LMFDB - Embedded newform 177.8.a.c.1.6

Newspace parameters

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

Newform invariants

Self dual:	yes
Analytic conductor:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
Defining polynomial:	$x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + 12724944 x^{10} + 71331230512 x^{9} + 50741131904 x^{8} - 7480805165760 x^{7} - 10751966150272 x^{6} + 413177144536320 x^{5} + 886760582981376 x^{4} - 10454479722123264 x^{3} - 29180140031461376 x^{2} + 79787300207378432 x + 248723246810300416$
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-8.14464$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-8.14464 q^{2} -27.0000 q^{3} -61.6648 q^{4} -54.3103 q^{5} +219.905 q^{6} -413.400 q^{7} +1544.75 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.14464 q^{2} -27.0000 q^{3} -61.6648 q^{4} -54.3103 q^{5} +219.905 q^{6} -413.400 q^{7} +1544.75 q^{8} +729.000 q^{9} +442.338 q^{10} +5302.90 q^{11} +1664.95 q^{12} -13494.1 q^{13} +3367.00 q^{14} +1466.38 q^{15} -4688.37 q^{16} +13725.3 q^{17} -5937.45 q^{18} -57847.2 q^{19} +3349.03 q^{20} +11161.8 q^{21} -43190.2 q^{22} -11834.5 q^{23} -41708.3 q^{24} -75175.4 q^{25} +109904. q^{26} -19683.0 q^{27} +25492.2 q^{28} -137312. q^{29} -11943.1 q^{30} +110476. q^{31} -159543. q^{32} -143178. q^{33} -111788. q^{34} +22451.9 q^{35} -44953.6 q^{36} +154147. q^{37} +471145. q^{38} +364339. q^{39} -83896.0 q^{40} +58042.4 q^{41} -90908.9 q^{42} -607469. q^{43} -327002. q^{44} -39592.2 q^{45} +96387.4 q^{46} -765556. q^{47} +126586. q^{48} -652643. q^{49} +612277. q^{50} -370584. q^{51} +832107. q^{52} +779953. q^{53} +160311. q^{54} -288002. q^{55} -638601. q^{56} +1.56188e6 q^{57} +1.11836e6 q^{58} -205379. q^{59} -90423.9 q^{60} +745383. q^{61} -899790. q^{62} -301369. q^{63} +1.89953e6 q^{64} +732866. q^{65} +1.16614e6 q^{66} -343978. q^{67} -846369. q^{68} +319530. q^{69} -182863. q^{70} +4.41562e6 q^{71} +1.12612e6 q^{72} +1.38449e6 q^{73} -1.25547e6 q^{74} +2.02974e6 q^{75} +3.56714e6 q^{76} -2.19222e6 q^{77} -2.96742e6 q^{78} -6.92496e6 q^{79} +254627. q^{80} +531441. q^{81} -472735. q^{82} +4.41025e6 q^{83} -688290. q^{84} -745427. q^{85} +4.94762e6 q^{86} +3.70742e6 q^{87} +8.19166e6 q^{88} -2.65103e6 q^{89} +322465. q^{90} +5.57844e6 q^{91} +729769. q^{92} -2.98286e6 q^{93} +6.23518e6 q^{94} +3.14170e6 q^{95} +4.30767e6 q^{96} +531245. q^{97} +5.31555e6 q^{98} +3.86581e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + O(q^{10}) $	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + 6521q^{10} - 1764q^{11} - 31482q^{12} + 18192q^{13} - 7827q^{14} + 8586q^{15} + 139226q^{16} - 15507q^{17} + 1458q^{18} + 52083q^{19} + 721q^{20} - 84915q^{21} - 234434q^{22} + 63823q^{23} - 63585q^{24} + 202153q^{25} - 367956q^{26} - 334611q^{27} + 182306q^{28} - 502955q^{29} - 176067q^{30} + 347531q^{31} - 243908q^{32} + 47628q^{33} - 330872q^{34} + 92641q^{35} + 850014q^{36} + 447615q^{37} + 775669q^{38} - 491184q^{39} + 2203270q^{40} + 940335q^{41} + 211329q^{42} + 478562q^{43} - 596924q^{44} - 231822q^{45} - 3078663q^{46} + 703121q^{47} - 3759102q^{48} + 1895082q^{49} - 876967q^{50} + 418689q^{51} + 6278296q^{52} - 1005974q^{53} - 39366q^{54} + 5212846q^{55} + 3425294q^{56} - 1406241q^{57} + 6710166q^{58} - 3491443q^{59} - 19467q^{60} + 11510749q^{61} + 5996234q^{62} + 2292705q^{63} + 29496941q^{64} + 11094180q^{65} + 6329718q^{66} + 14007144q^{67} + 19688159q^{68} - 1723221q^{69} + 30909708q^{70} + 5229074q^{71} + 1716795q^{72} + 5452211q^{73} + 12819662q^{74} - 5458131q^{75} + 41929340q^{76} + 9930777q^{77} + 9934812q^{78} + 15275654q^{79} + 36576105q^{80} + 9034497q^{81} + 32025935q^{82} + 7826609q^{83} - 4922262q^{84} + 11836945q^{85} + 51649136q^{86} + 13579785q^{87} + 30223741q^{88} - 6436185q^{89} + 4753809q^{90} + 11633535q^{91} + 43357972q^{92} - 9383337q^{93} - 4494252q^{94} + 23741055q^{95} + 6585516q^{96} + 26377540q^{97} + 26517816q^{98} - 1285956q^{99} + O(q^{100}) \)

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 $

$2$	−8.14464	−0.719892	−0.359946	−	0.932973i	$-0.617205\pi$
$2$	−8.14464	−0.719892	−0.359946	+	0.932973i	$0.617205\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−61.6648	−0.481756
$5$	−54.3103	−0.194307	−0.0971533	−	0.995269i	$-0.530974\pi$
$5$	−54.3103	−0.194307	−0.0971533	+	0.995269i	$0.530974\pi$
$6$	219.905	0.415630
$7$	−413.400	−0.455541	−0.227770	−	0.973715i	$-0.573144\pi$
$7$	−413.400	−0.455541	−0.227770	+	0.973715i	$0.573144\pi$
$8$	1544.75	1.06670
$9$	729.000	0.333333
$10$	442.338	0.139880
$11$	5302.90	1.20126	0.600632	−	0.799525i	$-0.294916\pi$
$11$	5302.90	1.20126	0.600632	+	0.799525i	$0.294916\pi$
$12$	1664.95	0.278142
$13$	−13494.1	−1.70349	−0.851747	−	0.523953i	$-0.824457\pi$
$13$	−13494.1	−1.70349	−0.851747	+	0.523953i	$0.824457\pi$
$14$	3367.00	0.327940
$15$	1466.38	0.112183
$16$	−4688.37	−0.286155
$17$	13725.3	0.677566	0.338783	−	0.940865i	$-0.389985\pi$
$17$	13725.3	0.677566	0.338783	+	0.940865i	$0.389985\pi$
$18$	−5937.45	−0.239964
$19$	−57847.2	−1.93484	−0.967420	−	0.253177i	$-0.918525\pi$
$19$	−57847.2	−1.93484	−0.967420	+	0.253177i	$0.918525\pi$
$20$	3349.03	0.0936083
$21$	11161.8	0.263007
$22$	−43190.2	−0.864780
$23$	−11834.5	−0.202815	−0.101408	−	0.994845i	$-0.532335\pi$
$23$	−11834.5	−0.202815	−0.101408	+	0.994845i	$0.532335\pi$
$24$	−41708.3	−0.615862
$25$	−75175.4	−0.962245
$26$	109904.	1.22633
$27$	−19683.0	−0.192450
$28$	25492.2	0.219460
$29$	−137312.	−1.04548	−0.522739	−	0.852493i	$-0.675090\pi$
$29$	−137312.	−1.04548	−0.522739	+	0.852493i	$0.675090\pi$
$30$	−11943.1	−0.0807596
$31$	110476.	0.666044	0.333022	−	0.942919i	$-0.391932\pi$
$31$	110476.	0.666044	0.333022	+	0.942919i	$0.391932\pi$
$32$	−159543.	−0.860703
$33$	−143178.	−0.693550
$34$	−111788.	−0.487774
$35$	22451.9	0.0885146
$36$	−44953.6	−0.160585
$37$	154147.	0.500297	0.250149	−	0.968207i	$-0.419520\pi$
$37$	154147.	0.500297	0.250149	+	0.968207i	$0.419520\pi$
$38$	471145.	1.39288
$39$	364339.	0.983513
$40$	−83896.0	−0.207268
$41$	58042.4	0.131523	0.0657615	−	0.997835i	$-0.479052\pi$
$41$	58042.4	0.131523	0.0657615	+	0.997835i	$0.479052\pi$
$42$	−90908.9	−0.189336
$43$	−607469.	−1.16516	−0.582578	−	0.812775i	$-0.697956\pi$
$43$	−607469.	−1.16516	−0.582578	+	0.812775i	$0.697956\pi$
$44$	−327002.	−0.578716
$45$	−39592.2	−0.0647689
$46$	96387.4	0.146005
$47$	−765556.	−1.07556	−0.537780	−	0.843085i	$-0.680737\pi$
$47$	−765556.	−1.07556	−0.537780	+	0.843085i	$0.680737\pi$
$48$	126586.	0.165212
$49$	−652643.	−0.792483
$50$	612277.	0.692712
$51$	−370584.	−0.391193
$52$	832107.	0.820668
$53$	779953.	0.719619	0.359810	−	0.933026i	$-0.382842\pi$
$53$	779953.	0.719619	0.359810	+	0.933026i	$0.382842\pi$
$54$	160311.	0.138543
$55$	−288002.	−0.233414
$56$	−638601.	−0.485927
$57$	1.56188e6	1.11708
$58$	1.11836e6	0.752630
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−90423.9	−0.0540448
$61$	745383.	0.420460	0.210230	−	0.977652i	$-0.432579\pi$
$61$	745383.	0.420460	0.210230	+	0.977652i	$0.432579\pi$
$62$	−899790.	−0.479480
$63$	−301369.	−0.151847
$64$	1.89953e6	0.905768
$65$	732866.	0.331000
$66$	1.16614e6	0.499281
$67$	−343978.	−0.139723	−0.0698616	−	0.997557i	$-0.522256\pi$
$67$	−343978.	−0.139723	−0.0698616	+	0.997557i	$0.522256\pi$
$68$	−846369.	−0.326421
$69$	319530.	0.117095
$70$	−182863.	−0.0637209
$71$	4.41562e6	1.46416	0.732078	−	0.681221i	$-0.238551\pi$
$71$	4.41562e6	1.46416	0.732078	+	0.681221i	$0.238551\pi$
$72$	1.12612e6	0.355568
$73$	1.38449e6	0.416544	0.208272	−	0.978071i	$-0.433216\pi$
$73$	1.38449e6	0.416544	0.208272	+	0.978071i	$0.433216\pi$
$74$	−1.25547e6	−0.360160
$75$	2.02974e6	0.555552
$76$	3.56714e6	0.932121
$77$	−2.19222e6	−0.547225
$78$	−2.96742e6	−0.708023
$79$	−6.92496e6	−1.58024	−0.790119	−	0.612953i	$-0.789981\pi$
$79$	−6.92496e6	−1.58024	−0.790119	+	0.612953i	$0.789981\pi$
$80$	254627.	0.0556019
$81$	531441.	0.111111
$82$	−472735.	−0.0946824
$83$	4.41025e6	0.846623	0.423312	−	0.905984i	$-0.360868\pi$
$83$	4.41025e6	0.846623	0.423312	+	0.905984i	$0.360868\pi$
$84$	−688290.	−0.126705
$85$	−745427.	−0.131655
$86$	4.94762e6	0.838787
$87$	3.70742e6	0.603607
$88$	8.19166e6	1.28139
$89$	−2.65103e6	−0.398612	−0.199306	−	0.979937i	$-0.563869\pi$
$89$	−2.65103e6	−0.398612	−0.199306	+	0.979937i	$0.563869\pi$
$90$	322465.	0.0466266
$91$	5.57844e6	0.776011
$92$	729769.	0.0977075
$93$	−2.98286e6	−0.384541
$94$	6.23518e6	0.774287
$95$	3.14170e6	0.375952
$96$	4.30767e6	0.496927
$97$	531245.	0.0591009	0.0295504	−	0.999563i	$-0.490592\pi$
$97$	531245.	0.0591009	0.0295504	+	0.999563i	$0.490592\pi$
$98$	5.31555e6	0.570502
$99$	3.86581e6	0.400422
$100$	4.63567e6	0.463567
$101$	2.90692e6	0.280742	0.140371	−	0.990099i	$-0.455170\pi$
$101$	2.90692e6	0.280742	0.140371	+	0.990099i	$0.455170\pi$
$102$	3.01827e6	0.281616
$103$	1.71445e7	1.54595	0.772974	−	0.634438i	$-0.218768\pi$
$103$	1.71445e7	1.54595	0.772974	+	0.634438i	$0.218768\pi$
$104$	−2.08450e7	−1.81712
$105$	−606201.	−0.0511039
$106$	−6.35244e6	−0.518048
$107$	−7.73354e6	−0.610289	−0.305144	−	0.952306i	$-0.598705\pi$
$107$	−7.73354e6	−0.610289	−0.305144	+	0.952306i	$0.598705\pi$
$108$	1.21375e6	0.0927140
$109$	5.26465e6	0.389383	0.194691	−	0.980865i	$-0.437629\pi$
$109$	5.26465e6	0.389383	0.194691	+	0.980865i	$0.437629\pi$
$110$	2.34567e6	0.168033
$111$	−4.16196e6	−0.288847
$112$	1.93817e6	0.130355
$113$	2.92949e7	1.90993	0.954966	−	0.296716i	$-0.0958915\pi$
$113$	2.92949e7	1.90993	0.954966	+	0.296716i	$0.0958915\pi$
$114$	−1.27209e7	−0.804177
$115$	642733.	0.0394083
$116$	8.46729e6	0.503665
$117$	−9.83716e6	−0.567831
$118$	1.67274e6	0.0937219
$119$	−5.67405e6	−0.308659
$120$	2.26519e6	0.119666
$121$	8.63353e6	0.443037
$122$	−6.07088e6	−0.302686
$123$	−1.56715e6	−0.0759349
$124$	−6.81249e6	−0.320871
$125$	8.32580e6	0.381277
$126$	2.45454e6	0.109313
$127$	1.91366e7	0.828995	0.414497	−	0.910051i	$-0.363957\pi$
$127$	1.91366e7	0.828995	0.414497	+	0.910051i	$0.363957\pi$
$128$	4.95050e6	0.208648
$129$	1.64017e7	0.672703
$130$	−5.96894e6	−0.238284
$131$	2.05015e6	0.0796775	0.0398387	−	0.999206i	$-0.487316\pi$
$131$	2.05015e6	0.0796775	0.0398387	+	0.999206i	$0.487316\pi$
$132$	8.82905e6	0.334122
$133$	2.39141e7	0.881399
$134$	2.80157e6	0.100586
$135$	1.06899e6	0.0373943
$136$	2.12022e7	0.722762
$137$	−1.22263e7	−0.406232	−0.203116	−	0.979155i	$-0.565107\pi$
$137$	−1.22263e7	−0.406232	−0.203116	+	0.979155i	$0.565107\pi$
$138$	−2.60246e6	−0.0842961
$139$	2.28834e7	0.722719	0.361359	−	0.932427i	$-0.382313\pi$
$139$	2.28834e7	0.722719	0.361359	+	0.932427i	$0.382313\pi$
$140$	−1.38449e6	−0.0426424
$141$	2.06700e7	0.620975
$142$	−3.59636e7	−1.05403
$143$	−7.15575e7	−2.04635
$144$	−3.41782e6	−0.0953851
$145$	7.45744e6	0.203143
$146$	−1.12762e7	−0.299866
$147$	1.76214e7	0.457540
$148$	−9.50542e6	−0.241021
$149$	−1.01691e7	−0.251843	−0.125921	−	0.992040i	$-0.540189\pi$
$149$	−1.01691e7	−0.251843	−0.125921	+	0.992040i	$0.540189\pi$
$150$	−1.65315e7	−0.399938
$151$	−5.75910e7	−1.36124	−0.680620	−	0.732636i	$-0.738290\pi$
$151$	−5.75910e7	−1.36124	−0.680620	+	0.732636i	$0.738290\pi$
$152$	−8.93597e7	−2.06390
$153$	1.00058e7	0.225855
$154$	1.78548e7	0.393943
$155$	−6.00000e6	−0.129417
$156$	−2.24669e7	−0.473813
$157$	−1.36932e7	−0.282395	−0.141197	−	0.989981i	$-0.545095\pi$
$157$	−1.36932e7	−0.282395	−0.141197	+	0.989981i	$0.545095\pi$
$158$	5.64014e7	1.13760
$159$	−2.10587e7	−0.415472
$160$	8.66484e6	0.167240
$161$	4.89236e6	0.0923907
$162$	−4.32840e6	−0.0799880
$163$	−5.01230e7	−0.906527	−0.453263	−	0.891377i	$-0.649740\pi$
$163$	−5.01230e7	−0.906527	−0.453263	+	0.891377i	$0.649740\pi$
$164$	−3.57917e6	−0.0633620
$165$	7.77606e6	0.134761
$166$	−3.59199e7	−0.609477
$167$	3.87403e6	0.0643659	0.0321829	−	0.999482i	$-0.489754\pi$
$167$	3.87403e6	0.0643659	0.0321829	+	0.999482i	$0.489754\pi$
$168$	1.72422e7	0.280550
$169$	1.19341e8	1.90189
$170$	6.07124e6	0.0947777
$171$	−4.21706e7	−0.644947
$172$	3.74594e7	0.561321
$173$	−5.96811e7	−0.876346	−0.438173	−	0.898891i	$-0.644374\pi$
$173$	−5.96811e7	−0.876346	−0.438173	+	0.898891i	$0.644374\pi$
$174$	−3.01956e7	−0.434531
$175$	3.10775e7	0.438342
$176$	−2.48619e7	−0.343748
$177$	5.54523e6	0.0751646
$178$	2.15917e7	0.286957
$179$	−1.10240e8	−1.43666	−0.718330	−	0.695703i	$-0.755093\pi$
$179$	−1.10240e8	−1.43666	−0.718330	+	0.695703i	$0.755093\pi$
$180$	2.44145e6	0.0312028
$181$	−5.56564e7	−0.697654	−0.348827	−	0.937187i	$-0.613420\pi$
$181$	−5.56564e7	−0.697654	−0.348827	+	0.937187i	$0.613420\pi$
$182$	−4.54344e7	−0.558644
$183$	−2.01253e7	−0.242753
$184$	−1.82813e7	−0.216344
$185$	−8.37176e6	−0.0972111
$186$	2.42943e7	0.276828
$187$	7.27840e7	0.813936
$188$	4.72079e7	0.518157
$189$	8.13695e6	0.0876689
$190$	−2.55881e7	−0.270645
$191$	1.30425e7	0.135439	0.0677194	−	0.997704i	$-0.478428\pi$
$191$	1.30425e7	0.135439	0.0677194	+	0.997704i	$0.478428\pi$
$192$	−5.12874e7	−0.522946
$193$	1.67962e8	1.68175	0.840873	−	0.541232i	$-0.182042\pi$
$193$	1.67962e8	1.68175	0.840873	+	0.541232i	$0.182042\pi$
$194$	−4.32680e6	−0.0425462
$195$	−1.97874e7	−0.191103
$196$	4.02451e7	0.381783
$197$	−3.14534e7	−0.293114	−0.146557	−	0.989202i	$-0.546819\pi$
$197$	−3.14534e7	−0.293114	−0.146557	+	0.989202i	$0.546819\pi$
$198$	−3.14857e7	−0.288260
$199$	−5.07710e6	−0.0456699	−0.0228350	−	0.999739i	$-0.507269\pi$
$199$	−5.07710e6	−0.0456699	−0.0228350	+	0.999739i	$0.507269\pi$
$200$	−1.16127e8	−1.02643
$201$	9.28739e6	0.0806692
$202$	−2.36758e7	−0.202104
$203$	5.67647e7	0.476258
$204$	2.28520e7	0.188459
$205$	−3.15230e6	−0.0255558
$206$	−1.39636e8	−1.11291
$207$	−8.62732e6	−0.0676051
$208$	6.32651e7	0.487464
$209$	−3.06758e8	−2.32426
$210$	4.93729e6	0.0367893
$211$	2.48172e7	0.181871	0.0909357	−	0.995857i	$-0.471014\pi$
$211$	2.48172e7	0.181871	0.0909357	+	0.995857i	$0.471014\pi$
$212$	−4.80956e7	−0.346681
$213$	−1.19222e8	−0.845330
$214$	6.29870e7	0.439342
$215$	3.29918e7	0.226398
$216$	−3.04054e7	−0.205287
$217$	−4.56709e7	−0.303410
$218$	−4.28787e7	−0.280313
$219$	−3.73813e7	−0.240492
$220$	1.77596e7	0.112448
$221$	−1.85210e8	−1.15423
$222$	3.38977e7	0.207938
$223$	−1.11098e8	−0.670868	−0.335434	−	0.942064i	$-0.608883\pi$
$223$	−1.11098e8	−0.670868	−0.335434	+	0.942064i	$0.608883\pi$
$224$	6.59552e7	0.392085
$225$	−5.48029e7	−0.320748
$226$	−2.38597e8	−1.37494
$227$	1.42670e8	0.809549	0.404774	−	0.914417i	$-0.367350\pi$
$227$	1.42670e8	0.809549	0.404774	+	0.914417i	$0.367350\pi$
$228$	−9.63127e7	−0.538160
$229$	−8.79526e7	−0.483977	−0.241989	−	0.970279i	$-0.577800\pi$
$229$	−8.79526e7	−0.483977	−0.241989	+	0.970279i	$0.577800\pi$
$230$	−5.23483e6	−0.0283697
$231$	5.91899e7	0.315941
$232$	−2.12113e8	−1.11521
$233$	2.33751e8	1.21062	0.605311	−	0.795989i	$-0.293049\pi$
$233$	2.33751e8	1.21062	0.605311	+	0.795989i	$0.293049\pi$
$234$	8.01202e7	0.408777
$235$	4.15776e7	0.208988
$236$	1.26646e7	0.0627193
$237$	1.86974e8	0.912351
$238$	4.62131e7	0.222201
$239$	2.35581e8	1.11621	0.558107	−	0.829769i	$-0.311528\pi$
$239$	2.35581e8	1.11621	0.558107	+	0.829769i	$0.311528\pi$
$240$	−6.87493e6	−0.0321017
$241$	1.34696e8	0.619862	0.309931	−	0.950759i	$-0.399694\pi$
$241$	1.34696e8	0.619862	0.309931	+	0.950759i	$0.399694\pi$
$242$	−7.03171e7	−0.318938
$243$	−1.43489e7	−0.0641500
$244$	−4.59639e7	−0.202559
$245$	3.54453e7	0.153985
$246$	1.27638e7	0.0546649
$247$	7.80594e8	3.29599
$248$	1.70658e8	0.710472
$249$	−1.19077e8	−0.488798
$250$	−6.78106e7	−0.274478
$251$	4.35229e8	1.73724	0.868621	−	0.495478i	$-0.165007\pi$
$251$	4.35229e8	1.73724	0.868621	+	0.495478i	$0.165007\pi$
$252$	1.85838e7	0.0731532
$253$	−6.27569e7	−0.243635
$254$	−1.55861e8	−0.596786
$255$	2.01265e7	0.0760113
$256$	−2.83460e8	−1.05597
$257$	2.77869e8	1.02112	0.510558	−	0.859844i	$-0.329439\pi$
$257$	2.77869e8	1.02112	0.510558	+	0.859844i	$0.329439\pi$
$258$	−1.33586e8	−0.484274
$259$	−6.37243e7	−0.227906
$260$	−4.51920e7	−0.159461
$261$	−1.00100e8	−0.348492
$262$	−1.66977e7	−0.0573592
$263$	1.34074e8	0.454463	0.227231	−	0.973841i	$-0.427033\pi$
$263$	1.34074e8	0.454463	0.227231	+	0.973841i	$0.427033\pi$
$264$	−2.21175e8	−0.739813
$265$	−4.23595e7	−0.139827
$266$	−1.94771e8	−0.634512
$267$	7.15779e7	0.230139
$268$	2.12113e7	0.0673124
$269$	4.06253e8	1.27252	0.636258	−	0.771476i	$-0.280481\pi$
$269$	4.06253e8	1.27252	0.636258	+	0.771476i	$0.280481\pi$
$270$	−8.70655e6	−0.0269199
$271$	4.61228e8	1.40774	0.703871	−	0.710328i	$-0.251453\pi$
$271$	4.61228e8	1.40774	0.703871	+	0.710328i	$0.251453\pi$
$272$	−6.43494e7	−0.193889
$273$	−1.50618e8	−0.448030
$274$	9.95791e7	0.292443
$275$	−3.98647e8	−1.15591
$276$	−1.97038e7	−0.0564114
$277$	−2.60294e8	−0.735843	−0.367922	−	0.929857i	$-0.619931\pi$
$277$	−2.60294e8	−0.735843	−0.367922	+	0.929857i	$0.619931\pi$
$278$	−1.86377e8	−0.520279
$279$	8.05372e7	0.222015
$280$	3.46826e7	0.0944188
$281$	−3.88226e8	−1.04379	−0.521894	−	0.853010i	$-0.674774\pi$
$281$	−3.88226e8	−1.04379	−0.521894	+	0.853010i	$0.674774\pi$
$282$	−1.68350e8	−0.447035
$283$	6.85015e8	1.79658	0.898292	−	0.439398i	$-0.144808\pi$
$283$	6.85015e8	1.79658	0.898292	+	0.439398i	$0.144808\pi$
$284$	−2.72288e8	−0.705365
$285$	−8.48260e7	−0.217056
$286$	5.82811e8	1.47315
$287$	−2.39947e7	−0.0599141
$288$	−1.16307e8	−0.286901
$289$	−2.21954e8	−0.540905
$290$	−6.07382e7	−0.146241
$291$	−1.43436e7	−0.0341219
$292$	−8.53744e7	−0.200672
$293$	−7.03513e7	−0.163394	−0.0816969	−	0.996657i	$-0.526034\pi$
$293$	−7.03513e7	−0.163394	−0.0816969	+	0.996657i	$0.526034\pi$
$294$	−1.43520e8	−0.329379
$295$	1.11542e7	0.0252966
$296$	2.38118e8	0.533669
$297$	−1.04377e8	−0.231183
$298$	8.28235e7	0.181299
$299$	1.59695e8	0.345495
$300$	−1.25163e8	−0.267641
$301$	2.51128e8	0.530776
$302$	4.69058e8	0.979946
$303$	−7.84868e7	−0.162087
$304$	2.71209e8	0.553665
$305$	−4.04820e7	−0.0816982
$306$	−8.14934e7	−0.162591
$307$	6.19217e8	1.22140	0.610701	−	0.791861i	$-0.290888\pi$
$307$	6.19217e8	1.22140	0.610701	+	0.791861i	$0.290888\pi$
$308$	1.35183e8	0.263629
$309$	−4.62902e8	−0.892553
$310$	4.88679e7	0.0931661
$311$	6.09567e8	1.14911	0.574553	−	0.818468i	$-0.305176\pi$
$311$	6.09567e8	1.14911	0.574553	+	0.818468i	$0.305176\pi$
$312$	5.62814e8	1.04912
$313$	−5.97609e8	−1.10157	−0.550785	−	0.834647i	$-0.685672\pi$
$313$	−5.97609e8	−1.10157	−0.550785	+	0.834647i	$0.685672\pi$
$314$	1.11526e8	0.203294
$315$	1.63674e7	0.0295049
$316$	4.27026e8	0.761289
$317$	−2.89237e8	−0.509972	−0.254986	−	0.966945i	$-0.582071\pi$
$317$	−2.89237e8	−0.509972	−0.254986	+	0.966945i	$0.582071\pi$
$318$	1.71516e8	0.299095
$319$	−7.28150e8	−1.25589
$320$	−1.03164e8	−0.175997
$321$	2.08806e8	0.352350
$322$	−3.98466e7	−0.0665113
$323$	−7.93972e8	−1.31098
$324$	−3.27712e7	−0.0535284
$325$	1.01442e9	1.63918
$326$	4.08234e8	0.652601
$327$	−1.42146e8	−0.224810
$328$	8.96611e7	0.140296
$329$	3.16481e8	0.489962
$330$	−6.33332e7	−0.0970136
$331$	−6.01918e8	−0.912304	−0.456152	−	0.889902i	$-0.650773\pi$
$331$	−6.01918e8	−0.912304	−0.456152	+	0.889902i	$0.650773\pi$
$332$	−2.71957e8	−0.407866
$333$	1.12373e8	0.166766
$334$	−3.15526e7	−0.0463365
$335$	1.86815e7	0.0271491
$336$	−5.23306e7	−0.0752607
$337$	4.06076e8	0.577966	0.288983	−	0.957334i	$-0.406683\pi$
$337$	4.06076e8	0.577966	0.288983	+	0.957334i	$0.406683\pi$
$338$	−9.71989e8	−1.36916
$339$	−7.90963e8	−1.10270
$340$	4.59666e7	0.0634258
$341$	5.85844e8	0.800095
$342$	3.43465e8	0.464292
$343$	6.10255e8	0.816549
$344$	−9.38388e8	−1.24288
$345$	−1.73538e7	−0.0227524
$346$	4.86082e8	0.630874
$347$	1.23529e8	0.158714	0.0793568	−	0.996846i	$-0.474713\pi$
$347$	1.23529e8	0.158714	0.0793568	+	0.996846i	$0.474713\pi$
$348$	−2.28617e8	−0.290791
$349$	−3.88573e8	−0.489309	−0.244655	−	0.969610i	$-0.578675\pi$
$349$	−3.88573e8	−0.489309	−0.244655	+	0.969610i	$0.578675\pi$
$350$	−2.53115e8	−0.315559
$351$	2.65603e8	0.327838
$352$	−8.46041e8	−1.03393
$353$	1.30943e8	0.158443	0.0792213	−	0.996857i	$-0.474757\pi$
$353$	1.30943e8	0.158443	0.0792213	+	0.996857i	$0.474757\pi$
$354$	−4.51640e7	−0.0541104
$355$	−2.39814e8	−0.284495
$356$	1.63475e8	0.192034
$357$	1.53199e8	0.178204
$358$	8.97866e8	1.03424
$359$	1.28579e9	1.46669	0.733346	−	0.679856i	$-0.237958\pi$
$359$	1.28579e9	1.46669	0.733346	+	0.679856i	$0.237958\pi$
$360$	−6.11602e7	−0.0690892
$361$	2.45243e9	2.74361
$362$	4.53301e8	0.502235
$363$	−2.33105e8	−0.255787
$364$	−3.43993e8	−0.373848
$365$	−7.51922e7	−0.0809372
$366$	1.63914e8	0.174756
$367$	1.23889e9	1.30828	0.654139	−	0.756374i	$-0.273031\pi$
$367$	1.23889e9	1.30828	0.654139	+	0.756374i	$0.273031\pi$
$368$	5.54843e7	0.0580367
$369$	4.23129e7	0.0438410
$370$	6.81850e7	0.0699814
$371$	−3.22433e8	−0.327816
$372$	1.83937e8	0.185255
$373$	−1.91108e8	−0.190676	−0.0953382	−	0.995445i	$-0.530393\pi$
$373$	−1.91108e8	−0.190676	−0.0953382	+	0.995445i	$0.530393\pi$
$374$	−5.92800e8	−0.585946
$375$	−2.24796e8	−0.220130
$376$	−1.18259e9	−1.14730
$377$	1.85289e9	1.78096
$378$	−6.62726e7	−0.0631121
$379$	−4.82547e8	−0.455305	−0.227653	−	0.973742i	$-0.573105\pi$
$379$	−4.82547e8	−0.455305	−0.227653	+	0.973742i	$0.573105\pi$
$380$	−1.93732e8	−0.181117
$381$	−5.16688e8	−0.478620
$382$	−1.06226e8	−0.0975012
$383$	−4.67810e8	−0.425475	−0.212738	−	0.977109i	$-0.568238\pi$
$383$	−4.67810e8	−0.425475	−0.212738	+	0.977109i	$0.568238\pi$
$384$	−1.33663e8	−0.120463
$385$	1.19060e8	0.106329
$386$	−1.36799e9	−1.21068
$387$	−4.42845e8	−0.388386
$388$	−3.27591e7	−0.0284722
$389$	2.37119e8	0.204241	0.102120	−	0.994772i	$-0.467437\pi$
$389$	2.37119e8	0.204241	0.102120	+	0.994772i	$0.467437\pi$
$390$	1.61161e8	0.137573
$391$	−1.62432e8	−0.137421
$392$	−1.00817e9	−0.845344
$393$	−5.53540e7	−0.0460018
$394$	2.56177e8	0.211010
$395$	3.76097e8	0.307051
$396$	−2.38384e8	−0.192905
$397$	−3.19338e8	−0.256144	−0.128072	−	0.991765i	$-0.540879\pi$
$397$	−3.19338e8	−0.256144	−0.128072	+	0.991765i	$0.540879\pi$
$398$	4.13512e7	0.0328774
$399$	−6.45679e8	−0.508876
$400$	3.52450e8	0.275351
$401$	−1.08909e9	−0.843451	−0.421725	−	0.906724i	$-0.638575\pi$
$401$	−1.08909e9	−0.843451	−0.421725	+	0.906724i	$0.638575\pi$
$402$	−7.56425e7	−0.0580731
$403$	−1.49077e9	−1.13460
$404$	−1.79254e8	−0.135249
$405$	−2.88627e7	−0.0215896
$406$	−4.62328e8	−0.342854
$407$	8.17424e8	0.600990
$408$	−5.72460e8	−0.417287
$409$	1.68562e9	1.21822	0.609112	−	0.793084i	$-0.291526\pi$
$409$	1.68562e9	1.21822	0.609112	+	0.793084i	$0.291526\pi$
$410$	2.56744e7	0.0183974
$411$	3.30111e8	0.234538
$412$	−1.05721e9	−0.744769
$413$	8.49037e7	0.0593064
$414$	7.02664e7	0.0486684
$415$	−2.39522e8	−0.164504
$416$	2.15288e9	1.46620
$417$	−6.17853e8	−0.417262
$418$	2.49843e9	1.67321
$419$	1.13922e9	0.756588	0.378294	−	0.925686i	$-0.376511\pi$
$419$	1.13922e9	0.756588	0.378294	+	0.925686i	$0.376511\pi$
$420$	3.73812e7	0.0246196
$421$	9.61423e8	0.627953	0.313977	−	0.949431i	$-0.398339\pi$
$421$	9.61423e8	0.627953	0.313977	+	0.949431i	$0.398339\pi$
$422$	−2.02127e8	−0.130928
$423$	−5.58091e8	−0.358520
$424$	1.20483e9	0.767621
$425$	−1.03181e9	−0.651984
$426$	9.71018e8	0.608546
$427$	−3.08141e8	−0.191537
$428$	4.76887e8	0.294010
$429$	1.93205e9	1.18146
$430$	−2.68707e8	−0.162982
$431$	2.62811e8	0.158115	0.0790575	−	0.996870i	$-0.474809\pi$
$431$	2.62811e8	0.158115	0.0790575	+	0.996870i	$0.474809\pi$
$432$	9.22812e7	0.0550706
$433$	−2.86742e9	−1.69740	−0.848698	−	0.528877i	$-0.822613\pi$
$433$	−2.86742e9	−1.69740	−0.848698	+	0.528877i	$0.822613\pi$
$434$	3.71973e8	0.218423
$435$	−2.01351e8	−0.117285
$436$	−3.24643e8	−0.187587
$437$	6.84590e8	0.392415
$438$	3.04457e8	0.173128
$439$	−2.91897e8	−0.164666	−0.0823330	−	0.996605i	$-0.526237\pi$
$439$	−2.91897e8	−0.164666	−0.0823330	+	0.996605i	$0.526237\pi$
$440$	−4.44892e8	−0.248983
$441$	−4.75777e8	−0.264161
$442$	1.50847e9	0.830920
$443$	−2.33184e9	−1.27434	−0.637169	−	0.770724i	$-0.719895\pi$
$443$	−2.33184e9	−1.27434	−0.637169	+	0.770724i	$0.719895\pi$
$444$	2.56646e8	0.139154
$445$	1.43979e8	0.0774529
$446$	9.04850e8	0.482953
$447$	2.74565e8	0.145401
$448$	−7.85267e8	−0.412614
$449$	−2.29986e9	−1.19905	−0.599527	−	0.800355i	$-0.704645\pi$
$449$	−2.29986e9	−1.19905	−0.599527	+	0.800355i	$0.704645\pi$
$450$	4.46350e8	0.230904
$451$	3.07793e8	0.157994
$452$	−1.80646e9	−0.920121
$453$	1.55496e9	0.785913
$454$	−1.16200e9	−0.582788
$455$	−3.02967e8	−0.150784
$456$	2.41271e9	1.19159
$457$	1.34778e9	0.660560	0.330280	−	0.943883i	$-0.392857\pi$
$457$	1.34778e9	0.660560	0.330280	+	0.943883i	$0.392857\pi$
$458$	7.16343e8	0.348411
$459$	−2.70156e8	−0.130398
$460$	−3.96340e7	−0.0189852
$461$	1.79615e9	0.853865	0.426932	−	0.904284i	$-0.359594\pi$
$461$	1.79615e9	0.853865	0.426932	+	0.904284i	$0.359594\pi$
$462$	−4.82080e8	−0.227443
$463$	−3.73066e9	−1.74684	−0.873418	−	0.486971i	$-0.838102\pi$
$463$	−3.73066e9	−1.74684	−0.873418	+	0.486971i	$0.838102\pi$
$464$	6.43768e8	0.299169
$465$	1.62000e8	0.0747188
$466$	−1.90382e9	−0.871517
$467$	−4.18677e9	−1.90226	−0.951129	−	0.308793i	$-0.900075\pi$
$467$	−4.18677e9	−1.90226	−0.951129	+	0.308793i	$0.900075\pi$
$468$	6.06606e8	0.273556
$469$	1.42200e8	0.0636496
$470$	−3.38635e8	−0.150449
$471$	3.69717e8	0.163041
$472$	−3.17260e8	−0.138873
$473$	−3.22134e9	−1.39966
$474$	−1.52284e9	−0.656794
$475$	4.34869e9	1.86179
$476$	3.49889e8	0.148698
$477$	5.68586e8	0.239873
$478$	−1.91872e9	−0.803553
$479$	4.05633e9	1.68639	0.843197	−	0.537605i	$-0.180671\pi$
$479$	4.05633e9	1.68639	0.843197	+	0.537605i	$0.180671\pi$
$480$	−2.33951e8	−0.0965562
$481$	−2.08006e9	−0.852254
$482$	−1.09705e9	−0.446233
$483$	−1.32094e8	−0.0533418
$484$	−5.32385e8	−0.213436
$485$	−2.88521e7	−0.0114837
$486$	1.16867e8	0.0461811
$487$	−3.44990e9	−1.35349	−0.676745	−	0.736218i	$-0.736610\pi$
$487$	−3.44990e9	−1.35349	−0.676745	+	0.736218i	$0.736610\pi$
$488$	1.15143e9	0.448507
$489$	1.35332e9	0.523383
$490$	−2.88689e8	−0.110852
$491$	−3.70056e9	−1.41086	−0.705428	−	0.708782i	$-0.749245\pi$
$491$	−3.70056e9	−1.41086	−0.705428	+	0.708782i	$0.749245\pi$
$492$	9.66376e7	0.0365821
$493$	−1.88465e9	−0.708380
$494$	−6.35766e9	−2.37276
$495$	−2.09953e8	−0.0778045
$496$	−5.17953e8	−0.190592
$497$	−1.82542e9	−0.666982
$498$	9.69838e8	0.351882
$499$	3.49353e9	1.25867	0.629336	−	0.777133i	$-0.283327\pi$
$499$	3.49353e9	1.25867	0.629336	+	0.777133i	$0.283327\pi$
$500$	−5.13408e8	−0.183682
$501$	−1.04599e8	−0.0371616
$502$	−3.54479e9	−1.25063
$503$	3.77577e9	1.32287	0.661436	−	0.750002i	$-0.269947\pi$
$503$	3.77577e9	1.32287	0.661436	+	0.750002i	$0.269947\pi$
$504$	−4.65540e8	−0.161976
$505$	−1.57876e8	−0.0545501
$506$	5.11132e8	0.175391
$507$	−3.22220e9	−1.09806
$508$	−1.18005e9	−0.399373
$509$	−2.35210e9	−0.790575	−0.395288	−	0.918557i	$-0.629355\pi$
$509$	−2.35210e9	−0.790575	−0.395288	+	0.918557i	$0.629355\pi$
$510$	−1.63923e8	−0.0547199
$511$	−5.72349e8	−0.189753
$512$	1.67502e9	0.551538
$513$	1.13861e9	0.372360
$514$	−2.26315e9	−0.735092
$515$	−9.31124e8	−0.300388
$516$	−1.01140e9	−0.324079
$517$	−4.05967e9	−1.29203
$518$	5.19011e8	0.164068
$519$	1.61139e9	0.505959
$520$	1.13210e9	0.353079
$521$	−1.51952e9	−0.470734	−0.235367	−	0.971907i	$-0.575629\pi$
$521$	−1.51952e9	−0.470734	−0.235367	+	0.971907i	$0.575629\pi$
$522$	8.15281e8	0.250877
$523$	5.57185e9	1.70311	0.851556	−	0.524264i	$-0.175659\pi$
$523$	5.57185e9	1.70311	0.851556	+	0.524264i	$0.175659\pi$
$524$	−1.26422e8	−0.0383851
$525$	−8.39093e8	−0.253077
$526$	−1.09198e9	−0.327164
$527$	1.51632e9	0.451289
$528$	6.71272e8	0.198463
$529$	−3.26477e9	−0.958866
$530$	3.45003e8	0.100660
$531$	−1.49721e8	−0.0433963
$532$	−1.47465e9	−0.424619
$533$	−7.83227e8	−0.224049
$534$	−5.82977e8	−0.165675
$535$	4.20011e8	0.118583
$536$	−5.31360e8	−0.149043
$537$	2.97648e9	0.829456
$538$	−3.30878e9	−0.916074
$539$	−3.46090e9	−0.951981
$540$	−6.59190e7	−0.0180149
$541$	−1.01713e9	−0.276177	−0.138088	−	0.990420i	$-0.544096\pi$
$541$	−1.01713e9	−0.276177	−0.138088	+	0.990420i	$0.544096\pi$
$542$	−3.75654e9	−1.01342
$543$	1.50272e9	0.402791
$544$	−2.18978e9	−0.583183
$545$	−2.85925e8	−0.0756596
$546$	1.22673e9	0.322533
$547$	−3.76396e8	−0.0983308	−0.0491654	−	0.998791i	$-0.515656\pi$
$547$	−3.76396e8	−0.0983308	−0.0491654	+	0.998791i	$0.515656\pi$
$548$	7.53934e8	0.195705
$549$	5.43384e8	0.140153
$550$	3.24684e9	0.832131
$551$	7.94310e9	2.02283
$552$	4.93595e8	0.124906
$553$	2.86278e9	0.719863
$554$	2.12000e9	0.529727
$555$	2.26038e8	0.0561248
$556$	−1.41110e9	−0.348174
$557$	7.16500e9	1.75680	0.878401	−	0.477924i	$-0.158611\pi$
$557$	7.16500e9	1.75680	0.878401	+	0.477924i	$0.158611\pi$
$558$	−6.55947e8	−0.159827
$559$	8.19721e9	1.98484
$560$	−1.05263e8	−0.0253289
$561$	−1.96517e9	−0.469926
$562$	3.16196e9	0.751414
$563$	4.65876e9	1.10025	0.550125	−	0.835082i	$-0.314580\pi$
$563$	4.65876e9	1.10025	0.550125	+	0.835082i	$0.314580\pi$
$564$	−1.27461e9	−0.299158
$565$	−1.59102e9	−0.371112
$566$	−5.57921e9	−1.29335
$567$	−2.19698e8	−0.0506157
$568$	6.82103e9	1.56182
$569$	−4.71634e9	−1.07328	−0.536639	−	0.843812i	$-0.680306\pi$
$569$	−4.71634e9	−1.07328	−0.536639	+	0.843812i	$0.680306\pi$
$570$	6.90878e8	0.156257
$571$	−8.11800e9	−1.82483	−0.912416	−	0.409265i	$-0.865785\pi$
$571$	−8.11800e9	−1.82483	−0.912416	+	0.409265i	$0.865785\pi$
$572$	4.41258e9	0.985840
$573$	−3.52147e8	−0.0781956
$574$	1.95429e8	0.0431317
$575$	8.89660e8	0.195158
$576$	1.38476e9	0.301923
$577$	−2.96457e9	−0.642460	−0.321230	−	0.947001i	$-0.604096\pi$
$577$	−2.96457e9	−0.642460	−0.321230	+	0.947001i	$0.604096\pi$
$578$	1.80774e9	0.389393
$579$	−4.53497e9	−0.970957
$580$	−4.59862e8	−0.0978654
$581$	−1.82320e9	−0.385671
$582$	1.16824e8	0.0245641
$583$	4.13601e9	0.864453
$584$	2.13870e9	0.444329
$585$	5.34260e8	0.110333
$586$	5.72986e8	0.117626
$587$	4.79349e9	0.978180	0.489090	−	0.872233i	$-0.337329\pi$
$587$	4.79349e9	0.978180	0.489090	+	0.872233i	$0.337329\pi$
$588$	−1.08662e9	−0.220423
$589$	−6.39075e9	−1.28869
$590$	−9.08470e7	−0.0182108
$591$	8.49242e8	0.169229
$592$	−7.22697e8	−0.143163
$593$	6.55987e9	1.29183	0.645913	−	0.763411i	$-0.276477\pi$
$593$	6.55987e9	1.29183	0.645913	+	0.763411i	$0.276477\pi$
$594$	8.50113e8	0.166427
$595$	3.08160e8	0.0599745
$596$	6.27073e8	0.121327
$597$	1.37082e8	0.0263675
$598$	−1.30066e9	−0.248719
$599$	8.15165e9	1.54971	0.774857	−	0.632137i	$-0.217822\pi$
$599$	8.15165e9	1.54971	0.774857	+	0.632137i	$0.217822\pi$
$600$	3.13544e9	0.592610
$601$	−3.63784e9	−0.683570	−0.341785	−	0.939778i	$-0.611031\pi$
$601$	−3.63784e9	−0.683570	−0.341785	+	0.939778i	$0.611031\pi$
$602$	−2.04534e9	−0.382102
$603$	−2.50760e8	−0.0465744
$604$	3.55133e9	0.655786
$605$	−4.68890e8	−0.0860849
$606$	6.39247e8	0.116685
$607$	4.53989e9	0.823920	0.411960	−	0.911202i	$-0.364844\pi$
$607$	4.53989e9	0.823920	0.411960	+	0.911202i	$0.364844\pi$
$608$	9.22913e9	1.66532
$609$	−1.53265e9	−0.274967
$610$	3.29712e8	0.0588139
$611$	1.03305e10	1.83221
$612$	−6.17003e8	−0.108807
$613$	5.71720e9	1.00247	0.501235	−	0.865311i	$-0.332879\pi$
$613$	5.71720e9	1.00247	0.501235	+	0.865311i	$0.332879\pi$
$614$	−5.04330e9	−0.879277
$615$	8.51122e7	0.0147546
$616$	−3.38643e9	−0.583727
$617$	−2.37562e9	−0.407172	−0.203586	−	0.979057i	$-0.565260\pi$
$617$	−2.37562e9	−0.407172	−0.203586	+	0.979057i	$0.565260\pi$
$618$	3.77017e9	0.642542
$619$	5.60279e9	0.949483	0.474742	−	0.880125i	$-0.342542\pi$
$619$	5.60279e9	0.949483	0.474742	+	0.880125i	$0.342542\pi$
$620$	3.69989e8	0.0623473
$621$	2.32938e8	0.0390318
$622$	−4.96470e9	−0.827231
$623$	1.09594e9	0.181584
$624$	−1.70816e9	−0.281437
$625$	5.42090e9	0.888160
$626$	4.86732e9	0.793011
$627$	8.28246e9	1.34191
$628$	8.44389e8	0.136045
$629$	2.11571e9	0.338984
$630$	−1.33307e8	−0.0212403
$631$	−1.14283e10	−1.81083	−0.905415	−	0.424527i	$-0.860440\pi$
$631$	−1.14283e10	−1.81083	−0.905415	+	0.424527i	$0.860440\pi$
$632$	−1.06974e10	−1.68565
$633$	−6.70065e8	−0.105003
$634$	2.35573e9	0.367124
$635$	−1.03932e9	−0.161079
$636$	1.29858e9	0.200156
$637$	8.80680e9	1.34999
$638$	5.93052e9	0.904108
$639$	3.21898e9	0.488052
$640$	−2.68863e8	−0.0405417
$641$	−8.14000e8	−0.122073	−0.0610367	−	0.998136i	$-0.519441\pi$
$641$	−8.14000e8	−0.122073	−0.0610367	+	0.998136i	$0.519441\pi$
$642$	−1.70065e9	−0.253654
$643$	−1.34257e10	−1.99158	−0.995792	−	0.0916394i	$-0.970789\pi$
$643$	−1.34257e10	−1.99158	−0.995792	+	0.0916394i	$0.970789\pi$
$644$	−3.01686e8	−0.0445098
$645$	−8.90779e8	−0.130711
$646$	6.46662e9	0.943765
$647$	−2.58413e9	−0.375102	−0.187551	−	0.982255i	$-0.560055\pi$
$647$	−2.58413e9	−0.375102	−0.187551	+	0.982255i	$0.560055\pi$
$648$	8.20945e8	0.118523
$649$	−1.08910e9	−0.156391
$650$	−8.26210e9	−1.18003
$651$	1.23311e9	0.175174
$652$	3.09082e9	0.436725
$653$	9.14859e9	1.28575	0.642877	−	0.765969i	$-0.277741\pi$
$653$	9.14859e9	1.28575	0.642877	+	0.765969i	$0.277741\pi$
$654$	1.15773e9	0.161839
$655$	−1.11344e8	−0.0154819
$656$	−2.72124e8	−0.0376360
$657$	1.00929e9	0.138848
$658$	−2.57763e9	−0.352719
$659$	−3.05757e9	−0.416176	−0.208088	−	0.978110i	$-0.566724\pi$
$659$	−3.05757e9	−0.416176	−0.208088	+	0.978110i	$0.566724\pi$
$660$	−4.79509e8	−0.0649221
$661$	−5.81198e9	−0.782743	−0.391371	−	0.920233i	$-0.627999\pi$
$661$	−5.81198e9	−0.782743	−0.391371	+	0.920233i	$0.627999\pi$
$662$	4.90241e9	0.656760
$663$	5.00068e9	0.666395
$664$	6.81275e9	0.903096
$665$	−1.29878e9	−0.171262
$666$	−9.15238e8	−0.120053
$667$	1.62501e9	0.212039
$668$	−2.38891e8	−0.0310086
$669$	2.99963e9	0.387326
$670$	−1.52154e8	−0.0195444
$671$	3.95269e9	0.505084
$672$	−1.78079e9	−0.226371
$673$	−7.68542e9	−0.971885	−0.485943	−	0.873991i	$-0.661524\pi$
$673$	−7.68542e9	−0.971885	−0.485943	+	0.873991i	$0.661524\pi$
$674$	−3.30734e9	−0.416073
$675$	1.47968e9	0.185184
$676$	−7.35913e9	−0.916248
$677$	5.12888e9	0.635276	0.317638	−	0.948212i	$-0.397110\pi$
$677$	5.12888e9	0.635276	0.317638	+	0.948212i	$0.397110\pi$
$678$	6.44211e9	0.793824
$679$	−2.19617e8	−0.0269229
$680$	−1.15150e9	−0.140437
$681$	−3.85210e9	−0.467393
$682$	−4.77149e9	−0.575982
$683$	9.14761e9	1.09859	0.549294	−	0.835629i	$-0.314897\pi$
$683$	9.14761e9	1.09859	0.549294	+	0.835629i	$0.314897\pi$
$684$	2.60044e9	0.310707
$685$	6.64016e8	0.0789335
$686$	−4.97031e9	−0.587827
$687$	2.37472e9	0.279424
$688$	2.84804e9	0.333416
$689$	−1.05247e10	−1.22587
$690$	1.41340e8	0.0163793
$691$	1.46307e10	1.68691	0.843455	−	0.537200i	$-0.180518\pi$
$691$	1.46307e10	1.68691	0.843455	+	0.537200i	$0.180518\pi$
$692$	3.68022e9	0.422185
$693$	−1.59813e9	−0.182408
$694$	−1.00610e9	−0.114257
$695$	−1.24281e9	−0.140429
$696$	5.72704e9	0.643869
$697$	7.96651e8	0.0891155
$698$	3.16479e9	0.352250
$699$	−6.31129e9	−0.698953
$700$	−1.91639e9	−0.211174
$701$	−5.51419e9	−0.604601	−0.302300	−	0.953213i	$-0.597755\pi$
$701$	−5.51419e9	−0.604601	−0.302300	+	0.953213i	$0.597755\pi$
$702$	−2.16325e9	−0.236008
$703$	−8.91696e9	−0.967996
$704$	1.00730e10	1.08807
$705$	−1.12260e9	−0.120660
$706$	−1.06649e9	−0.114061
$707$	−1.20172e9	−0.127890
$708$	−3.41945e8	−0.0362110
$709$	4.43575e9	0.467417	0.233709	−	0.972307i	$-0.424914\pi$
$709$	4.43575e9	0.467417	0.233709	+	0.972307i	$0.424914\pi$
$710$	1.95320e9	0.204806
$711$	−5.04830e9	−0.526746
$712$	−4.09519e9	−0.425201
$713$	−1.30743e9	−0.135084
$714$	−1.24775e9	−0.128288
$715$	3.88631e9	0.397619
$716$	6.79793e9	0.692119
$717$	−6.36069e9	−0.644447
$718$	−1.04723e10	−1.05586
$719$	−5.67887e9	−0.569785	−0.284893	−	0.958559i	$-0.591958\pi$
$719$	−5.67887e9	−0.569785	−0.284893	+	0.958559i	$0.591958\pi$
$720$	1.85623e8	0.0185340
$721$	−7.08754e9	−0.704242
$722$	−1.99742e10	−1.97510
$723$	−3.63679e9	−0.357877
$724$	3.43204e9	0.336099
$725$	1.03225e10	1.00601
$726$	1.89856e9	0.184139
$727$	−1.26294e10	−1.21903	−0.609514	−	0.792775i	$-0.708636\pi$
$727$	−1.26294e10	−1.21903	−0.609514	+	0.792775i	$0.708636\pi$
$728$	8.61731e9	0.827774
$729$	3.87420e8	0.0370370
$730$	6.12414e8	0.0582660
$731$	−8.33771e9	−0.789470
$732$	1.24102e9	0.116948
$733$	8.87757e9	0.832588	0.416294	−	0.909230i	$-0.363329\pi$
$733$	8.87757e9	0.832588	0.416294	+	0.909230i	$0.363329\pi$
$734$	−1.00903e10	−0.941819
$735$	−9.57023e8	−0.0889030
$736$	1.88811e9	0.174564
$737$	−1.82408e9	−0.167844
$738$	−3.44624e8	−0.0315608
$739$	−1.67534e10	−1.52703	−0.763515	−	0.645791i	$-0.776528\pi$
$739$	−1.67534e10	−1.52703	−0.763515	+	0.645791i	$0.776528\pi$
$740$	5.16243e8	0.0468320
$741$	−2.10760e10	−1.90294
$742$	2.62610e9	0.235992
$743$	1.87784e10	1.67957	0.839784	−	0.542921i	$-0.182682\pi$
$743$	1.87784e10	1.67957	0.839784	+	0.542921i	$0.182682\pi$
$744$	−4.60778e9	−0.410191
$745$	5.52286e8	0.0489347
$746$	1.55650e9	0.137266
$747$	3.21507e9	0.282208
$748$	−4.48821e9	−0.392118
$749$	3.19705e9	0.278011
$750$	1.83089e9	0.158470
$751$	2.58308e9	0.222535	0.111268	−	0.993790i	$-0.464509\pi$
$751$	2.58308e9	0.222535	0.111268	+	0.993790i	$0.464509\pi$
$752$	3.58921e9	0.307777
$753$	−1.17512e10	−1.00300
$754$	−1.50911e10	−1.28210
$755$	3.12778e9	0.264498
$756$	−5.01763e8	−0.0422350
$757$	5.60643e9	0.469733	0.234867	−	0.972028i	$-0.424535\pi$
$757$	5.60643e9	0.469733	0.234867	+	0.972028i	$0.424535\pi$
$758$	3.93018e9	0.327770
$759$	1.69444e9	0.140663
$760$	4.85315e9	0.401030
$761$	1.71960e8	0.0141443	0.00707216	−	0.999975i	$-0.497749\pi$
$761$	1.71960e8	0.0141443	0.00707216	+	0.999975i	$0.497749\pi$
$762$	4.20824e9	0.344555
$763$	−2.17641e9	−0.177380
$764$	−8.04260e8	−0.0652484
$765$	−5.43416e8	−0.0438852
$766$	3.81015e9	0.306296
$767$	2.77139e9	0.221776
$768$	7.65343e9	0.609666
$769$	−1.69708e10	−1.34574	−0.672869	−	0.739762i	$-0.734938\pi$
$769$	−1.69708e10	−1.34574	−0.672869	+	0.739762i	$0.734938\pi$
$770$	−9.69702e8	−0.0765457
$771$	−7.50247e9	−0.589541
$772$	−1.03573e10	−0.810191
$773$	−5.87486e9	−0.457477	−0.228739	−	0.973488i	$-0.573460\pi$
$773$	−5.87486e9	−0.457477	−0.228739	+	0.973488i	$0.573460\pi$
$774$	3.60681e9	0.279596
$775$	−8.30510e9	−0.640898
$776$	8.20642e8	0.0630431
$777$	1.72056e9	0.131582
$778$	−1.93125e9	−0.147031
$779$	−3.35759e9	−0.254476
$780$	1.22018e9	0.0920650
$781$	2.34156e10	1.75884
$782$	1.32295e9	0.0989280
$783$	2.70271e9	0.201202
$784$	3.05983e9	0.226773
$785$	7.43684e8	0.0548712
$786$	4.50839e8	0.0331163
$787$	1.81450e9	0.132692	0.0663461	−	0.997797i	$-0.478866\pi$
$787$	1.81450e9	0.132692	0.0663461	+	0.997797i	$0.478866\pi$
$788$	1.93957e9	0.141209
$789$	−3.61999e9	−0.262384
$790$	−3.06318e9	−0.221043
$791$	−1.21105e10	−0.870052
$792$	5.97172e9	0.427131
$793$	−1.00582e10	−0.716252
$794$	2.60089e9	0.184396
$795$	1.14371e9	0.0807290
$796$	3.13078e8	0.0220017
$797$	7.68250e9	0.537525	0.268762	−	0.963207i	$-0.413385\pi$
$797$	7.68250e9	0.537525	0.268762	+	0.963207i	$0.413385\pi$
$798$	5.25883e9	0.366335
$799$	−1.05075e10	−0.728763
$800$	1.19937e10	0.828207
$801$	−1.93260e9	−0.132871
$802$	8.87028e9	0.607193
$803$	7.34182e9	0.500379
$804$	−5.72705e8	−0.0388629
$805$	−2.65706e8	−0.0179521
$806$	1.21418e10	0.816791
$807$	−1.09688e10	−0.734688
$808$	4.49047e9	0.299469
$809$	−2.53283e10	−1.68185	−0.840924	−	0.541154i	$-0.817988\pi$
$809$	−2.53283e10	−1.68185	−0.840924	+	0.541154i	$0.817988\pi$
$810$	2.35077e8	0.0155422
$811$	−1.04893e9	−0.0690513	−0.0345256	−	0.999404i	$-0.510992\pi$
$811$	−1.04893e9	−0.0690513	−0.0345256	+	0.999404i	$0.510992\pi$
$812$	−3.50038e9	−0.229440
$813$	−1.24531e10	−0.812760
$814$	−6.65763e9	−0.432647
$815$	2.72220e9	0.176144
$816$	1.73743e9	0.111942
$817$	3.51404e10	2.25439
$818$	−1.37287e10	−0.876989
$819$	4.06668e9	0.258670
$820$	1.94386e8	0.0123117
$821$	−1.22269e10	−0.771110	−0.385555	−	0.922685i	$-0.625990\pi$
$821$	−1.22269e10	−0.771110	−0.385555	+	0.922685i	$0.625990\pi$
$822$	−2.68864e9	−0.168842
$823$	6.96726e8	0.0435675	0.0217837	−	0.999763i	$-0.493065\pi$
$823$	6.96726e8	0.0435675	0.0217837	+	0.999763i	$0.493065\pi$
$824$	2.64840e10	1.64907
$825$	1.07635e10	0.667365
$826$	−6.91510e8	−0.0426942
$827$	−2.23328e10	−1.37301	−0.686505	−	0.727125i	$-0.740856\pi$
$827$	−2.23328e10	−1.37301	−0.686505	+	0.727125i	$0.740856\pi$
$828$	5.32001e8	0.0325692
$829$	1.33734e10	0.815267	0.407633	−	0.913146i	$-0.366354\pi$
$829$	1.33734e10	0.815267	0.407633	+	0.913146i	$0.366354\pi$
$830$	1.95082e9	0.118425
$831$	7.02794e9	0.424839
$832$	−2.56324e10	−1.54297
$833$	−8.95774e9	−0.536959
$834$	5.03219e9	0.300383
$835$	−2.10400e8	−0.0125067
$836$	1.89162e10	1.11972
$837$	−2.17450e9	−0.128180
$838$	−9.27856e9	−0.544661
$839$	−1.68025e10	−0.982217	−0.491108	−	0.871098i	$-0.663408\pi$
$839$	−1.68025e10	−0.982217	−0.491108	+	0.871098i	$0.663408\pi$
$840$	−9.36430e8	−0.0545127
$841$	1.60463e9	0.0930226
$842$	−7.83045e9	−0.452058
$843$	1.04821e10	0.602631
$844$	−1.53035e9	−0.0876176
$845$	−6.48145e9	−0.369550
$846$	4.54545e9	0.258096
$847$	−3.56910e9	−0.201821
$848$	−3.65671e9	−0.205923
$849$	−1.84954e10	−1.03726
$850$	8.40370e9	0.469358
$851$	−1.82424e9	−0.101468
$852$	7.35177e9	0.407243
$853$	−6.95279e9	−0.383563	−0.191782	−	0.981438i	$-0.561427\pi$
$853$	−6.95279e9	−0.383563	−0.191782	+	0.981438i	$0.561427\pi$
$854$	2.50970e9	0.137886
$855$	2.29030e9	0.125317
$856$	−1.19464e10	−0.650997
$857$	−3.47269e10	−1.88466	−0.942330	−	0.334687i	$-0.891370\pi$
$857$	−3.47269e10	−1.88466	−0.942330	+	0.334687i	$0.891370\pi$
$858$	−1.57359e10	−0.850523
$859$	−1.72796e10	−0.930161	−0.465081	−	0.885268i	$-0.653975\pi$
$859$	−1.72796e10	−0.930161	−0.465081	+	0.885268i	$0.653975\pi$
$860$	−2.03443e9	−0.109068
$861$	6.47858e8	0.0345914
$862$	−2.14050e9	−0.113826
$863$	−3.64236e10	−1.92906	−0.964529	−	0.263977i	$-0.914966\pi$
$863$	−3.64236e10	−1.92906	−0.964529	+	0.263977i	$0.914966\pi$
$864$	3.14029e9	0.165642
$865$	3.24130e9	0.170280
$866$	2.33541e10	1.22194
$867$	5.99276e9	0.312291
$868$	2.81628e9	0.146170
$869$	−3.67224e10	−1.89828
$870$	1.63993e9	0.0844323
$871$	4.64165e9	0.238018
$872$	8.13258e9	0.415356
$873$	3.87278e8	0.0197003
$874$	−5.57575e9	−0.282496
$875$	−3.44188e9	−0.173687
$876$	2.30511e9	0.115858
$877$	−2.21634e9	−0.110953	−0.0554763	−	0.998460i	$-0.517668\pi$
$877$	−2.21634e9	−0.110953	−0.0554763	+	0.998460i	$0.517668\pi$
$878$	2.37740e9	0.118542
$879$	1.89949e9	0.0943354
$880$	1.35026e9	0.0667925
$881$	−2.32029e10	−1.14321	−0.571607	−	0.820528i	$-0.693680\pi$
$881$	−2.32029e10	−1.14321	−0.571607	+	0.820528i	$0.693680\pi$
$882$	3.87504e9	0.190167
$883$	1.94888e10	0.952624	0.476312	−	0.879276i	$-0.341973\pi$
$883$	1.94888e10	0.952624	0.476312	+	0.879276i	$0.341973\pi$
$884$	1.14209e10	0.556057
$885$	−3.01163e8	−0.0146050
$886$	1.89920e10	0.917386
$887$	9.83405e9	0.473151	0.236575	−	0.971613i	$-0.423975\pi$
$887$	9.83405e9	0.473151	0.236575	+	0.971613i	$0.423975\pi$
$888$	−6.42920e9	−0.308114
$889$	−7.91107e9	−0.377641
$890$	−1.17265e9	−0.0557577
$891$	2.81818e9	0.133474
$892$	6.85080e9	0.323195
$893$	4.42853e10	2.08104
$894$	−2.23623e9	−0.104673
$895$	5.98717e9	0.279152
$896$	−2.04654e9	−0.0950477
$897$	−4.31176e9	−0.199471
$898$	1.87315e10	0.863189
$899$	−1.51697e10	−0.696334
$900$	3.37941e9	0.154522
$901$	1.07051e10	0.487590
$902$	−2.50686e9	−0.113739
$903$	−6.78044e9	−0.306444
$904$	4.52534e10	2.03733
$905$	3.02272e9	0.135559
$906$	−1.26646e10	−0.565772
$907$	2.35757e10	1.04915	0.524577	−	0.851363i	$-0.324224\pi$
$907$	2.35757e10	1.04915	0.524577	+	0.851363i	$0.324224\pi$
$908$	−8.79773e9	−0.390005
$909$	2.11914e9	0.0935808
$910$	2.46756e9	0.108548
$911$	−2.65692e10	−1.16430	−0.582149	−	0.813082i	$-0.697788\pi$
$911$	−2.65692e10	−1.16430	−0.582149	+	0.813082i	$0.697788\pi$
$912$	−7.32265e9	−0.319658
$913$	2.33871e10	1.01702
$914$	−1.09772e10	−0.475532
$915$	1.09301e9	0.0471685
$916$	5.42358e9	0.233159
$917$	−8.47531e8	−0.0362964
$918$	2.20032e9	0.0938722
$919$	2.32295e10	0.987271	0.493636	−	0.869669i	$-0.335668\pi$
$919$	2.32295e10	0.987271	0.493636	+	0.869669i	$0.335668\pi$
$920$	9.92863e8	0.0420370
$921$	−1.67189e10	−0.705177
$922$	−1.46290e10	−0.614690
$923$	−5.95846e10	−2.49418
$924$	−3.64993e9	−0.152206
$925$	−1.15880e10	−0.481409
$926$	3.03849e10	1.25753
$927$	1.24983e10	0.515316
$928$	2.19071e10	0.899845
$929$	8.90068e9	0.364224	0.182112	−	0.983278i	$-0.441707\pi$
$929$	8.90068e9	0.364224	0.182112	+	0.983278i	$0.441707\pi$
$930$	−1.31943e9	−0.0537894
$931$	3.77536e10	1.53333
$932$	−1.44142e10	−0.583224
$933$	−1.64583e10	−0.663436
$934$	3.40997e10	1.36942
$935$	−3.95292e9	−0.158153
$936$	−1.51960e10	−0.605708
$937$	2.70936e10	1.07592	0.537959	−	0.842971i	$-0.319196\pi$
$937$	2.70936e10	1.07592	0.537959	+	0.842971i	$0.319196\pi$
$938$	−1.15817e9	−0.0458208
$939$	1.61355e10	0.635992
$940$	−2.56387e9	−0.100681
$941$	−4.63143e10	−1.81197	−0.905987	−	0.423306i	$-0.860869\pi$
$941$	−4.63143e10	−1.81197	−0.905987	+	0.423306i	$0.860869\pi$
$942$	−3.01121e9	−0.117372
$943$	−6.86900e8	−0.0266749
$944$	9.62892e8	0.0372542
$945$	−4.41921e8	−0.0170346
$946$	2.62367e10	1.00760
$947$	4.89914e10	1.87454	0.937271	−	0.348601i	$-0.113343\pi$
$947$	4.89914e10	1.87454	0.937271	+	0.348601i	$0.113343\pi$
$948$	−1.15297e10	−0.439531
$949$	−1.86824e10	−0.709580
$950$	−3.54185e10	−1.34029
$951$	7.80939e9	0.294432
$952$	−8.76500e9	−0.329248
$953$	3.63170e10	1.35921	0.679603	−	0.733580i	$-0.262152\pi$
$953$	3.63170e10	1.35921	0.679603	+	0.733580i	$0.262152\pi$
$954$	−4.63093e9	−0.172683
$955$	−7.08341e8	−0.0263166
$956$	−1.45270e10	−0.537743
$957$	1.96600e10	0.725091
$958$	−3.30374e10	−1.21402
$959$	5.05436e9	0.185055
$960$	2.78544e9	0.101612
$961$	−1.53076e10	−0.556385
$962$	1.69414e10	0.613530
$963$	−5.63775e9	−0.203430
$964$	−8.30599e9	−0.298622
$965$	−9.12207e9	−0.326774
$966$	1.07586e9	0.0384003
$967$	−3.38245e10	−1.20293	−0.601463	−	0.798901i	$-0.705415\pi$
$967$	−3.38245e10	−1.20293	−0.601463	+	0.798901i	$0.705415\pi$
$968$	1.33367e10	0.472589
$969$	2.14373e10	0.756896
$970$	2.34990e8	0.00826701
$971$	4.01598e10	1.40775	0.703873	−	0.710326i	$-0.251452\pi$
$971$	4.01598e10	1.40775	0.703873	+	0.710326i	$0.251452\pi$
$972$	8.84822e8	0.0309047
$973$	−9.46001e9	−0.329228
$974$	2.80982e10	0.974366
$975$	−2.73894e10	−0.946380
$976$	−3.49463e9	−0.120317
$977$	1.49500e10	0.512872	0.256436	−	0.966561i	$-0.417452\pi$
$977$	1.49500e10	0.512872	0.256436	+	0.966561i	$0.417452\pi$
$978$	−1.10223e10	−0.376779
$979$	−1.40582e10	−0.478838
$980$	−2.18572e9	−0.0741830
$981$	3.83793e9	0.129794
$982$	3.01398e10	1.01566
$983$	2.98689e10	1.00295	0.501477	−	0.865171i	$-0.332790\pi$
$983$	2.98689e10	1.00295	0.501477	+	0.865171i	$0.332790\pi$
$984$	−2.42085e9	−0.0810000
$985$	1.70825e9	0.0569539
$986$	1.53498e10	0.509957
$987$	−8.54499e9	−0.282879
$988$	−4.81351e10	−1.58786
$989$	7.18906e9	0.236312
$990$	1.71000e9	0.0560108
$991$	1.42111e10	0.463842	0.231921	−	0.972735i	$-0.425499\pi$
$991$	1.42111e10	0.463842	0.231921	+	0.972735i	$0.425499\pi$
$992$	−1.76257e10	−0.573266
$993$	1.62518e10	0.526719
$994$	1.48674e10	0.480155
$995$	2.75739e8	0.00887396
$996$	7.34284e9	0.235481
$997$	2.29718e10	0.734112	0.367056	−	0.930199i	$-0.380366\pi$
$997$	2.29718e10	0.734112	0.367056	+	0.930199i	$0.380366\pi$
$998$	−2.84536e10	−0.906108
$999$	−3.03407e9	−0.0962823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.6	✓	17
3.2	odd	2		531.8.a.c.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.6	✓	17	1.1	even	1	trivial
531.8.a.c.1.12		17	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-8.14464 q^{2} -27.0000 q^{3} -61.6648 q^{4} -54.3103 q^{5} +219.905 q^{6} -413.400 q^{7} +1544.75 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.14464 q^{2} -27.0000 q^{3} -61.6648 q^{4} -54.3103 q^{5} +219.905 q^{6} -413.400 q^{7} +1544.75 q^{8} +729.000 q^{9} +442.338 q^{10} +5302.90 q^{11} +1664.95 q^{12} -13494.1 q^{13} +3367.00 q^{14} +1466.38 q^{15} -4688.37 q^{16} +13725.3 q^{17} -5937.45 q^{18} -57847.2 q^{19} +3349.03 q^{20} +11161.8 q^{21} -43190.2 q^{22} -11834.5 q^{23} -41708.3 q^{24} -75175.4 q^{25} +109904. q^{26} -19683.0 q^{27} +25492.2 q^{28} -137312. q^{29} -11943.1 q^{30} +110476. q^{31} -159543. q^{32} -143178. q^{33} -111788. q^{34} +22451.9 q^{35} -44953.6 q^{36} +154147. q^{37} +471145. q^{38} +364339. q^{39} -83896.0 q^{40} +58042.4 q^{41} -90908.9 q^{42} -607469. q^{43} -327002. q^{44} -39592.2 q^{45} +96387.4 q^{46} -765556. q^{47} +126586. q^{48} -652643. q^{49} +612277. q^{50} -370584. q^{51} +832107. q^{52} +779953. q^{53} +160311. q^{54} -288002. q^{55} -638601. q^{56} +1.56188e6 q^{57} +1.11836e6 q^{58} -205379. q^{59} -90423.9 q^{60} +745383. q^{61} -899790. q^{62} -301369. q^{63} +1.89953e6 q^{64} +732866. q^{65} +1.16614e6 q^{66} -343978. q^{67} -846369. q^{68} +319530. q^{69} -182863. q^{70} +4.41562e6 q^{71} +1.12612e6 q^{72} +1.38449e6 q^{73} -1.25547e6 q^{74} +2.02974e6 q^{75} +3.56714e6 q^{76} -2.19222e6 q^{77} -2.96742e6 q^{78} -6.92496e6 q^{79} +254627. q^{80} +531441. q^{81} -472735. q^{82} +4.41025e6 q^{83} -688290. q^{84} -745427. q^{85} +4.94762e6 q^{86} +3.70742e6 q^{87} +8.19166e6 q^{88} -2.65103e6 q^{89} +322465. q^{90} +5.57844e6 q^{91} +729769. q^{92} -2.98286e6 q^{93} +6.23518e6 q^{94} +3.14170e6 q^{95} +4.30767e6 q^{96} +531245. q^{97} +5.31555e6 q^{98} +3.86581e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + O(q^{10}) \)	\( 17q + 2q^{2} - 459q^{3} + 1166q^{4} - 318q^{5} - 54q^{6} + 3145q^{7} + 2355q^{8} + 12393q^{9} + 6521q^{10} - 1764q^{11} - 31482q^{12} + 18192q^{13} - 7827q^{14} + 8586q^{15} + 139226q^{16} - 15507q^{17} + 1458q^{18} + 52083q^{19} + 721q^{20} - 84915q^{21} - 234434q^{22} + 63823q^{23} - 63585q^{24} + 202153q^{25} - 367956q^{26} - 334611q^{27} + 182306q^{28} - 502955q^{29} - 176067q^{30} + 347531q^{31} - 243908q^{32} + 47628q^{33} - 330872q^{34} + 92641q^{35} + 850014q^{36} + 447615q^{37} + 775669q^{38} - 491184q^{39} + 2203270q^{40} + 940335q^{41} + 211329q^{42} + 478562q^{43} - 596924q^{44} - 231822q^{45} - 3078663q^{46} + 703121q^{47} - 3759102q^{48} + 1895082q^{49} - 876967q^{50} + 418689q^{51} + 6278296q^{52} - 1005974q^{53} - 39366q^{54} + 5212846q^{55} + 3425294q^{56} - 1406241q^{57} + 6710166q^{58} - 3491443q^{59} - 19467q^{60} + 11510749q^{61} + 5996234q^{62} + 2292705q^{63} + 29496941q^{64} + 11094180q^{65} + 6329718q^{66} + 14007144q^{67} + 19688159q^{68} - 1723221q^{69} + 30909708q^{70} + 5229074q^{71} + 1716795q^{72} + 5452211q^{73} + 12819662q^{74} - 5458131q^{75} + 41929340q^{76} + 9930777q^{77} + 9934812q^{78} + 15275654q^{79} + 36576105q^{80} + 9034497q^{81} + 32025935q^{82} + 7826609q^{83} - 4922262q^{84} + 11836945q^{85} + 51649136q^{86} + 13579785q^{87} + 30223741q^{88} - 6436185q^{89} + 4753809q^{90} + 11633535q^{91} + 43357972q^{92} - 9383337q^{93} - 4494252q^{94} + 23741055q^{95} + 6585516q^{96} + 26377540q^{97} + 26517816q^{98} - 1285956q^{99} + O(q^{100}) \)

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