LMFDB - Embedded newform 3.40.a.b.1.2

Newspace parameters

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 40 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.9018654169$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
Defining polynomial:	$x^{3} - 3876249523 x - 18467420411022$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6}\cdot 5\cdot 7\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4792.65$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

$f(q)$	$=$	$q+264126. q^{2} -1.16226e9 q^{3} -4.79993e11 q^{4} -6.30487e13 q^{5} -3.06983e14 q^{6} -4.59086e16 q^{7} -2.71983e17 q^{8} +1.35085e18 q^{9} +O(q^{10})$	\(q+264126. q^{2} -1.16226e9 q^{3} -4.79993e11 q^{4} -6.30487e13 q^{5} -3.06983e14 q^{6} -4.59086e16 q^{7} -2.71983e17 q^{8} +1.35085e18 q^{9} -1.66528e19 q^{10} -1.42816e20 q^{11} +5.57878e20 q^{12} +2.23742e20 q^{13} -1.21256e22 q^{14} +7.32790e22 q^{15} +1.92041e23 q^{16} +3.05051e23 q^{17} +3.56795e23 q^{18} -1.47192e25 q^{19} +3.02629e25 q^{20} +5.33578e25 q^{21} -3.77213e25 q^{22} -5.75448e26 q^{23} +3.16116e26 q^{24} +2.15614e27 q^{25} +5.90959e25 q^{26} -1.57004e27 q^{27} +2.20358e28 q^{28} +1.59256e28 q^{29} +1.93549e28 q^{30} +2.90720e28 q^{31} +2.00247e29 q^{32} +1.65989e29 q^{33} +8.05717e28 q^{34} +2.89448e30 q^{35} -6.48400e29 q^{36} +4.49195e30 q^{37} -3.88772e30 q^{38} -2.60046e29 q^{39} +1.71482e31 q^{40} -3.98145e31 q^{41} +1.40932e31 q^{42} -1.13795e32 q^{43} +6.85506e31 q^{44} -8.51694e31 q^{45} -1.51990e32 q^{46} -4.87913e32 q^{47} -2.23202e32 q^{48} +1.19806e33 q^{49} +5.69493e32 q^{50} -3.54549e32 q^{51} -1.07395e32 q^{52} -5.94518e32 q^{53} -4.14689e32 q^{54} +9.00434e33 q^{55} +1.24864e34 q^{56} +1.71076e34 q^{57} +4.20636e33 q^{58} -2.61158e34 q^{59} -3.51734e34 q^{60} -4.20907e34 q^{61} +7.67866e33 q^{62} -6.20157e34 q^{63} -5.26854e34 q^{64} -1.41066e34 q^{65} +4.38420e34 q^{66} -4.97358e35 q^{67} -1.46422e35 q^{68} +6.68820e35 q^{69} +7.64506e35 q^{70} +8.30261e35 q^{71} -3.67409e35 q^{72} -5.71462e35 q^{73} +1.18644e36 q^{74} -2.50600e36 q^{75} +7.06513e36 q^{76} +6.55647e36 q^{77} -6.86849e34 q^{78} -1.34537e37 q^{79} -1.21080e37 q^{80} +1.82480e36 q^{81} -1.05160e37 q^{82} +2.31025e37 q^{83} -2.56114e37 q^{84} -1.92330e37 q^{85} -3.00563e37 q^{86} -1.85097e37 q^{87} +3.88435e37 q^{88} +5.53932e37 q^{89} -2.24954e37 q^{90} -1.02717e37 q^{91} +2.76211e38 q^{92} -3.37893e37 q^{93} -1.28870e38 q^{94} +9.28027e38 q^{95} -2.32740e38 q^{96} -5.58017e38 q^{97} +3.16438e38 q^{98} -1.92923e38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} + O(q^{10}) $	$ 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} - 39868781226579858780q^{10} - $$53\!\cdots\!40$$q^{11} - $$11\!\cdots\!44$$q^{12} + $$54\!\cdots\!90$$q^{13} + $$31\!\cdots\!52$$q^{14} + $$62\!\cdots\!10$$q^{15} + $$12\!\cdots\!36$$q^{16} + $$72\!\cdots\!58$$q^{17} + $$72\!\cdots\!86$$q^{18} - $$10\!\cdots\!24$$q^{19} + $$30\!\cdots\!60$$q^{20} + $$18\!\cdots\!76$$q^{21} - $$10\!\cdots\!24$$q^{22} + $$41\!\cdots\!64$$q^{23} - $$51\!\cdots\!32$$q^{24} - $$11\!\cdots\!75$$q^{25} + $$92\!\cdots\!76$$q^{26} - $$47\!\cdots\!89$$q^{27} + $$64\!\cdots\!56$$q^{28} + $$72\!\cdots\!62$$q^{29} + $$46\!\cdots\!60$$q^{30} - $$38\!\cdots\!56$$q^{31} + $$37\!\cdots\!12$$q^{32} + $$61\!\cdots\!80$$q^{33} + $$37\!\cdots\!44$$q^{34} + $$27\!\cdots\!20$$q^{35} + $$12\!\cdots\!48$$q^{36} + $$29\!\cdots\!22$$q^{37} + $$74\!\cdots\!92$$q^{38} - $$63\!\cdots\!30$$q^{39} + $$15\!\cdots\!00$$q^{40} - $$13\!\cdots\!26$$q^{41} - $$36\!\cdots\!84$$q^{42} - $$24\!\cdots\!28$$q^{43} - $$21\!\cdots\!12$$q^{44} - $$72\!\cdots\!70$$q^{45} - $$10\!\cdots\!56$$q^{46} - $$10\!\cdots\!04$$q^{47} - $$13\!\cdots\!12$$q^{48} + $$92\!\cdots\!43$$q^{49} - $$11\!\cdots\!50$$q^{50} - $$84\!\cdots\!86$$q^{51} + $$59\!\cdots\!88$$q^{52} + $$62\!\cdots\!34$$q^{53} - $$83\!\cdots\!62$$q^{54} + $$72\!\cdots\!40$$q^{55} + $$36\!\cdots\!00$$q^{56} + $$12\!\cdots\!08$$q^{57} + $$28\!\cdots\!84$$q^{58} - $$75\!\cdots\!56$$q^{59} - $$35\!\cdots\!20$$q^{60} - $$71\!\cdots\!98$$q^{61} - $$33\!\cdots\!16$$q^{62} - $$21\!\cdots\!92$$q^{63} - $$35\!\cdots\!56$$q^{64} - $$71\!\cdots\!60$$q^{65} + $$11\!\cdots\!08$$q^{66} - $$51\!\cdots\!72$$q^{67} + $$11\!\cdots\!92$$q^{68} - $$48\!\cdots\!88$$q^{69} + $$38\!\cdots\!20$$q^{70} + $$84\!\cdots\!76$$q^{71} + $$60\!\cdots\!44$$q^{72} + $$63\!\cdots\!14$$q^{73} + $$89\!\cdots\!12$$q^{74} + $$13\!\cdots\!25$$q^{75} + $$12\!\cdots\!36$$q^{76} - $$22\!\cdots\!36$$q^{77} - $$10\!\cdots\!92$$q^{78} - $$16\!\cdots\!00$$q^{79} - $$18\!\cdots\!80$$q^{80} + $$54\!\cdots\!63$$q^{81} - $$48\!\cdots\!36$$q^{82} + $$59\!\cdots\!48$$q^{83} - $$74\!\cdots\!52$$q^{84} - $$52\!\cdots\!80$$q^{85} + $$85\!\cdots\!00$$q^{86} - $$84\!\cdots\!54$$q^{87} - $$10\!\cdots\!64$$q^{88} + $$18\!\cdots\!86$$q^{89} - $$53\!\cdots\!20$$q^{90} + $$23\!\cdots\!24$$q^{91} + $$96\!\cdots\!32$$q^{92} + $$44\!\cdots\!52$$q^{93} - $$12\!\cdots\!20$$q^{94} + $$84\!\cdots\!00$$q^{95} - $$44\!\cdots\!04$$q^{96} - $$99\!\cdots\!42$$q^{97} + $$19\!\cdots\!10$$q^{98} - $$71\!\cdots\!60$$q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

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 $

$2$	264126.	0.356226	0.178113	−	0.984010i	$-0.443001\pi$
$2$	264126.	0.356226	0.178113	+	0.984010i	$0.443001\pi$
$3$	−1.16226e9	−0.577350
$3$	−1.16226e9	−0.577350
$4$	−4.79993e11	−0.873103
$5$	−6.30487e13	−1.47829	−0.739147	−	0.673544i	$-0.764771\pi$
$5$	−6.30487e13	−1.47829	−0.739147	+	0.673544i	$0.764771\pi$
$6$	−3.06983e14	−0.205667
$7$	−4.59086e16	−1.52224	−0.761119	−	0.648613i	$-0.775350\pi$
$7$	−4.59086e16	−1.52224	−0.761119	+	0.648613i	$0.775350\pi$
$8$	−2.71983e17	−0.667248
$9$	1.35085e18	0.333333
$10$	−1.66528e19	−0.526607
$11$	−1.42816e20	−0.704075	−0.352037	−	0.935986i	$-0.614511\pi$
$11$	−1.42816e20	−0.704075	−0.352037	+	0.935986i	$0.614511\pi$
$12$	5.57878e20	0.504086
$13$	2.23742e20	0.0424474	0.0212237	−	0.999775i	$-0.493244\pi$
$13$	2.23742e20	0.0424474	0.0212237	+	0.999775i	$0.493244\pi$
$14$	−1.21256e22	−0.542261
$15$	7.32790e22	0.853493
$16$	1.92041e23	0.635412
$17$	3.05051e23	0.309470	0.154735	−	0.987956i	$-0.450548\pi$
$17$	3.05051e23	0.309470	0.154735	+	0.987956i	$0.450548\pi$
$18$	3.56795e23	0.118742
$19$	−1.47192e25	−1.70683	−0.853413	−	0.521235i	$-0.825472\pi$
$19$	−1.47192e25	−1.70683	−0.853413	+	0.521235i	$0.825472\pi$
$20$	3.02629e25	1.29070
$21$	5.33578e25	0.878864
$22$	−3.77213e25	−0.250810
$23$	−5.75448e26	−1.60810	−0.804050	−	0.594562i	$-0.797325\pi$
$23$	−5.75448e26	−1.60810	−0.804050	+	0.594562i	$0.797325\pi$
$24$	3.16116e26	0.385236
$25$	2.15614e27	1.18535
$26$	5.90959e25	0.0151209
$27$	−1.57004e27	−0.192450
$28$	2.20358e28	1.32907
$29$	1.59256e28	0.484546	0.242273	−	0.970208i	$-0.422107\pi$
$29$	1.59256e28	0.484546	0.242273	+	0.970208i	$0.422107\pi$
$30$	1.93549e28	0.304037
$31$	2.90720e28	0.240947	0.120474	−	0.992717i	$-0.461559\pi$
$31$	2.90720e28	0.240947	0.120474	+	0.992717i	$0.461559\pi$
$32$	2.00247e29	0.893598
$33$	1.65989e29	0.406498
$34$	8.05717e28	0.110241
$35$	2.89448e30	2.25031
$36$	−6.48400e29	−0.291034
$37$	4.49195e30	1.18168	0.590842	−	0.806787i	$-0.298796\pi$
$37$	4.49195e30	1.18168	0.590842	+	0.806787i	$0.298796\pi$
$38$	−3.88772e30	−0.608016
$39$	−2.60046e29	−0.0245070
$40$	1.71482e31	0.986389
$41$	−3.98145e31	−1.41500	−0.707499	−	0.706715i	$-0.750176\pi$
$41$	−3.98145e31	−1.41500	−0.707499	+	0.706715i	$0.750176\pi$
$42$	1.40932e31	0.313074
$43$	−1.13795e32	−1.59768	−0.798840	−	0.601544i	$-0.794552\pi$
$43$	−1.13795e32	−1.59768	−0.798840	+	0.601544i	$0.794552\pi$
$44$	6.85506e31	0.614730
$45$	−8.51694e31	−0.492765
$46$	−1.51990e32	−0.572847
$47$	−4.87913e32	−1.20902	−0.604511	−	0.796597i	$-0.706631\pi$
$47$	−4.87913e32	−1.20902	−0.604511	+	0.796597i	$0.706631\pi$
$48$	−2.23202e32	−0.366855
$49$	1.19806e33	1.31721
$50$	5.69493e32	0.422253
$51$	−3.54549e32	−0.178672
$52$	−1.07395e32	−0.0370610
$53$	−5.94518e32	−0.141509	−0.0707547	−	0.997494i	$-0.522541\pi$
$53$	−5.94518e32	−0.141509	−0.0707547	+	0.997494i	$0.522541\pi$
$54$	−4.14689e32	−0.0685557
$55$	9.00434e33	1.04083
$56$	1.24864e34	1.01571
$57$	1.71076e34	0.985437
$58$	4.20636e33	0.172608
$59$	−2.61158e34	−0.767872	−0.383936	−	0.923360i	$-0.625432\pi$
$59$	−2.61158e34	−0.767872	−0.383936	+	0.923360i	$0.625432\pi$
$60$	−3.51734e34	−0.745188
$61$	−4.20907e34	−0.646032	−0.323016	−	0.946393i	$-0.604697\pi$
$61$	−4.20907e34	−0.646032	−0.323016	+	0.946393i	$0.604697\pi$
$62$	7.67866e33	0.0858317
$63$	−6.20157e34	−0.507413
$64$	−5.26854e34	−0.317089
$65$	−1.41066e34	−0.0627498
$66$	4.38420e34	0.144805
$67$	−4.97358e35	−1.22521	−0.612605	−	0.790389i	$-0.709878\pi$
$67$	−4.97358e35	−1.22521	−0.612605	+	0.790389i	$0.709878\pi$
$68$	−1.46422e35	−0.270199
$69$	6.68820e35	0.928437
$70$	7.64506e35	0.801621
$71$	8.30261e35	0.660202	0.330101	−	0.943946i	$-0.392917\pi$
$71$	8.30261e35	0.660202	0.330101	+	0.943946i	$0.392917\pi$
$72$	−3.67409e35	−0.222416
$73$	−5.71462e35	−0.264358	−0.132179	−	0.991226i	$-0.542197\pi$
$73$	−5.71462e35	−0.264358	−0.132179	+	0.991226i	$0.542197\pi$
$74$	1.18644e36	0.420947
$75$	−2.50600e36	−0.684364
$76$	7.06513e36	1.49024
$77$	6.55647e36	1.07177
$78$	−6.86849e34	−0.00873005
$79$	−1.34537e37	−1.33387	−0.666935	−	0.745116i	$-0.732394\pi$
$79$	−1.34537e37	−1.33387	−0.666935	+	0.745116i	$0.732394\pi$
$80$	−1.21080e37	−0.939325
$81$	1.82480e36	0.111111
$82$	−1.05160e37	−0.504059
$83$	2.31025e37	0.874252	0.437126	−	0.899400i	$-0.355996\pi$
$83$	2.31025e37	0.874252	0.437126	+	0.899400i	$0.355996\pi$
$84$	−2.56114e37	−0.767339
$85$	−1.92330e37	−0.457487
$86$	−3.00563e37	−0.569135
$87$	−1.85097e37	−0.279753
$88$	3.88435e37	0.469793
$89$	5.53932e37	0.537466	0.268733	−	0.963215i	$-0.413395\pi$
$89$	5.53932e37	0.537466	0.268733	+	0.963215i	$0.413395\pi$
$90$	−2.24954e37	−0.175536
$91$	−1.02717e37	−0.0646151
$92$	2.76211e38	1.40404
$93$	−3.37893e37	−0.139111
$94$	−1.28870e38	−0.430685
$95$	9.28027e38	2.52319
$96$	−2.32740e38	−0.515919
$97$	−5.58017e38	−1.01065	−0.505323	−	0.862930i	$-0.668627\pi$
$97$	−5.58017e38	−1.01065	−0.505323	+	0.862930i	$0.668627\pi$
$98$	3.16438e38	0.469224
$99$	−1.92923e38	−0.234692
$100$	−1.03493e39	−1.03493
$101$	−8.58640e38	−0.707203	−0.353602	−	0.935396i	$-0.615043\pi$
$101$	−8.58640e38	−0.707203	−0.353602	+	0.935396i	$0.615043\pi$
$102$	−9.36454e37	−0.0636478
$103$	7.23179e38	0.406368	0.203184	−	0.979141i	$-0.434871\pi$
$103$	7.23179e38	0.406368	0.203184	+	0.979141i	$0.434871\pi$
$104$	−6.08540e37	−0.0283230
$105$	−3.36414e39	−1.29922
$106$	−1.57027e38	−0.0504094
$107$	6.55460e39	1.75211	0.876057	−	0.482208i	$-0.160165\pi$
$107$	6.55460e39	1.75211	0.876057	+	0.482208i	$0.160165\pi$
$108$	7.53610e38	0.168029
$109$	−5.87754e39	−1.09491	−0.547456	−	0.836835i	$-0.684403\pi$
$109$	−5.87754e39	−1.09491	−0.547456	+	0.836835i	$0.684403\pi$
$110$	2.37828e39	0.370771
$111$	−5.22082e39	−0.682246
$112$	−8.81636e39	−0.967248
$113$	1.66536e40	1.53631	0.768154	−	0.640265i	$-0.221175\pi$
$113$	1.66536e40	1.53631	0.768154	+	0.640265i	$0.221175\pi$
$114$	4.51855e39	0.351038
$115$	3.62812e40	2.37724
$116$	−7.64418e39	−0.423058
$117$	3.02242e38	0.0141491
$118$	−6.89785e39	−0.273536
$119$	−1.40045e40	−0.471086
$120$	−1.99307e40	−0.569492
$121$	−2.07484e40	−0.504279
$122$	−1.11172e40	−0.230133
$123$	4.62748e40	0.816949
$124$	−1.39544e40	−0.210372
$125$	−2.12571e40	−0.274005
$126$	−1.63799e40	−0.180754
$127$	−1.17179e41	−1.10835	−0.554177	−	0.832399i	$-0.686967\pi$
$127$	−1.17179e41	−1.10835	−0.554177	+	0.832399i	$0.686967\pi$
$128$	−1.24003e41	−1.00655
$129$	1.32260e41	0.922420
$130$	−3.72592e39	−0.0223531
$131$	−2.69471e40	−0.139227	−0.0696133	−	0.997574i	$-0.522177\pi$
$131$	−2.69471e40	−0.139227	−0.0696133	+	0.997574i	$0.522177\pi$
$132$	−7.96737e40	−0.354914
$133$	6.75739e41	2.59820
$134$	−1.31365e41	−0.436452
$135$	9.89891e40	0.284498
$136$	−8.29687e40	−0.206493
$137$	1.62934e41	0.351528	0.175764	−	0.984432i	$-0.443760\pi$
$137$	1.62934e41	0.351528	0.175764	+	0.984432i	$0.443760\pi$
$138$	1.76653e41	0.330733
$139$	5.71049e41	0.928720	0.464360	−	0.885647i	$-0.346284\pi$
$139$	5.71049e41	0.928720	0.464360	+	0.885647i	$0.346284\pi$
$140$	−1.38933e42	−1.96476
$141$	5.67083e41	0.698029
$142$	2.19293e41	0.235181
$143$	−3.19538e40	−0.0298862
$144$	2.59419e41	0.211804
$145$	−1.00409e42	−0.716301
$146$	−1.50938e41	−0.0941711
$147$	−1.39246e42	−0.760490
$148$	−2.15611e42	−1.03173
$149$	−4.00637e41	−0.168120	−0.0840598	−	0.996461i	$-0.526789\pi$
$149$	−4.00637e41	−0.168120	−0.0840598	+	0.996461i	$0.526789\pi$
$150$	−6.61900e41	−0.243788
$151$	8.19755e41	0.265237	0.132618	−	0.991167i	$-0.457662\pi$
$151$	8.19755e41	0.265237	0.132618	+	0.991167i	$0.457662\pi$
$152$	4.00338e42	1.13888
$153$	4.12078e41	0.103157
$154$	1.73173e42	0.381792
$155$	−1.83295e42	−0.356191
$156$	1.24820e41	0.0213972
$157$	2.75060e42	0.416279	0.208139	−	0.978099i	$-0.433259\pi$
$157$	2.75060e42	0.416279	0.208139	+	0.978099i	$0.433259\pi$
$158$	−3.55347e42	−0.475159
$159$	6.90985e41	0.0817005
$160$	−1.26253e43	−1.32100
$161$	2.64180e43	2.44791
$162$	4.81977e41	0.0395807
$163$	−3.05226e41	−0.0222313	−0.0111156	−	0.999938i	$-0.503538\pi$
$163$	−3.05226e41	−0.0222313	−0.0111156	+	0.999938i	$0.503538\pi$
$164$	1.91107e43	1.23544
$165$	−1.04654e43	−0.600923
$166$	6.10197e42	0.311431
$167$	−8.60063e42	−0.390444	−0.195222	−	0.980759i	$-0.562543\pi$
$167$	−8.60063e42	−0.390444	−0.195222	+	0.980759i	$0.562543\pi$
$168$	−1.45124e43	−0.586421
$169$	−2.77337e43	−0.998198
$170$	−5.07994e42	−0.162969
$171$	−1.98835e43	−0.568942
$172$	5.46210e43	1.39494
$173$	−3.58571e43	−0.817856	−0.408928	−	0.912567i	$-0.634097\pi$
$173$	−3.58571e43	−0.817856	−0.408928	+	0.912567i	$0.634097\pi$
$174$	−4.88889e42	−0.0996551
$175$	−9.89856e43	−1.80439
$176$	−2.74265e43	−0.447377
$177$	3.03534e43	0.443331
$178$	1.46308e43	0.191459
$179$	1.32734e44	1.55721	0.778606	−	0.627514i	$-0.215927\pi$
$179$	1.32734e44	1.55721	0.778606	+	0.627514i	$0.215927\pi$
$180$	4.08807e43	0.430234
$181$	4.48145e43	0.423337	0.211668	−	0.977342i	$-0.432110\pi$
$181$	4.48145e43	0.423337	0.211668	+	0.977342i	$0.432110\pi$
$182$	−2.71301e42	−0.0230176
$183$	4.89204e43	0.372987
$184$	1.56512e44	1.07300
$185$	−2.83211e44	−1.74688
$186$	−8.92462e42	−0.0495550
$187$	−4.35661e43	−0.217890
$188$	2.34195e44	1.05560
$189$	7.20785e43	0.292955
$190$	2.45116e44	0.898826
$191$	−3.37653e44	−1.11769	−0.558843	−	0.829274i	$-0.688755\pi$
$191$	−3.37653e44	−1.11769	−0.558843	+	0.829274i	$0.688755\pi$
$192$	6.12342e43	0.183071
$193$	−3.65762e43	−0.0988168	−0.0494084	−	0.998779i	$-0.515734\pi$
$193$	−3.65762e43	−0.0988168	−0.0494084	+	0.998779i	$0.515734\pi$
$194$	−1.47387e44	−0.360018
$195$	1.63956e43	0.0362286
$196$	−5.75060e44	−1.15006
$197$	−2.25016e44	−0.407494	−0.203747	−	0.979024i	$-0.565312\pi$
$197$	−2.25016e44	−0.407494	−0.203747	+	0.979024i	$0.565312\pi$
$198$	−5.09559e43	−0.0836033
$199$	4.01172e43	0.0596617	0.0298308	−	0.999555i	$-0.490503\pi$
$199$	4.01172e43	0.0596617	0.0298308	+	0.999555i	$0.490503\pi$
$200$	−5.86435e44	−0.790924
$201$	5.78060e44	0.707375
$202$	−2.26789e44	−0.251924
$203$	−7.31122e44	−0.737593
$204$	1.70181e44	0.155999
$205$	2.51025e45	2.09178
$206$	1.91010e44	0.144759
$207$	−7.77344e44	−0.536033
$208$	4.29677e43	0.0269716
$209$	2.10214e45	1.20173
$210$	−8.88555e44	−0.462816
$211$	−2.64355e45	−1.25510	−0.627552	−	0.778575i	$-0.715943\pi$
$211$	−2.64355e45	−1.25510	−0.627552	+	0.778575i	$0.715943\pi$
$212$	2.85365e44	0.123552
$213$	−9.64981e44	−0.381168
$214$	1.73124e45	0.624149
$215$	7.17464e45	2.36184
$216$	4.27025e44	0.128412
$217$	−1.33466e45	−0.366779
$218$	−1.55241e45	−0.390036
$219$	6.64189e44	0.152627
$220$	−4.32202e45	−0.908751
$221$	6.82526e43	0.0131362
$222$	−1.37895e45	−0.243034
$223$	−6.61885e45	−1.06866	−0.534328	−	0.845277i	$-0.679435\pi$
$223$	−6.61885e45	−1.06866	−0.534328	+	0.845277i	$0.679435\pi$
$224$	−9.19308e45	−1.36027
$225$	2.91263e45	0.395117
$226$	4.39864e45	0.547273
$227$	1.14636e46	1.30863	0.654317	−	0.756220i	$-0.272956\pi$
$227$	1.14636e46	1.30863	0.654317	+	0.756220i	$0.272956\pi$
$228$	−8.21152e45	−0.860388
$229$	−5.43505e45	−0.522892	−0.261446	−	0.965218i	$-0.584199\pi$
$229$	−5.43505e45	−0.522892	−0.261446	+	0.965218i	$0.584199\pi$
$230$	9.58279e45	0.846836
$231$	−7.62034e45	−0.618786
$232$	−4.33149e45	−0.323312
$233$	−2.44861e46	−1.68066	−0.840328	−	0.542079i	$-0.817638\pi$
$233$	−2.44861e46	−1.68066	−0.840328	+	0.542079i	$0.817638\pi$
$234$	7.98298e43	0.00504029
$235$	3.07623e46	1.78729
$236$	1.25354e46	0.670432
$237$	1.56367e46	0.770110
$238$	−3.69894e45	−0.167813
$239$	3.20935e46	1.34171	0.670855	−	0.741589i	$-0.265927\pi$
$239$	3.20935e46	1.34171	0.670855	+	0.741589i	$0.265927\pi$
$240$	1.40726e46	0.542320
$241$	−4.03396e45	−0.143351	−0.0716753	−	0.997428i	$-0.522835\pi$
$241$	−4.03396e45	−0.143351	−0.0716753	+	0.997428i	$0.522835\pi$
$242$	−5.48020e45	−0.179637
$243$	−2.12090e45	−0.0641500
$244$	2.02032e46	0.564053
$245$	−7.55359e46	−1.94722
$246$	1.22224e46	0.291019
$247$	−3.29330e45	−0.0724504
$248$	−7.90710e45	−0.160772
$249$	−2.68512e46	−0.504750
$250$	−5.61455e45	−0.0976079
$251$	−9.02920e46	−1.45215	−0.726076	−	0.687615i	$-0.758658\pi$
$251$	−9.02920e46	−1.45215	−0.726076	+	0.687615i	$0.758658\pi$
$252$	2.97671e46	0.443023
$253$	8.21830e46	1.13222
$254$	−3.09501e46	−0.394824
$255$	2.23538e46	0.264130
$256$	−3.78821e45	−0.0414720
$257$	4.29725e45	0.0436008	0.0218004	−	0.999762i	$-0.493060\pi$
$257$	4.29725e45	0.0436008	0.0218004	+	0.999762i	$0.493060\pi$
$258$	3.49332e46	0.328590
$259$	−2.06219e47	−1.79880
$260$	6.77108e45	0.0547870
$261$	2.15131e46	0.161515
$262$	−7.11742e45	−0.0495961
$263$	1.26887e47	0.820879	0.410439	−	0.911888i	$-0.365375\pi$
$263$	1.26887e47	0.820879	0.410439	+	0.911888i	$0.365375\pi$
$264$	−4.51463e46	−0.271235
$265$	3.74835e46	0.209193
$266$	1.78480e47	0.925545
$267$	−6.43813e46	−0.310306
$268$	2.38729e47	1.06973
$269$	5.74667e46	0.239468	0.119734	−	0.992806i	$-0.461796\pi$
$269$	5.74667e46	0.239468	0.119734	+	0.992806i	$0.461796\pi$
$270$	2.61456e46	0.101346
$271$	−3.95688e46	−0.142709	−0.0713546	−	0.997451i	$-0.522732\pi$
$271$	−3.95688e46	−0.142709	−0.0713546	+	0.997451i	$0.522732\pi$
$272$	5.85824e46	0.196641
$273$	1.19384e46	0.0373055
$274$	4.30349e46	0.125223
$275$	−3.07931e47	−0.834577
$276$	−3.21029e47	−0.810621
$277$	4.47297e47	1.05254	0.526272	−	0.850316i	$-0.323589\pi$
$277$	4.47297e47	1.05254	0.526272	+	0.850316i	$0.323589\pi$
$278$	1.50829e47	0.330834
$279$	3.92720e46	0.0803158
$280$	−7.87249e47	−1.50152
$281$	3.99175e47	0.710215	0.355108	−	0.934825i	$-0.384444\pi$
$281$	3.99175e47	0.710215	0.355108	+	0.934825i	$0.384444\pi$
$282$	1.49781e47	0.248656
$283$	−8.24030e47	−1.27675	−0.638377	−	0.769724i	$-0.720394\pi$
$283$	−8.24030e47	−1.27675	−0.638377	+	0.769724i	$0.720394\pi$
$284$	−3.98520e47	−0.576424
$285$	−1.07861e48	−1.45676
$286$	−8.43983e45	−0.0106462
$287$	1.82783e48	2.15396
$288$	2.70505e47	0.297866
$289$	−8.78590e47	−0.904228
$290$	−2.65205e47	−0.255165
$291$	6.48562e47	0.583497
$292$	2.74298e47	0.230811
$293$	−6.28416e47	−0.494685	−0.247343	−	0.968928i	$-0.579557\pi$
$293$	−6.28416e47	−0.494685	−0.247343	+	0.968928i	$0.579557\pi$
$294$	−3.67783e47	−0.270906
$295$	1.64657e48	1.13514
$296$	−1.22174e48	−0.788476
$297$	2.24227e47	0.135499
$298$	−1.05818e47	−0.0598886
$299$	−1.28752e47	−0.0682597
$300$	1.20286e48	0.597520
$301$	5.22419e48	2.43205
$302$	2.16518e47	0.0944842
$303$	9.97964e47	0.408304
$304$	−2.82670e48	−1.08454
$305$	2.65376e48	0.955025
$306$	1.08840e47	0.0367471
$307$	−2.43683e48	−0.772018	−0.386009	−	0.922495i	$-0.626147\pi$
$307$	−2.43683e48	−0.772018	−0.386009	+	0.922495i	$0.626147\pi$
$308$	−3.14706e48	−0.935765
$309$	−8.40523e47	−0.234617
$310$	−4.84129e47	−0.126884
$311$	−6.81462e48	−1.67731	−0.838657	−	0.544660i	$-0.816659\pi$
$311$	−6.81462e48	−1.67731	−0.838657	+	0.544660i	$0.816659\pi$
$312$	7.07282e46	0.0163523
$313$	−2.62388e48	−0.569941	−0.284970	−	0.958536i	$-0.591984\pi$
$313$	−2.62388e48	−0.569941	−0.284970	+	0.958536i	$0.591984\pi$
$314$	7.26504e47	0.148289
$315$	3.91001e48	0.750105
$316$	6.45769e48	1.16461
$317$	−6.51955e48	−1.10551	−0.552754	−	0.833344i	$-0.686423\pi$
$317$	−6.51955e48	−1.10551	−0.552754	+	0.833344i	$0.686423\pi$
$318$	1.82507e47	0.0291039
$319$	−2.27443e48	−0.341156
$320$	3.32174e48	0.468750
$321$	−7.61816e48	−1.01158
$322$	6.97767e48	0.872009
$323$	−4.49011e48	−0.528211
$324$	−8.75892e47	−0.0970114
$325$	4.82419e47	0.0503152
$326$	−8.06181e46	−0.00791935
$327$	6.83124e48	0.632147
$328$	1.08289e49	0.944154
$329$	2.23994e49	1.84042
$330$	−2.76418e48	−0.214064
$331$	−2.04347e49	−1.49184	−0.745919	−	0.666036i	$-0.767990\pi$
$331$	−2.04347e49	−1.49184	−0.745919	+	0.666036i	$0.767990\pi$
$332$	−1.10891e49	−0.763312
$333$	6.06796e48	0.393895
$334$	−2.27165e48	−0.139087
$335$	3.13577e49	1.81122
$336$	1.02469e49	0.558441
$337$	−1.34582e49	−0.692154	−0.346077	−	0.938206i	$-0.612486\pi$
$337$	−1.34582e49	−0.692154	−0.346077	+	0.938206i	$0.612486\pi$
$338$	−7.32518e48	−0.355584
$339$	−1.93558e49	−0.886988
$340$	9.23173e48	0.399433
$341$	−4.15194e48	−0.169645
$342$	−5.25174e48	−0.202672
$343$	−1.32453e49	−0.482865
$344$	3.09504e49	1.06605
$345$	−4.21682e49	−1.37250
$346$	−9.47079e48	−0.291342
$347$	3.60982e49	1.04969	0.524844	−	0.851198i	$-0.324124\pi$
$347$	3.60982e49	1.04969	0.524844	+	0.851198i	$0.324124\pi$
$348$	8.88454e48	0.244253
$349$	1.29981e49	0.337896	0.168948	−	0.985625i	$-0.445963\pi$
$349$	1.29981e49	0.337896	0.168948	+	0.985625i	$0.445963\pi$
$350$	−2.61446e49	−0.642770
$351$	−3.51284e47	−0.00816901
$352$	−2.85985e49	−0.629160
$353$	−7.99353e49	−1.66392	−0.831959	−	0.554837i	$-0.812781\pi$
$353$	−7.99353e49	−1.66392	−0.831959	+	0.554837i	$0.812781\pi$
$354$	8.01711e48	0.157926
$355$	−5.23469e49	−0.975973
$356$	−2.65884e49	−0.469263
$357$	1.62768e49	0.271982
$358$	3.50584e49	0.554719
$359$	7.75277e49	1.16176	0.580878	−	0.813990i	$-0.302709\pi$
$359$	7.75277e49	1.16176	0.580878	+	0.813990i	$0.302709\pi$
$360$	2.31646e49	0.328796
$361$	1.42286e50	1.91326
$362$	1.18367e49	0.150804
$363$	2.41151e49	0.291146
$364$	4.93033e48	0.0564156
$365$	3.60299e49	0.390798
$366$	1.29211e49	0.132868
$367$	1.56697e49	0.152782	0.0763909	−	0.997078i	$-0.475660\pi$
$367$	1.56697e49	0.152782	0.0763909	+	0.997078i	$0.475660\pi$
$368$	−1.10510e50	−1.02181
$369$	−5.37834e49	−0.471666
$370$	−7.48034e49	−0.622283
$371$	2.72935e49	0.215411
$372$	1.62186e49	0.121458
$373$	5.67952e49	0.403636	0.201818	−	0.979423i	$-0.435315\pi$
$373$	5.67952e49	0.403636	0.201818	+	0.979423i	$0.435315\pi$
$374$	−1.15069e49	−0.0776180
$375$	2.47063e49	0.158197
$376$	1.32704e50	0.806718
$377$	3.56322e48	0.0205677
$378$	1.90378e49	0.104358
$379$	−3.40282e49	−0.177163	−0.0885817	−	0.996069i	$-0.528233\pi$
$379$	−3.40282e49	−0.177163	−0.0885817	+	0.996069i	$0.528233\pi$
$380$	−4.45447e50	−2.20301
$381$	1.36193e50	0.639908
$382$	−8.91828e49	−0.398149
$383$	−1.51395e50	−0.642295	−0.321147	−	0.947029i	$-0.604068\pi$
$383$	−1.51395e50	−0.642295	−0.321147	+	0.947029i	$0.604068\pi$
$384$	1.44124e50	0.581134
$385$	−4.13377e50	−1.58439
$386$	−9.66071e48	−0.0352011
$387$	−1.53721e50	−0.532560
$388$	2.67845e50	0.882398
$389$	3.64065e50	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$389$	3.64065e50	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$390$	4.33049e48	0.0129056
$391$	−1.75541e50	−0.497658
$392$	−3.25852e50	−0.878904
$393$	3.13196e49	0.0803825
$394$	−5.94324e49	−0.145160
$395$	8.48238e50	1.97185
$396$	9.26017e49	0.204910
$397$	6.19440e50	1.30492	0.652461	−	0.757823i	$-0.273737\pi$
$397$	6.19440e50	1.30492	0.652461	+	0.757823i	$0.273737\pi$
$398$	1.05960e49	0.0212530
$399$	−7.85385e50	−1.50007
$400$	4.14069e50	0.753187
$401$	1.98149e50	0.343302	0.171651	−	0.985158i	$-0.445090\pi$
$401$	1.98149e50	0.343302	0.171651	+	0.985158i	$0.445090\pi$
$402$	1.52680e50	0.251985
$403$	6.50462e48	0.0102276
$404$	4.12141e50	0.617461
$405$	−1.15051e50	−0.164255
$406$	−1.93108e50	−0.262750
$407$	−6.41521e50	−0.831994
$408$	9.64313e49	0.119219
$409$	−8.18635e50	−0.964908	−0.482454	−	0.875921i	$-0.660254\pi$
$409$	−8.18635e50	−0.964908	−0.482454	+	0.875921i	$0.660254\pi$
$410$	6.63021e50	0.745147
$411$	−1.89371e50	−0.202955
$412$	−3.47121e50	−0.354802
$413$	1.19894e51	1.16888
$414$	−2.05317e50	−0.190949
$415$	−1.45658e51	−1.29240
$416$	4.48037e49	0.0379310
$417$	−6.63708e50	−0.536197
$418$	5.55228e50	0.428089
$419$	−9.92910e50	−0.730696	−0.365348	−	0.930871i	$-0.619050\pi$
$419$	−9.92910e50	−0.730696	−0.365348	+	0.930871i	$0.619050\pi$
$420$	1.61476e51	1.13435
$421$	−6.39132e50	−0.428637	−0.214319	−	0.976764i	$-0.568753\pi$
$421$	−6.39132e50	−0.428637	−0.214319	+	0.976764i	$0.568753\pi$
$422$	−6.98230e50	−0.447101
$423$	−6.59098e50	−0.403007
$424$	1.61699e50	0.0944219
$425$	6.57733e50	0.366831
$426$	−2.54876e50	−0.135782
$427$	1.93232e51	0.983414
$428$	−3.14616e51	−1.52978
$429$	3.71387e49	0.0172548
$430$	1.89501e51	0.841349
$431$	3.21896e50	0.136587	0.0682935	−	0.997665i	$-0.478245\pi$
$431$	3.21896e50	0.136587	0.0682935	+	0.997665i	$0.478245\pi$
$432$	−3.01513e50	−0.122285
$433$	−4.43633e51	−1.71993	−0.859963	−	0.510356i	$-0.829514\pi$
$433$	−4.43633e51	−1.71993	−0.859963	+	0.510356i	$0.829514\pi$
$434$	−3.52517e50	−0.130656
$435$	1.16701e51	0.413556
$436$	2.82118e51	0.955970
$437$	8.47013e51	2.74475
$438$	1.75429e50	0.0543697
$439$	3.25569e51	0.965128	0.482564	−	0.875861i	$-0.339706\pi$
$439$	3.25569e51	0.965128	0.482564	+	0.875861i	$0.339706\pi$
$440$	−2.44903e51	−0.694491
$441$	1.61840e51	0.439069
$442$	1.80273e49	0.00467946
$443$	−4.09722e51	−1.01769	−0.508846	−	0.860858i	$-0.669928\pi$
$443$	−4.09722e51	−1.01769	−0.508846	+	0.860858i	$0.669928\pi$
$444$	2.50596e51	0.595671
$445$	−3.49246e51	−0.794533
$446$	−1.74821e51	−0.380683
$447$	4.65644e50	0.0970639
$448$	2.41871e51	0.482684
$449$	−8.07315e51	−1.54255	−0.771275	−	0.636502i	$-0.780381\pi$
$449$	−8.07315e51	−1.54255	−0.771275	+	0.636502i	$0.780381\pi$
$450$	7.69300e50	0.140751
$451$	5.68613e51	0.996264
$452$	−7.99362e51	−1.34136
$453$	−9.52770e50	−0.153134
$454$	3.02784e51	0.466170
$455$	6.47615e50	0.0955201
$456$	−4.65297e51	−0.657531
$457$	3.57503e51	0.484076	0.242038	−	0.970267i	$-0.422184\pi$
$457$	3.57503e51	0.484076	0.242038	+	0.970267i	$0.422184\pi$
$458$	−1.43554e51	−0.186268
$459$	−4.78943e50	−0.0595575
$460$	−1.74147e52	−2.07558
$461$	8.00610e51	0.914645	0.457323	−	0.889301i	$-0.348808\pi$
$461$	8.00610e51	0.914645	0.457323	+	0.889301i	$0.348808\pi$
$462$	−2.01273e51	−0.220428
$463$	−8.57929e51	−0.900787	−0.450393	−	0.892830i	$-0.648716\pi$
$463$	−8.57929e51	−0.900787	−0.450393	+	0.892830i	$0.648716\pi$
$464$	3.05837e51	0.307886
$465$	2.13037e51	0.205647
$466$	−6.46740e51	−0.598693
$467$	1.12846e52	1.00186	0.500932	−	0.865487i	$-0.332991\pi$
$467$	1.12846e52	1.00186	0.500932	+	0.865487i	$0.332991\pi$
$468$	−1.45074e50	−0.0123537
$469$	2.28330e52	1.86506
$470$	8.12510e51	0.636679
$471$	−3.19692e51	−0.240339
$472$	7.10306e51	0.512361
$473$	1.62518e52	1.12489
$474$	4.13006e51	0.274333
$475$	−3.17367e52	−2.02319
$476$	6.72205e51	0.411307
$477$	−8.03105e50	−0.0471698
$478$	8.47673e51	0.477952
$479$	−2.24291e52	−1.21414	−0.607071	−	0.794648i	$-0.707656\pi$
$479$	−2.24291e52	−1.21414	−0.607071	+	0.794648i	$0.707656\pi$
$480$	1.46739e52	0.762680
$481$	1.00504e51	0.0501594
$482$	−1.06547e51	−0.0510652
$483$	−3.07046e52	−1.41330
$484$	9.95912e51	0.440287
$485$	3.51822e52	1.49403
$486$	−5.60183e50	−0.0228519
$487$	6.05465e51	0.237287	0.118644	−	0.992937i	$-0.462145\pi$
$487$	6.05465e51	0.237287	0.118644	+	0.992937i	$0.462145\pi$
$488$	1.14480e52	0.431064
$489$	3.54753e50	0.0128352
$490$	−1.99510e52	−0.693650
$491$	−3.63912e52	−1.21593	−0.607963	−	0.793965i	$-0.708013\pi$
$491$	−3.63912e52	−1.21593	−0.607963	+	0.793965i	$0.708013\pi$
$492$	−2.22116e52	−0.713281
$493$	4.85811e51	0.149952
$494$	−8.69845e50	−0.0258087
$495$	1.21635e52	0.346943
$496$	5.58303e51	0.153101
$497$	−3.81161e52	−1.00498
$498$	−7.09209e51	−0.179805
$499$	−5.72391e52	−1.39551	−0.697754	−	0.716337i	$-0.745817\pi$
$499$	−5.72391e52	−1.39551	−0.697754	+	0.716337i	$0.745817\pi$
$500$	1.02033e52	0.239235
$501$	9.99619e51	0.225423
$502$	−2.38484e52	−0.517294
$503$	1.75324e52	0.365818	0.182909	−	0.983130i	$-0.441449\pi$
$503$	1.75324e52	0.365818	0.182909	+	0.983130i	$0.441449\pi$
$504$	1.68672e52	0.338570
$505$	5.41361e52	1.04545
$506$	2.17066e52	0.403327
$507$	3.22338e52	0.576310
$508$	5.62453e52	0.967707
$509$	−9.36160e52	−1.55008	−0.775039	−	0.631913i	$-0.782270\pi$
$509$	−9.36160e52	−1.55008	−0.775039	+	0.631913i	$0.782270\pi$
$510$	5.90422e51	0.0940901
$511$	2.62351e52	0.402415
$512$	6.71707e52	0.991780
$513$	2.31098e52	0.328479
$514$	1.13501e51	0.0155317
$515$	−4.55955e52	−0.600732
$516$	−6.34839e52	−0.805368
$517$	6.96817e52	0.851242
$518$	−5.44678e52	−0.640781
$519$	4.16754e52	0.472189
$520$	3.83676e51	0.0418697
$521$	−6.14605e52	−0.646042	−0.323021	−	0.946392i	$-0.604698\pi$
$521$	−6.14605e52	−0.646042	−0.323021	+	0.946392i	$0.604698\pi$
$522$	5.68217e51	0.0575359
$523$	−2.50871e52	−0.244719	−0.122359	−	0.992486i	$-0.539046\pi$
$523$	−2.50871e52	−0.244719	−0.122359	+	0.992486i	$0.539046\pi$
$524$	1.29344e52	0.121559
$525$	1.15047e53	1.04176
$526$	3.35140e52	0.292418
$527$	8.86844e51	0.0745659
$528$	3.18768e52	0.258293
$529$	2.03088e53	1.58598
$530$	9.90037e51	0.0745198
$531$	−3.52786e52	−0.255957
$532$	−3.24350e53	−2.26849
$533$	−8.90815e51	−0.0600630
$534$	−1.70048e52	−0.110539
$535$	−4.13259e53	−2.59014
$536$	1.35273e53	0.817519
$537$	−1.54271e53	−0.899056
$538$	1.51784e52	0.0853046
$539$	−1.71101e53	−0.927412
$540$	−4.75141e52	−0.248396
$541$	2.37622e53	1.19823	0.599114	−	0.800664i	$-0.295520\pi$
$541$	2.37622e53	1.19823	0.599114	+	0.800664i	$0.295520\pi$
$542$	−1.04511e52	−0.0508368
$543$	−5.20861e52	−0.244414
$544$	6.10856e52	0.276542
$545$	3.70571e53	1.61860
$546$	3.15323e51	0.0132892
$547$	1.01438e53	0.412524	0.206262	−	0.978497i	$-0.433870\pi$
$547$	1.01438e53	0.412524	0.206262	+	0.978497i	$0.433870\pi$
$548$	−7.82071e52	−0.306920
$549$	−5.68583e52	−0.215344
$550$	−8.13325e52	−0.297298
$551$	−2.34412e53	−0.827035
$552$	−1.81908e53	−0.619498
$553$	6.17641e53	2.03047
$554$	1.18143e53	0.374944
$555$	3.29166e53	1.00856
$556$	−2.74100e53	−0.810868
$557$	3.06102e53	0.874358	0.437179	−	0.899374i	$-0.355978\pi$
$557$	3.06102e53	0.874358	0.437179	+	0.899374i	$0.355978\pi$
$558$	1.03727e52	0.0286106
$559$	−2.54608e52	−0.0678174
$560$	5.55859e53	1.42988
$561$	5.06351e52	0.125799
$562$	1.05432e53	0.252997
$563$	1.09661e53	0.254179	0.127090	−	0.991891i	$-0.459436\pi$
$563$	1.09661e53	0.254179	0.127090	+	0.991891i	$0.459436\pi$
$564$	−2.72196e53	−0.609451
$565$	−1.04999e54	−2.27111
$566$	−2.17647e53	−0.454813
$567$	−8.37741e52	−0.169138
$568$	−2.25817e53	−0.440519
$569$	6.98263e53	1.31622	0.658112	−	0.752920i	$-0.271355\pi$
$569$	6.98263e53	1.31622	0.658112	+	0.752920i	$0.271355\pi$
$570$	−2.84888e53	−0.518938
$571$	−2.15970e53	−0.380180	−0.190090	−	0.981767i	$-0.560878\pi$
$571$	−2.15970e53	−0.380180	−0.190090	+	0.981767i	$0.560878\pi$
$572$	1.53376e52	0.0260937
$573$	3.92441e53	0.645296
$574$	4.82776e53	0.767298
$575$	−1.24075e54	−1.90616
$576$	−7.11702e52	−0.105696
$577$	2.02592e53	0.290867	0.145433	−	0.989368i	$-0.453542\pi$
$577$	2.02592e53	0.290867	0.145433	+	0.989368i	$0.453542\pi$
$578$	−2.32058e53	−0.322110
$579$	4.25111e52	0.0570519
$580$	4.81955e53	0.625404
$581$	−1.06061e54	−1.33082
$582$	1.71302e53	0.207857
$583$	8.49065e52	0.0996332
$584$	1.55428e53	0.176392
$585$	−1.90559e52	−0.0209166
$586$	−1.65981e53	−0.176220
$587$	−7.06852e53	−0.725914	−0.362957	−	0.931806i	$-0.618233\pi$
$587$	−7.06852e53	−0.725914	−0.362957	+	0.931806i	$0.618233\pi$
$588$	6.68370e53	0.663986
$589$	−4.27917e53	−0.411255
$590$	4.34900e53	0.404367
$591$	2.61527e53	0.235267
$592$	8.62641e53	0.750856
$593$	−1.68827e53	−0.142192	−0.0710959	−	0.997469i	$-0.522650\pi$
$593$	−1.68827e53	−0.142192	−0.0710959	+	0.997469i	$0.522650\pi$
$594$	5.92241e52	0.0482684
$595$	8.82962e53	0.696404
$596$	1.92303e53	0.146786
$597$	−4.66267e52	−0.0344457
$598$	−3.40066e52	−0.0243159
$599$	−8.66168e53	−0.599486	−0.299743	−	0.954020i	$-0.596901\pi$
$599$	−8.66168e53	−0.599486	−0.299743	+	0.954020i	$0.596901\pi$
$600$	6.81591e53	0.456640
$601$	1.01881e54	0.660758	0.330379	−	0.943848i	$-0.392823\pi$
$601$	1.01881e54	0.660758	0.330379	+	0.943848i	$0.392823\pi$
$602$	1.37984e54	0.866359
$603$	−6.71857e53	−0.408403
$604$	−3.93477e53	−0.231579
$605$	1.30816e54	0.745472
$606$	2.63588e53	0.145449
$607$	−3.59220e53	−0.191947	−0.0959734	−	0.995384i	$-0.530596\pi$
$607$	−3.59220e53	−0.191947	−0.0959734	+	0.995384i	$0.530596\pi$
$608$	−2.94748e54	−1.52522
$609$	8.49755e53	0.425850
$610$	7.00926e53	0.340205
$611$	−1.09166e53	−0.0513199
$612$	−1.97795e53	−0.0900663
$613$	9.11862e53	0.402207	0.201104	−	0.979570i	$-0.435547\pi$
$613$	9.11862e53	0.402207	0.201104	+	0.979570i	$0.435547\pi$
$614$	−6.43631e53	−0.275013
$615$	−2.91757e54	−1.20769
$616$	−1.78325e54	−0.715136
$617$	2.52497e54	0.981061	0.490530	−	0.871424i	$-0.336803\pi$
$617$	2.52497e54	0.981061	0.490530	+	0.871424i	$0.336803\pi$
$618$	−2.22004e53	−0.0835767
$619$	3.13318e53	0.114292	0.0571462	−	0.998366i	$-0.481800\pi$
$619$	3.13318e53	0.114292	0.0571462	+	0.998366i	$0.481800\pi$
$620$	8.79804e53	0.310991
$621$	9.03477e53	0.309479
$622$	−1.79992e54	−0.597503
$623$	−2.54302e54	−0.818151
$624$	−4.99397e52	−0.0155721
$625$	−2.58177e54	−0.780292
$626$	−6.93035e53	−0.203028
$627$	−2.44323e54	−0.693821
$628$	−1.32027e54	−0.363454
$629$	1.37027e54	0.365695
$630$	1.03273e54	0.267207
$631$	−3.45716e54	−0.867256	−0.433628	−	0.901092i	$-0.642767\pi$
$631$	−3.45716e54	−0.867256	−0.433628	+	0.901092i	$0.642767\pi$
$632$	3.65918e54	0.890022
$633$	3.07250e54	0.724635
$634$	−1.72198e54	−0.393811
$635$	7.38800e54	1.63847
$636$	−3.31668e53	−0.0713330
$637$	2.68055e53	0.0559121
$638$	−6.00734e53	−0.121529
$639$	1.12156e54	0.220067
$640$	7.81821e54	1.48798
$641$	3.85151e54	0.711050	0.355525	−	0.934667i	$-0.384302\pi$
$641$	3.85151e54	0.711050	0.355525	+	0.934667i	$0.384302\pi$
$642$	−2.01215e54	−0.360352
$643$	1.53024e54	0.265855	0.132928	−	0.991126i	$-0.457562\pi$
$643$	1.53024e54	0.265855	0.132928	+	0.991126i	$0.457562\pi$
$644$	−1.26805e55	−2.13728
$645$	−8.33881e54	−1.36361
$646$	−1.18595e54	−0.188163
$647$	1.27086e55	1.95644	0.978219	−	0.207577i	$-0.0665578\pi$
$647$	1.27086e55	1.95644	0.978219	+	0.207577i	$0.0665578\pi$
$648$	−4.96315e53	−0.0741387
$649$	3.72975e54	0.540639
$650$	1.27419e53	0.0179236
$651$	1.55122e54	0.211760
$652$	1.46507e53	0.0194102
$653$	9.19237e54	1.18201	0.591004	−	0.806669i	$-0.298732\pi$
$653$	9.19237e54	1.18201	0.591004	+	0.806669i	$0.298732\pi$
$654$	1.80431e54	0.225187
$655$	1.69898e54	0.205818
$656$	−7.64603e54	−0.899106
$657$	−7.71961e53	−0.0881192
$658$	5.91626e54	0.655605
$659$	−2.57996e54	−0.277554	−0.138777	−	0.990324i	$-0.544317\pi$
$659$	−2.57996e54	−0.277554	−0.138777	+	0.990324i	$0.544317\pi$
$660$	5.02332e54	0.524668
$661$	−1.12332e55	−1.13914	−0.569568	−	0.821944i	$-0.692890\pi$
$661$	−1.12332e55	−1.13914	−0.569568	+	0.821944i	$0.692890\pi$
$662$	−5.39732e54	−0.531432
$663$	−7.93273e52	−0.00758419
$664$	−6.28350e54	−0.583343
$665$	−4.26044e55	−3.84090
$666$	1.60270e54	0.140316
$667$	−9.16434e54	−0.779197
$668$	4.12825e54	0.340898
$669$	7.69283e54	0.616989
$670$	8.28239e54	0.645204
$671$	6.01121e54	0.454855
$672$	1.06848e55	0.785352
$673$	−1.50888e54	−0.107736	−0.0538681	−	0.998548i	$-0.517155\pi$
$673$	−1.50888e54	−0.107736	−0.0538681	+	0.998548i	$0.517155\pi$
$674$	−3.55464e54	−0.246563
$675$	−3.38524e54	−0.228121
$676$	1.33120e55	0.871530
$677$	5.88105e54	0.374090	0.187045	−	0.982351i	$-0.440109\pi$
$677$	5.88105e54	0.374090	0.187045	+	0.982351i	$0.440109\pi$
$678$	−5.11237e54	−0.315968
$679$	2.56178e55	1.53844
$680$	5.23106e54	0.305257
$681$	−1.33237e55	−0.755540
$682$	−1.09663e54	−0.0604319
$683$	1.21018e55	0.648109	0.324054	−	0.946038i	$-0.394954\pi$
$683$	1.21018e55	0.648109	0.324054	+	0.946038i	$0.394954\pi$
$684$	9.54394e54	0.496745
$685$	−1.02727e55	−0.519661
$686$	−3.49842e54	−0.172009
$687$	6.31695e54	0.301892
$688$	−2.18534e55	−1.01518
$689$	−1.33018e53	−0.00600671
$690$	−1.11377e55	−0.488921
$691$	1.62764e55	0.694601	0.347300	−	0.937754i	$-0.387098\pi$
$691$	1.62764e55	0.694601	0.347300	+	0.937754i	$0.387098\pi$
$692$	1.72112e55	0.714072
$693$	8.85682e54	0.357256
$694$	9.53445e54	0.373926
$695$	−3.60039e55	−1.37292
$696$	5.03433e54	0.186664
$697$	−1.21454e55	−0.437899
$698$	3.43312e54	0.120367
$699$	2.84592e55	0.970327
$700$	4.75124e55	1.57542
$701$	1.79427e55	0.578610	0.289305	−	0.957237i	$-0.406576\pi$
$701$	1.79427e55	0.578610	0.289305	+	0.957237i	$0.406576\pi$
$702$	−9.27831e52	−0.00291002
$703$	−6.61180e55	−2.01693
$704$	7.52430e54	0.223254
$705$	−3.57538e55	−1.03189
$706$	−2.11130e55	−0.592731
$707$	3.94190e55	1.07653
$708$	−1.45694e55	−0.387074
$709$	1.14395e55	0.295669	0.147834	−	0.989012i	$-0.452770\pi$
$709$	1.14395e55	0.295669	0.147834	+	0.989012i	$0.452770\pi$
$710$	−1.38261e55	−0.347667
$711$	−1.81740e55	−0.444623
$712$	−1.50660e55	−0.358623
$713$	−1.67294e55	−0.387467
$714$	4.29913e54	0.0968870
$715$	2.01465e54	0.0441805
$716$	−6.37114e55	−1.35961
$717$	−3.73011e55	−0.774636
$718$	2.04771e55	0.413848
$719$	6.82369e55	1.34216	0.671082	−	0.741383i	$-0.265830\pi$
$719$	6.82369e55	1.34216	0.671082	+	0.741383i	$0.265830\pi$
$720$	−1.63560e55	−0.313108
$721$	−3.32002e55	−0.618589
$722$	3.75815e55	0.681552
$723$	4.68852e54	0.0827635
$724$	−2.15107e55	−0.369617
$725$	3.43379e55	0.574357
$726$	6.36942e54	0.103714
$727$	4.73186e55	0.750085	0.375043	−	0.927008i	$-0.377628\pi$
$727$	4.73186e55	0.750085	0.375043	+	0.927008i	$0.377628\pi$
$728$	2.79372e54	0.0431143
$729$	2.46503e54	0.0370370
$730$	9.51643e54	0.139213
$731$	−3.47134e55	−0.494433
$732$	−2.34815e55	−0.325656
$733$	7.44240e54	0.100505	0.0502523	−	0.998737i	$-0.483997\pi$
$733$	7.44240e54	0.100505	0.0502523	+	0.998737i	$0.483997\pi$
$734$	4.13876e54	0.0544248
$735$	8.77925e55	1.12423
$736$	−1.15232e56	−1.43700
$737$	7.10305e55	0.862639
$738$	−1.42056e55	−0.168020
$739$	9.48337e55	1.09244	0.546218	−	0.837643i	$-0.316067\pi$
$739$	9.48337e55	1.09244	0.546218	+	0.837643i	$0.316067\pi$
$740$	1.35940e56	1.52520
$741$	3.82768e54	0.0418293
$742$	7.20891e54	0.0767350
$743$	−2.79365e55	−0.289661	−0.144830	−	0.989456i	$-0.546264\pi$
$743$	−2.79365e55	−0.289661	−0.144830	+	0.989456i	$0.546264\pi$
$744$	9.19012e54	0.0928215
$745$	2.52596e55	0.248530
$746$	1.50011e55	0.143786
$747$	3.12081e55	0.291417
$748$	2.09114e55	0.190240
$749$	−3.00912e56	−2.66713
$750$	6.52557e54	0.0563539
$751$	−8.12653e55	−0.683796	−0.341898	−	0.939737i	$-0.611070\pi$
$751$	−8.12653e55	−0.683796	−0.341898	+	0.939737i	$0.611070\pi$
$752$	−9.36995e55	−0.768227
$753$	1.04943e56	0.838400
$754$	9.41137e53	0.00732676
$755$	−5.16845e55	−0.392098
$756$	−3.45972e55	−0.255780
$757$	2.71381e56	1.95528	0.977642	−	0.210277i	$-0.0674367\pi$
$757$	2.71381e56	1.95528	0.977642	+	0.210277i	$0.0674367\pi$
$758$	−8.98771e54	−0.0631102
$759$	−9.55181e55	−0.653689
$760$	−2.52408e56	−1.68359
$761$	−2.53928e56	−1.65086	−0.825428	−	0.564507i	$-0.809066\pi$
$761$	−2.53928e56	−1.65086	−0.825428	+	0.564507i	$0.809066\pi$
$762$	3.59721e55	0.227952
$763$	2.69830e56	1.66671
$764$	1.62071e56	0.975855
$765$	−2.59810e55	−0.152496
$766$	−3.99872e55	−0.228802
$767$	−5.84319e54	−0.0325942
$768$	4.40289e54	0.0239439
$769$	−3.16540e56	−1.67828	−0.839140	−	0.543915i	$-0.816941\pi$
$769$	−3.16540e56	−1.67828	−0.839140	+	0.543915i	$0.816941\pi$
$770$	−1.09183e56	−0.564401
$771$	−4.99452e54	−0.0251729
$772$	1.75563e55	0.0862773
$773$	−8.83478e55	−0.423346	−0.211673	−	0.977341i	$-0.567891\pi$
$773$	−8.83478e55	−0.423346	−0.211673	+	0.977341i	$0.567891\pi$
$774$	−4.06016e55	−0.189712
$775$	6.26834e55	0.285607
$776$	1.51771e56	0.674352
$777$	2.39681e56	1.03854
$778$	9.61590e55	0.406338
$779$	5.86038e56	2.41516
$780$	−7.86976e54	−0.0316313
$781$	−1.18574e56	−0.464832
$782$	−4.63648e55	−0.177279
$783$	−2.50039e55	−0.0932508
$784$	2.30077e56	0.836969
$785$	−1.73422e56	−0.615382
$786$	8.27231e54	0.0286343
$787$	2.01468e56	0.680299	0.340149	−	0.940371i	$-0.389522\pi$
$787$	2.01468e56	0.680299	0.340149	+	0.940371i	$0.389522\pi$
$788$	1.08006e56	0.355784
$789$	−1.47475e56	−0.473934
$790$	2.24041e56	0.702425
$791$	−7.64544e56	−2.33863
$792$	5.24718e55	0.156598
$793$	−9.41744e54	−0.0274224
$794$	1.63610e56	0.464847
$795$	−4.35657e55	−0.120777
$796$	−1.92560e55	−0.0520908
$797$	4.87383e56	1.28657	0.643285	−	0.765627i	$-0.277571\pi$
$797$	4.87383e56	1.28657	0.643285	+	0.765627i	$0.277571\pi$
$798$	−2.07440e56	−0.534364
$799$	−1.48838e56	−0.374156
$800$	4.31762e56	1.05923
$801$	7.48279e55	0.179155
$802$	5.23362e55	0.122293
$803$	8.16138e55	0.186128
$804$	−2.77465e56	−0.617611
$805$	−1.66562e57	−3.61873
$806$	1.71804e54	0.00364333
$807$	−6.67913e55	−0.138257
$808$	2.33536e56	0.471880
$809$	2.97630e56	0.587057	0.293529	−	0.955950i	$-0.405170\pi$
$809$	2.97630e56	0.587057	0.293529	+	0.955950i	$0.405170\pi$
$810$	−3.03880e55	−0.0585119
$811$	−7.70370e56	−1.44808	−0.724041	−	0.689757i	$-0.757717\pi$
$811$	−7.70370e56	−1.44808	−0.724041	+	0.689757i	$0.757717\pi$
$812$	3.50934e56	0.643995
$813$	4.59893e55	0.0823932
$814$	−1.69442e56	−0.296378
$815$	1.92441e55	0.0328643
$816$	−6.80880e55	−0.113531
$817$	1.67498e57	2.72696
$818$	−2.16223e56	−0.343725
$819$	−1.38755e55	−0.0215384
$820$	−1.20490e57	−1.82634
$821$	4.31761e55	0.0639075	0.0319537	−	0.999489i	$-0.489827\pi$
$821$	4.31761e55	0.0639075	0.0319537	+	0.999489i	$0.489827\pi$
$822$	−5.00179e55	−0.0722977
$823$	4.12553e56	0.582348	0.291174	−	0.956670i	$-0.405954\pi$
$823$	4.12553e56	0.582348	0.291174	+	0.956670i	$0.405954\pi$
$824$	−1.96693e56	−0.271149
$825$	3.57897e56	0.481843
$826$	3.16671e56	0.416387
$827$	−6.96480e56	−0.894440	−0.447220	−	0.894424i	$-0.647586\pi$
$827$	−6.96480e56	−0.894440	−0.447220	+	0.894424i	$0.647586\pi$
$828$	3.73120e56	0.468012
$829$	1.42775e57	1.74920	0.874600	−	0.484845i	$-0.161124\pi$
$829$	1.42775e57	1.74920	0.874600	+	0.484845i	$0.161124\pi$
$830$	−3.84721e56	−0.460387
$831$	−5.19876e56	−0.607686
$832$	−1.17879e55	−0.0134596
$833$	3.65468e56	0.407636
$834$	−1.75302e56	−0.191007
$835$	5.42258e56	0.577192
$836$	−1.00901e57	−1.04924
$837$	−4.56443e55	−0.0463703
$838$	−2.62253e56	−0.260293
$839$	6.94535e56	0.673497	0.336749	−	0.941595i	$-0.390673\pi$
$839$	6.94535e56	0.673497	0.336749	+	0.941595i	$0.390673\pi$
$840$	9.14989e56	0.866902
$841$	−8.26620e56	−0.765216
$842$	−1.68811e56	−0.152692
$843$	−4.63946e56	−0.410043
$844$	1.26889e57	1.09584
$845$	1.74857e57	1.47563
$846$	−1.74085e56	−0.143562
$847$	9.52532e56	0.767632
$848$	−1.14172e56	−0.0899168
$849$	9.57738e56	0.737135
$850$	1.73724e56	0.130675
$851$	−2.58488e57	−1.90027
$852$	4.63184e56	0.332799
$853$	−4.76945e56	−0.334936	−0.167468	−	0.985878i	$-0.553559\pi$
$853$	−4.76945e56	−0.334936	−0.167468	+	0.985878i	$0.553559\pi$
$854$	5.10377e56	0.350318
$855$	1.25363e57	0.841064
$856$	−1.78274e57	−1.16909
$857$	−7.15190e56	−0.458454	−0.229227	−	0.973373i	$-0.573620\pi$
$857$	−7.15190e56	−0.458454	−0.229227	+	0.973373i	$0.573620\pi$
$858$	9.80928e54	0.00614660
$859$	−3.14874e57	−1.92872	−0.964362	−	0.264586i	$-0.914765\pi$
$859$	−3.14874e57	−1.92872	−0.964362	+	0.264586i	$0.914765\pi$
$860$	−3.44378e57	−2.06213
$861$	−2.12441e57	−1.24359
$862$	8.50211e55	0.0486558
$863$	6.33719e56	0.354557	0.177279	−	0.984161i	$-0.443271\pi$
$863$	6.33719e56	0.354557	0.177279	+	0.984161i	$0.443271\pi$
$864$	−3.14397e56	−0.171973
$865$	2.26074e57	1.20903
$866$	−1.17175e57	−0.612683
$867$	1.02115e57	0.522057
$868$	6.40626e56	0.320236
$869$	1.92140e57	0.939144
$870$	3.08238e56	0.147320
$871$	−1.11280e56	−0.0520070
$872$	1.59859e57	0.730577
$873$	−7.53799e56	−0.336882
$874$	2.23718e57	0.977750
$875$	9.75885e56	0.417101
$876$	−3.18806e56	−0.133259
$877$	−2.07724e57	−0.849171	−0.424585	−	0.905388i	$-0.639580\pi$
$877$	−2.07724e57	−0.849171	−0.424585	+	0.905388i	$0.639580\pi$
$878$	8.59911e56	0.343804
$879$	7.30384e56	0.285607
$880$	1.72921e57	0.661355
$881$	−1.44068e57	−0.538937	−0.269468	−	0.963009i	$-0.586848\pi$
$881$	−1.44068e57	−0.538937	−0.269468	+	0.963009i	$0.586848\pi$
$882$	4.27460e56	0.156408
$883$	−2.21527e57	−0.792852	−0.396426	−	0.918067i	$-0.629750\pi$
$883$	−2.21527e57	−0.792852	−0.396426	+	0.918067i	$0.629750\pi$
$884$	−3.27608e55	−0.0114693
$885$	−1.91374e57	−0.655374
$886$	−1.08218e57	−0.362528
$887$	4.62524e56	0.151574	0.0757868	−	0.997124i	$-0.475853\pi$
$887$	4.62524e56	0.151574	0.0757868	+	0.997124i	$0.475853\pi$
$888$	1.41998e57	0.455227
$889$	5.37954e57	1.68718
$890$	−9.22450e56	−0.283033
$891$	−2.60610e56	−0.0782305
$892$	3.17700e57	0.933046
$893$	7.18170e57	2.06359
$894$	1.22989e56	0.0345767
$895$	−8.36869e57	−2.30202
$896$	5.69280e57	1.53221
$897$	1.49643e56	0.0394097
$898$	−2.13233e57	−0.549497
$899$	4.62989e56	0.116750
$900$	−1.39804e57	−0.344978
$901$	−1.81358e56	−0.0437929
$902$	1.50185e57	0.354895
$903$	−6.07187e57	−1.40414
$904$	−4.52950e57	−1.02510
$905$	−2.82549e57	−0.625816
$906$	−2.51651e56	−0.0545505
$907$	5.47083e57	1.16068	0.580339	−	0.814375i	$-0.302920\pi$
$907$	5.47083e57	1.16068	0.580339	+	0.814375i	$0.302920\pi$
$908$	−5.50247e57	−1.14257
$909$	−1.15989e57	−0.235734
$910$	1.71052e56	0.0340267
$911$	−5.88844e56	−0.114655	−0.0573274	−	0.998355i	$-0.518258\pi$
$911$	−5.88844e56	−0.114655	−0.0573274	+	0.998355i	$0.518258\pi$
$912$	3.28536e57	0.626158
$913$	−3.29940e57	−0.615539
$914$	9.44258e56	0.172441
$915$	−3.08436e57	−0.551384
$916$	2.60879e57	0.456538
$917$	1.23710e57	0.211936
$918$	−1.26501e56	−0.0212159
$919$	−3.41668e57	−0.560986	−0.280493	−	0.959856i	$-0.590498\pi$
$919$	−3.41668e57	−0.560986	−0.280493	+	0.959856i	$0.590498\pi$
$920$	−9.86788e57	−1.58621
$921$	2.83224e57	0.445725
$922$	2.11462e57	0.325821
$923$	1.85764e56	0.0280239
$924$	3.65771e57	0.540264
$925$	9.68529e57	1.40071
$926$	−2.26601e57	−0.320884
$927$	9.76908e56	0.135456
$928$	3.18906e57	0.432989
$929$	−5.60274e57	−0.744893	−0.372447	−	0.928054i	$-0.621481\pi$
$929$	−5.60274e57	−0.744893	−0.372447	+	0.928054i	$0.621481\pi$
$930$	5.62685e56	0.0732568
$931$	−1.76345e58	−2.24824
$932$	1.17532e58	1.46739
$933$	7.92037e57	0.968397
$934$	2.98056e57	0.356890
$935$	2.74678e57	0.322105
$936$	−8.22047e55	−0.00944099
$937$	2.84316e57	0.319800	0.159900	−	0.987133i	$-0.448883\pi$
$937$	2.84316e57	0.319800	0.159900	+	0.987133i	$0.448883\pi$
$938$	6.03079e57	0.664383
$939$	3.04964e57	0.329055
$940$	−1.47657e58	−1.56049
$941$	−3.10342e57	−0.321250	−0.160625	−	0.987016i	$-0.551351\pi$
$941$	−3.10342e57	−0.321250	−0.160625	+	0.987016i	$0.551351\pi$
$942$	−8.44388e56	−0.0856149
$943$	2.29111e58	2.27546
$944$	−5.01531e57	−0.487915
$945$	−4.54445e57	−0.433073
$946$	4.29251e57	0.400714
$947$	1.09739e58	1.00354	0.501771	−	0.865000i	$-0.332682\pi$
$947$	1.09739e58	1.00354	0.501771	+	0.865000i	$0.332682\pi$
$948$	−7.50552e57	−0.672386
$949$	−1.27860e56	−0.0112213
$950$	−8.38249e57	−0.720713
$951$	7.57742e57	0.638265
$952$	3.80898e57	0.314332
$953$	−1.56833e58	−1.26802	−0.634009	−	0.773326i	$-0.718592\pi$
$953$	−1.56833e58	−1.26802	−0.634009	+	0.773326i	$0.718592\pi$
$954$	−2.12121e56	−0.0168031
$955$	2.12886e58	1.65227
$956$	−1.54047e58	−1.17145
$957$	2.64348e57	0.196967
$958$	−5.92410e57	−0.432509
$959$	−7.48006e57	−0.535109
$960$	−3.86073e57	−0.270633
$961$	−1.37130e58	−0.941944
$962$	2.65456e56	0.0178681
$963$	8.85429e57	0.584038
$964$	1.93627e57	0.125160
$965$	2.30608e57	0.146080
$966$	−8.10988e57	−0.503455
$967$	−6.70320e57	−0.407817	−0.203909	−	0.978990i	$-0.565365\pi$
$967$	−6.70320e57	−0.407817	−0.203909	+	0.978990i	$0.565365\pi$
$968$	5.64323e57	0.336479
$969$	5.21868e57	0.304963
$970$	9.29254e57	0.532213
$971$	−1.00902e57	−0.0566405	−0.0283202	−	0.999599i	$-0.509016\pi$
$971$	−1.00902e57	−0.0566405	−0.0283202	+	0.999599i	$0.509016\pi$
$972$	1.01802e57	0.0560096
$973$	−2.62161e58	−1.41373
$974$	1.59919e57	0.0845279
$975$	−5.60697e56	−0.0290495
$976$	−8.08315e57	−0.410496
$977$	−1.41653e58	−0.705150	−0.352575	−	0.935784i	$-0.614694\pi$
$977$	−1.41653e58	−0.705150	−0.352575	+	0.935784i	$0.614694\pi$
$978$	9.36994e55	0.00457224
$979$	−7.91101e57	−0.378416
$980$	3.62567e58	1.70012
$981$	−7.93968e57	−0.364970
$982$	−9.61185e57	−0.433145
$983$	−8.83216e57	−0.390187	−0.195094	−	0.980785i	$-0.562501\pi$
$983$	−8.83216e57	−0.390187	−0.195094	+	0.980785i	$0.562501\pi$
$984$	−1.25860e58	−0.545108
$985$	1.41869e58	0.602396
$986$	1.28315e57	0.0534169
$987$	−2.60340e58	−1.06257
$988$	1.58076e57	0.0632567
$989$	6.54832e58	2.56923
$990$	3.21270e57	0.123590
$991$	2.39176e58	0.902156	0.451078	−	0.892484i	$-0.351040\pi$
$991$	2.39176e58	0.902156	0.451078	+	0.892484i	$0.351040\pi$
$992$	5.82159e57	0.215310
$993$	2.37504e58	0.861313
$994$	−1.00675e58	−0.358002
$995$	−2.52933e57	−0.0881975
$996$	1.28884e58	0.440698
$997$	1.65650e58	0.555439	0.277719	−	0.960662i	$-0.410421\pi$
$997$	1.65650e58	0.555439	0.277719	+	0.960662i	$0.410421\pi$
$998$	−1.51183e58	−0.497116
$999$	−7.05255e57	−0.227415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.40.a.b.1.2	✓	3
3.2	odd	2		9.40.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.40.a.b.1.2	✓	3	1.1	even	1	trivial
9.40.a.c.1.2		3	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+264126. q^{2} -1.16226e9 q^{3} -4.79993e11 q^{4} -6.30487e13 q^{5} -3.06983e14 q^{6} -4.59086e16 q^{7} -2.71983e17 q^{8} +1.35085e18 q^{9} +O(q^{10})\)	\(q+264126. q^{2} -1.16226e9 q^{3} -4.79993e11 q^{4} -6.30487e13 q^{5} -3.06983e14 q^{6} -4.59086e16 q^{7} -2.71983e17 q^{8} +1.35085e18 q^{9} -1.66528e19 q^{10} -1.42816e20 q^{11} +5.57878e20 q^{12} +2.23742e20 q^{13} -1.21256e22 q^{14} +7.32790e22 q^{15} +1.92041e23 q^{16} +3.05051e23 q^{17} +3.56795e23 q^{18} -1.47192e25 q^{19} +3.02629e25 q^{20} +5.33578e25 q^{21} -3.77213e25 q^{22} -5.75448e26 q^{23} +3.16116e26 q^{24} +2.15614e27 q^{25} +5.90959e25 q^{26} -1.57004e27 q^{27} +2.20358e28 q^{28} +1.59256e28 q^{29} +1.93549e28 q^{30} +2.90720e28 q^{31} +2.00247e29 q^{32} +1.65989e29 q^{33} +8.05717e28 q^{34} +2.89448e30 q^{35} -6.48400e29 q^{36} +4.49195e30 q^{37} -3.88772e30 q^{38} -2.60046e29 q^{39} +1.71482e31 q^{40} -3.98145e31 q^{41} +1.40932e31 q^{42} -1.13795e32 q^{43} +6.85506e31 q^{44} -8.51694e31 q^{45} -1.51990e32 q^{46} -4.87913e32 q^{47} -2.23202e32 q^{48} +1.19806e33 q^{49} +5.69493e32 q^{50} -3.54549e32 q^{51} -1.07395e32 q^{52} -5.94518e32 q^{53} -4.14689e32 q^{54} +9.00434e33 q^{55} +1.24864e34 q^{56} +1.71076e34 q^{57} +4.20636e33 q^{58} -2.61158e34 q^{59} -3.51734e34 q^{60} -4.20907e34 q^{61} +7.67866e33 q^{62} -6.20157e34 q^{63} -5.26854e34 q^{64} -1.41066e34 q^{65} +4.38420e34 q^{66} -4.97358e35 q^{67} -1.46422e35 q^{68} +6.68820e35 q^{69} +7.64506e35 q^{70} +8.30261e35 q^{71} -3.67409e35 q^{72} -5.71462e35 q^{73} +1.18644e36 q^{74} -2.50600e36 q^{75} +7.06513e36 q^{76} +6.55647e36 q^{77} -6.86849e34 q^{78} -1.34537e37 q^{79} -1.21080e37 q^{80} +1.82480e36 q^{81} -1.05160e37 q^{82} +2.31025e37 q^{83} -2.56114e37 q^{84} -1.92330e37 q^{85} -3.00563e37 q^{86} -1.85097e37 q^{87} +3.88435e37 q^{88} +5.53932e37 q^{89} -2.24954e37 q^{90} -1.02717e37 q^{91} +2.76211e38 q^{92} -3.37893e37 q^{93} -1.28870e38 q^{94} +9.28027e38 q^{95} -2.32740e38 q^{96} -5.58017e38 q^{97} +3.16438e38 q^{98} -1.92923e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} + O(q^{10}) \)	\( 3q + 533574q^{2} - 3486784401q^{3} + 957442653732q^{4} - 53381973944430q^{5} - 620152499993058q^{6} - 1577312676222528q^{7} + 447338335366356696q^{8} + 4052555153018976267q^{9} - 39868781226579858780q^{10} - \)\(53\!\cdots\!40\)\(q^{11} - \)\(11\!\cdots\!44\)\(q^{12} + \)\(54\!\cdots\!90\)\(q^{13} + \)\(31\!\cdots\!52\)\(q^{14} + \)\(62\!\cdots\!10\)\(q^{15} + \)\(12\!\cdots\!36\)\(q^{16} + \)\(72\!\cdots\!58\)\(q^{17} + \)\(72\!\cdots\!86\)\(q^{18} - \)\(10\!\cdots\!24\)\(q^{19} + \)\(30\!\cdots\!60\)\(q^{20} + \)\(18\!\cdots\!76\)\(q^{21} - \)\(10\!\cdots\!24\)\(q^{22} + \)\(41\!\cdots\!64\)\(q^{23} - \)\(51\!\cdots\!32\)\(q^{24} - \)\(11\!\cdots\!75\)\(q^{25} + \)\(92\!\cdots\!76\)\(q^{26} - \)\(47\!\cdots\!89\)\(q^{27} + \)\(64\!\cdots\!56\)\(q^{28} + \)\(72\!\cdots\!62\)\(q^{29} + \)\(46\!\cdots\!60\)\(q^{30} - \)\(38\!\cdots\!56\)\(q^{31} + \)\(37\!\cdots\!12\)\(q^{32} + \)\(61\!\cdots\!80\)\(q^{33} + \)\(37\!\cdots\!44\)\(q^{34} + \)\(27\!\cdots\!20\)\(q^{35} + \)\(12\!\cdots\!48\)\(q^{36} + \)\(29\!\cdots\!22\)\(q^{37} + \)\(74\!\cdots\!92\)\(q^{38} - \)\(63\!\cdots\!30\)\(q^{39} + \)\(15\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!26\)\(q^{41} - \)\(36\!\cdots\!84\)\(q^{42} - \)\(24\!\cdots\!28\)\(q^{43} - \)\(21\!\cdots\!12\)\(q^{44} - \)\(72\!\cdots\!70\)\(q^{45} - \)\(10\!\cdots\!56\)\(q^{46} - \)\(10\!\cdots\!04\)\(q^{47} - \)\(13\!\cdots\!12\)\(q^{48} + \)\(92\!\cdots\!43\)\(q^{49} - \)\(11\!\cdots\!50\)\(q^{50} - \)\(84\!\cdots\!86\)\(q^{51} + \)\(59\!\cdots\!88\)\(q^{52} + \)\(62\!\cdots\!34\)\(q^{53} - \)\(83\!\cdots\!62\)\(q^{54} + \)\(72\!\cdots\!40\)\(q^{55} + \)\(36\!\cdots\!00\)\(q^{56} + \)\(12\!\cdots\!08\)\(q^{57} + \)\(28\!\cdots\!84\)\(q^{58} - \)\(75\!\cdots\!56\)\(q^{59} - \)\(35\!\cdots\!20\)\(q^{60} - \)\(71\!\cdots\!98\)\(q^{61} - \)\(33\!\cdots\!16\)\(q^{62} - \)\(21\!\cdots\!92\)\(q^{63} - \)\(35\!\cdots\!56\)\(q^{64} - \)\(71\!\cdots\!60\)\(q^{65} + \)\(11\!\cdots\!08\)\(q^{66} - \)\(51\!\cdots\!72\)\(q^{67} + \)\(11\!\cdots\!92\)\(q^{68} - \)\(48\!\cdots\!88\)\(q^{69} + \)\(38\!\cdots\!20\)\(q^{70} + \)\(84\!\cdots\!76\)\(q^{71} + \)\(60\!\cdots\!44\)\(q^{72} + \)\(63\!\cdots\!14\)\(q^{73} + \)\(89\!\cdots\!12\)\(q^{74} + \)\(13\!\cdots\!25\)\(q^{75} + \)\(12\!\cdots\!36\)\(q^{76} - \)\(22\!\cdots\!36\)\(q^{77} - \)\(10\!\cdots\!92\)\(q^{78} - \)\(16\!\cdots\!00\)\(q^{79} - \)\(18\!\cdots\!80\)\(q^{80} + \)\(54\!\cdots\!63\)\(q^{81} - \)\(48\!\cdots\!36\)\(q^{82} + \)\(59\!\cdots\!48\)\(q^{83} - \)\(74\!\cdots\!52\)\(q^{84} - \)\(52\!\cdots\!80\)\(q^{85} + \)\(85\!\cdots\!00\)\(q^{86} - \)\(84\!\cdots\!54\)\(q^{87} - \)\(10\!\cdots\!64\)\(q^{88} + \)\(18\!\cdots\!86\)\(q^{89} - \)\(53\!\cdots\!20\)\(q^{90} + \)\(23\!\cdots\!24\)\(q^{91} + \)\(96\!\cdots\!32\)\(q^{92} + \)\(44\!\cdots\!52\)\(q^{93} - \)\(12\!\cdots\!20\)\(q^{94} + \)\(84\!\cdots\!00\)\(q^{95} - \)\(44\!\cdots\!04\)\(q^{96} - \)\(99\!\cdots\!42\)\(q^{97} + \)\(19\!\cdots\!10\)\(q^{98} - \)\(71\!\cdots\!60\)\(q^{99} + O(q^{100}) \)

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Modular forms

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