LMFDB - Embedded newform 47.20.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-843.346 q^{2} +22834.2 q^{3} +186945. q^{4} -5.74638e6 q^{5} -1.92572e7 q^{6} -1.06332e8 q^{7} +2.84497e8 q^{8} -6.40859e8 q^{9} +O(q^{10})$	\(q-843.346 q^{2} +22834.2 q^{3} +186945. q^{4} -5.74638e6 q^{5} -1.92572e7 q^{6} -1.06332e8 q^{7} +2.84497e8 q^{8} -6.40859e8 q^{9} +4.84619e9 q^{10} -2.13765e7 q^{11} +4.26875e9 q^{12} +6.00396e10 q^{13} +8.96744e10 q^{14} -1.31214e11 q^{15} -3.37942e11 q^{16} -8.09041e11 q^{17} +5.40466e11 q^{18} -7.35070e11 q^{19} -1.07426e12 q^{20} -2.42800e12 q^{21} +1.80278e10 q^{22} -9.11480e12 q^{23} +6.49627e12 q^{24} +1.39474e13 q^{25} -5.06342e13 q^{26} -4.11729e13 q^{27} -1.98782e13 q^{28} -1.49639e13 q^{29} +1.10659e14 q^{30} -1.20833e14 q^{31} +1.35844e14 q^{32} -4.88116e11 q^{33} +6.82302e14 q^{34} +6.11022e14 q^{35} -1.19805e14 q^{36} -1.52413e15 q^{37} +6.19919e14 q^{38} +1.37096e15 q^{39} -1.63483e15 q^{40} -1.92039e15 q^{41} +2.04765e15 q^{42} +5.00272e15 q^{43} -3.99623e12 q^{44} +3.68262e15 q^{45} +7.68693e15 q^{46} -1.11913e15 q^{47} -7.71666e15 q^{48} -9.24802e13 q^{49} -1.17625e16 q^{50} -1.84738e16 q^{51} +1.12241e16 q^{52} -3.57989e16 q^{53} +3.47230e16 q^{54} +1.22837e14 q^{55} -3.02510e16 q^{56} -1.67848e16 q^{57} +1.26197e16 q^{58} -5.42554e16 q^{59} -2.45298e16 q^{60} -7.04491e16 q^{61} +1.01904e17 q^{62} +6.81436e16 q^{63} +6.26155e16 q^{64} -3.45011e17 q^{65} +4.11651e14 q^{66} -1.51365e17 q^{67} -1.51246e17 q^{68} -2.08129e17 q^{69} -5.15303e17 q^{70} -1.74547e17 q^{71} -1.82322e17 q^{72} +4.60160e16 q^{73} +1.28537e18 q^{74} +3.18479e17 q^{75} -1.37418e17 q^{76} +2.27300e15 q^{77} -1.15619e18 q^{78} -1.76923e18 q^{79} +1.94195e18 q^{80} -1.95306e17 q^{81} +1.61956e18 q^{82} -1.84812e18 q^{83} -4.53903e17 q^{84} +4.64906e18 q^{85} -4.21902e18 q^{86} -3.41688e17 q^{87} -6.08155e15 q^{88} +2.60629e18 q^{89} -3.10572e18 q^{90} -6.38411e18 q^{91} -1.70397e18 q^{92} -2.75914e18 q^{93} +9.43815e17 q^{94} +4.22399e18 q^{95} +3.10190e18 q^{96} +1.30524e19 q^{97} +7.79928e16 q^{98} +1.36993e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−843.346	−1.16472	−0.582359	−	0.812932i	$-0.697870\pi$
$2$	−843.346	−1.16472	−0.582359	+	0.812932i	$0.697870\pi$
$3$	22834.2	0.669784	0.334892	−	0.942257i	$-0.391300\pi$
$3$	22834.2	0.669784	0.334892	+	0.942257i	$0.391300\pi$
$4$	186945.	0.356569
$5$	−5.74638e6	−1.31577	−0.657884	−	0.753119i	$-0.728548\pi$
$5$	−5.74638e6	−1.31577	−0.657884	+	0.753119i	$0.728548\pi$
$6$	−1.92572e7	−0.780110
$7$	−1.06332e8	−0.995935	−0.497968	−	0.867196i	$-0.665920\pi$
$7$	−1.06332e8	−0.995935	−0.497968	+	0.867196i	$0.665920\pi$
$8$	2.84497e8	0.749416
$9$	−6.40859e8	−0.551390
$10$	4.84619e9	1.53250
$11$	−2.13765e7	−0.00273342	−0.00136671	−	0.999999i	$-0.500435\pi$
$11$	−2.13765e7	−0.00273342	−0.00136671	+	0.999999i	$0.500435\pi$
$12$	4.26875e9	0.238824
$13$	6.00396e10	1.57028	0.785138	−	0.619320i	$-0.212592\pi$
$13$	6.00396e10	1.57028	0.785138	+	0.619320i	$0.212592\pi$
$14$	8.96744e10	1.15998
$15$	−1.31214e11	−0.881280
$16$	−3.37942e11	−1.22943
$17$	−8.09041e11	−1.65465	−0.827324	−	0.561724i	$-0.810138\pi$
$17$	−8.09041e11	−1.65465	−0.827324	+	0.561724i	$0.810138\pi$
$18$	5.40466e11	0.642214
$19$	−7.35070e11	−0.522600	−0.261300	−	0.965258i	$-0.584151\pi$
$19$	−7.35070e11	−0.522600	−0.261300	+	0.965258i	$0.584151\pi$
$20$	−1.07426e12	−0.469163
$21$	−2.42800e12	−0.667061
$22$	1.80278e10	0.00318366
$23$	−9.11480e12	−1.05519	−0.527597	−	0.849495i	$-0.676907\pi$
$23$	−9.11480e12	−1.05519	−0.527597	+	0.849495i	$0.676907\pi$
$24$	6.49627e12	0.501946
$25$	1.39474e13	0.731246
$26$	−5.06342e13	−1.82893
$27$	−4.11729e13	−1.03910
$28$	−1.98782e13	−0.355120
$29$	−1.49639e13	−0.191541	−0.0957707	−	0.995403i	$-0.530532\pi$
$29$	−1.49639e13	−0.191541	−0.0957707	+	0.995403i	$0.530532\pi$
$30$	1.10659e14	1.02644
$31$	−1.20833e14	−0.820825	−0.410412	−	0.911900i	$-0.634615\pi$
$31$	−1.20833e14	−0.820825	−0.410412	+	0.911900i	$0.634615\pi$
$32$	1.35844e14	0.682522
$33$	−4.88116e11	−0.00183080
$34$	6.82302e14	1.92720
$35$	6.11022e14	1.31042
$36$	−1.19805e14	−0.196609
$37$	−1.52413e15	−1.92799	−0.963995	−	0.265922i	$-0.914324\pi$
$37$	−1.52413e15	−1.92799	−0.963995	+	0.265922i	$0.914324\pi$
$38$	6.19919e14	0.608682
$39$	1.37096e15	1.05175
$40$	−1.63483e15	−0.986057
$41$	−1.92039e15	−0.916102	−0.458051	−	0.888926i	$-0.651452\pi$
$41$	−1.92039e15	−0.916102	−0.458051	+	0.888926i	$0.651452\pi$
$42$	2.04765e15	0.776939
$43$	5.00272e15	1.51794	0.758971	−	0.651124i	$-0.225702\pi$
$43$	5.00272e15	1.51794	0.758971	+	0.651124i	$0.225702\pi$
$44$	−3.99623e12	−0.000974653 0
$45$	3.68262e15	0.725501
$46$	7.68693e15	1.22900
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	−7.71666e15	−0.823451
$49$	−9.24802e13	−0.00811308
$50$	−1.17625e16	−0.851696
$51$	−1.84738e16	−1.10826
$52$	1.12241e16	0.559912
$53$	−3.57989e16	−1.49022	−0.745108	−	0.666944i	$-0.767602\pi$
$53$	−3.57989e16	−1.49022	−0.745108	+	0.666944i	$0.767602\pi$
$54$	3.47230e16	1.21025
$55$	1.22837e14	0.00359654
$56$	−3.02510e16	−0.746369
$57$	−1.67848e16	−0.350029
$58$	1.26197e16	0.223092
$59$	−5.42554e16	−0.815358	−0.407679	−	0.913125i	$-0.633662\pi$
$59$	−5.42554e16	−0.815358	−0.407679	+	0.913125i	$0.633662\pi$
$60$	−2.45298e16	−0.314237
$61$	−7.04491e16	−0.771333	−0.385666	−	0.922638i	$-0.626028\pi$
$61$	−7.04491e16	−0.771333	−0.385666	+	0.922638i	$0.626028\pi$
$62$	1.01904e17	0.956030
$63$	6.81436e16	0.549148
$64$	6.26155e16	0.434482
$65$	−3.45011e17	−2.06612
$66$	4.11651e14	0.00213237
$67$	−1.51365e17	−0.679696	−0.339848	−	0.940480i	$-0.610376\pi$
$67$	−1.51365e17	−0.679696	−0.339848	+	0.940480i	$0.610376\pi$
$68$	−1.51246e17	−0.589997
$69$	−2.08129e17	−0.706752
$70$	−5.15303e17	−1.52627
$71$	−1.74547e17	−0.451812	−0.225906	−	0.974149i	$-0.572534\pi$
$71$	−1.74547e17	−0.451812	−0.225906	+	0.974149i	$0.572534\pi$
$72$	−1.82322e17	−0.413220
$73$	4.60160e16	0.0914832	0.0457416	−	0.998953i	$-0.485435\pi$
$73$	4.60160e16	0.0914832	0.0457416	+	0.998953i	$0.485435\pi$
$74$	1.28537e18	2.24556
$75$	3.18479e17	0.489777
$76$	−1.37418e17	−0.186343
$77$	2.27300e15	0.00272231
$78$	−1.15619e18	−1.22499
$79$	−1.76923e18	−1.66084	−0.830420	−	0.557139i	$-0.811899\pi$
$79$	−1.76923e18	−1.66084	−0.830420	+	0.557139i	$0.811899\pi$
$80$	1.94195e18	1.61764
$81$	−1.95306e17	−0.144580
$82$	1.61956e18	1.06700
$83$	−1.84812e18	−1.08515	−0.542573	−	0.840009i	$-0.682550\pi$
$83$	−1.84812e18	−1.08515	−0.542573	+	0.840009i	$0.682550\pi$
$84$	−4.53903e17	−0.237854
$85$	4.64906e18	2.17713
$86$	−4.21902e18	−1.76798
$87$	−3.41688e17	−0.128291
$88$	−6.08155e15	−0.00204847
$89$	2.60629e18	0.788530	0.394265	−	0.918997i	$-0.370999\pi$
$89$	2.60629e18	0.788530	0.394265	+	0.918997i	$0.370999\pi$
$90$	−3.10572e18	−0.845005
$91$	−6.38411e18	−1.56389
$92$	−1.70397e18	−0.376250
$93$	−2.75914e18	−0.549775
$94$	9.43815e17	0.169892
$95$	4.22399e18	0.687621
$96$	3.10190e18	0.457142
$97$	1.30524e19	1.74325	0.871626	−	0.490171i	$-0.163066\pi$
$97$	1.30524e19	1.74325	0.871626	+	0.490171i	$0.163066\pi$
$98$	7.79928e16	0.00944946
$99$	1.36993e16	0.00150718
$100$	2.60740e18	0.260740
$101$	6.17255e18	0.561580	0.280790	−	0.959769i	$-0.409404\pi$
$101$	6.17255e18	0.561580	0.280790	+	0.959769i	$0.409404\pi$
$102$	1.55798e19	1.29081
$103$	1.14289e19	0.863076	0.431538	−	0.902095i	$-0.357971\pi$
$103$	1.14289e19	0.863076	0.431538	+	0.902095i	$0.357971\pi$
$104$	1.70811e19	1.17679
$105$	1.39522e19	0.877698
$106$	3.01909e19	1.73568
$107$	1.56282e19	0.821792	0.410896	−	0.911682i	$-0.365216\pi$
$107$	1.56282e19	0.821792	0.410896	+	0.911682i	$0.365216\pi$
$108$	−7.69706e18	−0.370510
$109$	−2.58623e17	−0.0114055	−0.00570277	−	0.999984i	$-0.501815\pi$
$109$	−2.58623e17	−0.0114055	−0.00570277	+	0.999984i	$0.501815\pi$
$110$	−1.03595e17	−0.00418896
$111$	−3.48023e19	−1.29134
$112$	3.59340e19	1.22443
$113$	−3.71244e19	−1.16256	−0.581278	−	0.813705i	$-0.697447\pi$
$113$	−3.71244e19	−1.16256	−0.581278	+	0.813705i	$0.697447\pi$
$114$	1.41554e19	0.407685
$115$	5.23771e19	1.38839
$116$	−2.79742e18	−0.0682978
$117$	−3.84769e19	−0.865834
$118$	4.57561e19	0.949663
$119$	8.60267e19	1.64792
$120$	−3.73301e19	−0.660445
$121$	−6.11586e19	−0.999993
$122$	5.94130e19	0.898386
$123$	−4.38507e19	−0.613590
$124$	−2.25892e19	−0.292681
$125$	2.94564e19	0.353618
$126$	−5.74686e19	−0.639603
$127$	−3.46600e19	−0.357843	−0.178922	−	0.983863i	$-0.557261\pi$
$127$	−3.46600e19	−0.357843	−0.178922	+	0.983863i	$0.557261\pi$
$128$	−1.24028e20	−1.18857
$129$	1.14233e20	1.01669
$130$	2.90963e20	2.40645
$131$	4.19114e19	0.322296	0.161148	−	0.986930i	$-0.448480\pi$
$131$	4.19114e19	0.322296	0.161148	+	0.986930i	$0.448480\pi$
$132$	−9.12508e16	−0.000652807 0
$133$	7.81612e19	0.520476
$134$	1.27653e20	0.791655
$135$	2.36595e20	1.36721
$136$	−2.30170e20	−1.24002
$137$	−3.31270e20	−1.66470	−0.832352	−	0.554247i	$-0.813006\pi$
$137$	−3.31270e20	−1.66470	−0.832352	+	0.554247i	$0.813006\pi$
$138$	1.75525e20	0.823167
$139$	−2.48890e20	−1.08985	−0.544926	−	0.838484i	$-0.683442\pi$
$139$	−2.48890e20	−1.08985	−0.544926	+	0.838484i	$0.683442\pi$
$140$	1.14228e20	0.467256
$141$	−2.55545e19	−0.0976980
$142$	1.47204e20	0.526234
$143$	−1.28344e18	−0.00429222
$144$	2.16573e20	0.677894
$145$	8.59881e19	0.252024
$146$	−3.88074e19	−0.106552
$147$	−2.11171e18	−0.00543401
$148$	−2.84928e20	−0.687462
$149$	3.68444e20	0.833877	0.416938	−	0.908935i	$-0.363103\pi$
$149$	3.68444e20	0.833877	0.416938	+	0.908935i	$0.363103\pi$
$150$	−2.68588e20	−0.570452
$151$	−2.98488e19	−0.0595177	−0.0297588	−	0.999557i	$-0.509474\pi$
$151$	−2.98488e19	−0.0595177	−0.0297588	+	0.999557i	$0.509474\pi$
$152$	−2.09125e20	−0.391645
$153$	5.18481e20	0.912356
$154$	−1.91692e18	−0.00317072
$155$	6.94354e20	1.08002
$156$	2.56294e20	0.375020
$157$	1.13783e21	1.56686	0.783429	−	0.621481i	$-0.213469\pi$
$157$	1.13783e21	1.56686	0.783429	+	0.621481i	$0.213469\pi$
$158$	1.49208e21	1.93441
$159$	−8.17441e20	−0.998123
$160$	−7.80613e20	−0.898040
$161$	9.69191e20	1.05091
$162$	1.64710e20	0.168395
$163$	−1.46844e21	−1.41604	−0.708019	−	0.706193i	$-0.750411\pi$
$163$	−1.46844e21	−1.41604	−0.708019	+	0.706193i	$0.750411\pi$
$164$	−3.59008e20	−0.326654
$165$	2.80490e18	0.00240891
$166$	1.55861e21	1.26389
$167$	7.67982e20	0.588227	0.294113	−	0.955771i	$-0.404976\pi$
$167$	7.67982e20	0.588227	0.294113	+	0.955771i	$0.404976\pi$
$168$	−6.90759e20	−0.499906
$169$	2.14284e21	1.46577
$170$	−3.92077e21	−2.53575
$171$	4.71076e20	0.288156
$172$	9.35233e20	0.541252
$173$	−2.14374e21	−1.17418	−0.587089	−	0.809522i	$-0.699726\pi$
$173$	−2.14374e21	−1.17418	−0.587089	+	0.809522i	$0.699726\pi$
$174$	2.88162e20	0.149423
$175$	−1.48305e21	−0.728274
$176$	7.22403e18	0.00336054
$177$	−1.23888e21	−0.546114
$178$	−2.19801e21	−0.918415
$179$	2.88768e21	1.14405	0.572025	−	0.820236i	$-0.306158\pi$
$179$	2.88768e21	1.14405	0.572025	+	0.820236i	$0.306158\pi$
$180$	6.88447e20	0.258691
$181$	−2.24071e21	−0.798802	−0.399401	−	0.916776i	$-0.630782\pi$
$181$	−2.24071e21	−0.798802	−0.399401	+	0.916776i	$0.630782\pi$
$182$	5.38402e21	1.82150
$183$	−1.60865e21	−0.516626
$184$	−2.59313e21	−0.790779
$185$	8.75821e21	2.53679
$186$	2.32691e21	0.640333
$187$	1.72945e19	0.00452285
$188$	−2.09216e20	−0.0520110
$189$	4.37798e21	1.03487
$190$	−3.56229e21	−0.800885
$191$	4.48038e21	0.958292	0.479146	−	0.877735i	$-0.340946\pi$
$191$	4.48038e21	0.958292	0.479146	+	0.877735i	$0.340946\pi$
$192$	1.42978e21	0.291009
$193$	−7.68412e20	−0.148867	−0.0744337	−	0.997226i	$-0.523715\pi$
$193$	−7.68412e20	−0.148867	−0.0744337	+	0.997226i	$0.523715\pi$
$194$	−1.10077e22	−2.03040
$195$	−7.87805e21	−1.38385
$196$	−1.72887e19	−0.00289288
$197$	6.64290e21	1.05908	0.529539	−	0.848285i	$-0.322365\pi$
$197$	6.64290e21	1.05908	0.529539	+	0.848285i	$0.322365\pi$
$198$	−1.15533e19	−0.00175544
$199$	8.83267e21	1.27934	0.639672	−	0.768648i	$-0.279070\pi$
$199$	8.83267e21	1.27934	0.639672	+	0.768648i	$0.279070\pi$
$200$	3.96800e21	0.548007
$201$	−3.45630e21	−0.455250
$202$	−5.20560e21	−0.654083
$203$	1.59113e21	0.190763
$204$	−3.45359e21	−0.395170
$205$	1.10353e22	1.20538
$206$	−9.63848e21	−1.00524
$207$	5.84130e21	0.581823
$208$	−2.02899e22	−1.93054
$209$	1.57132e19	0.00142848
$210$	−1.17666e22	−1.02227
$211$	3.77122e21	0.313183	0.156592	−	0.987663i	$-0.449949\pi$
$211$	3.77122e21	0.313183	0.156592	+	0.987663i	$0.449949\pi$
$212$	−6.69243e21	−0.531365
$213$	−3.98565e21	−0.302617
$214$	−1.31800e22	−0.957157
$215$	−2.87475e22	−1.99726
$216$	−1.17136e22	−0.778715
$217$	1.28484e22	0.817489
$218$	2.18109e20	0.0132842
$219$	1.05074e21	0.0612740
$220$	2.29639e19	0.00128242
$221$	−4.85745e22	−2.59826
$222$	2.93504e22	1.50404
$223$	−7.98204e21	−0.391938	−0.195969	−	0.980610i	$-0.562785\pi$
$223$	−7.98204e21	−0.391938	−0.195969	+	0.980610i	$0.562785\pi$
$224$	−1.44445e22	−0.679747
$225$	−8.93833e21	−0.403202
$226$	3.13087e22	1.35405
$227$	−1.75647e21	−0.0728442	−0.0364221	−	0.999336i	$-0.511596\pi$
$227$	−1.75647e21	−0.0728442	−0.0364221	+	0.999336i	$0.511596\pi$
$228$	−3.13783e21	−0.124810
$229$	2.93074e22	1.11825	0.559126	−	0.829083i	$-0.311137\pi$
$229$	2.93074e22	1.11825	0.559126	+	0.829083i	$0.311137\pi$
$230$	−4.41720e22	−1.61709
$231$	5.19022e19	0.00182336
$232$	−4.25717e21	−0.143544
$233$	−2.52183e22	−0.816272	−0.408136	−	0.912921i	$-0.633821\pi$
$233$	−2.52183e22	−0.816272	−0.408136	+	0.912921i	$0.633821\pi$
$234$	3.24494e22	1.00845
$235$	6.43095e21	0.191925
$236$	−1.01428e22	−0.290732
$237$	−4.03991e22	−1.11240
$238$	−7.25503e22	−1.91937
$239$	−6.48680e22	−1.64911	−0.824556	−	0.565780i	$-0.808575\pi$
$239$	−6.48680e22	−1.64911	−0.824556	+	0.565780i	$0.808575\pi$
$240$	4.43429e22	1.08347
$241$	2.43517e22	0.571962	0.285981	−	0.958235i	$-0.407681\pi$
$241$	2.43517e22	0.571962	0.285981	+	0.958235i	$0.407681\pi$
$242$	5.15779e22	1.16471
$243$	4.33940e22	0.942259
$244$	−1.31701e22	−0.275034
$245$	5.31426e20	0.0106749
$246$	3.69814e22	0.714660
$247$	−4.41333e22	−0.820627
$248$	−3.43767e22	−0.615139
$249$	−4.22004e22	−0.726813
$250$	−2.48419e22	−0.411865
$251$	9.18931e22	1.46684	0.733419	−	0.679776i	$-0.237923\pi$
$251$	9.18931e22	1.46684	0.733419	+	0.679776i	$0.237923\pi$
$252$	1.27391e22	0.195809
$253$	1.94842e20	0.00288429
$254$	2.92304e22	0.416787
$255$	1.06158e23	1.45821
$256$	7.17700e22	0.949868
$257$	−1.24933e23	−1.59335	−0.796675	−	0.604408i	$-0.793410\pi$
$257$	−1.24933e23	−1.59335	−0.796675	+	0.604408i	$0.793410\pi$
$258$	−9.63381e22	−1.18416
$259$	1.62063e23	1.92015
$260$	−6.44980e22	−0.736715
$261$	9.58973e21	0.105614
$262$	−3.53458e22	−0.375384
$263$	8.94447e21	0.0916167	0.0458084	−	0.998950i	$-0.485414\pi$
$263$	8.94447e21	0.0916167	0.0458084	+	0.998950i	$0.485414\pi$
$264$	−1.38868e20	−0.00137203
$265$	2.05714e23	1.96078
$266$	−6.59170e22	−0.606208
$267$	5.95127e22	0.528145
$268$	−2.82969e22	−0.242359
$269$	−1.23696e23	−1.02260	−0.511302	−	0.859401i	$-0.670837\pi$
$269$	−1.23696e23	−1.02260	−0.511302	+	0.859401i	$0.670837\pi$
$270$	−1.99532e23	−1.59241
$271$	−3.96818e22	−0.305762	−0.152881	−	0.988245i	$-0.548855\pi$
$271$	−3.96818e22	−0.305762	−0.152881	+	0.988245i	$0.548855\pi$
$272$	2.73409e23	2.03427
$273$	−1.45776e23	−1.04747
$274$	2.79376e23	1.93891
$275$	−2.98147e20	−0.00199880
$276$	−3.89088e22	−0.252006
$277$	2.68993e23	1.68339	0.841693	−	0.539956i	$-0.181559\pi$
$277$	2.68993e23	1.68339	0.841693	+	0.539956i	$0.181559\pi$
$278$	2.09901e23	1.26937
$279$	7.74371e22	0.452594
$280$	1.73834e23	0.982049
$281$	2.31029e23	1.26170	0.630852	−	0.775904i	$-0.282706\pi$
$281$	2.31029e23	1.26170	0.630852	+	0.775904i	$0.282706\pi$
$282$	2.15513e22	0.113791
$283$	2.74065e22	0.139921	0.0699604	−	0.997550i	$-0.477713\pi$
$283$	2.74065e22	0.139921	0.0699604	+	0.997550i	$0.477713\pi$
$284$	−3.26307e22	−0.161102
$285$	9.64517e22	0.460557
$286$	1.08238e21	0.00499923
$287$	2.04199e23	0.912378
$288$	−8.70570e22	−0.376335
$289$	4.15475e23	1.73786
$290$	−7.25177e22	−0.293537
$291$	2.98043e23	1.16760
$292$	8.60245e21	0.0326201
$293$	−1.78156e23	−0.653971	−0.326985	−	0.945029i	$-0.606033\pi$
$293$	−1.78156e23	−0.653971	−0.326985	+	0.945029i	$0.606033\pi$
$294$	1.78091e21	0.00632909
$295$	3.11772e23	1.07282
$296$	−4.33609e23	−1.44487
$297$	8.80132e20	0.00284028
$298$	−3.10726e23	−0.971232
$299$	−5.47249e23	−1.65695
$300$	5.95380e22	0.174639
$301$	−5.31947e23	−1.51177
$302$	2.51729e22	0.0693214
$303$	1.40946e23	0.376137
$304$	2.48411e23	0.642499
$305$	4.04827e23	1.01490
$306$	−4.37259e23	−1.06264
$307$	−3.76334e23	−0.886664	−0.443332	−	0.896358i	$-0.646204\pi$
$307$	−3.76334e23	−0.886664	−0.443332	+	0.896358i	$0.646204\pi$
$308$	4.24926e20	0.000970691 0
$309$	2.60969e23	0.578074
$310$	−5.85581e23	−1.25791
$311$	−3.49580e23	−0.728322	−0.364161	−	0.931336i	$-0.618644\pi$
$311$	−3.49580e23	−0.728322	−0.364161	+	0.931336i	$0.618644\pi$
$312$	3.90034e23	0.788195
$313$	8.51662e22	0.166954	0.0834768	−	0.996510i	$-0.473398\pi$
$313$	8.51662e22	0.166954	0.0834768	+	0.996510i	$0.473398\pi$
$314$	−9.59582e23	−1.82495
$315$	−3.91579e23	−0.722552
$316$	−3.30749e23	−0.592204
$317$	−5.31917e23	−0.924232	−0.462116	−	0.886819i	$-0.652910\pi$
$317$	−5.31917e23	−0.924232	−0.462116	+	0.886819i	$0.652910\pi$
$318$	6.89386e23	1.16253
$319$	3.19875e20	0.000523563 0
$320$	−3.59812e23	−0.571678
$321$	3.56857e23	0.550423
$322$	−8.17364e23	−1.22401
$323$	5.94702e23	0.864720
$324$	−3.65114e22	−0.0515527
$325$	8.37398e23	1.14826
$326$	1.23841e24	1.64929
$327$	−5.90547e21	−0.00763925
$328$	−5.46346e23	−0.686541
$329$	1.18999e23	0.145272
$330$	−2.36550e21	−0.00280570
$331$	4.71765e23	0.543701	0.271850	−	0.962340i	$-0.412364\pi$
$331$	4.71765e23	0.543701	0.271850	+	0.962340i	$0.412364\pi$
$332$	−3.45497e23	−0.386930
$333$	9.76750e23	1.06307
$334$	−6.47675e23	−0.685119
$335$	8.69801e23	0.894323
$336$	8.20525e23	0.820103
$337$	−9.25357e23	−0.899136	−0.449568	−	0.893246i	$-0.648422\pi$
$337$	−9.25357e23	−0.899136	−0.449568	+	0.893246i	$0.648422\pi$
$338$	−1.80715e24	−1.70721
$339$	−8.47707e23	−0.778662
$340$	8.69118e23	0.776299
$341$	2.58299e21	0.00224366
$342$	−3.97281e23	−0.335621
$343$	1.22190e24	1.00402
$344$	1.42326e24	1.13757
$345$	1.19599e24	0.929922
$346$	1.80792e24	1.36759
$347$	−2.32568e24	−1.71167	−0.855836	−	0.517247i	$-0.826957\pi$
$347$	−2.32568e24	−1.71167	−0.855836	+	0.517247i	$0.826957\pi$
$348$	−6.38769e22	−0.0457448
$349$	−1.24736e24	−0.869262	−0.434631	−	0.900609i	$-0.643121\pi$
$349$	−1.24736e24	−0.869262	−0.434631	+	0.900609i	$0.643121\pi$
$350$	1.25073e24	0.848234
$351$	−2.47200e24	−1.63167
$352$	−2.90387e21	−0.00186562
$353$	−3.12178e23	−0.195228	−0.0976140	−	0.995224i	$-0.531121\pi$
$353$	−3.12178e23	−0.195228	−0.0976140	+	0.995224i	$0.531121\pi$
$354$	1.04480e24	0.636069
$355$	1.00301e24	0.594480
$356$	4.87233e23	0.281166
$357$	1.96435e24	1.10375
$358$	−2.43531e24	−1.33250
$359$	−2.37925e24	−1.26778	−0.633889	−	0.773424i	$-0.718543\pi$
$359$	−2.37925e24	−1.26778	−0.633889	+	0.773424i	$0.718543\pi$
$360$	1.04769e24	0.543702
$361$	−1.43809e24	−0.726889
$362$	1.88969e24	0.930379
$363$	−1.39651e24	−0.669779
$364$	−1.19348e24	−0.557637
$365$	−2.64425e23	−0.120371
$366$	1.35665e24	0.601724
$367$	−3.56663e24	−1.54145	−0.770726	−	0.637167i	$-0.780106\pi$
$367$	−3.56663e24	−1.54145	−0.770726	+	0.637167i	$0.780106\pi$
$368$	3.08028e24	1.29729
$369$	1.23070e24	0.505129
$370$	−7.38621e24	−2.95464
$371$	3.80656e24	1.48416
$372$	−5.15807e23	−0.196033
$373$	−1.06871e24	−0.395937	−0.197968	−	0.980208i	$-0.563434\pi$
$373$	−1.06871e24	−0.395937	−0.197968	+	0.980208i	$0.563434\pi$
$374$	−1.45852e22	−0.00526784
$375$	6.72614e23	0.236847
$376$	−3.18389e23	−0.109314
$377$	−8.98425e23	−0.300773
$378$	−3.69215e24	−1.20533
$379$	4.52540e24	1.44074	0.720368	−	0.693592i	$-0.243973\pi$
$379$	4.52540e24	1.44074	0.720368	+	0.693592i	$0.243973\pi$
$380$	7.89655e23	0.245184
$381$	−7.91434e23	−0.239678
$382$	−3.77851e24	−1.11614
$383$	−1.92748e24	−0.555396	−0.277698	−	0.960668i	$-0.589571\pi$
$383$	−1.92748e24	−0.555396	−0.277698	+	0.960668i	$0.589571\pi$
$384$	−2.83209e24	−0.796086
$385$	−1.30615e22	−0.00358192
$386$	6.48037e23	0.173389
$387$	−3.20604e24	−0.836978
$388$	2.44009e24	0.621590
$389$	−7.10885e24	−1.76717	−0.883584	−	0.468272i	$-0.844877\pi$
$389$	−7.10885e24	−1.76717	−0.883584	+	0.468272i	$0.844877\pi$
$390$	6.64393e24	1.61180
$391$	7.37425e24	1.74598
$392$	−2.63103e22	−0.00608007
$393$	9.57015e23	0.215869
$394$	−5.60226e24	−1.23353
$395$	1.01667e25	2.18528
$396$	2.56102e21	0.000537414 0
$397$	6.03382e24	1.23618	0.618091	−	0.786107i	$-0.287906\pi$
$397$	6.03382e24	1.23618	0.618091	+	0.786107i	$0.287906\pi$
$398$	−7.44900e24	−1.49008
$399$	1.78475e24	0.348606
$400$	−4.71342e24	−0.899014
$401$	−4.84878e23	−0.0903152	−0.0451576	−	0.998980i	$-0.514379\pi$
$401$	−4.84878e23	−0.0903152	−0.0451576	+	0.998980i	$0.514379\pi$
$402$	2.91486e24	0.530238
$403$	−7.25479e24	−1.28892
$404$	1.15393e24	0.200242
$405$	1.12230e24	0.190233
$406$	−1.34188e24	−0.222185
$407$	3.25805e22	0.00527000
$408$	−5.25575e24	−0.830545
$409$	2.48571e24	0.383776	0.191888	−	0.981417i	$-0.438539\pi$
$409$	2.48571e24	0.383776	0.191888	+	0.981417i	$0.438539\pi$
$410$	−9.30659e24	−1.40393
$411$	−7.56430e24	−1.11499
$412$	2.13657e24	0.307746
$413$	5.76906e24	0.812044
$414$	−4.92624e24	−0.677661
$415$	1.06200e25	1.42780
$416$	8.15604e24	1.07175
$417$	−5.68322e24	−0.729965
$418$	−1.32517e22	−0.00166378
$419$	−1.83878e24	−0.225682	−0.112841	−	0.993613i	$-0.535995\pi$
$419$	−1.83878e24	−0.225682	−0.112841	+	0.993613i	$0.535995\pi$
$420$	2.60830e24	0.312960
$421$	−1.66508e24	−0.195323	−0.0976617	−	0.995220i	$-0.531136\pi$
$421$	−1.66508e24	−0.195323	−0.0976617	+	0.995220i	$0.531136\pi$
$422$	−3.18044e24	−0.364770
$423$	7.17205e23	0.0804285
$424$	−1.01847e25	−1.11679
$425$	−1.12840e25	−1.20996
$426$	3.36128e24	0.352463
$427$	7.49096e24	0.768197
$428$	2.92161e24	0.293026
$429$	−2.93063e22	−0.00287486
$430$	2.42441e25	2.32625
$431$	−1.54891e25	−1.45376	−0.726880	−	0.686765i	$-0.759030\pi$
$431$	−1.54891e25	−1.45376	−0.726880	+	0.686765i	$0.759030\pi$
$432$	1.39141e25	1.27749
$433$	−1.52024e25	−1.36545	−0.682727	−	0.730674i	$-0.739206\pi$
$433$	−1.52024e25	−1.36545	−0.682727	+	0.730674i	$0.739206\pi$
$434$	−1.08357e25	−0.952144
$435$	1.96347e24	0.168802
$436$	−4.83483e22	−0.00406687
$437$	6.70002e24	0.551445
$438$	−8.86137e23	−0.0713669
$439$	1.68523e25	1.32815	0.664075	−	0.747666i	$-0.268826\pi$
$439$	1.68523e25	1.32815	0.664075	+	0.747666i	$0.268826\pi$
$440$	3.49469e22	0.00269531
$441$	5.92668e22	0.00447347
$442$	4.09652e25	3.02624
$443$	1.18083e25	0.853792	0.426896	−	0.904301i	$-0.359607\pi$
$443$	1.18083e25	0.853792	0.426896	+	0.904301i	$0.359607\pi$
$444$	−6.50611e24	−0.460451
$445$	−1.49768e25	−1.03752
$446$	6.73162e24	0.456498
$447$	8.41314e24	0.558517
$448$	−6.65801e24	−0.432716
$449$	−1.70111e25	−1.08241	−0.541205	−	0.840890i	$-0.682032\pi$
$449$	−1.70111e25	−1.08241	−0.541205	+	0.840890i	$0.682032\pi$
$450$	7.53810e24	0.469616
$451$	4.10513e22	0.00250409
$452$	−6.94022e24	−0.414532
$453$	−6.81575e23	−0.0398640
$454$	1.48131e24	0.0848429
$455$	3.66855e25	2.05772
$456$	−4.77522e24	−0.262317
$457$	−1.63078e24	−0.0877388	−0.0438694	−	0.999037i	$-0.513969\pi$
$457$	−1.63078e24	−0.0877388	−0.0438694	+	0.999037i	$0.513969\pi$
$458$	−2.47163e25	−1.30245
$459$	3.33106e25	1.71934
$460$	9.79164e24	0.495058
$461$	1.02930e25	0.509782	0.254891	−	0.966970i	$-0.417960\pi$
$461$	1.02930e25	0.509782	0.254891	+	0.966970i	$0.417960\pi$
$462$	−4.37715e22	−0.00212370
$463$	−8.20492e24	−0.389991	−0.194996	−	0.980804i	$-0.562469\pi$
$463$	−8.20492e24	−0.389991	−0.194996	+	0.980804i	$0.562469\pi$
$464$	5.05693e24	0.235486
$465$	1.58551e25	0.723377
$466$	2.12678e25	0.950727
$467$	3.92407e25	1.71880	0.859402	−	0.511300i	$-0.170836\pi$
$467$	3.92407e25	1.71880	0.859402	+	0.511300i	$0.170836\pi$
$468$	−7.19307e24	−0.308730
$469$	1.60949e25	0.676933
$470$	−5.42352e24	−0.223538
$471$	2.59814e25	1.04946
$472$	−1.54355e25	−0.611042
$473$	−1.06941e23	−0.00414917
$474$	3.40704e25	1.29564
$475$	−1.02523e25	−0.382149
$476$	1.60823e25	0.587599
$477$	2.29421e25	0.821690
$478$	5.47062e25	1.92075
$479$	−1.40735e25	−0.484412	−0.242206	−	0.970225i	$-0.577871\pi$
$479$	−1.40735e25	−0.484412	−0.242206	+	0.970225i	$0.577871\pi$
$480$	−1.78247e25	−0.601493
$481$	−9.15080e25	−3.02748
$482$	−2.05369e25	−0.666174
$483$	2.21307e25	0.703879
$484$	−1.14333e25	−0.356567
$485$	−7.50043e25	−2.29372
$486$	−3.65962e25	−1.09747
$487$	−2.91181e25	−0.856322	−0.428161	−	0.903702i	$-0.640838\pi$
$487$	−2.91181e25	−0.856322	−0.428161	+	0.903702i	$0.640838\pi$
$488$	−2.00425e25	−0.578049
$489$	−3.35308e25	−0.948440
$490$	−4.48176e23	−0.0124333
$491$	−3.92079e25	−1.06684	−0.533421	−	0.845850i	$-0.679094\pi$
$491$	−3.92079e25	−1.06684	−0.533421	+	0.845850i	$0.679094\pi$
$492$	−8.19768e24	−0.218787
$493$	1.21064e25	0.316934
$494$	3.72197e25	0.955800
$495$	−7.87215e22	−0.00198310
$496$	4.08347e25	1.00914
$497$	1.85599e25	0.449976
$498$	3.55896e25	0.846533
$499$	2.79040e25	0.651196	0.325598	−	0.945508i	$-0.394434\pi$
$499$	2.79040e25	0.651196	0.325598	+	0.945508i	$0.394434\pi$
$500$	5.50672e24	0.126089
$501$	1.75363e25	0.393985
$502$	−7.74977e25	−1.70845
$503$	−3.43814e24	−0.0743752	−0.0371876	−	0.999308i	$-0.511840\pi$
$503$	−3.43814e24	−0.0743752	−0.0371876	+	0.999308i	$0.511840\pi$
$504$	1.93866e25	0.411540
$505$	−3.54698e25	−0.738909
$506$	−1.64320e23	−0.00335938
$507$	4.89301e25	0.981748
$508$	−6.47951e24	−0.127596
$509$	7.92853e25	1.53241	0.766203	−	0.642599i	$-0.222144\pi$
$509$	7.92853e25	1.53241	0.766203	+	0.642599i	$0.222144\pi$
$510$	−8.95277e25	−1.69840
$511$	−4.89295e24	−0.0911113
$512$	4.49941e24	0.0822415
$513$	3.02650e25	0.543032
$514$	1.05361e26	1.85580
$515$	−6.56745e25	−1.13561
$516$	2.13553e25	0.362522
$517$	2.39231e22	0.000398710 0
$518$	−1.36675e26	−2.23644
$519$	−4.89507e25	−0.786446
$520$	−9.81545e25	−1.54838
$521$	−8.82204e24	−0.136650	−0.0683251	−	0.997663i	$-0.521766\pi$
$521$	−8.82204e24	−0.136650	−0.0683251	+	0.997663i	$0.521766\pi$
$522$	−8.08746e24	−0.123011
$523$	−7.85664e25	−1.17347	−0.586733	−	0.809780i	$-0.699586\pi$
$523$	−7.85664e25	−1.17347	−0.586733	+	0.809780i	$0.699586\pi$
$524$	7.83513e24	0.114921
$525$	−3.38643e25	−0.487786
$526$	−7.54328e24	−0.106708
$527$	9.77591e25	1.35818
$528$	1.64955e23	0.00225083
$529$	8.46406e24	0.113436
$530$	−1.73488e26	−2.28376
$531$	3.47700e25	0.449580
$532$	1.46118e25	0.185586
$533$	−1.15300e26	−1.43853
$534$	−5.01898e25	−0.615140
$535$	−8.98054e25	−1.08129
$536$	−4.30629e25	−0.509375
$537$	6.59379e25	0.766266
$538$	1.04318e26	1.19105
$539$	1.97690e21	2.21764e−5 0
$540$	4.42303e25	0.487505
$541$	−6.58347e25	−0.712985	−0.356493	−	0.934298i	$-0.616028\pi$
$541$	−6.58347e25	−0.712985	−0.356493	+	0.934298i	$0.616028\pi$
$542$	3.34655e25	0.356127
$543$	−5.11649e25	−0.535024
$544$	−1.09904e26	−1.12933
$545$	1.48615e24	0.0150071
$546$	1.22940e26	1.22001
$547$	1.59322e26	1.55380	0.776902	−	0.629621i	$-0.216790\pi$
$547$	1.59322e26	1.55380	0.776902	+	0.629621i	$0.216790\pi$
$548$	−6.19293e25	−0.593582
$549$	4.51479e25	0.425305
$550$	2.51441e23	0.00232804
$551$	1.09995e25	0.100100
$552$	−5.92122e25	−0.529651
$553$	1.88125e26	1.65409
$554$	−2.26855e26	−1.96067
$555$	1.99987e26	1.69910
$556$	−4.65288e25	−0.388608
$557$	4.50173e25	0.369620	0.184810	−	0.982774i	$-0.440833\pi$
$557$	4.50173e25	0.369620	0.184810	+	0.982774i	$0.440833\pi$
$558$	−6.53063e25	−0.527145
$559$	3.00361e26	2.38359
$560$	−2.06490e26	−1.61107
$561$	3.94906e23	0.00302933
$562$	−1.94838e26	−1.46953
$563$	4.47488e25	0.331858	0.165929	−	0.986138i	$-0.446938\pi$
$563$	4.47488e25	0.331858	0.165929	+	0.986138i	$0.446938\pi$
$564$	−4.77728e24	−0.0348361
$565$	2.13331e26	1.52966
$566$	−2.31132e25	−0.162968
$567$	2.07672e25	0.143992
$568$	−4.96581e25	−0.338595
$569$	−2.84482e26	−1.90760	−0.953802	−	0.300437i	$-0.902868\pi$
$569$	−2.84482e26	−1.90760	−0.953802	+	0.300437i	$0.902868\pi$
$570$	−8.13422e25	−0.536420
$571$	2.34625e26	1.52171	0.760855	−	0.648922i	$-0.224780\pi$
$571$	2.34625e26	1.52171	0.760855	+	0.648922i	$0.224780\pi$
$572$	−2.39932e23	−0.00153047
$573$	1.02306e26	0.641849
$574$	−1.72210e26	−1.06266
$575$	−1.27128e26	−0.771607
$576$	−4.01277e25	−0.239569
$577$	−3.53563e25	−0.207633	−0.103817	−	0.994596i	$-0.533105\pi$
$577$	−3.53563e25	−0.207633	−0.103817	+	0.994596i	$0.533105\pi$
$578$	−3.50389e26	−2.02412
$579$	−1.75461e25	−0.0997089
$580$	1.60750e25	0.0898641
$581$	1.96514e26	1.08074
$582$	−2.51353e26	−1.35993
$583$	7.65256e23	0.00407338
$584$	1.30914e25	0.0685589
$585$	2.21103e26	1.13924
$586$	1.50247e26	0.761692
$587$	2.23269e26	1.11370	0.556848	−	0.830615i	$-0.312011\pi$
$587$	2.23269e26	1.11370	0.556848	+	0.830615i	$0.312011\pi$
$588$	−3.94774e23	−0.00193760
$589$	8.88210e25	0.428963
$590$	−2.62932e26	−1.24954
$591$	1.51685e26	0.709354
$592$	5.15067e26	2.37032
$593$	−2.18872e26	−0.991223	−0.495612	−	0.868544i	$-0.665056\pi$
$593$	−2.18872e26	−0.991223	−0.495612	+	0.868544i	$0.665056\pi$
$594$	−7.42256e23	−0.00330813
$595$	−4.94342e26	−2.16828
$596$	6.88788e25	0.297335
$597$	2.01687e26	0.856884
$598$	4.61520e26	1.92988
$599$	3.54361e26	1.45845	0.729225	−	0.684274i	$-0.239881\pi$
$599$	3.54361e26	1.45845	0.729225	+	0.684274i	$0.239881\pi$
$600$	9.06062e25	0.367046
$601$	−3.87148e26	−1.54372	−0.771862	−	0.635790i	$-0.780674\pi$
$601$	−3.87148e26	−1.54372	−0.771862	+	0.635790i	$0.780674\pi$
$602$	4.48615e26	1.76079
$603$	9.70036e25	0.374778
$604$	−5.58009e24	−0.0212222
$605$	3.51441e26	1.31576
$606$	−1.18866e26	−0.438094
$607$	2.43999e26	0.885312	0.442656	−	0.896692i	$-0.354036\pi$
$607$	2.43999e26	0.885312	0.442656	+	0.896692i	$0.354036\pi$
$608$	−9.98550e25	−0.356686
$609$	3.63323e25	0.127770
$610$	−3.41410e26	−1.18207
$611$	−6.71922e25	−0.229048
$612$	9.69275e25	0.325318
$613$	−8.67574e25	−0.286703	−0.143351	−	0.989672i	$-0.545788\pi$
$613$	−8.67574e25	−0.286703	−0.143351	+	0.989672i	$0.545788\pi$
$614$	3.17380e26	1.03271
$615$	2.51983e26	0.807342
$616$	6.46661e23	0.00204014
$617$	−3.04548e26	−0.946122	−0.473061	−	0.881030i	$-0.656851\pi$
$617$	−3.04548e26	−0.946122	−0.473061	+	0.881030i	$0.656851\pi$
$618$	−2.20087e26	−0.673294
$619$	4.00087e26	1.20529	0.602647	−	0.798008i	$-0.294113\pi$
$619$	4.00087e26	1.20529	0.602647	+	0.798008i	$0.294113\pi$
$620$	1.29806e26	0.385100
$621$	3.75282e26	1.09645
$622$	2.94817e26	0.848290
$623$	−2.77131e26	−0.785325
$624$	−4.63305e26	−1.29305
$625$	−4.35293e26	−1.19653
$626$	−7.18246e25	−0.194454
$627$	3.58800e23	0.000956776 0
$628$	2.12711e26	0.558693
$629$	1.23308e27	3.19015
$630$	3.30237e26	0.841570
$631$	−3.64813e26	−0.915781	−0.457890	−	0.889009i	$-0.651395\pi$
$631$	−3.64813e26	−0.915781	−0.457890	+	0.889009i	$0.651395\pi$
$632$	−5.03341e26	−1.24466
$633$	8.61129e25	0.209765
$634$	4.48590e26	1.07647
$635$	1.99170e26	0.470839
$636$	−1.52817e26	−0.355900
$637$	−5.55248e24	−0.0127398
$638$	−2.69765e23	−0.000609803 0
$639$	1.11860e26	0.249125
$640$	7.12712e26	1.56388
$641$	−5.47342e26	−1.18333	−0.591667	−	0.806183i	$-0.701530\pi$
$641$	−5.47342e26	−1.18333	−0.591667	+	0.806183i	$0.701530\pi$
$642$	−3.00954e26	−0.641088
$643$	1.46790e26	0.308101	0.154051	−	0.988063i	$-0.450768\pi$
$643$	1.46790e26	0.308101	0.154051	+	0.988063i	$0.450768\pi$
$644$	1.81185e26	0.374721
$645$	−6.56428e26	−1.33773
$646$	−5.01540e26	−1.00716
$647$	−5.11722e26	−1.01261	−0.506307	−	0.862353i	$-0.668990\pi$
$647$	−5.11722e26	−1.01261	−0.506307	+	0.862353i	$0.668990\pi$
$648$	−5.55639e25	−0.108350
$649$	1.15979e24	0.00222872
$650$	−7.06216e26	−1.33740
$651$	2.93383e26	0.547541
$652$	−2.74518e26	−0.504916
$653$	5.61859e26	1.01848	0.509240	−	0.860625i	$-0.329927\pi$
$653$	5.61859e26	1.01848	0.509240	+	0.860625i	$0.329927\pi$
$654$	4.98035e24	0.00889757
$655$	−2.40839e26	−0.424067
$656$	6.48983e26	1.12628
$657$	−2.94897e25	−0.0504429
$658$	−1.00357e26	−0.169201
$659$	−5.00008e26	−0.830932	−0.415466	−	0.909609i	$-0.636382\pi$
$659$	−5.00008e26	−0.830932	−0.415466	+	0.909609i	$0.636382\pi$
$660$	5.24362e23	0.000858942 0
$661$	1.08708e27	1.75529	0.877645	−	0.479312i	$-0.159114\pi$
$661$	1.08708e27	1.75529	0.877645	+	0.479312i	$0.159114\pi$
$662$	−3.97862e26	−0.633259
$663$	−1.10916e27	−1.74027
$664$	−5.25785e26	−0.813226
$665$	−4.49144e26	−0.684826
$666$	−8.23739e26	−1.23818
$667$	1.36393e26	0.202114
$668$	1.43570e26	0.209744
$669$	−1.82264e26	−0.262514
$670$	−7.33544e26	−1.04163
$671$	1.50595e24	0.00210837
$672$	−3.29830e26	−0.455284
$673$	1.21119e27	1.64843	0.824215	−	0.566278i	$-0.191617\pi$
$673$	1.21119e27	1.64843	0.824215	+	0.566278i	$0.191617\pi$
$674$	7.80397e26	1.04724
$675$	−5.74255e26	−0.759835
$676$	4.00593e26	0.522648
$677$	−5.65556e26	−0.727585	−0.363792	−	0.931480i	$-0.618518\pi$
$677$	−5.65556e26	−0.727585	−0.363792	+	0.931480i	$0.618518\pi$
$678$	7.14911e26	0.906922
$679$	−1.38789e27	−1.73617
$680$	1.32264e27	1.63158
$681$	−4.01076e25	−0.0487898
$682$	−2.17836e24	−0.00261323
$683$	4.87069e26	0.576227	0.288114	−	0.957596i	$-0.406972\pi$
$683$	4.87069e26	0.576227	0.288114	+	0.957596i	$0.406972\pi$
$684$	8.80654e25	0.102748
$685$	1.90361e27	2.19036
$686$	−1.03048e27	−1.16940
$687$	6.69212e26	0.748987
$688$	−1.69063e27	−1.86620
$689$	−2.14935e27	−2.34005
$690$	−1.00863e27	−1.08310
$691$	−1.13848e27	−1.20583	−0.602914	−	0.797806i	$-0.705994\pi$
$691$	−1.13848e27	−1.20583	−0.602914	+	0.797806i	$0.705994\pi$
$692$	−4.00762e26	−0.418676
$693$	−1.45667e24	−0.00150105
$694$	1.96136e27	1.99362
$695$	1.43022e27	1.43399
$696$	−9.72093e25	−0.0961435
$697$	1.55368e27	1.51583
$698$	1.05196e27	1.01245
$699$	−5.75841e26	−0.546726
$700$	−2.77249e26	−0.259680
$701$	−8.66757e26	−0.800896	−0.400448	−	0.916319i	$-0.631146\pi$
$701$	−8.66757e26	−0.800896	−0.400448	+	0.916319i	$0.631146\pi$
$702$	2.08476e27	1.90043
$703$	1.12034e27	1.00757
$704$	−1.33850e24	−0.00118762
$705$	1.46846e26	0.128548
$706$	2.63274e26	0.227386
$707$	−6.56338e26	−0.559297
$708$	−2.31602e26	−0.194727
$709$	3.35892e26	0.278651	0.139325	−	0.990247i	$-0.455507\pi$
$709$	3.35892e26	0.278651	0.139325	+	0.990247i	$0.455507\pi$
$710$	−8.45888e26	−0.692402
$711$	1.13383e27	0.915770
$712$	7.41482e26	0.590937
$713$	1.10137e27	0.866130
$714$	−1.65663e27	−1.28556
$715$	7.37512e24	0.00564757
$716$	5.39837e26	0.407933
$717$	−1.48121e27	−1.10455
$718$	2.00654e27	1.47661
$719$	−8.34794e26	−0.606255	−0.303127	−	0.952950i	$-0.598031\pi$
$719$	−8.34794e26	−0.606255	−0.303127	+	0.952950i	$0.598031\pi$
$720$	−1.24451e27	−0.891951
$721$	−1.21525e27	−0.859568
$722$	1.21281e27	0.846621
$723$	5.56052e26	0.383091
$724$	−4.18889e26	−0.284828
$725$	−2.08707e26	−0.140064
$726$	1.17774e27	0.780104
$727$	−2.10320e27	−1.37500	−0.687502	−	0.726183i	$-0.741293\pi$
$727$	−2.10320e27	−1.37500	−0.687502	+	0.726183i	$0.741293\pi$
$728$	−1.81626e27	−1.17201
$729$	1.21787e27	0.775689
$730$	2.23002e26	0.140198
$731$	−4.04740e27	−2.51166
$732$	−3.00729e26	−0.184213
$733$	9.60397e26	0.580715	0.290357	−	0.956918i	$-0.406226\pi$
$733$	9.60397e26	0.580715	0.290357	+	0.956918i	$0.406226\pi$
$734$	3.00790e27	1.79536
$735$	1.21347e25	0.00714990
$736$	−1.23819e27	−0.720193
$737$	3.23565e24	0.00185789
$738$	−1.03791e27	−0.588333
$739$	2.87130e27	1.60678	0.803389	−	0.595454i	$-0.203028\pi$
$739$	2.87130e27	1.60678	0.803389	+	0.595454i	$0.203028\pi$
$740$	1.63730e27	0.904540
$741$	−1.00775e27	−0.549643
$742$	−3.21025e27	−1.72863
$743$	−2.42026e27	−1.28667	−0.643337	−	0.765583i	$-0.722451\pi$
$743$	−2.42026e27	−1.28667	−0.643337	+	0.765583i	$0.722451\pi$
$744$	−7.84966e26	−0.412010
$745$	−2.11722e27	−1.09719
$746$	9.01292e26	0.461155
$747$	1.18438e27	0.598339
$748$	3.23311e24	0.00161271
$749$	−1.66177e27	−0.818452
$750$	−5.67246e26	−0.275861
$751$	1.77713e27	0.853376	0.426688	−	0.904399i	$-0.359680\pi$
$751$	1.77713e27	0.853376	0.426688	+	0.904399i	$0.359680\pi$
$752$	3.78202e26	0.179330
$753$	2.09831e27	0.982465
$754$	7.57683e26	0.350316
$755$	1.71523e26	0.0783115
$756$	8.18441e26	0.369004
$757$	−5.83862e26	−0.259956	−0.129978	−	0.991517i	$-0.541491\pi$
$757$	−5.83862e26	−0.259956	−0.129978	+	0.991517i	$0.541491\pi$
$758$	−3.81648e27	−1.67805
$759$	4.44908e24	0.00193185
$760$	1.20171e27	0.515314
$761$	−4.00725e27	−1.69704	−0.848521	−	0.529162i	$-0.822506\pi$
$761$	−4.00725e27	−1.69704	−0.848521	+	0.529162i	$0.822506\pi$
$762$	6.67453e26	0.279157
$763$	2.74998e25	0.0113592
$764$	8.37585e26	0.341698
$765$	−2.97939e27	−1.20045
$766$	1.62554e27	0.646880
$767$	−3.25747e27	−1.28034
$768$	1.63881e27	0.636206
$769$	4.21501e27	1.61621	0.808107	−	0.589036i	$-0.200492\pi$
$769$	4.21501e27	1.61621	0.808107	+	0.589036i	$0.200492\pi$
$770$	1.10154e25	0.00417193
$771$	−2.85274e27	−1.06720
$772$	−1.43651e26	−0.0530815
$773$	−2.43184e27	−0.887627	−0.443813	−	0.896119i	$-0.646375\pi$
$773$	−2.43184e27	−0.887627	−0.443813	+	0.896119i	$0.646375\pi$
$774$	2.70380e27	0.974844
$775$	−1.68531e27	−0.600225
$776$	3.71338e27	1.30642
$777$	3.70058e27	1.28609
$778$	5.99522e27	2.05825
$779$	1.41162e27	0.478755
$780$	−1.47276e27	−0.493440
$781$	3.73120e24	0.00123499
$782$	−6.21904e27	−2.03357
$783$	6.16105e26	0.199030
$784$	3.12530e25	0.00997445
$785$	−6.53839e27	−2.06162
$786$	−8.07095e26	−0.251426
$787$	−6.05342e26	−0.186312	−0.0931560	−	0.995652i	$-0.529696\pi$
$787$	−6.05342e26	−0.186312	−0.0931560	+	0.995652i	$0.529696\pi$
$788$	1.24186e27	0.377635
$789$	2.04240e26	0.0613634
$790$	−8.57404e27	−2.54524
$791$	3.94750e27	1.15783
$792$	3.89741e24	0.00112950
$793$	−4.22974e27	−1.21121
$794$	−5.08860e27	−1.43980
$795$	4.69733e27	1.31330
$796$	1.65122e27	0.456175
$797$	4.69146e27	1.28072	0.640359	−	0.768075i	$-0.278785\pi$
$797$	4.69146e27	1.28072	0.640359	+	0.768075i	$0.278785\pi$
$798$	−1.50516e27	−0.406028
$799$	9.05423e26	0.241355
$800$	1.89468e27	0.499091
$801$	−1.67027e27	−0.434787
$802$	4.08920e26	0.105192
$803$	−9.83660e23	−0.000250062 0
$804$	−6.46139e26	−0.162328
$805$	−5.56934e27	−1.38275
$806$	6.11830e27	1.50123
$807$	−2.82450e27	−0.684924
$808$	1.75607e27	0.420857
$809$	4.62125e27	1.09458	0.547291	−	0.836942i	$-0.315659\pi$
$809$	4.62125e27	1.09458	0.547291	+	0.836942i	$0.315659\pi$
$810$	−9.46488e26	−0.221568
$811$	5.42914e26	0.125613	0.0628063	−	0.998026i	$-0.479995\pi$
$811$	5.42914e26	0.125613	0.0628063	+	0.998026i	$0.479995\pi$
$812$	2.97454e26	0.0680202
$813$	−9.06105e26	−0.204794
$814$	−2.74766e25	−0.00613807
$815$	8.43824e27	1.86318
$816$	6.24310e27	1.36252
$817$	−3.67735e27	−0.793277
$818$	−2.09631e27	−0.446992
$819$	4.09132e27	0.862315
$820$	2.06300e27	0.429801
$821$	−2.18087e27	−0.449129	−0.224564	−	0.974459i	$-0.572096\pi$
$821$	−2.18087e27	−0.449129	−0.224564	+	0.974459i	$0.572096\pi$
$822$	6.37933e27	1.29865
$823$	8.13808e26	0.163766	0.0818829	−	0.996642i	$-0.473907\pi$
$823$	8.13808e26	0.163766	0.0818829	+	0.996642i	$0.473907\pi$
$824$	3.25147e27	0.646803
$825$	−6.80796e24	−0.00133876
$826$	−4.86532e27	−0.945803
$827$	−1.46689e27	−0.281901	−0.140950	−	0.990017i	$-0.545016\pi$
$827$	−1.46689e27	−0.281901	−0.140950	+	0.990017i	$0.545016\pi$
$828$	1.09200e27	0.207460
$829$	3.43955e27	0.646002	0.323001	−	0.946399i	$-0.395308\pi$
$829$	3.43955e27	0.646002	0.323001	+	0.946399i	$0.395308\pi$
$830$	−8.95634e27	−1.66299
$831$	6.14226e27	1.12750
$832$	3.75941e27	0.682257
$833$	7.48203e25	0.0134243
$834$	4.79292e27	0.850204
$835$	−4.41312e27	−0.773970
$836$	2.93751e24	0.000509354 0
$837$	4.97506e27	0.852916
$838$	1.55073e27	0.262856
$839$	−4.86777e27	−0.815815	−0.407907	−	0.913023i	$-0.633741\pi$
$839$	−4.86777e27	−0.815815	−0.407907	+	0.913023i	$0.633741\pi$
$840$	3.96937e27	0.657761
$841$	−5.87934e27	−0.963312
$842$	1.40424e27	0.227497
$843$	5.27538e27	0.845068
$844$	7.05010e26	0.111671
$845$	−1.23136e28	−1.92861
$846$	−6.04852e26	−0.0936765
$847$	6.50310e27	0.995928
$848$	1.20980e28	1.83211
$849$	6.25806e26	0.0937167
$850$	9.51635e27	1.40926
$851$	1.38921e28	2.03440
$852$	−7.45097e26	−0.107904
$853$	−3.38801e27	−0.485209	−0.242604	−	0.970125i	$-0.578002\pi$
$853$	−3.38801e27	−0.485209	−0.242604	+	0.970125i	$0.578002\pi$
$854$	−6.31748e27	−0.894734
$855$	−2.70698e27	−0.379147
$856$	4.44616e27	0.615864
$857$	4.19172e27	0.574215	0.287108	−	0.957898i	$-0.407306\pi$
$857$	4.19172e27	0.574215	0.287108	+	0.957898i	$0.407306\pi$
$858$	2.47154e25	0.00334840
$859$	−5.36795e27	−0.719239	−0.359619	−	0.933099i	$-0.617093\pi$
$859$	−5.36795e27	−0.719239	−0.359619	+	0.933099i	$0.617093\pi$
$860$	−5.37420e27	−0.712162
$861$	4.66272e27	0.611096
$862$	1.30627e28	1.69322
$863$	1.90029e27	0.243622	0.121811	−	0.992553i	$-0.461130\pi$
$863$	1.90029e27	0.243622	0.121811	+	0.992553i	$0.461130\pi$
$864$	−5.59310e27	−0.709205
$865$	1.23188e28	1.54495
$866$	1.28209e28	1.59037
$867$	9.48706e27	1.16399
$868$	2.40194e27	0.291491
$869$	3.78200e25	0.00453977
$870$	−1.65589e27	−0.196606
$871$	−9.08790e27	−1.06731
$872$	−7.35776e25	−0.00854749
$873$	−8.36478e27	−0.961212
$874$	−5.65043e27	−0.642278
$875$	−3.13214e27	−0.352180
$876$	1.96430e26	0.0218484
$877$	−1.52964e28	−1.68303	−0.841515	−	0.540233i	$-0.818336\pi$
$877$	−1.52964e28	−1.68303	−0.841515	+	0.540233i	$0.818336\pi$
$878$	−1.42124e28	−1.54692
$879$	−4.06806e27	−0.438019
$880$	−4.15120e25	−0.00442169
$881$	−6.46269e27	−0.680992	−0.340496	−	0.940246i	$-0.610595\pi$
$881$	−6.46269e27	−0.680992	−0.340496	+	0.940246i	$0.610595\pi$
$882$	−4.99824e25	−0.00521033
$883$	4.75252e27	0.490114	0.245057	−	0.969509i	$-0.421193\pi$
$883$	4.75252e27	0.490114	0.245057	+	0.969509i	$0.421193\pi$
$884$	−9.08077e27	−0.926459
$885$	7.11908e27	0.718559
$886$	−9.95849e27	−0.994427
$887$	−3.77956e27	−0.373393	−0.186697	−	0.982418i	$-0.559778\pi$
$887$	−3.77956e27	−0.373393	−0.186697	+	0.982418i	$0.559778\pi$
$888$	−9.90114e27	−0.967747
$889$	3.68545e27	0.356389
$890$	1.26306e28	1.20842
$891$	4.17495e24	0.000395197 0
$892$	−1.49220e27	−0.139753
$893$	8.22640e26	0.0762291
$894$	−7.09519e27	−0.650515
$895$	−1.65937e28	−1.50530
$896$	1.31881e28	1.18374
$897$	−1.24960e28	−1.10980
$898$	1.43462e28	1.26070
$899$	1.80813e27	0.157222
$900$	−1.67098e27	−0.143769
$901$	2.89628e28	2.46578
$902$	−3.46205e25	−0.00291656
$903$	−1.21466e28	−1.01256
$904$	−1.05618e28	−0.871238
$905$	1.28760e28	1.05104
$906$	5.74804e26	0.0464303
$907$	1.98488e28	1.58659	0.793297	−	0.608834i	$-0.208363\pi$
$907$	1.98488e28	1.58659	0.793297	+	0.608834i	$0.208363\pi$
$908$	−3.28363e26	−0.0259740
$909$	−3.95574e27	−0.309650
$910$	−3.09386e28	−2.39667
$911$	−1.44352e27	−0.110662	−0.0553310	−	0.998468i	$-0.517621\pi$
$911$	−1.44352e27	−0.110662	−0.0553310	+	0.998468i	$0.517621\pi$
$912$	5.67229e27	0.430336
$913$	3.95063e25	0.00296616
$914$	1.37531e27	0.102191
$915$	9.24392e27	0.679760
$916$	5.47887e27	0.398735
$917$	−4.45651e27	−0.320986
$918$	−2.80923e28	−2.00255
$919$	8.06644e26	0.0569095	0.0284547	−	0.999595i	$-0.490941\pi$
$919$	8.06644e26	0.0569095	0.0284547	+	0.999595i	$0.490941\pi$
$920$	1.49011e28	1.04048
$921$	−8.59330e27	−0.593873
$922$	−8.68059e27	−0.593752
$923$	−1.04797e28	−0.709470
$924$	9.70285e24	0.000650153 0
$925$	−2.12576e28	−1.40983
$926$	6.91959e27	0.454230
$927$	−7.32428e27	−0.475891
$928$	−2.03275e27	−0.130731
$929$	−1.71336e28	−1.09069	−0.545343	−	0.838213i	$-0.683601\pi$
$929$	−1.71336e28	−1.09069	−0.545343	+	0.838213i	$0.683601\pi$
$930$	−1.33713e28	−0.842530
$931$	6.79794e25	0.00423990
$932$	−4.71444e27	−0.291058
$933$	−7.98240e27	−0.487818
$934$	−3.30935e28	−2.00192
$935$	−9.93806e25	−0.00595102
$936$	−1.09466e28	−0.648870
$937$	7.14216e27	0.419086	0.209543	−	0.977799i	$-0.432802\pi$
$937$	7.14216e27	0.419086	0.209543	+	0.977799i	$0.432802\pi$
$938$	−1.35736e28	−0.788437
$939$	1.94470e27	0.111823
$940$	1.20223e27	0.0684344
$941$	−1.44966e28	−0.816894	−0.408447	−	0.912782i	$-0.633929\pi$
$941$	−1.44966e28	−0.816894	−0.408447	+	0.912782i	$0.633929\pi$
$942$	−2.19113e28	−1.22232
$943$	1.75040e28	0.966666
$944$	1.83352e28	1.00242
$945$	−2.51575e28	−1.36165
$946$	9.01879e25	0.00483262
$947$	−2.49952e28	−1.32597	−0.662983	−	0.748635i	$-0.730710\pi$
$947$	−2.49952e28	−1.32597	−0.662983	+	0.748635i	$0.730710\pi$
$948$	−7.55241e27	−0.396649
$949$	2.76278e27	0.143654
$950$	8.64626e27	0.445097
$951$	−1.21459e28	−0.619036
$952$	2.44743e28	1.23498
$953$	4.30114e27	0.214882	0.107441	−	0.994211i	$-0.465734\pi$
$953$	4.30114e27	0.214882	0.107441	+	0.994211i	$0.465734\pi$
$954$	−1.93481e28	−0.957038
$955$	−2.57460e28	−1.26089
$956$	−1.21267e28	−0.588023
$957$	7.30410e24	0.000350674 0
$958$	1.18688e28	0.564203
$959$	3.52245e28	1.65794
$960$	−8.21604e27	−0.382901
$961$	−7.06997e27	−0.326246
$962$	7.71729e28	3.52616
$963$	−1.00154e28	−0.453128
$964$	4.55242e27	0.203944
$965$	4.41559e27	0.195875
$966$	−1.86639e28	−0.819821
$967$	3.69063e28	1.60527	0.802637	−	0.596467i	$-0.203430\pi$
$967$	3.69063e28	1.60527	0.802637	+	0.596467i	$0.203430\pi$
$968$	−1.73994e28	−0.749410
$969$	1.35796e28	0.579175
$970$	6.32546e28	2.67153
$971$	2.25962e28	0.945047	0.472523	−	0.881318i	$-0.343343\pi$
$971$	2.25962e28	0.945047	0.472523	+	0.881318i	$0.343343\pi$
$972$	8.11229e27	0.335980
$973$	2.64649e28	1.08542
$974$	2.45566e28	0.997375
$975$	1.91213e28	0.769085
$976$	2.38077e28	0.948298
$977$	2.19522e26	0.00865923	0.00432961	−	0.999991i	$-0.498622\pi$
$977$	2.19522e26	0.00865923	0.00432961	+	0.999991i	$0.498622\pi$
$978$	2.82781e28	1.10467
$979$	−5.57134e25	−0.00215538
$980$	9.93475e25	0.00380635
$981$	1.65741e26	0.00628890
$982$	3.30659e28	1.24257
$983$	−3.03494e28	−1.12951	−0.564757	−	0.825257i	$-0.691030\pi$
$983$	−3.03494e28	−1.12951	−0.564757	+	0.825257i	$0.691030\pi$
$984$	−1.24754e28	−0.459834
$985$	−3.81726e28	−1.39350
$986$	−1.02099e28	−0.369139
$987$	2.71725e27	0.0973009
$988$	−8.25051e27	−0.292610
$989$	−4.55987e28	−1.60173
$990$	6.63895e25	0.00230975
$991$	−4.68009e28	−1.61270	−0.806352	−	0.591436i	$-0.798561\pi$
$991$	−4.68009e28	−1.61270	−0.806352	+	0.591436i	$0.798561\pi$
$992$	−1.64145e28	−0.560231
$993$	1.07724e28	0.364162
$994$	−1.56524e28	−0.524095
$995$	−5.07559e28	−1.68332
$996$	−7.88916e27	−0.259159
$997$	−3.41935e28	−1.11260	−0.556301	−	0.830981i	$-0.687780\pi$
$997$	−3.41935e28	−1.11260	−0.556301	+	0.830981i	$0.687780\pi$
$998$	−2.35328e28	−0.758460
$999$	6.27527e28	2.00337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.11	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-843.346 q^{2} +22834.2 q^{3} +186945. q^{4} -5.74638e6 q^{5} -1.92572e7 q^{6} -1.06332e8 q^{7} +2.84497e8 q^{8} -6.40859e8 q^{9} +O(q^{10})\)	\(q-843.346 q^{2} +22834.2 q^{3} +186945. q^{4} -5.74638e6 q^{5} -1.92572e7 q^{6} -1.06332e8 q^{7} +2.84497e8 q^{8} -6.40859e8 q^{9} +4.84619e9 q^{10} -2.13765e7 q^{11} +4.26875e9 q^{12} +6.00396e10 q^{13} +8.96744e10 q^{14} -1.31214e11 q^{15} -3.37942e11 q^{16} -8.09041e11 q^{17} +5.40466e11 q^{18} -7.35070e11 q^{19} -1.07426e12 q^{20} -2.42800e12 q^{21} +1.80278e10 q^{22} -9.11480e12 q^{23} +6.49627e12 q^{24} +1.39474e13 q^{25} -5.06342e13 q^{26} -4.11729e13 q^{27} -1.98782e13 q^{28} -1.49639e13 q^{29} +1.10659e14 q^{30} -1.20833e14 q^{31} +1.35844e14 q^{32} -4.88116e11 q^{33} +6.82302e14 q^{34} +6.11022e14 q^{35} -1.19805e14 q^{36} -1.52413e15 q^{37} +6.19919e14 q^{38} +1.37096e15 q^{39} -1.63483e15 q^{40} -1.92039e15 q^{41} +2.04765e15 q^{42} +5.00272e15 q^{43} -3.99623e12 q^{44} +3.68262e15 q^{45} +7.68693e15 q^{46} -1.11913e15 q^{47} -7.71666e15 q^{48} -9.24802e13 q^{49} -1.17625e16 q^{50} -1.84738e16 q^{51} +1.12241e16 q^{52} -3.57989e16 q^{53} +3.47230e16 q^{54} +1.22837e14 q^{55} -3.02510e16 q^{56} -1.67848e16 q^{57} +1.26197e16 q^{58} -5.42554e16 q^{59} -2.45298e16 q^{60} -7.04491e16 q^{61} +1.01904e17 q^{62} +6.81436e16 q^{63} +6.26155e16 q^{64} -3.45011e17 q^{65} +4.11651e14 q^{66} -1.51365e17 q^{67} -1.51246e17 q^{68} -2.08129e17 q^{69} -5.15303e17 q^{70} -1.74547e17 q^{71} -1.82322e17 q^{72} +4.60160e16 q^{73} +1.28537e18 q^{74} +3.18479e17 q^{75} -1.37418e17 q^{76} +2.27300e15 q^{77} -1.15619e18 q^{78} -1.76923e18 q^{79} +1.94195e18 q^{80} -1.95306e17 q^{81} +1.61956e18 q^{82} -1.84812e18 q^{83} -4.53903e17 q^{84} +4.64906e18 q^{85} -4.21902e18 q^{86} -3.41688e17 q^{87} -6.08155e15 q^{88} +2.60629e18 q^{89} -3.10572e18 q^{90} -6.38411e18 q^{91} -1.70397e18 q^{92} -2.75914e18 q^{93} +9.43815e17 q^{94} +4.22399e18 q^{95} +3.10190e18 q^{96} +1.30524e19 q^{97} +7.79928e16 q^{98} +1.36993e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 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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