LMFDB - Embedded newform 10.20.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,20,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, 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("10.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	10.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:	$22.8816696556$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 2925852 $ x^2 - x - 2925852
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1710.01$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+512.000 q^{2} +51072.2 q^{3} +262144. q^{4} +1.95312e6 q^{5} +2.61490e7 q^{6} +2.72650e7 q^{7} +1.34218e8 q^{8} +1.44611e9 q^{9} +1.00000e9 q^{10} +8.90778e9 q^{11} +1.33883e10 q^{12} -3.88993e10 q^{13} +1.39597e10 q^{14} +9.97505e10 q^{15} +6.87195e10 q^{16} -4.92493e11 q^{17} +7.40410e11 q^{18} +7.02926e11 q^{19} +5.12000e11 q^{20} +1.39248e12 q^{21} +4.56078e12 q^{22} -5.93310e12 q^{23} +6.85480e12 q^{24} +3.81470e12 q^{25} -1.99164e13 q^{26} +1.44969e13 q^{27} +7.14735e12 q^{28} +1.42477e14 q^{29} +5.10722e13 q^{30} +2.10392e14 q^{31} +3.51844e13 q^{32} +4.54940e14 q^{33} -2.52156e14 q^{34} +5.32519e13 q^{35} +3.79090e14 q^{36} -1.00145e15 q^{37} +3.59898e14 q^{38} -1.98667e15 q^{39} +2.62144e14 q^{40} -4.08507e15 q^{41} +7.12952e14 q^{42} +3.21023e15 q^{43} +2.33512e15 q^{44} +2.82444e15 q^{45} -3.03774e15 q^{46} -6.44781e15 q^{47} +3.50966e15 q^{48} -1.06555e16 q^{49} +1.95312e15 q^{50} -2.51527e16 q^{51} -1.01972e16 q^{52} +1.88410e15 q^{53} +7.42243e15 q^{54} +1.73980e16 q^{55} +3.65944e15 q^{56} +3.59000e16 q^{57} +7.29480e16 q^{58} -4.28479e15 q^{59} +2.61490e16 q^{60} -1.19883e17 q^{61} +1.07721e17 q^{62} +3.94282e16 q^{63} +1.80144e16 q^{64} -7.59752e16 q^{65} +2.32929e17 q^{66} +1.93776e17 q^{67} -1.29104e17 q^{68} -3.03017e17 q^{69} +2.72650e16 q^{70} +3.68964e17 q^{71} +1.94094e17 q^{72} -9.09825e17 q^{73} -5.12740e17 q^{74} +1.94825e17 q^{75} +1.84268e17 q^{76} +2.42870e17 q^{77} -1.01718e18 q^{78} +5.25508e17 q^{79} +1.34218e17 q^{80} -9.40371e17 q^{81} -2.09156e18 q^{82} -2.77280e18 q^{83} +3.65031e17 q^{84} -9.61900e17 q^{85} +1.64364e18 q^{86} +7.27660e18 q^{87} +1.19558e18 q^{88} -3.88866e17 q^{89} +1.44611e18 q^{90} -1.06059e18 q^{91} -1.55533e18 q^{92} +1.07452e19 q^{93} -3.30128e18 q^{94} +1.37290e18 q^{95} +1.79694e18 q^{96} -9.73741e17 q^{97} -5.45562e18 q^{98} +1.28817e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 1024 q^{2} + 33724 q^{3} + 524288 q^{4} + 3906250 q^{5} + 17266688 q^{6} + 83061292 q^{7} + 268435456 q^{8} + 584812954 q^{9} + 2000000000 q^{10} + 3549480144 q^{11} + 8840544256 q^{12} + 30250225564 q^{13}+ \cdots + 17\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 1024 * q^2 + 33724 * q^3 + 524288 * q^4 + 3906250 * q^5 + 17266688 * q^6 + 83061292 * q^7 + 268435456 * q^8 + 584812954 * q^9 + 2000000000 * q^10 + 3549480144 * q^11 + 8840544256 * q^12 + 30250225564 * q^13 + 42527381504 * q^14 + 65867187500 * q^15 + 137438953472 * q^16 + 329655779412 * q^17 + 299424232448 * q^18 + 383076809800 * q^19 + 1024000000000 * q^20 + 424515195104 * q^21 + 1817333833728 * q^22 + 2082856096884 * q^23 + 4526358659072 * q^24 + 7629394531250 * q^25 + 15488115488768 * q^26 + 49602163340440 * q^27 + 21774019330048 * q^28 + 166587684602220 * q^29 + 33724000000000 * q^30 + 418151119038664 * q^31 + 70368744177664 * q^32 + 547897533578928 * q^33 + 168783759058944 * q^34 + 162229085937500 * q^35 + 153305207013376 * q^36 - 1292219637694628 * q^37 + 196135326617600 * q^38 - 3186297306918232 * q^39 + 524288000000000 * q^40 - 3127192714527996 * q^41 + 217351779893248 * q^42 - 1795992338357636 * q^43 + 930474922868736 * q^44 + 1142212800781250 * q^45 + 1066422321604608 * q^46 - 6761653310165988 * q^47 + 2317495633444864 * q^48 - 18941182438871454 * q^49 + 3906250000000000 * q^50 - 39415550773661256 * q^51 + 7929915130249216 * q^52 - 9787568571066516 * q^53 + 25396307630305280 * q^54 + 6932578406250000 * q^55 + 11148297896984576 * q^56 + 41448804721422800 * q^57 + 85292894516336640 * q^58 - 25484316660294360 * q^59 + 17266688000000000 * q^60 - 77840503559636276 * q^61 + 214093372947795968 * q^62 - 8629133041886116 * q^63 + 36028797018963968 * q^64 + 59082471804687500 * q^65 + 280523537192411136 * q^66 + 439654835073204532 * q^67 + 86417284638179328 * q^68 - 442079200728708192 * q^69 + 83061292000000000 * q^70 - 29427662567526696 * q^71 + 78492265990848512 * q^72 - 1463308911724217756 * q^73 - 661616454499649536 * q^74 + 128646850585937500 * q^75 + 100421287228211200 * q^76 - 56103061801470576 * q^77 - 1631384221142134784 * q^78 - 1235969155825112720 * q^79 + 268435456000000000 * q^80 - 548329353045127838 * q^81 - 1601122669838333952 * q^82 - 877205635969635396 * q^83 + 111284111305342976 * q^84 + 643858944164062500 * q^85 - 919548077239109632 * q^86 + 6858312722579528040 * q^87 + 476403160508792832 * q^88 + 4172929077000032820 * q^89 + 584812954000000000 * q^90 + 2797700455846427144 * q^91 + 546008228661559296 * q^92 + 7140934358593491968 * q^93 - 3461966494804985856 * q^94 + 748196894140625000 * q^95 + 1186557764323770368 * q^96 + 11254578228347861332 * q^97 - 9697885408702184448 * q^98 + 17496761012343831888 * q^99

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 $

$2$	512.000	0.707107
$2$	512.000	0.707107
$3$	51072.2	1.49807	0.749037	−	0.662529i	$-0.230517\pi$
$3$	51072.2	1.49807	0.749037	+	0.662529i	$0.230517\pi$
$4$	262144.	0.500000
$5$	1.95312e6	0.447214
$5$	1.95312e6	0.447214
$6$	2.61490e7	1.05930
$7$	2.72650e7	0.255372	0.127686	−	0.991815i	$-0.459245\pi$
$7$	2.72650e7	0.255372	0.127686	+	0.991815i	$0.459245\pi$
$8$	1.34218e8	0.353553
$9$	1.44611e9	1.24422
$10$	1.00000e9	0.316228
$11$	8.90778e9	1.13904	0.569520	−	0.821977i	$-0.307129\pi$
$11$	8.90778e9	1.13904	0.569520	+	0.821977i	$0.307129\pi$
$12$	1.33883e10	0.749037
$13$	−3.88993e10	−1.01737	−0.508686	−	0.860952i	$-0.669869\pi$
$13$	−3.88993e10	−1.01737	−0.508686	+	0.860952i	$0.669869\pi$
$14$	1.39597e10	0.180575
$15$	9.97505e10	0.669959
$16$	6.87195e10	0.250000
$17$	−4.92493e11	−1.00725	−0.503623	−	0.863924i	$-0.668000\pi$
$17$	−4.92493e11	−1.00725	−0.503623	+	0.863924i	$0.668000\pi$
$18$	7.40410e11	0.879799
$19$	7.02926e11	0.499747	0.249873	−	0.968278i	$-0.419611\pi$
$19$	7.02926e11	0.499747	0.249873	+	0.968278i	$0.419611\pi$
$20$	5.12000e11	0.223607
$21$	1.39248e12	0.382566
$22$	4.56078e12	0.805423
$23$	−5.93310e12	−0.686858	−0.343429	−	0.939179i	$-0.611588\pi$
$23$	−5.93310e12	−0.686858	−0.343429	+	0.939179i	$0.611588\pi$
$24$	6.85480e12	0.529649
$25$	3.81470e12	0.200000
$26$	−1.99164e13	−0.719391
$27$	1.44969e13	0.365864
$28$	7.14735e12	0.127686
$29$	1.42477e14	1.82374	0.911869	−	0.410481i	$-0.134639\pi$
$29$	1.42477e14	1.82374	0.911869	+	0.410481i	$0.134639\pi$
$30$	5.10722e13	0.473732
$31$	2.10392e14	1.42920	0.714600	−	0.699533i	$-0.246609\pi$
$31$	2.10392e14	1.42920	0.714600	+	0.699533i	$0.246609\pi$
$32$	3.51844e13	0.176777
$33$	4.54940e14	1.70637
$34$	−2.52156e14	−0.712230
$35$	5.32519e13	0.114206
$36$	3.79090e14	0.622112
$37$	−1.00145e15	−1.26681	−0.633404	−	0.773821i	$-0.718343\pi$
$37$	−1.00145e15	−1.26681	−0.633404	+	0.773821i	$0.718343\pi$
$38$	3.59898e14	0.353374
$39$	−1.98667e15	−1.52410
$40$	2.62144e14	0.158114
$41$	−4.08507e15	−1.94874	−0.974368	−	0.224961i	$-0.927775\pi$
$41$	−4.08507e15	−1.94874	−0.974368	+	0.224961i	$0.927775\pi$
$42$	7.12952e14	0.270515
$43$	3.21023e15	0.974060	0.487030	−	0.873385i	$-0.338080\pi$
$43$	3.21023e15	0.974060	0.487030	+	0.873385i	$0.338080\pi$
$44$	2.33512e15	0.569520
$45$	2.82444e15	0.556434
$46$	−3.03774e15	−0.485682
$47$	−6.44781e15	−0.840393	−0.420196	−	0.907433i	$-0.638039\pi$
$47$	−6.44781e15	−0.840393	−0.420196	+	0.907433i	$0.638039\pi$
$48$	3.50966e15	0.374518
$49$	−1.06555e16	−0.934785
$50$	1.95312e15	0.141421
$51$	−2.51527e16	−1.50893
$52$	−1.01972e16	−0.508686
$53$	1.88410e15	0.0784300	0.0392150	−	0.999231i	$-0.487514\pi$
$53$	1.88410e15	0.0784300	0.0392150	+	0.999231i	$0.487514\pi$
$54$	7.42243e15	0.258705
$55$	1.73980e16	0.509394
$56$	3.65944e15	0.0902877
$57$	3.59000e16	0.748658
$58$	7.29480e16	1.28958
$59$	−4.28479e15	−0.0643924	−0.0321962	−	0.999482i	$-0.510250\pi$
$59$	−4.28479e15	−0.0643924	−0.0321962	+	0.999482i	$0.510250\pi$
$60$	2.61490e16	0.334979
$61$	−1.19883e17	−1.31257	−0.656287	−	0.754511i	$-0.727874\pi$
$61$	−1.19883e17	−1.31257	−0.656287	+	0.754511i	$0.727874\pi$
$62$	1.07721e17	1.01060
$63$	3.94282e16	0.317740
$64$	1.80144e16	0.125000
$65$	−7.59752e16	−0.454983
$66$	2.32929e17	1.20658
$67$	1.93776e17	0.870141	0.435071	−	0.900396i	$-0.356723\pi$
$67$	1.93776e17	0.870141	0.435071	+	0.900396i	$0.356723\pi$
$68$	−1.29104e17	−0.503623
$69$	−3.03017e17	−1.02896
$70$	2.72650e16	0.0807558
$71$	3.68964e17	0.955058	0.477529	−	0.878616i	$-0.341532\pi$
$71$	3.68964e17	0.955058	0.477529	+	0.878616i	$0.341532\pi$
$72$	1.94094e17	0.439899
$73$	−9.09825e17	−1.80880	−0.904400	−	0.426685i	$-0.859681\pi$
$73$	−9.09825e17	−1.80880	−0.904400	+	0.426685i	$0.859681\pi$
$74$	−5.12740e17	−0.895769
$75$	1.94825e17	0.299615
$76$	1.84268e17	0.249873
$77$	2.42870e17	0.290879
$78$	−1.01718e18	−1.07770
$79$	5.25508e17	0.493313	0.246656	−	0.969103i	$-0.420668\pi$
$79$	5.25508e17	0.493313	0.246656	+	0.969103i	$0.420668\pi$
$80$	1.34218e17	0.111803
$81$	−9.40371e17	−0.696132
$82$	−2.09156e18	−1.37796
$83$	−2.77280e18	−1.62808	−0.814042	−	0.580807i	$-0.802737\pi$
$83$	−2.77280e18	−1.62808	−0.814042	+	0.580807i	$0.802737\pi$
$84$	3.65031e17	0.191283
$85$	−9.61900e17	−0.450454
$86$	1.64364e18	0.688764
$87$	7.27660e18	2.73209
$88$	1.19558e18	0.402712
$89$	−3.88866e17	−0.117651	−0.0588254	−	0.998268i	$-0.518736\pi$
$89$	−3.88866e17	−0.117651	−0.0588254	+	0.998268i	$0.518736\pi$
$90$	1.44611e18	0.393458
$91$	−1.06059e18	−0.259809
$92$	−1.55533e18	−0.343429
$93$	1.07452e19	2.14105
$94$	−3.30128e18	−0.594247
$95$	1.37290e18	0.223494
$96$	1.79694e18	0.264824
$97$	−9.73741e17	−0.130050	−0.0650252	−	0.997884i	$-0.520713\pi$
$97$	−9.73741e17	−0.130050	−0.0650252	+	0.997884i	$0.520713\pi$
$98$	−5.45562e18	−0.660993
$99$	1.28817e19	1.41722
$100$	1.00000e18	0.100000
$101$	−1.67461e19	−1.52356	−0.761781	−	0.647834i	$-0.775675\pi$
$101$	−1.67461e19	−1.52356	−0.761781	+	0.647834i	$0.775675\pi$
$102$	−1.28782e19	−1.06697
$103$	4.40800e18	0.332880	0.166440	−	0.986052i	$-0.446773\pi$
$103$	4.40800e18	0.332880	0.166440	+	0.986052i	$0.446773\pi$
$104$	−5.22098e18	−0.359695
$105$	2.71969e18	0.171089
$106$	9.64657e17	0.0554584
$107$	−8.71914e18	−0.458488	−0.229244	−	0.973369i	$-0.573625\pi$
$107$	−8.71914e18	−0.458488	−0.229244	+	0.973369i	$0.573625\pi$
$108$	3.80028e18	0.182932
$109$	4.17114e19	1.83951	0.919757	−	0.392487i	$-0.128385\pi$
$109$	4.17114e19	1.83951	0.919757	+	0.392487i	$0.128385\pi$
$110$	8.90778e18	0.360196
$111$	−5.11461e19	−1.89777
$112$	1.87363e18	0.0638431
$113$	−8.70592e18	−0.272627	−0.136314	−	0.990666i	$-0.543525\pi$
$113$	−8.70592e18	−0.272627	−0.136314	+	0.990666i	$0.543525\pi$
$114$	1.83808e19	0.529381
$115$	−1.15881e19	−0.307172
$116$	3.73494e19	0.911869
$117$	−5.62528e19	−1.26584
$118$	−2.19381e18	−0.0455323
$119$	−1.34278e19	−0.257222
$120$	1.33883e19	0.236866
$121$	1.81895e19	0.297413
$122$	−6.13801e19	−0.928130
$123$	−2.08634e20	−2.91935
$124$	5.51530e19	0.714600
$125$	7.45058e18	0.0894427
$126$	2.01873e19	0.224676
$127$	6.07257e19	0.626956	0.313478	−	0.949595i	$-0.398506\pi$
$127$	6.07257e19	0.626956	0.313478	+	0.949595i	$0.398506\pi$
$128$	9.22337e18	0.0883883
$129$	1.63954e20	1.45921
$130$	−3.88993e19	−0.321721
$131$	1.94831e20	1.49824	0.749120	−	0.662434i	$-0.230477\pi$
$131$	1.94831e20	1.49824	0.749120	+	0.662434i	$0.230477\pi$
$132$	1.19260e20	0.853183
$133$	1.91652e19	0.127622
$134$	9.92134e19	0.615283
$135$	2.83143e19	0.163620
$136$	−6.61013e19	−0.356115
$137$	1.21216e20	0.609135	0.304567	−	0.952491i	$-0.401488\pi$
$137$	1.21216e20	0.609135	0.304567	+	0.952491i	$0.401488\pi$
$138$	−1.55144e20	−0.727587
$139$	2.22493e20	0.974263	0.487131	−	0.873329i	$-0.338043\pi$
$139$	2.22493e20	0.974263	0.487131	+	0.873329i	$0.338043\pi$
$140$	1.39597e19	0.0571030
$141$	−3.29304e20	−1.25897
$142$	1.88910e20	0.675328
$143$	−3.46506e20	−1.15883
$144$	9.93761e19	0.311056
$145$	2.78275e20	0.815600
$146$	−4.65830e20	−1.27902
$147$	−5.44201e20	−1.40038
$148$	−2.62523e20	−0.633404
$149$	3.46894e20	0.785104	0.392552	−	0.919730i	$-0.371592\pi$
$149$	3.46894e20	0.785104	0.392552	+	0.919730i	$0.371592\pi$
$150$	9.97505e19	0.211860
$151$	−1.05205e19	−0.0209776	−0.0104888	−	0.999945i	$-0.503339\pi$
$151$	−1.05205e19	−0.0209776	−0.0104888	+	0.999945i	$0.503339\pi$
$152$	9.43451e19	0.176687
$153$	−7.12200e20	−1.25324
$154$	1.24350e20	0.205683
$155$	4.10922e20	0.639158
$156$	−5.20795e20	−0.762049
$157$	−3.07714e19	−0.0423741	−0.0211871	−	0.999776i	$-0.506745\pi$
$157$	−3.07714e19	−0.0423741	−0.0211871	+	0.999776i	$0.506745\pi$
$158$	2.69060e20	0.348825
$159$	9.62250e19	0.117494
$160$	6.87195e19	0.0790569
$161$	−1.61766e20	−0.175404
$162$	−4.81470e20	−0.492239
$163$	5.76318e20	0.555751	0.277875	−	0.960617i	$-0.410370\pi$
$163$	5.76318e20	0.555751	0.277875	+	0.960617i	$0.410370\pi$
$164$	−1.07088e21	−0.974368
$165$	8.88555e20	0.763110
$166$	−1.41967e21	−1.15123
$167$	6.89550e20	0.528153	0.264076	−	0.964502i	$-0.414933\pi$
$167$	6.89550e20	0.528153	0.264076	+	0.964502i	$0.414933\pi$
$168$	1.86896e20	0.135258
$169$	5.12350e19	0.0350464
$170$	−4.92493e20	−0.318519
$171$	1.01651e21	0.621797
$172$	8.41542e20	0.487030
$173$	−4.14244e19	−0.0226892	−0.0113446	−	0.999936i	$-0.503611\pi$
$173$	−4.14244e19	−0.0226892	−0.0113446	+	0.999936i	$0.503611\pi$
$174$	3.72562e21	1.93188
$175$	1.04008e20	0.0510744
$176$	6.12138e20	0.284760
$177$	−2.18834e20	−0.0964646
$178$	−1.99099e20	−0.0831917
$179$	3.65179e21	1.44678	0.723388	−	0.690441i	$-0.242584\pi$
$179$	3.65179e21	1.44678	0.723388	+	0.690441i	$0.242584\pi$
$180$	7.40410e20	0.278217
$181$	1.05232e21	0.375145	0.187573	−	0.982251i	$-0.439938\pi$
$181$	1.05232e21	0.375145	0.187573	+	0.982251i	$0.439938\pi$
$182$	−5.43021e20	−0.183712
$183$	−6.12269e21	−1.96633
$184$	−7.96327e20	−0.242841
$185$	−1.95595e21	−0.566534
$186$	5.50154e21	1.51395
$187$	−4.38702e21	−1.14729
$188$	−1.69025e21	−0.420196
$189$	3.95258e20	0.0934316
$190$	7.02926e20	0.158034
$191$	−6.63681e21	−1.41952	−0.709761	−	0.704442i	$-0.751197\pi$
$191$	−6.63681e21	−1.41952	−0.709761	+	0.704442i	$0.751197\pi$
$192$	9.20036e20	0.187259
$193$	−2.65526e21	−0.514414	−0.257207	−	0.966356i	$-0.582802\pi$
$193$	−2.65526e21	−0.514414	−0.257207	+	0.966356i	$0.582802\pi$
$194$	−4.98555e20	−0.0919596
$195$	−3.88022e21	−0.681597
$196$	−2.79328e21	−0.467393
$197$	1.02356e22	1.63186	0.815929	−	0.578153i	$-0.196226\pi$
$197$	1.02356e22	1.63186	0.815929	+	0.578153i	$0.196226\pi$
$198$	6.59541e21	1.00213
$199$	−2.53082e21	−0.366570	−0.183285	−	0.983060i	$-0.558673\pi$
$199$	−2.53082e21	−0.366570	−0.183285	+	0.983060i	$0.558673\pi$
$200$	5.12000e20	0.0707107
$201$	9.89659e21	1.30354
$202$	−8.57400e21	−1.07732
$203$	3.88462e21	0.465732
$204$	−6.59363e21	−0.754463
$205$	−7.97865e21	−0.871501
$206$	2.25689e21	0.235382
$207$	−8.57993e21	−0.854605
$208$	−2.67314e21	−0.254343
$209$	6.26151e21	0.569232
$210$	1.39248e21	0.120978
$211$	−1.43232e22	−1.18948	−0.594740	−	0.803918i	$-0.702745\pi$
$211$	−1.43232e22	−1.18948	−0.594740	+	0.803918i	$0.702745\pi$
$212$	4.93904e20	0.0392150
$213$	1.88438e22	1.43075
$214$	−4.46420e21	−0.324200
$215$	6.26998e21	0.435613
$216$	1.94574e21	0.129353
$217$	5.73633e21	0.364978
$218$	2.13562e22	1.30073
$219$	−4.64668e22	−2.70972
$220$	4.56078e21	0.254697
$221$	1.91576e22	1.02474
$222$	−2.61868e22	−1.34193
$223$	1.40599e22	0.690375	0.345187	−	0.938534i	$-0.387815\pi$
$223$	1.40599e22	0.690375	0.345187	+	0.938534i	$0.387815\pi$
$224$	9.59301e20	0.0451439
$225$	5.51648e21	0.248845
$226$	−4.45743e21	−0.192777
$227$	3.41441e22	1.41602	0.708011	−	0.706201i	$-0.249592\pi$
$227$	3.41441e22	1.41602	0.708011	+	0.706201i	$0.249592\pi$
$228$	9.41097e21	0.374329
$229$	2.26978e22	0.866057	0.433028	−	0.901380i	$-0.357445\pi$
$229$	2.26978e22	0.866057	0.433028	+	0.901380i	$0.357445\pi$
$230$	−5.93310e21	−0.217204
$231$	1.24039e22	0.435758
$232$	1.91229e22	0.644789
$233$	3.14636e22	1.01842	0.509211	−	0.860642i	$-0.329937\pi$
$233$	3.14636e22	1.01842	0.509211	+	0.860642i	$0.329937\pi$
$234$	−2.88014e22	−0.895083
$235$	−1.25934e22	−0.375835
$236$	−1.12323e21	−0.0321962
$237$	2.68389e22	0.739018
$238$	−6.87504e21	−0.181884
$239$	−1.24777e22	−0.317216	−0.158608	−	0.987342i	$-0.550701\pi$
$239$	−1.24777e22	−0.317216	−0.158608	+	0.987342i	$0.550701\pi$
$240$	6.85480e21	0.167490
$241$	−1.16264e21	−0.0273076	−0.0136538	−	0.999907i	$-0.504346\pi$
$241$	−1.16264e21	−0.0273076	−0.0136538	+	0.999907i	$0.504346\pi$
$242$	9.31301e21	0.210302
$243$	−6.48761e22	−1.40872
$244$	−3.14266e22	−0.656287
$245$	−2.08116e22	−0.418049
$246$	−1.06820e23	−2.06429
$247$	−2.73433e22	−0.508429
$248$	2.82383e22	0.505299
$249$	−1.41613e23	−2.43899
$250$	3.81470e21	0.0632456
$251$	1.09655e23	1.75036	0.875182	−	0.483793i	$-0.160741\pi$
$251$	1.09655e23	1.75036	0.875182	+	0.483793i	$0.160741\pi$
$252$	1.03359e22	0.158870
$253$	−5.28507e22	−0.782359
$254$	3.10916e22	0.443325
$255$	−4.91264e22	−0.674813
$256$	4.72237e21	0.0625000
$257$	−2.11998e22	−0.270375	−0.135187	−	0.990820i	$-0.543164\pi$
$257$	−2.11998e22	−0.270375	−0.135187	+	0.990820i	$0.543164\pi$
$258$	8.39442e22	1.03182
$259$	−2.73044e22	−0.323508
$260$	−1.99164e22	−0.227491
$261$	2.06037e23	2.26914
$262$	9.97536e22	1.05942
$263$	−1.06654e23	−1.09244	−0.546222	−	0.837641i	$-0.683934\pi$
$263$	−1.06654e23	−1.09244	−0.546222	+	0.837641i	$0.683934\pi$
$264$	6.10611e22	0.603291
$265$	3.67987e21	0.0350750
$266$	9.81261e21	0.0902420
$267$	−1.98603e22	−0.176250
$268$	5.07973e22	0.435071
$269$	9.27742e22	0.766974	0.383487	−	0.923546i	$-0.374723\pi$
$269$	9.27742e22	0.766974	0.383487	+	0.923546i	$0.374723\pi$
$270$	1.44969e22	0.115696
$271$	−9.46299e22	−0.729156	−0.364578	−	0.931173i	$-0.618787\pi$
$271$	−9.46299e22	−0.729156	−0.364578	+	0.931173i	$0.618787\pi$
$272$	−3.38438e22	−0.251811
$273$	−5.41666e22	−0.389212
$274$	6.20624e22	0.430723
$275$	3.39805e22	0.227808
$276$	−7.94340e22	−0.514482
$277$	−7.04507e21	−0.0440887	−0.0220444	−	0.999757i	$-0.507018\pi$
$277$	−7.04507e21	−0.0440887	−0.0220444	+	0.999757i	$0.507018\pi$
$278$	1.13916e23	0.688908
$279$	3.04251e23	1.77824
$280$	7.14735e21	0.0403779
$281$	−1.00259e22	−0.0547539	−0.0273770	−	0.999625i	$-0.508715\pi$
$281$	−1.00259e22	−0.0547539	−0.0273770	+	0.999625i	$0.508715\pi$
$282$	−1.68604e23	−0.890226
$283$	−2.12867e23	−1.08677	−0.543383	−	0.839485i	$-0.682857\pi$
$283$	−2.12867e23	−1.08677	−0.543383	+	0.839485i	$0.682857\pi$
$284$	9.67218e22	0.477529
$285$	7.01172e22	0.334810
$286$	−1.77411e23	−0.819415
$287$	−1.11379e23	−0.497653
$288$	5.08806e22	0.219950
$289$	3.47675e21	0.0145427
$290$	1.42477e23	0.576717
$291$	−4.97311e22	−0.194825
$292$	−2.38505e23	−0.904400
$293$	5.10289e23	1.87315	0.936577	−	0.350462i	$-0.113975\pi$
$293$	5.10289e23	1.87315	0.936577	+	0.350462i	$0.113975\pi$
$294$	−2.78631e23	−0.990216
$295$	−8.36872e21	−0.0287972
$296$	−1.34412e23	−0.447885
$297$	1.29135e23	0.416734
$298$	1.77610e23	0.555152
$299$	2.30793e23	0.698790
$300$	5.10722e22	0.149807
$301$	8.75268e22	0.248748
$302$	−5.38650e21	−0.0148334
$303$	−8.55260e23	−2.28241
$304$	4.83047e22	0.124937
$305$	−2.34146e23	−0.587001
$306$	−3.64646e23	−0.886173
$307$	−4.42100e23	−1.04161	−0.520806	−	0.853675i	$-0.674369\pi$
$307$	−4.42100e23	−1.04161	−0.520806	+	0.853675i	$0.674369\pi$
$308$	6.36670e22	0.145440
$309$	2.25126e23	0.498678
$310$	2.10392e23	0.451953
$311$	−3.04953e23	−0.635344	−0.317672	−	0.948201i	$-0.602901\pi$
$311$	−3.04953e23	−0.635344	−0.317672	+	0.948201i	$0.602901\pi$
$312$	−2.66647e23	−0.538850
$313$	−6.44559e23	−1.26355	−0.631774	−	0.775153i	$-0.717673\pi$
$313$	−6.44559e23	−1.26355	−0.631774	+	0.775153i	$0.717673\pi$
$314$	−1.57550e22	−0.0299630
$315$	7.70083e22	0.142098
$316$	1.37759e23	0.246656
$317$	1.02667e24	1.78389	0.891947	−	0.452140i	$-0.149339\pi$
$317$	1.02667e24	1.78389	0.891947	+	0.452140i	$0.149339\pi$
$318$	4.92672e22	0.0830807
$319$	1.26915e24	2.07731
$320$	3.51844e22	0.0559017
$321$	−4.45306e23	−0.686849
$322$	−8.28240e22	−0.124030
$323$	−3.46186e23	−0.503368
$324$	−2.46513e23	−0.348066
$325$	−1.48389e23	−0.203474
$326$	2.95075e23	0.392975
$327$	2.13030e24	2.75573
$328$	−5.48289e23	−0.688982
$329$	−1.75799e23	−0.214613
$330$	4.54940e23	0.539600
$331$	8.39874e23	0.967939	0.483970	−	0.875085i	$-0.339194\pi$
$331$	8.39874e23	0.967939	0.483970	+	0.875085i	$0.339194\pi$
$332$	−7.26873e23	−0.814042
$333$	−1.44820e24	−1.57619
$334$	3.53050e23	0.373460
$335$	3.78469e23	0.389139
$336$	9.56907e22	0.0956416
$337$	−7.88161e23	−0.765827	−0.382913	−	0.923784i	$-0.625079\pi$
$337$	−7.88161e23	−0.765827	−0.382913	+	0.923784i	$0.625079\pi$
$338$	2.62323e22	0.0247815
$339$	−4.44631e23	−0.408416
$340$	−2.52156e23	−0.225227
$341$	1.87413e24	1.62792
$342$	5.20453e23	0.439677
$343$	−6.01313e23	−0.494090
$344$	4.30870e23	0.344382
$345$	−5.91829e23	−0.460166
$346$	−2.12093e22	−0.0160437
$347$	−3.27984e23	−0.241392	−0.120696	−	0.992690i	$-0.538513\pi$
$347$	−3.27984e23	−0.241392	−0.120696	+	0.992690i	$0.538513\pi$
$348$	1.90752e24	1.36605
$349$	−1.57618e24	−1.09841	−0.549204	−	0.835689i	$-0.685069\pi$
$349$	−1.57618e24	−1.09841	−0.549204	+	0.835689i	$0.685069\pi$
$350$	5.32519e22	0.0361151
$351$	−5.63920e23	−0.372220
$352$	3.13415e23	0.201356
$353$	−1.44980e23	−0.0906667	−0.0453333	−	0.998972i	$-0.514435\pi$
$353$	−1.44980e23	−0.0906667	−0.0453333	+	0.998972i	$0.514435\pi$
$354$	−1.12043e23	−0.0682108
$355$	7.20633e23	0.427115
$356$	−1.01939e23	−0.0588254
$357$	−6.85788e23	−0.385338
$358$	1.86971e24	1.02303
$359$	7.64624e23	0.407428	0.203714	−	0.979030i	$-0.434699\pi$
$359$	7.64624e23	0.407428	0.203714	+	0.979030i	$0.434699\pi$
$360$	3.79090e23	0.196729
$361$	−1.48432e24	−0.750253
$362$	5.38786e23	0.265268
$363$	9.28978e23	0.445546
$364$	−2.78027e23	−0.129904
$365$	−1.77700e24	−0.808920
$366$	−3.13482e24	−1.39041
$367$	−2.08854e24	−0.902639	−0.451320	−	0.892362i	$-0.649047\pi$
$367$	−2.08854e24	−0.902639	−0.451320	+	0.892362i	$0.649047\pi$
$368$	−4.07719e23	−0.171714
$369$	−5.90747e24	−2.42466
$370$	−1.00145e24	−0.400600
$371$	5.13698e22	0.0200288
$372$	2.81679e24	1.07052
$373$	2.90964e24	1.07797	0.538984	−	0.842316i	$-0.318808\pi$
$373$	2.90964e24	1.07797	0.538984	+	0.842316i	$0.318808\pi$
$374$	−2.24615e24	−0.811258
$375$	3.80518e23	0.133992
$376$	−8.65410e23	−0.297124
$377$	−5.54224e24	−1.85542
$378$	2.02372e23	0.0660661
$379$	4.57048e24	1.45509	0.727544	−	0.686061i	$-0.240662\pi$
$379$	4.57048e24	1.45509	0.727544	+	0.686061i	$0.240662\pi$
$380$	3.59898e23	0.111747
$381$	3.10140e24	0.939226
$382$	−3.39805e24	−1.00375
$383$	4.74338e24	1.36678	0.683392	−	0.730052i	$-0.260504\pi$
$383$	4.74338e24	1.36678	0.683392	+	0.730052i	$0.260504\pi$
$384$	4.71058e23	0.132412
$385$	4.74356e23	0.130085
$386$	−1.35949e24	−0.363745
$387$	4.64235e24	1.21195
$388$	−2.55260e23	−0.0650252
$389$	−1.60295e24	−0.398472	−0.199236	−	0.979952i	$-0.563846\pi$
$389$	−1.60295e24	−0.398472	−0.199236	+	0.979952i	$0.563846\pi$
$390$	−1.98667e24	−0.481962
$391$	2.92201e24	0.691834
$392$	−1.43016e24	−0.330496
$393$	9.95047e24	2.24447
$394$	5.24060e24	1.15390
$395$	1.02638e24	0.220616
$396$	3.37685e24	0.708610
$397$	5.17477e24	1.06018	0.530092	−	0.847940i	$-0.322157\pi$
$397$	5.17477e24	1.06018	0.530092	+	0.847940i	$0.322157\pi$
$398$	−1.29578e24	−0.259204
$399$	9.78812e23	0.191186
$400$	2.62144e23	0.0500000
$401$	1.04892e24	0.195377	0.0976883	−	0.995217i	$-0.468855\pi$
$401$	1.04892e24	0.195377	0.0976883	+	0.995217i	$0.468855\pi$
$402$	5.06705e24	0.921739
$403$	−8.18410e24	−1.45403
$404$	−4.38989e24	−0.761781
$405$	−1.83666e24	−0.311320
$406$	1.98893e24	0.329322
$407$	−8.92066e24	−1.44295
$408$	−3.37594e24	−0.533486
$409$	−9.84304e24	−1.51970	−0.759850	−	0.650098i	$-0.774728\pi$
$409$	−9.84304e24	−1.51970	−0.759850	+	0.650098i	$0.774728\pi$
$410$	−4.08507e24	−0.616244
$411$	6.19076e24	0.912529
$412$	1.15553e24	0.166440
$413$	−1.16825e23	−0.0164440
$414$	−4.39292e24	−0.604297
$415$	−5.41562e24	−0.728101
$416$	−1.36865e24	−0.179848
$417$	1.13632e25	1.45952
$418$	3.20589e24	0.402508
$419$	1.39759e24	0.171533	0.0857664	−	0.996315i	$-0.472666\pi$
$419$	1.39759e24	0.171533	0.0857664	+	0.996315i	$0.472666\pi$
$420$	7.12952e23	0.0855444
$421$	2.96558e24	0.347880	0.173940	−	0.984756i	$-0.444350\pi$
$421$	2.96558e24	0.347880	0.173940	+	0.984756i	$0.444350\pi$
$422$	−7.33348e24	−0.841089
$423$	−9.32425e24	−1.04564
$424$	2.52879e23	0.0277292
$425$	−1.87871e24	−0.201449
$426$	9.64804e24	1.01169
$427$	−3.26861e24	−0.335195
$428$	−2.28567e24	−0.229244
$429$	−1.76969e25	−1.73601
$430$	3.21023e24	0.308025
$431$	−1.73742e25	−1.63069	−0.815343	−	0.578978i	$-0.803452\pi$
$431$	−1.73742e25	−1.63069	−0.815343	+	0.578978i	$0.803452\pi$
$432$	9.96221e23	0.0914661
$433$	1.97317e25	1.77227	0.886133	−	0.463432i	$-0.153382\pi$
$433$	1.97317e25	1.77227	0.886133	+	0.463432i	$0.153382\pi$
$434$	2.93700e24	0.258078
$435$	1.42121e25	1.22183
$436$	1.09344e25	0.919757
$437$	−4.17052e24	−0.343255
$438$	−2.37910e25	−1.91606
$439$	2.37490e25	1.87168	0.935840	−	0.352425i	$-0.114643\pi$
$439$	2.37490e25	1.87168	0.935840	+	0.352425i	$0.114643\pi$
$440$	2.33512e24	0.180098
$441$	−1.54091e25	−1.16308
$442$	9.80870e24	0.724603
$443$	−1.08663e25	−0.785679	−0.392840	−	0.919607i	$-0.628507\pi$
$443$	−1.08663e25	−0.785679	−0.392840	+	0.919607i	$0.628507\pi$
$444$	−1.34076e25	−0.948886
$445$	−7.59504e23	−0.0526150
$446$	7.19865e24	0.488169
$447$	1.77166e25	1.17614
$448$	4.91162e23	0.0319215
$449$	1.64022e25	1.04367	0.521834	−	0.853047i	$-0.325248\pi$
$449$	1.64022e25	1.04367	0.521834	+	0.853047i	$0.325248\pi$
$450$	2.82444e24	0.175960
$451$	−3.63889e25	−2.21969
$452$	−2.28220e24	−0.136314
$453$	−5.37306e23	−0.0314260
$454$	1.74818e25	1.00128
$455$	−2.07146e24	−0.116190
$456$	4.81841e24	0.264690
$457$	−1.90127e25	−1.02291	−0.511457	−	0.859309i	$-0.670894\pi$
$457$	−1.90127e25	−1.02291	−0.511457	+	0.859309i	$0.670894\pi$
$458$	1.16213e25	0.612395
$459$	−7.13963e24	−0.368515
$460$	−3.03774e24	−0.153586
$461$	−2.73913e25	−1.35660	−0.678302	−	0.734783i	$-0.737284\pi$
$461$	−2.73913e25	−1.35660	−0.678302	+	0.734783i	$0.737284\pi$
$462$	6.35082e24	0.308128
$463$	2.15999e25	1.02667	0.513337	−	0.858187i	$-0.328409\pi$
$463$	2.15999e25	1.02667	0.513337	+	0.858187i	$0.328409\pi$
$464$	9.79092e24	0.455935
$465$	2.09867e25	0.957505
$466$	1.61094e25	0.720133
$467$	6.57907e24	0.288174	0.144087	−	0.989565i	$-0.453976\pi$
$467$	6.57907e24	0.288174	0.144087	+	0.989565i	$0.453976\pi$
$468$	−1.47463e25	−0.632919
$469$	5.28330e24	0.222210
$470$	−6.44781e24	−0.265756
$471$	−1.57157e24	−0.0634796
$472$	−5.75094e23	−0.0227662
$473$	2.85960e25	1.10949
$474$	1.37415e25	0.522565
$475$	2.68145e24	0.0999494
$476$	−3.52002e24	−0.128611
$477$	2.72461e24	0.0975844
$478$	−6.38858e24	−0.224305
$479$	1.84209e25	0.634049	0.317024	−	0.948417i	$-0.397316\pi$
$479$	1.84209e25	0.634049	0.317024	+	0.948417i	$0.397316\pi$
$480$	3.50966e24	0.118433
$481$	3.89555e25	1.28882
$482$	−5.95271e23	−0.0193094
$483$	−8.26174e24	−0.262769
$484$	4.76826e24	0.148706
$485$	−1.90184e24	−0.0581603
$486$	−3.32165e25	−0.996116
$487$	−5.85949e25	−1.72320	−0.861598	−	0.507591i	$-0.830536\pi$
$487$	−5.85949e25	−1.72320	−0.861598	+	0.507591i	$0.830536\pi$
$488$	−1.60904e25	−0.464065
$489$	2.94339e25	0.832555
$490$	−1.06555e25	−0.295605
$491$	1.17567e24	0.0319896	0.0159948	−	0.999872i	$-0.494908\pi$
$491$	1.17567e24	0.0319896	0.0159948	+	0.999872i	$0.494908\pi$
$492$	−5.46921e25	−1.45967
$493$	−7.01687e25	−1.83695
$494$	−1.39998e25	−0.359513
$495$	2.51595e25	0.633800
$496$	1.44580e25	0.357300
$497$	1.00598e25	0.243895
$498$	−7.25059e25	−1.72462
$499$	−1.57255e25	−0.366985	−0.183492	−	0.983021i	$-0.558740\pi$
$499$	−1.57255e25	−0.366985	−0.183492	+	0.983021i	$0.558740\pi$
$500$	1.95313e24	0.0447214
$501$	3.52169e25	0.791211
$502$	5.61434e25	1.23769
$503$	−2.64249e24	−0.0571632	−0.0285816	−	0.999591i	$-0.509099\pi$
$503$	−2.64249e24	−0.0571632	−0.0285816	+	0.999591i	$0.509099\pi$
$504$	5.29197e24	0.112338
$505$	−3.27072e25	−0.681358
$506$	−2.70596e25	−0.553211
$507$	2.61669e24	0.0525020
$508$	1.59189e25	0.313478
$509$	7.94197e25	1.53500	0.767501	−	0.641048i	$-0.221500\pi$
$509$	7.94197e25	1.53500	0.767501	+	0.641048i	$0.221500\pi$
$510$	−2.51527e25	−0.477165
$511$	−2.48064e25	−0.461918
$512$	2.41785e24	0.0441942
$513$	1.01903e25	0.182840
$514$	−1.08543e25	−0.191184
$515$	8.60937e24	0.148868
$516$	4.29794e25	0.729606
$517$	−5.74356e25	−0.957241
$518$	−1.39798e25	−0.228755
$519$	−2.11564e24	−0.0339900
$520$	−1.01972e25	−0.160861
$521$	4.66972e25	0.723324	0.361662	−	0.932309i	$-0.382209\pi$
$521$	4.66972e25	0.723324	0.361662	+	0.932309i	$0.382209\pi$
$522$	1.05491e26	1.60452
$523$	−6.46849e25	−0.966132	−0.483066	−	0.875584i	$-0.660477\pi$
$523$	−6.46849e25	−0.966132	−0.483066	+	0.875584i	$0.660477\pi$
$524$	5.10739e25	0.749120
$525$	5.31190e24	0.0765133
$526$	−5.46070e25	−0.772474
$527$	−1.03617e26	−1.43955
$528$	3.12633e25	0.426591
$529$	−3.94138e25	−0.528226
$530$	1.88410e24	0.0248017
$531$	−6.19628e24	−0.0801186
$532$	5.02405e24	0.0638108
$533$	1.58906e26	1.98259
$534$	−1.01685e25	−0.124627
$535$	−1.70296e25	−0.205042
$536$	2.60082e25	0.307641
$537$	1.86505e26	2.16738
$538$	4.75004e25	0.542333
$539$	−9.49170e25	−1.06476
$540$	7.42243e24	0.0818098
$541$	1.28312e25	0.138961	0.0694805	−	0.997583i	$-0.477866\pi$
$541$	1.28312e25	0.138961	0.0694805	+	0.997583i	$0.477866\pi$
$542$	−4.84505e25	−0.515591
$543$	5.37441e25	0.561995
$544$	−1.73281e25	−0.178057
$545$	8.14676e25	0.822656
$546$	−2.77333e25	−0.275215
$547$	5.22682e25	0.509750	0.254875	−	0.966974i	$-0.417966\pi$
$547$	5.22682e25	0.509750	0.254875	+	0.966974i	$0.417966\pi$
$548$	3.17760e25	0.304567
$549$	−1.73364e26	−1.63314
$550$	1.73980e25	0.161085
$551$	1.00150e26	0.911408
$552$	−4.06702e25	−0.363793
$553$	1.43280e25	0.125978
$554$	−3.60708e24	−0.0311754
$555$	−9.98947e25	−0.848710
$556$	5.83252e25	0.487131
$557$	5.10671e25	0.419292	0.209646	−	0.977777i	$-0.432769\pi$
$557$	5.10671e25	0.419292	0.209646	+	0.977777i	$0.432769\pi$
$558$	1.55776e26	1.25741
$559$	−1.24876e26	−0.990981
$560$	3.65944e24	0.0285515
$561$	−2.24055e26	−1.71873
$562$	−5.13328e24	−0.0387169
$563$	1.95962e26	1.45325	0.726627	−	0.687032i	$-0.241087\pi$
$563$	1.95962e26	1.45325	0.726627	+	0.687032i	$0.241087\pi$
$564$	−8.63250e25	−0.629485
$565$	−1.70037e25	−0.121923
$566$	−1.08988e26	−0.768460
$567$	−2.56392e25	−0.177773
$568$	4.95215e25	0.337664
$569$	−2.04702e25	−0.137264	−0.0686320	−	0.997642i	$-0.521863\pi$
$569$	−2.04702e25	−0.137264	−0.0686320	+	0.997642i	$0.521863\pi$
$570$	3.59000e25	0.236746
$571$	−1.26019e26	−0.817322	−0.408661	−	0.912686i	$-0.634004\pi$
$571$	−1.26019e26	−0.817322	−0.408661	+	0.912686i	$0.634004\pi$
$572$	−9.08346e25	−0.579414
$573$	−3.38957e26	−2.12655
$574$	−5.70262e25	−0.351894
$575$	−2.26330e25	−0.137372
$576$	2.60509e25	0.155528
$577$	−1.24271e26	−0.729792	−0.364896	−	0.931048i	$-0.618895\pi$
$577$	−1.24271e26	−0.729792	−0.364896	+	0.931048i	$0.618895\pi$
$578$	1.78010e24	0.0102832
$579$	−1.35610e26	−0.770629
$580$	7.29480e25	0.407800
$581$	−7.56003e25	−0.415767
$582$	−2.54623e25	−0.137762
$583$	1.67831e25	0.0893349
$584$	−1.22115e26	−0.639508
$585$	−1.09869e26	−0.566100
$586$	2.61268e26	1.32452
$587$	3.67268e26	1.83198	0.915991	−	0.401199i	$-0.131407\pi$
$587$	3.67268e26	1.83198	0.915991	+	0.401199i	$0.131407\pi$
$588$	−1.42659e26	−0.700188
$589$	1.47890e26	0.714238
$590$	−4.28479e24	−0.0203627
$591$	5.22753e26	2.44464
$592$	−6.88188e25	−0.316702
$593$	−1.40519e26	−0.636378	−0.318189	−	0.948027i	$-0.603075\pi$
$593$	−1.40519e26	−0.636378	−0.318189	+	0.948027i	$0.603075\pi$
$594$	6.61173e25	0.294676
$595$	−2.62262e25	−0.115033
$596$	9.09361e25	0.392552
$597$	−1.29255e26	−0.549149
$598$	1.18166e26	0.494119
$599$	2.05613e26	0.846244	0.423122	−	0.906073i	$-0.360934\pi$
$599$	2.05613e26	0.846244	0.423122	+	0.906073i	$0.360934\pi$
$600$	2.61490e25	0.105930
$601$	2.32345e26	0.926457	0.463228	−	0.886239i	$-0.346691\pi$
$601$	2.32345e26	0.926457	0.463228	+	0.886239i	$0.346691\pi$
$602$	4.48137e25	0.175891
$603$	2.80222e26	1.08265
$604$	−2.75789e24	−0.0104888
$605$	3.55263e25	0.133007
$606$	−4.37893e26	−1.61391
$607$	2.30237e26	0.835376	0.417688	−	0.908591i	$-0.362841\pi$
$607$	2.30237e26	0.835376	0.417688	+	0.908591i	$0.362841\pi$
$608$	2.47320e25	0.0883436
$609$	1.98396e26	0.697701
$610$	−1.19883e26	−0.415073
$611$	2.50815e26	0.854992
$612$	−1.86699e26	−0.626619
$613$	−7.21990e25	−0.238592	−0.119296	−	0.992859i	$-0.538064\pi$
$613$	−7.21990e25	−0.238592	−0.119296	+	0.992859i	$0.538064\pi$
$614$	−2.26355e26	−0.736531
$615$	−4.07488e26	−1.30557
$616$	3.25975e25	0.102841
$617$	−1.44998e26	−0.450458	−0.225229	−	0.974306i	$-0.572313\pi$
$617$	−1.44998e26	−0.450458	−0.225229	+	0.974306i	$0.572313\pi$
$618$	1.15265e26	0.352619
$619$	−2.13817e26	−0.644141	−0.322071	−	0.946716i	$-0.604379\pi$
$619$	−2.13817e26	−0.644141	−0.322071	+	0.946716i	$0.604379\pi$
$620$	1.07721e26	0.319579
$621$	−8.60116e25	−0.251297
$622$	−1.56136e26	−0.449256
$623$	−1.06024e25	−0.0300448
$624$	−1.36523e26	−0.381025
$625$	1.45519e25	0.0400000
$626$	−3.30014e26	−0.893463
$627$	3.19789e26	0.852751
$628$	−8.06654e24	−0.0211871
$629$	4.93205e26	1.27599
$630$	3.94282e25	0.100478
$631$	1.60890e26	0.403877	0.201939	−	0.979398i	$-0.435276\pi$
$631$	1.60890e26	0.403877	0.201939	+	0.979398i	$0.435276\pi$
$632$	7.05325e25	0.174412
$633$	−7.31519e26	−1.78193
$634$	5.25656e26	1.26140
$635$	1.18605e26	0.280383
$636$	2.52248e25	0.0587469
$637$	4.14492e26	0.951024
$638$	6.49805e26	1.46888
$639$	5.33564e26	1.18831
$640$	1.80144e25	0.0395285
$641$	−5.97417e26	−1.29160	−0.645798	−	0.763509i	$-0.723475\pi$
$641$	−5.97417e26	−1.29160	−0.645798	+	0.763509i	$0.723475\pi$
$642$	−2.27997e26	−0.485675
$643$	−8.08712e26	−1.69742	−0.848710	−	0.528858i	$-0.822620\pi$
$643$	−8.08712e26	−1.69742	−0.848710	+	0.528858i	$0.822620\pi$
$644$	−4.24059e25	−0.0877022
$645$	3.20222e26	0.652580
$646$	−1.77247e26	−0.355935
$647$	−7.53176e26	−1.49041	−0.745205	−	0.666835i	$-0.767649\pi$
$647$	−7.53176e26	−1.49041	−0.745205	+	0.666835i	$0.767649\pi$
$648$	−1.26214e26	−0.246120
$649$	−3.81679e25	−0.0733456
$650$	−7.59752e25	−0.143878
$651$	2.92967e26	0.546764
$652$	1.51078e26	0.277875
$653$	1.75162e25	0.0317515	0.0158758	−	0.999874i	$-0.494946\pi$
$653$	1.75162e25	0.0317515	0.0158758	+	0.999874i	$0.494946\pi$
$654$	1.09071e27	1.94859
$655$	3.80530e26	0.670033
$656$	−2.80724e26	−0.487184
$657$	−1.31571e27	−2.25055
$658$	−9.00092e25	−0.151754
$659$	−1.10678e27	−1.83929	−0.919644	−	0.392754i	$-0.871523\pi$
$659$	−1.10678e27	−1.83929	−0.919644	+	0.392754i	$0.871523\pi$
$660$	2.32929e26	0.381555
$661$	−1.90870e26	−0.308194	−0.154097	−	0.988056i	$-0.549247\pi$
$661$	−1.90870e26	−0.308194	−0.154097	+	0.988056i	$0.549247\pi$
$662$	4.30015e26	0.684437
$663$	9.78423e26	1.53514
$664$	−3.72159e26	−0.575614
$665$	3.74321e25	0.0570741
$666$	−7.41480e26	−1.11454
$667$	−8.45327e26	−1.25265
$668$	1.80761e26	0.264076
$669$	7.18069e26	1.03423
$670$	1.93776e26	0.275163
$671$	−1.06789e27	−1.49508
$672$	4.89937e25	0.0676288
$673$	−1.19576e27	−1.62742	−0.813710	−	0.581270i	$-0.802556\pi$
$673$	−1.19576e27	−1.62742	−0.813710	+	0.581270i	$0.802556\pi$
$674$	−4.03538e26	−0.541521
$675$	5.53014e25	0.0731729
$676$	1.34309e25	0.0175232
$677$	4.22916e26	0.544079	0.272040	−	0.962286i	$-0.412302\pi$
$677$	4.22916e26	0.544079	0.272040	+	0.962286i	$0.412302\pi$
$678$	−2.27651e26	−0.288793
$679$	−2.65490e25	−0.0332113
$680$	−1.29104e26	−0.159259
$681$	1.74382e27	2.12131
$682$	9.59552e26	1.15111
$683$	7.22585e24	0.00854854	0.00427427	−	0.999991i	$-0.498639\pi$
$683$	7.22585e24	0.00854854	0.00427427	+	0.999991i	$0.498639\pi$
$684$	2.66472e26	0.310898
$685$	2.36749e26	0.272413
$686$	−3.07872e26	−0.349375
$687$	1.15923e27	1.29742
$688$	2.20605e26	0.243515
$689$	−7.32900e25	−0.0797925
$690$	−3.03017e26	−0.325387
$691$	−1.59913e26	−0.169372	−0.0846861	−	0.996408i	$-0.526989\pi$
$691$	−1.59913e26	−0.169372	−0.0846861	+	0.996408i	$0.526989\pi$
$692$	−1.08592e25	−0.0113446
$693$	3.51218e26	0.361919
$694$	−1.67928e26	−0.170690
$695$	4.34557e26	0.435703
$696$	9.76648e26	0.965941
$697$	2.01187e27	1.96285
$698$	−8.07003e26	−0.776691
$699$	1.60692e27	1.52567
$700$	2.72650e25	0.0255372
$701$	−3.07030e26	−0.283700	−0.141850	−	0.989888i	$-0.545305\pi$
$701$	−3.07030e26	−0.283700	−0.141850	+	0.989888i	$0.545305\pi$
$702$	−2.88727e26	−0.263199
$703$	−7.03942e26	−0.633084
$704$	1.60468e26	0.142380
$705$	−6.43172e26	−0.563028
$706$	−7.42296e25	−0.0641110
$707$	−4.56582e26	−0.389076
$708$	−5.73659e25	−0.0482323
$709$	−2.50359e26	−0.207694	−0.103847	−	0.994593i	$-0.533115\pi$
$709$	−2.50359e26	−0.207694	−0.103847	+	0.994593i	$0.533115\pi$
$710$	3.68964e26	0.302016
$711$	7.59944e26	0.613791
$712$	−5.21927e25	−0.0415958
$713$	−1.24828e27	−0.981657
$714$	−3.51124e26	−0.272475
$715$	−6.76770e26	−0.518244
$716$	9.57294e26	0.723388
$717$	−6.37264e26	−0.475212
$718$	3.91488e26	0.288095
$719$	−4.99484e26	−0.362741	−0.181371	−	0.983415i	$-0.558053\pi$
$719$	−4.99484e26	−0.362741	−0.181371	+	0.983415i	$0.558053\pi$
$720$	1.94094e26	0.139108
$721$	1.20184e26	0.0850083
$722$	−7.59969e26	−0.530509
$723$	−5.93786e25	−0.0409087
$724$	2.75858e26	0.187573
$725$	5.43505e26	0.364748
$726$	4.75637e26	0.315048
$727$	1.17305e27	0.766900	0.383450	−	0.923562i	$-0.374736\pi$
$727$	1.17305e27	0.766900	0.383450	+	0.923562i	$0.374736\pi$
$728$	−1.42350e26	−0.0918562
$729$	−2.22041e27	−1.41423
$730$	−9.09825e26	−0.571993
$731$	−1.58101e27	−0.981117
$732$	−1.60503e27	−0.983166
$733$	7.29500e26	0.441101	0.220550	−	0.975376i	$-0.429215\pi$
$733$	7.29500e26	0.441101	0.220550	+	0.975376i	$0.429215\pi$
$734$	−1.06933e27	−0.638262
$735$	−1.06289e27	−0.626267
$736$	−2.08752e26	−0.121420
$737$	1.72612e27	0.991126
$738$	−3.02463e27	−1.71450
$739$	2.41117e27	1.34929	0.674647	−	0.738141i	$-0.264296\pi$
$739$	2.41117e27	1.34929	0.674647	+	0.738141i	$0.264296\pi$
$740$	−5.12740e26	−0.283267
$741$	−1.39648e27	−0.761663
$742$	2.63013e25	0.0141625
$743$	1.98675e27	1.05621	0.528105	−	0.849179i	$-0.322903\pi$
$743$	1.98675e27	1.05621	0.528105	+	0.849179i	$0.322903\pi$
$744$	1.44220e27	0.756974
$745$	6.77527e26	0.351109
$746$	1.48974e27	0.762238
$747$	−4.00978e27	−2.02570
$748$	−1.15003e27	−0.573646
$749$	−2.37727e26	−0.117085
$750$	1.94825e26	0.0947465
$751$	4.77748e26	0.229414	0.114707	−	0.993399i	$-0.463407\pi$
$751$	4.77748e26	0.229414	0.114707	+	0.993399i	$0.463407\pi$
$752$	−4.43090e26	−0.210098
$753$	5.60033e27	2.62217
$754$	−2.83763e27	−1.31198
$755$	−2.05479e25	−0.00938147
$756$	1.03615e26	0.0467158
$757$	8.34040e25	0.0371344	0.0185672	−	0.999828i	$-0.494090\pi$
$757$	8.34040e25	0.0371344	0.0185672	+	0.999828i	$0.494090\pi$
$758$	2.34009e27	1.02890
$759$	−2.69920e27	−1.17203
$760$	1.84268e26	0.0790169
$761$	−2.96552e27	−1.25587	−0.627937	−	0.778264i	$-0.716100\pi$
$761$	−2.96552e27	−1.25587	−0.627937	+	0.778264i	$0.716100\pi$
$762$	1.58792e27	0.664133
$763$	1.13726e27	0.469761
$764$	−1.73980e27	−0.709761
$765$	−1.39102e27	−0.560465
$766$	2.42861e27	0.966462
$767$	1.66675e26	0.0655111
$768$	2.41182e26	0.0936296
$769$	9.68856e26	0.371500	0.185750	−	0.982597i	$-0.440528\pi$
$769$	9.68856e26	0.371500	0.185750	+	0.982597i	$0.440528\pi$
$770$	2.42870e26	0.0919841
$771$	−1.08272e27	−0.405041
$772$	−6.96060e26	−0.257207
$773$	5.16072e27	1.88367	0.941836	−	0.336074i	$-0.109099\pi$
$773$	5.16072e27	1.88367	0.941836	+	0.336074i	$0.109099\pi$
$774$	2.37688e27	0.856976
$775$	8.02582e26	0.285840
$776$	−1.30693e26	−0.0459798
$777$	−1.39450e27	−0.484638
$778$	−8.20709e26	−0.281762
$779$	−2.87150e27	−0.973875
$780$	−1.01718e27	−0.340799
$781$	3.28665e27	1.08785
$782$	1.49607e27	0.489201
$783$	2.06547e27	0.667241
$784$	−7.32242e26	−0.233696
$785$	−6.01004e25	−0.0189503
$786$	5.09464e27	1.58708
$787$	−4.95523e27	−1.52512	−0.762559	−	0.646919i	$-0.776057\pi$
$787$	−4.95523e27	−1.52512	−0.762559	+	0.646919i	$0.776057\pi$
$788$	2.68319e27	0.815929
$789$	−5.44708e27	−1.63656
$790$	5.25508e26	0.155999
$791$	−2.37367e26	−0.0696214
$792$	1.72895e27	0.501063
$793$	4.66336e27	1.33538
$794$	2.64948e27	0.749663
$795$	1.87939e26	0.0525449
$796$	−6.63439e26	−0.183285
$797$	9.51644e26	0.259789	0.129894	−	0.991528i	$-0.458536\pi$
$797$	9.51644e26	0.259789	0.129894	+	0.991528i	$0.458536\pi$
$798$	5.01152e26	0.135189
$799$	3.17550e27	0.846481
$800$	1.34218e26	0.0353553
$801$	−5.62344e26	−0.146384
$802$	5.37049e26	0.138152
$803$	−8.10452e27	−2.06030
$804$	2.59433e27	0.651768
$805$	−3.15949e26	−0.0784433
$806$	−4.19026e27	−1.02815
$807$	4.73819e27	1.14898
$808$	−2.24762e27	−0.538661
$809$	6.64620e26	0.157421	0.0787105	−	0.996898i	$-0.474920\pi$
$809$	6.64620e26	0.157421	0.0787105	+	0.996898i	$0.474920\pi$
$810$	−9.40371e26	−0.220136
$811$	−3.63702e27	−0.841487	−0.420743	−	0.907180i	$-0.638231\pi$
$811$	−3.63702e27	−0.841487	−0.420743	+	0.907180i	$0.638231\pi$
$812$	1.01833e27	0.232866
$813$	−4.83296e27	−1.09233
$814$	−4.56738e27	−1.02032
$815$	1.12562e27	0.248539
$816$	−1.72848e27	−0.377232
$817$	2.25655e27	0.486783
$818$	−5.03964e27	−1.07459
$819$	−1.53373e27	−0.323260
$820$	−2.09156e27	−0.435751
$821$	−4.44788e26	−0.0915996	−0.0457998	−	0.998951i	$-0.514584\pi$
$821$	−4.44788e26	−0.0915996	−0.0457998	+	0.998951i	$0.514584\pi$
$822$	3.16967e27	0.645255
$823$	−5.12412e27	−1.03115	−0.515574	−	0.856845i	$-0.672421\pi$
$823$	−5.12412e27	−1.03115	−0.515574	+	0.856845i	$0.672421\pi$
$824$	5.91631e26	0.117691
$825$	1.73546e27	0.341273
$826$	−5.98142e25	−0.0116277
$827$	−5.00813e27	−0.962439	−0.481219	−	0.876600i	$-0.659806\pi$
$827$	−5.00813e27	−0.962439	−0.481219	+	0.876600i	$0.659806\pi$
$828$	−2.24918e27	−0.427302
$829$	−3.98409e27	−0.748275	−0.374138	−	0.927373i	$-0.622061\pi$
$829$	−3.98409e27	−0.748275	−0.374138	+	0.927373i	$0.622061\pi$
$830$	−2.77280e27	−0.514845
$831$	−3.59807e26	−0.0660481
$832$	−7.00747e26	−0.127172
$833$	5.24777e27	0.941558
$834$	5.81797e27	1.03203
$835$	1.34678e27	0.236197
$836$	1.64142e27	0.284616
$837$	3.05004e27	0.522893
$838$	7.15567e26	0.121292
$839$	9.17325e27	1.53739	0.768696	−	0.639615i	$-0.220906\pi$
$839$	9.17325e27	1.53739	0.768696	+	0.639615i	$0.220906\pi$
$840$	3.65031e26	0.0604890
$841$	1.41963e28	2.32602
$842$	1.51838e27	0.245988
$843$	−5.12047e26	−0.0820254
$844$	−3.75474e27	−0.594740
$845$	1.00068e26	0.0156732
$846$	−4.77402e27	−0.739376
$847$	4.95936e26	0.0759509
$848$	1.29474e26	0.0196075
$849$	−1.08716e28	−1.62806
$850$	−9.61900e26	−0.142446
$851$	5.94167e27	0.870118
$852$	4.93980e27	0.715374
$853$	−7.79931e27	−1.11697	−0.558484	−	0.829516i	$-0.688617\pi$
$853$	−7.79931e27	−1.11697	−0.558484	+	0.829516i	$0.688617\pi$
$854$	−1.67353e27	−0.237019
$855$	1.98537e27	0.278076
$856$	−1.17026e27	−0.162100
$857$	5.48738e26	0.0751705	0.0375852	−	0.999293i	$-0.488033\pi$
$857$	5.48738e26	0.0751705	0.0375852	+	0.999293i	$0.488033\pi$
$858$	−9.06079e27	−1.22754
$859$	2.88785e27	0.386936	0.193468	−	0.981107i	$-0.438026\pi$
$859$	2.88785e27	0.386936	0.193468	+	0.981107i	$0.438026\pi$
$860$	1.64364e27	0.217806
$861$	−5.68839e27	−0.745521
$862$	−8.89559e27	−1.15307
$863$	−1.27182e27	−0.163051	−0.0815257	−	0.996671i	$-0.525979\pi$
$863$	−1.27182e27	−0.163051	−0.0815257	+	0.996671i	$0.525979\pi$
$864$	5.10065e26	0.0646763
$865$	−8.09071e25	−0.0101469
$866$	1.01026e28	1.25318
$867$	1.77566e26	0.0217860
$868$	1.50374e27	0.182489
$869$	4.68111e27	0.561903
$870$	7.27660e27	0.863964
$871$	−7.53776e27	−0.885258
$872$	5.59841e27	0.650367
$873$	−1.40814e27	−0.161812
$874$	−2.13531e27	−0.242718
$875$	2.03140e26	0.0228412
$876$	−1.21810e28	−1.35486
$877$	−7.93254e27	−0.872803	−0.436401	−	0.899752i	$-0.643747\pi$
$877$	−7.93254e27	−0.872803	−0.436401	+	0.899752i	$0.643747\pi$
$878$	1.21595e28	1.32348
$879$	2.60616e28	2.80612
$880$	1.19558e27	0.127349
$881$	−4.65349e27	−0.490351	−0.245176	−	0.969479i	$-0.578846\pi$
$881$	−4.65349e27	−0.490351	−0.245176	+	0.969479i	$0.578846\pi$
$882$	−7.88945e27	−0.822423
$883$	1.39322e28	1.43678	0.718392	−	0.695639i	$-0.244878\pi$
$883$	1.39322e28	1.43678	0.718392	+	0.695639i	$0.244878\pi$
$884$	5.02206e27	0.512372
$885$	−4.27409e26	−0.0431403
$886$	−5.56353e27	−0.555559
$887$	−2.98771e27	−0.295165	−0.147582	−	0.989050i	$-0.547149\pi$
$887$	−2.98771e27	−0.295165	−0.147582	+	0.989050i	$0.547149\pi$
$888$	−6.86471e27	−0.670964
$889$	1.65569e27	0.160107
$890$	−3.88866e26	−0.0372045
$891$	−8.37662e27	−0.792922
$892$	3.68571e27	0.345187
$893$	−4.53233e27	−0.419984
$894$	9.07092e27	0.831658
$895$	7.13239e27	0.647018
$896$	2.51475e26	0.0225719
$897$	1.17871e28	1.04684
$898$	8.39793e27	0.737984
$899$	2.99759e28	2.60649
$900$	1.44611e27	0.124422
$901$	−9.27904e26	−0.0789982
$902$	−1.86311e28	−1.56956
$903$	4.47019e27	0.372642
$904$	−1.16849e27	−0.0963883
$905$	2.05530e27	0.167770
$906$	−2.75101e26	−0.0222215
$907$	−1.01372e28	−0.810308	−0.405154	−	0.914248i	$-0.632782\pi$
$907$	−1.01372e28	−0.810308	−0.405154	+	0.914248i	$0.632782\pi$
$908$	8.95068e27	0.708011
$909$	−2.42167e28	−1.89565
$910$	−1.06059e27	−0.0821587
$911$	1.01665e28	0.779377	0.389688	−	0.920947i	$-0.372583\pi$
$911$	1.01665e28	0.779377	0.389688	+	0.920947i	$0.372583\pi$
$912$	2.46703e27	0.187164
$913$	−2.46995e28	−1.85445
$914$	−9.73448e27	−0.723309
$915$	−1.19584e28	−0.879371
$916$	5.95009e27	0.433028
$917$	5.31207e27	0.382609
$918$	−3.65549e27	−0.260580
$919$	−8.89132e27	−0.627291	−0.313645	−	0.949540i	$-0.601550\pi$
$919$	−8.89132e27	−0.627291	−0.313645	+	0.949540i	$0.601550\pi$
$920$	−1.55533e27	−0.108602
$921$	−2.25790e28	−1.56041
$922$	−1.40243e28	−0.959265
$923$	−1.43524e28	−0.971650
$924$	3.25162e27	0.217879
$925$	−3.82021e27	−0.253362
$926$	1.10592e28	0.725968
$927$	6.37446e27	0.414177
$928$	5.01295e27	0.322394
$929$	7.61744e26	0.0484909	0.0242454	−	0.999706i	$-0.492282\pi$
$929$	7.61744e26	0.0484909	0.0242454	+	0.999706i	$0.492282\pi$
$930$	1.07452e28	0.677058
$931$	−7.49004e27	−0.467156
$932$	8.24800e27	0.509211
$933$	−1.55746e28	−0.951791
$934$	3.36849e27	0.203770
$935$	−8.56840e27	−0.513085
$936$	−7.55012e27	−0.447541
$937$	−1.46040e28	−0.856931	−0.428465	−	0.903558i	$-0.640946\pi$
$937$	−1.46040e28	−0.856931	−0.428465	+	0.903558i	$0.640946\pi$
$938$	2.70505e27	0.157126
$939$	−3.29191e28	−1.89289
$940$	−3.30128e27	−0.187918
$941$	−1.23989e28	−0.698687	−0.349344	−	0.936995i	$-0.613595\pi$
$941$	−1.23989e28	−0.698687	−0.349344	+	0.936995i	$0.613595\pi$
$942$	−8.04642e26	−0.0448868
$943$	2.42371e28	1.33850
$944$	−2.94448e26	−0.0160981
$945$	7.71989e26	0.0417839
$946$	1.46412e28	0.784530
$947$	−1.35611e28	−0.719400	−0.359700	−	0.933068i	$-0.617121\pi$
$947$	−1.35611e28	−0.719400	−0.359700	+	0.933068i	$0.617121\pi$
$948$	7.03565e27	0.369509
$949$	3.53916e28	1.84022
$950$	1.37290e27	0.0706749
$951$	5.24345e28	2.67240
$952$	−1.80225e27	−0.0909419
$953$	−1.00835e28	−0.503764	−0.251882	−	0.967758i	$-0.581050\pi$
$953$	−1.00835e28	−0.503764	−0.251882	+	0.967758i	$0.581050\pi$
$954$	1.39500e27	0.0690026
$955$	−1.29625e28	−0.634830
$956$	−3.27095e27	−0.158608
$957$	6.48183e28	3.11196
$958$	9.43148e27	0.448340
$959$	3.30494e27	0.155556
$960$	1.79694e27	0.0837448
$961$	2.25941e28	1.04261
$962$	1.99452e28	0.911331
$963$	−1.26089e28	−0.570461
$964$	−3.04779e26	−0.0136538
$965$	−5.18605e27	−0.230053
$966$	−4.23001e27	−0.185806
$967$	1.24965e28	0.543547	0.271774	−	0.962361i	$-0.412390\pi$
$967$	1.24965e28	0.543547	0.271774	+	0.962361i	$0.412390\pi$
$968$	2.44135e27	0.105151
$969$	−1.76805e28	−0.754082
$970$	−9.73741e26	−0.0411256
$971$	−9.87663e27	−0.413072	−0.206536	−	0.978439i	$-0.566219\pi$
$971$	−9.87663e27	−0.413072	−0.206536	+	0.978439i	$0.566219\pi$
$972$	−1.70069e28	−0.704360
$973$	6.06627e27	0.248800
$974$	−3.00006e28	−1.21848
$975$	−7.57856e27	−0.304820
$976$	−8.23829e27	−0.328144
$977$	−2.84735e27	−0.112316	−0.0561581	−	0.998422i	$-0.517885\pi$
$977$	−2.84735e27	−0.112316	−0.0561581	+	0.998422i	$0.517885\pi$
$978$	1.50701e28	0.588705
$979$	−3.46393e27	−0.134009
$980$	−5.45562e27	−0.209024
$981$	6.03194e28	2.28877
$982$	6.01941e26	0.0226201
$983$	−2.10459e28	−0.783265	−0.391632	−	0.920122i	$-0.628090\pi$
$983$	−2.10459e28	−0.783265	−0.391632	+	0.920122i	$0.628090\pi$
$984$	−2.80023e28	−1.03215
$985$	1.99913e28	0.729789
$986$	−3.59264e28	−1.29892
$987$	−8.97846e27	−0.321506
$988$	−7.16789e27	−0.254214
$989$	−1.90466e28	−0.669041
$990$	1.28817e28	0.448164
$991$	5.03784e28	1.73598	0.867989	−	0.496583i	$-0.165412\pi$
$991$	5.03784e28	1.73598	0.867989	+	0.496583i	$0.165412\pi$
$992$	7.40251e27	0.252649
$993$	4.28943e28	1.45004
$994$	5.15062e27	0.172460
$995$	−4.94301e27	−0.163935
$996$	−3.71230e28	−1.21949
$997$	−1.44919e28	−0.471544	−0.235772	−	0.971808i	$-0.575762\pi$
$997$	−1.44919e28	−0.471544	−0.235772	+	0.971808i	$0.575762\pi$
$998$	−8.05144e27	−0.259498
$999$	−1.45179e28	−0.463480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.20.a.d.1.2	✓	2
3.2	odd	2		90.20.a.g.1.1		2
4.3	odd	2		80.20.a.d.1.1		2
5.2	odd	4		50.20.b.f.49.3		4
5.3	odd	4		50.20.b.f.49.2		4
5.4	even	2		50.20.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.20.a.d.1.2	✓	2	1.1	even	1	trivial
50.20.a.f.1.1		2	5.4	even	2
50.20.b.f.49.2		4	5.3	odd	4
50.20.b.f.49.3		4	5.2	odd	4
80.20.a.d.1.1		2	4.3	odd	2
90.20.a.g.1.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+512.000 q^{2} +51072.2 q^{3} +262144. q^{4} +1.95312e6 q^{5} +2.61490e7 q^{6} +2.72650e7 q^{7} +1.34218e8 q^{8} +1.44611e9 q^{9} +1.00000e9 q^{10} +8.90778e9 q^{11} +1.33883e10 q^{12} -3.88993e10 q^{13} +1.39597e10 q^{14} +9.97505e10 q^{15} +6.87195e10 q^{16} -4.92493e11 q^{17} +7.40410e11 q^{18} +7.02926e11 q^{19} +5.12000e11 q^{20} +1.39248e12 q^{21} +4.56078e12 q^{22} -5.93310e12 q^{23} +6.85480e12 q^{24} +3.81470e12 q^{25} -1.99164e13 q^{26} +1.44969e13 q^{27} +7.14735e12 q^{28} +1.42477e14 q^{29} +5.10722e13 q^{30} +2.10392e14 q^{31} +3.51844e13 q^{32} +4.54940e14 q^{33} -2.52156e14 q^{34} +5.32519e13 q^{35} +3.79090e14 q^{36} -1.00145e15 q^{37} +3.59898e14 q^{38} -1.98667e15 q^{39} +2.62144e14 q^{40} -4.08507e15 q^{41} +7.12952e14 q^{42} +3.21023e15 q^{43} +2.33512e15 q^{44} +2.82444e15 q^{45} -3.03774e15 q^{46} -6.44781e15 q^{47} +3.50966e15 q^{48} -1.06555e16 q^{49} +1.95312e15 q^{50} -2.51527e16 q^{51} -1.01972e16 q^{52} +1.88410e15 q^{53} +7.42243e15 q^{54} +1.73980e16 q^{55} +3.65944e15 q^{56} +3.59000e16 q^{57} +7.29480e16 q^{58} -4.28479e15 q^{59} +2.61490e16 q^{60} -1.19883e17 q^{61} +1.07721e17 q^{62} +3.94282e16 q^{63} +1.80144e16 q^{64} -7.59752e16 q^{65} +2.32929e17 q^{66} +1.93776e17 q^{67} -1.29104e17 q^{68} -3.03017e17 q^{69} +2.72650e16 q^{70} +3.68964e17 q^{71} +1.94094e17 q^{72} -9.09825e17 q^{73} -5.12740e17 q^{74} +1.94825e17 q^{75} +1.84268e17 q^{76} +2.42870e17 q^{77} -1.01718e18 q^{78} +5.25508e17 q^{79} +1.34218e17 q^{80} -9.40371e17 q^{81} -2.09156e18 q^{82} -2.77280e18 q^{83} +3.65031e17 q^{84} -9.61900e17 q^{85} +1.64364e18 q^{86} +7.27660e18 q^{87} +1.19558e18 q^{88} -3.88866e17 q^{89} +1.44611e18 q^{90} -1.06059e18 q^{91} -1.55533e18 q^{92} +1.07452e19 q^{93} -3.30128e18 q^{94} +1.37290e18 q^{95} +1.79694e18 q^{96} -9.73741e17 q^{97} -5.45562e18 q^{98} +1.28817e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 1024 q^{2} + 33724 q^{3} + 524288 q^{4} + 3906250 q^{5} + 17266688 q^{6} + 83061292 q^{7} + 268435456 q^{8} + 584812954 q^{9} + 2000000000 q^{10} + 3549480144 q^{11} + 8840544256 q^{12} + 30250225564 q^{13}+ \cdots + 17\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 1024 * q^2 + 33724 * q^3 + 524288 * q^4 + 3906250 * q^5 + 17266688 * q^6 + 83061292 * q^7 + 268435456 * q^8 + 584812954 * q^9 + 2000000000 * q^10 + 3549480144 * q^11 + 8840544256 * q^12 + 30250225564 * q^13 + 42527381504 * q^14 + 65867187500 * q^15 + 137438953472 * q^16 + 329655779412 * q^17 + 299424232448 * q^18 + 383076809800 * q^19 + 1024000000000 * q^20 + 424515195104 * q^21 + 1817333833728 * q^22 + 2082856096884 * q^23 + 4526358659072 * q^24 + 7629394531250 * q^25 + 15488115488768 * q^26 + 49602163340440 * q^27 + 21774019330048 * q^28 + 166587684602220 * q^29 + 33724000000000 * q^30 + 418151119038664 * q^31 + 70368744177664 * q^32 + 547897533578928 * q^33 + 168783759058944 * q^34 + 162229085937500 * q^35 + 153305207013376 * q^36 - 1292219637694628 * q^37 + 196135326617600 * q^38 - 3186297306918232 * q^39 + 524288000000000 * q^40 - 3127192714527996 * q^41 + 217351779893248 * q^42 - 1795992338357636 * q^43 + 930474922868736 * q^44 + 1142212800781250 * q^45 + 1066422321604608 * q^46 - 6761653310165988 * q^47 + 2317495633444864 * q^48 - 18941182438871454 * q^49 + 3906250000000000 * q^50 - 39415550773661256 * q^51 + 7929915130249216 * q^52 - 9787568571066516 * q^53 + 25396307630305280 * q^54 + 6932578406250000 * q^55 + 11148297896984576 * q^56 + 41448804721422800 * q^57 + 85292894516336640 * q^58 - 25484316660294360 * q^59 + 17266688000000000 * q^60 - 77840503559636276 * q^61 + 214093372947795968 * q^62 - 8629133041886116 * q^63 + 36028797018963968 * q^64 + 59082471804687500 * q^65 + 280523537192411136 * q^66 + 439654835073204532 * q^67 + 86417284638179328 * q^68 - 442079200728708192 * q^69 + 83061292000000000 * q^70 - 29427662567526696 * q^71 + 78492265990848512 * q^72 - 1463308911724217756 * q^73 - 661616454499649536 * q^74 + 128646850585937500 * q^75 + 100421287228211200 * q^76 - 56103061801470576 * q^77 - 1631384221142134784 * q^78 - 1235969155825112720 * q^79 + 268435456000000000 * q^80 - 548329353045127838 * q^81 - 1601122669838333952 * q^82 - 877205635969635396 * q^83 + 111284111305342976 * q^84 + 643858944164062500 * q^85 - 919548077239109632 * q^86 + 6858312722579528040 * q^87 + 476403160508792832 * q^88 + 4172929077000032820 * q^89 + 584812954000000000 * q^90 + 2797700455846427144 * q^91 + 546008228661559296 * q^92 + 7140934358593491968 * q^93 - 3461966494804985856 * q^94 + 748196894140625000 * q^95 + 1186557764323770368 * q^96 + 11254578228347861332 * q^97 - 9697885408702184448 * q^98 + 17496761012343831888 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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