LMFDB - Embedded newform 177.10.a.a.1.2

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			1.2
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-43.5628 q^{2} +81.0000 q^{3} +1385.72 q^{4} +1597.21 q^{5} -3528.58 q^{6} -10966.0 q^{7} -38061.5 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-43.5628 q^{2} +81.0000 q^{3} +1385.72 q^{4} +1597.21 q^{5} -3528.58 q^{6} -10966.0 q^{7} -38061.5 q^{8} +6561.00 q^{9} -69578.8 q^{10} +52965.0 q^{11} +112243. q^{12} -146184. q^{13} +477709. q^{14} +129374. q^{15} +948577. q^{16} -276332. q^{17} -285815. q^{18} +999877. q^{19} +2.21327e6 q^{20} -888246. q^{21} -2.30730e6 q^{22} +1.88611e6 q^{23} -3.08298e6 q^{24} +597945. q^{25} +6.36817e6 q^{26} +531441. q^{27} -1.51958e7 q^{28} -6.91128e6 q^{29} -5.63588e6 q^{30} -1.40963e6 q^{31} -2.18352e7 q^{32} +4.29017e6 q^{33} +1.20378e7 q^{34} -1.75150e7 q^{35} +9.09168e6 q^{36} +4.90587e6 q^{37} -4.35574e7 q^{38} -1.18409e7 q^{39} -6.07921e7 q^{40} +2.05841e7 q^{41} +3.86945e7 q^{42} -3.94179e6 q^{43} +7.33945e7 q^{44} +1.04793e7 q^{45} -8.21642e7 q^{46} +6.35577e6 q^{47} +7.68347e7 q^{48} +7.98995e7 q^{49} -2.60481e7 q^{50} -2.23829e7 q^{51} -2.02569e8 q^{52} -7.48000e7 q^{53} -2.31510e7 q^{54} +8.45961e7 q^{55} +4.17382e8 q^{56} +8.09900e7 q^{57} +3.01075e8 q^{58} +1.21174e7 q^{59} +1.79275e8 q^{60} -7.46185e7 q^{61} +6.14074e7 q^{62} -7.19479e7 q^{63} +4.65530e8 q^{64} -2.33486e8 q^{65} -1.86892e8 q^{66} +2.24949e7 q^{67} -3.82918e8 q^{68} +1.52775e8 q^{69} +7.63001e8 q^{70} -2.63688e8 q^{71} -2.49721e8 q^{72} +1.35213e8 q^{73} -2.13714e8 q^{74} +4.84335e7 q^{75} +1.38554e9 q^{76} -5.80815e8 q^{77} +5.15821e8 q^{78} +1.42336e8 q^{79} +1.51507e9 q^{80} +4.30467e7 q^{81} -8.96702e8 q^{82} -1.25542e7 q^{83} -1.23086e9 q^{84} -4.41360e8 q^{85} +1.71715e8 q^{86} -5.59814e8 q^{87} -2.01593e9 q^{88} -8.08199e8 q^{89} -4.56506e8 q^{90} +1.60305e9 q^{91} +2.61361e9 q^{92} -1.14180e8 q^{93} -2.76875e8 q^{94} +1.59701e9 q^{95} -1.76865e9 q^{96} -1.04265e8 q^{97} -3.48065e9 q^{98} +3.47504e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−43.5628	−1.92522	−0.962610	−	0.270889i	$-0.912682\pi$
$2$	−43.5628	−1.92522	−0.962610	+	0.270889i	$0.912682\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	1385.72	2.70648
$5$	1597.21	1.14287	0.571434	−	0.820648i	$-0.306387\pi$
$5$	1597.21	1.14287	0.571434	+	0.820648i	$0.306387\pi$
$6$	−3528.58	−1.11153
$7$	−10966.0	−1.72626	−0.863132	−	0.504979i	$-0.831500\pi$
$7$	−10966.0	−1.72626	−0.863132	+	0.504979i	$0.831500\pi$
$8$	−38061.5	−3.28534
$9$	6561.00	0.333333
$10$	−69578.8	−2.20027
$11$	52965.0	1.09074	0.545371	−	0.838195i	$-0.316389\pi$
$11$	52965.0	1.09074	0.545371	+	0.838195i	$0.316389\pi$
$12$	112243.	1.56258
$13$	−146184.	−1.41956	−0.709780	−	0.704423i	$-0.751206\pi$
$13$	−146184.	−1.41956	−0.709780	+	0.704423i	$0.751206\pi$
$14$	477709.	3.32344
$15$	129374.	0.659835
$16$	948577.	3.61853
$17$	−276332.	−0.802438	−0.401219	−	0.915982i	$-0.631413\pi$
$17$	−276332.	−0.802438	−0.401219	+	0.915982i	$0.631413\pi$
$18$	−285815.	−0.641740
$19$	999877.	1.76017	0.880086	−	0.474814i	$-0.157485\pi$
$19$	999877.	1.76017	0.880086	+	0.474814i	$0.157485\pi$
$20$	2.21327e6	3.09315
$21$	−888246.	−0.996659
$22$	−2.30730e6	−2.09992
$23$	1.88611e6	1.40537	0.702686	−	0.711500i	$-0.251984\pi$
$23$	1.88611e6	1.40537	0.702686	+	0.711500i	$0.251984\pi$
$24$	−3.08298e6	−1.89679
$25$	597945.	0.306148
$26$	6.36817e6	2.73297
$27$	531441.	0.192450
$28$	−1.51958e7	−4.67209
$29$	−6.91128e6	−1.81454	−0.907272	−	0.420543i	$-0.861839\pi$
$29$	−6.91128e6	−1.81454	−0.907272	+	0.420543i	$0.861839\pi$
$30$	−5.63588e6	−1.27033
$31$	−1.40963e6	−0.274143	−0.137072	−	0.990561i	$-0.543769\pi$
$31$	−1.40963e6	−0.274143	−0.137072	+	0.990561i	$0.543769\pi$
$32$	−2.18352e7	−3.68114
$33$	4.29017e6	0.629740
$34$	1.20378e7	1.54487
$35$	−1.75150e7	−1.97289
$36$	9.09168e6	0.902159
$37$	4.90587e6	0.430337	0.215168	−	0.976577i	$-0.430970\pi$
$37$	4.90587e6	0.430337	0.215168	+	0.976577i	$0.430970\pi$
$38$	−4.35574e7	−3.38872
$39$	−1.18409e7	−0.819583
$40$	−6.07921e7	−3.75471
$41$	2.05841e7	1.13764	0.568820	−	0.822462i	$-0.307400\pi$
$41$	2.05841e7	1.13764	0.568820	+	0.822462i	$0.307400\pi$
$42$	3.86945e7	1.91879
$43$	−3.94179e6	−0.175827	−0.0879135	−	0.996128i	$-0.528020\pi$
$43$	−3.94179e6	−0.175827	−0.0879135	+	0.996128i	$0.528020\pi$
$44$	7.33945e7	2.95207
$45$	1.04793e7	0.380956
$46$	−8.21642e7	−2.70565
$47$	6.35577e6	0.189989	0.0949943	−	0.995478i	$-0.469717\pi$
$47$	6.35577e6	0.189989	0.0949943	+	0.995478i	$0.469717\pi$
$48$	7.68347e7	2.08916
$49$	7.98995e7	1.97999
$50$	−2.60481e7	−0.589402
$51$	−2.23829e7	−0.463288
$52$	−2.02569e8	−3.84200
$53$	−7.48000e7	−1.30215	−0.651074	−	0.759014i	$-0.725681\pi$
$53$	−7.48000e7	−1.30215	−0.651074	+	0.759014i	$0.725681\pi$
$54$	−2.31510e7	−0.370509
$55$	8.45961e7	1.24657
$56$	4.17382e8	5.67137
$57$	8.09900e7	1.01624
$58$	3.01075e8	3.49340
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	1.79275e8	1.78583
$61$	−7.46185e7	−0.690021	−0.345010	−	0.938599i	$-0.612125\pi$
$61$	−7.46185e7	−0.690021	−0.345010	+	0.938599i	$0.612125\pi$
$62$	6.14074e7	0.527786
$63$	−7.19479e7	−0.575421
$64$	4.65530e8	3.46847
$65$	−2.33486e8	−1.62237
$66$	−1.86892e8	−1.21239
$67$	2.24949e7	0.136379	0.0681896	−	0.997672i	$-0.478278\pi$
$67$	2.24949e7	0.136379	0.0681896	+	0.997672i	$0.478278\pi$
$68$	−3.82918e8	−2.17178
$69$	1.52775e8	0.811392
$70$	7.63001e8	3.79825
$71$	−2.63688e8	−1.23148	−0.615741	−	0.787949i	$-0.711143\pi$
$71$	−2.63688e8	−1.23148	−0.615741	+	0.787949i	$0.711143\pi$
$72$	−2.49721e8	−1.09511
$73$	1.35213e8	0.557271	0.278636	−	0.960397i	$-0.410118\pi$
$73$	1.35213e8	0.557271	0.278636	+	0.960397i	$0.410118\pi$
$74$	−2.13714e8	−0.828494
$75$	4.84335e7	0.176755
$76$	1.38554e9	4.76386
$77$	−5.80815e8	−1.88291
$78$	5.15821e8	1.57788
$79$	1.42336e8	0.411142	0.205571	−	0.978642i	$-0.434095\pi$
$79$	1.42336e8	0.411142	0.205571	+	0.978642i	$0.434095\pi$
$80$	1.51507e9	4.13551
$81$	4.30467e7	0.111111
$82$	−8.96702e8	−2.19021
$83$	−1.25542e7	−0.0290360	−0.0145180	−	0.999895i	$-0.504621\pi$
$83$	−1.25542e7	−0.0290360	−0.0145180	+	0.999895i	$0.504621\pi$
$84$	−1.23086e9	−2.69743
$85$	−4.41360e8	−0.917080
$86$	1.71715e8	0.338506
$87$	−5.59814e8	−1.04763
$88$	−2.01593e9	−3.58346
$89$	−8.08199e8	−1.36541	−0.682705	−	0.730694i	$-0.739197\pi$
$89$	−8.08199e8	−1.36541	−0.682705	+	0.730694i	$0.739197\pi$
$90$	−4.56506e8	−0.733425
$91$	1.60305e9	2.45053
$92$	2.61361e9	3.80361
$93$	−1.14180e8	−0.158277
$94$	−2.76875e8	−0.365770
$95$	1.59701e9	2.01165
$96$	−1.76865e9	−2.12530
$97$	−1.04265e8	−0.119582	−0.0597909	−	0.998211i	$-0.519043\pi$
$97$	−1.04265e8	−0.119582	−0.0597909	+	0.998211i	$0.519043\pi$
$98$	−3.48065e9	−3.81191
$99$	3.47504e8	0.363581
$100$	8.28582e8	0.828582
$101$	−1.91315e9	−1.82938	−0.914689	−	0.404159i	$-0.867564\pi$
$101$	−1.91315e9	−1.82938	−0.914689	+	0.404159i	$0.867564\pi$
$102$	9.75061e8	0.891931
$103$	−3.75074e8	−0.328359	−0.164180	−	0.986430i	$-0.552498\pi$
$103$	−3.75074e8	−0.328359	−0.164180	+	0.986430i	$0.552498\pi$
$104$	5.56397e9	4.66374
$105$	−1.41871e9	−1.13905
$106$	3.25850e9	2.50692
$107$	3.35288e8	0.247281	0.123641	−	0.992327i	$-0.460543\pi$
$107$	3.35288e8	0.247281	0.123641	+	0.992327i	$0.460543\pi$
$108$	7.36426e8	0.520861
$109$	1.50110e9	1.01857	0.509283	−	0.860599i	$-0.329911\pi$
$109$	1.50110e9	1.01857	0.509283	+	0.860599i	$0.329911\pi$
$110$	−3.68524e9	−2.39993
$111$	3.97376e8	0.248455
$112$	−1.04021e10	−6.24654
$113$	−5.24785e8	−0.302781	−0.151390	−	0.988474i	$-0.548375\pi$
$113$	−5.24785e8	−0.302781	−0.151390	+	0.988474i	$0.548375\pi$
$114$	−3.52815e9	−1.95648
$115$	3.01251e9	1.60616
$116$	−9.57707e9	−4.91102
$117$	−9.59111e8	−0.473187
$118$	−5.27866e8	−0.250642
$119$	3.03026e9	1.38522
$120$	−4.92416e9	−2.16778
$121$	4.47347e8	0.189719
$122$	3.25059e9	1.32844
$123$	1.66731e9	0.656817
$124$	−1.95334e9	−0.741961
$125$	−2.16450e9	−0.792982
$126$	3.13425e9	1.10781
$127$	−5.21327e8	−0.177825	−0.0889126	−	0.996039i	$-0.528339\pi$
$127$	−5.21327e8	−0.177825	−0.0889126	+	0.996039i	$0.528339\pi$
$128$	−9.10015e9	−2.99643
$129$	−3.19285e8	−0.101514
$130$	1.01713e10	3.12342
$131$	3.86658e9	1.14711	0.573557	−	0.819166i	$-0.305563\pi$
$131$	3.86658e9	1.14711	0.573557	+	0.819166i	$0.305563\pi$
$132$	5.94495e9	1.70438
$133$	−1.09646e10	−3.03852
$134$	−9.79942e8	−0.262560
$135$	8.48821e8	0.219945
$136$	1.05176e10	2.63628
$137$	−1.63775e8	−0.0397197	−0.0198598	−	0.999803i	$-0.506322\pi$
$137$	−1.63775e8	−0.0397197	−0.0198598	+	0.999803i	$0.506322\pi$
$138$	−6.65530e9	−1.56211
$139$	5.02768e9	1.14235	0.571177	−	0.820827i	$-0.306487\pi$
$139$	5.02768e9	1.14235	0.571177	+	0.820827i	$0.306487\pi$
$140$	−2.42708e10	−5.33958
$141$	5.14817e8	0.109690
$142$	1.14870e10	2.37087
$143$	−7.74262e9	−1.54837
$144$	6.22361e9	1.20618
$145$	−1.10387e10	−2.07379
$146$	−5.89027e9	−1.07287
$147$	6.47186e9	1.14314
$148$	6.79815e9	1.16470
$149$	7.02775e9	1.16810	0.584048	−	0.811719i	$-0.301468\pi$
$149$	7.02775e9	1.16810	0.584048	+	0.811719i	$0.301468\pi$
$150$	−2.10990e9	−0.340292
$151$	−4.38989e9	−0.687159	−0.343580	−	0.939124i	$-0.611640\pi$
$151$	−4.38989e9	−0.687159	−0.343580	+	0.939124i	$0.611640\pi$
$152$	−3.80568e10	−5.78277
$153$	−1.81302e9	−0.267479
$154$	2.53019e10	3.62501
$155$	−2.25147e9	−0.313309
$156$	−1.64081e10	−2.21818
$157$	7.13429e9	0.937135	0.468568	−	0.883428i	$-0.344770\pi$
$157$	7.13429e9	0.937135	0.468568	+	0.883428i	$0.344770\pi$
$158$	−6.20053e9	−0.791538
$159$	−6.05880e9	−0.751796
$160$	−3.48753e10	−4.20705
$161$	−2.06831e10	−2.42604
$162$	−1.87523e9	−0.213913
$163$	−1.51240e10	−1.67812	−0.839061	−	0.544038i	$-0.816895\pi$
$163$	−1.51240e10	−1.67812	−0.839061	+	0.544038i	$0.816895\pi$
$164$	2.85238e10	3.07900
$165$	6.85229e9	0.719710
$166$	5.46895e8	0.0559007
$167$	−6.77132e9	−0.673674	−0.336837	−	0.941563i	$-0.609357\pi$
$167$	−6.77132e9	−0.673674	−0.336837	+	0.941563i	$0.609357\pi$
$168$	3.38080e10	3.27437
$169$	1.07652e10	1.01515
$170$	1.92269e10	1.76558
$171$	6.56019e9	0.586724
$172$	−5.46220e9	−0.475871
$173$	−1.25124e9	−0.106202	−0.0531009	−	0.998589i	$-0.516910\pi$
$173$	−1.25124e9	−0.106202	−0.0531009	+	0.998589i	$0.516910\pi$
$174$	2.43871e10	2.01692
$175$	−6.55707e9	−0.528492
$176$	5.02414e10	3.94689
$177$	9.81506e8	0.0751646
$178$	3.52074e10	2.62872
$179$	−1.64348e10	−1.19653	−0.598266	−	0.801297i	$-0.704143\pi$
$179$	−1.64348e10	−1.19653	−0.598266	+	0.801297i	$0.704143\pi$
$180$	1.45213e10	1.03105
$181$	−4.40038e7	−0.00304745	−0.00152372	−	0.999999i	$-0.500485\pi$
$181$	−4.40038e7	−0.00304745	−0.00152372	+	0.999999i	$0.500485\pi$
$182$	−6.98333e10	−4.71782
$183$	−6.04410e9	−0.398384
$184$	−7.17881e10	−4.61713
$185$	7.83570e9	0.491818
$186$	4.97400e9	0.304717
$187$	−1.46359e10	−0.875253
$188$	8.80729e9	0.514200
$189$	−5.82778e9	−0.332220
$190$	−6.95702e10	−3.87286
$191$	−1.43446e10	−0.779896	−0.389948	−	0.920837i	$-0.627507\pi$
$191$	−1.43446e10	−0.779896	−0.389948	+	0.920837i	$0.627507\pi$
$192$	3.77079e10	2.00252
$193$	−2.20418e10	−1.14351	−0.571754	−	0.820425i	$-0.693737\pi$
$193$	−2.20418e10	−1.14351	−0.571754	+	0.820425i	$0.693737\pi$
$194$	4.54206e9	0.230221
$195$	−1.89123e10	−0.936676
$196$	1.10718e11	5.35878
$197$	−3.24597e10	−1.53549	−0.767745	−	0.640755i	$-0.778621\pi$
$197$	−3.24597e10	−1.53549	−0.767745	+	0.640755i	$0.778621\pi$
$198$	−1.51382e10	−0.699973
$199$	−1.55333e10	−0.702141	−0.351070	−	0.936349i	$-0.614182\pi$
$199$	−1.55333e10	−0.702141	−0.351070	+	0.936349i	$0.614182\pi$
$200$	−2.27587e10	−1.00580
$201$	1.82209e9	0.0787386
$202$	8.33422e10	3.52196
$203$	7.57891e10	3.13238
$204$	−3.10163e10	−1.25388
$205$	3.28771e10	1.30017
$206$	1.63393e10	0.632164
$207$	1.23748e10	0.468458
$208$	−1.38666e11	−5.13673
$209$	5.29585e10	1.91989
$210$	6.18031e10	2.19292
$211$	7.41772e9	0.257632	0.128816	−	0.991669i	$-0.458882\pi$
$211$	7.41772e9	0.257632	0.128816	+	0.991669i	$0.458882\pi$
$212$	−1.03652e11	−3.52423
$213$	−2.13587e10	−0.710996
$214$	−1.46061e10	−0.476071
$215$	−6.29586e9	−0.200947
$216$	−2.02274e10	−0.632264
$217$	1.54580e10	0.473243
$218$	−6.53919e10	−1.96097
$219$	1.09523e10	0.321741
$220$	1.17226e11	3.37382
$221$	4.03952e10	1.13911
$222$	−1.73108e10	−0.478331
$223$	2.99814e10	0.811858	0.405929	−	0.913905i	$-0.366948\pi$
$223$	2.99814e10	0.811858	0.405929	+	0.913905i	$0.366948\pi$
$224$	2.39445e11	6.35461
$225$	3.92312e9	0.102049
$226$	2.28611e10	0.582920
$227$	3.94298e10	0.985618	0.492809	−	0.870138i	$-0.335970\pi$
$227$	3.94298e10	0.985618	0.492809	+	0.870138i	$0.335970\pi$
$228$	1.12229e11	2.75042
$229$	−1.03992e10	−0.249886	−0.124943	−	0.992164i	$-0.539875\pi$
$229$	−1.03992e10	−0.249886	−0.124943	+	0.992164i	$0.539875\pi$
$230$	−1.31233e11	−3.09221
$231$	−4.70460e10	−1.08710
$232$	2.63054e11	5.96140
$233$	−6.95843e10	−1.54671	−0.773356	−	0.633972i	$-0.781423\pi$
$233$	−6.95843e10	−1.54671	−0.773356	+	0.633972i	$0.781423\pi$
$234$	4.17815e10	0.910989
$235$	1.01515e10	0.217132
$236$	1.67912e10	0.352353
$237$	1.15292e10	0.237373
$238$	−1.32006e11	−2.66685
$239$	−4.09211e10	−0.811254	−0.405627	−	0.914039i	$-0.632947\pi$
$239$	−4.09211e10	−0.811254	−0.405627	+	0.914039i	$0.632947\pi$
$240$	1.22721e11	2.38764
$241$	−6.90087e10	−1.31773	−0.658866	−	0.752261i	$-0.728963\pi$
$241$	−6.90087e10	−1.31773	−0.658866	+	0.752261i	$0.728963\pi$
$242$	−1.94877e10	−0.365251
$243$	3.48678e9	0.0641500
$244$	−1.03400e11	−1.86752
$245$	1.27616e11	2.26286
$246$	−7.26329e10	−1.26452
$247$	−1.46166e11	−2.49867
$248$	5.36526e10	0.900654
$249$	−1.01689e9	−0.0167639
$250$	9.42918e10	1.52666
$251$	8.87595e10	1.41151	0.705754	−	0.708457i	$-0.250609\pi$
$251$	8.87595e10	1.41151	0.705754	+	0.708457i	$0.250609\pi$
$252$	−9.96994e10	−1.55736
$253$	9.98978e10	1.53290
$254$	2.27104e10	0.342353
$255$	−3.57501e10	−0.529477
$256$	1.58077e11	2.30032
$257$	9.45600e10	1.35210	0.676049	−	0.736857i	$-0.263691\pi$
$257$	9.45600e10	1.35210	0.676049	+	0.736857i	$0.263691\pi$
$258$	1.39089e10	0.195436
$259$	−5.37978e10	−0.742875
$260$	−3.23545e11	−4.39090
$261$	−4.53449e10	−0.604848
$262$	−1.68439e11	−2.20845
$263$	−1.00500e11	−1.29529	−0.647644	−	0.761943i	$-0.724246\pi$
$263$	−1.00500e11	−1.29529	−0.647644	+	0.761943i	$0.724246\pi$
$264$	−1.63290e11	−2.06891
$265$	−1.19471e11	−1.48818
$266$	4.77650e11	5.84982
$267$	−6.54641e10	−0.788320
$268$	3.11716e10	0.369107
$269$	−6.93801e9	−0.0807885	−0.0403942	−	0.999184i	$-0.512861\pi$
$269$	−6.93801e9	−0.0807885	−0.0403942	+	0.999184i	$0.512861\pi$
$270$	−3.69770e10	−0.423443
$271$	9.60064e10	1.08128	0.540640	−	0.841254i	$-0.318182\pi$
$271$	9.60064e10	1.08128	0.540640	+	0.841254i	$0.318182\pi$
$272$	−2.62122e11	−2.90365
$273$	1.29847e11	1.41482
$274$	7.13450e9	0.0764691
$275$	3.16702e10	0.333928
$276$	2.11702e11	2.19601
$277$	−1.82037e11	−1.85781	−0.928905	−	0.370318i	$-0.879249\pi$
$277$	−1.82037e11	−1.85781	−0.928905	+	0.370318i	$0.879249\pi$
$278$	−2.19020e11	−2.19928
$279$	−9.24858e9	−0.0913810
$280$	6.66646e11	6.48162
$281$	−1.73949e11	−1.66435	−0.832173	−	0.554517i	$-0.812903\pi$
$281$	−1.73949e11	−1.66435	−0.832173	+	0.554517i	$0.812903\pi$
$282$	−2.24269e10	−0.211178
$283$	−1.91984e11	−1.77921	−0.889603	−	0.456734i	$-0.849019\pi$
$283$	−1.91984e11	−1.77921	−0.889603	+	0.456734i	$0.849019\pi$
$284$	−3.65397e11	−3.33297
$285$	1.29358e11	1.16142
$286$	3.37290e11	2.98096
$287$	−2.25726e11	−1.96387
$288$	−1.43261e11	−1.22705
$289$	−4.22284e10	−0.356094
$290$	4.80879e11	3.99250
$291$	−8.44545e9	−0.0690405
$292$	1.87367e11	1.50824
$293$	−5.44405e10	−0.431536	−0.215768	−	0.976445i	$-0.569226\pi$
$293$	−5.44405e10	−0.431536	−0.215768	+	0.976445i	$0.569226\pi$
$294$	−2.81932e11	−2.20081
$295$	1.93539e10	0.148789
$296$	−1.86725e11	−1.41380
$297$	2.81478e10	0.209913
$298$	−3.06148e11	−2.24884
$299$	−2.75718e11	−1.99501
$300$	6.71151e10	0.478382
$301$	4.32257e10	0.303524
$302$	1.91236e11	1.32293
$303$	−1.54965e11	−1.05619
$304$	9.48460e11	6.36925
$305$	−1.19181e11	−0.788603
$306$	7.89800e10	0.514957
$307$	−6.62838e10	−0.425877	−0.212939	−	0.977066i	$-0.568303\pi$
$307$	−6.62838e10	−0.425877	−0.212939	+	0.977066i	$0.568303\pi$
$308$	−8.04844e11	−5.09605
$309$	−3.03810e10	−0.189578
$310$	9.80802e10	0.603190
$311$	8.07048e9	0.0489190	0.0244595	−	0.999701i	$-0.492214\pi$
$311$	8.07048e9	0.0489190	0.0244595	+	0.999701i	$0.492214\pi$
$312$	4.50681e11	2.69261
$313$	1.54810e10	0.0911696	0.0455848	−	0.998960i	$-0.485485\pi$
$313$	1.54810e10	0.0911696	0.0455848	+	0.998960i	$0.485485\pi$
$314$	−3.10790e11	−1.80419
$315$	−1.14916e11	−0.657631
$316$	1.97237e11	1.11274
$317$	−3.29987e11	−1.83540	−0.917699	−	0.397276i	$-0.869956\pi$
$317$	−3.29987e11	−1.83540	−0.917699	+	0.397276i	$0.869956\pi$
$318$	2.63938e11	1.44737
$319$	−3.66056e11	−1.97920
$320$	7.43547e11	3.96400
$321$	2.71583e10	0.142768
$322$	9.01012e11	4.67067
$323$	−2.76298e11	−1.41243
$324$	5.96505e10	0.300720
$325$	−8.74098e10	−0.434595
$326$	6.58845e11	3.23075
$327$	1.21589e11	0.588070
$328$	−7.83462e11	−3.73754
$329$	−6.96974e10	−0.327970
$330$	−2.98505e11	−1.38560
$331$	−1.41539e11	−0.648113	−0.324057	−	0.946038i	$-0.605047\pi$
$331$	−1.41539e11	−0.648113	−0.324057	+	0.946038i	$0.605047\pi$
$332$	−1.73965e10	−0.0785853
$333$	3.21874e10	0.143446
$334$	2.94978e11	1.29697
$335$	3.59291e10	0.155863
$336$	−8.42570e11	−3.60644
$337$	7.94755e10	0.335659	0.167830	−	0.985816i	$-0.446324\pi$
$337$	7.94755e10	0.335659	0.167830	+	0.985816i	$0.446324\pi$
$338$	−4.68960e11	−1.95439
$339$	−4.25076e10	−0.174811
$340$	−6.11599e11	−2.48206
$341$	−7.46610e10	−0.299019
$342$	−2.85780e11	−1.12957
$343$	−4.33661e11	−1.69171
$344$	1.50030e11	0.577652
$345$	2.44013e11	0.927315
$346$	5.45073e10	0.204462
$347$	2.42349e11	0.897343	0.448671	−	0.893697i	$-0.351897\pi$
$347$	2.42349e11	0.897343	0.448671	+	0.893697i	$0.351897\pi$
$348$	−7.75743e11	−2.83538
$349$	1.34335e11	0.484703	0.242352	−	0.970188i	$-0.422081\pi$
$349$	1.34335e11	0.484703	0.242352	+	0.970188i	$0.422081\pi$
$350$	2.85644e11	1.01746
$351$	−7.76880e10	−0.273194
$352$	−1.15650e12	−4.01517
$353$	2.89766e11	0.993258	0.496629	−	0.867963i	$-0.334571\pi$
$353$	2.89766e11	0.993258	0.496629	+	0.867963i	$0.334571\pi$
$354$	−4.27571e10	−0.144708
$355$	−4.21164e11	−1.40742
$356$	−1.11993e12	−3.69545
$357$	2.45451e11	0.799756
$358$	7.15943e11	2.30359
$359$	2.09948e11	0.667092	0.333546	−	0.942734i	$-0.391755\pi$
$359$	2.09948e11	0.667092	0.333546	+	0.942734i	$0.391755\pi$
$360$	−3.98857e11	−1.25157
$361$	6.77066e11	2.09821
$362$	1.91693e9	0.00586701
$363$	3.62351e10	0.109534
$364$	2.22137e12	6.63231
$365$	2.15964e11	0.636887
$366$	2.63298e11	0.766976
$367$	2.83366e11	0.815363	0.407681	−	0.913124i	$-0.366337\pi$
$367$	2.83366e11	0.815363	0.407681	+	0.913124i	$0.366337\pi$
$368$	1.78912e12	5.08539
$369$	1.35052e11	0.379214
$370$	−3.41345e11	−0.946859
$371$	8.20257e11	2.24785
$372$	−1.58221e11	−0.428372
$373$	−2.03235e11	−0.543636	−0.271818	−	0.962349i	$-0.587625\pi$
$373$	−2.03235e11	−0.543636	−0.271818	+	0.962349i	$0.587625\pi$
$374$	6.37582e11	1.68505
$375$	−1.75325e11	−0.457828
$376$	−2.41910e11	−0.624178
$377$	1.01032e12	2.57586
$378$	2.53874e11	0.639596
$379$	7.46197e10	0.185771	0.0928853	−	0.995677i	$-0.470391\pi$
$379$	7.46197e10	0.185771	0.0928853	+	0.995677i	$0.470391\pi$
$380$	2.21300e12	5.44447
$381$	−4.22275e10	−0.102667
$382$	6.24889e11	1.50147
$383$	−2.80797e11	−0.666803	−0.333401	−	0.942785i	$-0.608196\pi$
$383$	−2.80797e11	−0.666803	−0.333401	+	0.942785i	$0.608196\pi$
$384$	−7.37112e11	−1.72999
$385$	−9.27681e11	−2.15192
$386$	9.60203e11	2.20151
$387$	−2.58621e10	−0.0586090
$388$	−1.44481e11	−0.323645
$389$	4.02766e11	0.891824	0.445912	−	0.895077i	$-0.352879\pi$
$389$	4.02766e11	0.891824	0.445912	+	0.895077i	$0.352879\pi$
$390$	8.23874e11	1.80331
$391$	−5.21193e11	−1.12772
$392$	−3.04109e12	−6.50493
$393$	3.13193e11	0.662286
$394$	1.41404e12	2.95616
$395$	2.27339e11	0.469881
$396$	4.81541e11	0.984023
$397$	−1.15594e11	−0.233549	−0.116775	−	0.993158i	$-0.537255\pi$
$397$	−1.15594e11	−0.233549	−0.116775	+	0.993158i	$0.537255\pi$
$398$	6.76673e11	1.35178
$399$	−8.88136e11	−1.75429
$400$	5.67197e11	1.10781
$401$	−5.68027e11	−1.09703	−0.548516	−	0.836140i	$-0.684807\pi$
$401$	−5.68027e11	−1.09703	−0.548516	+	0.836140i	$0.684807\pi$
$402$	−7.93753e10	−0.151589
$403$	2.06065e11	0.389162
$404$	−2.65108e12	−4.95117
$405$	6.87545e10	0.126985
$406$	−3.30159e12	−6.03053
$407$	2.59840e11	0.469387
$408$	8.51926e11	1.52206
$409$	−4.33352e11	−0.765749	−0.382874	−	0.923800i	$-0.625066\pi$
$409$	−4.33352e11	−0.765749	−0.382874	+	0.923800i	$0.625066\pi$
$410$	−1.43222e12	−2.50312
$411$	−1.32658e10	−0.0229322
$412$	−5.19746e11	−0.888697
$413$	−1.32879e11	−0.224740
$414$	−5.39079e11	−0.901884
$415$	−2.00516e10	−0.0331843
$416$	3.19195e12	5.22559
$417$	4.07242e11	0.659539
$418$	−2.30702e12	−3.69622
$419$	−9.10366e11	−1.44296	−0.721478	−	0.692438i	$-0.756537\pi$
$419$	−9.10366e11	−1.44296	−0.721478	+	0.692438i	$0.756537\pi$
$420$	−1.96593e12	−3.08281
$421$	5.30818e11	0.823524	0.411762	−	0.911291i	$-0.364913\pi$
$421$	5.30818e11	0.823524	0.411762	+	0.911291i	$0.364913\pi$
$422$	−3.23136e11	−0.495998
$423$	4.17002e10	0.0633296
$424$	2.84700e12	4.27800
$425$	−1.65231e11	−0.245665
$426$	9.30445e11	1.36882
$427$	8.18266e11	1.19116
$428$	4.64614e11	0.669260
$429$	−6.27152e11	−0.893954
$430$	2.74265e11	0.386868
$431$	−1.05184e12	−1.46826	−0.734130	−	0.679009i	$-0.762410\pi$
$431$	−1.05184e12	−1.46826	−0.734130	+	0.679009i	$0.762410\pi$
$432$	5.04113e11	0.696387
$433$	3.32873e11	0.455074	0.227537	−	0.973769i	$-0.426933\pi$
$433$	3.32873e11	0.455074	0.227537	+	0.973769i	$0.426933\pi$
$434$	−6.73393e11	−0.911097
$435$	−8.94139e11	−1.19730
$436$	2.08009e12	2.75673
$437$	1.88588e12	2.47370
$438$	−4.77112e11	−0.619422
$439$	−1.34032e12	−1.72233	−0.861166	−	0.508323i	$-0.830265\pi$
$439$	−1.34032e12	−1.72233	−0.861166	+	0.508323i	$0.830265\pi$
$440$	−3.21985e12	−4.09543
$441$	5.24221e11	0.659995
$442$	−1.75973e12	−2.19303
$443$	2.01187e11	0.248189	0.124095	−	0.992270i	$-0.460397\pi$
$443$	2.01187e11	0.248189	0.124095	+	0.992270i	$0.460397\pi$
$444$	5.50650e11	0.672438
$445$	−1.29086e12	−1.56048
$446$	−1.30607e12	−1.56301
$447$	5.69248e11	0.674400
$448$	−5.10500e12	−5.98749
$449$	−6.42787e11	−0.746377	−0.373189	−	0.927756i	$-0.621736\pi$
$449$	−6.42787e11	−0.746377	−0.373189	+	0.927756i	$0.621736\pi$
$450$	−1.70902e11	−0.196467
$451$	1.09024e12	1.24087
$452$	−7.27203e11	−0.819469
$453$	−3.55581e11	−0.396732
$454$	−1.71767e12	−1.89753
$455$	2.56040e12	2.80064
$456$	−3.08260e12	−3.33868
$457$	1.43216e12	1.53592	0.767959	−	0.640499i	$-0.221272\pi$
$457$	1.43216e12	1.53592	0.767959	+	0.640499i	$0.221272\pi$
$458$	4.53020e11	0.481086
$459$	−1.46854e11	−0.154429
$460$	4.17448e12	4.34702
$461$	4.59275e11	0.473607	0.236804	−	0.971558i	$-0.423900\pi$
$461$	4.59275e11	0.473607	0.236804	+	0.971558i	$0.423900\pi$
$462$	2.04945e12	2.09290
$463$	1.91038e12	1.93199	0.965997	−	0.258553i	$-0.0832457\pi$
$463$	1.91038e12	1.93199	0.965997	+	0.258553i	$0.0832457\pi$
$464$	−6.55589e12	−6.56599
$465$	−1.82369e11	−0.180889
$466$	3.03128e12	2.97776
$467$	−4.19414e11	−0.408053	−0.204027	−	0.978965i	$-0.565403\pi$
$467$	−4.19414e11	−0.408053	−0.204027	+	0.978965i	$0.565403\pi$
$468$	−1.32905e12	−1.28067
$469$	−2.46680e11	−0.235426
$470$	−4.42227e11	−0.418027
$471$	5.77878e11	0.541055
$472$	−4.61205e11	−0.427715
$473$	−2.08777e11	−0.191782
$474$	−5.02243e11	−0.456995
$475$	5.97871e11	0.538873
$476$	4.19908e12	3.74906
$477$	−4.90763e11	−0.434049
$478$	1.78264e12	1.56184
$479$	−2.11271e12	−1.83371	−0.916855	−	0.399220i	$-0.869281\pi$
$479$	−2.11271e12	−1.83371	−0.916855	+	0.399220i	$0.869281\pi$
$480$	−2.82490e12	−2.42894
$481$	−7.17159e11	−0.610889
$482$	3.00621e12	2.53692
$483$	−1.67533e12	−1.40068
$484$	6.19896e11	0.513469
$485$	−1.66532e11	−0.136666
$486$	−1.51894e11	−0.123503
$487$	−5.93927e11	−0.478468	−0.239234	−	0.970962i	$-0.576896\pi$
$487$	−5.93927e11	−0.478468	−0.239234	+	0.970962i	$0.576896\pi$
$488$	2.84009e12	2.26695
$489$	−1.22505e12	−0.968864
$490$	−5.55931e12	−4.35651
$491$	−6.03440e11	−0.468562	−0.234281	−	0.972169i	$-0.575274\pi$
$491$	−6.03440e11	−0.468562	−0.234281	+	0.972169i	$0.575274\pi$
$492$	2.31042e12	1.77766
$493$	1.90981e12	1.45606
$494$	6.36738e12	4.81049
$495$	5.55035e11	0.415525
$496$	−1.33714e12	−0.991996
$497$	2.89160e12	2.12586
$498$	4.42985e10	0.0322743
$499$	−2.35555e12	−1.70075	−0.850375	−	0.526177i	$-0.823625\pi$
$499$	−2.35555e12	−1.70075	−0.850375	+	0.526177i	$0.823625\pi$
$500$	−2.99939e12	−2.14619
$501$	−5.48477e11	−0.388946
$502$	−3.86661e12	−2.71746
$503$	1.90452e12	1.32657	0.663285	−	0.748367i	$-0.269162\pi$
$503$	1.90452e12	1.32657	0.663285	+	0.748367i	$0.269162\pi$
$504$	2.73844e12	1.89046
$505$	−3.05570e12	−2.09074
$506$	−4.35183e12	−2.95117
$507$	8.71978e11	0.586097
$508$	−7.22411e11	−0.481280
$509$	−1.32499e12	−0.874951	−0.437475	−	0.899230i	$-0.644127\pi$
$509$	−1.32499e12	−0.874951	−0.437475	+	0.899230i	$0.644127\pi$
$510$	1.55737e12	1.01936
$511$	−1.48275e12	−0.961997
$512$	−2.22698e12	−1.43219
$513$	5.31375e11	0.338745
$514$	−4.11929e12	−2.60309
$515$	−5.99071e11	−0.375272
$516$	−4.42438e11	−0.274744
$517$	3.36633e11	0.207229
$518$	2.34358e12	1.43020
$519$	−1.01350e11	−0.0613156
$520$	8.88680e12	5.33004
$521$	1.19512e12	0.710625	0.355312	−	0.934748i	$-0.384374\pi$
$521$	1.19512e12	0.710625	0.355312	+	0.934748i	$0.384374\pi$
$522$	1.97535e12	1.16447
$523$	1.76481e12	1.03143	0.515717	−	0.856759i	$-0.327526\pi$
$523$	1.76481e12	1.03143	0.515717	+	0.856759i	$0.327526\pi$
$524$	5.35798e12	3.10463
$525$	−5.31122e11	−0.305125
$526$	4.37807e12	2.49372
$527$	3.89526e11	0.219983
$528$	4.06956e12	2.27874
$529$	1.75626e12	0.975073
$530$	5.20450e12	2.86508
$531$	7.95020e10	0.0433963
$532$	−1.51939e13	−8.22368
$533$	−3.00906e12	−1.61495
$534$	2.85180e12	1.51769
$535$	5.35524e11	0.282610
$536$	−8.56191e11	−0.448052
$537$	−1.33121e12	−0.690818
$538$	3.02239e11	0.155536
$539$	4.23188e12	2.15965
$540$	1.17622e12	0.595276
$541$	1.82271e12	0.914807	0.457403	−	0.889259i	$-0.348780\pi$
$541$	1.82271e12	0.914807	0.457403	+	0.889259i	$0.348780\pi$
$542$	−4.18231e12	−2.08170
$543$	−3.56431e9	−0.00175945
$544$	6.03376e12	2.95388
$545$	2.39756e12	1.16409
$546$	−5.65650e12	−2.72383
$547$	8.23239e10	0.0393172	0.0196586	−	0.999807i	$-0.493742\pi$
$547$	8.23239e10	0.0393172	0.0196586	+	0.999807i	$0.493742\pi$
$548$	−2.26946e11	−0.107500
$549$	−4.89572e11	−0.230007
$550$	−1.37964e12	−0.642886
$551$	−6.91043e12	−3.19391
$552$	−5.81484e12	−2.66570
$553$	−1.56085e12	−0.709739
$554$	7.93005e12	3.57669
$555$	6.34691e11	0.283952
$556$	6.96693e12	3.09175
$557$	−1.73608e12	−0.764225	−0.382113	−	0.924116i	$-0.624803\pi$
$557$	−1.73608e12	−0.764225	−0.382113	+	0.924116i	$0.624803\pi$
$558$	4.02894e11	0.175929
$559$	5.76225e11	0.249597
$560$	−1.66143e13	−7.13898
$561$	−1.18551e12	−0.505327
$562$	7.57770e12	3.20423
$563$	−1.36719e12	−0.573512	−0.286756	−	0.958004i	$-0.592577\pi$
$563$	−1.36719e12	−0.573512	−0.286756	+	0.958004i	$0.592577\pi$
$564$	7.13390e11	0.296873
$565$	−8.38190e11	−0.346039
$566$	8.36336e12	3.42537
$567$	−4.72050e11	−0.191807
$568$	1.00364e13	4.04584
$569$	9.42095e11	0.376782	0.188391	−	0.982094i	$-0.439673\pi$
$569$	9.42095e11	0.376782	0.188391	+	0.982094i	$0.439673\pi$
$570$	−5.63519e12	−2.23600
$571$	3.43206e12	1.35112	0.675558	−	0.737306i	$-0.263903\pi$
$571$	3.43206e12	1.35112	0.675558	+	0.737306i	$0.263903\pi$
$572$	−1.07291e13	−4.19064
$573$	−1.16191e12	−0.450273
$574$	9.83323e12	3.78088
$575$	1.12779e12	0.430252
$576$	3.05434e12	1.15616
$577$	2.01638e12	0.757322	0.378661	−	0.925535i	$-0.376385\pi$
$577$	2.01638e12	0.757322	0.378661	+	0.925535i	$0.376385\pi$
$578$	1.83959e12	0.685560
$579$	−1.78539e12	−0.660205
$580$	−1.52966e13	−5.61265
$581$	1.37669e11	0.0501238
$582$	3.67907e11	0.132918
$583$	−3.96179e12	−1.42031
$584$	−5.14642e12	−1.83083
$585$	−1.53190e12	−0.540790
$586$	2.37158e12	0.830803
$587$	−5.89110e11	−0.204797	−0.102399	−	0.994743i	$-0.532652\pi$
$587$	−5.89110e11	−0.204797	−0.102399	+	0.994743i	$0.532652\pi$
$588$	8.96816e12	3.09389
$589$	−1.40946e12	−0.482539
$590$	−8.43111e11	−0.286451
$591$	−2.62924e12	−0.886516
$592$	4.65360e12	1.55719
$593$	−2.77303e12	−0.920893	−0.460446	−	0.887687i	$-0.652311\pi$
$593$	−2.77303e12	−0.920893	−0.460446	+	0.887687i	$0.652311\pi$
$594$	−1.22620e12	−0.404130
$595$	4.83995e12	1.58312
$596$	9.73847e12	3.16142
$597$	−1.25820e12	−0.405381
$598$	1.20111e13	3.84084
$599$	−1.80709e12	−0.573533	−0.286766	−	0.958001i	$-0.592580\pi$
$599$	−1.80709e12	−0.573533	−0.286766	+	0.958001i	$0.592580\pi$
$600$	−1.84345e12	−0.580699
$601$	−1.82846e11	−0.0571678	−0.0285839	−	0.999591i	$-0.509100\pi$
$601$	−1.82846e11	−0.0571678	−0.0285839	+	0.999591i	$0.509100\pi$
$602$	−1.88303e12	−0.584350
$603$	1.47589e11	0.0454597
$604$	−6.08314e12	−1.85978
$605$	7.14506e11	0.216824
$606$	6.75072e12	2.03340
$607$	3.01684e12	0.901994	0.450997	−	0.892526i	$-0.351069\pi$
$607$	3.01684e12	0.901994	0.450997	+	0.892526i	$0.351069\pi$
$608$	−2.18325e13	−6.47943
$609$	6.13892e12	1.80848
$610$	5.19186e12	1.51823
$611$	−9.29109e11	−0.269700
$612$	−2.51232e12	−0.723926
$613$	−4.80257e12	−1.37373	−0.686866	−	0.726784i	$-0.741014\pi$
$613$	−4.80257e12	−1.37373	−0.686866	+	0.726784i	$0.741014\pi$
$614$	2.88750e12	0.819908
$615$	2.66305e12	0.750656
$616$	2.21067e13	6.18600
$617$	1.11287e12	0.309145	0.154572	−	0.987981i	$-0.450600\pi$
$617$	1.11287e12	0.309145	0.154572	+	0.987981i	$0.450600\pi$
$618$	1.32348e12	0.364980
$619$	1.60721e12	0.440012	0.220006	−	0.975499i	$-0.429392\pi$
$619$	1.60721e12	0.440012	0.220006	+	0.975499i	$0.429392\pi$
$620$	−3.11990e12	−0.847964
$621$	1.00236e12	0.270464
$622$	−3.51572e11	−0.0941798
$623$	8.86271e12	2.35706
$624$	−1.12320e13	−2.96569
$625$	−4.62502e12	−1.21242
$626$	−6.74396e11	−0.175522
$627$	4.28964e12	1.10845
$628$	9.88610e12	2.53633
$629$	−1.35565e12	−0.345319
$630$	5.00605e12	1.26608
$631$	−2.45294e12	−0.615964	−0.307982	−	0.951392i	$-0.599654\pi$
$631$	−2.45294e12	−0.615964	−0.307982	+	0.951392i	$0.599654\pi$
$632$	−5.41750e12	−1.35074
$633$	6.00835e11	0.148744
$634$	1.43752e13	3.53355
$635$	−8.32667e11	−0.203231
$636$	−8.39578e12	−2.03472
$637$	−1.16800e13	−2.81071
$638$	1.59464e13	3.81040
$639$	−1.73006e12	−0.410494
$640$	−1.45348e13	−3.42452
$641$	−6.74129e12	−1.57718	−0.788591	−	0.614918i	$-0.789189\pi$
$641$	−6.74129e12	−1.57718	−0.788591	+	0.614918i	$0.789189\pi$
$642$	−1.18309e12	−0.274860
$643$	6.95200e11	0.160384	0.0801919	−	0.996779i	$-0.474447\pi$
$643$	6.95200e11	0.160384	0.0801919	+	0.996779i	$0.474447\pi$
$644$	−2.86609e13	−6.56603
$645$	−5.09964e11	−0.116017
$646$	1.20363e13	2.71924
$647$	1.92451e11	0.0431769	0.0215884	−	0.999767i	$-0.493128\pi$
$647$	1.92451e11	0.0431769	0.0215884	+	0.999767i	$0.493128\pi$
$648$	−1.63842e12	−0.365038
$649$	6.41796e11	0.142003
$650$	3.80781e12	0.836692
$651$	1.25210e12	0.273227
$652$	−2.09576e13	−4.54180
$653$	−1.88242e12	−0.405142	−0.202571	−	0.979268i	$-0.564930\pi$
$653$	−1.88242e12	−0.405142	−0.202571	+	0.979268i	$0.564930\pi$
$654$	−5.29675e12	−1.13216
$655$	6.17573e12	1.31100
$656$	1.95256e13	4.11659
$657$	8.87134e11	0.185757
$658$	3.03621e12	0.631416
$659$	5.08014e12	1.04928	0.524640	−	0.851324i	$-0.324200\pi$
$659$	5.08014e12	1.04928	0.524640	+	0.851324i	$0.324200\pi$
$660$	9.49532e12	1.94788
$661$	−1.03648e12	−0.211181	−0.105591	−	0.994410i	$-0.533673\pi$
$661$	−1.03648e12	−0.211181	−0.105591	+	0.994410i	$0.533673\pi$
$662$	6.16584e12	1.24776
$663$	3.27201e12	0.657664
$664$	4.77831e11	0.0953932
$665$	−1.75128e13	−3.47263
$666$	−1.40217e12	−0.276165
$667$	−1.30354e13	−2.55011
$668$	−9.38313e12	−1.82328
$669$	2.42849e12	0.468727
$670$	−1.56517e12	−0.300072
$671$	−3.95217e12	−0.752635
$672$	1.93950e13	3.66884
$673$	8.29211e12	1.55811	0.779053	−	0.626958i	$-0.215700\pi$
$673$	8.29211e12	1.55811	0.779053	+	0.626958i	$0.215700\pi$
$674$	−3.46217e12	−0.646218
$675$	3.17773e11	0.0589182
$676$	1.49174e13	2.74748
$677$	4.71501e12	0.862648	0.431324	−	0.902197i	$-0.358047\pi$
$677$	4.71501e12	0.862648	0.431324	+	0.902197i	$0.358047\pi$
$678$	1.85175e12	0.336549
$679$	1.14337e12	0.206430
$680$	1.67988e13	3.01292
$681$	3.19382e12	0.569047
$682$	3.25244e12	0.575678
$683$	4.44301e12	0.781240	0.390620	−	0.920552i	$-0.372261\pi$
$683$	4.44301e12	0.781240	0.390620	+	0.920552i	$0.372261\pi$
$684$	9.09056e12	1.58795
$685$	−2.61583e11	−0.0453943
$686$	1.88915e13	3.25692
$687$	−8.42338e11	−0.144272
$688$	−3.73909e12	−0.636236
$689$	1.09345e13	1.84848
$690$	−1.06299e13	−1.78529
$691$	−8.76609e11	−0.146270	−0.0731349	−	0.997322i	$-0.523300\pi$
$691$	−8.76609e11	−0.146270	−0.0731349	+	0.997322i	$0.523300\pi$
$692$	−1.73386e12	−0.287432
$693$	−3.81072e12	−0.627636
$694$	−1.05574e13	−1.72758
$695$	8.03024e12	1.30556
$696$	2.13073e13	3.44182
$697$	−5.68806e12	−0.912886
$698$	−5.85202e12	−0.933161
$699$	−5.63633e12	−0.892995
$700$	−9.08623e12	−1.43035
$701$	−3.11983e12	−0.487978	−0.243989	−	0.969778i	$-0.578456\pi$
$701$	−3.11983e12	−0.487978	−0.243989	+	0.969778i	$0.578456\pi$
$702$	3.38430e12	0.525960
$703$	4.90527e12	0.757467
$704$	2.46568e13	3.78320
$705$	8.22270e11	0.125361
$706$	−1.26230e13	−1.91224
$707$	2.09796e13	3.15799
$708$	1.36009e12	0.203431
$709$	1.64768e12	0.244887	0.122443	−	0.992475i	$-0.460927\pi$
$709$	1.64768e12	0.244887	0.122443	+	0.992475i	$0.460927\pi$
$710$	1.83471e13	2.70960
$711$	9.33863e11	0.137047
$712$	3.07612e13	4.48584
$713$	−2.65871e12	−0.385273
$714$	−1.06925e13	−1.53971
$715$	−1.23666e13	−1.76959
$716$	−2.27739e13	−3.23839
$717$	−3.31461e12	−0.468378
$718$	−9.14590e12	−1.28430
$719$	1.69332e12	0.236298	0.118149	−	0.992996i	$-0.462304\pi$
$719$	1.69332e12	0.236298	0.118149	+	0.992996i	$0.462304\pi$
$720$	9.94040e12	1.37850
$721$	4.11306e12	0.566835
$722$	−2.94949e13	−4.03951
$723$	−5.58970e12	−0.760793
$724$	−6.09767e10	−0.00824785
$725$	−4.13257e12	−0.555519
$726$	−1.57850e12	−0.210878
$727$	−8.00586e12	−1.06293	−0.531463	−	0.847082i	$-0.678358\pi$
$727$	−8.00586e12	−1.06293	−0.531463	+	0.847082i	$0.678358\pi$
$728$	−6.10144e13	−8.05084
$729$	2.82430e11	0.0370370
$730$	−9.40797e12	−1.22615
$731$	1.08924e12	0.141090
$732$	−8.37540e12	−1.07822
$733$	1.40134e13	1.79299	0.896493	−	0.443058i	$-0.146106\pi$
$733$	1.40134e13	1.79299	0.896493	+	0.443058i	$0.146106\pi$
$734$	−1.23442e13	−1.56975
$735$	1.03369e13	1.30646
$736$	−4.11835e13	−5.17337
$737$	1.19145e12	0.148755
$738$	−5.88326e12	−0.730070
$739$	−1.20312e13	−1.48392	−0.741960	−	0.670444i	$-0.766104\pi$
$739$	−1.20312e13	−1.48392	−0.741960	+	0.670444i	$0.766104\pi$
$740$	1.08580e13	1.33109
$741$	−1.18394e13	−1.44261
$742$	−3.57327e13	−4.32761
$743$	−6.82684e12	−0.821808	−0.410904	−	0.911679i	$-0.634787\pi$
$743$	−6.82684e12	−0.821808	−0.410904	+	0.911679i	$0.634787\pi$
$744$	4.34586e12	0.519993
$745$	1.12248e13	1.33498
$746$	8.85347e12	1.04662
$747$	−8.23680e10	−0.00967867
$748$	−2.02813e13	−2.36885
$749$	−3.67677e12	−0.426872
$750$	7.63763e12	0.881420
$751$	1.18371e13	1.35789	0.678944	−	0.734190i	$-0.262438\pi$
$751$	1.18371e13	1.35789	0.678944	+	0.734190i	$0.262438\pi$
$752$	6.02894e12	0.687481
$753$	7.18952e12	0.814934
$754$	−4.40122e13	−4.95909
$755$	−7.01156e12	−0.785332
$756$	−8.07565e12	−0.899144
$757$	5.81566e12	0.643676	0.321838	−	0.946795i	$-0.395699\pi$
$757$	5.81566e12	0.643676	0.321838	+	0.946795i	$0.395699\pi$
$758$	−3.25064e12	−0.357650
$759$	8.09172e12	0.885020
$760$	−6.07846e13	−6.60894
$761$	−5.38603e12	−0.582154	−0.291077	−	0.956700i	$-0.594014\pi$
$761$	−5.38603e12	−0.582154	−0.291077	+	0.956700i	$0.594014\pi$
$762$	1.83955e12	0.197658
$763$	−1.64610e13	−1.75831
$764$	−1.98775e13	−2.11077
$765$	−2.89576e12	−0.305693
$766$	1.22323e13	1.28374
$767$	−1.77136e12	−0.184811
$768$	1.28042e13	1.32809
$769$	4.49355e12	0.463363	0.231681	−	0.972792i	$-0.425577\pi$
$769$	4.49355e12	0.463363	0.231681	+	0.972792i	$0.425577\pi$
$770$	4.04124e13	4.14291
$771$	7.65936e12	0.780634
$772$	−3.05437e13	−3.09488
$773$	8.71587e12	0.878017	0.439008	−	0.898483i	$-0.355330\pi$
$773$	8.71587e12	0.878017	0.439008	+	0.898483i	$0.355330\pi$
$774$	1.12662e12	0.112835
$775$	−8.42881e11	−0.0839283
$776$	3.96847e12	0.392867
$777$	−4.35762e12	−0.428899
$778$	−1.75456e13	−1.71696
$779$	2.05816e13	2.00244
$780$	−2.62071e13	−2.53509
$781$	−1.39662e13	−1.34323
$782$	2.27046e13	2.17112
$783$	−3.67294e12	−0.349209
$784$	7.57909e13	7.16465
$785$	1.13949e13	1.07102
$786$	−1.36436e13	−1.27505
$787$	−1.99079e13	−1.84986	−0.924930	−	0.380137i	$-0.875877\pi$
$787$	−1.99079e13	−1.84986	−0.924930	+	0.380137i	$0.875877\pi$
$788$	−4.49800e13	−4.15577
$789$	−8.14052e12	−0.747835
$790$	−9.90353e12	−0.904624
$791$	5.75479e12	0.522679
$792$	−1.32265e13	−1.19449
$793$	1.09080e13	0.979526
$794$	5.03560e12	0.449634
$795$	−9.67716e12	−0.859203
$796$	−2.15247e13	−1.90033
$797$	−2.67783e11	−0.0235082	−0.0117541	−	0.999931i	$-0.503742\pi$
$797$	−2.67783e11	−0.0235082	−0.0117541	+	0.999931i	$0.503742\pi$
$798$	3.86897e13	3.37740
$799$	−1.75630e12	−0.152454
$800$	−1.30562e13	−1.12697
$801$	−5.30259e12	−0.455137
$802$	2.47448e13	2.11203
$803$	7.16158e12	0.607839
$804$	2.52490e12	0.213104
$805$	−3.30351e13	−2.77265
$806$	−8.97675e12	−0.749224
$807$	−5.61979e11	−0.0466433
$808$	7.28174e13	6.01013
$809$	−5.14983e12	−0.422693	−0.211346	−	0.977411i	$-0.567785\pi$
$809$	−5.14983e12	−0.422693	−0.211346	+	0.977411i	$0.567785\pi$
$810$	−2.99514e12	−0.244475
$811$	−6.19815e12	−0.503116	−0.251558	−	0.967842i	$-0.580943\pi$
$811$	−6.19815e12	−0.503116	−0.251558	+	0.967842i	$0.580943\pi$
$812$	1.05022e14	8.47772
$813$	7.77652e12	0.624278
$814$	−1.13193e13	−0.903673
$815$	−2.41562e13	−1.91787
$816$	−2.12319e13	−1.67642
$817$	−3.94130e12	−0.309486
$818$	1.88780e13	1.47424
$819$	1.05176e13	0.816845
$820$	4.55583e13	3.51889
$821$	6.20987e12	0.477022	0.238511	−	0.971140i	$-0.423341\pi$
$821$	6.20987e12	0.477022	0.238511	+	0.971140i	$0.423341\pi$
$822$	5.77895e11	0.0441495
$823$	−1.59932e13	−1.21517	−0.607584	−	0.794255i	$-0.707861\pi$
$823$	−1.59932e13	−1.21517	−0.607584	+	0.794255i	$0.707861\pi$
$824$	1.42759e13	1.07877
$825$	2.56528e12	0.192794
$826$	5.78858e12	0.432675
$827$	2.11594e12	0.157300	0.0786500	−	0.996902i	$-0.474939\pi$
$827$	2.11594e12	0.157300	0.0786500	+	0.996902i	$0.474939\pi$
$828$	1.71479e13	1.26787
$829$	−1.83713e13	−1.35097	−0.675484	−	0.737374i	$-0.736065\pi$
$829$	−1.83713e13	−1.35097	−0.675484	+	0.737374i	$0.736065\pi$
$830$	8.73504e11	0.0638872
$831$	−1.47450e13	−1.07261
$832$	−6.80528e13	−4.92369
$833$	−2.20788e13	−1.58881
$834$	−1.77406e13	−1.26976
$835$	−1.08152e13	−0.769920
$836$	7.33854e13	5.19615
$837$	−7.49135e11	−0.0527588
$838$	3.96581e13	2.77801
$839$	−1.08393e13	−0.755221	−0.377611	−	0.925964i	$-0.623254\pi$
$839$	−1.08393e13	−0.755221	−0.377611	+	0.925964i	$0.623254\pi$
$840$	5.39983e13	3.74217
$841$	3.32587e13	2.29257
$842$	−2.31239e13	−1.58547
$843$	−1.40899e13	−0.960910
$844$	1.02788e13	0.697274
$845$	1.71942e13	1.16018
$846$	−1.81658e12	−0.121923
$847$	−4.90561e12	−0.327505
$848$	−7.09536e13	−4.71187
$849$	−1.55507e13	−1.02723
$850$	7.19794e12	0.472959
$851$	9.25301e12	0.604784
$852$	−2.95971e13	−1.92429
$853$	1.39415e13	0.901649	0.450825	−	0.892613i	$-0.351130\pi$
$853$	1.39415e13	0.901649	0.450825	+	0.892613i	$0.351130\pi$
$854$	−3.56459e13	−2.29324
$855$	1.04780e13	0.670548
$856$	−1.27616e13	−0.812403
$857$	−4.55558e12	−0.288489	−0.144245	−	0.989542i	$-0.546075\pi$
$857$	−4.55558e12	−0.288489	−0.144245	+	0.989542i	$0.546075\pi$
$858$	2.73205e13	1.72106
$859$	1.96628e13	1.23218	0.616092	−	0.787674i	$-0.288715\pi$
$859$	1.96628e13	1.23218	0.616092	+	0.787674i	$0.288715\pi$
$860$	−8.72426e12	−0.543858
$861$	−1.82838e13	−1.13384
$862$	4.58212e13	2.82673
$863$	1.15472e13	0.708644	0.354322	−	0.935123i	$-0.384712\pi$
$863$	1.15472e13	0.708644	0.354322	+	0.935123i	$0.384712\pi$
$864$	−1.16041e13	−0.708435
$865$	−1.99848e12	−0.121375
$866$	−1.45009e13	−0.876119
$867$	−3.42050e12	−0.205591
$868$	2.14204e13	1.28082
$869$	7.53881e12	0.448450
$870$	3.89512e13	2.30507
$871$	−3.28839e12	−0.193598
$872$	−5.71340e13	−3.34634
$873$	−6.84081e11	−0.0398606
$874$	−8.21540e13	−4.76242
$875$	2.37359e13	1.36890
$876$	1.51767e13	0.870783
$877$	2.43420e13	1.38950	0.694750	−	0.719251i	$-0.255515\pi$
$877$	2.43420e13	1.38950	0.694750	+	0.719251i	$0.255515\pi$
$878$	5.83879e13	3.31587
$879$	−4.40968e12	−0.249148
$880$	8.02459e13	4.51077
$881$	1.12417e13	0.628698	0.314349	−	0.949308i	$-0.398214\pi$
$881$	1.12417e13	0.628698	0.314349	+	0.949308i	$0.398214\pi$
$882$	−2.28365e13	−1.27064
$883$	1.39656e13	0.773101	0.386550	−	0.922268i	$-0.373667\pi$
$883$	1.39656e13	0.773101	0.386550	+	0.922268i	$0.373667\pi$
$884$	5.59763e13	3.08297
$885$	1.56767e12	0.0859032
$886$	−8.76425e12	−0.477819
$887$	−2.71387e13	−1.47208	−0.736042	−	0.676936i	$-0.763307\pi$
$887$	−2.71387e13	−1.47208	−0.736042	+	0.676936i	$0.763307\pi$
$888$	−1.51247e13	−0.816260
$889$	5.71687e12	0.306973
$890$	5.62335e13	3.00428
$891$	2.27997e12	0.121194
$892$	4.15457e13	2.19727
$893$	6.35498e12	0.334413
$894$	−2.47980e13	−1.29837
$895$	−2.62497e13	−1.36748
$896$	9.97922e13	5.17262
$897$	−2.23332e13	−1.15182
$898$	2.80016e13	1.43694
$899$	9.74235e12	0.497445
$900$	5.43632e12	0.276194
$901$	2.06697e13	1.04489
$902$	−4.74939e13	−2.38896
$903$	3.50128e12	0.175239
$904$	1.99741e13	0.994739
$905$	−7.02832e10	−0.00348283
$906$	1.54901e13	0.763796
$907$	−2.64168e13	−1.29613	−0.648065	−	0.761585i	$-0.724421\pi$
$907$	−2.64168e13	−1.29613	−0.648065	+	0.761585i	$0.724421\pi$
$908$	5.46385e13	2.66755
$909$	−1.25522e13	−0.609792
$910$	−1.11538e14	−5.39185
$911$	2.67036e13	1.28451	0.642255	−	0.766491i	$-0.277999\pi$
$911$	2.67036e13	1.28451	0.642255	+	0.766491i	$0.277999\pi$
$912$	7.68253e13	3.67729
$913$	−6.64933e11	−0.0316708
$914$	−6.23888e13	−2.95698
$915$	−9.65367e12	−0.455300
$916$	−1.44104e13	−0.676310
$917$	−4.24009e13	−1.98022
$918$	6.39738e12	0.297310
$919$	4.08123e12	0.188743	0.0943715	−	0.995537i	$-0.469916\pi$
$919$	4.08123e12	0.188743	0.0943715	+	0.995537i	$0.469916\pi$
$920$	−1.14660e14	−5.27677
$921$	−5.36898e12	−0.245880
$922$	−2.00073e13	−0.911799
$923$	3.85469e13	1.74816
$924$	−6.51923e13	−2.94220
$925$	2.93344e12	0.131747
$926$	−8.32216e13	−3.71952
$927$	−2.46086e12	−0.109453
$928$	1.50909e14	6.67959
$929$	−6.82957e12	−0.300831	−0.150416	−	0.988623i	$-0.548061\pi$
$929$	−6.82957e12	−0.300831	−0.150416	+	0.988623i	$0.548061\pi$
$930$	7.94450e12	0.348252
$931$	7.98897e13	3.48512
$932$	−9.64240e13	−4.18614
$933$	6.53709e11	0.0282434
$934$	1.82708e13	0.785593
$935$	−2.33766e13	−1.00030
$936$	3.65052e13	1.55458
$937$	1.15809e13	0.490812	0.245406	−	0.969420i	$-0.421079\pi$
$937$	1.15809e13	0.490812	0.245406	+	0.969420i	$0.421079\pi$
$938$	1.07460e13	0.453248
$939$	1.25396e12	0.0526368
$940$	1.40671e13	0.587663
$941$	3.00051e13	1.24750	0.623752	−	0.781622i	$-0.285608\pi$
$941$	3.00051e13	1.24750	0.623752	+	0.781622i	$0.285608\pi$
$942$	−2.51740e13	−1.04165
$943$	3.88239e13	1.59881
$944$	1.14943e13	0.471093
$945$	−9.30817e12	−0.379683
$946$	9.09491e12	0.369223
$947$	3.23056e13	1.30528	0.652640	−	0.757668i	$-0.273662\pi$
$947$	3.23056e13	1.30528	0.652640	+	0.757668i	$0.273662\pi$
$948$	1.59762e13	0.642443
$949$	−1.97660e13	−0.791080
$950$	−2.60449e13	−1.03745
$951$	−2.67290e13	−1.05967
$952$	−1.15336e14	−4.55092
$953$	2.22295e13	0.872994	0.436497	−	0.899706i	$-0.356219\pi$
$953$	2.22295e13	0.872994	0.436497	+	0.899706i	$0.356219\pi$
$954$	2.13790e13	0.835641
$955$	−2.29112e13	−0.891319
$956$	−5.67050e13	−2.19564
$957$	−2.96506e13	−1.14269
$958$	9.20356e13	3.53030
$959$	1.79596e12	0.0685666
$960$	6.02273e13	2.28862
$961$	−2.44526e13	−0.924846
$962$	3.12414e13	1.17610
$963$	2.19982e12	0.0824270
$964$	−9.56264e13	−3.56641
$965$	−3.52053e13	−1.30688
$966$	7.29820e13	2.69661
$967$	−3.16973e13	−1.16574	−0.582872	−	0.812564i	$-0.698071\pi$
$967$	−3.16973e13	−1.16574	−0.582872	+	0.812564i	$0.698071\pi$
$968$	−1.70267e13	−0.623291
$969$	−2.23801e13	−0.815466
$970$	7.25461e12	0.263113
$971$	3.75422e13	1.35529	0.677647	−	0.735387i	$-0.263000\pi$
$971$	3.75422e13	1.35529	0.677647	+	0.735387i	$0.263000\pi$
$972$	4.83169e12	0.173620
$973$	−5.51335e13	−1.97200
$974$	2.58731e13	0.921156
$975$	−7.08019e12	−0.250914
$976$	−7.07814e13	−2.49686
$977$	9.74926e11	0.0342331	0.0171166	−	0.999854i	$-0.494551\pi$
$977$	9.74926e11	0.0342331	0.0171166	+	0.999854i	$0.494551\pi$
$978$	5.33664e13	1.86528
$979$	−4.28063e13	−1.48931
$980$	1.76840e14	6.12438
$981$	9.84870e12	0.339522
$982$	2.62875e13	0.902086
$983$	−2.80063e13	−0.956676	−0.478338	−	0.878176i	$-0.658761\pi$
$983$	−2.80063e13	−0.956676	−0.478338	+	0.878176i	$0.658761\pi$
$984$	−6.34605e13	−2.15787
$985$	−5.18449e13	−1.75486
$986$	−8.31966e13	−2.80324
$987$	−5.64549e12	−0.189354
$988$	−2.02544e14	−6.76259
$989$	−7.43465e12	−0.247102
$990$	−2.41789e13	−0.799977
$991$	3.41237e13	1.12389	0.561947	−	0.827173i	$-0.310053\pi$
$991$	3.41237e13	1.12389	0.561947	+	0.827173i	$0.310053\pi$
$992$	3.07795e13	1.00916
$993$	−1.14647e13	−0.374188
$994$	−1.25966e14	−4.09275
$995$	−2.48099e13	−0.802455
$996$	−1.40912e12	−0.0453712
$997$	1.72440e13	0.552724	0.276362	−	0.961054i	$-0.410871\pi$
$997$	1.72440e13	0.552724	0.276362	+	0.961054i	$0.410871\pi$
$998$	1.02614e14	3.27432
$999$	2.60718e12	0.0828184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.2	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-43.5628 q^{2} +81.0000 q^{3} +1385.72 q^{4} +1597.21 q^{5} -3528.58 q^{6} -10966.0 q^{7} -38061.5 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-43.5628 q^{2} +81.0000 q^{3} +1385.72 q^{4} +1597.21 q^{5} -3528.58 q^{6} -10966.0 q^{7} -38061.5 q^{8} +6561.00 q^{9} -69578.8 q^{10} +52965.0 q^{11} +112243. q^{12} -146184. q^{13} +477709. q^{14} +129374. q^{15} +948577. q^{16} -276332. q^{17} -285815. q^{18} +999877. q^{19} +2.21327e6 q^{20} -888246. q^{21} -2.30730e6 q^{22} +1.88611e6 q^{23} -3.08298e6 q^{24} +597945. q^{25} +6.36817e6 q^{26} +531441. q^{27} -1.51958e7 q^{28} -6.91128e6 q^{29} -5.63588e6 q^{30} -1.40963e6 q^{31} -2.18352e7 q^{32} +4.29017e6 q^{33} +1.20378e7 q^{34} -1.75150e7 q^{35} +9.09168e6 q^{36} +4.90587e6 q^{37} -4.35574e7 q^{38} -1.18409e7 q^{39} -6.07921e7 q^{40} +2.05841e7 q^{41} +3.86945e7 q^{42} -3.94179e6 q^{43} +7.33945e7 q^{44} +1.04793e7 q^{45} -8.21642e7 q^{46} +6.35577e6 q^{47} +7.68347e7 q^{48} +7.98995e7 q^{49} -2.60481e7 q^{50} -2.23829e7 q^{51} -2.02569e8 q^{52} -7.48000e7 q^{53} -2.31510e7 q^{54} +8.45961e7 q^{55} +4.17382e8 q^{56} +8.09900e7 q^{57} +3.01075e8 q^{58} +1.21174e7 q^{59} +1.79275e8 q^{60} -7.46185e7 q^{61} +6.14074e7 q^{62} -7.19479e7 q^{63} +4.65530e8 q^{64} -2.33486e8 q^{65} -1.86892e8 q^{66} +2.24949e7 q^{67} -3.82918e8 q^{68} +1.52775e8 q^{69} +7.63001e8 q^{70} -2.63688e8 q^{71} -2.49721e8 q^{72} +1.35213e8 q^{73} -2.13714e8 q^{74} +4.84335e7 q^{75} +1.38554e9 q^{76} -5.80815e8 q^{77} +5.15821e8 q^{78} +1.42336e8 q^{79} +1.51507e9 q^{80} +4.30467e7 q^{81} -8.96702e8 q^{82} -1.25542e7 q^{83} -1.23086e9 q^{84} -4.41360e8 q^{85} +1.71715e8 q^{86} -5.59814e8 q^{87} -2.01593e9 q^{88} -8.08199e8 q^{89} -4.56506e8 q^{90} +1.60305e9 q^{91} +2.61361e9 q^{92} -1.14180e8 q^{93} -2.76875e8 q^{94} +1.59701e9 q^{95} -1.76865e9 q^{96} -1.04265e8 q^{97} -3.48065e9 q^{98} +3.47504e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \)	\( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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