LMFDB - Embedded newform 177.10.a.a.1.3

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-35.8479 q^{2} +81.0000 q^{3} +773.074 q^{4} +1881.24 q^{5} -2903.68 q^{6} -9737.47 q^{7} -9358.98 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-35.8479 q^{2} +81.0000 q^{3} +773.074 q^{4} +1881.24 q^{5} -2903.68 q^{6} -9737.47 q^{7} -9358.98 q^{8} +6561.00 q^{9} -67438.4 q^{10} -61627.4 q^{11} +62619.0 q^{12} +169936. q^{13} +349068. q^{14} +152380. q^{15} -60314.1 q^{16} +560769. q^{17} -235198. q^{18} -659805. q^{19} +1.45434e6 q^{20} -788735. q^{21} +2.20922e6 q^{22} -535600. q^{23} -758077. q^{24} +1.58592e6 q^{25} -6.09185e6 q^{26} +531441. q^{27} -7.52779e6 q^{28} +1.76519e6 q^{29} -5.46251e6 q^{30} -7.35837e6 q^{31} +6.95393e6 q^{32} -4.99182e6 q^{33} -2.01024e7 q^{34} -1.83185e7 q^{35} +5.07214e6 q^{36} -1.11914e7 q^{37} +2.36527e7 q^{38} +1.37648e7 q^{39} -1.76064e7 q^{40} +9.17749e6 q^{41} +2.82745e7 q^{42} +1.27647e7 q^{43} -4.76426e7 q^{44} +1.23428e7 q^{45} +1.92002e7 q^{46} +7.13479e6 q^{47} -4.88544e6 q^{48} +5.44648e7 q^{49} -5.68520e7 q^{50} +4.54223e7 q^{51} +1.31373e8 q^{52} -1.07603e8 q^{53} -1.90511e7 q^{54} -1.15936e8 q^{55} +9.11328e7 q^{56} -5.34442e7 q^{57} -6.32783e7 q^{58} +1.21174e7 q^{59} +1.17801e8 q^{60} -2.18590e7 q^{61} +2.63782e8 q^{62} -6.38876e7 q^{63} -2.18403e8 q^{64} +3.19690e8 q^{65} +1.78947e8 q^{66} +3.04061e8 q^{67} +4.33516e8 q^{68} -4.33836e7 q^{69} +6.56680e8 q^{70} -2.46812e8 q^{71} -6.14042e7 q^{72} -9.89167e7 q^{73} +4.01190e8 q^{74} +1.28460e8 q^{75} -5.10079e8 q^{76} +6.00096e8 q^{77} -4.93440e8 q^{78} -1.89951e7 q^{79} -1.13465e8 q^{80} +4.30467e7 q^{81} -3.28994e8 q^{82} -3.82819e8 q^{83} -6.09751e8 q^{84} +1.05494e9 q^{85} -4.57587e8 q^{86} +1.42980e8 q^{87} +5.76770e8 q^{88} +8.54743e8 q^{89} -4.42463e8 q^{90} -1.65475e9 q^{91} -4.14059e8 q^{92} -5.96028e8 q^{93} -2.55767e8 q^{94} -1.24125e9 q^{95} +5.63268e8 q^{96} +1.05008e9 q^{97} -1.95245e9 q^{98} -4.04338e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) $	\( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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 $

$2$	−35.8479	−1.58427	−0.792135	−	0.610346i	$-0.791030\pi$
$2$	−35.8479	−1.58427	−0.792135	+	0.610346i	$0.791030\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	773.074	1.50991
$5$	1881.24	1.34610	0.673051	−	0.739596i	$-0.264983\pi$
$5$	1881.24	1.34610	0.673051	+	0.739596i	$0.264983\pi$
$6$	−2903.68	−0.914679
$7$	−9737.47	−1.53287	−0.766435	−	0.642322i	$-0.777971\pi$
$7$	−9737.47	−1.53287	−0.766435	+	0.642322i	$0.777971\pi$
$8$	−9358.98	−0.807836
$9$	6561.00	0.333333
$10$	−67438.4	−2.13259
$11$	−61627.4	−1.26913	−0.634566	−	0.772868i	$-0.718821\pi$
$11$	−61627.4	−1.26913	−0.634566	+	0.772868i	$0.718821\pi$
$12$	62619.0	0.871747
$13$	169936.	1.65021	0.825107	−	0.564977i	$-0.191115\pi$
$13$	169936.	1.65021	0.825107	+	0.564977i	$0.191115\pi$
$14$	349068.	2.42848
$15$	152380.	0.777173
$16$	−60314.1	−0.230080
$17$	560769.	1.62841	0.814205	−	0.580578i	$-0.197173\pi$
$17$	560769.	1.62841	0.814205	+	0.580578i	$0.197173\pi$
$18$	−235198.	−0.528090
$19$	−659805.	−1.16151	−0.580757	−	0.814077i	$-0.697243\pi$
$19$	−659805.	−1.16151	−0.580757	+	0.814077i	$0.697243\pi$
$20$	1.45434e6	2.03250
$21$	−788735.	−0.885002
$22$	2.20922e6	2.01065
$23$	−535600.	−0.399085	−0.199543	−	0.979889i	$-0.563946\pi$
$23$	−535600.	−0.399085	−0.199543	+	0.979889i	$0.563946\pi$
$24$	−758077.	−0.466405
$25$	1.58592e6	0.811992
$26$	−6.09185e6	−2.61438
$27$	531441.	0.192450
$28$	−7.52779e6	−2.31450
$29$	1.76519e6	0.463446	0.231723	−	0.972782i	$-0.425564\pi$
$29$	1.76519e6	0.463446	0.231723	+	0.972782i	$0.425564\pi$
$30$	−5.46251e6	−1.23125
$31$	−7.35837e6	−1.43105	−0.715523	−	0.698589i	$-0.753812\pi$
$31$	−7.35837e6	−1.43105	−0.715523	+	0.698589i	$0.753812\pi$
$32$	6.95393e6	1.17235
$33$	−4.99182e6	−0.732734
$34$	−2.01024e7	−2.57984
$35$	−1.83185e7	−2.06340
$36$	5.07214e6	0.503304
$37$	−1.11914e7	−0.981699	−0.490849	−	0.871245i	$-0.663313\pi$
$37$	−1.11914e7	−0.981699	−0.490849	+	0.871245i	$0.663313\pi$
$38$	2.36527e7	1.84015
$39$	1.37648e7	0.952751
$40$	−1.76064e7	−1.08743
$41$	9.17749e6	0.507220	0.253610	−	0.967307i	$-0.418382\pi$
$41$	9.17749e6	0.507220	0.253610	+	0.967307i	$0.418382\pi$
$42$	2.82745e7	1.40208
$43$	1.27647e7	0.569379	0.284689	−	0.958620i	$-0.408110\pi$
$43$	1.27647e7	0.569379	0.284689	+	0.958620i	$0.408110\pi$
$44$	−4.76426e7	−1.91628
$45$	1.23428e7	0.448701
$46$	1.92002e7	0.632258
$47$	7.13479e6	0.213275	0.106638	−	0.994298i	$-0.465991\pi$
$47$	7.13479e6	0.213275	0.106638	+	0.994298i	$0.465991\pi$
$48$	−4.88544e6	−0.132837
$49$	5.44648e7	1.34969
$50$	−5.68520e7	−1.28641
$51$	4.54223e7	0.940163
$52$	1.31373e8	2.49168
$53$	−1.07603e8	−1.87320	−0.936602	−	0.350396i	$-0.886047\pi$
$53$	−1.07603e8	−1.87320	−0.936602	+	0.350396i	$0.886047\pi$
$54$	−1.90511e7	−0.304893
$55$	−1.15936e8	−1.70838
$56$	9.11328e7	1.23831
$57$	−5.34442e7	−0.670601
$58$	−6.32783e7	−0.734224
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	1.17801e8	1.17346
$61$	−2.18590e7	−0.202138	−0.101069	−	0.994879i	$-0.532226\pi$
$61$	−2.18590e7	−0.202138	−0.101069	+	0.994879i	$0.532226\pi$
$62$	2.63782e8	2.26716
$63$	−6.38876e7	−0.510956
$64$	−2.18403e8	−1.62723
$65$	3.19690e8	2.22136
$66$	1.78947e8	1.16085
$67$	3.04061e8	1.84342	0.921709	−	0.387883i	$-0.126794\pi$
$67$	3.04061e8	1.84342	0.921709	+	0.387883i	$0.126794\pi$
$68$	4.33516e8	2.45875
$69$	−4.33836e7	−0.230412
$70$	6.56680e8	3.26898
$71$	−2.46812e8	−1.15267	−0.576334	−	0.817214i	$-0.695517\pi$
$71$	−2.46812e8	−1.15267	−0.576334	+	0.817214i	$0.695517\pi$
$72$	−6.14042e7	−0.269279
$73$	−9.89167e7	−0.407678	−0.203839	−	0.979004i	$-0.565342\pi$
$73$	−9.89167e7	−0.407678	−0.203839	+	0.979004i	$0.565342\pi$
$74$	4.01190e8	1.55528
$75$	1.28460e8	0.468804
$76$	−5.10079e8	−1.75378
$77$	6.00096e8	1.94541
$78$	−4.93440e8	−1.50941
$79$	−1.89951e7	−0.0548679	−0.0274340	−	0.999624i	$-0.508734\pi$
$79$	−1.89951e7	−0.0548679	−0.0274340	+	0.999624i	$0.508734\pi$
$80$	−1.13465e8	−0.309711
$81$	4.30467e7	0.111111
$82$	−3.28994e8	−0.803574
$83$	−3.82819e8	−0.885405	−0.442703	−	0.896668i	$-0.645980\pi$
$83$	−3.82819e8	−0.885405	−0.442703	+	0.896668i	$0.645980\pi$
$84$	−6.09751e8	−1.33627
$85$	1.05494e9	2.19201
$86$	−4.57587e8	−0.902049
$87$	1.42980e8	0.267571
$88$	5.76770e8	1.02525
$89$	8.54743e8	1.44405	0.722023	−	0.691869i	$-0.243213\pi$
$89$	8.54743e8	1.44405	0.722023	+	0.691869i	$0.243213\pi$
$90$	−4.42463e8	−0.710863
$91$	−1.65475e9	−2.52956
$92$	−4.14059e8	−0.602583
$93$	−5.96028e8	−0.826215
$94$	−2.55767e8	−0.337886
$95$	−1.24125e9	−1.56352
$96$	5.63268e8	0.676854
$97$	1.05008e9	1.20434	0.602169	−	0.798369i	$-0.294303\pi$
$97$	1.05008e9	1.20434	0.602169	+	0.798369i	$0.294303\pi$
$98$	−1.95245e9	−2.13827
$99$	−4.04338e8	−0.423044
$100$	1.22604e9	1.22604
$101$	−1.45452e9	−1.39083	−0.695415	−	0.718608i	$-0.744779\pi$
$101$	−1.45452e9	−1.39083	−0.695415	+	0.718608i	$0.744779\pi$
$102$	−1.62829e9	−1.48947
$103$	1.64504e9	1.44015	0.720076	−	0.693895i	$-0.244107\pi$
$103$	1.64504e9	1.44015	0.720076	+	0.693895i	$0.244107\pi$
$104$	−1.59043e9	−1.33310
$105$	−1.48380e9	−1.19130
$106$	3.85736e9	2.96766
$107$	4.75094e8	0.350391	0.175195	−	0.984534i	$-0.443944\pi$
$107$	4.75094e8	0.350391	0.175195	+	0.984534i	$0.443944\pi$
$108$	4.10843e8	0.290582
$109$	−2.37857e9	−1.61398	−0.806988	−	0.590568i	$-0.798904\pi$
$109$	−2.37857e9	−1.61398	−0.806988	+	0.590568i	$0.798904\pi$
$110$	4.15606e9	2.70654
$111$	−9.06506e8	−0.566784
$112$	5.87307e8	0.352682
$113$	−1.39288e9	−0.803636	−0.401818	−	0.915720i	$-0.631622\pi$
$113$	−1.39288e9	−0.803636	−0.401818	+	0.915720i	$0.631622\pi$
$114$	1.91587e9	1.06241
$115$	−1.00759e9	−0.537209
$116$	1.36462e9	0.699763
$117$	1.11495e9	0.550071
$118$	−4.34382e8	−0.206254
$119$	−5.46047e9	−2.49614
$120$	−1.42612e9	−0.627828
$121$	1.43999e9	0.610698
$122$	7.83602e8	0.320240
$123$	7.43377e8	0.292844
$124$	−5.68856e9	−2.16075
$125$	−6.90795e8	−0.253078
$126$	2.29024e9	0.809493
$127$	4.26841e8	0.145596	0.0727980	−	0.997347i	$-0.476807\pi$
$127$	4.26841e8	0.145596	0.0727980	+	0.997347i	$0.476807\pi$
$128$	4.26889e9	1.40563
$129$	1.03394e9	0.328731
$130$	−1.14602e10	−3.51923
$131$	−2.55369e9	−0.757614	−0.378807	−	0.925476i	$-0.623666\pi$
$131$	−2.55369e9	−0.757614	−0.378807	+	0.925476i	$0.623666\pi$
$132$	−3.85905e9	−1.10636
$133$	6.42484e9	1.78045
$134$	−1.08999e10	−2.92047
$135$	9.99766e8	0.259058
$136$	−5.24822e9	−1.31549
$137$	−1.89733e9	−0.460150	−0.230075	−	0.973173i	$-0.573897\pi$
$137$	−1.89733e9	−0.460150	−0.230075	+	0.973173i	$0.573897\pi$
$138$	1.55521e9	0.365035
$139$	1.42180e9	0.323052	0.161526	−	0.986868i	$-0.448358\pi$
$139$	1.42180e9	0.323052	0.161526	+	0.986868i	$0.448358\pi$
$140$	−1.41615e10	−3.11555
$141$	5.77918e8	0.123135
$142$	8.84771e9	1.82614
$143$	−1.04727e10	−2.09434
$144$	−3.95721e8	−0.0766933
$145$	3.32073e9	0.623846
$146$	3.54596e9	0.645871
$147$	4.41165e9	0.779243
$148$	−8.65181e9	−1.48228
$149$	−9.87928e9	−1.64205	−0.821027	−	0.570890i	$-0.806598\pi$
$149$	−9.87928e9	−1.64205	−0.821027	+	0.570890i	$0.806598\pi$
$150$	−4.60502e9	−0.742712
$151$	−6.67305e9	−1.04455	−0.522274	−	0.852778i	$-0.674916\pi$
$151$	−6.67305e9	−1.04455	−0.522274	+	0.852778i	$0.674916\pi$
$152$	6.17510e9	0.938314
$153$	3.67920e9	0.542803
$154$	−2.15122e10	−3.08206
$155$	−1.38428e10	−1.92634
$156$	1.06412e10	1.43857
$157$	6.15305e9	0.808243	0.404122	−	0.914705i	$-0.367577\pi$
$157$	6.15305e9	0.808243	0.404122	+	0.914705i	$0.367577\pi$
$158$	6.80934e8	0.0869256
$159$	−8.71588e9	−1.08149
$160$	1.30820e10	1.57810
$161$	5.21539e9	0.611745
$162$	−1.54314e9	−0.176030
$163$	1.59815e10	1.77326	0.886630	−	0.462480i	$-0.153040\pi$
$163$	1.59815e10	1.77326	0.886630	+	0.462480i	$0.153040\pi$
$164$	7.09488e9	0.765857
$165$	−9.39080e9	−0.986335
$166$	1.37233e10	1.40272
$167$	−3.33847e9	−0.332141	−0.166071	−	0.986114i	$-0.553108\pi$
$167$	−3.33847e9	−0.332141	−0.166071	+	0.986114i	$0.553108\pi$
$168$	7.38176e9	0.714937
$169$	1.82737e10	1.72320
$170$	−3.78174e10	−3.47273
$171$	−4.32898e9	−0.387171
$172$	9.86803e9	0.859711
$173$	−6.91460e9	−0.586894	−0.293447	−	0.955975i	$-0.594802\pi$
$173$	−6.91460e9	−0.586894	−0.293447	+	0.955975i	$0.594802\pi$
$174$	−5.12554e9	−0.423904
$175$	−1.54429e10	−1.24468
$176$	3.71700e9	0.292002
$177$	9.81506e8	0.0751646
$178$	−3.06408e10	−2.28776
$179$	−3.30267e9	−0.240451	−0.120226	−	0.992747i	$-0.538362\pi$
$179$	−3.30267e9	−0.240451	−0.120226	+	0.992747i	$0.538362\pi$
$180$	9.54189e9	0.677498
$181$	−2.48966e10	−1.72419	−0.862096	−	0.506744i	$-0.830849\pi$
$181$	−2.48966e10	−1.72419	−0.862096	+	0.506744i	$0.830849\pi$
$182$	5.93192e10	4.00751
$183$	−1.77058e9	−0.116704
$184$	5.01267e9	0.322395
$185$	−2.10537e10	−1.32147
$186$	2.13664e10	1.30895
$187$	−3.45587e10	−2.06667
$188$	5.51572e9	0.322027
$189$	−5.17489e9	−0.295001
$190$	4.44962e10	2.47703
$191$	−1.74235e9	−0.0947295	−0.0473648	−	0.998878i	$-0.515082\pi$
$191$	−1.74235e9	−0.0947295	−0.0473648	+	0.998878i	$0.515082\pi$
$192$	−1.76907e10	−0.939482
$193$	−1.25460e10	−0.650875	−0.325438	−	0.945563i	$-0.605512\pi$
$193$	−1.25460e10	−0.650875	−0.325438	+	0.945563i	$0.605512\pi$
$194$	−3.76431e10	−1.90800
$195$	2.58949e10	1.28250
$196$	4.21053e10	2.03791
$197$	5.37321e9	0.254177	0.127088	−	0.991891i	$-0.459437\pi$
$197$	5.37321e9	0.254177	0.127088	+	0.991891i	$0.459437\pi$
$198$	1.44947e10	0.670216
$199$	−2.42720e10	−1.09715	−0.548576	−	0.836101i	$-0.684830\pi$
$199$	−2.42720e10	−1.09715	−0.548576	+	0.836101i	$0.684830\pi$
$200$	−1.48426e10	−0.655957
$201$	2.46289e10	1.06430
$202$	5.21416e10	2.20345
$203$	−1.71884e10	−0.710403
$204$	3.51148e10	1.41956
$205$	1.72650e10	0.682770
$206$	−5.89712e10	−2.28159
$207$	−3.51407e9	−0.133028
$208$	−1.02495e10	−0.379681
$209$	4.06621e10	1.47412
$210$	5.31911e10	1.88735
$211$	8.97002e9	0.311546	0.155773	−	0.987793i	$-0.450213\pi$
$211$	8.97002e9	0.311546	0.155773	+	0.987793i	$0.450213\pi$
$212$	−8.31855e10	−2.82837
$213$	−1.99918e10	−0.665493
$214$	−1.70311e10	−0.555113
$215$	2.40133e10	0.766442
$216$	−4.97374e9	−0.155468
$217$	7.16519e10	2.19361
$218$	8.52669e10	2.55697
$219$	−8.01226e9	−0.235373
$220$	−8.96270e10	−2.57951
$221$	9.52948e10	2.68722
$222$	3.24964e10	0.897939
$223$	−5.14153e10	−1.39226	−0.696130	−	0.717916i	$-0.745096\pi$
$223$	−5.14153e10	−1.39226	−0.696130	+	0.717916i	$0.745096\pi$
$224$	−6.77137e10	−1.79705
$225$	1.04052e10	0.270664
$226$	4.99317e10	1.27318
$227$	−2.13816e10	−0.534470	−0.267235	−	0.963631i	$-0.586110\pi$
$227$	−2.13816e10	−0.534470	−0.267235	+	0.963631i	$0.586110\pi$
$228$	−4.13164e10	−1.01255
$229$	4.05363e10	0.974057	0.487028	−	0.873386i	$-0.338081\pi$
$229$	4.05363e10	0.974057	0.487028	+	0.873386i	$0.338081\pi$
$230$	3.61200e10	0.851085
$231$	4.86077e10	1.12319
$232$	−1.65203e10	−0.374389
$233$	3.97623e10	0.883833	0.441916	−	0.897056i	$-0.354299\pi$
$233$	3.97623e10	0.883833	0.441916	+	0.897056i	$0.354299\pi$
$234$	−3.99686e10	−0.871461
$235$	1.34222e10	0.287091
$236$	9.36762e9	0.196574
$237$	−1.53860e9	−0.0316780
$238$	1.95747e11	3.95456
$239$	−3.15480e10	−0.625434	−0.312717	−	0.949846i	$-0.601239\pi$
$239$	−3.15480e10	−0.625434	−0.312717	+	0.949846i	$0.601239\pi$
$240$	−9.19067e9	−0.178812
$241$	−8.14750e10	−1.55578	−0.777889	−	0.628402i	$-0.783709\pi$
$241$	−8.14750e10	−1.55578	−0.777889	+	0.628402i	$0.783709\pi$
$242$	−5.16208e10	−0.967511
$243$	3.48678e9	0.0641500
$244$	−1.68987e10	−0.305210
$245$	1.02461e11	1.81682
$246$	−2.66485e10	−0.463943
$247$	−1.12125e11	−1.91675
$248$	6.88668e10	1.15605
$249$	−3.10083e10	−0.511189
$250$	2.47636e10	0.400943
$251$	−3.36364e9	−0.0534907	−0.0267453	−	0.999642i	$-0.508514\pi$
$251$	−3.36364e9	−0.0534907	−0.0267453	+	0.999642i	$0.508514\pi$
$252$	−4.93898e10	−0.771499
$253$	3.30077e10	0.506492
$254$	−1.53014e10	−0.230663
$255$	8.54500e10	1.26556
$256$	−4.12085e10	−0.599663
$257$	−6.90974e10	−0.988013	−0.494007	−	0.869458i	$-0.664468\pi$
$257$	−6.90974e10	−0.988013	−0.494007	+	0.869458i	$0.664468\pi$
$258$	−3.70645e10	−0.520798
$259$	1.08976e11	1.50482
$260$	2.47144e11	3.35405
$261$	1.15814e10	0.154482
$262$	9.15447e10	1.20027
$263$	−8.29232e10	−1.06875	−0.534374	−	0.845248i	$-0.679453\pi$
$263$	−8.29232e10	−1.06875	−0.534374	+	0.845248i	$0.679453\pi$
$264$	4.67184e10	0.591929
$265$	−2.02427e11	−2.52152
$266$	−2.30317e11	−2.82071
$267$	6.92342e10	0.833720
$268$	2.35062e11	2.78340
$269$	4.87849e10	0.568068	0.284034	−	0.958814i	$-0.408327\pi$
$269$	4.87849e10	0.568068	0.284034	+	0.958814i	$0.408327\pi$
$270$	−3.58395e10	−0.410417
$271$	−1.15620e11	−1.30218	−0.651088	−	0.759002i	$-0.725687\pi$
$271$	−1.15620e11	−1.30218	−0.651088	+	0.759002i	$0.725687\pi$
$272$	−3.38223e10	−0.374664
$273$	−1.34034e11	−1.46044
$274$	6.80152e10	0.729002
$275$	−9.77363e10	−1.03053
$276$	−3.35388e10	−0.347901
$277$	−7.34803e10	−0.749914	−0.374957	−	0.927042i	$-0.622343\pi$
$277$	−7.34803e10	−0.749914	−0.374957	+	0.927042i	$0.622343\pi$
$278$	−5.09686e10	−0.511801
$279$	−4.82782e10	−0.477016
$280$	1.71442e11	1.66689
$281$	−4.09307e10	−0.391626	−0.195813	−	0.980641i	$-0.562735\pi$
$281$	−4.09307e10	−0.391626	−0.195813	+	0.980641i	$0.562735\pi$
$282$	−2.07172e10	−0.195078
$283$	−1.88250e11	−1.74460	−0.872300	−	0.488970i	$-0.837373\pi$
$283$	−1.88250e11	−1.74460	−0.872300	+	0.488970i	$0.837373\pi$
$284$	−1.90804e11	−1.74043
$285$	−1.00541e11	−0.902697
$286$	3.75425e11	3.31800
$287$	−8.93655e10	−0.777502
$288$	4.56247e10	0.390782
$289$	1.95874e11	1.65172
$290$	−1.19041e11	−0.988341
$291$	8.50563e10	0.695325
$292$	−7.64700e10	−0.615557
$293$	9.87036e10	0.782400	0.391200	−	0.920306i	$-0.372060\pi$
$293$	9.87036e10	0.782400	0.391200	+	0.920306i	$0.372060\pi$
$294$	−1.58148e11	−1.23453
$295$	2.27956e10	0.175248
$296$	1.04740e11	0.793052
$297$	−3.27514e10	−0.244245
$298$	3.54152e11	2.60146
$299$	−9.10177e10	−0.658575
$300$	9.93089e10	0.707852
$301$	−1.24295e11	−0.872783
$302$	2.39215e11	1.65484
$303$	−1.17816e11	−0.802996
$304$	3.97956e10	0.267241
$305$	−4.11220e10	−0.272098
$306$	−1.31892e11	−0.859947
$307$	−1.14378e11	−0.734885	−0.367442	−	0.930046i	$-0.619766\pi$
$307$	−1.14378e11	−0.734885	−0.367442	+	0.930046i	$0.619766\pi$
$308$	4.63919e11	2.93740
$309$	1.33248e11	0.831472
$310$	4.96236e11	3.05184
$311$	−2.11753e10	−0.128354	−0.0641768	−	0.997939i	$-0.520442\pi$
$311$	−2.11753e10	−0.128354	−0.0641768	+	0.997939i	$0.520442\pi$
$312$	−1.28825e11	−0.769667
$313$	−9.81324e10	−0.577914	−0.288957	−	0.957342i	$-0.593308\pi$
$313$	−9.81324e10	−0.577914	−0.288957	+	0.957342i	$0.593308\pi$
$314$	−2.20574e11	−1.28048
$315$	−1.20188e11	−0.687800
$316$	−1.46846e10	−0.0828457
$317$	−4.64728e10	−0.258483	−0.129242	−	0.991613i	$-0.541254\pi$
$317$	−4.64728e10	−0.258483	−0.129242	+	0.991613i	$0.541254\pi$
$318$	3.12446e11	1.71338
$319$	−1.08784e11	−0.588175
$320$	−4.10868e11	−2.19042
$321$	3.84826e10	0.202298
$322$	−1.86961e11	−0.969169
$323$	−3.69998e11	−1.89142
$324$	3.32783e10	0.167768
$325$	2.69505e11	1.33996
$326$	−5.72902e11	−2.80932
$327$	−1.92664e11	−0.931829
$328$	−8.58919e10	−0.409751
$329$	−6.94748e10	−0.326923
$330$	3.36641e11	1.56262
$331$	5.07093e10	0.232200	0.116100	−	0.993238i	$-0.462961\pi$
$331$	5.07093e10	0.232200	0.116100	+	0.993238i	$0.462961\pi$
$332$	−2.95948e11	−1.33688
$333$	−7.34270e10	−0.327233
$334$	1.19677e11	0.526201
$335$	5.72010e11	2.48143
$336$	4.75718e10	0.203621
$337$	−3.44025e11	−1.45297	−0.726484	−	0.687184i	$-0.758847\pi$
$337$	−3.44025e11	−1.45297	−0.726484	+	0.687184i	$0.758847\pi$
$338$	−6.55075e11	−2.73002
$339$	−1.12823e11	−0.463980
$340$	8.15546e11	3.30973
$341$	4.53477e11	1.81619
$342$	1.55185e11	0.613384
$343$	−1.37407e11	−0.536026
$344$	−1.19464e11	−0.459965
$345$	−8.16148e10	−0.310158
$346$	2.47874e11	0.929799
$347$	−1.06614e11	−0.394758	−0.197379	−	0.980327i	$-0.563243\pi$
$347$	−1.06614e11	−0.394758	−0.197379	+	0.980327i	$0.563243\pi$
$348$	1.10534e11	0.404008
$349$	−3.09166e11	−1.11552	−0.557761	−	0.830002i	$-0.688339\pi$
$349$	−3.09166e11	−1.11552	−0.557761	+	0.830002i	$0.688339\pi$
$350$	5.53595e11	1.97191
$351$	9.03109e10	0.317584
$352$	−4.28553e11	−1.48786
$353$	−3.60113e11	−1.23439	−0.617195	−	0.786810i	$-0.711731\pi$
$353$	−3.60113e11	−1.23439	−0.617195	+	0.786810i	$0.711731\pi$
$354$	−3.51850e10	−0.119081
$355$	−4.64312e11	−1.55161
$356$	6.60780e11	2.18038
$357$	−4.42298e11	−1.44115
$358$	1.18394e11	0.380940
$359$	7.09609e10	0.225473	0.112736	−	0.993625i	$-0.464038\pi$
$359$	7.09609e10	0.225473	0.112736	+	0.993625i	$0.464038\pi$
$360$	−1.15516e11	−0.362477
$361$	1.12655e11	0.349116
$362$	8.92490e11	2.73159
$363$	1.16640e11	0.352587
$364$	−1.27924e12	−3.81941
$365$	−1.86086e11	−0.548776
$366$	6.34717e10	0.184891
$367$	3.13142e10	0.0901041	0.0450520	−	0.998985i	$-0.485655\pi$
$367$	3.13142e10	0.0901041	0.0450520	+	0.998985i	$0.485655\pi$
$368$	3.23042e10	0.0918215
$369$	6.02135e10	0.169073
$370$	7.54733e11	2.09356
$371$	1.04779e12	2.87138
$372$	−4.60774e11	−1.24751
$373$	6.03351e11	1.61391	0.806957	−	0.590610i	$-0.201113\pi$
$373$	6.03351e11	1.61391	0.806957	+	0.590610i	$0.201113\pi$
$374$	1.23886e12	3.27416
$375$	−5.59544e10	−0.146114
$376$	−6.67743e10	−0.172292
$377$	2.99968e11	0.764785
$378$	1.85509e11	0.467361
$379$	−1.57900e11	−0.393101	−0.196551	−	0.980494i	$-0.562974\pi$
$379$	−1.57900e11	−0.393101	−0.196551	+	0.980494i	$0.562974\pi$
$380$	−9.59578e11	−2.36077
$381$	3.45741e10	0.0840599
$382$	6.24597e10	0.150077
$383$	−7.59563e11	−1.80372	−0.901861	−	0.432027i	$-0.857799\pi$
$383$	−7.59563e11	−1.80372	−0.901861	+	0.432027i	$0.857799\pi$
$384$	3.45780e11	0.811540
$385$	1.12892e12	2.61873
$386$	4.49749e11	1.03116
$387$	8.37489e10	0.189793
$388$	8.11788e11	1.81844
$389$	−1.69262e11	−0.374788	−0.187394	−	0.982285i	$-0.560004\pi$
$389$	−1.69262e11	−0.374788	−0.187394	+	0.982285i	$0.560004\pi$
$390$	−9.28277e11	−2.03183
$391$	−3.00348e11	−0.649874
$392$	−5.09735e11	−1.09033
$393$	−2.06849e11	−0.437409
$394$	−1.92619e11	−0.402685
$395$	−3.57342e10	−0.0738579
$396$	−3.12583e11	−0.638759
$397$	2.11292e10	0.0426899	0.0213450	−	0.999772i	$-0.493205\pi$
$397$	2.11292e10	0.0426899	0.0213450	+	0.999772i	$0.493205\pi$
$398$	8.70101e11	1.73818
$399$	5.20412e11	1.02794
$400$	−9.56535e10	−0.186823
$401$	−1.24151e11	−0.239774	−0.119887	−	0.992788i	$-0.538253\pi$
$401$	−1.24151e11	−0.239774	−0.119887	+	0.992788i	$0.538253\pi$
$402$	−8.82896e11	−1.68613
$403$	−1.25045e12	−2.36153
$404$	−1.12445e12	−2.10003
$405$	8.09810e10	0.149567
$406$	6.16170e11	1.12547
$407$	6.89700e11	1.24591
$408$	−4.25106e11	−0.759498
$409$	5.91126e11	1.04454	0.522270	−	0.852780i	$-0.325085\pi$
$409$	5.91126e11	1.04454	0.522270	+	0.852780i	$0.325085\pi$
$410$	−6.18915e11	−1.08169
$411$	−1.53683e11	−0.265668
$412$	1.27174e12	2.17450
$413$	−1.17992e11	−0.199563
$414$	1.25972e11	0.210753
$415$	−7.20173e11	−1.19185
$416$	1.18172e12	1.93462
$417$	1.15166e11	0.186514
$418$	−1.45765e12	−2.33540
$419$	−5.16849e11	−0.819221	−0.409610	−	0.912261i	$-0.634335\pi$
$419$	−5.16849e11	−0.819221	−0.409610	+	0.912261i	$0.634335\pi$
$420$	−1.14709e12	−1.79876
$421$	4.07079e11	0.631552	0.315776	−	0.948834i	$-0.397735\pi$
$421$	4.07079e11	0.631552	0.315776	+	0.948834i	$0.397735\pi$
$422$	−3.21557e11	−0.493573
$423$	4.68114e10	0.0710918
$424$	1.00706e12	1.51324
$425$	8.89336e11	1.32226
$426$	7.16665e11	1.05432
$427$	2.12852e11	0.309850
$428$	3.67283e11	0.529059
$429$	−8.48290e11	−1.20917
$430$	−8.60828e11	−1.21425
$431$	−8.85168e11	−1.23560	−0.617800	−	0.786335i	$-0.711976\pi$
$431$	−8.85168e11	−1.23560	−0.617800	+	0.786335i	$0.711976\pi$
$432$	−3.20534e10	−0.0442789
$433$	6.74952e11	0.922735	0.461368	−	0.887209i	$-0.347359\pi$
$433$	6.74952e11	0.922735	0.461368	+	0.887209i	$0.347359\pi$
$434$	−2.56857e12	−3.47527
$435$	2.68979e11	0.360178
$436$	−1.83881e12	−2.43696
$437$	3.53392e11	0.463543
$438$	2.87223e11	0.372894
$439$	1.28318e12	1.64892	0.824458	−	0.565922i	$-0.191480\pi$
$439$	1.28318e12	1.64892	0.824458	+	0.565922i	$0.191480\pi$
$440$	1.08504e12	1.38009
$441$	3.57343e11	0.449896
$442$	−3.41612e12	−4.25729
$443$	1.44560e12	1.78332	0.891662	−	0.452701i	$-0.149539\pi$
$443$	1.44560e12	1.78332	0.891662	+	0.452701i	$0.149539\pi$
$444$	−7.00797e11	−0.855793
$445$	1.60797e12	1.94383
$446$	1.84313e12	2.20572
$447$	−8.00222e11	−0.948040
$448$	2.12670e12	2.49433
$449$	−7.76770e11	−0.901953	−0.450977	−	0.892536i	$-0.648924\pi$
$449$	−7.76770e11	−0.901953	−0.450977	+	0.892536i	$0.648924\pi$
$450$	−3.73006e11	−0.428805
$451$	−5.65585e11	−0.643730
$452$	−1.07680e12	−1.21342
$453$	−5.40517e11	−0.603070
$454$	7.66486e11	0.846745
$455$	−3.11297e12	−3.40505
$456$	5.00183e11	0.541736
$457$	7.01907e11	0.752760	0.376380	−	0.926465i	$-0.377169\pi$
$457$	7.01907e11	0.752760	0.376380	+	0.926465i	$0.377169\pi$
$458$	−1.45314e12	−1.54317
$459$	2.98016e11	0.313388
$460$	−7.78942e11	−0.811138
$461$	−4.87181e11	−0.502385	−0.251192	−	0.967937i	$-0.580823\pi$
$461$	−4.87181e11	−0.502385	−0.251192	+	0.967937i	$0.580823\pi$
$462$	−1.74249e12	−1.77943
$463$	1.22256e12	1.23639	0.618194	−	0.786025i	$-0.287864\pi$
$463$	1.22256e12	1.23639	0.618194	+	0.786025i	$0.287864\pi$
$464$	−1.06466e11	−0.106630
$465$	−1.12127e12	−1.11217
$466$	−1.42540e12	−1.40023
$467$	1.39487e12	1.35709	0.678543	−	0.734561i	$-0.262612\pi$
$467$	1.39487e12	1.35709	0.678543	+	0.734561i	$0.262612\pi$
$468$	8.61939e11	0.830558
$469$	−2.96078e12	−2.82572
$470$	−4.81159e11	−0.454829
$471$	4.98397e11	0.466639
$472$	−1.13406e11	−0.105171
$473$	−7.86653e11	−0.722617
$474$	5.51556e10	0.0501865
$475$	−1.04640e12	−0.943141
$476$	−4.22135e12	−3.76895
$477$	−7.05986e11	−0.624401
$478$	1.13093e12	0.990856
$479$	7.97510e11	0.692192	0.346096	−	0.938199i	$-0.387507\pi$
$479$	7.97510e11	0.692192	0.346096	+	0.938199i	$0.387507\pi$
$480$	1.05964e12	0.911115
$481$	−1.90183e12	−1.62001
$482$	2.92071e12	2.46477
$483$	4.22447e11	0.353191
$484$	1.11322e12	0.922100
$485$	1.97544e12	1.62116
$486$	−1.24994e11	−0.101631
$487$	−1.76341e12	−1.42060	−0.710302	−	0.703897i	$-0.751442\pi$
$487$	−1.76341e12	−1.42060	−0.710302	+	0.703897i	$0.751442\pi$
$488$	2.04578e11	0.163294
$489$	1.29450e12	1.02379
$490$	−3.67302e12	−2.87833
$491$	9.35179e11	0.726153	0.363077	−	0.931759i	$-0.381726\pi$
$491$	9.35179e11	0.726153	0.363077	+	0.931759i	$0.381726\pi$
$492$	5.74685e11	0.442168
$493$	9.89861e11	0.754680
$494$	4.01944e12	3.03664
$495$	−7.60654e11	−0.569461
$496$	4.43813e11	0.329255
$497$	2.40333e12	1.76689
$498$	1.11158e12	0.809861
$499$	2.32592e12	1.67935	0.839676	−	0.543088i	$-0.182745\pi$
$499$	2.32592e12	1.67935	0.839676	+	0.543088i	$0.182745\pi$
$500$	−5.34036e11	−0.382125
$501$	−2.70416e11	−0.191762
$502$	1.20580e11	0.0847436
$503$	−2.02638e12	−1.41145	−0.705723	−	0.708488i	$-0.749378\pi$
$503$	−2.02638e12	−1.41145	−0.705723	+	0.708488i	$0.749378\pi$
$504$	5.97922e11	0.412769
$505$	−2.73630e12	−1.87220
$506$	−1.18326e12	−0.802420
$507$	1.48017e12	0.994893
$508$	3.29980e11	0.219837
$509$	2.28341e12	1.50784	0.753919	−	0.656968i	$-0.228161\pi$
$509$	2.28341e12	1.50784	0.753919	+	0.656968i	$0.228161\pi$
$510$	−3.06321e12	−2.00498
$511$	9.63199e11	0.624917
$512$	−7.08433e11	−0.455600
$513$	−3.50648e11	−0.223534
$514$	2.47700e12	1.56528
$515$	3.09470e12	1.93859
$516$	7.99310e11	0.496354
$517$	−4.39699e11	−0.270675
$518$	−3.90658e12	−2.38403
$519$	−5.60083e11	−0.338844
$520$	−2.99197e12	−1.79449
$521$	1.64372e12	0.977367	0.488683	−	0.872461i	$-0.337477\pi$
$521$	1.64372e12	0.977367	0.488683	+	0.872461i	$0.337477\pi$
$522$	−4.15169e11	−0.244741
$523$	−3.11181e11	−0.181868	−0.0909339	−	0.995857i	$-0.528985\pi$
$523$	−3.11181e11	−0.181868	−0.0909339	+	0.995857i	$0.528985\pi$
$524$	−1.97420e12	−1.14393
$525$	−1.25087e12	−0.718615
$526$	2.97263e12	1.69319
$527$	−4.12634e12	−2.33033
$528$	3.01077e11	0.168587
$529$	−1.51429e12	−0.840731
$530$	7.25661e12	3.99477
$531$	7.95020e10	0.0433963
$532$	4.96688e12	2.68832
$533$	1.55958e12	0.837021
$534$	−2.48190e12	−1.32084
$535$	8.93764e11	0.471662
$536$	−2.84570e12	−1.48918
$537$	−2.67517e11	−0.138825
$538$	−1.74884e12	−0.899973
$539$	−3.35652e12	−1.71293
$540$	7.72893e11	0.391154
$541$	−8.12242e11	−0.407659	−0.203830	−	0.979006i	$-0.565339\pi$
$541$	−8.12242e11	−0.407659	−0.203830	+	0.979006i	$0.565339\pi$
$542$	4.14473e12	2.06300
$543$	−2.01662e12	−0.995463
$544$	3.89955e12	1.90906
$545$	−4.47465e12	−2.17258
$546$	4.80486e12	2.31374
$547$	−5.36570e11	−0.256261	−0.128131	−	0.991757i	$-0.540898\pi$
$547$	−5.36570e11	−0.256261	−0.128131	+	0.991757i	$0.540898\pi$
$548$	−1.46677e12	−0.694786
$549$	−1.43417e11	−0.0673792
$550$	3.50365e12	1.63263
$551$	−1.16468e12	−0.538299
$552$	4.06026e11	0.186135
$553$	1.84964e11	0.0841054
$554$	2.63412e12	1.18807
$555$	−1.70535e12	−0.762949
$556$	1.09916e12	0.487779
$557$	6.35994e11	0.279965	0.139983	−	0.990154i	$-0.455295\pi$
$557$	6.35994e11	0.279965	0.139983	+	0.990154i	$0.455295\pi$
$558$	1.73068e12	0.755721
$559$	2.16917e12	0.939596
$560$	1.10486e12	0.474747
$561$	−2.79926e12	−1.19319
$562$	1.46728e12	0.620441
$563$	5.11920e11	0.214741	0.107370	−	0.994219i	$-0.465757\pi$
$563$	5.11920e11	0.214741	0.107370	+	0.994219i	$0.465757\pi$
$564$	4.46774e11	0.185922
$565$	−2.62033e12	−1.08178
$566$	6.74837e12	2.76392
$567$	−4.19166e11	−0.170319
$568$	2.30991e12	0.931167
$569$	4.59360e11	0.183716	0.0918581	−	0.995772i	$-0.470719\pi$
$569$	4.59360e11	0.183716	0.0918581	+	0.995772i	$0.470719\pi$
$570$	3.60419e12	1.43012
$571$	3.99628e12	1.57323	0.786616	−	0.617442i	$-0.211831\pi$
$571$	3.99628e12	1.57323	0.786616	+	0.617442i	$0.211831\pi$
$572$	−8.09619e12	−3.16227
$573$	−1.41130e11	−0.0546921
$574$	3.20357e12	1.23177
$575$	−8.49420e11	−0.324054
$576$	−1.43294e12	−0.542410
$577$	−1.20235e12	−0.451584	−0.225792	−	0.974176i	$-0.572497\pi$
$577$	−1.20235e12	−0.451584	−0.225792	+	0.974176i	$0.572497\pi$
$578$	−7.02167e12	−2.61677
$579$	−1.01623e12	−0.375783
$580$	2.56717e12	0.941952
$581$	3.72769e12	1.35721
$582$	−3.04909e12	−1.10158
$583$	6.63133e12	2.37734
$584$	9.25760e11	0.329337
$585$	2.09748e12	0.740452
$586$	−3.53832e12	−1.23953
$587$	−4.83604e12	−1.68120	−0.840598	−	0.541660i	$-0.817796\pi$
$587$	−4.83604e12	−1.68120	−0.840598	+	0.541660i	$0.817796\pi$
$588$	3.41053e12	1.17659
$589$	4.85509e12	1.66218
$590$	−8.17176e11	−0.277640
$591$	4.35230e11	0.146749
$592$	6.75001e11	0.225869
$593$	−3.57818e12	−1.18827	−0.594136	−	0.804365i	$-0.702506\pi$
$593$	−3.57818e12	−1.18827	−0.594136	+	0.804365i	$0.702506\pi$
$594$	1.17407e12	0.386950
$595$	−1.02724e13	−3.36006
$596$	−7.63742e12	−2.47935
$597$	−1.96603e12	−0.633441
$598$	3.26280e12	1.04336
$599$	5.28387e12	1.67699	0.838496	−	0.544907i	$-0.183435\pi$
$599$	5.28387e12	1.67699	0.838496	+	0.544907i	$0.183435\pi$
$600$	−1.20225e12	−0.378717
$601$	2.67502e12	0.836359	0.418179	−	0.908365i	$-0.362668\pi$
$601$	2.67502e12	0.836359	0.418179	+	0.908365i	$0.362668\pi$
$602$	4.45574e12	1.38272
$603$	1.99494e12	0.614472
$604$	−5.15876e12	−1.57717
$605$	2.70897e12	0.822062
$606$	4.22347e12	1.27216
$607$	3.70644e12	1.10818	0.554088	−	0.832458i	$-0.313067\pi$
$607$	3.70644e12	1.10818	0.554088	+	0.832458i	$0.313067\pi$
$608$	−4.58824e12	−1.36170
$609$	−1.39226e12	−0.410151
$610$	1.47414e12	0.431076
$611$	1.21246e12	0.351950
$612$	2.84430e12	0.819584
$613$	6.45333e12	1.84592	0.922958	−	0.384900i	$-0.125764\pi$
$613$	6.45333e12	1.84592	0.922958	+	0.384900i	$0.125764\pi$
$614$	4.10021e12	1.16426
$615$	1.39847e12	0.394198
$616$	−5.61628e12	−1.57158
$617$	−6.71687e12	−1.86588	−0.932941	−	0.360031i	$-0.882766\pi$
$617$	−6.71687e12	−1.86588	−0.932941	+	0.360031i	$0.882766\pi$
$618$	−4.77667e12	−1.31728
$619$	−4.48065e12	−1.22669	−0.613343	−	0.789817i	$-0.710176\pi$
$619$	−4.48065e12	−1.22669	−0.613343	+	0.789817i	$0.710176\pi$
$620$	−1.07015e13	−2.90859
$621$	−2.84640e11	−0.0768039
$622$	7.59092e11	0.203347
$623$	−8.32304e12	−2.21353
$624$	−8.30212e11	−0.219209
$625$	−4.39705e12	−1.15266
$626$	3.51784e12	0.915571
$627$	3.29363e12	0.851081
$628$	4.75676e12	1.22037
$629$	−6.27581e12	−1.59861
$630$	4.30848e12	1.08966
$631$	3.31200e12	0.831683	0.415842	−	0.909437i	$-0.363487\pi$
$631$	3.31200e12	0.831683	0.415842	+	0.909437i	$0.363487\pi$
$632$	1.77774e11	0.0443243
$633$	7.26571e11	0.179871
$634$	1.66595e12	0.409507
$635$	8.02988e11	0.195987
$636$	−6.73803e12	−1.63296
$637$	9.25552e12	2.22727
$638$	3.89968e12	0.931828
$639$	−1.61934e12	−0.384223
$640$	8.03079e12	1.89212
$641$	3.34924e12	0.783584	0.391792	−	0.920054i	$-0.371855\pi$
$641$	3.34924e12	0.783584	0.391792	+	0.920054i	$0.371855\pi$
$642$	−1.37952e12	−0.320495
$643$	−3.43017e12	−0.791345	−0.395673	−	0.918392i	$-0.629489\pi$
$643$	−3.43017e12	−0.791345	−0.395673	+	0.918392i	$0.629489\pi$
$644$	4.03189e12	0.923681
$645$	1.94508e12	0.442505
$646$	1.32637e13	2.99652
$647$	5.54972e12	1.24509	0.622546	−	0.782583i	$-0.286098\pi$
$647$	5.54972e12	1.24509	0.622546	+	0.782583i	$0.286098\pi$
$648$	−4.02873e11	−0.0897596
$649$	−7.46762e11	−0.165227
$650$	−9.66120e12	−2.12286
$651$	5.80380e12	1.26648
$652$	1.23549e13	2.67746
$653$	−2.85530e11	−0.0614529	−0.0307265	−	0.999528i	$-0.509782\pi$
$653$	−2.85530e11	−0.0614529	−0.0307265	+	0.999528i	$0.509782\pi$
$654$	6.90662e12	1.47627
$655$	−4.80410e12	−1.01983
$656$	−5.53532e11	−0.116701
$657$	−6.48993e11	−0.135893
$658$	2.49053e12	0.517935
$659$	7.57432e11	0.156444	0.0782221	−	0.996936i	$-0.475076\pi$
$659$	7.57432e11	0.156444	0.0782221	+	0.996936i	$0.475076\pi$
$660$	−7.25978e12	−1.48928
$661$	5.28983e12	1.07779	0.538896	−	0.842372i	$-0.318841\pi$
$661$	5.28983e12	1.07779	0.538896	+	0.842372i	$0.318841\pi$
$662$	−1.81782e12	−0.367867
$663$	7.71888e12	1.55147
$664$	3.58279e12	0.715263
$665$	1.20866e13	2.39667
$666$	2.63221e12	0.518425
$667$	−9.45434e11	−0.184954
$668$	−2.58088e12	−0.501504
$669$	−4.16464e12	−0.803822
$670$	−2.05054e13	−3.93125
$671$	1.34712e12	0.256539
$672$	−5.48481e12	−1.03753
$673$	3.50601e12	0.658788	0.329394	−	0.944193i	$-0.393156\pi$
$673$	3.50601e12	0.658788	0.329394	+	0.944193i	$0.393156\pi$
$674$	1.23326e13	2.30189
$675$	8.42824e11	0.156268
$676$	1.41269e13	2.60189
$677$	−3.61379e12	−0.661171	−0.330585	−	0.943776i	$-0.607246\pi$
$677$	−3.61379e12	−0.661171	−0.330585	+	0.943776i	$0.607246\pi$
$678$	4.04447e12	0.735069
$679$	−1.02251e13	−1.84609
$680$	−9.87314e12	−1.77078
$681$	−1.73191e12	−0.308577
$682$	−1.62562e13	−2.87733
$683$	−1.51664e12	−0.266680	−0.133340	−	0.991070i	$-0.542570\pi$
$683$	−1.51664e12	−0.266680	−0.133340	+	0.991070i	$0.542570\pi$
$684$	−3.34663e12	−0.584594
$685$	−3.56932e12	−0.619409
$686$	4.92576e12	0.849209
$687$	3.28344e12	0.562372
$688$	−7.69889e11	−0.131003
$689$	−1.82857e13	−3.09119
$690$	2.92572e12	0.491374
$691$	7.69784e12	1.28445	0.642226	−	0.766515i	$-0.278011\pi$
$691$	7.69784e12	1.28445	0.642226	+	0.766515i	$0.278011\pi$
$692$	−5.34550e12	−0.886158
$693$	3.93723e12	0.648472
$694$	3.82189e12	0.625404
$695$	2.67474e12	0.434861
$696$	−1.33815e12	−0.216153
$697$	5.14645e12	0.825962
$698$	1.10830e13	1.76729
$699$	3.22075e12	0.510281
$700$	−1.19385e13	−1.87935
$701$	−6.31846e11	−0.0988280	−0.0494140	−	0.998778i	$-0.515735\pi$
$701$	−6.31846e11	−0.0988280	−0.0494140	+	0.998778i	$0.515735\pi$
$702$	−3.23746e12	−0.503138
$703$	7.38417e12	1.14026
$704$	1.34596e13	2.06517
$705$	1.08720e12	0.165752
$706$	1.29093e13	1.95561
$707$	1.41634e13	2.13196
$708$	7.58777e11	0.113492
$709$	−7.86914e12	−1.16955	−0.584775	−	0.811195i	$-0.698817\pi$
$709$	−7.86914e12	−1.16955	−0.584775	+	0.811195i	$0.698817\pi$
$710$	1.66446e13	2.45817
$711$	−1.24627e11	−0.0182893
$712$	−7.99952e12	−1.16655
$713$	3.94114e12	0.571109
$714$	1.58555e13	2.28316
$715$	−1.97016e13	−2.81920
$716$	−2.55321e12	−0.363060
$717$	−2.55539e12	−0.361094
$718$	−2.54380e12	−0.357210
$719$	1.18994e13	1.66052	0.830259	−	0.557378i	$-0.188193\pi$
$719$	1.18994e13	1.66052	0.830259	+	0.557378i	$0.188193\pi$
$720$	−7.44444e11	−0.103237
$721$	−1.60185e13	−2.20756
$722$	−4.03846e12	−0.553093
$723$	−6.59947e12	−0.898229
$724$	−1.92469e13	−2.60338
$725$	2.79945e12	0.376315
$726$	−4.18129e12	−0.558593
$727$	−9.95970e12	−1.32233	−0.661167	−	0.750238i	$-0.729939\pi$
$727$	−9.95970e12	−1.32233	−0.661167	+	0.750238i	$0.729939\pi$
$728$	1.54867e13	2.04347
$729$	2.82430e11	0.0370370
$730$	6.67079e12	0.869409
$731$	7.15802e12	0.927181
$732$	−1.36879e12	−0.176213
$733$	−2.10318e12	−0.269097	−0.134549	−	0.990907i	$-0.542958\pi$
$733$	−2.10318e12	−0.269097	−0.134549	+	0.990907i	$0.542958\pi$
$734$	−1.12255e12	−0.142749
$735$	8.29935e12	1.04894
$736$	−3.72453e12	−0.467865
$737$	−1.87385e13	−2.33954
$738$	−2.15853e12	−0.267858
$739$	−1.19388e13	−1.47251	−0.736256	−	0.676703i	$-0.763408\pi$
$739$	−1.19388e13	−1.47251	−0.736256	+	0.676703i	$0.763408\pi$
$740$	−1.62761e13	−1.99530
$741$	−9.08209e12	−1.10663
$742$	−3.75610e13	−4.54903
$743$	−9.79773e12	−1.17944	−0.589720	−	0.807608i	$-0.700762\pi$
$743$	−9.79773e12	−1.17944	−0.589720	+	0.807608i	$0.700762\pi$
$744$	5.57821e12	0.667447
$745$	−1.85853e13	−2.21037
$746$	−2.16289e13	−2.55687
$747$	−2.51168e12	−0.295135
$748$	−2.67165e13	−3.12048
$749$	−4.62621e12	−0.537103
$750$	2.00585e12	0.231485
$751$	−1.06936e13	−1.22672	−0.613359	−	0.789804i	$-0.710182\pi$
$751$	−1.06936e13	−1.22672	−0.613359	+	0.789804i	$0.710182\pi$
$752$	−4.30328e11	−0.0490704
$753$	−2.72455e11	−0.0308828
$754$	−1.07532e13	−1.21163
$755$	−1.25536e13	−1.40607
$756$	−4.00058e12	−0.445425
$757$	−5.82516e12	−0.644728	−0.322364	−	0.946616i	$-0.604477\pi$
$757$	−5.82516e12	−0.644728	−0.322364	+	0.946616i	$0.604477\pi$
$758$	5.66037e12	0.622778
$759$	2.67362e12	0.292423
$760$	1.16168e13	1.26307
$761$	6.06747e12	0.655808	0.327904	−	0.944711i	$-0.393658\pi$
$761$	6.06747e12	0.655808	0.327904	+	0.944711i	$0.393658\pi$
$762$	−1.23941e12	−0.133174
$763$	2.31613e13	2.47401
$764$	−1.34697e12	−0.143033
$765$	6.92145e12	0.730669
$766$	2.72288e13	2.85758
$767$	2.05918e12	0.214839
$768$	−3.33789e12	−0.346216
$769$	−8.69120e12	−0.896213	−0.448107	−	0.893980i	$-0.647902\pi$
$769$	−8.69120e12	−0.896213	−0.448107	+	0.893980i	$0.647902\pi$
$770$	−4.04695e13	−4.14877
$771$	−5.59689e12	−0.570430
$772$	−9.69900e12	−0.982764
$773$	−6.91962e12	−0.697067	−0.348534	−	0.937296i	$-0.613320\pi$
$773$	−6.91962e12	−0.697067	−0.348534	+	0.937296i	$0.613320\pi$
$774$	−3.00223e12	−0.300683
$775$	−1.16698e13	−1.16200
$776$	−9.82765e12	−0.972908
$777$	8.82708e12	0.868806
$778$	6.06769e12	0.593766
$779$	−6.05535e12	−0.589143
$780$	2.00186e13	1.93646
$781$	1.52104e13	1.46289
$782$	1.07668e13	1.02958
$783$	9.38092e11	0.0891903
$784$	−3.28499e12	−0.310536
$785$	1.15753e13	1.08798
$786$	7.41512e12	0.692973
$787$	−1.52860e13	−1.42039	−0.710195	−	0.704005i	$-0.751393\pi$
$787$	−1.52860e13	−1.42039	−0.710195	+	0.704005i	$0.751393\pi$
$788$	4.15389e12	0.383784
$789$	−6.71678e12	−0.617042
$790$	1.28100e12	0.117011
$791$	1.35631e13	1.23187
$792$	3.78419e12	0.341751
$793$	−3.71464e12	−0.333570
$794$	−7.57438e11	−0.0676324
$795$	−1.63966e13	−1.45580
$796$	−1.87641e13	−1.65660
$797$	−1.37425e13	−1.20644	−0.603219	−	0.797576i	$-0.706115\pi$
$797$	−1.37425e13	−1.20644	−0.603219	+	0.797576i	$0.706115\pi$
$798$	−1.86557e13	−1.62854
$799$	4.00097e12	0.347300
$800$	1.10284e13	0.951935
$801$	5.60797e12	0.481348
$802$	4.45056e12	0.379866
$803$	6.09599e12	0.517397
$804$	1.90400e13	1.60699
$805$	9.81138e12	0.823472
$806$	4.48261e13	3.74130
$807$	3.95158e12	0.327974
$808$	1.36128e13	1.12356
$809$	−3.57292e12	−0.293262	−0.146631	−	0.989191i	$-0.546843\pi$
$809$	−3.57292e12	−0.293262	−0.146631	+	0.989191i	$0.546843\pi$
$810$	−2.90300e12	−0.236954
$811$	1.71499e13	1.39209	0.696046	−	0.717998i	$-0.254941\pi$
$811$	1.71499e13	1.39209	0.696046	+	0.717998i	$0.254941\pi$
$812$	−1.32879e13	−1.07264
$813$	−9.36519e12	−0.751812
$814$	−2.47243e13	−1.97385
$815$	3.00649e13	2.38699
$816$	−2.73960e12	−0.216313
$817$	−8.42219e12	−0.661341
$818$	−2.11906e13	−1.65483
$819$	−1.08568e13	−0.843187
$820$	1.33471e13	1.03092
$821$	−6.68653e12	−0.513637	−0.256819	−	0.966460i	$-0.582674\pi$
$821$	−6.68653e12	−0.513637	−0.256819	+	0.966460i	$0.582674\pi$
$822$	5.50924e12	0.420890
$823$	1.36851e13	1.03979	0.519897	−	0.854229i	$-0.325970\pi$
$823$	1.36851e13	1.03979	0.519897	+	0.854229i	$0.325970\pi$
$824$	−1.53959e13	−1.16341
$825$	−7.91664e12	−0.594974
$826$	4.22979e12	0.316161
$827$	1.79247e13	1.33253	0.666265	−	0.745715i	$-0.267892\pi$
$827$	1.79247e13	1.33253	0.666265	+	0.745715i	$0.267892\pi$
$828$	−2.71664e12	−0.200861
$829$	6.90632e12	0.507869	0.253934	−	0.967221i	$-0.418275\pi$
$829$	6.90632e12	0.507869	0.253934	+	0.967221i	$0.418275\pi$
$830$	2.58167e13	1.88821
$831$	−5.95190e12	−0.432963
$832$	−3.71146e13	−2.68528
$833$	3.05421e13	2.19784
$834$	−4.12846e12	−0.295488
$835$	−6.28044e12	−0.447096
$836$	3.14348e13	2.22578
$837$	−3.91054e12	−0.275405
$838$	1.85280e13	1.29787
$839$	−2.60104e13	−1.81225	−0.906124	−	0.423011i	$-0.860973\pi$
$839$	−2.60104e13	−1.81225	−0.906124	+	0.423011i	$0.860973\pi$
$840$	1.38868e13	0.962379
$841$	−1.13913e13	−0.785218
$842$	−1.45929e13	−1.00055
$843$	−3.31539e12	−0.226105
$844$	6.93449e12	0.470407
$845$	3.43772e13	2.31961
$846$	−1.67809e12	−0.112629
$847$	−1.40219e13	−0.936120
$848$	6.49001e12	0.430987
$849$	−1.52483e13	−1.00725
$850$	−3.18808e13	−2.09481
$851$	5.99414e12	0.391781
$852$	−1.54551e13	−1.00484
$853$	1.41771e13	0.916888	0.458444	−	0.888723i	$-0.348407\pi$
$853$	1.41771e13	0.916888	0.458444	+	0.888723i	$0.348407\pi$
$854$	−7.63030e12	−0.490887
$855$	−8.14384e12	−0.521172
$856$	−4.44639e12	−0.283058
$857$	1.12350e13	0.711476	0.355738	−	0.934586i	$-0.384230\pi$
$857$	1.12350e13	0.711476	0.355738	+	0.934586i	$0.384230\pi$
$858$	3.04094e13	1.91565
$859$	2.44792e13	1.53401	0.767003	−	0.641643i	$-0.221747\pi$
$859$	2.44792e13	1.53401	0.767003	+	0.641643i	$0.221747\pi$
$860$	1.85641e13	1.15726
$861$	−7.23861e12	−0.448891
$862$	3.17315e13	1.95752
$863$	2.35658e13	1.44622	0.723110	−	0.690733i	$-0.242712\pi$
$863$	2.35658e13	1.44622	0.723110	+	0.690733i	$0.242712\pi$
$864$	3.69560e12	0.225618
$865$	−1.30080e13	−0.790020
$866$	−2.41956e13	−1.46186
$867$	1.58658e13	0.953620
$868$	5.53922e13	3.31215
$869$	1.17062e12	0.0696347
$870$	−9.64235e12	−0.570619
$871$	5.16708e13	3.04203
$872$	2.22610e13	1.30383
$873$	6.88956e12	0.401446
$874$	−1.26684e13	−0.734377
$875$	6.72659e12	0.387935
$876$	−6.19407e12	−0.355392
$877$	−2.44619e12	−0.139634	−0.0698170	−	0.997560i	$-0.522242\pi$
$877$	−2.44619e12	−0.139634	−0.0698170	+	0.997560i	$0.522242\pi$
$878$	−4.59995e13	−2.61233
$879$	7.99499e12	0.451719
$880$	6.99256e12	0.393065
$881$	−9.21734e12	−0.515483	−0.257741	−	0.966214i	$-0.582978\pi$
$881$	−9.21734e12	−0.515483	−0.257741	+	0.966214i	$0.582978\pi$
$882$	−1.28100e13	−0.712757
$883$	2.92106e12	0.161703	0.0808515	−	0.996726i	$-0.474236\pi$
$883$	2.92106e12	0.161703	0.0808515	+	0.996726i	$0.474236\pi$
$884$	7.36699e13	4.05747
$885$	1.84644e12	0.101179
$886$	−5.18217e13	−2.82527
$887$	1.35029e13	0.732436	0.366218	−	0.930529i	$-0.380652\pi$
$887$	1.35029e13	0.732436	0.366218	+	0.930529i	$0.380652\pi$
$888$	8.48397e12	0.457869
$889$	−4.15635e12	−0.223180
$890$	−5.76425e13	−3.07956
$891$	−2.65286e12	−0.141015
$892$	−3.97478e13	−2.10219
$893$	−4.70757e12	−0.247722
$894$	2.86863e13	1.50195
$895$	−6.21311e12	−0.323672
$896$	−4.15682e13	−2.15464
$897$	−7.37243e12	−0.380229
$898$	2.78456e13	1.42894
$899$	−1.29889e13	−0.663213
$900$	8.04402e12	0.408679
$901$	−6.03407e13	−3.05034
$902$	2.02751e13	1.01984
$903$	−1.00679e13	−0.503901
$904$	1.30359e13	0.649207
$905$	−4.68363e13	−2.32094
$906$	1.93764e13	0.955425
$907$	−8.48404e12	−0.416265	−0.208133	−	0.978101i	$-0.566739\pi$
$907$	−8.48404e12	−0.416265	−0.208133	+	0.978101i	$0.566739\pi$
$908$	−1.65296e13	−0.807002
$909$	−9.54312e12	−0.463610
$910$	1.11593e14	5.39452
$911$	2.66713e13	1.28295	0.641477	−	0.767142i	$-0.278322\pi$
$911$	2.66713e13	1.28295	0.641477	+	0.767142i	$0.278322\pi$
$912$	3.22344e12	0.154292
$913$	2.35922e13	1.12370
$914$	−2.51619e13	−1.19257
$915$	−3.33088e12	−0.157096
$916$	3.13376e13	1.47074
$917$	2.48665e13	1.16132
$918$	−1.06832e13	−0.496490
$919$	2.08506e13	0.964270	0.482135	−	0.876097i	$-0.339861\pi$
$919$	2.08506e13	0.964270	0.482135	+	0.876097i	$0.339861\pi$
$920$	9.43001e12	0.433977
$921$	−9.26461e12	−0.424286
$922$	1.74644e13	0.795913
$923$	−4.19423e13	−1.90215
$924$	3.75774e13	1.69591
$925$	−1.77488e13	−0.797132
$926$	−4.38262e13	−1.95877
$927$	1.07931e13	0.480051
$928$	1.22750e13	0.543319
$929$	1.22073e13	0.537712	0.268856	−	0.963180i	$-0.413355\pi$
$929$	1.22073e13	0.537712	0.268856	+	0.963180i	$0.413355\pi$
$930$	4.01952e13	1.76198
$931$	−3.59361e13	−1.56768
$932$	3.07392e13	1.33451
$933$	−1.71520e12	−0.0741050
$934$	−5.00031e13	−2.14999
$935$	−6.50131e13	−2.78195
$936$	−1.04348e13	−0.444368
$937$	3.42377e13	1.45103	0.725514	−	0.688207i	$-0.241602\pi$
$937$	3.42377e13	1.45103	0.725514	+	0.688207i	$0.241602\pi$
$938$	1.06138e14	4.47670
$939$	−7.94873e12	−0.333659
$940$	1.03764e13	0.433481
$941$	−7.47857e12	−0.310932	−0.155466	−	0.987841i	$-0.549688\pi$
$941$	−7.47857e12	−0.310932	−0.155466	+	0.987841i	$0.549688\pi$
$942$	−1.78665e13	−0.739283
$943$	−4.91546e12	−0.202424
$944$	−7.30848e11	−0.0299539
$945$	−9.73519e12	−0.397101
$946$	2.81999e13	1.14482
$947$	−2.42514e13	−0.979857	−0.489928	−	0.871763i	$-0.662977\pi$
$947$	−2.42514e13	−0.979857	−0.489928	+	0.871763i	$0.662977\pi$
$948$	−1.18945e12	−0.0478310
$949$	−1.68095e13	−0.672755
$950$	3.75113e13	1.49419
$951$	−3.76430e12	−0.149235
$952$	5.11044e13	2.01647
$953$	2.59499e13	1.01910	0.509551	−	0.860440i	$-0.329811\pi$
$953$	2.59499e13	1.01910	0.509551	+	0.860440i	$0.329811\pi$
$954$	2.53082e13	0.989220
$955$	−3.27777e12	−0.127516
$956$	−2.43890e13	−0.944350
$957$	−8.81149e12	−0.339583
$958$	−2.85891e13	−1.09662
$959$	1.84752e13	0.705350
$960$	−3.32803e13	−1.26464
$961$	2.77059e13	1.04789
$962$	6.81766e13	2.56654
$963$	3.11709e12	0.116797
$964$	−6.29862e13	−2.34909
$965$	−2.36020e13	−0.876145
$966$	−1.51438e13	−0.559550
$967$	1.84647e13	0.679085	0.339542	−	0.940591i	$-0.389728\pi$
$967$	1.84647e13	0.679085	0.339542	+	0.940591i	$0.389728\pi$
$968$	−1.34769e13	−0.493344
$969$	−2.99699e13	−1.09201
$970$	−7.08155e13	−2.56836
$971$	5.23071e13	1.88831	0.944157	−	0.329495i	$-0.106878\pi$
$971$	5.23071e13	1.88831	0.944157	+	0.329495i	$0.106878\pi$
$972$	2.69554e12	0.0968608
$973$	−1.38447e13	−0.495196
$974$	6.32146e13	2.25062
$975$	2.18299e13	0.773627
$976$	1.31841e12	0.0465078
$977$	2.96462e13	1.04098	0.520491	−	0.853867i	$-0.325749\pi$
$977$	2.96462e13	1.04098	0.520491	+	0.853867i	$0.325749\pi$
$978$	−4.64051e13	−1.62196
$979$	−5.26757e13	−1.83269
$980$	7.92100e13	2.74323
$981$	−1.56058e13	−0.537992
$982$	−3.35242e13	−1.15042
$983$	−1.15962e13	−0.396117	−0.198059	−	0.980190i	$-0.563464\pi$
$983$	−1.15962e13	−0.396117	−0.198059	+	0.980190i	$0.563464\pi$
$984$	−6.95724e12	−0.236570
$985$	1.01083e13	0.342148
$986$	−3.54845e13	−1.19562
$987$	−5.62746e12	−0.188749
$988$	−8.66807e13	−2.89412
$989$	−6.83675e12	−0.227230
$990$	2.72679e13	0.902180
$991$	2.04116e13	0.672273	0.336137	−	0.941813i	$-0.390880\pi$
$991$	2.04116e13	0.672273	0.336137	+	0.941813i	$0.390880\pi$
$992$	−5.11696e13	−1.67768
$993$	4.10745e12	0.134060
$994$	−8.61543e13	−2.79923
$995$	−4.56614e13	−1.47688
$996$	−2.39718e13	−0.771850
$997$	−5.11008e13	−1.63794	−0.818972	−	0.573833i	$-0.805456\pi$
$997$	−5.11008e13	−1.63794	−0.818972	+	0.573833i	$0.805456\pi$
$998$	−8.33793e13	−2.66055
$999$	−5.94759e12	−0.188928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.3	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.3	✓	21	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-35.8479 q^{2} +81.0000 q^{3} +773.074 q^{4} +1881.24 q^{5} -2903.68 q^{6} -9737.47 q^{7} -9358.98 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-35.8479 q^{2} +81.0000 q^{3} +773.074 q^{4} +1881.24 q^{5} -2903.68 q^{6} -9737.47 q^{7} -9358.98 q^{8} +6561.00 q^{9} -67438.4 q^{10} -61627.4 q^{11} +62619.0 q^{12} +169936. q^{13} +349068. q^{14} +152380. q^{15} -60314.1 q^{16} +560769. q^{17} -235198. q^{18} -659805. q^{19} +1.45434e6 q^{20} -788735. q^{21} +2.20922e6 q^{22} -535600. q^{23} -758077. q^{24} +1.58592e6 q^{25} -6.09185e6 q^{26} +531441. q^{27} -7.52779e6 q^{28} +1.76519e6 q^{29} -5.46251e6 q^{30} -7.35837e6 q^{31} +6.95393e6 q^{32} -4.99182e6 q^{33} -2.01024e7 q^{34} -1.83185e7 q^{35} +5.07214e6 q^{36} -1.11914e7 q^{37} +2.36527e7 q^{38} +1.37648e7 q^{39} -1.76064e7 q^{40} +9.17749e6 q^{41} +2.82745e7 q^{42} +1.27647e7 q^{43} -4.76426e7 q^{44} +1.23428e7 q^{45} +1.92002e7 q^{46} +7.13479e6 q^{47} -4.88544e6 q^{48} +5.44648e7 q^{49} -5.68520e7 q^{50} +4.54223e7 q^{51} +1.31373e8 q^{52} -1.07603e8 q^{53} -1.90511e7 q^{54} -1.15936e8 q^{55} +9.11328e7 q^{56} -5.34442e7 q^{57} -6.32783e7 q^{58} +1.21174e7 q^{59} +1.17801e8 q^{60} -2.18590e7 q^{61} +2.63782e8 q^{62} -6.38876e7 q^{63} -2.18403e8 q^{64} +3.19690e8 q^{65} +1.78947e8 q^{66} +3.04061e8 q^{67} +4.33516e8 q^{68} -4.33836e7 q^{69} +6.56680e8 q^{70} -2.46812e8 q^{71} -6.14042e7 q^{72} -9.89167e7 q^{73} +4.01190e8 q^{74} +1.28460e8 q^{75} -5.10079e8 q^{76} +6.00096e8 q^{77} -4.93440e8 q^{78} -1.89951e7 q^{79} -1.13465e8 q^{80} +4.30467e7 q^{81} -3.28994e8 q^{82} -3.82819e8 q^{83} -6.09751e8 q^{84} +1.05494e9 q^{85} -4.57587e8 q^{86} +1.42980e8 q^{87} +5.76770e8 q^{88} +8.54743e8 q^{89} -4.42463e8 q^{90} -1.65475e9 q^{91} -4.14059e8 q^{92} -5.96028e8 q^{93} -2.55767e8 q^{94} -1.24125e9 q^{95} +5.63268e8 q^{96} +1.05008e9 q^{97} -1.95245e9 q^{98} -4.04338e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \)	\( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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