LMFDB - Embedded newform 177.12.a.d.1.17

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:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q+23.7768 q^{2} +243.000 q^{3} -1482.66 q^{4} +6921.85 q^{5} +5777.76 q^{6} +24486.4 q^{7} -83947.8 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+23.7768 q^{2} +243.000 q^{3} -1482.66 q^{4} +6921.85 q^{5} +5777.76 q^{6} +24486.4 q^{7} -83947.8 q^{8} +59049.0 q^{9} +164579. q^{10} -888355. q^{11} -360287. q^{12} -914574. q^{13} +582209. q^{14} +1.68201e6 q^{15} +1.04049e6 q^{16} -3.69383e6 q^{17} +1.40400e6 q^{18} +4.55382e6 q^{19} -1.02628e7 q^{20} +5.95021e6 q^{21} -2.11222e7 q^{22} +7.76606e6 q^{23} -2.03993e7 q^{24} -916085. q^{25} -2.17456e7 q^{26} +1.43489e7 q^{27} -3.63052e7 q^{28} +2.05865e8 q^{29} +3.99928e7 q^{30} +3.06950e8 q^{31} +1.96665e8 q^{32} -2.15870e8 q^{33} -8.78273e7 q^{34} +1.69492e8 q^{35} -8.75499e7 q^{36} +2.90102e8 q^{37} +1.08275e8 q^{38} -2.22241e8 q^{39} -5.81075e8 q^{40} -7.24652e7 q^{41} +1.41477e8 q^{42} -5.44136e8 q^{43} +1.31713e9 q^{44} +4.08728e8 q^{45} +1.84652e8 q^{46} -4.59684e8 q^{47} +2.52838e8 q^{48} -1.37774e9 q^{49} -2.17816e7 q^{50} -8.97600e8 q^{51} +1.35601e9 q^{52} +2.43404e9 q^{53} +3.41171e8 q^{54} -6.14907e9 q^{55} -2.05558e9 q^{56} +1.10658e9 q^{57} +4.89480e9 q^{58} +7.14924e8 q^{59} -2.49386e9 q^{60} +1.80781e9 q^{61} +7.29829e9 q^{62} +1.44590e9 q^{63} +2.54513e9 q^{64} -6.33055e9 q^{65} -5.13270e9 q^{66} +1.65711e9 q^{67} +5.47671e9 q^{68} +1.88715e9 q^{69} +4.02996e9 q^{70} +2.44530e10 q^{71} -4.95704e9 q^{72} -3.35655e10 q^{73} +6.89770e9 q^{74} -2.22609e8 q^{75} -6.75179e9 q^{76} -2.17527e10 q^{77} -5.28419e9 q^{78} +2.48737e10 q^{79} +7.20210e9 q^{80} +3.48678e9 q^{81} -1.72299e9 q^{82} +6.34936e9 q^{83} -8.82216e9 q^{84} -2.55681e10 q^{85} -1.29378e10 q^{86} +5.00251e10 q^{87} +7.45755e10 q^{88} +8.37878e10 q^{89} +9.71825e9 q^{90} -2.23947e10 q^{91} -1.15145e10 q^{92} +7.45889e10 q^{93} -1.09298e10 q^{94} +3.15209e10 q^{95} +4.77895e10 q^{96} +1.27019e11 q^{97} -3.27582e10 q^{98} -5.24565e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) $	\( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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 $

$2$	23.7768	0.525398	0.262699	−	0.964878i	$-0.415387\pi$
$2$	23.7768	0.525398	0.262699	+	0.964878i	$0.415387\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1482.66	−0.723957
$5$	6921.85	0.990575	0.495287	−	0.868729i	$-0.335063\pi$
$5$	6921.85	0.990575	0.495287	+	0.868729i	$0.335063\pi$
$6$	5777.76	0.303338
$7$	24486.4	0.550664	0.275332	−	0.961349i	$-0.411212\pi$
$7$	24486.4	0.550664	0.275332	+	0.961349i	$0.411212\pi$
$8$	−83947.8	−0.905763
$9$	59049.0	0.333333
$10$	164579.	0.520446
$11$	−888355.	−1.66313	−0.831567	−	0.555425i	$-0.812556\pi$
$11$	−888355.	−1.66313	−0.831567	+	0.555425i	$0.812556\pi$
$12$	−360287.	−0.417977
$13$	−914574.	−0.683172	−0.341586	−	0.939850i	$-0.610964\pi$
$13$	−914574.	−0.683172	−0.341586	+	0.939850i	$0.610964\pi$
$14$	582209.	0.289317
$15$	1.68201e6	0.571909
$16$	1.04049e6	0.248072
$17$	−3.69383e6	−0.630968	−0.315484	−	0.948931i	$-0.602167\pi$
$17$	−3.69383e6	−0.630968	−0.315484	+	0.948931i	$0.602167\pi$
$18$	1.40400e6	0.175133
$19$	4.55382e6	0.421921	0.210961	−	0.977495i	$-0.432341\pi$
$19$	4.55382e6	0.421921	0.210961	+	0.977495i	$0.432341\pi$
$20$	−1.02628e7	−0.717134
$21$	5.95021e6	0.317926
$22$	−2.11222e7	−0.873806
$23$	7.76606e6	0.251593	0.125796	−	0.992056i	$-0.459851\pi$
$23$	7.76606e6	0.251593	0.125796	+	0.992056i	$0.459851\pi$
$24$	−2.03993e7	−0.522943
$25$	−916085.	−0.0187614
$26$	−2.17456e7	−0.358937
$27$	1.43489e7	0.192450
$28$	−3.63052e7	−0.398657
$29$	2.05865e8	1.86377	0.931886	−	0.362750i	$-0.118162\pi$
$29$	2.05865e8	1.86377	0.931886	+	0.362750i	$0.118162\pi$
$30$	3.99928e7	0.300479
$31$	3.06950e8	1.92566	0.962828	−	0.270114i	$-0.0870615\pi$
$31$	3.06950e8	1.92566	0.962828	+	0.270114i	$0.0870615\pi$
$32$	1.96665e8	1.03610
$33$	−2.15870e8	−0.960210
$34$	−8.78273e7	−0.331509
$35$	1.69492e8	0.545474
$36$	−8.75499e7	−0.241319
$37$	2.90102e8	0.687767	0.343884	−	0.939012i	$-0.388257\pi$
$37$	2.90102e8	0.687767	0.343884	+	0.939012i	$0.388257\pi$
$38$	1.08275e8	0.221676
$39$	−2.22241e8	−0.394430
$40$	−5.81075e8	−0.897226
$41$	−7.24652e7	−0.0976828	−0.0488414	−	0.998807i	$-0.515553\pi$
$41$	−7.24652e7	−0.0976828	−0.0488414	+	0.998807i	$0.515553\pi$
$42$	1.41477e8	0.167037
$43$	−5.44136e8	−0.564457	−0.282229	−	0.959347i	$-0.591074\pi$
$43$	−5.44136e8	−0.564457	−0.282229	+	0.959347i	$0.591074\pi$
$44$	1.31713e9	1.20404
$45$	4.08728e8	0.330192
$46$	1.84652e8	0.132186
$47$	−4.59684e8	−0.292362	−0.146181	−	0.989258i	$-0.546698\pi$
$47$	−4.59684e8	−0.292362	−0.146181	+	0.989258i	$0.546698\pi$
$48$	2.52838e8	0.143224
$49$	−1.37774e9	−0.696769
$50$	−2.17816e7	−0.00985721
$51$	−8.97600e8	−0.364290
$52$	1.35601e9	0.494588
$53$	2.43404e9	0.799485	0.399743	−	0.916627i	$-0.369100\pi$
$53$	2.43404e9	0.799485	0.399743	+	0.916627i	$0.369100\pi$
$54$	3.41171e8	0.101113
$55$	−6.14907e9	−1.64746
$56$	−2.05558e9	−0.498771
$57$	1.10658e9	0.243596
$58$	4.89480e9	0.979222
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−2.49386e9	−0.414037
$61$	1.80781e9	0.274055	0.137028	−	0.990567i	$-0.456245\pi$
$61$	1.80781e9	0.274055	0.137028	+	0.990567i	$0.456245\pi$
$62$	7.29829e9	1.01174
$63$	1.44590e9	0.183555
$64$	2.54513e9	0.296293
$65$	−6.33055e9	−0.676734
$66$	−5.13270e9	−0.504492
$67$	1.65711e9	0.149948	0.0749738	−	0.997186i	$-0.476113\pi$
$67$	1.65711e9	0.149948	0.0749738	+	0.997186i	$0.476113\pi$
$68$	5.47671e9	0.456794
$69$	1.88715e9	0.145257
$70$	4.02996e9	0.286591
$71$	2.44530e10	1.60846	0.804231	−	0.594317i	$-0.202578\pi$
$71$	2.44530e10	1.60846	0.804231	+	0.594317i	$0.202578\pi$
$72$	−4.95704e9	−0.301921
$73$	−3.35655e10	−1.89503	−0.947517	−	0.319705i	$-0.896416\pi$
$73$	−3.35655e10	−1.89503	−0.947517	+	0.319705i	$0.896416\pi$
$74$	6.89770e9	0.361351
$75$	−2.22609e8	−0.0108319
$76$	−6.75179e9	−0.305453
$77$	−2.17527e10	−0.915827
$78$	−5.28419e9	−0.207233
$79$	2.48737e10	0.909477	0.454739	−	0.890625i	$-0.349733\pi$
$79$	2.48737e10	0.909477	0.454739	+	0.890625i	$0.349733\pi$
$80$	7.20210e9	0.245733
$81$	3.48678e9	0.111111
$82$	−1.72299e9	−0.0513223
$83$	6.34936e9	0.176930	0.0884648	−	0.996079i	$-0.471804\pi$
$83$	6.34936e9	0.176930	0.0884648	+	0.996079i	$0.471804\pi$
$84$	−8.82216e9	−0.230165
$85$	−2.55681e10	−0.625021
$86$	−1.29378e10	−0.296565
$87$	5.00251e10	1.07605
$88$	7.45755e10	1.50640
$89$	8.37878e10	1.59051	0.795254	−	0.606276i	$-0.207337\pi$
$89$	8.37878e10	1.59051	0.795254	+	0.606276i	$0.207337\pi$
$90$	9.71825e9	0.173482
$91$	−2.23947e10	−0.376198
$92$	−1.15145e10	−0.182142
$93$	7.45889e10	1.11178
$94$	−1.09298e10	−0.153606
$95$	3.15209e10	0.417944
$96$	4.77895e10	0.598192
$97$	1.27019e11	1.50184	0.750921	−	0.660392i	$-0.229610\pi$
$97$	1.27019e11	1.50184	0.750921	+	0.660392i	$0.229610\pi$
$98$	−3.27582e10	−0.366081
$99$	−5.24565e10	−0.554378
$100$	1.35825e9	0.0135825
$101$	3.15002e10	0.298227	0.149113	−	0.988820i	$-0.452358\pi$
$101$	3.15002e10	0.298227	0.149113	+	0.988820i	$0.452358\pi$
$102$	−2.13420e10	−0.191397
$103$	1.13132e11	0.961568	0.480784	−	0.876839i	$-0.340352\pi$
$103$	1.13132e11	0.961568	0.480784	+	0.876839i	$0.340352\pi$
$104$	7.67765e10	0.618792
$105$	4.11864e10	0.314929
$106$	5.78736e10	0.420048
$107$	−2.48504e11	−1.71286	−0.856431	−	0.516262i	$-0.827323\pi$
$107$	−2.48504e11	−1.71286	−0.856431	+	0.516262i	$0.827323\pi$
$108$	−2.12746e10	−0.139326
$109$	2.02030e11	1.25768	0.628840	−	0.777535i	$-0.283530\pi$
$109$	2.02030e11	1.25768	0.628840	+	0.777535i	$0.283530\pi$
$110$	−1.46205e11	−0.865570
$111$	7.04948e10	0.397083
$112$	2.54778e10	0.136604
$113$	1.51738e11	0.774755	0.387377	−	0.921921i	$-0.373381\pi$
$113$	1.51738e11	0.774755	0.387377	+	0.921921i	$0.373381\pi$
$114$	2.63109e10	0.127985
$115$	5.37555e10	0.249221
$116$	−3.05228e11	−1.34929
$117$	−5.40047e10	−0.227724
$118$	1.69986e10	0.0684009
$119$	−9.04487e10	−0.347451
$120$	−1.41201e11	−0.518014
$121$	5.03864e11	1.76601
$122$	4.29839e10	0.143988
$123$	−1.76090e10	−0.0563972
$124$	−4.55104e11	−1.39409
$125$	−3.44322e11	−1.00916
$126$	3.43788e10	0.0964391
$127$	−2.49462e11	−0.670014	−0.335007	−	0.942216i	$-0.608739\pi$
$127$	−2.49462e11	−0.670014	−0.335007	+	0.942216i	$0.608739\pi$
$128$	−3.42254e11	−0.880428
$129$	−1.32225e11	−0.325890
$130$	−1.50520e11	−0.355554
$131$	−3.18121e11	−0.720444	−0.360222	−	0.932867i	$-0.617299\pi$
$131$	−3.18121e11	−0.720444	−0.360222	+	0.932867i	$0.617299\pi$
$132$	3.20063e11	0.695151
$133$	1.11507e11	0.232337
$134$	3.94007e10	0.0787821
$135$	9.93210e10	0.190636
$136$	3.10089e11	0.571508
$137$	6.28463e11	1.11254	0.556271	−	0.831001i	$-0.312232\pi$
$137$	6.28463e11	1.11254	0.556271	+	0.831001i	$0.312232\pi$
$138$	4.48704e10	0.0763177
$139$	1.09931e12	1.79696	0.898480	−	0.439015i	$-0.144673\pi$
$139$	1.09931e12	1.79696	0.898480	+	0.439015i	$0.144673\pi$
$140$	−2.51299e11	−0.394900
$141$	−1.11703e11	−0.168795
$142$	5.81413e11	0.845082
$143$	8.12467e11	1.13621
$144$	6.14397e10	0.0826905
$145$	1.42497e12	1.84621
$146$	−7.98079e11	−0.995646
$147$	−3.34791e11	−0.402280
$148$	−4.30124e11	−0.497914
$149$	−6.56389e11	−0.732212	−0.366106	−	0.930573i	$-0.619309\pi$
$149$	−6.56389e11	−0.732212	−0.366106	+	0.930573i	$0.619309\pi$
$150$	−5.29292e9	−0.00569106
$151$	−1.51015e12	−1.56548	−0.782741	−	0.622348i	$-0.786179\pi$
$151$	−1.51015e12	−1.56548	−0.782741	+	0.622348i	$0.786179\pi$
$152$	−3.82284e11	−0.382161
$153$	−2.18117e11	−0.210323
$154$	−5.17208e11	−0.481173
$155$	2.12466e12	1.90751
$156$	3.29510e11	0.285550
$157$	−1.32963e12	−1.11246	−0.556229	−	0.831029i	$-0.687752\pi$
$157$	−1.32963e12	−1.11246	−0.556229	+	0.831029i	$0.687752\pi$
$158$	5.91417e11	0.477837
$159$	5.91472e11	0.461583
$160$	1.36128e12	1.02633
$161$	1.90163e11	0.138543
$162$	8.29045e10	0.0583775
$163$	2.23220e12	1.51950	0.759752	−	0.650213i	$-0.225320\pi$
$163$	2.23220e12	1.51950	0.759752	+	0.650213i	$0.225320\pi$
$164$	1.07442e11	0.0707182
$165$	−1.49422e12	−0.951160
$166$	1.50967e11	0.0929584
$167$	6.78703e11	0.404333	0.202167	−	0.979351i	$-0.435202\pi$
$167$	6.78703e11	0.404333	0.202167	+	0.979351i	$0.435202\pi$
$168$	−4.99507e11	−0.287966
$169$	−9.55715e11	−0.533275
$170$	−6.07928e11	−0.328385
$171$	2.68899e11	0.140640
$172$	8.06772e11	0.408643
$173$	3.16596e12	1.55329	0.776645	−	0.629939i	$-0.216920\pi$
$173$	3.16596e12	1.55329	0.776645	+	0.629939i	$0.216920\pi$
$174$	1.18944e12	0.565354
$175$	−2.24317e10	−0.0103312
$176$	−9.24323e11	−0.412576
$177$	1.73727e11	0.0751646
$178$	1.99220e12	0.835649
$179$	−1.83525e12	−0.746454	−0.373227	−	0.927740i	$-0.621749\pi$
$179$	−1.83525e12	−0.746454	−0.373227	+	0.927740i	$0.621749\pi$
$180$	−6.06007e11	−0.239045
$181$	4.33122e11	0.165721	0.0828606	−	0.996561i	$-0.473594\pi$
$181$	4.33122e11	0.165721	0.0828606	+	0.996561i	$0.473594\pi$
$182$	−5.32473e11	−0.197654
$183$	4.39297e11	0.158226
$184$	−6.51944e11	−0.227883
$185$	2.00804e12	0.681285
$186$	1.77348e12	0.584126
$187$	3.28143e12	1.04938
$188$	6.81557e11	0.211658
$189$	3.51354e11	0.105975
$190$	7.49465e11	0.219587
$191$	−6.20522e12	−1.76634	−0.883169	−	0.469054i	$-0.844595\pi$
$191$	−6.20522e12	−1.76634	−0.883169	+	0.469054i	$0.844595\pi$
$192$	6.18468e11	0.171065
$193$	2.56884e12	0.690513	0.345256	−	0.938508i	$-0.387792\pi$
$193$	2.56884e12	0.690513	0.345256	+	0.938508i	$0.387792\pi$
$194$	3.02010e12	0.789064
$195$	−1.53832e12	−0.390712
$196$	2.04273e12	0.504431
$197$	6.44753e12	1.54821	0.774103	−	0.633060i	$-0.218201\pi$
$197$	6.44753e12	1.54821	0.774103	+	0.633060i	$0.218201\pi$
$198$	−1.24725e12	−0.291269
$199$	2.26246e12	0.513912	0.256956	−	0.966423i	$-0.417280\pi$
$199$	2.26246e12	0.513912	0.256956	+	0.966423i	$0.417280\pi$
$200$	7.69034e10	0.0169934
$201$	4.02677e11	0.0865723
$202$	7.48974e11	0.156688
$203$	5.04089e12	1.02631
$204$	1.33084e12	0.263730
$205$	−5.01593e11	−0.0967622
$206$	2.68991e12	0.505206
$207$	4.58578e11	0.0838642
$208$	−9.51603e11	−0.169476
$209$	−4.04541e12	−0.701711
$210$	9.79281e11	0.165463
$211$	6.14974e12	1.01229	0.506143	−	0.862450i	$-0.331071\pi$
$211$	6.14974e12	1.01229	0.506143	+	0.862450i	$0.331071\pi$
$212$	−3.60886e12	−0.578793
$213$	5.94207e12	0.928646
$214$	−5.90862e12	−0.899933
$215$	−3.76643e12	−0.559137
$216$	−1.20456e12	−0.174314
$217$	7.51612e12	1.06039
$218$	4.80362e12	0.660782
$219$	−8.15641e12	−1.09410
$220$	9.11700e12	1.19269
$221$	3.37828e12	0.431060
$222$	1.67614e12	0.208626
$223$	−1.23110e13	−1.49491	−0.747457	−	0.664310i	$-0.768726\pi$
$223$	−1.23110e13	−1.49491	−0.747457	+	0.664310i	$0.768726\pi$
$224$	4.81562e12	0.570542
$225$	−5.40939e10	−0.00625381
$226$	3.60785e12	0.407054
$227$	1.40310e13	1.54507	0.772534	−	0.634974i	$-0.218989\pi$
$227$	1.40310e13	1.54507	0.772534	+	0.634974i	$0.218989\pi$
$228$	−1.64069e12	−0.176353
$229$	−1.64351e12	−0.172455	−0.0862277	−	0.996275i	$-0.527481\pi$
$229$	−1.64351e12	−0.172455	−0.0862277	+	0.996275i	$0.527481\pi$
$230$	1.27813e12	0.130940
$231$	−5.28590e12	−0.528753
$232$	−1.72819e13	−1.68814
$233$	−1.93499e13	−1.84596	−0.922978	−	0.384853i	$-0.874252\pi$
$233$	−1.93499e13	−1.84596	−0.922978	+	0.384853i	$0.874252\pi$
$234$	−1.28406e12	−0.119646
$235$	−3.18187e12	−0.289607
$236$	−1.05999e12	−0.0942512
$237$	6.04432e12	0.525087
$238$	−2.15058e12	−0.182550
$239$	1.91104e13	1.58519	0.792594	−	0.609750i	$-0.208730\pi$
$239$	1.91104e13	1.58519	0.792594	+	0.609750i	$0.208730\pi$
$240$	1.75011e12	0.141874
$241$	−1.44086e12	−0.114164	−0.0570820	−	0.998369i	$-0.518180\pi$
$241$	−1.44086e12	−0.114164	−0.0570820	+	0.998369i	$0.518180\pi$
$242$	1.19803e13	0.927858
$243$	8.47289e11	0.0641500
$244$	−2.68037e12	−0.198404
$245$	−9.53652e12	−0.690202
$246$	−4.18686e11	−0.0296310
$247$	−4.16481e12	−0.288245
$248$	−2.57678e13	−1.74419
$249$	1.54289e12	0.102150
$250$	−8.18687e12	−0.530210
$251$	6.54826e12	0.414878	0.207439	−	0.978248i	$-0.433487\pi$
$251$	6.54826e12	0.414878	0.207439	+	0.978248i	$0.433487\pi$
$252$	−2.14378e12	−0.132886
$253$	−6.89902e12	−0.418432
$254$	−5.93140e12	−0.352024
$255$	−6.21305e12	−0.360856
$256$	−1.33501e13	−0.758867
$257$	−1.75348e12	−0.0975594	−0.0487797	−	0.998810i	$-0.515533\pi$
$257$	−1.75348e12	−0.0975594	−0.0487797	+	0.998810i	$0.515533\pi$
$258$	−3.14389e12	−0.171222
$259$	7.10357e12	0.378728
$260$	9.38608e12	0.489926
$261$	1.21561e13	0.621258
$262$	−7.56389e12	−0.378520
$263$	1.49939e13	0.734780	0.367390	−	0.930067i	$-0.380251\pi$
$263$	1.49939e13	0.734780	0.367390	+	0.930067i	$0.380251\pi$
$264$	1.81219e13	0.869723
$265$	1.68481e13	0.791950
$266$	2.65128e12	0.122069
$267$	2.03604e13	0.918280
$268$	−2.45694e12	−0.108556
$269$	2.22020e13	0.961069	0.480534	−	0.876976i	$-0.340443\pi$
$269$	2.22020e13	0.961069	0.480534	+	0.876976i	$0.340443\pi$
$270$	2.36153e12	0.100160
$271$	−8.63351e12	−0.358803	−0.179402	−	0.983776i	$-0.557416\pi$
$271$	−8.63351e12	−0.358803	−0.179402	+	0.983776i	$0.557416\pi$
$272$	−3.84338e12	−0.156525
$273$	−5.44190e12	−0.217198
$274$	1.49428e13	0.584527
$275$	8.13809e11	0.0312028
$276$	−2.79802e12	−0.105160
$277$	5.13042e13	1.89023	0.945114	−	0.326740i	$-0.105950\pi$
$277$	5.13042e13	1.89023	0.945114	+	0.326740i	$0.105950\pi$
$278$	2.61380e13	0.944118
$279$	1.81251e13	0.641885
$280$	−1.42284e13	−0.494070
$281$	2.26330e13	0.770651	0.385325	−	0.922781i	$-0.374089\pi$
$281$	2.26330e13	0.770651	0.385325	+	0.922781i	$0.374089\pi$
$282$	−2.65594e12	−0.0886847
$283$	2.57270e13	0.842486	0.421243	−	0.906948i	$-0.361594\pi$
$283$	2.57270e13	0.842486	0.421243	+	0.906948i	$0.361594\pi$
$284$	−3.62556e13	−1.16446
$285$	7.65957e12	0.241300
$286$	1.93178e13	0.596960
$287$	−1.77441e12	−0.0537904
$288$	1.16128e13	0.345366
$289$	−2.06275e13	−0.601879
$290$	3.38811e13	0.969993
$291$	3.08656e13	0.867089
$292$	4.97663e13	1.37192
$293$	−5.35154e13	−1.44779	−0.723896	−	0.689909i	$-0.757651\pi$
$293$	−5.35154e13	−1.44779	−0.723896	+	0.689909i	$0.757651\pi$
$294$	−7.96025e12	−0.211357
$295$	4.94860e12	0.128962
$296$	−2.43535e13	−0.622954
$297$	−1.27469e13	−0.320070
$298$	−1.56068e13	−0.384702
$299$	−7.10264e12	−0.171881
$300$	3.30054e11	0.00784185
$301$	−1.33240e13	−0.310826
$302$	−3.59066e13	−0.822500
$303$	7.65456e12	0.172181
$304$	4.73819e12	0.104667
$305$	1.25134e13	0.271472
$306$	−5.18612e12	−0.110503
$307$	7.26163e13	1.51975	0.759877	−	0.650067i	$-0.225259\pi$
$307$	7.26163e13	1.51975	0.759877	+	0.650067i	$0.225259\pi$
$308$	3.22519e13	0.663020
$309$	2.74910e13	0.555162
$310$	5.05177e13	1.00220
$311$	−5.96904e13	−1.16338	−0.581691	−	0.813410i	$-0.697609\pi$
$311$	−5.96904e13	−1.16338	−0.581691	+	0.813410i	$0.697609\pi$
$312$	1.86567e13	0.357260
$313$	−6.28890e13	−1.18326	−0.591630	−	0.806209i	$-0.701516\pi$
$313$	−6.28890e13	−1.18326	−0.591630	+	0.806209i	$0.701516\pi$
$314$	−3.16144e13	−0.584483
$315$	1.00083e13	0.181825
$316$	−3.68794e13	−0.658423
$317$	−9.60991e13	−1.68614	−0.843070	−	0.537804i	$-0.819254\pi$
$317$	−9.60991e13	−1.68614	−0.843070	+	0.537804i	$0.819254\pi$
$318$	1.40633e13	0.242515
$319$	−1.82881e14	−3.09970
$320$	1.76170e13	0.293500
$321$	−6.03864e13	−0.988921
$322$	4.52147e12	0.0727901
$323$	−1.68210e13	−0.266219
$324$	−5.16973e12	−0.0804397
$325$	8.37828e11	0.0128173
$326$	5.30746e13	0.798344
$327$	4.90933e13	0.726122
$328$	6.08330e12	0.0884775
$329$	−1.12560e13	−0.160993
$330$	−3.55278e13	−0.499737
$331$	−4.93954e13	−0.683333	−0.341667	−	0.939821i	$-0.610991\pi$
$331$	−4.93954e13	−0.683333	−0.341667	+	0.939821i	$0.610991\pi$
$332$	−9.41397e12	−0.128089
$333$	1.71302e13	0.229256
$334$	1.61374e13	0.212436
$335$	1.14703e13	0.148534
$336$	6.19111e12	0.0788683
$337$	6.72011e13	0.842193	0.421097	−	0.907016i	$-0.361645\pi$
$337$	6.72011e13	0.842193	0.421097	+	0.907016i	$0.361645\pi$
$338$	−2.27238e13	−0.280182
$339$	3.68724e13	0.447305
$340$	3.79090e13	0.452489
$341$	−2.72681e14	−3.20262
$342$	6.39354e12	0.0738921
$343$	−8.21537e13	−0.934349
$344$	4.56791e13	0.511265
$345$	1.30626e13	0.143888
$346$	7.52764e13	0.816094
$347$	−1.31316e14	−1.40121	−0.700607	−	0.713547i	$-0.747087\pi$
$347$	−1.31316e14	−1.40121	−0.700607	+	0.713547i	$0.747087\pi$
$348$	−7.41705e13	−0.779014
$349$	−5.29347e13	−0.547269	−0.273635	−	0.961834i	$-0.588226\pi$
$349$	−5.29347e13	−0.547269	−0.273635	+	0.961834i	$0.588226\pi$
$350$	−5.33353e11	−0.00542801
$351$	−1.31231e13	−0.131477
$352$	−1.74708e14	−1.72317
$353$	6.86471e13	0.666594	0.333297	−	0.942822i	$-0.391839\pi$
$353$	6.86471e13	0.666594	0.333297	+	0.942822i	$0.391839\pi$
$354$	4.13066e12	0.0394913
$355$	1.69260e14	1.59330
$356$	−1.24229e14	−1.15146
$357$	−2.19790e13	−0.200601
$358$	−4.36363e13	−0.392185
$359$	1.03179e14	0.913215	0.456607	−	0.889668i	$-0.349064\pi$
$359$	1.03179e14	0.913215	0.456607	+	0.889668i	$0.349064\pi$
$360$	−3.43119e13	−0.299075
$361$	−9.57530e13	−0.821983
$362$	1.02982e13	0.0870695
$363$	1.22439e14	1.01961
$364$	3.32038e13	0.272352
$365$	−2.32335e14	−1.87717
$366$	1.04451e13	0.0831315
$367$	5.44575e12	0.0426967	0.0213484	−	0.999772i	$-0.493204\pi$
$367$	5.44575e12	0.0426967	0.0213484	+	0.999772i	$0.493204\pi$
$368$	8.08049e12	0.0624129
$369$	−4.27900e12	−0.0325609
$370$	4.77448e13	0.357945
$371$	5.96010e13	0.440247
$372$	−1.10590e14	−0.804880
$373$	−7.26263e13	−0.520829	−0.260414	−	0.965497i	$-0.583859\pi$
$373$	−7.26263e13	−0.520829	−0.260414	+	0.965497i	$0.583859\pi$
$374$	7.80219e13	0.551344
$375$	−8.36703e13	−0.582638
$376$	3.85895e13	0.264811
$377$	−1.88279e14	−1.27328
$378$	8.35406e12	0.0556792
$379$	−2.08008e14	−1.36636	−0.683179	−	0.730251i	$-0.739403\pi$
$379$	−2.08008e14	−1.36636	−0.683179	+	0.730251i	$0.739403\pi$
$380$	−4.67349e13	−0.302574
$381$	−6.06193e13	−0.386833
$382$	−1.47540e14	−0.928030
$383$	2.06489e14	1.28027	0.640137	−	0.768261i	$-0.278878\pi$
$383$	2.06489e14	1.28027	0.640137	+	0.768261i	$0.278878\pi$
$384$	−8.31677e13	−0.508315
$385$	−1.50569e14	−0.907195
$386$	6.10787e13	0.362794
$387$	−3.21307e13	−0.188152
$388$	−1.88327e14	−1.08727
$389$	2.16026e14	1.22966	0.614828	−	0.788661i	$-0.289225\pi$
$389$	2.16026e14	1.22966	0.614828	+	0.788661i	$0.289225\pi$
$390$	−3.65764e13	−0.205279
$391$	−2.86865e13	−0.158747
$392$	1.15658e14	0.631108
$393$	−7.73034e13	−0.415949
$394$	1.53301e14	0.813424
$395$	1.72172e14	0.900905
$396$	7.77754e13	0.401346
$397$	−6.66369e13	−0.339131	−0.169565	−	0.985519i	$-0.554236\pi$
$397$	−6.66369e13	−0.339131	−0.169565	+	0.985519i	$0.554236\pi$
$398$	5.37940e13	0.270008
$399$	2.70962e13	0.134140
$400$	−9.53175e11	−0.00465418
$401$	9.42589e13	0.453971	0.226986	−	0.973898i	$-0.427113\pi$
$401$	9.42589e13	0.453971	0.226986	+	0.973898i	$0.427113\pi$
$402$	9.57437e12	0.0454849
$403$	−2.80729e14	−1.31556
$404$	−4.67043e13	−0.215903
$405$	2.41350e13	0.110064
$406$	1.19856e14	0.539222
$407$	−2.57714e14	−1.14385
$408$	7.53516e13	0.329960
$409$	1.68108e14	0.726288	0.363144	−	0.931733i	$-0.381703\pi$
$409$	1.68108e14	0.726288	0.363144	+	0.931733i	$0.381703\pi$
$410$	−1.19263e13	−0.0508386
$411$	1.52716e14	0.642326
$412$	−1.67737e14	−0.696135
$413$	1.75060e13	0.0716903
$414$	1.09035e13	0.0440620
$415$	4.39493e13	0.175262
$416$	−1.79864e14	−0.707835
$417$	2.67132e14	1.03747
$418$	−9.61869e13	−0.368677
$419$	−5.52023e13	−0.208824	−0.104412	−	0.994534i	$-0.533296\pi$
$419$	−5.52023e13	−0.208824	−0.104412	+	0.994534i	$0.533296\pi$
$420$	−6.10657e13	−0.227995
$421$	−2.98720e14	−1.10081	−0.550406	−	0.834897i	$-0.685527\pi$
$421$	−2.98720e14	−1.10081	−0.550406	+	0.834897i	$0.685527\pi$
$422$	1.46221e14	0.531853
$423$	−2.71439e13	−0.0974541
$424$	−2.04332e14	−0.724144
$425$	3.38386e12	0.0118379
$426$	1.41283e14	0.487908
$427$	4.42668e13	0.150912
$428$	3.68448e14	1.24004
$429$	1.97429e14	0.655989
$430$	−8.95536e13	−0.293769
$431$	−4.61512e14	−1.49471	−0.747357	−	0.664423i	$-0.768677\pi$
$431$	−4.61512e14	−1.49471	−0.747357	+	0.664423i	$0.768677\pi$
$432$	1.49299e13	0.0477414
$433$	−6.14093e13	−0.193888	−0.0969440	−	0.995290i	$-0.530907\pi$
$433$	−6.14093e13	−0.193888	−0.0969440	+	0.995290i	$0.530907\pi$
$434$	1.78709e14	0.557126
$435$	3.46267e14	1.06591
$436$	−2.99543e14	−0.910506
$437$	3.53653e13	0.106152
$438$	−1.93933e14	−0.574837
$439$	2.71791e14	0.795573	0.397786	−	0.917478i	$-0.369779\pi$
$439$	2.71791e14	0.795573	0.397786	+	0.917478i	$0.369779\pi$
$440$	5.16201e14	1.49221
$441$	−8.13542e13	−0.232256
$442$	8.03246e13	0.226478
$443$	2.08496e14	0.580600	0.290300	−	0.956936i	$-0.406245\pi$
$443$	2.08496e14	0.580600	0.290300	+	0.956936i	$0.406245\pi$
$444$	−1.04520e14	−0.287471
$445$	5.79967e14	1.57552
$446$	−2.92716e14	−0.785425
$447$	−1.59503e14	−0.422743
$448$	6.23213e13	0.163158
$449$	−1.30410e14	−0.337254	−0.168627	−	0.985680i	$-0.553933\pi$
$449$	−1.30410e14	−0.337254	−0.168627	+	0.985680i	$0.553933\pi$
$450$	−1.28618e12	−0.00328574
$451$	6.43748e13	0.162460
$452$	−2.24977e14	−0.560889
$453$	−3.66967e14	−0.903831
$454$	3.33613e14	0.811775
$455$	−1.55013e14	−0.372653
$456$	−9.28949e13	−0.220641
$457$	6.29919e14	1.47824	0.739121	−	0.673573i	$-0.235241\pi$
$457$	6.29919e14	1.47824	0.739121	+	0.673573i	$0.235241\pi$
$458$	−3.90773e13	−0.0906077
$459$	−5.30024e13	−0.121430
$460$	−7.97014e13	−0.180426
$461$	−4.96432e14	−1.11046	−0.555232	−	0.831696i	$-0.687371\pi$
$461$	−4.96432e14	−1.11046	−0.555232	+	0.831696i	$0.687371\pi$
$462$	−1.25682e14	−0.277806
$463$	4.11958e14	0.899824	0.449912	−	0.893073i	$-0.351455\pi$
$463$	4.11958e14	0.899824	0.449912	+	0.893073i	$0.351455\pi$
$464$	2.14200e14	0.462349
$465$	5.16294e14	1.10130
$466$	−4.60079e14	−0.969861
$467$	−2.15183e13	−0.0448297	−0.0224149	−	0.999749i	$-0.507135\pi$
$467$	−2.15183e13	−0.0448297	−0.0224149	+	0.999749i	$0.507135\pi$
$468$	8.00708e13	0.164863
$469$	4.05767e13	0.0825707
$470$	−7.56545e13	−0.152159
$471$	−3.23101e14	−0.642278
$472$	−6.00164e13	−0.117920
$473$	4.83386e14	0.938768
$474$	1.43714e14	0.275879
$475$	−4.17169e12	−0.00791584
$476$	1.34105e14	0.251540
$477$	1.43728e14	0.266495
$478$	4.54383e14	0.832854
$479$	2.18237e14	0.395443	0.197721	−	0.980258i	$-0.436646\pi$
$479$	2.18237e14	0.395443	0.197721	+	0.980258i	$0.436646\pi$
$480$	3.30792e14	0.592554
$481$	−2.65320e14	−0.469864
$482$	−3.42591e13	−0.0599815
$483$	4.62097e13	0.0799878
$484$	−7.47061e14	−1.27852
$485$	8.79207e14	1.48769
$486$	2.01458e13	0.0337043
$487$	−6.93472e14	−1.14715	−0.573574	−	0.819154i	$-0.694443\pi$
$487$	−6.93472e14	−1.14715	−0.573574	+	0.819154i	$0.694443\pi$
$488$	−1.51762e14	−0.248229
$489$	5.42425e14	0.877286
$490$	−2.26748e14	−0.362631
$491$	5.82804e14	0.921668	0.460834	−	0.887486i	$-0.347550\pi$
$491$	5.82804e14	0.921668	0.460834	+	0.887486i	$0.347550\pi$
$492$	2.61083e13	0.0408292
$493$	−7.60429e14	−1.17598
$494$	−9.90257e13	−0.151443
$495$	−3.63096e14	−0.549153
$496$	3.19378e14	0.477701
$497$	5.98766e14	0.885722
$498$	3.66851e13	0.0536695
$499$	−6.41955e14	−0.928863	−0.464431	−	0.885609i	$-0.653741\pi$
$499$	−6.41955e14	−0.928863	−0.464431	+	0.885609i	$0.653741\pi$
$500$	5.10514e14	0.730588
$501$	1.64925e14	0.233442
$502$	1.55697e14	0.217976
$503$	1.02609e15	1.42090	0.710448	−	0.703750i	$-0.248492\pi$
$503$	1.02609e15	1.42090	0.710448	+	0.703750i	$0.248492\pi$
$504$	−1.21380e14	−0.166257
$505$	2.18040e14	0.295416
$506$	−1.64037e14	−0.219843
$507$	−2.32239e14	−0.307887
$508$	3.69868e14	0.485062
$509$	4.61233e14	0.598374	0.299187	−	0.954194i	$-0.403285\pi$
$509$	4.61233e14	0.598374	0.299187	+	0.954194i	$0.403285\pi$
$510$	−1.47726e14	−0.189593
$511$	−8.21899e14	−1.04353
$512$	3.83513e14	0.481721
$513$	6.53424e13	0.0811988
$514$	−4.16921e13	−0.0512575
$515$	7.83082e14	0.952506
$516$	1.96045e14	0.235930
$517$	4.08363e14	0.486237
$518$	1.68900e14	0.198983
$519$	7.69329e14	0.896792
$520$	5.31436e14	0.612960
$521$	−4.43782e13	−0.0506479	−0.0253240	−	0.999679i	$-0.508062\pi$
$521$	−4.43782e13	−0.0506479	−0.0253240	+	0.999679i	$0.508062\pi$
$522$	2.89033e14	0.326407
$523$	3.21587e14	0.359367	0.179684	−	0.983724i	$-0.442493\pi$
$523$	3.21587e14	0.359367	0.179684	+	0.983724i	$0.442493\pi$
$524$	4.71667e14	0.521571
$525$	−5.45090e12	−0.00596474
$526$	3.56506e14	0.386052
$527$	−1.13382e15	−1.21503
$528$	−2.24610e14	−0.238201
$529$	−8.92498e14	−0.936701
$530$	4.00593e14	0.416089
$531$	4.22156e13	0.0433963
$532$	−1.65327e14	−0.168202
$533$	6.62748e13	0.0667342
$534$	4.84106e14	0.482462
$535$	−1.72011e15	−1.69672
$536$	−1.39111e14	−0.135817
$537$	−4.45965e14	−0.430965
$538$	5.27892e14	0.504943
$539$	1.22392e15	1.15882
$540$	−1.47260e14	−0.138012
$541$	−8.14845e14	−0.755945	−0.377972	−	0.925817i	$-0.623379\pi$
$541$	−8.14845e14	−0.755945	−0.377972	+	0.925817i	$0.623379\pi$
$542$	−2.05277e14	−0.188514
$543$	1.05249e14	0.0956792
$544$	−7.26445e14	−0.653746
$545$	1.39842e15	1.24583
$546$	−1.29391e14	−0.114115
$547$	8.04498e14	0.702416	0.351208	−	0.936297i	$-0.385771\pi$
$547$	8.04498e14	0.702416	0.351208	+	0.936297i	$0.385771\pi$
$548$	−9.31799e14	−0.805433
$549$	1.06749e14	0.0913518
$550$	1.93498e13	0.0163939
$551$	9.37471e14	0.786365
$552$	−1.58422e14	−0.131568
$553$	6.09069e14	0.500816
$554$	1.21985e15	0.993122
$555$	4.87955e14	0.393340
$556$	−1.62991e15	−1.30092
$557$	−1.28858e15	−1.01837	−0.509186	−	0.860656i	$-0.670053\pi$
$557$	−1.28858e15	−1.01837	−0.509186	+	0.860656i	$0.670053\pi$
$558$	4.30957e14	0.337245
$559$	4.97653e14	0.385622
$560$	1.76354e14	0.135316
$561$	7.97388e14	0.605862
$562$	5.38140e14	0.404898
$563$	−1.13486e15	−0.845564	−0.422782	−	0.906231i	$-0.638946\pi$
$563$	−1.13486e15	−0.845564	−0.422782	+	0.906231i	$0.638946\pi$
$564$	1.65618e14	0.122201
$565$	1.05031e15	0.767453
$566$	6.11704e14	0.442640
$567$	8.53789e13	0.0611849
$568$	−2.05277e15	−1.45689
$569$	−3.63483e14	−0.255486	−0.127743	−	0.991807i	$-0.540773\pi$
$569$	−3.63483e14	−0.255486	−0.127743	+	0.991807i	$0.540773\pi$
$570$	1.82120e14	0.126779
$571$	5.35440e14	0.369158	0.184579	−	0.982818i	$-0.440908\pi$
$571$	5.35440e14	0.369158	0.184579	+	0.982818i	$0.440908\pi$
$572$	−1.20462e15	−0.822565
$573$	−1.50787e15	−1.01980
$574$	−4.21899e13	−0.0282613
$575$	−7.11438e12	−0.00472024
$576$	1.50288e14	0.0987642
$577$	−1.71645e15	−1.11728	−0.558642	−	0.829409i	$-0.688678\pi$
$577$	−1.71645e15	−1.11728	−0.558642	+	0.829409i	$0.688678\pi$
$578$	−4.90456e14	−0.316226
$579$	6.24228e14	0.398668
$580$	−2.11275e15	−1.33657
$581$	1.55473e14	0.0974287
$582$	7.33885e14	0.455566
$583$	−2.16229e15	−1.32965
$584$	2.81775e15	1.71645
$585$	−3.73812e14	−0.225578
$586$	−1.27242e15	−0.760667
$587$	1.33142e15	0.788508	0.394254	−	0.919002i	$-0.371003\pi$
$587$	1.33142e15	0.788508	0.394254	+	0.919002i	$0.371003\pi$
$588$	4.96383e14	0.291234
$589$	1.39780e15	0.812475
$590$	1.17662e14	0.0677563
$591$	1.56675e15	0.893857
$592$	3.01848e14	0.170615
$593$	7.24920e14	0.405965	0.202983	−	0.979182i	$-0.434936\pi$
$593$	7.24920e14	0.405965	0.202983	+	0.979182i	$0.434936\pi$
$594$	−3.03081e14	−0.168164
$595$	−6.26072e14	−0.344177
$596$	9.73205e14	0.530090
$597$	5.49777e14	0.296707
$598$	−1.68878e14	−0.0903059
$599$	−1.70755e15	−0.904743	−0.452371	−	0.891830i	$-0.649422\pi$
$599$	−1.70755e15	−0.904743	−0.452371	+	0.891830i	$0.649422\pi$
$600$	1.86875e13	0.00981115
$601$	−1.03547e15	−0.538675	−0.269337	−	0.963046i	$-0.586805\pi$
$601$	−1.03547e15	−0.538675	−0.269337	+	0.963046i	$0.586805\pi$
$602$	−3.16801e14	−0.163307
$603$	9.78506e13	0.0499825
$604$	2.23905e15	1.13334
$605$	3.48767e15	1.74937
$606$	1.82001e14	0.0904636
$607$	3.90639e15	1.92414	0.962072	−	0.272797i	$-0.0879488\pi$
$607$	3.90639e15	1.92414	0.962072	+	0.272797i	$0.0879488\pi$
$608$	8.95576e14	0.437152
$609$	1.22494e15	0.592542
$610$	2.97528e14	0.142631
$611$	4.20415e14	0.199734
$612$	3.23394e14	0.152265
$613$	−1.81046e15	−0.844805	−0.422402	−	0.906408i	$-0.638813\pi$
$613$	−1.81046e15	−0.844805	−0.422402	+	0.906408i	$0.638813\pi$
$614$	1.72658e15	0.798475
$615$	−1.21887e14	−0.0558657
$616$	1.82609e15	0.829522
$617$	−1.18367e15	−0.532921	−0.266460	−	0.963846i	$-0.585854\pi$
$617$	−1.18367e15	−0.532921	−0.266460	+	0.963846i	$0.585854\pi$
$618$	6.53649e14	0.291681
$619$	−3.52172e15	−1.55760	−0.778800	−	0.627273i	$-0.784171\pi$
$619$	−3.52172e15	−1.55760	−0.778800	+	0.627273i	$0.784171\pi$
$620$	−3.15017e15	−1.38095
$621$	1.11435e14	0.0484190
$622$	−1.41925e15	−0.611238
$623$	2.05167e15	0.875835
$624$	−2.31239e14	−0.0978468
$625$	−2.33862e15	−0.980887
$626$	−1.49530e15	−0.621682
$627$	−9.83035e14	−0.405133
$628$	1.97140e15	0.805372
$629$	−1.07159e15	−0.433959
$630$	2.37965e14	0.0955302
$631$	−1.23880e15	−0.492992	−0.246496	−	0.969144i	$-0.579279\pi$
$631$	−1.23880e15	−0.492992	−0.246496	+	0.969144i	$0.579279\pi$
$632$	−2.08810e15	−0.823771
$633$	1.49439e15	0.584444
$634$	−2.28493e15	−0.885894
$635$	−1.72674e15	−0.663699
$636$	−8.76954e14	−0.334166
$637$	1.26005e15	0.476014
$638$	−4.34832e15	−1.62858
$639$	1.44392e15	0.536154
$640$	−2.36903e15	−0.872130
$641$	2.54832e15	0.930112	0.465056	−	0.885281i	$-0.346034\pi$
$641$	2.54832e15	0.930112	0.465056	+	0.885281i	$0.346034\pi$
$642$	−1.43579e15	−0.519577
$643$	1.45911e14	0.0523513	0.0261757	−	0.999657i	$-0.491667\pi$
$643$	1.45911e14	0.0523513	0.0261757	+	0.999657i	$0.491667\pi$
$644$	−2.81948e14	−0.100299
$645$	−9.15243e14	−0.322818
$646$	−3.99950e14	−0.139871
$647$	1.99009e14	0.0690080	0.0345040	−	0.999405i	$-0.489015\pi$
$647$	1.99009e14	0.0690080	0.0345040	+	0.999405i	$0.489015\pi$
$648$	−2.92708e14	−0.100640
$649$	−6.35107e14	−0.216521
$650$	1.99209e13	0.00673418
$651$	1.82642e15	0.612216
$652$	−3.30961e15	−1.10006
$653$	4.24825e14	0.140019	0.0700096	−	0.997546i	$-0.477697\pi$
$653$	4.24825e14	0.140019	0.0700096	+	0.997546i	$0.477697\pi$
$654$	1.16728e15	0.381503
$655$	−2.20199e15	−0.713654
$656$	−7.53991e13	−0.0242323
$657$	−1.98201e15	−0.631678
$658$	−2.67632e14	−0.0845855
$659$	−4.66835e15	−1.46317	−0.731583	−	0.681752i	$-0.761218\pi$
$659$	−4.66835e15	−1.46317	−0.731583	+	0.681752i	$0.761218\pi$
$660$	2.21543e15	0.688599
$661$	2.49961e14	0.0770484	0.0385242	−	0.999258i	$-0.487734\pi$
$661$	2.49961e14	0.0770484	0.0385242	+	0.999258i	$0.487734\pi$
$662$	−1.17446e15	−0.359022
$663$	8.20922e14	0.248873
$664$	−5.33015e14	−0.160256
$665$	7.71834e14	0.230147
$666$	4.07302e14	0.120450
$667$	1.59876e15	0.468911
$668$	−1.00629e15	−0.292720
$669$	−2.99157e15	−0.863089
$670$	2.72726e14	0.0780396
$671$	−1.60598e15	−0.455791
$672$	1.17019e15	0.329403
$673$	4.01308e15	1.12046	0.560228	−	0.828338i	$-0.310713\pi$
$673$	4.01308e15	1.12046	0.560228	+	0.828338i	$0.310713\pi$
$674$	1.59783e15	0.442486
$675$	−1.31448e13	−0.00361064
$676$	1.41700e15	0.386069
$677$	3.65865e15	0.988743	0.494371	−	0.869251i	$-0.335398\pi$
$677$	3.65865e15	0.988743	0.494371	+	0.869251i	$0.335398\pi$
$678$	8.76708e14	0.235013
$679$	3.11024e15	0.827010
$680$	2.14639e15	0.566121
$681$	3.40954e15	0.892045
$682$	−6.48348e15	−1.68265
$683$	6.60913e15	1.70149	0.850747	−	0.525575i	$-0.176150\pi$
$683$	6.60913e15	1.70149	0.850747	+	0.525575i	$0.176150\pi$
$684$	−3.98686e14	−0.101818
$685$	4.35013e15	1.10206
$686$	−1.95335e15	−0.490905
$687$	−3.99373e14	−0.0995672
$688$	−5.66167e14	−0.140026
$689$	−2.22611e15	−0.546186
$690$	3.10586e14	0.0755984
$691$	−4.05146e15	−0.978322	−0.489161	−	0.872193i	$-0.662697\pi$
$691$	−4.05146e15	−0.978322	−0.489161	+	0.872193i	$0.662697\pi$
$692$	−4.69406e15	−1.12451
$693$	−1.28447e15	−0.305276
$694$	−3.12226e15	−0.736195
$695$	7.60925e15	1.78002
$696$	−4.19950e15	−0.974646
$697$	2.67674e14	0.0616348
$698$	−1.25862e15	−0.287534
$699$	−4.70203e15	−1.06576
$700$	3.32586e13	0.00747938
$701$	3.60994e15	0.805473	0.402736	−	0.915316i	$-0.368059\pi$
$701$	3.60994e15	0.805473	0.402736	+	0.915316i	$0.368059\pi$
$702$	−3.12026e14	−0.0690775
$703$	1.32107e15	0.290183
$704$	−2.26098e15	−0.492774
$705$	−7.73193e14	−0.167205
$706$	1.63221e15	0.350227
$707$	7.71329e14	0.164223
$708$	−2.57578e14	−0.0544160
$709$	−4.47467e15	−0.938009	−0.469004	−	0.883196i	$-0.655387\pi$
$709$	−4.47467e15	−0.938009	−0.469004	+	0.883196i	$0.655387\pi$
$710$	4.02446e15	0.837117
$711$	1.46877e15	0.303159
$712$	−7.03381e15	−1.44062
$713$	2.38380e15	0.484481
$714$	−5.22591e14	−0.105395
$715$	5.62377e15	1.12550
$716$	2.72106e15	0.540401
$717$	4.64382e15	0.915208
$718$	2.45327e15	0.479801
$719$	5.79191e15	1.12412	0.562061	−	0.827096i	$-0.310009\pi$
$719$	5.79191e15	1.12412	0.562061	+	0.827096i	$0.310009\pi$
$720$	4.25277e14	0.0819111
$721$	2.77020e15	0.529501
$722$	−2.27670e15	−0.431868
$723$	−3.50130e14	−0.0659126
$724$	−6.42175e14	−0.119975
$725$	−1.88590e14	−0.0349670
$726$	2.91120e15	0.535699
$727$	−1.72964e15	−0.315875	−0.157938	−	0.987449i	$-0.550484\pi$
$727$	−1.72964e15	−0.315875	−0.157938	+	0.987449i	$0.550484\pi$
$728$	1.87998e15	0.340747
$729$	2.05891e14	0.0370370
$730$	−5.52418e15	−0.986262
$731$	2.00995e15	0.356155
$732$	−6.51331e14	−0.114549
$733$	−1.53166e15	−0.267356	−0.133678	−	0.991025i	$-0.542679\pi$
$733$	−1.53166e15	−0.267356	−0.133678	+	0.991025i	$0.542679\pi$
$734$	1.29482e14	0.0224328
$735$	−2.31737e15	−0.398488
$736$	1.52731e15	0.260675
$737$	−1.47210e15	−0.249383
$738$	−1.01741e14	−0.0171074
$739$	4.50150e15	0.751299	0.375650	−	0.926762i	$-0.377420\pi$
$739$	4.50150e15	0.751299	0.375650	+	0.926762i	$0.377420\pi$
$740$	−2.97726e15	−0.493221
$741$	−1.01205e15	−0.166418
$742$	1.41712e15	0.231305
$743$	9.19848e15	1.49031	0.745157	−	0.666889i	$-0.232375\pi$
$743$	9.19848e15	1.49031	0.745157	+	0.666889i	$0.232375\pi$
$744$	−6.26158e15	−1.00701
$745$	−4.54343e15	−0.725311
$746$	−1.72682e15	−0.273642
$747$	3.74923e14	0.0589765
$748$	−4.86526e15	−0.759709
$749$	−6.08497e15	−0.943211
$750$	−1.98941e15	−0.306117
$751$	−4.33394e15	−0.662008	−0.331004	−	0.943629i	$-0.607387\pi$
$751$	−4.33394e15	−0.662008	−0.331004	+	0.943629i	$0.607387\pi$
$752$	−4.78296e14	−0.0725268
$753$	1.59123e15	0.239530
$754$	−4.47666e15	−0.668977
$755$	−1.04531e16	−1.55073
$756$	−5.20940e14	−0.0767216
$757$	5.41348e15	0.791496	0.395748	−	0.918359i	$-0.370485\pi$
$757$	5.41348e15	0.791496	0.395748	+	0.918359i	$0.370485\pi$
$758$	−4.94577e15	−0.717882
$759$	−1.67646e15	−0.241582
$760$	−2.64611e15	−0.378559
$761$	−4.17764e15	−0.593356	−0.296678	−	0.954978i	$-0.595879\pi$
$761$	−4.17764e15	−0.593356	−0.296678	+	0.954978i	$0.595879\pi$
$762$	−1.44133e15	−0.203241
$763$	4.94699e15	0.692559
$764$	9.20027e15	1.27875
$765$	−1.50977e15	−0.208340
$766$	4.90963e15	0.672653
$767$	−6.53851e14	−0.0889415
$768$	−3.24408e15	−0.438132
$769$	−2.00420e15	−0.268748	−0.134374	−	0.990931i	$-0.542902\pi$
$769$	−2.00420e15	−0.268748	−0.134374	+	0.990931i	$0.542902\pi$
$770$	−3.58004e15	−0.476638
$771$	−4.26096e14	−0.0563259
$772$	−3.80873e15	−0.499902
$773$	−8.64697e15	−1.12688	−0.563439	−	0.826158i	$-0.690522\pi$
$773$	−8.64697e15	−1.12688	−0.563439	+	0.826158i	$0.690522\pi$
$774$	−7.63965e14	−0.0988549
$775$	−2.81193e14	−0.0361281
$776$	−1.06630e16	−1.36031
$777$	1.72617e15	0.218659
$778$	5.13641e15	0.646058
$779$	−3.29994e14	−0.0412144
$780$	2.28082e15	0.282859
$781$	−2.17229e16	−2.67509
$782$	−6.82072e14	−0.0834052
$783$	2.95393e15	0.358683
$784$	−1.43352e15	−0.172849
$785$	−9.20352e15	−1.10197
$786$	−1.83803e15	−0.218538
$787$	−2.22935e15	−0.263219	−0.131610	−	0.991302i	$-0.542015\pi$
$787$	−2.22935e15	−0.263219	−0.131610	+	0.991302i	$0.542015\pi$
$788$	−9.55952e15	−1.12084
$789$	3.64351e15	0.424226
$790$	4.09370e15	0.473334
$791$	3.71553e15	0.426629
$792$	4.40361e15	0.502135
$793$	−1.65337e15	−0.187227
$794$	−1.58441e15	−0.178179
$795$	4.09408e15	0.457233
$796$	−3.35447e15	−0.372050
$797$	2.86409e15	0.315476	0.157738	−	0.987481i	$-0.449580\pi$
$797$	2.86409e15	0.315476	0.157738	+	0.987481i	$0.449580\pi$
$798$	6.44260e14	0.0704766
$799$	1.69799e15	0.184471
$800$	−1.80162e14	−0.0194387
$801$	4.94759e15	0.530169
$802$	2.24117e15	0.238515
$803$	2.98181e16	3.15169
$804$	−5.97035e14	−0.0626746
$805$	1.31628e15	0.137237
$806$	−6.67483e15	−0.691190
$807$	5.39509e15	0.554873
$808$	−2.64438e15	−0.270123
$809$	−1.24502e16	−1.26316	−0.631581	−	0.775310i	$-0.717594\pi$
$809$	−1.24502e16	−1.26316	−0.631581	+	0.775310i	$0.717594\pi$
$810$	5.73853e14	0.0578273
$811$	−1.62012e16	−1.62156	−0.810778	−	0.585354i	$-0.800956\pi$
$811$	−1.62012e16	−1.62156	−0.810778	+	0.585354i	$0.800956\pi$
$812$	−7.47396e15	−0.743006
$813$	−2.09794e15	−0.207155
$814$	−6.12761e15	−0.600975
$815$	1.54510e16	1.50518
$816$	−9.33941e14	−0.0903699
$817$	−2.47790e15	−0.238156
$818$	3.99706e15	0.381590
$819$	−1.32238e15	−0.125399
$820$	7.43695e14	0.0700517
$821$	−7.47532e15	−0.699427	−0.349713	−	0.936857i	$-0.613721\pi$
$821$	−7.47532e15	−0.699427	−0.349713	+	0.936857i	$0.613721\pi$
$822$	3.63111e15	0.337477
$823$	−5.76646e13	−0.00532366	−0.00266183	−	0.999996i	$-0.500847\pi$
$823$	−5.76646e13	−0.00532366	−0.00266183	+	0.999996i	$0.500847\pi$
$824$	−9.49718e15	−0.870953
$825$	1.97756e14	0.0180149
$826$	4.16235e14	0.0376659
$827$	−4.43940e13	−0.00399065	−0.00199532	−	0.999998i	$-0.500635\pi$
$827$	−4.43940e13	−0.00399065	−0.00199532	+	0.999998i	$0.500635\pi$
$828$	−6.79918e14	−0.0607141
$829$	1.05447e16	0.935372	0.467686	−	0.883895i	$-0.345088\pi$
$829$	1.05447e16	0.935372	0.467686	+	0.883895i	$0.345088\pi$
$830$	1.04497e15	0.0920822
$831$	1.24669e16	1.09132
$832$	−2.32771e15	−0.202419
$833$	5.08914e15	0.439639
$834$	6.35154e15	0.545087
$835$	4.69788e15	0.400522
$836$	5.99799e15	0.508009
$837$	4.40440e15	0.370593
$838$	−1.31253e15	−0.109716
$839$	−6.14078e15	−0.509956	−0.254978	−	0.966947i	$-0.582068\pi$
$839$	−6.14078e15	−0.509956	−0.254978	+	0.966947i	$0.582068\pi$
$840$	−3.45751e15	−0.285251
$841$	3.01798e16	2.47365
$842$	−7.10261e15	−0.578364
$843$	5.49982e15	0.444935
$844$	−9.11800e15	−0.732852
$845$	−6.61532e15	−0.528249
$846$	−6.45394e14	−0.0512022
$847$	1.23378e16	0.972478
$848$	2.53259e15	0.198329
$849$	6.25165e15	0.486410
$850$	8.04573e13	0.00621959
$851$	2.25295e15	0.173037
$852$	−8.81010e15	−0.672300
$853$	1.02253e16	0.775277	0.387638	−	0.921812i	$-0.373291\pi$
$853$	1.02253e16	0.775277	0.387638	+	0.921812i	$0.373291\pi$
$854$	1.05252e15	0.0792890
$855$	1.86128e15	0.139315
$856$	2.08614e16	1.55145
$857$	−1.43797e15	−0.106257	−0.0531283	−	0.998588i	$-0.516919\pi$
$857$	−1.43797e15	−0.106257	−0.0531283	+	0.998588i	$0.516919\pi$
$858$	4.69424e15	0.344655
$859$	−5.05945e15	−0.369097	−0.184549	−	0.982823i	$-0.559082\pi$
$859$	−5.05945e15	−0.369097	−0.184549	+	0.982823i	$0.559082\pi$
$860$	5.58435e15	0.404792
$861$	−4.31183e14	−0.0310559
$862$	−1.09733e16	−0.785319
$863$	−1.23610e16	−0.879012	−0.439506	−	0.898240i	$-0.644846\pi$
$863$	−1.23610e16	−0.879012	−0.439506	+	0.898240i	$0.644846\pi$
$864$	2.82192e15	0.199397
$865$	2.19143e16	1.53865
$866$	−1.46012e15	−0.101868
$867$	−5.01249e15	−0.347495
$868$	−1.11439e16	−0.767677
$869$	−2.20967e16	−1.51258
$870$	8.23310e15	0.560025
$871$	−1.51555e15	−0.102440
$872$	−1.69600e16	−1.13916
$873$	7.50035e15	0.500614
$874$	8.40872e14	0.0557721
$875$	−8.43122e15	−0.555708
$876$	1.20932e16	0.792081
$877$	6.38167e15	0.415372	0.207686	−	0.978196i	$-0.433407\pi$
$877$	6.38167e15	0.415372	0.207686	+	0.978196i	$0.433407\pi$
$878$	6.46231e15	0.417992
$879$	−1.30042e16	−0.835884
$880$	−6.39802e15	−0.408687
$881$	−9.60382e15	−0.609644	−0.304822	−	0.952409i	$-0.598597\pi$
$881$	−9.60382e15	−0.609644	−0.304822	+	0.952409i	$0.598597\pi$
$882$	−1.93434e15	−0.122027
$883$	2.03319e16	1.27466	0.637329	−	0.770592i	$-0.280039\pi$
$883$	2.03319e16	1.27466	0.637329	+	0.770592i	$0.280039\pi$
$884$	−5.00885e15	−0.312069
$885$	1.20251e15	0.0744562
$886$	4.95737e15	0.305046
$887$	1.16294e16	0.711178	0.355589	−	0.934642i	$-0.384280\pi$
$887$	1.16294e16	0.711178	0.355589	+	0.934642i	$0.384280\pi$
$888$	−5.91789e15	−0.359663
$889$	−6.10844e15	−0.368952
$890$	1.37897e16	0.827773
$891$	−3.09750e15	−0.184793
$892$	1.82531e16	1.08225
$893$	−2.09332e15	−0.123354
$894$	−3.79246e15	−0.222108
$895$	−1.27033e16	−0.739418
$896$	−8.38058e15	−0.484820
$897$	−1.72594e15	−0.0992356
$898$	−3.10074e15	−0.177192
$899$	6.31903e16	3.58899
$900$	8.02032e13	0.00452749
$901$	−8.99092e15	−0.504450
$902$	1.53063e15	0.0853559
$903$	−3.23772e15	−0.179456
$904$	−1.27381e16	−0.701744
$905$	2.99801e15	0.164159
$906$	−8.72530e15	−0.474871
$907$	−2.64117e16	−1.42875	−0.714375	−	0.699763i	$-0.753289\pi$
$907$	−2.64117e16	−1.42875	−0.714375	+	0.699763i	$0.753289\pi$
$908$	−2.08033e16	−1.11856
$909$	1.86006e15	0.0994088
$910$	−3.68570e15	−0.195791
$911$	4.28301e15	0.226151	0.113075	−	0.993586i	$-0.463930\pi$
$911$	4.28301e15	0.226151	0.113075	+	0.993586i	$0.463930\pi$
$912$	1.15138e15	0.0604293
$913$	−5.64049e15	−0.294257
$914$	1.49774e16	0.776665
$915$	3.04075e15	0.156735
$916$	2.43677e15	0.124850
$917$	−7.78965e15	−0.396722
$918$	−1.26023e15	−0.0637990
$919$	8.05938e15	0.405571	0.202785	−	0.979223i	$-0.435001\pi$
$919$	8.05938e15	0.405571	0.202785	+	0.979223i	$0.435001\pi$
$920$	−4.51266e15	−0.225735
$921$	1.76458e16	0.877430
$922$	−1.18035e16	−0.583435
$923$	−2.23641e16	−1.09886
$924$	7.83721e15	0.382795
$925$	−2.65758e14	−0.0129035
$926$	9.79504e15	0.472765
$927$	6.68032e15	0.320523
$928$	4.04863e16	1.93105
$929$	2.56238e15	0.121495	0.0607474	−	0.998153i	$-0.480652\pi$
$929$	2.56238e15	0.121495	0.0607474	+	0.998153i	$0.480652\pi$
$930$	1.22758e16	0.578620
$931$	−6.27399e15	−0.293982
$932$	2.86894e16	1.33639
$933$	−1.45048e16	−0.671679
$934$	−5.11637e14	−0.0235534
$935$	2.27136e16	1.03949
$936$	4.53358e15	0.206264
$937$	1.21684e16	0.550385	0.275193	−	0.961389i	$-0.411258\pi$
$937$	1.21684e16	0.550385	0.275193	+	0.961389i	$0.411258\pi$
$938$	9.64783e14	0.0433825
$939$	−1.52820e16	−0.683156
$940$	4.71764e15	0.209663
$941$	2.93994e16	1.29896	0.649479	−	0.760379i	$-0.274987\pi$
$941$	2.93994e16	1.29896	0.649479	+	0.760379i	$0.274987\pi$
$942$	−7.68229e15	−0.337451
$943$	−5.62769e14	−0.0245763
$944$	7.43870e14	0.0322962
$945$	2.43202e15	0.104976
$946$	1.14934e16	0.493226
$947$	1.40267e16	0.598455	0.299228	−	0.954182i	$-0.403271\pi$
$947$	1.40267e16	0.598455	0.299228	+	0.954182i	$0.403271\pi$
$948$	−8.96169e15	−0.380141
$949$	3.06981e16	1.29464
$950$	−9.91894e13	−0.00415897
$951$	−2.33521e16	−0.973493
$952$	7.59297e15	0.314709
$953$	3.03827e16	1.25203	0.626015	−	0.779811i	$-0.284685\pi$
$953$	3.03827e16	1.25203	0.626015	+	0.779811i	$0.284685\pi$
$954$	3.41738e15	0.140016
$955$	−4.29516e16	−1.74969
$956$	−2.83343e16	−1.14761
$957$	−4.44401e16	−1.78961
$958$	5.18898e15	0.207765
$959$	1.53888e16	0.612637
$960$	4.28094e15	0.169452
$961$	6.88100e16	2.70815
$962$	−6.30845e15	−0.246865
$963$	−1.46739e16	−0.570954
$964$	2.13632e15	0.0826499
$965$	1.77811e16	0.684005
$966$	1.09872e15	0.0420254
$967$	−3.25574e16	−1.23824	−0.619120	−	0.785296i	$-0.712511\pi$
$967$	−3.25574e16	−1.23824	−0.619120	+	0.785296i	$0.712511\pi$
$968$	−4.22983e16	−1.59959
$969$	−4.08751e15	−0.153702
$970$	2.09047e16	0.781627
$971$	4.36365e16	1.62235	0.811174	−	0.584805i	$-0.198829\pi$
$971$	4.36365e16	1.62235	0.811174	+	0.584805i	$0.198829\pi$
$972$	−1.25624e15	−0.0464419
$973$	2.69182e16	0.989520
$974$	−1.64885e16	−0.602709
$975$	2.03592e14	0.00740007
$976$	1.88100e15	0.0679853
$977$	−1.98101e16	−0.711979	−0.355989	−	0.934490i	$-0.615856\pi$
$977$	−1.98101e16	−0.711979	−0.355989	+	0.934490i	$0.615856\pi$
$978$	1.28971e16	0.460924
$979$	−7.44334e16	−2.64523
$980$	1.41395e16	0.499677
$981$	1.19297e16	0.419227
$982$	1.38572e16	0.484242
$983$	−4.32181e16	−1.50183	−0.750916	−	0.660398i	$-0.770388\pi$
$983$	−4.32181e16	−1.50183	−0.750916	+	0.660398i	$0.770388\pi$
$984$	1.47824e15	0.0510825
$985$	4.46288e16	1.53361
$986$	−1.80805e16	−0.617858
$987$	−2.73522e15	−0.0929495
$988$	6.17501e15	0.208677
$989$	−4.22580e15	−0.142013
$990$	−8.63326e15	−0.288523
$991$	2.96218e16	0.984478	0.492239	−	0.870460i	$-0.336179\pi$
$991$	2.96218e16	0.984478	0.492239	+	0.870460i	$0.336179\pi$
$992$	6.03663e16	1.99517
$993$	−1.20031e16	−0.394523
$994$	1.42367e16	0.465356
$995$	1.56604e16	0.509068
$996$	−2.28759e15	−0.0739525
$997$	−4.68798e16	−1.50717	−0.753585	−	0.657350i	$-0.771677\pi$
$997$	−4.68798e16	−1.50717	−0.753585	+	0.657350i	$0.771677\pi$
$998$	−1.52636e16	−0.488022
$999$	4.16265e15	0.132361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.17	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.17	✓	28	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)

\(f(q)\)	\(=\)	\(q+23.7768 q^{2} +243.000 q^{3} -1482.66 q^{4} +6921.85 q^{5} +5777.76 q^{6} +24486.4 q^{7} -83947.8 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+23.7768 q^{2} +243.000 q^{3} -1482.66 q^{4} +6921.85 q^{5} +5777.76 q^{6} +24486.4 q^{7} -83947.8 q^{8} +59049.0 q^{9} +164579. q^{10} -888355. q^{11} -360287. q^{12} -914574. q^{13} +582209. q^{14} +1.68201e6 q^{15} +1.04049e6 q^{16} -3.69383e6 q^{17} +1.40400e6 q^{18} +4.55382e6 q^{19} -1.02628e7 q^{20} +5.95021e6 q^{21} -2.11222e7 q^{22} +7.76606e6 q^{23} -2.03993e7 q^{24} -916085. q^{25} -2.17456e7 q^{26} +1.43489e7 q^{27} -3.63052e7 q^{28} +2.05865e8 q^{29} +3.99928e7 q^{30} +3.06950e8 q^{31} +1.96665e8 q^{32} -2.15870e8 q^{33} -8.78273e7 q^{34} +1.69492e8 q^{35} -8.75499e7 q^{36} +2.90102e8 q^{37} +1.08275e8 q^{38} -2.22241e8 q^{39} -5.81075e8 q^{40} -7.24652e7 q^{41} +1.41477e8 q^{42} -5.44136e8 q^{43} +1.31713e9 q^{44} +4.08728e8 q^{45} +1.84652e8 q^{46} -4.59684e8 q^{47} +2.52838e8 q^{48} -1.37774e9 q^{49} -2.17816e7 q^{50} -8.97600e8 q^{51} +1.35601e9 q^{52} +2.43404e9 q^{53} +3.41171e8 q^{54} -6.14907e9 q^{55} -2.05558e9 q^{56} +1.10658e9 q^{57} +4.89480e9 q^{58} +7.14924e8 q^{59} -2.49386e9 q^{60} +1.80781e9 q^{61} +7.29829e9 q^{62} +1.44590e9 q^{63} +2.54513e9 q^{64} -6.33055e9 q^{65} -5.13270e9 q^{66} +1.65711e9 q^{67} +5.47671e9 q^{68} +1.88715e9 q^{69} +4.02996e9 q^{70} +2.44530e10 q^{71} -4.95704e9 q^{72} -3.35655e10 q^{73} +6.89770e9 q^{74} -2.22609e8 q^{75} -6.75179e9 q^{76} -2.17527e10 q^{77} -5.28419e9 q^{78} +2.48737e10 q^{79} +7.20210e9 q^{80} +3.48678e9 q^{81} -1.72299e9 q^{82} +6.34936e9 q^{83} -8.82216e9 q^{84} -2.55681e10 q^{85} -1.29378e10 q^{86} +5.00251e10 q^{87} +7.45755e10 q^{88} +8.37878e10 q^{89} +9.71825e9 q^{90} -2.23947e10 q^{91} -1.15145e10 q^{92} +7.45889e10 q^{93} -1.09298e10 q^{94} +3.15209e10 q^{95} +4.77895e10 q^{96} +1.27019e11 q^{97} -3.27582e10 q^{98} -5.24565e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \)	\( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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