LMFDB - Embedded newform 1368.2.e.g.379.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (of order $2$, degree $1$, 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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.4
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.g.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38840 + 0.268989i) q^{2} +(1.85529 - 0.746926i) q^{4} -3.66131i q^{5} +0.477575i q^{7} +(-2.37496 + 1.53608i) q^{8} +O(q^{10})$	\(q+(-1.38840 + 0.268989i) q^{2} +(1.85529 - 0.746926i) q^{4} -3.66131i q^{5} +0.477575i q^{7} +(-2.37496 + 1.53608i) q^{8} +(0.984850 + 5.08335i) q^{10} +6.02922 q^{11} +4.31300 q^{13} +(-0.128462 - 0.663064i) q^{14} +(2.88420 - 2.77153i) q^{16} +0.111078 q^{17} +(2.23153 + 3.74436i) q^{19} +(-2.73473 - 6.79279i) q^{20} +(-8.37094 + 1.62179i) q^{22} +7.73272i q^{23} -8.40518 q^{25} +(-5.98815 + 1.16015i) q^{26} +(0.356713 + 0.886040i) q^{28} -0.104336 q^{29} +6.47633 q^{31} +(-3.25891 + 4.62380i) q^{32} +(-0.154220 + 0.0298787i) q^{34} +1.74855 q^{35} +3.65969 q^{37} +(-4.10545 - 4.59840i) q^{38} +(5.62407 + 8.69548i) q^{40} +4.93627i q^{41} -0.796971 q^{43} +(11.1859 - 4.50338i) q^{44} +(-2.08001 - 10.7361i) q^{46} -3.88824i q^{47} +6.77192 q^{49} +(11.6697 - 2.26090i) q^{50} +(8.00186 - 3.22149i) q^{52} -6.35015 q^{53} -22.0748i q^{55} +(-0.733594 - 1.13422i) q^{56} +(0.144860 - 0.0280653i) q^{58} +8.57094i q^{59} +8.05083i q^{61} +(-8.99171 + 1.74206i) q^{62} +(3.28091 - 7.29628i) q^{64} -15.7912i q^{65} -12.2522i q^{67} +(0.206082 - 0.0829670i) q^{68} +(-2.42768 + 0.470340i) q^{70} +7.88798 q^{71} -13.9848 q^{73} +(-5.08110 + 0.984415i) q^{74} +(6.93691 + 5.28009i) q^{76} +2.87940i q^{77} -10.2206 q^{79} +(-10.1474 - 10.5600i) q^{80} +(-1.32780 - 6.85350i) q^{82} +6.98436 q^{83} -0.406691i q^{85} +(1.10651 - 0.214376i) q^{86} +(-14.3192 + 9.26137i) q^{88} -6.56953i q^{89} +2.05978i q^{91} +(5.77576 + 14.3464i) q^{92} +(1.04589 + 5.39842i) q^{94} +(13.7093 - 8.17034i) q^{95} -14.6725i q^{97} +(-9.40211 + 1.82157i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4}+O(q^{10}) $ 40 * q - 4 * q^4	$ 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.38840	+	0.268989i	−0.981745	+	0.190204i
$2$	−1.38840	+	0.268989i	−0.981745	+	0.190204i
$3$		0			0
$3$		0			0
$4$	1.85529	−	0.746926i	0.927645	−	0.373463i
$5$		−	3.66131i		−	1.63739i	−0.574231	−	0.818694i	$-0.694699\pi$
$5$		−	3.66131i		−	1.63739i	0.574231	−	0.818694i	$-0.305301\pi$
$6$		0			0
$7$			0.477575i			0.180506i	0.995919	+	0.0902532i	$0.0287676\pi$
$7$			0.477575i			0.180506i	−0.995919	+	0.0902532i	$0.971232\pi$
$8$	−2.37496	+	1.53608i	−0.839677	+	0.543087i
$9$		0			0
$10$	0.984850	+	5.08335i	0.311437	+	1.60750i
$11$	6.02922			1.81788			0.908939	−	0.416930i	$-0.136894\pi$
$11$	6.02922			1.81788			0.908939	+	0.416930i	$0.136894\pi$
$12$		0			0
$13$	4.31300			1.19621			0.598105	−	0.801418i	$-0.295920\pi$
$13$	4.31300			1.19621			0.598105	+	0.801418i	$0.295920\pi$
$14$	−0.128462	−	0.663064i	−0.0343330	−	0.177211i
$15$		0			0
$16$	2.88420	−	2.77153i	0.721051	−	0.692882i
$17$	0.111078			0.0269404			0.0134702	−	0.999909i	$-0.495712\pi$
$17$	0.111078			0.0269404			0.0134702	+	0.999909i	$0.495712\pi$
$18$		0			0
$19$	2.23153	+	3.74436i	0.511949	+	0.859016i
$19$	2.23153	+	3.74436i	0.511949	+	0.859016i
$20$	−2.73473	−	6.79279i	−0.611503	−	1.51891i
$21$		0			0
$22$	−8.37094	+	1.62179i	−1.78469	+	0.345767i
$23$			7.73272i			1.61238i	0.591655	+	0.806191i	$0.298475\pi$
$23$			7.73272i			1.61238i	−0.591655	+	0.806191i	$0.701525\pi$
$24$		0			0
$25$	−8.40518			−1.68104
$26$	−5.98815	+	1.16015i	−1.17437	+	0.227524i
$27$		0			0
$28$	0.356713	+	0.886040i	0.0674124	+	0.167446i
$29$	−0.104336			−0.0193748			−0.00968739	−	0.999953i	$-0.503084\pi$
$29$	−0.104336			−0.0193748			−0.00968739	+	0.999953i	$0.503084\pi$
$30$		0			0
$31$	6.47633			1.16318			0.581592	−	0.813481i	$-0.302430\pi$
$31$	6.47633			1.16318			0.581592	+	0.813481i	$0.302430\pi$
$32$	−3.25891	+	4.62380i	−0.576099	+	0.817380i
$33$		0			0
$34$	−0.154220	+	0.0298787i	−0.0264485	+	0.00512415i
$35$	1.74855			0.295559
$36$		0			0
$37$	3.65969			0.601650			0.300825	−	0.953679i	$-0.402738\pi$
$37$	3.65969			0.601650			0.300825	+	0.953679i	$0.402738\pi$
$38$	−4.10545	−	4.59840i	−0.665991	−	0.745959i
$39$		0			0
$40$	5.62407	+	8.69548i	0.889243	+	1.37488i
$41$			4.93627i			0.770915i	0.922726	+	0.385458i	$0.125956\pi$
$41$			4.93627i			0.770915i	−0.922726	+	0.385458i	$0.874044\pi$
$42$		0			0
$43$	−0.796971			−0.121537			−0.0607684	−	0.998152i	$-0.519355\pi$
$43$	−0.796971			−0.121537			−0.0607684	+	0.998152i	$0.519355\pi$
$44$	11.1859	−	4.50338i	1.68635	−	0.678910i
$45$		0			0
$46$	−2.08001	−	10.7361i	−0.306681	−	1.58295i
$47$		−	3.88824i		−	0.567159i	−0.958949	−	0.283579i	$-0.908478\pi$
$47$		−	3.88824i		−	0.567159i	0.958949	−	0.283579i	$-0.0915219\pi$
$48$		0			0
$49$	6.77192			0.967417
$50$	11.6697	−	2.26090i	1.65035	−	0.319739i
$51$		0			0
$52$	8.00186	−	3.22149i	1.10966	−	0.446740i
$53$	−6.35015			−0.872260			−0.436130	−	0.899884i	$-0.643651\pi$
$53$	−6.35015			−0.872260			−0.436130	+	0.899884i	$0.643651\pi$
$54$		0			0
$55$		−	22.0748i		−	2.97657i
$56$	−0.733594	−	1.13422i	−0.0980306	−	0.151567i
$57$		0			0
$58$	0.144860	−	0.0280653i	0.0190211	−	0.00368515i
$59$			8.57094i			1.11584i	0.829894	+	0.557921i	$0.188401\pi$
$59$			8.57094i			1.11584i	−0.829894	+	0.557921i	$0.811599\pi$
$60$		0			0
$61$			8.05083i			1.03080i	0.856949	+	0.515402i	$0.172357\pi$
$61$			8.05083i			1.03080i	−0.856949	+	0.515402i	$0.827643\pi$
$62$	−8.99171	+	1.74206i	−1.14195	+	0.221242i
$63$		0			0
$64$	3.28091	−	7.29628i	0.410114	−	0.912034i
$65$		−	15.7912i		−	1.95866i
$66$		0			0
$67$		−	12.2522i		−	1.49684i	−0.663223	−	0.748422i	$-0.730812\pi$
$67$		−	12.2522i		−	1.49684i	0.663223	−	0.748422i	$-0.269188\pi$
$68$	0.206082	−	0.0829670i	0.0249911	−	0.0100612i
$69$		0			0
$70$	−2.42768	+	0.470340i	−0.290163	+	0.0562164i
$71$	7.88798			0.936131			0.468066	−	0.883694i	$-0.344951\pi$
$71$	7.88798			0.936131			0.468066	+	0.883694i	$0.344951\pi$
$72$		0			0
$73$	−13.9848			−1.63680			−0.818401	−	0.574648i	$-0.805139\pi$
$73$	−13.9848			−1.63680			−0.818401	+	0.574648i	$0.805139\pi$
$74$	−5.08110	+	0.984415i	−0.590666	+	0.114436i
$75$		0			0
$76$	6.93691	+	5.28009i	0.795718	+	0.605668i
$77$			2.87940i			0.328139i
$78$		0			0
$79$	−10.2206			−1.14991			−0.574956	−	0.818184i	$-0.694981\pi$
$79$	−10.2206			−1.14991			−0.574956	+	0.818184i	$0.694981\pi$
$80$	−10.1474	−	10.5600i	−1.13452	−	1.18064i
$81$		0			0
$82$	−1.32780	−	6.85350i	−0.146631	−	0.756842i
$83$	6.98436			0.766633			0.383316	−	0.923617i	$-0.374782\pi$
$83$	6.98436			0.766633			0.383316	+	0.923617i	$0.374782\pi$
$84$		0			0
$85$		−	0.406691i		−	0.0441118i
$86$	1.10651	−	0.214376i	0.119318	−	0.0231168i
$87$		0			0
$88$	−14.3192	+	9.26137i	−1.52643	+	0.987265i
$89$		−	6.56953i		−	0.696368i	−0.937426	−	0.348184i	$-0.886798\pi$
$89$		−	6.56953i		−	0.696368i	0.937426	−	0.348184i	$-0.113202\pi$
$90$		0			0
$91$			2.05978i			0.215924i
$92$	5.77576	+	14.3464i	0.602165	+	1.49572i
$93$		0			0
$94$	1.04589	+	5.39842i	0.107876	+	0.556805i
$95$	13.7093	−	8.17034i	1.40654	−	0.838259i
$96$		0			0
$97$		−	14.6725i		−	1.48977i	−0.667192	−	0.744886i	$-0.732504\pi$
$97$		−	14.6725i		−	1.48977i	0.667192	−	0.744886i	$-0.267496\pi$
$98$	−9.40211	+	1.82157i	−0.949757	+	0.184006i
$99$		0			0
$100$	−15.5941	+	6.27805i	−1.55941	+	0.627805i
$101$		−	4.03481i		−	0.401478i	−0.979645	−	0.200739i	$-0.935666\pi$
$101$		−	4.03481i		−	0.401478i	0.979645	−	0.200739i	$-0.0643344\pi$
$102$		0			0
$103$	−11.7412			−1.15689			−0.578445	−	0.815721i	$-0.696340\pi$
$103$	−11.7412			−1.15689			−0.578445	+	0.815721i	$0.696340\pi$
$104$	−10.2432	+	6.62512i	−1.00443	+	0.649646i
$105$		0			0
$106$	8.81653	−	1.70812i	0.856337	−	0.165907i
$107$		−	0.308184i		−	0.0297932i	−0.999889	−	0.0148966i	$-0.995258\pi$
$107$		−	0.308184i		−	0.0297932i	0.999889	−	0.0148966i	$-0.00474192\pi$
$108$		0			0
$109$	−1.80709			−0.173088			−0.0865441	−	0.996248i	$-0.527582\pi$
$109$	−1.80709			−0.173088			−0.0865441	+	0.996248i	$0.527582\pi$
$110$	5.93788	+	30.6486i	0.566154	+	2.92223i
$111$		0			0
$112$	1.32361	+	1.37742i	0.125070	+	0.130154i
$113$		−	5.62063i		−	0.528744i	−0.964421	−	0.264372i	$-0.914835\pi$
$113$		−	5.62063i		−	0.528744i	0.964421	−	0.264372i	$-0.0851647\pi$
$114$		0			0
$115$	28.3119			2.64009
$116$	−0.193574	+	0.0779315i	−0.0179729	+	0.00723576i
$117$		0			0
$118$	−2.30549	−	11.8999i	−0.212237	−	1.09547i
$119$			0.0530480i			0.00486291i
$120$		0			0
$121$	25.3515			2.30468
$122$	−2.16558	−	11.1778i	−0.196063	−	1.01199i
$123$		0			0
$124$	12.0155	−	4.83734i	1.07902	−	0.434406i
$125$			12.4674i			1.11512i
$126$		0			0
$127$	10.1563			0.901222			0.450611	−	0.892720i	$-0.351206\pi$
$127$	10.1563			0.901222			0.450611	+	0.892720i	$0.351206\pi$
$128$	−2.59259	+	11.0127i	−0.229155	+	0.973390i
$129$		0			0
$130$	4.24766	+	21.9245i	0.372544	+	1.92290i
$131$	2.96824			0.259337			0.129668	−	0.991557i	$-0.458609\pi$
$131$	2.96824			0.259337			0.129668	+	0.991557i	$0.458609\pi$
$132$		0			0
$133$	−1.78821	+	1.06573i	−0.155058	+	0.0924101i
$134$	3.29570	+	17.0109i	0.284705	+	1.46952i
$135$		0			0
$136$	−0.263806	+	0.170625i	−0.0226212	+	0.0146309i
$137$	13.2242			1.12982			0.564910	−	0.825153i	$-0.308911\pi$
$137$	13.2242			1.12982			0.564910	+	0.825153i	$0.308911\pi$
$138$		0			0
$139$	−10.1509			−0.860984			−0.430492	−	0.902594i	$-0.641660\pi$
$139$	−10.1509			−0.860984			−0.430492	+	0.902594i	$0.641660\pi$
$140$	3.24407	−	1.30604i	0.274174	−	0.110380i
$141$		0			0
$142$	−10.9516	+	2.12178i	−0.919042	+	0.178056i
$143$	26.0040			2.17456
$144$		0			0
$145$			0.382008i			0.0317240i
$146$	19.4165	−	3.76176i	1.60692	−	0.311326i
$147$		0			0
$148$	6.78979	−	2.73352i	0.558117	−	0.224694i
$149$			4.46854i			0.366077i	0.983106	+	0.183038i	$0.0585933\pi$
$149$			4.46854i			0.366077i	−0.983106	+	0.183038i	$0.941407\pi$
$150$		0			0
$151$	12.8465			1.04543			0.522717	−	0.852506i	$-0.324919\pi$
$151$	12.8465			1.04543			0.522717	+	0.852506i	$0.324919\pi$
$152$	−11.0515	−	5.46491i	−0.896392	−	0.443263i
$153$		0			0
$154$	−0.774527	−	3.99775i	−0.0624132	−	0.322148i
$155$		−	23.7118i		−	1.90458i
$156$		0			0
$157$			17.0480i			1.36058i	0.732943	+	0.680290i	$0.238146\pi$
$157$			17.0480i			1.36058i	−0.732943	+	0.680290i	$0.761854\pi$
$158$	14.1903	−	2.74924i	1.12892	−	0.218718i
$159$		0			0
$160$	16.9292	+	11.9319i	1.33837	+	0.943297i
$161$	−3.69295			−0.291045
$162$		0			0
$163$	−0.203228			−0.0159181			−0.00795903	−	0.999968i	$-0.502533\pi$
$163$	−0.203228			−0.0159181			−0.00795903	+	0.999968i	$0.502533\pi$
$164$	3.68702	+	9.15821i	0.287908	+	0.715136i
$165$		0			0
$166$	−9.69706	+	1.87871i	−0.752638	+	0.145816i
$167$	−19.2702			−1.49117			−0.745587	−	0.666408i	$-0.767831\pi$
$167$	−19.2702			−1.49117			−0.745587	+	0.666408i	$0.767831\pi$
$168$		0			0
$169$	5.60196			0.430920
$170$	0.109395	+	0.564648i	0.00839022	+	0.0433065i
$171$		0			0
$172$	−1.47861	+	0.595278i	−0.112743	+	0.0453895i
$173$	−9.88821			−0.751787			−0.375893	−	0.926663i	$-0.622664\pi$
$173$	−9.88821			−0.751787			−0.375893	+	0.926663i	$0.622664\pi$
$174$		0			0
$175$		−	4.01410i		−	0.303438i
$176$	17.3895	−	16.7101i	1.31078	−	1.25957i
$177$		0			0
$178$	1.76713	+	9.12111i	0.132452	+	0.683656i
$179$		−	13.3538i		−	0.998110i	−0.866570	−	0.499055i	$-0.833681\pi$
$179$		−	13.3538i		−	0.998110i	0.866570	−	0.499055i	$-0.166319\pi$
$180$		0			0
$181$	−24.1122			−1.79225			−0.896123	−	0.443806i	$-0.853628\pi$
$181$	−24.1122			−1.79225			−0.896123	+	0.443806i	$0.853628\pi$
$182$	−0.554058	−	2.85979i	−0.0410695	−	0.211982i
$183$		0			0
$184$	−11.8781	−	18.3649i	−0.875664	−	1.35388i
$185$		−	13.3993i		−	0.985133i
$186$		0			0
$187$	0.669713			0.0489743
$188$	−2.90423	−	7.21382i	−0.211813	−	0.526122i
$189$		0			0
$190$	−16.8362	+	15.0313i	−1.22142	+	1.09049i
$191$		−	8.59245i		−	0.621728i	−0.950454	−	0.310864i	$-0.899382\pi$
$191$		−	8.59245i		−	0.621728i	0.950454	−	0.310864i	$-0.100618\pi$
$192$		0			0
$193$			15.4348i			1.11102i	0.831510	+	0.555510i	$0.187477\pi$
$193$			15.4348i			1.11102i	−0.831510	+	0.555510i	$0.812523\pi$
$194$	3.94675	+	20.3713i	0.283360	+	1.46258i
$195$		0			0
$196$	12.5639	−	5.05812i	0.897420	−	0.361295i
$197$			16.7351i			1.19233i	0.802863	+	0.596163i	$0.203309\pi$
$197$			16.7351i			1.19233i	−0.802863	+	0.596163i	$0.796691\pi$
$198$		0			0
$199$		−	20.4650i		−	1.45072i	−0.688367	−	0.725362i	$-0.741672\pi$
$199$		−	20.4650i		−	1.45072i	0.688367	−	0.725362i	$-0.258328\pi$
$200$	19.9620	−	12.9110i	1.41153	−	0.912948i
$201$		0			0
$202$	1.08532	+	5.60191i	0.0763627	+	0.394149i
$203$		−	0.0498284i		−	0.00349727i
$204$		0			0
$205$	18.0732			1.26229
$206$	16.3014	−	3.15824i	1.13577	−	0.220045i
$207$		0			0
$208$	12.4396	−	11.9536i	0.862529	−	0.828833i
$209$	13.4544	+	22.5756i	0.930661	+	1.56159i
$210$		0			0
$211$			1.64910i			0.113529i	0.998388	+	0.0567645i	$0.0180784\pi$
$211$			1.64910i			0.113529i	−0.998388	+	0.0567645i	$0.981922\pi$
$212$	−11.7814	+	4.74309i	−0.809148	+	0.325757i
$213$		0			0
$214$	0.0828979	+	0.427881i	0.00566678	+	0.0292494i
$215$			2.91796i			0.199003i
$216$		0			0
$217$			3.09293i			0.209962i
$218$	2.50896	−	0.486088i	0.169928	−	0.0329220i
$219$		0			0
$220$	−16.4883	−	40.9552i	−1.11164	−	2.76120i
$221$	0.479079			0.0322263
$222$		0			0
$223$	−3.00493			−0.201225			−0.100613	−	0.994926i	$-0.532080\pi$
$223$	−3.00493			−0.201225			−0.100613	+	0.994926i	$0.532080\pi$
$224$	−2.20821	−	1.55637i	−0.147542	−	0.103990i
$225$		0			0
$226$	1.51189	+	7.80366i	0.100569	+	0.519092i
$227$		−	25.9702i		−	1.72370i	−0.507161	−	0.861851i	$-0.669305\pi$
$227$		−	25.9702i		−	1.72370i	0.507161	−	0.861851i	$-0.330695\pi$
$228$		0			0
$229$		−	6.84507i		−	0.452335i	−0.974088	−	0.226168i	$-0.927380\pi$
$229$		−	6.84507i		−	0.452335i	0.974088	−	0.226168i	$-0.0726197\pi$
$230$	−39.3081	+	7.61557i	−2.59190	+	0.502156i
$231$		0			0
$232$	0.247795	−	0.160269i	0.0162685	−	0.0105222i
$233$	−20.9988			−1.37568			−0.687839	−	0.725863i	$-0.741440\pi$
$233$	−20.9988			−1.37568			−0.687839	+	0.725863i	$0.741440\pi$
$234$		0			0
$235$	−14.2361			−0.928658
$236$	6.40186	+	15.9016i	0.416725	+	1.03510i
$237$		0			0
$238$	−0.0142693	−	0.0736517i	−0.000924943	−	0.00477413i
$239$			13.0526i			0.844300i	0.906526	+	0.422150i	$0.138725\pi$
$239$			13.0526i			0.844300i	−0.906526	+	0.422150i	$0.861275\pi$
$240$		0			0
$241$		−	19.0062i		−	1.22430i	−0.790742	−	0.612149i	$-0.790305\pi$
$241$		−	19.0062i		−	1.22430i	0.790742	−	0.612149i	$-0.209695\pi$
$242$	−35.1979	+	6.81925i	−2.26261	+	0.438358i
$243$		0			0
$244$	6.01338	+	14.9366i	0.384967	+	0.956220i
$245$		−	24.7941i		−	1.58404i
$246$		0			0
$247$	9.62461	+	16.1494i	0.612399	+	1.02756i
$248$	−15.3810	+	9.94817i	−0.976698	+	0.631709i
$249$		0			0
$250$	−3.35359	−	17.3097i	−0.212100	−	1.09476i
$251$	−15.1767			−0.957944			−0.478972	−	0.877830i	$-0.658991\pi$
$251$	−15.1767			−0.957944			−0.478972	+	0.877830i	$0.658991\pi$
$252$		0			0
$253$			46.6222i			2.93111i
$254$	−14.1009	+	2.73192i	−0.884770	+	0.171416i
$255$		0			0
$256$	0.637262	−	15.9873i	0.0398289	−	0.999207i
$257$		−	1.62067i		−	0.101095i	−0.998722	−	0.0505473i	$-0.983903\pi$
$257$		−	1.62067i		−	0.101095i	0.998722	−	0.0505473i	$-0.0160966\pi$
$258$		0			0
$259$			1.74778i			0.108602i
$260$	−11.7949	−	29.2973i	−0.731487	−	1.81694i
$261$		0			0
$262$	−4.12110	+	0.798424i	−0.254602	+	0.0493268i
$263$		−	12.2459i		−	0.755113i	−0.925986	−	0.377557i	$-0.876764\pi$
$263$		−	12.2459i		−	0.755113i	0.925986	−	0.377557i	$-0.123236\pi$
$264$		0			0
$265$			23.2499i			1.42823i
$266$	2.19608	−	1.96066i	0.134650	−	0.120216i
$267$		0			0
$268$	−9.15148	−	22.7314i	−0.559016	−	1.38854i
$269$	12.3256			0.751502			0.375751	−	0.926721i	$-0.377385\pi$
$269$	12.3256			0.751502			0.375751	+	0.926721i	$0.377385\pi$
$270$		0			0
$271$			11.9166i			0.723885i	0.932200	+	0.361942i	$0.117886\pi$
$271$			11.9166i			0.723885i	−0.932200	+	0.361942i	$0.882114\pi$
$272$	0.320371	−	0.307856i	0.0194254	−	0.0186665i
$273$		0			0
$274$	−18.3604	+	3.55716i	−1.10919	+	0.214896i
$275$	−50.6767			−3.05592
$276$		0			0
$277$			14.4349i			0.867311i	0.901079	+	0.433656i	$0.142777\pi$
$277$			14.4349i			0.867311i	−0.901079	+	0.433656i	$0.857223\pi$
$278$	14.0934	−	2.73046i	0.845267	−	0.163762i
$279$		0			0
$280$	−4.15274	+	2.68591i	−0.248174	+	0.160514i
$281$			10.0963i			0.602292i	0.953578	+	0.301146i	$0.0973691\pi$
$281$			10.0963i			0.602292i	−0.953578	+	0.301146i	$0.902631\pi$
$282$		0			0
$283$	−12.3251			−0.732649			−0.366325	−	0.930487i	$-0.619384\pi$
$283$	−12.3251			−0.732649			−0.366325	+	0.930487i	$0.619384\pi$
$284$	14.6345	−	5.89174i	0.868398	−	0.349610i
$285$		0			0
$286$	−36.1039	+	6.99478i	−2.13487	+	0.413610i
$287$	−2.35744			−0.139155
$288$		0			0
$289$	−16.9877			−0.999274
$290$	−0.102756	−	0.530378i	−0.00603402	−	0.0311449i
$291$		0			0
$292$	−25.9459	+	10.4456i	−1.51837	+	0.611285i
$293$	−13.4269			−0.784405			−0.392203	−	0.919879i	$-0.628287\pi$
$293$	−13.4269			−0.784405			−0.392203	+	0.919879i	$0.628287\pi$
$294$		0			0
$295$	31.3809			1.82706
$296$	−8.69164	+	5.62158i	−0.505191	+	0.326748i
$297$		0			0
$298$	−1.20199	−	6.20410i	−0.0696292	−	0.359394i
$299$			33.3512i			1.92875i
$300$		0			0
$301$		−	0.380613i		−	0.0219382i
$302$	−17.8360	+	3.45556i	−1.02635	+	0.198845i
$303$		0			0
$304$	16.8138	+	4.61474i	0.964338	+	0.264674i
$305$	29.4766			1.68782
$306$		0			0
$307$			5.54628i			0.316543i	0.987396	+	0.158272i	$0.0505921\pi$
$307$			5.54628i			0.316543i	−0.987396	+	0.158272i	$0.949408\pi$
$308$	2.15070	+	5.34213i	0.122548	+	0.304396i
$309$		0			0
$310$	6.37822	+	32.9214i	0.362258	+	1.86981i
$311$		−	14.8688i		−	0.843134i	−0.906797	−	0.421567i	$-0.861480\pi$
$311$		−	14.8688i		−	0.843134i	0.906797	−	0.421567i	$-0.138520\pi$
$312$		0			0
$313$	−9.58377			−0.541707			−0.270853	−	0.962621i	$-0.587306\pi$
$313$	−9.58377			−0.541707			−0.270853	+	0.962621i	$0.587306\pi$
$314$	−4.58572	−	23.6694i	−0.258787	−	1.33574i
$315$		0			0
$316$	−18.9623	+	7.63406i	−1.06671	+	0.429449i
$317$	6.29299			0.353449			0.176725	−	0.984260i	$-0.443450\pi$
$317$	6.29299			0.353449			0.176725	+	0.984260i	$0.443450\pi$
$318$		0			0
$319$	−0.629067			−0.0352210
$320$	−26.7139	−	12.0124i	−1.49335	−	0.671515i
$321$		0			0
$322$	5.12728	−	0.993362i	0.285732	−	0.0553579i
$323$	0.247874	+	0.415916i	0.0137921	+	0.0231422i
$324$		0			0
$325$	−36.2515			−2.01087
$326$	0.282161	−	0.0546661i	0.0156275	−	0.00302767i
$327$		0			0
$328$	−7.58251	−	11.7235i	−0.418674	−	0.647320i
$329$	1.85693			0.102376
$330$		0			0
$331$			0.613453i			0.0337184i	0.999858	+	0.0168592i	$0.00536671\pi$
$331$			0.613453i			0.0337184i	−0.999858	+	0.0168592i	$0.994633\pi$
$332$	12.9580	−	5.21680i	0.711163	−	0.286309i
$333$		0			0
$334$	26.7547	−	5.18347i	1.46395	−	0.283627i
$335$	−44.8591			−2.45091
$336$		0			0
$337$		−	18.0411i		−	0.982762i	−0.870945	−	0.491381i	$-0.836492\pi$
$337$		−	18.0411i		−	0.982762i	0.870945	−	0.491381i	$-0.163508\pi$
$338$	−7.77774	+	1.50686i	−0.423053	+	0.0819625i
$339$		0			0
$340$	−0.303768	−	0.754529i	−0.0164741	−	0.0409201i
$341$	39.0472			2.11452
$342$		0			0
$343$			6.57713i			0.355131i
$344$	1.89278	−	1.22421i	0.102052	−	0.0660051i
$345$		0			0
$346$	13.7288	−	2.65982i	0.738063	−	0.142993i
$347$	35.7830			1.92093			0.960467	−	0.278394i	$-0.0898020\pi$
$347$	35.7830			1.92093			0.960467	+	0.278394i	$0.0898020\pi$
$348$		0			0
$349$		−	19.7659i		−	1.05804i	−0.848608	−	0.529022i	$-0.822559\pi$
$349$		−	19.7659i		−	1.05804i	0.848608	−	0.529022i	$-0.177441\pi$
$350$	1.07975	+	5.57317i	0.0577150	+	0.297898i
$351$		0			0
$352$	−19.6487	+	27.8779i	−1.04728	+	1.48590i
$353$	−33.7889			−1.79840			−0.899201	−	0.437537i	$-0.855851\pi$
$353$	−33.7889			−1.79840			−0.899201	+	0.437537i	$0.855851\pi$
$354$		0			0
$355$		−	28.8803i		−	1.53281i
$356$	−4.90695	−	12.1884i	−0.260068	−	0.645983i
$357$		0			0
$358$	3.59202	+	18.5404i	0.189844	+	0.979889i
$359$			1.09583i			0.0578356i	0.999582	+	0.0289178i	$0.00920611\pi$
$359$			1.09583i			0.0578356i	−0.999582	+	0.0289178i	$0.990794\pi$
$360$		0			0
$361$	−9.04051	+	16.7114i	−0.475816	+	0.879545i
$362$	33.4773	−	6.48591i	1.75953	−	0.340892i
$363$		0			0
$364$	1.53850	+	3.82149i	0.0806395	+	0.200301i
$365$			51.2028i			2.68008i
$366$		0			0
$367$			6.95430i			0.363011i	0.983390	+	0.181506i	$0.0580971\pi$
$367$			6.95430i			0.363011i	−0.983390	+	0.181506i	$0.941903\pi$
$368$	21.4314	+	22.3027i	1.11719	+	1.16261i
$369$		0			0
$370$	3.60425	+	18.6035i	0.187376	+	0.967149i
$371$		−	3.03267i		−	0.157449i
$372$		0			0
$373$	−11.8705			−0.614632			−0.307316	−	0.951607i	$-0.599431\pi$
$373$	−11.8705			−0.614632			−0.307316	+	0.951607i	$0.599431\pi$
$374$	−0.929827	+	0.180145i	−0.0480802	+	0.00931509i
$375$		0			0
$376$	5.97266	+	9.23444i	0.308016	+	0.476230i
$377$	−0.450003			−0.0231763
$378$		0			0
$379$			15.6688i			0.804852i	0.915453	+	0.402426i	$0.131833\pi$
$379$			15.6688i			0.804852i	−0.915453	+	0.402426i	$0.868167\pi$
$380$	19.3320	−	25.3982i	0.991712	−	1.30290i
$381$		0			0
$382$	2.31127	+	11.9297i	0.118255	+	0.610378i
$383$	−0.928843			−0.0474616			−0.0237308	−	0.999718i	$-0.507554\pi$
$383$	−0.928843			−0.0474616			−0.0237308	+	0.999718i	$0.507554\pi$
$384$		0			0
$385$	10.5424			0.537290
$386$	−4.15178	−	21.4296i	−0.211320	−	1.09074i
$387$		0			0
$388$	−10.9593	−	27.2218i	−0.556374	−	1.38198i
$389$		−	12.8829i		−	0.653191i	−0.945164	−	0.326596i	$-0.894098\pi$
$389$		−	12.8829i		−	0.653191i	0.945164	−	0.326596i	$-0.105902\pi$
$390$		0			0
$391$			0.858934i			0.0434382i
$392$	−16.0831	+	10.4022i	−0.812318	+	0.525392i
$393$		0			0
$394$	−4.50155	−	23.2350i	−0.226785	−	1.17056i
$395$			37.4209i			1.88285i
$396$		0			0
$397$		−	4.69481i		−	0.235626i	−0.993036	−	0.117813i	$-0.962412\pi$
$397$		−	4.69481i		−	0.235626i	0.993036	−	0.117813i	$-0.0375883\pi$
$398$	5.50485	+	28.4135i	0.275933	+	1.42424i
$399$		0			0
$400$	−24.2423	+	23.2952i	−1.21211	+	1.16476i
$401$		−	21.2932i		−	1.06333i	−0.846954	−	0.531665i	$-0.821566\pi$
$401$		−	21.2932i		−	1.06333i	0.846954	−	0.531665i	$-0.178434\pi$
$402$		0			0
$403$	27.9324			1.39141
$404$	−3.01370	−	7.48574i	−0.149937	−	0.372429i
$405$		0			0
$406$	0.0134033	+	0.0691816i	0.000665194	+	0.00343343i
$407$	22.0651			1.09373
$408$		0			0
$409$		−	35.4587i		−	1.75332i	−0.481109	−	0.876661i	$-0.659766\pi$
$409$		−	35.4587i		−	1.75332i	0.481109	−	0.876661i	$-0.340234\pi$
$410$	−25.0928	+	4.86148i	−1.23924	+	0.240092i
$411$		0			0
$412$	−21.7833	+	8.76977i	−1.07318	+	0.432056i
$413$	−4.09327			−0.201416
$414$		0			0
$415$		−	25.5719i		−	1.25527i
$416$	−14.0557	+	19.9424i	−0.689136	+	0.977758i
$417$		0			0
$418$	−24.7526	−	27.7248i	−1.21069	−	1.35606i
$419$	12.2871			0.600266			0.300133	−	0.953897i	$-0.402969\pi$
$419$	12.2871			0.600266			0.300133	+	0.953897i	$0.402969\pi$
$420$		0			0
$421$	−18.9376			−0.922963			−0.461481	−	0.887150i	$-0.652682\pi$
$421$	−18.9376			−0.922963			−0.461481	+	0.887150i	$0.652682\pi$
$422$	−0.443590	−	2.28961i	−0.0215936	−	0.111456i
$423$		0			0
$424$	15.0814	−	9.75434i	0.732416	−	0.473713i
$425$	−0.933630			−0.0452877
$426$		0			0
$427$	−3.84488			−0.186067
$428$	−0.230190	−	0.571770i	−0.0111267	−	0.0276376i
$429$		0			0
$430$	−0.784897	−	4.05128i	−0.0378511	−	0.195370i
$431$	−22.8465			−1.10048			−0.550238	−	0.835008i	$-0.685463\pi$
$431$	−22.8465			−1.10048			−0.550238	+	0.835008i	$0.685463\pi$
$432$		0			0
$433$			2.15376i			0.103503i	0.998660	+	0.0517516i	$0.0164804\pi$
$433$			2.15376i			0.103503i	−0.998660	+	0.0517516i	$0.983520\pi$
$434$	−0.831964	−	4.29422i	−0.0399355	−	0.206129i
$435$		0			0
$436$	−3.35268	+	1.34977i	−0.160564	+	0.0646420i
$437$	−28.9541	+	17.2558i	−1.38506	+	0.825458i
$438$		0			0
$439$	19.7107			0.940740			0.470370	−	0.882469i	$-0.344120\pi$
$439$	19.7107			0.940740			0.470370	+	0.882469i	$0.344120\pi$
$440$	33.9087	+	52.4269i	1.61653	+	2.49936i
$441$		0			0
$442$	−0.665152	+	0.128867i	−0.0316380	+	0.00612957i
$443$	8.46764			0.402309			0.201155	−	0.979559i	$-0.435531\pi$
$443$	8.46764			0.402309			0.201155	+	0.979559i	$0.435531\pi$
$444$		0			0
$445$	−24.0531			−1.14022
$446$	4.17204	−	0.808293i	0.197552	−	0.0382738i
$447$		0			0
$448$	3.48452	+	1.56688i	0.164628	+	0.0740281i
$449$			36.3479i			1.71536i	0.514181	+	0.857681i	$0.328096\pi$
$449$			36.3479i			1.71536i	−0.514181	+	0.857681i	$0.671904\pi$
$450$		0			0
$451$			29.7618i			1.40143i
$452$	−4.19819	−	10.4279i	−0.197466	−	0.490487i
$453$		0			0
$454$	6.98569	+	36.0569i	0.327855	+	1.69224i
$455$	7.54149			0.353551
$456$		0			0
$457$	−13.8319			−0.647029			−0.323515	−	0.946223i	$-0.604864\pi$
$457$	−13.8319			−0.647029			−0.323515	+	0.946223i	$0.604864\pi$
$458$	1.84125	+	9.50367i	0.0860358	+	0.444078i
$459$		0			0
$460$	52.5267	−	21.1469i	2.44907	−	0.985977i
$461$			13.5118i			0.629309i	0.949206	+	0.314654i	$0.101889\pi$
$461$			13.5118i			0.629309i	−0.949206	+	0.314654i	$0.898111\pi$
$462$		0			0
$463$		−	31.7531i		−	1.47569i	−0.674970	−	0.737846i	$-0.735843\pi$
$463$		−	31.7531i		−	1.47569i	0.674970	−	0.737846i	$-0.264157\pi$
$464$	−0.300927	+	0.289171i	−0.0139702	+	0.0134244i
$465$		0			0
$466$	29.1547	−	5.64844i	1.35056	−	0.261659i
$467$	−5.66145			−0.261980			−0.130990	−	0.991384i	$-0.541816\pi$
$467$	−5.66145			−0.261980			−0.130990	+	0.991384i	$0.541816\pi$
$468$		0			0
$469$	5.85134			0.270190
$470$	19.7653	−	3.82934i	0.911705	−	0.176634i
$471$		0			0
$472$	−13.1657	−	20.3557i	−0.605999	−	0.936946i
$473$	−4.80511			−0.220939
$474$		0			0
$475$	−18.7565	−	31.4720i	−0.860605	−	1.44404i
$476$	0.0396230	+	0.0984195i	0.00181612	+	0.00451105i
$477$		0			0
$478$	−3.51099	−	18.1221i	−0.160589	−	0.828887i
$479$			0.938852i			0.0428972i	0.999770	+	0.0214486i	$0.00682783\pi$
$479$			0.938852i			0.0428972i	−0.999770	+	0.0214486i	$0.993172\pi$
$480$		0			0
$481$	15.7842			0.719700
$482$	5.11246	+	26.3882i	0.232866	+	1.20195i
$483$		0			0
$484$	47.0343	−	18.9357i	2.13792	−	0.860712i
$485$	−53.7207			−2.43933
$486$		0			0
$487$	−20.9609			−0.949831			−0.474916	−	0.880031i	$-0.657521\pi$
$487$	−20.9609			−0.949831			−0.474916	+	0.880031i	$0.657521\pi$
$488$	−12.3667	−	19.1204i	−0.559816	−	0.865542i
$489$		0			0
$490$	6.66933	+	34.4240i	0.301290	+	1.55512i
$491$	−5.34859			−0.241379			−0.120689	−	0.992690i	$-0.538510\pi$
$491$	−5.34859			−0.241379			−0.120689	+	0.992690i	$0.538510\pi$
$492$		0			0
$493$	−0.0115895			−0.000521963
$494$	−17.7068	−	19.8329i	−0.796666	−	0.892325i
$495$		0			0
$496$	18.6791	−	17.9493i	0.838714	−	0.805949i
$497$			3.76710i			0.168978i
$498$		0			0
$499$	−31.8345			−1.42511			−0.712553	−	0.701618i	$-0.752461\pi$
$499$	−31.8345			−1.42511			−0.712553	+	0.701618i	$0.752461\pi$
$500$	9.31224	+	23.1307i	0.416456	+	1.03444i
$501$		0			0
$502$	21.0713	−	4.08236i	0.940457	−	0.182205i
$503$		−	7.01661i		−	0.312855i	−0.987689	−	0.156428i	$-0.950002\pi$
$503$		−	7.01661i		−	0.312855i	0.987689	−	0.156428i	$-0.0499978\pi$
$504$		0			0
$505$	−14.7727			−0.657375
$506$	−12.5408	−	64.7301i	−0.557509	−	2.87761i
$507$		0			0
$508$	18.8428	−	7.58597i	0.836014	−	0.336573i
$509$	39.7888			1.76361			0.881804	−	0.471617i	$-0.156329\pi$
$509$	39.7888			1.76361			0.881804	+	0.471617i	$0.156329\pi$
$510$		0			0
$511$		−	6.67881i		−	0.295453i
$512$	3.41563	+	22.3681i	0.150951	+	0.988541i
$513$		0			0
$514$	0.435942	+	2.25013i	0.0192286	+	0.0992491i
$515$			42.9880i			1.89428i
$516$		0			0
$517$		−	23.4431i		−	1.03102i
$518$	−0.470132	−	2.42661i	−0.0206564	−	0.106619i
$519$		0			0
$520$	24.2566	+	37.5036i	1.06372	+	1.64464i
$521$			22.1013i			0.968276i	0.874992	+	0.484138i	$0.160867\pi$
$521$			22.1013i			0.968276i	−0.874992	+	0.484138i	$0.839133\pi$
$522$		0			0
$523$			25.2015i			1.10199i	0.834510	+	0.550993i	$0.185751\pi$
$523$			25.2015i			1.10199i	−0.834510	+	0.550993i	$0.814249\pi$
$524$	5.50695	−	2.21706i	0.240572	−	0.0968526i
$525$		0			0
$526$	3.29400	+	17.0021i	0.143625	+	0.741329i
$527$	0.719377			0.0313366
$528$		0			0
$529$	−36.7949			−1.59978
$530$	−6.25395	−	32.2800i	−0.271654	−	1.40215i
$531$		0			0
$532$	−2.52164	+	3.31289i	−0.109327	+	0.143632i
$533$			21.2901i			0.922177i
$534$		0			0
$535$	−1.12836			−0.0487831
$536$	18.8204	+	29.0985i	0.812916	+	1.25686i
$537$		0			0
$538$	−17.1128	+	3.31543i	−0.737783	+	0.142939i
$539$	40.8294			1.75865
$540$		0			0
$541$		−	7.97150i		−	0.342722i	−0.985208	−	0.171361i	$-0.945184\pi$
$541$		−	7.97150i		−	0.342722i	0.985208	−	0.171361i	$-0.0548164\pi$
$542$	−3.20544	−	16.5450i	−0.137686	−	0.710670i
$543$		0			0
$544$	−0.361993	+	0.513602i	−0.0155203	+	0.0220205i
$545$			6.61633i			0.283412i
$546$		0			0
$547$			37.8368i			1.61779i	0.587956	+	0.808893i	$0.299933\pi$
$547$			37.8368i			1.61779i	−0.587956	+	0.808893i	$0.700067\pi$
$548$	24.5347	−	9.87749i	1.04807	−	0.421945i
$549$		0			0
$550$	70.3593	−	13.6314i	3.00013	−	0.581247i
$551$	−0.232830	−	0.390673i	−0.00991890	−	0.0166432i
$552$		0			0
$553$		−	4.88112i		−	0.207566i
$554$	−3.88283	−	20.0414i	−0.164966	−	0.851478i
$555$		0			0
$556$	−18.8328	+	7.58193i	−0.798688	+	0.321546i
$557$		−	1.42662i		−	0.0604480i	−0.999543	−	0.0302240i	$-0.990378\pi$
$557$		−	1.42662i		−	0.0604480i	0.999543	−	0.0302240i	$-0.00962206\pi$
$558$		0			0
$559$	−3.43733			−0.145384
$560$	5.04317	−	4.84615i	0.213113	−	0.204787i
$561$		0			0
$562$	−2.71578	−	14.0176i	−0.114558	−	0.591297i
$563$		−	14.7193i		−	0.620346i	−0.950680	−	0.310173i	$-0.899613\pi$
$563$		−	14.7193i		−	0.620346i	0.950680	−	0.310173i	$-0.100387\pi$
$564$		0			0
$565$	−20.5789			−0.865759
$566$	17.1121	−	3.31530i	0.719274	−	0.139353i
$567$		0			0
$568$	−18.7337	+	12.1166i	−0.786048	+	0.508400i
$569$			14.2289i			0.596506i	0.954487	+	0.298253i	$0.0964038\pi$
$569$			14.2289i			0.596506i	−0.954487	+	0.298253i	$0.903596\pi$
$570$		0			0
$571$	9.08617			0.380244			0.190122	−	0.981760i	$-0.439112\pi$
$571$	9.08617			0.380244			0.190122	+	0.981760i	$0.439112\pi$
$572$	48.2450	−	19.4231i	2.01722	−	0.812119i
$573$		0			0
$574$	3.27306	−	0.634124i	0.136615	−	0.0264678i
$575$		−	64.9949i		−	2.71047i
$576$		0			0
$577$	21.2120			0.883069			0.441534	−	0.897244i	$-0.354434\pi$
$577$	21.2120			0.883069			0.441534	+	0.897244i	$0.354434\pi$
$578$	23.5856	−	4.56949i	0.981032	−	0.190066i
$579$		0			0
$580$	0.285331	+	0.708735i	0.0118477	+	0.0294286i
$581$			3.33555i			0.138382i
$582$		0			0
$583$	−38.2864			−1.58566
$584$	33.2135	−	21.4819i	1.37438	−	0.888925i
$585$		0			0
$586$	18.6418	−	3.61167i	0.770085	−	0.149197i
$587$	16.0276			0.661531			0.330766	−	0.943713i	$-0.392693\pi$
$587$	16.0276			0.661531			0.330766	+	0.943713i	$0.392693\pi$
$588$		0			0
$589$	14.4522	+	24.2497i	0.595491	+	0.999193i
$590$	−43.5691	+	8.44109i	−1.79371	+	0.347514i
$591$		0			0
$592$	10.5553	−	10.1429i	0.433820	−	0.416872i
$593$	−18.5307			−0.760964			−0.380482	−	0.924788i	$-0.624242\pi$
$593$	−18.5307			−0.760964			−0.380482	+	0.924788i	$0.624242\pi$
$594$		0			0
$595$	0.194225			0.00796246
$596$	3.33767	+	8.29043i	0.136716	+	0.339589i
$597$		0			0
$598$	−8.97109	−	46.3047i	−0.366855	−	1.89354i
$599$	−11.9937			−0.490051			−0.245025	−	0.969517i	$-0.578796\pi$
$599$	−11.9937			−0.490051			−0.245025	+	0.969517i	$0.578796\pi$
$600$		0			0
$601$		−	30.4105i		−	1.24047i	−0.784416	−	0.620236i	$-0.787037\pi$
$601$		−	30.4105i		−	1.24047i	0.784416	−	0.620236i	$-0.212963\pi$
$602$	0.102381	+	0.528442i	0.00417272	+	0.0215377i
$603$		0			0
$604$	23.8340	−	9.59538i	0.969791	−	0.390431i
$605$		−	92.8195i		−	3.77365i
$606$		0			0
$607$	35.4092			1.43721			0.718607	−	0.695416i	$-0.244780\pi$
$607$	35.4092			1.43721			0.718607	+	0.695416i	$0.244780\pi$
$608$	−24.5855	−	1.88437i	−0.997076	−	0.0764213i
$609$		0			0
$610$	−40.9252	+	7.92887i	−1.65701	+	0.321030i
$611$		−	16.7700i		−	0.678441i
$612$		0			0
$613$		−	46.5620i		−	1.88062i	−0.340316	−	0.940311i	$-0.610534\pi$
$613$		−	46.5620i		−	1.88062i	0.340316	−	0.940311i	$-0.389466\pi$
$614$	−1.49189	−	7.70044i	−0.0602076	−	0.310764i
$615$		0			0
$616$	−4.42300	−	6.83848i	−0.178208	−	0.275530i
$617$	−32.9927			−1.32823			−0.664117	−	0.747629i	$-0.731192\pi$
$617$	−32.9927			−1.32823			−0.664117	+	0.747629i	$0.731192\pi$
$618$		0			0
$619$	9.77427			0.392861			0.196431	−	0.980518i	$-0.437065\pi$
$619$	9.77427			0.392861			0.196431	+	0.980518i	$0.437065\pi$
$620$	−17.7110	−	43.9923i	−0.711290	−	1.76678i
$621$		0			0
$622$	3.99955	+	20.6438i	0.160367	+	0.827742i
$623$	3.13744			0.125699
$624$		0			0
$625$	3.62116			0.144847
$626$	13.3061	−	2.57792i	0.531818	−	0.103035i
$627$		0			0
$628$	12.7336	+	31.6290i	0.508126	+	1.26214i
$629$	0.406511			0.0162087
$630$		0			0
$631$			24.1764i			0.962446i	0.876598	+	0.481223i	$0.159807\pi$
$631$			24.1764i			0.962446i	−0.876598	+	0.481223i	$0.840193\pi$
$632$	24.2737	−	15.6997i	0.965554	−	0.624502i
$633$		0			0
$634$	−8.73716	+	1.69274i	−0.346997	+	0.0672274i
$635$		−	37.1852i		−	1.47565i
$636$		0			0
$637$	29.2073			1.15723
$638$	0.873394	−	0.169212i	0.0345780	−	0.00669916i
$639$		0			0
$640$	40.3207	+	9.49226i	1.59382	+	0.375215i
$641$		−	46.9053i		−	1.85265i	−0.376726	−	0.926325i	$-0.622950\pi$
$641$		−	46.9053i		−	1.85265i	0.376726	−	0.926325i	$-0.377050\pi$
$642$		0			0
$643$	23.0731			0.909913			0.454957	−	0.890514i	$-0.349655\pi$
$643$	23.0731			0.909913			0.454957	+	0.890514i	$0.349655\pi$
$644$	−6.85150	+	2.75836i	−0.269987	+	0.108695i
$645$		0			0
$646$	−0.456024	−	0.510781i	−0.0179420	−	0.0200964i
$647$		−	43.8671i		−	1.72460i	−0.506402	−	0.862298i	$-0.669025\pi$
$647$		−	43.8671i		−	1.72460i	0.506402	−	0.862298i	$-0.330975\pi$
$648$		0			0
$649$			51.6761i			2.02846i
$650$	50.3315	−	9.75125i	1.97416	−	0.382476i
$651$		0			0
$652$	−0.377047	+	0.151796i	−0.0147663	+	0.00594481i
$653$		−	10.1868i		−	0.398641i	−0.979934	−	0.199320i	$-0.936127\pi$
$653$		−	10.1868i		−	0.398641i	0.979934	−	0.199320i	$-0.0638735\pi$
$654$		0			0
$655$		−	10.8677i		−	0.424634i
$656$	13.6810	+	14.2372i	0.534153	+	0.555869i
$657$		0			0
$658$	−2.57815	+	0.499493i	−0.100507	+	0.0194722i
$659$			32.1850i			1.25375i	0.779121	+	0.626874i	$0.215666\pi$
$659$			32.1850i			1.25375i	−0.779121	+	0.626874i	$0.784334\pi$
$660$		0			0
$661$	43.3863			1.68753			0.843765	−	0.536713i	$-0.180334\pi$
$661$	43.3863			1.68753			0.843765	+	0.536713i	$0.180334\pi$
$662$	−0.165012	−	0.851716i	−0.00641337	−	0.0331029i
$663$		0			0
$664$	−16.5876	+	10.7285i	−0.643724	+	0.416348i
$665$	3.90195	+	6.54720i	0.151311	+	0.253890i
$666$		0			0
$667$		−	0.806803i		−	0.0312395i
$668$	−35.7518	+	14.3934i	−1.38328	+	0.556898i
$669$		0			0
$670$	62.2822	−	12.0666i	2.40617	−	0.466173i
$671$			48.5402i			1.87387i
$672$		0			0
$673$			24.1792i			0.932041i	0.884774	+	0.466020i	$0.154313\pi$
$673$			24.1792i			0.932041i	−0.884774	+	0.466020i	$0.845687\pi$
$674$	4.85285	+	25.0482i	0.186925	+	0.964821i
$675$		0			0
$676$	10.3933	−	4.18425i	0.399741	−	0.160933i
$677$	40.6641			1.56285			0.781424	−	0.624001i	$-0.214494\pi$
$677$	40.6641			1.56285			0.781424	+	0.624001i	$0.214494\pi$
$678$		0			0
$679$	7.00724			0.268913
$680$	0.624710	+	0.965876i	0.0239565	+	0.0370396i
$681$		0			0
$682$	−54.2130	+	10.5033i	−2.07592	+	0.402190i
$683$			40.6935i			1.55709i	0.627586	+	0.778547i	$0.284043\pi$
$683$			40.6935i			1.55709i	−0.627586	+	0.778547i	$0.715957\pi$
$684$		0			0
$685$		−	48.4179i		−	1.84995i
$686$	−1.76917	−	9.13166i	−0.0675473	−	0.348648i
$687$		0			0
$688$	−2.29863	+	2.20883i	−0.0876343	+	0.0842107i
$689$	−27.3882			−1.04341
$690$		0			0
$691$	9.05312			0.344397			0.172198	−	0.985062i	$-0.444913\pi$
$691$	9.05312			0.344397			0.172198	+	0.985062i	$0.444913\pi$
$692$	−18.3455	+	7.38576i	−0.697391	+	0.280764i
$693$		0			0
$694$	−49.6810	+	9.62523i	−1.88587	+	0.365369i
$695$			37.1654i			1.40976i
$696$		0			0
$697$			0.548310i			0.0207687i
$698$	5.31680	+	27.4429i	0.201244	+	1.03873i
$699$		0			0
$700$	−2.99824	−	7.44733i	−0.113323	−	0.281483i
$701$			16.0571i			0.606470i	0.952916	+	0.303235i	$0.0980666\pi$
$701$			16.0571i			0.606470i	−0.952916	+	0.303235i	$0.901933\pi$
$702$		0			0
$703$	8.16673	+	13.7032i	0.308014	+	0.516826i
$704$	19.7813	−	43.9908i	0.745536	−	1.65797i
$705$		0			0
$706$	46.9124	−	9.08883i	1.76557	−	0.342063i
$707$	1.92692			0.0724694
$708$		0			0
$709$			7.26054i			0.272675i	0.990662	+	0.136338i	$0.0435332\pi$
$709$			7.26054i			0.272675i	−0.990662	+	0.136338i	$0.956467\pi$
$710$	7.76848	+	40.0974i	0.291546	+	1.50483i
$711$		0			0
$712$	10.0913	+	15.6024i	0.378188	+	0.584724i
$713$			50.0796i			1.87550i
$714$		0			0
$715$		−	95.2087i		−	3.56060i
$716$	−9.97429	−	24.7752i	−0.372757	−	0.925891i
$717$		0			0
$718$	−0.294765	−	1.52144i	−0.0110006	−	0.0567798i
$719$			38.3241i			1.42925i	0.699509	+	0.714624i	$0.253402\pi$
$719$			38.3241i			1.42925i	−0.699509	+	0.714624i	$0.746598\pi$
$720$		0			0
$721$		−	5.60728i		−	0.208826i
$722$	8.05664	−	25.6338i	0.299837	−	0.953990i
$723$		0			0
$724$	−44.7351	+	18.0100i	−1.66257	+	0.669337i
$725$	0.876966			0.0325697
$726$		0			0
$727$			36.7039i			1.36127i	0.732621	+	0.680637i	$0.238297\pi$
$727$			36.7039i			1.36127i	−0.732621	+	0.680637i	$0.761703\pi$
$728$	−3.16399	−	4.89190i	−0.117265	−	0.181306i
$729$		0			0
$730$	−13.7730	−	71.0898i	−0.509761	−	2.63115i
$731$	−0.0885259			−0.00327425
$732$		0			0
$733$			4.87598i			0.180098i	0.995937	+	0.0900492i	$0.0287024\pi$
$733$			4.87598i			0.180098i	−0.995937	+	0.0900492i	$0.971298\pi$
$734$	−1.87063	−	9.65532i	−0.0690461	−	0.356384i
$735$		0			0
$736$	−35.7545	−	25.2002i	−1.31793	−	0.928892i
$737$		−	73.8711i		−	2.72108i
$738$		0			0
$739$	27.4258			1.00888			0.504438	−	0.863448i	$-0.331700\pi$
$739$	27.4258			1.00888			0.504438	+	0.863448i	$0.331700\pi$
$740$	−10.0083	−	24.8595i	−0.367911	−	0.913854i
$741$		0			0
$742$	0.815754	+	4.21055i	0.0299473	+	0.154574i
$743$	−20.9491			−0.768550			−0.384275	−	0.923219i	$-0.625548\pi$
$743$	−20.9491			−0.768550			−0.384275	+	0.923219i	$0.625548\pi$
$744$		0			0
$745$	16.3607			0.599410
$746$	16.4810	−	3.19303i	0.603412	−	0.116905i
$747$		0			0
$748$	1.24251	−	0.500226i	0.0454307	−	0.0182901i
$749$	0.147181			0.00537787
$750$		0			0
$751$	37.4852			1.36785			0.683927	−	0.729550i	$-0.260271\pi$
$751$	37.4852			1.36785			0.683927	+	0.729550i	$0.260271\pi$
$752$	−10.7764	−	11.2145i	−0.392974	−	0.408950i
$753$		0			0
$754$	0.624782	−	0.121046i	0.0227532	−	0.00440822i
$755$		−	47.0350i		−	1.71178i
$756$		0			0
$757$			39.7181i			1.44358i	0.692112	+	0.721790i	$0.256680\pi$
$757$			39.7181i			1.44358i	−0.692112	+	0.721790i	$0.743320\pi$
$758$	−4.21473	−	21.7545i	−0.153086	−	0.790159i
$759$		0			0
$760$	−20.0087	+	40.4628i	−0.725792	+	1.46774i
$761$	−12.9445			−0.469238			−0.234619	−	0.972087i	$-0.575384\pi$
$761$	−12.9445			−0.469238			−0.234619	+	0.972087i	$0.575384\pi$
$762$		0			0
$763$		−	0.863023i		−	0.0312435i
$764$	−6.41792	−	15.9415i	−0.232192	−	0.576743i
$765$		0			0
$766$	1.28960	−	0.249848i	0.0465952	−	0.00902738i
$767$			36.9664i			1.33478i
$768$		0			0
$769$	13.6104			0.490803			0.245401	−	0.969422i	$-0.421080\pi$
$769$	13.6104			0.490803			0.245401	+	0.969422i	$0.421080\pi$
$770$	−14.6370	+	2.83578i	−0.527481	+	0.102194i
$771$		0			0
$772$	11.5286	+	28.6360i	0.414925	+	1.03063i
$773$	−5.54875			−0.199575			−0.0997873	−	0.995009i	$-0.531816\pi$
$773$	−5.54875			−0.199575			−0.0997873	+	0.995009i	$0.531816\pi$
$774$		0			0
$775$	−54.4347			−1.95535
$776$	22.5382	+	34.8468i	0.809075	+	1.25093i
$777$		0			0
$778$	3.46537	+	17.8866i	0.124239	+	0.641267i
$779$	−18.4832	+	11.0155i	−0.662228	+	0.394669i
$780$		0			0
$781$	47.5584			1.70177
$782$	−0.231043	−	1.19254i	−0.00826210	−	0.0426452i
$783$		0			0
$784$	19.5316	−	18.7686i	0.697557	−	0.670306i
$785$	62.4181			2.22780
$786$		0			0
$787$			25.5842i			0.911980i	0.889985	+	0.455990i	$0.150715\pi$
$787$			25.5842i			0.911980i	−0.889985	+	0.455990i	$0.849285\pi$
$788$	12.4999	+	31.0485i	0.445290	+	1.10606i
$789$		0			0
$790$	−10.0658	−	51.9551i	−0.358125	−	1.84848i
$791$	2.68427			0.0954417
$792$		0			0
$793$			34.7232i			1.23306i
$794$	1.26285	+	6.51826i	0.0448169	+	0.231324i
$795$		0			0
$796$	−15.2858	−	37.9685i	−0.541792	−	1.34576i
$797$	−19.9870			−0.707975			−0.353988	−	0.935250i	$-0.615174\pi$
$797$	−19.9870			−0.707975			−0.353988	+	0.935250i	$0.615174\pi$
$798$		0			0
$799$		−	0.431898i		−	0.0152795i
$800$	27.3917	−	38.8639i	0.968444	−	1.37405i
$801$		0			0
$802$	5.72762	+	29.5634i	0.202249	+	1.04392i
$803$	−84.3177			−2.97551
$804$		0			0
$805$			13.5210i			0.476554i
$806$	−38.7812	+	7.51350i	−1.36601	+	0.264652i
$807$		0			0
$808$	6.19779	+	9.58252i	0.218038	+	0.337112i
$809$	2.53016			0.0889557			0.0444779	−	0.999010i	$-0.485838\pi$
$809$	2.53016			0.0889557			0.0444779	+	0.999010i	$0.485838\pi$
$810$		0			0
$811$			31.0023i			1.08864i	0.838878	+	0.544319i	$0.183212\pi$
$811$			31.0023i			1.08864i	−0.838878	+	0.544319i	$0.816788\pi$
$812$	−0.0372181	−	0.0924462i	−0.00130610	−	0.00324423i
$813$		0			0
$814$	−30.6351	+	5.93525i	−1.07376	+	0.208031i
$815$			0.744081i			0.0260640i
$816$		0			0
$817$	−1.77847	−	2.98415i	−0.0622207	−	0.104402i
$818$	9.53799	+	49.2308i	0.333488	+	1.72131i
$819$		0			0
$820$	33.5310	−	13.4993i	1.17095	−	0.471417i
$821$		−	42.5684i		−	1.48565i	−0.669487	−	0.742824i	$-0.733486\pi$
$821$		−	42.5684i		−	1.48565i	0.669487	−	0.742824i	$-0.266514\pi$
$822$		0			0
$823$			9.56482i			0.333409i	0.986007	+	0.166704i	$0.0533125\pi$
$823$			9.56482i			0.333409i	−0.986007	+	0.166704i	$0.946687\pi$
$824$	27.8848	−	18.0354i	0.971414	−	0.628292i
$825$		0			0
$826$	5.68308	−	1.10104i	0.197740	−	0.0383102i
$827$			33.6462i			1.16999i	0.811035	+	0.584997i	$0.198904\pi$
$827$			33.6462i			1.16999i	−0.811035	+	0.584997i	$0.801096\pi$
$828$		0			0
$829$	21.3743			0.742360			0.371180	−	0.928561i	$-0.378953\pi$
$829$	21.3743			0.742360			0.371180	+	0.928561i	$0.378953\pi$
$830$	6.87855	+	35.5039i	0.238758	+	1.23236i
$831$		0			0
$832$	14.1506	−	31.4688i	0.490582	−	1.09099i
$833$	0.752211			0.0260626
$834$		0			0
$835$			70.5542i			2.44163i
$836$	41.8241	+	31.8348i	1.44652	+	1.10103i
$837$		0			0
$838$	−17.0594	+	3.30510i	−0.589307	+	0.114173i
$839$	11.0278			0.380720			0.190360	−	0.981714i	$-0.439034\pi$
$839$	11.0278			0.380720			0.190360	+	0.981714i	$0.439034\pi$
$840$		0			0
$841$	−28.9891			−0.999625
$842$	26.2929	−	5.09400i	0.906114	−	0.175551i
$843$		0			0
$844$	1.23176	+	3.05956i	0.0423988	+	0.105315i
$845$		−	20.5105i		−	0.705582i
$846$		0			0
$847$			12.1072i			0.416009i
$848$	−18.3151	+	17.5996i	−0.628944	+	0.604373i
$849$		0			0
$850$	1.29625	−	0.251136i	0.0444610	−	0.00861389i
$851$			28.2994i			0.970089i
$852$		0			0
$853$		−	0.0580014i		−	0.00198593i	−1.00000		0.000992965i	$-0.999684\pi$
$853$		−	0.0580014i		−	0.00198593i	1.00000		0.000992965i	$-0.000316071\pi$
$854$	5.33821	−	1.03423i	0.182670	−	0.0353906i
$855$		0			0
$856$	0.473395	+	0.731925i	0.0161803	+	0.0250167i
$857$		−	32.5174i		−	1.11077i	−0.831592	−	0.555386i	$-0.812570\pi$
$857$		−	32.5174i		−	1.11077i	0.831592	−	0.555386i	$-0.187430\pi$
$858$		0			0
$859$	−27.2215			−0.928784			−0.464392	−	0.885630i	$-0.653727\pi$
$859$	−27.2215			−0.928784			−0.464392	+	0.885630i	$0.653727\pi$
$860$	2.17950	+	5.41365i	0.0743202	+	0.184604i
$861$		0			0
$862$	31.7200	−	6.14545i	1.08039	−	0.209315i
$863$	41.7015			1.41954			0.709769	−	0.704435i	$-0.248800\pi$
$863$	41.7015			1.41954			0.709769	+	0.704435i	$0.248800\pi$
$864$		0			0
$865$			36.2038i			1.23097i
$866$	−0.579338	−	2.99028i	−0.0196867	−	0.101614i
$867$		0			0
$868$	2.31019	+	5.73829i	0.0784130	+	0.194770i
$869$	−61.6225			−2.09040
$870$		0			0
$871$		−	52.8437i		−	1.79054i
$872$	4.29178	−	2.77584i	0.145338	−	0.0940019i
$873$		0			0
$874$	35.5581	−	31.7462i	1.20277	−	1.07383i
$875$	−5.95413			−0.201286
$876$		0			0
$877$	42.0506			1.41995			0.709974	−	0.704228i	$-0.248707\pi$
$877$	42.0506			1.41995			0.709974	+	0.704228i	$0.248707\pi$
$878$	−27.3663	+	5.30195i	−0.923567	+	0.178932i
$879$		0			0
$880$	−61.1810	−	63.6683i	−2.06241	−	2.14626i
$881$	14.4430			0.486597			0.243298	−	0.969951i	$-0.421771\pi$
$881$	14.4430			0.486597			0.243298	+	0.969951i	$0.421771\pi$
$882$		0			0
$883$	−2.71398			−0.0913328			−0.0456664	−	0.998957i	$-0.514541\pi$
$883$	−2.71398			−0.0913328			−0.0456664	+	0.998957i	$0.514541\pi$
$884$	0.888830	−	0.357836i	0.0298946	−	0.0120353i
$885$		0			0
$886$	−11.7564	+	2.27770i	−0.394965	+	0.0765207i
$887$	19.2490			0.646319			0.323160	−	0.946344i	$-0.395255\pi$
$887$	19.2490			0.646319			0.323160	+	0.946344i	$0.395255\pi$
$888$		0			0
$889$			4.85038i			0.162676i
$890$	33.3952	−	6.47000i	1.11941	−	0.216875i
$891$		0			0
$892$	−5.57502	+	2.24446i	−0.186666	+	0.0751501i
$893$	14.5590	−	8.67675i	0.487198	−	0.290356i
$894$		0			0
$895$	−48.8924			−1.63429
$896$	−5.25937	−	1.23816i	−0.175703	−	0.0413639i
$897$		0			0
$898$	−9.77717	−	50.4653i	−0.326268	−	1.68405i
$899$	−0.675717			−0.0225364
$900$		0			0
$901$	−0.705361			−0.0234990
$902$	−8.00559	−	41.3212i	−0.266557	−	1.37585i
$903$		0			0
$904$	8.63374	+	13.3488i	0.287154	+	0.443974i
$905$			88.2822i			2.93460i
$906$		0			0
$907$		−	37.1775i		−	1.23446i	−0.786783	−	0.617230i	$-0.788255\pi$
$907$		−	37.1775i		−	1.23446i	0.786783	−	0.617230i	$-0.211745\pi$
$908$	−19.3978	−	48.1823i	−0.643739	−	1.59898i
$909$		0			0
$910$	−10.4706	+	2.02858i	−0.347096	+	0.0672466i
$911$	14.6570			0.485609			0.242804	−	0.970075i	$-0.421933\pi$
$911$	14.6570			0.485609			0.242804	+	0.970075i	$0.421933\pi$
$912$		0			0
$913$	42.1102			1.39364
$914$	19.2042	−	3.72062i	0.635217	−	0.123067i
$915$		0			0
$916$	−5.11276	−	12.6996i	−0.168930	−	0.419606i
$917$			1.41756i			0.0468119i
$918$		0			0
$919$			36.7289i			1.21157i	0.795627	+	0.605787i	$0.207142\pi$
$919$			36.7289i			1.21157i	−0.795627	+	0.605787i	$0.792858\pi$
$920$	−67.2397	+	43.4893i	−2.21683	+	1.43380i
$921$		0			0
$922$	−3.63453	−	18.7598i	−0.119697	−	0.617821i
$923$	34.0209			1.11981
$924$		0			0
$925$	−30.7604			−1.01139
$926$	8.54122	+	44.0859i	0.280682	+	1.44875i
$927$		0			0
$928$	0.340023	−	0.482430i	0.0111618	−	0.0158365i
$929$	42.5936			1.39745			0.698725	−	0.715390i	$-0.253751\pi$
$929$	42.5936			1.39745			0.698725	+	0.715390i	$0.253751\pi$
$930$		0			0
$931$	15.1118	+	25.3565i	0.495269	+	0.831027i
$932$	−38.9589	+	15.6846i	−1.27614	+	0.513765i
$933$		0			0
$934$	7.86033	−	1.52286i	0.257198	−	0.0498296i
$935$		−	2.45203i		−	0.0801898i
$936$		0			0
$937$	−6.27969			−0.205148			−0.102574	−	0.994725i	$-0.532708\pi$
$937$	−6.27969			−0.205148			−0.102574	+	0.994725i	$0.532708\pi$
$938$	−8.12398	+	1.57394i	−0.265257	+	0.0513911i
$939$		0			0
$940$	−26.4120	+	10.6333i	−0.861465	+	0.346819i
$941$	4.84526			0.157951			0.0789755	−	0.996877i	$-0.474835\pi$
$941$	4.84526			0.157951			0.0789755	+	0.996877i	$0.474835\pi$
$942$		0			0
$943$	−38.1707			−1.24301
$944$	23.7546	+	24.7203i	0.773146	+	0.804578i
$945$		0			0
$946$	6.67140	−	1.29252i	0.216906	−	0.0420234i
$947$	−15.0712			−0.489747			−0.244873	−	0.969555i	$-0.578746\pi$
$947$	−15.0712			−0.489747			−0.244873	+	0.969555i	$0.578746\pi$
$948$		0			0
$949$	−60.3166			−1.95796
$950$	34.5070	+	38.6504i	1.11956	+	1.25398i
$951$		0			0
$952$	−0.0814861	−	0.125987i	−0.00264098	−	0.00408327i
$953$			32.5858i			1.05556i	0.849381	+	0.527779i	$0.176975\pi$
$953$			32.5858i			1.05556i	−0.849381	+	0.527779i	$0.823025\pi$
$954$		0			0
$955$	−31.4596			−1.01801
$956$	9.74930	+	24.2163i	0.315315	+	0.783211i
$957$		0			0
$958$	−0.252540	−	1.30350i	−0.00815921	−	0.0421141i
$959$			6.31554i			0.203940i
$960$		0			0
$961$	10.9428			0.352995
$962$	−21.9148	+	4.24578i	−0.706561	+	0.136889i
$963$		0			0
$964$	−14.1962	−	35.2620i	−0.457230	−	1.13571i
$965$	56.5116			1.81917
$966$		0			0
$967$		−	34.7288i		−	1.11680i	−0.829571	−	0.558401i	$-0.811415\pi$
$967$		−	34.7288i		−	1.11680i	0.829571	−	0.558401i	$-0.188585\pi$
$968$	−60.2088	+	38.9419i	−1.93518	+	1.25164i
$969$		0			0
$970$	74.5857	−	14.4503i	2.39480	−	0.463970i
$971$		−	20.4304i		−	0.655642i	−0.944740	−	0.327821i	$-0.893686\pi$
$971$		−	20.4304i		−	0.655642i	0.944740	−	0.327821i	$-0.106314\pi$
$972$		0			0
$973$		−	4.84779i		−	0.155413i
$974$	29.1021	−	5.63826i	0.932492	−	0.180661i
$975$		0			0
$976$	22.3131	+	23.2202i	0.714225	+	0.743262i
$977$		−	9.40369i		−	0.300851i	−0.988621	−	0.150425i	$-0.951936\pi$
$977$		−	9.40369i		−	0.300851i	0.988621	−	0.150425i	$-0.0480643\pi$
$978$		0			0
$979$		−	39.6091i		−	1.26591i
$980$	−18.5194	−	46.0002i	−0.591579	−	1.46942i
$981$		0			0
$982$	7.42597	−	1.43871i	0.236972	−	0.0459111i
$983$	−15.6570			−0.499381			−0.249691	−	0.968326i	$-0.580329\pi$
$983$	−15.6570			−0.499381			−0.249691	+	0.968326i	$0.580329\pi$
$984$		0			0
$985$	61.2724			1.95230
$986$	0.0160908	−	0.00311743i	0.000512435	−	9.92793e-5i
$987$		0			0
$988$	29.9189	+	22.7730i	0.951846	+	0.724506i
$989$		−	6.16275i		−	0.195964i
$990$		0			0
$991$	24.7149			0.785094			0.392547	−	0.919732i	$-0.371594\pi$
$991$	24.7149			0.785094			0.392547	+	0.919732i	$0.371594\pi$
$992$	−21.1058	+	29.9452i	−0.670109	+	0.950762i
$993$		0			0
$994$	−1.01331	−	5.23023i	−0.0321402	−	0.165893i
$995$	−74.9286			−2.37540
$996$		0			0
$997$			2.67224i			0.0846306i	0.999104	+	0.0423153i	$0.0134734\pi$
$997$			2.67224i			0.0846306i	−0.999104	+	0.0423153i	$0.986527\pi$
$998$	44.1989	−	8.56311i	1.39909	−	0.271060i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.g.379.4		40
3.2	odd	2		456.2.e.a.379.37	yes	40
4.3	odd	2		5472.2.e.g.5167.39		40
8.3	odd	2	inner	1368.2.e.g.379.38		40
8.5	even	2		5472.2.e.g.5167.30		40
12.11	even	2		1824.2.e.a.1519.11		40
19.18	odd	2	inner	1368.2.e.g.379.37		40
24.5	odd	2		1824.2.e.a.1519.1		40
24.11	even	2		456.2.e.a.379.3	✓	40
57.56	even	2		456.2.e.a.379.4	yes	40
76.75	even	2		5472.2.e.g.5167.29		40
152.37	odd	2		5472.2.e.g.5167.40		40
152.75	even	2	inner	1368.2.e.g.379.3		40
228.227	odd	2		1824.2.e.a.1519.2		40
456.227	odd	2		456.2.e.a.379.38	yes	40
456.341	even	2		1824.2.e.a.1519.12		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.3	✓	40	24.11	even	2
456.2.e.a.379.4	yes	40	57.56	even	2
456.2.e.a.379.37	yes	40	3.2	odd	2
456.2.e.a.379.38	yes	40	456.227	odd	2
1368.2.e.g.379.3		40	152.75	even	2	inner
1368.2.e.g.379.4		40	1.1	even	1	trivial
1368.2.e.g.379.37		40	19.18	odd	2	inner
1368.2.e.g.379.38		40	8.3	odd	2	inner
1824.2.e.a.1519.1		40	24.5	odd	2
1824.2.e.a.1519.2		40	228.227	odd	2
1824.2.e.a.1519.11		40	12.11	even	2
1824.2.e.a.1519.12		40	456.341	even	2
5472.2.e.g.5167.29		40	76.75	even	2
5472.2.e.g.5167.30		40	8.5	even	2
5472.2.e.g.5167.39		40	4.3	odd	2
5472.2.e.g.5167.40		40	152.37	odd	2

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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38840 + 0.268989i) q^{2} +(1.85529 - 0.746926i) q^{4} -3.66131i q^{5} +0.477575i q^{7} +(-2.37496 + 1.53608i) q^{8} +O(q^{10})\)	\(q+(-1.38840 + 0.268989i) q^{2} +(1.85529 - 0.746926i) q^{4} -3.66131i q^{5} +0.477575i q^{7} +(-2.37496 + 1.53608i) q^{8} +(0.984850 + 5.08335i) q^{10} +6.02922 q^{11} +4.31300 q^{13} +(-0.128462 - 0.663064i) q^{14} +(2.88420 - 2.77153i) q^{16} +0.111078 q^{17} +(2.23153 + 3.74436i) q^{19} +(-2.73473 - 6.79279i) q^{20} +(-8.37094 + 1.62179i) q^{22} +7.73272i q^{23} -8.40518 q^{25} +(-5.98815 + 1.16015i) q^{26} +(0.356713 + 0.886040i) q^{28} -0.104336 q^{29} +6.47633 q^{31} +(-3.25891 + 4.62380i) q^{32} +(-0.154220 + 0.0298787i) q^{34} +1.74855 q^{35} +3.65969 q^{37} +(-4.10545 - 4.59840i) q^{38} +(5.62407 + 8.69548i) q^{40} +4.93627i q^{41} -0.796971 q^{43} +(11.1859 - 4.50338i) q^{44} +(-2.08001 - 10.7361i) q^{46} -3.88824i q^{47} +6.77192 q^{49} +(11.6697 - 2.26090i) q^{50} +(8.00186 - 3.22149i) q^{52} -6.35015 q^{53} -22.0748i q^{55} +(-0.733594 - 1.13422i) q^{56} +(0.144860 - 0.0280653i) q^{58} +8.57094i q^{59} +8.05083i q^{61} +(-8.99171 + 1.74206i) q^{62} +(3.28091 - 7.29628i) q^{64} -15.7912i q^{65} -12.2522i q^{67} +(0.206082 - 0.0829670i) q^{68} +(-2.42768 + 0.470340i) q^{70} +7.88798 q^{71} -13.9848 q^{73} +(-5.08110 + 0.984415i) q^{74} +(6.93691 + 5.28009i) q^{76} +2.87940i q^{77} -10.2206 q^{79} +(-10.1474 - 10.5600i) q^{80} +(-1.32780 - 6.85350i) q^{82} +6.98436 q^{83} -0.406691i q^{85} +(1.10651 - 0.214376i) q^{86} +(-14.3192 + 9.26137i) q^{88} -6.56953i q^{89} +2.05978i q^{91} +(5.77576 + 14.3464i) q^{92} +(1.04589 + 5.39842i) q^{94} +(13.7093 - 8.17034i) q^{95} -14.6725i q^{97} +(-9.40211 + 1.82157i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4}+O(q^{10}) \) 40 * q - 4 * q^4	\( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Introduction

L-functions

Modular forms

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