LMFDB - Embedded newform 47.20.a.b.1.7

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			1.7
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)

$f(q)$	$=$	$q-1080.46 q^{2} -39593.4 q^{3} +643107. q^{4} +8.62657e6 q^{5} +4.27791e7 q^{6} -1.13132e8 q^{7} -1.28380e8 q^{8} +4.05374e8 q^{9} +O(q^{10})$	\(q-1080.46 q^{2} -39593.4 q^{3} +643107. q^{4} +8.62657e6 q^{5} +4.27791e7 q^{6} -1.13132e8 q^{7} -1.28380e8 q^{8} +4.05374e8 q^{9} -9.32067e9 q^{10} -7.29953e9 q^{11} -2.54628e10 q^{12} +5.60554e10 q^{13} +1.22234e11 q^{14} -3.41555e11 q^{15} -1.98464e11 q^{16} -8.31360e11 q^{17} -4.37991e11 q^{18} +2.22916e12 q^{19} +5.54781e12 q^{20} +4.47927e12 q^{21} +7.88685e12 q^{22} +6.38725e12 q^{23} +5.08298e12 q^{24} +5.53442e13 q^{25} -6.05656e13 q^{26} +2.99677e13 q^{27} -7.27559e13 q^{28} -5.23398e13 q^{29} +3.69037e14 q^{30} -7.78443e13 q^{31} +2.81741e14 q^{32} +2.89013e14 q^{33} +8.98252e14 q^{34} -9.75939e14 q^{35} +2.60699e14 q^{36} -2.80684e14 q^{37} -2.40852e15 q^{38} -2.21942e15 q^{39} -1.10748e15 q^{40} +2.10309e15 q^{41} -4.83968e15 q^{42} -1.60155e15 q^{43} -4.69438e15 q^{44} +3.49699e15 q^{45} -6.90118e15 q^{46} -1.11913e15 q^{47} +7.85787e15 q^{48} +1.39991e15 q^{49} -5.97972e16 q^{50} +3.29164e16 q^{51} +3.60496e16 q^{52} +1.90244e16 q^{53} -3.23790e16 q^{54} -6.29699e16 q^{55} +1.45238e16 q^{56} -8.82599e16 q^{57} +5.65511e16 q^{58} -6.49192e16 q^{59} -2.19656e17 q^{60} +1.11763e17 q^{61} +8.41077e16 q^{62} -4.58607e16 q^{63} -2.00357e17 q^{64} +4.83566e17 q^{65} -3.12267e17 q^{66} -3.69325e17 q^{67} -5.34654e17 q^{68} -2.52893e17 q^{69} +1.05446e18 q^{70} +3.81213e17 q^{71} -5.20418e16 q^{72} +7.52794e15 q^{73} +3.03269e17 q^{74} -2.19126e18 q^{75} +1.43359e18 q^{76} +8.25809e17 q^{77} +2.39800e18 q^{78} +6.63803e17 q^{79} -1.71207e18 q^{80} -1.65767e18 q^{81} -2.27230e18 q^{82} -1.09876e18 q^{83} +2.88065e18 q^{84} -7.17178e18 q^{85} +1.73041e18 q^{86} +2.07231e18 q^{87} +9.37111e17 q^{88} -2.45388e18 q^{89} -3.77836e18 q^{90} -6.34165e18 q^{91} +4.10769e18 q^{92} +3.08212e18 q^{93} +1.20918e18 q^{94} +1.92300e19 q^{95} -1.11551e19 q^{96} +1.12931e19 q^{97} -1.51255e18 q^{98} -2.95904e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1080.46	−1.49219	−0.746095	−	0.665840i	$-0.768073\pi$
$2$	−1080.46	−1.49219	−0.746095	+	0.665840i	$0.768073\pi$
$3$	−39593.4	−1.16137	−0.580685	−	0.814128i	$-0.697215\pi$
$3$	−39593.4	−1.16137	−0.580685	+	0.814128i	$0.697215\pi$
$4$	643107.	1.22663
$5$	8.62657e6	1.97525	0.987627	−	0.156822i	$-0.0501248\pi$
$5$	8.62657e6	1.97525	0.987627	+	0.156822i	$0.0501248\pi$
$6$	4.27791e7	1.73298
$7$	−1.13132e8	−1.05963	−0.529814	−	0.848114i	$-0.677738\pi$
$7$	−1.13132e8	−1.05963	−0.529814	+	0.848114i	$0.677738\pi$
$8$	−1.28380e8	−0.338175
$9$	4.05374e8	0.348780
$10$	−9.32067e9	−2.94745
$11$	−7.29953e9	−0.933392	−0.466696	−	0.884418i	$-0.654556\pi$
$11$	−7.29953e9	−0.933392	−0.466696	+	0.884418i	$0.654556\pi$
$12$	−2.54628e10	−1.42457
$13$	5.60554e10	1.46607	0.733036	−	0.680189i	$-0.238102\pi$
$13$	5.60554e10	1.46607	0.733036	+	0.680189i	$0.238102\pi$
$14$	1.22234e11	1.58117
$15$	−3.41555e11	−2.29400
$16$	−1.98464e11	−0.722009
$17$	−8.31360e11	−1.70030	−0.850148	−	0.526544i	$-0.823488\pi$
$17$	−8.31360e11	−1.70030	−0.850148	+	0.526544i	$0.823488\pi$
$18$	−4.37991e11	−0.520446
$19$	2.22916e12	1.58483	0.792413	−	0.609985i	$-0.208825\pi$
$19$	2.22916e12	1.58483	0.792413	+	0.609985i	$0.208825\pi$
$20$	5.54781e12	2.42291
$21$	4.47927e12	1.23062
$22$	7.88685e12	1.39280
$23$	6.38725e12	0.739434	0.369717	−	0.929144i	$-0.379455\pi$
$23$	6.38725e12	0.739434	0.369717	+	0.929144i	$0.379455\pi$
$24$	5.08298e12	0.392746
$25$	5.53442e13	2.90163
$26$	−6.05656e13	−2.18766
$27$	2.99677e13	0.756307
$28$	−7.27559e13	−1.29977
$29$	−5.23398e13	−0.669964	−0.334982	−	0.942225i	$-0.608730\pi$
$29$	−5.23398e13	−0.669964	−0.334982	+	0.942225i	$0.608730\pi$
$30$	3.69037e14	3.42308
$31$	−7.78443e13	−0.528799	−0.264399	−	0.964413i	$-0.585174\pi$
$31$	−7.78443e13	−0.528799	−0.264399	+	0.964413i	$0.585174\pi$
$32$	2.81741e14	1.41555
$33$	2.89013e14	1.08401
$34$	8.98252e14	2.53716
$35$	−9.75939e14	−2.09303
$36$	2.60699e14	0.427824
$37$	−2.80684e14	−0.355060	−0.177530	−	0.984115i	$-0.556811\pi$
$37$	−2.80684e14	−0.355060	−0.177530	+	0.984115i	$0.556811\pi$
$38$	−2.40852e15	−2.36486
$39$	−2.21942e15	−1.70265
$40$	−1.10748e15	−0.667981
$41$	2.10309e15	1.00325	0.501627	−	0.865084i	$-0.332735\pi$
$41$	2.10309e15	1.00325	0.501627	+	0.865084i	$0.332735\pi$
$42$	−4.83968e15	−1.83632
$43$	−1.60155e15	−0.485949	−0.242974	−	0.970033i	$-0.578123\pi$
$43$	−1.60155e15	−0.485949	−0.242974	+	0.970033i	$0.578123\pi$
$44$	−4.69438e15	−1.14493
$45$	3.49699e15	0.688930
$46$	−6.90118e15	−1.10338
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	7.85787e15	0.838520
$49$	1.39991e15	0.122811
$50$	−5.97972e16	−4.32978
$51$	3.29164e16	1.97467
$52$	3.60496e16	1.79833
$53$	1.90244e16	0.791935	0.395968	−	0.918264i	$-0.370409\pi$
$53$	1.90244e16	0.791935	0.395968	+	0.918264i	$0.370409\pi$
$54$	−3.23790e16	−1.12855
$55$	−6.29699e16	−1.84369
$56$	1.45238e16	0.358339
$57$	−8.82599e16	−1.84057
$58$	5.65511e16	0.999713
$59$	−6.49192e16	−0.975617	−0.487808	−	0.872951i	$-0.662204\pi$
$59$	−6.49192e16	−0.975617	−0.487808	+	0.872951i	$0.662204\pi$
$60$	−2.19656e17	−2.81389
$61$	1.11763e17	1.22367	0.611835	−	0.790986i	$-0.290432\pi$
$61$	1.11763e17	1.22367	0.611835	+	0.790986i	$0.290432\pi$
$62$	8.41077e16	0.789068
$63$	−4.58607e16	−0.369577
$64$	−2.00357e17	−1.39026
$65$	4.83566e17	2.89587
$66$	−3.12267e17	−1.61755
$67$	−3.69325e17	−1.65843	−0.829217	−	0.558927i	$-0.811213\pi$
$67$	−3.69325e17	−1.65843	−0.829217	+	0.558927i	$0.811213\pi$
$68$	−5.34654e17	−2.08563
$69$	−2.52893e17	−0.858757
$70$	1.05446e18	3.12320
$71$	3.81213e17	0.986765	0.493383	−	0.869812i	$-0.335760\pi$
$71$	3.81213e17	0.986765	0.493383	+	0.869812i	$0.335760\pi$
$72$	−5.20418e16	−0.117949
$73$	7.52794e15	0.0149661	0.00748306	−	0.999972i	$-0.497618\pi$
$73$	7.52794e15	0.0149661	0.00748306	+	0.999972i	$0.497618\pi$
$74$	3.03269e17	0.529817
$75$	−2.19126e18	−3.36986
$76$	1.43359e18	1.94399
$77$	8.25809e17	0.989048
$78$	2.39800e18	2.54068
$79$	6.63803e17	0.623134	0.311567	−	0.950224i	$-0.399146\pi$
$79$	6.63803e17	0.623134	0.311567	+	0.950224i	$0.399146\pi$
$80$	−1.71207e18	−1.42615
$81$	−1.65767e18	−1.22713
$82$	−2.27230e18	−1.49704
$83$	−1.09876e18	−0.645149	−0.322574	−	0.946544i	$-0.604548\pi$
$83$	−1.09876e18	−0.645149	−0.322574	+	0.946544i	$0.604548\pi$
$84$	2.88065e18	1.50952
$85$	−7.17178e18	−3.35852
$86$	1.73041e18	0.725128
$87$	2.07231e18	0.778076
$88$	9.37111e17	0.315650
$89$	−2.45388e18	−0.742418	−0.371209	−	0.928549i	$-0.621057\pi$
$89$	−2.45388e18	−0.742418	−0.371209	+	0.928549i	$0.621057\pi$
$90$	−3.77836e18	−1.02801
$91$	−6.34165e18	−1.55349
$92$	4.10769e18	0.907012
$93$	3.08212e18	0.614131
$94$	1.20918e18	0.217658
$95$	1.92300e19	3.13043
$96$	−1.11551e19	−1.64398
$97$	1.12931e19	1.50828	0.754139	−	0.656715i	$-0.228054\pi$
$97$	1.12931e19	1.50828	0.754139	+	0.656715i	$0.228054\pi$
$98$	−1.51255e18	−0.183258
$99$	−2.95904e18	−0.325549
$100$	3.55922e19	3.55922
$101$	−4.28598e18	−0.389940	−0.194970	−	0.980809i	$-0.562461\pi$
$101$	−4.28598e18	−0.389940	−0.194970	+	0.980809i	$0.562461\pi$
$102$	−3.55648e19	−2.94659
$103$	−6.94263e18	−0.524289	−0.262144	−	0.965029i	$-0.584430\pi$
$103$	−6.94263e18	−0.524289	−0.262144	+	0.965029i	$0.584430\pi$
$104$	−7.19637e18	−0.495789
$105$	3.86407e19	2.43079
$106$	−2.05551e19	−1.18172
$107$	−1.67462e19	−0.880583	−0.440291	−	0.897855i	$-0.645125\pi$
$107$	−1.67462e19	−0.880583	−0.440291	+	0.897855i	$0.645125\pi$
$108$	1.92725e19	0.927709
$109$	−1.13856e19	−0.502114	−0.251057	−	0.967972i	$-0.580778\pi$
$109$	−1.13856e19	−0.502114	−0.251057	+	0.967972i	$0.580778\pi$
$110$	6.80365e19	2.75113
$111$	1.11132e19	0.412356
$112$	2.24526e19	0.765061
$113$	−2.02772e19	−0.634983	−0.317492	−	0.948261i	$-0.602841\pi$
$113$	−2.02772e19	−0.634983	−0.317492	+	0.948261i	$0.602841\pi$
$114$	9.53613e19	2.74648
$115$	5.51001e19	1.46057
$116$	−3.36601e19	−0.821798
$117$	2.27234e19	0.511337
$118$	7.01427e19	1.45581
$119$	9.40533e19	1.80168
$120$	4.38487e19	0.775773
$121$	−7.87599e18	−0.128779
$122$	−1.20755e20	−1.82595
$123$	−8.32683e19	−1.16515
$124$	−5.00622e19	−0.648641
$125$	3.12891e20	3.75620
$126$	4.95507e19	0.551480
$127$	−2.07926e19	−0.214671	−0.107335	−	0.994223i	$-0.534232\pi$
$127$	−2.07926e19	−0.214671	−0.107335	+	0.994223i	$0.534232\pi$
$128$	6.87650e19	0.658981
$129$	6.34108e19	0.564366
$130$	−5.22474e20	−4.32118
$131$	−7.28557e19	−0.560255	−0.280128	−	0.959963i	$-0.590377\pi$
$131$	−7.28557e19	−0.560255	−0.280128	+	0.959963i	$0.590377\pi$
$132$	1.85866e20	1.32968
$133$	−2.52189e20	−1.67933
$134$	3.99041e20	2.47470
$135$	2.58519e20	1.49390
$136$	1.06730e20	0.574997
$137$	2.18735e20	1.09919	0.549595	−	0.835431i	$-0.314782\pi$
$137$	2.18735e20	1.09919	0.549595	+	0.835431i	$0.314782\pi$
$138$	2.73241e20	1.28143
$139$	1.74562e20	0.764381	0.382191	−	0.924084i	$-0.375170\pi$
$139$	1.74562e20	0.764381	0.382191	+	0.924084i	$0.375170\pi$
$140$	−6.27634e20	−2.56738
$141$	4.43102e19	0.169403
$142$	−4.11886e20	−1.47244
$143$	−4.09178e20	−1.36842
$144$	−8.04523e19	−0.251823
$145$	−4.51513e20	−1.32335
$146$	−8.13365e18	−0.0223323
$147$	−5.54272e19	−0.142629
$148$	−1.80510e20	−0.435528
$149$	−2.40351e20	−0.543971	−0.271985	−	0.962301i	$-0.587680\pi$
$149$	−2.40351e20	−0.543971	−0.271985	+	0.962301i	$0.587680\pi$
$150$	2.36757e21	5.02848
$151$	−2.35211e20	−0.469004	−0.234502	−	0.972116i	$-0.575346\pi$
$151$	−2.35211e20	−0.469004	−0.234502	+	0.972116i	$0.575346\pi$
$152$	−2.86178e20	−0.535948
$153$	−3.37012e20	−0.593030
$154$	−8.92254e20	−1.47585
$155$	−6.71529e20	−1.04451
$156$	−1.42733e21	−2.08853
$157$	1.48912e20	0.205061	0.102531	−	0.994730i	$-0.467306\pi$
$157$	1.48912e20	0.205061	0.102531	+	0.994730i	$0.467306\pi$
$158$	−7.17213e20	−0.929835
$159$	−7.53239e20	−0.919730
$160$	2.43046e21	2.79607
$161$	−7.22602e20	−0.783525
$162$	1.79105e21	1.83111
$163$	8.88271e20	0.856571	0.428286	−	0.903643i	$-0.359118\pi$
$163$	8.88271e20	0.856571	0.428286	+	0.903643i	$0.359118\pi$
$164$	1.35251e21	1.23062
$165$	2.49319e21	2.14120
$166$	1.18716e21	0.962685
$167$	−2.50973e21	−1.92230	−0.961150	−	0.276026i	$-0.910982\pi$
$167$	−2.50973e21	−1.92230	−0.961150	+	0.276026i	$0.910982\pi$
$168$	−5.75047e20	−0.416165
$169$	1.68029e21	1.14937
$170$	7.74883e21	5.01154
$171$	9.03642e20	0.552756
$172$	−1.02997e21	−0.596079
$173$	2.21499e21	1.21320	0.606601	−	0.795007i	$-0.292533\pi$
$173$	2.21499e21	1.21320	0.606601	+	0.795007i	$0.292533\pi$
$174$	−2.23905e21	−1.16104
$175$	−6.26119e21	−3.07465
$176$	1.44870e21	0.673918
$177$	2.57037e21	1.13305
$178$	2.65132e21	1.10783
$179$	5.13600e20	0.203480	0.101740	−	0.994811i	$-0.467559\pi$
$179$	5.13600e20	0.203480	0.101740	+	0.994811i	$0.467559\pi$
$180$	2.24894e21	0.845062
$181$	−4.20314e21	−1.49840	−0.749199	−	0.662345i	$-0.769561\pi$
$181$	−4.20314e21	−1.49840	−0.749199	+	0.662345i	$0.769561\pi$
$182$	6.85190e21	2.31810
$183$	−4.42507e21	−1.42113
$184$	−8.19993e20	−0.250058
$185$	−2.42134e21	−0.701334
$186$	−3.33011e21	−0.916400
$187$	6.06854e21	1.58704
$188$	−7.19721e20	−0.178922
$189$	−3.39030e21	−0.801404
$190$	−2.07772e22	−4.67120
$191$	−1.14944e21	−0.245851	−0.122925	−	0.992416i	$-0.539228\pi$
$191$	−1.14944e21	−0.245851	−0.122925	+	0.992416i	$0.539228\pi$
$192$	7.93283e21	1.61460
$193$	8.17072e21	1.58294	0.791472	−	0.611205i	$-0.209315\pi$
$193$	8.17072e21	1.58294	0.791472	+	0.611205i	$0.209315\pi$
$194$	−1.22017e22	−2.25064
$195$	−1.91460e22	−3.36317
$196$	9.00293e20	0.150644
$197$	1.07750e22	1.71786	0.858928	−	0.512096i	$-0.171131\pi$
$197$	1.07750e22	1.71786	0.858928	+	0.512096i	$0.171131\pi$
$198$	3.19712e21	0.485781
$199$	1.14964e20	0.0166516	0.00832580	−	0.999965i	$-0.497350\pi$
$199$	1.14964e20	0.0166516	0.00832580	+	0.999965i	$0.497350\pi$
$200$	−7.10506e21	−0.981258
$201$	1.46228e22	1.92606
$202$	4.63084e21	0.581864
$203$	5.92130e21	0.709912
$204$	2.11688e22	2.42219
$205$	1.81424e22	1.98168
$206$	7.50124e21	0.782339
$207$	2.58923e21	0.257900
$208$	−1.11250e22	−1.05852
$209$	−1.62718e22	−1.47926
$210$	−4.17498e22	−3.62720
$211$	−2.12094e22	−1.76135	−0.880675	−	0.473721i	$-0.842910\pi$
$211$	−2.12094e22	−1.76135	−0.880675	+	0.473721i	$0.842910\pi$
$212$	1.22347e22	0.971412
$213$	−1.50935e22	−1.14600
$214$	1.80936e22	1.31400
$215$	−1.38159e22	−0.959872
$216$	−3.84725e21	−0.255764
$217$	8.80666e21	0.560330
$218$	1.23016e22	0.749250
$219$	−2.98057e20	−0.0173812
$220$	−4.04964e22	−2.26152
$221$	−4.66022e22	−2.49276
$222$	−1.20074e22	−0.615314
$223$	4.90057e21	0.240630	0.120315	−	0.992736i	$-0.461610\pi$
$223$	4.90057e21	0.240630	0.120315	+	0.992736i	$0.461610\pi$
$224$	−3.18738e22	−1.49996
$225$	2.24351e22	1.01203
$226$	2.19087e22	0.947516
$227$	3.52851e22	1.46334	0.731671	−	0.681658i	$-0.238741\pi$
$227$	3.52851e22	1.46334	0.731671	+	0.681658i	$0.238741\pi$
$228$	−5.67606e22	−2.25770
$229$	3.74557e22	1.42916	0.714580	−	0.699553i	$-0.246618\pi$
$229$	3.74557e22	1.42916	0.714580	+	0.699553i	$0.246618\pi$
$230$	−5.95335e22	−2.17945
$231$	−3.26966e22	−1.14865
$232$	6.71937e21	0.226565
$233$	1.34899e22	0.436645	0.218322	−	0.975877i	$-0.429942\pi$
$233$	1.34899e22	0.436645	0.218322	+	0.975877i	$0.429942\pi$
$234$	−2.45517e22	−0.763012
$235$	−9.65425e21	−0.288120
$236$	−4.17500e22	−1.19672
$237$	−2.62822e22	−0.723690
$238$	−1.01621e23	−2.68845
$239$	1.28652e22	0.327066	0.163533	−	0.986538i	$-0.447711\pi$
$239$	1.28652e22	0.327066	0.163533	+	0.986538i	$0.447711\pi$
$240$	6.77865e22	1.65629
$241$	−7.06032e22	−1.65830	−0.829149	−	0.559027i	$-0.811175\pi$
$241$	−7.06032e22	−1.65830	−0.829149	+	0.559027i	$0.811175\pi$
$242$	8.50970e21	0.192162
$243$	3.08026e22	0.668848
$244$	7.18755e22	1.50099
$245$	1.20764e22	0.242583
$246$	8.99682e22	1.73862
$247$	1.24956e23	2.32347
$248$	9.99362e21	0.178826
$249$	4.35035e22	0.749257
$250$	−3.38067e23	−5.60496
$251$	4.49294e22	0.717184	0.358592	−	0.933494i	$-0.383257\pi$
$251$	4.49294e22	0.717184	0.358592	+	0.933494i	$0.383257\pi$
$252$	−2.94933e22	−0.453335
$253$	−4.66239e22	−0.690182
$254$	2.24655e22	0.320329
$255$	2.83955e23	3.90048
$256$	3.07471e22	0.406935
$257$	1.07614e23	1.37247	0.686237	−	0.727378i	$-0.259261\pi$
$257$	1.07614e23	1.37247	0.686237	+	0.727378i	$0.259261\pi$
$258$	−6.85129e22	−0.842141
$259$	3.17543e22	0.376232
$260$	3.10985e23	3.55216
$261$	−2.12172e22	−0.233670
$262$	7.87177e22	0.836007
$263$	2.21733e22	0.227118	0.113559	−	0.993531i	$-0.463775\pi$
$263$	2.21733e22	0.227118	0.113559	+	0.993531i	$0.463775\pi$
$264$	−3.71034e22	−0.366586
$265$	1.64115e23	1.56427
$266$	2.72480e23	2.50587
$267$	9.71574e22	0.862222
$268$	−2.37516e23	−2.03429
$269$	4.86064e22	0.401834	0.200917	−	0.979608i	$-0.435608\pi$
$269$	4.86064e22	0.401834	0.200917	+	0.979608i	$0.435608\pi$
$270$	−2.79319e23	−2.22918
$271$	4.08472e22	0.314741	0.157371	−	0.987540i	$-0.449698\pi$
$271$	4.08472e22	0.314741	0.157371	+	0.987540i	$0.449698\pi$
$272$	1.64995e23	1.22763
$273$	2.51087e23	1.80418
$274$	−2.36334e23	−1.64020
$275$	−4.03986e23	−2.70836
$276$	−1.62637e23	−1.05338
$277$	1.04760e23	0.655598	0.327799	−	0.944748i	$-0.393693\pi$
$277$	1.04760e23	0.655598	0.327799	+	0.944748i	$0.393693\pi$
$278$	−1.88608e23	−1.14060
$279$	−3.15560e22	−0.184435
$280$	1.25291e23	0.707811
$281$	8.01354e22	0.437637	0.218819	−	0.975766i	$-0.429780\pi$
$281$	8.01354e22	0.437637	0.218819	+	0.975766i	$0.429780\pi$
$282$	−4.78754e22	−0.252782
$283$	2.17193e23	1.10885	0.554427	−	0.832233i	$-0.312938\pi$
$283$	2.17193e23	1.10885	0.554427	+	0.832233i	$0.312938\pi$
$284$	2.45161e23	1.21040
$285$	−7.61380e23	−3.63559
$286$	4.42101e23	2.04194
$287$	−2.37926e23	−1.06308
$288$	1.14210e23	0.493716
$289$	4.52087e23	1.89101
$290$	4.87842e23	1.97469
$291$	−4.47132e23	−1.75167
$292$	4.84128e21	0.0183579
$293$	−4.01186e23	−1.47266	−0.736332	−	0.676621i	$-0.763444\pi$
$293$	−4.01186e23	−1.47266	−0.736332	+	0.676621i	$0.763444\pi$
$294$	5.98869e22	0.212830
$295$	−5.60030e23	−1.92709
$296$	3.60342e22	0.120072
$297$	−2.18750e23	−0.705931
$298$	2.59689e23	0.811708
$299$	3.58040e23	1.08406
$300$	−1.40922e24	−4.13358
$301$	1.81186e23	0.514925
$302$	2.54136e23	0.699844
$303$	1.69697e23	0.452864
$304$	−4.42408e23	−1.14426
$305$	9.64130e23	2.41706
$306$	3.64128e23	0.884913
$307$	3.26155e23	0.768438	0.384219	−	0.923242i	$-0.374471\pi$
$307$	3.26155e23	0.768438	0.384219	+	0.923242i	$0.374471\pi$
$308$	5.31084e23	1.21320
$309$	2.74882e23	0.608893
$310$	7.25560e23	1.55861
$311$	−3.82878e23	−0.797696	−0.398848	−	0.917017i	$-0.630590\pi$
$311$	−3.82878e23	−0.797696	−0.398848	+	0.917017i	$0.630590\pi$
$312$	2.84929e23	0.575794
$313$	−4.95374e22	−0.0971095	−0.0485548	−	0.998821i	$-0.515462\pi$
$313$	−4.95374e22	−0.0971095	−0.0485548	+	0.998821i	$0.515462\pi$
$314$	−1.60894e23	−0.305990
$315$	−3.95620e23	−0.730009
$316$	4.26897e23	0.764355
$317$	8.64076e23	1.50137	0.750687	−	0.660658i	$-0.229723\pi$
$317$	8.64076e23	1.50137	0.750687	+	0.660658i	$0.229723\pi$
$318$	8.13846e23	1.37241
$319$	3.82056e23	0.625339
$320$	−1.72840e24	−2.74611
$321$	6.63038e23	1.02268
$322$	7.80743e23	1.16917
$323$	−1.85323e24	−2.69467
$324$	−1.06606e24	−1.50524
$325$	3.10234e24	4.25400
$326$	−9.59742e23	−1.27817
$327$	4.50793e23	0.583140
$328$	−2.69994e23	−0.339275
$329$	1.26609e23	0.154563
$330$	−2.69379e24	−3.19508
$331$	9.73403e23	1.12183	0.560915	−	0.827873i	$-0.310449\pi$
$331$	9.73403e23	1.12183	0.560915	+	0.827873i	$0.310449\pi$
$332$	−7.06619e23	−0.791359
$333$	−1.13782e23	−0.123838
$334$	2.71167e24	2.86844
$335$	−3.18601e24	−3.27583
$336$	−8.88975e23	−0.888519
$337$	1.59103e23	0.154594	0.0772972	−	0.997008i	$-0.475371\pi$
$337$	1.59103e23	0.154594	0.0772972	+	0.997008i	$0.475371\pi$
$338$	−1.81548e24	−1.71508
$339$	8.02842e23	0.737451
$340$	−4.61223e24	−4.11966
$341$	5.68226e23	0.493577
$342$	−9.76350e23	−0.824817
$343$	1.13120e24	0.929494
$344$	2.05607e23	0.164336
$345$	−2.18160e24	−1.69626
$346$	−2.39320e24	−1.81033
$347$	1.45729e24	1.07255	0.536275	−	0.844044i	$-0.319831\pi$
$347$	1.45729e24	1.07255	0.536275	+	0.844044i	$0.319831\pi$
$348$	1.33272e24	0.954411
$349$	1.37820e24	0.960440	0.480220	−	0.877148i	$-0.340557\pi$
$349$	1.37820e24	0.960440	0.480220	+	0.877148i	$0.340557\pi$
$350$	6.76496e24	4.58795
$351$	1.67985e24	1.10880
$352$	−2.05657e24	−1.32126
$353$	−6.15941e23	−0.385194	−0.192597	−	0.981278i	$-0.561691\pi$
$353$	−6.15941e23	−0.385194	−0.192597	+	0.981278i	$0.561691\pi$
$354$	−2.77719e24	−1.69073
$355$	3.28856e24	1.94911
$356$	−1.57811e24	−0.910672
$357$	−3.72389e24	−2.09242
$358$	−5.54925e23	−0.303631
$359$	−3.26739e24	−1.74102	−0.870509	−	0.492153i	$-0.836210\pi$
$359$	−3.26739e24	−1.74102	−0.870509	+	0.492153i	$0.836210\pi$
$360$	−4.48942e23	−0.232979
$361$	2.99072e24	1.51167
$362$	4.54133e24	2.23589
$363$	3.11837e23	0.149560
$364$	−4.07836e24	−1.90556
$365$	6.49403e22	0.0295619
$366$	4.78111e24	2.12060
$367$	8.29715e23	0.358592	0.179296	−	0.983795i	$-0.442618\pi$
$367$	8.29715e23	0.358592	0.179296	+	0.983795i	$0.442618\pi$
$368$	−1.26764e24	−0.533878
$369$	8.52537e23	0.349915
$370$	2.61617e24	1.04652
$371$	−2.15226e24	−0.839157
$372$	1.98213e24	0.753312
$373$	1.79169e24	0.663789	0.331894	−	0.943317i	$-0.392312\pi$
$373$	1.79169e24	0.663789	0.331894	+	0.943317i	$0.392312\pi$
$374$	−6.55682e24	−2.36817
$375$	−1.23884e25	−4.36234
$376$	1.43674e23	0.0493279
$377$	−2.93393e24	−0.982216
$378$	3.66309e24	1.19585
$379$	−1.66070e24	−0.528713	−0.264356	−	0.964425i	$-0.585159\pi$
$379$	−1.66070e24	−0.528713	−0.264356	+	0.964425i	$0.585159\pi$
$380$	1.23669e25	3.83988
$381$	8.23248e23	0.249312
$382$	1.24193e24	0.366856
$383$	1.49557e23	0.0430943	0.0215471	−	0.999768i	$-0.493141\pi$
$383$	1.49557e23	0.0430943	0.0215471	+	0.999768i	$0.493141\pi$
$384$	−2.72264e24	−0.765320
$385$	7.12389e24	1.95362
$386$	−8.82814e24	−2.36205
$387$	−6.49227e23	−0.169489
$388$	7.26267e24	1.85010
$389$	3.60368e24	0.895829	0.447915	−	0.894076i	$-0.352167\pi$
$389$	3.60368e24	0.895829	0.447915	+	0.894076i	$0.352167\pi$
$390$	2.06865e25	5.01849
$391$	−5.31011e24	−1.25726
$392$	−1.79720e23	−0.0415316
$393$	2.88460e24	0.650664
$394$	−1.16419e25	−2.56337
$395$	5.72634e24	1.23085
$396$	−1.90298e24	−0.399328
$397$	1.04079e24	0.213233	0.106617	−	0.994300i	$-0.465998\pi$
$397$	1.04079e24	0.213233	0.106617	+	0.994300i	$0.465998\pi$
$398$	−1.24214e23	−0.0248473
$399$	9.98500e24	1.95032
$400$	−1.09838e25	−2.09500
$401$	−1.37624e24	−0.256343	−0.128171	−	0.991752i	$-0.540911\pi$
$401$	−1.37624e24	−0.256343	−0.128171	+	0.991752i	$0.540911\pi$
$402$	−1.57994e25	−2.87404
$403$	−4.36359e24	−0.775258
$404$	−2.75635e24	−0.478312
$405$	−1.43000e25	−2.42390
$406$	−6.39773e24	−1.05932
$407$	2.04886e24	0.331411
$408$	−4.22579e24	−0.667785
$409$	7.99761e24	1.23478	0.617388	−	0.786658i	$-0.288191\pi$
$409$	7.99761e24	1.23478	0.617388	+	0.786658i	$0.288191\pi$
$410$	−1.96022e25	−2.95704
$411$	−8.66045e24	−1.27657
$412$	−4.46486e24	−0.643108
$413$	7.34443e24	1.03379
$414$	−2.79756e24	−0.384836
$415$	−9.47851e24	−1.27433
$416$	1.57931e25	2.07530
$417$	−6.91151e24	−0.887729
$418$	1.75810e25	2.20734
$419$	−6.45094e24	−0.791754	−0.395877	−	0.918304i	$-0.629559\pi$
$419$	−6.45094e24	−0.791754	−0.395877	+	0.918304i	$0.629559\pi$
$420$	2.48501e25	2.98168
$421$	−5.73720e24	−0.673007	−0.336504	−	0.941682i	$-0.609244\pi$
$421$	−5.73720e24	−0.673007	−0.336504	+	0.941682i	$0.609244\pi$
$422$	2.29160e25	2.62827
$423$	−4.53666e23	−0.0508748
$424$	−2.44234e24	−0.267813
$425$	−4.60109e25	−4.93363
$426$	1.63080e25	1.71005
$427$	−1.26439e25	−1.29663
$428$	−1.07696e25	−1.08015
$429$	1.62007e25	1.58924
$430$	1.49275e25	1.43231
$431$	1.02326e24	0.0960401	0.0480201	−	0.998846i	$-0.484709\pi$
$431$	1.02326e24	0.0960401	0.0480201	+	0.998846i	$0.484709\pi$
$432$	−5.94753e24	−0.546060
$433$	9.06423e24	0.814134	0.407067	−	0.913398i	$-0.366551\pi$
$433$	9.06423e24	0.814134	0.407067	+	0.913398i	$0.366551\pi$
$434$	−9.51525e24	−0.836119
$435$	1.78769e25	1.53690
$436$	−7.32214e24	−0.615908
$437$	1.42382e25	1.17187
$438$	3.22039e23	0.0259360
$439$	4.22149e24	0.332700	0.166350	−	0.986067i	$-0.446802\pi$
$439$	4.22149e24	0.332700	0.166350	+	0.986067i	$0.446802\pi$
$440$	8.08405e24	0.623488
$441$	5.67488e23	0.0428341
$442$	5.03519e25	3.71967
$443$	8.18313e24	0.591676	0.295838	−	0.955238i	$-0.404401\pi$
$443$	8.18313e24	0.591676	0.295838	+	0.955238i	$0.404401\pi$
$444$	7.14701e24	0.505809
$445$	−2.11686e25	−1.46646
$446$	−5.29487e24	−0.359066
$447$	9.51629e24	0.631752
$448$	2.26668e25	1.47316
$449$	2.33566e25	1.48617	0.743085	−	0.669197i	$-0.233362\pi$
$449$	2.33566e25	1.48617	0.743085	+	0.669197i	$0.233362\pi$
$450$	−2.42402e25	−1.51014
$451$	−1.53515e25	−0.936429
$452$	−1.30404e25	−0.778890
$453$	9.31281e24	0.544688
$454$	−3.81241e25	−2.18358
$455$	−5.47066e25	−3.06854
$456$	1.13308e25	0.622434
$457$	9.51260e24	0.511794	0.255897	−	0.966704i	$-0.417629\pi$
$457$	9.51260e24	0.511794	0.255897	+	0.966704i	$0.417629\pi$
$458$	−4.04694e25	−2.13258
$459$	−2.49140e25	−1.28595
$460$	3.54353e25	1.79158
$461$	5.56936e24	0.275833	0.137917	−	0.990444i	$-0.455959\pi$
$461$	5.56936e24	0.275833	0.137917	+	0.990444i	$0.455959\pi$
$462$	3.53273e25	1.71401
$463$	−1.46433e25	−0.696019	−0.348009	−	0.937491i	$-0.613142\pi$
$463$	−1.46433e25	−0.696019	−0.348009	+	0.937491i	$0.613142\pi$
$464$	1.03876e25	0.483720
$465$	2.65881e25	1.21307
$466$	−1.45753e25	−0.651557
$467$	2.75931e24	0.120862	0.0604310	−	0.998172i	$-0.480752\pi$
$467$	2.75931e24	0.120862	0.0604310	+	0.998172i	$0.480752\pi$
$468$	1.46136e25	0.627222
$469$	4.17824e25	1.75732
$470$	1.04310e25	0.429930
$471$	−5.89594e24	−0.238152
$472$	8.33431e24	0.329929
$473$	1.16906e25	0.453581
$474$	2.83969e25	1.07988
$475$	1.23371e26	4.59857
$476$	6.04864e25	2.21000
$477$	7.71199e24	0.276211
$478$	−1.39003e25	−0.488044
$479$	1.23869e25	0.426360	0.213180	−	0.977013i	$-0.431618\pi$
$479$	1.23869e25	0.426360	0.213180	+	0.977013i	$0.431618\pi$
$480$	−9.62299e25	−3.24727
$481$	−1.57339e25	−0.520544
$482$	7.62840e25	2.47450
$483$	2.86102e25	0.909963
$484$	−5.06511e24	−0.157964
$485$	9.74206e25	2.97923
$486$	−3.32810e25	−0.998048
$487$	−1.91495e25	−0.563160	−0.281580	−	0.959538i	$-0.590858\pi$
$487$	−1.91495e25	−0.563160	−0.281580	+	0.959538i	$0.590858\pi$
$488$	−1.43481e25	−0.413814
$489$	−3.51697e25	−0.994796
$490$	−1.30481e25	−0.361980
$491$	−4.84924e25	−1.31947	−0.659735	−	0.751498i	$-0.729331\pi$
$491$	−4.84924e25	−1.31947	−0.659735	+	0.751498i	$0.729331\pi$
$492$	−5.35505e25	−1.42921
$493$	4.35133e25	1.13914
$494$	−1.35010e26	−3.46706
$495$	−2.55263e25	−0.643042
$496$	1.54493e25	0.381798
$497$	−4.31274e25	−1.04560
$498$	−4.70038e25	−1.11803
$499$	5.96791e25	1.39273	0.696365	−	0.717688i	$-0.254799\pi$
$499$	5.96791e25	1.39273	0.696365	+	0.717688i	$0.254799\pi$
$500$	2.01223e26	4.60746
$501$	9.93689e25	2.23250
$502$	−4.85445e25	−1.07017
$503$	−1.64082e25	−0.354948	−0.177474	−	0.984126i	$-0.556793\pi$
$503$	−1.64082e25	−0.354948	−0.177474	+	0.984126i	$0.556793\pi$
$504$	5.88758e24	0.124982
$505$	−3.69733e25	−0.770230
$506$	5.03753e25	1.02988
$507$	−6.65282e25	−1.33484
$508$	−1.33719e25	−0.263321
$509$	−7.95536e25	−1.53759	−0.768796	−	0.639495i	$-0.779144\pi$
$509$	−7.95536e25	−1.53759	−0.768796	+	0.639495i	$0.779144\pi$
$510$	−3.06802e26	−5.82026
$511$	−8.51650e23	−0.0158585
$512$	−6.92737e25	−1.26620
$513$	6.68028e25	1.19861
$514$	−1.16273e26	−2.04799
$515$	−5.98911e25	−1.03560
$516$	4.07800e25	0.692269
$517$	8.16912e24	0.136149
$518$	−3.43093e25	−0.561409
$519$	−8.76988e25	−1.40898
$520$	−6.20800e25	−0.979309
$521$	8.74177e24	0.135407	0.0677035	−	0.997705i	$-0.478433\pi$
$521$	8.74177e24	0.135407	0.0677035	+	0.997705i	$0.478433\pi$
$522$	2.29244e25	0.348680
$523$	7.37236e25	1.10113	0.550567	−	0.834791i	$-0.314411\pi$
$523$	7.37236e25	1.10113	0.550567	+	0.834791i	$0.314411\pi$
$524$	−4.68540e25	−0.687226
$525$	2.47901e26	3.57080
$526$	−2.39574e25	−0.338903
$527$	6.47166e25	0.899115
$528$	−5.73588e25	−0.782668
$529$	−3.38185e25	−0.453237
$530$	−1.77320e26	−2.33419
$531$	−2.63166e25	−0.340276
$532$	−1.62184e26	−2.05991
$533$	1.17889e26	1.47084
$534$	−1.04975e26	−1.28660
$535$	−1.44462e26	−1.73937
$536$	4.74138e25	0.560841
$537$	−2.03352e25	−0.236315
$538$	−5.25173e25	−0.599613
$539$	−1.02187e25	−0.114631
$540$	1.66255e26	1.83246
$541$	5.09247e25	0.551512	0.275756	−	0.961228i	$-0.411072\pi$
$541$	5.09247e25	0.551512	0.275756	+	0.961228i	$0.411072\pi$
$542$	−4.41338e25	−0.469654
$543$	1.66416e26	1.74020
$544$	−2.34228e26	−2.40685
$545$	−9.82183e25	−0.991803
$546$	−2.71290e26	−2.69218
$547$	1.09334e26	1.06629	0.533144	−	0.846025i	$-0.321011\pi$
$547$	1.09334e26	1.06629	0.533144	+	0.846025i	$0.321011\pi$
$548$	1.40670e26	1.34830
$549$	4.53058e25	0.426792
$550$	4.36491e26	4.04138
$551$	−1.16674e26	−1.06178
$552$	3.24663e25	0.290410
$553$	−7.50972e25	−0.660291
$554$	−1.13189e26	−0.978276
$555$	9.58692e25	0.814508
$556$	1.12262e26	0.937613
$557$	1.33109e26	1.09290	0.546451	−	0.837491i	$-0.315978\pi$
$557$	1.33109e26	1.09290	0.546451	+	0.837491i	$0.315978\pi$
$558$	3.40951e25	0.275212
$559$	−8.97756e25	−0.712436
$560$	1.93689e26	1.51119
$561$	−2.40274e26	−1.84314
$562$	−8.65831e25	−0.653038
$563$	8.59090e25	0.637102	0.318551	−	0.947906i	$-0.396804\pi$
$563$	8.59090e25	0.637102	0.318551	+	0.947906i	$0.396804\pi$
$564$	2.84962e25	0.207795
$565$	−1.74922e26	−1.25425
$566$	−2.34668e26	−1.65462
$567$	1.87536e26	1.30030
$568$	−4.89400e25	−0.333699
$569$	−1.30684e26	−0.876309	−0.438154	−	0.898900i	$-0.644368\pi$
$569$	−1.30684e26	−0.876309	−0.438154	+	0.898900i	$0.644368\pi$
$570$	8.22641e26	5.42499
$571$	7.02595e25	0.455682	0.227841	−	0.973698i	$-0.426833\pi$
$571$	7.02595e25	0.455682	0.227841	+	0.973698i	$0.426833\pi$
$572$	−2.63145e26	−1.67855
$573$	4.55104e25	0.285523
$574$	2.57070e26	1.58631
$575$	3.53497e26	2.14556
$576$	−8.12197e25	−0.484895
$577$	−2.17407e25	−0.127674	−0.0638372	−	0.997960i	$-0.520334\pi$
$577$	−2.17407e25	−0.127674	−0.0638372	+	0.997960i	$0.520334\pi$
$578$	−4.88463e26	−2.82174
$579$	−3.23506e26	−1.83838
$580$	−2.90371e26	−1.62326
$581$	1.24304e26	0.683618
$582$	4.83108e26	2.61382
$583$	−1.38869e26	−0.739186
$584$	−9.66435e23	−0.00506116
$585$	1.96025e26	1.01002
$586$	4.33466e26	2.19749
$587$	1.69254e26	0.844259	0.422130	−	0.906535i	$-0.361283\pi$
$587$	1.69254e26	0.844259	0.422130	+	0.906535i	$0.361283\pi$
$588$	−3.56456e25	−0.174953
$589$	−1.73527e26	−0.838054
$590$	6.05090e26	2.87558
$591$	−4.26617e26	−1.99507
$592$	5.57059e25	0.256357
$593$	−3.21838e26	−1.45753	−0.728765	−	0.684764i	$-0.759905\pi$
$593$	−3.21838e26	−1.45753	−0.728765	+	0.684764i	$0.759905\pi$
$594$	2.36351e26	1.05338
$595$	8.11357e26	3.55878
$596$	−1.54571e26	−0.667251
$597$	−4.55179e24	−0.0193387
$598$	−3.86848e26	−1.61763
$599$	−6.65091e25	−0.273732	−0.136866	−	0.990590i	$-0.543703\pi$
$599$	−6.65091e25	−0.273732	−0.136866	+	0.990590i	$0.543703\pi$
$600$	2.81313e26	1.13960
$601$	6.28896e25	0.250768	0.125384	−	0.992108i	$-0.459984\pi$
$601$	6.28896e25	0.250768	0.125384	+	0.992108i	$0.459984\pi$
$602$	−1.95765e26	−0.768365
$603$	−1.49715e26	−0.578429
$604$	−1.51266e26	−0.575295
$605$	−6.79428e25	−0.254371
$606$	−1.83350e26	−0.675759
$607$	4.09760e26	1.48675	0.743373	−	0.668877i	$-0.233225\pi$
$607$	4.09760e26	1.48675	0.743373	+	0.668877i	$0.233225\pi$
$608$	6.28045e26	2.24340
$609$	−2.34444e26	−0.824471
$610$	−1.04170e27	−3.60671
$611$	−6.27333e25	−0.213849
$612$	−2.16735e26	−0.727428
$613$	9.92594e25	0.328018	0.164009	−	0.986459i	$-0.447557\pi$
$613$	9.92594e25	0.328018	0.164009	+	0.986459i	$0.447557\pi$
$614$	−3.52397e26	−1.14666
$615$	−7.18320e26	−2.30146
$616$	−1.06017e26	−0.334471
$617$	1.95800e26	0.608282	0.304141	−	0.952627i	$-0.401631\pi$
$617$	1.95800e26	0.608282	0.304141	+	0.952627i	$0.401631\pi$
$618$	−2.97000e26	−0.908584
$619$	1.59380e26	0.480147	0.240073	−	0.970755i	$-0.422829\pi$
$619$	1.59380e26	0.480147	0.240073	+	0.970755i	$0.422829\pi$
$620$	−4.31865e26	−1.28123
$621$	1.91411e26	0.559239
$622$	4.13685e26	1.19031
$623$	2.77612e26	0.786686
$624$	4.40476e26	1.22933
$625$	1.64357e27	4.51782
$626$	5.35232e25	0.144906
$627$	6.44255e26	1.71797
$628$	9.57665e25	0.251534
$629$	2.33350e26	0.603707
$630$	4.27452e26	1.08931
$631$	−2.56830e26	−0.644714	−0.322357	−	0.946618i	$-0.604475\pi$
$631$	−2.56830e26	−0.644714	−0.322357	+	0.946618i	$0.604475\pi$
$632$	−8.52188e25	−0.210728
$633$	8.39753e26	2.04558
$634$	−9.33600e26	−2.24034
$635$	−1.79368e26	−0.424029
$636$	−4.84414e26	−1.12817
$637$	7.84726e25	0.180050
$638$	−4.12797e26	−0.933124
$639$	1.54534e26	0.344164
$640$	5.93206e26	1.30165
$641$	−4.40974e25	−0.0953370	−0.0476685	−	0.998863i	$-0.515179\pi$
$641$	−4.40974e25	−0.0953370	−0.0476685	+	0.998863i	$0.515179\pi$
$642$	−7.16387e26	−1.52604
$643$	−2.50558e26	−0.525900	−0.262950	−	0.964809i	$-0.584695\pi$
$643$	−2.50558e26	−0.525900	−0.262950	+	0.964809i	$0.584695\pi$
$644$	−4.64710e26	−0.961096
$645$	5.47018e26	1.11477
$646$	2.00235e27	4.02096
$647$	−4.51427e26	−0.893298	−0.446649	−	0.894709i	$-0.647383\pi$
$647$	−4.51427e26	−0.893298	−0.446649	+	0.894709i	$0.647383\pi$
$648$	2.12812e26	0.414985
$649$	4.73880e26	0.910633
$650$	−3.35195e27	−6.34777
$651$	−3.48686e26	−0.650751
$652$	5.71254e26	1.05070
$653$	−6.29881e26	−1.14178	−0.570891	−	0.821026i	$-0.693402\pi$
$653$	−6.29881e26	−1.14178	−0.570891	+	0.821026i	$0.693402\pi$
$654$	−4.87064e26	−0.870156
$655$	−6.28494e26	−1.10665
$656$	−4.17388e26	−0.724358
$657$	3.05163e24	0.00521989
$658$	−1.36796e26	−0.230637
$659$	−7.78409e26	−1.29359	−0.646794	−	0.762664i	$-0.723891\pi$
$659$	−7.78409e26	−1.29359	−0.646794	+	0.762664i	$0.723891\pi$
$660$	1.60339e27	2.62646
$661$	4.87326e26	0.786875	0.393437	−	0.919351i	$-0.371286\pi$
$661$	4.87326e26	0.786875	0.393437	+	0.919351i	$0.371286\pi$
$662$	−1.05172e27	−1.67398
$663$	1.84514e27	2.89501
$664$	1.41058e26	0.218173
$665$	−2.17552e27	−3.31709
$666$	1.22937e26	0.184790
$667$	−3.34308e26	−0.495394
$668$	−1.61403e27	−2.35795
$669$	−1.94030e26	−0.279461
$670$	3.44236e27	4.88816
$671$	−8.15816e26	−1.14216
$672$	1.26199e27	1.74200
$673$	6.15031e25	0.0837055	0.0418527	−	0.999124i	$-0.486674\pi$
$673$	6.15031e25	0.0837055	0.0418527	+	0.999124i	$0.486674\pi$
$674$	−1.71904e26	−0.230684
$675$	1.65854e27	2.19452
$676$	1.08060e27	1.40985
$677$	1.10103e27	1.41647	0.708237	−	0.705975i	$-0.249491\pi$
$677$	1.10103e27	1.41647	0.708237	+	0.705975i	$0.249491\pi$
$678$	−8.67439e26	−1.10042
$679$	−1.27761e27	−1.59821
$680$	9.20711e26	1.13577
$681$	−1.39706e27	−1.69948
$682$	−6.13946e26	−0.736510
$683$	−2.06568e26	−0.244380	−0.122190	−	0.992507i	$-0.538992\pi$
$683$	−2.06568e26	−0.244380	−0.122190	+	0.992507i	$0.538992\pi$
$684$	5.81139e26	0.678027
$685$	1.88693e27	2.17118
$686$	−1.22222e27	−1.38698
$687$	−1.48300e27	−1.65978
$688$	3.17851e26	0.350859
$689$	1.06642e27	1.16103
$690$	2.35713e27	2.53115
$691$	4.40286e26	0.466330	0.233165	−	0.972437i	$-0.425092\pi$
$691$	4.40286e26	0.466330	0.233165	+	0.972437i	$0.425092\pi$
$692$	1.42447e27	1.48815
$693$	3.34761e26	0.344961
$694$	−1.57455e27	−1.60045
$695$	1.50587e27	1.50985
$696$	−2.66042e26	−0.263126
$697$	−1.74842e27	−1.70583
$698$	−1.48909e27	−1.43316
$699$	−5.34111e26	−0.507106
$700$	−4.02661e27	−3.77145
$701$	4.07132e26	0.376196	0.188098	−	0.982150i	$-0.439768\pi$
$701$	4.07132e26	0.376196	0.188098	+	0.982150i	$0.439768\pi$
$702$	−1.81502e27	−1.65454
$703$	−6.25690e26	−0.562709
$704$	1.46251e27	1.29766
$705$	3.82244e26	0.334614
$706$	6.65500e26	0.574782
$707$	4.84881e26	0.413191
$708$	1.65302e27	1.38984
$709$	−6.55122e26	−0.543480	−0.271740	−	0.962371i	$-0.587599\pi$
$709$	−6.55122e26	−0.543480	−0.271740	+	0.962371i	$0.587599\pi$
$710$	−3.55316e27	−2.90844
$711$	2.69088e26	0.217337
$712$	3.15028e26	0.251067
$713$	−4.97211e26	−0.391012
$714$	4.02351e27	3.12228
$715$	−3.52980e27	−2.70298
$716$	3.30300e26	0.249594
$717$	−5.09375e26	−0.379845
$718$	3.53028e27	2.59793
$719$	1.74912e27	1.27027	0.635134	−	0.772402i	$-0.280945\pi$
$719$	1.74912e27	1.27027	0.635134	+	0.772402i	$0.280945\pi$
$720$	−6.94027e26	−0.497413
$721$	7.85433e26	0.555551
$722$	−3.23136e27	−2.25570
$723$	2.79542e27	1.92590
$724$	−2.70307e27	−1.83798
$725$	−2.89670e27	−1.94399
$726$	−3.36928e26	−0.223172
$727$	−4.21334e25	−0.0275454	−0.0137727	−	0.999905i	$-0.504384\pi$
$727$	−4.21334e25	−0.0275454	−0.0137727	+	0.999905i	$0.504384\pi$
$728$	8.14138e26	0.525352
$729$	7.07073e26	0.450353
$730$	−7.01654e25	−0.0441119
$731$	1.33147e27	0.826257
$732$	−2.84579e27	−1.74320
$733$	9.20820e26	0.556785	0.278392	−	0.960467i	$-0.410198\pi$
$733$	9.20820e26	0.556785	0.278392	+	0.960467i	$0.410198\pi$
$734$	−8.96474e26	−0.535088
$735$	−4.78147e26	−0.281729
$736$	1.79955e27	1.04671
$737$	2.69590e27	1.54797
$738$	−9.21133e26	−0.522140
$739$	−2.51097e27	−1.40514	−0.702569	−	0.711616i	$-0.747964\pi$
$739$	−2.51097e27	−1.40514	−0.702569	+	0.711616i	$0.747964\pi$
$740$	−1.55718e27	−0.860277
$741$	−4.94744e27	−2.69841
$742$	2.32544e27	1.25218
$743$	2.47248e27	1.31444	0.657218	−	0.753701i	$-0.271733\pi$
$743$	2.47248e27	1.31444	0.657218	+	0.753701i	$0.271733\pi$
$744$	−3.95681e26	−0.207684
$745$	−2.07340e27	−1.07448
$746$	−1.93586e27	−0.990499
$747$	−4.45408e26	−0.225015
$748$	3.90272e27	1.94671
$749$	1.89453e27	0.933090
$750$	1.33852e28	6.50943
$751$	7.76411e26	0.372831	0.186416	−	0.982471i	$-0.440313\pi$
$751$	7.76411e26	0.372831	0.186416	+	0.982471i	$0.440313\pi$
$752$	2.22107e26	0.105316
$753$	−1.77891e27	−0.832916
$754$	3.17000e27	1.46565
$755$	−2.02906e27	−0.926403
$756$	−2.18033e27	−0.983026
$757$	−2.33359e27	−1.03900	−0.519498	−	0.854472i	$-0.673881\pi$
$757$	−2.33359e27	−1.03900	−0.519498	+	0.854472i	$0.673881\pi$
$758$	1.79433e27	0.788940
$759$	1.84600e27	0.801557
$760$	−2.46874e27	−1.05863
$761$	−1.50602e27	−0.637788	−0.318894	−	0.947790i	$-0.603311\pi$
$761$	−1.50602e27	−0.637788	−0.318894	+	0.947790i	$0.603311\pi$
$762$	−8.89487e26	−0.372021
$763$	1.28807e27	0.532054
$764$	−7.39216e26	−0.301568
$765$	−2.90725e27	−1.17138
$766$	−1.61591e26	−0.0643048
$767$	−3.63907e27	−1.43033
$768$	−1.21738e27	−0.472602
$769$	3.78500e27	1.45133	0.725664	−	0.688050i	$-0.241533\pi$
$769$	3.78500e27	1.45133	0.725664	+	0.688050i	$0.241533\pi$
$770$	−7.69709e27	−2.91517
$771$	−4.26080e27	−1.59395
$772$	5.25465e27	1.94169
$773$	−5.84341e26	−0.213286	−0.106643	−	0.994297i	$-0.534010\pi$
$773$	−5.84341e26	−0.213286	−0.106643	+	0.994297i	$0.534010\pi$
$774$	7.01464e26	0.252910
$775$	−4.30823e27	−1.53438
$776$	−1.44980e27	−0.510062
$777$	−1.25726e27	−0.436944
$778$	−3.89364e27	−1.33675
$779$	4.68811e27	1.58998
$780$	−1.23129e28	−4.12537
$781$	−2.78268e27	−0.921039
$782$	5.73736e27	1.87607
$783$	−1.56851e27	−0.506698
$784$	−2.77832e26	−0.0886707
$785$	1.28460e27	0.405048
$786$	−3.11670e27	−0.970914
$787$	2.79687e27	0.860821	0.430411	−	0.902633i	$-0.358369\pi$
$787$	2.79687e27	0.860821	0.430411	+	0.902633i	$0.358369\pi$
$788$	6.92946e27	2.10717
$789$	−8.77917e26	−0.263768
$790$	−6.18709e27	−1.83666
$791$	2.29399e27	0.672846
$792$	3.79880e26	0.110092
$793$	6.26491e27	1.79399
$794$	−1.12454e27	−0.318184
$795$	−6.49787e27	−1.81670
$796$	7.39339e25	0.0204253
$797$	1.35299e27	0.369351	0.184676	−	0.982800i	$-0.440877\pi$
$797$	1.35299e27	0.369351	0.184676	+	0.982800i	$0.440877\pi$
$798$	−1.07884e28	−2.91024
$799$	9.30401e26	0.248014
$800$	1.55927e28	4.10740
$801$	−9.94739e26	−0.258941
$802$	1.48697e27	0.382512
$803$	−5.49504e25	−0.0139693
$804$	9.40405e27	2.36256
$805$	−6.23357e27	−1.54766
$806$	4.71469e27	1.15683
$807$	−1.92449e27	−0.466678
$808$	5.50233e26	0.131868
$809$	2.53111e27	0.599515	0.299758	−	0.954015i	$-0.403094\pi$
$809$	2.53111e27	0.599515	0.299758	+	0.954015i	$0.403094\pi$
$810$	1.54506e28	3.61692
$811$	−3.84525e27	−0.889664	−0.444832	−	0.895614i	$-0.646737\pi$
$811$	−3.84525e27	−0.889664	−0.444832	+	0.895614i	$0.646737\pi$
$812$	3.80803e27	0.870800
$813$	−1.61728e27	−0.365531
$814$	−2.21372e27	−0.494527
$815$	7.66273e27	1.69195
$816$	−6.53272e27	−1.42573
$817$	−3.57011e27	−0.770144
$818$	−8.64110e27	−1.84252
$819$	−2.57074e27	−0.541827
$820$	1.16675e28	2.43079
$821$	4.21264e27	0.867550	0.433775	−	0.901021i	$-0.357181\pi$
$821$	4.21264e27	0.867550	0.433775	+	0.901021i	$0.357181\pi$
$822$	9.35728e27	1.90488
$823$	9.76309e26	0.196467	0.0982334	−	0.995163i	$-0.468681\pi$
$823$	9.76309e26	0.196467	0.0982334	+	0.995163i	$0.468681\pi$
$824$	8.91293e26	0.177301
$825$	1.59952e28	3.14540
$826$	−7.93537e27	−1.54261
$827$	5.96668e27	1.14665	0.573324	−	0.819329i	$-0.305654\pi$
$827$	5.96668e27	1.14665	0.573324	+	0.819329i	$0.305654\pi$
$828$	1.66515e27	0.316348
$829$	1.52128e27	0.285720	0.142860	−	0.989743i	$-0.454370\pi$
$829$	1.52128e27	0.285720	0.142860	+	0.989743i	$0.454370\pi$
$830$	1.02412e28	1.90155
$831$	−4.14780e27	−0.761392
$832$	−1.12311e28	−2.03822
$833$	−1.16383e27	−0.208815
$834$	7.46762e27	1.32466
$835$	−2.16504e28	−3.79703
$836$	−1.04645e28	−1.81451
$837$	−2.33282e27	−0.399934
$838$	6.96999e27	1.18145
$839$	6.72648e27	1.12733	0.563663	−	0.826005i	$-0.309392\pi$
$839$	6.72648e27	1.12733	0.563663	+	0.826005i	$0.309392\pi$
$840$	−4.96068e27	−0.822031
$841$	−3.36380e27	−0.551149
$842$	6.19882e27	1.00425
$843$	−3.17283e27	−0.508259
$844$	−1.36399e28	−2.16052
$845$	1.44951e28	2.27030
$846$	4.90169e26	0.0759149
$847$	8.91025e26	0.136458
$848$	−3.77566e27	−0.571784
$849$	−8.59939e27	−1.28779
$850$	4.97130e28	7.36191
$851$	−1.79280e27	−0.262544
$852$	−9.70676e27	−1.40572
$853$	2.66085e27	0.381070	0.190535	−	0.981680i	$-0.438978\pi$
$853$	2.66085e27	0.381070	0.190535	+	0.981680i	$0.438978\pi$
$854$	1.36613e28	1.93482
$855$	7.79533e27	1.09183
$856$	2.14987e27	0.297791
$857$	−1.05157e28	−1.44052	−0.720262	−	0.693702i	$-0.755978\pi$
$857$	−1.05157e28	−1.44052	−0.720262	+	0.693702i	$0.755978\pi$
$858$	−1.75043e28	−2.37145
$859$	1.21313e28	1.62544	0.812719	−	0.582655i	$-0.197986\pi$
$859$	1.21313e28	1.62544	0.812719	+	0.582655i	$0.197986\pi$
$860$	−8.88510e27	−1.17741
$861$	9.42030e27	1.23462
$862$	−1.10559e27	−0.143310
$863$	1.10564e27	0.141746	0.0708731	−	0.997485i	$-0.477421\pi$
$863$	1.10564e27	0.141746	0.0708731	+	0.997485i	$0.477421\pi$
$864$	8.44313e27	1.07059
$865$	1.91077e28	2.39638
$866$	−9.79355e27	−1.21484
$867$	−1.78997e28	−2.19616
$868$	5.66363e27	0.687318
$869$	−4.84545e27	−0.581629
$870$	−1.93153e28	−2.29334
$871$	−2.07027e28	−2.43139
$872$	1.46167e27	0.169802
$873$	4.57793e27	0.526058
$874$	−1.53838e28	−1.74866
$875$	−3.53980e28	−3.98017
$876$	−1.91682e26	−0.0213203
$877$	1.46138e28	1.60793	0.803963	−	0.594679i	$-0.202721\pi$
$877$	1.46138e28	1.60793	0.803963	+	0.594679i	$0.202721\pi$
$878$	−4.56115e27	−0.496452
$879$	1.58843e28	1.71031
$880$	1.24973e28	1.33116
$881$	−3.22595e27	−0.339928	−0.169964	−	0.985450i	$-0.554365\pi$
$881$	−3.22595e27	−0.339928	−0.169964	+	0.985450i	$0.554365\pi$
$882$	−6.13148e26	−0.0639166
$883$	2.01289e27	0.207584	0.103792	−	0.994599i	$-0.466902\pi$
$883$	2.01289e27	0.207584	0.103792	+	0.994599i	$0.466902\pi$
$884$	−2.99702e28	−3.05769
$885$	2.21735e28	2.23807
$886$	−8.84155e27	−0.882893
$887$	1.82749e28	1.80543	0.902714	−	0.430240i	$-0.141571\pi$
$887$	1.82749e28	1.80543	0.902714	+	0.430240i	$0.141571\pi$
$888$	−1.42671e27	−0.139449
$889$	2.35230e27	0.227471
$890$	2.28718e28	2.18824
$891$	1.21002e28	1.14540
$892$	3.15159e27	0.295164
$893$	−2.49472e27	−0.231171
$894$	−1.02820e28	−0.942693
$895$	4.43061e27	0.401924
$896$	−7.77951e27	−0.698274
$897$	−1.41760e28	−1.25900
$898$	−2.52358e28	−2.21765
$899$	4.07436e27	0.354276
$900$	1.44282e28	1.24139
$901$	−1.58161e28	−1.34652
$902$	1.65867e28	1.39733
$903$	−7.17378e27	−0.598018
$904$	2.60318e27	0.214735
$905$	−3.62587e28	−2.95972
$906$	−1.00621e28	−0.812777
$907$	−8.25511e27	−0.659862	−0.329931	−	0.944005i	$-0.607026\pi$
$907$	−8.25511e27	−0.659862	−0.329931	+	0.944005i	$0.607026\pi$
$908$	2.26921e28	1.79498
$909$	−1.73743e27	−0.136003
$910$	5.91084e28	4.57884
$911$	1.13910e28	0.873248	0.436624	−	0.899644i	$-0.356174\pi$
$911$	1.13910e28	0.873248	0.436624	+	0.899644i	$0.356174\pi$
$912$	1.75164e28	1.32891
$913$	8.02041e27	0.602177
$914$	−1.02780e28	−0.763694
$915$	−3.81732e28	−2.80710
$916$	2.40881e28	1.75305
$917$	8.24229e27	0.593662
$918$	2.69186e28	1.91887
$919$	−2.16813e28	−1.52964	−0.764818	−	0.644247i	$-0.777171\pi$
$919$	−2.16813e28	−1.52964	−0.764818	+	0.644247i	$0.777171\pi$
$920$	−7.07373e27	−0.493928
$921$	−1.29136e28	−0.892441
$922$	−6.01748e27	−0.411596
$923$	2.13691e28	1.44667
$924$	−2.10274e28	−1.40897
$925$	−1.55342e28	−1.03025
$926$	1.58216e28	1.03859
$927$	−2.81436e27	−0.182862
$928$	−1.47463e28	−0.948367
$929$	1.24064e28	0.789763	0.394881	−	0.918732i	$-0.370786\pi$
$929$	1.24064e28	0.789763	0.394881	+	0.918732i	$0.370786\pi$
$930$	−2.87274e28	−1.81012
$931$	3.12062e27	0.194634
$932$	8.67547e27	0.535601
$933$	1.51594e28	0.926420
$934$	−2.98132e27	−0.180349
$935$	5.23506e28	3.13481
$936$	−2.91722e27	−0.172921
$937$	2.04751e28	1.20143	0.600716	−	0.799462i	$-0.294882\pi$
$937$	2.04751e28	1.20143	0.600716	+	0.799462i	$0.294882\pi$
$938$	−4.51443e28	−2.62226
$939$	1.96135e27	0.112780
$940$	−6.20872e27	−0.353417
$941$	−1.53849e28	−0.866951	−0.433475	−	0.901165i	$-0.642713\pi$
$941$	−1.53849e28	−0.866951	−0.433475	+	0.901165i	$0.642713\pi$
$942$	6.37033e27	0.355368
$943$	1.34330e28	0.741840
$944$	1.28841e28	0.704404
$945$	−2.92467e28	−1.58298
$946$	−1.26312e28	−0.676829
$947$	−3.48863e27	−0.185068	−0.0925338	−	0.995710i	$-0.529497\pi$
$947$	−3.48863e27	−0.185068	−0.0925338	+	0.995710i	$0.529497\pi$
$948$	−1.69023e28	−0.887699
$949$	4.21982e26	0.0219414
$950$	−1.33297e29	−6.86195
$951$	−3.42117e28	−1.74365
$952$	−1.20745e28	−0.609283
$953$	−3.84961e28	−1.92324	−0.961621	−	0.274383i	$-0.911526\pi$
$953$	−3.84961e28	−1.92324	−0.961621	+	0.274383i	$0.911526\pi$
$954$	−8.33250e27	−0.412160
$955$	−9.91576e27	−0.485617
$956$	8.27368e27	0.401189
$957$	−1.51269e28	−0.726250
$958$	−1.33836e28	−0.636210
$959$	−2.47459e28	−1.16473
$960$	6.84330e28	3.18925
$961$	−1.56109e28	−0.720372
$962$	1.69998e28	0.776751
$963$	−6.78847e27	−0.307130
$964$	−4.54055e28	−2.03412
$965$	7.04852e28	3.12672
$966$	−3.09122e28	−1.35784
$967$	−9.27452e27	−0.403404	−0.201702	−	0.979447i	$-0.564647\pi$
$967$	−9.27452e27	−0.403404	−0.201702	+	0.979447i	$0.564647\pi$
$968$	1.01112e27	0.0435497
$969$	7.33757e28	3.12951
$970$	−1.05259e29	−4.44558
$971$	3.31418e28	1.38610	0.693048	−	0.720891i	$-0.256267\pi$
$971$	3.31418e28	1.38610	0.693048	+	0.720891i	$0.256267\pi$
$972$	1.98094e28	0.820429
$973$	−1.97486e28	−0.809960
$974$	2.06903e28	0.840341
$975$	−1.22832e29	−4.94047
$976$	−2.21809e28	−0.883500
$977$	2.48973e28	0.982096	0.491048	−	0.871133i	$-0.336614\pi$
$977$	2.48973e28	0.982096	0.491048	+	0.871133i	$0.336614\pi$
$978$	3.79994e28	1.48442
$979$	1.79122e28	0.692967
$980$	7.76644e27	0.297560
$981$	−4.61541e27	−0.175128
$982$	5.23941e28	1.96890
$983$	−1.01094e28	−0.376241	−0.188120	−	0.982146i	$-0.560240\pi$
$983$	−1.01094e28	−0.376241	−0.188120	+	0.982146i	$0.560240\pi$
$984$	1.06900e28	0.394024
$985$	9.29510e28	3.39320
$986$	−4.70144e28	−1.69981
$987$	−5.01289e27	−0.179504
$988$	8.03603e28	2.85004
$989$	−1.02295e28	−0.359327
$990$	2.75802e28	0.959540
$991$	−4.27997e28	−1.47483	−0.737414	−	0.675441i	$-0.763953\pi$
$991$	−4.27997e28	−1.47483	−0.737414	+	0.675441i	$0.763953\pi$
$992$	−2.19319e28	−0.748541
$993$	−3.85403e28	−1.30286
$994$	4.65974e28	1.56024
$995$	9.91741e26	0.0328911
$996$	2.79774e28	0.919061
$997$	1.79510e28	0.584096	0.292048	−	0.956404i	$-0.405663\pi$
$997$	1.79510e28	0.584096	0.292048	+	0.956404i	$0.405663\pi$
$998$	−6.44809e28	−2.07822
$999$	−8.41148e27	−0.268535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.7	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1080.46 q^{2} -39593.4 q^{3} +643107. q^{4} +8.62657e6 q^{5} +4.27791e7 q^{6} -1.13132e8 q^{7} -1.28380e8 q^{8} +4.05374e8 q^{9} +O(q^{10})\)	\(q-1080.46 q^{2} -39593.4 q^{3} +643107. q^{4} +8.62657e6 q^{5} +4.27791e7 q^{6} -1.13132e8 q^{7} -1.28380e8 q^{8} +4.05374e8 q^{9} -9.32067e9 q^{10} -7.29953e9 q^{11} -2.54628e10 q^{12} +5.60554e10 q^{13} +1.22234e11 q^{14} -3.41555e11 q^{15} -1.98464e11 q^{16} -8.31360e11 q^{17} -4.37991e11 q^{18} +2.22916e12 q^{19} +5.54781e12 q^{20} +4.47927e12 q^{21} +7.88685e12 q^{22} +6.38725e12 q^{23} +5.08298e12 q^{24} +5.53442e13 q^{25} -6.05656e13 q^{26} +2.99677e13 q^{27} -7.27559e13 q^{28} -5.23398e13 q^{29} +3.69037e14 q^{30} -7.78443e13 q^{31} +2.81741e14 q^{32} +2.89013e14 q^{33} +8.98252e14 q^{34} -9.75939e14 q^{35} +2.60699e14 q^{36} -2.80684e14 q^{37} -2.40852e15 q^{38} -2.21942e15 q^{39} -1.10748e15 q^{40} +2.10309e15 q^{41} -4.83968e15 q^{42} -1.60155e15 q^{43} -4.69438e15 q^{44} +3.49699e15 q^{45} -6.90118e15 q^{46} -1.11913e15 q^{47} +7.85787e15 q^{48} +1.39991e15 q^{49} -5.97972e16 q^{50} +3.29164e16 q^{51} +3.60496e16 q^{52} +1.90244e16 q^{53} -3.23790e16 q^{54} -6.29699e16 q^{55} +1.45238e16 q^{56} -8.82599e16 q^{57} +5.65511e16 q^{58} -6.49192e16 q^{59} -2.19656e17 q^{60} +1.11763e17 q^{61} +8.41077e16 q^{62} -4.58607e16 q^{63} -2.00357e17 q^{64} +4.83566e17 q^{65} -3.12267e17 q^{66} -3.69325e17 q^{67} -5.34654e17 q^{68} -2.52893e17 q^{69} +1.05446e18 q^{70} +3.81213e17 q^{71} -5.20418e16 q^{72} +7.52794e15 q^{73} +3.03269e17 q^{74} -2.19126e18 q^{75} +1.43359e18 q^{76} +8.25809e17 q^{77} +2.39800e18 q^{78} +6.63803e17 q^{79} -1.71207e18 q^{80} -1.65767e18 q^{81} -2.27230e18 q^{82} -1.09876e18 q^{83} +2.88065e18 q^{84} -7.17178e18 q^{85} +1.73041e18 q^{86} +2.07231e18 q^{87} +9.37111e17 q^{88} -2.45388e18 q^{89} -3.77836e18 q^{90} -6.34165e18 q^{91} +4.10769e18 q^{92} +3.08212e18 q^{93} +1.20918e18 q^{94} +1.92300e19 q^{95} -1.11551e19 q^{96} +1.12931e19 q^{97} -1.51255e18 q^{98} -2.95904e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 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

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Groups

Database

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