LMFDB - Embedded newform 177.10.a.d.1.4

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			1.4
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-32.9800 q^{2} +81.0000 q^{3} +575.677 q^{4} -958.538 q^{5} -2671.38 q^{6} -5513.62 q^{7} -2100.07 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-32.9800 q^{2} +81.0000 q^{3} +575.677 q^{4} -958.538 q^{5} -2671.38 q^{6} -5513.62 q^{7} -2100.07 q^{8} +6561.00 q^{9} +31612.5 q^{10} +29319.9 q^{11} +46629.8 q^{12} +137970. q^{13} +181839. q^{14} -77641.6 q^{15} -225487. q^{16} -339574. q^{17} -216381. q^{18} +86213.0 q^{19} -551808. q^{20} -446603. q^{21} -966968. q^{22} +1.13467e6 q^{23} -170106. q^{24} -1.03433e6 q^{25} -4.55026e6 q^{26} +531441. q^{27} -3.17406e6 q^{28} -919965. q^{29} +2.56062e6 q^{30} +1.08392e6 q^{31} +8.51177e6 q^{32} +2.37491e6 q^{33} +1.11991e7 q^{34} +5.28501e6 q^{35} +3.77702e6 q^{36} -2.63442e6 q^{37} -2.84330e6 q^{38} +1.11756e7 q^{39} +2.01299e6 q^{40} +9.33124e6 q^{41} +1.47289e7 q^{42} +6.15092e6 q^{43} +1.68788e7 q^{44} -6.28897e6 q^{45} -3.74214e7 q^{46} -5.67705e7 q^{47} -1.82644e7 q^{48} -9.95366e6 q^{49} +3.41121e7 q^{50} -2.75055e7 q^{51} +7.94264e7 q^{52} +5.09861e7 q^{53} -1.75269e7 q^{54} -2.81042e7 q^{55} +1.15790e7 q^{56} +6.98325e6 q^{57} +3.03404e7 q^{58} -1.21174e7 q^{59} -4.46965e7 q^{60} -9.11400e7 q^{61} -3.57475e7 q^{62} -3.61748e7 q^{63} -1.65269e8 q^{64} -1.32250e8 q^{65} -7.83244e7 q^{66} -9.97942e7 q^{67} -1.95485e8 q^{68} +9.19083e7 q^{69} -1.74299e8 q^{70} +1.19704e8 q^{71} -1.37785e7 q^{72} -6.25750e6 q^{73} +8.68832e7 q^{74} -8.37807e7 q^{75} +4.96308e7 q^{76} -1.61658e8 q^{77} -3.68571e8 q^{78} -2.70096e8 q^{79} +2.16137e8 q^{80} +4.30467e7 q^{81} -3.07744e8 q^{82} -4.06610e8 q^{83} -2.57099e8 q^{84} +3.25494e8 q^{85} -2.02857e8 q^{86} -7.45172e7 q^{87} -6.15737e7 q^{88} +9.88909e8 q^{89} +2.07410e8 q^{90} -7.60716e8 q^{91} +6.53204e8 q^{92} +8.77972e7 q^{93} +1.87229e9 q^{94} -8.26384e7 q^{95} +6.89453e8 q^{96} -1.09717e9 q^{97} +3.28271e8 q^{98} +1.92368e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−32.9800	−1.45752	−0.728761	−	0.684768i	$-0.759903\pi$
$2$	−32.9800	−1.45752	−0.728761	+	0.684768i	$0.759903\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	575.677	1.12437
$5$	−958.538	−0.685874	−0.342937	−	0.939358i	$-0.611422\pi$
$5$	−958.538	−0.685874	−0.342937	+	0.939358i	$0.611422\pi$
$6$	−2671.38	−0.841501
$7$	−5513.62	−0.867951	−0.433976	−	0.900925i	$-0.642890\pi$
$7$	−5513.62	−0.867951	−0.433976	+	0.900925i	$0.642890\pi$
$8$	−2100.07	−0.181271
$9$	6561.00	0.333333
$10$	31612.5	0.999676
$11$	29319.9	0.603803	0.301901	−	0.953339i	$-0.402379\pi$
$11$	29319.9	0.603803	0.301901	+	0.953339i	$0.402379\pi$
$12$	46629.8	0.649155
$13$	137970.	1.33980	0.669901	−	0.742450i	$-0.266336\pi$
$13$	137970.	1.33980	0.669901	+	0.742450i	$0.266336\pi$
$14$	181839.	1.26506
$15$	−77641.6	−0.395990
$16$	−225487.	−0.860163
$17$	−339574.	−0.986085	−0.493042	−	0.870005i	$-0.664115\pi$
$17$	−339574.	−0.986085	−0.493042	+	0.870005i	$0.664115\pi$
$18$	−216381.	−0.485841
$19$	86213.0	0.151768	0.0758842	−	0.997117i	$-0.475822\pi$
$19$	86213.0	0.151768	0.0758842	+	0.997117i	$0.475822\pi$
$20$	−551808.	−0.771176
$21$	−446603.	−0.501112
$22$	−966968.	−0.880055
$23$	1.13467e6	0.845463	0.422731	−	0.906255i	$-0.361071\pi$
$23$	1.13467e6	0.845463	0.422731	+	0.906255i	$0.361071\pi$
$24$	−170106.	−0.104657
$25$	−1.03433e6	−0.529577
$26$	−4.55026e6	−1.95279
$27$	531441.	0.192450
$28$	−3.17406e6	−0.975898
$29$	−919965.	−0.241535	−0.120768	−	0.992681i	$-0.538536\pi$
$29$	−919965.	−0.241535	−0.120768	+	0.992681i	$0.538536\pi$
$30$	2.56062e6	0.577163
$31$	1.08392e6	0.210799	0.105399	−	0.994430i	$-0.466388\pi$
$31$	1.08392e6	0.210799	0.105399	+	0.994430i	$0.466388\pi$
$32$	8.51177e6	1.43498
$33$	2.37491e6	0.348606
$34$	1.11991e7	1.43724
$35$	5.28501e6	0.595305
$36$	3.77702e6	0.374790
$37$	−2.63442e6	−0.231088	−0.115544	−	0.993302i	$-0.536861\pi$
$37$	−2.63442e6	−0.231088	−0.115544	+	0.993302i	$0.536861\pi$
$38$	−2.84330e6	−0.221206
$39$	1.11756e7	0.773535
$40$	2.01299e6	0.124329
$41$	9.33124e6	0.515718	0.257859	−	0.966183i	$-0.416983\pi$
$41$	9.33124e6	0.515718	0.257859	+	0.966183i	$0.416983\pi$
$42$	1.47289e7	0.730381
$43$	6.15092e6	0.274367	0.137184	−	0.990546i	$-0.456195\pi$
$43$	6.15092e6	0.274367	0.137184	+	0.990546i	$0.456195\pi$
$44$	1.68788e7	0.678897
$45$	−6.28897e6	−0.228625
$46$	−3.74214e7	−1.23228
$47$	−5.67705e7	−1.69700	−0.848501	−	0.529193i	$-0.822495\pi$
$47$	−5.67705e7	−1.69700	−0.848501	+	0.529193i	$0.822495\pi$
$48$	−1.82644e7	−0.496615
$49$	−9.95366e6	−0.246661
$50$	3.41121e7	0.771870
$51$	−2.75055e7	−0.569316
$52$	7.94264e7	1.50643
$53$	5.09861e7	0.887587	0.443793	−	0.896129i	$-0.353632\pi$
$53$	5.09861e7	0.887587	0.443793	+	0.896129i	$0.353632\pi$
$54$	−1.75269e7	−0.280500
$55$	−2.81042e7	−0.414132
$56$	1.15790e7	0.157334
$57$	6.98325e6	0.0876235
$58$	3.03404e7	0.352043
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−4.46965e7	−0.445238
$61$	−9.11400e7	−0.842801	−0.421400	−	0.906875i	$-0.638461\pi$
$61$	−9.11400e7	−0.842801	−0.421400	+	0.906875i	$0.638461\pi$
$62$	−3.57475e7	−0.307244
$63$	−3.61748e7	−0.289317
$64$	−1.65269e8	−1.23135
$65$	−1.32250e8	−0.918936
$66$	−7.83244e7	−0.508100
$67$	−9.97942e7	−0.605018	−0.302509	−	0.953146i	$-0.597824\pi$
$67$	−9.97942e7	−0.605018	−0.302509	+	0.953146i	$0.597824\pi$
$68$	−1.95485e8	−1.10872
$69$	9.19083e7	0.488128
$70$	−1.74299e8	−0.867670
$71$	1.19704e8	0.559043	0.279521	−	0.960139i	$-0.409824\pi$
$71$	1.19704e8	0.559043	0.279521	+	0.960139i	$0.409824\pi$
$72$	−1.37785e7	−0.0604237
$73$	−6.25750e6	−0.0257898	−0.0128949	−	0.999917i	$-0.504105\pi$
$73$	−6.25750e6	−0.0257898	−0.0128949	+	0.999917i	$0.504105\pi$
$74$	8.68832e7	0.336816
$75$	−8.37807e7	−0.305751
$76$	4.96308e7	0.170644
$77$	−1.61658e8	−0.524071
$78$	−3.68571e8	−1.12744
$79$	−2.70096e8	−0.780182	−0.390091	−	0.920776i	$-0.627557\pi$
$79$	−2.70096e8	−0.780182	−0.390091	+	0.920776i	$0.627557\pi$
$80$	2.16137e8	0.589963
$81$	4.30467e7	0.111111
$82$	−3.07744e8	−0.751670
$83$	−4.06610e8	−0.940431	−0.470215	−	0.882552i	$-0.655824\pi$
$83$	−4.06610e8	−0.940431	−0.470215	+	0.882552i	$0.655824\pi$
$84$	−2.57099e8	−0.563435
$85$	3.25494e8	0.676330
$86$	−2.02857e8	−0.399896
$87$	−7.45172e7	−0.139450
$88$	−6.15737e7	−0.109452
$89$	9.88909e8	1.67071	0.835355	−	0.549711i	$-0.185262\pi$
$89$	9.88909e8	1.67071	0.835355	+	0.549711i	$0.185262\pi$
$90$	2.07410e8	0.333225
$91$	−7.60716e8	−1.16288
$92$	6.53204e8	0.950612
$93$	8.77972e7	0.121705
$94$	1.87229e9	2.47342
$95$	−8.26384e7	−0.104094
$96$	6.89453e8	0.828484
$97$	−1.09717e9	−1.25835	−0.629177	−	0.777262i	$-0.716608\pi$
$97$	−1.09717e9	−1.25835	−0.629177	+	0.777262i	$0.716608\pi$
$98$	3.28271e8	0.359514
$99$	1.92368e8	0.201268
$100$	−5.95440e8	−0.595440
$101$	−5.16631e8	−0.494008	−0.247004	−	0.969014i	$-0.579446\pi$
$101$	−5.16631e8	−0.494008	−0.247004	+	0.969014i	$0.579446\pi$
$102$	9.07130e8	0.829791
$103$	−6.42155e8	−0.562176	−0.281088	−	0.959682i	$-0.590695\pi$
$103$	−6.42155e8	−0.562176	−0.281088	+	0.959682i	$0.590695\pi$
$104$	−2.89747e8	−0.242867
$105$	4.28086e8	0.343700
$106$	−1.68152e9	−1.29368
$107$	1.44354e9	1.06464	0.532319	−	0.846544i	$-0.321321\pi$
$107$	1.44354e9	1.06464	0.532319	+	0.846544i	$0.321321\pi$
$108$	3.05938e8	0.216385
$109$	1.04267e9	0.707501	0.353751	−	0.935340i	$-0.384906\pi$
$109$	1.04267e9	0.707501	0.353751	+	0.935340i	$0.384906\pi$
$110$	9.26875e8	0.603607
$111$	−2.13388e8	−0.133419
$112$	1.24325e9	0.746579
$113$	2.39521e9	1.38194	0.690971	−	0.722882i	$-0.257183\pi$
$113$	2.39521e9	1.38194	0.690971	+	0.722882i	$0.257183\pi$
$114$	−2.30307e8	−0.127713
$115$	−1.08762e9	−0.579881
$116$	−5.29603e8	−0.271575
$117$	9.05224e8	0.446601
$118$	3.99630e8	0.189753
$119$	1.87228e9	0.855873
$120$	1.63053e8	0.0717814
$121$	−1.49829e9	−0.635423
$122$	3.00579e9	1.22840
$123$	7.55831e8	0.297750
$124$	6.23986e8	0.237016
$125$	2.86359e9	1.04910
$126$	1.19304e9	0.421686
$127$	7.45551e8	0.254308	0.127154	−	0.991883i	$-0.459416\pi$
$127$	7.45551e8	0.254308	0.127154	+	0.991883i	$0.459416\pi$
$128$	1.09253e9	0.359738
$129$	4.98225e8	0.158406
$130$	4.36159e9	1.33937
$131$	6.45907e9	1.91624	0.958118	−	0.286374i	$-0.0924500\pi$
$131$	6.45907e9	1.91624	0.958118	+	0.286374i	$0.0924500\pi$
$132$	1.36718e9	0.391961
$133$	−4.75345e8	−0.131728
$134$	3.29121e9	0.881827
$135$	−5.09406e8	−0.131997
$136$	7.13128e8	0.178749
$137$	3.91437e9	0.949336	0.474668	−	0.880165i	$-0.342568\pi$
$137$	3.91437e9	0.949336	0.474668	+	0.880165i	$0.342568\pi$
$138$	−3.03113e9	−0.711457
$139$	1.24731e9	0.283405	0.141703	−	0.989909i	$-0.454742\pi$
$139$	1.24731e9	0.283405	0.141703	+	0.989909i	$0.454742\pi$
$140$	3.04246e9	0.669343
$141$	−4.59841e9	−0.979765
$142$	−3.94782e9	−0.814817
$143$	4.04527e9	0.808976
$144$	−1.47942e9	−0.286721
$145$	8.81822e8	0.165663
$146$	2.06372e8	0.0375892
$147$	−8.06246e8	−0.142410
$148$	−1.51658e9	−0.259829
$149$	−7.28493e9	−1.21084	−0.605421	−	0.795906i	$-0.706995\pi$
$149$	−7.28493e9	−1.21084	−0.605421	+	0.795906i	$0.706995\pi$
$150$	2.76308e9	0.445639
$151$	1.64429e9	0.257384	0.128692	−	0.991685i	$-0.458922\pi$
$151$	1.64429e9	0.257384	0.128692	+	0.991685i	$0.458922\pi$
$152$	−1.81053e8	−0.0275112
$153$	−2.22794e9	−0.328695
$154$	5.33149e9	0.763845
$155$	−1.03897e9	−0.144581
$156$	6.43354e9	0.869740
$157$	6.59444e9	0.866222	0.433111	−	0.901341i	$-0.357416\pi$
$157$	6.59444e9	0.866222	0.433111	+	0.901341i	$0.357416\pi$
$158$	8.90775e9	1.13713
$159$	4.12988e9	0.512448
$160$	−8.15885e9	−0.984213
$161$	−6.25614e9	−0.733820
$162$	−1.41968e9	−0.161947
$163$	7.39202e9	0.820199	0.410099	−	0.912041i	$-0.365494\pi$
$163$	7.39202e9	0.820199	0.410099	+	0.912041i	$0.365494\pi$
$164$	5.37178e9	0.579857
$165$	−2.27644e9	−0.239099
$166$	1.34100e10	1.37070
$167$	2.40304e9	0.239076	0.119538	−	0.992830i	$-0.461859\pi$
$167$	2.40304e9	0.239076	0.119538	+	0.992830i	$0.461859\pi$
$168$	9.37896e8	0.0908371
$169$	8.43133e9	0.795071
$170$	−1.07348e10	−0.985765
$171$	5.65643e8	0.0505895
$172$	3.54095e9	0.308490
$173$	7.67071e9	0.651071	0.325535	−	0.945530i	$-0.394455\pi$
$173$	7.67071e9	0.651071	0.325535	+	0.945530i	$0.394455\pi$
$174$	2.45757e9	0.203252
$175$	5.70290e9	0.459647
$176$	−6.61124e9	−0.519369
$177$	−9.81506e8	−0.0751646
$178$	−3.26142e10	−2.43510
$179$	1.22387e10	0.891037	0.445519	−	0.895273i	$-0.353019\pi$
$179$	1.22387e10	0.891037	0.445519	+	0.895273i	$0.353019\pi$
$180$	−3.62041e9	−0.257059
$181$	2.05532e10	1.42339	0.711697	−	0.702487i	$-0.247927\pi$
$181$	2.05532e10	1.42339	0.711697	+	0.702487i	$0.247927\pi$
$182$	2.50884e10	1.69493
$183$	−7.38234e9	−0.486591
$184$	−2.38289e9	−0.153258
$185$	2.52520e9	0.158497
$186$	−2.89555e9	−0.177387
$187$	−9.95626e9	−0.595400
$188$	−3.26815e10	−1.90806
$189$	−2.93016e9	−0.167037
$190$	2.72541e9	0.151719
$191$	−8.98521e8	−0.0488515	−0.0244257	−	0.999702i	$-0.507776\pi$
$191$	−8.98521e8	−0.0488515	−0.0244257	+	0.999702i	$0.507776\pi$
$192$	−1.33868e10	−0.710919
$193$	−1.81123e10	−0.939648	−0.469824	−	0.882760i	$-0.655683\pi$
$193$	−1.81123e10	−0.939648	−0.469824	+	0.882760i	$0.655683\pi$
$194$	3.61847e10	1.83408
$195$	−1.07122e10	−0.530548
$196$	−5.73009e9	−0.277338
$197$	6.57831e9	0.311183	0.155592	−	0.987821i	$-0.450272\pi$
$197$	6.57831e9	0.311183	0.155592	+	0.987821i	$0.450272\pi$
$198$	−6.34428e9	−0.293352
$199$	4.97840e9	0.225035	0.112518	−	0.993650i	$-0.464109\pi$
$199$	4.97840e9	0.225035	0.112518	+	0.993650i	$0.464109\pi$
$200$	2.17216e9	0.0959970
$201$	−8.08333e9	−0.349307
$202$	1.70385e10	0.720028
$203$	5.07233e9	0.209641
$204$	−1.58343e10	−0.640122
$205$	−8.94435e9	−0.353717
$206$	2.11783e10	0.819384
$207$	7.44457e9	0.281821
$208$	−3.11105e10	−1.15245
$209$	2.52775e9	0.0916381
$210$	−1.41182e10	−0.500950
$211$	6.78868e9	0.235784	0.117892	−	0.993026i	$-0.462386\pi$
$211$	6.78868e9	0.235784	0.117892	+	0.993026i	$0.462386\pi$
$212$	2.93516e10	0.997975
$213$	9.69600e9	0.322764
$214$	−4.76079e10	−1.55173
$215$	−5.89589e9	−0.188181
$216$	−1.11606e9	−0.0348856
$217$	−5.97630e9	−0.182963
$218$	−3.43872e10	−1.03120
$219$	−5.06858e8	−0.0148898
$220$	−1.61789e10	−0.465638
$221$	−4.68512e10	−1.32116
$222$	7.03754e9	0.194461
$223$	5.46776e10	1.48060	0.740299	−	0.672278i	$-0.234684\pi$
$223$	5.46776e10	1.48060	0.740299	+	0.672278i	$0.234684\pi$
$224$	−4.69306e10	−1.24549
$225$	−6.78624e9	−0.176526
$226$	−7.89938e10	−2.01421
$227$	7.36629e8	0.0184133	0.00920666	−	0.999958i	$-0.497069\pi$
$227$	7.36629e8	0.0184133	0.00920666	+	0.999958i	$0.497069\pi$
$228$	4.02010e9	0.0985212
$229$	1.70607e10	0.409955	0.204978	−	0.978767i	$-0.434288\pi$
$229$	1.70607e10	0.409955	0.204978	+	0.978767i	$0.434288\pi$
$230$	3.58698e10	0.845189
$231$	−1.30943e10	−0.302573
$232$	1.93199e9	0.0437833
$233$	−1.08113e10	−0.240311	−0.120156	−	0.992755i	$-0.538339\pi$
$233$	−1.08113e10	−0.240311	−0.120156	+	0.992755i	$0.538339\pi$
$234$	−2.98542e10	−0.650931
$235$	5.44167e10	1.16393
$236$	−6.97569e9	−0.146380
$237$	−2.18778e10	−0.450438
$238$	−6.17477e10	−1.24745
$239$	2.27031e10	0.450085	0.225043	−	0.974349i	$-0.427748\pi$
$239$	2.27031e10	0.450085	0.225043	+	0.974349i	$0.427748\pi$
$240$	1.75071e10	0.340615
$241$	−4.42553e10	−0.845062	−0.422531	−	0.906348i	$-0.638858\pi$
$241$	−4.42553e10	−0.845062	−0.422531	+	0.906348i	$0.638858\pi$
$242$	4.94136e10	0.926142
$243$	3.48678e9	0.0641500
$244$	−5.24672e10	−0.947619
$245$	9.54096e9	0.169178
$246$	−2.49273e10	−0.433977
$247$	1.18948e10	0.203340
$248$	−2.27630e9	−0.0382117
$249$	−3.29354e10	−0.542958
$250$	−9.44410e10	−1.52908
$251$	−1.28595e10	−0.204499	−0.102250	−	0.994759i	$-0.532604\pi$
$251$	−1.28595e10	−0.204499	−0.102250	+	0.994759i	$0.532604\pi$
$252$	−2.08250e10	−0.325299
$253$	3.32684e10	0.510493
$254$	−2.45882e10	−0.370660
$255$	2.63651e10	0.390479
$256$	4.85861e10	0.707021
$257$	1.16625e11	1.66760	0.833800	−	0.552067i	$-0.186161\pi$
$257$	1.16625e11	1.66760	0.833800	+	0.552067i	$0.186161\pi$
$258$	−1.64314e10	−0.230880
$259$	1.45252e10	0.200573
$260$	−7.61332e10	−1.03322
$261$	−6.03589e9	−0.0805117
$262$	−2.13020e11	−2.79296
$263$	5.05137e10	0.651041	0.325520	−	0.945535i	$-0.394460\pi$
$263$	5.05137e10	0.651041	0.325520	+	0.945535i	$0.394460\pi$
$264$	−4.98747e9	−0.0631921
$265$	−4.88722e10	−0.608773
$266$	1.56769e10	0.191996
$267$	8.01016e10	0.964585
$268$	−5.74492e10	−0.680264
$269$	9.77449e10	1.13817	0.569087	−	0.822277i	$-0.307297\pi$
$269$	9.77449e10	1.13817	0.569087	+	0.822277i	$0.307297\pi$
$270$	1.68002e10	0.192388
$271$	−1.23145e10	−0.138693	−0.0693463	−	0.997593i	$-0.522091\pi$
$271$	−1.23145e10	−0.138693	−0.0693463	+	0.997593i	$0.522091\pi$
$272$	7.65693e10	0.848193
$273$	−6.16180e10	−0.671391
$274$	−1.29096e11	−1.38368
$275$	−3.03264e10	−0.319760
$276$	5.29095e10	0.548836
$277$	3.89075e10	0.397077	0.198538	−	0.980093i	$-0.436381\pi$
$277$	3.89075e10	0.397077	0.198538	+	0.980093i	$0.436381\pi$
$278$	−4.11362e10	−0.413069
$279$	7.11157e9	0.0702662
$280$	−1.10989e10	−0.107912
$281$	1.86749e11	1.78682	0.893409	−	0.449244i	$-0.148307\pi$
$281$	1.86749e11	1.78682	0.893409	+	0.449244i	$0.148307\pi$
$282$	1.51655e11	1.42803
$283$	−4.26909e9	−0.0395637	−0.0197818	−	0.999804i	$-0.506297\pi$
$283$	−4.26909e9	−0.0395637	−0.0197818	+	0.999804i	$0.506297\pi$
$284$	6.89107e10	0.628571
$285$	−6.69371e9	−0.0600987
$286$	−1.33413e11	−1.17910
$287$	−5.14489e10	−0.447618
$288$	5.58457e10	0.478326
$289$	−3.27743e9	−0.0276372
$290$	−2.90824e10	−0.241457
$291$	−8.88711e10	−0.726511
$292$	−3.60230e9	−0.0289973
$293$	2.26975e11	1.79918	0.899590	−	0.436735i	$-0.143865\pi$
$293$	2.26975e11	1.79918	0.899590	+	0.436735i	$0.143865\pi$
$294$	2.65900e10	0.207565
$295$	1.16150e10	0.0892932
$296$	5.53247e9	0.0418896
$297$	1.55818e10	0.116202
$298$	2.40257e11	1.76483
$299$	1.56551e11	1.13275
$300$	−4.82306e10	−0.343777
$301$	−3.39138e10	−0.238137
$302$	−5.42285e10	−0.375143
$303$	−4.18471e10	−0.285216
$304$	−1.94399e10	−0.130546
$305$	8.73612e10	0.578055
$306$	7.34775e10	0.479080
$307$	3.32209e10	0.213446	0.106723	−	0.994289i	$-0.465964\pi$
$307$	3.32209e10	0.213446	0.106723	+	0.994289i	$0.465964\pi$
$308$	−9.30631e10	−0.589249
$309$	−5.20146e10	−0.324573
$310$	3.42653e10	0.210730
$311$	−1.65167e10	−0.100115	−0.0500577	−	0.998746i	$-0.515941\pi$
$311$	−1.65167e10	−0.100115	−0.0500577	+	0.998746i	$0.515941\pi$
$312$	−2.34695e10	−0.140220
$313$	8.71957e10	0.513506	0.256753	−	0.966477i	$-0.417347\pi$
$313$	8.71957e10	0.513506	0.256753	+	0.966477i	$0.417347\pi$
$314$	−2.17484e11	−1.26254
$315$	3.46749e10	0.198435
$316$	−1.55488e11	−0.877213
$317$	−1.00209e11	−0.557368	−0.278684	−	0.960383i	$-0.589898\pi$
$317$	−1.00209e11	−0.557368	−0.278684	+	0.960383i	$0.589898\pi$
$318$	−1.36203e11	−0.746905
$319$	−2.69733e10	−0.145840
$320$	1.58416e11	0.844549
$321$	1.16927e11	0.614669
$322$	2.06327e11	1.06956
$323$	−2.92757e10	−0.149656
$324$	2.47810e10	0.124930
$325$	−1.42707e11	−0.709529
$326$	−2.43789e11	−1.19546
$327$	8.44562e10	0.408476
$328$	−1.95962e10	−0.0934847
$329$	3.13011e11	1.47292
$330$	7.50769e10	0.348493
$331$	−2.47186e11	−1.13187	−0.565936	−	0.824449i	$-0.691485\pi$
$331$	−2.47186e11	−1.13187	−0.565936	+	0.824449i	$0.691485\pi$
$332$	−2.34076e11	−1.05739
$333$	−1.72845e10	−0.0770294
$334$	−7.92520e10	−0.348459
$335$	9.56565e10	0.414966
$336$	1.00703e11	0.431038
$337$	−7.13003e10	−0.301132	−0.150566	−	0.988600i	$-0.548110\pi$
$337$	−7.13003e10	−0.301132	−0.150566	+	0.988600i	$0.548110\pi$
$338$	−2.78065e11	−1.15883
$339$	1.94012e11	0.797865
$340$	1.87380e11	0.760444
$341$	3.17803e10	0.127281
$342$	−1.86549e10	−0.0737352
$343$	2.77375e11	1.08204
$344$	−1.29174e10	−0.0497348
$345$	−8.80976e10	−0.334794
$346$	−2.52980e11	−0.948950
$347$	−3.59303e11	−1.33039	−0.665194	−	0.746670i	$-0.731651\pi$
$347$	−3.59303e11	−1.33039	−0.665194	+	0.746670i	$0.731651\pi$
$348$	−4.28978e10	−0.156794
$349$	−1.90779e11	−0.688360	−0.344180	−	0.938904i	$-0.611843\pi$
$349$	−1.90779e11	−0.688360	−0.344180	+	0.938904i	$0.611843\pi$
$350$	−1.88081e11	−0.669945
$351$	7.33231e10	0.257845
$352$	2.49564e11	0.866443
$353$	1.88170e11	0.645005	0.322503	−	0.946569i	$-0.395476\pi$
$353$	1.88170e11	0.645005	0.322503	+	0.946569i	$0.395476\pi$
$354$	3.23700e10	0.109554
$355$	−1.14741e11	−0.383433
$356$	5.69292e11	1.87850
$357$	1.51655e11	0.494139
$358$	−4.03631e11	−1.29871
$359$	−4.34117e10	−0.137937	−0.0689686	−	0.997619i	$-0.521971\pi$
$359$	−4.34117e10	−0.137937	−0.0689686	+	0.997619i	$0.521971\pi$
$360$	1.32073e10	0.0414430
$361$	−3.15255e11	−0.976966
$362$	−6.77842e11	−2.07463
$363$	−1.21362e11	−0.366861
$364$	−4.37927e11	−1.30751
$365$	5.99805e9	0.0176886
$366$	2.43469e11	0.709217
$367$	−3.73765e11	−1.07548	−0.537739	−	0.843112i	$-0.680721\pi$
$367$	−3.73765e11	−1.07548	−0.537739	+	0.843112i	$0.680721\pi$
$368$	−2.55853e11	−0.727236
$369$	6.12223e10	0.171906
$370$	−8.32808e10	−0.231013
$371$	−2.81118e11	−0.770382
$372$	5.05428e10	0.136841
$373$	2.34265e11	0.626640	0.313320	−	0.949648i	$-0.398559\pi$
$373$	2.34265e11	0.626640	0.313320	+	0.949648i	$0.398559\pi$
$374$	3.28357e11	0.867809
$375$	2.31951e11	0.605696
$376$	1.19222e11	0.307617
$377$	−1.26928e11	−0.323609
$378$	9.66366e10	0.243460
$379$	5.95023e11	1.48135	0.740675	−	0.671864i	$-0.234506\pi$
$379$	5.95023e11	1.48135	0.740675	+	0.671864i	$0.234506\pi$
$380$	−4.75730e10	−0.117040
$381$	6.03897e10	0.146825
$382$	2.96332e10	0.0712021
$383$	−4.69626e11	−1.11521	−0.557606	−	0.830105i	$-0.688280\pi$
$383$	−4.69626e11	−1.11521	−0.557606	+	0.830105i	$0.688280\pi$
$384$	8.84945e10	0.207695
$385$	1.54956e11	0.359447
$386$	5.97342e11	1.36956
$387$	4.03562e10	0.0914557
$388$	−6.31618e11	−1.41485
$389$	−3.91024e11	−0.865826	−0.432913	−	0.901436i	$-0.642514\pi$
$389$	−3.91024e11	−0.865826	−0.432913	+	0.901436i	$0.642514\pi$
$390$	3.53289e11	0.773285
$391$	−3.85305e11	−0.833698
$392$	2.09034e10	0.0447125
$393$	5.23184e11	1.10634
$394$	−2.16952e11	−0.453556
$395$	2.58897e11	0.535107
$396$	1.10742e11	0.226299
$397$	1.93489e11	0.390929	0.195465	−	0.980711i	$-0.437379\pi$
$397$	1.93489e11	0.390929	0.195465	+	0.980711i	$0.437379\pi$
$398$	−1.64187e11	−0.327994
$399$	−3.85029e10	−0.0760529
$400$	2.33227e11	0.455522
$401$	−7.18517e11	−1.38767	−0.693837	−	0.720132i	$-0.744081\pi$
$401$	−7.18517e11	−1.38767	−0.693837	+	0.720132i	$0.744081\pi$
$402$	2.66588e11	0.509123
$403$	1.49548e11	0.282429
$404$	−2.97413e11	−0.555448
$405$	−4.12619e10	−0.0762082
$406$	−1.67285e11	−0.305556
$407$	−7.72410e10	−0.139532
$408$	5.77634e10	0.103201
$409$	3.48286e11	0.615433	0.307716	−	0.951478i	$-0.400435\pi$
$409$	3.48286e11	0.615433	0.307716	+	0.951478i	$0.400435\pi$
$410$	2.94984e11	0.515551
$411$	3.17064e11	0.548099
$412$	−3.69674e11	−0.632094
$413$	6.68105e10	0.112998
$414$	−2.45522e11	−0.410760
$415$	3.89751e11	0.645017
$416$	1.17437e12	1.92259
$417$	1.01032e11	0.163624
$418$	−8.33651e10	−0.133565
$419$	7.27209e11	1.15265	0.576323	−	0.817222i	$-0.304487\pi$
$419$	7.27209e11	1.15265	0.576323	+	0.817222i	$0.304487\pi$
$420$	2.46439e11	0.386445
$421$	−3.29826e11	−0.511700	−0.255850	−	0.966716i	$-0.582355\pi$
$421$	−3.29826e11	−0.511700	−0.255850	+	0.966716i	$0.582355\pi$
$422$	−2.23890e11	−0.343660
$423$	−3.72471e11	−0.565668
$424$	−1.07074e11	−0.160894
$425$	3.51231e11	0.522208
$426$	−3.19774e11	−0.470435
$427$	5.02511e11	0.731510
$428$	8.31013e11	1.19705
$429$	3.27667e11	0.467063
$430$	1.94446e11	0.274278
$431$	−3.37955e11	−0.471749	−0.235874	−	0.971784i	$-0.575795\pi$
$431$	−3.37955e11	−0.471749	−0.235874	+	0.971784i	$0.575795\pi$
$432$	−1.19833e11	−0.165538
$433$	−2.67392e11	−0.365554	−0.182777	−	0.983154i	$-0.558509\pi$
$433$	−2.67392e11	−0.365554	−0.182777	+	0.983154i	$0.558509\pi$
$434$	1.97098e11	0.266673
$435$	7.14275e10	0.0956454
$436$	6.00241e11	0.795493
$437$	9.78233e10	0.128315
$438$	1.67161e10	0.0217021
$439$	2.73505e11	0.351460	0.175730	−	0.984438i	$-0.443771\pi$
$439$	2.73505e11	0.351460	0.175730	+	0.984438i	$0.443771\pi$
$440$	5.90207e10	0.0750702
$441$	−6.53059e10	−0.0822203
$442$	1.54515e12	1.92562
$443$	9.56113e11	1.17949	0.589743	−	0.807591i	$-0.299229\pi$
$443$	9.56113e11	1.17949	0.589743	+	0.807591i	$0.299229\pi$
$444$	−1.22843e11	−0.150012
$445$	−9.47906e11	−1.14590
$446$	−1.80326e12	−2.15800
$447$	−5.90080e11	−0.699080
$448$	9.11228e11	1.06875
$449$	−5.34222e11	−0.620317	−0.310158	−	0.950685i	$-0.600382\pi$
$449$	−5.34222e11	−0.620317	−0.310158	+	0.950685i	$0.600382\pi$
$450$	2.23810e11	0.257290
$451$	2.73591e11	0.311392
$452$	1.37887e12	1.55381
$453$	1.33187e11	0.148601
$454$	−2.42940e10	−0.0268378
$455$	7.29175e11	0.797591
$456$	−1.46653e10	−0.0158836
$457$	1.04929e12	1.12531	0.562655	−	0.826692i	$-0.309780\pi$
$457$	1.04929e12	1.12531	0.562655	+	0.826692i	$0.309780\pi$
$458$	−5.62660e11	−0.597518
$459$	−1.80464e11	−0.189772
$460$	−6.26121e11	−0.652000
$461$	1.19364e12	1.23089	0.615446	−	0.788179i	$-0.288976\pi$
$461$	1.19364e12	1.23089	0.615446	+	0.788179i	$0.288976\pi$
$462$	4.31851e11	0.441006
$463$	−1.18352e12	−1.19691	−0.598453	−	0.801158i	$-0.704218\pi$
$463$	−1.18352e12	−1.19691	−0.598453	+	0.801158i	$0.704218\pi$
$464$	2.07440e11	0.207760
$465$	−8.41569e10	−0.0834741
$466$	3.56555e11	0.350259
$467$	−2.71301e11	−0.263952	−0.131976	−	0.991253i	$-0.542132\pi$
$467$	−2.71301e11	−0.263952	−0.131976	+	0.991253i	$0.542132\pi$
$468$	5.21117e11	0.502144
$469$	5.50227e11	0.525126
$470$	−1.79466e12	−1.69645
$471$	5.34149e11	0.500113
$472$	2.54473e10	0.0235995
$473$	1.80344e11	0.165664
$474$	7.21528e11	0.656524
$475$	−8.91726e10	−0.0803730
$476$	1.07783e12	0.962318
$477$	3.34520e11	0.295862
$478$	−7.48747e11	−0.656009
$479$	−1.66233e12	−1.44280	−0.721400	−	0.692519i	$-0.756501\pi$
$479$	−1.66233e12	−1.44280	−0.721400	+	0.692519i	$0.756501\pi$
$480$	−6.60867e11	−0.568236
$481$	−3.63473e11	−0.309613
$482$	1.45954e12	1.23170
$483$	−5.06747e11	−0.423671
$484$	−8.62533e11	−0.714450
$485$	1.05168e12	0.863072
$486$	−1.14994e11	−0.0935001
$487$	1.70962e12	1.37727	0.688635	−	0.725108i	$-0.258210\pi$
$487$	1.70962e12	1.37727	0.688635	+	0.725108i	$0.258210\pi$
$488$	1.91400e11	0.152775
$489$	5.98754e11	0.473542
$490$	−3.14660e11	−0.246581
$491$	−1.66144e12	−1.29008	−0.645041	−	0.764148i	$-0.723160\pi$
$491$	−1.66144e12	−1.29008	−0.645041	+	0.764148i	$0.723160\pi$
$492$	4.35115e11	0.334781
$493$	3.12396e11	0.238174
$494$	−3.92291e11	−0.296372
$495$	−1.84392e11	−0.138044
$496$	−2.44408e11	−0.181321
$497$	−6.60000e11	−0.485222
$498$	1.08621e12	0.791373
$499$	2.04870e12	1.47920	0.739598	−	0.673049i	$-0.235016\pi$
$499$	2.04870e12	1.47920	0.739598	+	0.673049i	$0.235016\pi$
$500$	1.64850e12	1.17957
$501$	1.94646e11	0.138031
$502$	4.24105e11	0.298062
$503$	−2.20450e12	−1.53552	−0.767759	−	0.640739i	$-0.778628\pi$
$503$	−2.20450e12	−1.53552	−0.767759	+	0.640739i	$0.778628\pi$
$504$	7.59696e10	0.0524448
$505$	4.95210e11	0.338827
$506$	−1.09719e12	−0.744054
$507$	6.82938e11	0.459035
$508$	4.29197e11	0.285937
$509$	1.04417e12	0.689511	0.344756	−	0.938692i	$-0.387962\pi$
$509$	1.04417e12	0.689511	0.344756	+	0.938692i	$0.387962\pi$
$510$	−8.69518e11	−0.569132
$511$	3.45015e10	0.0223843
$512$	−2.16174e12	−1.39024
$513$	4.58171e10	0.0292078
$514$	−3.84628e12	−2.43056
$515$	6.15530e11	0.385582
$516$	2.86817e11	0.178107
$517$	−1.66450e12	−1.02465
$518$	−4.79040e11	−0.292340
$519$	6.21328e11	0.375896
$520$	2.77734e11	0.166576
$521$	−1.07856e12	−0.641318	−0.320659	−	0.947195i	$-0.603904\pi$
$521$	−1.07856e12	−0.641318	−0.320659	+	0.947195i	$0.603904\pi$
$522$	1.99063e11	0.117348
$523$	−1.13837e12	−0.665315	−0.332657	−	0.943048i	$-0.607945\pi$
$523$	−1.13837e12	−0.665315	−0.332657	+	0.943048i	$0.607945\pi$
$524$	3.71834e12	2.15456
$525$	4.61935e11	0.265377
$526$	−1.66594e12	−0.948906
$527$	−3.68070e11	−0.207865
$528$	−5.35510e11	−0.299858
$529$	−5.13676e11	−0.285193
$530$	1.61180e12	0.887299
$531$	−7.95020e10	−0.0433963
$532$	−2.73645e11	−0.148110
$533$	1.28744e12	0.690960
$534$	−2.64175e12	−1.40590
$535$	−1.38369e12	−0.730207
$536$	2.09575e11	0.109672
$537$	9.91333e11	0.514441
$538$	−3.22362e12	−1.65891
$539$	−2.91840e11	−0.148934
$540$	−2.93254e11	−0.148413
$541$	7.84035e11	0.393503	0.196751	−	0.980453i	$-0.436961\pi$
$541$	7.84035e11	0.393503	0.196751	+	0.980453i	$0.436961\pi$
$542$	4.06130e11	0.202148
$543$	1.66481e12	0.821797
$544$	−2.89037e12	−1.41501
$545$	−9.99438e11	−0.485257
$546$	2.03216e12	0.978567
$547$	2.01623e12	0.962934	0.481467	−	0.876464i	$-0.340104\pi$
$547$	2.01623e12	0.962934	0.481467	+	0.876464i	$0.340104\pi$
$548$	2.25342e12	1.06740
$549$	−5.97970e11	−0.280934
$550$	1.00016e12	0.466057
$551$	−7.93129e10	−0.0366574
$552$	−1.93014e11	−0.0884835
$553$	1.48920e12	0.677160
$554$	−1.28317e12	−0.578748
$555$	2.04541e11	0.0915086
$556$	7.18048e11	0.318652
$557$	1.98586e12	0.874180	0.437090	−	0.899418i	$-0.356009\pi$
$557$	1.98586e12	0.874180	0.437090	+	0.899418i	$0.356009\pi$
$558$	−2.34539e11	−0.102415
$559$	8.48645e11	0.367598
$560$	−1.19170e12	−0.512059
$561$	−8.06457e11	−0.343755
$562$	−6.15898e12	−2.60433
$563$	−6.20064e11	−0.260105	−0.130053	−	0.991507i	$-0.541515\pi$
$563$	−6.20064e11	−0.260105	−0.130053	+	0.991507i	$0.541515\pi$
$564$	−2.64720e12	−1.10162
$565$	−2.29590e12	−0.947838
$566$	1.40794e11	0.0576649
$567$	−2.37343e11	−0.0964390
$568$	−2.51386e11	−0.101338
$569$	4.37693e12	1.75051	0.875255	−	0.483662i	$-0.160693\pi$
$569$	4.37693e12	1.75051	0.875255	+	0.483662i	$0.160693\pi$
$570$	2.20758e11	0.0875951
$571$	2.44447e12	0.962325	0.481162	−	0.876631i	$-0.340215\pi$
$571$	2.44447e12	0.962325	0.481162	+	0.876631i	$0.340215\pi$
$572$	2.32877e12	0.909588
$573$	−7.27802e10	−0.0282044
$574$	1.69678e12	0.652413
$575$	−1.17362e12	−0.447738
$576$	−1.08433e12	−0.410449
$577$	−2.44903e12	−0.919819	−0.459910	−	0.887966i	$-0.652118\pi$
$577$	−2.44903e12	−0.919819	−0.459910	+	0.887966i	$0.652118\pi$
$578$	1.08090e11	0.0402818
$579$	−1.46710e12	−0.542506
$580$	5.07644e11	0.186266
$581$	2.24189e12	0.816248
$582$	2.93096e12	1.05890
$583$	1.49491e12	0.535927
$584$	1.31412e10	0.00467494
$585$	−8.67691e11	−0.306312
$586$	−7.48564e12	−2.62234
$587$	4.47127e12	1.55439	0.777195	−	0.629260i	$-0.216642\pi$
$587$	4.47127e12	1.55439	0.777195	+	0.629260i	$0.216642\pi$
$588$	−4.64137e11	−0.160121
$589$	9.34476e10	0.0319926
$590$	−3.83060e11	−0.130147
$591$	5.32843e11	0.179662
$592$	5.94027e11	0.198774
$593$	−6.41097e11	−0.212901	−0.106450	−	0.994318i	$-0.533949\pi$
$593$	−6.41097e11	−0.212901	−0.106450	+	0.994318i	$0.533949\pi$
$594$	−5.13886e11	−0.169367
$595$	−1.79465e12	−0.587021
$596$	−4.19377e12	−1.36143
$597$	4.03250e11	0.129924
$598$	−5.16304e12	−1.65101
$599$	−2.76079e12	−0.876221	−0.438110	−	0.898921i	$-0.644352\pi$
$599$	−2.76079e12	−0.876221	−0.438110	+	0.898921i	$0.644352\pi$
$600$	1.75945e11	0.0554239
$601$	−8.81619e11	−0.275642	−0.137821	−	0.990457i	$-0.544010\pi$
$601$	−8.81619e11	−0.275642	−0.137821	+	0.990457i	$0.544010\pi$
$602$	1.11848e12	0.347090
$603$	−6.54750e11	−0.201673
$604$	9.46579e11	0.289395
$605$	1.43617e12	0.435820
$606$	1.38011e12	0.415708
$607$	−1.37826e12	−0.412080	−0.206040	−	0.978544i	$-0.566058\pi$
$607$	−1.37826e12	−0.412080	−0.206040	+	0.978544i	$0.566058\pi$
$608$	7.33825e11	0.217784
$609$	4.10859e11	0.121036
$610$	−2.88117e12	−0.842528
$611$	−7.83265e12	−2.27365
$612$	−1.28258e12	−0.369574
$613$	4.20522e12	1.20287	0.601433	−	0.798924i	$-0.294597\pi$
$613$	4.20522e12	1.20287	0.601433	+	0.798924i	$0.294597\pi$
$614$	−1.09562e12	−0.311102
$615$	−7.24493e11	−0.204219
$616$	3.39494e11	0.0949989
$617$	1.72073e12	0.478002	0.239001	−	0.971019i	$-0.423180\pi$
$617$	1.72073e12	0.478002	0.239001	+	0.971019i	$0.423180\pi$
$618$	1.71544e12	0.473072
$619$	2.41835e12	0.662081	0.331040	−	0.943617i	$-0.392600\pi$
$619$	2.41835e12	0.662081	0.331040	+	0.943617i	$0.392600\pi$
$620$	−5.98114e11	−0.162563
$621$	6.03010e11	0.162709
$622$	5.44719e11	0.145920
$623$	−5.45246e12	−1.45009
$624$	−2.51995e12	−0.665367
$625$	−7.24683e11	−0.189971
$626$	−2.87571e12	−0.748446
$627$	2.04748e11	0.0529073
$628$	3.79627e12	0.973953
$629$	8.94582e11	0.227873
$630$	−1.14358e12	−0.289223
$631$	−5.20973e12	−1.30823	−0.654113	−	0.756397i	$-0.726958\pi$
$631$	−5.20973e12	−1.30823	−0.654113	+	0.756397i	$0.726958\pi$
$632$	5.67220e11	0.141424
$633$	5.49883e11	0.136130
$634$	3.30490e12	0.812376
$635$	−7.14639e11	−0.174424
$636$	2.37748e12	0.576181
$637$	−1.37331e12	−0.330477
$638$	8.89577e11	0.212564
$639$	7.85376e11	0.186348
$640$	−1.04723e12	−0.246735
$641$	−6.57069e12	−1.53727	−0.768635	−	0.639688i	$-0.779063\pi$
$641$	−6.57069e12	−1.53727	−0.768635	+	0.639688i	$0.779063\pi$
$642$	−3.85624e12	−0.895893
$643$	−5.46128e12	−1.25993	−0.629963	−	0.776625i	$-0.716930\pi$
$643$	−5.46128e12	−1.25993	−0.629963	+	0.776625i	$0.716930\pi$
$644$	−3.60151e12	−0.825085
$645$	−4.77567e11	−0.108647
$646$	9.65510e11	0.218128
$647$	1.58624e12	0.355876	0.177938	−	0.984042i	$-0.443057\pi$
$647$	1.58624e12	0.355876	0.177938	+	0.984042i	$0.443057\pi$
$648$	−9.04010e10	−0.0201412
$649$	−3.55279e11	−0.0786084
$650$	4.70647e12	1.03415
$651$	−4.84080e11	−0.105634
$652$	4.25542e12	0.922207
$653$	2.41513e11	0.0519793	0.0259897	−	0.999662i	$-0.491726\pi$
$653$	2.41513e11	0.0519793	0.0259897	+	0.999662i	$0.491726\pi$
$654$	−2.78536e12	−0.595363
$655$	−6.19126e12	−1.31430
$656$	−2.10407e12	−0.443601
$657$	−4.10555e10	−0.00859660
$658$	−1.03231e13	−2.14681
$659$	2.47059e12	0.510290	0.255145	−	0.966903i	$-0.417877\pi$
$659$	2.47059e12	0.510290	0.255145	+	0.966903i	$0.417877\pi$
$660$	−1.31049e12	−0.268836
$661$	2.40593e12	0.490204	0.245102	−	0.969497i	$-0.421179\pi$
$661$	2.40593e12	0.490204	0.245102	+	0.969497i	$0.421179\pi$
$662$	8.15217e12	1.64973
$663$	−3.79494e12	−0.762771
$664$	8.53909e11	0.170473
$665$	4.55636e11	0.0903485
$666$	5.70041e11	0.112272
$667$	−1.04386e12	−0.204209
$668$	1.38337e12	0.268810
$669$	4.42888e12	0.854824
$670$	−3.15475e12	−0.604822
$671$	−2.67221e12	−0.508885
$672$	−3.80138e12	−0.719084
$673$	−4.41273e12	−0.829163	−0.414581	−	0.910012i	$-0.636072\pi$
$673$	−4.41273e12	−0.829163	−0.414581	+	0.910012i	$0.636072\pi$
$674$	2.35148e12	0.438906
$675$	−5.49685e11	−0.101917
$676$	4.85373e12	0.893954
$677$	−1.62377e12	−0.297081	−0.148541	−	0.988906i	$-0.547458\pi$
$677$	−1.62377e12	−0.297081	−0.148541	+	0.988906i	$0.547458\pi$
$678$	−6.39850e12	−1.16291
$679$	6.04939e12	1.09219
$680$	−6.83561e11	−0.122599
$681$	5.96669e10	0.0106309
$682$	−1.04811e12	−0.185515
$683$	9.25217e12	1.62686	0.813431	−	0.581662i	$-0.197597\pi$
$683$	9.25217e12	1.62686	0.813431	+	0.581662i	$0.197597\pi$
$684$	3.25628e11	0.0568812
$685$	−3.75208e12	−0.651125
$686$	−9.14781e12	−1.57710
$687$	1.38191e12	0.236688
$688$	−1.38695e12	−0.236001
$689$	7.03458e12	1.18919
$690$	2.90545e12	0.487970
$691$	5.15435e11	0.0860048	0.0430024	−	0.999075i	$-0.486308\pi$
$691$	5.15435e11	0.0860048	0.0430024	+	0.999075i	$0.486308\pi$
$692$	4.41585e12	0.732044
$693$	−1.06064e12	−0.174690
$694$	1.18498e13	1.93907
$695$	−1.19559e12	−0.194380
$696$	1.56491e11	0.0252783
$697$	−3.16865e12	−0.508541
$698$	6.29188e12	1.00330
$699$	−8.75712e11	−0.138744
$700$	3.28303e12	0.516813
$701$	3.50104e12	0.547603	0.273802	−	0.961786i	$-0.411719\pi$
$701$	3.50104e12	0.547603	0.273802	+	0.961786i	$0.411719\pi$
$702$	−2.41819e12	−0.375815
$703$	−2.27122e11	−0.0350719
$704$	−4.84565e12	−0.743491
$705$	4.40775e12	0.671995
$706$	−6.20582e12	−0.940109
$707$	2.84850e12	0.428775
$708$	−5.65031e11	−0.0845128
$709$	1.99580e12	0.296625	0.148313	−	0.988941i	$-0.452616\pi$
$709$	1.99580e12	0.296625	0.148313	+	0.988941i	$0.452616\pi$
$710$	3.78414e12	0.558862
$711$	−1.77210e12	−0.260061
$712$	−2.07678e12	−0.302851
$713$	1.22989e12	0.178222
$714$	−5.00156e12	−0.720218
$715$	−3.87755e12	−0.554856
$716$	7.04553e12	1.00186
$717$	1.83895e12	0.259857
$718$	1.43171e12	0.201046
$719$	−1.16662e13	−1.62798	−0.813989	−	0.580880i	$-0.802709\pi$
$719$	−1.16662e13	−1.62798	−0.813989	+	0.580880i	$0.802709\pi$
$720$	1.41808e12	0.196654
$721$	3.54060e12	0.487942
$722$	1.03971e13	1.42395
$723$	−3.58468e12	−0.487897
$724$	1.18320e13	1.60042
$725$	9.51547e11	0.127911
$726$	4.00250e12	0.534708
$727$	1.24565e13	1.65383	0.826917	−	0.562324i	$-0.190093\pi$
$727$	1.24565e13	1.65383	0.826917	+	0.562324i	$0.190093\pi$
$728$	1.59755e12	0.210797
$729$	2.82430e11	0.0370370
$730$	−1.97815e11	−0.0257815
$731$	−2.08869e12	−0.270549
$732$	−4.24984e12	−0.547108
$733$	9.57896e12	1.22560	0.612802	−	0.790236i	$-0.290042\pi$
$733$	9.57896e12	1.22560	0.612802	+	0.790236i	$0.290042\pi$
$734$	1.23267e13	1.56753
$735$	7.72817e11	0.0976751
$736$	9.65805e12	1.21322
$737$	−2.92595e12	−0.365312
$738$	−2.01911e12	−0.250557
$739$	1.19683e13	1.47616	0.738079	−	0.674714i	$-0.235733\pi$
$739$	1.19683e13	1.47616	0.738079	+	0.674714i	$0.235733\pi$
$740$	1.45370e12	0.178210
$741$	9.63482e11	0.117398
$742$	9.27126e12	1.12285
$743$	9.42113e12	1.13411	0.567053	−	0.823681i	$-0.308084\pi$
$743$	9.42113e12	1.13411	0.567053	+	0.823681i	$0.308084\pi$
$744$	−1.84380e11	−0.0220615
$745$	6.98289e12	0.830485
$746$	−7.72605e12	−0.913341
$747$	−2.66777e12	−0.313477
$748$	−5.73159e12	−0.669450
$749$	−7.95912e12	−0.924054
$750$	−7.64972e12	−0.882816
$751$	5.24381e12	0.601544	0.300772	−	0.953696i	$-0.402756\pi$
$751$	5.24381e12	0.601544	0.300772	+	0.953696i	$0.402756\pi$
$752$	1.28010e13	1.45970
$753$	−1.04162e12	−0.118068
$754$	4.18608e12	0.471668
$755$	−1.57611e12	−0.176533
$756$	−1.68683e12	−0.187812
$757$	1.12096e13	1.24067	0.620337	−	0.784335i	$-0.286996\pi$
$757$	1.12096e13	1.24067	0.620337	+	0.784335i	$0.286996\pi$
$758$	−1.96238e13	−2.15910
$759$	2.69474e12	0.294733
$760$	1.73546e11	0.0188692
$761$	9.44214e12	1.02056	0.510281	−	0.860008i	$-0.329541\pi$
$761$	9.44214e12	1.02056	0.510281	+	0.860008i	$0.329541\pi$
$762$	−1.99165e12	−0.214001
$763$	−5.74888e12	−0.614077
$764$	−5.17258e11	−0.0549271
$765$	2.13557e12	0.225443
$766$	1.54882e13	1.62545
$767$	−1.67184e12	−0.174427
$768$	3.93548e12	0.408199
$769$	1.11920e13	1.15409	0.577044	−	0.816713i	$-0.304206\pi$
$769$	1.11920e13	1.15409	0.577044	+	0.816713i	$0.304206\pi$
$770$	−5.11043e12	−0.523901
$771$	9.44661e12	0.962789
$772$	−1.04268e13	−1.05651
$773$	1.21128e13	1.22022	0.610109	−	0.792317i	$-0.291125\pi$
$773$	1.21128e13	1.22022	0.610109	+	0.792317i	$0.291125\pi$
$774$	−1.33095e12	−0.133299
$775$	−1.12113e12	−0.111634
$776$	2.30414e12	0.228103
$777$	1.17654e12	0.115801
$778$	1.28960e13	1.26196
$779$	8.04474e11	0.0782697
$780$	−6.16679e12	−0.596532
$781$	3.50970e12	0.337551
$782$	1.27073e13	1.21513
$783$	−4.88907e11	−0.0464835
$784$	2.24442e12	0.212169
$785$	−6.32102e12	−0.594119
$786$	−1.72546e13	−1.61251
$787$	−6.46327e11	−0.0600573	−0.0300286	−	0.999549i	$-0.509560\pi$
$787$	−6.46327e11	−0.0600573	−0.0300286	+	0.999549i	$0.509560\pi$
$788$	3.78698e12	0.349885
$789$	4.09161e12	0.375879
$790$	−8.53842e12	−0.779930
$791$	−1.32062e13	−1.19946
$792$	−4.03985e11	−0.0364840
$793$	−1.25746e13	−1.12919
$794$	−6.38124e12	−0.569788
$795$	−3.95864e12	−0.351475
$796$	2.86595e12	0.253023
$797$	5.88328e12	0.516484	0.258242	−	0.966080i	$-0.416857\pi$
$797$	5.88328e12	0.516484	0.258242	+	0.966080i	$0.416857\pi$
$798$	1.26983e12	0.110849
$799$	1.92778e13	1.67339
$800$	−8.80398e12	−0.759931
$801$	6.48823e12	0.556903
$802$	2.36967e13	2.02256
$803$	−1.83469e11	−0.0155719
$804$	−4.65339e12	−0.392751
$805$	5.99674e12	0.503308
$806$	−4.93210e12	−0.411646
$807$	7.91734e12	0.657125
$808$	1.08496e12	0.0895494
$809$	−1.11236e13	−0.913012	−0.456506	−	0.889720i	$-0.650899\pi$
$809$	−1.11236e13	−0.913012	−0.456506	+	0.889720i	$0.650899\pi$
$810$	1.36082e12	0.111075
$811$	1.91451e13	1.55405	0.777023	−	0.629472i	$-0.216729\pi$
$811$	1.91451e13	1.55405	0.777023	+	0.629472i	$0.216729\pi$
$812$	2.92003e12	0.235714
$813$	−9.97471e11	−0.0800743
$814$	2.54740e12	0.203371
$815$	−7.08554e12	−0.562553
$816$	6.20212e12	0.489705
$817$	5.30289e11	0.0416403
$818$	−1.14864e13	−0.897007
$819$	−4.99106e12	−0.387628
$820$	−5.14906e12	−0.397709
$821$	−1.79095e13	−1.37575	−0.687876	−	0.725828i	$-0.741457\pi$
$821$	−1.79095e13	−1.37575	−0.687876	+	0.725828i	$0.741457\pi$
$822$	−1.04568e13	−0.798867
$823$	6.67037e12	0.506816	0.253408	−	0.967359i	$-0.418448\pi$
$823$	6.67037e12	0.506816	0.253408	+	0.967359i	$0.418448\pi$
$824$	1.34857e12	0.101906
$825$	−2.45644e12	−0.184613
$826$	−2.20341e12	−0.164696
$827$	5.80949e11	0.0431880	0.0215940	−	0.999767i	$-0.493126\pi$
$827$	5.80949e11	0.0431880	0.0215940	+	0.999767i	$0.493126\pi$
$828$	4.28567e12	0.316871
$829$	2.16695e13	1.59351	0.796754	−	0.604304i	$-0.206549\pi$
$829$	2.16695e13	1.59351	0.796754	+	0.604304i	$0.206549\pi$
$830$	−1.28540e13	−0.940126
$831$	3.15151e12	0.229252
$832$	−2.28022e13	−1.64976
$833$	3.38000e12	0.243228
$834$	−3.33203e12	−0.238486
$835$	−2.30340e12	−0.163976
$836$	1.45517e12	0.103035
$837$	5.76037e11	0.0405682
$838$	−2.39833e13	−1.68001
$839$	1.21671e12	0.0847734	0.0423867	−	0.999101i	$-0.486504\pi$
$839$	1.21671e12	0.0847734	0.0423867	+	0.999101i	$0.486504\pi$
$840$	−8.99009e11	−0.0623028
$841$	−1.36608e13	−0.941661
$842$	1.08776e13	0.745814
$843$	1.51267e13	1.03162
$844$	3.90809e12	0.265108
$845$	−8.08175e12	−0.545319
$846$	1.22841e13	0.824473
$847$	8.26101e12	0.551516
$848$	−1.14967e13	−0.763469
$849$	−3.45797e11	−0.0228421
$850$	−1.15836e13	−0.761129
$851$	−2.98920e12	−0.195377
$852$	5.58177e12	0.362905
$853$	−5.36001e12	−0.346653	−0.173326	−	0.984864i	$-0.555452\pi$
$853$	−5.36001e12	−0.346653	−0.173326	+	0.984864i	$0.555452\pi$
$854$	−1.65728e13	−1.06619
$855$	−5.42190e11	−0.0346980
$856$	−3.03153e12	−0.192988
$857$	−1.30221e13	−0.824644	−0.412322	−	0.911038i	$-0.635282\pi$
$857$	−1.30221e13	−0.824644	−0.412322	+	0.911038i	$0.635282\pi$
$858$	−1.08064e13	−0.680754
$859$	2.19921e13	1.37816	0.689078	−	0.724688i	$-0.258016\pi$
$859$	2.19921e13	1.37816	0.689078	+	0.724688i	$0.258016\pi$
$860$	−3.39413e12	−0.211585
$861$	−4.16736e12	−0.258432
$862$	1.11457e13	0.687584
$863$	−2.89089e13	−1.77412	−0.887060	−	0.461654i	$-0.847256\pi$
$863$	−2.89089e13	−1.77412	−0.887060	+	0.461654i	$0.847256\pi$
$864$	4.52350e12	0.276161
$865$	−7.35267e12	−0.446552
$866$	8.81856e12	0.532804
$867$	−2.65472e11	−0.0159563
$868$	−3.44042e12	−0.205718
$869$	−7.91918e12	−0.471076
$870$	−2.35568e12	−0.139405
$871$	−1.37686e13	−0.810605
$872$	−2.18968e12	−0.128250
$873$	−7.19856e12	−0.419451
$874$	−3.22621e12	−0.187021
$875$	−1.57887e13	−0.910565
$876$	−2.91786e11	−0.0167416
$877$	1.72809e13	0.986435	0.493217	−	0.869906i	$-0.335821\pi$
$877$	1.72809e13	0.986435	0.493217	+	0.869906i	$0.335821\pi$
$878$	−9.02020e12	−0.512260
$879$	1.83850e13	1.03876
$880$	6.33712e12	0.356221
$881$	6.40170e12	0.358017	0.179009	−	0.983848i	$-0.442711\pi$
$881$	6.40170e12	0.358017	0.179009	+	0.983848i	$0.442711\pi$
$882$	2.15379e12	0.119838
$883$	5.02129e12	0.277966	0.138983	−	0.990295i	$-0.455617\pi$
$883$	5.02129e12	0.277966	0.138983	+	0.990295i	$0.455617\pi$
$884$	−2.69711e13	−1.48547
$885$	9.40811e11	0.0515534
$886$	−3.15326e13	−1.71912
$887$	2.62500e13	1.42388	0.711940	−	0.702240i	$-0.247817\pi$
$887$	2.62500e13	1.42388	0.711940	+	0.702240i	$0.247817\pi$
$888$	4.48130e11	0.0241850
$889$	−4.11068e12	−0.220727
$890$	3.12619e13	1.67017
$891$	1.26212e12	0.0670892
$892$	3.14766e13	1.66474
$893$	−4.89436e12	−0.257551
$894$	1.94608e13	1.01892
$895$	−1.17312e13	−0.611139
$896$	−6.02376e12	−0.312235
$897$	1.26806e13	0.653995
$898$	1.76186e13	0.904125
$899$	−9.97165e11	−0.0509153
$900$	−3.90668e12	−0.198480
$901$	−1.73136e13	−0.875236
$902$	−9.02301e12	−0.453860
$903$	−2.74702e12	−0.137489
$904$	−5.03010e12	−0.250506
$905$	−1.97010e13	−0.976269
$906$	−4.39251e12	−0.216589
$907$	−1.31166e13	−0.643559	−0.321780	−	0.946815i	$-0.604281\pi$
$907$	−1.31166e13	−0.643559	−0.321780	+	0.946815i	$0.604281\pi$
$908$	4.24060e11	0.0207034
$909$	−3.38961e12	−0.164669
$910$	−2.40482e13	−1.16251
$911$	3.00427e13	1.44513	0.722565	−	0.691303i	$-0.242963\pi$
$911$	3.00427e13	1.44513	0.722565	+	0.691303i	$0.242963\pi$
$912$	−1.57463e12	−0.0753705
$913$	−1.19218e13	−0.567835
$914$	−3.46055e13	−1.64016
$915$	7.07625e12	0.333740
$916$	9.82144e12	0.460941
$917$	−3.56128e13	−1.66320
$918$	5.95168e12	0.276597
$919$	−2.42329e13	−1.12069	−0.560345	−	0.828259i	$-0.689331\pi$
$919$	−2.42329e13	−1.12069	−0.560345	+	0.828259i	$0.689331\pi$
$920$	2.28409e12	0.105116
$921$	2.69089e12	0.123233
$922$	−3.93662e13	−1.79405
$923$	1.65156e13	0.749007
$924$	−7.53811e12	−0.340203
$925$	2.72486e12	0.122379
$926$	3.90323e13	1.74452
$927$	−4.21318e12	−0.187392
$928$	−7.83053e12	−0.346597
$929$	−1.06966e13	−0.471167	−0.235583	−	0.971854i	$-0.575700\pi$
$929$	−1.06966e13	−0.471167	−0.235583	+	0.971854i	$0.575700\pi$
$930$	2.77549e12	0.121665
$931$	−8.58134e11	−0.0374353
$932$	−6.22379e12	−0.270199
$933$	−1.33785e12	−0.0578016
$934$	8.94748e12	0.384716
$935$	9.54346e12	0.408370
$936$	−1.90103e12	−0.0809558
$937$	−2.83481e13	−1.20142	−0.600712	−	0.799465i	$-0.705116\pi$
$937$	−2.83481e13	−1.20142	−0.600712	+	0.799465i	$0.705116\pi$
$938$	−1.81464e13	−0.765383
$939$	7.06285e12	0.296473
$940$	3.13265e13	1.30869
$941$	−9.66030e12	−0.401641	−0.200820	−	0.979628i	$-0.564361\pi$
$941$	−9.66030e12	−0.401641	−0.200820	+	0.979628i	$0.564361\pi$
$942$	−1.76162e13	−0.728926
$943$	1.05879e13	0.436020
$944$	2.73230e12	0.111984
$945$	2.80867e12	0.114567
$946$	−5.94774e12	−0.241458
$947$	−4.49566e13	−1.81643	−0.908214	−	0.418506i	$-0.862554\pi$
$947$	−4.49566e13	−1.81643	−0.908214	+	0.418506i	$0.862554\pi$
$948$	−1.25945e13	−0.506459
$949$	−8.63350e11	−0.0345532
$950$	2.94091e12	0.117145
$951$	−8.11696e12	−0.321796
$952$	−3.93192e12	−0.155145
$953$	1.78252e13	0.700030	0.350015	−	0.936744i	$-0.386176\pi$
$953$	1.78252e13	0.700030	0.350015	+	0.936744i	$0.386176\pi$
$954$	−1.10325e13	−0.431226
$955$	8.61266e11	0.0335060
$956$	1.30697e13	0.506062
$957$	−2.18483e12	−0.0842005
$958$	5.48234e13	2.10291
$959$	−2.15824e13	−0.823977
$960$	1.28317e13	0.487601
$961$	−2.52647e13	−0.955564
$962$	1.19873e13	0.451267
$963$	9.47107e12	0.354879
$964$	−2.54768e13	−0.950162
$965$	1.73613e13	0.644480
$966$	1.67125e13	0.617510
$967$	3.12572e13	1.14956	0.574780	−	0.818308i	$-0.305088\pi$
$967$	3.12572e13	1.14956	0.574780	+	0.818308i	$0.305088\pi$
$968$	3.14652e12	0.115184
$969$	−2.37133e12	−0.0864042
$970$	−3.46844e13	−1.25795
$971$	−9.61953e12	−0.347270	−0.173635	−	0.984810i	$-0.555551\pi$
$971$	−9.61953e12	−0.347270	−0.173635	+	0.984810i	$0.555551\pi$
$972$	2.00726e12	0.0721283
$973$	−6.87719e12	−0.245982
$974$	−5.63831e13	−2.00740
$975$	−1.15593e13	−0.409647
$976$	2.05508e13	0.724946
$977$	1.16684e13	0.409719	0.204859	−	0.978791i	$-0.434326\pi$
$977$	1.16684e13	0.409719	0.204859	+	0.978791i	$0.434326\pi$
$978$	−1.97469e13	−0.690198
$979$	2.89947e13	1.00878
$980$	5.49251e12	0.190219
$981$	6.84095e12	0.235834
$982$	5.47941e13	1.88032
$983$	4.38643e13	1.49837	0.749187	−	0.662358i	$-0.230444\pi$
$983$	4.38643e13	1.49837	0.749187	+	0.662358i	$0.230444\pi$
$984$	−1.58730e12	−0.0539734
$985$	−6.30556e12	−0.213432
$986$	−1.03028e13	−0.347144
$987$	2.53539e13	0.850388
$988$	6.84759e12	0.228629
$989$	6.97927e12	0.231967
$990$	6.08123e12	0.201202
$991$	−3.26972e13	−1.07691	−0.538454	−	0.842655i	$-0.680991\pi$
$991$	−3.26972e13	−1.07691	−0.538454	+	0.842655i	$0.680991\pi$
$992$	9.22604e12	0.302491
$993$	−2.00220e13	−0.653487
$994$	2.17668e13	0.707221
$995$	−4.77198e12	−0.154346
$996$	−1.89602e13	−0.610485
$997$	3.11546e13	0.998606	0.499303	−	0.866428i	$-0.333589\pi$
$997$	3.11546e13	0.998606	0.499303	+	0.866428i	$0.333589\pi$
$998$	−6.75660e13	−2.15596
$999$	−1.40004e12	−0.0444730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-32.9800 q^{2} +81.0000 q^{3} +575.677 q^{4} -958.538 q^{5} -2671.38 q^{6} -5513.62 q^{7} -2100.07 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-32.9800 q^{2} +81.0000 q^{3} +575.677 q^{4} -958.538 q^{5} -2671.38 q^{6} -5513.62 q^{7} -2100.07 q^{8} +6561.00 q^{9} +31612.5 q^{10} +29319.9 q^{11} +46629.8 q^{12} +137970. q^{13} +181839. q^{14} -77641.6 q^{15} -225487. q^{16} -339574. q^{17} -216381. q^{18} +86213.0 q^{19} -551808. q^{20} -446603. q^{21} -966968. q^{22} +1.13467e6 q^{23} -170106. q^{24} -1.03433e6 q^{25} -4.55026e6 q^{26} +531441. q^{27} -3.17406e6 q^{28} -919965. q^{29} +2.56062e6 q^{30} +1.08392e6 q^{31} +8.51177e6 q^{32} +2.37491e6 q^{33} +1.11991e7 q^{34} +5.28501e6 q^{35} +3.77702e6 q^{36} -2.63442e6 q^{37} -2.84330e6 q^{38} +1.11756e7 q^{39} +2.01299e6 q^{40} +9.33124e6 q^{41} +1.47289e7 q^{42} +6.15092e6 q^{43} +1.68788e7 q^{44} -6.28897e6 q^{45} -3.74214e7 q^{46} -5.67705e7 q^{47} -1.82644e7 q^{48} -9.95366e6 q^{49} +3.41121e7 q^{50} -2.75055e7 q^{51} +7.94264e7 q^{52} +5.09861e7 q^{53} -1.75269e7 q^{54} -2.81042e7 q^{55} +1.15790e7 q^{56} +6.98325e6 q^{57} +3.03404e7 q^{58} -1.21174e7 q^{59} -4.46965e7 q^{60} -9.11400e7 q^{61} -3.57475e7 q^{62} -3.61748e7 q^{63} -1.65269e8 q^{64} -1.32250e8 q^{65} -7.83244e7 q^{66} -9.97942e7 q^{67} -1.95485e8 q^{68} +9.19083e7 q^{69} -1.74299e8 q^{70} +1.19704e8 q^{71} -1.37785e7 q^{72} -6.25750e6 q^{73} +8.68832e7 q^{74} -8.37807e7 q^{75} +4.96308e7 q^{76} -1.61658e8 q^{77} -3.68571e8 q^{78} -2.70096e8 q^{79} +2.16137e8 q^{80} +4.30467e7 q^{81} -3.07744e8 q^{82} -4.06610e8 q^{83} -2.57099e8 q^{84} +3.25494e8 q^{85} -2.02857e8 q^{86} -7.45172e7 q^{87} -6.15737e7 q^{88} +9.88909e8 q^{89} +2.07410e8 q^{90} -7.60716e8 q^{91} +6.53204e8 q^{92} +8.77972e7 q^{93} +1.87229e9 q^{94} -8.26384e7 q^{95} +6.89453e8 q^{96} -1.09717e9 q^{97} +3.28271e8 q^{98} +1.92368e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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