LMFDB - Embedded newform 47.20.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [47,20,Mod(1,47)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(47, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("47.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 47 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	47.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:	$107.543847381$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1265.30 q^{2} +61064.0 q^{3} +1.07670e6 q^{4} -1.52486e6 q^{5} -7.72644e7 q^{6} +6.24861e7 q^{7} -6.98970e8 q^{8} +2.56655e9 q^{9} +O(q^{10})$	\(q-1265.30 q^{2} +61064.0 q^{3} +1.07670e6 q^{4} -1.52486e6 q^{5} -7.72644e7 q^{6} +6.24861e7 q^{7} -6.98970e8 q^{8} +2.56655e9 q^{9} +1.92941e9 q^{10} -5.35249e9 q^{11} +6.57477e10 q^{12} +3.54072e10 q^{13} -7.90638e10 q^{14} -9.31139e10 q^{15} +3.19907e11 q^{16} -3.38946e11 q^{17} -3.24746e12 q^{18} -1.07323e12 q^{19} -1.64182e12 q^{20} +3.81565e12 q^{21} +6.77252e12 q^{22} +4.77620e11 q^{23} -4.26819e13 q^{24} -1.67483e13 q^{25} -4.48008e13 q^{26} +8.57512e13 q^{27} +6.72789e13 q^{28} +9.43429e13 q^{29} +1.17817e14 q^{30} +1.12053e14 q^{31} -3.83170e13 q^{32} -3.26845e14 q^{33} +4.28869e14 q^{34} -9.52825e13 q^{35} +2.76340e15 q^{36} +8.46180e14 q^{37} +1.35796e15 q^{38} +2.16210e15 q^{39} +1.06583e15 q^{40} +6.88735e13 q^{41} -4.82795e15 q^{42} +4.02348e15 q^{43} -5.76304e15 q^{44} -3.91362e15 q^{45} -6.04333e14 q^{46} -1.11913e15 q^{47} +1.95348e16 q^{48} -7.49438e15 q^{49} +2.11916e16 q^{50} -2.06974e16 q^{51} +3.81230e16 q^{52} -1.02170e16 q^{53} -1.08501e17 q^{54} +8.16180e15 q^{55} -4.36759e16 q^{56} -6.55357e16 q^{57} -1.19372e17 q^{58} +6.07531e15 q^{59} -1.00256e17 q^{60} +1.58603e17 q^{61} -1.41780e17 q^{62} +1.60373e17 q^{63} -1.19241e17 q^{64} -5.39910e16 q^{65} +4.13557e17 q^{66} +3.80548e17 q^{67} -3.64944e17 q^{68} +2.91654e16 q^{69} +1.20561e17 q^{70} +4.93119e17 q^{71} -1.79394e18 q^{72} -3.39005e17 q^{73} -1.07067e18 q^{74} -1.02272e18 q^{75} -1.15555e18 q^{76} -3.34457e17 q^{77} -2.73572e18 q^{78} +3.58125e17 q^{79} -4.87813e17 q^{80} +2.25331e18 q^{81} -8.71457e16 q^{82} -1.14552e18 q^{83} +4.10832e18 q^{84} +5.16845e17 q^{85} -5.09092e18 q^{86} +5.76095e18 q^{87} +3.74123e18 q^{88} -2.76040e18 q^{89} +4.95191e18 q^{90} +2.21246e18 q^{91} +5.14254e17 q^{92} +6.84237e18 q^{93} +1.41604e18 q^{94} +1.63652e18 q^{95} -2.33979e18 q^{96} +8.03827e18 q^{97} +9.48266e18 q^{98} -1.37374e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) $ 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9	$ 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9} - 197084160 q^{10} + 6183770516 q^{11} - 18595076275 q^{12} + 72670351796 q^{13} - 286195652197 q^{14} + 216978245574 q^{15} + 4395775708833 q^{16} + 1565738603712 q^{17} + 6109717535226 q^{18} + 3193929321662 q^{19} - 5906920535432 q^{20} - 7386396792532 q^{21} - 8877997844072 q^{22} - 24482520509106 q^{23} - 7153616576581 q^{24} + 205574470566045 q^{25} + 29760604099536 q^{26} + 37673737054348 q^{27} + 359478142575004 q^{28} + 236042103421602 q^{29} + 10\!\cdots\!54 q^{30}+ \cdots + 26\!\cdots\!62 q^{99}+O(q^{100}) $ 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9 - 197084160 * q^10 + 6183770516 * q^11 - 18595076275 * q^12 + 72670351796 * q^13 - 286195652197 * q^14 + 216978245574 * q^15 + 4395775708833 * q^16 + 1565738603712 * q^17 + 6109717535226 * q^18 + 3193929321662 * q^19 - 5906920535432 * q^20 - 7386396792532 * q^21 - 8877997844072 * q^22 - 24482520509106 * q^23 - 7153616576581 * q^24 + 205574470566045 * q^25 + 29760604099536 * q^26 + 37673737054348 * q^27 + 359478142575004 * q^28 + 236042103421602 * q^29 + 1030005166297154 * q^30 + 238097499775556 * q^31 + 980418196894414 * q^32 + 1875903246842268 * q^33 + 1649701857955214 * q^34 + 1575167660282324 * q^35 + 7318800726486641 * q^36 + 3601713987410012 * q^37 + 2042887131890906 * q^38 + 712786595145686 * q^39 - 38233381179154 * q^40 + 3933352398746224 * q^41 - 1818473706528187 * q^42 + 9956432184119776 * q^43 - 8374864809587786 * q^44 + 4814834336659374 * q^45 - 21420879452965494 * q^46 - 43646088451007913 * q^47 - 71590477049164572 * q^48 + 118361365545367441 * q^49 - 57666947668617547 * q^50 + 63071710735479788 * q^51 - 1295800694634632 * q^52 - 70710792109226748 * q^53 - 259379096268487409 * q^54 - 138894593750942388 * q^55 - 316931141949206936 * q^56 - 3219688617629350 * q^57 + 33593423193920552 * q^58 - 338601629983507156 * q^59 - 602000063011577726 * q^60 - 19162753603253692 * q^61 + 15505488837731256 * q^62 + 441133809282344796 * q^63 + 1575599177864752889 * q^64 + 991696997985687508 * q^65 - 223449751457078784 * q^66 + 789160046018441716 * q^67 + 793527065771503959 * q^68 + 1895066450986425554 * q^69 + 1371841313181399546 * q^70 + 901635006217520756 * q^71 + 4179441926330901705 * q^72 + 1704470931364824164 * q^73 - 936673704019194682 * q^74 + 2721299115185599300 * q^75 + 902909748895301048 * q^76 + 136895176815000502 * q^77 + 3735106483941260580 * q^78 - 384249994690730008 * q^79 - 1467637000368371240 * q^80 + 8095662645266644679 * q^81 + 6903936236738341456 * q^82 - 5730978816086659996 * q^83 - 10890678559479540867 * q^84 + 8583250605589725902 * q^85 + 15620118301833942618 * q^86 - 6279890617984303996 * q^87 + 17694374817110019346 * q^88 - 6455617251918472412 * q^89 - 170944452240128902 * q^90 - 1869573151265783134 * q^91 - 9347654291170404076 * q^92 + 11297106145565168410 * q^93 - 634546978249268889 * q^94 + 10375725689895196340 * q^95 + 38268359616807245724 * q^96 + 39090934998462984208 * q^97 + 41754136007920530767 * q^98 + 26521922158952497062 * 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 $

$2$	−1265.30	−1.74747	−0.873734	−	0.486404i	$-0.838308\pi$
$2$	−1265.30	−1.74747	−0.873734	+	0.486404i	$0.838308\pi$
$3$	61064.0	1.79115	0.895577	−	0.444906i	$-0.146763\pi$
$3$	61064.0	1.79115	0.895577	+	0.444906i	$0.146763\pi$
$4$	1.07670e6	2.05365
$5$	−1.52486e6	−0.349152	−0.174576	−	0.984644i	$-0.555855\pi$
$5$	−1.52486e6	−0.349152	−0.174576	+	0.984644i	$0.555855\pi$
$6$	−7.72644e7	−3.12999
$7$	6.24861e7	0.585264	0.292632	−	0.956225i	$-0.405469\pi$
$7$	6.24861e7	0.585264	0.292632	+	0.956225i	$0.405469\pi$
$8$	−6.98970e8	−1.84121
$9$	2.56655e9	2.20823
$10$	1.92941e9	0.610132
$11$	−5.35249e9	−0.684425	−0.342212	−	0.939623i	$-0.611176\pi$
$11$	−5.35249e9	−0.684425	−0.342212	+	0.939623i	$0.611176\pi$
$12$	6.57477e10	3.67840
$13$	3.54072e10	0.926040	0.463020	−	0.886348i	$-0.346766\pi$
$13$	3.54072e10	0.926040	0.463020	+	0.886348i	$0.346766\pi$
$14$	−7.90638e10	−1.02273
$15$	−9.31139e10	−0.625385
$16$	3.19907e11	1.16381
$17$	−3.38946e11	−0.693212	−0.346606	−	0.938011i	$-0.612666\pi$
$17$	−3.38946e11	−0.693212	−0.346606	+	0.938011i	$0.612666\pi$
$18$	−3.24746e12	−3.85882
$19$	−1.07323e12	−0.763016	−0.381508	−	0.924366i	$-0.624595\pi$
$19$	−1.07323e12	−0.763016	−0.381508	+	0.924366i	$0.624595\pi$
$20$	−1.64182e12	−0.717035
$21$	3.81565e12	1.04830
$22$	6.77252e12	1.19601
$23$	4.77620e11	0.0552927	0.0276464	−	0.999618i	$-0.491199\pi$
$23$	4.77620e11	0.0552927	0.0276464	+	0.999618i	$0.491199\pi$
$24$	−4.26819e13	−3.29789
$25$	−1.67483e13	−0.878093
$26$	−4.48008e13	−1.61823
$27$	8.57512e13	2.16414
$28$	6.72789e13	1.20193
$29$	9.43429e13	1.20761	0.603807	−	0.797131i	$-0.293650\pi$
$29$	9.43429e13	1.20761	0.603807	+	0.797131i	$0.293650\pi$
$30$	1.17817e14	1.09284
$31$	1.12053e14	0.761177	0.380588	−	0.924745i	$-0.375721\pi$
$31$	1.12053e14	0.761177	0.380588	+	0.924745i	$0.375721\pi$
$32$	−3.83170e13	−0.192516
$33$	−3.26845e14	−1.22591
$34$	4.28869e14	1.21137
$35$	−9.52825e13	−0.204346
$36$	2.76340e15	4.53493
$37$	8.46180e14	1.07040	0.535201	−	0.844725i	$-0.320236\pi$
$37$	8.46180e14	1.07040	0.535201	+	0.844725i	$0.320236\pi$
$38$	1.35796e15	1.33335
$39$	2.16210e15	1.65868
$40$	1.06583e15	0.642863
$41$	6.88735e13	0.0328553	0.0164276	−	0.999865i	$-0.494771\pi$
$41$	6.88735e13	0.0328553	0.0164276	+	0.999865i	$0.494771\pi$
$42$	−4.82795e15	−1.83187
$43$	4.02348e15	1.22082	0.610410	−	0.792085i	$-0.291005\pi$
$43$	4.02348e15	1.22082	0.610410	+	0.792085i	$0.291005\pi$
$44$	−5.76304e15	−1.40557
$45$	−3.91362e15	−0.771010
$46$	−6.04333e14	−0.0966223
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	1.95348e16	2.08457
$49$	−7.49438e15	−0.657466
$50$	2.11916e16	1.53444
$51$	−2.06974e16	−1.24165
$52$	3.81230e16	1.90176
$53$	−1.02170e16	−0.425305	−0.212653	−	0.977128i	$-0.568210\pi$
$53$	−1.02170e16	−0.425305	−0.212653	+	0.977128i	$0.568210\pi$
$54$	−1.08501e17	−3.78176
$55$	8.16180e15	0.238968
$56$	−4.36759e16	−1.07760
$57$	−6.55357e16	−1.36668
$58$	−1.19372e17	−2.11027
$59$	6.07531e15	0.0913008	0.0456504	−	0.998957i	$-0.485464\pi$
$59$	6.07531e15	0.0913008	0.0456504	+	0.998957i	$0.485464\pi$
$60$	−1.00256e17	−1.28432
$61$	1.58603e17	1.73651	0.868254	−	0.496120i	$-0.165242\pi$
$61$	1.58603e17	1.73651	0.868254	+	0.496120i	$0.165242\pi$
$62$	−1.41780e17	−1.33013
$63$	1.60373e17	1.29240
$64$	−1.19241e17	−0.827398
$65$	−5.39910e16	−0.323329
$66$	4.13557e17	2.14224
$67$	3.80548e17	1.70883	0.854415	−	0.519591i	$-0.173916\pi$
$67$	3.80548e17	1.70883	0.854415	+	0.519591i	$0.173916\pi$
$68$	−3.64944e17	−1.42361
$69$	2.91654e16	0.0990378
$70$	1.20561e17	0.357089
$71$	4.93119e17	1.27643	0.638215	−	0.769858i	$-0.279673\pi$
$71$	4.93119e17	1.27643	0.638215	+	0.769858i	$0.279673\pi$
$72$	−1.79394e18	−4.06583
$73$	−3.39005e17	−0.673967	−0.336983	−	0.941511i	$-0.609407\pi$
$73$	−3.39005e17	−0.673967	−0.336983	+	0.941511i	$0.609407\pi$
$74$	−1.07067e18	−1.87049
$75$	−1.02272e18	−1.57280
$76$	−1.15555e18	−1.56696
$77$	−3.34457e17	−0.400569
$78$	−2.73572e18	−2.89849
$79$	3.58125e17	0.336184	0.168092	−	0.985771i	$-0.446239\pi$
$79$	3.58125e17	0.336184	0.168092	+	0.985771i	$0.446239\pi$
$80$	−4.87813e17	−0.406348
$81$	2.25331e18	1.66807
$82$	−8.71457e16	−0.0574136
$83$	−1.14552e18	−0.672603	−0.336302	−	0.941754i	$-0.609176\pi$
$83$	−1.14552e18	−0.672603	−0.336302	+	0.941754i	$0.609176\pi$
$84$	4.10832e18	2.15283
$85$	5.16845e17	0.242036
$86$	−5.09092e18	−2.13335
$87$	5.76095e18	2.16302
$88$	3.74123e18	1.26017
$89$	−2.76040e18	−0.835154	−0.417577	−	0.908642i	$-0.637121\pi$
$89$	−2.76040e18	−0.835154	−0.417577	+	0.908642i	$0.637121\pi$
$90$	4.95191e18	1.34732
$91$	2.21246e18	0.541978
$92$	5.14254e17	0.113552
$93$	6.84237e18	1.36339
$94$	1.41604e18	0.254894
$95$	1.63652e18	0.266409
$96$	−2.33979e18	−0.344826
$97$	8.03827e18	1.07357	0.536786	−	0.843719i	$-0.319638\pi$
$97$	8.03827e18	1.07357	0.536786	+	0.843719i	$0.319638\pi$
$98$	9.48266e18	1.14890
$99$	−1.37374e19	−1.51137
$100$	−1.80329e19	−1.80329
$101$	−2.56642e18	−0.233493	−0.116747	−	0.993162i	$-0.537247\pi$
$101$	−2.56642e18	−0.233493	−0.116747	+	0.993162i	$0.537247\pi$
$102$	2.61885e19	2.16974
$103$	1.41640e19	1.06963	0.534814	−	0.844970i	$-0.320382\pi$
$103$	1.41640e19	1.06963	0.534814	+	0.844970i	$0.320382\pi$
$104$	−2.47486e19	−1.70504
$105$	−5.81833e18	−0.366016
$106$	1.29275e19	0.743207
$107$	−2.64026e19	−1.38836	−0.694178	−	0.719804i	$-0.744232\pi$
$107$	−2.64026e19	−1.38836	−0.694178	+	0.719804i	$0.744232\pi$
$108$	9.23285e19	4.44437
$109$	1.69871e18	0.0749149	0.0374574	−	0.999298i	$-0.488074\pi$
$109$	1.69871e18	0.0749149	0.0374574	+	0.999298i	$0.488074\pi$
$110$	−1.03271e19	−0.417590
$111$	5.16711e19	1.91725
$112$	1.99897e19	0.681139
$113$	−1.90746e19	−0.597325	−0.298663	−	0.954359i	$-0.596541\pi$
$113$	−1.90746e19	−0.597325	−0.298663	+	0.954359i	$0.596541\pi$
$114$	8.29224e19	2.38823
$115$	−7.28303e17	−0.0193056
$116$	1.01579e20	2.48001
$117$	9.08742e19	2.04491
$118$	−7.68711e18	−0.159545
$119$	−2.11794e19	−0.405712
$120$	6.50839e19	1.15147
$121$	−3.25099e19	−0.531563
$122$	−2.00680e20	−3.03449
$123$	4.20569e18	0.0588489
$124$	1.20647e20	1.56319
$125$	5.46232e19	0.655740
$126$	−2.02921e20	−2.25843
$127$	−1.60346e20	−1.65548	−0.827739	−	0.561114i	$-0.810373\pi$
$127$	−1.60346e20	−1.65548	−0.827739	+	0.561114i	$0.810373\pi$
$128$	1.70965e20	1.63837
$129$	2.45690e20	2.18668
$130$	6.83149e19	0.565007
$131$	−1.17054e20	−0.900141	−0.450070	−	0.892993i	$-0.648601\pi$
$131$	−1.17054e20	−0.900141	−0.450070	+	0.892993i	$0.648601\pi$
$132$	−3.51914e20	−2.51759
$133$	−6.70620e19	−0.446566
$134$	−4.81508e20	−2.98613
$135$	−1.30758e20	−0.755612
$136$	2.36913e20	1.27635
$137$	2.56028e19	0.128659	0.0643297	−	0.997929i	$-0.479509\pi$
$137$	2.56028e19	0.128659	0.0643297	+	0.997929i	$0.479509\pi$
$138$	−3.69030e19	−0.173065
$139$	1.19098e20	0.521510	0.260755	−	0.965405i	$-0.416028\pi$
$139$	1.19098e20	0.521510	0.260755	+	0.965405i	$0.416028\pi$
$140$	−1.02591e20	−0.419655
$141$	−6.83385e19	−0.261267
$142$	−6.23944e20	−2.23052
$143$	−1.89517e20	−0.633805
$144$	8.21055e20	2.56997
$145$	−1.43860e20	−0.421641
$146$	4.28943e20	1.17774
$147$	−4.57637e20	−1.17762
$148$	9.11084e20	2.19822
$149$	7.46612e20	1.68976	0.844881	−	0.534954i	$-0.179671\pi$
$149$	7.46612e20	1.68976	0.844881	+	0.534954i	$0.179671\pi$
$150$	1.29405e21	2.74842
$151$	8.94728e20	1.78406	0.892031	−	0.451974i	$-0.149280\pi$
$151$	8.94728e20	1.78406	0.892031	+	0.451974i	$0.149280\pi$
$152$	7.50156e20	1.40487
$153$	−8.69921e20	−1.53078
$154$	4.23189e20	0.699982
$155$	−1.70864e20	−0.265766
$156$	2.32794e21	3.40634
$157$	8.71151e18	0.0119963	0.00599814	−	0.999982i	$-0.498091\pi$
$157$	8.71151e18	0.0119963	0.00599814	+	0.999982i	$0.498091\pi$
$158$	−4.53136e20	−0.587471
$159$	−6.23888e20	−0.761787
$160$	5.84280e19	0.0672173
$161$	2.98446e19	0.0323609
$162$	−2.85112e21	−2.91489
$163$	1.49858e21	1.44510	0.722551	−	0.691318i	$-0.242970\pi$
$163$	1.49858e21	1.44510	0.722551	+	0.691318i	$0.242970\pi$
$164$	7.41562e19	0.0674731
$165$	4.98392e20	0.428029
$166$	1.44942e21	1.17535
$167$	−1.14801e21	−0.879308	−0.439654	−	0.898167i	$-0.644899\pi$
$167$	−1.14801e21	−0.879308	−0.439654	+	0.898167i	$0.644899\pi$
$168$	−2.66703e21	−1.93014
$169$	−2.08250e20	−0.142450
$170$	−6.53965e20	−0.422951
$171$	−2.75449e21	−1.68492
$172$	4.33209e21	2.50713
$173$	2.95542e21	1.61876	0.809378	−	0.587288i	$-0.199804\pi$
$173$	2.95542e21	1.61876	0.809378	+	0.587288i	$0.199804\pi$
$174$	−7.28934e21	−3.77981
$175$	−1.04654e21	−0.513916
$176$	−1.71230e21	−0.796543
$177$	3.70983e20	0.163534
$178$	3.49274e21	1.45940
$179$	3.08049e21	1.22044	0.610219	−	0.792233i	$-0.291081\pi$
$179$	3.08049e21	1.22044	0.610219	+	0.792233i	$0.291081\pi$
$180$	−4.21380e21	−1.58338
$181$	3.55691e21	1.26802	0.634011	−	0.773324i	$-0.281407\pi$
$181$	3.55691e21	1.26802	0.634011	+	0.773324i	$0.281407\pi$
$182$	−2.79943e21	−0.947090
$183$	9.68490e21	3.11035
$184$	−3.33842e20	−0.101806
$185$	−1.29031e21	−0.373733
$186$	−8.65767e21	−2.38247
$187$	1.81421e21	0.474451
$188$	−1.20497e21	−0.299555
$189$	5.35826e21	1.26659
$190$	−2.07070e21	−0.465540
$191$	7.40800e21	1.58447	0.792235	−	0.610217i	$-0.208918\pi$
$191$	7.40800e21	1.58447	0.792235	+	0.610217i	$0.208918\pi$
$192$	−7.28131e21	−1.48200
$193$	5.33930e21	1.03440	0.517202	−	0.855864i	$-0.326974\pi$
$193$	5.33930e21	1.03440	0.517202	+	0.855864i	$0.326974\pi$
$194$	−1.01708e22	−1.87603
$195$	−3.29690e21	−0.579132
$196$	−8.06921e21	−1.35020
$197$	2.87950e21	0.459080	0.229540	−	0.973299i	$-0.426278\pi$
$197$	2.87950e21	0.459080	0.229540	+	0.973299i	$0.426278\pi$
$198$	1.73820e22	2.64107
$199$	−1.03634e22	−1.50106	−0.750528	−	0.660838i	$-0.770201\pi$
$199$	−1.03634e22	−1.50106	−0.750528	+	0.660838i	$0.770201\pi$
$200$	1.17066e22	1.61675
$201$	2.32378e22	3.06078
$202$	3.24729e21	0.408022
$203$	5.89512e21	0.706773
$204$	−2.22849e22	−2.54991
$205$	−1.05022e20	−0.0114715
$206$	−1.79217e22	−1.86914
$207$	1.22583e21	0.122099
$208$	1.13270e22	1.07774
$209$	5.74446e21	0.522227
$210$	7.36194e21	0.639601
$211$	−8.21456e21	−0.682183	−0.341091	−	0.940030i	$-0.610797\pi$
$211$	−8.21456e21	−0.682183	−0.341091	+	0.940030i	$0.610797\pi$
$212$	−1.10006e22	−0.873426
$213$	3.01118e22	2.28628
$214$	3.34073e22	2.42611
$215$	−6.13525e21	−0.426252
$216$	−5.99375e22	−3.98463
$217$	7.00173e21	0.445490
$218$	−2.14938e21	−0.130911
$219$	−2.07010e22	−1.20718
$220$	8.78782e21	0.490756
$221$	−1.20011e22	−0.641942
$222$	−6.53796e22	−3.35034
$223$	−2.36373e22	−1.16065	−0.580324	−	0.814385i	$-0.697074\pi$
$223$	−2.36373e22	−1.16065	−0.580324	+	0.814385i	$0.697074\pi$
$224$	−2.39428e21	−0.112673
$225$	−4.29853e22	−1.93904
$226$	2.41352e22	1.04381
$227$	1.66491e21	0.0690469	0.0345235	−	0.999404i	$-0.489009\pi$
$227$	1.66491e21	0.0690469	0.0345235	+	0.999404i	$0.489009\pi$
$228$	−7.05624e22	−2.80667
$229$	−1.34768e22	−0.514223	−0.257111	−	0.966382i	$-0.582771\pi$
$229$	−1.34768e22	−0.514223	−0.257111	+	0.966382i	$0.582771\pi$
$230$	9.21523e20	0.0337359
$231$	−2.04232e22	−0.717482
$232$	−6.59428e22	−2.22347
$233$	5.37755e22	1.74062	0.870309	−	0.492506i	$-0.163919\pi$
$233$	5.37755e22	1.74062	0.870309	+	0.492506i	$0.163919\pi$
$234$	−1.14983e23	−3.57342
$235$	1.70652e21	0.0509291
$236$	6.54130e21	0.187499
$237$	2.18685e22	0.602157
$238$	2.67984e22	0.708969
$239$	4.42145e22	1.12405	0.562024	−	0.827121i	$-0.310023\pi$
$239$	4.42145e22	1.12405	0.562024	+	0.827121i	$0.310023\pi$
$240$	−2.97878e22	−0.727832
$241$	1.83964e22	0.432087	0.216043	−	0.976384i	$-0.430685\pi$
$241$	1.83964e22	0.432087	0.216043	+	0.976384i	$0.430685\pi$
$242$	4.11348e22	0.928889
$243$	3.79308e22	0.823630
$244$	1.70768e23	3.56617
$245$	1.14279e22	0.229555
$246$	−5.32146e21	−0.102837
$247$	−3.80001e22	−0.706583
$248$	−7.83214e22	−1.40149
$249$	−6.99497e22	−1.20474
$250$	−6.91148e22	−1.14588
$251$	−7.47088e22	−1.19254	−0.596268	−	0.802785i	$-0.703351\pi$
$251$	−7.47088e22	−1.19254	−0.596268	+	0.802785i	$0.703351\pi$
$252$	1.72674e23	2.65413
$253$	−2.55646e21	−0.0378437
$254$	2.02886e23	2.89289
$255$	3.15606e22	0.433525
$256$	−1.53805e23	−2.03560
$257$	−1.10047e23	−1.40350	−0.701751	−	0.712422i	$-0.747598\pi$
$257$	−1.10047e23	−1.40350	−0.701751	+	0.712422i	$0.747598\pi$
$258$	−3.10872e23	−3.82115
$259$	5.28745e22	0.626468
$260$	−5.81322e22	−0.664003
$261$	2.42135e23	2.66669
$262$	1.48109e23	1.57297
$263$	−1.46973e23	−1.50542	−0.752712	−	0.658349i	$-0.771255\pi$
$263$	−1.46973e23	−1.50542	−0.752712	+	0.658349i	$0.771255\pi$
$264$	2.28455e23	2.25716
$265$	1.55794e22	0.148496
$266$	8.48536e22	0.780360
$267$	−1.68561e23	−1.49589
$268$	4.09737e23	3.50933
$269$	8.93409e22	0.738590	0.369295	−	0.929312i	$-0.379599\pi$
$269$	8.93409e22	0.738590	0.369295	+	0.929312i	$0.379599\pi$
$270$	1.65449e23	1.32041
$271$	2.40768e23	1.85520	0.927598	−	0.373580i	$-0.121870\pi$
$271$	2.40768e23	1.85520	0.927598	+	0.373580i	$0.121870\pi$
$272$	−1.08431e23	−0.806770
$273$	1.35101e23	0.970767
$274$	−3.23952e22	−0.224828
$275$	8.96451e22	0.600988
$276$	3.14024e22	0.203388
$277$	2.15082e22	0.134601	0.0673003	−	0.997733i	$-0.478561\pi$
$277$	2.15082e22	0.134601	0.0673003	+	0.997733i	$0.478561\pi$
$278$	−1.50695e23	−0.911323
$279$	2.87588e23	1.68086
$280$	6.65996e22	0.376245
$281$	−1.28183e23	−0.700036	−0.350018	−	0.936743i	$-0.613825\pi$
$281$	−1.28183e23	−0.700036	−0.350018	+	0.936743i	$0.613825\pi$
$282$	8.64689e22	0.456555
$283$	1.26232e23	0.644464	0.322232	−	0.946661i	$-0.395567\pi$
$283$	1.26232e23	0.644464	0.322232	+	0.946661i	$0.395567\pi$
$284$	5.30942e23	2.62133
$285$	9.99327e22	0.477179
$286$	2.39796e23	1.10755
$287$	4.30363e21	0.0192290
$288$	−9.83423e22	−0.425120
$289$	−1.24188e23	−0.519457
$290$	1.82026e23	0.736804
$291$	4.90848e23	1.92293
$292$	−3.65007e23	−1.38409
$293$	−1.26080e23	−0.462810	−0.231405	−	0.972857i	$-0.574332\pi$
$293$	−1.26080e23	−0.462810	−0.231405	+	0.972857i	$0.574332\pi$
$294$	5.79049e23	2.05786
$295$	−9.26400e21	−0.0318779
$296$	−5.91455e23	−1.97084
$297$	−4.58983e23	−1.48119
$298$	−9.44690e23	−2.95281
$299$	1.69112e22	0.0512033
$300$	−1.10116e24	−3.22997
$301$	2.51412e23	0.714503
$302$	−1.13210e24	−3.11759
$303$	−1.56716e23	−0.418222
$304$	−3.43333e23	−0.888008
$305$	−2.41847e23	−0.606306
$306$	1.10071e24	2.67498
$307$	3.19976e23	0.753881	0.376940	−	0.926238i	$-0.376976\pi$
$307$	3.19976e23	0.753881	0.376940	+	0.926238i	$0.376976\pi$
$308$	−3.60110e23	−0.822628
$309$	8.64910e23	1.91587
$310$	2.16195e23	0.464418
$311$	−2.52063e23	−0.525153	−0.262577	−	0.964911i	$-0.584572\pi$
$311$	−2.52063e23	−0.525153	−0.262577	+	0.964911i	$0.584572\pi$
$312$	−1.51125e24	−3.05398
$313$	1.58945e23	0.311584	0.155792	−	0.987790i	$-0.450207\pi$
$313$	1.58945e23	0.311584	0.155792	+	0.987790i	$0.450207\pi$
$314$	−1.10227e22	−0.0209631
$315$	−2.44547e23	−0.451245
$316$	3.85593e23	0.690403
$317$	−8.29407e22	−0.144114	−0.0720568	−	0.997401i	$-0.522956\pi$
$317$	−8.29407e22	−0.144114	−0.0720568	+	0.997401i	$0.522956\pi$
$318$	7.89407e23	1.33120
$319$	−5.04970e23	−0.826521
$320$	1.81825e23	0.288888
$321$	−1.61225e24	−2.48676
$322$	−3.77624e22	−0.0565496
$323$	3.63767e23	0.528932
$324$	2.42614e24	3.42562
$325$	−5.93010e23	−0.813149
$326$	−1.89616e24	−2.52527
$327$	1.03730e23	0.134184
$328$	−4.81405e22	−0.0604935
$329$	−6.99301e22	−0.0853696
$330$	−6.30616e23	−0.747967
$331$	1.47391e24	1.69865	0.849327	−	0.527868i	$-0.177008\pi$
$331$	1.47391e24	1.69865	0.849327	+	0.527868i	$0.177008\pi$
$332$	−1.23338e24	−1.38129
$333$	2.17176e24	2.36370
$334$	1.45259e24	1.53656
$335$	−5.80282e23	−0.596642
$336$	1.22065e24	1.22002
$337$	1.30878e24	1.27170	0.635849	−	0.771814i	$-0.280650\pi$
$337$	1.30878e24	1.27170	0.635849	+	0.771814i	$0.280650\pi$
$338$	2.63500e23	0.248927
$339$	−1.16477e24	−1.06990
$340$	5.56488e23	0.497057
$341$	−5.99760e23	−0.520968
$342$	3.48527e24	2.94434
$343$	−1.18057e24	−0.970056
$344$	−2.81229e24	−2.24779
$345$	−4.44731e22	−0.0345793
$346$	−3.73950e24	−2.82872
$347$	2.62223e23	0.192992	0.0964961	−	0.995333i	$-0.469236\pi$
$347$	2.62223e23	0.192992	0.0964961	+	0.995333i	$0.469236\pi$
$348$	6.20282e24	4.44208
$349$	2.28702e24	1.59378	0.796890	−	0.604125i	$-0.206477\pi$
$349$	2.28702e24	1.59378	0.796890	+	0.604125i	$0.206477\pi$
$350$	1.32418e24	0.898053
$351$	3.03621e24	2.00408
$352$	2.05091e23	0.131763
$353$	−2.35039e24	−1.46987	−0.734937	−	0.678135i	$-0.762788\pi$
$353$	−2.35039e24	−1.46987	−0.734937	+	0.678135i	$0.762788\pi$
$354$	−4.69405e23	−0.285770
$355$	−7.51936e23	−0.445668
$356$	−2.97212e24	−1.71511
$357$	−1.29330e24	−0.726694
$358$	−3.89775e24	−2.13268
$359$	−9.40402e23	−0.501091	−0.250545	−	0.968105i	$-0.580610\pi$
$359$	−9.40402e23	−0.501091	−0.250545	+	0.968105i	$0.580610\pi$
$360$	2.73550e24	1.41959
$361$	−8.26597e23	−0.417807
$362$	−4.50057e24	−2.21583
$363$	−1.98518e24	−0.952111
$364$	2.38216e24	1.11303
$365$	5.16934e23	0.235317
$366$	−1.22543e25	−5.43525
$367$	1.72183e24	0.744153	0.372076	−	0.928202i	$-0.378646\pi$
$367$	1.72183e24	0.744153	0.372076	+	0.928202i	$0.378646\pi$
$368$	1.52794e23	0.0643504
$369$	1.76767e23	0.0725522
$370$	1.63263e24	0.653086
$371$	−6.38418e23	−0.248916
$372$	7.36719e24	2.79991
$373$	1.65981e24	0.614929	0.307464	−	0.951560i	$-0.400519\pi$
$373$	1.65981e24	0.614929	0.307464	+	0.951560i	$0.400519\pi$
$374$	−2.29552e24	−0.829089
$375$	3.33551e24	1.17453
$376$	7.82239e23	0.268568
$377$	3.34042e24	1.11830
$378$	−6.77982e24	−2.21333
$379$	4.17251e24	1.32839	0.664194	−	0.747560i	$-0.268775\pi$
$379$	4.17251e24	1.32839	0.664194	+	0.747560i	$0.268775\pi$
$380$	1.76205e24	0.547109
$381$	−9.79137e24	−2.96522
$382$	−9.37335e24	−2.76881
$383$	4.20924e24	1.21287	0.606437	−	0.795132i	$-0.292598\pi$
$383$	4.20924e24	1.21287	0.606437	+	0.795132i	$0.292598\pi$
$384$	1.04398e25	2.93457
$385$	5.09999e23	0.139860
$386$	−6.75583e24	−1.80759
$387$	1.03265e25	2.69586
$388$	8.65481e24	2.20473
$389$	5.15368e24	1.28114	0.640569	−	0.767901i	$-0.278699\pi$
$389$	5.15368e24	1.28114	0.640569	+	0.767901i	$0.278699\pi$
$390$	4.17158e24	1.01201
$391$	−1.61887e23	−0.0383296
$392$	5.23835e24	1.21053
$393$	−7.14781e24	−1.61229
$394$	−3.64344e24	−0.802227
$395$	−5.46090e23	−0.117379
$396$	−1.47911e25	−3.10382
$397$	−6.34296e24	−1.29952	−0.649759	−	0.760140i	$-0.725130\pi$
$397$	−6.34296e24	−1.29952	−0.649759	+	0.760140i	$0.725130\pi$
$398$	1.31128e25	2.62305
$399$	−4.09507e24	−0.799869
$400$	−5.35789e24	−1.02194
$401$	−1.85208e24	−0.344976	−0.172488	−	0.985012i	$-0.555181\pi$
$401$	−1.85208e24	−0.344976	−0.172488	+	0.985012i	$0.555181\pi$
$402$	−2.94028e25	−5.34862
$403$	3.96747e24	0.704880
$404$	−2.76327e24	−0.479512
$405$	−3.43598e24	−0.582409
$406$	−7.45911e24	−1.23506
$407$	−4.52918e24	−0.732609
$408$	1.44669e25	2.28614
$409$	2.33369e24	0.360306	0.180153	−	0.983639i	$-0.442341\pi$
$409$	2.33369e24	0.360306	0.180153	+	0.983639i	$0.442341\pi$
$410$	1.32885e23	0.0200461
$411$	1.56341e24	0.230449
$412$	1.52504e25	2.19664
$413$	3.79623e23	0.0534351
$414$	−1.55105e24	−0.213365
$415$	1.74675e24	0.234841
$416$	−1.35670e24	−0.178277
$417$	7.27258e24	0.934105
$418$	−7.26847e24	−0.912575
$419$	1.14436e25	1.40453	0.702263	−	0.711918i	$-0.252173\pi$
$419$	1.14436e25	1.40453	0.702263	+	0.711918i	$0.252173\pi$
$420$	−6.26460e24	−0.751667
$421$	−4.21036e24	−0.493901	−0.246950	−	0.969028i	$-0.579428\pi$
$421$	−4.21036e24	−0.493901	−0.246950	+	0.969028i	$0.579428\pi$
$422$	1.03939e25	1.19209
$423$	−2.87230e24	−0.322104
$424$	7.14135e24	0.783077
$425$	5.67677e24	0.608705
$426$	−3.81005e25	−3.99521
$427$	9.91046e24	1.01632
$428$	−2.84277e25	−2.85119
$429$	−1.15727e25	−1.13524
$430$	7.76294e24	0.744862
$431$	−1.73920e24	−0.163236	−0.0816180	−	0.996664i	$-0.526009\pi$
$431$	−1.73920e24	−0.163236	−0.0816180	+	0.996664i	$0.526009\pi$
$432$	2.74324e25	2.51865
$433$	−7.72402e24	−0.693759	−0.346879	−	0.937910i	$-0.612759\pi$
$433$	−7.72402e24	−0.693759	−0.346879	+	0.937910i	$0.612759\pi$
$434$	−8.85930e24	−0.778479
$435$	−8.78463e24	−0.755224
$436$	1.82901e24	0.153849
$437$	−5.12596e23	−0.0421892
$438$	2.61930e25	2.10951
$439$	−2.48383e25	−1.95754	−0.978768	−	0.204971i	$-0.934290\pi$
$439$	−2.48383e25	−1.95754	−0.978768	+	0.204971i	$0.934290\pi$
$440$	−5.70485e24	−0.439991
$441$	−1.92347e25	−1.45184
$442$	1.51851e25	1.12177
$443$	−7.07701e24	−0.511699	−0.255849	−	0.966717i	$-0.582355\pi$
$443$	−7.07701e24	−0.511699	−0.255849	+	0.966717i	$0.582355\pi$
$444$	5.56344e25	3.93736
$445$	4.20922e24	0.291596
$446$	2.99083e25	2.02820
$447$	4.55911e25	3.02663
$448$	−7.45089e24	−0.484247
$449$	−1.67536e25	−1.06603	−0.533014	−	0.846106i	$-0.678941\pi$
$449$	−1.67536e25	−1.06603	−0.533014	+	0.846106i	$0.678941\pi$
$450$	5.43894e25	3.38840
$451$	−3.68645e23	−0.0224870
$452$	−2.05377e25	−1.22669
$453$	5.46356e25	3.19553
$454$	−2.10661e24	−0.120657
$455$	−3.37369e24	−0.189233
$456$	4.58075e25	2.51635
$457$	−2.67788e25	−1.44075	−0.720373	−	0.693587i	$-0.756029\pi$
$457$	−2.67788e25	−1.44075	−0.720373	+	0.693587i	$0.756029\pi$
$458$	1.70523e25	0.898588
$459$	−2.90651e25	−1.50020
$460$	−7.84165e23	−0.0396468
$461$	2.93021e25	1.45124	0.725621	−	0.688095i	$-0.241553\pi$
$461$	2.93021e25	1.45124	0.725621	+	0.688095i	$0.241553\pi$
$462$	2.58416e25	1.25378
$463$	2.49414e24	0.118550	0.0592749	−	0.998242i	$-0.481121\pi$
$463$	2.49414e24	0.118550	0.0592749	+	0.998242i	$0.481121\pi$
$464$	3.01809e25	1.40544
$465$	−1.04336e25	−0.476029
$466$	−6.80423e25	−3.04167
$467$	−1.46743e25	−0.642758	−0.321379	−	0.946951i	$-0.604146\pi$
$467$	−1.46743e25	−0.642758	−0.321379	+	0.946951i	$0.604146\pi$
$468$	9.78444e25	4.19953
$469$	2.37790e25	1.00012
$470$	−2.15926e24	−0.0889969
$471$	5.31959e23	0.0214872
$472$	−4.24646e24	−0.168104
$473$	−2.15357e25	−0.835560
$474$	−2.76703e25	−1.05225
$475$	1.79748e25	0.669999
$476$	−2.28039e25	−0.833189
$477$	−2.62223e25	−0.939174
$478$	−5.59448e25	−1.96424
$479$	−1.45543e25	−0.500961	−0.250481	−	0.968122i	$-0.580589\pi$
$479$	−1.45543e25	−0.500961	−0.250481	+	0.968122i	$0.580589\pi$
$480$	3.56784e24	0.120397
$481$	2.99609e25	0.991234
$482$	−2.32770e25	−0.755058
$483$	1.82243e24	0.0579633
$484$	−3.50035e25	−1.09164
$485$	−1.22572e25	−0.374840
$486$	−4.79939e25	−1.43927
$487$	−1.44397e25	−0.424651	−0.212325	−	0.977199i	$-0.568104\pi$
$487$	−1.44397e25	−0.424651	−0.212325	+	0.977199i	$0.568104\pi$
$488$	−1.10858e26	−3.19728
$489$	9.15094e25	2.58840
$490$	−1.44597e25	−0.401141
$491$	−3.81745e25	−1.03872	−0.519361	−	0.854555i	$-0.673830\pi$
$491$	−3.81745e25	−1.03872	−0.519361	+	0.854555i	$0.673830\pi$
$492$	4.52827e24	0.120855
$493$	−3.19772e25	−0.837132
$494$	4.80816e25	1.23473
$495$	2.09476e25	0.527698
$496$	3.58463e25	0.885868
$497$	3.08131e25	0.747049
$498$	8.85075e25	2.10524
$499$	−7.78610e25	−1.81704	−0.908520	−	0.417841i	$-0.862787\pi$
$499$	−7.78610e25	−1.81704	−0.908520	+	0.417841i	$0.862787\pi$
$500$	5.88128e25	1.34666
$501$	−7.01023e25	−1.57498
$502$	9.45293e25	2.08392
$503$	−8.61336e24	−0.186327	−0.0931637	−	0.995651i	$-0.529698\pi$
$503$	−8.61336e24	−0.186327	−0.0931637	+	0.995651i	$0.529698\pi$
$504$	−1.12096e26	−2.37958
$505$	3.91342e24	0.0815246
$506$	3.23469e24	0.0661307
$507$	−1.27166e25	−0.255150
$508$	−1.72645e26	−3.39976
$509$	2.14289e25	0.414172	0.207086	−	0.978323i	$-0.433602\pi$
$509$	2.14289e25	0.414172	0.207086	+	0.978323i	$0.433602\pi$
$510$	−3.99337e25	−0.757571
$511$	−2.11831e25	−0.394449
$512$	1.04976e26	1.91877
$513$	−9.20307e25	−1.65127
$514$	1.39243e26	2.45258
$515$	−2.15981e25	−0.373463
$516$	2.64535e26	4.49066
$517$	5.99014e24	0.0998336
$518$	−6.69022e25	−1.09473
$519$	1.80470e26	2.89944
$520$	3.77381e25	0.595317
$521$	−9.07832e25	−1.40620	−0.703100	−	0.711091i	$-0.748201\pi$
$521$	−9.07832e25	−1.40620	−0.703100	+	0.711091i	$0.748201\pi$
$522$	−3.06374e26	−4.65996
$523$	−3.28492e25	−0.490635	−0.245318	−	0.969443i	$-0.578892\pi$
$523$	−3.28492e25	−0.490635	−0.245318	+	0.969443i	$0.578892\pi$
$524$	−1.26033e26	−1.84857
$525$	−6.39056e25	−0.920504
$526$	1.85966e26	2.63068
$527$	−3.79798e25	−0.527657
$528$	−1.04560e26	−1.42673
$529$	−7.43874e25	−0.996943
$530$	−1.97127e25	−0.259492
$531$	1.55926e25	0.201614
$532$	−7.22057e25	−0.917088
$533$	2.43862e24	0.0304253
$534$	2.13280e26	2.61402
$535$	4.02602e25	0.484747
$536$	−2.65992e26	−3.14632
$537$	1.88107e26	2.18599
$538$	−1.13043e26	−1.29066
$539$	4.01136e25	0.449986
$540$	−1.40788e26	−1.55176
$541$	−2.08808e25	−0.226137	−0.113069	−	0.993587i	$-0.536068\pi$
$541$	−2.08808e25	−0.226137	−0.113069	+	0.993587i	$0.536068\pi$
$542$	−3.04644e26	−3.24190
$543$	2.17199e26	2.27122
$544$	1.29874e25	0.133454
$545$	−2.59030e24	−0.0261567
$546$	−1.70944e26	−1.69638
$547$	1.12010e26	1.09239	0.546196	−	0.837657i	$-0.316075\pi$
$547$	1.12010e26	1.09239	0.546196	+	0.837657i	$0.316075\pi$
$548$	2.75665e25	0.264221
$549$	4.07061e26	3.83462
$550$	−1.13428e26	−1.05021
$551$	−1.01252e26	−0.921428
$552$	−2.03857e25	−0.182350
$553$	2.23778e25	0.196756
$554$	−2.72144e25	−0.235210
$555$	−7.87912e25	−0.669413
$556$	1.28233e26	1.07100
$557$	1.90166e26	1.56138	0.780688	−	0.624921i	$-0.214869\pi$
$557$	1.90166e26	1.56138	0.780688	+	0.624921i	$0.214869\pi$
$558$	−3.63886e26	−2.93724
$559$	1.42460e26	1.13053
$560$	−3.04815e25	−0.237821
$561$	1.10783e26	0.849816
$562$	1.62190e26	1.22329
$563$	5.82243e24	0.0431792	0.0215896	−	0.999767i	$-0.493127\pi$
$563$	5.82243e24	0.0431792	0.0215896	+	0.999767i	$0.493127\pi$
$564$	−7.35802e25	−0.536549
$565$	2.90861e25	0.208557
$566$	−1.59722e26	−1.12618
$567$	1.40801e26	0.976260
$568$	−3.44675e26	−2.35018
$569$	5.09715e24	0.0341791	0.0170896	−	0.999854i	$-0.494560\pi$
$569$	5.09715e24	0.0341791	0.0170896	+	0.999854i	$0.494560\pi$
$570$	−1.26445e26	−0.833855
$571$	1.47036e26	0.953629	0.476815	−	0.879004i	$-0.341791\pi$
$571$	1.47036e26	0.953629	0.476815	+	0.879004i	$0.341791\pi$
$572$	−2.04053e26	−1.30161
$573$	4.52362e26	2.83803
$574$	−5.44540e24	−0.0336021
$575$	−7.99932e24	−0.0485521
$576$	−3.06037e26	−1.82709
$577$	7.25153e25	0.425853	0.212926	−	0.977068i	$-0.431701\pi$
$577$	7.25153e25	0.425853	0.212926	+	0.977068i	$0.431701\pi$
$578$	1.57135e26	0.907735
$579$	3.26039e26	1.85278
$580$	−1.54894e26	−0.865901
$581$	−7.15788e25	−0.393651
$582$	−6.21072e26	−3.36026
$583$	5.46862e25	0.291089
$584$	2.36954e26	1.24092
$585$	−1.38570e26	−0.713986
$586$	1.59529e26	0.808746
$587$	−3.49601e26	−1.74386	−0.871929	−	0.489632i	$-0.837131\pi$
$587$	−3.49601e26	−1.74386	−0.871929	+	0.489632i	$0.837131\pi$
$588$	−4.92738e26	−2.41842
$589$	−1.20258e26	−0.580790
$590$	1.17218e25	0.0557056
$591$	1.75834e26	0.822282
$592$	2.70699e26	1.24575
$593$	−3.11117e25	−0.140898	−0.0704488	−	0.997515i	$-0.522443\pi$
$593$	−3.11117e25	−0.140898	−0.0704488	+	0.997515i	$0.522443\pi$
$594$	5.80752e26	2.58833
$595$	3.22957e25	0.141655
$596$	8.03879e26	3.47017
$597$	−6.32829e26	−2.68862
$598$	−2.13978e25	−0.0894761
$599$	1.33480e26	0.549364	0.274682	−	0.961535i	$-0.411427\pi$
$599$	1.33480e26	0.549364	0.274682	+	0.961535i	$0.411427\pi$
$600$	7.14849e26	2.89586
$601$	−2.08455e26	−0.831197	−0.415598	−	0.909548i	$-0.636428\pi$
$601$	−2.08455e26	−0.831197	−0.415598	+	0.909548i	$0.636428\pi$
$602$	−3.18112e26	−1.24857
$603$	9.76694e26	3.77350
$604$	9.63355e26	3.66383
$605$	4.95730e25	0.185596
$606$	1.98293e26	0.730830
$607$	−2.33799e26	−0.848303	−0.424151	−	0.905591i	$-0.639428\pi$
$607$	−2.33799e26	−0.848303	−0.424151	+	0.905591i	$0.639428\pi$
$608$	4.11229e25	0.146893
$609$	3.59979e26	1.26594
$610$	3.06009e26	1.05950
$611$	−3.96253e25	−0.135077
$612$	−9.36646e26	−3.14367
$613$	−7.07741e23	−0.00233884	−0.00116942	−	0.999999i	$-0.500372\pi$
$613$	−7.07741e23	−0.00233884	−0.00116942	+	0.999999i	$0.500372\pi$
$614$	−4.04866e26	−1.31738
$615$	−6.41308e24	−0.0205472
$616$	2.33775e26	0.737533
$617$	−9.23089e25	−0.286771	−0.143385	−	0.989667i	$-0.545799\pi$
$617$	−9.23089e25	−0.286771	−0.143385	+	0.989667i	$0.545799\pi$
$618$	−1.09437e27	−3.34792
$619$	3.47976e26	1.04831	0.524153	−	0.851624i	$-0.324382\pi$
$619$	3.47976e26	1.04831	0.524153	+	0.851624i	$0.324382\pi$
$620$	−1.83970e26	−0.545790
$621$	4.09565e25	0.119661
$622$	3.18936e26	0.917689
$623$	−1.72486e26	−0.488786
$624$	6.91672e26	1.93040
$625$	2.36156e26	0.649140
$626$	−2.01113e26	−0.544483
$627$	3.50779e26	0.935389
$628$	9.37970e24	0.0246361
$629$	−2.86810e26	−0.742015
$630$	3.09426e26	0.788536
$631$	−6.90132e25	−0.173242	−0.0866210	−	0.996241i	$-0.527607\pi$
$631$	−6.90132e25	−0.173242	−0.0866210	+	0.996241i	$0.527607\pi$
$632$	−2.50318e26	−0.618986
$633$	−5.01613e26	−1.22190
$634$	1.04945e26	0.251834
$635$	2.44505e26	0.578013
$636$	−6.71741e26	−1.56444
$637$	−2.65355e26	−0.608839
$638$	6.38939e26	1.44432
$639$	1.26561e27	2.81866
$640$	−2.60697e26	−0.572040
$641$	−4.38594e26	−0.948226	−0.474113	−	0.880464i	$-0.657231\pi$
$641$	−4.38594e26	−0.948226	−0.474113	+	0.880464i	$0.657231\pi$
$642$	2.03998e27	4.34553
$643$	−2.70170e26	−0.567066	−0.283533	−	0.958963i	$-0.591506\pi$
$643$	−2.70170e26	−0.567066	−0.283533	+	0.958963i	$0.591506\pi$
$644$	3.21337e25	0.0664577
$645$	−3.74642e26	−0.763483
$646$	−4.60275e26	−0.924291
$647$	2.84123e26	0.562231	0.281116	−	0.959674i	$-0.409296\pi$
$647$	2.84123e26	0.562231	0.281116	+	0.959674i	$0.409296\pi$
$648$	−1.57500e27	−3.07126
$649$	−3.25181e25	−0.0624885
$650$	7.50337e26	1.42095
$651$	4.27553e26	0.797941
$652$	1.61353e27	2.96773
$653$	−4.38186e26	−0.794298	−0.397149	−	0.917754i	$-0.630000\pi$
$653$	−4.38186e26	−0.794298	−0.397149	+	0.917754i	$0.630000\pi$
$654$	−1.31250e26	−0.234483
$655$	1.78491e26	0.314286
$656$	2.20331e25	0.0382374
$657$	−8.70071e26	−1.48828
$658$	8.84827e25	0.149181
$659$	7.83070e26	1.30134	0.650668	−	0.759363i	$-0.274489\pi$
$659$	7.83070e26	1.30134	0.650668	+	0.759363i	$0.274489\pi$
$660$	5.36619e26	0.879020
$661$	5.18238e25	0.0836788	0.0418394	−	0.999124i	$-0.486678\pi$
$661$	5.18238e25	0.0836788	0.0418394	+	0.999124i	$0.486678\pi$
$662$	−1.86494e27	−2.96834
$663$	−7.32837e26	−1.14982
$664$	8.00681e26	1.23840
$665$	1.02260e26	0.155919
$666$	−2.74793e27	−4.13049
$667$	4.50600e25	0.0667722
$668$	−1.23607e27	−1.80579
$669$	−1.44338e27	−2.07890
$670$	7.34232e26	1.04261
$671$	−8.48919e26	−1.18851
$672$	−1.46204e26	−0.201814
$673$	5.82850e26	0.793257	0.396629	−	0.917979i	$-0.370180\pi$
$673$	5.82850e26	0.793257	0.396629	+	0.917979i	$0.370180\pi$
$674$	−1.65601e27	−2.22225
$675$	−1.43619e27	−1.90031
$676$	−2.24223e26	−0.292541
$677$	6.81428e26	0.876652	0.438326	−	0.898816i	$-0.355571\pi$
$677$	6.81428e26	0.876652	0.438326	+	0.898816i	$0.355571\pi$
$678$	1.47379e27	1.86962
$679$	5.02280e26	0.628323
$680$	−3.61259e26	−0.445640
$681$	1.01666e26	0.123674
$682$	7.58878e26	0.910375
$683$	−8.43364e26	−0.997742	−0.498871	−	0.866676i	$-0.666252\pi$
$683$	−8.43364e26	−0.997742	−0.498871	+	0.866676i	$0.666252\pi$
$684$	−2.96577e27	−3.46022
$685$	−3.90406e25	−0.0449217
$686$	1.49377e27	1.69514
$687$	−8.22950e26	−0.921052
$688$	1.28714e27	1.42081
$689$	−3.61754e26	−0.393850
$690$	5.62719e25	0.0604261
$691$	1.43367e27	1.51848	0.759239	−	0.650812i	$-0.225571\pi$
$691$	1.43367e27	1.51848	0.759239	+	0.650812i	$0.225571\pi$
$692$	3.18211e27	3.32435
$693$	−8.58398e26	−0.884551
$694$	−3.31791e26	−0.337248
$695$	−1.81607e26	−0.182086
$696$	−4.02673e27	−3.98258
$697$	−2.33444e25	−0.0227757
$698$	−2.89377e27	−2.78508
$699$	3.28375e27	3.11772
$700$	−1.12681e27	−1.05540
$701$	−3.23277e26	−0.298713	−0.149356	−	0.988783i	$-0.547720\pi$
$701$	−3.23277e26	−0.298713	−0.149356	+	0.988783i	$0.547720\pi$
$702$	−3.84172e27	−3.50206
$703$	−9.08146e26	−0.816733
$704$	6.38235e26	0.566292
$705$	1.04207e26	0.0912218
$706$	2.97395e27	2.56856
$707$	−1.60365e26	−0.136655
$708$	3.99438e26	0.335841
$709$	1.24386e27	1.03189	0.515944	−	0.856622i	$-0.327441\pi$
$709$	1.24386e27	1.03189	0.515944	+	0.856622i	$0.327441\pi$
$710$	9.51427e26	0.778791
$711$	9.19144e26	0.742373
$712$	1.92943e27	1.53769
$713$	5.35185e25	0.0420875
$714$	1.63642e27	1.26987
$715$	2.88986e26	0.221294
$716$	3.31677e27	2.50635
$717$	2.69992e27	2.01334
$718$	1.18989e27	0.875640
$719$	−1.20259e26	−0.0873358	−0.0436679	−	0.999046i	$-0.513904\pi$
$719$	−1.20259e26	−0.0873358	−0.0436679	+	0.999046i	$0.513904\pi$
$720$	−1.25199e27	−0.897312
$721$	8.85054e26	0.626015
$722$	1.04590e27	0.730104
$723$	1.12336e27	0.773935
$724$	3.82973e27	2.60407
$725$	−1.58008e27	−1.06040
$726$	2.51186e27	1.66378
$727$	1.12398e27	0.734823	0.367412	−	0.930058i	$-0.380244\pi$
$727$	1.12398e27	0.734823	0.367412	+	0.930058i	$0.380244\pi$
$728$	−1.54644e27	−0.997897
$729$	−3.02734e26	−0.192819
$730$	−6.54078e26	−0.411209
$731$	−1.36374e27	−0.846288
$732$	1.04278e28	6.38757
$733$	−7.50774e26	−0.453964	−0.226982	−	0.973899i	$-0.572886\pi$
$733$	−7.50774e26	−0.453964	−0.226982	+	0.973899i	$0.572886\pi$
$734$	−2.17863e27	−1.30038
$735$	6.97831e26	0.411169
$736$	−1.83009e25	−0.0106447
$737$	−2.03688e27	−1.16957
$738$	−2.23664e26	−0.126783
$739$	1.57339e27	0.880469	0.440234	−	0.897883i	$-0.354895\pi$
$739$	1.57339e27	0.880469	0.440234	+	0.897883i	$0.354895\pi$
$740$	−1.38927e27	−0.767515
$741$	−2.32043e27	−1.26560
$742$	8.07791e26	0.434973
$743$	1.55311e27	0.825673	0.412836	−	0.910805i	$-0.364538\pi$
$743$	1.55311e27	0.825673	0.412836	+	0.910805i	$0.364538\pi$
$744$	−4.78261e27	−2.51028
$745$	−1.13848e27	−0.589984
$746$	−2.10016e27	−1.07457
$747$	−2.94002e27	−1.48527
$748$	1.95336e27	0.974355
$749$	−1.64980e27	−0.812555
$750$	−4.22042e27	−2.05246
$751$	−3.48262e27	−1.67235	−0.836174	−	0.548464i	$-0.815213\pi$
$751$	−3.48262e27	−1.67235	−0.836174	+	0.548464i	$0.815213\pi$
$752$	−3.58017e26	−0.169760
$753$	−4.56202e27	−2.13602
$754$	−4.22664e27	−1.95419
$755$	−1.36433e27	−0.622909
$756$	5.76925e27	2.60113
$757$	−3.08420e27	−1.37319	−0.686596	−	0.727039i	$-0.740896\pi$
$757$	−3.08420e27	−1.37319	−0.686596	+	0.727039i	$0.740896\pi$
$758$	−5.27949e27	−2.32132
$759$	−1.56107e26	−0.0677839
$760$	−1.14388e27	−0.490515
$761$	1.30961e27	0.554609	0.277305	−	0.960782i	$-0.410559\pi$
$761$	1.30961e27	0.554609	0.277305	+	0.960782i	$0.410559\pi$
$762$	1.23890e28	5.18162
$763$	1.06146e26	0.0438450
$764$	7.97620e27	3.25394
$765$	1.32651e27	0.534473
$766$	−5.32596e27	−2.11946
$767$	2.15110e26	0.0845482
$768$	−9.39197e27	−3.64607
$769$	−4.40893e27	−1.69057	−0.845285	−	0.534316i	$-0.820569\pi$
$769$	−4.40893e27	−1.69057	−0.845285	+	0.534316i	$0.820569\pi$
$770$	−6.45303e26	−0.244400
$771$	−6.71990e27	−2.51389
$772$	5.74883e27	2.12430
$773$	−2.60295e27	−0.950080	−0.475040	−	0.879964i	$-0.657566\pi$
$773$	−2.60295e27	−0.950080	−0.475040	+	0.879964i	$0.657566\pi$
$774$	−1.30661e28	−4.71093
$775$	−1.87669e27	−0.668384
$776$	−5.61851e27	−1.97667
$777$	3.22873e27	1.12210
$778$	−6.52096e27	−2.23875
$779$	−7.39170e25	−0.0250691
$780$	−3.54978e27	−1.18933
$781$	−2.63941e27	−0.873620
$782$	2.04837e26	0.0669797
$783$	8.09001e27	2.61344
$784$	−2.39750e27	−0.765167
$785$	−1.32838e25	−0.00418853
$786$	9.04413e27	2.81743
$787$	−2.79981e27	−0.861726	−0.430863	−	0.902417i	$-0.641791\pi$
$787$	−2.79981e27	−0.861726	−0.430863	+	0.902417i	$0.641791\pi$
$788$	3.10036e27	0.942787
$789$	−8.97478e27	−2.69645
$790$	6.90968e26	0.205117
$791$	−1.19190e27	−0.349593
$792$	9.60205e27	2.78275
$793$	5.61567e27	1.60808
$794$	8.02577e27	2.27087
$795$	9.51341e26	0.265980
$796$	−1.11583e28	−3.08264
$797$	−8.48781e26	−0.231708	−0.115854	−	0.993266i	$-0.536961\pi$
$797$	−8.48781e26	−0.231708	−0.115854	+	0.993266i	$0.536961\pi$
$798$	5.18150e27	1.39775
$799$	3.79325e26	0.101115
$800$	6.41744e26	0.169047
$801$	−7.08469e27	−1.84422
$802$	2.34344e27	0.602835
$803$	1.81452e27	0.461280
$804$	2.50202e28	6.28576
$805$	−4.55088e25	−0.0112989
$806$	−5.02004e27	−1.23176
$807$	5.45551e27	1.32293
$808$	1.79385e27	0.429910
$809$	7.96838e27	1.88738	0.943689	−	0.330833i	$-0.107330\pi$
$809$	7.96838e27	1.88738	0.943689	+	0.330833i	$0.107330\pi$
$810$	4.34755e27	1.01774
$811$	7.05819e27	1.63303	0.816517	−	0.577321i	$-0.195902\pi$
$811$	7.05819e27	1.63303	0.816517	+	0.577321i	$0.195902\pi$
$812$	6.34728e27	1.45146
$813$	1.47022e28	3.32294
$814$	5.73078e27	1.28021
$815$	−2.28513e27	−0.504560
$816$	−6.62124e27	−1.44505
$817$	−4.31812e27	−0.931505
$818$	−2.95282e27	−0.629623
$819$	5.67838e27	1.19682
$820$	−1.13078e26	−0.0235584
$821$	−3.64424e27	−0.750493	−0.375247	−	0.926925i	$-0.622442\pi$
$821$	−3.64424e27	−0.750493	−0.375247	+	0.926925i	$0.622442\pi$
$822$	−1.97818e27	−0.402702
$823$	−3.91082e27	−0.786991	−0.393495	−	0.919327i	$-0.628734\pi$
$823$	−3.91082e27	−0.786991	−0.393495	+	0.919327i	$0.628734\pi$
$824$	−9.90022e27	−1.96941
$825$	5.47409e27	1.07646
$826$	−4.80337e26	−0.0933761
$827$	−8.85065e27	−1.70088	−0.850438	−	0.526075i	$-0.823663\pi$
$827$	−8.85065e27	−1.70088	−0.850438	+	0.526075i	$0.823663\pi$
$828$	1.31986e27	0.250749
$829$	−8.03481e27	−1.50906	−0.754532	−	0.656264i	$-0.772136\pi$
$829$	−8.03481e27	−1.50906	−0.754532	+	0.656264i	$0.772136\pi$
$830$	−2.21017e27	−0.410377
$831$	1.31338e27	0.241090
$832$	−4.22198e27	−0.766204
$833$	2.54019e27	0.455763
$834$	−9.20201e27	−1.63232
$835$	1.75056e27	0.307012
$836$	6.18507e27	1.07247
$837$	9.60864e27	1.64729
$838$	−1.44796e28	−2.45436
$839$	6.74094e27	1.12975	0.564874	−	0.825177i	$-0.308925\pi$
$839$	6.74094e27	1.12975	0.564874	+	0.825177i	$0.308925\pi$
$840$	4.06684e27	0.673913
$841$	2.79731e27	0.458331
$842$	5.32738e27	0.863076
$843$	−7.82736e27	−1.25387
$844$	−8.84463e27	−1.40096
$845$	3.17552e26	0.0497366
$846$	3.63433e27	0.562867
$847$	−2.03142e27	−0.311105
$848$	−3.26847e27	−0.494976
$849$	7.70824e27	1.15434
$850$	−7.18283e27	−1.06369
$851$	4.04153e26	0.0591854
$852$	3.24214e28	4.69522
$853$	−4.05935e27	−0.581354	−0.290677	−	0.956821i	$-0.593880\pi$
$853$	−4.05935e27	−0.581354	−0.290677	+	0.956821i	$0.593880\pi$
$854$	−1.25397e28	−1.77598
$855$	4.20022e27	0.588293
$856$	1.84546e28	2.55626
$857$	2.63875e27	0.361477	0.180738	−	0.983531i	$-0.442151\pi$
$857$	2.63875e27	0.361477	0.180738	+	0.983531i	$0.442151\pi$
$858$	1.46429e28	1.98380
$859$	8.19819e26	0.109846	0.0549228	−	0.998491i	$-0.482509\pi$
$859$	8.19819e26	0.109846	0.0549228	+	0.998491i	$0.482509\pi$
$860$	−6.60583e27	−0.875371
$861$	2.62797e26	0.0344422
$862$	2.20062e27	0.285250
$863$	6.85725e27	0.879118	0.439559	−	0.898214i	$-0.355135\pi$
$863$	6.85725e27	0.879118	0.439559	+	0.898214i	$0.355135\pi$
$864$	−3.28573e27	−0.416630
$865$	−4.50660e27	−0.565192
$866$	9.77322e27	1.21232
$867$	−7.58340e27	−0.930428
$868$	7.53877e27	0.914878
$869$	−1.91686e27	−0.230093
$870$	1.11152e28	1.31973
$871$	1.34741e28	1.58245
$872$	−1.18735e27	−0.137934
$873$	2.06306e28	2.37070
$874$	6.48589e26	0.0737243
$875$	3.41319e27	0.383781
$876$	−2.22888e28	−2.47912
$877$	−7.48979e27	−0.824088	−0.412044	−	0.911164i	$-0.635185\pi$
$877$	−7.48979e27	−0.824088	−0.412044	+	0.911164i	$0.635185\pi$
$878$	3.14280e28	3.42073
$879$	−7.69893e27	−0.828965
$880$	2.61101e27	0.278115
$881$	−1.32028e28	−1.39122	−0.695610	−	0.718420i	$-0.744866\pi$
$881$	−1.32028e28	−1.39122	−0.695610	+	0.718420i	$0.744866\pi$
$882$	2.43377e28	2.53704
$883$	1.15130e28	1.18731	0.593654	−	0.804720i	$-0.297685\pi$
$883$	1.15130e28	1.18731	0.593654	+	0.804720i	$0.297685\pi$
$884$	−1.29216e28	−1.31832
$885$	−5.65696e26	−0.0570982
$886$	8.95455e27	0.894177
$887$	−1.11663e28	−1.10315	−0.551574	−	0.834126i	$-0.685973\pi$
$887$	−1.11663e28	−1.10315	−0.551574	+	0.834126i	$0.685973\pi$
$888$	−3.61166e28	−3.53007
$889$	−1.00194e28	−0.968892
$890$	−5.32593e27	−0.509554
$891$	−1.20608e28	−1.14167
$892$	−2.54503e28	−2.38356
$893$	1.20108e27	0.111297
$894$	−5.76865e28	−5.28893
$895$	−4.69731e27	−0.426119
$896$	1.06829e28	0.958879
$897$	1.03266e27	0.0917130
$898$	2.11984e28	1.86285
$899$	1.05714e28	0.919207
$900$	−4.62823e28	−3.98209
$901$	3.46300e27	0.294827
$902$	4.66447e26	0.0392953
$903$	1.53522e28	1.27979
$904$	1.33326e28	1.09980
$905$	−5.42379e27	−0.442732
$906$	−6.91306e28	−5.58409
$907$	−7.25657e27	−0.580045	−0.290023	−	0.957020i	$-0.593663\pi$
$907$	−7.25657e27	−0.580045	−0.290023	+	0.957020i	$0.593663\pi$
$908$	1.79261e27	0.141798
$909$	−6.58683e27	−0.515608
$910$	4.26873e27	0.330678
$911$	1.12246e28	0.860493	0.430246	−	0.902711i	$-0.358427\pi$
$911$	1.12246e28	0.860493	0.430246	+	0.902711i	$0.358427\pi$
$912$	−2.09653e28	−1.59056
$913$	6.13136e27	0.460346
$914$	3.38833e28	2.51766
$915$	−1.47681e28	−1.08599
$916$	−1.45105e28	−1.05603
$917$	−7.31427e27	−0.526820
$918$	3.67761e28	2.62156
$919$	1.22451e28	0.863902	0.431951	−	0.901897i	$-0.357825\pi$
$919$	1.22451e28	0.863902	0.431951	+	0.901897i	$0.357825\pi$
$920$	5.09062e26	0.0355456
$921$	1.95390e28	1.35032
$922$	−3.70760e28	−2.53600
$923$	1.74599e28	1.18203
$924$	−2.19897e28	−1.47345
$925$	−1.41721e28	−0.939912
$926$	−3.15584e27	−0.207162
$927$	3.63526e28	2.36199
$928$	−3.61493e27	−0.232485
$929$	−2.40659e28	−1.53198	−0.765988	−	0.642855i	$-0.777750\pi$
$929$	−2.40659e28	−1.53198	−0.765988	+	0.642855i	$0.777750\pi$
$930$	1.32017e28	0.831845
$931$	8.04319e27	0.501657
$932$	5.79002e28	3.57461
$933$	−1.53920e28	−0.940631
$934$	1.85674e28	1.12320
$935$	−2.76641e27	−0.165656
$936$	−6.35184e28	−3.76512
$937$	−1.30614e28	−0.766414	−0.383207	−	0.923663i	$-0.625180\pi$
$937$	−1.30614e28	−0.766414	−0.383207	+	0.923663i	$0.625180\pi$
$938$	−3.00876e28	−1.74767
$939$	9.70579e27	0.558095
$940$	1.83741e27	0.104590
$941$	−3.25797e28	−1.83588	−0.917942	−	0.396715i	$-0.870150\pi$
$941$	−3.25797e28	−1.83588	−0.917942	+	0.396715i	$0.870150\pi$
$942$	−6.73089e26	−0.0375482
$943$	3.28953e25	0.00181666
$944$	1.94353e27	0.106257
$945$	−8.17059e27	−0.442233
$946$	2.72491e28	1.46011
$947$	−1.04270e27	−0.0553140	−0.0276570	−	0.999617i	$-0.508805\pi$
$947$	−1.04270e27	−0.0553140	−0.0276570	+	0.999617i	$0.508805\pi$
$948$	2.35459e28	1.23662
$949$	−1.20032e28	−0.624120
$950$	−2.27435e28	−1.17080
$951$	−5.06469e27	−0.258130
$952$	1.48038e28	0.747002
$953$	−4.00251e26	−0.0199963	−0.00999817	−	0.999950i	$-0.503183\pi$
$953$	−4.00251e26	−0.0199963	−0.00999817	+	0.999950i	$0.503183\pi$
$954$	3.31791e28	1.64118
$955$	−1.12962e28	−0.553221
$956$	4.76059e28	2.30840
$957$	−3.08354e28	−1.48043
$958$	1.84156e28	0.875414
$959$	1.59982e27	0.0752997
$960$	1.11030e28	0.517443
$961$	−9.11490e27	−0.420610
$962$	−3.79096e28	−1.73215
$963$	−6.77635e28	−3.06581
$964$	1.98074e28	0.887353
$965$	−8.14168e27	−0.361164
$966$	−2.30592e27	−0.101289
$967$	1.76849e28	0.769222	0.384611	−	0.923079i	$-0.374336\pi$
$967$	1.76849e28	0.769222	0.384611	+	0.923079i	$0.374336\pi$
$968$	2.27234e28	0.978720
$969$	2.22131e28	0.947399
$970$	1.55091e28	0.655021
$971$	−2.74936e28	−1.14987	−0.574935	−	0.818199i	$-0.694973\pi$
$971$	−2.74936e28	−1.14987	−0.574935	+	0.818199i	$0.694973\pi$
$972$	4.08401e28	1.69144
$973$	7.44195e27	0.305221
$974$	1.82705e28	0.742064
$975$	−3.62116e28	−1.45648
$976$	5.07380e28	2.02097
$977$	6.43758e27	0.253936	0.126968	−	0.991907i	$-0.459475\pi$
$977$	6.43758e27	0.253936	0.126968	+	0.991907i	$0.459475\pi$
$978$	−1.15787e29	−4.52315
$979$	1.47750e28	0.571600
$980$	1.23044e28	0.471426
$981$	4.35982e27	0.165430
$982$	4.83023e28	1.81513
$983$	−1.96379e28	−0.730864	−0.365432	−	0.930838i	$-0.619079\pi$
$983$	−1.96379e28	−0.730864	−0.365432	+	0.930838i	$0.619079\pi$
$984$	−2.93965e27	−0.108353
$985$	−4.39083e27	−0.160289
$986$	4.04608e28	1.46286
$987$	−4.27021e27	−0.152910
$988$	−4.09147e28	−1.45107
$989$	1.92170e27	0.0675025
$990$	−2.65051e28	−0.922136
$991$	−5.24630e28	−1.80781	−0.903907	−	0.427729i	$-0.859314\pi$
$991$	−5.24630e28	−1.80781	−0.903907	+	0.427729i	$0.859314\pi$
$992$	−4.29351e27	−0.146539
$993$	9.00027e28	3.04255
$994$	−3.89878e28	−1.30544
$995$	1.58027e28	0.524097
$996$	−7.53149e28	−2.47410
$997$	2.85760e28	0.929816	0.464908	−	0.885359i	$-0.346087\pi$
$997$	2.85760e28	0.929816	0.464908	+	0.885359i	$0.346087\pi$
$998$	9.85177e28	3.17522
$999$	7.25610e28	2.31649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.3	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.3	✓	39	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:	\( N \)	\(=\)	\( 47 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	47.a (trivial)

\(f(q)\)	\(=\)	\(q-1265.30 q^{2} +61064.0 q^{3} +1.07670e6 q^{4} -1.52486e6 q^{5} -7.72644e7 q^{6} +6.24861e7 q^{7} -6.98970e8 q^{8} +2.56655e9 q^{9} +O(q^{10})\)	\(q-1265.30 q^{2} +61064.0 q^{3} +1.07670e6 q^{4} -1.52486e6 q^{5} -7.72644e7 q^{6} +6.24861e7 q^{7} -6.98970e8 q^{8} +2.56655e9 q^{9} +1.92941e9 q^{10} -5.35249e9 q^{11} +6.57477e10 q^{12} +3.54072e10 q^{13} -7.90638e10 q^{14} -9.31139e10 q^{15} +3.19907e11 q^{16} -3.38946e11 q^{17} -3.24746e12 q^{18} -1.07323e12 q^{19} -1.64182e12 q^{20} +3.81565e12 q^{21} +6.77252e12 q^{22} +4.77620e11 q^{23} -4.26819e13 q^{24} -1.67483e13 q^{25} -4.48008e13 q^{26} +8.57512e13 q^{27} +6.72789e13 q^{28} +9.43429e13 q^{29} +1.17817e14 q^{30} +1.12053e14 q^{31} -3.83170e13 q^{32} -3.26845e14 q^{33} +4.28869e14 q^{34} -9.52825e13 q^{35} +2.76340e15 q^{36} +8.46180e14 q^{37} +1.35796e15 q^{38} +2.16210e15 q^{39} +1.06583e15 q^{40} +6.88735e13 q^{41} -4.82795e15 q^{42} +4.02348e15 q^{43} -5.76304e15 q^{44} -3.91362e15 q^{45} -6.04333e14 q^{46} -1.11913e15 q^{47} +1.95348e16 q^{48} -7.49438e15 q^{49} +2.11916e16 q^{50} -2.06974e16 q^{51} +3.81230e16 q^{52} -1.02170e16 q^{53} -1.08501e17 q^{54} +8.16180e15 q^{55} -4.36759e16 q^{56} -6.55357e16 q^{57} -1.19372e17 q^{58} +6.07531e15 q^{59} -1.00256e17 q^{60} +1.58603e17 q^{61} -1.41780e17 q^{62} +1.60373e17 q^{63} -1.19241e17 q^{64} -5.39910e16 q^{65} +4.13557e17 q^{66} +3.80548e17 q^{67} -3.64944e17 q^{68} +2.91654e16 q^{69} +1.20561e17 q^{70} +4.93119e17 q^{71} -1.79394e18 q^{72} -3.39005e17 q^{73} -1.07067e18 q^{74} -1.02272e18 q^{75} -1.15555e18 q^{76} -3.34457e17 q^{77} -2.73572e18 q^{78} +3.58125e17 q^{79} -4.87813e17 q^{80} +2.25331e18 q^{81} -8.71457e16 q^{82} -1.14552e18 q^{83} +4.10832e18 q^{84} +5.16845e17 q^{85} -5.09092e18 q^{86} +5.76095e18 q^{87} +3.74123e18 q^{88} -2.76040e18 q^{89} +4.95191e18 q^{90} +2.21246e18 q^{91} +5.14254e17 q^{92} +6.84237e18 q^{93} +1.41604e18 q^{94} +1.63652e18 q^{95} -2.33979e18 q^{96} +8.03827e18 q^{97} +9.48266e18 q^{98} -1.37374e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9} - 197084160 q^{10} + 6183770516 q^{11} - 18595076275 q^{12} + 72670351796 q^{13} - 286195652197 q^{14} + 216978245574 q^{15} + 4395775708833 q^{16} + 1565738603712 q^{17} + 6109717535226 q^{18} + 3193929321662 q^{19} - 5906920535432 q^{20} - 7386396792532 q^{21} - 8877997844072 q^{22} - 24482520509106 q^{23} - 7153616576581 q^{24} + 205574470566045 q^{25} + 29760604099536 q^{26} + 37673737054348 q^{27} + 359478142575004 q^{28} + 236042103421602 q^{29} + 10\!\cdots\!54 q^{30}+ \cdots + 26\!\cdots\!62 q^{99}+O(q^{100}) \) 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9 - 197084160 * q^10 + 6183770516 * q^11 - 18595076275 * q^12 + 72670351796 * q^13 - 286195652197 * q^14 + 216978245574 * q^15 + 4395775708833 * q^16 + 1565738603712 * q^17 + 6109717535226 * q^18 + 3193929321662 * q^19 - 5906920535432 * q^20 - 7386396792532 * q^21 - 8877997844072 * q^22 - 24482520509106 * q^23 - 7153616576581 * q^24 + 205574470566045 * q^25 + 29760604099536 * q^26 + 37673737054348 * q^27 + 359478142575004 * q^28 + 236042103421602 * q^29 + 1030005166297154 * q^30 + 238097499775556 * q^31 + 980418196894414 * q^32 + 1875903246842268 * q^33 + 1649701857955214 * q^34 + 1575167660282324 * q^35 + 7318800726486641 * q^36 + 3601713987410012 * q^37 + 2042887131890906 * q^38 + 712786595145686 * q^39 - 38233381179154 * q^40 + 3933352398746224 * q^41 - 1818473706528187 * q^42 + 9956432184119776 * q^43 - 8374864809587786 * q^44 + 4814834336659374 * q^45 - 21420879452965494 * q^46 - 43646088451007913 * q^47 - 71590477049164572 * q^48 + 118361365545367441 * q^49 - 57666947668617547 * q^50 + 63071710735479788 * q^51 - 1295800694634632 * q^52 - 70710792109226748 * q^53 - 259379096268487409 * q^54 - 138894593750942388 * q^55 - 316931141949206936 * q^56 - 3219688617629350 * q^57 + 33593423193920552 * q^58 - 338601629983507156 * q^59 - 602000063011577726 * q^60 - 19162753603253692 * q^61 + 15505488837731256 * q^62 + 441133809282344796 * q^63 + 1575599177864752889 * q^64 + 991696997985687508 * q^65 - 223449751457078784 * q^66 + 789160046018441716 * q^67 + 793527065771503959 * q^68 + 1895066450986425554 * q^69 + 1371841313181399546 * q^70 + 901635006217520756 * q^71 + 4179441926330901705 * q^72 + 1704470931364824164 * q^73 - 936673704019194682 * q^74 + 2721299115185599300 * q^75 + 902909748895301048 * q^76 + 136895176815000502 * q^77 + 3735106483941260580 * q^78 - 384249994690730008 * q^79 - 1467637000368371240 * q^80 + 8095662645266644679 * q^81 + 6903936236738341456 * q^82 - 5730978816086659996 * q^83 - 10890678559479540867 * q^84 + 8583250605589725902 * q^85 + 15620118301833942618 * q^86 - 6279890617984303996 * q^87 + 17694374817110019346 * q^88 - 6455617251918472412 * q^89 - 170944452240128902 * q^90 - 1869573151265783134 * q^91 - 9347654291170404076 * q^92 + 11297106145565168410 * q^93 - 634546978249268889 * q^94 + 10375725689895196340 * q^95 + 38268359616807245724 * q^96 + 39090934998462984208 * q^97 + 41754136007920530767 * q^98 + 26521922158952497062 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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