LMFDB - Embedded newform 177.10.a.d.1.1

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:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-39.7571 q^{2} +81.0000 q^{3} +1068.63 q^{4} -1871.54 q^{5} -3220.33 q^{6} -43.1074 q^{7} -22129.9 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-39.7571 q^{2} +81.0000 q^{3} +1068.63 q^{4} -1871.54 q^{5} -3220.33 q^{6} -43.1074 q^{7} -22129.9 q^{8} +6561.00 q^{9} +74407.2 q^{10} +76107.0 q^{11} +86558.9 q^{12} -43732.0 q^{13} +1713.83 q^{14} -151595. q^{15} +332685. q^{16} +420385. q^{17} -260846. q^{18} -333780. q^{19} -1.99999e6 q^{20} -3491.70 q^{21} -3.02579e6 q^{22} -114536. q^{23} -1.79253e6 q^{24} +1.54955e6 q^{25} +1.73866e6 q^{26} +531441. q^{27} -46065.8 q^{28} +2.58705e6 q^{29} +6.02699e6 q^{30} -1.72886e6 q^{31} -1.89606e6 q^{32} +6.16467e6 q^{33} -1.67133e7 q^{34} +80677.4 q^{35} +7.01127e6 q^{36} +4.90694e6 q^{37} +1.32701e7 q^{38} -3.54229e6 q^{39} +4.14172e7 q^{40} +7.23989e6 q^{41} +138820. q^{42} -8.98509e6 q^{43} +8.13301e7 q^{44} -1.22792e7 q^{45} +4.55360e6 q^{46} +5.61464e7 q^{47} +2.69475e7 q^{48} -4.03517e7 q^{49} -6.16058e7 q^{50} +3.40512e7 q^{51} -4.67333e7 q^{52} -9.20424e7 q^{53} -2.11286e7 q^{54} -1.42438e8 q^{55} +953964. q^{56} -2.70362e7 q^{57} -1.02854e8 q^{58} -1.21174e7 q^{59} -1.61999e8 q^{60} -8.95394e7 q^{61} +6.87344e7 q^{62} -282828. q^{63} -9.49527e7 q^{64} +8.18464e7 q^{65} -2.45089e8 q^{66} -1.59831e8 q^{67} +4.49235e8 q^{68} -9.27738e6 q^{69} -3.20750e6 q^{70} +1.68944e8 q^{71} -1.45195e8 q^{72} -1.57076e8 q^{73} -1.95086e8 q^{74} +1.25514e8 q^{75} -3.56687e8 q^{76} -3.28077e6 q^{77} +1.40831e8 q^{78} +5.77979e8 q^{79} -6.22635e8 q^{80} +4.30467e7 q^{81} -2.87837e8 q^{82} -4.29141e8 q^{83} -3.73133e6 q^{84} -7.86769e8 q^{85} +3.57221e8 q^{86} +2.09551e8 q^{87} -1.68424e9 q^{88} -6.09435e8 q^{89} +4.88186e8 q^{90} +1.88517e6 q^{91} -1.22396e8 q^{92} -1.40037e8 q^{93} -2.23222e9 q^{94} +6.24684e8 q^{95} -1.53581e8 q^{96} +1.42423e9 q^{97} +1.60427e9 q^{98} +4.99338e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) $	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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 $

$2$	−39.7571	−1.75703	−0.878516	−	0.477712i	$-0.841466\pi$
$2$	−39.7571	−1.75703	−0.878516	+	0.477712i	$0.841466\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	1068.63	2.08716
$5$	−1871.54	−1.33917	−0.669584	−	0.742736i	$-0.733528\pi$
$5$	−1871.54	−1.33917	−0.669584	+	0.742736i	$0.733528\pi$
$6$	−3220.33	−1.01442
$7$	−43.1074	−0.00678595	−0.00339298	−	0.999994i	$-0.501080\pi$
$7$	−43.1074	−0.00678595	−0.00339298	+	0.999994i	$0.501080\pi$
$8$	−22129.9	−1.91018
$9$	6561.00	0.333333
$10$	74407.2	2.35296
$11$	76107.0	1.56732	0.783659	−	0.621191i	$-0.213351\pi$
$11$	76107.0	1.56732	0.783659	+	0.621191i	$0.213351\pi$
$12$	86558.9	1.20503
$13$	−43732.0	−0.424673	−0.212336	−	0.977197i	$-0.568107\pi$
$13$	−43732.0	−0.424673	−0.212336	+	0.977197i	$0.568107\pi$
$14$	1713.83	0.0119231
$15$	−151595.	−0.773169
$16$	332685.	1.26909
$17$	420385.	1.22075	0.610375	−	0.792113i	$-0.291019\pi$
$17$	420385.	1.22075	0.610375	+	0.792113i	$0.291019\pi$
$18$	−260846.	−0.585678
$19$	−333780.	−0.587583	−0.293791	−	0.955870i	$-0.594917\pi$
$19$	−333780.	−0.587583	−0.293791	+	0.955870i	$0.594917\pi$
$20$	−1.99999e6	−2.79507
$21$	−3491.70	−0.00391787
$22$	−3.02579e6	−2.75383
$23$	−114536.	−0.0853424	−0.0426712	−	0.999089i	$-0.513587\pi$
$23$	−114536.	−0.0853424	−0.0426712	+	0.999089i	$0.513587\pi$
$24$	−1.79253e6	−1.10285
$25$	1.54955e6	0.793372
$26$	1.73866e6	0.746164
$27$	531441.	0.192450
$28$	−46065.8	−0.0141634
$29$	2.58705e6	0.679226	0.339613	−	0.940565i	$-0.389704\pi$
$29$	2.58705e6	0.679226	0.339613	+	0.940565i	$0.389704\pi$
$30$	6.02699e6	1.35848
$31$	−1.72886e6	−0.336226	−0.168113	−	0.985768i	$-0.553767\pi$
$31$	−1.72886e6	−0.336226	−0.168113	+	0.985768i	$0.553767\pi$
$32$	−1.89606e6	−0.319652
$33$	6.16467e6	0.904892
$34$	−1.67133e7	−2.14490
$35$	80677.4	0.00908753
$36$	7.01127e6	0.695722
$37$	4.90694e6	0.430430	0.215215	−	0.976567i	$-0.430955\pi$
$37$	4.90694e6	0.430430	0.215215	+	0.976567i	$0.430955\pi$
$38$	1.32701e7	1.03240
$39$	−3.54229e6	−0.245185
$40$	4.14172e7	2.55806
$41$	7.23989e6	0.400133	0.200067	−	0.979782i	$-0.435884\pi$
$41$	7.23989e6	0.400133	0.200067	+	0.979782i	$0.435884\pi$
$42$	138820.	0.00688383
$43$	−8.98509e6	−0.400788	−0.200394	−	0.979715i	$-0.564222\pi$
$43$	−8.98509e6	−0.400788	−0.200394	+	0.979715i	$0.564222\pi$
$44$	8.13301e7	3.27125
$45$	−1.22792e7	−0.446389
$46$	4.55360e6	0.149949
$47$	5.61464e7	1.67835	0.839174	−	0.543864i	$-0.183039\pi$
$47$	5.61464e7	1.67835	0.839174	+	0.543864i	$0.183039\pi$
$48$	2.69475e7	0.732711
$49$	−4.03517e7	−0.999954
$50$	−6.16058e7	−1.39398
$51$	3.40512e7	0.704800
$52$	−4.67333e7	−0.886362
$53$	−9.20424e7	−1.60231	−0.801155	−	0.598457i	$-0.795781\pi$
$53$	−9.20424e7	−1.60231	−0.801155	+	0.598457i	$0.795781\pi$
$54$	−2.11286e7	−0.338141
$55$	−1.42438e8	−2.09890
$56$	953964.	0.0129624
$57$	−2.70362e7	−0.339241
$58$	−1.02854e8	−1.19342
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−1.61999e8	−1.61373
$61$	−8.95394e7	−0.827999	−0.413999	−	0.910277i	$-0.635868\pi$
$61$	−8.95394e7	−0.827999	−0.413999	+	0.910277i	$0.635868\pi$
$62$	6.87344e7	0.590761
$63$	−282828.	−0.00226198
$64$	−9.49527e7	−0.707453
$65$	8.18464e7	0.568708
$66$	−2.45089e8	−1.58993
$67$	−1.59831e8	−0.969004	−0.484502	−	0.874790i	$-0.660999\pi$
$67$	−1.59831e8	−0.969004	−0.484502	+	0.874790i	$0.660999\pi$
$68$	4.49235e8	2.54791
$69$	−9.27738e6	−0.0492725
$70$	−3.20750e6	−0.0159671
$71$	1.68944e8	0.789007	0.394504	−	0.918894i	$-0.370917\pi$
$71$	1.68944e8	0.789007	0.394504	+	0.918894i	$0.370917\pi$
$72$	−1.45195e8	−0.636728
$73$	−1.57076e8	−0.647378	−0.323689	−	0.946163i	$-0.604923\pi$
$73$	−1.57076e8	−0.647378	−0.323689	+	0.946163i	$0.604923\pi$
$74$	−1.95086e8	−0.756281
$75$	1.25514e8	0.458054
$76$	−3.56687e8	−1.22638
$77$	−3.28077e6	−0.0106357
$78$	1.40831e8	0.430798
$79$	5.77979e8	1.66951	0.834757	−	0.550619i	$-0.185608\pi$
$79$	5.77979e8	1.66951	0.834757	+	0.550619i	$0.185608\pi$
$80$	−6.22635e8	−1.69953
$81$	4.30467e7	0.111111
$82$	−2.87837e8	−0.703047
$83$	−4.29141e8	−0.992541	−0.496270	−	0.868168i	$-0.665297\pi$
$83$	−4.29141e8	−0.992541	−0.496270	+	0.868168i	$0.665297\pi$
$84$	−3.73133e6	−0.00817724
$85$	−7.86769e8	−1.63479
$86$	3.57221e8	0.704197
$87$	2.09551e8	0.392151
$88$	−1.68424e9	−2.99387
$89$	−6.09435e8	−1.02961	−0.514805	−	0.857308i	$-0.672135\pi$
$89$	−6.09435e8	−1.02961	−0.514805	+	0.857308i	$0.672135\pi$
$90$	4.88186e8	0.784321
$91$	1.88517e6	0.00288181
$92$	−1.22396e8	−0.178124
$93$	−1.40037e8	−0.194120
$94$	−2.23222e9	−2.94891
$95$	6.24684e8	0.786872
$96$	−1.53581e8	−0.184551
$97$	1.42423e9	1.63345	0.816727	−	0.577025i	$-0.195786\pi$
$97$	1.42423e9	1.63345	0.816727	+	0.577025i	$0.195786\pi$
$98$	1.60427e9	1.75695
$99$	4.99338e8	0.522440
$100$	1.65590e9	1.65590
$101$	−2.28375e8	−0.218374	−0.109187	−	0.994021i	$-0.534825\pi$
$101$	−2.28375e8	−0.218374	−0.109187	+	0.994021i	$0.534825\pi$
$102$	−1.35378e9	−1.23836
$103$	1.56336e9	1.36864	0.684321	−	0.729180i	$-0.260099\pi$
$103$	1.56336e9	1.36864	0.684321	+	0.729180i	$0.260099\pi$
$104$	9.67787e8	0.811203
$105$	6.53487e6	0.00524669
$106$	3.65934e9	2.81531
$107$	−1.24104e9	−0.915288	−0.457644	−	0.889136i	$-0.651307\pi$
$107$	−1.24104e9	−0.915288	−0.457644	+	0.889136i	$0.651307\pi$
$108$	5.67913e8	0.401675
$109$	−2.59764e9	−1.76263	−0.881314	−	0.472532i	$-0.843340\pi$
$109$	−2.59764e9	−1.76263	−0.881314	+	0.472532i	$0.843340\pi$
$110$	5.66291e9	3.68784
$111$	3.97462e8	0.248509
$112$	−1.43412e7	−0.00861200
$113$	6.59340e7	0.0380414	0.0190207	−	0.999819i	$-0.493945\pi$
$113$	6.59340e7	0.0380414	0.0190207	+	0.999819i	$0.493945\pi$
$114$	1.07488e9	0.596058
$115$	2.14358e8	0.114288
$116$	2.76460e9	1.41766
$117$	−2.86926e8	−0.141558
$118$	4.81751e8	0.228746
$119$	−1.81217e7	−0.00828395
$120$	3.35479e9	1.47690
$121$	3.43432e9	1.45649
$122$	3.55983e9	1.45482
$123$	5.86431e8	0.231017
$124$	−1.84751e9	−0.701760
$125$	7.55300e8	0.276710
$126$	1.12444e7	0.00397438
$127$	9.03648e8	0.308235	0.154118	−	0.988052i	$-0.450747\pi$
$127$	9.03648e8	0.308235	0.154118	+	0.988052i	$0.450747\pi$
$128$	4.74583e9	1.56267
$129$	−7.27792e8	−0.231395
$130$	−3.25398e9	−0.999239
$131$	−1.48993e9	−0.442024	−0.221012	−	0.975271i	$-0.570936\pi$
$131$	−1.48993e9	−0.442024	−0.221012	+	0.975271i	$0.570936\pi$
$132$	6.58774e9	1.88866
$133$	1.43884e7	0.00398731
$134$	6.35444e9	1.70257
$135$	−9.94616e8	−0.257723
$136$	−9.30309e9	−2.33186
$137$	3.80197e9	0.922074	0.461037	−	0.887381i	$-0.347478\pi$
$137$	3.80197e9	0.922074	0.461037	+	0.887381i	$0.347478\pi$
$138$	3.68842e8	0.0865734
$139$	−3.94690e8	−0.0896788	−0.0448394	−	0.998994i	$-0.514278\pi$
$139$	−3.94690e8	−0.0896788	−0.0448394	+	0.998994i	$0.514278\pi$
$140$	8.62142e7	0.0189672
$141$	4.54786e9	0.968994
$142$	−6.71674e9	−1.38631
$143$	−3.32831e9	−0.665598
$144$	2.18275e9	0.423031
$145$	−4.84178e9	−0.909598
$146$	6.24491e9	1.13746
$147$	−3.26849e9	−0.577324
$148$	5.24370e9	0.898379
$149$	2.09979e9	0.349009	0.174505	−	0.984656i	$-0.444168\pi$
$149$	2.09979e9	0.349009	0.174505	+	0.984656i	$0.444168\pi$
$150$	−4.99007e9	−0.804815
$151$	5.15317e9	0.806638	0.403319	−	0.915060i	$-0.367857\pi$
$151$	5.15317e9	0.806638	0.403319	+	0.915060i	$0.367857\pi$
$152$	7.38653e9	1.12239
$153$	2.75814e9	0.406917
$154$	1.30434e8	0.0186874
$155$	3.23563e9	0.450264
$156$	−3.78540e9	−0.511741
$157$	6.27151e9	0.823804	0.411902	−	0.911228i	$-0.364865\pi$
$157$	6.27151e9	0.823804	0.411902	+	0.911228i	$0.364865\pi$
$158$	−2.29788e10	−2.93339
$159$	−7.45544e9	−0.925094
$160$	3.54856e9	0.428068
$161$	4.93733e6	0.000579129 0
$162$	−1.71141e9	−0.195226
$163$	2.97767e9	0.330394	0.165197	−	0.986261i	$-0.447174\pi$
$163$	2.97767e9	0.330394	0.165197	+	0.986261i	$0.447174\pi$
$164$	7.73675e9	0.835144
$165$	−1.15374e10	−1.21180
$166$	1.70614e10	1.74393
$167$	−1.67149e9	−0.166295	−0.0831474	−	0.996537i	$-0.526497\pi$
$167$	−1.67149e9	−0.166295	−0.0831474	+	0.996537i	$0.526497\pi$
$168$	7.72711e7	0.00748385
$169$	−8.69201e9	−0.819653
$170$	3.12797e10	2.87238
$171$	−2.18993e9	−0.195861
$172$	−9.60172e9	−0.836510
$173$	1.34059e10	1.13786	0.568929	−	0.822387i	$-0.307358\pi$
$173$	1.34059e10	1.13786	0.568929	+	0.822387i	$0.307358\pi$
$174$	−8.33115e9	−0.689023
$175$	−6.67973e7	−0.00538378
$176$	2.53196e10	1.98907
$177$	−9.81506e8	−0.0751646
$178$	2.42294e10	1.80906
$179$	−1.19814e10	−0.872307	−0.436154	−	0.899872i	$-0.643660\pi$
$179$	−1.19814e10	−0.872307	−0.436154	+	0.899872i	$0.643660\pi$
$180$	−1.31219e10	−0.931688
$181$	1.22163e10	0.846027	0.423014	−	0.906123i	$-0.360972\pi$
$181$	1.22163e10	0.846027	0.423014	+	0.906123i	$0.360972\pi$
$182$	−7.49491e7	−0.00506343
$183$	−7.25269e9	−0.478045
$184$	2.53466e9	0.163020
$185$	−9.18356e9	−0.576419
$186$	5.56749e9	0.341076
$187$	3.19942e10	1.91330
$188$	5.99997e10	3.50299
$189$	−2.29090e7	−0.00130596
$190$	−2.48356e10	−1.38256
$191$	1.63472e10	0.888779	0.444390	−	0.895834i	$-0.353421\pi$
$191$	1.63472e10	0.888779	0.444390	+	0.895834i	$0.353421\pi$
$192$	−7.69117e9	−0.408448
$193$	3.04342e10	1.57890	0.789448	−	0.613817i	$-0.210367\pi$
$193$	3.04342e10	1.57890	0.789448	+	0.613817i	$0.210367\pi$
$194$	−5.66232e10	−2.87003
$195$	6.62956e9	0.328344
$196$	−4.31210e10	−2.08707
$197$	1.94201e10	0.918656	0.459328	−	0.888267i	$-0.348090\pi$
$197$	1.94201e10	0.918656	0.459328	+	0.888267i	$0.348090\pi$
$198$	−1.98522e10	−0.917944
$199$	1.94633e10	0.879786	0.439893	−	0.898050i	$-0.355016\pi$
$199$	1.94633e10	0.879786	0.439893	+	0.898050i	$0.355016\pi$
$200$	−3.42916e10	−1.51549
$201$	−1.29463e10	−0.559455
$202$	9.07952e9	0.383691
$203$	−1.11521e8	−0.00460919
$204$	3.63880e10	1.47103
$205$	−1.35498e10	−0.535846
$206$	−6.21545e10	−2.40475
$207$	−7.51468e8	−0.0284475
$208$	−1.45490e10	−0.538949
$209$	−2.54030e10	−0.920929
$210$	−2.59808e8	−0.00921860
$211$	−9.77363e9	−0.339457	−0.169728	−	0.985491i	$-0.554289\pi$
$211$	−9.77363e9	−0.339457	−0.169728	+	0.985491i	$0.554289\pi$
$212$	−9.83591e10	−3.34429
$213$	1.36845e10	0.455534
$214$	4.93400e10	1.60819
$215$	1.68160e10	0.536722
$216$	−1.17608e10	−0.367615
$217$	7.45266e7	0.00228161
$218$	1.03275e11	3.09699
$219$	−1.27232e10	−0.373764
$220$	−1.52213e11	−4.38076
$221$	−1.83843e10	−0.518419
$222$	−1.58020e10	−0.436639
$223$	−1.07041e10	−0.289853	−0.144926	−	0.989442i	$-0.546295\pi$
$223$	−1.07041e10	−0.289853	−0.144926	+	0.989442i	$0.546295\pi$
$224$	8.17343e7	0.00216914
$225$	1.01666e10	0.264457
$226$	−2.62134e9	−0.0668399
$227$	−7.59741e9	−0.189911	−0.0949553	−	0.995482i	$-0.530271\pi$
$227$	−7.59741e9	−0.189911	−0.0949553	+	0.995482i	$0.530271\pi$
$228$	−2.88916e10	−0.708052
$229$	3.95453e10	0.950244	0.475122	−	0.879920i	$-0.342404\pi$
$229$	3.95453e10	0.950244	0.475122	+	0.879920i	$0.342404\pi$
$230$	−8.52227e9	−0.200808
$231$	−2.65743e8	−0.00614055
$232$	−5.72513e10	−1.29745
$233$	8.75737e10	1.94658	0.973290	−	0.229581i	$-0.0737355\pi$
$233$	8.75737e10	1.94658	0.973290	+	0.229581i	$0.0737355\pi$
$234$	1.14073e10	0.248721
$235$	−1.05081e11	−2.24759
$236$	−1.29490e10	−0.271726
$237$	4.68163e10	0.963894
$238$	7.20466e8	0.0145552
$239$	3.19699e10	0.633797	0.316899	−	0.948459i	$-0.397358\pi$
$239$	3.19699e10	0.633797	0.316899	+	0.948459i	$0.397358\pi$
$240$	−5.04334e10	−0.981223
$241$	3.52544e10	0.673188	0.336594	−	0.941650i	$-0.390725\pi$
$241$	3.52544e10	0.673188	0.336594	+	0.941650i	$0.390725\pi$
$242$	−1.36539e11	−2.55910
$243$	3.48678e9	0.0641500
$244$	−9.56843e10	−1.72817
$245$	7.55201e10	1.33911
$246$	−2.33148e10	−0.405905
$247$	1.45969e10	0.249530
$248$	3.82595e10	0.642254
$249$	−3.47604e10	−0.573044
$250$	−3.00285e10	−0.486188
$251$	1.19741e10	0.190419	0.0952093	−	0.995457i	$-0.469648\pi$
$251$	1.19741e10	0.190419	0.0952093	+	0.995457i	$0.469648\pi$
$252$	−3.02238e8	−0.00472113
$253$	−8.71695e9	−0.133759
$254$	−3.59264e10	−0.541580
$255$	−6.37283e10	−0.943846
$256$	−1.40065e11	−2.03821
$257$	6.96218e10	0.995511	0.497755	−	0.867318i	$-0.334158\pi$
$257$	6.96218e10	0.995511	0.497755	+	0.867318i	$0.334158\pi$
$258$	2.89349e10	0.406568
$259$	−2.11525e8	−0.00292088
$260$	8.74634e10	1.18699
$261$	1.69736e10	0.226409
$262$	5.92354e10	0.776650
$263$	8.95325e10	1.15393	0.576965	−	0.816769i	$-0.304237\pi$
$263$	8.95325e10	1.15393	0.576965	+	0.816769i	$0.304237\pi$
$264$	−1.36424e11	−1.72851
$265$	1.72261e11	2.14576
$266$	−5.72041e8	−0.00700583
$267$	−4.93642e10	−0.594445
$268$	−1.70800e11	−2.02247
$269$	1.11073e11	1.29337	0.646685	−	0.762758i	$-0.276155\pi$
$269$	1.11073e11	1.29337	0.646685	+	0.762758i	$0.276155\pi$
$270$	3.95431e10	0.452828
$271$	−2.70781e10	−0.304970	−0.152485	−	0.988306i	$-0.548728\pi$
$271$	−2.70781e10	−0.304970	−0.152485	+	0.988306i	$0.548728\pi$
$272$	1.39856e11	1.54924
$273$	1.52699e8	0.00166381
$274$	−1.51155e11	−1.62011
$275$	1.17932e11	1.24347
$276$	−9.91407e9	−0.102840
$277$	−4.80043e10	−0.489916	−0.244958	−	0.969534i	$-0.578774\pi$
$277$	−4.80043e10	−0.489916	−0.244958	+	0.969534i	$0.578774\pi$
$278$	1.56917e10	0.157569
$279$	−1.13430e10	−0.112075
$280$	−1.78539e9	−0.0173589
$281$	−1.13338e11	−1.08442	−0.542208	−	0.840244i	$-0.682412\pi$
$281$	−1.13338e11	−1.08442	−0.542208	+	0.840244i	$0.682412\pi$
$282$	−1.80810e11	−1.70255
$283$	−6.41100e10	−0.594138	−0.297069	−	0.954856i	$-0.596009\pi$
$283$	−6.41100e10	−0.594138	−0.297069	+	0.954856i	$0.596009\pi$
$284$	1.80539e11	1.64679
$285$	5.05994e10	0.454301
$286$	1.32324e11	1.16948
$287$	−3.12093e8	−0.00271528
$288$	−1.24401e10	−0.106551
$289$	5.81354e10	0.490231
$290$	1.92495e11	1.59819
$291$	1.15362e11	0.943075
$292$	−1.67856e11	−1.35119
$293$	1.30027e11	1.03069	0.515345	−	0.856983i	$-0.327664\pi$
$293$	1.30027e11	1.03069	0.515345	+	0.856983i	$0.327664\pi$
$294$	1.29946e11	1.01438
$295$	2.26782e10	0.174345
$296$	−1.08590e11	−0.822202
$297$	4.04464e10	0.301631
$298$	−8.34814e10	−0.613221
$299$	5.00887e9	0.0362426
$300$	1.34128e11	0.956033
$301$	3.87324e8	0.00271972
$302$	−2.04875e11	−1.41729
$303$	−1.84983e10	−0.126079
$304$	−1.11044e11	−0.745696
$305$	1.67577e11	1.10883
$306$	−1.09656e11	−0.714966
$307$	9.33203e10	0.599589	0.299794	−	0.954004i	$-0.403082\pi$
$307$	9.33203e10	0.599589	0.299794	+	0.954004i	$0.403082\pi$
$308$	−3.50593e9	−0.0221986
$309$	1.26632e11	0.790186
$310$	−1.28639e11	−0.791128
$311$	1.57941e11	0.957352	0.478676	−	0.877992i	$-0.341117\pi$
$311$	1.57941e11	0.957352	0.478676	+	0.877992i	$0.341117\pi$
$312$	7.83907e10	0.468348
$313$	−8.35400e10	−0.491977	−0.245989	−	0.969273i	$-0.579113\pi$
$313$	−8.35400e10	−0.491977	−0.245989	+	0.969273i	$0.579113\pi$
$314$	−2.49337e11	−1.44745
$315$	5.29325e8	0.00302918
$316$	6.17645e11	3.48455
$317$	−1.98225e11	−1.10253	−0.551265	−	0.834330i	$-0.685855\pi$
$317$	−1.98225e11	−1.10253	−0.551265	+	0.834330i	$0.685855\pi$
$318$	2.96407e11	1.62542
$319$	1.96893e11	1.06456
$320$	1.77708e11	0.947398
$321$	−1.00524e11	−0.528442
$322$	−1.96294e8	−0.00101755
$323$	−1.40316e11	−0.717291
$324$	4.60009e10	0.231907
$325$	−6.77652e10	−0.336924
$326$	−1.18383e11	−0.580513
$327$	−2.10409e11	−1.01765
$328$	−1.60218e11	−0.764328
$329$	−2.42033e9	−0.0113892
$330$	4.58696e11	2.12918
$331$	−2.61910e10	−0.119930	−0.0599648	−	0.998200i	$-0.519099\pi$
$331$	−2.61910e10	−0.119930	−0.0599648	+	0.998200i	$0.519099\pi$
$332$	−4.58592e11	−2.07160
$333$	3.21944e10	0.143477
$334$	6.64535e10	0.292185
$335$	2.99132e11	1.29766
$336$	−1.16164e9	−0.00497214
$337$	1.09795e11	0.463714	0.231857	−	0.972750i	$-0.425520\pi$
$337$	1.09795e11	0.463714	0.231857	+	0.972750i	$0.425520\pi$
$338$	3.45569e11	1.44016
$339$	5.34065e9	0.0219632
$340$	−8.40763e11	−3.41208
$341$	−1.31578e11	−0.526974
$342$	8.70653e10	0.344134
$343$	3.47900e9	0.0135716
$344$	1.98839e11	0.765578
$345$	1.73630e10	0.0659841
$346$	−5.32980e11	−1.99925
$347$	4.82368e10	0.178606	0.0893029	−	0.996005i	$-0.471536\pi$
$347$	4.82368e10	0.178606	0.0893029	+	0.996005i	$0.471536\pi$
$348$	2.23932e11	0.818484
$349$	−3.17295e11	−1.14485	−0.572425	−	0.819957i	$-0.693997\pi$
$349$	−3.17295e11	−1.14485	−0.572425	+	0.819957i	$0.693997\pi$
$350$	2.65567e9	0.00945949
$351$	−2.32410e10	−0.0817283
$352$	−1.44304e11	−0.500997
$353$	2.17995e11	0.747239	0.373620	−	0.927582i	$-0.378117\pi$
$353$	2.17995e11	0.747239	0.373620	+	0.927582i	$0.378117\pi$
$354$	3.90219e10	0.132067
$355$	−3.16187e11	−1.05661
$356$	−6.51259e11	−2.14896
$357$	−1.46786e9	−0.00478274
$358$	4.76346e11	1.53267
$359$	−4.21124e11	−1.33809	−0.669044	−	0.743222i	$-0.733296\pi$
$359$	−4.21124e11	−1.33809	−0.669044	+	0.743222i	$0.733296\pi$
$360$	2.71738e11	0.852686
$361$	−2.11279e11	−0.654747
$362$	−4.85683e11	−1.48650
$363$	2.78180e11	0.840904
$364$	2.01455e9	0.00601481
$365$	2.93976e11	0.866949
$366$	2.88346e11	0.839942
$367$	−4.66968e11	−1.34366	−0.671831	−	0.740705i	$-0.734492\pi$
$367$	−4.66968e11	−1.34366	−0.671831	+	0.740705i	$0.734492\pi$
$368$	−3.81042e10	−0.108307
$369$	4.75009e10	0.133378
$370$	3.65112e11	1.01279
$371$	3.96771e9	0.0108732
$372$	−1.49648e11	−0.405161
$373$	−7.06913e11	−1.89093	−0.945467	−	0.325719i	$-0.894394\pi$
$373$	−7.06913e11	−1.89093	−0.945467	+	0.325719i	$0.894394\pi$
$374$	−1.27200e12	−3.36174
$375$	6.11793e10	0.159758
$376$	−1.24252e12	−3.20595
$377$	−1.13137e11	−0.288449
$378$	9.10797e8	0.00229461
$379$	4.89494e11	1.21863	0.609313	−	0.792930i	$-0.291445\pi$
$379$	4.89494e11	1.21863	0.609313	+	0.792930i	$0.291445\pi$
$380$	6.67555e11	1.64233
$381$	7.31955e10	0.177960
$382$	−6.49918e11	−1.56161
$383$	1.59864e11	0.379627	0.189814	−	0.981820i	$-0.439212\pi$
$383$	1.59864e11	0.379627	0.189814	+	0.981820i	$0.439212\pi$
$384$	3.84412e11	0.902208
$385$	6.14012e9	0.0142431
$386$	−1.20997e12	−2.77417
$387$	−5.89512e10	−0.133596
$388$	1.52197e12	3.40929
$389$	3.92974e11	0.870143	0.435072	−	0.900396i	$-0.356723\pi$
$389$	3.92974e11	0.870143	0.435072	+	0.900396i	$0.356723\pi$
$390$	−2.63572e11	−0.576911
$391$	−4.81490e10	−0.104182
$392$	8.92982e11	1.91010
$393$	−1.20684e11	−0.255202
$394$	−7.72087e11	−1.61411
$395$	−1.08171e12	−2.23576
$396$	5.33607e11	1.09042
$397$	8.13926e11	1.64448	0.822238	−	0.569144i	$-0.192725\pi$
$397$	8.13926e11	1.64448	0.822238	+	0.569144i	$0.192725\pi$
$398$	−7.73804e11	−1.54581
$399$	1.16546e9	0.00230207
$400$	5.15513e11	1.00686
$401$	−4.34991e11	−0.840099	−0.420050	−	0.907501i	$-0.637987\pi$
$401$	−4.34991e11	−0.840099	−0.420050	+	0.907501i	$0.637987\pi$
$402$	5.14709e11	0.982980
$403$	7.56064e10	0.142786
$404$	−2.44048e11	−0.455783
$405$	−8.05639e10	−0.148796
$406$	4.43376e9	0.00809850
$407$	3.73452e11	0.674622
$408$	−7.53550e11	−1.34630
$409$	−3.30766e11	−0.584475	−0.292237	−	0.956346i	$-0.594400\pi$
$409$	−3.30766e11	−0.584475	−0.292237	+	0.956346i	$0.594400\pi$
$410$	5.38700e11	0.941499
$411$	3.07959e11	0.532360
$412$	1.67065e12	2.85658
$413$	5.22348e8	0.000883456 0
$414$	2.98762e10	0.0499832
$415$	8.03156e11	1.32918
$416$	8.29186e10	0.135748
$417$	−3.19699e10	−0.0517761
$418$	1.00995e12	1.61810
$419$	7.85962e10	0.124577	0.0622886	−	0.998058i	$-0.480160\pi$
$419$	7.85962e10	0.124577	0.0622886	+	0.998058i	$0.480160\pi$
$420$	6.98335e9	0.0109507
$421$	1.15531e12	1.79238	0.896190	−	0.443671i	$-0.146324\pi$
$421$	1.15531e12	1.79238	0.896190	+	0.443671i	$0.146324\pi$
$422$	3.88571e11	0.596437
$423$	3.68377e11	0.559449
$424$	2.03689e12	3.06071
$425$	6.51409e11	0.968509
$426$	−5.44056e11	−0.800388
$427$	3.85981e9	0.00561876
$428$	−1.32621e12	−1.91036
$429$	−2.69593e11	−0.384283
$430$	−6.68555e11	−0.943038
$431$	9.27162e11	1.29422	0.647109	−	0.762397i	$-0.275978\pi$
$431$	9.27162e11	1.29422	0.647109	+	0.762397i	$0.275978\pi$
$432$	1.76802e11	0.244237
$433$	−5.34982e11	−0.731381	−0.365690	−	0.930737i	$-0.619167\pi$
$433$	−5.34982e11	−0.731381	−0.365690	+	0.930737i	$0.619167\pi$
$434$	−2.96296e9	−0.00400887
$435$	−3.92184e11	−0.525157
$436$	−2.77592e12	−3.67889
$437$	3.82297e10	0.0501457
$438$	5.05837e11	0.656716
$439$	−3.68635e11	−0.473703	−0.236852	−	0.971546i	$-0.576116\pi$
$439$	−3.68635e11	−0.473703	−0.236852	+	0.971546i	$0.576116\pi$
$440$	3.15214e12	4.00929
$441$	−2.64748e11	−0.333318
$442$	7.30906e11	0.910880
$443$	−1.14608e12	−1.41384	−0.706919	−	0.707294i	$-0.749916\pi$
$443$	−1.14608e12	−1.41384	−0.706919	+	0.707294i	$0.749916\pi$
$444$	4.24739e11	0.518680
$445$	1.14058e12	1.37882
$446$	4.25563e11	0.509281
$447$	1.70083e11	0.201501
$448$	4.09316e9	0.00480074
$449$	7.33272e11	0.851445	0.425722	−	0.904854i	$-0.360020\pi$
$449$	7.33272e11	0.851445	0.425722	+	0.904854i	$0.360020\pi$
$450$	−4.04196e11	−0.464660
$451$	5.51006e11	0.627137
$452$	7.04589e10	0.0793986
$453$	4.17407e11	0.465712
$454$	3.02051e11	0.333679
$455$	−3.52819e9	−0.00385923
$456$	5.98309e11	0.648013
$457$	6.95065e11	0.745422	0.372711	−	0.927947i	$-0.378428\pi$
$457$	6.95065e11	0.745422	0.372711	+	0.927947i	$0.378428\pi$
$458$	−1.57221e12	−1.66961
$459$	2.23410e11	0.234933
$460$	2.29069e11	0.238538
$461$	5.56679e11	0.574052	0.287026	−	0.957923i	$-0.407333\pi$
$461$	5.56679e11	0.574052	0.287026	+	0.957923i	$0.407333\pi$
$462$	1.05652e10	0.0107892
$463$	1.58767e12	1.60563	0.802815	−	0.596228i	$-0.203334\pi$
$463$	1.58767e12	1.60563	0.802815	+	0.596228i	$0.203334\pi$
$464$	8.60673e11	0.862000
$465$	2.62086e11	0.259960
$466$	−3.48168e12	−3.42020
$467$	−9.73788e10	−0.0947411	−0.0473706	−	0.998877i	$-0.515084\pi$
$467$	−9.73788e10	−0.0947411	−0.0473706	+	0.998877i	$0.515084\pi$
$468$	−3.06617e11	−0.295454
$469$	6.88992e9	0.00657561
$470$	4.17770e12	3.94909
$471$	5.07993e11	0.475623
$472$	2.68156e11	0.248685
$473$	−6.83828e11	−0.628162
$474$	−1.86128e12	−1.69359
$475$	−5.17210e11	−0.466172
$476$	−1.93654e10	−0.0172900
$477$	−6.03890e11	−0.534103
$478$	−1.27103e12	−1.11360
$479$	−4.31480e11	−0.374499	−0.187249	−	0.982312i	$-0.559957\pi$
$479$	−4.31480e11	−0.374499	−0.187249	+	0.982312i	$0.559957\pi$
$480$	2.87434e11	0.247145
$481$	−2.14590e11	−0.182792
$482$	−1.40161e12	−1.18281
$483$	3.99924e8	0.000334361 0
$484$	3.67002e12	3.03993
$485$	−2.66551e12	−2.18747
$486$	−1.38624e11	−0.112714
$487$	−2.09753e12	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$487$	−2.09753e12	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$488$	1.98150e12	1.58163
$489$	2.41191e11	0.190753
$490$	−3.00246e12	−2.35285
$491$	−1.32643e11	−0.102995	−0.0514976	−	0.998673i	$-0.516399\pi$
$491$	−1.32643e11	−0.102995	−0.0514976	+	0.998673i	$0.516399\pi$
$492$	6.26677e11	0.482171
$493$	1.08756e12	0.829165
$494$	−5.80329e11	−0.438433
$495$	−9.34533e11	−0.699635
$496$	−5.75165e11	−0.426702
$497$	−7.28275e9	−0.00535416
$498$	1.38197e12	1.00686
$499$	−3.85614e11	−0.278420	−0.139210	−	0.990263i	$-0.544456\pi$
$499$	−3.85614e11	−0.278420	−0.139210	+	0.990263i	$0.544456\pi$
$500$	8.07135e11	0.577538
$501$	−1.35390e11	−0.0960103
$502$	−4.76054e11	−0.334572
$503$	−1.68499e11	−0.117366	−0.0586829	−	0.998277i	$-0.518690\pi$
$503$	−1.68499e11	−0.117366	−0.0586829	+	0.998277i	$0.518690\pi$
$504$	6.25896e9	0.00432081
$505$	4.27413e11	0.292440
$506$	3.46561e11	0.235019
$507$	−7.04053e11	−0.473227
$508$	9.65664e11	0.643338
$509$	4.71940e11	0.311642	0.155821	−	0.987785i	$-0.450198\pi$
$509$	4.71940e11	0.311642	0.155821	+	0.987785i	$0.450198\pi$
$510$	2.53365e12	1.65837
$511$	6.77116e9	0.00439308
$512$	3.13870e12	2.01853
$513$	−1.77384e11	−0.113080
$514$	−2.76796e12	−1.74914
$515$	−2.92589e12	−1.83284
$516$	−7.77739e11	−0.482959
$517$	4.27314e12	2.63051
$518$	8.40964e9	0.00513208
$519$	1.08588e12	0.656943
$520$	−1.81126e12	−1.08634
$521$	−2.64327e12	−1.57171	−0.785853	−	0.618414i	$-0.787776\pi$
$521$	−2.64327e12	−1.57171	−0.785853	+	0.618414i	$0.787776\pi$
$522$	−6.74823e11	−0.397807
$523$	−3.72234e11	−0.217549	−0.108775	−	0.994066i	$-0.534693\pi$
$523$	−3.72234e11	−0.217549	−0.108775	+	0.994066i	$0.534693\pi$
$524$	−1.59218e12	−0.922576
$525$	−5.41058e9	−0.00310833
$526$	−3.55955e12	−2.02749
$527$	−7.26785e11	−0.410448
$528$	2.05089e12	1.14839
$529$	−1.78803e12	−0.992717
$530$	−6.84862e12	−3.77018
$531$	−7.95020e10	−0.0433963
$532$	1.53758e10	0.00832217
$533$	−3.16615e11	−0.169926
$534$	1.96258e12	1.04446
$535$	2.32266e12	1.22572
$536$	3.53706e12	1.85098
$537$	−9.70494e11	−0.503627
$538$	−4.41593e12	−2.27249
$539$	−3.07105e12	−1.56725
$540$	−1.06287e12	−0.537911
$541$	3.80779e12	1.91111	0.955554	−	0.294815i	$-0.0952579\pi$
$541$	3.80779e12	1.91111	0.955554	+	0.294815i	$0.0952579\pi$
$542$	1.07655e12	0.535842
$543$	9.89516e11	0.488454
$544$	−7.97075e11	−0.390215
$545$	4.86161e12	2.36045
$546$	−6.07088e9	−0.00292337
$547$	2.49470e12	1.19145	0.595725	−	0.803189i	$-0.296865\pi$
$547$	2.49470e12	1.19145	0.595725	+	0.803189i	$0.296865\pi$
$548$	4.06289e12	1.92452
$549$	−5.87468e11	−0.276000
$550$	−4.68863e12	−2.18481
$551$	−8.63506e11	−0.399101
$552$	2.05308e11	0.0941195
$553$	−2.49152e10	−0.0113292
$554$	1.90851e12	0.860798
$555$	−7.43868e11	−0.332796
$556$	−4.21777e11	−0.187174
$557$	3.97099e12	1.74804	0.874019	−	0.485892i	$-0.161505\pi$
$557$	3.97099e12	1.74804	0.874019	+	0.485892i	$0.161505\pi$
$558$	4.50966e11	0.196920
$559$	3.92936e11	0.170204
$560$	2.68402e10	0.0115329
$561$	2.59153e12	1.10465
$562$	4.50598e12	1.90535
$563$	3.54645e12	1.48767	0.743833	−	0.668365i	$-0.233006\pi$
$563$	3.54645e12	1.48767	0.743833	+	0.668365i	$0.233006\pi$
$564$	4.85997e12	2.02245
$565$	−1.23398e11	−0.0509438
$566$	2.54883e12	1.04392
$567$	−1.85563e9	−0.000753995 0
$568$	−3.73873e12	−1.50715
$569$	3.10044e12	1.23999	0.619994	−	0.784606i	$-0.287135\pi$
$569$	3.10044e12	1.23999	0.619994	+	0.784606i	$0.287135\pi$
$570$	−2.01169e12	−0.798221
$571$	−4.49759e12	−1.77059	−0.885294	−	0.465032i	$-0.846043\pi$
$571$	−4.49759e12	−1.77059	−0.885294	+	0.465032i	$0.846043\pi$
$572$	−3.55673e12	−1.38921
$573$	1.32413e12	0.513137
$574$	1.24079e10	0.00477084
$575$	−1.77479e11	−0.0677083
$576$	−6.22985e11	−0.235818
$577$	3.67193e12	1.37912	0.689562	−	0.724227i	$-0.257803\pi$
$577$	3.67193e12	1.37912	0.689562	+	0.724227i	$0.257803\pi$
$578$	−2.31130e12	−0.861351
$579$	2.46517e12	0.911576
$580$	−5.17407e12	−1.89848
$581$	1.84991e10	0.00673533
$582$	−4.58648e12	−1.65701
$583$	−7.00507e12	−2.51133
$584$	3.47609e12	1.23661
$585$	5.36994e11	0.189569
$586$	−5.16948e12	−1.81095
$587$	−3.14786e12	−1.09432	−0.547159	−	0.837029i	$-0.684291\pi$
$587$	−3.14786e12	−1.09432	−0.547159	+	0.837029i	$0.684291\pi$
$588$	−3.49280e12	−1.20497
$589$	5.77058e11	0.197561
$590$	−9.01619e11	−0.306330
$591$	1.57303e12	0.530387
$592$	1.63246e12	0.546256
$593$	1.66698e12	0.553584	0.276792	−	0.960930i	$-0.410729\pi$
$593$	1.66698e12	0.553584	0.276792	+	0.960930i	$0.410729\pi$
$594$	−1.60803e12	−0.529975
$595$	3.39156e10	0.0110936
$596$	2.24389e12	0.728440
$597$	1.57652e12	0.507945
$598$	−1.99138e11	−0.0636795
$599$	−1.17016e12	−0.371387	−0.185693	−	0.982608i	$-0.559453\pi$
$599$	−1.17016e12	−0.371387	−0.185693	+	0.982608i	$0.559453\pi$
$600$	−2.77762e12	−0.874967
$601$	−4.19866e12	−1.31273	−0.656366	−	0.754443i	$-0.727907\pi$
$601$	−4.19866e12	−1.31273	−0.656366	+	0.754443i	$0.727907\pi$
$602$	−1.53989e10	−0.00477865
$603$	−1.04865e12	−0.323001
$604$	5.50683e12	1.68359
$605$	−6.42749e12	−1.95048
$606$	7.35441e11	0.221524
$607$	−3.46965e12	−1.03738	−0.518689	−	0.854963i	$-0.673580\pi$
$607$	−3.46965e12	−1.03738	−0.518689	+	0.854963i	$0.673580\pi$
$608$	6.32867e11	0.187822
$609$	−9.03321e9	−0.00266112
$610$	−6.66238e12	−1.94825
$611$	−2.45540e12	−0.712748
$612$	2.94743e12	0.849302
$613$	−1.07824e12	−0.308420	−0.154210	−	0.988038i	$-0.549283\pi$
$613$	−1.07824e12	−0.308420	−0.154210	+	0.988038i	$0.549283\pi$
$614$	−3.71015e12	−1.05350
$615$	−1.09753e12	−0.309371
$616$	7.26033e10	0.0203162
$617$	3.25905e11	0.0905331	0.0452666	−	0.998975i	$-0.485586\pi$
$617$	3.25905e11	0.0905331	0.0452666	+	0.998975i	$0.485586\pi$
$618$	−5.03451e12	−1.38838
$619$	−3.86487e12	−1.05810	−0.529051	−	0.848590i	$-0.677452\pi$
$619$	−3.86487e12	−1.05810	−0.529051	+	0.848590i	$0.677452\pi$
$620$	3.45769e12	0.939774
$621$	−6.08689e10	−0.0164242
$622$	−6.27926e12	−1.68210
$623$	2.62712e10	0.00698688
$624$	−1.17847e12	−0.311162
$625$	−4.44005e12	−1.16393
$626$	3.32131e12	0.864420
$627$	−2.05764e12	−0.531699
$628$	6.70192e12	1.71941
$629$	2.06280e12	0.525448
$630$	−2.10444e10	−0.00532236
$631$	5.72504e12	1.43763	0.718813	−	0.695203i	$-0.244686\pi$
$631$	5.72504e12	1.43763	0.718813	+	0.695203i	$0.244686\pi$
$632$	−1.27906e13	−3.18908
$633$	−7.91664e11	−0.195986
$634$	7.88084e12	1.93718
$635$	−1.69122e12	−0.412779
$636$	−7.96709e12	−1.93082
$637$	1.76466e12	0.424653
$638$	−7.82789e12	−1.87047
$639$	1.10844e12	0.263002
$640$	−8.88203e12	−2.09268
$641$	2.78162e12	0.650785	0.325392	−	0.945579i	$-0.394504\pi$
$641$	2.78162e12	0.650785	0.325392	+	0.945579i	$0.394504\pi$
$642$	3.99654e12	0.928489
$643$	5.67681e12	1.30965	0.654824	−	0.755781i	$-0.272743\pi$
$643$	5.67681e12	1.30965	0.654824	+	0.755781i	$0.272743\pi$
$644$	5.27617e9	0.00120874
$645$	1.36210e12	0.309877
$646$	5.57856e12	1.26030
$647$	6.36165e10	0.0142725	0.00713626	−	0.999975i	$-0.497728\pi$
$647$	6.36165e10	0.0142725	0.00713626	+	0.999975i	$0.497728\pi$
$648$	−9.52621e11	−0.212243
$649$	−9.22216e11	−0.204048
$650$	2.69415e12	0.591986
$651$	6.03665e9	0.00131729
$652$	3.18202e12	0.689586
$653$	3.08169e12	0.663255	0.331627	−	0.943410i	$-0.392402\pi$
$653$	3.08169e12	0.663255	0.331627	+	0.943410i	$0.392402\pi$
$654$	8.36526e12	1.78805
$655$	2.78847e12	0.591944
$656$	2.40860e12	0.507806
$657$	−1.03058e12	−0.215793
$658$	9.62252e10	0.0200112
$659$	−7.50754e11	−0.155065	−0.0775324	−	0.996990i	$-0.524704\pi$
$659$	−7.50754e11	−0.155065	−0.0775324	+	0.996990i	$0.524704\pi$
$660$	−1.23292e13	−2.52923
$661$	−5.89525e12	−1.20115	−0.600573	−	0.799570i	$-0.705061\pi$
$661$	−5.89525e12	−1.20115	−0.600573	+	0.799570i	$0.705061\pi$
$662$	1.04128e12	0.210720
$663$	−1.48913e12	−0.299310
$664$	9.49686e12	1.89594
$665$	−2.69285e10	−0.00533967
$666$	−1.27996e12	−0.252094
$667$	−2.96309e11	−0.0579668
$668$	−1.78620e12	−0.347085
$669$	−8.67031e11	−0.167347
$670$	−1.18926e13	−2.28003
$671$	−6.81457e12	−1.29774
$672$	6.62048e9	0.00125236
$673$	−1.26722e11	−0.0238113	−0.0119057	−	0.999929i	$-0.503790\pi$
$673$	−1.26722e11	−0.0238113	−0.0119057	+	0.999929i	$0.503790\pi$
$674$	−4.36515e12	−0.814760
$675$	8.23497e11	0.152685
$676$	−9.28853e12	−1.71075
$677$	5.40759e12	0.989361	0.494681	−	0.869075i	$-0.335285\pi$
$677$	5.40759e12	0.989361	0.494681	+	0.869075i	$0.335285\pi$
$678$	−2.12329e11	−0.0385901
$679$	−6.13948e10	−0.0110845
$680$	1.74111e13	3.12275
$681$	−6.15390e11	−0.109645
$682$	5.23117e12	0.925910
$683$	−3.34048e12	−0.587376	−0.293688	−	0.955901i	$-0.594883\pi$
$683$	−3.34048e12	−0.587376	−0.293688	+	0.955901i	$0.594883\pi$
$684$	−2.34022e12	−0.408794
$685$	−7.11555e12	−1.23481
$686$	−1.38315e11	−0.0238457
$687$	3.20317e12	0.548623
$688$	−2.98920e12	−0.508636
$689$	4.02520e12	0.680458
$690$	−6.90304e11	−0.115936
$691$	−5.76394e12	−0.961764	−0.480882	−	0.876785i	$-0.659683\pi$
$691$	−5.76394e12	−0.961764	−0.480882	+	0.876785i	$0.659683\pi$
$692$	1.43259e13	2.37490
$693$	−2.15252e10	−0.00354525
$694$	−1.91776e12	−0.313816
$695$	7.38680e11	0.120095
$696$	−4.63736e12	−0.749081
$697$	3.04354e12	0.488463
$698$	1.26147e13	2.01154
$699$	7.09347e12	1.12386
$700$	−7.13815e10	−0.0112368
$701$	−5.48007e12	−0.857147	−0.428573	−	0.903507i	$-0.640984\pi$
$701$	−5.48007e12	−0.857147	−0.428573	+	0.903507i	$0.640984\pi$
$702$	9.23995e11	0.143599
$703$	−1.63784e12	−0.252913
$704$	−7.22656e12	−1.10880
$705$	−8.51153e12	−1.29765
$706$	−8.66684e12	−1.31292
$707$	9.84464e9	0.00148188
$708$	−1.04887e12	−0.156881
$709$	8.14487e12	1.21053	0.605265	−	0.796024i	$-0.293067\pi$
$709$	8.14487e12	1.21053	0.605265	+	0.796024i	$0.293067\pi$
$710$	1.25707e13	1.85651
$711$	3.79212e12	0.556505
$712$	1.34868e13	1.96674
$713$	1.98016e11	0.0286944
$714$	5.83578e10	0.00840343
$715$	6.22909e12	0.891348
$716$	−1.28037e13	−1.82065
$717$	2.58956e12	0.365923
$718$	1.67427e13	2.35107
$719$	9.83293e12	1.37215	0.686077	−	0.727529i	$-0.259331\pi$
$719$	9.83293e12	1.37215	0.686077	+	0.727529i	$0.259331\pi$
$720$	−4.08511e12	−0.566509
$721$	−6.73922e10	−0.00928754
$722$	8.39983e12	1.15041
$723$	2.85560e12	0.388665
$724$	1.30546e13	1.76580
$725$	4.00878e12	0.538879
$726$	−1.10596e13	−1.47750
$727$	−3.89292e12	−0.516857	−0.258428	−	0.966030i	$-0.583205\pi$
$727$	−3.89292e12	−0.516857	−0.258428	+	0.966030i	$0.583205\pi$
$728$	−4.17188e10	−0.00550479
$729$	2.82430e11	0.0370370
$730$	−1.16876e13	−1.52326
$731$	−3.77719e12	−0.489261
$732$	−7.75043e12	−0.997760
$733$	−8.99834e12	−1.15132	−0.575658	−	0.817691i	$-0.695254\pi$
$733$	−8.99834e12	−1.15132	−0.575658	+	0.817691i	$0.695254\pi$
$734$	1.85653e13	2.36086
$735$	6.11713e12	0.773134
$736$	2.17166e11	0.0272799
$737$	−1.21643e13	−1.51874
$738$	−1.88850e12	−0.234349
$739$	5.20306e12	0.641739	0.320870	−	0.947123i	$-0.396025\pi$
$739$	5.20306e12	0.641739	0.320870	+	0.947123i	$0.396025\pi$
$740$	−9.81381e12	−1.20308
$741$	1.18235e12	0.144066
$742$	−1.57745e11	−0.0191046
$743$	−1.31280e12	−0.158033	−0.0790165	−	0.996873i	$-0.525178\pi$
$743$	−1.31280e12	−0.158033	−0.0790165	+	0.996873i	$0.525178\pi$
$744$	3.09902e12	0.370806
$745$	−3.92984e12	−0.467382
$746$	2.81048e13	3.32243
$747$	−2.81559e12	−0.330847
$748$	3.41899e13	3.99338
$749$	5.34979e10	0.00621110
$750$	−2.43231e12	−0.280701
$751$	1.71718e13	1.96987	0.984933	−	0.172939i	$-0.0553262\pi$
$751$	1.71718e13	1.96987	0.984933	+	0.172939i	$0.0553262\pi$
$752$	1.86791e13	2.12998
$753$	9.69898e11	0.109938
$754$	4.49800e12	0.506814
$755$	−9.64439e12	−1.08022
$756$	−2.44813e10	−0.00272575
$757$	1.66475e13	1.84255	0.921273	−	0.388916i	$-0.127150\pi$
$757$	1.66475e13	1.84255	0.921273	+	0.388916i	$0.127150\pi$
$758$	−1.94609e13	−2.14117
$759$	−7.06073e11	−0.0772257
$760$	−1.38242e13	−1.50307
$761$	6.16014e12	0.665825	0.332912	−	0.942958i	$-0.391969\pi$
$761$	6.16014e12	0.665825	0.332912	+	0.942958i	$0.391969\pi$
$762$	−2.91004e12	−0.312681
$763$	1.11978e11	0.0119611
$764$	1.74691e13	1.85503
$765$	−5.16199e12	−0.544930
$766$	−6.35575e12	−0.667017
$767$	5.29917e11	0.0552877
$768$	−1.13452e13	−1.17676
$769$	1.33568e13	1.37731	0.688657	−	0.725087i	$-0.258200\pi$
$769$	1.33568e13	1.37731	0.688657	+	0.725087i	$0.258200\pi$
$770$	−2.44113e11	−0.0250255
$771$	5.63936e12	0.574758
$772$	3.25228e13	3.29542
$773$	−3.22073e12	−0.324449	−0.162225	−	0.986754i	$-0.551867\pi$
$773$	−3.22073e12	−0.324449	−0.162225	+	0.986754i	$0.551867\pi$
$774$	2.34373e12	0.234732
$775$	−2.67896e12	−0.266753
$776$	−3.15181e13	−3.12020
$777$	−1.71336e10	−0.00168637
$778$	−1.56235e13	−1.52887
$779$	−2.41653e12	−0.235111
$780$	7.08454e12	0.685308
$781$	1.28578e13	1.23663
$782$	1.91426e12	0.183051
$783$	1.37487e12	0.130717
$784$	−1.34244e13	−1.26903
$785$	−1.17374e13	−1.10321
$786$	4.79807e12	0.448399
$787$	1.14501e13	1.06395	0.531977	−	0.846759i	$-0.321449\pi$
$787$	1.14501e13	1.06395	0.531977	+	0.846759i	$0.321449\pi$
$788$	2.07529e13	1.91739
$789$	7.25213e12	0.666222
$790$	4.30058e13	3.92830
$791$	−2.84224e9	−0.000258147 0
$792$	−1.10503e13	−0.997956
$793$	3.91574e12	0.351629
$794$	−3.23593e13	−2.88940
$795$	1.39532e13	1.23886
$796$	2.07990e13	1.83626
$797$	7.25906e12	0.637262	0.318631	−	0.947879i	$-0.396777\pi$
$797$	7.25906e12	0.637262	0.318631	+	0.947879i	$0.396777\pi$
$798$	−4.63353e10	−0.00404482
$799$	2.36031e13	2.04884
$800$	−2.93805e12	−0.253603
$801$	−3.99850e12	−0.343203
$802$	1.72940e13	1.47608
$803$	−1.19546e13	−1.01465
$804$	−1.38348e13	−1.16767
$805$	−9.24043e9	−0.000775552 0
$806$	−3.00589e12	−0.250880
$807$	8.99690e12	0.746727
$808$	5.05392e12	0.417135
$809$	−1.85851e13	−1.52544	−0.762722	−	0.646726i	$-0.776138\pi$
$809$	−1.85851e13	−1.52544	−0.762722	+	0.646726i	$0.776138\pi$
$810$	3.20299e12	0.261440
$811$	2.15522e13	1.74944	0.874719	−	0.484630i	$-0.161046\pi$
$811$	2.15522e13	1.74944	0.874719	+	0.484630i	$0.161046\pi$
$812$	−1.19175e11	−0.00962014
$813$	−2.19333e12	−0.176074
$814$	−1.48474e13	−1.18533
$815$	−5.57284e12	−0.442453
$816$	1.13283e13	0.894457
$817$	2.99904e12	0.235496
$818$	1.31503e13	1.02694
$819$	1.23686e10	0.000960603 0
$820$	−1.44797e13	−1.11840
$821$	2.08276e13	1.59991	0.799954	−	0.600062i	$-0.204857\pi$
$821$	2.08276e13	1.59991	0.799954	+	0.600062i	$0.204857\pi$
$822$	−1.22436e13	−0.935373
$823$	−9.47540e12	−0.719943	−0.359972	−	0.932963i	$-0.617214\pi$
$823$	−9.47540e12	−0.719943	−0.359972	+	0.932963i	$0.617214\pi$
$824$	−3.45970e13	−2.61436
$825$	9.55249e12	0.717916
$826$	−2.07670e10	−0.00155226
$827$	3.45208e12	0.256629	0.128315	−	0.991734i	$-0.459043\pi$
$827$	3.45208e12	0.256629	0.128315	+	0.991734i	$0.459043\pi$
$828$	−8.03040e11	−0.0593746
$829$	−1.59708e13	−1.17444	−0.587222	−	0.809426i	$-0.699779\pi$
$829$	−1.59708e13	−1.17444	−0.587222	+	0.809426i	$0.699779\pi$
$830$	−3.19312e13	−2.33541
$831$	−3.88835e12	−0.282853
$832$	4.15247e12	0.300436
$833$	−1.69633e13	−1.22069
$834$	1.27103e12	0.0909723
$835$	3.12826e12	0.222697
$836$	−2.71463e13	−1.92213
$837$	−9.18786e11	−0.0647068
$838$	−3.12476e12	−0.218886
$839$	5.84124e12	0.406983	0.203491	−	0.979077i	$-0.434771\pi$
$839$	5.84124e12	0.406983	0.203491	+	0.979077i	$0.434771\pi$
$840$	−1.44616e11	−0.0100221
$841$	−7.81431e12	−0.538652
$842$	−4.59319e13	−3.14927
$843$	−9.18035e12	−0.626088
$844$	−1.04444e13	−0.708503
$845$	1.62675e13	1.09765
$846$	−1.46456e13	−0.982971
$847$	−1.48045e11	−0.00988366
$848$	−3.06211e13	−2.03348
$849$	−5.19291e12	−0.343025
$850$	−2.58982e13	−1.70170
$851$	−5.62019e11	−0.0367340
$852$	1.46236e13	0.950774
$853$	2.01733e10	0.00130468	0.000652342	−	1.00000i	$-0.499792\pi$
$853$	2.01733e10	0.00130468	0.000652342		1.00000i	$0.499792\pi$
$854$	−1.53455e11	−0.00987235
$855$	4.09855e12	0.262291
$856$	2.74641e13	1.74837
$857$	2.71965e12	0.172226	0.0861130	−	0.996285i	$-0.472555\pi$
$857$	2.71965e12	0.172226	0.0861130	+	0.996285i	$0.472555\pi$
$858$	1.07183e13	0.675198
$859$	−1.34952e13	−0.845688	−0.422844	−	0.906203i	$-0.638968\pi$
$859$	−1.34952e13	−0.845688	−0.422844	+	0.906203i	$0.638968\pi$
$860$	1.79700e13	1.12023
$861$	−2.52795e10	−0.00156767
$862$	−3.68613e13	−2.27399
$863$	−1.46281e13	−0.897717	−0.448859	−	0.893603i	$-0.648169\pi$
$863$	−1.46281e13	−0.897717	−0.448859	+	0.893603i	$0.648169\pi$
$864$	−1.00765e12	−0.0615171
$865$	−2.50897e13	−1.52378
$866$	2.12693e13	1.28506
$867$	4.70897e12	0.283035
$868$	7.96412e10	0.00476211
$869$	4.39882e13	2.61666
$870$	1.55921e13	0.922717
$871$	6.98975e12	0.411510
$872$	5.74857e13	3.36694
$873$	9.34436e12	0.544484
$874$	−1.51990e12	−0.0881077
$875$	−3.25590e10	−0.00187774
$876$	−1.35964e13	−0.780107
$877$	1.06900e13	0.610209	0.305105	−	0.952319i	$-0.401309\pi$
$877$	1.06900e13	0.610209	0.305105	+	0.952319i	$0.401309\pi$
$878$	1.46559e13	0.832312
$879$	1.05321e13	0.595069
$880$	−4.73868e13	−2.66370
$881$	−2.64579e13	−1.47967	−0.739833	−	0.672790i	$-0.765096\pi$
$881$	−2.64579e13	−1.47967	−0.739833	+	0.672790i	$0.765096\pi$
$882$	1.05256e13	0.585651
$883$	−1.05016e13	−0.581342	−0.290671	−	0.956823i	$-0.593879\pi$
$883$	−1.05016e13	−0.581342	−0.290671	+	0.956823i	$0.593879\pi$
$884$	−1.96460e13	−1.08203
$885$	1.83693e12	0.100658
$886$	4.55650e13	2.48416
$887$	1.51558e13	0.822098	0.411049	−	0.911613i	$-0.365162\pi$
$887$	1.51558e13	0.822098	0.411049	+	0.911613i	$0.365162\pi$
$888$	−8.79581e12	−0.474698
$889$	−3.89539e10	−0.00209167
$890$	−4.53464e13	−2.42263
$891$	3.27616e12	0.174147
$892$	−1.14387e13	−0.604971
$893$	−1.87405e13	−0.986168
$894$	−6.76200e12	−0.354043
$895$	2.24237e13	1.16817
$896$	−2.04580e11	−0.0106042
$897$	4.05719e11	0.0209247
$898$	−2.91528e13	−1.49602
$899$	−4.47264e12	−0.228374
$900$	1.08643e13	0.551966
$901$	−3.86932e13	−1.95602
$902$	−2.19064e13	−1.10190
$903$	3.13732e10	0.00157023
$904$	−1.45911e12	−0.0726660
$905$	−2.28633e13	−1.13297
$906$	−1.65949e13	−0.818272
$907$	1.91598e13	0.940067	0.470034	−	0.882649i	$-0.344242\pi$
$907$	1.91598e13	0.940067	0.470034	+	0.882649i	$0.344242\pi$
$908$	−8.11881e12	−0.396375
$909$	−1.49837e12	−0.0727915
$910$	1.40271e11	0.00678079
$911$	9.06518e12	0.436058	0.218029	−	0.975942i	$-0.430037\pi$
$911$	9.06518e12	0.436058	0.218029	+	0.975942i	$0.430037\pi$
$912$	−8.99452e12	−0.430528
$913$	−3.26606e13	−1.55563
$914$	−2.76338e13	−1.30973
$915$	1.35737e13	0.640183
$916$	4.22592e13	1.98332
$917$	6.42271e10	0.00299955
$918$	−8.88212e12	−0.412786
$919$	3.18663e13	1.47371	0.736854	−	0.676052i	$-0.236310\pi$
$919$	3.18663e13	1.47371	0.736854	+	0.676052i	$0.236310\pi$
$920$	−4.74374e12	−0.218311
$921$	7.55894e12	0.346173
$922$	−2.21320e13	−1.00863
$923$	−7.38828e12	−0.335070
$924$	−2.83980e11	−0.0128163
$925$	7.60357e12	0.341492
$926$	−6.31212e13	−2.82115
$927$	1.02572e13	0.456214
$928$	−4.90521e12	−0.217116
$929$	−1.82057e13	−0.801930	−0.400965	−	0.916093i	$-0.631325\pi$
$929$	−1.82057e13	−0.801930	−0.400965	+	0.916093i	$0.631325\pi$
$930$	−1.04198e13	−0.456758
$931$	1.34686e13	0.587556
$932$	9.35837e13	4.06283
$933$	1.27932e13	0.552728
$934$	3.87150e12	0.166463
$935$	−5.98786e13	−2.56224
$936$	6.34965e12	0.270401
$937$	2.86463e13	1.21406	0.607029	−	0.794679i	$-0.292361\pi$
$937$	2.86463e13	1.21406	0.607029	+	0.794679i	$0.292361\pi$
$938$	−2.73923e11	−0.0115536
$939$	−6.76674e12	−0.284043
$940$	−1.12292e14	−4.69109
$941$	2.02281e13	0.841012	0.420506	−	0.907290i	$-0.361853\pi$
$941$	2.02281e13	0.841012	0.420506	+	0.907290i	$0.361853\pi$
$942$	−2.01963e13	−0.835686
$943$	−8.29225e11	−0.0341483
$944$	−4.03126e12	−0.165222
$945$	4.28753e10	0.00174890
$946$	2.71870e13	1.10370
$947$	4.65361e13	1.88025	0.940124	−	0.340833i	$-0.110709\pi$
$947$	4.65361e13	1.88025	0.940124	+	0.340833i	$0.110709\pi$
$948$	5.00292e13	2.01181
$949$	6.86927e12	0.274924
$950$	2.05628e13	0.819079
$951$	−1.60562e13	−0.636546
$952$	4.01032e11	0.0158239
$953$	−7.93310e11	−0.0311548	−0.0155774	−	0.999879i	$-0.504959\pi$
$953$	−7.93310e11	−0.0311548	−0.0155774	+	0.999879i	$0.504959\pi$
$954$	2.40089e13	0.938437
$955$	−3.05946e13	−1.19022
$956$	3.41639e13	1.32284
$957$	1.59483e13	0.614626
$958$	1.71544e13	0.658007
$959$	−1.63893e11	−0.00625715
$960$	1.43944e13	0.546981
$961$	−2.34507e13	−0.886952
$962$	8.53150e12	0.321172
$963$	−8.14244e12	−0.305096
$964$	3.76738e13	1.40505
$965$	−5.69589e13	−2.11441
$966$	−1.58998e10	−0.000587483 0
$967$	2.13665e13	0.785805	0.392903	−	0.919580i	$-0.371471\pi$
$967$	2.13665e13	0.785805	0.392903	+	0.919580i	$0.371471\pi$
$968$	−7.60014e13	−2.78216
$969$	−1.13656e13	−0.414128
$970$	1.05973e14	3.84346
$971$	−3.68918e13	−1.33181	−0.665906	−	0.746036i	$-0.731955\pi$
$971$	−3.68918e13	−1.33181	−0.665906	+	0.746036i	$0.731955\pi$
$972$	3.72608e12	0.133892
$973$	1.70141e10	0.000608556 0
$974$	8.33918e13	2.96899
$975$	−5.48898e12	−0.194523
$976$	−2.97884e13	−1.05081
$977$	2.31976e13	0.814550	0.407275	−	0.913306i	$-0.366479\pi$
$977$	2.31976e13	0.814550	0.407275	+	0.913306i	$0.366479\pi$
$978$	−9.58906e12	−0.335159
$979$	−4.63823e13	−1.61373
$980$	8.07029e13	2.79494
$981$	−1.70431e13	−0.587542
$982$	5.27350e12	0.180966
$983$	−3.48605e13	−1.19081	−0.595405	−	0.803425i	$-0.703009\pi$
$983$	−3.48605e13	−1.19081	−0.595405	+	0.803425i	$0.703009\pi$
$984$	−1.29777e13	−0.441285
$985$	−3.63456e13	−1.23024
$986$	−4.32381e13	−1.45687
$987$	−1.96046e11	−0.00657555
$988$	1.55986e13	0.520811
$989$	1.02911e12	0.0342042
$990$	3.71543e13	1.22928
$991$	−5.67925e13	−1.87051	−0.935254	−	0.353977i	$-0.884829\pi$
$991$	−5.67925e13	−1.87051	−0.935254	+	0.353977i	$0.884829\pi$
$992$	3.27802e12	0.107475
$993$	−2.12147e12	−0.0692413
$994$	2.89541e11	0.00940744
$995$	−3.64264e13	−1.17818
$996$	−3.71459e13	−1.19604
$997$	−2.65675e13	−0.851575	−0.425787	−	0.904823i	$-0.640003\pi$
$997$	−2.65675e13	−0.851575	−0.425787	+	0.904823i	$0.640003\pi$
$998$	1.53309e13	0.489192
$999$	2.60775e12	0.0828364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.1	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.1	✓	22	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)

\(f(q)\)	\(=\)	\(q-39.7571 q^{2} +81.0000 q^{3} +1068.63 q^{4} -1871.54 q^{5} -3220.33 q^{6} -43.1074 q^{7} -22129.9 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-39.7571 q^{2} +81.0000 q^{3} +1068.63 q^{4} -1871.54 q^{5} -3220.33 q^{6} -43.1074 q^{7} -22129.9 q^{8} +6561.00 q^{9} +74407.2 q^{10} +76107.0 q^{11} +86558.9 q^{12} -43732.0 q^{13} +1713.83 q^{14} -151595. q^{15} +332685. q^{16} +420385. q^{17} -260846. q^{18} -333780. q^{19} -1.99999e6 q^{20} -3491.70 q^{21} -3.02579e6 q^{22} -114536. q^{23} -1.79253e6 q^{24} +1.54955e6 q^{25} +1.73866e6 q^{26} +531441. q^{27} -46065.8 q^{28} +2.58705e6 q^{29} +6.02699e6 q^{30} -1.72886e6 q^{31} -1.89606e6 q^{32} +6.16467e6 q^{33} -1.67133e7 q^{34} +80677.4 q^{35} +7.01127e6 q^{36} +4.90694e6 q^{37} +1.32701e7 q^{38} -3.54229e6 q^{39} +4.14172e7 q^{40} +7.23989e6 q^{41} +138820. q^{42} -8.98509e6 q^{43} +8.13301e7 q^{44} -1.22792e7 q^{45} +4.55360e6 q^{46} +5.61464e7 q^{47} +2.69475e7 q^{48} -4.03517e7 q^{49} -6.16058e7 q^{50} +3.40512e7 q^{51} -4.67333e7 q^{52} -9.20424e7 q^{53} -2.11286e7 q^{54} -1.42438e8 q^{55} +953964. q^{56} -2.70362e7 q^{57} -1.02854e8 q^{58} -1.21174e7 q^{59} -1.61999e8 q^{60} -8.95394e7 q^{61} +6.87344e7 q^{62} -282828. q^{63} -9.49527e7 q^{64} +8.18464e7 q^{65} -2.45089e8 q^{66} -1.59831e8 q^{67} +4.49235e8 q^{68} -9.27738e6 q^{69} -3.20750e6 q^{70} +1.68944e8 q^{71} -1.45195e8 q^{72} -1.57076e8 q^{73} -1.95086e8 q^{74} +1.25514e8 q^{75} -3.56687e8 q^{76} -3.28077e6 q^{77} +1.40831e8 q^{78} +5.77979e8 q^{79} -6.22635e8 q^{80} +4.30467e7 q^{81} -2.87837e8 q^{82} -4.29141e8 q^{83} -3.73133e6 q^{84} -7.86769e8 q^{85} +3.57221e8 q^{86} +2.09551e8 q^{87} -1.68424e9 q^{88} -6.09435e8 q^{89} +4.88186e8 q^{90} +1.88517e6 q^{91} -1.22396e8 q^{92} -1.40037e8 q^{93} -2.23222e9 q^{94} +6.24684e8 q^{95} -1.53581e8 q^{96} +1.42423e9 q^{97} +1.60427e9 q^{98} +4.99338e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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