LMFDB - Embedded newform 289.10.a.e.1.9

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			1.9
Root			$25.3822$ 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)

$f(q)$	$=$	$q+26.3822 q^{2} -66.0249 q^{3} +184.023 q^{4} +164.991 q^{5} -1741.89 q^{6} -5776.54 q^{7} -8652.77 q^{8} -15323.7 q^{9} +O(q^{10})$	\(q+26.3822 q^{2} -66.0249 q^{3} +184.023 q^{4} +164.991 q^{5} -1741.89 q^{6} -5776.54 q^{7} -8652.77 q^{8} -15323.7 q^{9} +4352.83 q^{10} -83760.0 q^{11} -12150.1 q^{12} -54843.6 q^{13} -152398. q^{14} -10893.5 q^{15} -322499. q^{16} -404274. q^{18} -415353. q^{19} +30362.1 q^{20} +381396. q^{21} -2.20978e6 q^{22} +645136. q^{23} +571298. q^{24} -1.92590e6 q^{25} -1.44690e6 q^{26} +2.31132e6 q^{27} -1.06302e6 q^{28} -2.89695e6 q^{29} -287395. q^{30} +3.57166e6 q^{31} -4.07804e6 q^{32} +5.53025e6 q^{33} -953076. q^{35} -2.81992e6 q^{36} -1.64472e7 q^{37} -1.09579e7 q^{38} +3.62104e6 q^{39} -1.42763e6 q^{40} +2.19135e7 q^{41} +1.00621e7 q^{42} +1.63180e7 q^{43} -1.54138e7 q^{44} -2.52827e6 q^{45} +1.70201e7 q^{46} +1.67476e7 q^{47} +2.12930e7 q^{48} -6.98519e6 q^{49} -5.08097e7 q^{50} -1.00925e7 q^{52} -1.54682e7 q^{53} +6.09777e7 q^{54} -1.38196e7 q^{55} +4.99831e7 q^{56} +2.74237e7 q^{57} -7.64280e7 q^{58} -8.58435e7 q^{59} -2.00466e6 q^{60} +1.58254e8 q^{61} +9.42285e7 q^{62} +8.85180e7 q^{63} +5.75318e7 q^{64} -9.04868e6 q^{65} +1.45900e8 q^{66} -6.70561e7 q^{67} -4.25951e7 q^{69} -2.51443e7 q^{70} +9.91611e7 q^{71} +1.32593e8 q^{72} -1.78647e8 q^{73} -4.33915e8 q^{74} +1.27158e8 q^{75} -7.64345e7 q^{76} +4.83843e8 q^{77} +9.55312e7 q^{78} -3.21915e8 q^{79} -5.32094e7 q^{80} +1.49012e8 q^{81} +5.78128e8 q^{82} -7.48591e8 q^{83} +7.01856e7 q^{84} +4.30505e8 q^{86} +1.91271e8 q^{87} +7.24756e8 q^{88} -1.10368e9 q^{89} -6.67015e7 q^{90} +3.16806e8 q^{91} +1.18720e8 q^{92} -2.35819e8 q^{93} +4.41840e8 q^{94} -6.85294e7 q^{95} +2.69252e8 q^{96} +5.39182e8 q^{97} -1.84285e8 q^{98} +1.28351e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	26.3822	1.16594	0.582971	−	0.812493i	$-0.301890\pi$
$2$	26.3822	1.16594	0.582971	+	0.812493i	$0.301890\pi$
$3$	−66.0249	−0.470611	−0.235306	−	0.971921i	$-0.575609\pi$
$3$	−66.0249	−0.470611	−0.235306	+	0.971921i	$0.575609\pi$
$4$	184.023	0.359420
$5$	164.991	0.118058	0.0590289	−	0.998256i	$-0.481200\pi$
$5$	164.991	0.118058	0.0590289	+	0.998256i	$0.481200\pi$
$6$	−1741.89	−0.548705
$7$	−5776.54	−0.909341	−0.454670	−	0.890660i	$-0.650243\pi$
$7$	−5776.54	−0.909341	−0.454670	+	0.890660i	$0.650243\pi$
$8$	−8652.77	−0.746879
$9$	−15323.7	−0.778525
$10$	4352.83	0.137649
$11$	−83760.0	−1.72492	−0.862461	−	0.506124i	$-0.831078\pi$
$11$	−83760.0	−1.72492	−0.862461	+	0.506124i	$0.831078\pi$
$12$	−12150.1	−0.169147
$13$	−54843.6	−0.532575	−0.266287	−	0.963894i	$-0.585797\pi$
$13$	−54843.6	−0.532575	−0.266287	+	0.963894i	$0.585797\pi$
$14$	−152398.	−1.06024
$15$	−10893.5	−0.0555593
$16$	−322499.	−1.23024
$17$	0	0
$17$	0	0
$18$	−404274.	−0.907715
$19$	−415353.	−0.731183	−0.365592	−	0.930775i	$-0.619133\pi$
$19$	−415353.	−0.731183	−0.365592	+	0.930775i	$0.619133\pi$
$20$	30362.1	0.0424323
$21$	381396.	0.427946
$22$	−2.20978e6	−2.01116
$23$	645136.	0.480702	0.240351	−	0.970686i	$-0.422737\pi$
$23$	645136.	0.480702	0.240351	+	0.970686i	$0.422737\pi$
$24$	571298.	0.351490
$25$	−1.92590e6	−0.986062
$26$	−1.44690e6	−0.620951
$27$	2.31132e6	0.836994
$28$	−1.06302e6	−0.326835
$29$	−2.89695e6	−0.760589	−0.380294	−	0.924866i	$-0.624177\pi$
$29$	−2.89695e6	−0.760589	−0.380294	+	0.924866i	$0.624177\pi$
$30$	−287395.	−0.0647789
$31$	3.57166e6	0.694613	0.347306	−	0.937752i	$-0.387096\pi$
$31$	3.57166e6	0.694613	0.347306	+	0.937752i	$0.387096\pi$
$32$	−4.07804e6	−0.687506
$33$	5.53025e6	0.811768
$34$	0	0
$35$	−953076.	−0.107355
$36$	−2.81992e6	−0.279817
$37$	−1.64472e7	−1.44273	−0.721365	−	0.692555i	$-0.756485\pi$
$37$	−1.64472e7	−1.44273	−0.721365	+	0.692555i	$0.756485\pi$
$38$	−1.09579e7	−0.852517
$39$	3.62104e6	0.250636
$40$	−1.42763e6	−0.0881749
$41$	2.19135e7	1.21111	0.605557	−	0.795802i	$-0.292950\pi$
$41$	2.19135e7	1.21111	0.605557	+	0.795802i	$0.292950\pi$
$42$	1.00621e7	0.498960
$43$	1.63180e7	0.727877	0.363938	−	0.931423i	$-0.381432\pi$
$43$	1.63180e7	0.727877	0.363938	+	0.931423i	$0.381432\pi$
$44$	−1.54138e7	−0.619971
$45$	−2.52827e6	−0.0919110
$46$	1.70201e7	0.560471
$47$	1.67476e7	0.500625	0.250313	−	0.968165i	$-0.419467\pi$
$47$	1.67476e7	0.500625	0.250313	+	0.968165i	$0.419467\pi$
$48$	2.12930e7	0.578963
$49$	−6.98519e6	−0.173100
$50$	−5.08097e7	−1.14969
$51$	0	0
$52$	−1.00925e7	−0.191418
$53$	−1.54682e7	−0.269277	−0.134638	−	0.990895i	$-0.542987\pi$
$53$	−1.54682e7	−0.269277	−0.134638	+	0.990895i	$0.542987\pi$
$54$	6.09777e7	0.975886
$55$	−1.38196e7	−0.203640
$56$	4.99831e7	0.679167
$57$	2.74237e7	0.344103
$58$	−7.64280e7	−0.886802
$59$	−8.58435e7	−0.922302	−0.461151	−	0.887322i	$-0.652563\pi$
$59$	−8.58435e7	−0.922302	−0.461151	+	0.887322i	$0.652563\pi$
$60$	−2.00466e6	−0.0199691
$61$	1.58254e8	1.46342	0.731711	−	0.681615i	$-0.238722\pi$
$61$	1.58254e8	1.46342	0.731711	+	0.681615i	$0.238722\pi$
$62$	9.42285e7	0.809878
$63$	8.85180e7	0.707945
$64$	5.75318e7	0.428645
$65$	−9.04868e6	−0.0628746
$66$	1.45900e8	0.946474
$67$	−6.70561e7	−0.406538	−0.203269	−	0.979123i	$-0.565157\pi$
$67$	−6.70561e7	−0.406538	−0.203269	+	0.979123i	$0.565157\pi$
$68$	0	0
$69$	−4.25951e7	−0.226224
$70$	−2.51443e7	−0.125169
$71$	9.91611e7	0.463104	0.231552	−	0.972823i	$-0.425620\pi$
$71$	9.91611e7	0.463104	0.231552	+	0.972823i	$0.425620\pi$
$72$	1.32593e8	0.581464
$73$	−1.78647e8	−0.736279	−0.368139	−	0.929771i	$-0.620005\pi$
$73$	−1.78647e8	−0.736279	−0.368139	+	0.929771i	$0.620005\pi$
$74$	−4.33915e8	−1.68214
$75$	1.27158e8	0.464052
$76$	−7.64345e7	−0.262802
$77$	4.83843e8	1.56854
$78$	9.55312e7	0.292227
$79$	−3.21915e8	−0.929865	−0.464932	−	0.885346i	$-0.653921\pi$
$79$	−3.21915e8	−0.929865	−0.464932	+	0.885346i	$0.653921\pi$
$80$	−5.32094e7	−0.145239
$81$	1.49012e8	0.384627
$82$	5.78128e8	1.41209
$83$	−7.48591e8	−1.73138	−0.865692	−	0.500577i	$-0.833121\pi$
$83$	−7.48591e8	−1.73138	−0.865692	+	0.500577i	$0.833121\pi$
$84$	7.01856e7	0.153812
$85$	0	0
$86$	4.30505e8	0.848662
$87$	1.91271e8	0.357942
$88$	7.24756e8	1.28831
$89$	−1.10368e9	−1.86462	−0.932309	−	0.361662i	$-0.882209\pi$
$89$	−1.10368e9	−1.86462	−0.932309	+	0.361662i	$0.882209\pi$
$90$	−6.67015e7	−0.107163
$91$	3.16806e8	0.484292
$92$	1.18720e8	0.172774
$93$	−2.35819e8	−0.326893
$94$	4.41840e8	0.583700
$95$	−6.85294e7	−0.0863219
$96$	2.69252e8	0.323548
$97$	5.39182e8	0.618391	0.309195	−	0.950999i	$-0.399940\pi$
$97$	5.39182e8	0.618391	0.309195	+	0.950999i	$0.399940\pi$
$98$	−1.84285e8	−0.201824
$99$	1.28351e9	1.34290
$100$	−3.54411e8	−0.354411
$101$	−7.02632e8	−0.671865	−0.335932	−	0.941886i	$-0.609051\pi$
$101$	−7.02632e8	−0.671865	−0.335932	+	0.941886i	$0.609051\pi$
$102$	0	0
$103$	−1.52332e9	−1.33360	−0.666799	−	0.745238i	$-0.732336\pi$
$103$	−1.52332e9	−1.33360	−0.666799	+	0.745238i	$0.732336\pi$
$104$	4.74549e8	0.397769
$105$	6.29268e7	0.0505223
$106$	−4.08086e8	−0.313961
$107$	−2.26705e9	−1.67199	−0.835996	−	0.548736i	$-0.815109\pi$
$107$	−2.26705e9	−1.67199	−0.835996	+	0.548736i	$0.815109\pi$
$108$	4.25335e8	0.300832
$109$	8.97007e8	0.608663	0.304331	−	0.952566i	$-0.401567\pi$
$109$	8.97007e8	0.608663	0.304331	+	0.952566i	$0.401567\pi$
$110$	−3.64593e8	−0.237433
$111$	1.08593e9	0.678965
$112$	1.86293e9	1.11870
$113$	2.03489e9	1.17405	0.587026	−	0.809568i	$-0.300299\pi$
$113$	2.03489e9	1.17405	0.587026	+	0.809568i	$0.300299\pi$
$114$	7.23498e8	0.401204
$115$	1.06442e8	0.0567506
$116$	−5.33105e8	−0.273371
$117$	8.40407e8	0.414623
$118$	−2.26474e9	−1.07535
$119$	0	0
$120$	9.42590e7	0.0414961
$121$	4.65779e9	1.97536
$122$	4.17509e9	1.70627
$123$	−1.44684e9	−0.569964
$124$	6.57268e8	0.249658
$125$	−6.40004e8	−0.234470
$126$	2.33530e9	0.825422
$127$	−5.08437e9	−1.73429	−0.867143	−	0.498059i	$-0.834046\pi$
$127$	−5.08437e9	−1.73429	−0.867143	+	0.498059i	$0.834046\pi$
$128$	3.60577e9	1.18728
$129$	−1.07739e9	−0.342547
$130$	−2.38725e8	−0.0733081
$131$	1.56203e8	0.0463413	0.0231706	−	0.999732i	$-0.492624\pi$
$131$	1.56203e8	0.0463413	0.0231706	+	0.999732i	$0.492624\pi$
$132$	1.01769e9	0.291765
$133$	2.39930e9	0.664895
$134$	−1.76909e9	−0.474000
$135$	3.81346e8	0.0988136
$136$	0	0
$137$	1.88812e9	0.457918	0.228959	−	0.973436i	$-0.426468\pi$
$137$	1.88812e9	0.457918	0.228959	+	0.973436i	$0.426468\pi$
$138$	−1.12375e9	−0.263764
$139$	8.04015e9	1.82683	0.913414	−	0.407033i	$-0.133437\pi$
$139$	8.04015e9	1.82683	0.913414	+	0.407033i	$0.133437\pi$
$140$	−1.75388e8	−0.0385854
$141$	−1.10576e9	−0.235600
$142$	2.61609e9	0.539952
$143$	4.59370e9	0.918650
$144$	4.94189e9	0.957771
$145$	−4.77970e8	−0.0897934
$146$	−4.71310e9	−0.858458
$147$	4.61197e8	0.0814626
$148$	−3.02667e9	−0.518546
$149$	1.09919e10	1.82699	0.913495	−	0.406850i	$-0.133373\pi$
$149$	1.09919e10	1.82699	0.913495	+	0.406850i	$0.133373\pi$
$150$	3.35470e9	0.541058
$151$	1.72635e8	0.0270229	0.0135114	−	0.999909i	$-0.495699\pi$
$151$	1.72635e8	0.0270229	0.0135114	+	0.999909i	$0.495699\pi$
$152$	3.59396e9	0.546105
$153$	0	0
$154$	1.27649e10	1.82883
$155$	5.89291e8	0.0820045
$156$	6.66355e8	0.0900835
$157$	1.63553e9	0.214837	0.107418	−	0.994214i	$-0.465742\pi$
$157$	1.63553e9	0.214837	0.107418	+	0.994214i	$0.465742\pi$
$158$	−8.49285e9	−1.08417
$159$	1.02129e9	0.126725
$160$	−6.72839e8	−0.0811654
$161$	−3.72665e9	−0.437122
$162$	3.93128e9	0.448452
$163$	5.08177e9	0.563859	0.281930	−	0.959435i	$-0.409026\pi$
$163$	5.08177e9	0.563859	0.281930	+	0.959435i	$0.409026\pi$
$164$	4.03259e9	0.435298
$165$	9.12440e8	0.0958355
$166$	−1.97495e10	−2.01869
$167$	2.55962e9	0.254655	0.127327	−	0.991861i	$-0.459360\pi$
$167$	2.55962e9	0.254655	0.127327	+	0.991861i	$0.459360\pi$
$168$	−3.30013e9	−0.319624
$169$	−7.59668e9	−0.716364
$170$	0	0
$171$	6.36475e9	0.569245
$172$	3.00288e9	0.261614
$173$	1.27890e9	0.108549	0.0542747	−	0.998526i	$-0.482715\pi$
$173$	1.27890e9	0.108549	0.0542747	+	0.998526i	$0.482715\pi$
$174$	5.04615e9	0.417339
$175$	1.11251e10	0.896667
$176$	2.70125e10	2.12206
$177$	5.66781e9	0.434046
$178$	−2.91177e10	−2.17404
$179$	−1.05831e9	−0.0770501	−0.0385250	−	0.999258i	$-0.512266\pi$
$179$	−1.05831e9	−0.0770501	−0.0385250	+	0.999258i	$0.512266\pi$
$180$	−4.65260e8	−0.0330346
$181$	−3.84880e9	−0.266546	−0.133273	−	0.991079i	$-0.542549\pi$
$181$	−3.84880e9	−0.266546	−0.133273	+	0.991079i	$0.542549\pi$
$182$	8.35806e9	0.564656
$183$	−1.04487e10	−0.688703
$184$	−5.58221e9	−0.359026
$185$	−2.71364e9	−0.170326
$186$	−6.22143e9	−0.381138
$187$	0	0
$188$	3.08195e9	0.179935
$189$	−1.33514e10	−0.761112
$190$	−1.80796e9	−0.100646
$191$	3.30020e10	1.79428	0.897139	−	0.441749i	$-0.145642\pi$
$191$	3.30020e10	1.79428	0.897139	+	0.441749i	$0.145642\pi$
$192$	−3.79853e9	−0.201725
$193$	2.85018e10	1.47865	0.739323	−	0.673351i	$-0.235146\pi$
$193$	2.85018e10	1.47865	0.739323	+	0.673351i	$0.235146\pi$
$194$	1.42248e10	0.721007
$195$	5.97439e8	0.0295895
$196$	−1.28544e9	−0.0622154
$197$	−3.06795e10	−1.45128	−0.725638	−	0.688077i	$-0.758455\pi$
$197$	−3.06795e10	−1.45128	−0.725638	+	0.688077i	$0.758455\pi$
$198$	3.38620e10	1.56574
$199$	−2.76572e10	−1.25017	−0.625086	−	0.780556i	$-0.714936\pi$
$199$	−2.76572e10	−1.25017	−0.625086	+	0.780556i	$0.714936\pi$
$200$	1.66644e10	0.736469
$201$	4.42737e9	0.191322
$202$	−1.85370e10	−0.783355
$203$	1.67343e10	0.691634
$204$	0	0
$205$	3.61553e9	0.142981
$206$	−4.01887e10	−1.55490
$207$	−9.88588e9	−0.374239
$208$	1.76870e10	0.655193
$209$	3.47900e10	1.26123
$210$	1.66015e9	0.0589061
$211$	−2.15664e10	−0.749041	−0.374521	−	0.927219i	$-0.622193\pi$
$211$	−2.15664e10	−0.749041	−0.374521	+	0.927219i	$0.622193\pi$
$212$	−2.84651e9	−0.0967835
$213$	−6.54710e9	−0.217942
$214$	−5.98099e10	−1.94945
$215$	2.69231e9	0.0859316
$216$	−1.99993e10	−0.625133
$217$	−2.06319e10	−0.631640
$218$	2.36651e10	0.709665
$219$	1.17951e10	0.346501
$220$	−2.54313e9	−0.0731925
$221$	0	0
$222$	2.86492e10	0.791634
$223$	−6.34535e9	−0.171824	−0.0859119	−	0.996303i	$-0.527380\pi$
$223$	−6.34535e9	−0.171824	−0.0859119	+	0.996303i	$0.527380\pi$
$224$	2.35570e10	0.625177
$225$	2.95120e10	0.767674
$226$	5.36849e10	1.36888
$227$	1.64079e10	0.410145	0.205073	−	0.978747i	$-0.434257\pi$
$227$	1.64079e10	0.410145	0.205073	+	0.978747i	$0.434257\pi$
$228$	5.04658e9	0.123678
$229$	−7.28411e10	−1.75032	−0.875159	−	0.483835i	$-0.839243\pi$
$229$	−7.28411e10	−1.75032	−0.875159	+	0.483835i	$0.839243\pi$
$230$	2.80817e9	0.0661679
$231$	−3.19457e10	−0.738173
$232$	2.50666e10	0.568068
$233$	−5.81677e10	−1.29295	−0.646473	−	0.762937i	$-0.723757\pi$
$233$	−5.81677e10	−1.29295	−0.646473	+	0.762937i	$0.723757\pi$
$234$	2.21718e10	0.483426
$235$	2.76320e9	0.0591027
$236$	−1.57972e10	−0.331494
$237$	2.12544e10	0.437605
$238$	0	0
$239$	4.95985e10	0.983281	0.491640	−	0.870798i	$-0.336397\pi$
$239$	4.95985e10	0.983281	0.491640	+	0.870798i	$0.336397\pi$
$240$	3.51315e9	0.0683511
$241$	−2.91135e10	−0.555927	−0.277963	−	0.960592i	$-0.589659\pi$
$241$	−2.91135e10	−0.555927	−0.277963	+	0.960592i	$0.589659\pi$
$242$	1.22883e11	2.30315
$243$	−5.53321e10	−1.01800
$244$	2.91223e10	0.525983
$245$	−1.15249e9	−0.0204357
$246$	−3.81709e10	−0.664544
$247$	2.27795e10	0.389410
$248$	−3.09048e10	−0.518792
$249$	4.94257e10	0.814809
$250$	−1.68847e10	−0.273379
$251$	−1.03901e11	−1.65229	−0.826144	−	0.563458i	$-0.809470\pi$
$251$	−1.03901e11	−1.65229	−0.826144	+	0.563458i	$0.809470\pi$
$252$	1.62894e10	0.254449
$253$	−5.40366e10	−0.829174
$254$	−1.34137e11	−2.02208
$255$	0	0
$256$	6.56722e10	0.955656
$257$	−8.68301e10	−1.24157	−0.620785	−	0.783981i	$-0.713186\pi$
$257$	−8.68301e10	−1.24157	−0.620785	+	0.783981i	$0.713186\pi$
$258$	−2.84240e10	−0.399390
$259$	9.50081e10	1.31193
$260$	−1.66517e9	−0.0225984
$261$	4.43920e10	0.592137
$262$	4.12098e9	0.0540312
$263$	1.65728e10	0.213596	0.106798	−	0.994281i	$-0.465940\pi$
$263$	1.65728e10	0.213596	0.106798	+	0.994281i	$0.465940\pi$
$264$	−4.78519e10	−0.606292
$265$	−2.55211e9	−0.0317902
$266$	6.32990e10	0.775229
$267$	7.28707e10	0.877510
$268$	−1.23399e10	−0.146118
$269$	−4.82317e10	−0.561626	−0.280813	−	0.959762i	$-0.590604\pi$
$269$	−4.82317e10	−0.561626	−0.280813	+	0.959762i	$0.590604\pi$
$270$	1.00608e10	0.115211
$271$	8.23997e10	0.928034	0.464017	−	0.885826i	$-0.346408\pi$
$271$	8.23997e10	0.928034	0.464017	+	0.885826i	$0.346408\pi$
$272$	0	0
$273$	−2.09171e10	−0.227913
$274$	4.98129e10	0.533905
$275$	1.61314e11	1.70088
$276$	−7.83847e9	−0.0813094
$277$	7.60846e9	0.0776493	0.0388247	−	0.999246i	$-0.487639\pi$
$277$	7.60846e9	0.0776493	0.0388247	+	0.999246i	$0.487639\pi$
$278$	2.12117e11	2.12997
$279$	−5.47311e10	−0.540774
$280$	8.24675e9	0.0801810
$281$	−1.09198e10	−0.104481	−0.0522405	−	0.998635i	$-0.516636\pi$
$281$	−1.09198e10	−0.104481	−0.0522405	+	0.998635i	$0.516636\pi$
$282$	−2.91724e10	−0.274696
$283$	−8.41546e10	−0.779900	−0.389950	−	0.920836i	$-0.627508\pi$
$283$	−8.41546e10	−0.779900	−0.389950	+	0.920836i	$0.627508\pi$
$284$	1.82479e10	0.166449
$285$	4.52465e9	0.0406240
$286$	1.21192e11	1.07109
$287$	−1.26584e11	−1.10131
$288$	6.24907e10	0.535241
$289$	0	0
$290$	−1.26099e10	−0.104694
$291$	−3.55995e10	−0.291022
$292$	−3.28751e10	−0.264633
$293$	−2.03804e11	−1.61550	−0.807751	−	0.589524i	$-0.799316\pi$
$293$	−2.03804e11	−1.61550	−0.807751	+	0.589524i	$0.799316\pi$
$294$	1.21674e10	0.0949806
$295$	−1.41634e10	−0.108885
$296$	1.42314e11	1.07755
$297$	−1.93596e11	−1.44375
$298$	2.89992e11	2.13016
$299$	−3.53816e10	−0.256010
$300$	2.33999e10	0.166790
$301$	−9.42614e10	−0.661888
$302$	4.55449e9	0.0315071
$303$	4.63912e10	0.316187
$304$	1.33951e11	0.899529
$305$	2.61104e10	0.172768
$306$	0	0
$307$	2.05276e11	1.31891	0.659455	−	0.751744i	$-0.270787\pi$
$307$	2.05276e11	1.31891	0.659455	+	0.751744i	$0.270787\pi$
$308$	8.90382e10	0.563765
$309$	1.00577e11	0.627606
$310$	1.55468e10	0.0956124
$311$	6.35962e9	0.0385487	0.0192743	−	0.999814i	$-0.493864\pi$
$311$	6.35962e9	0.0385487	0.0192743	+	0.999814i	$0.493864\pi$
$312$	−3.13320e10	−0.187195
$313$	3.19617e11	1.88227	0.941133	−	0.338037i	$-0.109763\pi$
$313$	3.19617e11	1.88227	0.941133	+	0.338037i	$0.109763\pi$
$314$	4.31488e10	0.250487
$315$	1.46047e10	0.0835784
$316$	−5.92398e10	−0.334212
$317$	5.43063e10	0.302053	0.151027	−	0.988530i	$-0.451742\pi$
$317$	5.43063e10	0.302053	0.151027	+	0.988530i	$0.451742\pi$
$318$	2.69439e10	0.147754
$319$	2.42648e11	1.31196
$320$	9.49222e9	0.0506049
$321$	1.49682e11	0.786858
$322$	−9.83175e10	−0.509659
$323$	0	0
$324$	2.74217e10	0.138242
$325$	1.05623e11	0.525152
$326$	1.34069e11	0.657427
$327$	−5.92248e10	−0.286443
$328$	−1.89613e11	−0.904555
$329$	−9.67433e10	−0.455239
$330$	2.40722e10	0.111739
$331$	−1.24105e11	−0.568283	−0.284141	−	0.958782i	$-0.591708\pi$
$331$	−1.24105e11	−0.568283	−0.284141	+	0.958782i	$0.591708\pi$
$332$	−1.37758e11	−0.622294
$333$	2.52033e11	1.12320
$334$	6.75286e10	0.296913
$335$	−1.10636e10	−0.0479950
$336$	−1.23000e11	−0.526475
$337$	−1.12724e11	−0.476081	−0.238041	−	0.971255i	$-0.576505\pi$
$337$	−1.12724e11	−0.476081	−0.238041	+	0.971255i	$0.576505\pi$
$338$	−2.00418e11	−0.835239
$339$	−1.34353e11	−0.552522
$340$	0	0
$341$	−2.99162e11	−1.19815
$342$	1.67916e11	0.663706
$343$	2.73454e11	1.06675
$344$	−1.41196e11	−0.543636
$345$	−7.02779e9	−0.0267075
$346$	3.37401e10	0.126562
$347$	−2.77880e11	−1.02890	−0.514452	−	0.857519i	$-0.672005\pi$
$347$	−2.77880e11	−1.02890	−0.514452	+	0.857519i	$0.672005\pi$
$348$	3.51982e10	0.128651
$349$	−2.69627e10	−0.0972857	−0.0486429	−	0.998816i	$-0.515490\pi$
$349$	−2.69627e10	−0.0972857	−0.0486429	+	0.998816i	$0.515490\pi$
$350$	2.93504e11	1.04546
$351$	−1.26761e11	−0.445762
$352$	3.41576e11	1.18589
$353$	4.08754e11	1.40112	0.700560	−	0.713593i	$-0.252934\pi$
$353$	4.08754e11	1.40112	0.700560	+	0.713593i	$0.252934\pi$
$354$	1.49530e11	0.506072
$355$	1.63607e10	0.0546731
$356$	−2.03103e11	−0.670181
$357$	0	0
$358$	−2.79205e10	−0.0898359
$359$	3.75018e11	1.19159	0.595796	−	0.803136i	$-0.296837\pi$
$359$	3.75018e11	1.19159	0.595796	+	0.803136i	$0.296837\pi$
$360$	2.18765e10	0.0686464
$361$	−1.50169e11	−0.465371
$362$	−1.01540e11	−0.310777
$363$	−3.07530e11	−0.929625
$364$	5.82996e10	0.174064
$365$	−2.94751e10	−0.0869235
$366$	−2.75660e11	−0.802987
$367$	3.22410e11	0.927707	0.463853	−	0.885912i	$-0.346466\pi$
$367$	3.22410e11	0.927707	0.463853	+	0.885912i	$0.346466\pi$
$368$	−2.08056e11	−0.591378
$369$	−3.35797e11	−0.942882
$370$	−7.15920e10	−0.198590
$371$	8.93528e10	0.244864
$372$	−4.33961e10	−0.117492
$373$	−2.11324e11	−0.565275	−0.282638	−	0.959227i	$-0.591209\pi$
$373$	−2.11324e11	−0.565275	−0.282638	+	0.959227i	$0.591209\pi$
$374$	0	0
$375$	4.22562e10	0.110344
$376$	−1.44913e11	−0.373906
$377$	1.58879e11	0.405070
$378$	−3.52240e11	−0.887413
$379$	−4.67354e11	−1.16351	−0.581755	−	0.813364i	$-0.697634\pi$
$379$	−4.67354e11	−1.16351	−0.581755	+	0.813364i	$0.697634\pi$
$380$	−1.26110e10	−0.0310258
$381$	3.35695e11	0.816175
$382$	8.70666e11	2.09202
$383$	6.63614e11	1.57587	0.787937	−	0.615756i	$-0.211149\pi$
$383$	6.63614e11	1.57587	0.787937	+	0.615756i	$0.211149\pi$
$384$	−2.38071e11	−0.558748
$385$	7.98296e10	0.185179
$386$	7.51942e11	1.72402
$387$	−2.50052e11	−0.566671
$388$	9.92220e10	0.222262
$389$	−1.12068e9	−0.00248146	−0.00124073	−	0.999999i	$-0.500395\pi$
$389$	−1.12068e9	−0.00248146	−0.00124073	+	0.999999i	$0.500395\pi$
$390$	1.57618e10	0.0344996
$391$	0	0
$392$	6.04412e10	0.129284
$393$	−1.03133e10	−0.0218087
$394$	−8.09393e11	−1.69210
$395$	−5.31131e10	−0.109778
$396$	2.36196e11	0.482663
$397$	−5.23692e11	−1.05808	−0.529040	−	0.848597i	$-0.677448\pi$
$397$	−5.23692e11	−1.05808	−0.529040	+	0.848597i	$0.677448\pi$
$398$	−7.29659e11	−1.45763
$399$	−1.58414e11	−0.312907
$400$	6.21102e11	1.21309
$401$	−4.63692e11	−0.895529	−0.447765	−	0.894152i	$-0.647780\pi$
$401$	−4.63692e11	−0.895529	−0.447765	+	0.894152i	$0.647780\pi$
$402$	1.16804e11	0.223070
$403$	−1.95883e11	−0.369933
$404$	−1.29301e11	−0.241482
$405$	2.45856e10	0.0454082
$406$	4.41490e11	0.806405
$407$	1.37762e12	2.48860
$408$	0	0
$409$	−9.57093e11	−1.69122	−0.845608	−	0.533804i	$-0.820762\pi$
$409$	−9.57093e11	−1.69122	−0.845608	+	0.533804i	$0.820762\pi$
$410$	9.53858e10	0.166708
$411$	−1.24663e11	−0.215501
$412$	−2.80327e11	−0.479322
$413$	4.95878e11	0.838687
$414$	−2.60812e11	−0.436341
$415$	−1.23511e11	−0.204403
$416$	2.23654e11	0.366148
$417$	−5.30850e11	−0.859725
$418$	9.17838e11	1.47053
$419$	−9.55806e11	−1.51498	−0.757490	−	0.652847i	$-0.773574\pi$
$419$	−9.55806e11	−1.51498	−0.757490	+	0.652847i	$0.773574\pi$
$420$	1.15800e10	0.0181587
$421$	−2.81196e11	−0.436255	−0.218127	−	0.975920i	$-0.569995\pi$
$421$	−2.81196e11	−0.436255	−0.218127	+	0.975920i	$0.569995\pi$
$422$	−5.68969e11	−0.873338
$423$	−2.56636e11	−0.389749
$424$	1.33843e11	0.201117
$425$	0	0
$426$	−1.72727e11	−0.254108
$427$	−9.14159e11	−1.33075
$428$	−4.17189e11	−0.600947
$429$	−3.03298e11	−0.432327
$430$	7.10293e10	0.100191
$431$	−7.09416e11	−0.990268	−0.495134	−	0.868816i	$-0.664881\pi$
$431$	−7.09416e11	−0.990268	−0.495134	+	0.868816i	$0.664881\pi$
$432$	−7.45398e11	−1.02970
$433$	3.80004e11	0.519509	0.259754	−	0.965675i	$-0.416358\pi$
$433$	3.80004e11	0.519509	0.259754	+	0.965675i	$0.416358\pi$
$434$	−5.44315e11	−0.736455
$435$	3.15579e10	0.0422578
$436$	1.65070e11	0.218766
$437$	−2.67959e11	−0.351481
$438$	3.11182e11	0.404000
$439$	−6.03199e11	−0.775123	−0.387561	−	0.921844i	$-0.626683\pi$
$439$	−6.03199e11	−0.775123	−0.387561	+	0.921844i	$0.626683\pi$
$440$	1.19578e11	0.152095
$441$	1.07039e11	0.134762
$442$	0	0
$443$	−1.25487e12	−1.54804	−0.774018	−	0.633164i	$-0.781756\pi$
$443$	−1.25487e12	−1.54804	−0.774018	+	0.633164i	$0.781756\pi$
$444$	1.99836e11	0.244034
$445$	−1.82098e11	−0.220133
$446$	−1.67405e11	−0.200337
$447$	−7.25742e11	−0.859802
$448$	−3.32335e11	−0.389785
$449$	3.37996e11	0.392467	0.196234	−	0.980557i	$-0.437129\pi$
$449$	3.37996e11	0.392467	0.196234	+	0.980557i	$0.437129\pi$
$450$	7.78592e11	0.895063
$451$	−1.83548e12	−2.08908
$452$	3.74466e11	0.421978
$453$	−1.13982e10	−0.0127173
$454$	4.32878e11	0.478206
$455$	5.22701e10	0.0571744
$456$	−2.37291e11	−0.257003
$457$	2.71721e11	0.291407	0.145704	−	0.989328i	$-0.453455\pi$
$457$	2.71721e11	0.291407	0.145704	+	0.989328i	$0.453455\pi$
$458$	−1.92171e12	−2.04077
$459$	0	0
$460$	1.95877e10	0.0203973
$461$	−1.31496e12	−1.35600	−0.677998	−	0.735064i	$-0.737152\pi$
$461$	−1.31496e12	−1.35600	−0.677998	+	0.735064i	$0.737152\pi$
$462$	−8.42799e11	−0.860667
$463$	1.78291e12	1.80308	0.901539	−	0.432698i	$-0.142439\pi$
$463$	1.78291e12	1.80308	0.901539	+	0.432698i	$0.142439\pi$
$464$	9.34264e11	0.935705
$465$	−3.89079e10	−0.0385922
$466$	−1.53459e12	−1.50750
$467$	1.44519e11	0.140605	0.0703024	−	0.997526i	$-0.477604\pi$
$467$	1.44519e11	0.140605	0.0703024	+	0.997526i	$0.477604\pi$
$468$	1.54654e11	0.149024
$469$	3.87352e11	0.369682
$470$	7.28995e10	0.0689103
$471$	−1.07985e11	−0.101105
$472$	7.42784e11	0.688848
$473$	−1.36679e12	−1.25553
$474$	5.60740e11	0.510222
$475$	7.99930e11	0.720992
$476$	0	0
$477$	2.37031e11	0.209639
$478$	1.30852e12	1.14645
$479$	−1.99283e12	−1.72966	−0.864829	−	0.502067i	$-0.832573\pi$
$479$	−1.99283e12	−1.72966	−0.864829	+	0.502067i	$0.832573\pi$
$480$	4.44241e10	0.0381974
$481$	9.02025e11	0.768362
$482$	−7.68079e11	−0.648178
$483$	2.46052e11	0.205715
$484$	8.57140e11	0.709982
$485$	8.89601e10	0.0730058
$486$	−1.45979e12	−1.18693
$487$	−1.82408e12	−1.46948	−0.734740	−	0.678349i	$-0.762696\pi$
$487$	−1.82408e12	−1.46948	−0.734740	+	0.678349i	$0.762696\pi$
$488$	−1.36933e12	−1.09300
$489$	−3.35523e11	−0.265359
$490$	−3.04053e10	−0.0238269
$491$	1.68204e12	1.30608	0.653039	−	0.757325i	$-0.273494\pi$
$491$	1.68204e12	1.30608	0.653039	+	0.757325i	$0.273494\pi$
$492$	−2.66252e11	−0.204856
$493$	0	0
$494$	6.00973e11	0.454029
$495$	2.11768e11	0.158539
$496$	−1.15186e12	−0.854539
$497$	−5.72808e11	−0.421119
$498$	1.30396e12	0.950019
$499$	2.30279e10	0.0166266	0.00831328	−	0.999965i	$-0.497354\pi$
$499$	2.30279e10	0.0166266	0.00831328	+	0.999965i	$0.497354\pi$
$500$	−1.17775e11	−0.0842733
$501$	−1.68999e11	−0.119843
$502$	−2.74113e12	−1.92647
$503$	6.75145e11	0.470264	0.235132	−	0.971963i	$-0.424448\pi$
$503$	6.75145e11	0.470264	0.235132	+	0.971963i	$0.424448\pi$
$504$	−7.65926e11	−0.528749
$505$	−1.15928e11	−0.0793189
$506$	−1.42561e12	−0.966768
$507$	5.01570e11	0.337129
$508$	−9.35642e11	−0.623337
$509$	2.78050e12	1.83609	0.918043	−	0.396481i	$-0.129769\pi$
$509$	2.78050e12	1.83609	0.918043	+	0.396481i	$0.129769\pi$
$510$	0	0
$511$	1.03196e12	0.669528
$512$	−1.13578e11	−0.0730429
$513$	−9.60012e11	−0.611996
$514$	−2.29077e12	−1.44760
$515$	−2.51334e11	−0.157442
$516$	−1.98265e11	−0.123118
$517$	−1.40278e12	−0.863539
$518$	2.50653e12	1.52964
$519$	−8.44390e10	−0.0510846
$520$	7.82962e10	0.0469597
$521$	1.68557e12	1.00225	0.501126	−	0.865374i	$-0.332919\pi$
$521$	1.68557e12	1.00225	0.501126	+	0.865374i	$0.332919\pi$
$522$	1.17116e12	0.690398
$523$	2.39587e12	1.40025	0.700124	−	0.714021i	$-0.253128\pi$
$523$	2.39587e12	1.40025	0.700124	+	0.714021i	$0.253128\pi$
$524$	2.87449e10	0.0166560
$525$	−7.34531e11	−0.421981
$526$	4.37227e11	0.249041
$527$	0	0
$528$	−1.78350e12	−0.998667
$529$	−1.38495e12	−0.768925
$530$	−6.73305e10	−0.0370655
$531$	1.31544e12	0.718035
$532$	4.41527e11	0.238976
$533$	−1.20182e12	−0.645009
$534$	1.92249e12	1.02313
$535$	−3.74042e11	−0.197392
$536$	5.80221e11	0.303635
$537$	6.98747e10	0.0362606
$538$	−1.27246e12	−0.654824
$539$	5.85079e11	0.298583
$540$	7.01764e10	0.0355156
$541$	−2.02996e12	−1.01882	−0.509412	−	0.860523i	$-0.670137\pi$
$541$	−2.02996e12	−1.01882	−0.509412	+	0.860523i	$0.670137\pi$
$542$	2.17389e12	1.08203
$543$	2.54117e11	0.125440
$544$	0	0
$545$	1.47998e11	0.0718574
$546$	−5.51840e11	−0.265734
$547$	2.99699e12	1.43134	0.715670	−	0.698439i	$-0.246122\pi$
$547$	2.99699e12	1.43134	0.715670	+	0.698439i	$0.246122\pi$
$548$	3.47458e11	0.164585
$549$	−2.42503e12	−1.13931
$550$	4.25582e12	1.98313
$551$	1.20326e12	0.556130
$552$	3.68565e11	0.168962
$553$	1.85956e12	0.845564
$554$	2.00728e11	0.0905346
$555$	1.79168e11	0.0801571
$556$	1.47957e12	0.656598
$557$	−2.35072e12	−1.03479	−0.517396	−	0.855746i	$-0.673098\pi$
$557$	−2.35072e12	−1.03479	−0.517396	+	0.855746i	$0.673098\pi$
$558$	−1.44393e12	−0.630510
$559$	−8.94936e11	−0.387649
$560$	3.07366e11	0.132072
$561$	0	0
$562$	−2.88090e11	−0.121819
$563$	1.06843e12	0.448186	0.224093	−	0.974568i	$-0.428058\pi$
$563$	1.06843e12	0.448186	0.224093	+	0.974568i	$0.428058\pi$
$564$	−2.03485e11	−0.0846793
$565$	3.35737e11	0.138606
$566$	−2.22019e12	−0.909318
$567$	−8.60775e11	−0.349757
$568$	−8.58018e11	−0.345883
$569$	−6.61622e11	−0.264609	−0.132305	−	0.991209i	$-0.542238\pi$
$569$	−6.61622e11	−0.264609	−0.132305	+	0.991209i	$0.542238\pi$
$570$	1.19370e11	0.0473653
$571$	1.31584e11	0.0518013	0.0259007	−	0.999665i	$-0.491755\pi$
$571$	1.31584e11	0.0518013	0.0259007	+	0.999665i	$0.491755\pi$
$572$	8.45346e11	0.330181
$573$	−2.17895e12	−0.844407
$574$	−3.33958e12	−1.28407
$575$	−1.24247e12	−0.474002
$576$	−8.81601e11	−0.333711
$577$	−3.61547e9	−0.00135792	−0.000678959	−	1.00000i	$-0.500216\pi$
$577$	−3.61547e9	−0.00135792	−0.000678959		1.00000i	$0.500216\pi$
$578$	0	0
$579$	−1.88183e12	−0.695868
$580$	−8.79575e10	−0.0322735
$581$	4.32427e12	1.57442
$582$	−9.39194e11	−0.339314
$583$	1.29562e12	0.464481
$584$	1.54579e12	0.549911
$585$	1.38659e11	0.0489495
$586$	−5.37680e12	−1.88358
$587$	1.61905e12	0.562846	0.281423	−	0.959584i	$-0.409194\pi$
$587$	1.61905e12	0.562846	0.281423	+	0.959584i	$0.409194\pi$
$588$	8.48708e10	0.0292793
$589$	−1.48350e12	−0.507889
$590$	−3.73662e11	−0.126953
$591$	2.02561e12	0.682986
$592$	5.30422e12	1.77490
$593$	−6.34063e11	−0.210565	−0.105283	−	0.994442i	$-0.533575\pi$
$593$	−6.34063e11	−0.210565	−0.105283	+	0.994442i	$0.533575\pi$
$594$	−5.10749e12	−1.68333
$595$	0	0
$596$	2.02277e12	0.656657
$597$	1.82606e12	0.588344
$598$	−9.33445e11	−0.298493
$599$	1.09199e12	0.346576	0.173288	−	0.984871i	$-0.444561\pi$
$599$	1.09199e12	0.346576	0.173288	+	0.984871i	$0.444561\pi$
$600$	−1.10027e12	−0.346591
$601$	−4.20600e12	−1.31502	−0.657512	−	0.753444i	$-0.728391\pi$
$601$	−4.20600e12	−1.31502	−0.657512	+	0.753444i	$0.728391\pi$
$602$	−2.48683e12	−0.771723
$603$	1.02755e12	0.316500
$604$	3.17688e10	0.00971257
$605$	7.68492e11	0.233206
$606$	1.22391e12	0.368656
$607$	6.33595e11	0.189436	0.0947181	−	0.995504i	$-0.469805\pi$
$607$	6.33595e11	0.189436	0.0947181	+	0.995504i	$0.469805\pi$
$608$	1.69383e12	0.502693
$609$	−1.10488e12	−0.325491
$610$	6.88851e11	0.201438
$611$	−9.18499e11	−0.266620
$612$	0	0
$613$	4.65062e12	1.33027	0.665133	−	0.746724i	$-0.268375\pi$
$613$	4.65062e12	1.33027	0.665133	+	0.746724i	$0.268375\pi$
$614$	5.41564e12	1.53777
$615$	−2.38715e11	−0.0672886
$616$	−4.18658e12	−1.17151
$617$	−2.62356e12	−0.728799	−0.364400	−	0.931243i	$-0.618726\pi$
$617$	−2.62356e12	−0.728799	−0.364400	+	0.931243i	$0.618726\pi$
$618$	2.65346e12	0.731752
$619$	6.55858e12	1.79557	0.897784	−	0.440437i	$-0.145176\pi$
$619$	6.55858e12	1.79557	0.897784	+	0.440437i	$0.145176\pi$
$620$	1.08443e11	0.0294740
$621$	1.49111e12	0.402345
$622$	1.67781e11	0.0449455
$623$	6.37548e12	1.69557
$624$	−1.16778e12	−0.308341
$625$	3.65593e12	0.958381
$626$	8.43223e12	2.19461
$627$	−2.29700e12	−0.593551
$628$	3.00974e11	0.0772167
$629$	0	0
$630$	3.85304e11	0.0974475
$631$	5.79881e11	0.145615	0.0728076	−	0.997346i	$-0.476804\pi$
$631$	5.79881e11	0.145615	0.0728076	+	0.997346i	$0.476804\pi$
$632$	2.78546e12	0.694496
$633$	1.42392e12	0.352507
$634$	1.43272e12	0.352177
$635$	−8.38875e11	−0.204746
$636$	1.87941e11	0.0455474
$637$	3.83093e11	0.0921885
$638$	6.40161e12	1.52966
$639$	−1.51952e12	−0.360538
$640$	5.94920e11	0.140168
$641$	5.03353e12	1.17764	0.588819	−	0.808265i	$-0.299593\pi$
$641$	5.03353e12	1.17764	0.588819	+	0.808265i	$0.299593\pi$
$642$	3.94894e12	0.917431
$643$	6.36495e12	1.46840	0.734202	−	0.678931i	$-0.237556\pi$
$643$	6.36495e12	1.46840	0.734202	+	0.678931i	$0.237556\pi$
$644$	−6.85790e11	−0.157110
$645$	−1.77760e11	−0.0404403
$646$	0	0
$647$	−3.40666e12	−0.764292	−0.382146	−	0.924102i	$-0.624815\pi$
$647$	−3.40666e12	−0.764292	−0.382146	+	0.924102i	$0.624815\pi$
$648$	−1.28937e12	−0.287269
$649$	7.19025e12	1.59090
$650$	2.78658e12	0.612297
$651$	1.36222e12	0.297257
$652$	9.35163e11	0.202662
$653$	2.99407e12	0.644397	0.322198	−	0.946672i	$-0.395578\pi$
$653$	2.99407e12	0.644397	0.322198	+	0.946672i	$0.395578\pi$
$654$	−1.56248e12	−0.333976
$655$	2.57720e10	0.00547095
$656$	−7.06710e12	−1.48996
$657$	2.73753e12	0.573212
$658$	−2.55231e12	−0.530782
$659$	−2.03535e12	−0.420392	−0.210196	−	0.977659i	$-0.567410\pi$
$659$	−2.03535e12	−0.420392	−0.210196	+	0.977659i	$0.567410\pi$
$660$	1.67910e11	0.0344452
$661$	−7.04693e12	−1.43580	−0.717900	−	0.696147i	$-0.754896\pi$
$661$	−7.04693e12	−1.43580	−0.717900	+	0.696147i	$0.754896\pi$
$662$	−3.27418e12	−0.662584
$663$	0	0
$664$	6.47739e12	1.29313
$665$	3.95863e11	0.0784960
$666$	6.64919e12	1.30959
$667$	−1.86893e12	−0.365617
$668$	4.71030e11	0.0915281
$669$	4.18951e11	0.0808622
$670$	−2.91884e11	−0.0559594
$671$	−1.32553e13	−2.52429
$672$	−1.55535e12	−0.294215
$673$	4.04986e12	0.760979	0.380489	−	0.924785i	$-0.375756\pi$
$673$	4.04986e12	0.760979	0.380489	+	0.924785i	$0.375756\pi$
$674$	−2.97391e12	−0.555083
$675$	−4.45137e12	−0.825328
$676$	−1.39796e12	−0.257476
$677$	8.15388e11	0.149182	0.0745908	−	0.997214i	$-0.476235\pi$
$677$	8.15388e11	0.149182	0.0745908	+	0.997214i	$0.476235\pi$
$678$	−3.54454e12	−0.644208
$679$	−3.11461e12	−0.562328
$680$	0	0
$681$	−1.08333e12	−0.193019
$682$	−7.89258e12	−1.39698
$683$	−3.55244e12	−0.624645	−0.312322	−	0.949976i	$-0.601107\pi$
$683$	−3.55244e12	−0.624645	−0.312322	+	0.949976i	$0.601107\pi$
$684$	1.17126e12	0.204598
$685$	3.11523e11	0.0540607
$686$	7.21434e12	1.24376
$687$	4.80933e12	0.823719
$688$	−5.26253e12	−0.895461
$689$	8.48332e11	0.143410
$690$	−1.85409e11	−0.0311394
$691$	−2.88386e11	−0.0481197	−0.0240598	−	0.999711i	$-0.507659\pi$
$691$	−2.88386e11	−0.0481197	−0.0240598	+	0.999711i	$0.507659\pi$
$692$	2.35346e11	0.0390148
$693$	−7.41427e12	−1.22115
$694$	−7.33110e12	−1.19964
$695$	1.32655e12	0.215671
$696$	−1.65502e12	−0.267339
$697$	0	0
$698$	−7.11337e11	−0.113429
$699$	3.84052e12	0.608474
$700$	2.04727e12	0.322280
$701$	1.10902e12	0.173463	0.0867315	−	0.996232i	$-0.472358\pi$
$701$	1.10902e12	0.173463	0.0867315	+	0.996232i	$0.472358\pi$
$702$	−3.34423e12	−0.519732
$703$	6.83141e12	1.05490
$704$	−4.81886e12	−0.739380
$705$	−1.82440e11	−0.0278144
$706$	1.07838e13	1.63362
$707$	4.05878e12	0.610954
$708$	1.04301e12	0.156005
$709$	7.04264e12	1.04671	0.523356	−	0.852114i	$-0.324680\pi$
$709$	7.04264e12	1.04671	0.523356	+	0.852114i	$0.324680\pi$
$710$	4.31631e11	0.0637456
$711$	4.93294e12	0.723923
$712$	9.54993e12	1.39264
$713$	2.30421e12	0.333902
$714$	0	0
$715$	7.57918e11	0.108454
$716$	−1.94753e11	−0.0276933
$717$	−3.27473e12	−0.462743
$718$	9.89382e12	1.38933
$719$	−1.73354e12	−0.241910	−0.120955	−	0.992658i	$-0.538596\pi$
$719$	−1.73354e12	−0.241910	−0.120955	+	0.992658i	$0.538596\pi$
$720$	8.15366e11	0.113072
$721$	8.79954e12	1.21269
$722$	−3.96181e12	−0.542595
$723$	1.92222e12	0.261625
$724$	−7.08269e11	−0.0958020
$725$	5.57924e12	0.749988
$726$	−8.11333e12	−1.08389
$727$	8.60821e11	0.114290	0.0571450	−	0.998366i	$-0.481800\pi$
$727$	8.60821e11	0.114290	0.0571450	+	0.998366i	$0.481800\pi$
$728$	−2.74125e12	−0.361707
$729$	7.20293e11	0.0944572
$730$	−7.77619e11	−0.101348
$731$	0	0
$732$	−1.92280e12	−0.247534
$733$	−1.51716e13	−1.94117	−0.970583	−	0.240766i	$-0.922602\pi$
$733$	−1.51716e13	−1.94117	−0.970583	+	0.240766i	$0.922602\pi$
$734$	8.50589e12	1.08165
$735$	7.60932e10	0.00961729
$736$	−2.63089e12	−0.330486
$737$	5.61662e12	0.701247
$738$	−8.85907e12	−1.09935
$739$	4.87991e12	0.601882	0.300941	−	0.953643i	$-0.402699\pi$
$739$	4.87991e12	0.601882	0.300941	+	0.953643i	$0.402699\pi$
$740$	−4.99373e11	−0.0612184
$741$	−1.50401e12	−0.183261
$742$	2.35733e12	0.285498
$743$	3.76850e12	0.453648	0.226824	−	0.973936i	$-0.427166\pi$
$743$	3.76850e12	0.453648	0.226824	+	0.973936i	$0.427166\pi$
$744$	2.04049e12	0.244149
$745$	1.81357e12	0.215690
$746$	−5.57521e12	−0.659078
$747$	1.14712e13	1.34793
$748$	0	0
$749$	1.30957e13	1.52041
$750$	1.11481e12	0.128655
$751$	−6.74548e12	−0.773808	−0.386904	−	0.922120i	$-0.626455\pi$
$751$	−6.74548e12	−0.773808	−0.386904	+	0.922120i	$0.626455\pi$
$752$	−5.40110e12	−0.615888
$753$	6.86002e12	0.777586
$754$	4.19159e12	0.472288
$755$	2.84831e10	0.00319026
$756$	−2.45697e12	−0.273559
$757$	−1.07821e13	−1.19336	−0.596682	−	0.802477i	$-0.703515\pi$
$757$	−1.07821e13	−1.19336	−0.596682	+	0.802477i	$0.703515\pi$
$758$	−1.23299e13	−1.35658
$759$	3.56776e12	0.390218
$760$	5.92969e11	0.0644720
$761$	−7.42380e12	−0.802408	−0.401204	−	0.915989i	$-0.631408\pi$
$761$	−7.42380e12	−0.802408	−0.401204	+	0.915989i	$0.631408\pi$
$762$	8.85640e12	0.951612
$763$	−5.18160e12	−0.553482
$764$	6.07312e12	0.644899
$765$	0	0
$766$	1.75076e13	1.83738
$767$	4.70796e12	0.491195
$768$	−4.33600e12	−0.449742
$769$	1.65746e13	1.70913	0.854565	−	0.519345i	$-0.173824\pi$
$769$	1.65746e13	1.70913	0.854565	+	0.519345i	$0.173824\pi$
$770$	2.10608e12	0.215907
$771$	5.73295e12	0.584297
$772$	5.24499e12	0.531455
$773$	8.48204e12	0.854462	0.427231	−	0.904143i	$-0.359489\pi$
$773$	8.48204e12	0.854462	0.427231	+	0.904143i	$0.359489\pi$
$774$	−6.59693e12	−0.660705
$775$	−6.87868e12	−0.684932
$776$	−4.66542e12	−0.461863
$777$	−6.27291e12	−0.617411
$778$	−2.95660e10	−0.00289324
$779$	−9.10185e12	−0.885546
$780$	1.09942e11	0.0106351
$781$	−8.30573e12	−0.798819
$782$	0	0
$783$	−6.69576e12	−0.636608
$784$	2.25272e12	0.212953
$785$	2.69847e11	0.0253632
$786$	−2.72087e11	−0.0254277
$787$	1.63530e13	1.51954	0.759768	−	0.650195i	$-0.225313\pi$
$787$	1.63530e13	1.51954	0.759768	+	0.650195i	$0.225313\pi$
$788$	−5.64573e12	−0.521617
$789$	−1.09421e12	−0.100521
$790$	−1.40124e12	−0.127995
$791$	−1.17546e13	−1.06761
$792$	−1.11059e13	−1.00298
$793$	−8.67920e12	−0.779382
$794$	−1.38162e13	−1.23366
$795$	1.68503e11	0.0149608
$796$	−5.08956e12	−0.449336
$797$	−1.73733e13	−1.52518	−0.762590	−	0.646883i	$-0.776072\pi$
$797$	−1.73733e13	−1.52518	−0.762590	+	0.646883i	$0.776072\pi$
$798$	−4.17931e12	−0.364831
$799$	0	0
$800$	7.85391e12	0.677924
$801$	1.69125e13	1.45165
$802$	−1.22332e13	−1.04413
$803$	1.49635e13	1.27002
$804$	8.14739e11	0.0687648
$805$	−6.14864e11	−0.0516057
$806$	−5.16783e12	−0.431321
$807$	3.18450e12	0.264308
$808$	6.07971e12	0.501802
$809$	−8.14620e12	−0.668631	−0.334316	−	0.942461i	$-0.608505\pi$
$809$	−8.14620e12	−0.668631	−0.334316	+	0.942461i	$0.608505\pi$
$810$	6.48624e11	0.0529433
$811$	6.41782e12	0.520947	0.260474	−	0.965481i	$-0.416121\pi$
$811$	6.41782e12	0.520947	0.260474	+	0.965481i	$0.416121\pi$
$812$	3.07950e12	0.248587
$813$	−5.44043e12	−0.436743
$814$	3.63447e13	2.90156
$815$	8.38445e11	0.0665680
$816$	0	0
$817$	−6.77772e12	−0.532212
$818$	−2.52503e13	−1.97186
$819$	−4.85464e12	−0.377033
$820$	6.65341e11	0.0513904
$821$	6.34823e12	0.487650	0.243825	−	0.969819i	$-0.421598\pi$
$821$	6.34823e12	0.487650	0.243825	+	0.969819i	$0.421598\pi$
$822$	−3.28889e12	−0.251262
$823$	1.96190e12	0.149066	0.0745329	−	0.997219i	$-0.476253\pi$
$823$	1.96190e12	0.149066	0.0745329	+	0.997219i	$0.476253\pi$
$824$	1.31810e13	0.996036
$825$	−1.06507e13	−0.800453
$826$	1.30824e13	0.977860
$827$	1.16150e13	0.863465	0.431732	−	0.902002i	$-0.357902\pi$
$827$	1.16150e13	0.863465	0.431732	+	0.902002i	$0.357902\pi$
$828$	−1.81923e12	−0.134509
$829$	7.30758e12	0.537376	0.268688	−	0.963227i	$-0.413410\pi$
$829$	7.30758e12	0.537376	0.268688	+	0.963227i	$0.413410\pi$
$830$	−3.25849e12	−0.238322
$831$	−5.02348e11	−0.0365426
$832$	−3.15525e12	−0.228286
$833$	0	0
$834$	−1.40050e13	−1.00239
$835$	4.22314e11	0.0300640
$836$	6.40216e12	0.453313
$837$	8.25524e12	0.581387
$838$	−2.52163e13	−1.76638
$839$	−1.23263e13	−0.858826	−0.429413	−	0.903108i	$-0.641280\pi$
$839$	−1.23263e13	−0.858826	−0.429413	+	0.903108i	$0.641280\pi$
$840$	−5.44491e11	−0.0377341
$841$	−6.11483e12	−0.421505
$842$	−7.41859e12	−0.508648
$843$	7.20981e11	0.0491699
$844$	−3.96871e12	−0.269220
$845$	−1.25338e12	−0.0845724
$846$	−6.77063e12	−0.454425
$847$	−2.69059e13	−1.79627
$848$	4.98849e12	0.331274
$849$	5.55630e12	0.367030
$850$	0	0
$851$	−1.06107e13	−0.693524
$852$	−1.20482e12	−0.0783327
$853$	−1.80405e13	−1.16675	−0.583376	−	0.812202i	$-0.698269\pi$
$853$	−1.80405e13	−1.16675	−0.583376	+	0.812202i	$0.698269\pi$
$854$	−2.41176e13	−1.55158
$855$	1.05013e12	0.0672038
$856$	1.96163e13	1.24878
$857$	−1.37524e13	−0.870895	−0.435448	−	0.900214i	$-0.643410\pi$
$857$	−1.37524e13	−0.870895	−0.435448	+	0.900214i	$0.643410\pi$
$858$	−8.00169e12	−0.504068
$859$	−9.46970e11	−0.0593427	−0.0296713	−	0.999560i	$-0.509446\pi$
$859$	−9.46970e11	−0.0593427	−0.0296713	+	0.999560i	$0.509446\pi$
$860$	4.95448e11	0.0308855
$861$	8.35772e12	0.518291
$862$	−1.87160e13	−1.15460
$863$	−1.77968e13	−1.09218	−0.546088	−	0.837728i	$-0.683884\pi$
$863$	−1.77968e13	−1.09218	−0.546088	+	0.837728i	$0.683884\pi$
$864$	−9.42563e12	−0.575438
$865$	2.11006e11	0.0128151
$866$	1.00254e13	0.605717
$867$	0	0
$868$	−3.79674e12	−0.227024
$869$	2.69636e13	1.60394
$870$	8.32569e11	0.0492701
$871$	3.67760e12	0.216512
$872$	−7.76160e12	−0.454597
$873$	−8.26227e12	−0.481433
$874$	−7.06937e12	−0.409807
$875$	3.69701e12	0.213213
$876$	2.17058e12	0.124539
$877$	2.60072e13	1.48455	0.742276	−	0.670095i	$-0.233747\pi$
$877$	2.60072e13	1.48455	0.742276	+	0.670095i	$0.233747\pi$
$878$	−1.59138e13	−0.903748
$879$	1.34561e13	0.760273
$880$	4.45682e12	0.250526
$881$	2.34952e13	1.31398	0.656989	−	0.753900i	$-0.271830\pi$
$881$	2.34952e13	1.31398	0.656989	+	0.753900i	$0.271830\pi$
$882$	2.82393e12	0.157125
$883$	9.42490e12	0.521739	0.260870	−	0.965374i	$-0.415991\pi$
$883$	9.42490e12	0.521739	0.260870	+	0.965374i	$0.415991\pi$
$884$	0	0
$885$	9.35136e11	0.0512425
$886$	−3.31062e13	−1.80492
$887$	9.43777e12	0.511933	0.255966	−	0.966686i	$-0.417606\pi$
$887$	9.43777e12	0.511933	0.255966	+	0.966686i	$0.417606\pi$
$888$	−9.39628e12	−0.507105
$889$	2.93701e13	1.57706
$890$	−4.80415e12	−0.256662
$891$	−1.24813e13	−0.663451
$892$	−1.16769e12	−0.0617569
$893$	−6.95618e12	−0.366049
$894$	−1.91467e13	−1.00248
$895$	−1.74611e11	−0.00909636
$896$	−2.08289e13	−1.07964
$897$	2.33607e12	0.120481
$898$	8.91711e12	0.457594
$899$	−1.03469e13	−0.528315
$900$	5.43088e12	0.275917
$901$	0	0
$902$	−4.84240e13	−2.43574
$903$	6.22360e12	0.311492
$904$	−1.76074e13	−0.876874
$905$	−6.35017e11	−0.0314678
$906$	−3.00710e11	−0.0148276
$907$	−1.43965e13	−0.706355	−0.353178	−	0.935556i	$-0.614899\pi$
$907$	−1.43965e13	−0.706355	−0.353178	+	0.935556i	$0.614899\pi$
$908$	3.01944e12	0.147414
$909$	1.07669e13	0.523064
$910$	1.37900e12	0.0666621
$911$	8.42261e12	0.405148	0.202574	−	0.979267i	$-0.435069\pi$
$911$	8.42261e12	0.405148	0.202574	+	0.979267i	$0.435069\pi$
$912$	−8.84411e12	−0.423328
$913$	6.27020e13	2.98650
$914$	7.16861e12	0.339764
$915$	−1.72394e12	−0.0813068
$916$	−1.34044e13	−0.629099
$917$	−9.02311e11	−0.0421400
$918$	0	0
$919$	4.07249e13	1.88339	0.941695	−	0.336469i	$-0.109233\pi$
$919$	4.07249e13	1.88339	0.941695	+	0.336469i	$0.109233\pi$
$920$	−9.21014e11	−0.0423859
$921$	−1.35533e13	−0.620694
$922$	−3.46916e13	−1.58101
$923$	−5.43835e12	−0.246638
$924$	−5.87874e12	−0.265314
$925$	3.16758e13	1.42262
$926$	4.70371e13	2.10228
$927$	2.33430e13	1.03824
$928$	1.18139e13	0.522909
$929$	−2.48550e13	−1.09482	−0.547410	−	0.836864i	$-0.684386\pi$
$929$	−2.48550e13	−1.09482	−0.547410	+	0.836864i	$0.684386\pi$
$930$	−1.02648e12	−0.0449963
$931$	2.90132e12	0.126568
$932$	−1.07042e13	−0.464710
$933$	−4.19893e11	−0.0181414
$934$	3.81275e12	0.163937
$935$	0	0
$936$	−7.27185e12	−0.309673
$937$	−1.96674e12	−0.0833526	−0.0416763	−	0.999131i	$-0.513270\pi$
$937$	−1.96674e12	−0.0833526	−0.0416763	+	0.999131i	$0.513270\pi$
$938$	1.02192e13	0.431028
$939$	−2.11027e13	−0.885815
$940$	5.08493e11	0.0212427
$941$	−2.86840e13	−1.19258	−0.596288	−	0.802770i	$-0.703358\pi$
$941$	−2.86840e13	−1.19258	−0.596288	+	0.802770i	$0.703358\pi$
$942$	−2.84890e12	−0.117882
$943$	1.41372e13	0.582185
$944$	2.76845e13	1.13465
$945$	−2.20286e12	−0.0898553
$946$	−3.60591e13	−1.46388
$947$	3.18106e13	1.28528	0.642640	−	0.766169i	$-0.277839\pi$
$947$	3.18106e13	1.28528	0.642640	+	0.766169i	$0.277839\pi$
$948$	3.91131e12	0.157284
$949$	9.79763e12	0.392124
$950$	2.11039e13	0.840635
$951$	−3.58557e12	−0.142150
$952$	0	0
$953$	−2.00740e13	−0.788343	−0.394171	−	0.919037i	$-0.628968\pi$
$953$	−2.00740e13	−0.788343	−0.394171	+	0.919037i	$0.628968\pi$
$954$	6.25340e12	0.244427
$955$	5.44502e12	0.211828
$956$	9.12726e12	0.353411
$957$	−1.60208e13	−0.617421
$958$	−5.25753e13	−2.01668
$959$	−1.09068e13	−0.416403
$960$	−6.26723e11	−0.0238152
$961$	−1.36828e13	−0.517513
$962$	2.37975e13	0.895865
$963$	3.47396e13	1.30169
$964$	−5.35755e12	−0.199811
$965$	4.70253e12	0.174566
$966$	6.49141e12	0.239851
$967$	−9.75077e12	−0.358608	−0.179304	−	0.983794i	$-0.557385\pi$
$967$	−9.75077e12	−0.358608	−0.179304	+	0.983794i	$0.557385\pi$
$968$	−4.03027e13	−1.47535
$969$	0	0
$970$	2.34697e12	0.0851205
$971$	3.82881e13	1.38222	0.691110	−	0.722750i	$-0.257122\pi$
$971$	3.82881e13	1.38222	0.691110	+	0.722750i	$0.257122\pi$
$972$	−1.01824e13	−0.365891
$973$	−4.64442e13	−1.66121
$974$	−4.81233e13	−1.71333
$975$	−6.97378e12	−0.247142
$976$	−5.10367e13	−1.80036
$977$	−7.30921e12	−0.256652	−0.128326	−	0.991732i	$-0.540960\pi$
$977$	−7.30921e12	−0.256652	−0.128326	+	0.991732i	$0.540960\pi$
$978$	−8.85186e12	−0.309393
$979$	9.24446e13	3.21632
$980$	−2.12085e11	−0.00734502
$981$	−1.37455e13	−0.473859
$982$	4.43759e13	1.52281
$983$	3.14313e13	1.07367	0.536836	−	0.843687i	$-0.319620\pi$
$983$	3.14313e13	1.07367	0.536836	+	0.843687i	$0.319620\pi$
$984$	1.25192e13	0.425694
$985$	−5.06183e12	−0.171334
$986$	0	0
$987$	6.38747e12	0.214240
$988$	4.19194e12	0.139962
$989$	1.05273e13	0.349892
$990$	5.58691e12	0.184848
$991$	5.32302e13	1.75318	0.876590	−	0.481238i	$-0.159813\pi$
$991$	5.32302e13	1.75318	0.876590	+	0.481238i	$0.159813\pi$
$992$	−1.45654e13	−0.477551
$993$	8.19404e12	0.267440
$994$	−1.51120e13	−0.491001
$995$	−4.56318e12	−0.147592
$996$	9.09547e12	0.292859
$997$	−2.49439e13	−0.799533	−0.399767	−	0.916617i	$-0.630909\pi$
$997$	−2.49439e13	−0.799533	−0.399767	+	0.916617i	$0.630909\pi$
$998$	6.07529e11	0.0193856
$999$	−3.80148e13	−1.20756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.e.1.9	yes	12
17.16	even	2		289.10.a.d.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.9	✓	12	17.16	even	2
289.10.a.e.1.9	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)

\(f(q)\)	\(=\)	\(q+26.3822 q^{2} -66.0249 q^{3} +184.023 q^{4} +164.991 q^{5} -1741.89 q^{6} -5776.54 q^{7} -8652.77 q^{8} -15323.7 q^{9} +O(q^{10})\)	\(q+26.3822 q^{2} -66.0249 q^{3} +184.023 q^{4} +164.991 q^{5} -1741.89 q^{6} -5776.54 q^{7} -8652.77 q^{8} -15323.7 q^{9} +4352.83 q^{10} -83760.0 q^{11} -12150.1 q^{12} -54843.6 q^{13} -152398. q^{14} -10893.5 q^{15} -322499. q^{16} -404274. q^{18} -415353. q^{19} +30362.1 q^{20} +381396. q^{21} -2.20978e6 q^{22} +645136. q^{23} +571298. q^{24} -1.92590e6 q^{25} -1.44690e6 q^{26} +2.31132e6 q^{27} -1.06302e6 q^{28} -2.89695e6 q^{29} -287395. q^{30} +3.57166e6 q^{31} -4.07804e6 q^{32} +5.53025e6 q^{33} -953076. q^{35} -2.81992e6 q^{36} -1.64472e7 q^{37} -1.09579e7 q^{38} +3.62104e6 q^{39} -1.42763e6 q^{40} +2.19135e7 q^{41} +1.00621e7 q^{42} +1.63180e7 q^{43} -1.54138e7 q^{44} -2.52827e6 q^{45} +1.70201e7 q^{46} +1.67476e7 q^{47} +2.12930e7 q^{48} -6.98519e6 q^{49} -5.08097e7 q^{50} -1.00925e7 q^{52} -1.54682e7 q^{53} +6.09777e7 q^{54} -1.38196e7 q^{55} +4.99831e7 q^{56} +2.74237e7 q^{57} -7.64280e7 q^{58} -8.58435e7 q^{59} -2.00466e6 q^{60} +1.58254e8 q^{61} +9.42285e7 q^{62} +8.85180e7 q^{63} +5.75318e7 q^{64} -9.04868e6 q^{65} +1.45900e8 q^{66} -6.70561e7 q^{67} -4.25951e7 q^{69} -2.51443e7 q^{70} +9.91611e7 q^{71} +1.32593e8 q^{72} -1.78647e8 q^{73} -4.33915e8 q^{74} +1.27158e8 q^{75} -7.64345e7 q^{76} +4.83843e8 q^{77} +9.55312e7 q^{78} -3.21915e8 q^{79} -5.32094e7 q^{80} +1.49012e8 q^{81} +5.78128e8 q^{82} -7.48591e8 q^{83} +7.01856e7 q^{84} +4.30505e8 q^{86} +1.91271e8 q^{87} +7.24756e8 q^{88} -1.10368e9 q^{89} -6.67015e7 q^{90} +3.16806e8 q^{91} +1.18720e8 q^{92} -2.35819e8 q^{93} +4.41840e8 q^{94} -6.85294e7 q^{95} +2.69252e8 q^{96} +5.39182e8 q^{97} -1.84285e8 q^{98} +1.28351e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 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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