LMFDB - Embedded newform 47.20.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-1437.04 q^{2} -44683.4 q^{3} +1.54079e6 q^{4} +3.89571e6 q^{5} +6.42118e7 q^{6} +1.74189e8 q^{7} -1.46076e9 q^{8} +8.34349e8 q^{9} +O(q^{10})$	\(q-1437.04 q^{2} -44683.4 q^{3} +1.54079e6 q^{4} +3.89571e6 q^{5} +6.42118e7 q^{6} +1.74189e8 q^{7} -1.46076e9 q^{8} +8.34349e8 q^{9} -5.59828e9 q^{10} -8.44656e9 q^{11} -6.88479e10 q^{12} +8.69560e9 q^{13} -2.50317e11 q^{14} -1.74074e11 q^{15} +1.29134e12 q^{16} +6.57108e11 q^{17} -1.19899e12 q^{18} +1.90007e12 q^{19} +6.00248e12 q^{20} -7.78339e12 q^{21} +1.21380e13 q^{22} -1.29115e13 q^{23} +6.52716e13 q^{24} -3.89695e12 q^{25} -1.24959e13 q^{26} +1.46523e13 q^{27} +2.68390e14 q^{28} +9.32683e13 q^{29} +2.50151e14 q^{30} +1.67699e12 q^{31} -1.08985e15 q^{32} +3.77421e14 q^{33} -9.44289e14 q^{34} +6.78591e14 q^{35} +1.28556e15 q^{36} +1.23478e15 q^{37} -2.73048e15 q^{38} -3.88549e14 q^{39} -5.69068e15 q^{40} -5.46877e14 q^{41} +1.11850e16 q^{42} +2.48854e15 q^{43} -1.30144e16 q^{44} +3.25038e15 q^{45} +1.85544e16 q^{46} -1.11913e15 q^{47} -5.77017e16 q^{48} +1.89431e16 q^{49} +5.60007e15 q^{50} -2.93618e16 q^{51} +1.33981e16 q^{52} +3.19315e16 q^{53} -2.10559e16 q^{54} -3.29053e16 q^{55} -2.54448e17 q^{56} -8.49018e16 q^{57} -1.34030e17 q^{58} +2.33696e16 q^{59} -2.68211e17 q^{60} -1.15922e16 q^{61} -2.40990e15 q^{62} +1.45335e17 q^{63} +8.89126e17 q^{64} +3.38755e16 q^{65} -5.42369e17 q^{66} +2.12794e16 q^{67} +1.01247e18 q^{68} +5.76932e17 q^{69} -9.75162e17 q^{70} +1.49996e17 q^{71} -1.21878e18 q^{72} +1.27009e16 q^{73} -1.77443e18 q^{74} +1.74129e17 q^{75} +2.92762e18 q^{76} -1.47130e18 q^{77} +5.58360e17 q^{78} -7.04511e16 q^{79} +5.03070e18 q^{80} -1.62445e18 q^{81} +7.85883e17 q^{82} -2.19521e18 q^{83} -1.19926e19 q^{84} +2.55990e18 q^{85} -3.57613e18 q^{86} -4.16755e18 q^{87} +1.23384e19 q^{88} +1.14262e18 q^{89} -4.67092e18 q^{90} +1.51468e18 q^{91} -1.98940e19 q^{92} -7.49339e16 q^{93} +1.60823e18 q^{94} +7.40213e18 q^{95} +4.86984e19 q^{96} +1.17721e18 q^{97} -2.72219e19 q^{98} -7.04738e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1437.04	−1.98465	−0.992324	−	0.123665i	$-0.960535\pi$
$2$	−1437.04	−1.98465	−0.992324	+	0.123665i	$0.960535\pi$
$3$	−44683.4	−1.31067	−0.655337	−	0.755337i	$-0.727473\pi$
$3$	−44683.4	−1.31067	−0.655337	+	0.755337i	$0.727473\pi$
$4$	1.54079e6	2.93883
$5$	3.89571e6	0.892013	0.446007	−	0.895030i	$-0.352846\pi$
$5$	3.89571e6	0.892013	0.446007	+	0.895030i	$0.352846\pi$
$6$	6.42118e7	2.60123
$7$	1.74189e8	1.63151	0.815757	−	0.578395i	$-0.196321\pi$
$7$	1.74189e8	1.63151	0.815757	+	0.578395i	$0.196321\pi$
$8$	−1.46076e9	−3.84789
$9$	8.34349e8	0.717867
$10$	−5.59828e9	−1.77033
$11$	−8.44656e9	−1.08006	−0.540032	−	0.841645i	$-0.681588\pi$
$11$	−8.44656e9	−1.08006	−0.540032	+	0.841645i	$0.681588\pi$
$12$	−6.88479e10	−3.85184
$13$	8.69560e9	0.227425	0.113712	−	0.993514i	$-0.463726\pi$
$13$	8.69560e9	0.227425	0.113712	+	0.993514i	$0.463726\pi$
$14$	−2.50317e11	−3.23798
$15$	−1.74074e11	−1.16914
$16$	1.29134e12	4.69788
$17$	6.57108e11	1.34392	0.671958	−	0.740589i	$-0.265454\pi$
$17$	6.57108e11	1.34392	0.671958	+	0.740589i	$0.265454\pi$
$18$	−1.19899e12	−1.42471
$19$	1.90007e12	1.35086	0.675431	−	0.737423i	$-0.263958\pi$
$19$	1.90007e12	1.35086	0.675431	+	0.737423i	$0.263958\pi$
$20$	6.00248e12	2.62147
$21$	−7.78339e12	−2.13838
$22$	1.21380e13	2.14355
$23$	−1.29115e13	−1.49473	−0.747366	−	0.664412i	$-0.768682\pi$
$23$	−1.29115e13	−1.49473	−0.747366	+	0.664412i	$0.768682\pi$
$24$	6.52716e13	5.04333
$25$	−3.89695e12	−0.204312
$26$	−1.24959e13	−0.451358
$27$	1.46523e13	0.369785
$28$	2.68390e14	4.79474
$29$	9.32683e13	1.19386	0.596930	−	0.802294i	$-0.296387\pi$
$29$	9.32683e13	1.19386	0.596930	+	0.802294i	$0.296387\pi$
$30$	2.50151e14	2.32033
$31$	1.67699e12	0.0113919	0.00569594	−	0.999984i	$-0.498187\pi$
$31$	1.67699e12	0.0113919	0.00569594	+	0.999984i	$0.498187\pi$
$32$	−1.08985e15	−5.47575
$33$	3.77421e14	1.41561
$34$	−9.44289e14	−2.66720
$35$	6.78591e14	1.45533
$36$	1.28556e15	2.10969
$37$	1.23478e15	1.56197	0.780986	−	0.624548i	$-0.214717\pi$
$37$	1.23478e15	1.56197	0.780986	+	0.624548i	$0.214717\pi$
$38$	−2.73048e15	−2.68099
$39$	−3.88549e14	−0.298080
$40$	−5.69068e15	−3.43237
$41$	−5.46877e14	−0.260881	−0.130441	−	0.991456i	$-0.541639\pi$
$41$	−5.46877e14	−0.260881	−0.130441	+	0.991456i	$0.541639\pi$
$42$	1.11850e16	4.24394
$43$	2.48854e15	0.755082	0.377541	−	0.925993i	$-0.376770\pi$
$43$	2.48854e15	0.755082	0.377541	+	0.925993i	$0.376770\pi$
$44$	−1.30144e16	−3.17412
$45$	3.25038e15	0.640346
$46$	1.85544e16	2.96652
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	−5.77017e16	−6.15739
$49$	1.89431e16	1.66183
$50$	5.60007e15	0.405488
$51$	−2.93618e16	−1.76144
$52$	1.33981e16	0.668362
$53$	3.19315e16	1.32923	0.664613	−	0.747188i	$-0.268597\pi$
$53$	3.19315e16	1.32923	0.664613	+	0.747188i	$0.268597\pi$
$54$	−2.10559e16	−0.733893
$55$	−3.29053e16	−0.963431
$56$	−2.54448e17	−6.27788
$57$	−8.49018e16	−1.77054
$58$	−1.34030e17	−2.36939
$59$	2.33696e16	0.351202	0.175601	−	0.984461i	$-0.443813\pi$
$59$	2.33696e16	0.351202	0.175601	+	0.984461i	$0.443813\pi$
$60$	−2.68211e17	−3.43590
$61$	−1.15922e16	−0.126921	−0.0634604	−	0.997984i	$-0.520214\pi$
$61$	−1.15922e16	−0.126921	−0.0634604	+	0.997984i	$0.520214\pi$
$62$	−2.40990e15	−0.0226089
$63$	1.45335e17	1.17121
$64$	8.89126e17	6.16955
$65$	3.38755e16	0.202866
$66$	−5.42369e17	−2.80949
$67$	2.12794e16	0.0955540	0.0477770	−	0.998858i	$-0.484786\pi$
$67$	2.12794e16	0.0955540	0.0477770	+	0.998858i	$0.484786\pi$
$68$	1.01247e18	3.94954
$69$	5.76932e17	1.95911
$70$	−9.75162e17	−2.88832
$71$	1.49996e17	0.388263	0.194131	−	0.980976i	$-0.437811\pi$
$71$	1.49996e17	0.388263	0.194131	+	0.980976i	$0.437811\pi$
$72$	−1.21878e18	−2.76227
$73$	1.27009e16	0.0252504	0.0126252	−	0.999920i	$-0.495981\pi$
$73$	1.27009e16	0.0252504	0.0126252	+	0.999920i	$0.495981\pi$
$74$	−1.77443e18	−3.09997
$75$	1.74129e17	0.267787
$76$	2.92762e18	3.96995
$77$	−1.47130e18	−1.76214
$78$	5.58360e17	0.591583
$79$	−7.04511e16	−0.0661349	−0.0330674	−	0.999453i	$-0.510528\pi$
$79$	−7.04511e16	−0.0661349	−0.0330674	+	0.999453i	$0.510528\pi$
$80$	5.03070e18	4.19057
$81$	−1.62445e18	−1.20253
$82$	7.85883e17	0.517757
$83$	−2.19521e18	−1.28894	−0.644472	−	0.764628i	$-0.722923\pi$
$83$	−2.19521e18	−1.28894	−0.644472	+	0.764628i	$0.722923\pi$
$84$	−1.19926e19	−6.28434
$85$	2.55990e18	1.19879
$86$	−3.57613e18	−1.49857
$87$	−4.16755e18	−1.56476
$88$	1.23384e19	4.15597
$89$	1.14262e18	0.345699	0.172849	−	0.984948i	$-0.444703\pi$
$89$	1.14262e18	0.345699	0.172849	+	0.984948i	$0.444703\pi$
$90$	−4.67092e18	−1.27086
$91$	1.51468e18	0.371046
$92$	−1.98940e19	−4.39276
$93$	−7.49339e16	−0.0149310
$94$	1.60823e18	0.289491
$95$	7.40213e18	1.20499
$96$	4.86984e19	7.17692
$97$	1.17721e18	0.157225	0.0786124	−	0.996905i	$-0.474951\pi$
$97$	1.17721e18	0.157225	0.0786124	+	0.996905i	$0.474951\pi$
$98$	−2.72219e19	−3.29816
$99$	−7.04738e18	−0.775342
$100$	−6.00439e18	−0.600439
$101$	5.35149e16	0.00486879	0.00243440	−	0.999997i	$-0.499225\pi$
$101$	5.35149e16	0.00486879	0.00243440	+	0.999997i	$0.499225\pi$
$102$	4.21941e19	3.49583
$103$	−2.29304e18	−0.173164	−0.0865821	−	0.996245i	$-0.527594\pi$
$103$	−2.29304e18	−0.173164	−0.0865821	+	0.996245i	$0.527594\pi$
$104$	−1.27021e19	−0.875105
$105$	−3.03218e19	−1.90746
$106$	−4.58868e19	−2.63804
$107$	2.83725e19	1.49194	0.745970	−	0.665979i	$-0.231986\pi$
$107$	2.83725e19	1.49194	0.745970	+	0.665979i	$0.231986\pi$
$108$	2.25761e19	1.08673
$109$	−1.87225e18	−0.0825681	−0.0412841	−	0.999147i	$-0.513145\pi$
$109$	−1.87225e18	−0.0825681	−0.0412841	+	0.999147i	$0.513145\pi$
$110$	4.72862e19	1.91207
$111$	−5.51743e19	−2.04724
$112$	2.24938e20	7.66465
$113$	−3.21619e19	−1.00716	−0.503578	−	0.863950i	$-0.667983\pi$
$113$	−3.21619e19	−1.00716	−0.503578	+	0.863950i	$0.667983\pi$
$114$	1.22007e20	3.51390
$115$	−5.02996e19	−1.33332
$116$	1.43707e20	3.50855
$117$	7.25516e18	0.163261
$118$	−3.35830e19	−0.697012
$119$	1.14461e20	2.19262
$120$	2.54279e20	4.49872
$121$	1.01853e19	0.166538
$122$	1.66584e19	0.251893
$123$	2.44363e19	0.341930
$124$	2.58390e18	0.0334788
$125$	−8.94861e19	−1.07426
$126$	−2.08852e20	−2.32444
$127$	−3.35635e19	−0.346522	−0.173261	−	0.984876i	$-0.555430\pi$
$127$	−3.35635e19	−0.346522	−0.173261	+	0.984876i	$0.555430\pi$
$128$	−7.06311e20	−6.76864
$129$	−1.11197e20	−0.989667
$130$	−4.86804e19	−0.402617
$131$	3.78907e19	0.291377	0.145689	−	0.989330i	$-0.453460\pi$
$131$	3.78907e19	0.291377	0.145689	+	0.989330i	$0.453460\pi$
$132$	5.81528e20	4.16024
$133$	3.30973e20	2.20395
$134$	−3.05793e19	−0.189641
$135$	5.70810e19	0.329853
$136$	−9.59874e20	−5.17124
$137$	2.66327e20	1.33835	0.669174	−	0.743106i	$-0.266648\pi$
$137$	2.66327e20	1.33835	0.669174	+	0.743106i	$0.266648\pi$
$138$	−8.29073e20	−3.88814
$139$	−2.23673e20	−0.979430	−0.489715	−	0.871883i	$-0.662899\pi$
$139$	−2.23673e20	−0.979430	−0.489715	+	0.871883i	$0.662899\pi$
$140$	1.04557e21	4.27697
$141$	5.00066e19	0.191181
$142$	−2.15550e20	−0.770564
$143$	−7.34479e19	−0.245633
$144$	1.07743e21	3.37245
$145$	3.63346e20	1.06494
$146$	−1.82517e19	−0.0501131
$147$	−8.46442e20	−2.17812
$148$	1.90254e21	4.59037
$149$	−5.28032e19	−0.119506	−0.0597531	−	0.998213i	$-0.519031\pi$
$149$	−5.28032e19	−0.119506	−0.0597531	+	0.998213i	$0.519031\pi$
$150$	−2.50230e20	−0.531463
$151$	−5.10259e20	−1.01744	−0.508721	−	0.860932i	$-0.669881\pi$
$151$	−5.10259e20	−1.01744	−0.508721	+	0.860932i	$0.669881\pi$
$152$	−2.77554e21	−5.19797
$153$	5.48257e20	0.964752
$154$	2.11432e21	3.49722
$155$	6.53308e18	0.0101617
$156$	−5.98674e20	−0.876005
$157$	5.60281e20	0.771541	0.385771	−	0.922595i	$-0.373936\pi$
$157$	5.60281e20	0.771541	0.385771	+	0.922595i	$0.373936\pi$
$158$	1.01241e20	0.131254
$159$	−1.42681e21	−1.74218
$160$	−4.24575e21	−4.88444
$161$	−2.24905e21	−2.43868
$162$	2.33439e21	2.38661
$163$	3.00583e20	0.289856	0.144928	−	0.989442i	$-0.453705\pi$
$163$	3.00583e20	0.289856	0.144928	+	0.989442i	$0.453705\pi$
$164$	−8.42623e20	−0.766685
$165$	1.47032e21	1.26274
$166$	3.15460e21	2.55810
$167$	5.55178e20	0.425231	0.212616	−	0.977136i	$-0.431802\pi$
$167$	5.55178e20	0.425231	0.212616	+	0.977136i	$0.431802\pi$
$168$	1.13696e22	8.22826
$169$	−1.38631e21	−0.948278
$170$	−3.67868e21	−2.37918
$171$	1.58532e21	0.969739
$172$	3.83432e21	2.21906
$173$	5.85226e19	0.0320542	0.0160271	−	0.999872i	$-0.494898\pi$
$173$	5.85226e19	0.0320542	0.0160271	+	0.999872i	$0.494898\pi$
$174$	5.98893e21	3.10550
$175$	−6.78807e20	−0.333338
$176$	−1.09074e22	−5.07401
$177$	−1.04423e21	−0.460311
$178$	−1.64199e21	−0.686090
$179$	−2.48051e21	−0.982738	−0.491369	−	0.870951i	$-0.663503\pi$
$179$	−2.48051e21	−0.982738	−0.491369	+	0.870951i	$0.663503\pi$
$180$	5.00816e21	1.88187
$181$	2.24394e21	0.799955	0.399978	−	0.916525i	$-0.369018\pi$
$181$	2.24394e21	0.799955	0.399978	+	0.916525i	$0.369018\pi$
$182$	−2.17666e21	−0.736396
$183$	5.17980e20	0.166352
$184$	1.88606e22	5.75157
$185$	4.81034e21	1.39330
$186$	1.07683e20	0.0296329
$187$	−5.55030e21	−1.45151
$188$	−1.72435e21	−0.428672
$189$	2.55227e21	0.603309
$190$	−1.06371e22	−2.39147
$191$	−4.29590e21	−0.918834	−0.459417	−	0.888221i	$-0.651942\pi$
$191$	−4.29590e21	−0.918834	−0.459417	+	0.888221i	$0.651942\pi$
$192$	−3.97292e22	−8.08627
$193$	6.91992e21	1.34062	0.670312	−	0.742080i	$-0.266160\pi$
$193$	6.91992e21	1.34062	0.670312	+	0.742080i	$0.266160\pi$
$194$	−1.69169e21	−0.312036
$195$	−1.51367e21	−0.265891
$196$	2.91873e22	4.88385
$197$	−5.06846e21	−0.808067	−0.404033	−	0.914744i	$-0.632392\pi$
$197$	−5.06846e21	−0.808067	−0.404033	+	0.914744i	$0.632392\pi$
$198$	1.01274e22	1.53878
$199$	−1.32130e22	−1.91380	−0.956902	−	0.290412i	$-0.906208\pi$
$199$	−1.32130e22	−1.91380	−0.956902	+	0.290412i	$0.906208\pi$
$200$	5.69249e21	0.786171
$201$	−9.50838e20	−0.125240
$202$	−7.69029e19	−0.00966284
$203$	1.62464e22	1.94780
$204$	−4.52405e22	−5.17655
$205$	−2.13047e21	−0.232709
$206$	3.29519e21	0.343670
$207$	−1.07727e22	−1.07302
$208$	1.12290e22	1.06841
$209$	−1.60491e22	−1.45902
$210$	4.35736e22	3.78565
$211$	−1.54665e21	−0.128442	−0.0642212	−	0.997936i	$-0.520456\pi$
$211$	−1.54665e21	−0.128442	−0.0642212	+	0.997936i	$0.520456\pi$
$212$	4.91998e22	3.90636
$213$	−6.70234e21	−0.508886
$214$	−4.07724e22	−2.96098
$215$	9.69463e21	0.673544
$216$	−2.14034e22	−1.42289
$217$	2.92115e20	0.0185860
$218$	2.69050e21	0.163869
$219$	−5.67520e20	−0.0330950
$220$	−5.07003e22	−2.83136
$221$	5.71395e21	0.305640
$222$	7.92875e22	4.06304
$223$	3.23139e22	1.58669	0.793346	−	0.608771i	$-0.208337\pi$
$223$	3.23139e22	1.58669	0.793346	+	0.608771i	$0.208337\pi$
$224$	−1.89841e23	−8.93375
$225$	−3.25141e21	−0.146669
$226$	4.62179e22	1.99885
$227$	3.27256e22	1.35719	0.678597	−	0.734511i	$-0.262588\pi$
$227$	3.27256e22	1.35719	0.678597	+	0.734511i	$0.262588\pi$
$228$	−1.30816e23	−5.20331
$229$	−2.69185e22	−1.02710	−0.513551	−	0.858059i	$-0.671670\pi$
$229$	−2.69185e22	−1.02710	−0.513551	+	0.858059i	$0.671670\pi$
$230$	7.22824e22	2.64617
$231$	6.57428e22	2.30959
$232$	−1.36242e23	−4.59384
$233$	3.21744e22	1.04143	0.520715	−	0.853731i	$-0.325666\pi$
$233$	3.21744e22	1.04143	0.520715	+	0.853731i	$0.325666\pi$
$234$	−1.04259e22	−0.324015
$235$	−4.35981e21	−0.130114
$236$	3.60076e22	1.03212
$237$	3.14800e21	0.0866813
$238$	−1.64485e23	−4.35157
$239$	−5.97415e22	−1.51878	−0.759391	−	0.650634i	$-0.774503\pi$
$239$	−5.97415e22	−1.51878	−0.759391	+	0.650634i	$0.774503\pi$
$240$	−2.24789e23	−5.49247
$241$	−2.96763e22	−0.697025	−0.348512	−	0.937304i	$-0.613313\pi$
$241$	−2.96763e22	−0.697025	−0.348512	+	0.937304i	$0.613313\pi$
$242$	−1.46367e22	−0.330519
$243$	5.55560e22	1.20635
$244$	−1.78612e22	−0.372998
$245$	7.37967e22	1.48238
$246$	−3.51159e22	−0.678611
$247$	1.65223e22	0.307219
$248$	−2.44968e21	−0.0438347
$249$	9.80895e22	1.68938
$250$	1.28595e23	2.13203
$251$	1.13235e23	1.80750	0.903751	−	0.428059i	$-0.140803\pi$
$251$	1.13235e23	1.80750	0.903751	+	0.428059i	$0.140803\pi$
$252$	2.23931e23	3.44198
$253$	1.09058e23	1.61441
$254$	4.82320e22	0.687725
$255$	−1.14385e23	−1.57122
$256$	5.48838e23	7.26381
$257$	−4.79153e22	−0.611097	−0.305548	−	0.952177i	$-0.598840\pi$
$257$	−4.79153e22	−0.611097	−0.305548	+	0.952177i	$0.598840\pi$
$258$	1.59794e23	1.96414
$259$	2.15086e23	2.54838
$260$	5.21951e22	0.596188
$261$	7.78183e22	0.857032
$262$	−5.44504e22	−0.578281
$263$	4.60611e22	0.471797	0.235898	−	0.971778i	$-0.424197\pi$
$263$	4.60611e22	0.471797	0.235898	+	0.971778i	$0.424197\pi$
$264$	−5.51320e23	−5.44712
$265$	1.24396e23	1.18569
$266$	−4.75621e23	−4.37406
$267$	−5.10563e22	−0.453098
$268$	3.27872e22	0.280817
$269$	2.41893e22	0.199975	0.0999877	−	0.994989i	$-0.468120\pi$
$269$	2.41893e22	0.199975	0.0999877	+	0.994989i	$0.468120\pi$
$270$	−8.20276e22	−0.654642
$271$	2.33360e22	0.179812	0.0899060	−	0.995950i	$-0.471343\pi$
$271$	2.33360e22	0.179812	0.0899060	+	0.995950i	$0.471343\pi$
$272$	8.48552e23	6.31355
$273$	−6.76812e22	−0.486321
$274$	−3.82722e23	−2.65615
$275$	3.29158e22	0.220670
$276$	8.88932e23	5.75748
$277$	−2.27940e23	−1.42647	−0.713235	−	0.700925i	$-0.752771\pi$
$277$	−2.27940e23	−1.42647	−0.713235	+	0.700925i	$0.752771\pi$
$278$	3.21427e23	1.94382
$279$	1.39920e21	0.00817785
$280$	−9.91256e23	−5.59995
$281$	6.41705e22	0.350449	0.175225	−	0.984528i	$-0.443935\pi$
$281$	6.41705e22	0.350449	0.175225	+	0.984528i	$0.443935\pi$
$282$	−7.18614e22	−0.379428
$283$	4.22340e22	0.215621	0.107811	−	0.994171i	$-0.465616\pi$
$283$	4.22340e22	0.215621	0.107811	+	0.994171i	$0.465616\pi$
$284$	2.31113e23	1.14104
$285$	−3.30753e23	−1.57935
$286$	1.05547e23	0.487495
$287$	−9.52601e22	−0.425631
$288$	−9.09318e23	−3.93086
$289$	1.92718e23	0.806109
$290$	−5.22142e23	−2.11353
$291$	−5.26016e22	−0.206070
$292$	1.95695e22	0.0742064
$293$	3.32181e23	1.21936	0.609680	−	0.792647i	$-0.291298\pi$
$293$	3.32181e23	1.21936	0.609680	+	0.792647i	$0.291298\pi$
$294$	1.21637e24	4.32281
$295$	9.10410e22	0.313277
$296$	−1.80371e24	−6.01030
$297$	−1.23761e23	−0.399391
$298$	7.58802e22	0.237178
$299$	−1.12274e23	−0.339939
$300$	2.68297e23	0.786979
$301$	4.33478e23	1.23193
$302$	7.33262e23	2.01926
$303$	−2.39123e21	−0.00638140
$304$	2.45365e24	6.34619
$305$	−4.51598e22	−0.113215
$306$	−7.87867e23	−1.91469
$307$	−3.90246e23	−0.919442	−0.459721	−	0.888063i	$-0.652051\pi$
$307$	−3.90246e23	−0.919442	−0.459721	+	0.888063i	$0.652051\pi$
$308$	−2.26697e24	−5.17862
$309$	1.02461e23	0.226962
$310$	−9.38828e21	−0.0201674
$311$	1.31504e23	0.273977	0.136989	−	0.990573i	$-0.456258\pi$
$311$	1.31504e23	0.273977	0.136989	+	0.990573i	$0.456258\pi$
$312$	5.67575e23	1.14698
$313$	2.34830e23	0.460343	0.230172	−	0.973150i	$-0.426071\pi$
$313$	2.34830e23	0.460343	0.230172	+	0.973150i	$0.426071\pi$
$314$	−8.05145e23	−1.53124
$315$	5.66182e23	1.04473
$316$	−1.08551e23	−0.194359
$317$	−5.41130e23	−0.940239	−0.470120	−	0.882603i	$-0.655789\pi$
$317$	−5.41130e23	−0.940239	−0.470120	+	0.882603i	$0.655789\pi$
$318$	2.05038e24	3.45762
$319$	−7.87797e23	−1.28944
$320$	3.46377e24	5.50332
$321$	−1.26778e24	−1.95545
$322$	3.23198e24	4.83991
$323$	1.24855e24	1.81544
$324$	−2.50293e24	−3.53404
$325$	−3.38863e22	−0.0464657
$326$	−4.31950e23	−0.575262
$327$	8.36586e22	0.108220
$328$	7.98853e23	1.00384
$329$	−1.94941e23	−0.237981
$330$	−2.11291e24	−2.50610
$331$	8.83320e23	1.01801	0.509005	−	0.860764i	$-0.330013\pi$
$331$	8.83320e23	1.01801	0.509005	+	0.860764i	$0.330013\pi$
$332$	−3.38236e24	−3.78798
$333$	1.03024e24	1.12129
$334$	−7.97812e23	−0.843935
$335$	8.28984e22	0.0852355
$336$	−1.00510e25	−10.0459
$337$	1.01065e24	0.982012	0.491006	−	0.871156i	$-0.336629\pi$
$337$	1.01065e24	0.982012	0.491006	+	0.871156i	$0.336629\pi$
$338$	1.99218e24	1.88200
$339$	1.43711e24	1.32005
$340$	3.94427e24	3.52304
$341$	−1.41648e22	−0.0123040
$342$	−2.27817e24	−1.92459
$343$	1.31412e24	1.07979
$344$	−3.63515e24	−2.90547
$345$	2.24756e24	1.74755
$346$	−8.40992e22	−0.0636164
$347$	1.61766e23	0.119057	0.0595287	−	0.998227i	$-0.481040\pi$
$347$	1.61766e23	0.119057	0.0595287	+	0.998227i	$0.481040\pi$
$348$	−6.42133e24	−4.59856
$349$	−3.01936e23	−0.210413	−0.105207	−	0.994450i	$-0.533550\pi$
$349$	−3.01936e23	−0.210413	−0.105207	+	0.994450i	$0.533550\pi$
$350$	9.75472e23	0.661559
$351$	1.27410e23	0.0840982
$352$	9.20551e24	5.91416
$353$	4.18795e23	0.261904	0.130952	−	0.991389i	$-0.458197\pi$
$353$	4.18795e23	0.261904	0.130952	+	0.991389i	$0.458197\pi$
$354$	1.50060e24	0.913555
$355$	5.84341e23	0.346335
$356$	1.76054e24	1.01595
$357$	−5.11452e24	−2.87380
$358$	3.56459e24	1.95039
$359$	−5.73449e23	−0.305561	−0.152780	−	0.988260i	$-0.548823\pi$
$359$	−5.73449e23	−0.305561	−0.152780	+	0.988260i	$0.548823\pi$
$360$	−4.74801e24	−2.46398
$361$	1.63186e24	0.824829
$362$	−3.22463e24	−1.58763
$363$	−4.55114e23	−0.218277
$364$	2.33381e24	1.09044
$365$	4.94790e22	0.0225237
$366$	−7.44357e23	−0.330150
$367$	3.17984e24	1.37429	0.687144	−	0.726521i	$-0.258864\pi$
$367$	3.17984e24	1.37429	0.687144	+	0.726521i	$0.258864\pi$
$368$	−1.66732e25	−7.02207
$369$	−4.56286e23	−0.187278
$370$	−6.91265e24	−2.76521
$371$	5.56213e24	2.16865
$372$	−1.15457e23	−0.0438798
$373$	−2.59474e24	−0.961304	−0.480652	−	0.876912i	$-0.659600\pi$
$373$	−2.59474e24	−0.961304	−0.480652	+	0.876912i	$0.659600\pi$
$374$	7.97600e24	2.88075
$375$	3.99855e24	1.40801
$376$	1.63478e24	0.561272
$377$	8.11024e23	0.271513
$378$	−3.66771e24	−1.19736
$379$	−2.36948e24	−0.754363	−0.377181	−	0.926139i	$-0.623107\pi$
$379$	−2.36948e24	−0.754363	−0.377181	+	0.926139i	$0.623107\pi$
$380$	1.14051e25	3.54125
$381$	1.49973e24	0.454178
$382$	6.17337e24	1.82356
$383$	4.59288e24	1.32342	0.661709	−	0.749761i	$-0.269831\pi$
$383$	4.59288e24	1.32342	0.661709	+	0.749761i	$0.269831\pi$
$384$	3.15604e25	8.87148
$385$	−5.73176e24	−1.57185
$386$	−9.94420e24	−2.66067
$387$	2.07631e24	0.542048
$388$	1.81383e24	0.462056
$389$	−4.42249e24	−1.09937	−0.549687	−	0.835371i	$-0.685253\pi$
$389$	−4.42249e24	−1.09937	−0.549687	+	0.835371i	$0.685253\pi$
$390$	2.17521e24	0.527700
$391$	−8.48427e24	−2.00879
$392$	−2.76712e25	−6.39456
$393$	−1.69309e24	−0.381901
$394$	7.28358e24	1.60373
$395$	−2.74457e23	−0.0589932
$396$	−1.08585e25	−2.27860
$397$	−5.67407e23	−0.116248	−0.0581239	−	0.998309i	$-0.518512\pi$
$397$	−5.67407e23	−0.116248	−0.0581239	+	0.998309i	$0.518512\pi$
$398$	1.89876e25	3.79823
$399$	−1.47890e25	−2.88866
$400$	−5.03230e24	−0.959835
$401$	6.20198e24	1.15521	0.577603	−	0.816318i	$-0.303988\pi$
$401$	6.20198e24	1.15521	0.577603	+	0.816318i	$0.303988\pi$
$402$	1.36639e24	0.248558
$403$	1.45825e22	0.00259079
$404$	8.24553e22	0.0143085
$405$	−6.32836e24	−1.07268
$406$	−2.33466e25	−3.86569
$407$	−1.04296e25	−1.68703
$408$	4.28905e25	6.77781
$409$	−1.04729e24	−0.161694	−0.0808472	−	0.996727i	$-0.525763\pi$
$409$	−1.04729e24	−0.161694	−0.0808472	+	0.996727i	$0.525763\pi$
$410$	3.06157e24	0.461846
$411$	−1.19004e25	−1.75414
$412$	−3.53310e24	−0.508900
$413$	4.07073e24	0.572990
$414$	1.54808e25	2.12956
$415$	−8.55189e24	−1.14975
$416$	−9.47693e24	−1.24532
$417$	9.99449e24	1.28371
$418$	2.30631e25	2.89564
$419$	1.34735e24	0.165366	0.0826831	−	0.996576i	$-0.473651\pi$
$419$	1.34735e24	0.165366	0.0826831	+	0.996576i	$0.473651\pi$
$420$	−4.67196e25	−5.60571
$421$	−2.33710e24	−0.274156	−0.137078	−	0.990560i	$-0.543771\pi$
$421$	−2.33710e24	−0.274156	−0.137078	+	0.990560i	$0.543771\pi$
$422$	2.22259e24	0.254913
$423$	−9.33745e23	−0.104712
$424$	−4.66441e25	−5.11471
$425$	−2.56072e24	−0.274579
$426$	9.63152e24	1.00996
$427$	−2.01924e24	−0.207073
$428$	4.37161e25	4.38456
$429$	3.28190e24	0.321945
$430$	−1.39316e25	−1.33675
$431$	−1.89409e25	−1.77774	−0.888869	−	0.458162i	$-0.848508\pi$
$431$	−1.89409e25	−1.77774	−0.888869	+	0.458162i	$0.848508\pi$
$432$	1.89211e25	1.73721
$433$	1.47758e25	1.32714	0.663568	−	0.748116i	$-0.269041\pi$
$433$	1.47758e25	1.32714	0.663568	+	0.748116i	$0.269041\pi$
$434$	−4.19780e23	−0.0368867
$435$	−1.62356e25	−1.39579
$436$	−2.88475e24	−0.242653
$437$	−2.45329e25	−2.01918
$438$	8.15548e23	0.0656819
$439$	5.74095e24	0.452450	0.226225	−	0.974075i	$-0.427362\pi$
$439$	5.74095e24	0.452450	0.226225	+	0.974075i	$0.427362\pi$
$440$	4.80666e25	3.70718
$441$	1.58051e25	1.19298
$442$	−8.21116e24	−0.606587
$443$	−7.29018e24	−0.527112	−0.263556	−	0.964644i	$-0.584895\pi$
$443$	−7.29018e24	−0.527112	−0.263556	+	0.964644i	$0.584895\pi$
$444$	−8.50120e25	−6.01648
$445$	4.45132e24	0.308368
$446$	−4.64363e25	−3.14903
$447$	2.35943e24	0.156634
$448$	1.54876e26	10.0657
$449$	2.14695e25	1.36610	0.683049	−	0.730373i	$-0.260654\pi$
$449$	2.14695e25	1.36610	0.683049	+	0.730373i	$0.260654\pi$
$450$	4.67241e24	0.291086
$451$	4.61923e24	0.281768
$452$	−4.95548e25	−2.95986
$453$	2.28001e25	1.33353
$454$	−4.70279e25	−2.69355
$455$	5.90076e24	0.330978
$456$	1.24021e26	6.81284
$457$	3.44509e25	1.85352	0.926759	−	0.375656i	$-0.122583\pi$
$457$	3.44509e25	1.85352	0.926759	+	0.375656i	$0.122583\pi$
$458$	3.86829e25	2.03843
$459$	9.62813e24	0.496960
$460$	−7.75012e25	−3.91840
$461$	−7.24457e24	−0.358801	−0.179400	−	0.983776i	$-0.557416\pi$
$461$	−7.24457e24	−0.358801	−0.179400	+	0.983776i	$0.557416\pi$
$462$	−9.44750e25	−4.58372
$463$	−3.20767e25	−1.52465	−0.762326	−	0.647193i	$-0.775943\pi$
$463$	−3.20767e25	−1.52465	−0.762326	+	0.647193i	$0.775943\pi$
$464$	1.20441e26	5.60861
$465$	−2.91920e23	−0.0133187
$466$	−4.62359e25	−2.06687
$467$	−1.64025e25	−0.718454	−0.359227	−	0.933250i	$-0.616960\pi$
$467$	−1.64025e25	−0.718454	−0.359227	+	0.933250i	$0.616960\pi$
$468$	1.11787e25	0.479795
$469$	3.70665e24	0.155898
$470$	6.26521e24	0.258230
$471$	−2.50353e25	−1.01124
$472$	−3.41372e25	−1.35139
$473$	−2.10196e25	−0.815537
$474$	−4.52380e24	−0.172032
$475$	−7.40449e24	−0.275998
$476$	1.76361e26	6.44372
$477$	2.66420e25	0.954206
$478$	8.58508e25	3.01425
$479$	−2.89807e25	−0.997521	−0.498760	−	0.866740i	$-0.666211\pi$
$479$	−2.89807e25	−0.997521	−0.498760	+	0.866740i	$0.666211\pi$
$480$	1.89715e26	6.40191
$481$	1.07372e25	0.355231
$482$	4.26460e25	1.38335
$483$	1.00495e26	3.19631
$484$	1.56934e25	0.489426
$485$	4.58605e24	0.140247
$486$	−7.98362e25	−2.39417
$487$	1.62863e25	0.478958	0.239479	−	0.970901i	$-0.423023\pi$
$487$	1.62863e25	0.478958	0.239479	+	0.970901i	$0.423023\pi$
$488$	1.69334e25	0.488377
$489$	−1.34311e25	−0.379907
$490$	−1.06049e26	−2.94200
$491$	8.56456e24	0.233040	0.116520	−	0.993188i	$-0.462826\pi$
$491$	8.56456e24	0.233040	0.116520	+	0.993188i	$0.462826\pi$
$492$	3.76513e25	1.00487
$493$	6.12874e25	1.60445
$494$	−2.37431e25	−0.609722
$495$	−2.74545e25	−0.691615
$496$	2.16557e24	0.0535177
$497$	2.61277e25	0.633455
$498$	−1.40958e26	−3.35283
$499$	6.87768e25	1.60504	0.802522	−	0.596623i	$-0.203491\pi$
$499$	6.87768e25	1.60504	0.802522	+	0.596623i	$0.203491\pi$
$500$	−1.37879e26	−3.15707
$501$	−2.48072e25	−0.557340
$502$	−1.62722e26	−3.58725
$503$	−2.88370e25	−0.623813	−0.311907	−	0.950113i	$-0.600968\pi$
$503$	−2.88370e25	−0.623813	−0.311907	+	0.950113i	$0.600968\pi$
$504$	−2.12299e26	−4.50668
$505$	2.08478e23	0.00434303
$506$	−1.56721e26	−3.20403
$507$	6.19450e25	1.24288
$508$	−5.17143e25	−1.01837
$509$	−3.96567e25	−0.766474	−0.383237	−	0.923650i	$-0.625191\pi$
$509$	−3.96567e25	−0.766474	−0.383237	+	0.923650i	$0.625191\pi$
$510$	1.64376e26	3.11833
$511$	2.21236e24	0.0411963
$512$	−4.18391e26	−7.64748
$513$	2.78404e25	0.499529
$514$	6.88562e25	1.21281
$515$	−8.93302e24	−0.154465
$516$	−1.71331e26	−2.90846
$517$	9.45280e24	0.157543
$518$	−3.09087e26	−5.05763
$519$	−2.61499e24	−0.0420127
$520$	−4.94838e25	−0.780605
$521$	1.04608e26	1.62034	0.810172	−	0.586193i	$-0.199374\pi$
$521$	1.04608e26	1.62034	0.810172	+	0.586193i	$0.199374\pi$
$522$	−1.11828e26	−1.70091
$523$	1.09350e25	0.163325	0.0816624	−	0.996660i	$-0.473977\pi$
$523$	1.09350e25	0.163325	0.0816624	+	0.996660i	$0.473977\pi$
$524$	5.83817e25	0.856307
$525$	3.03315e25	0.436898
$526$	−6.61916e25	−0.936351
$527$	1.10197e24	0.0153097
$528$	4.87381e26	6.65037
$529$	9.20923e25	1.23423
$530$	−1.78762e26	−2.35317
$531$	1.94984e25	0.252116
$532$	5.09960e26	6.47703
$533$	−4.75542e24	−0.0593308
$534$	7.33699e25	0.899240
$535$	1.10531e26	1.33083
$536$	−3.10840e25	−0.367681
$537$	1.10838e26	1.28805
$538$	−3.47609e25	−0.396881
$539$	−1.60004e26	−1.79489
$540$	8.79499e25	0.969382
$541$	1.24608e26	1.34949	0.674747	−	0.738049i	$-0.264253\pi$
$541$	1.24608e26	1.34949	0.674747	+	0.738049i	$0.264253\pi$
$542$	−3.35348e25	−0.356864
$543$	−1.00267e26	−1.04848
$544$	−7.16151e26	−7.35894
$545$	−7.29374e24	−0.0736518
$546$	9.72605e25	0.965176
$547$	5.33957e25	0.520747	0.260373	−	0.965508i	$-0.416154\pi$
$547$	5.33957e25	0.520747	0.260373	+	0.965508i	$0.416154\pi$
$548$	4.10354e26	3.93317
$549$	−9.67194e24	−0.0911122
$550$	−4.73013e25	−0.437953
$551$	1.77217e26	1.61274
$552$	−8.42756e26	−7.53843
$553$	−1.22718e25	−0.107900
$554$	3.27558e26	2.83104
$555$	−2.14943e26	−1.82616
$556$	−3.44634e26	−2.87838
$557$	−1.58829e26	−1.30409	−0.652043	−	0.758182i	$-0.726088\pi$
$557$	−1.58829e26	−1.30409	−0.652043	+	0.758182i	$0.726088\pi$
$558$	−2.01070e24	−0.0162302
$559$	2.16393e25	0.171724
$560$	8.76294e26	6.83697
$561$	2.48007e26	1.90246
$562$	−9.22154e25	−0.695518
$563$	1.29886e26	0.963236	0.481618	−	0.876381i	$-0.340049\pi$
$563$	1.29886e26	0.963236	0.481618	+	0.876381i	$0.340049\pi$
$564$	7.70498e25	0.561849
$565$	−1.25293e26	−0.898397
$566$	−6.06920e25	−0.427932
$567$	−2.82961e26	−1.96195
$568$	−2.19108e26	−1.49399
$569$	−1.19635e26	−0.802217	−0.401109	−	0.916031i	$-0.631375\pi$
$569$	−1.19635e26	−0.802217	−0.401109	+	0.916031i	$0.631375\pi$
$570$	4.75304e26	3.13444
$571$	−1.69654e26	−1.10033	−0.550163	−	0.835057i	$-0.685434\pi$
$571$	−1.69654e26	−1.10033	−0.550163	+	0.835057i	$0.685434\pi$
$572$	−1.13168e26	−0.721873
$573$	1.91956e26	1.20429
$574$	1.36893e26	0.844728
$575$	5.03156e25	0.305392
$576$	7.41841e26	4.42891
$577$	2.45240e26	1.44020	0.720098	−	0.693873i	$-0.244097\pi$
$577$	2.45240e26	1.44020	0.720098	+	0.693873i	$0.244097\pi$
$578$	−2.76944e26	−1.59984
$579$	−3.09206e26	−1.75712
$580$	5.59841e26	3.12967
$581$	−3.82382e26	−2.10293
$582$	7.55905e25	0.408977
$583$	−2.69711e26	−1.43565
$584$	−1.85529e25	−0.0971606
$585$	2.82640e25	0.145631
$586$	−4.77357e26	−2.42000
$587$	1.12643e25	0.0561878	0.0280939	−	0.999605i	$-0.491056\pi$
$587$	1.12643e25	0.0561878	0.0280939	+	0.999605i	$0.491056\pi$
$588$	−1.30419e27	−6.40113
$589$	3.18641e24	0.0153889
$590$	−1.30829e26	−0.621744
$591$	2.26476e26	1.05911
$592$	1.59453e27	7.33796
$593$	2.45637e26	1.11243	0.556216	−	0.831038i	$-0.312253\pi$
$593$	2.45637e26	1.11243	0.556216	+	0.831038i	$0.312253\pi$
$594$	1.77850e26	0.792651
$595$	4.45908e26	1.95584
$596$	−8.13587e25	−0.351208
$597$	5.90402e26	2.50837
$598$	1.61341e26	0.674659
$599$	4.03475e26	1.66059	0.830294	−	0.557325i	$-0.188172\pi$
$599$	4.03475e26	1.66059	0.830294	+	0.557325i	$0.188172\pi$
$600$	−2.54360e26	−1.03041
$601$	4.45924e26	1.77809	0.889044	−	0.457822i	$-0.151370\pi$
$601$	4.45924e26	1.77809	0.889044	+	0.457822i	$0.151370\pi$
$602$	−6.22924e26	−2.44494
$603$	1.77545e25	0.0685950
$604$	−7.86203e26	−2.99009
$605$	3.96789e25	0.148554
$606$	3.43629e24	0.0126648
$607$	−1.33702e25	−0.0485115	−0.0242558	−	0.999706i	$-0.507722\pi$
$607$	−1.33702e25	−0.0485115	−0.0242558	+	0.999706i	$0.507722\pi$
$608$	−2.07080e27	−7.39698
$609$	−7.25943e26	−2.55293
$610$	6.48964e25	0.224692
$611$	−9.73151e24	−0.0331733
$612$	8.44750e26	2.83524
$613$	1.47396e26	0.487094	0.243547	−	0.969889i	$-0.421689\pi$
$613$	1.47396e26	0.487094	0.243547	+	0.969889i	$0.421689\pi$
$614$	5.60799e26	1.82477
$615$	9.51968e25	0.305006
$616$	2.14921e27	6.78051
$617$	1.17670e26	0.365559	0.182780	−	0.983154i	$-0.441491\pi$
$617$	1.17670e26	0.365559	0.182780	+	0.983154i	$0.441491\pi$
$618$	−1.47240e26	−0.450439
$619$	9.63343e25	0.290215	0.145107	−	0.989416i	$-0.453647\pi$
$619$	9.63343e25	0.290215	0.145107	+	0.989416i	$0.453647\pi$
$620$	1.00661e25	0.0298635
$621$	−1.89183e26	−0.552730
$622$	−1.88976e26	−0.543749
$623$	1.99033e26	0.564012
$624$	−5.01750e26	−1.40034
$625$	−2.74283e26	−0.753944
$626$	−3.37459e26	−0.913619
$627$	7.17128e26	1.91230
$628$	8.63277e26	2.26743
$629$	8.11384e26	2.09916
$630$	−8.13625e26	−2.07343
$631$	6.97264e26	1.75032	0.875162	−	0.483830i	$-0.160755\pi$
$631$	6.97264e26	1.75032	0.875162	+	0.483830i	$0.160755\pi$
$632$	1.02912e26	0.254480
$633$	6.91095e25	0.168346
$634$	7.77624e26	1.86604
$635$	−1.30753e26	−0.309103
$636$	−2.19842e27	−5.11997
$637$	1.64721e26	0.377942
$638$	1.13209e27	2.55909
$639$	1.25149e26	0.278721
$640$	−2.75158e27	−6.03772
$641$	−3.22528e26	−0.697295	−0.348648	−	0.937254i	$-0.613359\pi$
$641$	−3.22528e26	−0.697295	−0.348648	+	0.937254i	$0.613359\pi$
$642$	1.82185e27	3.88087
$643$	5.66548e26	1.18914	0.594570	−	0.804044i	$-0.297322\pi$
$643$	5.66548e26	1.18914	0.594570	+	0.804044i	$0.297322\pi$
$644$	−3.46532e27	−7.16685
$645$	−4.33189e26	−0.882796
$646$	−1.79422e27	−3.60302
$647$	−9.01454e26	−1.78383	−0.891914	−	0.452205i	$-0.850638\pi$
$647$	−9.01454e26	−1.78383	−0.891914	+	0.452205i	$0.850638\pi$
$648$	2.37292e27	4.62722
$649$	−1.97392e26	−0.379320
$650$	4.86959e25	0.0922180
$651$	−1.30527e25	−0.0243602
$652$	4.63136e26	0.851837
$653$	5.15285e26	0.934054	0.467027	−	0.884243i	$-0.345325\pi$
$653$	5.15285e26	0.934054	0.467027	+	0.884243i	$0.345325\pi$
$654$	−1.20221e26	−0.214778
$655$	1.47611e26	0.259912
$656$	−7.06205e26	−1.22559
$657$	1.05970e25	0.0181264
$658$	2.80137e26	0.472308
$659$	−9.26386e26	−1.53950	−0.769752	−	0.638344i	$-0.779620\pi$
$659$	−9.26386e26	−1.53950	−0.769752	+	0.638344i	$0.779620\pi$
$660$	2.26546e27	3.71099
$661$	−8.01642e25	−0.129439	−0.0647197	−	0.997903i	$-0.520615\pi$
$661$	−8.01642e25	−0.129439	−0.0647197	+	0.997903i	$0.520615\pi$
$662$	−1.26936e27	−2.02039
$663$	−2.55319e26	−0.400594
$664$	3.20666e27	4.95971
$665$	1.28937e27	1.96595
$666$	−1.48049e27	−2.22536
$667$	−1.20424e27	−1.78450
$668$	8.55413e26	1.24968
$669$	−1.44389e27	−2.07964
$670$	−1.19128e26	−0.169162
$671$	9.79143e25	0.137083
$672$	8.48275e27	11.7092
$673$	−1.38414e27	−1.88381	−0.941907	−	0.335873i	$-0.890969\pi$
$673$	−1.38414e27	−1.88381	−0.941907	+	0.335873i	$0.890969\pi$
$674$	−1.45234e27	−1.94895
$675$	−5.70992e25	−0.0755516
$676$	−2.13601e27	−2.78683
$677$	−7.49459e25	−0.0964174	−0.0482087	−	0.998837i	$-0.515351\pi$
$677$	−7.49459e25	−0.0964174	−0.0482087	+	0.998837i	$0.515351\pi$
$678$	−2.06518e27	−2.61984
$679$	2.05057e26	0.256514
$680$	−3.73939e27	−4.61281
$681$	−1.46229e27	−1.77884
$682$	2.03554e25	0.0244190
$683$	−3.19948e26	−0.378514	−0.189257	−	0.981928i	$-0.560608\pi$
$683$	−3.19948e26	−0.378514	−0.189257	+	0.981928i	$0.560608\pi$
$684$	2.44265e27	2.84989
$685$	1.03753e27	1.19382
$686$	−1.88844e27	−2.14301
$687$	1.20281e27	1.34620
$688$	3.21356e27	3.54729
$689$	2.77663e26	0.302299
$690$	−3.22983e27	−3.46827
$691$	2.73582e26	0.289765	0.144882	−	0.989449i	$-0.453720\pi$
$691$	2.73582e26	0.289765	0.144882	+	0.989449i	$0.453720\pi$
$692$	9.01711e25	0.0942019
$693$	−1.22758e27	−1.26498
$694$	−2.32463e26	−0.236287
$695$	−8.71365e26	−0.873665
$696$	6.08777e27	6.02103
$697$	−3.59357e26	−0.350602
$698$	4.33894e26	0.417596
$699$	−1.43767e27	−1.36497
$700$	−1.04590e27	−0.979624
$701$	−1.18914e26	−0.109878	−0.0549390	−	0.998490i	$-0.517496\pi$
$701$	−1.18914e26	−0.109878	−0.0549390	+	0.998490i	$0.517496\pi$
$702$	−1.83094e26	−0.166905
$703$	2.34617e27	2.11001
$704$	−7.51006e27	−6.66351
$705$	1.94811e26	0.170536
$706$	−6.01825e26	−0.519787
$707$	9.32173e24	0.00794350
$708$	−1.60895e27	−1.35277
$709$	1.84409e27	1.52983	0.764915	−	0.644131i	$-0.222781\pi$
$709$	1.84409e27	1.52983	0.764915	+	0.644131i	$0.222781\pi$
$710$	−8.39720e26	−0.687354
$711$	−5.87808e25	−0.0474760
$712$	−1.66909e27	−1.33021
$713$	−2.16526e25	−0.0170278
$714$	7.34977e27	5.70349
$715$	−2.86132e26	−0.219108
$716$	−3.82196e27	−2.88810
$717$	2.66945e27	1.99063
$718$	8.24069e26	0.606431
$719$	1.84882e27	1.34267	0.671337	−	0.741152i	$-0.265720\pi$
$719$	1.84882e27	1.34267	0.671337	+	0.741152i	$0.265720\pi$
$720$	4.19735e27	3.00827
$721$	−3.99424e26	−0.282520
$722$	−2.34504e27	−1.63699
$723$	1.32604e27	0.913572
$724$	3.45745e27	2.35093
$725$	−3.63462e26	−0.243920
$726$	6.54016e26	0.433202
$727$	−2.60112e27	−1.70052	−0.850262	−	0.526360i	$-0.823556\pi$
$727$	−2.60112e27	−1.70052	−0.850262	+	0.526360i	$0.823556\pi$
$728$	−2.21258e27	−1.42775
$729$	−5.94405e26	−0.378591
$730$	−7.11033e25	−0.0447015
$731$	1.63524e27	1.01477
$732$	7.98099e26	0.488879
$733$	6.69675e26	0.404927	0.202463	−	0.979290i	$-0.435105\pi$
$733$	6.69675e26	0.404927	0.202463	+	0.979290i	$0.435105\pi$
$734$	−4.56955e27	−2.72748
$735$	−3.29749e27	−1.94292
$736$	1.40717e28	8.18478
$737$	−1.79738e26	−0.103204
$738$	6.55700e26	0.371681
$739$	−9.91650e26	−0.554928	−0.277464	−	0.960736i	$-0.589494\pi$
$739$	−9.91650e26	−0.554928	−0.277464	+	0.960736i	$0.589494\pi$
$740$	7.41174e27	4.09467
$741$	−7.38272e26	−0.402665
$742$	−7.99300e27	−4.30400
$743$	7.86751e26	0.418257	0.209129	−	0.977888i	$-0.432937\pi$
$743$	7.86751e26	0.418257	0.209129	+	0.977888i	$0.432937\pi$
$744$	1.09460e26	0.0574530
$745$	−2.05706e26	−0.106601
$746$	3.72875e27	1.90785
$747$	−1.83157e27	−0.925289
$748$	−8.55186e27	−4.26575
$749$	4.94219e27	2.43412
$750$	−5.74607e27	−2.79440
$751$	2.27305e27	1.09151	0.545757	−	0.837943i	$-0.316242\pi$
$751$	2.27305e27	1.09151	0.545757	+	0.837943i	$0.316242\pi$
$752$	−1.44518e27	−0.685256
$753$	−5.05971e27	−2.36905
$754$	−1.16547e27	−0.538858
$755$	−1.98782e27	−0.907571
$756$	3.93252e27	1.77302
$757$	−9.97715e26	−0.444217	−0.222109	−	0.975022i	$-0.571294\pi$
$757$	−9.97715e26	−0.444217	−0.222109	+	0.975022i	$0.571294\pi$
$758$	3.40503e27	1.49714
$759$	−4.87309e27	−2.11596
$760$	−1.08127e28	−4.63666
$761$	3.96267e27	1.67816	0.839081	−	0.544006i	$-0.183093\pi$
$761$	3.96267e27	1.67816	0.839081	+	0.544006i	$0.183093\pi$
$762$	−2.15517e27	−0.901383
$763$	−3.26126e26	−0.134711
$764$	−6.61909e27	−2.70030
$765$	2.13585e27	0.860572
$766$	−6.60015e27	−2.62652
$767$	2.03212e26	0.0798719
$768$	−2.45240e28	−9.52049
$769$	3.28540e27	1.25976	0.629881	−	0.776692i	$-0.283104\pi$
$769$	3.28540e27	1.25976	0.629881	+	0.776692i	$0.283104\pi$
$770$	8.23676e27	3.11957
$771$	2.14102e27	0.800949
$772$	1.06622e28	3.93986
$773$	3.68502e27	1.34504	0.672519	−	0.740080i	$-0.265212\pi$
$773$	3.68502e27	1.34504	0.672519	+	0.740080i	$0.265212\pi$
$774$	−2.98374e27	−1.07578
$775$	−6.53516e24	−0.00232750
$776$	−1.71961e27	−0.604984
$777$	−9.61077e27	−3.34009
$778$	6.35528e27	2.18187
$779$	−1.03911e27	−0.352414
$780$	−2.33226e27	−0.781408
$781$	−1.26695e27	−0.419348
$782$	1.21922e28	3.98675
$783$	1.36659e27	0.441471
$784$	2.44620e28	7.80710
$785$	2.18269e27	0.688225
$786$	2.43303e27	0.757938
$787$	−6.23435e27	−1.91881	−0.959403	−	0.282038i	$-0.908989\pi$
$787$	−6.23435e27	−1.91881	−0.959403	+	0.282038i	$0.908989\pi$
$788$	−7.80945e27	−2.37477
$789$	−2.05817e27	−0.618372
$790$	3.94405e26	0.117081
$791$	−5.60227e27	−1.64319
$792$	1.02945e28	2.98343
$793$	−1.00801e26	−0.0288649
$794$	8.15386e26	0.230711
$795$	−5.55843e27	−1.55405
$796$	−2.03585e28	−5.62434
$797$	3.30119e27	0.901189	0.450594	−	0.892729i	$-0.351212\pi$
$797$	3.30119e27	0.901189	0.450594	+	0.892729i	$0.351212\pi$
$798$	2.12524e28	5.73297
$799$	−7.35390e26	−0.196030
$800$	4.24710e27	1.11876
$801$	9.53345e26	0.248165
$802$	−8.91249e27	−2.29268
$803$	−1.07279e26	−0.0272720
$804$	−1.46504e27	−0.368059
$805$	−8.76166e27	−2.17533
$806$	−2.09556e25	−0.00514182
$807$	−1.08086e27	−0.262102
$808$	−7.81721e25	−0.0187346
$809$	3.68117e27	0.871917	0.435958	−	0.899967i	$-0.356410\pi$
$809$	3.68117e27	0.871917	0.435958	+	0.899967i	$0.356410\pi$
$810$	9.09410e27	2.12889
$811$	2.53232e27	0.585895	0.292948	−	0.956129i	$-0.405364\pi$
$811$	2.53232e27	0.585895	0.292948	+	0.956129i	$0.405364\pi$
$812$	2.50323e28	5.72424
$813$	−1.04273e27	−0.235675
$814$	1.49878e28	3.34816
$815$	1.17098e27	0.258556
$816$	−3.79162e28	−8.27501
$817$	4.72841e27	1.02001
$818$	1.50499e27	0.320906
$819$	1.26377e27	0.266362
$820$	−3.28261e27	−0.683893
$821$	−6.82525e27	−1.40559	−0.702795	−	0.711392i	$-0.748065\pi$
$821$	−6.82525e27	−1.40559	−0.702795	+	0.711392i	$0.748065\pi$
$822$	1.71013e28	3.48135
$823$	5.46028e26	0.109879	0.0549397	−	0.998490i	$-0.482503\pi$
$823$	5.46028e26	0.109879	0.0549397	+	0.998490i	$0.482503\pi$
$824$	3.34957e27	0.666317
$825$	−1.47079e27	−0.289227
$826$	−5.84980e27	−1.13718
$827$	−9.90451e27	−1.90340	−0.951702	−	0.307024i	$-0.900667\pi$
$827$	−9.90451e27	−1.90340	−0.951702	+	0.307024i	$0.900667\pi$
$828$	−1.65985e28	−3.15342
$829$	−3.90933e27	−0.734234	−0.367117	−	0.930175i	$-0.619655\pi$
$829$	−3.90933e27	−0.734234	−0.367117	+	0.930175i	$0.619655\pi$
$830$	1.22894e28	2.28186
$831$	1.01851e28	1.86964
$832$	7.73148e27	1.40311
$833$	1.24476e28	2.23337
$834$	−1.43625e28	−2.54772
$835$	2.16281e27	0.379312
$836$	−2.47283e28	−4.28780
$837$	2.45718e25	0.00421255
$838$	−1.93619e27	−0.328194
$839$	6.36087e27	1.06605	0.533026	−	0.846099i	$-0.321055\pi$
$839$	6.36087e27	1.06605	0.533026	+	0.846099i	$0.321055\pi$
$840$	4.42927e28	7.33972
$841$	2.59572e27	0.425300
$842$	3.35850e27	0.544103
$843$	−2.86736e27	−0.459325
$844$	−2.38306e27	−0.377470
$845$	−5.40065e27	−0.845877
$846$	1.34183e27	0.207816
$847$	1.77417e27	0.271708
$848$	4.12345e28	6.24454
$849$	−1.88716e27	−0.282609
$850$	3.67985e27	0.544942
$851$	−1.59429e28	−2.33473
$852$	−1.03269e28	−1.49553
$853$	4.13784e27	0.592594	0.296297	−	0.955096i	$-0.404248\pi$
$853$	4.13784e27	0.592594	0.296297	+	0.955096i	$0.404248\pi$
$854$	2.90173e27	0.410967
$855$	6.17596e27	0.865020
$856$	−4.14453e28	−5.74082
$857$	1.36672e28	1.87225	0.936123	−	0.351674i	$-0.114387\pi$
$857$	1.36672e28	1.87225	0.936123	+	0.351674i	$0.114387\pi$
$858$	−4.71622e27	−0.638948
$859$	−1.22217e28	−1.63756	−0.818778	−	0.574110i	$-0.805348\pi$
$859$	−1.22217e28	−1.63756	−0.818778	+	0.574110i	$0.805348\pi$
$860$	1.49374e28	1.97943
$861$	4.25655e27	0.557863
$862$	2.72189e28	3.52818
$863$	−9.08705e27	−1.16499	−0.582493	−	0.812836i	$-0.697923\pi$
$863$	−9.08705e27	−1.16499	−0.582493	+	0.812836i	$0.697923\pi$
$864$	−1.59688e28	−2.02485
$865$	2.27987e26	0.0285928
$866$	−2.12334e28	−2.63390
$867$	−8.61132e27	−1.05655
$868$	4.50088e26	0.0546210
$869$	5.95070e26	0.0714299
$870$	2.33311e28	2.77015
$871$	1.85037e26	0.0217313
$872$	2.73490e27	0.317713
$873$	9.82200e26	0.112866
$874$	3.52547e28	4.00736
$875$	−1.55875e28	−1.75267
$876$	−8.74431e26	−0.0972605
$877$	−1.06283e28	−1.16941	−0.584705	−	0.811246i	$-0.698790\pi$
$877$	−1.06283e28	−1.16941	−0.584705	+	0.811246i	$0.698790\pi$
$878$	−8.24996e27	−0.897954
$879$	−1.48430e28	−1.59818
$880$	−4.24921e28	−4.52608
$881$	1.66175e28	1.75103	0.875515	−	0.483190i	$-0.160522\pi$
$881$	1.66175e28	1.75103	0.875515	+	0.483190i	$0.160522\pi$
$882$	−2.27126e28	−2.36764
$883$	1.58538e26	0.0163496	0.00817480	−	0.999967i	$-0.497398\pi$
$883$	1.58538e26	0.0163496	0.00817480	+	0.999967i	$0.497398\pi$
$884$	8.80400e27	0.898222
$885$	−4.06803e27	−0.410603
$886$	1.04763e28	1.04613
$887$	1.22500e28	1.21021	0.605107	−	0.796144i	$-0.293130\pi$
$887$	1.22500e28	1.21021	0.605107	+	0.796144i	$0.293130\pi$
$888$	8.05961e28	7.87754
$889$	−5.84640e27	−0.565356
$890$	−6.39672e27	−0.612001
$891$	1.37210e28	1.29881
$892$	4.97889e28	4.66301
$893$	−2.12643e27	−0.197043
$894$	−3.39059e27	−0.310863
$895$	−9.66336e27	−0.876615
$896$	−1.23032e29	−11.0431
$897$	5.01677e27	0.445549
$898$	−3.08525e28	−2.71122
$899$	1.56410e26	0.0136003
$900$	−5.00975e27	−0.431035
$901$	2.09824e28	1.78637
$902$	−6.63801e27	−0.559211
$903$	−1.93693e28	−1.61465
$904$	4.69807e28	3.87543
$905$	8.74175e27	0.713571
$906$	−3.27647e28	−2.64660
$907$	1.44844e28	1.15779	0.578896	−	0.815401i	$-0.303484\pi$
$907$	1.44844e28	1.15779	0.578896	+	0.815401i	$0.303484\pi$
$908$	5.04233e28	3.98856
$909$	4.46501e25	0.00349514
$910$	−8.47962e27	−0.656875
$911$	−2.03813e28	−1.56246	−0.781228	−	0.624246i	$-0.785406\pi$
$911$	−2.03813e28	−1.56246	−0.781228	+	0.624246i	$0.785406\pi$
$912$	−1.09637e29	−8.31778
$913$	1.85420e28	1.39214
$914$	−4.95073e28	−3.67858
$915$	2.01790e27	0.148388
$916$	−4.14758e28	−3.01847
$917$	6.60016e27	0.475386
$918$	−1.38360e28	−0.986290
$919$	2.11489e28	1.49207	0.746036	−	0.665905i	$-0.231954\pi$
$919$	2.11489e28	1.49207	0.746036	+	0.665905i	$0.231954\pi$
$920$	7.34754e28	5.13047
$921$	1.74376e28	1.20509
$922$	1.04107e28	0.712093
$923$	1.30431e27	0.0883005
$924$	1.01296e29	6.78748
$925$	−4.81188e27	−0.319130
$926$	4.60955e28	3.02590
$927$	−1.91320e27	−0.124309
$928$	−1.01649e29	−6.53727
$929$	−2.74720e28	−1.74880	−0.874401	−	0.485205i	$-0.838745\pi$
$929$	−2.74720e28	−1.74880	−0.874401	+	0.485205i	$0.838745\pi$
$930$	4.19501e26	0.0264329
$931$	3.59932e28	2.24491
$932$	4.95741e28	3.06058
$933$	−5.87605e27	−0.359095
$934$	2.35710e28	1.42588
$935$	−2.16224e28	−1.29477
$936$	−1.05980e28	−0.628209
$937$	1.69922e28	0.997066	0.498533	−	0.866871i	$-0.333872\pi$
$937$	1.69922e28	0.997066	0.498533	+	0.866871i	$0.333872\pi$
$938$	−5.32660e27	−0.309402
$939$	−1.04930e28	−0.603360
$940$	−6.71755e27	−0.382381
$941$	−3.10851e26	−0.0175166	−0.00875831	−	0.999962i	$-0.502788\pi$
$941$	−3.10851e26	−0.0175166	−0.00875831	+	0.999962i	$0.502788\pi$
$942$	3.59767e28	2.00695
$943$	7.06102e27	0.389948
$944$	3.01781e28	1.64990
$945$	9.94291e27	0.538160
$946$	3.02060e28	1.61855
$947$	−2.35515e28	−1.24938	−0.624689	−	0.780873i	$-0.714774\pi$
$947$	−2.35515e28	−1.24938	−0.624689	+	0.780873i	$0.714774\pi$
$948$	4.85041e27	0.254741
$949$	1.10442e26	0.00574255
$950$	1.06405e28	0.547758
$951$	2.41795e28	1.23235
$952$	−1.67200e29	−8.43694
$953$	1.96270e28	0.980555	0.490278	−	0.871566i	$-0.336895\pi$
$953$	1.96270e28	0.980555	0.490278	+	0.871566i	$0.336895\pi$
$954$	−3.82856e28	−1.89376
$955$	−1.67356e28	−0.819612
$956$	−9.20491e28	−4.46344
$957$	3.52015e28	1.69004
$958$	4.16464e28	1.97973
$959$	4.63913e28	2.18353
$960$	−1.54773e29	−7.21306
$961$	−2.16678e28	−0.999870
$962$	−1.54297e28	−0.705009
$963$	2.36725e28	1.07101
$964$	−4.57250e28	−2.04844
$965$	2.69580e28	1.19585
$966$	−1.44416e29	−6.34355
$967$	−8.80381e26	−0.0382930	−0.0191465	−	0.999817i	$-0.506095\pi$
$967$	−8.80381e26	−0.0382930	−0.0191465	+	0.999817i	$0.506095\pi$
$968$	−1.48782e28	−0.640819
$969$	−5.57896e28	−2.37946
$970$	−6.59033e27	−0.278340
$971$	−1.01609e28	−0.424962	−0.212481	−	0.977165i	$-0.568154\pi$
$971$	−1.01609e28	−0.424962	−0.212481	+	0.977165i	$0.568154\pi$
$972$	8.56003e28	3.54524
$973$	−3.89615e28	−1.59795
$974$	−2.34041e28	−0.950564
$975$	1.51416e27	0.0609013
$976$	−1.49695e28	−0.596258
$977$	1.22974e28	0.485080	0.242540	−	0.970141i	$-0.422019\pi$
$977$	1.22974e28	0.485080	0.242540	+	0.970141i	$0.422019\pi$
$978$	1.93010e28	0.753981
$979$	−9.65123e27	−0.373376
$980$	1.13705e29	4.35646
$981$	−1.56211e27	−0.0592729
$982$	−1.23076e28	−0.462503
$983$	2.64717e28	0.985196	0.492598	−	0.870257i	$-0.336047\pi$
$983$	2.64717e28	0.985196	0.492598	+	0.870257i	$0.336047\pi$
$984$	−3.56955e28	−1.31571
$985$	−1.97453e28	−0.720806
$986$	−8.80723e28	−3.18426
$987$	8.71062e27	0.311915
$988$	2.54574e28	0.902865
$989$	−3.21309e28	−1.12865
$990$	3.94532e28	1.37261
$991$	1.73370e28	0.597411	0.298706	−	0.954345i	$-0.403445\pi$
$991$	1.73370e28	0.597411	0.298706	+	0.954345i	$0.403445\pi$
$992$	−1.82768e27	−0.0623790
$993$	−3.94698e28	−1.33428
$994$	−3.75466e28	−1.25719
$995$	−5.14740e28	−1.70714
$996$	1.51135e29	4.96481
$997$	2.39136e28	0.778110	0.389055	−	0.921214i	$-0.372802\pi$
$997$	2.39136e28	0.778110	0.389055	+	0.921214i	$0.372802\pi$
$998$	−9.88349e28	−3.18545
$999$	1.80923e28	0.577594

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1437.04 q^{2} -44683.4 q^{3} +1.54079e6 q^{4} +3.89571e6 q^{5} +6.42118e7 q^{6} +1.74189e8 q^{7} -1.46076e9 q^{8} +8.34349e8 q^{9} +O(q^{10})\)	\(q-1437.04 q^{2} -44683.4 q^{3} +1.54079e6 q^{4} +3.89571e6 q^{5} +6.42118e7 q^{6} +1.74189e8 q^{7} -1.46076e9 q^{8} +8.34349e8 q^{9} -5.59828e9 q^{10} -8.44656e9 q^{11} -6.88479e10 q^{12} +8.69560e9 q^{13} -2.50317e11 q^{14} -1.74074e11 q^{15} +1.29134e12 q^{16} +6.57108e11 q^{17} -1.19899e12 q^{18} +1.90007e12 q^{19} +6.00248e12 q^{20} -7.78339e12 q^{21} +1.21380e13 q^{22} -1.29115e13 q^{23} +6.52716e13 q^{24} -3.89695e12 q^{25} -1.24959e13 q^{26} +1.46523e13 q^{27} +2.68390e14 q^{28} +9.32683e13 q^{29} +2.50151e14 q^{30} +1.67699e12 q^{31} -1.08985e15 q^{32} +3.77421e14 q^{33} -9.44289e14 q^{34} +6.78591e14 q^{35} +1.28556e15 q^{36} +1.23478e15 q^{37} -2.73048e15 q^{38} -3.88549e14 q^{39} -5.69068e15 q^{40} -5.46877e14 q^{41} +1.11850e16 q^{42} +2.48854e15 q^{43} -1.30144e16 q^{44} +3.25038e15 q^{45} +1.85544e16 q^{46} -1.11913e15 q^{47} -5.77017e16 q^{48} +1.89431e16 q^{49} +5.60007e15 q^{50} -2.93618e16 q^{51} +1.33981e16 q^{52} +3.19315e16 q^{53} -2.10559e16 q^{54} -3.29053e16 q^{55} -2.54448e17 q^{56} -8.49018e16 q^{57} -1.34030e17 q^{58} +2.33696e16 q^{59} -2.68211e17 q^{60} -1.15922e16 q^{61} -2.40990e15 q^{62} +1.45335e17 q^{63} +8.89126e17 q^{64} +3.38755e16 q^{65} -5.42369e17 q^{66} +2.12794e16 q^{67} +1.01247e18 q^{68} +5.76932e17 q^{69} -9.75162e17 q^{70} +1.49996e17 q^{71} -1.21878e18 q^{72} +1.27009e16 q^{73} -1.77443e18 q^{74} +1.74129e17 q^{75} +2.92762e18 q^{76} -1.47130e18 q^{77} +5.58360e17 q^{78} -7.04511e16 q^{79} +5.03070e18 q^{80} -1.62445e18 q^{81} +7.85883e17 q^{82} -2.19521e18 q^{83} -1.19926e19 q^{84} +2.55990e18 q^{85} -3.57613e18 q^{86} -4.16755e18 q^{87} +1.23384e19 q^{88} +1.14262e18 q^{89} -4.67092e18 q^{90} +1.51468e18 q^{91} -1.98940e19 q^{92} -7.49339e16 q^{93} +1.60823e18 q^{94} +7.40213e18 q^{95} +4.86984e19 q^{96} +1.17721e18 q^{97} -2.72219e19 q^{98} -7.04738e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 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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