LMFDB - Embedded newform 49.14.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,14,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	49.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:	$52.5431551864$
Analytic rank:	$0$
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} - 5238x + 109872 $ x^3 - x^2 - 5238*x + 109872
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 7 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$23.2817$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+142.628 q^{2} +2125.59 q^{3} +12150.6 q^{4} +46903.4 q^{5} +303168. q^{6} +564608. q^{8} +2.92382e6 q^{9} +O(q^{10})$	\(q+142.628 q^{2} +2125.59 q^{3} +12150.6 q^{4} +46903.4 q^{5} +303168. q^{6} +564608. q^{8} +2.92382e6 q^{9} +6.68972e6 q^{10} -2.55738e6 q^{11} +2.58273e7 q^{12} -1.04520e7 q^{13} +9.96975e7 q^{15} -1.90092e7 q^{16} +1.58543e8 q^{17} +4.17017e8 q^{18} -3.16138e8 q^{19} +5.69906e8 q^{20} -3.64753e8 q^{22} -2.85822e8 q^{23} +1.20013e9 q^{24} +9.79229e8 q^{25} -1.49074e9 q^{26} +2.82596e9 q^{27} -2.45349e9 q^{29} +1.42196e10 q^{30} +3.82280e9 q^{31} -7.33650e9 q^{32} -5.43595e9 q^{33} +2.26126e10 q^{34} +3.55262e10 q^{36} -5.50455e9 q^{37} -4.50900e10 q^{38} -2.22166e10 q^{39} +2.64821e10 q^{40} +1.66721e10 q^{41} -3.18443e10 q^{43} -3.10738e10 q^{44} +1.37137e11 q^{45} -4.07661e10 q^{46} -2.02311e10 q^{47} -4.04057e10 q^{48} +1.39665e11 q^{50} +3.36997e11 q^{51} -1.26998e11 q^{52} +7.96490e10 q^{53} +4.03060e11 q^{54} -1.19950e11 q^{55} -6.71980e11 q^{57} -3.49936e11 q^{58} -3.65281e11 q^{59} +1.21139e12 q^{60} -2.52703e11 q^{61} +5.45236e11 q^{62} -8.90664e11 q^{64} -4.90234e11 q^{65} -7.75316e11 q^{66} +5.52124e11 q^{67} +1.92639e12 q^{68} -6.07541e11 q^{69} +8.14411e11 q^{71} +1.65081e12 q^{72} +1.53200e12 q^{73} -7.85100e11 q^{74} +2.08144e12 q^{75} -3.84127e12 q^{76} -3.16871e12 q^{78} +2.92952e12 q^{79} -8.91595e11 q^{80} +1.34533e12 q^{81} +2.37790e12 q^{82} +3.40105e12 q^{83} +7.43620e12 q^{85} -4.54188e12 q^{86} -5.21512e12 q^{87} -1.44392e12 q^{88} +2.92785e12 q^{89} +1.95595e13 q^{90} -3.47292e12 q^{92} +8.12571e12 q^{93} -2.88551e12 q^{94} -1.48280e13 q^{95} -1.55944e13 q^{96} -3.55436e12 q^{97} -7.47731e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 26 q^{2} + 1796 q^{3} + 17652 q^{4} + 24086 q^{5} + 288916 q^{6} - 560040 q^{8} - 136241 q^{9}+O(q^{10}) $ 3 * q + 26 * q^2 + 1796 * q^3 + 17652 * q^4 + 24086 * q^5 + 288916 * q^6 - 560040 * q^8 - 136241 * q^9	\( 3 q + 26 q^{2} + 1796 q^{3} + 17652 q^{4} + 24086 q^{5} + 288916 q^{6} - 560040 q^{8} - 136241 q^{9} + 11781480 q^{10} - 9339044 q^{11} + 28824376 q^{12} - 9219378 q^{13} + 95111824 q^{15} + 22016016 q^{16} + 161799306 q^{17} + 606492458 q^{18} - 351536172 q^{19} + 68483968 q^{20} - 82962528 q^{22} - 1258991568 q^{23} + 1339953360 q^{24} - 264033819 q^{25} + 592105696 q^{26} + 3831242840 q^{27} - 6748418342 q^{29} + 14249068640 q^{30} - 2961621120 q^{31} + 4217770336 q^{32} - 4066118848 q^{33} - 4547329068 q^{34} + 25822287476 q^{36} - 15165028062 q^{37} - 50788312340 q^{38} - 27201019328 q^{39} + 44426886720 q^{40} + 30348543778 q^{41} - 80250536052 q^{43} - 36470495776 q^{44} + 174799138718 q^{45} + 104345248704 q^{46} + 169583042880 q^{47} - 57669949472 q^{48} + 126343684270 q^{50} + 396306220872 q^{51} - 374907668016 q^{52} + 120814398690 q^{53} + 447197642200 q^{54} - 70923686328 q^{55} - 648921990728 q^{57} + 414757064340 q^{58} - 443036517780 q^{59} + 1226525703872 q^{60} + 312164967918 q^{61} + 1947956406408 q^{62} - 2035141631424 q^{64} + 32969416900 q^{65} - 722965868768 q^{66} + 1398804629172 q^{67} + 5080798627464 q^{68} - 643239052416 q^{69} + 980341716024 q^{71} + 3386556390360 q^{72} - 964409395470 q^{73} + 1492955795748 q^{74} + 2476757628364 q^{75} - 3033316968696 q^{76} - 3253765187344 q^{78} + 5421189462624 q^{79} - 179377360256 q^{80} + 5830367903443 q^{81} + 8267068838868 q^{82} + 5151799373700 q^{83} + 674264835492 q^{85} - 5617032798416 q^{86} - 5648416931128 q^{87} + 2215014098880 q^{88} + 15420753518162 q^{89} + 11482717432840 q^{90} - 16455265396992 q^{92} + 7009045069392 q^{93} - 18638542033128 q^{94} - 16359640125632 q^{95} - 17199777859264 q^{96} - 4897266340470 q^{97} + 2815692782188 q^{99}+O(q^{100}) \) 3 * q + 26 * q^2 + 1796 * q^3 + 17652 * q^4 + 24086 * q^5 + 288916 * q^6 - 560040 * q^8 - 136241 * q^9 + 11781480 * q^10 - 9339044 * q^11 + 28824376 * q^12 - 9219378 * q^13 + 95111824 * q^15 + 22016016 * q^16 + 161799306 * q^17 + 606492458 * q^18 - 351536172 * q^19 + 68483968 * q^20 - 82962528 * q^22 - 1258991568 * q^23 + 1339953360 * q^24 - 264033819 * q^25 + 592105696 * q^26 + 3831242840 * q^27 - 6748418342 * q^29 + 14249068640 * q^30 - 2961621120 * q^31 + 4217770336 * q^32 - 4066118848 * q^33 - 4547329068 * q^34 + 25822287476 * q^36 - 15165028062 * q^37 - 50788312340 * q^38 - 27201019328 * q^39 + 44426886720 * q^40 + 30348543778 * q^41 - 80250536052 * q^43 - 36470495776 * q^44 + 174799138718 * q^45 + 104345248704 * q^46 + 169583042880 * q^47 - 57669949472 * q^48 + 126343684270 * q^50 + 396306220872 * q^51 - 374907668016 * q^52 + 120814398690 * q^53 + 447197642200 * q^54 - 70923686328 * q^55 - 648921990728 * q^57 + 414757064340 * q^58 - 443036517780 * q^59 + 1226525703872 * q^60 + 312164967918 * q^61 + 1947956406408 * q^62 - 2035141631424 * q^64 + 32969416900 * q^65 - 722965868768 * q^66 + 1398804629172 * q^67 + 5080798627464 * q^68 - 643239052416 * q^69 + 980341716024 * q^71 + 3386556390360 * q^72 - 964409395470 * q^73 + 1492955795748 * q^74 + 2476757628364 * q^75 - 3033316968696 * q^76 - 3253765187344 * q^78 + 5421189462624 * q^79 - 179377360256 * q^80 + 5830367903443 * q^81 + 8267068838868 * q^82 + 5151799373700 * q^83 + 674264835492 * q^85 - 5617032798416 * q^86 - 5648416931128 * q^87 + 2215014098880 * q^88 + 15420753518162 * q^89 + 11482717432840 * q^90 - 16455265396992 * q^92 + 7009045069392 * q^93 - 18638542033128 * q^94 - 16359640125632 * q^95 - 17199777859264 * q^96 - 4897266340470 * q^97 + 2815692782188 * 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 $

$2$	142.628	1.57583	0.787913	−	0.615786i	$-0.211161\pi$
$2$	142.628	1.57583	0.787913	+	0.615786i	$0.211161\pi$
$3$	2125.59	1.68342	0.841708	−	0.539932i	$-0.181550\pi$
$3$	2125.59	1.68342	0.841708	+	0.539932i	$0.181550\pi$
$4$	12150.6	1.48323
$5$	46903.4	1.34245	0.671227	−	0.741252i	$-0.265767\pi$
$5$	46903.4	1.34245	0.671227	+	0.741252i	$0.265767\pi$
$6$	303168.	2.65277
$7$	0	0
$7$	0	0
$8$	564608.	0.761487
$9$	2.92382e6	1.83389
$10$	6.68972e6	2.11548
$11$	−2.55738e6	−0.435254	−0.217627	−	0.976032i	$-0.569832\pi$
$11$	−2.55738e6	−0.435254	−0.217627	+	0.976032i	$0.569832\pi$
$12$	2.58273e7	2.49689
$13$	−1.04520e7	−0.600574	−0.300287	−	0.953849i	$-0.597083\pi$
$13$	−1.04520e7	−0.600574	−0.300287	+	0.953849i	$0.597083\pi$
$14$	0	0
$15$	9.96975e7	2.25991
$16$	−1.90092e7	−0.283259
$17$	1.58543e8	1.59305	0.796524	−	0.604607i	$-0.206670\pi$
$17$	1.58543e8	1.59305	0.796524	+	0.604607i	$0.206670\pi$
$18$	4.17017e8	2.88990
$19$	−3.16138e8	−1.54162	−0.770812	−	0.637063i	$-0.780149\pi$
$19$	−3.16138e8	−1.54162	−0.770812	+	0.637063i	$0.780149\pi$
$20$	5.69906e8	1.99117
$21$	0	0
$22$	−3.64753e8	−0.685885
$23$	−2.85822e8	−0.402592	−0.201296	−	0.979530i	$-0.564515\pi$
$23$	−2.85822e8	−0.402592	−0.201296	+	0.979530i	$0.564515\pi$
$24$	1.20013e9	1.28190
$25$	9.79229e8	0.802184
$26$	−1.49074e9	−0.946401
$27$	2.82596e9	1.40379
$28$	0	0
$29$	−2.45349e9	−0.765945	−0.382973	−	0.923760i	$-0.625100\pi$
$29$	−2.45349e9	−0.765945	−0.382973	+	0.923760i	$0.625100\pi$
$30$	1.42196e10	3.56123
$31$	3.82280e9	0.773625	0.386812	−	0.922158i	$-0.373576\pi$
$31$	3.82280e9	0.773625	0.386812	+	0.922158i	$0.373576\pi$
$32$	−7.33650e9	−1.20785
$33$	−5.43595e9	−0.732714
$34$	2.26126e10	2.51037
$35$	0	0
$36$	3.55262e10	2.72008
$37$	−5.50455e9	−0.352704	−0.176352	−	0.984327i	$-0.556430\pi$
$37$	−5.50455e9	−0.352704	−0.176352	+	0.984327i	$0.556430\pi$
$38$	−4.50900e10	−2.42933
$39$	−2.22166e10	−1.01102
$40$	2.64821e10	1.02226
$41$	1.66721e10	0.548144	0.274072	−	0.961709i	$-0.411629\pi$
$41$	1.66721e10	0.548144	0.274072	+	0.961709i	$0.411629\pi$
$42$	0	0
$43$	−3.18443e10	−0.768223	−0.384112	−	0.923287i	$-0.625492\pi$
$43$	−3.18443e10	−0.768223	−0.384112	+	0.923287i	$0.625492\pi$
$44$	−3.10738e10	−0.645582
$45$	1.37137e11	2.46192
$46$	−4.07661e10	−0.634415
$47$	−2.02311e10	−0.273768	−0.136884	−	0.990587i	$-0.543709\pi$
$47$	−2.02311e10	−0.273768	−0.136884	+	0.990587i	$0.543709\pi$
$48$	−4.04057e10	−0.476842
$49$	0	0
$50$	1.39665e11	1.26410
$51$	3.36997e11	2.68176
$52$	−1.26998e11	−0.890790
$53$	7.96490e10	0.493613	0.246807	−	0.969065i	$-0.420619\pi$
$53$	7.96490e10	0.493613	0.246807	+	0.969065i	$0.420619\pi$
$54$	4.03060e11	2.21213
$55$	−1.19950e11	−0.584309
$56$	0	0
$57$	−6.71980e11	−2.59519
$58$	−3.49936e11	−1.20700
$59$	−3.65281e11	−1.12743	−0.563714	−	0.825970i	$-0.690628\pi$
$59$	−3.65281e11	−1.12743	−0.563714	+	0.825970i	$0.690628\pi$
$60$	1.21139e12	3.35197
$61$	−2.52703e11	−0.628009	−0.314004	−	0.949422i	$-0.601671\pi$
$61$	−2.52703e11	−0.628009	−0.314004	+	0.949422i	$0.601671\pi$
$62$	5.45236e11	1.21910
$63$	0	0
$64$	−8.90664e11	−1.62011
$65$	−4.90234e11	−0.806244
$66$	−7.75316e11	−1.15463
$67$	5.52124e11	0.745676	0.372838	−	0.927896i	$-0.378385\pi$
$67$	5.52124e11	0.745676	0.372838	+	0.927896i	$0.378385\pi$
$68$	1.92639e12	2.36286
$69$	−6.07541e11	−0.677730
$70$	0	0
$71$	8.14411e11	0.754509	0.377255	−	0.926110i	$-0.376868\pi$
$71$	8.14411e11	0.754509	0.377255	+	0.926110i	$0.376868\pi$
$72$	1.65081e12	1.39649
$73$	1.53200e12	1.18484	0.592422	−	0.805628i	$-0.298172\pi$
$73$	1.53200e12	1.18484	0.592422	+	0.805628i	$0.298172\pi$
$74$	−7.85100e11	−0.555801
$75$	2.08144e12	1.35041
$76$	−3.84127e12	−2.28658
$77$	0	0
$78$	−3.16871e12	−1.59319
$79$	2.92952e12	1.35588	0.677938	−	0.735119i	$-0.262874\pi$
$79$	2.92952e12	1.35588	0.677938	+	0.735119i	$0.262874\pi$
$80$	−8.91595e11	−0.380262
$81$	1.34533e12	0.529270
$82$	2.37790e12	0.863780
$83$	3.40105e12	1.14184	0.570920	−	0.821005i	$-0.306586\pi$
$83$	3.40105e12	1.14184	0.570920	+	0.821005i	$0.306586\pi$
$84$	0	0
$85$	7.43620e12	2.13859
$86$	−4.54188e12	−1.21059
$87$	−5.21512e12	−1.28941
$88$	−1.44392e12	−0.331440
$89$	2.92785e12	0.624474	0.312237	−	0.950004i	$-0.398922\pi$
$89$	2.92785e12	0.624474	0.312237	+	0.950004i	$0.398922\pi$
$90$	1.95595e13	3.87956
$91$	0	0
$92$	−3.47292e12	−0.597136
$93$	8.12571e12	1.30233
$94$	−2.88551e12	−0.431411
$95$	−1.48280e13	−2.06956
$96$	−1.55944e13	−2.03332
$97$	−3.55436e12	−0.433256	−0.216628	−	0.976254i	$-0.569506\pi$
$97$	−3.55436e12	−0.433256	−0.216628	+	0.976254i	$0.569506\pi$
$98$	0	0
$99$	−7.47731e12	−0.798209
$100$	1.18982e13	1.18982
$101$	8.77927e12	0.822942	0.411471	−	0.911423i	$-0.365015\pi$
$101$	8.77927e12	0.822942	0.411471	+	0.911423i	$0.365015\pi$
$102$	4.80651e13	4.22599
$103$	1.37349e13	1.13340	0.566701	−	0.823924i	$-0.308219\pi$
$103$	1.37349e13	1.13340	0.566701	+	0.823924i	$0.308219\pi$
$104$	−5.90127e12	−0.457329
$105$	0	0
$106$	1.13601e13	0.777849
$107$	2.11326e13	1.36131	0.680657	−	0.732602i	$-0.261694\pi$
$107$	2.11326e13	1.36131	0.680657	+	0.732602i	$0.261694\pi$
$108$	3.43372e13	2.08214
$109$	−2.83106e13	−1.61687	−0.808437	−	0.588583i	$-0.799686\pi$
$109$	−2.83106e13	−1.61687	−0.808437	+	0.588583i	$0.799686\pi$
$110$	−1.71082e13	−0.920770
$111$	−1.17004e13	−0.593748
$112$	0	0
$113$	−2.41000e13	−1.08895	−0.544475	−	0.838777i	$-0.683271\pi$
$113$	−2.41000e13	−1.08895	−0.544475	+	0.838777i	$0.683271\pi$
$114$	−9.58429e13	−4.08958
$115$	−1.34060e13	−0.540461
$116$	−2.98115e13	−1.13607
$117$	−3.05597e13	−1.10139
$118$	−5.20991e13	−1.77663
$119$	0	0
$120$	5.62901e13	1.72089
$121$	−2.79825e13	−0.810554
$122$	−3.60423e13	−0.989633
$123$	3.54380e13	0.922755
$124$	4.64494e13	1.14746
$125$	−1.13260e13	−0.265559
$126$	0	0
$127$	−3.92556e13	−0.830191	−0.415095	−	0.909778i	$-0.636252\pi$
$127$	−3.92556e13	−0.830191	−0.415095	+	0.909778i	$0.636252\pi$
$128$	−6.69327e13	−1.34516
$129$	−6.76881e13	−1.29324
$130$	−6.99208e13	−1.27050
$131$	−3.59881e13	−0.622150	−0.311075	−	0.950385i	$-0.600689\pi$
$131$	−3.59881e13	−0.622150	−0.311075	+	0.950385i	$0.600689\pi$
$132$	−6.60501e13	−1.08678
$133$	0	0
$134$	7.87481e13	1.17506
$135$	1.32547e14	1.88452
$136$	8.95146e13	1.21308
$137$	−1.19058e14	−1.53842	−0.769211	−	0.638995i	$-0.779351\pi$
$137$	−1.19058e14	−1.53842	−0.769211	+	0.638995i	$0.779351\pi$
$138$	−8.66521e13	−1.06798
$139$	−2.82105e13	−0.331753	−0.165876	−	0.986147i	$-0.553045\pi$
$139$	−2.82105e13	−0.331753	−0.165876	+	0.986147i	$0.553045\pi$
$140$	0	0
$141$	−4.30030e13	−0.460866
$142$	1.16157e14	1.18898
$143$	2.67297e13	0.261402
$144$	−5.55793e13	−0.519466
$145$	−1.15077e14	−1.02825
$146$	2.18506e14	1.86711
$147$	0	0
$148$	−6.68837e13	−0.523141
$149$	−9.09421e13	−0.680855	−0.340427	−	0.940271i	$-0.610572\pi$
$149$	−9.09421e13	−0.680855	−0.340427	+	0.940271i	$0.610572\pi$
$150$	2.96871e14	2.12801
$151$	2.27356e14	1.56084	0.780418	−	0.625258i	$-0.215006\pi$
$151$	2.27356e14	1.56084	0.780418	+	0.625258i	$0.215006\pi$
$152$	−1.78494e14	−1.17393
$153$	4.63550e14	2.92148
$154$	0	0
$155$	1.79302e14	1.03856
$156$	−2.69946e14	−1.49957
$157$	−1.65313e14	−0.880968	−0.440484	−	0.897761i	$-0.645193\pi$
$157$	−1.65313e14	−0.880968	−0.440484	+	0.897761i	$0.645193\pi$
$158$	4.17830e14	2.13662
$159$	1.69301e14	0.830957
$160$	−3.44107e14	−1.62149
$161$	0	0
$162$	1.91881e14	0.834037
$163$	2.09786e14	0.876107	0.438053	−	0.898949i	$-0.355668\pi$
$163$	2.09786e14	0.876107	0.438053	+	0.898949i	$0.355668\pi$
$164$	2.02576e14	0.813024
$165$	−2.54965e14	−0.983636
$166$	4.85084e14	1.79934
$167$	3.76960e14	1.34474	0.672370	−	0.740215i	$-0.265277\pi$
$167$	3.76960e14	1.34474	0.672370	+	0.740215i	$0.265277\pi$
$168$	0	0
$169$	−1.93631e14	−0.639311
$170$	1.06061e15	3.37005
$171$	−9.24330e14	−2.82717
$172$	−3.86929e14	−1.13945
$173$	−2.64470e14	−0.750027	−0.375013	−	0.927019i	$-0.622362\pi$
$173$	−2.64470e14	−0.750027	−0.375013	+	0.927019i	$0.622362\pi$
$174$	−7.43820e14	−2.03188
$175$	0	0
$176$	4.86137e13	0.123290
$177$	−7.76438e14	−1.89793
$178$	4.17592e14	0.984062
$179$	−6.08368e14	−1.38236	−0.691181	−	0.722682i	$-0.742909\pi$
$179$	−6.08368e14	−1.38236	−0.691181	+	0.722682i	$0.742909\pi$
$180$	1.66630e15	3.65159
$181$	−1.35548e14	−0.286537	−0.143269	−	0.989684i	$-0.545761\pi$
$181$	−1.35548e14	−0.286537	−0.143269	+	0.989684i	$0.545761\pi$
$182$	0	0
$183$	−5.37142e14	−1.05720
$184$	−1.61378e14	−0.306568
$185$	−2.58182e14	−0.473489
$186$	1.15895e15	2.05225
$187$	−4.05454e14	−0.693381
$188$	−2.45820e14	−0.406061
$189$	0	0
$190$	−2.11487e15	−3.26127
$191$	−4.40807e13	−0.0656949	−0.0328475	−	0.999460i	$-0.510458\pi$
$191$	−4.40807e13	−0.0656949	−0.0328475	+	0.999460i	$0.510458\pi$
$192$	−1.89319e15	−2.72732
$193$	1.12643e15	1.56885	0.784425	−	0.620224i	$-0.212958\pi$
$193$	1.12643e15	1.56885	0.784425	+	0.620224i	$0.212958\pi$
$194$	−5.06950e14	−0.682737
$195$	−1.04204e15	−1.35724
$196$	0	0
$197$	−3.37552e14	−0.411443	−0.205722	−	0.978611i	$-0.565954\pi$
$197$	−3.37552e14	−0.411443	−0.205722	+	0.978611i	$0.565954\pi$
$198$	−1.06647e15	−1.25784
$199$	1.07265e15	1.22437	0.612185	−	0.790715i	$-0.290291\pi$
$199$	1.07265e15	1.22437	0.612185	+	0.790715i	$0.290291\pi$
$200$	5.52881e14	0.610853
$201$	1.17359e15	1.25528
$202$	1.25217e15	1.29681
$203$	0	0
$204$	4.09473e15	3.97767
$205$	7.81978e14	0.735859
$206$	1.95898e15	1.78605
$207$	−8.35691e14	−0.738310
$208$	1.98683e14	0.170118
$209$	8.08485e14	0.670998
$210$	0	0
$211$	7.53958e14	0.588181	0.294091	−	0.955778i	$-0.404983\pi$
$211$	7.53958e14	0.588181	0.294091	+	0.955778i	$0.404983\pi$
$212$	9.67784e14	0.732142
$213$	1.73111e15	1.27015
$214$	3.01409e15	2.14520
$215$	−1.49361e15	−1.03130
$216$	1.59556e15	1.06897
$217$	0	0
$218$	−4.03787e15	−2.54791
$219$	3.25642e15	1.99459
$220$	−1.45747e15	−0.866665
$221$	−1.65709e15	−0.956743
$222$	−1.66880e15	−0.935644
$223$	−1.86136e14	−0.101356	−0.0506779	−	0.998715i	$-0.516138\pi$
$223$	−1.86136e14	−0.101356	−0.0506779	+	0.998715i	$0.516138\pi$
$224$	0	0
$225$	2.86309e15	1.47112
$226$	−3.43733e15	−1.71600
$227$	2.03298e15	0.986201	0.493100	−	0.869972i	$-0.335864\pi$
$227$	2.03298e15	0.986201	0.493100	+	0.869972i	$0.335864\pi$
$228$	−8.16498e15	−3.84927
$229$	−7.39258e14	−0.338739	−0.169370	−	0.985553i	$-0.554173\pi$
$229$	−7.39258e14	−0.338739	−0.169370	+	0.985553i	$0.554173\pi$
$230$	−1.91207e15	−0.851673
$231$	0	0
$232$	−1.38526e15	−0.583257
$233$	−7.64656e14	−0.313078	−0.156539	−	0.987672i	$-0.550034\pi$
$233$	−7.64656e14	−0.313078	−0.156539	+	0.987672i	$0.550034\pi$
$234$	−4.35865e15	−1.73560
$235$	−9.48907e14	−0.367521
$236$	−4.43839e15	−1.67224
$237$	6.22695e15	2.28250
$238$	0	0
$239$	2.95075e15	1.02411	0.512055	−	0.858953i	$-0.328885\pi$
$239$	2.95075e15	1.02411	0.512055	+	0.858953i	$0.328885\pi$
$240$	−1.89517e15	−0.640139
$241$	−4.67182e15	−1.53594	−0.767971	−	0.640484i	$-0.778734\pi$
$241$	−4.67182e15	−1.53594	−0.767971	+	0.640484i	$0.778734\pi$
$242$	−3.99108e15	−1.27729
$243$	−1.64587e15	−0.512808
$244$	−3.07049e15	−0.931481
$245$	0	0
$246$	5.05444e15	1.45410
$247$	3.30427e15	0.925859
$248$	2.15838e15	0.589105
$249$	7.22925e15	1.92219
$250$	−1.61540e15	−0.418475
$251$	−5.61936e15	−1.41843	−0.709214	−	0.704993i	$-0.750950\pi$
$251$	−5.61936e15	−1.41843	−0.709214	+	0.704993i	$0.750950\pi$
$252$	0	0
$253$	7.30956e14	0.175230
$254$	−5.59894e15	−1.30824
$255$	1.58063e16	3.60014
$256$	−2.25012e15	−0.499627
$257$	8.83366e15	1.91239	0.956193	−	0.292738i	$-0.0945664\pi$
$257$	8.83366e15	1.91239	0.956193	+	0.292738i	$0.0945664\pi$
$258$	−9.65419e15	−2.03792
$259$	0	0
$260$	−5.95664e15	−1.19584
$261$	−7.17357e15	−1.40466
$262$	−5.13289e15	−0.980400
$263$	−3.99118e15	−0.743685	−0.371842	−	0.928296i	$-0.621274\pi$
$263$	−3.99118e15	−0.743685	−0.371842	+	0.928296i	$0.621274\pi$
$264$	−3.06918e15	−0.557952
$265$	3.73581e15	0.662654
$266$	0	0
$267$	6.22342e15	1.05125
$268$	6.70865e15	1.10601
$269$	4.32644e14	0.0696211	0.0348106	−	0.999394i	$-0.488917\pi$
$269$	4.32644e14	0.0696211	0.0348106	+	0.999394i	$0.488917\pi$
$270$	1.89049e16	2.96968
$271$	1.03570e16	1.58830	0.794150	−	0.607722i	$-0.207917\pi$
$271$	1.03570e16	1.58830	0.794150	+	0.607722i	$0.207917\pi$
$272$	−3.01377e15	−0.451245
$273$	0	0
$274$	−1.69810e16	−2.42429
$275$	−2.50426e15	−0.349154
$276$	−7.38200e15	−1.00523
$277$	2.03537e15	0.270722	0.135361	−	0.990796i	$-0.456781\pi$
$277$	2.03537e15	0.270722	0.135361	+	0.990796i	$0.456781\pi$
$278$	−4.02359e15	−0.522785
$279$	1.11772e16	1.41874
$280$	0	0
$281$	7.82716e15	0.948447	0.474224	−	0.880404i	$-0.342729\pi$
$281$	7.82716e15	0.948447	0.474224	+	0.880404i	$0.342729\pi$
$282$	−6.13342e15	−0.726245
$283$	5.86025e15	0.678117	0.339058	−	0.940765i	$-0.389892\pi$
$283$	5.86025e15	0.678117	0.339058	+	0.940765i	$0.389892\pi$
$284$	9.89560e15	1.11911
$285$	−3.15182e16	−3.48393
$286$	3.81239e15	0.411925
$287$	0	0
$288$	−2.14506e16	−2.21507
$289$	1.52313e16	1.53780
$290$	−1.64132e16	−1.62034
$291$	−7.55512e15	−0.729351
$292$	1.86148e16	1.75740
$293$	−1.89116e16	−1.74618	−0.873092	−	0.487556i	$-0.837889\pi$
$293$	−1.89116e16	−1.74618	−0.873092	+	0.487556i	$0.837889\pi$
$294$	0	0
$295$	−1.71329e16	−1.51352
$296$	−3.10791e15	−0.268580
$297$	−7.22706e15	−0.611005
$298$	−1.29709e16	−1.07291
$299$	2.98741e15	0.241786
$300$	2.52908e16	2.00297
$301$	0	0
$302$	3.24273e16	2.45961
$303$	1.86611e16	1.38535
$304$	6.00952e15	0.436678
$305$	−1.18526e16	−0.843073
$306$	6.61151e16	4.60374
$307$	8.38573e15	0.571665	0.285832	−	0.958280i	$-0.407730\pi$
$307$	8.38573e15	0.571665	0.285832	+	0.958280i	$0.407730\pi$
$308$	0	0
$309$	2.91948e16	1.90799
$310$	2.55735e16	1.63658
$311$	−6.52334e15	−0.408816	−0.204408	−	0.978886i	$-0.565527\pi$
$311$	−6.52334e15	−0.408816	−0.204408	+	0.978886i	$0.565527\pi$
$312$	−1.25437e16	−0.769876
$313$	2.22060e16	1.33485	0.667425	−	0.744677i	$-0.267396\pi$
$313$	2.22060e16	1.33485	0.667425	+	0.744677i	$0.267396\pi$
$314$	−2.35782e16	−1.38825
$315$	0	0
$316$	3.55954e16	2.01108
$317$	−2.30356e16	−1.27501	−0.637507	−	0.770445i	$-0.720034\pi$
$317$	−2.30356e16	−1.27501	−0.637507	+	0.770445i	$0.720034\pi$
$318$	2.41470e16	1.30944
$319$	6.27452e15	0.333381
$320$	−4.17752e16	−2.17492
$321$	4.49193e16	2.29166
$322$	0	0
$323$	−5.01214e16	−2.45588
$324$	1.63466e16	0.785028
$325$	−1.02349e16	−0.481771
$326$	2.99213e16	1.38059
$327$	−6.01767e16	−2.72187
$328$	9.41320e15	0.417405
$329$	0	0
$330$	−3.63650e16	−1.55004
$331$	−4.29663e15	−0.179575	−0.0897875	−	0.995961i	$-0.528619\pi$
$331$	−4.29663e15	−0.179575	−0.0897875	+	0.995961i	$0.528619\pi$
$332$	4.13249e16	1.69361
$333$	−1.60943e16	−0.646822
$334$	5.37649e16	2.11908
$335$	2.58965e16	1.00104
$336$	0	0
$337$	3.52672e16	1.31153	0.655763	−	0.754967i	$-0.272347\pi$
$337$	3.52672e16	1.31153	0.655763	+	0.754967i	$0.272347\pi$
$338$	−2.76172e16	−1.00744
$339$	−5.12268e16	−1.83316
$340$	9.03545e16	3.17203
$341$	−9.77635e15	−0.336723
$342$	−1.31835e17	−4.45513
$343$	0	0
$344$	−1.79796e16	−0.584992
$345$	−2.84958e16	−0.909821
$346$	−3.77207e16	−1.18191
$347$	−1.24775e16	−0.383695	−0.191848	−	0.981425i	$-0.561448\pi$
$347$	−1.24775e16	−0.383695	−0.191848	+	0.981425i	$0.561448\pi$
$348$	−6.33670e16	−1.91249
$349$	5.21421e16	1.54463	0.772313	−	0.635242i	$-0.219100\pi$
$349$	5.21421e16	1.54463	0.772313	+	0.635242i	$0.219100\pi$
$350$	0	0
$351$	−2.95369e16	−0.843080
$352$	1.87622e16	0.525723
$353$	2.35467e16	0.647731	0.323865	−	0.946103i	$-0.395017\pi$
$353$	2.35467e16	0.647731	0.323865	+	0.946103i	$0.395017\pi$
$354$	−1.10741e17	−2.99081
$355$	3.81987e16	1.01289
$356$	3.55752e16	0.926238
$357$	0	0
$358$	−8.67701e16	−2.17836
$359$	6.41478e16	1.58150	0.790748	−	0.612142i	$-0.209692\pi$
$359$	6.41478e16	1.58150	0.790748	+	0.612142i	$0.209692\pi$
$360$	7.74287e16	1.87472
$361$	5.78902e16	1.37660
$362$	−1.93328e16	−0.451533
$363$	−5.94794e16	−1.36450
$364$	0	0
$365$	7.18563e16	1.59060
$366$	−7.66113e16	−1.66596
$367$	2.18188e16	0.466125	0.233062	−	0.972462i	$-0.425125\pi$
$367$	2.18188e16	0.466125	0.233062	+	0.972462i	$0.425125\pi$
$368$	5.43324e15	0.114038
$369$	4.87461e16	1.00524
$370$	−3.68239e16	−0.746137
$371$	0	0
$372$	9.87324e16	1.93166
$373$	5.19307e16	0.998428	0.499214	−	0.866479i	$-0.333622\pi$
$373$	5.19307e16	0.998428	0.499214	+	0.866479i	$0.333622\pi$
$374$	−5.78290e16	−1.09265
$375$	−2.40744e16	−0.447046
$376$	−1.14226e16	−0.208471
$377$	2.56439e16	0.460007
$378$	0	0
$379$	−2.67282e16	−0.463249	−0.231625	−	0.972805i	$-0.574404\pi$
$379$	−2.67282e16	−0.463249	−0.231625	+	0.972805i	$0.574404\pi$
$380$	−1.80169e17	−3.06963
$381$	−8.34415e16	−1.39756
$382$	−6.28713e15	−0.103524
$383$	−7.05610e16	−1.14228	−0.571140	−	0.820852i	$-0.693499\pi$
$383$	−7.05610e16	−1.14228	−0.571140	+	0.820852i	$0.693499\pi$
$384$	−1.42272e17	−2.26446
$385$	0	0
$386$	1.60660e17	2.47224
$387$	−9.31070e16	−1.40884
$388$	−4.31877e16	−0.642619
$389$	−9.17294e16	−1.34226	−0.671129	−	0.741340i	$-0.734191\pi$
$389$	−9.17294e16	−1.34226	−0.671129	+	0.741340i	$0.734191\pi$
$390$	−1.48623e17	−2.13878
$391$	−4.53150e16	−0.641348
$392$	0	0
$393$	−7.64959e16	−1.04734
$394$	−4.81442e16	−0.648363
$395$	1.37404e17	1.82020
$396$	−9.08540e16	−1.18393
$397$	6.36656e16	0.816143	0.408072	−	0.912950i	$-0.366201\pi$
$397$	6.36656e16	0.816143	0.408072	+	0.912950i	$0.366201\pi$
$398$	1.52989e17	1.92939
$399$	0	0
$400$	−1.86143e16	−0.227226
$401$	1.37375e17	1.64995	0.824974	−	0.565170i	$-0.191189\pi$
$401$	1.37375e17	1.64995	0.824974	+	0.565170i	$0.191189\pi$
$402$	1.67386e17	1.97811
$403$	−3.99558e16	−0.464619
$404$	1.06674e17	1.22061
$405$	6.31007e16	0.710520
$406$	0	0
$407$	1.40772e16	0.153516
$408$	1.90272e17	2.04213
$409$	−8.04679e16	−0.850004	−0.425002	−	0.905192i	$-0.639727\pi$
$409$	−8.04679e16	−0.850004	−0.425002	+	0.905192i	$0.639727\pi$
$410$	1.11532e17	1.15959
$411$	−2.53069e17	−2.58981
$412$	1.66888e17	1.68110
$413$	0	0
$414$	−1.19193e17	−1.16345
$415$	1.59521e17	1.53287
$416$	7.66810e16	0.725406
$417$	−5.99640e16	−0.558478
$418$	1.15312e17	1.05738
$419$	2.51544e15	0.0227103	0.0113552	−	0.999936i	$-0.496385\pi$
$419$	2.51544e15	0.0227103	0.0113552	+	0.999936i	$0.496385\pi$
$420$	0	0
$421$	7.71737e16	0.675516	0.337758	−	0.941233i	$-0.390331\pi$
$421$	7.71737e16	0.675516	0.337758	+	0.941233i	$0.390331\pi$
$422$	1.07535e17	0.926872
$423$	−5.91520e16	−0.502062
$424$	4.49705e16	0.375880
$425$	1.55250e17	1.27792
$426$	2.46903e17	2.00154
$427$	0	0
$428$	2.56774e17	2.01914
$429$	5.68164e16	0.440049
$430$	−2.13030e17	−1.62516
$431$	−5.33515e16	−0.400908	−0.200454	−	0.979703i	$-0.564242\pi$
$431$	−5.33515e16	−0.400908	−0.200454	+	0.979703i	$0.564242\pi$
$432$	−5.37192e16	−0.397635
$433$	−1.54954e17	−1.12988	−0.564938	−	0.825133i	$-0.691100\pi$
$433$	−1.54954e17	−1.12988	−0.564938	+	0.825133i	$0.691100\pi$
$434$	0	0
$435$	−2.44607e17	−1.73097
$436$	−3.43991e17	−2.39820
$437$	9.03592e16	0.620645
$438$	4.64455e17	3.14312
$439$	7.79267e15	0.0519598	0.0259799	−	0.999662i	$-0.491729\pi$
$439$	7.79267e15	0.0519598	0.0259799	+	0.999662i	$0.491729\pi$
$440$	−6.77247e16	−0.444944
$441$	0	0
$442$	−2.36346e17	−1.50766
$443$	−1.80572e17	−1.13508	−0.567540	−	0.823346i	$-0.692105\pi$
$443$	−1.80572e17	−1.13508	−0.567540	+	0.823346i	$0.692105\pi$
$444$	−1.42167e17	−0.880665
$445$	1.37326e17	0.838327
$446$	−2.65481e16	−0.159719
$447$	−1.93306e17	−1.14616
$448$	0	0
$449$	8.37235e16	0.482221	0.241111	−	0.970498i	$-0.422488\pi$
$449$	8.37235e16	0.482221	0.241111	+	0.970498i	$0.422488\pi$
$450$	4.08355e17	2.31823
$451$	−4.26369e16	−0.238582
$452$	−2.92830e17	−1.61516
$453$	4.83267e17	2.62754
$454$	2.89959e17	1.55408
$455$	0	0
$456$	−3.79406e17	−1.97621
$457$	−2.98139e17	−1.53096	−0.765481	−	0.643459i	$-0.777499\pi$
$457$	−2.98139e17	−1.53096	−0.765481	+	0.643459i	$0.777499\pi$
$458$	−1.05439e17	−0.533794
$459$	4.48036e17	2.23630
$460$	−1.62892e17	−0.801628
$461$	−1.72176e17	−0.835442	−0.417721	−	0.908575i	$-0.637171\pi$
$461$	−1.72176e17	−0.835442	−0.417721	+	0.908575i	$0.637171\pi$
$462$	0	0
$463$	2.90301e17	1.36953	0.684766	−	0.728763i	$-0.259904\pi$
$463$	2.90301e17	1.36953	0.684766	+	0.728763i	$0.259904\pi$
$464$	4.66389e16	0.216961
$465$	3.81124e17	1.74832
$466$	−1.09061e17	−0.493357
$467$	1.37166e16	0.0611908	0.0305954	−	0.999532i	$-0.490260\pi$
$467$	1.37166e16	0.0611908	0.0305954	+	0.999532i	$0.490260\pi$
$468$	−3.71319e17	−1.63361
$469$	0	0
$470$	−1.35340e17	−0.579150
$471$	−3.51389e17	−1.48304
$472$	−2.06241e17	−0.858522
$473$	8.14381e16	0.334372
$474$	8.88135e17	3.59683
$475$	−3.09571e17	−1.23667
$476$	0	0
$477$	2.32879e17	0.905234
$478$	4.20858e17	1.61382
$479$	2.17104e17	0.821271	0.410636	−	0.911800i	$-0.365307\pi$
$479$	2.17104e17	0.821271	0.410636	+	0.911800i	$0.365307\pi$
$480$	−7.31431e17	−2.72964
$481$	5.75334e16	0.211825
$482$	−6.66330e17	−2.42038
$483$	0	0
$484$	−3.40005e17	−1.20224
$485$	−1.66712e17	−0.581627
$486$	−2.34746e17	−0.808096
$487$	−4.38869e17	−1.49072	−0.745360	−	0.666662i	$-0.767723\pi$
$487$	−4.38869e17	−1.49072	−0.745360	+	0.666662i	$0.767723\pi$
$488$	−1.42678e17	−0.478220
$489$	4.45919e17	1.47485
$490$	0	0
$491$	−5.71580e17	−1.84097	−0.920486	−	0.390776i	$-0.872207\pi$
$491$	−5.71580e17	−1.84097	−0.920486	+	0.390776i	$0.872207\pi$
$492$	4.30594e17	1.36866
$493$	−3.88984e17	−1.22019
$494$	4.71280e17	1.45899
$495$	−3.50712e17	−1.07156
$496$	−7.26682e16	−0.219136
$497$	0	0
$498$	1.03109e18	3.02904
$499$	1.18330e17	0.343116	0.171558	−	0.985174i	$-0.445120\pi$
$499$	1.18330e17	0.343116	0.171558	+	0.985174i	$0.445120\pi$
$500$	−1.37618e17	−0.393885
$501$	8.01263e17	2.26376
$502$	−8.01475e17	−2.23520
$503$	5.92101e17	1.63006	0.815030	−	0.579418i	$-0.196720\pi$
$503$	5.92101e17	1.63006	0.815030	+	0.579418i	$0.196720\pi$
$504$	0	0
$505$	4.11778e17	1.10476
$506$	1.04254e17	0.276132
$507$	−4.11581e17	−1.07623
$508$	−4.76980e17	−1.23136
$509$	−2.51994e17	−0.642279	−0.321140	−	0.947032i	$-0.604066\pi$
$509$	−2.51994e17	−0.642279	−0.321140	+	0.947032i	$0.604066\pi$
$510$	2.25442e18	5.67320
$511$	0	0
$512$	2.27383e17	0.557833
$513$	−8.93394e17	−2.16411
$514$	1.25992e18	3.01359
$515$	6.44215e17	1.52154
$516$	−8.22452e17	−1.91817
$517$	5.17386e16	0.119159
$518$	0	0
$519$	−5.62155e17	−1.26261
$520$	−2.76790e17	−0.613944
$521$	−1.87770e17	−0.411321	−0.205661	−	0.978623i	$-0.565934\pi$
$521$	−1.87770e17	−0.411321	−0.205661	+	0.978623i	$0.565934\pi$
$522$	−1.02315e18	−2.21350
$523$	5.15934e17	1.10238	0.551192	−	0.834378i	$-0.314173\pi$
$523$	5.15934e17	1.10238	0.551192	+	0.834378i	$0.314173\pi$
$524$	−4.37277e17	−0.922791
$525$	0	0
$526$	−5.69252e17	−1.17192
$527$	6.06077e17	1.23242
$528$	1.03333e17	0.207548
$529$	−4.22342e17	−0.837920
$530$	5.32829e17	1.04423
$531$	−1.06801e18	−2.06758
$532$	0	0
$533$	−1.74256e17	−0.329201
$534$	8.87631e17	1.65659
$535$	9.91192e17	1.82750
$536$	3.11734e17	0.567822
$537$	−1.29314e18	−2.32709
$538$	6.17070e16	0.109711
$539$	0	0
$540$	1.61053e18	2.79518
$541$	1.53819e17	0.263771	0.131886	−	0.991265i	$-0.457897\pi$
$541$	1.53819e17	0.263771	0.131886	+	0.991265i	$0.457897\pi$
$542$	1.47719e18	2.50289
$543$	−2.88119e17	−0.482362
$544$	−1.16315e18	−1.92417
$545$	−1.32786e18	−2.17058
$546$	0	0
$547$	5.20357e17	0.830584	0.415292	−	0.909688i	$-0.363679\pi$
$547$	5.20357e17	0.830584	0.415292	+	0.909688i	$0.363679\pi$
$548$	−1.44663e18	−2.28183
$549$	−7.38856e17	−1.15170
$550$	−3.57177e17	−0.550206
$551$	7.75642e17	1.18080
$552$	−3.43023e17	−0.516082
$553$	0	0
$554$	2.90299e17	0.426611
$555$	−5.48790e17	−0.797080
$556$	−3.42775e17	−0.492065
$557$	−2.34926e16	−0.0333328	−0.0166664	−	0.999861i	$-0.505305\pi$
$557$	−2.34926e16	−0.0333328	−0.0166664	+	0.999861i	$0.505305\pi$
$558$	1.59417e18	2.23570
$559$	3.32836e17	0.461375
$560$	0	0
$561$	−8.61831e17	−1.16725
$562$	1.11637e18	1.49459
$563$	6.91217e17	0.914766	0.457383	−	0.889270i	$-0.348787\pi$
$563$	6.91217e17	0.914766	0.457383	+	0.889270i	$0.348787\pi$
$564$	−5.22513e17	−0.683570
$565$	−1.13037e18	−1.46187
$566$	8.35833e17	1.06859
$567$	0	0
$568$	4.59823e17	0.574549
$569$	1.93881e17	0.239500	0.119750	−	0.992804i	$-0.461791\pi$
$569$	1.93881e17	0.239500	0.119750	+	0.992804i	$0.461791\pi$
$570$	−4.49536e18	−5.49007
$571$	−4.22605e17	−0.510270	−0.255135	−	0.966905i	$-0.582120\pi$
$571$	−4.22605e17	−0.510270	−0.255135	+	0.966905i	$0.582120\pi$
$572$	3.24782e17	0.387720
$573$	−9.36977e16	−0.110592
$574$	0	0
$575$	−2.79885e17	−0.322953
$576$	−2.60414e18	−2.97111
$577$	4.05000e16	0.0456890	0.0228445	−	0.999739i	$-0.492728\pi$
$577$	4.05000e16	0.0456890	0.0228445	+	0.999739i	$0.492728\pi$
$578$	2.17240e18	2.42331
$579$	2.39433e18	2.64103
$580$	−1.39826e18	−1.52513
$581$	0	0
$582$	−1.07757e18	−1.14933
$583$	−2.03693e17	−0.214847
$584$	8.64983e17	0.902244
$585$	−1.43335e18	−1.47856
$586$	−2.69732e18	−2.75168
$587$	−1.02876e18	−1.03793	−0.518965	−	0.854795i	$-0.673683\pi$
$587$	−1.02876e18	−1.03793	−0.518965	+	0.854795i	$0.673683\pi$
$588$	0	0
$589$	−1.20853e18	−1.19264
$590$	−2.44363e18	−2.38505
$591$	−7.17497e17	−0.692630
$592$	1.04637e17	0.0999065
$593$	1.10083e18	1.03960	0.519800	−	0.854288i	$-0.326007\pi$
$593$	1.10083e18	1.03960	0.519800	+	0.854288i	$0.326007\pi$
$594$	−1.03078e18	−0.962838
$595$	0	0
$596$	−1.10500e18	−1.00986
$597$	2.28001e18	2.06112
$598$	4.26086e17	0.381013
$599$	−3.28930e17	−0.290958	−0.145479	−	0.989361i	$-0.546472\pi$
$599$	−3.28930e17	−0.290958	−0.145479	+	0.989361i	$0.546472\pi$
$600$	1.17520e18	1.02832
$601$	9.58353e17	0.829548	0.414774	−	0.909924i	$-0.363861\pi$
$601$	9.58353e17	0.829548	0.414774	+	0.909924i	$0.363861\pi$
$602$	0	0
$603$	1.61431e18	1.36749
$604$	2.76252e18	2.31508
$605$	−1.31248e18	−1.08813
$606$	2.66159e18	2.18308
$607$	3.56856e17	0.289579	0.144789	−	0.989462i	$-0.453750\pi$
$607$	3.56856e17	0.289579	0.144789	+	0.989462i	$0.453750\pi$
$608$	2.31935e18	1.86205
$609$	0	0
$610$	−1.69051e18	−1.32854
$611$	2.11455e17	0.164418
$612$	5.63242e18	4.33322
$613$	7.90362e17	0.601635	0.300818	−	0.953682i	$-0.402740\pi$
$613$	7.90362e17	0.601635	0.300818	+	0.953682i	$0.402740\pi$
$614$	1.19604e18	0.900845
$615$	1.66217e18	1.23876
$616$	0	0
$617$	−3.32371e16	−0.0242532	−0.0121266	−	0.999926i	$-0.503860\pi$
$617$	−3.32371e16	−0.0242532	−0.0121266	+	0.999926i	$0.503860\pi$
$618$	4.16399e18	3.00666
$619$	−2.32168e18	−1.65887	−0.829437	−	0.558601i	$-0.811338\pi$
$619$	−2.32168e18	−1.65887	−0.829437	+	0.558601i	$0.811338\pi$
$620$	2.17863e18	1.54042
$621$	−8.07722e17	−0.565154
$622$	−9.30408e17	−0.644223
$623$	0	0
$624$	4.22320e17	0.286379
$625$	−1.72657e18	−1.15868
$626$	3.16719e18	2.10349
$627$	1.71851e18	1.12957
$628$	−2.00866e18	−1.30668
$629$	−8.72707e17	−0.561874
$630$	0	0
$631$	2.08110e18	1.31251	0.656253	−	0.754541i	$-0.272140\pi$
$631$	2.08110e18	1.31251	0.656253	+	0.754541i	$0.272140\pi$
$632$	1.65403e18	1.03248
$633$	1.60261e18	0.990154
$634$	−3.28552e18	−2.00920
$635$	−1.84122e18	−1.11449
$636$	2.05711e18	1.23250
$637$	0	0
$638$	8.94919e17	0.525351
$639$	2.38119e18	1.38369
$640$	−3.13937e18	−1.80581
$641$	−8.17209e17	−0.465325	−0.232662	−	0.972558i	$-0.574744\pi$
$641$	−8.17209e17	−0.465325	−0.232662	+	0.972558i	$0.574744\pi$
$642$	6.40673e18	3.61126
$643$	1.98776e18	1.10916	0.554578	−	0.832132i	$-0.312880\pi$
$643$	1.98776e18	1.10916	0.554578	+	0.832132i	$0.312880\pi$
$644$	0	0
$645$	−3.17480e18	−1.73612
$646$	−7.14870e18	−3.87004
$647$	−3.43898e17	−0.184311	−0.0921556	−	0.995745i	$-0.529376\pi$
$647$	−3.43898e17	−0.184311	−0.0921556	+	0.995745i	$0.529376\pi$
$648$	7.59586e17	0.403032
$649$	9.34162e17	0.490718
$650$	−1.45978e18	−0.759188
$651$	0	0
$652$	2.54903e18	1.29947
$653$	8.17662e17	0.412703	0.206352	−	0.978478i	$-0.433841\pi$
$653$	8.17662e17	0.412703	0.206352	+	0.978478i	$0.433841\pi$
$654$	−8.58285e18	−4.28920
$655$	−1.68796e18	−0.835208
$656$	−3.16922e17	−0.155267
$657$	4.47930e18	2.17288
$658$	0	0
$659$	2.92851e18	1.39281	0.696405	−	0.717649i	$-0.254782\pi$
$659$	2.92851e18	1.39281	0.696405	+	0.717649i	$0.254782\pi$
$660$	−3.09798e18	−1.45896
$661$	−1.17201e17	−0.0546539	−0.0273270	−	0.999627i	$-0.508700\pi$
$661$	−1.17201e17	−0.0546539	−0.0273270	+	0.999627i	$0.508700\pi$
$662$	−6.12818e17	−0.282979
$663$	−3.52229e18	−1.61060
$664$	1.92026e18	0.869497
$665$	0	0
$666$	−2.29549e18	−1.01928
$667$	7.01262e17	0.308363
$668$	4.58030e18	1.99456
$669$	−3.95649e17	−0.170624
$670$	3.69355e18	1.57746
$671$	6.46257e17	0.273343
$672$	0	0
$673$	−2.94248e18	−1.22072	−0.610360	−	0.792124i	$-0.708975\pi$
$673$	−2.94248e18	−1.22072	−0.610360	+	0.792124i	$0.708975\pi$
$674$	5.03008e18	2.06674
$675$	2.76726e18	1.12610
$676$	−2.35274e18	−0.948245
$677$	8.12201e17	0.324218	0.162109	−	0.986773i	$-0.448170\pi$
$677$	8.12201e17	0.324218	0.162109	+	0.986773i	$0.448170\pi$
$678$	−7.30636e18	−2.88874
$679$	0	0
$680$	4.19854e18	1.62851
$681$	4.32129e18	1.66019
$682$	−1.39438e18	−0.530618
$683$	−3.05393e18	−1.15113	−0.575566	−	0.817755i	$-0.695218\pi$
$683$	−3.05393e18	−1.15113	−0.575566	+	0.817755i	$0.695218\pi$
$684$	−1.12312e19	−4.19335
$685$	−5.58424e18	−2.06526
$686$	0	0
$687$	−1.57136e18	−0.570239
$688$	6.05335e17	0.217606
$689$	−8.32489e17	−0.296452
$690$	−4.06428e18	−1.43372
$691$	2.13672e18	0.746691	0.373345	−	0.927692i	$-0.378211\pi$
$691$	2.13672e18	0.746691	0.373345	+	0.927692i	$0.378211\pi$
$692$	−3.21348e18	−1.11246
$693$	0	0
$694$	−1.77964e18	−0.604637
$695$	−1.32317e18	−0.445363
$696$	−2.94450e18	−0.981865
$697$	2.64324e18	0.873220
$698$	7.43690e18	2.43406
$699$	−1.62535e18	−0.527041
$700$	0	0
$701$	3.52548e18	1.12215	0.561076	−	0.827764i	$-0.310388\pi$
$701$	3.52548e18	1.12215	0.561076	+	0.827764i	$0.310388\pi$
$702$	−4.21277e18	−1.32855
$703$	1.74020e18	0.543737
$704$	2.27777e18	0.705159
$705$	−2.01699e18	−0.618692
$706$	3.35841e18	1.02071
$707$	0	0
$708$	−9.43421e18	−2.81507
$709$	−6.20913e18	−1.83582	−0.917910	−	0.396789i	$-0.870124\pi$
$709$	−6.20913e18	−1.83582	−0.917910	+	0.396789i	$0.870124\pi$
$710$	5.44818e18	1.59615
$711$	8.56537e18	2.48653
$712$	1.65309e18	0.475528
$713$	−1.09264e18	−0.311455
$714$	0	0
$715$	1.25371e18	0.350921
$716$	−7.39205e18	−2.05036
$717$	6.27209e18	1.72400
$718$	9.14925e18	2.49216
$719$	−4.49406e18	−1.21311	−0.606557	−	0.795040i	$-0.707450\pi$
$719$	−4.49406e18	−1.21311	−0.606557	+	0.795040i	$0.707450\pi$
$720$	−2.60686e18	−0.697360
$721$	0	0
$722$	8.25674e18	2.16929
$723$	−9.93037e18	−2.58563
$724$	−1.64699e18	−0.425001
$725$	−2.40253e18	−0.614429
$726$	−8.48340e18	−2.15022
$727$	1.52837e18	0.383933	0.191967	−	0.981401i	$-0.438513\pi$
$727$	1.52837e18	0.383933	0.191967	+	0.981401i	$0.438513\pi$
$728$	0	0
$729$	−5.64334e18	−1.39254
$730$	1.02487e19	2.50651
$731$	−5.04869e18	−1.22382
$732$	−6.52661e18	−1.56807
$733$	−7.27343e18	−1.73206	−0.866031	−	0.499991i	$-0.833337\pi$
$733$	−7.27343e18	−1.73206	−0.866031	+	0.499991i	$0.833337\pi$
$734$	3.11197e18	0.734532
$735$	0	0
$736$	2.09693e18	0.486272
$737$	−1.41199e18	−0.324559
$738$	6.95254e18	1.58408
$739$	−2.14454e18	−0.484335	−0.242168	−	0.970234i	$-0.577858\pi$
$739$	−2.14454e18	−0.484335	−0.242168	+	0.970234i	$0.577858\pi$
$740$	−3.13707e18	−0.702293
$741$	7.02352e18	1.55861
$742$	0	0
$743$	7.98286e18	1.74073	0.870365	−	0.492408i	$-0.163883\pi$
$743$	7.98286e18	1.74073	0.870365	+	0.492408i	$0.163883\pi$
$744$	4.58784e18	0.991709
$745$	−4.26550e18	−0.914017
$746$	7.40675e18	1.57335
$747$	9.94405e18	2.09401
$748$	−4.92652e18	−1.02844
$749$	0	0
$750$	−3.43367e18	−0.704467
$751$	−2.63224e18	−0.535385	−0.267693	−	0.963504i	$-0.586261\pi$
$751$	−2.63224e18	−0.535385	−0.267693	+	0.963504i	$0.586261\pi$
$752$	3.84576e17	0.0775472
$753$	−1.19445e19	−2.38781
$754$	3.65752e18	0.724892
$755$	1.06638e19	2.09535
$756$	0	0
$757$	−7.32086e16	−0.0141397	−0.00706983	−	0.999975i	$-0.502250\pi$
$757$	−7.32086e16	−0.0141397	−0.00706983	+	0.999975i	$0.502250\pi$
$758$	−3.81218e18	−0.730000
$759$	1.55371e18	0.294985
$760$	−8.37199e18	−1.57594
$761$	6.13714e18	1.14542	0.572711	−	0.819757i	$-0.305892\pi$
$761$	6.13714e18	1.14542	0.572711	+	0.819757i	$0.305892\pi$
$762$	−1.19011e19	−2.20231
$763$	0	0
$764$	−5.35608e17	−0.0974407
$765$	2.17421e19	3.92195
$766$	−1.00639e19	−1.80004
$767$	3.81791e18	0.677104
$768$	−4.78283e18	−0.841080
$769$	5.48582e17	0.0956577	0.0478289	−	0.998856i	$-0.484770\pi$
$769$	5.48582e17	0.0956577	0.0478289	+	0.998856i	$0.484770\pi$
$770$	0	0
$771$	1.87768e19	3.21934
$772$	1.36868e19	2.32696
$773$	5.93770e18	1.00104	0.500520	−	0.865725i	$-0.333142\pi$
$773$	5.93770e18	1.00104	0.500520	+	0.865725i	$0.333142\pi$
$774$	−1.32796e19	−2.22009
$775$	3.74339e18	0.620589
$776$	−2.00682e18	−0.329919
$777$	0	0
$778$	−1.30831e19	−2.11517
$779$	−5.27068e18	−0.845032
$780$	−1.26614e19	−2.01311
$781$	−2.08276e18	−0.328403
$782$	−6.46317e18	−1.01065
$783$	−6.93348e18	−1.07523
$784$	0	0
$785$	−7.75376e18	−1.18266
$786$	−1.09104e19	−1.65042
$787$	−1.58830e18	−0.238284	−0.119142	−	0.992877i	$-0.538014\pi$
$787$	−1.58830e18	−0.238284	−0.119142	+	0.992877i	$0.538014\pi$
$788$	−4.10146e18	−0.610265
$789$	−8.48362e18	−1.25193
$790$	1.95976e19	2.86832
$791$	0	0
$792$	−4.22175e18	−0.607826
$793$	2.64124e18	0.377166
$794$	9.08046e18	1.28610
$795$	7.94081e18	1.11552
$796$	1.30333e19	1.81602
$797$	−1.87643e17	−0.0259331	−0.0129665	−	0.999916i	$-0.504127\pi$
$797$	−1.87643e17	−0.0259331	−0.0129665	+	0.999916i	$0.504127\pi$
$798$	0	0
$799$	−3.20749e18	−0.436126
$800$	−7.18411e18	−0.968921
$801$	8.56050e18	1.14522
$802$	1.95935e19	2.60003
$803$	−3.91792e18	−0.515709
$804$	1.42598e19	1.86187
$805$	0	0
$806$	−5.69880e18	−0.732159
$807$	9.19625e17	0.117201
$808$	4.95685e18	0.626660
$809$	−9.94828e17	−0.124762	−0.0623811	−	0.998052i	$-0.519869\pi$
$809$	−9.94828e17	−0.124762	−0.0623811	+	0.998052i	$0.519869\pi$
$810$	8.99990e18	1.11966
$811$	2.60734e18	0.321782	0.160891	−	0.986972i	$-0.448563\pi$
$811$	2.60734e18	0.321782	0.160891	+	0.986972i	$0.448563\pi$
$812$	0	0
$813$	2.20147e19	2.67377
$814$	2.00780e18	0.241915
$815$	9.83968e18	1.17613
$816$	−6.40604e18	−0.759633
$817$	1.00672e19	1.18431
$818$	−1.14769e19	−1.33946
$819$	0	0
$820$	9.50152e18	1.09145
$821$	−9.39244e18	−1.07040	−0.535202	−	0.844724i	$-0.679765\pi$
$821$	−9.39244e18	−1.07040	−0.535202	+	0.844724i	$0.679765\pi$
$822$	−3.60946e19	−4.08109
$823$	8.22653e18	0.922821	0.461411	−	0.887187i	$-0.347343\pi$
$823$	8.22653e18	0.922821	0.461411	+	0.887187i	$0.347343\pi$
$824$	7.75485e18	0.863071
$825$	−5.32304e18	−0.587772
$826$	0	0
$827$	−8.03187e18	−0.873033	−0.436517	−	0.899696i	$-0.643788\pi$
$827$	−8.03187e18	−0.873033	−0.436517	+	0.899696i	$0.643788\pi$
$828$	−1.01542e19	−1.09508
$829$	−9.71593e18	−1.03963	−0.519816	−	0.854278i	$-0.674000\pi$
$829$	−9.71593e18	−1.03963	−0.519816	+	0.854278i	$0.674000\pi$
$830$	2.27521e19	2.41554
$831$	4.32636e18	0.455738
$832$	9.30921e18	0.972996
$833$	0	0
$834$	−8.55251e18	−0.880064
$835$	1.76807e19	1.80525
$836$	9.82360e18	0.995244
$837$	1.08031e19	1.08601
$838$	3.58771e17	0.0357875
$839$	−1.64141e19	−1.62467	−0.812333	−	0.583194i	$-0.801803\pi$
$839$	−1.64141e19	−1.62467	−0.812333	+	0.583194i	$0.801803\pi$
$840$	0	0
$841$	−4.24100e18	−0.413328
$842$	1.10071e19	1.06450
$843$	1.66374e19	1.59663
$844$	9.16106e18	0.872408
$845$	−9.08197e18	−0.858245
$846$	−8.43670e18	−0.791162
$847$	0	0
$848$	−1.51406e18	−0.139820
$849$	1.24565e19	1.14155
$850$	2.21429e19	2.01378
$851$	1.57332e18	0.141996
$852$	2.10340e19	1.88393
$853$	−1.52207e19	−1.35290	−0.676452	−	0.736487i	$-0.736483\pi$
$853$	−1.52207e19	−1.35290	−0.676452	+	0.736487i	$0.736483\pi$
$854$	0	0
$855$	−4.33542e19	−3.79535
$856$	1.19316e19	1.03662
$857$	−6.34551e18	−0.547131	−0.273565	−	0.961853i	$-0.588203\pi$
$857$	−6.34551e18	−0.547131	−0.273565	+	0.961853i	$0.588203\pi$
$858$	8.10359e18	0.693442
$859$	6.13885e18	0.521352	0.260676	−	0.965426i	$-0.416055\pi$
$859$	6.13885e18	0.521352	0.260676	+	0.965426i	$0.416055\pi$
$860$	−1.81483e19	−1.52966
$861$	0	0
$862$	−7.60939e18	−0.631761
$863$	−2.22996e18	−0.183750	−0.0918749	−	0.995771i	$-0.529286\pi$
$863$	−2.22996e18	−0.183750	−0.0918749	+	0.995771i	$0.529286\pi$
$864$	−2.07327e19	−1.69557
$865$	−1.24046e19	−1.00688
$866$	−2.21007e19	−1.78049
$867$	3.23754e19	2.58876
$868$	0	0
$869$	−7.49189e18	−0.590150
$870$	−3.48877e19	−2.72771
$871$	−5.77079e18	−0.447834
$872$	−1.59844e19	−1.23123
$873$	−1.03923e19	−0.794546
$874$	1.28877e19	0.978029
$875$	0	0
$876$	3.95675e19	2.95843
$877$	−4.71852e18	−0.350194	−0.175097	−	0.984551i	$-0.556024\pi$
$877$	−4.71852e18	−0.350194	−0.175097	+	0.984551i	$0.556024\pi$
$878$	1.11145e18	0.0818796
$879$	−4.01984e19	−2.93955
$880$	2.28015e18	0.165511
$881$	6.62467e18	0.477332	0.238666	−	0.971102i	$-0.423290\pi$
$881$	6.62467e18	0.477332	0.238666	+	0.971102i	$0.423290\pi$
$882$	0	0
$883$	−4.40822e17	−0.0312982	−0.0156491	−	0.999878i	$-0.504981\pi$
$883$	−4.40822e17	−0.0312982	−0.0156491	+	0.999878i	$0.504981\pi$
$884$	−2.01346e19	−1.41907
$885$	−3.64176e19	−2.54789
$886$	−2.57546e19	−1.78869
$887$	−1.27798e18	−0.0881088	−0.0440544	−	0.999029i	$-0.514027\pi$
$887$	−1.27798e18	−0.0881088	−0.0440544	+	0.999029i	$0.514027\pi$
$888$	−6.60616e18	−0.452131
$889$	0	0
$890$	1.95865e19	1.32106
$891$	−3.44053e18	−0.230367
$892$	−2.26167e18	−0.150334
$893$	6.39581e18	0.422047
$894$	−2.75707e19	−1.80615
$895$	−2.85346e19	−1.85576
$896$	0	0
$897$	6.35001e18	0.407027
$898$	1.19413e19	0.759897
$899$	−9.37921e18	−0.592554
$900$	3.47883e19	2.18201
$901$	1.26278e19	0.786350
$902$	−6.08119e18	−0.375964
$903$	0	0
$904$	−1.36071e19	−0.829221
$905$	−6.35765e18	−0.384663
$906$	6.89272e19	4.14054
$907$	2.66640e18	0.159029	0.0795147	−	0.996834i	$-0.474663\pi$
$907$	2.66640e18	0.159029	0.0795147	+	0.996834i	$0.474663\pi$
$908$	2.47020e19	1.46276
$909$	2.56690e19	1.50919
$910$	0	0
$911$	5.44284e17	0.0315468	0.0157734	−	0.999876i	$-0.494979\pi$
$911$	5.44284e17	0.0315468	0.0157734	+	0.999876i	$0.494979\pi$
$912$	1.27738e19	0.735111
$913$	−8.69778e18	−0.496991
$914$	−4.25229e19	−2.41253
$915$	−2.51938e19	−1.41924
$916$	−8.98244e18	−0.502428
$917$	0	0
$918$	6.39023e19	3.52403
$919$	−1.24879e19	−0.683815	−0.341908	−	0.939734i	$-0.611073\pi$
$919$	−1.24879e19	−0.683815	−0.341908	+	0.939734i	$0.611073\pi$
$920$	−7.56916e18	−0.411554
$921$	1.78246e19	0.962350
$922$	−2.45570e19	−1.31651
$923$	−8.51221e18	−0.453139
$924$	0	0
$925$	−5.39021e18	−0.282934
$926$	4.14049e19	2.15814
$927$	4.01584e19	2.07854
$928$	1.80001e19	0.925150
$929$	2.12743e19	1.08581	0.542905	−	0.839794i	$-0.317324\pi$
$929$	2.12743e19	1.08581	0.542905	+	0.839794i	$0.317324\pi$
$930$	5.43587e19	2.75505
$931$	0	0
$932$	−9.29104e18	−0.464367
$933$	−1.38660e19	−0.688207
$934$	1.95636e18	0.0964262
$935$	−1.90172e19	−0.930832
$936$	−1.72542e19	−0.838693
$937$	5.35693e17	0.0258588	0.0129294	−	0.999916i	$-0.495884\pi$
$937$	5.35693e17	0.0258588	0.0129294	+	0.999916i	$0.495884\pi$
$938$	0	0
$939$	4.72009e19	2.24711
$940$	−1.15298e19	−0.545119
$941$	−2.40612e19	−1.12976	−0.564878	−	0.825174i	$-0.691077\pi$
$941$	−2.40612e19	−1.12976	−0.564878	+	0.825174i	$0.691077\pi$
$942$	−5.01177e19	−2.33701
$943$	−4.76525e18	−0.220678
$944$	6.94369e18	0.319354
$945$	0	0
$946$	1.16153e19	0.526913
$947$	1.19606e19	0.538863	0.269431	−	0.963020i	$-0.413164\pi$
$947$	1.19606e19	0.538863	0.269431	+	0.963020i	$0.413164\pi$
$948$	7.56614e19	3.38548
$949$	−1.60125e19	−0.711587
$950$	−4.41534e19	−1.94877
$951$	−4.89644e19	−2.14638
$952$	0	0
$953$	3.46550e19	1.49852	0.749260	−	0.662276i	$-0.230409\pi$
$953$	3.46550e19	1.49852	0.749260	+	0.662276i	$0.230409\pi$
$954$	3.32150e19	1.42649
$955$	−2.06754e18	−0.0881925
$956$	3.58535e19	1.51899
$957$	1.33371e19	0.561219
$958$	3.09650e19	1.29418
$959$	0	0
$960$	−8.87971e19	−3.66130
$961$	−9.80376e18	−0.401505
$962$	8.20585e18	0.333800
$963$	6.17879e19	2.49650
$964$	−5.67655e19	−2.27816
$965$	5.28334e19	2.10611
$966$	0	0
$967$	−4.73453e19	−1.86211	−0.931054	−	0.364881i	$-0.881110\pi$
$967$	−4.73453e19	−1.86211	−0.931054	+	0.364881i	$0.881110\pi$
$968$	−1.57992e19	−0.617226
$969$	−1.06538e20	−4.13427
$970$	−2.37777e19	−0.916543
$971$	6.21967e18	0.238145	0.119073	−	0.992886i	$-0.462008\pi$
$971$	6.21967e18	0.238145	0.119073	+	0.992886i	$0.462008\pi$
$972$	−1.99983e19	−0.760612
$973$	0	0
$974$	−6.25948e19	−2.34912
$975$	−2.17552e19	−0.811022
$976$	4.80366e18	0.177889
$977$	−1.37438e19	−0.505584	−0.252792	−	0.967521i	$-0.581349\pi$
$977$	−1.37438e19	−0.505584	−0.252792	+	0.967521i	$0.581349\pi$
$978$	6.36004e19	2.32411
$979$	−7.48763e18	−0.271805
$980$	0	0
$981$	−8.27749e19	−2.96517
$982$	−8.15230e19	−2.90105
$983$	1.57601e19	0.557136	0.278568	−	0.960417i	$-0.410140\pi$
$983$	1.57601e19	0.557136	0.278568	+	0.960417i	$0.410140\pi$
$984$	2.00086e19	0.702666
$985$	−1.58323e19	−0.552344
$986$	−5.54798e19	−1.92280
$987$	0	0
$988$	4.01489e19	1.37326
$989$	9.10182e18	0.309280
$990$	−5.00211e19	−1.68859
$991$	2.72731e19	0.914653	0.457327	−	0.889299i	$-0.348807\pi$
$991$	2.72731e19	0.914653	0.457327	+	0.889299i	$0.348807\pi$
$992$	−2.80460e19	−0.934425
$993$	−9.13288e18	−0.302300
$994$	0	0
$995$	5.03109e19	1.64366
$996$	8.78398e19	2.85106
$997$	2.95863e19	0.954051	0.477026	−	0.878889i	$-0.341715\pi$
$997$	2.95863e19	0.954051	0.477026	+	0.878889i	$0.341715\pi$
$998$	1.68771e19	0.540691
$999$	−1.55556e19	−0.495122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.14.a.b.1.3		3
7.2	even	3		49.14.c.b.18.1		6
7.3	odd	6		49.14.c.c.30.1		6
7.4	even	3		49.14.c.b.30.1		6
7.5	odd	6		49.14.c.c.18.1		6
7.6	odd	2		7.14.a.a.1.3	✓	3
21.20	even	2		63.14.a.c.1.1		3
28.27	even	2		112.14.a.g.1.3		3
35.34	odd	2		175.14.a.a.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.14.a.a.1.3	✓	3	7.6	odd	2
49.14.a.b.1.3		3	1.1	even	1	trivial
49.14.c.b.18.1		6	7.2	even	3
49.14.c.b.30.1		6	7.4	even	3
49.14.c.c.18.1		6	7.5	odd	6
49.14.c.c.30.1		6	7.3	odd	6
63.14.a.c.1.1		3	21.20	even	2
112.14.a.g.1.3		3	28.27	even	2
175.14.a.a.1.1		3	35.34	odd	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+142.628 q^{2} +2125.59 q^{3} +12150.6 q^{4} +46903.4 q^{5} +303168. q^{6} +564608. q^{8} +2.92382e6 q^{9} +O(q^{10})\)	\(q+142.628 q^{2} +2125.59 q^{3} +12150.6 q^{4} +46903.4 q^{5} +303168. q^{6} +564608. q^{8} +2.92382e6 q^{9} +6.68972e6 q^{10} -2.55738e6 q^{11} +2.58273e7 q^{12} -1.04520e7 q^{13} +9.96975e7 q^{15} -1.90092e7 q^{16} +1.58543e8 q^{17} +4.17017e8 q^{18} -3.16138e8 q^{19} +5.69906e8 q^{20} -3.64753e8 q^{22} -2.85822e8 q^{23} +1.20013e9 q^{24} +9.79229e8 q^{25} -1.49074e9 q^{26} +2.82596e9 q^{27} -2.45349e9 q^{29} +1.42196e10 q^{30} +3.82280e9 q^{31} -7.33650e9 q^{32} -5.43595e9 q^{33} +2.26126e10 q^{34} +3.55262e10 q^{36} -5.50455e9 q^{37} -4.50900e10 q^{38} -2.22166e10 q^{39} +2.64821e10 q^{40} +1.66721e10 q^{41} -3.18443e10 q^{43} -3.10738e10 q^{44} +1.37137e11 q^{45} -4.07661e10 q^{46} -2.02311e10 q^{47} -4.04057e10 q^{48} +1.39665e11 q^{50} +3.36997e11 q^{51} -1.26998e11 q^{52} +7.96490e10 q^{53} +4.03060e11 q^{54} -1.19950e11 q^{55} -6.71980e11 q^{57} -3.49936e11 q^{58} -3.65281e11 q^{59} +1.21139e12 q^{60} -2.52703e11 q^{61} +5.45236e11 q^{62} -8.90664e11 q^{64} -4.90234e11 q^{65} -7.75316e11 q^{66} +5.52124e11 q^{67} +1.92639e12 q^{68} -6.07541e11 q^{69} +8.14411e11 q^{71} +1.65081e12 q^{72} +1.53200e12 q^{73} -7.85100e11 q^{74} +2.08144e12 q^{75} -3.84127e12 q^{76} -3.16871e12 q^{78} +2.92952e12 q^{79} -8.91595e11 q^{80} +1.34533e12 q^{81} +2.37790e12 q^{82} +3.40105e12 q^{83} +7.43620e12 q^{85} -4.54188e12 q^{86} -5.21512e12 q^{87} -1.44392e12 q^{88} +2.92785e12 q^{89} +1.95595e13 q^{90} -3.47292e12 q^{92} +8.12571e12 q^{93} -2.88551e12 q^{94} -1.48280e13 q^{95} -1.55944e13 q^{96} -3.55436e12 q^{97} -7.47731e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 26 q^{2} + 1796 q^{3} + 17652 q^{4} + 24086 q^{5} + 288916 q^{6} - 560040 q^{8} - 136241 q^{9}+O(q^{10}) \) 3 * q + 26 * q^2 + 1796 * q^3 + 17652 * q^4 + 24086 * q^5 + 288916 * q^6 - 560040 * q^8 - 136241 * q^9	\( 3 q + 26 q^{2} + 1796 q^{3} + 17652 q^{4} + 24086 q^{5} + 288916 q^{6} - 560040 q^{8} - 136241 q^{9} + 11781480 q^{10} - 9339044 q^{11} + 28824376 q^{12} - 9219378 q^{13} + 95111824 q^{15} + 22016016 q^{16} + 161799306 q^{17} + 606492458 q^{18} - 351536172 q^{19} + 68483968 q^{20} - 82962528 q^{22} - 1258991568 q^{23} + 1339953360 q^{24} - 264033819 q^{25} + 592105696 q^{26} + 3831242840 q^{27} - 6748418342 q^{29} + 14249068640 q^{30} - 2961621120 q^{31} + 4217770336 q^{32} - 4066118848 q^{33} - 4547329068 q^{34} + 25822287476 q^{36} - 15165028062 q^{37} - 50788312340 q^{38} - 27201019328 q^{39} + 44426886720 q^{40} + 30348543778 q^{41} - 80250536052 q^{43} - 36470495776 q^{44} + 174799138718 q^{45} + 104345248704 q^{46} + 169583042880 q^{47} - 57669949472 q^{48} + 126343684270 q^{50} + 396306220872 q^{51} - 374907668016 q^{52} + 120814398690 q^{53} + 447197642200 q^{54} - 70923686328 q^{55} - 648921990728 q^{57} + 414757064340 q^{58} - 443036517780 q^{59} + 1226525703872 q^{60} + 312164967918 q^{61} + 1947956406408 q^{62} - 2035141631424 q^{64} + 32969416900 q^{65} - 722965868768 q^{66} + 1398804629172 q^{67} + 5080798627464 q^{68} - 643239052416 q^{69} + 980341716024 q^{71} + 3386556390360 q^{72} - 964409395470 q^{73} + 1492955795748 q^{74} + 2476757628364 q^{75} - 3033316968696 q^{76} - 3253765187344 q^{78} + 5421189462624 q^{79} - 179377360256 q^{80} + 5830367903443 q^{81} + 8267068838868 q^{82} + 5151799373700 q^{83} + 674264835492 q^{85} - 5617032798416 q^{86} - 5648416931128 q^{87} + 2215014098880 q^{88} + 15420753518162 q^{89} + 11482717432840 q^{90} - 16455265396992 q^{92} + 7009045069392 q^{93} - 18638542033128 q^{94} - 16359640125632 q^{95} - 17199777859264 q^{96} - 4897266340470 q^{97} + 2815692782188 q^{99}+O(q^{100}) \) 3 * q + 26 * q^2 + 1796 * q^3 + 17652 * q^4 + 24086 * q^5 + 288916 * q^6 - 560040 * q^8 - 136241 * q^9 + 11781480 * q^10 - 9339044 * q^11 + 28824376 * q^12 - 9219378 * q^13 + 95111824 * q^15 + 22016016 * q^16 + 161799306 * q^17 + 606492458 * q^18 - 351536172 * q^19 + 68483968 * q^20 - 82962528 * q^22 - 1258991568 * q^23 + 1339953360 * q^24 - 264033819 * q^25 + 592105696 * q^26 + 3831242840 * q^27 - 6748418342 * q^29 + 14249068640 * q^30 - 2961621120 * q^31 + 4217770336 * q^32 - 4066118848 * q^33 - 4547329068 * q^34 + 25822287476 * q^36 - 15165028062 * q^37 - 50788312340 * q^38 - 27201019328 * q^39 + 44426886720 * q^40 + 30348543778 * q^41 - 80250536052 * q^43 - 36470495776 * q^44 + 174799138718 * q^45 + 104345248704 * q^46 + 169583042880 * q^47 - 57669949472 * q^48 + 126343684270 * q^50 + 396306220872 * q^51 - 374907668016 * q^52 + 120814398690 * q^53 + 447197642200 * q^54 - 70923686328 * q^55 - 648921990728 * q^57 + 414757064340 * q^58 - 443036517780 * q^59 + 1226525703872 * q^60 + 312164967918 * q^61 + 1947956406408 * q^62 - 2035141631424 * q^64 + 32969416900 * q^65 - 722965868768 * q^66 + 1398804629172 * q^67 + 5080798627464 * q^68 - 643239052416 * q^69 + 980341716024 * q^71 + 3386556390360 * q^72 - 964409395470 * q^73 + 1492955795748 * q^74 + 2476757628364 * q^75 - 3033316968696 * q^76 - 3253765187344 * q^78 + 5421189462624 * q^79 - 179377360256 * q^80 + 5830367903443 * q^81 + 8267068838868 * q^82 + 5151799373700 * q^83 + 674264835492 * q^85 - 5617032798416 * q^86 - 5648416931128 * q^87 + 2215014098880 * q^88 + 15420753518162 * q^89 + 11482717432840 * q^90 - 16455265396992 * q^92 + 7009045069392 * q^93 - 18638542033128 * q^94 - 16359640125632 * q^95 - 17199777859264 * q^96 - 4897266340470 * q^97 + 2815692782188 * q^99

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