LMFDB - Embedded newform 138.7.b.a.91.8

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			91.8
Character	$\chi$	$=$	138.91
Dual form			138.7.b.a.91.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685 q^{2} +15.5885 q^{3} +32.0000 q^{4} -155.973i q^{5} -88.1816 q^{6} +550.532i q^{7} -181.019 q^{8} +243.000 q^{9} +O(q^{10})$	\(q-5.65685 q^{2} +15.5885 q^{3} +32.0000 q^{4} -155.973i q^{5} -88.1816 q^{6} +550.532i q^{7} -181.019 q^{8} +243.000 q^{9} +882.319i q^{10} -1345.83i q^{11} +498.831 q^{12} -2413.94 q^{13} -3114.28i q^{14} -2431.38i q^{15} +1024.00 q^{16} -3856.03i q^{17} -1374.62 q^{18} +3565.26i q^{19} -4991.15i q^{20} +8581.95i q^{21} +7613.19i q^{22} +(-12123.3 + 1030.62i) q^{23} -2821.81 q^{24} -8702.69 q^{25} +13655.3 q^{26} +3788.00 q^{27} +17617.0i q^{28} +23972.5 q^{29} +13754.0i q^{30} -19606.0 q^{31} -5792.62 q^{32} -20979.5i q^{33} +21813.0i q^{34} +85868.4 q^{35} +7776.00 q^{36} -1214.74i q^{37} -20168.1i q^{38} -37629.5 q^{39} +28234.2i q^{40} -132912. q^{41} -48546.8i q^{42} -95969.6i q^{43} -43066.7i q^{44} -37901.5i q^{45} +(68579.6 - 5830.08i) q^{46} -33880.0 q^{47} +15962.6 q^{48} -185437. q^{49} +49229.8 q^{50} -60109.5i q^{51} -77246.0 q^{52} +223120. i q^{53} -21428.1 q^{54} -209914. q^{55} -99657.0i q^{56} +55576.9i q^{57} -135609. q^{58} -372613. q^{59} -77804.3i q^{60} +110196. i q^{61} +110908. q^{62} +133779. i q^{63} +32768.0 q^{64} +376510. i q^{65} +118678. i q^{66} -140901. i q^{67} -123393. i q^{68} +(-188983. + 16065.8i) q^{69} -485745. q^{70} -275824. q^{71} -43987.7 q^{72} -746746. q^{73} +6871.61i q^{74} -135661. q^{75} +114088. i q^{76} +740926. q^{77} +212865. q^{78} -957504. i q^{79} -159717. i q^{80} +59049.0 q^{81} +751866. q^{82} -617447. i q^{83} +274622. i q^{84} -601437. q^{85} +542886. i q^{86} +373695. q^{87} +243622. i q^{88} -409861. i q^{89} +214403. i q^{90} -1.32895e6i q^{91} +(-387945. + 32979.9i) q^{92} -305628. q^{93} +191654. q^{94} +556085. q^{95} -90298.0 q^{96} +1.13979e6i q^{97} +1.04899e6 q^{98} -327038. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$		−	155.973i		−	1.24779i	−0.781509	−	0.623893i	$-0.785550\pi$
$5$		−	155.973i		−	1.24779i	0.781509	−	0.623893i	$-0.214450\pi$
$6$	−88.1816			−0.408248
$7$			550.532i			1.60505i	0.596618	+	0.802525i	$0.296511\pi$
$7$			550.532i			1.60505i	−0.596618	+	0.802525i	$0.703489\pi$
$8$	−181.019			−0.353553
$9$	243.000			0.333333
$10$			882.319i			0.882319i
$11$		−	1345.83i		−	1.01115i	−0.862784	−	0.505573i	$-0.831281\pi$
$11$		−	1345.83i		−	1.01115i	0.862784	−	0.505573i	$-0.168719\pi$
$12$	498.831			0.288675
$13$	−2413.94			−1.09874			−0.549371	−	0.835578i	$-0.685133\pi$
$13$	−2413.94			−1.09874			−0.549371	+	0.835578i	$0.685133\pi$
$14$		−	3114.28i		−	1.13494i
$15$		−	2431.38i		−	0.720410i
$16$	1024.00			0.250000
$17$		−	3856.03i		−	0.784862i	−0.919781	−	0.392431i	$-0.871634\pi$
$17$		−	3856.03i		−	0.784862i	0.919781	−	0.392431i	$-0.128366\pi$
$18$	−1374.62			−0.235702
$19$			3565.26i			0.519793i	0.965637	+	0.259896i	$0.0836884\pi$
$19$			3565.26i			0.519793i	−0.965637	+	0.259896i	$0.916312\pi$
$20$		−	4991.15i		−	0.623893i
$21$			8581.95i			0.926676i
$22$			7613.19i			0.714988i
$23$	−12123.3	+	1030.62i	−0.996406	+	0.0847063i
$23$	−12123.3	+	1030.62i	−0.996406	+	0.0847063i
$24$	−2821.81			−0.204124
$25$	−8702.69			−0.556972
$26$	13655.3			0.776928
$27$	3788.00			0.192450
$28$			17617.0i			0.802525i
$29$	23972.5			0.982924			0.491462	−	0.870899i	$-0.336463\pi$
$29$	23972.5			0.982924			0.491462	+	0.870899i	$0.336463\pi$
$30$			13754.0i			0.509407i
$31$	−19606.0			−0.658119			−0.329060	−	0.944309i	$-0.606732\pi$
$31$	−19606.0			−0.658119			−0.329060	+	0.944309i	$0.606732\pi$
$32$	−5792.62			−0.176777
$33$		−	20979.5i		−	0.583785i
$34$			21813.0i			0.554981i
$35$	85868.4			2.00276
$36$	7776.00			0.166667
$37$		−	1214.74i		−	0.0239816i	−0.999928	−	0.0119908i	$-0.996183\pi$
$37$		−	1214.74i		−	0.0239816i	0.999928	−	0.0119908i	$-0.00381688\pi$
$38$		−	20168.1i		−	0.367549i
$39$	−37629.5			−0.634359
$40$			28234.2i			0.441159i
$41$	−132912.			−1.92847			−0.964237	−	0.265042i	$-0.914614\pi$
$41$	−132912.			−1.92847			−0.964237	+	0.265042i	$0.914614\pi$
$42$		−	48546.8i		−	0.655259i
$43$		−	95969.6i		−	1.20706i	−0.797341	−	0.603530i	$-0.793761\pi$
$43$		−	95969.6i		−	1.20706i	0.797341	−	0.603530i	$-0.206239\pi$
$44$		−	43066.7i		−	0.505573i
$45$		−	37901.5i		−	0.415929i
$46$	68579.6	−	5830.08i	0.704565	−	0.0598964i
$47$	−33880.0			−0.326325			−0.163163	−	0.986599i	$-0.552169\pi$
$47$	−33880.0			−0.326325			−0.163163	+	0.986599i	$0.552169\pi$
$48$	15962.6			0.144338
$49$	−185437.			−1.57619
$50$	49229.8			0.393839
$51$		−	60109.5i		−	0.453140i
$52$	−77246.0			−0.549371
$53$			223120.i			1.49869i	0.662182	+	0.749343i	$0.269631\pi$
$53$			223120.i			1.49869i	−0.662182	+	0.749343i	$0.730369\pi$
$54$	−21428.1			−0.136083
$55$	−209914.			−1.26169
$56$		−	99657.0i		−	0.567471i
$57$			55576.9i			0.300102i
$58$	−135609.			−0.695032
$59$	−372613.			−1.81427			−0.907136	−	0.420838i	$-0.861736\pi$
$59$	−372613.			−1.81427			−0.907136	+	0.420838i	$0.861736\pi$
$60$		−	77804.3i		−	0.360205i
$61$			110196.i			0.485486i	0.970091	+	0.242743i	$0.0780472\pi$
$61$			110196.i			0.485486i	−0.970091	+	0.242743i	$0.921953\pi$
$62$	110908.			0.465361
$63$			133779.i			0.535017i
$64$	32768.0			0.125000
$65$			376510.i			1.37100i
$66$			118678.i			0.412798i
$67$		−	140901.i		−	0.468480i	−0.972179	−	0.234240i	$-0.924740\pi$
$67$		−	140901.i		−	0.468480i	0.972179	−	0.234240i	$-0.0752601\pi$
$68$		−	123393.i		−	0.392431i
$69$	−188983.	+	16065.8i	−0.575275	+	0.0489052i
$70$	−485745.			−1.41617
$71$	−275824.			−0.770650			−0.385325	−	0.922781i	$-0.625911\pi$
$71$	−275824.			−0.770650			−0.385325	+	0.922781i	$0.625911\pi$
$72$	−43987.7			−0.117851
$73$	−746746.			−1.91957			−0.959786	−	0.280733i	$-0.909423\pi$
$73$	−746746.			−1.91957			−0.959786	+	0.280733i	$0.909423\pi$
$74$			6871.61i			0.0169576i
$75$	−135661.			−0.321568
$76$			114088.i			0.259896i
$77$	740926.			1.62294
$78$	212865.			0.448560
$79$		−	957504.i		−	1.94205i	−0.238988	−	0.971023i	$-0.576816\pi$
$79$		−	957504.i		−	1.94205i	0.238988	−	0.971023i	$-0.423184\pi$
$80$		−	159717.i		−	0.311947i
$81$	59049.0			0.111111
$82$	751866.			1.36364
$83$		−	617447.i		−	1.07986i	−0.841711	−	0.539928i	$-0.818452\pi$
$83$		−	617447.i		−	1.07986i	0.841711	−	0.539928i	$-0.181548\pi$
$84$			274622.i			0.463338i
$85$	−601437.			−0.979340
$86$			542886.i			0.853520i
$87$	373695.			0.567491
$88$			243622.i			0.357494i
$89$		−	409861.i		−	0.581389i	−0.956816	−	0.290694i	$-0.906114\pi$
$89$		−	409861.i		−	0.581389i	0.956816	−	0.290694i	$-0.0938863\pi$
$90$			214403.i			0.294106i
$91$		−	1.32895e6i		−	1.76354i
$92$	−387945.	+	32979.9i	−0.498203	+	0.0423532i
$93$	−305628.			−0.379965
$94$	191654.			0.230747
$95$	556085.			0.648591
$96$	−90298.0			−0.102062
$97$			1.13979e6i			1.24885i	0.781086	+	0.624423i	$0.214666\pi$
$97$			1.13979e6i			1.24885i	−0.781086	+	0.624423i	$0.785334\pi$
$98$	1.04899e6			1.11453
$99$		−	327038.i		−	0.337049i
$100$	−278486.			−0.278486
$101$	−183634.			−0.178234			−0.0891169	−	0.996021i	$-0.528404\pi$
$101$	−183634.			−0.178234			−0.0891169	+	0.996021i	$0.528404\pi$
$102$			340031.i			0.320419i
$103$			967563.i			0.885458i	0.896656	+	0.442729i	$0.145990\pi$
$103$			967563.i			0.885458i	−0.896656	+	0.442729i	$0.854010\pi$
$104$	436969.			0.388464
$105$	1.33856e6			1.15629
$106$		−	1.26216e6i		−	1.05973i
$107$		−	47140.3i		−	0.0384805i	−0.999815	−	0.0192403i	$-0.993875\pi$
$107$		−	47140.3i		−	0.0384805i	0.999815	−	0.0192403i	$-0.00612474\pi$
$108$	121216.			0.0962250
$109$			1.40723e6i			1.08664i	0.839525	+	0.543321i	$0.182833\pi$
$109$			1.40723e6i			1.08664i	−0.839525	+	0.543321i	$0.817167\pi$
$110$	1.18745e6			0.892153
$111$		−	18935.9i		−	0.0138458i
$112$			563745.i			0.401263i
$113$			1.68450e6i			1.16744i	0.811955	+	0.583721i	$0.198404\pi$
$113$			1.68450e6i			1.16744i	−0.811955	+	0.583721i	$0.801596\pi$
$114$		−	314390.i		−	0.212204i
$115$	160750.	+	1.89091e6i	0.105695	+	1.24330i
$116$	767121.			0.491462
$117$	−586587.			−0.366247
$118$	2.10782e6			1.28288
$119$	2.12287e6			1.25974
$120$			440128.i			0.254703i
$121$	−39710.4			−0.0224155
$122$		−	623364.i		−	0.343291i
$123$	−2.07190e6			−1.11340
$124$	−627393.			−0.329060
$125$		−	1.07970e6i		−	0.552805i
$126$		−	756770.i		−	0.378314i
$127$	2.13291e6			1.04127			0.520633	−	0.853781i	$-0.325696\pi$
$127$	2.13291e6			1.04127			0.520633	+	0.853781i	$0.325696\pi$
$128$	−185364.			−0.0883883
$129$		−	1.49602e6i		−	0.696896i
$130$		−	2.12986e6i		−	0.969441i
$131$	3.60774e6			1.60480			0.802400	−	0.596786i	$-0.203556\pi$
$131$	3.60774e6			1.60480			0.802400	+	0.596786i	$0.203556\pi$
$132$		−	671344.i		−	0.291893i
$133$	−1.96279e6			−0.834294
$134$			797059.i			0.331265i
$135$		−	590826.i		−	0.240137i
$136$			698015.i			0.277491i
$137$		−	2.85261e6i		−	1.10938i	−0.832057	−	0.554691i	$-0.812837\pi$
$137$		−	2.85261e6i		−	1.10938i	0.832057	−	0.554691i	$-0.187163\pi$
$138$	1.06905e6	−	90881.9i	0.406781	−	0.0345812i
$139$	−3.56726e6			−1.32828			−0.664141	−	0.747607i	$-0.731203\pi$
$139$	−3.56726e6			−1.32828			−0.664141	+	0.747607i	$0.731203\pi$
$140$	2.74779e6			1.00138
$141$	−528138.			−0.188404
$142$	1.56030e6			0.544932
$143$			3.24876e6i			1.11099i
$144$	248832.			0.0833333
$145$		−	3.73908e6i		−	1.22648i
$146$	4.22423e6			1.35734
$147$	−2.89067e6			−0.910012
$148$		−	38871.7i		−	0.0119908i
$149$			449820.i			0.135981i	0.997686	+	0.0679907i	$0.0216588\pi$
$149$			449820.i			0.135981i	−0.997686	+	0.0679907i	$0.978341\pi$
$150$	767417.			0.227383
$151$	34690.1			0.0100757			0.00503785	−	0.999987i	$-0.498396\pi$
$151$	34690.1			0.0100757			0.00503785	+	0.999987i	$0.498396\pi$
$152$		−	645381.i		−	0.183774i
$153$		−	937014.i		−	0.261621i
$154$	−4.19131e6			−1.14759
$155$			3.05802e6i			0.821193i
$156$	−1.20415e6			−0.317180
$157$			4.36553e6i			1.12808i	0.825749	+	0.564038i	$0.190753\pi$
$157$			4.36553e6i			1.12808i	−0.825749	+	0.564038i	$0.809247\pi$
$158$			5.41646e6i			1.37323i
$159$			3.47810e6i			0.865267i
$160$			903494.i			0.220580i
$161$	−567391.	−	6.67425e6i	−0.135958	−	1.59928i
$162$	−334032.			−0.0785674
$163$	810270.			0.187097			0.0935485	−	0.995615i	$-0.470179\pi$
$163$	810270.			0.187097			0.0935485	+	0.995615i	$0.470179\pi$
$164$	−4.25319e6			−0.964237
$165$	−3.27224e6			−0.728439
$166$			3.49281e6i			0.763573i
$167$	−1.80513e6			−0.387578			−0.193789	−	0.981043i	$-0.562078\pi$
$167$	−1.80513e6			−0.387578			−0.193789	+	0.981043i	$0.562078\pi$
$168$		−	1.55350e6i		−	0.327630i
$169$	1.00028e6			0.207234
$170$	3.40224e6			0.692498
$171$			866358.i			0.173264i
$172$		−	3.07103e6i		−	0.603530i
$173$	1.90407e6			0.367744			0.183872	−	0.982950i	$-0.441137\pi$
$173$	1.90407e6			0.367744			0.183872	+	0.982950i	$0.441137\pi$
$174$	−2.11394e6			−0.401277
$175$		−	4.79111e6i		−	0.893968i
$176$		−	1.37813e6i		−	0.252786i
$177$	−5.80847e6			−1.04747
$178$			2.31852e6i			0.411104i
$179$	1.20594e6			0.210265			0.105133	−	0.994458i	$-0.466473\pi$
$179$	1.20594e6			0.210265			0.105133	+	0.994458i	$0.466473\pi$
$180$		−	1.21285e6i		−	0.207964i
$181$		−	9.08285e6i		−	1.53175i	−0.642992	−	0.765873i	$-0.722307\pi$
$181$		−	9.08285e6i		−	1.53175i	0.642992	−	0.765873i	$-0.277693\pi$
$182$			7.51768e6i			1.24701i
$183$			1.71779e6i			0.280296i
$184$	2.19455e6	−	186562.i	0.352283	−	0.0299482i
$185$	−189467.			−0.0299239
$186$	1.72889e6			0.268676
$187$	−5.18957e6			−0.793610
$188$	−1.08416e6			−0.163163
$189$			2.08541e6i			0.308892i
$190$	−3.14569e6			−0.458623
$191$		−	1.01935e7i		−	1.46292i	−0.681882	−	0.731462i	$-0.738838\pi$
$191$		−	1.01935e7i		−	1.46292i	0.681882	−	0.731462i	$-0.261162\pi$
$192$	510803.			0.0721688
$193$	4.52496e6			0.629423			0.314712	−	0.949187i	$-0.398092\pi$
$193$	4.52496e6			0.629423			0.314712	+	0.949187i	$0.398092\pi$
$194$		−	6.44761e6i		−	0.883067i
$195$			5.86921e6i			0.791545i
$196$	−5.93398e6			−0.788094
$197$	1.37061e7			1.79274			0.896368	−	0.443311i	$-0.146196\pi$
$197$	1.37061e7			1.79274			0.896368	+	0.443311i	$0.146196\pi$
$198$			1.85001e6i			0.238329i
$199$		−	3.90073e6i		−	0.494979i	−0.968891	−	0.247490i	$-0.920394\pi$
$199$		−	3.90073e6i		−	0.494979i	0.968891	−	0.247490i	$-0.0796056\pi$
$200$	1.57535e6			0.196919
$201$		−	2.19644e6i		−	0.270477i
$202$	1.03879e6			0.126030
$203$			1.31977e7i			1.57764i
$204$		−	1.92350e6i		−	0.226570i
$205$			2.07308e7i			2.40632i
$206$		−	5.47337e6i		−	0.626113i
$207$	−2.94595e6	+	250441.i	−0.332135	+	0.0282354i
$208$	−2.47187e6			−0.274686
$209$	4.79825e6			0.525586
$210$	−7.57201e6			−0.817624
$211$	156196.			0.0166273			0.00831364	−	0.999965i	$-0.497354\pi$
$211$	156196.			0.0166273			0.00831364	+	0.999965i	$0.497354\pi$
$212$			7.13984e6i			0.749343i
$213$	−4.29967e6			−0.444935
$214$			266666.i			0.0272098i
$215$	−1.49687e7			−1.50615
$216$	−685700.			−0.0680414
$217$		−	1.07938e7i		−	1.05631i
$218$		−	7.96052e6i		−	0.768372i
$219$	−1.16406e7			−1.10827
$220$	−6.71726e6			−0.630847
$221$			9.30820e6i			0.862361i
$222$			107118.i			0.00979045i
$223$	1.89983e7			1.71317			0.856586	−	0.516005i	$-0.172581\pi$
$223$	1.89983e7			1.71317			0.856586	+	0.516005i	$0.172581\pi$
$224$		−	3.18902e6i		−	0.283736i
$225$	−2.11475e6			−0.185657
$226$		−	9.52896e6i		−	0.825506i
$227$		−	1.28489e7i		−	1.09847i	−0.835668	−	0.549235i	$-0.814919\pi$
$227$		−	1.28489e7i		−	1.09847i	0.835668	−	0.549235i	$-0.185081\pi$
$228$			1.77846e6i			0.150051i
$229$			1.16449e6i			0.0969683i	0.998824	+	0.0484841i	$0.0154390\pi$
$229$			1.16449e6i			0.0969683i	−0.998824	+	0.0484841i	$0.984561\pi$
$230$	−909337.	−	1.06966e7i	−0.0747380	−	0.879147i
$231$	1.15499e7			0.937005
$232$	−4.33949e6			−0.347516
$233$	−4.73834e6			−0.374592			−0.187296	−	0.982303i	$-0.559972\pi$
$233$	−4.73834e6			−0.374592			−0.187296	+	0.982303i	$0.559972\pi$
$234$	3.31823e6			0.258976
$235$			5.28438e6i			0.407184i
$236$	−1.19236e7			−0.907136
$237$		−	1.49260e7i		−	1.12124i
$238$	−1.20088e7			−0.890773
$239$	1.09966e7			0.805502			0.402751	−	0.915310i	$-0.368054\pi$
$239$	1.09966e7			0.805502			0.402751	+	0.915310i	$0.368054\pi$
$240$		−	2.48974e6i		−	0.180103i
$241$		−	8.65958e6i		−	0.618651i	−0.950956	−	0.309326i	$-0.899897\pi$
$241$		−	8.65958e6i		−	0.618651i	0.950956	−	0.309326i	$-0.100103\pi$
$242$	224636.			0.0158501
$243$	920483.			0.0641500
$244$			3.52628e6i			0.242743i
$245$			2.89232e7i			1.96675i
$246$	1.17204e7			0.787296
$247$		−	8.60631e6i		−	0.571118i
$248$	3.54907e6			0.232680
$249$		−	9.62505e6i		−	0.623455i
$250$			6.10769e6i			0.390892i
$251$			8.45460e6i			0.534653i	0.963606	+	0.267327i	$0.0861402\pi$
$251$			8.45460e6i			0.534653i	−0.963606	+	0.267327i	$0.913860\pi$
$252$			4.28094e6i			0.267508i
$253$	1.38705e6	+	1.63159e7i	0.0856504	+	1.00751i
$254$	−1.20656e7			−0.736286
$255$	−9.37548e6			−0.565422
$256$	1.04858e6			0.0625000
$257$	−1.02727e7			−0.605181			−0.302590	−	0.953121i	$-0.597851\pi$
$257$	−1.02727e7			−0.605181			−0.302590	+	0.953121i	$0.597851\pi$
$258$			8.46276e6i			0.492780i
$259$	668754.			0.0384917
$260$			1.20483e7i			0.685498i
$261$	5.82532e6			0.327641
$262$	−2.04085e7			−1.13477
$263$		−	4.67846e6i		−	0.257179i	−0.991698	−	0.128589i	$-0.958955\pi$
$263$		−	4.67846e6i		−	0.257179i	0.991698	−	0.128589i	$-0.0410449\pi$
$264$			3.79769e6i			0.206399i
$265$	3.48008e7			1.87004
$266$	1.11032e7			0.589935
$267$		−	6.38910e6i		−	0.335665i
$268$		−	4.50885e6i		−	0.234240i
$269$	−1.27885e7			−0.656998			−0.328499	−	0.944504i	$-0.606543\pi$
$269$	−1.27885e7			−0.656998			−0.328499	+	0.944504i	$0.606543\pi$
$270$			3.34222e6i			0.169802i
$271$	−3.23010e7			−1.62296			−0.811482	−	0.584378i	$-0.801339\pi$
$271$	−3.23010e7			−1.62296			−0.811482	+	0.584378i	$0.801339\pi$
$272$		−	3.94857e6i		−	0.196215i
$273$		−	2.07163e7i		−	1.01818i
$274$			1.61368e7i			0.784451i
$275$			1.17124e7i			0.563180i
$276$	−6.04746e6	+	514106.i	−0.287638	+	0.0244526i
$277$	−2.56930e6			−0.120886			−0.0604428	−	0.998172i	$-0.519251\pi$
$277$	−2.56930e6			−0.120886			−0.0604428	+	0.998172i	$0.519251\pi$
$278$	2.01795e7			0.939237
$279$	−4.76427e6			−0.219373
$280$	−1.55438e7			−0.708083
$281$			1.27353e7i			0.573971i	0.957935	+	0.286986i	$0.0926532\pi$
$281$			1.27353e7i			0.573971i	−0.957935	+	0.286986i	$0.907347\pi$
$282$	2.98760e6			0.133222
$283$		−	9.97919e6i		−	0.440287i	−0.975467	−	0.220144i	$-0.929347\pi$
$283$		−	9.97919e6i		−	0.440287i	0.975467	−	0.220144i	$-0.0706526\pi$
$284$	−8.82637e6			−0.385325
$285$	8.66851e6			0.374464
$286$		−	1.83778e7i		−	0.785587i
$287$		−	7.31725e7i		−	3.09530i
$288$	−1.40761e6			−0.0589256
$289$	9.26863e6			0.383992
$290$			2.11514e7i			0.867252i
$291$			1.77675e7i			0.721021i
$292$	−2.38959e7			−0.959786
$293$		−	6.78343e6i		−	0.269679i	−0.990867	−	0.134839i	$-0.956948\pi$
$293$		−	6.78343e6i		−	0.269679i	0.990867	−	0.134839i	$-0.0430518\pi$
$294$	1.63521e7			0.643476
$295$			5.81177e7i			2.26382i
$296$			219891.i			0.00847878i
$297$		−	5.09802e6i		−	0.194595i
$298$		−	2.54457e6i		−	0.0961534i
$299$	2.92648e7	−	2.48786e6i	1.09479	−	0.0930704i
$300$	−4.34117e6			−0.160784
$301$	5.28344e7			1.93739
$302$	−196237.			−0.00712459
$303$	−2.86258e6			−0.102903
$304$			3.65082e6i			0.129948i
$305$	1.71877e7			0.605783
$306$			5.30055e6i			0.184994i
$307$	−8.79454e6			−0.303947			−0.151974	−	0.988385i	$-0.548563\pi$
$307$	−8.79454e6			−0.303947			−0.151974	+	0.988385i	$0.548563\pi$
$308$	2.37096e7			0.811470
$309$			1.50828e7i			0.511219i
$310$		−	1.72988e7i		−	0.580671i
$311$	−1.53005e7			−0.508657			−0.254329	−	0.967118i	$-0.581854\pi$
$311$	−1.53005e7			−0.508657			−0.254329	+	0.967118i	$0.581854\pi$
$312$	6.81168e6			0.224280
$313$			1.24324e7i			0.405437i	0.979237	+	0.202719i	$0.0649777\pi$
$313$			1.24324e7i			0.405437i	−0.979237	+	0.202719i	$0.935022\pi$
$314$		−	2.46952e7i		−	0.797670i
$315$	2.08660e7			0.667587
$316$		−	3.06401e7i		−	0.971023i
$317$	2.02041e7			0.634253			0.317127	−	0.948383i	$-0.397282\pi$
$317$	2.02041e7			0.634253			0.317127	+	0.948383i	$0.397282\pi$
$318$		−	1.96751e7i		−	0.611836i
$319$		−	3.22631e7i		−	0.993879i
$320$		−	5.11093e6i		−	0.155973i
$321$		−	734844.i		−	0.0222167i
$322$	3.20965e6	+	3.77553e7i	0.0961368	+	1.13086i
$323$	1.37477e7			0.407965
$324$	1.88957e6			0.0555556
$325$	2.10077e7			0.611969
$326$	−4.58358e6			−0.132298
$327$			2.19366e7i			0.627373i
$328$	2.40597e7			0.681818
$329$		−	1.86521e7i		−	0.523768i
$330$	1.85106e7			0.515084
$331$	2.74012e7			0.755588			0.377794	−	0.925890i	$-0.376683\pi$
$331$	2.74012e7			0.755588			0.377794	+	0.925890i	$0.376683\pi$
$332$		−	1.97583e7i		−	0.539928i
$333$		−	295182.i		−	0.00799387i
$334$	1.02113e7			0.274059
$335$	−2.19769e7			−0.584563
$336$			8.78792e6i			0.231669i
$337$			1.60412e6i			0.0419128i	0.999780	+	0.0209564i	$0.00667112\pi$
$337$			1.60412e6i			0.0419128i	−0.999780	+	0.0209564i	$0.993329\pi$
$338$	−5.65844e6			−0.146537
$339$			2.62587e7i			0.674023i
$340$	−1.92460e7			−0.489670
$341$			2.63865e7i			0.665454i
$342$		−	4.90086e6i		−	0.122516i
$343$		−	3.73194e7i		−	0.924810i
$344$			1.73724e7i			0.426760i
$345$	2.50584e6	+	2.94763e7i	0.0610233	+	0.717821i
$346$	−1.07711e7			−0.260034
$347$	−4.07610e7			−0.975565			−0.487782	−	0.872965i	$-0.662194\pi$
$347$	−4.07610e7			−0.975565			−0.487782	+	0.872965i	$0.662194\pi$
$348$	1.19582e7			0.283746
$349$	538748.			0.0126739			0.00633694	−	0.999980i	$-0.497983\pi$
$349$	538748.			0.0126739			0.00633694	+	0.999980i	$0.497983\pi$
$350$			2.71026e7i			0.632131i
$351$	−9.14398e6			−0.211453
$352$			7.79591e6i			0.178747i
$353$	6.53499e7			1.48567			0.742833	−	0.669477i	$-0.233482\pi$
$353$	6.53499e7			1.48567			0.742833	+	0.669477i	$0.233482\pi$
$354$	3.28576e7			0.740673
$355$			4.30212e7i			0.961607i
$356$		−	1.31156e7i		−	0.290694i
$357$	3.30922e7			0.727313
$358$	−6.82184e6			−0.148680
$359$		−	5.97130e7i		−	1.29058i	−0.763937	−	0.645291i	$-0.776736\pi$
$359$		−	5.97130e7i		−	1.29058i	0.763937	−	0.645291i	$-0.223264\pi$
$360$			6.86091e6i			0.147053i
$361$	3.43348e7			0.729816
$362$			5.13804e7i			1.08311i
$363$	−619024.			−0.0129416
$364$		−	4.25264e7i		−	0.881768i
$365$			1.16473e8i			2.39522i
$366$		−	9.71728e6i		−	0.198199i
$367$		−	2.80969e7i		−	0.568408i	−0.958764	−	0.284204i	$-0.908271\pi$
$367$		−	2.80969e7i		−	0.568408i	0.958764	−	0.284204i	$-0.0917293\pi$
$368$	−1.24142e7	+	1.05536e6i	−0.249101	+	0.0211766i
$369$	−3.22977e7			−0.642825
$370$	1.07179e6			0.0211594
$371$	−1.22835e8			−2.40547
$372$	−9.78009e6			−0.189983
$373$		−	8.27278e7i		−	1.59414i	−0.603890	−	0.797068i	$-0.706383\pi$
$373$		−	8.27278e7i		−	1.59414i	0.603890	−	0.797068i	$-0.293617\pi$
$374$	2.93567e7			0.561167
$375$		−	1.68308e7i		−	0.319162i
$376$	6.13294e6			0.115373
$377$	−5.78682e7			−1.07998
$378$		−	1.17969e7i		−	0.218420i
$379$			3.96195e7i			0.727765i	0.931445	+	0.363882i	$0.118549\pi$
$379$			3.96195e7i			0.727765i	−0.931445	+	0.363882i	$0.881451\pi$
$380$	1.77947e7			0.324295
$381$	3.32488e7			0.601175
$382$			5.76630e7i			1.03444i
$383$			9.38916e7i			1.67121i	0.549332	+	0.835604i	$0.314882\pi$
$383$			9.38916e7i			1.67121i	−0.549332	+	0.835604i	$0.685118\pi$
$384$	−2.88954e6			−0.0510310
$385$		−	1.15565e8i		−	2.02508i
$386$	−2.55970e7			−0.445070
$387$		−	2.33206e7i		−	0.402353i
$388$			3.64732e7i			0.624423i
$389$		−	4.94758e7i		−	0.840512i	−0.907406	−	0.420256i	$-0.861940\pi$
$389$		−	4.94758e7i		−	0.840512i	0.907406	−	0.420256i	$-0.138060\pi$
$390$		−	3.32012e7i		−	0.559707i
$391$	3.97411e6	+	4.67477e7i	0.0664828	+	0.782041i
$392$	3.35677e7			0.557266
$393$	5.62391e7			0.926532
$394$	−7.75336e7			−1.26766
$395$	−1.49345e8			−2.42326
$396$		−	1.04652e7i		−	0.168524i
$397$	6.04357e7			0.965877			0.482938	−	0.875654i	$-0.339569\pi$
$397$	6.04357e7			0.965877			0.482938	+	0.875654i	$0.339569\pi$
$398$			2.20659e7i			0.350003i
$399$	−3.05969e7			−0.481680
$400$	−8.91155e6			−0.139243
$401$			1.10089e8i			1.70730i	0.520846	+	0.853651i	$0.325617\pi$
$401$			1.10089e8i			1.70730i	−0.520846	+	0.853651i	$0.674383\pi$
$402$			1.24249e7i			0.191256i
$403$	4.73277e7			0.723103
$404$	−5.87630e6			−0.0891169
$405$		−	9.21007e6i		−	0.138643i
$406$		−	7.46572e7i		−	1.11556i
$407$	−1.63484e6			−0.0242489
$408$			1.08810e7i			0.160209i
$409$	4.72897e7			0.691189			0.345594	−	0.938384i	$-0.387677\pi$
$409$	4.72897e7			0.691189			0.345594	+	0.938384i	$0.387677\pi$
$410$		−	1.17271e8i		−	1.70153i
$411$		−	4.44678e7i		−	0.640502i
$412$			3.09620e7i			0.442729i
$413$		−	2.05136e8i		−	2.91200i
$414$	1.66648e7	−	1.41671e6i	0.234855	−	0.0199655i
$415$	−9.63053e7			−1.34743
$416$	1.39830e7			0.194232
$417$	−5.56081e7			−0.766884
$418$	−2.71430e7			−0.371646
$419$		−	6.23716e7i		−	0.847900i	−0.905685	−	0.423950i	$-0.860643\pi$
$419$		−	6.23716e7i		−	0.847900i	0.905685	−	0.423950i	$-0.139357\pi$
$420$	4.28338e7			0.578147
$421$			3.50941e7i			0.470314i	0.971957	+	0.235157i	$0.0755604\pi$
$421$			3.50941e7i			0.470314i	−0.971957	+	0.235157i	$0.924440\pi$
$422$	−883576.			−0.0117573
$423$	−8.23285e6			−0.108775
$424$		−	4.03890e7i		−	0.529866i
$425$			3.35578e7i			0.437146i
$426$	2.43226e7			0.314617
$427$	−6.06666e7			−0.779230
$428$		−	1.50849e6i		−	0.0192403i
$429$			5.06432e7i			0.641429i
$430$	8.46758e7			1.06501
$431$		−	9.75350e7i		−	1.21823i	−0.793082	−	0.609114i	$-0.791525\pi$
$431$		−	9.75350e7i		−	1.21823i	0.793082	−	0.609114i	$-0.208475\pi$
$432$	3.87891e6			0.0481125
$433$			1.43764e8i			1.77087i	0.464766	+	0.885434i	$0.346139\pi$
$433$			1.43764e8i			1.77087i	−0.464766	+	0.885434i	$0.653861\pi$
$434$			6.10587e7i			0.746927i
$435$		−	5.82864e7i		−	0.708108i
$436$			4.50315e7i			0.543321i
$437$	−3.67443e6	−	4.32226e7i	−0.0440297	−	0.517925i
$438$	6.58493e7			0.783662
$439$	5.43646e7			0.642573			0.321286	−	0.946982i	$-0.395885\pi$
$439$	5.43646e7			0.642573			0.321286	+	0.946982i	$0.395885\pi$
$440$	3.79986e7			0.446076
$441$	−4.50612e7			−0.525396
$442$		−	5.26551e7i		−	0.609781i
$443$	−4.91980e7			−0.565896			−0.282948	−	0.959135i	$-0.591312\pi$
$443$	−4.91980e7			−0.565896			−0.282948	+	0.959135i	$0.591312\pi$
$444$		−	605949.i		−	0.00692289i
$445$	−6.39274e7			−0.725449
$446$	−1.07471e8			−1.21140
$447$			7.01200e6i			0.0785090i
$448$			1.80398e7i			0.200631i
$449$	−1.30938e8			−1.44653			−0.723263	−	0.690572i	$-0.757359\pi$
$449$	−1.30938e8			−1.44653			−0.723263	+	0.690572i	$0.757359\pi$
$450$	1.19628e7			0.131280
$451$			1.78878e8i			1.94997i
$452$			5.39039e7i			0.583721i
$453$	540765.			0.00581720
$454$			7.26843e7i			0.776736i
$455$	−2.07281e8			−2.20052
$456$		−	1.00605e7i		−	0.106102i
$457$			1.58822e7i			0.166404i	0.996533	+	0.0832019i	$0.0265146\pi$
$457$			1.58822e7i			0.166404i	−0.996533	+	0.0832019i	$0.973485\pi$
$458$		−	6.58735e6i		−	0.0685669i
$459$		−	1.46066e7i		−	0.151047i
$460$	5.14399e6	+	6.05090e7i	0.0528477	+	0.621651i
$461$	−1.36174e8			−1.38993			−0.694965	−	0.719044i	$-0.744580\pi$
$461$	−1.36174e8			−1.38993			−0.694965	+	0.719044i	$0.744580\pi$
$462$	−6.53360e7			−0.662562
$463$	−633116.			−0.00637882			−0.00318941	−	0.999995i	$-0.501015\pi$
$463$	−633116.			−0.00637882			−0.00318941	+	0.999995i	$0.501015\pi$
$464$	2.45479e7			0.245731
$465$			4.76698e7i			0.474116i
$466$	2.68041e7			0.264877
$467$			9.77046e7i			0.959322i	0.877454	+	0.479661i	$0.159240\pi$
$467$			9.77046e7i			0.959322i	−0.877454	+	0.479661i	$0.840760\pi$
$468$	−1.87708e7			−0.183124
$469$	7.75708e7			0.751934
$470$		−	2.98930e7i		−	0.287923i
$471$			6.80519e7i			0.651295i
$472$	6.74502e7			0.641442
$473$	−1.29159e8			−1.22051
$474$			8.44343e7i			0.792837i
$475$		−	3.10273e7i		−	0.289510i
$476$	6.79318e7			0.629871
$477$			5.42181e7i			0.499562i
$478$	−6.22064e7			−0.569576
$479$		−	1.17880e8i		−	1.07259i	−0.844030	−	0.536296i	$-0.819823\pi$
$479$		−	1.17880e8i		−	1.07259i	0.844030	−	0.536296i	$-0.180177\pi$
$480$			1.40841e7i			0.127352i
$481$			2.93231e6i			0.0263496i
$482$			4.89860e7i			0.437453i
$483$	−8.84475e6	−	1.04041e8i	−0.0784954	−	0.923346i
$484$	−1.27073e6			−0.0112077
$485$	1.77777e8			1.55829
$486$	−5.20704e6			−0.0453609
$487$	3.90651e7			0.338223			0.169111	−	0.985597i	$-0.445910\pi$
$487$	3.90651e7			0.338223			0.169111	+	0.985597i	$0.445910\pi$
$488$		−	1.99476e7i		−	0.171645i
$489$	1.26309e7			0.108020
$490$		−	1.63614e8i		−	1.39070i
$491$	2.52645e7			0.213435			0.106718	−	0.994289i	$-0.465966\pi$
$491$	2.52645e7			0.213435			0.106718	+	0.994289i	$0.465966\pi$
$492$	−6.63007e7			−0.556702
$493$		−	9.24387e7i		−	0.771459i
$494$			4.86846e7i			0.403842i
$495$	−5.10092e7			−0.420565
$496$	−2.00766e7			−0.164530
$497$		−	1.51850e8i		−	1.23693i
$498$			5.44475e7i			0.440849i
$499$	−1.40151e8			−1.12796			−0.563980	−	0.825789i	$-0.690730\pi$
$499$	−1.40151e8			−1.12796			−0.563980	+	0.825789i	$0.690730\pi$
$500$		−	3.45503e7i		−	0.276402i
$501$	−2.81392e7			−0.223768
$502$		−	4.78265e7i		−	0.378057i
$503$			6.27872e7i			0.493364i	0.969097	+	0.246682i	$0.0793402\pi$
$503$			6.27872e7i			0.493364i	−0.969097	+	0.246682i	$0.920660\pi$
$504$		−	2.42167e7i		−	0.189157i
$505$			2.86421e7i			0.222398i
$506$	−7.84632e6	−	9.22968e7i	−0.0605640	−	0.712418i
$507$	1.55928e7			0.119647
$508$	6.82532e7			0.520633
$509$	−9.76689e7			−0.740632			−0.370316	−	0.928906i	$-0.620751\pi$
$509$	−9.76689e7			−0.740632			−0.370316	+	0.928906i	$0.620751\pi$
$510$	5.30357e7			0.399814
$511$		−	4.11108e8i		−	3.08101i
$512$	−5.93164e6			−0.0441942
$513$			1.35052e7i			0.100034i
$514$	5.81111e7			0.427927
$515$	1.50914e8			1.10486
$516$		−	4.78726e7i		−	0.348448i
$517$			4.55969e7i			0.329962i
$518$	−3.78304e6			−0.0272177
$519$	2.96816e7			0.212317
$520$		−	6.81556e7i		−	0.484720i
$521$			9.55533e7i			0.675667i	0.941206	+	0.337833i	$0.109694\pi$
$521$			9.55533e7i			0.675667i	−0.941206	+	0.337833i	$0.890306\pi$
$522$	−3.29530e7			−0.231677
$523$			6.70304e7i			0.468562i	0.972169	+	0.234281i	$0.0752735\pi$
$523$			6.70304e7i			0.468562i	−0.972169	+	0.234281i	$0.924726\pi$
$524$	1.15448e8			0.802400
$525$		−	7.46860e7i		−	0.516133i
$526$			2.64653e7i			0.181853i
$527$			7.56014e7i			0.516533i
$528$		−	2.14830e7i		−	0.145946i
$529$	1.45912e8	−	2.49890e7i	0.985650	−	0.168804i
$530$	−1.96863e8			−1.32232
$531$	−9.05450e7			−0.604757
$532$	−6.28093e7			−0.417147
$533$	3.20842e8			2.11890
$534$			3.61422e7i			0.237351i
$535$	−7.35263e6			−0.0480155
$536$			2.55059e7i			0.165633i
$537$	1.87988e7			0.121397
$538$	7.23429e7			0.464568
$539$			2.49567e8i			1.59376i
$540$		−	1.89064e7i		−	0.120068i
$541$	−1.88707e8			−1.19178			−0.595889	−	0.803067i	$-0.703200\pi$
$541$	−1.88707e8			−1.19178			−0.595889	+	0.803067i	$0.703200\pi$
$542$	1.82722e8			1.14761
$543$		−	1.41588e8i		−	0.884354i
$544$			2.23365e7i			0.138745i
$545$	2.19491e8			1.35590
$546$			1.17189e8i			0.719961i
$547$	−2.13208e8			−1.30269			−0.651346	−	0.758781i	$-0.725795\pi$
$547$	−2.13208e8			−1.30269			−0.651346	+	0.758781i	$0.725795\pi$
$548$		−	9.12836e7i		−	0.554691i
$549$			2.67777e7i			0.161829i
$550$		−	6.62552e7i		−	0.398228i
$551$			8.54682e7i			0.510917i
$552$	3.42096e7	−	2.90822e6i	0.203391	−	0.0172906i
$553$	5.27137e8			3.11708
$554$	1.45341e7			0.0854791
$555$	−2.95350e6			−0.0172766
$556$	−1.14152e8			−0.664141
$557$			2.55425e8i			1.47808i	0.673660	+	0.739041i	$0.264721\pi$
$557$			2.55425e8i			1.47808i	−0.673660	+	0.739041i	$0.735279\pi$
$558$	2.69508e7			0.155120
$559$			2.31665e8i			1.32625i
$560$	8.79292e7			0.500690
$561$	−8.08975e7			−0.458191
$562$		−	7.20417e7i		−	0.405859i
$563$			2.42894e8i			1.36110i	0.732700	+	0.680552i	$0.238260\pi$
$563$			2.42894e8i			1.36110i	−0.732700	+	0.680552i	$0.761740\pi$
$564$	−1.69004e7			−0.0942019
$565$	2.62737e8			1.45672
$566$			5.64508e7i			0.311330i
$567$			3.25084e7i			0.178339i
$568$	4.99295e7			0.272466
$569$		−	1.78605e8i		−	0.969520i	−0.874647	−	0.484760i	$-0.838907\pi$
$569$		−	1.78605e8i		−	0.969520i	0.874647	−	0.484760i	$-0.161093\pi$
$570$	−4.90365e7			−0.264786
$571$			2.22442e8i			1.19484i	0.801930	+	0.597418i	$0.203807\pi$
$571$			2.22442e8i			1.19484i	−0.801930	+	0.597418i	$0.796193\pi$
$572$			1.03960e8i			0.555494i
$573$		−	1.58901e8i		−	0.844620i
$574$			4.13926e8i			2.18871i
$575$	1.05505e8	−	8.96918e6i	0.554970	−	0.0471790i
$576$	7.96262e6			0.0416667
$577$	4.27466e7			0.222523			0.111261	−	0.993791i	$-0.464511\pi$
$577$	4.27466e7			0.222523			0.111261	+	0.993791i	$0.464511\pi$
$578$	−5.24313e7			−0.271523
$579$	7.05372e7			0.363398
$580$		−	1.19650e8i		−	0.613240i
$581$	3.39925e8			1.73322
$582$		−	1.00508e8i		−	0.509839i
$583$	3.00283e8			1.51539
$584$	1.35175e8			0.678671
$585$			9.14919e7i			0.456999i
$586$			3.83729e7i			0.190692i
$587$	1.90913e8			0.943887			0.471944	−	0.881629i	$-0.343553\pi$
$587$	1.90913e8			0.943887			0.471944	+	0.881629i	$0.343553\pi$
$588$	−9.25016e7			−0.455006
$589$		−	6.99006e7i		−	0.342086i
$590$		−	3.28764e8i		−	1.60077i
$591$	2.13658e8			1.03504
$592$		−	1.24389e6i		−	0.00599540i
$593$	−3.65927e7			−0.175481			−0.0877406	−	0.996143i	$-0.527965\pi$
$593$	−3.65927e7			−0.175481			−0.0877406	+	0.996143i	$0.527965\pi$
$594$			2.88387e7i			0.137599i
$595$		−	3.31111e8i		−	1.57189i
$596$			1.43942e7i			0.0679907i
$597$		−	6.08064e7i		−	0.285776i
$598$	−1.65547e8	+	1.40734e7i	−0.774136	+	0.0658107i
$599$	2.56804e8			1.19487			0.597435	−	0.801917i	$-0.296187\pi$
$599$	2.56804e8			1.19487			0.597435	+	0.801917i	$0.296187\pi$
$600$	2.45573e7			0.113691
$601$	−4.13147e8			−1.90319			−0.951593	−	0.307360i	$-0.900554\pi$
$601$	−4.13147e8			−1.90319			−0.951593	+	0.307360i	$0.900554\pi$
$602$	−2.98876e8			−1.36994
$603$		−	3.42390e7i		−	0.156160i
$604$	1.11008e6			0.00503785
$605$			6.19376e6i			0.0279697i
$606$	1.61932e7			0.0727636
$607$	−3.54278e8			−1.58408			−0.792042	−	0.610467i	$-0.790982\pi$
$607$	−3.54278e8			−1.58408			−0.792042	+	0.610467i	$0.790982\pi$
$608$		−	2.06522e7i		−	0.0918872i
$609$			2.05731e8i			0.910852i
$610$	−9.72281e7			−0.428354
$611$	8.17843e7			0.358547
$612$		−	2.99845e7i		−	0.130810i
$613$		−	4.09123e8i		−	1.77612i	−0.459729	−	0.888059i	$-0.652053\pi$
$613$		−	4.09123e8i		−	1.77612i	0.459729	−	0.888059i	$-0.347947\pi$
$614$	4.97494e7			0.214923
$615$			3.23161e8i			1.38929i
$616$	−1.34122e8			−0.573796
$617$		−	3.31373e8i		−	1.41079i	−0.708816	−	0.705394i	$-0.750770\pi$
$617$		−	3.31373e8i		−	1.41079i	0.708816	−	0.705394i	$-0.249230\pi$
$618$		−	8.53213e7i		−	0.361487i
$619$		−	3.01187e8i		−	1.26989i	−0.772559	−	0.634943i	$-0.781024\pi$
$619$		−	3.01187e8i		−	1.26989i	0.772559	−	0.634943i	$-0.218976\pi$
$620$			9.78566e7i			0.410596i
$621$	−4.59229e7	+	3.90399e6i	−0.191758	+	0.0163017i
$622$	8.65529e7			0.359675
$623$	2.25642e8			0.933158
$624$	−3.85327e7			−0.158590
$625$	−3.04383e8			−1.24675
$626$		−	7.03285e7i		−	0.286687i
$627$	7.47973e7			0.303447
$628$			1.39697e8i			0.564038i
$629$	−4.68407e6			−0.0188222
$630$	−1.18036e8			−0.472055
$631$			9.17838e7i			0.365324i	0.983176	+	0.182662i	$0.0584714\pi$
$631$			9.17838e7i			0.365324i	−0.983176	+	0.182662i	$0.941529\pi$
$632$			1.73327e8i			0.686617i
$633$	2.43485e6			0.00959977
$634$	−1.14292e8			−0.448485
$635$		−	3.32677e8i		−	1.29928i
$636$			1.11299e8i			0.432633i
$637$	4.47633e8			1.73182
$638$			1.82507e8i			0.702779i
$639$	−6.70253e7			−0.256883
$640$			2.89118e7i			0.110290i
$641$		−	1.23179e8i		−	0.467696i	−0.972273	−	0.233848i	$-0.924868\pi$
$641$		−	1.23179e8i		−	0.467696i	0.972273	−	0.233848i	$-0.0751318\pi$
$642$			4.15691e6i			0.0157096i
$643$			4.63814e8i			1.74466i	0.488916	+	0.872331i	$0.337392\pi$
$643$			4.63814e8i			1.74466i	−0.488916	+	0.872331i	$0.662608\pi$
$644$	−1.81565e7	−	2.13576e8i	−0.0679790	−	0.799641i
$645$	−2.33339e8			−0.869577
$646$	−7.77689e7			−0.288475
$647$	−1.26012e8			−0.465265			−0.232633	−	0.972565i	$-0.574734\pi$
$647$	−1.26012e8			−0.465265			−0.232633	+	0.972565i	$0.574734\pi$
$648$	−1.06890e7			−0.0392837
$649$			5.01476e8i			1.83449i
$650$	−1.18838e8			−0.432727
$651$		−	1.68258e8i		−	0.609864i
$652$	2.59286e7			0.0935485
$653$	1.91338e8			0.687165			0.343583	−	0.939122i	$-0.388359\pi$
$653$	1.91338e8			0.687165			0.343583	+	0.939122i	$0.388359\pi$
$654$		−	1.24092e8i		−	0.443620i
$655$		−	5.62711e8i		−	2.00245i
$656$	−1.36102e8			−0.482118
$657$	−1.81459e8			−0.639857
$658$			1.05512e8i			0.370360i
$659$		−	4.49519e8i		−	1.57069i	−0.619056	−	0.785347i	$-0.712485\pi$
$659$		−	4.49519e8i		−	1.57069i	0.619056	−	0.785347i	$-0.287515\pi$
$660$	−1.04712e8			−0.364220
$661$			2.11445e8i			0.732138i	0.930588	+	0.366069i	$0.119297\pi$
$661$			2.11445e8i			0.732138i	−0.930588	+	0.366069i	$0.880703\pi$
$662$	−1.55004e8			−0.534281
$663$			1.45101e8i			0.497884i
$664$			1.11770e8i			0.381787i
$665$			3.06143e8i			1.04102i
$666$			1.66980e6i			0.00565252i
$667$	−2.90625e8	+	2.47066e7i	−0.979391	+	0.0832599i
$668$	−5.77641e7			−0.193789
$669$	2.96155e8			0.989100
$670$	1.24320e8			0.413348
$671$	1.48306e8			0.490897
$672$		−	4.97120e7i		−	0.163815i
$673$	−8.54195e7			−0.280228			−0.140114	−	0.990135i	$-0.544747\pi$
$673$	−8.54195e7			−0.280228			−0.140114	+	0.990135i	$0.544747\pi$
$674$		−	9.07426e6i		−	0.0296368i
$675$	−3.29657e7			−0.107189
$676$	3.20090e7			0.103617
$677$			2.76170e8i			0.890040i	0.895521	+	0.445020i	$0.146804\pi$
$677$			2.76170e8i			0.890040i	−0.895521	+	0.445020i	$0.853196\pi$
$678$		−	1.48542e8i		−	0.476606i
$679$	−6.27490e8			−2.00446
$680$	1.08872e8			0.346249
$681$		−	2.00294e8i		−	0.634202i
$682$		−	1.49264e8i		−	0.470547i
$683$	−5.58048e6			−0.0175150			−0.00875748	−	0.999962i	$-0.502788\pi$
$683$	−5.58048e6			−0.0175150			−0.00875748	+	0.999962i	$0.502788\pi$
$684$			2.77234e7i			0.0866321i
$685$	−4.44931e8			−1.38427
$686$			2.11111e8i			0.653939i
$687$			1.81526e7i			0.0559847i
$688$		−	9.82729e7i		−	0.301765i
$689$		−	5.38597e8i		−	1.64667i
$690$	−1.41752e7	−	1.66743e8i	−0.0431500	−	0.507576i
$691$	−5.82367e8			−1.76507			−0.882536	−	0.470245i	$-0.844166\pi$
$691$	−5.82367e8			−1.76507			−0.882536	+	0.470245i	$0.844166\pi$
$692$	6.09303e7			0.183872
$693$	1.80045e8			0.540980
$694$	2.30579e8			0.689829
$695$			5.56398e8i			1.65741i
$696$	−6.76460e7			−0.200638
$697$			5.12513e8i			1.51359i
$698$	−3.04762e6			−0.00896178
$699$	−7.38635e7			−0.216271
$700$		−	1.53316e8i		−	0.446984i
$701$		−	5.55924e7i		−	0.161384i	−0.996739	−	0.0806922i	$-0.974287\pi$
$701$		−	5.55924e7i		−	0.161384i	0.996739	−	0.0806922i	$-0.0257131\pi$
$702$	5.17262e7			0.149520
$703$	4.33086e6			0.0124655
$704$		−	4.41003e7i		−	0.126393i
$705$			8.23754e7i			0.235088i
$706$	−3.69675e8			−1.05052
$707$		−	1.01097e8i		−	0.286074i
$708$	−1.85871e8			−0.523735
$709$			5.65956e8i			1.58798i	0.607933	+	0.793988i	$0.291999\pi$
$709$			5.65956e8i			1.58798i	−0.607933	+	0.793988i	$0.708001\pi$
$710$		−	2.43365e8i		−	0.679959i
$711$		−	2.32673e8i		−	0.647348i
$712$			7.41928e7i			0.205552i
$713$	2.37689e8	−	2.02064e7i	0.655754	−	0.0557469i
$714$	−1.87198e8			−0.514288
$715$	5.06720e8			1.38628
$716$	3.85902e7			0.105133
$717$	1.71421e8			0.465057
$718$			3.37788e8i			0.912579i
$719$	2.88752e8			0.776853			0.388427	−	0.921480i	$-0.373019\pi$
$719$	2.88752e8			0.776853			0.388427	+	0.921480i	$0.373019\pi$
$720$		−	3.88112e7i		−	0.103982i
$721$	−5.32675e8			−1.42120
$722$	−1.94227e8			−0.516058
$723$		−	1.34990e8i		−	0.357179i
$724$		−	2.90651e8i		−	0.765873i
$725$	−2.08625e8			−0.547461
$726$	3.50173e6			0.00915108
$727$			4.29145e7i			0.111687i	0.998440	+	0.0558433i	$0.0177847\pi$
$727$			4.29145e7i			0.111687i	−0.998440	+	0.0558433i	$0.982215\pi$
$728$			2.40566e8i			0.623504i
$729$	1.43489e7			0.0370370
$730$		−	6.58868e8i		−	1.69367i
$731$	−3.70061e8			−0.947375
$732$			5.49692e7i			0.140148i
$733$		−	2.50539e8i		−	0.636156i	−0.948065	−	0.318078i	$-0.896963\pi$
$733$		−	2.50539e8i		−	0.636156i	0.948065	−	0.318078i	$-0.103037\pi$
$734$			1.58940e8i			0.401925i
$735$			4.50868e8i			1.13550i
$736$	7.02255e7	−	5.97000e6i	0.176141	−	0.0149741i
$737$	−1.89630e8			−0.473701
$738$	1.82703e8			0.454546
$739$	4.01203e8			0.994101			0.497051	−	0.867722i	$-0.334416\pi$
$739$	4.01203e8			0.994101			0.497051	+	0.867722i	$0.334416\pi$
$740$	−6.06295e6			−0.0149620
$741$		−	1.34159e8i		−	0.329735i
$742$	6.94858e8			1.70092
$743$			5.23752e8i			1.27691i	0.769660	+	0.638454i	$0.220426\pi$
$743$			5.23752e8i			1.27691i	−0.769660	+	0.638454i	$0.779574\pi$
$744$	5.53245e7			0.134338
$745$	7.01599e7			0.169676
$746$			4.67979e8i			1.12722i
$747$		−	1.50040e8i		−	0.359952i
$748$	−1.66066e8			−0.396805
$749$	2.59522e7			0.0617632
$750$			9.52094e7i			0.225682i
$751$		−	7.03204e8i		−	1.66020i	−0.557611	−	0.830102i	$-0.688282\pi$
$751$		−	7.03204e8i		−	1.66020i	0.557611	−	0.830102i	$-0.311718\pi$
$752$	−3.46932e7			−0.0815813
$753$			1.31794e8i			0.308682i
$754$	3.27352e8			0.763661
$755$		−	5.41073e6i		−	0.0125723i
$756$			6.67332e7i			0.154446i
$757$		−	3.04127e8i		−	0.701080i	−0.936548	−	0.350540i	$-0.885998\pi$
$757$		−	3.04127e8i		−	0.701080i	0.936548	−	0.350540i	$-0.114002\pi$
$758$		−	2.24122e8i		−	0.514608i
$759$	2.16219e7	+	2.54340e8i	0.0494503	+	0.581687i
$760$	−1.00662e8			−0.229311
$761$	−1.92200e8			−0.436113			−0.218056	−	0.975936i	$-0.569972\pi$
$761$	−1.92200e8			−0.436113			−0.218056	+	0.975936i	$0.569972\pi$
$762$	−1.88084e8			−0.425095
$763$	−7.74728e8			−1.74412
$764$		−	3.26191e8i		−	0.731462i
$765$	−1.46149e8			−0.326447
$766$		−	5.31131e8i		−	1.18172i
$767$	8.99465e8			1.99342
$768$	1.63457e7			0.0360844
$769$		−	3.67418e8i		−	0.807945i	−0.914771	−	0.403973i	$-0.867629\pi$
$769$		−	3.67418e8i		−	0.807945i	0.914771	−	0.403973i	$-0.132371\pi$
$770$			6.53732e8i			1.43195i
$771$	−1.60135e8			−0.349401
$772$	1.44799e8			0.314712
$773$			3.71696e8i			0.804729i	0.915479	+	0.402365i	$0.131812\pi$
$773$			3.71696e8i			0.804729i	−0.915479	+	0.402365i	$0.868188\pi$
$774$			1.31921e8i			0.284507i
$775$	1.70625e8			0.366554
$776$		−	2.06324e8i		−	0.441534i
$777$	1.04248e7			0.0222232
$778$			2.79877e8i			0.594332i
$779$		−	4.73867e8i		−	1.00241i
$780$			1.87815e8i			0.395772i
$781$			3.71214e8i			0.779240i
$782$	−2.24809e7	−	2.64445e8i	−0.0470104	−	0.552987i
$783$	9.08078e7			0.189164
$784$	−1.89887e8			−0.394047
$785$	6.80907e8			1.40760
$786$	−3.18136e8			−0.655157
$787$		−	4.39166e8i		−	0.900957i	−0.892787	−	0.450479i	$-0.851253\pi$
$787$		−	4.39166e8i		−	0.900957i	0.892787	−	0.450479i	$-0.148747\pi$
$788$	4.38596e8			0.896368
$789$		−	7.29299e7i		−	0.148482i
$790$	8.44824e8			1.71350
$791$	−9.27371e8			−1.87380
$792$			5.92002e7i			0.119165i
$793$		−	2.66007e8i		−	0.533424i
$794$	−3.41876e8			−0.682978
$795$	5.42490e8			1.07967
$796$		−	1.24823e8i		−	0.247490i
$797$		−	5.40594e8i		−	1.06782i	−0.845543	−	0.533908i	$-0.820723\pi$
$797$		−	5.40594e8i		−	1.06782i	0.845543	−	0.533908i	$-0.179277\pi$
$798$	1.73082e8			0.340599
$799$			1.30642e8i			0.256120i
$800$	5.04113e7			0.0984597
$801$		−	9.95962e7i		−	0.193796i
$802$		−	6.22757e8i		−	1.20724i
$803$			1.00500e9i			1.94097i
$804$		−	7.02859e7i		−	0.135238i
$805$	−1.04101e9	+	8.84978e7i	−1.99556	+	0.169647i
$806$	−2.67726e8			−0.511311
$807$	−1.99354e8			−0.379318
$808$	3.32414e7			0.0630151
$809$	−1.03036e8			−0.194601			−0.0973004	−	0.995255i	$-0.531021\pi$
$809$	−1.03036e8			−0.194601			−0.0973004	+	0.995255i	$0.531021\pi$
$810$			5.21000e7i			0.0980354i
$811$	3.63182e8			0.680866			0.340433	−	0.940269i	$-0.389426\pi$
$811$	3.63182e8			0.680866			0.340433	+	0.940269i	$0.389426\pi$
$812$			4.22325e8i			0.788821i
$813$	−5.03523e8			−0.937018
$814$	9.24805e6			0.0171466
$815$		−	1.26380e8i		−	0.233457i
$816$		−	6.15521e7i		−	0.113285i
$817$	3.42157e8			0.627420
$818$	−2.67511e8			−0.488744
$819$		−	3.22935e8i		−	0.587846i
$820$			6.63385e8i			1.20316i
$821$	−2.75797e8			−0.498380			−0.249190	−	0.968455i	$-0.580164\pi$
$821$	−2.75797e8			−0.498380			−0.249190	+	0.968455i	$0.580164\pi$
$822$			2.51548e8i			0.452903i
$823$	−4.81689e8			−0.864107			−0.432053	−	0.901848i	$-0.642211\pi$
$823$	−4.81689e8			−0.864107			−0.432053	+	0.901848i	$0.642211\pi$
$824$		−	1.75148e8i		−	0.313057i
$825$			1.82578e8i			0.325152i
$826$			1.16042e9i			2.05909i
$827$		−	9.59723e8i		−	1.69679i	−0.529360	−	0.848397i	$-0.677568\pi$
$827$		−	9.59723e8i		−	1.69679i	0.529360	−	0.848397i	$-0.322432\pi$
$828$	−9.42706e7	+	8.01412e6i	−0.166068	+	0.0141177i
$829$	1.10371e9			1.93728			0.968638	−	0.248478i	$-0.0799302\pi$
$829$	1.10371e9			1.93728			0.968638	+	0.248478i	$0.0799302\pi$
$830$	5.44785e8			0.952777
$831$	−4.00514e7			−0.0697934
$832$	−7.90999e7			−0.137343
$833$			7.15049e8i			1.23709i
$834$	3.14567e8			0.542269
$835$			2.81552e8i			0.483614i
$836$	1.53544e8			0.262793
$837$	−7.42675e7			−0.126655
$838$			3.52827e8i			0.599556i
$839$		−	2.07059e8i		−	0.350597i	−0.984515	−	0.175299i	$-0.943911\pi$
$839$		−	2.07059e8i		−	0.350597i	0.984515	−	0.175299i	$-0.0560891\pi$
$840$	−2.42304e8			−0.408812
$841$	−2.01414e7			−0.0338611
$842$		−	1.98522e8i		−	0.332562i
$843$			1.98524e8i			0.331382i
$844$	4.99826e6			0.00831364
$845$		−	1.56017e8i		−	0.258584i
$846$	4.65720e7			0.0769155
$847$		−	2.18619e7i		−	0.0359780i
$848$			2.28475e8i			0.374672i
$849$		−	1.55560e8i		−	0.254200i
$850$		−	1.89832e8i		−	0.309109i
$851$	1.25194e6	+	1.47266e7i	0.00203139	+	0.0238954i
$852$	−1.37590e8			−0.222468
$853$	9.42523e8			1.51860			0.759302	−	0.650738i	$-0.225540\pi$
$853$	9.42523e8			1.51860			0.759302	+	0.650738i	$0.225540\pi$
$854$	3.43182e8			0.550999
$855$	1.35129e8			0.216197
$856$			8.53330e6i			0.0136049i
$857$	3.95419e8			0.628226			0.314113	−	0.949386i	$-0.398293\pi$
$857$	3.95419e8			0.628226			0.314113	+	0.949386i	$0.398293\pi$
$858$		−	2.86481e8i		−	0.453559i
$859$	−7.24478e8			−1.14300			−0.571499	−	0.820603i	$-0.693638\pi$
$859$	−7.24478e8			−1.14300			−0.571499	+	0.820603i	$0.693638\pi$
$860$	−4.78999e8			−0.753076
$861$		−	1.14065e9i		−	1.78707i
$862$			5.51742e8i			0.861418i
$863$	−1.21660e9			−1.89285			−0.946423	−	0.322931i	$-0.895332\pi$
$863$	−1.21660e9			−1.89285			−0.946423	+	0.322931i	$0.895332\pi$
$864$	−2.19424e7			−0.0340207
$865$		−	2.96985e8i		−	0.458866i
$866$		−	8.13251e8i		−	1.25219i
$867$	1.44484e8			0.221698
$868$		−	3.45400e8i		−	0.528157i
$869$	−1.28864e9			−1.96369
$870$			3.29718e8i			0.500708i
$871$			3.40127e8i			0.514739i
$872$		−	2.54737e8i		−	0.384186i
$873$			2.76968e8i			0.416282i
$874$	2.07857e7	+	2.44504e8i	0.0311337	+	0.366228i
$875$	5.94408e8			0.887279
$876$	−3.72500e8			−0.554133
$877$	−8.36946e8			−1.24079			−0.620395	−	0.784289i	$-0.713028\pi$
$877$	−8.36946e8			−1.24079			−0.620395	+	0.784289i	$0.713028\pi$
$878$	−3.07532e8			−0.454368
$879$		−	1.05743e8i		−	0.155699i
$880$	−2.14952e8			−0.315424
$881$		−	1.21642e9i		−	1.77891i	−0.457020	−	0.889456i	$-0.651083\pi$
$881$		−	1.21642e9i		−	1.77891i	0.457020	−	0.889456i	$-0.348917\pi$
$882$	2.54904e8			0.371511
$883$	1.04726e9			1.52115			0.760574	−	0.649251i	$-0.224917\pi$
$883$	1.04726e9			1.52115			0.760574	+	0.649251i	$0.224917\pi$
$884$			2.97862e8i			0.431180i
$885$			9.05966e8i			1.30702i
$886$	2.78306e8			0.400149
$887$	8.71281e8			1.24850			0.624248	−	0.781226i	$-0.285405\pi$
$887$	8.71281e8			1.24850			0.624248	+	0.781226i	$0.285405\pi$
$888$			3.42777e6i			0.00489522i
$889$			1.17424e9i			1.67128i
$890$	3.61628e8			0.512970
$891$		−	7.94702e7i		−	0.112350i
$892$	6.07947e8			0.856586
$893$		−	1.20791e8i		−	0.169621i
$894$		−	3.96658e7i		−	0.0555142i
$895$		−	1.88095e8i		−	0.262366i
$896$		−	1.02049e8i		−	0.141868i
$897$	4.56193e8	−	3.87818e7i	0.632079	−	0.0537342i
$898$	7.40697e8			1.02285
$899$	−4.70006e8			−0.646881
$900$	−6.76721e7			−0.0928287
$901$	8.60356e8			1.17626
$902$		−	1.01189e9i		−	1.37884i
$903$	8.23607e8			1.11855
$904$		−	3.04927e8i		−	0.412753i
$905$	−1.41668e9			−1.91129
$906$	−3.05903e6			−0.00411338
$907$			3.88651e7i			0.0520880i	0.999661	+	0.0260440i	$0.00829101\pi$
$907$			3.88651e7i			0.0520880i	−0.999661	+	0.0260440i	$0.991709\pi$
$908$		−	4.11165e8i		−	0.549235i
$909$	−4.46232e7			−0.0594113
$910$	1.17256e9			1.55600
$911$			1.26440e9i			1.67236i	0.548456	+	0.836179i	$0.315216\pi$
$911$			1.26440e9i			1.67236i	−0.548456	+	0.836179i	$0.684784\pi$
$912$			5.69107e7i			0.0750256i
$913$	−8.30982e8			−1.09189
$914$		−	8.98435e7i		−	0.117665i
$915$	2.67929e8			0.349749
$916$			3.72637e7i			0.0484841i
$917$			1.98618e9i			2.57579i
$918$			8.26275e7i			0.106806i
$919$			2.10386e8i			0.271063i	0.990773	+	0.135531i	$0.0432742\pi$
$919$			2.10386e8i			0.271063i	−0.990773	+	0.135531i	$0.956726\pi$
$920$	−2.90988e7	−	3.42291e8i	−0.0373690	−	0.439574i
$921$	−1.37093e8			−0.175484
$922$	7.70319e8			0.982828
$923$	6.65822e8			0.846746
$924$	3.69596e8			0.468502
$925$			1.05715e7i			0.0133571i
$926$	3.58144e6			0.00451051
$927$			2.35118e8i			0.295153i
$928$	−1.38864e8			−0.173758
$929$	−6.40812e8			−0.799252			−0.399626	−	0.916678i	$-0.630860\pi$
$929$	−6.40812e8			−0.799252			−0.399626	+	0.916678i	$0.630860\pi$
$930$		−	2.69661e8i		−	0.335250i
$931$		−	6.61130e8i		−	0.819291i
$932$	−1.51627e8			−0.187296
$933$	−2.38512e8			−0.293673
$934$		−	5.52701e8i		−	0.678343i
$935$			8.09435e8i			0.990256i
$936$	1.06184e8			0.129488
$937$			1.09813e9i			1.33486i	0.744673	+	0.667429i	$0.232605\pi$
$937$			1.09813e9i			1.33486i	−0.744673	+	0.667429i	$0.767395\pi$
$938$	−4.38807e8			−0.531698
$939$			1.93803e8i			0.234079i
$940$			1.69100e8i			0.203592i
$941$			4.94221e8i			0.593133i	0.955012	+	0.296566i	$0.0958416\pi$
$941$			4.94221e8i			0.593133i	−0.955012	+	0.296566i	$0.904158\pi$
$942$		−	3.84960e8i		−	0.460535i
$943$	1.61133e9	−	1.36982e8i	1.92154	−	0.163354i
$944$	−3.81556e8			−0.453568
$945$	3.25269e8			0.385432
$946$	7.30635e8			0.863033
$947$	−3.15126e8			−0.371051			−0.185526	−	0.982639i	$-0.559399\pi$
$947$	−3.15126e8			−0.371051			−0.185526	+	0.982639i	$0.559399\pi$
$948$		−	4.77632e8i		−	0.560620i
$949$	1.80260e9			2.10911
$950$			1.75517e8i			0.204714i
$951$	3.14951e8			0.366186
$952$	−3.84280e8			−0.445386
$953$		−	1.28575e9i		−	1.48552i	−0.669557	−	0.742760i	$-0.733516\pi$
$953$		−	1.28575e9i		−	1.48552i	0.669557	−	0.742760i	$-0.266484\pi$
$954$		−	3.06704e8i		−	0.353244i
$955$	−1.58991e9			−1.82542
$956$	3.51893e8			0.402751
$957$		−	5.02931e8i		−	0.573816i
$958$			6.66831e8i			0.758436i
$959$	1.57046e9			1.78061
$960$		−	7.96716e7i		−	0.0900513i
$961$	−5.03107e8			−0.566879
$962$		−	1.65876e7i		−	0.0186320i
$963$		−	1.14551e7i		−	0.0128268i
$964$		−	2.77107e8i		−	0.309326i
$965$		−	7.05773e8i		−	0.785386i
$966$	5.00334e7	+	5.88547e8i	0.0555046	+	0.652904i
$967$	−9.71572e8			−1.07447			−0.537237	−	0.843432i	$-0.680532\pi$
$967$	−9.71572e8			−1.07447			−0.537237	+	0.843432i	$0.680532\pi$
$968$	7.18835e6			0.00792507
$969$	2.14306e8			0.235539
$970$	−1.00566e9			−1.10188
$971$		−	1.03765e9i		−	1.13342i	−0.823917	−	0.566711i	$-0.808216\pi$
$971$		−	1.03765e9i		−	1.13342i	0.823917	−	0.566711i	$-0.191784\pi$
$972$	2.94555e7			0.0320750
$973$		−	1.96389e9i		−	2.13196i
$974$	−2.20986e8			−0.239159
$975$	3.27478e8			0.353320
$976$			1.12841e8i			0.121372i
$977$		−	6.92476e8i		−	0.742542i	−0.928524	−	0.371271i	$-0.878922\pi$
$977$		−	6.92476e8i		−	0.742542i	0.928524	−	0.371271i	$-0.121078\pi$
$978$	−7.14509e7			−0.0763820
$979$	−5.51605e8			−0.587869
$980$			9.25543e8i			0.983373i
$981$			3.41958e8i			0.362214i
$982$	−1.42918e8			−0.150921
$983$		−	3.45909e8i		−	0.364167i	−0.983283	−	0.182084i	$-0.941716\pi$
$983$		−	3.45909e8i		−	0.364167i	0.983283	−	0.182084i	$-0.0582842\pi$
$984$	3.75054e8			0.393648
$985$		−	2.13779e9i		−	2.23695i
$986$			5.22912e8i			0.545504i
$987$		−	2.90757e8i		−	0.302398i
$988$		−	2.75402e8i		−	0.285559i
$989$	9.89084e7	+	1.16347e9i	0.102246	+	1.20272i
$990$	2.88552e8			0.297384
$991$	3.68259e8			0.378383			0.189192	−	0.981940i	$-0.439413\pi$
$991$	3.68259e8			0.378383			0.189192	+	0.981940i	$0.439413\pi$
$992$	1.13570e8			0.116340
$993$	4.27142e8			0.436239
$994$			8.58994e8i			0.874643i
$995$	−6.08411e8			−0.617629
$996$		−	3.08002e8i		−	0.311727i
$997$	1.16749e9			1.17806			0.589030	−	0.808111i	$-0.299510\pi$
$997$	1.16749e9			1.17806			0.589030	+	0.808111i	$0.299510\pi$
$998$	7.92812e8			0.797588
$999$		−	4.60143e6i		−	0.00461526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.7.b.a.91.8	✓	24
3.2	odd	2		414.7.b.c.91.22		24
23.22	odd	2	inner	138.7.b.a.91.11	yes	24
69.68	even	2		414.7.b.c.91.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.7.b.a.91.8	✓	24	1.1	even	1	trivial
138.7.b.a.91.11	yes	24	23.22	odd	2	inner
414.7.b.c.91.15		24	69.68	even	2
414.7.b.c.91.22		24	3.2	odd	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)

\(f(q)\)	\(=\)	\(q-5.65685 q^{2} +15.5885 q^{3} +32.0000 q^{4} -155.973i q^{5} -88.1816 q^{6} +550.532i q^{7} -181.019 q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-5.65685 q^{2} +15.5885 q^{3} +32.0000 q^{4} -155.973i q^{5} -88.1816 q^{6} +550.532i q^{7} -181.019 q^{8} +243.000 q^{9} +882.319i q^{10} -1345.83i q^{11} +498.831 q^{12} -2413.94 q^{13} -3114.28i q^{14} -2431.38i q^{15} +1024.00 q^{16} -3856.03i q^{17} -1374.62 q^{18} +3565.26i q^{19} -4991.15i q^{20} +8581.95i q^{21} +7613.19i q^{22} +(-12123.3 + 1030.62i) q^{23} -2821.81 q^{24} -8702.69 q^{25} +13655.3 q^{26} +3788.00 q^{27} +17617.0i q^{28} +23972.5 q^{29} +13754.0i q^{30} -19606.0 q^{31} -5792.62 q^{32} -20979.5i q^{33} +21813.0i q^{34} +85868.4 q^{35} +7776.00 q^{36} -1214.74i q^{37} -20168.1i q^{38} -37629.5 q^{39} +28234.2i q^{40} -132912. q^{41} -48546.8i q^{42} -95969.6i q^{43} -43066.7i q^{44} -37901.5i q^{45} +(68579.6 - 5830.08i) q^{46} -33880.0 q^{47} +15962.6 q^{48} -185437. q^{49} +49229.8 q^{50} -60109.5i q^{51} -77246.0 q^{52} +223120. i q^{53} -21428.1 q^{54} -209914. q^{55} -99657.0i q^{56} +55576.9i q^{57} -135609. q^{58} -372613. q^{59} -77804.3i q^{60} +110196. i q^{61} +110908. q^{62} +133779. i q^{63} +32768.0 q^{64} +376510. i q^{65} +118678. i q^{66} -140901. i q^{67} -123393. i q^{68} +(-188983. + 16065.8i) q^{69} -485745. q^{70} -275824. q^{71} -43987.7 q^{72} -746746. q^{73} +6871.61i q^{74} -135661. q^{75} +114088. i q^{76} +740926. q^{77} +212865. q^{78} -957504. i q^{79} -159717. i q^{80} +59049.0 q^{81} +751866. q^{82} -617447. i q^{83} +274622. i q^{84} -601437. q^{85} +542886. i q^{86} +373695. q^{87} +243622. i q^{88} -409861. i q^{89} +214403. i q^{90} -1.32895e6i q^{91} +(-387945. + 32979.9i) q^{92} -305628. q^{93} +191654. q^{94} +556085. q^{95} -90298.0 q^{96} +1.13979e6i q^{97} +1.04899e6 q^{98} -327038. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 768 q^{4} + 5832 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more