LMFDB - Embedded newform 177.10.a.a.1.7

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-24.8760 q^{2} +81.0000 q^{3} +106.816 q^{4} -222.031 q^{5} -2014.96 q^{6} -2494.49 q^{7} +10079.4 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-24.8760 q^{2} +81.0000 q^{3} +106.816 q^{4} -222.031 q^{5} -2014.96 q^{6} -2494.49 q^{7} +10079.4 q^{8} +6561.00 q^{9} +5523.25 q^{10} -17730.3 q^{11} +8652.13 q^{12} -12233.5 q^{13} +62052.9 q^{14} -17984.5 q^{15} -305424. q^{16} -170541. q^{17} -163212. q^{18} +800159. q^{19} -23716.6 q^{20} -202053. q^{21} +441059. q^{22} -44122.7 q^{23} +816428. q^{24} -1.90383e6 q^{25} +304322. q^{26} +531441. q^{27} -266452. q^{28} +2.97244e6 q^{29} +447383. q^{30} +3.78495e6 q^{31} +2.43711e6 q^{32} -1.43615e6 q^{33} +4.24237e6 q^{34} +553854. q^{35} +700823. q^{36} -1.62591e7 q^{37} -1.99048e7 q^{38} -990917. q^{39} -2.23793e6 q^{40} +4.70674e6 q^{41} +5.02629e6 q^{42} -2.93262e6 q^{43} -1.89389e6 q^{44} -1.45675e6 q^{45} +1.09760e6 q^{46} +5.72676e7 q^{47} -2.47394e7 q^{48} -3.41311e7 q^{49} +4.73596e7 q^{50} -1.38138e7 q^{51} -1.30674e6 q^{52} -7.27248e7 q^{53} -1.32201e7 q^{54} +3.93667e6 q^{55} -2.51428e7 q^{56} +6.48129e7 q^{57} -7.39425e7 q^{58} +1.21174e7 q^{59} -1.92104e6 q^{60} +1.75038e8 q^{61} -9.41546e7 q^{62} -1.63663e7 q^{63} +9.57516e7 q^{64} +2.71623e6 q^{65} +3.57258e7 q^{66} +2.04648e8 q^{67} -1.82166e7 q^{68} -3.57394e6 q^{69} -1.37777e7 q^{70} +4.00362e8 q^{71} +6.61306e7 q^{72} -2.17223e8 q^{73} +4.04463e8 q^{74} -1.54210e8 q^{75} +8.54702e7 q^{76} +4.42280e7 q^{77} +2.46501e7 q^{78} +3.33758e8 q^{79} +6.78137e7 q^{80} +4.30467e7 q^{81} -1.17085e8 q^{82} -3.31607e8 q^{83} -2.15826e7 q^{84} +3.78653e7 q^{85} +7.29519e7 q^{86} +2.40768e8 q^{87} -1.78710e8 q^{88} -9.11608e8 q^{89} +3.62380e7 q^{90} +3.05164e7 q^{91} -4.71303e6 q^{92} +3.06581e8 q^{93} -1.42459e9 q^{94} -1.77660e8 q^{95} +1.97406e8 q^{96} -4.51337e8 q^{97} +8.49047e8 q^{98} -1.16328e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) $	\( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−24.8760	−1.09938	−0.549688	−	0.835370i	$-0.685253\pi$
$2$	−24.8760	−1.09938	−0.549688	+	0.835370i	$0.685253\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	106.816	0.208626
$5$	−222.031	−0.158872	−0.0794362	−	0.996840i	$-0.525312\pi$
$5$	−222.031	−0.158872	−0.0794362	+	0.996840i	$0.525312\pi$
$6$	−2014.96	−0.634725
$7$	−2494.49	−0.392681	−0.196341	−	0.980536i	$-0.562906\pi$
$7$	−2494.49	−0.392681	−0.196341	+	0.980536i	$0.562906\pi$
$8$	10079.4	0.870017
$9$	6561.00	0.333333
$10$	5523.25	0.174660
$11$	−17730.3	−0.365131	−0.182565	−	0.983194i	$-0.558440\pi$
$11$	−17730.3	−0.365131	−0.182565	+	0.983194i	$0.558440\pi$
$12$	8652.13	0.120450
$13$	−12233.5	−0.118797	−0.0593987	−	0.998234i	$-0.518918\pi$
$13$	−12233.5	−0.118797	−0.0593987	+	0.998234i	$0.518918\pi$
$14$	62052.9	0.431704
$15$	−17984.5	−0.0917251
$16$	−305424.	−1.16510
$17$	−170541.	−0.495231	−0.247616	−	0.968858i	$-0.579647\pi$
$17$	−170541.	−0.495231	−0.247616	+	0.968858i	$0.579647\pi$
$18$	−163212.	−0.366458
$19$	800159.	1.40859	0.704296	−	0.709906i	$-0.251263\pi$
$19$	800159.	1.40859	0.704296	+	0.709906i	$0.251263\pi$
$20$	−23716.6	−0.0331449
$21$	−202053.	−0.226715
$22$	441059.	0.401416
$23$	−44122.7	−0.0328766	−0.0164383	−	0.999865i	$-0.505233\pi$
$23$	−44122.7	−0.0328766	−0.0164383	+	0.999865i	$0.505233\pi$
$24$	816428.	0.502305
$25$	−1.90383e6	−0.974760
$26$	304322.	0.130603
$27$	531441.	0.192450
$28$	−266452.	−0.0819235
$29$	2.97244e6	0.780409	0.390204	−	0.920728i	$-0.372404\pi$
$29$	2.97244e6	0.780409	0.390204	+	0.920728i	$0.372404\pi$
$30$	447383.	0.100840
$31$	3.78495e6	0.736093	0.368047	−	0.929807i	$-0.380027\pi$
$31$	3.78495e6	0.736093	0.368047	+	0.929807i	$0.380027\pi$
$32$	2.43711e6	0.410866
$33$	−1.43615e6	−0.210808
$34$	4.24237e6	0.544445
$35$	553854.	0.0623862
$36$	700823.	0.0695420
$37$	−1.62591e7	−1.42623	−0.713115	−	0.701047i	$-0.752716\pi$
$37$	−1.62591e7	−1.42623	−0.713115	+	0.701047i	$0.752716\pi$
$38$	−1.99048e7	−1.54857
$39$	−990917.	−0.0685877
$40$	−2.23793e6	−0.138222
$41$	4.70674e6	0.260131	0.130066	−	0.991505i	$-0.458481\pi$
$41$	4.70674e6	0.260131	0.130066	+	0.991505i	$0.458481\pi$
$42$	5.02629e6	0.249244
$43$	−2.93262e6	−0.130812	−0.0654060	−	0.997859i	$-0.520834\pi$
$43$	−2.93262e6	−0.130812	−0.0654060	+	0.997859i	$0.520834\pi$
$44$	−1.89389e6	−0.0761758
$45$	−1.45675e6	−0.0529575
$46$	1.09760e6	0.0361437
$47$	5.72676e7	1.71186	0.855931	−	0.517089i	$-0.172985\pi$
$47$	5.72676e7	1.71186	0.855931	+	0.517089i	$0.172985\pi$
$48$	−2.47394e7	−0.672671
$49$	−3.41311e7	−0.845801
$50$	4.73596e7	1.07163
$51$	−1.38138e7	−0.285922
$52$	−1.30674e6	−0.0247842
$53$	−7.27248e7	−1.26602	−0.633011	−	0.774143i	$-0.718181\pi$
$53$	−7.27248e7	−1.26602	−0.633011	+	0.774143i	$0.718181\pi$
$54$	−1.32201e7	−0.211575
$55$	3.93667e6	0.0580093
$56$	−2.51428e7	−0.341639
$57$	6.48129e7	0.813251
$58$	−7.39425e7	−0.857962
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−1.92104e6	−0.0191362
$61$	1.75038e8	1.61863	0.809314	−	0.587377i	$-0.199839\pi$
$61$	1.75038e8	1.61863	0.809314	+	0.587377i	$0.199839\pi$
$62$	−9.41546e7	−0.809243
$63$	−1.63663e7	−0.130894
$64$	9.57516e7	0.713405
$65$	2.71623e6	0.0188736
$66$	3.57258e7	0.231758
$67$	2.04648e8	1.24071	0.620357	−	0.784320i	$-0.286988\pi$
$67$	2.04648e8	1.24071	0.620357	+	0.784320i	$0.286988\pi$
$68$	−1.82166e7	−0.103318
$69$	−3.57394e6	−0.0189813
$70$	−1.37777e7	−0.0685859
$71$	4.00362e8	1.86978	0.934890	−	0.354938i	$-0.115498\pi$
$71$	4.00362e8	1.86978	0.934890	+	0.354938i	$0.115498\pi$
$72$	6.61306e7	0.290006
$73$	−2.17223e8	−0.895269	−0.447634	−	0.894217i	$-0.647733\pi$
$73$	−2.17223e8	−0.895269	−0.447634	+	0.894217i	$0.647733\pi$
$74$	4.04463e8	1.56796
$75$	−1.54210e8	−0.562778
$76$	8.54702e7	0.293869
$77$	4.42280e7	0.143380
$78$	2.46501e7	0.0754036
$79$	3.33758e8	0.964073	0.482036	−	0.876151i	$-0.339897\pi$
$79$	3.33758e8	0.964073	0.482036	+	0.876151i	$0.339897\pi$
$80$	6.78137e7	0.185103
$81$	4.30467e7	0.111111
$82$	−1.17085e8	−0.285982
$83$	−3.31607e8	−0.766959	−0.383479	−	0.923549i	$-0.625274\pi$
$83$	−3.31607e8	−0.766959	−0.383479	+	0.923549i	$0.625274\pi$
$84$	−2.15826e7	−0.0472985
$85$	3.78653e7	0.0786786
$86$	7.29519e7	0.143811
$87$	2.40768e8	0.450569
$88$	−1.78710e8	−0.317670
$89$	−9.11608e8	−1.54011	−0.770057	−	0.637975i	$-0.779772\pi$
$89$	−9.11608e8	−1.54011	−0.770057	+	0.637975i	$0.779772\pi$
$90$	3.62380e7	0.0582202
$91$	3.05164e7	0.0466495
$92$	−4.71303e6	−0.00685890
$93$	3.06581e8	0.424984
$94$	−1.42459e9	−1.88198
$95$	−1.77660e8	−0.223786
$96$	1.97406e8	0.237214
$97$	−4.51337e8	−0.517640	−0.258820	−	0.965926i	$-0.583334\pi$
$97$	−4.51337e8	−0.517640	−0.258820	+	0.965926i	$0.583334\pi$
$98$	8.49047e8	0.929853
$99$	−1.16328e8	−0.121710
$100$	−2.03360e8	−0.203360
$101$	−9.39227e8	−0.898099	−0.449050	−	0.893507i	$-0.648237\pi$
$101$	−9.39227e8	−0.898099	−0.449050	+	0.893507i	$0.648237\pi$
$102$	3.43632e8	0.314335
$103$	4.99025e8	0.436872	0.218436	−	0.975851i	$-0.429904\pi$
$103$	4.99025e8	0.436872	0.218436	+	0.975851i	$0.429904\pi$
$104$	−1.23306e8	−0.103356
$105$	4.48621e7	0.0360187
$106$	1.80910e9	1.39183
$107$	−1.84221e9	−1.35866	−0.679331	−	0.733832i	$-0.737730\pi$
$107$	−1.84221e9	−1.35866	−0.679331	+	0.733832i	$0.737730\pi$
$108$	5.67666e7	0.0401501
$109$	1.61168e9	1.09360	0.546801	−	0.837263i	$-0.315846\pi$
$109$	1.61168e9	1.09360	0.546801	+	0.837263i	$0.315846\pi$
$110$	−9.79288e7	−0.0637740
$111$	−1.31699e9	−0.823435
$112$	7.61877e8	0.457513
$113$	−2.32034e9	−1.33875	−0.669375	−	0.742925i	$-0.733438\pi$
$113$	−2.32034e9	−1.33875	−0.669375	+	0.742925i	$0.733438\pi$
$114$	−1.61229e9	−0.894068
$115$	9.79660e6	0.00522318
$116$	3.17506e8	0.162813
$117$	−8.02642e7	−0.0395991
$118$	−3.01432e8	−0.143126
$119$	4.25412e8	0.194468
$120$	−1.81272e8	−0.0798024
$121$	−2.04358e9	−0.866679
$122$	−4.35424e9	−1.77948
$123$	3.81246e8	0.150187
$124$	4.04295e8	0.153568
$125$	8.56363e8	0.313735
$126$	4.07129e8	0.143901
$127$	−6.43612e8	−0.219537	−0.109768	−	0.993957i	$-0.535011\pi$
$127$	−6.43612e8	−0.219537	−0.109768	+	0.993957i	$0.535011\pi$
$128$	−3.62972e9	−1.19517
$129$	−2.37542e8	−0.0755243
$130$	−6.75689e7	−0.0207492
$131$	−1.48253e9	−0.439827	−0.219914	−	0.975519i	$-0.570578\pi$
$131$	−1.48253e9	−0.439827	−0.219914	+	0.975519i	$0.570578\pi$
$132$	−1.53405e8	−0.0439801
$133$	−1.99599e9	−0.553128
$134$	−5.09083e9	−1.36401
$135$	−1.17996e8	−0.0305750
$136$	−1.71894e9	−0.430859
$137$	−4.89641e9	−1.18750	−0.593752	−	0.804648i	$-0.702354\pi$
$137$	−4.89641e9	−1.18750	−0.593752	+	0.804648i	$0.702354\pi$
$138$	8.89053e7	0.0208676
$139$	1.02222e9	0.232262	0.116131	−	0.993234i	$-0.462951\pi$
$139$	1.02222e9	0.232262	0.116131	+	0.993234i	$0.462951\pi$
$140$	5.91607e7	0.0130154
$141$	4.63868e9	0.988344
$142$	−9.95942e9	−2.05559
$143$	2.16904e8	0.0433766
$144$	−2.00389e9	−0.388367
$145$	−6.59974e8	−0.123986
$146$	5.40365e9	0.984236
$147$	−2.76462e9	−0.488324
$148$	−1.73674e9	−0.297549
$149$	−8.58555e9	−1.42702	−0.713510	−	0.700645i	$-0.752896\pi$
$149$	−8.58555e9	−1.42702	−0.713510	+	0.700645i	$0.752896\pi$
$150$	3.83613e9	0.618704
$151$	−7.12323e8	−0.111501	−0.0557507	−	0.998445i	$-0.517755\pi$
$151$	−7.12323e8	−0.111501	−0.0557507	+	0.998445i	$0.517755\pi$
$152$	8.06509e9	1.22550
$153$	−1.11892e9	−0.165077
$154$	−1.10022e9	−0.157629
$155$	−8.40377e8	−0.116945
$156$	−1.05846e8	−0.0143092
$157$	−1.19629e10	−1.57141	−0.785706	−	0.618601i	$-0.787700\pi$
$157$	−1.19629e10	−1.57141	−0.785706	+	0.618601i	$0.787700\pi$
$158$	−8.30257e9	−1.05988
$159$	−5.89071e9	−0.730938
$160$	−5.41114e8	−0.0652753
$161$	1.10063e8	0.0129100
$162$	−1.07083e9	−0.122153
$163$	−5.38110e9	−0.597073	−0.298536	−	0.954398i	$-0.596498\pi$
$163$	−5.38110e9	−0.597073	−0.298536	+	0.954398i	$0.596498\pi$
$164$	5.02757e8	0.0542701
$165$	3.18871e8	0.0334917
$166$	8.24906e9	0.843175
$167$	−1.56592e10	−1.55792	−0.778960	−	0.627074i	$-0.784253\pi$
$167$	−1.56592e10	−1.55792	−0.778960	+	0.627074i	$0.784253\pi$
$168$	−2.03657e9	−0.197246
$169$	−1.04548e10	−0.985887
$170$	−9.41939e8	−0.0864973
$171$	5.24984e9	0.469531
$172$	−3.13252e8	−0.0272908
$173$	−5.95860e9	−0.505751	−0.252875	−	0.967499i	$-0.581376\pi$
$173$	−5.95860e9	−0.505751	−0.252875	+	0.967499i	$0.581376\pi$
$174$	−5.98934e9	−0.495345
$175$	4.74907e9	0.382770
$176$	5.41526e9	0.425415
$177$	9.81506e8	0.0751646
$178$	2.26772e10	1.69316
$179$	4.50143e9	0.327727	0.163863	−	0.986483i	$-0.447604\pi$
$179$	4.50143e9	0.327727	0.163863	+	0.986483i	$0.447604\pi$
$180$	−1.55604e8	−0.0110483
$181$	1.42253e10	0.985163	0.492582	−	0.870266i	$-0.336053\pi$
$181$	1.42253e10	0.985163	0.492582	+	0.870266i	$0.336053\pi$
$182$	−7.59127e8	−0.0512853
$183$	1.41780e10	0.934515
$184$	−4.44728e8	−0.0286032
$185$	3.61003e9	0.226589
$186$	−7.62652e9	−0.467217
$187$	3.02374e9	0.180824
$188$	6.11713e9	0.357139
$189$	−1.32567e9	−0.0755715
$190$	4.41948e9	0.246025
$191$	−3.48150e10	−1.89285	−0.946425	−	0.322924i	$-0.895334\pi$
$191$	−3.48150e10	−1.89285	−0.946425	+	0.322924i	$0.895334\pi$
$192$	7.75588e9	0.411885
$193$	7.57616e9	0.393044	0.196522	−	0.980499i	$-0.437035\pi$
$193$	7.57616e9	0.393044	0.196522	+	0.980499i	$0.437035\pi$
$194$	1.12275e10	0.569081
$195$	2.20014e8	0.0108967
$196$	−3.64577e9	−0.176456
$197$	3.25173e10	1.53821	0.769105	−	0.639122i	$-0.220702\pi$
$197$	3.25173e10	1.53821	0.769105	+	0.639122i	$0.220702\pi$
$198$	2.89379e9	0.133805
$199$	−2.52469e10	−1.14122	−0.570611	−	0.821221i	$-0.693293\pi$
$199$	−2.52469e10	−1.14122	−0.570611	+	0.821221i	$0.693293\pi$
$200$	−1.91893e10	−0.848057
$201$	1.65765e10	0.716326
$202$	2.33642e10	0.987348
$203$	−7.41472e9	−0.306452
$204$	−1.47554e9	−0.0596507
$205$	−1.04504e9	−0.0413277
$206$	−1.24137e10	−0.480287
$207$	−2.89489e8	−0.0109589
$208$	3.73642e9	0.138411
$209$	−1.41871e10	−0.514321
$210$	−1.11599e9	−0.0395981
$211$	2.07497e10	0.720675	0.360338	−	0.932822i	$-0.382661\pi$
$211$	2.07497e10	0.720675	0.360338	+	0.932822i	$0.382661\pi$
$212$	−7.76821e9	−0.264125
$213$	3.24293e10	1.07952
$214$	4.58268e10	1.49368
$215$	6.51132e8	0.0207824
$216$	5.35658e9	0.167435
$217$	−9.44152e9	−0.289050
$218$	−4.00921e10	−1.20228
$219$	−1.75951e10	−0.516884
$220$	4.20502e8	0.0121022
$221$	2.08632e9	0.0588322
$222$	3.27615e10	0.905264
$223$	5.08398e10	1.37668	0.688338	−	0.725390i	$-0.258341\pi$
$223$	5.08398e10	1.37668	0.688338	+	0.725390i	$0.258341\pi$
$224$	−6.07934e9	−0.161339
$225$	−1.24910e10	−0.324920
$226$	5.77209e10	1.47179
$227$	−4.19962e10	−1.04977	−0.524884	−	0.851174i	$-0.675891\pi$
$227$	−4.19962e10	−1.04977	−0.524884	+	0.851174i	$0.675891\pi$
$228$	6.92308e9	0.169665
$229$	−5.74889e10	−1.38142	−0.690708	−	0.723134i	$-0.742701\pi$
$229$	−5.74889e10	−1.38142	−0.690708	+	0.723134i	$0.742701\pi$
$230$	−2.43700e8	−0.00574224
$231$	3.58247e9	0.0827805
$232$	2.99603e10	0.678969
$233$	8.28802e10	1.84225	0.921126	−	0.389264i	$-0.127270\pi$
$233$	8.28802e10	1.84225	0.921126	+	0.389264i	$0.127270\pi$
$234$	1.99666e9	0.0435343
$235$	−1.27152e10	−0.271968
$236$	1.29433e9	0.0271608
$237$	2.70344e10	0.556608
$238$	−1.05825e10	−0.213793
$239$	−3.92640e10	−0.778403	−0.389201	−	0.921153i	$-0.627249\pi$
$239$	−3.92640e10	−0.778403	−0.389201	+	0.921153i	$0.627249\pi$
$240$	5.49291e9	0.106869
$241$	4.09839e10	0.782595	0.391297	−	0.920264i	$-0.372026\pi$
$241$	4.09839e10	0.782595	0.391297	+	0.920264i	$0.372026\pi$
$242$	5.08363e10	0.952806
$243$	3.48678e9	0.0641500
$244$	1.86969e10	0.337688
$245$	7.57817e9	0.134375
$246$	−9.48388e9	−0.165112
$247$	−9.78878e9	−0.167337
$248$	3.81499e10	0.640414
$249$	−2.68601e10	−0.442804
$250$	−2.13029e10	−0.344912
$251$	−4.86170e10	−0.773137	−0.386569	−	0.922261i	$-0.626340\pi$
$251$	−4.86170e10	−0.773137	−0.386569	+	0.922261i	$0.626340\pi$
$252$	−1.74819e9	−0.0273078
$253$	7.82308e8	0.0120043
$254$	1.60105e10	0.241353
$255$	3.06709e9	0.0454251
$256$	4.12682e10	0.600531
$257$	−1.19445e11	−1.70793	−0.853965	−	0.520331i	$-0.825809\pi$
$257$	−1.19445e11	−1.70793	−0.853965	+	0.520331i	$0.825809\pi$
$258$	5.90910e9	0.0830296
$259$	4.05582e10	0.560054
$260$	2.90138e8	0.00393753
$261$	1.95022e10	0.260136
$262$	3.68794e10	0.483535
$263$	−1.23073e11	−1.58621	−0.793107	−	0.609083i	$-0.791538\pi$
$263$	−1.23073e11	−1.58621	−0.793107	+	0.609083i	$0.791538\pi$
$264$	−1.44755e10	−0.183407
$265$	1.61472e10	0.201136
$266$	4.96522e10	0.608095
$267$	−7.38402e10	−0.889186
$268$	2.18598e10	0.258845
$269$	−1.84342e10	−0.214654	−0.107327	−	0.994224i	$-0.534229\pi$
$269$	−1.84342e10	−0.214654	−0.107327	+	0.994224i	$0.534229\pi$
$270$	2.93528e9	0.0336134
$271$	1.45903e11	1.64325	0.821625	−	0.570028i	$-0.193068\pi$
$271$	1.45903e11	1.64325	0.821625	+	0.570028i	$0.193068\pi$
$272$	5.20873e10	0.576994
$273$	2.47183e9	0.0269331
$274$	1.21803e11	1.30551
$275$	3.37554e10	0.355915
$276$	−3.81755e8	−0.00395999
$277$	−1.10202e11	−1.12469	−0.562345	−	0.826903i	$-0.690101\pi$
$277$	−1.10202e11	−1.12469	−0.562345	+	0.826903i	$0.690101\pi$
$278$	−2.54288e10	−0.255344
$279$	2.48331e10	0.245364
$280$	5.58249e9	0.0542771
$281$	8.05599e10	0.770798	0.385399	−	0.922750i	$-0.374064\pi$
$281$	8.05599e10	0.770798	0.385399	+	0.922750i	$0.374064\pi$
$282$	−1.15392e11	−1.08656
$283$	−2.74018e8	−0.00253945	−0.00126973	−	0.999999i	$-0.500404\pi$
$283$	−2.74018e8	−0.00253945	−0.00126973	+	0.999999i	$0.500404\pi$
$284$	4.27653e10	0.390084
$285$	−1.43905e10	−0.129203
$286$	−5.39571e9	−0.0476872
$287$	−1.17409e10	−0.102149
$288$	1.59899e10	0.136955
$289$	−8.95037e10	−0.754746
$290$	1.64175e10	0.136307
$291$	−3.65583e10	−0.298860
$292$	−2.32030e10	−0.186776
$293$	−6.56715e10	−0.520562	−0.260281	−	0.965533i	$-0.583815\pi$
$293$	−6.56715e10	−0.520562	−0.260281	+	0.965533i	$0.583815\pi$
$294$	6.87728e10	0.536851
$295$	−2.69043e9	−0.0206834
$296$	−1.63882e11	−1.24085
$297$	−9.42260e9	−0.0702695
$298$	2.13574e11	1.56883
$299$	5.39776e8	0.00390565
$300$	−1.64722e10	−0.117410
$301$	7.31538e9	0.0513674
$302$	1.77198e10	0.122582
$303$	−7.60774e10	−0.518518
$304$	−2.44388e11	−1.64115
$305$	−3.88638e10	−0.257155
$306$	2.78342e10	0.181482
$307$	2.68465e10	0.172490	0.0862452	−	0.996274i	$-0.472513\pi$
$307$	2.68465e10	0.172490	0.0862452	+	0.996274i	$0.472513\pi$
$308$	4.72428e9	0.0299128
$309$	4.04210e10	0.252228
$310$	2.09052e10	0.128566
$311$	−2.14410e11	−1.29964	−0.649821	−	0.760088i	$-0.725156\pi$
$311$	−2.14410e11	−1.29964	−0.649821	+	0.760088i	$0.725156\pi$
$312$	−9.98780e9	−0.0596725
$313$	2.76816e11	1.63020	0.815102	−	0.579318i	$-0.196681\pi$
$313$	2.76816e11	1.63020	0.815102	+	0.579318i	$0.196681\pi$
$314$	2.97591e11	1.72757
$315$	3.63383e9	0.0207954
$316$	3.56508e10	0.201130
$317$	9.32046e10	0.518407	0.259203	−	0.965823i	$-0.416540\pi$
$317$	9.32046e10	0.518407	0.259203	+	0.965823i	$0.416540\pi$
$318$	1.46537e11	0.803575
$319$	−5.27022e10	−0.284951
$320$	−2.12598e10	−0.113340
$321$	−1.49219e11	−0.784424
$322$	−2.73794e9	−0.0141929
$323$	−1.36460e11	−0.697578
$324$	4.59810e9	0.0231807
$325$	2.32905e10	0.115799
$326$	1.33860e11	0.656407
$327$	1.30546e11	0.631391
$328$	4.74409e10	0.226319
$329$	−1.42853e11	−0.672216
$330$	−7.93223e9	−0.0368199
$331$	−2.31416e11	−1.05966	−0.529831	−	0.848103i	$-0.677745\pi$
$331$	−2.31416e11	−1.05966	−0.529831	+	0.848103i	$0.677745\pi$
$332$	−3.54211e10	−0.160007
$333$	−1.06676e11	−0.475410
$334$	3.89538e11	1.71274
$335$	−4.54383e10	−0.197115
$336$	6.17120e10	0.264145
$337$	−3.10705e11	−1.31224	−0.656121	−	0.754655i	$-0.727804\pi$
$337$	−3.10705e11	−1.31224	−0.656121	+	0.754655i	$0.727804\pi$
$338$	2.60075e11	1.08386
$339$	−1.87948e11	−0.772927
$340$	4.04464e9	0.0164144
$341$	−6.71083e10	−0.268770
$342$	−1.30595e11	−0.516190
$343$	1.85801e11	0.724812
$344$	−2.95589e10	−0.113809
$345$	7.93525e8	0.00301561
$346$	1.48226e11	0.556010
$347$	4.06988e11	1.50695	0.753475	−	0.657476i	$-0.228376\pi$
$347$	4.06988e11	1.50695	0.753475	+	0.657476i	$0.228376\pi$
$348$	2.57180e10	0.0940004
$349$	3.09331e11	1.11612	0.558058	−	0.829802i	$-0.311547\pi$
$349$	3.09331e11	1.11612	0.558058	+	0.829802i	$0.311547\pi$
$350$	−1.18138e11	−0.420808
$351$	−6.50140e9	−0.0228626
$352$	−4.32107e10	−0.150020
$353$	1.60790e11	0.551154	0.275577	−	0.961279i	$-0.411131\pi$
$353$	1.60790e11	0.551154	0.275577	+	0.961279i	$0.411131\pi$
$354$	−2.44160e10	−0.0826341
$355$	−8.88928e10	−0.297057
$356$	−9.73747e10	−0.321308
$357$	3.44583e10	0.112276
$358$	−1.11978e11	−0.360294
$359$	4.04099e10	0.128399	0.0641996	−	0.997937i	$-0.479551\pi$
$359$	4.04099e10	0.128399	0.0641996	+	0.997937i	$0.479551\pi$
$360$	−1.46831e10	−0.0460739
$361$	3.17567e11	0.984131
$362$	−3.53869e11	−1.08306
$363$	−1.65530e11	−0.500378
$364$	3.25965e9	0.00973230
$365$	4.82303e10	0.142234
$366$	−3.52693e11	−1.02738
$367$	4.75777e11	1.36901	0.684505	−	0.729009i	$-0.260019\pi$
$367$	4.75777e11	1.36901	0.684505	+	0.729009i	$0.260019\pi$
$368$	1.34761e10	0.0383045
$369$	3.08809e10	0.0867104
$370$	−8.98033e10	−0.249106
$371$	1.81411e11	0.497143
$372$	3.27479e10	0.0886626
$373$	−6.63497e11	−1.77480	−0.887400	−	0.461001i	$-0.847490\pi$
$373$	−6.63497e11	−1.77480	−0.887400	+	0.461001i	$0.847490\pi$
$374$	−7.52185e10	−0.198794
$375$	6.93654e10	0.181135
$376$	5.77221e11	1.48935
$377$	−3.63635e10	−0.0927106
$378$	3.29775e10	0.0830815
$379$	−1.62805e11	−0.405313	−0.202657	−	0.979250i	$-0.564957\pi$
$379$	−1.62805e11	−0.405313	−0.202657	+	0.979250i	$0.564957\pi$
$380$	−1.89770e10	−0.0466877
$381$	−5.21326e10	−0.126750
$382$	8.66058e11	2.08095
$383$	3.31529e11	0.787276	0.393638	−	0.919266i	$-0.371216\pi$
$383$	3.31529e11	0.787276	0.393638	+	0.919266i	$0.371216\pi$
$384$	−2.94007e11	−0.690029
$385$	−9.81998e9	−0.0227792
$386$	−1.88465e11	−0.432103
$387$	−1.92409e10	−0.0436040
$388$	−4.82102e10	−0.107993
$389$	−6.01100e11	−1.33099	−0.665494	−	0.746404i	$-0.731779\pi$
$389$	−6.01100e11	−1.33099	−0.665494	+	0.746404i	$0.731779\pi$
$390$	−5.47308e9	−0.0119796
$391$	7.52471e9	0.0162815
$392$	−3.44020e11	−0.735862
$393$	−1.20085e11	−0.253934
$394$	−8.08900e11	−1.69107
$395$	−7.41046e10	−0.153165
$396$	−1.24258e10	−0.0253919
$397$	−2.47379e11	−0.499811	−0.249905	−	0.968270i	$-0.580399\pi$
$397$	−2.47379e11	−0.499811	−0.249905	+	0.968270i	$0.580399\pi$
$398$	6.28043e11	1.25463
$399$	−1.61675e11	−0.319348
$400$	5.81475e11	1.13569
$401$	−5.01181e11	−0.967931	−0.483966	−	0.875087i	$-0.660804\pi$
$401$	−5.01181e11	−0.967931	−0.483966	+	0.875087i	$0.660804\pi$
$402$	−4.12358e11	−0.787511
$403$	−4.63034e10	−0.0874460
$404$	−1.00325e11	−0.187367
$405$	−9.55771e9	−0.0176525
$406$	1.84449e11	0.336906
$407$	2.88279e11	0.520761
$408$	−1.39234e11	−0.248757
$409$	3.05359e11	0.539580	0.269790	−	0.962919i	$-0.413046\pi$
$409$	3.05359e11	0.539580	0.269790	+	0.962919i	$0.413046\pi$
$410$	2.59965e10	0.0454347
$411$	−3.96609e11	−0.685606
$412$	5.33040e10	0.0911429
$413$	−3.02266e10	−0.0511227
$414$	7.20133e9	0.0120479
$415$	7.36270e10	0.121849
$416$	−2.98145e10	−0.0488098
$417$	8.28000e10	0.134097
$418$	3.52917e11	0.565431
$419$	8.08727e11	1.28186	0.640928	−	0.767601i	$-0.278550\pi$
$419$	8.08727e11	1.28186	0.640928	+	0.767601i	$0.278550\pi$
$420$	4.79202e9	0.00751444
$421$	−1.20078e12	−1.86292	−0.931459	−	0.363846i	$-0.881463\pi$
$421$	−1.20078e12	−1.86292	−0.931459	+	0.363846i	$0.881463\pi$
$422$	−5.16169e11	−0.792293
$423$	3.75733e11	0.570621
$424$	−7.33019e11	−1.10146
$425$	3.24680e11	0.482731
$426$	−8.06713e11	−1.18680
$427$	−4.36629e11	−0.635605
$428$	−1.96778e11	−0.283452
$429$	1.75692e10	0.0250435
$430$	−1.61976e10	−0.0228477
$431$	8.17289e11	1.14085	0.570424	−	0.821350i	$-0.306779\pi$
$431$	8.17289e11	1.14085	0.570424	+	0.821350i	$0.306779\pi$
$432$	−1.62315e11	−0.224224
$433$	4.47154e11	0.611310	0.305655	−	0.952142i	$-0.401125\pi$
$433$	4.47154e11	0.611310	0.305655	+	0.952142i	$0.401125\pi$
$434$	2.34867e11	0.317774
$435$	−5.34579e10	−0.0715831
$436$	1.72154e11	0.228154
$437$	−3.53052e10	−0.0463097
$438$	4.37696e11	0.568249
$439$	4.14846e11	0.533086	0.266543	−	0.963823i	$-0.414119\pi$
$439$	4.14846e11	0.533086	0.266543	+	0.963823i	$0.414119\pi$
$440$	3.96791e10	0.0504691
$441$	−2.23934e11	−0.281934
$442$	−5.18992e10	−0.0646786
$443$	−1.52484e12	−1.88108	−0.940540	−	0.339684i	$-0.889680\pi$
$443$	−1.52484e12	−1.88108	−0.940540	+	0.339684i	$0.889680\pi$
$444$	−1.40676e11	−0.171790
$445$	2.02405e11	0.244682
$446$	−1.26469e12	−1.51348
$447$	−6.95429e11	−0.823890
$448$	−2.38851e11	−0.280141
$449$	2.41329e10	0.0280221	0.0140111	−	0.999902i	$-0.495540\pi$
$449$	2.41329e10	0.0280221	0.0140111	+	0.999902i	$0.495540\pi$
$450$	3.10727e11	0.357209
$451$	−8.34518e10	−0.0949820
$452$	−2.47851e11	−0.279298
$453$	−5.76982e10	−0.0643754
$454$	1.04470e12	1.15409
$455$	−6.77559e9	−0.00741132
$456$	6.53272e11	0.707542
$457$	1.37101e12	1.47034	0.735170	−	0.677883i	$-0.237102\pi$
$457$	1.37101e12	1.47034	0.735170	+	0.677883i	$0.237102\pi$
$458$	1.43010e12	1.51869
$459$	−9.06323e10	−0.0953073
$460$	1.04644e9	0.00108969
$461$	8.56735e11	0.883471	0.441735	−	0.897145i	$-0.354363\pi$
$461$	8.56735e11	0.883471	0.441735	+	0.897145i	$0.354363\pi$
$462$	−8.91175e10	−0.0910069
$463$	−1.77854e12	−1.79866	−0.899328	−	0.437274i	$-0.855944\pi$
$463$	−1.77854e12	−1.79866	−0.899328	+	0.437274i	$0.855944\pi$
$464$	−9.07856e11	−0.909255
$465$	−6.80705e10	−0.0675182
$466$	−2.06173e12	−2.02533
$467$	−1.26353e12	−1.22931	−0.614654	−	0.788797i	$-0.710704\pi$
$467$	−1.26353e12	−1.22931	−0.614654	+	0.788797i	$0.710704\pi$
$468$	−8.57354e9	−0.00826141
$469$	−5.10492e11	−0.487205
$470$	3.16303e11	0.298995
$471$	−9.68999e11	−0.907255
$472$	1.22135e11	0.113267
$473$	5.19962e10	0.0477635
$474$	−6.72508e11	−0.611921
$475$	−1.52336e12	−1.37304
$476$	4.54410e10	0.0405710
$477$	−4.77147e11	−0.422007
$478$	9.76733e11	0.855757
$479$	−1.36613e12	−1.18572	−0.592862	−	0.805304i	$-0.702002\pi$
$479$	−1.36613e12	−1.18572	−0.592862	+	0.805304i	$0.702002\pi$
$480$	−4.38303e10	−0.0376867
$481$	1.98907e11	0.169433
$482$	−1.01952e12	−0.860365
$483$	8.91514e9	0.00745360
$484$	−2.18288e11	−0.180812
$485$	1.00211e11	0.0822388
$486$	−8.67373e10	−0.0705250
$487$	1.70385e12	1.37263	0.686313	−	0.727306i	$-0.259228\pi$
$487$	1.70385e12	1.37263	0.686313	+	0.727306i	$0.259228\pi$
$488$	1.76427e12	1.40823
$489$	−4.35869e11	−0.344720
$490$	−1.88515e11	−0.147728
$491$	1.97165e12	1.53096	0.765478	−	0.643462i	$-0.222503\pi$
$491$	1.97165e12	1.53096	0.765478	+	0.643462i	$0.222503\pi$
$492$	4.07233e10	0.0313329
$493$	−5.06922e11	−0.386483
$494$	2.43506e11	0.183966
$495$	2.58285e10	0.0193364
$496$	−1.15602e12	−0.857623
$497$	−9.98698e11	−0.734227
$498$	6.68174e11	0.486808
$499$	2.47891e12	1.78981	0.894907	−	0.446253i	$-0.147242\pi$
$499$	2.47891e12	1.78981	0.894907	+	0.446253i	$0.147242\pi$
$500$	9.14737e10	0.0654532
$501$	−1.26839e12	−0.899466
$502$	1.20940e12	0.849968
$503$	−1.22607e12	−0.854006	−0.427003	−	0.904250i	$-0.640431\pi$
$503$	−1.22607e12	−0.854006	−0.427003	+	0.904250i	$0.640431\pi$
$504$	−1.64962e11	−0.113880
$505$	2.08537e11	0.142683
$506$	−1.94607e10	−0.0131972
$507$	−8.46842e11	−0.569202
$508$	−6.87484e10	−0.0458011
$509$	−1.41506e12	−0.934427	−0.467213	−	0.884145i	$-0.654742\pi$
$509$	−1.41506e12	−0.934427	−0.467213	+	0.884145i	$0.654742\pi$
$510$	−7.62970e10	−0.0499392
$511$	5.41861e11	0.351555
$512$	8.31829e11	0.534957
$513$	4.25237e11	0.271084
$514$	2.97132e12	1.87766
$515$	−1.10799e11	−0.0694070
$516$	−2.53734e10	−0.0157563
$517$	−1.01537e12	−0.625054
$518$	−1.00893e12	−0.615710
$519$	−4.82647e11	−0.291995
$520$	2.73778e10	0.0164204
$521$	2.78794e11	0.165773	0.0828865	−	0.996559i	$-0.473586\pi$
$521$	2.78794e11	0.165773	0.0828865	+	0.996559i	$0.473586\pi$
$522$	−4.85137e11	−0.285987
$523$	2.29079e12	1.33884	0.669418	−	0.742886i	$-0.266544\pi$
$523$	2.29079e12	1.33884	0.669418	+	0.742886i	$0.266544\pi$
$524$	−1.58358e11	−0.0917593
$525$	3.84675e11	0.220992
$526$	3.06156e12	1.74384
$527$	−6.45489e11	−0.364536
$528$	4.38636e11	0.245613
$529$	−1.79921e12	−0.998919
$530$	−4.01677e11	−0.221124
$531$	7.95020e10	0.0433963
$532$	−2.13204e11	−0.115397
$533$	−5.75801e10	−0.0309029
$534$	1.83685e12	0.977549
$535$	4.09027e11	0.215854
$536$	2.06272e12	1.07944
$537$	3.64616e11	0.189213
$538$	4.58570e11	0.235986
$539$	6.05155e11	0.308828
$540$	−1.26040e10	−0.00637874
$541$	4.25469e11	0.213541	0.106770	−	0.994284i	$-0.465949\pi$
$541$	4.25469e11	0.213541	0.106770	+	0.994284i	$0.465949\pi$
$542$	−3.62950e12	−1.80655
$543$	1.15225e12	0.568784
$544$	−4.15627e11	−0.203474
$545$	−3.57843e11	−0.173743
$546$	−6.14893e10	−0.0296096
$547$	−1.78323e12	−0.851657	−0.425829	−	0.904804i	$-0.640017\pi$
$547$	−1.78323e12	−0.851657	−0.425829	+	0.904804i	$0.640017\pi$
$548$	−5.23017e11	−0.247744
$549$	1.14842e12	0.539542
$550$	−8.39700e11	−0.391284
$551$	2.37843e12	1.09928
$552$	−3.60230e10	−0.0165141
$553$	−8.32555e11	−0.378573
$554$	2.74140e12	1.23646
$555$	2.92413e11	0.130821
$556$	1.09190e11	0.0484560
$557$	−8.32903e11	−0.366645	−0.183323	−	0.983053i	$-0.558685\pi$
$557$	−8.32903e11	−0.366645	−0.183323	+	0.983053i	$0.558685\pi$
$558$	−6.17748e11	−0.269748
$559$	3.58763e10	0.0155401
$560$	−1.69160e11	−0.0726863
$561$	2.44923e11	0.104399
$562$	−2.00401e12	−0.847396
$563$	8.32713e10	0.0349307	0.0174654	−	0.999847i	$-0.494440\pi$
$563$	8.32713e10	0.0349307	0.0174654	+	0.999847i	$0.494440\pi$
$564$	4.95487e11	0.206194
$565$	5.15188e11	0.212690
$566$	6.81647e9	0.00279181
$567$	−1.07380e11	−0.0436312
$568$	4.03539e12	1.62674
$569$	−3.63936e12	−1.45553	−0.727763	−	0.685829i	$-0.759440\pi$
$569$	−3.63936e12	−1.45553	−0.727763	+	0.685829i	$0.759440\pi$
$570$	3.57978e11	0.142043
$571$	−1.64875e12	−0.649073	−0.324536	−	0.945873i	$-0.605208\pi$
$571$	−1.64875e12	−0.649073	−0.324536	+	0.945873i	$0.605208\pi$
$572$	2.31689e10	0.00904949
$573$	−2.82001e12	−1.09284
$574$	2.92067e11	0.112300
$575$	8.40019e10	0.0320468
$576$	6.28226e11	0.237802
$577$	−3.55485e11	−0.133515	−0.0667574	−	0.997769i	$-0.521265\pi$
$577$	−3.55485e11	−0.133515	−0.0667574	+	0.997769i	$0.521265\pi$
$578$	2.22650e12	0.829749
$579$	6.13669e11	0.226924
$580$	−7.04961e10	−0.0258666
$581$	8.27189e11	0.301170
$582$	9.09424e11	0.328559
$583$	1.28943e12	0.462264
$584$	−2.18947e12	−0.778899
$585$	1.78212e10	0.00629121
$586$	1.63365e12	0.572293
$587$	2.57122e12	0.893856	0.446928	−	0.894570i	$-0.352518\pi$
$587$	2.57122e12	0.893856	0.446928	+	0.894570i	$0.352518\pi$
$588$	−2.95307e11	−0.101877
$589$	3.02856e12	1.03686
$590$	6.69272e10	0.0227389
$591$	2.63390e12	0.888086
$592$	4.96594e12	1.66170
$593$	2.41018e12	0.800392	0.400196	−	0.916430i	$-0.368942\pi$
$593$	2.41018e12	0.800392	0.400196	+	0.916430i	$0.368942\pi$
$594$	2.34397e11	0.0772525
$595$	−9.44546e10	−0.0308956
$596$	−9.17078e11	−0.297713
$597$	−2.04500e12	−0.658884
$598$	−1.34275e10	−0.00429378
$599$	−4.24751e12	−1.34807	−0.674036	−	0.738698i	$-0.735441\pi$
$599$	−4.24751e12	−1.34807	−0.674036	+	0.738698i	$0.735441\pi$
$600$	−1.55434e12	−0.489626
$601$	2.12128e12	0.663227	0.331613	−	0.943415i	$-0.392407\pi$
$601$	2.12128e12	0.663227	0.331613	+	0.943415i	$0.392407\pi$
$602$	−1.81978e11	−0.0564721
$603$	1.34270e12	0.413571
$604$	−7.60878e10	−0.0232621
$605$	4.53739e11	0.137691
$606$	1.89250e12	0.570046
$607$	−7.37312e11	−0.220446	−0.110223	−	0.993907i	$-0.535156\pi$
$607$	−7.37312e11	−0.220446	−0.110223	+	0.993907i	$0.535156\pi$
$608$	1.95008e12	0.578743
$609$	−6.00592e11	−0.176930
$610$	9.66776e11	0.282710
$611$	−7.00586e11	−0.203365
$612$	−1.19519e11	−0.0344393
$613$	−1.75322e12	−0.501494	−0.250747	−	0.968053i	$-0.580676\pi$
$613$	−1.75322e12	−0.501494	−0.250747	+	0.968053i	$0.580676\pi$
$614$	−6.67834e11	−0.189632
$615$	−8.46484e10	−0.0238606
$616$	4.45790e11	0.124743
$617$	−3.50243e11	−0.0972940	−0.0486470	−	0.998816i	$-0.515491\pi$
$617$	−3.50243e11	−0.0972940	−0.0486470	+	0.998816i	$0.515491\pi$
$618$	−1.00551e12	−0.277294
$619$	3.58750e11	0.0982163	0.0491082	−	0.998793i	$-0.484362\pi$
$619$	3.58750e11	0.0982163	0.0491082	+	0.998793i	$0.484362\pi$
$620$	−8.97661e10	−0.0243977
$621$	−2.34486e10	−0.00632710
$622$	5.33367e12	1.42879
$623$	2.27399e12	0.604774
$624$	3.02650e11	0.0799116
$625$	3.52827e12	0.924916
$626$	−6.88608e12	−1.79221
$627$	−1.14915e12	−0.296943
$628$	−1.27784e12	−0.327837
$629$	2.77284e12	0.706314
$630$	−9.03953e10	−0.0228620
$631$	−1.63671e12	−0.410998	−0.205499	−	0.978657i	$-0.565882\pi$
$631$	−1.63671e12	−0.410998	−0.205499	+	0.978657i	$0.565882\pi$
$632$	3.36406e12	0.838760
$633$	1.68072e12	0.416082
$634$	−2.31856e12	−0.569924
$635$	1.42902e11	0.0348784
$636$	−6.29225e11	−0.152493
$637$	4.17545e11	0.100479
$638$	1.31102e12	0.313269
$639$	2.62678e12	0.623260
$640$	8.05910e11	0.189879
$641$	1.03690e11	0.0242592	0.0121296	−	0.999926i	$-0.496139\pi$
$641$	1.03690e11	0.0242592	0.0121296	+	0.999926i	$0.496139\pi$
$642$	3.71197e12	0.862376
$643$	5.90450e12	1.36218	0.681089	−	0.732201i	$-0.261507\pi$
$643$	5.90450e12	1.36218	0.681089	+	0.732201i	$0.261507\pi$
$644$	1.17566e10	0.00269336
$645$	5.27417e10	0.0119987
$646$	3.39457e12	0.766900
$647$	−1.37816e12	−0.309194	−0.154597	−	0.987978i	$-0.549408\pi$
$647$	−1.37816e12	−0.309194	−0.154597	+	0.987978i	$0.549408\pi$
$648$	4.33883e11	0.0966686
$649$	−2.14844e11	−0.0475360
$650$	−5.79376e11	−0.127306
$651$	−7.64763e11	−0.166883
$652$	−5.74790e11	−0.124565
$653$	3.68278e12	0.792624	0.396312	−	0.918116i	$-0.370290\pi$
$653$	3.68278e12	0.792624	0.396312	+	0.918116i	$0.370290\pi$
$654$	−3.24746e12	−0.694136
$655$	3.29167e11	0.0698764
$656$	−1.43755e12	−0.303079
$657$	−1.42520e12	−0.298423
$658$	3.55362e12	0.739018
$659$	2.25561e11	0.0465887	0.0232943	−	0.999729i	$-0.492585\pi$
$659$	2.25561e11	0.0465887	0.0232943	+	0.999729i	$0.492585\pi$
$660$	3.40606e10	0.00698723
$661$	4.85476e12	0.989148	0.494574	−	0.869135i	$-0.335324\pi$
$661$	4.85476e12	0.989148	0.494574	+	0.869135i	$0.335324\pi$
$662$	5.75671e12	1.16497
$663$	1.68992e11	0.0339668
$664$	−3.34238e12	−0.667267
$665$	4.43171e11	0.0878768
$666$	2.65368e12	0.522654
$667$	−1.31152e11	−0.0256572
$668$	−1.67266e12	−0.325022
$669$	4.11802e12	0.794825
$670$	1.13032e12	0.216704
$671$	−3.10347e12	−0.591011
$672$	−4.92427e11	−0.0931494
$673$	−8.95636e12	−1.68292	−0.841460	−	0.540319i	$-0.818304\pi$
$673$	−8.95636e12	−1.68292	−0.841460	+	0.540319i	$0.818304\pi$
$674$	7.72911e12	1.44265
$675$	−1.01177e12	−0.187593
$676$	−1.11675e12	−0.205682
$677$	−4.88016e12	−0.892863	−0.446432	−	0.894818i	$-0.647305\pi$
$677$	−4.88016e12	−0.892863	−0.446432	+	0.894818i	$0.647305\pi$
$678$	4.67539e12	0.849737
$679$	1.12585e12	0.203268
$680$	3.81658e11	0.0684517
$681$	−3.40169e12	−0.606084
$682$	1.66939e12	0.295480
$683$	4.85322e12	0.853369	0.426685	−	0.904400i	$-0.359681\pi$
$683$	4.85322e12	0.853369	0.426685	+	0.904400i	$0.359681\pi$
$684$	5.60770e11	0.0979562
$685$	1.08716e12	0.188662
$686$	−4.62200e12	−0.796840
$687$	−4.65660e12	−0.797561
$688$	8.95693e11	0.152409
$689$	8.89682e11	0.150400
$690$	−1.97397e10	−0.00331528
$691$	−2.42661e12	−0.404901	−0.202450	−	0.979293i	$-0.564890\pi$
$691$	−2.42661e12	−0.404901	−0.202450	+	0.979293i	$0.564890\pi$
$692$	−6.36476e11	−0.105513
$693$	2.90180e11	0.0477934
$694$	−1.01242e13	−1.65670
$695$	−2.26965e11	−0.0369001
$696$	2.42678e12	0.392003
$697$	−8.02690e11	−0.128825
$698$	−7.69493e12	−1.22703
$699$	6.71330e12	1.06363
$700$	5.07279e11	0.0798557
$701$	−2.58871e12	−0.404904	−0.202452	−	0.979292i	$-0.564891\pi$
$701$	−2.58871e12	−0.404904	−0.202452	+	0.979292i	$0.564891\pi$
$702$	1.61729e11	0.0251345
$703$	−1.30099e13	−2.00898
$704$	−1.69770e12	−0.260486
$705$	−1.02993e12	−0.157021
$706$	−3.99982e12	−0.605926
$707$	2.34289e12	0.352667
$708$	1.04841e11	0.0156813
$709$	−7.50290e12	−1.11512	−0.557559	−	0.830137i	$-0.688262\pi$
$709$	−7.50290e12	−1.11512	−0.557559	+	0.830137i	$0.688262\pi$
$710$	2.21130e12	0.326577
$711$	2.18979e12	0.321358
$712$	−9.18842e12	−1.33993
$713$	−1.67002e11	−0.0242002
$714$	−8.57186e11	−0.123434
$715$	−4.81595e10	−0.00689135
$716$	4.80827e11	0.0683722
$717$	−3.18039e12	−0.449411
$718$	−1.00524e12	−0.141159
$719$	−2.42649e12	−0.338609	−0.169304	−	0.985564i	$-0.554152\pi$
$719$	−2.42649e12	−0.338609	−0.169304	+	0.985564i	$0.554152\pi$
$720$	4.44925e11	0.0617008
$721$	−1.24481e12	−0.171552
$722$	−7.89980e12	−1.08193
$723$	3.31970e12	0.451831
$724$	1.51950e12	0.205531
$725$	−5.65901e12	−0.760711
$726$	4.11774e12	0.550103
$727$	1.31300e13	1.74325	0.871627	−	0.490169i	$-0.163065\pi$
$727$	1.31300e13	1.74325	0.871627	+	0.490169i	$0.163065\pi$
$728$	3.07586e11	0.0405859
$729$	2.82430e11	0.0370370
$730$	−1.19978e12	−0.156368
$731$	5.00131e11	0.0647822
$732$	1.51445e12	0.194964
$733$	−3.38940e11	−0.0433666	−0.0216833	−	0.999765i	$-0.506903\pi$
$733$	−3.38940e11	−0.0433666	−0.0216833	+	0.999765i	$0.506903\pi$
$734$	−1.18354e13	−1.50505
$735$	6.13832e11	0.0775812
$736$	−1.07532e11	−0.0135079
$737$	−3.62847e12	−0.453023
$738$	−7.68194e11	−0.0953273
$739$	−7.80178e12	−0.962262	−0.481131	−	0.876649i	$-0.659774\pi$
$739$	−7.80178e12	−0.962262	−0.481131	+	0.876649i	$0.659774\pi$
$740$	3.85611e11	0.0472723
$741$	−7.92891e11	−0.0966121
$742$	−4.51279e12	−0.546547
$743$	−5.12727e11	−0.0617215	−0.0308607	−	0.999524i	$-0.509825\pi$
$743$	−5.12727e11	−0.0617215	−0.0308607	+	0.999524i	$0.509825\pi$
$744$	3.09014e12	0.369743
$745$	1.90626e12	0.226714
$746$	1.65052e13	1.95117
$747$	−2.17567e12	−0.255653
$748$	3.22985e11	0.0377246
$749$	4.59536e12	0.533521
$750$	−1.72554e12	−0.199135
$751$	−9.33550e12	−1.07092	−0.535461	−	0.844560i	$-0.679862\pi$
$751$	−9.33550e12	−1.07092	−0.535461	+	0.844560i	$0.679862\pi$
$752$	−1.74909e13	−1.99449
$753$	−3.93798e12	−0.446371
$754$	9.04578e11	0.101924
$755$	1.58158e11	0.0177145
$756$	−1.41604e11	−0.0157662
$757$	−8.67301e12	−0.959928	−0.479964	−	0.877288i	$-0.659350\pi$
$757$	−8.67301e12	−0.959928	−0.479964	+	0.877288i	$0.659350\pi$
$758$	4.04993e12	0.445591
$759$	6.33669e10	0.00693066
$760$	−1.79070e12	−0.194698
$761$	2.14892e12	0.232268	0.116134	−	0.993234i	$-0.462950\pi$
$761$	2.14892e12	0.232268	0.116134	+	0.993234i	$0.462950\pi$
$762$	1.29685e12	0.139345
$763$	−4.02031e12	−0.429437
$764$	−3.71881e12	−0.394897
$765$	2.48434e11	0.0262262
$766$	−8.24712e12	−0.865511
$767$	−1.48238e11	−0.0154661
$768$	3.34272e12	0.346717
$769$	−1.38294e13	−1.42605	−0.713023	−	0.701140i	$-0.752675\pi$
$769$	−1.38294e13	−1.42605	−0.713023	+	0.701140i	$0.752675\pi$
$770$	2.44282e11	0.0250428
$771$	−9.67507e12	−0.986074
$772$	8.09259e11	0.0819992
$773$	−1.73146e13	−1.74424	−0.872118	−	0.489295i	$-0.837254\pi$
$773$	−1.73146e13	−1.74424	−0.872118	+	0.489295i	$0.837254\pi$
$774$	4.78637e11	0.0479372
$775$	−7.20590e12	−0.717514
$776$	−4.54918e12	−0.450356
$777$	3.28522e12	0.323347
$778$	1.49530e13	1.46325
$779$	3.76614e12	0.366419
$780$	2.35011e10	0.00227333
$781$	−7.09854e12	−0.682714
$782$	−1.87185e11	−0.0178995
$783$	1.57968e12	0.150190
$784$	1.04245e13	0.985444
$785$	2.65615e12	0.249654
$786$	2.98723e12	0.279169
$787$	−1.42737e13	−1.32633	−0.663165	−	0.748474i	$-0.730787\pi$
$787$	−1.42737e13	−1.32633	−0.663165	+	0.748474i	$0.730787\pi$
$788$	3.47338e12	0.320911
$789$	−9.96891e12	−0.915801
$790$	1.84343e12	0.168385
$791$	5.78807e12	0.525702
$792$	−1.17252e12	−0.105890
$793$	−2.14133e12	−0.192289
$794$	6.15380e12	0.549479
$795$	1.30792e12	0.116126
$796$	−2.69679e12	−0.238088
$797$	3.64156e12	0.319687	0.159843	−	0.987142i	$-0.448901\pi$
$797$	3.64156e12	0.319687	0.159843	+	0.987142i	$0.448901\pi$
$798$	4.02183e12	0.351084
$799$	−9.76646e12	−0.847768
$800$	−4.63984e12	−0.400496
$801$	−5.98106e12	−0.513372
$802$	1.24674e13	1.06412
$803$	3.85143e12	0.326890
$804$	1.77064e12	0.149444
$805$	−2.44375e10	−0.00205105
$806$	1.15184e12	0.0961360
$807$	−1.49317e12	−0.123931
$808$	−9.46680e12	−0.781362
$809$	1.26684e13	1.03981	0.519903	−	0.854225i	$-0.325968\pi$
$809$	1.26684e13	1.03981	0.519903	+	0.854225i	$0.325968\pi$
$810$	2.37758e11	0.0194067
$811$	2.26177e13	1.83592	0.917961	−	0.396670i	$-0.129834\pi$
$811$	2.26177e13	1.83592	0.917961	+	0.396670i	$0.129834\pi$
$812$	−7.92014e11	−0.0639338
$813$	1.18182e13	0.948731
$814$	−7.17124e12	−0.572512
$815$	1.19477e12	0.0948584
$816$	4.21907e12	0.333128
$817$	−2.34656e12	−0.184261
$818$	−7.59611e12	−0.593200
$819$	2.00218e11	0.0155498
$820$	−1.11628e11	−0.00862203
$821$	−1.76896e12	−0.135886	−0.0679428	−	0.997689i	$-0.521644\pi$
$821$	−1.76896e12	−0.135886	−0.0679428	+	0.997689i	$0.521644\pi$
$822$	9.86606e12	0.753739
$823$	−2.02207e13	−1.53638	−0.768189	−	0.640224i	$-0.778842\pi$
$823$	−2.02207e13	−1.53638	−0.768189	+	0.640224i	$0.778842\pi$
$824$	5.02985e12	0.380086
$825$	2.73419e12	0.205488
$826$	7.51918e11	0.0562031
$827$	−1.25520e13	−0.933120	−0.466560	−	0.884489i	$-0.654507\pi$
$827$	−1.25520e13	−0.933120	−0.466560	+	0.884489i	$0.654507\pi$
$828$	−3.09222e10	−0.00228630
$829$	4.15017e12	0.305190	0.152595	−	0.988289i	$-0.451237\pi$
$829$	4.15017e12	0.305190	0.152595	+	0.988289i	$0.451237\pi$
$830$	−1.83155e12	−0.133957
$831$	−8.92640e12	−0.649340
$832$	−1.17138e12	−0.0847507
$833$	5.82075e12	0.418867
$834$	−2.05974e12	−0.147423
$835$	3.47683e12	0.247511
$836$	−1.51541e12	−0.107301
$837$	2.01148e12	0.141661
$838$	−2.01179e13	−1.40924
$839$	1.24366e13	0.866506	0.433253	−	0.901272i	$-0.357366\pi$
$839$	1.24366e13	0.866506	0.433253	+	0.901272i	$0.357366\pi$
$840$	4.52181e11	0.0313369
$841$	−5.67174e12	−0.390962
$842$	2.98706e13	2.04805
$843$	6.52535e12	0.445021
$844$	2.21640e12	0.150352
$845$	2.32130e12	0.156630
$846$	−9.34674e12	−0.627326
$847$	5.09770e12	0.340329
$848$	2.22119e13	1.47504
$849$	−2.21954e10	−0.00146615
$850$	−8.07675e12	−0.530703
$851$	7.17397e11	0.0468896
$852$	3.46399e12	0.225215
$853$	−1.12775e13	−0.729358	−0.364679	−	0.931133i	$-0.618821\pi$
$853$	−1.12775e13	−0.729358	−0.364679	+	0.931133i	$0.618821\pi$
$854$	1.08616e13	0.698768
$855$	−1.16563e12	−0.0745955
$856$	−1.85683e13	−1.18206
$857$	6.20340e12	0.392840	0.196420	−	0.980520i	$-0.437068\pi$
$857$	6.20340e12	0.392840	0.196420	+	0.980520i	$0.437068\pi$
$858$	−4.37053e11	−0.0275322
$859$	−2.33530e12	−0.146343	−0.0731716	−	0.997319i	$-0.523312\pi$
$859$	−2.33530e12	−0.146343	−0.0731716	+	0.997319i	$0.523312\pi$
$860$	6.95517e10	0.00433575
$861$	−9.51013e11	−0.0589756
$862$	−2.03309e13	−1.25422
$863$	−8.44146e12	−0.518047	−0.259023	−	0.965871i	$-0.583401\pi$
$863$	−8.44146e12	−0.518047	−0.259023	+	0.965871i	$0.583401\pi$
$864$	1.29518e12	0.0790712
$865$	1.32299e12	0.0803499
$866$	−1.11234e13	−0.672059
$867$	−7.24980e12	−0.435753
$868$	−1.00851e12	−0.0603033
$869$	−5.91762e12	−0.352013
$870$	1.32982e12	0.0786966
$871$	−2.50357e12	−0.147394
$872$	1.62447e13	0.951452
$873$	−2.96122e12	−0.172547
$874$	8.78252e11	0.0509117
$875$	−2.13619e12	−0.123198
$876$	−1.87944e12	−0.107835
$877$	1.55888e13	0.889846	0.444923	−	0.895569i	$-0.353231\pi$
$877$	1.55888e13	0.889846	0.444923	+	0.895569i	$0.353231\pi$
$878$	−1.03197e13	−0.586061
$879$	−5.31939e12	−0.300547
$880$	−1.20236e12	−0.0675867
$881$	5.38270e11	0.0301029	0.0150515	−	0.999887i	$-0.495209\pi$
$881$	5.38270e11	0.0301029	0.0150515	+	0.999887i	$0.495209\pi$
$882$	5.57060e12	0.309951
$883$	5.19066e12	0.287342	0.143671	−	0.989625i	$-0.454109\pi$
$883$	5.19066e12	0.287342	0.143671	+	0.989625i	$0.454109\pi$
$884$	2.22853e11	0.0122739
$885$	−2.17925e11	−0.0119416
$886$	3.79319e13	2.06801
$887$	1.69013e13	0.916776	0.458388	−	0.888752i	$-0.348427\pi$
$887$	1.69013e13	0.916776	0.458388	+	0.888752i	$0.348427\pi$
$888$	−1.32744e13	−0.716402
$889$	1.60548e12	0.0862080
$890$	−5.03504e12	−0.268997
$891$	−7.63231e11	−0.0405701
$892$	5.43053e12	0.287210
$893$	4.58232e13	2.41132
$894$	1.72995e13	0.905764
$895$	−9.99457e11	−0.0520667
$896$	9.05429e12	0.469319
$897$	4.37219e10	0.00225493
$898$	−6.00331e11	−0.0308068
$899$	1.12505e13	0.574454
$900$	−1.33425e12	−0.0677867
$901$	1.24025e13	0.626973
$902$	2.07595e12	0.104421
$903$	5.92546e11	0.0296570
$904$	−2.33876e13	−1.16473
$905$	−3.15846e12	−0.156515
$906$	1.43530e12	0.0707727
$907$	3.37968e12	0.165822	0.0829112	−	0.996557i	$-0.473578\pi$
$907$	3.37968e12	0.165822	0.0829112	+	0.996557i	$0.473578\pi$
$908$	−4.48588e12	−0.219009
$909$	−6.16227e12	−0.299366
$910$	1.68550e11	0.00814783
$911$	3.39086e13	1.63109	0.815544	−	0.578696i	$-0.196438\pi$
$911$	3.39086e13	1.63109	0.815544	+	0.578696i	$0.196438\pi$
$912$	−1.97954e13	−0.947520
$913$	5.87948e12	0.280040
$914$	−3.41053e13	−1.61645
$915$	−3.14796e12	−0.148469
$916$	−6.14076e12	−0.288199
$917$	3.69815e12	0.172712
$918$	2.25457e12	0.104778
$919$	1.99191e13	0.921191	0.460596	−	0.887610i	$-0.347636\pi$
$919$	1.99191e13	0.921191	0.460596	+	0.887610i	$0.347636\pi$
$920$	9.87434e10	0.00454426
$921$	2.17457e12	0.0995874
$922$	−2.13121e13	−0.971266
$923$	−4.89785e12	−0.222125
$924$	3.82666e11	0.0172702
$925$	3.09546e13	1.39023
$926$	4.42429e13	1.97740
$927$	3.27410e12	0.145624
$928$	7.24417e12	0.320644
$929$	−9.51657e12	−0.419189	−0.209594	−	0.977788i	$-0.567214\pi$
$929$	−9.51657e12	−0.419189	−0.209594	+	0.977788i	$0.567214\pi$
$930$	1.69332e12	0.0742278
$931$	−2.73103e13	−1.19139
$932$	8.85297e12	0.384342
$933$	−1.73672e13	−0.750348
$934$	3.14317e13	1.35147
$935$	−6.71363e11	−0.0287280
$936$	−8.09012e11	−0.0344519
$937$	−1.61966e13	−0.686431	−0.343216	−	0.939257i	$-0.611516\pi$
$937$	−1.61966e13	−0.686431	−0.343216	+	0.939257i	$0.611516\pi$
$938$	1.26990e13	0.535621
$939$	2.24221e13	0.941198
$940$	−1.35819e12	−0.0567395
$941$	1.72664e12	0.0717874	0.0358937	−	0.999356i	$-0.488572\pi$
$941$	1.72664e12	0.0717874	0.0358937	+	0.999356i	$0.488572\pi$
$942$	2.41048e13	0.997413
$943$	−2.07674e11	−0.00855222
$944$	−3.70094e12	−0.151683
$945$	2.94341e11	0.0120062
$946$	−1.29346e12	−0.0525100
$947$	1.75876e13	0.710610	0.355305	−	0.934750i	$-0.384377\pi$
$947$	1.75876e13	0.710610	0.355305	+	0.934750i	$0.384377\pi$
$948$	2.88772e12	0.116123
$949$	2.65741e12	0.106356
$950$	3.78953e13	1.50948
$951$	7.54958e12	0.299302
$952$	4.28787e12	0.169190
$953$	3.21974e13	1.26445	0.632226	−	0.774784i	$-0.282141\pi$
$953$	3.21974e13	1.26445	0.632226	+	0.774784i	$0.282141\pi$
$954$	1.18695e13	0.463944
$955$	7.73001e12	0.300722
$956$	−4.19405e12	−0.162395
$957$	−4.26888e12	−0.164517
$958$	3.39840e13	1.30355
$959$	1.22140e13	0.466311
$960$	−1.72205e12	−0.0654371
$961$	−1.21138e13	−0.458167
$962$	−4.94801e12	−0.186270
$963$	−1.20867e13	−0.452887
$964$	4.37776e12	0.163270
$965$	−1.68214e12	−0.0624439
$966$	−2.21773e11	−0.00819430
$967$	−4.18164e13	−1.53790	−0.768950	−	0.639309i	$-0.779220\pi$
$967$	−4.18164e13	−1.53790	−0.768950	+	0.639309i	$0.779220\pi$
$968$	−2.05980e13	−0.754026
$969$	−1.10532e13	−0.402747
$970$	−2.49284e12	−0.0904112
$971$	−3.40994e13	−1.23101	−0.615503	−	0.788135i	$-0.711047\pi$
$971$	−3.40994e13	−1.23101	−0.615503	+	0.788135i	$0.711047\pi$
$972$	3.72446e11	0.0133834
$973$	−2.54992e12	−0.0912051
$974$	−4.23851e13	−1.50903
$975$	1.88653e12	0.0668565
$976$	−5.34607e13	−1.88586
$977$	4.01527e13	1.40990	0.704952	−	0.709255i	$-0.250969\pi$
$977$	4.01527e13	1.40990	0.704952	+	0.709255i	$0.250969\pi$
$978$	1.08427e13	0.378977
$979$	1.61631e13	0.562344
$980$	8.09473e11	0.0280340
$981$	1.05742e13	0.364534
$982$	−4.90468e13	−1.68309
$983$	1.78216e13	0.608775	0.304387	−	0.952548i	$-0.401548\pi$
$983$	1.78216e13	0.608775	0.304387	+	0.952548i	$0.401548\pi$
$984$	3.84271e12	0.130665
$985$	−7.21984e12	−0.244379
$986$	1.26102e13	0.424890
$987$	−1.15711e13	−0.388104
$988$	−1.04560e12	−0.0349108
$989$	1.29395e11	0.00430065
$990$	−6.42511e11	−0.0212580
$991$	−8.05274e12	−0.265223	−0.132612	−	0.991168i	$-0.542336\pi$
$991$	−8.05274e12	−0.265223	−0.132612	+	0.991168i	$0.542336\pi$
$992$	9.22435e12	0.302436
$993$	−1.87447e13	−0.611796
$994$	2.48436e13	0.807191
$995$	5.60560e12	0.181309
$996$	−2.86911e12	−0.0923803
$997$	7.38050e12	0.236569	0.118285	−	0.992980i	$-0.462261\pi$
$997$	7.38050e12	0.236569	0.118285	+	0.992980i	$0.462261\pi$
$998$	−6.16653e13	−1.96768
$999$	−8.64077e12	−0.274478

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.7	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.7	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-24.8760 q^{2} +81.0000 q^{3} +106.816 q^{4} -222.031 q^{5} -2014.96 q^{6} -2494.49 q^{7} +10079.4 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-24.8760 q^{2} +81.0000 q^{3} +106.816 q^{4} -222.031 q^{5} -2014.96 q^{6} -2494.49 q^{7} +10079.4 q^{8} +6561.00 q^{9} +5523.25 q^{10} -17730.3 q^{11} +8652.13 q^{12} -12233.5 q^{13} +62052.9 q^{14} -17984.5 q^{15} -305424. q^{16} -170541. q^{17} -163212. q^{18} +800159. q^{19} -23716.6 q^{20} -202053. q^{21} +441059. q^{22} -44122.7 q^{23} +816428. q^{24} -1.90383e6 q^{25} +304322. q^{26} +531441. q^{27} -266452. q^{28} +2.97244e6 q^{29} +447383. q^{30} +3.78495e6 q^{31} +2.43711e6 q^{32} -1.43615e6 q^{33} +4.24237e6 q^{34} +553854. q^{35} +700823. q^{36} -1.62591e7 q^{37} -1.99048e7 q^{38} -990917. q^{39} -2.23793e6 q^{40} +4.70674e6 q^{41} +5.02629e6 q^{42} -2.93262e6 q^{43} -1.89389e6 q^{44} -1.45675e6 q^{45} +1.09760e6 q^{46} +5.72676e7 q^{47} -2.47394e7 q^{48} -3.41311e7 q^{49} +4.73596e7 q^{50} -1.38138e7 q^{51} -1.30674e6 q^{52} -7.27248e7 q^{53} -1.32201e7 q^{54} +3.93667e6 q^{55} -2.51428e7 q^{56} +6.48129e7 q^{57} -7.39425e7 q^{58} +1.21174e7 q^{59} -1.92104e6 q^{60} +1.75038e8 q^{61} -9.41546e7 q^{62} -1.63663e7 q^{63} +9.57516e7 q^{64} +2.71623e6 q^{65} +3.57258e7 q^{66} +2.04648e8 q^{67} -1.82166e7 q^{68} -3.57394e6 q^{69} -1.37777e7 q^{70} +4.00362e8 q^{71} +6.61306e7 q^{72} -2.17223e8 q^{73} +4.04463e8 q^{74} -1.54210e8 q^{75} +8.54702e7 q^{76} +4.42280e7 q^{77} +2.46501e7 q^{78} +3.33758e8 q^{79} +6.78137e7 q^{80} +4.30467e7 q^{81} -1.17085e8 q^{82} -3.31607e8 q^{83} -2.15826e7 q^{84} +3.78653e7 q^{85} +7.29519e7 q^{86} +2.40768e8 q^{87} -1.78710e8 q^{88} -9.11608e8 q^{89} +3.62380e7 q^{90} +3.05164e7 q^{91} -4.71303e6 q^{92} +3.06581e8 q^{93} -1.42459e9 q^{94} -1.77660e8 q^{95} +1.97406e8 q^{96} -4.51337e8 q^{97} +8.49047e8 q^{98} -1.16328e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \)	\( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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