LMFDB - Embedded newform 59.18.a.b.1.19

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:	$0$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-70.2688 q^{2} -18018.4 q^{3} -126134. q^{4} -230878. q^{5} +1.26613e6 q^{6} +1.19779e7 q^{7} +1.80736e7 q^{8} +1.95522e8 q^{9} +O(q^{10})$	\(q-70.2688 q^{2} -18018.4 q^{3} -126134. q^{4} -230878. q^{5} +1.26613e6 q^{6} +1.19779e7 q^{7} +1.80736e7 q^{8} +1.95522e8 q^{9} +1.62235e7 q^{10} +4.59631e8 q^{11} +2.27274e9 q^{12} -5.60952e8 q^{13} -8.41676e8 q^{14} +4.16004e9 q^{15} +1.52627e10 q^{16} +3.57881e10 q^{17} -1.37391e10 q^{18} +4.33684e10 q^{19} +2.91216e10 q^{20} -2.15823e11 q^{21} -3.22977e10 q^{22} +3.91899e11 q^{23} -3.25656e11 q^{24} -7.09635e11 q^{25} +3.94174e10 q^{26} -1.19609e12 q^{27} -1.51083e12 q^{28} +3.55035e12 q^{29} -2.92321e11 q^{30} -4.06806e12 q^{31} -3.44143e12 q^{32} -8.28181e12 q^{33} -2.51479e12 q^{34} -2.76544e12 q^{35} -2.46620e13 q^{36} -2.44115e13 q^{37} -3.04744e12 q^{38} +1.01075e13 q^{39} -4.17279e12 q^{40} +2.37178e13 q^{41} +1.51656e13 q^{42} -9.53551e13 q^{43} -5.79753e13 q^{44} -4.51417e13 q^{45} -2.75383e13 q^{46} +7.47684e13 q^{47} -2.75009e14 q^{48} -8.91593e13 q^{49} +4.98652e13 q^{50} -6.44844e14 q^{51} +7.07553e13 q^{52} +7.46485e14 q^{53} +8.40479e13 q^{54} -1.06119e14 q^{55} +2.16484e14 q^{56} -7.81429e14 q^{57} -2.49479e14 q^{58} +1.46830e14 q^{59} -5.24724e14 q^{60} +1.35754e15 q^{61} +2.85857e14 q^{62} +2.34195e15 q^{63} -1.75868e15 q^{64} +1.29511e14 q^{65} +5.81953e14 q^{66} +4.35064e14 q^{67} -4.51411e15 q^{68} -7.06139e15 q^{69} +1.94324e14 q^{70} +2.50480e15 q^{71} +3.53378e15 q^{72} +7.36736e15 q^{73} +1.71537e15 q^{74} +1.27865e16 q^{75} -5.47024e15 q^{76} +5.50544e15 q^{77} -7.10238e14 q^{78} +1.82992e16 q^{79} -3.52381e15 q^{80} -3.69809e15 q^{81} -1.66662e15 q^{82} -1.33874e15 q^{83} +2.72227e16 q^{84} -8.26269e15 q^{85} +6.70049e15 q^{86} -6.39716e16 q^{87} +8.30718e15 q^{88} +8.69360e15 q^{89} +3.17205e15 q^{90} -6.71906e15 q^{91} -4.94319e16 q^{92} +7.32998e16 q^{93} -5.25388e15 q^{94} -1.00128e16 q^{95} +6.20090e16 q^{96} -1.02675e17 q^{97} +6.26511e15 q^{98} +8.98680e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9}+O(q^{10}) $ 44 * q + 783 * q^2 + 13122 * q^3 + 3063551 * q^4 + 2062778 * q^5 + 9982022 * q^6 + 13722970 * q^7 + 168939849 * q^8 + 2182805218 * q^9	\( 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9} + 246619918 q^{10} + 896501218 q^{11} + 2579890176 q^{12} + 5139901152 q^{13} - 1065727269 q^{14} + 52608606500 q^{15} + 170254553019 q^{16} + 31152575372 q^{17} + 371065029637 q^{18} + 222944612638 q^{19} + 632345964652 q^{20} + 518768862104 q^{21} - 1188197076091 q^{22} - 314739342184 q^{23} - 1830638682468 q^{24} + 8265149117122 q^{25} - 1422210694649 q^{26} + 1055641354104 q^{27} + 4733828767179 q^{28} + 7952343701542 q^{29} + 33815332595226 q^{30} + 22703202725740 q^{31} + 51508227606921 q^{32} + 39808250652964 q^{33} + 42559210973877 q^{34} + 53084789167044 q^{35} + 286899333699545 q^{36} + 70719636063816 q^{37} + 70760432282360 q^{38} + 89621954178128 q^{39} + 176727288274300 q^{40} + 77283001373080 q^{41} - 142968851337140 q^{42} + 218112956325030 q^{43} - 146577440549739 q^{44} + 156445227241670 q^{45} - 436430382603480 q^{46} - 206155334901712 q^{47} - 694457384549320 q^{48} + 17\!\cdots\!92 q^{49}+ \cdots - 33\!\cdots\!26 q^{99}+O(q^{100}) \) 44 * q + 783 * q^2 + 13122 * q^3 + 3063551 * q^4 + 2062778 * q^5 + 9982022 * q^6 + 13722970 * q^7 + 168939849 * q^8 + 2182805218 * q^9 + 246619918 * q^10 + 896501218 * q^11 + 2579890176 * q^12 + 5139901152 * q^13 - 1065727269 * q^14 + 52608606500 * q^15 + 170254553019 * q^16 + 31152575372 * q^17 + 371065029637 * q^18 + 222944612638 * q^19 + 632345964652 * q^20 + 518768862104 * q^21 - 1188197076091 * q^22 - 314739342184 * q^23 - 1830638682468 * q^24 + 8265149117122 * q^25 - 1422210694649 * q^26 + 1055641354104 * q^27 + 4733828767179 * q^28 + 7952343701542 * q^29 + 33815332595226 * q^30 + 22703202725740 * q^31 + 51508227606921 * q^32 + 39808250652964 * q^33 + 42559210973877 * q^34 + 53084789167044 * q^35 + 286899333699545 * q^36 + 70719636063816 * q^37 + 70760432282360 * q^38 + 89621954178128 * q^39 + 176727288274300 * q^40 + 77283001373080 * q^41 - 142968851337140 * q^42 + 218112956325030 * q^43 - 146577440549739 * q^44 + 156445227241670 * q^45 - 436430382603480 * q^46 - 206155334901712 * q^47 - 694457384549320 * q^48 + 1711133899986192 * q^49 - 636149584416999 * q^50 + 158951699286348 * q^51 - 3158033385800149 * q^52 - 404876214856866 * q^53 - 1832749628980958 * q^54 - 611379564042440 * q^55 - 2900007168369351 * q^56 - 1013357232316788 * q^57 - 455786716037158 * q^58 + 6460539254590124 * q^59 + 4624863641607938 * q^60 + 4875940646057436 * q^61 - 15281797209467076 * q^62 - 16054536748044808 * q^63 + 5329292222614591 * q^64 - 7625310499015476 * q^65 - 10349172696837322 * q^66 - 4206243743451792 * q^67 - 552954195428233 * q^68 + 8020251305435444 * q^69 + 3876379104148138 * q^70 + 19535505651668622 * q^71 + 71495174696263183 * q^72 + 33833193336852456 * q^73 + 40772046703252163 * q^74 + 75968477185276688 * q^75 + 38838328992025026 * q^76 + 53055532951436968 * q^77 + 73057936571746858 * q^78 + 61045424159854942 * q^79 + 80004004628116616 * q^80 + 155795318109062036 * q^81 + 52248236930642133 * q^82 + 1235564168216730 * q^83 + 164143534194509272 * q^84 + 113286530641911588 * q^85 + 50368241096487595 * q^86 + 18062036297697056 * q^87 - 116796176360505729 * q^88 + 5837731242014800 * q^89 + 269698982682069798 * q^90 - 57230636051197354 * q^91 + 85549613709158172 * q^92 - 42635139630610976 * q^93 + 217633917061493766 * q^94 - 190986541078108154 * q^95 + 173923507159625020 * q^96 + 233342043840904176 * q^97 + 216259456237342020 * q^98 - 333859997478074426 * 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 $

$2$	−70.2688	−0.194092	−0.0970459	−	0.995280i	$-0.530939\pi$
$2$	−70.2688	−0.194092	−0.0970459	+	0.995280i	$0.530939\pi$
$3$	−18018.4	−1.58557	−0.792784	−	0.609502i	$-0.791369\pi$
$3$	−18018.4	−1.58557	−0.792784	+	0.609502i	$0.791369\pi$
$4$	−126134.	−0.962328
$5$	−230878.	−0.264324	−0.132162	−	0.991228i	$-0.542192\pi$
$5$	−230878.	−0.264324	−0.132162	+	0.991228i	$0.542192\pi$
$6$	1.26613e6	0.307746
$7$	1.19779e7	0.785324	0.392662	−	0.919683i	$-0.371554\pi$
$7$	1.19779e7	0.785324	0.392662	+	0.919683i	$0.371554\pi$
$8$	1.80736e7	0.380872
$9$	1.95522e8	1.51403
$10$	1.62235e7	0.0513032
$11$	4.59631e8	0.646505	0.323252	−	0.946313i	$-0.395224\pi$
$11$	4.59631e8	0.646505	0.323252	+	0.946313i	$0.395224\pi$
$12$	2.27274e9	1.52584
$13$	−5.60952e8	−0.190725	−0.0953625	−	0.995443i	$-0.530401\pi$
$13$	−5.60952e8	−0.190725	−0.0953625	+	0.995443i	$0.530401\pi$
$14$	−8.41676e8	−0.152425
$15$	4.16004e9	0.419104
$16$	1.52627e10	0.888404
$17$	3.57881e10	1.24429	0.622147	−	0.782900i	$-0.286260\pi$
$17$	3.57881e10	1.24429	0.622147	+	0.782900i	$0.286260\pi$
$18$	−1.37391e10	−0.293861
$19$	4.33684e10	0.585825	0.292913	−	0.956139i	$-0.405376\pi$
$19$	4.33684e10	0.585825	0.292913	+	0.956139i	$0.405376\pi$
$20$	2.91216e10	0.254367
$21$	−2.15823e11	−1.24519
$22$	−3.22977e10	−0.125481
$23$	3.91899e11	1.04349	0.521744	−	0.853102i	$-0.325282\pi$
$23$	3.91899e11	1.04349	0.521744	+	0.853102i	$0.325282\pi$
$24$	−3.25656e11	−0.603899
$25$	−7.09635e11	−0.930133
$26$	3.94174e10	0.0370182
$27$	−1.19609e12	−0.815028
$28$	−1.51083e12	−0.755740
$29$	3.55035e12	1.31792	0.658960	−	0.752178i	$-0.270997\pi$
$29$	3.55035e12	1.31792	0.658960	+	0.752178i	$0.270997\pi$
$30$	−2.92321e11	−0.0813448
$31$	−4.06806e12	−0.856669	−0.428334	−	0.903620i	$-0.640899\pi$
$31$	−4.06806e12	−0.856669	−0.428334	+	0.903620i	$0.640899\pi$
$32$	−3.44143e12	−0.553304
$33$	−8.28181e12	−1.02508
$34$	−2.51479e12	−0.241508
$35$	−2.76544e12	−0.207580
$36$	−2.46620e13	−1.45699
$37$	−2.44115e13	−1.14256	−0.571282	−	0.820754i	$-0.693554\pi$
$37$	−2.44115e13	−1.14256	−0.571282	+	0.820754i	$0.693554\pi$
$38$	−3.04744e12	−0.113704
$39$	1.01075e13	0.302408
$40$	−4.17279e12	−0.100674
$41$	2.37178e13	0.463885	0.231943	−	0.972729i	$-0.425492\pi$
$41$	2.37178e13	0.463885	0.231943	+	0.972729i	$0.425492\pi$
$42$	1.51656e13	0.241680
$43$	−9.53551e13	−1.24412	−0.622060	−	0.782970i	$-0.713704\pi$
$43$	−9.53551e13	−1.24412	−0.622060	+	0.782970i	$0.713704\pi$
$44$	−5.79753e13	−0.622150
$45$	−4.51417e13	−0.400195
$46$	−2.75383e13	−0.202533
$47$	7.47684e13	0.458022	0.229011	−	0.973424i	$-0.426451\pi$
$47$	7.47684e13	0.458022	0.229011	+	0.973424i	$0.426451\pi$
$48$	−2.75009e14	−1.40863
$49$	−8.91593e13	−0.383266
$50$	4.98652e13	0.180531
$51$	−6.44844e14	−1.97292
$52$	7.07553e13	0.183540
$53$	7.46485e14	1.64693	0.823467	−	0.567364i	$-0.192037\pi$
$53$	7.46485e14	1.64693	0.823467	+	0.567364i	$0.192037\pi$
$54$	8.40479e13	0.158190
$55$	−1.06119e14	−0.170887
$56$	2.16484e14	0.299108
$57$	−7.81429e14	−0.928866
$58$	−2.49479e14	−0.255797
$59$	1.46830e14	0.130189
$59$	1.46830e14	0.130189
$60$	−5.24724e14	−0.403316
$61$	1.35754e15	0.906667	0.453334	−	0.891341i	$-0.350235\pi$
$61$	1.35754e15	0.906667	0.453334	+	0.891341i	$0.350235\pi$
$62$	2.85857e14	0.166272
$63$	2.34195e15	1.18900
$64$	−1.75868e15	−0.781012
$65$	1.29511e14	0.0504132
$66$	5.81953e14	0.198959
$67$	4.35064e14	0.130893	0.0654467	−	0.997856i	$-0.479153\pi$
$67$	4.35064e14	0.130893	0.0654467	+	0.997856i	$0.479153\pi$
$68$	−4.51411e15	−1.19742
$69$	−7.06139e15	−1.65452
$70$	1.94324e14	0.0402897
$71$	2.50480e15	0.460339	0.230170	−	0.973151i	$-0.426072\pi$
$71$	2.50480e15	0.460339	0.230170	+	0.973151i	$0.426072\pi$
$72$	3.53378e15	0.576651
$73$	7.36736e15	1.06922	0.534611	−	0.845099i	$-0.320458\pi$
$73$	7.36736e15	1.06922	0.534611	+	0.845099i	$0.320458\pi$
$74$	1.71537e15	0.221762
$75$	1.27865e16	1.47479
$76$	−5.47024e15	−0.563756
$77$	5.50544e15	0.507716
$78$	−7.10238e14	−0.0586948
$79$	1.82992e16	1.35707	0.678535	−	0.734568i	$-0.262615\pi$
$79$	1.82992e16	1.35707	0.678535	+	0.734568i	$0.262615\pi$
$80$	−3.52381e15	−0.234827
$81$	−3.69809e15	−0.221746
$82$	−1.66662e15	−0.0900364
$83$	−1.33874e15	−0.0652428	−0.0326214	−	0.999468i	$-0.510386\pi$
$83$	−1.33874e15	−0.0652428	−0.0326214	+	0.999468i	$0.510386\pi$
$84$	2.72227e16	1.19828
$85$	−8.26269e15	−0.328897
$86$	6.70049e15	0.241474
$87$	−6.39716e16	−2.08965
$88$	8.30718e15	0.246236
$89$	8.69360e15	0.234091	0.117045	−	0.993127i	$-0.462658\pi$
$89$	8.69360e15	0.234091	0.117045	+	0.993127i	$0.462658\pi$
$90$	3.17205e15	0.0776745
$91$	−6.71906e15	−0.149781
$92$	−4.94319e16	−1.00418
$93$	7.32998e16	1.35831
$94$	−5.25388e15	−0.0888984
$95$	−1.00128e16	−0.154848
$96$	6.20090e16	0.877302
$97$	−1.02675e17	−1.33016	−0.665082	−	0.746771i	$-0.731603\pi$
$97$	−1.02675e17	−1.33016	−0.665082	+	0.746771i	$0.731603\pi$
$98$	6.26511e15	0.0743888
$99$	8.98680e16	0.978827
$100$	8.95093e16	0.895093
$101$	−1.26611e16	−0.116342	−0.0581712	−	0.998307i	$-0.518527\pi$
$101$	−1.26611e16	−0.116342	−0.0581712	+	0.998307i	$0.518527\pi$
$102$	4.53124e16	0.382927
$103$	−8.83427e16	−0.687154	−0.343577	−	0.939125i	$-0.611639\pi$
$103$	−8.83427e16	−0.687154	−0.343577	+	0.939125i	$0.611639\pi$
$104$	−1.01384e16	−0.0726418
$105$	4.98288e16	0.329133
$106$	−5.24546e16	−0.319657
$107$	1.20869e16	0.0680069	0.0340034	−	0.999422i	$-0.489174\pi$
$107$	1.20869e16	0.0680069	0.0340034	+	0.999422i	$0.489174\pi$
$108$	1.50868e17	0.784325
$109$	−3.81924e17	−1.83591	−0.917955	−	0.396684i	$-0.870161\pi$
$109$	−3.81924e17	−1.83591	−0.917955	+	0.396684i	$0.870161\pi$
$110$	7.45683e15	0.0331678
$111$	4.39856e17	1.81161
$112$	1.82815e17	0.697685
$113$	8.44788e16	0.298938	0.149469	−	0.988766i	$-0.452244\pi$
$113$	8.44788e16	0.298938	0.149469	+	0.988766i	$0.452244\pi$
$114$	5.49100e16	0.180285
$115$	−9.04808e16	−0.275819
$116$	−4.47821e17	−1.26827
$117$	−1.09678e17	−0.288763
$118$	−1.03176e16	−0.0252686
$119$	4.28668e17	0.977175
$120$	7.51869e16	0.159625
$121$	−2.94186e17	−0.582031
$122$	−9.53924e16	−0.175977
$123$	−4.27355e17	−0.735522
$124$	5.13122e17	0.824396
$125$	3.39985e17	0.510181
$126$	−1.64566e17	−0.230776
$127$	8.32371e17	1.09140	0.545702	−	0.837979i	$-0.316263\pi$
$127$	8.32371e17	1.09140	0.545702	+	0.837979i	$0.316263\pi$
$128$	5.74655e17	0.704892
$129$	1.71814e18	1.97264
$130$	−9.10061e15	−0.00978480
$131$	1.50439e18	1.51549	0.757746	−	0.652550i	$-0.226301\pi$
$131$	1.50439e18	1.51549	0.757746	+	0.652550i	$0.226301\pi$
$132$	1.04462e18	0.986462
$133$	5.19465e17	0.460063
$134$	−3.05714e16	−0.0254053
$135$	2.76151e17	0.215432
$136$	6.46819e17	0.473917
$137$	−1.48165e18	−1.02005	−0.510024	−	0.860160i	$-0.670364\pi$
$137$	−1.48165e18	−1.02005	−0.510024	+	0.860160i	$0.670364\pi$
$138$	4.96195e17	0.321129
$139$	1.23714e18	0.752995	0.376498	−	0.926418i	$-0.377128\pi$
$139$	1.23714e18	0.752995	0.376498	+	0.926418i	$0.377128\pi$
$140$	3.48817e17	0.199760
$141$	−1.34721e18	−0.726226
$142$	−1.76010e17	−0.0893481
$143$	−2.57831e17	−0.123305
$144$	2.98419e18	1.34507
$145$	−8.19698e17	−0.348358
$146$	−5.17695e17	−0.207527
$147$	1.60651e18	0.607694
$148$	3.07913e18	1.09952
$149$	3.38829e18	1.14261	0.571304	−	0.820738i	$-0.306438\pi$
$149$	3.38829e18	1.14261	0.571304	+	0.820738i	$0.306438\pi$
$150$	−8.98490e17	−0.286245
$151$	−3.23649e18	−0.974474	−0.487237	−	0.873270i	$-0.661995\pi$
$151$	−3.23649e18	−0.974474	−0.487237	+	0.873270i	$0.661995\pi$
$152$	7.83822e17	0.223124
$153$	6.99737e18	1.88390
$154$	−3.86860e17	−0.0985436
$155$	9.39225e17	0.226438
$156$	−1.27490e18	−0.291015
$157$	−5.42912e17	−0.117377	−0.0586884	−	0.998276i	$-0.518692\pi$
$157$	−5.42912e17	−0.117377	−0.0586884	+	0.998276i	$0.518692\pi$
$158$	−1.28586e18	−0.263396
$159$	−1.34505e19	−2.61133
$160$	7.94549e17	0.146252
$161$	4.69415e18	0.819477
$162$	2.59860e17	0.0430390
$163$	7.55506e18	1.18753	0.593764	−	0.804640i	$-0.297641\pi$
$163$	7.55506e18	1.18753	0.593764	+	0.804640i	$0.297641\pi$
$164$	−2.99162e18	−0.446410
$165$	1.91209e18	0.270953
$166$	9.40716e16	0.0126631
$167$	−5.10793e18	−0.653363	−0.326682	−	0.945134i	$-0.605930\pi$
$167$	−5.10793e18	−0.653363	−0.326682	+	0.945134i	$0.605930\pi$
$168$	−3.90070e18	−0.474256
$169$	−8.33575e18	−0.963624
$170$	5.80609e17	0.0638363
$171$	8.47948e18	0.886956
$172$	1.20276e19	1.19725
$173$	1.34789e18	0.127721	0.0638607	−	0.997959i	$-0.479659\pi$
$173$	1.34789e18	0.127721	0.0638607	+	0.997959i	$0.479659\pi$
$174$	4.49521e18	0.405584
$175$	−8.49997e18	−0.730456
$176$	7.01520e18	0.574358
$177$	−2.64565e18	−0.206423
$178$	−6.10888e17	−0.0454351
$179$	−2.26031e19	−1.60294	−0.801469	−	0.598036i	$-0.795948\pi$
$179$	−2.26031e19	−1.60294	−0.801469	+	0.598036i	$0.795948\pi$
$180$	5.69391e18	0.385119
$181$	−3.19220e18	−0.205979	−0.102989	−	0.994682i	$-0.532841\pi$
$181$	−3.19220e18	−0.205979	−0.102989	+	0.994682i	$0.532841\pi$
$182$	4.72140e17	0.0290713
$183$	−2.44606e19	−1.43758
$184$	7.08302e18	0.397436
$185$	5.63608e18	0.302007
$186$	−5.15069e18	−0.263636
$187$	1.64494e19	0.804443
$188$	−9.43086e18	−0.440768
$189$	−1.43267e19	−0.640061
$190$	7.03587e17	0.0300547
$191$	1.84135e19	0.752234	0.376117	−	0.926572i	$-0.377259\pi$
$191$	1.84135e19	0.752234	0.376117	+	0.926572i	$0.377259\pi$
$192$	3.16886e19	1.23835
$193$	3.78120e19	1.41381	0.706907	−	0.707307i	$-0.250090\pi$
$193$	3.78120e19	1.41381	0.706907	+	0.707307i	$0.250090\pi$
$194$	7.21485e18	0.258174
$195$	−2.33359e18	−0.0799337
$196$	1.12460e19	0.368827
$197$	−2.53582e19	−0.796445	−0.398222	−	0.917289i	$-0.630373\pi$
$197$	−2.53582e19	−0.796445	−0.398222	+	0.917289i	$0.630373\pi$
$198$	−6.31491e18	−0.189982
$199$	−2.79788e19	−0.806451	−0.403225	−	0.915101i	$-0.632111\pi$
$199$	−2.79788e19	−0.806451	−0.403225	+	0.915101i	$0.632111\pi$
$200$	−1.28256e19	−0.354261
$201$	−7.83916e18	−0.207540
$202$	8.89677e17	0.0225811
$203$	4.25260e19	1.03499
$204$	8.13370e19	1.89859
$205$	−5.47590e18	−0.122616
$206$	6.20773e18	0.133371
$207$	7.66249e19	1.57987
$208$	−8.56163e18	−0.169441
$209$	1.99335e19	0.378739
$210$	−3.50141e18	−0.0638820
$211$	3.36032e19	0.588817	0.294408	−	0.955680i	$-0.404877\pi$
$211$	3.36032e19	0.588817	0.294408	+	0.955680i	$0.404877\pi$
$212$	−9.41574e19	−1.58489
$213$	−4.51325e19	−0.729899
$214$	−8.49331e17	−0.0131996
$215$	2.20154e19	0.328851
$216$	−2.16176e19	−0.310421
$217$	−4.87270e19	−0.672763
$218$	2.68373e19	0.356335
$219$	−1.32748e20	−1.69532
$220$	1.33852e19	0.164449
$221$	−2.00754e19	−0.237318
$222$	−3.09082e19	−0.351619
$223$	−7.30767e19	−0.800180	−0.400090	−	0.916476i	$-0.631021\pi$
$223$	−7.30767e19	−0.800180	−0.400090	+	0.916476i	$0.631021\pi$
$224$	−4.12212e19	−0.434523
$225$	−1.38749e20	−1.40825
$226$	−5.93622e18	−0.0580214
$227$	−9.28968e19	−0.874543	−0.437271	−	0.899330i	$-0.644055\pi$
$227$	−9.28968e19	−0.874543	−0.437271	+	0.899330i	$0.644055\pi$
$228$	9.85650e19	0.893874
$229$	−1.44255e20	−1.26046	−0.630229	−	0.776410i	$-0.717039\pi$
$229$	−1.44255e20	−1.26046	−0.630229	+	0.776410i	$0.717039\pi$
$230$	6.35798e18	0.0535343
$231$	−9.91991e19	−0.805019
$232$	6.41676e19	0.501958
$233$	−9.15214e19	−0.690235	−0.345118	−	0.938559i	$-0.612161\pi$
$233$	−9.15214e19	−0.690235	−0.345118	+	0.938559i	$0.612161\pi$
$234$	7.70697e18	0.0560466
$235$	−1.72624e19	−0.121066
$236$	−1.85204e19	−0.125284
$237$	−3.29722e20	−2.15173
$238$	−3.01220e19	−0.189662
$239$	−1.86519e20	−1.13329	−0.566645	−	0.823962i	$-0.691759\pi$
$239$	−1.86519e20	−1.13329	−0.566645	+	0.823962i	$0.691759\pi$
$240$	6.34934e19	0.372334
$241$	−1.49067e20	−0.843794	−0.421897	−	0.906644i	$-0.638636\pi$
$241$	−1.49067e20	−0.843794	−0.421897	+	0.906644i	$0.638636\pi$
$242$	2.06721e19	0.112968
$243$	2.21097e20	1.16662
$244$	−1.71232e20	−0.872512
$245$	2.05849e19	0.101306
$246$	3.00297e19	0.142759
$247$	−2.43276e19	−0.111731
$248$	−7.35243e19	−0.326281
$249$	2.41219e19	0.103447
$250$	−2.38903e19	−0.0990220
$251$	1.93098e20	0.773661	0.386831	−	0.922151i	$-0.373570\pi$
$251$	1.93098e20	0.773661	0.386831	+	0.922151i	$0.373570\pi$
$252$	−2.95400e20	−1.14421
$253$	1.80129e20	0.674621
$254$	−5.84897e19	−0.211833
$255$	1.48880e20	0.521490
$256$	1.90134e20	0.644199
$257$	2.36071e20	0.773767	0.386883	−	0.922129i	$-0.373552\pi$
$257$	2.36071e20	0.773767	0.386883	+	0.922129i	$0.373552\pi$
$258$	−1.20732e20	−0.382873
$259$	−2.92400e20	−0.897283
$260$	−1.63358e19	−0.0485141
$261$	6.94172e20	1.99537
$262$	−1.05711e20	−0.294145
$263$	−1.28283e20	−0.345576	−0.172788	−	0.984959i	$-0.555278\pi$
$263$	−1.28283e20	−0.345576	−0.172788	+	0.984959i	$0.555278\pi$
$264$	−1.49682e20	−0.390424
$265$	−1.72347e20	−0.435325
$266$	−3.65021e19	−0.0892944
$267$	−1.56645e20	−0.371167
$268$	−5.48765e19	−0.125962
$269$	7.89863e20	1.75654	0.878268	−	0.478168i	$-0.158699\pi$
$269$	7.89863e20	1.75654	0.878268	+	0.478168i	$0.158699\pi$
$270$	−1.94048e19	−0.0418136
$271$	1.57848e20	0.329610	0.164805	−	0.986326i	$-0.447301\pi$
$271$	1.57848e20	0.329610	0.164805	+	0.986326i	$0.447301\pi$
$272$	5.46223e20	1.10544
$273$	1.21067e20	0.237488
$274$	1.04114e20	0.197983
$275$	−3.26170e20	−0.601335
$276$	8.90683e20	1.59219
$277$	7.77614e20	1.34799	0.673994	−	0.738737i	$-0.264577\pi$
$277$	7.77614e20	1.34799	0.673994	+	0.738737i	$0.264577\pi$
$278$	−8.69321e19	−0.146150
$279$	−7.95395e20	−1.29702
$280$	−4.99814e19	−0.0790615
$281$	1.05782e21	1.62333	0.811665	−	0.584123i	$-0.198561\pi$
$281$	1.05782e21	1.62333	0.811665	+	0.584123i	$0.198561\pi$
$282$	9.46665e19	0.140954
$283$	−2.02675e20	−0.292830	−0.146415	−	0.989223i	$-0.546774\pi$
$283$	−2.02675e20	−0.292830	−0.146415	+	0.989223i	$0.546774\pi$
$284$	−3.15942e20	−0.442997
$285$	1.80415e20	0.245522
$286$	1.81175e19	0.0239324
$287$	2.84090e20	0.364301
$288$	−6.72875e20	−0.837718
$289$	4.53551e20	0.548270
$290$	5.75992e19	0.0676135
$291$	1.85004e21	2.10907
$292$	−9.29277e20	−1.02894
$293$	5.89538e20	0.634070	0.317035	−	0.948414i	$-0.397313\pi$
$293$	5.89538e20	0.634070	0.317035	+	0.948414i	$0.397313\pi$
$294$	−1.12887e20	−0.117949
$295$	−3.38999e19	−0.0344121
$296$	−4.41204e20	−0.435171
$297$	−5.49761e20	−0.526920
$298$	−2.38091e20	−0.221771
$299$	−2.19837e20	−0.199019
$300$	−1.61281e21	−1.41923
$301$	−1.14216e21	−0.977037
$302$	2.27424e20	0.189138
$303$	2.28132e20	0.184469
$304$	6.61918e20	0.520449
$305$	−3.13425e20	−0.239654
$306$	−4.91696e20	−0.365649
$307$	−1.00526e21	−0.727113	−0.363557	−	0.931572i	$-0.618438\pi$
$307$	−1.00526e21	−0.727113	−0.363557	+	0.931572i	$0.618438\pi$
$308$	−6.94425e20	−0.488590
$309$	1.59179e21	1.08953
$310$	−6.59982e19	−0.0439498
$311$	9.52288e20	0.617028	0.308514	−	0.951220i	$-0.400168\pi$
$311$	9.52288e20	0.617028	0.308514	+	0.951220i	$0.400168\pi$
$312$	1.82678e20	0.115179
$313$	1.83592e21	1.12649	0.563245	−	0.826290i	$-0.309553\pi$
$313$	1.83592e21	1.12649	0.563245	+	0.826290i	$0.309553\pi$
$314$	3.81498e19	0.0227819
$315$	−5.40705e20	−0.314283
$316$	−2.30816e21	−1.30595
$317$	−3.90570e20	−0.215127	−0.107564	−	0.994198i	$-0.534305\pi$
$317$	−3.90570e20	−0.215127	−0.107564	+	0.994198i	$0.534305\pi$
$318$	9.45147e20	0.506838
$319$	1.63185e21	0.852041
$320$	4.06041e20	0.206441
$321$	−2.17786e20	−0.107830
$322$	−3.29852e20	−0.159054
$323$	1.55208e21	0.728939
$324$	4.66456e20	0.213392
$325$	3.98071e20	0.177399
$326$	−5.30885e20	−0.230489
$327$	6.88165e21	2.91096
$328$	4.28664e20	0.176681
$329$	8.95572e20	0.359696
$330$	−1.34360e20	−0.0525898
$331$	1.12421e21	0.428856	0.214428	−	0.976740i	$-0.431211\pi$
$331$	1.12421e21	0.428856	0.214428	+	0.976740i	$0.431211\pi$
$332$	1.68861e20	0.0627850
$333$	−4.77299e21	−1.72987
$334$	3.58928e20	0.126812
$335$	−1.00447e20	−0.0345983
$336$	−3.29404e21	−1.10623
$337$	4.28566e21	1.40334	0.701672	−	0.712500i	$-0.252437\pi$
$337$	4.28566e21	1.40334	0.701672	+	0.712500i	$0.252437\pi$
$338$	5.85743e20	0.187032
$339$	−1.52217e21	−0.473987
$340$	1.04221e21	0.316507
$341$	−1.86981e21	−0.553840
$342$	−5.95842e20	−0.172151
$343$	−3.85438e21	−1.08631
$344$	−1.72341e21	−0.473850
$345$	1.63032e21	0.437331
$346$	−9.47148e19	−0.0247897
$347$	4.80612e21	1.22742	0.613712	−	0.789530i	$-0.289676\pi$
$347$	4.80612e21	1.22742	0.613712	+	0.789530i	$0.289676\pi$
$348$	8.06902e21	2.01093
$349$	−3.73313e21	−0.907940	−0.453970	−	0.891017i	$-0.649993\pi$
$349$	−3.73313e21	−0.907940	−0.453970	+	0.891017i	$0.649993\pi$
$350$	5.97282e20	0.141776
$351$	6.70951e20	0.155446
$352$	−1.58179e21	−0.357714
$353$	6.62915e21	1.46343	0.731717	−	0.681609i	$-0.238719\pi$
$353$	6.62915e21	1.46343	0.731717	+	0.681609i	$0.238719\pi$
$354$	1.85906e20	0.0400651
$355$	−5.78304e20	−0.121679
$356$	−1.09656e21	−0.225272
$357$	−7.72391e21	−1.54938
$358$	1.58829e21	0.311117
$359$	3.86545e21	0.739431	0.369715	−	0.929145i	$-0.379455\pi$
$359$	3.86545e21	0.739431	0.369715	+	0.929145i	$0.379455\pi$
$360$	−8.15871e20	−0.152423
$361$	−3.59957e21	−0.656809
$362$	2.24312e20	0.0399788
$363$	5.30076e21	0.922851
$364$	8.47504e20	0.144138
$365$	−1.70096e21	−0.282621
$366$	1.71882e21	0.279023
$367$	−6.86926e21	−1.08955	−0.544777	−	0.838581i	$-0.683386\pi$
$367$	−6.86926e21	−1.08955	−0.544777	+	0.838581i	$0.683386\pi$
$368$	5.98143e21	0.927040
$369$	4.63734e21	0.702336
$370$	−3.96041e20	−0.0586172
$371$	8.94136e21	1.29338
$372$	−9.24562e21	−1.30714
$373$	7.81662e20	0.108017	0.0540087	−	0.998540i	$-0.482800\pi$
$373$	7.81662e20	0.108017	0.0540087	+	0.998540i	$0.482800\pi$
$374$	−1.15588e21	−0.156136
$375$	−6.12598e21	−0.808927
$376$	1.35133e21	0.174448
$377$	−1.99158e21	−0.251360
$378$	1.00672e21	0.124231
$379$	−4.55003e21	−0.549011	−0.274506	−	0.961586i	$-0.588514\pi$
$379$	−4.55003e21	−0.549011	−0.274506	+	0.961586i	$0.588514\pi$
$380$	1.26296e21	0.149014
$381$	−1.49980e22	−1.73050
$382$	−1.29389e21	−0.146003
$383$	−6.47792e21	−0.714902	−0.357451	−	0.933932i	$-0.616354\pi$
$383$	−6.47792e21	−0.714902	−0.357451	+	0.933932i	$0.616354\pi$
$384$	−1.03544e22	−1.11766
$385$	−1.27108e21	−0.134202
$386$	−2.65700e21	−0.274410
$387$	−1.86440e22	−1.88363
$388$	1.29508e22	1.28005
$389$	1.16135e22	1.12303	0.561514	−	0.827468i	$-0.310219\pi$
$389$	1.16135e22	1.12303	0.561514	+	0.827468i	$0.310219\pi$
$390$	1.63978e20	0.0155145
$391$	1.40253e22	1.29841
$392$	−1.61143e21	−0.145975
$393$	−2.71066e22	−2.40292
$394$	1.78189e21	0.154583
$395$	−4.22488e21	−0.358707
$396$	−1.13354e22	−0.941953
$397$	−7.70885e20	−0.0627004	−0.0313502	−	0.999508i	$-0.509981\pi$
$397$	−7.70885e20	−0.0627004	−0.0313502	+	0.999508i	$0.509981\pi$
$398$	1.96604e21	0.156526
$399$	−9.35991e21	−0.729461
$400$	−1.08309e22	−0.826334
$401$	−6.30710e21	−0.471088	−0.235544	−	0.971864i	$-0.575687\pi$
$401$	−6.30710e21	−0.471088	−0.235544	+	0.971864i	$0.575687\pi$
$402$	5.50848e20	0.0402819
$403$	2.28199e21	0.163388
$404$	1.59699e21	0.111960
$405$	8.53808e20	0.0586128
$406$	−2.98825e21	−0.200884
$407$	−1.12203e22	−0.738673
$408$	−1.16546e22	−0.751428
$409$	−7.44011e21	−0.469820	−0.234910	−	0.972017i	$-0.575479\pi$
$409$	−7.44011e21	−0.469820	−0.234910	+	0.972017i	$0.575479\pi$
$410$	3.84785e20	0.0237988
$411$	2.66969e22	1.61736
$412$	1.11430e22	0.661268
$413$	1.75873e21	0.102241
$414$	−5.38433e21	−0.306640
$415$	3.09086e20	0.0172453
$416$	1.93048e21	0.105529
$417$	−2.22912e22	−1.19393
$418$	−1.40070e21	−0.0735101
$419$	2.77792e22	1.42857	0.714283	−	0.699857i	$-0.246753\pi$
$419$	2.77792e22	1.42857	0.714283	+	0.699857i	$0.246753\pi$
$420$	−6.28512e21	−0.316734
$421$	2.48434e19	0.00122691	0.000613455	−	1.00000i	$-0.499805\pi$
$421$	2.48434e19	0.00122691	0.000613455		1.00000i	$0.499805\pi$
$422$	−2.36126e21	−0.114285
$423$	1.46189e22	0.693459
$424$	1.34917e22	0.627271
$425$	−2.53965e22	−1.15736
$426$	3.17141e21	0.141668
$427$	1.62605e22	0.712028
$428$	−1.52457e21	−0.0654449
$429$	4.64570e21	0.195508
$430$	−1.54699e21	−0.0638273
$431$	−2.00290e22	−0.810219	−0.405109	−	0.914268i	$-0.632767\pi$
$431$	−2.00290e22	−0.810219	−0.405109	+	0.914268i	$0.632767\pi$
$432$	−1.82556e22	−0.724074
$433$	1.14951e22	0.447062	0.223531	−	0.974697i	$-0.428242\pi$
$433$	1.14951e22	0.447062	0.223531	+	0.974697i	$0.428242\pi$
$434$	3.42399e21	0.130578
$435$	1.47696e22	0.552346
$436$	4.81737e22	1.76675
$437$	1.69960e22	0.611302
$438$	9.32803e21	0.329049
$439$	3.42971e22	1.18661	0.593306	−	0.804977i	$-0.297822\pi$
$439$	3.42971e22	1.18661	0.593306	+	0.804977i	$0.297822\pi$
$440$	−1.91794e21	−0.0650861
$441$	−1.74326e22	−0.580275
$442$	1.41068e21	0.0460615
$443$	−1.48844e22	−0.476759	−0.238379	−	0.971172i	$-0.576616\pi$
$443$	−1.48844e22	−0.476759	−0.238379	+	0.971172i	$0.576616\pi$
$444$	−5.54810e22	−1.74337
$445$	−2.00716e21	−0.0618759
$446$	5.13501e21	0.155308
$447$	−6.10515e22	−1.81168
$448$	−2.10654e22	−0.613348
$449$	6.47377e22	1.84954	0.924769	−	0.380530i	$-0.124258\pi$
$449$	6.47377e22	1.84954	0.924769	+	0.380530i	$0.124258\pi$
$450$	9.74973e21	0.273329
$451$	1.09014e22	0.299904
$452$	−1.06557e22	−0.287676
$453$	5.83163e22	1.54510
$454$	6.52774e21	0.169742
$455$	1.55128e21	0.0395907
$456$	−1.41232e22	−0.353779
$457$	−4.79347e22	−1.17859	−0.589294	−	0.807918i	$-0.700594\pi$
$457$	−4.79347e22	−1.17859	−0.589294	+	0.807918i	$0.700594\pi$
$458$	1.01366e22	0.244645
$459$	−4.28059e22	−1.01414
$460$	1.14127e22	0.265429
$461$	1.84178e22	0.420513	0.210256	−	0.977646i	$-0.432570\pi$
$461$	1.84178e22	0.420513	0.210256	+	0.977646i	$0.432570\pi$
$462$	6.97060e21	0.156248
$463$	−3.18321e21	−0.0700531	−0.0350266	−	0.999386i	$-0.511152\pi$
$463$	−3.18321e21	−0.0700531	−0.0350266	+	0.999386i	$0.511152\pi$
$464$	5.41879e22	1.17084
$465$	−1.69233e22	−0.359034
$466$	6.43109e21	0.133969
$467$	−1.76869e22	−0.361792	−0.180896	−	0.983502i	$-0.557900\pi$
$467$	−1.76869e22	−0.361792	−0.180896	+	0.983502i	$0.557900\pi$
$468$	1.38342e22	0.277885
$469$	5.21118e21	0.102794
$470$	1.21301e21	0.0234980
$471$	9.78240e21	0.186109
$472$	2.65375e21	0.0495853
$473$	−4.38282e22	−0.804329
$474$	2.31692e22	0.417633
$475$	−3.07757e22	−0.544895
$476$	−5.40698e22	−0.940363
$477$	1.45954e23	2.49351
$478$	1.31065e22	0.219963
$479$	1.05593e22	0.174093	0.0870467	−	0.996204i	$-0.472257\pi$
$479$	1.05593e22	0.174093	0.0870467	+	0.996204i	$0.472257\pi$
$480$	−1.43165e22	−0.231892
$481$	1.36937e22	0.217915
$482$	1.04747e22	0.163774
$483$	−8.45809e22	−1.29934
$484$	3.71069e22	0.560105
$485$	2.37054e22	0.351595
$486$	−1.55362e22	−0.226432
$487$	7.48761e22	1.07238	0.536188	−	0.844099i	$-0.319864\pi$
$487$	7.48761e22	1.07238	0.536188	+	0.844099i	$0.319864\pi$
$488$	2.45355e22	0.345324
$489$	−1.36130e23	−1.88291
$490$	−1.44648e21	−0.0196628
$491$	9.06430e22	1.21099	0.605496	−	0.795848i	$-0.292975\pi$
$491$	9.06430e22	1.21099	0.605496	+	0.795848i	$0.292975\pi$
$492$	5.39042e22	0.707814
$493$	1.27061e23	1.63988
$494$	1.70947e21	0.0216862
$495$	−2.07485e22	−0.258728
$496$	−6.20894e22	−0.761068
$497$	3.00024e22	0.361515
$498$	−1.69502e21	−0.0200782
$499$	5.93866e22	0.691566	0.345783	−	0.938314i	$-0.387613\pi$
$499$	5.93866e22	0.691566	0.345783	+	0.938314i	$0.387613\pi$
$500$	−4.28837e22	−0.490962
$501$	9.20366e22	1.03595
$502$	−1.35688e22	−0.150161
$503$	2.74468e22	0.298651	0.149325	−	0.988788i	$-0.452290\pi$
$503$	2.74468e22	0.298651	0.149325	+	0.988788i	$0.452290\pi$
$504$	4.23274e22	0.452858
$505$	2.92316e21	0.0307521
$506$	−1.26575e22	−0.130938
$507$	1.50197e23	1.52789
$508$	−1.04991e23	−1.05029
$509$	−3.84997e22	−0.378753	−0.189376	−	0.981905i	$-0.560647\pi$
$509$	−3.84997e22	−0.378753	−0.189376	+	0.981905i	$0.560647\pi$
$510$	−1.04616e22	−0.101217
$511$	8.82458e22	0.839685
$512$	−8.86817e22	−0.829926
$513$	−5.18726e22	−0.477464
$514$	−1.65884e22	−0.150182
$515$	2.03964e22	0.181632
$516$	−2.16717e23	−1.89832
$517$	3.43659e22	0.296114
$518$	2.05466e22	0.174155
$519$	−2.42868e22	−0.202511
$520$	2.34073e21	0.0192010
$521$	2.03242e22	0.164018	0.0820091	−	0.996632i	$-0.473866\pi$
$521$	2.03242e22	0.164018	0.0820091	+	0.996632i	$0.473866\pi$
$522$	−4.87786e22	−0.387285
$523$	−7.01285e22	−0.547810	−0.273905	−	0.961757i	$-0.588315\pi$
$523$	−7.01285e22	−0.547810	−0.273905	+	0.961757i	$0.588315\pi$
$524$	−1.89755e23	−1.45840
$525$	1.53156e23	1.15819
$526$	9.01426e21	0.0670735
$527$	−1.45588e23	−1.06595
$528$	−1.26403e23	−0.910684
$529$	1.25349e22	0.0888684
$530$	1.21106e22	0.0844930
$531$	2.87086e22	0.197110
$532$	−6.55223e22	−0.442731
$533$	−1.33045e22	−0.0884745
$534$	1.10072e22	0.0720405
$535$	−2.79060e21	−0.0179759
$536$	7.86317e21	0.0498536
$537$	4.07271e23	2.54157
$538$	−5.55027e22	−0.340930
$539$	−4.09804e22	−0.247783
$540$	−3.48321e22	−0.207316
$541$	2.79054e23	1.63498	0.817488	−	0.575945i	$-0.195366\pi$
$541$	2.79054e23	1.63498	0.817488	+	0.575945i	$0.195366\pi$
$542$	−1.10918e22	−0.0639746
$543$	5.75183e22	0.326594
$544$	−1.23162e23	−0.688473
$545$	8.81778e22	0.485276
$546$	−8.50720e21	−0.0460945
$547$	1.64394e23	0.876990	0.438495	−	0.898734i	$-0.355512\pi$
$547$	1.64394e23	0.876990	0.438495	+	0.898734i	$0.355512\pi$
$548$	1.86887e23	0.981622
$549$	2.65428e23	1.37272
$550$	2.29196e22	0.116714
$551$	1.53973e23	0.772070
$552$	−1.27624e23	−0.630161
$553$	2.19187e23	1.06574
$554$	−5.46420e22	−0.261634
$555$	−1.01553e23	−0.478854
$556$	−1.56045e23	−0.724629
$557$	4.00358e23	1.83096	0.915480	−	0.402363i	$-0.131811\pi$
$557$	4.00358e23	1.83096	0.915480	+	0.402363i	$0.131811\pi$
$558$	5.58914e22	0.251741
$559$	5.34897e22	0.237285
$560$	−4.22080e22	−0.184415
$561$	−2.96391e23	−1.27550
$562$	−7.43315e22	−0.315075
$563$	−9.89748e22	−0.413241	−0.206620	−	0.978421i	$-0.566246\pi$
$563$	−9.89748e22	−0.413241	−0.206620	+	0.978421i	$0.566246\pi$
$564$	1.69929e23	0.698867
$565$	−1.95043e22	−0.0790166
$566$	1.42417e22	0.0568360
$567$	−4.42956e22	−0.174142
$568$	4.52708e22	0.175330
$569$	−3.12774e23	−1.19337	−0.596687	−	0.802474i	$-0.703517\pi$
$569$	−3.12774e23	−1.19337	−0.596687	+	0.802474i	$0.703517\pi$
$570$	−1.26775e22	−0.0476538
$571$	−1.84029e23	−0.681523	−0.340761	−	0.940150i	$-0.610685\pi$
$571$	−1.84029e23	−0.681523	−0.340761	+	0.940150i	$0.610685\pi$
$572$	3.25214e22	0.118660
$573$	−3.31782e23	−1.19272
$574$	−1.99627e22	−0.0707078
$575$	−2.78105e23	−0.970583
$576$	−3.43861e23	−1.18248
$577$	2.46710e23	0.835972	0.417986	−	0.908453i	$-0.362736\pi$
$577$	2.46710e23	0.835972	0.417986	+	0.908453i	$0.362736\pi$
$578$	−3.18705e22	−0.106415
$579$	−6.81311e23	−2.24170
$580$	1.03392e23	0.335235
$581$	−1.60354e22	−0.0512368
$582$	−1.30000e23	−0.409353
$583$	3.43108e23	1.06475
$584$	1.33154e23	0.407236
$585$	2.53223e22	0.0763271
$586$	−4.14261e22	−0.123068
$587$	−5.02239e23	−1.47057	−0.735287	−	0.677756i	$-0.762953\pi$
$587$	−5.02239e23	−1.47057	−0.735287	+	0.677756i	$0.762953\pi$
$588$	−2.02636e23	−0.584801
$589$	−1.76425e23	−0.501858
$590$	2.38210e21	0.00667911
$591$	4.56914e23	1.26282
$592$	−3.72585e23	−1.01506
$593$	3.80924e23	1.02300	0.511498	−	0.859285i	$-0.329091\pi$
$593$	3.80924e23	1.02300	0.511498	+	0.859285i	$0.329091\pi$
$594$	3.86310e22	0.102271
$595$	−9.89700e22	−0.258291
$596$	−4.27380e23	−1.09956
$597$	5.04133e23	1.27868
$598$	1.54477e22	0.0386280
$599$	−3.98989e23	−0.983633	−0.491816	−	0.870699i	$-0.663667\pi$
$599$	−3.98989e23	−0.983633	−0.491816	+	0.870699i	$0.663667\pi$
$600$	2.31097e23	0.561706
$601$	−5.53648e23	−1.32679	−0.663393	−	0.748271i	$-0.730884\pi$
$601$	−5.53648e23	−1.32679	−0.663393	+	0.748271i	$0.730884\pi$
$602$	8.02581e22	0.189635
$603$	8.50646e22	0.198176
$604$	4.08233e23	0.937764
$605$	6.79210e22	0.153845
$606$	−1.60305e22	−0.0358039
$607$	−2.30016e23	−0.506587	−0.253293	−	0.967390i	$-0.581514\pi$
$607$	−2.30016e23	−0.506587	−0.253293	+	0.967390i	$0.581514\pi$
$608$	−1.49249e23	−0.324139
$609$	−7.66249e23	−1.64105
$610$	2.20240e22	0.0465149
$611$	−4.19415e22	−0.0873562
$612$	−8.82608e23	−1.81293
$613$	8.70811e22	0.176405	0.0882023	−	0.996103i	$-0.471888\pi$
$613$	8.70811e22	0.176405	0.0882023	+	0.996103i	$0.471888\pi$
$614$	7.06383e22	0.141127
$615$	9.86669e22	0.194416
$616$	9.95030e22	0.193375
$617$	4.63073e23	0.887617	0.443808	−	0.896122i	$-0.353627\pi$
$617$	4.63073e23	0.887617	0.443808	+	0.896122i	$0.353627\pi$
$618$	−1.11853e23	−0.211469
$619$	2.68951e23	0.501536	0.250768	−	0.968047i	$-0.419317\pi$
$619$	2.68951e23	0.501536	0.250768	+	0.968047i	$0.419317\pi$
$620$	−1.18468e23	−0.217908
$621$	−4.68747e23	−0.850472
$622$	−6.69161e22	−0.119760
$623$	1.04131e23	0.183837
$624$	1.54267e23	0.268660
$625$	4.62914e23	0.795279
$626$	−1.29008e23	−0.218643
$627$	−3.59169e23	−0.600516
$628$	6.84798e22	0.112955
$629$	−8.73644e23	−1.42169
$630$	3.79946e22	0.0609997
$631$	−7.34142e23	−1.16287	−0.581434	−	0.813594i	$-0.697508\pi$
$631$	−7.34142e23	−1.16287	−0.581434	+	0.813594i	$0.697508\pi$
$632$	3.30732e23	0.516870
$633$	−6.05476e23	−0.933610
$634$	2.74449e22	0.0417545
$635$	−1.92176e23	−0.288485
$636$	1.69656e24	2.51295
$637$	5.00141e22	0.0730983
$638$	−1.14668e23	−0.165374
$639$	4.89744e23	0.696967
$640$	−1.32675e23	−0.186320
$641$	8.52931e23	1.18201	0.591005	−	0.806668i	$-0.298732\pi$
$641$	8.52931e23	1.18201	0.591005	+	0.806668i	$0.298732\pi$
$642$	1.53036e22	0.0209288
$643$	−8.00934e23	−1.08094	−0.540472	−	0.841362i	$-0.681754\pi$
$643$	−8.00934e23	−1.08094	−0.540472	+	0.841362i	$0.681754\pi$
$644$	−5.92093e23	−0.788606
$645$	−3.96682e23	−0.521416
$646$	−1.09062e23	−0.141481
$647$	−8.91454e23	−1.14133	−0.570667	−	0.821182i	$-0.693315\pi$
$647$	−8.91454e23	−1.14133	−0.570667	+	0.821182i	$0.693315\pi$
$648$	−6.68377e22	−0.0844567
$649$	6.74879e22	0.0841678
$650$	−2.79720e22	−0.0344318
$651$	8.77982e23	1.06671
$652$	−9.52953e23	−1.14279
$653$	7.41639e23	0.877871	0.438935	−	0.898519i	$-0.355356\pi$
$653$	7.41639e23	0.877871	0.438935	+	0.898519i	$0.355356\pi$
$654$	−4.83565e23	−0.564994
$655$	−3.47330e23	−0.400581
$656$	3.61996e23	0.412118
$657$	1.44048e24	1.61883
$658$	−6.29307e22	−0.0698140
$659$	−5.66251e23	−0.620130	−0.310065	−	0.950715i	$-0.600351\pi$
$659$	−5.66251e23	−0.620130	−0.310065	+	0.950715i	$0.600351\pi$
$660$	−2.41180e23	−0.260746
$661$	1.73316e24	1.84980	0.924901	−	0.380207i	$-0.124147\pi$
$661$	1.73316e24	1.84980	0.924901	+	0.380207i	$0.124147\pi$
$662$	−7.89971e22	−0.0832374
$663$	3.61727e23	0.376284
$664$	−2.41958e22	−0.0248492
$665$	−1.19933e23	−0.121606
$666$	3.35392e23	0.335755
$667$	1.39138e24	1.37523
$668$	6.44285e23	0.628750
$669$	1.31672e24	1.26874
$670$	7.05827e21	0.00671525
$671$	6.23966e23	0.586165
$672$	7.42740e23	0.688966
$673$	9.90342e23	0.907104	0.453552	−	0.891230i	$-0.350157\pi$
$673$	9.90342e23	0.907104	0.453552	+	0.891230i	$0.350157\pi$
$674$	−3.01148e23	−0.272378
$675$	8.48788e23	0.758084
$676$	1.05142e24	0.927323
$677$	1.24415e24	1.08360	0.541802	−	0.840506i	$-0.317742\pi$
$677$	1.24415e24	1.08360	0.541802	+	0.840506i	$0.317742\pi$
$678$	1.06961e23	0.0919970
$679$	−1.22984e24	−1.04461
$680$	−1.49336e23	−0.125268
$681$	1.67385e24	1.38665
$682$	1.31389e23	0.107496
$683$	−1.52784e24	−1.23453	−0.617264	−	0.786756i	$-0.711759\pi$
$683$	−1.52784e24	−1.23453	−0.617264	+	0.786756i	$0.711759\pi$
$684$	−1.06955e24	−0.853543
$685$	3.42080e23	0.269624
$686$	2.70843e23	0.210844
$687$	2.59924e24	1.99854
$688$	−1.45537e24	−1.10528
$689$	−4.18743e23	−0.314111
$690$	−1.14560e23	−0.0848823
$691$	−9.42634e23	−0.689890	−0.344945	−	0.938623i	$-0.612102\pi$
$691$	−9.42634e23	−0.689890	−0.344945	+	0.938623i	$0.612102\pi$
$692$	−1.70016e23	−0.122910
$693$	1.07643e24	0.768697
$694$	−3.37720e23	−0.238233
$695$	−2.85628e23	−0.199035
$696$	−1.15620e24	−0.795890
$697$	8.48814e23	0.577210
$698$	2.62322e23	0.176224
$699$	1.64907e24	1.09442
$700$	1.07214e24	0.702938
$701$	−1.62664e24	−1.05363	−0.526815	−	0.849980i	$-0.676614\pi$
$701$	−1.62664e24	−1.05363	−0.526815	+	0.849980i	$0.676614\pi$
$702$	−4.71469e22	−0.0301708
$703$	−1.05869e24	−0.669343
$704$	−8.08346e23	−0.504928
$705$	3.11040e23	0.191959
$706$	−4.65822e23	−0.284040
$707$	−1.51653e23	−0.0913665
$708$	3.33707e23	0.198647
$709$	−2.97117e24	−1.74757	−0.873785	−	0.486313i	$-0.838341\pi$
$709$	−2.97117e24	−1.74757	−0.873785	+	0.486313i	$0.838341\pi$
$710$	4.06367e22	0.0236169
$711$	3.57790e24	2.05464
$712$	1.57124e23	0.0891586
$713$	−1.59427e24	−0.893924
$714$	5.42750e23	0.300722
$715$	5.95275e22	0.0325924
$716$	2.85102e24	1.54255
$717$	3.36077e24	1.79691
$718$	−2.71621e23	−0.143518
$719$	−1.55702e24	−0.813013	−0.406507	−	0.913648i	$-0.633253\pi$
$719$	−1.55702e24	−0.813013	−0.406507	+	0.913648i	$0.633253\pi$
$720$	−6.88982e23	−0.355535
$721$	−1.05816e24	−0.539639
$722$	2.52937e23	0.127481
$723$	2.68594e24	1.33789
$724$	4.02646e23	0.198219
$725$	−2.51946e24	−1.22584
$726$	−3.72478e23	−0.179118
$727$	−3.79861e24	−1.80544	−0.902718	−	0.430234i	$-0.858431\pi$
$727$	−3.79861e24	−1.80544	−0.902718	+	0.430234i	$0.858431\pi$
$728$	−1.21437e23	−0.0570474
$729$	−3.50624e24	−1.62801
$730$	1.19524e23	0.0548545
$731$	−3.41258e24	−1.54805
$732$	3.08532e24	1.38343
$733$	2.86039e22	0.0126777	0.00633886	−	0.999980i	$-0.497982\pi$
$733$	2.86039e22	0.0126777	0.00633886	+	0.999980i	$0.497982\pi$
$734$	4.82695e23	0.211474
$735$	−3.70907e23	−0.160628
$736$	−1.34869e24	−0.577366
$737$	1.99969e23	0.0846232
$738$	−3.25860e23	−0.136318
$739$	3.44016e24	1.42266	0.711329	−	0.702859i	$-0.248093\pi$
$739$	3.44016e24	1.42266	0.711329	+	0.702859i	$0.248093\pi$
$740$	−7.10903e23	−0.290630
$741$	4.38344e23	0.177158
$742$	−6.28298e23	−0.251034
$743$	2.42958e24	0.959681	0.479841	−	0.877356i	$-0.340694\pi$
$743$	2.42958e24	0.959681	0.479841	+	0.877356i	$0.340694\pi$
$744$	1.32479e24	0.517341
$745$	−7.82281e23	−0.302019
$746$	−5.49264e22	−0.0209653
$747$	−2.61753e23	−0.0987795
$748$	−2.07483e24	−0.774138
$749$	1.44776e23	0.0534074
$750$	4.30465e23	0.157006
$751$	1.73948e24	0.627306	0.313653	−	0.949538i	$-0.398447\pi$
$751$	1.73948e24	0.627306	0.313653	+	0.949538i	$0.398447\pi$
$752$	1.14117e24	0.406909
$753$	−3.47931e24	−1.22669
$754$	1.39946e23	0.0487869
$755$	7.47234e23	0.257577
$756$	1.80709e24	0.615949
$757$	−1.64941e24	−0.555923	−0.277961	−	0.960592i	$-0.589659\pi$
$757$	−1.64941e24	−0.555923	−0.277961	+	0.960592i	$0.589659\pi$
$758$	3.19725e23	0.106559
$759$	−3.24564e24	−1.06966
$760$	−1.80967e23	−0.0589772
$761$	5.74503e24	1.85150	0.925748	−	0.378141i	$-0.123437\pi$
$761$	5.74503e24	1.85150	0.925748	+	0.378141i	$0.123437\pi$
$762$	1.05389e24	0.335875
$763$	−4.57466e24	−1.44179
$764$	−2.32258e24	−0.723896
$765$	−1.61554e24	−0.497960
$766$	4.55196e23	0.138757
$767$	−8.23649e22	−0.0248303
$768$	−3.42590e24	−1.02142
$769$	1.29705e24	0.382458	0.191229	−	0.981545i	$-0.438753\pi$
$769$	1.29705e24	0.382458	0.191229	+	0.981545i	$0.438753\pi$
$770$	8.93175e22	0.0260475
$771$	−4.25361e24	−1.22686
$772$	−4.76939e24	−1.36055
$773$	4.23996e23	0.119629	0.0598145	−	0.998210i	$-0.480949\pi$
$773$	4.23996e23	0.119629	0.0598145	+	0.998210i	$0.480949\pi$
$774$	1.31009e24	0.365598
$775$	2.88684e24	0.796815
$776$	−1.85570e24	−0.506622
$777$	5.26858e24	1.42270
$778$	−8.16064e23	−0.217970
$779$	1.02860e24	0.271756
$780$	2.94345e23	0.0769224
$781$	1.15129e24	0.297612
$782$	−9.85543e23	−0.252010
$783$	−4.24655e24	−1.07414
$784$	−1.36081e24	−0.340495
$785$	1.25346e23	0.0310256
$786$	1.90475e24	0.466387
$787$	6.16047e24	1.49220	0.746102	−	0.665831i	$-0.231923\pi$
$787$	6.16047e24	1.49220	0.746102	+	0.665831i	$0.231923\pi$
$788$	3.19854e24	0.766441
$789$	2.31144e24	0.547935
$790$	2.96877e23	0.0696221
$791$	1.01188e24	0.234763
$792$	1.62424e24	0.372808
$793$	−7.61513e23	−0.172924
$794$	5.41691e22	0.0121696
$795$	3.10541e24	0.690238
$796$	3.52909e24	0.776070
$797$	1.48019e24	0.322050	0.161025	−	0.986950i	$-0.448520\pi$
$797$	1.48019e24	0.322050	0.161025	+	0.986950i	$0.448520\pi$
$798$	6.57709e23	0.141582
$799$	2.67582e24	0.569915
$800$	2.44216e24	0.514646
$801$	1.69979e24	0.354420
$802$	4.43192e23	0.0914344
$803$	3.38627e24	0.691257
$804$	9.88786e23	0.199722
$805$	−1.08377e24	−0.216608
$806$	−1.60352e23	−0.0317123
$807$	−1.42320e25	−2.78511
$808$	−2.28830e23	−0.0443116
$809$	8.54444e24	1.63727	0.818637	−	0.574311i	$-0.194730\pi$
$809$	8.54444e24	1.63727	0.818637	+	0.574311i	$0.194730\pi$
$810$	−5.99960e22	−0.0113763
$811$	−3.50222e24	−0.657153	−0.328577	−	0.944477i	$-0.606569\pi$
$811$	−3.50222e24	−0.657153	−0.328577	+	0.944477i	$0.606569\pi$
$812$	−5.36398e24	−0.996004
$813$	−2.84417e24	−0.522619
$814$	7.88437e23	0.143370
$815$	−1.74430e24	−0.313892
$816$	−9.84205e24	−1.75275
$817$	−4.13540e24	−0.728836
$818$	5.22807e23	0.0911882
$819$	−1.31372e24	−0.226773
$820$	6.90699e23	0.117997
$821$	2.98807e24	0.505212	0.252606	−	0.967569i	$-0.418712\pi$
$821$	2.98807e24	0.505212	0.252606	+	0.967569i	$0.418712\pi$
$822$	−1.87596e24	−0.313916
$823$	7.76303e24	1.28568	0.642839	−	0.766001i	$-0.277756\pi$
$823$	7.76303e24	1.28568	0.642839	+	0.766001i	$0.277756\pi$
$824$	−1.59667e24	−0.261718
$825$	5.87706e24	0.953459
$826$	−1.23584e23	−0.0198441
$827$	−8.88486e24	−1.41206	−0.706031	−	0.708181i	$-0.749516\pi$
$827$	−8.88486e24	−1.41206	−0.706031	+	0.708181i	$0.749516\pi$
$828$	−9.66502e24	−1.52036
$829$	1.23508e24	0.192302	0.0961508	−	0.995367i	$-0.469347\pi$
$829$	1.23508e24	0.192302	0.0961508	+	0.995367i	$0.469347\pi$
$830$	−2.17191e22	−0.00334717
$831$	−1.40114e25	−2.13733
$832$	9.86538e23	0.148959
$833$	−3.19085e24	−0.476896
$834$	1.56638e24	0.231731
$835$	1.17931e24	0.172700
$836$	−2.51430e24	−0.364471
$837$	4.86577e24	0.698209
$838$	−1.95201e24	−0.277273
$839$	−1.74304e24	−0.245093	−0.122547	−	0.992463i	$-0.539106\pi$
$839$	−1.74304e24	−0.245093	−0.122547	+	0.992463i	$0.539106\pi$
$840$	9.00584e23	0.125358
$841$	5.34787e24	0.736911
$842$	−1.74571e21	−0.000238133 0
$843$	−1.90602e25	−2.57390
$844$	−4.23852e24	−0.566635
$845$	1.92454e24	0.254709
$846$	−1.02725e24	−0.134595
$847$	−3.52374e24	−0.457083
$848$	1.13934e25	1.46314
$849$	3.65188e24	0.464303
$850$	1.78458e24	0.224634
$851$	−9.56686e24	−1.19225
$852$	5.69276e24	0.702403
$853$	8.32752e24	1.01730	0.508650	−	0.860973i	$-0.330145\pi$
$853$	8.32752e24	1.01730	0.508650	+	0.860973i	$0.330145\pi$
$854$	−1.14261e24	−0.138199
$855$	−1.95772e24	−0.234444
$856$	2.18453e23	0.0259019
$857$	−1.57191e25	−1.84540	−0.922699	−	0.385522i	$-0.874021\pi$
$857$	−1.57191e25	−1.84540	−0.922699	+	0.385522i	$0.874021\pi$
$858$	−3.26448e23	−0.0379465
$859$	3.22934e24	0.371682	0.185841	−	0.982580i	$-0.440499\pi$
$859$	3.22934e24	0.371682	0.185841	+	0.982580i	$0.440499\pi$
$860$	−2.77689e24	−0.316463
$861$	−5.11884e24	−0.577624
$862$	1.40741e24	0.157257
$863$	−7.82567e24	−0.865824	−0.432912	−	0.901436i	$-0.642514\pi$
$863$	−7.82567e24	−0.865824	−0.432912	+	0.901436i	$0.642514\pi$
$864$	4.11626e24	0.450958
$865$	−3.11199e23	−0.0337599
$866$	−8.07750e23	−0.0867711
$867$	−8.17225e24	−0.869320
$868$	6.14615e24	0.647419
$869$	8.41090e24	0.877353
$870$	−1.03784e24	−0.107206
$871$	−2.44050e23	−0.0249646
$872$	−6.90273e24	−0.699247
$873$	−2.00752e25	−2.01391
$874$	−1.19429e24	−0.118649
$875$	4.07232e24	0.400658
$876$	1.67441e25	1.63146
$877$	1.53408e25	1.48031	0.740154	−	0.672437i	$-0.234753\pi$
$877$	1.53408e25	1.48031	0.740154	+	0.672437i	$0.234753\pi$
$878$	−2.41001e24	−0.230312
$879$	−1.06225e25	−1.00536
$880$	−1.61965e24	−0.151817
$881$	−1.94088e25	−1.80179	−0.900895	−	0.434036i	$-0.857089\pi$
$881$	−1.94088e25	−1.80179	−0.900895	+	0.434036i	$0.857089\pi$
$882$	1.22497e24	0.112627
$883$	−6.68163e23	−0.0608438	−0.0304219	−	0.999537i	$-0.509685\pi$
$883$	−6.68163e23	−0.0608438	−0.0304219	+	0.999537i	$0.509685\pi$
$884$	2.53220e24	0.228378
$885$	6.10821e23	0.0545628
$886$	1.04591e24	0.0925350
$887$	−1.46172e25	−1.28089	−0.640447	−	0.768002i	$-0.721251\pi$
$887$	−1.46172e25	−1.28089	−0.640447	+	0.768002i	$0.721251\pi$
$888$	7.94977e24	0.689993
$889$	9.97010e24	0.857106
$890$	1.41041e23	0.0120096
$891$	−1.69976e24	−0.143360
$892$	9.21748e24	0.770036
$893$	3.24259e24	0.268321
$894$	4.29002e24	0.351633
$895$	5.21855e24	0.423696
$896$	6.88319e24	0.553569
$897$	3.96110e24	0.315559
$898$	−4.54904e24	−0.358980
$899$	−1.44431e25	−1.12902
$900$	1.75010e25	1.35520
$901$	2.67153e25	2.04927
$902$	−7.66030e23	−0.0582090
$903$	2.05798e25	1.54916
$904$	1.52683e24	0.113857
$905$	7.37009e23	0.0544452
$906$	−4.09782e24	−0.299891
$907$	1.84289e25	1.33610	0.668049	−	0.744117i	$-0.267130\pi$
$907$	1.84289e25	1.33610	0.668049	+	0.744117i	$0.267130\pi$
$908$	1.17175e25	0.841597
$909$	−2.47551e24	−0.176146
$910$	−1.09007e23	−0.00768424
$911$	2.54837e23	0.0177974	0.00889868	−	0.999960i	$-0.497167\pi$
$911$	2.54837e23	0.0177974	0.00889868	+	0.999960i	$0.497167\pi$
$912$	−1.19267e25	−0.825208
$913$	−6.15327e23	−0.0421798
$914$	3.36831e24	0.228754
$915$	5.64741e24	0.379988
$916$	1.81955e25	1.21297
$917$	1.80195e25	1.19015
$918$	3.00792e24	0.196835
$919$	−6.70795e24	−0.434918	−0.217459	−	0.976069i	$-0.569777\pi$
$919$	−6.70795e24	−0.434918	−0.217459	+	0.976069i	$0.569777\pi$
$920$	−1.63531e24	−0.105052
$921$	1.81131e25	1.15289
$922$	−1.29419e24	−0.0816181
$923$	−1.40508e24	−0.0877981
$924$	1.25124e25	0.774692
$925$	1.73233e25	1.06274
$926$	2.23680e23	0.0135967
$927$	−1.72729e25	−1.04037
$928$	−1.22183e25	−0.729210
$929$	1.93492e25	1.14427	0.572135	−	0.820160i	$-0.306115\pi$
$929$	1.93492e25	1.14427	0.572135	+	0.820160i	$0.306115\pi$
$930$	1.18918e24	0.0696855
$931$	−3.86670e24	−0.224527
$932$	1.15440e25	0.664233
$933$	−1.71587e25	−0.978340
$934$	1.24284e24	0.0702208
$935$	−3.79779e24	−0.212634
$936$	−1.98228e24	−0.109982
$937$	−2.14055e25	−1.17690	−0.588448	−	0.808535i	$-0.700261\pi$
$937$	−2.14055e25	−1.17690	−0.588448	+	0.808535i	$0.700261\pi$
$938$	−3.66183e23	−0.0199514
$939$	−3.30804e25	−1.78613
$940$	2.17738e24	0.116506
$941$	2.48221e25	1.31621	0.658106	−	0.752925i	$-0.271358\pi$
$941$	2.48221e25	1.31621	0.658106	+	0.752925i	$0.271358\pi$
$942$	−6.87397e23	−0.0361223
$943$	9.29497e24	0.484059
$944$	2.24102e24	0.115660
$945$	3.30772e24	0.169184
$946$	3.07975e24	0.156114
$947$	−3.53328e24	−0.177502	−0.0887511	−	0.996054i	$-0.528288\pi$
$947$	−3.53328e24	−0.177502	−0.0887511	+	0.996054i	$0.528288\pi$
$948$	4.15893e25	2.07067
$949$	−4.13274e24	−0.203927
$950$	2.16257e24	0.105760
$951$	7.03745e24	0.341099
$952$	7.74757e24	0.372179
$953$	−1.56029e24	−0.0742874	−0.0371437	−	0.999310i	$-0.511826\pi$
$953$	−1.56029e24	−0.0742874	−0.0371437	+	0.999310i	$0.511826\pi$
$954$	−1.02560e25	−0.483969
$955$	−4.25127e24	−0.198834
$956$	2.35265e25	1.09060
$957$	−2.94034e25	−1.35097
$958$	−7.41987e23	−0.0337901
$959$	−1.77471e25	−0.801069
$960$	−7.31620e24	−0.327326
$961$	−6.00101e24	−0.266119
$962$	−9.62240e23	−0.0422956
$963$	2.36325e24	0.102964
$964$	1.88025e25	0.812007
$965$	−8.72995e24	−0.373705
$966$	5.94340e24	0.252191
$967$	2.82467e25	1.18807	0.594037	−	0.804438i	$-0.297533\pi$
$967$	2.82467e25	1.18807	0.594037	+	0.804438i	$0.297533\pi$
$968$	−5.31699e24	−0.221679
$969$	−2.79659e25	−1.15578
$970$	−1.66575e24	−0.0682417
$971$	4.22438e25	1.71553	0.857767	−	0.514038i	$-0.171851\pi$
$971$	4.22438e25	1.71553	0.857767	+	0.514038i	$0.171851\pi$
$972$	−2.78879e25	−1.12267
$973$	1.48184e25	0.591345
$974$	−5.26145e24	−0.208139
$975$	−7.17260e24	−0.281279
$976$	2.07196e25	0.805487
$977$	1.65376e25	0.637336	0.318668	−	0.947866i	$-0.396765\pi$
$977$	1.65376e25	0.637336	0.318668	+	0.947866i	$0.396765\pi$
$978$	9.56569e24	0.365457
$979$	3.99585e24	0.151341
$980$	−2.59646e24	−0.0974901
$981$	−7.46745e25	−2.77962
$982$	−6.36937e24	−0.235044
$983$	−4.30495e25	−1.57494	−0.787469	−	0.616354i	$-0.788609\pi$
$983$	−4.30495e25	−1.57494	−0.787469	+	0.616354i	$0.788609\pi$
$984$	−7.72384e24	−0.280140
$985$	5.85465e24	0.210520
$986$	−8.92839e24	−0.318287
$987$	−1.61368e25	−0.570323
$988$	3.06855e24	0.107522
$989$	−3.73696e25	−1.29822
$990$	1.45797e24	0.0502170
$991$	3.41382e24	0.116578	0.0582888	−	0.998300i	$-0.481436\pi$
$991$	3.41382e24	0.116578	0.0582888	+	0.998300i	$0.481436\pi$
$992$	1.39999e25	0.473998
$993$	−2.02565e25	−0.679980
$994$	−2.10823e24	−0.0701672
$995$	6.45968e24	0.213165
$996$	−3.04260e24	−0.0995500
$997$	4.02889e25	1.30700	0.653501	−	0.756925i	$-0.273299\pi$
$997$	4.02889e25	1.30700	0.653501	+	0.756925i	$0.273299\pi$
$998$	−4.17302e24	−0.134227
$999$	2.91984e25	0.931222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.18.a.b.1.19	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.18.a.b.1.19	✓	44	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)

\(f(q)\)	\(=\)	\(q-70.2688 q^{2} -18018.4 q^{3} -126134. q^{4} -230878. q^{5} +1.26613e6 q^{6} +1.19779e7 q^{7} +1.80736e7 q^{8} +1.95522e8 q^{9} +O(q^{10})\)	\(q-70.2688 q^{2} -18018.4 q^{3} -126134. q^{4} -230878. q^{5} +1.26613e6 q^{6} +1.19779e7 q^{7} +1.80736e7 q^{8} +1.95522e8 q^{9} +1.62235e7 q^{10} +4.59631e8 q^{11} +2.27274e9 q^{12} -5.60952e8 q^{13} -8.41676e8 q^{14} +4.16004e9 q^{15} +1.52627e10 q^{16} +3.57881e10 q^{17} -1.37391e10 q^{18} +4.33684e10 q^{19} +2.91216e10 q^{20} -2.15823e11 q^{21} -3.22977e10 q^{22} +3.91899e11 q^{23} -3.25656e11 q^{24} -7.09635e11 q^{25} +3.94174e10 q^{26} -1.19609e12 q^{27} -1.51083e12 q^{28} +3.55035e12 q^{29} -2.92321e11 q^{30} -4.06806e12 q^{31} -3.44143e12 q^{32} -8.28181e12 q^{33} -2.51479e12 q^{34} -2.76544e12 q^{35} -2.46620e13 q^{36} -2.44115e13 q^{37} -3.04744e12 q^{38} +1.01075e13 q^{39} -4.17279e12 q^{40} +2.37178e13 q^{41} +1.51656e13 q^{42} -9.53551e13 q^{43} -5.79753e13 q^{44} -4.51417e13 q^{45} -2.75383e13 q^{46} +7.47684e13 q^{47} -2.75009e14 q^{48} -8.91593e13 q^{49} +4.98652e13 q^{50} -6.44844e14 q^{51} +7.07553e13 q^{52} +7.46485e14 q^{53} +8.40479e13 q^{54} -1.06119e14 q^{55} +2.16484e14 q^{56} -7.81429e14 q^{57} -2.49479e14 q^{58} +1.46830e14 q^{59} -5.24724e14 q^{60} +1.35754e15 q^{61} +2.85857e14 q^{62} +2.34195e15 q^{63} -1.75868e15 q^{64} +1.29511e14 q^{65} +5.81953e14 q^{66} +4.35064e14 q^{67} -4.51411e15 q^{68} -7.06139e15 q^{69} +1.94324e14 q^{70} +2.50480e15 q^{71} +3.53378e15 q^{72} +7.36736e15 q^{73} +1.71537e15 q^{74} +1.27865e16 q^{75} -5.47024e15 q^{76} +5.50544e15 q^{77} -7.10238e14 q^{78} +1.82992e16 q^{79} -3.52381e15 q^{80} -3.69809e15 q^{81} -1.66662e15 q^{82} -1.33874e15 q^{83} +2.72227e16 q^{84} -8.26269e15 q^{85} +6.70049e15 q^{86} -6.39716e16 q^{87} +8.30718e15 q^{88} +8.69360e15 q^{89} +3.17205e15 q^{90} -6.71906e15 q^{91} -4.94319e16 q^{92} +7.32998e16 q^{93} -5.25388e15 q^{94} -1.00128e16 q^{95} +6.20090e16 q^{96} -1.02675e17 q^{97} +6.26511e15 q^{98} +8.98680e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9}+O(q^{10}) \) 44 * q + 783 * q^2 + 13122 * q^3 + 3063551 * q^4 + 2062778 * q^5 + 9982022 * q^6 + 13722970 * q^7 + 168939849 * q^8 + 2182805218 * q^9	\( 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9} + 246619918 q^{10} + 896501218 q^{11} + 2579890176 q^{12} + 5139901152 q^{13} - 1065727269 q^{14} + 52608606500 q^{15} + 170254553019 q^{16} + 31152575372 q^{17} + 371065029637 q^{18} + 222944612638 q^{19} + 632345964652 q^{20} + 518768862104 q^{21} - 1188197076091 q^{22} - 314739342184 q^{23} - 1830638682468 q^{24} + 8265149117122 q^{25} - 1422210694649 q^{26} + 1055641354104 q^{27} + 4733828767179 q^{28} + 7952343701542 q^{29} + 33815332595226 q^{30} + 22703202725740 q^{31} + 51508227606921 q^{32} + 39808250652964 q^{33} + 42559210973877 q^{34} + 53084789167044 q^{35} + 286899333699545 q^{36} + 70719636063816 q^{37} + 70760432282360 q^{38} + 89621954178128 q^{39} + 176727288274300 q^{40} + 77283001373080 q^{41} - 142968851337140 q^{42} + 218112956325030 q^{43} - 146577440549739 q^{44} + 156445227241670 q^{45} - 436430382603480 q^{46} - 206155334901712 q^{47} - 694457384549320 q^{48} + 17\!\cdots\!92 q^{49}+ \cdots - 33\!\cdots\!26 q^{99}+O(q^{100}) \) 44 * q + 783 * q^2 + 13122 * q^3 + 3063551 * q^4 + 2062778 * q^5 + 9982022 * q^6 + 13722970 * q^7 + 168939849 * q^8 + 2182805218 * q^9 + 246619918 * q^10 + 896501218 * q^11 + 2579890176 * q^12 + 5139901152 * q^13 - 1065727269 * q^14 + 52608606500 * q^15 + 170254553019 * q^16 + 31152575372 * q^17 + 371065029637 * q^18 + 222944612638 * q^19 + 632345964652 * q^20 + 518768862104 * q^21 - 1188197076091 * q^22 - 314739342184 * q^23 - 1830638682468 * q^24 + 8265149117122 * q^25 - 1422210694649 * q^26 + 1055641354104 * q^27 + 4733828767179 * q^28 + 7952343701542 * q^29 + 33815332595226 * q^30 + 22703202725740 * q^31 + 51508227606921 * q^32 + 39808250652964 * q^33 + 42559210973877 * q^34 + 53084789167044 * q^35 + 286899333699545 * q^36 + 70719636063816 * q^37 + 70760432282360 * q^38 + 89621954178128 * q^39 + 176727288274300 * q^40 + 77283001373080 * q^41 - 142968851337140 * q^42 + 218112956325030 * q^43 - 146577440549739 * q^44 + 156445227241670 * q^45 - 436430382603480 * q^46 - 206155334901712 * q^47 - 694457384549320 * q^48 + 1711133899986192 * q^49 - 636149584416999 * q^50 + 158951699286348 * q^51 - 3158033385800149 * q^52 - 404876214856866 * q^53 - 1832749628980958 * q^54 - 611379564042440 * q^55 - 2900007168369351 * q^56 - 1013357232316788 * q^57 - 455786716037158 * q^58 + 6460539254590124 * q^59 + 4624863641607938 * q^60 + 4875940646057436 * q^61 - 15281797209467076 * q^62 - 16054536748044808 * q^63 + 5329292222614591 * q^64 - 7625310499015476 * q^65 - 10349172696837322 * q^66 - 4206243743451792 * q^67 - 552954195428233 * q^68 + 8020251305435444 * q^69 + 3876379104148138 * q^70 + 19535505651668622 * q^71 + 71495174696263183 * q^72 + 33833193336852456 * q^73 + 40772046703252163 * q^74 + 75968477185276688 * q^75 + 38838328992025026 * q^76 + 53055532951436968 * q^77 + 73057936571746858 * q^78 + 61045424159854942 * q^79 + 80004004628116616 * q^80 + 155795318109062036 * q^81 + 52248236930642133 * q^82 + 1235564168216730 * q^83 + 164143534194509272 * q^84 + 113286530641911588 * q^85 + 50368241096487595 * q^86 + 18062036297697056 * q^87 - 116796176360505729 * q^88 + 5837731242014800 * q^89 + 269698982682069798 * q^90 - 57230636051197354 * q^91 + 85549613709158172 * q^92 - 42635139630610976 * q^93 + 217633917061493766 * q^94 - 190986541078108154 * q^95 + 173923507159625020 * q^96 + 233342043840904176 * q^97 + 216259456237342020 * q^98 - 333859997478074426 * q^99

Introduction

L-functions

Modular forms

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