LMFDB - Embedded newform 177.12.a.a.1.7

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$135.996742959$
Analytic rank:	$1$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-49.4794 q^{2} -243.000 q^{3} +400.209 q^{4} +6608.87 q^{5} +12023.5 q^{6} -17933.1 q^{7} +81531.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-49.4794 q^{2} -243.000 q^{3} +400.209 q^{4} +6608.87 q^{5} +12023.5 q^{6} -17933.1 q^{7} +81531.7 q^{8} +59049.0 q^{9} -327003. q^{10} +978139. q^{11} -97250.8 q^{12} +494374. q^{13} +887320. q^{14} -1.60596e6 q^{15} -4.85376e6 q^{16} -9.53772e6 q^{17} -2.92171e6 q^{18} +6.89884e6 q^{19} +2.64493e6 q^{20} +4.35775e6 q^{21} -4.83977e7 q^{22} +2.50424e7 q^{23} -1.98122e7 q^{24} -5.15090e6 q^{25} -2.44613e7 q^{26} -1.43489e7 q^{27} -7.17700e6 q^{28} -2.14527e8 q^{29} +7.94617e7 q^{30} +2.69999e8 q^{31} +7.31844e7 q^{32} -2.37688e8 q^{33} +4.71921e8 q^{34} -1.18518e8 q^{35} +2.36319e7 q^{36} -2.91399e8 q^{37} -3.41350e8 q^{38} -1.20133e8 q^{39} +5.38833e8 q^{40} -6.14837e8 q^{41} -2.15619e8 q^{42} -9.63348e8 q^{43} +3.91460e8 q^{44} +3.90247e8 q^{45} -1.23908e9 q^{46} -2.17341e9 q^{47} +1.17946e9 q^{48} -1.65573e9 q^{49} +2.54863e8 q^{50} +2.31767e9 q^{51} +1.97853e8 q^{52} +2.60466e9 q^{53} +7.09975e8 q^{54} +6.46440e9 q^{55} -1.46212e9 q^{56} -1.67642e9 q^{57} +1.06147e10 q^{58} +7.14924e8 q^{59} -6.42718e8 q^{60} +3.67189e9 q^{61} -1.33594e10 q^{62} -1.05893e9 q^{63} +6.31939e9 q^{64} +3.26726e9 q^{65} +1.17606e10 q^{66} +1.09092e10 q^{67} -3.81708e9 q^{68} -6.08530e9 q^{69} +5.86419e9 q^{70} -1.23634e10 q^{71} +4.81436e9 q^{72} +1.39653e10 q^{73} +1.44182e10 q^{74} +1.25167e9 q^{75} +2.76098e9 q^{76} -1.75411e10 q^{77} +5.94410e9 q^{78} +7.86947e9 q^{79} -3.20779e10 q^{80} +3.48678e9 q^{81} +3.04218e10 q^{82} +3.44891e10 q^{83} +1.74401e9 q^{84} -6.30336e10 q^{85} +4.76659e10 q^{86} +5.21301e10 q^{87} +7.97493e10 q^{88} +6.24194e10 q^{89} -1.93092e10 q^{90} -8.86567e9 q^{91} +1.00222e10 q^{92} -6.56098e10 q^{93} +1.07539e11 q^{94} +4.55936e10 q^{95} -1.77838e10 q^{96} -1.46326e11 q^{97} +8.19245e10 q^{98} +5.77581e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) $	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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 $

$2$	−49.4794	−1.09335	−0.546675	−	0.837345i	$-0.684107\pi$
$2$	−49.4794	−1.09335	−0.546675	+	0.837345i	$0.684107\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	400.209	0.195414
$5$	6608.87	0.945785	0.472893	−	0.881120i	$-0.343210\pi$
$5$	6608.87	0.945785	0.472893	+	0.881120i	$0.343210\pi$
$6$	12023.5	0.631246
$7$	−17933.1	−0.403289	−0.201645	−	0.979459i	$-0.564629\pi$
$7$	−17933.1	−0.403289	−0.201645	+	0.979459i	$0.564629\pi$
$8$	81531.7	0.879694
$9$	59049.0	0.333333
$10$	−327003.	−1.03407
$11$	978139.	1.83122	0.915610	−	0.402067i	$-0.131708\pi$
$11$	978139.	1.83122	0.915610	+	0.402067i	$0.131708\pi$
$12$	−97250.8	−0.112823
$13$	494374.	0.369290	0.184645	−	0.982805i	$-0.440887\pi$
$13$	494374.	0.369290	0.184645	+	0.982805i	$0.440887\pi$
$14$	887320.	0.440937
$15$	−1.60596e6	−0.546049
$16$	−4.85376e6	−1.15723
$17$	−9.53772e6	−1.62920	−0.814602	−	0.580020i	$-0.803045\pi$
$17$	−9.53772e6	−1.62920	−0.814602	+	0.580020i	$0.803045\pi$
$18$	−2.92171e6	−0.364450
$19$	6.89884e6	0.639192	0.319596	−	0.947554i	$-0.396453\pi$
$19$	6.89884e6	0.639192	0.319596	+	0.947554i	$0.396453\pi$
$20$	2.64493e6	0.184820
$21$	4.35775e6	0.232839
$22$	−4.83977e7	−2.00217
$23$	2.50424e7	0.811283	0.405641	−	0.914032i	$-0.367048\pi$
$23$	2.50424e7	0.811283	0.405641	+	0.914032i	$0.367048\pi$
$24$	−1.98122e7	−0.507891
$25$	−5.15090e6	−0.105490
$26$	−2.44613e7	−0.403763
$27$	−1.43489e7	−0.192450
$28$	−7.17700e6	−0.0788086
$29$	−2.14527e8	−1.94220	−0.971099	−	0.238679i	$-0.923286\pi$
$29$	−2.14527e8	−1.94220	−0.971099	+	0.238679i	$0.923286\pi$
$30$	7.94617e7	0.597023
$31$	2.69999e8	1.69384	0.846921	−	0.531718i	$-0.178454\pi$
$31$	2.69999e8	1.69384	0.846921	+	0.531718i	$0.178454\pi$
$32$	7.31844e7	0.385561
$33$	−2.37688e8	−1.05726
$34$	4.71921e8	1.78129
$35$	−1.18518e8	−0.381425
$36$	2.36319e7	0.0651382
$37$	−2.91399e8	−0.690841	−0.345420	−	0.938448i	$-0.612264\pi$
$37$	−2.91399e8	−0.690841	−0.345420	+	0.938448i	$0.612264\pi$
$38$	−3.41350e8	−0.698860
$39$	−1.20133e8	−0.213210
$40$	5.38833e8	0.832001
$41$	−6.14837e8	−0.828798	−0.414399	−	0.910095i	$-0.636008\pi$
$41$	−6.14837e8	−0.828798	−0.414399	+	0.910095i	$0.636008\pi$
$42$	−2.15619e8	−0.254575
$43$	−9.63348e8	−0.999325	−0.499662	−	0.866220i	$-0.666543\pi$
$43$	−9.63348e8	−0.999325	−0.499662	+	0.866220i	$0.666543\pi$
$44$	3.91460e8	0.357847
$45$	3.90247e8	0.315262
$46$	−1.23908e9	−0.887016
$47$	−2.17341e9	−1.38231	−0.691153	−	0.722708i	$-0.742897\pi$
$47$	−2.17341e9	−1.38231	−0.691153	+	0.722708i	$0.742897\pi$
$48$	1.17946e9	0.668126
$49$	−1.65573e9	−0.837358
$50$	2.54863e8	0.115338
$51$	2.31767e9	0.940622
$52$	1.97853e8	0.0721646
$53$	2.60466e9	0.855526	0.427763	−	0.903891i	$-0.359302\pi$
$53$	2.60466e9	0.855526	0.427763	+	0.903891i	$0.359302\pi$
$54$	7.09975e8	0.210415
$55$	6.46440e9	1.73194
$56$	−1.46212e9	−0.354771
$57$	−1.67642e9	−0.369038
$58$	1.06147e10	2.12350
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−6.42718e8	−0.106706
$61$	3.67189e9	0.556641	0.278321	−	0.960488i	$-0.410222\pi$
$61$	3.67189e9	0.556641	0.278321	+	0.960488i	$0.410222\pi$
$62$	−1.33594e10	−1.85196
$63$	−1.05893e9	−0.134430
$64$	6.31939e9	0.735674
$65$	3.26726e9	0.349269
$66$	1.17606e10	1.15595
$67$	1.09092e10	0.987151	0.493575	−	0.869703i	$-0.335690\pi$
$67$	1.09092e10	0.987151	0.493575	+	0.869703i	$0.335690\pi$
$68$	−3.81708e9	−0.318370
$69$	−6.08530e9	−0.468394
$70$	5.86419e9	0.417031
$71$	−1.23634e10	−0.813237	−0.406618	−	0.913598i	$-0.633292\pi$
$71$	−1.23634e10	−0.813237	−0.406618	+	0.913598i	$0.633292\pi$
$72$	4.81436e9	0.293231
$73$	1.39653e10	0.788450	0.394225	−	0.919014i	$-0.371013\pi$
$73$	1.39653e10	0.788450	0.394225	+	0.919014i	$0.371013\pi$
$74$	1.44182e10	0.755331
$75$	1.25167e9	0.0609049
$76$	2.76098e9	0.124907
$77$	−1.75411e10	−0.738512
$78$	5.94410e9	0.233113
$79$	7.86947e9	0.287738	0.143869	−	0.989597i	$-0.454046\pi$
$79$	7.86947e9	0.287738	0.143869	+	0.989597i	$0.454046\pi$
$80$	−3.20779e10	−1.09449
$81$	3.48678e9	0.111111
$82$	3.04218e10	0.906167
$83$	3.44891e10	0.961064	0.480532	−	0.876977i	$-0.340444\pi$
$83$	3.44891e10	0.961064	0.480532	+	0.876977i	$0.340444\pi$
$84$	1.74401e9	0.0455002
$85$	−6.30336e10	−1.54088
$86$	4.76659e10	1.09261
$87$	5.21301e10	1.12133
$88$	7.97493e10	1.61091
$89$	6.24194e10	1.18488	0.592440	−	0.805614i	$-0.298165\pi$
$89$	6.24194e10	1.18488	0.592440	+	0.805614i	$0.298165\pi$
$90$	−1.93092e10	−0.344691
$91$	−8.86567e9	−0.148931
$92$	1.00222e10	0.158536
$93$	−6.56098e10	−0.977940
$94$	1.07539e11	1.51134
$95$	4.55936e10	0.604538
$96$	−1.77838e10	−0.222604
$97$	−1.46326e11	−1.73012	−0.865059	−	0.501669i	$-0.832719\pi$
$97$	−1.46326e11	−1.73012	−0.865059	+	0.501669i	$0.832719\pi$
$98$	8.19245e10	0.915525
$99$	5.77581e10	0.610407
$100$	−2.06144e9	−0.0206144
$101$	−8.77236e10	−0.830517	−0.415259	−	0.909703i	$-0.636309\pi$
$101$	−8.77236e10	−0.830517	−0.415259	+	0.909703i	$0.636309\pi$
$102$	−1.14677e11	−1.02843
$103$	−7.67208e10	−0.652091	−0.326046	−	0.945354i	$-0.605716\pi$
$103$	−7.67208e10	−0.652091	−0.326046	+	0.945354i	$0.605716\pi$
$104$	4.03071e10	0.324862
$105$	2.87998e10	0.220216
$106$	−1.28877e11	−0.935389
$107$	1.37621e11	0.948580	0.474290	−	0.880369i	$-0.342705\pi$
$107$	1.37621e11	0.948580	0.474290	+	0.880369i	$0.342705\pi$
$108$	−5.74256e9	−0.0376075
$109$	−1.27808e11	−0.795635	−0.397817	−	0.917465i	$-0.630232\pi$
$109$	−1.27808e11	−0.795635	−0.397817	+	0.917465i	$0.630232\pi$
$110$	−3.19854e11	−1.89362
$111$	7.08099e10	0.398857
$112$	8.70432e10	0.466698
$113$	−7.20783e10	−0.368022	−0.184011	−	0.982924i	$-0.558908\pi$
$113$	−7.20783e10	−0.368022	−0.184011	+	0.982924i	$0.558908\pi$
$114$	8.29481e10	0.403487
$115$	1.65502e11	0.767299
$116$	−8.58557e10	−0.379533
$117$	2.91923e10	0.123097
$118$	−3.53740e10	−0.142342
$119$	1.71041e11	0.657041
$120$	−1.30936e11	−0.480356
$121$	6.71443e11	2.35337
$122$	−1.81683e11	−0.608604
$123$	1.49405e11	0.478507
$124$	1.08056e11	0.331001
$125$	−3.56741e11	−1.04556
$126$	5.23954e10	0.146979
$127$	−5.25572e11	−1.41160	−0.705800	−	0.708411i	$-0.749412\pi$
$127$	−5.25572e11	−1.41160	−0.705800	+	0.708411i	$0.749412\pi$
$128$	−4.62561e11	−1.18991
$129$	2.34094e11	0.576960
$130$	−1.61662e11	−0.381873
$131$	8.43429e11	1.91010	0.955051	−	0.296443i	$-0.0958005\pi$
$131$	8.43429e11	1.91010	0.955051	+	0.296443i	$0.0958005\pi$
$132$	−9.51247e10	−0.206603
$133$	−1.23718e11	−0.257779
$134$	−5.39783e11	−1.07930
$135$	−9.48301e10	−0.182016
$136$	−7.77626e11	−1.43320
$137$	−3.77154e11	−0.667660	−0.333830	−	0.942633i	$-0.608341\pi$
$137$	−3.77154e11	−0.667660	−0.333830	+	0.942633i	$0.608341\pi$
$138$	3.01097e11	0.512119
$139$	2.28213e11	0.373043	0.186522	−	0.982451i	$-0.440279\pi$
$139$	2.28213e11	0.373043	0.186522	+	0.982451i	$0.440279\pi$
$140$	−4.74319e10	−0.0745360
$141$	5.28140e11	0.798075
$142$	6.11733e11	0.889153
$143$	4.83566e11	0.676251
$144$	−2.86610e11	−0.385743
$145$	−1.41778e12	−1.83690
$146$	−6.90994e11	−0.862052
$147$	4.02342e11	0.483449
$148$	−1.16620e11	−0.135000
$149$	3.80245e10	0.0424170	0.0212085	−	0.999775i	$-0.493249\pi$
$149$	3.80245e10	0.0424170	0.0212085	+	0.999775i	$0.493249\pi$
$150$	−6.19318e10	−0.0665904
$151$	2.56888e11	0.266299	0.133150	−	0.991096i	$-0.457491\pi$
$151$	2.56888e11	0.266299	0.133150	+	0.991096i	$0.457491\pi$
$152$	5.62474e11	0.562293
$153$	−5.63193e11	−0.543068
$154$	8.67922e11	0.807452
$155$	1.78439e12	1.60201
$156$	−4.80782e10	−0.0416642
$157$	1.51998e11	0.127172	0.0635859	−	0.997976i	$-0.479746\pi$
$157$	1.51998e11	0.127172	0.0635859	+	0.997976i	$0.479746\pi$
$158$	−3.89377e11	−0.314598
$159$	−6.32931e11	−0.493938
$160$	4.83666e11	0.364658
$161$	−4.49088e11	−0.327182
$162$	−1.72524e11	−0.121483
$163$	−1.83131e12	−1.24661	−0.623304	−	0.781980i	$-0.714210\pi$
$163$	−1.83131e12	−1.24661	−0.623304	+	0.781980i	$0.714210\pi$
$164$	−2.46063e11	−0.161959
$165$	−1.57085e12	−0.999937
$166$	−1.70650e12	−1.05078
$167$	−2.90687e12	−1.73175	−0.865874	−	0.500262i	$-0.833237\pi$
$167$	−2.90687e12	−1.73175	−0.865874	+	0.500262i	$0.833237\pi$
$168$	3.55295e11	0.204827
$169$	−1.54775e12	−0.863625
$170$	3.11886e12	1.68472
$171$	4.07370e11	0.213064
$172$	−3.85540e11	−0.195283
$173$	−2.33226e12	−1.14426	−0.572129	−	0.820164i	$-0.693882\pi$
$173$	−2.33226e12	−1.14426	−0.572129	+	0.820164i	$0.693882\pi$
$174$	−2.57936e12	−1.22600
$175$	9.23718e10	0.0425432
$176$	−4.74765e12	−2.11914
$177$	−1.73727e11	−0.0751646
$178$	−3.08847e12	−1.29549
$179$	−9.95026e11	−0.404709	−0.202355	−	0.979312i	$-0.564859\pi$
$179$	−9.95026e11	−0.404709	−0.202355	+	0.979312i	$0.564859\pi$
$180$	1.56180e11	0.0616067
$181$	2.52323e12	0.965440	0.482720	−	0.875775i	$-0.339649\pi$
$181$	2.52323e12	0.965440	0.482720	+	0.875775i	$0.339649\pi$
$182$	4.38668e11	0.162833
$183$	−8.92269e11	−0.321377
$184$	2.04175e12	0.713680
$185$	−1.92582e12	−0.653387
$186$	3.24633e12	1.06923
$187$	−9.32921e12	−2.98343
$188$	−8.69820e11	−0.270123
$189$	2.57321e11	0.0776131
$190$	−2.25594e12	−0.660972
$191$	−4.70874e12	−1.34036	−0.670179	−	0.742199i	$-0.733783\pi$
$191$	−4.70874e12	−1.34036	−0.670179	+	0.742199i	$0.733783\pi$
$192$	−1.53561e12	−0.424742
$193$	3.14793e11	0.0846175	0.0423088	−	0.999105i	$-0.486529\pi$
$193$	3.14793e11	0.0846175	0.0423088	+	0.999105i	$0.486529\pi$
$194$	7.24010e12	1.89163
$195$	−7.93943e11	−0.201650
$196$	−6.62638e11	−0.163632
$197$	−7.57251e11	−0.181834	−0.0909171	−	0.995858i	$-0.528980\pi$
$197$	−7.57251e11	−0.181834	−0.0909171	+	0.995858i	$0.528980\pi$
$198$	−2.85784e12	−0.667388
$199$	7.43156e12	1.68806	0.844030	−	0.536295i	$-0.180177\pi$
$199$	7.43156e12	1.68806	0.844030	+	0.536295i	$0.180177\pi$
$200$	−4.19962e11	−0.0927993
$201$	−2.65095e12	−0.569932
$202$	4.34051e12	0.908046
$203$	3.84714e12	0.783267
$204$	9.27551e11	0.183811
$205$	−4.06338e12	−0.783865
$206$	3.79610e12	0.712964
$207$	1.47873e12	0.270428
$208$	−2.39958e12	−0.427352
$209$	6.74802e12	1.17050
$210$	−1.42500e12	−0.240773
$211$	−9.96014e12	−1.63950	−0.819751	−	0.572720i	$-0.805888\pi$
$211$	−9.96014e12	−1.63950	−0.819751	+	0.572720i	$0.805888\pi$
$212$	1.04241e12	0.167182
$213$	3.00431e12	0.469523
$214$	−6.80940e12	−1.03713
$215$	−6.36665e12	−0.945146
$216$	−1.16989e12	−0.169297
$217$	−4.84193e12	−0.683109
$218$	6.32388e12	0.869908
$219$	−3.39357e12	−0.455212
$220$	2.58711e12	0.338446
$221$	−4.71520e12	−0.601648
$222$	−3.50363e12	−0.436090
$223$	3.30929e12	0.401844	0.200922	−	0.979607i	$-0.435606\pi$
$223$	3.30929e12	0.401844	0.200922	+	0.979607i	$0.435606\pi$
$224$	−1.31242e12	−0.155493
$225$	−3.04156e11	−0.0351635
$226$	3.56639e12	0.402376
$227$	8.21619e12	0.904749	0.452374	−	0.891828i	$-0.350577\pi$
$227$	8.21619e12	0.904749	0.452374	+	0.891828i	$0.350577\pi$
$228$	−6.70917e11	−0.0721153
$229$	−8.95761e12	−0.939933	−0.469967	−	0.882684i	$-0.655734\pi$
$229$	−8.95761e12	−0.939933	−0.469967	+	0.882684i	$0.655734\pi$
$230$	−8.18893e12	−0.838927
$231$	4.26248e12	0.426380
$232$	−1.74908e13	−1.70854
$233$	1.42913e13	1.36337	0.681686	−	0.731645i	$-0.261247\pi$
$233$	1.42913e13	1.36337	0.681686	+	0.731645i	$0.261247\pi$
$234$	−1.44442e12	−0.134588
$235$	−1.43638e13	−1.30736
$236$	2.86119e11	0.0254408
$237$	−1.91228e12	−0.166125
$238$	−8.46301e12	−0.718376
$239$	4.12148e12	0.341873	0.170936	−	0.985282i	$-0.445321\pi$
$239$	4.12148e12	0.341873	0.170936	+	0.985282i	$0.445321\pi$
$240$	7.79494e12	0.631903
$241$	−1.92304e13	−1.52369	−0.761843	−	0.647762i	$-0.775705\pi$
$241$	−1.92304e13	−1.52369	−0.761843	+	0.647762i	$0.775705\pi$
$242$	−3.32226e13	−2.57306
$243$	−8.47289e11	−0.0641500
$244$	1.46952e12	0.108776
$245$	−1.09425e13	−0.791960
$246$	−7.39249e12	−0.523176
$247$	3.41061e12	0.236047
$248$	2.20135e13	1.49006
$249$	−8.38085e12	−0.554871
$250$	1.76513e13	1.14316
$251$	−2.89097e12	−0.183163	−0.0915817	−	0.995798i	$-0.529192\pi$
$251$	−2.89097e12	−0.183163	−0.0915817	+	0.995798i	$0.529192\pi$
$252$	−4.23794e11	−0.0262695
$253$	2.44949e13	1.48564
$254$	2.60050e13	1.54337
$255$	1.53172e13	0.889626
$256$	9.94513e12	0.565315
$257$	−1.53114e13	−0.851887	−0.425944	−	0.904750i	$-0.640058\pi$
$257$	−1.53114e13	−0.851887	−0.425944	+	0.904750i	$0.640058\pi$
$258$	−1.15828e13	−0.630820
$259$	5.22569e12	0.278609
$260$	1.30758e12	0.0682522
$261$	−1.26676e13	−0.647399
$262$	−4.17323e13	−2.08841
$263$	1.35532e13	0.664179	0.332089	−	0.943248i	$-0.392246\pi$
$263$	1.35532e13	0.664179	0.332089	+	0.943248i	$0.392246\pi$
$264$	−1.93791e13	−0.930061
$265$	1.72138e13	0.809143
$266$	6.12148e12	0.281843
$267$	−1.51679e13	−0.684091
$268$	4.36598e12	0.192904
$269$	1.50247e13	0.650380	0.325190	−	0.945649i	$-0.394572\pi$
$269$	1.50247e13	0.650380	0.325190	+	0.945649i	$0.394572\pi$
$270$	4.69214e12	0.199008
$271$	4.05690e13	1.68602	0.843010	−	0.537898i	$-0.180781\pi$
$271$	4.05690e13	1.68602	0.843010	+	0.537898i	$0.180781\pi$
$272$	4.62939e13	1.88536
$273$	2.15436e12	0.0859851
$274$	1.86613e13	0.729986
$275$	−5.03829e12	−0.193176
$276$	−2.43539e12	−0.0915310
$277$	−1.64608e13	−0.606474	−0.303237	−	0.952915i	$-0.598067\pi$
$277$	−1.64608e13	−0.606474	−0.303237	+	0.952915i	$0.598067\pi$
$278$	−1.12918e13	−0.407867
$279$	1.59432e13	0.564614
$280$	−9.66295e12	−0.335537
$281$	−2.07851e13	−0.707728	−0.353864	−	0.935297i	$-0.615132\pi$
$281$	−2.07851e13	−0.707728	−0.353864	+	0.935297i	$0.615132\pi$
$282$	−2.61320e13	−0.872575
$283$	5.01441e13	1.64208	0.821040	−	0.570871i	$-0.193395\pi$
$283$	5.01441e13	1.64208	0.821040	+	0.570871i	$0.193395\pi$
$284$	−4.94794e12	−0.158918
$285$	−1.10792e13	−0.349030
$286$	−2.39266e13	−0.739379
$287$	1.10260e13	0.334246
$288$	4.32146e12	0.128520
$289$	5.66962e13	1.65431
$290$	7.01510e13	2.00838
$291$	3.55571e13	0.998885
$292$	5.58903e12	0.154075
$293$	1.21982e13	0.330008	0.165004	−	0.986293i	$-0.447236\pi$
$293$	1.21982e13	0.330008	0.165004	+	0.986293i	$0.447236\pi$
$294$	−1.99076e13	−0.528579
$295$	4.72485e12	0.123131
$296$	−2.37582e13	−0.607728
$297$	−1.40352e13	−0.352419
$298$	−1.88143e12	−0.0463766
$299$	1.23803e13	0.299598
$300$	5.00929e11	0.0119017
$301$	1.72758e13	0.403017
$302$	−1.27106e13	−0.291158
$303$	2.13168e13	0.479499
$304$	−3.34853e13	−0.739690
$305$	2.42671e13	0.526463
$306$	2.78664e13	0.593764
$307$	−1.59534e13	−0.333880	−0.166940	−	0.985967i	$-0.553389\pi$
$307$	−1.59534e13	−0.333880	−0.166940	+	0.985967i	$0.553389\pi$
$308$	−7.02010e12	−0.144316
$309$	1.86431e13	0.376485
$310$	−8.82905e13	−1.75156
$311$	1.15687e13	0.225478	0.112739	−	0.993625i	$-0.464038\pi$
$311$	1.15687e13	0.225478	0.112739	+	0.993625i	$0.464038\pi$
$312$	−9.79464e12	−0.187559
$313$	−5.37759e13	−1.01180	−0.505899	−	0.862593i	$-0.668839\pi$
$313$	−5.37759e13	−1.01180	−0.505899	+	0.862593i	$0.668839\pi$
$314$	−7.52078e12	−0.139043
$315$	−6.99836e12	−0.127142
$316$	3.14943e12	0.0562281
$317$	2.98799e13	0.524267	0.262134	−	0.965032i	$-0.415574\pi$
$317$	2.98799e13	0.524267	0.262134	+	0.965032i	$0.415574\pi$
$318$	3.13170e13	0.540047
$319$	−2.09837e14	−3.55659
$320$	4.17641e13	0.695790
$321$	−3.34419e13	−0.547663
$322$	2.22206e13	0.357724
$323$	−6.57992e13	−1.04137
$324$	1.39544e12	0.0217127
$325$	−2.54647e12	−0.0389565
$326$	9.06120e13	1.36298
$327$	3.10575e13	0.459360
$328$	−5.01287e13	−0.729089
$329$	3.89761e13	0.557469
$330$	7.77246e13	1.09328
$331$	5.89326e13	0.815270	0.407635	−	0.913145i	$-0.366354\pi$
$331$	5.89326e13	0.815270	0.407635	+	0.913145i	$0.366354\pi$
$332$	1.38028e13	0.187806
$333$	−1.72068e13	−0.230280
$334$	1.43830e14	1.89341
$335$	7.20979e13	0.933632
$336$	−2.11515e13	−0.269448
$337$	−4.44507e13	−0.557075	−0.278538	−	0.960425i	$-0.589850\pi$
$337$	−4.44507e13	−0.557075	−0.278538	+	0.960425i	$0.589850\pi$
$338$	7.65819e13	0.944245
$339$	1.75150e13	0.212477
$340$	−2.52266e13	−0.301110
$341$	2.64097e14	3.10180
$342$	−2.01564e13	−0.232953
$343$	6.51521e13	0.740987
$344$	−7.85434e13	−0.879100
$345$	−4.02170e13	−0.443000
$346$	1.15399e14	1.25107
$347$	−1.71346e14	−1.82836	−0.914181	−	0.405305i	$-0.867165\pi$
$347$	−1.71346e14	−1.82836	−0.914181	+	0.405305i	$0.867165\pi$
$348$	2.08629e13	0.219124
$349$	−5.75830e13	−0.595325	−0.297663	−	0.954671i	$-0.596207\pi$
$349$	−5.75830e13	−0.595325	−0.297663	+	0.954671i	$0.596207\pi$
$350$	−4.57050e12	−0.0465146
$351$	−7.09373e12	−0.0710698
$352$	7.15845e13	0.706048
$353$	3.95768e13	0.384309	0.192154	−	0.981365i	$-0.438453\pi$
$353$	3.95768e13	0.384309	0.192154	+	0.981365i	$0.438453\pi$
$354$	8.59588e12	0.0821812
$355$	−8.17082e13	−0.769147
$356$	2.49808e13	0.231543
$357$	−4.15630e13	−0.379343
$358$	4.92333e13	0.442489
$359$	−1.03541e14	−0.916418	−0.458209	−	0.888845i	$-0.651509\pi$
$359$	−1.03541e14	−0.916418	−0.458209	+	0.888845i	$0.651509\pi$
$360$	3.18175e13	0.277334
$361$	−6.88963e13	−0.591434
$362$	−1.24848e14	−1.05556
$363$	−1.63161e14	−1.35872
$364$	−3.54812e12	−0.0291032
$365$	9.22949e13	0.745704
$366$	4.41489e13	0.351378
$367$	−7.22655e13	−0.566588	−0.283294	−	0.959033i	$-0.591427\pi$
$367$	−7.22655e13	−0.566588	−0.283294	+	0.959033i	$0.591427\pi$
$368$	−1.21550e14	−0.938839
$369$	−3.63055e13	−0.276266
$370$	9.52882e13	0.714381
$371$	−4.67096e13	−0.345024
$372$	−2.62576e13	−0.191104
$373$	−8.53528e12	−0.0612096	−0.0306048	−	0.999532i	$-0.509743\pi$
$373$	−8.53528e12	−0.0612096	−0.0306048	+	0.999532i	$0.509743\pi$
$374$	4.61604e14	3.26194
$375$	8.66880e13	0.603652
$376$	−1.77202e14	−1.21601
$377$	−1.06057e14	−0.717233
$378$	−1.27321e13	−0.0848583
$379$	8.02058e13	0.526854	0.263427	−	0.964679i	$-0.415147\pi$
$379$	8.02058e13	0.526854	0.263427	+	0.964679i	$0.415147\pi$
$380$	1.82469e13	0.118136
$381$	1.27714e14	0.814988
$382$	2.32985e14	1.46548
$383$	−4.42970e13	−0.274651	−0.137325	−	0.990526i	$-0.543851\pi$
$383$	−4.42970e13	−0.274651	−0.137325	+	0.990526i	$0.543851\pi$
$384$	1.12402e14	0.686995
$385$	−1.15927e14	−0.698473
$386$	−1.55758e13	−0.0925166
$387$	−5.68847e13	−0.333108
$388$	−5.85608e13	−0.338090
$389$	−1.10253e14	−0.627578	−0.313789	−	0.949493i	$-0.601598\pi$
$389$	−1.10253e14	−0.627578	−0.313789	+	0.949493i	$0.601598\pi$
$390$	3.92838e13	0.220474
$391$	−2.38847e14	−1.32175
$392$	−1.34994e14	−0.736618
$393$	−2.04953e14	−1.10280
$394$	3.74683e13	0.198808
$395$	5.20084e13	0.272138
$396$	2.31153e13	0.119282
$397$	−3.54712e12	−0.0180521	−0.00902606	−	0.999959i	$-0.502873\pi$
$397$	−3.54712e12	−0.0180521	−0.00902606	+	0.999959i	$0.502873\pi$
$398$	−3.67709e14	−1.84564
$399$	3.00634e13	0.148829
$400$	2.50013e13	0.122076
$401$	2.96303e14	1.42706	0.713529	−	0.700625i	$-0.247096\pi$
$401$	2.96303e14	1.42706	0.713529	+	0.700625i	$0.247096\pi$
$402$	1.31167e14	0.623135
$403$	1.33481e14	0.625519
$404$	−3.51077e13	−0.162295
$405$	2.30437e13	0.105087
$406$	−1.90354e14	−0.856386
$407$	−2.85028e14	−1.26508
$408$	1.88963e14	0.827459
$409$	−1.60718e14	−0.694364	−0.347182	−	0.937798i	$-0.612861\pi$
$409$	−1.60718e14	−0.694364	−0.347182	+	0.937798i	$0.612861\pi$
$410$	2.01054e14	0.857039
$411$	9.16484e13	0.385474
$412$	−3.07043e13	−0.127428
$413$	−1.28208e13	−0.0525038
$414$	−7.31665e13	−0.295672
$415$	2.27934e14	0.908960
$416$	3.61805e13	0.142384
$417$	−5.54558e13	−0.215377
$418$	−3.33888e14	−1.27977
$419$	2.71067e14	1.02541	0.512707	−	0.858564i	$-0.328643\pi$
$419$	2.71067e14	1.02541	0.512707	+	0.858564i	$0.328643\pi$
$420$	1.15259e13	0.0430334
$421$	−2.58859e14	−0.953921	−0.476960	−	0.878925i	$-0.658261\pi$
$421$	−2.58859e14	−0.953921	−0.476960	+	0.878925i	$0.658261\pi$
$422$	4.92822e14	1.79255
$423$	−1.28338e14	−0.460769
$424$	2.12362e14	0.752600
$425$	4.91279e13	0.171865
$426$	−1.48651e14	−0.513353
$427$	−6.58485e13	−0.224488
$428$	5.50772e13	0.185366
$429$	−1.17507e14	−0.390434
$430$	3.15018e14	1.03338
$431$	−6.24636e13	−0.202303	−0.101151	−	0.994871i	$-0.532253\pi$
$431$	−6.24636e13	−0.202303	−0.101151	+	0.994871i	$0.532253\pi$
$432$	6.96462e13	0.222709
$433$	4.04003e14	1.27556	0.637780	−	0.770219i	$-0.279853\pi$
$433$	4.04003e14	1.27556	0.637780	+	0.770219i	$0.279853\pi$
$434$	2.39576e14	0.746877
$435$	3.44521e14	1.06054
$436$	−5.11501e13	−0.155479
$437$	1.72763e14	0.518565
$438$	1.67912e14	0.497706
$439$	−3.42771e14	−1.00334	−0.501671	−	0.865059i	$-0.667281\pi$
$439$	−3.42771e14	−1.00334	−0.501671	+	0.865059i	$0.667281\pi$
$440$	5.27053e14	1.52358
$441$	−9.77692e13	−0.279119
$442$	2.33305e14	0.657812
$443$	−3.25901e14	−0.907538	−0.453769	−	0.891119i	$-0.649921\pi$
$443$	−3.25901e14	−0.907538	−0.453769	+	0.891119i	$0.649921\pi$
$444$	2.83387e13	0.0779425
$445$	4.12522e14	1.12064
$446$	−1.63742e14	−0.439357
$447$	−9.23996e12	−0.0244894
$448$	−1.13326e14	−0.296690
$449$	1.57380e14	0.407000	0.203500	−	0.979075i	$-0.434768\pi$
$449$	1.57380e14	0.407000	0.203500	+	0.979075i	$0.434768\pi$
$450$	1.50494e13	0.0384460
$451$	−6.01396e14	−1.51771
$452$	−2.88464e13	−0.0719167
$453$	−6.24237e13	−0.153748
$454$	−4.06532e14	−0.989207
$455$	−5.85921e13	−0.140856
$456$	−1.36681e14	−0.324640
$457$	−1.55301e14	−0.364447	−0.182224	−	0.983257i	$-0.558329\pi$
$457$	−1.55301e14	−0.364447	−0.182224	+	0.983257i	$0.558329\pi$
$458$	4.43217e14	1.02768
$459$	1.36856e14	0.313541
$460$	6.62353e13	0.149941
$461$	−5.55644e13	−0.124292	−0.0621458	−	0.998067i	$-0.519794\pi$
$461$	−5.55644e13	−0.124292	−0.0621458	+	0.998067i	$0.519794\pi$
$462$	−2.10905e14	−0.466183
$463$	−2.11155e14	−0.461217	−0.230609	−	0.973047i	$-0.574072\pi$
$463$	−2.11155e14	−0.461217	−0.230609	+	0.973047i	$0.574072\pi$
$464$	1.04126e15	2.24756
$465$	−4.33607e14	−0.924921
$466$	−7.07125e14	−1.49064
$467$	5.95058e14	1.23970	0.619850	−	0.784720i	$-0.287193\pi$
$467$	5.95058e14	1.23970	0.619850	+	0.784720i	$0.287193\pi$
$468$	1.16830e13	0.0240549
$469$	−1.95637e14	−0.398107
$470$	7.10713e14	1.42941
$471$	−3.69356e13	−0.0734226
$472$	5.82890e13	0.114526
$473$	−9.42288e14	−1.82998
$474$	9.46185e13	0.181633
$475$	−3.55352e13	−0.0674286
$476$	6.84522e13	0.128395
$477$	1.53802e14	0.285175
$478$	−2.03928e14	−0.373787
$479$	−7.93679e14	−1.43813	−0.719067	−	0.694941i	$-0.755431\pi$
$479$	−7.93679e14	−1.43813	−0.719067	+	0.694941i	$0.755431\pi$
$480$	−1.17531e14	−0.210536
$481$	−1.44060e14	−0.255120
$482$	9.51510e14	1.66592
$483$	1.09128e14	0.188898
$484$	2.68718e14	0.459882
$485$	−9.67048e14	−1.63632
$486$	4.19233e13	0.0701384
$487$	4.48179e14	0.741383	0.370691	−	0.928756i	$-0.379121\pi$
$487$	4.48179e14	0.741383	0.370691	+	0.928756i	$0.379121\pi$
$488$	2.99375e14	0.489674
$489$	4.45008e14	0.719729
$490$	5.41429e14	0.865890
$491$	1.28873e14	0.203804	0.101902	−	0.994794i	$-0.467507\pi$
$491$	1.28873e14	0.203804	0.101902	+	0.994794i	$0.467507\pi$
$492$	5.97934e13	0.0935072
$493$	2.04610e15	3.16424
$494$	−1.68755e14	−0.258082
$495$	3.81716e14	0.577314
$496$	−1.31051e15	−1.96016
$497$	2.21714e14	0.327970
$498$	4.14679e14	0.606668
$499$	3.76743e14	0.545120	0.272560	−	0.962139i	$-0.412130\pi$
$499$	3.76743e14	0.545120	0.272560	+	0.962139i	$0.412130\pi$
$500$	−1.42771e14	−0.204317
$501$	7.06369e14	0.999825
$502$	1.43044e14	0.200262
$503$	−8.75394e14	−1.21222	−0.606108	−	0.795383i	$-0.707270\pi$
$503$	−8.75394e14	−1.21222	−0.606108	+	0.795383i	$0.707270\pi$
$504$	−8.63366e13	−0.118257
$505$	−5.79754e14	−0.785491
$506$	−1.21199e15	−1.62432
$507$	3.76104e14	0.498614
$508$	−2.10339e14	−0.275847
$509$	4.28083e14	0.555367	0.277683	−	0.960673i	$-0.410433\pi$
$509$	4.28083e14	0.555367	0.277683	+	0.960673i	$0.410433\pi$
$510$	−7.57884e14	−0.972673
$511$	−2.50441e14	−0.317974
$512$	4.55247e14	0.571824
$513$	−9.89908e13	−0.123013
$514$	7.57597e14	0.931411
$515$	−5.07038e14	−0.616738
$516$	9.36863e13	0.112746
$517$	−2.12590e15	−2.53131
$518$	−2.58564e14	−0.304617
$519$	5.66740e14	0.660638
$520$	2.66385e14	0.307249
$521$	1.67398e15	1.91049	0.955243	−	0.295822i	$-0.0955935\pi$
$521$	1.67398e15	1.91049	0.955243	+	0.295822i	$0.0955935\pi$
$522$	6.26786e14	0.707834
$523$	−1.29093e15	−1.44259	−0.721294	−	0.692629i	$-0.756452\pi$
$523$	−1.29093e15	−1.44259	−0.721294	+	0.692629i	$0.756452\pi$
$524$	3.37548e14	0.373261
$525$	−2.24463e13	−0.0245623
$526$	−6.70603e14	−0.726180
$527$	−2.57518e15	−2.75962
$528$	1.15368e15	1.22349
$529$	−3.25690e14	−0.341820
$530$	−8.51730e14	−0.884677
$531$	4.22156e13	0.0433963
$532$	−4.95129e13	−0.0503738
$533$	−3.03960e14	−0.306067
$534$	7.50499e14	0.747951
$535$	9.09520e14	0.897153
$536$	8.89449e14	0.868390
$537$	2.41791e14	0.233659
$538$	−7.43411e14	−0.711094
$539$	−1.61953e15	−1.53339
$540$	−3.79519e13	−0.0355686
$541$	−1.55979e15	−1.44704	−0.723519	−	0.690304i	$-0.757477\pi$
$541$	−1.55979e15	−1.44704	−0.723519	+	0.690304i	$0.757477\pi$
$542$	−2.00733e15	−1.84341
$543$	−6.13146e14	−0.557397
$544$	−6.98012e14	−0.628158
$545$	−8.44670e14	−0.752500
$546$	−1.06596e14	−0.0940119
$547$	−6.95998e14	−0.607683	−0.303842	−	0.952723i	$-0.598269\pi$
$547$	−6.95998e14	−0.607683	−0.303842	+	0.952723i	$0.598269\pi$
$548$	−1.50940e14	−0.130470
$549$	2.16821e14	0.185547
$550$	2.49292e14	0.211209
$551$	−1.47999e15	−1.24144
$552$	−4.96144e14	−0.412044
$553$	−1.41124e14	−0.116042
$554$	8.14471e14	0.663089
$555$	4.67973e14	0.377233
$556$	9.13329e13	0.0728980
$557$	−1.13537e15	−0.897294	−0.448647	−	0.893709i	$-0.648094\pi$
$557$	−1.13537e15	−0.897294	−0.448647	+	0.893709i	$0.648094\pi$
$558$	−7.88858e14	−0.617321
$559$	−4.76254e14	−0.369040
$560$	5.75257e14	0.441396
$561$	2.26700e15	1.72249
$562$	1.02843e15	0.773794
$563$	−2.40860e15	−1.79460	−0.897301	−	0.441418i	$-0.854475\pi$
$563$	−2.40860e15	−1.79460	−0.897301	+	0.441418i	$0.854475\pi$
$564$	2.11366e14	0.155955
$565$	−4.76357e14	−0.348069
$566$	−2.48110e15	−1.79537
$567$	−6.25289e13	−0.0448099
$568$	−1.00801e15	−0.715399
$569$	−2.65432e15	−1.86567	−0.932837	−	0.360300i	$-0.882674\pi$
$569$	−2.65432e15	−1.86567	−0.932837	+	0.360300i	$0.882674\pi$
$570$	5.48194e14	0.381612
$571$	−2.55697e15	−1.76290	−0.881448	−	0.472281i	$-0.843431\pi$
$571$	−2.55697e15	−1.76290	−0.881448	+	0.472281i	$0.843431\pi$
$572$	1.93528e14	0.132149
$573$	1.14422e15	0.773856
$574$	−5.45557e14	−0.365447
$575$	−1.28991e14	−0.0855826
$576$	3.73154e14	0.245225
$577$	1.06655e15	0.694248	0.347124	−	0.937819i	$-0.387158\pi$
$577$	1.06655e15	0.694248	0.347124	+	0.937819i	$0.387158\pi$
$578$	−2.80529e15	−1.80874
$579$	−7.64948e13	−0.0488539
$580$	−5.67409e14	−0.358957
$581$	−6.18498e14	−0.387587
$582$	−1.75934e15	−1.09213
$583$	2.54771e15	1.56666
$584$	1.13861e15	0.693595
$585$	1.92928e14	0.116423
$586$	−6.03560e14	−0.360814
$587$	9.19059e14	0.544294	0.272147	−	0.962256i	$-0.412266\pi$
$587$	9.19059e14	0.544294	0.272147	+	0.962256i	$0.412266\pi$
$588$	1.61021e14	0.0944729
$589$	1.86268e15	1.08269
$590$	−2.33782e14	−0.134625
$591$	1.84012e14	0.104982
$592$	1.41438e15	0.799460
$593$	3.09077e15	1.73088	0.865438	−	0.501016i	$-0.167040\pi$
$593$	3.09077e15	1.73088	0.865438	+	0.501016i	$0.167040\pi$
$594$	6.94454e14	0.385317
$595$	1.13039e15	0.621419
$596$	1.52178e13	0.00828889
$597$	−1.80587e15	−0.974602
$598$	−6.12569e14	−0.327566
$599$	1.52727e15	0.809225	0.404613	−	0.914488i	$-0.367406\pi$
$599$	1.52727e15	0.809225	0.404613	+	0.914488i	$0.367406\pi$
$600$	1.02051e14	0.0535777
$601$	−7.54230e14	−0.392368	−0.196184	−	0.980567i	$-0.562855\pi$
$601$	−7.54230e14	−0.392368	−0.196184	+	0.980567i	$0.562855\pi$
$602$	−8.54798e14	−0.440639
$603$	6.44180e14	0.329050
$604$	1.02809e14	0.0520387
$605$	4.43749e15	2.22578
$606$	−1.05474e15	−0.524261
$607$	−5.78289e14	−0.284844	−0.142422	−	0.989806i	$-0.545489\pi$
$607$	−5.78289e14	−0.284844	−0.142422	+	0.989806i	$0.545489\pi$
$608$	5.04887e14	0.246448
$609$	−9.34856e14	−0.452220
$610$	−1.20072e15	−0.575609
$611$	−1.07448e15	−0.510471
$612$	−2.25395e14	−0.106123
$613$	1.84316e15	0.860062	0.430031	−	0.902814i	$-0.358503\pi$
$613$	1.84316e15	0.860062	0.430031	+	0.902814i	$0.358503\pi$
$614$	7.89362e14	0.365048
$615$	9.87402e14	0.452565
$616$	−1.43015e15	−0.649664
$617$	1.67834e15	0.755635	0.377817	−	0.925880i	$-0.376675\pi$
$617$	1.67834e15	0.755635	0.377817	+	0.925880i	$0.376675\pi$
$618$	−9.22451e14	−0.411630
$619$	−3.54325e15	−1.56712	−0.783562	−	0.621314i	$-0.786599\pi$
$619$	−3.54325e15	−1.56712	−0.783562	+	0.621314i	$0.786599\pi$
$620$	7.14129e14	0.313056
$621$	−3.59331e14	−0.156131
$622$	−5.72414e14	−0.246526
$623$	−1.11937e15	−0.477850
$624$	5.83097e14	0.246732
$625$	−2.10615e15	−0.883381
$626$	2.66080e15	1.10625
$627$	−1.63977e15	−0.675789
$628$	6.08311e13	0.0248512
$629$	2.77928e15	1.12552
$630$	3.46274e14	0.139010
$631$	1.61670e15	0.643380	0.321690	−	0.946845i	$-0.395749\pi$
$631$	1.61670e15	0.643380	0.321690	+	0.946845i	$0.395749\pi$
$632$	6.41611e14	0.253121
$633$	2.42031e15	0.946567
$634$	−1.47844e15	−0.573207
$635$	−3.47344e15	−1.33507
$636$	−2.53305e14	−0.0965226
$637$	−8.18550e14	−0.309228
$638$	1.03826e16	3.88860
$639$	−7.30047e14	−0.271079
$640$	−3.05701e15	−1.12540
$641$	2.08616e15	0.761429	0.380714	−	0.924693i	$-0.375678\pi$
$641$	2.08616e15	0.761429	0.380714	+	0.924693i	$0.375678\pi$
$642$	1.65468e15	0.598787
$643$	−2.94568e15	−1.05688	−0.528439	−	0.848971i	$-0.677222\pi$
$643$	−2.94568e15	−1.05688	−0.528439	+	0.848971i	$0.677222\pi$
$644$	−1.79729e14	−0.0639361
$645$	1.54709e15	0.545681
$646$	3.25570e15	1.13859
$647$	−4.38575e15	−1.52079	−0.760396	−	0.649459i	$-0.774995\pi$
$647$	−4.38575e15	−1.52079	−0.760396	+	0.649459i	$0.774995\pi$
$648$	2.84283e14	0.0977437
$649$	6.99295e14	0.238405
$650$	1.25998e14	0.0425931
$651$	1.17659e15	0.394393
$652$	−7.32906e14	−0.243605
$653$	−3.53489e15	−1.16507	−0.582537	−	0.812804i	$-0.697940\pi$
$653$	−3.53489e15	−1.16507	−0.582537	+	0.812804i	$0.697940\pi$
$654$	−1.53670e15	−0.502241
$655$	5.57412e15	1.80655
$656$	2.98427e15	0.959108
$657$	8.24636e14	0.262817
$658$	−1.92851e15	−0.609509
$659$	4.08134e15	1.27918	0.639592	−	0.768714i	$-0.279103\pi$
$659$	4.08134e15	1.27918	0.639592	+	0.768714i	$0.279103\pi$
$660$	−6.28667e14	−0.195402
$661$	−1.34229e15	−0.413751	−0.206876	−	0.978367i	$-0.566330\pi$
$661$	−1.34229e15	−0.413751	−0.206876	+	0.978367i	$0.566330\pi$
$662$	−2.91595e15	−0.891376
$663$	1.14579e15	0.347362
$664$	2.81195e15	0.845442
$665$	−8.17635e14	−0.243804
$666$	8.51382e14	0.251777
$667$	−5.37227e15	−1.57567
$668$	−1.16335e15	−0.338409
$669$	−8.04157e14	−0.232005
$670$	−3.56736e15	−1.02079
$671$	3.59162e15	1.01933
$672$	3.18919e14	0.0897738
$673$	−2.73009e14	−0.0762244	−0.0381122	−	0.999273i	$-0.512134\pi$
$673$	−2.73009e14	−0.0762244	−0.0381122	+	0.999273i	$0.512134\pi$
$674$	2.19939e15	0.609078
$675$	7.39098e13	0.0203016
$676$	−6.19425e14	−0.168765
$677$	3.93378e15	1.06310	0.531549	−	0.847028i	$-0.321610\pi$
$677$	3.93378e15	1.06310	0.531549	+	0.847028i	$0.321610\pi$
$678$	−8.66633e14	−0.232312
$679$	2.62408e15	0.697739
$680$	−5.13924e15	−1.35550
$681$	−1.99653e15	−0.522357
$682$	−1.30673e16	−3.39135
$683$	−7.36548e15	−1.89621	−0.948107	−	0.317952i	$-0.897005\pi$
$683$	−7.36548e15	−1.89621	−0.948107	+	0.317952i	$0.897005\pi$
$684$	1.63033e14	0.0416358
$685$	−2.49256e15	−0.631463
$686$	−3.22368e15	−0.810158
$687$	2.17670e15	0.542671
$688$	4.67586e15	1.15645
$689$	1.28767e15	0.315937
$690$	1.98991e15	0.484355
$691$	1.57534e15	0.380403	0.190202	−	0.981745i	$-0.439086\pi$
$691$	1.57534e15	0.380403	0.190202	+	0.981745i	$0.439086\pi$
$692$	−9.33392e14	−0.223605
$693$	−1.03578e15	−0.246171
$694$	8.47810e15	1.99904
$695$	1.50823e15	0.352819
$696$	4.25025e15	0.986425
$697$	5.86415e15	1.35028
$698$	2.84917e15	0.650899
$699$	−3.47279e15	−0.787143
$700$	3.69680e13	0.00831355
$701$	4.21744e15	0.941021	0.470511	−	0.882394i	$-0.344070\pi$
$701$	4.21744e15	0.941021	0.470511	+	0.882394i	$0.344070\pi$
$702$	3.50993e14	0.0777042
$703$	−2.01031e15	−0.441580
$704$	6.18124e15	1.34718
$705$	3.49041e15	0.754807
$706$	−1.95824e15	−0.420184
$707$	1.57316e15	0.334939
$708$	−6.95269e13	−0.0146883
$709$	−5.25660e14	−0.110192	−0.0550960	−	0.998481i	$-0.517546\pi$
$709$	−5.25660e14	−0.110192	−0.0550960	+	0.998481i	$0.517546\pi$
$710$	4.04287e15	0.840947
$711$	4.64684e14	0.0959125
$712$	5.08916e15	1.04233
$713$	6.76142e15	1.37419
$714$	2.05651e15	0.414754
$715$	3.19583e15	0.639588
$716$	−3.98218e14	−0.0790860
$717$	−1.00152e15	−0.197380
$718$	5.12315e15	1.00197
$719$	1.25727e15	0.244016	0.122008	−	0.992529i	$-0.461067\pi$
$719$	1.25727e15	0.244016	0.122008	+	0.992529i	$0.461067\pi$
$720$	−1.89417e15	−0.364830
$721$	1.37584e15	0.262981
$722$	3.40895e15	0.646644
$723$	4.67300e15	0.879701
$724$	1.00982e15	0.188661
$725$	1.10501e15	0.204883
$726$	8.07309e15	1.48555
$727$	−2.64385e15	−0.482834	−0.241417	−	0.970421i	$-0.577612\pi$
$727$	−2.64385e15	−0.482834	−0.241417	+	0.970421i	$0.577612\pi$
$728$	−7.22833e14	−0.131013
$729$	2.05891e14	0.0370370
$730$	−4.56669e15	−0.815316
$731$	9.18814e15	1.62810
$732$	−3.57094e14	−0.0628017
$733$	−6.39802e15	−1.11680	−0.558398	−	0.829573i	$-0.688584\pi$
$733$	−6.39802e15	−1.11680	−0.558398	+	0.829573i	$0.688584\pi$
$734$	3.57565e15	0.619479
$735$	2.65903e15	0.457239
$736$	1.83271e15	0.312799
$737$	1.06708e16	1.80769
$738$	1.79637e15	0.302056
$739$	−5.73297e15	−0.956831	−0.478416	−	0.878134i	$-0.658789\pi$
$739$	−5.73297e15	−0.956831	−0.478416	+	0.878134i	$0.658789\pi$
$740$	−7.70729e14	−0.127681
$741$	−8.28777e14	−0.136282
$742$	2.31116e15	0.377232
$743$	1.44597e15	0.234271	0.117136	−	0.993116i	$-0.462629\pi$
$743$	1.44597e15	0.234271	0.117136	+	0.993116i	$0.462629\pi$
$744$	−5.34928e15	−0.860288
$745$	2.51299e14	0.0401173
$746$	4.22320e14	0.0669235
$747$	2.03655e15	0.320355
$748$	−3.73363e15	−0.583006
$749$	−2.46798e15	−0.382552
$750$	−4.28927e15	−0.660003
$751$	−4.83205e15	−0.738094	−0.369047	−	0.929411i	$-0.620316\pi$
$751$	−4.83205e15	−0.738094	−0.369047	+	0.929411i	$0.620316\pi$
$752$	1.05492e16	1.59964
$753$	7.02507e14	0.105749
$754$	5.24762e15	0.784187
$755$	1.69774e15	0.251862
$756$	1.02982e14	0.0151667
$757$	−2.48126e15	−0.362781	−0.181390	−	0.983411i	$-0.558060\pi$
$757$	−2.48126e15	−0.362781	−0.181390	+	0.983411i	$0.558060\pi$
$758$	−3.96853e15	−0.576036
$759$	−5.95226e15	−0.857733
$760$	3.71732e15	0.531808
$761$	−3.20037e15	−0.454552	−0.227276	−	0.973830i	$-0.572982\pi$
$761$	−3.20037e15	−0.454552	−0.227276	+	0.973830i	$0.572982\pi$
$762$	−6.31921e15	−0.891067
$763$	2.29201e15	0.320871
$764$	−1.88448e15	−0.261925
$765$	−3.72207e15	−0.513626
$766$	2.19179e15	0.300289
$767$	3.53440e14	0.0480774
$768$	−2.41667e15	−0.326385
$769$	−9.86048e15	−1.32222	−0.661109	−	0.750289i	$-0.729914\pi$
$769$	−9.86048e15	−1.32222	−0.661109	+	0.750289i	$0.729914\pi$
$770$	5.73599e15	0.763676
$771$	3.72066e15	0.491837
$772$	1.25983e14	0.0165355
$773$	−1.27501e16	−1.66160	−0.830801	−	0.556570i	$-0.812117\pi$
$773$	−1.27501e16	−1.66160	−0.830801	+	0.556570i	$0.812117\pi$
$774$	2.81462e15	0.364204
$775$	−1.39074e15	−0.178684
$776$	−1.19302e16	−1.52197
$777$	−1.26984e15	−0.160855
$778$	5.45525e15	0.686162
$779$	−4.24166e15	−0.529761
$780$	−3.17743e14	−0.0394054
$781$	−1.20931e16	−1.48922
$782$	1.18180e16	1.44513
$783$	3.07823e15	0.373776
$784$	8.03652e15	0.969013
$785$	1.00454e15	0.120277
$786$	1.01410e16	1.20574
$787$	1.71079e15	0.201992	0.100996	−	0.994887i	$-0.467797\pi$
$787$	1.71079e15	0.201992	0.100996	+	0.994887i	$0.467797\pi$
$788$	−3.03058e14	−0.0355330
$789$	−3.29342e15	−0.383464
$790$	−2.57334e15	−0.297542
$791$	1.29259e15	0.148419
$792$	4.70912e15	0.536971
$793$	1.81529e15	0.205562
$794$	1.75509e14	0.0197373
$795$	−4.18296e15	−0.467159
$796$	2.97418e15	0.329872
$797$	4.08760e15	0.450244	0.225122	−	0.974331i	$-0.427722\pi$
$797$	4.08760e15	0.450244	0.225122	+	0.974331i	$0.427722\pi$
$798$	−1.48752e15	−0.162722
$799$	2.07294e16	2.25206
$800$	−3.76965e14	−0.0406730
$801$	3.68580e15	0.394960
$802$	−1.46609e16	−1.56027
$803$	1.36600e16	1.44383
$804$	−1.06093e15	−0.111373
$805$	−2.96797e15	−0.309444
$806$	−6.60453e15	−0.683911
$807$	−3.65100e15	−0.375497
$808$	−7.15225e15	−0.730601
$809$	−3.69053e15	−0.374431	−0.187215	−	0.982319i	$-0.559946\pi$
$809$	−3.69053e15	−0.374431	−0.187215	+	0.982319i	$0.559946\pi$
$810$	−1.14019e15	−0.114897
$811$	−6.57565e15	−0.658148	−0.329074	−	0.944304i	$-0.606737\pi$
$811$	−6.57565e15	−0.658148	−0.329074	+	0.944304i	$0.606737\pi$
$812$	1.53966e15	0.153062
$813$	−9.85826e15	−0.973424
$814$	1.41030e16	1.38318
$815$	−1.21029e16	−1.17902
$816$	−1.12494e16	−1.08851
$817$	−6.64598e15	−0.638760
$818$	7.95225e15	0.759183
$819$	−5.23509e14	−0.0496435
$820$	−1.62620e15	−0.153179
$821$	−1.74407e15	−0.163183	−0.0815917	−	0.996666i	$-0.526000\pi$
$821$	−1.74407e15	−0.163183	−0.0815917	+	0.996666i	$0.526000\pi$
$822$	−4.53471e15	−0.421458
$823$	1.16565e16	1.07614	0.538068	−	0.842901i	$-0.319154\pi$
$823$	1.16565e16	1.07614	0.538068	+	0.842901i	$0.319154\pi$
$824$	−6.25517e15	−0.573640
$825$	1.22431e15	0.111530
$826$	6.34367e14	0.0574050
$827$	−1.26350e16	−1.13578	−0.567892	−	0.823103i	$-0.692241\pi$
$827$	−1.26350e16	−1.13578	−0.567892	+	0.823103i	$0.692241\pi$
$828$	5.91800e14	0.0528455
$829$	−1.58439e16	−1.40544	−0.702721	−	0.711466i	$-0.748032\pi$
$829$	−1.58439e16	−1.40544	−0.702721	+	0.711466i	$0.748032\pi$
$830$	−1.12780e16	−0.993812
$831$	3.99998e15	0.350148
$832$	3.12414e15	0.271677
$833$	1.57919e16	1.36423
$834$	2.74392e15	0.235482
$835$	−1.92111e16	−1.63786
$836$	2.70062e15	0.228733
$837$	−3.87419e15	−0.325980
$838$	−1.34122e16	−1.12114
$839$	9.87033e15	0.819673	0.409837	−	0.912159i	$-0.365586\pi$
$839$	9.87033e15	0.819673	0.409837	+	0.912159i	$0.365586\pi$
$840$	2.34810e15	0.193723
$841$	3.38214e16	2.77213
$842$	1.28082e16	1.04297
$843$	5.05077e15	0.408607
$844$	−3.98614e15	−0.320382
$845$	−1.02289e16	−0.816804
$846$	6.35008e15	0.503782
$847$	−1.20411e16	−0.949088
$848$	−1.26424e16	−0.990038
$849$	−1.21850e16	−0.948055
$850$	−2.43082e15	−0.187909
$851$	−7.29731e15	−0.560467
$852$	1.20235e15	0.0917515
$853$	2.03104e15	0.153992	0.0769962	−	0.997031i	$-0.475467\pi$
$853$	2.03104e15	0.153992	0.0769962	+	0.997031i	$0.475467\pi$
$854$	3.25814e15	0.245444
$855$	2.69225e15	0.201513
$856$	1.12205e16	0.834460
$857$	1.13646e16	0.839765	0.419883	−	0.907578i	$-0.362071\pi$
$857$	1.13646e16	0.839765	0.419883	+	0.907578i	$0.362071\pi$
$858$	5.81415e15	0.426881
$859$	−1.95756e16	−1.42808	−0.714041	−	0.700104i	$-0.753137\pi$
$859$	−1.95756e16	−1.42808	−0.714041	+	0.700104i	$0.753137\pi$
$860$	−2.54799e15	−0.184695
$861$	−2.67931e15	−0.192977
$862$	3.09066e15	0.221188
$863$	2.61983e16	1.86300	0.931500	−	0.363741i	$-0.118501\pi$
$863$	2.61983e16	1.86300	0.931500	+	0.363741i	$0.118501\pi$
$864$	−1.05012e15	−0.0742013
$865$	−1.54136e16	−1.08222
$866$	−1.99898e16	−1.39463
$867$	−1.37772e16	−0.955114
$868$	−1.93778e15	−0.133489
$869$	7.69743e15	0.526911
$870$	−1.70467e16	−1.15954
$871$	5.39325e15	0.364545
$872$	−1.04204e16	−0.699915
$873$	−8.64038e15	−0.576706
$874$	−8.54822e15	−0.566973
$875$	6.39747e15	0.421662
$876$	−1.35814e15	−0.0889550
$877$	3.54322e15	0.230622	0.115311	−	0.993329i	$-0.463214\pi$
$877$	3.54322e15	0.230622	0.115311	+	0.993329i	$0.463214\pi$
$878$	1.69601e16	1.09700
$879$	−2.96417e15	−0.190530
$880$	−3.13767e16	−2.00425
$881$	−2.91262e16	−1.84891	−0.924457	−	0.381285i	$-0.875482\pi$
$881$	−2.91262e16	−1.84891	−0.924457	+	0.381285i	$0.875482\pi$
$882$	4.83756e15	0.305175
$883$	2.14395e16	1.34410	0.672049	−	0.740507i	$-0.265414\pi$
$883$	2.14395e16	1.34410	0.672049	+	0.740507i	$0.265414\pi$
$884$	−1.88707e15	−0.117571
$885$	−1.14814e15	−0.0710896
$886$	1.61254e16	0.992257
$887$	9.83610e15	0.601510	0.300755	−	0.953701i	$-0.402761\pi$
$887$	9.83610e15	0.601510	0.300755	+	0.953701i	$0.402761\pi$
$888$	5.77325e15	0.350872
$889$	9.42515e15	0.569283
$890$	−2.04113e16	−1.22525
$891$	3.41056e15	0.203469
$892$	1.32441e15	0.0785262
$893$	−1.49940e16	−0.883559
$894$	4.57188e14	0.0267755
$895$	−6.57600e15	−0.382768
$896$	8.29517e15	0.479878
$897$	−3.00841e15	−0.172973
$898$	−7.78706e15	−0.444994
$899$	−5.79221e16	−3.28978
$900$	−1.21726e14	−0.00687145
$901$	−2.48425e16	−1.39383
$902$	2.97567e16	1.65939
$903$	−4.19803e15	−0.232682
$904$	−5.87667e15	−0.323746
$905$	1.66757e16	0.913099
$906$	3.08868e15	0.168100
$907$	−1.91807e16	−1.03759	−0.518793	−	0.854900i	$-0.673618\pi$
$907$	−1.91807e16	−1.03759	−0.518793	+	0.854900i	$0.673618\pi$
$908$	3.28819e15	0.176801
$909$	−5.17999e15	−0.276839
$910$	2.89910e15	0.154005
$911$	−1.87431e16	−0.989672	−0.494836	−	0.868986i	$-0.664772\pi$
$911$	−1.87431e16	−0.989672	−0.494836	+	0.868986i	$0.664772\pi$
$912$	8.13694e15	0.427060
$913$	3.37351e16	1.75992
$914$	7.68419e15	0.398468
$915$	−5.89690e15	−0.303954
$916$	−3.58491e15	−0.183677
$917$	−1.51253e16	−0.770324
$918$	−6.77154e15	−0.342810
$919$	3.72180e16	1.87291	0.936456	−	0.350786i	$-0.114085\pi$
$919$	3.72180e16	1.87291	0.936456	+	0.350786i	$0.114085\pi$
$920$	1.34936e16	0.674988
$921$	3.87666e15	0.192766
$922$	2.74929e15	0.135894
$923$	−6.11215e15	−0.300320
$924$	1.70588e15	0.0833208
$925$	1.50097e15	0.0728771
$926$	1.04478e16	0.504272
$927$	−4.53028e15	−0.217364
$928$	−1.57000e16	−0.748836
$929$	−1.68328e16	−0.798125	−0.399062	−	0.916924i	$-0.630664\pi$
$929$	−1.68328e16	−0.798125	−0.399062	+	0.916924i	$0.630664\pi$
$930$	2.14546e16	1.01126
$931$	−1.14226e16	−0.535232
$932$	5.71951e15	0.266423
$933$	−2.81120e15	−0.130180
$934$	−2.94431e16	−1.35543
$935$	−6.16556e16	−2.82169
$936$	2.38010e15	0.108287
$937$	−1.40828e16	−0.636974	−0.318487	−	0.947927i	$-0.603175\pi$
$937$	−1.40828e16	−0.636974	−0.318487	+	0.947927i	$0.603175\pi$
$938$	9.67999e15	0.435271
$939$	1.30675e16	0.584162
$940$	−5.74853e15	−0.255478
$941$	3.64793e16	1.61177	0.805887	−	0.592070i	$-0.201689\pi$
$941$	3.64793e16	1.61177	0.805887	+	0.592070i	$0.201689\pi$
$942$	1.82755e15	0.0802767
$943$	−1.53970e16	−0.672390
$944$	−3.47007e15	−0.150658
$945$	1.70060e15	0.0734053
$946$	4.66238e16	2.00081
$947$	−1.27686e16	−0.544777	−0.272389	−	0.962187i	$-0.587814\pi$
$947$	−1.27686e16	−0.544777	−0.272389	+	0.962187i	$0.587814\pi$
$948$	−7.65312e14	−0.0324633
$949$	6.90408e15	0.291167
$950$	1.75826e15	0.0737231
$951$	−7.26081e15	−0.302686
$952$	1.39453e16	0.577995
$953$	1.72977e16	0.712814	0.356407	−	0.934331i	$-0.384002\pi$
$953$	1.72977e16	0.712814	0.356407	+	0.934331i	$0.384002\pi$
$954$	−7.61004e15	−0.311796
$955$	−3.11195e16	−1.26769
$956$	1.64945e15	0.0668069
$957$	5.09905e16	2.05340
$958$	3.92707e16	1.57238
$959$	6.76355e15	0.269260
$960$	−1.01487e16	−0.401714
$961$	4.74910e16	1.86910
$962$	7.12799e15	0.278936
$963$	8.12638e15	0.316193
$964$	−7.69619e15	−0.297750
$965$	2.08043e15	0.0800300
$966$	−5.39960e15	−0.206532
$967$	3.00509e16	1.14291	0.571455	−	0.820634i	$-0.306379\pi$
$967$	3.00509e16	1.14291	0.571455	+	0.820634i	$0.306379\pi$
$968$	5.47439e16	2.07024
$969$	1.59892e16	0.601238
$970$	4.78489e16	1.78907
$971$	−1.80996e16	−0.672921	−0.336461	−	0.941698i	$-0.609230\pi$
$971$	−1.80996e16	−0.672921	−0.336461	+	0.941698i	$0.609230\pi$
$972$	−3.39092e14	−0.0125358
$973$	−4.09257e15	−0.150444
$974$	−2.21756e16	−0.810591
$975$	6.18793e14	0.0224916
$976$	−1.78225e16	−0.644161
$977$	1.47747e16	0.531004	0.265502	−	0.964110i	$-0.414462\pi$
$977$	1.47747e16	0.531004	0.265502	+	0.964110i	$0.414462\pi$
$978$	−2.20187e16	−0.786916
$979$	6.10548e16	2.16978
$980$	−4.37929e15	−0.154761
$981$	−7.54696e15	−0.265212
$982$	−6.37654e15	−0.222829
$983$	−4.87943e16	−1.69561	−0.847803	−	0.530311i	$-0.822075\pi$
$983$	−4.87943e16	−1.69561	−0.847803	+	0.530311i	$0.822075\pi$
$984$	1.21813e16	0.420940
$985$	−5.00457e15	−0.171976
$986$	−1.01240e17	−3.45962
$987$	−9.47120e15	−0.321855
$988$	1.36496e15	0.0461270
$989$	−2.41245e16	−0.810735
$990$	−1.88871e16	−0.631206
$991$	8.57060e15	0.284843	0.142422	−	0.989806i	$-0.454511\pi$
$991$	8.57060e15	0.284843	0.142422	+	0.989806i	$0.454511\pi$
$992$	1.97597e16	0.653080
$993$	−1.43206e16	−0.470697
$994$	−1.09703e16	−0.358586
$995$	4.91143e16	1.59654
$996$	−3.35409e15	−0.108430
$997$	−4.60960e16	−1.48197	−0.740987	−	0.671520i	$-0.765642\pi$
$997$	−4.60960e16	−1.48197	−0.740987	+	0.671520i	$0.765642\pi$
$998$	−1.86410e16	−0.596007
$999$	4.18125e15	0.132952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.7	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.7	✓	26	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-49.4794 q^{2} -243.000 q^{3} +400.209 q^{4} +6608.87 q^{5} +12023.5 q^{6} -17933.1 q^{7} +81531.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-49.4794 q^{2} -243.000 q^{3} +400.209 q^{4} +6608.87 q^{5} +12023.5 q^{6} -17933.1 q^{7} +81531.7 q^{8} +59049.0 q^{9} -327003. q^{10} +978139. q^{11} -97250.8 q^{12} +494374. q^{13} +887320. q^{14} -1.60596e6 q^{15} -4.85376e6 q^{16} -9.53772e6 q^{17} -2.92171e6 q^{18} +6.89884e6 q^{19} +2.64493e6 q^{20} +4.35775e6 q^{21} -4.83977e7 q^{22} +2.50424e7 q^{23} -1.98122e7 q^{24} -5.15090e6 q^{25} -2.44613e7 q^{26} -1.43489e7 q^{27} -7.17700e6 q^{28} -2.14527e8 q^{29} +7.94617e7 q^{30} +2.69999e8 q^{31} +7.31844e7 q^{32} -2.37688e8 q^{33} +4.71921e8 q^{34} -1.18518e8 q^{35} +2.36319e7 q^{36} -2.91399e8 q^{37} -3.41350e8 q^{38} -1.20133e8 q^{39} +5.38833e8 q^{40} -6.14837e8 q^{41} -2.15619e8 q^{42} -9.63348e8 q^{43} +3.91460e8 q^{44} +3.90247e8 q^{45} -1.23908e9 q^{46} -2.17341e9 q^{47} +1.17946e9 q^{48} -1.65573e9 q^{49} +2.54863e8 q^{50} +2.31767e9 q^{51} +1.97853e8 q^{52} +2.60466e9 q^{53} +7.09975e8 q^{54} +6.46440e9 q^{55} -1.46212e9 q^{56} -1.67642e9 q^{57} +1.06147e10 q^{58} +7.14924e8 q^{59} -6.42718e8 q^{60} +3.67189e9 q^{61} -1.33594e10 q^{62} -1.05893e9 q^{63} +6.31939e9 q^{64} +3.26726e9 q^{65} +1.17606e10 q^{66} +1.09092e10 q^{67} -3.81708e9 q^{68} -6.08530e9 q^{69} +5.86419e9 q^{70} -1.23634e10 q^{71} +4.81436e9 q^{72} +1.39653e10 q^{73} +1.44182e10 q^{74} +1.25167e9 q^{75} +2.76098e9 q^{76} -1.75411e10 q^{77} +5.94410e9 q^{78} +7.86947e9 q^{79} -3.20779e10 q^{80} +3.48678e9 q^{81} +3.04218e10 q^{82} +3.44891e10 q^{83} +1.74401e9 q^{84} -6.30336e10 q^{85} +4.76659e10 q^{86} +5.21301e10 q^{87} +7.97493e10 q^{88} +6.24194e10 q^{89} -1.93092e10 q^{90} -8.86567e9 q^{91} +1.00222e10 q^{92} -6.56098e10 q^{93} +1.07539e11 q^{94} +4.55936e10 q^{95} -1.77838e10 q^{96} -1.46326e11 q^{97} +8.19245e10 q^{98} +5.77581e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \)	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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