LMFDB - Embedded newform 731.2.d.d.560.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(560,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.560");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			560.1
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79374 q^{2} -1.46205i q^{3} +5.80499 q^{4} -1.65611i q^{5} +4.08460i q^{6} +2.54474i q^{7} -10.6302 q^{8} +0.862404 q^{9} +O(q^{10})$	\(q-2.79374 q^{2} -1.46205i q^{3} +5.80499 q^{4} -1.65611i q^{5} +4.08460i q^{6} +2.54474i q^{7} -10.6302 q^{8} +0.862404 q^{9} +4.62675i q^{10} +3.40942i q^{11} -8.48720i q^{12} -3.78460 q^{13} -7.10934i q^{14} -2.42132 q^{15} +18.0879 q^{16} +(1.31248 - 3.90863i) q^{17} -2.40933 q^{18} -0.391596 q^{19} -9.61372i q^{20} +3.72054 q^{21} -9.52504i q^{22} -6.71034i q^{23} +15.5419i q^{24} +2.25729 q^{25} +10.5732 q^{26} -5.64704i q^{27} +14.7722i q^{28} -3.12547i q^{29} +6.76455 q^{30} +4.70114i q^{31} -29.2727 q^{32} +4.98475 q^{33} +(-3.66672 + 10.9197i) q^{34} +4.21437 q^{35} +5.00625 q^{36} -6.05175i q^{37} +1.09402 q^{38} +5.53328i q^{39} +17.6047i q^{40} -4.77526i q^{41} -10.3942 q^{42} -1.00000 q^{43} +19.7917i q^{44} -1.42824i q^{45} +18.7469i q^{46} +3.54294 q^{47} -26.4455i q^{48} +0.524308 q^{49} -6.30629 q^{50} +(-5.71462 - 1.91891i) q^{51} -21.9696 q^{52} +10.1812 q^{53} +15.7764i q^{54} +5.64638 q^{55} -27.0510i q^{56} +0.572534i q^{57} +8.73175i q^{58} -12.1593 q^{59} -14.0558 q^{60} -4.63742i q^{61} -13.1338i q^{62} +2.19459i q^{63} +45.6045 q^{64} +6.26772i q^{65} -13.9261 q^{66} +7.31570 q^{67} +(7.61891 - 22.6896i) q^{68} -9.81086 q^{69} -11.7739 q^{70} -10.2675i q^{71} -9.16750 q^{72} -5.85190i q^{73} +16.9070i q^{74} -3.30028i q^{75} -2.27321 q^{76} -8.67608 q^{77} -15.4586i q^{78} -14.7632i q^{79} -29.9557i q^{80} -5.66905 q^{81} +13.3409i q^{82} -7.29952 q^{83} +21.5977 q^{84} +(-6.47313 - 2.17361i) q^{85} +2.79374 q^{86} -4.56960 q^{87} -36.2427i q^{88} -5.50827 q^{89} +3.99013i q^{90} -9.63082i q^{91} -38.9534i q^{92} +6.87331 q^{93} -9.89805 q^{94} +0.648527i q^{95} +42.7982i q^{96} -1.97083i q^{97} -1.46478 q^{98} +2.94030i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$1$

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 $

$2$	−2.79374			−1.97547			−0.987737	−	0.156128i	$-0.950099\pi$
$2$	−2.79374			−1.97547			−0.987737	+	0.156128i	$0.950099\pi$
$3$		−	1.46205i		−	0.844116i	−0.906569	−	0.422058i	$-0.861308\pi$
$3$		−	1.46205i		−	0.844116i	0.906569	−	0.422058i	$-0.138692\pi$
$4$	5.80499			2.90250
$5$		−	1.65611i		−	0.740636i	−0.928905	−	0.370318i	$-0.879249\pi$
$5$		−	1.65611i		−	0.740636i	0.928905	−	0.370318i	$-0.120751\pi$
$6$			4.08460i			1.66753i
$7$			2.54474i			0.961821i	0.876770	+	0.480910i	$0.159694\pi$
$7$			2.54474i			0.961821i	−0.876770	+	0.480910i	$0.840306\pi$
$8$	−10.6302			−3.75833
$9$	0.862404			0.287468
$10$			4.62675i			1.46311i
$11$			3.40942i			1.02798i	0.857797	+	0.513989i	$0.171833\pi$
$11$			3.40942i			1.02798i	−0.857797	+	0.513989i	$0.828167\pi$
$12$		−	8.48720i		−	2.45004i
$13$	−3.78460			−1.04966			−0.524830	−	0.851207i	$-0.675871\pi$
$13$	−3.78460			−1.04966			−0.524830	+	0.851207i	$0.675871\pi$
$14$		−	7.10934i		−	1.90005i
$15$	−2.42132			−0.625183
$16$	18.0879			4.52199
$17$	1.31248	−	3.90863i	0.318322	−	0.947983i
$17$	1.31248	−	3.90863i	0.318322	−	0.947983i
$18$	−2.40933			−0.567886
$19$	−0.391596			−0.0898383			−0.0449192	−	0.998991i	$-0.514303\pi$
$19$	−0.391596			−0.0898383			−0.0449192	+	0.998991i	$0.514303\pi$
$20$		−	9.61372i		−	2.14969i
$21$	3.72054			0.811888
$22$		−	9.52504i		−	2.03074i
$23$		−	6.71034i		−	1.39920i	−0.714534	−	0.699601i	$-0.753361\pi$
$23$		−	6.71034i		−	1.39920i	0.714534	−	0.699601i	$-0.246639\pi$
$24$			15.5419i			3.17247i
$25$	2.25729			0.451458
$26$	10.5732			2.07357
$27$		−	5.64704i		−	1.08677i
$28$			14.7722i			2.79168i
$29$		−	3.12547i		−	0.580385i	−0.956968	−	0.290192i	$-0.906281\pi$
$29$		−	3.12547i		−	0.580385i	0.956968	−	0.290192i	$-0.0937193\pi$
$30$	6.76455			1.23503
$31$			4.70114i			0.844350i	0.906514	+	0.422175i	$0.138733\pi$
$31$			4.70114i			0.844350i	−0.906514	+	0.422175i	$0.861267\pi$
$32$	−29.2727			−5.17474
$33$	4.98475			0.867733
$34$	−3.66672	+	10.9197i	−0.628837	+	1.87271i
$35$	4.21437			0.712359
$36$	5.00625			0.834375
$37$		−	6.05175i		−	0.994902i	−0.867492	−	0.497451i	$-0.834270\pi$
$37$		−	6.05175i		−	0.994902i	0.867492	−	0.497451i	$-0.165730\pi$
$38$	1.09402			0.177473
$39$			5.53328i			0.886034i
$40$			17.6047i			2.78355i
$41$		−	4.77526i		−	0.745771i	−0.927877	−	0.372885i	$-0.878368\pi$
$41$		−	4.77526i		−	0.745771i	0.927877	−	0.372885i	$-0.121632\pi$
$42$	−10.3942			−1.60386
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$			19.7917i			2.98370i
$45$		−	1.42824i		−	0.212909i
$46$			18.7469i			2.76409i
$47$	3.54294			0.516790			0.258395	−	0.966039i	$-0.416806\pi$
$47$	3.54294			0.516790			0.258395	+	0.966039i	$0.416806\pi$
$48$		−	26.4455i		−	3.81708i
$49$	0.524308			0.0749012
$50$	−6.30629			−0.891844
$51$	−5.71462	−	1.91891i	−0.800207	−	0.268701i
$52$	−21.9696			−3.04663
$53$	10.1812			1.39849			0.699247	−	0.714880i	$-0.253519\pi$
$53$	10.1812			1.39849			0.699247	+	0.714880i	$0.253519\pi$
$54$			15.7764i			2.14689i
$55$	5.64638			0.761358
$56$		−	27.0510i		−	3.61484i
$57$			0.572534i			0.0758340i
$58$			8.73175i			1.14653i
$59$	−12.1593			−1.58301			−0.791503	−	0.611166i	$-0.790701\pi$
$59$	−12.1593			−1.58301			−0.791503	+	0.611166i	$0.790701\pi$
$60$	−14.0558			−1.81459
$61$		−	4.63742i		−	0.593761i	−0.954915	−	0.296881i	$-0.904054\pi$
$61$		−	4.63742i		−	0.593761i	0.954915	−	0.296881i	$-0.0959463\pi$
$62$		−	13.1338i		−	1.66799i
$63$			2.19459i			0.276493i
$64$	45.6045			5.70057
$65$			6.26772i			0.777415i
$66$	−13.9261			−1.71418
$67$	7.31570			0.893755			0.446878	−	0.894595i	$-0.352536\pi$
$67$	7.31570			0.893755			0.446878	+	0.894595i	$0.352536\pi$
$68$	7.61891	−	22.6896i	0.923929	−	2.75152i
$69$	−9.81086			−1.18109
$70$	−11.7739			−1.40725
$71$		−	10.2675i		−	1.21853i	−0.792966	−	0.609265i	$-0.791464\pi$
$71$		−	10.2675i		−	1.21853i	0.792966	−	0.609265i	$-0.208536\pi$
$72$	−9.16750			−1.08040
$73$		−	5.85190i		−	0.684913i	−0.939534	−	0.342456i	$-0.888741\pi$
$73$		−	5.85190i		−	0.684913i	0.939534	−	0.342456i	$-0.111259\pi$
$74$			16.9070i			1.96540i
$75$		−	3.30028i		−	0.381083i
$76$	−2.27321			−0.260755
$77$	−8.67608			−0.988731
$78$		−	15.4586i		−	1.75034i
$79$		−	14.7632i		−	1.66099i	−0.557029	−	0.830493i	$-0.688059\pi$
$79$		−	14.7632i		−	1.66099i	0.557029	−	0.830493i	$-0.311941\pi$
$80$		−	29.9557i		−	3.34915i
$81$	−5.66905			−0.629894
$82$			13.3409i			1.47325i
$83$	−7.29952			−0.801227			−0.400613	−	0.916247i	$-0.631203\pi$
$83$	−7.29952			−0.801227			−0.400613	+	0.916247i	$0.631203\pi$
$84$	21.5977			2.35650
$85$	−6.47313	−	2.17361i	−0.702110	−	0.235761i
$86$	2.79374			0.301257
$87$	−4.56960			−0.489912
$88$		−	36.2427i		−	3.86348i
$89$	−5.50827			−0.583876			−0.291938	−	0.956437i	$-0.594300\pi$
$89$	−5.50827			−0.583876			−0.291938	+	0.956437i	$0.594300\pi$
$90$			3.99013i			0.420596i
$91$		−	9.63082i		−	1.00958i
$92$		−	38.9534i		−	4.06118i
$93$	6.87331			0.712729
$94$	−9.89805			−1.02091
$95$			0.648527i			0.0665375i
$96$			42.7982i			4.36808i
$97$		−	1.97083i		−	0.200107i	−0.994982	−	0.100054i	$-0.968099\pi$
$97$		−	1.97083i		−	0.200107i	0.994982	−	0.100054i	$-0.0319014\pi$
$98$	−1.46478			−0.147965
$99$			2.94030i			0.295511i
$100$	13.1036			1.31036
$101$	7.92324			0.788391			0.394196	−	0.919027i	$-0.371023\pi$
$101$	7.92324			0.788391			0.394196	+	0.919027i	$0.371023\pi$
$102$	15.9652	+	5.36093i	1.58079	+	0.530812i
$103$	7.72884			0.761545			0.380773	−	0.924669i	$-0.375658\pi$
$103$	7.72884			0.761545			0.380773	+	0.924669i	$0.375658\pi$
$104$	40.2309			3.94497
$105$		−	6.16163i		−	0.601314i
$106$	−28.4436			−2.76269
$107$			10.0014i			0.966871i	0.875380	+	0.483435i	$0.160611\pi$
$107$			10.0014i			0.966871i	−0.875380	+	0.483435i	$0.839389\pi$
$108$		−	32.7810i		−	3.15435i
$109$		−	12.8056i		−	1.22655i	−0.789870	−	0.613275i	$-0.789852\pi$
$109$		−	12.8056i		−	1.22655i	0.789870	−	0.613275i	$-0.210148\pi$
$110$	−15.7745			−1.50404
$111$	−8.84797			−0.839812
$112$			46.0291i			4.34934i
$113$			12.0286i			1.13156i	0.824557	+	0.565779i	$0.191424\pi$
$113$			12.0286i			1.13156i	−0.824557	+	0.565779i	$0.808576\pi$
$114$		−	1.59951i		−	0.149808i
$115$	−11.1131			−1.03630
$116$		−	18.1433i		−	1.68456i
$117$	−3.26386			−0.301744
$118$	33.9699			3.12718
$119$	9.94645	+	3.33991i	0.911789	+	0.306169i
$120$	25.7391			2.34964
$121$	−0.624139			−0.0567399
$122$			12.9558i			1.17296i
$123$	−6.98168			−0.629517
$124$			27.2901i			2.45072i
$125$		−	12.0189i		−	1.07500i
$126$		−	6.13113i		−	0.546204i
$127$	−19.1934			−1.70314			−0.851569	−	0.524242i	$-0.824349\pi$
$127$	−19.1934			−1.70314			−0.851569	+	0.524242i	$0.824349\pi$
$128$	−68.8618			−6.08658
$129$			1.46205i			0.128726i
$130$		−	17.5104i		−	1.53576i
$131$			2.79227i			0.243961i	0.992532	+	0.121981i	$0.0389246\pi$
$131$			2.79227i			0.243961i	−0.992532	+	0.121981i	$0.961075\pi$
$132$	28.9364			2.51859
$133$		−	0.996510i		−	0.0864083i
$134$	−20.4382			−1.76559
$135$	−9.35212			−0.804903
$136$	−13.9518	+	41.5494i	−1.19636	+	3.56283i
$137$	1.70070			0.145301			0.0726504	−	0.997357i	$-0.476854\pi$
$137$	1.70070			0.145301			0.0726504	+	0.997357i	$0.476854\pi$
$138$	27.4090			2.33321
$139$			18.7895i			1.59370i	0.604174	+	0.796852i	$0.293503\pi$
$139$			18.7895i			1.59370i	−0.604174	+	0.796852i	$0.706497\pi$
$140$	24.4644			2.06762
$141$		−	5.17995i		−	0.436231i
$142$			28.6848i			2.40718i
$143$		−	12.9033i		−	1.07903i
$144$	15.5991			1.29993
$145$	−5.17613			−0.429854
$146$			16.3487i			1.35303i
$147$		−	0.766566i		−	0.0632253i
$148$		−	35.1304i		−	2.88770i
$149$	−13.3367			−1.09259			−0.546294	−	0.837594i	$-0.683962\pi$
$149$	−13.3367			−1.09259			−0.546294	+	0.837594i	$0.683962\pi$
$150$			9.22013i			0.752820i
$151$	12.4731			1.01505			0.507525	−	0.861637i	$-0.330561\pi$
$151$	12.4731			1.01505			0.507525	+	0.861637i	$0.330561\pi$
$152$	4.16273			0.337642
$153$	1.13189	−	3.37082i	0.0915075	−	0.272515i
$154$	24.2387			1.95321
$155$	7.78562			0.625356
$156$			32.1207i			2.57171i
$157$	−2.73448			−0.218235			−0.109118	−	0.994029i	$-0.534803\pi$
$157$	−2.73448			−0.218235			−0.109118	+	0.994029i	$0.534803\pi$
$158$			41.2445i			3.28123i
$159$		−	14.8854i		−	1.18049i
$160$			48.4789i			3.83260i
$161$	17.0760			1.34578
$162$	15.8378			1.24434
$163$			9.39136i			0.735588i	0.929907	+	0.367794i	$0.119887\pi$
$163$			9.39136i			0.735588i	−0.929907	+	0.367794i	$0.880113\pi$
$164$		−	27.7204i		−	2.16460i
$165$		−	8.25530i		−	0.642674i
$166$	20.3930			1.58280
$167$			21.1455i			1.63629i	0.575014	+	0.818144i	$0.304997\pi$
$167$			21.1455i			1.63629i	−0.575014	+	0.818144i	$0.695003\pi$
$168$	−39.5499			−3.05134
$169$	1.32320			0.101784
$170$	18.0843	+	6.07250i	1.38700	+	0.465739i
$171$	−0.337714			−0.0258256
$172$	−5.80499			−0.442627
$173$			0.663285i			0.0504286i	0.999682	+	0.0252143i	$0.00802682\pi$
$173$			0.663285i			0.0504286i	−0.999682	+	0.0252143i	$0.991973\pi$
$174$	12.7663			0.967808
$175$			5.74422i			0.434222i
$176$			61.6694i			4.64851i
$177$			17.7775i			1.33624i
$178$	15.3887			1.15343
$179$	5.34535			0.399530			0.199765	−	0.979844i	$-0.435982\pi$
$179$	5.34535			0.399530			0.199765	+	0.979844i	$0.435982\pi$
$180$		−	8.29091i		−	0.617968i
$181$			13.3345i			0.991145i	0.868567	+	0.495572i	$0.165042\pi$
$181$			13.3345i			0.991145i	−0.868567	+	0.495572i	$0.834958\pi$
$182$			26.9060i			1.99441i
$183$	−6.78015			−0.501203
$184$			71.3320i			5.25866i
$185$	−10.0224			−0.736860
$186$	−19.2023			−1.40798
$187$	13.3262	+	4.47478i	0.974506	+	0.327228i
$188$	20.5667			1.49998
$189$	14.3702			1.04528
$190$		−	1.81182i		−	0.131443i
$191$	−5.61606			−0.406364			−0.203182	−	0.979141i	$-0.565128\pi$
$191$	−5.61606			−0.406364			−0.203182	+	0.979141i	$0.565128\pi$
$192$		−	66.6762i		−	4.81194i
$193$		−	18.6972i		−	1.34586i	−0.739708	−	0.672929i	$-0.765036\pi$
$193$		−	18.6972i		−	1.34586i	0.739708	−	0.672929i	$-0.234964\pi$
$194$			5.50598i			0.395307i
$195$	9.16374			0.656229
$196$	3.04361			0.217400
$197$		−	23.7683i		−	1.69342i	−0.532054	−	0.846710i	$-0.678580\pi$
$197$		−	23.7683i		−	1.69342i	0.532054	−	0.846710i	$-0.321420\pi$
$198$		−	8.21443i		−	0.583774i
$199$		−	22.1182i		−	1.56792i	−0.620813	−	0.783959i	$-0.713197\pi$
$199$		−	22.1182i		−	1.56792i	0.620813	−	0.783959i	$-0.286803\pi$
$200$	−23.9954			−1.69673
$201$		−	10.6959i		−	0.754433i
$202$	−22.1355			−1.55745
$203$	7.95350			0.558226
$204$	−33.1733	−	11.1392i	−2.32260	−	0.779903i
$205$	−7.90837			−0.552345
$206$	−21.5924			−1.50441
$207$		−	5.78702i		−	0.402226i
$208$	−68.4557			−4.74655
$209$		−	1.33512i		−	0.0923519i
$210$			17.2140i			1.18788i
$211$		−	16.1020i		−	1.10851i	−0.832349	−	0.554253i	$-0.813004\pi$
$211$		−	16.1020i		−	1.10851i	0.832349	−	0.554253i	$-0.186996\pi$
$212$	59.1017			4.05912
$213$	−15.0117			−1.02858
$214$		−	27.9413i		−	1.91003i
$215$			1.65611i			0.112946i
$216$			60.0289i			4.08445i
$217$	−11.9632			−0.812113
$218$			35.7754i			2.42302i
$219$	−8.55578			−0.578146
$220$	32.7772			2.20984
$221$	−4.96720	+	14.7926i	−0.334130	+	0.995059i
$222$	24.7189			1.65903
$223$	−0.273345			−0.0183045			−0.00915227	−	0.999958i	$-0.502913\pi$
$223$	−0.273345			−0.0183045			−0.00915227	+	0.999958i	$0.502913\pi$
$224$		−	74.4914i		−	4.97717i
$225$	1.94670			0.129780
$226$		−	33.6049i		−	2.23536i
$227$		−	8.62264i		−	0.572305i	−0.958184	−	0.286152i	$-0.907624\pi$
$227$		−	8.62264i		−	0.572305i	0.958184	−	0.286152i	$-0.0923764\pi$
$228$			3.32355i			0.220108i
$229$	−18.6025			−1.22929			−0.614645	−	0.788804i	$-0.710701\pi$
$229$	−18.6025			−1.22929			−0.614645	+	0.788804i	$0.710701\pi$
$230$	31.0470			2.04718
$231$			12.6849i			0.834604i
$232$			33.2242i			2.18128i
$233$			17.7622i			1.16364i	0.813317	+	0.581821i	$0.197660\pi$
$233$			17.7622i			1.16364i	−0.813317	+	0.581821i	$0.802340\pi$
$234$	9.11837			0.596086
$235$		−	5.86750i		−	0.382753i
$236$	−70.5846			−4.59467
$237$	−21.5845			−1.40207
$238$	−27.7878	−	9.33084i	−1.80122	−	0.604829i
$239$	20.1567			1.30383			0.651915	−	0.758292i	$-0.273966\pi$
$239$	20.1567			1.30383			0.651915	+	0.758292i	$0.273966\pi$
$240$	−43.7968			−2.82707
$241$			16.1475i			1.04015i	0.854121	+	0.520075i	$0.174096\pi$
$241$			16.1475i			1.04015i	−0.854121	+	0.520075i	$0.825904\pi$
$242$	1.74368			0.112088
$243$		−	8.65267i		−	0.555069i
$244$		−	26.9202i		−	1.72339i
$245$		−	0.868314i		−	0.0554745i
$246$	19.5050			1.24359
$247$	1.48203			0.0942996
$248$		−	49.9739i		−	3.17335i
$249$			10.6723i			0.676328i
$250$			33.5777i			2.12364i
$251$	17.8269			1.12522			0.562612	−	0.826721i	$-0.309796\pi$
$251$	17.8269			1.12522			0.562612	+	0.826721i	$0.309796\pi$
$252$			12.7396i			0.802519i
$253$	22.8783			1.43835
$254$	53.6214			3.36451
$255$	−3.17793	+	9.46406i	−0.199010	+	0.592662i
$256$	101.173			6.32332
$257$	−25.4097			−1.58502			−0.792508	−	0.609861i	$-0.791225\pi$
$257$	−25.4097			−1.58502			−0.792508	+	0.609861i	$0.791225\pi$
$258$		−	4.08460i		−	0.254296i
$259$	15.4001			0.956917
$260$			36.3841i			2.25644i
$261$		−	2.69542i		−	0.166842i
$262$		−	7.80087i		−	0.481939i
$263$	17.6259			1.08686			0.543430	−	0.839455i	$-0.317125\pi$
$263$	17.6259			1.08686			0.543430	+	0.839455i	$0.317125\pi$
$264$	−52.9887			−3.26123
$265$		−	16.8612i		−	1.03577i
$266$			2.78399i			0.170697i
$267$			8.05338i			0.492859i
$268$	42.4676			2.59412
$269$		−	1.19300i		−	0.0727385i	−0.999338	−	0.0363692i	$-0.988421\pi$
$269$		−	1.19300i		−	0.0727385i	0.999338	−	0.0363692i	$-0.0115792\pi$
$270$	26.1274			1.59006
$271$	30.5550			1.85608			0.928041	−	0.372478i	$-0.121492\pi$
$271$	30.5550			1.85608			0.928041	+	0.372478i	$0.121492\pi$
$272$	23.7400	−	70.6991i	1.43945	−	4.28677i
$273$	−14.0808			−0.852206
$274$	−4.75132			−0.287038
$275$			7.69606i			0.464090i
$276$	−56.9520			−3.42811
$277$		−	3.02740i		−	0.181899i	−0.995856	−	0.0909494i	$-0.971010\pi$
$277$		−	3.02740i		−	0.181899i	0.995856	−	0.0909494i	$-0.0289901\pi$
$278$		−	52.4930i		−	3.14832i
$279$			4.05428i			0.242724i
$280$	−44.7995			−2.67728
$281$	21.1527			1.26186			0.630932	−	0.775838i	$-0.282673\pi$
$281$	21.1527			1.26186			0.630932	+	0.775838i	$0.282673\pi$
$282$			14.4715i			0.861763i
$283$			16.4611i			0.978509i	0.872141	+	0.489255i	$0.162731\pi$
$283$			16.4611i			0.978509i	−0.872141	+	0.489255i	$0.837269\pi$
$284$		−	59.6029i		−	3.53678i
$285$	0.948180			0.0561654
$286$			36.0485i			2.13159i
$287$	12.1518			0.717298
$288$	−25.2449			−1.48757
$289$	−13.5548	−	10.2600i	−0.797342	−	0.603528i
$290$	14.4608			0.849165
$291$	−2.88145			−0.168914
$292$		−	33.9702i		−	1.98796i
$293$	−4.91985			−0.287421			−0.143710	−	0.989620i	$-0.545903\pi$
$293$	−4.91985			−0.287421			−0.143710	+	0.989620i	$0.545903\pi$
$294$			2.14159i			0.124900i
$295$			20.1372i			1.17243i
$296$			64.3311i			3.73917i
$297$	19.2531			1.11718
$298$	37.2594			2.15838
$299$			25.3959i			1.46868i
$300$		−	19.1581i		−	1.10609i
$301$		−	2.54474i		−	0.146676i
$302$	−34.8467			−2.00520
$303$		−	11.5842i		−	0.665494i
$304$	−7.08317			−0.406248
$305$	−7.68009			−0.439761
$306$	−3.16219	+	9.41720i	−0.180771	+	0.538346i
$307$	−11.3181			−0.645958			−0.322979	−	0.946406i	$-0.604684\pi$
$307$	−11.3181			−0.645958			−0.322979	+	0.946406i	$0.604684\pi$
$308$	−50.3646			−2.86979
$309$		−	11.3000i		−	0.642832i
$310$	−21.7510			−1.23537
$311$			25.8639i			1.46661i	0.679901	+	0.733304i	$0.262023\pi$
$311$			25.8639i			1.46661i	−0.679901	+	0.733304i	$0.737977\pi$
$312$		−	58.8197i		−	3.33001i
$313$		−	1.66362i		−	0.0940331i	−0.998894	−	0.0470166i	$-0.985029\pi$
$313$		−	1.66362i		−	0.0940331i	0.998894	−	0.0470166i	$-0.0149714\pi$
$314$	7.63943			0.431118
$315$	3.63449			0.204780
$316$		−	85.7001i		−	4.82101i
$317$			16.7523i			0.940900i	0.882427	+	0.470450i	$0.155908\pi$
$317$			16.7523i			0.940900i	−0.882427	+	0.470450i	$0.844092\pi$
$318$			41.5860i			2.33203i
$319$	10.6560			0.596623
$320$		−	75.5262i		−	4.22204i
$321$	14.6225			0.816151
$322$	−47.7061			−2.65855
$323$	−0.513961	+	1.53061i	−0.0285975	+	0.0851652i
$324$	−32.9088			−1.82826
$325$	−8.54295			−0.473878
$326$		−	26.2370i		−	1.45314i
$327$	−18.7224			−1.03535
$328$			50.7618i			2.80285i
$329$			9.01584i			0.497059i
$330$			23.0632i			1.26959i
$331$	17.9659			0.987497			0.493748	−	0.869605i	$-0.335626\pi$
$331$	17.9659			0.987497			0.493748	+	0.869605i	$0.335626\pi$
$332$	−42.3737			−2.32556
$333$		−	5.21906i		−	0.286002i
$334$		−	59.0751i		−	3.23244i
$335$		−	12.1156i		−	0.661947i
$336$	67.2969			3.67135
$337$		−	1.40894i		−	0.0767501i	−0.999263	−	0.0383750i	$-0.987782\pi$
$337$		−	1.40894i		−	0.0767501i	0.999263	−	0.0383750i	$-0.0122182\pi$
$338$	−3.69667			−0.201072
$339$	17.5865			0.955166
$340$	−37.5765	−	12.6178i	−2.03787	−	0.684295i
$341$	−16.0282			−0.867974
$342$	0.943486			0.0510179
$343$			19.1474i			1.03386i
$344$	10.6302			0.573140
$345$			16.2479i			0.874757i
$346$		−	1.85305i		−	0.0996205i
$347$			13.2695i			0.712342i	0.934421	+	0.356171i	$0.115918\pi$
$347$			13.2695i			0.712342i	−0.934421	+	0.356171i	$0.884082\pi$
$348$	−26.5265			−1.42197
$349$	−1.26967			−0.0679637			−0.0339818	−	0.999422i	$-0.510819\pi$
$349$	−1.26967			−0.0679637			−0.0339818	+	0.999422i	$0.510819\pi$
$350$		−	16.0479i		−	0.857794i
$351$			21.3718i			1.14074i
$352$		−	99.8030i		−	5.31952i
$353$	−10.0176			−0.533182			−0.266591	−	0.963810i	$-0.585897\pi$
$353$	−10.0176			−0.533182			−0.266591	+	0.963810i	$0.585897\pi$
$354$		−	49.6658i		−	2.63971i
$355$	−17.0042			−0.902488
$356$	−31.9755			−1.69470
$357$	4.88312	−	14.5422i	0.258442	−	0.769656i
$358$	−14.9335			−0.789261
$359$	22.6635			1.19613			0.598066	−	0.801447i	$-0.295936\pi$
$359$	22.6635			1.19613			0.598066	+	0.801447i	$0.295936\pi$
$360$			15.1824i			0.800183i
$361$	−18.8467			−0.991929
$362$		−	37.2531i		−	1.95798i
$363$			0.912524i			0.0478951i
$364$		−	55.9068i		−	2.93031i
$365$	−9.69140			−0.507271
$366$	18.9420			0.990114
$367$		−	0.197645i		−	0.0103170i	−0.999987	−	0.00515850i	$-0.998358\pi$
$367$		−	0.197645i		−	0.0103170i	0.999987	−	0.00515850i	$-0.00164201\pi$
$368$		−	121.376i		−	6.32717i
$369$		−	4.11821i		−	0.214385i
$370$	27.9999			1.45565
$371$			25.9085i			1.34510i
$372$	39.8995			2.06869
$373$	32.9519			1.70618			0.853091	−	0.521762i	$-0.174725\pi$
$373$	32.9519			1.70618			0.853091	+	0.521762i	$0.174725\pi$
$374$	−37.2299	−	12.5014i	−1.92511	−	0.646431i
$375$	−17.5722			−0.907427
$376$	−37.6620			−1.94227
$377$			11.8286i			0.609206i
$378$	−40.1467			−2.06492
$379$		−	12.6811i		−	0.651382i	−0.945476	−	0.325691i	$-0.894403\pi$
$379$		−	12.6811i		−	0.651382i	0.945476	−	0.325691i	$-0.105597\pi$
$380$			3.76469i			0.193125i
$381$			28.0617i			1.43765i
$382$	15.6898			0.802760
$383$	37.0563			1.89349			0.946743	−	0.321990i	$-0.104352\pi$
$383$	37.0563			1.89349			0.946743	+	0.321990i	$0.104352\pi$
$384$			100.680i			5.13778i
$385$			14.3686i			0.732290i
$386$			52.2353i			2.65871i
$387$	−0.862404			−0.0438385
$388$		−	11.4406i		−	0.580811i
$389$	−15.3281			−0.777166			−0.388583	−	0.921414i	$-0.627035\pi$
$389$	−15.3281			−0.777166			−0.388583	+	0.921414i	$0.627035\pi$
$390$	−25.6011			−1.29636
$391$	−26.2282	−	8.80716i	−1.32642	−	0.445397i
$392$	−5.57348			−0.281504
$393$	4.08244			0.205932
$394$			66.4025i			3.34531i
$395$	−24.4495			−1.23019
$396$			17.0684i			0.857720i
$397$		−	5.29692i		−	0.265845i	−0.991126	−	0.132922i	$-0.957564\pi$
$397$		−	5.29692i		−	0.265845i	0.991126	−	0.132922i	$-0.0424361\pi$
$398$			61.7925i			3.09738i
$399$	−1.45695			−0.0729387
$400$	40.8298			2.04149
$401$			0.819961i			0.0409469i	0.999790	+	0.0204735i	$0.00651736\pi$
$401$			0.819961i			0.0409469i	−0.999790	+	0.0204735i	$0.993483\pi$
$402$			29.8817i			1.49036i
$403$		−	17.7919i		−	0.886280i
$404$	45.9943			2.28830
$405$			9.38858i			0.466522i
$406$	−22.2200			−1.10276
$407$	20.6330			1.02274
$408$	60.7474	+	20.3983i	3.00744	+	1.00987i
$409$	7.19648			0.355843			0.177922	−	0.984045i	$-0.443063\pi$
$409$	7.19648			0.355843			0.177922	+	0.984045i	$0.443063\pi$
$410$	22.0939			1.09114
$411$		−	2.48652i		−	0.122651i
$412$	44.8658			2.21038
$413$		−	30.9422i		−	1.52257i
$414$			16.1674i			0.794587i
$415$			12.0888i			0.593417i
$416$	110.786			5.43171
$417$	27.4712			1.34527
$418$			3.72997i			0.182439i
$419$			18.9629i			0.926397i	0.886255	+	0.463198i	$0.153298\pi$
$419$			18.9629i			0.926397i	−0.886255	+	0.463198i	$0.846702\pi$
$420$		−	35.7682i		−	1.74531i
$421$	12.9413			0.630718			0.315359	−	0.948972i	$-0.397875\pi$
$421$	12.9413			0.630718			0.315359	+	0.948972i	$0.397875\pi$
$422$			44.9847i			2.18982i
$423$	3.05544			0.148561
$424$	−108.228			−5.25600
$425$	2.96264	−	8.82293i	0.143709	−	0.427975i
$426$	41.9387			2.03194
$427$	11.8010			0.571092
$428$			58.0580i			2.80634i
$429$	−18.8653			−0.910824
$430$		−	4.62675i		−	0.223122i
$431$		−	2.72681i		−	0.131346i	−0.997841	−	0.0656729i	$-0.979081\pi$
$431$		−	2.72681i		−	0.131346i	0.997841	−	0.0656729i	$-0.0209194\pi$
$432$		−	102.143i		−	4.91437i
$433$	−9.49565			−0.456332			−0.228166	−	0.973622i	$-0.573273\pi$
$433$	−9.49565			−0.456332			−0.228166	+	0.973622i	$0.573273\pi$
$434$	33.4220			1.60431
$435$			7.56776i			0.362846i
$436$		−	74.3361i		−	3.56006i
$437$			2.62774i			0.125702i
$438$	23.9026			1.14211
$439$		−	20.1383i		−	0.961151i	−0.876953	−	0.480575i	$-0.840428\pi$
$439$		−	20.1383i		−	0.961151i	0.876953	−	0.480575i	$-0.159572\pi$
$440$	−60.0220			−2.86143
$441$	0.452166			0.0215317
$442$	13.8771	−	41.3267i	0.660065	−	1.96571i
$443$	−14.7892			−0.702654			−0.351327	−	0.936253i	$-0.614269\pi$
$443$	−14.7892			−0.702654			−0.351327	+	0.936253i	$0.614269\pi$
$444$	−51.3624			−2.43755
$445$			9.12232i			0.432439i
$446$	0.763656			0.0361602
$447$			19.4990i			0.922271i
$448$			116.052i			5.48292i
$449$			8.47763i			0.400084i	0.979787	+	0.200042i	$0.0641079\pi$
$449$			8.47763i			0.400084i	−0.979787	+	0.200042i	$0.935892\pi$
$450$	−5.43857			−0.256377
$451$	16.2809			0.766636
$452$			69.8261i			3.28434i
$453$		−	18.2364i		−	0.856819i
$454$			24.0894i			1.13057i
$455$	−15.9497			−0.747734
$456$		−	6.08613i		−	0.285009i
$457$	32.0961			1.50139			0.750696	−	0.660648i	$-0.229718\pi$
$457$	32.0961			1.50139			0.750696	+	0.660648i	$0.229718\pi$
$458$	51.9707			2.42843
$459$	−22.0722	−	7.41160i	−1.03024	−	0.345944i
$460$	−64.5113			−3.00785
$461$	−6.16175			−0.286982			−0.143491	−	0.989652i	$-0.545833\pi$
$461$	−6.16175			−0.286982			−0.143491	+	0.989652i	$0.545833\pi$
$462$		−	35.4383i		−	1.64874i
$463$	−3.26234			−0.151614			−0.0758068	−	0.997123i	$-0.524153\pi$
$463$	−3.26234			−0.151614			−0.0758068	+	0.997123i	$0.524153\pi$
$464$		−	56.5333i		−	2.62449i
$465$		−	11.3830i		−	0.527873i
$466$		−	49.6231i		−	2.29875i
$467$	−13.8701			−0.641834			−0.320917	−	0.947107i	$-0.603991\pi$
$467$	−13.8701			−0.641834			−0.320917	+	0.947107i	$0.603991\pi$
$468$	−18.9467			−0.875809
$469$			18.6165i			0.859632i
$470$			16.3923i			0.756119i
$471$			3.99795i			0.184216i
$472$	129.255			5.94946
$473$		−	3.40942i		−	0.156765i
$474$	60.3016			2.76974
$475$	−0.883947			−0.0405583
$476$	57.7390	+	19.3881i	2.64646	+	0.888654i
$477$	8.78030			0.402022
$478$	−56.3127			−2.57568
$479$		−	37.3132i		−	1.70488i	−0.522823	−	0.852441i	$-0.675121\pi$
$479$		−	37.3132i		−	1.70488i	0.522823	−	0.852441i	$-0.324879\pi$
$480$	70.8787			3.23516
$481$			22.9035i			1.04431i
$482$		−	45.1118i		−	2.05479i
$483$		−	24.9661i		−	1.13600i
$484$	−3.62312			−0.164687
$485$	−3.26391			−0.148207
$486$			24.1733i			1.09652i
$487$			22.1719i			1.00470i	0.864663	+	0.502352i	$0.167532\pi$
$487$			22.1719i			1.00470i	−0.864663	+	0.502352i	$0.832468\pi$
$488$			49.2966i			2.23155i
$489$	13.7307			0.620922
$490$			2.42584i			0.109588i
$491$	−8.84932			−0.399364			−0.199682	−	0.979861i	$-0.563991\pi$
$491$	−8.84932			−0.399364			−0.199682	+	0.979861i	$0.563991\pi$
$492$	−40.5286			−1.82717
$493$	−12.2163	−	4.10210i	−0.550195	−	0.184749i
$494$	−4.14042			−0.186286
$495$	4.86946			0.218866
$496$			85.0340i			3.81814i
$497$	26.1282			1.17201
$498$		−	29.8156i		−	1.33607i
$499$			2.30346i			0.103117i	0.998670	+	0.0515586i	$0.0164189\pi$
$499$			2.30346i			0.103117i	−0.998670	+	0.0515586i	$0.983581\pi$
$500$		−	69.7696i		−	3.12019i
$501$	30.9158			1.38122
$502$	−49.8038			−2.22285
$503$			35.9013i			1.60076i	0.599492	+	0.800381i	$0.295369\pi$
$503$			35.9013i			1.60076i	−0.599492	+	0.800381i	$0.704631\pi$
$504$		−	23.3289i		−	1.03915i
$505$		−	13.1218i		−	0.583911i
$506$	−63.9162			−2.84142
$507$		−	1.93458i		−	0.0859178i
$508$	−111.418			−4.94335
$509$	−4.47397			−0.198305			−0.0991527	−	0.995072i	$-0.531613\pi$
$509$	−4.47397			−0.198305			−0.0991527	+	0.995072i	$0.531613\pi$
$510$	8.87831	−	26.4401i	0.393138	−	1.17079i
$511$	14.8915			0.658763
$512$	−144.928			−6.40497
$513$			2.21136i			0.0976338i
$514$	70.9883			3.13116
$515$		−	12.7998i		−	0.564028i
$516$			8.48720i			0.373628i
$517$			12.0794i			0.531249i
$518$	−43.0240			−1.89036
$519$	0.969757			0.0425676
$520$		−	66.6269i		−	2.92178i
$521$		−	4.62973i		−	0.202832i	−0.994844	−	0.101416i	$-0.967663\pi$
$521$		−	4.62973i		−	0.202832i	0.994844	−	0.101416i	$-0.0323373\pi$
$522$			7.53030i			0.329592i
$523$	7.63705			0.333945			0.166972	−	0.985962i	$-0.446601\pi$
$523$	7.63705			0.333945			0.166972	+	0.985962i	$0.446601\pi$
$524$			16.2091i			0.708097i
$525$	8.39834			0.366534
$526$	−49.2422			−2.14706
$527$	18.3750	+	6.17014i	0.800429	+	0.268775i
$528$	90.1639			3.92388
$529$	−22.0286			−0.957765
$530$			47.1058i			2.04615i
$531$	−10.4862			−0.455063
$532$		−	5.78473i		−	0.250800i
$533$			18.0725i			0.782805i
$534$		−	22.4991i		−	0.973630i
$535$	16.5634			0.716099
$536$	−77.7671			−3.35903
$537$		−	7.81518i		−	0.337250i
$538$			3.33293i			0.143693i
$539$			1.78759i			0.0769968i
$540$	−54.2890			−2.33623
$541$		−	26.6213i		−	1.14454i	−0.820066	−	0.572270i	$-0.806063\pi$
$541$		−	26.6213i		−	1.14454i	0.820066	−	0.572270i	$-0.193937\pi$
$542$	−85.3627			−3.66664
$543$	19.4957			0.836641
$544$	−38.4198	+	114.416i	−1.64723	+	4.90556i
$545$	−21.2074			−0.908427
$546$	39.3380			1.68351
$547$			26.3709i			1.12754i	0.825932	+	0.563770i	$0.190649\pi$
$547$			26.3709i			1.12754i	−0.825932	+	0.563770i	$0.809351\pi$
$548$	9.87256			0.421735
$549$		−	3.99933i		−	0.170687i
$550$		−	21.5008i		−	0.916797i
$551$			1.22392i			0.0521408i
$552$	104.291			4.43892
$553$	37.5684			1.59757
$554$			8.45777i			0.359336i
$555$			14.6532i			0.621995i
$556$			109.073i			4.62572i
$557$	−44.2433			−1.87465			−0.937325	−	0.348457i	$-0.886706\pi$
$557$	−44.2433			−1.87465			−0.937325	+	0.348457i	$0.886706\pi$
$558$		−	11.3266i		−	0.479494i
$559$	3.78460			0.160072
$560$	76.2293			3.22128
$561$	6.54236	−	19.4835i	0.276219	−	0.822596i
$562$	−59.0952			−2.49278
$563$	−35.6549			−1.50267			−0.751337	−	0.659919i	$-0.770591\pi$
$563$	−35.6549			−1.50267			−0.751337	+	0.659919i	$0.770591\pi$
$564$		−	30.0696i		−	1.26616i
$565$	19.9208			0.838072
$566$		−	45.9880i		−	1.93302i
$567$		−	14.4262i		−	0.605845i
$568$			109.145i			4.57964i
$569$	−4.24642			−0.178019			−0.0890097	−	0.996031i	$-0.528370\pi$
$569$	−4.24642			−0.178019			−0.0890097	+	0.996031i	$0.528370\pi$
$570$	−2.64897			−0.110953
$571$		−	16.0385i		−	0.671189i	−0.942007	−	0.335594i	$-0.891063\pi$
$571$		−	16.0385i		−	0.671189i	0.942007	−	0.335594i	$-0.108937\pi$
$572$		−	74.9035i		−	3.13187i
$573$			8.21096i			0.343018i
$574$	−33.9490			−1.41700
$575$		−	15.1472i		−	0.631681i
$576$	39.3295			1.63873
$577$	12.3700			0.514969			0.257484	−	0.966282i	$-0.417106\pi$
$577$	12.3700			0.514969			0.257484	+	0.966282i	$0.417106\pi$
$578$	37.8686	+	28.6637i	1.57513	+	1.19225i
$579$	−27.3363			−1.13606
$580$	−30.0474			−1.24765
$581$		−	18.5754i		−	0.770636i
$582$	8.05003			0.333685
$583$			34.7119i			1.43762i
$584$			62.2066i			2.57413i
$585$			5.40531i			0.223482i
$586$	13.7448			0.567792
$587$	−32.6343			−1.34696			−0.673481	−	0.739204i	$-0.735202\pi$
$587$	−32.6343			−1.34696			−0.673481	+	0.739204i	$0.735202\pi$
$588$		−	4.44991i		−	0.183511i
$589$		−	1.84095i		−	0.0758550i
$590$		−	56.2580i		−	2.31611i
$591$	−34.7505			−1.42944
$592$		−	109.464i		−	4.49893i
$593$	41.8212			1.71739			0.858696	−	0.512486i	$-0.171275\pi$
$593$	41.8212			1.71739			0.858696	+	0.512486i	$0.171275\pi$
$594$	−53.7882			−2.20696
$595$	5.53126	−	16.4724i	0.226760	−	0.675304i
$596$	−77.4196			−3.17123
$597$	−32.3379			−1.32350
$598$		−	70.9497i		−	2.90135i
$599$	21.9914			0.898545			0.449273	−	0.893395i	$-0.351683\pi$
$599$	21.9914			0.898545			0.449273	+	0.893395i	$0.351683\pi$
$600$			35.0825i			1.43224i
$601$			13.8945i			0.566767i	0.959007	+	0.283383i	$0.0914569\pi$
$601$			13.8945i			0.566767i	−0.959007	+	0.283383i	$0.908543\pi$
$602$			7.10934i			0.289755i
$603$	6.30909			0.256926
$604$	72.4064			2.94618
$605$			1.03364i			0.0420236i
$606$			32.3632i			1.31467i
$607$		−	10.4505i		−	0.424171i	−0.977251	−	0.212086i	$-0.931974\pi$
$607$		−	10.4505i		−	0.424171i	0.977251	−	0.212086i	$-0.0680256\pi$
$608$	11.4631			0.464890
$609$		−	11.6284i		−	0.471208i
$610$	21.4562			0.868736
$611$	−13.4086			−0.542454
$612$	6.57058	−	19.5676i	0.265600	−	0.790973i
$613$	20.2398			0.817479			0.408740	−	0.912651i	$-0.365968\pi$
$613$	20.2398			0.817479			0.408740	+	0.912651i	$0.365968\pi$
$614$	31.6198			1.27607
$615$			11.5625i			0.466243i
$616$	92.2281			3.71598
$617$		−	17.3971i		−	0.700380i	−0.936679	−	0.350190i	$-0.886117\pi$
$617$		−	17.3971i		−	0.700380i	0.936679	−	0.350190i	$-0.113883\pi$
$618$			31.5692i			1.26990i
$619$		−	15.1841i		−	0.610301i	−0.952304	−	0.305151i	$-0.901293\pi$
$619$		−	15.1841i		−	0.610301i	0.952304	−	0.305151i	$-0.0987068\pi$
$620$	45.1954			1.81509
$621$	−37.8935			−1.52061
$622$		−	72.2571i		−	2.89725i
$623$		−	14.0171i		−	0.561584i
$624$			100.086i			4.00664i
$625$	−8.61817			−0.344727
$626$			4.64771i			0.185760i
$627$	−1.95201			−0.0779557
$628$	−15.8736			−0.633427
$629$	−23.6541	−	7.94278i	−0.943149	−	0.316699i
$630$	−10.1538			−0.404538
$631$	18.8434			0.750142			0.375071	−	0.926996i	$-0.377618\pi$
$631$	18.8434			0.750142			0.375071	+	0.926996i	$0.377618\pi$
$632$			156.935i			6.24254i
$633$	−23.5419			−0.935707
$634$		−	46.8015i		−	1.85872i
$635$			31.7864i			1.26141i
$636$		−	86.4098i		−	3.42637i
$637$	−1.98430			−0.0786207
$638$	−29.7702			−1.17861
$639$		−	8.85476i		−	0.350289i
$640$			114.043i			4.50794i
$641$			25.1534i			0.993499i	0.867894	+	0.496749i	$0.165473\pi$
$641$			25.1534i			0.993499i	−0.867894	+	0.496749i	$0.834527\pi$
$642$	−40.8516			−1.61228
$643$			37.2072i			1.46731i	0.679523	+	0.733654i	$0.262187\pi$
$643$			37.2072i			1.46731i	−0.679523	+	0.733654i	$0.737813\pi$
$644$	99.1263			3.90612
$645$	2.42132			0.0953395
$646$	1.43587	−	4.27612i	0.0564937	−	0.168242i
$647$	21.2060			0.833694			0.416847	−	0.908977i	$-0.363135\pi$
$647$	21.2060			0.833694			0.416847	+	0.908977i	$0.363135\pi$
$648$	60.2629			2.36735
$649$		−	41.4561i		−	1.62730i
$650$	23.8668			0.936133
$651$			17.4908i			0.685518i
$652$			54.5168i			2.13504i
$653$			5.67344i			0.222019i	0.993819	+	0.111009i	$0.0354084\pi$
$653$			5.67344i			0.222019i	−0.993819	+	0.111009i	$0.964592\pi$
$654$	52.3055			2.04531
$655$	4.62431			0.180687
$656$		−	86.3747i		−	3.37237i
$657$		−	5.04670i		−	0.196891i
$658$		−	25.1879i		−	0.981928i
$659$	−8.05844			−0.313912			−0.156956	−	0.987606i	$-0.550168\pi$
$659$	−8.05844			−0.313912			−0.156956	+	0.987606i	$0.550168\pi$
$660$		−	47.9220i		−	1.86536i
$661$	−30.6584			−1.19247			−0.596236	−	0.802809i	$-0.703338\pi$
$661$	−30.6584			−1.19247			−0.596236	+	0.802809i	$0.703338\pi$
$662$	−50.1922			−1.95077
$663$	21.6276	+	7.26230i	0.839945	+	0.282044i
$664$	77.5951			3.01127
$665$	−1.65033			−0.0639971
$666$			14.5807i			0.564990i
$667$	−20.9729			−0.812075
$668$			122.749i			4.74932i
$669$			0.399645i			0.0154512i
$670$			33.8479i			1.30766i
$671$	15.8109			0.610374
$672$	−108.910			−4.20131
$673$		−	41.4496i		−	1.59776i	−0.601488	−	0.798882i	$-0.705425\pi$
$673$		−	41.4496i		−	1.59776i	0.601488	−	0.798882i	$-0.294575\pi$
$674$			3.93623i			0.151618i
$675$		−	12.7470i		−	0.490633i
$676$	7.68115			0.295429
$677$			20.2044i			0.776519i	0.921550	+	0.388259i	$0.126924\pi$
$677$			20.2044i			0.776519i	−0.921550	+	0.388259i	$0.873076\pi$
$678$	−49.1321			−1.88691
$679$	5.01524			0.192467
$680$	68.8105	+	23.1058i	2.63876	+	0.886067i
$681$	−12.6067			−0.483092
$682$	44.7785			1.71466
$683$			9.79171i			0.374669i	0.982296	+	0.187335i	$0.0599849\pi$
$683$			9.79171i			0.374669i	−0.982296	+	0.187335i	$0.940015\pi$
$684$	−1.96043			−0.0749588
$685$		−	2.81655i		−	0.107615i
$686$		−	53.4929i		−	2.04237i
$687$			27.1979i			1.03766i
$688$	−18.0879			−0.689597
$689$	−38.5317			−1.46794
$690$		−	45.3924i		−	1.72806i
$691$			30.5502i			1.16219i	0.813837	+	0.581093i	$0.197375\pi$
$691$			30.5502i			1.16219i	−0.813837	+	0.581093i	$0.802625\pi$
$692$			3.85037i			0.146369i
$693$	−7.48229			−0.284229
$694$		−	37.0714i		−	1.40721i
$695$	31.1175			1.18035
$696$	48.5756			1.84125
$697$	−18.6647	−	6.26742i	−0.706978	−	0.237395i
$698$	3.54712			0.134260
$699$	25.9693			0.982250
$700$			33.3451i			1.26033i
$701$	32.3586			1.22217			0.611083	−	0.791567i	$-0.290734\pi$
$701$	32.3586			1.22217			0.611083	+	0.791567i	$0.290734\pi$
$702$		−	59.7072i		−	2.25350i
$703$			2.36984i			0.0893803i
$704$			155.485i			5.86006i
$705$	−8.57859			−0.323088
$706$	27.9866			1.05329
$707$			20.1626i			0.758291i
$708$			103.198i			3.87843i
$709$			0.391967i			0.0147206i	0.999973	+	0.00736032i	$0.00234288\pi$
$709$			0.391967i			0.0147206i	−0.999973	+	0.00736032i	$0.997657\pi$
$710$	47.5053			1.78284
$711$		−	12.7318i		−	0.477481i
$712$	58.5539			2.19440
$713$	31.5462			1.18142
$714$	−13.6422	+	40.6272i	−0.510545	+	1.52043i
$715$	−21.3693			−0.799166
$716$	31.0297			1.15963
$717$		−	29.4702i		−	1.10058i
$718$	−63.3159			−2.36293
$719$		−	38.2255i		−	1.42557i	−0.701382	−	0.712786i	$-0.747433\pi$
$719$		−	38.2255i		−	1.42557i	0.701382	−	0.712786i	$-0.252567\pi$
$720$		−	25.8339i		−	0.962773i
$721$			19.6679i			0.732470i
$722$	52.6527			1.95953
$723$	23.6084			0.878007
$724$			77.4066i			2.87679i
$725$		−	7.05509i		−	0.262020i
$726$		−	2.54936i		−	0.0946155i
$727$	−33.5452			−1.24412			−0.622062	−	0.782968i	$-0.713705\pi$
$727$	−33.5452			−1.24412			−0.622062	+	0.782968i	$0.713705\pi$
$728$			102.377i			3.79435i
$729$	−29.6578			−1.09844
$730$	27.0753			1.00210
$731$	−1.31248	+	3.90863i	−0.0485437	+	0.144566i
$732$	−39.3587			−1.45474
$733$	−19.5193			−0.720963			−0.360482	−	0.932766i	$-0.617388\pi$
$733$	−19.5193			−0.720963			−0.360482	+	0.932766i	$0.617388\pi$
$734$			0.552170i			0.0203810i
$735$	−1.26952			−0.0468269
$736$			196.430i			7.24050i
$737$			24.9423i			0.918761i
$738$			11.5052i			0.423513i
$739$	−40.1566			−1.47718			−0.738592	−	0.674153i	$-0.764509\pi$
$739$	−40.1566			−1.47718			−0.738592	+	0.674153i	$0.764509\pi$
$740$	−58.1798			−2.13873
$741$		−	2.16681i		−	0.0795998i
$742$		−	72.3815i		−	2.65721i
$743$		−	5.59817i		−	0.205377i	−0.994714	−	0.102689i	$-0.967255\pi$
$743$		−	5.59817i		−	0.205377i	0.994714	−	0.102689i	$-0.0327445\pi$
$744$	−73.0644			−2.67867
$745$			22.0871i			0.809210i
$746$	−92.0590			−3.37052
$747$	−6.29514			−0.230327
$748$	77.3583	+	25.9761i	2.82850	+	0.949779i
$749$	−25.4509			−0.929956
$750$	49.0923			1.79260
$751$		−	16.5539i		−	0.604059i	−0.953299	−	0.302029i	$-0.902336\pi$
$751$		−	16.5539i		−	0.604059i	0.953299	−	0.302029i	$-0.0976641\pi$
$752$	64.0844			2.33692
$753$		−	26.0639i		−	0.949820i
$754$		−	33.0462i		−	1.20347i
$755$		−	20.6569i		−	0.751782i
$756$	83.4190			3.03392
$757$	41.4538			1.50666			0.753332	−	0.657640i	$-0.228445\pi$
$757$	41.4538			1.50666			0.753332	+	0.657640i	$0.228445\pi$
$758$			35.4276i			1.28679i
$759$		−	33.4493i		−	1.21413i
$760$		−	6.89395i		−	0.250070i
$761$	19.6506			0.712334			0.356167	−	0.934422i	$-0.384083\pi$
$761$	19.6506			0.712334			0.356167	+	0.934422i	$0.384083\pi$
$762$		−	78.3973i		−	2.84003i
$763$	32.5868			1.17972
$764$	−32.6012			−1.17947
$765$	−5.58246	−	1.87453i	−0.201834	−	0.0677737i
$766$	−103.526			−3.74053
$767$	46.0181			1.66162
$768$		−	147.920i		−	5.33762i
$769$	25.5536			0.921487			0.460744	−	0.887533i	$-0.347583\pi$
$769$	25.5536			0.921487			0.460744	+	0.887533i	$0.347583\pi$
$770$		−	40.1420i		−	1.44662i
$771$			37.1504i			1.33794i
$772$		−	108.537i		−	3.90634i
$773$	7.74195			0.278459			0.139229	−	0.990260i	$-0.455537\pi$
$773$	7.74195			0.278459			0.139229	+	0.990260i	$0.455537\pi$
$774$	2.40933			0.0866017
$775$			10.6119i			0.381189i
$776$			20.9502i			0.752069i
$777$		−	22.5158i		−	0.807749i
$778$	42.8228			1.53527
$779$			1.86997i			0.0669988i
$780$	53.1954			1.90470
$781$	35.0063			1.25262
$782$	73.2749	+	24.6049i	2.62031	+	0.879870i
$783$	−17.6496			−0.630746
$784$	9.48366			0.338702
$785$			4.52861i			0.161633i
$786$	−11.4053			−0.406813
$787$		−	21.1598i		−	0.754265i	−0.926159	−	0.377132i	$-0.876910\pi$
$787$		−	21.1598i		−	0.754265i	0.926159	−	0.377132i	$-0.123090\pi$
$788$		−	137.975i		−	4.91515i
$789$		−	25.7700i		−	0.917436i
$790$	68.3055			2.43020
$791$	−30.6097			−1.08836
$792$		−	31.2558i		−	1.11063i
$793$			17.5508i			0.623247i
$794$			14.7982i			0.525169i
$795$	−24.6519			−0.874314
$796$		−	128.396i		−	4.55087i
$797$	−14.6769			−0.519882			−0.259941	−	0.965624i	$-0.583703\pi$
$797$	−14.6769			−0.519882			−0.259941	+	0.965624i	$0.583703\pi$
$798$	4.07034			0.144088
$799$	4.65002	−	13.8480i	0.164506	−	0.489908i
$800$	−66.0771			−2.33618
$801$	−4.75036			−0.167846
$802$		−	2.29076i		−	0.0808896i
$803$	19.9516			0.704076
$804$		−	62.0898i		−	2.18974i
$805$		−	28.2798i		−	0.996734i
$806$			49.7061i			1.75082i
$807$	−1.74423			−0.0613997
$808$	−84.2253			−2.96304
$809$			21.2449i			0.746929i	0.927644	+	0.373465i	$0.121830\pi$
$809$			21.2449i			0.746929i	−0.927644	+	0.373465i	$0.878170\pi$
$810$		−	26.2293i		−	0.921602i
$811$			1.51406i			0.0531658i	0.999647	+	0.0265829i	$0.00846259\pi$
$811$			1.51406i			0.0531658i	−0.999647	+	0.0265829i	$0.991537\pi$
$812$	46.1700			1.62025
$813$		−	44.6729i		−	1.56675i
$814$	−57.6431			−2.02039
$815$	15.5531			0.544803
$816$	−103.366	−	34.7091i	−3.61853	−	1.21506i
$817$	0.391596			0.0137002
$818$	−20.1051			−0.702959
$819$		−	8.30566i		−	0.290223i
$820$	−45.9080			−1.60318
$821$			18.1541i			0.633582i	0.948495	+	0.316791i	$0.102605\pi$
$821$			18.1541i			0.633582i	−0.948495	+	0.316791i	$0.897395\pi$
$822$			6.94668i			0.242293i
$823$		−	13.6683i		−	0.476446i	−0.971211	−	0.238223i	$-0.923435\pi$
$823$		−	13.6683i		−	0.476446i	0.971211	−	0.238223i	$-0.0765648\pi$
$824$	−82.1588			−2.86214
$825$	11.2520			0.391746
$826$			86.4446i			3.00779i
$827$		−	15.4282i		−	0.536490i	−0.963351	−	0.268245i	$-0.913556\pi$
$827$		−	15.4282i		−	0.536490i	0.963351	−	0.268245i	$-0.0864436\pi$
$828$		−	33.5936i		−	1.16746i
$829$	−56.8738			−1.97531			−0.987655	−	0.156646i	$-0.949932\pi$
$829$	−56.8738			−1.97531			−0.987655	+	0.156646i	$0.949932\pi$
$830$		−	33.7731i		−	1.17228i
$831$	−4.42621			−0.153544
$832$	−172.595			−5.98365
$833$	0.688142	−	2.04933i	0.0238427	−	0.0710050i
$834$	−76.7475			−2.65755
$835$	35.0193			1.21189
$836$		−	7.75033i		−	0.268051i
$837$	26.5475			0.917616
$838$		−	52.9774i		−	1.83007i
$839$		−	1.62422i		−	0.0560744i	−0.999607	−	0.0280372i	$-0.991074\pi$
$839$		−	1.62422i		−	0.0560744i	0.999607	−	0.0280372i	$-0.00892568\pi$
$840$			65.4991i			2.25994i
$841$	19.2315			0.663154
$842$	−36.1545			−1.24597
$843$		−	30.9263i		−	1.06516i
$844$		−	93.4718i		−	3.21743i
$845$		−	2.19136i		−	0.0753852i
$846$	−8.53612			−0.293478
$847$		−	1.58827i		−	0.0545736i
$848$	184.157			6.32397
$849$	24.0669			0.825976
$850$	−8.27686	+	24.6490i	−0.283894	+	0.845453i
$851$	−40.6093			−1.39207
$852$	−87.1425			−2.98545
$853$			38.8069i			1.32872i	0.747411	+	0.664362i	$0.231296\pi$
$853$			38.8069i			1.32872i	−0.747411	+	0.664362i	$0.768704\pi$
$854$	−32.9690			−1.12818
$855$			0.559293i			0.0191274i
$856$		−	106.316i		−	3.63382i
$857$		−	6.56334i		−	0.224199i	−0.993697	−	0.112100i	$-0.964242\pi$
$857$		−	6.56334i		−	0.224199i	0.993697	−	0.112100i	$-0.0357576\pi$
$858$	52.7047			1.79931
$859$	−4.22224			−0.144061			−0.0720305	−	0.997402i	$-0.522948\pi$
$859$	−4.22224			−0.144061			−0.0720305	+	0.997402i	$0.522948\pi$
$860$			9.61372i			0.327825i
$861$		−	17.7666i		−	0.605483i
$862$			7.61800i			0.259470i
$863$	4.70002			0.159991			0.0799953	−	0.996795i	$-0.474509\pi$
$863$	4.70002			0.159991			0.0799953	+	0.996795i	$0.474509\pi$
$864$			165.304i			5.62376i
$865$	1.09847			0.0373493
$866$	26.5284			0.901472
$867$	−15.0006	+	19.8178i	−0.509448	+	0.673049i
$868$	−69.4461			−2.35716
$869$	50.3338			1.70746
$870$		−	21.1424i		−	0.716794i
$871$	−27.6870			−0.938138
$872$			136.125i			4.60978i
$873$		−	1.69965i		−	0.0575245i
$874$		−	7.34123i		−	0.248321i
$875$	30.5849			1.03396
$876$	−49.6662			−1.67807
$877$		−	23.1496i		−	0.781706i	−0.920453	−	0.390853i	$-0.872180\pi$
$877$		−	23.1496i		−	0.781706i	0.920453	−	0.390853i	$-0.127820\pi$
$878$			56.2613i			1.89873i
$879$			7.19308i			0.242616i
$880$	102.131			3.44285
$881$		−	10.6783i		−	0.359760i	−0.983689	−	0.179880i	$-0.942429\pi$
$881$		−	10.6783i		−	0.359760i	0.983689	−	0.179880i	$-0.0575710\pi$
$882$	−1.26323			−0.0425353
$883$	−10.8709			−0.365835			−0.182918	−	0.983128i	$-0.558554\pi$
$883$	−10.8709			−0.365835			−0.182918	+	0.983128i	$0.558554\pi$
$884$	−28.8345	+	85.8710i	−0.969811	+	2.88815i
$885$	29.4416			0.989667
$886$	41.3171			1.38807
$887$			5.56670i			0.186912i	0.995623	+	0.0934558i	$0.0297914\pi$
$887$			5.56670i			0.186912i	−0.995623	+	0.0934558i	$0.970209\pi$
$888$	94.0554			3.15629
$889$		−	48.8422i		−	1.63811i
$890$		−	25.4854i		−	0.854273i
$891$		−	19.3282i		−	0.647518i
$892$	−1.58677			−0.0531289
$893$	−1.38740			−0.0464276
$894$		−	54.4752i		−	1.82192i
$895$		−	8.85250i		−	0.295906i
$896$		−	175.235i		−	5.85420i
$897$	37.1302			1.23974
$898$		−	23.6843i		−	0.790356i
$899$	14.6933			0.490048
$900$	11.3006			0.376686
$901$	13.3626	−	39.7945i	0.445172	−	1.32575i
$902$	−45.4846			−1.51447
$903$	−3.72054			−0.123812
$904$		−	127.866i		−	4.25277i
$905$	22.0834			0.734077
$906$			50.9477i			1.69262i
$907$			31.9477i			1.06081i	0.847745	+	0.530404i	$0.177960\pi$
$907$			31.9477i			1.06081i	−0.847745	+	0.530404i	$0.822040\pi$
$908$		−	50.0544i		−	1.66111i
$909$	6.83303			0.226637
$910$	44.5594			1.47713
$911$			50.9592i			1.68836i	0.536064	+	0.844178i	$0.319911\pi$
$911$			50.9592i			1.68836i	−0.536064	+	0.844178i	$0.680089\pi$
$912$			10.3560i			0.342920i
$913$		−	24.8871i		−	0.823644i
$914$	−89.6682			−2.96596
$915$			11.2287i			0.371209i
$916$	−107.988			−3.56801
$917$	−7.10559			−0.234647
$918$	61.6640	+	20.7061i	2.03521	+	0.683403i
$919$	19.6276			0.647455			0.323727	−	0.946150i	$-0.395064\pi$
$919$	19.6276			0.647455			0.323727	+	0.946150i	$0.395064\pi$
$920$	118.134			3.89475
$921$			16.5476i			0.545263i
$922$	17.2143			0.566924
$923$			38.8585i			1.27904i
$924$			73.6356i			2.42243i
$925$		−	13.6606i		−	0.449157i
$926$	9.11412			0.299509
$927$	6.66538			0.218920
$928$			91.4910i			3.00334i
$929$			33.2774i			1.09180i	0.837851	+	0.545898i	$0.183812\pi$
$929$			33.2774i			1.09180i	−0.837851	+	0.545898i	$0.816188\pi$
$930$			31.8011i			1.04280i
$931$	−0.205317			−0.00672900
$932$			103.110i			3.37747i
$933$	37.8144			1.23799
$934$	38.7496			1.26793
$935$	7.41074	−	22.0696i	0.242357	−	0.721754i
$936$	34.6953			1.13405
$937$	−23.7915			−0.777236			−0.388618	−	0.921399i	$-0.627047\pi$
$937$	−23.7915			−0.777236			−0.388618	+	0.921399i	$0.627047\pi$
$938$		−	52.0098i		−	1.69818i
$939$	−2.43229			−0.0793749
$940$		−	34.0608i		−	1.11094i
$941$		−	19.2086i		−	0.626183i	−0.949723	−	0.313092i	$-0.898635\pi$
$941$		−	19.2086i		−	0.626183i	0.949723	−	0.313092i	$-0.101365\pi$
$942$		−	11.1692i		−	0.363914i
$943$	−32.0436			−1.04348
$944$	−219.937			−7.15833
$945$		−	23.7987i		−	0.774172i
$946$			9.52504i			0.309686i
$947$		−	37.8228i		−	1.22908i	−0.788887	−	0.614538i	$-0.789342\pi$
$947$		−	37.8228i		−	1.22908i	0.788887	−	0.614538i	$-0.210658\pi$
$948$	−125.298			−4.06949
$949$			22.1471i			0.718925i
$950$	2.46952			0.0801218
$951$	24.4927			0.794229
$952$	−105.732	−	35.5038i	−3.42681	−	1.15068i
$953$	26.1740			0.847858			0.423929	−	0.905695i	$-0.360651\pi$
$953$	26.1740			0.847858			0.423929	+	0.905695i	$0.360651\pi$
$954$	−24.5299			−0.794185
$955$			9.30082i			0.300967i
$956$	117.010			3.78436
$957$		−	15.5797i		−	0.503619i
$958$			104.243i			3.36795i
$959$			4.32784i			0.139753i
$960$	−110.423			−3.56390
$961$	8.89927			0.287073
$962$		−	63.9863i		−	2.06300i
$963$			8.62524i			0.277944i
$964$			93.7359i			3.01903i
$965$	−30.9647			−0.996790
$966$			69.7487i			2.24413i
$967$	−51.8490			−1.66735			−0.833676	−	0.552254i	$-0.813768\pi$
$967$	−51.8490			−1.66735			−0.833676	+	0.552254i	$0.813768\pi$
$968$	6.63470			0.213247
$969$	2.23782	+	0.751437i	0.0718893	+	0.0241396i
$970$	9.11853			0.292778
$971$	−40.9058			−1.31273			−0.656365	−	0.754444i	$-0.727907\pi$
$971$	−40.9058			−1.31273			−0.656365	+	0.754444i	$0.727907\pi$
$972$		−	50.2287i		−	1.61109i
$973$	−47.8143			−1.53286
$974$		−	61.9425i		−	1.98477i
$975$			12.4902i			0.400008i
$976$		−	83.8815i		−	2.68498i
$977$	−25.9090			−0.828901			−0.414450	−	0.910072i	$-0.636026\pi$
$977$	−25.9090			−0.828901			−0.414450	+	0.910072i	$0.636026\pi$
$978$	−38.3599			−1.22661
$979$		−	18.7800i		−	0.600212i
$980$		−	5.04055i		−	0.161015i
$981$		−	11.0436i		−	0.352594i
$982$	24.7227			0.788934
$983$			48.8234i			1.55722i	0.627505	+	0.778612i	$0.284076\pi$
$983$			48.8234i			1.55722i	−0.627505	+	0.778612i	$0.715924\pi$
$984$	74.2164			2.36593
$985$	−39.3630			−1.25421
$986$	34.1292	+	11.4602i	1.08690	+	0.364968i
$987$	13.1816			0.419576
$988$	8.60320			0.273704
$989$			6.71034i			0.213376i
$990$	−13.6040			−0.432364
$991$			5.00169i			0.158884i	0.996839	+	0.0794419i	$0.0253138\pi$
$991$			5.00169i			0.158884i	−0.996839	+	0.0794419i	$0.974686\pi$
$992$		−	137.615i		−	4.36929i
$993$		−	26.2671i		−	0.833562i
$994$	−72.9953			−2.31527
$995$	−36.6302			−1.16126
$996$			61.9525i			1.96304i
$997$		−	1.47230i		−	0.0466283i	−0.999728	−	0.0233141i	$-0.992578\pi$
$997$		−	1.47230i		−	0.0466283i	0.999728	−	0.0233141i	$-0.00742179\pi$
$998$		−	6.43528i		−	0.203705i
$999$	−34.1744			−1.08123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.1	✓	34
17.16	even	2	inner	731.2.d.d.560.2	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.1	✓	34	1.1	even	1	trivial
731.2.d.d.560.2	yes	34	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.79374 q^{2} -1.46205i q^{3} +5.80499 q^{4} -1.65611i q^{5} +4.08460i q^{6} +2.54474i q^{7} -10.6302 q^{8} +0.862404 q^{9} +O(q^{10})\)	\(q-2.79374 q^{2} -1.46205i q^{3} +5.80499 q^{4} -1.65611i q^{5} +4.08460i q^{6} +2.54474i q^{7} -10.6302 q^{8} +0.862404 q^{9} +4.62675i q^{10} +3.40942i q^{11} -8.48720i q^{12} -3.78460 q^{13} -7.10934i q^{14} -2.42132 q^{15} +18.0879 q^{16} +(1.31248 - 3.90863i) q^{17} -2.40933 q^{18} -0.391596 q^{19} -9.61372i q^{20} +3.72054 q^{21} -9.52504i q^{22} -6.71034i q^{23} +15.5419i q^{24} +2.25729 q^{25} +10.5732 q^{26} -5.64704i q^{27} +14.7722i q^{28} -3.12547i q^{29} +6.76455 q^{30} +4.70114i q^{31} -29.2727 q^{32} +4.98475 q^{33} +(-3.66672 + 10.9197i) q^{34} +4.21437 q^{35} +5.00625 q^{36} -6.05175i q^{37} +1.09402 q^{38} +5.53328i q^{39} +17.6047i q^{40} -4.77526i q^{41} -10.3942 q^{42} -1.00000 q^{43} +19.7917i q^{44} -1.42824i q^{45} +18.7469i q^{46} +3.54294 q^{47} -26.4455i q^{48} +0.524308 q^{49} -6.30629 q^{50} +(-5.71462 - 1.91891i) q^{51} -21.9696 q^{52} +10.1812 q^{53} +15.7764i q^{54} +5.64638 q^{55} -27.0510i q^{56} +0.572534i q^{57} +8.73175i q^{58} -12.1593 q^{59} -14.0558 q^{60} -4.63742i q^{61} -13.1338i q^{62} +2.19459i q^{63} +45.6045 q^{64} +6.26772i q^{65} -13.9261 q^{66} +7.31570 q^{67} +(7.61891 - 22.6896i) q^{68} -9.81086 q^{69} -11.7739 q^{70} -10.2675i q^{71} -9.16750 q^{72} -5.85190i q^{73} +16.9070i q^{74} -3.30028i q^{75} -2.27321 q^{76} -8.67608 q^{77} -15.4586i q^{78} -14.7632i q^{79} -29.9557i q^{80} -5.66905 q^{81} +13.3409i q^{82} -7.29952 q^{83} +21.5977 q^{84} +(-6.47313 - 2.17361i) q^{85} +2.79374 q^{86} -4.56960 q^{87} -36.2427i q^{88} -5.50827 q^{89} +3.99013i q^{90} -9.63082i q^{91} -38.9534i q^{92} +6.87331 q^{93} -9.89805 q^{94} +0.648527i q^{95} +42.7982i q^{96} -1.97083i q^{97} -1.46478 q^{98} +2.94030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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