LMFDB - Embedded newform 177.10.a.d.1.10

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			1.10
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-6.00717 q^{2} +81.0000 q^{3} -475.914 q^{4} +2084.99 q^{5} -486.580 q^{6} -6970.40 q^{7} +5934.56 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-6.00717 q^{2} +81.0000 q^{3} -475.914 q^{4} +2084.99 q^{5} -486.580 q^{6} -6970.40 q^{7} +5934.56 q^{8} +6561.00 q^{9} -12524.9 q^{10} -39367.9 q^{11} -38549.0 q^{12} -185559. q^{13} +41872.3 q^{14} +168884. q^{15} +208018. q^{16} +311978. q^{17} -39413.0 q^{18} -320095. q^{19} -992274. q^{20} -564602. q^{21} +236490. q^{22} +573097. q^{23} +480700. q^{24} +2.39404e6 q^{25} +1.11468e6 q^{26} +531441. q^{27} +3.31731e6 q^{28} +896559. q^{29} -1.01451e6 q^{30} +7.63959e6 q^{31} -4.28809e6 q^{32} -3.18880e6 q^{33} -1.87410e6 q^{34} -1.45332e7 q^{35} -3.12247e6 q^{36} -1.40613e7 q^{37} +1.92287e6 q^{38} -1.50303e7 q^{39} +1.23735e7 q^{40} +7.43518e6 q^{41} +3.39166e6 q^{42} +3.38470e7 q^{43} +1.87357e7 q^{44} +1.36796e7 q^{45} -3.44269e6 q^{46} -3.46557e7 q^{47} +1.68495e7 q^{48} +8.23280e6 q^{49} -1.43814e7 q^{50} +2.52702e7 q^{51} +8.83102e7 q^{52} +2.21693e7 q^{53} -3.19245e6 q^{54} -8.20816e7 q^{55} -4.13662e7 q^{56} -2.59277e7 q^{57} -5.38578e6 q^{58} -1.21174e7 q^{59} -8.03742e7 q^{60} +1.30661e7 q^{61} -4.58923e7 q^{62} -4.57328e7 q^{63} -8.07460e7 q^{64} -3.86888e8 q^{65} +1.91557e7 q^{66} +2.44148e8 q^{67} -1.48475e8 q^{68} +4.64208e7 q^{69} +8.73032e7 q^{70} +3.04234e8 q^{71} +3.89367e7 q^{72} +2.17807e8 q^{73} +8.44685e7 q^{74} +1.93918e8 q^{75} +1.52338e8 q^{76} +2.74410e8 q^{77} +9.02894e7 q^{78} -4.29738e7 q^{79} +4.33715e8 q^{80} +4.30467e7 q^{81} -4.46644e7 q^{82} -8.56942e8 q^{83} +2.68702e8 q^{84} +6.50470e8 q^{85} -2.03325e8 q^{86} +7.26213e7 q^{87} -2.33631e8 q^{88} -6.49239e8 q^{89} -8.21756e7 q^{90} +1.29342e9 q^{91} -2.72745e8 q^{92} +6.18807e8 q^{93} +2.08182e8 q^{94} -6.67394e8 q^{95} -3.47336e8 q^{96} +1.14836e9 q^{97} -4.94558e7 q^{98} -2.58293e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.00717	−0.265482	−0.132741	−	0.991151i	$-0.542378\pi$
$2$	−6.00717	−0.265482	−0.132741	+	0.991151i	$0.542378\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−475.914	−0.929519
$5$	2084.99	1.49189	0.745947	−	0.666005i	$-0.231997\pi$
$5$	2084.99	1.49189	0.745947	+	0.666005i	$0.231997\pi$
$6$	−486.580	−0.153276
$7$	−6970.40	−1.09728	−0.548638	−	0.836060i	$-0.684854\pi$
$7$	−6970.40	−1.09728	−0.548638	+	0.836060i	$0.684854\pi$
$8$	5934.56	0.512252
$9$	6561.00	0.333333
$10$	−12524.9	−0.396071
$11$	−39367.9	−0.810728	−0.405364	−	0.914155i	$-0.632855\pi$
$11$	−39367.9	−0.810728	−0.405364	+	0.914155i	$0.632855\pi$
$12$	−38549.0	−0.536658
$13$	−185559.	−1.80193	−0.900964	−	0.433895i	$-0.857139\pi$
$13$	−185559.	−1.80193	−0.900964	+	0.433895i	$0.857139\pi$
$14$	41872.3	0.291307
$15$	168884.	0.861346
$16$	208018.	0.793526
$17$	311978.	0.905949	0.452974	−	0.891524i	$-0.350363\pi$
$17$	311978.	0.905949	0.452974	+	0.891524i	$0.350363\pi$
$18$	−39413.0	−0.0884939
$19$	−320095.	−0.563492	−0.281746	−	0.959489i	$-0.590914\pi$
$19$	−320095.	−0.563492	−0.281746	+	0.959489i	$0.590914\pi$
$20$	−992274.	−1.38675
$21$	−564602.	−0.633513
$22$	236490.	0.215233
$23$	573097.	0.427024	0.213512	−	0.976940i	$-0.431510\pi$
$23$	573097.	0.427024	0.213512	+	0.976940i	$0.431510\pi$
$24$	480700.	0.295749
$25$	2.39404e6	1.22575
$26$	1.11468e6	0.478379
$27$	531441.	0.192450
$28$	3.31731e6	1.01994
$29$	896559.	0.235390	0.117695	−	0.993050i	$-0.462449\pi$
$29$	896559.	0.235390	0.117695	+	0.993050i	$0.462449\pi$
$30$	−1.01451e6	−0.228672
$31$	7.63959e6	1.48574	0.742869	−	0.669436i	$-0.233464\pi$
$31$	7.63959e6	1.48574	0.742869	+	0.669436i	$0.233464\pi$
$32$	−4.28809e6	−0.722919
$33$	−3.18880e6	−0.468074
$34$	−1.87410e6	−0.240513
$35$	−1.45332e7	−1.63702
$36$	−3.12247e6	−0.309840
$37$	−1.40613e7	−1.23344	−0.616719	−	0.787183i	$-0.711538\pi$
$37$	−1.40613e7	−1.23344	−0.616719	+	0.787183i	$0.711538\pi$
$38$	1.92287e6	0.149597
$39$	−1.50303e7	−1.04034
$40$	1.23735e7	0.764226
$41$	7.43518e6	0.410927	0.205463	−	0.978665i	$-0.434130\pi$
$41$	7.43518e6	0.410927	0.205463	+	0.978665i	$0.434130\pi$
$42$	3.39166e6	0.168186
$43$	3.38470e7	1.50978	0.754888	−	0.655853i	$-0.227691\pi$
$43$	3.38470e7	1.50978	0.754888	+	0.655853i	$0.227691\pi$
$44$	1.87357e7	0.753588
$45$	1.36796e7	0.497298
$46$	−3.44269e6	−0.113367
$47$	−3.46557e7	−1.03594	−0.517969	−	0.855399i	$-0.673312\pi$
$47$	−3.46557e7	−1.03594	−0.517969	+	0.855399i	$0.673312\pi$
$48$	1.68495e7	0.458142
$49$	8.23280e6	0.204017
$50$	−1.43814e7	−0.325414
$51$	2.52702e7	0.523050
$52$	8.83102e7	1.67493
$53$	2.21693e7	0.385932	0.192966	−	0.981205i	$-0.438189\pi$
$53$	2.21693e7	0.385932	0.192966	+	0.981205i	$0.438189\pi$
$54$	−3.19245e6	−0.0510920
$55$	−8.20816e7	−1.20952
$56$	−4.13662e7	−0.562082
$57$	−2.59277e7	−0.325332
$58$	−5.38578e6	−0.0624917
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−8.03742e7	−0.800638
$61$	1.30661e7	0.120827	0.0604133	−	0.998173i	$-0.480758\pi$
$61$	1.30661e7	0.120827	0.0604133	+	0.998173i	$0.480758\pi$
$62$	−4.58923e7	−0.394436
$63$	−4.57328e7	−0.365759
$64$	−8.07460e7	−0.601604
$65$	−3.86888e8	−2.68829
$66$	1.91557e7	0.124265
$67$	2.44148e8	1.48018	0.740092	−	0.672505i	$-0.234782\pi$
$67$	2.44148e8	1.48018	0.740092	+	0.672505i	$0.234782\pi$
$68$	−1.48475e8	−0.842097
$69$	4.64208e7	0.246543
$70$	8.73032e7	0.434599
$71$	3.04234e8	1.42084	0.710420	−	0.703778i	$-0.248505\pi$
$71$	3.04234e8	1.42084	0.710420	+	0.703778i	$0.248505\pi$
$72$	3.89367e7	0.170751
$73$	2.17807e8	0.897673	0.448837	−	0.893614i	$-0.351839\pi$
$73$	2.17807e8	0.897673	0.448837	+	0.893614i	$0.351839\pi$
$74$	8.44685e7	0.327455
$75$	1.93918e8	0.707687
$76$	1.52338e8	0.523777
$77$	2.74410e8	0.889593
$78$	9.02894e7	0.276192
$79$	−4.29738e7	−0.124132	−0.0620658	−	0.998072i	$-0.519769\pi$
$79$	−4.29738e7	−0.124132	−0.0620658	+	0.998072i	$0.519769\pi$
$80$	4.33715e8	1.18386
$81$	4.30467e7	0.111111
$82$	−4.46644e7	−0.109094
$83$	−8.56942e8	−1.98198	−0.990991	−	0.133925i	$-0.957242\pi$
$83$	−8.56942e8	−1.98198	−0.990991	+	0.133925i	$0.957242\pi$
$84$	2.68702e8	0.588863
$85$	6.50470e8	1.35158
$86$	−2.03325e8	−0.400818
$87$	7.26213e7	0.135902
$88$	−2.33631e8	−0.415297
$89$	−6.49239e8	−1.09686	−0.548428	−	0.836198i	$-0.684774\pi$
$89$	−6.49239e8	−1.09686	−0.548428	+	0.836198i	$0.684774\pi$
$90$	−8.21756e7	−0.132024
$91$	1.29342e9	1.97721
$92$	−2.72745e8	−0.396927
$93$	6.18807e8	0.857792
$94$	2.08182e8	0.275023
$95$	−6.67394e8	−0.840671
$96$	−3.47336e8	−0.417377
$97$	1.14836e9	1.31706	0.658528	−	0.752556i	$-0.271179\pi$
$97$	1.14836e9	1.31706	0.658528	+	0.752556i	$0.271179\pi$
$98$	−4.94558e7	−0.0541627
$99$	−2.58293e8	−0.270243
$100$	−1.13936e9	−1.13936
$101$	8.98191e8	0.858860	0.429430	−	0.903100i	$-0.358714\pi$
$101$	8.98191e8	0.858860	0.429430	+	0.903100i	$0.358714\pi$
$102$	−1.51802e8	−0.138860
$103$	−6.04439e8	−0.529157	−0.264579	−	0.964364i	$-0.585233\pi$
$103$	−6.04439e8	−0.529157	−0.264579	+	0.964364i	$0.585233\pi$
$104$	−1.10121e9	−0.923041
$105$	−1.17719e9	−0.945135
$106$	−1.33175e8	−0.102458
$107$	2.30250e9	1.69814	0.849068	−	0.528283i	$-0.177164\pi$
$107$	2.30250e9	1.69814	0.849068	+	0.528283i	$0.177164\pi$
$108$	−2.52920e8	−0.178886
$109$	1.44302e9	0.979159	0.489580	−	0.871959i	$-0.337150\pi$
$109$	1.44302e9	0.979159	0.489580	+	0.871959i	$0.337150\pi$
$110$	4.93077e8	0.321106
$111$	−1.13896e9	−0.712126
$112$	−1.44997e9	−0.870718
$113$	4.83813e8	0.279141	0.139571	−	0.990212i	$-0.455428\pi$
$113$	4.83813e8	0.279141	0.139571	+	0.990212i	$0.455428\pi$
$114$	1.55752e8	0.0863698
$115$	1.19490e9	0.637075
$116$	−4.26685e8	−0.218799
$117$	−1.21745e9	−0.600642
$118$	7.27910e7	0.0345628
$119$	−2.17461e9	−0.994077
$120$	1.00225e9	0.441226
$121$	−8.08116e8	−0.342720
$122$	−7.84903e7	−0.0320772
$123$	6.02250e8	0.237249
$124$	−3.63579e9	−1.38102
$125$	9.19310e8	0.336796
$126$	2.74724e8	0.0971023
$127$	1.35220e9	0.461237	0.230619	−	0.973044i	$-0.425925\pi$
$127$	1.35220e9	0.461237	0.230619	+	0.973044i	$0.425925\pi$
$128$	2.68056e9	0.882634
$129$	2.74161e9	0.871670
$130$	2.32410e9	0.713691
$131$	4.03325e9	1.19656	0.598280	−	0.801287i	$-0.295851\pi$
$131$	4.03325e9	1.19656	0.598280	+	0.801287i	$0.295851\pi$
$132$	1.51759e9	0.435084
$133$	2.23119e9	0.618307
$134$	−1.46664e9	−0.392962
$135$	1.10805e9	0.287115
$136$	1.85145e9	0.464074
$137$	4.79550e8	0.116303	0.0581515	−	0.998308i	$-0.481479\pi$
$137$	4.79550e8	0.116303	0.0581515	+	0.998308i	$0.481479\pi$
$138$	−2.78858e8	−0.0654526
$139$	2.01524e9	0.457890	0.228945	−	0.973439i	$-0.426472\pi$
$139$	2.01524e9	0.457890	0.228945	+	0.973439i	$0.426472\pi$
$140$	6.91654e9	1.52164
$141$	−2.80711e9	−0.598099
$142$	−1.82758e9	−0.377207
$143$	7.30507e9	1.46087
$144$	1.36481e9	0.264509
$145$	1.86931e9	0.351177
$146$	−1.30840e9	−0.238316
$147$	6.66857e8	0.117789
$148$	6.69196e9	1.14650
$149$	6.27978e9	1.04377	0.521887	−	0.853015i	$-0.325228\pi$
$149$	6.27978e9	1.04377	0.521887	+	0.853015i	$0.325228\pi$
$150$	−1.16489e9	−0.187878
$151$	9.86636e9	1.54440	0.772201	−	0.635378i	$-0.219156\pi$
$151$	9.86636e9	1.54440	0.772201	+	0.635378i	$0.219156\pi$
$152$	−1.89963e9	−0.288650
$153$	2.04689e9	0.301983
$154$	−1.64843e9	−0.236171
$155$	1.59284e10	2.21657
$156$	7.15312e9	0.967019
$157$	1.21615e10	1.59750	0.798748	−	0.601666i	$-0.205496\pi$
$157$	1.21615e10	1.59750	0.798748	+	0.601666i	$0.205496\pi$
$158$	2.58151e8	0.0329547
$159$	1.79571e9	0.222818
$160$	−8.94062e9	−1.07852
$161$	−3.99471e9	−0.468564
$162$	−2.58589e8	−0.0294980
$163$	−1.18179e10	−1.31128	−0.655642	−	0.755072i	$-0.727602\pi$
$163$	−1.18179e10	−1.31128	−0.655642	+	0.755072i	$0.727602\pi$
$164$	−3.53851e9	−0.381964
$165$	−6.64861e9	−0.698317
$166$	5.14779e9	0.526180
$167$	5.66807e9	0.563911	0.281956	−	0.959427i	$-0.409017\pi$
$167$	5.66807e9	0.563911	0.281956	+	0.959427i	$0.409017\pi$
$168$	−3.35067e9	−0.324518
$169$	2.38277e10	2.24694
$170$	−3.90748e9	−0.358820
$171$	−2.10015e9	−0.187831
$172$	−1.61083e10	−1.40337
$173$	1.76972e10	1.50210	0.751049	−	0.660246i	$-0.229548\pi$
$173$	1.76972e10	1.50210	0.751049	+	0.660246i	$0.229548\pi$
$174$	−4.36248e8	−0.0360796
$175$	−1.66874e10	−1.34499
$176$	−8.18924e9	−0.643334
$177$	−9.81506e8	−0.0751646
$178$	3.90009e9	0.291195
$179$	1.59584e10	1.16186	0.580928	−	0.813955i	$-0.302690\pi$
$179$	1.59584e10	1.16186	0.580928	+	0.813955i	$0.302690\pi$
$180$	−6.51031e9	−0.462248
$181$	−9.26360e9	−0.641543	−0.320772	−	0.947157i	$-0.603942\pi$
$181$	−9.26360e9	−0.641543	−0.320772	+	0.947157i	$0.603942\pi$
$182$	−7.76979e9	−0.524914
$183$	1.05836e9	0.0697592
$184$	3.40108e9	0.218744
$185$	−2.93176e10	−1.84016
$186$	−3.71727e9	−0.227728
$187$	−1.22819e10	−0.734478
$188$	1.64931e10	0.962925
$189$	−3.70435e9	−0.211171
$190$	4.00915e9	0.223183
$191$	−1.65202e10	−0.898182	−0.449091	−	0.893486i	$-0.648252\pi$
$191$	−1.65202e10	−0.898182	−0.449091	+	0.893486i	$0.648252\pi$
$192$	−6.54042e9	−0.347336
$193$	1.33694e8	0.00693591	0.00346796	−	0.999994i	$-0.498896\pi$
$193$	1.33694e8	0.00693591	0.00346796	+	0.999994i	$0.498896\pi$
$194$	−6.89837e9	−0.349654
$195$	−3.13380e10	−1.55208
$196$	−3.91811e9	−0.189637
$197$	6.83918e9	0.323524	0.161762	−	0.986830i	$-0.448282\pi$
$197$	6.83918e9	0.323524	0.161762	+	0.986830i	$0.448282\pi$
$198$	1.55161e9	0.0717445
$199$	−1.06544e9	−0.0481605	−0.0240803	−	0.999710i	$-0.507666\pi$
$199$	−1.06544e9	−0.0481605	−0.0240803	+	0.999710i	$0.507666\pi$
$200$	1.42076e10	0.627893
$201$	1.97760e10	0.854585
$202$	−5.39558e9	−0.228012
$203$	−6.24937e9	−0.258288
$204$	−1.20264e10	−0.486185
$205$	1.55023e10	0.613059
$206$	3.63096e9	0.140482
$207$	3.76009e9	0.142341
$208$	−3.85996e10	−1.42988
$209$	1.26015e10	0.456839
$210$	7.07156e9	0.250916
$211$	−1.58072e10	−0.549013	−0.274507	−	0.961585i	$-0.588515\pi$
$211$	−1.58072e10	−0.549013	−0.274507	+	0.961585i	$0.588515\pi$
$212$	−1.05507e10	−0.358731
$213$	2.46430e10	0.820323
$214$	−1.38315e10	−0.450824
$215$	7.05706e10	2.25243
$216$	3.15387e9	0.0985830
$217$	−5.32510e10	−1.63027
$218$	−8.66846e9	−0.259949
$219$	1.76423e10	0.518272
$220$	3.90638e10	1.12427
$221$	−5.78903e10	−1.63245
$222$	6.84195e9	0.189056
$223$	−2.32521e10	−0.629636	−0.314818	−	0.949152i	$-0.601943\pi$
$223$	−2.32521e10	−0.629636	−0.314818	+	0.949152i	$0.601943\pi$
$224$	2.98897e10	0.793242
$225$	1.57073e10	0.408583
$226$	−2.90634e9	−0.0741069
$227$	2.67471e10	0.668591	0.334296	−	0.942468i	$-0.391502\pi$
$227$	2.67471e10	0.668591	0.334296	+	0.942468i	$0.391502\pi$
$228$	1.23394e10	0.302403
$229$	−5.20429e10	−1.25055	−0.625276	−	0.780404i	$-0.715014\pi$
$229$	−5.20429e10	−1.25055	−0.625276	+	0.780404i	$0.715014\pi$
$230$	−7.17795e9	−0.169132
$231$	2.22272e10	0.513607
$232$	5.32068e9	0.120579
$233$	−3.89449e10	−0.865663	−0.432832	−	0.901475i	$-0.642486\pi$
$233$	−3.89449e10	−0.865663	−0.432832	+	0.901475i	$0.642486\pi$
$234$	7.31344e9	0.159460
$235$	−7.22566e10	−1.54551
$236$	5.76682e9	0.121013
$237$	−3.48088e9	−0.0716674
$238$	1.30632e10	0.263909
$239$	1.34283e10	0.266214	0.133107	−	0.991102i	$-0.457505\pi$
$239$	1.34283e10	0.266214	0.133107	+	0.991102i	$0.457505\pi$
$240$	3.51309e10	0.683500
$241$	−1.42708e10	−0.272504	−0.136252	−	0.990674i	$-0.543506\pi$
$241$	−1.42708e10	−0.272504	−0.136252	+	0.990674i	$0.543506\pi$
$242$	4.85448e9	0.0909859
$243$	3.48678e9	0.0641500
$244$	−6.21835e9	−0.112311
$245$	1.71653e10	0.304371
$246$	−3.61781e9	−0.0629852
$247$	5.93966e10	1.01537
$248$	4.53376e10	0.761073
$249$	−6.94123e10	−1.14430
$250$	−5.52245e9	−0.0894132
$251$	−9.85654e10	−1.56745	−0.783724	−	0.621110i	$-0.786682\pi$
$251$	−9.85654e10	−1.56745	−0.783724	+	0.621110i	$0.786682\pi$
$252$	2.17649e10	0.339980
$253$	−2.25616e10	−0.346201
$254$	−8.12289e9	−0.122450
$255$	5.26880e10	0.780335
$256$	2.52394e10	0.367281
$257$	−9.44707e10	−1.35082	−0.675411	−	0.737442i	$-0.736034\pi$
$257$	−9.44707e10	−1.35082	−0.675411	+	0.737442i	$0.736034\pi$
$258$	−1.64693e10	−0.231412
$259$	9.80127e10	1.35342
$260$	1.84126e11	2.49881
$261$	5.88232e9	0.0784633
$262$	−2.42284e10	−0.317665
$263$	3.07403e10	0.396194	0.198097	−	0.980182i	$-0.436524\pi$
$263$	3.07403e10	0.396194	0.198097	+	0.980182i	$0.436524\pi$
$264$	−1.89241e10	−0.239772
$265$	4.62227e10	0.575770
$266$	−1.34031e10	−0.164149
$267$	−5.25884e10	−0.633270
$268$	−1.16193e11	−1.37586
$269$	−6.19302e10	−0.721137	−0.360568	−	0.932733i	$-0.617417\pi$
$269$	−6.19302e10	−0.721137	−0.360568	+	0.932733i	$0.617417\pi$
$270$	−6.65622e9	−0.0762239
$271$	−5.29125e10	−0.595931	−0.297966	−	0.954577i	$-0.596308\pi$
$271$	−5.29125e10	−0.595931	−0.297966	+	0.954577i	$0.596308\pi$
$272$	6.48970e10	0.718894
$273$	1.04767e11	1.14154
$274$	−2.88073e9	−0.0308763
$275$	−9.42485e10	−0.993750
$276$	−2.20923e10	−0.229166
$277$	4.92700e10	0.502833	0.251416	−	0.967879i	$-0.419104\pi$
$277$	4.92700e10	0.502833	0.251416	+	0.967879i	$0.419104\pi$
$278$	−1.21059e10	−0.121561
$279$	5.01234e10	0.495246
$280$	−8.62481e10	−0.838568
$281$	−1.04213e11	−0.997111	−0.498556	−	0.866858i	$-0.666136\pi$
$281$	−1.04213e11	−0.997111	−0.498556	+	0.866858i	$0.666136\pi$
$282$	1.68628e10	0.158784
$283$	1.29363e11	1.19887	0.599435	−	0.800423i	$-0.295392\pi$
$283$	1.29363e11	1.19887	0.599435	+	0.800423i	$0.295392\pi$
$284$	−1.44789e11	−1.32070
$285$	−5.40589e10	−0.485362
$286$	−4.38828e10	−0.387835
$287$	−5.18262e10	−0.450900
$288$	−2.81342e10	−0.240973
$289$	−2.12577e10	−0.179257
$290$	−1.12293e10	−0.0932311
$291$	9.30169e10	0.760403
$292$	−1.03657e11	−0.834405
$293$	1.85348e10	0.146921	0.0734604	−	0.997298i	$-0.476596\pi$
$293$	1.85348e10	0.146921	0.0734604	+	0.997298i	$0.476596\pi$
$294$	−4.00592e9	−0.0312708
$295$	−2.52645e10	−0.194228
$296$	−8.34476e10	−0.631831
$297$	−2.09217e10	−0.156025
$298$	−3.77237e10	−0.277103
$299$	−1.06343e11	−0.769467
$300$	−9.22881e10	−0.657809
$301$	−2.35927e11	−1.65664
$302$	−5.92688e10	−0.410011
$303$	7.27534e10	0.495863
$304$	−6.65856e10	−0.447146
$305$	2.72427e10	0.180260
$306$	−1.22960e10	−0.0801709
$307$	2.80374e11	1.80142	0.900709	−	0.434424i	$-0.143048\pi$
$307$	2.80374e11	1.80142	0.900709	+	0.434424i	$0.143048\pi$
$308$	−1.30595e11	−0.826894
$309$	−4.89595e10	−0.305509
$310$	−9.56848e10	−0.588458
$311$	2.75615e11	1.67063	0.835315	−	0.549771i	$-0.185285\pi$
$311$	2.75615e11	1.67063	0.835315	+	0.549771i	$0.185285\pi$
$312$	−8.91982e10	−0.532918
$313$	1.54872e11	0.912060	0.456030	−	0.889964i	$-0.349271\pi$
$313$	1.54872e11	0.912060	0.456030	+	0.889964i	$0.349271\pi$
$314$	−7.30563e10	−0.424106
$315$	−9.53522e10	−0.545674
$316$	2.04518e10	0.115383
$317$	−1.30019e11	−0.723168	−0.361584	−	0.932340i	$-0.617764\pi$
$317$	−1.30019e11	−0.723168	−0.361584	+	0.932340i	$0.617764\pi$
$318$	−1.07872e10	−0.0591541
$319$	−3.52956e10	−0.190837
$320$	−1.68354e11	−0.897530
$321$	1.86502e11	0.980419
$322$	2.39969e10	0.124395
$323$	−9.98626e10	−0.510495
$324$	−2.04865e10	−0.103280
$325$	−4.44237e11	−2.20871
$326$	7.09922e10	0.348122
$327$	1.16885e11	0.565318
$328$	4.41246e10	0.210498
$329$	2.41564e11	1.13671
$330$	3.99393e10	0.185390
$331$	−1.78508e11	−0.817396	−0.408698	−	0.912670i	$-0.634017\pi$
$331$	−1.78508e11	−0.817396	−0.408698	+	0.912670i	$0.634017\pi$
$332$	4.07831e11	1.84229
$333$	−9.22561e10	−0.411146
$334$	−3.40490e10	−0.149708
$335$	5.09044e11	2.20828
$336$	−1.17447e11	−0.502709
$337$	3.18272e10	0.134420	0.0672100	−	0.997739i	$-0.478590\pi$
$337$	3.18272e10	0.134420	0.0672100	+	0.997739i	$0.478590\pi$
$338$	−1.43137e11	−0.596522
$339$	3.91888e10	0.161162
$340$	−3.09568e11	−1.25632
$341$	−3.00755e11	−1.20453
$342$	1.26159e10	0.0498656
$343$	2.23895e11	0.873414
$344$	2.00867e11	0.773386
$345$	9.67868e10	0.367816
$346$	−1.06310e11	−0.398780
$347$	−9.04488e10	−0.334904	−0.167452	−	0.985880i	$-0.553554\pi$
$347$	−9.04488e10	−0.334904	−0.167452	+	0.985880i	$0.553554\pi$
$348$	−3.45615e10	−0.126324
$349$	−5.17329e11	−1.86660	−0.933302	−	0.359092i	$-0.883086\pi$
$349$	−5.17329e11	−1.86660	−0.933302	+	0.359092i	$0.883086\pi$
$350$	1.00244e11	0.357070
$351$	−9.86137e10	−0.346781
$352$	1.68813e11	0.586091
$353$	3.58289e11	1.22814	0.614068	−	0.789253i	$-0.289532\pi$
$353$	3.58289e11	1.22814	0.614068	+	0.789253i	$0.289532\pi$
$354$	5.89607e9	0.0199548
$355$	6.34324e11	2.11975
$356$	3.08982e11	1.01955
$357$	−1.76143e11	−0.573930
$358$	−9.58650e10	−0.308451
$359$	1.13310e11	0.360033	0.180016	−	0.983664i	$-0.442385\pi$
$359$	1.13310e11	0.360033	0.180016	+	0.983664i	$0.442385\pi$
$360$	8.11824e10	0.254742
$361$	−2.20227e11	−0.682476
$362$	5.56480e10	0.170318
$363$	−6.54574e10	−0.197869
$364$	−6.15557e11	−1.83786
$365$	4.54124e11	1.33923
$366$	−6.35772e9	−0.0185198
$367$	5.94459e11	1.71050	0.855252	−	0.518212i	$-0.173402\pi$
$367$	5.94459e11	1.71050	0.855252	+	0.518212i	$0.173402\pi$
$368$	1.19214e11	0.338855
$369$	4.87822e10	0.136976
$370$	1.76116e11	0.488529
$371$	−1.54529e11	−0.423474
$372$	−2.94499e11	−0.797334
$373$	−5.26553e11	−1.40849	−0.704243	−	0.709959i	$-0.748713\pi$
$373$	−5.26553e11	−1.40849	−0.704243	+	0.709959i	$0.748713\pi$
$374$	7.37795e10	0.194991
$375$	7.44641e10	0.194449
$376$	−2.05666e11	−0.530662
$377$	−1.66365e11	−0.424155
$378$	2.22527e10	0.0560620
$379$	7.85785e11	1.95626	0.978131	−	0.207989i	$-0.0666920\pi$
$379$	7.85785e11	1.95626	0.978131	+	0.207989i	$0.0666920\pi$
$380$	3.17622e11	0.781420
$381$	1.09528e11	0.266295
$382$	9.92394e10	0.238451
$383$	4.44736e11	1.05611	0.528053	−	0.849211i	$-0.322922\pi$
$383$	4.44736e11	1.05611	0.528053	+	0.849211i	$0.322922\pi$
$384$	2.17125e11	0.509589
$385$	5.72141e11	1.32718
$386$	−8.03121e8	−0.00184136
$387$	2.22070e11	0.503259
$388$	−5.46519e11	−1.22423
$389$	−5.50601e11	−1.21917	−0.609584	−	0.792722i	$-0.708663\pi$
$389$	−5.50601e11	−1.21917	−0.609584	+	0.792722i	$0.708663\pi$
$390$	1.88252e11	0.412050
$391$	1.78793e11	0.386862
$392$	4.88581e10	0.104508
$393$	3.26694e11	0.690835
$394$	−4.10841e10	−0.0858896
$395$	−8.95999e10	−0.185191
$396$	1.22925e11	0.251196
$397$	3.53364e11	0.713946	0.356973	−	0.934115i	$-0.383809\pi$
$397$	3.53364e11	0.713946	0.356973	+	0.934115i	$0.383809\pi$
$398$	6.40029e9	0.0127857
$399$	1.80726e11	0.356980
$400$	4.98004e11	0.972665
$401$	−5.64703e11	−1.09061	−0.545306	−	0.838237i	$-0.683587\pi$
$401$	−5.64703e11	−1.09061	−0.545306	+	0.838237i	$0.683587\pi$
$402$	−1.18797e11	−0.226877
$403$	−1.41760e12	−2.67719
$404$	−4.27462e11	−0.798327
$405$	8.97518e10	0.165766
$406$	3.75410e10	0.0685707
$407$	5.53563e11	0.999983
$408$	1.49968e11	0.267933
$409$	5.11455e11	0.903759	0.451880	−	0.892079i	$-0.350754\pi$
$409$	5.11455e11	0.903759	0.451880	+	0.892079i	$0.350754\pi$
$410$	−9.31246e10	−0.162756
$411$	3.88435e10	0.0671476
$412$	2.87661e11	0.491862
$413$	8.44628e10	0.142853
$414$	−2.25875e10	−0.0377890
$415$	−1.78671e12	−2.95691
$416$	7.95695e11	1.30265
$417$	1.63235e11	0.264363
$418$	−7.56992e10	−0.121282
$419$	3.01888e11	0.478500	0.239250	−	0.970958i	$-0.423098\pi$
$419$	3.01888e11	0.478500	0.239250	+	0.970958i	$0.423098\pi$
$420$	5.60240e11	0.878521
$421$	6.20585e11	0.962790	0.481395	−	0.876504i	$-0.340130\pi$
$421$	6.20585e11	0.962790	0.481395	+	0.876504i	$0.340130\pi$
$422$	9.49562e10	0.145753
$423$	−2.27376e11	−0.345313
$424$	1.31565e11	0.197694
$425$	7.46889e11	1.11047
$426$	−1.48034e11	−0.217781
$427$	−9.10760e10	−0.132580
$428$	−1.09579e12	−1.57845
$429$	5.91711e11	0.843435
$430$	−4.23929e11	−0.597978
$431$	−4.33998e10	−0.0605814	−0.0302907	−	0.999541i	$-0.509643\pi$
$431$	−4.33998e10	−0.0605814	−0.0302907	+	0.999541i	$0.509643\pi$
$432$	1.10549e11	0.152714
$433$	−9.53516e11	−1.30356	−0.651782	−	0.758406i	$-0.725978\pi$
$433$	−9.53516e11	−1.30356	−0.651782	+	0.758406i	$0.725978\pi$
$434$	3.19887e11	0.432806
$435$	1.51414e11	0.202752
$436$	−6.86754e11	−0.910148
$437$	−1.83446e11	−0.240625
$438$	−1.05980e11	−0.137592
$439$	−2.66042e11	−0.341869	−0.170934	−	0.985282i	$-0.554679\pi$
$439$	−2.66042e11	−0.341869	−0.170934	+	0.985282i	$0.554679\pi$
$440$	−4.87118e11	−0.619580
$441$	5.40154e10	0.0680055
$442$	3.47757e11	0.433387
$443$	−8.41868e11	−1.03855	−0.519275	−	0.854607i	$-0.673798\pi$
$443$	−8.41868e11	−1.03855	−0.519275	+	0.854607i	$0.673798\pi$
$444$	5.42049e11	0.661935
$445$	−1.35366e12	−1.63639
$446$	1.39679e11	0.167157
$447$	5.08662e11	0.602623
$448$	5.62831e11	0.660126
$449$	−1.19292e12	−1.38517	−0.692583	−	0.721338i	$-0.743527\pi$
$449$	−1.19292e12	−1.38517	−0.692583	+	0.721338i	$0.743527\pi$
$450$	−9.43565e10	−0.108471
$451$	−2.92708e11	−0.333150
$452$	−2.30253e11	−0.259467
$453$	7.99175e11	0.891661
$454$	−1.60674e11	−0.177499
$455$	2.69676e12	2.94979
$456$	−1.53870e11	−0.166652
$457$	4.51300e11	0.483997	0.241998	−	0.970277i	$-0.422197\pi$
$457$	4.51300e11	0.483997	0.241998	+	0.970277i	$0.422197\pi$
$458$	3.12630e11	0.331999
$459$	1.65798e11	0.174350
$460$	−5.68669e11	−0.592174
$461$	3.74613e11	0.386304	0.193152	−	0.981169i	$-0.438129\pi$
$461$	3.74613e11	0.386304	0.193152	+	0.981169i	$0.438129\pi$
$462$	−1.33522e11	−0.136353
$463$	−1.27942e11	−0.129390	−0.0646948	−	0.997905i	$-0.520607\pi$
$463$	−1.27942e11	−0.129390	−0.0646948	+	0.997905i	$0.520607\pi$
$464$	1.86500e11	0.186788
$465$	1.29020e12	1.27974
$466$	2.33948e11	0.229818
$467$	1.24686e12	1.21309	0.606544	−	0.795050i	$-0.292555\pi$
$467$	1.24686e12	1.21309	0.606544	+	0.795050i	$0.292555\pi$
$468$	5.79403e11	0.558309
$469$	−1.70181e12	−1.62417
$470$	4.34057e11	0.410305
$471$	9.85083e11	0.922314
$472$	−7.19112e10	−0.0666895
$473$	−1.33249e12	−1.22402
$474$	2.09102e10	0.0190264
$475$	−7.66322e11	−0.690701
$476$	1.03493e12	0.924014
$477$	1.45453e11	0.128644
$478$	−8.06661e10	−0.0706750
$479$	1.89190e12	1.64206	0.821031	−	0.570884i	$-0.193399\pi$
$479$	1.89190e12	1.64206	0.821031	+	0.570884i	$0.193399\pi$
$480$	−7.24190e11	−0.622683
$481$	2.60920e12	2.22257
$482$	8.57273e10	0.0723449
$483$	−3.23572e11	−0.270526
$484$	3.84593e11	0.318565
$485$	2.39431e12	1.96491
$486$	−2.09457e10	−0.0170307
$487$	−8.53099e11	−0.687256	−0.343628	−	0.939106i	$-0.611656\pi$
$487$	−8.53099e11	−0.687256	−0.343628	+	0.939106i	$0.611656\pi$
$488$	7.75417e10	0.0618936
$489$	−9.57252e11	−0.757071
$490$	−1.03115e11	−0.0808050
$491$	3.54150e11	0.274993	0.137496	−	0.990502i	$-0.456094\pi$
$491$	3.54150e11	0.274993	0.137496	+	0.990502i	$0.456094\pi$
$492$	−2.86619e11	−0.220527
$493$	2.79707e11	0.213251
$494$	−3.56805e11	−0.269563
$495$	−5.38537e11	−0.403174
$496$	1.58917e12	1.17897
$497$	−2.12063e12	−1.55906
$498$	4.16971e11	0.303790
$499$	1.13264e12	0.817787	0.408893	−	0.912582i	$-0.365915\pi$
$499$	1.13264e12	0.817787	0.408893	+	0.912582i	$0.365915\pi$
$500$	−4.37512e11	−0.313058
$501$	4.59113e11	0.325574
$502$	5.92099e11	0.416129
$503$	−2.19217e12	−1.52692	−0.763462	−	0.645852i	$-0.776502\pi$
$503$	−2.19217e12	−1.52692	−0.763462	+	0.645852i	$0.776502\pi$
$504$	−2.71404e11	−0.187361
$505$	1.87272e12	1.28133
$506$	1.35531e11	0.0919099
$507$	1.93004e12	1.29727
$508$	−6.43531e11	−0.428729
$509$	8.24907e11	0.544722	0.272361	−	0.962195i	$-0.412196\pi$
$509$	8.24907e11	0.544722	0.272361	+	0.962195i	$0.412196\pi$
$510$	−3.16506e11	−0.207165
$511$	−1.51820e12	−0.984996
$512$	−1.52406e12	−0.980140
$513$	−1.70112e11	−0.108444
$514$	5.67501e11	0.358618
$515$	−1.26025e12	−0.789447
$516$	−1.30477e12	−0.810234
$517$	1.36432e12	0.839864
$518$	−5.88779e11	−0.359309
$519$	1.43348e12	0.867237
$520$	−2.29601e12	−1.37708
$521$	−2.63163e12	−1.56479	−0.782395	−	0.622783i	$-0.786002\pi$
$521$	−2.63163e12	−1.56479	−0.782395	+	0.622783i	$0.786002\pi$
$522$	−3.53361e10	−0.0208306
$523$	−2.33142e12	−1.36258	−0.681292	−	0.732011i	$-0.738582\pi$
$523$	−2.33142e12	−1.36258	−0.681292	+	0.732011i	$0.738582\pi$
$524$	−1.91948e12	−1.11223
$525$	−1.35168e12	−0.776529
$526$	−1.84662e11	−0.105182
$527$	2.38338e12	1.34600
$528$	−6.63328e11	−0.371429
$529$	−1.47271e12	−0.817650
$530$	−2.77667e11	−0.152856
$531$	−7.95020e10	−0.0433963
$532$	−1.06185e12	−0.574729
$533$	−1.37967e12	−0.740460
$534$	3.15907e11	0.168122
$535$	4.80068e12	2.53344
$536$	1.44891e12	0.758228
$537$	1.29263e12	0.670797
$538$	3.72025e11	0.191449
$539$	−3.24108e11	−0.165402
$540$	−5.27335e11	−0.266879
$541$	1.55823e12	0.782069	0.391035	−	0.920376i	$-0.372117\pi$
$541$	1.55823e12	0.782069	0.391035	+	0.920376i	$0.372117\pi$
$542$	3.17854e11	0.158209
$543$	−7.50351e11	−0.370395
$544$	−1.33779e12	−0.654927
$545$	3.00868e12	1.46080
$546$	−6.29353e11	−0.303059
$547$	−2.18819e12	−1.04506	−0.522530	−	0.852621i	$-0.675012\pi$
$547$	−2.18819e12	−1.04506	−0.522530	+	0.852621i	$0.675012\pi$
$548$	−2.28224e11	−0.108106
$549$	8.57268e10	0.0402755
$550$	5.66166e11	0.263823
$551$	−2.86984e11	−0.132640
$552$	2.75487e11	0.126292
$553$	2.99545e11	0.136207
$554$	−2.95973e11	−0.133493
$555$	−2.37472e12	−1.06242
$556$	−9.59083e11	−0.425618
$557$	−2.09021e12	−0.920115	−0.460058	−	0.887889i	$-0.652171\pi$
$557$	−2.09021e12	−0.920115	−0.460058	+	0.887889i	$0.652171\pi$
$558$	−3.01099e11	−0.131479
$559$	−6.28063e12	−2.72051
$560$	−3.02316e12	−1.29902
$561$	−9.94835e11	−0.424051
$562$	6.26025e11	0.264715
$563$	−2.00077e12	−0.839287	−0.419643	−	0.907689i	$-0.637845\pi$
$563$	−2.00077e12	−0.839287	−0.419643	+	0.907689i	$0.637845\pi$
$564$	1.33594e12	0.555945
$565$	1.00874e12	0.416450
$566$	−7.77107e11	−0.318278
$567$	−3.00053e11	−0.121920
$568$	1.80550e12	0.727829
$569$	4.13455e12	1.65357	0.826786	−	0.562517i	$-0.190167\pi$
$569$	4.13455e12	1.65357	0.826786	+	0.562517i	$0.190167\pi$
$570$	3.24741e11	0.128855
$571$	−4.71661e11	−0.185681	−0.0928404	−	0.995681i	$-0.529595\pi$
$571$	−4.71661e11	−0.185681	−0.0928404	+	0.995681i	$0.529595\pi$
$572$	−3.47659e12	−1.35791
$573$	−1.33813e12	−0.518566
$574$	3.11328e11	0.119706
$575$	1.37202e12	0.523425
$576$	−5.29774e11	−0.200535
$577$	−6.67106e11	−0.250555	−0.125278	−	0.992122i	$-0.539982\pi$
$577$	−6.67106e11	−0.250555	−0.125278	+	0.992122i	$0.539982\pi$
$578$	1.27698e11	0.0475894
$579$	1.08292e10	0.00400445
$580$	−8.89632e11	−0.326426
$581$	5.97322e12	2.17478
$582$	−5.58768e11	−0.201873
$583$	−8.72759e11	−0.312886
$584$	1.29259e12	0.459835
$585$	−2.53837e12	−0.896095
$586$	−1.11342e11	−0.0390048
$587$	8.89904e11	0.309365	0.154683	−	0.987964i	$-0.450564\pi$
$587$	8.89904e11	0.309365	0.154683	+	0.987964i	$0.450564\pi$
$588$	−3.17367e11	−0.109487
$589$	−2.44540e12	−0.837203
$590$	1.51768e11	0.0515640
$591$	5.53973e11	0.186786
$592$	−2.92500e12	−0.978765
$593$	3.07082e12	1.01979	0.509893	−	0.860238i	$-0.329685\pi$
$593$	3.07082e12	1.01979	0.509893	+	0.860238i	$0.329685\pi$
$594$	1.25680e11	0.0414217
$595$	−4.53403e12	−1.48306
$596$	−2.98864e12	−0.970208
$597$	−8.63009e10	−0.0278055
$598$	6.38822e11	0.204279
$599$	4.06896e12	1.29141	0.645703	−	0.763589i	$-0.276564\pi$
$599$	4.06896e12	1.29141	0.645703	+	0.763589i	$0.276564\pi$
$600$	1.15082e12	0.362514
$601$	4.36201e12	1.36380	0.681902	−	0.731444i	$-0.261153\pi$
$601$	4.36201e12	1.36380	0.681902	+	0.731444i	$0.261153\pi$
$602$	1.41725e12	0.439808
$603$	1.60185e12	0.493395
$604$	−4.69554e12	−1.43555
$605$	−1.68491e12	−0.511302
$606$	−4.37042e11	−0.131643
$607$	1.66672e11	0.0498326	0.0249163	−	0.999690i	$-0.492068\pi$
$607$	1.66672e11	0.0498326	0.0249163	+	0.999690i	$0.492068\pi$
$608$	1.37260e12	0.407359
$609$	−5.06199e11	−0.149123
$610$	−1.63651e11	−0.0478559
$611$	6.43068e12	1.86669
$612$	−9.74142e11	−0.280699
$613$	6.34195e12	1.81406	0.907028	−	0.421071i	$-0.138346\pi$
$613$	6.34195e12	1.81406	0.907028	+	0.421071i	$0.138346\pi$
$614$	−1.68425e12	−0.478243
$615$	1.25568e12	0.353950
$616$	1.62850e12	0.455696
$617$	−1.22926e12	−0.341476	−0.170738	−	0.985317i	$-0.554615\pi$
$617$	−1.22926e12	−0.341476	−0.170738	+	0.985317i	$0.554615\pi$
$618$	2.94108e11	0.0811071
$619$	−6.37479e12	−1.74525	−0.872625	−	0.488390i	$-0.837584\pi$
$619$	−6.37479e12	−1.74525	−0.872625	+	0.488390i	$0.837584\pi$
$620$	−7.58057e12	−2.06034
$621$	3.04567e11	0.0821809
$622$	−1.65566e12	−0.443522
$623$	4.52546e12	1.20356
$624$	−3.12657e12	−0.825539
$625$	−2.75912e12	−0.723286
$626$	−9.30342e11	−0.242135
$627$	1.02072e12	0.263756
$628$	−5.78784e12	−1.48490
$629$	−4.38681e12	−1.11743
$630$	5.72796e11	0.144866
$631$	6.92899e12	1.73995	0.869977	−	0.493092i	$-0.164133\pi$
$631$	6.92899e12	1.73995	0.869977	+	0.493092i	$0.164133\pi$
$632$	−2.55031e11	−0.0635867
$633$	−1.28038e12	−0.316973
$634$	7.81044e11	0.191988
$635$	2.81932e12	0.688117
$636$	−8.54605e11	−0.207114
$637$	−1.52767e12	−0.367623
$638$	2.12027e11	0.0506638
$639$	1.99608e12	0.473614
$640$	5.58893e12	1.31680
$641$	−2.35358e12	−0.550641	−0.275321	−	0.961352i	$-0.588784\pi$
$641$	−2.35358e12	−0.550641	−0.275321	+	0.961352i	$0.588784\pi$
$642$	−1.12035e12	−0.260283
$643$	−4.24079e12	−0.978357	−0.489178	−	0.872184i	$-0.662703\pi$
$643$	−4.24079e12	−0.978357	−0.489178	+	0.872184i	$0.662703\pi$
$644$	1.90114e12	0.435539
$645$	5.71622e12	1.30044
$646$	5.99891e11	0.135527
$647$	−2.88401e12	−0.647035	−0.323517	−	0.946222i	$-0.604865\pi$
$647$	−2.88401e12	−0.647035	−0.323517	+	0.946222i	$0.604865\pi$
$648$	2.55463e11	0.0569169
$649$	4.77035e11	0.105548
$650$	2.66860e12	0.586373
$651$	−4.31333e12	−0.941235
$652$	5.62432e12	1.21886
$653$	−3.51257e12	−0.755990	−0.377995	−	0.925808i	$-0.623386\pi$
$653$	−3.51257e12	−0.755990	−0.377995	+	0.925808i	$0.623386\pi$
$654$	−7.02146e11	−0.150082
$655$	8.40928e12	1.78514
$656$	1.54665e12	0.326081
$657$	1.42903e12	0.299224
$658$	−1.45111e12	−0.301776
$659$	−3.31529e12	−0.684758	−0.342379	−	0.939562i	$-0.611233\pi$
$659$	−3.31529e12	−0.684758	−0.342379	+	0.939562i	$0.611233\pi$
$660$	3.16416e12	0.649100
$661$	−2.28687e12	−0.465945	−0.232972	−	0.972483i	$-0.574845\pi$
$661$	−2.28687e12	−0.465945	−0.232972	+	0.972483i	$0.574845\pi$
$662$	1.07233e12	0.217004
$663$	−4.68912e12	−0.942498
$664$	−5.08557e12	−1.01527
$665$	4.65200e12	0.922449
$666$	5.54198e11	0.109152
$667$	5.13815e11	0.100517
$668$	−2.69751e12	−0.524166
$669$	−1.88342e12	−0.363520
$670$	−3.05791e12	−0.586258
$671$	−5.14386e11	−0.0979575
$672$	2.42107e12	0.457978
$673$	−2.07786e12	−0.390435	−0.195217	−	0.980760i	$-0.562541\pi$
$673$	−2.07786e12	−0.390435	−0.195217	+	0.980760i	$0.562541\pi$
$674$	−1.91191e11	−0.0356860
$675$	1.27229e12	0.235896
$676$	−1.13399e13	−2.08858
$677$	2.27593e12	0.416400	0.208200	−	0.978086i	$-0.433240\pi$
$677$	2.27593e12	0.416400	0.208200	+	0.978086i	$0.433240\pi$
$678$	−2.35414e11	−0.0427857
$679$	−8.00450e12	−1.44517
$680$	3.86025e12	0.692350
$681$	2.16652e12	0.386011
$682$	1.80668e12	0.319781
$683$	−9.62632e12	−1.69265	−0.846325	−	0.532667i	$-0.821190\pi$
$683$	−9.62632e12	−1.69265	−0.846325	+	0.532667i	$0.821190\pi$
$684$	9.99488e11	0.174592
$685$	9.99855e11	0.173512
$686$	−1.34497e12	−0.231876
$687$	−4.21547e12	−0.722006
$688$	7.04080e12	1.19805
$689$	−4.11372e12	−0.695421
$690$	−5.81414e11	−0.0976483
$691$	3.42976e12	0.572286	0.286143	−	0.958187i	$-0.407627\pi$
$691$	3.42976e12	0.572286	0.286143	+	0.958187i	$0.407627\pi$
$692$	−8.42237e12	−1.39623
$693$	1.80040e12	0.296531
$694$	5.43341e11	0.0889108
$695$	4.20176e12	0.683124
$696$	4.30975e11	0.0696163
$697$	2.31961e12	0.372279
$698$	3.10768e12	0.495549
$699$	−3.15454e12	−0.499791
$700$	7.94178e12	1.25019
$701$	−7.51204e12	−1.17497	−0.587485	−	0.809235i	$-0.699882\pi$
$701$	−7.51204e12	−1.17497	−0.587485	+	0.809235i	$0.699882\pi$
$702$	5.92389e11	0.0920640
$703$	4.50095e12	0.695033
$704$	3.17880e12	0.487737
$705$	−5.85279e12	−0.892301
$706$	−2.15230e12	−0.326048
$707$	−6.26074e12	−0.942407
$708$	4.67113e11	0.0698670
$709$	1.66785e12	0.247885	0.123942	−	0.992289i	$-0.460446\pi$
$709$	1.66785e12	0.247885	0.123942	+	0.992289i	$0.460446\pi$
$710$	−3.81049e12	−0.562754
$711$	−2.81951e11	−0.0413772
$712$	−3.85295e12	−0.561867
$713$	4.37822e12	0.634447
$714$	1.05812e12	0.152368
$715$	1.52310e13	2.17947
$716$	−7.59485e12	−1.07997
$717$	1.08769e12	0.153699
$718$	−6.80670e11	−0.0955821
$719$	−4.70556e11	−0.0656646	−0.0328323	−	0.999461i	$-0.510453\pi$
$719$	−4.70556e11	−0.0656646	−0.0328323	+	0.999461i	$0.510453\pi$
$720$	2.84560e12	0.394619
$721$	4.21318e12	0.580632
$722$	1.32294e12	0.181185
$723$	−1.15594e12	−0.157330
$724$	4.40867e12	0.596327
$725$	2.14640e12	0.288529
$726$	3.93213e11	0.0525307
$727$	3.60837e12	0.479078	0.239539	−	0.970887i	$-0.423004\pi$
$727$	3.60837e12	0.479078	0.239539	+	0.970887i	$0.423004\pi$
$728$	7.67588e12	1.01283
$729$	2.82430e11	0.0370370
$730$	−2.72800e12	−0.355542
$731$	1.05595e13	1.36778
$732$	−5.03686e11	−0.0648426
$733$	7.63962e12	0.977470	0.488735	−	0.872432i	$-0.337458\pi$
$733$	7.63962e12	0.977470	0.488735	+	0.872432i	$0.337458\pi$
$734$	−3.57101e12	−0.454108
$735$	1.39039e12	0.175729
$736$	−2.45749e12	−0.308704
$737$	−9.61158e12	−1.20003
$738$	−2.93043e11	−0.0363645
$739$	−1.87258e11	−0.0230962	−0.0115481	−	0.999933i	$-0.503676\pi$
$739$	−1.87258e11	−0.0230962	−0.0115481	+	0.999933i	$0.503676\pi$
$740$	1.39527e13	1.71046
$741$	4.81112e12	0.586225
$742$	9.28280e11	0.112425
$743$	−9.93138e11	−0.119553	−0.0597764	−	0.998212i	$-0.519039\pi$
$743$	−9.93138e11	−0.119553	−0.0597764	+	0.998212i	$0.519039\pi$
$744$	3.67235e12	0.439406
$745$	1.30933e13	1.55720
$746$	3.16309e12	0.373927
$747$	−5.62240e12	−0.660661
$748$	5.84514e12	0.682712
$749$	−1.60493e13	−1.86333
$750$	−4.47318e11	−0.0516227
$751$	1.41702e13	1.62553	0.812766	−	0.582590i	$-0.197961\pi$
$751$	1.41702e13	1.62553	0.812766	+	0.582590i	$0.197961\pi$
$752$	−7.20901e12	−0.822044
$753$	−7.98380e12	−0.904966
$754$	9.99380e11	0.112606
$755$	2.05712e13	2.30409
$756$	1.76295e12	0.196288
$757$	−2.14614e12	−0.237535	−0.118767	−	0.992922i	$-0.537894\pi$
$757$	−2.14614e12	−0.237535	−0.118767	+	0.992922i	$0.537894\pi$
$758$	−4.72034e12	−0.519352
$759$	−1.82749e12	−0.199879
$760$	−3.96069e12	−0.430636
$761$	5.13455e11	0.0554972	0.0277486	−	0.999615i	$-0.491166\pi$
$761$	5.13455e11	0.0554972	0.0277486	+	0.999615i	$0.491166\pi$
$762$	−6.57954e11	−0.0706965
$763$	−1.00584e13	−1.07441
$764$	7.86218e12	0.834878
$765$	4.26773e12	0.450527
$766$	−2.67160e12	−0.280377
$767$	2.24849e12	0.234591
$768$	2.04439e12	0.212050
$769$	1.32023e13	1.36138	0.680692	−	0.732570i	$-0.261679\pi$
$769$	1.32023e13	1.36138	0.680692	+	0.732570i	$0.261679\pi$
$770$	−3.43694e12	−0.352342
$771$	−7.65213e12	−0.779897
$772$	−6.36268e10	−0.00644707
$773$	−1.99216e12	−0.200686	−0.100343	−	0.994953i	$-0.531994\pi$
$773$	−1.99216e12	−0.200686	−0.100343	+	0.994953i	$0.531994\pi$
$774$	−1.33401e12	−0.133606
$775$	1.82895e13	1.82115
$776$	6.81500e12	0.674665
$777$	7.93903e12	0.781399
$778$	3.30755e12	0.323667
$779$	−2.37997e12	−0.231554
$780$	1.49142e13	1.44269
$781$	−1.19771e13	−1.15192
$782$	−1.07404e12	−0.102705
$783$	4.76468e11	0.0453008
$784$	1.71257e12	0.161892
$785$	2.53566e13	2.38329
$786$	−1.96250e12	−0.183404
$787$	1.14986e13	1.06846	0.534229	−	0.845340i	$-0.320602\pi$
$787$	1.14986e13	1.06846	0.534229	+	0.845340i	$0.320602\pi$
$788$	−3.25486e12	−0.300721
$789$	2.48997e12	0.228742
$790$	5.38241e11	0.0491649
$791$	−3.37237e12	−0.306295
$792$	−1.53285e12	−0.138432
$793$	−2.42454e12	−0.217721
$794$	−2.12272e12	−0.189540
$795$	3.74404e12	0.332421
$796$	5.07059e11	0.0447661
$797$	−8.15663e12	−0.716058	−0.358029	−	0.933710i	$-0.616551\pi$
$797$	−8.15663e12	−0.716058	−0.358029	+	0.933710i	$0.616551\pi$
$798$	−1.08565e12	−0.0947716
$799$	−1.08118e13	−0.938507
$800$	−1.02659e13	−0.886118
$801$	−4.25966e12	−0.365619
$802$	3.39226e12	0.289538
$803$	−8.57459e12	−0.727769
$804$	−9.41165e12	−0.794353
$805$	−8.32892e12	−0.699048
$806$	8.51573e12	0.710746
$807$	−5.01635e12	−0.416348
$808$	5.33037e12	0.439953
$809$	1.29744e13	1.06493	0.532464	−	0.846453i	$-0.321266\pi$
$809$	1.29744e13	1.06493	0.532464	+	0.846453i	$0.321266\pi$
$810$	−5.39154e11	−0.0440079
$811$	1.26001e13	1.02278	0.511389	−	0.859349i	$-0.329131\pi$
$811$	1.26001e13	1.02278	0.511389	+	0.859349i	$0.329131\pi$
$812$	2.97416e12	0.240084
$813$	−4.28591e12	−0.344061
$814$	−3.32535e12	−0.265477
$815$	−2.46402e13	−1.95630
$816$	5.25666e12	0.415054
$817$	−1.08343e13	−0.850748
$818$	−3.07240e12	−0.239931
$819$	8.48613e12	0.659071
$820$	−7.37774e12	−0.569851
$821$	1.56350e13	1.20103	0.600516	−	0.799613i	$-0.294962\pi$
$821$	1.56350e13	1.20103	0.600516	+	0.799613i	$0.294962\pi$
$822$	−2.33339e11	−0.0178265
$823$	−5.24256e12	−0.398331	−0.199166	−	0.979966i	$-0.563823\pi$
$823$	−5.24256e12	−0.398331	−0.199166	+	0.979966i	$0.563823\pi$
$824$	−3.58708e12	−0.271062
$825$	−7.63413e12	−0.573742
$826$	−5.07382e11	−0.0379249
$827$	−2.12406e13	−1.57903	−0.789517	−	0.613729i	$-0.789669\pi$
$827$	−2.12406e13	−1.57903	−0.789517	+	0.613729i	$0.789669\pi$
$828$	−1.78948e12	−0.132309
$829$	−5.92257e12	−0.435527	−0.217763	−	0.976002i	$-0.569876\pi$
$829$	−5.92257e12	−0.435527	−0.217763	+	0.976002i	$0.569876\pi$
$830$	1.07331e13	0.785006
$831$	3.99087e12	0.290311
$832$	1.49831e13	1.08405
$833$	2.56845e12	0.184829
$834$	−9.80579e11	−0.0701835
$835$	1.18178e13	0.841296
$836$	−5.99722e12	−0.424641
$837$	4.05999e12	0.285931
$838$	−1.81349e12	−0.127033
$839$	−8.63296e12	−0.601493	−0.300747	−	0.953704i	$-0.597236\pi$
$839$	−8.63296e12	−0.601493	−0.300747	+	0.953704i	$0.597236\pi$
$840$	−6.98609e12	−0.484147
$841$	−1.37033e13	−0.944592
$842$	−3.72795e12	−0.255603
$843$	−8.44126e12	−0.575682
$844$	7.52285e12	0.510319
$845$	4.96804e13	3.35220
$846$	1.36588e12	0.0916742
$847$	5.63288e12	0.376059
$848$	4.61162e12	0.306247
$849$	1.04784e13	0.692168
$850$	−4.48668e12	−0.294809
$851$	−8.05848e12	−0.526708
$852$	−1.17279e13	−0.762506
$853$	6.69552e12	0.433026	0.216513	−	0.976280i	$-0.430532\pi$
$853$	6.69552e12	0.433026	0.216513	+	0.976280i	$0.430532\pi$
$854$	5.47109e11	0.0351976
$855$	−4.37877e12	−0.280224
$856$	1.36643e13	0.869874
$857$	−6.92268e12	−0.438390	−0.219195	−	0.975681i	$-0.570343\pi$
$857$	−6.92268e12	−0.438390	−0.219195	+	0.975681i	$0.570343\pi$
$858$	−3.55451e12	−0.223917
$859$	−7.38422e12	−0.462738	−0.231369	−	0.972866i	$-0.574321\pi$
$859$	−7.38422e12	−0.462738	−0.231369	+	0.972866i	$0.574321\pi$
$860$	−3.35855e13	−2.09368
$861$	−4.19792e12	−0.260327
$862$	2.60709e11	0.0160833
$863$	2.45681e13	1.50773	0.753865	−	0.657029i	$-0.228187\pi$
$863$	2.45681e13	1.50773	0.753865	+	0.657029i	$0.228187\pi$
$864$	−2.27887e12	−0.139126
$865$	3.68985e13	2.24097
$866$	5.72793e12	0.346072
$867$	−1.72187e12	−0.103494
$868$	2.53429e13	1.51536
$869$	1.69179e12	0.100637
$870$	−9.09571e11	−0.0538270
$871$	−4.53038e13	−2.66718
$872$	8.56370e12	0.501576
$873$	7.53437e12	0.439019
$874$	1.10199e12	0.0638815
$875$	−6.40795e12	−0.369558
$876$	−8.39623e12	−0.481744
$877$	7.18173e12	0.409950	0.204975	−	0.978767i	$-0.434289\pi$
$877$	7.18173e12	0.409950	0.204975	+	0.978767i	$0.434289\pi$
$878$	1.59816e12	0.0907599
$879$	1.50132e12	0.0848248
$880$	−1.70744e13	−0.959786
$881$	1.52735e12	0.0854177	0.0427088	−	0.999088i	$-0.486401\pi$
$881$	1.52735e12	0.0854177	0.0427088	+	0.999088i	$0.486401\pi$
$882$	−3.24480e11	−0.0180542
$883$	−8.48668e12	−0.469802	−0.234901	−	0.972019i	$-0.575477\pi$
$883$	−8.48668e12	−0.469802	−0.234901	+	0.972019i	$0.575477\pi$
$884$	2.75508e13	1.51740
$885$	−2.04643e12	−0.112138
$886$	5.05724e12	0.275716
$887$	−2.03638e13	−1.10459	−0.552297	−	0.833648i	$-0.686248\pi$
$887$	−2.03638e13	−1.10459	−0.552297	+	0.833648i	$0.686248\pi$
$888$	−6.75925e12	−0.364788
$889$	−9.42537e12	−0.506105
$890$	8.13163e12	0.434433
$891$	−1.69466e12	−0.0900809
$892$	1.10660e13	0.585259
$893$	1.10931e13	0.583743
$894$	−3.05562e12	−0.159985
$895$	3.32731e13	1.73337
$896$	−1.86846e13	−0.968493
$897$	−8.61381e12	−0.444252
$898$	7.16605e12	0.367736
$899$	6.84934e12	0.349728
$900$	−7.47533e12	−0.379786
$901$	6.91633e12	0.349635
$902$	1.75834e12	0.0884452
$903$	−1.91101e13	−0.956463
$904$	2.87122e12	0.142991
$905$	−1.93145e13	−0.957115
$906$	−4.80078e12	−0.236720
$907$	−2.75665e13	−1.35254	−0.676269	−	0.736655i	$-0.736404\pi$
$907$	−2.75665e13	−1.35254	−0.676269	+	0.736655i	$0.736404\pi$
$908$	−1.27293e13	−0.621469
$909$	5.89303e12	0.286287
$910$	−1.61999e13	−0.783116
$911$	−2.40644e13	−1.15755	−0.578777	−	0.815486i	$-0.696470\pi$
$911$	−2.40644e13	−1.15755	−0.578777	+	0.815486i	$0.696470\pi$
$912$	−5.39343e12	−0.258160
$913$	3.37360e13	1.60685
$914$	−2.71103e12	−0.128492
$915$	2.20666e12	0.104073
$916$	2.47679e13	1.16241
$917$	−2.81134e13	−1.31296
$918$	−9.95975e11	−0.0462867
$919$	−2.04595e12	−0.0946185	−0.0473092	−	0.998880i	$-0.515065\pi$
$919$	−2.04595e12	−0.0946185	−0.0473092	+	0.998880i	$0.515065\pi$
$920$	7.09120e12	0.326343
$921$	2.27103e13	1.04005
$922$	−2.25036e12	−0.102557
$923$	−5.64534e13	−2.56025
$924$	−1.05782e13	−0.477408
$925$	−3.36633e13	−1.51189
$926$	7.68570e11	0.0343506
$927$	−3.96572e12	−0.176386
$928$	−3.84453e12	−0.170168
$929$	1.09000e13	0.480128	0.240064	−	0.970757i	$-0.422832\pi$
$929$	1.09000e13	0.480128	0.240064	+	0.970757i	$0.422832\pi$
$930$	−7.75047e12	−0.339746
$931$	−2.63528e12	−0.114962
$932$	1.85344e13	0.804651
$933$	2.23248e13	0.964539
$934$	−7.49011e12	−0.322053
$935$	−2.56076e13	−1.09576
$936$	−7.22505e12	−0.307680
$937$	2.11912e13	0.898105	0.449053	−	0.893505i	$-0.351762\pi$
$937$	2.11912e13	0.898105	0.449053	+	0.893505i	$0.351762\pi$
$938$	1.02230e13	0.431188
$939$	1.25446e13	0.526578
$940$	3.43879e13	1.43658
$941$	6.28519e11	0.0261315	0.0130658	−	0.999915i	$-0.495841\pi$
$941$	6.28519e11	0.0261315	0.0130658	+	0.999915i	$0.495841\pi$
$942$	−5.91756e12	−0.244858
$943$	4.26108e12	0.175476
$944$	−2.52063e12	−0.103308
$945$	−7.72353e12	−0.315045
$946$	8.00447e12	0.324954
$947$	−1.19856e13	−0.484269	−0.242134	−	0.970243i	$-0.577848\pi$
$947$	−1.19856e13	−0.484269	−0.242134	+	0.970243i	$0.577848\pi$
$948$	1.65660e12	0.0666162
$949$	−4.04160e13	−1.61754
$950$	4.60342e12	0.183368
$951$	−1.05315e13	−0.417521
$952$	−1.29054e13	−0.509218
$953$	−2.35282e13	−0.923995	−0.461998	−	0.886881i	$-0.652867\pi$
$953$	−2.35282e13	−0.923995	−0.461998	+	0.886881i	$0.652867\pi$
$954$	−8.73759e11	−0.0341526
$955$	−3.44443e13	−1.33999
$956$	−6.39072e12	−0.247451
$957$	−2.85895e12	−0.110180
$958$	−1.13650e13	−0.435937
$959$	−3.34265e12	−0.127617
$960$	−1.36367e13	−0.518189
$961$	3.19237e13	1.20742
$962$	−1.56739e13	−0.590050
$963$	1.51067e13	0.566045
$964$	6.79170e12	0.253298
$965$	2.78750e11	0.0103477
$966$	1.94375e12	0.0718196
$967$	3.66589e13	1.34822	0.674109	−	0.738632i	$-0.264528\pi$
$967$	3.66589e13	1.34822	0.674109	+	0.738632i	$0.264528\pi$
$968$	−4.79581e12	−0.175559
$969$	−8.08887e12	−0.294735
$970$	−1.43830e13	−0.521647
$971$	2.79106e13	1.00759	0.503793	−	0.863824i	$-0.331937\pi$
$971$	2.79106e13	1.00759	0.503793	+	0.863824i	$0.331937\pi$
$972$	−1.65941e12	−0.0596287
$973$	−1.40471e13	−0.502432
$974$	5.12470e12	0.182454
$975$	−3.59832e13	−1.27520
$976$	2.71799e12	0.0958790
$977$	2.08276e13	0.731331	0.365665	−	0.930746i	$-0.380841\pi$
$977$	2.08276e13	0.731331	0.365665	+	0.930746i	$0.380841\pi$
$978$	5.75037e12	0.200988
$979$	2.55592e13	0.889253
$980$	−8.16920e12	−0.282919
$981$	9.46766e12	0.326386
$982$	−2.12744e12	−0.0730055
$983$	−5.69777e11	−0.0194632	−0.00973160	−	0.999953i	$-0.503098\pi$
$983$	−5.69777e11	−0.0194632	−0.00973160	+	0.999953i	$0.503098\pi$
$984$	3.57409e12	0.121531
$985$	1.42596e13	0.482663
$986$	−1.68024e12	−0.0566143
$987$	1.95667e13	0.656281
$988$	−2.82677e13	−0.943808
$989$	1.93976e13	0.644711
$990$	3.23508e12	0.107035
$991$	−1.93568e13	−0.637532	−0.318766	−	0.947833i	$-0.603268\pi$
$991$	−1.93568e13	−0.637532	−0.318766	+	0.947833i	$0.603268\pi$
$992$	−3.27593e13	−1.07407
$993$	−1.44592e13	−0.471924
$994$	1.27390e13	0.413901
$995$	−2.22143e12	−0.0718504
$996$	3.30343e13	1.06365
$997$	−1.00007e11	−0.00320555	−0.00160277	−	0.999999i	$-0.500510\pi$
$997$	−1.00007e11	−0.00320555	−0.00160277	+	0.999999i	$0.500510\pi$
$998$	−6.80396e12	−0.217107
$999$	−7.47274e12	−0.237375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-6.00717 q^{2} +81.0000 q^{3} -475.914 q^{4} +2084.99 q^{5} -486.580 q^{6} -6970.40 q^{7} +5934.56 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-6.00717 q^{2} +81.0000 q^{3} -475.914 q^{4} +2084.99 q^{5} -486.580 q^{6} -6970.40 q^{7} +5934.56 q^{8} +6561.00 q^{9} -12524.9 q^{10} -39367.9 q^{11} -38549.0 q^{12} -185559. q^{13} +41872.3 q^{14} +168884. q^{15} +208018. q^{16} +311978. q^{17} -39413.0 q^{18} -320095. q^{19} -992274. q^{20} -564602. q^{21} +236490. q^{22} +573097. q^{23} +480700. q^{24} +2.39404e6 q^{25} +1.11468e6 q^{26} +531441. q^{27} +3.31731e6 q^{28} +896559. q^{29} -1.01451e6 q^{30} +7.63959e6 q^{31} -4.28809e6 q^{32} -3.18880e6 q^{33} -1.87410e6 q^{34} -1.45332e7 q^{35} -3.12247e6 q^{36} -1.40613e7 q^{37} +1.92287e6 q^{38} -1.50303e7 q^{39} +1.23735e7 q^{40} +7.43518e6 q^{41} +3.39166e6 q^{42} +3.38470e7 q^{43} +1.87357e7 q^{44} +1.36796e7 q^{45} -3.44269e6 q^{46} -3.46557e7 q^{47} +1.68495e7 q^{48} +8.23280e6 q^{49} -1.43814e7 q^{50} +2.52702e7 q^{51} +8.83102e7 q^{52} +2.21693e7 q^{53} -3.19245e6 q^{54} -8.20816e7 q^{55} -4.13662e7 q^{56} -2.59277e7 q^{57} -5.38578e6 q^{58} -1.21174e7 q^{59} -8.03742e7 q^{60} +1.30661e7 q^{61} -4.58923e7 q^{62} -4.57328e7 q^{63} -8.07460e7 q^{64} -3.86888e8 q^{65} +1.91557e7 q^{66} +2.44148e8 q^{67} -1.48475e8 q^{68} +4.64208e7 q^{69} +8.73032e7 q^{70} +3.04234e8 q^{71} +3.89367e7 q^{72} +2.17807e8 q^{73} +8.44685e7 q^{74} +1.93918e8 q^{75} +1.52338e8 q^{76} +2.74410e8 q^{77} +9.02894e7 q^{78} -4.29738e7 q^{79} +4.33715e8 q^{80} +4.30467e7 q^{81} -4.46644e7 q^{82} -8.56942e8 q^{83} +2.68702e8 q^{84} +6.50470e8 q^{85} -2.03325e8 q^{86} +7.26213e7 q^{87} -2.33631e8 q^{88} -6.49239e8 q^{89} -8.21756e7 q^{90} +1.29342e9 q^{91} -2.72745e8 q^{92} +6.18807e8 q^{93} +2.08182e8 q^{94} -6.67394e8 q^{95} -3.47336e8 q^{96} +1.14836e9 q^{97} -4.94558e7 q^{98} -2.58293e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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