LMFDB - Embedded newform 138.7.b.a.91.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,7,Mod(91,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("138.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	138.b (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:	$31.7474635395$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.12
Character	$\chi$	$=$	138.91
Dual form			138.7.b.a.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685 q^{2} +15.5885 q^{3} +32.0000 q^{4} +203.893i q^{5} -88.1816 q^{6} -33.7438i q^{7} -181.019 q^{8} +243.000 q^{9} +O(q^{10})$	\(q-5.65685 q^{2} +15.5885 q^{3} +32.0000 q^{4} +203.893i q^{5} -88.1816 q^{6} -33.7438i q^{7} -181.019 q^{8} +243.000 q^{9} -1153.39i q^{10} -2593.83i q^{11} +498.831 q^{12} +4009.82 q^{13} +190.884i q^{14} +3178.38i q^{15} +1024.00 q^{16} -3231.21i q^{17} -1374.62 q^{18} +5487.27i q^{19} +6524.57i q^{20} -526.014i q^{21} +14672.9i q^{22} +(10320.2 - 6444.40i) q^{23} -2821.81 q^{24} -25947.3 q^{25} -22683.0 q^{26} +3788.00 q^{27} -1079.80i q^{28} +30010.5 q^{29} -17979.6i q^{30} +2749.15 q^{31} -5792.62 q^{32} -40433.8i q^{33} +18278.5i q^{34} +6880.12 q^{35} +7776.00 q^{36} +80778.1i q^{37} -31040.7i q^{38} +62506.9 q^{39} -36908.6i q^{40} -121979. q^{41} +2975.59i q^{42} +31853.7i q^{43} -83002.6i q^{44} +49546.0i q^{45} +(-58379.6 + 36455.0i) q^{46} +111467. q^{47} +15962.6 q^{48} +116510. q^{49} +146780. q^{50} -50369.6i q^{51} +128314. q^{52} +67038.7i q^{53} -21428.1 q^{54} +528864. q^{55} +6108.28i q^{56} +85538.1i q^{57} -169765. q^{58} -159596. q^{59} +101708. i q^{60} +193201. i q^{61} -15551.5 q^{62} -8199.75i q^{63} +32768.0 q^{64} +817574. i q^{65} +228728. i q^{66} +156790. i q^{67} -103399. i q^{68} +(160875. - 100458. i) q^{69} -38919.9 q^{70} +400367. q^{71} -43987.7 q^{72} +590418. q^{73} -456950. i q^{74} -404478. q^{75} +175593. i q^{76} -87525.8 q^{77} -353593. q^{78} -465617. i q^{79} +208786. i q^{80} +59049.0 q^{81} +690018. q^{82} -615758. i q^{83} -16832.5i q^{84} +658822. q^{85} -180192. i q^{86} +467818. q^{87} +469534. i q^{88} +351448. i q^{89} -280274. i q^{90} -135307. i q^{91} +(330245. - 206221. i) q^{92} +42855.0 q^{93} -630553. q^{94} -1.11882e6 q^{95} -90298.0 q^{96} -1.30800e6i q^{97} -659082. q^{98} -630301. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 768 q^{4} + 5832 q^{9}+O(q^{10}) $ 24 * q + 768 * q^4 + 5832 * q^9	$ 24 q + 768 q^{4} + 5832 q^{9} - 768 q^{13} + 24576 q^{16} - 44104 q^{23} - 119448 q^{25} - 53888 q^{26} + 3456 q^{29} + 50976 q^{31} + 149008 q^{35} + 186624 q^{36} + 11664 q^{39} - 3920 q^{41} - 150720 q^{46} + 441088 q^{47} - 32472 q^{49} + 8320 q^{50} - 24576 q^{52} + 826176 q^{55} - 307200 q^{58} - 1210160 q^{59} + 783744 q^{62} + 786432 q^{64} + 361584 q^{69} - 2480064 q^{70} + 1531264 q^{71} + 593472 q^{73} + 23328 q^{75} + 1068784 q^{77} + 171072 q^{78} + 1417176 q^{81} + 1454592 q^{82} - 1318272 q^{85} + 697248 q^{87} - 1411328 q^{92} - 983664 q^{93} + 1115712 q^{94} + 4047632 q^{95} - 2409344 q^{98}+O(q^{100}) $ 24 * q + 768 * q^4 + 5832 * q^9 - 768 * q^13 + 24576 * q^16 - 44104 * q^23 - 119448 * q^25 - 53888 * q^26 + 3456 * q^29 + 50976 * q^31 + 149008 * q^35 + 186624 * q^36 + 11664 * q^39 - 3920 * q^41 - 150720 * q^46 + 441088 * q^47 - 32472 * q^49 + 8320 * q^50 - 24576 * q^52 + 826176 * q^55 - 307200 * q^58 - 1210160 * q^59 + 783744 * q^62 + 786432 * q^64 + 361584 * q^69 - 2480064 * q^70 + 1531264 * q^71 + 593472 * q^73 + 23328 * q^75 + 1068784 * q^77 + 171072 * q^78 + 1417176 * q^81 + 1454592 * q^82 - 1318272 * q^85 + 697248 * q^87 - 1411328 * q^92 - 983664 * q^93 + 1115712 * q^94 + 4047632 * q^95 - 2409344 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$-1$

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 $

$2$	−5.65685			−0.707107
$2$	−5.65685			−0.707107
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	32.0000			0.500000
$5$			203.893i			1.63114i	0.578656	+	0.815571i	$0.303577\pi$
$5$			203.893i			1.63114i	−0.578656	+	0.815571i	$0.696423\pi$
$6$	−88.1816			−0.408248
$7$		−	33.7438i		−	0.0983785i	−0.998789	−	0.0491892i	$-0.984336\pi$
$7$		−	33.7438i		−	0.0983785i	0.998789	−	0.0491892i	$-0.0156637\pi$
$8$	−181.019			−0.353553
$9$	243.000			0.333333
$10$		−	1153.39i		−	1.15339i
$11$		−	2593.83i		−	1.94878i	−0.224857	−	0.974392i	$-0.572191\pi$
$11$		−	2593.83i		−	1.94878i	0.224857	−	0.974392i	$-0.427809\pi$
$12$	498.831			0.288675
$13$	4009.82			1.82513			0.912567	−	0.408926i	$-0.134097\pi$
$13$	4009.82			1.82513			0.912567	+	0.408926i	$0.134097\pi$
$14$			190.884i			0.0695641i
$15$			3178.38i			0.941741i
$16$	1024.00			0.250000
$17$		−	3231.21i		−	0.657687i	−0.944384	−	0.328843i	$-0.893341\pi$
$17$		−	3231.21i		−	0.657687i	0.944384	−	0.328843i	$-0.106659\pi$
$18$	−1374.62			−0.235702
$19$			5487.27i			0.800010i	0.916513	+	0.400005i	$0.130992\pi$
$19$			5487.27i			0.800010i	−0.916513	+	0.400005i	$0.869008\pi$
$20$			6524.57i			0.815571i
$21$		−	526.014i		−	0.0567988i
$22$			14672.9i			1.37800i
$23$	10320.2	−	6444.40i	0.848209	−	0.529662i
$23$	10320.2	−	6444.40i	0.848209	−	0.529662i
$24$	−2821.81			−0.204124
$25$	−25947.3			−1.66063
$26$	−22683.0			−1.29057
$27$	3788.00			0.192450
$28$		−	1079.80i		−	0.0491892i
$29$	30010.5			1.23049			0.615247	−	0.788334i	$-0.289056\pi$
$29$	30010.5			1.23049			0.615247	+	0.788334i	$0.289056\pi$
$30$		−	17979.6i		−	0.665911i
$31$	2749.15			0.0922811			0.0461406	−	0.998935i	$-0.485308\pi$
$31$	2749.15			0.0922811			0.0461406	+	0.998935i	$0.485308\pi$
$32$	−5792.62			−0.176777
$33$		−	40433.8i		−	1.12513i
$34$			18278.5i			0.465055i
$35$	6880.12			0.160469
$36$	7776.00			0.166667
$37$			80778.1i			1.59473i	0.603494	+	0.797367i	$0.293775\pi$
$37$			80778.1i			1.59473i	−0.603494	+	0.797367i	$0.706225\pi$
$38$		−	31040.7i		−	0.565693i
$39$	62506.9			1.05374
$40$		−	36908.6i		−	0.576696i
$41$	−121979.			−1.76984			−0.884920	−	0.465744i	$-0.845787\pi$
$41$	−121979.			−1.76984			−0.884920	+	0.465744i	$0.845787\pi$
$42$			2975.59i			0.0401628i
$43$			31853.7i			0.400640i	0.979731	+	0.200320i	$0.0641982\pi$
$43$			31853.7i			0.400640i	−0.979731	+	0.200320i	$0.935802\pi$
$44$		−	83002.6i		−	0.974392i
$45$			49546.0i			0.543714i
$46$	−58379.6	+	36455.0i	−0.599774	+	0.374528i
$47$	111467.			1.07363			0.536813	−	0.843701i	$-0.319628\pi$
$47$	111467.			1.07363			0.536813	+	0.843701i	$0.319628\pi$
$48$	15962.6			0.144338
$49$	116510.			0.990322
$50$	146780.			1.17424
$51$		−	50369.6i		−	0.379716i
$52$	128314.			0.912567
$53$			67038.7i			0.450296i	0.974325	+	0.225148i	$0.0722865\pi$
$53$			67038.7i			0.450296i	−0.974325	+	0.225148i	$0.927713\pi$
$54$	−21428.1			−0.136083
$55$	528864.			3.17874
$56$			6108.28i			0.0347820i
$57$			85538.1i			0.461886i
$58$	−169765.			−0.870091
$59$	−159596.			−0.777079			−0.388540	−	0.921432i	$-0.627020\pi$
$59$	−159596.			−0.777079			−0.388540	+	0.921432i	$0.627020\pi$
$60$			101708.i			0.470870i
$61$			193201.i			0.851177i	0.904917	+	0.425588i	$0.139933\pi$
$61$			193201.i			0.851177i	−0.904917	+	0.425588i	$0.860067\pi$
$62$	−15551.5			−0.0652526
$63$		−	8199.75i		−	0.0327928i
$64$	32768.0			0.125000
$65$			817574.i			2.97706i
$66$			228728.i			0.795588i
$67$			156790.i			0.521308i	0.965432	+	0.260654i	$0.0839382\pi$
$67$			156790.i			0.521308i	−0.965432	+	0.260654i	$0.916062\pi$
$68$		−	103399.i		−	0.328843i
$69$	160875.	−	100458.i	0.489714	−	0.305801i
$70$	−38919.9			−0.113469
$71$	400367.			1.11862			0.559310	−	0.828958i	$-0.311066\pi$
$71$	400367.			1.11862			0.559310	+	0.828958i	$0.311066\pi$
$72$	−43987.7			−0.117851
$73$	590418.			1.51772			0.758859	−	0.651255i	$-0.225757\pi$
$73$	590418.			1.51772			0.758859	+	0.651255i	$0.225757\pi$
$74$		−	456950.i		−	1.12765i
$75$	−404478.			−0.958764
$76$			175593.i			0.400005i
$77$	−87525.8			−0.191718
$78$	−353593.			−0.745108
$79$		−	465617.i		−	0.944381i	−0.881496	−	0.472191i	$-0.843463\pi$
$79$		−	465617.i		−	0.944381i	0.881496	−	0.472191i	$-0.156537\pi$
$80$			208786.i			0.407786i
$81$	59049.0			0.111111
$82$	690018.			1.25147
$83$		−	615758.i		−	1.07690i	−0.842657	−	0.538451i	$-0.819010\pi$
$83$		−	615758.i		−	1.07690i	0.842657	−	0.538451i	$-0.180990\pi$
$84$		−	16832.5i		−	0.0283994i
$85$	658822.			1.07278
$86$		−	180192.i		−	0.283295i
$87$	467818.			0.710427
$88$			469534.i			0.688999i
$89$			351448.i			0.498529i	0.968435	+	0.249265i	$0.0801889\pi$
$89$			351448.i			0.498529i	−0.968435	+	0.249265i	$0.919811\pi$
$90$		−	280274.i		−	0.384464i
$91$		−	135307.i		−	0.179554i
$92$	330245.	−	206221.i	0.424104	−	0.264831i
$93$	42855.0			0.0532785
$94$	−630553.			−0.759168
$95$	−1.11882e6			−1.30493
$96$	−90298.0			−0.102062
$97$		−	1.30800e6i		−	1.43315i	−0.697510	−	0.716575i	$-0.745709\pi$
$97$		−	1.30800e6i		−	1.43315i	0.697510	−	0.716575i	$-0.254291\pi$
$98$	−659082.			−0.700263
$99$		−	630301.i		−	0.649595i
$100$	−830314.			−0.830314
$101$	−636938.			−0.618206			−0.309103	−	0.951029i	$-0.600029\pi$
$101$	−636938.			−0.618206			−0.309103	+	0.951029i	$0.600029\pi$
$102$			284934.i			0.268499i
$103$			1.39478e6i			1.27642i	0.769863	+	0.638209i	$0.220324\pi$
$103$			1.39478e6i			1.27642i	−0.769863	+	0.638209i	$0.779676\pi$
$104$	−725855.			−0.645283
$105$	107251.			0.0926470
$106$		−	379228.i		−	0.318407i
$107$		−	1.60279e6i		−	1.30835i	−0.756342	−	0.654176i	$-0.773015\pi$
$107$		−	1.60279e6i		−	1.30835i	0.756342	−	0.654176i	$-0.226985\pi$
$108$	121216.			0.0962250
$109$			152408.i			0.117687i	0.998267	+	0.0588434i	$0.0187413\pi$
$109$			152408.i			0.117687i	−0.998267	+	0.0588434i	$0.981259\pi$
$110$	−2.99170e6			−2.24771
$111$			1.25921e6i			0.920720i
$112$		−	34553.7i		−	0.0245946i
$113$			532659.i			0.369159i	0.982818	+	0.184580i	$0.0590924\pi$
$113$			532659.i			0.369159i	−0.982818	+	0.184580i	$0.940908\pi$
$114$		−	483877.i		−	0.326603i
$115$	1.31397e6	+	2.10421e6i	0.863955	+	1.38355i
$116$	960337.			0.615247
$117$	974387.			0.608378
$118$	902810.			0.549478
$119$	−109034.			−0.0647022
$120$		−	575347.i		−	0.332956i
$121$	−4.95640e6			−2.79776
$122$		−	1.09291e6i		−	0.601873i
$123$	−1.90147e6			−1.02182
$124$	87972.7			0.0461406
$125$		−	2.10464e6i		−	1.07758i
$126$			46384.8i			0.0231880i
$127$	821603.			0.401098			0.200549	−	0.979684i	$-0.435727\pi$
$127$	821603.			0.401098			0.200549	+	0.979684i	$0.435727\pi$
$128$	−185364.			−0.0883883
$129$			496550.i			0.231310i
$130$		−	4.62490e6i		−	2.10510i
$131$	−1.10460e6			−0.491352			−0.245676	−	0.969352i	$-0.579010\pi$
$131$	−1.10460e6			−0.491352			−0.245676	+	0.969352i	$0.579010\pi$
$132$		−	1.29388e6i		−	0.562565i
$133$	185162.			0.0787038
$134$		−	886939.i		−	0.368620i
$135$			772345.i			0.313914i
$136$			584912.i			0.232527i
$137$			3.80784e6i			1.48087i	0.672127	+	0.740436i	$0.265381\pi$
$137$			3.80784e6i			1.48087i	−0.672127	+	0.740436i	$0.734619\pi$
$138$	−910048.	+	568278.i	−0.346280	+	0.216234i
$139$	487348.			0.181466			0.0907329	−	0.995875i	$-0.471079\pi$
$139$	487348.			0.181466			0.0907329	+	0.995875i	$0.471079\pi$
$140$	220164.			0.0802347
$141$	1.73760e6			0.619858
$142$	−2.26482e6			−0.790984
$143$		−	1.04008e7i		−	3.55679i
$144$	248832.			0.0833333
$145$			6.11894e6i			2.00711i
$146$	−3.33991e6			−1.07319
$147$	1.81622e6			0.571762
$148$			2.58490e6i			0.797367i
$149$			121884.i			0.0368459i	0.999830	+	0.0184229i	$0.00586454\pi$
$149$			121884.i			0.0368459i	−0.999830	+	0.0184229i	$0.994135\pi$
$150$	2.28808e6			0.677948
$151$	1.69528e6			0.492392			0.246196	−	0.969220i	$-0.420819\pi$
$151$	1.69528e6			0.492392			0.246196	+	0.969220i	$0.420819\pi$
$152$		−	993302.i		−	0.282846i
$153$		−	785185.i		−	0.219229i
$154$	495121.			0.135565
$155$			560531.i			0.150524i
$156$	2.00022e6			0.526871
$157$		−	1.95602e6i		−	0.505446i	−0.967539	−	0.252723i	$-0.918674\pi$
$157$		−	1.95602e6i		−	0.505446i	0.967539	−	0.252723i	$-0.0813261\pi$
$158$			2.63393e6i			0.667778i
$159$			1.04503e6i			0.259978i
$160$		−	1.18107e6i		−	0.288348i
$161$	−217459.	−	348241.i	−0.0521074	−	0.0834455i
$162$	−334032.			−0.0785674
$163$	−787492.			−0.181837			−0.0909187	−	0.995858i	$-0.528980\pi$
$163$	−787492.			−0.181837			−0.0909187	+	0.995858i	$0.528980\pi$
$164$	−3.90333e6			−0.884920
$165$	8.24417e6			1.83525
$166$			3.48325e6i			0.761484i
$167$	5.41973e6			1.16367			0.581833	−	0.813309i	$-0.302336\pi$
$167$	5.41973e6			1.16367			0.581833	+	0.813309i	$0.302336\pi$
$168$			95218.7i			0.0200814i
$169$	1.12519e7			2.33112
$170$	−3.72686e6			−0.758571
$171$			1.33341e6i			0.266670i
$172$			1.01932e6i			0.200320i
$173$	−7.54362e6			−1.45694			−0.728470	−	0.685078i	$-0.759768\pi$
$173$	−7.54362e6			−1.45694			−0.728470	+	0.685078i	$0.759768\pi$
$174$	−2.64638e6			−0.502347
$175$			875561.i			0.163370i
$176$		−	2.65608e6i		−	0.487196i
$177$	−2.48785e6			−0.448647
$178$		−	1.98809e6i		−	0.352513i
$179$	1.69691e6			0.295869			0.147934	−	0.988997i	$-0.452738\pi$
$179$	1.69691e6			0.295869			0.147934	+	0.988997i	$0.452738\pi$
$180$			1.58547e6i			0.271857i
$181$		−	2.60307e6i		−	0.438985i	−0.975614	−	0.219492i	$-0.929560\pi$
$181$		−	2.60307e6i		−	0.438985i	0.975614	−	0.219492i	$-0.0704401\pi$
$182$			765410.i			0.126964i
$183$			3.01171e6i			0.491427i
$184$	−1.86815e6	+	1.16656e6i	−0.299887	+	0.187264i
$185$	−1.64701e7			−2.60124
$186$	−242424.			−0.0376736
$187$	−8.38122e6			−1.28169
$188$	3.56694e6			0.536813
$189$		−	127821.i		−	0.0189329i
$190$	6.32898e6			0.922726
$191$			1.10223e7i			1.58187i	0.611902	+	0.790934i	$0.290405\pi$
$191$			1.10223e7i			1.58187i	−0.611902	+	0.790934i	$0.709595\pi$
$192$	510803.			0.0721688
$193$	5.12899e6			0.713445			0.356722	−	0.934210i	$-0.383894\pi$
$193$	5.12899e6			0.713445			0.356722	+	0.934210i	$0.383894\pi$
$194$			7.39915e6i			1.01339i
$195$			1.27447e7i			1.71880i
$196$	3.72833e6			0.495161
$197$	4.29658e6			0.561984			0.280992	−	0.959710i	$-0.409337\pi$
$197$	4.29658e6			0.561984			0.280992	+	0.959710i	$0.409337\pi$
$198$			3.56552e6i			0.459333i
$199$		−	1.03380e7i		−	1.31183i	−0.754833	−	0.655917i	$-0.772282\pi$
$199$		−	1.03380e7i		−	1.31183i	0.754833	−	0.655917i	$-0.227718\pi$
$200$	4.69696e6			0.587120
$201$			2.44412e6i			0.300977i
$202$	3.60307e6			0.437137
$203$		−	1.01267e6i		−	0.121054i
$204$		−	1.61183e6i		−	0.189858i
$205$		−	2.48707e7i		−	2.88686i
$206$		−	7.89004e6i		−	0.902563i
$207$	2.50780e6	−	1.56599e6i	0.282736	−	0.176554i
$208$	4.10606e6			0.456284
$209$	1.42331e7			1.55905
$210$	−606701.			−0.0655113
$211$	−1.62452e7			−1.72933			−0.864667	−	0.502346i	$-0.832470\pi$
$211$	−1.62452e7			−1.72933			−0.864667	+	0.502346i	$0.832470\pi$
$212$			2.14524e6i			0.225148i
$213$	6.24110e6			0.645836
$214$			9.06674e6i			0.925145i
$215$	−6.49474e6			−0.653501
$216$	−685700.			−0.0680414
$217$		−	92766.7i		−	0.00907848i
$218$		−	862148.i		−	0.0832171i
$219$	9.20370e6			0.876254
$220$	1.69236e7			1.58937
$221$		−	1.29566e7i		−	1.20037i
$222$		−	7.12314e6i		−	0.651048i
$223$	−5.83554e6			−0.526219			−0.263110	−	0.964766i	$-0.584748\pi$
$223$	−5.83554e6			−0.526219			−0.263110	+	0.964766i	$0.584748\pi$
$224$			195465.i			0.0173910i
$225$	−6.30519e6			−0.553542
$226$		−	3.01317e6i		−	0.261035i
$227$			1.12366e6i			0.0960634i	0.998846	+	0.0480317i	$0.0152948\pi$
$227$			1.12366e6i			0.0960634i	−0.998846	+	0.0480317i	$0.984705\pi$
$228$			2.73722e6i			0.230943i
$229$			1.87885e7i			1.56453i	0.622944	+	0.782266i	$0.285936\pi$
$229$			1.87885e7i			1.56453i	−0.622944	+	0.782266i	$0.714064\pi$
$230$	−7.43292e6	−	1.19032e7i	−0.610908	−	0.978317i
$231$	−1.36439e6			−0.110689
$232$	−5.43249e6			−0.435046
$233$	1.13567e7			0.897810			0.448905	−	0.893579i	$-0.351814\pi$
$233$	1.13567e7			0.897810			0.448905	+	0.893579i	$0.351814\pi$
$234$	−5.51196e6			−0.430188
$235$			2.27273e7i			1.75124i
$236$	−5.10706e6			−0.388540
$237$		−	7.25825e6i		−	0.545239i
$238$	616787.			0.0457514
$239$	−1.80143e6			−0.131954			−0.0659772	−	0.997821i	$-0.521016\pi$
$239$	−1.80143e6			−0.131954			−0.0659772	+	0.997821i	$0.521016\pi$
$240$			3.25466e6i			0.235435i
$241$			3.33358e6i			0.238155i	0.992885	+	0.119077i	$0.0379936\pi$
$241$			3.33358e6i			0.238155i	−0.992885	+	0.119077i	$0.962006\pi$
$242$	2.80376e7			1.97831
$243$	920483.			0.0641500
$244$			6.18243e6i			0.425588i
$245$			2.37556e7i			1.61536i
$246$	1.07563e7			0.722534
$247$			2.20030e7i			1.46013i
$248$	−497649.			−0.0326263
$249$		−	9.59872e6i		−	0.621749i
$250$			1.19057e7i			0.761962i
$251$		−	2.45714e7i		−	1.55385i	−0.629592	−	0.776926i	$-0.716778\pi$
$251$		−	2.45714e7i		−	1.55385i	0.629592	−	0.776926i	$-0.283222\pi$
$252$		−	262392.i		−	0.0163964i
$253$	−1.67157e7	−	2.67687e7i	−1.03220	−	1.65298i
$254$	−4.64769e6			−0.283619
$255$	1.02700e7			0.619370
$256$	1.04858e6			0.0625000
$257$	−2.63033e7			−1.54957			−0.774783	−	0.632227i	$-0.782141\pi$
$257$	−2.63033e7			−1.54957			−0.774783	+	0.632227i	$0.782141\pi$
$258$		−	2.80891e6i		−	0.163561i
$259$	2.72576e6			0.156888
$260$			2.61624e7i			1.48853i
$261$	7.29256e6			0.410165
$262$	6.24858e6			0.347438
$263$		−	1.92094e7i		−	1.05596i	−0.849258	−	0.527978i	$-0.822950\pi$
$263$		−	1.92094e7i		−	1.05596i	0.849258	−	0.527978i	$-0.177050\pi$
$264$			7.31930e6i			0.397794i
$265$	−1.36687e7			−0.734497
$266$	−1.04743e6			−0.0556520
$267$			5.47853e6i			0.287826i
$268$			5.01729e6i			0.260654i
$269$	−4.77453e6			−0.245287			−0.122643	−	0.992451i	$-0.539137\pi$
$269$	−4.77453e6			−0.245287			−0.122643	+	0.992451i	$0.539137\pi$
$270$		−	4.36904e6i		−	0.221970i
$271$	2.41673e7			1.21428			0.607142	−	0.794593i	$-0.292316\pi$
$271$	2.41673e7			1.21428			0.607142	+	0.794593i	$0.292316\pi$
$272$		−	3.30876e6i		−	0.164422i
$273$		−	2.10922e6i		−	0.103666i
$274$		−	2.15404e7i		−	1.04713i
$275$			6.73029e7i			3.23620i
$276$	5.14801e6	−	3.21466e6i	0.244857	−	0.152900i
$277$	−9.10742e6			−0.428505			−0.214253	−	0.976778i	$-0.568732\pi$
$277$	−9.10742e6			−0.428505			−0.214253	+	0.976778i	$0.568732\pi$
$278$	−2.75686e6			−0.128316
$279$	668043.			0.0307604
$280$	−1.24544e6			−0.0567345
$281$		−	3.68293e7i		−	1.65987i	−0.557858	−	0.829936i	$-0.688377\pi$
$281$		−	3.68293e7i		−	1.65987i	0.557858	−	0.829936i	$-0.311623\pi$
$282$	−9.82934e6			−0.438306
$283$		−	1.16216e7i		−	0.512749i	−0.966578	−	0.256375i	$-0.917472\pi$
$283$		−	1.16216e7i		−	0.512749i	0.966578	−	0.256375i	$-0.0825280\pi$
$284$	1.28117e7			0.559310
$285$	−1.74406e7			−0.753402
$286$			5.88358e7i			2.51503i
$287$			4.11604e6i			0.174114i
$288$	−1.40761e6			−0.0589256
$289$	1.36968e7			0.567448
$290$		−	3.46139e7i		−	1.41924i
$291$		−	2.03897e7i		−	0.827430i
$292$	1.88934e7			0.758859
$293$			2.22176e7i			0.883273i	0.897194	+	0.441636i	$0.145602\pi$
$293$			2.22176e7i			0.883273i	−0.897194	+	0.441636i	$0.854398\pi$
$294$	−1.02741e7			−0.404297
$295$		−	3.25404e7i		−	1.26753i
$296$		−	1.46224e7i		−	0.563824i
$297$		−	9.82542e6i		−	0.375044i
$298$		−	689482.i		−	0.0260540i
$299$	4.13820e7	−	2.58409e7i	1.54810	−	0.966705i
$300$	−1.29433e7			−0.479382
$301$	1.07487e6			0.0394144
$302$	−9.58997e6			−0.348174
$303$	−9.92888e6			−0.356921
$304$			5.61897e6i			0.200003i
$305$	−3.93923e7			−1.38839
$306$			4.44168e6i			0.155018i
$307$	−6.36874e6			−0.220109			−0.110055	−	0.993926i	$-0.535103\pi$
$307$	−6.36874e6			−0.220109			−0.110055	+	0.993926i	$0.535103\pi$
$308$	−2.80082e6			−0.0958592
$309$			2.17424e7i			0.736940i
$310$		−	3.17084e6i		−	0.106436i
$311$	2.65152e7			0.881481			0.440741	−	0.897634i	$-0.354716\pi$
$311$	2.65152e7			0.881481			0.440741	+	0.897634i	$0.354716\pi$
$312$	−1.13150e7			−0.372554
$313$		−	6.87253e6i		−	0.224122i	−0.993701	−	0.112061i	$-0.964255\pi$
$313$		−	6.87253e6i		−	0.224122i	0.993701	−	0.112061i	$-0.0357451\pi$
$314$			1.10649e7i			0.357404i
$315$	1.67187e6			0.0534898
$316$		−	1.48997e7i		−	0.472191i
$317$	−2.15637e7			−0.676934			−0.338467	−	0.940978i	$-0.609908\pi$
$317$	−2.15637e7			−0.676934			−0.338467	+	0.940978i	$0.609908\pi$
$318$		−	5.91158e6i		−	0.183833i
$319$		−	7.78423e7i		−	2.39797i
$320$			6.68116e6i			0.203893i
$321$		−	2.49850e7i		−	0.755378i
$322$	1.23013e6	+	1.96995e6i	0.0368455	+	0.0590049i
$323$	1.77305e7			0.526156
$324$	1.88957e6			0.0555556
$325$	−1.04044e8			−3.03087
$326$	4.45473e6			0.128578
$327$			2.37580e6i			0.0679465i
$328$	2.20806e7			0.625733
$329$		−	3.76132e6i		−	0.105622i
$330$	−4.66361e7			−1.29772
$331$	1.04486e7			0.288121			0.144061	−	0.989569i	$-0.453984\pi$
$331$	1.04486e7			0.288121			0.144061	+	0.989569i	$0.453984\pi$
$332$		−	1.97043e7i		−	0.538451i
$333$			1.96291e7i			0.531578i
$334$	−3.06586e7			−0.822836
$335$	−3.19684e7			−0.850328
$336$		−	538638.i		−	0.0141997i
$337$		−	4.73012e6i		−	0.123590i	−0.998089	−	0.0617949i	$-0.980318\pi$
$337$		−	4.73012e6i		−	0.123590i	0.998089	−	0.0617949i	$-0.0196825\pi$
$338$	−6.36501e7			−1.64835
$339$			8.30333e6i			0.213134i
$340$	2.10823e7			0.536390
$341$		−	7.13082e6i		−	0.179836i
$342$		−	7.54289e6i		−	0.188564i
$343$		−	7.90143e6i		−	0.195805i
$344$		−	5.76613e6i		−	0.141648i
$345$	2.04827e7	+	3.28013e7i	0.498805	+	0.798793i
$346$	4.26732e7			1.03021
$347$	1.29524e7			0.310001			0.155000	−	0.987914i	$-0.450462\pi$
$347$	1.29524e7			0.310001			0.155000	+	0.987914i	$0.450462\pi$
$348$	1.49702e7			0.355213
$349$	−4.28996e7			−1.00920			−0.504600	−	0.863353i	$-0.668360\pi$
$349$	−4.28996e7			−1.00920			−0.504600	+	0.863353i	$0.668360\pi$
$350$		−	4.95292e6i		−	0.115520i
$351$	1.51892e7			0.351247
$352$			1.50251e7i			0.344500i
$353$	−3.57462e7			−0.812654			−0.406327	−	0.913728i	$-0.633191\pi$
$353$	−3.57462e7			−0.812654			−0.406327	+	0.913728i	$0.633191\pi$
$354$	1.40734e7			0.317241
$355$			8.16319e7i			1.82463i
$356$			1.12463e7i			0.249265i
$357$	−1.69966e6			−0.0373558
$358$	−9.59917e6			−0.209211
$359$		−	2.03417e7i		−	0.439647i	−0.975540	−	0.219823i	$-0.929452\pi$
$359$		−	2.03417e7i		−	0.439647i	0.975540	−	0.219823i	$-0.0705481\pi$
$360$		−	8.96878e6i		−	0.192232i
$361$	1.69357e7			0.359983
$362$			1.47252e7i			0.310409i
$363$	−7.72626e7			−1.61529
$364$		−	4.32981e6i		−	0.0897770i
$365$			1.20382e8i			2.47561i
$366$		−	1.70368e7i		−	0.347492i
$367$			1.24670e7i			0.252210i	0.992017	+	0.126105i	$0.0402477\pi$
$367$			1.24670e7i			0.252210i	−0.992017	+	0.126105i	$0.959752\pi$
$368$	1.05678e7	−	6.59907e6i	0.212052	−	0.132416i
$369$	−2.96409e7			−0.589946
$370$	9.31688e7			1.83935
$371$	2.26214e6			0.0442994
$372$	1.37136e6			0.0266393
$373$		−	6.54965e7i		−	1.26209i	−0.775745	−	0.631047i	$-0.782626\pi$
$373$		−	6.54965e7i		−	1.26209i	0.775745	−	0.631047i	$-0.217374\pi$
$374$	4.74114e7			0.906291
$375$		−	3.28081e7i		−	0.622140i
$376$	−2.01777e7			−0.379584
$377$	1.20337e8			2.24582
$378$			723067.i			0.0133876i
$379$			7.94040e7i			1.45856i	0.684215	+	0.729281i	$0.260145\pi$
$379$			7.94040e7i			1.45856i	−0.684215	+	0.729281i	$0.739855\pi$
$380$	−3.58021e7			−0.652466
$381$	1.28075e7			0.231574
$382$		−	6.23513e7i		−	1.11855i
$383$			1.75197e7i			0.311839i	0.987770	+	0.155920i	$0.0498341\pi$
$383$			1.75197e7i			0.311839i	−0.987770	+	0.155920i	$0.950166\pi$
$384$	−2.88954e6			−0.0510310
$385$		−	1.78459e7i		−	0.312720i
$386$	−2.90140e7			−0.504482
$387$			7.74045e6i			0.133547i
$388$		−	4.18559e7i		−	0.716575i
$389$		−	6.61863e6i		−	0.112440i	−0.998418	−	0.0562198i	$-0.982095\pi$
$389$		−	6.61863e6i		−	0.112440i	0.998418	−	0.0562198i	$-0.0179048\pi$
$390$		−	7.20950e7i		−	1.21538i
$391$	−2.08232e7	−	3.33466e7i	−0.348352	−	0.557855i
$392$	−2.10906e7			−0.350132
$393$	−1.72191e7			−0.283682
$394$	−2.43051e7			−0.397383
$395$	9.49359e7			1.54042
$396$		−	2.01696e7i		−	0.324797i
$397$	−2.15833e7			−0.344942			−0.172471	−	0.985015i	$-0.555175\pi$
$397$	−2.15833e7			−0.344942			−0.172471	+	0.985015i	$0.555175\pi$
$398$			5.84808e7i			0.927607i
$399$	2.88638e6			0.0454397
$400$	−2.65700e7			−0.415157
$401$		−	1.14160e8i		−	1.77044i	−0.465177	−	0.885218i	$-0.654009\pi$
$401$		−	1.14160e8i		−	1.77044i	0.465177	−	0.885218i	$-0.345991\pi$
$402$		−	1.38260e7i		−	0.212823i
$403$	1.10236e7			0.168425
$404$	−2.03820e7			−0.309103
$405$			1.20397e7i			0.181238i
$406$			5.72853e6i			0.0855983i
$407$	2.09525e8			3.10779
$408$			9.11788e6i			0.134250i
$409$	−7.91210e7			−1.15644			−0.578219	−	0.815882i	$-0.696252\pi$
$409$	−7.91210e7			−1.15644			−0.578219	+	0.815882i	$0.696252\pi$
$410$			1.40690e8i			2.04132i
$411$			5.93584e7i			0.854982i
$412$			4.46328e7i			0.638209i
$413$			5.38537e6i			0.0764479i
$414$	−1.41862e7	+	8.85857e6i	−0.199925	+	0.124843i
$415$	1.25549e8			1.75658
$416$	−2.32274e7			−0.322641
$417$	7.59701e6			0.104769
$418$	−8.05143e7			−1.10241
$419$			1.82747e7i			0.248433i	0.992255	+	0.124217i	$0.0396417\pi$
$419$			1.82747e7i			0.248433i	−0.992255	+	0.124217i	$0.960358\pi$
$420$	3.43202e6			0.0463235
$421$		−	5.58147e7i		−	0.748001i	−0.927428	−	0.374001i	$-0.877986\pi$
$421$		−	5.58147e7i		−	0.748001i	0.927428	−	0.374001i	$-0.122014\pi$
$422$	9.18970e7			1.22282
$423$	2.70865e7			0.357875
$424$		−	1.21353e7i		−	0.159204i
$425$			8.38413e7i			1.09217i
$426$	−3.53050e7			−0.456675
$427$	6.51934e6			0.0837375
$428$		−	5.12892e7i		−	0.654176i
$429$		−	1.62132e8i		−	2.05352i
$430$	3.67398e7			0.462095
$431$			2.26801e6i			0.0283278i	0.999900	+	0.0141639i	$0.00450865\pi$
$431$			2.26801e6i			0.0283278i	−0.999900	+	0.0141639i	$0.995491\pi$
$432$	3.87891e6			0.0481125
$433$		−	1.02154e8i		−	1.25833i	−0.777274	−	0.629163i	$-0.783398\pi$
$433$		−	1.02154e8i		−	1.25833i	0.777274	−	0.629163i	$-0.216602\pi$
$434$			524768.i			0.00641945i
$435$			9.53848e7i			1.15881i
$436$			4.87705e6i			0.0588434i
$437$	3.53622e7	+	5.66295e7i	0.423735	+	0.678576i
$438$	−5.20640e7			−0.619605
$439$	1.61254e7			0.190598			0.0952990	−	0.995449i	$-0.469619\pi$
$439$	1.61254e7			0.190598			0.0952990	+	0.995449i	$0.469619\pi$
$440$	−9.57345e7			−1.12386
$441$	2.83120e7			0.330107
$442$			7.32935e7i			0.848787i
$443$	1.06117e8			1.22060			0.610302	−	0.792169i	$-0.291048\pi$
$443$	1.06117e8			1.22060			0.610302	+	0.792169i	$0.291048\pi$
$444$			4.02946e7i			0.460360i
$445$	−7.16577e7			−0.813172
$446$	3.30108e7			0.372093
$447$			1.89999e6i			0.0212730i
$448$		−	1.10572e6i		−	0.0122973i
$449$	3.77407e7			0.416937			0.208468	−	0.978029i	$-0.433152\pi$
$449$	3.77407e7			0.416937			0.208468	+	0.978029i	$0.433152\pi$
$450$	3.56676e7			0.391414
$451$			3.16393e8i			3.44903i
$452$			1.70451e7i			0.184580i
$453$	2.64268e7			0.284283
$454$		−	6.35639e6i		−	0.0679271i
$455$	2.75881e7			0.292878
$456$		−	1.54840e7i		−	0.163301i
$457$			1.49571e7i			0.156711i	0.996925	+	0.0783554i	$0.0249669\pi$
$457$			1.49571e7i			0.156711i	−0.996925	+	0.0783554i	$0.975033\pi$
$458$		−	1.06284e8i		−	1.10629i
$459$		−	1.22398e7i		−	0.126572i
$460$	4.20470e7	+	6.73346e7i	0.431977	+	0.691775i
$461$	−1.12876e8			−1.15212			−0.576060	−	0.817407i	$-0.695411\pi$
$461$	−1.12876e8			−1.15212			−0.576060	+	0.817407i	$0.695411\pi$
$462$	7.71817e6			0.0782687
$463$	−7.86214e7			−0.792133			−0.396066	−	0.918222i	$-0.629625\pi$
$463$	−7.86214e7			−0.792133			−0.396066	+	0.918222i	$0.629625\pi$
$464$	3.07308e7			0.307624
$465$			8.73782e6i			0.0869049i
$466$	−6.42432e7			−0.634848
$467$			8.36411e7i			0.821238i	0.911807	+	0.410619i	$0.134687\pi$
$467$			8.36411e7i			0.821238i	−0.911807	+	0.410619i	$0.865313\pi$
$468$	3.11804e7			0.304189
$469$	5.29070e6			0.0512855
$470$		−	1.28565e8i		−	1.23831i
$471$		−	3.04914e7i		−	0.291819i
$472$	2.88899e7			0.274739
$473$	8.26231e7			0.780761
$474$			4.10588e7i			0.385542i
$475$		−	1.42380e8i		−	1.32852i
$476$	−3.48907e6			−0.0323511
$477$			1.62904e7i			0.150099i
$478$	1.01904e7			0.0933058
$479$			1.38160e8i			1.25712i	0.777762	+	0.628558i	$0.216355\pi$
$479$			1.38160e8i			1.25712i	−0.777762	+	0.628558i	$0.783645\pi$
$480$		−	1.84111e7i		−	0.166478i
$481$			3.23906e8i			2.91061i
$482$		−	1.88575e7i		−	0.168401i
$483$	−3.38985e6	−	5.42855e6i	−0.0300842	−	0.0481773i
$484$	−1.58605e8			−1.39888
$485$	2.66691e8			2.33767
$486$	−5.20704e6			−0.0453609
$487$	3.22179e7			0.278940			0.139470	−	0.990226i	$-0.455460\pi$
$487$	3.22179e7			0.278940			0.139470	+	0.990226i	$0.455460\pi$
$488$		−	3.49731e7i		−	0.300936i
$489$	−1.22758e7			−0.104984
$490$		−	1.34382e8i		−	1.14223i
$491$	4.89186e7			0.413266			0.206633	−	0.978419i	$-0.433749\pi$
$491$	4.89186e7			0.413266			0.206633	+	0.978419i	$0.433749\pi$
$492$	−6.08469e7			−0.510909
$493$		−	9.69705e7i		−	0.809280i
$494$		−	1.24468e8i		−	1.03247i
$495$	1.28514e8			1.05958
$496$	2.81513e6			0.0230703
$497$		−	1.35099e7i		−	0.110048i
$498$			5.42986e7i			0.439643i
$499$	−6.90945e7			−0.556086			−0.278043	−	0.960569i	$-0.589686\pi$
$499$	−6.90945e7			−0.556086			−0.278043	+	0.960569i	$0.589686\pi$
$500$		−	6.73486e7i		−	0.538789i
$501$	8.44852e7			0.671842
$502$			1.38997e8i			1.09874i
$503$			1.32771e8i			1.04328i	0.853166	+	0.521640i	$0.174680\pi$
$503$			1.32771e8i			1.04328i	−0.853166	+	0.521640i	$0.825320\pi$
$504$			1.48431e6i			0.0115940i
$505$		−	1.29867e8i		−	1.00838i
$506$	9.45582e7	+	1.51427e8i	0.729874	+	1.16883i
$507$	1.75399e8			1.34587
$508$	2.62913e7			0.200549
$509$	−5.13727e7			−0.389564			−0.194782	−	0.980847i	$-0.562400\pi$
$509$	−5.13727e7			−0.389564			−0.194782	+	0.980847i	$0.562400\pi$
$510$	−5.80960e7			−0.437961
$511$		−	1.99230e7i		−	0.149311i
$512$	−5.93164e6			−0.0441942
$513$			2.07858e7i			0.153962i
$514$	1.48794e8			1.09571
$515$	−2.84385e8			−2.08202
$516$			1.58896e7i			0.115655i
$517$		−	2.89127e8i		−	2.09226i
$518$	−1.54192e7			−0.110936
$519$	−1.17593e8			−0.841165
$520$		−	1.47997e8i		−	1.05255i
$521$			1.53373e8i			1.08451i	0.840213	+	0.542257i	$0.182430\pi$
$521$			1.53373e8i			1.08451i	−0.840213	+	0.542257i	$0.817570\pi$
$522$	−4.12530e7			−0.290030
$523$		−	2.02000e8i		−	1.41204i	−0.708193	−	0.706019i	$-0.750489\pi$
$523$		−	2.02000e8i		−	1.41204i	0.708193	−	0.706019i	$-0.249511\pi$
$524$	−3.53473e7			−0.245676
$525$			1.36486e7i			0.0943217i
$526$			1.08665e8i			0.746674i
$527$		−	8.88308e6i		−	0.0606921i
$528$		−	4.14042e7i		−	0.281283i
$529$	6.49753e7	−	1.33014e8i	0.438916	−	0.898528i
$530$	7.73219e7			0.519368
$531$	−3.87818e7			−0.259026
$532$	5.92517e6			0.0393519
$533$	−4.89114e8			−3.23020
$534$		−	3.09912e7i		−	0.203524i
$535$	3.26797e8			2.13411
$536$		−	2.83821e7i		−	0.184310i
$537$	2.64522e7			0.170820
$538$	2.70088e7			0.173444
$539$		−	3.02208e8i		−	1.92992i
$540$			2.47150e7i			0.156957i
$541$	−7.94230e6			−0.0501597			−0.0250798	−	0.999685i	$-0.507984\pi$
$541$	−7.94230e6			−0.0501597			−0.0250798	+	0.999685i	$0.507984\pi$
$542$	−1.36711e8			−0.858628
$543$		−	4.05778e7i		−	0.253448i
$544$			1.87172e7i			0.116264i
$545$	−3.10749e7			−0.191964
$546$			1.19316e7i			0.0733026i
$547$	−2.96476e8			−1.81145			−0.905727	−	0.423863i	$-0.860674\pi$
$547$	−2.96476e8			−1.81145			−0.905727	+	0.423863i	$0.860674\pi$
$548$			1.21851e8i			0.740436i
$549$			4.69478e7i			0.283726i
$550$		−	3.80723e8i		−	2.28834i
$551$			1.64676e8i			0.984409i
$552$	−2.91215e7	+	1.81849e7i	−0.173140	+	0.108117i
$553$	−1.57117e7			−0.0929068
$554$	5.15193e7			0.302999
$555$	−2.56743e8			−1.50183
$556$	1.55951e7			0.0907329
$557$		−	4.04715e7i		−	0.234198i	−0.993120	−	0.117099i	$-0.962640\pi$
$557$		−	4.04715e7i		−	0.234198i	0.993120	−	0.117099i	$-0.0373595\pi$
$558$	−3.77902e6			−0.0217509
$559$			1.27728e8i			0.731222i
$560$	7.04525e6			0.0401173
$561$	−1.30650e8			−0.739983
$562$			2.08338e8i			1.17371i
$563$		−	2.48158e8i		−	1.39060i	−0.718719	−	0.695300i	$-0.755271\pi$
$563$		−	2.48158e8i		−	1.39060i	0.718719	−	0.695300i	$-0.244729\pi$
$564$	5.56032e7			0.309929
$565$	−1.08605e8			−0.602152
$566$			6.57414e7i			0.362568i
$567$		−	1.99254e6i		−	0.0109309i
$568$	−7.24741e7			−0.395492
$569$		−	1.01298e7i		−	0.0549872i	−0.999622	−	0.0274936i	$-0.991247\pi$
$569$		−	1.01298e7i		−	0.0549872i	0.999622	−	0.0274936i	$-0.00875260\pi$
$570$	9.86590e7			0.532736
$571$		−	1.12617e8i		−	0.604919i	−0.953162	−	0.302460i	$-0.902192\pi$
$571$		−	1.12617e8i		−	0.604919i	0.953162	−	0.302460i	$-0.0978077\pi$
$572$		−	3.32826e8i		−	1.77840i
$573$			1.71820e8i			0.913292i
$574$		−	2.32838e7i		−	0.123117i
$575$	−2.67780e8	+	1.67215e8i	−1.40856	+	0.879572i
$576$	7.96262e6			0.0416667
$577$	−2.55084e8			−1.32787			−0.663935	−	0.747790i	$-0.731115\pi$
$577$	−2.55084e8			−1.32787			−0.663935	+	0.747790i	$0.731115\pi$
$578$	−7.74809e7			−0.401247
$579$	7.99531e7			0.411907
$580$			1.95806e8i			1.00356i
$581$	−2.07780e7			−0.105944
$582$			1.15341e8i			0.585081i
$583$	1.73887e8			0.877529
$584$	−1.06877e8			−0.536594
$585$			1.98670e8i			0.992352i
$586$		−	1.25682e8i		−	0.624568i
$587$	−3.38682e8			−1.67447			−0.837236	−	0.546841i	$-0.815830\pi$
$587$	−3.38682e8			−1.67447			−0.837236	+	0.546841i	$0.815830\pi$
$588$	5.81189e7			0.285881
$589$			1.50853e7i			0.0738258i
$590$			1.84076e8i			0.896277i
$591$	6.69770e7			0.324462
$592$			8.27168e7i			0.398684i
$593$	−3.45172e8			−1.65528			−0.827639	−	0.561261i	$-0.810316\pi$
$593$	−3.45172e8			−1.65528			−0.827639	+	0.561261i	$0.810316\pi$
$594$			5.55810e7i			0.265196i
$595$		−	2.22312e7i		−	0.105539i
$596$			3.90030e6i			0.0184229i
$597$		−	1.61154e8i		−	0.757388i
$598$	−2.34092e8	+	1.46178e8i	−1.09467	+	0.683564i
$599$	−2.74458e8			−1.27701			−0.638507	−	0.769616i	$-0.720448\pi$
$599$	−2.74458e8			−1.27701			−0.638507	+	0.769616i	$0.720448\pi$
$600$	7.32184e7			0.338974
$601$	2.03299e8			0.936509			0.468255	−	0.883594i	$-0.344883\pi$
$601$	2.03299e8			0.936509			0.468255	+	0.883594i	$0.344883\pi$
$602$	−6.08036e6			−0.0278702
$603$			3.81000e7i			0.173769i
$604$	5.42490e7			0.246196
$605$		−	1.01057e9i		−	4.56354i
$606$	5.61662e7			0.252381
$607$	−6.59874e7			−0.295050			−0.147525	−	0.989058i	$-0.547131\pi$
$607$	−6.59874e7			−0.295050			−0.147525	+	0.989058i	$0.547131\pi$
$608$		−	3.17857e7i		−	0.141423i
$609$		−	1.57860e7i		−	0.0698907i
$610$	2.22837e8			0.981741
$611$	4.46963e8			1.95951
$612$		−	2.51259e7i		−	0.109614i
$613$			3.77934e8i			1.64072i	0.571846	+	0.820361i	$0.306227\pi$
$613$			3.77934e8i			1.64072i	−0.571846	+	0.820361i	$0.693773\pi$
$614$	3.60270e7			0.155641
$615$		−	3.87695e8i		−	1.66673i
$616$	1.58439e7			0.0677827
$617$		−	3.82983e8i		−	1.63051i	−0.579101	−	0.815256i	$-0.696596\pi$
$617$		−	3.82983e8i		−	1.63051i	0.579101	−	0.815256i	$-0.303404\pi$
$618$		−	1.22994e8i		−	0.521095i
$619$			4.36109e8i			1.83875i	0.393382	+	0.919375i	$0.371305\pi$
$619$			4.36109e8i			1.83875i	−0.393382	+	0.919375i	$0.628695\pi$
$620$			1.79370e7i			0.0752618i
$621$	3.90927e7	−	2.44114e7i	0.163238	−	0.101934i
$622$	−1.49992e8			−0.623301
$623$	1.18592e7			0.0490445
$624$	6.40071e7			0.263436
$625$	2.36952e7			0.0970557
$626$			3.88769e7i			0.158478i
$627$	2.21871e8			0.900116
$628$		−	6.25927e7i		−	0.252723i
$629$	2.61011e8			1.04884
$630$	−9.45753e6			−0.0378230
$631$		−	5.07572e7i		−	0.202027i	−0.994885	−	0.101014i	$-0.967791\pi$
$631$		−	5.07572e7i		−	0.202027i	0.994885	−	0.101014i	$-0.0322085\pi$
$632$			8.42856e7i			0.333889i
$633$	−2.53238e8			−0.998431
$634$	1.21983e8			0.478665
$635$			1.67519e8i			0.654249i
$636$			3.34410e7i			0.129989i
$637$	4.67186e8			1.80747
$638$			4.40342e8i			1.69562i
$639$	9.72891e7			0.372874
$640$		−	3.77944e7i		−	0.144174i
$641$		−	4.83596e8i		−	1.83615i	−0.396402	−	0.918077i	$-0.629742\pi$
$641$		−	4.83596e8i		−	1.83615i	0.396402	−	0.918077i	$-0.370258\pi$
$642$			1.41337e8i			0.534133i
$643$		−	2.69061e6i		−	0.0101209i	−0.999987	−	0.00506043i	$-0.998389\pi$
$643$		−	2.69061e6i		−	0.0101209i	0.999987	−	0.00506043i	$-0.00161079\pi$
$644$	−6.95868e6	−	1.11437e7i	−0.0260537	−	0.0417227i
$645$	−1.01243e8			−0.377299
$646$	−1.00299e8			−0.372049
$647$	−4.58921e8			−1.69444			−0.847218	−	0.531245i	$-0.821724\pi$
$647$	−4.58921e8			−1.69444			−0.847218	+	0.531245i	$0.821724\pi$
$648$	−1.06890e7			−0.0392837
$649$			4.13964e8i			1.51436i
$650$	5.88562e8			2.14315
$651$		−	1.44609e6i		−	0.00524146i
$652$	−2.51997e7			−0.0909187
$653$	1.36879e8			0.491584			0.245792	−	0.969323i	$-0.420952\pi$
$653$	1.36879e8			0.491584			0.245792	+	0.969323i	$0.420952\pi$
$654$		−	1.34396e7i		−	0.0480454i
$655$		−	2.25221e8i		−	0.801465i
$656$	−1.24907e8			−0.442460
$657$	1.43472e8			0.505906
$658$			2.12773e7i			0.0746858i
$659$			2.29136e8i			0.800641i	0.916375	+	0.400320i	$0.131101\pi$
$659$			2.29136e8i			0.800641i	−0.916375	+	0.400320i	$0.868899\pi$
$660$	2.63813e8			0.917625
$661$			2.95149e8i			1.02197i	0.859590	+	0.510984i	$0.170719\pi$
$661$			2.95149e8i			1.02197i	−0.859590	+	0.510984i	$0.829281\pi$
$662$	−5.91063e7			−0.203732
$663$		−	2.01973e8i		−	0.693032i
$664$			1.11464e8i			0.380742i
$665$			3.77531e7i			0.128377i
$666$		−	1.11039e8i		−	0.375883i
$667$	3.09713e8	−	1.93400e8i	1.04372	−	0.651747i
$668$	1.73431e8			0.581833
$669$	−9.09671e7			−0.303813
$670$	1.80841e8			0.601273
$671$	5.01131e8			1.65876
$672$			3.04700e6i			0.0100407i
$673$	−1.61901e7			−0.0531134			−0.0265567	−	0.999647i	$-0.508454\pi$
$673$	−1.61901e7			−0.0531134			−0.0265567	+	0.999647i	$0.508454\pi$
$674$			2.67576e7i			0.0873911i
$675$	−9.82883e7			−0.319588
$676$	3.60059e8			1.16556
$677$			1.19911e8i			0.386451i	0.981154	+	0.193225i	$0.0618948\pi$
$677$			1.19911e8i			0.386451i	−0.981154	+	0.193225i	$0.938105\pi$
$678$		−	4.69707e7i		−	0.150709i
$679$	−4.41368e7			−0.140991
$680$	−1.19259e8			−0.379285
$681$			1.75161e7i			0.0554622i
$682$			4.03380e7i			0.127163i
$683$	−2.15755e8			−0.677173			−0.338586	−	0.940935i	$-0.609949\pi$
$683$	−2.15755e8			−0.677173			−0.338586	+	0.940935i	$0.609949\pi$
$684$			4.26690e7i			0.133335i
$685$	−7.76392e8			−2.41551
$686$			4.46972e7i			0.138455i
$687$			2.92883e8i			0.903283i
$688$			3.26182e7i			0.100160i
$689$			2.68813e8i			0.821851i
$690$	−1.15868e8	−	1.85552e8i	−0.352708	−	0.564832i
$691$	−1.20685e7			−0.0365779			−0.0182890	−	0.999833i	$-0.505822\pi$
$691$	−1.20685e7			−0.0365779			−0.0182890	+	0.999833i	$0.505822\pi$
$692$	−2.41396e8			−0.728470
$693$	−2.12688e7			−0.0639061
$694$	−7.32700e7			−0.219204
$695$			9.93668e7i			0.295997i
$696$	−8.46841e7			−0.251174
$697$			3.94141e8i			1.16400i
$698$	2.42677e8			0.713612
$699$	1.77033e8			0.518351
$700$			2.80180e7i			0.0816850i
$701$			2.53095e8i			0.734734i	0.930076	+	0.367367i	$0.119741\pi$
$701$			2.53095e8i			0.734734i	−0.930076	+	0.367367i	$0.880259\pi$
$702$	−8.59230e7			−0.248369
$703$	−4.43251e8			−1.27580
$704$		−	8.49947e7i		−	0.243598i
$705$			3.54284e8i			1.01108i
$706$	2.02211e8			0.574633
$707$			2.14927e7i			0.0608181i
$708$	−7.96112e7			−0.224323
$709$		−	2.68381e8i		−	0.753031i	−0.926410	−	0.376515i	$-0.877122\pi$
$709$		−	2.68381e8i		−	0.753031i	0.926410	−	0.376515i	$-0.122878\pi$
$710$		−	4.61780e8i		−	1.29021i
$711$		−	1.13145e8i		−	0.314794i
$712$		−	6.36188e7i		−	0.176257i
$713$	2.83716e7	−	1.77166e7i	0.0782736	−	0.0488778i
$714$	9.61475e6			0.0264146
$715$	2.12065e9			5.80164
$716$	5.43011e7			0.147934
$717$	−2.80815e7			−0.0761839
$718$			1.15070e8i			0.310877i
$719$	−5.12392e8			−1.37853			−0.689264	−	0.724510i	$-0.742066\pi$
$719$	−5.12392e8			−1.37853			−0.689264	+	0.724510i	$0.742066\pi$
$720$			5.07351e7i			0.135929i
$721$	4.70651e7			0.125572
$722$	−9.58030e7			−0.254547
$723$			5.19653e7i			0.137499i
$724$		−	8.32981e7i		−	0.219492i
$725$	−7.78693e8			−2.04339
$726$	4.37063e8			1.14218
$727$			2.72582e8i			0.709405i	0.934979	+	0.354702i	$0.115418\pi$
$727$			2.72582e8i			0.709405i	−0.934979	+	0.354702i	$0.884582\pi$
$728$			2.44931e7i			0.0634819i
$729$	1.43489e7			0.0370370
$730$		−	6.80983e8i		−	1.75052i
$731$	1.02926e8			0.263496
$732$			9.63746e7i			0.245714i
$733$			2.13837e8i			0.542963i	0.962444	+	0.271482i	$0.0875136\pi$
$733$			2.13837e8i			0.542963i	−0.962444	+	0.271482i	$0.912486\pi$
$734$		−	7.05239e7i		−	0.178340i
$735$			3.70314e8i			0.932626i
$736$	−5.97807e7	+	3.73300e7i	−0.149944	+	0.0936319i
$737$	4.06687e8			1.01592
$738$	1.67674e8			0.417155
$739$	1.90058e8			0.470926			0.235463	−	0.971883i	$-0.424339\pi$
$739$	1.90058e8			0.470926			0.235463	+	0.971883i	$0.424339\pi$
$740$	−5.27042e8			−1.30062
$741$			3.42992e8i			0.843005i
$742$	−1.27966e7			−0.0313244
$743$		−	3.99601e8i		−	0.974226i	−0.873339	−	0.487113i	$-0.838050\pi$
$743$		−	3.99601e8i		−	0.974226i	0.873339	−	0.487113i	$-0.161950\pi$
$744$	−7.75758e6			−0.0188368
$745$	−2.48513e7			−0.0601009
$746$			3.70504e8i			0.892435i
$747$		−	1.49629e8i		−	0.358967i
$748$	−2.68199e8			−0.640844
$749$	−5.40842e7			−0.128714
$750$			1.85591e8i			0.439919i
$751$			1.83487e8i			0.433197i	0.976261	+	0.216598i	$0.0694962\pi$
$751$			1.83487e8i			0.433197i	−0.976261	+	0.216598i	$0.930504\pi$
$752$	1.14142e8			0.268406
$753$		−	3.83031e8i		−	0.897117i
$754$	−6.80728e8			−1.58803
$755$			3.45656e8i			0.803162i
$756$		−	4.09029e6i		−	0.00946647i
$757$			2.11689e8i			0.487990i	0.969776	+	0.243995i	$0.0784581\pi$
$757$			2.11689e8i			0.487990i	−0.969776	+	0.243995i	$0.921542\pi$
$758$		−	4.49177e8i		−	1.03136i
$759$	−2.60572e8	−	4.17283e8i	−0.595939	−	0.954346i
$760$	2.02527e8			0.461363
$761$	3.19833e8			0.725721			0.362860	−	0.931844i	$-0.381800\pi$
$761$	3.19833e8			0.725721			0.362860	+	0.931844i	$0.381800\pi$
$762$	−7.24503e7			−0.163748
$763$	5.14282e6			0.0115778
$764$			3.52712e8i			0.790934i
$765$	1.60094e8			0.357594
$766$		−	9.91065e7i		−	0.220504i
$767$	−6.39950e8			−1.41827
$768$	1.63457e7			0.0360844
$769$		−	1.22652e8i		−	0.269710i	−0.990865	−	0.134855i	$-0.956943\pi$
$769$		−	1.22652e8i		−	0.269710i	0.990865	−	0.134855i	$-0.0430568\pi$
$770$			1.00952e8i			0.221126i
$771$	−4.10027e8			−0.894643
$772$	1.64128e8			0.356722
$773$			2.40409e8i			0.520490i	0.965543	+	0.260245i	$0.0838034\pi$
$773$			2.40409e8i			0.520490i	−0.965543	+	0.260245i	$0.916197\pi$
$774$		−	4.37866e7i		−	0.0944318i
$775$	−7.13329e7			−0.153245
$776$			2.36773e8i			0.506695i
$777$	4.24904e7			0.0905791
$778$			3.74407e7i			0.0795069i
$779$		−	6.69332e8i		−	1.41589i
$780$			4.07831e8i			0.859402i
$781$		−	1.03848e9i		−	2.17995i
$782$	1.17794e8	+	1.88637e8i	0.246322	+	0.394463i
$783$	1.13680e8			0.236809
$784$	1.19307e8			0.247580
$785$	3.98819e8			0.824454
$786$	9.74058e7			0.200594
$787$		−	4.21078e8i		−	0.863850i	−0.901910	−	0.431925i	$-0.857835\pi$
$787$		−	4.21078e8i		−	0.863850i	0.901910	−	0.431925i	$-0.142165\pi$
$788$	1.37491e8			0.280992
$789$		−	2.99445e8i		−	0.609657i
$790$	−5.37039e8			−1.08924
$791$	1.79739e7			0.0363173
$792$			1.14097e8i			0.229666i
$793$			7.74701e8i			1.55351i
$794$	1.22093e8			0.243911
$795$	−2.13074e8			−0.424062
$796$		−	3.30817e8i		−	0.655917i
$797$		−	2.64341e8i		−	0.522144i	−0.965319	−	0.261072i	$-0.915924\pi$
$797$		−	2.64341e8i		−	0.522144i	0.965319	−	0.261072i	$-0.0840760\pi$
$798$	−1.63278e7			−0.0321307
$799$		−	3.60174e8i		−	0.706109i
$800$	1.50303e8			0.293560
$801$			8.54018e7i			0.166176i
$802$			6.45785e8i			1.25189i
$803$		−	1.53144e9i		−	2.95770i
$804$			7.82117e7i			0.150489i
$805$	7.10040e7	−	4.43383e7i	0.136112	−	0.0849946i
$806$	−6.23588e7			−0.119095
$807$	−7.44276e7			−0.141616
$808$	1.15298e8			0.218569
$809$	4.17196e8			0.787943			0.393971	−	0.919123i	$-0.371101\pi$
$809$	4.17196e8			0.787943			0.393971	+	0.919123i	$0.371101\pi$
$810$		−	6.81067e7i		−	0.128155i
$811$	4.51507e8			0.846452			0.423226	−	0.906024i	$-0.360898\pi$
$811$	4.51507e8			0.846452			0.423226	+	0.906024i	$0.360898\pi$
$812$		−	3.24055e7i		−	0.0605271i
$813$	3.76731e8			0.701067
$814$	−1.18525e9			−2.19754
$815$		−	1.60564e8i		−	0.296603i
$816$		−	5.15785e7i		−	0.0949289i
$817$	−1.74790e8			−0.320516
$818$	4.47576e8			0.817724
$819$		−	3.28795e7i		−	0.0598513i
$820$		−	7.95861e8i		−	1.44343i
$821$	8.80657e8			1.59139			0.795697	−	0.605695i	$-0.207105\pi$
$821$	8.80657e8			1.59139			0.795697	+	0.605695i	$0.207105\pi$
$822$		−	3.35782e8i		−	0.604563i
$823$	2.76316e8			0.495686			0.247843	−	0.968800i	$-0.420278\pi$
$823$	2.76316e8			0.495686			0.247843	+	0.968800i	$0.420278\pi$
$824$		−	2.52481e8i		−	0.451282i
$825$			1.04915e9i			1.86842i
$826$		−	3.04643e7i		−	0.0540568i
$827$			8.50421e8i			1.50355i	0.659421	+	0.751774i	$0.270802\pi$
$827$			8.50421e8i			1.50355i	−0.659421	+	0.751774i	$0.729198\pi$
$828$	8.02495e7	−	5.01117e7i	0.141368	−	0.0882770i
$829$	5.10034e8			0.895231			0.447616	−	0.894226i	$-0.352273\pi$
$829$	5.10034e8			0.895231			0.447616	+	0.894226i	$0.352273\pi$
$830$	−7.10211e8			−1.24209
$831$	−1.41971e8			−0.247398
$832$	1.31394e8			0.228142
$833$		−	3.76470e8i		−	0.651321i
$834$	−4.29752e7			−0.0740831
$835$			1.10504e9i			1.89810i
$836$	4.55458e8			0.779524
$837$	1.04138e7			0.0177595
$838$		−	1.03378e8i		−	0.175669i
$839$			2.75191e8i			0.465960i	0.972482	+	0.232980i	$0.0748476\pi$
$839$			2.75191e8i			0.465960i	−0.972482	+	0.232980i	$0.925152\pi$
$840$	−1.94144e7			−0.0327557
$841$	3.05809e8			0.514118
$842$			3.15736e8i			0.528917i
$843$		−	5.74112e8i		−	0.958328i
$844$	−5.19848e8			−0.864667
$845$			2.29417e9i			3.80239i
$846$	−1.53224e8			−0.253056
$847$			1.67248e8i			0.275239i
$848$			6.86476e7i			0.112574i
$849$		−	1.81162e8i		−	0.296036i
$850$		−	4.74278e8i		−	0.772282i
$851$	5.20566e8	+	8.33642e8i	0.844671	+	1.35267i
$852$	1.99715e8			0.322918
$853$	−9.04348e8			−1.45710			−0.728548	−	0.684994i	$-0.759805\pi$
$853$	−9.04348e8			−1.45710			−0.728548	+	0.684994i	$0.759805\pi$
$854$	−3.68790e7			−0.0592114
$855$	−2.71872e8			−0.434977
$856$			2.90136e8i			0.462573i
$857$	−2.00435e8			−0.318442			−0.159221	−	0.987243i	$-0.550898\pi$
$857$	−2.00435e8			−0.318442			−0.159221	+	0.987243i	$0.550898\pi$
$858$			9.17159e8i			1.45205i
$859$	−8.00222e8			−1.26250			−0.631250	−	0.775580i	$-0.717458\pi$
$859$	−8.00222e8			−1.26250			−0.631250	+	0.775580i	$0.717458\pi$
$860$	−2.07832e8			−0.326751
$861$			6.41627e7i			0.100525i
$862$		−	1.28298e7i		−	0.0200308i
$863$	−5.10212e8			−0.793814			−0.396907	−	0.917859i	$-0.629916\pi$
$863$	−5.10212e8			−0.793814			−0.396907	+	0.917859i	$0.629916\pi$
$864$	−2.19424e7			−0.0340207
$865$		−	1.53809e9i		−	2.37648i
$866$			5.77872e8i			0.889770i
$867$	2.13512e8			0.327616
$868$		−	2.96853e6i		−	0.00453924i
$869$	−1.20773e9			−1.84039
$870$		−	5.39578e8i		−	0.819400i
$871$			6.28700e8i			0.951457i
$872$		−	2.75888e7i		−	0.0416086i
$873$		−	3.17843e8i		−	0.477717i
$874$	−2.00039e8	−	3.20345e8i	−0.299626	−	0.479826i
$875$	−7.10187e7			−0.106010
$876$	2.94518e8			0.438127
$877$	8.77639e7			0.130112			0.0650560	−	0.997882i	$-0.479277\pi$
$877$	8.77639e7			0.130112			0.0650560	+	0.997882i	$0.479277\pi$
$878$	−9.12193e7			−0.134773
$879$			3.46339e8i			0.509958i
$880$	5.41556e8			0.794686
$881$		−	4.14993e8i		−	0.606895i	−0.952848	−	0.303447i	$-0.901862\pi$
$881$		−	4.14993e8i		−	0.606895i	0.952848	−	0.303447i	$-0.0981377\pi$
$882$	−1.60157e8			−0.233421
$883$	−1.10770e7			−0.0160894			−0.00804472	−	0.999968i	$-0.502561\pi$
$883$	−1.10770e7			−0.0160894			−0.00804472	+	0.999968i	$0.502561\pi$
$884$		−	4.14611e8i		−	0.600183i
$885$		−	5.07255e8i		−	0.731807i
$886$	−6.00290e8			−0.863097
$887$	4.31069e7			0.0617698			0.0308849	−	0.999523i	$-0.490167\pi$
$887$	4.31069e7			0.0617698			0.0308849	+	0.999523i	$0.490167\pi$
$888$		−	2.27941e8i		−	0.325524i
$889$		−	2.77240e7i		−	0.0394594i
$890$	4.05357e8			0.575000
$891$		−	1.53163e8i		−	0.216532i
$892$	−1.86737e8			−0.263110
$893$			6.11650e8i			0.858911i
$894$		−	1.07480e7i		−	0.0150423i
$895$			3.45988e8i			0.482605i
$896$			6.25488e6i			0.00869551i
$897$	6.45081e8	−	4.02820e8i	0.893793	−	0.558127i
$898$	−2.13493e8			−0.294819
$899$	8.25034e7			0.113551
$900$	−2.01766e8			−0.276771
$901$	2.16616e8			0.296154
$902$		−	1.78979e9i		−	2.43884i
$903$	1.67555e7			0.0227559
$904$		−	9.64216e7i		−	0.130518i
$905$	5.30747e8			0.716047
$906$	−1.49493e8			−0.201018
$907$		−	6.87747e8i		−	0.921737i	−0.887469	−	0.460868i	$-0.847538\pi$
$907$		−	6.87747e8i		−	0.921737i	0.887469	−	0.460868i	$-0.152462\pi$
$908$			3.59572e7i			0.0480317i
$909$	−1.54776e8			−0.206069
$910$	−1.56062e8			−0.207096
$911$			3.81242e8i			0.504249i	0.967695	+	0.252125i	$0.0811293\pi$
$911$			3.81242e8i			0.504249i	−0.967695	+	0.252125i	$0.918871\pi$
$912$			8.75910e7i			0.115472i
$913$	−1.59717e9			−2.09865
$914$		−	8.46102e7i		−	0.110811i
$915$	−6.14065e8			−0.801588
$916$			6.01231e8i			0.782266i
$917$			3.72736e7i			0.0483385i
$918$			6.92389e7i			0.0894998i
$919$			4.86233e8i			0.626467i	0.949676	+	0.313233i	$0.101412\pi$
$919$			4.86233e8i			0.626467i	−0.949676	+	0.313233i	$0.898588\pi$
$920$	−2.37853e8	−	3.80902e8i	−0.305454	−	0.489159i
$921$	−9.92788e7			−0.127080
$922$	6.38521e8			0.814672
$923$	1.60540e9			2.04163
$924$	−4.36605e7			−0.0553443
$925$		−	2.09597e9i		−	2.64826i
$926$	4.44750e8			0.560123
$927$			3.38931e8i			0.425472i
$928$	−1.73840e8			−0.217523
$929$	8.56011e8			1.06766			0.533829	−	0.845592i	$-0.320752\pi$
$929$	8.56011e8			1.06766			0.533829	+	0.845592i	$0.320752\pi$
$930$		−	4.94286e7i		−	0.0614510i
$931$			6.39324e8i			0.792268i
$932$	3.63414e8			0.448905
$933$	4.13331e8			0.508924
$934$		−	4.73145e8i		−	0.580703i
$935$		−	1.70887e9i		−	2.09062i
$936$	−1.76383e8			−0.215094
$937$			2.22251e8i			0.270162i	0.990835	+	0.135081i	$0.0431295\pi$
$937$			2.22251e8i			0.270162i	−0.990835	+	0.135081i	$0.956870\pi$
$938$	−2.99287e7			−0.0362643
$939$		−	1.07132e8i		−	0.129397i
$940$			7.27274e8i			0.875618i
$941$		−	2.78171e8i		−	0.333843i	−0.985970	−	0.166922i	$-0.946617\pi$
$941$		−	2.78171e8i		−	0.333843i	0.985970	−	0.166922i	$-0.0533827\pi$
$942$			1.72485e8i			0.206347i
$943$	−1.25884e9	+	7.86082e8i	−1.50119	+	0.937417i
$944$	−1.63426e8			−0.194270
$945$	2.60619e7			0.0308823
$946$	−4.67387e8			−0.552081
$947$	−1.13787e9			−1.33981			−0.669903	−	0.742449i	$-0.733664\pi$
$947$	−1.13787e9			−1.33981			−0.669903	+	0.742449i	$0.733664\pi$
$948$		−	2.32264e8i		−	0.272619i
$949$	2.36747e9			2.77004
$950$			8.05422e8i			0.939405i
$951$	−3.36145e8			−0.390828
$952$	1.97372e7			0.0228757
$953$		−	6.71876e8i		−	0.776266i	−0.921603	−	0.388133i	$-0.873120\pi$
$953$		−	6.71876e8i		−	0.776266i	0.921603	−	0.388133i	$-0.126880\pi$
$954$		−	9.21524e7i		−	0.106136i
$955$	−2.24736e9			−2.58025
$956$	−5.76458e7			−0.0659772
$957$		−	1.21344e9i		−	1.38447i
$958$		−	7.81551e8i		−	0.888916i
$959$	1.28491e8			0.145686
$960$			1.04149e8i			0.117718i
$961$	−8.79946e8			−0.991484
$962$		−	1.83229e9i		−	2.05811i
$963$		−	3.89478e8i		−	0.436118i
$964$			1.06674e8i			0.119077i
$965$			1.04577e9i			1.16373i
$966$	1.91759e7	+	3.07085e7i	0.0212727	+	0.0340665i
$967$	−1.31309e8			−0.145216			−0.0726082	−	0.997361i	$-0.523132\pi$
$967$	−1.31309e8			−0.145216			−0.0726082	+	0.997361i	$0.523132\pi$
$968$	8.97204e8			0.989157
$969$	2.76392e8			0.303776
$970$	−1.50863e9			−1.65298
$971$		−	1.19993e8i		−	0.131069i	−0.997850	−	0.0655344i	$-0.979125\pi$
$971$		−	1.19993e8i		−	0.131069i	0.997850	−	0.0655344i	$-0.0208752\pi$
$972$	2.94555e7			0.0320750
$973$		−	1.64450e7i		−	0.0178523i
$974$	−1.82252e8			−0.197240
$975$	−1.62189e9			−1.74987
$976$			1.97838e8i			0.212794i
$977$			1.27440e9i			1.36654i	0.730168	+	0.683268i	$0.239442\pi$
$977$			1.27440e9i			1.36654i	−0.730168	+	0.683268i	$0.760558\pi$
$978$	6.94423e7			0.0742348
$979$	9.11596e8			0.971525
$980$			7.60180e8i			0.807678i
$981$			3.70351e7i			0.0392289i
$982$	−2.76726e8			−0.292223
$983$			4.71331e8i			0.496210i	0.968733	+	0.248105i	$0.0798078\pi$
$983$			4.71331e8i			0.496210i	−0.968733	+	0.248105i	$0.920192\pi$
$984$	3.44202e8			0.361267
$985$			8.76042e8i			0.916677i
$986$			5.48548e8i			0.572247i
$987$		−	5.86332e7i		−	0.0609807i
$988$			7.04095e8i			0.730063i
$989$	2.05278e8	+	3.28735e8i	0.212204	+	0.339826i
$990$	−7.26984e8			−0.749237
$991$	8.48764e8			0.872100			0.436050	−	0.899922i	$-0.356377\pi$
$991$	8.48764e8			0.872100			0.436050	+	0.899922i	$0.356377\pi$
$992$	−1.59248e7			−0.0163131
$993$	1.62878e8			0.166347
$994$			7.64235e7i			0.0778158i
$995$	2.10785e9			2.13979
$996$		−	3.07159e8i		−	0.310875i
$997$	−3.65324e7			−0.0368632			−0.0184316	−	0.999830i	$-0.505867\pi$
$997$	−3.65324e7			−0.0368632			−0.0184316	+	0.999830i	$0.505867\pi$
$998$	3.90857e8			0.393212
$999$			3.05987e8i			0.306907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.7.b.a.91.12	yes	24
3.2	odd	2		414.7.b.c.91.13		24
23.22	odd	2	inner	138.7.b.a.91.7	✓	24
69.68	even	2		414.7.b.c.91.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.7.b.a.91.7	✓	24	23.22	odd	2	inner
138.7.b.a.91.12	yes	24	1.1	even	1	trivial
414.7.b.c.91.13		24	3.2	odd	2
414.7.b.c.91.24		24	69.68	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	138.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685 q^{2} +15.5885 q^{3} +32.0000 q^{4} +203.893i q^{5} -88.1816 q^{6} -33.7438i q^{7} -181.019 q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-5.65685 q^{2} +15.5885 q^{3} +32.0000 q^{4} +203.893i q^{5} -88.1816 q^{6} -33.7438i q^{7} -181.019 q^{8} +243.000 q^{9} -1153.39i q^{10} -2593.83i q^{11} +498.831 q^{12} +4009.82 q^{13} +190.884i q^{14} +3178.38i q^{15} +1024.00 q^{16} -3231.21i q^{17} -1374.62 q^{18} +5487.27i q^{19} +6524.57i q^{20} -526.014i q^{21} +14672.9i q^{22} +(10320.2 - 6444.40i) q^{23} -2821.81 q^{24} -25947.3 q^{25} -22683.0 q^{26} +3788.00 q^{27} -1079.80i q^{28} +30010.5 q^{29} -17979.6i q^{30} +2749.15 q^{31} -5792.62 q^{32} -40433.8i q^{33} +18278.5i q^{34} +6880.12 q^{35} +7776.00 q^{36} +80778.1i q^{37} -31040.7i q^{38} +62506.9 q^{39} -36908.6i q^{40} -121979. q^{41} +2975.59i q^{42} +31853.7i q^{43} -83002.6i q^{44} +49546.0i q^{45} +(-58379.6 + 36455.0i) q^{46} +111467. q^{47} +15962.6 q^{48} +116510. q^{49} +146780. q^{50} -50369.6i q^{51} +128314. q^{52} +67038.7i q^{53} -21428.1 q^{54} +528864. q^{55} +6108.28i q^{56} +85538.1i q^{57} -169765. q^{58} -159596. q^{59} +101708. i q^{60} +193201. i q^{61} -15551.5 q^{62} -8199.75i q^{63} +32768.0 q^{64} +817574. i q^{65} +228728. i q^{66} +156790. i q^{67} -103399. i q^{68} +(160875. - 100458. i) q^{69} -38919.9 q^{70} +400367. q^{71} -43987.7 q^{72} +590418. q^{73} -456950. i q^{74} -404478. q^{75} +175593. i q^{76} -87525.8 q^{77} -353593. q^{78} -465617. i q^{79} +208786. i q^{80} +59049.0 q^{81} +690018. q^{82} -615758. i q^{83} -16832.5i q^{84} +658822. q^{85} -180192. i q^{86} +467818. q^{87} +469534. i q^{88} +351448. i q^{89} -280274. i q^{90} -135307. i q^{91} +(330245. - 206221. i) q^{92} +42855.0 q^{93} -630553. q^{94} -1.11882e6 q^{95} -90298.0 q^{96} -1.30800e6i q^{97} -659082. q^{98} -630301. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 768 q^{4} + 5832 q^{9}+O(q^{10}) \) 24 * q + 768 * q^4 + 5832 * q^9	\( 24 q + 768 q^{4} + 5832 q^{9} - 768 q^{13} + 24576 q^{16} - 44104 q^{23} - 119448 q^{25} - 53888 q^{26} + 3456 q^{29} + 50976 q^{31} + 149008 q^{35} + 186624 q^{36} + 11664 q^{39} - 3920 q^{41} - 150720 q^{46} + 441088 q^{47} - 32472 q^{49} + 8320 q^{50} - 24576 q^{52} + 826176 q^{55} - 307200 q^{58} - 1210160 q^{59} + 783744 q^{62} + 786432 q^{64} + 361584 q^{69} - 2480064 q^{70} + 1531264 q^{71} + 593472 q^{73} + 23328 q^{75} + 1068784 q^{77} + 171072 q^{78} + 1417176 q^{81} + 1454592 q^{82} - 1318272 q^{85} + 697248 q^{87} - 1411328 q^{92} - 983664 q^{93} + 1115712 q^{94} + 4047632 q^{95} - 2409344 q^{98}+O(q^{100}) \) 24 * q + 768 * q^4 + 5832 * q^9 - 768 * q^13 + 24576 * q^16 - 44104 * q^23 - 119448 * q^25 - 53888 * q^26 + 3456 * q^29 + 50976 * q^31 + 149008 * q^35 + 186624 * q^36 + 11664 * q^39 - 3920 * q^41 - 150720 * q^46 + 441088 * q^47 - 32472 * q^49 + 8320 * q^50 - 24576 * q^52 + 826176 * q^55 - 307200 * q^58 - 1210160 * q^59 + 783744 * q^62 + 786432 * q^64 + 361584 * q^69 - 2480064 * q^70 + 1531264 * q^71 + 593472 * q^73 + 23328 * q^75 + 1068784 * q^77 + 171072 * q^78 + 1417176 * q^81 + 1454592 * q^82 - 1318272 * q^85 + 697248 * q^87 - 1411328 * q^92 - 983664 * q^93 + 1115712 * q^94 + 4047632 * q^95 - 2409344 * q^98

Introduction

L-functions

Modular forms

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Database

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