LMFDB - Embedded newform 1368.2.e.f.379.18

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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.18
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.f.379.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26128 - 0.639662i) q^{2} +(1.18166 - 1.61359i) q^{4} +1.96435i q^{5} -1.25539i q^{7} +(0.458259 - 2.79106i) q^{8} +O(q^{10})$	\(q+(1.26128 - 0.639662i) q^{2} +(1.18166 - 1.61359i) q^{4} +1.96435i q^{5} -1.25539i q^{7} +(0.458259 - 2.79106i) q^{8} +(1.25652 + 2.47760i) q^{10} +3.11106 q^{11} +0.401637 q^{13} +(-0.803023 - 1.58339i) q^{14} +(-1.20734 - 3.81344i) q^{16} +4.88644 q^{17} +(-2.50466 + 3.56744i) q^{19} +(3.16965 + 2.32120i) q^{20} +(3.92392 - 1.99003i) q^{22} -3.34225i q^{23} +1.14134 q^{25} +(0.506577 - 0.256912i) q^{26} +(-2.02568 - 1.48344i) q^{28} +3.79561 q^{29} -2.06495 q^{31} +(-3.96211 - 4.03753i) q^{32} +(6.16318 - 3.12567i) q^{34} +2.46601 q^{35} -1.55353 q^{37} +(-0.877128 + 6.10169i) q^{38} +(5.48261 + 0.900181i) q^{40} -2.92028i q^{41} +2.08998 q^{43} +(3.67623 - 5.01997i) q^{44} +(-2.13791 - 4.21552i) q^{46} -4.59290i q^{47} +5.42401 q^{49} +(1.43955 - 0.730070i) q^{50} +(0.474600 - 0.648077i) q^{52} +1.83304 q^{53} +6.11121i q^{55} +(-3.50385 - 0.575292i) q^{56} +(4.78734 - 2.42791i) q^{58} -7.40388i q^{59} +1.71150i q^{61} +(-2.60448 + 1.32087i) q^{62} +(-7.58000 - 2.55806i) q^{64} +0.788954i q^{65} +10.2314i q^{67} +(5.77413 - 7.88471i) q^{68} +(3.11034 - 1.57742i) q^{70} -8.84074 q^{71} +6.14134 q^{73} +(-1.95944 + 0.993733i) q^{74} +(2.79672 + 8.25702i) q^{76} -3.90558i q^{77} +1.51739 q^{79} +(7.49093 - 2.37164i) q^{80} +(-1.86799 - 3.68330i) q^{82} +3.55077 q^{83} +9.59867i q^{85} +(2.63606 - 1.33688i) q^{86} +(1.42567 - 8.68315i) q^{88} -5.11730i q^{89} -0.504209i q^{91} +(-5.39302 - 3.94942i) q^{92} +(-2.93790 - 5.79294i) q^{94} +(-7.00770 - 4.92003i) q^{95} +9.40618i q^{97} +(6.84120 - 3.46953i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{4}+O(q^{10}) $ 24 * q + 20 * q^4	$ 24 q + 20 q^{4} - 12 q^{16} + 24 q^{19} - 40 q^{25} - 40 q^{28} - 72 q^{49} - 104 q^{58} + 20 q^{64} + 80 q^{73} - 12 q^{76} + 56 q^{82}+O(q^{100}) $ 24 * q + 20 * q^4 - 12 * q^16 + 24 * q^19 - 40 * q^25 - 40 * q^28 - 72 * q^49 - 104 * q^58 + 20 * q^64 + 80 * q^73 - 12 * q^76 + 56 * q^82

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 $

$2$	1.26128	−	0.639662i	0.891861	−	0.452310i
$2$	1.26128	−	0.639662i	0.891861	−	0.452310i
$3$		0			0
$3$		0			0
$4$	1.18166	−	1.61359i	0.590832	−	0.806795i
$5$			1.96435i			0.878483i	0.898369	+	0.439242i	$0.144753\pi$
$5$			1.96435i			0.878483i	−0.898369	+	0.439242i	$0.855247\pi$
$6$		0			0
$7$		−	1.25539i		−	0.474491i	−0.971450	−	0.237245i	$-0.923755\pi$
$7$		−	1.25539i		−	0.474491i	0.971450	−	0.237245i	$-0.0762446\pi$
$8$	0.458259	−	2.79106i	0.162019	−	0.986788i
$9$		0			0
$10$	1.25652	+	2.47760i	0.397346	+	0.783485i
$11$	3.11106			0.938020			0.469010	−	0.883193i	$-0.344611\pi$
$11$	3.11106			0.938020			0.469010	+	0.883193i	$0.344611\pi$
$12$		0			0
$13$	0.401637			0.111394			0.0556970	−	0.998448i	$-0.482262\pi$
$13$	0.401637			0.111394			0.0556970	+	0.998448i	$0.482262\pi$
$14$	−0.803023	−	1.58339i	−0.214617	−	0.423180i
$15$		0			0
$16$	−1.20734	−	3.81344i	−0.301835	−	0.953360i
$17$	4.88644			1.18514			0.592568	−	0.805520i	$-0.298114\pi$
$17$	4.88644			1.18514			0.592568	+	0.805520i	$0.298114\pi$
$18$		0			0
$19$	−2.50466	+	3.56744i	−0.574609	+	0.818428i
$19$	−2.50466	+	3.56744i	−0.574609	+	0.818428i
$20$	3.16965	+	2.32120i	0.708755	+	0.519036i
$21$		0			0
$22$	3.92392	−	1.99003i	0.836583	−	0.424275i
$23$		−	3.34225i		−	0.696907i	−0.937326	−	0.348454i	$-0.886707\pi$
$23$		−	3.34225i		−	0.696907i	0.937326	−	0.348454i	$-0.113293\pi$
$24$		0			0
$25$	1.14134			0.228267
$26$	0.506577	−	0.256912i	0.0993479	−	0.0503846i
$27$		0			0
$28$	−2.02568	−	1.48344i	−0.382817	−	0.280344i
$29$	3.79561			0.704827			0.352414	−	0.935844i	$-0.385361\pi$
$29$	3.79561			0.704827			0.352414	+	0.935844i	$0.385361\pi$
$30$		0			0
$31$	−2.06495			−0.370876			−0.185438	−	0.982656i	$-0.559370\pi$
$31$	−2.06495			−0.370876			−0.185438	+	0.982656i	$0.559370\pi$
$32$	−3.96211	−	4.03753i	−0.700409	−	0.713742i
$33$		0			0
$34$	6.16318	−	3.12567i	1.05698	−	0.536049i
$35$	2.46601			0.416832
$36$		0			0
$37$	−1.55353			−0.255398			−0.127699	−	0.991813i	$-0.540759\pi$
$37$	−1.55353			−0.255398			−0.127699	+	0.991813i	$0.540759\pi$
$38$	−0.877128	+	6.10169i	−0.142289	+	0.989825i
$39$		0			0
$40$	5.48261	+	0.900181i	0.866876	+	0.142331i
$41$		−	2.92028i		−	0.456071i	−0.973653	−	0.228035i	$-0.926770\pi$
$41$		−	2.92028i		−	0.456071i	0.973653	−	0.228035i	$-0.0732302\pi$
$42$		0			0
$43$	2.08998			0.318720			0.159360	−	0.987221i	$-0.449057\pi$
$43$	2.08998			0.318720			0.159360	+	0.987221i	$0.449057\pi$
$44$	3.67623	−	5.01997i	0.554212	−	0.756789i
$45$		0			0
$46$	−2.13791	−	4.21552i	−0.315218	−	0.621545i
$47$		−	4.59290i		−	0.669943i	−0.942228	−	0.334971i	$-0.891273\pi$
$47$		−	4.59290i		−	0.669943i	0.942228	−	0.334971i	$-0.108727\pi$
$48$		0			0
$49$	5.42401			0.774858
$50$	1.43955	−	0.730070i	0.203583	−	0.103247i
$51$		0			0
$52$	0.474600	−	0.648077i	0.0658151	−	0.0898720i
$53$	1.83304			0.251787			0.125894	−	0.992044i	$-0.459820\pi$
$53$	1.83304			0.251787			0.125894	+	0.992044i	$0.459820\pi$
$54$		0			0
$55$			6.11121i			0.824035i
$56$	−3.50385	−	0.575292i	−0.468222	−	0.0768766i
$57$		0			0
$58$	4.78734	−	2.42791i	0.628608	−	0.318800i
$59$		−	7.40388i		−	0.963903i	−0.876198	−	0.481952i	$-0.839928\pi$
$59$		−	7.40388i		−	0.963903i	0.876198	−	0.481952i	$-0.160072\pi$
$60$		0			0
$61$			1.71150i			0.219135i	0.993979	+	0.109568i	$0.0349466\pi$
$61$			1.71150i			0.219135i	−0.993979	+	0.109568i	$0.965053\pi$
$62$	−2.60448	+	1.32087i	−0.330770	+	0.167751i
$63$		0			0
$64$	−7.58000	−	2.55806i	−0.947500	−	0.319757i
$65$			0.788954i			0.0978577i
$66$		0			0
$67$			10.2314i			1.24996i	0.780639	+	0.624982i	$0.214894\pi$
$67$			10.2314i			1.24996i	−0.780639	+	0.624982i	$0.785106\pi$
$68$	5.77413	−	7.88471i	0.700217	−	0.956162i
$69$		0			0
$70$	3.11034	−	1.57742i	0.371757	−	0.188537i
$71$	−8.84074			−1.04920			−0.524601	−	0.851348i	$-0.675786\pi$
$71$	−8.84074			−1.04920			−0.524601	+	0.851348i	$0.675786\pi$
$72$		0			0
$73$	6.14134			0.718789			0.359395	−	0.933186i	$-0.382983\pi$
$73$	6.14134			0.718789			0.359395	+	0.933186i	$0.382983\pi$
$74$	−1.95944	+	0.993733i	−0.227780	+	0.115519i
$75$		0			0
$76$	2.79672	+	8.25702i	0.320805	+	0.947145i
$77$		−	3.90558i		−	0.445082i
$78$		0			0
$79$	1.51739			0.170719			0.0853597	−	0.996350i	$-0.472796\pi$
$79$	1.51739			0.170719			0.0853597	+	0.996350i	$0.472796\pi$
$80$	7.49093	−	2.37164i	0.837511	−	0.265157i
$81$		0			0
$82$	−1.86799	−	3.68330i	−0.206285	−	0.406752i
$83$	3.55077			0.389747			0.194874	−	0.980828i	$-0.437570\pi$
$83$	3.55077			0.389747			0.194874	+	0.980828i	$0.437570\pi$
$84$		0			0
$85$			9.59867i			1.04112i
$86$	2.63606	−	1.33688i	0.284254	−	0.144160i
$87$		0			0
$88$	1.42567	−	8.68315i	0.151977	−	0.925626i
$89$		−	5.11730i		−	0.542433i	−0.962518	−	0.271216i	$-0.912574\pi$
$89$		−	5.11730i		−	0.542433i	0.962518	−	0.271216i	$-0.0874259\pi$
$90$		0			0
$91$		−	0.504209i		−	0.0528554i
$92$	−5.39302	−	3.94942i	−0.562261	−	0.411755i
$93$		0			0
$94$	−2.93790	−	5.79294i	−0.303022	−	0.597496i
$95$	−7.00770	−	4.92003i	−0.718975	−	0.504785i
$96$		0			0
$97$			9.40618i			0.955053i	0.878617	+	0.477526i	$0.158467\pi$
$97$			9.40618i			0.955053i	−0.878617	+	0.477526i	$0.841533\pi$
$98$	6.84120	−	3.46953i	0.691066	−	0.350476i
$99$		0			0
$100$	1.34868	−	1.84165i	0.134868	−	0.184165i
$101$			13.2549i			1.31892i	0.751742	+	0.659458i	$0.229214\pi$
$101$			13.2549i			1.31892i	−0.751742	+	0.659458i	$0.770786\pi$
$102$		0			0
$103$	−8.49863			−0.837395			−0.418697	−	0.908126i	$-0.637513\pi$
$103$	−8.49863			−0.837395			−0.418697	+	0.908126i	$0.637513\pi$
$104$	0.184054	−	1.12099i	0.0180480	−	0.109922i
$105$		0			0
$106$	2.31198	−	1.17252i	0.224559	−	0.113886i
$107$		−	4.91093i		−	0.474757i	−0.971417	−	0.237379i	$-0.923712\pi$
$107$		−	4.91093i		−	0.474757i	0.971417	−	0.237379i	$-0.0762882\pi$
$108$		0			0
$109$	−16.1902			−1.55074			−0.775372	−	0.631505i	$-0.782438\pi$
$109$	−16.1902			−1.55074			−0.775372	+	0.631505i	$0.782438\pi$
$110$	3.90911	+	7.70795i	0.372719	+	0.734924i
$111$		0			0
$112$	−4.78734	+	1.51568i	−0.452361	+	0.143218i
$113$			8.17825i			0.769345i	0.923053	+	0.384673i	$0.125686\pi$
$113$			8.17825i			0.769345i	−0.923053	+	0.384673i	$0.874314\pi$
$114$		0			0
$115$	6.56534			0.612222
$116$	4.48514	−	6.12456i	0.416435	−	0.568651i
$117$		0			0
$118$	−4.73599	−	9.33838i	−0.435983	−	0.859668i
$119$		−	6.13437i		−	0.562337i
$120$		0			0
$121$	−1.32131			−0.120119
$122$	1.09478	+	2.15869i	0.0991170	+	0.195438i
$123$		0			0
$124$	−2.44008	+	3.33198i	−0.219125	+	0.299221i
$125$			12.0637i			1.07901i
$126$		0			0
$127$	−14.7826			−1.31175			−0.655873	−	0.754871i	$-0.727700\pi$
$127$	−14.7826			−1.31175			−0.655873	+	0.754871i	$0.727700\pi$
$128$	−11.1968	+	1.62221i	−0.989667	+	0.143384i
$129$		0			0
$130$	0.504664	+	0.995094i	0.0442620	+	0.0872755i
$131$	15.7897			1.37955			0.689775	−	0.724024i	$-0.257710\pi$
$131$	15.7897			1.37955			0.689775	+	0.724024i	$0.257710\pi$
$132$		0			0
$133$	4.47852	+	3.14432i	0.388337	+	0.272647i
$134$	6.54464	+	12.9047i	0.565371	+	1.11479i
$135$		0			0
$136$	2.23926	−	13.6383i	0.192015	−	1.16948i
$137$	−14.0143			−1.19732			−0.598660	−	0.801003i	$-0.704300\pi$
$137$	−14.0143			−1.19732			−0.598660	+	0.801003i	$0.704300\pi$
$138$		0			0
$139$	−4.37266			−0.370884			−0.185442	−	0.982655i	$-0.559372\pi$
$139$	−4.37266			−0.370884			−0.185442	+	0.982655i	$0.559372\pi$
$140$	2.91400	−	3.97913i	0.246278	−	0.336298i
$141$		0			0
$142$	−11.1507	+	5.65509i	−0.935743	+	0.474564i
$143$	1.24952			0.104490
$144$		0			0
$145$			7.45590i			0.619179i
$146$	7.74596	−	3.92838i	0.641060	−	0.325115i
$147$		0			0
$148$	−1.83575	+	2.50676i	−0.150898	+	0.206054i
$149$			6.84807i			0.561016i	0.959852	+	0.280508i	$0.0905029\pi$
$149$			6.84807i			0.561016i	−0.959852	+	0.280508i	$0.909497\pi$
$150$		0			0
$151$	−17.3060			−1.40834			−0.704171	−	0.710031i	$-0.748681\pi$
$151$	−17.3060			−1.40834			−0.704171	+	0.710031i	$0.748681\pi$
$152$	8.80915	+	8.62548i	0.714517	+	0.699618i
$153$		0			0
$154$	−2.49825	−	4.92604i	−0.201315	−	0.396951i
$155$		−	4.05628i		−	0.325808i
$156$		0			0
$157$			13.8209i			1.10303i	0.834164	+	0.551516i	$0.185950\pi$
$157$			13.8209i			1.10303i	−0.834164	+	0.551516i	$0.814050\pi$
$158$	1.91385	−	0.970615i	0.152258	−	0.0772180i
$159$		0			0
$160$	7.93112	−	7.78296i	0.627010	−	0.615297i
$161$	−4.19581			−0.330676
$162$		0			0
$163$	1.27334			0.0997360			0.0498680	−	0.998756i	$-0.484120\pi$
$163$	1.27334			0.0997360			0.0498680	+	0.998756i	$0.484120\pi$
$164$	−4.71213	−	3.45079i	−0.367956	−	0.269461i
$165$		0			0
$166$	4.47852	−	2.27129i	0.347600	−	0.176286i
$167$	−8.84074			−0.684117			−0.342058	−	0.939679i	$-0.611124\pi$
$167$	−8.84074			−0.684117			−0.342058	+	0.939679i	$0.611124\pi$
$168$		0			0
$169$	−12.8387			−0.987591
$170$	6.13991	+	12.1066i	0.470910	+	0.928537i
$171$		0			0
$172$	2.46966	−	3.37238i	0.188310	−	0.257141i
$173$	15.8484			1.20493			0.602467	−	0.798144i	$-0.294184\pi$
$173$	15.8484			1.20493			0.602467	+	0.798144i	$0.294184\pi$
$174$		0			0
$175$		−	1.43282i		−	0.108311i
$176$	−3.75611	−	11.8638i	−0.283127	−	0.894271i
$177$		0			0
$178$	−3.27334	−	6.45436i	−0.245347	−	0.483774i
$179$		−	11.5916i		−	0.866393i	−0.901299	−	0.433197i	$-0.857386\pi$
$179$		−	11.5916i		−	0.866393i	0.901299	−	0.433197i	$-0.142614\pi$
$180$		0			0
$181$	−25.3101			−1.88128			−0.940641	−	0.339402i	$-0.889775\pi$
$181$	−25.3101			−1.88128			−0.940641	+	0.339402i	$0.889775\pi$
$182$	−0.322523	−	0.635949i	−0.0239070	−	0.0471397i
$183$		0			0
$184$	−9.32841	−	1.53162i	−0.687700	−	0.112912i
$185$		−	3.05167i		−	0.224363i
$186$		0			0
$187$	15.2020			1.11168
$188$	−7.41105	−	5.42726i	−0.540506	−	0.395824i
$189$		0			0
$190$	−11.9858	−	1.72299i	−0.869545	−	0.124998i
$191$		−	22.6901i		−	1.64180i	−0.571073	−	0.820899i	$-0.693473\pi$
$191$		−	22.6901i		−	1.64180i	0.571073	−	0.820899i	$-0.306527\pi$
$192$		0			0
$193$		−	13.0069i		−	0.936257i	−0.883660	−	0.468129i	$-0.844928\pi$
$193$		−	13.0069i		−	0.936257i	0.883660	−	0.468129i	$-0.155072\pi$
$194$	6.01678	+	11.8638i	0.431980	+	0.851774i
$195$		0			0
$196$	6.40936	−	8.75212i	0.457811	−	0.625151i
$197$			5.77092i			0.411161i	0.978640	+	0.205580i	$0.0659082\pi$
$197$			5.77092i			0.411161i	−0.978640	+	0.205580i	$0.934092\pi$
$198$		0			0
$199$			20.4527i			1.44986i	0.688825	+	0.724928i	$0.258127\pi$
$199$			20.4527i			1.44986i	−0.688825	+	0.724928i	$0.741873\pi$
$200$	0.523028	−	3.18553i	0.0369837	−	0.225251i
$201$		0			0
$202$	8.47869	+	16.7182i	0.596558	+	1.17629i
$203$		−	4.76495i		−	0.334434i
$204$		0			0
$205$	5.73644			0.400651
$206$	−10.7192	+	5.43625i	−0.746840	+	0.378762i
$207$		0			0
$208$	−0.484912	−	1.53162i	−0.0336226	−	0.106199i
$209$	−7.79216	+	11.0985i	−0.538995	+	0.767702i
$210$		0			0
$211$		−	12.1817i		−	0.838621i	−0.907843	−	0.419311i	$-0.862272\pi$
$211$		−	12.1817i		−	0.838621i	0.907843	−	0.419311i	$-0.137728\pi$
$212$	2.16603	−	2.95777i	0.148764	−	0.203140i
$213$		0			0
$214$	−3.14134	−	6.19407i	−0.214737	−	0.423418i
$215$			4.10546i			0.279990i
$216$		0			0
$217$			2.59231i			0.175977i
$218$	−20.4205	+	10.3563i	−1.38305	+	0.701416i
$219$		0			0
$220$	9.86097	+	7.22139i	0.664827	+	0.486866i
$221$	1.96257			0.132017
$222$		0			0
$223$	21.9834			1.47212			0.736060	−	0.676916i	$-0.236684\pi$
$223$	21.9834			1.47212			0.736060	+	0.676916i	$0.236684\pi$
$224$	−5.06866	+	4.97397i	−0.338664	+	0.332338i
$225$		0			0
$226$	5.23132	+	10.3151i	0.347982	+	0.686149i
$227$			20.9715i			1.39193i	0.718077	+	0.695964i	$0.245023\pi$
$227$			20.9715i			1.39193i	−0.718077	+	0.695964i	$0.754977\pi$
$228$		0			0
$229$		−	9.59867i		−	0.634298i	−0.948376	−	0.317149i	$-0.897274\pi$
$229$		−	9.59867i		−	0.634298i	0.948376	−	0.317149i	$-0.102726\pi$
$230$	8.28075	−	4.19960i	0.546016	−	0.276914i
$231$		0			0
$232$	1.73937	−	10.5938i	0.114196	−	0.695515i
$233$	−9.81847			−0.643229			−0.321615	−	0.946871i	$-0.604226\pi$
$233$	−9.81847			−0.643229			−0.321615	+	0.946871i	$0.604226\pi$
$234$		0			0
$235$	9.02205			0.588533
$236$	−11.9468	−	8.74890i	−0.777672	−	0.569505i
$237$		0			0
$238$	−3.92392	−	7.73717i	−0.254350	−	0.501526i
$239$			5.71955i			0.369967i	0.982742	+	0.184983i	$0.0592232\pi$
$239$			5.71955i			0.369967i	−0.982742	+	0.184983i	$0.940777\pi$
$240$		0			0
$241$			17.8705i			1.15114i	0.817752	+	0.575570i	$0.195220\pi$
$241$			17.8705i			1.15114i	−0.817752	+	0.575570i	$0.804780\pi$
$242$	−1.66654	+	0.845189i	−0.107129	+	0.0543308i
$243$		0			0
$244$	2.76166	+	2.02242i	0.176797	+	0.129472i
$245$			10.6546i			0.680700i
$246$		0			0
$247$	−1.00597	+	1.43282i	−0.0640080	+	0.0911679i
$248$	−0.946282	+	5.76339i	−0.0600890	+	0.365976i
$249$		0			0
$250$	7.71671	+	15.2158i	0.488048	+	0.962329i
$251$	−6.66183			−0.420491			−0.210245	−	0.977649i	$-0.567426\pi$
$251$	−6.66183			−0.420491			−0.210245	+	0.977649i	$0.567426\pi$
$252$		0			0
$253$		−	10.3979i		−	0.653713i
$254$	−18.6451	+	9.45590i	−1.16990	+	0.593316i
$255$		0			0
$256$	−13.0847	+	9.20824i	−0.817791	+	0.575515i
$257$			9.82186i			0.612671i	0.951924	+	0.306335i	$0.0991029\pi$
$257$			9.82186i			0.612671i	−0.951924	+	0.306335i	$0.900897\pi$
$258$		0			0
$259$			1.95028i			0.121184i
$260$	1.27305	+	0.932279i	0.0789511	+	0.0578175i
$261$		0			0
$262$	19.9152	−	10.1001i	1.23037	−	0.623983i
$263$		−	7.49394i		−	0.462096i	−0.972942	−	0.231048i	$-0.925784\pi$
$263$		−	7.49394i		−	0.462096i	0.972942	−	0.231048i	$-0.0742155\pi$
$264$		0			0
$265$			3.60072i			0.221191i
$266$	7.65997	+	1.10113i	0.469663	+	0.0675148i
$267$		0			0
$268$	16.5093	+	12.0901i	1.00846	+	0.738519i
$269$	25.9387			1.58151			0.790755	−	0.612133i	$-0.209688\pi$
$269$	25.9387			1.58151			0.790755	+	0.612133i	$0.209688\pi$
$270$		0			0
$271$			20.2753i			1.23164i	0.787888	+	0.615818i	$0.211175\pi$
$271$			20.2753i			1.23164i	−0.787888	+	0.615818i	$0.788825\pi$
$272$	−5.89960	−	18.6342i	−0.357716	−	1.12986i
$273$		0			0
$274$	−17.6760	+	8.96441i	−1.06784	+	0.541560i
$275$	3.55077			0.214119
$276$		0			0
$277$		−	3.31004i		−	0.198881i	−0.995044	−	0.0994405i	$-0.968295\pi$
$277$		−	3.31004i		−	0.198881i	0.995044	−	0.0994405i	$-0.0317053\pi$
$278$	−5.51515	+	2.79702i	−0.330777	+	0.167754i
$279$		0			0
$280$	1.13007	−	6.88278i	0.0675348	−	0.411325i
$281$			31.9439i			1.90562i	0.303574	+	0.952808i	$0.401820\pi$
$281$			31.9439i			1.90562i	−0.303574	+	0.952808i	$0.598180\pi$
$282$		0			0
$283$	−13.1834			−0.783669			−0.391835	−	0.920036i	$-0.628159\pi$
$283$	−13.1834			−0.783669			−0.391835	+	0.920036i	$0.628159\pi$
$284$	−10.4468	+	14.2653i	−0.619903	+	0.846491i
$285$		0			0
$286$	1.57599	−	0.799268i	0.0931903	−	0.0472617i
$287$	−3.66607			−0.216402
$288$		0			0
$289$	6.87732			0.404548
$290$	4.76926	+	9.40400i	0.280061	+	0.552222i
$291$		0			0
$292$	7.25700	−	9.90959i	0.424684	−	0.579915i
$293$	−8.25722			−0.482392			−0.241196	−	0.970476i	$-0.577540\pi$
$293$	−8.25722			−0.482392			−0.241196	+	0.970476i	$0.577540\pi$
$294$		0			0
$295$	14.5438			0.846773
$296$	−0.711919	+	4.33598i	−0.0413794	+	0.252024i
$297$		0			0
$298$	4.38045	+	8.63735i	0.253753	+	0.500348i
$299$		−	1.34237i		−	0.0776313i
$300$		0			0
$301$		−	2.62374i		−	0.151230i
$302$	−21.8277	+	11.0700i	−1.25604	+	0.637006i
$303$		0			0
$304$	16.6282	+	5.24427i	0.953694	+	0.300780i
$305$	−3.36199			−0.192507
$306$		0			0
$307$			19.3166i			1.10245i	0.834355	+	0.551227i	$0.185840\pi$
$307$			19.3166i			1.10245i	−0.834355	+	0.551227i	$0.814160\pi$
$308$	−6.30200	−	4.61508i	−0.359090	−	0.262969i
$309$		0			0
$310$	−2.59465	−	5.11611i	−0.147366	−	0.290576i
$311$		−	19.7891i		−	1.12213i	−0.827770	−	0.561067i	$-0.810391\pi$
$311$		−	19.7891i		−	1.12213i	0.827770	−	0.561067i	$-0.189609\pi$
$312$		0			0
$313$	−0.385375			−0.0217827			−0.0108913	−	0.999941i	$-0.503467\pi$
$313$	−0.385375			−0.0217827			−0.0108913	+	0.999941i	$0.503467\pi$
$314$	8.84074	+	17.4321i	0.498912	+	0.983751i
$315$		0			0
$316$	1.79304	−	2.44844i	0.100866	−	0.137735i
$317$	17.8110			1.00037			0.500183	−	0.865920i	$-0.333266\pi$
$317$	17.8110			1.00037			0.500183	+	0.865920i	$0.333266\pi$
$318$		0			0
$319$	11.8084			0.661142
$320$	5.02491	−	14.8898i	0.280901	−	0.832363i
$321$		0			0
$322$	−5.29210	+	2.68390i	−0.294917	+	0.149568i
$323$	−12.2389	+	17.4321i	−0.680991	+	0.969949i
$324$		0			0
$325$	0.458402			0.0254276
$326$	1.60605	−	0.814510i	0.0889506	−	0.0451115i
$327$		0			0
$328$	−8.15066	−	1.33825i	−0.450045	−	0.0738922i
$329$	−5.76585			−0.317882
$330$		0			0
$331$			0.504209i			0.0277138i	0.999904	+	0.0138569i	$0.00441093\pi$
$331$			0.504209i			0.0277138i	−0.999904	+	0.0138569i	$0.995589\pi$
$332$	4.19581	−	5.72948i	0.230275	−	0.314446i
$333$		0			0
$334$	−11.1507	+	5.65509i	−0.610137	+	0.309433i
$335$	−20.0980			−1.09807
$336$		0			0
$337$			6.81387i			0.371175i	0.982628	+	0.185588i	$0.0594189\pi$
$337$			6.81387i			0.371175i	−0.982628	+	0.185588i	$0.940581\pi$
$338$	−16.1932	+	8.21243i	−0.880794	+	0.446697i
$339$		0			0
$340$	15.4883	+	11.3424i	0.839972	+	0.615129i
$341$	−6.42418			−0.347889
$342$		0			0
$343$		−	15.5969i		−	0.842154i
$344$	0.957755	−	5.83327i	0.0516387	−	0.314509i
$345$		0			0
$346$	19.9894	−	10.1377i	1.07463	−	0.545004i
$347$	−6.66183			−0.357626			−0.178813	−	0.983883i	$-0.557226\pi$
$347$	−6.66183			−0.357626			−0.178813	+	0.983883i	$0.557226\pi$
$348$		0			0
$349$		−	26.8426i		−	1.43685i	−0.695603	−	0.718426i	$-0.744863\pi$
$349$		−	26.8426i		−	1.43685i	0.695603	−	0.718426i	$-0.255137\pi$
$350$	−0.916519	−	1.80719i	−0.0489900	−	0.0965981i
$351$		0			0
$352$	−12.3264	−	12.5610i	−0.656997	−	0.669504i
$353$	−23.8328			−1.26849			−0.634245	−	0.773132i	$-0.718689\pi$
$353$	−23.8328			−1.26849			−0.634245	+	0.773132i	$0.718689\pi$
$354$		0			0
$355$		−	17.3663i		−	0.921707i
$356$	−8.25722	−	6.04693i	−0.437632	−	0.320487i
$357$		0			0
$358$	−7.41468	−	14.6202i	−0.391878	−	0.772702i
$359$		−	17.8064i		−	0.939785i	−0.882724	−	0.469893i	$-0.844293\pi$
$359$		−	17.8064i		−	0.939785i	0.882724	−	0.469893i	$-0.155707\pi$
$360$		0			0
$361$	−6.45331	−	17.8705i	−0.339648	−	0.940553i
$362$	−31.9231	+	16.1899i	−1.67784	+	0.850922i
$363$		0			0
$364$	−0.813586	−	0.595805i	−0.0426435	−	0.0312287i
$365$			12.0637i			0.631444i
$366$		0			0
$367$		−	23.1409i		−	1.20795i	−0.797004	−	0.603974i	$-0.793583\pi$
$367$		−	23.1409i		−	1.20795i	0.797004	−	0.603974i	$-0.206417\pi$
$368$	−12.7455	+	4.03523i	−0.664404	+	0.210351i
$369$		0			0
$370$	−1.95204	−	3.84902i	−0.101482	−	0.200101i
$371$		−	2.30117i		−	0.119471i
$372$		0			0
$373$	26.4052			1.36721			0.683605	−	0.729852i	$-0.260411\pi$
$373$	26.4052			1.36721			0.683605	+	0.729852i	$0.260411\pi$
$374$	19.1740	−	9.72416i	0.991465	−	0.502824i
$375$		0			0
$376$	−12.8190	−	2.10474i	−0.661091	−	0.108544i
$377$	1.52446			0.0785135
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−16.2197	+	5.49373i	−0.832051	+	0.281822i
$381$		0			0
$382$	−14.5140	−	28.6186i	−0.742601	−	1.46426i
$383$	−2.49903			−0.127695			−0.0638473	−	0.997960i	$-0.520337\pi$
$383$	−2.49903			−0.127695			−0.0638473	+	0.997960i	$0.520337\pi$
$384$		0			0
$385$	7.67192			0.390997
$386$	−8.32003	−	16.4054i	−0.423478	−	0.835011i
$387$		0			0
$388$	15.1777	+	11.1149i	0.770531	+	0.564276i
$389$			17.0615i			0.865053i	0.901621	+	0.432526i	$0.142378\pi$
$389$			17.0615i			0.865053i	−0.901621	+	0.432526i	$0.857622\pi$
$390$		0			0
$391$		−	16.3317i		−	0.825930i
$392$	2.48560	−	15.1387i	0.125542	−	0.764621i
$393$		0			0
$394$	3.69144	+	7.27876i	0.185972	+	0.366698i
$395$			2.98068i			0.149974i
$396$		0			0
$397$			13.9339i			0.699323i	0.936876	+	0.349662i	$0.113703\pi$
$397$			13.9339i			0.699323i	−0.936876	+	0.349662i	$0.886297\pi$
$398$	13.0828	+	25.7967i	0.655784	+	1.29307i
$399$		0			0
$400$	−1.37798	−	4.35242i	−0.0688990	−	0.217621i
$401$		−	14.0188i		−	0.700066i	−0.936737	−	0.350033i	$-0.886170\pi$
$401$		−	14.0188i		−	0.700066i	0.936737	−	0.350033i	$-0.113830\pi$
$402$		0			0
$403$	−0.829359			−0.0413133
$404$	21.3880	+	15.6629i	1.06409	+	0.779258i
$405$		0			0
$406$	−3.04796	−	6.00995i	−0.151268	−	0.298269i
$407$	−4.83312			−0.239569
$408$		0			0
$409$		−	34.7326i		−	1.71742i	−0.512465	−	0.858708i	$-0.671268\pi$
$409$		−	34.7326i		−	1.71742i	0.512465	−	0.858708i	$-0.328732\pi$
$410$	7.23527	−	3.66939i	0.357325	−	0.181218i
$411$		0			0
$412$	−10.0425	+	13.7133i	−0.494760	+	0.675606i
$413$	−9.29472			−0.457363
$414$		0			0
$415$			6.97494i			0.342386i
$416$	−1.59133	−	1.62162i	−0.0780213	−	0.0795065i
$417$		0			0
$418$	−2.72880	+	18.9827i	−0.133470	+	0.928476i
$419$	18.2557			0.891848			0.445924	−	0.895071i	$-0.352875\pi$
$419$	18.2557			0.891848			0.445924	+	0.895071i	$0.352875\pi$
$420$		0			0
$421$	11.6057			0.565626			0.282813	−	0.959175i	$-0.408732\pi$
$421$	11.6057			0.565626			0.282813	+	0.959175i	$0.408732\pi$
$422$	−7.79216	−	15.3645i	−0.379316	−	0.747934i
$423$		0			0
$424$	0.840006	−	5.11611i	0.0407943	−	0.248460i
$425$	5.57707			0.270528
$426$		0			0
$427$	2.14859			0.103978
$428$	−7.92422	−	5.80307i	−0.383032	−	0.280502i
$429$		0			0
$430$	2.62611	+	5.17814i	0.126642	+	0.249712i
$431$	4.91559			0.236776			0.118388	−	0.992967i	$-0.462227\pi$
$431$	4.91559			0.236776			0.118388	+	0.992967i	$0.462227\pi$
$432$		0			0
$433$			24.6844i			1.18626i	0.805108	+	0.593128i	$0.202107\pi$
$433$			24.6844i			1.18626i	−0.805108	+	0.593128i	$0.797893\pi$
$434$	1.65820	+	3.26963i	0.0795962	+	0.156947i
$435$		0			0
$436$	−19.1314	+	26.1244i	−0.916229	+	1.25113i
$437$	11.9233	+	8.37122i	0.570368	+	0.400450i
$438$		0			0
$439$	18.4011			0.878237			0.439119	−	0.898429i	$-0.355291\pi$
$439$	18.4011			0.878237			0.439119	+	0.898429i	$0.355291\pi$
$440$	17.0567	+	2.80052i	0.813147	+	0.133509i
$441$		0			0
$442$	2.47536	−	1.25539i	0.117741	−	0.0597126i
$443$	−6.66183			−0.316513			−0.158256	−	0.987398i	$-0.550587\pi$
$443$	−6.66183			−0.316513			−0.158256	+	0.987398i	$0.550587\pi$
$444$		0			0
$445$	10.0522			0.476518
$446$	27.7273	−	14.0620i	1.31293	−	0.665854i
$447$		0			0
$448$	−3.21134	+	9.51581i	−0.151722	+	0.449580i
$449$		−	2.40339i		−	0.113423i	−0.998391	−	0.0567115i	$-0.981938\pi$
$449$		−	2.40339i		−	0.113423i	0.998391	−	0.0567115i	$-0.0180615\pi$
$450$		0			0
$451$		−	9.08516i		−	0.427804i
$452$	13.1963	+	9.66395i	0.620704	+	0.454554i
$453$		0			0
$454$	13.4147	+	26.4510i	0.629582	+	1.24141i
$455$	0.990441			0.0464326
$456$		0			0
$457$	−13.7746			−0.644349			−0.322175	−	0.946680i	$-0.604414\pi$
$457$	−13.7746			−0.644349			−0.322175	+	0.946680i	$0.604414\pi$
$458$	−6.13991	−	12.1066i	−0.286899	−	0.565706i
$459$		0			0
$460$	7.75803	−	10.5938i	0.361720	−	0.493937i
$461$			6.19380i			0.288474i	0.989543	+	0.144237i	$0.0460727\pi$
$461$			6.19380i			0.288474i	−0.989543	+	0.144237i	$0.953927\pi$
$462$		0			0
$463$		−	32.6751i		−	1.51854i	−0.650774	−	0.759271i	$-0.725556\pi$
$463$		−	32.6751i		−	1.51854i	0.650774	−	0.759271i	$-0.274444\pi$
$464$	−4.58259	−	14.4743i	−0.212742	−	0.671954i
$465$		0			0
$466$	−12.3839	+	6.28051i	−0.573671	+	0.290939i
$467$	−23.5362			−1.08913			−0.544564	−	0.838720i	$-0.683305\pi$
$467$	−23.5362			−1.08913			−0.544564	+	0.838720i	$0.683305\pi$
$468$		0			0
$469$	12.8444			0.593097
$470$	11.3793	−	5.77106i	0.524890	−	0.266199i
$471$		0			0
$472$	−20.6647	−	3.39290i	−0.951168	−	0.156171i
$473$	6.50207			0.298965
$474$		0			0
$475$	−2.85866	+	4.07165i	−0.131164	+	0.186820i
$476$	−9.89835	−	7.24876i	−0.453690	−	0.332246i
$477$		0			0
$478$	3.65858	+	7.21397i	0.167340	+	0.329959i
$479$			1.31334i			0.0600081i	0.999550	+	0.0300041i	$0.00955202\pi$
$479$			1.31334i			0.0600081i	−0.999550	+	0.0300041i	$0.990448\pi$
$480$		0			0
$481$	−0.623954			−0.0284498
$482$	11.4311	+	22.5397i	0.520672	+	1.02666i
$483$		0			0
$484$	−1.56134	+	2.13204i	−0.0709700	+	0.0969111i
$485$	−18.4770			−0.838998
$486$		0			0
$487$	−26.4413			−1.19817			−0.599086	−	0.800685i	$-0.704469\pi$
$487$	−26.4413			−1.19817			−0.599086	+	0.800685i	$0.704469\pi$
$488$	4.77690	+	0.784312i	0.216240	+	0.0355041i
$489$		0			0
$490$	6.81537	+	13.4385i	0.307887	+	0.607090i
$491$	25.1228			1.13378			0.566889	−	0.823794i	$-0.308147\pi$
$491$	25.1228			1.13378			0.566889	+	0.823794i	$0.308147\pi$
$492$		0			0
$493$	18.5470			0.835317
$494$	−0.352287	+	2.45066i	−0.0158501	+	0.110261i
$495$		0			0
$496$	2.49310	+	7.87456i	0.111943	+	0.353578i
$497$			11.0985i			0.497837i
$498$		0			0
$499$	−9.30472			−0.416536			−0.208268	−	0.978072i	$-0.566783\pi$
$499$	−9.30472			−0.416536			−0.208268	+	0.978072i	$0.566783\pi$
$500$	19.4659	+	14.2553i	0.870541	+	0.637515i
$501$		0			0
$502$	−8.40244	+	4.26132i	−0.375019	+	0.190192i
$503$			0.887197i			0.0395582i	0.999804	+	0.0197791i	$0.00629629\pi$
$503$			0.887197i			0.0395582i	−0.999804	+	0.0197791i	$0.993704\pi$
$504$		0			0
$505$	−26.0373			−1.15865
$506$	−6.65117	−	13.1147i	−0.295681	−	0.583021i
$507$		0			0
$508$	−17.4681	+	23.8531i	−0.775022	+	1.05831i
$509$	17.5519			0.777976			0.388988	−	0.921243i	$-0.372825\pi$
$509$	17.5519			0.777976			0.388988	+	0.921243i	$0.372825\pi$
$510$		0			0
$511$		−	7.70974i		−	0.341059i
$512$	−10.6133	+	19.9839i	−0.469045	+	0.883174i
$513$		0			0
$514$	6.28267	+	12.3881i	0.277117	+	0.546417i
$515$		−	16.6943i		−	0.735637i
$516$		0			0
$517$		−	14.2888i		−	0.628420i
$518$	1.24752	+	2.45985i	0.0548128	+	0.108079i
$519$		0			0
$520$	2.20202	+	0.361546i	0.0965648	+	0.0158548i
$521$		−	18.4878i		−	0.809967i	−0.914324	−	0.404983i	$-0.867277\pi$
$521$		−	18.4878i		−	0.809967i	0.914324	−	0.404983i	$-0.132723\pi$
$522$		0			0
$523$			10.7356i			0.469436i	0.972064	+	0.234718i	$0.0754166\pi$
$523$			10.7356i			0.469436i	−0.972064	+	0.234718i	$0.924583\pi$
$524$	18.6581	−	25.4780i	0.815082	−	1.11301i
$525$		0			0
$526$	−4.79359	−	9.45198i	−0.209011	−	0.412126i
$527$	−10.0903			−0.439538
$528$		0			0
$529$	11.8294			0.514320
$530$	2.30325	+	4.54153i	0.100047	+	0.197271i
$531$		0			0
$532$	10.3657	−	3.51096i	0.449412	−	0.152219i
$533$		−	1.17289i		−	0.0508036i
$534$		0			0
$535$	9.64677			0.417066
$536$	28.5564	+	4.68864i	1.23345	+	0.202518i
$537$		0			0
$538$	32.7160	−	16.5920i	1.41049	−	0.715332i
$539$	16.8744			0.726833
$540$		0			0
$541$			37.9269i			1.63060i	0.579036	+	0.815302i	$0.303429\pi$
$541$			37.9269i			1.63060i	−0.579036	+	0.815302i	$0.696571\pi$
$542$	12.9693	+	25.5729i	0.557081	+	1.09845i
$543$		0			0
$544$	−19.3606	−	19.7292i	−0.830080	−	0.845882i
$545$		−	31.8033i		−	1.36230i
$546$		0			0
$547$		−	37.1871i		−	1.59000i	−0.606607	−	0.795002i	$-0.707470\pi$
$547$		−	37.1871i		−	1.59000i	0.606607	−	0.795002i	$-0.292530\pi$
$548$	−16.5602	+	22.6133i	−0.707416	+	0.965992i
$549$		0			0
$550$	4.47852	−	2.27129i	0.190965	−	0.0968482i
$551$	−9.50673	+	13.5406i	−0.405000	+	0.576850i
$552$		0			0
$553$		−	1.90490i		−	0.0810048i
$554$	−2.11731	−	4.17489i	−0.0899558	−	0.177374i
$555$		0			0
$556$	−5.16701	+	7.05567i	−0.219130	+	0.299227i
$557$			6.61994i			0.280496i	0.990116	+	0.140248i	$0.0447900\pi$
$557$			6.61994i			0.280496i	−0.990116	+	0.140248i	$0.955210\pi$
$558$		0			0
$559$	0.839414			0.0355035
$560$	−2.97732	−	9.40400i	−0.125815	−	0.397391i
$561$		0			0
$562$	20.4333	+	40.2903i	0.861928	+	1.69954i
$563$		−	37.4740i		−	1.57934i	−0.613532	−	0.789670i	$-0.710252\pi$
$563$		−	37.4740i		−	1.57934i	0.613532	−	0.789670i	$-0.289748\pi$
$564$		0			0
$565$	−16.0649			−0.675857
$566$	−16.6279	+	8.43290i	−0.698924	+	0.354461i
$567$		0			0
$568$	−4.05135	+	24.6750i	−0.169991	+	1.03534i
$569$			23.1924i			0.972276i	0.873882	+	0.486138i	$0.161595\pi$
$569$			23.1924i			0.972276i	−0.873882	+	0.486138i	$0.838405\pi$
$570$		0			0
$571$	−30.6027			−1.28068			−0.640341	−	0.768091i	$-0.721207\pi$
$571$	−30.6027			−1.28068			−0.640341	+	0.768091i	$0.721207\pi$
$572$	1.47651	−	2.01621i	0.0617359	−	0.0843018i
$573$		0			0
$574$	−4.62395	+	2.34505i	−0.193000	+	0.0978805i
$575$		−	3.81463i		−	0.159081i
$576$		0			0
$577$	32.2814			1.34389			0.671945	−	0.740601i	$-0.265459\pi$
$577$	32.2814			1.34389			0.671945	+	0.740601i	$0.265459\pi$
$578$	8.67424	−	4.39916i	0.360801	−	0.182981i
$579$		0			0
$580$	12.0308	+	8.81037i	0.499550	+	0.365831i
$581$		−	4.45758i		−	0.184931i
$582$		0			0
$583$	5.70269			0.236181
$584$	2.81432	−	17.1408i	0.116458	−	0.709292i
$585$		0			0
$586$	−10.4147	+	5.28183i	−0.430226	+	0.218190i
$587$	−9.97823			−0.411845			−0.205923	−	0.978568i	$-0.566020\pi$
$587$	−9.97823			−0.411845			−0.205923	+	0.978568i	$0.566020\pi$
$588$		0			0
$589$	5.17200	−	7.36659i	0.213109	−	0.303535i
$590$	18.3438	−	9.30312i	0.755204	−	0.383004i
$591$		0			0
$592$	1.87564	+	5.92429i	0.0770882	+	0.243487i
$593$	21.5721			0.885859			0.442930	−	0.896556i	$-0.353939\pi$
$593$	21.5721			0.885859			0.442930	+	0.896556i	$0.353939\pi$
$594$		0			0
$595$	12.0500			0.494003
$596$	11.0500	+	8.09212i	0.452624	+	0.331466i
$597$		0			0
$598$	−0.858664	−	1.69311i	−0.0351134	−	0.0692363i
$599$	36.6125			1.49595			0.747973	−	0.663730i	$-0.231027\pi$
$599$	36.6125			1.49595			0.747973	+	0.663730i	$0.231027\pi$
$600$		0			0
$601$		−	46.0890i		−	1.88001i	−0.341159	−	0.940005i	$-0.610820\pi$
$601$		−	46.0890i		−	1.88001i	0.341159	−	0.940005i	$-0.389180\pi$
$602$	−1.67830	−	3.30927i	−0.0684026	−	0.134876i
$603$		0			0
$604$	−20.4499	+	27.9248i	−0.832093	+	1.13624i
$605$		−	2.59550i		−	0.105522i
$606$		0			0
$607$	−0.600582			−0.0243769			−0.0121884	−	0.999926i	$-0.503880\pi$
$607$	−0.600582			−0.0243769			−0.0121884	+	0.999926i	$0.503880\pi$
$608$	24.3274	−	4.02194i	0.986608	−	0.163111i
$609$		0			0
$610$	−4.24041	+	2.15054i	−0.171689	+	0.0870726i
$611$		−	1.84468i		−	0.0746276i
$612$		0			0
$613$			21.5952i			0.872220i	0.899893	+	0.436110i	$0.143644\pi$
$613$			21.5952i			0.872220i	−0.899893	+	0.436110i	$0.856356\pi$
$614$	12.3561	+	24.3636i	0.498651	+	0.983236i
$615$		0			0
$616$	−10.9007	−	1.78977i	−0.439201	−	0.0721118i
$617$	16.5945			0.668068			0.334034	−	0.942561i	$-0.391590\pi$
$617$	16.5945			0.668068			0.334034	+	0.942561i	$0.391590\pi$
$618$		0			0
$619$	−30.4626			−1.22440			−0.612198	−	0.790704i	$-0.709715\pi$
$619$	−30.4626			−1.22440			−0.612198	+	0.790704i	$0.709715\pi$
$620$	−6.54517	−	4.79316i	−0.262860	−	0.192498i
$621$		0			0
$622$	−12.6583	−	24.9596i	−0.507552	−	1.00079i
$623$	−6.42418			−0.257379
$624$		0			0
$625$	−17.9907			−0.719627
$626$	−0.486067	+	0.246510i	−0.0194271	+	0.00985252i
$627$		0			0
$628$	22.3013	+	16.3317i	0.889920	+	0.651706i
$629$	−7.59122			−0.302682
$630$		0			0
$631$		−	7.54402i		−	0.300323i	−0.988661	−	0.150161i	$-0.952021\pi$
$631$		−	7.54402i		−	0.300323i	0.988661	−	0.150161i	$-0.0479793\pi$
$632$	0.695357	−	4.23511i	0.0276598	−	0.168464i
$633$		0			0
$634$	22.4647	−	11.3930i	0.892188	−	0.452475i
$635$		−	29.0382i		−	1.15235i
$636$		0			0
$637$	2.17848			0.0863145
$638$	14.8937	−	7.55337i	0.589647	−	0.299041i
$639$		0			0
$640$	−3.18658	−	21.9944i	−0.125961	−	0.869406i
$641$		−	46.0941i		−	1.82061i	−0.413939	−	0.910305i	$-0.635847\pi$
$641$		−	46.0941i		−	1.82061i	0.413939	−	0.910305i	$-0.364153\pi$
$642$		0			0
$643$	−11.7674			−0.464059			−0.232030	−	0.972709i	$-0.574537\pi$
$643$	−11.7674			−0.464059			−0.232030	+	0.972709i	$0.574537\pi$
$644$	−4.95804	+	6.77032i	−0.195374	+	0.266788i
$645$		0			0
$646$	−4.28604	+	29.8156i	−0.168632	+	1.17308i
$647$			22.2904i			0.876324i	0.898896	+	0.438162i	$0.144370\pi$
$647$			22.2904i			0.876324i	−0.898896	+	0.438162i	$0.855630\pi$
$648$		0			0
$649$		−	23.0339i		−	0.904161i
$650$	0.578175	−	0.293223i	0.0226779	−	0.0115011i
$651$		0			0
$652$	1.50466	−	2.05465i	0.0589272	−	0.0804664i
$653$		−	33.8039i		−	1.32285i	−0.750011	−	0.661425i	$-0.769952\pi$
$653$		−	33.8039i		−	1.32285i	0.750011	−	0.661425i	$-0.230048\pi$
$654$		0			0
$655$			31.0164i			1.21191i
$656$	−11.1363	+	3.52577i	−0.434800	+	0.137658i
$657$		0			0
$658$	−7.27237	+	3.68820i	−0.283506	+	0.143781i
$659$			16.2065i			0.631317i	0.948873	+	0.315659i	$0.102225\pi$
$659$			16.2065i			0.631317i	−0.948873	+	0.315659i	$0.897775\pi$
$660$		0			0
$661$	0.564440			0.0219542			0.0109771	−	0.999940i	$-0.496506\pi$
$661$	0.564440			0.0219542			0.0109771	+	0.999940i	$0.496506\pi$
$662$	0.322523	+	0.635949i	0.0125352	+	0.0247169i
$663$		0			0
$664$	1.62717	−	9.91039i	0.0631465	−	0.384598i
$665$	−6.17654	+	8.79736i	−0.239516	+	0.341147i
$666$		0			0
$667$		−	12.6859i		−	0.491200i
$668$	−10.4468	+	14.2653i	−0.404198	+	0.551942i
$669$		0			0
$670$	−25.3493	+	12.8560i	−0.979329	+	0.496669i
$671$			5.32459i			0.205553i
$672$		0			0
$673$		−	15.5992i		−	0.601305i	−0.953734	−	0.300653i	$-0.902796\pi$
$673$		−	15.5992i		−	0.601305i	0.953734	−	0.300653i	$-0.0972045\pi$
$674$	4.35858	+	8.59421i	0.167886	+	0.331037i
$675$		0			0
$676$	−15.1710	+	20.7164i	−0.583501	+	0.796783i
$677$	−3.79561			−0.145877			−0.0729386	−	0.997336i	$-0.523238\pi$
$677$	−3.79561			−0.145877			−0.0729386	+	0.997336i	$0.523238\pi$
$678$		0			0
$679$	11.8084			0.453164
$680$	26.7904	+	4.39868i	1.02737	+	0.168682i
$681$		0			0
$682$	−8.10270	+	4.10931i	−0.310269	+	0.157353i
$683$			40.6152i			1.55410i	0.629440	+	0.777049i	$0.283284\pi$
$683$			40.6152i			1.55410i	−0.629440	+	0.777049i	$0.716716\pi$
$684$		0			0
$685$		−	27.5289i		−	1.05183i
$686$	−9.97676	−	19.6721i	−0.380914	−	0.751085i
$687$		0			0
$688$	−2.52332	−	7.97003i	−0.0962007	−	0.303855i
$689$	0.736215			0.0280476
$690$		0			0
$691$	6.90069			0.262514			0.131257	−	0.991348i	$-0.458099\pi$
$691$	6.90069			0.262514			0.131257	+	0.991348i	$0.458099\pi$
$692$	18.7275	−	25.5729i	0.711914	−	0.972135i
$693$		0			0
$694$	−8.40244	+	4.26132i	−0.318952	+	0.161757i
$695$		−	8.58942i		−	0.325815i
$696$		0			0
$697$		−	14.2698i		−	0.540506i
$698$	−17.1702	−	33.8561i	−0.649902	−	1.28147i
$699$		0			0
$700$	−2.31198	−	1.69311i	−0.0873845	−	0.0639935i
$701$		−	42.5932i		−	1.60872i	−0.594139	−	0.804362i	$-0.702507\pi$
$701$		−	42.5932i		−	1.60872i	0.594139	−	0.804362i	$-0.297493\pi$
$702$		0			0
$703$	3.89107	−	5.54212i	0.146754	−	0.209025i
$704$	−23.5818	−	7.95826i	−0.888773	−	0.299938i
$705$		0			0
$706$	−30.0598	+	15.2449i	−1.13132	+	0.573750i
$707$	16.6401			0.625814
$708$		0			0
$709$		−	34.2854i		−	1.28761i	−0.765188	−	0.643807i	$-0.777354\pi$
$709$		−	34.2854i		−	1.28761i	0.765188	−	0.643807i	$-0.222646\pi$
$710$	−11.1086	−	21.9038i	−0.416897	−	0.822035i
$711$		0			0
$712$	−14.2827	−	2.34505i	−0.535266	−	0.0878845i
$713$			6.90158i			0.258466i
$714$		0			0
$715$			2.45448i			0.0917925i
$716$	−18.7040	−	13.6973i	−0.699001	−	0.511893i
$717$		0			0
$718$	−11.3901	−	22.4589i	−0.425074	−	0.838158i
$719$			7.09419i			0.264568i	0.991212	+	0.132284i	$0.0422312\pi$
$719$			7.09419i			0.264568i	−0.991212	+	0.132284i	$0.957769\pi$
$720$		0			0
$721$			10.6691i			0.397336i
$722$	−19.5705	−	18.4118i	−0.728340	−	0.685216i
$723$		0			0
$724$	−29.9080	+	40.8401i	−1.11152	+	1.51781i
$725$	4.33207			0.160889
$726$		0			0
$727$			35.8722i			1.33043i	0.746653	+	0.665213i	$0.231659\pi$
$727$			35.8722i			1.33043i	−0.746653	+	0.665213i	$0.768341\pi$
$728$	−1.40728	−	0.231058i	−0.0521571	−	0.00856359i
$729$		0			0
$730$	7.71671	+	15.2158i	0.285608	+	0.563160i
$731$	10.2126			0.377726
$732$		0			0
$733$		−	27.6419i		−	1.02098i	−0.859885	−	0.510488i	$-0.829465\pi$
$733$		−	27.6419i		−	1.02098i	0.859885	−	0.510488i	$-0.170535\pi$
$734$	−14.8024	−	29.1872i	−0.546366	−	1.07732i
$735$		0			0
$736$	−13.4945	+	13.2424i	−0.497412	+	0.488120i
$737$			31.8305i			1.17249i
$738$		0			0
$739$	−33.7860			−1.24284			−0.621419	−	0.783478i	$-0.713444\pi$
$739$	−33.7860			−1.24284			−0.621419	+	0.783478i	$0.713444\pi$
$740$	−4.92414	−	3.60605i	−0.181015	−	0.132561i
$741$		0			0
$742$	−1.47197	−	2.90242i	−0.0540377	−	0.106551i
$743$	−7.67370			−0.281521			−0.140760	−	0.990044i	$-0.544955\pi$
$743$	−7.67370			−0.281521			−0.140760	+	0.990044i	$0.544955\pi$
$744$		0			0
$745$	−13.4520			−0.492843
$746$	33.3044	−	16.8904i	1.21936	−	0.618402i
$747$		0			0
$748$	17.9637	−	24.5298i	0.656817	−	0.896899i
$749$	−6.16511			−0.225268
$750$		0			0
$751$	20.6688			0.754214			0.377107	−	0.926170i	$-0.376919\pi$
$751$	20.6688			0.754214			0.377107	+	0.926170i	$0.376919\pi$
$752$	−17.5147	+	5.54519i	−0.638697	+	0.202212i
$753$		0			0
$754$	1.92277	−	0.975138i	0.0700232	−	0.0355124i
$755$		−	33.9950i		−	1.23720i
$756$		0			0
$757$			34.7298i			1.26228i	0.775671	+	0.631138i	$0.217412\pi$
$757$			34.7298i			1.26228i	−0.775671	+	0.631138i	$0.782588\pi$
$758$		0			0
$759$		0			0
$760$	−16.9434	+	17.3042i	−0.614603	+	0.627691i
$761$	41.1634			1.49217			0.746087	−	0.665849i	$-0.231930\pi$
$761$	41.1634			1.49217			0.746087	+	0.665849i	$0.231930\pi$
$762$		0			0
$763$			20.3250i			0.735814i
$764$	−36.6125	−	26.8121i	−1.32459	−	0.970027i
$765$		0			0
$766$	−3.15198	+	1.59854i	−0.113886	+	0.0577575i
$767$		−	2.97367i		−	0.107373i
$768$		0			0
$769$	31.2466			1.12678			0.563390	−	0.826191i	$-0.309497\pi$
$769$	31.2466			1.12678			0.563390	+	0.826191i	$0.309497\pi$
$770$	9.67645	−	4.90744i	0.348715	−	0.176852i
$771$		0			0
$772$	−20.9878	−	15.3698i	−0.755367	−	0.553171i
$773$	−35.2334			−1.26726			−0.633629	−	0.773637i	$-0.718435\pi$
$773$	−35.2334			−1.26726			−0.633629	+	0.773637i	$0.718435\pi$
$774$		0			0
$775$	−2.35680			−0.0846588
$776$	26.2532	+	4.31047i	0.942434	+	0.154737i
$777$		0			0
$778$	10.9136	+	21.5194i	0.391272	+	0.771507i
$779$	10.4179	+	7.31432i	0.373261	+	0.262063i
$780$		0			0
$781$	−27.5041			−0.984173
$782$	−10.4468	−	20.5989i	−0.373576	−	0.736615i
$783$		0			0
$784$	−6.54862	−	20.6841i	−0.233879	−	0.738719i
$785$	−27.1492			−0.968995
$786$		0			0
$787$			26.9557i			0.960866i	0.877032	+	0.480433i	$0.159520\pi$
$787$			26.9557i			0.960866i	−0.877032	+	0.480433i	$0.840480\pi$
$788$	9.31189	+	6.81929i	0.331722	+	0.242927i
$789$		0			0
$790$	1.90663	+	3.75947i	0.0678347	+	0.133756i
$791$	10.2669			0.365047
$792$		0			0
$793$			0.687402i			0.0244104i
$794$	8.91300	+	17.5746i	0.316311	+	0.623699i
$795$		0			0
$796$	33.0023	+	24.1683i	1.16974	+	0.856621i
$797$	−30.4003			−1.07683			−0.538417	−	0.842679i	$-0.680977\pi$
$797$	−30.4003			−1.07683			−0.538417	+	0.842679i	$0.680977\pi$
$798$		0			0
$799$		−	22.4429i		−	0.793974i
$800$	−4.52210	−	4.60818i	−0.159880	−	0.162924i
$801$		0			0
$802$	−8.96731	−	17.6817i	−0.316647	−	0.624362i
$803$	19.1061			0.674238
$804$		0			0
$805$		−	8.24204i		−	0.290494i
$806$	−1.04606	+	0.530510i	−0.0368457	+	0.0186864i
$807$		0			0
$808$	36.9953	+	6.07420i	1.30149	+	0.213690i
$809$	2.71694			0.0955225			0.0477612	−	0.998859i	$-0.484791\pi$
$809$	2.71694			0.0955225			0.0477612	+	0.998859i	$0.484791\pi$
$810$		0			0
$811$		−	18.3747i		−	0.645223i	−0.946531	−	0.322612i	$-0.895439\pi$
$811$		−	18.3747i		−	0.645223i	0.946531	−	0.322612i	$-0.104561\pi$
$812$	−7.68868	−	5.63058i	−0.269820	−	0.197594i
$813$		0			0
$814$	−6.09592	+	3.09156i	−0.213662	+	0.108359i
$815$			2.50129i			0.0876164i
$816$		0			0
$817$	−5.23471	+	7.45590i	−0.183139	+	0.260849i
$818$	−22.2171	−	43.8076i	−0.776804	−	1.53170i
$819$		0			0
$820$	6.77855	−	9.25627i	0.236717	−	0.323243i
$821$			7.72021i			0.269437i	0.990884	+	0.134719i	$0.0430130\pi$
$821$			7.72021i			0.269437i	−0.990884	+	0.134719i	$0.956987\pi$
$822$		0			0
$823$		−	26.3865i		−	0.919776i	−0.887977	−	0.459888i	$-0.847890\pi$
$823$		−	26.3865i		−	0.919776i	0.887977	−	0.459888i	$-0.152110\pi$
$824$	−3.89458	+	23.7202i	−0.135674	+	0.826331i
$825$		0			0
$826$	−11.7233	+	5.94549i	−0.407905	+	0.206870i
$827$			45.4697i			1.58114i	0.612373	+	0.790569i	$0.290215\pi$
$827$			45.4697i			1.58114i	−0.612373	+	0.790569i	$0.709785\pi$
$828$		0			0
$829$	16.8307			0.584555			0.292277	−	0.956334i	$-0.405587\pi$
$829$	16.8307			0.584555			0.292277	+	0.956334i	$0.405587\pi$
$830$	4.46161	+	8.79736i	0.154865	+	0.305361i
$831$		0			0
$832$	−3.04440	−	1.02741i	−0.105546	−	0.0356190i
$833$	26.5041			0.918313
$834$		0			0
$835$		−	17.3663i		−	0.600985i
$836$	8.70075	+	25.6881i	0.300922	+	0.888441i
$837$		0			0
$838$	23.0256	−	11.6775i	0.795405	−	0.403391i
$839$	−45.7123			−1.57816			−0.789082	−	0.614288i	$-0.789443\pi$
$839$	−45.7123			−1.57816			−0.789082	+	0.614288i	$0.789443\pi$
$840$		0			0
$841$	−14.5933			−0.503218
$842$	14.6380	−	7.42372i	0.504460	−	0.255838i
$843$		0			0
$844$	−19.6562	−	14.3947i	−0.676595	−	0.495484i
$845$		−	25.2197i		−	0.867582i
$846$		0			0
$847$			1.65875i			0.0569952i
$848$	−2.21310	−	6.99018i	−0.0759981	−	0.240044i
$849$		0			0
$850$	7.03426	−	3.56744i	0.241273	−	0.122362i
$851$			5.19228i			0.177989i
$852$		0			0
$853$		−	36.7727i		−	1.25907i	−0.776970	−	0.629537i	$-0.783244\pi$
$853$		−	36.7727i		−	1.25907i	0.776970	−	0.629537i	$-0.216756\pi$
$854$	2.70998	−	1.37437i	0.0927337	−	0.0470301i
$855$		0			0
$856$	−13.7067	−	2.25048i	−0.468485	−	0.0769198i
$857$			6.42314i			0.219410i	0.993964	+	0.109705i	$0.0349907\pi$
$857$			6.42314i			0.219410i	−0.993964	+	0.109705i	$0.965009\pi$
$858$		0			0
$859$	26.0500			0.888816			0.444408	−	0.895825i	$-0.353414\pi$
$859$	26.0500			0.888816			0.444408	+	0.895825i	$0.353414\pi$
$860$	6.62452	+	4.85127i	0.225894	+	0.165427i
$861$		0			0
$862$	6.19995	−	3.14432i	0.211171	−	0.107096i
$863$	49.3784			1.68086			0.840430	−	0.541921i	$-0.182303\pi$
$863$	49.3784			1.68086			0.840430	+	0.541921i	$0.182303\pi$
$864$		0			0
$865$			31.1319i			1.05851i
$866$	15.7897	+	31.1340i	0.536555	+	1.05797i
$867$		0			0
$868$	4.18292	+	3.06324i	0.141977	+	0.103973i
$869$	4.72068			0.160138
$870$		0			0
$871$			4.10931i			0.139239i
$872$	−7.41933	+	45.1879i	−0.251250	+	1.53025i
$873$		0			0
$874$	20.3934	+	2.93158i	0.689817	+	0.0991623i
$875$	15.1446			0.511982
$876$		0			0
$877$	7.69536			0.259854			0.129927	−	0.991524i	$-0.458526\pi$
$877$	7.69536			0.259854			0.129927	+	0.991524i	$0.458526\pi$
$878$	23.2090	−	11.7705i	0.783266	−	0.397235i
$879$		0			0
$880$	23.3047	−	7.37830i	0.785602	−	0.248722i
$881$	23.1421			0.779678			0.389839	−	0.920883i	$-0.372531\pi$
$881$	23.1421			0.779678			0.389839	+	0.920883i	$0.372531\pi$
$882$		0			0
$883$	38.5899			1.29865			0.649327	−	0.760509i	$-0.275050\pi$
$883$	38.5899			1.29865			0.649327	+	0.760509i	$0.275050\pi$
$884$	2.31910	−	3.16679i	0.0779999	−	0.106511i
$885$		0			0
$886$	−8.40244	+	4.26132i	−0.282285	+	0.143162i
$887$	30.4474			1.02232			0.511161	−	0.859485i	$-0.329215\pi$
$887$	30.4474			1.02232			0.511161	+	0.859485i	$0.329215\pi$
$888$		0			0
$889$			18.5579i			0.622412i
$890$	12.6786	−	6.42999i	0.424988	−	0.215534i
$891$		0			0
$892$	25.9771	−	35.4723i	0.869776	−	1.18770i
$893$	16.3849	+	11.5037i	0.548300	+	0.384955i
$894$		0			0
$895$	22.7698			0.761112
$896$	2.03650	+	14.0563i	0.0680346	+	0.469588i
$897$		0			0
$898$	−1.53736	−	3.03135i	−0.0513023	−	0.101158i
$899$	−7.83775			−0.261403
$900$		0			0
$901$	8.95703			0.298402
$902$	−5.81144	−	11.4590i	−0.193500	−	0.381541i
$903$		0			0
$904$	22.8260	+	3.74776i	0.759180	+	0.124649i
$905$		−	49.7178i		−	1.65268i
$906$		0			0
$907$		−	10.0936i		−	0.335152i	−0.985859	−	0.167576i	$-0.946406\pi$
$907$		−	10.0936i		−	0.335152i	0.985859	−	0.167576i	$-0.0535939\pi$
$908$	33.8394	+	24.7813i	1.12300	+	0.822395i
$909$		0			0
$910$	1.24923	−	0.633548i	0.0414114	−	0.0210019i
$911$	49.1193			1.62739			0.813697	−	0.581289i	$-0.197451\pi$
$911$	49.1193			1.62739			0.813697	+	0.581289i	$0.197451\pi$
$912$		0			0
$913$	11.0466			0.365591
$914$	−17.3737	+	8.81111i	−0.574670	+	0.291445i
$915$		0			0
$916$	−15.4883	−	11.3424i	−0.511748	−	0.374764i
$917$		−	19.8221i		−	0.654584i
$918$		0			0
$919$		−	10.2322i		−	0.337530i	−0.985656	−	0.168765i	$-0.946022\pi$
$919$		−	10.2322i		−	0.337530i	0.985656	−	0.168765i	$-0.0539779\pi$
$920$	3.00863	−	18.3242i	0.0991916	−	0.604133i
$921$		0			0
$922$	3.96194	+	7.81212i	0.130479	+	0.257279i
$923$	−3.55077			−0.116875
$924$		0			0
$925$	−1.77310			−0.0582991
$926$	−20.9011	−	41.2126i	−0.686851	−	1.35433i
$927$		0			0
$928$	−15.0386	−	15.3249i	−0.493667	−	0.503065i
$929$	2.58019			0.0846532			0.0423266	−	0.999104i	$-0.486523\pi$
$929$	2.58019			0.0846532			0.0423266	+	0.999104i	$0.486523\pi$
$930$		0			0
$931$	−13.5853	+	19.3498i	−0.445241	+	0.634166i
$932$	−11.6021	+	15.8430i	−0.380041	+	0.518954i
$933$		0			0
$934$	−29.6858	+	15.0552i	−0.971350	+	0.492623i
$935$			29.8621i			0.976594i
$936$		0			0
$937$	−9.71601			−0.317408			−0.158704	−	0.987326i	$-0.550732\pi$
$937$	−9.71601			−0.317408			−0.158704	+	0.987326i	$0.550732\pi$
$938$	16.2003	−	8.21605i	0.528960	−	0.268263i
$939$		0			0
$940$	10.6610	−	14.5579i	0.347724	−	0.474826i
$941$	−24.7717			−0.807533			−0.403766	−	0.914862i	$-0.632299\pi$
$941$	−24.7717			−0.807533			−0.403766	+	0.914862i	$0.632299\pi$
$942$		0			0
$943$	−9.76031			−0.317839
$944$	−28.2343	+	8.93900i	−0.918947	+	0.290940i
$945$		0			0
$946$	8.20094	−	4.15913i	0.266636	−	0.135225i
$947$	−43.3785			−1.40961			−0.704806	−	0.709400i	$-0.748966\pi$
$947$	−43.3785			−1.40961			−0.704806	+	0.709400i	$0.748966\pi$
$948$		0			0
$949$	2.46659			0.0800688
$950$	−1.00110	+	6.96408i	−0.0324799	+	0.225945i
$951$		0			0
$952$	−17.1214	−	2.81113i	−0.554907	−	0.0911093i
$953$		−	1.09947i		−	0.0356154i	−0.999841	−	0.0178077i	$-0.994331\pi$
$953$		−	1.09947i		−	0.0356154i	0.999841	−	0.0178077i	$-0.00566867\pi$
$954$		0			0
$955$	44.5713			1.44229
$956$	9.22900	+	6.75859i	0.298487	+	0.218588i
$957$		0			0
$958$	0.840095	+	1.65649i	0.0271422	+	0.0535189i
$959$			17.5933i			0.568118i
$960$		0			0
$961$	−26.7360			−0.862451
$962$	−0.786981	+	0.399120i	−0.0253733	+	0.0128681i
$963$		0			0
$964$	28.8356	+	21.1169i	0.928734	+	0.680130i
$965$	25.5501			0.822486
$966$		0			0
$967$		−	18.4508i		−	0.593339i	−0.954980	−	0.296669i	$-0.904124\pi$
$967$		−	18.4508i		−	0.593339i	0.954980	−	0.296669i	$-0.0958760\pi$
$968$	−0.605501	+	3.68784i	−0.0194615	+	0.118532i
$969$		0			0
$970$	−23.3047	+	11.8190i	−0.748269	+	0.379487i
$971$		−	22.0471i		−	0.707525i	−0.935335	−	0.353763i	$-0.884902\pi$
$971$		−	22.0471i		−	0.707525i	0.935335	−	0.353763i	$-0.115098\pi$
$972$		0			0
$973$			5.48937i			0.175981i
$974$	−33.3500	+	16.9135i	−1.06860	+	0.541944i
$975$		0			0
$976$	6.52671	−	2.06636i	0.208915	−	0.0661427i
$977$		−	7.59567i		−	0.243007i	−0.992591	−	0.121503i	$-0.961228\pi$
$977$		−	7.59567i		−	0.243007i	0.992591	−	0.121503i	$-0.0387716\pi$
$978$		0			0
$979$		−	15.9202i		−	0.508813i
$980$	17.1922	+	12.5902i	0.549185	+	0.402179i
$981$		0			0
$982$	31.6870	−	16.0701i	1.01117	−	0.512819i
$983$	2.75811			0.0879699			0.0439850	−	0.999032i	$-0.485995\pi$
$983$	2.75811			0.0879699			0.0439850	+	0.999032i	$0.485995\pi$
$984$		0			0
$985$	−11.3361			−0.361198
$986$	23.3930	−	11.8638i	0.744986	−	0.377822i
$987$		0			0
$988$	1.12326	+	3.31632i	0.0357358	+	0.105506i
$989$		−	6.98525i		−	0.222118i
$990$		0			0
$991$	−51.8481			−1.64701			−0.823504	−	0.567310i	$-0.807984\pi$
$991$	−51.8481			−1.64701			−0.823504	+	0.567310i	$0.807984\pi$
$992$	8.18156	+	8.33730i	0.259765	+	0.264710i
$993$		0			0
$994$	7.09931	+	13.9984i	0.225177	+	0.444002i
$995$	−40.1763			−1.27367
$996$		0			0
$997$			39.1940i			1.24129i	0.784094	+	0.620643i	$0.213128\pi$
$997$			39.1940i			1.24129i	−0.784094	+	0.620643i	$0.786872\pi$
$998$	−11.7359	+	5.95188i	−0.371493	+	0.188403i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.f.379.18	yes	24
3.2	odd	2	inner	1368.2.e.f.379.8	yes	24
4.3	odd	2		5472.2.e.f.5167.18		24
8.3	odd	2	inner	1368.2.e.f.379.5	✓	24
8.5	even	2		5472.2.e.f.5167.11		24
12.11	even	2		5472.2.e.f.5167.19		24
19.18	odd	2	inner	1368.2.e.f.379.7	yes	24
24.5	odd	2		5472.2.e.f.5167.10		24
24.11	even	2	inner	1368.2.e.f.379.19	yes	24
57.56	even	2	inner	1368.2.e.f.379.17	yes	24
76.75	even	2		5472.2.e.f.5167.12		24
152.37	odd	2		5472.2.e.f.5167.17		24
152.75	even	2	inner	1368.2.e.f.379.20	yes	24
228.227	odd	2		5472.2.e.f.5167.9		24
456.227	odd	2	inner	1368.2.e.f.379.6	yes	24
456.341	even	2		5472.2.e.f.5167.20		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.e.f.379.5	✓	24	8.3	odd	2	inner
1368.2.e.f.379.6	yes	24	456.227	odd	2	inner
1368.2.e.f.379.7	yes	24	19.18	odd	2	inner
1368.2.e.f.379.8	yes	24	3.2	odd	2	inner
1368.2.e.f.379.17	yes	24	57.56	even	2	inner
1368.2.e.f.379.18	yes	24	1.1	even	1	trivial
1368.2.e.f.379.19	yes	24	24.11	even	2	inner
1368.2.e.f.379.20	yes	24	152.75	even	2	inner
5472.2.e.f.5167.9		24	228.227	odd	2
5472.2.e.f.5167.10		24	24.5	odd	2
5472.2.e.f.5167.11		24	8.5	even	2
5472.2.e.f.5167.12		24	76.75	even	2
5472.2.e.f.5167.17		24	152.37	odd	2
5472.2.e.f.5167.18		24	4.3	odd	2
5472.2.e.f.5167.19		24	12.11	even	2
5472.2.e.f.5167.20		24	456.341	even	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)

\(f(q)\)	\(=\)	\(q+(1.26128 - 0.639662i) q^{2} +(1.18166 - 1.61359i) q^{4} +1.96435i q^{5} -1.25539i q^{7} +(0.458259 - 2.79106i) q^{8} +O(q^{10})\)	\(q+(1.26128 - 0.639662i) q^{2} +(1.18166 - 1.61359i) q^{4} +1.96435i q^{5} -1.25539i q^{7} +(0.458259 - 2.79106i) q^{8} +(1.25652 + 2.47760i) q^{10} +3.11106 q^{11} +0.401637 q^{13} +(-0.803023 - 1.58339i) q^{14} +(-1.20734 - 3.81344i) q^{16} +4.88644 q^{17} +(-2.50466 + 3.56744i) q^{19} +(3.16965 + 2.32120i) q^{20} +(3.92392 - 1.99003i) q^{22} -3.34225i q^{23} +1.14134 q^{25} +(0.506577 - 0.256912i) q^{26} +(-2.02568 - 1.48344i) q^{28} +3.79561 q^{29} -2.06495 q^{31} +(-3.96211 - 4.03753i) q^{32} +(6.16318 - 3.12567i) q^{34} +2.46601 q^{35} -1.55353 q^{37} +(-0.877128 + 6.10169i) q^{38} +(5.48261 + 0.900181i) q^{40} -2.92028i q^{41} +2.08998 q^{43} +(3.67623 - 5.01997i) q^{44} +(-2.13791 - 4.21552i) q^{46} -4.59290i q^{47} +5.42401 q^{49} +(1.43955 - 0.730070i) q^{50} +(0.474600 - 0.648077i) q^{52} +1.83304 q^{53} +6.11121i q^{55} +(-3.50385 - 0.575292i) q^{56} +(4.78734 - 2.42791i) q^{58} -7.40388i q^{59} +1.71150i q^{61} +(-2.60448 + 1.32087i) q^{62} +(-7.58000 - 2.55806i) q^{64} +0.788954i q^{65} +10.2314i q^{67} +(5.77413 - 7.88471i) q^{68} +(3.11034 - 1.57742i) q^{70} -8.84074 q^{71} +6.14134 q^{73} +(-1.95944 + 0.993733i) q^{74} +(2.79672 + 8.25702i) q^{76} -3.90558i q^{77} +1.51739 q^{79} +(7.49093 - 2.37164i) q^{80} +(-1.86799 - 3.68330i) q^{82} +3.55077 q^{83} +9.59867i q^{85} +(2.63606 - 1.33688i) q^{86} +(1.42567 - 8.68315i) q^{88} -5.11730i q^{89} -0.504209i q^{91} +(-5.39302 - 3.94942i) q^{92} +(-2.93790 - 5.79294i) q^{94} +(-7.00770 - 4.92003i) q^{95} +9.40618i q^{97} +(6.84120 - 3.46953i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4}+O(q^{10}) \) 24 * q + 20 * q^4	\( 24 q + 20 q^{4} - 12 q^{16} + 24 q^{19} - 40 q^{25} - 40 q^{28} - 72 q^{49} - 104 q^{58} + 20 q^{64} + 80 q^{73} - 12 q^{76} + 56 q^{82}+O(q^{100}) \) 24 * q + 20 * q^4 - 12 * q^16 + 24 * q^19 - 40 * q^25 - 40 * q^28 - 72 * q^49 - 104 * q^58 + 20 * q^64 + 80 * q^73 - 12 * q^76 + 56 * q^82

Introduction

L-functions

Modular forms

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Database

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