LMFDB - Embedded newform 1352.2.o.f.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1352,2,Mod(361,1352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1352, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1352.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$1.30512 - 1.13871i$ of defining polynomial
Character	$\chi$	$=$	1352.361
Dual form			1352.2.o.f.1161.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.63871 + 2.83834i) q^{3} +2.61023i q^{5} +(0.971521 + 0.560908i) q^{7} +(-3.87076 + 6.70436i) q^{9} +(-0.971521 + 0.560908i) q^{11} +(-7.40872 + 4.27743i) q^{15} +(2.77743 - 4.81064i) q^{17} +(1.45204 + 0.838335i) q^{19} +3.67667i q^{21} +(1.63871 + 2.83834i) q^{23} -1.81333 q^{25} -15.5400 q^{27} +(0.167192 + 0.289586i) q^{29} -0.129717i q^{31} +(-3.18409 - 1.83834i) q^{33} +(-1.46410 + 2.53590i) q^{35} +(3.92356 - 2.26527i) q^{37} +(-4.96410 + 2.86603i) q^{41} +(-2.24895 + 3.89529i) q^{43} +(-17.5000 - 10.1036i) q^{45} -10.7985i q^{47} +(-2.87076 - 4.97231i) q^{49} +18.2056 q^{51} +4.14771 q^{53} +(-1.46410 - 2.53590i) q^{55} +5.49516i q^{57} +(0.549538 + 0.317276i) q^{59} +(-2.35387 + 4.07702i) q^{61} +(-7.52106 + 4.34229i) q^{63} +(12.4372 - 7.18062i) q^{67} +(-5.37076 + 9.30244i) q^{69} +(7.45204 + 4.30244i) q^{71} -9.94462i q^{73} +(-2.97152 - 5.14683i) q^{75} -1.25847 q^{77} +13.5970 q^{79} +(-13.8533 - 23.9947i) q^{81} +5.75637i q^{83} +(12.5569 + 7.24974i) q^{85} +(-0.547961 + 0.949096i) q^{87} +(-12.4235 + 7.17272i) q^{89} +(0.368180 - 0.212569i) q^{93} +(-2.18825 + 3.79016i) q^{95} +(-7.80107 - 4.50395i) q^{97} -8.68457i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 6 q^{7} - 6 q^{9} - 6 q^{11} + 6 q^{19} + 2 q^{23} - 20 q^{25} - 28 q^{27} - 8 q^{29} - 6 q^{33} + 16 q^{35} + 24 q^{37} - 12 q^{41} + 6 q^{43} - 30 q^{45} + 2 q^{49} + 68 q^{51} + 20 q^{53}+ \cdots - 30 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 + 6 * q^7 - 6 * q^9 - 6 * q^11 + 6 * q^19 + 2 * q^23 - 20 * q^25 - 28 * q^27 - 8 * q^29 - 6 * q^33 + 16 * q^35 + 24 * q^37 - 12 * q^41 + 6 * q^43 - 30 * q^45 + 2 * q^49 + 68 * q^51 + 20 * q^53 + 16 * q^55 - 18 * q^59 - 4 * q^61 - 36 * q^63 + 42 * q^67 - 18 * q^69 + 54 * q^71 - 22 * q^75 - 60 * q^77 + 16 * q^79 - 20 * q^81 - 6 * q^85 - 10 * q^87 + 18 * q^89 - 36 * q^93 + 16 * q^95 - 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.63871	+	2.83834i	0.946112	+	1.63871i	0.753510	+	0.657437i	$0.228359\pi$
$3$	1.63871	+	2.83834i	0.946112	+	1.63871i	0.192602	+	0.981277i	$0.438307\pi$
$4$		0			0
$5$			2.61023i			1.16733i	0.811994	+	0.583666i	$0.198382\pi$
$5$			2.61023i			1.16733i	−0.811994	+	0.583666i	$0.801618\pi$
$6$		0			0
$7$	0.971521	+	0.560908i	0.367200	+	0.212003i	0.672235	−	0.740338i	$-0.265335\pi$
$7$	0.971521	+	0.560908i	0.367200	+	0.212003i	−0.305034	+	0.952341i	$0.598668\pi$
$8$		0			0
$9$	−3.87076	+	6.70436i	−1.29025	+	2.23479i
$10$		0			0
$11$	−0.971521	+	0.560908i	−0.292925	+	0.169120i	−0.639260	−	0.768991i	$-0.720759\pi$
$11$	−0.971521	+	0.560908i	−0.292925	+	0.169120i	0.346335	+	0.938111i	$0.387426\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−7.40872	+	4.27743i	−1.91292	+	1.10443i
$16$		0			0
$17$	2.77743	−	4.81064i	0.673625	−	1.16675i	−0.303244	−	0.952913i	$-0.598070\pi$
$17$	2.77743	−	4.81064i	0.673625	−	1.16675i	0.976869	−	0.213840i	$-0.0685970\pi$
$18$		0			0
$19$	1.45204	+	0.838335i	0.333121	+	0.192327i	0.657226	−	0.753694i	$-0.271730\pi$
$19$	1.45204	+	0.838335i	0.333121	+	0.192327i	−0.324105	+	0.946021i	$0.605063\pi$
$20$		0			0
$21$			3.67667i			0.802315i
$22$		0			0
$23$	1.63871	+	2.83834i	0.341695	+	0.591834i	0.984748	−	0.173988i	$-0.0556656\pi$
$23$	1.63871	+	2.83834i	0.341695	+	0.591834i	−0.643052	+	0.765822i	$0.722332\pi$
$24$		0			0
$25$	−1.81333			−0.362665
$26$		0			0
$27$	−15.5400			−2.99068
$28$		0			0
$29$	0.167192	+	0.289586i	0.0310468	+	0.0537747i	0.881131	−	0.472872i	$-0.156783\pi$
$29$	0.167192	+	0.289586i	0.0310468	+	0.0537747i	−0.850084	+	0.526646i	$0.823449\pi$
$30$		0			0
$31$		−	0.129717i		−	0.0232978i	−0.999932	−	0.0116489i	$-0.996292\pi$
$31$		−	0.129717i		−	0.0232978i	0.999932	−	0.0116489i	$-0.00370805\pi$
$32$		0			0
$33$	−3.18409	−	1.83834i	−0.554279	−	0.320013i
$34$		0			0
$35$	−1.46410	+	2.53590i	−0.247478	+	0.428645i
$36$		0			0
$37$	3.92356	−	2.26527i	0.645029	−	0.372408i	−0.141520	−	0.989935i	$-0.545199\pi$
$37$	3.92356	−	2.26527i	0.645029	−	0.372408i	0.786549	+	0.617528i	$0.211866\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.96410	+	2.86603i	−0.775262	+	0.447598i	−0.834749	−	0.550631i	$-0.814387\pi$
$41$	−4.96410	+	2.86603i	−0.775262	+	0.447598i	0.0594862	+	0.998229i	$0.481054\pi$
$42$		0			0
$43$	−2.24895	+	3.89529i	−0.342961	+	0.594027i	−0.984981	−	0.172661i	$-0.944763\pi$
$43$	−2.24895	+	3.89529i	−0.342961	+	0.594027i	0.642020	+	0.766688i	$0.278097\pi$
$44$		0			0
$45$	−17.5000	−	10.1036i	−2.60874	−	1.50616i
$46$		0			0
$47$		−	10.7985i		−	1.57512i	−0.616237	−	0.787561i	$-0.711344\pi$
$47$		−	10.7985i		−	1.57512i	0.616237	−	0.787561i	$-0.288656\pi$
$48$		0			0
$49$	−2.87076	−	4.97231i	−0.410109	−	0.710330i
$50$		0			0
$51$	18.2056			2.54930
$52$		0			0
$53$	4.14771			0.569732			0.284866	−	0.958567i	$-0.408051\pi$
$53$	4.14771			0.569732			0.284866	+	0.958567i	$0.408051\pi$
$54$		0			0
$55$	−1.46410	−	2.53590i	−0.197419	−	0.341940i
$56$		0			0
$57$			5.49516i			0.727852i
$58$		0			0
$59$	0.549538	+	0.317276i	0.0715438	+	0.0413058i	0.535345	−	0.844633i	$-0.320182\pi$
$59$	0.549538	+	0.317276i	0.0715438	+	0.0413058i	−0.463801	+	0.885939i	$0.653515\pi$
$60$		0			0
$61$	−2.35387	+	4.07702i	−0.301382	+	0.522009i	−0.976449	−	0.215748i	$-0.930781\pi$
$61$	−2.35387	+	4.07702i	−0.301382	+	0.522009i	0.675067	+	0.737756i	$0.264115\pi$
$62$		0			0
$63$	−7.52106	+	4.34229i	−0.947564	+	0.547077i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	12.4372	−	7.18062i	1.51945	−	0.877252i	0.519708	−	0.854344i	$-0.326041\pi$
$67$	12.4372	−	7.18062i	1.51945	−	0.877252i	0.999738	−	0.0229086i	$-0.00729269\pi$
$68$		0			0
$69$	−5.37076	+	9.30244i	−0.646564	+	1.11988i
$70$		0			0
$71$	7.45204	+	4.30244i	0.884394	+	0.510605i	0.872105	−	0.489319i	$-0.162755\pi$
$71$	7.45204	+	4.30244i	0.884394	+	0.510605i	0.0122896	+	0.999924i	$0.496088\pi$
$72$		0			0
$73$		−	9.94462i		−	1.16393i	−0.813214	−	0.581965i	$-0.802284\pi$
$73$		−	9.94462i		−	1.16393i	0.813214	−	0.581965i	$-0.197716\pi$
$74$		0			0
$75$	−2.97152	−	5.14683i	−0.343122	−	0.594304i
$76$		0			0
$77$	−1.25847			−0.143416
$78$		0			0
$79$	13.5970			1.52978			0.764889	−	0.644162i	$-0.222794\pi$
$79$	13.5970			1.52978			0.764889	+	0.644162i	$0.222794\pi$
$80$		0			0
$81$	−13.8533	−	23.9947i	−1.53926	−	2.66608i
$82$		0			0
$83$			5.75637i			0.631843i	0.948785	+	0.315922i	$0.102314\pi$
$83$			5.75637i			0.631843i	−0.948785	+	0.315922i	$0.897686\pi$
$84$		0			0
$85$	12.5569	+	7.24974i	1.36199	+	0.786344i
$86$		0			0
$87$	−0.547961	+	0.949096i	−0.0587476	+	0.101754i
$88$		0			0
$89$	−12.4235	+	7.17272i	−1.31689	+	0.760307i	−0.983227	−	0.182386i	$-0.941618\pi$
$89$	−12.4235	+	7.17272i	−1.31689	+	0.760307i	−0.333663	+	0.942692i	$0.608285\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.368180	−	0.212569i	0.0381785	−	0.0220424i
$94$		0			0
$95$	−2.18825	+	3.79016i	−0.224510	+	0.388863i
$96$		0			0
$97$	−7.80107	−	4.50395i	−0.792079	−	0.457307i	0.0486151	−	0.998818i	$-0.484519\pi$
$97$	−7.80107	−	4.50395i	−0.792079	−	0.457307i	−0.840694	+	0.541511i	$0.817853\pi$
$98$		0			0
$99$		−	8.68457i		−	0.872832i
$100$		0			0
$101$	−1.44462	−	2.50215i	−0.143745	−	0.248974i	0.785159	−	0.619294i	$-0.212581\pi$
$101$	−1.44462	−	2.50215i	−0.143745	−	0.248974i	−0.928904	+	0.370321i	$0.879248\pi$
$102$		0			0
$103$	5.22047			0.514388			0.257194	−	0.966360i	$-0.417202\pi$
$103$	5.22047			0.514388			0.257194	+	0.966360i	$0.417202\pi$
$104$		0			0
$105$	−9.59697			−0.936569
$106$		0			0
$107$	−2.91614	−	5.05090i	−0.281914	−	0.488289i	0.689942	−	0.723865i	$-0.257636\pi$
$107$	−2.91614	−	5.05090i	−0.281914	−	0.488289i	−0.971856	+	0.235575i	$0.924303\pi$
$108$		0			0
$109$			2.92820i			0.280471i	0.990118	+	0.140236i	$0.0447860\pi$
$109$			2.92820i			0.280471i	−0.990118	+	0.140236i	$0.955214\pi$
$110$		0			0
$111$	12.8592	+	7.42425i	1.22054	+	0.704679i
$112$		0			0
$113$	−2.44304	+	4.23147i	−0.229822	+	0.398064i	−0.957755	−	0.287585i	$-0.907148\pi$
$113$	−2.44304	+	4.23147i	−0.229822	+	0.398064i	0.727933	+	0.685648i	$0.240481\pi$
$114$		0			0
$115$	−7.40872	+	4.27743i	−0.690867	+	0.398872i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.39666	−	3.11576i	0.494711	−	0.285621i
$120$		0			0
$121$	−4.87076	+	8.43641i	−0.442797	+	0.766946i
$122$		0			0
$123$	−16.2695	−	9.39319i	−1.46697	−	0.846955i
$124$		0			0
$125$			8.31797i			0.743982i
$126$		0			0
$127$	−5.15977	−	8.93699i	−0.457856	−	0.793030i	0.540992	−	0.841028i	$-0.318049\pi$
$127$	−5.15977	−	8.93699i	−0.457856	−	0.793030i	−0.998847	+	0.0479985i	$0.984716\pi$
$128$		0			0
$129$	−14.7415			−1.29792
$130$		0			0
$131$	−0.110761			−0.00967723			−0.00483861	−	0.999988i	$-0.501540\pi$
$131$	−0.110761			−0.00967723			−0.00483861	+	0.999988i	$0.501540\pi$
$132$		0			0
$133$	0.940458	+	1.62892i	0.0815480	+	0.141245i
$134$		0			0
$135$		−	40.5631i		−	3.49111i
$136$		0			0
$137$	−6.02106	−	3.47626i	−0.514414	−	0.296997i	0.220232	−	0.975447i	$-0.429318\pi$
$137$	−6.02106	−	3.47626i	−0.514414	−	0.296997i	−0.734646	+	0.678451i	$0.762652\pi$
$138$		0			0
$139$	5.21515	−	9.03291i	0.442344	−	0.766161i	−0.555519	−	0.831504i	$-0.687481\pi$
$139$	5.21515	−	9.03291i	0.442344	−	0.766161i	0.997863	+	0.0653421i	$0.0208139\pi$
$140$		0			0
$141$	30.6497	−	17.6956i	2.58117	−	1.49024i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−0.755887	+	0.436411i	−0.0627730	+	0.0362420i
$146$		0			0
$147$	9.40872	−	16.2964i	0.776018	−	1.34410i
$148$		0			0
$149$	8.31587	+	4.80117i	0.681262	+	0.393327i	0.800330	−	0.599559i	$-0.204657\pi$
$149$	8.31587	+	4.80117i	0.681262	+	0.393327i	−0.119068	+	0.992886i	$0.537991\pi$
$150$		0			0
$151$			13.7267i			1.11706i	0.829484	+	0.558531i	$0.188635\pi$
$151$			13.7267i			1.11706i	−0.829484	+	0.558531i	$0.811365\pi$
$152$		0			0
$153$	21.5015	+	37.2417i	1.73830	+	3.01082i
$154$		0			0
$155$	0.338591			0.0271963
$156$		0			0
$157$	8.96200			0.715245			0.357623	−	0.933866i	$-0.383587\pi$
$157$	8.96200			0.715245			0.357623	+	0.933866i	$0.383587\pi$
$158$		0			0
$159$	6.79691	+	11.7726i	0.539030	+	0.933627i
$160$		0			0
$161$			3.67667i			0.289762i
$162$		0			0
$163$	1.89972	+	1.09681i	0.148798	+	0.0859085i	0.572550	−	0.819869i	$-0.305954\pi$
$163$	1.89972	+	1.09681i	0.148798	+	0.0859085i	−0.423753	+	0.905778i	$0.639287\pi$
$164$		0			0
$165$	4.79849	−	8.31122i	0.373562	−	0.647028i
$166$		0			0
$167$	−12.9715	+	7.48911i	−1.00377	+	0.579525i	−0.909361	−	0.416009i	$-0.863428\pi$
$167$	−12.9715	+	7.48911i	−1.00377	+	0.579525i	−0.0944059	+	0.995534i	$0.530095\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−11.2410	+	6.49000i	−0.859621	+	0.496302i
$172$		0			0
$173$	−1.99742	+	3.45963i	−0.151861	+	0.263030i	−0.931912	−	0.362686i	$-0.881860\pi$
$173$	−1.99742	+	3.45963i	−0.151861	+	0.263030i	0.780051	+	0.625716i	$0.215193\pi$
$174$		0			0
$175$	−1.76168	−	1.01711i	−0.133171	−	0.0768862i
$176$		0			0
$177$			2.07970i			0.156320i
$178$		0			0
$179$	−4.30591	−	7.45805i	−0.321839	−	0.557441i	0.659029	−	0.752118i	$-0.270967\pi$
$179$	−4.30591	−	7.45805i	−0.321839	−	0.557441i	−0.980867	+	0.194677i	$0.937634\pi$
$180$		0			0
$181$	15.6308			1.16183			0.580913	−	0.813966i	$-0.302696\pi$
$181$	15.6308			1.16183			0.580913	+	0.813966i	$0.302696\pi$
$182$		0			0
$183$	−15.4293			−1.14056
$184$		0			0
$185$	5.91288	+	10.2414i	0.434724	+	0.752964i
$186$		0			0
$187$			6.23152i			0.455694i
$188$		0			0
$189$	−15.0975	−	8.71652i	−1.09818	−	0.634033i
$190$		0			0
$191$	−13.5280	+	23.4311i	−0.978848	+	1.69541i	−0.312246	+	0.950001i	$0.601081\pi$
$191$	−13.5280	+	23.4311i	−0.978848	+	1.69541i	−0.666602	+	0.745414i	$0.732252\pi$
$192$		0			0
$193$	−20.7426	+	11.9757i	−1.49308	+	0.862032i	−0.999969	−	0.00793192i	$-0.997475\pi$
$193$	−20.7426	+	11.9757i	−1.49308	+	0.862032i	−0.493115	+	0.869964i	$0.664142\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.95941	+	5.17272i	−0.638332	+	0.368541i	−0.783972	−	0.620797i	$-0.786809\pi$
$197$	−8.95941	+	5.17272i	−0.638332	+	0.368541i	0.145640	+	0.989338i	$0.453476\pi$
$198$		0			0
$199$	6.78642	−	11.7544i	0.481077	−	0.833250i	−0.518687	−	0.854964i	$-0.673579\pi$
$199$	6.78642	−	11.7544i	0.481077	−	0.833250i	0.999764	+	0.0217145i	$0.00691247\pi$
$200$		0			0
$201$	40.7620	+	23.5340i	2.87513	+	1.65996i
$202$		0			0
$203$			0.375118i			0.0263281i
$204$		0			0
$205$	−7.48100	−	12.9575i	−0.522496	−	0.904989i
$206$		0			0
$207$	−25.3723			−1.76350
$208$		0			0
$209$	−1.88092			−0.130106
$210$		0			0
$211$	0.973098	+	1.68546i	0.0669909	+	0.116032i	0.897575	−	0.440861i	$-0.145327\pi$
$211$	0.973098	+	1.68546i	0.0669909	+	0.116032i	−0.830585	+	0.556893i	$0.811994\pi$
$212$		0			0
$213$			28.2018i			1.93236i
$214$		0			0
$215$	−10.1676	−	5.87028i	−0.693427	−	0.400350i
$216$		0			0
$217$	0.0727592	−	0.126023i	0.00493922	−	0.00855498i
$218$		0			0
$219$	28.2262	−	16.2964i	1.90735	−	1.10121i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	20.7156	−	11.9602i	1.38722	−	0.800911i	0.394218	−	0.919017i	$-0.371016\pi$
$223$	20.7156	−	11.9602i	1.38722	−	0.800911i	0.993001	+	0.118106i	$0.0376823\pi$
$224$		0			0
$225$	7.01896	−	12.1572i	0.467930	−	0.810479i
$226$		0			0
$227$	15.3084	+	8.83834i	1.01606	+	0.586621i	0.912959	−	0.408050i	$-0.133791\pi$
$227$	15.3084	+	8.83834i	1.01606	+	0.586621i	0.103098	+	0.994671i	$0.467125\pi$
$228$		0			0
$229$		−	10.9282i		−	0.722156i	−0.932536	−	0.361078i	$-0.882409\pi$
$229$		−	10.9282i		−	0.722156i	0.932536	−	0.361078i	$-0.117591\pi$
$230$		0			0
$231$	−2.06227	−	3.57196i	−0.135688	−	0.235018i
$232$		0			0
$233$	−11.5970			−0.759743			−0.379871	−	0.925039i	$-0.624032\pi$
$233$	−11.5970			−0.759743			−0.379871	+	0.925039i	$0.624032\pi$
$234$		0			0
$235$	28.1866			1.83869
$236$		0			0
$237$	22.2815	+	38.5928i	1.44734	+	2.50687i
$238$		0			0
$239$			18.0221i			1.16575i	0.812561	+	0.582877i	$0.198073\pi$
$239$			18.0221i			1.16575i	−0.812561	+	0.582877i	$0.801927\pi$
$240$		0			0
$241$	0.709837	+	0.409825i	0.0457246	+	0.0263991i	0.522688	−	0.852524i	$-0.324929\pi$
$241$	0.709837	+	0.409825i	0.0457246	+	0.0263991i	−0.476963	+	0.878923i	$0.658263\pi$
$242$		0			0
$243$	22.0933	−	38.2667i	1.41729	−	2.45481i
$244$		0			0
$245$	12.9789	−	7.49337i	0.829191	−	0.478734i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−16.3385	+	9.43304i	−1.03541	+	0.597795i
$250$		0			0
$251$	7.17873	−	12.4339i	0.453117	−	0.784822i	−0.545460	−	0.838137i	$-0.683645\pi$
$251$	7.17873	−	12.4339i	0.453117	−	0.784822i	0.998578	+	0.0533143i	$0.0169785\pi$
$252$		0			0
$253$	−3.18409	−	1.83834i	−0.200182	−	0.115575i
$254$		0			0
$255$			47.5210i			2.97588i
$256$		0			0
$257$	−10.2985	−	17.8375i	−0.642402	−	1.11267i	−0.984895	−	0.173152i	$-0.944605\pi$
$257$	−10.2985	−	17.8375i	−0.642402	−	1.11267i	0.342493	−	0.939520i	$-0.388729\pi$
$258$		0			0
$259$	5.08243			0.315807
$260$		0			0
$261$	−2.58865			−0.160233
$262$		0			0
$263$	14.5115	+	25.1347i	0.894820	+	1.54987i	0.834028	+	0.551723i	$0.186029\pi$
$263$	14.5115	+	25.1347i	0.894820	+	1.54987i	0.0607920	+	0.998150i	$0.480637\pi$
$264$		0			0
$265$			10.8265i			0.665066i
$266$		0			0
$267$	−40.7172	−	23.5081i	−2.49185	−	1.43867i
$268$		0			0
$269$	4.31381	−	7.47173i	0.263017	−	0.455560i	−0.704025	−	0.710175i	$-0.748616\pi$
$269$	4.31381	−	7.47173i	0.263017	−	0.455560i	0.967042	+	0.254616i	$0.0819490\pi$
$270$		0			0
$271$	13.8459	−	7.99395i	0.841080	−	0.485598i	−0.0165513	−	0.999863i	$-0.505269\pi$
$271$	13.8459	−	7.99395i	0.841080	−	0.485598i	0.857631	+	0.514265i	$0.171935\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.76168	−	1.01711i	0.106234	−	0.0613340i
$276$		0			0
$277$	−14.3728	+	24.8945i	−0.863579	+	1.49576i	0.00487180	+	0.999988i	$0.498449\pi$
$277$	−14.3728	+	24.8945i	−0.863579	+	1.49576i	−0.868451	+	0.495775i	$0.834884\pi$
$278$		0			0
$279$	0.869668	+	0.502103i	0.0520657	+	0.0300601i
$280$		0			0
$281$		−	5.83386i		−	0.348019i	−0.984744	−	0.174009i	$-0.944328\pi$
$281$		−	5.83386i		−	0.348019i	0.984744	−	0.174009i	$-0.0556723\pi$
$282$		0			0
$283$	13.8459	+	23.9818i	0.823055	+	1.42557i	0.903397	+	0.428805i	$0.141065\pi$
$283$	13.8459	+	23.9818i	0.823055	+	1.42557i	−0.0803425	+	0.996767i	$0.525601\pi$
$284$		0			0
$285$	−14.3437			−0.849646
$286$		0			0
$287$	−6.43031			−0.379569
$288$		0			0
$289$	−6.92820	−	12.0000i	−0.407541	−	0.705882i
$290$		0			0
$291$		−	29.5227i		−	1.73065i
$292$		0			0
$293$	13.7980	+	7.96626i	0.806085	+	0.465394i	0.845595	−	0.533826i	$-0.179246\pi$
$293$	13.7980	+	7.96626i	0.806085	+	0.465394i	−0.0395092	+	0.999219i	$0.512579\pi$
$294$		0			0
$295$	−0.828165	+	1.43442i	−0.0482176	+	0.0835154i
$296$		0			0
$297$	15.0975	−	8.71652i	0.876043	−	0.505784i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−4.36980	+	2.52291i	−0.251871	+	0.145418i
$302$		0			0
$303$	4.73464	−	8.20063i	0.271998	−	0.471114i
$304$		0			0
$305$	−10.6420	−	6.14415i	−0.609358	−	0.351813i
$306$		0			0
$307$		−	20.3955i		−	1.16403i	−0.813178	−	0.582015i	$-0.802264\pi$
$307$		−	20.3955i		−	1.16403i	0.813178	−	0.582015i	$-0.197736\pi$
$308$		0			0
$309$	8.55485	+	14.8174i	0.486669	+	0.842935i
$310$		0			0
$311$	12.9989			0.737103			0.368551	−	0.929607i	$-0.379854\pi$
$311$	12.9989			0.737103			0.368551	+	0.929607i	$0.379854\pi$
$312$		0			0
$313$	−9.51274			−0.537692			−0.268846	−	0.963183i	$-0.586642\pi$
$313$	−9.51274			−0.537692			−0.268846	+	0.963183i	$0.586642\pi$
$314$		0			0
$315$	−11.3344	−	19.6317i	−0.638620	−	1.10612i
$316$		0			0
$317$		−	19.1354i		−	1.07475i	−0.843343	−	0.537376i	$-0.819416\pi$
$317$		−	19.1354i		−	1.07475i	0.843343	−	0.537376i	$-0.180584\pi$
$318$		0			0
$319$	−0.324862	−	0.187559i	−0.0181888	−	0.0105013i
$320$		0			0
$321$	9.55744	−	16.5540i	0.533444	−	0.923952i
$322$		0			0
$323$	8.06587	−	4.65683i	0.448797	−	0.259113i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−8.31122	+	4.79849i	−0.459612	+	0.265357i
$328$		0			0
$329$	6.05696	−	10.4910i	0.333931	−	0.578385i
$330$		0			0
$331$	9.78896	+	5.65166i	0.538050	+	0.310643i	0.744288	−	0.667858i	$-0.232789\pi$
$331$	9.78896	+	5.65166i	0.538050	+	0.310643i	−0.206238	+	0.978502i	$0.566122\pi$
$332$		0			0
$333$			35.0733i			1.92200i
$334$		0			0
$335$	18.7431	+	32.4640i	1.02405	+	1.77370i
$336$		0			0
$337$	−5.14035			−0.280013			−0.140006	−	0.990151i	$-0.544712\pi$
$337$	−5.14035			−0.280013			−0.140006	+	0.990151i	$0.544712\pi$
$338$		0			0
$339$	−16.0138			−0.869750
$340$		0			0
$341$	0.0727592	+	0.126023i	0.00394013	+	0.00682451i
$342$		0			0
$343$		−	14.2937i		−	0.771785i
$344$		0			0
$345$	−24.2815	−	14.0190i	−1.30727	−	0.754755i
$346$		0			0
$347$	4.36129	−	7.55397i	0.234126	−	0.405518i	−0.724892	−	0.688862i	$-0.758110\pi$
$347$	4.36129	−	7.55397i	0.234126	−	0.405518i	0.959018	+	0.283344i	$0.0914438\pi$
$348$		0			0
$349$	−23.4625	+	13.5461i	−1.25592	+	0.725104i	−0.972278	−	0.233827i	$-0.924875\pi$
$349$	−23.4625	+	13.5461i	−1.25592	+	0.725104i	−0.283639	+	0.958931i	$0.591542\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	19.9524	−	11.5195i	1.06196	−	0.613123i	0.135986	−	0.990711i	$-0.456580\pi$
$353$	19.9524	−	11.5195i	1.06196	−	0.613123i	0.925974	+	0.377588i	$0.123246\pi$
$354$		0			0
$355$	−11.2304	+	19.4516i	−0.596046	+	1.03238i
$356$		0			0
$357$	17.6872	+	10.2117i	0.936104	+	0.540460i
$358$		0			0
$359$			1.13392i			0.0598462i	0.999552	+	0.0299231i	$0.00952624\pi$
$359$			1.13392i			0.0598462i	−0.999552	+	0.0299231i	$0.990474\pi$
$360$		0			0
$361$	−8.09439	−	14.0199i	−0.426020	−	0.737889i
$362$		0			0
$363$	−31.9272			−1.67574
$364$		0			0
$365$	25.9578			1.35869
$366$		0			0
$367$	−14.3992	−	24.9401i	−0.751632	−	1.30186i	−0.947031	−	0.321141i	$-0.895934\pi$
$367$	−14.3992	−	24.9401i	−0.751632	−	1.30186i	0.195399	−	0.980724i	$-0.437400\pi$
$368$		0			0
$369$		−	44.3748i		−	2.31006i
$370$		0			0
$371$	4.02959	+	2.32648i	0.209206	+	0.120785i
$372$		0			0
$373$	11.8939	−	20.6008i	0.615842	−	1.06667i	−0.374394	−	0.927270i	$-0.622149\pi$
$373$	11.8939	−	20.6008i	0.615842	−	1.06667i	0.990236	−	0.139400i	$-0.0445173\pi$
$374$		0			0
$375$	−23.6092	+	13.6308i	−1.21917	+	0.703890i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	12.9434	−	7.47289i	0.664859	−	0.383856i	−0.129267	−	0.991610i	$-0.541262\pi$
$379$	12.9434	−	7.47289i	0.664859	−	0.383856i	0.794126	+	0.607753i	$0.207929\pi$
$380$		0			0
$381$	16.9108	−	29.2903i	0.866365	−	1.50059i
$382$		0			0
$383$	3.92940	+	2.26864i	0.200783	+	0.115922i	0.597021	−	0.802226i	$-0.296351\pi$
$383$	3.92940	+	2.26864i	0.200783	+	0.115922i	−0.396238	+	0.918148i	$0.629684\pi$
$384$		0			0
$385$		−	3.28491i		−	0.167414i
$386$		0			0
$387$	−17.4103	−	30.1555i	−0.885015	−	1.53289i
$388$		0			0
$389$	−9.51685			−0.482524			−0.241262	−	0.970460i	$-0.577561\pi$
$389$	−9.51685			−0.482524			−0.241262	+	0.970460i	$0.577561\pi$
$390$		0			0
$391$	18.2056			0.920698
$392$		0			0
$393$	−0.181505	−	0.314377i	−0.00915574	−	0.0158582i
$394$		0			0
$395$			35.4913i			1.78576i
$396$		0			0
$397$	29.8307	+	17.2227i	1.49716	+	0.864385i	0.999995	−	0.00327253i	$-0.00104168\pi$
$397$	29.8307	+	17.2227i	1.49716	+	0.864385i	0.497163	+	0.867657i	$0.334375\pi$
$398$		0			0
$399$	−3.08228	+	5.33867i	−0.154307	+	0.267268i
$400$		0			0
$401$	12.2605	−	7.07859i	0.612259	−	0.353488i	−0.161590	−	0.986858i	$-0.551662\pi$
$401$	12.2605	−	7.07859i	0.612259	−	0.353488i	0.773849	+	0.633370i	$0.218329\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	62.6318	−	36.1605i	3.11220	−	1.79683i
$406$		0			0
$407$	−2.54121	+	4.40151i	−0.125963	+	0.218175i
$408$		0			0
$409$	0.299539	+	0.172939i	0.0148112	+	0.00855127i	0.507387	−	0.861718i	$-0.330611\pi$
$409$	0.299539	+	0.172939i	0.0148112	+	0.00855127i	−0.492576	+	0.870269i	$0.663945\pi$
$410$		0			0
$411$		−	22.7864i		−	1.12397i
$412$		0			0
$413$	0.355925	+	0.616481i	0.0175139	+	0.0303350i
$414$		0			0
$415$	−15.0255			−0.737571
$416$		0			0
$417$	34.1846			1.67403
$418$		0			0
$419$	6.98890	+	12.1051i	0.341430	+	0.591374i	0.984699	−	0.174266i	$-0.0557554\pi$
$419$	6.98890	+	12.1051i	0.341430	+	0.591374i	−0.643268	+	0.765641i	$0.722422\pi$
$420$		0			0
$421$		−	22.1609i		−	1.08006i	−0.841647	−	0.540028i	$-0.818414\pi$
$421$		−	22.1609i		−	1.08006i	0.841647	−	0.540028i	$-0.181586\pi$
$422$		0			0
$423$	72.3969	+	41.7984i	3.52006	+	2.03231i
$424$		0			0
$425$	−5.03638	+	8.72327i	−0.244300	+	0.423141i
$426$		0			0
$427$	−4.57366	+	2.64061i	−0.221335	+	0.127788i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−22.2109	+	12.8235i	−1.06986	+	0.617686i	−0.928144	−	0.372221i	$-0.878596\pi$
$431$	−22.2109	+	12.8235i	−1.06986	+	0.617686i	−0.141719	+	0.989907i	$0.545263\pi$
$432$		0			0
$433$	−5.07802	+	8.79538i	−0.244034	+	0.422679i	−0.961860	−	0.273544i	$-0.911804\pi$
$433$	−5.07802	+	8.79538i	−0.244034	+	0.422679i	0.717826	+	0.696223i	$0.245137\pi$
$434$		0			0
$435$	−2.47736	−	1.43031i	−0.118780	−	0.0685779i
$436$		0			0
$437$			5.49516i			0.262869i
$438$		0			0
$439$	−10.6982	−	18.5298i	−0.510598	−	0.884381i	−0.999925	−	0.0122808i	$-0.996091\pi$
$439$	−10.6982	−	18.5298i	−0.510598	−	0.884381i	0.489327	−	0.872100i	$-0.337243\pi$
$440$		0			0
$441$	44.4482			2.11658
$442$		0			0
$443$	10.6688			0.506889			0.253444	−	0.967350i	$-0.418437\pi$
$443$	10.6688			0.506889			0.253444	+	0.967350i	$0.418437\pi$
$444$		0			0
$445$	−18.7225	−	32.4283i	−0.887531	−	1.53725i
$446$		0			0
$447$			31.4710i			1.48852i
$448$		0			0
$449$	8.62407	+	4.97911i	0.406995	+	0.234979i	0.689498	−	0.724288i	$-0.257831\pi$
$449$	8.62407	+	4.97911i	0.406995	+	0.234979i	−0.282503	+	0.959266i	$0.591165\pi$
$450$		0			0
$451$	3.21515	−	5.56881i	0.151396	−	0.262225i
$452$		0			0
$453$	−38.9609	+	22.4941i	−1.83054	+	1.05687i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	23.2035	−	13.3966i	1.08542	−	0.626665i	0.153063	−	0.988216i	$-0.451086\pi$
$457$	23.2035	−	13.3966i	1.08542	−	0.626665i	0.932352	+	0.361552i	$0.117753\pi$
$458$		0			0
$459$	−43.1613	+	74.7575i	−2.01460	+	3.48938i
$460$		0			0
$461$	−27.7410	−	16.0163i	−1.29203	−	0.745952i	−0.313014	−	0.949749i	$-0.601339\pi$
$461$	−27.7410	−	16.0163i	−1.29203	−	0.745952i	−0.979013	+	0.203796i	$0.934672\pi$
$462$		0			0
$463$		−	21.7564i		−	1.01110i	−0.862796	−	0.505552i	$-0.831289\pi$
$463$		−	21.7564i		−	1.01110i	0.862796	−	0.505552i	$-0.168711\pi$
$464$		0			0
$465$	0.554854	+	0.961036i	0.0257308	+	0.0445670i
$466$		0			0
$467$	33.7322			1.56094			0.780469	−	0.625195i	$-0.214980\pi$
$467$	33.7322			1.56094			0.780469	+	0.625195i	$0.214980\pi$
$468$		0			0
$469$	16.1107			0.743922
$470$		0			0
$471$	14.6861	+	25.4372i	0.676702	+	1.17208i
$472$		0			0
$473$		−	5.04581i		−	0.232007i
$474$		0			0
$475$	−2.63302	−	1.52017i	−0.120811	−	0.0697504i
$476$		0			0
$477$	−16.0548	+	27.8077i	−0.735099	+	1.27323i
$478$		0			0
$479$	9.17041	−	5.29454i	0.419007	−	0.241914i	−0.275646	−	0.961259i	$-0.588892\pi$
$479$	9.17041	−	5.29454i	0.419007	−	0.241914i	0.694652	+	0.719346i	$0.255558\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−10.4356	+	6.02501i	−0.474837	+	0.274147i
$484$		0			0
$485$	11.7564	−	20.3626i	0.533829	−	0.924619i
$486$		0			0
$487$	19.0612	+	11.0050i	0.863746	+	0.498684i	0.865265	−	0.501315i	$-0.167150\pi$
$487$	19.0612	+	11.0050i	0.863746	+	0.498684i	−0.00151867	+	0.999999i	$0.500483\pi$
$488$		0			0
$489$			7.18941i			0.325116i
$490$		0			0
$491$	−8.25727	−	14.3020i	−0.372645	−	0.645441i	0.617326	−	0.786707i	$-0.288216\pi$
$491$	−8.25727	−	14.3020i	−0.372645	−	0.645441i	−0.989972	+	0.141266i	$0.954883\pi$
$492$		0			0
$493$	1.85746			0.0836557
$494$		0			0
$495$	22.6688			1.01889
$496$		0			0
$497$	4.82654	+	8.35982i	0.216500	+	0.374989i
$498$		0			0
$499$		−	11.1236i		−	0.497960i	−0.968509	−	0.248980i	$-0.919905\pi$
$499$		−	11.1236i		−	0.497960i	0.968509	−	0.248980i	$-0.0800954\pi$
$500$		0			0
$501$	−42.5132	−	24.5450i	−1.89935	−	1.09659i
$502$		0			0
$503$	14.6361	−	25.3504i	0.652591	−	1.13032i	−0.329901	−	0.944015i	$-0.607015\pi$
$503$	14.6361	−	25.3504i	0.652591	−	1.13032i	0.982492	−	0.186305i	$-0.0596512\pi$
$504$		0			0
$505$	6.53121	−	3.77080i	0.290635	−	0.167798i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−24.4571	+	14.1203i	−1.08404	+	0.625871i	−0.931983	−	0.362501i	$-0.881923\pi$
$509$	−24.4571	+	14.1203i	−1.08404	+	0.625871i	−0.152057	+	0.988372i	$0.548590\pi$
$510$		0			0
$511$	5.57802	−	9.66141i	0.246757	−	0.427396i
$512$		0			0
$513$	−22.5647	−	13.0277i	−0.996256	−	0.575189i
$514$		0			0
$515$			13.6267i			0.600462i
$516$		0			0
$517$	6.05696	+	10.4910i	0.266385	+	0.461392i
$518$		0			0
$519$	−13.0928			−0.574709
$520$		0			0
$521$	−18.6401			−0.816636			−0.408318	−	0.912840i	$-0.633884\pi$
$521$	−18.6401			−0.816636			−0.408318	+	0.912840i	$0.633884\pi$
$522$		0			0
$523$	−17.6561	−	30.5812i	−0.772047	−	1.33722i	−0.936439	−	0.350830i	$-0.885900\pi$
$523$	−17.6561	−	30.5812i	−0.772047	−	1.33722i	0.164392	−	0.986395i	$-0.447434\pi$
$524$		0			0
$525$		−	6.66700i		−	0.290972i
$526$		0			0
$527$	−0.624022	−	0.360279i	−0.0271828	−	0.0156940i
$528$		0			0
$529$	6.12924	−	10.6161i	0.266489	−	0.461572i
$530$		0			0
$531$	−4.25426	+	2.45620i	−0.184619	+	0.106590i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	13.1840	−	7.61181i	0.569996	−	0.329087i
$536$		0			0
$537$	14.1123	−	24.4432i	0.608990	−	1.05480i
$538$		0			0
$539$	5.57802	+	3.22047i	0.240262	+	0.138715i
$540$		0			0
$541$		−	45.2196i		−	1.94414i	−0.234682	−	0.972072i	$-0.575405\pi$
$541$		−	45.2196i		−	1.94414i	0.234682	−	0.972072i	$-0.424595\pi$
$542$		0			0
$543$	25.6144	+	44.3654i	1.09922	+	1.90390i
$544$		0			0
$545$	−7.64330			−0.327403
$546$		0			0
$547$	−37.8808			−1.61967			−0.809834	−	0.586660i	$-0.800443\pi$
$547$	−37.8808			−1.61967			−0.809834	+	0.586660i	$0.800443\pi$
$548$		0			0
$549$	−18.2225	−	31.5623i	−0.777719	−	1.34705i
$550$		0			0
$551$			0.560653i			0.0238846i
$552$		0			0
$553$	13.2097	+	7.62665i	0.561736	+	0.324318i
$554$		0			0
$555$	−19.3790	+	33.5655i	−0.822595	+	1.42478i
$556$		0			0
$557$	17.8759	−	10.3206i	0.757426	−	0.437300i	−0.0709450	−	0.997480i	$-0.522601\pi$
$557$	17.8759	−	10.3206i	0.757426	−	0.437300i	0.828371	+	0.560180i	$0.189268\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−17.6872	+	10.2117i	−0.746752	+	0.431138i
$562$		0			0
$563$	−10.2300	+	17.7189i	−0.431143	+	0.746761i	−0.996972	−	0.0777613i	$-0.975223\pi$
$563$	−10.2300	+	17.7189i	−0.431143	+	0.746761i	0.565829	+	0.824522i	$0.308556\pi$
$564$		0			0
$565$	−11.0451	−	6.37691i	−0.464673	−	0.268279i
$566$		0			0
$567$		−	31.0818i		−	1.30531i
$568$		0			0
$569$	−10.5681	−	18.3044i	−0.443037	−	0.767362i	0.554877	−	0.831933i	$-0.312765\pi$
$569$	−10.5681	−	18.3044i	−0.443037	−	0.767362i	−0.997913	+	0.0645708i	$0.979432\pi$
$570$		0			0
$571$	−13.9221			−0.582621			−0.291310	−	0.956629i	$-0.594091\pi$
$571$	−13.9221			−0.582621			−0.291310	+	0.956629i	$0.594091\pi$
$572$		0			0
$573$	−88.6738			−3.70440
$574$		0			0
$575$	−2.97152	−	5.14683i	−0.123921	−	0.214637i
$576$		0			0
$577$		−	26.2420i		−	1.09247i	−0.837633	−	0.546234i	$-0.816061\pi$
$577$		−	26.2420i		−	1.09247i	0.837633	−	0.546234i	$-0.183939\pi$
$578$		0			0
$579$	−67.9823	−	39.2496i	−2.82525	−	1.63116i
$580$		0			0
$581$	−3.22879	+	5.59243i	−0.133953	+	0.232013i
$582$		0			0
$583$	−4.02959	+	2.32648i	−0.166889	+	0.0963531i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−21.3670	+	12.3362i	−0.881910	+	0.509171i	−0.871288	−	0.490773i	$-0.836715\pi$
$587$	−21.3670	+	12.3362i	−0.881910	+	0.509171i	−0.0106221	+	0.999944i	$0.503381\pi$
$588$		0			0
$589$	0.108746	−	0.188354i	0.00448081	−	0.00776099i
$590$		0			0
$591$	−29.3638	−	16.9532i	−1.20787	−	0.697362i
$592$		0			0
$593$			40.3506i			1.65700i	0.559988	+	0.828501i	$0.310806\pi$
$593$			40.3506i			1.65700i	−0.559988	+	0.828501i	$0.689194\pi$
$594$		0			0
$595$	8.13287	+	14.0865i	0.333415	+	0.577492i
$596$		0			0
$597$	44.4840			1.82061
$598$		0			0
$599$	−4.96104			−0.202702			−0.101351	−	0.994851i	$-0.532317\pi$
$599$	−4.96104			−0.202702			−0.101351	+	0.994851i	$0.532317\pi$
$600$		0			0
$601$	7.73846	+	13.4034i	0.315658	+	0.546737i	0.979577	−	0.201068i	$-0.0644413\pi$
$601$	7.73846	+	13.4034i	0.315658	+	0.546737i	−0.663919	+	0.747805i	$0.731108\pi$
$602$		0			0
$603$			111.178i			4.52752i
$604$		0			0
$605$	−22.0210	−	12.7138i	−0.895282	−	0.516891i
$606$		0			0
$607$	−11.2167	+	19.4279i	−0.455273	+	0.788556i	−0.998704	−	0.0508979i	$-0.983792\pi$
$607$	−11.2167	+	19.4279i	−0.455273	+	0.788556i	0.543431	+	0.839454i	$0.317125\pi$
$608$		0			0
$609$	−1.06471	+	0.614711i	−0.0431443	+	0.0249094i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−14.3634	+	8.29274i	−0.580134	+	0.334941i	−0.761187	−	0.648533i	$-0.775383\pi$
$613$	−14.3634	+	8.29274i	−0.580134	+	0.334941i	0.181053	+	0.983473i	$0.442050\pi$
$614$		0			0
$615$	24.5184	−	42.4672i	0.988679	−	1.71244i
$616$		0			0
$617$	−28.6107	−	16.5184i	−1.15182	−	0.665005i	−0.202492	−	0.979284i	$-0.564904\pi$
$617$	−28.6107	−	16.5184i	−1.15182	−	0.665005i	−0.949331	+	0.314279i	$0.898237\pi$
$618$		0			0
$619$			35.3913i			1.42249i	0.702942	+	0.711247i	$0.251869\pi$
$619$			35.3913i			1.42249i	−0.702942	+	0.711247i	$0.748131\pi$
$620$		0			0
$621$	−25.4656	−	44.1078i	−1.02190	−	1.76998i
$622$		0			0
$623$	−16.0929			−0.644750
$624$		0			0
$625$	−30.7785			−1.23114
$626$		0			0
$627$	−3.08228	−	5.33867i	−0.123094	−	0.213206i
$628$		0			0
$629$		−	25.1665i		−	1.00345i
$630$		0			0
$631$	5.58850	+	3.22652i	0.222475	+	0.128446i	0.607096	−	0.794629i	$-0.292334\pi$
$631$	5.58850	+	3.22652i	0.222475	+	0.128446i	−0.384621	+	0.923075i	$0.625668\pi$
$632$		0			0
$633$	−3.18926	+	5.52396i	−0.126762	+	0.219558i
$634$		0			0
$635$	23.3276	−	13.4682i	0.925729	−	0.534470i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−57.6902	+	33.3074i	−2.28219	+	1.31762i
$640$		0			0
$641$	−10.8871	+	18.8571i	−0.430016	+	0.744810i	−0.996874	−	0.0790058i	$-0.974825\pi$
$641$	−10.8871	+	18.8571i	−0.430016	+	0.744810i	0.566858	+	0.823815i	$0.308159\pi$
$642$		0			0
$643$	−34.8552	−	20.1237i	−1.37456	−	0.793600i	−0.383058	−	0.923724i	$-0.625129\pi$
$643$	−34.8552	−	20.1237i	−1.37456	−	0.793600i	−0.991498	+	0.130125i	$0.958462\pi$
$644$		0			0
$645$		−	38.4789i		−	1.51510i
$646$		0			0
$647$	18.8105	+	32.5808i	0.739519	+	1.28088i	0.952712	+	0.303874i	$0.0982803\pi$
$647$	18.8105	+	32.5808i	0.739519	+	1.28088i	−0.213193	+	0.977010i	$0.568386\pi$
$648$		0			0
$649$	−0.711850			−0.0279426
$650$		0			0
$651$	0.476926			0.0186922
$652$		0			0
$653$	15.3559	+	26.5972i	0.600924	+	1.04083i	0.992681	+	0.120762i	$0.0385338\pi$
$653$	15.3559	+	26.5972i	0.600924	+	1.04083i	−0.391758	+	0.920068i	$0.628133\pi$
$654$		0			0
$655$		−	0.289112i		−	0.0112965i
$656$		0			0
$657$	66.6723	+	38.4933i	2.60113	+	1.50177i
$658$		0			0
$659$	−6.88489	+	11.9250i	−0.268197	+	0.464531i	−0.968396	−	0.249417i	$-0.919761\pi$
$659$	−6.88489	+	11.9250i	−0.268197	+	0.464531i	0.700199	+	0.713947i	$0.253094\pi$
$660$		0			0
$661$	8.85492	−	5.11239i	0.344416	−	0.198849i	−0.317807	−	0.948155i	$-0.602946\pi$
$661$	8.85492	−	5.11239i	0.344416	−	0.198849i	0.662223	+	0.749307i	$0.269613\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.25187	+	2.45482i	−0.164880	+	0.0951937i
$666$		0			0
$667$	−0.547961	+	0.949096i	−0.0212171	+	0.0367491i
$668$		0			0
$669$	67.8938	+	39.1985i	2.62493	+	1.51550i
$670$		0			0
$671$		−	5.28121i		−	0.203879i
$672$		0			0
$673$	2.13077	+	3.69060i	0.0821351	+	0.142262i	0.904167	−	0.427180i	$-0.140493\pi$
$673$	2.13077	+	3.69060i	0.0821351	+	0.142262i	−0.822032	+	0.569442i	$0.807159\pi$
$674$		0			0
$675$	28.1791			1.08461
$676$		0			0
$677$	−4.47885			−0.172136			−0.0860681	−	0.996289i	$-0.527430\pi$
$677$	−4.47885			−0.172136			−0.0860681	+	0.996289i	$0.527430\pi$
$678$		0			0
$679$	−5.05260	−	8.75137i	−0.193901	−	0.335847i
$680$		0			0
$681$			57.9340i			2.22004i
$682$		0			0
$683$	−17.4014	−	10.0467i	−0.665846	−	0.384426i	0.128655	−	0.991689i	$-0.458934\pi$
$683$	−17.4014	−	10.0467i	−0.665846	−	0.384426i	−0.794501	+	0.607263i	$0.792267\pi$
$684$		0			0
$685$	9.07386	−	15.7164i	0.346694	−	0.600492i
$686$		0			0
$687$	31.0179	−	17.9082i	1.18341	−	0.683240i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	32.6571	−	18.8546i	1.24233	−	0.717261i	0.272764	−	0.962081i	$-0.412062\pi$
$691$	32.6571	−	18.8546i	1.24233	−	0.717261i	0.969569	+	0.244820i	$0.0787288\pi$
$692$		0			0
$693$	4.87125	−	8.43724i	0.185043	−	0.320504i
$694$		0			0
$695$	23.5780	+	13.6128i	0.894365	+	0.516362i
$696$		0			0
$697$			31.8407i			1.20605i
$698$		0			0
$699$	−19.0041	−	32.9161i	−0.718802	−	1.24500i
$700$		0			0
$701$	−17.2849			−0.652842			−0.326421	−	0.945225i	$-0.605843\pi$
$701$	−17.2849			−0.652842			−0.326421	+	0.945225i	$0.605843\pi$
$702$		0			0
$703$	7.59622			0.286497
$704$		0			0
$705$	46.1897	+	80.0030i	1.73961	+	3.01309i
$706$		0			0
$707$		−	3.24119i		−	0.121898i
$708$		0			0
$709$	−15.7410	−	9.08807i	−0.591166	−	0.341310i	0.174393	−	0.984676i	$-0.444204\pi$
$709$	−15.7410	−	9.08807i	−0.591166	−	0.341310i	−0.765558	+	0.643366i	$0.777537\pi$
$710$		0			0
$711$	−52.6307	+	91.1590i	−1.97380	+	3.41873i
$712$		0			0
$713$	0.368180	−	0.212569i	0.0137884	−	0.00796076i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−51.1528	+	29.5331i	−1.91034	+	1.10293i
$718$		0			0
$719$	−9.95668	+	17.2455i	−0.371322	+	0.643148i	−0.989769	−	0.142678i	$-0.954429\pi$
$719$	−9.95668	+	17.2455i	−0.371322	+	0.643148i	0.618448	+	0.785826i	$0.287762\pi$
$720$		0			0
$721$	5.07180	+	2.92820i	0.188884	+	0.109052i
$722$		0			0
$723$			2.68634i			0.0999061i
$724$		0			0
$725$	−0.303174	−	0.525113i	−0.0112596	−	0.0195022i
$726$		0			0
$727$	38.7446			1.43696			0.718479	−	0.695549i	$-0.244839\pi$
$727$	38.7446			1.43696			0.718479	+	0.695549i	$0.244839\pi$
$728$		0			0
$729$	61.6983			2.28512
$730$		0			0
$731$	12.4926	+	21.6378i	0.462055	+	0.800302i
$732$		0			0
$733$			3.19477i			0.118001i	0.998258	+	0.0590007i	$0.0187914\pi$
$733$			3.19477i			0.118001i	−0.998258	+	0.0590007i	$0.981209\pi$
$734$		0			0
$735$	42.5374	+	24.5590i	1.56902	+	0.905871i
$736$		0			0
$737$	−8.05534	+	13.9523i	−0.296722	+	0.513938i
$738$		0			0
$739$	−35.2234	+	20.3362i	−1.29571	+	0.748080i	−0.979661	−	0.200661i	$-0.935691\pi$
$739$	−35.2234	+	20.3362i	−1.29571	+	0.748080i	−0.316053	+	0.948742i	$0.602358\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	12.0464	−	6.95498i	0.441939	−	0.255154i	−0.262481	−	0.964937i	$-0.584541\pi$
$743$	12.0464	−	6.95498i	0.441939	−	0.255154i	0.704420	+	0.709784i	$0.251207\pi$
$744$		0			0
$745$	−12.5322	+	21.7064i	−0.459143	+	0.795260i
$746$		0			0
$747$	−38.5928	−	22.2815i	−1.41204	−	0.815239i
$748$		0			0
$749$		−	6.54275i		−	0.239067i
$750$		0			0
$751$	−8.79317	−	15.2302i	−0.320867	−	0.555759i	0.659800	−	0.751441i	$-0.270641\pi$
$751$	−8.79317	−	15.2302i	−0.320867	−	0.555759i	−0.980667	+	0.195683i	$0.937308\pi$
$752$		0			0
$753$	47.0555			1.71480
$754$		0			0
$755$	−35.8299			−1.30398
$756$		0			0
$757$	−11.0553	−	19.1484i	−0.401813	−	0.695961i	0.592132	−	0.805841i	$-0.298286\pi$
$757$	−11.0553	−	19.1484i	−0.401813	−	0.695961i	−0.993945	+	0.109881i	$0.964953\pi$
$758$		0			0
$759$		−	12.0500i		−	0.437388i
$760$		0			0
$761$	−21.0765	−	12.1685i	−0.764022	−	0.441108i	0.0667160	−	0.997772i	$-0.478748\pi$
$761$	−21.0765	−	12.1685i	−0.764022	−	0.441108i	−0.830738	+	0.556664i	$0.812081\pi$
$762$		0			0
$763$	−1.64245	+	2.84481i	−0.0594608	+	0.102989i
$764$		0			0
$765$	−97.2097	+	56.1240i	−3.51462	+	2.02917i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−6.14197	+	3.54607i	−0.221485	+	0.127875i	−0.606638	−	0.794978i	$-0.707482\pi$
$769$	−6.14197	+	3.54607i	−0.221485	+	0.127875i	0.385153	+	0.922853i	$0.374149\pi$
$770$		0			0
$771$	33.7525	−	58.4611i	1.21557	−	2.10543i
$772$		0			0
$773$	−0.840035	−	0.484994i	−0.0302140	−	0.0174440i	0.484817	−	0.874616i	$-0.338886\pi$
$773$	−0.840035	−	0.484994i	−0.0302140	−	0.0174440i	−0.515031	+	0.857172i	$0.672220\pi$
$774$		0			0
$775$			0.235219i			0.00844931i
$776$		0			0
$777$	8.32865	+	14.4256i	0.298789	+	0.517517i
$778$		0			0
$779$	−9.61076			−0.344341
$780$		0			0
$781$	−9.65309			−0.345415
$782$		0			0
$783$	−2.59817	−	4.50017i	−0.0928511	−	0.160823i
$784$		0			0
$785$			23.3929i			0.834929i
$786$		0			0
$787$	0.0361875	+	0.0208929i	0.00128994	+	0.000744750i	0.500645	−	0.865653i	$-0.333096\pi$
$787$	0.0361875	+	0.0208929i	0.00128994	+	0.000744750i	−0.499355	+	0.866398i	$0.666430\pi$
$788$		0			0
$789$	−47.5605	+	82.3772i	−1.69320	+	2.93271i
$790$		0			0
$791$	−4.74693	+	2.74064i	−0.168782	+	0.0974461i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−30.7292	+	17.7415i	−1.08985	+	0.629227i
$796$		0			0
$797$	19.6671	−	34.0645i	0.696646	−	1.20663i	−0.272977	−	0.962021i	$-0.588008\pi$
$797$	19.6671	−	34.0645i	0.696646	−	1.20663i	0.969623	−	0.244606i	$-0.0786585\pi$
$798$		0			0
$799$	−51.9477	−	29.9920i	−1.83778	−	1.06104i
$800$		0			0
$801$		−	111.056i		−	3.92396i
$802$		0			0
$803$	5.57802	+	9.66141i	0.196844	+	0.340944i
$804$		0			0
$805$	−9.59697			−0.338249
$806$		0			0
$807$	28.2764			0.995376
$808$		0			0
$809$	0.404078	+	0.699884i	0.0142066	+	0.0246066i	0.873041	−	0.487646i	$-0.162144\pi$
$809$	0.404078	+	0.699884i	0.0142066	+	0.0246066i	−0.858835	+	0.512253i	$0.828811\pi$
$810$		0			0
$811$		−	24.3955i		−	0.856640i	−0.903627	−	0.428320i	$-0.859106\pi$
$811$		−	24.3955i		−	0.856640i	0.903627	−	0.428320i	$-0.140894\pi$
$812$		0			0
$813$	45.3790	+	26.1996i	1.59151	+	0.918859i
$814$		0			0
$815$	−2.86292	+	4.95873i	−0.100284	+	0.173697i
$816$		0			0
$817$	−6.53112	+	3.77075i	−0.228495	+	0.131922i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.0406	−	8.68369i	0.524920	−	0.303063i	−0.214025	−	0.976828i	$-0.568657\pi$
$821$	15.0406	−	8.68369i	0.524920	−	0.303063i	0.738945	+	0.673765i	$0.235324\pi$
$822$		0			0
$823$	2.83865	−	4.91669i	0.0989491	−	0.171385i	−0.812301	−	0.583239i	$-0.801785\pi$
$823$	2.83865	−	4.91669i	0.0989491	−	0.171385i	0.911250	+	0.411854i	$0.135119\pi$
$824$		0			0
$825$	5.77379	+	3.33350i	0.201018	+	0.116058i
$826$		0			0
$827$			14.5094i			0.504540i	0.967657	+	0.252270i	$0.0811772\pi$
$827$			14.5094i			0.504540i	−0.967657	+	0.252270i	$0.918823\pi$
$828$		0			0
$829$	23.7516	+	41.1390i	0.824928	+	1.42882i	0.901974	+	0.431790i	$0.142118\pi$
$829$	23.7516	+	41.1390i	0.824928	+	1.42882i	−0.0770456	+	0.997028i	$0.524549\pi$
$830$		0			0
$831$	−94.2118			−3.26817
$832$		0			0
$833$	−31.8934			−1.10504
$834$		0			0
$835$	−19.5483	−	33.8587i	−0.676498	−	1.17173i
$836$		0			0
$837$			2.01580i			0.0696763i
$838$		0			0
$839$	−1.78192	−	1.02879i	−0.0615188	−	0.0355179i	0.468925	−	0.883238i	$-0.344641\pi$
$839$	−1.78192	−	1.02879i	−0.0615188	−	0.0355179i	−0.530444	+	0.847720i	$0.677975\pi$
$840$		0			0
$841$	14.4441	−	25.0179i	0.498072	−	0.862686i
$842$		0			0
$843$	16.5584	−	9.56002i	0.570303	−	0.329265i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−9.46410	+	5.46410i	−0.325190	+	0.187749i
$848$		0			0
$849$	−45.3790	+	78.5987i	−1.55740	+	2.69750i
$850$		0			0
$851$	12.8592	+	7.42425i	0.440807	+	0.254500i
$852$		0			0
$853$			4.10363i			0.140506i	0.997529	+	0.0702528i	$0.0223806\pi$
$853$			4.10363i			0.140506i	−0.997529	+	0.0702528i	$0.977619\pi$
$854$		0			0
$855$	−16.9404	−	29.3417i	−0.579350	−	1.00346i
$856$		0			0
$857$	35.9776			1.22897			0.614486	−	0.788928i	$-0.289364\pi$
$857$	35.9776			1.22897			0.614486	+	0.788928i	$0.289364\pi$
$858$		0			0
$859$	12.7711			0.435745			0.217872	−	0.975977i	$-0.430088\pi$
$859$	12.7711			0.435745			0.217872	+	0.975977i	$0.430088\pi$
$860$		0			0
$861$	−10.5374	−	18.2514i	−0.359115	−	0.622005i
$862$		0			0
$863$		−	34.2815i		−	1.16696i	−0.812128	−	0.583479i	$-0.801691\pi$
$863$		−	34.2815i		−	1.16696i	0.812128	−	0.583479i	$-0.198309\pi$
$864$		0			0
$865$	−9.03043	−	5.21372i	−0.307044	−	0.177272i
$866$		0			0
$867$	22.7067	−	39.3291i	0.771159	−	1.33569i
$868$		0			0
$869$	−13.2097	+	7.62665i	−0.448110	+	0.258716i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	60.3922	−	34.8675i	2.04397	−	1.18008i
$874$		0			0
$875$	−4.66562	+	8.08108i	−0.157727	+	0.273190i
$876$		0			0
$877$	39.4625	+	22.7837i	1.33255	+	0.769351i	0.985691	−	0.168565i	$-0.0539132\pi$
$877$	39.4625	+	22.7837i	1.33255	+	0.769351i	0.346864	+	0.937915i	$0.387247\pi$
$878$		0			0
$879$			52.2176i			1.76126i
$880$		0			0
$881$	−6.88302	−	11.9217i	−0.231895	−	0.401654i	0.726471	−	0.687197i	$-0.241159\pi$
$881$	−6.88302	−	11.9217i	−0.231895	−	0.401654i	−0.958366	+	0.285544i	$0.907826\pi$
$882$		0			0
$883$	−1.44199			−0.0485269			−0.0242634	−	0.999706i	$-0.507724\pi$
$883$	−1.44199			−0.0485269			−0.0242634	+	0.999706i	$0.507724\pi$
$884$		0			0
$885$	−5.42850			−0.182477
$886$		0			0
$887$	−13.2859	−	23.0118i	−0.446097	−	0.772662i	0.552031	−	0.833824i	$-0.313853\pi$
$887$	−13.2859	−	23.0118i	−0.446097	−	0.772662i	−0.998128	+	0.0611612i	$0.980520\pi$
$888$		0			0
$889$		−	11.5766i		−	0.388268i
$890$		0			0
$891$	26.9176	+	15.5409i	0.901774	+	0.520640i
$892$		0			0
$893$	9.05275	−	15.6798i	0.302939	−	0.524705i
$894$		0			0
$895$	19.4673	−	11.2394i	0.650719	−	0.375693i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.0375641	−	0.0216877i	0.00125283	−	0.000723324i
$900$		0			0
$901$	11.5200	−	19.9532i	0.383786	−	0.664736i
$902$		0			0
$903$	−14.3217	−	8.26864i	−0.476597	−	0.275163i
$904$		0			0
$905$			40.8000i			1.35624i
$906$		0			0
$907$	−5.03911	−	8.72800i	−0.167321	−	0.289808i	0.770156	−	0.637855i	$-0.220178\pi$
$907$	−5.03911	−	8.72800i	−0.167321	−	0.289808i	−0.937477	+	0.348047i	$0.886845\pi$
$908$		0			0
$909$	22.3671			0.741871
$910$		0			0
$911$	−44.5252			−1.47518			−0.737592	−	0.675246i	$-0.764037\pi$
$911$	−44.5252			−1.47518			−0.737592	+	0.675246i	$0.764037\pi$
$912$		0			0
$913$	−3.22879	−	5.59243i	−0.106857	−	0.185083i
$914$		0			0
$915$		−	40.2740i		−	1.33142i
$916$		0			0
$917$	−0.107607	−	0.0621267i	−0.00355348	−	0.00205160i
$918$		0			0
$919$	16.7591	−	29.0275i	0.552830	−	0.957530i	−0.445239	−	0.895412i	$-0.646881\pi$
$919$	16.7591	−	29.0275i	0.552830	−	0.957530i	0.998069	−	0.0621180i	$-0.0197855\pi$
$920$		0			0
$921$	57.8891	−	33.4223i	1.90751	−	1.10130i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−7.11469	+	4.10767i	−0.233930	+	0.135059i
$926$		0			0
$927$	−20.2072	+	34.9999i	−0.663692	+	1.14955i
$928$		0			0
$929$	−15.1077	−	8.72243i	−0.495667	−	0.286174i	0.231255	−	0.972893i	$-0.425717\pi$
$929$	−15.1077	−	8.72243i	−0.495667	−	0.286174i	−0.726923	+	0.686719i	$0.759050\pi$
$930$		0			0
$931$		−	9.62665i		−	0.315501i
$932$		0			0
$933$	21.3016	+	36.8954i	0.697382	+	1.20790i
$934$		0			0
$935$	−16.2657			−0.531947
$936$		0			0
$937$	17.0052			0.555535			0.277767	−	0.960648i	$-0.410406\pi$
$937$	17.0052			0.555535			0.277767	+	0.960648i	$0.410406\pi$
$938$		0			0
$939$	−15.5886	−	27.0003i	−0.508716	−	0.881123i
$940$		0			0
$941$			15.7406i			0.513128i	0.966527	+	0.256564i	$0.0825904\pi$
$941$			15.7406i			0.513128i	−0.966527	+	0.256564i	$0.917410\pi$
$942$		0			0
$943$	−16.2695	−	9.39319i	−0.529807	−	0.305884i
$944$		0			0
$945$	22.7522	−	39.4079i	0.740128	−	1.28194i
$946$		0			0
$947$	28.2102	−	16.2872i	0.916709	−	0.529262i	0.0341252	−	0.999418i	$-0.489136\pi$
$947$	28.2102	−	16.2872i	0.916709	−	0.529262i	0.882584	+	0.470155i	$0.155802\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	54.3127	−	31.3575i	1.76121	−	1.01684i
$952$		0			0
$953$	15.6154	−	27.0466i	0.505831	−	0.876125i	−0.494146	−	0.869379i	$-0.664519\pi$
$953$	15.6154	−	27.0466i	0.505831	−	0.876125i	0.999977	−	0.00674630i	$-0.00214743\pi$
$954$		0			0
$955$	−61.1607	−	35.3111i	−1.97911	−	1.14264i
$956$		0			0
$957$		−	1.22942i		−	0.0397416i
$958$		0			0
$959$	−3.89972	−	6.75452i	−0.125929	−	0.218115i
$960$		0			0
$961$	30.9832			0.999457
$962$		0			0
$963$	45.1508			1.45496
$964$		0			0
$965$	−31.2595	−	54.1430i	−1.00628	−	1.74292i
$966$		0			0
$967$		−	37.8998i		−	1.21877i	−0.792873	−	0.609387i	$-0.791415\pi$
$967$		−	37.8998i		−	1.21877i	0.792873	−	0.609387i	$-0.208585\pi$
$968$		0			0
$969$	26.4353	+	15.2624i	0.849224	+	0.490300i
$970$		0			0
$971$	13.6628	−	23.6647i	0.438461	−	0.759437i	−0.559110	−	0.829094i	$-0.688857\pi$
$971$	13.6628	−	23.6647i	0.438461	−	0.759437i	0.997571	+	0.0696563i	$0.0221903\pi$
$972$		0			0
$973$	10.1333	−	5.85044i	0.324858	−	0.187557i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25.8089	+	14.9008i	−0.825700	+	0.476718i	−0.852378	−	0.522926i	$-0.824840\pi$
$977$	−25.8089	+	14.9008i	−0.825700	+	0.476718i	0.0266779	+	0.999644i	$0.491507\pi$
$978$		0			0
$979$	8.04647	−	13.9369i	0.257166	−	0.445425i
$980$		0			0
$981$	−19.6317	−	11.3344i	−0.626793	−	0.361879i
$982$		0			0
$983$		−	16.0704i		−	0.512565i	−0.966602	−	0.256282i	$-0.917502\pi$
$983$		−	16.0704i		−	0.512565i	0.966602	−	0.256282i	$-0.0824977\pi$
$984$		0			0
$985$	−13.5020	−	23.3862i	−0.430210	−	0.745145i
$986$		0			0
$987$	39.7025			1.26374
$988$		0			0
$989$	−14.7415			−0.468753
$990$		0			0
$991$	−15.9772	−	27.6733i	−0.507533	−	0.879073i	−0.999962	−	0.00872027i	$-0.997224\pi$
$991$	−15.9772	−	27.6733i	−0.507533	−	0.879073i	0.492429	−	0.870353i	$-0.336109\pi$
$992$		0			0
$993$			37.0458i			1.17561i
$994$		0			0
$995$	30.6818	+	17.7142i	0.972679	+	0.561577i
$996$		0			0
$997$	4.39599	−	7.61407i	0.139222	−	0.241140i	−0.787980	−	0.615701i	$-0.788873\pi$
$997$	4.39599	−	7.61407i	0.139222	−	0.241140i	0.927202	+	0.374561i	$0.122206\pi$
$998$		0			0
$999$	−60.9722	+	35.2023i	−1.92907	+	1.11375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.o.f.361.4		8
13.2	odd	12		1352.2.a.l.1.1		4
13.3	even	3		1352.2.f.f.337.2		8
13.4	even	6	inner	1352.2.o.f.1161.4		8
13.5	odd	4		1352.2.i.l.1329.4		8
13.6	odd	12		1352.2.i.l.529.4		8
13.7	odd	12		1352.2.i.k.529.4		8
13.8	odd	4		1352.2.i.k.1329.4		8
13.9	even	3		104.2.o.a.17.4	✓	8
13.10	even	6		1352.2.f.f.337.1		8
13.11	odd	12		1352.2.a.k.1.1		4
13.12	even	2		104.2.o.a.49.4	yes	8
39.35	odd	6		936.2.bi.b.433.2		8
39.38	odd	2		936.2.bi.b.361.3		8
52.3	odd	6		2704.2.f.q.337.8		8
52.11	even	12		2704.2.a.bd.1.4		4
52.15	even	12		2704.2.a.be.1.4		4
52.23	odd	6		2704.2.f.q.337.7		8
52.35	odd	6		208.2.w.c.17.1		8
52.51	odd	2		208.2.w.c.49.1		8
104.35	odd	6		832.2.w.i.641.4		8
104.51	odd	2		832.2.w.i.257.4		8
104.61	even	6		832.2.w.g.641.1		8
104.77	even	2		832.2.w.g.257.1		8
156.35	even	6		1872.2.by.n.433.2		8
156.155	even	2		1872.2.by.n.1297.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.o.a.17.4	✓	8	13.9	even	3
104.2.o.a.49.4	yes	8	13.12	even	2
208.2.w.c.17.1		8	52.35	odd	6
208.2.w.c.49.1		8	52.51	odd	2
832.2.w.g.257.1		8	104.77	even	2
832.2.w.g.641.1		8	104.61	even	6
832.2.w.i.257.4		8	104.51	odd	2
832.2.w.i.641.4		8	104.35	odd	6
936.2.bi.b.361.3		8	39.38	odd	2
936.2.bi.b.433.2		8	39.35	odd	6
1352.2.a.k.1.1		4	13.11	odd	12
1352.2.a.l.1.1		4	13.2	odd	12
1352.2.f.f.337.1		8	13.10	even	6
1352.2.f.f.337.2		8	13.3	even	3
1352.2.i.k.529.4		8	13.7	odd	12
1352.2.i.k.1329.4		8	13.8	odd	4
1352.2.i.l.529.4		8	13.6	odd	12
1352.2.i.l.1329.4		8	13.5	odd	4
1352.2.o.f.361.4		8	1.1	even	1	trivial
1352.2.o.f.1161.4		8	13.4	even	6	inner
1872.2.by.n.433.2		8	156.35	even	6
1872.2.by.n.1297.3		8	156.155	even	2
2704.2.a.bd.1.4		4	52.11	even	12
2704.2.a.be.1.4		4	52.15	even	12
2704.2.f.q.337.7		8	52.23	odd	6
2704.2.f.q.337.8		8	52.3	odd	6

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:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.63871 + 2.83834i) q^{3} +2.61023i q^{5} +(0.971521 + 0.560908i) q^{7} +(-3.87076 + 6.70436i) q^{9} +(-0.971521 + 0.560908i) q^{11} +(-7.40872 + 4.27743i) q^{15} +(2.77743 - 4.81064i) q^{17} +(1.45204 + 0.838335i) q^{19} +3.67667i q^{21} +(1.63871 + 2.83834i) q^{23} -1.81333 q^{25} -15.5400 q^{27} +(0.167192 + 0.289586i) q^{29} -0.129717i q^{31} +(-3.18409 - 1.83834i) q^{33} +(-1.46410 + 2.53590i) q^{35} +(3.92356 - 2.26527i) q^{37} +(-4.96410 + 2.86603i) q^{41} +(-2.24895 + 3.89529i) q^{43} +(-17.5000 - 10.1036i) q^{45} -10.7985i q^{47} +(-2.87076 - 4.97231i) q^{49} +18.2056 q^{51} +4.14771 q^{53} +(-1.46410 - 2.53590i) q^{55} +5.49516i q^{57} +(0.549538 + 0.317276i) q^{59} +(-2.35387 + 4.07702i) q^{61} +(-7.52106 + 4.34229i) q^{63} +(12.4372 - 7.18062i) q^{67} +(-5.37076 + 9.30244i) q^{69} +(7.45204 + 4.30244i) q^{71} -9.94462i q^{73} +(-2.97152 - 5.14683i) q^{75} -1.25847 q^{77} +13.5970 q^{79} +(-13.8533 - 23.9947i) q^{81} +5.75637i q^{83} +(12.5569 + 7.24974i) q^{85} +(-0.547961 + 0.949096i) q^{87} +(-12.4235 + 7.17272i) q^{89} +(0.368180 - 0.212569i) q^{93} +(-2.18825 + 3.79016i) q^{95} +(-7.80107 - 4.50395i) q^{97} -8.68457i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 6 q^{7} - 6 q^{9} - 6 q^{11} + 6 q^{19} + 2 q^{23} - 20 q^{25} - 28 q^{27} - 8 q^{29} - 6 q^{33} + 16 q^{35} + 24 q^{37} - 12 q^{41} + 6 q^{43} - 30 q^{45} + 2 q^{49} + 68 q^{51} + 20 q^{53}+ \cdots - 30 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 + 6 * q^7 - 6 * q^9 - 6 * q^11 + 6 * q^19 + 2 * q^23 - 20 * q^25 - 28 * q^27 - 8 * q^29 - 6 * q^33 + 16 * q^35 + 24 * q^37 - 12 * q^41 + 6 * q^43 - 30 * q^45 + 2 * q^49 + 68 * q^51 + 20 * q^53 + 16 * q^55 - 18 * q^59 - 4 * q^61 - 36 * q^63 + 42 * q^67 - 18 * q^69 + 54 * q^71 - 22 * q^75 - 60 * q^77 + 16 * q^79 - 20 * q^81 - 6 * q^85 - 10 * q^87 + 18 * q^89 - 36 * q^93 + 16 * q^95 - 30 * q^97

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