LMFDB - Embedded newform 588.4.k.e.521.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(509,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("588.509");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.k (of order $6$, degree $2$, not 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:	$34.6931230834$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.10
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93946 - 4.82063i) q^{3} +(3.83273 + 6.63849i) q^{5} +(-19.4770 + 18.6988i) q^{9} +O(q^{10})$	\(q+(-1.93946 - 4.82063i) q^{3} +(3.83273 + 6.63849i) q^{5} +(-19.4770 + 18.6988i) q^{9} +(-1.13857 - 0.657354i) q^{11} +23.9754i q^{13} +(24.5683 - 31.3513i) q^{15} +(29.5490 - 51.1804i) q^{17} +(-24.4639 + 14.1243i) q^{19} +(-65.7234 + 37.9454i) q^{23} +(33.1203 - 57.3661i) q^{25} +(127.915 + 57.6258i) q^{27} -302.001i q^{29} +(-80.9549 - 46.7393i) q^{31} +(-0.960652 + 6.76354i) q^{33} +(-133.433 - 231.113i) q^{37} +(115.576 - 46.4992i) q^{39} +142.471 q^{41} +284.654 q^{43} +(-198.782 - 57.6302i) q^{45} +(104.876 + 181.651i) q^{47} +(-304.031 - 43.1827i) q^{51} +(-545.190 - 314.765i) q^{53} -10.0779i q^{55} +(115.535 + 90.5383i) q^{57} +(-365.186 + 632.521i) q^{59} +(471.964 - 272.488i) q^{61} +(-159.160 + 91.8912i) q^{65} +(240.556 - 416.655i) q^{67} +(310.389 + 243.235i) q^{69} +46.5477i q^{71} +(-834.095 - 481.565i) q^{73} +(-340.776 - 48.4018i) q^{75} +(-630.818 - 1092.61i) q^{79} +(29.7071 - 728.394i) q^{81} -841.130 q^{83} +453.014 q^{85} +(-1455.84 + 585.719i) q^{87} +(-641.169 - 1110.54i) q^{89} +(-68.3045 + 480.903i) q^{93} +(-187.528 - 108.269i) q^{95} -60.2806i q^{97} +(34.4677 - 8.48666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 64 q^{9}+O(q^{10}) $ 48 * q + 64 * q^9	$ 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) $ 48 * q + 64 * q^9 - 192 * q^15 - 456 * q^25 + 432 * q^37 - 688 * q^39 + 1248 * q^43 + 1536 * q^51 - 2720 * q^57 + 528 * q^67 - 3744 * q^79 - 3408 * q^81 + 13824 * q^85 + 5088 * q^93 - 15472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.93946	−	4.82063i	−0.373249	−	0.927731i
$3$	−1.93946	−	4.82063i	−0.373249	−	0.927731i
$4$		0			0
$5$	3.83273	+	6.63849i	0.342810	+	0.593764i	0.984953	−	0.172820i	$-0.0552879\pi$
$5$	3.83273	+	6.63849i	0.342810	+	0.593764i	−0.642143	+	0.766585i	$0.721955\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−19.4770	+	18.6988i	−0.721370	+	0.692549i
$10$		0			0
$11$	−1.13857	−	0.657354i	−0.0312084	−	0.0180182i	0.484315	−	0.874894i	$-0.339069\pi$
$11$	−1.13857	−	0.657354i	−0.0312084	−	0.0180182i	−0.515523	+	0.856876i	$0.672402\pi$
$12$		0			0
$13$			23.9754i			0.511505i	0.966742	+	0.255753i	$0.0823233\pi$
$13$			23.9754i			0.511505i	−0.966742	+	0.255753i	$0.917677\pi$
$14$		0			0
$15$	24.5683	−	31.3513i	0.422900	−	0.539658i
$16$		0			0
$17$	29.5490	−	51.1804i	0.421570	−	0.730181i	−0.574523	−	0.818488i	$-0.694813\pi$
$17$	29.5490	−	51.1804i	0.421570	−	0.730181i	0.996093	+	0.0883076i	$0.0281458\pi$
$18$		0			0
$19$	−24.4639	+	14.1243i	−0.295390	+	0.170544i	−0.640370	−	0.768066i	$-0.721219\pi$
$19$	−24.4639	+	14.1243i	−0.295390	+	0.170544i	0.344980	+	0.938610i	$0.387886\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−65.7234	+	37.9454i	−0.595838	+	0.344008i	−0.767403	−	0.641165i	$-0.778451\pi$
$23$	−65.7234	+	37.9454i	−0.595838	+	0.344008i	0.171564	+	0.985173i	$0.445118\pi$
$24$		0			0
$25$	33.1203	−	57.3661i	0.264963	−	0.458929i
$26$		0			0
$27$	127.915	+	57.6258i	0.911751	+	0.410744i
$28$		0			0
$29$		−	302.001i		−	1.93380i	−0.255151	−	0.966901i	$-0.582125\pi$
$29$		−	302.001i		−	1.93380i	0.255151	−	0.966901i	$-0.417875\pi$
$30$		0			0
$31$	−80.9549	−	46.7393i	−0.469030	−	0.270795i	0.246804	−	0.969066i	$-0.420620\pi$
$31$	−80.9549	−	46.7393i	−0.469030	−	0.270795i	−0.715834	+	0.698271i	$0.753953\pi$
$32$		0			0
$33$	−0.960652	+	6.76354i	−0.00506752	+	0.0356782i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−133.433	−	231.113i	−0.592871	−	1.02688i	−0.993843	−	0.110793i	$-0.964661\pi$
$37$	−133.433	−	231.113i	−0.592871	−	1.02688i	0.400972	−	0.916090i	$-0.368672\pi$
$38$		0			0
$39$	115.576	−	46.4992i	0.474540	−	0.190919i
$40$		0			0
$41$	142.471			0.542688			0.271344	−	0.962482i	$-0.412532\pi$
$41$	142.471			0.542688			0.271344	+	0.962482i	$0.412532\pi$
$42$		0			0
$43$	284.654			1.00952			0.504760	−	0.863260i	$-0.331581\pi$
$43$	284.654			1.00952			0.504760	+	0.863260i	$0.331581\pi$
$44$		0			0
$45$	−198.782	−	57.6302i	−0.658504	−	0.190911i
$46$		0			0
$47$	104.876	+	181.651i	0.325484	+	0.563755i	0.981610	−	0.190896i	$-0.0611393\pi$
$47$	104.876	+	181.651i	0.325484	+	0.563755i	−0.656126	+	0.754651i	$0.727806\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−304.031	−	43.1827i	−0.834762	−	0.118564i
$52$		0			0
$53$	−545.190	−	314.765i	−1.41297	−	0.815780i	−0.417306	−	0.908766i	$-0.637026\pi$
$53$	−545.190	−	314.765i	−1.41297	−	0.815780i	−0.995667	+	0.0929859i	$0.970359\pi$
$54$		0			0
$55$		−	10.0779i		−	0.0247072i
$56$		0			0
$57$	115.535	+	90.5383i	0.268473	+	0.210387i
$58$		0			0
$59$	−365.186	+	632.521i	−0.805817	+	1.39572i	0.109922	+	0.993940i	$0.464940\pi$
$59$	−365.186	+	632.521i	−0.805817	+	1.39572i	−0.915738	+	0.401775i	$0.868393\pi$
$60$		0			0
$61$	471.964	−	272.488i	0.990635	−	0.571943i	0.0851710	−	0.996366i	$-0.472856\pi$
$61$	471.964	−	272.488i	0.990635	−	0.571943i	0.905464	+	0.424423i	$0.139523\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−159.160	+	91.8912i	−0.303714	+	0.175349i
$66$		0			0
$67$	240.556	−	416.655i	0.438635	−	0.759739i	−0.558949	−	0.829202i	$-0.688795\pi$
$67$	240.556	−	416.655i	0.438635	−	0.759739i	0.997585	+	0.0694632i	$0.0221286\pi$
$68$		0			0
$69$	310.389	+	243.235i	0.541543	+	0.424377i
$70$		0			0
$71$			46.5477i			0.0778056i	0.999243	+	0.0389028i	$0.0123863\pi$
$71$			46.5477i			0.0778056i	−0.999243	+	0.0389028i	$0.987614\pi$
$72$		0			0
$73$	−834.095	−	481.565i	−1.33731	−	0.772095i	−0.350900	−	0.936413i	$-0.614124\pi$
$73$	−834.095	−	481.565i	−1.33731	−	0.772095i	−0.986407	+	0.164318i	$0.947458\pi$
$74$		0			0
$75$	−340.776	−	48.4018i	−0.524659	−	0.0745194i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−630.818	−	1092.61i	−0.898386	−	1.55605i	−0.829557	−	0.558422i	$-0.811407\pi$
$79$	−630.818	−	1092.61i	−0.898386	−	1.55605i	−0.0688294	−	0.997628i	$-0.521926\pi$
$80$		0			0
$81$	29.7071	−	728.394i	0.0407504	−	0.999169i
$82$		0			0
$83$	−841.130			−1.11236			−0.556181	−	0.831061i	$-0.687734\pi$
$83$	−841.130			−1.11236			−0.556181	+	0.831061i	$0.687734\pi$
$84$		0			0
$85$	453.014			0.578074
$86$		0			0
$87$	−1455.84	+	585.719i	−1.79405	+	0.721790i
$88$		0			0
$89$	−641.169	−	1110.54i	−0.763638	−	1.32266i	−0.940964	−	0.338507i	$-0.890078\pi$
$89$	−641.169	−	1110.54i	−0.763638	−	1.32266i	0.177326	−	0.984152i	$-0.443255\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−68.3045	+	480.903i	−0.0761596	+	0.536207i
$94$		0			0
$95$	−187.528	−	108.269i	−0.202525	−	0.116928i
$96$		0			0
$97$		−	60.2806i		−	0.0630986i	−0.999502	−	0.0315493i	$-0.989956\pi$
$97$		−	60.2806i		−	0.0630986i	0.999502	−	0.0315493i	$-0.0100441\pi$
$98$		0			0
$99$	34.4677	−	8.48666i	0.0349913	−	0.00861557i
$100$		0			0
$101$	−584.358	+	1012.14i	−0.575701	+	0.997144i	0.420264	+	0.907402i	$0.361938\pi$
$101$	−584.358	+	1012.14i	−0.575701	+	0.997144i	−0.995965	+	0.0897419i	$0.971396\pi$
$102$		0			0
$103$	−15.8686	+	9.16173i	−0.0151804	+	0.00876439i	−0.507571	−	0.861610i	$-0.669456\pi$
$103$	−15.8686	+	9.16173i	−0.0151804	+	0.00876439i	0.492391	+	0.870374i	$0.336123\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−824.968	+	476.295i	−0.745352	+	0.430329i	−0.824012	−	0.566572i	$-0.808269\pi$
$107$	−824.968	+	476.295i	−0.745352	+	0.430329i	0.0786602	+	0.996901i	$0.474936\pi$
$108$		0			0
$109$	353.940	−	613.042i	0.311021	−	0.538704i	−0.667563	−	0.744554i	$-0.732662\pi$
$109$	353.940	−	613.042i	0.311021	−	0.538704i	0.978584	+	0.205849i	$0.0659957\pi$
$110$		0			0
$111$	−855.322	+	1091.46i	−0.731383	+	0.933309i
$112$		0			0
$113$		−	9.01287i		−	0.00750318i	−0.999993	−	0.00375159i	$-0.998806\pi$
$113$		−	9.01287i		−	0.00750318i	0.999993	−	0.00375159i	$-0.00119417\pi$
$114$		0			0
$115$	−503.801	−	290.870i	−0.408519	−	0.235858i
$116$		0			0
$117$	−448.311	−	466.968i	−0.354243	−	0.368985i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−664.636	−	1151.18i	−0.499351	−	0.864901i
$122$		0			0
$123$	−276.316	−	686.800i	−0.202558	−	0.503469i
$124$		0			0
$125$	1465.95			1.04895
$126$		0			0
$127$	387.174			0.270521			0.135260	−	0.990810i	$-0.456813\pi$
$127$	387.174			0.270521			0.135260	+	0.990810i	$0.456813\pi$
$128$		0			0
$129$	−552.075	−	1372.21i	−0.376802	−	0.936563i
$130$		0			0
$131$	705.778	+	1222.44i	0.470718	+	0.815308i	0.999439	−	0.0334876i	$-0.0106614\pi$
$131$	705.778	+	1222.44i	0.470718	+	0.815308i	−0.528721	+	0.848796i	$0.677328\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	107.716	+	1070.03i	0.0686718	+	0.682172i
$136$		0			0
$137$	−631.197	−	364.422i	−0.393626	−	0.227260i	0.290104	−	0.956995i	$-0.406310\pi$
$137$	−631.197	−	364.422i	−0.393626	−	0.227260i	−0.683730	+	0.729735i	$0.739643\pi$
$138$		0			0
$139$		−	1262.40i		−	0.770324i	−0.922849	−	0.385162i	$-0.874146\pi$
$139$		−	1262.40i		−	0.770324i	0.922849	−	0.385162i	$-0.125854\pi$
$140$		0			0
$141$	672.269	−	857.874i	0.401527	−	0.512383i
$142$		0			0
$143$	15.7603	−	27.2977i	0.00921639	−	0.0159632i
$144$		0			0
$145$	2004.83	−	1157.49i	1.14822	−	0.662927i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−817.509	+	471.989i	−0.449483	+	0.259509i	−0.707612	−	0.706601i	$-0.750227\pi$
$149$	−817.509	+	471.989i	−0.449483	+	0.259509i	0.258129	+	0.966111i	$0.416894\pi$
$150$		0			0
$151$	−153.771	+	266.339i	−0.0828722	+	0.143539i	−0.904483	−	0.426511i	$-0.859743\pi$
$151$	−153.771	+	266.339i	−0.0828722	+	0.143539i	0.821610	+	0.570050i	$0.193076\pi$
$152$		0			0
$153$	381.488	+	1549.37i	0.201578	+	0.818689i
$154$		0			0
$155$		−	716.557i		−	0.371324i
$156$		0			0
$157$	1614.46	+	932.111i	0.820690	+	0.473825i	0.850654	−	0.525726i	$-0.176206\pi$
$157$	1614.46	+	932.111i	0.820690	+	0.473825i	−0.0299645	+	0.999551i	$0.509539\pi$
$158$		0			0
$159$	−459.996	+	3238.63i	−0.229434	+	1.61535i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1620.61	−	2806.98i	−0.778749	−	1.34883i	−0.932663	−	0.360749i	$-0.882521\pi$
$163$	−1620.61	−	2806.98i	−0.778749	−	1.34883i	0.153913	−	0.988084i	$-0.450812\pi$
$164$		0			0
$165$	−48.5816	+	19.5456i	−0.0229217	+	0.00922195i
$166$		0			0
$167$	2021.13			0.936523			0.468262	−	0.883590i	$-0.344881\pi$
$167$	2021.13			0.936523			0.468262	+	0.883590i	$0.344881\pi$
$168$		0			0
$169$	1622.18			0.738362
$170$		0			0
$171$	212.377	−	732.546i	0.0949758	−	0.327597i
$172$		0			0
$173$	−350.294	−	606.727i	−0.153944	−	0.266639i	0.778730	−	0.627359i	$-0.215864\pi$
$173$	−350.294	−	606.727i	−0.153944	−	0.266639i	−0.932674	+	0.360720i	$0.882531\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3757.41	+	533.680i	1.59562	+	0.226632i
$178$		0			0
$179$	2484.84	+	1434.62i	1.03757	+	0.599043i	0.919145	−	0.393920i	$-0.128881\pi$
$179$	2484.84	+	1434.62i	1.03757	+	0.599043i	0.118428	+	0.992963i	$0.462215\pi$
$180$		0			0
$181$		−	1974.33i		−	0.810778i	−0.914144	−	0.405389i	$-0.867136\pi$
$181$		−	1974.33i		−	0.810778i	0.914144	−	0.405389i	$-0.132864\pi$
$182$		0			0
$183$	−2228.92	−	1746.68i	−0.900363	−	0.705566i
$184$		0			0
$185$	1022.83	−	1771.59i	0.406485	−	0.704052i
$186$		0			0
$187$	−67.2873	+	38.8483i	−0.0263130	+	0.0151918i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	941.978	−	543.851i	0.356854	−	0.206030i	−0.310846	−	0.950460i	$-0.600612\pi$
$191$	941.978	−	543.851i	0.356854	−	0.206030i	0.667700	+	0.744431i	$0.267279\pi$
$192$		0			0
$193$	−1917.52	+	3321.24i	−0.715161	+	1.23870i	0.247736	+	0.968828i	$0.420314\pi$
$193$	−1917.52	+	3321.24i	−0.715161	+	1.23870i	−0.962897	+	0.269868i	$0.913020\pi$
$194$		0			0
$195$	751.658	+	589.034i	0.276038	+	0.216316i
$196$		0			0
$197$		−	1635.24i		−	0.591400i	−0.955281	−	0.295700i	$-0.904447\pi$
$197$		−	1635.24i		−	0.591400i	0.955281	−	0.295700i	$-0.0955528\pi$
$198$		0			0
$199$	3734.89	+	2156.34i	1.33045	+	0.768134i	0.985368	−	0.170439i	$-0.0545187\pi$
$199$	3734.89	+	2156.34i	1.33045	+	0.768134i	0.345079	+	0.938574i	$0.387852\pi$
$200$		0			0
$201$	−2475.09	−	351.546i	−0.868554	−	0.123364i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	546.053	+	945.791i	0.186039	+	0.322229i
$206$		0			0
$207$	570.560	−	1968.02i	0.191578	−	0.660804i
$208$		0			0
$209$	37.1386			0.0122915
$210$		0			0
$211$	−2882.49			−0.940468			−0.470234	−	0.882542i	$-0.655831\pi$
$211$	−2882.49			−0.940468			−0.470234	+	0.882542i	$0.655831\pi$
$212$		0			0
$213$	224.390	−	90.2774i	0.0721827	−	0.0290409i
$214$		0			0
$215$	1091.00	+	1889.67i	0.346073	+	0.599417i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−703.755	+	4954.84i	−0.217148	+	1.52885i
$220$		0			0
$221$	1227.07	+	708.449i	0.373491	+	0.215635i
$222$		0			0
$223$		−	3378.49i		−	1.01453i	−0.861790	−	0.507265i	$-0.830656\pi$
$223$		−	3378.49i		−	1.01453i	0.861790	−	0.507265i	$-0.169344\pi$
$224$		0			0
$225$	427.594	+	1736.63i	0.126695	+	0.514557i
$226$		0			0
$227$	2538.84	−	4397.39i	0.742328	−	1.28575i	−0.209105	−	0.977893i	$-0.567055\pi$
$227$	2538.84	−	4397.39i	0.742328	−	1.28575i	0.951433	−	0.307857i	$-0.0996117\pi$
$228$		0			0
$229$	3784.94	−	2185.24i	1.09221	−	0.630587i	0.158046	−	0.987432i	$-0.449481\pi$
$229$	3784.94	−	2185.24i	1.09221	−	0.630587i	0.934164	+	0.356844i	$0.116147\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3335.56	−	1925.79i	0.937854	−	0.541470i	0.0485671	−	0.998820i	$-0.484535\pi$
$233$	3335.56	−	1925.79i	0.937854	−	0.541470i	0.889287	+	0.457350i	$0.151201\pi$
$234$		0			0
$235$	−803.925	+	1392.44i	−0.223159	+	0.386522i
$236$		0			0
$237$	−4043.62	+	5160.01i	−1.10827	+	1.41426i
$238$		0			0
$239$			7067.79i			1.91288i	0.291937	+	0.956438i	$0.405700\pi$
$239$			7067.79i			1.91288i	−0.291937	+	0.956438i	$0.594300\pi$
$240$		0			0
$241$	2636.64	+	1522.26i	0.704733	+	0.406878i	0.809108	−	0.587660i	$-0.199951\pi$
$241$	2636.64	+	1522.26i	0.704733	+	0.406878i	−0.104375	+	0.994538i	$0.533284\pi$
$242$		0			0
$243$	−3568.94	+	1269.48i	−0.942171	+	0.335134i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−338.634	−	586.532i	−0.0872340	−	0.151094i
$248$		0			0
$249$	1631.34	+	4054.78i	0.415188	+	1.03197i
$250$		0			0
$251$	−5439.29			−1.36783			−0.683914	−	0.729562i	$-0.739724\pi$
$251$	−5439.29			−1.36783			−0.683914	+	0.729562i	$0.739724\pi$
$252$		0			0
$253$	99.7744			0.0247935
$254$		0			0
$255$	−878.602	−	2183.81i	−0.215765	−	0.536297i
$256$		0			0
$257$	−1139.37	−	1973.45i	−0.276545	−	0.478990i	0.693979	−	0.719996i	$-0.255856\pi$
$257$	−1139.37	−	1973.45i	−0.276545	−	0.478990i	−0.970524	+	0.241005i	$0.922523\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5647.08	+	5882.08i	1.33925	+	1.39499i
$262$		0			0
$263$	−1003.97	−	579.643i	−0.235390	−	0.135902i	0.377666	−	0.925942i	$-0.376727\pi$
$263$	−1003.97	−	579.643i	−0.235390	−	0.135902i	−0.613056	+	0.790039i	$0.710060\pi$
$264$		0			0
$265$		−	4825.65i		−	1.11863i
$266$		0			0
$267$	−4109.97	+	5244.68i	−0.942045	+	1.20213i
$268$		0			0
$269$	−1873.94	+	3245.77i	−0.424745	+	0.735680i	−0.996397	−	0.0848164i	$-0.972970\pi$
$269$	−1873.94	+	3245.77i	−0.424745	+	0.735680i	0.571651	+	0.820497i	$0.306303\pi$
$270$		0			0
$271$	−1771.74	+	1022.91i	−0.397142	+	0.229290i	−0.685250	−	0.728308i	$-0.740307\pi$
$271$	−1771.74	+	1022.91i	−0.397142	+	0.229290i	0.288108	+	0.957598i	$0.406974\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−75.4197	+	43.5436i	−0.0165381	+	0.00954827i
$276$		0			0
$277$	−2421.58	+	4194.29i	−0.525265	+	0.909785i	0.474302	+	0.880362i	$0.342700\pi$
$277$	−2421.58	+	4194.29i	−0.525265	+	0.909785i	−0.999567	+	0.0294232i	$0.990633\pi$
$278$		0			0
$279$	2450.73	−	603.420i	0.525883	−	0.129483i
$280$		0			0
$281$			827.961i			0.175772i	0.996131	+	0.0878862i	$0.0280112\pi$
$281$			827.961i			0.175772i	−0.996131	+	0.0878862i	$0.971989\pi$
$282$		0			0
$283$	7402.44	+	4273.80i	1.55487	+	0.897707i	0.997734	+	0.0672878i	$0.0214346\pi$
$283$	7402.44	+	4273.80i	1.55487	+	0.897707i	0.557140	+	0.830419i	$0.311899\pi$
$284$		0			0
$285$	−158.224	+	1113.98i	−0.0328854	+	0.231532i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	710.211	+	1230.12i	0.144557	+	0.250381i
$290$		0			0
$291$	−290.590	+	116.912i	−0.0585385	+	0.0235515i
$292$		0			0
$293$	−7266.94			−1.44894			−0.724469	−	0.689307i	$-0.757915\pi$
$293$	−7266.94			−1.44894			−0.724469	+	0.689307i	$0.757915\pi$
$294$		0			0
$295$	−5598.64			−1.10497
$296$		0			0
$297$	−107.760	−	149.697i	−0.0210534	−	0.0292467i
$298$		0			0
$299$	−909.756	−	1575.74i	−0.175962	−	0.304775i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	6012.49	+	853.977i	1.13996	+	0.161913i
$304$		0			0
$305$	3617.82	+	2088.75i	0.679199	+	0.392136i
$306$		0			0
$307$		−	4124.73i		−	0.766811i	−0.923580	−	0.383406i	$-0.874751\pi$
$307$		−	4124.73i		−	0.766811i	0.923580	−	0.383406i	$-0.125249\pi$
$308$		0			0
$309$	74.9418	+	58.7278i	0.0137971	+	0.0108120i
$310$		0			0
$311$	1649.15	−	2856.41i	0.300691	−	0.520812i	−0.675602	−	0.737267i	$-0.736116\pi$
$311$	1649.15	−	2856.41i	0.300691	−	0.520812i	0.976293	+	0.216455i	$0.0694495\pi$
$312$		0			0
$313$	5188.30	−	2995.47i	0.936934	−	0.540939i	0.0479358	−	0.998850i	$-0.484736\pi$
$313$	5188.30	−	2995.47i	0.936934	−	0.540939i	0.888998	+	0.457912i	$0.151402\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6144.35	−	3547.44i	1.08865	−	0.628531i	0.155432	−	0.987847i	$-0.450323\pi$
$317$	6144.35	−	3547.44i	1.08865	−	0.628531i	0.933216	+	0.359316i	$0.116990\pi$
$318$		0			0
$319$	−198.522	+	343.850i	−0.0348436	+	0.0603508i
$320$		0			0
$321$	3896.04	+	3053.11i	0.677431	+	0.530866i
$322$		0			0
$323$			1669.43i			0.287584i
$324$		0			0
$325$	1375.37	+	794.072i	0.234744	+	0.135530i
$326$		0			0
$327$	−3641.70	−	517.245i	−0.615861	−	0.0874731i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4581.91	−	7936.10i	−0.760860	−	1.31785i	−0.942408	−	0.334466i	$-0.891444\pi$
$331$	−4581.91	−	7936.10i	−0.760860	−	1.31785i	0.181548	−	0.983382i	$-0.441889\pi$
$332$		0			0
$333$	6920.41	+	2006.34i	1.13885	+	0.330170i
$334$		0			0
$335$	3687.94			0.601474
$336$		0			0
$337$	1546.78			0.250025			0.125012	−	0.992155i	$-0.460103\pi$
$337$	1546.78			0.250025			0.125012	+	0.992155i	$0.460103\pi$
$338$		0			0
$339$	−43.4477	+	17.4801i	−0.00696094	+	0.00280055i
$340$		0			0
$341$	61.4486	+	106.432i	0.00975844	+	0.0169021i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−425.074	+	2992.77i	−0.0663340	+	0.467030i
$346$		0			0
$347$	−7966.18	−	4599.27i	−1.23241	−	0.711533i	−0.264879	−	0.964282i	$-0.585332\pi$
$347$	−7966.18	−	4599.27i	−1.23241	−	0.711533i	−0.967532	+	0.252749i	$0.918665\pi$
$348$		0			0
$349$		−	6916.38i		−	1.06082i	−0.847742	−	0.530409i	$-0.822038\pi$
$349$		−	6916.38i		−	1.06082i	0.847742	−	0.530409i	$-0.177962\pi$
$350$		0			0
$351$	−1381.60	+	3066.81i	−0.210098	+	0.466365i
$352$		0			0
$353$	−1376.71	+	2384.52i	−0.207577	+	0.359534i	−0.950951	−	0.309343i	$-0.899891\pi$
$353$	−1376.71	+	2384.52i	−0.207577	+	0.359534i	0.743374	+	0.668876i	$0.233224\pi$
$354$		0			0
$355$	−309.007	+	178.405i	−0.0461982	+	0.0266725i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3079.84	−	1778.15i	0.452780	−	0.261413i	−0.256224	−	0.966618i	$-0.582478\pi$
$359$	3079.84	−	1778.15i	0.452780	−	0.261413i	0.709004	+	0.705205i	$0.249145\pi$
$360$		0			0
$361$	−3030.51	+	5249.00i	−0.441830	+	0.765272i
$362$		0			0
$363$	−4260.40	+	5436.64i	−0.616013	+	0.786087i
$364$		0			0
$365$		−	7382.84i		−	1.05873i
$366$		0			0
$367$	4788.83	+	2764.83i	0.681131	+	0.393251i	0.800281	−	0.599625i	$-0.204684\pi$
$367$	4788.83	+	2764.83i	0.681131	+	0.393251i	−0.119150	+	0.992876i	$0.538017\pi$
$368$		0			0
$369$	−2774.90	+	2664.04i	−0.391479	+	0.375838i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	566.970	+	982.020i	0.0787039	+	0.136319i	0.902691	−	0.430289i	$-0.141588\pi$
$373$	566.970	+	982.020i	0.0787039	+	0.136319i	−0.823987	+	0.566609i	$0.808255\pi$
$374$		0			0
$375$	−2843.15	−	7066.80i	−0.391519	−	0.973141i
$376$		0			0
$377$	7240.60			0.989150
$378$		0			0
$379$	4071.36			0.551799			0.275900	−	0.961186i	$-0.411024\pi$
$379$	4071.36			0.551799			0.275900	+	0.961186i	$0.411024\pi$
$380$		0			0
$381$	−750.908	−	1866.42i	−0.100972	−	0.250970i
$382$		0			0
$383$	7069.27	+	12244.3i	0.943140	+	1.63357i	0.759433	+	0.650586i	$0.225477\pi$
$383$	7069.27	+	12244.3i	0.943140	+	1.63357i	0.183707	+	0.982981i	$0.441190\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5544.21	+	5322.70i	−0.728237	+	0.699142i
$388$		0			0
$389$	9257.16	+	5344.63i	1.20657	+	0.696615i	0.962009	−	0.273018i	$-0.0880219\pi$
$389$	9257.16	+	5344.63i	1.20657	+	0.696615i	0.244564	+	0.969633i	$0.421355\pi$
$390$		0			0
$391$			4485.00i			0.580093i
$392$		0			0
$393$	4524.12	−	5773.18i	0.580692	−	0.741013i
$394$		0			0
$395$	4835.51	−	8375.35i	0.615952	−	1.06686i
$396$		0			0
$397$	8778.93	−	5068.52i	1.10983	−	0.640760i	0.171043	−	0.985263i	$-0.445286\pi$
$397$	8778.93	−	5068.52i	1.10983	−	0.640760i	0.938785	+	0.344504i	$0.111953\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7292.21	+	4210.16i	−0.908119	+	0.524303i	−0.879825	−	0.475297i	$-0.842341\pi$
$401$	−7292.21	+	4210.16i	−0.908119	+	0.524303i	−0.0282934	+	0.999600i	$0.509007\pi$
$402$		0			0
$403$	1120.59	−	1940.92i	0.138513	−	0.239911i
$404$		0			0
$405$	4949.30	−	2594.53i	0.607241	−	0.318329i
$406$		0			0
$407$			350.851i			0.0427298i
$408$		0			0
$409$	−8021.64	−	4631.30i	−0.969792	−	0.559909i	−0.0706189	−	0.997503i	$-0.522497\pi$
$409$	−8021.64	−	4631.30i	−0.969792	−	0.559909i	−0.899173	+	0.437594i	$0.855831\pi$
$410$		0			0
$411$	−532.563	+	3749.55i	−0.0639158	+	0.450004i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−3223.83	−	5583.83i	−0.381329	−	0.660480i
$416$		0			0
$417$	−6085.55	+	2448.37i	−0.714654	+	0.287523i
$418$		0			0
$419$	−883.038			−0.102958			−0.0514788	−	0.998674i	$-0.516393\pi$
$419$	−883.038			−0.102958			−0.0514788	+	0.998674i	$0.516393\pi$
$420$		0			0
$421$	6313.53			0.730886			0.365443	−	0.930834i	$-0.380918\pi$
$421$	6313.53			0.730886			0.365443	+	0.930834i	$0.380918\pi$
$422$		0			0
$423$	−5439.33	−	1576.95i	−0.625223	−	0.181262i
$424$		0			0
$425$	−1957.35	−	3390.22i	−0.223401	−	0.386941i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−162.158	−	23.0320i	−0.0182496	−	0.00259206i
$430$		0			0
$431$	−6291.22	−	3632.24i	−0.703103	−	0.405937i	0.105399	−	0.994430i	$-0.466388\pi$
$431$	−6291.22	−	3632.24i	−0.703103	−	0.405937i	−0.808502	+	0.588493i	$0.799721\pi$
$432$		0			0
$433$			4242.72i			0.470883i	0.971889	+	0.235441i	$0.0756536\pi$
$433$			4242.72i			0.470883i	−0.971889	+	0.235441i	$0.924346\pi$
$434$		0			0
$435$	−9468.13	−	7419.66i	−1.04359	−	0.817806i
$436$		0			0
$437$	1071.90	−	1856.59i	0.117337	−	0.203233i
$438$		0			0
$439$	−9430.55	+	5444.73i	−1.02528	+	0.591943i	−0.915628	−	0.402028i	$-0.868306\pi$
$439$	−9430.55	+	5444.73i	−1.02528	+	0.591943i	−0.109648	+	0.993971i	$0.534972\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13925.6	+	8039.92i	−1.49351	+	0.862276i	−0.999972	−	0.00745048i	$-0.997628\pi$
$443$	−13925.6	+	8039.92i	−1.49351	+	0.862276i	−0.493534	+	0.869727i	$0.664295\pi$
$444$		0			0
$445$	4914.86	−	8512.78i	0.523565	−	0.906842i
$446$		0			0
$447$	3860.81	+	3025.51i	0.408524	+	0.320138i
$448$		0			0
$449$		−	13638.3i		−	1.43348i	−0.697341	−	0.716740i	$-0.745634\pi$
$449$		−	13638.3i		−	1.43348i	0.697341	−	0.716740i	$-0.254366\pi$
$450$		0			0
$451$	−162.213	−	93.6538i	−0.0169364	−	0.00977824i
$452$		0			0
$453$	1582.16	+	224.720i	0.164098	+	0.0233074i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−939.399	−	1627.09i	−0.0961559	−	0.166547i	0.813935	−	0.580957i	$-0.197321\pi$
$457$	−939.399	−	1627.09i	−0.0961559	−	0.166547i	−0.910090	+	0.414410i	$0.863988\pi$
$458$		0			0
$459$	6729.08	−	4843.96i	0.684284	−	0.492585i
$460$		0			0
$461$	2579.48			0.260604			0.130302	−	0.991474i	$-0.458405\pi$
$461$	2579.48			0.260604			0.130302	+	0.991474i	$0.458405\pi$
$462$		0			0
$463$	6099.88			0.612280			0.306140	−	0.951986i	$-0.400962\pi$
$463$	6099.88			0.612280			0.306140	+	0.951986i	$0.400962\pi$
$464$		0			0
$465$	−3454.26	+	1389.73i	−0.344489	+	0.138596i
$466$		0			0
$467$	−9526.74	−	16500.8i	−0.943993	−	1.63504i	−0.757755	−	0.652540i	$-0.773704\pi$
$467$	−9526.74	−	16500.8i	−0.943993	−	1.63504i	−0.186239	−	0.982505i	$-0.559630\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1362.18	−	9590.53i	0.133261	−	0.938234i
$472$		0			0
$473$	−324.099	−	187.119i	−0.0315054	−	0.0181897i
$474$		0			0
$475$			1871.20i			0.180751i
$476$		0			0
$477$	16504.4	−	4063.73i	1.58425	−	0.390074i
$478$		0			0
$479$	−8990.07	+	15571.3i	−0.857551	+	1.48532i	0.0167077	+	0.999860i	$0.494682\pi$
$479$	−8990.07	+	15571.3i	−0.857551	+	1.48532i	−0.874258	+	0.485461i	$0.838652\pi$
$480$		0			0
$481$	5541.01	−	3199.10i	0.525256	−	0.303257i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	400.172	−	231.039i	0.0374657	−	0.0216308i
$486$		0			0
$487$	6157.30	−	10664.8i	0.572924	−	0.992333i	−0.423340	−	0.905971i	$-0.639142\pi$
$487$	6157.30	−	10664.8i	0.572924	−	0.992333i	0.996264	−	0.0863623i	$-0.0275243\pi$
$488$		0			0
$489$	−10388.3	+	13256.4i	−0.960688	+	1.22592i
$490$		0			0
$491$			6650.90i			0.611305i	0.952143	+	0.305653i	$0.0988747\pi$
$491$			6650.90i			0.611305i	−0.952143	+	0.305653i	$0.901125\pi$
$492$		0			0
$493$	−15456.6	−	8923.85i	−1.41203	−	0.815233i
$494$		0			0
$495$	188.444	+	196.286i	0.0171110	+	0.0178231i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6376.49	−	11044.4i	−0.572046	−	0.990813i	−0.996356	−	0.0852957i	$-0.972816\pi$
$499$	−6376.49	−	11044.4i	−0.572046	−	0.990813i	0.424310	−	0.905517i	$-0.360517\pi$
$500$		0			0
$501$	−3919.89	−	9743.10i	−0.349556	−	0.868842i
$502$		0			0
$503$	7044.47			0.624448			0.312224	−	0.950009i	$-0.398926\pi$
$503$	7044.47			0.624448			0.312224	+	0.950009i	$0.398926\pi$
$504$		0			0
$505$	−8958.76			−0.789425
$506$		0			0
$507$	−3146.15	−	7819.94i	−0.275593	−	0.685002i
$508$		0			0
$509$	2386.47	+	4133.49i	0.207816	+	0.359948i	0.951026	−	0.309110i	$-0.100031\pi$
$509$	2386.47	+	4133.49i	0.207816	+	0.359948i	−0.743210	+	0.669058i	$0.766698\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−3943.23	+	396.951i	−0.339372	+	0.0341634i
$514$		0			0
$515$	−121.640	−	70.2289i	−0.0104080	−	0.00600904i
$516$		0			0
$517$		−	275.763i		−	0.0234585i
$518$		0			0
$519$	−2245.43	+	2865.36i	−0.189910	+	0.242342i
$520$		0			0
$521$	−7491.53	+	12975.7i	−0.629961	+	1.09113i	0.357597	+	0.933876i	$0.383596\pi$
$521$	−7491.53	+	12975.7i	−0.629961	+	1.09113i	−0.987559	+	0.157249i	$0.949737\pi$
$522$		0			0
$523$	−4638.56	+	2678.07i	−0.387820	+	0.223908i	−0.681215	−	0.732083i	$-0.738548\pi$
$523$	−4638.56	+	2678.07i	−0.387820	+	0.223908i	0.293395	+	0.955991i	$0.405215\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4784.27	+	2762.20i	−0.395458	+	0.228318i
$528$		0			0
$529$	−3203.79	+	5549.12i	−0.263318	+	0.456080i
$530$		0			0
$531$	−4714.68	−	19148.2i	−0.385310	−	1.56490i
$532$		0			0
$533$			3415.79i			0.277588i
$534$		0			0
$535$	−6323.76	−	3651.03i	−0.511028	−	0.295042i
$536$		0			0
$537$	2096.54	−	14760.9i	0.168478	−	1.18618i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.18626	+	7.25082i	0.000332683	+	0.000576224i	0.866192	−	0.499712i	$-0.166561\pi$
$541$	4.18626	+	7.25082i	0.000332683	+	0.000576224i	−0.865859	+	0.500288i	$0.833227\pi$
$542$		0			0
$543$	−9517.52	+	3829.13i	−0.752184	+	0.302622i
$544$		0			0
$545$	5426.23			0.426485
$546$		0			0
$547$	10274.7			0.803137			0.401568	−	0.915829i	$-0.368465\pi$
$547$	10274.7			0.803137			0.401568	+	0.915829i	$0.368465\pi$
$548$		0			0
$549$	−4097.22	+	14132.4i	−0.318516	+	1.09865i
$550$		0			0
$551$	4265.55	+	7388.15i	0.329798	+	0.571226i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−10523.9	−	1494.75i	−0.804891	−	0.114322i
$556$		0			0
$557$	−13316.1	−	7688.05i	−1.01296	−	0.584835i	−0.100906	−	0.994896i	$-0.532174\pi$
$557$	−13316.1	−	7688.05i	−1.01296	−	0.584835i	−0.912058	+	0.410061i	$0.865507\pi$
$558$		0			0
$559$			6824.68i			0.516375i
$560$		0			0
$561$	317.775	+	249.023i	0.0239152	+	0.0187411i
$562$		0			0
$563$	−9229.97	+	15986.8i	−0.690936	+	1.19674i	0.280596	+	0.959826i	$0.409468\pi$
$563$	−9229.97	+	15986.8i	−0.690936	+	1.19674i	−0.971532	+	0.236910i	$0.923865\pi$
$564$		0			0
$565$	59.8318	−	34.5439i	0.00445512	−	0.00257217i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3033.11	−	1751.17i	0.223471	−	0.129021i	−0.384086	−	0.923297i	$-0.625483\pi$
$569$	3033.11	−	1751.17i	0.223471	−	0.129021i	0.607556	+	0.794277i	$0.292150\pi$
$570$		0			0
$571$	5593.74	−	9688.63i	0.409966	−	0.710082i	−0.584920	−	0.811091i	$-0.698874\pi$
$571$	5593.74	−	9688.63i	0.409966	−	0.710082i	0.994885	+	0.101009i	$0.0322072\pi$
$572$		0			0
$573$	−4448.64	−	3486.15i	−0.324336	−	0.254164i
$574$		0			0
$575$			5027.06i			0.364596i
$576$		0			0
$577$	−8346.61	−	4818.92i	−0.602208	−	0.347685i	0.167702	−	0.985838i	$-0.446365\pi$
$577$	−8346.61	−	4818.92i	−0.602208	−	0.347685i	−0.769910	+	0.638153i	$0.779699\pi$
$578$		0			0
$579$	19729.4	+	2802.25i	1.41611	+	0.201136i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	413.825	+	716.765i	0.0293977	+	0.0509183i
$584$		0			0
$585$	1381.70	−	4765.87i	0.0976521	−	0.336828i
$586$		0			0
$587$	−3998.01			−0.281117			−0.140559	−	0.990072i	$-0.544890\pi$
$587$	−3998.01			−0.281117			−0.140559	+	0.990072i	$0.544890\pi$
$588$		0			0
$589$	2640.63			0.184729
$590$		0			0
$591$	−7882.87	+	3171.47i	−0.548660	+	0.220739i
$592$		0			0
$593$	−5716.00	−	9900.41i	−0.395832	−	0.685600i	0.597375	−	0.801962i	$-0.296210\pi$
$593$	−5716.00	−	9900.41i	−0.395832	−	0.685600i	−0.993207	+	0.116361i	$0.962877\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3151.25	−	22186.6i	0.216034	−	1.52100i
$598$		0			0
$599$	−700.491	−	404.428i	−0.0477818	−	0.0275868i	0.475919	−	0.879489i	$-0.342116\pi$
$599$	−700.491	−	404.428i	−0.0477818	−	0.0275868i	−0.523701	+	0.851902i	$0.675449\pi$
$600$		0			0
$601$			6813.76i			0.462461i	0.972899	+	0.231231i	$0.0742752\pi$
$601$			6813.76i			0.462461i	−0.972899	+	0.231231i	$0.925725\pi$
$602$		0			0
$603$	3105.66	+	12613.3i	0.209738	+	0.851830i
$604$		0			0
$605$	5094.74	−	8824.35i	0.342365	−	0.592993i
$606$		0			0
$607$	2799.03	−	1616.02i	0.187165	−	0.108060i	−0.403490	−	0.914984i	$-0.632203\pi$
$607$	2799.03	−	1616.02i	0.187165	−	0.108060i	0.590655	+	0.806924i	$0.298870\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4355.15	+	2514.44i	−0.288364	+	0.166487i
$612$		0			0
$613$	6607.92	−	11445.2i	0.435385	−	0.754110i	−0.561942	−	0.827177i	$-0.689945\pi$
$613$	6607.92	−	11445.2i	0.435385	−	0.754110i	0.997327	+	0.0730673i	$0.0232788\pi$
$614$		0			0
$615$	3500.26	−	4466.64i	0.229503	−	0.292866i
$616$		0			0
$617$			23412.7i			1.52765i	0.645422	+	0.763826i	$0.276681\pi$
$617$			23412.7i			1.52765i	−0.645422	+	0.763826i	$0.723319\pi$
$618$		0			0
$619$	−9042.06	−	5220.44i	−0.587126	−	0.338977i	0.176834	−	0.984241i	$-0.443414\pi$
$619$	−9042.06	−	5220.44i	−0.587126	−	0.338977i	−0.763960	+	0.645263i	$0.776748\pi$
$620$		0			0
$621$	−10593.7	+	1066.43i	−0.684555	+	0.0689117i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	1478.55	+	2560.92i	0.0946271	+	0.163899i
$626$		0			0
$627$	−72.0287	−	179.031i	−0.00458780	−	0.0114032i
$628$		0			0
$629$	−15771.3			−0.999747
$630$		0			0
$631$	−1116.76			−0.0704556			−0.0352278	−	0.999379i	$-0.511216\pi$
$631$	−1116.76			−0.0704556			−0.0352278	+	0.999379i	$0.511216\pi$
$632$		0			0
$633$	5590.47	+	13895.4i	0.351029	+	0.872502i
$634$		0			0
$635$	1483.93	+	2570.25i	0.0927372	+	0.160626i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−870.388	−	906.610i	−0.0538842	−	0.0561267i
$640$		0			0
$641$	−1197.94	−	691.630i	−0.0738155	−	0.0426174i	0.462638	−	0.886547i	$-0.346903\pi$
$641$	−1197.94	−	691.630i	−0.0738155	−	0.0426174i	−0.536453	+	0.843930i	$0.680236\pi$
$642$		0			0
$643$			13841.5i			0.848918i	0.905447	+	0.424459i	$0.139536\pi$
$643$			13841.5i			0.848918i	−0.905447	+	0.424459i	$0.860464\pi$
$644$		0			0
$645$	6993.46	−	8924.27i	0.426926	−	0.544795i
$646$		0			0
$647$	−1188.54	+	2058.62i	−0.0722201	+	0.125089i	−0.899874	−	0.436150i	$-0.856342\pi$
$647$	−1188.54	+	2058.62i	−0.0722201	+	0.125089i	0.827654	+	0.561239i	$0.189675\pi$
$648$		0			0
$649$	831.581	−	480.113i	0.0502964	−	0.0290387i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4812.62	−	2778.57i	0.288411	−	0.166514i	−0.348814	−	0.937192i	$-0.613416\pi$
$653$	4812.62	−	2778.57i	0.288411	−	0.166514i	0.637225	+	0.770678i	$0.280082\pi$
$654$		0			0
$655$	−5410.12	+	9370.60i	−0.322734	+	0.558992i
$656$		0			0
$657$	25250.4	−	6217.17i	1.49941	−	0.369185i
$658$		0			0
$659$		−	32145.5i		−	1.90017i	−0.311991	−	0.950085i	$-0.600996\pi$
$659$		−	32145.5i		−	1.90017i	0.311991	−	0.950085i	$-0.399004\pi$
$660$		0			0
$661$	602.813	+	348.034i	0.0354715	+	0.0204795i	0.517631	−	0.855604i	$-0.326814\pi$
$661$	602.813	+	348.034i	0.0354715	+	0.0204795i	−0.482159	+	0.876084i	$0.660147\pi$
$662$		0			0
$663$	1035.32	−	7289.26i	0.0606464	−	0.426985i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11459.6	+	19848.6i	0.665243	+	1.15223i
$668$		0			0
$669$	−16286.5	+	6552.44i	−0.941212	+	0.378673i
$670$		0			0
$671$	−716.485			−0.0412215
$672$		0			0
$673$	−12403.6			−0.710436			−0.355218	−	0.934783i	$-0.615593\pi$
$673$	−12403.6			−0.710436			−0.355218	+	0.934783i	$0.615593\pi$
$674$		0			0
$675$	7542.36	−	5429.40i	0.430082	−	0.309597i
$676$		0			0
$677$	−9752.83	−	16892.4i	−0.553666	−	0.958977i	−0.998006	−	0.0631191i	$-0.979895\pi$
$677$	−9752.83	−	16892.4i	−0.553666	−	0.958977i	0.444340	−	0.895858i	$-0.353438\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−26122.2	−	3710.23i	−1.46990	−	0.208776i
$682$		0			0
$683$	25452.0	+	14694.7i	1.42591	+	0.823247i	0.996795	−	0.0800044i	$-0.0254934\pi$
$683$	25452.0	+	14694.7i	1.42591	+	0.823247i	0.429111	+	0.903252i	$0.358827\pi$
$684$		0			0
$685$		−	5586.92i		−	0.311628i
$686$		0			0
$687$	−17875.0	−	14007.6i	−0.992682	−	0.777911i
$688$		0			0
$689$	7546.62	−	13071.1i	0.417276	−	0.722743i
$690$		0			0
$691$	−27416.6	+	15829.0i	−1.50937	+	0.871436i	−0.509432	+	0.860511i	$0.670144\pi$
$691$	−27416.6	+	15829.0i	−1.50937	+	0.871436i	−0.999940	+	0.0109252i	$0.996522\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8380.40	−	4838.43i	0.457391	−	0.264075i
$696$		0			0
$697$	4209.87	−	7291.72i	0.228781	−	0.396260i
$698$		0			0
$699$	−15752.7	−	12344.5i	−0.852392	−	0.667973i
$700$		0			0
$701$		−	5372.77i		−	0.289482i	−0.989470	−	0.144741i	$-0.953765\pi$
$701$		−	5372.77i		−	0.289482i	0.989470	−	0.144741i	$-0.0462349\pi$
$702$		0			0
$703$	6528.59	+	3769.28i	0.350257	+	0.202221i
$704$		0			0
$705$	8271.61	+	1174.85i	0.441882	+	0.0627622i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	16713.7	+	28949.0i	0.885328	+	1.53343i	0.845337	+	0.534233i	$0.179400\pi$
$709$	16713.7	+	28949.0i	0.885328	+	1.53343i	0.0399911	+	0.999200i	$0.487267\pi$
$710$		0			0
$711$	32716.9	+	9485.17i	1.72571	+	0.500312i
$712$		0			0
$713$	7094.18			0.372621
$714$		0			0
$715$	241.620			0.0126379
$716$		0			0
$717$	34071.2	−	13707.7i	1.77463	−	0.713979i
$718$		0			0
$719$	13795.7	+	23894.9i	0.715567	+	1.23940i	0.962740	+	0.270428i	$0.0871651\pi$
$719$	13795.7	+	23894.9i	0.715567	+	1.23940i	−0.247173	+	0.968971i	$0.579502\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2224.62	−	15662.6i	0.114432	−	0.805670i
$724$		0			0
$725$	−17324.6	−	10002.4i	−0.887477	−	0.512385i
$726$		0			0
$727$			16801.8i			0.857143i	0.903508	+	0.428572i	$0.140983\pi$
$727$			16801.8i			0.857143i	−0.903508	+	0.428572i	$0.859017\pi$
$728$		0			0
$729$	13041.5	+	14742.4i	0.662578	+	0.748993i
$730$		0			0
$731$	8411.25	−	14568.7i	0.425583	−	0.737131i
$732$		0			0
$733$	−14820.4	+	8556.57i	−0.746800	+	0.431165i	−0.824537	−	0.565809i	$-0.808564\pi$
$733$	−14820.4	+	8556.57i	−0.746800	+	0.431165i	0.0777364	+	0.996974i	$0.475231\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−547.780	+	316.261i	−0.0273782	+	0.0158068i
$738$		0			0
$739$	−9855.83	+	17070.8i	−0.490599	+	0.849742i	−0.999941	−	0.0108215i	$-0.996555\pi$
$739$	−9855.83	+	17070.8i	−0.490599	+	0.849742i	0.509342	+	0.860564i	$0.329889\pi$
$740$		0			0
$741$	−2170.69	+	2769.99i	−0.107614	+	0.137325i
$742$		0			0
$743$		−	17443.3i		−	0.861283i	−0.902523	−	0.430642i	$-0.858287\pi$
$743$		−	17443.3i		−	0.861283i	0.902523	−	0.430642i	$-0.141713\pi$
$744$		0			0
$745$	−6266.59	−	3618.02i	−0.308175	−	0.177925i
$746$		0			0
$747$	16382.7	−	15728.1i	0.802424	−	0.770365i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	9793.78	+	16963.3i	0.475872	+	0.824235i	0.999618	−	0.0276399i	$-0.00879916\pi$
$751$	9793.78	+	16963.3i	0.475872	+	0.824235i	−0.523746	+	0.851875i	$0.675466\pi$
$752$		0			0
$753$	10549.3	+	26220.8i	0.510541	+	1.26898i
$754$		0			0
$755$	−2357.45			−0.113638
$756$		0			0
$757$	−4635.88			−0.222581			−0.111291	−	0.993788i	$-0.535498\pi$
$757$	−4635.88			−0.222581			−0.111291	+	0.993788i	$0.535498\pi$
$758$		0			0
$759$	−193.508	−	480.976i	−0.00925416	−	0.0230017i
$760$		0			0
$761$	9585.45	+	16602.5i	0.456600	+	0.790854i	0.998779	−	0.0494092i	$-0.0157338\pi$
$761$	9585.45	+	16602.5i	0.456600	+	0.790854i	−0.542179	+	0.840263i	$0.682400\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−8823.35	+	8470.83i	−0.417005	+	0.400345i
$766$		0			0
$767$	−15164.9	−	8755.47i	−0.713916	−	0.412180i
$768$		0			0
$769$			22223.5i			1.04213i	0.853517	+	0.521065i	$0.174465\pi$
$769$			22223.5i			1.04213i	−0.853517	+	0.521065i	$0.825535\pi$
$770$		0			0
$771$	−7303.52	+	9319.93i	−0.341154	+	0.435342i
$772$		0			0
$773$	10497.8	−	18182.7i	0.488460	−	0.846037i	−0.511452	−	0.859312i	$-0.670892\pi$
$773$	10497.8	−	18182.7i	0.488460	−	0.846037i	0.999912	+	0.0132746i	$0.00422555\pi$
$774$		0			0
$775$	−5362.50	+	3096.04i	−0.248551	+	0.143501i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3485.40	+	2012.30i	−0.160305	+	0.0925520i
$780$		0			0
$781$	30.5983	−	52.9979i	0.00140191	−	0.00242819i
$782$		0			0
$783$	17403.1	−	38630.5i	0.794299	−	1.76315i
$784$		0			0
$785$			14290.1i			0.649728i
$786$		0			0
$787$	20245.5	+	11688.7i	0.916994	+	0.529427i	0.882675	−	0.469984i	$-0.155740\pi$
$787$	20245.5	+	11688.7i	0.916994	+	0.529427i	0.0343191	+	0.999411i	$0.489074\pi$
$788$		0			0
$789$	−847.085	+	5963.97i	−0.0382218	+	0.269104i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6533.01	+	11315.5i	0.292552	+	0.506715i
$794$		0			0
$795$	−23262.7	+	9359.14i	−1.03779	+	0.417528i
$796$		0			0
$797$	5445.93			0.242039			0.121019	−	0.992650i	$-0.461384\pi$
$797$	5445.93			0.242039			0.121019	+	0.992650i	$0.461384\pi$
$798$		0			0
$799$	12396.0			0.548858
$800$		0			0
$801$	33253.8	+	9640.82i	1.46687	+	0.425270i
$802$		0			0
$803$	633.118	+	1096.59i	0.0278235	+	0.0481916i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	19281.1	+	2738.57i	0.841049	+	0.119457i
$808$		0			0
$809$	28161.4	+	16259.0i	1.22386	+	0.706597i	0.965739	−	0.259516i	$-0.0835629\pi$
$809$	28161.4	+	16259.0i	1.22386	+	0.706597i	0.258122	+	0.966112i	$0.416896\pi$
$810$		0			0
$811$			16408.0i			0.710437i	0.934783	+	0.355218i	$0.115594\pi$
$811$			16408.0i			0.710437i	−0.934783	+	0.355218i	$0.884406\pi$
$812$		0			0
$813$	8367.31	+	6557.01i	0.360953	+	0.282859i
$814$		0			0
$815$	12422.7	−	21516.8i	0.533926	−	0.924787i
$816$		0			0
$817$	−6963.76	+	4020.53i	−0.298202	+	0.172167i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10550.2	−	6091.13i	0.448481	−	0.258931i	−0.258707	−	0.965956i	$-0.583297\pi$
$821$	10550.2	−	6091.13i	0.448481	−	0.258931i	0.707188	+	0.707025i	$0.249963\pi$
$822$		0			0
$823$	−2231.32	+	3864.75i	−0.0945064	+	0.163690i	−0.909402	−	0.415917i	$-0.863461\pi$
$823$	−2231.32	+	3864.75i	−0.0945064	+	0.163690i	0.814896	+	0.579607i	$0.196794\pi$
$824$		0			0
$825$	356.181	+	279.120i	0.0150311	+	0.0117790i
$826$		0			0
$827$		−	2442.53i		−	0.102703i	−0.998681	−	0.0513513i	$-0.983647\pi$
$827$		−	2442.53i		−	0.102703i	0.998681	−	0.0513513i	$-0.0163528\pi$
$828$		0			0
$829$	8327.05	+	4807.62i	0.348866	+	0.201418i	0.664186	−	0.747567i	$-0.268778\pi$
$829$	8327.05	+	4807.62i	0.348866	+	0.201418i	−0.315319	+	0.948986i	$0.602112\pi$
$830$		0			0
$831$	24915.7	+	3538.87i	1.04009	+	0.147728i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	7746.43	+	13417.2i	0.321050	+	0.556074i
$836$		0			0
$837$	−7661.95	−	10643.8i	−0.316411	−	0.439548i
$838$		0			0
$839$	−19611.2			−0.806979			−0.403489	−	0.914984i	$-0.632203\pi$
$839$	−19611.2			−0.806979			−0.403489	+	0.914984i	$0.632203\pi$
$840$		0			0
$841$	−66815.9			−2.73959
$842$		0			0
$843$	3991.30	−	1605.80i	0.163069	−	0.0656068i
$844$		0			0
$845$	6217.39	+	10768.8i	0.253118	+	0.438413i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	6245.69	−	43973.3i	0.252475	−	1.77757i
$850$		0			0
$851$	17539.3	+	10126.3i	0.706511	+	0.407904i
$852$		0			0
$853$		−	49160.6i		−	1.97330i	−0.162848	−	0.986651i	$-0.552068\pi$
$853$		−	49160.6i		−	1.97330i	0.162848	−	0.986651i	$-0.447932\pi$
$854$		0			0
$855$	5676.98	−	1397.79i	0.227074	−	0.0559104i
$856$		0			0
$857$	5684.31	−	9845.52i	0.226572	−	0.392435i	−0.730218	−	0.683215i	$-0.760581\pi$
$857$	5684.31	−	9845.52i	0.226572	−	0.392435i	0.956790	+	0.290780i	$0.0939147\pi$
$858$		0			0
$859$	6120.51	−	3533.68i	0.243107	−	0.140358i	−0.373497	−	0.927631i	$-0.621841\pi$
$859$	6120.51	−	3533.68i	0.243107	−	0.140358i	0.616604	+	0.787273i	$0.288508\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	23350.3	−	13481.3i	0.921035	−	0.531760i	0.0370701	−	0.999313i	$-0.488198\pi$
$863$	23350.3	−	13481.3i	0.921035	−	0.531760i	0.883965	+	0.467553i	$0.154864\pi$
$864$		0			0
$865$	2685.17	−	4650.85i	0.105547	−	0.182813i
$866$		0			0
$867$	4552.54	−	5809.44i	0.178330	−	0.227565i
$868$		0			0
$869$			1658.68i			0.0647491i
$870$		0			0
$871$	9989.45	+	5767.41i	0.388610	+	0.224364i
$872$		0			0
$873$	1127.18	+	1174.08i	0.0436989	+	0.0455175i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19303.6	+	33434.9i	0.743258	+	1.28736i	0.951004	+	0.309177i	$0.100054\pi$
$877$	19303.6	+	33434.9i	0.743258	+	1.28736i	−0.207747	+	0.978183i	$0.566613\pi$
$878$		0			0
$879$	14093.9	+	35031.2i	0.540815	+	1.34423i
$880$		0			0
$881$	3460.09			0.132320			0.0661598	−	0.997809i	$-0.478925\pi$
$881$	3460.09			0.132320			0.0661598	+	0.997809i	$0.478925\pi$
$882$		0			0
$883$	10380.8			0.395631			0.197815	−	0.980239i	$-0.436615\pi$
$883$	10380.8			0.395631			0.197815	+	0.980239i	$0.436615\pi$
$884$		0			0
$885$	10858.3	+	26989.0i	0.412428	+	1.02511i
$886$		0			0
$887$	−22566.0	−	39085.4i	−0.854217	−	1.47955i	−0.877369	−	0.479815i	$-0.840704\pi$
$887$	−22566.0	−	39085.4i	−0.854217	−	1.47955i	0.0231523	−	0.999732i	$-0.492630\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−512.637	+	809.801i	−0.0192749	+	0.0304482i
$892$		0			0
$893$	−5131.37	−	2962.60i	−0.192290	−	0.111019i
$894$		0			0
$895$			21994.1i			0.821431i
$896$		0			0
$897$	−5831.65	+	7441.69i	−0.217071	+	0.277002i
$898$		0			0
$899$	−14115.3	+	24448.5i	−0.523663	+	0.907011i
$900$		0			0
$901$	−32219.6	+	18602.0i	−1.19133	+	0.687817i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13106.6	−	7567.08i	0.481411	−	0.277943i
$906$		0			0
$907$	−21491.9	+	37225.1i	−0.786800	+	1.36278i	0.141118	+	0.989993i	$0.454930\pi$
$907$	−21491.9	+	37225.1i	−0.786800	+	1.36278i	−0.927918	+	0.372785i	$0.878403\pi$
$908$		0			0
$909$	−7544.26	−	30640.2i	−0.275278	−	1.11801i
$910$		0			0
$911$			45726.0i			1.66297i	0.555545	+	0.831487i	$0.312510\pi$
$911$			45726.0i			1.66297i	−0.555545	+	0.831487i	$0.687490\pi$
$912$		0			0
$913$	957.686	+	552.920i	0.0347150	+	0.0200427i
$914$		0			0
$915$	3052.48	−	21491.2i	0.110286	−	0.776479i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	12581.6	+	21791.9i	0.451608	+	0.782208i	0.998486	−	0.0550040i	$-0.0175172\pi$
$919$	12581.6	+	21791.9i	0.451608	+	0.782208i	−0.546878	+	0.837212i	$0.684184\pi$
$920$		0			0
$921$	−19883.8	+	7999.75i	−0.711395	+	0.286211i
$922$		0			0
$923$	−1116.00			−0.0397980
$924$		0			0
$925$	−17677.4			−0.628355
$926$		0			0
$927$	137.759	−	475.167i	0.00488089	−	0.0168355i
$928$		0			0
$929$	10145.7	+	17572.8i	0.358309	+	0.620609i	0.987678	−	0.156497i	$-0.0500202\pi$
$929$	10145.7	+	17572.8i	0.358309	+	0.620609i	−0.629370	+	0.777106i	$0.716687\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−16968.2	−	2410.06i	−0.595406	−	0.0845678i
$934$		0			0
$935$	−515.788	−	297.791i	−0.0180407	−	0.0104158i
$936$		0			0
$937$			25708.8i			0.896339i	0.893949	+	0.448170i	$0.147924\pi$
$937$			25708.8i			0.896339i	−0.893949	+	0.448170i	$0.852076\pi$
$938$		0			0
$939$	−24502.5	−	19201.3i	−0.851555	−	0.667318i
$940$		0			0
$941$	−4571.93	+	7918.81i	−0.158385	+	0.274332i	−0.934287	−	0.356523i	$-0.883962\pi$
$941$	−4571.93	+	7918.81i	−0.158385	+	0.274332i	0.775901	+	0.630854i	$0.217296\pi$
$942$		0			0
$943$	−9363.68	+	5406.12i	−0.323354	+	0.186689i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	38004.7	−	21942.0i	1.30411	−	0.752925i	0.323000	−	0.946399i	$-0.395309\pi$
$947$	38004.7	−	21942.0i	1.30411	−	0.752925i	0.981105	+	0.193474i	$0.0619754\pi$
$948$		0			0
$949$	11545.7	−	19997.7i	0.394931	−	0.684040i
$950$		0			0
$951$	−29017.7	−	22739.6i	−0.989445	−	0.775374i
$952$		0			0
$953$			29621.5i			1.00686i	0.864037	+	0.503429i	$0.167928\pi$
$953$			29621.5i			1.00686i	−0.864037	+	0.503429i	$0.832072\pi$
$954$		0			0
$955$	7220.70	+	4168.87i	0.244666	+	0.141258i
$956$		0			0
$957$	2042.60	+	290.118i	0.0689947	+	0.00979958i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−10526.4	−	18232.2i	−0.353341	−	0.612004i
$962$		0			0
$963$	7161.73	−	24702.7i	0.239650	−	0.826620i
$964$		0			0
$965$	−29397.4			−0.980658
$966$		0			0
$967$	39437.0			1.31149			0.655744	−	0.754983i	$-0.272355\pi$
$967$	39437.0			1.31149			0.655744	+	0.754983i	$0.272355\pi$
$968$		0			0
$969$	8047.72	−	3237.80i	0.266801	−	0.107341i
$970$		0			0
$971$	−11231.4	−	19453.3i	−0.371197	−	0.642931i	0.618553	−	0.785743i	$-0.287719\pi$
$971$	−11231.4	−	19453.3i	−0.371197	−	0.642931i	−0.989750	+	0.142812i	$0.954386\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1160.45	−	8170.24i	0.0381171	−	0.268366i
$976$		0			0
$977$	23589.9	+	13619.6i	0.772474	+	0.445988i	0.833756	−	0.552132i	$-0.186186\pi$
$977$	23589.9	+	13619.6i	0.772474	+	0.445988i	−0.0612826	+	0.998120i	$0.519519\pi$
$978$		0			0
$979$			1685.90i			0.0550374i
$980$		0			0
$981$	4569.48	+	18558.5i	0.148718	+	0.604003i
$982$		0			0
$983$	−4358.40	+	7548.98i	−0.141416	+	0.244939i	−0.928030	−	0.372506i	$-0.878499\pi$
$983$	−4358.40	+	7548.98i	−0.141416	+	0.244939i	0.786614	+	0.617445i	$0.211832\pi$
$984$		0			0
$985$	10855.5	−	6267.42i	0.351152	−	0.202738i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−18708.4	+	10801.3i	−0.601510	+	0.347282i
$990$		0			0
$991$	14888.8	−	25788.1i	0.477252	−	0.826625i	−0.522408	−	0.852696i	$-0.674966\pi$
$991$	14888.8	−	25788.1i	0.477252	−	0.826625i	0.999660	+	0.0260705i	$0.00829944\pi$
$992$		0			0
$993$	−29370.6	+	37479.4i	−0.938618	+	1.19776i
$994$		0			0
$995$			33058.7i			1.05330i
$996$		0			0
$997$	−46504.6	−	26849.5i	−1.47725	−	0.852890i	−0.477579	−	0.878589i	$-0.658486\pi$
$997$	−46504.6	−	26849.5i	−1.47725	−	0.852890i	−0.999670	+	0.0256990i	$0.991819\pi$
$998$		0			0
$999$	−3750.02	−	37252.0i	−0.118764	−	1.17978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.e.521.10		48
3.2	odd	2	inner	588.4.k.e.521.3		48
7.2	even	3	inner	588.4.k.e.509.22		48
7.3	odd	6		588.4.f.d.293.19	yes	24
7.4	even	3		588.4.f.d.293.6	yes	24
7.5	odd	6	inner	588.4.k.e.509.3		48
7.6	odd	2	inner	588.4.k.e.521.15		48
21.2	odd	6	inner	588.4.k.e.509.15		48
21.5	even	6	inner	588.4.k.e.509.10		48
21.11	odd	6		588.4.f.d.293.20	yes	24
21.17	even	6		588.4.f.d.293.5	✓	24
21.20	even	2	inner	588.4.k.e.521.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.f.d.293.5	✓	24	21.17	even	6
588.4.f.d.293.6	yes	24	7.4	even	3
588.4.f.d.293.19	yes	24	7.3	odd	6
588.4.f.d.293.20	yes	24	21.11	odd	6
588.4.k.e.509.3		48	7.5	odd	6	inner
588.4.k.e.509.10		48	21.5	even	6	inner
588.4.k.e.509.15		48	21.2	odd	6	inner
588.4.k.e.509.22		48	7.2	even	3	inner
588.4.k.e.521.3		48	3.2	odd	2	inner
588.4.k.e.521.10		48	1.1	even	1	trivial
588.4.k.e.521.15		48	7.6	odd	2	inner
588.4.k.e.521.22		48	21.20	even	2	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93946 - 4.82063i) q^{3} +(3.83273 + 6.63849i) q^{5} +(-19.4770 + 18.6988i) q^{9} +O(q^{10})\)	\(q+(-1.93946 - 4.82063i) q^{3} +(3.83273 + 6.63849i) q^{5} +(-19.4770 + 18.6988i) q^{9} +(-1.13857 - 0.657354i) q^{11} +23.9754i q^{13} +(24.5683 - 31.3513i) q^{15} +(29.5490 - 51.1804i) q^{17} +(-24.4639 + 14.1243i) q^{19} +(-65.7234 + 37.9454i) q^{23} +(33.1203 - 57.3661i) q^{25} +(127.915 + 57.6258i) q^{27} -302.001i q^{29} +(-80.9549 - 46.7393i) q^{31} +(-0.960652 + 6.76354i) q^{33} +(-133.433 - 231.113i) q^{37} +(115.576 - 46.4992i) q^{39} +142.471 q^{41} +284.654 q^{43} +(-198.782 - 57.6302i) q^{45} +(104.876 + 181.651i) q^{47} +(-304.031 - 43.1827i) q^{51} +(-545.190 - 314.765i) q^{53} -10.0779i q^{55} +(115.535 + 90.5383i) q^{57} +(-365.186 + 632.521i) q^{59} +(471.964 - 272.488i) q^{61} +(-159.160 + 91.8912i) q^{65} +(240.556 - 416.655i) q^{67} +(310.389 + 243.235i) q^{69} +46.5477i q^{71} +(-834.095 - 481.565i) q^{73} +(-340.776 - 48.4018i) q^{75} +(-630.818 - 1092.61i) q^{79} +(29.7071 - 728.394i) q^{81} -841.130 q^{83} +453.014 q^{85} +(-1455.84 + 585.719i) q^{87} +(-641.169 - 1110.54i) q^{89} +(-68.3045 + 480.903i) q^{93} +(-187.528 - 108.269i) q^{95} -60.2806i q^{97} +(34.4677 - 8.48666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 48 * q + 64 * q^9	\( 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) \) 48 * q + 64 * q^9 - 192 * q^15 - 456 * q^25 + 432 * q^37 - 688 * q^39 + 1248 * q^43 + 1536 * q^51 - 2720 * q^57 + 528 * q^67 - 3744 * q^79 - 3408 * q^81 + 13824 * q^85 + 5088 * q^93 - 15472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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