LMFDB - Embedded newform 98.10.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,10,Mod(1,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, 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("98.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.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:	$50.4735119441$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 1115x + 2100 $ x^3 - x^2 - 1115*x + 2100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.88624$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} +13.9747 q^{3} +256.000 q^{4} +1718.94 q^{5} +223.595 q^{6} +4096.00 q^{8} -19487.7 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} +13.9747 q^{3} +256.000 q^{4} +1718.94 q^{5} +223.595 q^{6} +4096.00 q^{8} -19487.7 q^{9} +27503.0 q^{10} -71323.4 q^{11} +3577.52 q^{12} -156547. q^{13} +24021.6 q^{15} +65536.0 q^{16} -511711. q^{17} -311803. q^{18} +194494. q^{19} +440048. q^{20} -1.14118e6 q^{22} -108156. q^{23} +57240.3 q^{24} +1.00162e6 q^{25} -2.50475e6 q^{26} -547398. q^{27} +4.21769e6 q^{29} +384346. q^{30} -3.16733e6 q^{31} +1.04858e6 q^{32} -996722. q^{33} -8.18738e6 q^{34} -4.98885e6 q^{36} +1.44137e7 q^{37} +3.11190e6 q^{38} -2.18769e6 q^{39} +7.04077e6 q^{40} -7.69007e6 q^{41} -3.64544e7 q^{43} -1.82588e7 q^{44} -3.34982e7 q^{45} -1.73050e6 q^{46} -1.82379e7 q^{47} +915845. q^{48} +1.60259e7 q^{50} -7.15100e6 q^{51} -4.00760e7 q^{52} +4.52073e7 q^{53} -8.75837e6 q^{54} -1.22601e8 q^{55} +2.71799e6 q^{57} +6.74831e7 q^{58} +9.78147e7 q^{59} +6.14953e6 q^{60} -1.14670e8 q^{61} -5.06773e7 q^{62} +1.67772e7 q^{64} -2.69094e8 q^{65} -1.59476e7 q^{66} +2.01616e8 q^{67} -1.30998e8 q^{68} -1.51145e6 q^{69} +2.08831e7 q^{71} -7.98217e7 q^{72} -8.84783e6 q^{73} +2.30620e8 q^{74} +1.39973e7 q^{75} +4.97905e7 q^{76} -3.50031e7 q^{78} +3.84488e7 q^{79} +1.12652e8 q^{80} +3.75927e8 q^{81} -1.23041e8 q^{82} -5.55300e8 q^{83} -8.79600e8 q^{85} -5.83270e8 q^{86} +5.89409e7 q^{87} -2.92141e8 q^{88} +1.64919e8 q^{89} -5.35970e8 q^{90} -2.76880e7 q^{92} -4.42624e7 q^{93} -2.91806e8 q^{94} +3.34323e8 q^{95} +1.46535e7 q^{96} -1.57025e8 q^{97} +1.38993e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 48 q^{2} - 233 q^{3} + 768 q^{4} - 733 q^{5} - 3728 q^{6} + 12288 q^{8} + 15058 q^{9}+O(q^{10}) $ 3 * q + 48 * q^2 - 233 * q^3 + 768 * q^4 - 733 * q^5 - 3728 * q^6 + 12288 * q^8 + 15058 * q^9	\( 3 q + 48 q^{2} - 233 q^{3} + 768 q^{4} - 733 q^{5} - 3728 q^{6} + 12288 q^{8} + 15058 q^{9} - 11728 q^{10} - 7339 q^{11} - 59648 q^{12} - 98518 q^{13} + 369119 q^{15} + 196608 q^{16} - 306665 q^{17} + 240928 q^{18} - 377991 q^{19} - 187648 q^{20} - 117424 q^{22} + 2267255 q^{23} - 954368 q^{24} + 142612 q^{25} - 1576288 q^{26} - 10674179 q^{27} - 6542978 q^{29} + 5905904 q^{30} - 6654517 q^{31} + 3145728 q^{32} + 3747977 q^{33} - 4906640 q^{34} + 3854848 q^{36} + 22287969 q^{37} - 6047856 q^{38} - 3151974 q^{39} - 3002368 q^{40} - 34048098 q^{41} - 62824140 q^{43} - 1878784 q^{44} - 86300638 q^{45} + 36276080 q^{46} - 52703019 q^{47} - 15269888 q^{48} + 2281792 q^{50} - 97736333 q^{51} - 25220608 q^{52} + 12091125 q^{53} - 170786864 q^{54} - 188717699 q^{55} - 79258835 q^{57} - 104687648 q^{58} - 12949897 q^{59} + 94494464 q^{60} - 160252153 q^{61} - 106472272 q^{62} + 50331648 q^{64} - 334191270 q^{65} + 59967632 q^{66} + 480890225 q^{67} - 78506240 q^{68} - 565616581 q^{69} - 37210720 q^{71} + 61677568 q^{72} + 251382283 q^{73} + 356607504 q^{74} + 16322324 q^{75} - 96765696 q^{76} - 50431584 q^{78} - 286494785 q^{79} - 48037888 q^{80} + 2165894587 q^{81} - 544769568 q^{82} - 1147591172 q^{83} - 1194592537 q^{85} - 1005186240 q^{86} + 1412199358 q^{87} - 30060544 q^{88} - 901243845 q^{89} - 1380810208 q^{90} + 580417280 q^{92} - 710456889 q^{93} - 843248304 q^{94} + 887366177 q^{95} - 244318208 q^{96} - 314853938 q^{97} - 628109434 q^{99}+O(q^{100}) \) 3 * q + 48 * q^2 - 233 * q^3 + 768 * q^4 - 733 * q^5 - 3728 * q^6 + 12288 * q^8 + 15058 * q^9 - 11728 * q^10 - 7339 * q^11 - 59648 * q^12 - 98518 * q^13 + 369119 * q^15 + 196608 * q^16 - 306665 * q^17 + 240928 * q^18 - 377991 * q^19 - 187648 * q^20 - 117424 * q^22 + 2267255 * q^23 - 954368 * q^24 + 142612 * q^25 - 1576288 * q^26 - 10674179 * q^27 - 6542978 * q^29 + 5905904 * q^30 - 6654517 * q^31 + 3145728 * q^32 + 3747977 * q^33 - 4906640 * q^34 + 3854848 * q^36 + 22287969 * q^37 - 6047856 * q^38 - 3151974 * q^39 - 3002368 * q^40 - 34048098 * q^41 - 62824140 * q^43 - 1878784 * q^44 - 86300638 * q^45 + 36276080 * q^46 - 52703019 * q^47 - 15269888 * q^48 + 2281792 * q^50 - 97736333 * q^51 - 25220608 * q^52 + 12091125 * q^53 - 170786864 * q^54 - 188717699 * q^55 - 79258835 * q^57 - 104687648 * q^58 - 12949897 * q^59 + 94494464 * q^60 - 160252153 * q^61 - 106472272 * q^62 + 50331648 * q^64 - 334191270 * q^65 + 59967632 * q^66 + 480890225 * q^67 - 78506240 * q^68 - 565616581 * q^69 - 37210720 * q^71 + 61677568 * q^72 + 251382283 * q^73 + 356607504 * q^74 + 16322324 * q^75 - 96765696 * q^76 - 50431584 * q^78 - 286494785 * q^79 - 48037888 * q^80 + 2165894587 * q^81 - 544769568 * q^82 - 1147591172 * q^83 - 1194592537 * q^85 - 1005186240 * q^86 + 1412199358 * q^87 - 30060544 * q^88 - 901243845 * q^89 - 1380810208 * q^90 + 580417280 * q^92 - 710456889 * q^93 - 843248304 * q^94 + 887366177 * q^95 - 244318208 * q^96 - 314853938 * q^97 - 628109434 * 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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	13.9747	0.0996085	0.0498042	−	0.998759i	$-0.484140\pi$
$3$	13.9747	0.0996085	0.0498042	+	0.998759i	$0.484140\pi$
$4$	256.000	0.500000
$5$	1718.94	1.22997	0.614986	−	0.788538i	$-0.289162\pi$
$5$	1718.94	1.22997	0.614986	+	0.788538i	$0.289162\pi$
$6$	223.595	0.0704338
$7$	0	0
$7$	0	0
$8$	4096.00	0.353553
$9$	−19487.7	−0.990078
$10$	27503.0	0.869721
$11$	−71323.4	−1.46881	−0.734404	−	0.678712i	$-0.762538\pi$
$11$	−71323.4	−1.46881	−0.734404	+	0.678712i	$0.762538\pi$
$12$	3577.52	0.0498042
$13$	−156547.	−1.52019	−0.760097	−	0.649809i	$-0.774849\pi$
$13$	−156547.	−1.52019	−0.760097	+	0.649809i	$0.774849\pi$
$14$	0	0
$15$	24021.6	0.122516
$16$	65536.0	0.250000
$17$	−511711.	−1.48595	−0.742976	−	0.669318i	$-0.766587\pi$
$17$	−511711.	−1.48595	−0.742976	+	0.669318i	$0.766587\pi$
$18$	−311803.	−0.700091
$19$	194494.	0.342385	0.171193	−	0.985238i	$-0.445238\pi$
$19$	194494.	0.342385	0.171193	+	0.985238i	$0.445238\pi$
$20$	440048.	0.614986
$21$	0	0
$22$	−1.14118e6	−1.03860
$23$	−108156.	−0.0805890	−0.0402945	−	0.999188i	$-0.512830\pi$
$23$	−108156.	−0.0805890	−0.0402945	+	0.999188i	$0.512830\pi$
$24$	57240.3	0.0352169
$25$	1.00162e6	0.512830
$26$	−2.50475e6	−1.07494
$27$	−547398.	−0.198229
$28$	0	0
$29$	4.21769e6	1.10735	0.553674	−	0.832734i	$-0.313226\pi$
$29$	4.21769e6	1.10735	0.553674	+	0.832734i	$0.313226\pi$
$30$	384346.	0.0866316
$31$	−3.16733e6	−0.615979	−0.307990	−	0.951390i	$-0.599656\pi$
$31$	−3.16733e6	−0.615979	−0.307990	+	0.951390i	$0.599656\pi$
$32$	1.04858e6	0.176777
$33$	−996722.	−0.146306
$34$	−8.18738e6	−1.05073
$35$	0	0
$36$	−4.98885e6	−0.495039
$37$	1.44137e7	1.26435	0.632177	−	0.774824i	$-0.282162\pi$
$37$	1.44137e7	1.26435	0.632177	+	0.774824i	$0.282162\pi$
$38$	3.11190e6	0.242103
$39$	−2.18769e6	−0.151424
$40$	7.04077e6	0.434861
$41$	−7.69007e6	−0.425014	−0.212507	−	0.977160i	$-0.568163\pi$
$41$	−7.69007e6	−0.425014	−0.212507	+	0.977160i	$0.568163\pi$
$42$	0	0
$43$	−3.64544e7	−1.62608	−0.813040	−	0.582208i	$-0.802189\pi$
$43$	−3.64544e7	−1.62608	−0.813040	+	0.582208i	$0.802189\pi$
$44$	−1.82588e7	−0.734404
$45$	−3.34982e7	−1.21777
$46$	−1.73050e6	−0.0569851
$47$	−1.82379e7	−0.545173	−0.272587	−	0.962131i	$-0.587879\pi$
$47$	−1.82379e7	−0.545173	−0.272587	+	0.962131i	$0.587879\pi$
$48$	915845.	0.0249021
$49$	0	0
$50$	1.60259e7	0.362625
$51$	−7.15100e6	−0.148013
$52$	−4.00760e7	−0.760097
$53$	4.52073e7	0.786987	0.393494	−	0.919327i	$-0.371266\pi$
$53$	4.52073e7	0.786987	0.393494	+	0.919327i	$0.371266\pi$
$54$	−8.75837e6	−0.140169
$55$	−1.22601e8	−1.80659
$56$	0	0
$57$	2.71799e6	0.0341045
$58$	6.74831e7	0.783013
$59$	9.78147e7	1.05092	0.525461	−	0.850818i	$-0.323893\pi$
$59$	9.78147e7	1.05092	0.525461	+	0.850818i	$0.323893\pi$
$60$	6.14953e6	0.0612578
$61$	−1.14670e8	−1.06039	−0.530197	−	0.847874i	$-0.677882\pi$
$61$	−1.14670e8	−1.06039	−0.530197	+	0.847874i	$0.677882\pi$
$62$	−5.06773e7	−0.435563
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−2.69094e8	−1.86980
$66$	−1.59476e7	−0.103454
$67$	2.01616e8	1.22233	0.611166	−	0.791503i	$-0.290701\pi$
$67$	2.01616e8	1.22233	0.611166	+	0.791503i	$0.290701\pi$
$68$	−1.30998e8	−0.742976
$69$	−1.51145e6	−0.00802735
$70$	0	0
$71$	2.08831e7	0.0975288	0.0487644	−	0.998810i	$-0.484472\pi$
$71$	2.08831e7	0.0975288	0.0487644	+	0.998810i	$0.484472\pi$
$72$	−7.98217e7	−0.350045
$73$	−8.84783e6	−0.0364657	−0.0182328	−	0.999834i	$-0.505804\pi$
$73$	−8.84783e6	−0.0364657	−0.0182328	+	0.999834i	$0.505804\pi$
$74$	2.30620e8	0.894033
$75$	1.39973e7	0.0510822
$76$	4.97905e7	0.171193
$77$	0	0
$78$	−3.50031e7	−0.107073
$79$	3.84488e7	0.111061	0.0555304	−	0.998457i	$-0.482315\pi$
$79$	3.84488e7	0.111061	0.0555304	+	0.998457i	$0.482315\pi$
$80$	1.12652e8	0.307493
$81$	3.75927e8	0.970333
$82$	−1.23041e8	−0.300530
$83$	−5.55300e8	−1.28433	−0.642164	−	0.766567i	$-0.721963\pi$
$83$	−5.55300e8	−1.28433	−0.642164	+	0.766567i	$0.721963\pi$
$84$	0	0
$85$	−8.79600e8	−1.82768
$86$	−5.83270e8	−1.14981
$87$	5.89409e7	0.110301
$88$	−2.92141e8	−0.519302
$89$	1.64919e8	0.278622	0.139311	−	0.990249i	$-0.455511\pi$
$89$	1.64919e8	0.278622	0.139311	+	0.990249i	$0.455511\pi$
$90$	−5.35970e8	−0.861092
$91$	0	0
$92$	−2.76880e7	−0.0402945
$93$	−4.42624e7	−0.0613567
$94$	−2.91806e8	−0.385496
$95$	3.34323e8	0.421124
$96$	1.46535e7	0.0176085
$97$	−1.57025e8	−0.180093	−0.0900466	−	0.995938i	$-0.528702\pi$
$97$	−1.57025e8	−0.180093	−0.0900466	+	0.995938i	$0.528702\pi$
$98$	0	0
$99$	1.38993e9	1.45424
$100$	2.56415e8	0.256415
$101$	−1.62774e8	−0.155646	−0.0778230	−	0.996967i	$-0.524797\pi$
$101$	−1.62774e8	−0.155646	−0.0778230	+	0.996967i	$0.524797\pi$
$102$	−1.14416e8	−0.104661
$103$	−1.35406e9	−1.18541	−0.592705	−	0.805419i	$-0.701940\pi$
$103$	−1.35406e9	−1.18541	−0.592705	+	0.805419i	$0.701940\pi$
$104$	−6.41216e8	−0.537470
$105$	0	0
$106$	7.23318e8	0.556484
$107$	8.78604e6	0.00647987	0.00323993	−	0.999995i	$-0.498969\pi$
$107$	8.78604e6	0.00647987	0.00323993	+	0.999995i	$0.498969\pi$
$108$	−1.40134e8	−0.0991143
$109$	7.22869e8	0.490501	0.245251	−	0.969460i	$-0.421130\pi$
$109$	7.22869e8	0.490501	0.245251	+	0.969460i	$0.421130\pi$
$110$	−1.96161e9	−1.27745
$111$	2.01427e8	0.125940
$112$	0	0
$113$	−2.94124e9	−1.69698	−0.848492	−	0.529209i	$-0.822489\pi$
$113$	−2.94124e9	−1.69698	−0.848492	+	0.529209i	$0.822489\pi$
$114$	4.34879e7	0.0241155
$115$	−1.85914e8	−0.0991222
$116$	1.07973e9	0.553674
$117$	3.05074e9	1.50511
$118$	1.56504e9	0.743113
$119$	0	0
$120$	9.83925e7	0.0433158
$121$	2.72909e9	1.15740
$122$	−1.83473e9	−0.749812
$123$	−1.07466e8	−0.0423350
$124$	−8.10837e8	−0.307990
$125$	−1.63558e9	−0.599205
$126$	0	0
$127$	−6.47761e8	−0.220952	−0.110476	−	0.993879i	$-0.535238\pi$
$127$	−6.47761e8	−0.220952	−0.110476	+	0.993879i	$0.535238\pi$
$128$	2.68435e8	0.0883883
$129$	−5.09439e8	−0.161971
$130$	−4.30551e9	−1.32215
$131$	2.94753e9	0.874456	0.437228	−	0.899351i	$-0.355960\pi$
$131$	2.94753e9	0.874456	0.437228	+	0.899351i	$0.355960\pi$
$132$	−2.55161e8	−0.0731529
$133$	0	0
$134$	3.22586e9	0.864319
$135$	−9.40943e8	−0.243816
$136$	−2.09597e9	−0.525364
$137$	−7.71337e9	−1.87069	−0.935344	−	0.353739i	$-0.884910\pi$
$137$	−7.71337e9	−1.87069	−0.935344	+	0.353739i	$0.884910\pi$
$138$	−2.41832e7	−0.00567619
$139$	5.40626e9	1.22837	0.614187	−	0.789161i	$-0.289484\pi$
$139$	5.40626e9	1.22837	0.614187	+	0.789161i	$0.289484\pi$
$140$	0	0
$141$	−2.54869e8	−0.0543038
$142$	3.34130e8	0.0689632
$143$	1.11655e10	2.23288
$144$	−1.27715e9	−0.247520
$145$	7.24995e9	1.36201
$146$	−1.41565e8	−0.0257851
$147$	0	0
$148$	3.68991e9	0.632177
$149$	3.10602e7	0.00516257	0.00258129	−	0.999997i	$-0.499178\pi$
$149$	3.10602e7	0.00516257	0.00258129	+	0.999997i	$0.499178\pi$
$150$	2.23957e8	0.0361206
$151$	8.16700e9	1.27840	0.639199	−	0.769041i	$-0.279266\pi$
$151$	8.16700e9	1.27840	0.639199	+	0.769041i	$0.279266\pi$
$152$	7.96648e8	0.121051
$153$	9.97208e9	1.47121
$154$	0	0
$155$	−5.44445e9	−0.757637
$156$	−5.60049e8	−0.0757121
$157$	−1.54411e8	−0.0202829	−0.0101415	−	0.999949i	$-0.503228\pi$
$157$	−1.54411e8	−0.0202829	−0.0101415	+	0.999949i	$0.503228\pi$
$158$	6.15180e8	0.0785318
$159$	6.31758e8	0.0783906
$160$	1.80244e9	0.217430
$161$	0	0
$162$	6.01483e9	0.686129
$163$	1.14467e10	1.27010	0.635048	−	0.772473i	$-0.280980\pi$
$163$	1.14467e10	1.27010	0.635048	+	0.772473i	$0.280980\pi$
$164$	−1.96866e9	−0.212507
$165$	−1.71330e9	−0.179952
$166$	−8.88479e9	−0.908157
$167$	1.71056e10	1.70182	0.850911	−	0.525310i	$-0.176051\pi$
$167$	1.71056e10	1.70182	0.850911	+	0.525310i	$0.176051\pi$
$168$	0	0
$169$	1.39024e10	1.31099
$170$	−1.40736e10	−1.29236
$171$	−3.79024e9	−0.338988
$172$	−9.33233e9	−0.813040
$173$	1.81936e9	0.154423	0.0772113	−	0.997015i	$-0.475398\pi$
$173$	1.81936e9	0.154423	0.0772113	+	0.997015i	$0.475398\pi$
$174$	9.43054e8	0.0779947
$175$	0	0
$176$	−4.67425e9	−0.367202
$177$	1.36693e9	0.104681
$178$	2.63870e9	0.197015
$179$	−2.36314e9	−0.172048	−0.0860241	−	0.996293i	$-0.527416\pi$
$179$	−2.36314e9	−0.172048	−0.0860241	+	0.996293i	$0.527416\pi$
$180$	−8.57553e9	−0.608884
$181$	−1.65554e10	−1.14653	−0.573265	−	0.819370i	$-0.694323\pi$
$181$	−1.65554e10	−1.14653	−0.573265	+	0.819370i	$0.694323\pi$
$182$	0	0
$183$	−1.60248e9	−0.105624
$184$	−4.43008e8	−0.0284925
$185$	2.47763e10	1.55512
$186$	−7.08199e8	−0.0433858
$187$	3.64970e10	2.18258
$188$	−4.66890e9	−0.272587
$189$	0	0
$190$	5.34917e9	0.297780
$191$	−3.36529e9	−0.182967	−0.0914835	−	0.995807i	$-0.529161\pi$
$191$	−3.36529e9	−0.182967	−0.0914835	+	0.995807i	$0.529161\pi$
$192$	2.34456e8	0.0124511
$193$	−4.72385e9	−0.245069	−0.122534	−	0.992464i	$-0.539102\pi$
$193$	−4.72385e9	−0.245069	−0.122534	+	0.992464i	$0.539102\pi$
$194$	−2.51241e9	−0.127345
$195$	−3.76051e9	−0.186248
$196$	0	0
$197$	−1.66982e10	−0.789897	−0.394949	−	0.918703i	$-0.629238\pi$
$197$	−1.66982e10	−0.789897	−0.394949	+	0.918703i	$0.629238\pi$
$198$	2.22389e10	1.02830
$199$	−2.61827e10	−1.18352	−0.591759	−	0.806115i	$-0.701566\pi$
$199$	−2.61827e10	−1.18352	−0.591759	+	0.806115i	$0.701566\pi$
$200$	4.10264e9	0.181313
$201$	2.81752e9	0.121755
$202$	−2.60438e9	−0.110058
$203$	0	0
$204$	−1.83066e9	−0.0740067
$205$	−1.32187e10	−0.522755
$206$	−2.16649e10	−0.838212
$207$	2.10772e9	0.0797894
$208$	−1.02595e10	−0.380049
$209$	−1.38720e10	−0.502898
$210$	0	0
$211$	−3.90431e10	−1.35604	−0.678021	−	0.735042i	$-0.737162\pi$
$211$	−3.90431e10	−1.35604	−0.678021	+	0.735042i	$0.737162\pi$
$212$	1.15731e10	0.393494
$213$	2.91835e8	0.00971469
$214$	1.40577e8	0.00458196
$215$	−6.26628e10	−2.00003
$216$	−2.24214e9	−0.0700844
$217$	0	0
$218$	1.15659e10	0.346837
$219$	−1.23646e8	−0.00363229
$220$	−3.13857e10	−0.903296
$221$	8.01068e10	2.25894
$222$	3.22283e9	0.0890532
$223$	−4.53210e10	−1.22723	−0.613617	−	0.789603i	$-0.710286\pi$
$223$	−4.53210e10	−1.22723	−0.613617	+	0.789603i	$0.710286\pi$
$224$	0	0
$225$	−1.95193e10	−0.507742
$226$	−4.70598e10	−1.19995
$227$	−7.50843e9	−0.187686	−0.0938432	−	0.995587i	$-0.529915\pi$
$227$	−7.50843e9	−0.187686	−0.0938432	+	0.995587i	$0.529915\pi$
$228$	6.95806e8	0.0170522
$229$	−4.18474e10	−1.00556	−0.502781	−	0.864414i	$-0.667690\pi$
$229$	−4.18474e10	−1.00556	−0.502781	+	0.864414i	$0.667690\pi$
$230$	−2.97462e9	−0.0700900
$231$	0	0
$232$	1.72757e10	0.391506
$233$	3.04921e10	0.677776	0.338888	−	0.940827i	$-0.389949\pi$
$233$	3.04921e10	0.677776	0.338888	+	0.940827i	$0.389949\pi$
$234$	4.88118e10	1.06427
$235$	−3.13498e10	−0.670547
$236$	2.50406e10	0.525461
$237$	5.37309e8	0.0110626
$238$	0	0
$239$	4.29290e10	0.851060	0.425530	−	0.904944i	$-0.360088\pi$
$239$	4.29290e10	0.851060	0.425530	+	0.904944i	$0.360088\pi$
$240$	1.57428e9	0.0306289
$241$	8.41066e9	0.160603	0.0803015	−	0.996771i	$-0.474412\pi$
$241$	8.41066e9	0.160603	0.0803015	+	0.996771i	$0.474412\pi$
$242$	4.36654e10	0.818404
$243$	1.60279e10	0.294882
$244$	−2.93556e10	−0.530197
$245$	0	0
$246$	−1.71946e9	−0.0299353
$247$	−3.04474e10	−0.520492
$248$	−1.29734e10	−0.217781
$249$	−7.76013e9	−0.127930
$250$	−2.61692e10	−0.423702
$251$	−8.14744e10	−1.29566	−0.647828	−	0.761787i	$-0.724322\pi$
$251$	−8.14744e10	−1.29566	−0.647828	+	0.761787i	$0.724322\pi$
$252$	0	0
$253$	7.71407e9	0.118370
$254$	−1.03642e10	−0.156237
$255$	−1.22921e10	−0.182052
$256$	4.29497e9	0.0625000
$257$	−3.81037e10	−0.544839	−0.272420	−	0.962179i	$-0.587824\pi$
$257$	−3.81037e10	−0.544839	−0.272420	+	0.962179i	$0.587824\pi$
$258$	−8.15102e9	−0.114531
$259$	0	0
$260$	−6.88881e10	−0.934898
$261$	−8.21931e10	−1.09636
$262$	4.71606e10	0.618334
$263$	−5.66482e10	−0.730105	−0.365053	−	0.930987i	$-0.618949\pi$
$263$	−5.66482e10	−0.730105	−0.365053	+	0.930987i	$0.618949\pi$
$264$	−4.08257e9	−0.0517269
$265$	7.77086e10	0.967972
$266$	0	0
$267$	2.30469e9	0.0277531
$268$	5.16138e10	0.611166
$269$	−1.42135e11	−1.65507	−0.827534	−	0.561416i	$-0.810257\pi$
$269$	−1.42135e11	−1.65507	−0.827534	+	0.561416i	$0.810257\pi$
$270$	−1.50551e10	−0.172404
$271$	3.72665e10	0.419717	0.209859	−	0.977732i	$-0.432700\pi$
$271$	3.72665e10	0.419717	0.209859	+	0.977732i	$0.432700\pi$
$272$	−3.35355e10	−0.371488
$273$	0	0
$274$	−1.23414e11	−1.32278
$275$	−7.14390e10	−0.753249
$276$	−3.86931e8	−0.00401367
$277$	1.57394e11	1.60631	0.803157	−	0.595767i	$-0.203152\pi$
$277$	1.57394e11	1.60631	0.803157	+	0.595767i	$0.203152\pi$
$278$	8.65002e10	0.868591
$279$	6.17240e10	0.609867
$280$	0	0
$281$	9.66888e10	0.925119	0.462560	−	0.886588i	$-0.346931\pi$
$281$	9.66888e10	0.925119	0.462560	+	0.886588i	$0.346931\pi$
$282$	−4.07790e9	−0.0383986
$283$	1.99126e11	1.84540	0.922698	−	0.385524i	$-0.125979\pi$
$283$	1.99126e11	1.84540	0.922698	+	0.385524i	$0.125979\pi$
$284$	5.34608e9	0.0487644
$285$	4.67206e9	0.0419475
$286$	1.78647e11	1.57888
$287$	0	0
$288$	−2.04343e10	−0.175023
$289$	1.43261e11	1.20806
$290$	1.15999e11	0.963083
$291$	−2.19438e9	−0.0179388
$292$	−2.26505e9	−0.0182328
$293$	−7.28364e10	−0.577357	−0.288679	−	0.957426i	$-0.593216\pi$
$293$	−7.28364e10	−0.577357	−0.288679	+	0.957426i	$0.593216\pi$
$294$	0	0
$295$	1.68137e11	1.29260
$296$	5.90386e10	0.447016
$297$	3.90423e10	0.291160
$298$	4.96963e8	0.00365049
$299$	1.69315e10	0.122511
$300$	3.58332e9	0.0255411
$301$	0	0
$302$	1.30672e11	0.903965
$303$	−2.27471e9	−0.0155037
$304$	1.27464e10	0.0855963
$305$	−1.97111e11	−1.30425
$306$	1.59553e11	1.04030
$307$	1.17824e11	0.757027	0.378514	−	0.925596i	$-0.376435\pi$
$307$	1.17824e11	0.757027	0.378514	+	0.925596i	$0.376435\pi$
$308$	0	0
$309$	−1.89225e10	−0.118077
$310$	−8.71111e10	−0.535730
$311$	−1.81389e11	−1.09948	−0.549742	−	0.835335i	$-0.685274\pi$
$311$	−1.81389e11	−1.09948	−0.549742	+	0.835335i	$0.685274\pi$
$312$	−8.96079e9	−0.0535366
$313$	−2.84435e11	−1.67507	−0.837537	−	0.546381i	$-0.816005\pi$
$313$	−2.84435e11	−1.67507	−0.837537	+	0.546381i	$0.816005\pi$
$314$	−2.47058e9	−0.0143422
$315$	0	0
$316$	9.84288e9	0.0555304
$317$	−1.01749e11	−0.565929	−0.282964	−	0.959130i	$-0.591318\pi$
$317$	−1.01749e11	−0.565929	−0.282964	+	0.959130i	$0.591318\pi$
$318$	1.01081e10	0.0554305
$319$	−3.00820e11	−1.62648
$320$	2.88390e10	0.153746
$321$	1.22782e8	0.000645449 0
$322$	0	0
$323$	−9.95248e10	−0.508768
$324$	9.62373e10	0.485166
$325$	−1.56801e11	−0.779601
$326$	1.83147e11	0.898093
$327$	1.01019e10	0.0488581
$328$	−3.14985e10	−0.150265
$329$	0	0
$330$	−2.74128e10	−0.127245
$331$	3.03966e11	1.39187	0.695935	−	0.718105i	$-0.254990\pi$
$331$	3.03966e11	1.39187	0.695935	+	0.718105i	$0.254990\pi$
$332$	−1.42157e11	−0.642164
$333$	−2.80890e11	−1.25181
$334$	2.73689e11	1.20337
$335$	3.46566e11	1.50343
$336$	0	0
$337$	−1.72473e10	−0.0728427	−0.0364213	−	0.999337i	$-0.511596\pi$
$337$	−1.72473e10	−0.0728427	−0.0364213	+	0.999337i	$0.511596\pi$
$338$	2.22439e11	0.927012
$339$	−4.11029e10	−0.169034
$340$	−2.25178e11	−0.913840
$341$	2.25905e11	0.904755
$342$	−6.06439e10	−0.239701
$343$	0	0
$344$	−1.49317e11	−0.574906
$345$	−2.59808e9	−0.00987341
$346$	2.91097e10	0.109193
$347$	3.16834e11	1.17314	0.586569	−	0.809899i	$-0.300478\pi$
$347$	3.16834e11	1.17314	0.586569	+	0.809899i	$0.300478\pi$
$348$	1.50889e10	0.0551506
$349$	−9.59821e10	−0.346318	−0.173159	−	0.984894i	$-0.555398\pi$
$349$	−9.59821e10	−0.346318	−0.173159	+	0.984894i	$0.555398\pi$
$350$	0	0
$351$	8.56934e10	0.301346
$352$	−7.47880e10	−0.259651
$353$	2.62190e11	0.898731	0.449365	−	0.893348i	$-0.351650\pi$
$353$	2.62190e11	0.898731	0.449365	+	0.893348i	$0.351650\pi$
$354$	2.18709e10	0.0740204
$355$	3.58968e10	0.119958
$356$	4.22192e10	0.139311
$357$	0	0
$358$	−3.78102e10	−0.121656
$359$	−1.08533e11	−0.344855	−0.172427	−	0.985022i	$-0.555161\pi$
$359$	−1.08533e11	−0.344855	−0.172427	+	0.985022i	$0.555161\pi$
$360$	−1.37208e11	−0.430546
$361$	−2.84860e11	−0.882772
$362$	−2.64886e11	−0.810719
$363$	3.81381e10	0.115287
$364$	0	0
$365$	−1.52089e10	−0.0448517
$366$	−2.56397e10	−0.0746876
$367$	−2.12536e11	−0.611554	−0.305777	−	0.952103i	$-0.598916\pi$
$367$	−2.12536e11	−0.611554	−0.305777	+	0.952103i	$0.598916\pi$
$368$	−7.08812e9	−0.0201473
$369$	1.49862e11	0.420797
$370$	3.96421e11	1.09963
$371$	0	0
$372$	−1.13312e10	−0.0306784
$373$	−3.17831e11	−0.850170	−0.425085	−	0.905153i	$-0.639756\pi$
$373$	−3.17831e11	−0.850170	−0.425085	+	0.905153i	$0.639756\pi$
$374$	5.83952e11	1.54332
$375$	−2.28567e10	−0.0596859
$376$	−7.47024e10	−0.192748
$377$	−6.60266e11	−1.68338
$378$	0	0
$379$	6.09315e11	1.51693	0.758465	−	0.651714i	$-0.225950\pi$
$379$	6.09315e11	1.51693	0.758465	+	0.651714i	$0.225950\pi$
$380$	8.55867e10	0.210562
$381$	−9.05225e9	−0.0220087
$382$	−5.38447e10	−0.129377
$383$	−3.40063e11	−0.807542	−0.403771	−	0.914860i	$-0.632301\pi$
$383$	−3.40063e11	−0.807542	−0.403771	+	0.914860i	$0.632301\pi$
$384$	3.75130e9	0.00880423
$385$	0	0
$386$	−7.55816e10	−0.173290
$387$	7.10413e11	1.60995
$388$	−4.01985e10	−0.0900466
$389$	7.54884e11	1.67150	0.835751	−	0.549108i	$-0.185033\pi$
$389$	7.54884e11	1.67150	0.835751	+	0.549108i	$0.185033\pi$
$390$	−6.01681e10	−0.131697
$391$	5.53447e10	0.119751
$392$	0	0
$393$	4.11908e10	0.0871032
$394$	−2.67171e11	−0.558542
$395$	6.60910e10	0.136602
$396$	3.55822e11	0.727118
$397$	2.69388e11	0.544279	0.272140	−	0.962258i	$-0.412269\pi$
$397$	2.69388e11	0.544279	0.272140	+	0.962258i	$0.412269\pi$
$398$	−4.18923e11	−0.836874
$399$	0	0
$400$	6.56422e10	0.128207
$401$	−3.56166e11	−0.687865	−0.343932	−	0.938994i	$-0.611759\pi$
$401$	−3.56166e11	−0.687865	−0.343932	+	0.938994i	$0.611759\pi$
$402$	4.50804e10	0.0860935
$403$	4.95836e11	0.936408
$404$	−4.16700e10	−0.0778230
$405$	6.46195e11	1.19348
$406$	0	0
$407$	−1.02804e12	−1.85709
$408$	−2.92905e10	−0.0523307
$409$	8.74402e10	0.154510	0.0772549	−	0.997011i	$-0.475384\pi$
$409$	8.74402e10	0.154510	0.0772549	+	0.997011i	$0.475384\pi$
$410$	−2.11500e11	−0.369643
$411$	−1.07792e11	−0.186336
$412$	−3.46638e11	−0.592705
$413$	0	0
$414$	3.37234e10	0.0564197
$415$	−9.54525e11	−1.57969
$416$	−1.64151e11	−0.268735
$417$	7.55508e10	0.122356
$418$	−2.21952e11	−0.355603
$419$	−4.46048e9	−0.00706999	−0.00353499	−	0.999994i	$-0.501125\pi$
$419$	−4.46048e9	−0.00706999	−0.00353499	+	0.999994i	$0.501125\pi$
$420$	0	0
$421$	−9.34684e10	−0.145009	−0.0725046	−	0.997368i	$-0.523099\pi$
$421$	−9.34684e10	−0.145009	−0.0725046	+	0.997368i	$0.523099\pi$
$422$	−6.24690e11	−0.958867
$423$	3.55415e11	0.539764
$424$	1.85169e11	0.278242
$425$	−5.12541e11	−0.762041
$426$	4.66936e9	0.00686932
$427$	0	0
$428$	2.24923e9	0.00323993
$429$	1.56034e11	0.222413
$430$	−1.00261e12	−1.41424
$431$	−4.99124e11	−0.696724	−0.348362	−	0.937360i	$-0.613262\pi$
$431$	−4.99124e11	−0.696724	−0.348362	+	0.937360i	$0.613262\pi$
$432$	−3.58743e10	−0.0495572
$433$	−1.04168e12	−1.42410	−0.712049	−	0.702130i	$-0.752232\pi$
$433$	−1.04168e12	−1.42410	−0.712049	+	0.702130i	$0.752232\pi$
$434$	0	0
$435$	1.01316e11	0.135667
$436$	1.85054e11	0.245251
$437$	−2.10357e10	−0.0275925
$438$	−1.97833e9	−0.00256842
$439$	2.00279e11	0.257363	0.128681	−	0.991686i	$-0.458926\pi$
$439$	2.00279e11	0.257363	0.128681	+	0.991686i	$0.458926\pi$
$440$	−5.02172e11	−0.638727
$441$	0	0
$442$	1.28171e12	1.59731
$443$	2.26102e11	0.278925	0.139463	−	0.990227i	$-0.455462\pi$
$443$	2.26102e11	0.278925	0.139463	+	0.990227i	$0.455462\pi$
$444$	5.15654e10	0.0629701
$445$	2.83485e11	0.342697
$446$	−7.25136e11	−0.867786
$447$	4.34056e8	0.000514236 0
$448$	0	0
$449$	−1.20089e12	−1.39443	−0.697213	−	0.716864i	$-0.745577\pi$
$449$	−1.20089e12	−1.39443	−0.697213	+	0.716864i	$0.745577\pi$
$450$	−3.12309e11	−0.359028
$451$	5.48482e11	0.624264
$452$	−7.52958e11	−0.848492
$453$	1.14131e11	0.127339
$454$	−1.20135e11	−0.132714
$455$	0	0
$456$	1.11329e10	0.0120578
$457$	3.29728e11	0.353616	0.176808	−	0.984245i	$-0.443423\pi$
$457$	3.29728e11	0.353616	0.176808	+	0.984245i	$0.443423\pi$
$458$	−6.69558e11	−0.711040
$459$	2.80110e11	0.294558
$460$	−4.75939e10	−0.0495611
$461$	−1.38928e12	−1.43263	−0.716317	−	0.697775i	$-0.754173\pi$
$461$	−1.38928e12	−1.43263	−0.716317	+	0.697775i	$0.754173\pi$
$462$	0	0
$463$	−6.88123e7	−6.95908e−5 0	−3.47954e−5	−	1.00000i	$-0.500011\pi$
$463$	−6.88123e7	−6.95908e−5 0	−3.47954e−5		1.00000i	$0.500011\pi$
$464$	2.76411e11	0.276837
$465$	−7.60844e10	−0.0754670
$466$	4.87874e11	0.479260
$467$	1.07890e12	1.04968	0.524839	−	0.851202i	$-0.324126\pi$
$467$	1.07890e12	1.04968	0.524839	+	0.851202i	$0.324126\pi$
$468$	7.80989e11	0.752556
$469$	0	0
$470$	−5.01597e11	−0.474149
$471$	−2.15785e9	−0.00202035
$472$	4.00649e11	0.371557
$473$	2.60005e12	2.38840
$474$	8.59695e9	0.00782243
$475$	1.94809e11	0.175585
$476$	0	0
$477$	−8.80988e11	−0.779179
$478$	6.86864e11	0.601790
$479$	6.23810e11	0.541430	0.270715	−	0.962659i	$-0.412740\pi$
$479$	6.23810e11	0.541430	0.270715	+	0.962659i	$0.412740\pi$
$480$	2.51885e10	0.0216579
$481$	−2.25642e12	−1.92206
$482$	1.34571e11	0.113563
$483$	0	0
$484$	6.98646e11	0.578699
$485$	−2.69917e11	−0.221509
$486$	2.56446e11	0.208513
$487$	−1.49693e12	−1.20592	−0.602962	−	0.797770i	$-0.706013\pi$
$487$	−1.49693e12	−1.20592	−0.602962	+	0.797770i	$0.706013\pi$
$488$	−4.69690e11	−0.374906
$489$	1.59964e11	0.126512
$490$	0	0
$491$	6.91050e11	0.536590	0.268295	−	0.963337i	$-0.413540\pi$
$491$	6.91050e11	0.536590	0.268295	+	0.963337i	$0.413540\pi$
$492$	−2.75114e10	−0.0211675
$493$	−2.15824e12	−1.64547
$494$	−4.87159e11	−0.368044
$495$	2.38920e12	1.78867
$496$	−2.07574e11	−0.153995
$497$	0	0
$498$	−1.24162e11	−0.0904601
$499$	1.37492e12	0.992714	0.496357	−	0.868118i	$-0.334671\pi$
$499$	1.37492e12	0.992714	0.496357	+	0.868118i	$0.334671\pi$
$500$	−4.18708e11	−0.299603
$501$	2.39045e11	0.169516
$502$	−1.30359e12	−0.916167
$503$	2.02197e12	1.40837	0.704187	−	0.710015i	$-0.251312\pi$
$503$	2.02197e12	1.40837	0.704187	+	0.710015i	$0.251312\pi$
$504$	0	0
$505$	−2.79798e11	−0.191440
$506$	1.23425e11	0.0837001
$507$	1.94282e11	0.130586
$508$	−1.65827e11	−0.110476
$509$	1.14808e12	0.758125	0.379062	−	0.925371i	$-0.376247\pi$
$509$	1.14808e12	0.758125	0.379062	+	0.925371i	$0.376247\pi$
$510$	−1.96674e11	−0.128730
$511$	0	0
$512$	6.87195e10	0.0441942
$513$	−1.06466e11	−0.0678706
$514$	−6.09660e11	−0.385260
$515$	−2.32754e12	−1.45802
$516$	−1.30416e11	−0.0809857
$517$	1.30079e12	0.800755
$518$	0	0
$519$	2.54250e10	0.0153818
$520$	−1.10221e12	−0.661073
$521$	1.30064e12	0.773372	0.386686	−	0.922212i	$-0.373620\pi$
$521$	1.30064e12	0.773372	0.386686	+	0.922212i	$0.373620\pi$
$522$	−1.31509e12	−0.775244
$523$	2.24172e12	1.31016	0.655079	−	0.755560i	$-0.272635\pi$
$523$	2.24172e12	1.31016	0.655079	+	0.755560i	$0.272635\pi$
$524$	7.54569e11	0.437228
$525$	0	0
$526$	−9.06371e11	−0.516262
$527$	1.62076e12	0.915316
$528$	−6.53212e10	−0.0365764
$529$	−1.78945e12	−0.993505
$530$	1.24334e12	0.684459
$531$	−1.90618e12	−1.04049
$532$	0	0
$533$	1.20386e12	0.646104
$534$	3.68750e10	0.0196244
$535$	1.51026e10	0.00797005
$536$	8.25821e11	0.432160
$537$	−3.30241e10	−0.0171375
$538$	−2.27416e12	−1.17031
$539$	0	0
$540$	−2.40881e11	−0.121908
$541$	−1.16232e11	−0.0583364	−0.0291682	−	0.999575i	$-0.509286\pi$
$541$	−1.16232e11	−0.0583364	−0.0291682	+	0.999575i	$0.509286\pi$
$542$	5.96264e11	0.296785
$543$	−2.31356e11	−0.114204
$544$	−5.36568e11	−0.262682
$545$	1.24257e12	0.603303
$546$	0	0
$547$	1.58473e12	0.756854	0.378427	−	0.925631i	$-0.376465\pi$
$547$	1.58473e12	0.756854	0.378427	+	0.925631i	$0.376465\pi$
$548$	−1.97462e12	−0.935344
$549$	2.23466e12	1.04987
$550$	−1.14302e12	−0.532627
$551$	8.20316e11	0.379139
$552$	−6.19089e9	−0.00283810
$553$	0	0
$554$	2.51831e12	1.13584
$555$	3.46241e11	0.154903
$556$	1.38400e12	0.614187
$557$	1.51057e12	0.664956	0.332478	−	0.943111i	$-0.392115\pi$
$557$	1.51057e12	0.664956	0.332478	+	0.943111i	$0.392115\pi$
$558$	9.87585e11	0.431241
$559$	5.70682e12	2.47196
$560$	0	0
$561$	5.10034e11	0.217403
$562$	1.54702e12	0.654158
$563$	6.06023e11	0.254215	0.127108	−	0.991889i	$-0.459431\pi$
$563$	6.06023e11	0.254215	0.127108	+	0.991889i	$0.459431\pi$
$564$	−6.52464e10	−0.0271519
$565$	−5.05581e12	−2.08724
$566$	3.18602e12	1.30489
$567$	0	0
$568$	8.55372e10	0.0344816
$569$	−3.20263e11	−0.128086	−0.0640431	−	0.997947i	$-0.520400\pi$
$569$	−3.20263e11	−0.128086	−0.0640431	+	0.997947i	$0.520400\pi$
$570$	7.47529e10	0.0296614
$571$	−3.05228e12	−1.20160	−0.600802	−	0.799398i	$-0.705152\pi$
$571$	−3.05228e12	−1.20160	−0.600802	+	0.799398i	$0.705152\pi$
$572$	2.85836e12	1.11644
$573$	−4.70289e10	−0.0182251
$574$	0	0
$575$	−1.08331e11	−0.0413285
$576$	−3.26949e11	−0.123760
$577$	−2.82965e12	−1.06278	−0.531389	−	0.847128i	$-0.678330\pi$
$577$	−2.82965e12	−1.06278	−0.531389	+	0.847128i	$0.678330\pi$
$578$	2.29217e12	0.854224
$579$	−6.60142e10	−0.0244109
$580$	1.85599e12	0.681003
$581$	0	0
$582$	−3.51101e10	−0.0126846
$583$	−3.22434e12	−1.15593
$584$	−3.62407e10	−0.0128926
$585$	5.24403e12	1.85124
$586$	−1.16538e12	−0.408253
$587$	2.10206e12	0.730756	0.365378	−	0.930859i	$-0.380940\pi$
$587$	2.10206e12	0.730756	0.365378	+	0.930859i	$0.380940\pi$
$588$	0	0
$589$	−6.16027e11	−0.210902
$590$	2.69020e12	0.914008
$591$	−2.33351e11	−0.0786804
$592$	9.44618e11	0.316088
$593$	5.93069e12	1.96951	0.984756	−	0.173940i	$-0.0556498\pi$
$593$	5.93069e12	1.96951	0.984756	+	0.173940i	$0.0556498\pi$
$594$	6.24677e11	0.205881
$595$	0	0
$596$	7.95141e9	0.00258129
$597$	−3.65894e11	−0.117888
$598$	2.70904e11	0.0866284
$599$	−3.15214e12	−1.00043	−0.500213	−	0.865902i	$-0.666745\pi$
$599$	−3.15214e12	−1.00043	−0.500213	+	0.865902i	$0.666745\pi$
$600$	5.73331e10	0.0180603
$601$	−6.20966e12	−1.94148	−0.970740	−	0.240132i	$-0.922809\pi$
$601$	−6.20966e12	−1.94148	−0.970740	+	0.240132i	$0.922809\pi$
$602$	0	0
$603$	−3.92904e12	−1.21020
$604$	2.09075e12	0.639199
$605$	4.69113e12	1.42357
$606$	−3.63953e10	−0.0109627
$607$	−4.55039e12	−1.36050	−0.680251	−	0.732979i	$-0.738129\pi$
$607$	−4.55039e12	−1.36050	−0.680251	+	0.732979i	$0.738129\pi$
$608$	2.03942e11	0.0605257
$609$	0	0
$610$	−3.15378e12	−0.922247
$611$	2.85509e12	0.828769
$612$	2.55285e12	0.735605
$613$	−6.97263e11	−0.199445	−0.0997227	−	0.995015i	$-0.531796\pi$
$613$	−6.97263e11	−0.199445	−0.0997227	+	0.995015i	$0.531796\pi$
$614$	1.88519e12	0.535299
$615$	−1.84728e11	−0.0520708
$616$	0	0
$617$	3.02922e12	0.841488	0.420744	−	0.907179i	$-0.361769\pi$
$617$	3.02922e12	0.841488	0.420744	+	0.907179i	$0.361769\pi$
$618$	−3.02760e11	−0.0834930
$619$	−3.16385e12	−0.866181	−0.433090	−	0.901350i	$-0.642577\pi$
$619$	−3.16385e12	−0.866181	−0.433090	+	0.901350i	$0.642577\pi$
$620$	−1.39378e12	−0.378818
$621$	5.92045e10	0.0159751
$622$	−2.90222e12	−0.777452
$623$	0	0
$624$	−1.43373e11	−0.0378561
$625$	−4.76774e12	−1.24984
$626$	−4.55096e12	−1.18446
$627$	−1.93857e11	−0.0500929
$628$	−3.95293e10	−0.0101415
$629$	−7.37567e12	−1.87877
$630$	0	0
$631$	6.97874e12	1.75245	0.876223	−	0.481906i	$-0.160055\pi$
$631$	6.97874e12	1.75245	0.876223	+	0.481906i	$0.160055\pi$
$632$	1.57486e11	0.0392659
$633$	−5.45615e11	−0.135073
$634$	−1.62798e12	−0.400172
$635$	−1.11346e12	−0.271765
$636$	1.61730e11	0.0391953
$637$	0	0
$638$	−4.81312e12	−1.15010
$639$	−4.06964e11	−0.0965611
$640$	4.61424e11	0.108715
$641$	−2.99448e12	−0.700585	−0.350293	−	0.936640i	$-0.613918\pi$
$641$	−2.99448e12	−0.700585	−0.350293	+	0.936640i	$0.613918\pi$
$642$	1.96451e9	0.000456402 0
$643$	−1.46030e12	−0.336894	−0.168447	−	0.985711i	$-0.553875\pi$
$643$	−1.46030e12	−0.336894	−0.168447	+	0.985711i	$0.553875\pi$
$644$	0	0
$645$	−8.75693e11	−0.199220
$646$	−1.59240e12	−0.359754
$647$	−4.15901e12	−0.933084	−0.466542	−	0.884499i	$-0.654500\pi$
$647$	−4.15901e12	−0.933084	−0.466542	+	0.884499i	$0.654500\pi$
$648$	1.53980e12	0.343064
$649$	−6.97648e12	−1.54360
$650$	−2.50881e12	−0.551261
$651$	0	0
$652$	2.93036e12	0.635048
$653$	1.58494e12	0.341118	0.170559	−	0.985347i	$-0.445443\pi$
$653$	1.58494e12	0.341118	0.170559	+	0.985347i	$0.445443\pi$
$654$	1.61630e11	0.0345479
$655$	5.06663e12	1.07556
$656$	−5.03976e11	−0.106253
$657$	1.72424e11	0.0361039
$658$	0	0
$659$	−3.00036e12	−0.619711	−0.309855	−	0.950784i	$-0.600281\pi$
$659$	−3.00036e12	−0.619711	−0.309855	+	0.950784i	$0.600281\pi$
$660$	−4.38606e11	−0.0899759
$661$	−6.89840e12	−1.40554	−0.702768	−	0.711419i	$-0.748053\pi$
$661$	−6.89840e12	−1.40554	−0.702768	+	0.711419i	$0.748053\pi$
$662$	4.86345e12	0.984201
$663$	1.11947e12	0.225009
$664$	−2.27451e12	−0.454079
$665$	0	0
$666$	−4.49425e12	−0.885162
$667$	−4.56169e11	−0.0892400
$668$	4.37903e12	0.850911
$669$	−6.33347e11	−0.122243
$670$	5.54505e12	1.06309
$671$	8.17869e12	1.55752
$672$	0	0
$673$	−4.53756e12	−0.852618	−0.426309	−	0.904578i	$-0.640186\pi$
$673$	−4.53756e12	−0.852618	−0.426309	+	0.904578i	$0.640186\pi$
$674$	−2.75956e11	−0.0515076
$675$	−5.48285e11	−0.101658
$676$	3.55902e12	0.655496
$677$	−1.04279e13	−1.90787	−0.953936	−	0.300011i	$-0.903010\pi$
$677$	−1.04279e13	−1.90787	−0.953936	+	0.300011i	$0.903010\pi$
$678$	−6.57646e11	−0.119525
$679$	0	0
$680$	−3.60284e12	−0.646182
$681$	−1.04928e11	−0.0186952
$682$	3.61448e12	0.639759
$683$	4.02493e12	0.707726	0.353863	−	0.935297i	$-0.384868\pi$
$683$	4.02493e12	0.707726	0.353863	+	0.935297i	$0.384868\pi$
$684$	−9.70302e11	−0.169494
$685$	−1.32588e13	−2.30089
$686$	0	0
$687$	−5.84804e11	−0.100162
$688$	−2.38908e12	−0.406520
$689$	−7.07707e12	−1.19637
$690$	−4.15693e10	−0.00698156
$691$	−4.05726e12	−0.676989	−0.338494	−	0.940968i	$-0.609918\pi$
$691$	−4.05726e12	−0.676989	−0.338494	+	0.940968i	$0.609918\pi$
$692$	4.65756e11	0.0772113
$693$	0	0
$694$	5.06934e12	0.829534
$695$	9.29303e12	1.51086
$696$	2.41422e11	0.0389973
$697$	3.93510e12	0.631550
$698$	−1.53571e12	−0.244884
$699$	4.26118e11	0.0675122
$700$	0	0
$701$	2.14575e11	0.0335621	0.0167810	−	0.999859i	$-0.494658\pi$
$701$	2.14575e11	0.0335621	0.0167810	+	0.999859i	$0.494658\pi$
$702$	1.37110e12	0.213084
$703$	2.80338e12	0.432896
$704$	−1.19661e12	−0.183601
$705$	−4.38103e11	−0.0667922
$706$	4.19504e12	0.635499
$707$	0	0
$708$	3.49934e11	0.0523403
$709$	−8.55470e12	−1.27144	−0.635721	−	0.771919i	$-0.719297\pi$
$709$	−8.55470e12	−1.27144	−0.635721	+	0.771919i	$0.719297\pi$
$710$	5.74348e11	0.0848228
$711$	−7.49278e11	−0.109959
$712$	6.75508e11	0.0985077
$713$	3.42566e11	0.0496412
$714$	0	0
$715$	1.91927e13	2.74637
$716$	−6.04963e11	−0.0860241
$717$	5.99919e11	0.0847727
$718$	−1.73653e12	−0.243849
$719$	6.49482e12	0.906331	0.453166	−	0.891426i	$-0.350295\pi$
$719$	6.49482e12	0.906331	0.453166	+	0.891426i	$0.350295\pi$
$720$	−2.19533e12	−0.304442
$721$	0	0
$722$	−4.55776e12	−0.624214
$723$	1.17536e11	0.0159974
$724$	−4.23818e12	−0.573265
$725$	4.22453e12	0.567881
$726$	6.10210e11	0.0815200
$727$	−5.36028e12	−0.711677	−0.355838	−	0.934548i	$-0.615805\pi$
$727$	−5.36028e12	−0.711677	−0.355838	+	0.934548i	$0.615805\pi$
$728$	0	0
$729$	−7.17538e12	−0.940960
$730$	−2.43342e11	−0.0317150
$731$	1.86541e13	2.41628
$732$	−4.10236e11	−0.0528121
$733$	−3.46664e12	−0.443548	−0.221774	−	0.975098i	$-0.571185\pi$
$733$	−3.46664e12	−0.443548	−0.221774	+	0.975098i	$0.571185\pi$
$734$	−3.40057e12	−0.432434
$735$	0	0
$736$	−1.13410e11	−0.0142463
$737$	−1.43800e13	−1.79537
$738$	2.39779e12	0.297548
$739$	−4.24093e12	−0.523071	−0.261536	−	0.965194i	$-0.584229\pi$
$739$	−4.24093e12	−0.523071	−0.261536	+	0.965194i	$0.584229\pi$
$740$	6.34273e12	0.777559
$741$	−4.25493e11	−0.0518454
$742$	0	0
$743$	−7.87489e12	−0.947970	−0.473985	−	0.880533i	$-0.657185\pi$
$743$	−7.87489e12	−0.947970	−0.473985	+	0.880533i	$0.657185\pi$
$744$	−1.81299e11	−0.0216929
$745$	5.33905e10	0.00634982
$746$	−5.08529e12	−0.601161
$747$	1.08215e13	1.27159
$748$	9.34324e12	1.09129
$749$	0	0
$750$	−3.65706e11	−0.0422043
$751$	−1.10534e13	−1.26799	−0.633997	−	0.773336i	$-0.718587\pi$
$751$	−1.10534e13	−1.26799	−0.633997	+	0.773336i	$0.718587\pi$
$752$	−1.19524e12	−0.136293
$753$	−1.13858e12	−0.129058
$754$	−1.05643e13	−1.19033
$755$	1.40386e13	1.57239
$756$	0	0
$757$	−3.02707e12	−0.335035	−0.167518	−	0.985869i	$-0.553575\pi$
$757$	−3.02707e12	−0.335035	−0.167518	+	0.985869i	$0.553575\pi$
$758$	9.74904e12	1.07263
$759$	1.07802e11	0.0117906
$760$	1.36939e12	0.148890
$761$	1.31649e13	1.42294	0.711472	−	0.702714i	$-0.248029\pi$
$761$	1.31649e13	1.42294	0.711472	+	0.702714i	$0.248029\pi$
$762$	−1.44836e11	−0.0155625
$763$	0	0
$764$	−8.61515e11	−0.0914835
$765$	1.71414e13	1.80955
$766$	−5.44101e12	−0.571018
$767$	−1.53126e13	−1.59760
$768$	6.00208e10	0.00622553
$769$	5.52244e12	0.569460	0.284730	−	0.958608i	$-0.408096\pi$
$769$	5.52244e12	0.569460	0.284730	+	0.958608i	$0.408096\pi$
$770$	0	0
$771$	−5.32487e11	−0.0542706
$772$	−1.20930e12	−0.122534
$773$	1.98588e12	0.200053	0.100027	−	0.994985i	$-0.468107\pi$
$773$	1.98588e12	0.200053	0.100027	+	0.994985i	$0.468107\pi$
$774$	1.13666e13	1.13840
$775$	−3.17247e12	−0.315892
$776$	−6.43176e11	−0.0636725
$777$	0	0
$778$	1.20781e13	1.18193
$779$	−1.49567e12	−0.145518
$780$	−9.62689e11	−0.0931238
$781$	−1.48946e12	−0.143251
$782$	8.85516e11	0.0846771
$783$	−2.30876e12	−0.219508
$784$	0	0
$785$	−2.65424e11	−0.0249474
$786$	6.59054e11	0.0615913
$787$	−1.41096e13	−1.31108	−0.655538	−	0.755162i	$-0.727558\pi$
$787$	−1.41096e13	−1.31108	−0.655538	+	0.755162i	$0.727558\pi$
$788$	−4.27473e12	−0.394949
$789$	−7.91641e11	−0.0727246
$790$	1.05746e12	0.0965919
$791$	0	0
$792$	5.69316e12	0.514150
$793$	1.79513e13	1.61201
$794$	4.31022e12	0.384863
$795$	1.08595e12	0.0964182
$796$	−6.70276e12	−0.591759
$797$	9.54651e12	0.838074	0.419037	−	0.907969i	$-0.362368\pi$
$797$	9.54651e12	0.838074	0.419037	+	0.907969i	$0.362368\pi$
$798$	0	0
$799$	9.33254e12	0.810101
$800$	1.05028e12	0.0906564
$801$	−3.21389e12	−0.275857
$802$	−5.69866e12	−0.486394
$803$	6.31058e11	0.0535611
$804$	7.21286e11	0.0608773
$805$	0	0
$806$	7.93337e12	0.662141
$807$	−1.98629e12	−0.164859
$808$	−6.66721e11	−0.0550292
$809$	1.84755e13	1.51645	0.758225	−	0.651993i	$-0.226067\pi$
$809$	1.84755e13	1.51645	0.758225	+	0.651993i	$0.226067\pi$
$810$	1.03391e13	0.843919
$811$	1.08163e13	0.877981	0.438991	−	0.898492i	$-0.355336\pi$
$811$	1.08163e13	0.877981	0.438991	+	0.898492i	$0.355336\pi$
$812$	0	0
$813$	5.20787e11	0.0418074
$814$	−1.64486e13	−1.31316
$815$	1.96762e13	1.56218
$816$	−4.68648e11	−0.0370034
$817$	−7.09016e12	−0.556746
$818$	1.39904e12	0.109255
$819$	0	0
$820$	−3.38400e12	−0.261377
$821$	−8.98463e12	−0.690170	−0.345085	−	0.938571i	$-0.612150\pi$
$821$	−8.98463e12	−0.690170	−0.345085	+	0.938571i	$0.612150\pi$
$822$	−1.72467e12	−0.131760
$823$	−2.09468e13	−1.59154	−0.795770	−	0.605599i	$-0.792934\pi$
$823$	−2.09468e13	−1.59154	−0.795770	+	0.605599i	$0.792934\pi$
$824$	−5.54621e12	−0.419106
$825$	−9.98338e11	−0.0750300
$826$	0	0
$827$	−7.58139e12	−0.563604	−0.281802	−	0.959473i	$-0.590932\pi$
$827$	−7.58139e12	−0.563604	−0.281802	+	0.959473i	$0.590932\pi$
$828$	5.39575e11	0.0398947
$829$	1.32905e13	0.977340	0.488670	−	0.872469i	$-0.337482\pi$
$829$	1.32905e13	0.977340	0.488670	+	0.872469i	$0.337482\pi$
$830$	−1.52724e13	−1.11701
$831$	2.19954e12	0.160002
$832$	−2.62642e12	−0.190024
$833$	0	0
$834$	1.20881e12	0.0865190
$835$	2.94034e13	2.09319
$836$	−3.55123e12	−0.251449
$837$	1.73379e12	0.122105
$838$	−7.13677e10	−0.00499924
$839$	−6.44356e12	−0.448949	−0.224474	−	0.974480i	$-0.572067\pi$
$839$	−6.44356e12	−0.448949	−0.224474	+	0.974480i	$0.572067\pi$
$840$	0	0
$841$	3.28177e12	0.226218
$842$	−1.49550e12	−0.102537
$843$	1.35119e12	0.0921497
$844$	−9.99504e12	−0.678021
$845$	2.38974e13	1.61248
$846$	5.68664e12	0.381671
$847$	0	0
$848$	2.96271e12	0.196747
$849$	2.78272e12	0.183817
$850$	−8.20065e12	−0.538844
$851$	−1.55893e12	−0.101893
$852$	7.47097e10	0.00485734
$853$	1.11447e13	0.720769	0.360384	−	0.932804i	$-0.382646\pi$
$853$	1.11447e13	0.720769	0.360384	+	0.932804i	$0.382646\pi$
$854$	0	0
$855$	−6.51519e12	−0.416946
$856$	3.59876e10	0.00229098
$857$	−5.91032e12	−0.374281	−0.187140	−	0.982333i	$-0.559922\pi$
$857$	−5.91032e12	−0.374281	−0.187140	+	0.982333i	$0.559922\pi$
$858$	2.49654e12	0.157270
$859$	1.78076e13	1.11593	0.557964	−	0.829865i	$-0.311583\pi$
$859$	1.78076e13	1.11593	0.557964	+	0.829865i	$0.311583\pi$
$860$	−1.60417e13	−1.00002
$861$	0	0
$862$	−7.98598e12	−0.492658
$863$	1.43048e13	0.877873	0.438937	−	0.898518i	$-0.355355\pi$
$863$	1.43048e13	0.877873	0.438937	+	0.898518i	$0.355355\pi$
$864$	−5.73988e11	−0.0350422
$865$	3.12736e12	0.189935
$866$	−1.66669e13	−1.00699
$867$	2.00202e12	0.120333
$868$	0	0
$869$	−2.74230e12	−0.163127
$870$	1.62105e12	0.0959312
$871$	−3.15624e13	−1.85818
$872$	2.96087e12	0.173418
$873$	3.06007e12	0.178306
$874$	−3.36572e11	−0.0195108
$875$	0	0
$876$	−3.16533e10	−0.00181614
$877$	6.03456e12	0.344467	0.172233	−	0.985056i	$-0.444902\pi$
$877$	6.03456e12	0.344467	0.172233	+	0.985056i	$0.444902\pi$
$878$	3.20447e12	0.181983
$879$	−1.01787e12	−0.0575096
$880$	−8.03475e12	−0.451648
$881$	−1.54875e12	−0.0866142	−0.0433071	−	0.999062i	$-0.513789\pi$
$881$	−1.54875e12	−0.0866142	−0.0433071	+	0.999062i	$0.513789\pi$
$882$	0	0
$883$	−2.01052e13	−1.11297	−0.556487	−	0.830857i	$-0.687851\pi$
$883$	−2.01052e13	−1.11297	−0.556487	+	0.830857i	$0.687851\pi$
$884$	2.05073e13	1.12947
$885$	2.34967e12	0.128754
$886$	3.61764e12	0.197230
$887$	2.15625e13	1.16962	0.584809	−	0.811171i	$-0.301170\pi$
$887$	2.15625e13	1.16962	0.584809	+	0.811171i	$0.301170\pi$
$888$	8.25046e11	0.0445266
$889$	0	0
$890$	4.53576e12	0.242323
$891$	−2.68124e13	−1.42523
$892$	−1.16022e13	−0.613617
$893$	−3.54716e12	−0.186659
$894$	6.94490e9	0.000363620 0
$895$	−4.06208e12	−0.211614
$896$	0	0
$897$	2.36612e11	0.0122031
$898$	−1.92143e13	−0.986008
$899$	−1.33588e13	−0.682103
$900$	−4.99694e12	−0.253871
$901$	−2.31331e13	−1.16943
$902$	8.77571e12	0.441421
$903$	0	0
$904$	−1.20473e13	−0.599974
$905$	−2.84577e13	−1.41020
$906$	1.82610e12	0.0900425
$907$	−2.21054e12	−0.108459	−0.0542295	−	0.998528i	$-0.517270\pi$
$907$	−2.21054e12	−0.108459	−0.0542295	+	0.998528i	$0.517270\pi$
$908$	−1.92216e12	−0.0938432
$909$	3.17208e12	0.154102
$910$	0	0
$911$	7.06459e11	0.0339824	0.0169912	−	0.999856i	$-0.494591\pi$
$911$	7.06459e11	0.0339824	0.0169912	+	0.999856i	$0.494591\pi$
$912$	1.78126e11	0.00852612
$913$	3.96059e13	1.88643
$914$	5.27564e12	0.250045
$915$	−2.75457e12	−0.129915
$916$	−1.07129e13	−0.502781
$917$	0	0
$918$	4.48176e12	0.208284
$919$	1.65966e13	0.767537	0.383768	−	0.923429i	$-0.374626\pi$
$919$	1.65966e13	0.767537	0.383768	+	0.923429i	$0.374626\pi$
$920$	−7.61502e11	−0.0350450
$921$	1.64655e12	0.0754063
$922$	−2.22285e13	−1.01303
$923$	−3.26919e12	−0.148263
$924$	0	0
$925$	1.44371e13	0.648398
$926$	−1.10100e9	−4.92081e−5 0
$927$	2.63874e13	1.17365
$928$	4.42257e12	0.195753
$929$	−1.78781e13	−0.787501	−0.393751	−	0.919217i	$-0.628823\pi$
$929$	−1.78781e13	−0.787501	−0.393751	+	0.919217i	$0.628823\pi$
$930$	−1.21735e12	−0.0533632
$931$	0	0
$932$	7.80599e12	0.338888
$933$	−2.53485e12	−0.109518
$934$	1.72624e13	0.742234
$935$	6.27361e13	2.68451
$936$	1.24958e13	0.532137
$937$	−4.36868e13	−1.85149	−0.925747	−	0.378143i	$-0.876563\pi$
$937$	−4.36868e13	−1.85149	−0.925747	+	0.378143i	$0.876563\pi$
$938$	0	0
$939$	−3.97489e12	−0.166852
$940$	−8.02555e12	−0.335274
$941$	−6.40704e12	−0.266381	−0.133191	−	0.991090i	$-0.542522\pi$
$941$	−6.40704e12	−0.266381	−0.133191	+	0.991090i	$0.542522\pi$
$942$	−3.45256e10	−0.00142861
$943$	8.31728e11	0.0342514
$944$	6.41039e12	0.262730
$945$	0	0
$946$	4.16009e13	1.68885
$947$	−1.04173e13	−0.420901	−0.210451	−	0.977604i	$-0.567493\pi$
$947$	−1.04173e13	−0.420901	−0.210451	+	0.977604i	$0.567493\pi$
$948$	1.37551e11	0.00553129
$949$	1.38510e12	0.0554349
$950$	3.11695e12	0.124158
$951$	−1.42190e12	−0.0563713
$952$	0	0
$953$	6.40900e12	0.251694	0.125847	−	0.992050i	$-0.459835\pi$
$953$	6.40900e12	0.251694	0.125847	+	0.992050i	$0.459835\pi$
$954$	−1.40958e13	−0.550963
$955$	−5.78473e12	−0.225044
$956$	1.09898e13	0.425530
$957$	−4.20387e12	−0.162011
$958$	9.98096e12	0.382849
$959$	0	0
$960$	4.03016e11	0.0153144
$961$	−1.64076e13	−0.620570
$962$	−3.61028e13	−1.35910
$963$	−1.71220e11	−0.00641557
$964$	2.15313e12	0.0803015
$965$	−8.12000e12	−0.301428
$966$	0	0
$967$	1.24456e12	0.0457718	0.0228859	−	0.999738i	$-0.492715\pi$
$967$	1.24456e12	0.0457718	0.0228859	+	0.999738i	$0.492715\pi$
$968$	1.11783e13	0.409202
$969$	−1.39083e12	−0.0506776
$970$	−4.31867e12	−0.156631
$971$	−3.77827e13	−1.36398	−0.681988	−	0.731364i	$-0.738884\pi$
$971$	−3.77827e13	−1.36398	−0.681988	+	0.731364i	$0.738884\pi$
$972$	4.10314e12	0.147441
$973$	0	0
$974$	−2.39508e13	−0.852717
$975$	−2.19124e12	−0.0776549
$976$	−7.51504e12	−0.265099
$977$	−1.27808e13	−0.448780	−0.224390	−	0.974499i	$-0.572039\pi$
$977$	−1.27808e13	−0.448780	−0.224390	+	0.974499i	$0.572039\pi$
$978$	2.55943e12	0.0894577
$979$	−1.17626e13	−0.409242
$980$	0	0
$981$	−1.40871e13	−0.485635
$982$	1.10568e13	0.379427
$983$	2.29492e13	0.783929	0.391964	−	0.919980i	$-0.371796\pi$
$983$	2.29492e13	0.783929	0.391964	+	0.919980i	$0.371796\pi$
$984$	−4.40182e11	−0.0149677
$985$	−2.87031e13	−0.971551
$986$	−3.45319e13	−1.16352
$987$	0	0
$988$	−7.79454e12	−0.260246
$989$	3.94277e12	0.131044
$990$	3.82273e13	1.26478
$991$	2.75191e13	0.906363	0.453182	−	0.891418i	$-0.350289\pi$
$991$	2.75191e13	0.906363	0.453182	+	0.891418i	$0.350289\pi$
$992$	−3.32119e12	−0.108891
$993$	4.24782e12	0.138642
$994$	0	0
$995$	−4.50063e13	−1.45569
$996$	−1.98659e12	−0.0639650
$997$	−2.83723e13	−0.909423	−0.454712	−	0.890639i	$-0.650258\pi$
$997$	−2.83723e13	−0.909423	−0.454712	+	0.890639i	$0.650258\pi$
$998$	2.19987e13	0.701955
$999$	−7.89004e12	−0.250631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.i.1.2		3
7.2	even	3		98.10.c.k.67.2		6
7.3	odd	6		14.10.c.a.9.2	✓	6
7.4	even	3		98.10.c.k.79.2		6
7.5	odd	6		14.10.c.a.11.2	yes	6
7.6	odd	2		98.10.a.j.1.2		3
21.5	even	6		126.10.g.f.109.1		6
21.17	even	6		126.10.g.f.37.1		6
28.3	even	6		112.10.i.b.65.2		6
28.19	even	6		112.10.i.b.81.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.a.9.2	✓	6	7.3	odd	6
14.10.c.a.11.2	yes	6	7.5	odd	6
98.10.a.i.1.2		3	1.1	even	1	trivial
98.10.a.j.1.2		3	7.6	odd	2
98.10.c.k.67.2		6	7.2	even	3
98.10.c.k.79.2		6	7.4	even	3
112.10.i.b.65.2		6	28.3	even	6
112.10.i.b.81.2		6	28.19	even	6
126.10.g.f.37.1		6	21.17	even	6
126.10.g.f.109.1		6	21.5	even	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +13.9747 q^{3} +256.000 q^{4} +1718.94 q^{5} +223.595 q^{6} +4096.00 q^{8} -19487.7 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} +13.9747 q^{3} +256.000 q^{4} +1718.94 q^{5} +223.595 q^{6} +4096.00 q^{8} -19487.7 q^{9} +27503.0 q^{10} -71323.4 q^{11} +3577.52 q^{12} -156547. q^{13} +24021.6 q^{15} +65536.0 q^{16} -511711. q^{17} -311803. q^{18} +194494. q^{19} +440048. q^{20} -1.14118e6 q^{22} -108156. q^{23} +57240.3 q^{24} +1.00162e6 q^{25} -2.50475e6 q^{26} -547398. q^{27} +4.21769e6 q^{29} +384346. q^{30} -3.16733e6 q^{31} +1.04858e6 q^{32} -996722. q^{33} -8.18738e6 q^{34} -4.98885e6 q^{36} +1.44137e7 q^{37} +3.11190e6 q^{38} -2.18769e6 q^{39} +7.04077e6 q^{40} -7.69007e6 q^{41} -3.64544e7 q^{43} -1.82588e7 q^{44} -3.34982e7 q^{45} -1.73050e6 q^{46} -1.82379e7 q^{47} +915845. q^{48} +1.60259e7 q^{50} -7.15100e6 q^{51} -4.00760e7 q^{52} +4.52073e7 q^{53} -8.75837e6 q^{54} -1.22601e8 q^{55} +2.71799e6 q^{57} +6.74831e7 q^{58} +9.78147e7 q^{59} +6.14953e6 q^{60} -1.14670e8 q^{61} -5.06773e7 q^{62} +1.67772e7 q^{64} -2.69094e8 q^{65} -1.59476e7 q^{66} +2.01616e8 q^{67} -1.30998e8 q^{68} -1.51145e6 q^{69} +2.08831e7 q^{71} -7.98217e7 q^{72} -8.84783e6 q^{73} +2.30620e8 q^{74} +1.39973e7 q^{75} +4.97905e7 q^{76} -3.50031e7 q^{78} +3.84488e7 q^{79} +1.12652e8 q^{80} +3.75927e8 q^{81} -1.23041e8 q^{82} -5.55300e8 q^{83} -8.79600e8 q^{85} -5.83270e8 q^{86} +5.89409e7 q^{87} -2.92141e8 q^{88} +1.64919e8 q^{89} -5.35970e8 q^{90} -2.76880e7 q^{92} -4.42624e7 q^{93} -2.91806e8 q^{94} +3.34323e8 q^{95} +1.46535e7 q^{96} -1.57025e8 q^{97} +1.38993e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 48 q^{2} - 233 q^{3} + 768 q^{4} - 733 q^{5} - 3728 q^{6} + 12288 q^{8} + 15058 q^{9}+O(q^{10}) \) 3 * q + 48 * q^2 - 233 * q^3 + 768 * q^4 - 733 * q^5 - 3728 * q^6 + 12288 * q^8 + 15058 * q^9	\( 3 q + 48 q^{2} - 233 q^{3} + 768 q^{4} - 733 q^{5} - 3728 q^{6} + 12288 q^{8} + 15058 q^{9} - 11728 q^{10} - 7339 q^{11} - 59648 q^{12} - 98518 q^{13} + 369119 q^{15} + 196608 q^{16} - 306665 q^{17} + 240928 q^{18} - 377991 q^{19} - 187648 q^{20} - 117424 q^{22} + 2267255 q^{23} - 954368 q^{24} + 142612 q^{25} - 1576288 q^{26} - 10674179 q^{27} - 6542978 q^{29} + 5905904 q^{30} - 6654517 q^{31} + 3145728 q^{32} + 3747977 q^{33} - 4906640 q^{34} + 3854848 q^{36} + 22287969 q^{37} - 6047856 q^{38} - 3151974 q^{39} - 3002368 q^{40} - 34048098 q^{41} - 62824140 q^{43} - 1878784 q^{44} - 86300638 q^{45} + 36276080 q^{46} - 52703019 q^{47} - 15269888 q^{48} + 2281792 q^{50} - 97736333 q^{51} - 25220608 q^{52} + 12091125 q^{53} - 170786864 q^{54} - 188717699 q^{55} - 79258835 q^{57} - 104687648 q^{58} - 12949897 q^{59} + 94494464 q^{60} - 160252153 q^{61} - 106472272 q^{62} + 50331648 q^{64} - 334191270 q^{65} + 59967632 q^{66} + 480890225 q^{67} - 78506240 q^{68} - 565616581 q^{69} - 37210720 q^{71} + 61677568 q^{72} + 251382283 q^{73} + 356607504 q^{74} + 16322324 q^{75} - 96765696 q^{76} - 50431584 q^{78} - 286494785 q^{79} - 48037888 q^{80} + 2165894587 q^{81} - 544769568 q^{82} - 1147591172 q^{83} - 1194592537 q^{85} - 1005186240 q^{86} + 1412199358 q^{87} - 30060544 q^{88} - 901243845 q^{89} - 1380810208 q^{90} + 580417280 q^{92} - 710456889 q^{93} - 843248304 q^{94} + 887366177 q^{95} - 244318208 q^{96} - 314853938 q^{97} - 628109434 q^{99}+O(q^{100}) \) 3 * q + 48 * q^2 - 233 * q^3 + 768 * q^4 - 733 * q^5 - 3728 * q^6 + 12288 * q^8 + 15058 * q^9 - 11728 * q^10 - 7339 * q^11 - 59648 * q^12 - 98518 * q^13 + 369119 * q^15 + 196608 * q^16 - 306665 * q^17 + 240928 * q^18 - 377991 * q^19 - 187648 * q^20 - 117424 * q^22 + 2267255 * q^23 - 954368 * q^24 + 142612 * q^25 - 1576288 * q^26 - 10674179 * q^27 - 6542978 * q^29 + 5905904 * q^30 - 6654517 * q^31 + 3145728 * q^32 + 3747977 * q^33 - 4906640 * q^34 + 3854848 * q^36 + 22287969 * q^37 - 6047856 * q^38 - 3151974 * q^39 - 3002368 * q^40 - 34048098 * q^41 - 62824140 * q^43 - 1878784 * q^44 - 86300638 * q^45 + 36276080 * q^46 - 52703019 * q^47 - 15269888 * q^48 + 2281792 * q^50 - 97736333 * q^51 - 25220608 * q^52 + 12091125 * q^53 - 170786864 * q^54 - 188717699 * q^55 - 79258835 * q^57 - 104687648 * q^58 - 12949897 * q^59 + 94494464 * q^60 - 160252153 * q^61 - 106472272 * q^62 + 50331648 * q^64 - 334191270 * q^65 + 59967632 * q^66 + 480890225 * q^67 - 78506240 * q^68 - 565616581 * q^69 - 37210720 * q^71 + 61677568 * q^72 + 251382283 * q^73 + 356607504 * q^74 + 16322324 * q^75 - 96765696 * q^76 - 50431584 * q^78 - 286494785 * q^79 - 48037888 * q^80 + 2165894587 * q^81 - 544769568 * q^82 - 1147591172 * q^83 - 1194592537 * q^85 - 1005186240 * q^86 + 1412199358 * q^87 - 30060544 * q^88 - 901243845 * q^89 - 1380810208 * q^90 + 580417280 * q^92 - 710456889 * q^93 - 843248304 * q^94 + 887366177 * q^95 - 244318208 * q^96 - 314853938 * q^97 - 628109434 * q^99

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