LMFDB - Embedded newform 59.18.a.b.1.28

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			1.28
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)

$f(q)$	$=$	$q+272.894 q^{2} -10486.4 q^{3} -56601.1 q^{4} +682316. q^{5} -2.86168e6 q^{6} -1.24000e7 q^{7} -5.12148e7 q^{8} -1.91748e7 q^{9} +O(q^{10})$	\(q+272.894 q^{2} -10486.4 q^{3} -56601.1 q^{4} +682316. q^{5} -2.86168e6 q^{6} -1.24000e7 q^{7} -5.12148e7 q^{8} -1.91748e7 q^{9} +1.86200e8 q^{10} -1.11028e9 q^{11} +5.93543e8 q^{12} -4.87181e8 q^{13} -3.38387e9 q^{14} -7.15506e9 q^{15} -6.55738e9 q^{16} +9.03991e9 q^{17} -5.23268e9 q^{18} -6.84630e10 q^{19} -3.86198e10 q^{20} +1.30031e11 q^{21} -3.02989e11 q^{22} -4.89532e11 q^{23} +5.37061e11 q^{24} -2.97385e11 q^{25} -1.32949e11 q^{26} +1.55530e12 q^{27} +7.01851e11 q^{28} +1.91227e12 q^{29} -1.95257e12 q^{30} -8.62758e12 q^{31} +4.92336e12 q^{32} +1.16429e13 q^{33} +2.46694e12 q^{34} -8.46068e12 q^{35} +1.08531e12 q^{36} +4.24919e12 q^{37} -1.86831e13 q^{38} +5.10879e12 q^{39} -3.49447e13 q^{40} -6.70407e13 q^{41} +3.54847e13 q^{42} -7.22603e13 q^{43} +6.28432e13 q^{44} -1.30833e13 q^{45} -1.33590e14 q^{46} -1.99549e14 q^{47} +6.87635e13 q^{48} -7.88716e13 q^{49} -8.11544e13 q^{50} -9.47965e13 q^{51} +2.75750e13 q^{52} +6.25678e14 q^{53} +4.24430e14 q^{54} -7.57563e14 q^{55} +6.35061e14 q^{56} +7.17933e14 q^{57} +5.21846e14 q^{58} +1.46830e14 q^{59} +4.04984e14 q^{60} -8.26838e14 q^{61} -2.35441e15 q^{62} +2.37767e14 q^{63} +2.20304e15 q^{64} -3.32411e14 q^{65} +3.17728e15 q^{66} +1.53814e15 q^{67} -5.11669e14 q^{68} +5.13345e15 q^{69} -2.30887e15 q^{70} +3.47766e14 q^{71} +9.82033e14 q^{72} +1.10827e16 q^{73} +1.15958e15 q^{74} +3.11851e15 q^{75} +3.87508e15 q^{76} +1.37675e16 q^{77} +1.39416e15 q^{78} -4.86985e15 q^{79} -4.47420e15 q^{80} -1.38333e16 q^{81} -1.82950e16 q^{82} +6.61166e15 q^{83} -7.35991e15 q^{84} +6.16808e15 q^{85} -1.97194e16 q^{86} -2.00529e16 q^{87} +5.68629e16 q^{88} +4.46264e16 q^{89} -3.57034e15 q^{90} +6.04102e15 q^{91} +2.77080e16 q^{92} +9.04726e16 q^{93} -5.44556e16 q^{94} -4.67134e16 q^{95} -5.16285e16 q^{96} +3.21445e16 q^{97} -2.15236e16 q^{98} +2.12894e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	272.894	0.753769	0.376885	−	0.926260i	$-0.376995\pi$
$2$	272.894	0.753769	0.376885	+	0.926260i	$0.376995\pi$
$3$	−10486.4	−0.922778	−0.461389	−	0.887198i	$-0.652649\pi$
$3$	−10486.4	−0.922778	−0.461389	+	0.887198i	$0.652649\pi$
$4$	−56601.1	−0.431832
$5$	682316.	0.781161	0.390580	−	0.920569i	$-0.372274\pi$
$5$	682316.	0.781161	0.390580	+	0.920569i	$0.372274\pi$
$6$	−2.86168e6	−0.695562
$7$	−1.24000e7	−0.812993	−0.406496	−	0.913652i	$-0.633250\pi$
$7$	−1.24000e7	−0.812993	−0.406496	+	0.913652i	$0.633250\pi$
$8$	−5.12148e7	−1.07927
$9$	−1.91748e7	−0.148480
$10$	1.86200e8	0.588815
$11$	−1.11028e9	−1.56169	−0.780846	−	0.624723i	$-0.785212\pi$
$11$	−1.11028e9	−1.56169	−0.780846	+	0.624723i	$0.785212\pi$
$12$	5.93543e8	0.398485
$13$	−4.87181e8	−0.165642	−0.0828212	−	0.996564i	$-0.526393\pi$
$13$	−4.87181e8	−0.165642	−0.0828212	+	0.996564i	$0.526393\pi$
$14$	−3.38387e9	−0.612809
$15$	−7.15506e9	−0.720838
$16$	−6.55738e9	−0.381689
$17$	9.03991e9	0.314303	0.157151	−	0.987575i	$-0.449769\pi$
$17$	9.03991e9	0.314303	0.157151	+	0.987575i	$0.449769\pi$
$18$	−5.23268e9	−0.111920
$19$	−6.84630e10	−0.924805	−0.462403	−	0.886670i	$-0.653012\pi$
$19$	−6.84630e10	−0.924805	−0.462403	+	0.886670i	$0.653012\pi$
$20$	−3.86198e10	−0.337330
$21$	1.30031e11	0.750212
$22$	−3.02989e11	−1.17716
$23$	−4.89532e11	−1.30345	−0.651725	−	0.758455i	$-0.725955\pi$
$23$	−4.89532e11	−1.30345	−0.651725	+	0.758455i	$0.725955\pi$
$24$	5.37061e11	0.995928
$25$	−2.97385e11	−0.389788
$26$	−1.32949e11	−0.124856
$27$	1.55530e12	1.05979
$28$	7.01851e11	0.351076
$29$	1.91227e12	0.709849	0.354924	−	0.934895i	$-0.384507\pi$
$29$	1.91227e12	0.709849	0.354924	+	0.934895i	$0.384507\pi$
$30$	−1.95257e12	−0.543346
$31$	−8.62758e12	−1.81683	−0.908416	−	0.418067i	$-0.862708\pi$
$31$	−8.62758e12	−1.81683	−0.908416	+	0.418067i	$0.862708\pi$
$32$	4.92336e12	0.791565
$33$	1.16429e13	1.44110
$34$	2.46694e12	0.236912
$35$	−8.46068e12	−0.635078
$36$	1.08531e12	0.0641186
$37$	4.24919e12	0.198880	0.0994401	−	0.995044i	$-0.468295\pi$
$37$	4.24919e12	0.198880	0.0994401	+	0.995044i	$0.468295\pi$
$38$	−1.86831e13	−0.697090
$39$	5.10879e12	0.152851
$40$	−3.49447e13	−0.843084
$41$	−6.70407e13	−1.31122	−0.655610	−	0.755100i	$-0.727588\pi$
$41$	−6.70407e13	−1.31122	−0.655610	+	0.755100i	$0.727588\pi$
$42$	3.54847e13	0.565487
$43$	−7.22603e13	−0.942796	−0.471398	−	0.881921i	$-0.656251\pi$
$43$	−7.22603e13	−0.942796	−0.471398	+	0.881921i	$0.656251\pi$
$44$	6.28432e13	0.674389
$45$	−1.30833e13	−0.115987
$46$	−1.33590e14	−0.982501
$47$	−1.99549e14	−1.22241	−0.611206	−	0.791472i	$-0.709315\pi$
$47$	−1.99549e14	−1.22241	−0.611206	+	0.791472i	$0.709315\pi$
$48$	6.87635e13	0.352215
$49$	−7.88716e13	−0.339043
$50$	−8.11544e13	−0.293810
$51$	−9.47965e13	−0.290032
$52$	2.75750e13	0.0715297
$53$	6.25678e14	1.38040	0.690202	−	0.723617i	$-0.257522\pi$
$53$	6.25678e14	1.38040	0.690202	+	0.723617i	$0.257522\pi$
$54$	4.24430e14	0.798839
$55$	−7.57563e14	−1.21993
$56$	6.35061e14	0.877440
$57$	7.17933e14	0.853390
$58$	5.21846e14	0.535062
$59$	1.46830e14	0.130189
$59$	1.46830e14	0.130189
$60$	4.04984e14	0.311281
$61$	−8.26838e14	−0.552226	−0.276113	−	0.961125i	$-0.589046\pi$
$61$	−8.26838e14	−0.552226	−0.276113	+	0.961125i	$0.589046\pi$
$62$	−2.35441e15	−1.36947
$63$	2.37767e14	0.120714
$64$	2.20304e15	0.978347
$65$	−3.32411e14	−0.129393
$66$	3.17728e15	1.08625
$67$	1.53814e15	0.462764	0.231382	−	0.972863i	$-0.425675\pi$
$67$	1.53814e15	0.462764	0.231382	+	0.972863i	$0.425675\pi$
$68$	−5.11669e14	−0.135726
$69$	5.13345e15	1.20280
$70$	−2.30887e15	−0.478702
$71$	3.47766e14	0.0639133	0.0319566	−	0.999489i	$-0.489826\pi$
$71$	3.47766e14	0.0639133	0.0319566	+	0.999489i	$0.489826\pi$
$72$	9.82033e14	0.160251
$73$	1.10827e16	1.60843	0.804214	−	0.594340i	$-0.202587\pi$
$73$	1.10827e16	1.60843	0.804214	+	0.594340i	$0.202587\pi$
$74$	1.15958e15	0.149910
$75$	3.11851e15	0.359688
$76$	3.87508e15	0.399360
$77$	1.37675e16	1.26965
$78$	1.39416e15	0.115215
$79$	−4.86985e15	−0.361148	−0.180574	−	0.983561i	$-0.557795\pi$
$79$	−4.86985e15	−0.361148	−0.180574	+	0.983561i	$0.557795\pi$
$80$	−4.47420e15	−0.298161
$81$	−1.38333e16	−0.829473
$82$	−1.82950e16	−0.988357
$83$	6.61166e15	0.322216	0.161108	−	0.986937i	$-0.448493\pi$
$83$	6.61166e15	0.322216	0.161108	+	0.986937i	$0.448493\pi$
$84$	−7.35991e15	−0.323965
$85$	6.16808e15	0.245521
$86$	−1.97194e16	−0.710651
$87$	−2.00529e16	−0.655033
$88$	5.68629e16	1.68549
$89$	4.46264e16	1.20165	0.600823	−	0.799382i	$-0.294840\pi$
$89$	4.46264e16	1.20165	0.600823	+	0.799382i	$0.294840\pi$
$90$	−3.57034e15	−0.0874275
$91$	6.04102e15	0.134666
$92$	2.77080e16	0.562872
$93$	9.04726e16	1.67653
$94$	−5.44556e16	−0.921416
$95$	−4.67134e16	−0.722421
$96$	−5.16285e16	−0.730439
$97$	3.21445e16	0.416435	0.208217	−	0.978083i	$-0.433234\pi$
$97$	3.21445e16	0.416435	0.208217	+	0.978083i	$0.433234\pi$
$98$	−2.15236e16	−0.255560
$99$	2.12894e16	0.231881
$100$	1.68323e16	0.168323
$101$	3.96859e16	0.364674	0.182337	−	0.983236i	$-0.441634\pi$
$101$	3.96859e16	0.364674	0.182337	+	0.983236i	$0.441634\pi$
$102$	−2.58694e16	−0.218617
$103$	2.32575e17	1.80903	0.904515	−	0.426442i	$-0.140233\pi$
$103$	2.32575e17	1.80903	0.904515	+	0.426442i	$0.140233\pi$
$104$	2.49509e16	0.178773
$105$	8.87224e16	0.586036
$106$	1.70744e17	1.04051
$107$	−3.13781e17	−1.76549	−0.882743	−	0.469856i	$-0.844306\pi$
$107$	−3.13781e17	−1.76549	−0.882743	+	0.469856i	$0.844306\pi$
$108$	−8.80314e16	−0.457652
$109$	−2.96181e17	−1.42374	−0.711872	−	0.702309i	$-0.752152\pi$
$109$	−2.96181e17	−1.42374	−0.711872	+	0.702309i	$0.752152\pi$
$110$	−2.06734e17	−0.919548
$111$	−4.45589e16	−0.183522
$112$	8.13112e16	0.310311
$113$	−1.67150e17	−0.591479	−0.295739	−	0.955269i	$-0.595566\pi$
$113$	−1.67150e17	−0.591479	−0.295739	+	0.955269i	$0.595566\pi$
$114$	1.95919e17	0.643259
$115$	−3.34016e17	−1.01820
$116$	−1.08236e17	−0.306535
$117$	9.34159e15	0.0245947
$118$	4.00691e16	0.0981324
$119$	−1.12095e17	−0.255526
$120$	3.66445e17	0.777979
$121$	7.27280e17	1.43889
$122$	−2.25639e17	−0.416251
$123$	7.03018e17	1.20997
$124$	4.88330e17	0.784566
$125$	−7.23476e17	−1.08565
$126$	6.48850e16	0.0909902
$127$	9.69423e17	1.27111	0.635553	−	0.772057i	$-0.280772\pi$
$127$	9.69423e17	1.27111	0.635553	+	0.772057i	$0.280772\pi$
$128$	−4.41184e16	−0.0541172
$129$	7.57753e17	0.869992
$130$	−9.07129e16	−0.0975328
$131$	−9.62838e17	−0.969945	−0.484973	−	0.874529i	$-0.661170\pi$
$131$	−9.62838e17	−0.969945	−0.484973	+	0.874529i	$0.661170\pi$
$132$	−6.59001e17	−0.622311
$133$	8.48938e17	0.751860
$134$	4.19749e17	0.348818
$135$	1.06120e18	0.827868
$136$	−4.62977e17	−0.339218
$137$	1.90298e18	1.31012	0.655058	−	0.755579i	$-0.272644\pi$
$137$	1.90298e18	1.31012	0.655058	+	0.755579i	$0.272644\pi$
$138$	1.40089e18	0.906631
$139$	−2.75395e17	−0.167622	−0.0838109	−	0.996482i	$-0.526709\pi$
$139$	−2.75395e17	−0.167622	−0.0838109	+	0.996482i	$0.526709\pi$
$140$	4.78884e17	0.274247
$141$	2.09256e18	1.12801
$142$	9.49031e16	0.0481759
$143$	5.40908e17	0.258683
$144$	1.25736e17	0.0566734
$145$	1.30477e18	0.554506
$146$	3.02440e18	1.21238
$147$	8.27082e17	0.312861
$148$	−2.40509e17	−0.0858828
$149$	4.77133e18	1.60900	0.804501	−	0.593951i	$-0.202433\pi$
$149$	4.77133e18	1.60900	0.804501	+	0.593951i	$0.202433\pi$
$150$	8.51020e17	0.271122
$151$	−7.22349e17	−0.217492	−0.108746	−	0.994070i	$-0.534683\pi$
$151$	−7.22349e17	−0.217492	−0.108746	+	0.994070i	$0.534683\pi$
$152$	3.50632e18	0.998115
$153$	−1.73338e17	−0.0466679
$154$	3.75705e18	0.957020
$155$	−5.88674e18	−1.41924
$156$	−2.89163e17	−0.0660060
$157$	−1.04403e18	−0.225717	−0.112859	−	0.993611i	$-0.536001\pi$
$157$	−1.04403e18	−0.225717	−0.112859	+	0.993611i	$0.536001\pi$
$158$	−1.32895e18	−0.272222
$159$	−6.56113e18	−1.27381
$160$	3.35928e18	0.618339
$161$	6.07018e18	1.05970
$162$	−3.77501e18	−0.625231
$163$	2.51417e17	0.0395185	0.0197592	−	0.999805i	$-0.493710\pi$
$163$	2.51417e17	0.0395185	0.0197592	+	0.999805i	$0.493710\pi$
$164$	3.79457e18	0.566227
$165$	7.94414e18	1.12573
$166$	1.80428e18	0.242876
$167$	−2.59432e18	−0.331843	−0.165922	−	0.986139i	$-0.553060\pi$
$167$	−2.59432e18	−0.331843	−0.165922	+	0.986139i	$0.553060\pi$
$168$	−6.65953e18	−0.809682
$169$	−8.41307e18	−0.972563
$170$	1.68323e18	0.185066
$171$	1.31276e18	0.137316
$172$	4.09001e18	0.407129
$173$	−1.49666e19	−1.41818	−0.709090	−	0.705118i	$-0.750894\pi$
$173$	−1.49666e19	−1.41818	−0.709090	+	0.705118i	$0.750894\pi$
$174$	−5.47230e18	−0.493744
$175$	3.68756e18	0.316895
$176$	7.28054e18	0.596082
$177$	−1.53973e18	−0.120135
$178$	1.21783e19	0.905764
$179$	7.18128e18	0.509274	0.254637	−	0.967037i	$-0.418044\pi$
$179$	7.18128e18	0.509274	0.254637	+	0.967037i	$0.418044\pi$
$180$	7.40527e17	0.0500869
$181$	−4.65234e18	−0.300195	−0.150097	−	0.988671i	$-0.547959\pi$
$181$	−4.65234e18	−0.300195	−0.150097	+	0.988671i	$0.547959\pi$
$182$	1.64856e18	0.101507
$183$	8.67058e18	0.509582
$184$	2.50713e19	1.40678
$185$	2.89929e18	0.155357
$186$	2.46894e19	1.26372
$187$	−1.00369e19	−0.490845
$188$	1.12947e19	0.527876
$189$	−1.92856e19	−0.861604
$190$	−1.27478e19	−0.544539
$191$	7.02101e18	0.286824	0.143412	−	0.989663i	$-0.454193\pi$
$191$	7.02101e18	0.286824	0.143412	+	0.989663i	$0.454193\pi$
$192$	−2.31021e19	−0.902797
$193$	−5.11830e19	−1.91377	−0.956883	−	0.290474i	$-0.906187\pi$
$193$	−5.11830e19	−1.91377	−0.956883	+	0.290474i	$0.906187\pi$
$194$	8.77204e18	0.313896
$195$	3.48581e18	0.119401
$196$	4.46422e18	0.146409
$197$	3.02638e18	0.0950520	0.0475260	−	0.998870i	$-0.484866\pi$
$197$	3.02638e18	0.0950520	0.0475260	+	0.998870i	$0.484866\pi$
$198$	5.80975e18	0.174785
$199$	−5.51429e19	−1.58942	−0.794709	−	0.606991i	$-0.792377\pi$
$199$	−5.51429e19	−1.58942	−0.794709	+	0.606991i	$0.792377\pi$
$200$	1.52305e19	0.420687
$201$	−1.61296e19	−0.427029
$202$	1.08300e19	0.274880
$203$	−2.37120e19	−0.577102
$204$	5.36558e18	0.125245
$205$	−4.57429e19	−1.02427
$206$	6.34681e19	1.36359
$207$	9.38668e18	0.193537
$208$	3.19463e18	0.0632240
$209$	7.60133e19	1.44426
$210$	2.42118e19	0.441736
$211$	−6.14073e19	−1.07602	−0.538009	−	0.842939i	$-0.680823\pi$
$211$	−6.14073e19	−1.07602	−0.538009	+	0.842939i	$0.680823\pi$
$212$	−3.54140e19	−0.596102
$213$	−3.64683e18	−0.0589778
$214$	−8.56288e19	−1.33077
$215$	−4.93043e19	−0.736475
$216$	−7.96541e19	−1.14380
$217$	1.06982e20	1.47707
$218$	−8.08259e19	−1.07317
$219$	−1.16218e20	−1.48422
$220$	4.28789e19	0.526806
$221$	−4.40407e18	−0.0520619
$222$	−1.21598e19	−0.138333
$223$	1.11868e20	1.22494	0.612471	−	0.790493i	$-0.290176\pi$
$223$	1.11868e20	1.22494	0.612471	+	0.790493i	$0.290176\pi$
$224$	−6.10494e19	−0.643537
$225$	5.70229e18	0.0578759
$226$	−4.56141e19	−0.445838
$227$	1.38291e20	1.30189	0.650946	−	0.759124i	$-0.274372\pi$
$227$	1.38291e20	1.30189	0.650946	+	0.759124i	$0.274372\pi$
$228$	−4.06358e19	−0.368521
$229$	−9.10168e19	−0.795279	−0.397640	−	0.917542i	$-0.630171\pi$
$229$	−9.10168e19	−0.795279	−0.397640	+	0.917542i	$0.630171\pi$
$230$	−9.11507e19	−0.767491
$231$	−1.44372e20	−1.17160
$232$	−9.79364e19	−0.766119
$233$	2.94994e19	0.222478	0.111239	−	0.993794i	$-0.464518\pi$
$233$	2.94994e19	0.222478	0.111239	+	0.993794i	$0.464518\pi$
$234$	2.54926e18	0.0185387
$235$	−1.36155e20	−0.954900
$236$	−8.31076e18	−0.0562197
$237$	5.10673e19	0.333259
$238$	−3.05899e19	−0.192608
$239$	−9.67493e19	−0.587849	−0.293924	−	0.955829i	$-0.594961\pi$
$239$	−9.67493e19	−0.587849	−0.293924	+	0.955829i	$0.594961\pi$
$240$	4.69184e19	0.275136
$241$	−1.12973e20	−0.639484	−0.319742	−	0.947505i	$-0.603596\pi$
$241$	−1.12973e20	−0.639484	−0.319742	+	0.947505i	$0.603596\pi$
$242$	1.98470e20	1.08459
$243$	−5.57894e19	−0.294373
$244$	4.67999e19	0.238469
$245$	−5.38154e19	−0.264847
$246$	1.91849e20	0.912035
$247$	3.33539e19	0.153187
$248$	4.41860e20	1.96085
$249$	−6.93328e19	−0.297334
$250$	−1.97432e20	−0.818328
$251$	−4.91324e20	−1.96853	−0.984264	−	0.176705i	$-0.943456\pi$
$251$	−4.91324e20	−1.96853	−0.984264	+	0.176705i	$0.943456\pi$
$252$	−1.34578e19	−0.0521280
$253$	5.43519e20	2.03559
$254$	2.64549e20	0.958121
$255$	−6.46811e19	−0.226562
$256$	−3.00797e20	−1.01914
$257$	2.88871e20	0.946831	0.473415	−	0.880839i	$-0.343021\pi$
$257$	2.88871e20	0.946831	0.473415	+	0.880839i	$0.343021\pi$
$258$	2.06786e20	0.655773
$259$	−5.26898e19	−0.161688
$260$	1.88148e19	0.0558762
$261$	−3.66673e19	−0.105399
$262$	−2.62752e20	−0.731115
$263$	−1.25563e20	−0.338249	−0.169124	−	0.985595i	$-0.554094\pi$
$263$	−1.25563e20	−0.338249	−0.169124	+	0.985595i	$0.554094\pi$
$264$	−5.96289e20	−1.55533
$265$	4.26910e20	1.07832
$266$	2.31670e20	0.566729
$267$	−4.67972e20	−1.10885
$268$	−8.70604e19	−0.199836
$269$	−1.37674e20	−0.306166	−0.153083	−	0.988213i	$-0.548920\pi$
$269$	−1.37674e20	−0.306166	−0.153083	+	0.988213i	$0.548920\pi$
$270$	2.89595e20	0.624022
$271$	1.13270e20	0.236525	0.118263	−	0.992982i	$-0.462268\pi$
$271$	1.13270e20	0.236525	0.118263	+	0.992982i	$0.462268\pi$
$272$	−5.92781e19	−0.119966
$273$	−6.33488e19	−0.124267
$274$	5.19312e20	0.987525
$275$	3.30181e20	0.608729
$276$	−2.90559e20	−0.519406
$277$	−9.62390e20	−1.66830	−0.834148	−	0.551540i	$-0.814040\pi$
$277$	−9.62390e20	−1.66830	−0.834148	+	0.551540i	$0.814040\pi$
$278$	−7.51536e19	−0.126348
$279$	1.65432e20	0.269764
$280$	4.33312e20	0.685421
$281$	−1.78218e20	−0.273494	−0.136747	−	0.990606i	$-0.543665\pi$
$281$	−1.78218e20	−0.273494	−0.136747	+	0.990606i	$0.543665\pi$
$282$	5.71045e20	0.850263
$283$	9.55660e20	1.38076	0.690381	−	0.723446i	$-0.257443\pi$
$283$	9.55660e20	1.38076	0.690381	+	0.723446i	$0.257443\pi$
$284$	−1.96839e19	−0.0275998
$285$	4.89857e20	0.666635
$286$	1.47610e20	0.194987
$287$	8.31301e20	1.06601
$288$	−9.44044e19	−0.117532
$289$	−7.45520e20	−0.901214
$290$	3.56064e20	0.417969
$291$	−3.37082e20	−0.384277
$292$	−6.27293e20	−0.694571
$293$	1.65023e21	1.77488	0.887440	−	0.460923i	$-0.152482\pi$
$293$	1.65023e21	1.77488	0.887440	+	0.460923i	$0.152482\pi$
$294$	2.25706e20	0.235825
$295$	1.00185e20	0.101698
$296$	−2.17621e20	−0.214646
$297$	−1.72682e21	−1.65507
$298$	1.30207e21	1.21282
$299$	2.38491e20	0.215907
$300$	−1.76511e20	−0.155325
$301$	8.96024e20	0.766487
$302$	−1.97124e20	−0.163939
$303$	−4.16164e20	−0.336513
$304$	4.48937e20	0.352988
$305$	−5.64164e20	−0.431377
$306$	−4.73030e19	−0.0351768
$307$	−2.91700e20	−0.210989	−0.105495	−	0.994420i	$-0.533643\pi$
$307$	−2.91700e20	−0.210989	−0.105495	+	0.994420i	$0.533643\pi$
$308$	−7.79252e20	−0.548273
$309$	−2.43888e21	−1.66933
$310$	−1.60645e21	−1.06978
$311$	1.47303e21	0.954438	0.477219	−	0.878784i	$-0.341645\pi$
$311$	1.47303e21	0.954438	0.477219	+	0.878784i	$0.341645\pi$
$312$	−2.61646e20	−0.164968
$313$	9.23024e20	0.566352	0.283176	−	0.959068i	$-0.408612\pi$
$313$	9.23024e20	0.566352	0.283176	+	0.959068i	$0.408612\pi$
$314$	−2.84908e20	−0.170139
$315$	1.62232e20	0.0942967
$316$	2.75638e20	0.155955
$317$	−3.01534e21	−1.66086	−0.830428	−	0.557125i	$-0.811904\pi$
$317$	−3.01534e21	−1.66086	−0.830428	+	0.557125i	$0.811904\pi$
$318$	−1.79049e21	−0.960156
$319$	−2.12316e21	−1.10857
$320$	1.50317e21	0.764246
$321$	3.29044e21	1.62915
$322$	1.65651e21	0.798767
$323$	−6.18900e20	−0.290669
$324$	7.82978e20	0.358193
$325$	1.44880e20	0.0645654
$326$	6.86101e19	0.0297878
$327$	3.10588e21	1.31380
$328$	3.43347e21	1.41516
$329$	2.47440e21	0.993812
$330$	2.16791e21	0.848539
$331$	−4.53137e21	−1.72859	−0.864295	−	0.502985i	$-0.832235\pi$
$331$	−4.53137e21	−1.72859	−0.864295	+	0.502985i	$0.832235\pi$
$332$	−3.74227e20	−0.139143
$333$	−8.14774e19	−0.0295298
$334$	−7.07973e20	−0.250133
$335$	1.04950e21	0.361493
$336$	−8.52664e20	−0.286348
$337$	1.01547e21	0.332516	0.166258	−	0.986082i	$-0.446832\pi$
$337$	1.01547e21	0.332516	0.166258	+	0.986082i	$0.446832\pi$
$338$	−2.29587e21	−0.733088
$339$	1.75281e21	0.545803
$340$	−3.49120e20	−0.106024
$341$	9.57906e21	2.83733
$342$	3.58245e20	0.103504
$343$	3.86261e21	1.08863
$344$	3.70080e21	1.01753
$345$	3.50263e21	0.939577
$346$	−4.08429e21	−1.06898
$347$	−1.92457e21	−0.491510	−0.245755	−	0.969332i	$-0.579036\pi$
$347$	−1.92457e21	−0.491510	−0.245755	+	0.969332i	$0.579036\pi$
$348$	1.13501e21	0.282864
$349$	6.11605e21	1.48749	0.743746	−	0.668462i	$-0.233047\pi$
$349$	6.11605e21	1.48749	0.743746	+	0.668462i	$0.233047\pi$
$350$	1.00631e21	0.238866
$351$	−7.57710e20	−0.175547
$352$	−5.46632e21	−1.23618
$353$	−8.03271e21	−1.77328	−0.886640	−	0.462461i	$-0.846967\pi$
$353$	−8.03271e21	−1.77328	−0.886640	+	0.462461i	$0.846967\pi$
$354$	−4.20182e20	−0.0905544
$355$	2.37286e20	0.0499265
$356$	−2.52590e21	−0.518909
$357$	1.17547e21	0.235794
$358$	1.95973e21	0.383875
$359$	5.28363e21	1.01072	0.505359	−	0.862909i	$-0.331360\pi$
$359$	5.28363e21	1.01072	0.505359	+	0.862909i	$0.331360\pi$
$360$	6.70057e20	0.125182
$361$	−7.93206e20	−0.144735
$362$	−1.26959e21	−0.226278
$363$	−7.62658e21	−1.32777
$364$	−3.41928e20	−0.0581531
$365$	7.56191e21	1.25644
$366$	2.36615e21	0.384107
$367$	−3.50477e21	−0.555902	−0.277951	−	0.960595i	$-0.589655\pi$
$367$	−3.50477e21	−0.555902	−0.277951	+	0.960595i	$0.589655\pi$
$368$	3.21005e21	0.497513
$369$	1.28549e21	0.194691
$370$	7.91198e20	0.117104
$371$	−7.75838e21	−1.12226
$372$	−5.12085e21	−0.723980
$373$	−8.69484e21	−1.20154	−0.600768	−	0.799424i	$-0.705138\pi$
$373$	−8.69484e21	−1.20154	−0.600768	+	0.799424i	$0.705138\pi$
$374$	−2.73900e21	−0.369984
$375$	7.58668e21	1.00181
$376$	1.02198e22	1.31931
$377$	−9.31620e20	−0.117581
$378$	−5.26292e21	−0.649451
$379$	−1.18557e22	−1.43052	−0.715261	−	0.698857i	$-0.753692\pi$
$379$	−1.18557e22	−1.43052	−0.715261	+	0.698857i	$0.753692\pi$
$380$	2.64403e21	0.311965
$381$	−1.01658e22	−1.17295
$382$	1.91599e21	0.216199
$383$	4.46504e21	0.492760	0.246380	−	0.969173i	$-0.420759\pi$
$383$	4.46504e21	0.492760	0.246380	+	0.969173i	$0.420759\pi$
$384$	4.62645e20	0.0499381
$385$	9.39375e21	0.991797
$386$	−1.39675e22	−1.44254
$387$	1.38558e21	0.139987
$388$	−1.81941e21	−0.179830
$389$	−1.31672e22	−1.27328	−0.636639	−	0.771162i	$-0.719676\pi$
$389$	−1.31672e22	−1.27328	−0.636639	+	0.771162i	$0.719676\pi$
$390$	9.51255e20	0.0900011
$391$	−4.42533e21	−0.409678
$392$	4.03939e21	0.365919
$393$	1.00967e22	0.895044
$394$	8.25881e20	0.0716472
$395$	−3.32277e21	−0.282114
$396$	−1.20500e21	−0.100134
$397$	−1.35407e22	−1.10134	−0.550672	−	0.834721i	$-0.685629\pi$
$397$	−1.35407e22	−1.10134	−0.550672	+	0.834721i	$0.685629\pi$
$398$	−1.50481e22	−1.19805
$399$	−8.90233e21	−0.693800
$400$	1.95006e21	0.148778
$401$	5.24638e21	0.391862	0.195931	−	0.980618i	$-0.437227\pi$
$401$	5.24638e21	0.391862	0.195931	+	0.980618i	$0.437227\pi$
$402$	−4.40167e21	−0.321881
$403$	4.20319e21	0.300945
$404$	−2.24626e21	−0.157478
$405$	−9.43866e21	−0.647952
$406$	−6.47086e21	−0.435002
$407$	−4.71780e21	−0.310590
$408$	4.85498e21	0.313023
$409$	−1.67361e21	−0.105683	−0.0528417	−	0.998603i	$-0.516828\pi$
$409$	−1.67361e21	−0.105683	−0.0528417	+	0.998603i	$0.516828\pi$
$410$	−1.24829e22	−0.772066
$411$	−1.99555e22	−1.20895
$412$	−1.31640e22	−0.781197
$413$	−1.82069e21	−0.105843
$414$	2.56156e21	0.145882
$415$	4.51124e21	0.251702
$416$	−2.39857e21	−0.131117
$417$	2.88791e21	0.154678
$418$	2.07435e22	1.08864
$419$	2.58546e21	0.132959	0.0664797	−	0.997788i	$-0.478823\pi$
$419$	2.58546e21	0.132959	0.0664797	+	0.997788i	$0.478823\pi$
$420$	−5.02178e21	−0.253069
$421$	5.00366e21	0.247110	0.123555	−	0.992338i	$-0.460570\pi$
$421$	5.00366e21	0.247110	0.123555	+	0.992338i	$0.460570\pi$
$422$	−1.67577e22	−0.811069
$423$	3.82631e21	0.181504
$424$	−3.20440e22	−1.48983
$425$	−2.68833e21	−0.122512
$426$	−9.95196e20	−0.0444556
$427$	1.02528e22	0.448956
$428$	1.77603e22	0.762393
$429$	−5.67220e21	−0.238707
$430$	−1.34548e22	−0.555133
$431$	−1.35119e22	−0.546586	−0.273293	−	0.961931i	$-0.588113\pi$
$431$	−1.35119e22	−0.546586	−0.273293	+	0.961931i	$0.588113\pi$
$432$	−1.01987e22	−0.404512
$433$	−9.28638e21	−0.361160	−0.180580	−	0.983560i	$-0.557797\pi$
$433$	−9.28638e21	−0.361160	−0.180580	+	0.983560i	$0.557797\pi$
$434$	2.91946e22	1.11337
$435$	−1.36824e22	−0.511686
$436$	1.67642e22	0.614818
$437$	3.35148e22	1.20544
$438$	−3.17152e22	−1.11876
$439$	−2.07018e22	−0.716243	−0.358122	−	0.933675i	$-0.616583\pi$
$439$	−2.07018e22	−0.716243	−0.358122	+	0.933675i	$0.616583\pi$
$440$	3.87984e22	1.31664
$441$	1.51235e21	0.0503412
$442$	−1.20184e21	−0.0392427
$443$	1.21568e22	0.389391	0.194696	−	0.980864i	$-0.437628\pi$
$443$	1.21568e22	0.389391	0.194696	+	0.980864i	$0.437628\pi$
$444$	2.52208e21	0.0792508
$445$	3.04493e22	0.938679
$446$	3.05281e22	0.923324
$447$	−5.00343e22	−1.48475
$448$	−2.73176e22	−0.795389
$449$	1.65002e22	0.471407	0.235703	−	0.971825i	$-0.424261\pi$
$449$	1.65002e22	0.471407	0.235703	+	0.971825i	$0.424261\pi$
$450$	1.55612e21	0.0436251
$451$	7.44341e22	2.04772
$452$	9.46085e21	0.255419
$453$	7.57487e21	0.200697
$454$	3.77388e22	0.981326
$455$	4.12188e21	0.105196
$456$	−3.67688e22	−0.921039
$457$	7.33995e22	1.80470	0.902351	−	0.431002i	$-0.141840\pi$
$457$	7.33995e22	1.80470	0.902351	+	0.431002i	$0.141840\pi$
$458$	−2.48379e22	−0.599457
$459$	1.40597e22	0.333096
$460$	1.89056e22	0.439693
$461$	2.76787e22	0.631958	0.315979	−	0.948766i	$-0.397667\pi$
$461$	2.76787e22	0.631958	0.315979	+	0.948766i	$0.397667\pi$
$462$	−3.93981e22	−0.883117
$463$	2.49341e22	0.548726	0.274363	−	0.961626i	$-0.411533\pi$
$463$	2.49341e22	0.548726	0.274363	+	0.961626i	$0.411533\pi$
$464$	−1.25395e22	−0.270942
$465$	6.17309e22	1.30964
$466$	8.05019e21	0.167697
$467$	1.41906e22	0.290273	0.145136	−	0.989412i	$-0.453638\pi$
$467$	1.41906e22	0.290273	0.145136	+	0.989412i	$0.453638\pi$
$468$	−5.28744e20	−0.0106208
$469$	−1.90729e22	−0.376224
$470$	−3.71559e22	−0.719774
$471$	1.09481e22	0.208287
$472$	−7.51989e21	−0.140509
$473$	8.02293e22	1.47236
$474$	1.39360e22	0.251201
$475$	2.03598e22	0.360478
$476$	6.34467e21	0.110344
$477$	−1.19972e22	−0.204963
$478$	−2.64023e22	−0.443102
$479$	9.38040e21	0.154657	0.0773285	−	0.997006i	$-0.475361\pi$
$479$	9.38040e21	0.154657	0.0773285	+	0.997006i	$0.475361\pi$
$480$	−3.52269e22	−0.570590
$481$	−2.07012e21	−0.0329430
$482$	−3.08296e22	−0.482023
$483$	−6.36545e22	−0.977865
$484$	−4.11648e22	−0.621356
$485$	2.19327e22	0.325303
$486$	−1.52246e22	−0.221889
$487$	6.77866e22	0.970840	0.485420	−	0.874281i	$-0.338667\pi$
$487$	6.77866e22	0.970840	0.485420	+	0.874281i	$0.338667\pi$
$488$	4.23463e22	0.596001
$489$	−2.63647e21	−0.0364668
$490$	−1.46859e22	−0.199633
$491$	−2.37561e22	−0.317382	−0.158691	−	0.987328i	$-0.550727\pi$
$491$	−2.37561e22	−0.317382	−0.158691	+	0.987328i	$0.550727\pi$
$492$	−3.97916e22	−0.522501
$493$	1.72867e22	0.223108
$494$	9.10205e21	0.115468
$495$	1.45261e22	0.181136
$496$	5.65743e22	0.693466
$497$	−4.31228e21	−0.0519610
$498$	−1.89205e22	−0.224121
$499$	6.36278e21	0.0740956	0.0370478	−	0.999313i	$-0.488205\pi$
$499$	6.36278e21	0.0740956	0.0370478	+	0.999313i	$0.488205\pi$
$500$	4.09495e22	0.468817
$501$	2.72051e22	0.306218
$502$	−1.34079e23	−1.48382
$503$	−7.44153e22	−0.809719	−0.404860	−	0.914379i	$-0.632680\pi$
$503$	−7.44153e22	−0.809719	−0.404860	+	0.914379i	$0.632680\pi$
$504$	−1.21772e22	−0.130283
$505$	2.70783e22	0.284869
$506$	1.48323e23	1.53437
$507$	8.82231e22	0.897459
$508$	−5.48704e22	−0.548904
$509$	1.19377e23	1.17441	0.587203	−	0.809440i	$-0.300229\pi$
$509$	1.19377e23	1.17441	0.587203	+	0.809440i	$0.300229\pi$
$510$	−1.76511e22	−0.170775
$511$	−1.37425e23	−1.30764
$512$	−7.63028e22	−0.714078
$513$	−1.06480e23	−0.980102
$514$	7.88310e22	0.713692
$515$	1.58689e23	1.41314
$516$	−4.28896e22	−0.375690
$517$	2.21556e23	1.90903
$518$	−1.43787e22	−0.121876
$519$	1.56946e23	1.30866
$520$	1.70244e22	0.139651
$521$	1.44144e23	1.16326	0.581628	−	0.813455i	$-0.302416\pi$
$521$	1.44144e23	1.16326	0.581628	+	0.813455i	$0.302416\pi$
$522$	−1.00063e22	−0.0794463
$523$	−9.64165e21	−0.0753160	−0.0376580	−	0.999291i	$-0.511990\pi$
$523$	−9.64165e21	−0.0753160	−0.0376580	+	0.999291i	$0.511990\pi$
$524$	5.44976e22	0.418853
$525$	−3.86693e22	−0.292424
$526$	−3.42652e22	−0.254962
$527$	−7.79926e22	−0.571036
$528$	−7.63469e22	−0.550051
$529$	9.85917e22	0.698984
$530$	1.16501e23	0.812802
$531$	−2.81544e21	−0.0193305
$532$	−4.80508e22	−0.324677
$533$	3.26609e22	0.217194
$534$	−1.27707e23	−0.835819
$535$	−2.14098e23	−1.37913
$536$	−7.87755e22	−0.499448
$537$	−7.53061e22	−0.469947
$538$	−3.75703e22	−0.230779
$539$	8.75698e22	0.529480
$540$	−6.00652e22	−0.357500
$541$	−1.98268e22	−0.116165	−0.0580826	−	0.998312i	$-0.518499\pi$
$541$	−1.98268e22	−0.116165	−0.0580826	+	0.998312i	$0.518499\pi$
$542$	3.09108e22	0.178286
$543$	4.87865e22	0.277013
$544$	4.45067e22	0.248791
$545$	−2.02089e23	−1.11217
$546$	−1.72875e22	−0.0936686
$547$	−1.18324e22	−0.0631219	−0.0315610	−	0.999502i	$-0.510048\pi$
$547$	−1.18324e22	−0.0631219	−0.0315610	+	0.999502i	$0.510048\pi$
$548$	−1.07711e23	−0.565750
$549$	1.58544e22	0.0819948
$550$	9.01043e22	0.458841
$551$	−1.30920e23	−0.656472
$552$	−2.62908e23	−1.29814
$553$	6.03859e22	0.293611
$554$	−2.62630e23	−1.25751
$555$	−3.04032e22	−0.143360
$556$	1.55877e22	0.0723844
$557$	−2.69182e23	−1.23105	−0.615526	−	0.788117i	$-0.711056\pi$
$557$	−2.69182e23	−1.23105	−0.615526	+	0.788117i	$0.711056\pi$
$558$	4.51454e22	0.203340
$559$	3.52038e22	0.156167
$560$	5.54799e22	0.242403
$561$	1.05251e23	0.452941
$562$	−4.86346e22	−0.206151
$563$	4.25159e23	1.77513	0.887565	−	0.460682i	$-0.152395\pi$
$563$	4.25159e23	1.77513	0.887565	+	0.460682i	$0.152395\pi$
$564$	−1.18441e23	−0.487112
$565$	−1.14049e23	−0.462040
$566$	2.60794e23	1.04078
$567$	1.71532e23	0.674356
$568$	−1.78108e22	−0.0689797
$569$	−4.36790e23	−1.66655	−0.833274	−	0.552860i	$-0.813537\pi$
$569$	−4.36790e23	−1.66655	−0.833274	+	0.552860i	$0.813537\pi$
$570$	1.33679e23	0.502489
$571$	1.93256e22	0.0715692	0.0357846	−	0.999360i	$-0.488607\pi$
$571$	1.93256e22	0.0715692	0.0357846	+	0.999360i	$0.488607\pi$
$572$	−3.06160e22	−0.111707
$573$	−7.36254e22	−0.264675
$574$	2.26857e23	0.803528
$575$	1.45579e23	0.508069
$576$	−4.22429e22	−0.145265
$577$	−9.55375e22	−0.323727	−0.161864	−	0.986813i	$-0.551750\pi$
$577$	−9.55375e22	−0.323727	−0.161864	+	0.986813i	$0.551750\pi$
$578$	−2.03448e23	−0.679307
$579$	5.36727e23	1.76598
$580$	−7.38514e22	−0.239453
$581$	−8.19843e22	−0.261959
$582$	−9.19874e22	−0.289656
$583$	−6.94679e23	−2.15577
$584$	−5.67599e23	−1.73593
$585$	6.37392e21	0.0192124
$586$	4.50337e23	1.33785
$587$	−4.37934e22	−0.128229	−0.0641143	−	0.997943i	$-0.520422\pi$
$587$	−4.37934e22	−0.128229	−0.0641143	+	0.997943i	$0.520422\pi$
$588$	−4.68137e22	−0.135103
$589$	5.90670e23	1.68022
$590$	2.73398e22	0.0766572
$591$	−3.17360e22	−0.0877119
$592$	−2.78635e22	−0.0759105
$593$	5.09618e23	1.36861	0.684306	−	0.729195i	$-0.260105\pi$
$593$	5.09618e23	1.36861	0.684306	+	0.729195i	$0.260105\pi$
$594$	−4.71237e23	−1.24754
$595$	−7.64839e22	−0.199607
$596$	−2.70063e23	−0.694818
$597$	5.78252e23	1.46668
$598$	6.50826e22	0.162744
$599$	4.80755e23	1.18521	0.592606	−	0.805493i	$-0.298099\pi$
$599$	4.80755e23	1.18521	0.592606	+	0.805493i	$0.298099\pi$
$600$	−1.59714e23	−0.388201
$601$	−7.25537e23	−1.73871	−0.869354	−	0.494190i	$-0.835465\pi$
$601$	−7.25537e23	−1.73871	−0.869354	+	0.494190i	$0.835465\pi$
$602$	2.44519e23	0.577754
$603$	−2.94935e22	−0.0687115
$604$	4.08857e22	0.0939199
$605$	4.96235e23	1.12400
$606$	−1.13568e23	−0.253653
$607$	6.93131e23	1.52655	0.763276	−	0.646072i	$-0.223590\pi$
$607$	6.93131e23	1.52655	0.763276	+	0.646072i	$0.223590\pi$
$608$	−3.37068e23	−0.732043
$609$	2.48655e23	0.532537
$610$	−1.53957e23	−0.325159
$611$	9.72164e22	0.202483
$612$	9.81114e21	0.0201527
$613$	−3.80731e23	−0.771266	−0.385633	−	0.922652i	$-0.626017\pi$
$613$	−3.80731e23	−0.771266	−0.385633	+	0.922652i	$0.626017\pi$
$614$	−7.96031e22	−0.159037
$615$	4.79680e23	0.945177
$616$	−7.05097e23	−1.37029
$617$	−8.12208e23	−1.55684	−0.778419	−	0.627745i	$-0.783978\pi$
$617$	−8.12208e23	−1.55684	−0.778419	+	0.627745i	$0.783978\pi$
$618$	−6.65554e23	−1.25829
$619$	−8.70370e23	−1.62306	−0.811528	−	0.584314i	$-0.801364\pi$
$619$	−8.70370e23	−1.62306	−0.811528	+	0.584314i	$0.801364\pi$
$620$	3.33196e23	0.612872
$621$	−7.61367e23	−1.38139
$622$	4.01980e23	0.719426
$623$	−5.53365e23	−0.976930
$624$	−3.35003e22	−0.0583417
$625$	−2.66752e23	−0.458277
$626$	2.51887e23	0.426899
$627$	−7.97108e23	−1.33273
$628$	5.90930e22	0.0974718
$629$	3.84123e22	0.0625086
$630$	4.42720e22	0.0710780
$631$	−7.06052e23	−1.11837	−0.559187	−	0.829042i	$-0.688887\pi$
$631$	−7.06052e23	−1.11837	−0.559187	+	0.829042i	$0.688887\pi$
$632$	2.49408e23	0.389776
$633$	6.43944e23	0.992925
$634$	−8.22867e23	−1.25190
$635$	6.61453e23	0.992938
$636$	3.71367e23	0.550070
$637$	3.84247e22	0.0561598
$638$	−5.79396e23	−0.835603
$639$	−6.66834e21	−0.00948987
$640$	−3.01027e22	−0.0422742
$641$	1.20846e24	1.67471	0.837356	−	0.546658i	$-0.184100\pi$
$641$	1.20846e24	1.67471	0.837356	+	0.546658i	$0.184100\pi$
$642$	8.97941e23	1.22800
$643$	1.55294e23	0.209585	0.104793	−	0.994494i	$-0.466582\pi$
$643$	1.55294e23	0.209585	0.104793	+	0.994494i	$0.466582\pi$
$644$	−3.43578e23	−0.457611
$645$	5.17027e23	0.679603
$646$	−1.68894e23	−0.219097
$647$	−3.17250e23	−0.406177	−0.203089	−	0.979160i	$-0.565098\pi$
$647$	−3.17250e23	−0.406177	−0.203089	+	0.979160i	$0.565098\pi$
$648$	7.08468e23	0.895226
$649$	−1.63023e23	−0.203315
$650$	3.95369e22	0.0486675
$651$	−1.12186e24	−1.36301
$652$	−1.42305e22	−0.0170653
$653$	1.49960e24	1.77506	0.887531	−	0.460748i	$-0.152419\pi$
$653$	1.49960e24	1.77506	0.887531	+	0.460748i	$0.152419\pi$
$654$	8.47576e23	0.990302
$655$	−6.56959e23	−0.757683
$656$	4.39611e23	0.500479
$657$	−2.12509e23	−0.238820
$658$	6.75247e23	0.749105
$659$	8.13097e23	0.890464	0.445232	−	0.895415i	$-0.353121\pi$
$659$	8.13097e23	0.890464	0.445232	+	0.895415i	$0.353121\pi$
$660$	−4.49647e23	−0.486125
$661$	−5.62216e23	−0.600055	−0.300027	−	0.953931i	$-0.596996\pi$
$661$	−5.62216e23	−0.600055	−0.300027	+	0.953931i	$0.596996\pi$
$662$	−1.23658e24	−1.30296
$663$	4.61830e22	0.0480416
$664$	−3.38615e23	−0.347758
$665$	5.79244e23	0.587323
$666$	−2.22347e22	−0.0222587
$667$	−9.36117e23	−0.925253
$668$	1.46841e23	0.143300
$669$	−1.17310e24	−1.13035
$670$	2.86401e23	0.272483
$671$	9.18024e23	0.862407
$672$	6.40191e23	0.593842
$673$	−1.77846e23	−0.162898	−0.0814492	−	0.996677i	$-0.525955\pi$
$673$	−1.77846e23	−0.162898	−0.0814492	+	0.996677i	$0.525955\pi$
$674$	2.77115e23	0.250640
$675$	−4.62521e23	−0.413094
$676$	4.76189e23	0.419983
$677$	1.16757e24	1.01690	0.508450	−	0.861092i	$-0.330219\pi$
$677$	1.16757e24	1.01690	0.508450	+	0.861092i	$0.330219\pi$
$678$	4.78329e23	0.411410
$679$	−3.98591e23	−0.338559
$680$	−3.15897e23	−0.264984
$681$	−1.45018e24	−1.20136
$682$	2.61406e24	2.13870
$683$	−8.05116e23	−0.650552	−0.325276	−	0.945619i	$-0.605457\pi$
$683$	−8.05116e23	−0.650552	−0.325276	+	0.945619i	$0.605457\pi$
$684$	−7.43038e22	−0.0592972
$685$	1.29843e24	1.02341
$686$	1.05408e24	0.820577
$687$	9.54441e23	0.733866
$688$	4.73838e23	0.359855
$689$	−3.04818e23	−0.228653
$690$	9.55846e23	0.708224
$691$	5.39840e23	0.395095	0.197548	−	0.980293i	$-0.436702\pi$
$691$	5.39840e23	0.395095	0.197548	+	0.980293i	$0.436702\pi$
$692$	8.47125e23	0.612415
$693$	−2.63988e23	−0.188518
$694$	−5.25202e23	−0.370485
$695$	−1.87906e23	−0.130940
$696$	1.02700e24	0.706958
$697$	−6.06042e23	−0.412120
$698$	1.66903e24	1.12123
$699$	−3.09343e23	−0.205298
$700$	−2.08720e23	−0.136845
$701$	−1.07222e24	−0.694511	−0.347256	−	0.937771i	$-0.612886\pi$
$701$	−1.07222e24	−0.694511	−0.347256	+	0.937771i	$0.612886\pi$
$702$	−2.06774e23	−0.132322
$703$	−2.90912e23	−0.183925
$704$	−2.44600e24	−1.52788
$705$	1.42778e24	0.881160
$706$	−2.19208e24	−1.33664
$707$	−4.92103e23	−0.296477
$708$	8.71502e22	0.0518783
$709$	3.48137e23	0.204765	0.102383	−	0.994745i	$-0.467353\pi$
$709$	3.48137e23	0.204765	0.102383	+	0.994745i	$0.467353\pi$
$710$	6.47539e22	0.0376331
$711$	9.33783e22	0.0536234
$712$	−2.28553e24	−1.29690
$713$	4.22348e24	2.36815
$714$	3.20779e23	0.177734
$715$	3.69070e23	0.202073
$716$	−4.06468e23	−0.219921
$717$	1.01456e24	0.542454
$718$	1.44187e24	0.761848
$719$	1.52393e24	0.795736	0.397868	−	0.917443i	$-0.369750\pi$
$719$	1.52393e24	0.795736	0.397868	+	0.917443i	$0.369750\pi$
$720$	8.57919e22	0.0442711
$721$	−2.88391e24	−1.47073
$722$	−2.16461e23	−0.109097
$723$	1.18468e24	0.590101
$724$	2.63327e23	0.129634
$725$	−5.68679e23	−0.276690
$726$	−2.08124e24	−1.00083
$727$	−2.61452e24	−1.24265	−0.621326	−	0.783552i	$-0.713406\pi$
$727$	−2.61452e24	−1.24265	−0.621326	+	0.783552i	$0.713406\pi$
$728$	−3.09390e23	−0.145341
$729$	2.37146e24	1.10111
$730$	2.06360e24	0.947067
$731$	−6.53227e23	−0.296324
$732$	−4.90764e23	−0.220054
$733$	1.85910e24	0.823986	0.411993	−	0.911187i	$-0.364833\pi$
$733$	1.85910e24	0.823986	0.411993	+	0.911187i	$0.364833\pi$
$734$	−9.56430e23	−0.419022
$735$	5.64331e23	0.244395
$736$	−2.41014e24	−1.03177
$737$	−1.70777e24	−0.722696
$738$	3.50802e23	0.146752
$739$	3.67104e24	1.51814	0.759069	−	0.651011i	$-0.225655\pi$
$739$	3.67104e24	1.51814	0.759069	+	0.651011i	$0.225655\pi$
$740$	−1.64103e23	−0.0670883
$741$	−3.49763e23	−0.141358
$742$	−2.11721e24	−0.845924
$743$	−3.34740e24	−1.32222	−0.661109	−	0.750290i	$-0.729914\pi$
$743$	−3.34740e24	−1.32222	−0.661109	+	0.750290i	$0.729914\pi$
$744$	−4.63354e24	−1.80943
$745$	3.25556e24	1.25689
$746$	−2.37277e24	−0.905681
$747$	−1.26777e23	−0.0478428
$748$	5.68097e23	0.211962
$749$	3.89087e24	1.43533
$750$	2.07036e24	0.755135
$751$	1.46393e24	0.527935	0.263967	−	0.964532i	$-0.414969\pi$
$751$	1.46393e24	0.527935	0.263967	+	0.964532i	$0.414969\pi$
$752$	1.30852e24	0.466582
$753$	5.15224e24	1.81651
$754$	−2.54233e23	−0.0886290
$755$	−4.92870e23	−0.169896
$756$	1.09159e24	0.372068
$757$	2.08613e24	0.703114	0.351557	−	0.936166i	$-0.385652\pi$
$757$	2.08613e24	0.703114	0.351557	+	0.936166i	$0.385652\pi$
$758$	−3.23535e24	−1.07828
$759$	−5.69958e24	−1.87840
$760$	2.39242e24	0.779688
$761$	1.34436e24	0.433256	0.216628	−	0.976254i	$-0.430494\pi$
$761$	1.34436e24	0.433256	0.216628	+	0.976254i	$0.430494\pi$
$762$	−2.77418e24	−0.884133
$763$	3.67263e24	1.15749
$764$	−3.97396e23	−0.123860
$765$	−1.18272e23	−0.0364551
$766$	1.21848e24	0.371427
$767$	−7.15330e22	−0.0215648
$768$	3.15429e24	0.940439
$769$	−4.08381e24	−1.20418	−0.602090	−	0.798428i	$-0.705665\pi$
$769$	−4.08381e24	−1.20418	−0.602090	+	0.798428i	$0.705665\pi$
$770$	2.56349e24	0.747586
$771$	−3.02923e24	−0.873715
$772$	2.89701e24	0.826425
$773$	−1.57985e24	−0.445748	−0.222874	−	0.974847i	$-0.571544\pi$
$773$	−1.57985e24	−0.445748	−0.222874	+	0.974847i	$0.571544\pi$
$774$	3.78115e23	0.105518
$775$	2.56571e24	0.708179
$776$	−1.64627e24	−0.449446
$777$	5.52528e23	0.149202
$778$	−3.59326e24	−0.959758
$779$	4.58980e24	1.21262
$780$	−1.97300e23	−0.0515613
$781$	−3.86118e23	−0.0998129
$782$	−1.20764e24	−0.308803
$783$	2.97414e24	0.752292
$784$	5.17191e23	0.129409
$785$	−7.12356e23	−0.176321
$786$	2.75534e24	0.674657
$787$	−2.11727e24	−0.512850	−0.256425	−	0.966564i	$-0.582545\pi$
$787$	−2.11727e24	−0.512850	−0.256425	+	0.966564i	$0.582545\pi$
$788$	−1.71297e23	−0.0410465
$789$	1.31670e24	0.312129
$790$	−9.06764e23	−0.212649
$791$	2.07265e24	0.480868
$792$	−1.09033e24	−0.250262
$793$	4.02820e23	0.0914721
$794$	−3.69518e24	−0.830160
$795$	−4.47677e24	−0.995047
$796$	3.12114e24	0.686361
$797$	−3.10685e24	−0.675966	−0.337983	−	0.941152i	$-0.609745\pi$
$797$	−3.10685e24	−0.675966	−0.337983	+	0.941152i	$0.609745\pi$
$798$	−2.42939e24	−0.522965
$799$	−1.80390e24	−0.384208
$800$	−1.46413e24	−0.308543
$801$	−8.55702e23	−0.178421
$802$	1.43170e24	0.295373
$803$	−1.23049e25	−2.51187
$804$	9.12953e23	0.184405
$805$	4.14178e24	0.827793
$806$	1.14702e24	0.226843
$807$	1.44371e24	0.282523
$808$	−2.03251e24	−0.393582
$809$	6.59983e24	1.26465	0.632325	−	0.774703i	$-0.282101\pi$
$809$	6.59983e24	1.26465	0.632325	+	0.774703i	$0.282101\pi$
$810$	−2.57575e24	−0.488406
$811$	2.09068e24	0.392292	0.196146	−	0.980575i	$-0.437157\pi$
$811$	2.09068e24	0.392292	0.196146	+	0.980575i	$0.437157\pi$
$812$	1.34213e24	0.249211
$813$	−1.18780e24	−0.218260
$814$	−1.28746e24	−0.234113
$815$	1.71546e23	0.0308703
$816$	6.21616e23	0.110702
$817$	4.94716e24	0.871903
$818$	−4.56718e23	−0.0796609
$819$	−1.15835e23	−0.0199953
$820$	2.58910e24	0.442314
$821$	−3.96635e24	−0.670617	−0.335308	−	0.942108i	$-0.608841\pi$
$821$	−3.96635e24	−0.670617	−0.335308	+	0.942108i	$0.608841\pi$
$822$	−5.44573e24	−0.911267
$823$	−1.05625e25	−1.74932	−0.874658	−	0.484740i	$-0.838914\pi$
$823$	−1.05625e25	−1.74932	−0.874658	+	0.484740i	$0.838914\pi$
$824$	−1.19113e25	−1.95243
$825$	−3.46242e24	−0.561722
$826$	−4.96855e23	−0.0797810
$827$	3.58787e24	0.570217	0.285109	−	0.958495i	$-0.407970\pi$
$827$	3.58787e24	0.570217	0.285109	+	0.958495i	$0.407970\pi$
$828$	−5.31296e23	−0.0835754
$829$	−2.00561e24	−0.312273	−0.156136	−	0.987736i	$-0.549904\pi$
$829$	−2.00561e24	−0.312273	−0.156136	+	0.987736i	$0.549904\pi$
$830$	1.23109e24	0.189726
$831$	1.00920e25	1.53947
$832$	−1.07328e24	−0.162056
$833$	−7.12993e23	−0.106562
$834$	7.88094e23	0.116591
$835$	−1.77014e24	−0.259223
$836$	−4.30243e24	−0.623678
$837$	−1.34184e25	−1.92547
$838$	7.05556e23	0.100221
$839$	−7.72479e24	−1.08620	−0.543101	−	0.839668i	$-0.682750\pi$
$839$	−7.72479e24	−1.08620	−0.543101	+	0.839668i	$0.682750\pi$
$840$	−4.54390e24	−0.632492
$841$	−3.60038e24	−0.496115
$842$	1.36547e24	0.186264
$843$	1.86887e24	0.252374
$844$	3.47572e24	0.464658
$845$	−5.74037e24	−0.759728
$846$	1.04417e24	0.136812
$847$	−9.01824e24	−1.16980
$848$	−4.10281e24	−0.526885
$849$	−1.00215e25	−1.27414
$850$	−7.33629e23	−0.0923454
$851$	−2.08012e24	−0.259231
$852$	2.06414e23	0.0254685
$853$	−1.15330e25	−1.40888	−0.704441	−	0.709763i	$-0.748802\pi$
$853$	−1.15330e25	−1.40888	−0.704441	+	0.709763i	$0.748802\pi$
$854$	2.79791e24	0.338409
$855$	8.95719e23	0.107265
$856$	1.60702e25	1.90544
$857$	1.08547e25	1.27433	0.637165	−	0.770728i	$-0.280107\pi$
$857$	1.08547e25	1.27433	0.637165	+	0.770728i	$0.280107\pi$
$858$	−1.54791e24	−0.179930
$859$	−1.32309e24	−0.152282	−0.0761410	−	0.997097i	$-0.524260\pi$
$859$	−1.32309e24	−0.152282	−0.0761410	+	0.997097i	$0.524260\pi$
$860$	2.79068e24	0.318034
$861$	−8.71739e24	−0.983693
$862$	−3.68731e24	−0.412000
$863$	4.31993e23	0.0477952	0.0238976	−	0.999714i	$-0.492392\pi$
$863$	4.31993e23	0.0477952	0.0238976	+	0.999714i	$0.492392\pi$
$864$	7.65728e24	0.838895
$865$	−1.02119e25	−1.10783
$866$	−2.53419e24	−0.272231
$867$	7.81785e24	0.831620
$868$	−6.05528e24	−0.637847
$869$	5.40691e24	0.564002
$870$	−3.73384e24	−0.385693
$871$	−7.49352e23	−0.0766535
$872$	1.51688e25	1.53661
$873$	−6.16365e23	−0.0618325
$874$	9.14599e24	0.908622
$875$	8.97107e24	0.882624
$876$	6.57807e24	0.640934
$877$	1.08744e25	1.04933	0.524663	−	0.851310i	$-0.324191\pi$
$877$	1.08744e25	1.04933	0.524663	+	0.851310i	$0.324191\pi$
$878$	−5.64940e24	−0.539882
$879$	−1.73050e25	−1.63782
$880$	4.96763e24	0.465636
$881$	1.05432e25	0.978762	0.489381	−	0.872070i	$-0.337223\pi$
$881$	1.05432e25	0.978762	0.489381	+	0.872070i	$0.337223\pi$
$882$	4.12710e23	0.0379456
$883$	8.11960e24	0.739382	0.369691	−	0.929155i	$-0.379464\pi$
$883$	8.11960e24	0.739382	0.369691	+	0.929155i	$0.379464\pi$
$884$	2.49275e23	0.0224820
$885$	−1.05058e24	−0.0938451
$886$	3.31750e24	0.293511
$887$	1.58225e25	1.38651	0.693257	−	0.720691i	$-0.256175\pi$
$887$	1.58225e25	1.38651	0.693257	+	0.720691i	$0.256175\pi$
$888$	2.28207e24	0.198070
$889$	−1.20208e25	−1.03340
$890$	8.30942e24	0.707547
$891$	1.53588e25	1.29538
$892$	−6.33186e24	−0.528969
$893$	1.36617e25	1.13049
$894$	−1.36540e25	−1.11916
$895$	4.89990e24	0.397825
$896$	5.47066e23	0.0439969
$897$	−2.50092e24	−0.199234
$898$	4.50280e24	0.355332
$899$	−1.64983e25	−1.28968
$900$	−3.22756e23	−0.0249927
$901$	5.65608e24	0.433865
$902$	2.03126e25	1.54351
$903$	−9.39610e24	−0.707297
$904$	8.56054e24	0.638366
$905$	−3.17436e24	−0.234501
$906$	2.06713e24	0.151279
$907$	1.19475e25	0.866197	0.433098	−	0.901347i	$-0.357420\pi$
$907$	1.19475e25	0.866197	0.433098	+	0.901347i	$0.357420\pi$
$908$	−7.82743e24	−0.562198
$909$	−7.60969e23	−0.0541469
$910$	1.12484e24	0.0792934
$911$	−1.60357e25	−1.11991	−0.559954	−	0.828524i	$-0.689181\pi$
$911$	−1.60357e25	−1.11991	−0.559954	+	0.828524i	$0.689181\pi$
$912$	−4.70775e24	−0.325730
$913$	−7.34081e24	−0.503202
$914$	2.00303e25	1.36033
$915$	5.91608e24	0.398065
$916$	5.15164e24	0.343427
$917$	1.19391e25	0.788559
$918$	3.83681e24	0.251078
$919$	−1.78911e25	−1.16000	−0.579998	−	0.814618i	$-0.696946\pi$
$919$	−1.78911e25	−1.16000	−0.579998	+	0.814618i	$0.696946\pi$
$920$	1.71065e25	1.09892
$921$	3.05889e24	0.194696
$922$	7.55334e24	0.476350
$923$	−1.69425e23	−0.0105868
$924$	8.17158e24	0.505935
$925$	−1.26364e24	−0.0775211
$926$	6.80436e24	0.413613
$927$	−4.45957e24	−0.268606
$928$	9.41478e24	0.561891
$929$	−4.96163e24	−0.293421	−0.146710	−	0.989179i	$-0.546869\pi$
$929$	−4.96163e24	−0.293421	−0.146710	+	0.989179i	$0.546869\pi$
$930$	1.68460e25	0.987168
$931$	5.39979e24	0.313548
$932$	−1.66970e24	−0.0960731
$933$	−1.54468e25	−0.880735
$934$	3.87251e24	0.218799
$935$	−6.84831e24	−0.383429
$936$	−4.78428e23	−0.0265443
$937$	−6.42591e24	−0.353304	−0.176652	−	0.984273i	$-0.556527\pi$
$937$	−6.42591e24	−0.353304	−0.176652	+	0.984273i	$0.556527\pi$
$938$	−5.20486e24	−0.283586
$939$	−9.67923e24	−0.522617
$940$	7.70653e24	0.412356
$941$	−7.38864e24	−0.391790	−0.195895	−	0.980625i	$-0.562761\pi$
$941$	−7.38864e24	−0.391790	−0.195895	+	0.980625i	$0.562761\pi$
$942$	2.98767e24	0.157000
$943$	3.28186e25	1.70911
$944$	−9.62822e23	−0.0496917
$945$	−1.31589e25	−0.673051
$946$	2.18941e25	1.10982
$947$	−1.63085e25	−0.819291	−0.409646	−	0.912245i	$-0.634348\pi$
$947$	−1.63085e25	−0.819291	−0.409646	+	0.912245i	$0.634348\pi$
$948$	−2.89047e24	−0.143912
$949$	−5.39928e24	−0.266424
$950$	5.55607e24	0.271717
$951$	3.16202e25	1.53260
$952$	5.74090e24	0.275782
$953$	1.75856e25	0.837273	0.418637	−	0.908154i	$-0.362508\pi$
$953$	1.75856e25	0.837273	0.418637	+	0.908154i	$0.362508\pi$
$954$	−3.27397e24	−0.154495
$955$	4.79054e24	0.224056
$956$	5.47611e24	0.253852
$957$	2.22644e25	1.02296
$958$	2.55985e24	0.116576
$959$	−2.35969e25	−1.06512
$960$	−1.57629e25	−0.705230
$961$	5.18851e25	2.30088
$962$	−5.64924e23	−0.0248314
$963$	6.01668e24	0.262140
$964$	6.39439e24	0.276149
$965$	−3.49230e25	−1.49496
$966$	−1.73709e25	−0.737084
$967$	−5.68755e24	−0.239222	−0.119611	−	0.992821i	$-0.538165\pi$
$967$	−5.68755e24	−0.239222	−0.119611	+	0.992821i	$0.538165\pi$
$968$	−3.72475e25	−1.55295
$969$	6.49005e24	0.268223
$970$	5.98530e24	0.245203
$971$	4.01583e25	1.63084	0.815421	−	0.578869i	$-0.196506\pi$
$971$	4.01583e25	1.63084	0.815421	+	0.578869i	$0.196506\pi$
$972$	3.15774e24	0.127120
$973$	3.41489e24	0.136275
$974$	1.84985e25	0.731789
$975$	−1.51928e24	−0.0595796
$976$	5.42189e24	0.210779
$977$	−4.43583e25	−1.70951	−0.854754	−	0.519033i	$-0.826292\pi$
$977$	−4.43583e25	−1.70951	−0.854754	+	0.519033i	$0.826292\pi$
$978$	−7.19476e23	−0.0274875
$979$	−4.95479e25	−1.87660
$980$	3.04601e24	0.114369
$981$	5.67921e24	0.211398
$982$	−6.48288e24	−0.239233
$983$	−4.89816e25	−1.79196	−0.895980	−	0.444095i	$-0.853525\pi$
$983$	−4.89816e25	−1.79196	−0.895980	+	0.444095i	$0.853525\pi$
$984$	−3.60049e25	−1.30588
$985$	2.06495e24	0.0742508
$986$	4.71744e24	0.168172
$987$	−2.59476e25	−0.917068
$988$	−1.88786e24	−0.0661510
$989$	3.53737e25	1.22889
$990$	3.96409e24	0.136535
$991$	2.20549e25	0.753146	0.376573	−	0.926387i	$-0.377102\pi$
$991$	2.20549e25	0.753146	0.376573	+	0.926387i	$0.377102\pi$
$992$	−4.24767e25	−1.43814
$993$	4.75180e25	1.59510
$994$	−1.17679e24	−0.0391666
$995$	−3.76248e25	−1.24159
$996$	3.92431e24	0.128398
$997$	2.28496e25	0.741258	0.370629	−	0.928781i	$-0.379142\pi$
$997$	2.28496e25	0.741258	0.370629	+	0.928781i	$0.379142\pi$
$998$	1.73636e24	0.0558510
$999$	6.60875e24	0.210772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.18.a.b.1.28	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.18.a.b.1.28	✓	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)

\(f(q)\)	\(=\)	\(q+272.894 q^{2} -10486.4 q^{3} -56601.1 q^{4} +682316. q^{5} -2.86168e6 q^{6} -1.24000e7 q^{7} -5.12148e7 q^{8} -1.91748e7 q^{9} +O(q^{10})\)	\(q+272.894 q^{2} -10486.4 q^{3} -56601.1 q^{4} +682316. q^{5} -2.86168e6 q^{6} -1.24000e7 q^{7} -5.12148e7 q^{8} -1.91748e7 q^{9} +1.86200e8 q^{10} -1.11028e9 q^{11} +5.93543e8 q^{12} -4.87181e8 q^{13} -3.38387e9 q^{14} -7.15506e9 q^{15} -6.55738e9 q^{16} +9.03991e9 q^{17} -5.23268e9 q^{18} -6.84630e10 q^{19} -3.86198e10 q^{20} +1.30031e11 q^{21} -3.02989e11 q^{22} -4.89532e11 q^{23} +5.37061e11 q^{24} -2.97385e11 q^{25} -1.32949e11 q^{26} +1.55530e12 q^{27} +7.01851e11 q^{28} +1.91227e12 q^{29} -1.95257e12 q^{30} -8.62758e12 q^{31} +4.92336e12 q^{32} +1.16429e13 q^{33} +2.46694e12 q^{34} -8.46068e12 q^{35} +1.08531e12 q^{36} +4.24919e12 q^{37} -1.86831e13 q^{38} +5.10879e12 q^{39} -3.49447e13 q^{40} -6.70407e13 q^{41} +3.54847e13 q^{42} -7.22603e13 q^{43} +6.28432e13 q^{44} -1.30833e13 q^{45} -1.33590e14 q^{46} -1.99549e14 q^{47} +6.87635e13 q^{48} -7.88716e13 q^{49} -8.11544e13 q^{50} -9.47965e13 q^{51} +2.75750e13 q^{52} +6.25678e14 q^{53} +4.24430e14 q^{54} -7.57563e14 q^{55} +6.35061e14 q^{56} +7.17933e14 q^{57} +5.21846e14 q^{58} +1.46830e14 q^{59} +4.04984e14 q^{60} -8.26838e14 q^{61} -2.35441e15 q^{62} +2.37767e14 q^{63} +2.20304e15 q^{64} -3.32411e14 q^{65} +3.17728e15 q^{66} +1.53814e15 q^{67} -5.11669e14 q^{68} +5.13345e15 q^{69} -2.30887e15 q^{70} +3.47766e14 q^{71} +9.82033e14 q^{72} +1.10827e16 q^{73} +1.15958e15 q^{74} +3.11851e15 q^{75} +3.87508e15 q^{76} +1.37675e16 q^{77} +1.39416e15 q^{78} -4.86985e15 q^{79} -4.47420e15 q^{80} -1.38333e16 q^{81} -1.82950e16 q^{82} +6.61166e15 q^{83} -7.35991e15 q^{84} +6.16808e15 q^{85} -1.97194e16 q^{86} -2.00529e16 q^{87} +5.68629e16 q^{88} +4.46264e16 q^{89} -3.57034e15 q^{90} +6.04102e15 q^{91} +2.77080e16 q^{92} +9.04726e16 q^{93} -5.44556e16 q^{94} -4.67134e16 q^{95} -5.16285e16 q^{96} +3.21445e16 q^{97} -2.15236e16 q^{98} +2.12894e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 783 q^{2} + 13122 q^{3} + 3063551 q^{4} + 2062778 q^{5} + 9982022 q^{6} + 13722970 q^{7} + 168939849 q^{8} + 2182805218 q^{9}+O(q^{10}) \) 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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