LMFDB - Embedded newform 177.14.a.b.1.2

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$189.798744245$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-169.081 q^{2} -729.000 q^{3} +20396.4 q^{4} +15031.4 q^{5} +123260. q^{6} -257399. q^{7} -2.06354e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q-169.081 q^{2} -729.000 q^{3} +20396.4 q^{4} +15031.4 q^{5} +123260. q^{6} -257399. q^{7} -2.06354e6 q^{8} +531441. q^{9} -2.54153e6 q^{10} -4.81287e6 q^{11} -1.48690e7 q^{12} -3.34772e7 q^{13} +4.35214e7 q^{14} -1.09579e7 q^{15} +1.81818e8 q^{16} -1.05741e8 q^{17} -8.98566e7 q^{18} +1.32508e8 q^{19} +3.06587e8 q^{20} +1.87644e8 q^{21} +8.13765e8 q^{22} +7.80853e8 q^{23} +1.50432e9 q^{24} -9.94759e8 q^{25} +5.66035e9 q^{26} -3.87420e8 q^{27} -5.25002e9 q^{28} -9.46595e8 q^{29} +1.85277e9 q^{30} +7.66826e9 q^{31} -1.38374e10 q^{32} +3.50858e9 q^{33} +1.78788e10 q^{34} -3.86908e9 q^{35} +1.08395e10 q^{36} +1.25449e10 q^{37} -2.24046e10 q^{38} +2.44048e10 q^{39} -3.10179e10 q^{40} -2.31196e10 q^{41} -3.17271e10 q^{42} +2.54394e10 q^{43} -9.81653e10 q^{44} +7.98831e9 q^{45} -1.32027e11 q^{46} +9.37427e9 q^{47} -1.32545e11 q^{48} -3.06346e10 q^{49} +1.68195e11 q^{50} +7.70852e10 q^{51} -6.82814e11 q^{52} +1.13282e11 q^{53} +6.55055e10 q^{54} -7.23442e10 q^{55} +5.31153e11 q^{56} -9.65985e10 q^{57} +1.60051e11 q^{58} -4.21805e10 q^{59} -2.23502e11 q^{60} -1.44401e11 q^{61} -1.29656e12 q^{62} -1.36793e11 q^{63} +8.50198e11 q^{64} -5.03209e11 q^{65} -5.93235e11 q^{66} -4.28988e11 q^{67} -2.15674e12 q^{68} -5.69242e11 q^{69} +6.54188e11 q^{70} +1.96469e12 q^{71} -1.09665e12 q^{72} -1.02505e12 q^{73} -2.12110e12 q^{74} +7.25180e11 q^{75} +2.70269e12 q^{76} +1.23883e12 q^{77} -4.12640e12 q^{78} +7.60306e11 q^{79} +2.73298e12 q^{80} +2.82430e11 q^{81} +3.90909e12 q^{82} +1.79334e12 q^{83} +3.82727e12 q^{84} -1.58944e12 q^{85} -4.30132e12 q^{86} +6.90068e11 q^{87} +9.93153e12 q^{88} +8.56658e12 q^{89} -1.35067e12 q^{90} +8.61700e12 q^{91} +1.59266e13 q^{92} -5.59016e12 q^{93} -1.58501e12 q^{94} +1.99179e12 q^{95} +1.00875e13 q^{96} +1.76137e12 q^{97} +5.17973e12 q^{98} -2.55775e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) $	\( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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 $

$2$	−169.081	−1.86810	−0.934050	−	0.357142i	$-0.883751\pi$
$2$	−169.081	−1.86810	−0.934050	+	0.357142i	$0.883751\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	20396.4	2.48980
$5$	15031.4	0.430224	0.215112	−	0.976589i	$-0.430988\pi$
$5$	15031.4	0.430224	0.215112	+	0.976589i	$0.430988\pi$
$6$	123260.	1.07855
$7$	−257399.	−0.826933	−0.413466	−	0.910519i	$-0.635682\pi$
$7$	−257399.	−0.826933	−0.413466	+	0.910519i	$0.635682\pi$
$8$	−2.06354e6	−2.78309
$9$	531441.	0.333333
$10$	−2.54153e6	−0.803702
$11$	−4.81287e6	−0.819127	−0.409564	−	0.912282i	$-0.634319\pi$
$11$	−4.81287e6	−0.819127	−0.409564	+	0.912282i	$0.634319\pi$
$12$	−1.48690e7	−1.43749
$13$	−3.34772e7	−1.92361	−0.961804	−	0.273738i	$-0.911740\pi$
$13$	−3.34772e7	−1.92361	−0.961804	+	0.273738i	$0.911740\pi$
$14$	4.35214e7	1.54479
$15$	−1.09579e7	−0.248390
$16$	1.81818e8	2.70929
$17$	−1.05741e8	−1.06249	−0.531246	−	0.847218i	$-0.678276\pi$
$17$	−1.05741e8	−1.06249	−0.531246	+	0.847218i	$0.678276\pi$
$18$	−8.98566e7	−0.622700
$19$	1.32508e8	0.646166	0.323083	−	0.946371i	$-0.395281\pi$
$19$	1.32508e8	0.646166	0.323083	+	0.946371i	$0.395281\pi$
$20$	3.06587e8	1.07117
$21$	1.87644e8	0.477430
$22$	8.13765e8	1.53021
$23$	7.80853e8	1.09986	0.549931	−	0.835210i	$-0.314654\pi$
$23$	7.80853e8	1.09986	0.549931	+	0.835210i	$0.314654\pi$
$24$	1.50432e9	1.60682
$25$	−9.94759e8	−0.814907
$26$	5.66035e9	3.59349
$27$	−3.87420e8	−0.192450
$28$	−5.25002e9	−2.05889
$29$	−9.46595e8	−0.295514	−0.147757	−	0.989024i	$-0.547205\pi$
$29$	−9.46595e8	−0.295514	−0.147757	+	0.989024i	$0.547205\pi$
$30$	1.85277e9	0.464018
$31$	7.66826e9	1.55184	0.775918	−	0.630834i	$-0.217287\pi$
$31$	7.66826e9	1.55184	0.775918	+	0.630834i	$0.217287\pi$
$32$	−1.38374e10	−2.27814
$33$	3.50858e9	0.472923
$34$	1.78788e10	1.98484
$35$	−3.86908e9	−0.355767
$36$	1.08395e10	0.829932
$37$	1.25449e10	0.803812	0.401906	−	0.915681i	$-0.368348\pi$
$37$	1.25449e10	0.803812	0.401906	+	0.915681i	$0.368348\pi$
$38$	−2.24046e10	−1.20710
$39$	2.44048e10	1.11060
$40$	−3.10179e10	−1.19735
$41$	−2.31196e10	−0.760125	−0.380063	−	0.924961i	$-0.624098\pi$
$41$	−2.31196e10	−0.760125	−0.380063	+	0.924961i	$0.624098\pi$
$42$	−3.17271e10	−0.891887
$43$	2.54394e10	0.613708	0.306854	−	0.951757i	$-0.400724\pi$
$43$	2.54394e10	0.613708	0.306854	+	0.951757i	$0.400724\pi$
$44$	−9.81653e10	−2.03946
$45$	7.98831e9	0.143408
$46$	−1.32027e11	−2.05465
$47$	9.37427e9	0.126853	0.0634266	−	0.997987i	$-0.479797\pi$
$47$	9.37427e9	0.126853	0.0634266	+	0.997987i	$0.479797\pi$
$48$	−1.32545e11	−1.56421
$49$	−3.06346e10	−0.316182
$50$	1.68195e11	1.52233
$51$	7.70852e10	0.613430
$52$	−6.82814e11	−4.78940
$53$	1.13282e11	0.702050	0.351025	−	0.936366i	$-0.385833\pi$
$53$	1.13282e11	0.702050	0.351025	+	0.936366i	$0.385833\pi$
$54$	6.55055e10	0.359516
$55$	−7.23442e10	−0.352409
$56$	5.31153e11	2.30143
$57$	−9.65985e10	−0.373064
$58$	1.60051e11	0.552049
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−2.23502e11	−0.618441
$61$	−1.44401e11	−0.358860	−0.179430	−	0.983771i	$-0.557425\pi$
$61$	−1.44401e11	−0.358860	−0.179430	+	0.983771i	$0.557425\pi$
$62$	−1.29656e12	−2.89898
$63$	−1.36793e11	−0.275644
$64$	8.50198e11	1.54650
$65$	−5.03209e11	−0.827583
$66$	−5.93235e11	−0.883468
$67$	−4.28988e11	−0.579374	−0.289687	−	0.957121i	$-0.593551\pi$
$67$	−4.28988e11	−0.579374	−0.289687	+	0.957121i	$0.593551\pi$
$68$	−2.15674e12	−2.64539
$69$	−5.69242e11	−0.635006
$70$	6.54188e11	0.664608
$71$	1.96469e12	1.82019	0.910093	−	0.414405i	$-0.136010\pi$
$71$	1.96469e12	1.82019	0.910093	+	0.414405i	$0.136010\pi$
$72$	−1.09665e12	−0.927697
$73$	−1.02505e12	−0.792767	−0.396383	−	0.918085i	$-0.629735\pi$
$73$	−1.02505e12	−0.792767	−0.396383	+	0.918085i	$0.629735\pi$
$74$	−2.12110e12	−1.50160
$75$	7.25180e11	0.470487
$76$	2.70269e12	1.60882
$77$	1.23883e12	0.677363
$78$	−4.12640e12	−2.07470
$79$	7.60306e11	0.351894	0.175947	−	0.984400i	$-0.443701\pi$
$79$	7.60306e11	0.351894	0.175947	+	0.984400i	$0.443701\pi$
$80$	2.73298e12	1.16560
$81$	2.82430e11	0.111111
$82$	3.90909e12	1.41999
$83$	1.79334e12	0.602080	0.301040	−	0.953611i	$-0.402666\pi$
$83$	1.79334e12	0.602080	0.301040	+	0.953611i	$0.402666\pi$
$84$	3.82727e12	1.18870
$85$	−1.58944e12	−0.457110
$86$	−4.30132e12	−1.14647
$87$	6.90068e11	0.170615
$88$	9.93153e12	2.27971
$89$	8.56658e12	1.82714	0.913571	−	0.406680i	$-0.133313\pi$
$89$	8.56658e12	1.82714	0.913571	+	0.406680i	$0.133313\pi$
$90$	−1.35067e12	−0.267901
$91$	8.61700e12	1.59069
$92$	1.59266e13	2.73843
$93$	−5.59016e12	−0.895953
$94$	−1.58501e12	−0.236974
$95$	1.99179e12	0.277997
$96$	1.00875e13	1.31528
$97$	1.76137e12	0.214701	0.107351	−	0.994221i	$-0.465763\pi$
$97$	1.76137e12	0.214701	0.107351	+	0.994221i	$0.465763\pi$
$98$	5.17973e12	0.590660
$99$	−2.55775e12	−0.273042
$100$	−2.02895e13	−2.02895
$101$	8.40147e12	0.787529	0.393765	−	0.919211i	$-0.371173\pi$
$101$	8.40147e12	0.787529	0.393765	+	0.919211i	$0.371173\pi$
$102$	−1.30337e13	−1.14595
$103$	−6.08513e12	−0.502143	−0.251072	−	0.967969i	$-0.580783\pi$
$103$	−6.08513e12	−0.502143	−0.251072	+	0.967969i	$0.580783\pi$
$104$	6.90813e13	5.35358
$105$	2.82056e12	0.205402
$106$	−1.91539e13	−1.31150
$107$	−1.19993e13	−0.772966	−0.386483	−	0.922297i	$-0.626310\pi$
$107$	−1.19993e13	−0.772966	−0.386483	+	0.922297i	$0.626310\pi$
$108$	−7.90199e12	−0.479162
$109$	1.59918e12	0.0913323	0.0456661	−	0.998957i	$-0.485459\pi$
$109$	1.59918e12	0.0913323	0.0456661	+	0.998957i	$0.485459\pi$
$110$	1.22320e13	0.658334
$111$	−9.14520e12	−0.464081
$112$	−4.67997e13	−2.24040
$113$	2.23014e13	1.00768	0.503838	−	0.863798i	$-0.331921\pi$
$113$	2.23014e13	1.00768	0.503838	+	0.863798i	$0.331921\pi$
$114$	1.63330e13	0.696921
$115$	1.17373e13	0.473187
$116$	−1.93072e13	−0.735769
$117$	−1.77911e13	−0.641203
$118$	7.13193e12	0.243206
$119$	2.72177e13	0.878609
$120$	2.26120e13	0.691292
$121$	−1.13590e13	−0.329030
$122$	2.44154e13	0.670386
$123$	1.68542e13	0.438858
$124$	1.56405e14	3.86376
$125$	−3.33016e13	−0.780817
$126$	2.31290e13	0.514931
$127$	1.38017e13	0.291883	0.145942	−	0.989293i	$-0.453379\pi$
$127$	1.38017e13	0.291883	0.145942	+	0.989293i	$0.453379\pi$
$128$	−3.03962e13	−0.610877
$129$	−1.85453e13	−0.354324
$130$	8.50832e13	1.54601
$131$	9.95920e13	1.72171	0.860857	−	0.508846i	$-0.169928\pi$
$131$	9.95920e13	1.72171	0.860857	+	0.508846i	$0.169928\pi$
$132$	7.15625e13	1.17748
$133$	−3.41075e13	−0.534336
$134$	7.25338e13	1.08233
$135$	−5.82348e12	−0.0827967
$136$	2.18200e14	2.95701
$137$	−1.22658e14	−1.58493	−0.792466	−	0.609915i	$-0.791203\pi$
$137$	−1.22658e14	−1.58493	−0.792466	+	0.609915i	$0.791203\pi$
$138$	9.62480e13	1.18625
$139$	−1.56326e13	−0.183837	−0.0919187	−	0.995767i	$-0.529300\pi$
$139$	−1.56326e13	−0.183837	−0.0919187	+	0.995767i	$0.529300\pi$
$140$	−7.89153e13	−0.885787
$141$	−6.83384e12	−0.0732387
$142$	−3.32193e14	−3.40029
$143$	1.61121e14	1.57568
$144$	9.66253e13	0.903098
$145$	−1.42287e13	−0.127137
$146$	1.73316e14	1.48097
$147$	2.23326e13	0.182548
$148$	2.55870e14	2.00133
$149$	1.74212e13	0.130427	0.0652135	−	0.997871i	$-0.479227\pi$
$149$	1.74212e13	0.130427	0.0652135	+	0.997871i	$0.479227\pi$
$150$	−1.22614e14	−0.878916
$151$	−2.42138e14	−1.66232	−0.831158	−	0.556037i	$-0.812321\pi$
$151$	−2.42138e14	−1.66232	−0.831158	+	0.556037i	$0.812321\pi$
$152$	−2.73436e14	−1.79834
$153$	−5.61951e13	−0.354164
$154$	−2.09463e14	−1.26538
$155$	1.15265e14	0.667638
$156$	4.97771e14	2.76516
$157$	5.46292e13	0.291123	0.145562	−	0.989349i	$-0.453501\pi$
$157$	5.46292e13	0.291123	0.145562	+	0.989349i	$0.453501\pi$
$158$	−1.28553e14	−0.657374
$159$	−8.25826e13	−0.405329
$160$	−2.07996e14	−0.980112
$161$	−2.00991e14	−0.909512
$162$	−4.77535e13	−0.207567
$163$	−1.72738e13	−0.0721389	−0.0360694	−	0.999349i	$-0.511484\pi$
$163$	−1.72738e13	−0.0721389	−0.0360694	+	0.999349i	$0.511484\pi$
$164$	−4.71557e14	−1.89256
$165$	5.27389e13	0.203463
$166$	−3.03219e14	−1.12475
$167$	1.44703e14	0.516203	0.258101	−	0.966118i	$-0.416903\pi$
$167$	1.44703e14	0.516203	0.258101	+	0.966118i	$0.416903\pi$
$168$	−3.87211e14	−1.32873
$169$	8.17845e14	2.70027
$170$	2.68744e14	0.853927
$171$	7.04203e13	0.215389
$172$	5.18872e14	1.52801
$173$	2.42499e13	0.0687719	0.0343860	−	0.999409i	$-0.489052\pi$
$173$	2.42499e13	0.0687719	0.0343860	+	0.999409i	$0.489052\pi$
$174$	−1.16677e14	−0.318726
$175$	2.56050e14	0.673873
$176$	−8.75064e14	−2.21926
$177$	3.07496e13	0.0751646
$178$	−1.44845e15	−3.41328
$179$	1.43017e14	0.324970	0.162485	−	0.986711i	$-0.448049\pi$
$179$	1.43017e14	0.324970	0.162485	+	0.986711i	$0.448049\pi$
$180$	1.62933e14	0.357057
$181$	−7.37868e14	−1.55980	−0.779898	−	0.625907i	$-0.784729\pi$
$181$	−7.37868e14	−1.55980	−0.779898	+	0.625907i	$0.784729\pi$
$182$	−1.45697e15	−2.97158
$183$	1.05268e14	0.207188
$184$	−1.61132e15	−3.06102
$185$	1.88567e14	0.345820
$186$	9.45191e14	1.67373
$187$	5.08918e14	0.870316
$188$	1.91201e14	0.315839
$189$	9.97218e13	0.159143
$190$	−3.36773e14	−0.519325
$191$	−1.08478e14	−0.161668	−0.0808339	−	0.996728i	$-0.525758\pi$
$191$	−1.08478e14	−0.161668	−0.0808339	+	0.996728i	$0.525758\pi$
$192$	−6.19794e14	−0.892872
$193$	−5.50034e14	−0.766067	−0.383034	−	0.923734i	$-0.625121\pi$
$193$	−5.50034e14	−0.766067	−0.383034	+	0.923734i	$0.625121\pi$
$194$	−2.97814e14	−0.401083
$195$	3.66840e14	0.477806
$196$	−6.24836e14	−0.787230
$197$	1.39304e15	1.69799	0.848993	−	0.528404i	$-0.177209\pi$
$197$	1.39304e15	1.69799	0.848993	+	0.528404i	$0.177209\pi$
$198$	4.32468e14	0.510071
$199$	8.63797e14	0.985977	0.492989	−	0.870036i	$-0.335904\pi$
$199$	8.63797e14	0.985977	0.492989	+	0.870036i	$0.335904\pi$
$200$	2.05272e15	2.26796
$201$	3.12733e14	0.334502
$202$	−1.42053e15	−1.47118
$203$	2.43653e14	0.244370
$204$	1.57226e15	1.52732
$205$	−3.47520e14	−0.327024
$206$	1.02888e15	0.938054
$207$	4.14977e14	0.366621
$208$	−6.08674e15	−5.21162
$209$	−6.37744e14	−0.529292
$210$	−4.76903e14	−0.383711
$211$	4.70340e14	0.366924	0.183462	−	0.983027i	$-0.441270\pi$
$211$	4.70340e14	0.366924	0.183462	+	0.983027i	$0.441270\pi$
$212$	2.31055e15	1.74796
$213$	−1.43226e15	−1.05088
$214$	2.02885e15	1.44398
$215$	3.82390e14	0.264032
$216$	7.99456e14	0.535606
$217$	−1.97380e15	−1.28326
$218$	−2.70391e14	−0.170618
$219$	7.47260e14	0.457704
$220$	−1.47556e15	−0.877426
$221$	3.53991e15	2.04382
$222$	1.54628e15	0.866950
$223$	1.64133e15	0.893744	0.446872	−	0.894598i	$-0.352538\pi$
$223$	1.64133e15	0.893744	0.446872	+	0.894598i	$0.352538\pi$
$224$	3.56174e15	1.88387
$225$	−5.28656e14	−0.271636
$226$	−3.77074e15	−1.88244
$227$	−2.58555e15	−1.25425	−0.627125	−	0.778918i	$-0.715769\pi$
$227$	−2.58555e15	−1.25425	−0.627125	+	0.778918i	$0.715769\pi$
$228$	−1.97026e15	−0.928854
$229$	−2.74237e15	−1.25659	−0.628297	−	0.777974i	$-0.716248\pi$
$229$	−2.74237e15	−1.25659	−0.628297	+	0.777974i	$0.716248\pi$
$230$	−1.98456e15	−0.883961
$231$	−9.03106e14	−0.391076
$232$	1.95333e15	0.822441
$233$	−1.40319e15	−0.574516	−0.287258	−	0.957853i	$-0.592744\pi$
$233$	−1.40319e15	−0.574516	−0.287258	+	0.957853i	$0.592744\pi$
$234$	3.00814e15	1.19783
$235$	1.40909e14	0.0545753
$236$	−8.60332e14	−0.324144
$237$	−5.54263e14	−0.203166
$238$	−4.60199e15	−1.64133
$239$	−9.69016e14	−0.336314	−0.168157	−	0.985760i	$-0.553782\pi$
$239$	−9.69016e14	−0.336314	−0.168157	+	0.985760i	$0.553782\pi$
$240$	−1.99234e15	−0.672962
$241$	3.93767e15	1.29458	0.647289	−	0.762245i	$-0.275903\pi$
$241$	3.93767e15	1.29458	0.647289	+	0.762245i	$0.275903\pi$
$242$	1.92060e15	0.614662
$243$	−2.05891e14	−0.0641500
$244$	−2.94525e15	−0.893488
$245$	−4.60482e14	−0.136029
$246$	−2.84972e15	−0.819831
$247$	−4.43600e15	−1.24297
$248$	−1.58237e16	−4.31890
$249$	−1.30734e15	−0.347611
$250$	5.63066e15	1.45864
$251$	7.77142e15	1.96165	0.980825	−	0.194892i	$-0.0624357\pi$
$251$	7.77142e15	1.96165	0.980825	+	0.194892i	$0.0624357\pi$
$252$	−2.79008e15	−0.686298
$253$	−3.75814e15	−0.900927
$254$	−2.33361e15	−0.545267
$255$	1.15870e15	0.263912
$256$	−1.82540e15	−0.405321
$257$	−8.48906e15	−1.83778	−0.918892	−	0.394510i	$-0.870914\pi$
$257$	−8.48906e15	−1.83778	−0.918892	+	0.394510i	$0.870914\pi$
$258$	3.13566e15	0.661913
$259$	−3.22904e15	−0.664698
$260$	−1.02637e16	−2.06051
$261$	−5.03060e14	−0.0985045
$262$	−1.68391e16	−3.21633
$263$	4.59142e15	0.855528	0.427764	−	0.903890i	$-0.359301\pi$
$263$	4.59142e15	0.855528	0.427764	+	0.903890i	$0.359301\pi$
$264$	−7.24008e15	−1.31619
$265$	1.70279e15	0.302039
$266$	5.76694e15	0.998193
$267$	−6.24503e15	−1.05490
$268$	−8.74983e15	−1.44252
$269$	1.05501e16	1.69773	0.848865	−	0.528609i	$-0.177286\pi$
$269$	1.05501e16	1.69773	0.848865	+	0.528609i	$0.177286\pi$
$270$	9.84641e14	0.154673
$271$	2.76727e15	0.424376	0.212188	−	0.977229i	$-0.431941\pi$
$271$	2.76727e15	0.424376	0.212188	+	0.977229i	$0.431941\pi$
$272$	−1.92256e16	−2.87860
$273$	−6.28179e15	−0.918388
$274$	2.07391e16	2.96081
$275$	4.78765e15	0.667513
$276$	−1.16105e16	−1.58104
$277$	−8.05495e15	−1.07138	−0.535691	−	0.844414i	$-0.679949\pi$
$277$	−8.05495e15	−1.07138	−0.535691	+	0.844414i	$0.679949\pi$
$278$	2.64317e15	0.343426
$279$	4.07523e15	0.517279
$280$	7.98398e15	0.990131
$281$	9.17393e14	0.111164	0.0555820	−	0.998454i	$-0.482299\pi$
$281$	9.17393e14	0.111164	0.0555820	+	0.998454i	$0.482299\pi$
$282$	1.15547e15	0.136817
$283$	−1.16050e16	−1.34287	−0.671433	−	0.741065i	$-0.734321\pi$
$283$	−1.16050e16	−1.34287	−0.671433	+	0.741065i	$0.734321\pi$
$284$	4.00727e16	4.53189
$285$	−1.45201e15	−0.160501
$286$	−2.72425e16	−2.94353
$287$	5.95097e15	0.628572
$288$	−7.35378e15	−0.759380
$289$	1.27659e15	0.128889
$290$	2.40580e15	0.237505
$291$	−1.28404e15	−0.123958
$292$	−2.09073e16	−1.97383
$293$	−1.53153e16	−1.41411	−0.707057	−	0.707156i	$-0.749978\pi$
$293$	−1.53153e16	−1.41411	−0.707057	+	0.707156i	$0.749978\pi$
$294$	−3.77602e15	−0.341018
$295$	−6.34033e14	−0.0560104
$296$	−2.58868e16	−2.23708
$297$	1.86460e15	0.157641
$298$	−2.94560e15	−0.243651
$299$	−2.61407e16	−2.11570
$300$	1.47911e16	1.17142
$301$	−6.54808e15	−0.507495
$302$	4.09410e16	3.10537
$303$	−6.12468e15	−0.454680
$304$	2.40923e16	1.75065
$305$	−2.17055e15	−0.154390
$306$	9.50153e15	0.661614
$307$	−1.73057e15	−0.117975	−0.0589874	−	0.998259i	$-0.518787\pi$
$307$	−1.73057e15	−0.117975	−0.0589874	+	0.998259i	$0.518787\pi$
$308$	2.52677e16	1.68650
$309$	4.43606e15	0.289913
$310$	−1.94891e16	−1.24721
$311$	2.75558e16	1.72691	0.863456	−	0.504423i	$-0.168295\pi$
$311$	2.75558e16	1.72691	0.863456	+	0.504423i	$0.168295\pi$
$312$	−5.03603e16	−3.09089
$313$	7.57965e15	0.455628	0.227814	−	0.973705i	$-0.426842\pi$
$313$	7.57965e15	0.455628	0.227814	+	0.973705i	$0.426842\pi$
$314$	−9.23676e15	−0.543847
$315$	−2.05619e15	−0.118589
$316$	1.55075e16	0.876146
$317$	2.65849e16	1.47146	0.735732	−	0.677273i	$-0.236838\pi$
$317$	2.65849e16	1.47146	0.735732	+	0.677273i	$0.236838\pi$
$318$	1.39632e16	0.757195
$319$	4.55584e15	0.242063
$320$	1.27797e16	0.665342
$321$	8.74747e15	0.446272
$322$	3.39838e16	1.69906
$323$	−1.40116e16	−0.686546
$324$	5.76055e15	0.276644
$325$	3.33017e16	1.56756
$326$	2.92068e15	0.134763
$327$	−1.16580e15	−0.0527307
$328$	4.77081e16	2.11550
$329$	−2.41293e15	−0.104899
$330$	−8.91716e15	−0.380090
$331$	8.69548e15	0.363422	0.181711	−	0.983352i	$-0.441836\pi$
$331$	8.69548e15	0.363422	0.181711	+	0.983352i	$0.441836\pi$
$332$	3.65777e16	1.49906
$333$	6.66685e15	0.267937
$334$	−2.44665e16	−0.964319
$335$	−6.44831e15	−0.249261
$336$	3.41170e16	1.29350
$337$	6.16978e15	0.229443	0.114722	−	0.993398i	$-0.463402\pi$
$337$	6.16978e15	0.229443	0.114722	+	0.993398i	$0.463402\pi$
$338$	−1.38282e17	−5.04438
$339$	−1.62577e16	−0.581783
$340$	−3.24188e16	−1.13811
$341$	−3.69063e16	−1.27115
$342$	−1.19067e16	−0.402368
$343$	3.28245e16	1.08839
$344$	−5.24951e16	−1.70800
$345$	−8.55651e15	−0.273195
$346$	−4.10021e15	−0.128473
$347$	2.83759e15	0.0872585	0.0436292	−	0.999048i	$-0.486108\pi$
$347$	2.83759e15	0.0872585	0.0436292	+	0.999048i	$0.486108\pi$
$348$	1.40749e16	0.424796
$349$	6.03272e16	1.78710	0.893548	−	0.448968i	$-0.148208\pi$
$349$	6.03272e16	1.78710	0.893548	+	0.448968i	$0.148208\pi$
$350$	−4.32933e16	−1.25886
$351$	1.29697e16	0.370199
$352$	6.65977e16	1.86609
$353$	−7.92367e15	−0.217967	−0.108983	−	0.994044i	$-0.534760\pi$
$353$	−7.92367e15	−0.217967	−0.108983	+	0.994044i	$0.534760\pi$
$354$	−5.19918e15	−0.140415
$355$	2.95321e16	0.783088
$356$	1.74727e17	4.54921
$357$	−1.98417e16	−0.507265
$358$	−2.41815e16	−0.607076
$359$	1.88282e16	0.464190	0.232095	−	0.972693i	$-0.425442\pi$
$359$	1.88282e16	0.464190	0.232095	+	0.972693i	$0.425442\pi$
$360$	−1.64842e16	−0.399118
$361$	−2.44946e16	−0.582469
$362$	1.24759e17	2.91385
$363$	8.28073e15	0.189966
$364$	1.75756e17	3.96051
$365$	−1.54079e16	−0.341068
$366$	−1.77988e16	−0.387048
$367$	−2.52607e16	−0.539655	−0.269827	−	0.962909i	$-0.586967\pi$
$367$	−2.52607e16	−0.539655	−0.269827	+	0.962909i	$0.586967\pi$
$368$	1.41973e17	2.97985
$369$	−1.22867e16	−0.253375
$370$	−3.18831e16	−0.646026
$371$	−2.91587e16	−0.580548
$372$	−1.14019e17	−2.23074
$373$	8.77358e16	1.68682	0.843412	−	0.537268i	$-0.180544\pi$
$373$	8.77358e16	1.68682	0.843412	+	0.537268i	$0.180544\pi$
$374$	−8.60483e16	−1.62584
$375$	2.42768e16	0.450805
$376$	−1.93441e16	−0.353044
$377$	3.16893e16	0.568452
$378$	−1.68611e16	−0.297296
$379$	8.32382e16	1.44267	0.721336	−	0.692585i	$-0.243528\pi$
$379$	8.32382e16	1.44267	0.721336	+	0.692585i	$0.243528\pi$
$380$	4.06253e16	0.692155
$381$	−1.00614e16	−0.168519
$382$	1.83415e16	0.302011
$383$	4.84608e15	0.0784509	0.0392255	−	0.999230i	$-0.487511\pi$
$383$	4.84608e15	0.0784509	0.0392255	+	0.999230i	$0.487511\pi$
$384$	2.21588e16	0.352690
$385$	1.86214e16	0.291418
$386$	9.30003e16	1.43109
$387$	1.35195e16	0.204569
$388$	3.59256e16	0.534562
$389$	−2.86897e16	−0.419811	−0.209905	−	0.977722i	$-0.567316\pi$
$389$	−2.86897e16	−0.419811	−0.209905	+	0.977722i	$0.567316\pi$
$390$	−6.20256e16	−0.892588
$391$	−8.25682e16	−1.16859
$392$	6.32156e16	0.879964
$393$	−7.26026e16	−0.994032
$394$	−2.35537e17	−3.17201
$395$	1.14285e16	0.151394
$396$	−5.21690e16	−0.679820
$397$	−1.12294e17	−1.43953	−0.719763	−	0.694220i	$-0.755750\pi$
$397$	−1.12294e17	−1.43953	−0.719763	+	0.694220i	$0.755750\pi$
$398$	−1.46052e17	−1.84190
$399$	2.48644e16	0.308499
$400$	−1.80865e17	−2.20782
$401$	−6.86571e16	−0.824607	−0.412304	−	0.911047i	$-0.635276\pi$
$401$	−6.86571e16	−0.824607	−0.412304	+	0.911047i	$0.635276\pi$
$402$	−5.28772e16	−0.624883
$403$	−2.56712e17	−2.98513
$404$	1.71360e17	1.96079
$405$	4.24532e15	0.0478027
$406$	−4.11971e16	−0.456507
$407$	−6.03767e16	−0.658424
$408$	−1.59068e17	−1.70723
$409$	−1.01572e17	−1.07294	−0.536469	−	0.843920i	$-0.680242\pi$
$409$	−1.01572e17	−1.07294	−0.536469	+	0.843920i	$0.680242\pi$
$410$	5.87591e16	0.610914
$411$	8.94174e16	0.915061
$412$	−1.24115e17	−1.25023
$413$	1.08572e16	0.107657
$414$	−7.01648e16	−0.684884
$415$	2.69564e16	0.259030
$416$	4.63238e17	4.38225
$417$	1.13961e16	0.106139
$418$	1.07831e17	0.988771
$419$	−8.75813e16	−0.790715	−0.395358	−	0.918527i	$-0.629379\pi$
$419$	−8.75813e16	−0.790715	−0.395358	+	0.918527i	$0.629379\pi$
$420$	5.75293e16	0.511409
$421$	−1.51127e17	−1.32284	−0.661420	−	0.750016i	$-0.730046\pi$
$421$	−1.51127e17	−1.32284	−0.661420	+	0.750016i	$0.730046\pi$
$422$	−7.95256e16	−0.685450
$423$	4.98187e15	0.0422844
$424$	−2.33762e17	−1.95387
$425$	1.05187e17	0.865832
$426$	2.42168e17	1.96316
$427$	3.71686e16	0.296753
$428$	−2.44742e17	−1.92453
$429$	−1.17457e17	−0.909720
$430$	−6.46549e16	−0.493238
$431$	−2.09940e16	−0.157758	−0.0788791	−	0.996884i	$-0.525134\pi$
$431$	−2.09940e16	−0.157758	−0.0788791	+	0.996884i	$0.525134\pi$
$432$	−7.04399e16	−0.521404
$433$	2.00541e17	1.46228	0.731142	−	0.682225i	$-0.238988\pi$
$433$	2.00541e17	1.46228	0.731142	+	0.682225i	$0.238988\pi$
$434$	3.33733e17	2.39727
$435$	1.03727e16	0.0734027
$436$	3.26175e16	0.227399
$437$	1.03469e17	0.710694
$438$	−1.26348e17	−0.855037
$439$	−2.34587e17	−1.56417	−0.782085	−	0.623172i	$-0.785844\pi$
$439$	−2.34587e17	−1.56417	−0.782085	+	0.623172i	$0.785844\pi$
$440$	1.49285e17	0.980785
$441$	−1.62805e16	−0.105394
$442$	−5.98532e17	−3.81806
$443$	−1.56695e17	−0.984989	−0.492494	−	0.870316i	$-0.663915\pi$
$443$	−1.56695e17	−0.984989	−0.492494	+	0.870316i	$0.663915\pi$
$444$	−1.86529e17	−1.15547
$445$	1.28768e17	0.786081
$446$	−2.77517e17	−1.66960
$447$	−1.27001e16	−0.0753020
$448$	−2.18840e17	−1.27885
$449$	2.39276e17	1.37815	0.689076	−	0.724689i	$-0.258017\pi$
$449$	2.39276e17	1.37815	0.689076	+	0.724689i	$0.258017\pi$
$450$	8.93857e16	0.507443
$451$	1.11272e17	0.622639
$452$	4.54868e17	2.50891
$453$	1.76519e17	0.959738
$454$	4.37167e17	2.34307
$455$	1.29526e17	0.684356
$456$	1.99334e17	1.03827
$457$	−1.14996e17	−0.590509	−0.295254	−	0.955419i	$-0.595404\pi$
$457$	−1.14996e17	−0.590509	−0.295254	+	0.955419i	$0.595404\pi$
$458$	4.63683e17	2.34744
$459$	4.09662e16	0.204477
$460$	2.39399e17	1.17814
$461$	2.49498e17	1.21063	0.605314	−	0.795987i	$-0.293048\pi$
$461$	2.49498e17	1.21063	0.605314	+	0.795987i	$0.293048\pi$
$462$	1.52698e17	0.730569
$463$	−3.34372e17	−1.57744	−0.788722	−	0.614750i	$-0.789257\pi$
$463$	−3.34372e17	−1.57744	−0.788722	+	0.614750i	$0.789257\pi$
$464$	−1.72108e17	−0.800633
$465$	−8.40281e16	−0.385461
$466$	2.37252e17	1.07325
$467$	−5.83675e16	−0.260382	−0.130191	−	0.991489i	$-0.541559\pi$
$467$	−5.83675e16	−0.260382	−0.130191	+	0.991489i	$0.541559\pi$
$468$	−3.62875e17	−1.59647
$469$	1.10421e17	0.479104
$470$	−2.38250e16	−0.101952
$471$	−3.98247e16	−0.168080
$472$	8.70411e16	0.362327
$473$	−1.22436e17	−0.502705
$474$	9.37154e16	0.379535
$475$	−1.31814e17	−0.526565
$476$	5.55143e17	2.18756
$477$	6.02027e16	0.234017
$478$	1.63842e17	0.628268
$479$	−7.63797e16	−0.288933	−0.144466	−	0.989510i	$-0.546147\pi$
$479$	−7.63797e16	−0.288933	−0.144466	+	0.989510i	$0.546147\pi$
$480$	1.51629e17	0.565868
$481$	−4.19966e17	−1.54622
$482$	−6.65785e17	−2.41840
$483$	1.46522e17	0.525107
$484$	−2.31683e17	−0.819219
$485$	2.64759e16	0.0923697
$486$	3.48123e16	0.119839
$487$	−1.51731e16	−0.0515390	−0.0257695	−	0.999668i	$-0.508204\pi$
$487$	−1.51731e16	−0.0515390	−0.0257695	+	0.999668i	$0.508204\pi$
$488$	2.97976e17	0.998739
$489$	1.25926e16	0.0416494
$490$	7.78587e16	0.254116
$491$	−5.62266e17	−1.81097	−0.905486	−	0.424376i	$-0.860493\pi$
$491$	−5.62266e17	−1.81097	−0.905486	+	0.424376i	$0.860493\pi$
$492$	3.43765e17	1.09267
$493$	1.00094e17	0.313981
$494$	7.50043e17	2.32199
$495$	−3.84467e16	−0.117470
$496$	1.39422e18	4.20438
$497$	−5.05711e17	−1.50517
$498$	2.21047e17	0.649372
$499$	−3.04338e17	−0.882476	−0.441238	−	0.897390i	$-0.645460\pi$
$499$	−3.04338e17	−0.882476	−0.441238	+	0.897390i	$0.645460\pi$
$500$	−6.79232e17	−1.94408
$501$	−1.05488e17	−0.298030
$502$	−1.31400e18	−3.66456
$503$	1.36107e17	0.374705	0.187353	−	0.982293i	$-0.440009\pi$
$503$	1.36107e17	0.374705	0.187353	+	0.982293i	$0.440009\pi$
$504$	2.82276e17	0.767143
$505$	1.26286e17	0.338814
$506$	6.35430e17	1.68302
$507$	−5.96209e17	−1.55900
$508$	2.81506e17	0.726730
$509$	−4.90782e17	−1.25090	−0.625450	−	0.780264i	$-0.715085\pi$
$509$	−4.90782e17	−1.25090	−0.625450	+	0.780264i	$0.715085\pi$
$510$	−1.95914e17	−0.493015
$511$	2.63847e17	0.655565
$512$	5.57647e17	1.36806
$513$	−5.13364e16	−0.124355
$514$	1.43534e18	3.43316
$515$	−9.14681e16	−0.216034
$516$	−3.78258e17	−0.882196
$517$	−4.51171e16	−0.103909
$518$	5.45969e17	1.24172
$519$	−1.76782e16	−0.0397055
$520$	1.03839e18	2.30324
$521$	2.22597e17	0.487611	0.243806	−	0.969824i	$-0.421604\pi$
$521$	2.22597e17	0.487611	0.243806	+	0.969824i	$0.421604\pi$
$522$	8.50579e16	0.184016
$523$	−6.36879e17	−1.36081	−0.680403	−	0.732838i	$-0.738195\pi$
$523$	−6.36879e17	−1.36081	−0.680403	+	0.732838i	$0.738195\pi$
$524$	2.03132e18	4.28672
$525$	−1.86661e17	−0.389061
$526$	−7.76322e17	−1.59821
$527$	−8.10850e17	−1.64881
$528$	6.37922e17	1.28129
$529$	1.05695e17	0.209696
$530$	−2.87910e17	−0.564239
$531$	−2.24165e16	−0.0433963
$532$	−6.95671e17	−1.33039
$533$	7.73978e17	1.46218
$534$	1.05592e18	1.97066
$535$	−1.80366e17	−0.332549
$536$	8.85233e17	1.61245
$537$	−1.04259e17	−0.187621
$538$	−1.78383e18	−3.17153
$539$	1.47440e17	0.258994
$540$	−1.18778e17	−0.206147
$541$	7.84768e17	1.34573	0.672867	−	0.739763i	$-0.265063\pi$
$541$	7.84768e17	1.34573	0.672867	+	0.739763i	$0.265063\pi$
$542$	−4.67893e17	−0.792777
$543$	5.37905e17	0.900548
$544$	1.46318e18	2.42051
$545$	2.40379e16	0.0392934
$546$	1.06213e18	1.71564
$547$	8.71489e16	0.139105	0.0695527	−	0.997578i	$-0.477843\pi$
$547$	8.71489e16	0.139105	0.0695527	+	0.997578i	$0.477843\pi$
$548$	−2.50178e18	−3.94616
$549$	−7.67404e16	−0.119620
$550$	−8.09500e17	−1.24698
$551$	−1.25432e17	−0.190951
$552$	1.17465e18	1.76728
$553$	−1.95702e17	−0.290993
$554$	1.36194e18	2.00145
$555$	−1.37465e17	−0.199659
$556$	−3.18848e17	−0.457718
$557$	3.40843e17	0.483610	0.241805	−	0.970325i	$-0.422260\pi$
$557$	3.40843e17	0.483610	0.241805	+	0.970325i	$0.422260\pi$
$558$	−6.89044e17	−0.966328
$559$	−8.51638e17	−1.18053
$560$	−7.03466e17	−0.963876
$561$	−3.71001e17	−0.502477
$562$	−1.55114e17	−0.207666
$563$	−7.11918e17	−0.942162	−0.471081	−	0.882090i	$-0.656136\pi$
$563$	−7.11918e17	−0.942162	−0.471081	+	0.882090i	$0.656136\pi$
$564$	−1.39386e17	−0.182349
$565$	3.35221e17	0.433527
$566$	1.96218e18	2.50861
$567$	−7.26972e16	−0.0918814
$568$	−4.05422e18	−5.06574
$569$	−1.09261e18	−1.34969	−0.674845	−	0.737959i	$-0.735790\pi$
$569$	−1.09261e18	−1.34969	−0.674845	+	0.737959i	$0.735790\pi$
$570$	2.45508e17	0.299833
$571$	4.69203e17	0.566534	0.283267	−	0.959041i	$-0.408582\pi$
$571$	4.69203e17	0.566534	0.283267	+	0.959041i	$0.408582\pi$
$572$	3.28629e18	3.92312
$573$	7.90802e16	0.0933389
$574$	−1.00620e18	−1.17424
$575$	−7.76761e17	−0.896285
$576$	4.51830e17	0.515500
$577$	6.98382e17	0.787863	0.393931	−	0.919140i	$-0.371115\pi$
$577$	6.98382e17	0.787863	0.393931	+	0.919140i	$0.371115\pi$
$578$	−2.15847e17	−0.240777
$579$	4.00975e17	0.442289
$580$	−2.90214e17	−0.316546
$581$	−4.61604e17	−0.497880
$582$	2.17107e17	0.231565
$583$	−5.45212e17	−0.575068
$584$	2.11522e18	2.20634
$585$	−2.67426e17	−0.275861
$586$	2.58952e18	2.64171
$587$	−1.12669e18	−1.13673	−0.568364	−	0.822777i	$-0.692424\pi$
$587$	−1.12669e18	−1.13673	−0.568364	+	0.822777i	$0.692424\pi$
$588$	4.55506e17	0.454507
$589$	1.01611e18	1.00274
$590$	1.07203e17	0.104633
$591$	−1.01553e18	−0.980333
$592$	2.28088e18	2.17776
$593$	−1.00836e18	−0.952269	−0.476135	−	0.879372i	$-0.657963\pi$
$593$	−1.00836e18	−0.952269	−0.476135	+	0.879372i	$0.657963\pi$
$594$	−3.15269e17	−0.294489
$595$	4.09120e17	0.377999
$596$	3.55330e17	0.324737
$597$	−6.29708e17	−0.569254
$598$	4.41990e18	3.95235
$599$	7.20482e17	0.637307	0.318654	−	0.947871i	$-0.396769\pi$
$599$	7.20482e17	0.637307	0.318654	+	0.947871i	$0.396769\pi$
$600$	−1.49643e18	−1.30941
$601$	−1.82789e18	−1.58222	−0.791108	−	0.611676i	$-0.790496\pi$
$601$	−1.82789e18	−1.58222	−0.791108	+	0.611676i	$0.790496\pi$
$602$	1.10716e18	0.948051
$603$	−2.27982e17	−0.193125
$604$	−4.93875e18	−4.13883
$605$	−1.70742e17	−0.141557
$606$	1.03557e18	0.849388
$607$	−1.46250e16	−0.0118678	−0.00593390	−	0.999982i	$-0.501889\pi$
$607$	−1.46250e16	−0.0118678	−0.00593390	+	0.999982i	$0.501889\pi$
$608$	−1.83357e18	−1.47206
$609$	−1.77623e17	−0.141087
$610$	3.66998e17	0.288416
$611$	−3.13824e17	−0.244016
$612$	−1.14618e18	−0.881796
$613$	2.16294e18	1.64646	0.823231	−	0.567706i	$-0.192169\pi$
$613$	2.16294e18	1.64646	0.823231	+	0.567706i	$0.192169\pi$
$614$	2.92606e17	0.220389
$615$	2.53342e17	0.188808
$616$	−2.55637e18	−1.88516
$617$	−6.90608e17	−0.503939	−0.251970	−	0.967735i	$-0.581078\pi$
$617$	−6.90608e17	−0.503939	−0.251970	+	0.967735i	$0.581078\pi$
$618$	−7.50053e17	−0.541586
$619$	−1.72650e18	−1.23361	−0.616805	−	0.787116i	$-0.711573\pi$
$619$	−1.72650e18	−1.23361	−0.616805	+	0.787116i	$0.711573\pi$
$620$	2.35099e18	1.66228
$621$	−3.02518e17	−0.211669
$622$	−4.65916e18	−3.22605
$623$	−2.20503e18	−1.51092
$624$	4.43723e18	3.00893
$625$	7.13736e17	0.478980
$626$	−1.28157e18	−0.851159
$627$	4.64916e17	0.305587
$628$	1.11424e18	0.724838
$629$	−1.32651e18	−0.854044
$630$	3.47662e17	0.221536
$631$	−7.24337e17	−0.456825	−0.228413	−	0.973564i	$-0.573354\pi$
$631$	−7.24337e17	−0.456825	−0.228413	+	0.973564i	$0.573354\pi$
$632$	−1.56892e18	−0.979354
$633$	−3.42878e17	−0.211844
$634$	−4.49500e18	−2.74884
$635$	2.07459e17	0.125575
$636$	−1.68439e18	−1.00919
$637$	1.02556e18	0.608211
$638$	−7.70306e17	−0.452198
$639$	1.04412e18	0.606728
$640$	−4.56897e17	−0.262814
$641$	−3.82643e17	−0.217880	−0.108940	−	0.994048i	$-0.534746\pi$
$641$	−3.82643e17	−0.217880	−0.108940	+	0.994048i	$0.534746\pi$
$642$	−1.47903e18	−0.833681
$643$	1.78480e18	0.995908	0.497954	−	0.867203i	$-0.334085\pi$
$643$	1.78480e18	0.995908	0.497954	+	0.867203i	$0.334085\pi$
$644$	−4.09950e18	−2.26450
$645$	−2.78762e17	−0.152439
$646$	2.36909e18	1.28254
$647$	2.66447e18	1.42802	0.714008	−	0.700137i	$-0.246878\pi$
$647$	2.66447e18	1.42802	0.714008	+	0.700137i	$0.246878\pi$
$648$	−5.82804e17	−0.309232
$649$	2.03009e17	0.106641
$650$	−5.63069e18	−2.92836
$651$	1.43890e18	0.740893
$652$	−3.52324e17	−0.179611
$653$	−8.25665e17	−0.416743	−0.208371	−	0.978050i	$-0.566816\pi$
$653$	−8.25665e17	−0.416743	−0.208371	+	0.978050i	$0.566816\pi$
$654$	1.97115e17	0.0985063
$655$	1.49701e18	0.740724
$656$	−4.20355e18	−2.05940
$657$	−5.44752e17	−0.264256
$658$	4.07981e17	0.195962
$659$	−3.82149e18	−1.81752	−0.908758	−	0.417324i	$-0.862968\pi$
$659$	−3.82149e18	−1.81752	−0.908758	+	0.417324i	$0.862968\pi$
$660$	1.07569e18	0.506582
$661$	2.35646e18	1.09888	0.549440	−	0.835533i	$-0.314841\pi$
$661$	2.35646e18	1.09888	0.549440	+	0.835533i	$0.314841\pi$
$662$	−1.47024e18	−0.678909
$663$	−2.58059e18	−1.18000
$664$	−3.70062e18	−1.67564
$665$	−5.12684e17	−0.229884
$666$	−1.12724e18	−0.500534
$667$	−7.39152e17	−0.325024
$668$	2.95142e18	1.28524
$669$	−1.19653e18	−0.516003
$670$	1.09029e18	0.465645
$671$	6.94980e17	0.293952
$672$	−2.59651e18	−1.08765
$673$	−4.43044e18	−1.83802	−0.919008	−	0.394238i	$-0.871008\pi$
$673$	−4.43044e18	−1.83802	−0.919008	+	0.394238i	$0.871008\pi$
$674$	−1.04319e18	−0.428623
$675$	3.85390e17	0.156829
$676$	1.66811e19	6.72313
$677$	2.85814e18	1.14093	0.570463	−	0.821323i	$-0.306764\pi$
$677$	2.85814e18	1.14093	0.570463	+	0.821323i	$0.306764\pi$
$678$	2.74887e18	1.08683
$679$	−4.53375e17	−0.177543
$680$	3.27986e18	1.27218
$681$	1.88486e18	0.724142
$682$	6.24016e18	2.37464
$683$	7.49096e17	0.282360	0.141180	−	0.989984i	$-0.454910\pi$
$683$	7.49096e17	0.282360	0.141180	+	0.989984i	$0.454910\pi$
$684$	1.43632e18	0.536274
$685$	−1.84372e18	−0.681877
$686$	−5.55000e18	−2.03323
$687$	1.99919e18	0.725495
$688$	4.62533e18	1.66271
$689$	−3.79236e18	−1.35047
$690$	1.44674e18	0.510355
$691$	−1.53441e18	−0.536210	−0.268105	−	0.963390i	$-0.586397\pi$
$691$	−1.53441e18	−0.536210	−0.268105	+	0.963390i	$0.586397\pi$
$692$	4.94612e17	0.171228
$693$	6.58364e17	0.225788
$694$	−4.79782e17	−0.163008
$695$	−2.34979e17	−0.0790913
$696$	−1.42398e18	−0.474836
$697$	2.44469e18	0.807627
$698$	−1.02002e19	−3.33847
$699$	1.02292e18	0.331697
$700$	5.22251e18	1.67781
$701$	1.98402e18	0.631508	0.315754	−	0.948841i	$-0.397743\pi$
$701$	1.98402e18	0.631508	0.315754	+	0.948841i	$0.397743\pi$
$702$	−2.19294e18	−0.691568
$703$	1.66230e18	0.519396
$704$	−4.09189e18	−1.26678
$705$	−1.02722e17	−0.0315091
$706$	1.33974e18	0.407184
$707$	−2.16253e18	−0.651234
$708$	6.27182e17	0.187145
$709$	1.60737e18	0.475243	0.237621	−	0.971358i	$-0.423632\pi$
$709$	1.60737e18	0.475243	0.237621	+	0.971358i	$0.423632\pi$
$710$	−4.99333e18	−1.46289
$711$	4.04058e17	0.117298
$712$	−1.76774e19	−5.08510
$713$	5.98778e18	1.70681
$714$	3.35485e18	0.947622
$715$	2.42188e18	0.677896
$716$	2.91703e18	0.809109
$717$	7.06413e17	0.194171
$718$	−3.18350e18	−0.867154
$719$	−5.71365e17	−0.154232	−0.0771162	−	0.997022i	$-0.524571\pi$
$719$	−5.71365e17	−0.154232	−0.0771162	+	0.997022i	$0.524571\pi$
$720$	1.45242e18	0.388535
$721$	1.56631e18	0.415239
$722$	4.14157e18	1.08811
$723$	−2.87056e18	−0.747425
$724$	−1.50499e19	−3.88357
$725$	9.41635e17	0.240816
$726$	−1.40011e18	−0.354875
$727$	−5.03265e18	−1.26422	−0.632110	−	0.774879i	$-0.717811\pi$
$727$	−5.03265e18	−1.26422	−0.632110	+	0.774879i	$0.717811\pi$
$728$	−1.77815e19	−4.42705
$729$	1.50095e17	0.0370370
$730$	2.60519e18	0.637149
$731$	−2.68999e18	−0.652059
$732$	2.14709e18	0.515856
$733$	−7.24584e18	−1.72549	−0.862746	−	0.505637i	$-0.831257\pi$
$733$	−7.24584e18	−1.72549	−0.862746	+	0.505637i	$0.831257\pi$
$734$	4.27111e18	1.00813
$735$	3.35691e17	0.0785366
$736$	−1.08050e19	−2.50564
$737$	2.06466e18	0.474581
$738$	2.07745e18	0.473330
$739$	−7.01404e18	−1.58409	−0.792044	−	0.610464i	$-0.790983\pi$
$739$	−7.01404e18	−1.58409	−0.792044	+	0.610464i	$0.790983\pi$
$740$	3.84609e18	0.861021
$741$	3.23384e18	0.717630
$742$	4.93019e18	1.08452
$743$	1.10490e18	0.240932	0.120466	−	0.992717i	$-0.461561\pi$
$743$	1.10490e18	0.240932	0.120466	+	0.992717i	$0.461561\pi$
$744$	1.15355e19	2.49352
$745$	2.61865e17	0.0561128
$746$	−1.48345e19	−3.15115
$747$	9.53053e17	0.200693
$748$	1.03801e19	2.16691
$749$	3.08861e18	0.639191
$750$	−4.10475e18	−0.842149
$751$	5.73835e18	1.16715	0.583576	−	0.812059i	$-0.301653\pi$
$751$	5.73835e18	1.16715	0.583576	+	0.812059i	$0.301653\pi$
$752$	1.70441e18	0.343682
$753$	−5.66537e18	−1.13256
$754$	−5.35807e18	−1.06193
$755$	−3.63968e18	−0.715169
$756$	2.03397e18	0.396234
$757$	−5.65708e18	−1.09262	−0.546310	−	0.837583i	$-0.683968\pi$
$757$	−5.65708e18	−1.09262	−0.546310	+	0.837583i	$0.683968\pi$
$758$	−1.40740e19	−2.69506
$759$	2.73968e18	0.520150
$760$	−4.11012e18	−0.773689
$761$	−5.36784e18	−1.00184	−0.500921	−	0.865493i	$-0.667005\pi$
$761$	−5.36784e18	−1.00184	−0.500921	+	0.865493i	$0.667005\pi$
$762$	1.70120e18	0.314810
$763$	−4.11627e17	−0.0755257
$764$	−2.21256e18	−0.402520
$765$	−8.44693e17	−0.152370
$766$	−8.19380e17	−0.146554
$767$	1.41208e18	0.250433
$768$	1.33072e18	0.234012
$769$	1.14119e19	1.98993	0.994964	−	0.100234i	$-0.0319590\pi$
$769$	1.14119e19	1.98993	0.994964	+	0.100234i	$0.0319590\pi$
$770$	−3.14852e18	−0.544398
$771$	6.18853e18	1.06104
$772$	−1.12187e19	−1.90735
$773$	−8.22705e18	−1.38700	−0.693502	−	0.720455i	$-0.743933\pi$
$773$	−8.22705e18	−1.38700	−0.693502	+	0.720455i	$0.743933\pi$
$774$	−2.28590e18	−0.382156
$775$	−7.62807e18	−1.26460
$776$	−3.63465e18	−0.597533
$777$	2.35397e18	0.383764
$778$	4.85089e18	0.784248
$779$	−3.06354e18	−0.491167
$780$	7.48221e18	1.18964
$781$	−9.45581e18	−1.49096
$782$	1.39607e19	2.18305
$783$	3.66730e17	0.0568716
$784$	−5.56991e18	−0.856631
$785$	8.21154e17	0.125248
$786$	1.22757e19	1.85695
$787$	3.97239e18	0.595958	0.297979	−	0.954572i	$-0.403687\pi$
$787$	3.97239e18	0.595958	0.297979	+	0.954572i	$0.403687\pi$
$788$	2.84131e19	4.22764
$789$	−3.34714e18	−0.493939
$790$	−1.93234e18	−0.282818
$791$	−5.74035e18	−0.833281
$792$	5.27802e18	0.759902
$793$	4.83412e18	0.690306
$794$	1.89869e19	2.68918
$795$	−1.24133e18	−0.174382
$796$	1.76184e19	2.45488
$797$	6.01437e18	0.831210	0.415605	−	0.909545i	$-0.363570\pi$
$797$	6.01437e18	0.831210	0.415605	+	0.909545i	$0.363570\pi$
$798$	−4.20410e18	−0.576307
$799$	−9.91245e17	−0.134780
$800$	1.37649e19	1.85647
$801$	4.55263e18	0.609047
$802$	1.16086e19	1.54045
$803$	4.93342e18	0.649377
$804$	6.37862e18	0.832842
$805$	−3.02118e18	−0.391294
$806$	4.34051e19	5.57651
$807$	−7.69106e18	−0.980185
$808$	−1.73368e19	−2.19176
$809$	−3.84204e18	−0.481833	−0.240916	−	0.970546i	$-0.577448\pi$
$809$	−3.84204e18	−0.481833	−0.240916	+	0.970546i	$0.577448\pi$
$810$	−7.17803e17	−0.0893002
$811$	3.86489e18	0.476982	0.238491	−	0.971145i	$-0.423347\pi$
$811$	3.86489e18	0.476982	0.238491	+	0.971145i	$0.423347\pi$
$812$	4.96965e18	0.608431
$813$	−2.01734e18	−0.245014
$814$	1.02086e19	1.23000
$815$	−2.59650e17	−0.0310359
$816$	1.40154e19	1.66196
$817$	3.37093e18	0.396557
$818$	1.71740e19	2.00436
$819$	4.57943e18	0.530232
$820$	−7.08817e18	−0.814224
$821$	3.29104e17	0.0375061	0.0187531	−	0.999824i	$-0.494030\pi$
$821$	3.29104e17	0.0375061	0.0187531	+	0.999824i	$0.494030\pi$
$822$	−1.51188e19	−1.70943
$823$	−9.44893e17	−0.105995	−0.0529973	−	0.998595i	$-0.516877\pi$
$823$	−9.44893e17	−0.105995	−0.0529973	+	0.998595i	$0.516877\pi$
$824$	1.25569e19	1.39751
$825$	−3.49019e18	−0.385389
$826$	−1.83575e18	−0.201115
$827$	1.72578e19	1.87586	0.937929	−	0.346827i	$-0.112741\pi$
$827$	1.72578e19	1.87586	0.937929	+	0.346827i	$0.112741\pi$
$828$	8.46405e18	0.912811
$829$	−2.53625e18	−0.271387	−0.135693	−	0.990751i	$-0.543326\pi$
$829$	−2.53625e18	−0.271387	−0.135693	+	0.990751i	$0.543326\pi$
$830$	−4.55782e18	−0.483893
$831$	5.87206e18	0.618563
$832$	−2.84622e19	−2.97486
$833$	3.23933e18	0.335941
$834$	−1.92687e18	−0.198277
$835$	2.17509e18	0.222083
$836$	−1.30077e19	−1.31783
$837$	−2.97084e18	−0.298651
$838$	1.48083e19	1.47713
$839$	−9.36061e18	−0.926513	−0.463256	−	0.886224i	$-0.653319\pi$
$839$	−9.36061e18	−0.926513	−0.463256	+	0.886224i	$0.653319\pi$
$840$	−5.82032e18	−0.571652
$841$	−9.36459e18	−0.912672
$842$	2.55526e19	2.47120
$843$	−6.68780e17	−0.0641806
$844$	9.59325e18	0.913566
$845$	1.22934e19	1.16172
$846$	−8.42340e17	−0.0789914
$847$	2.92380e18	0.272086
$848$	2.05967e19	1.90206
$849$	8.46004e18	0.775305
$850$	−1.77851e19	−1.61746
$851$	9.79569e18	0.884082
$852$	−2.92130e19	−2.61649
$853$	5.94715e18	0.528615	0.264308	−	0.964438i	$-0.414857\pi$
$853$	5.94715e18	0.528615	0.264308	+	0.964438i	$0.414857\pi$
$854$	−6.28451e18	−0.554364
$855$	1.05852e18	0.0926655
$856$	2.47609e19	2.15123
$857$	9.17213e18	0.790852	0.395426	−	0.918498i	$-0.370597\pi$
$857$	9.17213e18	0.790852	0.395426	+	0.918498i	$0.370597\pi$
$858$	1.98598e19	1.69945
$859$	−1.84411e19	−1.56614	−0.783072	−	0.621931i	$-0.786348\pi$
$859$	−1.84411e19	−1.56614	−0.783072	+	0.621931i	$0.786348\pi$
$860$	7.79939e18	0.657386
$861$	−4.33826e18	−0.362906
$862$	3.54968e18	0.294708
$863$	4.45527e17	0.0367116	0.0183558	−	0.999832i	$-0.494157\pi$
$863$	4.45527e17	0.0367116	0.0183558	+	0.999832i	$0.494157\pi$
$864$	5.36090e18	0.438428
$865$	3.64511e17	0.0295874
$866$	−3.39077e19	−2.73169
$867$	−9.30632e17	−0.0744139
$868$	−4.02586e19	−3.19507
$869$	−3.65925e18	−0.288246
$870$	−1.75383e18	−0.137124
$871$	1.43613e19	1.11449
$872$	−3.29996e18	−0.254186
$873$	9.36064e17	0.0715670
$874$	−1.74947e19	−1.32765
$875$	8.57180e18	0.645683
$876$	1.52414e19	1.13959
$877$	2.22386e19	1.65048	0.825238	−	0.564785i	$-0.191041\pi$
$877$	2.22386e19	1.65048	0.825238	+	0.564785i	$0.191041\pi$
$878$	3.96642e19	2.92203
$879$	1.11648e19	0.816439
$880$	−1.31535e19	−0.954778
$881$	2.93798e18	0.211693	0.105846	−	0.994382i	$-0.466245\pi$
$881$	2.93798e18	0.211693	0.105846	+	0.994382i	$0.466245\pi$
$882$	2.75272e18	0.196887
$883$	6.62315e18	0.470240	0.235120	−	0.971966i	$-0.424452\pi$
$883$	6.62315e18	0.470240	0.235120	+	0.971966i	$0.424452\pi$
$884$	7.22015e19	5.08869
$885$	4.62210e17	0.0323376
$886$	2.64942e19	1.84006
$887$	6.99765e18	0.482446	0.241223	−	0.970470i	$-0.422452\pi$
$887$	6.99765e18	0.482446	0.241223	+	0.970470i	$0.422452\pi$
$888$	1.88715e19	1.29158
$889$	−3.55255e18	−0.241368
$890$	−2.17722e19	−1.46848
$891$	−1.35930e18	−0.0910141
$892$	3.34772e19	2.22524
$893$	1.24217e18	0.0819682
$894$	2.14734e18	0.140672
$895$	2.14975e18	0.139810
$896$	7.82395e18	0.505154
$897$	1.90566e19	1.22150
$898$	−4.04570e19	−2.57453
$899$	−7.25874e18	−0.458589
$900$	−1.07827e19	−0.676318
$901$	−1.19786e19	−0.745922
$902$	−1.88139e19	−1.16315
$903$	4.77355e18	0.293002
$904$	−4.60197e19	−2.80446
$905$	−1.10912e19	−0.671062
$906$	−2.98460e19	−1.79289
$907$	−5.93077e18	−0.353723	−0.176862	−	0.984236i	$-0.556595\pi$
$907$	−5.93077e18	−0.353723	−0.176862	+	0.984236i	$0.556595\pi$
$908$	−5.27359e19	−3.12283
$909$	4.46489e18	0.262510
$910$	−2.19004e19	−1.27844
$911$	2.70660e19	1.56876	0.784378	−	0.620283i	$-0.212982\pi$
$911$	2.70660e19	1.56876	0.784378	+	0.620283i	$0.212982\pi$
$912$	−1.75633e19	−1.01074
$913$	−8.63109e18	−0.493180
$914$	1.94436e19	1.10313
$915$	1.58233e18	0.0891372
$916$	−5.59345e19	−3.12866
$917$	−2.56349e19	−1.42374
$918$	−6.92662e18	−0.381983
$919$	−1.30576e19	−0.715008	−0.357504	−	0.933912i	$-0.616372\pi$
$919$	−1.30576e19	−0.715008	−0.357504	+	0.933912i	$0.616372\pi$
$920$	−2.42204e19	−1.31692
$921$	1.26158e18	0.0681128
$922$	−4.21854e19	−2.26157
$923$	−6.57724e19	−3.50132
$924$	−1.84201e19	−0.973699
$925$	−1.24791e19	−0.655032
$926$	5.65360e19	2.94682
$927$	−3.23389e18	−0.167381
$928$	1.30984e19	0.673221
$929$	−2.70921e19	−1.38274	−0.691371	−	0.722500i	$-0.742993\pi$
$929$	−2.70921e19	−1.38274	−0.691371	+	0.722500i	$0.742993\pi$
$930$	1.42076e19	0.720079
$931$	−4.05933e18	−0.204306
$932$	−2.86200e19	−1.43043
$933$	−2.00882e19	−0.997034
$934$	9.86884e18	0.486420
$935$	7.64975e18	0.374431
$936$	3.67127e19	1.78453
$937$	3.25888e19	1.57312	0.786558	−	0.617516i	$-0.211861\pi$
$937$	3.25888e19	1.57312	0.786558	+	0.617516i	$0.211861\pi$
$938$	−1.86702e19	−0.895014
$939$	−5.52556e18	−0.263057
$940$	2.87403e18	0.135881
$941$	−2.45508e19	−1.15274	−0.576372	−	0.817187i	$-0.695532\pi$
$941$	−2.45508e19	−1.15274	−0.576372	+	0.817187i	$0.695532\pi$
$942$	6.73360e18	0.313990
$943$	−1.80530e19	−0.836033
$944$	−7.66916e18	−0.352720
$945$	1.49896e18	0.0684673
$946$	2.07017e19	0.939103
$947$	8.54835e18	0.385130	0.192565	−	0.981284i	$-0.438319\pi$
$947$	8.54835e18	0.385130	0.192565	+	0.981284i	$0.438319\pi$
$948$	−1.13050e19	−0.505843
$949$	3.43157e19	1.52497
$950$	2.22872e19	0.983677
$951$	−1.93804e19	−0.849550
$952$	−5.61647e19	−2.44525
$953$	−1.91407e19	−0.827663	−0.413831	−	0.910354i	$-0.635810\pi$
$953$	−1.91407e19	−0.827663	−0.413831	+	0.910354i	$0.635810\pi$
$954$	−1.01791e19	−0.437167
$955$	−1.63057e18	−0.0695534
$956$	−1.97645e19	−0.837353
$957$	−3.32121e18	−0.139755
$958$	1.29144e19	0.539756
$959$	3.15720e19	1.31063
$960$	−9.31639e18	−0.384136
$961$	3.43847e19	1.40819
$962$	7.10083e19	2.88849
$963$	−6.37691e18	−0.257655
$964$	8.03143e19	3.22324
$965$	−8.26779e18	−0.329581
$966$	−2.47742e19	−0.980952
$967$	1.56848e19	0.616891	0.308445	−	0.951242i	$-0.400191\pi$
$967$	1.56848e19	0.616891	0.308445	+	0.951242i	$0.400191\pi$
$968$	2.34398e19	0.915721
$969$	1.02144e19	0.396378
$970$	−4.47657e18	−0.172556
$971$	−1.81360e19	−0.694409	−0.347205	−	0.937789i	$-0.612869\pi$
$971$	−1.81360e19	−0.694409	−0.347205	+	0.937789i	$0.612869\pi$
$972$	−4.19944e18	−0.159721
$973$	4.02381e18	0.152021
$974$	2.56548e18	0.0962800
$975$	−2.42770e19	−0.905032
$976$	−2.62546e19	−0.972256
$977$	1.19351e18	0.0439047	0.0219523	−	0.999759i	$-0.493012\pi$
$977$	1.19351e18	0.0439047	0.0219523	+	0.999759i	$0.493012\pi$
$978$	−2.12918e18	−0.0778052
$979$	−4.12298e19	−1.49666
$980$	−9.39217e18	−0.338686
$981$	8.49868e17	0.0304441
$982$	9.50685e19	3.38308
$983$	−2.48473e19	−0.878378	−0.439189	−	0.898395i	$-0.644734\pi$
$983$	−2.48473e19	−0.878378	−0.439189	+	0.898395i	$0.644734\pi$
$984$	−3.47792e19	−1.22138
$985$	2.09394e19	0.730515
$986$	−1.69240e19	−0.586547
$987$	1.75903e18	0.0605635
$988$	−9.04785e19	−3.09475
$989$	1.98644e19	0.674994
$990$	6.50061e18	0.219445
$991$	−4.39355e19	−1.47346	−0.736728	−	0.676189i	$-0.763630\pi$
$991$	−4.39355e19	−1.47346	−0.736728	+	0.676189i	$0.763630\pi$
$992$	−1.06109e20	−3.53530
$993$	−6.33900e18	−0.209822
$994$	8.55062e19	2.81181
$995$	1.29841e19	0.424191
$996$	−2.66651e19	−0.865481
$997$	2.88935e19	0.931712	0.465856	−	0.884860i	$-0.345746\pi$
$997$	2.88935e19	0.931712	0.465856	+	0.884860i	$0.345746\pi$
$998$	5.14578e19	1.64855
$999$	−4.86013e18	−0.154694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.2	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.2	✓	31	1.1	even	1	trivial

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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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-169.081 q^{2} -729.000 q^{3} +20396.4 q^{4} +15031.4 q^{5} +123260. q^{6} -257399. q^{7} -2.06354e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-169.081 q^{2} -729.000 q^{3} +20396.4 q^{4} +15031.4 q^{5} +123260. q^{6} -257399. q^{7} -2.06354e6 q^{8} +531441. q^{9} -2.54153e6 q^{10} -4.81287e6 q^{11} -1.48690e7 q^{12} -3.34772e7 q^{13} +4.35214e7 q^{14} -1.09579e7 q^{15} +1.81818e8 q^{16} -1.05741e8 q^{17} -8.98566e7 q^{18} +1.32508e8 q^{19} +3.06587e8 q^{20} +1.87644e8 q^{21} +8.13765e8 q^{22} +7.80853e8 q^{23} +1.50432e9 q^{24} -9.94759e8 q^{25} +5.66035e9 q^{26} -3.87420e8 q^{27} -5.25002e9 q^{28} -9.46595e8 q^{29} +1.85277e9 q^{30} +7.66826e9 q^{31} -1.38374e10 q^{32} +3.50858e9 q^{33} +1.78788e10 q^{34} -3.86908e9 q^{35} +1.08395e10 q^{36} +1.25449e10 q^{37} -2.24046e10 q^{38} +2.44048e10 q^{39} -3.10179e10 q^{40} -2.31196e10 q^{41} -3.17271e10 q^{42} +2.54394e10 q^{43} -9.81653e10 q^{44} +7.98831e9 q^{45} -1.32027e11 q^{46} +9.37427e9 q^{47} -1.32545e11 q^{48} -3.06346e10 q^{49} +1.68195e11 q^{50} +7.70852e10 q^{51} -6.82814e11 q^{52} +1.13282e11 q^{53} +6.55055e10 q^{54} -7.23442e10 q^{55} +5.31153e11 q^{56} -9.65985e10 q^{57} +1.60051e11 q^{58} -4.21805e10 q^{59} -2.23502e11 q^{60} -1.44401e11 q^{61} -1.29656e12 q^{62} -1.36793e11 q^{63} +8.50198e11 q^{64} -5.03209e11 q^{65} -5.93235e11 q^{66} -4.28988e11 q^{67} -2.15674e12 q^{68} -5.69242e11 q^{69} +6.54188e11 q^{70} +1.96469e12 q^{71} -1.09665e12 q^{72} -1.02505e12 q^{73} -2.12110e12 q^{74} +7.25180e11 q^{75} +2.70269e12 q^{76} +1.23883e12 q^{77} -4.12640e12 q^{78} +7.60306e11 q^{79} +2.73298e12 q^{80} +2.82430e11 q^{81} +3.90909e12 q^{82} +1.79334e12 q^{83} +3.82727e12 q^{84} -1.58944e12 q^{85} -4.30132e12 q^{86} +6.90068e11 q^{87} +9.93153e12 q^{88} +8.56658e12 q^{89} -1.35067e12 q^{90} +8.61700e12 q^{91} +1.59266e13 q^{92} -5.59016e12 q^{93} -1.58501e12 q^{94} +1.99179e12 q^{95} +1.00875e13 q^{96} +1.76137e12 q^{97} +5.17973e12 q^{98} -2.55775e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \)	\( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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