LMFDB - Embedded newform 289.10.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + \cdots + 245077910606835 $ x^12 - 5x^11 - 4542x^10 + 30079x^9 + 7481825x^8 - 58373994x^7 - 5553197164x^6 + 45662797046x^5 + 1825619566875x^4 - 13493392282513x^3 - 214257360688838x^2 + 1064197876989579*x + 245077910606835
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$41.9032$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+42.9032 q^{2} +45.1099 q^{3} +1328.68 q^{4} +608.765 q^{5} +1935.36 q^{6} -521.377 q^{7} +35038.3 q^{8} -17648.1 q^{9} +O(q^{10})$	\(q+42.9032 q^{2} +45.1099 q^{3} +1328.68 q^{4} +608.765 q^{5} +1935.36 q^{6} -521.377 q^{7} +35038.3 q^{8} -17648.1 q^{9} +26118.0 q^{10} +61800.5 q^{11} +59936.8 q^{12} +157939. q^{13} -22368.7 q^{14} +27461.3 q^{15} +822971. q^{16} -757160. q^{18} -327081. q^{19} +808857. q^{20} -23519.3 q^{21} +2.65144e6 q^{22} +1.00286e6 q^{23} +1.58058e6 q^{24} -1.58253e6 q^{25} +6.77607e6 q^{26} -1.68400e6 q^{27} -692745. q^{28} +6.67486e6 q^{29} +1.17818e6 q^{30} -8.67994e6 q^{31} +1.73684e7 q^{32} +2.78781e6 q^{33} -317396. q^{35} -2.34487e7 q^{36} +6.88467e6 q^{37} -1.40328e7 q^{38} +7.12459e6 q^{39} +2.13301e7 q^{40} +4.90825e6 q^{41} -1.00905e6 q^{42} -2.42986e7 q^{43} +8.21133e7 q^{44} -1.07435e7 q^{45} +4.30261e7 q^{46} +5.28966e7 q^{47} +3.71241e7 q^{48} -4.00818e7 q^{49} -6.78956e7 q^{50} +2.09850e8 q^{52} -4.52618e7 q^{53} -7.22491e7 q^{54} +3.76220e7 q^{55} -1.82682e7 q^{56} -1.47546e7 q^{57} +2.86373e8 q^{58} -2.13981e7 q^{59} +3.64874e7 q^{60} +1.97696e8 q^{61} -3.72397e8 q^{62} +9.20131e6 q^{63} +3.23800e8 q^{64} +9.61475e7 q^{65} +1.19606e8 q^{66} -2.13859e7 q^{67} +4.52391e7 q^{69} -1.36173e7 q^{70} +1.17030e8 q^{71} -6.18360e8 q^{72} +8.46531e7 q^{73} +2.95374e8 q^{74} -7.13878e7 q^{75} -4.34587e8 q^{76} -3.22214e7 q^{77} +3.05668e8 q^{78} +5.55650e8 q^{79} +5.00996e8 q^{80} +2.71402e8 q^{81} +2.10580e8 q^{82} +5.63701e8 q^{83} -3.12497e7 q^{84} -1.04249e9 q^{86} +3.01102e8 q^{87} +2.16539e9 q^{88} -4.63389e8 q^{89} -4.60933e8 q^{90} -8.23456e7 q^{91} +1.33249e9 q^{92} -3.91551e8 q^{93} +2.26943e9 q^{94} -1.99116e8 q^{95} +7.83488e8 q^{96} +1.16241e8 q^{97} -1.71964e9 q^{98} -1.09066e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) $ 12 * q + 17 * q^2 + 74 * q^3 + 2987 * q^4 + 454 * q^5 + 2674 * q^6 - 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9} - 2449 q^{10} + 152886 q^{11} + 41717 q^{12} + 23478 q^{13} + 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} - 2477218 q^{20} - 1395256 q^{21} + 2391095 q^{22} + 2012428 q^{23} + 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} + 3231638 q^{27} - 5978216 q^{28} + 12772842 q^{29} + 181633 q^{30} + 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} + 1352872 q^{37} + 3704404 q^{38} - 1380780 q^{39} + 44739331 q^{40} + 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} + 148233417 q^{44} - 79449336 q^{45} + 31855859 q^{46} + 133558002 q^{47} - 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} - 50215469 q^{54} - 91197532 q^{55} + 267350757 q^{56} + 49507694 q^{57} + 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} + 262041240 q^{61} - 314328847 q^{62} + 218532626 q^{63} + 595820098 q^{64} + 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} + 204290852 q^{71} - 208030791 q^{72} + 673538852 q^{73} + 1274510282 q^{74} + 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} + 165043245 q^{78} + 434002980 q^{79} + 599590757 q^{80} - 389011392 q^{81} - 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} - 262108460 q^{88} + 911678128 q^{89} - 2734590475 q^{90} - 560105446 q^{91} - 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} - 1116511966 q^{95} + 2204198979 q^{96} - 3589270998 q^{97} - 2677144485 q^{98} + 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 + 74 * q^3 + 2987 * q^4 + 454 * q^5 + 2674 * q^6 - 5524 * q^7 - 12036 * q^8 + 71898 * q^9 - 2449 * q^10 + 152886 * q^11 + 41717 * q^12 + 23478 * q^13 + 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 - 2477218 * q^20 - 1395256 * q^21 + 2391095 * q^22 + 2012428 * q^23 + 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 + 3231638 * q^27 - 5978216 * q^28 + 12772842 * q^29 + 181633 * q^30 + 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 + 1352872 * q^37 + 3704404 * q^38 - 1380780 * q^39 + 44739331 * q^40 + 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 + 148233417 * q^44 - 79449336 * q^45 + 31855859 * q^46 + 133558002 * q^47 - 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 - 50215469 * q^54 - 91197532 * q^55 + 267350757 * q^56 + 49507694 * q^57 + 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 + 262041240 * q^61 - 314328847 * q^62 + 218532626 * q^63 + 595820098 * q^64 + 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 + 204290852 * q^71 - 208030791 * q^72 + 673538852 * q^73 + 1274510282 * q^74 + 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 + 165043245 * q^78 + 434002980 * q^79 + 599590757 * q^80 - 389011392 * q^81 - 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 - 262108460 * q^88 + 911678128 * q^89 - 2734590475 * q^90 - 560105446 * q^91 - 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 - 1116511966 * q^95 + 2204198979 * q^96 - 3589270998 * q^97 - 2677144485 * q^98 + 2056683494 * q^99

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 $

$2$	42.9032	1.89607	0.948036	−	0.318164i	$-0.103066\pi$
$2$	42.9032	1.89607	0.948036	+	0.318164i	$0.103066\pi$
$3$	45.1099	0.321533	0.160767	−	0.986992i	$-0.448603\pi$
$3$	45.1099	0.321533	0.160767	+	0.986992i	$0.448603\pi$
$4$	1328.68	2.59509
$5$	608.765	0.435597	0.217798	−	0.975994i	$-0.430112\pi$
$5$	608.765	0.435597	0.217798	+	0.975994i	$0.430112\pi$
$6$	1935.36	0.609650
$7$	−521.377	−0.0820750	−0.0410375	−	0.999158i	$-0.513066\pi$
$7$	−521.377	−0.0820750	−0.0410375	+	0.999158i	$0.513066\pi$
$8$	35038.3	3.02440
$9$	−17648.1	−0.896616
$10$	26118.0	0.825923
$11$	61800.5	1.27270	0.636348	−	0.771402i	$-0.280444\pi$
$11$	61800.5	1.27270	0.636348	+	0.771402i	$0.280444\pi$
$12$	59936.8	0.834407
$13$	157939.	1.53371	0.766855	−	0.641820i	$-0.221821\pi$
$13$	157939.	1.53371	0.766855	+	0.641820i	$0.221821\pi$
$14$	−22368.7	−0.155620
$15$	27461.3	0.140059
$16$	822971.	3.13938
$17$	0	0
$17$	0	0
$18$	−757160.	−1.70005
$19$	−327081.	−0.575790	−0.287895	−	0.957662i	$-0.592955\pi$
$19$	−327081.	−0.575790	−0.287895	+	0.957662i	$0.592955\pi$
$20$	808857.	1.13041
$21$	−23519.3	−0.0263899
$22$	2.65144e6	2.41312
$23$	1.00286e6	0.747251	0.373626	−	0.927580i	$-0.378114\pi$
$23$	1.00286e6	0.747251	0.373626	+	0.927580i	$0.378114\pi$
$24$	1.58058e6	0.972444
$25$	−1.58253e6	−0.810255
$26$	6.77607e6	2.90802
$27$	−1.68400e6	−0.609826
$28$	−692745.	−0.212992
$29$	6.67486e6	1.75247	0.876236	−	0.481882i	$-0.160047\pi$
$29$	6.67486e6	1.75247	0.876236	+	0.481882i	$0.160047\pi$
$30$	1.17818e6	0.265562
$31$	−8.67994e6	−1.68806	−0.844032	−	0.536292i	$-0.819824\pi$
$31$	−8.67994e6	−1.68806	−0.844032	+	0.536292i	$0.819824\pi$
$32$	1.73684e7	2.92810
$33$	2.78781e6	0.409215
$34$	0	0
$35$	−317396.	−0.0357516
$36$	−2.34487e7	−2.32680
$37$	6.88467e6	0.603914	0.301957	−	0.953322i	$-0.402360\pi$
$37$	6.88467e6	0.603914	0.301957	+	0.953322i	$0.402360\pi$
$38$	−1.40328e7	−1.09174
$39$	7.12459e6	0.493139
$40$	2.13301e7	1.31742
$41$	4.90825e6	0.271269	0.135634	−	0.990759i	$-0.456693\pi$
$41$	4.90825e6	0.271269	0.135634	+	0.990759i	$0.456693\pi$
$42$	−1.00905e6	−0.0500370
$43$	−2.42986e7	−1.08386	−0.541931	−	0.840423i	$-0.682307\pi$
$43$	−2.42986e7	−1.08386	−0.541931	+	0.840423i	$0.682307\pi$
$44$	8.21133e7	3.30276
$45$	−1.07435e7	−0.390563
$46$	4.30261e7	1.41684
$47$	5.28966e7	1.58120	0.790601	−	0.612332i	$-0.209769\pi$
$47$	5.28966e7	1.58120	0.790601	+	0.612332i	$0.209769\pi$
$48$	3.71241e7	1.00942
$49$	−4.00818e7	−0.993264
$50$	−6.78956e7	−1.53630
$51$	0	0
$52$	2.09850e8	3.98011
$53$	−4.52618e7	−0.787935	−0.393967	−	0.919124i	$-0.628898\pi$
$53$	−4.52618e7	−0.787935	−0.393967	+	0.919124i	$0.628898\pi$
$54$	−7.22491e7	−1.15627
$55$	3.76220e7	0.554383
$56$	−1.82682e7	−0.248227
$57$	−1.47546e7	−0.185136
$58$	2.86373e8	3.32281
$59$	−2.13981e7	−0.229901	−0.114950	−	0.993371i	$-0.536671\pi$
$59$	−2.13981e7	−0.229901	−0.114950	+	0.993371i	$0.536671\pi$
$60$	3.64874e7	0.363465
$61$	1.97696e8	1.82816	0.914079	−	0.405537i	$-0.132915\pi$
$61$	1.97696e8	1.82816	0.914079	+	0.405537i	$0.132915\pi$
$62$	−3.72397e8	−3.20069
$63$	9.20131e6	0.0735898
$64$	3.23800e8	2.41250
$65$	9.61475e7	0.668079
$66$	1.19606e8	0.775900
$67$	−2.13859e7	−0.129655	−0.0648276	−	0.997896i	$-0.520650\pi$
$67$	−2.13859e7	−0.129655	−0.0648276	+	0.997896i	$0.520650\pi$
$68$	0	0
$69$	4.52391e7	0.240266
$70$	−1.36173e7	−0.0677876
$71$	1.17030e8	0.546555	0.273277	−	0.961935i	$-0.411892\pi$
$71$	1.17030e8	0.546555	0.273277	+	0.961935i	$0.411892\pi$
$72$	−6.18360e8	−2.71172
$73$	8.46531e7	0.348891	0.174445	−	0.984667i	$-0.444187\pi$
$73$	8.46531e7	0.348891	0.174445	+	0.984667i	$0.444187\pi$
$74$	2.95374e8	1.14506
$75$	−7.13878e7	−0.260524
$76$	−4.34587e8	−1.49423
$77$	−3.22214e7	−0.104457
$78$	3.05668e8	0.935027
$79$	5.55650e8	1.60502	0.802509	−	0.596640i	$-0.203498\pi$
$79$	5.55650e8	1.60502	0.802509	+	0.596640i	$0.203498\pi$
$80$	5.00996e8	1.36751
$81$	2.71402e8	0.700537
$82$	2.10580e8	0.514344
$83$	5.63701e8	1.30376	0.651880	−	0.758322i	$-0.273981\pi$
$83$	5.63701e8	1.30376	0.651880	+	0.758322i	$0.273981\pi$
$84$	−3.12497e7	−0.0684839
$85$	0	0
$86$	−1.04249e9	−2.05508
$87$	3.01102e8	0.563478
$88$	2.16539e9	3.84914
$89$	−4.63389e8	−0.782872	−0.391436	−	0.920205i	$-0.628022\pi$
$89$	−4.63389e8	−0.782872	−0.391436	+	0.920205i	$0.628022\pi$
$90$	−4.60933e8	−0.740536
$91$	−8.23456e7	−0.125879
$92$	1.33249e9	1.93918
$93$	−3.91551e8	−0.542769
$94$	2.26943e9	2.99807
$95$	−1.99116e8	−0.250813
$96$	7.83488e8	0.941482
$97$	1.16241e8	0.133317	0.0666584	−	0.997776i	$-0.478766\pi$
$97$	1.16241e8	0.133317	0.0666584	+	0.997776i	$0.478766\pi$
$98$	−1.71964e9	−1.88330
$99$	−1.09066e9	−1.14112
$100$	−2.10268e9	−2.10268
$101$	−8.16304e8	−0.780559	−0.390280	−	0.920696i	$-0.627622\pi$
$101$	−8.16304e8	−0.780559	−0.390280	+	0.920696i	$0.627622\pi$
$102$	0	0
$103$	1.08441e8	0.0949351	0.0474675	−	0.998873i	$-0.484885\pi$
$103$	1.08441e8	0.0949351	0.0474675	+	0.998873i	$0.484885\pi$
$104$	5.53391e9	4.63855
$105$	−1.43177e7	−0.0114953
$106$	−1.94187e9	−1.49398
$107$	−1.90252e9	−1.40314	−0.701571	−	0.712600i	$-0.747518\pi$
$107$	−1.90252e9	−1.40314	−0.701571	+	0.712600i	$0.747518\pi$
$108$	−2.23751e9	−1.58255
$109$	−2.19601e9	−1.49010	−0.745049	−	0.667010i	$-0.767574\pi$
$109$	−2.19601e9	−1.49010	−0.745049	+	0.667010i	$0.767574\pi$
$110$	1.61410e9	1.05115
$111$	3.10567e8	0.194179
$112$	−4.29078e8	−0.257665
$113$	−1.76648e8	−0.101919	−0.0509595	−	0.998701i	$-0.516228\pi$
$113$	−1.76648e8	−0.101919	−0.0509595	+	0.998701i	$0.516228\pi$
$114$	−6.33019e8	−0.351031
$115$	6.10509e8	0.325500
$116$	8.86878e9	4.54782
$117$	−2.78732e9	−1.37515
$118$	−9.18046e8	−0.435908
$119$	0	0
$120$	9.62200e8	0.423594
$121$	1.46136e9	0.619757
$122$	8.48179e9	3.46632
$123$	2.21411e8	0.0872219
$124$	−1.15329e10	−4.38067
$125$	−2.15238e9	−0.788542
$126$	3.94766e8	0.139531
$127$	2.70081e8	0.0921248	0.0460624	−	0.998939i	$-0.485333\pi$
$127$	2.70081e8	0.0921248	0.0460624	+	0.998939i	$0.485333\pi$
$128$	4.99943e9	1.64617
$129$	−1.09611e9	−0.348498
$130$	4.12504e9	1.26673
$131$	−9.89524e8	−0.293566	−0.146783	−	0.989169i	$-0.546892\pi$
$131$	−9.89524e8	−0.293566	−0.146783	+	0.989169i	$0.546892\pi$
$132$	3.70412e9	1.06195
$133$	1.70533e8	0.0472580
$134$	−9.17522e8	−0.245836
$135$	−1.02516e9	−0.265638
$136$	0	0
$137$	−1.50274e9	−0.364452	−0.182226	−	0.983257i	$-0.558330\pi$
$137$	−1.50274e9	−0.364452	−0.182226	+	0.983257i	$0.558330\pi$
$138$	1.94090e9	0.455562
$139$	5.26249e8	0.119571	0.0597853	−	0.998211i	$-0.480958\pi$
$139$	5.26249e8	0.119571	0.0597853	+	0.998211i	$0.480958\pi$
$140$	−4.21719e8	−0.0927785
$141$	2.38616e9	0.508409
$142$	5.02095e9	1.03631
$143$	9.76069e9	1.95195
$144$	−1.45239e10	−2.81482
$145$	4.06342e9	0.763372
$146$	3.63189e9	0.661522
$147$	−1.80808e9	−0.319367
$148$	9.14754e9	1.56721
$149$	−7.33464e9	−1.21910	−0.609552	−	0.792746i	$-0.708651\pi$
$149$	−7.33464e9	−1.21910	−0.609552	+	0.792746i	$0.708651\pi$
$150$	−3.06276e9	−0.493972
$151$	5.02244e9	0.786174	0.393087	−	0.919501i	$-0.371407\pi$
$151$	5.02244e9	0.786174	0.393087	+	0.919501i	$0.371407\pi$
$152$	−1.14604e10	−1.74142
$153$	0	0
$154$	−1.38240e9	−0.198057
$155$	−5.28405e9	−0.735316
$156$	9.46633e9	1.27974
$157$	−8.86110e9	−1.16396	−0.581981	−	0.813202i	$-0.697722\pi$
$157$	−8.86110e9	−1.16396	−0.581981	+	0.813202i	$0.697722\pi$
$158$	2.38392e10	3.04323
$159$	−2.04175e9	−0.253347
$160$	1.05733e10	1.27547
$161$	−5.22870e8	−0.0613306
$162$	1.16440e10	1.32827
$163$	1.42326e10	1.57921	0.789604	−	0.613616i	$-0.210286\pi$
$163$	1.42326e10	1.57921	0.789604	+	0.613616i	$0.210286\pi$
$164$	6.52151e9	0.703965
$165$	1.69712e9	0.178253
$166$	2.41846e10	2.47202
$167$	−1.59934e9	−0.159117	−0.0795584	−	0.996830i	$-0.525351\pi$
$167$	−1.59934e9	−0.159117	−0.0795584	+	0.996830i	$0.525351\pi$
$168$	−8.24076e8	−0.0798134
$169$	1.43401e10	1.35227
$170$	0	0
$171$	5.77236e9	0.516263
$172$	−3.22852e10	−2.81271
$173$	−1.01489e10	−0.861417	−0.430708	−	0.902491i	$-0.641736\pi$
$173$	−1.01489e10	−0.861417	−0.430708	+	0.902491i	$0.641736\pi$
$174$	1.29182e10	1.06840
$175$	8.25095e8	0.0665017
$176$	5.08600e10	3.99548
$177$	−9.65265e8	−0.0739208
$178$	−1.98809e10	−1.48438
$179$	−5.75525e9	−0.419011	−0.209506	−	0.977807i	$-0.567185\pi$
$179$	−5.75525e9	−0.419011	−0.209506	+	0.977807i	$0.567185\pi$
$180$	−1.42748e10	−1.01355
$181$	8.62193e9	0.597105	0.298553	−	0.954393i	$-0.403496\pi$
$181$	8.62193e9	0.597105	0.298553	+	0.954393i	$0.403496\pi$
$182$	−3.53289e9	−0.238676
$183$	8.91804e9	0.587814
$184$	3.51387e10	2.25998
$185$	4.19115e9	0.263063
$186$	−1.67988e10	−1.02913
$187$	0	0
$188$	7.02828e10	4.10335
$189$	8.78000e8	0.0500514
$190$	−8.54270e9	−0.475558
$191$	−1.83321e9	−0.0996696	−0.0498348	−	0.998757i	$-0.515869\pi$
$191$	−1.83321e9	−0.0996696	−0.0498348	+	0.998757i	$0.515869\pi$
$192$	1.46066e10	0.775699
$193$	1.17253e9	0.0608298	0.0304149	−	0.999537i	$-0.490317\pi$
$193$	1.17253e9	0.0608298	0.0304149	+	0.999537i	$0.490317\pi$
$194$	4.98709e9	0.252778
$195$	4.33720e9	0.214810
$196$	−5.32560e10	−2.57760
$197$	−8.26722e9	−0.391076	−0.195538	−	0.980696i	$-0.562645\pi$
$197$	−8.26722e9	−0.391076	−0.195538	+	0.980696i	$0.562645\pi$
$198$	−4.67929e10	−2.16365
$199$	−2.04984e10	−0.926577	−0.463289	−	0.886207i	$-0.653331\pi$
$199$	−2.04984e10	−0.926577	−0.463289	+	0.886207i	$0.653331\pi$
$200$	−5.54492e10	−2.45053
$201$	−9.64714e8	−0.0416885
$202$	−3.50221e10	−1.48000
$203$	−3.48012e9	−0.143834
$204$	0	0
$205$	2.98797e9	0.118164
$206$	4.65247e9	0.180004
$207$	−1.76986e10	−0.669998
$208$	1.29979e11	4.81490
$209$	−2.02138e10	−0.732807
$210$	−6.14276e8	−0.0217960
$211$	−2.19986e10	−0.764053	−0.382027	−	0.924151i	$-0.624774\pi$
$211$	−2.19986e10	−0.764053	−0.382027	+	0.924151i	$0.624774\pi$
$212$	−6.01386e10	−2.04476
$213$	5.27920e9	0.175736
$214$	−8.16240e10	−2.66046
$215$	−1.47922e10	−0.472127
$216$	−5.90046e10	−1.84435
$217$	4.52552e9	0.138548
$218$	−9.42158e10	−2.82533
$219$	3.81869e9	0.112180
$220$	4.99877e10	1.43867
$221$	0	0
$222$	1.33243e10	0.368176
$223$	−3.91109e10	−1.05907	−0.529536	−	0.848287i	$-0.677634\pi$
$223$	−3.91109e10	−1.05907	−0.529536	+	0.848287i	$0.677634\pi$
$224$	−9.05550e9	−0.240324
$225$	2.79286e10	0.726488
$226$	−7.57875e9	−0.193246
$227$	−1.31363e10	−0.328366	−0.164183	−	0.986430i	$-0.552499\pi$
$227$	−1.31363e10	−0.328366	−0.164183	+	0.986430i	$0.552499\pi$
$228$	−1.96042e10	−0.480443
$229$	5.92730e10	1.42429	0.712143	−	0.702034i	$-0.247725\pi$
$229$	5.92730e10	1.42429	0.712143	+	0.702034i	$0.247725\pi$
$230$	2.61928e10	0.617172
$231$	−1.45350e9	−0.0335863
$232$	2.33876e11	5.30017
$233$	−1.02513e10	−0.227865	−0.113933	−	0.993488i	$-0.536345\pi$
$233$	−1.02513e10	−0.227865	−0.113933	+	0.993488i	$0.536345\pi$
$234$	−1.19585e11	−2.60738
$235$	3.22016e10	0.688766
$236$	−2.84313e10	−0.596612
$237$	2.50653e10	0.516067
$238$	0	0
$239$	−7.75597e10	−1.53761	−0.768804	−	0.639484i	$-0.779148\pi$
$239$	−7.75597e10	−1.53761	−0.768804	+	0.639484i	$0.779148\pi$
$240$	2.25999e10	0.439699
$241$	9.35303e10	1.78598	0.892988	−	0.450081i	$-0.148605\pi$
$241$	9.35303e10	1.78598	0.892988	+	0.450081i	$0.148605\pi$
$242$	6.26968e10	1.17510
$243$	4.53891e10	0.835072
$244$	2.62675e11	4.74422
$245$	−2.44004e10	−0.432663
$246$	9.49922e9	0.165379
$247$	−5.16587e10	−0.883095
$248$	−3.04131e11	−5.10538
$249$	2.54285e10	0.419202
$250$	−9.23441e10	−1.49513
$251$	3.66158e9	0.0582287	0.0291143	−	0.999576i	$-0.490731\pi$
$251$	3.66158e9	0.0582287	0.0291143	+	0.999576i	$0.490731\pi$
$252$	1.22256e10	0.190972
$253$	6.19775e10	0.951024
$254$	1.15873e10	0.174675
$255$	0	0
$256$	4.87056e10	0.708760
$257$	3.77419e10	0.539665	0.269833	−	0.962907i	$-0.413032\pi$
$257$	3.77419e10	0.539665	0.269833	+	0.962907i	$0.413032\pi$
$258$	−4.70266e10	−0.660777
$259$	−3.58951e9	−0.0495662
$260$	1.27750e11	1.73372
$261$	−1.17799e11	−1.57130
$262$	−4.24537e10	−0.556621
$263$	−9.23359e10	−1.19006	−0.595031	−	0.803703i	$-0.702860\pi$
$263$	−9.23359e10	−1.19006	−0.595031	+	0.803703i	$0.702860\pi$
$264$	9.76804e10	1.23763
$265$	−2.75538e10	−0.343222
$266$	7.31640e9	0.0896045
$267$	−2.09034e10	−0.251720
$268$	−2.84150e10	−0.336466
$269$	−1.61183e11	−1.87686	−0.938432	−	0.345465i	$-0.887721\pi$
$269$	−1.61183e11	−1.87686	−0.938432	+	0.345465i	$0.887721\pi$
$270$	−4.39827e10	−0.503669
$271$	1.65120e10	0.185968	0.0929839	−	0.995668i	$-0.470359\pi$
$271$	1.65120e10	0.185968	0.0929839	+	0.995668i	$0.470359\pi$
$272$	0	0
$273$	−3.71460e9	−0.0404744
$274$	−6.44722e10	−0.691027
$275$	−9.78012e10	−1.03121
$276$	6.01084e10	0.623512
$277$	−1.44923e11	−1.47904	−0.739519	−	0.673136i	$-0.764947\pi$
$277$	−1.44923e11	−1.47904	−0.739519	+	0.673136i	$0.764947\pi$
$278$	2.25778e10	0.226714
$279$	1.53184e11	1.51355
$280$	−1.11210e10	−0.108127
$281$	9.07854e10	0.868635	0.434318	−	0.900760i	$-0.356990\pi$
$281$	9.07854e10	0.868635	0.434318	+	0.900760i	$0.356990\pi$
$282$	1.02374e11	0.963980
$283$	−8.89698e10	−0.824525	−0.412262	−	0.911065i	$-0.635261\pi$
$283$	−8.89698e10	−0.824525	−0.412262	+	0.911065i	$0.635261\pi$
$284$	1.55495e11	1.41836
$285$	−8.98209e9	−0.0806446
$286$	4.18765e11	3.70103
$287$	−2.55905e9	−0.0222644
$288$	−3.06520e11	−2.62538
$289$	0	0
$290$	1.74334e11	1.44741
$291$	5.24360e9	0.0428658
$292$	1.12477e11	0.905402
$293$	1.35425e11	1.07348	0.536742	−	0.843746i	$-0.319655\pi$
$293$	1.35425e11	1.07348	0.536742	+	0.843746i	$0.319655\pi$
$294$	−7.75726e10	−0.605543
$295$	−1.30264e10	−0.100144
$296$	2.41227e11	1.82648
$297$	−1.04072e11	−0.776123
$298$	−3.14680e11	−2.31151
$299$	1.58391e11	1.14607
$300$	−9.48518e10	−0.676083
$301$	1.26688e10	0.0889579
$302$	2.15479e11	1.49064
$303$	−3.68234e10	−0.250976
$304$	−2.69178e11	−1.80763
$305$	1.20350e11	0.796340
$306$	0	0
$307$	1.86260e11	1.19673	0.598365	−	0.801223i	$-0.295817\pi$
$307$	1.86260e11	1.19673	0.598365	+	0.801223i	$0.295817\pi$
$308$	−4.28120e10	−0.271074
$309$	4.89177e9	0.0305248
$310$	−2.26702e11	−1.39421
$311$	−8.60973e10	−0.521876	−0.260938	−	0.965356i	$-0.584032\pi$
$311$	−8.60973e10	−0.521876	−0.260938	+	0.965356i	$0.584032\pi$
$312$	2.49634e11	1.49145
$313$	−1.46998e11	−0.865689	−0.432845	−	0.901469i	$-0.642490\pi$
$313$	−1.46998e11	−0.865689	−0.432845	+	0.901469i	$0.642490\pi$
$314$	−3.80169e11	−2.20696
$315$	5.60144e9	0.0320555
$316$	7.38284e11	4.16516
$317$	−7.37113e10	−0.409984	−0.204992	−	0.978764i	$-0.565717\pi$
$317$	−7.37113e10	−0.409984	−0.204992	+	0.978764i	$0.565717\pi$
$318$	−8.75977e10	−0.480365
$319$	4.12510e11	2.23037
$320$	1.97118e11	1.05088
$321$	−8.58223e10	−0.451157
$322$	−2.24328e10	−0.116287
$323$	0	0
$324$	3.60608e11	1.81795
$325$	−2.49943e11	−1.24270
$326$	6.10623e11	2.99429
$327$	−9.90617e10	−0.479116
$328$	1.71977e11	0.820423
$329$	−2.75791e10	−0.129777
$330$	7.28121e10	0.337980
$331$	−7.65947e10	−0.350730	−0.175365	−	0.984503i	$-0.556111\pi$
$331$	−7.65947e10	−0.350730	−0.175365	+	0.984503i	$0.556111\pi$
$332$	7.48981e11	3.38337
$333$	−1.21501e11	−0.541479
$334$	−6.86167e10	−0.301697
$335$	−1.30190e10	−0.0564774
$336$	−1.93557e10	−0.0828479
$337$	−6.61967e9	−0.0279577	−0.0139789	−	0.999902i	$-0.504450\pi$
$337$	−6.61967e9	−0.0279577	−0.0139789	+	0.999902i	$0.504450\pi$
$338$	6.15236e11	2.56399
$339$	−7.96856e9	−0.0327703
$340$	0	0
$341$	−5.36425e11	−2.14839
$342$	2.47653e11	0.978871
$343$	4.19372e10	0.163597
$344$	−8.51384e11	−3.27803
$345$	2.75400e10	0.104659
$346$	−4.35422e11	−1.63331
$347$	3.89348e11	1.44163	0.720817	−	0.693126i	$-0.243767\pi$
$347$	3.89348e11	1.44163	0.720817	+	0.693126i	$0.243767\pi$
$348$	4.00070e11	1.46227
$349$	2.64912e11	0.955846	0.477923	−	0.878402i	$-0.341390\pi$
$349$	2.64912e11	0.955846	0.477923	+	0.878402i	$0.341390\pi$
$350$	3.53992e10	0.126092
$351$	−2.65969e11	−0.935295
$352$	1.07338e12	3.72658
$353$	−3.76148e11	−1.28935	−0.644677	−	0.764455i	$-0.723008\pi$
$353$	−3.76148e11	−1.28935	−0.644677	+	0.764455i	$0.723008\pi$
$354$	−4.14129e10	−0.140159
$355$	7.12436e10	0.238077
$356$	−6.15698e11	−2.03162
$357$	0	0
$358$	−2.46919e11	−0.794475
$359$	−3.37031e11	−1.07089	−0.535445	−	0.844570i	$-0.679856\pi$
$359$	−3.37031e11	−1.07089	−0.535445	+	0.844570i	$0.679856\pi$
$360$	−3.76436e11	−1.18122
$361$	−2.15706e11	−0.668465
$362$	3.69908e11	1.13215
$363$	6.59216e10	0.199273
$364$	−1.09411e11	−0.326667
$365$	5.15338e10	0.151976
$366$	3.82613e11	1.11454
$367$	−3.17691e11	−0.914128	−0.457064	−	0.889434i	$-0.651099\pi$
$367$	−3.17691e11	−0.914128	−0.457064	+	0.889434i	$0.651099\pi$
$368$	8.25327e11	2.34591
$369$	−8.66213e10	−0.243224
$370$	1.79814e11	0.498786
$371$	2.35985e10	0.0646697
$372$	−5.20248e11	−1.40853
$373$	5.76449e11	1.54195	0.770976	−	0.636864i	$-0.219769\pi$
$373$	5.76449e11	1.54195	0.770976	+	0.636864i	$0.219769\pi$
$374$	0	0
$375$	−9.70938e10	−0.253543
$376$	1.85341e12	4.78218
$377$	1.05422e12	2.68778
$378$	3.76690e10	0.0949011
$379$	−6.26659e11	−1.56011	−0.780054	−	0.625712i	$-0.784809\pi$
$379$	−6.26659e11	−1.56011	−0.780054	+	0.625712i	$0.784809\pi$
$380$	−2.64562e11	−0.650880
$381$	1.21833e10	0.0296212
$382$	−7.86507e10	−0.188981
$383$	−2.84238e11	−0.674976	−0.337488	−	0.941330i	$-0.609577\pi$
$383$	−2.84238e11	−0.674976	−0.337488	+	0.941330i	$0.609577\pi$
$384$	2.25524e11	0.529299
$385$	−1.96153e10	−0.0455010
$386$	5.03053e10	0.115338
$387$	4.28825e11	0.971808
$388$	1.54447e11	0.345968
$389$	1.71613e11	0.379994	0.189997	−	0.981785i	$-0.439152\pi$
$389$	1.71613e11	0.379994	0.189997	+	0.981785i	$0.439152\pi$
$390$	1.86080e11	0.407295
$391$	0	0
$392$	−1.40440e12	−3.00402
$393$	−4.46373e10	−0.0943912
$394$	−3.54690e11	−0.741509
$395$	3.38261e11	0.699141
$396$	−1.44914e12	−2.96131
$397$	−3.18468e11	−0.643441	−0.321720	−	0.946835i	$-0.604261\pi$
$397$	−3.18468e11	−0.643441	−0.321720	+	0.946835i	$0.604261\pi$
$398$	−8.79448e11	−1.75686
$399$	7.69271e9	0.0151950
$400$	−1.30238e12	−2.54370
$401$	1.86235e11	0.359677	0.179838	−	0.983696i	$-0.442443\pi$
$401$	1.86235e11	0.359677	0.179838	+	0.983696i	$0.442443\pi$
$402$	−4.13893e10	−0.0790443
$403$	−1.37090e12	−2.58900
$404$	−1.08461e12	−2.02562
$405$	1.65220e11	0.305152
$406$	−1.49308e11	−0.272720
$407$	4.25476e11	0.768600
$408$	0	0
$409$	4.24350e11	0.749842	0.374921	−	0.927057i	$-0.377670\pi$
$409$	4.24350e11	0.749842	0.374921	+	0.927057i	$0.377670\pi$
$410$	1.28194e11	0.224047
$411$	−6.77883e10	−0.117184
$412$	1.44084e11	0.246365
$413$	1.11565e10	0.0188691
$414$	−7.59328e11	−1.27036
$415$	3.43162e11	0.567914
$416$	2.74315e12	4.49085
$417$	2.37390e10	0.0384460
$418$	−8.67236e11	−1.38945
$419$	5.26304e11	0.834207	0.417103	−	0.908859i	$-0.363045\pi$
$419$	5.26304e11	0.834207	0.417103	+	0.908859i	$0.363045\pi$
$420$	−1.90237e10	−0.0298314
$421$	3.44361e10	0.0534250	0.0267125	−	0.999643i	$-0.491496\pi$
$421$	3.44361e10	0.0534250	0.0267125	+	0.999643i	$0.491496\pi$
$422$	−9.43809e11	−1.44870
$423$	−9.33524e11	−1.41773
$424$	−1.58590e12	−2.38303
$425$	0	0
$426$	2.26494e11	0.333207
$427$	−1.03074e11	−0.150046
$428$	−2.52784e12	−3.64127
$429$	4.40304e11	0.627617
$430$	−6.34631e11	−0.895186
$431$	−1.08210e12	−1.51050	−0.755248	−	0.655440i	$-0.772483\pi$
$431$	−1.08210e12	−1.51050	−0.755248	+	0.655440i	$0.772483\pi$
$432$	−1.38588e12	−1.91448
$433$	−9.55386e11	−1.30612	−0.653061	−	0.757306i	$-0.726515\pi$
$433$	−9.55386e11	−1.30612	−0.653061	+	0.757306i	$0.726515\pi$
$434$	1.94159e11	0.262697
$435$	1.83301e11	0.245449
$436$	−2.91780e12	−3.86693
$437$	−3.28018e11	−0.430260
$438$	1.63834e11	0.212701
$439$	−7.09198e11	−0.911334	−0.455667	−	0.890150i	$-0.650599\pi$
$439$	−7.09198e11	−0.911334	−0.455667	+	0.890150i	$0.650599\pi$
$440$	1.31821e12	1.67667
$441$	7.07367e11	0.890576
$442$	0	0
$443$	−8.77067e11	−1.08197	−0.540986	−	0.841032i	$-0.681949\pi$
$443$	−8.77067e11	−1.08197	−0.540986	+	0.841032i	$0.681949\pi$
$444$	4.12645e11	0.503910
$445$	−2.82095e11	−0.341017
$446$	−1.67798e12	−2.00808
$447$	−3.30865e11	−0.391983
$448$	−1.68822e11	−0.198006
$449$	3.55376e11	0.412648	0.206324	−	0.978484i	$-0.433850\pi$
$449$	3.55376e11	0.412648	0.206324	+	0.978484i	$0.433850\pi$
$450$	1.19823e12	1.37747
$451$	3.03332e11	0.345243
$452$	−2.34709e11	−0.264488
$453$	2.26562e11	0.252781
$454$	−5.63591e11	−0.622605
$455$	−5.01291e10	−0.0548326
$456$	−5.16977e11	−0.559924
$457$	7.35302e11	0.788575	0.394288	−	0.918987i	$-0.370991\pi$
$457$	7.35302e11	0.788575	0.394288	+	0.918987i	$0.370991\pi$
$458$	2.54300e12	2.70055
$459$	0	0
$460$	8.11173e11	0.844701
$461$	−1.52864e12	−1.57634	−0.788170	−	0.615457i	$-0.788971\pi$
$461$	−1.52864e12	−1.57634	−0.788170	+	0.615457i	$0.788971\pi$
$462$	−6.23599e10	−0.0636820
$463$	9.71471e11	0.982461	0.491230	−	0.871030i	$-0.336547\pi$
$463$	9.71471e11	0.982461	0.491230	+	0.871030i	$0.336547\pi$
$464$	5.49321e12	5.50168
$465$	−2.38363e11	−0.236429
$466$	−4.39814e11	−0.432049
$467$	−1.42256e12	−1.38402	−0.692012	−	0.721886i	$-0.743275\pi$
$467$	−1.42256e12	−1.38402	−0.692012	+	0.721886i	$0.743275\pi$
$468$	−3.70346e12	−3.56863
$469$	1.11501e10	0.0106415
$470$	1.38155e12	1.30595
$471$	−3.99723e11	−0.374253
$472$	−7.49753e11	−0.695311
$473$	−1.50167e12	−1.37943
$474$	1.07538e12	0.978499
$475$	5.17616e11	0.466537
$476$	0	0
$477$	7.98784e11	0.706475
$478$	−3.32756e12	−2.91542
$479$	1.72566e12	1.49777	0.748884	−	0.662701i	$-0.230590\pi$
$479$	1.72566e12	1.49777	0.748884	+	0.662701i	$0.230590\pi$
$480$	4.76960e11	0.410107
$481$	1.08735e12	0.926229
$482$	4.01275e12	3.38634
$483$	−2.35866e10	−0.0197199
$484$	1.94168e12	1.60832
$485$	7.07632e10	0.0580724
$486$	1.94734e12	1.58336
$487$	−1.49100e12	−1.20115	−0.600577	−	0.799567i	$-0.705062\pi$
$487$	−1.49100e12	−1.20115	−0.600577	+	0.799567i	$0.705062\pi$
$488$	6.92694e12	5.52907
$489$	6.42030e11	0.507768
$490$	−1.04685e12	−0.820359
$491$	1.24376e12	0.965765	0.482882	−	0.875685i	$-0.339590\pi$
$491$	1.24376e12	0.965765	0.482882	+	0.875685i	$0.339590\pi$
$492$	2.94185e11	0.226348
$493$	0	0
$494$	−2.21633e12	−1.67441
$495$	−6.63957e11	−0.497069
$496$	−7.14333e12	−5.29948
$497$	−6.10166e10	−0.0448585
$498$	1.09096e12	0.794838
$499$	−1.00661e12	−0.726789	−0.363395	−	0.931635i	$-0.618382\pi$
$499$	−1.00661e12	−0.726789	−0.363395	+	0.931635i	$0.618382\pi$
$500$	−2.85984e12	−2.04633
$501$	−7.21460e10	−0.0511614
$502$	1.57093e11	0.110406
$503$	1.23875e11	0.0862838	0.0431419	−	0.999069i	$-0.486263\pi$
$503$	1.23875e11	0.0862838	0.0431419	+	0.999069i	$0.486263\pi$
$504$	3.22399e11	0.222565
$505$	−4.96938e11	−0.340009
$506$	2.65903e12	1.80321
$507$	6.46881e11	0.434799
$508$	3.58852e11	0.239072
$509$	3.20582e11	0.211694	0.105847	−	0.994382i	$-0.466245\pi$
$509$	3.20582e11	0.211694	0.105847	+	0.994382i	$0.466245\pi$
$510$	0	0
$511$	−4.41362e10	−0.0286352
$512$	−4.70080e11	−0.302313
$513$	5.50805e11	0.351132
$514$	1.61925e12	1.02324
$515$	6.60152e10	0.0413534
$516$	−1.45638e12	−0.904382
$517$	3.26903e12	2.01239
$518$	−1.54001e11	−0.0939811
$519$	−4.57818e11	−0.276974
$520$	3.36885e12	2.02054
$521$	−1.33721e12	−0.795114	−0.397557	−	0.917578i	$-0.630142\pi$
$521$	−1.33721e12	−0.795114	−0.397557	+	0.917578i	$0.630142\pi$
$522$	−5.05393e12	−2.97929
$523$	−1.12920e12	−0.659951	−0.329975	−	0.943990i	$-0.607040\pi$
$523$	−1.12920e12	−0.659951	−0.329975	+	0.943990i	$0.607040\pi$
$524$	−1.31476e12	−0.761828
$525$	3.72199e10	0.0213825
$526$	−3.96150e12	−2.25644
$527$	0	0
$528$	2.29429e12	1.28468
$529$	−7.95417e11	−0.441616
$530$	−1.18215e12	−0.650773
$531$	3.77635e11	0.206133
$532$	2.26584e11	0.122639
$533$	7.75202e11	0.416047
$534$	−8.96824e11	−0.477278
$535$	−1.15819e12	−0.611204
$536$	−7.49325e11	−0.392129
$537$	−2.59619e11	−0.134726
$538$	−6.91524e12	−3.55867
$539$	−2.47707e12	−1.26412
$540$	−1.36212e12	−0.689354
$541$	−1.33317e12	−0.669111	−0.334555	−	0.942376i	$-0.608586\pi$
$541$	−1.33317e12	−0.669111	−0.334555	+	0.942376i	$0.608586\pi$
$542$	7.08417e11	0.352608
$543$	3.88934e11	0.191989
$544$	0	0
$545$	−1.33685e12	−0.649082
$546$	−1.59368e11	−0.0767423
$547$	−1.05771e11	−0.0505152	−0.0252576	−	0.999681i	$-0.508041\pi$
$547$	−1.05771e11	−0.0505152	−0.0252576	+	0.999681i	$0.508041\pi$
$548$	−1.99666e12	−0.945784
$549$	−3.48896e12	−1.63916
$550$	−4.19598e12	−1.95525
$551$	−2.18322e12	−1.00906
$552$	1.58510e12	0.726660
$553$	−2.89703e11	−0.131732
$554$	−6.21767e12	−2.80436
$555$	1.89062e11	0.0845836
$556$	6.99218e11	0.310296
$557$	1.73381e12	0.763227	0.381614	−	0.924322i	$-0.375369\pi$
$557$	1.73381e12	0.763227	0.381614	+	0.924322i	$0.375369\pi$
$558$	6.57210e12	2.86979
$559$	−3.83769e12	−1.66233
$560$	−2.61208e11	−0.112238
$561$	0	0
$562$	3.89498e12	1.64699
$563$	1.47444e12	0.618501	0.309250	−	0.950981i	$-0.399922\pi$
$563$	1.47444e12	0.618501	0.309250	+	0.950981i	$0.399922\pi$
$564$	3.17045e12	1.31936
$565$	−1.07537e11	−0.0443956
$566$	−3.81709e12	−1.56336
$567$	−1.41503e11	−0.0574966
$568$	4.10053e12	1.65300
$569$	−2.62398e12	−1.04943	−0.524716	−	0.851277i	$-0.675829\pi$
$569$	−2.62398e12	−1.04943	−0.524716	+	0.851277i	$0.675829\pi$
$570$	−3.85360e11	−0.152908
$571$	1.79653e12	0.707250	0.353625	−	0.935387i	$-0.384949\pi$
$571$	1.79653e12	0.707250	0.353625	+	0.935387i	$0.384949\pi$
$572$	1.29689e13	5.06547
$573$	−8.26961e10	−0.0320471
$574$	−1.09791e11	−0.0422148
$575$	−1.58706e12	−0.605464
$576$	−5.71446e12	−2.16309
$577$	3.73704e12	1.40358	0.701789	−	0.712385i	$-0.252385\pi$
$577$	3.73704e12	1.40358	0.701789	+	0.712385i	$0.252385\pi$
$578$	0	0
$579$	5.28927e10	0.0195588
$580$	5.39900e12	1.98101
$581$	−2.93901e11	−0.107006
$582$	2.24967e11	0.0812766
$583$	−2.79720e12	−1.00280
$584$	2.96610e12	1.05518
$585$	−1.69682e12	−0.599011
$586$	5.81018e12	2.03540
$587$	2.29209e12	0.796818	0.398409	−	0.917208i	$-0.369562\pi$
$587$	2.29209e12	0.796818	0.398409	+	0.917208i	$0.369562\pi$
$588$	−2.40237e12	−0.828786
$589$	2.83905e12	0.971971
$590$	−5.58874e11	−0.189880
$591$	−3.72934e11	−0.125744
$592$	5.66588e12	1.89592
$593$	6.85605e11	0.227681	0.113841	−	0.993499i	$-0.463685\pi$
$593$	6.85605e11	0.227681	0.113841	+	0.993499i	$0.463685\pi$
$594$	−4.46503e12	−1.47158
$595$	0	0
$596$	−9.74542e12	−3.16368
$597$	−9.24682e11	−0.297926
$598$	6.79547e12	2.17302
$599$	−2.58472e11	−0.0820339	−0.0410170	−	0.999158i	$-0.513060\pi$
$599$	−2.58472e11	−0.0820339	−0.0410170	+	0.999158i	$0.513060\pi$
$600$	−2.50131e12	−0.787928
$601$	−5.17541e12	−1.61812	−0.809058	−	0.587729i	$-0.800022\pi$
$601$	−5.17541e12	−1.61812	−0.809058	+	0.587729i	$0.800022\pi$
$602$	5.43530e11	0.168671
$603$	3.77420e11	0.116251
$604$	6.67324e12	2.04019
$605$	8.89623e11	0.269964
$606$	−1.57984e12	−0.475868
$607$	1.85386e12	0.554278	0.277139	−	0.960830i	$-0.410614\pi$
$607$	1.85386e12	0.554278	0.277139	+	0.960830i	$0.410614\pi$
$608$	−5.68089e12	−1.68597
$609$	−1.56988e11	−0.0462475
$610$	5.16342e12	1.50992
$611$	8.35441e12	2.42510
$612$	0	0
$613$	−2.59651e12	−0.742709	−0.371355	−	0.928491i	$-0.621107\pi$
$613$	−2.59651e12	−0.742709	−0.371355	+	0.928491i	$0.621107\pi$
$614$	7.99114e12	2.26909
$615$	1.34787e11	0.0379936
$616$	−1.12898e12	−0.315918
$617$	5.08891e12	1.41365	0.706825	−	0.707389i	$-0.250127\pi$
$617$	5.08891e12	1.41365	0.706825	+	0.707389i	$0.250127\pi$
$618$	2.09872e11	0.0578772
$619$	1.49604e12	0.409576	0.204788	−	0.978806i	$-0.434349\pi$
$619$	1.49604e12	0.409576	0.204788	+	0.978806i	$0.434349\pi$
$620$	−7.02083e12	−1.90821
$621$	−1.68882e12	−0.455693
$622$	−3.69385e12	−0.989515
$623$	2.41601e11	0.0642542
$624$	5.86333e12	1.54815
$625$	1.78058e12	0.466769
$626$	−6.30668e12	−1.64141
$627$	−9.11842e11	−0.235622
$628$	−1.17736e13	−3.02058
$629$	0	0
$630$	2.40320e11	0.0607795
$631$	3.16897e12	0.795766	0.397883	−	0.917436i	$-0.369745\pi$
$631$	3.16897e12	0.795766	0.397883	+	0.917436i	$0.369745\pi$
$632$	1.94691e13	4.85421
$633$	−9.92354e11	−0.245669
$634$	−3.16245e12	−0.777359
$635$	1.64416e11	0.0401293
$636$	−2.71285e12	−0.657458
$637$	−6.33046e12	−1.52338
$638$	1.76980e13	4.22893
$639$	−2.06535e12	−0.490050
$640$	3.04348e12	0.717068
$641$	1.14784e12	0.268546	0.134273	−	0.990944i	$-0.457130\pi$
$641$	1.14784e12	0.268546	0.134273	+	0.990944i	$0.457130\pi$
$642$	−3.68205e12	−0.855426
$643$	2.17534e12	0.501855	0.250928	−	0.968006i	$-0.419264\pi$
$643$	2.17534e12	0.501855	0.250928	+	0.968006i	$0.419264\pi$
$644$	−6.94729e11	−0.159158
$645$	−6.67273e11	−0.151805
$646$	0	0
$647$	−2.40281e12	−0.539076	−0.269538	−	0.962990i	$-0.586871\pi$
$647$	−2.40281e12	−0.539076	−0.269538	+	0.962990i	$0.586871\pi$
$648$	9.50949e12	2.11870
$649$	−1.32241e12	−0.292594
$650$	−1.07233e13	−2.35624
$651$	2.04146e11	0.0445478
$652$	1.89106e13	4.09818
$653$	6.54607e12	1.40887	0.704435	−	0.709768i	$-0.251200\pi$
$653$	6.54607e12	1.40887	0.704435	+	0.709768i	$0.251200\pi$
$654$	−4.25006e12	−0.908439
$655$	−6.02388e11	−0.127876
$656$	4.03935e12	0.851616
$657$	−1.49397e12	−0.312821
$658$	−1.18323e12	−0.246067
$659$	−3.95943e12	−0.817802	−0.408901	−	0.912579i	$-0.634088\pi$
$659$	−3.95943e12	−0.817802	−0.408901	+	0.912579i	$0.634088\pi$
$660$	2.25494e12	0.462581
$661$	−1.85422e12	−0.377793	−0.188897	−	0.981997i	$-0.560491\pi$
$661$	−1.85422e12	−0.377793	−0.188897	+	0.981997i	$0.560491\pi$
$662$	−3.28616e12	−0.665009
$663$	0	0
$664$	1.97512e13	3.94309
$665$	1.03814e11	0.0205854
$666$	−5.21279e12	−1.02668
$667$	6.69397e12	1.30954
$668$	−2.12501e12	−0.412922
$669$	−1.76429e12	−0.340527
$670$	−5.58555e11	−0.107085
$671$	1.22177e13	2.32669
$672$	−4.08493e11	−0.0772721
$673$	6.80080e12	1.27789	0.638943	−	0.769254i	$-0.279372\pi$
$673$	6.80080e12	1.27789	0.638943	+	0.769254i	$0.279372\pi$
$674$	−2.84005e11	−0.0530098
$675$	2.66498e12	0.494114
$676$	1.90535e13	3.50925
$677$	8.48518e12	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$677$	8.48518e12	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$678$	−3.41877e11	−0.0621349
$679$	−6.06052e10	−0.0109420
$680$	0	0
$681$	−5.92579e11	−0.105581
$682$	−2.30143e13	−4.07351
$683$	9.08140e12	1.59683	0.798417	−	0.602105i	$-0.205671\pi$
$683$	9.08140e12	1.59683	0.798417	+	0.602105i	$0.205671\pi$
$684$	7.66964e12	1.33975
$685$	−9.14814e11	−0.158754
$686$	1.79924e12	0.310192
$687$	2.67380e12	0.457956
$688$	−1.99971e13	−3.40266
$689$	−7.14858e12	−1.20846
$690$	1.18155e12	0.198441
$691$	−1.23372e12	−0.205857	−0.102928	−	0.994689i	$-0.532821\pi$
$691$	−1.23372e12	−0.205857	−0.102928	+	0.994689i	$0.532821\pi$
$692$	−1.34847e13	−2.23545
$693$	5.68646e11	0.0936575
$694$	1.67043e13	2.73344
$695$	3.20362e11	0.0520846
$696$	1.05501e13	1.70418
$697$	0	0
$698$	1.13656e13	1.81235
$699$	−4.62436e11	−0.0732663
$700$	1.09629e12	0.172578
$701$	−7.03809e11	−0.110084	−0.0550420	−	0.998484i	$-0.517529\pi$
$701$	−7.03809e11	−0.110084	−0.0550420	+	0.998484i	$0.517529\pi$
$702$	−1.14109e13	−1.77339
$703$	−2.25184e12	−0.347728
$704$	2.00110e13	3.07038
$705$	1.45261e12	0.221461
$706$	−1.61379e13	−2.44471
$707$	4.25602e11	0.0640644
$708$	−1.28253e12	−0.191831
$709$	2.00854e12	0.298519	0.149260	−	0.988798i	$-0.452311\pi$
$709$	2.00854e12	0.298519	0.149260	+	0.988798i	$0.452311\pi$
$710$	3.05658e12	0.451412
$711$	−9.80617e12	−1.43908
$712$	−1.62364e13	−2.36772
$713$	−8.70480e12	−1.26141
$714$	0	0
$715$	5.94197e12	0.850263
$716$	−7.64691e12	−1.08737
$717$	−3.49871e12	−0.494393
$718$	−1.44597e13	−2.03048
$719$	1.25258e13	1.74793	0.873967	−	0.485985i	$-0.161539\pi$
$719$	1.25258e13	1.74793	0.873967	+	0.485985i	$0.161539\pi$
$720$	−8.84162e12	−1.22613
$721$	−5.65387e10	−0.00779179
$722$	−9.25446e12	−1.26746
$723$	4.21914e12	0.574251
$724$	1.14558e13	1.54954
$725$	−1.05632e13	−1.41995
$726$	2.82825e12	0.377835
$727$	9.59868e12	1.27440	0.637201	−	0.770697i	$-0.280092\pi$
$727$	9.59868e12	1.27440	0.637201	+	0.770697i	$0.280092\pi$
$728$	−2.88525e12	−0.380709
$729$	−3.29451e12	−0.432033
$730$	2.21097e12	0.288157
$731$	0	0
$732$	1.18493e13	1.52543
$733$	8.21658e12	1.05129	0.525646	−	0.850703i	$-0.323824\pi$
$733$	8.21658e12	1.05129	0.525646	+	0.850703i	$0.323824\pi$
$734$	−1.36299e13	−1.73325
$735$	−1.10070e12	−0.139116
$736$	1.74182e13	2.18803
$737$	−1.32166e12	−0.165012
$738$	−3.71633e12	−0.461170
$739$	−1.96560e12	−0.242435	−0.121218	−	0.992626i	$-0.538680\pi$
$739$	−1.96560e12	−0.242435	−0.121218	+	0.992626i	$0.538680\pi$
$740$	5.56871e12	0.682671
$741$	−2.33032e12	−0.283945
$742$	1.01245e12	0.122618
$743$	6.68465e12	0.804690	0.402345	−	0.915488i	$-0.368195\pi$
$743$	6.68465e12	0.804690	0.402345	+	0.915488i	$0.368195\pi$
$744$	−1.37193e13	−1.64155
$745$	−4.46508e12	−0.531038
$746$	2.47315e13	2.92365
$747$	−9.94825e12	−1.16897
$748$	0	0
$749$	9.91929e11	0.115163
$750$	−4.16563e12	−0.480735
$751$	−9.93363e12	−1.13954	−0.569768	−	0.821805i	$-0.692967\pi$
$751$	−9.93363e12	−1.13954	−0.569768	+	0.821805i	$0.692967\pi$
$752$	4.35323e13	4.96400
$753$	1.65174e11	0.0187225
$754$	4.52293e13	5.09623
$755$	3.05749e12	0.342455
$756$	1.16658e12	0.129888
$757$	−5.21690e12	−0.577406	−0.288703	−	0.957419i	$-0.593224\pi$
$757$	−5.21690e12	−0.577406	−0.288703	+	0.957419i	$0.593224\pi$
$758$	−2.68857e13	−2.95808
$759$	2.79580e12	0.305786
$760$	−6.97668e12	−0.758556
$761$	−1.43150e13	−1.54725	−0.773624	−	0.633645i	$-0.781558\pi$
$761$	−1.43150e13	−1.54725	−0.773624	+	0.633645i	$0.781558\pi$
$762$	5.22703e11	0.0561639
$763$	1.14495e12	0.122300
$764$	−2.43576e12	−0.258651
$765$	0	0
$766$	−1.21947e13	−1.27980
$767$	−3.37958e12	−0.352601
$768$	2.19710e12	0.227890
$769$	2.93738e12	0.302895	0.151447	−	0.988465i	$-0.451607\pi$
$769$	2.93738e12	0.302895	0.151447	+	0.988465i	$0.451607\pi$
$770$	−8.41557e11	−0.0862731
$771$	1.70253e12	0.173520
$772$	1.55792e12	0.157858
$773$	9.90255e11	0.0997561	0.0498780	−	0.998755i	$-0.484117\pi$
$773$	9.90255e11	0.0997561	0.0498780	+	0.998755i	$0.484117\pi$
$774$	1.83979e13	1.84262
$775$	1.37363e13	1.36776
$776$	4.07288e12	0.403203
$777$	−1.61922e11	−0.0159372
$778$	7.36275e12	0.720496
$779$	−1.60540e12	−0.156194
$780$	5.76277e12	0.557450
$781$	7.23250e12	0.695598
$782$	0	0
$783$	−1.12405e13	−1.06870
$784$	−3.29861e13	−3.11824
$785$	−5.39433e12	−0.507019
$786$	−1.91508e12	−0.178972
$787$	1.12776e13	1.04793	0.523963	−	0.851741i	$-0.324453\pi$
$787$	1.12776e13	1.04793	0.523963	+	0.851741i	$0.324453\pi$
$788$	−1.09845e13	−1.01488
$789$	−4.16526e12	−0.382645
$790$	1.45125e13	1.32562
$791$	9.21001e10	0.00836500
$792$	−3.82150e13	−3.45120
$793$	3.12238e13	2.80386
$794$	−1.36633e13	−1.22001
$795$	−1.24295e12	−0.110357
$796$	−2.72359e13	−2.40455
$797$	−1.25891e13	−1.10518	−0.552589	−	0.833454i	$-0.686360\pi$
$797$	−1.25891e13	−1.10518	−0.552589	+	0.833454i	$0.686360\pi$
$798$	3.30042e11	0.0288108
$799$	0	0
$800$	−2.74861e13	−2.37251
$801$	8.17794e12	0.701936
$802$	7.99009e12	0.681973
$803$	5.23160e12	0.444032
$804$	−1.28180e12	−0.108185
$805$	−3.18305e11	−0.0267154
$806$	−5.88159e13	−4.90893
$807$	−7.27093e12	−0.603474
$808$	−2.86019e13	−2.36072
$809$	−1.18891e13	−0.975843	−0.487922	−	0.872887i	$-0.662245\pi$
$809$	−1.18891e13	−0.975843	−0.487922	+	0.872887i	$0.662245\pi$
$810$	7.08848e12	0.578589
$811$	1.79717e13	1.45880	0.729400	−	0.684088i	$-0.239799\pi$
$811$	1.79717e13	1.45880	0.729400	+	0.684088i	$0.239799\pi$
$812$	−4.62398e12	−0.373262
$813$	7.44855e11	0.0597949
$814$	1.82543e13	1.45732
$815$	8.66430e12	0.687899
$816$	0	0
$817$	7.94763e12	0.624077
$818$	1.82060e13	1.42175
$819$	1.45324e12	0.112865
$820$	3.97007e12	0.306645
$821$	−4.69789e12	−0.360876	−0.180438	−	0.983586i	$-0.557752\pi$
$821$	−4.69789e12	−0.360876	−0.180438	+	0.983586i	$0.557752\pi$
$822$	−2.90834e12	−0.222188
$823$	−4.48513e12	−0.340781	−0.170391	−	0.985377i	$-0.554503\pi$
$823$	−4.48513e12	−0.340781	−0.170391	+	0.985377i	$0.554503\pi$
$824$	3.79960e12	0.287121
$825$	−4.41180e12	−0.331568
$826$	4.78648e11	0.0357772
$827$	9.93346e12	0.738458	0.369229	−	0.929338i	$-0.379622\pi$
$827$	9.93346e12	0.738458	0.369229	+	0.929338i	$0.379622\pi$
$828$	−2.35159e13	−1.73870
$829$	−1.76224e13	−1.29589	−0.647947	−	0.761685i	$-0.724372\pi$
$829$	−1.76224e13	−1.29589	−0.647947	+	0.761685i	$0.724372\pi$
$830$	1.47227e13	1.07680
$831$	−6.53747e12	−0.475560
$832$	5.11406e13	3.70007
$833$	0	0
$834$	1.01848e12	0.0728963
$835$	−9.73621e11	−0.0693108
$836$	−2.68577e13	−1.90170
$837$	1.46170e13	1.02942
$838$	2.25801e13	1.58172
$839$	2.31842e11	0.0161533	0.00807667	−	0.999967i	$-0.497429\pi$
$839$	2.31842e11	0.0161533	0.00807667	+	0.999967i	$0.497429\pi$
$840$	−5.01669e11	−0.0347665
$841$	3.00466e13	2.07116
$842$	1.47742e12	0.101298
$843$	4.09532e12	0.279295
$844$	−2.92292e13	−1.98278
$845$	8.72976e12	0.589043
$846$	−4.00511e13	−2.68812
$847$	−7.61917e11	−0.0508666
$848$	−3.72491e13	−2.47363
$849$	−4.01342e12	−0.265112
$850$	0	0
$851$	6.90438e12	0.451276
$852$	7.01438e12	0.456049
$853$	−5.57436e12	−0.360516	−0.180258	−	0.983619i	$-0.557693\pi$
$853$	−5.57436e12	−0.360516	−0.180258	+	0.983619i	$0.557693\pi$
$854$	−4.42221e12	−0.284498
$855$	3.51401e12	0.224883
$856$	−6.66610e13	−4.24366
$857$	2.37998e13	1.50716	0.753580	−	0.657357i	$-0.228325\pi$
$857$	2.37998e13	1.50716	0.753580	+	0.657357i	$0.228325\pi$
$858$	1.88904e13	1.19001
$859$	−1.05899e13	−0.663623	−0.331812	−	0.943346i	$-0.607660\pi$
$859$	−1.05899e13	−0.663623	−0.331812	+	0.943346i	$0.607660\pi$
$860$	−1.96541e13	−1.22521
$861$	−1.15438e11	−0.00715874
$862$	−4.64255e13	−2.86401
$863$	−1.01406e13	−0.622320	−0.311160	−	0.950358i	$-0.600718\pi$
$863$	−1.01406e13	−0.622320	−0.311160	+	0.950358i	$0.600718\pi$
$864$	−2.92485e13	−1.78563
$865$	−6.17832e12	−0.375230
$866$	−4.09891e13	−2.47650
$867$	0	0
$868$	6.01299e12	0.359544
$869$	3.43395e13	2.04270
$870$	7.86418e12	0.465390
$871$	−3.37765e12	−0.198854
$872$	−7.69445e13	−4.50665
$873$	−2.05142e12	−0.119534
$874$	−1.40730e13	−0.815804
$875$	1.12220e12	0.0647195
$876$	5.07383e12	0.291117
$877$	6.58970e12	0.376156	0.188078	−	0.982154i	$-0.439774\pi$
$877$	6.58970e12	0.376156	0.188078	+	0.982154i	$0.439774\pi$
$878$	−3.04269e13	−1.72795
$879$	6.10902e12	0.345161
$880$	3.09618e13	1.74042
$881$	7.41843e12	0.414878	0.207439	−	0.978248i	$-0.433487\pi$
$881$	7.41843e12	0.414878	0.207439	+	0.978248i	$0.433487\pi$
$882$	3.03483e13	1.68860
$883$	−1.13514e13	−0.628388	−0.314194	−	0.949359i	$-0.601734\pi$
$883$	−1.13514e13	−0.628388	−0.314194	+	0.949359i	$0.601734\pi$
$884$	0	0
$885$	−5.87620e11	−0.0321997
$886$	−3.76290e13	−2.05149
$887$	−1.70949e13	−0.927281	−0.463640	−	0.886023i	$-0.653457\pi$
$887$	−1.70949e13	−0.927281	−0.463640	+	0.886023i	$0.653457\pi$
$888$	1.08817e13	0.587273
$889$	−1.40814e11	−0.00756114
$890$	−1.21028e13	−0.646592
$891$	1.67728e13	0.891571
$892$	−5.19660e13	−2.74838
$893$	−1.73015e13	−0.910440
$894$	−1.41952e13	−0.743227
$895$	−3.50360e12	−0.182520
$896$	−2.60659e12	−0.135110
$897$	7.14500e12	0.368499
$898$	1.52468e13	0.782410
$899$	−5.79374e13	−2.95829
$900$	3.71083e13	1.88530
$901$	0	0
$902$	1.30139e13	0.654604
$903$	5.71486e11	0.0286029
$904$	−6.18944e12	−0.308243
$905$	5.24873e12	0.260097
$906$	9.72022e12	0.479291
$907$	3.89667e13	1.91188	0.955940	−	0.293562i	$-0.0948406\pi$
$907$	3.89667e13	1.91188	0.955940	+	0.293562i	$0.0948406\pi$
$908$	−1.74540e13	−0.852138
$909$	1.44062e13	0.699862
$910$	−2.15070e12	−0.103967
$911$	2.22052e13	1.06813	0.534063	−	0.845445i	$-0.320665\pi$
$911$	2.22052e13	1.06813	0.534063	+	0.845445i	$0.320665\pi$
$912$	−1.21426e13	−0.581212
$913$	3.48370e13	1.65929
$914$	3.15468e13	1.49519
$915$	5.42899e12	0.256050
$916$	7.87551e13	3.69614
$917$	5.15915e11	0.0240944
$918$	0	0
$919$	8.46248e11	0.0391361	0.0195681	−	0.999809i	$-0.493771\pi$
$919$	8.46248e11	0.0391361	0.0195681	+	0.999809i	$0.493771\pi$
$920$	2.13912e13	0.984442
$921$	8.40216e12	0.384789
$922$	−6.55834e13	−2.98885
$923$	1.84835e13	0.838256
$924$	−1.93125e12	−0.0871593
$925$	−1.08952e13	−0.489325
$926$	4.16792e13	1.86282
$927$	−1.91378e12	−0.0851203
$928$	1.15932e14	5.13141
$929$	3.10807e13	1.36905	0.684527	−	0.728988i	$-0.260009\pi$
$929$	3.10807e13	1.36905	0.684527	+	0.728988i	$0.260009\pi$
$930$	−1.02265e13	−0.448285
$931$	1.31100e13	0.571912
$932$	−1.36208e13	−0.591330
$933$	−3.88384e12	−0.167801
$934$	−6.10322e13	−2.62421
$935$	0	0
$936$	−9.76629e13	−4.15900
$937$	−2.09786e13	−0.889097	−0.444549	−	0.895755i	$-0.646636\pi$
$937$	−2.09786e13	−0.889097	−0.444549	+	0.895755i	$0.646636\pi$
$938$	4.78375e11	0.0201769
$939$	−6.63106e12	−0.278348
$940$	4.27857e13	1.78741
$941$	−1.07388e13	−0.446481	−0.223240	−	0.974763i	$-0.571663\pi$
$941$	−1.07388e13	−0.446481	−0.223240	+	0.974763i	$0.571663\pi$
$942$	−1.71494e13	−0.709610
$943$	4.92231e12	0.202706
$944$	−1.76100e13	−0.721747
$945$	5.34496e11	0.0218022
$946$	−6.44264e13	−2.61549
$947$	1.85891e13	0.751077	0.375538	−	0.926807i	$-0.377458\pi$
$947$	1.85891e13	0.751077	0.375538	+	0.926807i	$0.377458\pi$
$948$	3.33039e13	1.33924
$949$	1.33700e13	0.535098
$950$	2.22074e13	0.884588
$951$	−3.32511e12	−0.131824
$952$	0	0
$953$	2.44750e13	0.961181	0.480591	−	0.876945i	$-0.340422\pi$
$953$	2.44750e13	0.961181	0.480591	+	0.876945i	$0.340422\pi$
$954$	3.42704e13	1.33953
$955$	−1.11600e12	−0.0434158
$956$	−1.03052e14	−3.99023
$957$	1.86083e13	0.717137
$958$	7.40362e13	2.83988
$959$	7.83493e11	0.0299124
$960$	8.89199e12	0.337892
$961$	4.89017e13	1.84956
$962$	4.66510e13	1.75620
$963$	3.35758e13	1.25808
$964$	1.24272e14	4.63476
$965$	7.13796e11	0.0264973
$966$	−1.01194e12	−0.0373902
$967$	3.69182e13	1.35775	0.678877	−	0.734252i	$-0.262467\pi$
$967$	3.69182e13	1.35775	0.678877	+	0.734252i	$0.262467\pi$
$968$	5.12035e13	1.87439
$969$	0	0
$970$	3.03597e12	0.110109
$971$	2.54109e13	0.917348	0.458674	−	0.888605i	$-0.348325\pi$
$971$	2.54109e13	0.917348	0.458674	+	0.888605i	$0.348325\pi$
$972$	6.03078e13	2.16708
$973$	−2.74374e11	−0.00981376
$974$	−6.39688e13	−2.27747
$975$	−1.12749e13	−0.399568
$976$	1.62698e14	5.73929
$977$	−3.64533e13	−1.28001	−0.640003	−	0.768373i	$-0.721067\pi$
$977$	−3.64533e13	−1.28001	−0.640003	+	0.768373i	$0.721067\pi$
$978$	2.75452e13	0.962765
$979$	−2.86377e13	−0.996359
$980$	−3.24204e13	−1.12280
$981$	3.87554e13	1.33605
$982$	5.33615e13	1.83116
$983$	−6.57654e12	−0.224650	−0.112325	−	0.993672i	$-0.535830\pi$
$983$	−6.57654e12	−0.224650	−0.112325	+	0.993672i	$0.535830\pi$
$984$	7.75786e12	0.263794
$985$	−5.03280e12	−0.170352
$986$	0	0
$987$	−1.24409e12	−0.0417277
$988$	−6.86381e13	−2.29171
$989$	−2.43682e13	−0.809917
$990$	−2.84859e13	−0.942478
$991$	3.54759e13	1.16843	0.584214	−	0.811600i	$-0.301403\pi$
$991$	3.54759e13	1.16843	0.584214	+	0.811600i	$0.301403\pi$
$992$	−1.50757e14	−4.94282
$993$	−3.45518e12	−0.112771
$994$	−2.61781e12	−0.0850548
$995$	−1.24787e13	−0.403614
$996$	3.37864e13	1.08787
$997$	−2.00321e13	−0.642094	−0.321047	−	0.947063i	$-0.604035\pi$
$997$	−2.00321e13	−0.642094	−0.321047	+	0.947063i	$0.604035\pi$
$998$	−4.31868e13	−1.37804
$999$	−1.15938e13	−0.368282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.e.1.12	yes	12
17.16	even	2		289.10.a.d.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.12	✓	12	17.16	even	2
289.10.a.e.1.12	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+42.9032 q^{2} +45.1099 q^{3} +1328.68 q^{4} +608.765 q^{5} +1935.36 q^{6} -521.377 q^{7} +35038.3 q^{8} -17648.1 q^{9} +O(q^{10})\)	\(q+42.9032 q^{2} +45.1099 q^{3} +1328.68 q^{4} +608.765 q^{5} +1935.36 q^{6} -521.377 q^{7} +35038.3 q^{8} -17648.1 q^{9} +26118.0 q^{10} +61800.5 q^{11} +59936.8 q^{12} +157939. q^{13} -22368.7 q^{14} +27461.3 q^{15} +822971. q^{16} -757160. q^{18} -327081. q^{19} +808857. q^{20} -23519.3 q^{21} +2.65144e6 q^{22} +1.00286e6 q^{23} +1.58058e6 q^{24} -1.58253e6 q^{25} +6.77607e6 q^{26} -1.68400e6 q^{27} -692745. q^{28} +6.67486e6 q^{29} +1.17818e6 q^{30} -8.67994e6 q^{31} +1.73684e7 q^{32} +2.78781e6 q^{33} -317396. q^{35} -2.34487e7 q^{36} +6.88467e6 q^{37} -1.40328e7 q^{38} +7.12459e6 q^{39} +2.13301e7 q^{40} +4.90825e6 q^{41} -1.00905e6 q^{42} -2.42986e7 q^{43} +8.21133e7 q^{44} -1.07435e7 q^{45} +4.30261e7 q^{46} +5.28966e7 q^{47} +3.71241e7 q^{48} -4.00818e7 q^{49} -6.78956e7 q^{50} +2.09850e8 q^{52} -4.52618e7 q^{53} -7.22491e7 q^{54} +3.76220e7 q^{55} -1.82682e7 q^{56} -1.47546e7 q^{57} +2.86373e8 q^{58} -2.13981e7 q^{59} +3.64874e7 q^{60} +1.97696e8 q^{61} -3.72397e8 q^{62} +9.20131e6 q^{63} +3.23800e8 q^{64} +9.61475e7 q^{65} +1.19606e8 q^{66} -2.13859e7 q^{67} +4.52391e7 q^{69} -1.36173e7 q^{70} +1.17030e8 q^{71} -6.18360e8 q^{72} +8.46531e7 q^{73} +2.95374e8 q^{74} -7.13878e7 q^{75} -4.34587e8 q^{76} -3.22214e7 q^{77} +3.05668e8 q^{78} +5.55650e8 q^{79} +5.00996e8 q^{80} +2.71402e8 q^{81} +2.10580e8 q^{82} +5.63701e8 q^{83} -3.12497e7 q^{84} -1.04249e9 q^{86} +3.01102e8 q^{87} +2.16539e9 q^{88} -4.63389e8 q^{89} -4.60933e8 q^{90} -8.23456e7 q^{91} +1.33249e9 q^{92} -3.91551e8 q^{93} +2.26943e9 q^{94} -1.99116e8 q^{95} +7.83488e8 q^{96} +1.16241e8 q^{97} -1.71964e9 q^{98} -1.09066e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 12 * q + 17 * q^2 + 74 * q^3 + 2987 * q^4 + 454 * q^5 + 2674 * q^6 - 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9} - 2449 q^{10} + 152886 q^{11} + 41717 q^{12} + 23478 q^{13} + 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} - 2477218 q^{20} - 1395256 q^{21} + 2391095 q^{22} + 2012428 q^{23} + 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} + 3231638 q^{27} - 5978216 q^{28} + 12772842 q^{29} + 181633 q^{30} + 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} + 1352872 q^{37} + 3704404 q^{38} - 1380780 q^{39} + 44739331 q^{40} + 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} + 148233417 q^{44} - 79449336 q^{45} + 31855859 q^{46} + 133558002 q^{47} - 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} - 50215469 q^{54} - 91197532 q^{55} + 267350757 q^{56} + 49507694 q^{57} + 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} + 262041240 q^{61} - 314328847 q^{62} + 218532626 q^{63} + 595820098 q^{64} + 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} + 204290852 q^{71} - 208030791 q^{72} + 673538852 q^{73} + 1274510282 q^{74} + 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} + 165043245 q^{78} + 434002980 q^{79} + 599590757 q^{80} - 389011392 q^{81} - 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} - 262108460 q^{88} + 911678128 q^{89} - 2734590475 q^{90} - 560105446 q^{91} - 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} - 1116511966 q^{95} + 2204198979 q^{96} - 3589270998 q^{97} - 2677144485 q^{98} + 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 + 74 * q^3 + 2987 * q^4 + 454 * q^5 + 2674 * q^6 - 5524 * q^7 - 12036 * q^8 + 71898 * q^9 - 2449 * q^10 + 152886 * q^11 + 41717 * q^12 + 23478 * q^13 + 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 - 2477218 * q^20 - 1395256 * q^21 + 2391095 * q^22 + 2012428 * q^23 + 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 + 3231638 * q^27 - 5978216 * q^28 + 12772842 * q^29 + 181633 * q^30 + 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 + 1352872 * q^37 + 3704404 * q^38 - 1380780 * q^39 + 44739331 * q^40 + 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 + 148233417 * q^44 - 79449336 * q^45 + 31855859 * q^46 + 133558002 * q^47 - 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 - 50215469 * q^54 - 91197532 * q^55 + 267350757 * q^56 + 49507694 * q^57 + 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 + 262041240 * q^61 - 314328847 * q^62 + 218532626 * q^63 + 595820098 * q^64 + 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 + 204290852 * q^71 - 208030791 * q^72 + 673538852 * q^73 + 1274510282 * q^74 + 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 + 165043245 * q^78 + 434002980 * q^79 + 599590757 * q^80 - 389011392 * q^81 - 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 - 262108460 * q^88 + 911678128 * q^89 - 2734590475 * q^90 - 560105446 * q^91 - 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 - 1116511966 * q^95 + 2204198979 * q^96 - 3589270998 * q^97 - 2677144485 * q^98 + 2056683494 * q^99

Introduction

L-functions

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