LMFDB - Embedded newform 289.10.a.d.1.10

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			1.10
Root			$25.6779$ 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)

$f(q)$	$=$	$q+26.6779 q^{2} -248.720 q^{3} +199.710 q^{4} +2486.89 q^{5} -6635.33 q^{6} +7643.33 q^{7} -8331.23 q^{8} +42178.6 q^{9} +O(q^{10})$	\(q+26.6779 q^{2} -248.720 q^{3} +199.710 q^{4} +2486.89 q^{5} -6635.33 q^{6} +7643.33 q^{7} -8331.23 q^{8} +42178.6 q^{9} +66345.1 q^{10} -36423.7 q^{11} -49672.0 q^{12} -22928.9 q^{13} +203908. q^{14} -618540. q^{15} -324511. q^{16} +1.12524e6 q^{18} +65495.7 q^{19} +496658. q^{20} -1.90105e6 q^{21} -971709. q^{22} -1.26237e6 q^{23} +2.07214e6 q^{24} +4.23151e6 q^{25} -611694. q^{26} -5.59511e6 q^{27} +1.52645e6 q^{28} -3.05958e6 q^{29} -1.65013e7 q^{30} -5.62658e6 q^{31} -4.39170e6 q^{32} +9.05931e6 q^{33} +1.90081e7 q^{35} +8.42351e6 q^{36} -1.60507e7 q^{37} +1.74729e6 q^{38} +5.70287e6 q^{39} -2.07189e7 q^{40} +3.10368e7 q^{41} -5.07160e7 q^{42} -2.74384e6 q^{43} -7.27420e6 q^{44} +1.04894e8 q^{45} -3.36774e7 q^{46} +2.40543e7 q^{47} +8.07125e7 q^{48} +1.80669e7 q^{49} +1.12888e8 q^{50} -4.57914e6 q^{52} +6.76529e7 q^{53} -1.49266e8 q^{54} -9.05819e7 q^{55} -6.36783e7 q^{56} -1.62901e7 q^{57} -8.16231e7 q^{58} +7.10522e7 q^{59} -1.23529e8 q^{60} -6.08297e7 q^{61} -1.50105e8 q^{62} +3.22385e8 q^{63} +4.89887e7 q^{64} -5.70216e7 q^{65} +2.41683e8 q^{66} -2.86525e8 q^{67} +3.13977e8 q^{69} +5.07097e8 q^{70} +2.41217e7 q^{71} -3.51400e8 q^{72} -3.36309e7 q^{73} -4.28198e8 q^{74} -1.05246e9 q^{75} +1.30802e7 q^{76} -2.78399e8 q^{77} +1.52141e8 q^{78} -3.66433e8 q^{79} -8.07025e8 q^{80} +5.61413e8 q^{81} +8.27997e8 q^{82} -6.48526e7 q^{83} -3.79659e8 q^{84} -7.31999e7 q^{86} +7.60978e8 q^{87} +3.03454e8 q^{88} -4.02237e8 q^{89} +2.79834e9 q^{90} -1.75253e8 q^{91} -2.52108e8 q^{92} +1.39944e9 q^{93} +6.41719e8 q^{94} +1.62881e8 q^{95} +1.09230e9 q^{96} +2.35780e8 q^{97} +4.81987e8 q^{98} -1.53630e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	26.6779	1.17901	0.589504	−	0.807766i	$-0.299323\pi$
$2$	26.6779	1.17901	0.589504	+	0.807766i	$0.299323\pi$
$3$	−248.720	−1.77282	−0.886411	−	0.462900i	$-0.846809\pi$
$3$	−248.720	−1.77282	−0.886411	+	0.462900i	$0.846809\pi$
$4$	199.710	0.390059
$5$	2486.89	1.77947	0.889737	−	0.456473i	$-0.150887\pi$
$5$	2486.89	1.77947	0.889737	+	0.456473i	$0.150887\pi$
$6$	−6635.33	−2.09017
$7$	7643.33	1.20321	0.601605	−	0.798794i	$-0.294528\pi$
$7$	7643.33	1.20321	0.601605	+	0.798794i	$0.294528\pi$
$8$	−8331.23	−0.719125
$9$	42178.6	2.14290
$10$	66345.1	2.09801
$11$	−36423.7	−0.750097	−0.375048	−	0.927005i	$-0.622374\pi$
$11$	−36423.7	−0.750097	−0.375048	+	0.927005i	$0.622374\pi$
$12$	−49672.0	−0.691506
$13$	−22928.9	−0.222658	−0.111329	−	0.993784i	$-0.535511\pi$
$13$	−22928.9	−0.222658	−0.111329	+	0.993784i	$0.535511\pi$
$14$	203908.	1.41859
$15$	−618540.	−3.15469
$16$	−324511.	−1.23791
$17$	0	0
$17$	0	0
$18$	1.12524e6	2.52649
$19$	65495.7	0.115298	0.0576490	−	0.998337i	$-0.481640\pi$
$19$	65495.7	0.115298	0.0576490	+	0.998337i	$0.481640\pi$
$20$	496658.	0.694101
$21$	−1.90105e6	−2.13308
$22$	−971709.	−0.884370
$23$	−1.26237e6	−0.940614	−0.470307	−	0.882503i	$-0.655857\pi$
$23$	−1.26237e6	−0.940614	−0.470307	+	0.882503i	$0.655857\pi$
$24$	2.07214e6	1.27488
$25$	4.23151e6	2.16653
$26$	−611694.	−0.262515
$27$	−5.59511e6	−2.02615
$28$	1.52645e6	0.469323
$29$	−3.05958e6	−0.803287	−0.401643	−	0.915796i	$-0.631561\pi$
$29$	−3.05958e6	−0.803287	−0.401643	+	0.915796i	$0.631561\pi$
$30$	−1.65013e7	−3.71941
$31$	−5.62658e6	−1.09425	−0.547125	−	0.837051i	$-0.684278\pi$
$31$	−5.62658e6	−1.09425	−0.547125	+	0.837051i	$0.684278\pi$
$32$	−4.39170e6	−0.740384
$33$	9.05931e6	1.32979
$34$	0	0
$35$	1.90081e7	2.14108
$36$	8.42351e6	0.835857
$37$	−1.60507e7	−1.40794	−0.703972	−	0.710227i	$-0.748592\pi$
$37$	−1.60507e7	−1.40794	−0.703972	+	0.710227i	$0.748592\pi$
$38$	1.74729e6	0.135937
$39$	5.70287e6	0.394732
$40$	−2.07189e7	−1.27966
$41$	3.10368e7	1.71534	0.857669	−	0.514202i	$-0.171912\pi$
$41$	3.10368e7	1.71534	0.857669	+	0.514202i	$0.171912\pi$
$42$	−5.07160e7	−2.51491
$43$	−2.74384e6	−0.122391	−0.0611957	−	0.998126i	$-0.519491\pi$
$43$	−2.74384e6	−0.122391	−0.0611957	+	0.998126i	$0.519491\pi$
$44$	−7.27420e6	−0.292582
$45$	1.04894e8	3.81323
$46$	−3.36774e7	−1.10899
$47$	2.40543e7	0.719039	0.359520	−	0.933137i	$-0.382941\pi$
$47$	2.40543e7	0.719039	0.359520	+	0.933137i	$0.382941\pi$
$48$	8.07125e7	2.19460
$49$	1.80669e7	0.447714
$50$	1.12888e8	2.55436
$51$	0	0
$52$	−4.57914e6	−0.0868497
$53$	6.76529e7	1.17773	0.588864	−	0.808232i	$-0.299575\pi$
$53$	6.76529e7	1.17773	0.588864	+	0.808232i	$0.299575\pi$
$54$	−1.49266e8	−2.38885
$55$	−9.05819e7	−1.33478
$56$	−6.36783e7	−0.865258
$57$	−1.62901e7	−0.204403
$58$	−8.16231e7	−0.947081
$59$	7.10522e7	0.763385	0.381693	−	0.924289i	$-0.375341\pi$
$59$	7.10522e7	0.763385	0.381693	+	0.924289i	$0.375341\pi$
$60$	−1.23529e8	−1.23052
$61$	−6.08297e7	−0.562511	−0.281256	−	0.959633i	$-0.590751\pi$
$61$	−6.08297e7	−0.562511	−0.281256	+	0.959633i	$0.590751\pi$
$62$	−1.50105e8	−1.29013
$63$	3.22385e8	2.57835
$64$	4.89887e7	0.364994
$65$	−5.70216e7	−0.396214
$66$	2.41683e8	1.56783
$67$	−2.86525e8	−1.73710	−0.868552	−	0.495597i	$-0.834949\pi$
$67$	−2.86525e8	−1.73710	−0.868552	+	0.495597i	$0.834949\pi$
$68$	0	0
$69$	3.13977e8	1.66754
$70$	5.07097e8	2.52435
$71$	2.41217e7	0.112653	0.0563267	−	0.998412i	$-0.482061\pi$
$71$	2.41217e7	0.112653	0.0563267	+	0.998412i	$0.482061\pi$
$72$	−3.51400e8	−1.54101
$73$	−3.36309e7	−0.138607	−0.0693035	−	0.997596i	$-0.522078\pi$
$73$	−3.36309e7	−0.138607	−0.0693035	+	0.997596i	$0.522078\pi$
$74$	−4.28198e8	−1.65998
$75$	−1.05246e9	−3.84087
$76$	1.30802e7	0.0449731
$77$	−2.78399e8	−0.902524
$78$	1.52141e8	0.465392
$79$	−3.66433e8	−1.05846	−0.529228	−	0.848480i	$-0.677518\pi$
$79$	−3.66433e8	−1.05846	−0.529228	+	0.848480i	$0.677518\pi$
$80$	−8.07025e8	−2.20284
$81$	5.61413e8	1.44911
$82$	8.27997e8	2.02240
$83$	−6.48526e7	−0.149995	−0.0749974	−	0.997184i	$-0.523895\pi$
$83$	−6.48526e7	−0.149995	−0.0749974	+	0.997184i	$0.523895\pi$
$84$	−3.79659e8	−0.832026
$85$	0	0
$86$	−7.31999e7	−0.144300
$87$	7.60978e8	1.42408
$88$	3.03454e8	0.539413
$89$	−4.02237e8	−0.679558	−0.339779	−	0.940505i	$-0.610352\pi$
$89$	−4.02237e8	−0.679558	−0.339779	+	0.940505i	$0.610352\pi$
$90$	2.79834e9	4.49583
$91$	−1.75253e8	−0.267904
$92$	−2.52108e8	−0.366895
$93$	1.39944e9	1.93991
$94$	6.41719e8	0.847753
$95$	1.62881e8	0.205170
$96$	1.09230e9	1.31257
$97$	2.35780e8	0.270418	0.135209	−	0.990817i	$-0.456829\pi$
$97$	2.35780e8	0.270418	0.135209	+	0.990817i	$0.456829\pi$
$98$	4.81987e8	0.527859
$99$	−1.53630e9	−1.60738
$100$	8.45076e8	0.845076
$101$	1.58074e9	1.51152	0.755759	−	0.654850i	$-0.227268\pi$
$101$	1.58074e9	1.51152	0.755759	+	0.654850i	$0.227268\pi$
$102$	0	0
$103$	−6.79231e8	−0.594634	−0.297317	−	0.954779i	$-0.596092\pi$
$103$	−6.79231e8	−0.594634	−0.297317	+	0.954779i	$0.596092\pi$
$104$	1.91026e8	0.160119
$105$	−4.72770e9	−3.79576
$106$	1.80484e9	1.38855
$107$	1.53610e8	0.113290	0.0566450	−	0.998394i	$-0.481960\pi$
$107$	1.53610e8	0.113290	0.0566450	+	0.998394i	$0.481960\pi$
$108$	−1.11740e9	−0.790319
$109$	−2.74984e9	−1.86590	−0.932949	−	0.360008i	$-0.882774\pi$
$109$	−2.74984e9	−1.86590	−0.932949	+	0.360008i	$0.882774\pi$
$110$	−2.41653e9	−1.57371
$111$	3.99212e9	2.49603
$112$	−2.48035e9	−1.48947
$113$	−1.25971e9	−0.726806	−0.363403	−	0.931632i	$-0.618385\pi$
$113$	−1.25971e9	−0.726806	−0.363403	+	0.931632i	$0.618385\pi$
$114$	−4.34586e8	−0.240992
$115$	−3.13938e9	−1.67380
$116$	−6.11030e8	−0.313329
$117$	−9.67108e8	−0.477132
$118$	1.89552e9	0.900037
$119$	0	0
$120$	5.15320e9	2.26862
$121$	−1.03126e9	−0.437355
$122$	−1.62281e9	−0.663205
$123$	−7.71947e9	−3.04099
$124$	−1.12369e9	−0.426823
$125$	5.66609e9	2.07581
$126$	8.60056e9	3.03990
$127$	−5.99446e8	−0.204472	−0.102236	−	0.994760i	$-0.532600\pi$
$127$	−5.99446e8	−0.204472	−0.102236	+	0.994760i	$0.532600\pi$
$128$	3.55546e9	1.17072
$129$	6.82448e8	0.216978
$130$	−1.52122e9	−0.467139
$131$	−2.60491e9	−0.772808	−0.386404	−	0.922330i	$-0.626283\pi$
$131$	−2.60491e9	−0.772808	−0.386404	+	0.922330i	$0.626283\pi$
$132$	1.80924e9	0.518696
$133$	5.00605e8	0.138728
$134$	−7.64389e9	−2.04806
$135$	−1.39144e10	−3.60548
$136$	0	0
$137$	−5.23591e9	−1.26984	−0.634921	−	0.772577i	$-0.718967\pi$
$137$	−5.23591e9	−1.26984	−0.634921	+	0.772577i	$0.718967\pi$
$138$	8.37624e9	1.96604
$139$	−3.86994e9	−0.879301	−0.439651	−	0.898169i	$-0.644898\pi$
$139$	−3.86994e9	−0.879301	−0.439651	+	0.898169i	$0.644898\pi$
$140$	3.79612e9	0.835149
$141$	−5.98279e9	−1.27473
$142$	6.43515e8	0.132819
$143$	8.35155e8	0.167015
$144$	−1.36874e10	−2.65272
$145$	−7.60884e9	−1.42943
$146$	−8.97201e8	−0.163419
$147$	−4.49360e9	−0.793718
$148$	−3.20549e9	−0.549182
$149$	4.17809e9	0.694448	0.347224	−	0.937782i	$-0.387124\pi$
$149$	4.17809e9	0.694448	0.347224	+	0.937782i	$0.387124\pi$
$150$	−2.80774e10	−4.52842
$151$	−7.62654e9	−1.19380	−0.596899	−	0.802316i	$-0.703601\pi$
$151$	−7.62654e9	−1.19380	−0.596899	+	0.802316i	$0.703601\pi$
$152$	−5.45660e8	−0.0829136
$153$	0	0
$154$	−7.42709e9	−1.06408
$155$	−1.39927e10	−1.94719
$156$	1.13892e9	0.153969
$157$	2.75115e9	0.361382	0.180691	−	0.983540i	$-0.442167\pi$
$157$	2.75115e9	0.361382	0.180691	+	0.983540i	$0.442167\pi$
$158$	−9.77566e9	−1.24793
$159$	−1.68266e10	−2.08790
$160$	−1.09217e10	−1.31750
$161$	−9.64871e9	−1.13176
$162$	1.49773e10	1.70851
$163$	−2.03030e9	−0.225277	−0.112638	−	0.993636i	$-0.535930\pi$
$163$	−2.03030e9	−0.225277	−0.112638	+	0.993636i	$0.535930\pi$
$164$	6.19837e9	0.669084
$165$	2.25295e10	2.36632
$166$	−1.73013e9	−0.176845
$167$	−4.82082e9	−0.479620	−0.239810	−	0.970820i	$-0.577085\pi$
$167$	−4.82082e9	−0.479620	−0.239810	+	0.970820i	$0.577085\pi$
$168$	1.58381e10	1.53395
$169$	−1.00788e10	−0.950424
$170$	0	0
$171$	2.76252e9	0.247072
$172$	−5.47974e8	−0.0477399
$173$	1.37527e10	1.16730	0.583649	−	0.812006i	$-0.301624\pi$
$173$	1.37527e10	1.16730	0.583649	+	0.812006i	$0.301624\pi$
$174$	2.03013e10	1.67901
$175$	3.23428e10	2.60679
$176$	1.18199e10	0.928555
$177$	−1.76721e10	−1.35335
$178$	−1.07308e10	−0.801205
$179$	9.44751e9	0.687826	0.343913	−	0.939001i	$-0.388247\pi$
$179$	9.44751e9	0.687826	0.343913	+	0.939001i	$0.388247\pi$
$180$	2.09484e10	1.48739
$181$	−1.27539e10	−0.883261	−0.441630	−	0.897197i	$-0.645600\pi$
$181$	−1.27539e10	−0.883261	−0.441630	+	0.897197i	$0.645600\pi$
$182$	−4.67538e9	−0.315861
$183$	1.51295e10	0.997232
$184$	1.05171e10	0.676419
$185$	−3.99163e10	−2.50540
$186$	3.73342e10	2.28717
$187$	0	0
$188$	4.80390e9	0.280468
$189$	−4.27653e10	−2.43788
$190$	4.34532e9	0.241897
$191$	3.74399e9	0.203556	0.101778	−	0.994807i	$-0.467547\pi$
$191$	3.74399e9	0.203556	0.101778	+	0.994807i	$0.467547\pi$
$192$	−1.21845e10	−0.647069
$193$	−3.30655e9	−0.171541	−0.0857704	−	0.996315i	$-0.527335\pi$
$193$	−3.30655e9	−0.171541	−0.0857704	+	0.996315i	$0.527335\pi$
$194$	6.29013e9	0.318824
$195$	1.41824e10	0.702416
$196$	3.60815e9	0.174635
$197$	2.41732e10	1.14350	0.571750	−	0.820428i	$-0.306265\pi$
$197$	2.41732e10	1.14350	0.571750	+	0.820428i	$0.306265\pi$
$198$	−4.09853e10	−1.89511
$199$	−2.69574e10	−1.21854	−0.609270	−	0.792963i	$-0.708537\pi$
$199$	−2.69574e10	−1.21854	−0.609270	+	0.792963i	$0.708537\pi$
$200$	−3.52537e10	−1.55801
$201$	7.12645e10	3.07958
$202$	4.21707e10	1.78209
$203$	−2.33854e10	−0.966522
$204$	0	0
$205$	7.71852e10	3.05240
$206$	−1.81205e10	−0.701079
$207$	−5.32450e10	−2.01564
$208$	7.44068e9	0.275631
$209$	−2.38560e9	−0.0864847
$210$	−1.26125e11	−4.47523
$211$	−1.09942e10	−0.381851	−0.190926	−	0.981604i	$-0.561149\pi$
$211$	−1.09942e10	−0.381851	−0.190926	+	0.981604i	$0.561149\pi$
$212$	1.35110e10	0.459384
$213$	−5.99954e9	−0.199714
$214$	4.09798e9	0.133570
$215$	−6.82364e9	−0.217792
$216$	4.66141e10	1.45705
$217$	−4.30058e10	−1.31661
$218$	−7.33599e10	−2.19991
$219$	8.36466e9	0.245725
$220$	−1.80901e10	−0.520643
$221$	0	0
$222$	1.06501e11	2.94284
$223$	4.45866e10	1.20735	0.603674	−	0.797232i	$-0.293703\pi$
$223$	4.45866e10	1.20735	0.603674	+	0.797232i	$0.293703\pi$
$224$	−3.35672e10	−0.890838
$225$	1.78479e11	4.64265
$226$	−3.36065e10	−0.856910
$227$	−1.49234e10	−0.373036	−0.186518	−	0.982452i	$-0.559720\pi$
$227$	−1.49234e10	−0.373036	−0.186518	+	0.982452i	$0.559720\pi$
$228$	−3.25330e9	−0.0797292
$229$	5.36534e10	1.28925	0.644626	−	0.764498i	$-0.277013\pi$
$229$	5.36534e10	1.28925	0.644626	+	0.764498i	$0.277013\pi$
$230$	−8.37520e10	−1.97342
$231$	6.92433e10	1.60001
$232$	2.54900e10	0.577663
$233$	−2.83632e10	−0.630454	−0.315227	−	0.949016i	$-0.602081\pi$
$233$	−2.83632e10	−0.630454	−0.315227	+	0.949016i	$0.602081\pi$
$234$	−2.58004e10	−0.562542
$235$	5.98205e10	1.27951
$236$	1.41899e10	0.297766
$237$	9.11392e10	1.87645
$238$	0	0
$239$	−7.73827e10	−1.53410	−0.767050	−	0.641588i	$-0.778276\pi$
$239$	−7.73827e10	−1.53410	−0.767050	+	0.641588i	$0.778276\pi$
$240$	2.00723e11	3.90523
$241$	5.94132e10	1.13450	0.567252	−	0.823544i	$-0.308007\pi$
$241$	5.94132e10	1.13450	0.567252	+	0.823544i	$0.308007\pi$
$242$	−2.75118e10	−0.515645
$243$	−2.95062e10	−0.542856
$244$	−1.21483e10	−0.219413
$245$	4.49304e10	0.796696
$246$	−2.05939e11	−3.58535
$247$	−1.50174e9	−0.0256720
$248$	4.68763e10	0.786903
$249$	1.61301e10	0.265914
$250$	1.51159e11	2.44740
$251$	1.06016e11	1.68593	0.842964	−	0.537971i	$-0.180809\pi$
$251$	1.06016e11	1.68593	0.842964	+	0.537971i	$0.180809\pi$
$252$	6.43837e10	1.00571
$253$	4.59802e10	0.705551
$254$	−1.59920e10	−0.241074
$255$	0	0
$256$	6.97701e10	1.01529
$257$	−1.30721e11	−1.86915	−0.934577	−	0.355762i	$-0.884221\pi$
$257$	−1.30721e11	−1.86915	−0.934577	+	0.355762i	$0.884221\pi$
$258$	1.82063e10	0.255819
$259$	−1.22681e11	−1.69405
$260$	−1.13878e10	−0.154547
$261$	−1.29049e11	−1.72136
$262$	−6.94935e10	−0.911147
$263$	−8.85385e10	−1.14112	−0.570560	−	0.821256i	$-0.693274\pi$
$263$	−8.85385e10	−1.14112	−0.570560	+	0.821256i	$0.693274\pi$
$264$	−7.54752e10	−0.956283
$265$	1.68245e11	2.09574
$266$	1.33551e10	0.163561
$267$	1.00044e11	1.20474
$268$	−5.72220e10	−0.677574
$269$	−1.21204e11	−1.41133	−0.705667	−	0.708543i	$-0.749353\pi$
$269$	−1.21204e11	−1.41133	−0.705667	+	0.708543i	$0.749353\pi$
$270$	−3.71208e11	−4.25089
$271$	7.02021e10	0.790658	0.395329	−	0.918540i	$-0.370631\pi$
$271$	7.02021e10	0.790658	0.395329	+	0.918540i	$0.370631\pi$
$272$	0	0
$273$	4.35889e10	0.474946
$274$	−1.39683e11	−1.49715
$275$	−1.54127e11	−1.62511
$276$	6.27044e10	0.650440
$277$	5.73626e10	0.585423	0.292712	−	0.956201i	$-0.405442\pi$
$277$	5.73626e10	0.585423	0.292712	+	0.956201i	$0.405442\pi$
$278$	−1.03242e11	−1.03670
$279$	−2.37321e11	−2.34486
$280$	−1.58361e11	−1.53971
$281$	−5.07750e9	−0.0485815	−0.0242908	−	0.999705i	$-0.507733\pi$
$281$	−5.07750e9	−0.0485815	−0.0242908	+	0.999705i	$0.507733\pi$
$282$	−1.59608e11	−1.50291
$283$	−1.57533e11	−1.45993	−0.729965	−	0.683485i	$-0.760464\pi$
$283$	−1.57533e11	−1.45993	−0.729965	+	0.683485i	$0.760464\pi$
$284$	4.81735e9	0.0439415
$285$	−4.05117e10	−0.363730
$286$	2.22802e10	0.196912
$287$	2.37225e11	2.06391
$288$	−1.85236e11	−1.58657
$289$	0	0
$290$	−2.02988e11	−1.68531
$291$	−5.86433e10	−0.479402
$292$	−6.71643e9	−0.0540649
$293$	1.40704e11	1.11532	0.557661	−	0.830069i	$-0.311699\pi$
$293$	1.40704e11	1.11532	0.557661	+	0.830069i	$0.311699\pi$
$294$	−1.19880e11	−0.935799
$295$	1.76699e11	1.35842
$296$	1.33722e11	1.01249
$297$	2.03795e11	1.51981
$298$	1.11463e11	0.818760
$299$	2.89447e10	0.209435
$300$	−2.10187e11	−1.49817
$301$	−2.09721e10	−0.147263
$302$	−2.03460e11	−1.40750
$303$	−3.93161e11	−2.67965
$304$	−2.12541e10	−0.142729
$305$	−1.51277e11	−1.00097
$306$	0	0
$307$	3.62814e10	0.233110	0.116555	−	0.993184i	$-0.462815\pi$
$307$	3.62814e10	0.233110	0.116555	+	0.993184i	$0.462815\pi$
$308$	−5.55991e10	−0.352038
$309$	1.68938e11	1.05418
$310$	−3.73296e11	−2.29575
$311$	1.97553e11	1.19746	0.598730	−	0.800951i	$-0.295672\pi$
$311$	1.97553e11	1.19746	0.598730	+	0.800951i	$0.295672\pi$
$312$	−4.75119e10	−0.283862
$313$	−3.01127e10	−0.177337	−0.0886687	−	0.996061i	$-0.528261\pi$
$313$	−3.01127e10	−0.177337	−0.0886687	+	0.996061i	$0.528261\pi$
$314$	7.33950e10	0.426072
$315$	8.01737e11	4.58811
$316$	−7.31805e10	−0.412860
$317$	1.53142e11	0.851783	0.425891	−	0.904774i	$-0.359961\pi$
$317$	1.53142e11	0.851783	0.425891	+	0.904774i	$0.359961\pi$
$318$	−4.48899e11	−2.46165
$319$	1.11441e11	0.602543
$320$	1.21830e11	0.649498
$321$	−3.82058e10	−0.200843
$322$	−2.57407e11	−1.33435
$323$	0	0
$324$	1.12120e11	0.565237
$325$	−9.70237e10	−0.482395
$326$	−5.41642e10	−0.265603
$327$	6.83940e11	3.30790
$328$	−2.58575e11	−1.23354
$329$	1.83855e11	0.865156
$330$	6.01040e11	2.78991
$331$	−1.97770e11	−0.905598	−0.452799	−	0.891613i	$-0.649575\pi$
$331$	−1.97770e11	−0.905598	−0.452799	+	0.891613i	$0.649575\pi$
$332$	−1.29517e10	−0.0585069
$333$	−6.76995e11	−3.01708
$334$	−1.28609e11	−0.565475
$335$	−7.12557e11	−3.09113
$336$	6.16912e11	2.64056
$337$	−2.77785e11	−1.17321	−0.586603	−	0.809875i	$-0.699535\pi$
$337$	−2.77785e11	−1.17321	−0.586603	+	0.809875i	$0.699535\pi$
$338$	−2.68880e11	−1.12056
$339$	3.13316e11	1.28850
$340$	0	0
$341$	2.04941e11	0.820794
$342$	7.36982e10	0.291299
$343$	−1.70345e11	−0.664516
$344$	2.28596e10	0.0880147
$345$	7.80826e11	2.96735
$346$	3.66894e11	1.37625
$347$	−4.74603e11	−1.75731	−0.878655	−	0.477458i	$-0.841558\pi$
$347$	−4.74603e11	−1.75731	−0.878655	+	0.477458i	$0.841558\pi$
$348$	1.51975e11	0.555477
$349$	−1.38895e11	−0.501155	−0.250578	−	0.968096i	$-0.580621\pi$
$349$	−1.38895e11	−0.501155	−0.250578	+	0.968096i	$0.580621\pi$
$350$	8.62838e11	3.07343
$351$	1.28290e11	0.451138
$352$	1.59962e11	0.555360
$353$	4.16142e11	1.42644	0.713222	−	0.700938i	$-0.247235\pi$
$353$	4.16142e11	1.42644	0.713222	+	0.700938i	$0.247235\pi$
$354$	−4.71455e11	−1.59561
$355$	5.99879e10	0.200464
$356$	−8.03309e10	−0.265068
$357$	0	0
$358$	2.52040e11	0.810952
$359$	7.66520e10	0.243556	0.121778	−	0.992557i	$-0.461140\pi$
$359$	7.66520e10	0.243556	0.121778	+	0.992557i	$0.461140\pi$
$360$	−8.73893e11	−2.74219
$361$	−3.18398e11	−0.986706
$362$	−3.40247e11	−1.04137
$363$	2.56495e11	0.775352
$364$	−3.49998e10	−0.104498
$365$	−8.36363e10	−0.246648
$366$	4.03625e11	1.17574
$367$	−3.30418e11	−0.950749	−0.475374	−	0.879784i	$-0.657687\pi$
$367$	−3.30418e11	−0.950749	−0.475374	+	0.879784i	$0.657687\pi$
$368$	4.09653e11	1.16440
$369$	1.30909e12	3.67579
$370$	−1.06488e12	−2.95389
$371$	5.17094e11	1.41705
$372$	2.79483e11	0.756680
$373$	−2.54050e11	−0.679561	−0.339781	−	0.940505i	$-0.610353\pi$
$373$	−2.54050e11	−0.679561	−0.339781	+	0.940505i	$0.610353\pi$
$374$	0	0
$375$	−1.40927e12	−3.68004
$376$	−2.00402e11	−0.517079
$377$	7.01527e10	0.178858
$378$	−1.14089e12	−2.87428
$379$	−9.88045e9	−0.0245980	−0.0122990	−	0.999924i	$-0.503915\pi$
$379$	−9.88045e9	−0.0245980	−0.0122990	+	0.999924i	$0.503915\pi$
$380$	3.25290e10	0.0800284
$381$	1.49094e11	0.362492
$382$	9.98819e10	0.239995
$383$	−7.86927e11	−1.86870	−0.934351	−	0.356354i	$-0.884020\pi$
$383$	−7.86927e11	−1.86870	−0.934351	+	0.356354i	$0.884020\pi$
$384$	−8.84315e11	−2.07547
$385$	−6.92347e11	−1.60602
$386$	−8.82118e10	−0.202248
$387$	−1.15731e11	−0.262272
$388$	4.70878e10	0.105479
$389$	1.26382e11	0.279842	0.139921	−	0.990163i	$-0.455315\pi$
$389$	1.26382e11	0.279842	0.139921	+	0.990163i	$0.455315\pi$
$390$	3.78357e11	0.828154
$391$	0	0
$392$	−1.50519e11	−0.321962
$393$	6.47893e11	1.37005
$394$	6.44891e11	1.34820
$395$	−9.11279e11	−1.88349
$396$	−3.06816e11	−0.626973
$397$	5.44547e11	1.10022	0.550108	−	0.835094i	$-0.314587\pi$
$397$	5.44547e11	1.10022	0.550108	+	0.835094i	$0.314587\pi$
$398$	−7.19168e11	−1.43667
$399$	−1.24511e11	−0.245939
$400$	−1.37317e12	−2.68198
$401$	−4.39004e10	−0.0847849	−0.0423925	−	0.999101i	$-0.513498\pi$
$401$	−4.39004e10	−0.0847849	−0.0423925	+	0.999101i	$0.513498\pi$
$402$	1.90119e12	3.63084
$403$	1.29011e11	0.243643
$404$	3.15689e11	0.589582
$405$	1.39617e12	2.57865
$406$	−6.23872e11	−1.13954
$407$	5.84625e11	1.05609
$408$	0	0
$409$	4.80426e11	0.848929	0.424465	−	0.905444i	$-0.360462\pi$
$409$	4.80426e11	0.848929	0.424465	+	0.905444i	$0.360462\pi$
$410$	2.05914e12	3.59880
$411$	1.30227e12	2.25120
$412$	−1.35650e11	−0.231943
$413$	5.43076e11	0.918513
$414$	−1.42046e12	−2.37645
$415$	−1.61281e11	−0.266912
$416$	1.00697e11	0.164852
$417$	9.62532e11	1.55884
$418$	−6.36428e10	−0.101966
$419$	−1.06468e12	−1.68755	−0.843773	−	0.536700i	$-0.819671\pi$
$419$	−1.06468e12	−1.68755	−0.843773	+	0.536700i	$0.819671\pi$
$420$	−9.44171e11	−1.48057
$421$	2.57586e11	0.399625	0.199813	−	0.979834i	$-0.435967\pi$
$421$	2.57586e11	0.399625	0.199813	+	0.979834i	$0.435967\pi$
$422$	−2.93303e11	−0.450206
$423$	1.01458e12	1.54083
$424$	−5.63632e11	−0.846934
$425$	0	0
$426$	−1.60055e11	−0.235465
$427$	−4.64941e11	−0.676819
$428$	3.06774e10	0.0441898
$429$	−2.07720e11	−0.296087
$430$	−1.82040e11	−0.256779
$431$	−1.22706e12	−1.71284	−0.856419	−	0.516281i	$-0.827316\pi$
$431$	−1.22706e12	−1.71284	−0.856419	+	0.516281i	$0.827316\pi$
$432$	1.81568e12	2.50820
$433$	−2.43685e11	−0.333145	−0.166572	−	0.986029i	$-0.553270\pi$
$433$	−2.43685e11	−0.333145	−0.166572	+	0.986029i	$0.553270\pi$
$434$	−1.14730e12	−1.55230
$435$	1.89247e12	2.53412
$436$	−5.49171e11	−0.727811
$437$	−8.26798e10	−0.108451
$438$	2.23152e11	0.289712
$439$	1.14718e12	1.47415	0.737074	−	0.675812i	$-0.236207\pi$
$439$	1.14718e12	1.47415	0.737074	+	0.675812i	$0.236207\pi$
$440$	7.54658e11	0.959872
$441$	7.62036e11	0.959405
$442$	0	0
$443$	−5.82318e11	−0.718363	−0.359181	−	0.933268i	$-0.616944\pi$
$443$	−5.82318e11	−0.718363	−0.359181	+	0.933268i	$0.616944\pi$
$444$	7.97269e11	0.973602
$445$	−1.00032e12	−1.20926
$446$	1.18948e12	1.42347
$447$	−1.03918e12	−1.23113
$448$	3.74437e11	0.439164
$449$	−7.46199e11	−0.866455	−0.433227	−	0.901285i	$-0.642625\pi$
$449$	−7.46199e11	−0.866455	−0.433227	+	0.901285i	$0.642625\pi$
$450$	4.76145e12	5.47372
$451$	−1.13048e12	−1.28667
$452$	−2.51578e11	−0.283498
$453$	1.89687e12	2.11639
$454$	−3.98125e11	−0.439813
$455$	−4.35835e11	−0.476728
$456$	1.35717e11	0.146991
$457$	−5.50976e11	−0.590895	−0.295447	−	0.955359i	$-0.595469\pi$
$457$	−5.50976e11	−0.590895	−0.295447	+	0.955359i	$0.595469\pi$
$458$	1.43136e12	1.52004
$459$	0	0
$460$	−6.26966e11	−0.652881
$461$	−1.08634e12	−1.12024	−0.560120	−	0.828411i	$-0.689245\pi$
$461$	−1.08634e12	−1.12024	−0.560120	+	0.828411i	$0.689245\pi$
$462$	1.84727e12	1.88643
$463$	−6.27197e10	−0.0634293	−0.0317146	−	0.999497i	$-0.510097\pi$
$463$	−6.27197e10	−0.0634293	−0.0317146	+	0.999497i	$0.510097\pi$
$464$	9.92868e11	0.994399
$465$	3.48026e12	3.45202
$466$	−7.56670e11	−0.743310
$467$	3.31434e11	0.322457	0.161228	−	0.986917i	$-0.448454\pi$
$467$	3.31434e11	0.322457	0.161228	+	0.986917i	$0.448454\pi$
$468$	−1.93142e11	−0.186110
$469$	−2.19001e12	−2.09010
$470$	1.59589e12	1.50856
$471$	−6.84267e11	−0.640666
$472$	−5.91953e11	−0.548969
$473$	9.99409e10	0.0918054
$474$	2.43140e12	2.21235
$475$	2.77146e11	0.249797
$476$	0	0
$477$	2.85351e12	2.52375
$478$	−2.06441e12	−1.80872
$479$	−4.15195e11	−0.360365	−0.180182	−	0.983633i	$-0.557669\pi$
$479$	−4.15195e11	−0.360365	−0.180182	+	0.983633i	$0.557669\pi$
$480$	2.71644e12	2.33568
$481$	3.68024e11	0.313490
$482$	1.58502e12	1.33759
$483$	2.39983e12	2.00640
$484$	−2.05953e11	−0.170594
$485$	5.86360e11	0.481201
$486$	−7.87162e11	−0.640031
$487$	9.70548e10	0.0781874	0.0390937	−	0.999236i	$-0.487553\pi$
$487$	9.70548e10	0.0781874	0.0390937	+	0.999236i	$0.487553\pi$
$488$	5.06786e11	0.404516
$489$	5.04976e11	0.399375
$490$	1.19865e12	0.939311
$491$	1.65593e12	1.28581	0.642904	−	0.765946i	$-0.277729\pi$
$491$	1.65593e12	1.28581	0.642904	+	0.765946i	$0.277729\pi$
$492$	−1.54166e12	−1.18617
$493$	0	0
$494$	−4.00634e10	−0.0302675
$495$	−3.82062e12	−2.86029
$496$	1.82589e12	1.35459
$497$	1.84370e11	0.135546
$498$	4.30318e11	0.313515
$499$	7.78441e11	0.562048	0.281024	−	0.959701i	$-0.409326\pi$
$499$	7.78441e11	0.562048	0.281024	+	0.959701i	$0.409326\pi$
$500$	1.13158e12	0.809690
$501$	1.19903e12	0.850280
$502$	2.82828e12	1.98772
$503$	1.31683e12	0.917219	0.458610	−	0.888638i	$-0.348348\pi$
$503$	1.31683e12	0.917219	0.458610	+	0.888638i	$0.348348\pi$
$504$	−2.68586e12	−1.85416
$505$	3.93112e12	2.68971
$506$	1.22666e12	0.831850
$507$	2.50679e12	1.68493
$508$	−1.19716e11	−0.0797562
$509$	1.31058e12	0.865436	0.432718	−	0.901529i	$-0.357555\pi$
$509$	1.31058e12	0.865436	0.432718	+	0.901529i	$0.357555\pi$
$510$	0	0
$511$	−2.57052e11	−0.166773
$512$	4.09225e10	0.0263177
$513$	−3.66456e11	−0.233611
$514$	−3.48735e12	−2.20375
$515$	−1.68917e12	−1.05814
$516$	1.36292e11	0.0846344
$517$	−8.76148e11	−0.539349
$518$	−3.27286e12	−1.99730
$519$	−3.42058e12	−2.06941
$520$	4.75060e11	0.284927
$521$	−1.25440e12	−0.745878	−0.372939	−	0.927856i	$-0.621650\pi$
$521$	−1.25440e12	−0.745878	−0.372939	+	0.927856i	$0.621650\pi$
$522$	−3.44275e12	−2.02950
$523$	8.10021e11	0.473411	0.236706	−	0.971581i	$-0.423932\pi$
$523$	8.10021e11	0.473411	0.236706	+	0.971581i	$0.423932\pi$
$524$	−5.20227e11	−0.301441
$525$	−8.04430e12	−4.62138
$526$	−2.36202e12	−1.34539
$527$	0	0
$528$	−2.93985e12	−1.64616
$529$	−2.07575e11	−0.115246
$530$	4.48844e12	2.47089
$531$	2.99689e12	1.63585
$532$	9.99761e10	0.0541120
$533$	−7.11639e11	−0.381933
$534$	2.66897e12	1.42039
$535$	3.82010e11	0.201597
$536$	2.38711e12	1.24920
$537$	−2.34978e12	−1.21939
$538$	−3.23346e12	−1.66397
$539$	−6.58063e11	−0.335829
$540$	−2.77886e12	−1.40635
$541$	−3.73267e12	−1.87341	−0.936703	−	0.350126i	$-0.886139\pi$
$541$	−3.73267e12	−1.87341	−0.936703	+	0.350126i	$0.886139\pi$
$542$	1.87285e12	0.932192
$543$	3.17215e12	1.56586
$544$	0	0
$545$	−6.83855e12	−3.32032
$546$	1.16286e12	0.559965
$547$	8.25146e11	0.394083	0.197042	−	0.980395i	$-0.436867\pi$
$547$	8.25146e11	0.394083	0.197042	+	0.980395i	$0.436867\pi$
$548$	−1.04567e12	−0.495313
$549$	−2.56571e12	−1.20540
$550$	−4.11179e12	−1.91601
$551$	−2.00389e11	−0.0926173
$552$	−2.61581e12	−1.19917
$553$	−2.80077e12	−1.27354
$554$	1.53031e12	0.690218
$555$	9.92798e12	4.44163
$556$	−7.72868e11	−0.342980
$557$	−2.50302e12	−1.10183	−0.550917	−	0.834560i	$-0.685722\pi$
$557$	−2.50302e12	−1.10183	−0.550917	+	0.834560i	$0.685722\pi$
$558$	−6.33123e12	−2.76461
$559$	6.29132e10	0.0272514
$560$	−6.16836e12	−2.65047
$561$	0	0
$562$	−1.35457e11	−0.0572780
$563$	1.82021e12	0.763544	0.381772	−	0.924256i	$-0.375314\pi$
$563$	1.82021e12	0.763544	0.381772	+	0.924256i	$0.375314\pi$
$564$	−1.19483e12	−0.497220
$565$	−3.13277e12	−1.29333
$566$	−4.20264e12	−1.72127
$567$	4.29107e12	1.74358
$568$	−2.00963e11	−0.0810119
$569$	2.42769e11	0.0970930	0.0485465	−	0.998821i	$-0.484541\pi$
$569$	2.42769e11	0.0970930	0.0485465	+	0.998821i	$0.484541\pi$
$570$	−1.08077e12	−0.428840
$571$	1.47469e12	0.580549	0.290275	−	0.956943i	$-0.406253\pi$
$571$	1.47469e12	0.580549	0.290275	+	0.956943i	$0.406253\pi$
$572$	1.66789e11	0.0651457
$573$	−9.31206e11	−0.360869
$574$	6.32865e12	2.43337
$575$	−5.34172e12	−2.03787
$576$	2.06627e12	0.782144
$577$	−1.65922e12	−0.623177	−0.311589	−	0.950217i	$-0.600861\pi$
$577$	−1.65922e12	−0.623177	−0.311589	+	0.950217i	$0.600861\pi$
$578$	0	0
$579$	8.22405e11	0.304111
$580$	−1.51956e12	−0.557562
$581$	−4.95690e11	−0.180475
$582$	−1.56448e12	−0.565219
$583$	−2.46417e12	−0.883410
$584$	2.80186e11	0.0996757
$585$	−2.40509e12	−0.849045
$586$	3.75367e12	1.31497
$587$	4.07096e12	1.41522	0.707612	−	0.706601i	$-0.249772\pi$
$587$	4.07096e12	1.41522	0.707612	+	0.706601i	$0.249772\pi$
$588$	−8.97418e11	−0.309597
$589$	−3.68517e11	−0.126165
$590$	4.71397e12	1.60159
$591$	−6.01236e12	−2.02722
$592$	5.20863e12	1.74291
$593$	−1.14534e12	−0.380353	−0.190176	−	0.981750i	$-0.560906\pi$
$593$	−1.14534e12	−0.380353	−0.190176	+	0.981750i	$0.560906\pi$
$594$	5.43681e12	1.79187
$595$	0	0
$596$	8.34409e11	0.270876
$597$	6.70485e12	2.16025
$598$	7.72184e11	0.246925
$599$	−6.69763e11	−0.212569	−0.106285	−	0.994336i	$-0.533895\pi$
$599$	−6.69763e11	−0.212569	−0.106285	+	0.994336i	$0.533895\pi$
$600$	8.76829e12	2.76207
$601$	−4.67723e12	−1.46236	−0.731179	−	0.682186i	$-0.761030\pi$
$601$	−4.67723e12	−1.46236	−0.731179	+	0.682186i	$0.761030\pi$
$602$	−5.59491e11	−0.173624
$603$	−1.20852e13	−3.72243
$604$	−1.52310e12	−0.465652
$605$	−2.56463e12	−0.778262
$606$	−1.04887e13	−3.15933
$607$	−5.69539e11	−0.170284	−0.0851422	−	0.996369i	$-0.527134\pi$
$607$	−5.69539e11	−0.170284	−0.0851422	+	0.996369i	$0.527134\pi$
$608$	−2.87637e11	−0.0853648
$609$	5.81641e12	1.71347
$610$	−4.03575e12	−1.18016
$611$	−5.51539e11	−0.160100
$612$	0	0
$613$	8.07974e11	0.231114	0.115557	−	0.993301i	$-0.463135\pi$
$613$	8.07974e11	0.231114	0.115557	+	0.993301i	$0.463135\pi$
$614$	9.67911e11	0.274839
$615$	−1.91975e13	−5.41136
$616$	2.31940e12	0.649027
$617$	2.81815e12	0.782855	0.391428	−	0.920209i	$-0.371981\pi$
$617$	2.81815e12	0.782855	0.391428	+	0.920209i	$0.371981\pi$
$618$	4.50692e12	1.24289
$619$	7.58669e11	0.207704	0.103852	−	0.994593i	$-0.466883\pi$
$619$	7.58669e11	0.207704	0.103852	+	0.994593i	$0.466883\pi$
$620$	−2.79449e12	−0.759520
$621$	7.06309e12	1.90582
$622$	5.27029e12	1.41182
$623$	−3.07443e12	−0.817652
$624$	−1.85065e12	−0.488644
$625$	5.82628e12	1.52733
$626$	−8.03344e11	−0.209082
$627$	5.93346e11	0.153322
$628$	5.49434e11	0.140960
$629$	0	0
$630$	2.13887e13	5.40942
$631$	1.03233e12	0.259231	0.129615	−	0.991564i	$-0.458626\pi$
$631$	1.03233e12	0.259231	0.129615	+	0.991564i	$0.458626\pi$
$632$	3.05284e12	0.761161
$633$	2.73449e12	0.676954
$634$	4.08552e12	1.00426
$635$	−1.49076e12	−0.363852
$636$	−3.36045e12	−0.814406
$637$	−4.14253e11	−0.0996870
$638$	2.97302e12	0.710403
$639$	1.01742e12	0.241405
$640$	8.84205e12	2.08326
$641$	5.28188e12	1.23574	0.617871	−	0.786280i	$-0.287995\pi$
$641$	5.28188e12	1.23574	0.617871	+	0.786280i	$0.287995\pi$
$642$	−1.01925e12	−0.236795
$643$	−9.88170e11	−0.227972	−0.113986	−	0.993482i	$-0.536362\pi$
$643$	−9.88170e11	−0.227972	−0.113986	+	0.993482i	$0.536362\pi$
$644$	−1.92695e12	−0.441452
$645$	1.69717e12	0.386107
$646$	0	0
$647$	−3.03022e12	−0.679837	−0.339918	−	0.940455i	$-0.610399\pi$
$647$	−3.03022e12	−0.679837	−0.339918	+	0.940455i	$0.610399\pi$
$648$	−4.67726e12	−1.04209
$649$	−2.58799e12	−0.572613
$650$	−2.58839e12	−0.568747
$651$	1.06964e13	2.33412
$652$	−4.05472e11	−0.0878713
$653$	6.25827e12	1.34693	0.673465	−	0.739219i	$-0.264805\pi$
$653$	6.25827e12	1.34693	0.673465	+	0.739219i	$0.264805\pi$
$654$	1.82461e13	3.90004
$655$	−6.47812e12	−1.37519
$656$	−1.00718e13	−2.12344
$657$	−1.41850e12	−0.297020
$658$	4.90487e12	1.02003
$659$	5.50577e12	1.13719	0.568596	−	0.822617i	$-0.307487\pi$
$659$	5.50577e12	1.13719	0.568596	+	0.822617i	$0.307487\pi$
$660$	4.49938e12	0.923007
$661$	8.86306e12	1.80583	0.902915	−	0.429819i	$-0.141423\pi$
$661$	8.86306e12	1.80583	0.902915	+	0.429819i	$0.141423\pi$
$662$	−5.27610e12	−1.06771
$663$	0	0
$664$	5.40302e11	0.107865
$665$	1.24495e12	0.246862
$666$	−1.80608e13	−3.55716
$667$	3.86232e12	0.755582
$668$	−9.62768e11	−0.187080
$669$	−1.10896e13	−2.14041
$670$	−1.90095e13	−3.64447
$671$	2.21564e12	0.421938
$672$	8.34883e12	1.57930
$673$	−6.54876e12	−1.23053	−0.615263	−	0.788322i	$-0.710950\pi$
$673$	−6.54876e12	−1.23053	−0.615263	+	0.788322i	$0.710950\pi$
$674$	−7.41072e12	−1.38322
$675$	−2.36757e13	−4.38972
$676$	−2.01283e12	−0.370722
$677$	6.06506e12	1.10965	0.554825	−	0.831967i	$-0.312785\pi$
$677$	6.06506e12	1.10965	0.554825	+	0.831967i	$0.312785\pi$
$678$	8.35861e12	1.51915
$679$	1.80215e12	0.325369
$680$	0	0
$681$	3.71174e12	0.661327
$682$	5.46740e12	0.967722
$683$	4.07884e12	0.717206	0.358603	−	0.933490i	$-0.383253\pi$
$683$	4.07884e12	0.717206	0.358603	+	0.933490i	$0.383253\pi$
$684$	5.51704e11	0.0963726
$685$	−1.30211e13	−2.25965
$686$	−4.54444e12	−0.783469
$687$	−1.33447e13	−2.28561
$688$	8.90408e11	0.151510
$689$	−1.55121e12	−0.262230
$690$	2.08308e13	3.49852
$691$	4.46929e12	0.745741	0.372870	−	0.927883i	$-0.378374\pi$
$691$	4.46929e12	0.745741	0.372870	+	0.927883i	$0.378374\pi$
$692$	2.74657e12	0.455316
$693$	−1.17425e13	−1.93401
$694$	−1.26614e13	−2.07188
$695$	−9.62412e12	−1.56469
$696$	−6.33988e12	−1.02409
$697$	0	0
$698$	−3.70543e12	−0.590866
$699$	7.05449e12	1.11768
$700$	6.45919e12	1.01680
$701$	6.58540e12	1.03003	0.515016	−	0.857180i	$-0.327786\pi$
$701$	6.58540e12	1.03003	0.515016	+	0.857180i	$0.327786\pi$
$702$	3.42249e12	0.531895
$703$	−1.05125e12	−0.162333
$704$	−1.78435e12	−0.273781
$705$	−1.48785e13	−2.26835
$706$	1.11018e13	1.68179
$707$	1.20821e13	1.81867
$708$	−3.52930e12	−0.527885
$709$	2.55085e12	0.379120	0.189560	−	0.981869i	$-0.439294\pi$
$709$	2.55085e12	0.379120	0.189560	+	0.981869i	$0.439294\pi$
$710$	1.60035e12	0.236349
$711$	−1.54556e13	−2.26816
$712$	3.35113e12	0.488687
$713$	7.10282e12	1.02927
$714$	0	0
$715$	2.07694e12	0.297199
$716$	1.88677e12	0.268293
$717$	1.92466e13	2.71968
$718$	2.04491e12	0.287154
$719$	9.48887e12	1.32414	0.662071	−	0.749441i	$-0.269678\pi$
$719$	9.48887e12	1.32414	0.662071	+	0.749441i	$0.269678\pi$
$720$	−3.40392e13	−4.72045
$721$	−5.19159e12	−0.715470
$722$	−8.49419e12	−1.16333
$723$	−1.47772e13	−2.01127
$724$	−2.54708e12	−0.344524
$725$	−1.29466e13	−1.74035
$726$	6.84275e12	0.914146
$727$	1.44804e13	1.92254	0.961269	−	0.275612i	$-0.0888805\pi$
$727$	1.44804e13	1.92254	0.961269	+	0.275612i	$0.0888805\pi$
$728$	1.46007e12	0.192656
$729$	−3.71153e12	−0.486719
$730$	−2.23124e12	−0.290799
$731$	0	0
$732$	3.02153e12	0.388980
$733$	9.75007e12	1.24750	0.623749	−	0.781625i	$-0.285609\pi$
$733$	9.75007e12	1.24750	0.623749	+	0.781625i	$0.285609\pi$
$734$	−8.81485e12	−1.12094
$735$	−1.11751e13	−1.41240
$736$	5.54394e12	0.696416
$737$	1.04363e13	1.30300
$738$	3.49238e13	4.33379
$739$	−1.57482e13	−1.94237	−0.971184	−	0.238329i	$-0.923400\pi$
$739$	−1.57482e13	−1.94237	−0.971184	+	0.238329i	$0.923400\pi$
$740$	−7.97170e12	−0.977256
$741$	3.73514e11	0.0455118
$742$	1.37950e13	1.67072
$743$	6.24284e12	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$743$	6.24284e12	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$744$	−1.16591e13	−1.39504
$745$	1.03905e13	1.23575
$746$	−6.77751e12	−0.801208
$747$	−2.73539e12	−0.321423
$748$	0	0
$749$	1.17409e12	0.136312
$750$	−3.75963e13	−4.33880
$751$	1.32705e13	1.52233	0.761165	−	0.648558i	$-0.224628\pi$
$751$	1.32705e13	1.52233	0.761165	+	0.648558i	$0.224628\pi$
$752$	−7.80590e12	−0.890108
$753$	−2.63682e13	−2.98885
$754$	1.87153e12	0.210875
$755$	−1.89664e13	−2.12434
$756$	−8.54067e12	−0.950919
$757$	5.96072e12	0.659731	0.329866	−	0.944028i	$-0.392997\pi$
$757$	5.96072e12	0.659731	0.329866	+	0.944028i	$0.392997\pi$
$758$	−2.63590e11	−0.0290013
$759$	−1.14362e13	−1.25082
$760$	−1.35700e12	−0.147543
$761$	1.28434e13	1.38819	0.694094	−	0.719884i	$-0.255805\pi$
$761$	1.28434e13	1.38819	0.694094	+	0.719884i	$0.255805\pi$
$762$	3.97752e12	0.427381
$763$	−2.10179e13	−2.24507
$764$	7.47714e11	0.0793991
$765$	0	0
$766$	−2.09936e13	−2.20321
$767$	−1.62915e12	−0.169974
$768$	−1.73532e13	−1.79992
$769$	1.27241e13	1.31208	0.656039	−	0.754727i	$-0.272230\pi$
$769$	1.27241e13	1.31208	0.656039	+	0.754727i	$0.272230\pi$
$770$	−1.84704e13	−1.89351
$771$	3.25128e13	3.31367
$772$	−6.60352e11	−0.0669111
$773$	8.70178e12	0.876598	0.438299	−	0.898829i	$-0.355581\pi$
$773$	8.70178e12	0.876598	0.438299	+	0.898829i	$0.355581\pi$
$774$	−3.08747e12	−0.309221
$775$	−2.38089e13	−2.37073
$776$	−1.96434e12	−0.194464
$777$	3.05131e13	3.00325
$778$	3.37162e12	0.329936
$779$	2.03278e12	0.197775
$780$	2.83238e12	0.273984
$781$	−8.78600e11	−0.0845010
$782$	0	0
$783$	1.71187e13	1.62758
$784$	−5.86291e12	−0.554231
$785$	6.84182e12	0.643070
$786$	1.72844e13	1.61530
$787$	−8.49469e12	−0.789335	−0.394667	−	0.918824i	$-0.629140\pi$
$787$	−8.49469e12	−0.789335	−0.394667	+	0.918824i	$0.629140\pi$
$788$	4.82764e12	0.446033
$789$	2.20213e13	2.02300
$790$	−2.43110e13	−2.22065
$791$	−9.62841e12	−0.874501
$792$	1.27993e13	1.15591
$793$	1.39476e12	0.125247
$794$	1.45274e13	1.29716
$795$	−4.18460e13	−3.71537
$796$	−5.38368e12	−0.475303
$797$	3.81262e12	0.334704	0.167352	−	0.985897i	$-0.446478\pi$
$797$	3.81262e12	0.334704	0.167352	+	0.985897i	$0.446478\pi$
$798$	−3.32168e12	−0.289965
$799$	0	0
$800$	−1.85835e13	−1.60407
$801$	−1.69658e13	−1.45622
$802$	−1.17117e12	−0.0999621
$803$	1.22496e12	0.103969
$804$	1.42323e13	1.20122
$805$	−2.39953e13	−2.01393
$806$	3.44175e12	0.287257
$807$	3.01457e13	2.50204
$808$	−1.31695e13	−1.08697
$809$	1.14733e13	0.941718	0.470859	−	0.882208i	$-0.343944\pi$
$809$	1.14733e13	0.941718	0.470859	+	0.882208i	$0.343944\pi$
$810$	3.72470e13	3.04024
$811$	−1.17175e13	−0.951132	−0.475566	−	0.879680i	$-0.657757\pi$
$811$	−1.17175e13	−0.951132	−0.475566	+	0.879680i	$0.657757\pi$
$812$	−4.67030e12	−0.377001
$813$	−1.74607e13	−1.40169
$814$	1.55966e13	1.24514
$815$	−5.04914e12	−0.400874
$816$	0	0
$817$	−1.79710e11	−0.0141115
$818$	1.28168e13	1.00089
$819$	−7.39193e12	−0.574090
$820$	1.54147e13	1.19062
$821$	4.10840e12	0.315594	0.157797	−	0.987472i	$-0.449561\pi$
$821$	4.10840e12	0.315594	0.157797	+	0.987472i	$0.449561\pi$
$822$	3.47419e13	2.65418
$823$	2.29450e13	1.74337	0.871683	−	0.490070i	$-0.163029\pi$
$823$	2.29450e13	1.74337	0.871683	+	0.490070i	$0.163029\pi$
$824$	5.65883e12	0.427616
$825$	3.83345e13	2.88103
$826$	1.44881e13	1.08293
$827$	−1.38558e13	−1.03005	−0.515025	−	0.857175i	$-0.672217\pi$
$827$	−1.38558e13	−1.03005	−0.515025	+	0.857175i	$0.672217\pi$
$828$	−1.06336e13	−0.786218
$829$	2.37981e12	0.175003	0.0875017	−	0.996164i	$-0.472112\pi$
$829$	2.37981e12	0.175003	0.0875017	+	0.996164i	$0.472112\pi$
$830$	−4.30265e12	−0.314691
$831$	−1.42672e13	−1.03785
$832$	−1.12326e12	−0.0812687
$833$	0	0
$834$	2.56783e13	1.83789
$835$	−1.19889e13	−0.853471
$836$	−4.76429e11	−0.0337342
$837$	3.14813e13	2.21712
$838$	−2.84034e13	−1.98963
$839$	−8.17795e12	−0.569791	−0.284895	−	0.958559i	$-0.591959\pi$
$839$	−8.17795e12	−0.569791	−0.284895	+	0.958559i	$0.591959\pi$
$840$	3.93876e13	2.72962
$841$	−5.14613e12	−0.354731
$842$	6.87185e12	0.471161
$843$	1.26287e12	0.0861264
$844$	−2.19567e12	−0.148945
$845$	−2.50648e13	−1.69125
$846$	2.70668e13	1.81665
$847$	−7.88226e12	−0.526230
$848$	−2.19542e13	−1.45793
$849$	3.91815e13	2.58819
$850$	0	0
$851$	2.02619e13	1.32433
$852$	−1.19817e12	−0.0779005
$853$	2.66126e13	1.72114	0.860570	−	0.509332i	$-0.170107\pi$
$853$	2.66126e13	1.72114	0.860570	+	0.509332i	$0.170107\pi$
$854$	−1.24037e13	−0.797975
$855$	6.87009e12	0.439658
$856$	−1.27976e12	−0.0814696
$857$	−2.11808e13	−1.34131	−0.670654	−	0.741770i	$-0.733986\pi$
$857$	−2.11808e13	−1.34131	−0.670654	+	0.741770i	$0.733986\pi$
$858$	−5.54153e12	−0.349089
$859$	−1.07671e13	−0.674731	−0.337366	−	0.941374i	$-0.609536\pi$
$859$	−1.07671e13	−0.674731	−0.337366	+	0.941374i	$0.609536\pi$
$860$	−1.36275e12	−0.0849520
$861$	−5.90025e13	−3.65895
$862$	−3.27353e13	−2.01945
$863$	−1.87450e13	−1.15037	−0.575185	−	0.818024i	$-0.695070\pi$
$863$	−1.87450e13	−1.15037	−0.575185	+	0.818024i	$0.695070\pi$
$864$	2.45720e13	1.50013
$865$	3.42016e13	2.07718
$866$	−6.50100e12	−0.392780
$867$	0	0
$868$	−8.58871e12	−0.513557
$869$	1.33468e13	0.793944
$870$	5.04871e13	2.98775
$871$	6.56970e12	0.386780
$872$	2.29095e13	1.34181
$873$	9.94489e12	0.579477
$874$	−2.20572e12	−0.127864
$875$	4.33078e13	2.49764
$876$	1.67051e12	0.0958475
$877$	−1.87509e13	−1.07035	−0.535173	−	0.844742i	$-0.679754\pi$
$877$	−1.87509e13	−1.07035	−0.535173	+	0.844742i	$0.679754\pi$
$878$	3.06043e13	1.73803
$879$	−3.49958e13	−1.97727
$880$	2.93949e13	1.65234
$881$	3.17297e13	1.77450	0.887248	−	0.461293i	$-0.152614\pi$
$881$	3.17297e13	1.77450	0.887248	+	0.461293i	$0.152614\pi$
$882$	2.03295e13	1.13115
$883$	−2.91895e13	−1.61586	−0.807930	−	0.589278i	$-0.799412\pi$
$883$	−2.91895e13	−1.61586	−0.807930	+	0.589278i	$0.799412\pi$
$884$	0	0
$885$	−4.39486e13	−2.40824
$886$	−1.55350e13	−0.846955
$887$	−1.37213e13	−0.744283	−0.372142	−	0.928176i	$-0.621376\pi$
$887$	−1.37213e13	−0.744283	−0.372142	+	0.928176i	$0.621376\pi$
$888$	−3.32593e13	−1.79496
$889$	−4.58177e12	−0.246023
$890$	−2.66864e13	−1.42572
$891$	−2.04488e13	−1.08697
$892$	8.90440e12	0.470937
$893$	1.57546e12	0.0829038
$894$	−2.77230e13	−1.45152
$895$	2.34949e13	1.22397
$896$	2.71756e13	1.40862
$897$	−7.19913e12	−0.371291
$898$	−1.99070e13	−1.02156
$899$	1.72150e13	0.878997
$900$	3.56441e13	1.81091
$901$	0	0
$902$	−3.01587e13	−1.51699
$903$	5.21618e12	0.261070
$904$	1.04950e13	0.522664
$905$	−3.17175e13	−1.57174
$906$	5.06046e13	2.49524
$907$	3.08384e12	0.151307	0.0756535	−	0.997134i	$-0.475896\pi$
$907$	3.08384e12	0.151307	0.0756535	+	0.997134i	$0.475896\pi$
$908$	−2.98036e12	−0.145506
$909$	6.66732e13	3.23902
$910$	−1.16272e13	−0.562066
$911$	3.98667e13	1.91769	0.958844	−	0.283935i	$-0.0916400\pi$
$911$	3.98667e13	1.91769	0.958844	+	0.283935i	$0.0916400\pi$
$912$	5.28632e12	0.253033
$913$	2.36217e12	0.112511
$914$	−1.46989e13	−0.696669
$915$	3.76256e13	1.77455
$916$	1.07151e13	0.502885
$917$	−1.99102e13	−0.929850
$918$	0	0
$919$	−6.40742e12	−0.296322	−0.148161	−	0.988963i	$-0.547335\pi$
$919$	−6.40742e12	−0.296322	−0.148161	+	0.988963i	$0.547335\pi$
$920$	2.61549e13	1.20367
$921$	−9.02390e12	−0.413263
$922$	−2.89812e13	−1.32077
$923$	−5.53082e11	−0.0250832
$924$	1.38286e13	0.624100
$925$	−6.79185e13	−3.05036
$926$	−1.67323e12	−0.0747836
$927$	−2.86490e13	−1.27424
$928$	1.34367e13	0.594741
$929$	1.00272e13	0.441683	0.220842	−	0.975310i	$-0.429120\pi$
$929$	1.00272e13	0.441683	0.220842	+	0.975310i	$0.429120\pi$
$930$	9.28461e13	4.06996
$931$	1.18330e12	0.0516206
$932$	−5.66442e12	−0.245914
$933$	−4.91353e13	−2.12288
$934$	8.84197e12	0.380179
$935$	0	0
$936$	8.05720e12	0.343117
$937$	−1.07556e13	−0.455832	−0.227916	−	0.973681i	$-0.573191\pi$
$937$	−1.07556e13	−0.455832	−0.227916	+	0.973681i	$0.573191\pi$
$938$	−5.84248e13	−2.46425
$939$	7.48963e12	0.314388
$940$	1.19468e13	0.499086
$941$	2.19364e13	0.912036	0.456018	−	0.889971i	$-0.349275\pi$
$941$	2.19364e13	0.912036	0.456018	+	0.889971i	$0.349275\pi$
$942$	−1.82548e13	−0.755350
$943$	−3.91799e13	−1.61347
$944$	−2.30573e13	−0.945005
$945$	−1.06353e14	−4.33815
$946$	2.66621e12	0.108239
$947$	1.94272e13	0.784938	0.392469	−	0.919765i	$-0.371621\pi$
$947$	1.94272e13	0.784938	0.392469	+	0.919765i	$0.371621\pi$
$948$	1.82014e13	0.731928
$949$	7.71118e11	0.0308619
$950$	7.39366e12	0.294512
$951$	−3.80896e13	−1.51006
$952$	0	0
$953$	1.46823e13	0.576603	0.288301	−	0.957540i	$-0.406910\pi$
$953$	1.46823e13	0.576603	0.288301	+	0.957540i	$0.406910\pi$
$954$	7.61256e13	2.97552
$955$	9.31090e12	0.362224
$956$	−1.54541e13	−0.598390
$957$	−2.77177e13	−1.06820
$958$	−1.10765e13	−0.424873
$959$	−4.00198e13	−1.52789
$960$	−3.03014e13	−1.15144
$961$	5.21877e12	0.197385
$962$	9.81811e12	0.369607
$963$	6.47904e12	0.242768
$964$	1.18654e13	0.442524
$965$	−8.22303e12	−0.305252
$966$	6.40223e13	2.36556
$967$	1.70290e13	0.626281	0.313141	−	0.949707i	$-0.398619\pi$
$967$	1.70290e13	0.626281	0.313141	+	0.949707i	$0.398619\pi$
$968$	8.59166e12	0.314513
$969$	0	0
$970$	1.56429e13	0.567340
$971$	−4.10571e13	−1.48218	−0.741091	−	0.671404i	$-0.765691\pi$
$971$	−4.10571e13	−1.48218	−0.741091	+	0.671404i	$0.765691\pi$
$972$	−5.89269e12	−0.211746
$973$	−2.95792e13	−1.05798
$974$	2.58922e12	0.0921836
$975$	2.41317e13	0.855200
$976$	1.97399e13	0.696340
$977$	−1.64980e13	−0.579303	−0.289652	−	0.957132i	$-0.593539\pi$
$977$	−1.64980e13	−0.579303	−0.289652	+	0.957132i	$0.593539\pi$
$978$	1.34717e13	0.470867
$979$	1.46510e13	0.509735
$980$	8.97307e12	0.310759
$981$	−1.15984e14	−3.99842
$982$	4.41769e13	1.51598
$983$	1.84714e12	0.0630969	0.0315485	−	0.999502i	$-0.489956\pi$
$983$	1.84714e12	0.0630969	0.0315485	+	0.999502i	$0.489956\pi$
$984$	6.43127e13	2.18685
$985$	6.01162e13	2.03483
$986$	0	0
$987$	−4.57284e13	−1.53377
$988$	−2.99914e11	−0.0100136
$989$	3.46374e12	0.115123
$990$	−1.01926e14	−3.37230
$991$	3.88397e13	1.27922	0.639609	−	0.768700i	$-0.279096\pi$
$991$	3.88397e13	1.27922	0.639609	+	0.768700i	$0.279096\pi$
$992$	2.47102e13	0.810166
$993$	4.91895e13	1.60546
$994$	4.91860e12	0.159810
$995$	−6.70403e13	−2.16836
$996$	3.22136e12	0.103722
$997$	2.44157e13	0.782601	0.391301	−	0.920263i	$-0.372025\pi$
$997$	2.44157e13	0.782601	0.391301	+	0.920263i	$0.372025\pi$
$998$	2.07672e13	0.662658
$999$	8.98053e13	2.85271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.d.1.10	✓	12
17.16	even	2		289.10.a.e.1.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.10	✓	12	1.1	even	1	trivial
289.10.a.e.1.10	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)

\(f(q)\)	\(=\)	\(q+26.6779 q^{2} -248.720 q^{3} +199.710 q^{4} +2486.89 q^{5} -6635.33 q^{6} +7643.33 q^{7} -8331.23 q^{8} +42178.6 q^{9} +O(q^{10})\)	\(q+26.6779 q^{2} -248.720 q^{3} +199.710 q^{4} +2486.89 q^{5} -6635.33 q^{6} +7643.33 q^{7} -8331.23 q^{8} +42178.6 q^{9} +66345.1 q^{10} -36423.7 q^{11} -49672.0 q^{12} -22928.9 q^{13} +203908. q^{14} -618540. q^{15} -324511. q^{16} +1.12524e6 q^{18} +65495.7 q^{19} +496658. q^{20} -1.90105e6 q^{21} -971709. q^{22} -1.26237e6 q^{23} +2.07214e6 q^{24} +4.23151e6 q^{25} -611694. q^{26} -5.59511e6 q^{27} +1.52645e6 q^{28} -3.05958e6 q^{29} -1.65013e7 q^{30} -5.62658e6 q^{31} -4.39170e6 q^{32} +9.05931e6 q^{33} +1.90081e7 q^{35} +8.42351e6 q^{36} -1.60507e7 q^{37} +1.74729e6 q^{38} +5.70287e6 q^{39} -2.07189e7 q^{40} +3.10368e7 q^{41} -5.07160e7 q^{42} -2.74384e6 q^{43} -7.27420e6 q^{44} +1.04894e8 q^{45} -3.36774e7 q^{46} +2.40543e7 q^{47} +8.07125e7 q^{48} +1.80669e7 q^{49} +1.12888e8 q^{50} -4.57914e6 q^{52} +6.76529e7 q^{53} -1.49266e8 q^{54} -9.05819e7 q^{55} -6.36783e7 q^{56} -1.62901e7 q^{57} -8.16231e7 q^{58} +7.10522e7 q^{59} -1.23529e8 q^{60} -6.08297e7 q^{61} -1.50105e8 q^{62} +3.22385e8 q^{63} +4.89887e7 q^{64} -5.70216e7 q^{65} +2.41683e8 q^{66} -2.86525e8 q^{67} +3.13977e8 q^{69} +5.07097e8 q^{70} +2.41217e7 q^{71} -3.51400e8 q^{72} -3.36309e7 q^{73} -4.28198e8 q^{74} -1.05246e9 q^{75} +1.30802e7 q^{76} -2.78399e8 q^{77} +1.52141e8 q^{78} -3.66433e8 q^{79} -8.07025e8 q^{80} +5.61413e8 q^{81} +8.27997e8 q^{82} -6.48526e7 q^{83} -3.79659e8 q^{84} -7.31999e7 q^{86} +7.60978e8 q^{87} +3.03454e8 q^{88} -4.02237e8 q^{89} +2.79834e9 q^{90} -1.75253e8 q^{91} -2.52108e8 q^{92} +1.39944e9 q^{93} +6.41719e8 q^{94} +1.62881e8 q^{95} +1.09230e9 q^{96} +2.35780e8 q^{97} +4.81987e8 q^{98} -1.53630e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 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

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