LMFDB - Embedded newform 21.30.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.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:	$111.883889004$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 678740466 x^{5} - 2954969748680 x^{4} + \cdots - 14\!\cdots\!64 $ x^7 - x^6 - 678740466x^5 - 2954969748680x^4 + 92148363808982720x^3 + 418126965823508980224x^2 - 2978683903673490966301184*x - 14143029174281721602229028864
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{12}\cdot 5^{3}\cdot 7^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-17887.0$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+44469.9 q^{2} -4.78297e6 q^{3} +1.44070e9 q^{4} +4.26822e9 q^{5} -2.12698e11 q^{6} +6.78223e11 q^{7} +4.01934e13 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q+44469.9 q^{2} -4.78297e6 q^{3} +1.44070e9 q^{4} +4.26822e9 q^{5} -2.12698e11 q^{6} +6.78223e11 q^{7} +4.01934e13 q^{8} +2.28768e13 q^{9} +1.89808e14 q^{10} +3.33625e13 q^{11} -6.89084e15 q^{12} +2.47459e16 q^{13} +3.01605e16 q^{14} -2.04148e16 q^{15} +1.01392e18 q^{16} +3.50547e17 q^{17} +1.01733e18 q^{18} -4.86600e18 q^{19} +6.14924e18 q^{20} -3.24392e18 q^{21} +1.48363e18 q^{22} -6.35651e19 q^{23} -1.92244e20 q^{24} -1.68047e20 q^{25} +1.10045e21 q^{26} -1.09419e20 q^{27} +9.77118e20 q^{28} +1.29288e21 q^{29} -9.07843e20 q^{30} +6.01040e21 q^{31} +2.35105e22 q^{32} -1.59572e20 q^{33} +1.55888e22 q^{34} +2.89481e21 q^{35} +3.29587e22 q^{36} +1.93119e22 q^{37} -2.16391e23 q^{38} -1.18359e23 q^{39} +1.71554e23 q^{40} +1.89783e23 q^{41} -1.44257e23 q^{42} +6.08342e23 q^{43} +4.80654e22 q^{44} +9.76432e22 q^{45} -2.82673e24 q^{46} -5.68500e23 q^{47} -4.84957e24 q^{48} +4.59987e23 q^{49} -7.47303e24 q^{50} -1.67665e24 q^{51} +3.56515e25 q^{52} -1.42621e25 q^{53} -4.86585e24 q^{54} +1.42398e23 q^{55} +2.72601e25 q^{56} +2.32739e25 q^{57} +5.74941e25 q^{58} +7.70985e25 q^{59} -2.94116e25 q^{60} -4.19815e25 q^{61} +2.67282e26 q^{62} +1.55156e25 q^{63} +5.01163e26 q^{64} +1.05621e26 q^{65} -7.09614e24 q^{66} -4.17723e26 q^{67} +5.05034e26 q^{68} +3.04030e26 q^{69} +1.28732e26 q^{70} +6.10132e25 q^{71} +9.19495e26 q^{72} +5.13641e26 q^{73} +8.58800e26 q^{74} +8.03763e26 q^{75} -7.01046e27 q^{76} +2.26272e25 q^{77} -5.26341e27 q^{78} +3.72792e27 q^{79} +4.32765e27 q^{80} +5.23348e26 q^{81} +8.43964e27 q^{82} +3.79754e27 q^{83} -4.67353e27 q^{84} +1.49621e27 q^{85} +2.70529e28 q^{86} -6.18379e27 q^{87} +1.34095e27 q^{88} +9.29132e27 q^{89} +4.34219e27 q^{90} +1.67832e28 q^{91} -9.15784e28 q^{92} -2.87476e28 q^{93} -2.52812e28 q^{94} -2.07692e28 q^{95} -1.12450e29 q^{96} -7.85268e28 q^{97} +2.04556e28 q^{98} +7.63227e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9}+O(q^{10}) $ 7 * q + 60870 * q^2 - 33480783 * q^3 + 2201135476 * q^4 - 2861618502 * q^5 - 291139323030 * q^6 + 4747561509943 * q^7 + 9964333994280 * q^8 + 160137547184727 * q^9	$ 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9} - 472777770164028 q^{10} + 135879674344284 q^{11} - 10\!\cdots\!44 q^{12}+ \cdots + 31\!\cdots\!24 q^{99}+O(q^{100}) $ 7 * q + 60870 * q^2 - 33480783 * q^3 + 2201135476 * q^4 - 2861618502 * q^5 - 291139323030 * q^6 + 4747561509943 * q^7 + 9964333994280 * q^8 + 160137547184727 * q^9 - 472777770164028 * q^10 + 135879674344284 * q^11 - 10527962746508244 * q^12 + 12138994948536170 * q^13 + 41283438444318630 * q^14 + 13687032584892438 * q^15 + 1300607396354614288 * q^16 - 385869676567281066 * q^17 + 1392510356733476070 * q^18 + 726075641163594644 * q^19 + 8133031378709443032 * q^20 - 22707439527650560767 * q^21 - 40013549861901162600 * q^22 + 81623233895572110192 * q^23 - 47659100600287417320 * q^24 - 344687932818137236151 * q^25 + 557803893676418715300 * q^26 - 765932923920586514463 * q^27 + 1492860866289666291124 * q^28 + 2523262928009462965506 * q^29 + 2261281418583670839132 * q^30 + 3097457398331417166752 * q^31 + 3797011810352053176480 * q^32 - 649908270118805699196 * q^33 + 63335711497801752433500 * q^34 - 1940815693747992252198 * q^35 + 50354919449703789296436 * q^36 + 12145140799949814343466 * q^37 - 108697233906951781953720 * q^38 - 58060436530005096488730 * q^39 - 475320691810097154363216 * q^40 - 262433505631892547251154 * q^41 - 197457406292584233412470 * q^42 - 193139951479227114687580 * q^43 - 2430431685366465708769488 * q^44 - 65464652555530399288422 * q^45 - 6981072827049021325022880 * q^46 - 1146871717647137318395248 * q^47 - 6220764857934833146461072 * q^48 + 3219905755813179726837607 * q^49 + 4481749443828030876391386 * q^50 + 1845602701061331752964954 * q^51 + 1236271786388417967514040 * q^52 - 6665695659633633475901814 * q^53 - 6660333868435157305051830 * q^54 + 5317495916141118544489032 * q^55 + 6758041220494331589303720 * q^56 - 3472797283340597110818036 * q^57 - 19887500189096257342540140 * q^58 + 252077122803863627555062380 * q^59 - 38900036960394526029322008 * q^60 + 286844596551467198960110586 * q^61 + 655482484647841866799404480 * q^62 + 108608979330127274981177223 * q^63 + 523821984648801603783498304 * q^64 + 677830247031279033073631964 * q^65 + 191383568569427541779759400 * q^66 - 21966489249761249366283412 * q^67 - 230093364489444117467612568 * q^68 - 390401397402270640312920048 * q^69 - 320648792055345340923275772 * q^70 + 236873286033551829517504320 * q^71 + 227952000739056108131623080 * q^72 + 1436061741885259500381870806 * q^73 - 3275022628978202210175964380 * q^74 + 1648631697343233038255912319 * q^75 - 4562877250128321487477927888 * q^76 + 92156730271501723638745116 * q^77 - 2667958731533606746299725700 * q^78 + 442695609959843509130102048 * q^79 + 7254106132718389061591220192 * q^80 + 3663433431191523760494580647 * q^81 + 4421292535141977509208500940 * q^82 + 4700059828307966195559697476 * q^83 - 7140307244776618890791067156 * q^84 - 13424791113423208631620606908 * q^85 + 12752722226530676548320081000 * q^86 - 12068688363518493070663267314 * q^87 + 4553745967919270581660489440 * q^88 + 52994579350095331884835317486 * q^89 - 10815638925361721529772342908 * q^90 + 8232946455294689831821448330 * q^91 + 54926079962260892072539429536 * q^92 - 14815042715039820034642646688 * q^93 - 26892181494551465508576501600 * q^94 - 74456487258213633048885368328 * q^95 - 18160989781547749429455369120 * q^96 + 74985775395694126905639860942 * q^97 + 27999380479478321424657876870 * q^98 + 3108491108821873976277792924 * 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 $

$2$	44469.9	1.91925	0.959625	−	0.281283i	$-0.0907600\pi$
$2$	44469.9	1.91925	0.959625	+	0.281283i	$0.0907600\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	1.44070e9	2.68352
$5$	4.26822e9	0.312739	0.156369	−	0.987699i	$-0.450021\pi$
$5$	4.26822e9	0.312739	0.156369	+	0.987699i	$0.450021\pi$
$6$	−2.12698e11	−1.10808
$7$	6.78223e11	0.377964
$7$	6.78223e11	0.377964
$8$	4.01934e13	3.23109
$9$	2.28768e13	0.333333
$10$	1.89808e14	0.600224
$11$	3.33625e13	0.0264889	0.0132445	−	0.999912i	$-0.495784\pi$
$11$	3.33625e13	0.0264889	0.0132445	+	0.999912i	$0.495784\pi$
$12$	−6.89084e15	−1.54933
$13$	2.47459e16	1.74311	0.871554	−	0.490299i	$-0.163112\pi$
$13$	2.47459e16	1.74311	0.871554	+	0.490299i	$0.163112\pi$
$14$	3.01605e16	0.725408
$15$	−2.04148e16	−0.180560
$16$	1.01392e18	3.51776
$17$	3.50547e17	0.504936	0.252468	−	0.967605i	$-0.418758\pi$
$17$	3.50547e17	0.504936	0.252468	+	0.967605i	$0.418758\pi$
$18$	1.01733e18	0.639750
$19$	−4.86600e18	−1.39716	−0.698578	−	0.715534i	$-0.746184\pi$
$19$	−4.86600e18	−1.39716	−0.698578	+	0.715534i	$0.746184\pi$
$20$	6.14924e18	0.839241
$21$	−3.24392e18	−0.218218
$22$	1.48363e18	0.0508389
$23$	−6.35651e19	−1.14331	−0.571656	−	0.820493i	$-0.693699\pi$
$23$	−6.35651e19	−1.14331	−0.571656	+	0.820493i	$0.693699\pi$
$24$	−1.92244e20	−1.86547
$25$	−1.68047e20	−0.902194
$26$	1.10045e21	3.34546
$27$	−1.09419e20	−0.192450
$28$	9.77118e20	1.01427
$29$	1.29288e21	0.806837	0.403419	−	0.915016i	$-0.367822\pi$
$29$	1.29288e21	0.806837	0.403419	+	0.915016i	$0.367822\pi$
$30$	−9.07843e20	−0.346539
$31$	6.01040e21	1.42613	0.713064	−	0.701099i	$-0.247307\pi$
$31$	6.01040e21	1.42613	0.713064	+	0.701099i	$0.247307\pi$
$32$	2.35105e22	3.52036
$33$	−1.59572e20	−0.0152934
$34$	1.55888e22	0.969099
$35$	2.89481e21	0.118204
$36$	3.29587e22	0.894506
$37$	1.93119e22	0.352290	0.176145	−	0.984364i	$-0.443637\pi$
$37$	1.93119e22	0.352290	0.176145	+	0.984364i	$0.443637\pi$
$38$	−2.16391e23	−2.68149
$39$	−1.18359e23	−1.00638
$40$	1.71554e23	1.01049
$41$	1.89783e23	0.781433	0.390716	−	0.920511i	$-0.372227\pi$
$41$	1.89783e23	0.781433	0.390716	+	0.920511i	$0.372227\pi$
$42$	−1.44257e23	−0.418815
$43$	6.08342e23	1.25561	0.627805	−	0.778370i	$-0.283953\pi$
$43$	6.08342e23	1.25561	0.627805	+	0.778370i	$0.283953\pi$
$44$	4.80654e22	0.0710836
$45$	9.76432e22	0.104246
$46$	−2.82673e24	−2.19430
$47$	−5.68500e23	−0.323081	−0.161541	−	0.986866i	$-0.551646\pi$
$47$	−5.68500e23	−0.323081	−0.161541	+	0.986866i	$0.551646\pi$
$48$	−4.84957e24	−2.03098
$49$	4.59987e23	0.142857
$50$	−7.47303e24	−1.73154
$51$	−1.67665e24	−0.291525
$52$	3.56515e25	4.67767
$53$	−1.42621e25	−1.41965	−0.709827	−	0.704376i	$-0.751227\pi$
$53$	−1.42621e25	−1.41965	−0.709827	+	0.704376i	$0.751227\pi$
$54$	−4.86585e24	−0.369360
$55$	1.42398e23	0.00828412
$56$	2.72601e25	1.22124
$57$	2.32739e25	0.806649
$58$	5.74941e25	1.54852
$59$	7.70985e25	1.62066	0.810329	−	0.585975i	$-0.199288\pi$
$59$	7.70985e25	1.62066	0.810329	+	0.585975i	$0.199288\pi$
$60$	−2.94116e25	−0.484536
$61$	−4.19815e25	−0.544221	−0.272111	−	0.962266i	$-0.587722\pi$
$61$	−4.19815e25	−0.544221	−0.272111	+	0.962266i	$0.587722\pi$
$62$	2.67282e26	2.73710
$63$	1.55156e25	0.125988
$64$	5.01163e26	3.23869
$65$	1.05621e26	0.545138
$66$	−7.09614e24	−0.0293518
$67$	−4.17723e26	−1.38932	−0.694662	−	0.719336i	$-0.744446\pi$
$67$	−4.17723e26	−1.38932	−0.694662	+	0.719336i	$0.744446\pi$
$68$	5.05034e26	1.35501
$69$	3.04030e26	0.660092
$70$	1.28732e26	0.226863
$71$	6.10132e25	0.0875342	0.0437671	−	0.999042i	$-0.486064\pi$
$71$	6.10132e25	0.0875342	0.0437671	+	0.999042i	$0.486064\pi$
$72$	9.19495e26	1.07703
$73$	5.13641e26	0.492582	0.246291	−	0.969196i	$-0.420788\pi$
$73$	5.13641e26	0.492582	0.246291	+	0.969196i	$0.420788\pi$
$74$	8.58800e26	0.676133
$75$	8.03763e26	0.520882
$76$	−7.01046e27	−3.74930
$77$	2.26272e25	0.0100119
$78$	−5.26341e27	−1.93150
$79$	3.72792e27	1.13730	0.568648	−	0.822581i	$-0.307467\pi$
$79$	3.72792e27	1.13730	0.568648	+	0.822581i	$0.307467\pi$
$80$	4.32765e27	1.10014
$81$	5.23348e26	0.111111
$82$	8.43964e27	1.49976
$83$	3.79754e27	0.566070	0.283035	−	0.959110i	$-0.408659\pi$
$83$	3.79754e27	0.566070	0.283035	+	0.959110i	$0.408659\pi$
$84$	−4.67353e27	−0.585592
$85$	1.49621e27	0.157913
$86$	2.70529e28	2.40983
$87$	−6.18379e27	−0.465828
$88$	1.34095e27	0.0855882
$89$	9.29132e27	0.503410	0.251705	−	0.967804i	$-0.419009\pi$
$89$	9.29132e27	0.503410	0.251705	+	0.967804i	$0.419009\pi$
$90$	4.34219e27	0.200075
$91$	1.67832e28	0.658833
$92$	−9.15784e28	−3.06810
$93$	−2.87476e28	−0.823376
$94$	−2.52812e28	−0.620073
$95$	−2.07692e28	−0.436945
$96$	−1.12450e29	−2.03248
$97$	−7.85268e28	−1.22132	−0.610658	−	0.791895i	$-0.709095\pi$
$97$	−7.85268e28	−1.22132	−0.610658	+	0.791895i	$0.709095\pi$
$98$	2.04556e28	0.274179
$99$	7.63227e26	0.00882964
$100$	−2.42106e29	−2.42106
$101$	1.44969e28	0.125492	0.0627460	−	0.998030i	$-0.480014\pi$
$101$	1.44969e28	0.125492	0.0627460	+	0.998030i	$0.480014\pi$
$102$	−7.45607e28	−0.559509
$103$	1.82187e29	1.18680	0.593399	−	0.804909i	$-0.297786\pi$
$103$	1.82187e29	1.18680	0.593399	+	0.804909i	$0.297786\pi$
$104$	9.94621e29	5.63215
$105$	−1.38458e28	−0.0682452
$106$	−6.34234e29	−2.72467
$107$	4.80933e29	1.80310	0.901549	−	0.432676i	$-0.142431\pi$
$107$	4.80933e29	1.80310	0.901549	+	0.432676i	$0.142431\pi$
$108$	−1.57640e29	−0.516444
$109$	−4.39919e29	−1.26092	−0.630462	−	0.776220i	$-0.717134\pi$
$109$	−4.39919e29	−1.26092	−0.630462	+	0.776220i	$0.717134\pi$
$110$	6.33245e27	0.0158993
$111$	−9.23683e28	−0.203395
$112$	6.87667e29	1.32959
$113$	2.69636e29	0.458290	0.229145	−	0.973392i	$-0.426407\pi$
$113$	2.69636e29	0.458290	0.229145	+	0.973392i	$0.426407\pi$
$114$	1.03499e30	1.54816
$115$	−2.71310e29	−0.357558
$116$	1.86265e30	2.16516
$117$	5.66107e29	0.581036
$118$	3.42856e30	3.11045
$119$	2.37749e29	0.190848
$120$	−8.20538e29	−0.583406
$121$	−1.58520e30	−0.999298
$122$	−1.86692e30	−1.04450
$123$	−9.07727e29	−0.451160
$124$	8.65920e30	3.82704
$125$	−1.51228e30	−0.594890
$126$	6.89976e29	0.241803
$127$	−2.56551e30	−0.801715	−0.400858	−	0.916140i	$-0.631288\pi$
$127$	−2.56551e30	−0.801715	−0.400858	+	0.916140i	$0.631288\pi$
$128$	9.66459e30	2.69550
$129$	−2.90968e30	−0.724927
$130$	4.69696e30	1.04626
$131$	3.44616e30	0.686913	0.343456	−	0.939169i	$-0.388402\pi$
$131$	3.44616e30	0.686913	0.343456	+	0.939169i	$0.388402\pi$
$132$	−2.29896e29	−0.0410401
$133$	−3.30023e30	−0.528075
$134$	−1.85761e31	−2.66646
$135$	−4.67024e29	−0.0601866
$136$	1.40896e31	1.63150
$137$	−8.72389e30	−0.908368	−0.454184	−	0.890908i	$-0.650069\pi$
$137$	−8.72389e30	−0.908368	−0.454184	+	0.890908i	$0.650069\pi$
$138$	1.35202e31	1.26688
$139$	1.77954e31	1.50174	0.750868	−	0.660452i	$-0.229635\pi$
$139$	1.77954e31	1.50174	0.750868	+	0.660452i	$0.229635\pi$
$140$	4.17056e30	0.317203
$141$	2.71912e30	0.186531
$142$	2.71325e30	0.168000
$143$	8.25584e29	0.0461731
$144$	2.31953e31	1.17259
$145$	5.51828e30	0.252329
$146$	2.28416e31	0.945387
$147$	−2.20010e30	−0.0824786
$148$	2.78227e31	0.945377
$149$	−4.95990e31	−1.52852	−0.764262	−	0.644906i	$-0.776896\pi$
$149$	−4.95990e31	−1.52852	−0.764262	+	0.644906i	$0.776896\pi$
$150$	3.57433e31	0.999703
$151$	−5.48894e31	−1.39419	−0.697096	−	0.716978i	$-0.745525\pi$
$151$	−5.48894e31	−1.39419	−0.697096	+	0.716978i	$0.745525\pi$
$152$	−1.95581e32	−4.51434
$153$	8.01938e30	0.168312
$154$	1.00623e30	0.0192153
$155$	2.56537e31	0.446006
$156$	−1.70520e32	−2.70065
$157$	−2.95415e31	−0.426470	−0.213235	−	0.977001i	$-0.568400\pi$
$157$	−2.95415e31	−0.426470	−0.213235	+	0.977001i	$0.568400\pi$
$158$	1.65780e32	2.18276
$159$	6.82151e31	0.819638
$160$	1.00348e32	1.10095
$161$	−4.31113e31	−0.432132
$162$	2.32732e31	0.213250
$163$	4.38395e31	0.367406	0.183703	−	0.982982i	$-0.441192\pi$
$163$	4.38395e31	0.367406	0.183703	+	0.982982i	$0.441192\pi$
$164$	2.73421e32	2.09699
$165$	−6.81088e29	−0.00478284
$166$	1.68876e32	1.08643
$167$	−1.25976e32	−0.742849	−0.371425	−	0.928463i	$-0.621131\pi$
$167$	−1.25976e32	−0.742849	−0.371425	+	0.928463i	$0.621131\pi$
$168$	−1.30384e32	−0.705082
$169$	4.10821e32	2.03843
$170$	6.65364e31	0.303075
$171$	−1.11319e32	−0.465719
$172$	8.76440e32	3.36946
$173$	−3.29329e32	−1.16402	−0.582011	−	0.813181i	$-0.697734\pi$
$173$	−3.29329e32	−1.16402	−0.582011	+	0.813181i	$0.697734\pi$
$174$	−2.74992e32	−0.894040
$175$	−1.13973e32	−0.340997
$176$	3.38270e31	0.0931816
$177$	−3.68760e32	−0.935688
$178$	4.13184e32	0.966170
$179$	6.70010e32	1.44448	0.722241	−	0.691642i	$-0.243112\pi$
$179$	6.70010e32	1.44448	0.722241	+	0.691642i	$0.243112\pi$
$180$	1.40675e32	0.279747
$181$	−2.89463e32	−0.531196	−0.265598	−	0.964084i	$-0.585569\pi$
$181$	−2.89463e32	−0.531196	−0.265598	+	0.964084i	$0.585569\pi$
$182$	7.46349e32	1.26447
$183$	2.00796e32	0.314206
$184$	−2.55489e33	−3.69415
$185$	8.24276e31	0.110175
$186$	−1.27840e33	−1.58026
$187$	1.16951e31	0.0133752
$188$	−8.19040e32	−0.866994
$189$	−7.42105e31	−0.0727393
$190$	−9.23604e32	−0.838607
$191$	−2.74876e32	−0.231288	−0.115644	−	0.993291i	$-0.536893\pi$
$191$	−2.74876e32	−0.231288	−0.115644	+	0.993291i	$0.536893\pi$
$192$	−2.39705e33	−1.86986
$193$	−1.63178e33	−1.18054	−0.590272	−	0.807205i	$-0.700979\pi$
$193$	−1.63178e33	−1.18054	−0.590272	+	0.807205i	$0.700979\pi$
$194$	−3.49208e33	−2.34401
$195$	−5.05182e32	−0.314736
$196$	6.62704e32	0.383360
$197$	−2.87354e33	−1.54404	−0.772018	−	0.635600i	$-0.780753\pi$
$197$	−2.87354e33	−1.54404	−0.772018	+	0.635600i	$0.780753\pi$
$198$	3.39406e31	0.0169463
$199$	9.25318e32	0.429459	0.214729	−	0.976674i	$-0.431113\pi$
$199$	9.25318e32	0.429459	0.214729	+	0.976674i	$0.431113\pi$
$200$	−6.75437e33	−2.91507
$201$	1.99795e33	0.802126
$202$	6.44678e32	0.240851
$203$	8.76858e32	0.304956
$204$	−2.41556e33	−0.782313
$205$	8.10036e32	0.244384
$206$	8.10182e33	2.27776
$207$	−1.45417e33	−0.381104
$208$	2.50905e34	6.13183
$209$	−1.62342e32	−0.0370092
$210$	−6.15720e32	−0.130980
$211$	−4.27276e33	−0.848423	−0.424212	−	0.905563i	$-0.639449\pi$
$211$	−4.27276e33	−0.848423	−0.424212	+	0.905563i	$0.639449\pi$
$212$	−2.05474e34	−3.80967
$213$	−2.91824e32	−0.0505379
$214$	2.13870e34	3.46060
$215$	2.59654e33	0.392678
$216$	−4.39792e33	−0.621824
$217$	4.07639e33	0.539026
$218$	−1.95632e34	−2.42003
$219$	−2.45673e33	−0.284392
$220$	2.05154e32	0.0222306
$221$	8.67459e33	0.880159
$222$	−4.10761e33	−0.390365
$223$	−7.10808e33	−0.632895	−0.316448	−	0.948610i	$-0.602490\pi$
$223$	−7.10808e33	−0.632895	−0.316448	+	0.948610i	$0.602490\pi$
$224$	1.59454e34	1.33057
$225$	−3.84437e33	−0.300731
$226$	1.19907e34	0.879573
$227$	−2.38068e34	−1.63805	−0.819023	−	0.573761i	$-0.805484\pi$
$227$	−2.38068e34	−1.63805	−0.819023	+	0.573761i	$0.805484\pi$
$228$	3.35308e34	2.16466
$229$	−9.98797e33	−0.605150	−0.302575	−	0.953126i	$-0.597846\pi$
$229$	−9.98797e33	−0.605150	−0.302575	+	0.953126i	$0.597846\pi$
$230$	−1.20651e34	−0.686244
$231$	−1.08225e32	−0.00578036
$232$	5.19650e34	2.60697
$233$	−3.33807e34	−1.57339	−0.786693	−	0.617345i	$-0.788208\pi$
$233$	−3.33807e34	−1.57339	−0.786693	+	0.617345i	$0.788208\pi$
$234$	2.51747e34	1.11515
$235$	−2.42648e33	−0.101040
$236$	1.11076e35	4.34907
$237$	−1.78305e34	−0.656618
$238$	1.05727e34	0.366285
$239$	5.31641e34	1.73320	0.866600	−	0.499004i	$-0.166301\pi$
$239$	5.31641e34	1.73320	0.866600	+	0.499004i	$0.166301\pi$
$240$	−2.06990e34	−0.635166
$241$	4.27142e34	1.23403	0.617015	−	0.786951i	$-0.288342\pi$
$241$	4.27142e34	1.23403	0.617015	+	0.786951i	$0.288342\pi$
$242$	−7.04936e34	−1.91790
$243$	−2.50316e33	−0.0641500
$244$	−6.04829e34	−1.46043
$245$	1.96332e33	0.0446770
$246$	−4.03665e34	−0.865889
$247$	−1.20414e35	−2.43540
$248$	2.41578e35	4.60796
$249$	−1.81635e34	−0.326820
$250$	−6.72509e34	−1.14174
$251$	−5.61546e34	−0.899739	−0.449870	−	0.893094i	$-0.648530\pi$
$251$	−5.61546e34	−0.899739	−0.449870	+	0.893094i	$0.648530\pi$
$252$	2.23533e34	0.338092
$253$	−2.12069e33	−0.0302851
$254$	−1.14088e35	−1.53869
$255$	−7.15633e33	−0.0911712
$256$	1.60724e35	1.93464
$257$	1.47198e34	0.167445	0.0837226	−	0.996489i	$-0.473319\pi$
$257$	1.47198e34	0.167445	0.0837226	+	0.996489i	$0.473319\pi$
$258$	−1.29393e35	−1.39132
$259$	1.30978e34	0.133153
$260$	1.52168e35	1.46289
$261$	2.95769e34	0.268946
$262$	1.53250e35	1.31836
$263$	−1.50439e34	−0.122462	−0.0612310	−	0.998124i	$-0.519503\pi$
$263$	−1.50439e34	−0.122462	−0.0612310	+	0.998124i	$0.519503\pi$
$264$	−6.41372e33	−0.0494144
$265$	−6.08737e34	−0.443981
$266$	−1.46761e35	−1.01351
$267$	−4.44401e34	−0.290644
$268$	−6.01815e35	−3.72828
$269$	−2.35186e35	−1.38039	−0.690196	−	0.723622i	$-0.742476\pi$
$269$	−2.35186e35	−1.38039	−0.690196	+	0.723622i	$0.742476\pi$
$270$	−2.07685e34	−0.115513
$271$	−8.69571e34	−0.458406	−0.229203	−	0.973379i	$-0.573612\pi$
$271$	−8.69571e34	−0.458406	−0.229203	+	0.973379i	$0.573612\pi$
$272$	3.55428e35	1.77624
$273$	−8.02737e34	−0.380378
$274$	−3.87951e35	−1.74339
$275$	−5.60646e33	−0.0238982
$276$	4.38017e35	1.77137
$277$	1.53444e35	0.588835	0.294418	−	0.955677i	$-0.404874\pi$
$277$	1.53444e35	0.588835	0.294418	+	0.955677i	$0.404874\pi$
$278$	7.91361e35	2.88221
$279$	1.37499e35	0.475376
$280$	1.16352e35	0.381929
$281$	−4.39186e35	−1.36901	−0.684505	−	0.729008i	$-0.739982\pi$
$281$	−4.39186e35	−1.36901	−0.684505	+	0.729008i	$0.739982\pi$
$282$	1.20919e35	0.358000
$283$	−3.98971e35	−1.12212	−0.561059	−	0.827776i	$-0.689606\pi$
$283$	−3.98971e35	−1.12212	−0.561059	+	0.827776i	$0.689606\pi$
$284$	8.79020e34	0.234900
$285$	9.93383e34	0.252270
$286$	3.67137e34	0.0886177
$287$	1.28715e35	0.295354
$288$	5.37844e35	1.17345
$289$	−3.59086e35	−0.745039
$290$	2.45398e35	0.484283
$291$	3.75591e35	0.705127
$292$	7.40005e35	1.32185
$293$	2.98938e35	0.508160	0.254080	−	0.967183i	$-0.418227\pi$
$293$	2.98938e35	0.508160	0.254080	+	0.967183i	$0.418227\pi$
$294$	−9.78383e34	−0.158297
$295$	3.29073e35	0.506843
$296$	7.76211e35	1.13828
$297$	−3.65049e33	−0.00509780
$298$	−2.20566e36	−2.93362
$299$	−1.57297e36	−1.99292
$300$	1.15798e36	1.39780
$301$	4.12591e35	0.474576
$302$	−2.44093e36	−2.67580
$303$	−6.93384e34	−0.0724529
$304$	−4.93376e36	−4.91486
$305$	−1.79186e35	−0.170199
$306$	3.56621e35	0.323033
$307$	1.27388e36	1.10058	0.550290	−	0.834974i	$-0.314517\pi$
$307$	1.27388e36	1.10058	0.550290	+	0.834974i	$0.314517\pi$
$308$	3.25991e34	0.0268671
$309$	−8.71393e35	−0.685198
$310$	1.14082e36	0.855997
$311$	1.40268e35	0.100446	0.0502231	−	0.998738i	$-0.484007\pi$
$311$	1.40268e35	0.100446	0.0502231	+	0.998738i	$0.484007\pi$
$312$	−4.75724e36	−3.25172
$313$	−2.30564e36	−1.50452	−0.752260	−	0.658867i	$-0.771036\pi$
$313$	−2.30564e36	−1.50452	−0.752260	+	0.658867i	$0.771036\pi$
$314$	−1.31371e36	−0.818502
$315$	6.62239e34	0.0394014
$316$	5.37083e36	3.05196
$317$	2.63394e36	1.42971	0.714854	−	0.699274i	$-0.246493\pi$
$317$	2.63394e36	1.42971	0.714854	+	0.699274i	$0.246493\pi$
$318$	3.03352e36	1.57309
$319$	4.31336e34	0.0213723
$320$	2.13908e36	1.01286
$321$	−2.30029e36	−1.04102
$322$	−1.91716e36	−0.829368
$323$	−1.70576e36	−0.705475
$324$	7.53989e35	0.298169
$325$	−4.15847e36	−1.57262
$326$	1.94954e36	0.705143
$327$	2.10412e36	0.727994
$328$	7.62802e36	2.52488
$329$	−3.85570e35	−0.122113
$330$	−3.02879e34	−0.00917946
$331$	−2.88274e36	−0.836179	−0.418090	−	0.908406i	$-0.637300\pi$
$331$	−2.88274e36	−0.836179	−0.418090	+	0.908406i	$0.637300\pi$
$332$	5.47113e36	1.51906
$333$	4.41795e35	0.117430
$334$	−5.60216e36	−1.42571
$335$	−1.78293e36	−0.434496
$336$	−3.28909e36	−0.767637
$337$	7.40449e36	1.65524	0.827621	−	0.561287i	$-0.189694\pi$
$337$	7.40449e36	1.65524	0.827621	+	0.561287i	$0.189694\pi$
$338$	1.82692e37	3.91225
$339$	−1.28966e36	−0.264594
$340$	2.15560e36	0.423763
$341$	2.00522e35	0.0377766
$342$	−4.95033e36	−0.893831
$343$	3.11973e35	0.0539949
$344$	2.44513e37	4.05700
$345$	1.29767e36	0.206436
$346$	−1.46452e37	−2.23405
$347$	−5.68749e36	−0.832038	−0.416019	−	0.909356i	$-0.636575\pi$
$347$	−5.68749e36	−0.832038	−0.416019	+	0.909356i	$0.636575\pi$
$348$	−8.90900e36	−1.25006
$349$	9.35615e36	1.25930	0.629649	−	0.776880i	$-0.283199\pi$
$349$	9.35615e36	1.25930	0.629649	+	0.776880i	$0.283199\pi$
$350$	−5.06838e36	−0.654459
$351$	−2.70767e36	−0.335461
$352$	7.84368e35	0.0932505
$353$	8.10014e36	0.924186	0.462093	−	0.886831i	$-0.347099\pi$
$353$	8.10014e36	0.924186	0.462093	+	0.886831i	$0.347099\pi$
$354$	−1.63987e37	−1.79582
$355$	2.60418e35	0.0273754
$356$	1.33860e37	1.35091
$357$	−1.13715e36	−0.110186
$358$	2.97953e37	2.77232
$359$	−9.10637e36	−0.813722	−0.406861	−	0.913490i	$-0.633377\pi$
$359$	−9.10637e36	−0.813722	−0.406861	+	0.913490i	$0.633377\pi$
$360$	3.92461e36	0.336830
$361$	1.15481e37	0.952046
$362$	−1.28724e37	−1.01950
$363$	7.58194e36	0.576945
$364$	2.41797e37	1.76799
$365$	2.19233e36	0.154049
$366$	8.92940e36	0.603040
$367$	1.49545e37	0.970762	0.485381	−	0.874303i	$-0.338681\pi$
$367$	1.49545e37	0.970762	0.485381	+	0.874303i	$0.338681\pi$
$368$	−6.44502e37	−4.02189
$369$	4.34163e36	0.260478
$370$	3.66555e36	0.211453
$371$	−9.67287e36	−0.536579
$372$	−4.14167e37	−2.20954
$373$	−2.12975e36	−0.109283	−0.0546413	−	0.998506i	$-0.517402\pi$
$373$	−2.12975e36	−0.109283	−0.0546413	+	0.998506i	$0.517402\pi$
$374$	5.20081e35	0.0256704
$375$	7.23318e36	0.343460
$376$	−2.28499e37	−1.04391
$377$	3.19934e37	1.40641
$378$	−3.30013e36	−0.139605
$379$	2.91578e37	1.18710	0.593549	−	0.804798i	$-0.297726\pi$
$379$	2.91578e37	1.18710	0.593549	+	0.804798i	$0.297726\pi$
$380$	−2.99222e37	−1.17255
$381$	1.22708e37	0.462871
$382$	−1.22237e37	−0.443900
$383$	5.61402e37	1.96287	0.981436	−	0.191789i	$-0.0614290\pi$
$383$	5.61402e37	1.96287	0.981436	+	0.191789i	$0.0614290\pi$
$384$	−4.62254e37	−1.55625
$385$	9.65779e34	0.00313110
$386$	−7.25654e37	−2.26576
$387$	1.39169e37	0.418537
$388$	−1.13134e38	−3.27742
$389$	−5.50867e37	−1.53737	−0.768684	−	0.639629i	$-0.779088\pi$
$389$	−5.50867e37	−1.53737	−0.768684	+	0.639629i	$0.779088\pi$
$390$	−2.24654e37	−0.604056
$391$	−2.22825e37	−0.577300
$392$	1.84884e37	0.461585
$393$	−1.64829e37	−0.396589
$394$	−1.27786e38	−2.96339
$395$	1.59116e37	0.355677
$396$	1.09958e36	0.0236945
$397$	−3.53475e37	−0.734339	−0.367169	−	0.930154i	$-0.619673\pi$
$397$	−3.53475e37	−0.734339	−0.367169	+	0.930154i	$0.619673\pi$
$398$	4.11488e37	0.824239
$399$	1.57849e37	0.304885
$400$	−1.70387e38	−3.17370
$401$	4.31451e37	0.775064	0.387532	−	0.921856i	$-0.373328\pi$
$401$	4.31451e37	0.775064	0.387532	+	0.921856i	$0.373328\pi$
$402$	8.88489e37	1.53948
$403$	1.48733e38	2.48590
$404$	2.08858e37	0.336760
$405$	2.23376e36	0.0347488
$406$	3.89938e37	0.585286
$407$	6.44294e35	0.00933179
$408$	−6.73904e37	−0.941945
$409$	6.53972e37	0.882209	0.441104	−	0.897456i	$-0.354587\pi$
$409$	6.53972e37	0.882209	0.441104	+	0.897456i	$0.354587\pi$
$410$	3.60222e37	0.469035
$411$	4.17261e37	0.524447
$412$	2.62477e38	3.18479
$413$	5.22900e37	0.612551
$414$	−6.46666e37	−0.731434
$415$	1.62087e37	0.177032
$416$	5.81788e38	6.13637
$417$	−8.51149e37	−0.867028
$418$	−7.21933e36	−0.0710299
$419$	−2.26965e37	−0.215703	−0.107851	−	0.994167i	$-0.534397\pi$
$419$	−2.26965e37	−0.215703	−0.107851	+	0.994167i	$0.534397\pi$
$420$	−1.99476e37	−0.183137
$421$	−3.66863e37	−0.325397	−0.162698	−	0.986676i	$-0.552020\pi$
$421$	−3.66863e37	−0.325397	−0.162698	+	0.986676i	$0.552020\pi$
$422$	−1.90009e38	−1.62834
$423$	−1.30055e37	−0.107694
$424$	−5.73241e38	−4.58704
$425$	−5.89082e37	−0.455551
$426$	−1.29774e37	−0.0969949
$427$	−2.84728e37	−0.205696
$428$	6.92881e38	4.83865
$429$	−3.94875e36	−0.0266580
$430$	1.15468e38	0.753648
$431$	−2.31592e36	−0.0146151	−0.00730756	−	0.999973i	$-0.502326\pi$
$431$	−2.31592e36	−0.0146151	−0.00730756	+	0.999973i	$0.502326\pi$
$432$	−1.10943e38	−0.676992
$433$	−1.25743e38	−0.742010	−0.371005	−	0.928631i	$-0.620987\pi$
$433$	−1.25743e38	−0.742010	−0.371005	+	0.928631i	$0.620987\pi$
$434$	1.81277e38	1.03453
$435$	−2.63938e37	−0.145682
$436$	−6.33793e38	−3.38371
$437$	3.09308e38	1.59739
$438$	−1.09251e38	−0.545820
$439$	−1.99699e38	−0.965250	−0.482625	−	0.875827i	$-0.660317\pi$
$439$	−1.99699e38	−0.965250	−0.482625	+	0.875827i	$0.660317\pi$
$440$	5.72347e36	0.0267668
$441$	1.05230e37	0.0476190
$442$	3.85758e38	1.68924
$443$	−1.08558e38	−0.460054	−0.230027	−	0.973184i	$-0.573881\pi$
$443$	−1.08558e38	−0.460054	−0.230027	+	0.973184i	$0.573881\pi$
$444$	−1.33075e38	−0.545814
$445$	3.96574e37	0.157436
$446$	−3.16096e38	−1.21468
$447$	2.37231e38	0.882493
$448$	3.39900e38	1.22411
$449$	−3.58212e38	−1.24902	−0.624509	−	0.781018i	$-0.714701\pi$
$449$	−3.58212e38	−1.24902	−0.624509	+	0.781018i	$0.714701\pi$
$450$	−1.70959e38	−0.577179
$451$	6.33163e36	0.0206993
$452$	3.88465e38	1.22983
$453$	2.62534e38	0.804937
$454$	−1.05869e39	−3.14382
$455$	7.16346e37	0.206043
$456$	9.35458e38	2.60636
$457$	−4.40120e38	−1.18792	−0.593958	−	0.804496i	$-0.702436\pi$
$457$	−4.40120e38	−1.18792	−0.593958	+	0.804496i	$0.702436\pi$
$458$	−4.44164e38	−1.16143
$459$	−3.83565e37	−0.0971750
$460$	−3.90877e38	−0.959515
$461$	−7.85783e37	−0.186913	−0.0934565	−	0.995623i	$-0.529792\pi$
$461$	−7.85783e37	−0.186913	−0.0934565	+	0.995623i	$0.529792\pi$
$462$	−4.81277e36	−0.0110940
$463$	5.76796e38	1.28854	0.644270	−	0.764798i	$-0.277161\pi$
$463$	5.76796e38	1.28854	0.644270	+	0.764798i	$0.277161\pi$
$464$	1.31088e39	2.83826
$465$	−1.22701e38	−0.257502
$466$	−1.48444e39	−3.01972
$467$	−2.26025e38	−0.445720	−0.222860	−	0.974851i	$-0.571539\pi$
$467$	−2.26025e38	−0.445720	−0.222860	+	0.974851i	$0.571539\pi$
$468$	8.15592e38	1.55922
$469$	−2.83309e38	−0.525115
$470$	−1.07906e38	−0.193921
$471$	1.41296e38	0.246222
$472$	3.09885e39	5.23650
$473$	2.02958e37	0.0332598
$474$	−7.92922e38	−1.26021
$475$	8.17716e38	1.26051
$476$	3.42526e38	0.512144
$477$	−3.26271e38	−0.473218
$478$	2.36420e39	3.32644
$479$	−9.68370e38	−1.32183	−0.660916	−	0.750460i	$-0.729832\pi$
$479$	−9.68370e38	−1.32183	−0.660916	+	0.750460i	$0.729832\pi$
$480$	−4.79961e38	−0.635635
$481$	4.77891e38	0.614080
$482$	1.89950e39	2.36841
$483$	2.06200e38	0.249491
$484$	−2.28380e39	−2.68164
$485$	−3.35170e38	−0.381953
$486$	−1.11315e38	−0.123120
$487$	−1.36854e39	−1.46922	−0.734612	−	0.678487i	$-0.762636\pi$
$487$	−1.36854e39	−1.46922	−0.734612	+	0.678487i	$0.762636\pi$
$488$	−1.68738e39	−1.75843
$489$	−2.09683e38	−0.212122
$490$	8.73089e37	0.0857463
$491$	1.08091e39	1.03064	0.515322	−	0.856997i	$-0.327672\pi$
$491$	1.08091e39	1.03064	0.515322	+	0.856997i	$0.327672\pi$
$492$	−1.30776e39	−1.21070
$493$	4.53213e38	0.407401
$494$	−5.35478e39	−4.67413
$495$	3.25762e36	0.00276137
$496$	6.09409e39	5.01677
$497$	4.13806e37	0.0330848
$498$	−8.07730e38	−0.627250
$499$	−1.15691e38	−0.0872655	−0.0436328	−	0.999048i	$-0.513893\pi$
$499$	−1.15691e38	−0.0872655	−0.0436328	+	0.999048i	$0.513893\pi$
$500$	−2.17875e39	−1.59640
$501$	6.02542e38	0.428884
$502$	−2.49719e39	−1.72682
$503$	−7.17451e37	−0.0482010	−0.0241005	−	0.999710i	$-0.507672\pi$
$503$	−7.17451e37	−0.0482010	−0.0241005	+	0.999710i	$0.507672\pi$
$504$	6.23623e38	0.407080
$505$	6.18761e37	0.0392463
$506$	−9.43069e37	−0.0581247
$507$	−1.96494e39	−1.17689
$508$	−3.69614e39	−2.15142
$509$	2.72089e39	1.53923	0.769614	−	0.638510i	$-0.220449\pi$
$509$	2.72089e39	1.53923	0.769614	+	0.638510i	$0.220449\pi$
$510$	−3.18241e38	−0.174980
$511$	3.48363e38	0.186178
$512$	1.95873e39	1.01756
$513$	5.32433e38	0.268883
$514$	6.54590e38	0.321369
$515$	7.77613e38	0.371158
$516$	−4.19199e39	−1.94536
$517$	−1.89666e37	−0.00855808
$518$	5.82458e38	0.255554
$519$	1.57517e39	0.672049
$520$	4.24526e39	1.76139
$521$	−1.64928e39	−0.665499	−0.332750	−	0.943015i	$-0.607976\pi$
$521$	−1.64928e39	−0.665499	−0.332750	+	0.943015i	$0.607976\pi$
$522$	1.31528e39	0.516174
$523$	−3.22038e39	−1.22923	−0.614614	−	0.788828i	$-0.710688\pi$
$523$	−3.22038e39	−1.22923	−0.614614	+	0.788828i	$0.710688\pi$
$524$	4.96489e39	1.84334
$525$	5.45130e38	0.196875
$526$	−6.69000e38	−0.235035
$527$	2.10693e39	0.720104
$528$	−1.61794e38	−0.0537984
$529$	9.49461e38	0.307164
$530$	−2.70705e39	−0.852111
$531$	1.76377e39	0.540220
$532$	−4.75466e39	−1.41710
$533$	4.69635e39	1.36212
$534$	−1.97625e39	−0.557819
$535$	2.05273e39	0.563899
$536$	−1.67897e40	−4.48903
$537$	−3.20464e39	−0.833972
$538$	−1.04587e40	−2.64932
$539$	1.53463e37	0.00378413
$540$	−6.72844e38	−0.161512
$541$	9.25631e38	0.216311	0.108155	−	0.994134i	$-0.465506\pi$
$541$	9.25631e38	0.216311	0.108155	+	0.994134i	$0.465506\pi$
$542$	−3.86698e39	−0.879796
$543$	1.38449e39	0.306686
$544$	8.24152e39	1.77756
$545$	−1.87767e39	−0.394340
$546$	−3.56977e39	−0.730039
$547$	4.97772e39	0.991322	0.495661	−	0.868516i	$-0.334926\pi$
$547$	4.97772e39	0.991322	0.495661	+	0.868516i	$0.334926\pi$
$548$	−1.25685e40	−2.43762
$549$	−9.60403e38	−0.181407
$550$	−2.49319e38	−0.0458665
$551$	−6.29114e39	−1.12728
$552$	1.22200e40	2.13282
$553$	2.52836e39	0.429858
$554$	6.82365e39	1.13012
$555$	−3.94248e38	−0.0636095
$556$	2.56379e40	4.02994
$557$	8.12164e39	1.24378	0.621890	−	0.783105i	$-0.286365\pi$
$557$	8.12164e39	1.24378	0.621890	+	0.783105i	$0.286365\pi$
$558$	6.11455e39	0.912366
$559$	1.50540e40	2.18867
$560$	2.93511e39	0.415814
$561$	−5.59373e37	−0.00772219
$562$	−1.95306e40	−2.62747
$563$	8.07680e39	1.05893	0.529465	−	0.848332i	$-0.322393\pi$
$563$	8.07680e39	1.05893	0.529465	+	0.848332i	$0.322393\pi$
$564$	3.91744e39	0.500560
$565$	1.15087e39	0.143325
$566$	−1.77422e40	−2.15362
$567$	3.54946e38	0.0419961
$568$	2.45233e39	0.282831
$569$	1.03436e40	1.16291	0.581453	−	0.813580i	$-0.302484\pi$
$569$	1.03436e40	1.16291	0.581453	+	0.813580i	$0.302484\pi$
$570$	4.41757e39	0.484170
$571$	2.97584e39	0.317970	0.158985	−	0.987281i	$-0.449178\pi$
$571$	2.97584e39	0.317970	0.158985	+	0.987281i	$0.449178\pi$
$572$	1.18942e39	0.123906
$573$	1.31472e39	0.133534
$574$	5.72396e39	0.566858
$575$	1.06819e40	1.03149
$576$	1.14650e40	1.07956
$577$	−2.87800e39	−0.264266	−0.132133	−	0.991232i	$-0.542183\pi$
$577$	−2.87800e39	−0.264266	−0.132133	+	0.991232i	$0.542183\pi$
$578$	−1.59685e40	−1.42992
$579$	7.80478e39	0.681587
$580$	7.95021e39	0.677131
$581$	2.57558e39	0.213954
$582$	1.67025e40	1.35331
$583$	−4.75818e38	−0.0376051
$584$	2.06450e40	1.59158
$585$	2.41627e39	0.181713
$586$	1.32937e40	0.975285
$587$	−1.41483e40	−1.01263	−0.506316	−	0.862348i	$-0.668993\pi$
$587$	−1.41483e40	−1.01263	−0.506316	+	0.862348i	$0.668993\pi$
$588$	−3.16969e39	−0.221333
$589$	−2.92466e40	−1.99252
$590$	1.46339e40	0.972758
$591$	1.37441e40	0.891450
$592$	1.95808e40	1.23927
$593$	1.63398e40	1.00914	0.504572	−	0.863370i	$-0.331650\pi$
$593$	1.63398e40	1.00914	0.504572	+	0.863370i	$0.331650\pi$
$594$	−1.62337e38	−0.00978395
$595$	1.01476e39	0.0596856
$596$	−7.14575e40	−4.10182
$597$	−4.42577e39	−0.247948
$598$	−6.99501e40	−3.82491
$599$	9.49273e39	0.506643	0.253322	−	0.967382i	$-0.418477\pi$
$599$	9.49273e39	0.506643	0.253322	+	0.967382i	$0.418477\pi$
$600$	3.23059e40	1.68302
$601$	−1.54534e39	−0.0785860	−0.0392930	−	0.999228i	$-0.512511\pi$
$601$	−1.54534e39	−0.0785860	−0.0392930	+	0.999228i	$0.512511\pi$
$602$	1.83479e40	0.910830
$603$	−9.55616e39	−0.463108
$604$	−7.90793e40	−3.74134
$605$	−6.76597e39	−0.312519
$606$	−3.08347e39	−0.139055
$607$	2.00086e40	0.881009	0.440504	−	0.897750i	$-0.354800\pi$
$607$	2.00086e40	0.881009	0.440504	+	0.897750i	$0.354800\pi$
$608$	−1.14402e41	−4.91849
$609$	−4.19399e39	−0.176066
$610$	−7.96841e39	−0.326655
$611$	−1.40680e40	−0.563166
$612$	1.15536e40	0.451669
$613$	1.23276e39	0.0470656	0.0235328	−	0.999723i	$-0.492509\pi$
$613$	1.23276e39	0.0470656	0.0235328	+	0.999723i	$0.492509\pi$
$614$	5.66493e40	2.11229
$615$	−3.87438e39	−0.141095
$616$	9.09464e38	0.0323493
$617$	5.43229e40	1.88733	0.943665	−	0.330901i	$-0.107353\pi$
$617$	5.43229e40	1.88733	0.943665	+	0.330901i	$0.107353\pi$
$618$	−3.87508e40	−1.31507
$619$	−5.72969e40	−1.89940	−0.949700	−	0.313161i	$-0.898612\pi$
$619$	−5.72969e40	−1.89940	−0.949700	+	0.313161i	$0.898612\pi$
$620$	3.69594e40	1.19687
$621$	6.95523e39	0.220031
$622$	6.23772e39	0.192781
$623$	6.30158e39	0.190271
$624$	−1.20007e41	−3.54021
$625$	2.48464e40	0.716149
$626$	−1.02531e41	−2.88755
$627$	7.76476e38	0.0213673
$628$	−4.25606e40	−1.14444
$629$	6.76973e39	0.177884
$630$	2.94497e39	0.0756211
$631$	1.27656e40	0.320344	0.160172	−	0.987089i	$-0.448795\pi$
$631$	1.27656e40	0.320344	0.160172	+	0.987089i	$0.448795\pi$
$632$	1.49838e41	3.67471
$633$	2.04365e40	0.489837
$634$	1.17131e41	2.74397
$635$	−1.09502e40	−0.250728
$636$	9.82777e40	2.19951
$637$	1.13828e40	0.249016
$638$	1.91815e39	0.0410187
$639$	1.39579e39	0.0291781
$640$	4.12506e40	0.842987
$641$	1.02517e37	0.000204812 0	0.000102406	−	1.00000i	$-0.499967\pi$
$641$	1.02517e37	0.000204812 0	0.000102406		1.00000i	$0.499967\pi$
$642$	−1.02294e41	−1.99798
$643$	3.29308e40	0.628845	0.314422	−	0.949283i	$-0.398189\pi$
$643$	3.29308e40	0.628845	0.314422	+	0.949283i	$0.398189\pi$
$644$	−6.21106e40	−1.15963
$645$	−1.24192e40	−0.226713
$646$	−7.58550e40	−1.35398
$647$	1.03953e41	1.81437	0.907184	−	0.420734i	$-0.138228\pi$
$647$	1.03953e41	1.81437	0.907184	+	0.420734i	$0.138228\pi$
$648$	2.10351e40	0.359010
$649$	2.57220e39	0.0429295
$650$	−1.84927e41	−3.01826
$651$	−1.94973e40	−0.311207
$652$	6.31598e40	0.985940
$653$	−6.23026e40	−0.951185	−0.475592	−	0.879666i	$-0.657766\pi$
$653$	−6.23026e40	−0.951185	−0.475592	+	0.879666i	$0.657766\pi$
$654$	9.35700e40	1.39720
$655$	1.47090e40	0.214824
$656$	1.92426e41	2.74889
$657$	1.17505e40	0.164194
$658$	−1.71463e40	−0.234366
$659$	2.38999e40	0.319563	0.159782	−	0.987152i	$-0.448921\pi$
$659$	2.38999e40	0.319563	0.159782	+	0.987152i	$0.448921\pi$
$660$	−9.81245e38	−0.0128348
$661$	−6.15815e40	−0.788005	−0.394002	−	0.919109i	$-0.628910\pi$
$661$	−6.15815e40	−0.788005	−0.394002	+	0.919109i	$0.628910\pi$
$662$	−1.28195e41	−1.60484
$663$	−4.14903e40	−0.508160
$664$	1.52636e41	1.82902
$665$	−1.40861e40	−0.165150
$666$	1.96466e40	0.225378
$667$	−8.21818e40	−0.922467
$668$	−1.81495e41	−1.99345
$669$	3.39977e40	0.365402
$670$	−7.92869e40	−0.833905
$671$	−1.40061e39	−0.0144158
$672$	−7.62661e40	−0.768205
$673$	−1.22028e41	−1.20294	−0.601468	−	0.798897i	$-0.705417\pi$
$673$	−1.22028e41	−1.20294	−0.601468	+	0.798897i	$0.705417\pi$
$674$	3.29277e41	3.17682
$675$	1.83875e40	0.173627
$676$	5.91871e41	5.47016
$677$	−1.52165e41	−1.37651	−0.688256	−	0.725467i	$-0.741624\pi$
$677$	−1.52165e41	−1.37651	−0.688256	+	0.725467i	$0.741624\pi$
$678$	−5.73511e40	−0.507822
$679$	−5.32587e40	−0.461614
$680$	6.01377e40	0.510232
$681$	1.13867e41	0.945726
$682$	8.91719e39	0.0725028
$683$	4.11663e40	0.327673	0.163837	−	0.986487i	$-0.447613\pi$
$683$	4.11663e40	0.327673	0.163837	+	0.986487i	$0.447613\pi$
$684$	−1.60377e41	−1.24977
$685$	−3.72355e40	−0.284082
$686$	1.38734e40	0.103630
$687$	4.77722e40	0.349383
$688$	6.16812e41	4.41693
$689$	−3.52928e41	−2.47461
$690$	5.77071e40	0.396203
$691$	−1.91665e41	−1.28858	−0.644288	−	0.764783i	$-0.722846\pi$
$691$	−1.91665e41	−1.28858	−0.644288	+	0.764783i	$0.722846\pi$
$692$	−4.74465e41	−3.12368
$693$	5.17638e38	0.00333729
$694$	−2.52922e41	−1.59689
$695$	7.59548e40	0.469651
$696$	−2.48547e41	−1.50513
$697$	6.65278e40	0.394574
$698$	4.16067e41	2.41691
$699$	1.59659e41	0.908395
$700$	−1.64202e41	−0.915073
$701$	2.38848e40	0.130380	0.0651900	−	0.997873i	$-0.479235\pi$
$701$	2.38848e40	0.130380	0.0651900	+	0.997873i	$0.479235\pi$
$702$	−1.20410e41	−0.643834
$703$	−9.39718e40	−0.492204
$704$	1.67200e40	0.0857894
$705$	1.16058e40	0.0583355
$706$	3.60213e41	1.77374
$707$	9.83216e39	0.0474315
$708$	−5.31273e41	−2.51094
$709$	−1.23369e41	−0.571261	−0.285630	−	0.958340i	$-0.592203\pi$
$709$	−1.23369e41	−0.571261	−0.285630	+	0.958340i	$0.592203\pi$
$710$	1.15808e40	0.0525402
$711$	8.52828e40	0.379099
$712$	3.73449e41	1.62657
$713$	−3.82052e41	−1.63051
$714$	−5.05688e40	−0.211475
$715$	3.52378e39	0.0144401
$716$	9.65285e41	3.87629
$717$	−2.54282e41	−1.00066
$718$	−4.04960e41	−1.56173
$719$	1.89927e41	0.717825	0.358912	−	0.933371i	$-0.383148\pi$
$719$	1.89927e41	0.717825	0.358912	+	0.933371i	$0.383148\pi$
$720$	9.90028e40	0.366713
$721$	1.23563e41	0.448567
$722$	5.13545e41	1.82721
$723$	−2.04301e41	−0.712467
$724$	−4.17031e41	−1.42547
$725$	−2.17264e41	−0.727924
$726$	3.37169e41	1.10730
$727$	−9.49906e40	−0.305796	−0.152898	−	0.988242i	$-0.548861\pi$
$727$	−9.49906e40	−0.305796	−0.152898	+	0.988242i	$0.548861\pi$
$728$	6.74575e41	2.12875
$729$	1.19725e40	0.0370370
$730$	9.74930e40	0.295659
$731$	2.13252e41	0.634003
$732$	2.89288e41	0.843179
$733$	−4.19554e41	−1.19889	−0.599447	−	0.800415i	$-0.704613\pi$
$733$	−4.19554e41	−1.19889	−0.599447	+	0.800415i	$0.704613\pi$
$734$	6.65023e41	1.86313
$735$	−9.39052e39	−0.0257943
$736$	−1.49445e42	−4.02487
$737$	−1.39363e40	−0.0368017
$738$	1.93072e41	0.499921
$739$	−6.86683e41	−1.74346	−0.871730	−	0.489986i	$-0.837002\pi$
$739$	−6.86683e41	−1.74346	−0.871730	+	0.489986i	$0.837002\pi$
$740$	1.18754e41	0.295656
$741$	5.75934e41	1.40608
$742$	−4.30152e41	−1.02983
$743$	2.44827e40	0.0574806	0.0287403	−	0.999587i	$-0.490850\pi$
$743$	2.44827e40	0.0574806	0.0287403	+	0.999587i	$0.490850\pi$
$744$	−1.15546e42	−2.66040
$745$	−2.11700e41	−0.478029
$746$	−9.47100e40	−0.209741
$747$	8.68755e40	0.188690
$748$	1.68492e40	0.0358927
$749$	3.26180e41	0.681507
$750$	3.21659e41	0.659185
$751$	−4.48251e40	−0.0901036	−0.0450518	−	0.998985i	$-0.514345\pi$
$751$	−4.48251e40	−0.0901036	−0.0450518	+	0.998985i	$0.514345\pi$
$752$	−5.76416e41	−1.13652
$753$	2.68586e41	0.519465
$754$	1.42274e42	2.69924
$755$	−2.34280e41	−0.436018
$756$	−1.06915e41	−0.195197
$757$	4.69163e41	0.840299	0.420150	−	0.907455i	$-0.361978\pi$
$757$	4.69163e41	0.840299	0.420150	+	0.907455i	$0.361978\pi$
$758$	1.29665e42	2.27834
$759$	1.01432e40	0.0174851
$760$	−8.34783e41	−1.41181
$761$	1.03587e42	1.71881	0.859405	−	0.511295i	$-0.170834\pi$
$761$	1.03587e42	1.71881	0.859405	+	0.511295i	$0.170834\pi$
$762$	5.45680e41	0.888364
$763$	−2.98363e41	−0.476584
$764$	−3.96015e41	−0.620666
$765$	3.42285e40	0.0526377
$766$	2.49655e42	3.76724
$767$	1.90787e42	2.82498
$768$	−7.68737e41	−1.11697
$769$	−8.27534e41	−1.17992	−0.589962	−	0.807431i	$-0.700857\pi$
$769$	−8.27534e41	−1.17992	−0.589962	+	0.807431i	$0.700857\pi$
$770$	4.29481e39	0.00600937
$771$	−7.04045e40	−0.0966745
$772$	−2.35092e42	−3.16801
$773$	9.94627e40	0.131540	0.0657700	−	0.997835i	$-0.479050\pi$
$773$	9.94627e40	0.131540	0.0657700	+	0.997835i	$0.479050\pi$
$774$	6.18884e41	0.803277
$775$	−1.01003e42	−1.28665
$776$	−3.15626e42	−3.94618
$777$	−6.26463e40	−0.0768760
$778$	−2.44970e42	−2.95059
$779$	−9.23485e41	−1.09178
$780$	−7.27817e41	−0.844599
$781$	2.03555e39	0.00231869
$782$	−9.90902e41	−1.10798
$783$	−1.41465e41	−0.155276
$784$	4.66391e41	0.502537
$785$	−1.26090e41	−0.133374
$786$	−7.32992e41	−0.761154
$787$	1.51930e42	1.54885	0.774425	−	0.632666i	$-0.218040\pi$
$787$	1.51930e42	1.54885	0.774425	+	0.632666i	$0.218040\pi$
$788$	−4.13992e42	−4.14345
$789$	7.19544e40	0.0707034
$790$	7.07587e41	0.682633
$791$	1.82873e41	0.173217
$792$	3.06766e40	0.0285294
$793$	−1.03887e42	−0.948637
$794$	−1.57190e42	−1.40938
$795$	2.91157e41	0.256333
$796$	1.33311e42	1.15246
$797$	−6.21474e41	−0.527566	−0.263783	−	0.964582i	$-0.584970\pi$
$797$	−6.21474e41	−0.527566	−0.263783	+	0.964582i	$0.584970\pi$
$798$	7.01954e41	0.585150
$799$	−1.99286e41	−0.163135
$800$	−3.95086e42	−3.17605
$801$	2.12556e41	0.167803
$802$	1.91866e42	1.48754
$803$	1.71363e40	0.0130480
$804$	2.87846e42	2.15252
$805$	−1.84009e41	−0.135144
$806$	6.61413e42	4.77106
$807$	1.12489e42	0.796970
$808$	5.82681e41	0.405477
$809$	−2.08679e42	−1.42635	−0.713174	−	0.700987i	$-0.752743\pi$
$809$	−2.08679e42	−1.42635	−0.713174	+	0.700987i	$0.752743\pi$
$810$	9.93353e40	0.0666916
$811$	1.12627e42	0.742748	0.371374	−	0.928483i	$-0.378887\pi$
$811$	1.12627e42	0.742748	0.371374	+	0.928483i	$0.378887\pi$
$812$	1.26329e42	0.818355
$813$	4.15913e41	0.264661
$814$	2.86517e40	0.0179100
$815$	1.87117e41	0.114902
$816$	−1.70000e42	−1.02551
$817$	−2.96019e42	−1.75428
$818$	2.90821e42	1.69318
$819$	3.83947e41	0.219611
$820$	1.16702e42	0.655810
$821$	2.00158e42	1.10509	0.552545	−	0.833483i	$-0.313657\pi$
$821$	2.00158e42	1.10509	0.552545	+	0.833483i	$0.313657\pi$
$822$	1.85556e42	1.00654
$823$	−6.09027e41	−0.324593	−0.162296	−	0.986742i	$-0.551890\pi$
$823$	−6.09027e41	−0.324593	−0.162296	+	0.986742i	$0.551890\pi$
$824$	7.32269e42	3.83465
$825$	2.68155e40	0.0137976
$826$	2.32533e42	1.17564
$827$	−9.52191e41	−0.473036	−0.236518	−	0.971627i	$-0.576006\pi$
$827$	−9.52191e41	−0.473036	−0.236518	+	0.971627i	$0.576006\pi$
$828$	−2.09502e42	−1.02270
$829$	1.28436e42	0.616091	0.308045	−	0.951372i	$-0.400325\pi$
$829$	1.28436e42	0.616091	0.308045	+	0.951372i	$0.400325\pi$
$830$	7.20801e41	0.339769
$831$	−7.33919e41	−0.339964
$832$	1.24017e43	5.64539
$833$	1.61247e41	0.0721337
$834$	−3.78506e42	−1.66404
$835$	−5.37695e41	−0.232318
$836$	−2.33887e41	−0.0993148
$837$	−6.57652e41	−0.274459
$838$	−1.00931e42	−0.413988
$839$	1.07192e42	0.432131	0.216065	−	0.976379i	$-0.430678\pi$
$839$	1.07192e42	0.432131	0.216065	+	0.976379i	$0.430678\pi$
$840$	−5.56508e41	−0.220507
$841$	−8.96158e41	−0.349014
$842$	−1.63144e42	−0.624518
$843$	2.10061e42	0.790398
$844$	−6.15577e42	−2.27676
$845$	1.75348e42	0.637496
$846$	−5.78352e41	−0.206691
$847$	−1.07512e42	−0.377699
$848$	−1.44607e43	−4.99400
$849$	1.90827e42	0.647855
$850$	−2.61965e42	−0.874315
$851$	−1.22756e42	−0.402778
$852$	−4.20432e41	−0.135619
$853$	−4.87303e42	−1.54539	−0.772694	−	0.634778i	$-0.781092\pi$
$853$	−4.87303e42	−1.54539	−0.772694	+	0.634778i	$0.781092\pi$
$854$	−1.26618e42	−0.394783
$855$	−4.75132e41	−0.145648
$856$	1.93303e43	5.82598
$857$	4.74751e42	1.40684	0.703418	−	0.710776i	$-0.251656\pi$
$857$	4.74751e42	1.40684	0.703418	+	0.710776i	$0.251656\pi$
$858$	−1.75600e41	−0.0511635
$859$	4.10289e42	1.17541	0.587704	−	0.809076i	$-0.300032\pi$
$859$	4.10289e42	1.17541	0.587704	+	0.809076i	$0.300032\pi$
$860$	3.74084e42	1.05376
$861$	−6.15641e41	−0.170523
$862$	−1.02989e41	−0.0280501
$863$	1.19544e42	0.320162	0.160081	−	0.987104i	$-0.448824\pi$
$863$	1.19544e42	0.320162	0.160081	+	0.987104i	$0.448824\pi$
$864$	−2.57249e42	−0.677493
$865$	−1.40565e42	−0.364035
$866$	−5.59179e42	−1.42410
$867$	1.71750e42	0.430149
$868$	5.87287e42	1.44649
$869$	1.24373e41	0.0301258
$870$	−1.17373e42	−0.279601
$871$	−1.03369e43	−2.42174
$872$	−1.76818e43	−4.07416
$873$	−1.79644e42	−0.407105
$874$	1.37549e43	3.06578
$875$	−1.02566e42	−0.224847
$876$	−3.53942e42	−0.763172
$877$	9.09651e40	0.0192921	0.00964607	−	0.999953i	$-0.496930\pi$
$877$	9.09651e40	0.0192921	0.00964607	+	0.999953i	$0.496930\pi$
$878$	−8.88059e42	−1.85256
$879$	−1.42981e42	−0.293386
$880$	1.44381e41	0.0291415
$881$	−2.71938e42	−0.539908	−0.269954	−	0.962873i	$-0.587009\pi$
$881$	−2.71938e42	−0.539908	−0.269954	+	0.962873i	$0.587009\pi$
$882$	4.67958e41	0.0913928
$883$	−5.66116e41	−0.108762	−0.0543808	−	0.998520i	$-0.517318\pi$
$883$	−5.66116e41	−0.108762	−0.0543808	+	0.998520i	$0.517318\pi$
$884$	1.24975e43	2.36192
$885$	−1.57395e42	−0.292626
$886$	−4.82758e42	−0.882959
$887$	−3.74902e41	−0.0674567	−0.0337284	−	0.999431i	$-0.510738\pi$
$887$	−3.74902e41	−0.0674567	−0.0337284	+	0.999431i	$0.510738\pi$
$888$	−3.71259e42	−0.657188
$889$	−1.73999e42	−0.303020
$890$	1.76356e42	0.302159
$891$	1.74602e40	0.00294321
$892$	−1.02406e43	−1.69839
$893$	2.76632e42	0.451395
$894$	1.05496e43	1.69373
$895$	2.85975e42	0.451746
$896$	6.55475e42	1.01880
$897$	7.52349e42	1.15061
$898$	−1.59297e43	−2.39718
$899$	7.77070e42	1.15065
$900$	−5.53860e42	−0.807019
$901$	−4.99952e42	−0.716835
$902$	2.81567e41	0.0397272
$903$	−1.97341e42	−0.273997
$904$	1.08376e43	1.48078
$905$	−1.23549e42	−0.166125
$906$	1.16749e43	1.54488
$907$	−3.53978e42	−0.460968	−0.230484	−	0.973076i	$-0.574031\pi$
$907$	−3.53978e42	−0.460968	−0.230484	+	0.973076i	$0.574031\pi$
$908$	−3.42985e43	−4.39573
$909$	3.31643e41	0.0418307
$910$	3.18558e42	0.395448
$911$	−3.15682e42	−0.385685	−0.192843	−	0.981230i	$-0.561771\pi$
$911$	−3.15682e42	−0.385685	−0.192843	+	0.981230i	$0.561771\pi$
$912$	2.35980e43	2.83759
$913$	1.26695e41	0.0149946
$914$	−1.95721e43	−2.27991
$915$	8.57043e41	0.0982645
$916$	−1.43897e43	−1.62393
$917$	2.33727e42	0.259629
$918$	−1.70571e42	−0.186503
$919$	−3.80667e42	−0.409704	−0.204852	−	0.978793i	$-0.565671\pi$
$919$	−3.80667e42	−0.409704	−0.204852	+	0.978793i	$0.565671\pi$
$920$	−1.09049e43	−1.15530
$921$	−6.09292e42	−0.635420
$922$	−3.49437e42	−0.358733
$923$	1.50983e42	0.152582
$924$	−1.55920e41	−0.0155117
$925$	−3.24531e42	−0.317834
$926$	2.56501e43	2.47303
$927$	4.16784e42	0.395599
$928$	3.03961e43	2.84036
$929$	−8.87177e42	−0.816173	−0.408087	−	0.912943i	$-0.633804\pi$
$929$	−8.87177e42	−0.816173	−0.408087	+	0.912943i	$0.633804\pi$
$930$	−5.45650e42	−0.494210
$931$	−2.23830e42	−0.199594
$932$	−4.80918e43	−4.22221
$933$	−6.70898e41	−0.0579926
$934$	−1.00513e43	−0.855447
$935$	4.99173e40	0.00418295
$936$	2.27537e43	1.87738
$937$	2.93793e42	0.238681	0.119340	−	0.992853i	$-0.461922\pi$
$937$	2.93793e42	0.238681	0.119340	+	0.992853i	$0.461922\pi$
$938$	−1.25987e43	−1.00783
$939$	1.10278e43	0.868635
$940$	−3.49584e42	−0.271143
$941$	1.52042e43	1.16122	0.580610	−	0.814182i	$-0.302814\pi$
$941$	1.52042e43	1.16122	0.580610	+	0.814182i	$0.302814\pi$
$942$	6.28343e42	0.472562
$943$	−1.20636e43	−0.893422
$944$	7.81720e43	5.70108
$945$	−3.16747e41	−0.0227484
$946$	9.02552e41	0.0638338
$947$	−1.62703e43	−1.13324	−0.566620	−	0.823980i	$-0.691749\pi$
$947$	−1.62703e43	−1.13324	−0.566620	+	0.823980i	$0.691749\pi$
$948$	−2.56885e43	−1.76205
$949$	1.27105e43	0.858624
$950$	3.63638e43	2.41923
$951$	−1.25981e43	−0.825442
$952$	9.55592e42	0.616647
$953$	1.76610e43	1.12245	0.561227	−	0.827662i	$-0.310329\pi$
$953$	1.76610e43	1.12245	0.561227	+	0.827662i	$0.310329\pi$
$954$	−1.45092e43	−0.908224
$955$	−1.17323e42	−0.0723328
$956$	7.65937e43	4.65108
$957$	−2.06306e41	−0.0123393
$958$	−4.30633e43	−2.53693
$959$	−5.91674e42	−0.343331
$960$	−1.02311e43	−0.584778
$961$	1.83630e43	1.03384
$962$	2.12518e43	1.17857
$963$	1.10022e43	0.601033
$964$	6.15386e43	3.31154
$965$	−6.96482e42	−0.369202
$966$	9.16970e42	0.478836
$967$	−1.60062e43	−0.823386	−0.411693	−	0.911323i	$-0.635062\pi$
$967$	−1.60062e43	−0.823386	−0.411693	+	0.911323i	$0.635062\pi$
$968$	−6.37144e43	−3.22883
$969$	8.15860e42	0.407306
$970$	−1.49050e43	−0.733063
$971$	3.06260e43	1.48392	0.741962	−	0.670442i	$-0.233896\pi$
$971$	3.06260e43	1.48392	0.741962	+	0.670442i	$0.233896\pi$
$972$	−3.60630e42	−0.172148
$973$	1.20693e43	0.567603
$974$	−6.08590e43	−2.81981
$975$	1.98898e43	0.907954
$976$	−4.25661e43	−1.91444
$977$	4.08278e43	1.80919	0.904597	−	0.426267i	$-0.140172\pi$
$977$	4.08278e43	1.80919	0.904597	+	0.426267i	$0.140172\pi$
$978$	−9.32459e42	−0.407114
$979$	3.09981e41	0.0133348
$980$	2.82857e42	0.119892
$981$	−1.00639e43	−0.420308
$982$	4.80680e43	1.97806
$983$	−2.58811e42	−0.104944	−0.0524719	−	0.998622i	$-0.516710\pi$
$983$	−2.58811e42	−0.104944	−0.0524719	+	0.998622i	$0.516710\pi$
$984$	−3.64846e43	−1.45774
$985$	−1.22649e43	−0.482880
$986$	2.01544e43	0.781905
$987$	1.84417e42	0.0705021
$988$	−1.73480e44	−6.53543
$989$	−3.86693e43	−1.43556
$990$	1.44866e41	0.00529976
$991$	−2.87510e43	−1.03654	−0.518269	−	0.855218i	$-0.673423\pi$
$991$	−2.87510e43	−1.03654	−0.518269	+	0.855218i	$0.673423\pi$
$992$	1.41307e44	5.02048
$993$	1.37881e43	0.482768
$994$	1.84019e42	0.0634981
$995$	3.94946e42	0.134309
$996$	−2.61682e43	−0.877029
$997$	1.13965e43	0.376437	0.188219	−	0.982127i	$-0.439729\pi$
$997$	1.13965e43	0.376437	0.188219	+	0.982127i	$0.439729\pi$
$998$	−5.14478e42	−0.167484
$999$	−2.11309e42	−0.0677983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.c.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.c.1.7	✓	7	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q+44469.9 q^{2} -4.78297e6 q^{3} +1.44070e9 q^{4} +4.26822e9 q^{5} -2.12698e11 q^{6} +6.78223e11 q^{7} +4.01934e13 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q+44469.9 q^{2} -4.78297e6 q^{3} +1.44070e9 q^{4} +4.26822e9 q^{5} -2.12698e11 q^{6} +6.78223e11 q^{7} +4.01934e13 q^{8} +2.28768e13 q^{9} +1.89808e14 q^{10} +3.33625e13 q^{11} -6.89084e15 q^{12} +2.47459e16 q^{13} +3.01605e16 q^{14} -2.04148e16 q^{15} +1.01392e18 q^{16} +3.50547e17 q^{17} +1.01733e18 q^{18} -4.86600e18 q^{19} +6.14924e18 q^{20} -3.24392e18 q^{21} +1.48363e18 q^{22} -6.35651e19 q^{23} -1.92244e20 q^{24} -1.68047e20 q^{25} +1.10045e21 q^{26} -1.09419e20 q^{27} +9.77118e20 q^{28} +1.29288e21 q^{29} -9.07843e20 q^{30} +6.01040e21 q^{31} +2.35105e22 q^{32} -1.59572e20 q^{33} +1.55888e22 q^{34} +2.89481e21 q^{35} +3.29587e22 q^{36} +1.93119e22 q^{37} -2.16391e23 q^{38} -1.18359e23 q^{39} +1.71554e23 q^{40} +1.89783e23 q^{41} -1.44257e23 q^{42} +6.08342e23 q^{43} +4.80654e22 q^{44} +9.76432e22 q^{45} -2.82673e24 q^{46} -5.68500e23 q^{47} -4.84957e24 q^{48} +4.59987e23 q^{49} -7.47303e24 q^{50} -1.67665e24 q^{51} +3.56515e25 q^{52} -1.42621e25 q^{53} -4.86585e24 q^{54} +1.42398e23 q^{55} +2.72601e25 q^{56} +2.32739e25 q^{57} +5.74941e25 q^{58} +7.70985e25 q^{59} -2.94116e25 q^{60} -4.19815e25 q^{61} +2.67282e26 q^{62} +1.55156e25 q^{63} +5.01163e26 q^{64} +1.05621e26 q^{65} -7.09614e24 q^{66} -4.17723e26 q^{67} +5.05034e26 q^{68} +3.04030e26 q^{69} +1.28732e26 q^{70} +6.10132e25 q^{71} +9.19495e26 q^{72} +5.13641e26 q^{73} +8.58800e26 q^{74} +8.03763e26 q^{75} -7.01046e27 q^{76} +2.26272e25 q^{77} -5.26341e27 q^{78} +3.72792e27 q^{79} +4.32765e27 q^{80} +5.23348e26 q^{81} +8.43964e27 q^{82} +3.79754e27 q^{83} -4.67353e27 q^{84} +1.49621e27 q^{85} +2.70529e28 q^{86} -6.18379e27 q^{87} +1.34095e27 q^{88} +9.29132e27 q^{89} +4.34219e27 q^{90} +1.67832e28 q^{91} -9.15784e28 q^{92} -2.87476e28 q^{93} -2.52812e28 q^{94} -2.07692e28 q^{95} -1.12450e29 q^{96} -7.85268e28 q^{97} +2.04556e28 q^{98} +7.63227e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9}+O(q^{10}) \) 7 * q + 60870 * q^2 - 33480783 * q^3 + 2201135476 * q^4 - 2861618502 * q^5 - 291139323030 * q^6 + 4747561509943 * q^7 + 9964333994280 * q^8 + 160137547184727 * q^9	\( 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9} - 472777770164028 q^{10} + 135879674344284 q^{11} - 10\!\cdots\!44 q^{12}+ \cdots + 31\!\cdots\!24 q^{99}+O(q^{100}) \) 7 * q + 60870 * q^2 - 33480783 * q^3 + 2201135476 * q^4 - 2861618502 * q^5 - 291139323030 * q^6 + 4747561509943 * q^7 + 9964333994280 * q^8 + 160137547184727 * q^9 - 472777770164028 * q^10 + 135879674344284 * q^11 - 10527962746508244 * q^12 + 12138994948536170 * q^13 + 41283438444318630 * q^14 + 13687032584892438 * q^15 + 1300607396354614288 * q^16 - 385869676567281066 * q^17 + 1392510356733476070 * q^18 + 726075641163594644 * q^19 + 8133031378709443032 * q^20 - 22707439527650560767 * q^21 - 40013549861901162600 * q^22 + 81623233895572110192 * q^23 - 47659100600287417320 * q^24 - 344687932818137236151 * q^25 + 557803893676418715300 * q^26 - 765932923920586514463 * q^27 + 1492860866289666291124 * q^28 + 2523262928009462965506 * q^29 + 2261281418583670839132 * q^30 + 3097457398331417166752 * q^31 + 3797011810352053176480 * q^32 - 649908270118805699196 * q^33 + 63335711497801752433500 * q^34 - 1940815693747992252198 * q^35 + 50354919449703789296436 * q^36 + 12145140799949814343466 * q^37 - 108697233906951781953720 * q^38 - 58060436530005096488730 * q^39 - 475320691810097154363216 * q^40 - 262433505631892547251154 * q^41 - 197457406292584233412470 * q^42 - 193139951479227114687580 * q^43 - 2430431685366465708769488 * q^44 - 65464652555530399288422 * q^45 - 6981072827049021325022880 * q^46 - 1146871717647137318395248 * q^47 - 6220764857934833146461072 * q^48 + 3219905755813179726837607 * q^49 + 4481749443828030876391386 * q^50 + 1845602701061331752964954 * q^51 + 1236271786388417967514040 * q^52 - 6665695659633633475901814 * q^53 - 6660333868435157305051830 * q^54 + 5317495916141118544489032 * q^55 + 6758041220494331589303720 * q^56 - 3472797283340597110818036 * q^57 - 19887500189096257342540140 * q^58 + 252077122803863627555062380 * q^59 - 38900036960394526029322008 * q^60 + 286844596551467198960110586 * q^61 + 655482484647841866799404480 * q^62 + 108608979330127274981177223 * q^63 + 523821984648801603783498304 * q^64 + 677830247031279033073631964 * q^65 + 191383568569427541779759400 * q^66 - 21966489249761249366283412 * q^67 - 230093364489444117467612568 * q^68 - 390401397402270640312920048 * q^69 - 320648792055345340923275772 * q^70 + 236873286033551829517504320 * q^71 + 227952000739056108131623080 * q^72 + 1436061741885259500381870806 * q^73 - 3275022628978202210175964380 * q^74 + 1648631697343233038255912319 * q^75 - 4562877250128321487477927888 * q^76 + 92156730271501723638745116 * q^77 - 2667958731533606746299725700 * q^78 + 442695609959843509130102048 * q^79 + 7254106132718389061591220192 * q^80 + 3663433431191523760494580647 * q^81 + 4421292535141977509208500940 * q^82 + 4700059828307966195559697476 * q^83 - 7140307244776618890791067156 * q^84 - 13424791113423208631620606908 * q^85 + 12752722226530676548320081000 * q^86 - 12068688363518493070663267314 * q^87 + 4553745967919270581660489440 * q^88 + 52994579350095331884835317486 * q^89 - 10815638925361721529772342908 * q^90 + 8232946455294689831821448330 * q^91 + 54926079962260892072539429536 * q^92 - 14815042715039820034642646688 * q^93 - 26892181494551465508576501600 * q^94 - 74456487258213633048885368328 * q^95 - 18160989781547749429455369120 * q^96 + 74985775395694126905639860942 * q^97 + 27999380479478321424657876870 * q^98 + 3108491108821873976277792924 * q^99

Introduction

L-functions

Modular forms

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