LMFDB - Embedded newform 177.12.a.b.1.13

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-17.2441 q^{2} +243.000 q^{3} -1750.64 q^{4} +7994.91 q^{5} -4190.32 q^{6} +1325.62 q^{7} +65504.2 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-17.2441 q^{2} +243.000 q^{3} -1750.64 q^{4} +7994.91 q^{5} -4190.32 q^{6} +1325.62 q^{7} +65504.2 q^{8} +59049.0 q^{9} -137865. q^{10} +134920. q^{11} -425406. q^{12} -29851.6 q^{13} -22859.1 q^{14} +1.94276e6 q^{15} +2.45575e6 q^{16} -3.25895e6 q^{17} -1.01825e6 q^{18} -1.09243e7 q^{19} -1.39962e7 q^{20} +322125. q^{21} -2.32657e6 q^{22} +185019. q^{23} +1.59175e7 q^{24} +1.50905e7 q^{25} +514764. q^{26} +1.43489e7 q^{27} -2.32068e6 q^{28} +1.68886e7 q^{29} -3.35012e7 q^{30} -5.53827e7 q^{31} -1.76500e8 q^{32} +3.27855e7 q^{33} +5.61977e7 q^{34} +1.05982e7 q^{35} -1.03374e8 q^{36} -7.21695e8 q^{37} +1.88379e8 q^{38} -7.25393e6 q^{39} +5.23700e8 q^{40} -8.63631e8 q^{41} -5.55476e6 q^{42} +1.00149e9 q^{43} -2.36196e8 q^{44} +4.72092e8 q^{45} -3.19049e6 q^{46} +3.01812e9 q^{47} +5.96748e8 q^{48} -1.97557e9 q^{49} -2.60222e8 q^{50} -7.91925e8 q^{51} +5.22594e7 q^{52} +2.68649e9 q^{53} -2.47434e8 q^{54} +1.07867e9 q^{55} +8.68335e7 q^{56} -2.65460e9 q^{57} -2.91229e8 q^{58} -7.14924e8 q^{59} -3.40108e9 q^{60} -1.08583e10 q^{61} +9.55025e8 q^{62} +7.82764e7 q^{63} -1.98580e9 q^{64} -2.38661e8 q^{65} -5.65356e8 q^{66} +1.61605e10 q^{67} +5.70525e9 q^{68} +4.49597e7 q^{69} -1.82756e8 q^{70} +3.75065e9 q^{71} +3.86795e9 q^{72} -2.36110e10 q^{73} +1.24450e10 q^{74} +3.66699e9 q^{75} +1.91245e10 q^{76} +1.78852e8 q^{77} +1.25088e8 q^{78} -4.18117e10 q^{79} +1.96335e10 q^{80} +3.48678e9 q^{81} +1.48925e10 q^{82} +2.14444e10 q^{83} -5.63926e8 q^{84} -2.60550e10 q^{85} -1.72697e10 q^{86} +4.10393e9 q^{87} +8.83780e9 q^{88} +2.25760e10 q^{89} -8.14080e9 q^{90} -3.95718e7 q^{91} -3.23902e8 q^{92} -1.34580e10 q^{93} -5.20448e10 q^{94} -8.73387e10 q^{95} -4.28894e10 q^{96} -3.27724e10 q^{97} +3.40669e10 q^{98} +7.96687e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) $	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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 $

$2$	−17.2441	−0.381044	−0.190522	−	0.981683i	$-0.561018\pi$
$2$	−17.2441	−0.381044	−0.190522	+	0.981683i	$0.561018\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1750.64	−0.854805
$5$	7994.91	1.14414	0.572069	−	0.820205i	$-0.306141\pi$
$5$	7994.91	1.14414	0.572069	+	0.820205i	$0.306141\pi$
$6$	−4190.32	−0.219996
$7$	1325.62	0.0298112	0.0149056	−	0.999889i	$-0.495255\pi$
$7$	1325.62	0.0298112	0.0149056	+	0.999889i	$0.495255\pi$
$8$	65504.2	0.706763
$9$	59049.0	0.333333
$10$	−137865.	−0.435968
$11$	134920.	0.252590	0.126295	−	0.991993i	$-0.459691\pi$
$11$	134920.	0.252590	0.126295	+	0.991993i	$0.459691\pi$
$12$	−425406.	−0.493522
$13$	−29851.6	−0.0222987	−0.0111493	−	0.999938i	$-0.503549\pi$
$13$	−29851.6	−0.0222987	−0.0111493	+	0.999938i	$0.503549\pi$
$14$	−22859.1	−0.0113594
$15$	1.94276e6	0.660569
$16$	2.45575e6	0.585497
$17$	−3.25895e6	−0.556684	−0.278342	−	0.960482i	$-0.589785\pi$
$17$	−3.25895e6	−0.556684	−0.278342	+	0.960482i	$0.589785\pi$
$18$	−1.01825e6	−0.127015
$19$	−1.09243e7	−1.01216	−0.506079	−	0.862487i	$-0.668905\pi$
$19$	−1.09243e7	−1.01216	−0.506079	+	0.862487i	$0.668905\pi$
$20$	−1.39962e7	−0.978016
$21$	322125.	0.0172115
$22$	−2.32657e6	−0.0962479
$23$	185019.	0.00599396	0.00299698	−	0.999996i	$-0.499046\pi$
$23$	185019.	0.00599396	0.00299698	+	0.999996i	$0.499046\pi$
$24$	1.59175e7	0.408050
$25$	1.50905e7	0.309054
$26$	514764.	0.00849678
$27$	1.43489e7	0.192450
$28$	−2.32068e6	−0.0254828
$29$	1.68886e7	0.152899	0.0764495	−	0.997073i	$-0.475642\pi$
$29$	1.68886e7	0.152899	0.0764495	+	0.997073i	$0.475642\pi$
$30$	−3.35012e7	−0.251706
$31$	−5.53827e7	−0.347444	−0.173722	−	0.984795i	$-0.555579\pi$
$31$	−5.53827e7	−0.347444	−0.173722	+	0.984795i	$0.555579\pi$
$32$	−1.76500e8	−0.929864
$33$	3.27855e7	0.145833
$34$	5.61977e7	0.212121
$35$	1.05982e7	0.0341081
$36$	−1.03374e8	−0.284935
$37$	−7.21695e8	−1.71098	−0.855489	−	0.517821i	$-0.826743\pi$
$37$	−7.21695e8	−1.71098	−0.855489	+	0.517821i	$0.826743\pi$
$38$	1.88379e8	0.385677
$39$	−7.25393e6	−0.0128741
$40$	5.23700e8	0.808635
$41$	−8.63631e8	−1.16417	−0.582086	−	0.813128i	$-0.697763\pi$
$41$	−8.63631e8	−1.16417	−0.582086	+	0.813128i	$0.697763\pi$
$42$	−5.55476e6	−0.00655834
$43$	1.00149e9	1.03889	0.519444	−	0.854505i	$-0.326139\pi$
$43$	1.00149e9	1.03889	0.519444	+	0.854505i	$0.326139\pi$
$44$	−2.36196e8	−0.215915
$45$	4.72092e8	0.381380
$46$	−3.19049e6	−0.00228397
$47$	3.01812e9	1.91954	0.959772	−	0.280779i	$-0.0905929\pi$
$47$	3.01812e9	1.91954	0.959772	+	0.280779i	$0.0905929\pi$
$48$	5.96748e8	0.338037
$49$	−1.97557e9	−0.999111
$50$	−2.60222e8	−0.117763
$51$	−7.91925e8	−0.321402
$52$	5.22594e7	0.0190610
$53$	2.68649e9	0.882405	0.441203	−	0.897407i	$-0.354552\pi$
$53$	2.68649e9	0.882405	0.441203	+	0.897407i	$0.354552\pi$
$54$	−2.47434e8	−0.0733320
$55$	1.07867e9	0.288998
$56$	8.68335e7	0.0210694
$57$	−2.65460e9	−0.584369
$58$	−2.91229e8	−0.0582613
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−3.40108e9	−0.564658
$61$	−1.08583e10	−1.64607	−0.823035	−	0.567990i	$-0.807721\pi$
$61$	−1.08583e10	−1.64607	−0.823035	+	0.567990i	$0.807721\pi$
$62$	9.55025e8	0.132392
$63$	7.82764e7	0.00993706
$64$	−1.98580e9	−0.231178
$65$	−2.38661e8	−0.0255128
$66$	−5.65356e8	−0.0555687
$67$	1.61605e10	1.46233	0.731163	−	0.682203i	$-0.238978\pi$
$67$	1.61605e10	1.46233	0.731163	+	0.682203i	$0.238978\pi$
$68$	5.70525e9	0.475856
$69$	4.49597e7	0.00346062
$70$	−1.82756e8	−0.0129967
$71$	3.75065e9	0.246710	0.123355	−	0.992363i	$-0.460635\pi$
$71$	3.75065e9	0.246710	0.123355	+	0.992363i	$0.460635\pi$
$72$	3.86795e9	0.235588
$73$	−2.36110e10	−1.33302	−0.666512	−	0.745495i	$-0.732213\pi$
$73$	−2.36110e10	−1.33302	−0.666512	+	0.745495i	$0.732213\pi$
$74$	1.24450e10	0.651959
$75$	3.66699e9	0.178432
$76$	1.91245e10	0.865197
$77$	1.78852e8	0.00752999
$78$	1.25088e8	0.00490562
$79$	−4.18117e10	−1.52879	−0.764397	−	0.644746i	$-0.776963\pi$
$79$	−4.18117e10	−1.52879	−0.764397	+	0.644746i	$0.776963\pi$
$80$	1.96335e10	0.669890
$81$	3.48678e9	0.111111
$82$	1.48925e10	0.443601
$83$	2.14444e10	0.597564	0.298782	−	0.954321i	$-0.403420\pi$
$83$	2.14444e10	0.597564	0.298782	+	0.954321i	$0.403420\pi$
$84$	−5.63926e8	−0.0147125
$85$	−2.60550e10	−0.636924
$86$	−1.72697e10	−0.395862
$87$	4.10393e9	0.0882762
$88$	8.83780e9	0.178521
$89$	2.25760e10	0.428550	0.214275	−	0.976773i	$-0.431261\pi$
$89$	2.25760e10	0.428550	0.214275	+	0.976773i	$0.431261\pi$
$90$	−8.14080e9	−0.145323
$91$	−3.95718e7	−0.000664749 0
$92$	−3.23902e8	−0.00512367
$93$	−1.34580e10	−0.200597
$94$	−5.20448e10	−0.731432
$95$	−8.73387e10	−1.15805
$96$	−4.28894e10	−0.536857
$97$	−3.27724e10	−0.387493	−0.193747	−	0.981052i	$-0.562064\pi$
$97$	−3.27724e10	−0.387493	−0.193747	+	0.981052i	$0.562064\pi$
$98$	3.40669e10	0.380706
$99$	7.96687e9	0.0841965
$100$	−2.64181e10	−0.264181
$101$	8.33085e10	0.788718	0.394359	−	0.918957i	$-0.370967\pi$
$101$	8.33085e10	0.788718	0.394359	+	0.918957i	$0.370967\pi$
$102$	1.36560e10	0.122468
$103$	2.29703e11	1.95237	0.976187	−	0.216932i	$-0.0696051\pi$
$103$	2.29703e11	1.95237	0.976187	+	0.216932i	$0.0696051\pi$
$104$	−1.95540e9	−0.0157599
$105$	2.57536e9	0.0196923
$106$	−4.63261e10	−0.336236
$107$	−1.56240e11	−1.07692	−0.538459	−	0.842652i	$-0.680993\pi$
$107$	−1.56240e11	−1.07692	−0.538459	+	0.842652i	$0.680993\pi$
$108$	−2.51198e10	−0.164507
$109$	−2.21150e11	−1.37670	−0.688352	−	0.725377i	$-0.741666\pi$
$109$	−2.21150e11	−1.37670	−0.688352	+	0.725377i	$0.741666\pi$
$110$	−1.86007e10	−0.110121
$111$	−1.75372e11	−0.987833
$112$	3.25539e9	0.0174544
$113$	3.63850e11	1.85777	0.928883	−	0.370373i	$-0.120770\pi$
$113$	3.63850e11	1.85777	0.928883	+	0.370373i	$0.120770\pi$
$114$	4.57762e10	0.222671
$115$	1.47921e9	0.00685793
$116$	−2.95659e10	−0.130699
$117$	−1.76271e9	−0.00743289
$118$	1.23282e10	0.0496078
$119$	−4.32012e9	−0.0165954
$120$	1.27259e11	0.466866
$121$	−2.67108e11	−0.936198
$122$	1.87242e11	0.627226
$123$	−2.09862e11	−0.672135
$124$	9.69552e10	0.296997
$125$	−2.69729e11	−0.790539
$126$	−1.34981e9	−0.00378646
$127$	−3.83293e11	−1.02946	−0.514732	−	0.857351i	$-0.672108\pi$
$127$	−3.83293e11	−1.02946	−0.514732	+	0.857351i	$0.672108\pi$
$128$	3.95715e11	1.01795
$129$	2.43361e11	0.599802
$130$	4.11549e9	0.00972149
$131$	4.10464e11	0.929571	0.464785	−	0.885423i	$-0.346131\pi$
$131$	4.10464e11	0.929571	0.464785	+	0.885423i	$0.346131\pi$
$132$	−5.73956e10	−0.124659
$133$	−1.44814e10	−0.0301736
$134$	−2.78674e11	−0.557211
$135$	1.14718e11	0.220190
$136$	−2.13475e11	−0.393444
$137$	2.08833e11	0.369689	0.184845	−	0.982768i	$-0.440822\pi$
$137$	2.08833e11	0.369689	0.184845	+	0.982768i	$0.440822\pi$
$138$	−7.75290e8	−0.00131865
$139$	4.49732e11	0.735145	0.367572	−	0.929995i	$-0.380189\pi$
$139$	4.49732e11	0.735145	0.367572	+	0.929995i	$0.380189\pi$
$140$	−1.85536e10	−0.0291558
$141$	7.33403e11	1.10825
$142$	−6.46767e10	−0.0940073
$143$	−4.02756e9	−0.00563241
$144$	1.45010e11	0.195166
$145$	1.35023e11	0.174938
$146$	4.07150e11	0.507941
$147$	−4.80063e11	−0.576837
$148$	1.26343e12	1.46255
$149$	1.77907e10	0.0198458	0.00992288	−	0.999951i	$-0.496841\pi$
$149$	1.77907e10	0.0198458	0.00992288	+	0.999951i	$0.496841\pi$
$150$	−6.32340e10	−0.0679906
$151$	−1.59845e12	−1.65701	−0.828506	−	0.559980i	$-0.810809\pi$
$151$	−1.59845e12	−1.65701	−0.828506	+	0.559980i	$0.810809\pi$
$152$	−7.15586e11	−0.715356
$153$	−1.92438e11	−0.185561
$154$	−3.08414e9	−0.00286926
$155$	−4.42780e11	−0.397524
$156$	1.26990e10	0.0110049
$157$	−1.19670e12	−1.00124	−0.500619	−	0.865668i	$-0.666894\pi$
$157$	−1.19670e12	−1.00124	−0.500619	+	0.865668i	$0.666894\pi$
$158$	7.21005e11	0.582538
$159$	6.52817e11	0.509457
$160$	−1.41110e12	−1.06389
$161$	2.45265e8	0.000178687 0
$162$	−6.01265e10	−0.0423383
$163$	−1.67271e12	−1.13865	−0.569324	−	0.822113i	$-0.692795\pi$
$163$	−1.67271e12	−1.13865	−0.569324	+	0.822113i	$0.692795\pi$
$164$	1.51191e12	0.995140
$165$	2.62117e11	0.166853
$166$	−3.69790e11	−0.227699
$167$	−1.38696e12	−0.826274	−0.413137	−	0.910669i	$-0.635567\pi$
$167$	−1.38696e12	−0.826274	−0.413137	+	0.910669i	$0.635567\pi$
$168$	2.11005e10	0.0121644
$169$	−1.79127e12	−0.999503
$170$	4.49295e11	0.242696
$171$	−6.45068e11	−0.337386
$172$	−1.75324e12	−0.888047
$173$	−3.50693e12	−1.72058	−0.860288	−	0.509808i	$-0.829717\pi$
$173$	−3.50693e12	−1.72058	−0.860288	+	0.509808i	$0.829717\pi$
$174$	−7.07685e10	−0.0336372
$175$	2.00042e10	0.00921325
$176$	3.31329e11	0.147890
$177$	−1.73727e11	−0.0751646
$178$	−3.89302e11	−0.163297
$179$	−4.28803e12	−1.74408	−0.872039	−	0.489436i	$-0.837203\pi$
$179$	−4.28803e12	−1.74408	−0.872039	+	0.489436i	$0.837203\pi$
$180$	−8.26463e11	−0.326005
$181$	−1.32012e12	−0.505105	−0.252553	−	0.967583i	$-0.581270\pi$
$181$	−1.32012e12	−0.505105	−0.252553	+	0.967583i	$0.581270\pi$
$182$	6.82380e8	0.000253299 0
$183$	−2.63857e12	−0.950359
$184$	1.21195e10	0.00423631
$185$	−5.76989e12	−1.95760
$186$	2.32071e11	0.0764363
$187$	−4.39696e11	−0.140613
$188$	−5.28364e12	−1.64084
$189$	1.90212e10	0.00573716
$190$	1.50608e12	0.441268
$191$	4.44766e11	0.126604	0.0633021	−	0.997994i	$-0.479837\pi$
$191$	4.44766e11	0.126604	0.0633021	+	0.997994i	$0.479837\pi$
$192$	−4.82550e11	−0.133471
$193$	−4.40420e12	−1.18386	−0.591932	−	0.805988i	$-0.701635\pi$
$193$	−4.40420e12	−1.18386	−0.591932	+	0.805988i	$0.701635\pi$
$194$	5.65131e11	0.147652
$195$	−5.79946e10	−0.0147298
$196$	3.45851e12	0.854045
$197$	−1.08074e12	−0.259511	−0.129756	−	0.991546i	$-0.541419\pi$
$197$	−1.08074e12	−0.259511	−0.129756	+	0.991546i	$0.541419\pi$
$198$	−1.37382e11	−0.0320826
$199$	1.76499e12	0.400914	0.200457	−	0.979703i	$-0.435757\pi$
$199$	1.76499e12	0.400914	0.200457	+	0.979703i	$0.435757\pi$
$200$	9.88491e11	0.218428
$201$	3.92701e12	0.844274
$202$	−1.43658e12	−0.300536
$203$	2.23878e10	0.00455810
$204$	1.38638e12	0.274736
$205$	−6.90465e12	−1.33197
$206$	−3.96103e12	−0.743941
$207$	1.09252e10	0.00199799
$208$	−7.33081e10	−0.0130558
$209$	−1.47390e12	−0.255660
$210$	−4.44098e10	−0.00750366
$211$	−9.48437e12	−1.56119	−0.780593	−	0.625039i	$-0.785083\pi$
$211$	−9.48437e12	−1.56119	−0.780593	+	0.625039i	$0.785083\pi$
$212$	−4.70308e12	−0.754285
$213$	9.11409e11	0.142438
$214$	2.69422e12	0.410353
$215$	8.00680e12	1.18863
$216$	9.39913e11	0.136017
$217$	−7.34163e10	−0.0103577
$218$	3.81353e12	0.524585
$219$	−5.73746e12	−0.769621
$220$	−1.88837e12	−0.247037
$221$	9.72848e10	0.0124133
$222$	3.02413e12	0.376408
$223$	1.52602e13	1.85303	0.926514	−	0.376260i	$-0.122790\pi$
$223$	1.52602e13	1.85303	0.926514	+	0.376260i	$0.122790\pi$
$224$	−2.33971e11	−0.0277203
$225$	8.91079e11	0.103018
$226$	−6.27427e12	−0.707892
$227$	1.23239e12	0.135709	0.0678543	−	0.997695i	$-0.478385\pi$
$227$	1.23239e12	0.135709	0.0678543	+	0.997695i	$0.478385\pi$
$228$	4.64725e12	0.499522
$229$	9.34468e11	0.0980549	0.0490275	−	0.998797i	$-0.484388\pi$
$229$	9.34468e11	0.0980549	0.0490275	+	0.998797i	$0.484388\pi$
$230$	−2.55077e10	−0.00261317
$231$	4.34610e10	0.00434744
$232$	1.10627e12	0.108063
$233$	−1.10618e13	−1.05528	−0.527641	−	0.849468i	$-0.676923\pi$
$233$	−1.10618e13	−1.05528	−0.527641	+	0.849468i	$0.676923\pi$
$234$	3.03963e10	0.00283226
$235$	2.41296e13	2.19623
$236$	1.25158e12	0.111286
$237$	−1.01602e13	−0.882649
$238$	7.44966e10	0.00632359
$239$	−1.79204e13	−1.48648	−0.743240	−	0.669024i	$-0.766712\pi$
$239$	−1.79204e13	−1.48648	−0.743240	+	0.669024i	$0.766712\pi$
$240$	4.77095e12	0.386761
$241$	−9.45537e11	−0.0749177	−0.0374589	−	0.999298i	$-0.511926\pi$
$241$	−9.45537e11	−0.0749177	−0.0374589	+	0.999298i	$0.511926\pi$
$242$	4.60604e12	0.356733
$243$	8.47289e11	0.0641500
$244$	1.90090e13	1.40707
$245$	−1.57945e13	−1.14312
$246$	3.61889e12	0.256113
$247$	3.26107e11	0.0225698
$248$	−3.62780e12	−0.245561
$249$	5.21099e12	0.345004
$250$	4.65124e12	0.301230
$251$	−1.19285e13	−0.755752	−0.377876	−	0.925856i	$-0.623345\pi$
$251$	−1.19285e13	−0.755752	−0.377876	+	0.925856i	$0.623345\pi$
$252$	−1.37034e11	−0.00849425
$253$	2.49627e10	0.00151401
$254$	6.60955e12	0.392271
$255$	−6.33137e12	−0.367728
$256$	−2.75683e12	−0.156707
$257$	1.72401e13	0.959196	0.479598	−	0.877488i	$-0.340783\pi$
$257$	1.72401e13	0.959196	0.479598	+	0.877488i	$0.340783\pi$
$258$	−4.19655e12	−0.228551
$259$	−9.56692e11	−0.0510063
$260$	4.17809e11	0.0218084
$261$	9.97254e11	0.0509663
$262$	−7.07807e12	−0.354208
$263$	−1.30175e13	−0.637928	−0.318964	−	0.947767i	$-0.603335\pi$
$263$	−1.30175e13	−0.637928	−0.318964	+	0.947767i	$0.603335\pi$
$264$	2.14758e12	0.103069
$265$	2.14783e13	1.00959
$266$	2.49719e11	0.0114975
$267$	5.48596e12	0.247423
$268$	−2.82913e13	−1.25000
$269$	2.39837e13	1.03819	0.519096	−	0.854716i	$-0.326269\pi$
$269$	2.39837e13	1.03819	0.519096	+	0.854716i	$0.326269\pi$
$270$	−1.97821e12	−0.0839020
$271$	8.58896e12	0.356952	0.178476	−	0.983944i	$-0.442883\pi$
$271$	8.58896e12	0.356952	0.178476	+	0.983944i	$0.442883\pi$
$272$	−8.00318e12	−0.325937
$273$	−9.61594e9	−0.000383793 0
$274$	−3.60114e12	−0.140868
$275$	2.03601e12	0.0780637
$276$	−7.87083e10	−0.00295815
$277$	3.88767e13	1.43235	0.716177	−	0.697919i	$-0.245890\pi$
$277$	3.88767e13	1.43235	0.716177	+	0.697919i	$0.245890\pi$
$278$	−7.75523e12	−0.280123
$279$	−3.27029e12	−0.115815
$280$	6.94226e11	0.0241064
$281$	−5.40461e13	−1.84026	−0.920130	−	0.391612i	$-0.871917\pi$
$281$	−5.40461e13	−1.84026	−0.920130	+	0.391612i	$0.871917\pi$
$282$	−1.26469e13	−0.422292
$283$	−3.02124e13	−0.989371	−0.494686	−	0.869072i	$-0.664717\pi$
$283$	−3.02124e13	−0.989371	−0.494686	+	0.869072i	$0.664717\pi$
$284$	−6.56605e12	−0.210889
$285$	−2.12233e13	−0.668600
$286$	6.94517e10	0.00214620
$287$	−1.14484e12	−0.0347053
$288$	−1.04221e13	−0.309955
$289$	−2.36511e13	−0.690103
$290$	−2.32835e12	−0.0666590
$291$	−7.96370e12	−0.223719
$292$	4.13343e13	1.13948
$293$	5.03877e13	1.36318	0.681589	−	0.731735i	$-0.261289\pi$
$293$	5.03877e13	1.36318	0.681589	+	0.731735i	$0.261289\pi$
$294$	8.27826e12	0.219801
$295$	−5.71576e12	−0.148954
$296$	−4.72740e13	−1.20926
$297$	1.93595e12	0.0486109
$298$	−3.06784e11	−0.00756211
$299$	−5.52312e9	−0.000133657 0
$300$	−6.41959e12	−0.152525
$301$	1.32759e12	0.0309705
$302$	2.75638e13	0.631395
$303$	2.02440e13	0.455366
$304$	−2.68273e13	−0.592615
$305$	−8.68113e13	−1.88333
$306$	3.31842e12	0.0707071
$307$	−4.20907e13	−0.880897	−0.440448	−	0.897778i	$-0.645181\pi$
$307$	−4.20907e13	−0.880897	−0.440448	+	0.897778i	$0.645181\pi$
$308$	−3.13106e11	−0.00643668
$309$	5.58179e13	1.12720
$310$	7.63534e12	0.151474
$311$	9.40628e12	0.183331	0.0916655	−	0.995790i	$-0.470781\pi$
$311$	9.40628e12	0.183331	0.0916655	+	0.995790i	$0.470781\pi$
$312$	−4.75163e11	−0.00909897
$313$	7.43970e13	1.39979	0.699893	−	0.714248i	$-0.253231\pi$
$313$	7.43970e13	1.39979	0.699893	+	0.714248i	$0.253231\pi$
$314$	2.06360e13	0.381516
$315$	6.25813e11	0.0113694
$316$	7.31973e13	1.30682
$317$	2.30400e13	0.404257	0.202128	−	0.979359i	$-0.435214\pi$
$317$	2.30400e13	0.404257	0.202128	+	0.979359i	$0.435214\pi$
$318$	−1.12573e13	−0.194126
$319$	2.27860e12	0.0386207
$320$	−1.58763e13	−0.264499
$321$	−3.79664e13	−0.621758
$322$	−4.22937e9	−6.80877e−5 0
$323$	3.56017e13	0.563452
$324$	−6.10411e12	−0.0949784
$325$	−4.50475e11	−0.00689148
$326$	2.88444e13	0.433875
$327$	−5.37394e13	−0.794840
$328$	−5.65714e13	−0.822793
$329$	4.00087e12	0.0572239
$330$	−4.51997e12	−0.0635783
$331$	−1.02273e13	−0.141483	−0.0707417	−	0.997495i	$-0.522537\pi$
$331$	−1.02273e13	−0.141483	−0.0707417	+	0.997495i	$0.522537\pi$
$332$	−3.75415e13	−0.510801
$333$	−4.26154e13	−0.570326
$334$	2.39169e13	0.314847
$335$	1.29202e14	1.67310
$336$	7.91060e11	0.0100773
$337$	−2.55314e13	−0.319971	−0.159986	−	0.987119i	$-0.551145\pi$
$337$	−2.55314e13	−0.319971	−0.159986	+	0.987119i	$0.551145\pi$
$338$	3.08888e13	0.380855
$339$	8.84156e13	1.07258
$340$	4.56130e13	0.544446
$341$	−7.47222e12	−0.0877608
$342$	1.11236e13	0.128559
$343$	−5.24003e12	−0.0595959
$344$	6.56015e13	0.734248
$345$	3.59449e11	0.00395943
$346$	6.04739e13	0.655616
$347$	9.22758e13	0.984636	0.492318	−	0.870415i	$-0.336150\pi$
$347$	9.22758e13	0.984636	0.492318	+	0.870415i	$0.336150\pi$
$348$	−7.18450e12	−0.0754590
$349$	8.18322e13	0.846027	0.423013	−	0.906123i	$-0.360972\pi$
$349$	8.18322e13	0.846027	0.423013	+	0.906123i	$0.360972\pi$
$350$	−3.44955e11	−0.00351066
$351$	−4.28337e11	−0.00429138
$352$	−2.38133e13	−0.234874
$353$	1.64332e14	1.59573	0.797867	−	0.602833i	$-0.205961\pi$
$353$	1.64332e14	1.59573	0.797867	+	0.602833i	$0.205961\pi$
$354$	2.99576e12	0.0286411
$355$	2.99862e13	0.282270
$356$	−3.95224e13	−0.366327
$357$	−1.04979e12	−0.00958136
$358$	7.39432e13	0.664571
$359$	4.41523e13	0.390781	0.195391	−	0.980725i	$-0.437403\pi$
$359$	4.41523e13	0.390781	0.195391	+	0.980725i	$0.437403\pi$
$360$	3.09240e13	0.269545
$361$	2.84965e12	0.0244625
$362$	2.27643e13	0.192468
$363$	−6.49073e13	−0.540514
$364$	6.92760e10	0.000568231 0
$365$	−1.88767e14	−1.52516
$366$	4.54998e13	0.362129
$367$	−8.52900e13	−0.668705	−0.334353	−	0.942448i	$-0.608518\pi$
$367$	−8.52900e13	−0.668705	−0.334353	+	0.942448i	$0.608518\pi$
$368$	4.54362e11	0.00350945
$369$	−5.09965e13	−0.388057
$370$	9.94966e13	0.745931
$371$	3.56126e12	0.0263055
$372$	2.35601e13	0.171471
$373$	2.26293e14	1.62283	0.811414	−	0.584471i	$-0.198698\pi$
$373$	2.26293e14	1.62283	0.811414	+	0.584471i	$0.198698\pi$
$374$	7.58217e12	0.0535796
$375$	−6.55442e13	−0.456418
$376$	1.97699e14	1.35666
$377$	−5.04151e11	−0.00340944
$378$	−3.28003e11	−0.00218611
$379$	2.21395e13	0.145429	0.0727147	−	0.997353i	$-0.476834\pi$
$379$	2.21395e13	0.145429	0.0727147	+	0.997353i	$0.476834\pi$
$380$	1.52899e14	0.989906
$381$	−9.31403e13	−0.594361
$382$	−7.66960e12	−0.0482419
$383$	−2.57233e14	−1.59490	−0.797451	−	0.603384i	$-0.793819\pi$
$383$	−2.57233e14	−1.59490	−0.797451	+	0.603384i	$0.793819\pi$
$384$	9.61587e13	0.587715
$385$	1.42991e12	0.00861536
$386$	7.59465e13	0.451105
$387$	5.91368e13	0.346296
$388$	5.73728e13	0.331231
$389$	1.48946e14	0.847825	0.423913	−	0.905703i	$-0.360656\pi$
$389$	1.48946e14	0.847825	0.423913	+	0.905703i	$0.360656\pi$
$390$	1.00006e12	0.00561271
$391$	−6.02969e11	−0.00333674
$392$	−1.29408e14	−0.706135
$393$	9.97426e13	0.536688
$394$	1.86364e13	0.0988854
$395$	−3.34281e14	−1.74915
$396$	−1.39471e13	−0.0719716
$397$	−3.16206e14	−1.60925	−0.804623	−	0.593786i	$-0.797632\pi$
$397$	−3.16206e14	−1.60925	−0.804623	+	0.593786i	$0.797632\pi$
$398$	−3.04357e13	−0.152766
$399$	−3.51899e12	−0.0174207
$400$	3.70585e13	0.180950
$401$	1.69636e14	0.817004	0.408502	−	0.912757i	$-0.366051\pi$
$401$	1.69636e14	0.817004	0.408502	+	0.912757i	$0.366051\pi$
$402$	−6.77177e13	−0.321706
$403$	1.65326e12	0.00774754
$404$	−1.45843e14	−0.674200
$405$	2.78765e13	0.127127
$406$	−3.86058e11	−0.00173684
$407$	−9.73709e13	−0.432175
$408$	−5.18744e13	−0.227155
$409$	−1.55395e14	−0.671366	−0.335683	−	0.941975i	$-0.608967\pi$
$409$	−1.55395e14	−0.671366	−0.335683	+	0.941975i	$0.608967\pi$
$410$	1.19065e14	0.507541
$411$	5.07465e13	0.213440
$412$	−4.02128e14	−1.66890
$413$	−9.47717e11	−0.00388109
$414$	−1.88395e11	−0.000761322 0
$415$	1.71446e14	0.683696
$416$	5.26879e12	0.0207347
$417$	1.09285e14	0.424436
$418$	2.54161e13	0.0974180
$419$	5.61588e13	0.212442	0.106221	−	0.994343i	$-0.466125\pi$
$419$	5.61588e13	0.212442	0.106221	+	0.994343i	$0.466125\pi$
$420$	−4.50854e12	−0.0168331
$421$	4.27803e13	0.157649	0.0788247	−	0.996888i	$-0.474883\pi$
$421$	4.27803e13	0.157649	0.0788247	+	0.996888i	$0.474883\pi$
$422$	1.63549e14	0.594882
$423$	1.78217e14	0.639848
$424$	1.75976e14	0.623652
$425$	−4.91792e13	−0.172045
$426$	−1.57164e13	−0.0542752
$427$	−1.43940e13	−0.0490713
$428$	2.73521e14	0.920554
$429$	−9.78698e11	−0.00325187
$430$	−1.38070e14	−0.452922
$431$	−2.22098e14	−0.719317	−0.359658	−	0.933084i	$-0.617107\pi$
$431$	−2.22098e14	−0.719317	−0.359658	+	0.933084i	$0.617107\pi$
$432$	3.52374e13	0.112679
$433$	4.37273e14	1.38061	0.690303	−	0.723521i	$-0.257477\pi$
$433$	4.37273e14	1.38061	0.690303	+	0.723521i	$0.257477\pi$
$434$	1.26600e12	0.00394675
$435$	3.28105e13	0.101000
$436$	3.87154e14	1.17681
$437$	−2.02120e12	−0.00606683
$438$	9.89374e13	0.293260
$439$	−1.67284e14	−0.489667	−0.244833	−	0.969565i	$-0.578733\pi$
$439$	−1.67284e14	−0.489667	−0.244833	+	0.969565i	$0.578733\pi$
$440$	7.06574e13	0.204253
$441$	−1.16655e14	−0.333037
$442$	−1.67759e12	−0.00473002
$443$	−5.50257e14	−1.53231	−0.766153	−	0.642659i	$-0.777831\pi$
$443$	−5.50257e14	−1.53231	−0.766153	+	0.642659i	$0.777831\pi$
$444$	3.07013e14	0.844405
$445$	1.80493e14	0.490321
$446$	−2.63148e14	−0.706086
$447$	4.32313e12	0.0114579
$448$	−2.63241e12	−0.00689168
$449$	1.21006e14	0.312933	0.156467	−	0.987683i	$-0.449990\pi$
$449$	1.21006e14	0.312933	0.156467	+	0.987683i	$0.449990\pi$
$450$	−1.53659e13	−0.0392544
$451$	−1.16521e14	−0.294058
$452$	−6.36971e14	−1.58803
$453$	−3.88423e14	−0.956677
$454$	−2.12515e13	−0.0517110
$455$	−3.16373e11	−0.000760566 0
$456$	−1.73887e14	−0.413011
$457$	6.51012e14	1.52774	0.763871	−	0.645369i	$-0.223296\pi$
$457$	6.51012e14	1.52774	0.763871	+	0.645369i	$0.223296\pi$
$458$	−1.61141e13	−0.0373633
$459$	−4.67624e13	−0.107134
$460$	−2.58957e12	−0.00586219
$461$	1.38009e14	0.308710	0.154355	−	0.988015i	$-0.450670\pi$
$461$	1.38009e14	0.308710	0.154355	+	0.988015i	$0.450670\pi$
$462$	−7.49446e11	−0.00165657
$463$	−1.78732e14	−0.390396	−0.195198	−	0.980764i	$-0.562535\pi$
$463$	−1.78732e14	−0.390396	−0.195198	+	0.980764i	$0.562535\pi$
$464$	4.14742e13	0.0895219
$465$	−1.07596e14	−0.229511
$466$	1.90751e14	0.402109
$467$	6.46209e14	1.34626	0.673132	−	0.739523i	$-0.264949\pi$
$467$	6.46209e14	1.34626	0.673132	+	0.739523i	$0.264949\pi$
$468$	3.08586e12	0.00635367
$469$	2.14227e13	0.0435937
$470$	−4.16093e14	−0.836859
$471$	−2.90798e14	−0.578065
$472$	−4.68305e13	−0.0920127
$473$	1.35120e14	0.262412
$474$	1.75204e14	0.336328
$475$	−1.64853e14	−0.312811
$476$	7.56299e12	0.0141858
$477$	1.58635e14	0.294135
$478$	3.09021e14	0.566415
$479$	−2.06190e14	−0.373613	−0.186806	−	0.982397i	$-0.559814\pi$
$479$	−2.06190e14	−0.373613	−0.186806	+	0.982397i	$0.559814\pi$
$480$	−3.42897e14	−0.614239
$481$	2.15437e13	0.0381525
$482$	1.63049e13	0.0285470
$483$	5.95994e10	0.000103165 0
$484$	4.67611e14	0.800267
$485$	−2.62013e14	−0.443346
$486$	−1.46107e13	−0.0244440
$487$	−1.41182e14	−0.233545	−0.116772	−	0.993159i	$-0.537255\pi$
$487$	−1.41182e14	−0.233545	−0.116772	+	0.993159i	$0.537255\pi$
$488$	−7.11265e14	−1.16338
$489$	−4.06469e14	−0.657398
$490$	2.72362e14	0.435580
$491$	−2.31067e14	−0.365417	−0.182709	−	0.983167i	$-0.558487\pi$
$491$	−2.31067e14	−0.365417	−0.182709	+	0.983167i	$0.558487\pi$
$492$	3.67393e14	0.574544
$493$	−5.50391e13	−0.0851164
$494$	−5.62342e12	−0.00860008
$495$	6.36944e13	0.0963325
$496$	−1.36006e14	−0.203427
$497$	4.97193e12	0.00735471
$498$	−8.98589e13	−0.131462
$499$	5.09795e14	0.737637	0.368818	−	0.929501i	$-0.379762\pi$
$499$	5.09795e14	0.737637	0.368818	+	0.929501i	$0.379762\pi$
$500$	4.72199e14	0.675757
$501$	−3.37032e14	−0.477050
$502$	2.05696e14	0.287975
$503$	−2.71402e14	−0.375828	−0.187914	−	0.982185i	$-0.560173\pi$
$503$	−2.71402e14	−0.375828	−0.187914	+	0.982185i	$0.560173\pi$
$504$	5.12743e12	0.00702315
$505$	6.66044e14	0.902402
$506$	−4.30460e11	−0.000576906 0
$507$	−4.35278e14	−0.577063
$508$	6.71009e14	0.879990
$509$	−1.29361e15	−1.67825	−0.839123	−	0.543941i	$-0.816931\pi$
$509$	−1.29361e15	−1.67825	−0.839123	+	0.543941i	$0.816931\pi$
$510$	1.09179e14	0.140121
$511$	−3.12991e13	−0.0397390
$512$	−7.62885e14	−0.958240
$513$	−1.56751e14	−0.194790
$514$	−2.97290e14	−0.365496
$515$	1.83646e15	2.23379
$516$	−4.26038e14	−0.512714
$517$	4.07204e14	0.484857
$518$	1.64973e13	0.0194357
$519$	−8.52185e14	−0.993376
$520$	−1.56333e13	−0.0180315
$521$	6.01854e14	0.686884	0.343442	−	0.939174i	$-0.388407\pi$
$521$	6.01854e14	0.686884	0.343442	+	0.939174i	$0.388407\pi$
$522$	−1.71968e13	−0.0194204
$523$	−1.06743e15	−1.19284	−0.596418	−	0.802674i	$-0.703410\pi$
$523$	−1.06743e15	−1.19284	−0.596418	+	0.802674i	$0.703410\pi$
$524$	−7.18574e14	−0.794602
$525$	4.86103e12	0.00531927
$526$	2.24475e14	0.243079
$527$	1.80490e14	0.193417
$528$	8.05130e13	0.0853846
$529$	−9.52776e14	−0.999964
$530$	−3.70373e14	−0.384700
$531$	−4.22156e13	−0.0433963
$532$	2.53518e13	0.0257926
$533$	2.57807e13	0.0259595
$534$	−9.46005e13	−0.0942793
$535$	−1.24913e15	−1.23214
$536$	1.05858e15	1.03352
$537$	−1.04199e15	−1.00694
$538$	−4.13577e14	−0.395598
$539$	−2.66543e14	−0.252365
$540$	−2.00830e14	−0.188219
$541$	2.76164e14	0.256202	0.128101	−	0.991761i	$-0.459112\pi$
$541$	2.76164e14	0.256202	0.128101	+	0.991761i	$0.459112\pi$
$542$	−1.48109e14	−0.136014
$543$	−3.20790e14	−0.291623
$544$	5.75204e14	0.517640
$545$	−1.76807e15	−1.57514
$546$	1.65818e11	0.000146242 0
$547$	−3.59061e14	−0.313500	−0.156750	−	0.987638i	$-0.550102\pi$
$547$	−3.59061e14	−0.313500	−0.156750	+	0.987638i	$0.550102\pi$
$548$	−3.65592e14	−0.316012
$549$	−6.41173e14	−0.548690
$550$	−3.51091e13	−0.0297457
$551$	−1.84496e14	−0.154758
$552$	2.94505e12	0.00244584
$553$	−5.54263e13	−0.0455751
$554$	−6.70393e14	−0.545790
$555$	−1.40208e15	−1.13022
$556$	−7.87320e14	−0.628405
$557$	3.36952e14	0.266296	0.133148	−	0.991096i	$-0.457491\pi$
$557$	3.36952e14	0.266296	0.133148	+	0.991096i	$0.457491\pi$
$558$	5.63933e13	0.0441305
$559$	−2.98960e13	−0.0231658
$560$	2.60266e13	0.0199702
$561$	−1.06846e14	−0.0811827
$562$	9.31976e14	0.701221
$563$	2.16086e15	1.61001	0.805007	−	0.593265i	$-0.202162\pi$
$563$	2.16086e15	1.61001	0.805007	+	0.593265i	$0.202162\pi$
$564$	−1.28393e15	−0.947338
$565$	2.90895e15	2.12554
$566$	5.20985e14	0.376994
$567$	4.62214e12	0.00331235
$568$	2.45683e14	0.174365
$569$	−8.33757e14	−0.586033	−0.293016	−	0.956107i	$-0.594659\pi$
$569$	−8.33757e14	−0.586033	−0.293016	+	0.956107i	$0.594659\pi$
$570$	3.65977e14	0.254766
$571$	−1.16917e15	−0.806080	−0.403040	−	0.915182i	$-0.632046\pi$
$571$	−1.16917e15	−0.806080	−0.403040	+	0.915182i	$0.632046\pi$
$572$	7.05082e12	0.00481461
$573$	1.08078e14	0.0730950
$574$	1.97418e13	0.0132243
$575$	2.79204e12	0.00185246
$576$	−1.17260e14	−0.0770592
$577$	−8.63090e14	−0.561810	−0.280905	−	0.959736i	$-0.590635\pi$
$577$	−8.63090e14	−0.561810	−0.280905	+	0.959736i	$0.590635\pi$
$578$	4.07843e14	0.262960
$579$	−1.07022e15	−0.683504
$580$	−2.36376e14	−0.149538
$581$	2.84271e13	0.0178141
$582$	1.37327e14	0.0852470
$583$	3.62461e14	0.222886
$584$	−1.54662e15	−0.942132
$585$	−1.40927e13	−0.00850425
$586$	−8.68890e14	−0.519431
$587$	−1.15770e15	−0.685627	−0.342813	−	0.939404i	$-0.611380\pi$
$587$	−1.15770e15	−0.685627	−0.342813	+	0.939404i	$0.611380\pi$
$588$	8.40419e14	0.493083
$589$	6.05016e14	0.351668
$590$	9.85631e13	0.0567582
$591$	−2.62620e14	−0.149829
$592$	−1.77230e15	−1.00177
$593$	3.40899e14	0.190908	0.0954542	−	0.995434i	$-0.469570\pi$
$593$	3.40899e14	0.190908	0.0954542	+	0.995434i	$0.469570\pi$
$594$	−3.33837e13	−0.0185229
$595$	−3.45390e13	−0.0189874
$596$	−3.11451e13	−0.0169643
$597$	4.28893e14	0.231468
$598$	9.52412e10	5.09294e−5 0
$599$	6.59440e14	0.349404	0.174702	−	0.984621i	$-0.444104\pi$
$599$	6.59440e14	0.349404	0.174702	+	0.984621i	$0.444104\pi$
$600$	2.40203e14	0.126109
$601$	−7.80789e14	−0.406185	−0.203093	−	0.979160i	$-0.565099\pi$
$601$	−7.80789e14	−0.406185	−0.203093	+	0.979160i	$0.565099\pi$
$602$	−2.28931e13	−0.0118011
$603$	9.54263e14	0.487442
$604$	2.79831e15	1.41642
$605$	−2.13551e15	−1.07114
$606$	−3.49089e14	−0.173515
$607$	3.21551e15	1.58384	0.791921	−	0.610623i	$-0.209081\pi$
$607$	3.21551e15	1.58384	0.791921	+	0.610623i	$0.209081\pi$
$608$	1.92813e15	0.941168
$609$	5.44024e12	0.00263162
$610$	1.49698e15	0.717633
$611$	−9.00956e13	−0.0428033
$612$	3.36889e14	0.158619
$613$	3.43995e15	1.60517	0.802583	−	0.596541i	$-0.203459\pi$
$613$	3.43995e15	1.60517	0.802583	+	0.596541i	$0.203459\pi$
$614$	7.25816e14	0.335661
$615$	−1.67783e15	−0.769015
$616$	1.17155e13	0.00532192
$617$	−2.37363e15	−1.06867	−0.534337	−	0.845272i	$-0.679439\pi$
$617$	−2.37363e15	−1.06867	−0.534337	+	0.845272i	$0.679439\pi$
$618$	−9.62530e14	−0.429515
$619$	−5.35918e14	−0.237028	−0.118514	−	0.992952i	$-0.537813\pi$
$619$	−5.35918e14	−0.237028	−0.118514	+	0.992952i	$0.537813\pi$
$620$	7.75149e14	0.339806
$621$	2.65483e12	0.00115354
$622$	−1.62203e14	−0.0698573
$623$	2.99271e13	0.0127756
$624$	−1.78139e13	−0.00753777
$625$	−2.89330e15	−1.21354
$626$	−1.28291e15	−0.533381
$627$	−3.58158e14	−0.147606
$628$	2.09499e15	0.855863
$629$	2.35197e15	0.952474
$630$	−1.07916e13	−0.00433224
$631$	1.90985e15	0.760044	0.380022	−	0.924978i	$-0.375916\pi$
$631$	1.90985e15	0.760044	0.380022	+	0.924978i	$0.375916\pi$
$632$	−2.73884e15	−1.08049
$633$	−2.30470e15	−0.901352
$634$	−3.97305e14	−0.154040
$635$	−3.06440e15	−1.17785
$636$	−1.14285e15	−0.435487
$637$	5.89739e13	0.0222788
$638$	−3.92925e13	−0.0147162
$639$	2.21472e14	0.0822365
$640$	3.16371e15	1.16468
$641$	4.57415e15	1.66952	0.834760	−	0.550614i	$-0.185606\pi$
$641$	4.57415e15	1.66952	0.834760	+	0.550614i	$0.185606\pi$
$642$	6.54696e14	0.236918
$643$	−6.28032e14	−0.225331	−0.112666	−	0.993633i	$-0.535939\pi$
$643$	−6.28032e14	−0.225331	−0.112666	+	0.993633i	$0.535939\pi$
$644$	−4.29371e11	−0.000152743 0
$645$	1.94565e15	0.686257
$646$	−6.13919e14	−0.214700
$647$	−4.79908e15	−1.66412	−0.832060	−	0.554686i	$-0.812838\pi$
$647$	−4.79908e15	−1.66412	−0.832060	+	0.554686i	$0.812838\pi$
$648$	2.28399e14	0.0785292
$649$	−9.64573e13	−0.0328844
$650$	7.76804e12	0.00262596
$651$	−1.78402e13	−0.00598003
$652$	2.92832e15	0.973322
$653$	−3.50364e15	−1.15478	−0.577388	−	0.816470i	$-0.695928\pi$
$653$	−3.50364e15	−1.15478	−0.577388	+	0.816470i	$0.695928\pi$
$654$	9.26687e14	0.302869
$655$	3.28162e15	1.06356
$656$	−2.12086e15	−0.681619
$657$	−1.39420e15	−0.444341
$658$	−6.89915e13	−0.0218048
$659$	3.69398e15	1.15778	0.578889	−	0.815407i	$-0.303487\pi$
$659$	3.69398e15	1.15778	0.578889	+	0.815407i	$0.303487\pi$
$660$	−4.58873e14	−0.142627
$661$	−3.57572e15	−1.10219	−0.551093	−	0.834444i	$-0.685789\pi$
$661$	−3.57572e15	−1.10219	−0.551093	+	0.834444i	$0.685789\pi$
$662$	1.76360e14	0.0539114
$663$	2.36402e13	0.00716683
$664$	1.40470e15	0.422336
$665$	−1.15778e14	−0.0345228
$666$	7.34864e14	0.217320
$667$	3.12472e12	0.000916471 0
$668$	2.42807e15	0.706303
$669$	3.70822e15	1.06985
$670$	−2.22797e15	−0.637527
$671$	−1.46500e15	−0.415780
$672$	−5.68550e13	−0.0160043
$673$	−1.82280e15	−0.508927	−0.254464	−	0.967082i	$-0.581899\pi$
$673$	−1.82280e15	−0.508927	−0.254464	+	0.967082i	$0.581899\pi$
$674$	4.40267e14	0.121923
$675$	2.16532e14	0.0594774
$676$	3.13587e15	0.854380
$677$	−3.90103e15	−1.05424	−0.527122	−	0.849789i	$-0.676729\pi$
$677$	−3.90103e15	−1.05424	−0.527122	+	0.849789i	$0.676729\pi$
$678$	−1.52465e15	−0.408701
$679$	−4.34437e13	−0.0115516
$680$	−1.70671e15	−0.450154
$681$	2.99472e14	0.0783514
$682$	1.28852e14	0.0334407
$683$	−1.94562e15	−0.500891	−0.250446	−	0.968131i	$-0.580577\pi$
$683$	−1.94562e15	−0.500891	−0.250446	+	0.968131i	$0.580577\pi$
$684$	1.12928e15	0.288399
$685$	1.66960e15	0.422976
$686$	9.03596e13	0.0227087
$687$	2.27076e14	0.0566120
$688$	2.45940e15	0.608266
$689$	−8.01960e13	−0.0196765
$690$	−6.19837e12	−0.00150872
$691$	−6.12024e15	−1.47788	−0.738941	−	0.673771i	$-0.764674\pi$
$691$	−6.12024e15	−1.47788	−0.738941	+	0.673771i	$0.764674\pi$
$692$	6.13938e15	1.47076
$693$	1.05610e13	0.00251000
$694$	−1.59121e15	−0.375190
$695$	3.59557e15	0.841107
$696$	2.68824e14	0.0623904
$697$	2.81453e15	0.648075
$698$	−1.41112e15	−0.322374
$699$	−2.68802e15	−0.609267
$700$	−3.50203e13	−0.00787553
$701$	6.24454e15	1.39332	0.696661	−	0.717401i	$-0.254668\pi$
$701$	6.24454e15	1.39332	0.696661	+	0.717401i	$0.254668\pi$
$702$	7.38629e12	0.00163521
$703$	7.88400e15	1.73178
$704$	−2.67924e14	−0.0583931
$705$	5.86349e15	1.26799
$706$	−2.83375e15	−0.608046
$707$	1.10435e14	0.0235126
$708$	3.04133e14	0.0642511
$709$	1.48232e15	0.310734	0.155367	−	0.987857i	$-0.450344\pi$
$709$	1.48232e15	0.310734	0.155367	+	0.987857i	$0.450344\pi$
$710$	−5.17084e14	−0.107557
$711$	−2.46894e15	−0.509598
$712$	1.47882e15	0.302883
$713$	−1.02469e13	−0.00208257
$714$	1.81027e13	0.00365092
$715$	−3.22000e13	−0.00644426
$716$	7.50680e15	1.49085
$717$	−4.35466e15	−0.858220
$718$	−7.61366e14	−0.148905
$719$	−8.47515e15	−1.64490	−0.822448	−	0.568840i	$-0.807393\pi$
$719$	−8.47515e15	−1.64490	−0.822448	+	0.568840i	$0.807393\pi$
$720$	1.15934e15	0.223297
$721$	3.04499e14	0.0582026
$722$	−4.91396e13	−0.00932131
$723$	−2.29765e14	−0.0432538
$724$	2.31106e15	0.431767
$725$	2.54857e14	0.0472540
$726$	1.11927e15	0.205960
$727$	1.05823e16	1.93260	0.966301	−	0.257415i	$-0.0828706\pi$
$727$	1.05823e16	1.93260	0.966301	+	0.257415i	$0.0828706\pi$
$728$	−2.59212e12	−0.000469820 0
$729$	2.05891e14	0.0370370
$730$	3.25513e15	0.581155
$731$	−3.26380e15	−0.578332
$732$	4.61919e15	0.812372
$733$	6.21466e15	1.08479	0.542395	−	0.840124i	$-0.317518\pi$
$733$	6.21466e15	1.08479	0.542395	+	0.840124i	$0.317518\pi$
$734$	1.47075e15	0.254806
$735$	−3.83806e15	−0.659982
$736$	−3.26559e13	−0.00557357
$737$	2.18037e15	0.369368
$738$	8.79389e14	0.147867
$739$	−9.46484e14	−0.157968	−0.0789840	−	0.996876i	$-0.525168\pi$
$739$	−9.46484e14	−0.157968	−0.0789840	+	0.996876i	$0.525168\pi$
$740$	1.01010e16	1.67336
$741$	7.92440e13	0.0130307
$742$	−6.14108e13	−0.0100236
$743$	2.09825e15	0.339953	0.169977	−	0.985448i	$-0.445631\pi$
$743$	2.09825e15	0.339953	0.169977	+	0.985448i	$0.445631\pi$
$744$	−8.81555e14	−0.141775
$745$	1.42235e14	0.0227063
$746$	−3.90222e15	−0.618370
$747$	1.26627e15	0.199188
$748$	7.69751e14	0.120196
$749$	−2.07115e14	−0.0321042
$750$	1.13025e15	0.173915
$751$	5.77633e14	0.0882332	0.0441166	−	0.999026i	$-0.485953\pi$
$751$	5.77633e14	0.0882332	0.0441166	+	0.999026i	$0.485953\pi$
$752$	7.41175e15	1.12389
$753$	−2.89862e15	−0.436333
$754$	8.69363e12	0.00129915
$755$	−1.27795e16	−1.89585
$756$	−3.32992e13	−0.00490416
$757$	5.59338e15	0.817800	0.408900	−	0.912579i	$-0.365913\pi$
$757$	5.59338e15	0.817800	0.408900	+	0.912579i	$0.365913\pi$
$758$	−3.81776e14	−0.0554150
$759$	6.06595e12	0.000874116 0
$760$	−5.72105e15	−0.818466
$761$	−1.23287e16	−1.75107	−0.875533	−	0.483158i	$-0.839490\pi$
$761$	−1.23287e16	−1.75107	−0.875533	+	0.483158i	$0.839490\pi$
$762$	1.60612e15	0.226478
$763$	−2.93160e14	−0.0410412
$764$	−7.78626e14	−0.108222
$765$	−1.53852e15	−0.212308
$766$	4.43576e15	0.607728
$767$	2.13416e13	0.00290304
$768$	−6.69909e14	−0.0904751
$769$	7.07708e15	0.948985	0.474492	−	0.880260i	$-0.342632\pi$
$769$	7.07708e15	0.948985	0.474492	+	0.880260i	$0.342632\pi$
$770$	−2.46574e13	−0.00328283
$771$	4.18934e15	0.553792
$772$	7.71017e15	1.01197
$773$	7.41041e15	0.965728	0.482864	−	0.875695i	$-0.339597\pi$
$773$	7.41041e15	0.965728	0.482864	+	0.875695i	$0.339597\pi$
$774$	−1.01976e15	−0.131954
$775$	−8.35753e14	−0.107379
$776$	−2.14673e15	−0.273866
$777$	−2.32476e14	−0.0294485
$778$	−2.56844e15	−0.323059
$779$	9.43454e15	1.17832
$780$	1.01528e14	0.0125911
$781$	5.06037e14	0.0623163
$782$	1.03977e13	0.00127145
$783$	2.42333e14	0.0294254
$784$	−4.85151e15	−0.584977
$785$	−9.56751e15	−1.14555
$786$	−1.71997e15	−0.204502
$787$	−1.46049e16	−1.72440	−0.862200	−	0.506568i	$-0.830914\pi$
$787$	−1.46049e16	−1.72440	−0.862200	+	0.506568i	$0.830914\pi$
$788$	1.89199e15	0.221832
$789$	−3.16326e15	−0.368308
$790$	5.76437e15	0.666504
$791$	4.82326e14	0.0553822
$792$	5.21863e14	0.0595070
$793$	3.24138e14	0.0367052
$794$	5.45269e15	0.613194
$795$	5.21922e15	0.582890
$796$	−3.08987e15	−0.342703
$797$	1.41948e16	1.56353	0.781767	−	0.623571i	$-0.214319\pi$
$797$	1.41948e16	1.56353	0.781767	+	0.623571i	$0.214319\pi$
$798$	6.06817e13	0.00663808
$799$	−9.83590e15	−1.06858
$800$	−2.66347e15	−0.287378
$801$	1.33309e15	0.142850
$802$	−2.92522e15	−0.311315
$803$	−3.18558e15	−0.336708
$804$	−6.87478e15	−0.721690
$805$	1.96087e12	0.000204443 0
$806$	−2.85090e13	−0.00295216
$807$	5.82803e15	0.599401
$808$	5.45705e15	0.557436
$809$	−1.91599e15	−0.194391	−0.0971956	−	0.995265i	$-0.530987\pi$
$809$	−1.91599e15	−0.194391	−0.0971956	+	0.995265i	$0.530987\pi$
$810$	−4.80706e14	−0.0484409
$811$	1.00041e16	1.00130	0.500648	−	0.865651i	$-0.333095\pi$
$811$	1.00041e16	1.00130	0.500648	+	0.865651i	$0.333095\pi$
$812$	−3.91930e13	−0.00389629
$813$	2.08712e15	0.206086
$814$	1.67907e15	0.164678
$815$	−1.33732e16	−1.30277
$816$	−1.94477e15	−0.188180
$817$	−1.09405e16	−1.05152
$818$	2.67965e15	0.255820
$819$	−2.33667e12	−0.000221583 0
$820$	1.20876e16	1.13858
$821$	−1.46063e16	−1.36663	−0.683317	−	0.730122i	$-0.739463\pi$
$821$	−1.46063e16	−1.36663	−0.683317	+	0.730122i	$0.739463\pi$
$822$	−8.75078e14	−0.0813302
$823$	5.76089e15	0.531852	0.265926	−	0.963993i	$-0.414322\pi$
$823$	5.76089e15	0.531852	0.265926	+	0.963993i	$0.414322\pi$
$824$	1.50465e16	1.37987
$825$	4.94749e14	0.0450701
$826$	1.63425e13	0.00147887
$827$	1.07854e16	0.969519	0.484760	−	0.874647i	$-0.338907\pi$
$827$	1.07854e16	0.969519	0.484760	+	0.874647i	$0.338907\pi$
$828$	−1.91261e13	−0.00170789
$829$	−1.84718e15	−0.163854	−0.0819272	−	0.996638i	$-0.526108\pi$
$829$	−1.84718e15	−0.163854	−0.0819272	+	0.996638i	$0.526108\pi$
$830$	−2.95644e15	−0.260519
$831$	9.44703e15	0.826970
$832$	5.92793e13	0.00515495
$833$	6.43828e15	0.556189
$834$	−1.88452e15	−0.161729
$835$	−1.10886e16	−0.945372
$836$	2.58027e15	0.218540
$837$	−7.94681e14	−0.0668656
$838$	−9.68408e14	−0.0809499
$839$	−1.40672e16	−1.16820	−0.584100	−	0.811682i	$-0.698552\pi$
$839$	−1.40672e16	−1.16820	−0.584100	+	0.811682i	$0.698552\pi$
$840$	1.68697e14	0.0139178
$841$	−1.19153e16	−0.976622
$842$	−7.37708e14	−0.0600714
$843$	−1.31332e16	−1.06247
$844$	1.66037e16	1.33451
$845$	−1.43210e16	−1.14357
$846$	−3.07319e15	−0.243811
$847$	−3.54084e14	−0.0279092
$848$	6.59736e15	0.516646
$849$	−7.34161e15	−0.571214
$850$	8.48051e14	0.0655568
$851$	−1.33528e14	−0.0102555
$852$	−1.59555e15	−0.121757
$853$	2.39241e16	1.81391	0.906954	−	0.421230i	$-0.138401\pi$
$853$	2.39241e16	1.81391	0.906954	+	0.421230i	$0.138401\pi$
$854$	2.48211e14	0.0186983
$855$	−5.15726e15	−0.386016
$856$	−1.02344e16	−0.761125
$857$	2.19672e16	1.62323	0.811614	−	0.584194i	$-0.198589\pi$
$857$	2.19672e16	1.62323	0.811614	+	0.584194i	$0.198589\pi$
$858$	1.68768e13	0.00123911
$859$	−2.63625e14	−0.0192320	−0.00961601	−	0.999954i	$-0.503061\pi$
$859$	−2.63625e14	−0.0192320	−0.00961601	+	0.999954i	$0.503061\pi$
$860$	−1.40170e16	−1.01605
$861$	−2.78197e14	−0.0200371
$862$	3.82988e15	0.274092
$863$	−5.79310e14	−0.0411957	−0.0205978	−	0.999788i	$-0.506557\pi$
$863$	−5.79310e14	−0.0411957	−0.0205978	+	0.999788i	$0.506557\pi$
$864$	−2.53258e15	−0.178952
$865$	−2.80376e16	−1.96858
$866$	−7.54039e15	−0.526072
$867$	−5.74723e15	−0.398431
$868$	1.28526e14	0.00885383
$869$	−5.64122e15	−0.386157
$870$	−5.65788e14	−0.0384856
$871$	−4.82417e14	−0.0326079
$872$	−1.44862e16	−0.973004
$873$	−1.93518e15	−0.129164
$874$	3.48538e13	0.00231173
$875$	−3.57558e14	−0.0235669
$876$	1.00442e16	0.657876
$877$	−1.32387e16	−0.861680	−0.430840	−	0.902428i	$-0.641783\pi$
$877$	−1.32387e16	−0.861680	−0.430840	+	0.902428i	$0.641783\pi$
$878$	2.88467e15	0.186585
$879$	1.22442e16	0.787031
$880$	2.64895e15	0.169207
$881$	2.12452e16	1.34863	0.674317	−	0.738442i	$-0.264438\pi$
$881$	2.12452e16	1.34863	0.674317	+	0.738442i	$0.264438\pi$
$882$	2.01162e15	0.126902
$883$	6.50488e15	0.407807	0.203904	−	0.978991i	$-0.434637\pi$
$883$	6.50488e15	0.407807	0.203904	+	0.978991i	$0.434637\pi$
$884$	−1.70311e14	−0.0106110
$885$	−1.38893e15	−0.0859987
$886$	9.48869e15	0.583876
$887$	−1.40683e15	−0.0860326	−0.0430163	−	0.999074i	$-0.513697\pi$
$887$	−1.40683e15	−0.0860326	−0.0430163	+	0.999074i	$0.513697\pi$
$888$	−1.14876e16	−0.698164
$889$	−5.08101e14	−0.0306895
$890$	−3.11244e15	−0.186834
$891$	4.70436e14	0.0280655
$892$	−2.67150e16	−1.58398
$893$	−3.29708e16	−1.94288
$894$	−7.45485e13	−0.00436599
$895$	−3.42824e16	−1.99547
$896$	5.24567e14	0.0303464
$897$	−1.34212e12	−7.71671e−5 0
$898$	−2.08664e15	−0.119242
$899$	−9.35336e14	−0.0531238
$900$	−1.55996e15	−0.0880602
$901$	−8.75514e15	−0.491221
$902$	2.00930e15	0.112049
$903$	3.22604e14	0.0178808
$904$	2.38337e16	1.31300
$905$	−1.05543e16	−0.577911
$906$	6.69801e15	0.364536
$907$	4.31251e15	0.233287	0.116643	−	0.993174i	$-0.462787\pi$
$907$	4.31251e15	0.233287	0.116643	+	0.993174i	$0.462787\pi$
$908$	−2.15748e15	−0.116004
$909$	4.91928e15	0.262906
$910$	5.45557e12	0.000289809 0
$911$	−7.59414e14	−0.0400984	−0.0200492	−	0.999799i	$-0.506382\pi$
$911$	−7.59414e14	−0.0400984	−0.0200492	+	0.999799i	$0.506382\pi$
$912$	−6.51904e15	−0.342146
$913$	2.89327e15	0.150939
$914$	−1.12261e16	−0.582138
$915$	−2.10951e16	−1.08734
$916$	−1.63592e15	−0.0838179
$917$	5.44118e14	0.0277116
$918$	8.06375e14	0.0408228
$919$	2.69528e16	1.35634	0.678170	−	0.734905i	$-0.262773\pi$
$919$	2.69528e16	1.35634	0.678170	+	0.734905i	$0.262773\pi$
$920$	9.68946e13	0.00484693
$921$	−1.02280e16	−0.508586
$922$	−2.37983e15	−0.117632
$923$	−1.11963e14	−0.00550129
$924$	−7.60846e13	−0.00371622
$925$	−1.08907e16	−0.528784
$926$	3.08207e15	0.148758
$927$	1.35638e16	0.650791
$928$	−2.98083e15	−0.142175
$929$	−2.52655e16	−1.19796	−0.598980	−	0.800764i	$-0.704427\pi$
$929$	−2.52655e16	−1.19796	−0.598980	+	0.800764i	$0.704427\pi$
$930$	1.85539e15	0.0874538
$931$	2.15817e16	1.01126
$932$	1.93652e16	0.902060
$933$	2.28573e15	0.105846
$934$	−1.11433e16	−0.512986
$935$	−3.51533e15	−0.160880
$936$	−1.15465e14	−0.00525329
$937$	7.21858e15	0.326500	0.163250	−	0.986585i	$-0.447802\pi$
$937$	7.21858e15	0.326500	0.163250	+	0.986585i	$0.447802\pi$
$938$	−3.69415e14	−0.0166111
$939$	1.80785e16	0.808167
$940$	−4.22423e16	−1.87734
$941$	−1.23022e16	−0.543551	−0.271775	−	0.962361i	$-0.587611\pi$
$941$	−1.23022e16	−0.543551	−0.271775	+	0.962361i	$0.587611\pi$
$942$	5.01455e15	0.220268
$943$	−1.59788e14	−0.00697800
$944$	−1.75568e15	−0.0762252
$945$	1.52073e14	0.00656411
$946$	−2.33003e15	−0.0999907
$947$	−1.82694e16	−0.779470	−0.389735	−	0.920927i	$-0.627433\pi$
$947$	−1.82694e16	−0.779470	−0.389735	+	0.920927i	$0.627433\pi$
$948$	1.77869e16	0.754493
$949$	7.04824e14	0.0297246
$950$	2.84274e15	0.119195
$951$	5.59873e15	0.233398
$952$	−2.82986e14	−0.0117290
$953$	−4.67260e15	−0.192552	−0.0962759	−	0.995355i	$-0.530693\pi$
$953$	−4.67260e15	−0.192552	−0.0962759	+	0.995355i	$0.530693\pi$
$954$	−2.73551e15	−0.112079
$955$	3.55587e15	0.144853
$956$	3.13722e16	1.27065
$957$	5.53701e14	0.0222977
$958$	3.55556e15	0.142363
$959$	2.76833e14	0.0110209
$960$	−3.85794e15	−0.152709
$961$	−2.23412e16	−0.879283
$962$	−3.71502e14	−0.0145378
$963$	−9.22583e15	−0.358972
$964$	1.65530e15	0.0640401
$965$	−3.52112e16	−1.35450
$966$	−1.02774e12	−3.93105e−5 0
$967$	−3.47991e16	−1.32349	−0.661747	−	0.749727i	$-0.730185\pi$
$967$	−3.47991e16	−1.32349	−0.661747	+	0.749727i	$0.730185\pi$
$968$	−1.74967e16	−0.661671
$969$	8.65121e15	0.325309
$970$	4.51818e15	0.168935
$971$	1.97264e16	0.733402	0.366701	−	0.930339i	$-0.380487\pi$
$971$	1.97264e16	0.733402	0.366701	+	0.930339i	$0.380487\pi$
$972$	−1.48330e15	−0.0548358
$973$	5.96173e14	0.0219155
$974$	2.43456e15	0.0889909
$975$	−1.09465e14	−0.00397880
$976$	−2.66653e16	−0.963769
$977$	3.00929e16	1.08154	0.540771	−	0.841170i	$-0.318133\pi$
$977$	3.00929e16	1.08154	0.540771	+	0.841170i	$0.318133\pi$
$978$	7.00919e15	0.250498
$979$	3.04594e15	0.108247
$980$	2.76505e16	0.977147
$981$	−1.30587e16	−0.458901
$982$	3.98454e15	0.139240
$983$	4.40527e16	1.53084	0.765418	−	0.643533i	$-0.222532\pi$
$983$	4.40527e16	1.53084	0.765418	+	0.643533i	$0.222532\pi$
$984$	−1.37468e16	−0.475040
$985$	−8.64041e15	−0.296917
$986$	9.49100e14	0.0324331
$987$	9.72212e14	0.0330382
$988$	−5.70896e14	−0.0192927
$989$	1.85294e14	0.00622706
$990$	−1.09835e15	−0.0367070
$991$	3.88270e14	0.0129041	0.00645206	−	0.999979i	$-0.497946\pi$
$991$	3.88270e14	0.0129041	0.00645206	+	0.999979i	$0.497946\pi$
$992$	9.77503e15	0.323076
$993$	−2.48522e15	−0.0816855
$994$	−8.57365e13	−0.00280247
$995$	1.41110e16	0.458701
$996$	−9.12258e15	−0.294911
$997$	5.91431e15	0.190143	0.0950715	−	0.995470i	$-0.469692\pi$
$997$	5.91431e15	0.190143	0.0950715	+	0.995470i	$0.469692\pi$
$998$	−8.79096e15	−0.281072
$999$	−1.03555e16	−0.329278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.13	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.13	✓	27	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-17.2441 q^{2} +243.000 q^{3} -1750.64 q^{4} +7994.91 q^{5} -4190.32 q^{6} +1325.62 q^{7} +65504.2 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-17.2441 q^{2} +243.000 q^{3} -1750.64 q^{4} +7994.91 q^{5} -4190.32 q^{6} +1325.62 q^{7} +65504.2 q^{8} +59049.0 q^{9} -137865. q^{10} +134920. q^{11} -425406. q^{12} -29851.6 q^{13} -22859.1 q^{14} +1.94276e6 q^{15} +2.45575e6 q^{16} -3.25895e6 q^{17} -1.01825e6 q^{18} -1.09243e7 q^{19} -1.39962e7 q^{20} +322125. q^{21} -2.32657e6 q^{22} +185019. q^{23} +1.59175e7 q^{24} +1.50905e7 q^{25} +514764. q^{26} +1.43489e7 q^{27} -2.32068e6 q^{28} +1.68886e7 q^{29} -3.35012e7 q^{30} -5.53827e7 q^{31} -1.76500e8 q^{32} +3.27855e7 q^{33} +5.61977e7 q^{34} +1.05982e7 q^{35} -1.03374e8 q^{36} -7.21695e8 q^{37} +1.88379e8 q^{38} -7.25393e6 q^{39} +5.23700e8 q^{40} -8.63631e8 q^{41} -5.55476e6 q^{42} +1.00149e9 q^{43} -2.36196e8 q^{44} +4.72092e8 q^{45} -3.19049e6 q^{46} +3.01812e9 q^{47} +5.96748e8 q^{48} -1.97557e9 q^{49} -2.60222e8 q^{50} -7.91925e8 q^{51} +5.22594e7 q^{52} +2.68649e9 q^{53} -2.47434e8 q^{54} +1.07867e9 q^{55} +8.68335e7 q^{56} -2.65460e9 q^{57} -2.91229e8 q^{58} -7.14924e8 q^{59} -3.40108e9 q^{60} -1.08583e10 q^{61} +9.55025e8 q^{62} +7.82764e7 q^{63} -1.98580e9 q^{64} -2.38661e8 q^{65} -5.65356e8 q^{66} +1.61605e10 q^{67} +5.70525e9 q^{68} +4.49597e7 q^{69} -1.82756e8 q^{70} +3.75065e9 q^{71} +3.86795e9 q^{72} -2.36110e10 q^{73} +1.24450e10 q^{74} +3.66699e9 q^{75} +1.91245e10 q^{76} +1.78852e8 q^{77} +1.25088e8 q^{78} -4.18117e10 q^{79} +1.96335e10 q^{80} +3.48678e9 q^{81} +1.48925e10 q^{82} +2.14444e10 q^{83} -5.63926e8 q^{84} -2.60550e10 q^{85} -1.72697e10 q^{86} +4.10393e9 q^{87} +8.83780e9 q^{88} +2.25760e10 q^{89} -8.14080e9 q^{90} -3.95718e7 q^{91} -3.23902e8 q^{92} -1.34580e10 q^{93} -5.20448e10 q^{94} -8.73387e10 q^{95} -4.28894e10 q^{96} -3.27724e10 q^{97} +3.40669e10 q^{98} +7.96687e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \)	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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