LMFDB - Embedded newform 177.12.a.a.1.19

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:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q+38.1800 q^{2} -243.000 q^{3} -590.285 q^{4} +118.373 q^{5} -9277.75 q^{6} -24998.6 q^{7} -100730. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+38.1800 q^{2} -243.000 q^{3} -590.285 q^{4} +118.373 q^{5} -9277.75 q^{6} -24998.6 q^{7} -100730. q^{8} +59049.0 q^{9} +4519.50 q^{10} +78307.6 q^{11} +143439. q^{12} +516458. q^{13} -954447. q^{14} -28764.7 q^{15} -2.63696e6 q^{16} +707304. q^{17} +2.25449e6 q^{18} +1.93229e7 q^{19} -69874.0 q^{20} +6.07465e6 q^{21} +2.98979e6 q^{22} -4.56770e6 q^{23} +2.44773e7 q^{24} -4.88141e7 q^{25} +1.97184e7 q^{26} -1.43489e7 q^{27} +1.47563e7 q^{28} +1.21637e8 q^{29} -1.09824e6 q^{30} +5.43729e7 q^{31} +1.05615e8 q^{32} -1.90288e7 q^{33} +2.70049e7 q^{34} -2.95916e6 q^{35} -3.48557e7 q^{36} +3.64765e8 q^{37} +7.37749e8 q^{38} -1.25499e8 q^{39} -1.19237e7 q^{40} -9.48045e7 q^{41} +2.31931e8 q^{42} -1.12923e9 q^{43} -4.62238e7 q^{44} +6.98983e6 q^{45} -1.74395e8 q^{46} -1.05885e9 q^{47} +6.40782e8 q^{48} -1.35240e9 q^{49} -1.86372e9 q^{50} -1.71875e8 q^{51} -3.04857e8 q^{52} +1.10685e9 q^{53} -5.47842e8 q^{54} +9.26954e6 q^{55} +2.51810e9 q^{56} -4.69546e9 q^{57} +4.64409e9 q^{58} +7.14924e8 q^{59} +1.69794e7 q^{60} +9.70538e9 q^{61} +2.07596e9 q^{62} -1.47614e9 q^{63} +9.43290e9 q^{64} +6.11348e7 q^{65} -7.26519e8 q^{66} -1.88824e10 q^{67} -4.17511e8 q^{68} +1.10995e9 q^{69} -1.12981e8 q^{70} -1.71949e9 q^{71} -5.94799e9 q^{72} -6.45985e9 q^{73} +1.39268e10 q^{74} +1.18618e10 q^{75} -1.14060e10 q^{76} -1.95758e9 q^{77} -4.79157e9 q^{78} +3.94200e9 q^{79} -3.12146e8 q^{80} +3.48678e9 q^{81} -3.61964e9 q^{82} +1.19778e10 q^{83} -3.58578e9 q^{84} +8.37260e7 q^{85} -4.31142e10 q^{86} -2.95577e10 q^{87} -7.88791e9 q^{88} +2.13002e10 q^{89} +2.66872e8 q^{90} -1.29107e10 q^{91} +2.69624e9 q^{92} -1.32126e10 q^{93} -4.04270e10 q^{94} +2.28732e9 q^{95} -2.56645e10 q^{96} -4.49781e10 q^{97} -5.16346e10 q^{98} +4.62399e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) $	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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 $

$2$	38.1800	0.843668	0.421834	−	0.906673i	$-0.361387\pi$
$2$	38.1800	0.843668	0.421834	+	0.906673i	$0.361387\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−590.285	−0.288225
$5$	118.373	0.0169402	0.00847011	−	0.999964i	$-0.497304\pi$
$5$	118.373	0.0169402	0.00847011	+	0.999964i	$0.497304\pi$
$6$	−9277.75	−0.487092
$7$	−24998.6	−0.562181	−0.281090	−	0.959681i	$-0.590696\pi$
$7$	−24998.6	−0.562181	−0.281090	+	0.959681i	$0.590696\pi$
$8$	−100730.	−1.08683
$9$	59049.0	0.333333
$10$	4519.50	0.0142919
$11$	78307.6	0.146604	0.0733018	−	0.997310i	$-0.476646\pi$
$11$	78307.6	0.146604	0.0733018	+	0.997310i	$0.476646\pi$
$12$	143439.	0.166407
$13$	516458.	0.385786	0.192893	−	0.981220i	$-0.438213\pi$
$13$	516458.	0.385786	0.192893	+	0.981220i	$0.438213\pi$
$14$	−954447.	−0.474294
$15$	−28764.7	−0.00978044
$16$	−2.63696e6	−0.628701
$17$	707304.	0.120820	0.0604098	−	0.998174i	$-0.480759\pi$
$17$	707304.	0.120820	0.0604098	+	0.998174i	$0.480759\pi$
$18$	2.25449e6	0.281223
$19$	1.93229e7	1.79031	0.895153	−	0.445758i	$-0.147066\pi$
$19$	1.93229e7	1.79031	0.895153	+	0.445758i	$0.147066\pi$
$20$	−69874.0	−0.00488259
$21$	6.07465e6	0.324575
$22$	2.98979e6	0.123685
$23$	−4.56770e6	−0.147977	−0.0739885	−	0.997259i	$-0.523573\pi$
$23$	−4.56770e6	−0.147977	−0.0739885	+	0.997259i	$0.523573\pi$
$24$	2.44773e7	0.627484
$25$	−4.88141e7	−0.999713
$26$	1.97184e7	0.325475
$27$	−1.43489e7	−0.192450
$28$	1.47563e7	0.162035
$29$	1.21637e8	1.10122	0.550612	−	0.834761i	$-0.314394\pi$
$29$	1.21637e8	1.10122	0.550612	+	0.834761i	$0.314394\pi$
$30$	−1.09824e6	−0.00825144
$31$	5.43729e7	0.341109	0.170555	−	0.985348i	$-0.445444\pi$
$31$	5.43729e7	0.341109	0.170555	+	0.985348i	$0.445444\pi$
$32$	1.05615e8	0.556419
$33$	−1.90288e7	−0.0846416
$34$	2.70049e7	0.101932
$35$	−2.95916e6	−0.00952346
$36$	−3.48557e7	−0.0960750
$37$	3.64765e8	0.864777	0.432388	−	0.901687i	$-0.357671\pi$
$37$	3.64765e8	0.864777	0.432388	+	0.901687i	$0.357671\pi$
$38$	7.37749e8	1.51042
$39$	−1.25499e8	−0.222734
$40$	−1.19237e7	−0.0184112
$41$	−9.48045e7	−0.127796	−0.0638980	−	0.997956i	$-0.520353\pi$
$41$	−9.48045e7	−0.127796	−0.0638980	+	0.997956i	$0.520353\pi$
$42$	2.31931e8	0.273834
$43$	−1.12923e9	−1.17141	−0.585703	−	0.810526i	$-0.699182\pi$
$43$	−1.12923e9	−1.17141	−0.585703	+	0.810526i	$0.699182\pi$
$44$	−4.62238e7	−0.0422548
$45$	6.98983e6	0.00564674
$46$	−1.74395e8	−0.124843
$47$	−1.05885e9	−0.673437	−0.336719	−	0.941605i	$-0.609317\pi$
$47$	−1.05885e9	−0.673437	−0.336719	+	0.941605i	$0.609317\pi$
$48$	6.40782e8	0.362981
$49$	−1.35240e9	−0.683953
$50$	−1.86372e9	−0.843426
$51$	−1.71875e8	−0.0697552
$52$	−3.04857e8	−0.111193
$53$	1.10685e9	0.363555	0.181778	−	0.983340i	$-0.441815\pi$
$53$	1.10685e9	0.363555	0.181778	+	0.983340i	$0.441815\pi$
$54$	−5.47842e8	−0.162364
$55$	9.26954e6	0.00248349
$56$	2.51810e9	0.610997
$57$	−4.69546e9	−1.03363
$58$	4.64409e9	0.929067
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	1.69794e7	0.00281897
$61$	9.70538e9	1.47129	0.735645	−	0.677367i	$-0.236879\pi$
$61$	9.70538e9	1.47129	0.735645	+	0.677367i	$0.236879\pi$
$62$	2.07596e9	0.287783
$63$	−1.47614e9	−0.187394
$64$	9.43290e9	1.09813
$65$	6.11348e7	0.00653529
$66$	−7.26519e8	−0.0714094
$67$	−1.88824e10	−1.70862	−0.854311	−	0.519762i	$-0.826020\pi$
$67$	−1.88824e10	−1.70862	−0.854311	+	0.519762i	$0.826020\pi$
$68$	−4.17511e8	−0.0348232
$69$	1.10995e9	0.0854346
$70$	−1.12981e8	−0.00803464
$71$	−1.71949e9	−0.113104	−0.0565520	−	0.998400i	$-0.518011\pi$
$71$	−1.71949e9	−0.113104	−0.0565520	+	0.998400i	$0.518011\pi$
$72$	−5.94799e9	−0.362278
$73$	−6.45985e9	−0.364709	−0.182354	−	0.983233i	$-0.558372\pi$
$73$	−6.45985e9	−0.364709	−0.182354	+	0.983233i	$0.558372\pi$
$74$	1.39268e10	0.729584
$75$	1.18618e10	0.577185
$76$	−1.14060e10	−0.516011
$77$	−1.95758e9	−0.0824177
$78$	−4.79157e9	−0.187913
$79$	3.94200e9	0.144134	0.0720671	−	0.997400i	$-0.477040\pi$
$79$	3.94200e9	0.144134	0.0720671	+	0.997400i	$0.477040\pi$
$80$	−3.12146e8	−0.0106503
$81$	3.48678e9	0.111111
$82$	−3.61964e9	−0.107817
$83$	1.19778e10	0.333771	0.166885	−	0.985976i	$-0.446629\pi$
$83$	1.19778e10	0.333771	0.166885	+	0.985976i	$0.446629\pi$
$84$	−3.58578e9	−0.0935507
$85$	8.37260e7	0.00204671
$86$	−4.31142e10	−0.988278
$87$	−2.95577e10	−0.635792
$88$	−7.88791e9	−0.159334
$89$	2.13002e10	0.404332	0.202166	−	0.979351i	$-0.435202\pi$
$89$	2.13002e10	0.404332	0.202166	+	0.979351i	$0.435202\pi$
$90$	2.66872e8	0.00476397
$91$	−1.29107e10	−0.216881
$92$	2.69624e9	0.0426507
$93$	−1.32126e10	−0.196940
$94$	−4.04270e10	−0.568157
$95$	2.28732e9	0.0303282
$96$	−2.56645e10	−0.321248
$97$	−4.49781e10	−0.531810	−0.265905	−	0.963999i	$-0.585671\pi$
$97$	−4.49781e10	−0.531810	−0.265905	+	0.963999i	$0.585671\pi$
$98$	−5.16346e10	−0.577029
$99$	4.62399e9	0.0488678
$100$	2.88142e10	0.288142
$101$	−6.75570e10	−0.639592	−0.319796	−	0.947486i	$-0.603614\pi$
$101$	−6.75570e10	−0.639592	−0.319796	+	0.947486i	$0.603614\pi$
$102$	−6.56219e9	−0.0588502
$103$	−9.45356e9	−0.0803509	−0.0401755	−	0.999193i	$-0.512792\pi$
$103$	−9.45356e9	−0.0803509	−0.0401755	+	0.999193i	$0.512792\pi$
$104$	−5.20227e10	−0.419285
$105$	7.19077e8	0.00549837
$106$	4.22595e10	0.306720
$107$	−2.46903e11	−1.70182	−0.850912	−	0.525308i	$-0.823950\pi$
$107$	−2.46903e11	−1.70182	−0.850912	+	0.525308i	$0.823950\pi$
$108$	8.46994e9	0.0554689
$109$	−6.18565e10	−0.385070	−0.192535	−	0.981290i	$-0.561671\pi$
$109$	−6.18565e10	−0.385070	−0.192535	+	0.981290i	$0.561671\pi$
$110$	3.53911e8	0.00209524
$111$	−8.86380e10	−0.499279
$112$	6.59204e10	0.353444
$113$	−2.13710e11	−1.09117	−0.545586	−	0.838055i	$-0.683693\pi$
$113$	−2.13710e11	−1.09117	−0.545586	+	0.838055i	$0.683693\pi$
$114$	−1.79273e11	−0.872043
$115$	−5.40694e8	−0.00250676
$116$	−7.18003e10	−0.317400
$117$	3.04963e10	0.128595
$118$	2.72958e10	0.109836
$119$	−1.76816e10	−0.0679224
$120$	2.89746e9	0.0106297
$121$	−2.79180e11	−0.978507
$122$	3.70552e11	1.24128
$123$	2.30375e10	0.0737831
$124$	−3.20955e10	−0.0983162
$125$	−1.15582e10	−0.0338756
$126$	−5.63591e10	−0.158098
$127$	2.58686e11	0.694787	0.347394	−	0.937719i	$-0.387067\pi$
$127$	2.58686e11	0.694787	0.347394	+	0.937719i	$0.387067\pi$
$128$	1.43848e11	0.370041
$129$	2.74404e11	0.676312
$130$	2.33413e9	0.00551362
$131$	−4.89314e10	−0.110814	−0.0554071	−	0.998464i	$-0.517646\pi$
$131$	−4.89314e10	−0.110814	−0.0554071	+	0.998464i	$0.517646\pi$
$132$	1.12324e10	0.0243958
$133$	−4.83045e11	−1.00648
$134$	−7.20931e11	−1.44151
$135$	−1.69853e9	−0.00326015
$136$	−7.12466e10	−0.131311
$137$	−3.61771e11	−0.640429	−0.320214	−	0.947345i	$-0.603755\pi$
$137$	−3.61771e11	−0.640429	−0.320214	+	0.947345i	$0.603755\pi$
$138$	4.23780e10	0.0720784
$139$	−5.60774e11	−0.916657	−0.458328	−	0.888783i	$-0.651552\pi$
$139$	−5.60774e11	−0.916657	−0.458328	+	0.888783i	$0.651552\pi$
$140$	1.74675e9	0.00274490
$141$	2.57301e11	0.388809
$142$	−6.56501e10	−0.0954223
$143$	4.04426e10	0.0565576
$144$	−1.55710e11	−0.209567
$145$	1.43985e10	0.0186550
$146$	−2.46637e11	−0.307693
$147$	3.28633e11	0.394880
$148$	−2.15315e11	−0.249250
$149$	1.48332e11	0.165467	0.0827333	−	0.996572i	$-0.473635\pi$
$149$	1.48332e11	0.165467	0.0827333	+	0.996572i	$0.473635\pi$
$150$	4.52885e11	0.486952
$151$	7.02729e11	0.728475	0.364238	−	0.931306i	$-0.381330\pi$
$151$	7.02729e11	0.728475	0.364238	+	0.931306i	$0.381330\pi$
$152$	−1.94639e12	−1.94577
$153$	4.17656e10	0.0402732
$154$	−7.47405e10	−0.0695331
$155$	6.43631e9	0.00577846
$156$	7.40803e10	0.0641974
$157$	−6.12975e11	−0.512855	−0.256428	−	0.966563i	$-0.582546\pi$
$157$	−6.12975e11	−0.512855	−0.256428	+	0.966563i	$0.582546\pi$
$158$	1.50506e11	0.121601
$159$	−2.68964e11	−0.209899
$160$	1.25020e10	0.00942585
$161$	1.14186e11	0.0831899
$162$	1.33126e11	0.0937408
$163$	6.05132e11	0.411925	0.205962	−	0.978560i	$-0.433968\pi$
$163$	6.05132e11	0.411925	0.205962	+	0.978560i	$0.433968\pi$
$164$	5.59616e10	0.0368340
$165$	−2.25250e9	−0.00143385
$166$	4.57314e11	0.281592
$167$	1.19419e12	0.711429	0.355714	−	0.934595i	$-0.384238\pi$
$167$	1.19419e12	0.711429	0.355714	+	0.934595i	$0.384238\pi$
$168$	−6.11899e11	−0.352759
$169$	−1.52543e12	−0.851169
$170$	3.19666e9	0.00172674
$171$	1.14100e12	0.596769
$172$	6.66570e11	0.337629
$173$	−4.78670e11	−0.234846	−0.117423	−	0.993082i	$-0.537463\pi$
$173$	−4.78670e11	−0.234846	−0.117423	+	0.993082i	$0.537463\pi$
$174$	−1.12851e12	−0.536397
$175$	1.22028e12	0.562020
$176$	−2.06495e11	−0.0921698
$177$	−1.73727e11	−0.0751646
$178$	8.13241e11	0.341122
$179$	−2.16926e12	−0.882308	−0.441154	−	0.897431i	$-0.645431\pi$
$179$	−2.16926e12	−0.882308	−0.441154	+	0.897431i	$0.645431\pi$
$180$	−4.12599e9	−0.00162753
$181$	1.23590e12	0.472881	0.236441	−	0.971646i	$-0.424019\pi$
$181$	1.23590e12	0.472881	0.236441	+	0.971646i	$0.424019\pi$
$182$	−4.92931e11	−0.182976
$183$	−2.35841e12	−0.849450
$184$	4.60104e11	0.160826
$185$	4.31785e10	0.0146495
$186$	−5.04458e11	−0.166151
$187$	5.53873e10	0.0177126
$188$	6.25024e11	0.194101
$189$	3.58702e11	0.108192
$190$	8.73298e10	0.0255869
$191$	3.89010e12	1.10733	0.553665	−	0.832740i	$-0.313229\pi$
$191$	3.89010e12	1.10733	0.553665	+	0.832740i	$0.313229\pi$
$192$	−2.29219e12	−0.634008
$193$	−3.05506e12	−0.821210	−0.410605	−	0.911813i	$-0.634682\pi$
$193$	−3.05506e12	−0.821210	−0.410605	+	0.911813i	$0.634682\pi$
$194$	−1.71726e12	−0.448671
$195$	−1.48558e10	−0.00377315
$196$	7.98300e11	0.197132
$197$	−5.41761e12	−1.30090	−0.650450	−	0.759549i	$-0.725419\pi$
$197$	−5.41761e12	−1.30090	−0.650450	+	0.759549i	$0.725419\pi$
$198$	1.76544e11	0.0412282
$199$	2.53133e12	0.574986	0.287493	−	0.957783i	$-0.407178\pi$
$199$	2.53133e12	0.574986	0.287493	+	0.957783i	$0.407178\pi$
$200$	4.91704e12	1.08652
$201$	4.58842e12	0.986473
$202$	−2.57933e12	−0.539603
$203$	−3.04074e12	−0.619087
$204$	1.01455e11	0.0201052
$205$	−1.12223e10	−0.00216489
$206$	−3.60937e11	−0.0677895
$207$	−2.69718e11	−0.0493257
$208$	−1.36188e12	−0.242544
$209$	1.51313e12	0.262465
$210$	2.74544e10	0.00463880
$211$	−8.82774e12	−1.45310	−0.726551	−	0.687112i	$-0.758878\pi$
$211$	−8.82774e12	−1.45310	−0.726551	+	0.687112i	$0.758878\pi$
$212$	−6.53355e11	−0.104786
$213$	4.17836e11	0.0653007
$214$	−9.42675e12	−1.43577
$215$	−1.33671e11	−0.0198439
$216$	1.44536e12	0.209161
$217$	−1.35925e12	−0.191765
$218$	−2.36169e12	−0.324871
$219$	1.56974e12	0.210565
$220$	−5.47167e9	−0.000715805 0
$221$	3.65293e11	0.0466105
$222$	−3.38420e12	−0.421226
$223$	−1.48106e11	−0.0179844	−0.00899218	−	0.999960i	$-0.502862\pi$
$223$	−1.48106e11	−0.0179844	−0.00899218	+	0.999960i	$0.502862\pi$
$224$	−2.64023e12	−0.312808
$225$	−2.88242e12	−0.333238
$226$	−8.15946e12	−0.920587
$227$	−1.46590e13	−1.61422	−0.807111	−	0.590400i	$-0.798970\pi$
$227$	−1.46590e13	−1.61422	−0.807111	+	0.590400i	$0.798970\pi$
$228$	2.77166e12	0.297919
$229$	1.16723e13	1.22478	0.612392	−	0.790554i	$-0.290207\pi$
$229$	1.16723e13	1.22478	0.612392	+	0.790554i	$0.290207\pi$
$230$	−2.06437e10	−0.00211487
$231$	4.75692e11	0.0475839
$232$	−1.22524e13	−1.19685
$233$	−7.50544e12	−0.716009	−0.358005	−	0.933720i	$-0.616543\pi$
$233$	−7.50544e12	−0.716009	−0.358005	+	0.933720i	$0.616543\pi$
$234$	1.16435e12	0.108492
$235$	−1.25340e11	−0.0114082
$236$	−4.22009e11	−0.0375237
$237$	−9.57905e11	−0.0832159
$238$	−6.75084e11	−0.0573040
$239$	4.48254e12	0.371823	0.185911	−	0.982567i	$-0.440476\pi$
$239$	4.48254e12	0.371823	0.185911	+	0.982567i	$0.440476\pi$
$240$	7.58515e10	0.00614897
$241$	2.28198e13	1.80808	0.904041	−	0.427445i	$-0.140586\pi$
$241$	2.28198e13	1.80808	0.904041	+	0.427445i	$0.140586\pi$
$242$	−1.06591e13	−0.825535
$243$	−8.47289e11	−0.0641500
$244$	−5.72894e12	−0.424063
$245$	−1.60088e11	−0.0115863
$246$	8.79572e11	0.0622484
$247$	9.97946e12	0.690675
$248$	−5.47698e12	−0.370729
$249$	−2.91061e12	−0.192703
$250$	−4.41294e11	−0.0285797
$251$	−1.04956e13	−0.664972	−0.332486	−	0.943108i	$-0.607887\pi$
$251$	−1.04956e13	−0.664972	−0.332486	+	0.943108i	$0.607887\pi$
$252$	8.71343e11	0.0540115
$253$	−3.57686e11	−0.0216940
$254$	9.87663e12	0.586170
$255$	−2.03454e10	−0.00118167
$256$	−1.38264e13	−0.785942
$257$	−1.84143e13	−1.02452	−0.512262	−	0.858829i	$-0.671192\pi$
$257$	−1.84143e13	−1.02452	−0.512262	+	0.858829i	$0.671192\pi$
$258$	1.04768e13	0.570582
$259$	−9.11861e12	−0.486161
$260$	−3.60870e10	−0.00188364
$261$	7.18252e12	0.367075
$262$	−1.86820e12	−0.0934904
$263$	−1.21552e13	−0.595668	−0.297834	−	0.954618i	$-0.596264\pi$
$263$	−1.21552e13	−0.595668	−0.297834	+	0.954618i	$0.596264\pi$
$264$	1.91676e12	0.0919913
$265$	1.31021e11	0.00615870
$266$	−1.84427e13	−0.849131
$267$	−5.17594e12	−0.233441
$268$	1.11460e13	0.492467
$269$	−3.42443e13	−1.48235	−0.741175	−	0.671312i	$-0.765731\pi$
$269$	−3.42443e13	−1.48235	−0.741175	+	0.671312i	$0.765731\pi$
$270$	−6.48499e10	−0.00275048
$271$	8.60560e12	0.357643	0.178822	−	0.983882i	$-0.442772\pi$
$271$	8.60560e12	0.357643	0.178822	+	0.983882i	$0.442772\pi$
$272$	−1.86514e12	−0.0759594
$273$	3.13730e12	0.125217
$274$	−1.38124e13	−0.540309
$275$	−3.82252e12	−0.146561
$276$	−6.55187e11	−0.0246244
$277$	2.62981e13	0.968915	0.484457	−	0.874815i	$-0.339017\pi$
$277$	2.62981e13	0.968915	0.484457	+	0.874815i	$0.339017\pi$
$278$	−2.14104e13	−0.773354
$279$	3.21067e12	0.113703
$280$	2.98076e11	0.0103504
$281$	−9.46162e12	−0.322167	−0.161083	−	0.986941i	$-0.551499\pi$
$281$	−9.46162e12	−0.322167	−0.161083	+	0.986941i	$0.551499\pi$
$282$	9.82376e12	0.328026
$283$	−2.59883e13	−0.851046	−0.425523	−	0.904948i	$-0.639910\pi$
$283$	−2.59883e13	−0.851046	−0.425523	+	0.904948i	$0.639910\pi$
$284$	1.01499e12	0.0325994
$285$	−5.55818e11	−0.0175100
$286$	1.54410e12	0.0477158
$287$	2.36998e12	0.0718445
$288$	6.23647e12	0.185473
$289$	−3.37716e13	−0.985403
$290$	5.49737e11	0.0157386
$291$	1.09297e13	0.307041
$292$	3.81315e12	0.105118
$293$	2.86354e13	0.774697	0.387348	−	0.921933i	$-0.373391\pi$
$293$	2.86354e13	0.774697	0.387348	+	0.921933i	$0.373391\pi$
$294$	1.25472e13	0.333148
$295$	8.46280e10	0.00220543
$296$	−3.67427e13	−0.939869
$297$	−1.12363e12	−0.0282139
$298$	5.66332e12	0.139599
$299$	−2.35902e12	−0.0570875
$300$	−7.00186e12	−0.166359
$301$	2.82292e13	0.658542
$302$	2.68302e13	0.614591
$303$	1.64164e13	0.369269
$304$	−5.09538e13	−1.12557
$305$	1.14886e12	0.0249240
$306$	1.59461e12	0.0339772
$307$	−3.67740e13	−0.769625	−0.384813	−	0.922995i	$-0.625734\pi$
$307$	−3.67740e13	−0.769625	−0.384813	+	0.922995i	$0.625734\pi$
$308$	1.15553e12	0.0237548
$309$	2.29722e12	0.0463906
$310$	2.45738e11	0.00487510
$311$	7.76531e13	1.51348	0.756740	−	0.653716i	$-0.226791\pi$
$311$	7.76531e13	1.51348	0.756740	+	0.653716i	$0.226791\pi$
$312$	1.26415e13	0.242074
$313$	8.63382e13	1.62446	0.812230	−	0.583338i	$-0.198254\pi$
$313$	8.63382e13	1.62446	0.812230	+	0.583338i	$0.198254\pi$
$314$	−2.34034e13	−0.432680
$315$	−1.74736e11	−0.00317449
$316$	−2.32690e12	−0.0415431
$317$	7.03310e13	1.23402	0.617008	−	0.786956i	$-0.288344\pi$
$317$	7.03310e13	1.23402	0.617008	+	0.786956i	$0.288344\pi$
$318$	−1.02691e13	−0.177085
$319$	9.52508e12	0.161443
$320$	1.11660e12	0.0186026
$321$	5.99973e13	0.982549
$322$	4.35963e12	0.0701846
$323$	1.36672e13	0.216304
$324$	−2.05820e12	−0.0320250
$325$	−2.52104e13	−0.385675
$326$	2.31039e13	0.347528
$327$	1.50311e13	0.222320
$328$	9.54964e12	0.138893
$329$	2.64698e13	0.378594
$330$	−8.60004e10	−0.00120969
$331$	−1.27120e13	−0.175857	−0.0879286	−	0.996127i	$-0.528025\pi$
$331$	−1.27120e13	−0.175857	−0.0879286	+	0.996127i	$0.528025\pi$
$332$	−7.07033e12	−0.0962011
$333$	2.15390e13	0.288259
$334$	4.55941e13	0.600209
$335$	−2.23517e12	−0.0289444
$336$	−1.60186e13	−0.204061
$337$	−1.20215e13	−0.150659	−0.0753294	−	0.997159i	$-0.524001\pi$
$337$	−1.20215e13	−0.150659	−0.0753294	+	0.997159i	$0.524001\pi$
$338$	−5.82410e13	−0.718104
$339$	5.19315e13	0.629989
$340$	−4.94222e10	−0.000589913 0
$341$	4.25782e12	0.0500078
$342$	4.35633e13	0.503475
$343$	8.32384e13	0.946686
$344$	1.13748e14	1.27312
$345$	1.31389e11	0.00144728
$346$	−1.82757e13	−0.198132
$347$	1.61543e13	0.172376	0.0861879	−	0.996279i	$-0.472531\pi$
$347$	1.61543e13	0.172376	0.0861879	+	0.996279i	$0.472531\pi$
$348$	1.74475e13	0.183251
$349$	1.06002e14	1.09591	0.547954	−	0.836509i	$-0.315407\pi$
$349$	1.06002e14	1.09591	0.547954	+	0.836509i	$0.315407\pi$
$350$	4.65905e13	0.474158
$351$	−7.41060e12	−0.0742445
$352$	8.27048e12	0.0815729
$353$	6.62164e13	0.642991	0.321495	−	0.946911i	$-0.395815\pi$
$353$	6.62164e13	0.642991	0.321495	+	0.946911i	$0.395815\pi$
$354$	−6.63289e12	−0.0634139
$355$	−2.03542e11	−0.00191601
$356$	−1.25732e13	−0.116539
$357$	4.29663e12	0.0392150
$358$	−8.28225e13	−0.744375
$359$	−1.63008e13	−0.144275	−0.0721374	−	0.997395i	$-0.522982\pi$
$359$	−1.63008e13	−0.144275	−0.0721374	+	0.997395i	$0.522982\pi$
$360$	−7.04084e11	−0.00613706
$361$	2.56884e14	2.20520
$362$	4.71868e13	0.398955
$363$	6.78406e13	0.564942
$364$	7.62099e12	0.0625106
$365$	−7.64673e11	−0.00617825
$366$	−9.00441e13	−0.716653
$367$	−6.31664e13	−0.495248	−0.247624	−	0.968856i	$-0.579650\pi$
$367$	−6.31664e13	−0.495248	−0.247624	+	0.968856i	$0.579650\pi$
$368$	1.20449e13	0.0930334
$369$	−5.59811e12	−0.0425987
$370$	1.64856e12	0.0123593
$371$	−2.76696e13	−0.204384
$372$	7.79921e12	0.0567629
$373$	1.55068e13	0.111205	0.0556024	−	0.998453i	$-0.482292\pi$
$373$	1.55068e13	0.111205	0.0556024	+	0.998453i	$0.482292\pi$
$374$	2.11469e12	0.0149435
$375$	2.80865e12	0.0195581
$376$	1.06658e14	0.731914
$377$	6.28202e13	0.424837
$378$	1.36953e13	0.0912779
$379$	−8.86462e13	−0.582297	−0.291148	−	0.956678i	$-0.594037\pi$
$379$	−8.86462e13	−0.582297	−0.291148	+	0.956678i	$0.594037\pi$
$380$	−1.35017e12	−0.00874134
$381$	−6.28606e13	−0.401136
$382$	1.48524e14	0.934218
$383$	−1.41516e13	−0.0877430	−0.0438715	−	0.999037i	$-0.513969\pi$
$383$	−1.41516e13	−0.0877430	−0.0438715	+	0.999037i	$0.513969\pi$
$384$	−3.49552e13	−0.213643
$385$	−2.31725e11	−0.00139617
$386$	−1.16642e14	−0.692828
$387$	−6.66802e13	−0.390469
$388$	2.65499e13	0.153281
$389$	−1.11304e14	−0.633560	−0.316780	−	0.948499i	$-0.602602\pi$
$389$	−1.11304e14	−0.633560	−0.316780	+	0.948499i	$0.602602\pi$
$390$	−5.67194e11	−0.00318329
$391$	−3.23075e12	−0.0178785
$392$	1.36227e14	0.743343
$393$	1.18903e13	0.0639786
$394$	−2.06845e14	−1.09753
$395$	4.66627e11	0.00244166
$396$	−2.72947e12	−0.0140849
$397$	1.49667e14	0.761691	0.380846	−	0.924639i	$-0.375633\pi$
$397$	1.49667e14	0.761691	0.380846	+	0.924639i	$0.375633\pi$
$398$	9.66464e13	0.485097
$399$	1.17380e14	0.581089
$400$	1.28721e14	0.628521
$401$	−2.70108e14	−1.30090	−0.650450	−	0.759549i	$-0.725419\pi$
$401$	−2.70108e14	−1.30090	−0.650450	+	0.759549i	$0.725419\pi$
$402$	1.75186e14	0.832255
$403$	2.80813e13	0.131595
$404$	3.98779e13	0.184346
$405$	4.12742e11	0.00188225
$406$	−1.16096e14	−0.522303
$407$	2.85639e13	0.126779
$408$	1.73129e13	0.0758123
$409$	−1.60681e14	−0.694204	−0.347102	−	0.937827i	$-0.612834\pi$
$409$	−1.60681e14	−0.694204	−0.347102	+	0.937827i	$0.612834\pi$
$410$	−4.28469e11	−0.00182645
$411$	8.79104e13	0.369752
$412$	5.58029e12	0.0231591
$413$	−1.78721e13	−0.0731897
$414$	−1.02978e13	−0.0416145
$415$	1.41785e12	0.00565415
$416$	5.45458e13	0.214658
$417$	1.36268e14	0.529232
$418$	5.77714e13	0.221433
$419$	4.24501e14	1.60584	0.802919	−	0.596088i	$-0.203279\pi$
$419$	4.24501e14	1.60584	0.802919	+	0.596088i	$0.203279\pi$
$420$	−4.24460e11	−0.00158477
$421$	−1.38573e14	−0.510654	−0.255327	−	0.966855i	$-0.582183\pi$
$421$	−1.38573e14	−0.510654	−0.255327	+	0.966855i	$0.582183\pi$
$422$	−3.37044e14	−1.22594
$423$	−6.25242e13	−0.224479
$424$	−1.11493e14	−0.395124
$425$	−3.45264e13	−0.120785
$426$	1.59530e13	0.0550921
$427$	−2.42621e14	−0.827131
$428$	1.45743e14	0.490508
$429$	−9.82755e12	−0.0326535
$430$	−5.10357e12	−0.0167416
$431$	2.32465e14	0.752893	0.376447	−	0.926438i	$-0.377146\pi$
$431$	2.32465e14	0.752893	0.376447	+	0.926438i	$0.377146\pi$
$432$	3.78376e13	0.120994
$433$	−3.58882e13	−0.113310	−0.0566551	−	0.998394i	$-0.518044\pi$
$433$	−3.58882e13	−0.113310	−0.0566551	+	0.998394i	$0.518044\pi$
$434$	−5.18961e13	−0.161786
$435$	−3.49884e12	−0.0107704
$436$	3.65130e13	0.110987
$437$	−8.82612e13	−0.264924
$438$	5.99328e13	0.177647
$439$	3.49088e14	1.02183	0.510916	−	0.859631i	$-0.329306\pi$
$439$	3.49088e14	1.02183	0.510916	+	0.859631i	$0.329306\pi$
$440$	−9.33719e11	−0.00269915
$441$	−7.98577e13	−0.227984
$442$	1.39469e13	0.0393238
$443$	−1.39270e14	−0.387826	−0.193913	−	0.981019i	$-0.562118\pi$
$443$	−1.39270e14	−0.387826	−0.193913	+	0.981019i	$0.562118\pi$
$444$	5.23216e13	0.143905
$445$	2.52137e12	0.00684947
$446$	−5.65468e12	−0.0151728
$447$	−3.60447e13	−0.0955322
$448$	−2.35809e14	−0.617350
$449$	4.43677e14	1.14739	0.573696	−	0.819068i	$-0.305509\pi$
$449$	4.43677e14	1.14739	0.573696	+	0.819068i	$0.305509\pi$
$450$	−1.10051e14	−0.281142
$451$	−7.42391e12	−0.0187354
$452$	1.26150e14	0.314503
$453$	−1.70763e14	−0.420585
$454$	−5.59683e14	−1.36187
$455$	−1.52828e12	−0.00367402
$456$	4.72973e14	1.12339
$457$	−2.75578e14	−0.646703	−0.323352	−	0.946279i	$-0.604810\pi$
$457$	−2.75578e14	−0.646703	−0.323352	+	0.946279i	$0.604810\pi$
$458$	4.45647e14	1.03331
$459$	−1.01490e13	−0.0232517
$460$	3.19163e11	0.000722512 0
$461$	−6.83076e14	−1.52797	−0.763983	−	0.645236i	$-0.776759\pi$
$461$	−6.83076e14	−1.52797	−0.763983	+	0.645236i	$0.776759\pi$
$462$	1.81619e13	0.0401450
$463$	−5.88016e14	−1.28438	−0.642190	−	0.766545i	$-0.721974\pi$
$463$	−5.88016e14	−1.28438	−0.642190	+	0.766545i	$0.721974\pi$
$464$	−3.20752e14	−0.692341
$465$	−1.56402e12	−0.00333620
$466$	−2.86558e14	−0.604074
$467$	−7.88305e13	−0.164230	−0.0821148	−	0.996623i	$-0.526167\pi$
$467$	−7.88305e13	−0.164230	−0.0821148	+	0.996623i	$0.526167\pi$
$468$	−1.80015e13	−0.0370644
$469$	4.72033e14	0.960554
$470$	−4.78548e12	−0.00962470
$471$	1.48953e14	0.296097
$472$	−7.20142e13	−0.141494
$473$	−8.84277e13	−0.171732
$474$	−3.65728e13	−0.0702066
$475$	−9.43230e14	−1.78979
$476$	1.04372e13	0.0195769
$477$	6.53582e13	0.121185
$478$	1.71144e14	0.313695
$479$	−6.85495e13	−0.124211	−0.0621054	−	0.998070i	$-0.519781\pi$
$479$	−6.85495e13	−0.124211	−0.0621054	+	0.998070i	$0.519781\pi$
$480$	−3.03799e12	−0.00544202
$481$	1.88386e14	0.333619
$482$	8.71261e14	1.52542
$483$	−2.77472e13	−0.0480297
$484$	1.64795e14	0.282030
$485$	−5.32421e12	−0.00900897
$486$	−3.23495e13	−0.0541213
$487$	−6.19920e14	−1.02548	−0.512739	−	0.858544i	$-0.671369\pi$
$487$	−6.19920e14	−1.02548	−0.512739	+	0.858544i	$0.671369\pi$
$488$	−9.77621e14	−1.59905
$489$	−1.47047e14	−0.237825
$490$	−6.11216e12	−0.00977499
$491$	−1.56199e14	−0.247018	−0.123509	−	0.992343i	$-0.539415\pi$
$491$	−1.56199e14	−0.247018	−0.123509	+	0.992343i	$0.539415\pi$
$492$	−1.35987e13	−0.0212661
$493$	8.60341e13	0.133049
$494$	3.81016e14	0.582700
$495$	5.47357e11	0.000827832 0
$496$	−1.43380e14	−0.214456
$497$	4.29848e13	0.0635850
$498$	−1.11127e14	−0.162577
$499$	−5.75189e14	−0.832257	−0.416128	−	0.909306i	$-0.636613\pi$
$499$	−5.75189e14	−0.832257	−0.416128	+	0.909306i	$0.636613\pi$
$500$	6.82265e12	0.00976378
$501$	−2.90187e14	−0.410744
$502$	−4.00724e14	−0.561015
$503$	4.51069e14	0.624624	0.312312	−	0.949980i	$-0.398897\pi$
$503$	4.51069e14	0.624624	0.312312	+	0.949980i	$0.398897\pi$
$504$	1.48691e14	0.203666
$505$	−7.99695e12	−0.0108348
$506$	−1.36565e13	−0.0183025
$507$	3.70680e14	0.491423
$508$	−1.52698e14	−0.200255
$509$	7.55708e14	0.980407	0.490204	−	0.871608i	$-0.336922\pi$
$509$	7.55708e14	0.980407	0.490204	+	0.871608i	$0.336922\pi$
$510$	−7.76788e11	−0.000996935 0
$511$	1.61487e14	0.205032
$512$	−8.22495e14	−1.03312
$513$	−2.77262e14	−0.344545
$514$	−7.03058e14	−0.864358
$515$	−1.11905e12	−0.00136116
$516$	−1.61976e14	−0.194930
$517$	−8.29162e13	−0.0987283
$518$	−3.48149e14	−0.410158
$519$	1.16317e14	0.135588
$520$	−6.15810e12	−0.00710278
$521$	1.42188e15	1.62276	0.811382	−	0.584517i	$-0.198716\pi$
$521$	1.42188e15	1.62276	0.811382	+	0.584517i	$0.198716\pi$
$522$	2.74229e14	0.309689
$523$	−6.61743e14	−0.739486	−0.369743	−	0.929134i	$-0.620554\pi$
$523$	−6.61743e14	−0.739486	−0.369743	+	0.929134i	$0.620554\pi$
$524$	2.88835e13	0.0319394
$525$	−2.96529e14	−0.324482
$526$	−4.64084e14	−0.502545
$527$	3.84582e13	0.0412127
$528$	5.01782e13	0.0532143
$529$	−9.31946e14	−0.978103
$530$	5.00239e12	0.00519590
$531$	4.22156e13	0.0433963
$532$	2.85134e14	0.290092
$533$	−4.89625e13	−0.0493019
$534$	−1.97618e14	−0.196947
$535$	−2.92267e13	−0.0288293
$536$	1.90202e15	1.85699
$537$	5.27131e14	0.509401
$538$	−1.30745e15	−1.25061
$539$	−1.05903e14	−0.100270
$540$	1.00262e12	0.000939655 0
$541$	−1.00319e15	−0.930675	−0.465338	−	0.885133i	$-0.654067\pi$
$541$	−1.00319e15	−0.930675	−0.465338	+	0.885133i	$0.654067\pi$
$542$	3.28562e14	0.301732
$543$	−3.00324e14	−0.273018
$544$	7.47021e13	0.0672263
$545$	−7.32216e12	−0.00652317
$546$	1.19782e14	0.105641
$547$	−2.23450e15	−1.95097	−0.975486	−	0.220062i	$-0.929374\pi$
$547$	−2.23450e15	−1.95097	−0.975486	+	0.220062i	$0.929374\pi$
$548$	2.13548e14	0.184588
$549$	5.73093e14	0.490430
$550$	−1.45944e14	−0.123649
$551$	2.35037e15	1.97153
$552$	−1.11805e14	−0.0928532
$553$	−9.85443e13	−0.0810295
$554$	1.00406e15	0.817442
$555$	−1.04924e13	−0.00845789
$556$	3.31017e14	0.264203
$557$	−1.28284e15	−1.01384	−0.506921	−	0.861992i	$-0.669217\pi$
$557$	−1.28284e15	−1.01384	−0.506921	+	0.861992i	$0.669217\pi$
$558$	1.22583e14	0.0959276
$559$	−5.83202e14	−0.451912
$560$	7.80321e12	0.00598741
$561$	−1.34591e13	−0.0102264
$562$	−3.61245e14	−0.271802
$563$	−1.02356e15	−0.762633	−0.381316	−	0.924445i	$-0.624529\pi$
$563$	−1.02356e15	−0.762633	−0.381316	+	0.924445i	$0.624529\pi$
$564$	−1.51881e14	−0.112065
$565$	−2.52976e13	−0.0184847
$566$	−9.92235e14	−0.718000
$567$	−8.71646e13	−0.0624645
$568$	1.73204e14	0.122925
$569$	−8.08918e13	−0.0568574	−0.0284287	−	0.999596i	$-0.509050\pi$
$569$	−8.08918e13	−0.0568574	−0.0284287	+	0.999596i	$0.509050\pi$
$570$	−2.12211e13	−0.0147726
$571$	−2.70125e15	−1.86237	−0.931185	−	0.364546i	$-0.881224\pi$
$571$	−2.70125e15	−1.86237	−0.931185	+	0.364546i	$0.881224\pi$
$572$	−2.38726e13	−0.0163013
$573$	−9.45294e14	−0.639317
$574$	9.04858e13	0.0606129
$575$	2.22968e14	0.147935
$576$	5.57003e14	0.366045
$577$	−1.21212e15	−0.789000	−0.394500	−	0.918896i	$-0.629082\pi$
$577$	−1.21212e15	−0.789000	−0.394500	+	0.918896i	$0.629082\pi$
$578$	−1.28940e15	−0.831352
$579$	7.42379e14	0.474126
$580$	−8.49924e12	−0.00537683
$581$	−2.99429e14	−0.187640
$582$	4.17295e14	0.259040
$583$	8.66746e13	0.0532985
$584$	6.50699e14	0.396378
$585$	3.60995e12	0.00217843
$586$	1.09330e15	0.653587
$587$	2.45076e15	1.45141	0.725706	−	0.688005i	$-0.241513\pi$
$587$	2.45076e15	1.45141	0.725706	+	0.688005i	$0.241513\pi$
$588$	−1.93987e14	−0.113814
$589$	1.05064e15	0.610690
$590$	3.23110e12	0.00186065
$591$	1.31648e15	0.751074
$592$	−9.61873e14	−0.543686
$593$	1.66723e15	0.933674	0.466837	−	0.884343i	$-0.345393\pi$
$593$	1.66723e15	0.933674	0.466837	+	0.884343i	$0.345393\pi$
$594$	−4.29002e13	−0.0238031
$595$	−2.09303e12	−0.00115062
$596$	−8.75581e13	−0.0476916
$597$	−6.15114e14	−0.331968
$598$	−9.00676e13	−0.0481629
$599$	−3.13480e15	−1.66097	−0.830485	−	0.557040i	$-0.811937\pi$
$599$	−3.13480e15	−1.66097	−0.830485	+	0.557040i	$0.811937\pi$
$600$	−1.19484e15	−0.627304
$601$	−2.87675e15	−1.49655	−0.748277	−	0.663387i	$-0.769118\pi$
$601$	−2.87675e15	−1.49655	−0.748277	+	0.663387i	$0.769118\pi$
$602$	1.07779e15	0.555591
$603$	−1.11499e15	−0.569541
$604$	−4.14810e14	−0.209965
$605$	−3.30474e13	−0.0165761
$606$	6.26777e14	0.311540
$607$	1.38720e14	0.0683286	0.0341643	−	0.999416i	$-0.489123\pi$
$607$	1.38720e14	0.0683286	0.0341643	+	0.999416i	$0.489123\pi$
$608$	2.04079e15	0.996160
$609$	7.38901e14	0.357430
$610$	4.38634e13	0.0210275
$611$	−5.46852e14	−0.259803
$612$	−2.46536e13	−0.0116077
$613$	−2.58931e14	−0.120824	−0.0604118	−	0.998174i	$-0.519241\pi$
$613$	−2.58931e14	−0.120824	−0.0604118	+	0.998174i	$0.519241\pi$
$614$	−1.40403e15	−0.649308
$615$	2.72702e12	0.00124990
$616$	1.97187e14	0.0895743
$617$	1.07625e15	0.484555	0.242277	−	0.970207i	$-0.422106\pi$
$617$	1.07625e15	0.484555	0.242277	+	0.970207i	$0.422106\pi$
$618$	8.77078e13	0.0391383
$619$	2.20936e15	0.977164	0.488582	−	0.872518i	$-0.337514\pi$
$619$	2.20936e15	0.977164	0.488582	+	0.872518i	$0.337514\pi$
$620$	−3.79925e12	−0.00166550
$621$	6.55415e13	0.0284782
$622$	2.96480e15	1.27687
$623$	−5.32474e14	−0.227308
$624$	3.30937e14	0.140033
$625$	2.38213e15	0.999139
$626$	3.29639e15	1.37050
$627$	−3.67691e14	−0.151534
$628$	3.61830e14	0.147818
$629$	2.58000e14	0.104482
$630$	−6.67142e12	−0.00267821
$631$	−1.37298e14	−0.0546389	−0.0273195	−	0.999627i	$-0.508697\pi$
$631$	−1.37298e14	−0.0546389	−0.0273195	+	0.999627i	$0.508697\pi$
$632$	−3.97076e14	−0.156650
$633$	2.14514e15	0.838949
$634$	2.68524e15	1.04110
$635$	3.06215e13	0.0117698
$636$	1.58765e14	0.0604981
$637$	−6.98456e14	−0.263859
$638$	3.63668e14	0.136204
$639$	−1.01534e14	−0.0377014
$640$	1.70278e13	0.00626858
$641$	4.28931e15	1.56555	0.782777	−	0.622303i	$-0.213803\pi$
$641$	4.28931e15	1.56555	0.782777	+	0.622303i	$0.213803\pi$
$642$	2.29070e15	0.828945
$643$	−4.12032e15	−1.47833	−0.739164	−	0.673525i	$-0.764779\pi$
$643$	−4.12032e15	−1.47833	−0.739164	+	0.673525i	$0.764779\pi$
$644$	−6.74022e13	−0.0239774
$645$	3.24821e13	0.0114569
$646$	5.21813e14	0.182489
$647$	−3.73194e15	−1.29408	−0.647040	−	0.762456i	$-0.723993\pi$
$647$	−3.73194e15	−1.29408	−0.647040	+	0.762456i	$0.723993\pi$
$648$	−3.51223e14	−0.120759
$649$	5.59840e13	0.0190862
$650$	−9.62535e14	−0.325382
$651$	3.30297e14	0.110716
$652$	−3.57200e14	−0.118727
$653$	1.38669e14	0.0457042	0.0228521	−	0.999739i	$-0.492725\pi$
$653$	1.38669e14	0.0457042	0.0228521	+	0.999739i	$0.492725\pi$
$654$	5.73890e14	0.187565
$655$	−5.79217e12	−0.00187722
$656$	2.49996e14	0.0803456
$657$	−3.81447e14	−0.121570
$658$	1.01062e15	0.319407
$659$	−8.65288e14	−0.271201	−0.135600	−	0.990764i	$-0.543296\pi$
$659$	−8.65288e14	−0.271201	−0.135600	+	0.990764i	$0.543296\pi$
$660$	1.32961e12	0.000413270 0
$661$	−5.98330e15	−1.84431	−0.922153	−	0.386825i	$-0.873572\pi$
$661$	−5.98330e15	−1.84431	−0.922153	+	0.386825i	$0.873572\pi$
$662$	−4.85345e14	−0.148365
$663$	−8.87662e13	−0.0269106
$664$	−1.20652e15	−0.362753
$665$	−5.71796e13	−0.0170499
$666$	8.22361e14	0.243195
$667$	−5.55600e14	−0.162956
$668$	−7.04910e14	−0.205052
$669$	3.59897e13	0.0103833
$670$	−8.53390e13	−0.0244195
$671$	7.60006e14	0.215696
$672$	6.41576e14	0.180600
$673$	−6.00946e15	−1.67785	−0.838924	−	0.544248i	$-0.816815\pi$
$673$	−6.00946e15	−1.67785	−0.838924	+	0.544248i	$0.816815\pi$
$674$	−4.58981e14	−0.127106
$675$	7.00429e14	0.192395
$676$	9.00439e14	0.245328
$677$	−2.25463e14	−0.0609309	−0.0304654	−	0.999536i	$-0.509699\pi$
$677$	−2.25463e14	−0.0609309	−0.0304654	+	0.999536i	$0.509699\pi$
$678$	1.98275e15	0.531501
$679$	1.12439e15	0.298973
$680$	−8.43370e12	−0.00222443
$681$	3.56215e15	0.931972
$682$	1.62564e14	0.0421900
$683$	2.92558e15	0.753178	0.376589	−	0.926381i	$-0.377097\pi$
$683$	2.92558e15	0.753178	0.376589	+	0.926381i	$0.377097\pi$
$684$	−6.73513e14	−0.172004
$685$	−4.28241e13	−0.0108490
$686$	3.17804e15	0.798688
$687$	−2.83636e15	−0.707129
$688$	2.97775e15	0.736465
$689$	5.71640e14	0.140255
$690$	5.01642e12	0.00122102
$691$	5.93173e14	0.143236	0.0716180	−	0.997432i	$-0.477184\pi$
$691$	5.93173e14	0.143236	0.0716180	+	0.997432i	$0.477184\pi$
$692$	2.82552e14	0.0676885
$693$	−1.15593e14	−0.0274726
$694$	6.16772e14	0.145428
$695$	−6.63807e13	−0.0155284
$696$	2.97734e15	0.691000
$697$	−6.70556e13	−0.0154403
$698$	4.04716e15	0.924582
$699$	1.82382e15	0.413388
$700$	−7.20315e14	−0.161988
$701$	2.81888e15	0.628967	0.314483	−	0.949263i	$-0.398169\pi$
$701$	2.81888e15	0.628967	0.314483	+	0.949263i	$0.398169\pi$
$702$	−2.82937e14	−0.0626377
$703$	7.04832e15	1.54822
$704$	7.38668e14	0.160990
$705$	3.04576e13	0.00658651
$706$	2.52815e15	0.542471
$707$	1.68883e15	0.359566
$708$	1.02548e14	0.0216643
$709$	−7.68258e15	−1.61047	−0.805235	−	0.592955i	$-0.797961\pi$
$709$	−7.68258e15	−1.61047	−0.805235	+	0.592955i	$0.797961\pi$
$710$	−7.77122e12	−0.00161647
$711$	2.32771e14	0.0480447
$712$	−2.14556e15	−0.439442
$713$	−2.48359e14	−0.0504764
$714$	1.64045e14	0.0330845
$715$	4.78732e12	0.000958097 0
$716$	1.28048e15	0.254303
$717$	−1.08926e15	−0.214672
$718$	−6.22367e14	−0.121720
$719$	−6.63705e15	−1.28815	−0.644075	−	0.764962i	$-0.722758\pi$
$719$	−6.63705e15	−1.28815	−0.644075	+	0.764962i	$0.722758\pi$
$720$	−1.84319e13	−0.00355011
$721$	2.36326e14	0.0451717
$722$	9.80784e15	1.86045
$723$	−5.54521e15	−1.04390
$724$	−7.29534e14	−0.136296
$725$	−5.93759e15	−1.10091
$726$	2.59016e15	0.476623
$727$	−4.84956e15	−0.885652	−0.442826	−	0.896608i	$-0.646024\pi$
$727$	−4.84956e15	−0.885652	−0.442826	+	0.896608i	$0.646024\pi$
$728$	1.30049e15	0.235714
$729$	2.05891e14	0.0370370
$730$	−2.91953e13	−0.00521239
$731$	−7.98712e14	−0.141529
$732$	1.39213e15	0.244833
$733$	−3.68177e15	−0.642665	−0.321333	−	0.946966i	$-0.604131\pi$
$733$	−3.68177e15	−0.642665	−0.321333	+	0.946966i	$0.604131\pi$
$734$	−2.41170e15	−0.417825
$735$	3.89013e13	0.00668936
$736$	−4.82419e14	−0.0823372
$737$	−1.47864e15	−0.250490
$738$	−2.13736e14	−0.0359391
$739$	−8.18857e14	−0.136667	−0.0683335	−	0.997663i	$-0.521768\pi$
$739$	−8.18857e14	−0.136667	−0.0683335	+	0.997663i	$0.521768\pi$
$740$	−2.54876e13	−0.00422235
$741$	−2.42501e15	−0.398761
$742$	−1.05643e15	−0.172432
$743$	−6.97943e15	−1.13079	−0.565394	−	0.824821i	$-0.691276\pi$
$743$	−6.97943e15	−1.13079	−0.565394	+	0.824821i	$0.691276\pi$
$744$	1.33091e15	0.214040
$745$	1.75585e13	0.00280304
$746$	5.92051e14	0.0938200
$747$	7.07279e14	0.111257
$748$	−3.26943e13	−0.00510521
$749$	6.17221e15	0.956733
$750$	1.07234e14	0.0165005
$751$	8.78726e15	1.34225	0.671126	−	0.741343i	$-0.265811\pi$
$751$	8.78726e15	1.34225	0.671126	+	0.741343i	$0.265811\pi$
$752$	2.79216e15	0.423391
$753$	2.55044e15	0.383922
$754$	2.39848e15	0.358421
$755$	8.31844e13	0.0123405
$756$	−2.11736e14	−0.0311836
$757$	−8.53584e14	−0.124801	−0.0624006	−	0.998051i	$-0.519876\pi$
$757$	−8.53584e14	−0.124801	−0.0624006	+	0.998051i	$0.519876\pi$
$758$	−3.38451e15	−0.491265
$759$	8.69177e13	0.0125250
$760$	−2.30401e14	−0.0329617
$761$	4.67837e14	0.0664476	0.0332238	−	0.999448i	$-0.489423\pi$
$761$	4.67837e14	0.0664476	0.0332238	+	0.999448i	$0.489423\pi$
$762$	−2.40002e15	−0.338425
$763$	1.54633e15	0.216479
$764$	−2.29626e15	−0.319160
$765$	4.94393e12	0.000682236 0
$766$	−5.40309e14	−0.0740259
$767$	3.69228e14	0.0502250
$768$	3.35982e15	0.453764
$769$	1.20552e16	1.61652	0.808259	−	0.588828i	$-0.200410\pi$
$769$	1.20552e16	1.61652	0.808259	+	0.588828i	$0.200410\pi$
$770$	−8.84728e12	−0.00117791
$771$	4.47467e15	0.591510
$772$	1.80335e15	0.236693
$773$	−3.00579e15	−0.391717	−0.195858	−	0.980632i	$-0.562749\pi$
$773$	−3.00579e15	−0.391717	−0.195858	+	0.980632i	$0.562749\pi$
$774$	−2.54585e15	−0.329426
$775$	−2.65417e15	−0.341011
$776$	4.53063e15	0.577989
$777$	2.21582e15	0.280685
$778$	−4.24959e15	−0.534514
$779$	−1.83190e15	−0.228794
$780$	8.76913e12	0.00108752
$781$	−1.34649e14	−0.0165815
$782$	−1.23350e14	−0.0150835
$783$	−1.74535e15	−0.211931
$784$	3.56623e15	0.430002
$785$	−7.25599e13	−0.00868788
$786$	4.53973e14	0.0539767
$787$	4.13814e14	0.0488590	0.0244295	−	0.999702i	$-0.492223\pi$
$787$	4.13814e14	0.0488590	0.0244295	+	0.999702i	$0.492223\pi$
$788$	3.19793e15	0.374952
$789$	2.95370e15	0.343909
$790$	1.78158e13	0.00205995
$791$	5.34245e15	0.613436
$792$	−4.65773e14	−0.0531112
$793$	5.01242e15	0.567603
$794$	5.71430e15	0.642614
$795$	−3.18381e13	−0.00355573
$796$	−1.49421e15	−0.165725
$797$	−1.22642e16	−1.35088	−0.675442	−	0.737413i	$-0.736047\pi$
$797$	−1.22642e16	−1.35088	−0.675442	+	0.737413i	$0.736047\pi$
$798$	4.48157e15	0.490246
$799$	−7.48931e14	−0.0813644
$800$	−5.15551e15	−0.556259
$801$	1.25775e15	0.134777
$802$	−1.03127e16	−1.09753
$803$	−5.05855e14	−0.0534676
$804$	−2.70848e15	−0.284326
$805$	1.35166e13	0.00140925
$806$	1.07215e15	0.111023
$807$	8.32137e15	0.855835
$808$	6.80501e15	0.695130
$809$	4.94885e14	0.0502096	0.0251048	−	0.999685i	$-0.492008\pi$
$809$	4.94885e14	0.0502096	0.0251048	+	0.999685i	$0.492008\pi$
$810$	1.57585e13	0.00158799
$811$	−4.78177e15	−0.478602	−0.239301	−	0.970945i	$-0.576918\pi$
$811$	−4.78177e15	−0.478602	−0.239301	+	0.970945i	$0.576918\pi$
$812$	1.79490e15	0.178436
$813$	−2.09116e15	−0.206485
$814$	1.09057e15	0.106960
$815$	7.16314e13	0.00697809
$816$	4.53228e14	0.0438552
$817$	−2.18201e16	−2.09718
$818$	−6.13482e15	−0.585678
$819$	−7.62364e14	−0.0722938
$820$	6.62436e12	0.000623976 0
$821$	1.15726e16	1.08279	0.541393	−	0.840770i	$-0.317897\pi$
$821$	1.15726e16	1.08279	0.541393	+	0.840770i	$0.317897\pi$
$822$	3.35642e15	0.311948
$823$	−9.85164e15	−0.909514	−0.454757	−	0.890615i	$-0.650274\pi$
$823$	−9.85164e15	−0.909514	−0.454757	+	0.890615i	$0.650274\pi$
$824$	9.52256e14	0.0873281
$825$	9.28872e14	0.0846173
$826$	−6.82357e14	−0.0617478
$827$	7.54016e15	0.677798	0.338899	−	0.940823i	$-0.389945\pi$
$827$	7.54016e15	0.677798	0.338899	+	0.940823i	$0.389945\pi$
$828$	1.59210e14	0.0142169
$829$	−1.77254e16	−1.57234	−0.786169	−	0.618012i	$-0.787938\pi$
$829$	−1.77254e16	−1.57234	−0.786169	+	0.618012i	$0.787938\pi$
$830$	5.41338e13	0.00477022
$831$	−6.39044e15	−0.559403
$832$	4.87169e15	0.423645
$833$	−9.56557e14	−0.0826349
$834$	5.20273e15	0.446496
$835$	1.41360e14	0.0120518
$836$	−8.93178e14	−0.0756490
$837$	−7.80192e14	−0.0656465
$838$	1.62075e16	1.35479
$839$	−9.41894e15	−0.782188	−0.391094	−	0.920351i	$-0.627903\pi$
$839$	−9.41894e15	−0.782188	−0.391094	+	0.920351i	$0.627903\pi$
$840$	−7.24325e13	−0.00597582
$841$	2.59497e15	0.212693
$842$	−5.29072e15	−0.430822
$843$	2.29917e15	0.186003
$844$	5.21088e15	0.418820
$845$	−1.80570e14	−0.0144190
$846$	−2.38717e15	−0.189386
$847$	6.97909e15	0.550098
$848$	−2.91872e15	−0.228568
$849$	6.31516e15	0.491352
$850$	−1.31822e15	−0.101902
$851$	−1.66614e15	−0.127967
$852$	−2.46642e14	−0.0188213
$853$	1.95835e16	1.48481	0.742404	−	0.669952i	$-0.233685\pi$
$853$	1.95835e16	1.48481	0.742404	+	0.669952i	$0.233685\pi$
$854$	−9.26327e15	−0.697824
$855$	1.35064e14	0.0101094
$856$	2.48704e16	1.84960
$857$	−4.29029e15	−0.317024	−0.158512	−	0.987357i	$-0.550670\pi$
$857$	−4.29029e15	−0.317024	−0.158512	+	0.987357i	$0.550670\pi$
$858$	−3.75216e14	−0.0275487
$859$	1.07177e16	0.781880	0.390940	−	0.920416i	$-0.372150\pi$
$859$	1.07177e16	0.781880	0.390940	+	0.920416i	$0.372150\pi$
$860$	7.89041e13	0.00571950
$861$	−5.75904e14	−0.0414794
$862$	8.87554e15	0.635192
$863$	−2.33202e16	−1.65833	−0.829167	−	0.559001i	$-0.811185\pi$
$863$	−2.33202e16	−1.65833	−0.829167	+	0.559001i	$0.811185\pi$
$864$	−1.51546e15	−0.107083
$865$	−5.66618e13	−0.00397834
$866$	−1.37021e15	−0.0955961
$867$	8.20650e15	0.568922
$868$	8.02342e14	0.0552715
$869$	3.08688e14	0.0211306
$870$	−1.33586e14	−0.00908668
$871$	−9.75197e15	−0.659162
$872$	6.23080e15	0.418507
$873$	−2.65591e15	−0.177270
$874$	−3.36982e15	−0.223508
$875$	2.88939e14	0.0190442
$876$	−9.26595e14	−0.0606900
$877$	2.18713e16	1.42356	0.711781	−	0.702402i	$-0.247889\pi$
$877$	2.18713e16	1.42356	0.711781	+	0.702402i	$0.247889\pi$
$878$	1.33282e16	0.862087
$879$	−6.95841e15	−0.447271
$880$	−2.44434e13	−0.00156138
$881$	−1.76902e16	−1.12296	−0.561482	−	0.827489i	$-0.689769\pi$
$881$	−1.76902e16	−1.12296	−0.561482	+	0.827489i	$0.689769\pi$
$882$	−3.04897e15	−0.192343
$883$	6.93163e15	0.434562	0.217281	−	0.976109i	$-0.430281\pi$
$883$	6.93163e15	0.434562	0.217281	+	0.976109i	$0.430281\pi$
$884$	−2.15627e14	−0.0134343
$885$	−2.05646e13	−0.00127330
$886$	−5.31733e15	−0.327196
$887$	1.95770e16	1.19720	0.598600	−	0.801048i	$-0.295724\pi$
$887$	1.95770e16	1.19720	0.598600	+	0.801048i	$0.295724\pi$
$888$	8.92849e15	0.542633
$889$	−6.46677e15	−0.390596
$890$	9.62661e13	0.00577868
$891$	2.73042e14	0.0162893
$892$	8.74245e13	0.00518354
$893$	−2.04601e16	−1.20566
$894$	−1.37619e15	−0.0805974
$895$	−2.56783e14	−0.0149465
$896$	−3.59600e15	−0.208030
$897$	5.73243e14	0.0329595
$898$	1.69396e16	0.968018
$899$	6.61374e15	0.375638
$900$	1.70145e15	0.0960474
$901$	7.82878e14	0.0439246
$902$	−2.83445e14	−0.0158064
$903$	−6.85971e15	−0.380209
$904$	2.15270e16	1.18592
$905$	1.46298e14	0.00801071
$906$	−6.51975e15	−0.354834
$907$	−7.72373e15	−0.417818	−0.208909	−	0.977935i	$-0.566991\pi$
$907$	−7.72373e15	−0.417818	−0.208909	+	0.977935i	$0.566991\pi$
$908$	8.65301e15	0.465259
$909$	−3.98917e15	−0.213197
$910$	−5.83499e13	−0.00309965
$911$	1.78083e14	0.00940311	0.00470156	−	0.999989i	$-0.498503\pi$
$911$	1.78083e14	0.00940311	0.00470156	+	0.999989i	$0.498503\pi$
$912$	1.23818e16	0.649847
$913$	9.37955e14	0.0489320
$914$	−1.05216e16	−0.545603
$915$	−2.79173e14	−0.0143899
$916$	−6.88995e15	−0.353013
$917$	1.22322e15	0.0622976
$918$	−3.87491e14	−0.0196167
$919$	9.91685e14	0.0499043	0.0249522	−	0.999689i	$-0.492057\pi$
$919$	9.91685e14	0.0499043	0.0249522	+	0.999689i	$0.492057\pi$
$920$	5.44640e13	0.00272443
$921$	8.93607e15	0.444343
$922$	−2.60799e16	−1.28910
$923$	−8.88043e14	−0.0436340
$924$	−2.80794e14	−0.0137149
$925$	−1.78057e16	−0.864529
$926$	−2.24505e16	−1.08359
$927$	−5.58223e14	−0.0267836
$928$	1.28467e16	0.612741
$929$	−1.04273e16	−0.494409	−0.247205	−	0.968963i	$-0.579512\pi$
$929$	−1.04273e16	−0.494409	−0.247205	+	0.968963i	$0.579512\pi$
$930$	−5.97144e13	−0.00281464
$931$	−2.61322e16	−1.22449
$932$	4.43035e15	0.206372
$933$	−1.88697e16	−0.873808
$934$	−3.00975e15	−0.138555
$935$	6.55638e12	0.000300055 0
$936$	−3.07189e15	−0.139762
$937$	−2.29193e16	−1.03665	−0.518326	−	0.855183i	$-0.673445\pi$
$937$	−2.29193e16	−1.03665	−0.518326	+	0.855183i	$0.673445\pi$
$938$	1.80222e16	0.810389
$939$	−2.09802e16	−0.937882
$940$	7.39862e13	0.00328812
$941$	1.18608e15	0.0524049	0.0262025	−	0.999657i	$-0.491659\pi$
$941$	1.18608e15	0.0524049	0.0262025	+	0.999657i	$0.491659\pi$
$942$	5.68703e15	0.249808
$943$	4.33038e14	0.0189109
$944$	−1.88523e15	−0.0818500
$945$	4.24608e13	0.00183279
$946$	−3.37617e15	−0.144885
$947$	−1.55576e16	−0.663769	−0.331885	−	0.943320i	$-0.607685\pi$
$947$	−1.55576e16	−0.663769	−0.331885	+	0.943320i	$0.607685\pi$
$948$	5.65437e14	0.0239849
$949$	−3.33624e15	−0.140700
$950$	−3.60126e16	−1.50999
$951$	−1.70904e16	−0.712460
$952$	1.78106e15	0.0738204
$953$	9.11804e15	0.375743	0.187871	−	0.982194i	$-0.439841\pi$
$953$	9.11804e15	0.375743	0.187871	+	0.982194i	$0.439841\pi$
$954$	2.49538e15	0.102240
$955$	4.60484e14	0.0187584
$956$	−2.64598e15	−0.107169
$957$	−2.31459e15	−0.0932093
$958$	−2.61722e15	−0.104793
$959$	9.04377e15	0.360037
$960$	−2.71335e14	−0.0107402
$961$	−2.24521e16	−0.883644
$962$	7.19258e15	0.281463
$963$	−1.45794e16	−0.567275
$964$	−1.34702e16	−0.521134
$965$	−3.61637e14	−0.0139115
$966$	−1.05939e15	−0.0405211
$967$	−1.89068e16	−0.719071	−0.359535	−	0.933131i	$-0.617065\pi$
$967$	−1.89068e16	−0.719071	−0.359535	+	0.933131i	$0.617065\pi$
$968$	2.81217e16	1.06347
$969$	−3.32112e15	−0.124883
$970$	−2.03278e14	−0.00760058
$971$	−4.50296e16	−1.67414	−0.837070	−	0.547095i	$-0.815734\pi$
$971$	−4.50296e16	−1.67414	−0.837070	+	0.547095i	$0.815734\pi$
$972$	5.00142e14	0.0184896
$973$	1.40186e16	0.515327
$974$	−2.36686e16	−0.865163
$975$	6.12613e15	0.222670
$976$	−2.55927e16	−0.925002
$977$	1.08082e16	0.388449	0.194224	−	0.980957i	$-0.437781\pi$
$977$	1.08082e16	0.388449	0.194224	+	0.980957i	$0.437781\pi$
$978$	−5.61426e15	−0.200645
$979$	1.66797e15	0.0592765
$980$	9.44974e13	0.00333946
$981$	−3.65257e15	−0.128357
$982$	−5.96367e15	−0.208401
$983$	−3.83117e16	−1.33133	−0.665666	−	0.746250i	$-0.731853\pi$
$983$	−3.83117e16	−1.33133	−0.665666	+	0.746250i	$0.731853\pi$
$984$	−2.32056e15	−0.0801900
$985$	−6.41301e14	−0.0220375
$986$	3.28479e15	0.112249
$987$	−6.43216e15	−0.218581
$988$	−5.89072e15	−0.199070
$989$	5.15800e15	0.173341
$990$	2.08981e13	0.000698415 0
$991$	−1.85561e16	−0.616712	−0.308356	−	0.951271i	$-0.599779\pi$
$991$	−1.85561e16	−0.616712	−0.308356	+	0.951271i	$0.599779\pi$
$992$	5.74261e15	0.189800
$993$	3.08902e15	0.101531
$994$	1.64116e15	0.0536446
$995$	2.99642e14	0.00974039
$996$	1.71809e15	0.0555417
$997$	2.11779e16	0.680863	0.340431	−	0.940269i	$-0.389427\pi$
$997$	2.11779e16	0.680863	0.340431	+	0.940269i	$0.389427\pi$
$998$	−2.19607e16	−0.702148
$999$	−5.23398e15	−0.166426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.19	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.19	✓	26	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)

\(f(q)\)	\(=\)	\(q+38.1800 q^{2} -243.000 q^{3} -590.285 q^{4} +118.373 q^{5} -9277.75 q^{6} -24998.6 q^{7} -100730. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+38.1800 q^{2} -243.000 q^{3} -590.285 q^{4} +118.373 q^{5} -9277.75 q^{6} -24998.6 q^{7} -100730. q^{8} +59049.0 q^{9} +4519.50 q^{10} +78307.6 q^{11} +143439. q^{12} +516458. q^{13} -954447. q^{14} -28764.7 q^{15} -2.63696e6 q^{16} +707304. q^{17} +2.25449e6 q^{18} +1.93229e7 q^{19} -69874.0 q^{20} +6.07465e6 q^{21} +2.98979e6 q^{22} -4.56770e6 q^{23} +2.44773e7 q^{24} -4.88141e7 q^{25} +1.97184e7 q^{26} -1.43489e7 q^{27} +1.47563e7 q^{28} +1.21637e8 q^{29} -1.09824e6 q^{30} +5.43729e7 q^{31} +1.05615e8 q^{32} -1.90288e7 q^{33} +2.70049e7 q^{34} -2.95916e6 q^{35} -3.48557e7 q^{36} +3.64765e8 q^{37} +7.37749e8 q^{38} -1.25499e8 q^{39} -1.19237e7 q^{40} -9.48045e7 q^{41} +2.31931e8 q^{42} -1.12923e9 q^{43} -4.62238e7 q^{44} +6.98983e6 q^{45} -1.74395e8 q^{46} -1.05885e9 q^{47} +6.40782e8 q^{48} -1.35240e9 q^{49} -1.86372e9 q^{50} -1.71875e8 q^{51} -3.04857e8 q^{52} +1.10685e9 q^{53} -5.47842e8 q^{54} +9.26954e6 q^{55} +2.51810e9 q^{56} -4.69546e9 q^{57} +4.64409e9 q^{58} +7.14924e8 q^{59} +1.69794e7 q^{60} +9.70538e9 q^{61} +2.07596e9 q^{62} -1.47614e9 q^{63} +9.43290e9 q^{64} +6.11348e7 q^{65} -7.26519e8 q^{66} -1.88824e10 q^{67} -4.17511e8 q^{68} +1.10995e9 q^{69} -1.12981e8 q^{70} -1.71949e9 q^{71} -5.94799e9 q^{72} -6.45985e9 q^{73} +1.39268e10 q^{74} +1.18618e10 q^{75} -1.14060e10 q^{76} -1.95758e9 q^{77} -4.79157e9 q^{78} +3.94200e9 q^{79} -3.12146e8 q^{80} +3.48678e9 q^{81} -3.61964e9 q^{82} +1.19778e10 q^{83} -3.58578e9 q^{84} +8.37260e7 q^{85} -4.31142e10 q^{86} -2.95577e10 q^{87} -7.88791e9 q^{88} +2.13002e10 q^{89} +2.66872e8 q^{90} -1.29107e10 q^{91} +2.69624e9 q^{92} -1.32126e10 q^{93} -4.04270e10 q^{94} +2.28732e9 q^{95} -2.56645e10 q^{96} -4.49781e10 q^{97} -5.16346e10 q^{98} +4.62399e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \)	\( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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