LMFDB - Embedded newform 177.14.a.b.1.3

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$189.798744245$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-159.673 q^{2} -729.000 q^{3} +17303.4 q^{4} -10788.6 q^{5} +116402. q^{6} +188818. q^{7} -1.45485e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q-159.673 q^{2} -729.000 q^{3} +17303.4 q^{4} -10788.6 q^{5} +116402. q^{6} +188818. q^{7} -1.45485e6 q^{8} +531441. q^{9} +1.72264e6 q^{10} +7.69789e6 q^{11} -1.26142e7 q^{12} +8.10554e6 q^{13} -3.01492e7 q^{14} +7.86486e6 q^{15} +9.05501e7 q^{16} -3.84238e7 q^{17} -8.48567e7 q^{18} +2.90246e8 q^{19} -1.86679e8 q^{20} -1.37649e8 q^{21} -1.22914e9 q^{22} +6.02860e8 q^{23} +1.06058e9 q^{24} -1.10431e9 q^{25} -1.29424e9 q^{26} -3.87420e8 q^{27} +3.26720e9 q^{28} +6.20361e9 q^{29} -1.25581e9 q^{30} -4.12563e9 q^{31} -2.54027e9 q^{32} -5.61176e9 q^{33} +6.13525e9 q^{34} -2.03708e9 q^{35} +9.19575e9 q^{36} +2.05036e9 q^{37} -4.63444e10 q^{38} -5.90894e9 q^{39} +1.56957e10 q^{40} -1.51019e10 q^{41} +2.19787e10 q^{42} -8.13939e10 q^{43} +1.33200e11 q^{44} -5.73348e9 q^{45} -9.62605e10 q^{46} -3.75187e10 q^{47} -6.60110e10 q^{48} -6.12366e10 q^{49} +1.76328e11 q^{50} +2.80110e10 q^{51} +1.40254e11 q^{52} -4.24339e10 q^{53} +6.18605e10 q^{54} -8.30491e10 q^{55} -2.74702e11 q^{56} -2.11589e11 q^{57} -9.90549e11 q^{58} -4.21805e10 q^{59} +1.36089e11 q^{60} -7.71030e11 q^{61} +6.58751e11 q^{62} +1.00346e11 q^{63} -3.36173e11 q^{64} -8.74472e10 q^{65} +8.96046e11 q^{66} +2.56447e10 q^{67} -6.64864e11 q^{68} -4.39485e11 q^{69} +3.25266e11 q^{70} -1.41029e12 q^{71} -7.73166e11 q^{72} -1.45810e12 q^{73} -3.27386e11 q^{74} +8.05042e11 q^{75} +5.02224e12 q^{76} +1.45350e12 q^{77} +9.43498e11 q^{78} +3.78082e12 q^{79} -9.76905e11 q^{80} +2.82430e11 q^{81} +2.41136e12 q^{82} -1.30021e12 q^{83} -2.38179e12 q^{84} +4.14538e11 q^{85} +1.29964e13 q^{86} -4.52244e12 q^{87} -1.11993e13 q^{88} +8.93336e11 q^{89} +9.15482e11 q^{90} +1.53048e12 q^{91} +1.04316e13 q^{92} +3.00758e12 q^{93} +5.99072e12 q^{94} -3.13133e12 q^{95} +1.85186e12 q^{96} +9.58195e12 q^{97} +9.77783e12 q^{98} +4.09097e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) $	\( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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 $

$2$	−159.673	−1.76415	−0.882076	−	0.471106i	$-0.843855\pi$
$2$	−159.673	−1.76415	−0.882076	+	0.471106i	$0.843855\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	17303.4	2.11223
$5$	−10788.6	−0.308787	−0.154393	−	0.988009i	$-0.549342\pi$
$5$	−10788.6	−0.308787	−0.154393	+	0.988009i	$0.549342\pi$
$6$	116402.	1.01853
$7$	188818.	0.606606	0.303303	−	0.952894i	$-0.401911\pi$
$7$	188818.	0.606606	0.303303	+	0.952894i	$0.401911\pi$
$8$	−1.45485e6	−1.96215
$9$	531441.	0.333333
$10$	1.72264e6	0.544747
$11$	7.69789e6	1.31014	0.655072	−	0.755566i	$-0.272638\pi$
$11$	7.69789e6	1.31014	0.655072	+	0.755566i	$0.272638\pi$
$12$	−1.26142e7	−1.21950
$13$	8.10554e6	0.465747	0.232874	−	0.972507i	$-0.425187\pi$
$13$	8.10554e6	0.465747	0.232874	+	0.972507i	$0.425187\pi$
$14$	−3.01492e7	−1.07015
$15$	7.86486e6	0.178278
$16$	9.05501e7	1.34930
$17$	−3.84238e7	−0.386085	−0.193042	−	0.981190i	$-0.561836\pi$
$17$	−3.84238e7	−0.386085	−0.193042	+	0.981190i	$0.561836\pi$
$18$	−8.48567e7	−0.588051
$19$	2.90246e8	1.41536	0.707681	−	0.706532i	$-0.249742\pi$
$19$	2.90246e8	1.41536	0.707681	+	0.706532i	$0.249742\pi$
$20$	−1.86679e8	−0.652230
$21$	−1.37649e8	−0.350224
$22$	−1.22914e9	−2.31129
$23$	6.02860e8	0.849153	0.424576	−	0.905392i	$-0.360423\pi$
$23$	6.02860e8	0.849153	0.424576	+	0.905392i	$0.360423\pi$
$24$	1.06058e9	1.13285
$25$	−1.10431e9	−0.904651
$26$	−1.29424e9	−0.821649
$27$	−3.87420e8	−0.192450
$28$	3.26720e9	1.28129
$29$	6.20361e9	1.93668	0.968340	−	0.249635i	$-0.0803107\pi$
$29$	6.20361e9	1.93668	0.968340	+	0.249635i	$0.0803107\pi$
$30$	−1.25581e9	−0.314510
$31$	−4.12563e9	−0.834909	−0.417455	−	0.908698i	$-0.637078\pi$
$31$	−4.12563e9	−0.834909	−0.417455	+	0.908698i	$0.637078\pi$
$32$	−2.54027e9	−0.418221
$33$	−5.61176e9	−0.756412
$34$	6.13525e9	0.681113
$35$	−2.03708e9	−0.187312
$36$	9.19575e9	0.704078
$37$	2.05036e9	0.131377	0.0656883	−	0.997840i	$-0.479076\pi$
$37$	2.05036e9	0.131377	0.0656883	+	0.997840i	$0.479076\pi$
$38$	−4.63444e10	−2.49691
$39$	−5.90894e9	−0.268899
$40$	1.56957e10	0.605886
$41$	−1.51019e10	−0.496520	−0.248260	−	0.968693i	$-0.579859\pi$
$41$	−1.51019e10	−0.496520	−0.248260	+	0.968693i	$0.579859\pi$
$42$	2.19787e10	0.617849
$43$	−8.13939e10	−1.96357	−0.981786	−	0.189992i	$-0.939154\pi$
$43$	−8.13939e10	−1.96357	−0.981786	+	0.189992i	$0.939154\pi$
$44$	1.33200e11	2.76733
$45$	−5.73348e9	−0.102929
$46$	−9.62605e10	−1.49804
$47$	−3.75187e10	−0.507705	−0.253853	−	0.967243i	$-0.581698\pi$
$47$	−3.75187e10	−0.507705	−0.253853	+	0.967243i	$0.581698\pi$
$48$	−6.60110e10	−0.779019
$49$	−6.12366e10	−0.632029
$50$	1.76328e11	1.59594
$51$	2.80110e10	0.222906
$52$	1.40254e11	0.983768
$53$	−4.24339e10	−0.262978	−0.131489	−	0.991318i	$-0.541976\pi$
$53$	−4.24339e10	−0.262978	−0.131489	+	0.991318i	$0.541976\pi$
$54$	6.18605e10	0.339511
$55$	−8.30491e10	−0.404555
$56$	−2.74702e11	−1.19025
$57$	−2.11589e11	−0.817159
$58$	−9.90549e11	−3.41660
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.36089e11	0.376565
$61$	−7.71030e11	−1.91614	−0.958070	−	0.286535i	$-0.907497\pi$
$61$	−7.71030e11	−1.91614	−0.958070	+	0.286535i	$0.907497\pi$
$62$	6.58751e11	1.47291
$63$	1.00346e11	0.202202
$64$	−3.36173e11	−0.611495
$65$	−8.74472e10	−0.143817
$66$	8.96046e11	1.33443
$67$	2.56447e10	0.0346347	0.0173174	−	0.999850i	$-0.494487\pi$
$67$	2.56447e10	0.0346347	0.0173174	+	0.999850i	$0.494487\pi$
$68$	−6.64864e11	−0.815502
$69$	−4.39485e11	−0.490259
$70$	3.25266e11	0.330447
$71$	−1.41029e12	−1.30656	−0.653282	−	0.757115i	$-0.726608\pi$
$71$	−1.41029e12	−1.30656	−0.653282	+	0.757115i	$0.726608\pi$
$72$	−7.73166e11	−0.654051
$73$	−1.45810e12	−1.12769	−0.563844	−	0.825881i	$-0.690678\pi$
$73$	−1.45810e12	−1.12769	−0.563844	+	0.825881i	$0.690678\pi$
$74$	−3.27386e11	−0.231768
$75$	8.05042e11	0.522300
$76$	5.02224e12	2.98958
$77$	1.45350e12	0.794742
$78$	9.43498e11	0.474380
$79$	3.78082e12	1.74989	0.874943	−	0.484227i	$-0.160899\pi$
$79$	3.78082e12	1.74989	0.874943	+	0.484227i	$0.160899\pi$
$80$	−9.76905e11	−0.416646
$81$	2.82430e11	0.111111
$82$	2.41136e12	0.875937
$83$	−1.30021e12	−0.436521	−0.218261	−	0.975891i	$-0.570038\pi$
$83$	−1.30021e12	−0.436521	−0.218261	+	0.975891i	$0.570038\pi$
$84$	−2.38179e12	−0.739756
$85$	4.14538e11	0.119218
$86$	1.29964e13	3.46404
$87$	−4.52244e12	−1.11814
$88$	−1.11993e13	−2.57070
$89$	8.93336e11	0.190537	0.0952686	−	0.995452i	$-0.469629\pi$
$89$	8.93336e11	0.190537	0.0952686	+	0.995452i	$0.469629\pi$
$90$	9.15482e11	0.181582
$91$	1.53048e12	0.282525
$92$	1.04316e13	1.79361
$93$	3.00758e12	0.482035
$94$	5.99072e12	0.895669
$95$	−3.13133e12	−0.437045
$96$	1.85186e12	0.241460
$97$	9.58195e12	1.16799	0.583993	−	0.811759i	$-0.301490\pi$
$97$	9.58195e12	1.16799	0.583993	+	0.811759i	$0.301490\pi$
$98$	9.77783e12	1.11500
$99$	4.09097e12	0.436715
$100$	−1.91083e13	−1.91083
$101$	1.29711e12	0.121587	0.0607936	−	0.998150i	$-0.480637\pi$
$101$	1.29711e12	0.121587	0.0607936	+	0.998150i	$0.480637\pi$
$102$	−4.47259e12	−0.393241
$103$	−8.37017e12	−0.690704	−0.345352	−	0.938473i	$-0.612241\pi$
$103$	−8.37017e12	−0.690704	−0.345352	+	0.938473i	$0.612241\pi$
$104$	−1.17923e13	−0.913867
$105$	1.48503e12	0.108145
$106$	6.77555e12	0.463934
$107$	−1.60096e11	−0.0103130	−0.00515652	−	0.999987i	$-0.501641\pi$
$107$	−1.60096e11	−0.0103130	−0.00515652	+	0.999987i	$0.501641\pi$
$108$	−6.70370e12	−0.406500
$109$	−4.01913e12	−0.229541	−0.114770	−	0.993392i	$-0.536613\pi$
$109$	−4.01913e12	−0.229541	−0.114770	+	0.993392i	$0.536613\pi$
$110$	1.32607e13	0.713697
$111$	−1.49471e12	−0.0758503
$112$	1.70975e13	0.818494
$113$	−1.96393e13	−0.887394	−0.443697	−	0.896177i	$-0.646333\pi$
$113$	−1.96393e13	−0.887394	−0.443697	+	0.896177i	$0.646333\pi$
$114$	3.37850e13	1.44159
$115$	−6.50400e12	−0.262207
$116$	1.07344e14	4.09072
$117$	4.30762e12	0.155249
$118$	6.73509e12	0.229673
$119$	−7.25513e12	−0.234202
$120$	−1.14422e13	−0.349809
$121$	2.47347e13	0.716477
$122$	1.23113e14	3.38036
$123$	1.10093e13	0.286666
$124$	−7.13875e13	−1.76352
$125$	2.50835e13	0.588131
$126$	−1.60225e13	−0.356715
$127$	−6.34911e13	−1.34273	−0.671365	−	0.741127i	$-0.734292\pi$
$127$	−6.34911e13	−1.34273	−0.671365	+	0.741127i	$0.734292\pi$
$128$	7.44877e13	1.49699
$129$	5.93361e13	1.13367
$130$	1.39629e13	0.253714
$131$	9.15084e13	1.58197	0.790984	−	0.611837i	$-0.209569\pi$
$131$	9.15084e13	1.58197	0.790984	+	0.611837i	$0.209569\pi$
$132$	−9.71027e13	−1.59772
$133$	5.48037e13	0.858567
$134$	−4.09476e12	−0.0611009
$135$	4.17971e12	0.0594260
$136$	5.59008e13	0.757557
$137$	1.26357e14	1.63273	0.816367	−	0.577534i	$-0.195985\pi$
$137$	1.26357e14	1.63273	0.816367	+	0.577534i	$0.195985\pi$
$138$	7.01739e13	0.864891
$139$	−2.79722e13	−0.328950	−0.164475	−	0.986381i	$-0.552593\pi$
$139$	−2.79722e13	−0.328950	−0.164475	+	0.986381i	$0.552593\pi$
$140$	−3.52484e13	−0.395647
$141$	2.73511e13	0.293124
$142$	2.25186e14	2.30498
$143$	6.23956e13	0.610196
$144$	4.81220e13	0.449767
$145$	−6.69281e13	−0.598021
$146$	2.32819e14	1.98941
$147$	4.46415e13	0.364902
$148$	3.54782e13	0.277498
$149$	−2.51209e14	−1.88072	−0.940361	−	0.340177i	$-0.889513\pi$
$149$	−2.51209e14	−1.88072	−0.940361	+	0.340177i	$0.889513\pi$
$150$	−1.28543e14	−0.921418
$151$	2.18580e14	1.50058	0.750291	−	0.661108i	$-0.229913\pi$
$151$	2.18580e14	1.50058	0.750291	+	0.661108i	$0.229913\pi$
$152$	−4.22263e14	−2.77715
$153$	−2.04200e13	−0.128695
$154$	−2.32085e14	−1.40205
$155$	4.45096e13	0.257809
$156$	−1.02245e14	−0.567979
$157$	−7.47896e13	−0.398560	−0.199280	−	0.979943i	$-0.563860\pi$
$157$	−7.47896e13	−0.398560	−0.199280	+	0.979943i	$0.563860\pi$
$158$	−6.03694e14	−3.08706
$159$	3.09343e13	0.151831
$160$	2.74059e13	0.129141
$161$	1.13831e14	0.515101
$162$	−4.50963e13	−0.196017
$163$	−4.02010e14	−1.67887	−0.839436	−	0.543459i	$-0.817115\pi$
$163$	−4.02010e14	−1.67887	−0.839436	+	0.543459i	$0.817115\pi$
$164$	−2.61315e14	−1.04877
$165$	6.05428e13	0.233570
$166$	2.07608e14	0.770090
$167$	3.79547e14	1.35397	0.676984	−	0.735998i	$-0.263287\pi$
$167$	3.79547e14	1.35397	0.676984	+	0.735998i	$0.263287\pi$
$168$	2.00258e14	0.687193
$169$	−2.37175e14	−0.783079
$170$	−6.61905e13	−0.210319
$171$	1.54248e14	0.471787
$172$	−1.40839e15	−4.14752
$173$	−5.55455e14	−1.57525	−0.787624	−	0.616156i	$-0.788689\pi$
$173$	−5.55455e14	−1.57525	−0.787624	+	0.616156i	$0.788689\pi$
$174$	7.22110e14	1.97257
$175$	−2.08514e14	−0.548767
$176$	6.97044e14	1.76778
$177$	3.07496e13	0.0751646
$178$	−1.42641e14	−0.336137
$179$	5.64535e14	1.28276	0.641381	−	0.767222i	$-0.278362\pi$
$179$	5.64535e14	1.28276	0.641381	+	0.767222i	$0.278362\pi$
$180$	−9.92089e13	−0.217410
$181$	3.34847e14	0.707840	0.353920	−	0.935276i	$-0.384849\pi$
$181$	3.34847e14	0.707840	0.353920	+	0.935276i	$0.384849\pi$
$182$	−2.44375e14	−0.498418
$183$	5.62081e14	1.10628
$184$	−8.77070e14	−1.66617
$185$	−2.21204e13	−0.0405673
$186$	−4.80230e14	−0.850383
$187$	−2.95782e14	−0.505827
$188$	−6.49202e14	−1.07239
$189$	−7.31521e13	−0.116741
$190$	4.99989e14	0.771013
$191$	−3.68079e14	−0.548559	−0.274280	−	0.961650i	$-0.588439\pi$
$191$	−3.68079e14	−0.548559	−0.274280	+	0.961650i	$0.588439\pi$
$192$	2.45070e14	0.353047
$193$	−1.19941e14	−0.167049	−0.0835244	−	0.996506i	$-0.526618\pi$
$193$	−1.19941e14	−0.167049	−0.0835244	+	0.996506i	$0.526618\pi$
$194$	−1.52998e15	−2.06051
$195$	6.37490e13	0.0830325
$196$	−1.05960e15	−1.33499
$197$	−1.52574e15	−1.85974	−0.929868	−	0.367894i	$-0.880079\pi$
$197$	−1.52574e15	−1.85974	−0.929868	+	0.367894i	$0.880079\pi$
$198$	−6.53217e14	−0.770431
$199$	2.96360e14	0.338279	0.169140	−	0.985592i	$-0.445901\pi$
$199$	2.96360e14	0.338279	0.169140	+	0.985592i	$0.445901\pi$
$200$	1.60660e15	1.77506
$201$	−1.86950e13	−0.0199964
$202$	−2.07113e14	−0.214498
$203$	1.17136e15	1.17480
$204$	4.84686e14	0.470830
$205$	1.62928e14	0.153319
$206$	1.33649e15	1.21851
$207$	3.20385e14	0.283051
$208$	7.33958e14	0.628433
$209$	2.23428e15	1.85433
$210$	−2.37119e14	−0.190784
$211$	−2.99534e14	−0.233674	−0.116837	−	0.993151i	$-0.537275\pi$
$211$	−2.99534e14	−0.233674	−0.116837	+	0.993151i	$0.537275\pi$
$212$	−7.34252e14	−0.555472
$213$	1.02810e15	0.754345
$214$	2.55630e13	0.0181938
$215$	8.78123e14	0.606325
$216$	5.63638e14	0.377616
$217$	−7.78994e14	−0.506461
$218$	6.41746e14	0.404945
$219$	1.06296e15	0.651071
$220$	−1.43703e15	−0.854515
$221$	−3.11446e14	−0.179818
$222$	2.38665e14	0.133812
$223$	−2.32263e14	−0.126473	−0.0632367	−	0.997999i	$-0.520142\pi$
$223$	−2.32263e14	−0.126473	−0.0632367	+	0.997999i	$0.520142\pi$
$224$	−4.79650e14	−0.253695
$225$	−5.86876e14	−0.301550
$226$	3.13586e15	1.56550
$227$	−7.29458e14	−0.353861	−0.176930	−	0.984223i	$-0.556617\pi$
$227$	−7.29458e14	−0.353861	−0.176930	+	0.984223i	$0.556617\pi$
$228$	−3.66122e15	−1.72603
$229$	−1.84328e15	−0.844620	−0.422310	−	0.906451i	$-0.638781\pi$
$229$	−1.84328e15	−0.844620	−0.422310	+	0.906451i	$0.638781\pi$
$230$	1.03851e15	0.462573
$231$	−1.05960e15	−0.458844
$232$	−9.02532e15	−3.80006
$233$	−2.70339e15	−1.10687	−0.553434	−	0.832893i	$-0.686683\pi$
$233$	−2.70339e15	−1.10687	−0.553434	+	0.832893i	$0.686683\pi$
$234$	−6.87810e14	−0.273883
$235$	4.04773e14	0.156773
$236$	−7.29868e14	−0.274990
$237$	−2.75622e15	−1.01030
$238$	1.15845e15	0.413167
$239$	2.63090e15	0.913100	0.456550	−	0.889698i	$-0.349085\pi$
$239$	2.63090e15	0.913100	0.456550	+	0.889698i	$0.349085\pi$
$240$	7.12164e14	0.240551
$241$	−5.27704e15	−1.73492	−0.867460	−	0.497507i	$-0.834249\pi$
$241$	−5.27704e15	−1.73492	−0.867460	+	0.497507i	$0.834249\pi$
$242$	−3.94947e15	−1.26398
$243$	−2.05891e14	−0.0641500
$244$	−1.33415e16	−4.04734
$245$	6.60655e14	0.195162
$246$	−1.75788e15	−0.505722
$247$	2.35260e15	0.659201
$248$	6.00216e15	1.63822
$249$	9.47852e14	0.252026
$250$	−4.00516e15	−1.03755
$251$	3.52800e15	0.890531	0.445265	−	0.895399i	$-0.353109\pi$
$251$	3.52800e15	0.890531	0.445265	+	0.895399i	$0.353109\pi$
$252$	1.73633e15	0.427098
$253$	4.64075e15	1.11251
$254$	1.01378e16	2.36878
$255$	−3.02198e14	−0.0688305
$256$	−9.13973e15	−2.02943
$257$	−2.69146e15	−0.582669	−0.291335	−	0.956621i	$-0.594099\pi$
$257$	−2.69146e15	−0.582669	−0.291335	+	0.956621i	$0.594099\pi$
$258$	−9.47437e15	−1.99996
$259$	3.87145e14	0.0796939
$260$	−1.51314e15	−0.303774
$261$	3.29686e15	0.645560
$262$	−1.46114e16	−2.79083
$263$	−2.03595e15	−0.379363	−0.189682	−	0.981846i	$-0.560746\pi$
$263$	−2.03595e15	−0.379363	−0.189682	+	0.981846i	$0.560746\pi$
$264$	8.16426e15	1.48420
$265$	4.57801e14	0.0812042
$266$	−8.75066e15	−1.51464
$267$	−6.51242e14	−0.110007
$268$	4.43741e14	0.0731566
$269$	−4.93105e15	−0.793504	−0.396752	−	0.917926i	$-0.629863\pi$
$269$	−4.93105e15	−0.793504	−0.396752	+	0.917926i	$0.629863\pi$
$270$	−6.67386e14	−0.104837
$271$	1.06198e16	1.62860	0.814301	−	0.580443i	$-0.197121\pi$
$271$	1.06198e16	1.62860	0.814301	+	0.580443i	$0.197121\pi$
$272$	−3.47928e15	−0.520945
$273$	−1.11572e15	−0.163116
$274$	−2.01758e16	−2.88039
$275$	−8.50085e15	−1.18522
$276$	−7.60460e15	−1.03554
$277$	6.73410e15	0.895697	0.447849	−	0.894109i	$-0.352190\pi$
$277$	6.73410e15	0.895697	0.447849	+	0.894109i	$0.352190\pi$
$278$	4.46640e15	0.580319
$279$	−2.19253e15	−0.278303
$280$	2.96364e15	0.367534
$281$	7.63531e15	0.925200	0.462600	−	0.886567i	$-0.346917\pi$
$281$	7.63531e15	0.925200	0.462600	+	0.886567i	$0.346917\pi$
$282$	−4.36723e15	−0.517115
$283$	2.87879e15	0.333118	0.166559	−	0.986031i	$-0.446734\pi$
$283$	2.87879e15	0.333118	0.166559	+	0.986031i	$0.446734\pi$
$284$	−2.44029e16	−2.75977
$285$	2.28274e15	0.252328
$286$	−9.96288e15	−1.07648
$287$	−2.85152e15	−0.301192
$288$	−1.35001e15	−0.139407
$289$	−8.42819e15	−0.850938
$290$	1.06866e16	1.05500
$291$	−6.98524e15	−0.674337
$292$	−2.52301e16	−2.38194
$293$	3.05609e15	0.282181	0.141090	−	0.989997i	$-0.454939\pi$
$293$	3.05609e15	0.282181	0.141090	+	0.989997i	$0.454939\pi$
$294$	−7.12804e15	−0.643743
$295$	4.55067e14	0.0402006
$296$	−2.98296e15	−0.257781
$297$	−2.98232e15	−0.252137
$298$	4.01113e16	3.31788
$299$	4.88651e15	0.395491
$300$	1.39300e16	1.10322
$301$	−1.53687e16	−1.19111
$302$	−3.49013e16	−2.64726
$303$	−9.45593e14	−0.0701984
$304$	2.62818e16	1.90975
$305$	8.31830e15	0.591678
$306$	3.26052e15	0.227038
$307$	2.36580e16	1.61279	0.806397	−	0.591375i	$-0.201415\pi$
$307$	2.36580e16	1.61279	0.806397	+	0.591375i	$0.201415\pi$
$308$	2.51506e16	1.67868
$309$	6.10185e15	0.398778
$310$	−7.10698e15	−0.454814
$311$	−3.10338e16	−1.94488	−0.972438	−	0.233162i	$-0.925093\pi$
$311$	−3.10338e16	−1.94488	−0.972438	+	0.233162i	$0.925093\pi$
$312$	8.59661e15	0.527621
$313$	−2.34297e16	−1.40841	−0.704205	−	0.709997i	$-0.748696\pi$
$313$	−2.34297e16	−1.40841	−0.704205	+	0.709997i	$0.748696\pi$
$314$	1.19419e16	0.703120
$315$	−1.08259e15	−0.0624373
$316$	6.54211e16	3.69617
$317$	−1.29438e16	−0.716435	−0.358218	−	0.933638i	$-0.616615\pi$
$317$	−1.29438e16	−0.716435	−0.358218	+	0.933638i	$0.616615\pi$
$318$	−4.93937e15	−0.267852
$319$	4.77547e16	2.53733
$320$	3.62682e15	0.188822
$321$	1.16710e14	0.00595423
$322$	−1.81757e16	−0.908718
$323$	−1.11524e16	−0.546450
$324$	4.88700e15	0.234693
$325$	−8.95103e15	−0.421339
$326$	6.41901e16	2.96179
$327$	2.92994e15	0.132525
$328$	2.19710e16	0.974247
$329$	−7.08422e15	−0.307977
$330$	−9.66704e15	−0.412053
$331$	−4.31442e16	−1.80319	−0.901593	−	0.432584i	$-0.857602\pi$
$331$	−4.31442e16	−1.80319	−0.901593	+	0.432584i	$0.857602\pi$
$332$	−2.24981e16	−0.922035
$333$	1.08964e15	0.0437922
$334$	−6.06034e16	−2.38861
$335$	−2.76670e14	−0.0106947
$336$	−1.24641e16	−0.472558
$337$	3.15609e16	1.17369	0.586847	−	0.809698i	$-0.300369\pi$
$337$	3.15609e16	1.17369	0.586847	+	0.809698i	$0.300369\pi$
$338$	3.78705e16	1.38147
$339$	1.43171e16	0.512337
$340$	7.17293e15	0.251816
$341$	−3.17586e16	−1.09385
$342$	−2.46293e16	−0.832304
$343$	−2.98570e16	−0.989999
$344$	1.18416e17	3.85283
$345$	4.74141e15	0.151385
$346$	8.86910e16	2.77898
$347$	1.98681e16	0.610962	0.305481	−	0.952198i	$-0.401183\pi$
$347$	1.98681e16	0.610962	0.305481	+	0.952198i	$0.401183\pi$
$348$	−7.82536e16	−2.36178
$349$	5.59919e16	1.65867	0.829334	−	0.558753i	$-0.188720\pi$
$349$	5.59919e16	1.65867	0.829334	+	0.558753i	$0.188720\pi$
$350$	3.32940e16	0.968109
$351$	−3.14025e15	−0.0896331
$352$	−1.95547e16	−0.547930
$353$	3.58540e16	0.986284	0.493142	−	0.869949i	$-0.335848\pi$
$353$	3.58540e16	0.986284	0.493142	+	0.869949i	$0.335848\pi$
$354$	−4.90988e15	−0.132602
$355$	1.52151e16	0.403449
$356$	1.54578e16	0.402459
$357$	5.28899e15	0.135216
$358$	−9.01410e16	−2.26299
$359$	4.28853e16	1.05729	0.528646	−	0.848843i	$-0.322700\pi$
$359$	4.28853e16	1.05729	0.528646	+	0.848843i	$0.322700\pi$
$360$	8.34135e15	0.201962
$361$	4.21895e16	1.00325
$362$	−5.34659e16	−1.24874
$363$	−1.80316e16	−0.413658
$364$	2.64825e16	0.596760
$365$	1.57308e16	0.348215
$366$	−8.97490e16	−1.95165
$367$	−3.10176e16	−0.662642	−0.331321	−	0.943518i	$-0.607494\pi$
$367$	−3.10176e16	−0.662642	−0.331321	+	0.943518i	$0.607494\pi$
$368$	5.45891e16	1.14576
$369$	−8.02577e15	−0.165507
$370$	3.53203e15	0.0715670
$371$	−8.01230e15	−0.159524
$372$	5.20415e16	1.01817
$373$	−1.79979e15	−0.0346030	−0.0173015	−	0.999850i	$-0.505508\pi$
$373$	−1.79979e15	−0.0346030	−0.0173015	+	0.999850i	$0.505508\pi$
$374$	4.72284e16	0.892356
$375$	−1.82859e16	−0.339557
$376$	5.45840e16	0.996195
$377$	5.02837e16	0.902004
$378$	1.16804e16	0.205950
$379$	−7.40780e16	−1.28391	−0.641955	−	0.766743i	$-0.721876\pi$
$379$	−7.40780e16	−1.28391	−0.641955	+	0.766743i	$0.721876\pi$
$380$	−5.41828e16	−0.923141
$381$	4.62850e16	0.775226
$382$	5.87722e16	0.967743
$383$	1.40044e16	0.226712	0.113356	−	0.993554i	$-0.463840\pi$
$383$	1.40044e16	0.226712	0.113356	+	0.993554i	$0.463840\pi$
$384$	−5.43015e16	−0.864289
$385$	−1.56812e16	−0.245406
$386$	1.91512e16	0.294700
$387$	−4.32560e16	−0.654524
$388$	1.65801e17	2.46706
$389$	−1.46668e16	−0.214617	−0.107308	−	0.994226i	$-0.534223\pi$
$389$	−1.46668e16	−0.214617	−0.107308	+	0.994226i	$0.534223\pi$
$390$	−1.01790e16	−0.146482
$391$	−2.31642e16	−0.327845
$392$	8.90900e16	1.24014
$393$	−6.67096e16	−0.913350
$394$	2.43620e17	3.28086
$395$	−4.07896e16	−0.540341
$396$	7.07878e16	0.922444
$397$	−1.34858e17	−1.72878	−0.864390	−	0.502823i	$-0.832295\pi$
$397$	−1.34858e17	−1.72878	−0.864390	+	0.502823i	$0.832295\pi$
$398$	−4.73207e16	−0.596776
$399$	−3.99519e16	−0.495694
$400$	−9.99953e16	−1.22065
$401$	−9.96784e16	−1.19719	−0.598595	−	0.801052i	$-0.704274\pi$
$401$	−9.96784e16	−1.19719	−0.598595	+	0.801052i	$0.704274\pi$
$402$	2.98508e15	0.0352766
$403$	−3.34405e16	−0.388857
$404$	2.24444e16	0.256821
$405$	−3.04701e15	−0.0343096
$406$	−1.87034e17	−2.07253
$407$	1.57834e16	0.172122
$408$	−4.07517e16	−0.437376
$409$	−8.75972e16	−0.925313	−0.462656	−	0.886538i	$-0.653104\pi$
$409$	−8.75972e16	−0.925313	−0.462656	+	0.886538i	$0.653104\pi$
$410$	−2.60151e16	−0.270478
$411$	−9.21142e16	−0.942659
$412$	−1.44833e17	−1.45893
$413$	−7.96446e15	−0.0789734
$414$	−5.11568e16	−0.499345
$415$	1.40274e16	0.134792
$416$	−2.05903e16	−0.194785
$417$	2.03917e16	0.189920
$418$	−3.56754e17	−3.27132
$419$	2.19132e16	0.197841	0.0989203	−	0.995095i	$-0.468461\pi$
$419$	2.19132e16	0.197841	0.0989203	+	0.995095i	$0.468461\pi$
$420$	2.56961e16	0.228427
$421$	2.77673e16	0.243052	0.121526	−	0.992588i	$-0.461221\pi$
$421$	2.77673e16	0.243052	0.121526	+	0.992588i	$0.461221\pi$
$422$	4.78274e16	0.412236
$423$	−1.99390e16	−0.169235
$424$	6.17349e16	0.516003
$425$	4.24318e16	0.349272
$426$	−1.64160e17	−1.33078
$427$	−1.45585e17	−1.16234
$428$	−2.77021e15	−0.0217835
$429$	−4.54864e16	−0.352297
$430$	−1.40212e17	−1.06965
$431$	2.11622e17	1.59023	0.795114	−	0.606460i	$-0.207411\pi$
$431$	2.11622e17	1.59023	0.795114	+	0.606460i	$0.207411\pi$
$432$	−3.50809e16	−0.259673
$433$	−2.12581e17	−1.55008	−0.775040	−	0.631912i	$-0.782270\pi$
$433$	−2.12581e17	−1.55008	−0.775040	+	0.631912i	$0.782270\pi$
$434$	1.24384e17	0.893475
$435$	4.87906e16	0.345268
$436$	−6.95447e16	−0.484844
$437$	1.74978e17	1.20186
$438$	−1.69725e17	−1.14859
$439$	1.48280e16	0.0988695	0.0494347	−	0.998777i	$-0.484258\pi$
$439$	1.48280e16	0.0988695	0.0494347	+	0.998777i	$0.484258\pi$
$440$	1.20824e17	0.793798
$441$	−3.25437e16	−0.210676
$442$	4.97295e16	0.317226
$443$	1.33915e17	0.841790	0.420895	−	0.907109i	$-0.361716\pi$
$443$	1.33915e17	0.841790	0.420895	+	0.907109i	$0.361716\pi$
$444$	−2.58636e16	−0.160214
$445$	−9.63781e15	−0.0588353
$446$	3.70862e16	0.223118
$447$	1.83132e17	1.08584
$448$	−6.34756e16	−0.370937
$449$	−9.57945e16	−0.551746	−0.275873	−	0.961194i	$-0.588967\pi$
$449$	−9.57945e16	−0.551746	−0.275873	+	0.961194i	$0.588967\pi$
$450$	9.37081e16	0.531981
$451$	−1.16253e17	−0.650512
$452$	−3.39827e17	−1.87438
$453$	−1.59345e17	−0.866361
$454$	1.16475e17	0.624264
$455$	−1.65116e16	−0.0872400
$456$	3.07830e17	1.60339
$457$	2.24606e17	1.15336	0.576681	−	0.816969i	$-0.304348\pi$
$457$	2.24606e17	1.15336	0.576681	+	0.816969i	$0.304348\pi$
$458$	2.94322e17	1.49004
$459$	1.48862e16	0.0743021
$460$	−1.12541e17	−0.553843
$461$	1.30695e17	0.634166	0.317083	−	0.948398i	$-0.397297\pi$
$461$	1.30695e17	0.634166	0.317083	+	0.948398i	$0.397297\pi$
$462$	1.69190e17	0.809471
$463$	5.86683e16	0.276775	0.138387	−	0.990378i	$-0.455808\pi$
$463$	5.86683e16	0.276775	0.138387	+	0.990378i	$0.455808\pi$
$464$	5.61738e17	2.61316
$465$	−3.24475e16	−0.148846
$466$	4.31659e17	1.95268
$467$	3.78140e17	1.68692	0.843458	−	0.537196i	$-0.180516\pi$
$467$	3.78140e17	1.68692	0.843458	+	0.537196i	$0.180516\pi$
$468$	7.45366e16	0.327923
$469$	4.84219e15	0.0210096
$470$	−6.46312e16	−0.276571
$471$	5.45216e16	0.230109
$472$	6.13663e16	0.255450
$473$	−6.26561e17	−2.57256
$474$	4.40093e17	1.78232
$475$	−3.20521e17	−1.28041
$476$	−1.25539e17	−0.494689
$477$	−2.25511e16	−0.0876594
$478$	−4.20084e17	−1.61085
$479$	2.31664e17	0.876350	0.438175	−	0.898890i	$-0.355625\pi$
$479$	2.31664e17	0.876350	0.438175	+	0.898890i	$0.355625\pi$
$480$	−1.99789e16	−0.0745596
$481$	1.66192e16	0.0611883
$482$	8.42600e17	3.06066
$483$	−8.29829e16	−0.297394
$484$	4.27996e17	1.51337
$485$	−1.03375e17	−0.360658
$486$	3.28752e16	0.113170
$487$	2.94479e17	1.00027	0.500134	−	0.865948i	$-0.333284\pi$
$487$	2.94479e17	1.00027	0.500134	+	0.865948i	$0.333284\pi$
$488$	1.12173e18	3.75976
$489$	2.93065e17	0.969297
$490$	−1.05489e17	−0.344296
$491$	−3.67443e17	−1.18348	−0.591739	−	0.806130i	$-0.701558\pi$
$491$	−3.67443e17	−1.18348	−0.591739	+	0.806130i	$0.701558\pi$
$492$	1.90498e17	0.605505
$493$	−2.38367e17	−0.747723
$494$	−3.75646e17	−1.16293
$495$	−4.41357e16	−0.134852
$496$	−3.73576e17	−1.12654
$497$	−2.66290e17	−0.792570
$498$	−1.51346e17	−0.444612
$499$	8.41582e16	0.244030	0.122015	−	0.992528i	$-0.461064\pi$
$499$	8.41582e16	0.244030	0.122015	+	0.992528i	$0.461064\pi$
$500$	4.34031e17	1.24227
$501$	−2.76690e17	−0.781714
$502$	−5.63325e17	−1.57103
$503$	−1.88108e17	−0.517863	−0.258932	−	0.965896i	$-0.583370\pi$
$503$	−1.88108e17	−0.517863	−0.258932	+	0.965896i	$0.583370\pi$
$504$	−1.45988e17	−0.396751
$505$	−1.39939e16	−0.0375445
$506$	−7.41002e17	−1.96264
$507$	1.72901e17	0.452111
$508$	−1.09861e18	−2.83616
$509$	−1.17080e17	−0.298413	−0.149206	−	0.988806i	$-0.547672\pi$
$509$	−1.17080e17	−0.298413	−0.149206	+	0.988806i	$0.547672\pi$
$510$	4.82529e16	0.121427
$511$	−2.75316e17	−0.684063
$512$	8.49164e17	2.08323
$513$	−1.12447e17	−0.272386
$514$	4.29753e17	1.02792
$515$	9.03021e16	0.213280
$516$	1.02672e18	2.39457
$517$	−2.88815e17	−0.665167
$518$	−6.18165e16	−0.140592
$519$	4.04926e17	0.909470
$520$	1.27222e17	0.282190
$521$	−2.25724e17	−0.494461	−0.247230	−	0.968957i	$-0.579520\pi$
$521$	−2.25724e17	−0.494461	−0.247230	+	0.968957i	$0.579520\pi$
$522$	−5.26418e17	−1.13887
$523$	1.23001e17	0.262814	0.131407	−	0.991328i	$-0.458050\pi$
$523$	1.23001e17	0.262814	0.131407	+	0.991328i	$0.458050\pi$
$524$	1.58341e18	3.34149
$525$	1.52007e17	0.316831
$526$	3.25086e17	0.669254
$527$	1.58523e17	0.322346
$528$	−5.08145e17	−1.02063
$529$	−1.40596e17	−0.278939
$530$	−7.30984e16	−0.143257
$531$	−2.24165e16	−0.0433963
$532$	9.48292e17	1.81350
$533$	−1.22409e17	−0.231253
$534$	1.03986e17	0.194069
$535$	1.72721e15	0.00318453
$536$	−3.73091e16	−0.0679586
$537$	−4.11546e17	−0.740604
$538$	7.87354e17	1.39986
$539$	−4.71393e17	−0.828049
$540$	7.23233e16	0.125522
$541$	−4.04571e17	−0.693765	−0.346883	−	0.937909i	$-0.612760\pi$
$541$	−4.04571e17	−0.693765	−0.346883	+	0.937909i	$0.612760\pi$
$542$	−1.69569e18	−2.87310
$543$	−2.44103e17	−0.408672
$544$	9.76071e16	0.161469
$545$	4.33606e16	0.0708791
$546$	1.78150e17	0.287762
$547$	−1.11019e18	−1.77206	−0.886032	−	0.463624i	$-0.846549\pi$
$547$	−1.11019e18	−1.77206	−0.886032	+	0.463624i	$0.846549\pi$
$548$	2.18641e18	3.44872
$549$	−4.09757e17	−0.638713
$550$	1.35736e18	2.09091
$551$	1.80057e18	2.74110
$552$	6.39384e17	0.961962
$553$	7.13888e17	1.06149
$554$	−1.07525e18	−1.58015
$555$	1.61258e16	0.0234216
$556$	−4.84015e17	−0.694820
$557$	4.52746e17	0.642385	0.321193	−	0.947014i	$-0.395916\pi$
$557$	4.52746e17	0.642385	0.321193	+	0.947014i	$0.395916\pi$
$558$	3.50087e17	0.490969
$559$	−6.59742e17	−0.914528
$560$	−1.84458e17	−0.252740
$561$	2.15625e17	0.292039
$562$	−1.21915e18	−1.63219
$563$	−1.39911e18	−1.85160	−0.925799	−	0.378017i	$-0.876606\pi$
$563$	−1.39911e18	−1.85160	−0.925799	+	0.378017i	$0.876606\pi$
$564$	4.73268e17	0.619146
$565$	2.11880e17	0.274015
$566$	−4.59665e17	−0.587671
$567$	5.33279e16	0.0674007
$568$	2.05176e18	2.56368
$569$	−8.98613e16	−0.111005	−0.0555026	−	0.998459i	$-0.517676\pi$
$569$	−8.98613e16	−0.111005	−0.0555026	+	0.998459i	$0.517676\pi$
$570$	−3.64492e17	−0.445145
$571$	−8.09016e16	−0.0976838	−0.0488419	−	0.998807i	$-0.515553\pi$
$571$	−8.09016e16	−0.0976838	−0.0488419	+	0.998807i	$0.515553\pi$
$572$	1.07966e18	1.28888
$573$	2.68329e17	0.316711
$574$	4.55310e17	0.531349
$575$	−6.65745e17	−0.768187
$576$	−1.78656e17	−0.203832
$577$	−1.57286e15	−0.00177438	−0.000887190	−	1.00000i	$-0.500282\pi$
$577$	−1.57286e15	−0.00177438	−0.000887190		1.00000i	$0.500282\pi$
$578$	1.34575e18	1.50119
$579$	8.74366e16	0.0964457
$580$	−1.15809e18	−1.26316
$581$	−2.45503e17	−0.264797
$582$	1.11535e18	1.18963
$583$	−3.26651e17	−0.344539
$584$	2.12132e18	2.21270
$585$	−4.64730e16	−0.0479389
$586$	−4.87975e17	−0.497810
$587$	−5.97841e17	−0.603167	−0.301584	−	0.953440i	$-0.597515\pi$
$587$	−5.97841e17	−0.603167	−0.301584	+	0.953440i	$0.597515\pi$
$588$	7.72451e17	0.770759
$589$	−1.19745e18	−1.18170
$590$	−7.26619e16	−0.0709200
$591$	1.11227e18	1.07372
$592$	1.85660e17	0.177267
$593$	5.99958e17	0.566585	0.283292	−	0.959034i	$-0.408573\pi$
$593$	5.99958e17	0.566585	0.283292	+	0.959034i	$0.408573\pi$
$594$	4.76195e17	0.444809
$595$	7.82724e16	0.0723183
$596$	−4.34678e18	−3.97253
$597$	−2.16047e17	−0.195306
$598$	−7.80243e17	−0.697706
$599$	−2.68993e17	−0.237939	−0.118970	−	0.992898i	$-0.537959\pi$
$599$	−2.68993e17	−0.237939	−0.118970	+	0.992898i	$0.537959\pi$
$600$	−1.17121e18	−1.02483
$601$	−3.33071e17	−0.288306	−0.144153	−	0.989555i	$-0.546046\pi$
$601$	−3.33071e17	−0.288306	−0.144153	+	0.989555i	$0.546046\pi$
$602$	2.45396e18	2.10131
$603$	1.36286e16	0.0115449
$604$	3.78218e18	3.16958
$605$	−2.66852e17	−0.221239
$606$	1.50986e17	0.123841
$607$	3.32104e17	0.269493	0.134747	−	0.990880i	$-0.456978\pi$
$607$	3.32104e17	0.269493	0.134747	+	0.990880i	$0.456978\pi$
$608$	−7.37304e17	−0.591934
$609$	−8.53919e17	−0.678272
$610$	−1.32821e18	−1.04381
$611$	−3.04109e17	−0.236462
$612$	−3.53336e17	−0.271834
$613$	−6.68632e17	−0.508972	−0.254486	−	0.967076i	$-0.581906\pi$
$613$	−6.68632e17	−0.508972	−0.254486	+	0.967076i	$0.581906\pi$
$614$	−3.77754e18	−2.84521
$615$	−1.18774e17	−0.0885186
$616$	−2.11462e18	−1.55940
$617$	−2.07671e18	−1.51538	−0.757691	−	0.652613i	$-0.773673\pi$
$617$	−2.07671e18	−1.51538	−0.757691	+	0.652613i	$0.773673\pi$
$618$	−9.74300e17	−0.703506
$619$	−2.42821e18	−1.73499	−0.867495	−	0.497446i	$-0.834271\pi$
$619$	−2.42821e18	−1.73499	−0.867495	+	0.497446i	$0.834271\pi$
$620$	7.70169e17	0.544553
$621$	−2.33561e17	−0.163420
$622$	4.95525e18	3.43106
$623$	1.68678e17	0.115581
$624$	−5.35055e17	−0.362826
$625$	1.07742e18	0.723044
$626$	3.74109e18	2.48465
$627$	−1.62879e18	−1.07060
$628$	−1.29412e18	−0.841852
$629$	−7.87825e16	−0.0507225
$630$	1.72860e17	0.110149
$631$	1.99224e18	1.25647	0.628234	−	0.778024i	$-0.283778\pi$
$631$	1.99224e18	1.25647	0.628234	+	0.778024i	$0.283778\pi$
$632$	−5.50051e18	−3.43354
$633$	2.18360e17	0.134911
$634$	2.06678e18	1.26390
$635$	6.84978e17	0.414617
$636$	5.35270e17	0.320702
$637$	−4.96356e17	−0.294366
$638$	−7.62513e18	−4.47624
$639$	−7.49488e17	−0.435521
$640$	−8.03615e17	−0.462251
$641$	1.44405e18	0.822254	0.411127	−	0.911578i	$-0.365135\pi$
$641$	1.44405e18	0.822254	0.411127	+	0.911578i	$0.365135\pi$
$642$	−1.86354e16	−0.0105042
$643$	−3.04746e18	−1.70046	−0.850230	−	0.526411i	$-0.823537\pi$
$643$	−3.04746e18	−1.70046	−0.850230	+	0.526411i	$0.823537\pi$
$644$	1.96967e18	1.08802
$645$	−6.40151e17	−0.350062
$646$	1.78073e18	0.964021
$647$	−2.39541e18	−1.28381	−0.641907	−	0.766783i	$-0.721856\pi$
$647$	−2.39541e18	−1.28381	−0.641907	+	0.766783i	$0.721856\pi$
$648$	−4.10892e17	−0.218017
$649$	−3.24701e17	−0.170566
$650$	1.42924e18	0.743306
$651$	5.67887e17	0.292405
$652$	−6.95615e18	−3.54617
$653$	1.00343e18	0.506466	0.253233	−	0.967405i	$-0.418506\pi$
$653$	1.00343e18	0.506466	0.253233	+	0.967405i	$0.418506\pi$
$654$	−4.67833e17	−0.233795
$655$	−9.87244e17	−0.488491
$656$	−1.36748e18	−0.669954
$657$	−7.74895e17	−0.375896
$658$	1.13116e18	0.543319
$659$	−2.20142e18	−1.04700	−0.523502	−	0.852024i	$-0.675375\pi$
$659$	−2.20142e18	−1.04700	−0.523502	+	0.852024i	$0.675375\pi$
$660$	1.04760e18	0.493355
$661$	1.93163e18	0.900772	0.450386	−	0.892834i	$-0.351286\pi$
$661$	1.93163e18	0.900772	0.450386	+	0.892834i	$0.351286\pi$
$662$	6.88896e18	3.18110
$663$	2.27044e17	0.103818
$664$	1.89161e18	0.856521
$665$	−5.91253e17	−0.265114
$666$	−1.73986e17	−0.0772561
$667$	3.73991e18	1.64454
$668$	6.56746e18	2.85990
$669$	1.69320e17	0.0730194
$670$	4.41766e16	0.0188671
$671$	−5.93530e18	−2.51042
$672$	3.49665e17	0.146471
$673$	1.18529e18	0.491729	0.245865	−	0.969304i	$-0.420928\pi$
$673$	1.18529e18	0.491729	0.245865	+	0.969304i	$0.420928\pi$
$674$	−5.03942e18	−2.07057
$675$	4.27832e17	0.174100
$676$	−4.10394e18	−1.65405
$677$	−2.82296e18	−1.12688	−0.563440	−	0.826157i	$-0.690522\pi$
$677$	−2.82296e18	−1.12688	−0.563440	+	0.826157i	$0.690522\pi$
$678$	−2.28605e18	−0.903841
$679$	1.80925e18	0.708508
$680$	−6.03090e17	−0.233924
$681$	5.31775e17	0.204302
$682$	5.07099e18	1.92972
$683$	1.91965e18	0.723580	0.361790	−	0.932260i	$-0.382166\pi$
$683$	1.91965e18	0.723580	0.361790	+	0.932260i	$0.382166\pi$
$684$	2.66903e18	0.996525
$685$	−1.36321e18	−0.504166
$686$	4.76736e18	1.74651
$687$	1.34375e18	0.487642
$688$	−7.37022e18	−2.64945
$689$	−3.43950e17	−0.122481
$690$	−7.57075e17	−0.267067
$691$	−5.30676e18	−1.85448	−0.927240	−	0.374468i	$-0.877825\pi$
$691$	−5.30676e18	−1.85448	−0.927240	+	0.374468i	$0.877825\pi$
$692$	−9.61127e18	−3.32729
$693$	7.72451e17	0.264914
$694$	−3.17239e18	−1.07783
$695$	3.01780e17	0.101575
$696$	6.57946e18	2.19397
$697$	5.80273e17	0.191699
$698$	−8.94038e18	−2.92615
$699$	1.97077e18	0.639050
$700$	−3.60801e18	−1.15912
$701$	1.94249e18	0.618288	0.309144	−	0.951015i	$-0.399958\pi$
$701$	1.94249e18	0.618288	0.309144	+	0.951015i	$0.399958\pi$
$702$	5.01413e17	0.158127
$703$	5.95107e17	0.185945
$704$	−2.58782e18	−0.801147
$705$	−2.95079e17	−0.0905127
$706$	−5.72491e18	−1.73996
$707$	2.44918e17	0.0737555
$708$	5.32074e17	0.158765
$709$	1.39382e18	0.412105	0.206052	−	0.978541i	$-0.433938\pi$
$709$	1.39382e18	0.412105	0.206052	+	0.978541i	$0.433938\pi$
$710$	−2.42943e18	−0.711746
$711$	2.00928e18	0.583295
$712$	−1.29967e18	−0.373863
$713$	−2.48718e18	−0.708965
$714$	−8.44508e17	−0.238542
$715$	−6.73158e17	−0.188420
$716$	9.76840e18	2.70950
$717$	−1.91793e18	−0.527178
$718$	−6.84762e18	−1.86522
$719$	−1.25268e18	−0.338143	−0.169072	−	0.985604i	$-0.554077\pi$
$719$	−1.25268e18	−0.338143	−0.169072	+	0.985604i	$0.554077\pi$
$720$	−5.19167e17	−0.138882
$721$	−1.58044e18	−0.418986
$722$	−6.73653e18	−1.76988
$723$	3.84696e18	1.00166
$724$	5.79399e18	1.49512
$725$	−6.85071e18	−1.75202
$726$	2.87916e18	0.729757
$727$	1.06674e18	0.267970	0.133985	−	0.990983i	$-0.457223\pi$
$727$	1.06674e18	0.267970	0.133985	+	0.990983i	$0.457223\pi$
$728$	−2.22661e18	−0.554358
$729$	1.50095e17	0.0370370
$730$	−2.51178e18	−0.614305
$731$	3.12746e18	0.758105
$732$	9.72592e18	2.33673
$733$	5.83547e17	0.138963	0.0694816	−	0.997583i	$-0.477865\pi$
$733$	5.83547e17	0.138963	0.0694816	+	0.997583i	$0.477865\pi$
$734$	4.95267e18	1.16900
$735$	−4.81618e17	−0.112677
$736$	−1.53143e18	−0.355134
$737$	1.97410e17	0.0453765
$738$	1.28150e18	0.291979
$739$	6.34195e18	1.43230	0.716150	−	0.697946i	$-0.245902\pi$
$739$	6.34195e18	1.43230	0.716150	+	0.697946i	$0.245902\pi$
$740$	−3.82758e17	−0.0856877
$741$	−1.71504e18	−0.380590
$742$	1.27935e18	0.281425
$743$	−1.18973e17	−0.0259430	−0.0129715	−	0.999916i	$-0.504129\pi$
$743$	−1.18973e17	−0.0259430	−0.0129715	+	0.999916i	$0.504129\pi$
$744$	−4.37558e18	−0.945826
$745$	2.71019e18	0.580742
$746$	2.87377e17	0.0610450
$747$	−6.90984e17	−0.145507
$748$	−5.11805e18	−1.06843
$749$	−3.02291e16	−0.00625595
$750$	2.91976e18	0.599031
$751$	3.88050e18	0.789274	0.394637	−	0.918837i	$-0.370870\pi$
$751$	3.88050e18	0.789274	0.394637	+	0.918837i	$0.370870\pi$
$752$	−3.39732e18	−0.685047
$753$	−2.57191e18	−0.514148
$754$	−8.02894e18	−1.59127
$755$	−2.35816e18	−0.463360
$756$	−1.26578e18	−0.246585
$757$	3.34912e18	0.646857	0.323428	−	0.946253i	$-0.395165\pi$
$757$	3.34912e18	0.646857	0.323428	+	0.946253i	$0.395165\pi$
$758$	1.18282e19	2.26501
$759$	−3.38311e18	−0.642309
$760$	4.55561e18	0.857548
$761$	7.46644e18	1.39352	0.696760	−	0.717304i	$-0.254624\pi$
$761$	7.46644e18	1.39352	0.696760	+	0.717304i	$0.254624\pi$
$762$	−7.39047e18	−1.36762
$763$	−7.58885e17	−0.139241
$764$	−6.36902e18	−1.15869
$765$	2.20302e17	0.0397393
$766$	−2.23613e18	−0.399954
$767$	−3.41896e17	−0.0606351
$768$	6.66286e18	1.17169
$769$	4.87854e18	0.850686	0.425343	−	0.905032i	$-0.360154\pi$
$769$	4.87854e18	0.850686	0.425343	+	0.905032i	$0.360154\pi$
$770$	2.50386e18	0.432933
$771$	1.96207e18	0.336404
$772$	−2.07538e18	−0.352846
$773$	−3.71918e18	−0.627020	−0.313510	−	0.949585i	$-0.601505\pi$
$773$	−3.71918e18	−0.627020	−0.313510	+	0.949585i	$0.601505\pi$
$774$	6.90682e18	1.15468
$775$	4.55597e18	0.755301
$776$	−1.39403e19	−2.29177
$777$	−2.82228e17	−0.0460113
$778$	2.34189e18	0.378617
$779$	−4.38326e18	−0.702755
$780$	1.10308e18	0.175384
$781$	−1.08563e19	−1.71179
$782$	3.69870e18	0.578369
$783$	−2.40341e18	−0.372714
$784$	−5.54498e18	−0.852797
$785$	8.06872e17	0.123070
$786$	1.06517e19	1.61129
$787$	−8.05087e17	−0.120783	−0.0603916	−	0.998175i	$-0.519235\pi$
$787$	−8.05087e17	−0.120783	−0.0603916	+	0.998175i	$0.519235\pi$
$788$	−2.64006e19	−3.92820
$789$	1.48421e18	0.219025
$790$	6.51299e18	0.953244
$791$	−3.70826e18	−0.538299
$792$	−5.95174e18	−0.856901
$793$	−6.24962e18	−0.892437
$794$	2.15332e19	3.04983
$795$	−3.33737e17	−0.0468833
$796$	5.12805e18	0.714525
$797$	8.26045e16	0.0114163	0.00570814	−	0.999984i	$-0.498183\pi$
$797$	8.26045e16	0.0114163	0.00570814	+	0.999984i	$0.498183\pi$
$798$	6.37923e18	0.874480
$799$	1.44161e18	0.196017
$800$	2.80525e18	0.378344
$801$	4.74755e17	0.0635124
$802$	1.59159e19	2.11202
$803$	−1.12243e19	−1.47743
$804$	−3.23487e17	−0.0422370
$805$	−1.22807e18	−0.159056
$806$	5.33954e18	0.686003
$807$	3.59473e18	0.458130
$808$	−1.88710e18	−0.238572
$809$	1.38254e19	1.73385	0.866925	−	0.498439i	$-0.166093\pi$
$809$	1.38254e19	1.73385	0.866925	+	0.498439i	$0.166093\pi$
$810$	4.86525e17	0.0605274
$811$	4.71473e18	0.581864	0.290932	−	0.956744i	$-0.406035\pi$
$811$	4.71473e18	0.581864	0.290932	+	0.956744i	$0.406035\pi$
$812$	2.02685e19	2.48146
$813$	−7.74181e18	−0.940273
$814$	−2.52018e18	−0.303650
$815$	4.33711e18	0.518413
$816$	2.53640e18	0.300768
$817$	−2.36242e19	−2.77916
$818$	1.39869e19	1.63239
$819$	8.13357e17	0.0941751
$820$	2.81921e18	0.323845
$821$	3.15464e18	0.359516	0.179758	−	0.983711i	$-0.442468\pi$
$821$	3.15464e18	0.359516	0.179758	+	0.983711i	$0.442468\pi$
$822$	1.47081e19	1.66299
$823$	6.03428e18	0.676903	0.338452	−	0.940984i	$-0.390097\pi$
$823$	6.03428e18	0.676903	0.338452	+	0.940984i	$0.390097\pi$
$824$	1.21773e19	1.35527
$825$	6.19712e18	0.684289
$826$	1.27171e18	0.139321
$827$	1.18728e19	1.29053	0.645265	−	0.763958i	$-0.276747\pi$
$827$	1.18728e19	1.29053	0.645265	+	0.763958i	$0.276747\pi$
$828$	5.54375e18	0.597870
$829$	2.32766e17	0.0249067	0.0124533	−	0.999922i	$-0.496036\pi$
$829$	2.32766e17	0.0249067	0.0124533	+	0.999922i	$0.496036\pi$
$830$	−2.23979e18	−0.237794
$831$	−4.90916e18	−0.517131
$832$	−2.72487e18	−0.284802
$833$	2.35295e18	0.244017
$834$	−3.25601e18	−0.335047
$835$	−4.09477e18	−0.418087
$836$	3.86607e19	3.91677
$837$	1.59835e18	0.160678
$838$	−3.49895e18	−0.349021
$839$	7.84977e18	0.776970	0.388485	−	0.921455i	$-0.372999\pi$
$839$	7.84977e18	0.776970	0.388485	+	0.921455i	$0.372999\pi$
$840$	−2.16049e18	−0.212196
$841$	2.82242e19	2.75073
$842$	−4.43368e18	−0.428781
$843$	−5.56614e18	−0.534165
$844$	−5.18296e18	−0.493573
$845$	2.55878e18	0.241804
$846$	3.18371e18	0.298556
$847$	4.67037e18	0.434620
$848$	−3.84239e18	−0.354837
$849$	−2.09864e18	−0.192326
$850$	−6.77521e18	−0.616169
$851$	1.23608e18	0.111559
$852$	1.77897e19	1.59335
$853$	−3.39791e18	−0.302025	−0.151013	−	0.988532i	$-0.548253\pi$
$853$	−3.39791e18	−0.302025	−0.151013	+	0.988532i	$0.548253\pi$
$854$	2.32459e19	2.05055
$855$	−1.66412e18	−0.145682
$856$	2.32916e17	0.0202357
$857$	1.52503e18	0.131493	0.0657467	−	0.997836i	$-0.479057\pi$
$857$	1.52503e18	0.131493	0.0657467	+	0.997836i	$0.479057\pi$
$858$	7.26294e18	0.621506
$859$	7.91165e17	0.0671911	0.0335955	−	0.999436i	$-0.489304\pi$
$859$	7.91165e17	0.0671911	0.0335955	+	0.999436i	$0.489304\pi$
$860$	1.51945e19	1.28070
$861$	2.07875e18	0.173893
$862$	−3.37904e19	−2.80540
$863$	−5.10763e18	−0.420871	−0.210436	−	0.977608i	$-0.567488\pi$
$863$	−5.10763e18	−0.420871	−0.210436	+	0.977608i	$0.567488\pi$
$864$	9.84154e17	0.0804867
$865$	5.99256e18	0.486416
$866$	3.39435e19	2.73458
$867$	6.14415e18	0.491290
$868$	−1.34793e19	−1.06976
$869$	2.91043e19	2.29260
$870$	−7.79053e18	−0.609105
$871$	2.07864e17	0.0161310
$872$	5.84722e18	0.450394
$873$	5.09224e18	0.389329
$874$	−2.79392e19	−2.12026
$875$	4.73623e18	0.356764
$876$	1.83928e19	1.37522
$877$	1.59731e19	1.18547	0.592735	−	0.805398i	$-0.298048\pi$
$877$	1.59731e19	1.18547	0.592735	+	0.805398i	$0.298048\pi$
$878$	−2.36762e18	−0.174421
$879$	−2.22789e18	−0.162917
$880$	−7.52010e18	−0.545866
$881$	−5.20802e18	−0.375257	−0.187629	−	0.982240i	$-0.560080\pi$
$881$	−5.20802e18	−0.375257	−0.187629	+	0.982240i	$0.560080\pi$
$882$	5.19634e18	0.371665
$883$	−6.44610e18	−0.457670	−0.228835	−	0.973465i	$-0.573492\pi$
$883$	−6.44610e18	−0.457670	−0.228835	+	0.973465i	$0.573492\pi$
$884$	−5.38909e18	−0.379818
$885$	−3.31744e17	−0.0232098
$886$	−2.13825e19	−1.48505
$887$	−7.23479e18	−0.498795	−0.249398	−	0.968401i	$-0.580233\pi$
$887$	−7.23479e18	−0.498795	−0.249398	+	0.968401i	$0.580233\pi$
$888$	2.17457e18	0.148830
$889$	−1.19883e19	−0.814509
$890$	1.53890e18	0.103794
$891$	2.17411e18	0.145572
$892$	−4.01895e18	−0.267141
$893$	−1.08896e19	−0.718586
$894$	−2.92411e19	−1.91558
$895$	−6.09052e18	−0.396100
$896$	1.40646e19	0.908085
$897$	−3.56227e18	−0.228337
$898$	1.52958e19	0.973364
$899$	−2.55938e19	−1.61695
$900$	−1.01550e19	−0.636945
$901$	1.63047e18	0.101532
$902$	1.85624e19	1.14760
$903$	1.12037e19	0.687690
$904$	2.85722e19	1.74120
$905$	−3.61251e18	−0.218572
$906$	2.54430e19	1.52839
$907$	1.89021e18	0.112736	0.0563680	−	0.998410i	$-0.482048\pi$
$907$	1.89021e18	0.112736	0.0563680	+	0.998410i	$0.482048\pi$
$908$	−1.26221e19	−0.747437
$909$	6.89337e17	0.0405291
$910$	2.63646e18	0.153905
$911$	−2.22775e19	−1.29121	−0.645605	−	0.763671i	$-0.723395\pi$
$911$	−2.22775e19	−1.29121	−0.645605	+	0.763671i	$0.723395\pi$
$912$	−1.91594e19	−1.10259
$913$	−1.00089e19	−0.571906
$914$	−3.58634e19	−2.03471
$915$	−6.06404e18	−0.341606
$916$	−3.18951e19	−1.78404
$917$	1.72785e19	0.959632
$918$	−2.37692e18	−0.131080
$919$	1.55361e19	0.850727	0.425363	−	0.905023i	$-0.360146\pi$
$919$	1.55361e19	0.850727	0.425363	+	0.905023i	$0.360146\pi$
$920$	9.46233e18	0.514490
$921$	−1.72467e19	−0.931147
$922$	−2.08684e19	−1.11877
$923$	−1.14312e19	−0.608529
$924$	−1.83348e19	−0.969187
$925$	−2.26423e18	−0.118850
$926$	−9.36773e18	−0.488273
$927$	−4.44825e18	−0.230235
$928$	−1.57589e19	−0.809960
$929$	5.57626e18	0.284604	0.142302	−	0.989823i	$-0.454550\pi$
$929$	5.57626e18	0.284604	0.142302	+	0.989823i	$0.454550\pi$
$930$	5.18099e18	0.262587
$931$	−1.77737e19	−0.894549
$932$	−4.67780e19	−2.33796
$933$	2.26236e19	1.12287
$934$	−6.03787e19	−2.97598
$935$	3.19107e18	0.156193
$936$	−6.26693e18	−0.304622
$937$	−1.53589e19	−0.741402	−0.370701	−	0.928752i	$-0.620883\pi$
$937$	−1.53589e19	−0.741402	−0.370701	+	0.928752i	$0.620883\pi$
$938$	−7.73167e17	−0.0370642
$939$	1.70803e19	0.813146
$940$	7.00395e18	0.331140
$941$	−8.38429e18	−0.393671	−0.196836	−	0.980437i	$-0.563067\pi$
$941$	−8.38429e18	−0.393671	−0.196836	+	0.980437i	$0.563067\pi$
$942$	−8.70562e18	−0.405947
$943$	−9.10434e18	−0.421621
$944$	−3.81945e18	−0.175664
$945$	7.89206e17	0.0360482
$946$	1.00045e20	4.53839
$947$	2.70215e19	1.21740	0.608702	−	0.793399i	$-0.291691\pi$
$947$	2.70215e19	1.21740	0.608702	+	0.793399i	$0.291691\pi$
$948$	−4.76920e19	−2.13398
$949$	−1.18187e19	−0.525218
$950$	5.11785e19	2.25883
$951$	9.43604e18	0.413634
$952$	1.05551e19	0.459539
$953$	−1.64697e19	−0.712168	−0.356084	−	0.934454i	$-0.615888\pi$
$953$	−1.64697e19	−0.712168	−0.356084	+	0.934454i	$0.615888\pi$
$954$	3.60080e18	0.154645
$955$	3.97104e18	0.169388
$956$	4.55236e19	1.92868
$957$	−3.48132e19	−1.46493
$958$	−3.69904e19	−1.54601
$959$	2.38585e19	0.990426
$960$	−2.64395e18	−0.109016
$961$	−7.39673e18	−0.302927
$962$	−2.65364e18	−0.107945
$963$	−8.50817e16	−0.00343768
$964$	−9.13108e19	−3.66456
$965$	1.29399e18	0.0515824
$966$	1.32501e19	0.524648
$967$	3.71084e19	1.45949	0.729743	−	0.683721i	$-0.239639\pi$
$967$	3.71084e19	1.45949	0.729743	+	0.683721i	$0.239639\pi$
$968$	−3.59853e19	−1.40584
$969$	8.13007e18	0.315493
$970$	1.65063e19	0.636257
$971$	4.23409e19	1.62119	0.810597	−	0.585604i	$-0.199143\pi$
$971$	4.23409e19	1.62119	0.810597	+	0.585604i	$0.199143\pi$
$972$	−3.56262e18	−0.135500
$973$	−5.28166e18	−0.199543
$974$	−4.70204e19	−1.76463
$975$	6.52530e18	0.243260
$976$	−6.98168e19	−2.58545
$977$	−4.15029e19	−1.52673	−0.763367	−	0.645964i	$-0.776455\pi$
$977$	−4.15029e19	−1.52673	−0.763367	+	0.645964i	$0.776455\pi$
$978$	−4.67946e19	−1.70999
$979$	6.87680e18	0.249631
$980$	1.14316e19	0.412228
$981$	−2.13593e18	−0.0765135
$982$	5.86707e19	2.08784
$983$	−1.04911e19	−0.370873	−0.185436	−	0.982656i	$-0.559370\pi$
$983$	−1.04911e19	−0.370873	−0.185436	+	0.982656i	$0.559370\pi$
$984$	−1.60168e19	−0.562482
$985$	1.64606e19	0.574261
$986$	3.80607e19	1.31910
$987$	5.16439e18	0.177811
$988$	4.07080e19	1.39239
$989$	−4.90691e19	−1.66737
$990$	7.04728e18	0.237899
$991$	−2.39742e19	−0.804017	−0.402009	−	0.915636i	$-0.631688\pi$
$991$	−2.39742e19	−0.804017	−0.402009	+	0.915636i	$0.631688\pi$
$992$	1.04802e19	0.349176
$993$	3.14521e19	1.04107
$994$	4.25192e19	1.39821
$995$	−3.19730e18	−0.104456
$996$	1.64011e19	0.532337
$997$	3.65502e18	0.117861	0.0589307	−	0.998262i	$-0.481231\pi$
$997$	3.65502e18	0.117861	0.0589307	+	0.998262i	$0.481231\pi$
$998$	−1.34378e19	−0.430506
$999$	−7.94350e17	−0.0252834

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.3	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.3	✓	31	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-159.673 q^{2} -729.000 q^{3} +17303.4 q^{4} -10788.6 q^{5} +116402. q^{6} +188818. q^{7} -1.45485e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-159.673 q^{2} -729.000 q^{3} +17303.4 q^{4} -10788.6 q^{5} +116402. q^{6} +188818. q^{7} -1.45485e6 q^{8} +531441. q^{9} +1.72264e6 q^{10} +7.69789e6 q^{11} -1.26142e7 q^{12} +8.10554e6 q^{13} -3.01492e7 q^{14} +7.86486e6 q^{15} +9.05501e7 q^{16} -3.84238e7 q^{17} -8.48567e7 q^{18} +2.90246e8 q^{19} -1.86679e8 q^{20} -1.37649e8 q^{21} -1.22914e9 q^{22} +6.02860e8 q^{23} +1.06058e9 q^{24} -1.10431e9 q^{25} -1.29424e9 q^{26} -3.87420e8 q^{27} +3.26720e9 q^{28} +6.20361e9 q^{29} -1.25581e9 q^{30} -4.12563e9 q^{31} -2.54027e9 q^{32} -5.61176e9 q^{33} +6.13525e9 q^{34} -2.03708e9 q^{35} +9.19575e9 q^{36} +2.05036e9 q^{37} -4.63444e10 q^{38} -5.90894e9 q^{39} +1.56957e10 q^{40} -1.51019e10 q^{41} +2.19787e10 q^{42} -8.13939e10 q^{43} +1.33200e11 q^{44} -5.73348e9 q^{45} -9.62605e10 q^{46} -3.75187e10 q^{47} -6.60110e10 q^{48} -6.12366e10 q^{49} +1.76328e11 q^{50} +2.80110e10 q^{51} +1.40254e11 q^{52} -4.24339e10 q^{53} +6.18605e10 q^{54} -8.30491e10 q^{55} -2.74702e11 q^{56} -2.11589e11 q^{57} -9.90549e11 q^{58} -4.21805e10 q^{59} +1.36089e11 q^{60} -7.71030e11 q^{61} +6.58751e11 q^{62} +1.00346e11 q^{63} -3.36173e11 q^{64} -8.74472e10 q^{65} +8.96046e11 q^{66} +2.56447e10 q^{67} -6.64864e11 q^{68} -4.39485e11 q^{69} +3.25266e11 q^{70} -1.41029e12 q^{71} -7.73166e11 q^{72} -1.45810e12 q^{73} -3.27386e11 q^{74} +8.05042e11 q^{75} +5.02224e12 q^{76} +1.45350e12 q^{77} +9.43498e11 q^{78} +3.78082e12 q^{79} -9.76905e11 q^{80} +2.82430e11 q^{81} +2.41136e12 q^{82} -1.30021e12 q^{83} -2.38179e12 q^{84} +4.14538e11 q^{85} +1.29964e13 q^{86} -4.52244e12 q^{87} -1.11993e13 q^{88} +8.93336e11 q^{89} +9.15482e11 q^{90} +1.53048e12 q^{91} +1.04316e13 q^{92} +3.00758e12 q^{93} +5.99072e12 q^{94} -3.13133e12 q^{95} +1.85186e12 q^{96} +9.58195e12 q^{97} +9.77783e12 q^{98} +4.09097e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \)	\( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about