LMFDB - Embedded newform 289.10.a.d.1.7

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:	$1$
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			1.7
Root			$4.74483$ 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)

$f(q)$	$=$	$q+5.74483 q^{2} +214.211 q^{3} -478.997 q^{4} -2392.81 q^{5} +1230.60 q^{6} +2771.45 q^{7} -5693.11 q^{8} +26203.3 q^{9} +O(q^{10})$	\(q+5.74483 q^{2} +214.211 q^{3} -478.997 q^{4} -2392.81 q^{5} +1230.60 q^{6} +2771.45 q^{7} -5693.11 q^{8} +26203.3 q^{9} -13746.3 q^{10} -54405.8 q^{11} -102606. q^{12} +187831. q^{13} +15921.5 q^{14} -512565. q^{15} +212541. q^{16} +150533. q^{18} +756343. q^{19} +1.14615e6 q^{20} +593675. q^{21} -312552. q^{22} -648115. q^{23} -1.21953e6 q^{24} +3.77240e6 q^{25} +1.07906e6 q^{26} +1.39672e6 q^{27} -1.32752e6 q^{28} -1.04851e6 q^{29} -2.94460e6 q^{30} -8.10714e6 q^{31} +4.13588e6 q^{32} -1.16543e7 q^{33} -6.63154e6 q^{35} -1.25513e7 q^{36} +8.95189e6 q^{37} +4.34506e6 q^{38} +4.02354e7 q^{39} +1.36225e7 q^{40} -3.34853e6 q^{41} +3.41056e6 q^{42} +1.81251e7 q^{43} +2.60602e7 q^{44} -6.26994e7 q^{45} -3.72331e6 q^{46} +2.47206e7 q^{47} +4.55285e7 q^{48} -3.26727e7 q^{49} +2.16718e7 q^{50} -8.99704e7 q^{52} -5.72785e7 q^{53} +8.02389e6 q^{54} +1.30183e8 q^{55} -1.57782e7 q^{56} +1.62017e8 q^{57} -6.02352e6 q^{58} +9.17398e7 q^{59} +2.45517e8 q^{60} +1.39714e7 q^{61} -4.65741e7 q^{62} +7.26211e7 q^{63} -8.50608e7 q^{64} -4.49443e8 q^{65} -6.69521e7 q^{66} -1.95676e8 q^{67} -1.38833e8 q^{69} -3.80971e7 q^{70} -5.02281e7 q^{71} -1.49178e8 q^{72} -1.39690e8 q^{73} +5.14271e7 q^{74} +8.08089e8 q^{75} -3.62286e8 q^{76} -1.50783e8 q^{77} +2.31145e8 q^{78} -1.15006e8 q^{79} -5.08568e8 q^{80} -2.16568e8 q^{81} -1.92367e7 q^{82} -5.34414e8 q^{83} -2.84368e8 q^{84} +1.04126e8 q^{86} -2.24603e8 q^{87} +3.09738e8 q^{88} -329484. q^{89} -3.60197e8 q^{90} +5.20563e8 q^{91} +3.10445e8 q^{92} -1.73664e9 q^{93} +1.42016e8 q^{94} -1.80978e9 q^{95} +8.85950e8 q^{96} +8.51166e8 q^{97} -1.87699e8 q^{98} -1.42561e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.74483	0.253888	0.126944	−	0.991910i	$-0.459483\pi$
$2$	5.74483	0.253888	0.126944	+	0.991910i	$0.459483\pi$
$3$	214.211	1.52685	0.763424	−	0.645898i	$-0.223517\pi$
$3$	214.211	1.52685	0.763424	+	0.645898i	$0.223517\pi$
$4$	−478.997	−0.935541
$5$	−2392.81	−1.71215	−0.856076	−	0.516849i	$-0.827105\pi$
$5$	−2392.81	−1.71215	−0.856076	+	0.516849i	$0.827105\pi$
$6$	1230.60	0.387648
$7$	2771.45	0.436281	0.218140	−	0.975917i	$-0.430001\pi$
$7$	2771.45	0.436281	0.218140	+	0.975917i	$0.430001\pi$
$8$	−5693.11	−0.491411
$9$	26203.3	1.33126
$10$	−13746.3	−0.434695
$11$	−54405.8	−1.12041	−0.560207	−	0.828353i	$-0.689278\pi$
$11$	−54405.8	−1.12041	−0.560207	+	0.828353i	$0.689278\pi$
$12$	−102606.	−1.42843
$13$	187831.	1.82399	0.911993	−	0.410205i	$-0.134543\pi$
$13$	187831.	1.82399	0.911993	+	0.410205i	$0.134543\pi$
$14$	15921.5	0.110766
$15$	−512565.	−2.61420
$16$	212541.	0.810778
$17$	0	0
$17$	0	0
$18$	150533.	0.337992
$19$	756343.	1.33146	0.665729	−	0.746193i	$-0.268120\pi$
$19$	756343.	1.33146	0.665729	+	0.746193i	$0.268120\pi$
$20$	1.14615e6	1.60179
$21$	593675.	0.666134
$22$	−312552.	−0.284460
$23$	−648115.	−0.482922	−0.241461	−	0.970411i	$-0.577627\pi$
$23$	−648115.	−0.482922	−0.241461	+	0.970411i	$0.577627\pi$
$24$	−1.21953e6	−0.750309
$25$	3.77240e6	1.93147
$26$	1.07906e6	0.463088
$27$	1.39672e6	0.505791
$28$	−1.32752e6	−0.408158
$29$	−1.04851e6	−0.275285	−0.137642	−	0.990482i	$-0.543953\pi$
$29$	−1.04851e6	−0.275285	−0.137642	+	0.990482i	$0.543953\pi$
$30$	−2.94460e6	−0.663713
$31$	−8.10714e6	−1.57667	−0.788333	−	0.615249i	$-0.789056\pi$
$31$	−8.10714e6	−1.57667	−0.788333	+	0.615249i	$0.789056\pi$
$32$	4.13588e6	0.697257
$33$	−1.16543e7	−1.71070
$34$	0	0
$35$	−6.63154e6	−0.746979
$36$	−1.25513e7	−1.24545
$37$	8.95189e6	0.785248	0.392624	−	0.919699i	$-0.371567\pi$
$37$	8.95189e6	0.785248	0.392624	+	0.919699i	$0.371567\pi$
$38$	4.34506e6	0.338041
$39$	4.02354e7	2.78495
$40$	1.36225e7	0.841370
$41$	−3.34853e6	−0.185066	−0.0925329	−	0.995710i	$-0.529496\pi$
$41$	−3.34853e6	−0.185066	−0.0925329	+	0.995710i	$0.529496\pi$
$42$	3.41056e6	0.169123
$43$	1.81251e7	0.808486	0.404243	−	0.914652i	$-0.367535\pi$
$43$	1.81251e7	0.808486	0.404243	+	0.914652i	$0.367535\pi$
$44$	2.60602e7	1.04819
$45$	−6.26994e7	−2.27933
$46$	−3.72331e6	−0.122608
$47$	2.47206e7	0.738957	0.369479	−	0.929239i	$-0.379536\pi$
$47$	2.47206e7	0.738957	0.369479	+	0.929239i	$0.379536\pi$
$48$	4.55285e7	1.23793
$49$	−3.26727e7	−0.809659
$50$	2.16718e7	0.490376
$51$	0	0
$52$	−8.99704e7	−1.70641
$53$	−5.72785e7	−0.997127	−0.498563	−	0.866853i	$-0.666139\pi$
$53$	−5.72785e7	−0.997127	−0.498563	+	0.866853i	$0.666139\pi$
$54$	8.02389e6	0.128414
$55$	1.30183e8	1.91832
$56$	−1.57782e7	−0.214393
$57$	1.62017e8	2.03294
$58$	−6.02352e6	−0.0698915
$59$	9.17398e7	0.985652	0.492826	−	0.870128i	$-0.335964\pi$
$59$	9.17398e7	0.985652	0.492826	+	0.870128i	$0.335964\pi$
$60$	2.45517e8	2.44569
$61$	1.39714e7	0.129198	0.0645989	−	0.997911i	$-0.479423\pi$
$61$	1.39714e7	0.129198	0.0645989	+	0.997911i	$0.479423\pi$
$62$	−4.65741e7	−0.400297
$63$	7.26211e7	0.580805
$64$	−8.50608e7	−0.633752
$65$	−4.49443e8	−3.12294
$66$	−6.69521e7	−0.434327
$67$	−1.95676e8	−1.18632	−0.593160	−	0.805085i	$-0.702120\pi$
$67$	−1.95676e8	−1.18632	−0.593160	+	0.805085i	$0.702120\pi$
$68$	0	0
$69$	−1.38833e8	−0.737348
$70$	−3.80971e7	−0.189649
$71$	−5.02281e7	−0.234576	−0.117288	−	0.993098i	$-0.537420\pi$
$71$	−5.02281e7	−0.234576	−0.117288	+	0.993098i	$0.537420\pi$
$72$	−1.49178e8	−0.654197
$73$	−1.39690e8	−0.575721	−0.287860	−	0.957672i	$-0.592944\pi$
$73$	−1.39690e8	−0.575721	−0.287860	+	0.957672i	$0.592944\pi$
$74$	5.14271e7	0.199365
$75$	8.08089e8	2.94906
$76$	−3.62286e8	−1.24563
$77$	−1.50783e8	−0.488815
$78$	2.31145e8	0.707065
$79$	−1.15006e8	−0.332199	−0.166100	−	0.986109i	$-0.553117\pi$
$79$	−1.15006e8	−0.332199	−0.166100	+	0.986109i	$0.553117\pi$
$80$	−5.08568e8	−1.38818
$81$	−2.16568e8	−0.558999
$82$	−1.92367e7	−0.0469860
$83$	−5.34414e8	−1.23602	−0.618012	−	0.786169i	$-0.712062\pi$
$83$	−5.34414e8	−1.23602	−0.618012	+	0.786169i	$0.712062\pi$
$84$	−2.84368e8	−0.623196
$85$	0	0
$86$	1.04126e8	0.205265
$87$	−2.24603e8	−0.420318
$88$	3.09738e8	0.550583
$89$	−329484.	−0.000556646 0	−0.000278323	−	1.00000i	$-0.500089\pi$
$89$	−329484.	−0.000556646 0	−0.000278323		1.00000i	$0.500089\pi$
$90$	−3.60197e8	−0.578694
$91$	5.20563e8	0.795770
$92$	3.10445e8	0.451793
$93$	−1.73664e9	−2.40733
$94$	1.42016e8	0.187612
$95$	−1.80978e9	−2.27966
$96$	8.85950e8	1.06461
$97$	8.51166e8	0.976206	0.488103	−	0.872786i	$-0.337689\pi$
$97$	8.51166e8	0.976206	0.488103	+	0.872786i	$0.337689\pi$
$98$	−1.87699e8	−0.205563
$99$	−1.42561e9	−1.49157
$100$	−1.80697e9	−1.80697
$101$	2.75119e8	0.263072	0.131536	−	0.991311i	$-0.458009\pi$
$101$	2.75119e8	0.263072	0.131536	+	0.991311i	$0.458009\pi$
$102$	0	0
$103$	−1.05790e9	−0.926140	−0.463070	−	0.886322i	$-0.653252\pi$
$103$	−1.05790e9	−0.926140	−0.463070	+	0.886322i	$0.653252\pi$
$104$	−1.06934e9	−0.896326
$105$	−1.42055e9	−1.14052
$106$	−3.29055e8	−0.253159
$107$	−1.85456e9	−1.36777	−0.683887	−	0.729588i	$-0.739712\pi$
$107$	−1.85456e9	−1.36777	−0.683887	+	0.729588i	$0.739712\pi$
$108$	−6.69022e8	−0.473188
$109$	−2.81820e9	−1.91229	−0.956144	−	0.292897i	$-0.905381\pi$
$109$	−2.81820e9	−1.91229	−0.956144	+	0.292897i	$0.905381\pi$
$110$	7.47877e8	0.487038
$111$	1.91759e9	1.19895
$112$	5.89045e8	0.353727
$113$	1.77880e7	0.0102630	0.00513149	−	0.999987i	$-0.498367\pi$
$113$	1.77880e7	0.0102630	0.00513149	+	0.999987i	$0.498367\pi$
$114$	9.30760e8	0.516138
$115$	1.55081e9	0.826836
$116$	5.02234e8	0.257540
$117$	4.92178e9	2.42821
$118$	5.27029e8	0.250245
$119$	0	0
$120$	2.91809e9	1.28464
$121$	6.02048e8	0.255327
$122$	8.02632e7	0.0328018
$123$	−7.17291e8	−0.282567
$124$	3.88329e9	1.47504
$125$	−4.35317e9	−1.59482
$126$	4.17196e8	0.147459
$127$	−8.58453e8	−0.292819	−0.146410	−	0.989224i	$-0.546772\pi$
$127$	−8.58453e8	−0.292819	−0.146410	+	0.989224i	$0.546772\pi$
$128$	−2.60623e9	−0.858159
$129$	3.88259e9	1.23443
$130$	−2.58197e9	−0.792878
$131$	−4.96254e9	−1.47225	−0.736127	−	0.676843i	$-0.763348\pi$
$131$	−4.96254e9	−1.47225	−0.736127	+	0.676843i	$0.763348\pi$
$132$	5.58238e9	1.60043
$133$	2.09617e9	0.580890
$134$	−1.12413e9	−0.301192
$135$	−3.34207e9	−0.865991
$136$	0	0
$137$	6.38074e9	1.54749	0.773746	−	0.633496i	$-0.218381\pi$
$137$	6.38074e9	1.54749	0.773746	+	0.633496i	$0.218381\pi$
$138$	−7.97573e8	−0.187204
$139$	1.91051e9	0.434094	0.217047	−	0.976161i	$-0.430358\pi$
$139$	1.91051e9	0.434094	0.217047	+	0.976161i	$0.430358\pi$
$140$	3.17649e9	0.698829
$141$	5.29543e9	1.12828
$142$	−2.88552e8	−0.0595561
$143$	−1.02191e10	−2.04362
$144$	5.56926e9	1.07936
$145$	2.50889e9	0.471330
$146$	−8.02494e8	−0.146169
$147$	−6.99884e9	−1.23623
$148$	−4.28793e9	−0.734632
$149$	−1.06531e10	−1.77068	−0.885338	−	0.464947i	$-0.846073\pi$
$149$	−1.06531e10	−1.77068	−0.885338	+	0.464947i	$0.846073\pi$
$150$	4.64233e9	0.748730
$151$	2.72110e9	0.425940	0.212970	−	0.977059i	$-0.431686\pi$
$151$	2.72110e9	0.425940	0.212970	+	0.977059i	$0.431686\pi$
$152$	−4.30594e9	−0.654293
$153$	0	0
$154$	−8.66223e8	−0.124104
$155$	1.93988e10	2.69949
$156$	−1.92726e10	−2.60543
$157$	1.00371e10	1.31844	0.659221	−	0.751949i	$-0.270886\pi$
$157$	1.00371e10	1.31844	0.659221	+	0.751949i	$0.270886\pi$
$158$	−6.60690e8	−0.0843414
$159$	−1.22697e10	−1.52246
$160$	−9.89636e9	−1.19381
$161$	−1.79622e9	−0.210689
$162$	−1.24414e9	−0.141923
$163$	1.41986e9	0.157544	0.0787718	−	0.996893i	$-0.474900\pi$
$163$	1.41986e9	0.157544	0.0787718	+	0.996893i	$0.474900\pi$
$164$	1.60393e9	0.173137
$165$	2.78865e10	2.92898
$166$	−3.07012e9	−0.313811
$167$	−3.46700e9	−0.344929	−0.172465	−	0.985016i	$-0.555173\pi$
$167$	−3.46700e9	−0.344929	−0.172465	+	0.985016i	$0.555173\pi$
$168$	−3.37985e9	−0.327345
$169$	2.46759e10	2.32693
$170$	0	0
$171$	1.98187e10	1.77252
$172$	−8.68187e9	−0.756371
$173$	1.26979e9	0.107777	0.0538884	−	0.998547i	$-0.482838\pi$
$173$	1.26979e9	0.107777	0.0538884	+	0.998547i	$0.482838\pi$
$174$	−1.29030e9	−0.106714
$175$	1.04550e10	0.842662
$176$	−1.15634e10	−0.908407
$177$	1.96517e10	1.50494
$178$	−1.89283e6	−0.000141326 0
$179$	−1.46690e9	−0.106798	−0.0533990	−	0.998573i	$-0.517006\pi$
$179$	−1.46690e9	−0.106798	−0.0533990	+	0.998573i	$0.517006\pi$
$180$	3.00328e10	2.13241
$181$	3.04190e9	0.210665	0.105332	−	0.994437i	$-0.466409\pi$
$181$	3.04190e9	0.210665	0.105332	+	0.994437i	$0.466409\pi$
$182$	2.99055e9	0.202036
$183$	2.99282e9	0.197265
$184$	3.68979e9	0.237313
$185$	−2.14201e10	−1.34446
$186$	−9.97668e9	−0.611192
$187$	0	0
$188$	−1.18411e10	−0.691325
$189$	3.87093e9	0.220667
$190$	−1.03969e10	−0.578779
$191$	−1.92930e10	−1.04894	−0.524470	−	0.851429i	$-0.675736\pi$
$191$	−1.92930e10	−1.04894	−0.524470	+	0.851429i	$0.675736\pi$
$192$	−1.82209e10	−0.967644
$193$	−9.31475e9	−0.483240	−0.241620	−	0.970371i	$-0.577679\pi$
$193$	−9.31475e9	−0.483240	−0.241620	+	0.970371i	$0.577679\pi$
$194$	4.88980e9	0.247847
$195$	−9.62755e10	−4.76826
$196$	1.56501e10	0.757469
$197$	1.52996e10	0.723741	0.361871	−	0.932228i	$-0.382138\pi$
$197$	1.52996e10	0.723741	0.361871	+	0.932228i	$0.382138\pi$
$198$	−8.18990e9	−0.378691
$199$	−9.26535e9	−0.418816	−0.209408	−	0.977828i	$-0.567154\pi$
$199$	−9.26535e9	−0.418816	−0.209408	+	0.977828i	$0.567154\pi$
$200$	−2.14767e10	−0.949144
$201$	−4.19160e10	−1.81133
$202$	1.58051e9	0.0667908
$203$	−2.90590e9	−0.120101
$204$	0	0
$205$	8.01238e9	0.316861
$206$	−6.07745e9	−0.235136
$207$	−1.69827e10	−0.642896
$208$	3.99216e10	1.47885
$209$	−4.11495e10	−1.49179
$210$	−8.16081e9	−0.289565
$211$	4.82301e9	0.167513	0.0837563	−	0.996486i	$-0.473308\pi$
$211$	4.82301e9	0.167513	0.0837563	+	0.996486i	$0.473308\pi$
$212$	2.74362e10	0.932853
$213$	−1.07594e10	−0.358162
$214$	−1.06541e10	−0.347261
$215$	−4.33699e10	−1.38425
$216$	−7.95165e9	−0.248551
$217$	−2.24685e10	−0.687869
$218$	−1.61901e10	−0.485507
$219$	−2.99231e10	−0.879038
$220$	−6.23571e10	−1.79467
$221$	0	0
$222$	1.10162e10	0.304400
$223$	−3.58214e10	−0.969997	−0.484998	−	0.874515i	$-0.661180\pi$
$223$	−3.58214e10	−0.969997	−0.484998	+	0.874515i	$0.661180\pi$
$224$	1.14624e10	0.304200
$225$	9.88492e10	2.57129
$226$	1.02189e8	0.00260565
$227$	−4.23736e10	−1.05920	−0.529601	−	0.848247i	$-0.677658\pi$
$227$	−4.23736e10	−1.05920	−0.529601	+	0.848247i	$0.677658\pi$
$228$	−7.76056e10	−1.90189
$229$	−3.96186e10	−0.952005	−0.476002	−	0.879444i	$-0.657915\pi$
$229$	−3.96186e10	−0.952005	−0.476002	+	0.879444i	$0.657915\pi$
$230$	8.90915e9	0.209924
$231$	−3.22994e10	−0.746346
$232$	5.96929e9	0.135278
$233$	3.79889e10	0.844414	0.422207	−	0.906500i	$-0.361256\pi$
$233$	3.79889e10	0.844414	0.422207	+	0.906500i	$0.361256\pi$
$234$	2.82748e10	0.616493
$235$	−5.91517e10	−1.26521
$236$	−4.39431e10	−0.922118
$237$	−2.46355e10	−0.507218
$238$	0	0
$239$	5.70449e10	1.13090	0.565452	−	0.824781i	$-0.308702\pi$
$239$	5.70449e10	1.13090	0.565452	+	0.824781i	$0.308702\pi$
$240$	−1.08941e11	−2.11953
$241$	3.13263e10	0.598180	0.299090	−	0.954225i	$-0.403317\pi$
$241$	3.13263e10	0.598180	0.299090	+	0.954225i	$0.403317\pi$
$242$	3.45866e9	0.0648245
$243$	−7.38827e10	−1.35930
$244$	−6.69225e9	−0.120870
$245$	7.81794e10	1.38626
$246$	−4.12071e9	−0.0717405
$247$	1.42065e11	2.42856
$248$	4.61548e10	0.774790
$249$	−1.14477e11	−1.88722
$250$	−2.50082e10	−0.404904
$251$	8.86015e10	1.40899	0.704497	−	0.709707i	$-0.251173\pi$
$251$	8.86015e10	1.40899	0.704497	+	0.709707i	$0.251173\pi$
$252$	−3.47853e10	−0.543367
$253$	3.52612e10	0.541072
$254$	−4.93166e9	−0.0743433
$255$	0	0
$256$	2.85788e10	0.415876
$257$	−1.14775e11	−1.64115	−0.820577	−	0.571536i	$-0.806348\pi$
$257$	−1.14775e11	−1.64115	−0.820577	+	0.571536i	$0.806348\pi$
$258$	2.23048e10	0.313408
$259$	2.48097e10	0.342588
$260$	2.15282e11	2.92164
$261$	−2.74745e10	−0.366477
$262$	−2.85089e10	−0.373788
$263$	−1.02138e11	−1.31640	−0.658198	−	0.752845i	$-0.728681\pi$
$263$	−1.02138e11	−1.31640	−0.658198	+	0.752845i	$0.728681\pi$
$264$	6.63493e10	0.840657
$265$	1.37056e11	1.70723
$266$	1.20421e10	0.147481
$267$	−7.05791e7	−0.000849915 0
$268$	9.37284e10	1.10985
$269$	4.82426e10	0.561753	0.280876	−	0.959744i	$-0.409375\pi$
$269$	4.82426e10	0.561753	0.280876	+	0.959744i	$0.409375\pi$
$270$	−1.91996e10	−0.219865
$271$	1.38998e10	0.156547	0.0782737	−	0.996932i	$-0.475059\pi$
$271$	1.38998e10	0.156547	0.0782737	+	0.996932i	$0.475059\pi$
$272$	0	0
$273$	1.11510e11	1.21502
$274$	3.66563e10	0.392890
$275$	−2.05240e11	−2.16404
$276$	6.65007e10	0.689819
$277$	−3.59889e10	−0.367290	−0.183645	−	0.982993i	$-0.558790\pi$
$277$	−3.59889e10	−0.367290	−0.183645	+	0.982993i	$0.558790\pi$
$278$	1.09756e10	0.110211
$279$	−2.12434e11	−2.09896
$280$	3.77541e10	0.367073
$281$	−1.26399e11	−1.20939	−0.604695	−	0.796457i	$-0.706705\pi$
$281$	−1.26399e11	−1.20939	−0.604695	+	0.796457i	$0.706705\pi$
$282$	3.04213e10	0.286456
$283$	1.63530e11	1.51551	0.757753	−	0.652541i	$-0.226297\pi$
$283$	1.63530e11	1.51551	0.757753	+	0.652541i	$0.226297\pi$
$284$	2.40591e10	0.219456
$285$	−3.87675e11	−3.48070
$286$	−5.87069e10	−0.518850
$287$	−9.28027e9	−0.0807406
$288$	1.08374e11	0.928234
$289$	0	0
$290$	1.44131e10	0.119665
$291$	1.82329e11	1.49052
$292$	6.69110e10	0.538610
$293$	3.31692e10	0.262924	0.131462	−	0.991321i	$-0.458033\pi$
$293$	3.31692e10	0.262924	0.131462	+	0.991321i	$0.458033\pi$
$294$	−4.02071e10	−0.313863
$295$	−2.19515e11	−1.68759
$296$	−5.09641e10	−0.385879
$297$	−7.59895e10	−0.566695
$298$	−6.12005e10	−0.449554
$299$	−1.21736e11	−0.880842
$300$	−3.87072e11	−2.75896
$301$	5.02328e10	0.352727
$302$	1.56322e10	0.108141
$303$	5.89335e10	0.401671
$304$	1.60754e11	1.07952
$305$	−3.34308e10	−0.221206
$306$	0	0
$307$	−1.85856e11	−1.19414	−0.597069	−	0.802190i	$-0.703668\pi$
$307$	−1.85856e11	−1.19414	−0.597069	+	0.802190i	$0.703668\pi$
$308$	7.22246e10	0.457306
$309$	−2.26613e11	−1.41408
$310$	1.11443e11	0.685369
$311$	−1.31514e11	−0.797169	−0.398584	−	0.917132i	$-0.630498\pi$
$311$	−1.31514e11	−0.797169	−0.398584	+	0.917132i	$0.630498\pi$
$312$	−2.29064e11	−1.36855
$313$	2.18617e11	1.28746	0.643730	−	0.765253i	$-0.277386\pi$
$313$	2.18617e11	1.28746	0.643730	+	0.765253i	$0.277386\pi$
$314$	5.76616e10	0.334737
$315$	−1.73768e11	−0.994427
$316$	5.50875e10	0.310786
$317$	2.52877e11	1.40651	0.703255	−	0.710938i	$-0.251729\pi$
$317$	2.52877e11	1.40651	0.703255	+	0.710938i	$0.251729\pi$
$318$	−7.04872e10	−0.386535
$319$	5.70452e10	0.308433
$320$	2.03534e11	1.08508
$321$	−3.97267e11	−2.08838
$322$	−1.03190e10	−0.0534915
$323$	0	0
$324$	1.03735e11	0.522966
$325$	7.08572e11	3.52297
$326$	8.15685e9	0.0399984
$327$	−6.03690e11	−2.91977
$328$	1.90635e10	0.0909433
$329$	6.85120e10	0.322393
$330$	1.60203e11	0.743633
$331$	−1.66489e11	−0.762359	−0.381179	−	0.924501i	$-0.624482\pi$
$331$	−1.66489e11	−0.762359	−0.381179	+	0.924501i	$0.624482\pi$
$332$	2.55983e11	1.15635
$333$	2.34569e11	1.04537
$334$	−1.99173e10	−0.0875734
$335$	4.68216e11	2.03116
$336$	1.26180e11	0.540087
$337$	−6.08599e9	−0.0257038	−0.0128519	−	0.999917i	$-0.504091\pi$
$337$	−6.08599e9	−0.0257038	−0.0128519	+	0.999917i	$0.504091\pi$
$338$	1.41759e11	0.590779
$339$	3.81037e9	0.0156700
$340$	0	0
$341$	4.41076e11	1.76652
$342$	1.13855e11	0.450023
$343$	−2.02389e11	−0.789519
$344$	−1.03188e11	−0.397298
$345$	3.32201e11	1.26245
$346$	7.29474e9	0.0273632
$347$	−2.11321e11	−0.782455	−0.391227	−	0.920294i	$-0.627949\pi$
$347$	−2.11321e11	−0.782455	−0.391227	+	0.920294i	$0.627949\pi$
$348$	1.07584e11	0.393225
$349$	−3.73753e11	−1.34856	−0.674280	−	0.738476i	$-0.735546\pi$
$349$	−3.73753e11	−1.34856	−0.674280	+	0.738476i	$0.735546\pi$
$350$	6.00623e10	0.213942
$351$	2.62346e11	0.922555
$352$	−2.25016e11	−0.781217
$353$	−1.80915e10	−0.0620137	−0.0310069	−	0.999519i	$-0.509871\pi$
$353$	−1.80915e10	−0.0620137	−0.0310069	+	0.999519i	$0.509871\pi$
$354$	1.12895e11	0.382086
$355$	1.20186e11	0.401630
$356$	1.57822e8	0.000520766 0
$357$	0	0
$358$	−8.42712e9	−0.0271147
$359$	−5.20752e11	−1.65465	−0.827325	−	0.561724i	$-0.810138\pi$
$359$	−5.20752e11	−1.65465	−0.827325	+	0.561724i	$0.810138\pi$
$360$	3.56954e11	1.12009
$361$	2.49368e11	0.772783
$362$	1.74752e10	0.0534853
$363$	1.28965e11	0.389846
$364$	−2.49348e11	−0.744475
$365$	3.34251e11	0.985722
$366$	1.71932e10	0.0500833
$367$	−1.32647e11	−0.381680	−0.190840	−	0.981621i	$-0.561121\pi$
$367$	−1.32647e11	−0.381680	−0.190840	+	0.981621i	$0.561121\pi$
$368$	−1.37751e11	−0.391542
$369$	−8.77424e10	−0.246372
$370$	−1.23055e11	−0.341343
$371$	−1.58745e11	−0.435027
$372$	8.31843e11	2.25216
$373$	5.72714e11	1.53196	0.765981	−	0.642863i	$-0.222254\pi$
$373$	5.72714e11	1.53196	0.765981	+	0.642863i	$0.222254\pi$
$374$	0	0
$375$	−9.32496e11	−2.43504
$376$	−1.40737e11	−0.363131
$377$	−1.96943e11	−0.502116
$378$	2.22378e10	0.0560246
$379$	−4.74284e11	−1.18076	−0.590380	−	0.807125i	$-0.701022\pi$
$379$	−4.74284e11	−1.18076	−0.590380	+	0.807125i	$0.701022\pi$
$380$	8.66881e11	2.13272
$381$	−1.83890e11	−0.447090
$382$	−1.10835e11	−0.266313
$383$	−7.47734e10	−0.177563	−0.0887816	−	0.996051i	$-0.528297\pi$
$383$	−7.47734e10	−0.177563	−0.0887816	+	0.996051i	$0.528297\pi$
$384$	−5.58283e11	−1.31028
$385$	3.60795e11	0.836926
$386$	−5.35116e10	−0.122689
$387$	4.74937e11	1.07631
$388$	−4.07706e11	−0.913280
$389$	−8.27117e11	−1.83144	−0.915722	−	0.401813i	$-0.868380\pi$
$389$	−8.27117e11	−1.83144	−0.915722	+	0.401813i	$0.868380\pi$
$390$	−5.53086e11	−1.21060
$391$	0	0
$392$	1.86009e11	0.397875
$393$	−1.06303e12	−2.24791
$394$	8.78938e10	0.183749
$395$	2.75187e11	0.568776
$396$	6.82864e11	1.39542
$397$	2.68894e11	0.543280	0.271640	−	0.962399i	$-0.412434\pi$
$397$	2.68894e11	0.543280	0.271640	+	0.962399i	$0.412434\pi$
$398$	−5.32278e10	−0.106332
$399$	4.49022e11	0.886930
$400$	8.01787e11	1.56599
$401$	−9.25888e11	−1.78817	−0.894085	−	0.447897i	$-0.852173\pi$
$401$	−9.25888e11	−1.78817	−0.894085	+	0.447897i	$0.852173\pi$
$402$	−2.40800e11	−0.459875
$403$	−1.52277e12	−2.87582
$404$	−1.31781e11	−0.246115
$405$	5.18205e11	0.957092
$406$	−1.66939e10	−0.0304923
$407$	−4.87035e11	−0.879803
$408$	0	0
$409$	−5.35602e11	−0.946428	−0.473214	−	0.880948i	$-0.656906\pi$
$409$	−5.35602e11	−0.946428	−0.473214	+	0.880948i	$0.656906\pi$
$410$	4.60297e10	0.0804472
$411$	1.36682e12	2.36279
$412$	5.06731e11	0.866442
$413$	2.54252e11	0.430021
$414$	−9.75629e10	−0.163224
$415$	1.27875e12	2.11626
$416$	7.76845e11	1.27179
$417$	4.09253e11	0.662796
$418$	−2.36397e11	−0.378746
$419$	−6.58106e11	−1.04312	−0.521558	−	0.853216i	$-0.674649\pi$
$419$	−6.58106e11	−1.04312	−0.521558	+	0.853216i	$0.674649\pi$
$420$	6.80438e11	1.06701
$421$	1.03482e12	1.60544	0.802721	−	0.596354i	$-0.203385\pi$
$421$	1.03482e12	1.60544	0.802721	+	0.596354i	$0.203385\pi$
$422$	2.77074e10	0.0425294
$423$	6.47762e11	0.983748
$424$	3.26093e11	0.489999
$425$	0	0
$426$	−6.18109e10	−0.0909330
$427$	3.87210e10	0.0563665
$428$	8.88330e11	1.27961
$429$	−2.18904e12	−3.12030
$430$	−2.49152e11	−0.351445
$431$	2.74186e11	0.382735	0.191367	−	0.981518i	$-0.438708\pi$
$431$	2.74186e11	0.382735	0.191367	+	0.981518i	$0.438708\pi$
$432$	2.96859e11	0.410084
$433$	−3.31146e11	−0.452714	−0.226357	−	0.974044i	$-0.572682\pi$
$433$	−3.31146e11	−0.452714	−0.226357	+	0.974044i	$0.572682\pi$
$434$	−1.29078e11	−0.174642
$435$	5.37431e11	0.719649
$436$	1.34991e12	1.78902
$437$	−4.90197e11	−0.642990
$438$	−1.71903e11	−0.223177
$439$	2.78778e11	0.358235	0.179117	−	0.983828i	$-0.442676\pi$
$439$	2.78778e11	0.358235	0.179117	+	0.983828i	$0.442676\pi$
$440$	−7.41144e11	−0.942683
$441$	−8.56131e11	−1.07787
$442$	0	0
$443$	−5.18773e11	−0.639972	−0.319986	−	0.947422i	$-0.603678\pi$
$443$	−5.18773e11	−0.639972	−0.319986	+	0.947422i	$0.603678\pi$
$444$	−9.18520e11	−1.12167
$445$	7.88392e8	0.000953064 0
$446$	−2.05788e11	−0.246271
$447$	−2.28202e12	−2.70355
$448$	−2.35742e11	−0.276494
$449$	7.83174e11	0.909389	0.454694	−	0.890648i	$-0.349749\pi$
$449$	7.83174e11	0.909389	0.454694	+	0.890648i	$0.349749\pi$
$450$	5.67872e11	0.652821
$451$	1.82179e11	0.207350
$452$	−8.52038e9	−0.00960143
$453$	5.82889e11	0.650345
$454$	−2.43429e11	−0.268919
$455$	−1.24561e12	−1.36248
$456$	−9.22380e11	−0.999006
$457$	8.02805e11	0.860968	0.430484	−	0.902598i	$-0.358343\pi$
$457$	8.02805e11	0.860968	0.430484	+	0.902598i	$0.358343\pi$
$458$	−2.27602e11	−0.241703
$459$	0	0
$460$	−7.42835e11	−0.773538
$461$	4.80563e11	0.495560	0.247780	−	0.968816i	$-0.420299\pi$
$461$	4.80563e11	0.495560	0.247780	+	0.968816i	$0.420299\pi$
$462$	−1.85554e11	−0.189488
$463$	1.56434e12	1.58204	0.791018	−	0.611792i	$-0.209551\pi$
$463$	1.56434e12	1.58204	0.791018	+	0.611792i	$0.209551\pi$
$464$	−2.22851e11	−0.223195
$465$	4.15543e12	4.12172
$466$	2.18240e11	0.214386
$467$	3.55237e11	0.345615	0.172808	−	0.984956i	$-0.444716\pi$
$467$	3.55237e11	0.345615	0.172808	+	0.984956i	$0.444716\pi$
$468$	−2.35752e12	−2.27169
$469$	−5.42307e11	−0.517568
$470$	−3.39816e11	−0.321221
$471$	2.15006e12	2.01306
$472$	−5.22284e11	−0.484360
$473$	−9.86111e11	−0.905839
$474$	−1.41527e11	−0.128777
$475$	2.85323e12	2.57167
$476$	0	0
$477$	−1.50089e12	−1.32744
$478$	3.27713e11	0.287123
$479$	2.60014e11	0.225676	0.112838	−	0.993613i	$-0.464006\pi$
$479$	2.60014e11	0.225676	0.112838	+	0.993613i	$0.464006\pi$
$480$	−2.11991e12	−1.82277
$481$	1.68144e12	1.43228
$482$	1.79964e11	0.151871
$483$	−3.84769e11	−0.321690
$484$	−2.88379e11	−0.238869
$485$	−2.03668e12	−1.67141
$486$	−4.24443e11	−0.345109
$487$	1.36381e12	1.09868	0.549341	−	0.835598i	$-0.314879\pi$
$487$	1.36381e12	1.09868	0.549341	+	0.835598i	$0.314879\pi$
$488$	−7.95405e10	−0.0634891
$489$	3.04149e11	0.240545
$490$	4.49127e11	0.351955
$491$	−1.00959e12	−0.783935	−0.391968	−	0.919979i	$-0.628206\pi$
$491$	−1.00959e12	−0.783935	−0.391968	+	0.919979i	$0.628206\pi$
$492$	3.43580e11	0.264353
$493$	0	0
$494$	8.16136e11	0.616583
$495$	3.41121e12	2.55379
$496$	−1.72309e12	−1.27833
$497$	−1.39205e11	−0.102341
$498$	−6.57653e11	−0.479142
$499$	−1.18599e12	−0.856306	−0.428153	−	0.903706i	$-0.640836\pi$
$499$	−1.18599e12	−0.856306	−0.428153	+	0.903706i	$0.640836\pi$
$500$	2.08515e12	1.49201
$501$	−7.42670e11	−0.526655
$502$	5.09000e11	0.357727
$503$	−7.08530e11	−0.493517	−0.246759	−	0.969077i	$-0.579365\pi$
$503$	−7.08530e11	−0.493517	−0.246759	+	0.969077i	$0.579365\pi$
$504$	−4.13440e11	−0.285414
$505$	−6.58307e11	−0.450420
$506$	2.02570e11	0.137372
$507$	5.28584e12	3.55286
$508$	4.11196e11	0.273944
$509$	1.69865e11	0.112170	0.0560848	−	0.998426i	$-0.482138\pi$
$509$	1.69865e11	0.112170	0.0560848	+	0.998426i	$0.482138\pi$
$510$	0	0
$511$	−3.87143e11	−0.251176
$512$	1.49857e12	0.963745
$513$	1.05640e12	0.673440
$514$	−6.59365e11	−0.416669
$515$	2.53135e12	1.58569
$516$	−1.85975e12	−1.15486
$517$	−1.34495e12	−0.827938
$518$	1.42528e11	0.0869791
$519$	2.72003e11	0.164559
$520$	2.55873e12	1.53465
$521$	1.46893e12	0.873437	0.436718	−	0.899598i	$-0.356141\pi$
$521$	1.46893e12	0.873437	0.436718	+	0.899598i	$0.356141\pi$
$522$	−1.57836e11	−0.0930441
$523$	4.36238e11	0.254956	0.127478	−	0.991841i	$-0.459312\pi$
$523$	4.36238e11	0.254956	0.127478	+	0.991841i	$0.459312\pi$
$524$	2.37704e12	1.37735
$525$	2.23958e12	1.28662
$526$	−5.86766e11	−0.334217
$527$	0	0
$528$	−2.47702e12	−1.38700
$529$	−1.38110e12	−0.766787
$530$	7.87366e11	0.433446
$531$	2.40388e12	1.31216
$532$	−1.00406e12	−0.543446
$533$	−6.28956e11	−0.337558
$534$	−4.05465e8	−0.000215783 0
$535$	4.43761e12	2.34184
$536$	1.11401e12	0.582970
$537$	−3.14227e11	−0.163064
$538$	2.77145e11	0.142622
$539$	1.77758e12	0.907154
$540$	1.60084e12	0.810170
$541$	−1.76198e12	−0.884326	−0.442163	−	0.896935i	$-0.645789\pi$
$541$	−1.76198e12	−0.884326	−0.442163	+	0.896935i	$0.645789\pi$
$542$	7.98518e10	0.0397455
$543$	6.51609e11	0.321653
$544$	0	0
$545$	6.74342e12	3.27413
$546$	6.40608e11	0.308479
$547$	1.91468e12	0.914436	0.457218	−	0.889355i	$-0.348846\pi$
$547$	1.91468e12	0.914436	0.457218	+	0.889355i	$0.348846\pi$
$548$	−3.05635e12	−1.44774
$549$	3.66096e11	0.171996
$550$	−1.17907e12	−0.549425
$551$	−7.93035e11	−0.366531
$552$	7.90392e11	0.362340
$553$	−3.18733e11	−0.144932
$554$	−2.06750e11	−0.0932505
$555$	−4.58842e12	−2.05279
$556$	−9.15131e11	−0.406113
$557$	−3.94456e12	−1.73640	−0.868202	−	0.496212i	$-0.834724\pi$
$557$	−3.94456e12	−1.73640	−0.868202	+	0.496212i	$0.834724\pi$
$558$	−1.22039e12	−0.532901
$559$	3.40445e12	1.47467
$560$	−1.40947e12	−0.605634
$561$	0	0
$562$	−7.26143e11	−0.307050
$563$	−6.33213e11	−0.265621	−0.132810	−	0.991141i	$-0.542400\pi$
$563$	−6.33213e11	−0.265621	−0.132810	+	0.991141i	$0.542400\pi$
$564$	−2.53649e12	−1.05555
$565$	−4.25632e10	−0.0175718
$566$	9.39450e11	0.384769
$567$	−6.00206e11	−0.243880
$568$	2.85954e11	0.115273
$569$	3.78056e12	1.51200	0.755998	−	0.654574i	$-0.227152\pi$
$569$	3.78056e12	1.51200	0.755998	+	0.654574i	$0.227152\pi$
$570$	−2.22713e12	−0.883707
$571$	−2.35055e12	−0.925350	−0.462675	−	0.886528i	$-0.653110\pi$
$571$	−2.35055e12	−0.925350	−0.462675	+	0.886528i	$0.653110\pi$
$572$	4.89491e12	1.91189
$573$	−4.13278e12	−1.60157
$574$	−5.33136e10	−0.0204991
$575$	−2.44495e12	−0.932747
$576$	−2.22887e12	−0.843692
$577$	4.52438e11	0.169929	0.0849646	−	0.996384i	$-0.472922\pi$
$577$	4.52438e11	0.169929	0.0849646	+	0.996384i	$0.472922\pi$
$578$	0	0
$579$	−1.99532e12	−0.737835
$580$	−1.20175e12	−0.440948
$581$	−1.48110e12	−0.539253
$582$	1.04745e12	0.378425
$583$	3.11629e12	1.11719
$584$	7.95269e11	0.282915
$585$	−1.17769e13	−4.15746
$586$	1.90551e11	0.0667533
$587$	4.70909e12	1.63706	0.818532	−	0.574461i	$-0.194788\pi$
$587$	4.70909e12	1.63706	0.818532	+	0.574461i	$0.194788\pi$
$588$	3.35242e12	1.15654
$589$	−6.13178e12	−2.09927
$590$	−1.26108e12	−0.428458
$591$	3.27735e12	1.10504
$592$	1.90264e12	0.636662
$593$	1.91105e12	0.634639	0.317320	−	0.948319i	$-0.397217\pi$
$593$	1.91105e12	0.634639	0.317320	+	0.948319i	$0.397217\pi$
$594$	−4.36546e11	−0.143877
$595$	0	0
$596$	5.10282e12	1.65654
$597$	−1.98474e12	−0.639468
$598$	−6.99352e11	−0.223635
$599$	2.70870e12	0.859687	0.429844	−	0.902903i	$-0.358569\pi$
$599$	2.70870e12	0.859687	0.429844	+	0.902903i	$0.358569\pi$
$600$	−4.60054e12	−1.44920
$601$	−3.94720e11	−0.123411	−0.0617055	−	0.998094i	$-0.519654\pi$
$601$	−3.94720e11	−0.123411	−0.0617055	+	0.998094i	$0.519654\pi$
$602$	2.88579e11	0.0895530
$603$	−5.12736e12	−1.57931
$604$	−1.30340e12	−0.398484
$605$	−1.44058e12	−0.437159
$606$	3.38563e11	0.101979
$607$	−2.49938e12	−0.747280	−0.373640	−	0.927574i	$-0.621890\pi$
$607$	−2.49938e12	−0.747280	−0.373640	+	0.927574i	$0.621890\pi$
$608$	3.12815e12	0.928369
$609$	−6.22475e11	−0.183377
$610$	−1.92054e11	−0.0561616
$611$	4.64330e12	1.34785
$612$	0	0
$613$	7.55741e11	0.216173	0.108086	−	0.994142i	$-0.465528\pi$
$613$	7.55741e11	0.216173	0.108086	+	0.994142i	$0.465528\pi$
$614$	−1.06771e12	−0.303177
$615$	1.71634e12	0.483799
$616$	8.58424e11	0.240209
$617$	8.69538e11	0.241549	0.120775	−	0.992680i	$-0.461462\pi$
$617$	8.69538e11	0.241549	0.120775	+	0.992680i	$0.461462\pi$
$618$	−1.30186e12	−0.359017
$619$	5.11649e12	1.40076	0.700380	−	0.713770i	$-0.253014\pi$
$619$	5.11649e12	1.40076	0.700380	+	0.713770i	$0.253014\pi$
$620$	−9.29197e12	−2.52549
$621$	−9.05232e11	−0.244257
$622$	−7.55526e11	−0.202392
$623$	−9.13149e8	−0.000242854 0
$624$	8.55165e12	2.25798
$625$	3.04832e12	0.799100
$626$	1.25591e12	0.326870
$627$	−8.81467e12	−2.27773
$628$	−4.80775e12	−1.23346
$629$	0	0
$630$	−9.98269e11	−0.252473
$631$	−2.72352e12	−0.683909	−0.341954	−	0.939717i	$-0.611089\pi$
$631$	−2.72352e12	−0.683909	−0.341954	+	0.939717i	$0.611089\pi$
$632$	6.54742e11	0.163246
$633$	1.03314e12	0.255766
$634$	1.45273e12	0.357096
$635$	2.05411e12	0.501351
$636$	5.87714e12	1.42432
$637$	−6.13693e12	−1.47681
$638$	3.27715e11	0.0783075
$639$	−1.31614e12	−0.312283
$640$	6.23621e12	1.46930
$641$	1.98245e12	0.463812	0.231906	−	0.972738i	$-0.425504\pi$
$641$	1.98245e12	0.463812	0.231906	+	0.972738i	$0.425504\pi$
$642$	−2.28223e12	−0.530215
$643$	−3.56013e12	−0.821327	−0.410664	−	0.911787i	$-0.634703\pi$
$643$	−3.56013e12	−0.821327	−0.410664	+	0.911787i	$0.634703\pi$
$644$	8.60382e11	0.197108
$645$	−9.29029e12	−2.11354
$646$	0	0
$647$	−2.63327e12	−0.590782	−0.295391	−	0.955377i	$-0.595450\pi$
$647$	−2.63327e12	−0.590782	−0.295391	+	0.955377i	$0.595450\pi$
$648$	1.23294e12	0.274698
$649$	−4.99118e12	−1.10434
$650$	4.07063e12	0.894440
$651$	−4.81300e12	−1.05027
$652$	−6.80108e11	−0.147389
$653$	3.30135e12	0.710529	0.355265	−	0.934766i	$-0.384391\pi$
$653$	3.30135e12	0.710529	0.355265	+	0.934766i	$0.384391\pi$
$654$	−3.46810e12	−0.741295
$655$	1.18744e13	2.52073
$656$	−7.11698e11	−0.150047
$657$	−3.66033e12	−0.766437
$658$	3.93590e11	0.0818516
$659$	1.52476e11	0.0314933	0.0157466	−	0.999876i	$-0.494987\pi$
$659$	1.52476e11	0.0314933	0.0157466	+	0.999876i	$0.494987\pi$
$660$	−1.33576e13	−2.74018
$661$	−4.44682e12	−0.906031	−0.453015	−	0.891503i	$-0.649652\pi$
$661$	−4.44682e12	−0.906031	−0.453015	+	0.891503i	$0.649652\pi$
$662$	−9.56451e11	−0.193554
$663$	0	0
$664$	3.04248e12	0.607395
$665$	−5.01572e12	−0.994572
$666$	1.34756e12	0.265408
$667$	6.79556e11	0.132941
$668$	1.66068e12	0.322695
$669$	−7.67333e12	−1.48104
$670$	2.68982e12	0.515687
$671$	−7.60124e11	−0.144755
$672$	2.45537e12	0.464467
$673$	7.47229e12	1.40406	0.702030	−	0.712147i	$-0.252277\pi$
$673$	7.47229e12	1.40406	0.702030	+	0.712147i	$0.252277\pi$
$674$	−3.49630e10	−0.00652587
$675$	5.26897e12	0.976919
$676$	−1.18197e13	−2.17693
$677$	−4.51253e12	−0.825602	−0.412801	−	0.910821i	$-0.635449\pi$
$677$	−4.51253e12	−0.825602	−0.412801	+	0.910821i	$0.635449\pi$
$678$	2.18899e10	0.00397842
$679$	2.35896e12	0.425900
$680$	0	0
$681$	−9.07689e12	−1.61724
$682$	2.53390e12	0.448498
$683$	−1.09640e13	−1.92786	−0.963932	−	0.266150i	$-0.914248\pi$
$683$	−1.09640e13	−1.92786	−0.963932	+	0.266150i	$0.914248\pi$
$684$	−9.49309e12	−1.65827
$685$	−1.52679e13	−2.64954
$686$	−1.16269e12	−0.200449
$687$	−8.48673e12	−1.45357
$688$	3.85232e12	0.655502
$689$	−1.07587e13	−1.81875
$690$	1.90844e12	0.320521
$691$	−7.36009e12	−1.22809	−0.614047	−	0.789269i	$-0.710460\pi$
$691$	−7.36009e12	−1.22809	−0.614047	+	0.789269i	$0.710460\pi$
$692$	−6.08226e11	−0.100830
$693$	−3.95101e12	−0.650742
$694$	−1.21400e12	−0.198656
$695$	−4.57149e12	−0.743235
$696$	1.27869e12	0.206549
$697$	0	0
$698$	−2.14715e12	−0.342383
$699$	8.13764e12	1.28929
$700$	−5.00792e12	−0.788345
$701$	7.59917e12	1.18860	0.594299	−	0.804244i	$-0.297430\pi$
$701$	7.59917e12	1.18860	0.594299	+	0.804244i	$0.297430\pi$
$702$	1.50713e12	0.234226
$703$	6.77070e12	1.04553
$704$	4.62781e12	0.710065
$705$	−1.26709e13	−1.93178
$706$	−1.03932e11	−0.0157445
$707$	7.62479e11	0.114773
$708$	−9.41308e12	−1.40793
$709$	−1.17955e13	−1.75311	−0.876554	−	0.481303i	$-0.840164\pi$
$709$	−1.17955e13	−1.75311	−0.876554	+	0.481303i	$0.840164\pi$
$710$	6.90448e11	0.101969
$711$	−3.01354e12	−0.442245
$712$	1.87579e9	0.000273542 0
$713$	5.25435e12	0.761406
$714$	0	0
$715$	2.44523e13	3.49899
$716$	7.02643e11	0.0999139
$717$	1.22196e13	1.72672
$718$	−2.99163e12	−0.420096
$719$	1.01005e13	1.40949	0.704745	−	0.709461i	$-0.251062\pi$
$719$	1.01005e13	1.40949	0.704745	+	0.709461i	$0.251062\pi$
$720$	−1.33262e13	−1.84803
$721$	−2.93191e12	−0.404057
$722$	1.43257e12	0.196200
$723$	6.71043e12	0.913330
$724$	−1.45706e12	−0.197086
$725$	−3.95541e12	−0.531704
$726$	7.40883e11	0.0989772
$727$	−4.77545e12	−0.634029	−0.317015	−	0.948421i	$-0.602680\pi$
$727$	−4.77545e12	−0.634029	−0.317015	+	0.948421i	$0.602680\pi$
$728$	−2.96362e12	−0.391050
$729$	−1.15638e13	−1.51644
$730$	1.92021e12	0.250263
$731$	0	0
$732$	−1.43355e12	−0.184550
$733$	−1.00540e13	−1.28639	−0.643194	−	0.765703i	$-0.722391\pi$
$733$	−1.00540e13	−1.28639	−0.643194	+	0.765703i	$0.722391\pi$
$734$	−7.62033e11	−0.0969040
$735$	1.67469e13	2.11661
$736$	−2.68052e12	−0.336721
$737$	1.06459e13	1.32917
$738$	−5.04065e11	−0.0625508
$739$	1.96727e12	0.242640	0.121320	−	0.992613i	$-0.461287\pi$
$739$	1.96727e12	0.242640	0.121320	+	0.992613i	$0.461287\pi$
$740$	1.02602e13	1.25780
$741$	3.04318e13	3.70805
$742$	−9.11960e11	−0.110448
$743$	−1.21609e12	−0.146392	−0.0731958	−	0.997318i	$-0.523320\pi$
$743$	−1.21609e12	−0.146392	−0.0731958	+	0.997318i	$0.523320\pi$
$744$	9.88686e12	1.18299
$745$	2.54909e13	3.03167
$746$	3.29014e12	0.388947
$747$	−1.40034e13	−1.64547
$748$	0	0
$749$	−5.13983e12	−0.596733
$750$	−5.35703e12	−0.618227
$751$	−2.62861e12	−0.301542	−0.150771	−	0.988569i	$-0.548176\pi$
$751$	−2.62861e12	−0.301542	−0.150771	+	0.988569i	$0.548176\pi$
$752$	5.25414e12	0.599130
$753$	1.89794e13	2.15132
$754$	−1.13140e12	−0.127481
$755$	−6.51106e12	−0.729274
$756$	−1.85416e12	−0.206443
$757$	−5.49224e12	−0.607880	−0.303940	−	0.952691i	$-0.598302\pi$
$757$	−5.49224e12	−0.607880	−0.303940	+	0.952691i	$0.598302\pi$
$758$	−2.72468e12	−0.299781
$759$	7.55334e12	0.826135
$760$	1.03033e13	1.12025
$761$	−2.75245e12	−0.297501	−0.148751	−	0.988875i	$-0.547525\pi$
$761$	−2.75245e12	−0.297501	−0.148751	+	0.988875i	$0.547525\pi$
$762$	−1.05642e12	−0.113511
$763$	−7.81051e12	−0.834294
$764$	9.24131e12	0.981326
$765$	0	0
$766$	−4.29561e11	−0.0450811
$767$	1.72315e13	1.79782
$768$	6.12189e12	0.634980
$769$	3.05192e12	0.314705	0.157353	−	0.987542i	$-0.449704\pi$
$769$	3.05192e12	0.314705	0.157353	+	0.987542i	$0.449704\pi$
$770$	2.07270e12	0.212485
$771$	−2.45861e13	−2.50579
$772$	4.46174e12	0.452091
$773$	1.48497e13	1.49592	0.747962	−	0.663741i	$-0.231032\pi$
$773$	1.48497e13	1.49592	0.747962	+	0.663741i	$0.231032\pi$
$774$	2.72843e12	0.273262
$775$	−3.05833e13	−3.04528
$776$	−4.84578e12	−0.479718
$777$	5.31451e12	0.523080
$778$	−4.75164e12	−0.464982
$779$	−2.53264e12	−0.246408
$780$	4.61157e13	4.46090
$781$	2.73270e12	0.262822
$782$	0	0
$783$	−1.46447e12	−0.139237
$784$	−6.94427e12	−0.656454
$785$	−2.40169e13	−2.25737
$786$	−6.10692e12	−0.570717
$787$	2.19892e12	0.204325	0.102163	−	0.994768i	$-0.467424\pi$
$787$	2.19892e12	0.204325	0.102163	+	0.994768i	$0.467424\pi$
$788$	−7.32848e12	−0.677089
$789$	−2.18791e13	−2.00994
$790$	1.58090e12	0.144405
$791$	4.92984e10	0.00447754
$792$	8.11616e12	0.732972
$793$	2.62425e12	0.235655
$794$	1.54475e12	0.137932
$795$	2.93590e13	2.60669
$796$	4.43807e12	0.391819
$797$	5.00936e12	0.439764	0.219882	−	0.975526i	$-0.429433\pi$
$797$	5.00936e12	0.439764	0.219882	+	0.975526i	$0.429433\pi$
$798$	2.57955e12	0.225181
$799$	0	0
$800$	1.56022e13	1.34673
$801$	−8.63357e9	−0.000741044 0
$802$	−5.31907e12	−0.453995
$803$	7.59994e12	0.645046
$804$	2.00776e13	1.69457
$805$	4.29800e12	0.360732
$806$	−8.74805e12	−0.730136
$807$	1.03341e13	0.857711
$808$	−1.56628e12	−0.129276
$809$	1.09260e13	0.896794	0.448397	−	0.893834i	$-0.351995\pi$
$809$	1.09260e13	0.896794	0.448397	+	0.893834i	$0.351995\pi$
$810$	2.97700e12	0.242994
$811$	1.46137e13	1.18622	0.593110	−	0.805121i	$-0.297900\pi$
$811$	1.46137e13	1.18622	0.593110	+	0.805121i	$0.297900\pi$
$812$	1.39192e12	0.112360
$813$	2.97748e12	0.239024
$814$	−2.79793e12	−0.223371
$815$	−3.39745e12	−0.269739
$816$	0	0
$817$	1.37088e13	1.07647
$818$	−3.07694e12	−0.240287
$819$	1.36405e13	1.05938
$820$	−3.83790e12	−0.296437
$821$	−2.54363e13	−1.95393	−0.976966	−	0.213395i	$-0.931548\pi$
$821$	−2.54363e13	−1.95393	−0.976966	+	0.213395i	$0.931548\pi$
$822$	7.85217e12	0.599883
$823$	−1.24645e13	−0.947059	−0.473530	−	0.880778i	$-0.657020\pi$
$823$	−1.24645e13	−0.947059	−0.473530	+	0.880778i	$0.657020\pi$
$824$	6.02273e12	0.455115
$825$	−4.39647e13	−3.30416
$826$	1.46063e12	0.109177
$827$	1.30304e13	0.968688	0.484344	−	0.874878i	$-0.339058\pi$
$827$	1.30304e13	0.968688	0.484344	+	0.874878i	$0.339058\pi$
$828$	8.13468e12	0.601456
$829$	−1.86534e13	−1.37171	−0.685857	−	0.727736i	$-0.740573\pi$
$829$	−1.86534e13	−1.37171	−0.685857	+	0.727736i	$0.740573\pi$
$830$	7.34620e12	0.537293
$831$	−7.70920e12	−0.560796
$832$	−1.59770e13	−1.15596
$833$	0	0
$834$	2.35109e12	0.168276
$835$	8.29587e12	0.590572
$836$	1.97105e13	1.39563
$837$	−1.13234e13	−0.797463
$838$	−3.78071e12	−0.264835
$839$	−1.53435e13	−1.06905	−0.534523	−	0.845154i	$-0.679509\pi$
$839$	−1.53435e13	−1.06905	−0.534523	+	0.845154i	$0.679509\pi$
$840$	8.08733e12	0.560465
$841$	−1.34078e13	−0.924218
$842$	5.94486e12	0.407603
$843$	−2.70761e13	−1.84656
$844$	−2.31021e12	−0.156715
$845$	−5.90446e13	−3.98405
$846$	3.72128e12	0.249762
$847$	1.66855e12	0.111394
$848$	−1.21740e13	−0.808448
$849$	3.50298e13	2.31395
$850$	0	0
$851$	−5.80185e12	−0.379213
$852$	5.15372e12	0.335075
$853$	3.21915e11	0.0208195	0.0104098	−	0.999946i	$-0.496686\pi$
$853$	3.21915e11	0.0208195	0.0104098	+	0.999946i	$0.496686\pi$
$854$	2.22445e11	0.0143108
$855$	−4.74223e13	−3.03483
$856$	1.05582e13	0.672139
$857$	2.41023e13	1.52632	0.763158	−	0.646212i	$-0.223648\pi$
$857$	2.41023e13	1.52632	0.763158	+	0.646212i	$0.223648\pi$
$858$	−1.25757e13	−0.792206
$859$	−1.10638e13	−0.693325	−0.346662	−	0.937990i	$-0.612685\pi$
$859$	−1.10638e13	−0.693325	−0.346662	+	0.937990i	$0.612685\pi$
$860$	2.07740e13	1.29502
$861$	−1.98794e12	−0.123279
$862$	1.57515e12	0.0971718
$863$	−1.31635e13	−0.807833	−0.403917	−	0.914796i	$-0.632351\pi$
$863$	−1.31635e13	−0.807833	−0.403917	+	0.914796i	$0.632351\pi$
$864$	5.77665e12	0.352666
$865$	−3.03837e12	−0.184530
$866$	−1.90238e12	−0.114939
$867$	0	0
$868$	1.07624e13	0.643529
$869$	6.25700e12	0.372201
$870$	3.08745e12	0.182710
$871$	−3.67540e13	−2.16383
$872$	1.60443e13	0.939719
$873$	2.23033e13	1.29959
$874$	−2.81610e12	−0.163247
$875$	−1.20646e13	−0.695787
$876$	1.43331e13	0.822376
$877$	−2.24289e12	−0.128030	−0.0640148	−	0.997949i	$-0.520390\pi$
$877$	−2.24289e12	−0.128030	−0.0640148	+	0.997949i	$0.520390\pi$
$878$	1.60153e12	0.0909515
$879$	7.10520e12	0.401445
$880$	2.76691e13	1.55533
$881$	−4.14357e12	−0.231730	−0.115865	−	0.993265i	$-0.536964\pi$
$881$	−4.14357e12	−0.231730	−0.115865	+	0.993265i	$0.536964\pi$
$882$	−4.91833e12	−0.273658
$883$	2.44077e13	1.35115	0.675575	−	0.737292i	$-0.263896\pi$
$883$	2.44077e13	1.35115	0.675575	+	0.737292i	$0.263896\pi$
$884$	0	0
$885$	−4.70226e13	−2.57669
$886$	−2.98026e12	−0.162481
$887$	1.89165e13	1.02609	0.513043	−	0.858363i	$-0.328518\pi$
$887$	1.89165e13	1.02609	0.513043	+	0.858363i	$0.328518\pi$
$888$	−1.09171e13	−0.589179
$889$	−2.37916e12	−0.127751
$890$	4.52918e9	0.000241971 0
$891$	1.17825e13	0.626310
$892$	1.71583e13	0.907472
$893$	1.86973e13	0.983891
$894$	−1.31098e13	−0.686400
$895$	3.51002e12	0.182855
$896$	−7.22304e12	−0.374398
$897$	−2.60771e13	−1.34491
$898$	4.49920e12	0.230883
$899$	8.50043e12	0.434033
$900$	−4.73485e13	−2.40555
$901$	0	0
$902$	1.04659e12	0.0526438
$903$	1.07604e13	0.538560
$904$	−1.01269e11	−0.00504333
$905$	−7.27869e12	−0.360690
$906$	3.34860e12	0.165115
$907$	−5.03338e12	−0.246960	−0.123480	−	0.992347i	$-0.539405\pi$
$907$	−5.03338e12	−0.246960	−0.123480	+	0.992347i	$0.539405\pi$
$908$	2.02968e13	0.990927
$909$	7.20903e12	0.350219
$910$	−7.15580e12	−0.345917
$911$	−3.95603e13	−1.90295	−0.951475	−	0.307726i	$-0.900432\pi$
$911$	−3.95603e13	−1.90295	−0.951475	+	0.307726i	$0.900432\pi$
$912$	3.44352e13	1.64826
$913$	2.90753e13	1.38486
$914$	4.61198e12	0.218589
$915$	−7.16124e12	−0.337748
$916$	1.89772e13	0.890639
$917$	−1.37534e13	−0.642316
$918$	0	0
$919$	−1.78697e13	−0.826413	−0.413206	−	0.910637i	$-0.635591\pi$
$919$	−1.78697e13	−0.826413	−0.413206	+	0.910637i	$0.635591\pi$
$920$	−8.82895e12	−0.406316
$921$	−3.98124e13	−1.82327
$922$	2.76075e12	0.125817
$923$	−9.43437e12	−0.427864
$924$	1.54713e13	0.698237
$925$	3.37701e13	1.51668
$926$	8.98686e12	0.401660
$927$	−2.77204e13	−1.23294
$928$	−4.33652e12	−0.191944
$929$	3.82222e13	1.68363	0.841813	−	0.539770i	$-0.181489\pi$
$929$	3.82222e13	1.68363	0.841813	+	0.539770i	$0.181489\pi$
$930$	2.38723e13	1.04645
$931$	−2.47118e13	−1.07803
$932$	−1.81966e13	−0.789983
$933$	−2.81717e13	−1.21716
$934$	2.04078e12	0.0877475
$935$	0	0
$936$	−2.80202e13	−1.19325
$937$	−2.31069e13	−0.979295	−0.489647	−	0.871921i	$-0.662874\pi$
$937$	−2.31069e13	−0.979295	−0.489647	+	0.871921i	$0.662874\pi$
$938$	−3.11546e12	−0.131404
$939$	4.68300e13	1.96575
$940$	2.83335e13	1.18365
$941$	2.39775e13	0.996900	0.498450	−	0.866919i	$-0.333903\pi$
$941$	2.39775e13	0.996900	0.498450	+	0.866919i	$0.333903\pi$
$942$	1.23517e13	0.511092
$943$	2.17023e12	0.0893723
$944$	1.94984e13	0.799145
$945$	−9.26238e12	−0.377815
$946$	−5.66504e12	−0.229982
$947$	3.67999e12	0.148686	0.0743432	−	0.997233i	$-0.476314\pi$
$947$	3.67999e12	0.148686	0.0743432	+	0.997233i	$0.476314\pi$
$948$	1.18003e13	0.474523
$949$	−2.62381e13	−1.05011
$950$	1.63913e13	0.652916
$951$	5.41690e13	2.14753
$952$	0	0
$953$	−3.84204e13	−1.50884	−0.754422	−	0.656390i	$-0.772083\pi$
$953$	−3.84204e13	−1.50884	−0.754422	+	0.656390i	$0.772083\pi$
$954$	−8.62233e12	−0.337021
$955$	4.61645e13	1.79594
$956$	−2.73243e13	−1.05801
$957$	1.22197e13	0.470930
$958$	1.49373e12	0.0572965
$959$	1.76839e13	0.675141
$960$	4.35992e13	1.65675
$961$	3.92860e13	1.48588
$962$	9.65958e12	0.363639
$963$	−4.85956e13	−1.82087
$964$	−1.50052e13	−0.559622
$965$	2.22884e13	0.827382
$966$	−2.21043e12	−0.0816733
$967$	−1.42714e13	−0.524866	−0.262433	−	0.964950i	$-0.584525\pi$
$967$	−1.42714e13	−0.524866	−0.262433	+	0.964950i	$0.584525\pi$
$968$	−3.42753e12	−0.125470
$969$	0	0
$970$	−1.17003e13	−0.424352
$971$	−6.93223e12	−0.250257	−0.125129	−	0.992141i	$-0.539934\pi$
$971$	−6.93223e12	−0.250257	−0.125129	+	0.992141i	$0.539934\pi$
$972$	3.53896e13	1.27168
$973$	5.29490e12	0.189387
$974$	7.83483e12	0.278942
$975$	1.51784e14	5.37904
$976$	2.96948e12	0.104751
$977$	−8.04380e12	−0.282446	−0.141223	−	0.989978i	$-0.545103\pi$
$977$	−8.04380e12	−0.282446	−0.141223	+	0.989978i	$0.545103\pi$
$978$	1.74728e12	0.0610715
$979$	1.79259e10	0.000623674 0
$980$	−3.74477e13	−1.29690
$981$	−7.38462e13	−2.54576
$982$	−5.79995e12	−0.199032
$983$	3.25832e13	1.11302	0.556509	−	0.830841i	$-0.312140\pi$
$983$	3.25832e13	1.11302	0.556509	+	0.830841i	$0.312140\pi$
$984$	4.08361e12	0.138857
$985$	−3.66091e13	−1.23916
$986$	0	0
$987$	1.46760e13	0.492245
$988$	−6.80485e13	−2.27202
$989$	−1.17471e13	−0.390435
$990$	1.95968e13	0.648377
$991$	1.06994e13	0.352394	0.176197	−	0.984355i	$-0.443620\pi$
$991$	1.06994e13	0.352394	0.176197	+	0.984355i	$0.443620\pi$
$992$	−3.35301e13	−1.09934
$993$	−3.56637e13	−1.16401
$994$	−7.99706e11	−0.0259831
$995$	2.21702e13	0.717076
$996$	5.48343e13	1.76557
$997$	−8.82824e11	−0.0282974	−0.0141487	−	0.999900i	$-0.504504\pi$
$997$	−8.82824e11	−0.0282974	−0.0141487	+	0.999900i	$0.504504\pi$
$998$	−6.81332e12	−0.217406
$999$	1.25032e13	0.397171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.d.1.7	✓	12
17.16	even	2		289.10.a.e.1.7	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.7	✓	12	1.1	even	1	trivial
289.10.a.e.1.7	yes	12	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+5.74483 q^{2} +214.211 q^{3} -478.997 q^{4} -2392.81 q^{5} +1230.60 q^{6} +2771.45 q^{7} -5693.11 q^{8} +26203.3 q^{9} +O(q^{10})\)	\(q+5.74483 q^{2} +214.211 q^{3} -478.997 q^{4} -2392.81 q^{5} +1230.60 q^{6} +2771.45 q^{7} -5693.11 q^{8} +26203.3 q^{9} -13746.3 q^{10} -54405.8 q^{11} -102606. q^{12} +187831. q^{13} +15921.5 q^{14} -512565. q^{15} +212541. q^{16} +150533. q^{18} +756343. q^{19} +1.14615e6 q^{20} +593675. q^{21} -312552. q^{22} -648115. q^{23} -1.21953e6 q^{24} +3.77240e6 q^{25} +1.07906e6 q^{26} +1.39672e6 q^{27} -1.32752e6 q^{28} -1.04851e6 q^{29} -2.94460e6 q^{30} -8.10714e6 q^{31} +4.13588e6 q^{32} -1.16543e7 q^{33} -6.63154e6 q^{35} -1.25513e7 q^{36} +8.95189e6 q^{37} +4.34506e6 q^{38} +4.02354e7 q^{39} +1.36225e7 q^{40} -3.34853e6 q^{41} +3.41056e6 q^{42} +1.81251e7 q^{43} +2.60602e7 q^{44} -6.26994e7 q^{45} -3.72331e6 q^{46} +2.47206e7 q^{47} +4.55285e7 q^{48} -3.26727e7 q^{49} +2.16718e7 q^{50} -8.99704e7 q^{52} -5.72785e7 q^{53} +8.02389e6 q^{54} +1.30183e8 q^{55} -1.57782e7 q^{56} +1.62017e8 q^{57} -6.02352e6 q^{58} +9.17398e7 q^{59} +2.45517e8 q^{60} +1.39714e7 q^{61} -4.65741e7 q^{62} +7.26211e7 q^{63} -8.50608e7 q^{64} -4.49443e8 q^{65} -6.69521e7 q^{66} -1.95676e8 q^{67} -1.38833e8 q^{69} -3.80971e7 q^{70} -5.02281e7 q^{71} -1.49178e8 q^{72} -1.39690e8 q^{73} +5.14271e7 q^{74} +8.08089e8 q^{75} -3.62286e8 q^{76} -1.50783e8 q^{77} +2.31145e8 q^{78} -1.15006e8 q^{79} -5.08568e8 q^{80} -2.16568e8 q^{81} -1.92367e7 q^{82} -5.34414e8 q^{83} -2.84368e8 q^{84} +1.04126e8 q^{86} -2.24603e8 q^{87} +3.09738e8 q^{88} -329484. q^{89} -3.60197e8 q^{90} +5.20563e8 q^{91} +3.10445e8 q^{92} -1.73664e9 q^{93} +1.42016e8 q^{94} -1.80978e9 q^{95} +8.85950e8 q^{96} +8.51166e8 q^{97} -1.87699e8 q^{98} -1.42561e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 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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