LMFDB - Embedded newform 59.18.a.a.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [59,18,Mod(1,59)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(59, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("59.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	59.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:	$108.101031533$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+82.4113 q^{2} -9693.66 q^{3} -124280. q^{4} -870585. q^{5} -798867. q^{6} +2.16368e6 q^{7} -2.10439e7 q^{8} -3.51731e7 q^{9} +O(q^{10})$	\(q+82.4113 q^{2} -9693.66 q^{3} -124280. q^{4} -870585. q^{5} -798867. q^{6} +2.16368e6 q^{7} -2.10439e7 q^{8} -3.51731e7 q^{9} -7.17460e7 q^{10} -2.73963e8 q^{11} +1.20473e9 q^{12} -8.21057e7 q^{13} +1.78312e8 q^{14} +8.43915e9 q^{15} +1.45554e10 q^{16} -3.86242e10 q^{17} -2.89866e9 q^{18} +1.08365e11 q^{19} +1.08197e11 q^{20} -2.09740e10 q^{21} -2.25776e10 q^{22} -1.93992e11 q^{23} +2.03993e11 q^{24} -5.02192e9 q^{25} -6.76644e9 q^{26} +1.59280e12 q^{27} -2.68904e11 q^{28} +3.45569e12 q^{29} +6.95481e11 q^{30} +4.47542e12 q^{31} +3.95780e12 q^{32} +2.65570e12 q^{33} -3.18307e12 q^{34} -1.88367e12 q^{35} +4.37132e12 q^{36} +2.09426e13 q^{37} +8.93053e12 q^{38} +7.95905e11 q^{39} +1.83205e13 q^{40} +1.12091e13 q^{41} -1.72850e12 q^{42} +9.61406e12 q^{43} +3.40482e13 q^{44} +3.06211e13 q^{45} -1.59871e13 q^{46} -1.08631e14 q^{47} -1.41095e14 q^{48} -2.27949e14 q^{49} -4.13862e11 q^{50} +3.74410e14 q^{51} +1.02041e13 q^{52} +5.20989e14 q^{53} +1.31264e14 q^{54} +2.38508e14 q^{55} -4.55324e13 q^{56} -1.05046e15 q^{57} +2.84788e14 q^{58} -1.46830e14 q^{59} -1.04882e15 q^{60} +2.21303e14 q^{61} +3.68825e14 q^{62} -7.61035e13 q^{63} -1.58164e15 q^{64} +7.14800e13 q^{65} +2.18860e14 q^{66} -1.74865e15 q^{67} +4.80024e15 q^{68} +1.88049e15 q^{69} -1.55236e14 q^{70} -2.43624e11 q^{71} +7.40179e14 q^{72} -9.81922e15 q^{73} +1.72591e15 q^{74} +4.86808e13 q^{75} -1.34677e16 q^{76} -5.92768e14 q^{77} +6.55916e13 q^{78} -1.42398e16 q^{79} -1.26717e16 q^{80} -1.08978e16 q^{81} +9.23754e14 q^{82} +2.31627e16 q^{83} +2.60666e15 q^{84} +3.36257e16 q^{85} +7.92307e14 q^{86} -3.34983e16 q^{87} +5.76524e15 q^{88} +2.63626e16 q^{89} +2.52353e15 q^{90} -1.77651e14 q^{91} +2.41094e16 q^{92} -4.33832e16 q^{93} -8.95243e15 q^{94} -9.43413e16 q^{95} -3.83656e16 q^{96} +1.70108e16 q^{97} -1.87856e16 q^{98} +9.63611e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 15 q^{2} + 2080511 q^{4} - 1062222 q^{5} - 3454906 q^{6} - 43925040 q^{7} + 17944905 q^{8} + 1407964240 q^{9}+O(q^{10}) $ 38 * q + 15 * q^2 + 2080511 * q^4 - 1062222 * q^5 - 3454906 * q^6 - 43925040 * q^7 + 17944905 * q^8 + 1407964240 * q^9	\( 38 q + 15 q^{2} + 2080511 q^{4} - 1062222 q^{5} - 3454906 q^{6} - 43925040 q^{7} + 17944905 q^{8} + 1407964240 q^{9} - 753380082 q^{10} - 1247087592 q^{11} - 12806174710 q^{13} - 9920461605 q^{14} - 26267835313 q^{15} + 150793103155 q^{16} - 32714582925 q^{17} - 321256617405 q^{18} - 275283244180 q^{19} - 219435764020 q^{20} - 301109113003 q^{21} + 141637789665 q^{22} + 101540066360 q^{23} + 2412933601890 q^{24} + 4991161115804 q^{25} + 990445756111 q^{26} - 1179423443835 q^{27} - 10869216693165 q^{28} - 12862783749830 q^{29} - 27886581579060 q^{30} - 7513791056524 q^{31} - 31047860166815 q^{32} - 16499870737070 q^{33} - 62883745276639 q^{34} - 41836456706373 q^{35} - 74757290464031 q^{36} - 113711477231480 q^{37} - 86782161105620 q^{38} - 63680125347522 q^{39} - 53946909479582 q^{40} - 40841718887048 q^{41} - 8891162142170 q^{42} - 81961546008910 q^{43} - 24535596549333 q^{44} - 43121875478149 q^{45} - 432155860006696 q^{46} + 48939724777580 q^{47} + 513518246048640 q^{48} + 888582051628886 q^{49} + 20\!\cdots\!21 q^{50}+ \cdots - 51\!\cdots\!14 q^{99}+O(q^{100}) \) 38 * q + 15 * q^2 + 2080511 * q^4 - 1062222 * q^5 - 3454906 * q^6 - 43925040 * q^7 + 17944905 * q^8 + 1407964240 * q^9 - 753380082 * q^10 - 1247087592 * q^11 - 12806174710 * q^13 - 9920461605 * q^14 - 26267835313 * q^15 + 150793103155 * q^16 - 32714582925 * q^17 - 321256617405 * q^18 - 275283244180 * q^19 - 219435764020 * q^20 - 301109113003 * q^21 + 141637789665 * q^22 + 101540066360 * q^23 + 2412933601890 * q^24 + 4991161115804 * q^25 + 990445756111 * q^26 - 1179423443835 * q^27 - 10869216693165 * q^28 - 12862783749830 * q^29 - 27886581579060 * q^30 - 7513791056524 * q^31 - 31047860166815 * q^32 - 16499870737070 * q^33 - 62883745276639 * q^34 - 41836456706373 * q^35 - 74757290464031 * q^36 - 113711477231480 * q^37 - 86782161105620 * q^38 - 63680125347522 * q^39 - 53946909479582 * q^40 - 40841718887048 * q^41 - 8891162142170 * q^42 - 81961546008910 * q^43 - 24535596549333 * q^44 - 43121875478149 * q^45 - 432155860006696 * q^46 + 48939724777580 * q^47 + 513518246048640 * q^48 + 888582051628886 * q^49 + 2057077370177321 * q^50 + 569659539952336 * q^51 - 370273252291135 * q^52 - 433723261090750 * q^53 + 1096466631267392 * q^54 + 79796671313772 * q^55 + 2323327792351993 * q^56 + 887203937605935 * q^57 - 295587621090020 * q^58 - 5579556628964198 * q^59 + 592426170977334 * q^60 - 6025444644348168 * q^61 + 7570949891683260 * q^62 + 9980846882585340 * q^63 + 13715521778988675 * q^64 + 4776848418760040 * q^65 + 20125410682117558 * q^66 - 6448471666351340 * q^67 - 1025381952060385 * q^68 - 16162390563538664 * q^69 - 18060178308372494 * q^70 - 863248182916719 * q^71 - 15920098968926535 * q^72 - 15893509015624410 * q^73 - 29377392966301269 * q^74 - 76871360452990700 * q^75 - 76061521963339558 * q^76 - 47308441379226170 * q^77 - 62616737236958550 * q^78 - 56867622838588436 * q^79 - 110758045028448708 * q^80 + 20733776554374430 * q^81 - 22335528426891945 * q^82 - 20340278534672400 * q^83 - 60706646448603304 * q^84 - 138649838511113872 * q^85 - 126684793482322437 * q^86 + 98988867535735775 * q^87 - 129449914775692245 * q^88 + 46444572410639724 * q^89 - 92592608336160718 * q^90 - 57065301260365760 * q^91 - 252639467544196520 * q^92 - 51058891330353870 * q^93 - 23726593342614318 * q^94 + 397700906642915716 * q^95 - 348083640855946590 * q^96 - 45861521042958940 * q^97 - 457813795136007510 * q^98 - 514992036448276814 * 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 $

$2$	82.4113	0.227631	0.113816	−	0.993502i	$-0.463693\pi$
$2$	82.4113	0.227631	0.113816	+	0.993502i	$0.463693\pi$
$3$	−9693.66	−0.853016	−0.426508	−	0.904484i	$-0.640256\pi$
$3$	−9693.66	−0.853016	−0.426508	+	0.904484i	$0.640256\pi$
$4$	−124280.	−0.948184
$5$	−870585.	−0.996703	−0.498352	−	0.866975i	$-0.666061\pi$
$5$	−870585.	−0.996703	−0.498352	+	0.866975i	$0.666061\pi$
$6$	−798867.	−0.194173
$7$	2.16368e6	0.141860	0.0709301	−	0.997481i	$-0.477403\pi$
$7$	2.16368e6	0.141860	0.0709301	+	0.997481i	$0.477403\pi$
$8$	−2.10439e7	−0.443467
$9$	−3.51731e7	−0.272364
$10$	−7.17460e7	−0.226881
$11$	−2.73963e8	−0.385348	−0.192674	−	0.981263i	$-0.561716\pi$
$11$	−2.73963e8	−0.385348	−0.192674	+	0.981263i	$0.561716\pi$
$12$	1.20473e9	0.808816
$13$	−8.21057e7	−0.0279161	−0.0139581	−	0.999903i	$-0.504443\pi$
$13$	−8.21057e7	−0.0279161	−0.0139581	+	0.999903i	$0.504443\pi$
$14$	1.78312e8	0.0322918
$15$	8.43915e9	0.850204
$16$	1.45554e10	0.847237
$17$	−3.86242e10	−1.34290	−0.671451	−	0.741049i	$-0.734328\pi$
$17$	−3.86242e10	−1.34290	−0.671451	+	0.741049i	$0.734328\pi$
$18$	−2.89866e9	−0.0619984
$19$	1.08365e11	1.46381	0.731906	−	0.681406i	$-0.238631\pi$
$19$	1.08365e11	1.46381	0.731906	+	0.681406i	$0.238631\pi$
$20$	1.08197e11	0.945058
$21$	−2.09740e10	−0.121009
$22$	−2.25776e10	−0.0877172
$23$	−1.93992e11	−0.516532	−0.258266	−	0.966074i	$-0.583151\pi$
$23$	−1.93992e11	−0.516532	−0.258266	+	0.966074i	$0.583151\pi$
$24$	2.03993e11	0.378285
$25$	−5.02192e9	−0.00658233
$26$	−6.76644e9	−0.00635458
$27$	1.59280e12	1.08535
$28$	−2.68904e11	−0.134510
$29$	3.45569e12	1.28278	0.641390	−	0.767215i	$-0.278358\pi$
$29$	3.45569e12	1.28278	0.641390	+	0.767215i	$0.278358\pi$
$30$	6.95481e11	0.193533
$31$	4.47542e12	0.942452	0.471226	−	0.882013i	$-0.343812\pi$
$31$	4.47542e12	0.942452	0.471226	+	0.882013i	$0.343812\pi$
$32$	3.95780e12	0.636325
$33$	2.65570e12	0.328708
$34$	−3.18307e12	−0.305686
$35$	−1.88367e12	−0.141393
$36$	4.37132e12	0.258251
$37$	2.09426e13	0.980203	0.490102	−	0.871665i	$-0.336960\pi$
$37$	2.09426e13	0.980203	0.490102	+	0.871665i	$0.336960\pi$
$38$	8.93053e12	0.333209
$39$	7.95905e11	0.0238129
$40$	1.83205e13	0.442005
$41$	1.12091e13	0.219234	0.109617	−	0.993974i	$-0.465038\pi$
$41$	1.12091e13	0.219234	0.109617	+	0.993974i	$0.465038\pi$
$42$	−1.72850e12	−0.0275454
$43$	9.61406e12	0.125437	0.0627184	−	0.998031i	$-0.480023\pi$
$43$	9.61406e12	0.125437	0.0627184	+	0.998031i	$0.480023\pi$
$44$	3.40482e13	0.365381
$45$	3.06211e13	0.271466
$46$	−1.59871e13	−0.117579
$47$	−1.08631e14	−0.665461	−0.332730	−	0.943022i	$-0.607970\pi$
$47$	−1.08631e14	−0.665461	−0.332730	+	0.943022i	$0.607970\pi$
$48$	−1.41095e14	−0.722707
$49$	−2.27949e14	−0.979876
$50$	−4.13862e11	−0.00149834
$51$	3.74410e14	1.14552
$52$	1.02041e13	0.0264696
$53$	5.20989e14	1.14943	0.574716	−	0.818353i	$-0.305113\pi$
$53$	5.20989e14	1.14943	0.574716	+	0.818353i	$0.305113\pi$
$54$	1.31264e14	0.247059
$55$	2.38508e14	0.384078
$56$	−4.55324e13	−0.0629104
$57$	−1.05046e15	−1.24865
$58$	2.84788e14	0.292000
$59$	−1.46830e14	−0.130189
$59$	−1.46830e14	−0.130189
$60$	−1.04882e15	−0.806150
$61$	2.21303e14	0.147803	0.0739015	−	0.997266i	$-0.476455\pi$
$61$	2.21303e14	0.147803	0.0739015	+	0.997266i	$0.476455\pi$
$62$	3.68825e14	0.214531
$63$	−7.61035e13	−0.0386376
$64$	−1.58164e15	−0.702390
$65$	7.14800e13	0.0278241
$66$	2.18860e14	0.0748242
$67$	−1.74865e15	−0.526098	−0.263049	−	0.964782i	$-0.584728\pi$
$67$	−1.74865e15	−0.526098	−0.263049	+	0.964782i	$0.584728\pi$
$68$	4.80024e15	1.27332
$69$	1.88049e15	0.440610
$70$	−1.55236e14	−0.0321853
$71$	−2.43624e11	−4.47737e−5 0	−2.23869e−5	−	1.00000i	$-0.500007\pi$
$71$	−2.43624e11	−4.47737e−5 0	−2.23869e−5		1.00000i	$0.500007\pi$
$72$	7.40179e14	0.120784
$73$	−9.81922e15	−1.42506	−0.712529	−	0.701642i	$-0.752450\pi$
$73$	−9.81922e15	−1.42506	−0.712529	+	0.701642i	$0.752450\pi$
$74$	1.72591e15	0.223125
$75$	4.86808e13	0.00561483
$76$	−1.34677e16	−1.38796
$77$	−5.92768e14	−0.0546656
$78$	6.55916e13	0.00542056
$79$	−1.42398e16	−1.05602	−0.528012	−	0.849237i	$-0.677062\pi$
$79$	−1.42398e16	−1.05602	−0.528012	+	0.849237i	$0.677062\pi$
$80$	−1.26717e16	−0.844444
$81$	−1.08978e16	−0.653454
$82$	9.23754e14	0.0499044
$83$	2.31627e16	1.12882	0.564410	−	0.825495i	$-0.309104\pi$
$83$	2.31627e16	1.12882	0.564410	+	0.825495i	$0.309104\pi$
$84$	2.60666e15	0.114739
$85$	3.36257e16	1.33847
$86$	7.92307e14	0.0285533
$87$	−3.34983e16	−1.09423
$88$	5.76524e15	0.170889
$89$	2.63626e16	0.709861	0.354930	−	0.934893i	$-0.384505\pi$
$89$	2.63626e16	0.709861	0.354930	+	0.934893i	$0.384505\pi$
$90$	2.52353e15	0.0617941
$91$	−1.77651e14	−0.00396019
$92$	2.41094e16	0.489767
$93$	−4.33832e16	−0.803926
$94$	−8.95243e15	−0.151480
$95$	−9.43413e16	−1.45899
$96$	−3.83656e16	−0.542795
$97$	1.70108e16	0.220376	0.110188	−	0.993911i	$-0.464855\pi$
$97$	1.70108e16	0.220376	0.110188	+	0.993911i	$0.464855\pi$
$98$	−1.87856e16	−0.223050
$99$	9.63611e15	0.104955
$100$	6.24126e14	0.00624126
$101$	9.50898e16	0.873780	0.436890	−	0.899515i	$-0.356080\pi$
$101$	9.50898e16	0.873780	0.436890	+	0.899515i	$0.356080\pi$
$102$	3.08556e16	0.260755
$103$	−1.17754e17	−0.915927	−0.457964	−	0.888971i	$-0.651421\pi$
$103$	−1.17754e17	−0.915927	−0.457964	+	0.888971i	$0.651421\pi$
$104$	1.72783e15	0.0123799
$105$	1.82597e16	0.120610
$106$	4.29353e16	0.261646
$107$	7.43085e16	0.418097	0.209048	−	0.977905i	$-0.432963\pi$
$107$	7.43085e16	0.418097	0.209048	+	0.977905i	$0.432963\pi$
$108$	−1.97953e17	−1.02911
$109$	2.39705e17	1.15226	0.576131	−	0.817357i	$-0.304562\pi$
$109$	2.39705e17	1.15226	0.576131	+	0.817357i	$0.304562\pi$
$110$	1.96557e16	0.0874281
$111$	−2.03011e17	−0.836129
$112$	3.14933e16	0.120189
$113$	6.38595e16	0.225974	0.112987	−	0.993596i	$-0.463958\pi$
$113$	6.38595e16	0.225974	0.112987	+	0.993596i	$0.463958\pi$
$114$	−8.65696e16	−0.284233
$115$	1.68886e17	0.514829
$116$	−4.29475e17	−1.21631
$117$	2.88791e15	0.00760334
$118$	−1.21005e16	−0.0296350
$119$	−8.35707e16	−0.190504
$120$	−1.77593e17	−0.377038
$121$	−4.30392e17	−0.851507
$122$	1.82379e16	0.0336446
$123$	−1.08657e17	−0.187010
$124$	−5.56206e17	−0.893618
$125$	6.68575e17	1.00326
$126$	−6.27178e15	−0.00879511
$127$	3.05206e17	0.400186	0.200093	−	0.979777i	$-0.435876\pi$
$127$	3.05206e17	0.400186	0.200093	+	0.979777i	$0.435876\pi$
$128$	−6.49102e17	−0.796211
$129$	−9.31954e16	−0.107000
$130$	5.89076e15	0.00633363
$131$	−1.28345e18	−1.29292	−0.646460	−	0.762948i	$-0.723751\pi$
$131$	−1.28345e18	−1.29292	−0.646460	+	0.762948i	$0.723751\pi$
$132$	−3.30051e17	−0.311676
$133$	2.34469e17	0.207657
$134$	−1.44108e17	−0.119756
$135$	−1.38666e18	−1.08177
$136$	8.12805e17	0.595533
$137$	−1.08748e18	−0.748684	−0.374342	−	0.927291i	$-0.622131\pi$
$137$	−1.08748e18	−0.748684	−0.374342	+	0.927291i	$0.622131\pi$
$138$	1.54974e17	0.100297
$139$	−2.86610e18	−1.74448	−0.872239	−	0.489080i	$-0.837333\pi$
$139$	−2.86610e18	−1.74448	−0.872239	+	0.489080i	$0.837333\pi$
$140$	2.34103e17	0.134066
$141$	1.05303e18	0.567649
$142$	−2.00773e13	−1.01919e−5 0
$143$	2.24939e16	0.0107574
$144$	−5.11959e17	−0.230757
$145$	−3.00847e18	−1.27855
$146$	−8.09214e17	−0.324388
$147$	2.20966e18	0.835850
$148$	−2.60276e18	−0.929413
$149$	7.10408e17	0.239566	0.119783	−	0.992800i	$-0.461780\pi$
$149$	7.10408e17	0.239566	0.119783	+	0.992800i	$0.461780\pi$
$150$	4.01184e15	0.00127811
$151$	−3.58726e18	−1.08009	−0.540043	−	0.841637i	$-0.681592\pi$
$151$	−3.58726e18	−1.08009	−0.540043	+	0.841637i	$0.681592\pi$
$152$	−2.28043e18	−0.649153
$153$	1.35853e18	0.365758
$154$	−4.88508e16	−0.0124436
$155$	−3.89623e18	−0.939345
$156$	−9.89154e16	−0.0225790
$157$	5.21787e18	1.12810	0.564048	−	0.825742i	$-0.309243\pi$
$157$	5.21787e18	1.12810	0.564048	+	0.825742i	$0.309243\pi$
$158$	−1.17352e18	−0.240384
$159$	−5.05029e18	−0.980484
$160$	−3.44560e18	−0.634227
$161$	−4.19738e17	−0.0732753
$162$	−8.98100e17	−0.148747
$163$	−3.34237e18	−0.525364	−0.262682	−	0.964882i	$-0.584607\pi$
$163$	−3.34237e18	−0.525364	−0.262682	+	0.964882i	$0.584607\pi$
$164$	−1.39307e18	−0.207874
$165$	−2.31201e18	−0.327625
$166$	1.90886e18	0.256955
$167$	1.32093e19	1.68962	0.844808	−	0.535069i	$-0.179714\pi$
$167$	1.32093e19	1.68962	0.844808	+	0.535069i	$0.179714\pi$
$168$	4.41376e17	0.0536635
$169$	−8.64367e18	−0.999221
$170$	2.77113e18	0.304678
$171$	−3.81155e18	−0.398689
$172$	−1.19484e18	−0.118937
$173$	1.27552e19	1.20864	0.604319	−	0.796743i	$-0.293445\pi$
$173$	1.27552e19	1.20864	0.604319	+	0.796743i	$0.293445\pi$
$174$	−2.76064e18	−0.249081
$175$	−1.08658e16	−0.000933770 0
$176$	−3.98764e18	−0.326481
$177$	1.42332e18	0.111053
$178$	2.17257e18	0.161586
$179$	8.64803e18	0.613291	0.306645	−	0.951824i	$-0.400793\pi$
$179$	8.64803e18	0.613291	0.306645	+	0.951824i	$0.400793\pi$
$180$	−3.80561e18	−0.257400
$181$	−5.94721e18	−0.383748	−0.191874	−	0.981420i	$-0.561456\pi$
$181$	−5.94721e18	−0.383748	−0.191874	+	0.981420i	$0.561456\pi$
$182$	−1.46404e16	−0.000901462 0
$183$	−2.14524e18	−0.126078
$184$	4.08235e18	0.229065
$185$	−1.82323e19	−0.976972
$186$	−3.57526e18	−0.182999
$187$	1.05816e19	0.517485
$188$	1.35007e19	0.630979
$189$	3.44631e18	0.153968
$190$	−7.77478e18	−0.332111
$191$	1.09952e19	0.449179	0.224589	−	0.974453i	$-0.427896\pi$
$191$	1.09952e19	0.449179	0.224589	+	0.974453i	$0.427896\pi$
$192$	1.53319e19	0.599150
$193$	−3.57181e18	−0.133552	−0.0667761	−	0.997768i	$-0.521271\pi$
$193$	−3.57181e18	−0.133552	−0.0667761	+	0.997768i	$0.521271\pi$
$194$	1.40188e18	0.0501645
$195$	−6.92903e17	−0.0237344
$196$	2.83296e19	0.929103
$197$	2.65772e17	0.00834730	0.00417365	−	0.999991i	$-0.498671\pi$
$197$	2.65772e17	0.00834730	0.00417365	+	0.999991i	$0.498671\pi$
$198$	7.94124e17	0.0238910
$199$	−4.44052e19	−1.27992	−0.639960	−	0.768408i	$-0.721049\pi$
$199$	−4.44052e19	−1.27992	−0.639960	+	0.768408i	$0.721049\pi$
$200$	1.05681e17	0.00291905
$201$	1.69508e19	0.448770
$202$	7.83647e18	0.198899
$203$	7.47703e18	0.181975
$204$	−4.65319e19	−1.08616
$205$	−9.75845e18	−0.218511
$206$	−9.70430e18	−0.208494
$207$	6.82330e18	0.140685
$208$	−1.19508e18	−0.0236516
$209$	−2.96881e19	−0.564077
$210$	1.50480e18	0.0274546
$211$	7.96072e19	1.39493	0.697463	−	0.716621i	$-0.254312\pi$
$211$	7.96072e19	1.39493	0.697463	+	0.716621i	$0.254312\pi$
$212$	−6.47487e19	−1.08987
$213$	2.36160e15	3.81927e−5 0
$214$	6.12386e18	0.0951718
$215$	−8.36985e18	−0.125023
$216$	−3.35187e19	−0.481316
$217$	9.68339e18	0.133696
$218$	1.97544e19	0.262291
$219$	9.51842e19	1.21560
$220$	−2.96418e19	−0.364176
$221$	3.17127e18	0.0374886
$222$	−1.67304e19	−0.190329
$223$	1.12608e20	1.23304	0.616520	−	0.787339i	$-0.288542\pi$
$223$	1.12608e20	1.23304	0.616520	+	0.787339i	$0.288542\pi$
$224$	8.56343e18	0.0902692
$225$	1.76636e17	0.00179279
$226$	5.26274e18	0.0514387
$227$	1.41789e20	1.33482	0.667410	−	0.744691i	$-0.267403\pi$
$227$	1.41789e20	1.33482	0.667410	+	0.744691i	$0.267403\pi$
$228$	1.30551e20	1.18395
$229$	4.81628e19	0.420833	0.210417	−	0.977612i	$-0.432518\pi$
$229$	4.81628e19	0.420833	0.210417	+	0.977612i	$0.432518\pi$
$230$	1.39181e19	0.117191
$231$	5.74610e18	0.0466306
$232$	−7.27213e19	−0.568871
$233$	1.35973e20	1.02548	0.512741	−	0.858544i	$-0.328630\pi$
$233$	1.35973e20	1.02548	0.512741	+	0.858544i	$0.328630\pi$
$234$	2.37997e17	0.00173076
$235$	9.45726e19	0.663267
$236$	1.82481e19	0.123443
$237$	1.38036e20	0.900805
$238$	−6.88716e18	−0.0433647
$239$	2.40462e20	1.46105	0.730523	−	0.682888i	$-0.239276\pi$
$239$	2.40462e20	1.46105	0.730523	+	0.682888i	$0.239276\pi$
$240$	1.22835e20	0.720324
$241$	6.45461e19	0.365363	0.182682	−	0.983172i	$-0.441522\pi$
$241$	6.45461e19	0.365363	0.182682	+	0.983172i	$0.441522\pi$
$242$	−3.54691e19	−0.193829
$243$	−1.00055e20	−0.527940
$244$	−2.75036e19	−0.140145
$245$	1.98449e20	0.976645
$246$	−8.95456e18	−0.0425692
$247$	−8.89743e18	−0.0408639
$248$	−9.41803e19	−0.417946
$249$	−2.24531e20	−0.962901
$250$	5.50981e19	0.228374
$251$	−2.03904e20	−0.816956	−0.408478	−	0.912768i	$-0.633940\pi$
$251$	−2.03904e20	−0.816956	−0.408478	+	0.912768i	$0.633940\pi$
$252$	9.45817e18	0.0366355
$253$	5.31465e19	0.199045
$254$	2.51524e19	0.0910947
$255$	−3.25956e20	−1.14174
$256$	1.53816e20	0.521148
$257$	2.41389e20	0.791198	0.395599	−	0.918423i	$-0.370537\pi$
$257$	2.41389e20	0.791198	0.395599	+	0.918423i	$0.370537\pi$
$258$	−7.68035e18	−0.0243564
$259$	4.53132e19	0.139052
$260$	−8.88356e18	−0.0263824
$261$	−1.21547e20	−0.349383
$262$	−1.05770e20	−0.294309
$263$	1.61153e20	0.434125	0.217063	−	0.976158i	$-0.430352\pi$
$263$	1.61153e20	0.434125	0.217063	+	0.976158i	$0.430352\pi$
$264$	−5.58863e19	−0.145771
$265$	−4.53565e20	−1.14564
$266$	1.93229e19	0.0472691
$267$	−2.55550e20	−0.605522
$268$	2.17323e20	0.498838
$269$	1.01868e20	0.226540	0.113270	−	0.993564i	$-0.463868\pi$
$269$	1.01868e20	0.226540	0.113270	+	0.993564i	$0.463868\pi$
$270$	−1.14277e20	−0.246244
$271$	−4.03080e20	−0.841690	−0.420845	−	0.907133i	$-0.638266\pi$
$271$	−4.03080e20	−0.841690	−0.420845	+	0.907133i	$0.638266\pi$
$272$	−5.62192e20	−1.13776
$273$	1.72209e18	0.00337810
$274$	−8.96210e19	−0.170424
$275$	1.37582e18	0.00253649
$276$	−2.33708e20	−0.417779
$277$	−3.56056e20	−0.617221	−0.308610	−	0.951189i	$-0.599864\pi$
$277$	−3.56056e20	−0.617221	−0.308610	+	0.951189i	$0.599864\pi$
$278$	−2.36199e20	−0.397097
$279$	−1.57414e20	−0.256690
$280$	3.96398e19	0.0627030
$281$	3.32136e20	0.509697	0.254848	−	0.966981i	$-0.417974\pi$
$281$	3.32136e20	0.509697	0.254848	+	0.966981i	$0.417974\pi$
$282$	8.67818e19	0.129215
$283$	−9.56353e20	−1.38176	−0.690882	−	0.722968i	$-0.742777\pi$
$283$	−9.56353e20	−1.38176	−0.690882	+	0.722968i	$0.742777\pi$
$284$	3.02776e16	4.24538e−5 0
$285$	9.14513e20	1.24454
$286$	1.85375e18	0.00244872
$287$	2.42529e19	0.0311005
$288$	−1.39208e20	−0.173312
$289$	6.64592e20	0.803384
$290$	−2.47932e20	−0.291038
$291$	−1.64897e20	−0.187985
$292$	1.22034e21	1.35122
$293$	−3.37440e20	−0.362929	−0.181465	−	0.983397i	$-0.558084\pi$
$293$	−3.37440e20	−0.362929	−0.181465	+	0.983397i	$0.558084\pi$
$294$	1.82101e20	0.190265
$295$	1.27828e20	0.129760
$296$	−4.40714e20	−0.434688
$297$	−4.36367e20	−0.418236
$298$	5.85456e19	0.0545326
$299$	1.59279e19	0.0144196
$300$	−6.05006e18	−0.00532389
$301$	2.08018e19	0.0177945
$302$	−2.95630e20	−0.245861
$303$	−9.21768e20	−0.745348
$304$	1.57730e21	1.24020
$305$	−1.92663e20	−0.147316
$306$	1.11958e20	0.0832578
$307$	9.04175e20	0.653998	0.326999	−	0.945025i	$-0.393963\pi$
$307$	9.04175e20	0.653998	0.326999	+	0.945025i	$0.393963\pi$
$308$	7.36695e19	0.0518330
$309$	1.14147e21	0.781301
$310$	−3.21093e20	−0.213824
$311$	−4.74717e20	−0.307590	−0.153795	−	0.988103i	$-0.549149\pi$
$311$	−4.74717e20	−0.307590	−0.153795	+	0.988103i	$0.549149\pi$
$312$	−1.67490e19	−0.0105602
$313$	−8.26796e20	−0.507308	−0.253654	−	0.967295i	$-0.581632\pi$
$313$	−8.26796e20	−0.507308	−0.253654	+	0.967295i	$0.581632\pi$
$314$	4.30011e20	0.256790
$315$	6.62545e19	0.0385102
$316$	1.76973e21	1.00130
$317$	−1.67448e21	−0.922311	−0.461156	−	0.887319i	$-0.652565\pi$
$317$	−1.67448e21	−0.922311	−0.461156	+	0.887319i	$0.652565\pi$
$318$	−4.16200e20	−0.223189
$319$	−9.46730e20	−0.494317
$320$	1.37695e21	0.700074
$321$	−7.20322e20	−0.356643
$322$	−3.45911e19	−0.0166797
$323$	−4.18553e21	−1.96575
$324$	1.35438e21	0.619595
$325$	4.12328e17	0.000183753 0
$326$	−2.75449e20	−0.119589
$327$	−2.32362e21	−0.982898
$328$	−2.35883e20	−0.0972229
$329$	−2.35044e20	−0.0944024
$330$	−1.90536e20	−0.0745775
$331$	−2.94884e21	−1.12490	−0.562450	−	0.826831i	$-0.690141\pi$
$331$	−2.94884e21	−1.12490	−0.562450	+	0.826831i	$0.690141\pi$
$332$	−2.87866e21	−1.07033
$333$	−7.36616e20	−0.266972
$334$	1.08859e21	0.384609
$335$	1.52235e21	0.524364
$336$	−3.05286e20	−0.102523
$337$	7.47095e20	0.244637	0.122318	−	0.992491i	$-0.460967\pi$
$337$	7.47095e20	0.244637	0.122318	+	0.992491i	$0.460967\pi$
$338$	−7.12336e20	−0.227454
$339$	−6.19032e20	−0.192759
$340$	−4.17901e21	−1.26912
$341$	−1.22610e21	−0.363172
$342$	−3.14114e20	−0.0907540
$343$	−9.96549e20	−0.280866
$344$	−2.02317e20	−0.0556271
$345$	−1.63713e21	−0.439158
$346$	1.05117e21	0.275123
$347$	3.04718e21	0.778212	0.389106	−	0.921193i	$-0.372784\pi$
$347$	3.04718e21	0.778212	0.389106	+	0.921193i	$0.372784\pi$
$348$	4.16318e21	1.03753
$349$	−1.23494e21	−0.300351	−0.150176	−	0.988659i	$-0.547984\pi$
$349$	−1.23494e21	−0.300351	−0.150176	+	0.988659i	$0.547984\pi$
$350$	−8.95468e17	−0.000212555 0
$351$	−1.30778e20	−0.0302987
$352$	−1.08429e21	−0.245207
$353$	−7.12489e21	−1.57287	−0.786436	−	0.617672i	$-0.788076\pi$
$353$	−7.12489e21	−1.57287	−0.786436	+	0.617672i	$0.788076\pi$
$354$	1.17298e20	0.0252792
$355$	2.12095e17	4.46261e−5 0
$356$	−3.27635e21	−0.673078
$357$	8.10106e20	0.162503
$358$	7.12695e20	0.139604
$359$	6.84319e21	1.30905	0.654524	−	0.756041i	$-0.272869\pi$
$359$	6.84319e21	1.30905	0.654524	+	0.756041i	$0.272869\pi$
$360$	−6.44389e20	−0.120386
$361$	6.26268e21	1.14274
$362$	−4.90117e20	−0.0873529
$363$	4.17207e21	0.726349
$364$	2.20785e19	0.00375499
$365$	8.54846e21	1.42036
$366$	−1.76792e20	−0.0286994
$367$	−9.65431e21	−1.53130	−0.765649	−	0.643258i	$-0.777582\pi$
$367$	−9.65431e21	−1.53130	−0.765649	+	0.643258i	$0.777582\pi$
$368$	−2.82364e21	−0.437625
$369$	−3.94258e20	−0.0597113
$370$	−1.50255e21	−0.222389
$371$	1.12725e21	0.163059
$372$	5.39168e21	0.762270
$373$	5.38619e21	0.744314	0.372157	−	0.928170i	$-0.378618\pi$
$373$	5.38619e21	0.744314	0.372157	+	0.928170i	$0.378618\pi$
$374$	8.72042e20	0.117796
$375$	−6.48094e21	−0.855800
$376$	2.28602e21	0.295110
$377$	−2.83732e20	−0.0358102
$378$	2.84015e20	0.0350478
$379$	1.59930e22	1.92974	0.964868	−	0.262736i	$-0.0846248\pi$
$379$	1.59930e22	1.92974	0.964868	+	0.262736i	$0.0846248\pi$
$380$	1.17248e22	1.38339
$381$	−2.95857e21	−0.341365
$382$	9.06128e20	0.102247
$383$	−7.54518e21	−0.832683	−0.416342	−	0.909208i	$-0.636688\pi$
$383$	−7.54518e21	−0.832683	−0.416342	+	0.909208i	$0.636688\pi$
$384$	6.29217e21	0.679180
$385$	5.16055e20	0.0544854
$386$	−2.94357e20	−0.0304006
$387$	−3.38156e20	−0.0341644
$388$	−2.11411e21	−0.208957
$389$	−5.51437e21	−0.533241	−0.266621	−	0.963802i	$-0.585907\pi$
$389$	−5.51437e21	−0.533241	−0.266621	+	0.963802i	$0.585907\pi$
$390$	−5.71030e19	−0.00540269
$391$	7.49279e21	0.693652
$392$	4.79694e21	0.434543
$393$	1.24413e22	1.10288
$394$	2.19026e19	0.00190010
$395$	1.23969e22	1.05254
$396$	−1.19758e21	−0.0995165
$397$	2.29977e22	1.87053	0.935265	−	0.353949i	$-0.115161\pi$
$397$	2.29977e22	1.87053	0.935265	+	0.353949i	$0.115161\pi$
$398$	−3.65949e21	−0.291350
$399$	−2.27286e21	−0.177134
$400$	−7.30961e19	−0.00557679
$401$	−1.44008e22	−1.07562	−0.537812	−	0.843065i	$-0.680749\pi$
$401$	−1.44008e22	−1.07562	−0.537812	+	0.843065i	$0.680749\pi$
$402$	1.39694e21	0.102154
$403$	−3.67457e20	−0.0263096
$404$	−1.18178e22	−0.828504
$405$	9.48744e21	0.651300
$406$	6.16191e20	0.0414233
$407$	−5.73749e21	−0.377720
$408$	−7.87906e21	−0.507999
$409$	−3.00547e22	−1.89786	−0.948931	−	0.315484i	$-0.897833\pi$
$409$	−3.00547e22	−1.89786	−0.948931	+	0.315484i	$0.897833\pi$
$410$	−8.04206e20	−0.0497399
$411$	1.05417e22	0.638639
$412$	1.46346e22	0.868468
$413$	−3.17695e20	−0.0184686
$414$	5.62317e20	0.0320242
$415$	−2.01651e22	−1.12510
$416$	−3.24958e20	−0.0177637
$417$	2.77830e22	1.48807
$418$	−2.44663e21	−0.128401
$419$	7.79594e21	0.400912	0.200456	−	0.979703i	$-0.435758\pi$
$419$	7.79594e21	0.400912	0.200456	+	0.979703i	$0.435758\pi$
$420$	−2.26932e21	−0.114361
$421$	3.15344e22	1.55735	0.778677	−	0.627425i	$-0.215891\pi$
$421$	3.15344e22	1.55735	0.778677	+	0.627425i	$0.215891\pi$
$422$	6.56053e21	0.317529
$423$	3.82089e21	0.181247
$424$	−1.09636e22	−0.509735
$425$	1.93968e20	0.00883941
$426$	1.94623e17	8.69385e−6 0
$427$	4.78830e20	0.0209674
$428$	−9.23509e21	−0.396433
$429$	−2.18048e20	−0.00917626
$430$	−6.89770e20	−0.0284592
$431$	−1.16709e22	−0.472116	−0.236058	−	0.971739i	$-0.575856\pi$
$431$	−1.16709e22	−0.472116	−0.236058	+	0.971739i	$0.575856\pi$
$432$	2.31838e22	0.919546
$433$	4.98677e22	1.93942	0.969712	−	0.244253i	$-0.0785426\pi$
$433$	4.98677e22	1.93942	0.969712	+	0.244253i	$0.0785426\pi$
$434$	7.98020e20	0.0304335
$435$	2.91631e22	1.09062
$436$	−2.97906e22	−1.09256
$437$	−2.10220e22	−0.756106
$438$	7.84425e21	0.276708
$439$	1.37707e21	0.0476438	0.0238219	−	0.999716i	$-0.492417\pi$
$439$	1.37707e21	0.0476438	0.0238219	+	0.999716i	$0.492417\pi$
$440$	−5.01913e21	−0.170326
$441$	8.01767e21	0.266883
$442$	2.61349e20	0.00853357
$443$	−7.44793e21	−0.238563	−0.119282	−	0.992860i	$-0.538059\pi$
$443$	−7.44793e21	−0.238563	−0.119282	+	0.992860i	$0.538059\pi$
$444$	2.52302e22	0.792804
$445$	−2.29509e22	−0.707520
$446$	9.28015e21	0.280678
$447$	−6.88645e21	−0.204353
$448$	−3.42217e21	−0.0996412
$449$	−5.77985e22	−1.65129	−0.825644	−	0.564191i	$-0.809188\pi$
$449$	−5.77985e22	−1.65129	−0.825644	+	0.564191i	$0.809188\pi$
$450$	1.45568e19	0.000408094 0
$451$	−3.07087e21	−0.0844813
$452$	−7.93648e21	−0.214265
$453$	3.47737e22	0.921331
$454$	1.16850e22	0.303847
$455$	1.54660e20	0.00394713
$456$	2.21057e22	0.553738
$457$	−6.92765e22	−1.70333	−0.851664	−	0.524088i	$-0.824406\pi$
$457$	−6.92765e22	−1.70333	−0.851664	+	0.524088i	$0.824406\pi$
$458$	3.96915e21	0.0957947
$459$	−6.15206e22	−1.45751
$460$	−2.09893e22	−0.488153
$461$	−4.35415e22	−0.994136	−0.497068	−	0.867712i	$-0.665590\pi$
$461$	−4.35415e22	−0.994136	−0.497068	+	0.867712i	$0.665590\pi$
$462$	4.73543e20	0.0106146
$463$	−4.78581e22	−1.05322	−0.526608	−	0.850108i	$-0.676536\pi$
$463$	−4.78581e22	−1.05322	−0.526608	+	0.850108i	$0.676536\pi$
$464$	5.02991e22	1.08682
$465$	3.77687e22	0.801276
$466$	1.12057e22	0.233431
$467$	−7.31902e22	−1.49713	−0.748564	−	0.663062i	$-0.769257\pi$
$467$	−7.31902e22	−1.49713	−0.748564	+	0.663062i	$0.769257\pi$
$468$	−3.58911e20	−0.00720936
$469$	−3.78352e21	−0.0746324
$470$	7.79385e21	0.150980
$471$	−5.05803e22	−0.962284
$472$	3.08989e21	0.0577345
$473$	−2.63389e21	−0.0483368
$474$	1.13757e22	0.205051
$475$	−5.44202e20	−0.00963529
$476$	1.03862e22	0.180633
$477$	−1.83248e22	−0.313064
$478$	1.98168e22	0.332580
$479$	−1.15387e22	−0.190241	−0.0951205	−	0.995466i	$-0.530324\pi$
$479$	−1.15387e22	−0.190241	−0.0951205	+	0.995466i	$0.530324\pi$
$480$	3.34005e22	0.541006
$481$	−1.71951e21	−0.0273635
$482$	5.31932e21	0.0831681
$483$	4.06879e21	0.0625050
$484$	5.34892e22	0.807385
$485$	−1.48093e22	−0.219650
$486$	−8.24563e21	−0.120175
$487$	−3.05365e22	−0.437345	−0.218672	−	0.975798i	$-0.570173\pi$
$487$	−3.05365e22	−0.437345	−0.218672	+	0.975798i	$0.570173\pi$
$488$	−4.65708e21	−0.0655458
$489$	3.23998e22	0.448144
$490$	1.63544e22	0.222315
$491$	−7.71916e22	−1.03128	−0.515641	−	0.856805i	$-0.672446\pi$
$491$	−7.71916e22	−1.03128	−0.515641	+	0.856805i	$0.672446\pi$
$492$	1.35039e22	0.177320
$493$	−1.33473e23	−1.72265
$494$	−7.33248e20	−0.00930190
$495$	−8.38905e21	−0.104609
$496$	6.51416e22	0.798480
$497$	−5.27125e17	−6.35161e−6 0
$498$	−1.85039e22	−0.219186
$499$	−1.00285e23	−1.16783	−0.583915	−	0.811815i	$-0.698480\pi$
$499$	−1.00285e23	−1.16783	−0.583915	+	0.811815i	$0.698480\pi$
$500$	−8.30908e22	−0.951279
$501$	−1.28046e23	−1.44127
$502$	−1.68040e22	−0.185965
$503$	1.17368e23	1.27709	0.638546	−	0.769584i	$-0.279536\pi$
$503$	1.17368e23	1.27709	0.638546	+	0.769584i	$0.279536\pi$
$504$	1.60151e21	0.0171345
$505$	−8.27837e22	−0.870899
$506$	4.37987e21	0.0453088
$507$	8.37889e22	0.852351
$508$	−3.79311e22	−0.379450
$509$	8.71897e22	0.857757	0.428878	−	0.903362i	$-0.358909\pi$
$509$	8.71897e22	0.857757	0.428878	+	0.903362i	$0.358909\pi$
$510$	−2.68624e22	−0.259896
$511$	−2.12457e22	−0.202159
$512$	9.77552e22	0.914840
$513$	1.72604e23	1.58874
$514$	1.98931e22	0.180101
$515$	1.02515e23	0.912908
$516$	1.15824e22	0.101455
$517$	2.97609e22	0.256434
$518$	3.73432e21	0.0316525
$519$	−1.23645e23	−1.03099
$520$	−1.50422e21	−0.0123391
$521$	−1.64033e23	−1.32376	−0.661882	−	0.749608i	$-0.730242\pi$
$521$	−1.64033e23	−1.32376	−0.661882	+	0.749608i	$0.730242\pi$
$522$	−1.00169e22	−0.0795303
$523$	5.80399e22	0.453380	0.226690	−	0.973967i	$-0.427210\pi$
$523$	5.80399e22	0.453380	0.226690	+	0.973967i	$0.427210\pi$
$524$	1.59507e23	1.22593
$525$	1.05330e20	0.000796521 0
$526$	1.32808e22	0.0988204
$527$	−1.72860e23	−1.26562
$528$	3.86548e22	0.278494
$529$	−1.03417e23	−0.733195
$530$	−3.73788e22	−0.260784
$531$	5.16448e21	0.0354587
$532$	−2.91399e22	−0.196897
$533$	−9.20330e20	−0.00612015
$534$	−2.10602e22	−0.137836
$535$	−6.46919e22	−0.416718
$536$	3.67984e22	0.233307
$537$	−8.38311e22	−0.523147
$538$	8.39508e21	0.0515674
$539$	6.24495e22	0.377593
$540$	1.72335e23	1.02572
$541$	5.81472e22	0.340684	0.170342	−	0.985385i	$-0.445513\pi$
$541$	5.81472e22	0.340684	0.170342	+	0.985385i	$0.445513\pi$
$542$	−3.32183e22	−0.191595
$543$	5.76503e22	0.327343
$544$	−1.52867e23	−0.854521
$545$	−2.08683e23	−1.14846
$546$	1.41919e20	0.000768961 0
$547$	−2.54239e23	−1.35628	−0.678141	−	0.734932i	$-0.737214\pi$
$547$	−2.54239e23	−1.35628	−0.678141	+	0.734932i	$0.737214\pi$
$548$	1.35153e23	0.709890
$549$	−7.78391e21	−0.0402562
$550$	1.13383e20	0.000577383 0
$551$	3.74478e23	1.87775
$552$	−3.95729e22	−0.195396
$553$	−3.08104e22	−0.149808
$554$	−2.93430e22	−0.140499
$555$	1.76738e23	0.833373
$556$	3.56200e23	1.65409
$557$	2.82126e23	1.29025	0.645125	−	0.764077i	$-0.276805\pi$
$557$	2.82126e23	1.29025	0.645125	+	0.764077i	$0.276805\pi$
$558$	−1.29727e22	−0.0584305
$559$	−7.89369e20	−0.00350171
$560$	−2.74176e22	−0.119793
$561$	−1.02574e23	−0.441423
$562$	2.73717e22	0.116023
$563$	−2.62615e23	−1.09648	−0.548238	−	0.836323i	$-0.684701\pi$
$563$	−2.62615e23	−1.09648	−0.548238	+	0.836323i	$0.684701\pi$
$564$	−1.30871e23	−0.538236
$565$	−5.55951e22	−0.225229
$566$	−7.88143e22	−0.314532
$567$	−2.35794e22	−0.0926992
$568$	5.12679e18	1.98557e−5 0
$569$	3.17162e23	1.21011	0.605057	−	0.796182i	$-0.293150\pi$
$569$	3.17162e23	1.21011	0.605057	+	0.796182i	$0.293150\pi$
$570$	7.53661e22	0.283296
$571$	−4.56127e23	−1.68919	−0.844595	−	0.535406i	$-0.820159\pi$
$571$	−4.56127e23	−1.68919	−0.844595	+	0.535406i	$0.820159\pi$
$572$	−2.79555e21	−0.0102000
$573$	−1.06584e23	−0.383157
$574$	1.99871e21	0.00707945
$575$	9.74212e20	0.00339998
$576$	5.56312e22	0.191305
$577$	−3.62212e22	−0.122735	−0.0613675	−	0.998115i	$-0.519546\pi$
$577$	−3.62212e22	−0.122735	−0.0613675	+	0.998115i	$0.519546\pi$
$578$	5.47698e22	0.182875
$579$	3.46239e22	0.113922
$580$	3.73894e23	1.21230
$581$	5.01167e22	0.160135
$582$	−1.35894e22	−0.0427911
$583$	−1.42731e23	−0.442932
$584$	2.06635e23	0.631967
$585$	−2.51417e21	−0.00757827
$586$	−2.78089e22	−0.0826139
$587$	−2.69899e23	−0.790272	−0.395136	−	0.918623i	$-0.629303\pi$
$587$	−2.69899e23	−0.790272	−0.395136	+	0.918623i	$0.629303\pi$
$588$	−2.74617e23	−0.792539
$589$	4.84980e23	1.37957
$590$	1.05345e22	0.0295373
$591$	−2.57630e21	−0.00712038
$592$	3.04829e23	0.830465
$593$	2.24371e21	0.00602562	0.00301281	−	0.999995i	$-0.499041\pi$
$593$	2.24371e21	0.00602562	0.00301281	+	0.999995i	$0.499041\pi$
$594$	−3.59615e22	−0.0952036
$595$	7.27553e22	0.189876
$596$	−8.82897e22	−0.227152
$597$	4.30449e23	1.09179
$598$	1.31263e21	0.00328234
$599$	4.10096e23	1.01101	0.505507	−	0.862823i	$-0.331306\pi$
$599$	4.10096e23	1.01101	0.505507	+	0.862823i	$0.331306\pi$
$600$	−1.02443e21	−0.00248999
$601$	−2.07254e23	−0.496673	−0.248337	−	0.968674i	$-0.579884\pi$
$601$	−2.07254e23	−0.496673	−0.248337	+	0.968674i	$0.579884\pi$
$602$	1.71430e21	0.00405058
$603$	6.15054e22	0.143290
$604$	4.45826e23	1.02412
$605$	3.74692e23	0.848700
$606$	−7.59641e22	−0.169664
$607$	2.58553e23	0.569438	0.284719	−	0.958611i	$-0.408100\pi$
$607$	2.58553e23	0.569438	0.284719	+	0.958611i	$0.408100\pi$
$608$	4.28889e23	0.931460
$609$	−7.24798e22	−0.155228
$610$	−1.58776e22	−0.0335337
$611$	8.91924e21	0.0185771
$612$	−1.68839e23	−0.346805
$613$	−6.98944e22	−0.141589	−0.0707943	−	0.997491i	$-0.522553\pi$
$613$	−6.98944e22	−0.141589	−0.0707943	+	0.997491i	$0.522553\pi$
$614$	7.45142e22	0.148870
$615$	9.45951e22	0.186393
$616$	1.24742e22	0.0242424
$617$	1.10882e23	0.212538	0.106269	−	0.994337i	$-0.466110\pi$
$617$	1.10882e23	0.212538	0.106269	+	0.994337i	$0.466110\pi$
$618$	9.40702e22	0.177848
$619$	2.33109e23	0.434699	0.217349	−	0.976094i	$-0.430259\pi$
$619$	2.33109e23	0.434699	0.217349	+	0.976094i	$0.430259\pi$
$620$	4.84225e23	0.890672
$621$	−3.08990e23	−0.560616
$622$	−3.91220e22	−0.0700170
$623$	5.70403e22	0.100701
$624$	1.15847e22	0.0201752
$625$	−5.78220e23	−0.993374
$626$	−6.81373e22	−0.115479
$627$	2.87786e23	0.481167
$628$	−6.48479e23	−1.06964
$629$	−8.08892e23	−1.31632
$630$	5.46012e21	0.00876612
$631$	4.82440e23	0.764176	0.382088	−	0.924126i	$-0.375205\pi$
$631$	4.82440e23	0.764176	0.382088	+	0.924126i	$0.375205\pi$
$632$	2.99661e23	0.468312
$633$	−7.71685e23	−1.18989
$634$	−1.37996e23	−0.209947
$635$	−2.65708e23	−0.398867
$636$	6.27652e23	0.929679
$637$	1.87159e22	0.0273543
$638$	−7.80212e22	−0.112522
$639$	8.56899e18	1.21947e−5 0
$640$	5.65098e23	0.793586
$641$	−5.26804e22	−0.0730055	−0.0365027	−	0.999334i	$-0.511622\pi$
$641$	−5.26804e22	−0.0730055	−0.0365027	+	0.999334i	$0.511622\pi$
$642$	−5.93626e22	−0.0811831
$643$	2.22624e21	0.00300455	0.00150228	−	0.999999i	$-0.499522\pi$
$643$	2.22624e21	0.00300455	0.00150228	+	0.999999i	$0.499522\pi$
$644$	5.21651e22	0.0694785
$645$	8.11345e22	0.106647
$646$	−3.44935e23	−0.447467
$647$	−4.66422e23	−0.597163	−0.298581	−	0.954384i	$-0.596513\pi$
$647$	−4.66422e23	−0.597163	−0.298581	+	0.954384i	$0.596513\pi$
$648$	2.29332e23	0.289786
$649$	4.02260e22	0.0501681
$650$	3.39805e19	4.18279e−5 0
$651$	−9.38675e22	−0.114045
$652$	4.15392e23	0.498142
$653$	−1.17388e24	−1.38951	−0.694756	−	0.719245i	$-0.744488\pi$
$653$	−1.17388e24	−1.38951	−0.694756	+	0.719245i	$0.744488\pi$
$654$	−1.91492e23	−0.223738
$655$	1.11735e24	1.28866
$656$	1.63153e23	0.185743
$657$	3.45372e23	0.388134
$658$	−1.93702e22	−0.0214889
$659$	6.24504e23	0.683926	0.341963	−	0.939713i	$-0.388908\pi$
$659$	6.24504e23	0.683926	0.341963	+	0.939713i	$0.388908\pi$
$660$	2.87338e23	0.310648
$661$	7.82011e23	0.834643	0.417321	−	0.908759i	$-0.362969\pi$
$661$	7.82011e23	0.834643	0.417321	+	0.908759i	$0.362969\pi$
$662$	−2.43018e23	−0.256062
$663$	−3.07412e22	−0.0319784
$664$	−4.87433e23	−0.500595
$665$	−2.04125e23	−0.206972
$666$	−6.07055e22	−0.0607711
$667$	−6.70377e23	−0.662597
$668$	−1.64165e24	−1.60207
$669$	−1.09158e24	−1.05180
$670$	1.25458e23	0.119361
$671$	−6.06287e22	−0.0569556
$672$	−8.30110e22	−0.0770011
$673$	−9.68722e23	−0.887301	−0.443651	−	0.896200i	$-0.646317\pi$
$673$	−9.68722e23	−0.887301	−0.443651	+	0.896200i	$0.646317\pi$
$674$	6.15690e22	0.0556869
$675$	−7.99889e21	−0.00714411
$676$	1.07424e24	0.947445
$677$	−9.11599e23	−0.793962	−0.396981	−	0.917827i	$-0.629942\pi$
$677$	−9.11599e23	−0.793962	−0.396981	+	0.917827i	$0.629942\pi$
$678$	−5.10152e22	−0.0438780
$679$	3.68060e22	0.0312626
$680$	−7.07616e23	−0.593570
$681$	−1.37445e24	−1.13862
$682$	−1.01044e23	−0.0826692
$683$	−2.17931e23	−0.176094	−0.0880468	−	0.996116i	$-0.528063\pi$
$683$	−2.17931e23	−0.176094	−0.0880468	+	0.996116i	$0.528063\pi$
$684$	4.73701e23	0.378031
$685$	9.46748e23	0.746216
$686$	−8.21268e22	−0.0639337
$687$	−4.66874e23	−0.358977
$688$	1.39937e23	0.106275
$689$	−4.27762e22	−0.0320877
$690$	−1.34918e23	−0.0999659
$691$	−1.26873e23	−0.0928550	−0.0464275	−	0.998922i	$-0.514784\pi$
$691$	−1.26873e23	−0.0928550	−0.0464275	+	0.998922i	$0.514784\pi$
$692$	−1.58522e24	−1.14601
$693$	2.08495e22	0.0148889
$694$	2.51122e23	0.177145
$695$	2.49518e24	1.73873
$696$	7.04935e23	0.485256
$697$	−4.32942e23	−0.294409
$698$	−1.01773e23	−0.0683693
$699$	−1.31808e24	−0.874752
$700$	1.35041e21	0.000885386 0
$701$	−8.54540e23	−0.553515	−0.276757	−	0.960940i	$-0.589260\pi$
$701$	−8.54540e23	−0.553515	−0.276757	+	0.960940i	$0.589260\pi$
$702$	−1.07776e22	−0.00689692
$703$	2.26946e24	1.43483
$704$	4.33310e23	0.270665
$705$	−9.16755e23	−0.565777
$706$	−5.87171e23	−0.358034
$707$	2.05744e23	0.123955
$708$	−1.76891e23	−0.105299
$709$	−7.36640e23	−0.433274	−0.216637	−	0.976252i	$-0.569509\pi$
$709$	−7.36640e23	−0.433274	−0.216637	+	0.976252i	$0.569509\pi$
$710$	1.74790e19	1.01583e−5 0
$711$	5.00858e23	0.287622
$712$	−5.54772e23	−0.314800
$713$	−8.68195e23	−0.486806
$714$	6.67618e22	0.0369908
$715$	−1.95828e22	−0.0107220
$716$	−1.07478e24	−0.581513
$717$	−2.33096e24	−1.24630
$718$	5.63956e23	0.297980
$719$	−3.16939e24	−1.65493	−0.827467	−	0.561514i	$-0.810219\pi$
$719$	−3.16939e24	−1.65493	−0.827467	+	0.561514i	$0.810219\pi$
$720$	4.45704e23	0.229996
$721$	−2.54784e23	−0.129934
$722$	5.16116e23	0.260124
$723$	−6.25688e23	−0.311661
$724$	7.39122e23	0.363863
$725$	−1.73542e22	−0.00844367
$726$	3.43826e23	0.165340
$727$	−1.52540e24	−0.725005	−0.362502	−	0.931983i	$-0.618078\pi$
$727$	−1.52540e24	−0.725005	−0.362502	+	0.931983i	$0.618078\pi$
$728$	3.73847e21	0.00175621
$729$	2.37724e24	1.10380
$730$	7.04490e23	0.323318
$731$	−3.71336e23	−0.168449
$732$	2.66611e23	0.119546
$733$	2.39175e23	0.106006	0.0530031	−	0.998594i	$-0.483121\pi$
$733$	2.39175e23	0.106006	0.0530031	+	0.998594i	$0.483121\pi$
$734$	−7.95624e23	−0.348571
$735$	−1.92370e24	−0.833094
$736$	−7.67781e23	−0.328682
$737$	4.79064e23	0.202731
$738$	−3.24913e22	−0.0135921
$739$	1.36437e24	0.564228	0.282114	−	0.959381i	$-0.408964\pi$
$739$	1.36437e24	0.564228	0.282114	+	0.959381i	$0.408964\pi$
$740$	2.26592e24	0.926349
$741$	8.62486e22	0.0348576
$742$	9.28985e22	0.0371172
$743$	4.47038e24	1.76579	0.882895	−	0.469570i	$-0.155591\pi$
$743$	4.47038e24	1.76579	0.882895	+	0.469570i	$0.155591\pi$
$744$	9.12952e23	0.356515
$745$	−6.18470e23	−0.238776
$746$	4.43882e23	0.169429
$747$	−8.14702e23	−0.307450
$748$	−1.31508e24	−0.490671
$749$	1.60780e23	0.0593113
$750$	−5.34103e23	−0.194807
$751$	2.13210e24	0.768895	0.384448	−	0.923147i	$-0.374392\pi$
$751$	2.13210e24	0.768895	0.384448	+	0.923147i	$0.374392\pi$
$752$	−1.58117e24	−0.563803
$753$	1.97657e24	0.696876
$754$	−2.33827e22	−0.00815152
$755$	3.12301e24	1.07653
$756$	−4.28309e23	−0.145990
$757$	9.31156e23	0.313839	0.156920	−	0.987611i	$-0.449844\pi$
$757$	9.31156e23	0.313839	0.156920	+	0.987611i	$0.449844\pi$
$758$	1.31801e24	0.439268
$759$	−5.15185e23	−0.169788
$760$	1.98531e24	0.647013
$761$	−4.56816e24	−1.47222	−0.736109	−	0.676863i	$-0.763339\pi$
$761$	−4.56816e24	−1.47222	−0.736109	+	0.676863i	$0.763339\pi$
$762$	−2.43819e23	−0.0777053
$763$	5.18645e23	0.163460
$764$	−1.36649e24	−0.425904
$765$	−1.18272e24	−0.364552
$766$	−6.21807e23	−0.189545
$767$	1.20556e22	0.00363437
$768$	−1.49104e24	−0.444547
$769$	7.90010e23	0.232948	0.116474	−	0.993194i	$-0.462841\pi$
$769$	7.90010e23	0.232948	0.116474	+	0.993194i	$0.462841\pi$
$770$	4.25287e22	0.0124026
$771$	−2.33994e24	−0.674904
$772$	4.43906e23	0.126632
$773$	2.16522e24	0.610910	0.305455	−	0.952207i	$-0.401191\pi$
$773$	2.16522e24	0.610910	0.305455	+	0.952207i	$0.401191\pi$
$774$	−2.78679e22	−0.00777688
$775$	−2.24752e22	−0.00620352
$776$	−3.57974e23	−0.0977297
$777$	−4.39251e23	−0.118613
$778$	−4.54446e23	−0.121382
$779$	1.21468e24	0.320917
$780$	8.61142e22	0.0225046
$781$	6.67437e19	1.72535e−5 0
$782$	6.17491e23	0.157897
$783$	5.50422e24	1.39226
$784$	−3.31789e24	−0.830187
$785$	−4.54260e24	−1.12438
$786$	1.02530e24	0.251050
$787$	−4.35665e24	−1.05528	−0.527640	−	0.849468i	$-0.676923\pi$
$787$	−4.35665e24	−1.05528	−0.527640	+	0.849468i	$0.676923\pi$
$788$	−3.30302e22	−0.00791478
$789$	−1.56216e24	−0.370316
$790$	1.02165e24	0.239591
$791$	1.38172e23	0.0320567
$792$	−2.02781e23	−0.0465440
$793$	−1.81702e22	−0.00412609
$794$	1.89527e24	0.425791
$795$	4.39670e24	0.977252
$796$	5.51870e24	1.21360
$797$	−6.82691e24	−1.48535	−0.742675	−	0.669652i	$-0.766443\pi$
$797$	−6.82691e24	−1.48535	−0.742675	+	0.669652i	$0.766443\pi$
$798$	−1.87309e23	−0.0403213
$799$	4.19579e24	0.893648
$800$	−1.98757e22	−0.00418850
$801$	−9.27254e23	−0.193340
$802$	−1.18679e24	−0.244845
$803$	2.69010e24	0.549144
$804$	−2.10665e24	−0.425517
$805$	3.65417e23	0.0730338
$806$	−3.02826e22	−0.00598888
$807$	−9.87475e23	−0.193242
$808$	−2.00106e24	−0.387493
$809$	1.60220e24	0.307012	0.153506	−	0.988148i	$-0.450944\pi$
$809$	1.60220e24	0.307012	0.153506	+	0.988148i	$0.450944\pi$
$810$	7.81872e23	0.148256
$811$	2.70019e24	0.506661	0.253330	−	0.967380i	$-0.418474\pi$
$811$	2.70019e24	0.506661	0.253330	+	0.967380i	$0.418474\pi$
$812$	−9.29248e23	−0.172546
$813$	3.90732e24	0.717975
$814$	−4.72834e23	−0.0859807
$815$	2.90982e24	0.523632
$816$	5.44970e24	0.970524
$817$	1.04183e24	0.183616
$818$	−2.47685e24	−0.432012
$819$	6.24853e21	0.00107861
$820$	1.21278e24	0.207189
$821$	−1.01213e25	−1.71127	−0.855634	−	0.517582i	$-0.826832\pi$
$821$	−1.01213e25	−1.71127	−0.855634	+	0.517582i	$0.826832\pi$
$822$	8.68756e23	0.145374
$823$	−6.27574e24	−1.03936	−0.519681	−	0.854361i	$-0.673949\pi$
$823$	−6.27574e24	−1.03936	−0.519681	+	0.854361i	$0.673949\pi$
$824$	2.47801e24	0.406184
$825$	−1.33367e22	−0.00216366
$826$	−2.61816e22	−0.00420403
$827$	1.11592e25	1.77352	0.886760	−	0.462229i	$-0.152950\pi$
$827$	1.11592e25	1.77352	0.886760	+	0.462229i	$0.152950\pi$
$828$	−8.48002e23	−0.133395
$829$	1.97400e24	0.307351	0.153675	−	0.988121i	$-0.450889\pi$
$829$	1.97400e24	0.307351	0.153675	+	0.988121i	$0.450889\pi$
$830$	−1.66183e24	−0.256107
$831$	3.45149e24	0.526499
$832$	1.29862e23	0.0196080
$833$	8.80436e24	1.31588
$834$	2.28963e24	0.338730
$835$	−1.14998e25	−1.68405
$836$	3.68964e24	0.534849
$837$	7.12843e24	1.02289
$838$	6.42473e23	0.0912601
$839$	6.08158e24	0.855145	0.427572	−	0.903981i	$-0.359369\pi$
$839$	6.08158e24	0.855145	0.427572	+	0.903981i	$0.359369\pi$
$840$	−3.84255e23	−0.0534866
$841$	4.68466e24	0.645523
$842$	2.59879e24	0.354502
$843$	−3.21961e24	−0.434780
$844$	−9.89361e24	−1.32265
$845$	7.52505e24	0.995927
$846$	3.14885e23	0.0412575
$847$	−9.31232e23	−0.120795
$848$	7.58321e24	0.973841
$849$	9.27056e24	1.17867
$850$	1.59851e22	0.00201213
$851$	−4.06270e24	−0.506306
$852$	−2.93501e20	−3.62137e−5 0
$853$	−8.58941e24	−1.04929	−0.524646	−	0.851320i	$-0.675802\pi$
$853$	−8.58941e24	−1.04929	−0.524646	+	0.851320i	$0.675802\pi$
$854$	3.94610e22	0.00477283
$855$	3.31827e24	0.397375
$856$	−1.56374e24	−0.185412
$857$	−6.18790e24	−0.726451	−0.363226	−	0.931701i	$-0.618325\pi$
$857$	−6.18790e24	−0.726451	−0.363226	+	0.931701i	$0.618325\pi$
$858$	−1.79696e22	−0.00208880
$859$	1.20392e25	1.38566	0.692828	−	0.721103i	$-0.256365\pi$
$859$	1.20392e25	1.38566	0.692828	+	0.721103i	$0.256365\pi$
$860$	1.04021e24	0.118545
$861$	−2.35099e23	−0.0265292
$862$	−9.61816e23	−0.107468
$863$	1.20653e25	1.33489	0.667447	−	0.744657i	$-0.267387\pi$
$863$	1.20653e25	1.33489	0.667447	+	0.744657i	$0.267387\pi$
$864$	6.30397e24	0.690633
$865$	−1.11045e25	−1.20465
$866$	4.10966e24	0.441473
$867$	−6.44233e24	−0.685299
$868$	−1.20346e24	−0.126769
$869$	3.90117e24	0.406937
$870$	2.40337e24	0.248260
$871$	1.43574e23	0.0146866
$872$	−5.04432e24	−0.510990
$873$	−5.98322e23	−0.0600225
$874$	−1.73245e24	−0.172113
$875$	1.44659e24	0.142323
$876$	−1.18295e25	−1.15261
$877$	6.01843e24	0.580747	0.290373	−	0.956913i	$-0.406220\pi$
$877$	6.01843e24	0.580747	0.290373	+	0.956913i	$0.406220\pi$
$878$	1.13486e23	0.0108452
$879$	3.27103e24	0.309584
$880$	3.47158e24	0.325405
$881$	9.79107e24	0.908940	0.454470	−	0.890762i	$-0.349829\pi$
$881$	9.79107e24	0.908940	0.454470	+	0.890762i	$0.349829\pi$
$882$	6.60746e23	0.0607508
$883$	3.03669e24	0.276525	0.138263	−	0.990396i	$-0.455848\pi$
$883$	3.03669e24	0.276525	0.138263	+	0.990396i	$0.455848\pi$
$884$	−3.94127e23	−0.0355461
$885$	−1.23912e24	−0.110687
$886$	−6.13793e23	−0.0543045
$887$	−4.68275e23	−0.0410346	−0.0205173	−	0.999789i	$-0.506531\pi$
$887$	−4.68275e23	−0.0410346	−0.0205173	+	0.999789i	$0.506531\pi$
$888$	4.27214e24	0.370796
$889$	6.60370e23	0.0567705
$890$	−1.89141e24	−0.161054
$891$	2.98558e24	0.251807
$892$	−1.39949e25	−1.16915
$893$	−1.17719e25	−0.974109
$894$	−5.67521e23	−0.0465172
$895$	−7.52884e24	−0.611269
$896$	−1.40445e24	−0.112951
$897$	−1.54399e23	−0.0123001
$898$	−4.76325e24	−0.375885
$899$	1.54657e25	1.20896
$900$	−2.19524e22	−0.00169989
$901$	−2.01228e25	−1.54357
$902$	−2.53074e23	−0.0192306
$903$	−2.01645e23	−0.0151790
$904$	−1.34385e24	−0.100212
$905$	5.17755e24	0.382483
$906$	2.86574e24	0.209724
$907$	−2.47841e24	−0.179685	−0.0898423	−	0.995956i	$-0.528636\pi$
$907$	−2.47841e24	−0.179685	−0.0898423	+	0.995956i	$0.528636\pi$
$908$	−1.76216e25	−1.26565
$909$	−3.34460e24	−0.237986
$910$	1.27457e22	0.000898490 0
$911$	−2.44197e25	−1.70543	−0.852714	−	0.522378i	$-0.825045\pi$
$911$	−2.44197e25	−1.70543	−0.852714	+	0.522378i	$0.825045\pi$
$912$	−1.52899e25	−1.05791
$913$	−6.34570e24	−0.434989
$914$	−5.70917e24	−0.387730
$915$	1.86761e24	0.125663
$916$	−5.98569e24	−0.399027
$917$	−2.77697e24	−0.183414
$918$	−5.06999e24	−0.331775
$919$	−7.57916e24	−0.491405	−0.245702	−	0.969345i	$-0.579019\pi$
$919$	−7.57916e24	−0.491405	−0.245702	+	0.969345i	$0.579019\pi$
$920$	−3.55403e24	−0.228310
$921$	−8.76477e24	−0.557871
$922$	−3.58831e24	−0.226296
$923$	2.00029e19	1.24991e−6 0
$924$	−7.14127e23	−0.0442144
$925$	−1.05172e23	−0.00645202
$926$	−3.94405e24	−0.239745
$927$	4.14179e24	0.249465
$928$	1.36769e25	0.816264
$929$	−3.88806e24	−0.229932	−0.114966	−	0.993369i	$-0.536676\pi$
$929$	−3.88806e24	−0.229932	−0.114966	+	0.993369i	$0.536676\pi$
$930$	3.11257e24	0.182395
$931$	−2.47018e25	−1.43435
$932$	−1.68988e25	−0.972345
$933$	4.60175e24	0.262379
$934$	−6.03169e24	−0.340793
$935$	−9.21217e24	−0.515779
$936$	−6.07730e22	−0.00337183
$937$	6.58913e24	0.362278	0.181139	−	0.983458i	$-0.442022\pi$
$937$	6.58913e24	0.362278	0.181139	+	0.983458i	$0.442022\pi$
$938$	−3.11805e23	−0.0169887
$939$	8.01468e24	0.432742
$940$	−1.17535e25	−0.628899
$941$	3.15517e25	1.67306	0.836529	−	0.547922i	$-0.184581\pi$
$941$	3.15517e25	1.67306	0.836529	+	0.547922i	$0.184581\pi$
$942$	−4.16838e24	−0.219046
$943$	−2.17447e24	−0.113241
$944$	−2.13718e24	−0.110301
$945$	−3.00030e24	−0.153460
$946$	−2.17062e23	−0.0110030
$947$	5.30449e24	0.266483	0.133241	−	0.991084i	$-0.457461\pi$
$947$	5.30449e24	0.266483	0.133241	+	0.991084i	$0.457461\pi$
$948$	−1.71551e25	−0.854129
$949$	8.06214e23	0.0397821
$950$	−4.48484e22	−0.00219329
$951$	1.62319e25	0.786746
$952$	1.75865e24	0.0844824
$953$	3.12610e25	1.48838	0.744188	−	0.667970i	$-0.232837\pi$
$953$	3.12610e25	1.48838	0.744188	+	0.667970i	$0.232837\pi$
$954$	−1.51017e24	−0.0712630
$955$	−9.57224e24	−0.447698
$956$	−2.98847e25	−1.38534
$957$	9.17728e24	0.421660
$958$	−9.50917e23	−0.0433048
$959$	−2.35297e24	−0.106208
$960$	−1.33477e25	−0.597175
$961$	−2.52076e24	−0.111785
$962$	−1.41707e23	−0.00622878
$963$	−2.61366e24	−0.113874
$964$	−8.02181e24	−0.346432
$965$	3.10956e24	0.133112
$966$	3.35314e23	0.0142281
$967$	−2.31470e25	−0.973575	−0.486788	−	0.873520i	$-0.661831\pi$
$967$	−2.31470e25	−0.973575	−0.486788	+	0.873520i	$0.661831\pi$
$968$	9.05712e24	0.377615
$969$	4.05731e25	1.67682
$970$	−1.22046e24	−0.0499991
$971$	1.64757e25	0.669082	0.334541	−	0.942381i	$-0.391419\pi$
$971$	1.64757e25	0.669082	0.334541	+	0.942381i	$0.391419\pi$
$972$	1.24348e25	0.500584
$973$	−6.20134e24	−0.247472
$974$	−2.51656e24	−0.0995532
$975$	−3.99697e21	−0.000156744 0
$976$	3.22116e24	0.125224
$977$	1.18564e25	0.456929	0.228465	−	0.973552i	$-0.426629\pi$
$977$	1.18564e25	0.456929	0.228465	+	0.973552i	$0.426629\pi$
$978$	2.67011e24	0.102012
$979$	−7.22236e24	−0.273543
$980$	−2.46633e25	−0.926040
$981$	−8.43115e24	−0.313834
$982$	−6.36146e24	−0.234752
$983$	4.06962e25	1.48884	0.744421	−	0.667710i	$-0.232725\pi$
$983$	4.06962e25	1.48884	0.744421	+	0.667710i	$0.232725\pi$
$984$	2.28657e24	0.0829327
$985$	−2.31377e23	−0.00831978
$986$	−1.09997e25	−0.392128
$987$	2.27843e24	0.0805268
$988$	1.10578e24	0.0387465
$989$	−1.86505e24	−0.0647921
$990$	−6.91352e23	−0.0238122
$991$	−1.22384e25	−0.417924	−0.208962	−	0.977924i	$-0.567009\pi$
$991$	−1.22384e25	−0.417924	−0.208962	+	0.977924i	$0.567009\pi$
$992$	1.77128e25	0.599705
$993$	2.85851e25	0.959557
$994$	−4.34410e19	−1.44582e−6 0
$995$	3.86585e25	1.27570
$996$	2.79048e25	0.913008
$997$	4.51209e25	1.46376	0.731878	−	0.681436i	$-0.238644\pi$
$997$	4.51209e25	1.46376	0.731878	+	0.681436i	$0.238644\pi$
$998$	−8.26458e24	−0.265834
$999$	3.33573e25	1.06386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.18.a.a.1.21	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.18.a.a.1.21	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	59.a (trivial)

\(f(q)\)	\(=\)	\(q+82.4113 q^{2} -9693.66 q^{3} -124280. q^{4} -870585. q^{5} -798867. q^{6} +2.16368e6 q^{7} -2.10439e7 q^{8} -3.51731e7 q^{9} +O(q^{10})\)	\(q+82.4113 q^{2} -9693.66 q^{3} -124280. q^{4} -870585. q^{5} -798867. q^{6} +2.16368e6 q^{7} -2.10439e7 q^{8} -3.51731e7 q^{9} -7.17460e7 q^{10} -2.73963e8 q^{11} +1.20473e9 q^{12} -8.21057e7 q^{13} +1.78312e8 q^{14} +8.43915e9 q^{15} +1.45554e10 q^{16} -3.86242e10 q^{17} -2.89866e9 q^{18} +1.08365e11 q^{19} +1.08197e11 q^{20} -2.09740e10 q^{21} -2.25776e10 q^{22} -1.93992e11 q^{23} +2.03993e11 q^{24} -5.02192e9 q^{25} -6.76644e9 q^{26} +1.59280e12 q^{27} -2.68904e11 q^{28} +3.45569e12 q^{29} +6.95481e11 q^{30} +4.47542e12 q^{31} +3.95780e12 q^{32} +2.65570e12 q^{33} -3.18307e12 q^{34} -1.88367e12 q^{35} +4.37132e12 q^{36} +2.09426e13 q^{37} +8.93053e12 q^{38} +7.95905e11 q^{39} +1.83205e13 q^{40} +1.12091e13 q^{41} -1.72850e12 q^{42} +9.61406e12 q^{43} +3.40482e13 q^{44} +3.06211e13 q^{45} -1.59871e13 q^{46} -1.08631e14 q^{47} -1.41095e14 q^{48} -2.27949e14 q^{49} -4.13862e11 q^{50} +3.74410e14 q^{51} +1.02041e13 q^{52} +5.20989e14 q^{53} +1.31264e14 q^{54} +2.38508e14 q^{55} -4.55324e13 q^{56} -1.05046e15 q^{57} +2.84788e14 q^{58} -1.46830e14 q^{59} -1.04882e15 q^{60} +2.21303e14 q^{61} +3.68825e14 q^{62} -7.61035e13 q^{63} -1.58164e15 q^{64} +7.14800e13 q^{65} +2.18860e14 q^{66} -1.74865e15 q^{67} +4.80024e15 q^{68} +1.88049e15 q^{69} -1.55236e14 q^{70} -2.43624e11 q^{71} +7.40179e14 q^{72} -9.81922e15 q^{73} +1.72591e15 q^{74} +4.86808e13 q^{75} -1.34677e16 q^{76} -5.92768e14 q^{77} +6.55916e13 q^{78} -1.42398e16 q^{79} -1.26717e16 q^{80} -1.08978e16 q^{81} +9.23754e14 q^{82} +2.31627e16 q^{83} +2.60666e15 q^{84} +3.36257e16 q^{85} +7.92307e14 q^{86} -3.34983e16 q^{87} +5.76524e15 q^{88} +2.63626e16 q^{89} +2.52353e15 q^{90} -1.77651e14 q^{91} +2.41094e16 q^{92} -4.33832e16 q^{93} -8.95243e15 q^{94} -9.43413e16 q^{95} -3.83656e16 q^{96} +1.70108e16 q^{97} -1.87856e16 q^{98} +9.63611e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 15 q^{2} + 2080511 q^{4} - 1062222 q^{5} - 3454906 q^{6} - 43925040 q^{7} + 17944905 q^{8} + 1407964240 q^{9}+O(q^{10}) \) 38 * q + 15 * q^2 + 2080511 * q^4 - 1062222 * q^5 - 3454906 * q^6 - 43925040 * q^7 + 17944905 * q^8 + 1407964240 * q^9	\( 38 q + 15 q^{2} + 2080511 q^{4} - 1062222 q^{5} - 3454906 q^{6} - 43925040 q^{7} + 17944905 q^{8} + 1407964240 q^{9} - 753380082 q^{10} - 1247087592 q^{11} - 12806174710 q^{13} - 9920461605 q^{14} - 26267835313 q^{15} + 150793103155 q^{16} - 32714582925 q^{17} - 321256617405 q^{18} - 275283244180 q^{19} - 219435764020 q^{20} - 301109113003 q^{21} + 141637789665 q^{22} + 101540066360 q^{23} + 2412933601890 q^{24} + 4991161115804 q^{25} + 990445756111 q^{26} - 1179423443835 q^{27} - 10869216693165 q^{28} - 12862783749830 q^{29} - 27886581579060 q^{30} - 7513791056524 q^{31} - 31047860166815 q^{32} - 16499870737070 q^{33} - 62883745276639 q^{34} - 41836456706373 q^{35} - 74757290464031 q^{36} - 113711477231480 q^{37} - 86782161105620 q^{38} - 63680125347522 q^{39} - 53946909479582 q^{40} - 40841718887048 q^{41} - 8891162142170 q^{42} - 81961546008910 q^{43} - 24535596549333 q^{44} - 43121875478149 q^{45} - 432155860006696 q^{46} + 48939724777580 q^{47} + 513518246048640 q^{48} + 888582051628886 q^{49} + 20\!\cdots\!21 q^{50}+ \cdots - 51\!\cdots\!14 q^{99}+O(q^{100}) \) 38 * q + 15 * q^2 + 2080511 * q^4 - 1062222 * q^5 - 3454906 * q^6 - 43925040 * q^7 + 17944905 * q^8 + 1407964240 * q^9 - 753380082 * q^10 - 1247087592 * q^11 - 12806174710 * q^13 - 9920461605 * q^14 - 26267835313 * q^15 + 150793103155 * q^16 - 32714582925 * q^17 - 321256617405 * q^18 - 275283244180 * q^19 - 219435764020 * q^20 - 301109113003 * q^21 + 141637789665 * q^22 + 101540066360 * q^23 + 2412933601890 * q^24 + 4991161115804 * q^25 + 990445756111 * q^26 - 1179423443835 * q^27 - 10869216693165 * q^28 - 12862783749830 * q^29 - 27886581579060 * q^30 - 7513791056524 * q^31 - 31047860166815 * q^32 - 16499870737070 * q^33 - 62883745276639 * q^34 - 41836456706373 * q^35 - 74757290464031 * q^36 - 113711477231480 * q^37 - 86782161105620 * q^38 - 63680125347522 * q^39 - 53946909479582 * q^40 - 40841718887048 * q^41 - 8891162142170 * q^42 - 81961546008910 * q^43 - 24535596549333 * q^44 - 43121875478149 * q^45 - 432155860006696 * q^46 + 48939724777580 * q^47 + 513518246048640 * q^48 + 888582051628886 * q^49 + 2057077370177321 * q^50 + 569659539952336 * q^51 - 370273252291135 * q^52 - 433723261090750 * q^53 + 1096466631267392 * q^54 + 79796671313772 * q^55 + 2323327792351993 * q^56 + 887203937605935 * q^57 - 295587621090020 * q^58 - 5579556628964198 * q^59 + 592426170977334 * q^60 - 6025444644348168 * q^61 + 7570949891683260 * q^62 + 9980846882585340 * q^63 + 13715521778988675 * q^64 + 4776848418760040 * q^65 + 20125410682117558 * q^66 - 6448471666351340 * q^67 - 1025381952060385 * q^68 - 16162390563538664 * q^69 - 18060178308372494 * q^70 - 863248182916719 * q^71 - 15920098968926535 * q^72 - 15893509015624410 * q^73 - 29377392966301269 * q^74 - 76871360452990700 * q^75 - 76061521963339558 * q^76 - 47308441379226170 * q^77 - 62616737236958550 * q^78 - 56867622838588436 * q^79 - 110758045028448708 * q^80 + 20733776554374430 * q^81 - 22335528426891945 * q^82 - 20340278534672400 * q^83 - 60706646448603304 * q^84 - 138649838511113872 * q^85 - 126684793482322437 * q^86 + 98988867535735775 * q^87 - 129449914775692245 * q^88 + 46444572410639724 * q^89 - 92592608336160718 * q^90 - 57065301260365760 * q^91 - 252639467544196520 * q^92 - 51058891330353870 * q^93 - 23726593342614318 * q^94 + 397700906642915716 * q^95 - 348083640855946590 * q^96 - 45861521042958940 * q^97 - 457813795136007510 * q^98 - 514992036448276814 * q^99

Introduction

L-functions

Modular forms

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