LMFDB - Embedded newform 177.12.a.b.1.4

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:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-71.6191 q^{2} +243.000 q^{3} +3081.30 q^{4} -9710.01 q^{5} -17403.4 q^{6} +37645.0 q^{7} -74003.9 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-71.6191 q^{2} +243.000 q^{3} +3081.30 q^{4} -9710.01 q^{5} -17403.4 q^{6} +37645.0 q^{7} -74003.9 q^{8} +59049.0 q^{9} +695422. q^{10} +60655.0 q^{11} +748755. q^{12} +624964. q^{13} -2.69610e6 q^{14} -2.35953e6 q^{15} -1.01041e6 q^{16} +2.49028e6 q^{17} -4.22904e6 q^{18} -1.44054e7 q^{19} -2.99194e7 q^{20} +9.14772e6 q^{21} -4.34406e6 q^{22} +1.14743e7 q^{23} -1.79829e7 q^{24} +4.54562e7 q^{25} -4.47593e7 q^{26} +1.43489e7 q^{27} +1.15995e8 q^{28} -1.23449e8 q^{29} +1.68988e8 q^{30} +2.37452e8 q^{31} +2.23924e8 q^{32} +1.47392e7 q^{33} -1.78352e8 q^{34} -3.65533e8 q^{35} +1.81948e8 q^{36} -4.08733e8 q^{37} +1.03170e9 q^{38} +1.51866e8 q^{39} +7.18578e8 q^{40} -2.82822e8 q^{41} -6.55152e8 q^{42} +1.04999e9 q^{43} +1.86896e8 q^{44} -5.73366e8 q^{45} -8.21780e8 q^{46} -2.58355e9 q^{47} -2.45529e8 q^{48} -5.60184e8 q^{49} -3.25553e9 q^{50} +6.05138e8 q^{51} +1.92570e9 q^{52} -1.74096e9 q^{53} -1.02766e9 q^{54} -5.88961e8 q^{55} -2.78587e9 q^{56} -3.50052e9 q^{57} +8.84130e9 q^{58} -7.14924e8 q^{59} -7.27042e9 q^{60} +1.03848e10 q^{61} -1.70061e10 q^{62} +2.22290e9 q^{63} -1.39679e10 q^{64} -6.06840e9 q^{65} -1.05561e9 q^{66} +1.41202e10 q^{67} +7.67329e9 q^{68} +2.78826e9 q^{69} +2.61791e10 q^{70} -1.38159e10 q^{71} -4.36986e9 q^{72} +1.71356e10 q^{73} +2.92731e10 q^{74} +1.10459e10 q^{75} -4.43874e10 q^{76} +2.28336e9 q^{77} -1.08765e10 q^{78} +1.65750e10 q^{79} +9.81105e9 q^{80} +3.48678e9 q^{81} +2.02554e10 q^{82} +1.81884e10 q^{83} +2.81869e10 q^{84} -2.41806e10 q^{85} -7.51994e10 q^{86} -2.99981e10 q^{87} -4.48871e9 q^{88} -9.62794e10 q^{89} +4.10640e10 q^{90} +2.35267e10 q^{91} +3.53558e10 q^{92} +5.77008e10 q^{93} +1.85031e11 q^{94} +1.39877e11 q^{95} +5.44136e10 q^{96} +6.76303e10 q^{97} +4.01199e10 q^{98} +3.58162e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) $	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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 $

$2$	−71.6191	−1.58257	−0.791287	−	0.611445i	$-0.790589\pi$
$2$	−71.6191	−1.58257	−0.791287	+	0.611445i	$0.790589\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	3081.30	1.50454
$5$	−9710.01	−1.38958	−0.694792	−	0.719211i	$-0.744503\pi$
$5$	−9710.01	−1.38958	−0.694792	+	0.719211i	$0.744503\pi$
$6$	−17403.4	−0.913699
$7$	37645.0	0.846579	0.423290	−	0.905994i	$-0.360875\pi$
$7$	37645.0	0.846579	0.423290	+	0.905994i	$0.360875\pi$
$8$	−74003.9	−0.798472
$9$	59049.0	0.333333
$10$	695422.	2.19912
$11$	60655.0	0.113555	0.0567776	−	0.998387i	$-0.481917\pi$
$11$	60655.0	0.113555	0.0567776	+	0.998387i	$0.481917\pi$
$12$	748755.	0.868647
$13$	624964.	0.466838	0.233419	−	0.972376i	$-0.425009\pi$
$13$	624964.	0.466838	0.233419	+	0.972376i	$0.425009\pi$
$14$	−2.69610e6	−1.33977
$15$	−2.35953e6	−0.802276
$16$	−1.01041e6	−0.240899
$17$	2.49028e6	0.425382	0.212691	−	0.977120i	$-0.431777\pi$
$17$	2.49028e6	0.425382	0.212691	+	0.977120i	$0.431777\pi$
$18$	−4.22904e6	−0.527525
$19$	−1.44054e7	−1.33469	−0.667346	−	0.744748i	$-0.732570\pi$
$19$	−1.44054e7	−1.33469	−0.667346	+	0.744748i	$0.732570\pi$
$20$	−2.99194e7	−2.09068
$21$	9.14772e6	0.488773
$22$	−4.34406e6	−0.179709
$23$	1.14743e7	0.371727	0.185863	−	0.982576i	$-0.440492\pi$
$23$	1.14743e7	0.371727	0.185863	+	0.982576i	$0.440492\pi$
$24$	−1.79829e7	−0.460998
$25$	4.54562e7	0.930942
$26$	−4.47593e7	−0.738806
$27$	1.43489e7	0.192450
$28$	1.15995e8	1.27371
$29$	−1.23449e8	−1.11763	−0.558815	−	0.829292i	$-0.688744\pi$
$29$	−1.23449e8	−1.11763	−0.558815	+	0.829292i	$0.688744\pi$
$30$	1.68988e8	1.26966
$31$	2.37452e8	1.48966	0.744828	−	0.667256i	$-0.232531\pi$
$31$	2.37452e8	1.48966	0.744828	+	0.667256i	$0.232531\pi$
$32$	2.23924e8	1.17971
$33$	1.47392e7	0.0655611
$34$	−1.78352e8	−0.673198
$35$	−3.65533e8	−1.17639
$36$	1.81948e8	0.501513
$37$	−4.08733e8	−0.969015	−0.484507	−	0.874787i	$-0.661001\pi$
$37$	−4.08733e8	−0.969015	−0.484507	+	0.874787i	$0.661001\pi$
$38$	1.03170e9	2.11225
$39$	1.51866e8	0.269529
$40$	7.18578e8	1.10954
$41$	−2.82822e8	−0.381243	−0.190621	−	0.981664i	$-0.561050\pi$
$41$	−2.82822e8	−0.381243	−0.190621	+	0.981664i	$0.561050\pi$
$42$	−6.55152e8	−0.773519
$43$	1.04999e9	1.08920	0.544601	−	0.838695i	$-0.316681\pi$
$43$	1.04999e9	1.08920	0.544601	+	0.838695i	$0.316681\pi$
$44$	1.86896e8	0.170848
$45$	−5.73366e8	−0.463195
$46$	−8.21780e8	−0.588285
$47$	−2.58355e9	−1.64315	−0.821577	−	0.570098i	$-0.806905\pi$
$47$	−2.58355e9	−1.64315	−0.821577	+	0.570098i	$0.806905\pi$
$48$	−2.45529e8	−0.139083
$49$	−5.60184e8	−0.283304
$50$	−3.25553e9	−1.47329
$51$	6.05138e8	0.245594
$52$	1.92570e9	0.702376
$53$	−1.74096e9	−0.571835	−0.285918	−	0.958254i	$-0.592298\pi$
$53$	−1.74096e9	−0.571835	−0.285918	+	0.958254i	$0.592298\pi$
$54$	−1.02766e9	−0.304566
$55$	−5.88961e8	−0.157794
$56$	−2.78587e9	−0.675969
$57$	−3.50052e9	−0.770585
$58$	8.84130e9	1.76873
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−7.27042e9	−1.20706
$61$	1.03848e10	1.57429	0.787146	−	0.616766i	$-0.211558\pi$
$61$	1.03848e10	1.57429	0.787146	+	0.616766i	$0.211558\pi$
$62$	−1.70061e10	−2.35749
$63$	2.22290e9	0.282193
$64$	−1.39679e10	−1.62608
$65$	−6.06840e9	−0.648710
$66$	−1.05561e9	−0.103755
$67$	1.41202e10	1.27770	0.638850	−	0.769331i	$-0.279410\pi$
$67$	1.41202e10	1.27770	0.638850	+	0.769331i	$0.279410\pi$
$68$	7.67329e9	0.640004
$69$	2.78826e9	0.214616
$70$	2.61791e10	1.86173
$71$	−1.38159e10	−0.908778	−0.454389	−	0.890803i	$-0.650142\pi$
$71$	−1.38159e10	−0.908778	−0.454389	+	0.890803i	$0.650142\pi$
$72$	−4.36986e9	−0.266157
$73$	1.71356e10	0.967442	0.483721	−	0.875222i	$-0.339285\pi$
$73$	1.71356e10	0.967442	0.483721	+	0.875222i	$0.339285\pi$
$74$	2.92731e10	1.53354
$75$	1.10459e10	0.537480
$76$	−4.43874e10	−2.00810
$77$	2.28336e9	0.0961334
$78$	−1.08765e10	−0.426550
$79$	1.65750e10	0.606044	0.303022	−	0.952984i	$-0.402004\pi$
$79$	1.65750e10	0.606044	0.303022	+	0.952984i	$0.402004\pi$
$80$	9.81105e9	0.334750
$81$	3.48678e9	0.111111
$82$	2.02554e10	0.603345
$83$	1.81884e10	0.506834	0.253417	−	0.967357i	$-0.418446\pi$
$83$	1.81884e10	0.506834	0.253417	+	0.967357i	$0.418446\pi$
$84$	2.81869e10	0.735378
$85$	−2.41806e10	−0.591104
$86$	−7.51994e10	−1.72374
$87$	−2.99981e10	−0.645264
$88$	−4.48871e9	−0.0906706
$89$	−9.62794e10	−1.82763	−0.913815	−	0.406131i	$-0.866878\pi$
$89$	−9.62794e10	−1.82763	−0.913815	+	0.406131i	$0.866878\pi$
$90$	4.10640e10	0.733040
$91$	2.35267e10	0.395215
$92$	3.53558e10	0.559278
$93$	5.77008e10	0.860053
$94$	1.85031e11	2.60041
$95$	1.39877e11	1.85467
$96$	5.44136e10	0.681108
$97$	6.76303e10	0.799644	0.399822	−	0.916593i	$-0.369072\pi$
$97$	6.76303e10	0.799644	0.399822	+	0.916593i	$0.369072\pi$
$98$	4.01199e10	0.448349
$99$	3.58162e9	0.0378517
$100$	1.40064e11	1.40064
$101$	9.72443e10	0.920654	0.460327	−	0.887749i	$-0.347732\pi$
$101$	9.72443e10	0.920654	0.460327	+	0.887749i	$0.347732\pi$
$102$	−4.33395e10	−0.388671
$103$	1.68362e11	1.43100	0.715500	−	0.698613i	$-0.246199\pi$
$103$	1.68362e11	1.43100	0.715500	+	0.698613i	$0.246199\pi$
$104$	−4.62497e10	−0.372757
$105$	−8.88245e10	−0.679190
$106$	1.24686e11	0.904971
$107$	2.85563e10	0.196830	0.0984151	−	0.995145i	$-0.468623\pi$
$107$	2.85563e10	0.196830	0.0984151	+	0.995145i	$0.468623\pi$
$108$	4.42133e10	0.289549
$109$	1.07166e11	0.667134	0.333567	−	0.942726i	$-0.391748\pi$
$109$	1.07166e11	0.667134	0.333567	+	0.942726i	$0.391748\pi$
$110$	4.21809e10	0.249721
$111$	−9.93222e10	−0.559461
$112$	−3.80367e10	−0.203940
$113$	2.67933e11	1.36803	0.684015	−	0.729468i	$-0.260232\pi$
$113$	2.67933e11	1.36803	0.684015	+	0.729468i	$0.260232\pi$
$114$	2.50704e11	1.21951
$115$	−1.11416e11	−0.516545
$116$	−3.80383e11	−1.68152
$117$	3.69035e10	0.155613
$118$	5.12022e10	0.206034
$119$	9.37465e10	0.360120
$120$	1.74615e11	0.640595
$121$	−2.81633e11	−0.987105
$122$	−7.43753e11	−2.49143
$123$	−6.87257e10	−0.220111
$124$	7.31659e11	2.24125
$125$	3.27417e10	0.0959613
$126$	−1.59202e11	−0.446591
$127$	−4.93391e11	−1.32517	−0.662583	−	0.748988i	$-0.730540\pi$
$127$	−4.93391e11	−1.32517	−0.662583	+	0.748988i	$0.730540\pi$
$128$	5.41775e11	1.39368
$129$	2.55148e11	0.628851
$130$	4.34614e11	1.02663
$131$	−3.92825e11	−0.889625	−0.444813	−	0.895624i	$-0.646730\pi$
$131$	−3.92825e11	−0.889625	−0.444813	+	0.895624i	$0.646730\pi$
$132$	4.54158e10	0.0986393
$133$	−5.42292e11	−1.12992
$134$	−1.01127e12	−2.02205
$135$	−1.39328e11	−0.267425
$136$	−1.84290e11	−0.339656
$137$	1.35467e11	0.239811	0.119906	−	0.992785i	$-0.461741\pi$
$137$	1.35467e11	0.239811	0.119906	+	0.992785i	$0.461741\pi$
$138$	−1.99693e11	−0.339646
$139$	−3.25168e11	−0.531529	−0.265764	−	0.964038i	$-0.585624\pi$
$139$	−3.25168e11	−0.531529	−0.265764	+	0.964038i	$0.585624\pi$
$140$	−1.12632e12	−1.76993
$141$	−6.27802e11	−0.948675
$142$	9.89481e11	1.43821
$143$	3.79072e10	0.0530119
$144$	−5.96634e10	−0.0802998
$145$	1.19869e12	1.55304
$146$	−1.22724e12	−1.53105
$147$	−1.36125e11	−0.163566
$148$	−1.25943e12	−1.45792
$149$	−8.60761e11	−0.960192	−0.480096	−	0.877216i	$-0.659398\pi$
$149$	−8.60761e11	−0.960192	−0.480096	+	0.877216i	$0.659398\pi$
$150$	−7.91094e11	−0.850602
$151$	−2.95852e11	−0.306691	−0.153346	−	0.988173i	$-0.549005\pi$
$151$	−2.95852e11	−0.306691	−0.153346	+	0.988173i	$0.549005\pi$
$152$	1.06606e12	1.06571
$153$	1.47049e11	0.141794
$154$	−1.63532e11	−0.152138
$155$	−2.30566e12	−2.07000
$156$	4.67945e11	0.405517
$157$	8.60052e11	0.719576	0.359788	−	0.933034i	$-0.382849\pi$
$157$	8.60052e11	0.719576	0.359788	+	0.933034i	$0.382849\pi$
$158$	−1.18709e12	−0.959109
$159$	−4.23053e11	−0.330149
$160$	−2.17431e12	−1.63931
$161$	4.31950e11	0.314696
$162$	−2.49720e11	−0.175842
$163$	−4.52373e11	−0.307939	−0.153970	−	0.988076i	$-0.549206\pi$
$163$	−4.52373e11	−0.307939	−0.153970	+	0.988076i	$0.549206\pi$
$164$	−8.71458e11	−0.573595
$165$	−1.43117e11	−0.0911027
$166$	−1.30264e12	−0.802102
$167$	−3.57279e11	−0.212846	−0.106423	−	0.994321i	$-0.533940\pi$
$167$	−3.57279e11	−0.212846	−0.106423	+	0.994321i	$0.533940\pi$
$168$	−6.76967e11	−0.390271
$169$	−1.40158e12	−0.782062
$170$	1.73180e12	0.935466
$171$	−8.50626e11	−0.444898
$172$	3.23533e12	1.63875
$173$	1.16482e12	0.571486	0.285743	−	0.958306i	$-0.407760\pi$
$173$	1.16482e12	0.571486	0.285743	+	0.958306i	$0.407760\pi$
$174$	2.14844e12	1.02118
$175$	1.71120e12	0.788116
$176$	−6.12862e10	−0.0273554
$177$	−1.73727e11	−0.0751646
$178$	6.89544e12	2.89236
$179$	−5.99613e11	−0.243882	−0.121941	−	0.992537i	$-0.538912\pi$
$179$	−5.99613e11	−0.243882	−0.121941	+	0.992537i	$0.538912\pi$
$180$	−1.76671e12	−0.696895
$181$	2.40799e11	0.0921347	0.0460673	−	0.998938i	$-0.485331\pi$
$181$	2.40799e11	0.0921347	0.0460673	+	0.998938i	$0.485331\pi$
$182$	−1.68496e12	−0.625457
$183$	2.52351e12	0.908918
$184$	−8.49144e11	−0.296813
$185$	3.96880e12	1.34653
$186$	−4.13248e12	−1.36110
$187$	1.51048e11	0.0483043
$188$	−7.96068e12	−2.47219
$189$	5.40164e11	0.162924
$190$	−1.00179e13	−2.93515
$191$	−1.64656e12	−0.468699	−0.234350	−	0.972152i	$-0.575296\pi$
$191$	−1.64656e12	−0.468699	−0.234350	+	0.972152i	$0.575296\pi$
$192$	−3.39421e12	−0.938820
$193$	1.54565e12	0.415476	0.207738	−	0.978185i	$-0.433390\pi$
$193$	1.54565e12	0.415476	0.207738	+	0.978185i	$0.433390\pi$
$194$	−4.84362e12	−1.26550
$195$	−1.47462e12	−0.374533
$196$	−1.72609e12	−0.426242
$197$	1.38427e12	0.332397	0.166199	−	0.986092i	$-0.446851\pi$
$197$	1.38427e12	0.332397	0.166199	+	0.986092i	$0.446851\pi$
$198$	−2.56512e11	−0.0599032
$199$	−1.07613e12	−0.244441	−0.122221	−	0.992503i	$-0.539002\pi$
$199$	−1.07613e12	−0.244441	−0.122221	+	0.992503i	$0.539002\pi$
$200$	−3.36393e12	−0.743331
$201$	3.43120e12	0.737680
$202$	−6.96455e12	−1.45700
$203$	−4.64723e12	−0.946163
$204$	1.86461e12	0.369507
$205$	2.74620e12	0.529769
$206$	−1.20579e13	−2.26466
$207$	6.77547e11	0.123909
$208$	−6.31467e11	−0.112461
$209$	−8.73761e11	−0.151561
$210$	6.36153e12	1.07487
$211$	−9.00351e12	−1.48204	−0.741018	−	0.671486i	$-0.765657\pi$
$211$	−9.00351e12	−1.48204	−0.741018	+	0.671486i	$0.765657\pi$
$212$	−5.36441e12	−0.860349
$213$	−3.35726e12	−0.524683
$214$	−2.04518e12	−0.311498
$215$	−1.01954e13	−1.51354
$216$	−1.06187e12	−0.153666
$217$	8.93886e12	1.26111
$218$	−7.67517e12	−1.05579
$219$	4.16396e12	0.558553
$220$	−1.81476e12	−0.237408
$221$	1.55633e12	0.198585
$222$	7.11337e12	0.885388
$223$	2.56413e12	0.311360	0.155680	−	0.987808i	$-0.450243\pi$
$223$	2.56413e12	0.311360	0.155680	+	0.987808i	$0.450243\pi$
$224$	8.42962e12	0.998720
$225$	2.68414e12	0.310314
$226$	−1.91892e13	−2.16501
$227$	4.72205e12	0.519982	0.259991	−	0.965611i	$-0.416280\pi$
$227$	4.72205e12	0.519982	0.259991	+	0.965611i	$0.416280\pi$
$228$	−1.07861e13	−1.15938
$229$	−1.74449e13	−1.83051	−0.915256	−	0.402873i	$-0.868012\pi$
$229$	−1.74449e13	−1.83051	−0.915256	+	0.402873i	$0.868012\pi$
$230$	7.97949e12	0.817471
$231$	5.54855e11	0.0555027
$232$	9.13570e12	0.892396
$233$	6.59376e11	0.0629036	0.0314518	−	0.999505i	$-0.489987\pi$
$233$	6.59376e11	0.0629036	0.0314518	+	0.999505i	$0.489987\pi$
$234$	−2.64299e12	−0.246269
$235$	2.50863e13	2.28330
$236$	−2.20289e12	−0.195874
$237$	4.02772e12	0.349899
$238$	−6.71404e12	−0.569916
$239$	−9.06209e12	−0.751692	−0.375846	−	0.926682i	$-0.622648\pi$
$239$	−9.06209e12	−0.751692	−0.375846	+	0.926682i	$0.622648\pi$
$240$	2.38408e12	0.193268
$241$	−2.24055e13	−1.77525	−0.887626	−	0.460565i	$-0.847647\pi$
$241$	−2.24055e13	−1.77525	−0.887626	+	0.460565i	$0.847647\pi$
$242$	2.01703e13	1.56217
$243$	8.47289e11	0.0641500
$244$	3.19988e13	2.36859
$245$	5.43940e12	0.393674
$246$	4.92207e12	0.348341
$247$	−9.00287e12	−0.623085
$248$	−1.75723e13	−1.18945
$249$	4.41979e12	0.292621
$250$	−2.34493e12	−0.151866
$251$	1.13619e13	0.719857	0.359929	−	0.932980i	$-0.382801\pi$
$251$	1.13619e13	0.719857	0.359929	+	0.932980i	$0.382801\pi$
$252$	6.84941e12	0.424571
$253$	6.95975e11	0.0422115
$254$	3.53362e13	2.09717
$255$	−5.87590e12	−0.341274
$256$	−1.01951e13	−0.579525
$257$	1.61056e12	0.0896074	0.0448037	−	0.998996i	$-0.485734\pi$
$257$	1.61056e12	0.0896074	0.0448037	+	0.998996i	$0.485734\pi$
$258$	−1.82734e13	−0.995204
$259$	−1.53867e13	−0.820348
$260$	−1.86986e13	−0.976011
$261$	−7.28953e12	−0.372544
$262$	2.81338e13	1.40790
$263$	−1.14324e13	−0.560251	−0.280125	−	0.959963i	$-0.590376\pi$
$263$	−1.14324e13	−0.560251	−0.280125	+	0.959963i	$0.590376\pi$
$264$	−1.09076e12	−0.0523487
$265$	1.69047e13	0.794613
$266$	3.88384e13	1.78819
$267$	−2.33959e13	−1.05518
$268$	4.35085e13	1.92235
$269$	−3.96300e13	−1.71548	−0.857742	−	0.514081i	$-0.828133\pi$
$269$	−3.96300e13	−1.71548	−0.857742	+	0.514081i	$0.828133\pi$
$270$	9.97855e12	0.423221
$271$	6.17718e12	0.256720	0.128360	−	0.991728i	$-0.459029\pi$
$271$	6.17718e12	0.256720	0.128360	+	0.991728i	$0.459029\pi$
$272$	−2.51619e12	−0.102474
$273$	5.71699e12	0.228178
$274$	−9.70201e12	−0.379519
$275$	2.75715e12	0.105713
$276$	8.59145e12	0.322899
$277$	−5.13723e13	−1.89274	−0.946368	−	0.323090i	$-0.895278\pi$
$277$	−5.13723e13	−1.89274	−0.946368	+	0.323090i	$0.895278\pi$
$278$	2.32883e13	0.841184
$279$	1.40213e13	0.496552
$280$	2.70508e13	0.939316
$281$	1.65407e13	0.563210	0.281605	−	0.959530i	$-0.409133\pi$
$281$	1.65407e13	0.563210	0.281605	+	0.959530i	$0.409133\pi$
$282$	4.49626e13	1.50135
$283$	9.14231e12	0.299385	0.149693	−	0.988733i	$-0.452172\pi$
$283$	9.14231e12	0.299385	0.149693	+	0.988733i	$0.452172\pi$
$284$	−4.25708e13	−1.36729
$285$	3.39901e13	1.07079
$286$	−2.71488e12	−0.0838952
$287$	−1.06468e13	−0.322752
$288$	1.32225e13	0.393238
$289$	−2.80704e13	−0.819050
$290$	−8.58491e13	−2.45780
$291$	1.64342e13	0.461675
$292$	5.28000e13	1.45555
$293$	−1.46326e13	−0.395866	−0.197933	−	0.980216i	$-0.563423\pi$
$293$	−1.46326e13	−0.395866	−0.197933	+	0.980216i	$0.563423\pi$
$294$	9.74914e12	0.258855
$295$	6.94192e12	0.180908
$296$	3.02478e13	0.773731
$297$	8.70333e11	0.0218537
$298$	6.16470e13	1.51958
$299$	7.17103e12	0.173536
$300$	3.40356e13	0.808660
$301$	3.95268e13	0.922096
$302$	2.11887e13	0.485362
$303$	2.36304e13	0.531540
$304$	1.45553e13	0.321527
$305$	−1.00837e14	−2.18761
$306$	−1.05315e13	−0.224399
$307$	9.77088e12	0.204490	0.102245	−	0.994759i	$-0.467397\pi$
$307$	9.77088e12	0.204490	0.102245	+	0.994759i	$0.467397\pi$
$308$	7.03570e12	0.144637
$309$	4.09120e13	0.826188
$310$	1.65129e14	3.27593
$311$	−3.39024e13	−0.660767	−0.330383	−	0.943847i	$-0.607178\pi$
$311$	−3.39024e13	−0.660767	−0.330383	+	0.943847i	$0.607178\pi$
$312$	−1.12387e13	−0.215211
$313$	−6.89569e13	−1.29743	−0.648714	−	0.761032i	$-0.724693\pi$
$313$	−6.89569e13	−1.29743	−0.648714	+	0.761032i	$0.724693\pi$
$314$	−6.15962e13	−1.13878
$315$	−2.15843e13	−0.392131
$316$	5.10724e13	0.911817
$317$	−6.46132e13	−1.13369	−0.566847	−	0.823823i	$-0.691837\pi$
$317$	−6.46132e13	−1.13369	−0.566847	+	0.823823i	$0.691837\pi$
$318$	3.02987e13	0.522485
$319$	−7.48780e12	−0.126913
$320$	1.35629e14	2.25958
$321$	6.93919e12	0.113640
$322$	−3.09359e13	−0.498030
$323$	−3.58735e13	−0.567754
$324$	1.07438e13	0.167171
$325$	2.84085e13	0.434599
$326$	3.23986e13	0.487337
$327$	2.60415e13	0.385170
$328$	2.09299e13	0.304412
$329$	−9.72575e13	−1.39106
$330$	1.02499e13	0.144177
$331$	−9.99966e13	−1.38335	−0.691674	−	0.722210i	$-0.743126\pi$
$331$	−9.99966e13	−1.38335	−0.691674	+	0.722210i	$0.743126\pi$
$332$	5.60439e13	0.762552
$333$	−2.41353e13	−0.323005
$334$	2.55880e13	0.336845
$335$	−1.37107e14	−1.77547
$336$	−9.24291e12	−0.117745
$337$	−1.23806e14	−1.55159	−0.775795	−	0.630985i	$-0.782651\pi$
$337$	−1.23806e14	−1.55159	−0.775795	+	0.630985i	$0.782651\pi$
$338$	1.00380e14	1.23767
$339$	6.51078e13	0.789832
$340$	−7.45078e13	−0.889339
$341$	1.44026e13	0.169158
$342$	6.09211e13	0.704083
$343$	−9.55245e13	−1.08642
$344$	−7.77033e13	−0.869698
$345$	−2.70740e13	−0.298227
$346$	−8.34234e13	−0.904418
$347$	9.04500e13	0.965154	0.482577	−	0.875854i	$-0.339701\pi$
$347$	9.04500e13	0.965154	0.482577	+	0.875854i	$0.339701\pi$
$348$	−9.24330e13	−0.970826
$349$	−4.98058e12	−0.0514920	−0.0257460	−	0.999669i	$-0.508196\pi$
$349$	−4.98058e12	−0.0514920	−0.0257460	+	0.999669i	$0.508196\pi$
$350$	−1.22554e14	−1.24725
$351$	8.96754e12	0.0898430
$352$	1.35821e13	0.133963
$353$	−9.99494e13	−0.970554	−0.485277	−	0.874361i	$-0.661281\pi$
$353$	−9.99494e13	−0.970554	−0.485277	+	0.874361i	$0.661281\pi$
$354$	1.24421e13	0.118954
$355$	1.34152e14	1.26282
$356$	−2.96665e14	−2.74974
$357$	2.27804e13	0.207915
$358$	4.29437e13	0.385961
$359$	7.76199e13	0.686995	0.343498	−	0.939154i	$-0.388388\pi$
$359$	7.76199e13	0.686995	0.343498	+	0.939154i	$0.388388\pi$
$360$	4.24313e13	0.369848
$361$	9.10260e13	0.781404
$362$	−1.72458e13	−0.145810
$363$	−6.84367e13	−0.569905
$364$	7.24928e13	0.594617
$365$	−1.66387e14	−1.34434
$366$	−1.80732e14	−1.43843
$367$	1.26252e14	0.989861	0.494930	−	0.868933i	$-0.335194\pi$
$367$	1.26252e14	0.989861	0.494930	+	0.868933i	$0.335194\pi$
$368$	−1.15937e13	−0.0895487
$369$	−1.67003e13	−0.127081
$370$	−2.84242e14	−2.13098
$371$	−6.55383e13	−0.484104
$372$	1.77793e14	1.29398
$373$	2.49748e14	1.79103	0.895515	−	0.445031i	$-0.146807\pi$
$373$	2.49748e14	1.79103	0.895515	+	0.445031i	$0.146807\pi$
$374$	−1.08179e13	−0.0764452
$375$	7.95623e12	0.0554033
$376$	1.91193e14	1.31201
$377$	−7.71511e13	−0.521752
$378$	−3.86861e13	−0.257840
$379$	5.89118e13	0.386978	0.193489	−	0.981102i	$-0.438020\pi$
$379$	5.89118e13	0.386978	0.193489	+	0.981102i	$0.438020\pi$
$380$	4.31002e14	2.79042
$381$	−1.19894e14	−0.765085
$382$	1.17925e14	0.741752
$383$	−1.30460e14	−0.808881	−0.404440	−	0.914564i	$-0.632534\pi$
$383$	−1.30460e14	−0.808881	−0.404440	+	0.914564i	$0.632534\pi$
$384$	1.31651e14	0.804644
$385$	−2.21714e13	−0.133585
$386$	−1.10698e14	−0.657521
$387$	6.20009e13	0.363068
$388$	2.08389e14	1.20310
$389$	1.05199e14	0.598807	0.299403	−	0.954127i	$-0.403212\pi$
$389$	1.05199e14	0.598807	0.299403	+	0.954127i	$0.403212\pi$
$390$	1.05611e14	0.592726
$391$	2.85743e13	0.158126
$392$	4.14558e13	0.226210
$393$	−9.54565e13	−0.513625
$394$	−9.91404e13	−0.526043
$395$	−1.60943e14	−0.842148
$396$	1.10360e13	0.0569494
$397$	−2.32327e14	−1.18237	−0.591184	−	0.806537i	$-0.701339\pi$
$397$	−2.32327e14	−1.18237	−0.591184	+	0.806537i	$0.701339\pi$
$398$	7.70718e13	0.386846
$399$	−1.31777e14	−0.652361
$400$	−4.59292e13	−0.224264
$401$	−3.00084e14	−1.44527	−0.722635	−	0.691230i	$-0.757069\pi$
$401$	−3.00084e14	−1.44527	−0.722635	+	0.691230i	$0.757069\pi$
$402$	−2.45740e14	−1.16743
$403$	1.48399e14	0.695428
$404$	2.99639e14	1.38516
$405$	−3.38567e13	−0.154398
$406$	3.32830e14	1.49737
$407$	−2.47917e13	−0.110037
$408$	−4.47826e13	−0.196100
$409$	3.69758e14	1.59749	0.798747	−	0.601667i	$-0.205497\pi$
$409$	3.69758e14	1.59749	0.798747	+	0.601667i	$0.205497\pi$
$410$	−1.96681e14	−0.838398
$411$	3.29184e13	0.138455
$412$	5.18774e14	2.15300
$413$	−2.69133e13	−0.110215
$414$	−4.85253e13	−0.196095
$415$	−1.76610e14	−0.704288
$416$	1.39945e14	0.550735
$417$	−7.90159e13	−0.306878
$418$	6.25780e13	0.239857
$419$	1.12710e14	0.426370	0.213185	−	0.977012i	$-0.431616\pi$
$419$	1.12710e14	0.426370	0.213185	+	0.977012i	$0.431616\pi$
$420$	−2.73695e14	−1.02187
$421$	4.47083e14	1.64754	0.823772	−	0.566922i	$-0.191866\pi$
$421$	4.47083e14	1.64754	0.823772	+	0.566922i	$0.191866\pi$
$422$	6.44824e14	2.34543
$423$	−1.52556e14	−0.547718
$424$	1.28838e14	0.456594
$425$	1.13199e14	0.396006
$426$	2.40444e14	0.830350
$427$	3.90937e14	1.33276
$428$	8.79906e13	0.296139
$429$	9.21144e12	0.0306064
$430$	7.30187e14	2.39529
$431$	2.16562e14	0.701386	0.350693	−	0.936490i	$-0.385946\pi$
$431$	2.16562e14	0.701386	0.350693	+	0.936490i	$0.385946\pi$
$432$	−1.44982e13	−0.0463611
$433$	−4.32371e14	−1.36513	−0.682563	−	0.730827i	$-0.739135\pi$
$433$	−4.32371e14	−1.36513	−0.682563	+	0.730827i	$0.739135\pi$
$434$	−6.40193e14	−1.99580
$435$	2.91282e14	0.896649
$436$	3.30212e14	1.00373
$437$	−1.65292e14	−0.496141
$438$	−2.98219e14	−0.883951
$439$	−3.18492e14	−0.932275	−0.466137	−	0.884712i	$-0.654355\pi$
$439$	−3.18492e14	−0.932275	−0.466137	+	0.884712i	$0.654355\pi$
$440$	4.35854e13	0.125994
$441$	−3.30783e13	−0.0944346
$442$	−1.11463e14	−0.314275
$443$	4.44114e14	1.23673	0.618364	−	0.785892i	$-0.287796\pi$
$443$	4.44114e14	1.23673	0.618364	+	0.785892i	$0.287796\pi$
$444$	−3.06041e14	−0.841731
$445$	9.34874e14	2.53964
$446$	−1.83641e14	−0.492751
$447$	−2.09165e14	−0.554367
$448$	−5.25823e14	−1.37661
$449$	−1.82168e14	−0.471105	−0.235552	−	0.971862i	$-0.575690\pi$
$449$	−1.82168e14	−0.471105	−0.235552	+	0.971862i	$0.575690\pi$
$450$	−1.92236e14	−0.491095
$451$	−1.71546e13	−0.0432921
$452$	8.25583e14	2.05825
$453$	−7.18921e13	−0.177068
$454$	−3.38189e14	−0.822910
$455$	−2.28445e14	−0.549185
$456$	2.59052e14	0.615290
$457$	1.57071e14	0.368602	0.184301	−	0.982870i	$-0.440998\pi$
$457$	1.57071e14	0.368602	0.184301	+	0.982870i	$0.440998\pi$
$458$	1.24939e15	2.89692
$459$	3.57328e13	0.0818648
$460$	−3.43305e14	−0.777163
$461$	−6.23903e14	−1.39560	−0.697801	−	0.716292i	$-0.745838\pi$
$461$	−6.23903e14	−1.39560	−0.697801	+	0.716292i	$0.745838\pi$
$462$	−3.97382e13	−0.0878371
$463$	−3.29305e14	−0.719288	−0.359644	−	0.933090i	$-0.617102\pi$
$463$	−3.29305e14	−0.719288	−0.359644	+	0.933090i	$0.617102\pi$
$464$	1.24733e14	0.269237
$465$	−5.60275e14	−1.19512
$466$	−4.72240e13	−0.0995497
$467$	7.60322e14	1.58400	0.791999	−	0.610522i	$-0.209040\pi$
$467$	7.60322e14	1.58400	0.791999	+	0.610522i	$0.209040\pi$
$468$	1.13711e14	0.234125
$469$	5.31554e14	1.08167
$470$	−1.79666e15	−3.61349
$471$	2.08993e14	0.415447
$472$	5.29072e13	0.103952
$473$	6.36872e13	0.123685
$474$	−2.88462e14	−0.553742
$475$	−6.54815e14	−1.24252
$476$	2.88861e14	0.541814
$477$	−1.02802e14	−0.190612
$478$	6.49019e14	1.18961
$479$	−5.26864e13	−0.0954669	−0.0477335	−	0.998860i	$-0.515200\pi$
$479$	−5.26864e13	−0.0954669	−0.0477335	+	0.998860i	$0.515200\pi$
$480$	−5.28357e14	−0.946456
$481$	−2.55443e14	−0.452373
$482$	1.60466e15	2.80947
$483$	1.04964e14	0.181690
$484$	−8.67794e14	−1.48514
$485$	−6.56691e14	−1.11117
$486$	−6.06821e13	−0.101522
$487$	−3.58994e14	−0.593851	−0.296926	−	0.954901i	$-0.595961\pi$
$487$	−3.58994e14	−0.593851	−0.296926	+	0.954901i	$0.595961\pi$
$488$	−7.68518e14	−1.25703
$489$	−1.09927e14	−0.177789
$490$	−3.89565e14	−0.623019
$491$	8.18417e14	1.29427	0.647137	−	0.762373i	$-0.275966\pi$
$491$	8.18417e14	1.29427	0.647137	+	0.762373i	$0.275966\pi$
$492$	−2.11764e14	−0.331165
$493$	−3.07422e14	−0.475420
$494$	6.44777e14	0.986078
$495$	−3.47775e13	−0.0525981
$496$	−2.39923e14	−0.358857
$497$	−5.20098e14	−0.769352
$498$	−3.16541e14	−0.463094
$499$	1.37376e13	0.0198774	0.00993869	−	0.999951i	$-0.496836\pi$
$499$	1.37376e13	0.0198774	0.00993869	+	0.999951i	$0.496836\pi$
$500$	1.00887e14	0.144378
$501$	−8.68187e13	−0.122887
$502$	−8.13731e14	−1.13923
$503$	5.86134e14	0.811658	0.405829	−	0.913949i	$-0.366983\pi$
$503$	5.86134e14	0.811658	0.405829	+	0.913949i	$0.366983\pi$
$504$	−1.64503e14	−0.225323
$505$	−9.44243e14	−1.27933
$506$	−4.98451e13	−0.0668028
$507$	−3.40584e14	−0.451524
$508$	−1.52028e15	−1.99377
$509$	−9.93752e14	−1.28923	−0.644615	−	0.764507i	$-0.722982\pi$
$509$	−9.93752e14	−1.28923	−0.644615	+	0.764507i	$0.722982\pi$
$510$	4.20827e14	0.540091
$511$	6.45071e14	0.819016
$512$	−3.79391e14	−0.476544
$513$	−2.06702e14	−0.256862
$514$	−1.15347e14	−0.141810
$515$	−1.63480e15	−1.98849
$516$	7.86186e14	0.946132
$517$	−1.56705e14	−0.186589
$518$	1.10198e15	1.29826
$519$	2.83051e14	0.329947
$520$	4.49085e14	0.517977
$521$	8.59337e14	0.980745	0.490372	−	0.871513i	$-0.336861\pi$
$521$	8.59337e14	0.980745	0.490372	+	0.871513i	$0.336861\pi$
$522$	5.22070e14	0.589578
$523$	4.92525e13	0.0550388	0.0275194	−	0.999621i	$-0.491239\pi$
$523$	4.92525e13	0.0550388	0.0275194	+	0.999621i	$0.491239\pi$
$524$	−1.21041e15	−1.33848
$525$	4.15820e14	0.455019
$526$	8.18781e14	0.886638
$527$	5.91321e14	0.633673
$528$	−1.48925e13	−0.0157936
$529$	−8.21150e14	−0.861819
$530$	−1.21070e15	−1.25753
$531$	−4.22156e13	−0.0433963
$532$	−1.67096e15	−1.70001
$533$	−1.76753e14	−0.177979
$534$	1.67559e15	1.66990
$535$	−2.77282e14	−0.273512
$536$	−1.04495e15	−1.02021
$537$	−1.45706e14	−0.140805
$538$	2.83827e15	2.71488
$539$	−3.39780e13	−0.0321706
$540$	−4.29311e14	−0.402352
$541$	4.94069e14	0.458356	0.229178	−	0.973385i	$-0.426396\pi$
$541$	4.94069e14	0.458356	0.229178	+	0.973385i	$0.426396\pi$
$542$	−4.42404e14	−0.406278
$543$	5.85142e13	0.0531940
$544$	5.57634e14	0.501829
$545$	−1.04059e15	−0.927039
$546$	−4.09446e14	−0.361108
$547$	5.68865e12	0.00496682	0.00248341	−	0.999997i	$-0.499210\pi$
$547$	5.68865e12	0.00496682	0.00248341	+	0.999997i	$0.499210\pi$
$548$	4.17413e14	0.360806
$549$	6.13214e14	0.524764
$550$	−1.97464e14	−0.167299
$551$	1.77833e15	1.49169
$552$	−2.06342e14	−0.171365
$553$	6.23964e14	0.513064
$554$	3.67924e15	2.99540
$555$	9.64419e14	0.777418
$556$	−1.00194e15	−0.799706
$557$	2.04927e15	1.61956	0.809778	−	0.586737i	$-0.199588\pi$
$557$	2.04927e15	1.61956	0.809778	+	0.586737i	$0.199588\pi$
$558$	−1.00419e15	−0.785830
$559$	6.56205e14	0.508481
$560$	3.69336e14	0.283392
$561$	3.67047e13	0.0278885
$562$	−1.18463e15	−0.891321
$563$	−1.25655e15	−0.936234	−0.468117	−	0.883667i	$-0.655067\pi$
$563$	−1.25655e15	−0.936234	−0.468117	+	0.883667i	$0.655067\pi$
$564$	−1.93444e15	−1.42732
$565$	−2.60164e15	−1.90099
$566$	−6.54764e14	−0.473800
$567$	1.31260e14	0.0940643
$568$	1.02243e15	0.725633
$569$	−2.63511e15	−1.85217	−0.926085	−	0.377316i	$-0.876847\pi$
$569$	−2.63511e15	−1.85217	−0.926085	+	0.377316i	$0.876847\pi$
$570$	−2.43434e15	−1.69461
$571$	1.17266e15	0.808485	0.404242	−	0.914652i	$-0.367535\pi$
$571$	1.17266e15	0.808485	0.404242	+	0.914652i	$0.367535\pi$
$572$	1.16803e14	0.0797585
$573$	−4.00114e14	−0.270604
$574$	7.62515e14	0.510779
$575$	5.21578e14	0.346056
$576$	−8.24793e14	−0.542028
$577$	−1.41481e15	−0.920938	−0.460469	−	0.887676i	$-0.652319\pi$
$577$	−1.41481e15	−0.920938	−0.460469	+	0.887676i	$0.652319\pi$
$578$	2.01038e15	1.29621
$579$	3.75593e14	0.239875
$580$	3.69352e15	2.33661
$581$	6.84702e14	0.429075
$582$	−1.17700e15	−0.730635
$583$	−1.05598e14	−0.0649349
$584$	−1.26810e15	−0.772475
$585$	−3.58333e14	−0.216237
$586$	1.04797e15	0.626487
$587$	−7.67307e14	−0.454422	−0.227211	−	0.973846i	$-0.572961\pi$
$587$	−7.67307e14	−0.454422	−0.227211	+	0.973846i	$0.572961\pi$
$588$	−4.19441e14	−0.246091
$589$	−3.42059e15	−1.98823
$590$	−4.97174e14	−0.286301
$591$	3.36378e14	0.191910
$592$	4.12986e14	0.233435
$593$	7.93935e14	0.444615	0.222307	−	0.974977i	$-0.428641\pi$
$593$	7.93935e14	0.444615	0.222307	+	0.974977i	$0.428641\pi$
$594$	−6.23325e13	−0.0345851
$595$	−9.10279e14	−0.500416
$596$	−2.65226e15	−1.44465
$597$	−2.61501e14	−0.141128
$598$	−5.13583e14	−0.274634
$599$	−7.13533e14	−0.378065	−0.189033	−	0.981971i	$-0.560535\pi$
$599$	−7.13533e14	−0.378065	−0.189033	+	0.981971i	$0.560535\pi$
$600$	−8.17436e14	−0.429162
$601$	1.02257e15	0.531967	0.265984	−	0.963978i	$-0.414303\pi$
$601$	1.02257e15	0.531967	0.265984	+	0.963978i	$0.414303\pi$
$602$	−2.83088e15	−1.45929
$603$	8.33783e14	0.425900
$604$	−9.11608e14	−0.461429
$605$	2.73466e15	1.37167
$606$	−1.69239e15	−0.841201
$607$	−2.89132e14	−0.142416	−0.0712078	−	0.997462i	$-0.522685\pi$
$607$	−2.89132e14	−0.142416	−0.0712078	+	0.997462i	$0.522685\pi$
$608$	−3.22572e15	−1.57455
$609$	−1.12928e15	−0.546267
$610$	7.22185e15	3.46206
$611$	−1.61462e15	−0.767087
$612$	4.53100e14	0.213335
$613$	1.49684e15	0.698463	0.349232	−	0.937036i	$-0.386443\pi$
$613$	1.49684e15	0.698463	0.349232	+	0.937036i	$0.386443\pi$
$614$	−6.99782e14	−0.323621
$615$	6.67327e14	0.305862
$616$	−1.68977e14	−0.0767598
$617$	−3.99373e15	−1.79808	−0.899042	−	0.437863i	$-0.855736\pi$
$617$	−3.99373e15	−1.79808	−0.899042	+	0.437863i	$0.855736\pi$
$618$	−2.93008e15	−1.30750
$619$	−2.08009e15	−0.919989	−0.459995	−	0.887922i	$-0.652149\pi$
$619$	−2.08009e15	−0.919989	−0.459995	+	0.887922i	$0.652149\pi$
$620$	−7.10442e15	−3.11440
$621$	1.64644e14	0.0715388
$622$	2.42806e15	1.04571
$623$	−3.62443e15	−1.54723
$624$	−1.53446e14	−0.0649294
$625$	−2.53746e15	−1.06429
$626$	4.93863e15	2.05328
$627$	−2.12324e14	−0.0875039
$628$	2.65008e15	1.08263
$629$	−1.01786e15	−0.412202
$630$	1.54585e15	0.620576
$631$	−3.76713e15	−1.49916	−0.749581	−	0.661912i	$-0.769745\pi$
$631$	−3.76713e15	−1.49916	−0.749581	+	0.661912i	$0.769745\pi$
$632$	−1.22661e15	−0.483909
$633$	−2.18785e15	−0.855653
$634$	4.62754e15	1.79415
$635$	4.79083e15	1.84143
$636$	−1.30355e15	−0.496723
$637$	−3.50095e14	−0.132257
$638$	5.36269e14	0.200849
$639$	−8.15814e14	−0.302926
$640$	−5.26064e15	−1.93664
$641$	3.19313e15	1.16546	0.582731	−	0.812665i	$-0.301984\pi$
$641$	3.19313e15	1.16546	0.582731	+	0.812665i	$0.301984\pi$
$642$	−4.96979e14	−0.179844
$643$	−1.62229e15	−0.582061	−0.291030	−	0.956714i	$-0.593998\pi$
$643$	−1.62229e15	−0.582061	−0.291030	+	0.956714i	$0.593998\pi$
$644$	1.33097e15	0.473473
$645$	−2.47749e15	−0.873842
$646$	2.56923e15	0.898513
$647$	1.56046e15	0.541102	0.270551	−	0.962706i	$-0.412794\pi$
$647$	1.56046e15	0.541102	0.270551	+	0.962706i	$0.412794\pi$
$648$	−2.58036e14	−0.0887191
$649$	−4.33637e13	−0.0147836
$650$	−2.03459e15	−0.687786
$651$	2.17214e15	0.728103
$652$	−1.39390e15	−0.463307
$653$	−3.73978e15	−1.23260	−0.616301	−	0.787511i	$-0.711370\pi$
$653$	−3.73978e15	−1.23260	−0.616301	+	0.787511i	$0.711370\pi$
$654$	−1.86507e15	−0.609560
$655$	3.81434e15	1.23621
$656$	2.85765e14	0.0918412
$657$	1.01184e15	0.322481
$658$	6.96550e15	2.20145
$659$	−8.52327e14	−0.267139	−0.133569	−	0.991039i	$-0.542644\pi$
$659$	−8.52327e14	−0.267139	−0.133569	+	0.991039i	$0.542644\pi$
$660$	−4.40988e14	−0.137068
$661$	6.46071e14	0.199146	0.0995732	−	0.995030i	$-0.468252\pi$
$661$	6.46071e14	0.199146	0.0995732	+	0.995030i	$0.468252\pi$
$662$	7.16167e15	2.18925
$663$	3.78189e14	0.114653
$664$	−1.34601e15	−0.404692
$665$	5.26566e15	1.57012
$666$	1.72855e15	0.511179
$667$	−1.41649e15	−0.415453
$668$	−1.10088e15	−0.320236
$669$	6.23084e14	0.179764
$670$	9.81949e15	2.80981
$671$	6.29892e14	0.178769
$672$	2.04840e15	0.576611
$673$	−5.08949e15	−1.42099	−0.710495	−	0.703702i	$-0.751529\pi$
$673$	−5.08949e15	−1.42099	−0.710495	+	0.703702i	$0.751529\pi$
$674$	8.86687e15	2.45551
$675$	6.52246e14	0.179160
$676$	−4.31869e15	−1.17664
$677$	−3.90992e14	−0.105665	−0.0528324	−	0.998603i	$-0.516825\pi$
$677$	−3.90992e14	−0.105665	−0.0528324	+	0.998603i	$0.516825\pi$
$678$	−4.66296e15	−1.24997
$679$	2.54594e15	0.676962
$680$	1.78946e15	0.471980
$681$	1.14746e15	0.300212
$682$	−1.03150e15	−0.267705
$683$	−1.81796e15	−0.468026	−0.234013	−	0.972233i	$-0.575186\pi$
$683$	−1.81796e15	−0.468026	−0.234013	+	0.972233i	$0.575186\pi$
$684$	−2.62103e15	−0.669366
$685$	−1.31538e15	−0.333238
$686$	6.84138e15	1.71934
$687$	−4.23910e15	−1.05685
$688$	−1.06092e15	−0.262388
$689$	−1.08803e15	−0.266954
$690$	1.93902e15	0.471967
$691$	4.28858e15	1.03558	0.517791	−	0.855507i	$-0.326754\pi$
$691$	4.28858e15	1.03558	0.517791	+	0.855507i	$0.326754\pi$
$692$	3.58916e15	0.859823
$693$	1.34830e14	0.0320445
$694$	−6.47795e15	−1.52743
$695$	3.15739e15	0.738604
$696$	2.21997e15	0.515225
$697$	−7.04306e14	−0.162174
$698$	3.56705e14	0.0814899
$699$	1.60228e14	0.0363174
$700$	5.27270e15	1.18575
$701$	4.36940e15	0.974929	0.487464	−	0.873143i	$-0.337922\pi$
$701$	4.36940e15	0.974929	0.487464	+	0.873143i	$0.337922\pi$
$702$	−6.42248e14	−0.142183
$703$	5.88798e15	1.29334
$704$	−8.47226e14	−0.184650
$705$	6.09596e15	1.31826
$706$	7.15829e15	1.53597
$707$	3.66076e15	0.779407
$708$	−5.35303e14	−0.113088
$709$	−5.54169e14	−0.116168	−0.0580842	−	0.998312i	$-0.518499\pi$
$709$	−5.54169e14	−0.116168	−0.0580842	+	0.998312i	$0.518499\pi$
$710$	−9.60787e15	−1.99851
$711$	9.78736e14	0.202015
$712$	7.12505e15	1.45931
$713$	2.72460e15	0.553745
$714$	−1.63151e15	−0.329041
$715$	−3.68079e14	−0.0736644
$716$	−1.84759e15	−0.366930
$717$	−2.20209e15	−0.433990
$718$	−5.55907e15	−1.08722
$719$	−1.11509e15	−0.216422	−0.108211	−	0.994128i	$-0.534512\pi$
$719$	−1.11509e15	−0.216422	−0.108211	+	0.994128i	$0.534512\pi$
$720$	5.79333e14	0.111583
$721$	6.33798e15	1.21145
$722$	−6.51920e15	−1.23663
$723$	−5.44453e15	−1.02494
$724$	7.41974e14	0.138620
$725$	−5.61151e15	−1.04045
$726$	4.90138e15	0.901917
$727$	8.02340e15	1.46528	0.732638	−	0.680619i	$-0.238289\pi$
$727$	8.02340e15	1.46528	0.732638	+	0.680619i	$0.238289\pi$
$728$	−1.74107e15	−0.315568
$729$	2.05891e14	0.0370370
$730$	1.19165e16	2.12752
$731$	2.61477e15	0.463327
$732$	7.77570e15	1.36750
$733$	−9.57279e14	−0.167096	−0.0835481	−	0.996504i	$-0.526625\pi$
$733$	−9.57279e14	−0.167096	−0.0835481	+	0.996504i	$0.526625\pi$
$734$	−9.04204e15	−1.56653
$735$	1.32177e15	0.227288
$736$	2.56938e15	0.438531
$737$	8.56460e14	0.145089
$738$	1.19606e15	0.201115
$739$	−9.01924e14	−0.150531	−0.0752654	−	0.997164i	$-0.523980\pi$
$739$	−9.01924e14	−0.150531	−0.0752654	+	0.997164i	$0.523980\pi$
$740$	1.22291e16	2.02590
$741$	−2.18770e15	−0.359738
$742$	4.69379e15	0.766130
$743$	2.27033e15	0.367833	0.183916	−	0.982942i	$-0.441122\pi$
$743$	2.27033e15	0.367833	0.183916	+	0.982942i	$0.441122\pi$
$744$	−4.27008e15	−0.686728
$745$	8.35800e15	1.33427
$746$	−1.78867e16	−2.83444
$747$	1.07401e15	0.168945
$748$	4.65424e14	0.0726758
$749$	1.07500e15	0.166632
$750$	−5.69818e14	−0.0876798
$751$	−3.58007e15	−0.546855	−0.273427	−	0.961893i	$-0.588157\pi$
$751$	−3.58007e15	−0.546855	−0.273427	+	0.961893i	$0.588157\pi$
$752$	2.61043e15	0.395835
$753$	2.76095e15	0.415610
$754$	5.52549e15	0.825712
$755$	2.87273e15	0.426173
$756$	1.66441e15	0.245126
$757$	−9.09591e15	−1.32990	−0.664950	−	0.746888i	$-0.731547\pi$
$757$	−9.09591e15	−1.32990	−0.664950	+	0.746888i	$0.731547\pi$
$758$	−4.21921e15	−0.612422
$759$	1.69122e14	0.0243708
$760$	−1.03514e16	−1.48090
$761$	−6.24456e15	−0.886924	−0.443462	−	0.896293i	$-0.646250\pi$
$761$	−6.24456e15	−0.886924	−0.443462	+	0.896293i	$0.646250\pi$
$762$	8.58670e15	1.21080
$763$	4.03428e15	0.564782
$764$	−5.07355e15	−0.705177
$765$	−1.42784e15	−0.197035
$766$	9.34344e15	1.28011
$767$	−4.46802e14	−0.0607771
$768$	−2.47741e15	−0.334589
$769$	9.24521e15	1.23972	0.619858	−	0.784714i	$-0.287190\pi$
$769$	9.24521e15	1.23972	0.619858	+	0.784714i	$0.287190\pi$
$770$	1.58790e15	0.211409
$771$	3.91365e14	0.0517349
$772$	4.76261e15	0.625100
$773$	−1.06718e15	−0.139075	−0.0695376	−	0.997579i	$-0.522152\pi$
$773$	−1.06718e15	−0.139075	−0.0695376	+	0.997579i	$0.522152\pi$
$774$	−4.44045e15	−0.574581
$775$	1.07936e16	1.38678
$776$	−5.00491e15	−0.638493
$777$	−3.73898e15	−0.473628
$778$	−7.53422e15	−0.947656
$779$	4.07417e15	0.508842
$780$	−4.54375e15	−0.563500
$781$	−8.38002e14	−0.103196
$782$	−2.04646e15	−0.250246
$783$	−1.77136e15	−0.215088
$784$	5.66013e14	0.0682478
$785$	−8.35111e15	−0.999911
$786$	6.83651e15	0.812850
$787$	1.31820e16	1.55640	0.778201	−	0.628016i	$-0.216133\pi$
$787$	1.31820e16	1.55640	0.778201	+	0.628016i	$0.216133\pi$
$788$	4.26536e15	0.500105
$789$	−2.77808e15	−0.323461
$790$	1.15266e16	1.33276
$791$	1.00863e16	1.15815
$792$	−2.65054e14	−0.0302235
$793$	6.49014e15	0.734940
$794$	1.66391e16	1.87119
$795$	4.10785e15	0.458770
$796$	−3.31589e15	−0.367772
$797$	8.00193e14	0.0881401	0.0440701	−	0.999028i	$-0.485968\pi$
$797$	8.00193e14	0.0881401	0.0440701	+	0.999028i	$0.485968\pi$
$798$	9.43774e15	1.03241
$799$	−6.43376e15	−0.698968
$800$	1.01787e16	1.09824
$801$	−5.68520e15	−0.609210
$802$	2.14918e16	2.28725
$803$	1.03936e15	0.109858
$804$	1.05726e16	1.10987
$805$	−4.19424e15	−0.437296
$806$	−1.06282e16	−1.10057
$807$	−9.63009e15	−0.990435
$808$	−7.19646e15	−0.735116
$809$	−6.00294e15	−0.609042	−0.304521	−	0.952506i	$-0.598496\pi$
$809$	−6.00294e15	−0.609042	−0.304521	+	0.952506i	$0.598496\pi$
$810$	2.42479e15	0.244347
$811$	−2.41855e15	−0.242070	−0.121035	−	0.992648i	$-0.538621\pi$
$811$	−2.41855e15	−0.242070	−0.121035	+	0.992648i	$0.538621\pi$
$812$	−1.43195e16	−1.42354
$813$	1.50105e15	0.148217
$814$	1.77556e15	0.174141
$815$	4.39255e15	0.427907
$816$	−6.11435e14	−0.0591636
$817$	−1.51256e16	−1.45375
$818$	−2.64817e16	−2.52815
$819$	1.38923e15	0.131738
$820$	8.46187e15	0.797058
$821$	−1.95856e16	−1.83252	−0.916260	−	0.400584i	$-0.868807\pi$
$821$	−1.95856e16	−1.83252	−0.916260	+	0.400584i	$0.868807\pi$
$822$	−2.35759e15	−0.219115
$823$	−8.60498e15	−0.794421	−0.397211	−	0.917727i	$-0.630022\pi$
$823$	−8.60498e15	−0.794421	−0.397211	+	0.917727i	$0.630022\pi$
$824$	−1.24595e16	−1.14261
$825$	6.69986e14	0.0610336
$826$	1.92751e15	0.174424
$827$	−9.60942e15	−0.863807	−0.431904	−	0.901920i	$-0.642158\pi$
$827$	−9.60942e15	−0.863807	−0.431904	+	0.901920i	$0.642158\pi$
$828$	2.08772e15	0.186426
$829$	−1.43126e16	−1.26960	−0.634800	−	0.772676i	$-0.718918\pi$
$829$	−1.43126e16	−1.26960	−0.634800	+	0.772676i	$0.718918\pi$
$830$	1.26486e16	1.11459
$831$	−1.24835e16	−1.09277
$832$	−8.72946e15	−0.759118
$833$	−1.39502e15	−0.120512
$834$	5.65905e15	0.485658
$835$	3.46918e15	0.295768
$836$	−2.69232e15	−0.228030
$837$	3.40717e15	0.286684
$838$	−8.07222e15	−0.674763
$839$	−4.75190e15	−0.394618	−0.197309	−	0.980341i	$-0.563220\pi$
$839$	−4.75190e15	−0.394618	−0.197309	+	0.980341i	$0.563220\pi$
$840$	6.57336e15	0.542314
$841$	3.03912e15	0.249098
$842$	−3.20197e16	−2.60736
$843$	4.01940e15	0.325169
$844$	−2.77425e16	−2.22978
$845$	1.36094e16	1.08674
$846$	1.09259e16	0.866804
$847$	−1.06020e16	−0.835663
$848$	1.75907e15	0.137755
$849$	2.22158e15	0.172850
$850$	−8.10718e15	−0.626709
$851$	−4.68993e15	−0.360209
$852$	−1.03447e16	−0.789406
$853$	3.78608e15	0.287058	0.143529	−	0.989646i	$-0.454155\pi$
$853$	3.78608e15	0.287058	0.143529	+	0.989646i	$0.454155\pi$
$854$	−2.79985e16	−2.10920
$855$	8.25959e15	0.618222
$856$	−2.11328e15	−0.157163
$857$	4.05160e15	0.299386	0.149693	−	0.988733i	$-0.452171\pi$
$857$	4.05160e15	0.299386	0.149693	+	0.988733i	$0.452171\pi$
$858$	−6.59715e14	−0.0484369
$859$	−1.59860e16	−1.16621	−0.583107	−	0.812395i	$-0.698163\pi$
$859$	−1.59860e16	−1.16621	−0.583107	+	0.812395i	$0.698163\pi$
$860$	−3.14151e16	−2.27718
$861$	−2.58718e15	−0.186341
$862$	−1.55100e16	−1.11000
$863$	1.06600e16	0.758052	0.379026	−	0.925386i	$-0.376259\pi$
$863$	1.06600e16	0.758052	0.379026	+	0.925386i	$0.376259\pi$
$864$	3.21307e15	0.227036
$865$	−1.13104e16	−0.794127
$866$	3.09660e16	2.16041
$867$	−6.82111e15	−0.472879
$868$	2.75433e16	1.89739
$869$	1.00536e15	0.0688194
$870$	−2.08613e16	−1.41901
$871$	8.82460e15	0.596479
$872$	−7.93074e15	−0.532688
$873$	3.99350e15	0.266548
$874$	1.18381e16	0.785179
$875$	1.23256e15	0.0812388
$876$	1.28304e16	0.840365
$877$	5.94643e15	0.387043	0.193521	−	0.981096i	$-0.438009\pi$
$877$	5.94643e15	0.387043	0.193521	+	0.981096i	$0.438009\pi$
$878$	2.28101e16	1.47539
$879$	−3.55571e15	−0.228553
$880$	5.95089e14	0.0380126
$881$	2.84161e16	1.80384	0.901918	−	0.431907i	$-0.142159\pi$
$881$	2.84161e16	1.80384	0.901918	+	0.431907i	$0.142159\pi$
$882$	2.36904e15	0.149450
$883$	−8.18053e15	−0.512858	−0.256429	−	0.966563i	$-0.582546\pi$
$883$	−8.18053e15	−0.512858	−0.256429	+	0.966563i	$0.582546\pi$
$884$	4.79553e15	0.298778
$885$	1.68689e15	0.104447
$886$	−3.18071e16	−1.95721
$887$	−1.99589e16	−1.22055	−0.610277	−	0.792188i	$-0.708942\pi$
$887$	−1.99589e16	−1.22055	−0.610277	+	0.792188i	$0.708942\pi$
$888$	7.35023e15	0.446714
$889$	−1.85737e16	−1.12186
$890$	−6.69548e16	−4.01918
$891$	2.11491e14	0.0126172
$892$	7.90085e15	0.468454
$893$	3.72171e16	2.19311
$894$	1.49802e16	0.877327
$895$	5.82224e15	0.338894
$896$	2.03951e16	1.17986
$897$	1.74256e15	0.100191
$898$	1.30467e16	0.745558
$899$	−2.93132e16	−1.66489
$900$	8.27064e15	0.466880
$901$	−4.33547e15	−0.243248
$902$	1.22859e15	0.0685130
$903$	9.60502e15	0.532372
$904$	−1.98281e16	−1.09233
$905$	−2.33816e15	−0.128029
$906$	5.14885e15	0.280224
$907$	−2.33057e16	−1.26073	−0.630366	−	0.776298i	$-0.717095\pi$
$907$	−2.33057e16	−1.26073	−0.630366	+	0.776298i	$0.717095\pi$
$908$	1.45500e16	0.782334
$909$	5.74218e15	0.306885
$910$	1.63610e16	0.869125
$911$	−1.41043e16	−0.744731	−0.372366	−	0.928086i	$-0.621453\pi$
$911$	−1.41043e16	−0.744731	−0.372366	+	0.928086i	$0.621453\pi$
$912$	3.53694e15	0.185634
$913$	1.10322e15	0.0575536
$914$	−1.12493e16	−0.583340
$915$	−2.45034e16	−1.26302
$916$	−5.37528e16	−2.75408
$917$	−1.47879e16	−0.753138
$918$	−2.55915e15	−0.129557
$919$	−2.24983e16	−1.13218	−0.566088	−	0.824345i	$-0.691544\pi$
$919$	−2.24983e16	−1.13218	−0.566088	+	0.824345i	$0.691544\pi$
$920$	8.24519e15	0.412447
$921$	2.37432e15	0.118062
$922$	4.46833e16	2.20864
$923$	−8.63442e15	−0.424252
$924$	1.70967e15	0.0835060
$925$	−1.85794e16	−0.902097
$926$	2.35845e16	1.13833
$927$	9.94162e15	0.477000
$928$	−2.76432e16	−1.31848
$929$	−1.50141e16	−0.711888	−0.355944	−	0.934507i	$-0.615841\pi$
$929$	−1.50141e16	−0.711888	−0.355944	+	0.934507i	$0.615841\pi$
$930$	4.01264e16	1.89136
$931$	8.06969e15	0.378124
$932$	2.03173e15	0.0946410
$933$	−8.23828e15	−0.381494
$934$	−5.44536e16	−2.50679
$935$	−1.46668e15	−0.0671229
$936$	−2.73100e15	−0.124252
$937$	−3.18844e15	−0.144215	−0.0721075	−	0.997397i	$-0.522972\pi$
$937$	−3.18844e15	−0.144215	−0.0721075	+	0.997397i	$0.522972\pi$
$938$	−3.80694e16	−1.71183
$939$	−1.67565e16	−0.749071
$940$	7.72983e16	3.43532
$941$	5.16849e15	0.228360	0.114180	−	0.993460i	$-0.463576\pi$
$941$	5.16849e15	0.228360	0.114180	+	0.993460i	$0.463576\pi$
$942$	−1.49679e16	−0.657476
$943$	−3.24519e15	−0.141718
$944$	7.22363e14	0.0313624
$945$	−5.24500e15	−0.226397
$946$	−4.56122e15	−0.195740
$947$	3.76798e16	1.60762	0.803811	−	0.594885i	$-0.202802\pi$
$947$	3.76798e16	1.60762	0.803811	+	0.594885i	$0.202802\pi$
$948$	1.24106e16	0.526438
$949$	1.07092e16	0.451639
$950$	4.68973e16	1.96638
$951$	−1.57010e16	−0.654538
$952$	−6.93760e15	−0.287545
$953$	2.04664e15	0.0843396	0.0421698	−	0.999110i	$-0.486573\pi$
$953$	2.04664e15	0.0843396	0.0421698	+	0.999110i	$0.486573\pi$
$954$	7.36257e15	0.301657
$955$	1.59881e16	0.651297
$956$	−2.79230e16	−1.13095
$957$	−1.81953e15	−0.0732731
$958$	3.77335e15	0.151083
$959$	5.09964e15	0.203019
$960$	3.29578e16	1.30457
$961$	3.09748e16	1.21908
$962$	1.82946e16	0.715914
$963$	1.68622e15	0.0656101
$964$	−6.90379e16	−2.67094
$965$	−1.50083e16	−0.577339
$966$	−7.51742e15	−0.287538
$967$	−2.18214e16	−0.829923	−0.414961	−	0.909839i	$-0.636205\pi$
$967$	−2.18214e16	−0.829923	−0.414961	+	0.909839i	$0.636205\pi$
$968$	2.08419e16	0.788176
$969$	−8.71727e15	−0.327793
$970$	4.70316e16	1.75851
$971$	−7.42026e15	−0.275876	−0.137938	−	0.990441i	$-0.544047\pi$
$971$	−7.42026e15	−0.275876	−0.137938	+	0.990441i	$0.544047\pi$
$972$	2.61075e15	0.0965163
$973$	−1.22409e16	−0.449981
$974$	2.57108e16	0.939813
$975$	6.90325e15	0.250916
$976$	−1.04929e16	−0.379246
$977$	−3.89311e16	−1.39919	−0.699595	−	0.714540i	$-0.746636\pi$
$977$	−3.89311e16	−1.39919	−0.699595	+	0.714540i	$0.746636\pi$
$978$	7.87285e15	0.281364
$979$	−5.83983e15	−0.207537
$980$	1.67604e16	0.592299
$981$	6.32807e15	0.222378
$982$	−5.86143e16	−2.04829
$983$	2.02760e16	0.704591	0.352295	−	0.935889i	$-0.385401\pi$
$983$	2.02760e16	0.704591	0.352295	+	0.935889i	$0.385401\pi$
$984$	5.08597e15	0.175752
$985$	−1.34413e16	−0.461894
$986$	2.20173e16	0.752387
$987$	−2.36336e16	−0.803129
$988$	−2.77405e16	−0.937457
$989$	1.20479e16	0.404886
$990$	2.49074e15	0.0832404
$991$	−1.25418e16	−0.416827	−0.208414	−	0.978041i	$-0.566830\pi$
$991$	−1.25418e16	−0.416827	−0.208414	+	0.978041i	$0.566830\pi$
$992$	5.31712e16	1.75737
$993$	−2.42992e16	−0.798676
$994$	3.72490e16	1.21756
$995$	1.04493e16	0.339672
$996$	1.36187e16	0.440259
$997$	8.28428e15	0.266337	0.133169	−	0.991093i	$-0.457485\pi$
$997$	8.28428e15	0.266337	0.133169	+	0.991093i	$0.457485\pi$
$998$	−9.83877e14	−0.0314574
$999$	−5.86487e15	−0.186487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.4	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.4	✓	27	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)

\(f(q)\)	\(=\)	\(q-71.6191 q^{2} +243.000 q^{3} +3081.30 q^{4} -9710.01 q^{5} -17403.4 q^{6} +37645.0 q^{7} -74003.9 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-71.6191 q^{2} +243.000 q^{3} +3081.30 q^{4} -9710.01 q^{5} -17403.4 q^{6} +37645.0 q^{7} -74003.9 q^{8} +59049.0 q^{9} +695422. q^{10} +60655.0 q^{11} +748755. q^{12} +624964. q^{13} -2.69610e6 q^{14} -2.35953e6 q^{15} -1.01041e6 q^{16} +2.49028e6 q^{17} -4.22904e6 q^{18} -1.44054e7 q^{19} -2.99194e7 q^{20} +9.14772e6 q^{21} -4.34406e6 q^{22} +1.14743e7 q^{23} -1.79829e7 q^{24} +4.54562e7 q^{25} -4.47593e7 q^{26} +1.43489e7 q^{27} +1.15995e8 q^{28} -1.23449e8 q^{29} +1.68988e8 q^{30} +2.37452e8 q^{31} +2.23924e8 q^{32} +1.47392e7 q^{33} -1.78352e8 q^{34} -3.65533e8 q^{35} +1.81948e8 q^{36} -4.08733e8 q^{37} +1.03170e9 q^{38} +1.51866e8 q^{39} +7.18578e8 q^{40} -2.82822e8 q^{41} -6.55152e8 q^{42} +1.04999e9 q^{43} +1.86896e8 q^{44} -5.73366e8 q^{45} -8.21780e8 q^{46} -2.58355e9 q^{47} -2.45529e8 q^{48} -5.60184e8 q^{49} -3.25553e9 q^{50} +6.05138e8 q^{51} +1.92570e9 q^{52} -1.74096e9 q^{53} -1.02766e9 q^{54} -5.88961e8 q^{55} -2.78587e9 q^{56} -3.50052e9 q^{57} +8.84130e9 q^{58} -7.14924e8 q^{59} -7.27042e9 q^{60} +1.03848e10 q^{61} -1.70061e10 q^{62} +2.22290e9 q^{63} -1.39679e10 q^{64} -6.06840e9 q^{65} -1.05561e9 q^{66} +1.41202e10 q^{67} +7.67329e9 q^{68} +2.78826e9 q^{69} +2.61791e10 q^{70} -1.38159e10 q^{71} -4.36986e9 q^{72} +1.71356e10 q^{73} +2.92731e10 q^{74} +1.10459e10 q^{75} -4.43874e10 q^{76} +2.28336e9 q^{77} -1.08765e10 q^{78} +1.65750e10 q^{79} +9.81105e9 q^{80} +3.48678e9 q^{81} +2.02554e10 q^{82} +1.81884e10 q^{83} +2.81869e10 q^{84} -2.41806e10 q^{85} -7.51994e10 q^{86} -2.99981e10 q^{87} -4.48871e9 q^{88} -9.62794e10 q^{89} +4.10640e10 q^{90} +2.35267e10 q^{91} +3.53558e10 q^{92} +5.77008e10 q^{93} +1.85031e11 q^{94} +1.39877e11 q^{95} +5.44136e10 q^{96} +6.76303e10 q^{97} +4.01199e10 q^{98} +3.58162e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \)	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about