LMFDB - Embedded newform 177.12.a.c.1.20

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

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q+43.4861 q^{2} -243.000 q^{3} -156.959 q^{4} +1833.80 q^{5} -10567.1 q^{6} +33856.7 q^{7} -95885.1 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+43.4861 q^{2} -243.000 q^{3} -156.959 q^{4} +1833.80 q^{5} -10567.1 q^{6} +33856.7 q^{7} -95885.1 q^{8} +59049.0 q^{9} +79745.0 q^{10} +908207. q^{11} +38141.1 q^{12} +503420. q^{13} +1.47230e6 q^{14} -445614. q^{15} -3.84821e6 q^{16} +4.40755e6 q^{17} +2.56781e6 q^{18} +1.49769e6 q^{19} -287833. q^{20} -8.22718e6 q^{21} +3.94944e7 q^{22} -1.40606e7 q^{23} +2.33001e7 q^{24} -4.54653e7 q^{25} +2.18918e7 q^{26} -1.43489e7 q^{27} -5.31413e6 q^{28} -7.57535e7 q^{29} -1.93780e7 q^{30} -1.41318e8 q^{31} +2.90288e7 q^{32} -2.20694e8 q^{33} +1.91667e8 q^{34} +6.20866e7 q^{35} -9.26830e6 q^{36} -4.72854e8 q^{37} +6.51288e7 q^{38} -1.22331e8 q^{39} -1.75834e8 q^{40} +1.06497e9 q^{41} -3.57768e8 q^{42} +1.00349e9 q^{43} -1.42552e8 q^{44} +1.08284e8 q^{45} -6.11442e8 q^{46} +1.98049e9 q^{47} +9.35116e8 q^{48} -8.31050e8 q^{49} -1.97711e9 q^{50} -1.07103e9 q^{51} -7.90166e7 q^{52} +4.29679e9 q^{53} -6.23978e8 q^{54} +1.66547e9 q^{55} -3.24635e9 q^{56} -3.63939e8 q^{57} -3.29422e9 q^{58} -7.14924e8 q^{59} +6.99434e7 q^{60} +6.72663e8 q^{61} -6.14535e9 q^{62} +1.99920e9 q^{63} +9.14349e9 q^{64} +9.23174e8 q^{65} -9.59714e9 q^{66} -5.16613e9 q^{67} -6.91806e8 q^{68} +3.41673e9 q^{69} +2.69990e9 q^{70} -1.10100e10 q^{71} -5.66192e9 q^{72} +1.07298e10 q^{73} -2.05626e10 q^{74} +1.10481e10 q^{75} -2.35077e8 q^{76} +3.07489e10 q^{77} -5.31970e9 q^{78} +5.11404e10 q^{79} -7.05687e9 q^{80} +3.48678e9 q^{81} +4.63113e10 q^{82} -6.20725e10 q^{83} +1.29133e9 q^{84} +8.08258e9 q^{85} +4.36380e10 q^{86} +1.84081e10 q^{87} -8.70835e10 q^{88} +4.27674e10 q^{89} +4.70886e9 q^{90} +1.70442e10 q^{91} +2.20695e9 q^{92} +3.43402e10 q^{93} +8.61237e10 q^{94} +2.74647e9 q^{95} -7.05400e9 q^{96} +1.93882e10 q^{97} -3.61391e10 q^{98} +5.36287e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) $	\( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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 $

$2$	43.4861	0.960916	0.480458	−	0.877018i	$-0.340470\pi$
$2$	43.4861	0.960916	0.480458	+	0.877018i	$0.340470\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−156.959	−0.0766403
$5$	1833.80	0.262433	0.131216	−	0.991354i	$-0.458112\pi$
$5$	1833.80	0.262433	0.131216	+	0.991354i	$0.458112\pi$
$6$	−10567.1	−0.554785
$7$	33856.7	0.761387	0.380694	−	0.924701i	$-0.375685\pi$
$7$	33856.7	0.761387	0.380694	+	0.924701i	$0.375685\pi$
$8$	−95885.1	−1.03456
$9$	59049.0	0.333333
$10$	79745.0	0.252176
$11$	908207.	1.70030	0.850149	−	0.526541i	$-0.176511\pi$
$11$	908207.	1.70030	0.850149	+	0.526541i	$0.176511\pi$
$12$	38141.1	0.0442483
$13$	503420.	0.376047	0.188024	−	0.982165i	$-0.439792\pi$
$13$	503420.	0.376047	0.188024	+	0.982165i	$0.439792\pi$
$14$	1.47230e6	0.731629
$15$	−445614.	−0.151516
$16$	−3.84821e6	−0.917486
$17$	4.40755e6	0.752884	0.376442	−	0.926440i	$-0.377147\pi$
$17$	4.40755e6	0.752884	0.376442	+	0.926440i	$0.377147\pi$
$18$	2.56781e6	0.320305
$19$	1.49769e6	0.138764	0.0693821	−	0.997590i	$-0.477897\pi$
$19$	1.49769e6	0.138764	0.0693821	+	0.997590i	$0.477897\pi$
$20$	−287833.	−0.0201129
$21$	−8.22718e6	−0.439587
$22$	3.94944e7	1.63384
$23$	−1.40606e7	−0.455514	−0.227757	−	0.973718i	$-0.573139\pi$
$23$	−1.40606e7	−0.455514	−0.227757	+	0.973718i	$0.573139\pi$
$24$	2.33001e7	0.597304
$25$	−4.54653e7	−0.931129
$26$	2.18918e7	0.361350
$27$	−1.43489e7	−0.192450
$28$	−5.31413e6	−0.0583530
$29$	−7.57535e7	−0.685826	−0.342913	−	0.939367i	$-0.611414\pi$
$29$	−7.57535e7	−0.685826	−0.342913	+	0.939367i	$0.611414\pi$
$30$	−1.93780e7	−0.145594
$31$	−1.41318e8	−0.886558	−0.443279	−	0.896384i	$-0.646185\pi$
$31$	−1.41318e8	−0.886558	−0.443279	+	0.896384i	$0.646185\pi$
$32$	2.90288e7	0.152934
$33$	−2.20694e8	−0.981668
$34$	1.91667e8	0.723458
$35$	6.20866e7	0.199813
$36$	−9.26830e6	−0.0255468
$37$	−4.72854e8	−1.12103	−0.560515	−	0.828144i	$-0.689397\pi$
$37$	−4.72854e8	−1.12103	−0.560515	+	0.828144i	$0.689397\pi$
$38$	6.51288e7	0.133341
$39$	−1.22331e8	−0.217111
$40$	−1.75834e8	−0.271503
$41$	1.06497e9	1.43557	0.717787	−	0.696263i	$-0.245155\pi$
$41$	1.06497e9	1.43557	0.717787	+	0.696263i	$0.245155\pi$
$42$	−3.57768e8	−0.422406
$43$	1.00349e9	1.04097	0.520485	−	0.853871i	$-0.325751\pi$
$43$	1.00349e9	1.04097	0.520485	+	0.853871i	$0.325751\pi$
$44$	−1.42552e8	−0.130311
$45$	1.08284e8	0.0874775
$46$	−6.11442e8	−0.437711
$47$	1.98049e9	1.25960	0.629802	−	0.776756i	$-0.283136\pi$
$47$	1.98049e9	1.25960	0.629802	+	0.776756i	$0.283136\pi$
$48$	9.35116e8	0.529711
$49$	−8.31050e8	−0.420290
$50$	−1.97711e9	−0.894737
$51$	−1.07103e9	−0.434678
$52$	−7.90166e7	−0.0288204
$53$	4.29679e9	1.41132	0.705662	−	0.708548i	$-0.250650\pi$
$53$	4.29679e9	1.41132	0.705662	+	0.708548i	$0.250650\pi$
$54$	−6.23978e8	−0.184928
$55$	1.66547e9	0.446214
$56$	−3.24635e9	−0.787701
$57$	−3.63939e8	−0.0801156
$58$	−3.29422e9	−0.659021
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	6.99434e7	0.0116122
$61$	6.72663e8	0.101973	0.0509863	−	0.998699i	$-0.483764\pi$
$61$	6.72663e8	0.101973	0.0509863	+	0.998699i	$0.483764\pi$
$62$	−6.14535e9	−0.851907
$63$	1.99920e9	0.253796
$64$	9.14349e9	1.06444
$65$	9.23174e8	0.0986871
$66$	−9.59714e9	−0.943301
$67$	−5.16613e9	−0.467470	−0.233735	−	0.972300i	$-0.575095\pi$
$67$	−5.16613e9	−0.467470	−0.233735	+	0.972300i	$0.575095\pi$
$68$	−6.91806e8	−0.0577013
$69$	3.41673e9	0.262991
$70$	2.69990e9	0.192003
$71$	−1.10100e10	−0.724215	−0.362107	−	0.932136i	$-0.617943\pi$
$71$	−1.10100e10	−0.724215	−0.362107	+	0.932136i	$0.617943\pi$
$72$	−5.66192e9	−0.344854
$73$	1.07298e10	0.605783	0.302892	−	0.953025i	$-0.402048\pi$
$73$	1.07298e10	0.605783	0.302892	+	0.953025i	$0.402048\pi$
$74$	−2.05626e10	−1.07722
$75$	1.10481e10	0.537588
$76$	−2.35077e8	−0.0106349
$77$	3.07489e10	1.29459
$78$	−5.31970e9	−0.208625
$79$	5.11404e10	1.86989	0.934943	−	0.354798i	$-0.115451\pi$
$79$	5.11404e10	1.86989	0.934943	+	0.354798i	$0.115451\pi$
$80$	−7.05687e9	−0.240778
$81$	3.48678e9	0.111111
$82$	4.63113e10	1.37947
$83$	−6.20725e10	−1.72970	−0.864848	−	0.502035i	$-0.832585\pi$
$83$	−6.20725e10	−1.72970	−0.864848	+	0.502035i	$0.832585\pi$
$84$	1.29133e9	0.0336901
$85$	8.08258e9	0.197581
$86$	4.36380e10	1.00029
$87$	1.84081e10	0.395962
$88$	−8.70835e10	−1.75906
$89$	4.27674e10	0.811835	0.405918	−	0.913910i	$-0.366952\pi$
$89$	4.27674e10	0.811835	0.405918	+	0.913910i	$0.366952\pi$
$90$	4.70886e9	0.0840586
$91$	1.70442e10	0.286317
$92$	2.20695e9	0.0349108
$93$	3.43402e10	0.511854
$94$	8.61237e10	1.21037
$95$	2.74647e9	0.0364163
$96$	−7.05400e9	−0.0882965
$97$	1.93882e10	0.229241	0.114621	−	0.993409i	$-0.463435\pi$
$97$	1.93882e10	0.229241	0.114621	+	0.993409i	$0.463435\pi$
$98$	−3.61391e10	−0.403863
$99$	5.36287e10	0.566766
$100$	7.13621e9	0.0713621
$101$	8.04521e10	0.761675	0.380838	−	0.924642i	$-0.375636\pi$
$101$	8.04521e10	0.761675	0.380838	+	0.924642i	$0.375636\pi$
$102$	−4.65751e10	−0.417689
$103$	−3.11508e9	−0.0264767	−0.0132384	−	0.999912i	$-0.504214\pi$
$103$	−3.11508e9	−0.0264767	−0.0132384	+	0.999912i	$0.504214\pi$
$104$	−4.82705e10	−0.389044
$105$	−1.50870e10	−0.115362
$106$	1.86851e11	1.35616
$107$	2.77619e10	0.191354	0.0956771	−	0.995412i	$-0.469498\pi$
$107$	2.77619e10	0.191354	0.0956771	+	0.995412i	$0.469498\pi$
$108$	2.25220e9	0.0147494
$109$	−2.05970e11	−1.28221	−0.641104	−	0.767454i	$-0.721523\pi$
$109$	−2.05970e11	−1.28221	−0.641104	+	0.767454i	$0.721523\pi$
$110$	7.24250e10	0.428774
$111$	1.14904e11	0.647228
$112$	−1.30288e11	−0.698562
$113$	3.60171e11	1.83898	0.919492	−	0.393109i	$-0.128601\pi$
$113$	3.60171e11	1.83898	0.919492	+	0.393109i	$0.128601\pi$
$114$	−1.58263e10	−0.0769844
$115$	−2.57844e10	−0.119542
$116$	1.18902e10	0.0525619
$117$	2.97265e10	0.125349
$118$	−3.10893e10	−0.125101
$119$	1.49225e11	0.573236
$120$	4.27278e10	0.156752
$121$	5.39529e11	1.89102
$122$	2.92515e10	0.0979871
$123$	−2.58787e11	−0.828829
$124$	2.21811e10	0.0679461
$125$	−1.72916e11	−0.506791
$126$	8.69376e10	0.243876
$127$	6.11224e11	1.64165	0.820823	−	0.571182i	$-0.193515\pi$
$127$	6.11224e11	1.64165	0.820823	+	0.571182i	$0.193515\pi$
$128$	3.38164e11	0.869906
$129$	−2.43849e11	−0.601005
$130$	4.01452e10	0.0948300
$131$	4.87280e10	0.110354	0.0551768	−	0.998477i	$-0.482428\pi$
$131$	4.87280e10	0.110354	0.0551768	+	0.998477i	$0.482428\pi$
$132$	3.46401e10	0.0752354
$133$	5.07069e10	0.105653
$134$	−2.24655e11	−0.449200
$135$	−2.63131e10	−0.0505052
$136$	−4.22618e11	−0.778904
$137$	1.10392e12	1.95422	0.977109	−	0.212738i	$-0.0682381\pi$
$137$	1.10392e12	1.95422	0.977109	+	0.212738i	$0.0682381\pi$
$138$	1.48580e11	0.252712
$139$	6.89351e11	1.12683	0.563416	−	0.826174i	$-0.309487\pi$
$139$	6.89351e11	1.12683	0.563416	+	0.826174i	$0.309487\pi$
$140$	−9.74507e9	−0.0153137
$141$	−4.81259e11	−0.727233
$142$	−4.78783e11	−0.695909
$143$	4.57210e11	0.639393
$144$	−2.27233e11	−0.305829
$145$	−1.38917e11	−0.179983
$146$	4.66599e11	0.582107
$147$	2.01945e11	0.242654
$148$	7.42189e10	0.0859162
$149$	7.47587e11	0.833945	0.416972	−	0.908919i	$-0.363091\pi$
$149$	7.47587e11	0.833945	0.416972	+	0.908919i	$0.363091\pi$
$150$	4.80437e11	0.516577
$151$	−4.44145e11	−0.460417	−0.230209	−	0.973141i	$-0.573941\pi$
$151$	−4.44145e11	−0.460417	−0.230209	+	0.973141i	$0.573941\pi$
$152$	−1.43606e11	−0.143560
$153$	2.60261e11	0.250961
$154$	1.33715e12	1.24399
$155$	−2.59149e11	−0.232662
$156$	1.92010e10	0.0166395
$157$	−2.16780e12	−1.81372	−0.906860	−	0.421432i	$-0.861528\pi$
$157$	−2.16780e12	−1.81372	−0.906860	+	0.421432i	$0.861528\pi$
$158$	2.22390e12	1.79680
$159$	−1.04412e12	−0.814829
$160$	5.32331e10	0.0401349
$161$	−4.76047e11	−0.346823
$162$	1.51627e11	0.106768
$163$	−1.17833e12	−0.802114	−0.401057	−	0.916053i	$-0.631357\pi$
$163$	−1.17833e12	−0.802114	−0.401057	+	0.916053i	$0.631357\pi$
$164$	−1.67157e11	−0.110023
$165$	−4.04710e11	−0.257622
$166$	−2.69929e12	−1.66209
$167$	−2.26313e12	−1.34825	−0.674124	−	0.738619i	$-0.735478\pi$
$167$	−2.26313e12	−1.34825	−0.674124	+	0.738619i	$0.735478\pi$
$168$	7.88864e11	0.454780
$169$	−1.53873e12	−0.858588
$170$	3.51480e11	0.189859
$171$	8.84372e10	0.0462548
$172$	−1.57508e11	−0.0797803
$173$	7.73542e11	0.379516	0.189758	−	0.981831i	$-0.439230\pi$
$173$	7.73542e11	0.379516	0.189758	+	0.981831i	$0.439230\pi$
$174$	8.00497e11	0.380486
$175$	−1.53931e12	−0.708950
$176$	−3.49498e12	−1.56000
$177$	1.73727e11	0.0751646
$178$	1.85979e12	0.780105
$179$	4.62740e12	1.88211	0.941055	−	0.338253i	$-0.109836\pi$
$179$	4.62740e12	1.88211	0.941055	+	0.338253i	$0.109836\pi$
$180$	−1.69962e10	−0.00670431
$181$	2.35718e12	0.901905	0.450953	−	0.892548i	$-0.351084\pi$
$181$	2.35718e12	0.901905	0.450953	+	0.892548i	$0.351084\pi$
$182$	7.41184e11	0.275127
$183$	−1.63457e11	−0.0588739
$184$	1.34821e12	0.471257
$185$	−8.67121e11	−0.294195
$186$	1.49332e12	0.491849
$187$	4.00297e12	1.28013
$188$	−3.10856e11	−0.0965365
$189$	−4.85807e11	−0.146529
$190$	1.19433e11	0.0349930
$191$	−1.88163e12	−0.535614	−0.267807	−	0.963473i	$-0.586299\pi$
$191$	−1.88163e12	−0.535614	−0.267807	+	0.963473i	$0.586299\pi$
$192$	−2.22187e12	−0.614556
$193$	1.29316e12	0.347605	0.173803	−	0.984780i	$-0.444395\pi$
$193$	1.29316e12	0.347605	0.173803	+	0.984780i	$0.444395\pi$
$194$	8.43117e11	0.220282
$195$	−2.24331e11	−0.0569770
$196$	1.30441e11	0.0322111
$197$	−1.85691e12	−0.445888	−0.222944	−	0.974831i	$-0.571567\pi$
$197$	−1.85691e12	−0.445888	−0.222944	+	0.974831i	$0.571567\pi$
$198$	2.33210e12	0.544615
$199$	5.68634e12	1.29164	0.645819	−	0.763491i	$-0.276516\pi$
$199$	5.68634e12	1.29164	0.645819	+	0.763491i	$0.276516\pi$
$200$	4.35944e12	0.963310
$201$	1.25537e12	0.269894
$202$	3.49855e12	0.731906
$203$	−2.56476e12	−0.522179
$204$	1.68109e11	0.0333138
$205$	1.95294e12	0.376741
$206$	−1.35463e11	−0.0254419
$207$	−8.30266e11	−0.151838
$208$	−1.93727e12	−0.345018
$209$	1.36021e12	0.235941
$210$	−6.56076e11	−0.110853
$211$	1.34650e12	0.221642	0.110821	−	0.993840i	$-0.464652\pi$
$211$	1.34650e12	0.221642	0.110821	+	0.993840i	$0.464652\pi$
$212$	−6.74422e11	−0.108164
$213$	2.67544e12	0.418125
$214$	1.20726e12	0.183875
$215$	1.84021e12	0.273185
$216$	1.37585e12	0.199101
$217$	−4.78455e12	−0.675013
$218$	−8.95684e12	−1.23209
$219$	−2.60735e12	−0.349749
$220$	−2.61412e11	−0.0341980
$221$	2.21885e12	0.283120
$222$	4.99671e12	0.621931
$223$	−8.91880e12	−1.08300	−0.541501	−	0.840700i	$-0.682144\pi$
$223$	−8.91880e12	−1.08300	−0.541501	+	0.840700i	$0.682144\pi$
$224$	9.82820e11	0.116442
$225$	−2.68468e12	−0.310376
$226$	1.56624e13	1.76711
$227$	5.85027e12	0.644219	0.322109	−	0.946702i	$-0.395608\pi$
$227$	5.85027e12	0.644219	0.322109	+	0.946702i	$0.395608\pi$
$228$	5.71237e10	0.00614009
$229$	4.86887e12	0.510897	0.255448	−	0.966823i	$-0.417777\pi$
$229$	4.86887e12	0.510897	0.255448	+	0.966823i	$0.417777\pi$
$230$	−1.12126e12	−0.114870
$231$	−7.47199e12	−0.747429
$232$	7.26363e12	0.709529
$233$	1.90023e13	1.81280	0.906398	−	0.422425i	$-0.138821\pi$
$233$	1.90023e13	1.81280	0.906398	+	0.422425i	$0.138821\pi$
$234$	1.29269e12	0.120450
$235$	3.63183e12	0.330561
$236$	1.12214e11	0.00997772
$237$	−1.24271e13	−1.07958
$238$	6.48922e12	0.550832
$239$	6.07560e12	0.503965	0.251983	−	0.967732i	$-0.418917\pi$
$239$	6.07560e12	0.503965	0.251983	+	0.967732i	$0.418917\pi$
$240$	1.71482e12	0.139013
$241$	−2.48442e12	−0.196848	−0.0984242	−	0.995145i	$-0.531380\pi$
$241$	−2.48442e12	−0.196848	−0.0984242	+	0.995145i	$0.531380\pi$
$242$	2.34620e13	1.81711
$243$	−8.47289e11	−0.0641500
$244$	−1.05581e11	−0.00781522
$245$	−1.52398e12	−0.110298
$246$	−1.12536e13	−0.796435
$247$	7.53969e11	0.0521819
$248$	1.35502e13	0.917198
$249$	1.50836e13	0.998640
$250$	−7.51942e12	−0.486984
$251$	−1.58043e12	−0.100131	−0.0500656	−	0.998746i	$-0.515943\pi$
$251$	−1.58043e12	−0.100131	−0.0500656	+	0.998746i	$0.515943\pi$
$252$	−3.13794e11	−0.0194510
$253$	−1.27700e13	−0.774510
$254$	2.65797e13	1.57748
$255$	−1.96407e12	−0.114074
$256$	−4.02045e12	−0.228536
$257$	−3.16358e13	−1.76014	−0.880068	−	0.474847i	$-0.842503\pi$
$257$	−3.16358e13	−1.76014	−0.880068	+	0.474847i	$0.842503\pi$
$258$	−1.06040e13	−0.577515
$259$	−1.60093e13	−0.853539
$260$	−1.44901e11	−0.00756341
$261$	−4.47317e12	−0.228609
$262$	2.11899e12	0.106040
$263$	2.99328e13	1.46686	0.733432	−	0.679762i	$-0.237917\pi$
$263$	2.99328e13	1.46686	0.733432	+	0.679762i	$0.237917\pi$
$264$	2.11613e13	1.01560
$265$	7.87947e12	0.370378
$266$	2.20505e12	0.101524
$267$	−1.03925e13	−0.468713
$268$	8.10873e11	0.0358271
$269$	4.52704e13	1.95964	0.979820	−	0.199880i	$-0.0640553\pi$
$269$	4.52704e13	1.95964	0.979820	+	0.199880i	$0.0640553\pi$
$270$	−1.14425e12	−0.0485312
$271$	2.56171e12	0.106463	0.0532316	−	0.998582i	$-0.483048\pi$
$271$	2.56171e12	0.106463	0.0532316	+	0.998582i	$0.483048\pi$
$272$	−1.69612e13	−0.690760
$273$	−4.14173e12	−0.165305
$274$	4.80050e13	1.87784
$275$	−4.12919e13	−1.58320
$276$	−5.36289e11	−0.0201557
$277$	−2.63263e13	−0.969953	−0.484977	−	0.874527i	$-0.661172\pi$
$277$	−2.63263e13	−0.969953	−0.484977	+	0.874527i	$0.661172\pi$
$278$	2.99772e13	1.08279
$279$	−8.34466e12	−0.295519
$280$	−5.95317e12	−0.206719
$281$	3.76679e13	1.28259	0.641293	−	0.767296i	$-0.278398\pi$
$281$	3.76679e13	1.28259	0.641293	+	0.767296i	$0.278398\pi$
$282$	−2.09281e13	−0.698810
$283$	2.92810e11	0.00958873	0.00479437	−	0.999989i	$-0.498474\pi$
$283$	2.92810e11	0.00958873	0.00479437	+	0.999989i	$0.498474\pi$
$284$	1.72813e12	0.0555041
$285$	−6.67393e11	−0.0210249
$286$	1.98823e13	0.614403
$287$	3.60563e13	1.09303
$288$	1.71412e12	0.0509780
$289$	−1.48454e13	−0.433166
$290$	−6.04096e12	−0.172949
$291$	−4.71133e12	−0.132352
$292$	−1.68415e12	−0.0464274
$293$	1.90466e13	0.515283	0.257641	−	0.966241i	$-0.417055\pi$
$293$	1.90466e13	0.515283	0.257641	+	0.966241i	$0.417055\pi$
$294$	8.78181e12	0.233170
$295$	−1.31103e12	−0.0341658
$296$	4.53396e13	1.15977
$297$	−1.30318e13	−0.327223
$298$	3.25096e13	0.801351
$299$	−7.07841e12	−0.171295
$300$	−1.73410e12	−0.0412009
$301$	3.39750e13	0.792581
$302$	−1.93141e13	−0.442422
$303$	−1.95499e13	−0.439753
$304$	−5.76344e12	−0.127314
$305$	1.23353e12	0.0267609
$306$	1.13177e13	0.241153
$307$	−2.57069e12	−0.0538008	−0.0269004	−	0.999638i	$-0.508564\pi$
$307$	−2.57069e12	−0.0538008	−0.0269004	+	0.999638i	$0.508564\pi$
$308$	−4.82633e12	−0.0992175
$309$	7.56964e11	0.0152863
$310$	−1.12694e13	−0.223568
$311$	−6.65354e13	−1.29679	−0.648397	−	0.761303i	$-0.724560\pi$
$311$	−6.65354e13	−1.29679	−0.648397	+	0.761303i	$0.724560\pi$
$312$	1.17297e13	0.224615
$313$	−2.87328e13	−0.540610	−0.270305	−	0.962775i	$-0.587125\pi$
$313$	−2.87328e13	−0.540610	−0.270305	+	0.962775i	$0.587125\pi$
$314$	−9.42690e13	−1.74283
$315$	3.66615e12	0.0666043
$316$	−8.02697e12	−0.143309
$317$	6.54043e13	1.14757	0.573786	−	0.819005i	$-0.305474\pi$
$317$	6.54043e13	1.14757	0.573786	+	0.819005i	$0.305474\pi$
$318$	−4.54047e13	−0.782982
$319$	−6.87999e13	−1.16611
$320$	1.67674e13	0.279344
$321$	−6.74613e12	−0.110478
$322$	−2.07014e13	−0.333267
$323$	6.60115e12	0.104473
$324$	−5.47284e11	−0.00851559
$325$	−2.28882e13	−0.350149
$326$	−5.12411e13	−0.770764
$327$	5.00508e13	0.740284
$328$	−1.02115e14	−1.48519
$329$	6.70528e13	0.959046
$330$	−1.75993e13	−0.247553
$331$	−2.33819e13	−0.323463	−0.161732	−	0.986835i	$-0.551708\pi$
$331$	−2.33819e13	−0.323463	−0.161732	+	0.986835i	$0.551708\pi$
$332$	9.74286e12	0.132564
$333$	−2.79216e13	−0.373677
$334$	−9.84148e13	−1.29555
$335$	−9.47367e12	−0.122679
$336$	3.16600e13	0.403315
$337$	−9.97413e13	−1.25000	−0.625001	−	0.780624i	$-0.714901\pi$
$337$	−9.97413e13	−1.25000	−0.625001	+	0.780624i	$0.714901\pi$
$338$	−6.69133e13	−0.825031
$339$	−8.75217e13	−1.06174
$340$	−1.26864e12	−0.0151427
$341$	−1.28346e14	−1.50741
$342$	3.84579e12	0.0444469
$343$	−9.50824e13	−1.08139
$344$	−9.62201e13	−1.07695
$345$	6.26562e12	0.0690175
$346$	3.36383e13	0.364683
$347$	−8.88536e13	−0.948119	−0.474059	−	0.880493i	$-0.657212\pi$
$347$	−8.88536e13	−0.948119	−0.474059	+	0.880493i	$0.657212\pi$
$348$	−2.88933e12	−0.0303466
$349$	1.09785e14	1.13502	0.567511	−	0.823366i	$-0.307907\pi$
$349$	1.09785e14	1.13502	0.567511	+	0.823366i	$0.307907\pi$
$350$	−6.69384e13	−0.681241
$351$	−7.22353e12	−0.0723703
$352$	2.63642e13	0.260034
$353$	−1.01555e14	−0.986147	−0.493073	−	0.869988i	$-0.664127\pi$
$353$	−1.01555e14	−0.986147	−0.493073	+	0.869988i	$0.664127\pi$
$354$	7.55469e12	0.0722269
$355$	−2.01902e13	−0.190058
$356$	−6.71275e12	−0.0622193
$357$	−3.62617e13	−0.330958
$358$	2.01227e14	1.80855
$359$	−1.37962e14	−1.22107	−0.610535	−	0.791989i	$-0.709045\pi$
$359$	−1.37962e14	−1.22107	−0.610535	+	0.791989i	$0.709045\pi$
$360$	−1.03828e13	−0.0905008
$361$	−1.14247e14	−0.980744
$362$	1.02505e14	0.866655
$363$	−1.31106e14	−1.09178
$364$	−2.67524e12	−0.0219435
$365$	1.96764e13	0.158977
$366$	−7.10811e12	−0.0565729
$367$	2.32302e14	1.82134	0.910668	−	0.413140i	$-0.135568\pi$
$367$	2.32302e14	1.82134	0.910668	+	0.413140i	$0.135568\pi$
$368$	5.41083e13	0.417928
$369$	6.28853e13	0.478524
$370$	−3.77077e13	−0.282697
$371$	1.45475e14	1.07456
$372$	−5.39001e12	−0.0392287
$373$	2.28454e14	1.63833	0.819163	−	0.573561i	$-0.194439\pi$
$373$	2.28454e14	1.63833	0.819163	+	0.573561i	$0.194439\pi$
$374$	1.74073e14	1.23010
$375$	4.20185e13	0.292596
$376$	−1.89899e14	−1.30314
$377$	−3.81359e13	−0.257903
$378$	−2.11258e13	−0.140802
$379$	−2.46243e14	−1.61751	−0.808757	−	0.588142i	$-0.799859\pi$
$379$	−2.46243e14	−1.61751	−0.808757	+	0.588142i	$0.799859\pi$
$380$	−4.31085e11	−0.00279096
$381$	−1.48527e14	−0.947805
$382$	−8.18249e13	−0.514680
$383$	3.47857e12	0.0215679	0.0107839	−	0.999942i	$-0.496567\pi$
$383$	3.47857e12	0.0215679	0.0107839	+	0.999942i	$0.496567\pi$
$384$	−8.21738e13	−0.502240
$385$	5.63875e13	0.339741
$386$	5.62344e13	0.334020
$387$	5.92553e13	0.346990
$388$	−3.04316e12	−0.0175691
$389$	4.32209e13	0.246021	0.123010	−	0.992405i	$-0.460745\pi$
$389$	4.32209e13	0.246021	0.123010	+	0.992405i	$0.460745\pi$
$390$	−9.75529e12	−0.0547501
$391$	−6.19729e13	−0.342949
$392$	7.96853e13	0.434815
$393$	−1.18409e13	−0.0637126
$394$	−8.07496e13	−0.428461
$395$	9.37814e13	0.490719
$396$	−8.41754e12	−0.0434372
$397$	2.65109e14	1.34920	0.674600	−	0.738183i	$-0.264316\pi$
$397$	2.65109e14	1.34920	0.674600	+	0.738183i	$0.264316\pi$
$398$	2.47277e14	1.24116
$399$	−1.23218e13	−0.0609990
$400$	1.74960e14	0.854298
$401$	−2.39946e14	−1.15563	−0.577816	−	0.816167i	$-0.696095\pi$
$401$	−2.39946e14	−1.15563	−0.577816	+	0.816167i	$0.696095\pi$
$402$	5.45911e13	0.259346
$403$	−7.11422e13	−0.333388
$404$	−1.26277e13	−0.0583750
$405$	6.39408e12	0.0291592
$406$	−1.11532e14	−0.501770
$407$	−4.29450e14	−1.90609
$408$	1.02696e14	0.449701
$409$	−3.90926e12	−0.0168895	−0.00844473	−	0.999964i	$-0.502688\pi$
$409$	−3.90926e12	−0.0168895	−0.00844473	+	0.999964i	$0.502688\pi$
$410$	8.49258e13	0.362017
$411$	−2.68252e14	−1.12827
$412$	4.88941e11	0.00202918
$413$	−2.42050e13	−0.0991242
$414$	−3.61050e13	−0.145904
$415$	−1.13829e14	−0.453928
$416$	1.46137e13	0.0575104
$417$	−1.67512e14	−0.650576
$418$	5.91504e13	0.226719
$419$	1.38759e11	0.000524909 0	0.000262454	−	1.00000i	$-0.499916\pi$
$419$	1.38759e11	0.000524909 0	0.000262454		1.00000i	$0.499916\pi$
$420$	2.36805e12	0.00884138
$421$	−5.33323e13	−0.196534	−0.0982672	−	0.995160i	$-0.531330\pi$
$421$	−5.33323e13	−0.196534	−0.0982672	+	0.995160i	$0.531330\pi$
$422$	5.85539e13	0.212979
$423$	1.16946e14	0.419868
$424$	−4.11998e14	−1.46010
$425$	−2.00390e14	−0.701032
$426$	1.16344e14	0.401783
$427$	2.27742e13	0.0776406
$428$	−4.35749e12	−0.0146654
$429$	−1.11102e14	−0.369154
$430$	8.00236e13	0.262507
$431$	1.33808e14	0.433369	0.216685	−	0.976242i	$-0.430476\pi$
$431$	1.33808e14	0.433369	0.216685	+	0.976242i	$0.430476\pi$
$432$	5.52177e13	0.176570
$433$	4.98813e13	0.157491	0.0787453	−	0.996895i	$-0.474909\pi$
$433$	4.98813e13	0.157491	0.0787453	+	0.996895i	$0.474909\pi$
$434$	−2.08061e14	−0.648631
$435$	3.37568e13	0.103913
$436$	3.23290e13	0.0982689
$437$	−2.10585e13	−0.0632091
$438$	−1.13383e14	−0.336080
$439$	2.35666e14	0.689831	0.344915	−	0.938634i	$-0.387908\pi$
$439$	2.35666e14	0.689831	0.344915	+	0.938634i	$0.387908\pi$
$440$	−1.59694e14	−0.461635
$441$	−4.90727e13	−0.140097
$442$	9.64891e13	0.272054
$443$	−3.17843e14	−0.885100	−0.442550	−	0.896744i	$-0.645926\pi$
$443$	−3.17843e14	−0.885100	−0.442550	+	0.896744i	$0.645926\pi$
$444$	−1.80352e13	−0.0496037
$445$	7.84270e13	0.213052
$446$	−3.87844e14	−1.04067
$447$	−1.81664e14	−0.481478
$448$	3.09569e14	0.810453
$449$	5.56046e13	0.143799	0.0718995	−	0.997412i	$-0.477094\pi$
$449$	5.56046e13	0.143799	0.0718995	+	0.997412i	$0.477094\pi$
$450$	−1.16746e14	−0.298246
$451$	9.67212e14	2.44090
$452$	−5.65323e13	−0.140940
$453$	1.07927e14	0.265822
$454$	2.54405e14	0.619040
$455$	3.12556e13	0.0751390
$456$	3.48963e13	0.0828845
$457$	5.44106e14	1.27686	0.638432	−	0.769679i	$-0.279584\pi$
$457$	5.44106e14	1.27686	0.638432	+	0.769679i	$0.279584\pi$
$458$	2.11728e14	0.490929
$459$	−6.32435e13	−0.144893
$460$	4.04711e12	0.00916172
$461$	−6.66619e14	−1.49116	−0.745578	−	0.666419i	$-0.767826\pi$
$461$	−6.66619e14	−1.49116	−0.745578	+	0.666419i	$0.767826\pi$
$462$	−3.24928e14	−0.718217
$463$	−1.75744e14	−0.383870	−0.191935	−	0.981408i	$-0.561476\pi$
$463$	−1.75744e14	−0.383870	−0.191935	+	0.981408i	$0.561476\pi$
$464$	2.91516e14	0.629236
$465$	6.29731e13	0.134327
$466$	8.26336e14	1.74194
$467$	−6.97107e14	−1.45230	−0.726151	−	0.687536i	$-0.758692\pi$
$467$	−6.97107e14	−1.45230	−0.726151	+	0.687536i	$0.758692\pi$
$468$	−4.66585e12	−0.00960680
$469$	−1.74908e14	−0.355926
$470$	1.57934e14	0.317642
$471$	5.26774e14	1.04715
$472$	6.85506e13	0.134688
$473$	9.11381e14	1.76996
$474$	−5.40407e14	−1.03738
$475$	−6.80930e13	−0.129207
$476$	−2.34223e13	−0.0439330
$477$	2.53721e14	0.470442
$478$	2.64204e14	0.484268
$479$	8.55969e14	1.55100	0.775501	−	0.631346i	$-0.217497\pi$
$479$	8.55969e14	1.55100	0.775501	+	0.631346i	$0.217497\pi$
$480$	−1.29356e13	−0.0231719
$481$	−2.38044e14	−0.421561
$482$	−1.08038e14	−0.189155
$483$	1.15679e14	0.200238
$484$	−8.46842e13	−0.144928
$485$	3.55541e13	0.0601604
$486$	−3.68453e13	−0.0616428
$487$	3.99285e14	0.660502	0.330251	−	0.943893i	$-0.392867\pi$
$487$	3.99285e14	0.660502	0.330251	+	0.943893i	$0.392867\pi$
$488$	−6.44984e13	−0.105497
$489$	2.86335e14	0.463100
$490$	−6.62721e13	−0.105987
$491$	3.99664e14	0.632043	0.316022	−	0.948752i	$-0.397653\pi$
$491$	3.99664e14	0.632043	0.316022	+	0.948752i	$0.397653\pi$
$492$	4.06191e13	0.0635217
$493$	−3.33887e14	−0.516347
$494$	3.27872e13	0.0501424
$495$	9.83446e13	0.148738
$496$	5.43820e14	0.813404
$497$	−3.72763e14	−0.551408
$498$	6.55927e14	0.959609
$499$	8.97290e14	1.29831	0.649157	−	0.760654i	$-0.275122\pi$
$499$	8.97290e14	1.29831	0.649157	+	0.760654i	$0.275122\pi$
$500$	2.71407e13	0.0388407
$501$	5.49941e14	0.778411
$502$	−6.87267e13	−0.0962177
$503$	2.80375e14	0.388253	0.194126	−	0.980977i	$-0.437813\pi$
$503$	2.80375e14	0.388253	0.194126	+	0.980977i	$0.437813\pi$
$504$	−1.91694e14	−0.262567
$505$	1.47533e14	0.199888
$506$	−5.55316e14	−0.744239
$507$	3.73911e14	0.495706
$508$	−9.59373e13	−0.125816
$509$	7.16559e14	0.929617	0.464808	−	0.885411i	$-0.346123\pi$
$509$	7.16559e14	0.929617	0.464808	+	0.885411i	$0.346123\pi$
$510$	−8.54096e13	−0.109615
$511$	3.63277e14	0.461236
$512$	−8.67393e14	−1.08951
$513$	−2.14902e13	−0.0267052
$514$	−1.37572e15	−1.69134
$515$	−5.71244e12	−0.00694835
$516$	3.82744e13	0.0460612
$517$	1.79869e15	2.14170
$518$	−6.96181e14	−0.820179
$519$	−1.87971e14	−0.219114
$520$	−8.85186e13	−0.102098
$521$	−9.72152e14	−1.10950	−0.554749	−	0.832017i	$-0.687186\pi$
$521$	−9.72152e14	−1.10950	−0.554749	+	0.832017i	$0.687186\pi$
$522$	−1.94521e14	−0.219674
$523$	−8.37926e14	−0.936367	−0.468184	−	0.883631i	$-0.655091\pi$
$523$	−8.37926e14	−0.936367	−0.468184	+	0.883631i	$0.655091\pi$
$524$	−7.64831e12	−0.00845753
$525$	3.74051e14	0.409312
$526$	1.30166e15	1.40953
$527$	−6.22864e14	−0.667475
$528$	8.49279e14	0.900667
$529$	−7.55108e14	−0.792507
$530$	3.42647e14	0.355902
$531$	−4.22156e13	−0.0433963
$532$	−7.95893e12	−0.00809731
$533$	5.36127e14	0.539843
$534$	−4.51928e14	−0.450394
$535$	5.09098e13	0.0502176
$536$	4.95355e14	0.483626
$537$	−1.12446e15	−1.08664
$538$	1.96863e15	1.88305
$539$	−7.54766e14	−0.714618
$540$	4.13009e12	0.00387073
$541$	−1.47807e15	−1.37123	−0.685613	−	0.727966i	$-0.740466\pi$
$541$	−1.47807e15	−1.37123	−0.685613	+	0.727966i	$0.740466\pi$
$542$	1.11399e14	0.102302
$543$	−5.72795e14	−0.520715
$544$	1.27946e14	0.115142
$545$	−3.77709e14	−0.336493
$546$	−1.80108e14	−0.158845
$547$	1.93870e15	1.69270	0.846352	−	0.532624i	$-0.178794\pi$
$547$	1.93870e15	1.69270	0.846352	+	0.532624i	$0.178794\pi$
$548$	−1.73270e14	−0.149772
$549$	3.97201e13	0.0339909
$550$	−1.79562e15	−1.52132
$551$	−1.13455e14	−0.0951681
$552$	−3.27614e14	−0.272080
$553$	1.73145e15	1.42371
$554$	−1.14483e15	−0.932044
$555$	2.10711e14	0.169854
$556$	−1.08200e14	−0.0863607
$557$	6.82212e14	0.539157	0.269579	−	0.962978i	$-0.413116\pi$
$557$	6.82212e14	0.539157	0.269579	+	0.962978i	$0.413116\pi$
$558$	−3.62877e14	−0.283969
$559$	5.05179e14	0.391454
$560$	−2.38922e14	−0.183325
$561$	−9.72721e14	−0.739082
$562$	1.63803e15	1.23246
$563$	2.01142e15	1.49867	0.749336	−	0.662190i	$-0.230373\pi$
$563$	2.01142e15	1.49867	0.749336	+	0.662190i	$0.230373\pi$
$564$	7.55381e13	0.0557354
$565$	6.60484e14	0.482609
$566$	1.27332e13	0.00921397
$567$	1.18051e14	0.0845986
$568$	1.05570e15	0.749244
$569$	−3.82268e14	−0.268689	−0.134345	−	0.990935i	$-0.542893\pi$
$569$	−3.82268e14	−0.268689	−0.134345	+	0.990935i	$0.542893\pi$
$570$	−2.90223e13	−0.0202032
$571$	7.65105e14	0.527500	0.263750	−	0.964591i	$-0.415041\pi$
$571$	7.65105e14	0.527500	0.263750	+	0.964591i	$0.415041\pi$
$572$	−7.17634e13	−0.0490033
$573$	4.57237e14	0.309237
$574$	1.56795e15	1.05031
$575$	6.39271e14	0.424142
$576$	5.39914e14	0.354814
$577$	−1.17709e15	−0.766199	−0.383099	−	0.923707i	$-0.625143\pi$
$577$	−1.17709e15	−0.766199	−0.383099	+	0.923707i	$0.625143\pi$
$578$	−6.45569e14	−0.416236
$579$	−3.14237e14	−0.200690
$580$	2.18043e13	0.0137940
$581$	−2.10157e15	−1.31697
$582$	−2.04877e14	−0.127180
$583$	3.90238e15	2.39967
$584$	−1.02883e15	−0.626720
$585$	5.45125e13	0.0328957
$586$	8.28263e14	0.495144
$587$	−9.35500e14	−0.554031	−0.277016	−	0.960865i	$-0.589345\pi$
$587$	−9.35500e14	−0.554031	−0.277016	+	0.960865i	$0.589345\pi$
$588$	−3.16972e13	−0.0185971
$589$	−2.11650e14	−0.123023
$590$	−5.70116e13	−0.0328305
$591$	4.51228e14	0.257433
$592$	1.81964e15	1.02853
$593$	3.41994e14	0.191522	0.0957609	−	0.995404i	$-0.469472\pi$
$593$	3.41994e14	0.191522	0.0957609	+	0.995404i	$0.469472\pi$
$594$	−5.66701e14	−0.314434
$595$	2.73649e14	0.150436
$596$	−1.17341e14	−0.0639138
$597$	−1.38178e15	−0.745727
$598$	−3.07812e14	−0.164600
$599$	−3.20513e15	−1.69824	−0.849118	−	0.528203i	$-0.822866\pi$
$599$	−3.20513e15	−1.69824	−0.849118	+	0.528203i	$0.822866\pi$
$600$	−1.05934e15	−0.556167
$601$	−1.84194e15	−0.958221	−0.479110	−	0.877755i	$-0.659041\pi$
$601$	−1.84194e15	−0.958221	−0.479110	+	0.877755i	$0.659041\pi$
$602$	1.47744e15	0.761604
$603$	−3.05055e14	−0.155823
$604$	6.97127e13	0.0352865
$605$	9.89390e14	0.496264
$606$	−8.50147e14	−0.422566
$607$	−1.61378e15	−0.794889	−0.397444	−	0.917626i	$-0.630103\pi$
$607$	−1.61378e15	−0.794889	−0.397444	+	0.917626i	$0.630103\pi$
$608$	4.34762e13	0.0212218
$609$	6.23238e14	0.301480
$610$	5.36415e13	0.0257150
$611$	9.97018e14	0.473671
$612$	−4.08505e13	−0.0192338
$613$	1.38006e15	0.643968	0.321984	−	0.946745i	$-0.395650\pi$
$613$	1.38006e15	0.643968	0.321984	+	0.946745i	$0.395650\pi$
$614$	−1.11789e14	−0.0516981
$615$	−4.74565e14	−0.217512
$616$	−2.94836e15	−1.33933
$617$	−5.39967e14	−0.243108	−0.121554	−	0.992585i	$-0.538788\pi$
$617$	−5.39967e14	−0.243108	−0.121554	+	0.992585i	$0.538788\pi$
$618$	3.29174e13	0.0146889
$619$	1.93355e15	0.855178	0.427589	−	0.903973i	$-0.359363\pi$
$619$	1.93355e15	0.855178	0.427589	+	0.903973i	$0.359363\pi$
$620$	4.06758e13	0.0178313
$621$	2.01755e14	0.0876637
$622$	−2.89337e15	−1.24611
$623$	1.44796e15	0.618121
$624$	4.70757e14	0.199196
$625$	1.90289e15	0.798131
$626$	−1.24948e15	−0.519481
$627$	−3.30532e14	−0.136220
$628$	3.40256e14	0.139004
$629$	−2.08413e15	−0.844006
$630$	1.59427e14	0.0640011
$631$	−2.03258e15	−0.808884	−0.404442	−	0.914564i	$-0.632534\pi$
$631$	−2.03258e15	−0.808884	−0.404442	+	0.914564i	$0.632534\pi$
$632$	−4.90360e15	−1.93451
$633$	−3.27199e14	−0.127965
$634$	2.84418e15	1.10272
$635$	1.12086e15	0.430822
$636$	1.63884e14	0.0624487
$637$	−4.18368e14	−0.158049
$638$	−2.99184e15	−1.12053
$639$	−6.50131e14	−0.241405
$640$	6.20126e14	0.228292
$641$	5.25486e15	1.91797	0.958986	−	0.283454i	$-0.0914804\pi$
$641$	5.25486e15	1.91797	0.958986	+	0.283454i	$0.0914804\pi$
$642$	−2.93363e14	−0.106160
$643$	−8.43519e14	−0.302646	−0.151323	−	0.988484i	$-0.548353\pi$
$643$	−8.43519e14	−0.302646	−0.151323	+	0.988484i	$0.548353\pi$
$644$	7.47200e13	0.0265806
$645$	−4.47171e14	−0.157723
$646$	2.87058e14	0.100390
$647$	−1.85214e15	−0.642244	−0.321122	−	0.947038i	$-0.604060\pi$
$647$	−1.85214e15	−0.642244	−0.321122	+	0.947038i	$0.604060\pi$
$648$	−3.34331e14	−0.114951
$649$	−6.49300e14	−0.221360
$650$	−9.95316e14	−0.336463
$651$	1.16265e15	0.389719
$652$	1.84950e14	0.0614743
$653$	−1.21454e15	−0.400304	−0.200152	−	0.979765i	$-0.564144\pi$
$653$	−1.21454e15	−0.400304	−0.200152	+	0.979765i	$0.564144\pi$
$654$	2.17651e15	0.711350
$655$	8.93575e13	0.0289604
$656$	−4.09823e15	−1.31712
$657$	6.33586e14	0.201928
$658$	2.91587e15	0.921563
$659$	1.11485e15	0.349418	0.174709	−	0.984620i	$-0.444101\pi$
$659$	1.11485e15	0.349418	0.174709	+	0.984620i	$0.444101\pi$
$660$	6.35231e13	0.0197442
$661$	2.64586e15	0.815565	0.407782	−	0.913079i	$-0.366302\pi$
$661$	2.64586e15	0.815565	0.407782	+	0.913079i	$0.366302\pi$
$662$	−1.01679e15	−0.310821
$663$	−5.39180e14	−0.163459
$664$	5.95182e15	1.78948
$665$	9.29865e13	0.0277269
$666$	−1.21420e15	−0.359072
$667$	1.06514e15	0.312403
$668$	3.55220e14	0.103330
$669$	2.16727e15	0.625272
$670$	−4.11973e14	−0.117885
$671$	6.10918e14	0.173384
$672$	−2.38825e14	−0.0672278
$673$	1.24861e14	0.0348614	0.0174307	−	0.999848i	$-0.494451\pi$
$673$	1.24861e14	0.0348614	0.0174307	+	0.999848i	$0.494451\pi$
$674$	−4.33736e15	−1.20115
$675$	6.52377e14	0.179196
$676$	2.41518e14	0.0658025
$677$	−2.13566e15	−0.577159	−0.288579	−	0.957456i	$-0.593183\pi$
$677$	−2.13566e15	−0.577159	−0.288579	+	0.957456i	$0.593183\pi$
$678$	−3.80598e15	−1.02024
$679$	6.56420e14	0.174541
$680$	−7.74999e14	−0.204410
$681$	−1.42161e15	−0.371940
$682$	−5.58125e15	−1.44850
$683$	−1.84879e15	−0.475962	−0.237981	−	0.971270i	$-0.576486\pi$
$683$	−1.84879e15	−0.475962	−0.237981	+	0.971270i	$0.576486\pi$
$684$	−1.38811e13	−0.00354498
$685$	2.02437e15	0.512851
$686$	−4.13476e15	−1.03913
$687$	−1.18314e15	−0.294966
$688$	−3.86166e15	−0.955076
$689$	2.16309e15	0.530725
$690$	2.72467e14	0.0663200
$691$	−2.47818e15	−0.598417	−0.299208	−	0.954188i	$-0.596723\pi$
$691$	−2.47818e15	−0.598417	−0.299208	+	0.954188i	$0.596723\pi$
$692$	−1.21415e14	−0.0290862
$693$	1.81569e15	0.431529
$694$	−3.86389e15	−0.911063
$695$	1.26413e15	0.295717
$696$	−1.76506e15	−0.409647
$697$	4.69390e15	1.08082
$698$	4.77413e15	1.09066
$699$	−4.61756e15	−1.04662
$700$	2.41608e14	0.0543341
$701$	−3.03287e15	−0.676713	−0.338356	−	0.941018i	$-0.609871\pi$
$701$	−3.03287e15	−0.676713	−0.338356	+	0.941018i	$0.609871\pi$
$702$	−3.14123e14	−0.0695418
$703$	−7.08190e14	−0.155559
$704$	8.30419e15	1.80987
$705$	−8.82534e14	−0.190850
$706$	−4.41624e15	−0.947604
$707$	2.72384e15	0.579930
$708$	−2.72680e13	−0.00576064
$709$	6.12649e15	1.28427	0.642137	−	0.766590i	$-0.278048\pi$
$709$	6.12649e15	1.28427	0.642137	+	0.766590i	$0.278048\pi$
$710$	−8.77994e14	−0.182629
$711$	3.01979e15	0.623295
$712$	−4.10076e15	−0.839893
$713$	1.98702e15	0.403839
$714$	−1.57688e15	−0.318023
$715$	8.38434e14	0.167797
$716$	−7.26314e14	−0.144246
$717$	−1.47637e15	−0.290965
$718$	−5.99943e15	−1.17335
$719$	5.78193e15	1.12218	0.561092	−	0.827754i	$-0.310382\pi$
$719$	5.78193e15	1.12218	0.561092	+	0.827754i	$0.310382\pi$
$720$	−4.16701e14	−0.0802594
$721$	−1.05466e14	−0.0201590
$722$	−4.96816e15	−0.942413
$723$	6.03715e14	0.113650
$724$	−3.69982e14	−0.0691223
$725$	3.44416e15	0.638592
$726$	−5.70127e15	−1.04911
$727$	5.16468e15	0.943201	0.471601	−	0.881812i	$-0.343676\pi$
$727$	5.16468e15	0.943201	0.471601	+	0.881812i	$0.343676\pi$
$728$	−1.63428e15	−0.296213
$729$	2.05891e14	0.0370370
$730$	8.55650e14	0.152764
$731$	4.42295e15	0.783730
$732$	2.56561e13	0.00451212
$733$	8.31193e14	0.145087	0.0725437	−	0.997365i	$-0.476888\pi$
$733$	8.31193e14	0.145087	0.0725437	+	0.997365i	$0.476888\pi$
$734$	1.01019e16	1.75015
$735$	3.70328e14	0.0636804
$736$	−4.08163e14	−0.0696636
$737$	−4.69192e15	−0.794839
$738$	2.73464e15	0.459822
$739$	2.62994e15	0.438936	0.219468	−	0.975620i	$-0.429568\pi$
$739$	2.62994e15	0.438936	0.219468	+	0.975620i	$0.429568\pi$
$740$	1.36103e14	0.0225472
$741$	−1.83214e14	−0.0301272
$742$	6.32615e15	1.03257
$743$	−2.00258e15	−0.324452	−0.162226	−	0.986754i	$-0.551867\pi$
$743$	−2.00258e15	−0.324452	−0.162226	+	0.986754i	$0.551867\pi$
$744$	−3.29271e15	−0.529544
$745$	1.37093e15	0.218854
$746$	9.93457e15	1.57429
$747$	−3.66532e15	−0.576565
$748$	−6.28304e14	−0.0981094
$749$	9.39925e14	0.145695
$750$	1.82722e15	0.281160
$751$	−1.05836e16	−1.61665	−0.808324	−	0.588738i	$-0.799625\pi$
$751$	−1.05836e16	−1.61665	−0.808324	+	0.588738i	$0.799625\pi$
$752$	−7.62134e15	−1.15567
$753$	3.84044e14	0.0578108
$754$	−1.65838e15	−0.247823
$755$	−8.14475e14	−0.120828
$756$	7.62519e13	0.0112300
$757$	−1.76057e15	−0.257411	−0.128705	−	0.991683i	$-0.541082\pi$
$757$	−1.76057e15	−0.257411	−0.128705	+	0.991683i	$0.541082\pi$
$758$	−1.07081e16	−1.55430
$759$	3.10310e15	0.447164
$760$	−2.63346e14	−0.0376749
$761$	−8.82470e15	−1.25338	−0.626692	−	0.779267i	$-0.715592\pi$
$761$	−8.82470e15	−1.25338	−0.626692	+	0.779267i	$0.715592\pi$
$762$	−6.45887e15	−0.910761
$763$	−6.97347e15	−0.976257
$764$	2.95340e14	0.0410496
$765$	4.77268e14	0.0658604
$766$	1.51269e14	0.0207249
$767$	−3.59907e14	−0.0489572
$768$	9.76969e14	0.131945
$769$	1.21909e16	1.63471	0.817355	−	0.576134i	$-0.195440\pi$
$769$	1.21909e16	1.63471	0.817355	+	0.576134i	$0.195440\pi$
$770$	2.45207e15	0.326463
$771$	7.68749e15	1.01622
$772$	−2.02973e14	−0.0266406
$773$	−6.91060e15	−0.900594	−0.450297	−	0.892879i	$-0.648682\pi$
$773$	−6.91060e15	−0.900594	−0.450297	+	0.892879i	$0.648682\pi$
$774$	2.57678e15	0.333428
$775$	6.42505e15	0.825500
$776$	−1.85904e15	−0.237164
$777$	3.89026e15	0.492791
$778$	1.87951e15	0.236405
$779$	1.59499e15	0.199206
$780$	3.52109e13	0.00436674
$781$	−9.99938e15	−1.23138
$782$	−2.69496e15	−0.329545
$783$	1.08698e15	0.131987
$784$	3.19806e15	0.385610
$785$	−3.97531e15	−0.475979
$786$	−5.14914e14	−0.0612225
$787$	−4.59089e15	−0.542046	−0.271023	−	0.962573i	$-0.587362\pi$
$787$	−4.59089e15	−0.542046	−0.271023	+	0.962573i	$0.587362\pi$
$788$	2.91459e14	0.0341730
$789$	−7.27366e15	−0.846895
$790$	4.07819e15	0.471540
$791$	1.21942e16	1.40018
$792$	−5.14220e15	−0.586354
$793$	3.38632e14	0.0383465
$794$	1.15286e16	1.29647
$795$	−1.91471e15	−0.213838
$796$	−8.92524e14	−0.0989915
$797$	1.32732e16	1.46202	0.731012	−	0.682365i	$-0.239048\pi$
$797$	1.32732e16	1.46202	0.731012	+	0.682365i	$0.239048\pi$
$798$	−5.35826e14	−0.0586149
$799$	8.72910e15	0.948336
$800$	−1.31980e15	−0.142401
$801$	2.52537e15	0.270612
$802$	−1.04343e16	−1.11047
$803$	9.74491e15	1.03001
$804$	−1.97042e14	−0.0206848
$805$	−8.72976e14	−0.0910176
$806$	−3.09370e15	−0.320357
$807$	−1.10007e16	−1.13140
$808$	−7.71415e15	−0.787999
$809$	−1.20145e16	−1.21896	−0.609480	−	0.792802i	$-0.708622\pi$
$809$	−1.20145e16	−1.21896	−0.609480	+	0.792802i	$0.708622\pi$
$810$	2.78053e14	0.0280195
$811$	−3.59147e15	−0.359465	−0.179733	−	0.983715i	$-0.557523\pi$
$811$	−3.59147e15	−0.359465	−0.179733	+	0.983715i	$0.557523\pi$
$812$	4.02564e14	0.0400200
$813$	−6.22496e14	−0.0614665
$814$	−1.86751e16	−1.83159
$815$	−2.16083e15	−0.210501
$816$	4.12157e15	0.398811
$817$	1.50292e15	0.144449
$818$	−1.69998e14	−0.0162294
$819$	1.00644e15	0.0954392
$820$	−3.06533e14	−0.0288736
$821$	−9.48394e15	−0.887363	−0.443682	−	0.896185i	$-0.646328\pi$
$821$	−9.48394e15	−0.887363	−0.443682	+	0.896185i	$0.646328\pi$
$822$	−1.16652e16	−1.08417
$823$	2.01774e16	1.86280	0.931399	−	0.364000i	$-0.118589\pi$
$823$	2.01774e16	1.86280	0.931399	+	0.364000i	$0.118589\pi$
$824$	2.98689e14	0.0273918
$825$	1.00339e16	0.914060
$826$	−1.05258e15	−0.0952500
$827$	−7.62814e15	−0.685707	−0.342853	−	0.939389i	$-0.611393\pi$
$827$	−7.62814e15	−0.685707	−0.342853	+	0.939389i	$0.611393\pi$
$828$	1.30318e14	0.0116369
$829$	2.04342e15	0.181262	0.0906311	−	0.995885i	$-0.471112\pi$
$829$	2.04342e15	0.181262	0.0906311	+	0.995885i	$0.471112\pi$
$830$	−4.94997e15	−0.436187
$831$	6.39729e15	0.560003
$832$	4.60302e15	0.400281
$833$	−3.66289e15	−0.316429
$834$	−7.28445e15	−0.625149
$835$	−4.15014e15	−0.353824
$836$	−2.13499e14	−0.0180826
$837$	2.02775e15	0.170618
$838$	6.03408e12	0.000504393 0
$839$	4.12678e15	0.342705	0.171352	−	0.985210i	$-0.445186\pi$
$839$	4.12678e15	0.342705	0.171352	+	0.985210i	$0.445186\pi$
$840$	1.44662e15	0.119349
$841$	−6.46191e15	−0.529643
$842$	−2.31921e15	−0.188853
$843$	−9.15329e15	−0.740501
$844$	−2.11345e14	−0.0169867
$845$	−2.82173e15	−0.225322
$846$	5.08552e15	0.403458
$847$	1.82667e16	1.43980
$848$	−1.65350e16	−1.29487
$849$	−7.11529e13	−0.00553606
$850$	−8.71420e15	−0.673633
$851$	6.64863e15	0.510645
$852$	−4.19935e14	−0.0320453
$853$	2.28613e16	1.73333	0.866665	−	0.498891i	$-0.166259\pi$
$853$	2.28613e16	1.73333	0.866665	+	0.498891i	$0.166259\pi$
$854$	9.90359e14	0.0746061
$855$	1.62176e14	0.0121388
$856$	−2.66195e15	−0.197968
$857$	−2.52878e16	−1.86860	−0.934299	−	0.356491i	$-0.883973\pi$
$857$	−2.52878e16	−1.86860	−0.934299	+	0.356491i	$0.883973\pi$
$858$	−4.83140e15	−0.354726
$859$	−1.05091e16	−0.766658	−0.383329	−	0.923612i	$-0.625222\pi$
$859$	−1.05091e16	−0.766658	−0.383329	+	0.923612i	$0.625222\pi$
$860$	−2.88839e14	−0.0209370
$861$	−8.76168e15	−0.631059
$862$	5.81880e15	0.416432
$863$	−4.46292e15	−0.317366	−0.158683	−	0.987330i	$-0.550725\pi$
$863$	−4.46292e15	−0.317366	−0.158683	+	0.987330i	$0.550725\pi$
$864$	−4.16532e14	−0.0294322
$865$	1.41852e15	0.0995974
$866$	2.16914e15	0.151335
$867$	3.60744e15	0.250088
$868$	7.50980e14	0.0517333
$869$	4.64461e16	3.17936
$870$	1.46795e15	0.0998519
$871$	−2.60074e15	−0.175791
$872$	1.97495e16	1.32652
$873$	1.14485e15	0.0764137
$874$	−9.15752e14	−0.0607386
$875$	−5.85435e15	−0.385864
$876$	4.09248e14	0.0268049
$877$	−3.44854e15	−0.224459	−0.112230	−	0.993682i	$-0.535799\pi$
$877$	−3.44854e15	−0.224459	−0.112230	+	0.993682i	$0.535799\pi$
$878$	1.02482e16	0.662870
$879$	−4.62833e15	−0.297499
$880$	−6.40910e15	−0.409395
$881$	−9.92748e15	−0.630190	−0.315095	−	0.949060i	$-0.602036\pi$
$881$	−9.92748e15	−0.630190	−0.315095	+	0.949060i	$0.602036\pi$
$882$	−2.13398e15	−0.134621
$883$	−1.29961e16	−0.814761	−0.407381	−	0.913258i	$-0.633558\pi$
$883$	−1.29961e16	−0.814761	−0.407381	+	0.913258i	$0.633558\pi$
$884$	−3.48269e14	−0.0216984
$885$	3.18580e14	0.0197256
$886$	−1.38217e16	−0.850506
$887$	6.94619e15	0.424783	0.212391	−	0.977185i	$-0.431875\pi$
$887$	6.94619e15	0.424783	0.212391	+	0.977185i	$0.431875\pi$
$888$	−1.10175e16	−0.669596
$889$	2.06940e16	1.24993
$890$	3.41048e15	0.204725
$891$	3.16672e15	0.188922
$892$	1.39989e15	0.0830017
$893$	2.96616e15	0.174788
$894$	−7.89984e15	−0.462660
$895$	8.48574e15	0.493927
$896$	1.14491e16	0.662335
$897$	1.72005e15	0.0988971
$898$	2.41803e15	0.138179
$899$	1.07053e16	0.608024
$900$	4.21386e14	0.0237874
$901$	1.89383e16	1.06256
$902$	4.20603e16	2.34550
$903$	−8.25593e15	−0.457597
$904$	−3.45351e16	−1.90254
$905$	4.32261e15	0.236689
$906$	4.69333e15	0.255433
$907$	−1.03723e15	−0.0561093	−0.0280547	−	0.999606i	$-0.508931\pi$
$907$	−1.03723e15	−0.0561093	−0.0280547	+	0.999606i	$0.508931\pi$
$908$	−9.18254e14	−0.0493732
$909$	4.75062e15	0.253892
$910$	1.35919e15	0.0722023
$911$	1.03483e16	0.546407	0.273204	−	0.961956i	$-0.411917\pi$
$911$	1.03483e16	0.546407	0.273204	+	0.961956i	$0.411917\pi$
$912$	1.40052e15	0.0735049
$913$	−5.63747e16	−2.94100
$914$	2.36610e16	1.22696
$915$	−2.99748e14	−0.0154504
$916$	−7.64215e14	−0.0391553
$917$	1.64977e15	0.0840217
$918$	−2.75021e15	−0.139230
$919$	−2.38504e15	−0.120022	−0.0600108	−	0.998198i	$-0.519114\pi$
$919$	−2.38504e15	−0.120022	−0.0600108	+	0.998198i	$0.519114\pi$
$920$	2.47234e15	0.123673
$921$	6.24678e14	0.0310619
$922$	−2.89887e16	−1.43288
$923$	−5.54267e15	−0.272339
$924$	1.17280e15	0.0572832
$925$	2.14984e16	1.04382
$926$	−7.64241e15	−0.368867
$927$	−1.83942e14	−0.00882557
$928$	−2.19903e15	−0.104886
$929$	−1.95390e16	−0.926436	−0.463218	−	0.886244i	$-0.653305\pi$
$929$	−1.95390e16	−0.926436	−0.463218	+	0.886244i	$0.653305\pi$
$930$	2.73846e15	0.129077
$931$	−1.24466e15	−0.0583212
$932$	−2.98259e15	−0.138933
$933$	1.61681e16	0.748704
$934$	−3.03145e16	−1.39554
$935$	7.34066e15	0.335947
$936$	−2.85033e15	−0.129681
$937$	1.28648e16	0.581882	0.290941	−	0.956741i	$-0.406032\pi$
$937$	1.28648e16	0.581882	0.290941	+	0.956741i	$0.406032\pi$
$938$	−7.60607e15	−0.342015
$939$	6.98207e15	0.312121
$940$	−5.70049e14	−0.0253343
$941$	1.79692e15	0.0793937	0.0396968	−	0.999212i	$-0.487361\pi$
$941$	1.79692e15	0.0793937	0.0396968	+	0.999212i	$0.487361\pi$
$942$	2.29074e16	1.00623
$943$	−1.49741e16	−0.653924
$944$	2.75118e15	0.119446
$945$	−8.90874e14	−0.0384540
$946$	3.96324e16	1.70078
$947$	1.58619e16	0.676755	0.338378	−	0.941010i	$-0.390122\pi$
$947$	1.58619e16	0.676755	0.338378	+	0.941010i	$0.390122\pi$
$948$	1.95055e15	0.0827393
$949$	5.40162e15	0.227803
$950$	−2.96110e15	−0.124158
$951$	−1.58932e16	−0.662552
$952$	−1.43085e16	−0.593048
$953$	1.77159e16	0.730048	0.365024	−	0.930998i	$-0.381061\pi$
$953$	1.77159e16	0.730048	0.365024	+	0.930998i	$0.381061\pi$
$954$	1.10333e16	0.452055
$955$	−3.45055e15	−0.140562
$956$	−9.53623e14	−0.0386241
$957$	1.67184e16	0.673253
$958$	3.72227e16	1.49038
$959$	3.73750e16	1.48792
$960$	−4.07447e15	−0.161280
$961$	−5.43781e15	−0.214016
$962$	−1.03516e16	−0.405084
$963$	1.63931e15	0.0637847
$964$	3.89954e14	0.0150865
$965$	2.37140e15	0.0912230
$966$	5.03044e15	0.192412
$967$	3.19757e16	1.21611	0.608057	−	0.793894i	$-0.291949\pi$
$967$	3.19757e16	1.21611	0.608057	+	0.793894i	$0.291949\pi$
$968$	−5.17328e16	−1.95637
$969$	−1.60408e15	−0.0603177
$970$	1.54611e15	0.0578091
$971$	4.28910e16	1.59463	0.797316	−	0.603563i	$-0.206253\pi$
$971$	4.28910e16	1.59463	0.797316	+	0.603563i	$0.206253\pi$
$972$	1.32990e14	0.00491648
$973$	2.33391e16	0.857955
$974$	1.73634e16	0.634687
$975$	5.56182e15	0.202158
$976$	−2.58855e15	−0.0935584
$977$	−5.46717e16	−1.96491	−0.982455	−	0.186499i	$-0.940286\pi$
$977$	−5.46717e16	−1.96491	−0.982455	+	0.186499i	$0.940286\pi$
$978$	1.24516e16	0.445001
$979$	3.88417e16	1.38036
$980$	2.39203e14	0.00845326
$981$	−1.21623e16	−0.427403
$982$	1.73798e16	0.607341
$983$	3.39763e16	1.18068	0.590339	−	0.807155i	$-0.298994\pi$
$983$	3.39763e16	1.18068	0.590339	+	0.807155i	$0.298994\pi$
$984$	2.48138e16	0.857474
$985$	−3.40520e15	−0.117016
$986$	−1.45195e16	−0.496166
$987$	−1.62938e16	−0.553706
$988$	−1.18342e14	−0.00399924
$989$	−1.41098e16	−0.474177
$990$	4.27662e15	0.142925
$991$	1.82981e16	0.608137	0.304069	−	0.952650i	$-0.401655\pi$
$991$	1.82981e16	0.608137	0.304069	+	0.952650i	$0.401655\pi$
$992$	−4.10228e15	−0.135585
$993$	5.68179e15	0.186752
$994$	−1.62100e16	−0.529856
$995$	1.04276e16	0.338968
$996$	−2.36751e15	−0.0765361
$997$	−6.67267e15	−0.214524	−0.107262	−	0.994231i	$-0.534208\pi$
$997$	−6.67267e15	−0.214524	−0.107262	+	0.994231i	$0.534208\pi$
$998$	3.90197e16	1.24757
$999$	6.78494e15	0.215743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.20	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+43.4861 q^{2} -243.000 q^{3} -156.959 q^{4} +1833.80 q^{5} -10567.1 q^{6} +33856.7 q^{7} -95885.1 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+43.4861 q^{2} -243.000 q^{3} -156.959 q^{4} +1833.80 q^{5} -10567.1 q^{6} +33856.7 q^{7} -95885.1 q^{8} +59049.0 q^{9} +79745.0 q^{10} +908207. q^{11} +38141.1 q^{12} +503420. q^{13} +1.47230e6 q^{14} -445614. q^{15} -3.84821e6 q^{16} +4.40755e6 q^{17} +2.56781e6 q^{18} +1.49769e6 q^{19} -287833. q^{20} -8.22718e6 q^{21} +3.94944e7 q^{22} -1.40606e7 q^{23} +2.33001e7 q^{24} -4.54653e7 q^{25} +2.18918e7 q^{26} -1.43489e7 q^{27} -5.31413e6 q^{28} -7.57535e7 q^{29} -1.93780e7 q^{30} -1.41318e8 q^{31} +2.90288e7 q^{32} -2.20694e8 q^{33} +1.91667e8 q^{34} +6.20866e7 q^{35} -9.26830e6 q^{36} -4.72854e8 q^{37} +6.51288e7 q^{38} -1.22331e8 q^{39} -1.75834e8 q^{40} +1.06497e9 q^{41} -3.57768e8 q^{42} +1.00349e9 q^{43} -1.42552e8 q^{44} +1.08284e8 q^{45} -6.11442e8 q^{46} +1.98049e9 q^{47} +9.35116e8 q^{48} -8.31050e8 q^{49} -1.97711e9 q^{50} -1.07103e9 q^{51} -7.90166e7 q^{52} +4.29679e9 q^{53} -6.23978e8 q^{54} +1.66547e9 q^{55} -3.24635e9 q^{56} -3.63939e8 q^{57} -3.29422e9 q^{58} -7.14924e8 q^{59} +6.99434e7 q^{60} +6.72663e8 q^{61} -6.14535e9 q^{62} +1.99920e9 q^{63} +9.14349e9 q^{64} +9.23174e8 q^{65} -9.59714e9 q^{66} -5.16613e9 q^{67} -6.91806e8 q^{68} +3.41673e9 q^{69} +2.69990e9 q^{70} -1.10100e10 q^{71} -5.66192e9 q^{72} +1.07298e10 q^{73} -2.05626e10 q^{74} +1.10481e10 q^{75} -2.35077e8 q^{76} +3.07489e10 q^{77} -5.31970e9 q^{78} +5.11404e10 q^{79} -7.05687e9 q^{80} +3.48678e9 q^{81} +4.63113e10 q^{82} -6.20725e10 q^{83} +1.29133e9 q^{84} +8.08258e9 q^{85} +4.36380e10 q^{86} +1.84081e10 q^{87} -8.70835e10 q^{88} +4.27674e10 q^{89} +4.70886e9 q^{90} +1.70442e10 q^{91} +2.20695e9 q^{92} +3.43402e10 q^{93} +8.61237e10 q^{94} +2.74647e9 q^{95} -7.05400e9 q^{96} +1.93882e10 q^{97} -3.61391e10 q^{98} +5.36287e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \)	\( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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