LMFDB - Embedded newform 177.8.a.b.1.16

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$55.2921495107$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
Defining polynomial:	$x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} - 89298188 x^{10} + 64650816672 x^{9} + 33122051904 x^{8} - 6210397064704 x^{7} - 2735256748800 x^{6} + 288860762071040 x^{5} - 34502173230080 x^{4} - 5633463408885760 x^{3} + 4719471961341952 x^{2} + 37636623107620864 x - 58321181718347776$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$18.2619$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q+16.2619 q^{2} +27.0000 q^{3} +136.450 q^{4} -30.6671 q^{5} +439.072 q^{6} -1356.62 q^{7} +137.421 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+16.2619 q^{2} +27.0000 q^{3} +136.450 q^{4} -30.6671 q^{5} +439.072 q^{6} -1356.62 q^{7} +137.421 q^{8} +729.000 q^{9} -498.706 q^{10} +1825.79 q^{11} +3684.16 q^{12} -1173.55 q^{13} -22061.2 q^{14} -828.012 q^{15} -15230.9 q^{16} +13185.9 q^{17} +11854.9 q^{18} -18595.5 q^{19} -4184.54 q^{20} -36628.7 q^{21} +29690.8 q^{22} -14566.3 q^{23} +3710.36 q^{24} -77184.5 q^{25} -19084.3 q^{26} +19683.0 q^{27} -185111. q^{28} -183281. q^{29} -13465.1 q^{30} -265230. q^{31} -265274. q^{32} +49296.2 q^{33} +214428. q^{34} +41603.6 q^{35} +99472.4 q^{36} -260898. q^{37} -302399. q^{38} -31686.0 q^{39} -4214.29 q^{40} +719268. q^{41} -595654. q^{42} -707870. q^{43} +249129. q^{44} -22356.3 q^{45} -236876. q^{46} +1.30218e6 q^{47} -411235. q^{48} +1.01687e6 q^{49} -1.25517e6 q^{50} +356019. q^{51} -160132. q^{52} -1.80784e6 q^{53} +320084. q^{54} -55991.6 q^{55} -186427. q^{56} -502078. q^{57} -2.98051e6 q^{58} -205379. q^{59} -112983. q^{60} +1.38182e6 q^{61} -4.31315e6 q^{62} -988975. q^{63} -2.36431e6 q^{64} +35989.5 q^{65} +801652. q^{66} +2.41963e6 q^{67} +1.79922e6 q^{68} -393290. q^{69} +676555. q^{70} +2.72507e6 q^{71} +100180. q^{72} +3.97598e6 q^{73} -4.24271e6 q^{74} -2.08398e6 q^{75} -2.53736e6 q^{76} -2.47690e6 q^{77} -515275. q^{78} -6.91787e6 q^{79} +467089. q^{80} +531441. q^{81} +1.16967e7 q^{82} +8.32910e6 q^{83} -4.99800e6 q^{84} -404374. q^{85} -1.15113e7 q^{86} -4.94860e6 q^{87} +250901. q^{88} -6.71890e6 q^{89} -363557. q^{90} +1.59207e6 q^{91} -1.98758e6 q^{92} -7.16121e6 q^{93} +2.11760e7 q^{94} +570270. q^{95} -7.16240e6 q^{96} -4.77557e6 q^{97} +1.65363e7 q^{98} +1.33100e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17q - 32q^{2} + 459q^{3} + 1166q^{4} - 1072q^{5} - 864q^{6} - 2407q^{7} - 6645q^{8} + 12393q^{9} + O(q^{10}) $	\( 17q - 32q^{2} + 459q^{3} + 1166q^{4} - 1072q^{5} - 864q^{6} - 2407q^{7} - 6645q^{8} + 12393q^{9} - 6391q^{10} - 8888q^{11} + 31482q^{12} - 12702q^{13} - 17555q^{14} - 28944q^{15} + 139226q^{16} - 36167q^{17} - 23328q^{18} - 71037q^{19} - 274883q^{20} - 64989q^{21} - 325182q^{22} - 269995q^{23} - 179415q^{24} + 97329q^{25} - 336906q^{26} + 334611q^{27} - 901362q^{28} - 543825q^{29} - 172557q^{30} - 633109q^{31} - 837062q^{32} - 239976q^{33} - 529288q^{34} - 287621q^{35} + 850014q^{36} - 867607q^{37} - 1727169q^{38} - 342954q^{39} - 815662q^{40} - 1428939q^{41} - 473985q^{42} - 477060q^{43} - 1667926q^{44} - 781488q^{45} + 5305549q^{46} - 1217849q^{47} + 3759102q^{48} + 4350738q^{49} + 4561369q^{50} - 976509q^{51} + 4175994q^{52} - 3487068q^{53} - 629856q^{54} - 960484q^{55} - 5363196q^{56} - 1917999q^{57} - 3082906q^{58} - 3491443q^{59} - 7421841q^{60} + 998917q^{61} - 5742614q^{62} - 1754703q^{63} + 17531621q^{64} - 6075816q^{65} - 8779914q^{66} - 356026q^{67} - 16149231q^{68} - 7289865q^{69} - 548798q^{70} - 12879428q^{71} - 4844205q^{72} - 6176157q^{73} - 5971906q^{74} + 2627883q^{75} - 17624580q^{76} + 239687q^{77} - 9096462q^{78} - 18886490q^{79} - 70463349q^{80} + 9034497q^{81} - 19351611q^{82} - 22824893q^{83} - 24336774q^{84} - 7973079q^{85} - 27502196q^{86} - 14683275q^{87} - 62527651q^{88} - 30609647q^{89} - 4659039q^{90} - 36301521q^{91} - 41388548q^{92} - 17093943q^{93} + 1010176q^{94} - 29303629q^{95} - 22600674q^{96} - 26249806q^{97} - 93110852q^{98} - 6479352q^{99} + O(q^{100}) \)

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 $

$2$	16.2619	1.43737	0.718683	−	0.695338i	$-0.244745\pi$
$2$	16.2619	1.43737	0.718683	+	0.695338i	$0.244745\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	136.450	1.06602
$5$	−30.6671	−0.109718	−0.0548590	−	0.998494i	$-0.517471\pi$
$5$	−30.6671	−0.109718	−0.0548590	+	0.998494i	$0.517471\pi$
$6$	439.072	0.829863
$7$	−1356.62	−1.49491	−0.747455	−	0.664313i	$-0.768724\pi$
$7$	−1356.62	−1.49491	−0.747455	+	0.664313i	$0.768724\pi$
$8$	137.421	0.0948936
$9$	729.000	0.333333
$10$	−498.706	−0.157705
$11$	1825.79	0.413595	0.206798	−	0.978384i	$-0.433696\pi$
$11$	1825.79	0.413595	0.206798	+	0.978384i	$0.433696\pi$
$12$	3684.16	0.615466
$13$	−1173.55	−0.148150	−0.0740750	−	0.997253i	$-0.523600\pi$
$13$	−1173.55	−0.148150	−0.0740750	+	0.997253i	$0.523600\pi$
$14$	−22061.2	−2.14873
$15$	−828.012	−0.0633457
$16$	−15230.9	−0.929622
$17$	13185.9	0.650937	0.325468	−	0.945553i	$-0.394478\pi$
$17$	13185.9	0.650937	0.325468	+	0.945553i	$0.394478\pi$
$18$	11854.9	0.479122
$19$	−18595.5	−0.621971	−0.310985	−	0.950415i	$-0.600659\pi$
$19$	−18595.5	−0.621971	−0.310985	+	0.950415i	$0.600659\pi$
$20$	−4184.54	−0.116961
$21$	−36628.7	−0.863086
$22$	29690.8	0.594488
$23$	−14566.3	−0.249633	−0.124817	−	0.992180i	$-0.539834\pi$
$23$	−14566.3	−0.249633	−0.124817	+	0.992180i	$0.539834\pi$
$24$	3710.36	0.0547869
$25$	−77184.5	−0.987962
$26$	−19084.3	−0.212946
$27$	19683.0	0.192450
$28$	−185111.	−1.59360
$29$	−183281.	−1.39549	−0.697743	−	0.716348i	$-0.745812\pi$
$29$	−183281.	−1.39549	−0.697743	+	0.716348i	$0.745812\pi$
$30$	−13465.1	−0.0910509
$31$	−265230.	−1.59903	−0.799515	−	0.600646i	$-0.794910\pi$
$31$	−265230.	−1.59903	−0.799515	+	0.600646i	$0.794910\pi$
$32$	−265274.	−1.43110
$33$	49296.2	0.238789
$34$	214428.	0.935634
$35$	41603.6	0.164018
$36$	99472.4	0.355340
$37$	−260898.	−0.846769	−0.423385	−	0.905950i	$-0.639158\pi$
$37$	−260898.	−0.846769	−0.423385	+	0.905950i	$0.639158\pi$
$38$	−302399.	−0.893999
$39$	−31686.0	−0.0855344
$40$	−4214.29	−0.0104115
$41$	719268.	1.62985	0.814924	−	0.579568i	$-0.196779\pi$
$41$	719268.	1.62985	0.814924	+	0.579568i	$0.196779\pi$
$42$	−595654.	−1.24057
$43$	−707870.	−1.35773	−0.678866	−	0.734262i	$-0.737528\pi$
$43$	−707870.	−1.35773	−0.678866	+	0.734262i	$0.737528\pi$
$44$	249129.	0.440900
$45$	−22356.3	−0.0365727
$46$	−236876.	−0.358814
$47$	1.30218e6	1.82948	0.914742	−	0.404038i	$-0.132394\pi$
$47$	1.30218e6	1.82948	0.914742	+	0.404038i	$0.132394\pi$
$48$	−411235.	−0.536718
$49$	1.01687e6	1.23475
$50$	−1.25517e6	−1.42006
$51$	356019.	0.375818
$52$	−160132.	−0.157931
$53$	−1.80784e6	−1.66799	−0.833996	−	0.551770i	$-0.813953\pi$
$53$	−1.80784e6	−1.66799	−0.833996	+	0.551770i	$0.813953\pi$
$54$	320084.	0.276621
$55$	−55991.6	−0.0453788
$56$	−186427.	−0.141857
$57$	−502078.	−0.359095
$58$	−2.98051e6	−2.00582
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−112983.	−0.0675277
$61$	1.38182e6	0.779468	0.389734	−	0.920928i	$-0.372567\pi$
$61$	1.38182e6	0.779468	0.389734	+	0.920928i	$0.372567\pi$
$62$	−4.31315e6	−2.29839
$63$	−988975.	−0.498303
$64$	−2.36431e6	−1.12739
$65$	35989.5	0.0162547
$66$	801652.	0.343228
$67$	2.41963e6	0.982849	0.491424	−	0.870920i	$-0.336476\pi$
$67$	2.41963e6	0.982849	0.491424	+	0.870920i	$0.336476\pi$
$68$	1.79922e6	0.693911
$69$	−393290.	−0.144126
$70$	676555.	0.235754
$71$	2.72507e6	0.903595	0.451797	−	0.892121i	$-0.350783\pi$
$71$	2.72507e6	0.903595	0.451797	+	0.892121i	$0.350783\pi$
$72$	100180.	0.0316312
$73$	3.97598e6	1.19623	0.598115	−	0.801411i	$-0.295917\pi$
$73$	3.97598e6	1.19623	0.598115	+	0.801411i	$0.295917\pi$
$74$	−4.24271e6	−1.21712
$75$	−2.08398e6	−0.570400
$76$	−2.53736e6	−0.663033
$77$	−2.47690e6	−0.618287
$78$	−515275.	−0.122944
$79$	−6.91787e6	−1.57862	−0.789310	−	0.613995i	$-0.789562\pi$
$79$	−6.91787e6	−1.57862	−0.789310	+	0.613995i	$0.789562\pi$
$80$	467089.	0.101996
$81$	531441.	0.111111
$82$	1.16967e7	2.34269
$83$	8.32910e6	1.59891	0.799456	−	0.600725i	$-0.205121\pi$
$83$	8.32910e6	1.59891	0.799456	+	0.600725i	$0.205121\pi$
$84$	−4.99800e6	−0.920066
$85$	−404374.	−0.0714195
$86$	−1.15113e7	−1.95156
$87$	−4.94860e6	−0.805684
$88$	250901.	0.0392476
$89$	−6.71890e6	−1.01026	−0.505130	−	0.863043i	$-0.668556\pi$
$89$	−6.71890e6	−1.01026	−0.505130	+	0.863043i	$0.668556\pi$
$90$	−363557.	−0.0525683
$91$	1.59207e6	0.221471
$92$	−1.98758e6	−0.266114
$93$	−7.16121e6	−0.923200
$94$	2.11760e7	2.62964
$95$	570270.	0.0682414
$96$	−7.16240e6	−0.826246
$97$	−4.77557e6	−0.531281	−0.265640	−	0.964072i	$-0.585583\pi$
$97$	−4.77557e6	−0.531281	−0.265640	+	0.964072i	$0.585583\pi$
$98$	1.65363e7	1.77479
$99$	1.33100e6	0.137865
$100$	−1.05319e7	−1.05319
$101$	1.79352e7	1.73213	0.866066	−	0.499930i	$-0.166641\pi$
$101$	1.79352e7	1.73213	0.866066	+	0.499930i	$0.166641\pi$
$102$	5.78956e6	0.540188
$103$	−1.83344e7	−1.65324	−0.826619	−	0.562762i	$-0.809739\pi$
$103$	−1.83344e7	−1.65324	−0.826619	+	0.562762i	$0.809739\pi$
$104$	−161271.	−0.0140585
$105$	1.12330e6	0.0946961
$106$	−2.93990e7	−2.39752
$107$	1.58268e7	1.24896	0.624480	−	0.781041i	$-0.285311\pi$
$107$	1.58268e7	1.24896	0.624480	+	0.781041i	$0.285311\pi$
$108$	2.68575e6	0.205155
$109$	4.43687e6	0.328159	0.164079	−	0.986447i	$-0.447535\pi$
$109$	4.43687e6	0.328159	0.164079	+	0.986447i	$0.447535\pi$
$110$	−910531.	−0.0652260
$111$	−7.04425e6	−0.488882
$112$	2.06626e7	1.38970
$113$	2.03544e7	1.32704	0.663520	−	0.748159i	$-0.269062\pi$
$113$	2.03544e7	1.32704	0.663520	+	0.748159i	$0.269062\pi$
$114$	−8.16476e6	−0.516151
$115$	446707.	0.0273892
$116$	−2.50088e7	−1.48761
$117$	−855521.	−0.0493833
$118$	−3.33986e6	−0.187129
$119$	−1.78883e7	−0.973091
$120$	−113786.	−0.00601110
$121$	−1.61537e7	−0.828939
$122$	2.24711e7	1.12038
$123$	1.94202e7	0.940993
$124$	−3.61907e7	−1.70460
$125$	4.76289e6	0.218115
$126$	−1.60827e7	−0.716244
$127$	−9.80807e6	−0.424884	−0.212442	−	0.977174i	$-0.568142\pi$
$127$	−9.80807e6	−0.424884	−0.212442	+	0.977174i	$0.568142\pi$
$128$	−4.49319e6	−0.189374
$129$	−1.91125e7	−0.783887
$130$	585259.	0.0233640
$131$	−2.55344e7	−0.992377	−0.496189	−	0.868215i	$-0.665268\pi$
$131$	−2.55344e7	−0.992377	−0.496189	+	0.868215i	$0.665268\pi$
$132$	6.72649e6	0.254554
$133$	2.52270e7	0.929790
$134$	3.93478e7	1.41271
$135$	−603621.	−0.0211152
$136$	1.81202e6	0.0617698
$137$	−5.60036e6	−0.186078	−0.0930388	−	0.995662i	$-0.529658\pi$
$137$	−5.60036e6	−0.186078	−0.0930388	+	0.995662i	$0.529658\pi$
$138$	−6.39566e6	−0.207161
$139$	−994215.	−0.0313999	−0.0157000	−	0.999877i	$-0.504998\pi$
$139$	−994215.	−0.0313999	−0.0157000	+	0.999877i	$0.504998\pi$
$140$	5.67683e6	0.174847
$141$	3.51589e7	1.05625
$142$	4.43149e7	1.29880
$143$	−2.14266e6	−0.0612741
$144$	−1.11033e7	−0.309874
$145$	5.62071e6	0.153110
$146$	6.46572e7	1.71942
$147$	2.74556e7	0.712885
$148$	−3.55997e7	−0.902672
$149$	2.61359e7	0.647269	0.323635	−	0.946182i	$-0.395095\pi$
$149$	2.61359e7	0.647269	0.323635	+	0.946182i	$0.395095\pi$
$150$	−3.38896e7	−0.819873
$151$	−7.02885e7	−1.66136	−0.830682	−	0.556747i	$-0.812049\pi$
$151$	−7.02885e7	−1.66136	−0.830682	+	0.556747i	$0.812049\pi$
$152$	−2.55540e6	−0.0590211
$153$	9.61253e6	0.216979
$154$	−4.02791e7	−0.888705
$155$	8.13383e6	0.175442
$156$	−4.32357e6	−0.0911813
$157$	−2.28654e7	−0.471553	−0.235776	−	0.971807i	$-0.575763\pi$
$157$	−2.28654e7	−0.471553	−0.235776	+	0.971807i	$0.575763\pi$
$158$	−1.12498e8	−2.26905
$159$	−4.88117e7	−0.963016
$160$	8.13519e6	0.157017
$161$	1.97609e7	0.373179
$162$	8.64226e6	0.159707
$163$	−6.26397e7	−1.13290	−0.566452	−	0.824095i	$-0.691684\pi$
$163$	−6.26397e7	−1.13290	−0.566452	+	0.824095i	$0.691684\pi$
$164$	9.81444e7	1.73745
$165$	−1.51177e6	−0.0261995
$166$	1.35447e8	2.29822
$167$	−2.02935e7	−0.337171	−0.168586	−	0.985687i	$-0.553920\pi$
$167$	−2.02935e7	−0.337171	−0.168586	+	0.985687i	$0.553920\pi$
$168$	−5.03354e6	−0.0819014
$169$	−6.13713e7	−0.978052
$170$	−6.57590e6	−0.102656
$171$	−1.35561e7	−0.207324
$172$	−9.65892e7	−1.44737
$173$	−4.43065e7	−0.650588	−0.325294	−	0.945613i	$-0.605463\pi$
$173$	−4.43065e7	−0.650588	−0.325294	+	0.945613i	$0.605463\pi$
$174$	−8.04737e7	−1.15806
$175$	1.04710e8	1.47691
$176$	−2.78084e7	−0.384487
$177$	−5.54523e6	−0.0751646
$178$	−1.09262e8	−1.45211
$179$	1.30339e8	1.69858	0.849292	−	0.527923i	$-0.177029\pi$
$179$	1.30339e8	1.69858	0.849292	+	0.527923i	$0.177029\pi$
$180$	−3.05053e6	−0.0389872
$181$	−8.67394e7	−1.08728	−0.543640	−	0.839319i	$-0.682954\pi$
$181$	−8.67394e7	−1.08728	−0.543640	+	0.839319i	$0.682954\pi$
$182$	2.58901e7	0.318334
$183$	3.73092e7	0.450026
$184$	−2.00171e6	−0.0236886
$185$	8.00099e6	0.0929058
$186$	−1.16455e8	−1.32698
$187$	2.40746e7	0.269224
$188$	1.77683e8	1.95027
$189$	−2.67023e7	−0.287695
$190$	9.27369e6	0.0980878
$191$	−1.00406e8	−1.04266	−0.521330	−	0.853355i	$-0.674564\pi$
$191$	−1.00406e8	−1.04266	−0.521330	+	0.853355i	$0.674564\pi$
$192$	−6.38364e7	−0.650900
$193$	1.63066e8	1.63272	0.816361	−	0.577542i	$-0.195988\pi$
$193$	1.63066e8	1.63272	0.816361	+	0.577542i	$0.195988\pi$
$194$	−7.76600e7	−0.763645
$195$	971717.	0.00938466
$196$	1.38753e8	1.31627
$197$	1.22832e8	1.14467	0.572335	−	0.820020i	$-0.306038\pi$
$197$	1.22832e8	1.14467	0.572335	+	0.820020i	$0.306038\pi$
$198$	2.16446e7	0.198163
$199$	1.85902e8	1.67224	0.836119	−	0.548549i	$-0.184820\pi$
$199$	1.85902e8	1.67224	0.836119	+	0.548549i	$0.184820\pi$
$200$	−1.06067e7	−0.0937513
$201$	6.53299e7	0.567448
$202$	2.91661e8	2.48971
$203$	2.48643e8	2.08612
$204$	4.85790e7	0.400630
$205$	−2.20579e7	−0.178824
$206$	−2.98152e8	−2.37631
$207$	−1.06188e7	−0.0832110
$208$	1.78743e7	0.137724
$209$	−3.39514e7	−0.257244
$210$	1.82670e7	0.136113
$211$	4.25639e6	0.0311927	0.0155963	−	0.999878i	$-0.495035\pi$
$211$	4.25639e6	0.0311927	0.0155963	+	0.999878i	$0.495035\pi$
$212$	−2.46680e8	−1.77811
$213$	7.35769e7	0.521691
$214$	2.57374e8	1.79521
$215$	2.17083e7	0.148968
$216$	2.70485e6	0.0182623
$217$	3.59816e8	2.39040
$218$	7.21521e7	0.471684
$219$	1.07352e8	0.690643
$220$	−7.64008e6	−0.0483747
$221$	−1.54744e7	−0.0964362
$222$	−1.14553e8	−0.702703
$223$	−1.01090e8	−0.610437	−0.305219	−	0.952282i	$-0.598730\pi$
$223$	−1.01090e8	−0.610437	−0.305219	+	0.952282i	$0.598730\pi$
$224$	3.59876e8	2.13937
$225$	−5.62675e7	−0.329321
$226$	3.31002e8	1.90744
$227$	−1.56725e8	−0.889299	−0.444650	−	0.895705i	$-0.646672\pi$
$227$	−1.56725e8	−0.889299	−0.444650	+	0.895705i	$0.646672\pi$
$228$	−6.85088e7	−0.382802
$229$	2.30104e8	1.26619	0.633097	−	0.774072i	$-0.281783\pi$
$229$	2.30104e8	1.26619	0.633097	+	0.774072i	$0.281783\pi$
$230$	7.26431e6	0.0393683
$231$	−6.68762e7	−0.356968
$232$	−2.51866e7	−0.132423
$233$	9.45434e7	0.489649	0.244825	−	0.969567i	$-0.421270\pi$
$233$	9.45434e7	0.489649	0.244825	+	0.969567i	$0.421270\pi$
$234$	−1.39124e7	−0.0709819
$235$	−3.99341e7	−0.200727
$236$	−2.80241e7	−0.138784
$237$	−1.86783e8	−0.911417
$238$	−2.90898e8	−1.39869
$239$	−2.18199e8	−1.03385	−0.516927	−	0.856029i	$-0.672924\pi$
$239$	−2.18199e8	−1.03385	−0.516927	+	0.856029i	$0.672924\pi$
$240$	1.26114e7	0.0588876
$241$	−7.52814e7	−0.346440	−0.173220	−	0.984883i	$-0.555417\pi$
$241$	−7.52814e7	−0.346440	−0.173220	+	0.984883i	$0.555417\pi$
$242$	−2.62690e8	−1.19149
$243$	1.43489e7	0.0641500
$244$	1.88550e8	0.830927
$245$	−3.11845e7	−0.135475
$246$	3.15811e8	1.35255
$247$	2.18228e7	0.0921450
$248$	−3.64481e7	−0.151738
$249$	2.24886e8	0.923132
$250$	7.74539e7	0.313511
$251$	−2.48536e8	−0.992046	−0.496023	−	0.868309i	$-0.665207\pi$
$251$	−2.48536e8	−0.992046	−0.496023	+	0.868309i	$0.665207\pi$
$252$	−1.34946e8	−0.531201
$253$	−2.65950e7	−0.103247
$254$	−1.59498e8	−0.610714
$255$	−1.09181e7	−0.0412340
$256$	2.29564e8	0.855193
$257$	9.48986e7	0.348734	0.174367	−	0.984681i	$-0.444212\pi$
$257$	9.48986e7	0.348734	0.174367	+	0.984681i	$0.444212\pi$
$258$	−3.10806e8	−1.12673
$259$	3.53939e8	1.26584
$260$	4.91079e6	0.0173278
$261$	−1.33612e8	−0.465162
$262$	−4.15239e8	−1.42641
$263$	7.74187e7	0.262422	0.131211	−	0.991354i	$-0.458113\pi$
$263$	7.74187e7	0.262422	0.131211	+	0.991354i	$0.458113\pi$
$264$	6.77432e6	0.0226596
$265$	5.54412e7	0.183009
$266$	4.10240e8	1.33645
$267$	−1.81410e8	−0.583274
$268$	3.30159e8	1.04774
$269$	−1.48368e8	−0.464738	−0.232369	−	0.972628i	$-0.574648\pi$
$269$	−1.48368e8	−0.464738	−0.232369	+	0.972628i	$0.574648\pi$
$270$	−9.81604e6	−0.0303503
$271$	2.14037e8	0.653275	0.326637	−	0.945150i	$-0.394084\pi$
$271$	2.14037e8	0.653275	0.326637	+	0.945150i	$0.394084\pi$
$272$	−2.00834e8	−0.605125
$273$	4.29858e7	0.127866
$274$	−9.10727e7	−0.267462
$275$	−1.40922e8	−0.408616
$276$	−5.36647e7	−0.153641
$277$	−4.49384e8	−1.27039	−0.635196	−	0.772351i	$-0.719081\pi$
$277$	−4.49384e8	−1.27039	−0.635196	+	0.772351i	$0.719081\pi$
$278$	−1.61679e7	−0.0451331
$279$	−1.93353e8	−0.533010
$280$	5.71719e6	0.0155643
$281$	5.47292e7	0.147145	0.0735727	−	0.997290i	$-0.476560\pi$
$281$	5.47292e7	0.147145	0.0735727	+	0.997290i	$0.476560\pi$
$282$	5.71751e8	1.51822
$283$	−6.96310e8	−1.82621	−0.913104	−	0.407727i	$-0.866322\pi$
$283$	−6.96310e8	−1.82621	−0.913104	+	0.407727i	$0.866322\pi$
$284$	3.71837e8	0.963249
$285$	1.53973e7	0.0393992
$286$	−3.48438e7	−0.0880733
$287$	−9.75773e8	−2.43648
$288$	−1.93385e8	−0.477034
$289$	−2.36471e8	−0.576281
$290$	9.14036e7	0.220075
$291$	−1.28940e8	−0.306735
$292$	5.42525e8	1.27520
$293$	−1.58823e8	−0.368874	−0.184437	−	0.982844i	$-0.559046\pi$
$293$	−1.58823e8	−0.368874	−0.184437	+	0.982844i	$0.559046\pi$
$294$	4.46480e8	1.02468
$295$	6.29838e6	0.0142841
$296$	−3.58528e7	−0.0803530
$297$	3.59370e7	0.0795964
$298$	4.25020e8	0.930363
$299$	1.70944e7	0.0369831
$300$	−2.84360e8	−0.608057
$301$	9.60310e8	2.02969
$302$	−1.14303e9	−2.38799
$303$	4.84250e8	1.00005
$304$	2.83227e8	0.578198
$305$	−4.23765e7	−0.0855216
$306$	1.56318e8	0.311878
$307$	2.01551e8	0.397558	0.198779	−	0.980044i	$-0.436302\pi$
$307$	2.01551e8	0.397558	0.198779	+	0.980044i	$0.436302\pi$
$308$	−3.37974e8	−0.659106
$309$	−4.95028e8	−0.954497
$310$	1.32272e8	0.252175
$311$	3.80395e8	0.717090	0.358545	−	0.933513i	$-0.383273\pi$
$311$	3.80395e8	0.717090	0.358545	+	0.933513i	$0.383273\pi$
$312$	−4.35431e6	−0.00811667
$313$	1.43971e8	0.265382	0.132691	−	0.991157i	$-0.457638\pi$
$313$	1.43971e8	0.265382	0.132691	+	0.991157i	$0.457638\pi$
$314$	−3.71836e8	−0.677794
$315$	3.03290e7	0.0546728
$316$	−9.43947e8	−1.68284
$317$	−3.85345e8	−0.679426	−0.339713	−	0.940529i	$-0.610330\pi$
$317$	−3.85345e8	−0.679426	−0.339713	+	0.940529i	$0.610330\pi$
$318$	−7.93772e8	−1.38421
$319$	−3.34633e8	−0.577166
$320$	7.25066e7	0.123695
$321$	4.27322e8	0.721087
$322$	3.21351e8	0.536394
$323$	−2.45198e8	−0.404864
$324$	7.25154e7	0.118447
$325$	9.05803e7	0.146367
$326$	−1.01864e9	−1.62840
$327$	1.19796e8	0.189463
$328$	9.88423e7	0.154662
$329$	−1.76656e9	−2.73491
$330$	−2.45843e7	−0.0376582
$331$	−5.09634e8	−0.772432	−0.386216	−	0.922408i	$-0.626218\pi$
$331$	−5.09634e8	−0.772432	−0.386216	+	0.922408i	$0.626218\pi$
$332$	1.13651e9	1.70447
$333$	−1.90195e8	−0.282256
$334$	−3.30012e8	−0.484638
$335$	−7.42030e7	−0.107836
$336$	5.57889e8	0.802344
$337$	3.29994e8	0.469679	0.234840	−	0.972034i	$-0.424543\pi$
$337$	3.29994e8	0.469679	0.234840	+	0.972034i	$0.424543\pi$
$338$	−9.98016e8	−1.40582
$339$	5.49569e8	0.766167
$340$	−5.51770e7	−0.0761345
$341$	−4.84253e8	−0.661351
$342$	−2.20449e8	−0.298000
$343$	−2.62274e8	−0.350935
$344$	−9.72760e7	−0.128840
$345$	1.20611e7	0.0158132
$346$	−7.20510e8	−0.935133
$347$	−1.54205e9	−1.98128	−0.990642	−	0.136488i	$-0.956418\pi$
$347$	−1.54205e9	−1.98128	−0.990642	+	0.136488i	$0.956418\pi$
$348$	−6.75238e8	−0.858874
$349$	−3.37260e8	−0.424694	−0.212347	−	0.977194i	$-0.568111\pi$
$349$	−3.37260e8	−0.424694	−0.212347	+	0.977194i	$0.568111\pi$
$350$	1.70279e9	2.12286
$351$	−2.30991e7	−0.0285115
$352$	−4.84334e8	−0.591896
$353$	−8.38966e8	−1.01516	−0.507578	−	0.861606i	$-0.669459\pi$
$353$	−8.38966e8	−1.01516	−0.507578	+	0.861606i	$0.669459\pi$
$354$	−9.01762e7	−0.108039
$355$	−8.35701e7	−0.0991406
$356$	−9.16797e8	−1.07696
$357$	−4.82983e8	−0.561814
$358$	2.11956e9	2.44149
$359$	−5.75290e8	−0.656231	−0.328115	−	0.944638i	$-0.606413\pi$
$359$	−5.75290e8	−0.656231	−0.328115	+	0.944638i	$0.606413\pi$
$360$	−3.07222e6	−0.00347051
$361$	−5.48079e8	−0.613152
$362$	−1.41055e9	−1.56282
$363$	−4.36149e8	−0.478588
$364$	2.17238e8	0.236092
$365$	−1.21932e8	−0.131248
$366$	6.06720e8	0.646852
$367$	−1.63254e8	−0.172398	−0.0861990	−	0.996278i	$-0.527472\pi$
$367$	−1.63254e8	−0.172398	−0.0861990	+	0.996278i	$0.527472\pi$
$368$	2.21859e8	0.232065
$369$	5.24346e8	0.543283
$370$	1.30112e8	0.133540
$371$	2.45255e9	2.49350
$372$	−9.77150e8	−0.984149
$373$	−5.02935e8	−0.501801	−0.250900	−	0.968013i	$-0.580727\pi$
$373$	−5.02935e8	−0.501801	−0.250900	+	0.968013i	$0.580727\pi$
$374$	3.91500e8	0.386974
$375$	1.28598e8	0.125929
$376$	1.78947e8	0.173606
$377$	2.15091e8	0.206741
$378$	−4.34232e8	−0.413523
$379$	1.84658e9	1.74234	0.871168	−	0.490986i	$-0.163363\pi$
$379$	1.84658e9	1.74234	0.871168	+	0.490986i	$0.163363\pi$
$380$	7.78136e7	0.0727466
$381$	−2.64818e8	−0.245307
$382$	−1.63279e9	−1.49868
$383$	78579.0	7.14679e−5 0	3.57339e−5	−	1.00000i	$-0.499989\pi$
$383$	78579.0	7.14679e−5 0	3.57339e−5		1.00000i	$0.499989\pi$
$384$	−1.21316e8	−0.109335
$385$	7.59593e7	0.0678372
$386$	2.65176e9	2.34682
$387$	−5.16037e8	−0.452577
$388$	−6.51629e8	−0.566355
$389$	1.01883e9	0.877561	0.438780	−	0.898594i	$-0.355411\pi$
$389$	1.01883e9	0.877561	0.438780	+	0.898594i	$0.355411\pi$
$390$	1.58020e7	0.0134892
$391$	−1.92070e8	−0.162495
$392$	1.39739e8	0.117170
$393$	−6.89430e8	−0.572949
$394$	1.99749e9	1.64531
$395$	2.12151e8	0.173203
$396$	1.81615e8	0.146967
$397$	3.45551e8	0.277170	0.138585	−	0.990351i	$-0.455745\pi$
$397$	3.45551e8	0.277170	0.138585	+	0.990351i	$0.455745\pi$
$398$	3.02312e9	2.40362
$399$	6.81129e8	0.536814
$400$	1.17559e9	0.918431
$401$	−2.15091e9	−1.66578	−0.832890	−	0.553439i	$-0.813315\pi$
$401$	−2.15091e9	−1.66578	−0.832890	+	0.553439i	$0.813315\pi$
$402$	1.06239e9	0.815630
$403$	3.11262e8	0.236896
$404$	2.44726e9	1.84649
$405$	−1.62978e7	−0.0121909
$406$	4.04342e9	2.99852
$407$	−4.76344e8	−0.350220
$408$	4.89244e7	0.0356628
$409$	−2.23244e8	−0.161342	−0.0806710	−	0.996741i	$-0.525706\pi$
$409$	−2.23244e8	−0.161342	−0.0806710	+	0.996741i	$0.525706\pi$
$410$	−3.58704e8	−0.257035
$411$	−1.51210e8	−0.107432
$412$	−2.50173e9	−1.76238
$413$	2.78621e8	0.194621
$414$	−1.72683e8	−0.119605
$415$	−2.55429e8	−0.175429
$416$	3.11314e8	0.212017
$417$	−2.68438e7	−0.0181287
$418$	−5.52115e8	−0.369754
$419$	−1.16588e9	−0.774291	−0.387146	−	0.922019i	$-0.626539\pi$
$419$	−1.16588e9	−0.774291	−0.387146	+	0.922019i	$0.626539\pi$
$420$	1.53274e8	0.100948
$421$	−9.44097e8	−0.616637	−0.308318	−	0.951283i	$-0.599766\pi$
$421$	−9.44097e8	−0.616637	−0.308318	+	0.951283i	$0.599766\pi$
$422$	6.92171e7	0.0448353
$423$	9.49290e8	0.609828
$424$	−2.48434e8	−0.158282
$425$	−1.01775e9	−0.643101
$426$	1.19650e9	0.749860
$427$	−1.87461e9	−1.16523
$428$	2.15957e9	1.33142
$429$	−5.78518e7	−0.0353766
$430$	3.53019e8	0.214121
$431$	−1.01990e9	−0.613600	−0.306800	−	0.951774i	$-0.599258\pi$
$431$	−1.01990e9	−0.613600	−0.306800	+	0.951774i	$0.599258\pi$
$432$	−2.99790e8	−0.178906
$433$	−4.96072e8	−0.293655	−0.146827	−	0.989162i	$-0.546906\pi$
$433$	−4.96072e8	−0.293655	−0.146827	+	0.989162i	$0.546906\pi$
$434$	5.85130e9	3.43588
$435$	1.51759e8	0.0883980
$436$	6.05413e8	0.349824
$437$	2.70868e8	0.155265
$438$	1.74574e9	0.992707
$439$	1.84581e9	1.04126	0.520632	−	0.853781i	$-0.325697\pi$
$439$	1.84581e9	1.04126	0.520632	+	0.853781i	$0.325697\pi$
$440$	−7.69440e6	−0.00430616
$441$	7.41300e8	0.411584
$442$	−2.51643e8	−0.138614
$443$	2.12406e8	0.116079	0.0580394	−	0.998314i	$-0.481515\pi$
$443$	2.12406e8	0.116079	0.0580394	+	0.998314i	$0.481515\pi$
$444$	−9.61191e8	−0.521158
$445$	2.06049e8	0.110844
$446$	−1.64392e9	−0.877421
$447$	7.05669e8	0.373701
$448$	3.20747e9	1.68535
$449$	−3.53221e9	−1.84155	−0.920777	−	0.390090i	$-0.872444\pi$
$449$	−3.53221e9	−1.84155	−0.920777	+	0.390090i	$0.872444\pi$
$450$	−9.15019e8	−0.473354
$451$	1.31323e9	0.674098
$452$	2.77737e9	1.41465
$453$	−1.89779e9	−0.959189
$454$	−2.54865e9	−1.27825
$455$	−4.88241e7	−0.0242993
$456$	−6.89959e7	−0.0340758
$457$	2.05595e9	1.00764	0.503821	−	0.863808i	$-0.331927\pi$
$457$	2.05595e9	1.00764	0.503821	+	0.863808i	$0.331927\pi$
$458$	3.74194e9	1.81998
$459$	2.59538e8	0.125273
$460$	6.09533e7	0.0291975
$461$	−1.34533e9	−0.639551	−0.319776	−	0.947493i	$-0.603608\pi$
$461$	−1.34533e9	−0.639551	−0.319776	+	0.947493i	$0.603608\pi$
$462$	−1.08754e9	−0.513094
$463$	1.16277e9	0.544452	0.272226	−	0.962233i	$-0.412240\pi$
$463$	1.16277e9	0.544452	0.272226	+	0.962233i	$0.412240\pi$
$464$	2.79155e9	1.29727
$465$	2.19613e8	0.101292
$466$	1.53746e9	0.703805
$467$	3.37053e9	1.53140	0.765700	−	0.643198i	$-0.222393\pi$
$467$	3.37053e9	1.53140	0.765700	+	0.643198i	$0.222393\pi$
$468$	−1.16736e8	−0.0526436
$469$	−3.28251e9	−1.46927
$470$	−6.49406e8	−0.288519
$471$	−6.17366e8	−0.272251
$472$	−2.82233e7	−0.0123541
$473$	−1.29242e9	−0.561552
$474$	−3.03744e9	−1.31004
$475$	1.43528e9	0.614484
$476$	−2.44086e9	−1.03733
$477$	−1.31791e9	−0.555998
$478$	−3.54833e9	−1.48603
$479$	−1.66586e9	−0.692571	−0.346286	−	0.938129i	$-0.612557\pi$
$479$	−1.66586e9	−0.692571	−0.346286	+	0.938129i	$0.612557\pi$
$480$	2.19650e8	0.0906541
$481$	3.06178e8	0.125449
$482$	−1.22422e9	−0.497961
$483$	5.33545e8	0.215455
$484$	−2.20418e9	−0.883665
$485$	1.46453e8	0.0582910
$486$	2.33341e8	0.0922070
$487$	−1.02449e9	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$487$	−1.02449e9	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$488$	1.89891e8	0.0739665
$489$	−1.69127e9	−0.654082
$490$	−5.07121e8	−0.194727
$491$	2.27469e9	0.867235	0.433618	−	0.901097i	$-0.357237\pi$
$491$	2.27469e9	0.867235	0.433618	+	0.901097i	$0.357237\pi$
$492$	2.64990e9	1.00312
$493$	−2.41673e9	−0.908373
$494$	3.54881e8	0.132446
$495$	−4.08179e7	−0.0151263
$496$	4.03970e9	1.48649
$497$	−3.69688e9	−1.35079
$498$	3.65707e9	1.32688
$499$	2.02609e9	0.729971	0.364986	−	0.931013i	$-0.381074\pi$
$499$	2.02609e9	0.729971	0.364986	+	0.931013i	$0.381074\pi$
$500$	6.49899e8	0.232515
$501$	−5.47926e8	−0.194666
$502$	−4.04168e9	−1.42593
$503$	1.54149e9	0.540073	0.270037	−	0.962850i	$-0.412964\pi$
$503$	1.54149e9	0.540073	0.270037	+	0.962850i	$0.412964\pi$
$504$	−1.35906e8	−0.0472858
$505$	−5.50020e8	−0.190046
$506$	−4.32486e8	−0.148404
$507$	−1.65702e9	−0.564678
$508$	−1.33832e9	−0.452935
$509$	3.87817e9	1.30351	0.651755	−	0.758430i	$-0.274033\pi$
$509$	3.87817e9	1.30351	0.651755	+	0.758430i	$0.274033\pi$
$510$	−1.77549e8	−0.0592684
$511$	−5.39389e9	−1.78825
$512$	4.30828e9	1.41860
$513$	−3.66015e8	−0.119698
$514$	1.54323e9	0.501258
$515$	5.62262e8	0.181390
$516$	−2.60791e9	−0.835638
$517$	2.37750e9	0.756666
$518$	5.75574e9	1.81948
$519$	−1.19628e9	−0.375617
$520$	4.94570e6	0.00154247
$521$	−4.39564e8	−0.136173	−0.0680864	−	0.997679i	$-0.521689\pi$
$521$	−4.39564e8	−0.136173	−0.0680864	+	0.997679i	$0.521689\pi$
$522$	−2.17279e9	−0.668607
$523$	−6.36830e9	−1.94656	−0.973280	−	0.229623i	$-0.926251\pi$
$523$	−6.36830e9	−1.94656	−0.973280	+	0.229623i	$0.926251\pi$
$524$	−3.48419e9	−1.05789
$525$	2.82717e9	0.852696
$526$	1.25898e9	0.377197
$527$	−3.49730e9	−1.04087
$528$	−7.50828e8	−0.221984
$529$	−3.19265e9	−0.937683
$530$	9.01581e8	0.263051
$531$	−1.49721e8	−0.0433963
$532$	3.44224e9	0.991174
$533$	−8.44100e8	−0.241462
$534$	−2.95008e9	−0.838378
$535$	−4.85361e8	−0.137033
$536$	3.32507e8	0.0932661
$537$	3.51914e9	0.980678
$538$	−2.41276e9	−0.667999
$539$	1.85659e9	0.510688
$540$	−8.23643e7	−0.0225092
$541$	−1.34859e9	−0.366175	−0.183088	−	0.983097i	$-0.558609\pi$
$541$	−1.34859e9	−0.366175	−0.183088	+	0.983097i	$0.558609\pi$
$542$	3.48065e9	0.938995
$543$	−2.34196e9	−0.627741
$544$	−3.49788e9	−0.931556
$545$	−1.36066e8	−0.0360049
$546$	6.99032e8	0.183790
$547$	−2.38331e9	−0.622622	−0.311311	−	0.950308i	$-0.600768\pi$
$547$	−2.38331e9	−0.622622	−0.311311	+	0.950308i	$0.600768\pi$
$548$	−7.64172e8	−0.198362
$549$	1.00735e9	0.259823
$550$	−2.29167e9	−0.587331
$551$	3.40821e9	0.867951
$552$	−5.40462e7	−0.0136766
$553$	9.38492e9	2.35989
$554$	−7.30785e9	−1.82602
$555$	2.16027e8	0.0536392
$556$	−1.35661e8	−0.0334729
$557$	−2.39992e8	−0.0588442	−0.0294221	−	0.999567i	$-0.509367\pi$
$557$	−2.39992e8	−0.0588442	−0.0294221	+	0.999567i	$0.509367\pi$
$558$	−3.14429e9	−0.766130
$559$	8.30724e8	0.201148
$560$	−6.33661e8	−0.152475
$561$	6.50016e8	0.155437
$562$	8.90002e8	0.211502
$563$	−1.44852e9	−0.342093	−0.171047	−	0.985263i	$-0.554715\pi$
$563$	−1.44852e9	−0.342093	−0.171047	+	0.985263i	$0.554715\pi$
$564$	4.79745e9	1.12599
$565$	−6.24211e8	−0.145600
$566$	−1.13234e10	−2.62493
$567$	−7.20963e8	−0.166101
$568$	3.74481e8	0.0857454
$569$	7.46267e9	1.69825	0.849124	−	0.528193i	$-0.177130\pi$
$569$	7.46267e9	1.69825	0.849124	+	0.528193i	$0.177130\pi$
$570$	2.50390e8	0.0566310
$571$	1.56608e9	0.352036	0.176018	−	0.984387i	$-0.443678\pi$
$571$	1.56608e9	0.352036	0.176018	+	0.984387i	$0.443678\pi$
$572$	−2.92367e8	−0.0653194
$573$	−2.71096e9	−0.601980
$574$	−1.58679e10	−3.50211
$575$	1.12429e9	0.246628
$576$	−1.72358e9	−0.375797
$577$	−6.11728e7	−0.0132569	−0.00662847	−	0.999978i	$-0.502110\pi$
$577$	−6.11728e7	−0.0132569	−0.00662847	+	0.999978i	$0.502110\pi$
$578$	−3.84547e9	−0.828327
$579$	4.40278e9	0.942653
$580$	7.66948e8	0.163218
$581$	−1.12994e10	−2.39023
$582$	−2.09682e9	−0.440890
$583$	−3.30073e9	−0.689874
$584$	5.46382e8	0.113515
$585$	2.62364e7	0.00541824
$586$	−2.58277e9	−0.530206
$587$	2.95616e9	0.603245	0.301623	−	0.953427i	$-0.402472\pi$
$587$	2.95616e9	0.603245	0.301623	+	0.953427i	$0.402472\pi$
$588$	3.74632e9	0.759949
$589$	4.93208e9	0.994550
$590$	1.02424e8	0.0205314
$591$	3.31647e9	0.660875
$592$	3.97372e9	0.787175
$593$	1.97406e8	0.0388748	0.0194374	−	0.999811i	$-0.493812\pi$
$593$	1.97406e8	0.0388748	0.0194374	+	0.999811i	$0.493812\pi$
$594$	5.84404e8	0.114409
$595$	5.48581e8	0.106766
$596$	3.56625e9	0.690002
$597$	5.01935e9	0.965467
$598$	2.77987e8	0.0531583
$599$	8.20815e8	0.156046	0.0780228	−	0.996952i	$-0.475139\pi$
$599$	8.20815e8	0.156046	0.0780228	+	0.996952i	$0.475139\pi$
$600$	−2.86382e8	−0.0541273
$601$	9.75118e9	1.83230	0.916150	−	0.400837i	$-0.131280\pi$
$601$	9.75118e9	1.83230	0.916150	+	0.400837i	$0.131280\pi$
$602$	1.56165e10	2.91740
$603$	1.76391e9	0.327616
$604$	−9.59089e9	−1.77105
$605$	4.95386e8	0.0909495
$606$	7.87484e9	1.43743
$607$	−5.21137e9	−0.945784	−0.472892	−	0.881120i	$-0.656790\pi$
$607$	−5.21137e9	−0.945784	−0.472892	+	0.881120i	$0.656790\pi$
$608$	4.93290e9	0.890103
$609$	6.71336e9	1.20442
$610$	−6.89124e8	−0.122926
$611$	−1.52818e9	−0.271038
$612$	1.31163e9	0.231304
$613$	−1.02466e9	−0.179666	−0.0898330	−	0.995957i	$-0.528633\pi$
$613$	−1.02466e9	−0.179666	−0.0898330	+	0.995957i	$0.528633\pi$
$614$	3.27761e9	0.571437
$615$	−5.95562e8	−0.103244
$616$	−3.40377e8	−0.0586715
$617$	−1.71355e9	−0.293696	−0.146848	−	0.989159i	$-0.546913\pi$
$617$	−1.71355e9	−0.293696	−0.146848	+	0.989159i	$0.546913\pi$
$618$	−8.05010e9	−1.37196
$619$	3.38211e9	0.573153	0.286577	−	0.958057i	$-0.407483\pi$
$619$	3.38211e9	0.573153	0.286577	+	0.958057i	$0.407483\pi$
$620$	1.10987e9	0.187025
$621$	−2.86709e8	−0.0480419
$622$	6.18596e9	1.03072
$623$	9.11499e9	1.51025
$624$	4.82607e8	0.0795147
$625$	5.88398e9	0.964031
$626$	2.34125e9	0.381451
$627$	−9.16688e8	−0.148520
$628$	−3.12000e9	−0.502684
$629$	−3.44018e9	−0.551193
$630$	4.93208e8	0.0785848
$631$	2.96207e8	0.0469345	0.0234673	−	0.999725i	$-0.492529\pi$
$631$	2.96207e8	0.0469345	0.0234673	+	0.999725i	$0.492529\pi$
$632$	−9.50658e8	−0.149801
$633$	1.14922e8	0.0180091
$634$	−6.26645e9	−0.976583
$635$	3.00785e8	0.0466174
$636$	−6.66037e9	−1.02659
$637$	−1.19336e9	−0.182929
$638$	−5.44177e9	−0.829599
$639$	1.98658e9	0.301198
$640$	1.37793e8	0.0207777
$641$	5.82615e9	0.873732	0.436866	−	0.899526i	$-0.356088\pi$
$641$	5.82615e9	0.873732	0.436866	+	0.899526i	$0.356088\pi$
$642$	6.94909e9	1.03647
$643$	−5.33573e9	−0.791508	−0.395754	−	0.918357i	$-0.629517\pi$
$643$	−5.33573e9	−0.791508	−0.395754	+	0.918357i	$0.629517\pi$
$644$	2.69639e9	0.397816
$645$	5.86125e8	0.0860065
$646$	−3.98740e9	−0.581937
$647$	1.10418e10	1.60279	0.801393	−	0.598138i	$-0.204093\pi$
$647$	1.10418e10	1.60279	0.801393	+	0.598138i	$0.204093\pi$
$648$	7.30310e7	0.0105437
$649$	−3.74978e8	−0.0538455
$650$	1.47301e9	0.210382
$651$	9.71503e9	1.38010
$652$	−8.54722e9	−1.20770
$653$	−7.56490e9	−1.06318	−0.531590	−	0.847002i	$-0.678405\pi$
$653$	−7.56490e9	−1.06318	−0.531590	+	0.847002i	$0.678405\pi$
$654$	1.94811e9	0.272327
$655$	7.83068e8	0.108882
$656$	−1.09551e10	−1.51514
$657$	2.89849e9	0.398743
$658$	−2.87277e10	−3.93107
$659$	−5.59162e9	−0.761095	−0.380547	−	0.924761i	$-0.624264\pi$
$659$	−5.59162e9	−0.761095	−0.380547	+	0.924761i	$0.624264\pi$
$660$	−2.06282e8	−0.0279292
$661$	−1.88074e9	−0.253293	−0.126647	−	0.991948i	$-0.540421\pi$
$661$	−1.88074e9	−0.253293	−0.126647	+	0.991948i	$0.540421\pi$
$662$	−8.28763e9	−1.11027
$663$	−4.17808e8	−0.0556775
$664$	1.14459e9	0.151727
$665$	−7.73639e8	−0.102015
$666$	−3.09293e9	−0.405705
$667$	2.66973e9	0.348359
$668$	−2.76906e9	−0.359431
$669$	−2.72943e9	−0.352436
$670$	−1.20668e9	−0.155000
$671$	2.52291e9	0.322384
$672$	9.71665e9	1.23516
$673$	8.51715e9	1.07706	0.538532	−	0.842605i	$-0.318979\pi$
$673$	8.51715e9	1.07706	0.538532	+	0.842605i	$0.318979\pi$
$674$	5.36634e9	0.675101
$675$	−1.51922e9	−0.190133
$676$	−8.37414e9	−1.04262
$677$	−1.19888e10	−1.48497	−0.742484	−	0.669864i	$-0.766352\pi$
$677$	−1.19888e10	−1.48497	−0.742484	+	0.669864i	$0.766352\pi$
$678$	8.93705e9	1.10126
$679$	6.47863e9	0.794216
$680$	−5.55693e7	−0.00677725
$681$	−4.23158e9	−0.513437
$682$	−7.87489e9	−0.950603
$683$	−7.29599e9	−0.876217	−0.438109	−	0.898922i	$-0.644351\pi$
$683$	−7.29599e9	−0.876217	−0.438109	+	0.898922i	$0.644351\pi$
$684$	−1.84974e9	−0.221011
$685$	1.71747e8	0.0204161
$686$	−4.26509e9	−0.504422
$687$	6.21282e9	0.731038
$688$	1.07815e10	1.26218
$689$	2.12160e9	0.247113
$690$	1.96136e8	0.0227293
$691$	2.48922e9	0.287006	0.143503	−	0.989650i	$-0.454163\pi$
$691$	2.48922e9	0.287006	0.143503	+	0.989650i	$0.454163\pi$
$692$	−6.04564e9	−0.693540
$693$	−1.80566e9	−0.206096
$694$	−2.50768e10	−2.84783
$695$	3.04897e7	0.00344513
$696$	−6.80039e8	−0.0764543
$697$	9.48420e9	1.06093
$698$	−5.48450e9	−0.610440
$699$	2.55267e9	0.282699
$700$	1.42877e10	1.57442
$701$	1.04516e10	1.14596	0.572980	−	0.819570i	$-0.305787\pi$
$701$	1.04516e10	1.14596	0.572980	+	0.819570i	$0.305787\pi$
$702$	−3.75636e8	−0.0409814
$703$	4.85153e9	0.526666
$704$	−4.31673e9	−0.466284
$705$	−1.07822e9	−0.115890
$706$	−1.36432e10	−1.45915
$707$	−2.43312e10	−2.58938
$708$	−7.56650e8	−0.0801269
$709$	4.68714e9	0.493908	0.246954	−	0.969027i	$-0.420570\pi$
$709$	4.68714e9	0.493908	0.246954	+	0.969027i	$0.420570\pi$
$710$	−1.35901e9	−0.142501
$711$	−5.04313e9	−0.526207
$712$	−9.23316e8	−0.0958673
$713$	3.86342e9	0.399171
$714$	−7.85423e9	−0.807533
$715$	6.57092e7	0.00672287
$716$	1.77847e10	1.81072
$717$	−5.89136e9	−0.596896
$718$	−9.35533e9	−0.943243
$719$	−1.88048e10	−1.88676	−0.943381	−	0.331710i	$-0.892374\pi$
$719$	−1.88048e10	−1.88676	−0.943381	+	0.331710i	$0.892374\pi$
$720$	3.40508e8	0.0339988
$721$	2.48727e10	2.47144
$722$	−8.91283e9	−0.881324
$723$	−2.03260e9	−0.200017
$724$	−1.18356e10	−1.15906
$725$	1.41465e10	1.37869
$726$	−7.09263e9	−0.687906
$727$	−1.41494e10	−1.36574	−0.682869	−	0.730541i	$-0.739268\pi$
$727$	−1.41494e10	−1.36574	−0.682869	+	0.730541i	$0.739268\pi$
$728$	2.18783e8	0.0210162
$729$	3.87420e8	0.0370370
$730$	−1.98285e9	−0.188651
$731$	−9.33391e9	−0.883798
$732$	5.09086e9	0.479736
$733$	−1.16913e10	−1.09647	−0.548237	−	0.836323i	$-0.684701\pi$
$733$	−1.16913e10	−1.09647	−0.548237	+	0.836323i	$0.684701\pi$
$734$	−2.65482e9	−0.247799
$735$	−8.41982e8	−0.0782163
$736$	3.86407e9	0.357250
$737$	4.41772e9	0.406502
$738$	8.52688e9	0.780896
$739$	8.53323e9	0.777782	0.388891	−	0.921284i	$-0.372858\pi$
$739$	8.53323e9	0.777782	0.388891	+	0.921284i	$0.372858\pi$
$740$	1.09174e9	0.0990393
$741$	5.89216e8	0.0531999
$742$	3.98832e10	3.58407
$743$	−2.88722e9	−0.258237	−0.129119	−	0.991629i	$-0.541215\pi$
$743$	−2.88722e9	−0.258237	−0.129119	+	0.991629i	$0.541215\pi$
$744$	−9.84098e8	−0.0876058
$745$	−8.01512e8	−0.0710171
$746$	−8.17870e9	−0.721271
$747$	6.07191e9	0.532971
$748$	3.28500e9	0.286998
$749$	−2.14709e10	−1.86708
$750$	2.09125e9	0.181006
$751$	1.71155e10	1.47452	0.737258	−	0.675611i	$-0.236120\pi$
$751$	1.71155e10	1.47452	0.737258	+	0.675611i	$0.236120\pi$
$752$	−1.98334e10	−1.70073
$753$	−6.71048e9	−0.572758
$754$	3.49779e9	0.297162
$755$	2.15554e9	0.182281
$756$	−3.64355e9	−0.306689
$757$	1.12521e10	0.942751	0.471375	−	0.881933i	$-0.343758\pi$
$757$	1.12521e10	0.942751	0.471375	+	0.881933i	$0.343758\pi$
$758$	3.00290e10	2.50437
$759$	−7.18064e8	−0.0596097
$760$	7.83669e7	0.00647567
$761$	9.66355e9	0.794859	0.397430	−	0.917633i	$-0.369902\pi$
$761$	9.66355e9	0.794859	0.397430	+	0.917633i	$0.369902\pi$
$762$	−4.30645e9	−0.352596
$763$	−6.01915e9	−0.490568
$764$	−1.37004e10	−1.11150
$765$	−2.94788e8	−0.0238065
$766$	1.27785e6	0.000102725 0
$767$	2.41023e8	0.0192875
$768$	6.19823e9	0.493746
$769$	6.93012e8	0.0549539	0.0274769	−	0.999622i	$-0.491253\pi$
$769$	6.93012e8	0.0549539	0.0274769	+	0.999622i	$0.491253\pi$
$770$	1.23524e9	0.0975069
$771$	2.56226e9	0.201342
$772$	2.22504e10	1.74051
$773$	−6.71030e8	−0.0522533	−0.0261266	−	0.999659i	$-0.508317\pi$
$773$	−6.71030e8	−0.0522533	−0.0261266	+	0.999659i	$0.508317\pi$
$774$	−8.39176e9	−0.650519
$775$	2.04716e10	1.57978
$776$	−6.56262e8	−0.0504152
$777$	9.55636e9	0.730835
$778$	1.65681e10	1.26138
$779$	−1.33751e10	−1.01372
$780$	1.32591e8	0.0100042
$781$	4.97540e9	0.373723
$782$	−3.12343e9	−0.233565
$783$	−3.60753e9	−0.268561
$784$	−1.54879e10	−1.14785
$785$	7.01216e8	0.0517378
$786$	−1.12115e10	−0.823538
$787$	−1.62943e10	−1.19158	−0.595790	−	0.803141i	$-0.703161\pi$
$787$	−1.62943e10	−1.19158	−0.595790	+	0.803141i	$0.703161\pi$
$788$	1.67605e10	1.22024
$789$	2.09031e9	0.151510
$790$	3.44999e9	0.248956
$791$	−2.76132e10	−1.98380
$792$	1.82907e8	0.0130825
$793$	−1.62165e9	−0.115478
$794$	5.61933e9	0.398394
$795$	1.49691e9	0.105660
$796$	2.53664e10	1.78264
$797$	6.31608e9	0.441920	0.220960	−	0.975283i	$-0.429081\pi$
$797$	6.31608e9	0.441920	0.220960	+	0.975283i	$0.429081\pi$
$798$	1.10765e10	0.771599
$799$	1.71704e10	1.19088
$800$	2.04751e10	1.41387
$801$	−4.89808e9	−0.336753
$802$	−3.49780e10	−2.39433
$803$	7.25929e9	0.494755
$804$	8.91430e9	0.604910
$805$	−6.06011e8	−0.0409444
$806$	5.06172e9	0.340506
$807$	−4.00595e9	−0.268317
$808$	2.46466e9	0.164368
$809$	−5.93171e9	−0.393876	−0.196938	−	0.980416i	$-0.563100\pi$
$809$	−5.93171e9	−0.393876	−0.196938	+	0.980416i	$0.563100\pi$
$810$	−2.65033e8	−0.0175228
$811$	3.74376e9	0.246454	0.123227	−	0.992379i	$-0.460676\pi$
$811$	3.74376e9	0.246454	0.123227	+	0.992379i	$0.460676\pi$
$812$	3.39274e10	2.22385
$813$	5.77899e9	0.377168
$814$	−7.74628e9	−0.503394
$815$	1.92098e9	0.124300
$816$	−5.42251e9	−0.349369
$817$	1.31632e10	0.844470
$818$	−3.63037e9	−0.231907
$819$	1.16062e9	0.0738236
$820$	−3.00981e9	−0.190629
$821$	2.22338e10	1.40221	0.701103	−	0.713060i	$-0.252691\pi$
$821$	2.22338e10	1.40221	0.701103	+	0.713060i	$0.252691\pi$
$822$	−2.45896e9	−0.154419
$823$	−2.57937e10	−1.61292	−0.806462	−	0.591286i	$-0.798620\pi$
$823$	−2.57937e10	−1.61292	−0.806462	+	0.591286i	$0.798620\pi$
$824$	−2.51952e9	−0.156882
$825$	−3.80491e9	−0.235915
$826$	4.53092e9	0.279741
$827$	2.36853e10	1.45616	0.728082	−	0.685490i	$-0.240412\pi$
$827$	2.36853e10	1.45616	0.728082	+	0.685490i	$0.240412\pi$
$828$	−1.44895e9	−0.0887046
$829$	−3.07672e10	−1.87563	−0.937815	−	0.347137i	$-0.887154\pi$
$829$	−3.07672e10	−1.87563	−0.937815	+	0.347137i	$0.887154\pi$
$830$	−4.15377e9	−0.252156
$831$	−1.21334e10	−0.733462
$832$	2.77465e9	0.167023
$833$	1.34084e10	0.803746
$834$	−4.36532e8	−0.0260576
$835$	6.22344e8	0.0369937
$836$	−4.63268e9	−0.274227
$837$	−5.22052e9	−0.307733
$838$	−1.89594e10	−1.11294
$839$	−9.92051e9	−0.579919	−0.289959	−	0.957039i	$-0.593642\pi$
$839$	−9.92051e9	−0.579919	−0.289959	+	0.957039i	$0.593642\pi$
$840$	1.54364e8	0.00898605
$841$	1.63422e10	0.947379
$842$	−1.53528e10	−0.886332
$843$	1.47769e9	0.0849544
$844$	5.80786e8	0.0332520
$845$	1.88208e9	0.107310
$846$	1.54373e10	0.876546
$847$	2.19144e10	1.23919
$848$	2.75351e10	1.55060
$849$	−1.88004e10	−1.05436
$850$	−1.65505e10	−0.924371
$851$	3.80032e9	0.211382
$852$	1.00396e10	0.556132
$853$	1.89035e10	1.04285	0.521424	−	0.853298i	$-0.325401\pi$
$853$	1.89035e10	1.04285	0.521424	+	0.853298i	$0.325401\pi$
$854$	−3.04847e10	−1.67487
$855$	4.15727e8	0.0227471
$856$	2.17492e9	0.118518
$857$	1.56380e10	0.848688	0.424344	−	0.905501i	$-0.360505\pi$
$857$	1.56380e10	0.848688	0.424344	+	0.905501i	$0.360505\pi$
$858$	−9.40782e8	−0.0508491
$859$	3.59002e10	1.93251	0.966254	−	0.257592i	$-0.0829291\pi$
$859$	3.59002e10	1.93251	0.966254	+	0.257592i	$0.0829291\pi$
$860$	2.96211e9	0.158802
$861$	−2.63459e10	−1.40670
$862$	−1.65855e10	−0.881968
$863$	−3.31160e10	−1.75388	−0.876941	−	0.480599i	$-0.840419\pi$
$863$	−3.31160e10	−1.75388	−0.876941	+	0.480599i	$0.840419\pi$
$864$	−5.22139e9	−0.275415
$865$	1.35875e9	0.0713812
$866$	−8.06708e9	−0.422089
$867$	−6.38470e9	−0.332716
$868$	4.90970e10	2.54822
$869$	−1.26306e10	−0.652910
$870$	2.46790e9	0.127060
$871$	−2.83956e9	−0.145609
$872$	6.09718e8	0.0311402
$873$	−3.48139e9	−0.177094
$874$	4.40483e9	0.223172
$875$	−6.46143e9	−0.326062
$876$	1.46482e10	0.736239
$877$	3.12644e10	1.56513	0.782567	−	0.622566i	$-0.213910\pi$
$877$	3.12644e10	1.56513	0.782567	+	0.622566i	$0.213910\pi$
$878$	3.00164e10	1.49668
$879$	−4.28823e9	−0.212969
$880$	8.52804e8	0.0421852
$881$	−1.15281e9	−0.0567991	−0.0283996	−	0.999597i	$-0.509041\pi$
$881$	−1.15281e9	−0.0567991	−0.0283996	+	0.999597i	$0.509041\pi$
$882$	1.20550e10	0.591597
$883$	−7.36328e9	−0.359922	−0.179961	−	0.983674i	$-0.557597\pi$
$883$	−7.36328e9	−0.359922	−0.179961	+	0.983674i	$0.557597\pi$
$884$	−2.11149e9	−0.102803
$885$	1.70056e8	0.00824691
$886$	3.45413e9	0.166848
$887$	2.01350e10	0.968765	0.484383	−	0.874856i	$-0.339044\pi$
$887$	2.01350e10	0.968765	0.484383	+	0.874856i	$0.339044\pi$
$888$	−9.68025e8	−0.0463918
$889$	1.33058e10	0.635163
$890$	3.35076e9	0.159323
$891$	9.70298e8	0.0459550
$892$	−1.37938e10	−0.650738
$893$	−2.42147e10	−1.13789
$894$	1.14755e10	0.537145
$895$	−3.99710e9	−0.186365
$896$	6.09554e9	0.283096
$897$	4.61548e8	0.0213522
$898$	−5.74406e10	−2.64698
$899$	4.86117e10	2.23142
$900$	−7.67773e9	−0.351062
$901$	−2.38380e10	−1.08576
$902$	2.13557e10	0.968925
$903$	2.59284e10	1.17184
$904$	2.79712e9	0.125928
$905$	2.66005e9	0.119294
$906$	−3.08617e10	−1.37870
$907$	−4.37196e10	−1.94559	−0.972793	−	0.231677i	$-0.925579\pi$
$907$	−4.37196e10	−1.94559	−0.972793	+	0.231677i	$0.925579\pi$
$908$	−2.13852e10	−0.948010
$909$	1.30747e10	0.577377
$910$	−7.93974e8	−0.0349270
$911$	2.71783e10	1.19099	0.595494	−	0.803360i	$-0.296956\pi$
$911$	2.71783e10	1.19099	0.595494	+	0.803360i	$0.296956\pi$
$912$	7.64712e9	0.333823
$913$	1.52071e10	0.661302
$914$	3.34337e10	1.44835
$915$	−1.14417e9	−0.0493759
$916$	3.13978e10	1.34979
$917$	3.46405e10	1.48351
$918$	4.22059e9	0.180063
$919$	−1.97736e10	−0.840393	−0.420196	−	0.907433i	$-0.638039\pi$
$919$	−1.97736e10	−0.840393	−0.420196	+	0.907433i	$0.638039\pi$
$920$	6.13867e7	0.00259906
$921$	5.44188e9	0.229530
$922$	−2.18777e10	−0.919269
$923$	−3.19802e9	−0.133868
$924$	−9.12529e9	−0.380535
$925$	2.01373e10	0.836576
$926$	1.89088e10	0.782576
$927$	−1.33657e10	−0.551079
$928$	4.86198e10	1.99708
$929$	−3.68821e10	−1.50925	−0.754625	−	0.656156i	$-0.772181\pi$
$929$	−3.68821e10	−1.50925	−0.754625	+	0.656156i	$0.772181\pi$
$930$	3.57134e9	0.145593
$931$	−1.89092e10	−0.767981
$932$	1.29005e10	0.521976
$933$	1.02707e10	0.414012
$934$	5.48113e10	2.20118
$935$	−7.38300e8	−0.0295388
$936$	−1.17566e8	−0.00468616
$937$	−2.54302e10	−1.00986	−0.504930	−	0.863160i	$-0.668482\pi$
$937$	−2.54302e10	−1.00986	−0.504930	+	0.863160i	$0.668482\pi$
$938$	−5.33800e10	−2.11188
$939$	3.88723e9	0.153218
$940$	−5.44903e9	−0.213979
$941$	−1.08449e10	−0.424288	−0.212144	−	0.977238i	$-0.568045\pi$
$941$	−1.08449e10	−0.424288	−0.212144	+	0.977238i	$0.568045\pi$
$942$	−1.00396e10	−0.391324
$943$	−1.04771e10	−0.406864
$944$	3.12811e9	0.121027
$945$	8.18883e8	0.0315654
$946$	−2.10172e10	−0.807155
$947$	−2.44245e9	−0.0934547	−0.0467273	−	0.998908i	$-0.514879\pi$
$947$	−2.44245e9	−0.0934547	−0.0467273	+	0.998908i	$0.514879\pi$
$948$	−2.54866e10	−0.971588
$949$	−4.66603e9	−0.177221
$950$	2.33405e10	0.883237
$951$	−1.04043e10	−0.392267
$952$	−2.45822e9	−0.0923402
$953$	−3.90381e10	−1.46104	−0.730522	−	0.682890i	$-0.760723\pi$
$953$	−3.90381e10	−1.46104	−0.730522	+	0.682890i	$0.760723\pi$
$954$	−2.14318e10	−0.799172
$955$	3.07916e9	0.114398
$956$	−2.97733e10	−1.10211
$957$	−9.03508e9	−0.333227
$958$	−2.70901e10	−0.995478
$959$	7.59756e9	0.278169
$960$	1.95768e9	0.0714154
$961$	4.28343e10	1.55690
$962$	4.97905e9	0.180316
$963$	1.15377e10	0.416320
$964$	−1.02722e10	−0.369312
$965$	−5.00076e9	−0.179139
$966$	8.67648e9	0.309687
$967$	−2.52051e10	−0.896388	−0.448194	−	0.893936i	$-0.647933\pi$
$967$	−2.52051e10	−0.896388	−0.448194	+	0.893936i	$0.647933\pi$
$968$	−2.21985e9	−0.0786610
$969$	−6.62036e9	−0.233748
$970$	2.38161e9	0.0837855
$971$	−6.22835e9	−0.218326	−0.109163	−	0.994024i	$-0.534817\pi$
$971$	−6.22835e9	−0.218326	−0.109163	+	0.994024i	$0.534817\pi$
$972$	1.95791e9	0.0683852
$973$	1.34877e9	0.0469400
$974$	−1.66601e10	−0.577726
$975$	2.44567e9	0.0845048
$976$	−2.10465e10	−0.724611
$977$	1.86878e10	0.641103	0.320551	−	0.947231i	$-0.396132\pi$
$977$	1.86878e10	0.641103	0.320551	+	0.947231i	$0.396132\pi$
$978$	−2.75034e10	−0.940155
$979$	−1.22673e10	−0.417839
$980$	−4.25514e9	−0.144419
$981$	3.23448e9	0.109386
$982$	3.69908e10	1.24653
$983$	4.26187e10	1.43108	0.715538	−	0.698574i	$-0.246182\pi$
$983$	4.26187e10	1.43108	0.715538	+	0.698574i	$0.246182\pi$
$984$	2.66874e9	0.0892943
$985$	−3.76691e9	−0.125591
$986$	−3.93007e10	−1.30566
$987$	−4.76972e10	−1.57900
$988$	2.97773e9	0.0982283
$989$	1.03111e10	0.338935
$990$	−6.63777e8	−0.0217420
$991$	−3.72023e9	−0.121426	−0.0607130	−	0.998155i	$-0.519337\pi$
$991$	−3.72023e9	−0.121426	−0.0607130	+	0.998155i	$0.519337\pi$
$992$	7.03586e10	2.28837
$993$	−1.37601e10	−0.445964
$994$	−6.01185e10	−1.94158
$995$	−5.70107e9	−0.183474
$996$	3.06857e10	0.984077
$997$	3.00026e10	0.958794	0.479397	−	0.877598i	$-0.340855\pi$
$997$	3.00026e10	0.958794	0.479397	+	0.877598i	$0.340855\pi$
$998$	3.29481e10	1.04924
$999$	−5.13526e9	−0.162961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.16	✓	17
3.2	odd	2		531.8.a.d.1.2		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.16	✓	17	1.1	even	1	trivial
531.8.a.d.1.2		17	3.2	odd	2

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+16.2619 q^{2} +27.0000 q^{3} +136.450 q^{4} -30.6671 q^{5} +439.072 q^{6} -1356.62 q^{7} +137.421 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+16.2619 q^{2} +27.0000 q^{3} +136.450 q^{4} -30.6671 q^{5} +439.072 q^{6} -1356.62 q^{7} +137.421 q^{8} +729.000 q^{9} -498.706 q^{10} +1825.79 q^{11} +3684.16 q^{12} -1173.55 q^{13} -22061.2 q^{14} -828.012 q^{15} -15230.9 q^{16} +13185.9 q^{17} +11854.9 q^{18} -18595.5 q^{19} -4184.54 q^{20} -36628.7 q^{21} +29690.8 q^{22} -14566.3 q^{23} +3710.36 q^{24} -77184.5 q^{25} -19084.3 q^{26} +19683.0 q^{27} -185111. q^{28} -183281. q^{29} -13465.1 q^{30} -265230. q^{31} -265274. q^{32} +49296.2 q^{33} +214428. q^{34} +41603.6 q^{35} +99472.4 q^{36} -260898. q^{37} -302399. q^{38} -31686.0 q^{39} -4214.29 q^{40} +719268. q^{41} -595654. q^{42} -707870. q^{43} +249129. q^{44} -22356.3 q^{45} -236876. q^{46} +1.30218e6 q^{47} -411235. q^{48} +1.01687e6 q^{49} -1.25517e6 q^{50} +356019. q^{51} -160132. q^{52} -1.80784e6 q^{53} +320084. q^{54} -55991.6 q^{55} -186427. q^{56} -502078. q^{57} -2.98051e6 q^{58} -205379. q^{59} -112983. q^{60} +1.38182e6 q^{61} -4.31315e6 q^{62} -988975. q^{63} -2.36431e6 q^{64} +35989.5 q^{65} +801652. q^{66} +2.41963e6 q^{67} +1.79922e6 q^{68} -393290. q^{69} +676555. q^{70} +2.72507e6 q^{71} +100180. q^{72} +3.97598e6 q^{73} -4.24271e6 q^{74} -2.08398e6 q^{75} -2.53736e6 q^{76} -2.47690e6 q^{77} -515275. q^{78} -6.91787e6 q^{79} +467089. q^{80} +531441. q^{81} +1.16967e7 q^{82} +8.32910e6 q^{83} -4.99800e6 q^{84} -404374. q^{85} -1.15113e7 q^{86} -4.94860e6 q^{87} +250901. q^{88} -6.71890e6 q^{89} -363557. q^{90} +1.59207e6 q^{91} -1.98758e6 q^{92} -7.16121e6 q^{93} +2.11760e7 q^{94} +570270. q^{95} -7.16240e6 q^{96} -4.77557e6 q^{97} +1.65363e7 q^{98} +1.33100e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17q - 32q^{2} + 459q^{3} + 1166q^{4} - 1072q^{5} - 864q^{6} - 2407q^{7} - 6645q^{8} + 12393q^{9} + O(q^{10}) \)	\( 17q - 32q^{2} + 459q^{3} + 1166q^{4} - 1072q^{5} - 864q^{6} - 2407q^{7} - 6645q^{8} + 12393q^{9} - 6391q^{10} - 8888q^{11} + 31482q^{12} - 12702q^{13} - 17555q^{14} - 28944q^{15} + 139226q^{16} - 36167q^{17} - 23328q^{18} - 71037q^{19} - 274883q^{20} - 64989q^{21} - 325182q^{22} - 269995q^{23} - 179415q^{24} + 97329q^{25} - 336906q^{26} + 334611q^{27} - 901362q^{28} - 543825q^{29} - 172557q^{30} - 633109q^{31} - 837062q^{32} - 239976q^{33} - 529288q^{34} - 287621q^{35} + 850014q^{36} - 867607q^{37} - 1727169q^{38} - 342954q^{39} - 815662q^{40} - 1428939q^{41} - 473985q^{42} - 477060q^{43} - 1667926q^{44} - 781488q^{45} + 5305549q^{46} - 1217849q^{47} + 3759102q^{48} + 4350738q^{49} + 4561369q^{50} - 976509q^{51} + 4175994q^{52} - 3487068q^{53} - 629856q^{54} - 960484q^{55} - 5363196q^{56} - 1917999q^{57} - 3082906q^{58} - 3491443q^{59} - 7421841q^{60} + 998917q^{61} - 5742614q^{62} - 1754703q^{63} + 17531621q^{64} - 6075816q^{65} - 8779914q^{66} - 356026q^{67} - 16149231q^{68} - 7289865q^{69} - 548798q^{70} - 12879428q^{71} - 4844205q^{72} - 6176157q^{73} - 5971906q^{74} + 2627883q^{75} - 17624580q^{76} + 239687q^{77} - 9096462q^{78} - 18886490q^{79} - 70463349q^{80} + 9034497q^{81} - 19351611q^{82} - 22824893q^{83} - 24336774q^{84} - 7973079q^{85} - 27502196q^{86} - 14683275q^{87} - 62527651q^{88} - 30609647q^{89} - 4659039q^{90} - 36301521q^{91} - 41388548q^{92} - 17093943q^{93} + 1010176q^{94} - 29303629q^{95} - 22600674q^{96} - 26249806q^{97} - 93110852q^{98} - 6479352q^{99} + O(q^{100}) \)

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