LMFDB - Embedded newform 177.10.a.d.1.6

Newspace parameters

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

Newform invariants

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-20.0625 q^{2} +81.0000 q^{3} -109.497 q^{4} +2619.85 q^{5} -1625.06 q^{6} -4642.93 q^{7} +12468.8 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-20.0625 q^{2} +81.0000 q^{3} -109.497 q^{4} +2619.85 q^{5} -1625.06 q^{6} -4642.93 q^{7} +12468.8 q^{8} +6561.00 q^{9} -52560.7 q^{10} +94387.2 q^{11} -8869.24 q^{12} +101912. q^{13} +93148.8 q^{14} +212208. q^{15} -194092. q^{16} -174668. q^{17} -131630. q^{18} +598100. q^{19} -286865. q^{20} -376078. q^{21} -1.89364e6 q^{22} -811615. q^{23} +1.00997e6 q^{24} +4.91050e6 q^{25} -2.04461e6 q^{26} +531441. q^{27} +508387. q^{28} +7.22901e6 q^{29} -4.25742e6 q^{30} +7.32811e6 q^{31} -2.49004e6 q^{32} +7.64536e6 q^{33} +3.50427e6 q^{34} -1.21638e7 q^{35} -718409. q^{36} +715607. q^{37} -1.19994e7 q^{38} +8.25488e6 q^{39} +3.26663e7 q^{40} -2.55171e7 q^{41} +7.54505e6 q^{42} -8.78795e6 q^{43} -1.03351e7 q^{44} +1.71888e7 q^{45} +1.62830e7 q^{46} +7.96566e6 q^{47} -1.57215e7 q^{48} -1.87968e7 q^{49} -9.85168e7 q^{50} -1.41481e7 q^{51} -1.11590e7 q^{52} -1.41564e7 q^{53} -1.06620e7 q^{54} +2.47281e8 q^{55} -5.78917e7 q^{56} +4.84461e7 q^{57} -1.45032e8 q^{58} -1.21174e7 q^{59} -2.32361e7 q^{60} -1.20131e8 q^{61} -1.47020e8 q^{62} -3.04623e7 q^{63} +1.49332e8 q^{64} +2.66994e8 q^{65} -1.53385e8 q^{66} -1.23118e8 q^{67} +1.91255e7 q^{68} -6.57408e7 q^{69} +2.44036e8 q^{70} -3.13097e8 q^{71} +8.18076e7 q^{72} -1.28195e8 q^{73} -1.43569e7 q^{74} +3.97750e8 q^{75} -6.54901e7 q^{76} -4.38234e8 q^{77} -1.65613e8 q^{78} -3.90227e8 q^{79} -5.08492e8 q^{80} +4.30467e7 q^{81} +5.11936e8 q^{82} +5.79282e8 q^{83} +4.11793e7 q^{84} -4.57603e8 q^{85} +1.76308e8 q^{86} +5.85550e8 q^{87} +1.17689e9 q^{88} +1.25314e8 q^{89} -3.44851e8 q^{90} -4.73171e8 q^{91} +8.88693e7 q^{92} +5.93577e8 q^{93} -1.59811e8 q^{94} +1.56693e9 q^{95} -2.01693e8 q^{96} +5.54861e8 q^{97} +3.77110e8 q^{98} +6.19275e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) $	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−20.0625	−0.886645	−0.443322	−	0.896362i	$-0.646200\pi$
$2$	−20.0625	−0.886645	−0.443322	+	0.896362i	$0.646200\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−109.497	−0.213861
$5$	2619.85	1.87461	0.937307	−	0.348506i	$-0.113311\pi$
$5$	2619.85	1.87461	0.937307	+	0.348506i	$0.113311\pi$
$6$	−1625.06	−0.511905
$7$	−4642.93	−0.730889	−0.365444	−	0.930833i	$-0.619083\pi$
$7$	−4642.93	−0.730889	−0.365444	+	0.930833i	$0.619083\pi$
$8$	12468.8	1.07626
$9$	6561.00	0.333333
$10$	−52560.7	−1.66212
$11$	94387.2	1.94378	0.971888	−	0.235445i	$-0.0756546\pi$
$11$	94387.2	1.94378	0.971888	+	0.235445i	$0.0756546\pi$
$12$	−8869.24	−0.123473
$13$	101912.	0.989647	0.494824	−	0.868993i	$-0.335233\pi$
$13$	101912.	0.989647	0.494824	+	0.868993i	$0.335233\pi$
$14$	93148.8	0.648039
$15$	212208.	1.08231
$16$	−194092.	−0.740402
$17$	−174668.	−0.507215	−0.253608	−	0.967307i	$-0.581617\pi$
$17$	−174668.	−0.507215	−0.253608	+	0.967307i	$0.581617\pi$
$18$	−131630.	−0.295548
$19$	598100.	1.05289	0.526445	−	0.850209i	$-0.323525\pi$
$19$	598100.	1.05289	0.526445	+	0.850209i	$0.323525\pi$
$20$	−286865.	−0.400907
$21$	−376078.	−0.421979
$22$	−1.89364e6	−1.72344
$23$	−811615.	−0.604749	−0.302374	−	0.953189i	$-0.597779\pi$
$23$	−811615.	−0.604749	−0.302374	+	0.953189i	$0.597779\pi$
$24$	1.00997e6	0.621381
$25$	4.91050e6	2.51418
$26$	−2.04461e6	−0.877466
$27$	531441.	0.192450
$28$	508387.	0.156309
$29$	7.22901e6	1.89796	0.948982	−	0.315331i	$-0.102116\pi$
$29$	7.22901e6	1.89796	0.948982	+	0.315331i	$0.102116\pi$
$30$	−4.25742e6	−0.959623
$31$	7.32811e6	1.42516	0.712581	−	0.701590i	$-0.247526\pi$
$31$	7.32811e6	1.42516	0.712581	+	0.701590i	$0.247526\pi$
$32$	−2.49004e6	−0.419790
$33$	7.64536e6	1.12224
$34$	3.50427e6	0.449720
$35$	−1.21638e7	−1.37013
$36$	−718409.	−0.0712870
$37$	715607.	0.0627721	0.0313861	−	0.999507i	$-0.490008\pi$
$37$	715607.	0.0627721	0.0313861	+	0.999507i	$0.490008\pi$
$38$	−1.19994e7	−0.933539
$39$	8.25488e6	0.571373
$40$	3.26663e7	2.01758
$41$	−2.55171e7	−1.41027	−0.705137	−	0.709071i	$-0.749115\pi$
$41$	−2.55171e7	−1.41027	−0.705137	+	0.709071i	$0.749115\pi$
$42$	7.54505e6	0.374145
$43$	−8.78795e6	−0.391994	−0.195997	−	0.980604i	$-0.562794\pi$
$43$	−8.78795e6	−0.391994	−0.195997	+	0.980604i	$0.562794\pi$
$44$	−1.03351e7	−0.415698
$45$	1.71888e7	0.624871
$46$	1.62830e7	0.536197
$47$	7.96566e6	0.238112	0.119056	−	0.992888i	$-0.462013\pi$
$47$	7.96566e6	0.238112	0.119056	+	0.992888i	$0.462013\pi$
$48$	−1.57215e7	−0.427472
$49$	−1.87968e7	−0.465801
$50$	−9.85168e7	−2.22918
$51$	−1.41481e7	−0.292841
$52$	−1.11590e7	−0.211647
$53$	−1.41564e7	−0.246441	−0.123220	−	0.992379i	$-0.539322\pi$
$53$	−1.41564e7	−0.246441	−0.123220	+	0.992379i	$0.539322\pi$
$54$	−1.06620e7	−0.170635
$55$	2.47281e8	3.64383
$56$	−5.78917e7	−0.786629
$57$	4.84461e7	0.607886
$58$	−1.45032e8	−1.68282
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−2.32361e7	−0.231464
$61$	−1.20131e8	−1.11089	−0.555444	−	0.831554i	$-0.687452\pi$
$61$	−1.20131e8	−1.11089	−0.555444	+	0.831554i	$0.687452\pi$
$62$	−1.47020e8	−1.26361
$63$	−3.04623e7	−0.243630
$64$	1.49332e8	1.11261
$65$	2.66994e8	1.85521
$66$	−1.53385e8	−0.995028
$67$	−1.23118e8	−0.746423	−0.373212	−	0.927746i	$-0.621743\pi$
$67$	−1.23118e8	−0.746423	−0.373212	+	0.927746i	$0.621743\pi$
$68$	1.91255e7	0.108474
$69$	−6.57408e7	−0.349152
$70$	2.44036e8	1.21482
$71$	−3.13097e8	−1.46223	−0.731115	−	0.682254i	$-0.761000\pi$
$71$	−3.13097e8	−1.46223	−0.731115	+	0.682254i	$0.761000\pi$
$72$	8.18076e7	0.358755
$73$	−1.28195e8	−0.528348	−0.264174	−	0.964475i	$-0.585099\pi$
$73$	−1.28195e8	−0.528348	−0.264174	+	0.964475i	$0.585099\pi$
$74$	−1.43569e7	−0.0556566
$75$	3.97750e8	1.45156
$76$	−6.54901e7	−0.225172
$77$	−4.38234e8	−1.42068
$78$	−1.65613e8	−0.506605
$79$	−3.90227e8	−1.12718	−0.563592	−	0.826053i	$-0.690581\pi$
$79$	−3.90227e8	−1.12718	−0.563592	+	0.826053i	$0.690581\pi$
$80$	−5.08492e8	−1.38797
$81$	4.30467e7	0.111111
$82$	5.11936e8	1.25041
$83$	5.79282e8	1.33980	0.669898	−	0.742453i	$-0.266338\pi$
$83$	5.79282e8	1.33980	0.669898	+	0.742453i	$0.266338\pi$
$84$	4.11793e7	0.0902448
$85$	−4.57603e8	−0.950832
$86$	1.76308e8	0.347560
$87$	5.85550e8	1.09579
$88$	1.17689e9	2.09201
$89$	1.25314e8	0.211712	0.105856	−	0.994381i	$-0.466242\pi$
$89$	1.25314e8	0.211712	0.105856	+	0.994381i	$0.466242\pi$
$90$	−3.44851e8	−0.554039
$91$	−4.73171e8	−0.723322
$92$	8.88693e7	0.129332
$93$	5.93577e8	0.822818
$94$	−1.59811e8	−0.211121
$95$	1.56693e9	1.97376
$96$	−2.01693e8	−0.242366
$97$	5.54861e8	0.636373	0.318186	−	0.948028i	$-0.396926\pi$
$97$	5.54861e8	0.636373	0.318186	+	0.948028i	$0.396926\pi$
$98$	3.77110e8	0.413000
$99$	6.19275e8	0.647925
$100$	−5.37684e8	−0.537684
$101$	−9.65044e8	−0.922785	−0.461393	−	0.887196i	$-0.652650\pi$
$101$	−9.65044e8	−0.922785	−0.461393	+	0.887196i	$0.652650\pi$
$102$	2.83846e8	0.259646
$103$	−4.46300e8	−0.390715	−0.195357	−	0.980732i	$-0.562587\pi$
$103$	−4.46300e8	−0.390715	−0.195357	+	0.980732i	$0.562587\pi$
$104$	1.27072e9	1.06512
$105$	−9.85268e8	−0.791047
$106$	2.84013e8	0.218506
$107$	8.14950e8	0.601040	0.300520	−	0.953775i	$-0.402840\pi$
$107$	8.14950e8	0.601040	0.300520	+	0.953775i	$0.402840\pi$
$108$	−5.81911e7	−0.0411576
$109$	9.99145e8	0.677968	0.338984	−	0.940792i	$-0.389917\pi$
$109$	9.99145e8	0.677968	0.338984	+	0.940792i	$0.389917\pi$
$110$	−4.96106e9	−3.23078
$111$	5.79642e7	0.0362415
$112$	9.01157e8	0.541152
$113$	−2.39006e9	−1.37897	−0.689487	−	0.724298i	$-0.742164\pi$
$113$	−2.39006e9	−1.37897	−0.689487	+	0.724298i	$0.742164\pi$
$114$	−9.71949e8	−0.538979
$115$	−2.12631e9	−1.13367
$116$	−7.91554e8	−0.405900
$117$	6.68645e8	0.329882
$118$	2.43104e8	0.115431
$119$	8.10970e8	0.370718
$120$	2.64597e9	1.16485
$121$	6.55100e9	2.77826
$122$	2.41012e9	0.984964
$123$	−2.06688e9	−0.814222
$124$	−8.02405e8	−0.304787
$125$	7.74788e9	2.83849
$126$	6.11149e8	0.216013
$127$	3.72987e9	1.27226	0.636131	−	0.771581i	$-0.280534\pi$
$127$	3.72987e9	1.27226	0.636131	+	0.771581i	$0.280534\pi$
$128$	−1.72106e9	−0.566697
$129$	−7.11824e8	−0.226318
$130$	−5.35657e9	−1.64491
$131$	−5.89914e9	−1.75012	−0.875060	−	0.484014i	$-0.839179\pi$
$131$	−5.89914e9	−1.75012	−0.875060	+	0.484014i	$0.839179\pi$
$132$	−8.37143e8	−0.240003
$133$	−2.77694e9	−0.769545
$134$	2.47005e9	0.661812
$135$	1.39230e9	0.360770
$136$	−2.17789e9	−0.545897
$137$	6.38085e9	1.54752	0.773760	−	0.633479i	$-0.218374\pi$
$137$	6.38085e9	1.54752	0.773760	+	0.633479i	$0.218374\pi$
$138$	1.31892e9	0.309574
$139$	−2.76211e9	−0.627588	−0.313794	−	0.949491i	$-0.601600\pi$
$139$	−2.76211e9	−0.627588	−0.313794	+	0.949491i	$0.601600\pi$
$140$	1.33190e9	0.293018
$141$	6.45218e8	0.137474
$142$	6.28149e9	1.29648
$143$	9.61919e9	1.92365
$144$	−1.27344e9	−0.246801
$145$	1.89389e10	3.55795
$146$	2.57192e9	0.468457
$147$	−1.52254e9	−0.268931
$148$	−7.83567e7	−0.0134245
$149$	6.08916e9	1.01209	0.506045	−	0.862507i	$-0.331107\pi$
$149$	6.08916e9	1.01209	0.506045	+	0.862507i	$0.331107\pi$
$150$	−7.97986e9	−1.28702
$151$	−2.28550e9	−0.357755	−0.178877	−	0.983871i	$-0.557247\pi$
$151$	−2.28550e9	−0.357755	−0.178877	+	0.983871i	$0.557247\pi$
$152$	7.45757e9	1.13319
$153$	−1.14599e9	−0.169072
$154$	8.79206e9	1.25964
$155$	1.91986e10	2.67163
$156$	−9.03883e8	−0.122194
$157$	1.20766e10	1.58635	0.793173	−	0.608996i	$-0.208428\pi$
$157$	1.20766e10	1.58635	0.793173	+	0.608996i	$0.208428\pi$
$158$	7.82891e9	0.999412
$159$	−1.14667e9	−0.142283
$160$	−6.52354e9	−0.786943
$161$	3.76828e9	0.442004
$162$	−8.63624e8	−0.0985161
$163$	7.24899e9	0.804328	0.402164	−	0.915568i	$-0.368258\pi$
$163$	7.24899e9	0.804328	0.402164	+	0.915568i	$0.368258\pi$
$164$	2.79404e9	0.301603
$165$	2.00297e10	2.10376
$166$	−1.16218e10	−1.18792
$167$	7.99480e9	0.795396	0.397698	−	0.917516i	$-0.369809\pi$
$167$	7.99480e9	0.795396	0.397698	+	0.917516i	$0.369809\pi$
$168$	−4.68923e9	−0.454161
$169$	−2.18435e8	−0.0205983
$170$	9.18066e9	0.843050
$171$	3.92414e9	0.350963
$172$	9.62253e8	0.0838322
$173$	−1.17866e10	−1.00041	−0.500207	−	0.865906i	$-0.666743\pi$
$173$	−1.17866e10	−1.00041	−0.500207	+	0.865906i	$0.666743\pi$
$174$	−1.17476e10	−0.971576
$175$	−2.27991e10	−1.83758
$176$	−1.83198e10	−1.43918
$177$	−9.81506e8	−0.0751646
$178$	−2.51411e9	−0.187713
$179$	−1.07231e10	−0.780694	−0.390347	−	0.920668i	$-0.627645\pi$
$179$	−1.07231e10	−0.780694	−0.390347	+	0.920668i	$0.627645\pi$
$180$	−1.88212e9	−0.133636
$181$	−2.63189e10	−1.82270	−0.911348	−	0.411637i	$-0.864957\pi$
$181$	−2.63189e10	−1.82270	−0.911348	+	0.411637i	$0.864957\pi$
$182$	9.49298e9	0.641330
$183$	−9.73060e9	−0.641372
$184$	−1.01198e10	−0.650869
$185$	1.87478e9	0.117673
$186$	−1.19086e10	−0.729547
$187$	−1.64864e10	−0.985912
$188$	−8.72214e8	−0.0509229
$189$	−2.46745e9	−0.140660
$190$	−3.14366e10	−1.75002
$191$	4.47796e9	0.243461	0.121731	−	0.992563i	$-0.461156\pi$
$191$	4.47796e9	0.243461	0.121731	+	0.992563i	$0.461156\pi$
$192$	1.20959e10	0.642364
$193$	2.23390e10	1.15893	0.579464	−	0.814998i	$-0.303262\pi$
$193$	2.23390e10	1.15893	0.579464	+	0.814998i	$0.303262\pi$
$194$	−1.11319e10	−0.564236
$195$	2.16266e10	1.07110
$196$	2.05819e9	0.0996167
$197$	−1.08202e10	−0.511843	−0.255921	−	0.966698i	$-0.582379\pi$
$197$	−1.08202e10	−0.511843	−0.255921	+	0.966698i	$0.582379\pi$
$198$	−1.24242e10	−0.574480
$199$	6.34469e9	0.286795	0.143398	−	0.989665i	$-0.454197\pi$
$199$	6.34469e9	0.286795	0.143398	+	0.989665i	$0.454197\pi$
$200$	6.12279e10	2.70591
$201$	−9.97256e9	−0.430948
$202$	1.93612e10	0.818183
$203$	−3.35638e10	−1.38720
$204$	1.54917e9	0.0626272
$205$	−6.68510e10	−2.64372
$206$	8.95389e9	0.346425
$207$	−5.32501e9	−0.201583
$208$	−1.97803e10	−0.732737
$209$	5.64530e10	2.04658
$210$	1.97669e10	0.701378
$211$	2.33646e10	0.811498	0.405749	−	0.913985i	$-0.367011\pi$
$211$	2.33646e10	0.811498	0.405749	+	0.913985i	$0.367011\pi$
$212$	1.55009e9	0.0527041
$213$	−2.53608e10	−0.844219
$214$	−1.63499e10	−0.532909
$215$	−2.30231e10	−0.734837
$216$	6.62641e9	0.207127
$217$	−3.40239e10	−1.04164
$218$	−2.00453e10	−0.601117
$219$	−1.03838e10	−0.305042
$220$	−2.70764e10	−0.779273
$221$	−1.78007e10	−0.501964
$222$	−1.16291e9	−0.0321333
$223$	4.97717e10	1.34775	0.673877	−	0.738844i	$-0.264628\pi$
$223$	4.97717e10	1.34775	0.673877	+	0.738844i	$0.264628\pi$
$224$	1.15611e10	0.306820
$225$	3.22178e10	0.838058
$226$	4.79506e10	1.22266
$227$	−2.07221e10	−0.517985	−0.258992	−	0.965879i	$-0.583390\pi$
$227$	−2.07221e10	−0.517985	−0.258992	+	0.965879i	$0.583390\pi$
$228$	−5.30470e9	−0.130003
$229$	−6.32264e10	−1.51928	−0.759641	−	0.650342i	$-0.774626\pi$
$229$	−6.32264e10	−1.51928	−0.759641	+	0.650342i	$0.774626\pi$
$230$	4.26591e10	1.00516
$231$	−3.54969e10	−0.820232
$232$	9.01368e10	2.04271
$233$	5.89052e9	0.130934	0.0654669	−	0.997855i	$-0.479146\pi$
$233$	5.89052e9	0.130934	0.0654669	+	0.997855i	$0.479146\pi$
$234$	−1.34147e10	−0.292489
$235$	2.08688e10	0.446368
$236$	1.32681e9	0.0278423
$237$	−3.16084e10	−0.650780
$238$	−1.62701e10	−0.328695
$239$	−5.30021e10	−1.05076	−0.525379	−	0.850868i	$-0.676076\pi$
$239$	−5.30021e10	−1.05076	−0.525379	+	0.850868i	$0.676076\pi$
$240$	−4.11879e10	−0.801344
$241$	8.88739e10	1.69706	0.848531	−	0.529146i	$-0.177488\pi$
$241$	8.88739e10	1.69706	0.848531	+	0.529146i	$0.177488\pi$
$242$	−1.31429e11	−2.46333
$243$	3.48678e9	0.0641500
$244$	1.31540e10	0.237576
$245$	−4.92447e10	−0.873197
$246$	4.14668e10	0.721926
$247$	6.09536e10	1.04199
$248$	9.13725e10	1.53385
$249$	4.69218e10	0.773531
$250$	−1.55442e11	−2.51673
$251$	5.90117e10	0.938440	0.469220	−	0.883081i	$-0.344535\pi$
$251$	5.90117e10	0.938440	0.469220	+	0.883081i	$0.344535\pi$
$252$	3.33552e9	0.0521029
$253$	−7.66061e10	−1.17550
$254$	−7.48304e10	−1.12804
$255$	−3.70659e10	−0.548963
$256$	−4.19290e10	−0.610147
$257$	−8.45554e10	−1.20904	−0.604522	−	0.796588i	$-0.706636\pi$
$257$	−8.45554e10	−1.20904	−0.604522	+	0.796588i	$0.706636\pi$
$258$	1.42810e10	0.200664
$259$	−3.32252e9	−0.0458795
$260$	−2.92350e10	−0.396756
$261$	4.74295e10	0.632654
$262$	1.18351e11	1.55174
$263$	3.27803e10	0.422485	0.211243	−	0.977434i	$-0.432249\pi$
$263$	3.27803e10	0.422485	0.211243	+	0.977434i	$0.432249\pi$
$264$	9.53283e10	1.20783
$265$	−3.70878e10	−0.461981
$266$	5.57123e10	0.682313
$267$	1.01504e10	0.122232
$268$	1.34810e10	0.159631
$269$	−4.94973e9	−0.0576363	−0.0288182	−	0.999585i	$-0.509174\pi$
$269$	−4.94973e9	−0.0576363	−0.0288182	+	0.999585i	$0.509174\pi$
$270$	−2.79329e10	−0.319874
$271$	−1.06262e11	−1.19679	−0.598393	−	0.801203i	$-0.704194\pi$
$271$	−1.06262e11	−1.19679	−0.598393	+	0.801203i	$0.704194\pi$
$272$	3.39016e10	0.375543
$273$	−3.83268e10	−0.417610
$274$	−1.28016e11	−1.37210
$275$	4.63488e11	4.88699
$276$	7.19841e9	0.0746699
$277$	2.17004e10	0.221467	0.110733	−	0.993850i	$-0.464680\pi$
$277$	2.17004e10	0.221467	0.110733	+	0.993850i	$0.464680\pi$
$278$	5.54148e10	0.556448
$279$	4.80797e10	0.475054
$280$	−1.51668e11	−1.47463
$281$	−6.09824e10	−0.583481	−0.291740	−	0.956498i	$-0.594234\pi$
$281$	−6.09824e10	−0.583481	−0.291740	+	0.956498i	$0.594234\pi$
$282$	−1.29447e10	−0.121891
$283$	−2.24580e10	−0.208129	−0.104065	−	0.994571i	$-0.533185\pi$
$283$	−2.24580e10	−0.208129	−0.104065	+	0.994571i	$0.533185\pi$
$284$	3.42831e10	0.312714
$285$	1.26922e11	1.13955
$286$	−1.92985e11	−1.70560
$287$	1.18474e11	1.03075
$288$	−1.63372e10	−0.139930
$289$	−8.80791e10	−0.742733
$290$	−3.79962e11	−3.15464
$291$	4.49437e10	0.367410
$292$	1.40370e10	0.112993
$293$	5.49774e10	0.435793	0.217896	−	0.975972i	$-0.430081\pi$
$293$	5.49774e10	0.435793	0.217896	+	0.975972i	$0.430081\pi$
$294$	3.05459e10	0.238446
$295$	−3.17457e10	−0.244054
$296$	8.92274e9	0.0675594
$297$	5.01612e10	0.374080
$298$	−1.22164e11	−0.897365
$299$	−8.27133e10	−0.598488
$300$	−4.35524e10	−0.310432
$301$	4.08019e10	0.286504
$302$	4.58529e10	0.317202
$303$	−7.81685e10	−0.532770
$304$	−1.16087e11	−0.779562
$305$	−3.14725e11	−2.08249
$306$	2.29915e10	0.149907
$307$	1.69953e11	1.09196	0.545979	−	0.837799i	$-0.316158\pi$
$307$	1.69953e11	1.09196	0.545979	+	0.837799i	$0.316158\pi$
$308$	4.79852e10	0.303829
$309$	−3.61503e10	−0.225579
$310$	−3.85171e11	−2.36879
$311$	7.45434e10	0.451843	0.225922	−	0.974145i	$-0.427461\pi$
$311$	7.45434e10	0.451843	0.225922	+	0.974145i	$0.427461\pi$
$312$	1.02928e11	0.614948
$313$	−1.89734e11	−1.11737	−0.558683	−	0.829381i	$-0.688693\pi$
$313$	−1.89734e11	−1.11737	−0.558683	+	0.829381i	$0.688693\pi$
$314$	−2.42288e11	−1.40653
$315$	−7.98067e10	−0.456711
$316$	4.27286e10	0.241061
$317$	−3.01500e11	−1.67695	−0.838475	−	0.544940i	$-0.816552\pi$
$317$	−3.01500e11	−1.67695	−0.838475	+	0.544940i	$0.816552\pi$
$318$	2.30051e10	0.126154
$319$	6.82326e11	3.68921
$320$	3.91227e11	2.08571
$321$	6.60109e10	0.347011
$322$	−7.56010e10	−0.391901
$323$	−1.04469e11	−0.534041
$324$	−4.71348e9	−0.0237623
$325$	5.00439e11	2.48815
$326$	−1.45433e11	−0.713153
$327$	8.09308e10	0.391425
$328$	−3.18167e11	−1.51783
$329$	−3.69840e10	−0.174033
$330$	−4.01846e11	−1.86529
$331$	6.12456e10	0.280446	0.140223	−	0.990120i	$-0.455218\pi$
$331$	6.12456e10	0.280446	0.140223	+	0.990120i	$0.455218\pi$
$332$	−6.34295e10	−0.286530
$333$	4.69510e9	0.0209240
$334$	−1.60395e11	−0.705234
$335$	−3.22551e11	−1.39925
$336$	7.29937e10	0.312434
$337$	3.11346e11	1.31495	0.657473	−	0.753478i	$-0.271625\pi$
$337$	3.11346e11	1.31495	0.657473	+	0.753478i	$0.271625\pi$
$338$	4.38234e9	0.0182634
$339$	−1.93595e11	−0.796151
$340$	5.01061e10	0.203346
$341$	6.91680e11	2.77020
$342$	−7.87279e10	−0.311180
$343$	2.74631e11	1.07134
$344$	−1.09575e11	−0.421889
$345$	−1.72231e11	−0.654524
$346$	2.36468e11	0.887012
$347$	9.84171e10	0.364408	0.182204	−	0.983261i	$-0.441677\pi$
$347$	9.84171e10	0.364408	0.182204	+	0.983261i	$0.441677\pi$
$348$	−6.41158e10	−0.234347
$349$	−1.25695e11	−0.453529	−0.226765	−	0.973950i	$-0.572815\pi$
$349$	−1.25695e11	−0.453529	−0.226765	+	0.973950i	$0.572815\pi$
$350$	4.57407e11	1.62928
$351$	5.41602e10	0.190458
$352$	−2.35028e11	−0.815977
$353$	3.19345e11	1.09465	0.547324	−	0.836921i	$-0.315647\pi$
$353$	3.19345e11	1.09465	0.547324	+	0.836921i	$0.315647\pi$
$354$	1.96915e10	0.0666443
$355$	−8.20266e11	−2.74112
$356$	−1.37215e10	−0.0452768
$357$	6.56886e10	0.214034
$358$	2.15132e11	0.692198
$359$	2.19489e10	0.0697410	0.0348705	−	0.999392i	$-0.488898\pi$
$359$	2.19489e10	0.0697410	0.0348705	+	0.999392i	$0.488898\pi$
$360$	2.14324e11	0.672526
$361$	3.50362e10	0.108576
$362$	5.28022e11	1.61608
$363$	5.30631e11	1.60403
$364$	5.18107e10	0.154690
$365$	−3.35853e11	−0.990448
$366$	1.95220e11	0.568669
$367$	−2.12729e11	−0.612110	−0.306055	−	0.952014i	$-0.599009\pi$
$367$	−2.12729e11	−0.612110	−0.306055	+	0.952014i	$0.599009\pi$
$368$	1.57528e11	0.447757
$369$	−1.67418e11	−0.470091
$370$	−3.76128e10	−0.104335
$371$	6.57275e10	0.180121
$372$	−6.49948e10	−0.175969
$373$	−2.24274e11	−0.599914	−0.299957	−	0.953953i	$-0.596972\pi$
$373$	−2.24274e11	−0.599914	−0.299957	+	0.953953i	$0.596972\pi$
$374$	3.30758e11	0.874154
$375$	6.27578e11	1.63880
$376$	9.93219e10	0.256271
$377$	7.36723e11	1.87831
$378$	4.95031e10	0.124715
$379$	−4.97926e11	−1.23962	−0.619809	−	0.784752i	$-0.712790\pi$
$379$	−4.97926e11	−1.23962	−0.619809	+	0.784752i	$0.712790\pi$
$380$	−1.71574e11	−0.422110
$381$	3.02119e11	0.734541
$382$	−8.98390e10	−0.215864
$383$	3.98168e11	0.945521	0.472761	−	0.881191i	$-0.343257\pi$
$383$	3.98168e11	0.945521	0.472761	+	0.881191i	$0.343257\pi$
$384$	−1.39406e11	−0.327183
$385$	−1.14811e12	−2.66323
$386$	−4.48177e11	−1.02756
$387$	−5.76577e10	−0.130665
$388$	−6.07555e10	−0.136095
$389$	−4.13365e11	−0.915293	−0.457647	−	0.889134i	$-0.651308\pi$
$389$	−4.13365e11	−0.915293	−0.457647	+	0.889134i	$0.651308\pi$
$390$	−4.33882e11	−0.949688
$391$	1.41763e11	0.306738
$392$	−2.34372e11	−0.501325
$393$	−4.77831e11	−1.01043
$394$	2.17080e11	0.453823
$395$	−1.02234e12	−2.11303
$396$	−6.78086e10	−0.138566
$397$	6.21335e10	0.125536	0.0627680	−	0.998028i	$-0.480007\pi$
$397$	6.21335e10	0.125536	0.0627680	+	0.998028i	$0.480007\pi$
$398$	−1.27290e11	−0.254285
$399$	−2.24932e11	−0.444297
$400$	−9.53089e11	−1.86150
$401$	3.10487e11	0.599645	0.299823	−	0.953995i	$-0.403072\pi$
$401$	3.10487e11	0.599645	0.299823	+	0.953995i	$0.403072\pi$
$402$	2.00074e11	0.382098
$403$	7.46823e11	1.41041
$404$	1.05669e11	0.197348
$405$	1.12776e11	0.208290
$406$	6.73373e11	1.22995
$407$	6.75442e10	0.122015
$408$	−1.76409e11	−0.315174
$409$	−7.93556e11	−1.40224	−0.701121	−	0.713043i	$-0.747317\pi$
$409$	−7.93556e11	−1.40224	−0.701121	+	0.713043i	$0.747317\pi$
$410$	1.34120e12	2.34404
$411$	5.16849e11	0.893461
$412$	4.88685e10	0.0835586
$413$	5.62601e10	0.0951536
$414$	1.06833e11	0.178732
$415$	1.51763e12	2.51160
$416$	−2.53765e11	−0.415444
$417$	−2.23731e11	−0.362338
$418$	−1.13259e12	−1.81459
$419$	6.60242e10	0.104650	0.0523251	−	0.998630i	$-0.483337\pi$
$419$	6.60242e10	0.104650	0.0523251	+	0.998630i	$0.483337\pi$
$420$	1.07884e11	0.169174
$421$	−3.88291e11	−0.602404	−0.301202	−	0.953560i	$-0.597388\pi$
$421$	−3.88291e11	−0.602404	−0.301202	+	0.953560i	$0.597388\pi$
$422$	−4.68752e11	−0.719510
$423$	5.22627e10	0.0793707
$424$	−1.76513e11	−0.265235
$425$	−8.57705e11	−1.27523
$426$	5.08801e11	0.748522
$427$	5.57760e11	0.811936
$428$	−8.92344e10	−0.128539
$429$	7.79155e11	1.11062
$430$	4.61901e11	0.651540
$431$	9.04844e10	0.126307	0.0631533	−	0.998004i	$-0.479884\pi$
$431$	9.04844e10	0.126307	0.0631533	+	0.998004i	$0.479884\pi$
$432$	−1.03148e11	−0.142491
$433$	−9.10222e11	−1.24438	−0.622188	−	0.782868i	$-0.713756\pi$
$433$	−9.10222e11	−1.24438	−0.622188	+	0.782868i	$0.713756\pi$
$434$	6.82605e11	0.923561
$435$	1.53405e12	2.05418
$436$	−1.09403e11	−0.144991
$437$	−4.85427e11	−0.636733
$438$	2.08326e11	0.270464
$439$	5.83572e11	0.749901	0.374951	−	0.927045i	$-0.377660\pi$
$439$	5.83572e11	0.749901	0.374951	+	0.927045i	$0.377660\pi$
$440$	3.08328e12	3.92172
$441$	−1.23326e11	−0.155267
$442$	3.57127e11	0.445064
$443$	−2.48193e11	−0.306177	−0.153088	−	0.988213i	$-0.548922\pi$
$443$	−2.48193e11	−0.306177	−0.153088	+	0.988213i	$0.548922\pi$
$444$	−6.34689e9	−0.00775065
$445$	3.28304e11	0.396877
$446$	−9.98543e11	−1.19498
$447$	4.93222e11	0.584331
$448$	−6.93337e11	−0.813192
$449$	3.24622e11	0.376938	0.188469	−	0.982079i	$-0.439648\pi$
$449$	3.24622e11	0.376938	0.188469	+	0.982079i	$0.439648\pi$
$450$	−6.46369e11	−0.743060
$451$	−2.40849e12	−2.74126
$452$	2.61704e11	0.294909
$453$	−1.85126e11	−0.206550
$454$	4.15736e11	0.459268
$455$	−1.23964e12	−1.35595
$456$	6.04063e11	0.654246
$457$	4.72129e11	0.506335	0.253167	−	0.967423i	$-0.418528\pi$
$457$	4.72129e11	0.506335	0.253167	+	0.967423i	$0.418528\pi$
$458$	1.26848e12	1.34706
$459$	−9.28255e10	−0.0976136
$460$	2.32824e11	0.242448
$461$	−3.91642e11	−0.403864	−0.201932	−	0.979400i	$-0.564722\pi$
$461$	−3.91642e11	−0.403864	−0.201932	+	0.979400i	$0.564722\pi$
$462$	7.12157e11	0.727255
$463$	3.19127e11	0.322738	0.161369	−	0.986894i	$-0.448409\pi$
$463$	3.19127e11	0.322738	0.161369	+	0.986894i	$0.448409\pi$
$464$	−1.40309e12	−1.40526
$465$	1.55508e12	1.54247
$466$	−1.18178e11	−0.116092
$467$	3.42865e11	0.333578	0.166789	−	0.985993i	$-0.446660\pi$
$467$	3.42865e11	0.333578	0.166789	+	0.985993i	$0.446660\pi$
$468$	−7.32145e10	−0.0705490
$469$	5.71629e11	0.545553
$470$	−4.18681e11	−0.395770
$471$	9.78209e11	0.915878
$472$	−1.51089e11	−0.140118
$473$	−8.29470e11	−0.761949
$474$	6.34142e11	0.577011
$475$	2.93697e12	2.64715
$476$	−8.87987e10	−0.0792821
$477$	−9.28804e10	−0.0821470
$478$	1.06335e12	0.931649
$479$	−1.63372e12	−1.41797	−0.708987	−	0.705222i	$-0.750848\pi$
$479$	−1.63372e12	−1.41797	−0.708987	+	0.705222i	$0.750848\pi$
$480$	−5.28407e11	−0.454342
$481$	7.29290e10	0.0621223
$482$	−1.78303e12	−1.50469
$483$	3.05230e11	0.255191
$484$	−7.17314e11	−0.594162
$485$	1.45365e12	1.19295
$486$	−6.99535e10	−0.0568783
$487$	6.17831e11	0.497725	0.248862	−	0.968539i	$-0.419943\pi$
$487$	6.17831e11	0.497725	0.248862	+	0.968539i	$0.419943\pi$
$488$	−1.49788e12	−1.19561
$489$	5.87168e11	0.464379
$490$	9.87972e11	0.774216
$491$	1.56189e12	1.21279	0.606393	−	0.795165i	$-0.292616\pi$
$491$	1.56189e12	1.21279	0.606393	+	0.795165i	$0.292616\pi$
$492$	2.26317e11	0.174130
$493$	−1.26267e12	−0.962676
$494$	−1.22288e12	−0.923874
$495$	1.62241e12	1.21461
$496$	−1.42233e12	−1.05519
$497$	1.45369e12	1.06873
$498$	−9.41368e11	−0.685847
$499$	4.28815e11	0.309612	0.154806	−	0.987945i	$-0.450525\pi$
$499$	4.28815e11	0.309612	0.154806	+	0.987945i	$0.450525\pi$
$500$	−8.48368e11	−0.607043
$501$	6.47579e11	0.459222
$502$	−1.18392e12	−0.832063
$503$	−2.85102e11	−0.198584	−0.0992920	−	0.995058i	$-0.531658\pi$
$503$	−2.85102e11	−0.198584	−0.0992920	+	0.995058i	$0.531658\pi$
$504$	−3.79827e11	−0.262210
$505$	−2.52827e12	−1.72987
$506$	1.53691e12	1.04225
$507$	−1.76932e10	−0.0118924
$508$	−4.08408e11	−0.272087
$509$	2.89839e12	1.91394	0.956968	−	0.290195i	$-0.0937201\pi$
$509$	2.89839e12	1.91394	0.956968	+	0.290195i	$0.0937201\pi$
$510$	7.43633e11	0.486735
$511$	5.95203e11	0.386164
$512$	1.72238e12	1.10768
$513$	3.17855e11	0.202629
$514$	1.69639e12	1.07199
$515$	−1.16924e12	−0.732439
$516$	7.79425e10	0.0484006
$517$	7.51856e11	0.462836
$518$	6.66579e10	0.0406788
$519$	−9.54712e11	−0.577589
$520$	3.32909e12	1.99669
$521$	−2.83708e12	−1.68695	−0.843473	−	0.537172i	$-0.819493\pi$
$521$	−2.83708e12	−1.68695	−0.843473	+	0.537172i	$0.819493\pi$
$522$	−9.51554e11	−0.560940
$523$	2.70892e12	1.58321	0.791606	−	0.611032i	$-0.209245\pi$
$523$	2.70892e12	1.58321	0.791606	+	0.611032i	$0.209245\pi$
$524$	6.45937e11	0.374283
$525$	−1.84673e12	−1.06093
$526$	−6.57654e11	−0.374595
$527$	−1.27998e12	−0.722864
$528$	−1.48390e12	−0.830909
$529$	−1.14243e12	−0.634279
$530$	7.44073e11	0.409613
$531$	−7.95020e10	−0.0433963
$532$	3.04066e11	0.164576
$533$	−2.60050e12	−1.39567
$534$	−2.03643e11	−0.108376
$535$	2.13505e12	1.12672
$536$	−1.53513e12	−0.803348
$537$	−8.68569e11	−0.450734
$538$	9.93039e10	0.0511030
$539$	−1.77417e12	−0.905413
$540$	−1.52452e11	−0.0771545
$541$	−2.37196e12	−1.19047	−0.595236	−	0.803551i	$-0.702941\pi$
$541$	−2.37196e12	−1.19047	−0.595236	+	0.803551i	$0.702941\pi$
$542$	2.13188e12	1.06112
$543$	−2.13183e12	−1.05233
$544$	4.34929e11	0.212924
$545$	2.61761e12	1.27093
$546$	7.68932e11	0.370272
$547$	−3.31592e12	−1.58365	−0.791827	−	0.610745i	$-0.790870\pi$
$547$	−3.31592e12	−1.58365	−0.791827	+	0.610745i	$0.790870\pi$
$548$	−6.98683e11	−0.330954
$549$	−7.88179e11	−0.370296
$550$	−9.29873e12	−4.33303
$551$	4.32367e12	1.99835
$552$	−8.19707e11	−0.375779
$553$	1.81180e12	0.823847
$554$	−4.35364e11	−0.196363
$555$	1.51858e11	0.0679388
$556$	3.02442e11	0.134217
$557$	2.66734e12	1.17417	0.587084	−	0.809526i	$-0.300276\pi$
$557$	2.66734e12	1.17417	0.587084	+	0.809526i	$0.300276\pi$
$558$	−9.64599e11	−0.421204
$559$	−8.95598e11	−0.387936
$560$	2.36090e12	1.01445
$561$	−1.33540e12	−0.569217
$562$	1.22346e12	0.517340
$563$	1.91035e12	0.801356	0.400678	−	0.916219i	$-0.368775\pi$
$563$	1.91035e12	0.801356	0.400678	+	0.916219i	$0.368775\pi$
$564$	−7.06494e10	−0.0294003
$565$	−6.26161e12	−2.58504
$566$	4.50564e11	0.184537
$567$	−1.99863e11	−0.0812099
$568$	−3.90393e12	−1.57374
$569$	9.95402e11	0.398101	0.199051	−	0.979989i	$-0.436214\pi$
$569$	9.95402e11	0.398101	0.199051	+	0.979989i	$0.436214\pi$
$570$	−2.54636e12	−1.01038
$571$	−4.29714e12	−1.69168	−0.845838	−	0.533439i	$-0.820899\pi$
$571$	−4.29714e12	−1.69168	−0.845838	+	0.533439i	$0.820899\pi$
$572$	−1.05327e12	−0.411394
$573$	3.62715e11	0.140562
$574$	−2.37689e12	−0.913913
$575$	−3.98543e12	−1.52044
$576$	9.79764e11	0.370869
$577$	−4.74470e12	−1.78204	−0.891021	−	0.453962i	$-0.850010\pi$
$577$	−4.74470e12	−1.78204	−0.891021	+	0.453962i	$0.850010\pi$
$578$	1.76709e12	0.658540
$579$	1.80946e12	0.669108
$580$	−2.07375e12	−0.760906
$581$	−2.68957e12	−0.979242
$582$	−9.01683e11	−0.325762
$583$	−1.33619e12	−0.479026
$584$	−1.59844e12	−0.568641
$585$	1.75175e12	0.618402
$586$	−1.10298e12	−0.386393
$587$	5.62007e12	1.95376	0.976879	−	0.213794i	$-0.0685822\pi$
$587$	5.62007e12	1.95376	0.976879	+	0.213794i	$0.0685822\pi$
$588$	1.66713e11	0.0575137
$589$	4.38294e12	1.50054
$590$	6.36897e11	0.216389
$591$	−8.76435e11	−0.295513
$592$	−1.38894e11	−0.0464766
$593$	−2.19578e12	−0.729193	−0.364597	−	0.931166i	$-0.618793\pi$
$593$	−2.19578e12	−0.729193	−0.364597	+	0.931166i	$0.618793\pi$
$594$	−1.00636e12	−0.331676
$595$	2.12462e12	0.694953
$596$	−6.66744e11	−0.216447
$597$	5.13920e11	0.165581
$598$	1.65944e12	0.530646
$599$	1.86738e12	0.592667	0.296334	−	0.955085i	$-0.404236\pi$
$599$	1.86738e12	0.592667	0.296334	+	0.955085i	$0.404236\pi$
$600$	4.95946e12	1.56226
$601$	4.35928e12	1.36295	0.681475	−	0.731842i	$-0.261339\pi$
$601$	4.35928e12	1.36295	0.681475	+	0.731842i	$0.261339\pi$
$602$	−8.18587e11	−0.254027
$603$	−8.07778e11	−0.248808
$604$	2.50255e11	0.0765098
$605$	1.71626e13	5.20817
$606$	1.56825e12	0.472378
$607$	2.75537e12	0.823817	0.411908	−	0.911225i	$-0.364862\pi$
$607$	2.75537e12	0.823817	0.411908	+	0.911225i	$0.364862\pi$
$608$	−1.48929e12	−0.441992
$609$	−2.71867e12	−0.800900
$610$	6.31417e12	1.84643
$611$	8.11796e11	0.235647
$612$	1.25483e11	0.0361578
$613$	−3.60906e12	−1.03234	−0.516169	−	0.856487i	$-0.672642\pi$
$613$	−3.60906e12	−1.03234	−0.516169	+	0.856487i	$0.672642\pi$
$614$	−3.40968e12	−0.968178
$615$	−5.41493e12	−1.52635
$616$	−5.46423e12	−1.52903
$617$	−2.90935e12	−0.808189	−0.404095	−	0.914717i	$-0.632413\pi$
$617$	−2.90935e12	−0.808189	−0.404095	+	0.914717i	$0.632413\pi$
$618$	7.25265e11	0.200009
$619$	−2.61466e10	−0.00715825	−0.00357912	−	0.999994i	$-0.501139\pi$
$619$	−2.61466e10	−0.00715825	−0.00357912	+	0.999994i	$0.501139\pi$
$620$	−2.10218e12	−0.571357
$621$	−4.31326e11	−0.116384
$622$	−1.49553e12	−0.400624
$623$	−5.81825e11	−0.154738
$624$	−1.60221e12	−0.423046
$625$	1.07075e13	2.80690
$626$	3.80654e12	0.990707
$627$	4.57269e12	1.18159
$628$	−1.32235e12	−0.339258
$629$	−1.24993e11	−0.0318390
$630$	1.60112e12	0.404941
$631$	−2.64461e12	−0.664093	−0.332047	−	0.943263i	$-0.607739\pi$
$631$	−2.64461e12	−0.664093	−0.332047	+	0.943263i	$0.607739\pi$
$632$	−4.86564e12	−1.21315
$633$	1.89253e12	0.468518
$634$	6.04883e12	1.48686
$635$	9.77169e12	2.38500
$636$	1.25557e11	0.0304287
$637$	−1.91562e12	−0.460979
$638$	−1.36892e13	−3.27102
$639$	−2.05423e12	−0.487410
$640$	−4.50892e12	−1.06234
$641$	4.50041e11	0.105291	0.0526455	−	0.998613i	$-0.483235\pi$
$641$	4.50041e11	0.105291	0.0526455	+	0.998613i	$0.483235\pi$
$642$	−1.32434e12	−0.307675
$643$	−7.34415e12	−1.69431	−0.847153	−	0.531349i	$-0.821685\pi$
$643$	−7.34415e12	−1.69431	−0.847153	+	0.531349i	$0.821685\pi$
$644$	−4.12614e11	−0.0945274
$645$	−1.86487e12	−0.424259
$646$	2.09590e12	0.473505
$647$	5.31477e12	1.19238	0.596190	−	0.802843i	$-0.296680\pi$
$647$	5.31477e12	1.19238	0.596190	+	0.802843i	$0.296680\pi$
$648$	5.36740e11	0.119585
$649$	−1.14372e12	−0.253058
$650$	−1.00400e13	−2.20610
$651$	−2.75594e12	−0.601388
$652$	−7.93741e11	−0.172014
$653$	3.21840e12	0.692678	0.346339	−	0.938109i	$-0.387425\pi$
$653$	3.21840e12	0.692678	0.346339	+	0.938109i	$0.387425\pi$
$654$	−1.62367e12	−0.347055
$655$	−1.54549e13	−3.28080
$656$	4.95266e12	1.04417
$657$	−8.41091e11	−0.176116
$658$	7.41991e11	0.154306
$659$	−4.67442e12	−0.965479	−0.482740	−	0.875764i	$-0.660358\pi$
$659$	−4.67442e12	−0.965479	−0.482740	+	0.875764i	$0.660358\pi$
$660$	−2.19319e12	−0.449913
$661$	4.37429e12	0.891252	0.445626	−	0.895219i	$-0.352981\pi$
$661$	4.37429e12	0.891252	0.445626	+	0.895219i	$0.352981\pi$
$662$	−1.22874e12	−0.248656
$663$	−1.44186e12	−0.289809
$664$	7.22293e12	1.44197
$665$	−7.27517e12	−1.44260
$666$	−9.41953e10	−0.0185522
$667$	−5.86717e12	−1.14779
$668$	−8.75405e11	−0.170104
$669$	4.03151e12	0.778126
$670$	6.47117e12	1.24064
$671$	−1.13388e13	−2.15932
$672$	9.36449e11	0.177142
$673$	−5.15555e12	−0.968741	−0.484370	−	0.874863i	$-0.660951\pi$
$673$	−5.15555e12	−0.968741	−0.484370	+	0.874863i	$0.660951\pi$
$674$	−6.24636e12	−1.16589
$675$	2.60964e12	0.483853
$676$	2.39179e10	0.00440517
$677$	9.72694e12	1.77962	0.889810	−	0.456331i	$-0.150837\pi$
$677$	9.72694e12	1.77962	0.889810	+	0.456331i	$0.150837\pi$
$678$	3.88400e12	0.705903
$679$	−2.57618e12	−0.465118
$680$	−5.70575e12	−1.02335
$681$	−1.67849e12	−0.299059
$682$	−1.38768e13	−2.45618
$683$	−6.89717e12	−1.21277	−0.606384	−	0.795172i	$-0.707381\pi$
$683$	−6.89717e12	−1.21277	−0.606384	+	0.795172i	$0.707381\pi$
$684$	−4.29680e11	−0.0750573
$685$	1.67169e13	2.90100
$686$	−5.50979e12	−0.949896
$687$	−5.12134e12	−0.877158
$688$	1.70567e12	0.290233
$689$	−1.44271e12	−0.243890
$690$	3.45539e12	0.580331
$691$	−1.93434e12	−0.322762	−0.161381	−	0.986892i	$-0.551595\pi$
$691$	−1.93434e12	−0.322762	−0.161381	+	0.986892i	$0.551595\pi$
$692$	1.29059e12	0.213950
$693$	−2.87525e12	−0.473561
$694$	−1.97449e12	−0.323100
$695$	−7.23632e12	−1.17648
$696$	7.30108e12	1.17936
$697$	4.45701e12	0.715313
$698$	2.52176e12	0.402119
$699$	4.77132e11	0.0755947
$700$	2.49643e12	0.392987
$701$	−1.76848e12	−0.276611	−0.138306	−	0.990390i	$-0.544166\pi$
$701$	−1.76848e12	−0.276611	−0.138306	+	0.990390i	$0.544166\pi$
$702$	−1.08659e12	−0.168868
$703$	4.28005e11	0.0660921
$704$	1.40950e13	2.16266
$705$	1.69038e12	0.257711
$706$	−6.40686e12	−0.970564
$707$	4.48063e12	0.674454
$708$	1.07472e11	0.0160748
$709$	7.22441e12	1.07373	0.536864	−	0.843669i	$-0.319609\pi$
$709$	7.22441e12	1.07373	0.536864	+	0.843669i	$0.319609\pi$
$710$	1.64566e13	2.43040
$711$	−2.56028e12	−0.375728
$712$	1.56251e12	0.227857
$713$	−5.94760e12	−0.861865
$714$	−1.31788e12	−0.189772
$715$	2.52009e13	3.60610
$716$	1.17414e12	0.166960
$717$	−4.29317e12	−0.606655
$718$	−4.40350e11	−0.0618355
$719$	3.55344e12	0.495871	0.247936	−	0.968777i	$-0.420248\pi$
$719$	3.55344e12	0.495871	0.247936	+	0.968777i	$0.420248\pi$
$720$	−3.33622e12	−0.462656
$721$	2.07214e12	0.285569
$722$	−7.02913e11	−0.0962684
$723$	7.19879e12	0.979799
$724$	2.88184e12	0.389803
$725$	3.54980e13	4.77181
$726$	−1.06458e13	−1.42221
$727$	6.89027e12	0.914811	0.457405	−	0.889258i	$-0.348779\pi$
$727$	6.89027e12	0.914811	0.457405	+	0.889258i	$0.348779\pi$
$728$	−5.89986e12	−0.778485
$729$	2.82430e11	0.0370370
$730$	6.73805e12	0.878175
$731$	1.53497e12	0.198825
$732$	1.06547e12	0.137164
$733$	−3.14265e12	−0.402094	−0.201047	−	0.979582i	$-0.564434\pi$
$733$	−3.14265e12	−0.402094	−0.201047	+	0.979582i	$0.564434\pi$
$734$	4.26787e12	0.542724
$735$	−3.98882e12	−0.504141
$736$	2.02095e12	0.253867
$737$	−1.16208e13	−1.45088
$738$	3.35881e12	0.416804
$739$	1.41697e13	1.74768	0.873840	−	0.486214i	$-0.161623\pi$
$739$	1.41697e13	1.74768	0.873840	+	0.486214i	$0.161623\pi$
$740$	−2.05283e11	−0.0251658
$741$	4.93724e12	0.601593
$742$	−1.31866e12	−0.159703
$743$	−1.25170e13	−1.50678	−0.753392	−	0.657572i	$-0.771584\pi$
$743$	−1.25170e13	−1.50678	−0.753392	+	0.657572i	$0.771584\pi$
$744$	7.40117e12	0.885569
$745$	1.59527e13	1.89728
$746$	4.49949e12	0.531911
$747$	3.80067e12	0.446598
$748$	1.80521e12	0.210848
$749$	−3.78376e12	−0.439294
$750$	−1.25908e13	−1.45304
$751$	9.03491e12	1.03644	0.518220	−	0.855248i	$-0.326595\pi$
$751$	9.03491e12	1.03644	0.518220	+	0.855248i	$0.326595\pi$
$752$	−1.54607e12	−0.176299
$753$	4.77995e12	0.541808
$754$	−1.47805e13	−1.66540
$755$	−5.98768e12	−0.670652
$756$	2.70177e11	0.0300816
$757$	−1.39440e13	−1.54331	−0.771657	−	0.636039i	$-0.780572\pi$
$757$	−1.39440e13	−1.54331	−0.771657	+	0.636039i	$0.780572\pi$
$758$	9.98963e12	1.09910
$759$	−6.20509e12	−0.678673
$760$	1.95377e13	2.12429
$761$	−1.41470e13	−1.52909	−0.764547	−	0.644568i	$-0.777037\pi$
$761$	−1.41470e13	−1.52909	−0.764547	+	0.644568i	$0.777037\pi$
$762$	−6.06126e12	−0.651277
$763$	−4.63897e12	−0.495520
$764$	−4.90322e11	−0.0520669
$765$	−3.00233e12	−0.316944
$766$	−7.98823e12	−0.838342
$767$	−1.23491e12	−0.128841
$768$	−3.39625e12	−0.352269
$769$	7.29078e12	0.751805	0.375903	−	0.926659i	$-0.377333\pi$
$769$	7.29078e12	0.751805	0.375903	+	0.926659i	$0.377333\pi$
$770$	2.30339e13	2.36134
$771$	−6.84898e12	−0.698042
$772$	−2.44605e12	−0.247850
$773$	−1.14023e12	−0.114864	−0.0574320	−	0.998349i	$-0.518291\pi$
$773$	−1.14023e12	−0.114864	−0.0574320	+	0.998349i	$0.518291\pi$
$774$	1.15676e12	0.115853
$775$	3.59847e13	3.58311
$776$	6.91843e12	0.684905
$777$	−2.69124e11	−0.0264885
$778$	8.29312e12	0.811540
$779$	−1.52618e13	−1.48486
$780$	−2.36804e12	−0.229067
$781$	−2.95523e13	−2.84225
$782$	−2.84411e12	−0.271967
$783$	3.84179e12	0.365263
$784$	3.64830e12	0.344880
$785$	3.16390e13	2.97379
$786$	9.58647e12	0.895895
$787$	−7.37896e11	−0.0685660	−0.0342830	−	0.999412i	$-0.510915\pi$
$787$	−7.37896e11	−0.0685660	−0.0342830	+	0.999412i	$0.510915\pi$
$788$	1.18478e12	0.109463
$789$	2.65520e12	0.243922
$790$	2.05106e13	1.87351
$791$	1.10969e13	1.00788
$792$	7.72159e12	0.697338
$793$	−1.22428e13	−1.09939
$794$	−1.24655e12	−0.111306
$795$	−3.00411e12	−0.266725
$796$	−6.94724e11	−0.0613343
$797$	−4.78686e12	−0.420231	−0.210116	−	0.977677i	$-0.567384\pi$
$797$	−4.78686e12	−0.420231	−0.210116	+	0.977677i	$0.567384\pi$
$798$	4.51270e12	0.393934
$799$	−1.39134e12	−0.120774
$800$	−1.22273e13	−1.05542
$801$	8.22185e11	0.0705705
$802$	−6.22915e12	−0.531672
$803$	−1.21000e13	−1.02699
$804$	1.09196e12	0.0921629
$805$	9.87232e12	0.828587
$806$	−1.49831e13	−1.25053
$807$	−4.00928e11	−0.0332764
$808$	−1.20329e13	−0.993160
$809$	−1.29881e13	−1.06605	−0.533025	−	0.846100i	$-0.678945\pi$
$809$	−1.29881e13	−1.06605	−0.533025	+	0.846100i	$0.678945\pi$
$810$	−2.26257e12	−0.184680
$811$	6.81318e12	0.553039	0.276520	−	0.961008i	$-0.410819\pi$
$811$	6.81318e12	0.553039	0.276520	+	0.961008i	$0.410819\pi$
$812$	3.67513e12	0.296668
$813$	−8.60723e12	−0.690965
$814$	−1.35510e12	−0.108184
$815$	1.89913e13	1.50780
$816$	2.74603e12	0.216820
$817$	−5.25607e12	−0.412726
$818$	1.59207e13	1.24329
$819$	−3.10447e12	−0.241107
$820$	7.31997e12	0.565388
$821$	−1.67652e13	−1.28784	−0.643922	−	0.765091i	$-0.722694\pi$
$821$	−1.67652e13	−1.28784	−0.643922	+	0.765091i	$0.722694\pi$
$822$	−1.03693e13	−0.792183
$823$	−3.68616e12	−0.280075	−0.140038	−	0.990146i	$-0.544722\pi$
$823$	−3.68616e12	−0.280075	−0.140038	+	0.990146i	$0.544722\pi$
$824$	−5.56482e12	−0.420512
$825$	3.75426e13	2.82151
$826$	−1.12872e12	−0.0843675
$827$	−8.35656e12	−0.621231	−0.310615	−	0.950536i	$-0.600535\pi$
$827$	−8.35656e12	−0.621231	−0.310615	+	0.950536i	$0.600535\pi$
$828$	5.83071e11	0.0431107
$829$	−1.32045e13	−0.971013	−0.485507	−	0.874233i	$-0.661365\pi$
$829$	−1.32045e13	−0.971013	−0.485507	+	0.874233i	$0.661365\pi$
$830$	−3.04475e13	−2.22690
$831$	1.75773e12	0.127864
$832$	1.52187e13	1.10109
$833$	3.28319e12	0.236261
$834$	4.48860e12	0.321265
$835$	2.09452e13	1.49106
$836$	−6.18143e12	−0.437684
$837$	3.89446e12	0.274273
$838$	−1.32461e12	−0.0927876
$839$	2.94279e11	0.0205036	0.0102518	−	0.999947i	$-0.496737\pi$
$839$	2.94279e11	0.0205036	0.0102518	+	0.999947i	$0.496737\pi$
$840$	−1.22851e13	−0.851375
$841$	3.77514e13	2.60226
$842$	7.79009e12	0.534119
$843$	−4.93958e12	−0.336873
$844$	−2.55835e12	−0.173548
$845$	−5.72266e11	−0.0386138
$846$	−1.04852e12	−0.0703736
$847$	−3.04159e13	−2.03060
$848$	2.74765e12	0.182465
$849$	−1.81910e12	−0.120163
$850$	1.72077e13	1.13067
$851$	−5.80798e11	−0.0379614
$852$	2.77693e12	0.180545
$853$	1.03099e13	0.666782	0.333391	−	0.942789i	$-0.391807\pi$
$853$	1.03099e13	0.666782	0.333391	+	0.942789i	$0.391807\pi$
$854$	−1.11900e13	−0.719899
$855$	1.02807e13	0.657920
$856$	1.01614e13	0.646878
$857$	−1.79877e12	−0.113910	−0.0569549	−	0.998377i	$-0.518139\pi$
$857$	−1.79877e12	−0.113910	−0.0569549	+	0.998377i	$0.518139\pi$
$858$	−1.56318e13	−0.984726
$859$	1.54668e13	0.969240	0.484620	−	0.874725i	$-0.338958\pi$
$859$	1.54668e13	0.969240	0.484620	+	0.874725i	$0.338958\pi$
$860$	2.52096e12	0.157153
$861$	9.59641e12	0.595106
$862$	−1.81534e12	−0.111989
$863$	−2.07216e13	−1.27167	−0.635836	−	0.771825i	$-0.719344\pi$
$863$	−2.07216e13	−1.27167	−0.635836	+	0.771825i	$0.719344\pi$
$864$	−1.32331e12	−0.0807885
$865$	−3.08791e13	−1.87539
$866$	1.82613e13	1.10332
$867$	−7.13441e12	−0.428817
$868$	3.72551e12	0.222765
$869$	−3.68324e13	−2.19099
$870$	−3.07769e13	−1.82133
$871$	−1.25472e13	−0.738696
$872$	1.24581e13	0.729673
$873$	3.64044e12	0.212124
$874$	9.73887e12	0.564556
$875$	−3.59729e13	−2.07462
$876$	1.13700e12	0.0652365
$877$	−1.00413e11	−0.00573182	−0.00286591	−	0.999996i	$-0.500912\pi$
$877$	−1.00413e11	−0.00573182	−0.00286591	+	0.999996i	$0.500912\pi$
$878$	−1.17079e13	−0.664896
$879$	4.45317e12	0.251605
$880$	−4.79952e13	−2.69790
$881$	3.37574e13	1.88789	0.943946	−	0.330100i	$-0.107082\pi$
$881$	3.37574e13	1.88789	0.943946	+	0.330100i	$0.107082\pi$
$882$	2.47422e12	0.137667
$883$	1.65265e13	0.914864	0.457432	−	0.889245i	$-0.348769\pi$
$883$	1.65265e13	0.914864	0.457432	+	0.889245i	$0.348769\pi$
$884$	1.94912e12	0.107351
$885$	−2.57140e12	−0.140905
$886$	4.97936e12	0.271470
$887$	2.28789e13	1.24102	0.620510	−	0.784198i	$-0.286926\pi$
$887$	2.28789e13	1.24102	0.620510	+	0.784198i	$0.286926\pi$
$888$	7.22742e11	0.0390054
$889$	−1.73175e13	−0.929882
$890$	−6.58659e12	−0.351889
$891$	4.06306e12	0.215975
$892$	−5.44984e12	−0.288232
$893$	4.76426e12	0.250706
$894$	−9.89526e12	−0.518094
$895$	−2.80929e13	−1.46350
$896$	7.99077e12	0.414193
$897$	−6.69978e12	−0.345537
$898$	−6.51273e12	−0.334210
$899$	5.29750e13	2.70491
$900$	−3.52774e12	−0.179228
$901$	2.47267e12	0.124999
$902$	4.83202e13	2.43052
$903$	3.30495e12	0.165413
$904$	−2.98011e13	−1.48414
$905$	−6.89516e13	−3.41685
$906$	3.71408e12	0.183136
$907$	−5.90929e12	−0.289936	−0.144968	−	0.989436i	$-0.546308\pi$
$907$	−5.90929e12	−0.289936	−0.144968	+	0.989436i	$0.546308\pi$
$908$	2.26900e12	0.110777
$909$	−6.33165e12	−0.307595
$910$	2.48702e13	1.20225
$911$	−1.93776e13	−0.932110	−0.466055	−	0.884756i	$-0.654325\pi$
$911$	−1.93776e13	−0.932110	−0.466055	+	0.884756i	$0.654325\pi$
$912$	−9.40301e12	−0.450080
$913$	5.46768e13	2.60426
$914$	−9.47208e12	−0.448939
$915$	−2.54927e13	−1.20232
$916$	6.92309e12	0.324915
$917$	2.73893e13	1.27914
$918$	1.86231e12	0.0865486
$919$	−1.84541e12	−0.0853439	−0.0426720	−	0.999089i	$-0.513587\pi$
$919$	−1.84541e12	−0.0853439	−0.0426720	+	0.999089i	$0.513587\pi$
$920$	−2.65125e13	−1.22013
$921$	1.37662e13	0.630442
$922$	7.85731e12	0.358084
$923$	−3.19083e13	−1.44709
$924$	3.88680e12	0.175416
$925$	3.51399e12	0.157820
$926$	−6.40249e12	−0.286154
$927$	−2.92818e12	−0.130238
$928$	−1.80005e13	−0.796745
$929$	−3.06785e13	−1.35134	−0.675668	−	0.737206i	$-0.736145\pi$
$929$	−3.06785e13	−1.35134	−0.675668	+	0.737206i	$0.736145\pi$
$930$	−3.11988e13	−1.36762
$931$	−1.12423e13	−0.490437
$932$	−6.44993e11	−0.0280016
$933$	6.03802e12	0.260872
$934$	−6.87873e12	−0.295765
$935$	−4.31919e13	−1.84820
$936$	8.33718e12	0.355040
$937$	8.12349e12	0.344282	0.172141	−	0.985072i	$-0.444931\pi$
$937$	8.12349e12	0.344282	0.172141	+	0.985072i	$0.444931\pi$
$938$	−1.14683e13	−0.483711
$939$	−1.53685e13	−0.645112
$940$	−2.28507e12	−0.0954607
$941$	−2.62020e13	−1.08939	−0.544693	−	0.838635i	$-0.683354\pi$
$941$	−2.62020e13	−1.08939	−0.544693	+	0.838635i	$0.683354\pi$
$942$	−1.96253e13	−0.812058
$943$	2.07100e13	0.852861
$944$	2.35188e12	0.0963922
$945$	−6.46434e12	−0.263682
$946$	1.66412e13	0.675578
$947$	1.74982e13	0.706998	0.353499	−	0.935435i	$-0.384992\pi$
$947$	1.74982e13	0.706998	0.353499	+	0.935435i	$0.384992\pi$
$948$	3.46101e12	0.139176
$949$	−1.30647e13	−0.522878
$950$	−5.89229e13	−2.34708
$951$	−2.44215e13	−0.968187
$952$	1.01118e13	0.398990
$953$	3.99984e13	1.57081	0.785407	−	0.618980i	$-0.212454\pi$
$953$	3.99984e13	1.57081	0.785407	+	0.618980i	$0.212454\pi$
$954$	1.86341e12	0.0728352
$955$	1.17316e13	0.456396
$956$	5.80356e12	0.224716
$957$	5.52684e13	2.12997
$958$	3.27765e13	1.25724
$959$	−2.96259e13	−1.13107
$960$	3.16893e13	1.20418
$961$	2.72616e13	1.03109
$962$	−1.46314e12	−0.0550804
$963$	5.34688e12	0.200347
$964$	−9.73141e12	−0.362935
$965$	5.85250e13	2.17254
$966$	−6.12368e12	−0.226264
$967$	6.64062e12	0.244225	0.122112	−	0.992516i	$-0.461033\pi$
$967$	6.64062e12	0.244225	0.122112	+	0.992516i	$0.461033\pi$
$968$	8.16829e13	2.99014
$969$	−8.46197e12	−0.308329
$970$	−2.91639e13	−1.05773
$971$	2.22077e13	0.801708	0.400854	−	0.916142i	$-0.368713\pi$
$971$	2.22077e13	0.801708	0.400854	+	0.916142i	$0.368713\pi$
$972$	−3.81792e11	−0.0137192
$973$	1.28243e13	0.458697
$974$	−1.23952e13	−0.441305
$975$	4.05356e13	1.43653
$976$	2.33165e13	0.822505
$977$	−1.67680e13	−0.588785	−0.294392	−	0.955685i	$-0.595117\pi$
$977$	−1.67680e13	−0.588785	−0.294392	+	0.955685i	$0.595117\pi$
$978$	−1.17800e13	−0.411739
$979$	1.18280e13	0.411520
$980$	5.39214e12	0.186743
$981$	6.55539e12	0.225989
$982$	−3.13354e13	−1.07531
$983$	−1.63039e13	−0.556930	−0.278465	−	0.960446i	$-0.589826\pi$
$983$	−1.63039e13	−0.556930	−0.278465	+	0.960446i	$0.589826\pi$
$984$	−2.57715e13	−0.876318
$985$	−2.83473e13	−0.959508
$986$	2.53324e13	0.853551
$987$	−2.99571e12	−0.100478
$988$	−6.67423e12	−0.222841
$989$	7.13243e12	0.237058
$990$	−3.25495e13	−1.07693
$991$	3.73024e13	1.22859	0.614293	−	0.789078i	$-0.289441\pi$
$991$	3.73024e13	1.22859	0.614293	+	0.789078i	$0.289441\pi$
$992$	−1.82473e13	−0.598268
$993$	4.96089e12	0.161915
$994$	−2.91646e13	−0.947582
$995$	1.66222e13	0.537630
$996$	−5.13779e12	−0.165428
$997$	−4.09992e12	−0.131416	−0.0657078	−	0.997839i	$-0.520931\pi$
$997$	−4.09992e12	−0.131416	−0.0657078	+	0.997839i	$0.520931\pi$
$998$	−8.60309e12	−0.274516
$999$	3.80303e11	0.0120805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.6	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.6	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-20.0625 q^{2} +81.0000 q^{3} -109.497 q^{4} +2619.85 q^{5} -1625.06 q^{6} -4642.93 q^{7} +12468.8 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-20.0625 q^{2} +81.0000 q^{3} -109.497 q^{4} +2619.85 q^{5} -1625.06 q^{6} -4642.93 q^{7} +12468.8 q^{8} +6561.00 q^{9} -52560.7 q^{10} +94387.2 q^{11} -8869.24 q^{12} +101912. q^{13} +93148.8 q^{14} +212208. q^{15} -194092. q^{16} -174668. q^{17} -131630. q^{18} +598100. q^{19} -286865. q^{20} -376078. q^{21} -1.89364e6 q^{22} -811615. q^{23} +1.00997e6 q^{24} +4.91050e6 q^{25} -2.04461e6 q^{26} +531441. q^{27} +508387. q^{28} +7.22901e6 q^{29} -4.25742e6 q^{30} +7.32811e6 q^{31} -2.49004e6 q^{32} +7.64536e6 q^{33} +3.50427e6 q^{34} -1.21638e7 q^{35} -718409. q^{36} +715607. q^{37} -1.19994e7 q^{38} +8.25488e6 q^{39} +3.26663e7 q^{40} -2.55171e7 q^{41} +7.54505e6 q^{42} -8.78795e6 q^{43} -1.03351e7 q^{44} +1.71888e7 q^{45} +1.62830e7 q^{46} +7.96566e6 q^{47} -1.57215e7 q^{48} -1.87968e7 q^{49} -9.85168e7 q^{50} -1.41481e7 q^{51} -1.11590e7 q^{52} -1.41564e7 q^{53} -1.06620e7 q^{54} +2.47281e8 q^{55} -5.78917e7 q^{56} +4.84461e7 q^{57} -1.45032e8 q^{58} -1.21174e7 q^{59} -2.32361e7 q^{60} -1.20131e8 q^{61} -1.47020e8 q^{62} -3.04623e7 q^{63} +1.49332e8 q^{64} +2.66994e8 q^{65} -1.53385e8 q^{66} -1.23118e8 q^{67} +1.91255e7 q^{68} -6.57408e7 q^{69} +2.44036e8 q^{70} -3.13097e8 q^{71} +8.18076e7 q^{72} -1.28195e8 q^{73} -1.43569e7 q^{74} +3.97750e8 q^{75} -6.54901e7 q^{76} -4.38234e8 q^{77} -1.65613e8 q^{78} -3.90227e8 q^{79} -5.08492e8 q^{80} +4.30467e7 q^{81} +5.11936e8 q^{82} +5.79282e8 q^{83} +4.11793e7 q^{84} -4.57603e8 q^{85} +1.76308e8 q^{86} +5.85550e8 q^{87} +1.17689e9 q^{88} +1.25314e8 q^{89} -3.44851e8 q^{90} -4.73171e8 q^{91} +8.88693e7 q^{92} +5.93577e8 q^{93} -1.59811e8 q^{94} +1.56693e9 q^{95} -2.01693e8 q^{96} +5.54861e8 q^{97} +3.77110e8 q^{98} +6.19275e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about