LMFDB - Embedded newform 177.14.a.a.1.12

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:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-44.2174 q^{2} +729.000 q^{3} -6236.82 q^{4} +14897.9 q^{5} -32234.5 q^{6} +473501. q^{7} +638005. q^{8} +531441. q^{9} +O(q^{10})$	\(q-44.2174 q^{2} +729.000 q^{3} -6236.82 q^{4} +14897.9 q^{5} -32234.5 q^{6} +473501. q^{7} +638005. q^{8} +531441. q^{9} -658745. q^{10} -5.62449e6 q^{11} -4.54664e6 q^{12} -1.37488e7 q^{13} -2.09370e7 q^{14} +1.08605e7 q^{15} +2.28811e7 q^{16} +1.90754e8 q^{17} -2.34989e7 q^{18} -2.39269e8 q^{19} -9.29153e7 q^{20} +3.45182e8 q^{21} +2.48700e8 q^{22} +8.48230e8 q^{23} +4.65106e8 q^{24} -9.98757e8 q^{25} +6.07938e8 q^{26} +3.87420e8 q^{27} -2.95314e9 q^{28} -2.26512e9 q^{29} -4.80225e8 q^{30} +6.87064e8 q^{31} -6.23828e9 q^{32} -4.10025e9 q^{33} -8.43464e9 q^{34} +7.05415e9 q^{35} -3.31450e9 q^{36} -1.85095e10 q^{37} +1.05798e10 q^{38} -1.00229e10 q^{39} +9.50491e9 q^{40} -2.65666e10 q^{41} -1.52630e10 q^{42} -8.00165e10 q^{43} +3.50790e10 q^{44} +7.91734e9 q^{45} -3.75065e10 q^{46} -1.28932e11 q^{47} +1.66804e10 q^{48} +1.27314e11 q^{49} +4.41624e10 q^{50} +1.39060e11 q^{51} +8.57491e10 q^{52} +2.46479e11 q^{53} -1.71307e10 q^{54} -8.37929e10 q^{55} +3.02096e11 q^{56} -1.74427e11 q^{57} +1.00157e11 q^{58} +4.21805e10 q^{59} -6.77353e10 q^{60} +6.06790e11 q^{61} -3.03802e10 q^{62} +2.51638e11 q^{63} +8.83981e10 q^{64} -2.04828e11 q^{65} +1.81303e11 q^{66} +1.30921e11 q^{67} -1.18970e12 q^{68} +6.18360e11 q^{69} -3.11916e11 q^{70} -1.05368e12 q^{71} +3.39062e11 q^{72} -1.45214e12 q^{73} +8.18440e11 q^{74} -7.28094e11 q^{75} +1.49228e12 q^{76} -2.66320e12 q^{77} +4.43187e11 q^{78} +9.47431e10 q^{79} +3.40880e11 q^{80} +2.82430e11 q^{81} +1.17471e12 q^{82} +4.49947e12 q^{83} -2.15284e12 q^{84} +2.84182e12 q^{85} +3.53812e12 q^{86} -1.65127e12 q^{87} -3.58845e12 q^{88} +4.97158e11 q^{89} -3.50084e11 q^{90} -6.51009e12 q^{91} -5.29026e12 q^{92} +5.00869e11 q^{93} +5.70103e12 q^{94} -3.56459e12 q^{95} -4.54771e12 q^{96} -1.63570e12 q^{97} -5.62949e12 q^{98} -2.98909e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) $	\( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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 $

$2$	−44.2174	−0.488538	−0.244269	−	0.969708i	$-0.578548\pi$
$2$	−44.2174	−0.488538	−0.244269	+	0.969708i	$0.578548\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−6236.82	−0.761331
$5$	14897.9	0.426402	0.213201	−	0.977008i	$-0.431611\pi$
$5$	14897.9	0.426402	0.213201	+	0.977008i	$0.431611\pi$
$6$	−32234.5	−0.282057
$7$	473501.	1.52119	0.760595	−	0.649227i	$-0.224907\pi$
$7$	473501.	1.52119	0.760595	+	0.649227i	$0.224907\pi$
$8$	638005.	0.860477
$9$	531441.	0.333333
$10$	−658745.	−0.208313
$11$	−5.62449e6	−0.957262	−0.478631	−	0.878016i	$-0.658867\pi$
$11$	−5.62449e6	−0.957262	−0.478631	+	0.878016i	$0.658867\pi$
$12$	−4.54664e6	−0.439555
$13$	−1.37488e7	−0.790014	−0.395007	−	0.918678i	$-0.629258\pi$
$13$	−1.37488e7	−0.790014	−0.395007	+	0.918678i	$0.629258\pi$
$14$	−2.09370e7	−0.743159
$15$	1.08605e7	0.246183
$16$	2.28811e7	0.340956
$17$	1.90754e8	1.91670	0.958352	−	0.285588i	$-0.0921890\pi$
$17$	1.90754e8	1.91670	0.958352	+	0.285588i	$0.0921890\pi$
$18$	−2.34989e7	−0.162846
$19$	−2.39269e8	−1.16678	−0.583388	−	0.812194i	$-0.698273\pi$
$19$	−2.39269e8	−1.16678	−0.583388	+	0.812194i	$0.698273\pi$
$20$	−9.29153e7	−0.324633
$21$	3.45182e8	0.878259
$22$	2.48700e8	0.467659
$23$	8.48230e8	1.19477	0.597383	−	0.801956i	$-0.296207\pi$
$23$	8.48230e8	1.19477	0.597383	+	0.801956i	$0.296207\pi$
$24$	4.65106e8	0.496796
$25$	−9.98757e8	−0.818182
$26$	6.07938e8	0.385951
$27$	3.87420e8	0.192450
$28$	−2.95314e9	−1.15813
$29$	−2.26512e9	−0.707137	−0.353568	−	0.935409i	$-0.615032\pi$
$29$	−2.26512e9	−0.707137	−0.353568	+	0.935409i	$0.615032\pi$
$30$	−4.80225e8	−0.120270
$31$	6.87064e8	0.139042	0.0695210	−	0.997580i	$-0.477853\pi$
$31$	6.87064e8	0.139042	0.0695210	+	0.997580i	$0.477853\pi$
$32$	−6.23828e9	−1.02705
$33$	−4.10025e9	−0.552676
$34$	−8.43464e9	−0.936383
$35$	7.05415e9	0.648638
$36$	−3.31450e9	−0.253777
$37$	−1.85095e10	−1.18599	−0.592997	−	0.805205i	$-0.702055\pi$
$37$	−1.85095e10	−1.18599	−0.592997	+	0.805205i	$0.702055\pi$
$38$	1.05798e10	0.570014
$39$	−1.00229e10	−0.456115
$40$	9.50491e9	0.366909
$41$	−2.65666e10	−0.873456	−0.436728	−	0.899593i	$-0.643863\pi$
$41$	−2.65666e10	−0.873456	−0.436728	+	0.899593i	$0.643863\pi$
$42$	−1.52630e10	−0.429063
$43$	−8.00165e10	−1.93034	−0.965172	−	0.261617i	$-0.915744\pi$
$43$	−8.00165e10	−1.93034	−0.965172	+	0.261617i	$0.915744\pi$
$44$	3.50790e10	0.728793
$45$	7.91734e9	0.142134
$46$	−3.75065e10	−0.583688
$47$	−1.28932e11	−1.74471	−0.872357	−	0.488869i	$-0.837410\pi$
$47$	−1.28932e11	−1.74471	−0.872357	+	0.488869i	$0.837410\pi$
$48$	1.66804e10	0.196851
$49$	1.27314e11	1.31402
$50$	4.41624e10	0.399713
$51$	1.39060e11	1.10661
$52$	8.57491e10	0.601462
$53$	2.46479e11	1.52752	0.763760	−	0.645500i	$-0.223351\pi$
$53$	2.46479e11	1.52752	0.763760	+	0.645500i	$0.223351\pi$
$54$	−1.71307e10	−0.0940191
$55$	−8.37929e10	−0.408178
$56$	3.02096e11	1.30895
$57$	−1.74427e11	−0.673638
$58$	1.00157e11	0.345463
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−6.77353e10	−0.187427
$61$	6.06790e11	1.50798	0.753989	−	0.656888i	$-0.228127\pi$
$61$	6.06790e11	1.50798	0.753989	+	0.656888i	$0.228127\pi$
$62$	−3.03802e10	−0.0679272
$63$	2.51638e11	0.507063
$64$	8.83981e10	0.160795
$65$	−2.04828e11	−0.336863
$66$	1.81303e11	0.270003
$67$	1.30921e11	0.176817	0.0884086	−	0.996084i	$-0.471822\pi$
$67$	1.30921e11	0.176817	0.0884086	+	0.996084i	$0.471822\pi$
$68$	−1.18970e12	−1.45925
$69$	6.18360e11	0.689798
$70$	−3.11916e11	−0.316884
$71$	−1.05368e12	−0.976175	−0.488088	−	0.872795i	$-0.662305\pi$
$71$	−1.05368e12	−0.976175	−0.488088	+	0.872795i	$0.662305\pi$
$72$	3.39062e11	0.286826
$73$	−1.45214e12	−1.12308	−0.561538	−	0.827451i	$-0.689790\pi$
$73$	−1.45214e12	−1.12308	−0.561538	+	0.827451i	$0.689790\pi$
$74$	8.18440e11	0.579403
$75$	−7.28094e11	−0.472377
$76$	1.49228e12	0.888303
$77$	−2.66320e12	−1.45618
$78$	4.43187e11	0.222829
$79$	9.47431e10	0.0438502	0.0219251	−	0.999760i	$-0.493020\pi$
$79$	9.47431e10	0.0438502	0.0219251	+	0.999760i	$0.493020\pi$
$80$	3.40880e11	0.145384
$81$	2.82430e11	0.111111
$82$	1.17471e12	0.426716
$83$	4.49947e12	1.51062	0.755308	−	0.655370i	$-0.227487\pi$
$83$	4.49947e12	1.51062	0.755308	+	0.655370i	$0.227487\pi$
$84$	−2.15284e12	−0.668646
$85$	2.84182e12	0.817286
$86$	3.53812e12	0.943046
$87$	−1.65127e12	−0.408265
$88$	−3.58845e12	−0.823702
$89$	4.97158e11	0.106038	0.0530188	−	0.998594i	$-0.483116\pi$
$89$	4.97158e11	0.106038	0.0530188	+	0.998594i	$0.483116\pi$
$90$	−3.50084e11	−0.0694378
$91$	−6.51009e12	−1.20176
$92$	−5.29026e12	−0.909612
$93$	5.00869e11	0.0802759
$94$	5.70103e12	0.852359
$95$	−3.56459e12	−0.497515
$96$	−4.54771e12	−0.592965
$97$	−1.63570e12	−0.199382	−0.0996911	−	0.995018i	$-0.531785\pi$
$97$	−1.63570e12	−0.199382	−0.0996911	+	0.995018i	$0.531785\pi$
$98$	−5.62949e12	−0.641947
$99$	−2.98909e12	−0.319087
$100$	6.22907e12	0.622907
$101$	7.02588e12	0.658585	0.329293	−	0.944228i	$-0.393190\pi$
$101$	7.02588e12	0.658585	0.329293	+	0.944228i	$0.393190\pi$
$102$	−6.14885e12	−0.540621
$103$	−6.28234e12	−0.518417	−0.259209	−	0.965821i	$-0.583462\pi$
$103$	−6.28234e12	−0.518417	−0.259209	+	0.965821i	$0.583462\pi$
$104$	−8.77183e12	−0.679788
$105$	5.14247e12	0.374491
$106$	−1.08987e13	−0.746251
$107$	−2.66456e12	−0.171645	−0.0858223	−	0.996310i	$-0.527352\pi$
$107$	−2.66456e12	−0.171645	−0.0858223	+	0.996310i	$0.527352\pi$
$108$	−2.41627e12	−0.146518
$109$	2.75266e13	1.57210	0.786050	−	0.618163i	$-0.212123\pi$
$109$	2.75266e13	1.57210	0.786050	+	0.618163i	$0.212123\pi$
$110$	3.70510e12	0.199410
$111$	−1.34934e13	−0.684734
$112$	1.08342e13	0.518658
$113$	5.68272e12	0.256771	0.128386	−	0.991724i	$-0.459021\pi$
$113$	5.68272e12	0.256771	0.128386	+	0.991724i	$0.459021\pi$
$114$	7.71270e12	0.329098
$115$	1.26368e13	0.509450
$116$	1.41271e13	0.538365
$117$	−7.30670e12	−0.263338
$118$	−1.86511e12	−0.0636022
$119$	9.03221e13	2.91567
$120$	6.92908e12	0.211835
$121$	−2.88780e12	−0.0836492
$122$	−2.68307e13	−0.736704
$123$	−1.93671e13	−0.504290
$124$	−4.28509e12	−0.105857
$125$	−3.30652e13	−0.775276
$126$	−1.11268e13	−0.247720
$127$	−3.37035e13	−0.712773	−0.356386	−	0.934339i	$-0.615991\pi$
$127$	−3.37035e13	−0.712773	−0.356386	+	0.934339i	$0.615991\pi$
$128$	4.71953e13	0.948492
$129$	−5.83320e13	−1.11448
$130$	9.05698e12	0.164570
$131$	4.65155e13	0.804144	0.402072	−	0.915608i	$-0.368290\pi$
$131$	4.65155e13	0.804144	0.402072	+	0.915608i	$0.368290\pi$
$132$	2.55726e13	0.420769
$133$	−1.13294e14	−1.77489
$134$	−5.78900e12	−0.0863818
$135$	5.77174e12	0.0820611
$136$	1.21702e14	1.64928
$137$	−1.23746e14	−1.59900	−0.799498	−	0.600669i	$-0.794901\pi$
$137$	−1.23746e14	−1.59900	−0.799498	+	0.600669i	$0.794901\pi$
$138$	−2.73423e13	−0.336993
$139$	1.38699e13	0.163108	0.0815541	−	0.996669i	$-0.474012\pi$
$139$	1.38699e13	0.163108	0.0815541	+	0.996669i	$0.474012\pi$
$140$	−4.39955e13	−0.493828
$141$	−9.39914e13	−1.00731
$142$	4.65908e13	0.476899
$143$	7.73303e13	0.756250
$144$	1.21600e13	0.113652
$145$	−3.37454e13	−0.301524
$146$	6.42098e13	0.548665
$147$	9.28118e13	0.758649
$148$	1.15440e14	0.902934
$149$	−8.35651e13	−0.625625	−0.312813	−	0.949815i	$-0.601271\pi$
$149$	−8.35651e13	−0.625625	−0.312813	+	0.949815i	$0.601271\pi$
$150$	3.21944e13	0.230774
$151$	−5.63763e13	−0.387032	−0.193516	−	0.981097i	$-0.561989\pi$
$151$	−5.63763e13	−0.387032	−0.193516	+	0.981097i	$0.561989\pi$
$152$	−1.52655e14	−1.00398
$153$	1.01374e14	0.638902
$154$	1.17760e14	0.711398
$155$	1.02358e13	0.0592877
$156$	6.25111e13	0.347254
$157$	7.91560e12	0.0421829	0.0210914	−	0.999778i	$-0.493286\pi$
$157$	7.91560e12	0.0421829	0.0210914	+	0.999778i	$0.493286\pi$
$158$	−4.18929e12	−0.0214225
$159$	1.79683e14	0.881914
$160$	−9.29370e13	−0.437934
$161$	4.01638e14	1.81747
$162$	−1.24883e13	−0.0542820
$163$	−1.46318e13	−0.0611053	−0.0305526	−	0.999533i	$-0.509727\pi$
$163$	−1.46318e13	−0.0611053	−0.0305526	+	0.999533i	$0.509727\pi$
$164$	1.65691e14	0.664989
$165$	−6.10850e13	−0.235662
$166$	−1.98955e14	−0.737993
$167$	−2.35885e14	−0.841479	−0.420739	−	0.907182i	$-0.638229\pi$
$167$	−2.35885e14	−0.841479	−0.420739	+	0.907182i	$0.638229\pi$
$168$	2.20228e14	0.755722
$169$	−1.13844e14	−0.375879
$170$	−1.25658e14	−0.399275
$171$	−1.27157e14	−0.388925
$172$	4.99049e14	1.46963
$173$	−9.02605e13	−0.255975	−0.127988	−	0.991776i	$-0.540852\pi$
$173$	−9.02605e13	−0.255975	−0.127988	+	0.991776i	$0.540852\pi$
$174$	7.30148e13	0.199453
$175$	−4.72912e14	−1.24461
$176$	−1.28695e14	−0.326384
$177$	3.07496e13	0.0751646
$178$	−2.19830e13	−0.0518033
$179$	−4.73759e14	−1.07650	−0.538248	−	0.842787i	$-0.680914\pi$
$179$	−4.73759e14	−1.07650	−0.538248	+	0.842787i	$0.680914\pi$
$180$	−4.93790e13	−0.108211
$181$	−3.94362e14	−0.833652	−0.416826	−	0.908986i	$-0.636858\pi$
$181$	−3.94362e14	−0.833652	−0.416826	+	0.908986i	$0.636858\pi$
$182$	2.87859e14	0.587105
$183$	4.42350e14	0.870631
$184$	5.41175e14	1.02807
$185$	−2.75751e14	−0.505710
$186$	−2.21471e13	−0.0392178
$187$	−1.07289e15	−1.83479
$188$	8.04126e14	1.32831
$189$	1.83444e14	0.292753
$190$	1.57617e14	0.243055
$191$	1.12171e15	1.67172	0.835860	−	0.548943i	$-0.184969\pi$
$191$	1.12171e15	1.67172	0.835860	+	0.548943i	$0.184969\pi$
$192$	6.44422e13	0.0928352
$193$	−9.55941e14	−1.33140	−0.665700	−	0.746219i	$-0.731867\pi$
$193$	−9.55941e14	−1.33140	−0.665700	+	0.746219i	$0.731867\pi$
$194$	7.23262e13	0.0974058
$195$	−1.49320e14	−0.194488
$196$	−7.94034e14	−1.00040
$197$	1.29129e15	1.57395	0.786976	−	0.616983i	$-0.211645\pi$
$197$	1.29129e15	1.57395	0.786976	+	0.616983i	$0.211645\pi$
$198$	1.32170e14	0.155886
$199$	−2.34104e14	−0.267217	−0.133609	−	0.991034i	$-0.542657\pi$
$199$	−2.34104e14	−0.267217	−0.133609	+	0.991034i	$0.542657\pi$
$200$	−6.37212e14	−0.704026
$201$	9.54417e13	0.102085
$202$	−3.10666e14	−0.321744
$203$	−1.07253e15	−1.07569
$204$	−8.67290e14	−0.842496
$205$	−3.95786e14	−0.372443
$206$	2.77789e14	0.253266
$207$	4.50784e14	0.398255
$208$	−3.14589e14	−0.269360
$209$	1.34576e15	1.11691
$210$	−2.27387e14	−0.182953
$211$	−2.23736e15	−1.74542	−0.872709	−	0.488241i	$-0.837639\pi$
$211$	−2.23736e15	−1.74542	−0.872709	+	0.488241i	$0.837639\pi$
$212$	−1.53725e15	−1.16295
$213$	−7.68130e14	−0.563595
$214$	1.17820e14	0.0838549
$215$	−1.19208e15	−0.823102
$216$	2.47176e14	0.165599
$217$	3.25325e14	0.211509
$218$	−1.21715e15	−0.768030
$219$	−1.05861e15	−0.648409
$220$	5.22602e14	0.310759
$221$	−2.62265e15	−1.51422
$222$	5.96643e14	0.334518
$223$	−3.19039e15	−1.73725	−0.868626	−	0.495468i	$-0.834996\pi$
$223$	−3.19039e15	−1.73725	−0.868626	+	0.495468i	$0.834996\pi$
$224$	−2.95383e15	−1.56233
$225$	−5.30780e14	−0.272727
$226$	−2.51275e14	−0.125442
$227$	−6.78365e14	−0.329075	−0.164538	−	0.986371i	$-0.552613\pi$
$227$	−6.78365e14	−0.329075	−0.164538	+	0.986371i	$0.552613\pi$
$228$	1.08787e15	0.512862
$229$	2.07816e15	0.952245	0.476123	−	0.879379i	$-0.342042\pi$
$229$	2.07816e15	0.952245	0.476123	+	0.879379i	$0.342042\pi$
$230$	−5.58767e14	−0.248886
$231$	−1.94147e15	−0.840724
$232$	−1.44515e15	−0.608474
$233$	8.65199e13	0.0354244	0.0177122	−	0.999843i	$-0.494362\pi$
$233$	8.65199e13	0.0354244	0.0177122	+	0.999843i	$0.494362\pi$
$234$	3.23083e14	0.128650
$235$	−1.92081e15	−0.743949
$236$	−2.63073e14	−0.0991168
$237$	6.90677e13	0.0253169
$238$	−3.99381e15	−1.42442
$239$	−2.97537e15	−1.03265	−0.516326	−	0.856392i	$-0.672701\pi$
$239$	−2.97537e15	−1.03265	−0.516326	+	0.856392i	$0.672701\pi$
$240$	2.48502e14	0.0839375
$241$	1.38612e15	0.455710	0.227855	−	0.973695i	$-0.426829\pi$
$241$	1.38612e15	0.455710	0.227855	+	0.973695i	$0.426829\pi$
$242$	1.27691e14	0.0408658
$243$	2.05891e14	0.0641500
$244$	−3.78444e15	−1.14807
$245$	1.89671e15	0.560300
$246$	8.56361e14	0.246365
$247$	3.28967e15	0.921769
$248$	4.38350e14	0.119642
$249$	3.28012e15	0.872154
$250$	1.46206e15	0.378751
$251$	−4.33970e15	−1.09542	−0.547710	−	0.836668i	$-0.684500\pi$
$251$	−4.33970e15	−1.09542	−0.547710	+	0.836668i	$0.684500\pi$
$252$	−1.56942e15	−0.386043
$253$	−4.77087e15	−1.14370
$254$	1.49028e15	0.348216
$255$	2.07169e15	0.471860
$256$	−2.81101e15	−0.624169
$257$	6.59104e14	0.142688	0.0713442	−	0.997452i	$-0.477271\pi$
$257$	6.59104e14	0.142688	0.0713442	+	0.997452i	$0.477271\pi$
$258$	2.57929e15	0.544468
$259$	−8.76424e15	−1.80412
$260$	1.27748e15	0.256464
$261$	−1.20378e15	−0.235712
$262$	−2.05679e15	−0.392855
$263$	−3.76994e15	−0.702461	−0.351231	−	0.936289i	$-0.614237\pi$
$263$	−3.76994e15	−0.702461	−0.351231	+	0.936289i	$0.614237\pi$
$264$	−2.61598e15	−0.475564
$265$	3.67201e15	0.651337
$266$	5.00956e15	0.867099
$267$	3.62428e14	0.0612208
$268$	−8.16533e14	−0.134616
$269$	−9.46874e14	−0.152371	−0.0761855	−	0.997094i	$-0.524274\pi$
$269$	−9.46874e14	−0.152371	−0.0761855	+	0.997094i	$0.524274\pi$
$270$	−2.55211e14	−0.0400899
$271$	1.35782e15	0.208230	0.104115	−	0.994565i	$-0.466799\pi$
$271$	1.35782e15	0.208230	0.104115	+	0.994565i	$0.466799\pi$
$272$	4.36467e15	0.653511
$273$	−4.74586e15	−0.693837
$274$	5.47172e15	0.781169
$275$	5.61750e15	0.783214
$276$	−3.85660e15	−0.525165
$277$	1.45446e16	1.93456	0.967280	−	0.253712i	$-0.0816517\pi$
$277$	1.45446e16	1.93456	0.967280	+	0.253712i	$0.0816517\pi$
$278$	−6.13289e14	−0.0796845
$279$	3.65134e14	0.0463473
$280$	4.50058e15	0.558138
$281$	−1.08921e16	−1.31984	−0.659918	−	0.751337i	$-0.729409\pi$
$281$	−1.08921e16	−1.31984	−0.659918	+	0.751337i	$0.729409\pi$
$282$	4.15605e15	0.492110
$283$	1.28425e15	0.148607	0.0743034	−	0.997236i	$-0.476327\pi$
$283$	1.28425e15	0.148607	0.0743034	+	0.997236i	$0.476327\pi$
$284$	6.57159e15	0.743193
$285$	−2.59859e15	−0.287241
$286$	−3.41934e15	−0.369457
$287$	−1.25793e16	−1.32869
$288$	−3.31528e15	−0.342349
$289$	2.64824e16	2.67376
$290$	1.49213e15	0.147306
$291$	−1.19242e15	−0.115113
$292$	9.05673e15	0.855033
$293$	−1.63989e16	−1.51417	−0.757085	−	0.653316i	$-0.773377\pi$
$293$	−1.63989e16	−1.51417	−0.757085	+	0.653316i	$0.773377\pi$
$294$	−4.10390e15	−0.370628
$295$	6.28400e14	0.0555128
$296$	−1.18091e16	−1.02052
$297$	−2.17904e15	−0.184225
$298$	3.69503e15	0.305642
$299$	−1.16622e16	−0.943881
$300$	4.54099e15	0.359635
$301$	−3.78879e16	−2.93642
$302$	2.49281e15	0.189080
$303$	5.12187e15	0.380234
$304$	−5.47474e15	−0.397819
$305$	9.03988e15	0.643004
$306$	−4.48251e15	−0.312128
$307$	1.15451e16	0.787043	0.393522	−	0.919315i	$-0.371257\pi$
$307$	1.15451e16	0.787043	0.393522	+	0.919315i	$0.371257\pi$
$308$	1.66099e16	1.10863
$309$	−4.57983e15	−0.299308
$310$	−4.52599e14	−0.0289643
$311$	−2.58262e15	−0.161852	−0.0809260	−	0.996720i	$-0.525788\pi$
$311$	−2.58262e15	−0.161852	−0.0809260	+	0.996720i	$0.525788\pi$
$312$	−6.39467e15	−0.392476
$313$	1.58178e16	0.950839	0.475420	−	0.879759i	$-0.342296\pi$
$313$	1.58178e16	0.950839	0.475420	+	0.879759i	$0.342296\pi$
$314$	−3.50007e14	−0.0206079
$315$	3.74886e15	0.216213
$316$	−5.90896e14	−0.0333845
$317$	1.23606e15	0.0684157	0.0342079	−	0.999415i	$-0.489109\pi$
$317$	1.23606e15	0.0684157	0.0342079	+	0.999415i	$0.489109\pi$
$318$	−7.94513e15	−0.430848
$319$	1.27401e16	0.676915
$320$	1.31694e15	0.0685634
$321$	−1.94246e15	−0.0990991
$322$	−1.77594e16	−0.887901
$323$	−4.56414e16	−2.23636
$324$	−1.76146e15	−0.0845923
$325$	1.37318e16	0.646375
$326$	6.46980e14	0.0298522
$327$	2.00669e16	0.907653
$328$	−1.69496e16	−0.751589
$329$	−6.10494e16	−2.65404
$330$	2.70102e15	0.115130
$331$	2.43886e15	0.101931	0.0509654	−	0.998700i	$-0.483770\pi$
$331$	2.43886e15	0.101931	0.0509654	+	0.998700i	$0.483770\pi$
$332$	−2.80624e16	−1.15008
$333$	−9.83668e15	−0.395331
$334$	1.04302e16	0.411094
$335$	1.95045e15	0.0753951
$336$	7.89816e15	0.299447
$337$	−3.73870e16	−1.39036	−0.695179	−	0.718837i	$-0.744675\pi$
$337$	−3.73870e16	−1.39036	−0.695179	+	0.718837i	$0.744675\pi$
$338$	5.03390e15	0.183631
$339$	4.14270e15	0.148247
$340$	−1.77240e16	−0.622225
$341$	−3.86438e15	−0.133100
$342$	5.62256e15	0.190005
$343$	1.44062e16	0.477681
$344$	−5.10509e16	−1.66102
$345$	9.21224e15	0.294131
$346$	3.99108e15	0.125054
$347$	6.97870e15	0.214602	0.107301	−	0.994227i	$-0.465779\pi$
$347$	6.97870e15	0.214602	0.107301	+	0.994227i	$0.465779\pi$
$348$	1.02987e16	0.310825
$349$	3.93172e16	1.16471	0.582354	−	0.812935i	$-0.302132\pi$
$349$	3.93172e16	1.16471	0.582354	+	0.812935i	$0.302132\pi$
$350$	2.09109e16	0.608039
$351$	−5.32659e15	−0.152038
$352$	3.50872e16	0.983152
$353$	2.99842e15	0.0824817	0.0412408	−	0.999149i	$-0.486869\pi$
$353$	2.99842e15	0.0824817	0.0412408	+	0.999149i	$0.486869\pi$
$354$	−1.35967e15	−0.0367207
$355$	−1.56975e16	−0.416243
$356$	−3.10069e15	−0.0807296
$357$	6.58448e16	1.68336
$358$	2.09484e16	0.525909
$359$	−2.98048e16	−0.734806	−0.367403	−	0.930062i	$-0.619753\pi$
$359$	−2.98048e16	−0.734806	−0.367403	+	0.930062i	$0.619753\pi$
$360$	5.05130e15	0.122303
$361$	1.51965e16	0.361366
$362$	1.74377e16	0.407270
$363$	−2.10520e15	−0.0482949
$364$	4.06023e16	0.914937
$365$	−2.16338e16	−0.478882
$366$	−1.95596e16	−0.425336
$367$	−2.33299e16	−0.498406	−0.249203	−	0.968451i	$-0.580169\pi$
$367$	−2.33299e16	−0.498406	−0.249203	+	0.968451i	$0.580169\pi$
$368$	1.94085e16	0.407362
$369$	−1.41186e16	−0.291152
$370$	1.21930e16	0.247058
$371$	1.16708e17	2.32365
$372$	−3.12383e15	−0.0611165
$373$	−8.12135e16	−1.56142	−0.780712	−	0.624892i	$-0.785143\pi$
$373$	−8.12135e16	−1.56142	−0.780712	+	0.624892i	$0.785143\pi$
$374$	4.74405e16	0.896364
$375$	−2.41045e16	−0.447606
$376$	−8.22592e16	−1.50129
$377$	3.11427e16	0.558648
$378$	−8.11141e15	−0.143021
$379$	−1.05622e17	−1.83062	−0.915309	−	0.402752i	$-0.868054\pi$
$379$	−1.05622e17	−1.83062	−0.915309	+	0.402752i	$0.868054\pi$
$380$	2.22317e16	0.378774
$381$	−2.45699e16	−0.411520
$382$	−4.95991e16	−0.816698
$383$	7.65692e14	0.0123955	0.00619773	−	0.999981i	$-0.498027\pi$
$383$	7.65692e14	0.0123955	0.00619773	+	0.999981i	$0.498027\pi$
$384$	3.44053e16	0.547612
$385$	−3.96760e16	−0.620917
$386$	4.22692e16	0.650439
$387$	−4.25241e16	−0.643448
$388$	1.02016e16	0.151796
$389$	−6.70250e16	−0.980764	−0.490382	−	0.871507i	$-0.663143\pi$
$389$	−6.70250e16	−0.980764	−0.490382	+	0.871507i	$0.663143\pi$
$390$	6.60254e15	0.0950147
$391$	1.61803e17	2.29001
$392$	8.12269e16	1.13068
$393$	3.39098e16	0.464273
$394$	−5.70973e16	−0.768935
$395$	1.41147e15	0.0186978
$396$	1.86424e16	0.242931
$397$	1.20104e17	1.53964	0.769820	−	0.638262i	$-0.220346\pi$
$397$	1.20104e17	1.53964	0.769820	+	0.638262i	$0.220346\pi$
$398$	1.03515e16	0.130546
$399$	−8.25912e16	−1.02473
$400$	−2.28527e16	−0.278964
$401$	−6.36394e16	−0.764342	−0.382171	−	0.924092i	$-0.624823\pi$
$401$	−6.36394e16	−0.764342	−0.382171	+	0.924092i	$0.624823\pi$
$402$	−4.22018e15	−0.0498726
$403$	−9.44633e15	−0.109845
$404$	−4.38192e16	−0.501401
$405$	4.20760e15	0.0473780
$406$	4.74246e16	0.525515
$407$	1.04106e17	1.13531
$408$	8.87207e16	0.952212
$409$	6.97030e16	0.736292	0.368146	−	0.929768i	$-0.379993\pi$
$409$	6.97030e16	0.736292	0.368146	+	0.929768i	$0.379993\pi$
$410$	1.75006e16	0.181953
$411$	−9.02108e16	−0.923180
$412$	3.91819e16	0.394687
$413$	1.99725e16	0.198042
$414$	−1.99325e16	−0.194563
$415$	6.70325e16	0.644129
$416$	8.57692e16	0.811381
$417$	1.01111e16	0.0941706
$418$	−5.95062e16	−0.545653
$419$	4.45589e16	0.402294	0.201147	−	0.979561i	$-0.435533\pi$
$419$	4.45589e16	0.402294	0.201147	+	0.979561i	$0.435533\pi$
$420$	−3.20727e16	−0.285112
$421$	−9.19806e16	−0.805123	−0.402562	−	0.915393i	$-0.631880\pi$
$421$	−9.19806e16	−0.805123	−0.402562	+	0.915393i	$0.631880\pi$
$422$	9.89301e16	0.852702
$423$	−6.85197e16	−0.581572
$424$	1.57255e17	1.31440
$425$	−1.90517e17	−1.56821
$426$	3.39647e16	0.275337
$427$	2.87316e17	2.29392
$428$	1.66184e16	0.130678
$429$	5.63738e16	0.436621
$430$	5.27104e16	0.402116
$431$	−3.66494e16	−0.275400	−0.137700	−	0.990474i	$-0.543971\pi$
$431$	−3.66494e16	−0.275400	−0.137700	+	0.990474i	$0.543971\pi$
$432$	8.86462e15	0.0656169
$433$	−4.93879e16	−0.360122	−0.180061	−	0.983655i	$-0.557630\pi$
$433$	−4.93879e16	−0.360122	−0.180061	+	0.983655i	$0.557630\pi$
$434$	−1.43850e16	−0.103330
$435$	−2.46004e16	−0.174085
$436$	−1.71678e17	−1.19689
$437$	−2.02955e17	−1.39402
$438$	4.68089e16	0.316772
$439$	−5.19055e16	−0.346094	−0.173047	−	0.984914i	$-0.555361\pi$
$439$	−5.19055e16	−0.346094	−0.173047	+	0.984914i	$0.555361\pi$
$440$	−5.34603e16	−0.351228
$441$	6.76598e16	0.438006
$442$	1.15967e17	0.739755
$443$	−1.57657e17	−0.991033	−0.495517	−	0.868598i	$-0.665021\pi$
$443$	−1.57657e17	−0.991033	−0.495517	+	0.868598i	$0.665021\pi$
$444$	8.41559e16	0.521309
$445$	7.40660e15	0.0452146
$446$	1.41071e17	0.848713
$447$	−6.09190e16	−0.361205
$448$	4.18566e16	0.244600
$449$	−1.00305e17	−0.577724	−0.288862	−	0.957371i	$-0.593277\pi$
$449$	−1.00305e17	−0.577724	−0.288862	+	0.957371i	$0.593277\pi$
$450$	2.34697e16	0.133238
$451$	1.49424e17	0.836127
$452$	−3.54421e16	−0.195488
$453$	−4.10983e16	−0.223453
$454$	2.99955e16	0.160766
$455$	−9.69864e16	−0.512433
$456$	−1.11285e17	−0.579650
$457$	−5.63806e16	−0.289517	−0.144759	−	0.989467i	$-0.546241\pi$
$457$	−5.63806e16	−0.289517	−0.144759	+	0.989467i	$0.546241\pi$
$458$	−9.18909e16	−0.465208
$459$	7.39019e16	0.368870
$460$	−7.88136e16	−0.387860
$461$	−1.20880e17	−0.586541	−0.293270	−	0.956030i	$-0.594744\pi$
$461$	−1.20880e17	−0.586541	−0.293270	+	0.956030i	$0.594744\pi$
$462$	8.58469e16	0.410726
$463$	1.67790e17	0.791572	0.395786	−	0.918343i	$-0.370472\pi$
$463$	1.67790e17	0.791572	0.395786	+	0.918343i	$0.370472\pi$
$464$	−5.18284e16	−0.241102
$465$	7.46188e15	0.0342298
$466$	−3.82569e15	−0.0173062
$467$	3.70336e17	1.65210	0.826049	−	0.563598i	$-0.190583\pi$
$467$	3.70336e17	1.65210	0.826049	+	0.563598i	$0.190583\pi$
$468$	4.55706e16	0.200487
$469$	6.19914e16	0.268972
$470$	8.49332e16	0.363447
$471$	5.77048e15	0.0243543
$472$	2.69114e16	0.112025
$473$	4.50052e17	1.84784
$474$	−3.05399e15	−0.0123683
$475$	2.38971e17	0.954634
$476$	−5.63323e17	−2.21979
$477$	1.30989e17	0.509173
$478$	1.31563e17	0.504489
$479$	6.66464e16	0.252114	0.126057	−	0.992023i	$-0.459768\pi$
$479$	6.66464e16	0.252114	0.126057	+	0.992023i	$0.459768\pi$
$480$	−6.77511e16	−0.252842
$481$	2.54484e17	0.936951
$482$	−6.12904e16	−0.222632
$483$	2.92794e17	1.04931
$484$	1.80107e16	0.0636847
$485$	−2.43684e16	−0.0850169
$486$	−9.10397e15	−0.0313397
$487$	3.56614e16	0.121132	0.0605662	−	0.998164i	$-0.480709\pi$
$487$	3.56614e16	0.121132	0.0605662	+	0.998164i	$0.480709\pi$
$488$	3.87135e17	1.29758
$489$	−1.06666e16	−0.0352791
$490$	−8.38674e16	−0.273727
$491$	2.91939e16	0.0940293	0.0470146	−	0.998894i	$-0.485029\pi$
$491$	2.91939e16	0.0940293	0.0470146	+	0.998894i	$0.485029\pi$
$492$	1.20789e17	0.383932
$493$	−4.32079e17	−1.35537
$494$	−1.45461e17	−0.450319
$495$	−4.45310e16	−0.136059
$496$	1.57208e16	0.0474071
$497$	−4.98916e17	−1.48495
$498$	−1.45038e17	−0.426080
$499$	6.02093e17	1.74586	0.872932	−	0.487842i	$-0.162216\pi$
$499$	6.02093e17	1.74586	0.872932	+	0.487842i	$0.162216\pi$
$500$	2.06222e17	0.590241
$501$	−1.71960e17	−0.485828
$502$	1.91890e17	0.535154
$503$	−2.10322e17	−0.579020	−0.289510	−	0.957175i	$-0.593492\pi$
$503$	−2.10322e17	−0.579020	−0.289510	+	0.957175i	$0.593492\pi$
$504$	1.60546e17	0.436316
$505$	1.04671e17	0.280822
$506$	2.10955e17	0.558743
$507$	−8.29925e16	−0.217014
$508$	2.10203e17	0.542656
$509$	4.81081e17	1.22618	0.613088	−	0.790015i	$-0.289927\pi$
$509$	4.81081e17	1.22618	0.613088	+	0.790015i	$0.289927\pi$
$510$	−9.16047e16	−0.230522
$511$	−6.87589e17	−1.70841
$512$	−2.62328e17	−0.643562
$513$	−9.26976e16	−0.224546
$514$	−2.91438e16	−0.0697086
$515$	−9.35935e16	−0.221054
$516$	3.63807e17	0.848491
$517$	7.25177e17	1.67015
$518$	3.87532e17	0.881381
$519$	−6.57999e16	−0.147787
$520$	−1.30682e17	−0.289863
$521$	5.80316e16	0.127122	0.0635608	−	0.997978i	$-0.479754\pi$
$521$	5.80316e16	0.127122	0.0635608	+	0.997978i	$0.479754\pi$
$522$	5.32278e16	0.115154
$523$	−2.89417e17	−0.618391	−0.309195	−	0.950999i	$-0.600060\pi$
$523$	−2.89417e17	−0.618391	−0.309195	+	0.950999i	$0.600060\pi$
$524$	−2.90109e17	−0.612220
$525$	−3.44753e17	−0.718576
$526$	1.66697e17	0.343179
$527$	1.31060e17	0.266502
$528$	−9.38185e16	−0.188438
$529$	2.15458e17	0.427466
$530$	−1.62367e17	−0.318203
$531$	2.24165e16	0.0433963
$532$	7.06594e17	1.35128
$533$	3.65260e17	0.690042
$534$	−1.60256e16	−0.0299087
$535$	−3.96962e16	−0.0731896
$536$	8.35285e16	0.152147
$537$	−3.45370e17	−0.621515
$538$	4.18683e16	0.0744390
$539$	−7.16076e17	−1.25786
$540$	−3.59973e16	−0.0624756
$541$	−2.95677e17	−0.507032	−0.253516	−	0.967331i	$-0.581587\pi$
$541$	−2.95677e17	−0.507032	−0.253516	+	0.967331i	$0.581587\pi$
$542$	−6.00395e16	−0.101728
$543$	−2.87490e17	−0.481309
$544$	−1.18998e18	−1.96854
$545$	4.10087e17	0.670346
$546$	2.09849e17	0.338965
$547$	−9.39910e17	−1.50027	−0.750134	−	0.661286i	$-0.770011\pi$
$547$	−9.39910e17	−1.50027	−0.750134	+	0.661286i	$0.770011\pi$
$548$	7.71781e17	1.21736
$549$	3.22473e17	0.502659
$550$	−2.48391e17	−0.382630
$551$	5.41971e17	0.825070
$552$	3.94517e17	0.593555
$553$	4.48609e16	0.0667044
$554$	−6.43122e17	−0.945105
$555$	−2.01023e17	−0.291972
$556$	−8.65039e16	−0.124179
$557$	6.16218e17	0.874330	0.437165	−	0.899381i	$-0.355983\pi$
$557$	6.16218e17	0.874330	0.437165	+	0.899381i	$0.355983\pi$
$558$	−1.61453e16	−0.0226424
$559$	1.10013e18	1.52500
$560$	1.61407e17	0.221157
$561$	−7.82139e17	−1.05932
$562$	4.81620e17	0.644790
$563$	−6.77170e17	−0.896175	−0.448088	−	0.893990i	$-0.647895\pi$
$563$	−6.77170e17	−0.896175	−0.448088	+	0.893990i	$0.647895\pi$
$564$	5.86208e17	0.766897
$565$	8.46603e16	0.109488
$566$	−5.67863e16	−0.0726001
$567$	1.33731e17	0.169021
$568$	−6.72250e17	−0.839976
$569$	−4.29749e17	−0.530866	−0.265433	−	0.964129i	$-0.585515\pi$
$569$	−4.29749e17	−0.530866	−0.265433	+	0.964129i	$0.585515\pi$
$570$	1.14903e17	0.140328
$571$	1.18834e18	1.43485	0.717423	−	0.696637i	$-0.245321\pi$
$571$	1.18834e18	1.43485	0.717423	+	0.696637i	$0.245321\pi$
$572$	−4.82295e17	−0.575757
$573$	8.17726e17	0.965168
$574$	5.56224e17	0.649117
$575$	−8.47176e17	−0.977536
$576$	4.69784e16	0.0535984
$577$	−2.62221e17	−0.295818	−0.147909	−	0.989001i	$-0.547254\pi$
$577$	−2.62221e17	−0.295818	−0.147909	+	0.989001i	$0.547254\pi$
$578$	−1.17098e18	−1.30623
$579$	−6.96881e17	−0.768685
$580$	2.10464e17	0.229560
$581$	2.13050e18	2.29793
$582$	5.27258e16	0.0562372
$583$	−1.38632e18	−1.46224
$584$	−9.26471e17	−0.966381
$585$	−1.08854e17	−0.112288
$586$	7.25116e17	0.739729
$587$	−1.57347e18	−1.58749	−0.793745	−	0.608250i	$-0.791872\pi$
$587$	−1.57347e18	−1.58749	−0.793745	+	0.608250i	$0.791872\pi$
$588$	−5.78851e17	−0.577583
$589$	−1.64393e17	−0.162231
$590$	−2.77862e16	−0.0271201
$591$	9.41347e17	0.908722
$592$	−4.23518e17	−0.404371
$593$	−8.97746e17	−0.847809	−0.423904	−	0.905707i	$-0.639341\pi$
$593$	−8.97746e17	−0.847809	−0.423904	+	0.905707i	$0.639341\pi$
$594$	9.63516e16	0.0900010
$595$	1.34561e18	1.24325
$596$	5.21181e17	0.476308
$597$	−1.70662e17	−0.154278
$598$	5.15672e17	0.461122
$599$	9.76390e17	0.863673	0.431836	−	0.901952i	$-0.357866\pi$
$599$	9.76390e17	0.863673	0.431836	+	0.901952i	$0.357866\pi$
$600$	−4.64527e17	−0.406470
$601$	1.28535e18	1.11260	0.556299	−	0.830982i	$-0.312221\pi$
$601$	1.28535e18	1.11260	0.556299	+	0.830982i	$0.312221\pi$
$602$	1.67530e18	1.43455
$603$	6.95770e16	0.0589390
$604$	3.51609e17	0.294659
$605$	−4.30220e16	−0.0356682
$606$	−2.26476e17	−0.185759
$607$	−2.35015e18	−1.90708	−0.953539	−	0.301269i	$-0.902590\pi$
$607$	−2.35015e18	−1.90708	−0.953539	+	0.301269i	$0.902590\pi$
$608$	1.49262e18	1.19833
$609$	−7.81877e17	−0.621049
$610$	−3.99720e17	−0.314132
$611$	1.77267e18	1.37835
$612$	−6.32254e17	−0.486416
$613$	1.19210e18	0.907444	0.453722	−	0.891143i	$-0.350096\pi$
$613$	1.19210e18	0.907444	0.453722	+	0.891143i	$0.350096\pi$
$614$	−5.10495e17	−0.384500
$615$	−2.88528e17	−0.215030
$616$	−1.69914e18	−1.25301
$617$	−1.32168e18	−0.964435	−0.482218	−	0.876051i	$-0.660169\pi$
$617$	−1.32168e18	−0.964435	−0.482218	+	0.876051i	$0.660169\pi$
$618$	2.02508e17	0.146223
$619$	−1.31387e18	−0.938780	−0.469390	−	0.882991i	$-0.655526\pi$
$619$	−1.31387e18	−0.938780	−0.469390	+	0.882991i	$0.655526\pi$
$620$	−6.38387e16	−0.0451376
$621$	3.28622e17	0.229933
$622$	1.14197e17	0.0790708
$623$	2.35405e17	0.161303
$624$	−2.29336e17	−0.155515
$625$	7.26584e17	0.487603
$626$	−6.99421e17	−0.464521
$627$	9.81063e17	0.644848
$628$	−4.93682e16	−0.0321151
$629$	−3.53075e18	−2.27320
$630$	−1.65765e17	−0.105628
$631$	2.19393e17	0.138367	0.0691834	−	0.997604i	$-0.477961\pi$
$631$	2.19393e17	0.138367	0.0691834	+	0.997604i	$0.477961\pi$
$632$	6.04465e16	0.0377320
$633$	−1.63103e18	−1.00772
$634$	−5.46555e16	−0.0334237
$635$	−5.02110e17	−0.303928
$636$	−1.12065e18	−0.671429
$637$	−1.75042e18	−1.03809
$638$	−5.63335e17	−0.330699
$639$	−5.59967e17	−0.325392
$640$	7.03109e17	0.404439
$641$	9.07607e17	0.516798	0.258399	−	0.966038i	$-0.416805\pi$
$641$	9.07607e17	0.516798	0.258399	+	0.966038i	$0.416805\pi$
$642$	8.58906e16	0.0484136
$643$	1.88340e18	1.05092	0.525462	−	0.850817i	$-0.323893\pi$
$643$	1.88340e18	1.05092	0.525462	+	0.850817i	$0.323893\pi$
$644$	−2.50494e18	−1.38369
$645$	−8.69023e17	−0.475218
$646$	2.01814e18	1.09255
$647$	1.34923e18	0.723118	0.361559	−	0.932349i	$-0.382245\pi$
$647$	1.34923e18	0.723118	0.361559	+	0.932349i	$0.382245\pi$
$648$	1.80191e17	0.0956085
$649$	−2.37244e17	−0.124625
$650$	−6.07182e17	−0.315778
$651$	2.37162e17	0.122115
$652$	9.12560e16	0.0465213
$653$	1.71614e18	0.866199	0.433100	−	0.901346i	$-0.357420\pi$
$653$	1.71614e18	0.866199	0.433100	+	0.901346i	$0.357420\pi$
$654$	−8.87305e17	−0.443422
$655$	6.92981e17	0.342889
$656$	−6.07875e17	−0.297810
$657$	−7.71726e17	−0.374359
$658$	2.69944e18	1.29660
$659$	−1.28135e18	−0.609415	−0.304708	−	0.952446i	$-0.598559\pi$
$659$	−1.28135e18	−0.609415	−0.304708	+	0.952446i	$0.598559\pi$
$660$	3.80977e17	0.179417
$661$	−1.79244e18	−0.835864	−0.417932	−	0.908478i	$-0.637245\pi$
$661$	−1.79244e18	−0.835864	−0.417932	+	0.908478i	$0.637245\pi$
$662$	−1.07840e17	−0.0497971
$663$	−1.91191e18	−0.874237
$664$	2.87069e18	1.29985
$665$	−1.68784e18	−0.756815
$666$	4.34952e17	0.193134
$667$	−1.92134e18	−0.844863
$668$	1.47117e18	0.640644
$669$	−2.32580e18	−1.00300
$670$	−8.62438e16	−0.0368334
$671$	−3.41289e18	−1.44353
$672$	−2.15334e18	−0.902013
$673$	6.34042e16	0.0263039	0.0131519	−	0.999914i	$-0.495813\pi$
$673$	6.34042e16	0.0263039	0.0131519	+	0.999914i	$0.495813\pi$
$674$	1.65316e18	0.679242
$675$	−3.86939e17	−0.157459
$676$	7.10026e17	0.286168
$677$	−9.29177e17	−0.370913	−0.185457	−	0.982652i	$-0.559376\pi$
$677$	−9.29177e17	−0.370913	−0.185457	+	0.982652i	$0.559376\pi$
$678$	−1.83179e17	−0.0724242
$679$	−7.74504e17	−0.303298
$680$	1.81310e18	0.703256
$681$	−4.94528e17	−0.189992
$682$	1.70873e17	0.0650242
$683$	−3.07516e18	−1.15913	−0.579566	−	0.814925i	$-0.696778\pi$
$683$	−3.07516e18	−1.15913	−0.579566	+	0.814925i	$0.696778\pi$
$684$	7.93057e17	0.296101
$685$	−1.84355e18	−0.681814
$686$	−6.37005e17	−0.233365
$687$	1.51498e18	0.549779
$688$	−1.83087e18	−0.658162
$689$	−3.38880e18	−1.20676
$690$	−4.07341e17	−0.143694
$691$	−2.73730e18	−0.956565	−0.478283	−	0.878206i	$-0.658741\pi$
$691$	−2.73730e18	−0.956565	−0.478283	+	0.878206i	$0.658741\pi$
$692$	5.62939e17	0.194882
$693$	−1.41533e18	−0.485392
$694$	−3.08580e17	−0.104841
$695$	2.06631e17	0.0695497
$696$	−1.05352e18	−0.351303
$697$	−5.06768e18	−1.67416
$698$	−1.73850e18	−0.569004
$699$	6.30730e16	0.0204523
$700$	2.94947e18	0.947560
$701$	−4.73652e17	−0.150762	−0.0753811	−	0.997155i	$-0.524017\pi$
$701$	−4.73652e17	−0.150762	−0.0753811	+	0.997155i	$0.524017\pi$
$702$	2.35528e17	0.0742764
$703$	4.42873e18	1.38379
$704$	−4.97194e17	−0.153923
$705$	−1.40027e18	−0.429519
$706$	−1.32582e17	−0.0402954
$707$	3.32676e18	1.00183
$708$	−1.91780e17	−0.0572251
$709$	2.44513e18	0.722938	0.361469	−	0.932384i	$-0.382275\pi$
$709$	2.44513e18	0.722938	0.361469	+	0.932384i	$0.382275\pi$
$710$	6.94103e17	0.203350
$711$	5.03503e16	0.0146167
$712$	3.17189e17	0.0912428
$713$	5.82788e17	0.166123
$714$	−2.91148e18	−0.822387
$715$	1.15206e18	0.322466
$716$	2.95475e18	0.819570
$717$	−2.16904e18	−0.596202
$718$	1.31789e18	0.358981
$719$	4.08649e18	1.10309	0.551547	−	0.834144i	$-0.314038\pi$
$719$	4.08649e18	1.10309	0.551547	+	0.834144i	$0.314038\pi$
$720$	1.81158e17	0.0484614
$721$	−2.97469e18	−0.788611
$722$	−6.71950e17	−0.176541
$723$	1.01048e18	0.263104
$724$	2.45957e18	0.634685
$725$	2.26230e18	0.578566
$726$	9.30866e16	0.0235939
$727$	7.13650e18	1.79272	0.896358	−	0.443331i	$-0.146203\pi$
$727$	7.13650e18	1.79272	0.896358	+	0.443331i	$0.146203\pi$
$728$	−4.15347e18	−1.03409
$729$	1.50095e17	0.0370370
$730$	9.56589e17	0.233952
$731$	−1.52635e19	−3.69990
$732$	−2.75886e18	−0.662838
$733$	2.80764e18	0.668598	0.334299	−	0.942467i	$-0.391501\pi$
$733$	2.80764e18	0.668598	0.334299	+	0.942467i	$0.391501\pi$
$734$	1.03159e18	0.243490
$735$	1.38270e18	0.323489
$736$	−5.29150e18	−1.22708
$737$	−7.36366e17	−0.169260
$738$	6.24287e17	0.142239
$739$	4.67894e18	1.05672	0.528359	−	0.849021i	$-0.322808\pi$
$739$	4.67894e18	1.05672	0.528359	+	0.849021i	$0.322808\pi$
$740$	1.71981e18	0.385013
$741$	2.39817e18	0.532183
$742$	−5.16053e18	−1.13519
$743$	7.01746e18	1.53022	0.765108	−	0.643902i	$-0.222686\pi$
$743$	7.01746e18	1.53022	0.765108	+	0.643902i	$0.222686\pi$
$744$	3.19557e17	0.0690755
$745$	−1.24494e18	−0.266768
$746$	3.59105e18	0.762814
$747$	2.39120e18	0.503539
$748$	6.69145e18	1.39688
$749$	−1.26167e18	−0.261104
$750$	1.06584e18	0.218672
$751$	6.91693e18	1.40687	0.703434	−	0.710760i	$-0.251649\pi$
$751$	6.91693e18	1.40687	0.703434	+	0.710760i	$0.251649\pi$
$752$	−2.95011e18	−0.594870
$753$	−3.16364e18	−0.632441
$754$	−1.37705e18	−0.272920
$755$	−8.39887e17	−0.165031
$756$	−1.14411e18	−0.222882
$757$	−4.84887e18	−0.936520	−0.468260	−	0.883591i	$-0.655119\pi$
$757$	−4.84887e18	−0.936520	−0.468260	+	0.883591i	$0.655119\pi$
$758$	4.67031e18	0.894326
$759$	−3.47796e18	−0.660318
$760$	−2.27423e18	−0.428100
$761$	−9.04988e18	−1.68905	−0.844525	−	0.535517i	$-0.820117\pi$
$761$	−9.04988e18	−1.68905	−0.844525	+	0.535517i	$0.820117\pi$
$762$	1.08642e18	0.201043
$763$	1.30339e19	2.39146
$764$	−6.99590e18	−1.27273
$765$	1.51026e18	0.272429
$766$	−3.38569e16	−0.00605565
$767$	−5.79934e17	−0.102851
$768$	−2.04922e18	−0.360364
$769$	−2.90761e18	−0.507007	−0.253504	−	0.967334i	$-0.581583\pi$
$769$	−2.90761e18	−0.507007	−0.253504	+	0.967334i	$0.581583\pi$
$770$	1.75437e18	0.303341
$771$	4.80487e17	0.0823811
$772$	5.96204e18	1.01364
$773$	1.55467e18	0.262103	0.131052	−	0.991376i	$-0.458165\pi$
$773$	1.55467e18	0.262103	0.131052	+	0.991376i	$0.458165\pi$
$774$	1.88030e18	0.314349
$775$	−6.86209e17	−0.113762
$776$	−1.04358e18	−0.171564
$777$	−6.38913e18	−1.04161
$778$	2.96367e18	0.479140
$779$	6.35656e18	1.01913
$780$	9.31282e17	0.148070
$781$	5.92639e18	0.934456
$782$	−7.15451e18	−1.11876
$783$	−8.77552e17	−0.136088
$784$	2.91309e18	0.448022
$785$	1.17926e17	0.0179869
$786$	−1.49940e18	−0.226815
$787$	5.65108e18	0.847805	0.423902	−	0.905708i	$-0.360660\pi$
$787$	5.65108e18	0.847805	0.423902	+	0.905708i	$0.360660\pi$
$788$	−8.05352e18	−1.19830
$789$	−2.74829e18	−0.405566
$790$	−6.24115e16	−0.00913458
$791$	2.69077e18	0.390597
$792$	−1.90705e18	−0.274567
$793$	−8.34267e18	−1.19132
$794$	−5.31068e18	−0.752172
$795$	2.67690e18	0.376050
$796$	1.46007e18	0.203441
$797$	−2.10870e18	−0.291430	−0.145715	−	0.989327i	$-0.546548\pi$
$797$	−2.10870e18	−0.291430	−0.145715	+	0.989327i	$0.546548\pi$
$798$	3.65197e18	0.500620
$799$	−2.45943e19	−3.34410
$800$	6.23052e18	0.840310
$801$	2.64210e17	0.0353458
$802$	2.81397e18	0.373410
$803$	8.16754e18	1.07508
$804$	−5.95253e17	−0.0777208
$805$	5.98354e18	0.774971
$806$	4.17692e17	0.0536634
$807$	−6.90271e17	−0.0879714
$808$	4.48255e18	0.566697
$809$	4.06041e18	0.509219	0.254609	−	0.967044i	$-0.418053\pi$
$809$	4.06041e18	0.509219	0.254609	+	0.967044i	$0.418053\pi$
$810$	−1.86049e17	−0.0231459
$811$	7.82447e17	0.0965650	0.0482825	−	0.998834i	$-0.484625\pi$
$811$	7.82447e17	0.0965650	0.0482825	+	0.998834i	$0.484625\pi$
$812$	6.68920e18	0.818955
$813$	9.89854e17	0.120222
$814$	−4.60331e18	−0.554640
$815$	−2.17983e17	−0.0260554
$816$	3.18184e18	0.377305
$817$	1.91454e19	2.25228
$818$	−3.08208e18	−0.359706
$819$	−3.45973e18	−0.400587
$820$	2.46845e18	0.283553
$821$	8.67478e18	0.988617	0.494308	−	0.869287i	$-0.335421\pi$
$821$	8.67478e18	0.988617	0.494308	+	0.869287i	$0.335421\pi$
$822$	3.98888e18	0.451008
$823$	−2.87394e18	−0.322388	−0.161194	−	0.986923i	$-0.551534\pi$
$823$	−2.87394e18	−0.322388	−0.161194	+	0.986923i	$0.551534\pi$
$824$	−4.00816e18	−0.446086
$825$	4.09516e18	0.452189
$826$	−8.83132e17	−0.0967510
$827$	−8.01024e18	−0.870682	−0.435341	−	0.900266i	$-0.643372\pi$
$827$	−8.01024e18	−0.870682	−0.435341	+	0.900266i	$0.643372\pi$
$828$	−2.81146e18	−0.303204
$829$	−9.97891e18	−1.06777	−0.533886	−	0.845556i	$-0.679269\pi$
$829$	−9.97891e18	−1.06777	−0.533886	+	0.845556i	$0.679269\pi$
$830$	−2.96400e18	−0.314681
$831$	1.06030e19	1.11692
$832$	−1.21537e18	−0.127030
$833$	2.42856e19	2.51858
$834$	−4.47088e17	−0.0460059
$835$	−3.51418e18	−0.358808
$836$	−8.39330e18	−0.850338
$837$	2.66183e17	0.0267586
$838$	−1.97028e18	−0.196536
$839$	1.57978e19	1.56366	0.781831	−	0.623491i	$-0.214286\pi$
$839$	1.57978e19	1.56366	0.781831	+	0.623491i	$0.214286\pi$
$840$	3.28092e18	0.322241
$841$	−5.12988e18	−0.499958
$842$	4.06714e18	0.393333
$843$	−7.94033e18	−0.762008
$844$	1.39540e19	1.32884
$845$	−1.69604e18	−0.160275
$846$	3.02976e18	0.284120
$847$	−1.36737e18	−0.127246
$848$	5.63973e18	0.520817
$849$	9.36221e17	0.0857982
$850$	8.42415e18	0.766131
$851$	−1.57003e19	−1.41699
$852$	4.79069e18	0.429082
$853$	7.10936e17	0.0631919	0.0315960	−	0.999501i	$-0.489941\pi$
$853$	7.10936e17	0.0631919	0.0315960	+	0.999501i	$0.489941\pi$
$854$	−1.27043e19	−1.12067
$855$	−1.89437e18	−0.165838
$856$	−1.70000e18	−0.147696
$857$	1.28817e19	1.11070	0.555350	−	0.831617i	$-0.312584\pi$
$857$	1.28817e19	1.11070	0.555350	+	0.831617i	$0.312584\pi$
$858$	−2.49270e18	−0.213306
$859$	2.25964e19	1.91904	0.959519	−	0.281645i	$-0.0908800\pi$
$859$	2.25964e19	1.91904	0.959519	+	0.281645i	$0.0908800\pi$
$860$	7.43476e18	0.626653
$861$	−9.17032e18	−0.767121
$862$	1.62054e18	0.134543
$863$	−1.69103e19	−1.39341	−0.696707	−	0.717356i	$-0.745352\pi$
$863$	−1.69103e19	−1.39341	−0.696707	+	0.717356i	$0.745352\pi$
$864$	−2.41684e18	−0.197655
$865$	−1.34469e18	−0.109148
$866$	2.18381e18	0.175933
$867$	1.93057e19	1.54369
$868$	−2.02899e18	−0.161029
$869$	−5.32882e17	−0.0419761
$870$	1.08776e18	0.0850471
$871$	−1.80002e18	−0.139688
$872$	1.75621e19	1.35276
$873$	−8.69276e17	−0.0664608
$874$	8.97414e18	0.681033
$875$	−1.56564e19	−1.17934
$876$	6.60236e18	0.493654
$877$	−2.01142e19	−1.49281	−0.746405	−	0.665491i	$-0.768222\pi$
$877$	−2.01142e19	−1.49281	−0.746405	+	0.665491i	$0.768222\pi$
$878$	2.29513e18	0.169080
$879$	−1.19548e19	−0.874207
$880$	−1.91728e18	−0.139171
$881$	−1.66197e19	−1.19751	−0.598754	−	0.800933i	$-0.704337\pi$
$881$	−1.66197e19	−1.19751	−0.598754	+	0.800933i	$0.704337\pi$
$882$	−2.99174e18	−0.213982
$883$	1.56643e19	1.11216	0.556079	−	0.831129i	$-0.312305\pi$
$883$	1.56643e19	1.11216	0.556079	+	0.831129i	$0.312305\pi$
$884$	1.63570e19	1.15282
$885$	4.58104e17	0.0320503
$886$	6.97117e18	0.484157
$887$	1.06391e19	0.733504	0.366752	−	0.930319i	$-0.380470\pi$
$887$	1.06391e19	0.733504	0.366752	+	0.930319i	$0.380470\pi$
$888$	−8.60885e18	−0.589197
$889$	−1.59586e19	−1.08426
$890$	−3.27500e17	−0.0220890
$891$	−1.58852e18	−0.106362
$892$	1.98979e19	1.32262
$893$	3.08494e19	2.03569
$894$	2.69368e18	0.176462
$895$	−7.05799e18	−0.459020
$896$	2.23470e19	1.44284
$897$	−8.50174e18	−0.544950
$898$	4.43521e18	0.282240
$899$	−1.55628e18	−0.0983217
$900$	3.31038e18	0.207636
$901$	4.70168e19	2.92781
$902$	−6.60713e18	−0.408479
$903$	−2.76203e19	−1.69534
$904$	3.62560e18	0.220945
$905$	−5.87516e18	−0.355471
$906$	1.81726e18	0.109165
$907$	8.52215e18	0.508278	0.254139	−	0.967168i	$-0.418208\pi$
$907$	8.52215e18	0.508278	0.254139	+	0.967168i	$0.418208\pi$
$908$	4.23084e18	0.250535
$909$	3.73384e18	0.219528
$910$	4.28849e18	0.250343
$911$	−1.45978e19	−0.846092	−0.423046	−	0.906108i	$-0.639039\pi$
$911$	−1.45978e19	−0.846092	−0.423046	+	0.906108i	$0.639039\pi$
$912$	−3.99109e18	−0.229681
$913$	−2.53073e19	−1.44606
$914$	2.49300e18	0.141440
$915$	6.59007e18	0.371239
$916$	−1.29611e19	−0.724974
$917$	2.20251e19	1.22326
$918$	−3.26775e18	−0.180207
$919$	3.06603e19	1.67890	0.839450	−	0.543437i	$-0.182877\pi$
$919$	3.06603e19	1.67890	0.839450	+	0.543437i	$0.182877\pi$
$920$	8.06235e18	0.438370
$921$	8.41639e18	0.454400
$922$	5.34499e18	0.286547
$923$	1.44868e19	0.771192
$924$	1.21086e19	0.640069
$925$	1.84864e19	0.970358
$926$	−7.41925e18	−0.386713
$927$	−3.33869e18	−0.172806
$928$	1.41304e19	0.726262
$929$	−3.57344e19	−1.82383	−0.911916	−	0.410378i	$-0.865397\pi$
$929$	−3.57344e19	−1.82383	−0.911916	+	0.410378i	$0.865397\pi$
$930$	−3.29945e17	−0.0167225
$931$	−3.04622e19	−1.53316
$932$	−5.39609e17	−0.0269697
$933$	−1.88273e18	−0.0934453
$934$	−1.63753e19	−0.807112
$935$	−1.59838e19	−0.782357
$936$	−4.66171e18	−0.226596
$937$	3.54595e19	1.71169	0.855844	−	0.517233i	$-0.173038\pi$
$937$	3.54595e19	1.71169	0.855844	+	0.517233i	$0.173038\pi$
$938$	−2.74110e18	−0.131403
$939$	1.15312e19	0.548967
$940$	1.19798e19	0.566392
$941$	−3.26670e19	−1.53383	−0.766915	−	0.641749i	$-0.778209\pi$
$941$	−3.26670e19	−1.53383	−0.766915	+	0.641749i	$0.778209\pi$
$942$	−2.55155e17	−0.0118980
$943$	−2.25346e19	−1.04358
$944$	9.65139e17	0.0443886
$945$	2.73292e18	0.124830
$946$	−1.99001e19	−0.902742
$947$	−1.43139e19	−0.644886	−0.322443	−	0.946589i	$-0.604504\pi$
$947$	−1.43139e19	−0.644886	−0.322443	+	0.946589i	$0.604504\pi$
$948$	−4.30763e17	−0.0192745
$949$	1.99652e19	0.887246
$950$	−1.05667e19	−0.466375
$951$	9.01091e17	0.0394998
$952$	5.76259e19	2.50887
$953$	5.17993e18	0.223986	0.111993	−	0.993709i	$-0.464277\pi$
$953$	5.17993e18	0.223986	0.111993	+	0.993709i	$0.464277\pi$
$954$	−5.79200e18	−0.248750
$955$	1.67111e19	0.712824
$956$	1.85568e19	0.786190
$957$	9.28755e18	0.390817
$958$	−2.94693e18	−0.123167
$959$	−5.85938e19	−2.43238
$960$	9.60051e17	0.0395851
$961$	−2.39455e19	−0.980667
$962$	−1.12526e19	−0.457736
$963$	−1.41605e18	−0.0572149
$964$	−8.64496e18	−0.346946
$965$	−1.42415e19	−0.567712
$966$	−1.29466e19	−0.512630
$967$	7.35443e18	0.289252	0.144626	−	0.989486i	$-0.453802\pi$
$967$	7.35443e18	0.289252	0.144626	+	0.989486i	$0.453802\pi$
$968$	−1.84243e18	−0.0719782
$969$	−3.32726e19	−1.29117
$970$	1.07751e18	0.0415340
$971$	4.34657e18	0.166426	0.0832131	−	0.996532i	$-0.473482\pi$
$971$	4.34657e18	0.166426	0.0832131	+	0.996532i	$0.473482\pi$
$972$	−1.28411e18	−0.0488394
$973$	6.56739e18	0.248119
$974$	−1.57685e18	−0.0591777
$975$	1.00105e19	0.373185
$976$	1.38841e19	0.514153
$977$	1.39032e19	0.511445	0.255722	−	0.966750i	$-0.417687\pi$
$977$	1.39032e19	0.511445	0.255722	+	0.966750i	$0.417687\pi$
$978$	4.71649e17	0.0172352
$979$	−2.79626e18	−0.101506
$980$	−1.18294e19	−0.426573
$981$	1.46288e19	0.524033
$982$	−1.29088e18	−0.0459369
$983$	−5.29076e19	−1.87034	−0.935170	−	0.354199i	$-0.884753\pi$
$983$	−5.29076e19	−1.87034	−0.935170	+	0.354199i	$0.884753\pi$
$984$	−1.23563e19	−0.433930
$985$	1.92374e19	0.671136
$986$	1.91054e19	0.662150
$987$	−4.45050e19	−1.53231
$988$	−2.05171e19	−0.701771
$989$	−6.78724e19	−2.30631
$990$	1.96904e18	0.0664702
$991$	−7.55353e18	−0.253321	−0.126660	−	0.991946i	$-0.540426\pi$
$991$	−7.55353e18	−0.253321	−0.126660	+	0.991946i	$0.540426\pi$
$992$	−4.28610e18	−0.142803
$993$	1.77793e18	0.0588498
$994$	2.20608e19	0.725453
$995$	−3.48765e18	−0.113942
$996$	−2.04575e19	−0.663998
$997$	3.67023e19	1.18352	0.591759	−	0.806115i	$-0.298434\pi$
$997$	3.67023e19	1.18352	0.591759	+	0.806115i	$0.298434\pi$
$998$	−2.66230e19	−0.852920
$999$	−7.17094e18	−0.228245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.12	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.12	✓	30	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)

\(f(q)\)	\(=\)	\(q-44.2174 q^{2} +729.000 q^{3} -6236.82 q^{4} +14897.9 q^{5} -32234.5 q^{6} +473501. q^{7} +638005. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-44.2174 q^{2} +729.000 q^{3} -6236.82 q^{4} +14897.9 q^{5} -32234.5 q^{6} +473501. q^{7} +638005. q^{8} +531441. q^{9} -658745. q^{10} -5.62449e6 q^{11} -4.54664e6 q^{12} -1.37488e7 q^{13} -2.09370e7 q^{14} +1.08605e7 q^{15} +2.28811e7 q^{16} +1.90754e8 q^{17} -2.34989e7 q^{18} -2.39269e8 q^{19} -9.29153e7 q^{20} +3.45182e8 q^{21} +2.48700e8 q^{22} +8.48230e8 q^{23} +4.65106e8 q^{24} -9.98757e8 q^{25} +6.07938e8 q^{26} +3.87420e8 q^{27} -2.95314e9 q^{28} -2.26512e9 q^{29} -4.80225e8 q^{30} +6.87064e8 q^{31} -6.23828e9 q^{32} -4.10025e9 q^{33} -8.43464e9 q^{34} +7.05415e9 q^{35} -3.31450e9 q^{36} -1.85095e10 q^{37} +1.05798e10 q^{38} -1.00229e10 q^{39} +9.50491e9 q^{40} -2.65666e10 q^{41} -1.52630e10 q^{42} -8.00165e10 q^{43} +3.50790e10 q^{44} +7.91734e9 q^{45} -3.75065e10 q^{46} -1.28932e11 q^{47} +1.66804e10 q^{48} +1.27314e11 q^{49} +4.41624e10 q^{50} +1.39060e11 q^{51} +8.57491e10 q^{52} +2.46479e11 q^{53} -1.71307e10 q^{54} -8.37929e10 q^{55} +3.02096e11 q^{56} -1.74427e11 q^{57} +1.00157e11 q^{58} +4.21805e10 q^{59} -6.77353e10 q^{60} +6.06790e11 q^{61} -3.03802e10 q^{62} +2.51638e11 q^{63} +8.83981e10 q^{64} -2.04828e11 q^{65} +1.81303e11 q^{66} +1.30921e11 q^{67} -1.18970e12 q^{68} +6.18360e11 q^{69} -3.11916e11 q^{70} -1.05368e12 q^{71} +3.39062e11 q^{72} -1.45214e12 q^{73} +8.18440e11 q^{74} -7.28094e11 q^{75} +1.49228e12 q^{76} -2.66320e12 q^{77} +4.43187e11 q^{78} +9.47431e10 q^{79} +3.40880e11 q^{80} +2.82430e11 q^{81} +1.17471e12 q^{82} +4.49947e12 q^{83} -2.15284e12 q^{84} +2.84182e12 q^{85} +3.53812e12 q^{86} -1.65127e12 q^{87} -3.58845e12 q^{88} +4.97158e11 q^{89} -3.50084e11 q^{90} -6.51009e12 q^{91} -5.29026e12 q^{92} +5.00869e11 q^{93} +5.70103e12 q^{94} -3.56459e12 q^{95} -4.54771e12 q^{96} -1.63570e12 q^{97} -5.62949e12 q^{98} -2.98909e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \)	\( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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