LMFDB - Embedded newform 936.2.j.a.755.48

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(755,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.755"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.j (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			755.48
Character	$\chi$	$=$	936.755
Dual form			936.2.j.a.755.47

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40511 + 0.160221i) q^{2} +(1.94866 + 0.450256i) q^{4} -3.43430 q^{5} -1.48385i q^{7} +(2.66594 + 0.944875i) q^{8} +(-4.82556 - 0.550247i) q^{10} -4.11313i q^{11} -1.00000i q^{13} +(0.237744 - 2.08497i) q^{14} +(3.59454 + 1.75479i) q^{16} -6.57820i q^{17} +7.48832 q^{19} +(-6.69227 - 1.54631i) q^{20} +(0.659011 - 5.77940i) q^{22} +2.95626 q^{23} +6.79440 q^{25} +(0.160221 - 1.40511i) q^{26} +(0.668113 - 2.89152i) q^{28} -2.46896 q^{29} -4.42928i q^{31} +(4.76956 + 3.04159i) q^{32} +(1.05397 - 9.24308i) q^{34} +5.09598i q^{35} +9.06101i q^{37} +(10.5219 + 1.19979i) q^{38} +(-9.15562 - 3.24498i) q^{40} -2.36415i q^{41} -11.0152 q^{43} +(1.85196 - 8.01509i) q^{44} +(4.15386 + 0.473655i) q^{46} +4.15658 q^{47} +4.79819 q^{49} +(9.54686 + 1.08861i) q^{50} +(0.450256 - 1.94866i) q^{52} -11.6774 q^{53} +14.1257i q^{55} +(1.40205 - 3.95585i) q^{56} +(-3.46915 - 0.395579i) q^{58} +9.65991i q^{59} -13.0229i q^{61} +(0.709664 - 6.22362i) q^{62} +(6.21442 + 5.03795i) q^{64} +3.43430i q^{65} -5.33582 q^{67} +(2.96187 - 12.8187i) q^{68} +(-0.816484 + 7.16041i) q^{70} -4.14842 q^{71} +2.91895 q^{73} +(-1.45176 + 12.7317i) q^{74} +(14.5922 + 3.37166i) q^{76} -6.10327 q^{77} -6.01233i q^{79} +(-12.3447 - 6.02647i) q^{80} +(0.378786 - 3.32188i) q^{82} -7.31280i q^{83} +22.5915i q^{85} +(-15.4775 - 1.76487i) q^{86} +(3.88639 - 10.9653i) q^{88} +1.95737i q^{89} -1.48385 q^{91} +(5.76074 + 1.33107i) q^{92} +(5.84044 + 0.665971i) q^{94} -25.7171 q^{95} +15.3919 q^{97} +(6.74197 + 0.768771i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) $ 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	1.40511	+	0.160221i	0.993562	+	0.113293i
$2$	1.40511	+	0.160221i	0.993562	+	0.113293i
$3$		0			0
$3$		0			0
$4$	1.94866	+	0.450256i	0.974329	+	0.225128i
$5$	−3.43430			−1.53586			−0.767932	−	0.640531i	$-0.778714\pi$
$5$	−3.43430			−1.53586			−0.767932	+	0.640531i	$0.778714\pi$
$6$		0			0
$7$		−	1.48385i		−	0.560843i	−0.959877	−	0.280421i	$-0.909526\pi$
$7$		−	1.48385i		−	0.560843i	0.959877	−	0.280421i	$-0.0904742\pi$
$8$	2.66594	+	0.944875i	0.942551	+	0.334064i
$9$		0			0
$10$	−4.82556	−	0.550247i	−1.52598	−	0.174003i
$11$		−	4.11313i		−	1.24016i	−0.784540	−	0.620078i	$-0.787101\pi$
$11$		−	4.11313i		−	1.24016i	0.784540	−	0.620078i	$-0.212899\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.237744	−	2.08497i	0.0635398	−	0.557232i
$15$		0			0
$16$	3.59454	+	1.75479i	0.898635	+	0.438698i
$17$		−	6.57820i		−	1.59545i	−0.603024	−	0.797723i	$-0.706038\pi$
$17$		−	6.57820i		−	1.59545i	0.603024	−	0.797723i	$-0.293962\pi$
$18$		0			0
$19$	7.48832			1.71794			0.858970	−	0.512027i	$-0.171105\pi$
$19$	7.48832			1.71794			0.858970	+	0.512027i	$0.171105\pi$
$20$	−6.69227	−	1.54631i	−1.49644	−	0.345766i
$21$		0			0
$22$	0.659011	−	5.77940i	0.140502	−	1.23217i
$23$	2.95626			0.616423			0.308211	−	0.951318i	$-0.400270\pi$
$23$	2.95626			0.616423			0.308211	+	0.951318i	$0.400270\pi$
$24$		0			0
$25$	6.79440			1.35888
$26$	0.160221	−	1.40511i	0.0314219	−	0.275564i
$27$		0			0
$28$	0.668113	−	2.89152i	0.126261	−	0.546445i
$29$	−2.46896			−0.458474			−0.229237	−	0.973371i	$-0.573623\pi$
$29$	−2.46896			−0.458474			−0.229237	+	0.973371i	$0.573623\pi$
$30$		0			0
$31$		−	4.42928i		−	0.795522i	−0.917489	−	0.397761i	$-0.869787\pi$
$31$		−	4.42928i		−	0.795522i	0.917489	−	0.397761i	$-0.130213\pi$
$32$	4.76956	+	3.04159i	0.843147	+	0.537682i
$33$		0			0
$34$	1.05397	−	9.24308i	0.180754	−	1.58517i
$35$			5.09598i			0.861378i
$36$		0			0
$37$			9.06101i			1.48962i	0.667276	+	0.744810i	$0.267460\pi$
$37$			9.06101i			1.48962i	−0.667276	+	0.744810i	$0.732540\pi$
$38$	10.5219	+	1.19979i	1.70688	+	0.194631i
$39$		0			0
$40$	−9.15562	−	3.24498i	−1.44763	−	0.513076i
$41$		−	2.36415i		−	0.369218i	−0.982812	−	0.184609i	$-0.940898\pi$
$41$		−	2.36415i		−	0.369218i	0.982812	−	0.184609i	$-0.0591018\pi$
$42$		0			0
$43$	−11.0152			−1.67980			−0.839901	−	0.542740i	$-0.817387\pi$
$43$	−11.0152			−1.67980			−0.839901	+	0.542740i	$0.817387\pi$
$44$	1.85196	−	8.01509i	0.279194	−	1.20832i
$45$		0			0
$46$	4.15386	+	0.473655i	0.612454	+	0.0698366i
$47$	4.15658			0.606299			0.303149	−	0.952943i	$-0.401962\pi$
$47$	4.15658			0.606299			0.303149	+	0.952943i	$0.401962\pi$
$48$		0			0
$49$	4.79819			0.685455
$50$	9.54686	+	1.08861i	1.35013	+	0.153952i
$51$		0			0
$52$	0.450256	−	1.94866i	0.0624393	−	0.270230i
$53$	−11.6774			−1.60401			−0.802007	−	0.597315i	$-0.796234\pi$
$53$	−11.6774			−1.60401			−0.802007	+	0.597315i	$0.796234\pi$
$54$		0			0
$55$			14.1257i			1.90471i
$56$	1.40205	−	3.95585i	0.187357	−	0.528623i
$57$		0			0
$58$	−3.46915	−	0.395579i	−0.455522	−	0.0519421i
$59$			9.65991i			1.25761i	0.777562	+	0.628807i	$0.216456\pi$
$59$			9.65991i			1.25761i	−0.777562	+	0.628807i	$0.783544\pi$
$60$		0			0
$61$		−	13.0229i		−	1.66741i	−0.552206	−	0.833707i	$-0.686214\pi$
$61$		−	13.0229i		−	1.66741i	0.552206	−	0.833707i	$-0.313786\pi$
$62$	0.709664	−	6.22362i	0.0901274	−	0.790400i
$63$		0			0
$64$	6.21442	+	5.03795i	0.776803	+	0.629744i
$65$			3.43430i			0.425972i
$66$		0			0
$67$	−5.33582			−0.651875			−0.325937	−	0.945391i	$-0.605680\pi$
$67$	−5.33582			−0.651875			−0.325937	+	0.945391i	$0.605680\pi$
$68$	2.96187	−	12.8187i	0.359180	−	1.55449i
$69$		0			0
$70$	−0.816484	+	7.16041i	−0.0975885	+	0.855833i
$71$	−4.14842			−0.492327			−0.246164	−	0.969228i	$-0.579170\pi$
$71$	−4.14842			−0.492327			−0.246164	+	0.969228i	$0.579170\pi$
$72$		0			0
$73$	2.91895			0.341637			0.170818	−	0.985303i	$-0.445359\pi$
$73$	2.91895			0.341637			0.170818	+	0.985303i	$0.445359\pi$
$74$	−1.45176	+	12.7317i	−0.168764	+	1.48003i
$75$		0			0
$76$	14.5922	+	3.37166i	1.67384	+	0.386756i
$77$	−6.10327			−0.695533
$78$		0			0
$79$		−	6.01233i		−	0.676440i	−0.941067	−	0.338220i	$-0.890175\pi$
$79$		−	6.01233i		−	0.676440i	0.941067	−	0.338220i	$-0.109825\pi$
$80$	−12.3447	−	6.02647i	−1.38018	−	0.673780i
$81$		0			0
$82$	0.378786	−	3.32188i	0.0418299	−	0.366840i
$83$		−	7.31280i		−	0.802685i	−0.915928	−	0.401342i	$-0.868544\pi$
$83$		−	7.31280i		−	0.802685i	0.915928	−	0.401342i	$-0.131456\pi$
$84$		0			0
$85$			22.5915i			2.45039i
$86$	−15.4775	−	1.76487i	−1.66899	−	0.190310i
$87$		0			0
$88$	3.88639	−	10.9653i	0.414291	−	1.16891i
$89$			1.95737i			0.207481i	0.994604	+	0.103740i	$0.0330811\pi$
$89$			1.95737i			0.207481i	−0.994604	+	0.103740i	$0.966919\pi$
$90$		0			0
$91$	−1.48385			−0.155550
$92$	5.76074	+	1.33107i	0.600599	+	0.138774i
$93$		0			0
$94$	5.84044	+	0.665971i	0.602395	+	0.0686897i
$95$	−25.7171			−2.63852
$96$		0			0
$97$	15.3919			1.56281			0.781406	−	0.624023i	$-0.214503\pi$
$97$	15.3919			1.56281			0.781406	+	0.624023i	$0.214503\pi$
$98$	6.74197	+	0.768771i	0.681042	+	0.0776576i
$99$		0			0
$100$	13.2400	+	3.05922i	1.32400	+	0.305922i
$101$	1.77864			0.176981			0.0884907	−	0.996077i	$-0.471796\pi$
$101$	1.77864			0.176981			0.0884907	+	0.996077i	$0.471796\pi$
$102$		0			0
$103$			0.165835i			0.0163403i	0.999967	+	0.00817013i	$0.00260066\pi$
$103$			0.165835i			0.0163403i	−0.999967	+	0.00817013i	$0.997399\pi$
$104$	0.944875	−	2.66594i	0.0926526	−	0.261416i
$105$		0			0
$106$	−16.4080	−	1.87097i	−1.59369	−	0.181724i
$107$			11.2981i			1.09223i	0.837710	+	0.546116i	$0.183894\pi$
$107$			11.2981i			1.09223i	−0.837710	+	0.546116i	$0.816106\pi$
$108$		0			0
$109$			6.75654i			0.647159i	0.946201	+	0.323580i	$0.104886\pi$
$109$			6.75654i			0.647159i	−0.946201	+	0.323580i	$0.895114\pi$
$110$	−2.26324	+	19.8482i	−0.215791	+	1.89245i
$111$		0			0
$112$	2.60385	−	5.33376i	0.246040	−	0.503993i
$113$			10.7906i			1.01509i	0.861625	+	0.507546i	$0.169447\pi$
$113$			10.7906i			1.01509i	−0.861625	+	0.507546i	$0.830553\pi$
$114$		0			0
$115$	−10.1527			−0.946742
$116$	−4.81115	−	1.11166i	−0.446704	−	0.103215i
$117$		0			0
$118$	−1.54772	+	13.5732i	−0.142479	+	1.24952i
$119$	−9.76106			−0.894795
$120$		0			0
$121$	−5.91786			−0.537987
$122$	2.08655	−	18.2986i	0.188907	−	1.65668i
$123$		0			0
$124$	1.99431	−	8.63115i	0.179094	−	0.775100i
$125$	−6.16250			−0.551190
$126$		0			0
$127$			21.8477i			1.93867i	0.245746	+	0.969334i	$0.420967\pi$
$127$			21.8477i			1.93867i	−0.245746	+	0.969334i	$0.579033\pi$
$128$	7.92475	+	8.07455i	0.700456	+	0.713696i
$129$		0			0
$130$	−0.550247	+	4.82556i	−0.0482598	+	0.423230i
$131$			3.06648i			0.267919i	0.990987	+	0.133960i	$0.0427692\pi$
$131$			3.06648i			0.267919i	−0.990987	+	0.133960i	$0.957231\pi$
$132$		0			0
$133$		−	11.1116i		−	0.963494i
$134$	−7.49741	−	0.854912i	−0.647678	−	0.0738531i
$135$		0			0
$136$	6.21557	−	17.5370i	0.532981	−	1.50379i
$137$		−	12.5259i		−	1.07016i	−0.844801	−	0.535081i	$-0.820281\pi$
$137$		−	12.5259i		−	1.07016i	0.844801	−	0.535081i	$-0.179719\pi$
$138$		0			0
$139$	−6.34023			−0.537771			−0.268885	−	0.963172i	$-0.586655\pi$
$139$	−6.34023			−0.537771			−0.268885	+	0.963172i	$0.586655\pi$
$140$	−2.29450	+	9.93033i	−0.193920	+	0.839266i
$141$		0			0
$142$	−5.82898	−	0.664665i	−0.489157	−	0.0557774i
$143$	−4.11313			−0.343957
$144$		0			0
$145$	8.47913			0.704154
$146$	4.10144	+	0.467677i	0.339437	+	0.0387052i
$147$		0			0
$148$	−4.07977	+	17.6568i	−0.335355	+	1.45138i
$149$	11.8939			0.974386			0.487193	−	0.873294i	$-0.338021\pi$
$149$	11.8939			0.974386			0.487193	+	0.873294i	$0.338021\pi$
$150$		0			0
$151$			10.7651i			0.876055i	0.898962	+	0.438027i	$0.144323\pi$
$151$			10.7651i			0.876055i	−0.898962	+	0.438027i	$0.855677\pi$
$152$	19.9634	+	7.07553i	1.61924	+	0.573901i
$153$		0			0
$154$	−8.57576	−	0.977873i	−0.691054	−	0.0787993i
$155$			15.2115i			1.22181i
$156$		0			0
$157$		−	6.23480i		−	0.497591i	−0.968556	−	0.248796i	$-0.919965\pi$
$157$		−	6.23480i		−	0.497591i	0.968556	−	0.248796i	$-0.0800348\pi$
$158$	0.963302	−	8.44797i	0.0766362	−	0.672084i
$159$		0			0
$160$	−16.3801	−	10.4457i	−1.29496	−	0.825807i
$161$		−	4.38665i		−	0.345716i
$162$		0			0
$163$	10.3506			0.810718			0.405359	−	0.914158i	$-0.367147\pi$
$163$	10.3506			0.810718			0.405359	+	0.914158i	$0.367147\pi$
$164$	1.06447	−	4.60691i	0.0831212	−	0.359739i
$165$		0			0
$166$	1.17167	−	10.2753i	0.0909389	−	0.797517i
$167$	3.90946			0.302523			0.151262	−	0.988494i	$-0.451666\pi$
$167$	3.90946			0.302523			0.151262	+	0.988494i	$0.451666\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−3.61963	+	31.7435i	−0.277613	+	2.43461i
$171$		0			0
$172$	−21.4648	−	4.95966i	−1.63668	−	0.378170i
$173$	11.0575			0.840683			0.420341	−	0.907366i	$-0.361910\pi$
$173$	11.0575			0.840683			0.420341	+	0.907366i	$0.361910\pi$
$174$		0			0
$175$		−	10.0819i		−	0.762118i
$176$	7.21768	−	14.7848i	0.544053	−	1.11445i
$177$		0			0
$178$	−0.313612	+	2.75032i	−0.0235062	+	0.206145i
$179$		−	3.06653i		−	0.229203i	−0.993412	−	0.114602i	$-0.963441\pi$
$179$		−	3.06653i		−	0.229203i	0.993412	−	0.114602i	$-0.0365592\pi$
$180$		0			0
$181$		−	15.7696i		−	1.17215i	−0.810258	−	0.586073i	$-0.800673\pi$
$181$		−	15.7696i		−	1.17215i	0.810258	−	0.586073i	$-0.199327\pi$
$182$	−2.08497	−	0.237744i	−0.154548	−	0.0176228i
$183$		0			0
$184$	7.88120	+	2.79329i	0.581009	+	0.205924i
$185$		−	31.1182i		−	2.28786i
$186$		0			0
$187$	−27.0570			−1.97860
$188$	8.09975	+	1.87152i	0.590735	+	0.136495i
$189$		0			0
$190$	−36.1353	−	4.12043i	−2.62153	−	0.298927i
$191$	−11.0790			−0.801648			−0.400824	−	0.916155i	$-0.631276\pi$
$191$	−11.0790			−0.801648			−0.400824	+	0.916155i	$0.631276\pi$
$192$		0			0
$193$	7.62208			0.548649			0.274325	−	0.961637i	$-0.411546\pi$
$193$	7.62208			0.548649			0.274325	+	0.961637i	$0.411546\pi$
$194$	21.6273	+	2.46611i	1.55275	+	0.177056i
$195$		0			0
$196$	9.35003	+	2.16041i	0.667859	+	0.154315i
$197$	24.0203			1.71138			0.855688	−	0.517493i	$-0.173135\pi$
$197$	24.0203			1.71138			0.855688	+	0.517493i	$0.173135\pi$
$198$		0			0
$199$		−	9.37481i		−	0.664562i	−0.943180	−	0.332281i	$-0.892182\pi$
$199$		−	9.37481i		−	0.664562i	0.943180	−	0.332281i	$-0.107818\pi$
$200$	18.1134	+	6.41985i	1.28081	+	0.453952i
$201$		0			0
$202$	2.49918	+	0.284976i	0.175842	+	0.0200508i
$203$			3.66356i			0.257132i
$204$		0			0
$205$			8.11918i			0.567068i
$206$	−0.0265703	+	0.233017i	−0.00185124	+	0.0162350i
$207$		0			0
$208$	1.75479	−	3.59454i	0.121673	−	0.249236i
$209$		−	30.8005i		−	2.13051i
$210$		0			0
$211$	2.85230			0.196360			0.0981801	−	0.995169i	$-0.468698\pi$
$211$	2.85230			0.196360			0.0981801	+	0.995169i	$0.468698\pi$
$212$	−22.7553	−	5.25782i	−1.56284	−	0.361108i
$213$		0			0
$214$	−1.81020	+	15.8751i	−0.123743	+	1.08520i
$215$	37.8294			2.57995
$216$		0			0
$217$	−6.57239			−0.446163
$218$	−1.08254	+	9.49367i	−0.0733189	+	0.642992i
$219$		0			0
$220$	−6.36019	+	27.5262i	−0.428804	+	1.85582i
$221$	−6.57820			−0.442497
$222$		0			0
$223$			12.1492i			0.813571i	0.913524	+	0.406786i	$0.133350\pi$
$223$			12.1492i			0.813571i	−0.913524	+	0.406786i	$0.866650\pi$
$224$	4.51327	−	7.07732i	0.301555	−	0.472873i
$225$		0			0
$226$	−1.72888	+	15.1619i	−0.115003	+	1.00856i
$227$			28.9612i			1.92222i	0.276164	+	0.961111i	$0.410937\pi$
$227$			28.9612i			1.92222i	−0.276164	+	0.961111i	$0.589063\pi$
$228$		0			0
$229$			7.83253i			0.517588i	0.965932	+	0.258794i	$0.0833251\pi$
$229$			7.83253i			0.517588i	−0.965932	+	0.258794i	$0.916675\pi$
$230$	−14.2656	−	1.62667i	−0.940646	−	0.107260i
$231$		0			0
$232$	−6.58208	−	2.33286i	−0.432135	−	0.153159i
$233$			21.1736i			1.38713i	0.720393	+	0.693566i	$0.243961\pi$
$233$			21.1736i			1.38713i	−0.720393	+	0.693566i	$0.756039\pi$
$234$		0			0
$235$	−14.2749			−0.931193
$236$	−4.34943	+	18.8239i	−0.283124	+	1.22533i
$237$		0			0
$238$	−13.7153	−	1.56393i	−0.889034	−	0.101374i
$239$	9.63791			0.623425			0.311712	−	0.950177i	$-0.399097\pi$
$239$	9.63791			0.623425			0.311712	+	0.950177i	$0.399097\pi$
$240$		0			0
$241$	−6.60721			−0.425608			−0.212804	−	0.977095i	$-0.568260\pi$
$241$	−6.60721			−0.425608			−0.212804	+	0.977095i	$0.568260\pi$
$242$	−8.31523	−	0.948166i	−0.534523	−	0.0609504i
$243$		0			0
$244$	5.86365	−	25.3772i	0.375382	−	1.62461i
$245$	−16.4784			−1.05277
$246$		0			0
$247$		−	7.48832i		−	0.476471i
$248$	4.18511	−	11.8082i	0.265755	−	0.749820i
$249$		0			0
$250$	−8.65897	−	0.987362i	−0.547642	−	0.0624463i
$251$			26.3839i			1.66534i	0.553771	+	0.832669i	$0.313188\pi$
$251$			26.3839i			1.66534i	−0.553771	+	0.832669i	$0.686812\pi$
$252$		0			0
$253$		−	12.1595i		−	0.764460i
$254$	−3.50046	+	30.6984i	−0.219638	+	1.92619i
$255$		0			0
$256$	9.84142	+	12.6153i	0.615089	+	0.788458i
$257$			12.4536i			0.776832i	0.921484	+	0.388416i	$0.126978\pi$
$257$			12.4536i			0.776832i	−0.921484	+	0.388416i	$0.873022\pi$
$258$		0			0
$259$	13.4452			0.835443
$260$	−1.54631	+	6.69227i	−0.0958983	+	0.415037i
$261$		0			0
$262$	−0.491314	+	4.30873i	−0.0303535	+	0.266194i
$263$	−12.3191			−0.759631			−0.379816	−	0.925062i	$-0.624013\pi$
$263$	−12.3191			−0.759631			−0.379816	+	0.925062i	$0.624013\pi$
$264$		0			0
$265$	40.1037			2.46355
$266$	1.78031	−	15.6129i	0.109158	−	0.957290i
$267$		0			0
$268$	−10.3977	−	2.40249i	−0.635141	−	0.146755i
$269$	5.67847			0.346223			0.173111	−	0.984902i	$-0.444618\pi$
$269$	5.67847			0.346223			0.173111	+	0.984902i	$0.444618\pi$
$270$		0			0
$271$			24.5812i			1.49320i	0.665274	+	0.746600i	$0.268315\pi$
$271$			24.5812i			1.49320i	−0.665274	+	0.746600i	$0.731685\pi$
$272$	11.5434	−	23.6456i	0.699919	−	1.43372i
$273$		0			0
$274$	2.00692	−	17.6003i	0.121242	−	1.06327i
$275$		−	27.9463i		−	1.68522i
$276$		0			0
$277$		−	25.1434i		−	1.51072i	−0.655310	−	0.755360i	$-0.727462\pi$
$277$		−	25.1434i		−	1.51072i	0.655310	−	0.755360i	$-0.272538\pi$
$278$	−8.90870	−	1.01584i	−0.534309	−	0.0609259i
$279$		0			0
$280$	−4.81507	+	13.5856i	−0.287755	+	0.811893i
$281$			1.73983i			0.103789i	0.998653	+	0.0518947i	$0.0165260\pi$
$281$			1.73983i			0.103789i	−0.998653	+	0.0518947i	$0.983474\pi$
$282$		0			0
$283$	−32.9825			−1.96060			−0.980302	−	0.197502i	$-0.936717\pi$
$283$	−32.9825			−1.96060			−0.980302	+	0.197502i	$0.936717\pi$
$284$	−8.08386	−	1.86785i	−0.479689	−	0.110837i
$285$		0			0
$286$	−5.77940	−	0.659011i	−0.341743	−	0.0389681i
$287$	−3.50804			−0.207073
$288$		0			0
$289$	−26.2727			−1.54545
$290$	11.9141	+	1.35854i	0.699620	+	0.0797760i
$291$		0			0
$292$	5.68803	+	1.31427i	0.332867	+	0.0769120i
$293$	12.7025			0.742090			0.371045	−	0.928615i	$-0.379000\pi$
$293$	12.7025			0.742090			0.371045	+	0.928615i	$0.379000\pi$
$294$		0			0
$295$		−	33.1750i		−	1.93152i
$296$	−8.56152	+	24.1561i	−0.497628	+	1.40404i
$297$		0			0
$298$	16.7122	+	1.90565i	0.968112	+	0.110391i
$299$		−	2.95626i		−	0.170965i
$300$		0			0
$301$			16.3449i			0.942104i
$302$	−1.72480	+	15.1262i	−0.0992513	+	0.870415i
$303$		0			0
$304$	26.9171	+	13.1404i	1.54380	+	0.753656i
$305$			44.7246i			2.56092i
$306$		0			0
$307$	−4.14718			−0.236692			−0.118346	−	0.992972i	$-0.537759\pi$
$307$	−4.14718			−0.236692			−0.118346	+	0.992972i	$0.537759\pi$
$308$	−11.8932	−	2.74804i	−0.677678	−	0.156584i
$309$		0			0
$310$	−2.43720	+	21.3738i	−0.138424	+	1.21395i
$311$	13.8548			0.785635			0.392817	−	0.919617i	$-0.371500\pi$
$311$	13.8548			0.785635			0.392817	+	0.919617i	$0.371500\pi$
$312$		0			0
$313$	−27.5845			−1.55917			−0.779585	−	0.626297i	$-0.784570\pi$
$313$	−27.5845			−1.55917			−0.779585	+	0.626297i	$0.784570\pi$
$314$	0.998947	−	8.76057i	0.0563738	−	0.494388i
$315$		0			0
$316$	2.70709	−	11.7160i	0.152286	−	0.659075i
$317$	−5.43165			−0.305072			−0.152536	−	0.988298i	$-0.548744\pi$
$317$	−5.43165			−0.305072			−0.152536	+	0.988298i	$0.548744\pi$
$318$		0			0
$319$			10.1551i			0.568579i
$320$	−21.3422	−	17.3018i	−1.19306	−	0.967201i
$321$		0			0
$322$	0.702833	−	6.16371i	0.0391674	−	0.343490i
$323$		−	49.2597i		−	2.74088i
$324$		0			0
$325$		−	6.79440i		−	0.376885i
$326$	14.5436	+	1.65838i	0.805498	+	0.0918490i
$327$		0			0
$328$	2.23382	−	6.30266i	0.123342	−	0.348006i
$329$		−	6.16774i		−	0.340038i
$330$		0			0
$331$	1.82454			0.100286			0.0501430	−	0.998742i	$-0.484032\pi$
$331$	1.82454			0.100286			0.0501430	+	0.998742i	$0.484032\pi$
$332$	3.29263	−	14.2502i	0.180707	−	0.782079i
$333$		0			0
$334$	5.49322	+	0.626379i	0.300576	+	0.0342739i
$335$	18.3248			1.00119
$336$		0			0
$337$	−0.724485			−0.0394652			−0.0197326	−	0.999805i	$-0.506281\pi$
$337$	−0.724485			−0.0394652			−0.0197326	+	0.999805i	$0.506281\pi$
$338$	−1.40511	−	0.160221i	−0.0764278	−	0.00871488i
$339$		0			0
$340$	−10.1719	+	44.0231i	−0.551651	+	2.38749i
$341$	−18.2182			−0.986572
$342$		0			0
$343$		−	17.5067i		−	0.945275i
$344$	−29.3658	−	10.4080i	−1.58330	−	0.561160i
$345$		0			0
$346$	15.5369	+	1.77164i	0.835270	+	0.0952438i
$347$		−	21.2480i		−	1.14065i	−0.821419	−	0.570325i	$-0.806817\pi$
$347$		−	21.2480i		−	1.14065i	0.821419	−	0.570325i	$-0.193183\pi$
$348$		0			0
$349$		−	14.8566i		−	0.795257i	−0.917546	−	0.397629i	$-0.869833\pi$
$349$		−	14.8566i		−	0.795257i	0.917546	−	0.397629i	$-0.130167\pi$
$350$	1.61533	−	14.1661i	0.0863429	−	0.757211i
$351$		0			0
$352$	12.5105	−	19.6178i	0.666810	−	1.04563i
$353$		−	4.19368i		−	0.223207i	−0.993753	−	0.111604i	$-0.964401\pi$
$353$		−	4.19368i		−	0.223207i	0.993753	−	0.111604i	$-0.0355987\pi$
$354$		0			0
$355$	14.2469			0.756148
$356$	−0.881318	+	3.81425i	−0.0467098	+	0.202155i
$357$		0			0
$358$	0.491323	−	4.30881i	0.0259672	−	0.227728i
$359$	21.0005			1.10836			0.554182	−	0.832396i	$-0.313031\pi$
$359$	21.0005			1.10836			0.554182	+	0.832396i	$0.313031\pi$
$360$		0			0
$361$	37.0750			1.95131
$362$	2.52662	−	22.1580i	0.132796	−	1.16460i
$363$		0			0
$364$	−2.89152	−	0.668113i	−0.151557	−	0.0350186i
$365$	−10.0245			−0.524708
$366$		0			0
$367$		−	16.3564i		−	0.853799i	−0.904299	−	0.426900i	$-0.859606\pi$
$367$		−	16.3564i		−	0.853799i	0.904299	−	0.426900i	$-0.140394\pi$
$368$	10.6264	+	5.18761i	0.553939	+	0.270423i
$369$		0			0
$370$	4.98579	−	43.7244i	0.259199	−	2.27313i
$371$			17.3275i			0.899600i
$372$		0			0
$373$			17.7555i			0.919345i	0.888089	+	0.459672i	$0.152033\pi$
$373$			17.7555i			0.919345i	−0.888089	+	0.459672i	$0.847967\pi$
$374$	−38.0180	−	4.33510i	−1.96586	−	0.224163i
$375$		0			0
$376$	11.0812	+	3.92744i	0.571467	+	0.202542i
$377$			2.46896i			0.127158i
$378$		0			0
$379$	−10.1380			−0.520757			−0.260378	−	0.965507i	$-0.583847\pi$
$379$	−10.1380			−0.520757			−0.260378	+	0.965507i	$0.583847\pi$
$380$	−50.1139	−	11.5793i	−2.57079	−	0.594005i
$381$		0			0
$382$	−15.5672	−	1.77509i	−0.796487	−	0.0908215i
$383$	9.25148			0.472728			0.236364	−	0.971665i	$-0.424044\pi$
$383$	9.25148			0.472728			0.236364	+	0.971665i	$0.424044\pi$
$384$		0			0
$385$	20.9605			1.06824
$386$	10.7099	+	1.22122i	0.545117	+	0.0621584i
$387$		0			0
$388$	29.9936	+	6.93030i	1.52269	+	0.351833i
$389$	25.2900			1.28225			0.641127	−	0.767435i	$-0.278467\pi$
$389$	25.2900			1.28225			0.641127	+	0.767435i	$0.278467\pi$
$390$		0			0
$391$		−	19.4468i		−	0.983469i
$392$	12.7917	+	4.53369i	0.646076	+	0.228986i
$393$		0			0
$394$	33.7511	+	3.84856i	1.70036	+	0.193888i
$395$			20.6481i			1.03892i
$396$		0			0
$397$			15.7899i			0.792474i	0.918148	+	0.396237i	$0.129684\pi$
$397$			15.7899i			0.792474i	−0.918148	+	0.396237i	$0.870316\pi$
$398$	1.50204	−	13.1726i	0.0752906	−	0.660284i
$399$		0			0
$400$	24.4227	+	11.9227i	1.22114	+	0.596137i
$401$		−	10.7963i		−	0.539141i	−0.962981	−	0.269571i	$-0.913118\pi$
$401$		−	10.7963i		−	0.539141i	0.962981	−	0.269571i	$-0.0868818\pi$
$402$		0			0
$403$	−4.42928			−0.220638
$404$	3.46596	+	0.800844i	0.172438	+	0.0398435i
$405$		0			0
$406$	−0.586980	+	5.14770i	−0.0291313	+	0.255476i
$407$	37.2691			1.84736
$408$		0			0
$409$	−26.6099			−1.31577			−0.657887	−	0.753117i	$-0.728549\pi$
$409$	−26.6099			−1.31577			−0.657887	+	0.753117i	$0.728549\pi$
$410$	−1.30086	+	11.4083i	−0.0642451	+	0.563417i
$411$		0			0
$412$	−0.0746684	+	0.323157i	−0.00367865	+	0.0159208i
$413$	14.3339			0.705323
$414$		0			0
$415$			25.1143i			1.23281i
$416$	3.04159	−	4.76956i	0.149126	−	0.233847i
$417$		0			0
$418$	4.93488	−	43.2780i	0.241373	−	2.11680i
$419$		−	6.79469i		−	0.331942i	−0.986131	−	0.165971i	$-0.946924\pi$
$419$		−	6.79469i		−	0.331942i	0.986131	−	0.165971i	$-0.0530759\pi$
$420$		0			0
$421$			1.59188i			0.0775835i	0.999247	+	0.0387918i	$0.0123509\pi$
$421$			1.59188i			0.0775835i	−0.999247	+	0.0387918i	$0.987649\pi$
$422$	4.00778	+	0.456998i	0.195096	+	0.0222463i
$423$		0			0
$424$	−31.1312	−	11.0337i	−1.51186	−	0.535843i
$425$		−	44.6949i		−	2.16802i
$426$		0			0
$427$	−19.3241			−0.935158
$428$	−5.08705	+	22.0162i	−0.245892	+	1.06419i
$429$		0			0
$430$	53.1545	+	6.06108i	2.56334	+	0.292291i
$431$	−16.2055			−0.780589			−0.390295	−	0.920690i	$-0.627627\pi$
$431$	−16.2055			−0.780589			−0.390295	+	0.920690i	$0.627627\pi$
$432$		0			0
$433$	13.0208			0.625739			0.312870	−	0.949796i	$-0.398710\pi$
$433$	13.0208			0.625739			0.312870	+	0.949796i	$0.398710\pi$
$434$	−9.23492	−	1.05304i	−0.443290	−	0.0505473i
$435$		0			0
$436$	−3.04217	+	13.1662i	−0.145694	+	0.630546i
$437$	22.1374			1.05898
$438$		0			0
$439$		−	24.1906i		−	1.15455i	−0.816549	−	0.577276i	$-0.804116\pi$
$439$		−	24.1906i		−	1.15455i	0.816549	−	0.577276i	$-0.195884\pi$
$440$	−13.3470	+	37.6583i	−0.636295	+	1.79529i
$441$		0			0
$442$	−9.24308	−	1.05397i	−0.439648	−	0.0501320i
$443$			20.5907i			0.978295i	0.872201	+	0.489147i	$0.162692\pi$
$443$			20.5907i			0.978295i	−0.872201	+	0.489147i	$0.837308\pi$
$444$		0			0
$445$		−	6.72220i		−	0.318663i
$446$	−1.94656	+	17.0710i	−0.0921723	+	0.808333i
$447$		0			0
$448$	7.47556	−	9.22128i	0.353187	−	0.435664i
$449$		−	40.3421i		−	1.90386i	−0.306316	−	0.951930i	$-0.599096\pi$
$449$		−	40.3421i		−	1.90386i	0.306316	−	0.951930i	$-0.400904\pi$
$450$		0			0
$451$	−9.72405			−0.457887
$452$	−4.85852	+	21.0271i	−0.228525	+	0.989033i
$453$		0			0
$454$	−4.64019	+	40.6936i	−0.217775	+	1.90985i
$455$	5.09598			0.238903
$456$		0			0
$457$	−7.86556			−0.367935			−0.183968	−	0.982932i	$-0.558894\pi$
$457$	−7.86556			−0.367935			−0.183968	+	0.982932i	$0.558894\pi$
$458$	−1.25494	+	11.0056i	−0.0586394	+	0.514256i
$459$		0			0
$460$	−19.7841	−	4.57130i	−0.922438	−	0.213138i
$461$	−22.9618			−1.06944			−0.534719	−	0.845030i	$-0.679583\pi$
$461$	−22.9618			−1.06944			−0.534719	+	0.845030i	$0.679583\pi$
$462$		0			0
$463$		−	10.0614i		−	0.467594i	−0.972285	−	0.233797i	$-0.924885\pi$
$463$		−	10.0614i		−	0.467594i	0.972285	−	0.233797i	$-0.0751152\pi$
$464$	−8.87476	−	4.33250i	−0.412001	−	0.201131i
$465$		0			0
$466$	−3.39246	+	29.7513i	−0.157153	+	1.37820i
$467$			21.4264i			0.991494i	0.868467	+	0.495747i	$0.165106\pi$
$467$			21.4264i			0.991494i	−0.868467	+	0.495747i	$0.834894\pi$
$468$		0			0
$469$			7.91757i			0.365599i
$470$	−20.0578	−	2.28714i	−0.925197	−	0.105498i
$471$		0			0
$472$	−9.12741	+	25.7527i	−0.420123	+	1.18536i
$473$			45.3069i			2.08322i
$474$		0			0
$475$	50.8786			2.33447
$476$	−19.0210	−	4.39497i	−0.871825	−	0.201443i
$477$		0			0
$478$	13.5423	+	1.54420i	0.619411	+	0.0706299i
$479$	8.85381			0.404541			0.202270	−	0.979330i	$-0.435168\pi$
$479$	8.85381			0.404541			0.202270	+	0.979330i	$0.435168\pi$
$480$		0			0
$481$	9.06101			0.413146
$482$	−9.28385	−	1.05861i	−0.422868	−	0.0482186i
$483$		0			0
$484$	−11.5319	−	2.66455i	−0.524177	−	0.121116i
$485$	−52.8604			−2.40027
$486$		0			0
$487$		−	8.83371i		−	0.400293i	−0.979766	−	0.200147i	$-0.935858\pi$
$487$		−	8.83371i		−	0.400293i	0.979766	−	0.200147i	$-0.0641419\pi$
$488$	12.3050	−	34.7183i	0.557023	−	1.57162i
$489$		0			0
$490$	−23.1539	−	2.64019i	−1.04599	−	0.119272i
$491$		−	29.1663i		−	1.31626i	−0.752906	−	0.658128i	$-0.771349\pi$
$491$		−	29.1663i		−	1.31626i	0.752906	−	0.658128i	$-0.228651\pi$
$492$		0			0
$493$			16.2413i			0.731471i
$494$	1.19979	−	10.5219i	0.0539810	−	0.473403i
$495$		0			0
$496$	7.77246	−	15.9212i	0.348994	−	0.714884i
$497$			6.15564i			0.276118i
$498$		0			0
$499$	31.5806			1.41374			0.706870	−	0.707343i	$-0.250106\pi$
$499$	31.5806			1.41374			0.706870	+	0.707343i	$0.250106\pi$
$500$	−12.0086	−	2.77470i	−0.537041	−	0.124088i
$501$		0			0
$502$	−4.22726	+	37.0723i	−0.188672	+	1.65462i
$503$	−32.4054			−1.44488			−0.722442	−	0.691431i	$-0.756981\pi$
$503$	−32.4054			−1.44488			−0.722442	+	0.691431i	$0.756981\pi$
$504$		0			0
$505$	−6.10838			−0.271819
$506$	1.94821	−	17.0854i	0.0866083	−	0.759538i
$507$		0			0
$508$	−9.83705	+	42.5737i	−0.436449	+	1.88890i
$509$	7.52326			0.333463			0.166731	−	0.986002i	$-0.446679\pi$
$509$	7.52326			0.333463			0.166731	+	0.986002i	$0.446679\pi$
$510$		0			0
$511$		−	4.33128i		−	0.191605i
$512$	11.8070	+	19.3027i	0.521802	+	0.853067i
$513$		0			0
$514$	−1.99532	+	17.4986i	−0.0880100	+	0.771831i
$515$		−	0.569528i		−	0.0250964i
$516$		0			0
$517$		−	17.0965i		−	0.751905i
$518$	18.8919	+	2.15420i	0.830064	+	0.0946502i
$519$		0			0
$520$	−3.24498	+	9.15562i	−0.142302	+	0.401500i
$521$		−	12.4067i		−	0.543549i	−0.962361	−	0.271775i	$-0.912390\pi$
$521$		−	12.4067i		−	0.543549i	0.962361	−	0.271775i	$-0.0876105\pi$
$522$		0			0
$523$	18.9625			0.829174			0.414587	−	0.910010i	$-0.363926\pi$
$523$	18.9625			0.829174			0.414587	+	0.910010i	$0.363926\pi$
$524$	−1.38070	+	5.97551i	−0.0603161	+	0.261042i
$525$		0			0
$526$	−17.3097	−	1.97379i	−0.754740	−	0.0860612i
$527$	−29.1367			−1.26921
$528$		0			0
$529$	−14.2605			−0.620023
$530$	56.3500	+	6.42545i	2.44769	+	0.279104i
$531$		0			0
$532$	5.00304	−	21.6526i	0.216909	−	0.938760i
$533$	−2.36415			−0.102403
$534$		0			0
$535$		−	38.8011i		−	1.67752i
$536$	−14.2250	−	5.04169i	−0.614425	−	0.217768i
$537$		0			0
$538$	7.97887	+	0.909811i	0.343993	+	0.0392247i
$539$		−	19.7356i		−	0.850072i
$540$		0			0
$541$			18.2295i			0.783748i	0.920019	+	0.391874i	$0.128173\pi$
$541$			18.2295i			0.783748i	−0.920019	+	0.391874i	$0.871827\pi$
$542$	−3.93842	+	34.5392i	−0.169170	+	1.48359i
$543$		0			0
$544$	20.0082	−	31.3751i	0.857844	−	1.34520i
$545$		−	23.2040i		−	0.993949i
$546$		0			0
$547$	24.0359			1.02770			0.513849	−	0.857880i	$-0.328219\pi$
$547$	24.0359			1.02770			0.513849	+	0.857880i	$0.328219\pi$
$548$	5.63987	−	24.4087i	0.240923	−	1.04269i
$549$		0			0
$550$	4.47758	−	39.2675i	0.190925	−	1.67437i
$551$	−18.4884			−0.787630
$552$		0			0
$553$	−8.92140			−0.379376
$554$	4.02850	−	35.3292i	0.171155	−	1.50099i
$555$		0			0
$556$	−12.3549	−	2.85472i	−0.523966	−	0.121067i
$557$	26.7567			1.13372			0.566859	−	0.823815i	$-0.308158\pi$
$557$	26.7567			1.13372			0.566859	+	0.823815i	$0.308158\pi$
$558$		0			0
$559$			11.0152i			0.465893i
$560$	−8.94238	+	18.3177i	−0.377885	+	0.774065i
$561$		0			0
$562$	−0.278757	+	2.44464i	−0.0117587	+	0.103121i
$563$		−	13.2621i		−	0.558932i	−0.960156	−	0.279466i	$-0.909843\pi$
$563$		−	13.2621i		−	0.558932i	0.960156	−	0.279466i	$-0.0901574\pi$
$564$		0			0
$565$		−	37.0580i		−	1.55904i
$566$	−46.3440	−	5.28449i	−1.94798	−	0.222124i
$567$		0			0
$568$	−11.0594	−	3.91974i	−0.464043	−	0.164469i
$569$			27.8794i			1.16877i	0.811478	+	0.584383i	$0.198663\pi$
$569$			27.8794i			1.16877i	−0.811478	+	0.584383i	$0.801337\pi$
$570$		0			0
$571$	26.2805			1.09981			0.549903	−	0.835229i	$-0.314665\pi$
$571$	26.2805			1.09981			0.549903	+	0.835229i	$0.314665\pi$
$572$	−8.01509	−	1.85196i	−0.335128	−	0.0774344i
$573$		0			0
$574$	−4.92917	−	0.562062i	−0.205740	−	0.0234600i
$575$	20.0860			0.837644
$576$		0			0
$577$	−14.5803			−0.606986			−0.303493	−	0.952834i	$-0.598153\pi$
$577$	−14.5803			−0.606986			−0.303493	+	0.952834i	$0.598153\pi$
$578$	−36.9159	−	4.20943i	−1.53550	−	0.175089i
$579$		0			0
$580$	16.5229	+	3.81778i	0.686078	+	0.158525i
$581$	−10.8511			−0.450180
$582$		0			0
$583$			48.0307i			1.98923i
$584$	7.78172	+	2.75804i	0.322010	+	0.114128i
$585$		0			0
$586$	17.8484	+	2.03521i	0.737312	+	0.0840739i
$587$			6.62727i			0.273537i	0.990603	+	0.136768i	$0.0436716\pi$
$587$			6.62727i			0.273537i	−0.990603	+	0.136768i	$0.956328\pi$
$588$		0			0
$589$		−	33.1679i		−	1.36666i
$590$	5.31534	−	46.6145i	0.218829	−	1.91909i
$591$		0			0
$592$	−15.9002	+	32.5702i	−0.653493	+	1.33862i
$593$			31.2980i			1.28525i	0.766179	+	0.642627i	$0.222155\pi$
$593$			31.2980i			1.28525i	−0.766179	+	0.642627i	$0.777845\pi$
$594$		0			0
$595$	33.5224			1.37428
$596$	23.1771	+	5.35530i	0.949372	+	0.219361i
$597$		0			0
$598$	0.473655	−	4.15386i	0.0193692	−	0.169864i
$599$	23.5010			0.960225			0.480113	−	0.877207i	$-0.340596\pi$
$599$	23.5010			0.960225			0.480113	+	0.877207i	$0.340596\pi$
$600$		0			0
$601$	−7.71826			−0.314834			−0.157417	−	0.987532i	$-0.550317\pi$
$601$	−7.71826			−0.314834			−0.157417	+	0.987532i	$0.550317\pi$
$602$	−2.61880	+	22.9664i	−0.106734	+	0.936039i
$603$		0			0
$604$	−4.84707	+	20.9776i	−0.197225	+	0.853566i
$605$	20.3237			0.826275
$606$		0			0
$607$		−	40.1656i		−	1.63027i	−0.579270	−	0.815136i	$-0.696662\pi$
$607$		−	40.1656i		−	1.63027i	0.579270	−	0.815136i	$-0.303338\pi$
$608$	35.7160	+	22.7764i	1.44848	+	0.923706i
$609$		0			0
$610$	−7.16583	+	62.8429i	−0.290136	+	2.54443i
$611$		−	4.15658i		−	0.168157i
$612$		0			0
$613$			6.53797i			0.264066i	0.991245	+	0.132033i	$0.0421505\pi$
$613$			6.53797i			0.264066i	−0.991245	+	0.132033i	$0.957850\pi$
$614$	−5.82724	−	0.664466i	−0.235168	−	0.0268157i
$615$		0			0
$616$	−16.2709	−	5.76683i	−0.655575	−	0.232352i
$617$		−	15.2512i		−	0.613991i	−0.951711	−	0.306996i	$-0.900676\pi$
$617$		−	15.2512i		−	0.613991i	0.951711	−	0.306996i	$-0.0993237\pi$
$618$		0			0
$619$	15.8477			0.636973			0.318486	−	0.947927i	$-0.396826\pi$
$619$	15.8477			0.636973			0.318486	+	0.947927i	$0.396826\pi$
$620$	−6.84905	+	29.6419i	−0.275065	+	1.19045i
$621$		0			0
$622$	19.4675	+	2.21983i	0.780576	+	0.0890072i
$623$	2.90445			0.116364
$624$		0			0
$625$	−12.8081			−0.512326
$626$	−38.7592	−	4.41962i	−1.54913	−	0.176644i
$627$		0			0
$628$	2.80726	−	12.1495i	0.112022	−	0.484818i
$629$	59.6051			2.37661
$630$		0			0
$631$			30.2794i			1.20540i	0.797967	+	0.602701i	$0.205909\pi$
$631$			30.2794i			1.20540i	−0.797967	+	0.602701i	$0.794091\pi$
$632$	5.68090	−	16.0285i	0.225974	−	0.637579i
$633$		0			0
$634$	−7.63206	−	0.870265i	−0.303108	−	0.0345627i
$635$		−	75.0314i		−	2.97753i
$636$		0			0
$637$		−	4.79819i		−	0.190111i
$638$	−1.62707	+	14.2691i	−0.0644163	+	0.564918i
$639$		0			0
$640$	−27.2160	−	27.7304i	−1.07581	−	1.09614i
$641$		−	7.03695i		−	0.277943i	−0.990296	−	0.138971i	$-0.955620\pi$
$641$		−	7.03695i		−	0.277943i	0.990296	−	0.138971i	$-0.0443796\pi$
$642$		0			0
$643$	−5.27680			−0.208097			−0.104048	−	0.994572i	$-0.533180\pi$
$643$	−5.27680			−0.208097			−0.104048	+	0.994572i	$0.533180\pi$
$644$	1.97511	−	8.54807i	0.0778304	−	0.336841i
$645$		0			0
$646$	7.89244	−	69.2151i	0.310524	−	2.72323i
$647$	−9.40269			−0.369658			−0.184829	−	0.982771i	$-0.559173\pi$
$647$	−9.40269			−0.369658			−0.184829	+	0.982771i	$0.559173\pi$
$648$		0			0
$649$	39.7325			1.55964
$650$	1.08861	−	9.54686i	0.0426986	−	0.374459i
$651$		0			0
$652$	20.1697	+	4.66040i	0.789906	+	0.182515i
$653$	−21.0712			−0.824578			−0.412289	−	0.911053i	$-0.635271\pi$
$653$	−21.0712			−0.824578			−0.412289	+	0.911053i	$0.635271\pi$
$654$		0			0
$655$		−	10.5312i		−	0.411488i
$656$	4.14858	−	8.49802i	0.161975	−	0.331792i
$657$		0			0
$658$	0.988202	−	8.66634i	0.0385241	−	0.337849i
$659$		−	18.4813i		−	0.719930i	−0.932966	−	0.359965i	$-0.882789\pi$
$659$		−	18.4813i		−	0.719930i	0.932966	−	0.359965i	$-0.117211\pi$
$660$		0			0
$661$		−	8.57840i		−	0.333661i	−0.985986	−	0.166831i	$-0.946647\pi$
$661$		−	8.57840i		−	0.333661i	0.985986	−	0.166831i	$-0.0533533\pi$
$662$	2.56368	+	0.292331i	0.0996403	+	0.0113617i
$663$		0			0
$664$	6.90968	−	19.4955i	0.268148	−	0.756571i
$665$			38.1604i			1.47980i
$666$		0			0
$667$	−7.29888			−0.282614
$668$	7.61821	+	1.76026i	0.294757	+	0.0681065i
$669$		0			0
$670$	25.7483	+	2.93602i	0.994745	+	0.113428i
$671$	−53.5650			−2.06785
$672$		0			0
$673$	−1.55751			−0.0600376			−0.0300188	−	0.999549i	$-0.509557\pi$
$673$	−1.55751			−0.0600376			−0.0300188	+	0.999549i	$0.509557\pi$
$674$	−1.01798	−	0.116078i	−0.0392111	−	0.00447115i
$675$		0			0
$676$	−1.94866	−	0.450256i	−0.0749484	−	0.0173175i
$677$	27.1384			1.04301			0.521507	−	0.853247i	$-0.325370\pi$
$677$	27.1384			1.04301			0.521507	+	0.853247i	$0.325370\pi$
$678$		0			0
$679$		−	22.8393i		−	0.876492i
$680$	−21.3461	+	60.2274i	−0.818586	+	2.30962i
$681$		0			0
$682$	−25.5986	−	2.91894i	−0.980220	−	0.111772i
$683$		−	6.05171i		−	0.231562i	−0.993275	−	0.115781i	$-0.963063\pi$
$683$		−	6.05171i		−	0.231562i	0.993275	−	0.115781i	$-0.0369371\pi$
$684$		0			0
$685$			43.0177i			1.64362i
$686$	2.80495	−	24.5989i	0.107094	−	0.939189i
$687$		0			0
$688$	−39.5945	−	19.3294i	−1.50953	−	0.736925i
$689$			11.6774i			0.444873i
$690$		0			0
$691$	−34.4081			−1.30895			−0.654473	−	0.756085i	$-0.727110\pi$
$691$	−34.4081			−1.30895			−0.654473	+	0.756085i	$0.727110\pi$
$692$	21.5472	+	4.97868i	0.819102	+	0.189261i
$693$		0			0
$694$	3.40437	−	29.8557i	0.129228	−	1.13331i
$695$	21.7742			0.825943
$696$		0			0
$697$	−15.5518			−0.589067
$698$	2.38035	−	20.8752i	0.0900974	−	0.790137i
$699$		0			0
$700$	4.53942	−	19.6461i	0.171574	−	0.742554i
$701$	49.7859			1.88039			0.940193	−	0.340642i	$-0.110644\pi$
$701$	49.7859			1.88039			0.940193	+	0.340642i	$0.110644\pi$
$702$		0			0
$703$			67.8518i			2.55908i
$704$	20.7218	−	25.5607i	0.780980	−	0.963357i
$705$		0			0
$706$	0.671917	−	5.89258i	0.0252879	−	0.221770i
$707$		−	2.63924i		−	0.0992587i
$708$		0			0
$709$		−	11.9217i		−	0.447727i	−0.974620	−	0.223864i	$-0.928133\pi$
$709$		−	11.9217i		−	0.447727i	0.974620	−	0.223864i	$-0.0718670\pi$
$710$	20.0185	+	2.28266i	0.751279	+	0.0856666i
$711$		0			0
$712$	−1.84947	+	5.21823i	−0.0693118	+	0.195561i
$713$		−	13.0941i		−	0.490378i
$714$		0			0
$715$	14.1257			0.528272
$716$	1.38072	−	5.97562i	0.0516001	−	0.223319i
$717$		0			0
$718$	29.5080	+	3.36472i	1.10123	+	0.125570i
$719$	−12.0486			−0.449336			−0.224668	−	0.974435i	$-0.572130\pi$
$719$	−12.0486			−0.449336			−0.224668	+	0.974435i	$0.572130\pi$
$720$		0			0
$721$	0.246075			0.00916431
$722$	52.0944	+	5.94019i	1.93875	+	0.221071i
$723$		0			0
$724$	7.10036	−	30.7296i	0.263883	−	1.14206i
$725$	−16.7751			−0.623011
$726$		0			0
$727$			32.1438i			1.19215i	0.802929	+	0.596074i	$0.203274\pi$
$727$			32.1438i			1.19215i	−0.802929	+	0.596074i	$0.796726\pi$
$728$	−3.95585	−	1.40205i	−0.146614	−	0.0519635i
$729$		0			0
$730$	−14.0856	−	1.60614i	−0.521330	−	0.0594460i
$731$			72.4601i			2.68003i
$732$		0			0
$733$		−	9.56968i		−	0.353464i	−0.984259	−	0.176732i	$-0.943447\pi$
$733$		−	9.56968i		−	0.353464i	0.984259	−	0.176732i	$-0.0565526\pi$
$734$	2.62065	−	22.9826i	0.0967298	−	0.848302i
$735$		0			0
$736$	14.1001	+	8.99173i	0.519735	+	0.331440i
$737$			21.9470i			0.808426i
$738$		0			0
$739$	−42.5861			−1.56656			−0.783278	−	0.621672i	$-0.786454\pi$
$739$	−42.5861			−1.56656			−0.783278	+	0.621672i	$0.786454\pi$
$740$	14.0112	−	60.6387i	0.515060	−	2.22912i
$741$		0			0
$742$	−2.77623	+	24.3470i	−0.101919	+	0.893808i
$743$	6.02679			0.221101			0.110551	−	0.993870i	$-0.464739\pi$
$743$	6.02679			0.221101			0.110551	+	0.993870i	$0.464739\pi$
$744$		0			0
$745$	−40.8472			−1.49652
$746$	−2.84481	+	24.9484i	−0.104156	+	0.913426i
$747$		0			0
$748$	−52.7248	−	12.1826i	−1.92781	−	0.445439i
$749$	16.7647			0.612570
$750$		0			0
$751$			29.2953i			1.06900i	0.845168	+	0.534501i	$0.179500\pi$
$751$			29.2953i			1.06900i	−0.845168	+	0.534501i	$0.820500\pi$
$752$	14.9410	+	7.29392i	0.544841	+	0.265982i
$753$		0			0
$754$	−0.395579	+	3.46915i	−0.0144061	+	0.126339i
$755$		−	36.9707i		−	1.34550i
$756$		0			0
$757$		−	34.8134i		−	1.26532i	−0.774431	−	0.632658i	$-0.781964\pi$
$757$		−	34.8134i		−	1.26532i	0.774431	−	0.632658i	$-0.218036\pi$
$758$	−14.2451	−	1.62433i	−0.517404	−	0.0589983i
$759$		0			0
$760$	−68.5602	−	24.2995i	−2.48694	−	0.881434i
$761$			17.7411i			0.643114i	0.946890	+	0.321557i	$0.104206\pi$
$761$			17.7411i			0.643114i	−0.946890	+	0.321557i	$0.895794\pi$
$762$		0			0
$763$	10.0257			0.362955
$764$	−21.5892	−	4.98839i	−0.781069	−	0.180473i
$765$		0			0
$766$	12.9993	+	1.48228i	0.469685	+	0.0535570i
$767$	9.65991			0.348799
$768$		0			0
$769$	14.2239			0.512928			0.256464	−	0.966554i	$-0.417443\pi$
$769$	14.2239			0.512928			0.256464	+	0.966554i	$0.417443\pi$
$770$	29.4517	+	3.35831i	1.06137	+	0.121025i
$771$		0			0
$772$	14.8528	+	3.43189i	0.534565	+	0.123516i
$773$	−46.4252			−1.66980			−0.834899	−	0.550403i	$-0.814474\pi$
$773$	−46.4252			−1.66980			−0.834899	+	0.550403i	$0.814474\pi$
$774$		0			0
$775$		−	30.0943i		−	1.08102i
$776$	41.0339	+	14.5434i	1.47303	+	0.522079i
$777$		0			0
$778$	35.5352	+	4.05199i	1.27400	+	0.145271i
$779$		−	17.7035i		−	0.634293i
$780$		0			0
$781$			17.0630i			0.610562i
$782$	3.11580	−	27.3249i	0.111421	−	0.977137i
$783$		0			0
$784$	17.2473	+	8.41981i	0.615974	+	0.300708i
$785$			21.4122i			0.764233i
$786$		0			0
$787$	−9.64648			−0.343860			−0.171930	−	0.985109i	$-0.555000\pi$
$787$	−9.64648			−0.343860			−0.171930	+	0.985109i	$0.555000\pi$
$788$	46.8073	+	10.8153i	1.66744	+	0.385278i
$789$		0			0
$790$	−3.30826	+	29.0128i	−0.117703	+	1.03223i
$791$	16.0116			0.569306
$792$		0			0
$793$	−13.0229			−0.462458
$794$	−2.52988	+	22.1866i	−0.0897821	+	0.787372i
$795$		0			0
$796$	4.22106	−	18.2683i	0.149612	−	0.647503i
$797$	−12.0174			−0.425677			−0.212839	−	0.977087i	$-0.568271\pi$
$797$	−12.0174			−0.425677			−0.212839	+	0.977087i	$0.568271\pi$
$798$		0			0
$799$		−	27.3428i		−	0.967318i
$800$	32.4063	+	20.6658i	1.14574	+	0.730646i
$801$		0			0
$802$	1.72980	−	15.1700i	0.0610812	−	0.535670i
$803$		−	12.0060i		−	0.423683i
$804$		0			0
$805$			15.0650i			0.530973i
$806$	−6.22362	−	0.709664i	−0.219218	−	0.0249969i
$807$		0			0
$808$	4.74174	+	1.68059i	0.166814	+	0.0591230i
$809$		−	13.3426i		−	0.469102i	−0.972104	−	0.234551i	$-0.924638\pi$
$809$		−	13.3426i		−	0.469102i	0.972104	−	0.234551i	$-0.0753620\pi$
$810$		0			0
$811$	−11.5782			−0.406565			−0.203283	−	0.979120i	$-0.565161\pi$
$811$	−11.5782			−0.406565			−0.203283	+	0.979120i	$0.565161\pi$
$812$	−1.64954	+	7.13903i	−0.0578876	+	0.250531i
$813$		0			0
$814$	52.3672	+	5.97130i	1.83547	+	0.209294i
$815$	−35.5469			−1.24515
$816$		0			0
$817$	−82.4853			−2.88580
$818$	−37.3897	−	4.26346i	−1.30730	−	0.149068i
$819$		0			0
$820$	−3.65571	+	15.8215i	−0.127663	+	0.552511i
$821$	−34.6761			−1.21020			−0.605102	−	0.796148i	$-0.706868\pi$
$821$	−34.6761			−1.21020			−0.605102	+	0.796148i	$0.706868\pi$
$822$		0			0
$823$			11.4656i			0.399666i	0.979830	+	0.199833i	$0.0640399\pi$
$823$			11.4656i			0.399666i	−0.979830	+	0.199833i	$0.935960\pi$
$824$	−0.156694	+	0.442107i	−0.00545868	+	0.0154015i
$825$		0			0
$826$	20.1406	+	2.29659i	0.700782	+	0.0799085i
$827$			31.3392i			1.08977i	0.838511	+	0.544885i	$0.183427\pi$
$827$			31.3392i			1.08977i	−0.838511	+	0.544885i	$0.816573\pi$
$828$		0			0
$829$		−	51.7029i		−	1.79572i	−0.440284	−	0.897859i	$-0.645122\pi$
$829$		−	51.7029i		−	1.79572i	0.440284	−	0.897859i	$-0.354878\pi$
$830$	−4.02385	+	35.2884i	−0.139670	+	1.22488i
$831$		0			0
$832$	5.03795	−	6.21442i	0.174659	−	0.215446i
$833$		−	31.5634i		−	1.09361i
$834$		0			0
$835$	−13.4263			−0.464635
$836$	13.8681	−	60.0196i	0.479638	−	2.07582i
$837$		0			0
$838$	1.08865	−	9.54728i	0.0376069	−	0.329805i
$839$	−44.6953			−1.54305			−0.771526	−	0.636198i	$-0.780506\pi$
$839$	−44.6953			−1.54305			−0.771526	+	0.636198i	$0.780506\pi$
$840$		0			0
$841$	−22.9042			−0.789802
$842$	−0.255053	+	2.23677i	−0.00878971	+	0.0770840i
$843$		0			0
$844$	5.55815	+	1.28426i	0.191319	+	0.0442062i
$845$	3.43430			0.118143
$846$		0			0
$847$			8.78122i			0.301726i
$848$	−41.9749	−	20.4914i	−1.44142	−	0.703677i
$849$		0			0
$850$	7.16106	−	62.8011i	0.245622	−	2.15406i
$851$			26.7867i			0.918236i
$852$		0			0
$853$		−	19.0904i		−	0.653642i	−0.945086	−	0.326821i	$-0.894022\pi$
$853$		−	19.0904i		−	0.653642i	0.945086	−	0.326821i	$-0.105978\pi$
$854$	−27.1524	−	3.09612i	−0.929137	−	0.105947i
$855$		0			0
$856$	−10.6753	+	30.1201i	−0.364875	+	1.02948i
$857$			55.8671i			1.90839i	0.299193	+	0.954193i	$0.403283\pi$
$857$			55.8671i			1.90839i	−0.299193	+	0.954193i	$0.596717\pi$
$858$		0			0
$859$	−9.28709			−0.316871			−0.158436	−	0.987369i	$-0.550645\pi$
$859$	−9.28709			−0.316871			−0.158436	+	0.987369i	$0.550645\pi$
$860$	73.7167	+	17.0329i	2.51372	+	0.580818i
$861$		0			0
$862$	−22.7704	−	2.59646i	−0.775563	−	0.0884356i
$863$	−49.0184			−1.66860			−0.834302	−	0.551307i	$-0.814129\pi$
$863$	−49.0184			−1.66860			−0.834302	+	0.551307i	$0.814129\pi$
$864$		0			0
$865$	−37.9746			−1.29117
$866$	18.2956	+	2.08621i	0.621711	+	0.0708922i
$867$		0			0
$868$	−12.8073	−	2.95926i	−0.434710	−	0.100444i
$869$	−24.7295			−0.838891
$870$		0			0
$871$			5.33582i			0.180798i
$872$	−6.38408	+	18.0125i	−0.216192	+	0.609980i
$873$		0			0
$874$	31.1055	+	3.54688i	1.05216	+	0.119975i
$875$			9.14422i			0.309131i
$876$		0			0
$877$			20.8671i			0.704631i	0.935881	+	0.352316i	$0.114606\pi$
$877$			20.8671i			0.704631i	−0.935881	+	0.352316i	$0.885394\pi$
$878$	3.87584	−	33.9904i	0.130803	−	1.14712i
$879$		0			0
$880$	−24.7877	+	50.7755i	−0.835592	+	1.71164i
$881$		−	7.48262i		−	0.252096i	−0.992024	−	0.126048i	$-0.959771\pi$
$881$		−	7.48262i		−	0.252096i	0.992024	−	0.126048i	$-0.0402293\pi$
$882$		0			0
$883$	58.6643			1.97421			0.987105	−	0.160071i	$-0.0511724\pi$
$883$	58.6643			1.97421			0.987105	+	0.160071i	$0.0511724\pi$
$884$	−12.8187	−	2.96187i	−0.431138	−	0.0996185i
$885$		0			0
$886$	−3.29907	+	28.9322i	−0.110834	+	0.971996i
$887$	32.5991			1.09457			0.547285	−	0.836947i	$-0.315662\pi$
$887$	32.5991			1.09457			0.547285	+	0.836947i	$0.315662\pi$
$888$		0			0
$889$	32.4187			1.08729
$890$	1.07704	−	9.44541i	0.0361024	−	0.316611i
$891$		0			0
$892$	−5.47025	+	23.6747i	−0.183158	+	0.792686i
$893$	31.1258			1.04158
$894$		0			0
$895$			10.5314i			0.352025i
$896$	11.9814	−	11.7591i	0.400271	−	0.392846i
$897$		0			0
$898$	6.46365	−	56.6850i	0.215695	−	1.89160i
$899$			10.9357i			0.364726i
$900$		0			0
$901$			76.8162i			2.55912i
$902$	−13.6633	−	1.55800i	−0.454939	−	0.0518756i
$903$		0			0
$904$	−10.1957	+	28.7670i	−0.339105	+	0.956775i
$905$			54.1575i			1.80026i
$906$		0			0
$907$	−27.7859			−0.922615			−0.461308	−	0.887240i	$-0.652620\pi$
$907$	−27.7859			−0.922615			−0.461308	+	0.887240i	$0.652620\pi$
$908$	−13.0399	+	56.4355i	−0.432746	+	1.87288i
$909$		0			0
$910$	7.16041	+	0.816484i	0.237365	+	0.0270662i
$911$	−35.8904			−1.18910			−0.594551	−	0.804058i	$-0.702670\pi$
$911$	−35.8904			−1.18910			−0.594551	+	0.804058i	$0.702670\pi$
$912$		0			0
$913$	−30.0785			−0.995454
$914$	−11.0520	−	1.26023i	−0.365567	−	0.0416847i
$915$		0			0
$916$	−3.52664	+	15.2629i	−0.116524	+	0.504301i
$917$	4.55019			0.150261
$918$		0			0
$919$		−	10.5323i		−	0.347429i	−0.984796	−	0.173715i	$-0.944423\pi$
$919$		−	10.5323i		−	0.347429i	0.984796	−	0.173715i	$-0.0555770\pi$
$920$	−27.0664	−	9.59300i	−0.892352	−	0.316272i
$921$		0			0
$922$	−32.2638	−	3.67897i	−1.06255	−	0.121160i
$923$			4.14842i			0.136547i
$924$		0			0
$925$			61.5641i			2.02422i
$926$	1.61205	−	14.1374i	0.0529754	−	0.464584i
$927$		0			0
$928$	−11.7758	−	7.50956i	−0.386561	−	0.246513i
$929$			27.6997i			0.908799i	0.890798	+	0.454400i	$0.150146\pi$
$929$			27.6997i			0.908799i	−0.890798	+	0.454400i	$0.849854\pi$
$930$		0			0
$931$	35.9304			1.17757
$932$	−9.53356	+	41.2602i	−0.312282	+	1.35152i
$933$		0			0
$934$	−3.43296	+	30.1064i	−0.112330	+	0.985110i
$935$	92.9217			3.03887
$936$		0			0
$937$	−42.5811			−1.39106			−0.695532	−	0.718495i	$-0.744831\pi$
$937$	−42.5811			−1.39106			−0.695532	+	0.718495i	$0.744831\pi$
$938$	−1.26856	+	11.1250i	−0.0414200	+	0.363245i
$939$		0			0
$940$	−27.8169	−	6.42737i	−0.907288	−	0.209638i
$941$	21.1059			0.688033			0.344017	−	0.938964i	$-0.388212\pi$
$941$	21.1059			0.688033			0.344017	+	0.938964i	$0.388212\pi$
$942$		0			0
$943$		−	6.98903i		−	0.227594i
$944$	−16.9511	+	34.7229i	−0.551712	+	1.13014i
$945$		0			0
$946$	−7.25913	+	63.6612i	−0.236015	+	2.06980i
$947$			31.1667i			1.01278i	0.862304	+	0.506391i	$0.169021\pi$
$947$			31.1667i			1.01278i	−0.862304	+	0.506391i	$0.830979\pi$
$948$		0			0
$949$		−	2.91895i		−	0.0947530i
$950$	71.4900	+	8.15183i	2.31944	+	0.264480i
$951$		0			0
$952$	−26.0224	−	9.22298i	−0.843389	−	0.298918i
$953$			10.0942i			0.326984i	0.986545	+	0.163492i	$0.0522759\pi$
$953$			10.0942i			0.326984i	−0.986545	+	0.163492i	$0.947724\pi$
$954$		0			0
$955$	38.0486			1.23122
$956$	18.7810	+	4.33953i	0.607421	+	0.140350i
$957$		0			0
$958$	12.4406	+	1.41857i	0.401936	+	0.0458318i
$959$	−18.5866			−0.600192
$960$		0			0
$961$	11.3815			0.367144
$962$	12.7317	+	1.45176i	0.410486	+	0.0468068i
$963$		0			0
$964$	−12.8752	−	2.97494i	−0.414682	−	0.0958162i
$965$	−26.1765			−0.842651
$966$		0			0
$967$			43.6067i			1.40230i	0.713015	+	0.701149i	$0.247329\pi$
$967$			43.6067i			1.40230i	−0.713015	+	0.701149i	$0.752671\pi$
$968$	−15.7766	−	5.59163i	−0.507080	−	0.179722i
$969$		0			0
$970$	−74.2746	−	8.46935i	−2.38481	−	0.271935i
$971$		−	32.6183i		−	1.04677i	−0.852096	−	0.523386i	$-0.824669\pi$
$971$		−	32.6183i		−	1.04677i	0.852096	−	0.523386i	$-0.175331\pi$
$972$		0			0
$973$			9.40795i			0.301605i
$974$	1.41535	−	12.4123i	0.0453506	−	0.397716i
$975$		0			0
$976$	22.8525	−	46.8114i	0.731491	−	1.49840i
$977$			18.8377i			0.602672i	0.953518	+	0.301336i	$0.0974326\pi$
$977$			18.8377i			0.602672i	−0.953518	+	0.301336i	$0.902567\pi$
$978$		0			0
$979$	8.05093			0.257309
$980$	−32.1108	−	7.41950i	−1.02574	−	0.237007i
$981$		0			0
$982$	4.67305	−	40.9818i	0.149123	−	1.30778i
$983$	30.7835			0.981841			0.490920	−	0.871204i	$-0.336661\pi$
$983$	30.7835			0.981841			0.490920	+	0.871204i	$0.336661\pi$
$984$		0			0
$985$	−82.4928			−2.62844
$986$	−2.60220	+	22.8208i	−0.0828708	+	0.726761i
$987$		0			0
$988$	3.37166	−	14.5922i	0.107267	−	0.464239i
$989$	−32.5638			−1.03547
$990$		0			0
$991$			54.0367i			1.71653i	0.513206	+	0.858265i	$0.328458\pi$
$991$			54.0367i			1.71653i	−0.513206	+	0.858265i	$0.671542\pi$
$992$	13.4721	−	21.1257i	0.427738	−	0.670742i
$993$		0			0
$994$	−0.986263	+	8.64934i	−0.0312824	+	0.274340i
$995$			32.1959i			1.02068i
$996$		0			0
$997$			55.9698i			1.77258i	0.463130	+	0.886290i	$0.346726\pi$
$997$			55.9698i			1.77258i	−0.463130	+	0.886290i	$0.653274\pi$
$998$	44.3741	+	5.05987i	1.40464	+	0.160168i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.j.a.755.48	yes	48
3.2	odd	2	inner	936.2.j.a.755.1	✓	48
4.3	odd	2		3744.2.j.a.2159.5		48
8.3	odd	2	inner	936.2.j.a.755.2	yes	48
8.5	even	2		3744.2.j.a.2159.44		48
12.11	even	2		3744.2.j.a.2159.43		48
24.5	odd	2		3744.2.j.a.2159.6		48
24.11	even	2	inner	936.2.j.a.755.47	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.j.a.755.1	✓	48	3.2	odd	2	inner
936.2.j.a.755.2	yes	48	8.3	odd	2	inner
936.2.j.a.755.47	yes	48	24.11	even	2	inner
936.2.j.a.755.48	yes	48	1.1	even	1	trivial
3744.2.j.a.2159.5		48	4.3	odd	2
3744.2.j.a.2159.6		48	24.5	odd	2
3744.2.j.a.2159.43		48	12.11	even	2
3744.2.j.a.2159.44		48	8.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40511 + 0.160221i) q^{2} +(1.94866 + 0.450256i) q^{4} -3.43430 q^{5} -1.48385i q^{7} +(2.66594 + 0.944875i) q^{8} +(-4.82556 - 0.550247i) q^{10} -4.11313i q^{11} -1.00000i q^{13} +(0.237744 - 2.08497i) q^{14} +(3.59454 + 1.75479i) q^{16} -6.57820i q^{17} +7.48832 q^{19} +(-6.69227 - 1.54631i) q^{20} +(0.659011 - 5.77940i) q^{22} +2.95626 q^{23} +6.79440 q^{25} +(0.160221 - 1.40511i) q^{26} +(0.668113 - 2.89152i) q^{28} -2.46896 q^{29} -4.42928i q^{31} +(4.76956 + 3.04159i) q^{32} +(1.05397 - 9.24308i) q^{34} +5.09598i q^{35} +9.06101i q^{37} +(10.5219 + 1.19979i) q^{38} +(-9.15562 - 3.24498i) q^{40} -2.36415i q^{41} -11.0152 q^{43} +(1.85196 - 8.01509i) q^{44} +(4.15386 + 0.473655i) q^{46} +4.15658 q^{47} +4.79819 q^{49} +(9.54686 + 1.08861i) q^{50} +(0.450256 - 1.94866i) q^{52} -11.6774 q^{53} +14.1257i q^{55} +(1.40205 - 3.95585i) q^{56} +(-3.46915 - 0.395579i) q^{58} +9.65991i q^{59} -13.0229i q^{61} +(0.709664 - 6.22362i) q^{62} +(6.21442 + 5.03795i) q^{64} +3.43430i q^{65} -5.33582 q^{67} +(2.96187 - 12.8187i) q^{68} +(-0.816484 + 7.16041i) q^{70} -4.14842 q^{71} +2.91895 q^{73} +(-1.45176 + 12.7317i) q^{74} +(14.5922 + 3.37166i) q^{76} -6.10327 q^{77} -6.01233i q^{79} +(-12.3447 - 6.02647i) q^{80} +(0.378786 - 3.32188i) q^{82} -7.31280i q^{83} +22.5915i q^{85} +(-15.4775 - 1.76487i) q^{86} +(3.88639 - 10.9653i) q^{88} +1.95737i q^{89} -1.48385 q^{91} +(5.76074 + 1.33107i) q^{92} +(5.84044 + 0.665971i) q^{94} -25.7171 q^{95} +15.3919 q^{97} +(6.74197 + 0.768771i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) \) 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Introduction

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