LMFDB - Embedded newform 21.30.a.c.1.5

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			1.5
Root			$-6093.44$ 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)

$f(q)$	$=$	$q+20882.9 q^{2} -4.78297e6 q^{3} -1.00776e8 q^{4} -7.49509e9 q^{5} -9.98822e10 q^{6} +6.78223e11 q^{7} -1.33159e13 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q+20882.9 q^{2} -4.78297e6 q^{3} -1.00776e8 q^{4} -7.49509e9 q^{5} -9.98822e10 q^{6} +6.78223e11 q^{7} -1.33159e13 q^{8} +2.28768e13 q^{9} -1.56519e14 q^{10} +1.86927e15 q^{11} +4.82010e14 q^{12} -1.18400e16 q^{13} +1.41632e16 q^{14} +3.58488e16 q^{15} -2.23971e17 q^{16} -5.24569e17 q^{17} +4.77733e17 q^{18} -3.74134e18 q^{19} +7.55328e17 q^{20} -3.24392e18 q^{21} +3.90358e19 q^{22} -6.15693e19 q^{23} +6.36896e19 q^{24} -1.30088e20 q^{25} -2.47253e20 q^{26} -1.09419e20 q^{27} -6.83489e19 q^{28} -2.31332e21 q^{29} +7.48625e20 q^{30} +5.54242e21 q^{31} +2.47177e21 q^{32} -8.94068e21 q^{33} -1.09545e22 q^{34} -5.08334e21 q^{35} -2.30544e21 q^{36} +7.11445e22 q^{37} -7.81300e22 q^{38} +5.66302e22 q^{39} +9.98039e22 q^{40} -7.27141e22 q^{41} -6.77424e22 q^{42} -8.73297e23 q^{43} -1.88379e23 q^{44} -1.71464e23 q^{45} -1.28574e24 q^{46} +3.11079e24 q^{47} +1.07124e24 q^{48} +4.59987e23 q^{49} -2.71662e24 q^{50} +2.50900e24 q^{51} +1.19319e24 q^{52} +9.30877e24 q^{53} -2.28498e24 q^{54} -1.40104e25 q^{55} -9.03116e24 q^{56} +1.78947e25 q^{57} -4.83088e25 q^{58} +6.67667e25 q^{59} -3.61271e24 q^{60} +9.98143e25 q^{61} +1.15742e26 q^{62} +1.55156e25 q^{63} +1.71861e26 q^{64} +8.87416e25 q^{65} -1.86707e26 q^{66} +3.21812e26 q^{67} +5.28642e25 q^{68} +2.94484e26 q^{69} -1.06155e26 q^{70} -1.09406e27 q^{71} -3.04625e26 q^{72} +6.92677e26 q^{73} +1.48570e27 q^{74} +6.22208e26 q^{75} +3.77039e26 q^{76} +1.26778e27 q^{77} +1.18260e27 q^{78} -3.20253e27 q^{79} +1.67868e27 q^{80} +5.23348e26 q^{81} -1.51848e27 q^{82} -7.17951e26 q^{83} +3.26910e26 q^{84} +3.93169e27 q^{85} -1.82370e28 q^{86} +1.10645e28 q^{87} -2.48911e28 q^{88} +1.19260e28 q^{89} -3.58065e27 q^{90} -8.03014e27 q^{91} +6.20473e27 q^{92} -2.65092e28 q^{93} +6.49622e28 q^{94} +2.80417e28 q^{95} -1.18224e28 q^{96} -9.45294e28 q^{97} +9.60584e27 q^{98} +4.27630e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	20882.9	0.901271	0.450635	−	0.892708i	$-0.351197\pi$
$2$	20882.9	0.901271	0.450635	+	0.892708i	$0.351197\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	−1.00776e8	−0.187711
$5$	−7.49509e9	−0.549176	−0.274588	−	0.961562i	$-0.588541\pi$
$5$	−7.49509e9	−0.549176	−0.274588	+	0.961562i	$0.588541\pi$
$6$	−9.98822e10	−0.520349
$7$	6.78223e11	0.377964
$7$	6.78223e11	0.377964
$8$	−1.33159e13	−1.07045
$9$	2.28768e13	0.333333
$10$	−1.56519e14	−0.494956
$11$	1.86927e15	1.48415	0.742077	−	0.670314i	$-0.233841\pi$
$11$	1.86927e15	1.48415	0.742077	+	0.670314i	$0.233841\pi$
$12$	4.82010e14	0.108375
$13$	−1.18400e16	−0.834011	−0.417006	−	0.908904i	$-0.636920\pi$
$13$	−1.18400e16	−0.834011	−0.417006	+	0.908904i	$0.636920\pi$
$14$	1.41632e16	0.340648
$15$	3.58488e16	0.317067
$16$	−2.23971e17	−0.777054
$17$	−5.24569e17	−0.755602	−0.377801	−	0.925887i	$-0.623320\pi$
$17$	−5.24569e17	−0.755602	−0.377801	+	0.925887i	$0.623320\pi$
$18$	4.77733e17	0.300424
$19$	−3.74134e18	−1.07424	−0.537119	−	0.843507i	$-0.680487\pi$
$19$	−3.74134e18	−1.07424	−0.537119	+	0.843507i	$0.680487\pi$
$20$	7.55328e17	0.103086
$21$	−3.24392e18	−0.218218
$22$	3.90358e19	1.33763
$23$	−6.15693e19	−1.10742	−0.553708	−	0.832711i	$-0.686788\pi$
$23$	−6.15693e19	−1.10742	−0.553708	+	0.832711i	$0.686788\pi$
$24$	6.36896e19	0.618024
$25$	−1.30088e20	−0.698406
$26$	−2.47253e20	−0.751670
$27$	−1.09419e20	−0.192450
$28$	−6.83489e19	−0.0709479
$29$	−2.31332e21	−1.44366	−0.721830	−	0.692071i	$-0.756699\pi$
$29$	−2.31332e21	−1.44366	−0.721830	+	0.692071i	$0.756699\pi$
$30$	7.48625e20	0.285763
$31$	5.54242e21	1.31509	0.657544	−	0.753416i	$-0.271595\pi$
$31$	5.54242e21	1.31509	0.657544	+	0.753416i	$0.271595\pi$
$32$	2.47177e21	0.370113
$33$	−8.94068e21	−0.856877
$34$	−1.09545e22	−0.681003
$35$	−5.08334e21	−0.207569
$36$	−2.30544e21	−0.0625702
$37$	7.11445e22	1.29783	0.648913	−	0.760863i	$-0.275224\pi$
$37$	7.11445e22	1.29783	0.648913	+	0.760863i	$0.275224\pi$
$38$	−7.81300e22	−0.968179
$39$	5.66302e22	0.481517
$40$	9.98039e22	0.587865
$41$	−7.27141e22	−0.299401	−0.149700	−	0.988731i	$-0.547831\pi$
$41$	−7.27141e22	−0.299401	−0.149700	+	0.988731i	$0.547831\pi$
$42$	−6.77424e22	−0.196673
$43$	−8.73297e23	−1.80248	−0.901238	−	0.433324i	$-0.857341\pi$
$43$	−8.73297e23	−1.80248	−0.901238	+	0.433324i	$0.857341\pi$
$44$	−1.88379e23	−0.278592
$45$	−1.71464e23	−0.183059
$46$	−1.28574e24	−0.998082
$47$	3.11079e24	1.76788	0.883938	−	0.467605i	$-0.154883\pi$
$47$	3.11079e24	1.76788	0.883938	+	0.467605i	$0.154883\pi$
$48$	1.07124e24	0.448632
$49$	4.59987e23	0.142857
$50$	−2.71662e24	−0.629453
$51$	2.50900e24	0.436247
$52$	1.19319e24	0.156553
$53$	9.30877e24	0.926599	0.463300	−	0.886202i	$-0.346665\pi$
$53$	9.30877e24	0.926599	0.463300	+	0.886202i	$0.346665\pi$
$54$	−2.28498e24	−0.173450
$55$	−1.40104e25	−0.815062
$56$	−9.03116e24	−0.404592
$57$	1.78947e25	0.620211
$58$	−4.83088e25	−1.30113
$59$	6.67667e25	1.40348	0.701739	−	0.712434i	$-0.252407\pi$
$59$	6.67667e25	1.40348	0.701739	+	0.712434i	$0.252407\pi$
$60$	−3.61271e24	−0.0595168
$61$	9.98143e25	1.29393	0.646964	−	0.762521i	$-0.276038\pi$
$61$	9.98143e25	1.29393	0.646964	+	0.762521i	$0.276038\pi$
$62$	1.15742e26	1.18525
$63$	1.55156e25	0.125988
$64$	1.71861e26	1.11063
$65$	8.87416e25	0.458019
$66$	−1.86707e26	−0.772278
$67$	3.21812e26	1.07033	0.535165	−	0.844747i	$-0.320249\pi$
$67$	3.21812e26	1.07033	0.535165	+	0.844747i	$0.320249\pi$
$68$	5.28642e25	0.141835
$69$	2.94484e26	0.639367
$70$	−1.06155e26	−0.187076
$71$	−1.09406e27	−1.56963	−0.784813	−	0.619733i	$-0.787241\pi$
$71$	−1.09406e27	−1.56963	−0.784813	+	0.619733i	$0.787241\pi$
$72$	−3.04625e26	−0.356816
$73$	6.92677e26	0.664277	0.332138	−	0.943231i	$-0.392230\pi$
$73$	6.92677e26	0.664277	0.332138	+	0.943231i	$0.392230\pi$
$74$	1.48570e27	1.16969
$75$	6.22208e26	0.403225
$76$	3.77039e26	0.201646
$77$	1.26778e27	0.560958
$78$	1.18260e27	0.433977
$79$	−3.20253e27	−0.977014	−0.488507	−	0.872560i	$-0.662458\pi$
$79$	−3.20253e27	−0.977014	−0.488507	+	0.872560i	$0.662458\pi$
$80$	1.67868e27	0.426739
$81$	5.23348e26	0.111111
$82$	−1.51848e27	−0.269841
$83$	−7.17951e26	−0.107019	−0.0535097	−	0.998567i	$-0.517041\pi$
$83$	−7.17951e26	−0.107019	−0.0535097	+	0.998567i	$0.517041\pi$
$84$	3.26910e26	0.0409618
$85$	3.93169e27	0.414959
$86$	−1.82370e28	−1.62452
$87$	1.10645e28	0.833497
$88$	−2.48911e28	−1.58871
$89$	1.19260e28	0.646162	0.323081	−	0.946371i	$-0.395281\pi$
$89$	1.19260e28	0.646162	0.323081	+	0.946371i	$0.395281\pi$
$90$	−3.58065e27	−0.164985
$91$	−8.03014e27	−0.315227
$92$	6.20473e27	0.207874
$93$	−2.65092e28	−0.759267
$94$	6.49622e28	1.59333
$95$	2.80417e28	0.589945
$96$	−1.18224e28	−0.213685
$97$	−9.45294e28	−1.47020	−0.735101	−	0.677958i	$-0.762865\pi$
$97$	−9.45294e28	−1.47020	−0.735101	+	0.677958i	$0.762865\pi$
$98$	9.60584e27	0.128753
$99$	4.27630e28	0.494718
$100$	1.31098e28	0.131098
$101$	−1.46638e29	−1.26937	−0.634683	−	0.772773i	$-0.718869\pi$
$101$	−1.46638e29	−1.26937	−0.634683	+	0.772773i	$0.718869\pi$
$102$	5.23951e28	0.393177
$103$	1.71781e29	1.11901	0.559507	−	0.828826i	$-0.310991\pi$
$103$	1.71781e29	1.11901	0.559507	+	0.828826i	$0.310991\pi$
$104$	1.57660e29	0.892767
$105$	2.43135e28	0.119840
$106$	1.94394e29	0.835117
$107$	−8.58763e28	−0.321965	−0.160982	−	0.986957i	$-0.551466\pi$
$107$	−8.58763e28	−0.321965	−0.160982	+	0.986957i	$0.551466\pi$
$108$	1.10268e28	0.0361249
$109$	−7.63934e28	−0.218963	−0.109482	−	0.993989i	$-0.534919\pi$
$109$	−7.63934e28	−0.218963	−0.109482	+	0.993989i	$0.534919\pi$
$110$	−2.92577e29	−0.734592
$111$	−3.40282e29	−0.749300
$112$	−1.51902e29	−0.293699
$113$	8.15067e29	1.38534	0.692669	−	0.721255i	$-0.256435\pi$
$113$	8.15067e29	1.38534	0.692669	+	0.721255i	$0.256435\pi$
$114$	3.73693e29	0.558978
$115$	4.61467e29	0.608166
$116$	2.33128e29	0.270990
$117$	−2.70861e29	−0.278004
$118$	1.39428e30	1.26491
$119$	−3.55775e29	−0.285591
$120$	−4.77359e29	−0.339404
$121$	1.90788e30	1.20271
$122$	2.08441e30	1.16618
$123$	3.47789e29	0.172859
$124$	−5.58545e29	−0.246856
$125$	2.37109e30	0.932724
$126$	3.24010e29	0.113549
$127$	4.87035e30	1.52197	0.760985	−	0.648770i	$-0.224716\pi$
$127$	4.87035e30	1.52197	0.760985	+	0.648770i	$0.224716\pi$
$128$	2.26193e30	0.630862
$129$	4.17695e30	1.04066
$130$	1.85318e30	0.412799
$131$	−5.93848e30	−1.18370	−0.591850	−	0.806048i	$-0.701602\pi$
$131$	−5.93848e30	−1.18370	−0.591850	+	0.806048i	$0.701602\pi$
$132$	9.01009e29	0.160845
$133$	−2.53746e30	−0.406023
$134$	6.72036e30	0.964658
$135$	8.20105e29	0.105689
$136$	6.98511e30	0.808834
$137$	1.53250e31	1.59570	0.797851	−	0.602855i	$-0.205970\pi$
$137$	1.53250e31	1.59570	0.797851	+	0.602855i	$0.205970\pi$
$138$	6.14968e30	0.576243
$139$	−3.55635e29	−0.0300116	−0.0150058	−	0.999887i	$-0.504777\pi$
$139$	−3.55635e29	−0.0300116	−0.0150058	+	0.999887i	$0.504777\pi$
$140$	5.12281e29	0.0389629
$141$	−1.48788e31	−1.02068
$142$	−2.28472e31	−1.41466
$143$	−2.21321e31	−1.23780
$144$	−5.12373e30	−0.259018
$145$	1.73385e31	0.792823
$146$	1.44651e31	0.598694
$147$	−2.20010e30	−0.0824786
$148$	−7.16969e30	−0.243616
$149$	2.06084e31	0.635101	0.317550	−	0.948241i	$-0.397140\pi$
$149$	2.06084e31	0.635101	0.317550	+	0.948241i	$0.397140\pi$
$150$	1.29935e31	0.363415
$151$	3.13180e31	0.795479	0.397740	−	0.917498i	$-0.369795\pi$
$151$	3.13180e31	0.795479	0.397740	+	0.917498i	$0.369795\pi$
$152$	4.98194e31	1.14992
$153$	−1.20005e31	−0.251867
$154$	2.64750e31	0.505575
$155$	−4.15409e31	−0.722215
$156$	−5.70699e30	−0.0903858
$157$	1.04672e32	1.51107	0.755535	−	0.655108i	$-0.227377\pi$
$157$	1.04672e32	1.51107	0.755535	+	0.655108i	$0.227377\pi$
$158$	−6.68781e31	−0.880554
$159$	−4.45235e31	−0.534972
$160$	−1.85262e31	−0.203257
$161$	−4.17577e31	−0.418564
$162$	1.09290e31	0.100141
$163$	4.66532e31	0.390986	0.195493	−	0.980705i	$-0.437369\pi$
$163$	4.66532e31	0.390986	0.195493	+	0.980705i	$0.437369\pi$
$164$	7.32786e30	0.0562007
$165$	6.70112e31	0.470576
$166$	−1.49929e31	−0.0964535
$167$	1.02569e32	0.604821	0.302410	−	0.953178i	$-0.402209\pi$
$167$	1.02569e32	0.604821	0.302410	+	0.953178i	$0.402209\pi$
$168$	4.31957e31	0.233591
$169$	−6.13532e31	−0.304425
$170$	8.21050e31	0.373990
$171$	−8.55899e31	−0.358079
$172$	8.80078e31	0.338344
$173$	3.74933e32	1.32521	0.662605	−	0.748969i	$-0.269451\pi$
$173$	3.74933e32	1.32521	0.662605	+	0.748969i	$0.269451\pi$
$174$	2.31059e32	0.751207
$175$	−8.82288e31	−0.263973
$176$	−4.18662e32	−1.15327
$177$	−3.19343e32	−0.810298
$178$	2.49050e32	0.582367
$179$	−6.82498e32	−1.47141	−0.735703	−	0.677304i	$-0.763148\pi$
$179$	−6.82498e32	−1.47141	−0.735703	+	0.677304i	$0.763148\pi$
$180$	1.72795e31	0.0343621
$181$	3.82358e32	0.701666	0.350833	−	0.936438i	$-0.385898\pi$
$181$	3.82358e32	0.701666	0.350833	+	0.936438i	$0.385898\pi$
$182$	−1.67692e32	−0.284105
$183$	−4.77409e32	−0.747050
$184$	8.19852e32	1.18543
$185$	−5.33234e32	−0.712735
$186$	−5.53589e32	−0.684305
$187$	−9.80563e32	−1.12143
$188$	−3.13494e32	−0.331849
$189$	−7.42105e31	−0.0727393
$190$	5.85591e32	0.531700
$191$	−1.28426e33	−1.08061	−0.540304	−	0.841470i	$-0.681691\pi$
$191$	−1.28426e33	−1.08061	−0.540304	+	0.841470i	$0.681691\pi$
$192$	−8.22006e32	−0.641220
$193$	−1.16221e33	−0.840818	−0.420409	−	0.907335i	$-0.638113\pi$
$193$	−1.16221e33	−0.840818	−0.420409	+	0.907335i	$0.638113\pi$
$194$	−1.97405e33	−1.32505
$195$	−4.24448e32	−0.264437
$196$	−4.63558e31	−0.0268158
$197$	−6.70165e32	−0.360099	−0.180049	−	0.983658i	$-0.557626\pi$
$197$	−6.70165e32	−0.360099	−0.180049	+	0.983658i	$0.557626\pi$
$198$	8.93014e32	0.445875
$199$	−3.13429e32	−0.145469	−0.0727343	−	0.997351i	$-0.523173\pi$
$199$	−3.13429e32	−0.145469	−0.0727343	+	0.997351i	$0.523173\pi$
$200$	1.73224e33	0.747608
$201$	−1.53922e33	−0.617955
$202$	−3.06222e33	−1.14404
$203$	−1.56895e33	−0.545652
$204$	−2.52848e32	−0.0818882
$205$	5.44998e32	0.164424
$206$	3.58728e33	1.00853
$207$	−1.40851e33	−0.369139
$208$	2.65181e33	0.648072
$209$	−6.99359e33	−1.59433
$210$	5.07735e32	0.108008
$211$	3.04944e33	0.605514	0.302757	−	0.953068i	$-0.402093\pi$
$211$	3.04944e33	0.605514	0.302757	+	0.953068i	$0.402093\pi$
$212$	−9.38104e32	−0.173933
$213$	5.23287e33	0.906224
$214$	−1.79334e33	−0.290178
$215$	6.54544e33	0.989877
$216$	1.45701e33	0.206008
$217$	3.75900e33	0.497057
$218$	−1.59531e33	−0.197345
$219$	−3.31305e33	−0.383520
$220$	1.41191e33	0.152996
$221$	6.21088e33	0.630181
$222$	−7.10607e33	−0.675322
$223$	8.66178e32	0.0771235	0.0385617	−	0.999256i	$-0.487722\pi$
$223$	8.66178e32	0.0771235	0.0385617	+	0.999256i	$0.487722\pi$
$224$	1.67641e33	0.139889
$225$	−2.97600e33	−0.232802
$226$	1.70209e34	1.24857
$227$	−5.11378e33	−0.351858	−0.175929	−	0.984403i	$-0.556293\pi$
$227$	−5.11378e33	−0.351858	−0.175929	+	0.984403i	$0.556293\pi$
$228$	−1.80336e33	−0.116420
$229$	2.66384e34	1.61396	0.806981	−	0.590577i	$-0.201100\pi$
$229$	2.66384e34	1.61396	0.806981	+	0.590577i	$0.201100\pi$
$230$	9.63677e33	0.548123
$231$	−6.06378e33	−0.323869
$232$	3.08040e34	1.54536
$233$	−1.32196e34	−0.623101	−0.311551	−	0.950230i	$-0.600848\pi$
$233$	−1.32196e34	−0.623101	−0.311551	+	0.950230i	$0.600848\pi$
$234$	−5.65635e33	−0.250557
$235$	−2.33156e34	−0.970875
$236$	−6.72850e33	−0.263448
$237$	1.53176e34	0.564079
$238$	−7.42960e33	−0.257395
$239$	2.85089e34	0.929417	0.464709	−	0.885464i	$-0.346159\pi$
$239$	2.85089e34	0.929417	0.464709	+	0.885464i	$0.346159\pi$
$240$	−8.02907e33	−0.246378
$241$	2.06600e34	0.596874	0.298437	−	0.954429i	$-0.403535\pi$
$241$	2.06600e34	0.596874	0.298437	+	0.954429i	$0.403535\pi$
$242$	3.98419e34	1.08397
$243$	−2.50316e33	−0.0641500
$244$	−1.00589e34	−0.242884
$245$	−3.44764e33	−0.0784537
$246$	7.26284e33	0.155793
$247$	4.42974e34	0.895926
$248$	−7.38024e34	−1.40774
$249$	3.43394e33	0.0617877
$250$	4.95152e34	0.840637
$251$	5.83252e34	0.934517	0.467258	−	0.884121i	$-0.345242\pi$
$251$	5.83252e34	0.934517	0.467258	+	0.884121i	$0.345242\pi$
$252$	−1.56360e33	−0.0236493
$253$	−1.15090e35	−1.64358
$254$	1.01707e35	1.37171
$255$	−1.88052e34	−0.239577
$256$	−4.50316e34	−0.542048
$257$	−6.45531e34	−0.734323	−0.367162	−	0.930157i	$-0.619670\pi$
$257$	−6.45531e34	−0.734323	−0.367162	+	0.930157i	$0.619670\pi$
$258$	8.72268e34	0.937917
$259$	4.82518e34	0.490532
$260$	−8.94306e33	−0.0859750
$261$	−5.29213e34	−0.481220
$262$	−1.24013e35	−1.06683
$263$	−2.50069e34	−0.203564	−0.101782	−	0.994807i	$-0.532454\pi$
$263$	−2.50069e34	−0.203564	−0.101782	+	0.994807i	$0.532454\pi$
$264$	1.19053e35	0.917243
$265$	−6.97700e34	−0.508866
$266$	−5.29895e34	−0.365937
$267$	−5.70419e34	−0.373062
$268$	−3.24311e34	−0.200912
$269$	1.60023e35	0.939234	0.469617	−	0.882870i	$-0.344392\pi$
$269$	1.60023e35	0.939234	0.469617	+	0.882870i	$0.344392\pi$
$270$	1.71261e34	0.0952544
$271$	−6.58380e34	−0.347074	−0.173537	−	0.984827i	$-0.555520\pi$
$271$	−6.58380e34	−0.347074	−0.173537	+	0.984827i	$0.555520\pi$
$272$	1.17488e35	0.587144
$273$	3.84079e34	0.181996
$274$	3.20030e35	1.43816
$275$	−2.43171e35	−1.03654
$276$	−2.96770e34	−0.120016
$277$	−3.49022e35	−1.33936	−0.669678	−	0.742651i	$-0.733568\pi$
$277$	−3.49022e35	−1.33936	−0.669678	+	0.742651i	$0.733568\pi$
$278$	−7.42668e33	−0.0270486
$279$	1.26793e35	0.438363
$280$	6.76893e34	0.222192
$281$	1.59964e35	0.498633	0.249317	−	0.968422i	$-0.419794\pi$
$281$	1.59964e35	0.498633	0.249317	+	0.968422i	$0.419794\pi$
$282$	−3.10712e35	−0.919912
$283$	−3.97233e35	−1.11723	−0.558614	−	0.829428i	$-0.688667\pi$
$283$	−3.97233e35	−1.11723	−0.558614	+	0.829428i	$0.688667\pi$
$284$	1.10256e35	0.294635
$285$	−1.34122e35	−0.340605
$286$	−4.62183e35	−1.11559
$287$	−4.93164e34	−0.113163
$288$	5.65463e34	0.123371
$289$	−2.06796e35	−0.429065
$290$	3.62078e35	0.714548
$291$	4.52131e35	0.848821
$292$	−6.98055e34	−0.124692
$293$	1.76818e35	0.300571	0.150286	−	0.988643i	$-0.451981\pi$
$293$	1.76818e35	0.300571	0.150286	+	0.988643i	$0.451981\pi$
$294$	−4.59444e34	−0.0743356
$295$	−5.00422e35	−0.770756
$296$	−9.47354e35	−1.38926
$297$	−2.04534e35	−0.285626
$298$	4.30362e35	0.572398
$299$	7.28979e35	0.923598
$300$	−6.27039e34	−0.0756896
$301$	−5.92291e35	−0.681272
$302$	6.54011e35	0.716942
$303$	7.01365e35	0.732868
$304$	8.37950e35	0.834740
$305$	−7.48117e35	−0.710594
$306$	−2.50604e35	−0.227001
$307$	−1.35114e36	−1.16733	−0.583664	−	0.811995i	$-0.698381\pi$
$307$	−1.35114e36	−1.16733	−0.583664	+	0.811995i	$0.698381\pi$
$308$	−1.27763e35	−0.105298
$309$	−8.21623e35	−0.646063
$310$	−8.67494e35	−0.650912
$311$	−1.16879e36	−0.836973	−0.418487	−	0.908223i	$-0.637439\pi$
$311$	−1.16879e36	−0.836973	−0.418487	+	0.908223i	$0.637439\pi$
$312$	−7.54083e35	−0.515439
$313$	1.23118e36	0.803392	0.401696	−	0.915773i	$-0.368421\pi$
$313$	1.23118e36	0.803392	0.401696	+	0.915773i	$0.368421\pi$
$314$	2.18585e36	1.36188
$315$	−1.16291e35	−0.0691897
$316$	3.22740e35	0.183396
$317$	5.42375e35	0.294402	0.147201	−	0.989107i	$-0.452974\pi$
$317$	5.42375e35	0.294402	0.147201	+	0.989107i	$0.452974\pi$
$318$	−9.29780e35	−0.482155
$319$	−4.32423e36	−2.14261
$320$	−1.28811e36	−0.609929
$321$	4.10744e35	0.185886
$322$	−8.72022e35	−0.377239
$323$	1.96259e36	0.811696
$324$	−5.27411e34	−0.0208567
$325$	1.54024e36	0.582478
$326$	9.74252e35	0.352384
$327$	3.65387e35	0.126419
$328$	9.68255e35	0.320493
$329$	2.10981e36	0.668194
$330$	1.39939e36	0.424117
$331$	3.75074e36	1.08796	0.543978	−	0.839100i	$-0.316918\pi$
$331$	3.75074e36	1.08796	0.543978	+	0.839100i	$0.316918\pi$
$332$	7.23525e34	0.0200887
$333$	1.62756e36	0.432609
$334$	2.14193e36	0.545107
$335$	−2.41201e36	−0.587800
$336$	7.26543e35	0.169567
$337$	−4.58919e36	−1.02589	−0.512947	−	0.858420i	$-0.671446\pi$
$337$	−4.58919e36	−1.02589	−0.512947	+	0.858420i	$0.671446\pi$
$338$	−1.28123e36	−0.274369
$339$	−3.89844e36	−0.799826
$340$	−3.96221e35	−0.0778922
$341$	1.03603e37	1.95179
$342$	−1.78736e36	−0.322726
$343$	3.11973e35	0.0539949
$344$	1.16288e37	1.92946
$345$	−2.20718e36	−0.351125
$346$	7.82967e36	1.19437
$347$	−5.95136e36	−0.870640	−0.435320	−	0.900276i	$-0.643365\pi$
$347$	−5.95136e36	−0.870640	−0.435320	+	0.900276i	$0.643365\pi$
$348$	−1.11504e36	−0.156456
$349$	1.38536e37	1.86464	0.932318	−	0.361639i	$-0.117783\pi$
$349$	1.38536e37	1.86464	0.932318	+	0.361639i	$0.117783\pi$
$350$	−1.84247e36	−0.237911
$351$	1.29552e36	0.160506
$352$	4.62042e36	0.549305
$353$	1.09061e37	1.24433	0.622166	−	0.782885i	$-0.286253\pi$
$353$	1.09061e37	1.24433	0.622166	+	0.782885i	$0.286253\pi$
$354$	−6.66880e36	−0.730298
$355$	8.20009e36	0.862001
$356$	−1.20186e36	−0.121291
$357$	1.70166e36	0.164886
$358$	−1.42525e37	−1.32614
$359$	7.58827e36	0.678068	0.339034	−	0.940774i	$-0.389900\pi$
$359$	7.58827e36	0.678068	0.339034	+	0.940774i	$0.389900\pi$
$360$	2.28319e36	0.195955
$361$	1.86781e36	0.153985
$362$	7.98473e36	0.632391
$363$	−9.12531e36	−0.694387
$364$	8.09248e35	0.0591714
$365$	−5.19167e36	−0.364805
$366$	−9.96967e36	−0.673294
$367$	1.12685e37	0.731490	0.365745	−	0.930715i	$-0.380814\pi$
$367$	1.12685e37	0.731490	0.365745	+	0.930715i	$0.380814\pi$
$368$	1.37897e37	0.860522
$369$	−1.66347e36	−0.0998002
$370$	−1.11355e37	−0.642367
$371$	6.31342e36	0.350222
$372$	2.67150e36	0.142522
$373$	−3.28474e37	−1.68548	−0.842738	−	0.538324i	$-0.819058\pi$
$373$	−3.28474e37	−1.68548	−0.842738	+	0.538324i	$0.819058\pi$
$374$	−2.04770e37	−1.01071
$375$	−1.13409e37	−0.538508
$376$	−4.14230e37	−1.89242
$377$	2.73896e37	1.20403
$378$	−1.54973e36	−0.0655578
$379$	1.44955e37	0.590152	0.295076	−	0.955474i	$-0.404655\pi$
$379$	1.44955e37	0.590152	0.295076	+	0.955474i	$0.404655\pi$
$380$	−2.82594e36	−0.110739
$381$	−2.32947e37	−0.878709
$382$	−2.68190e37	−0.973920
$383$	−3.76949e37	−1.31795	−0.658977	−	0.752163i	$-0.729011\pi$
$383$	−3.76949e37	−1.31795	−0.658977	+	0.752163i	$0.729011\pi$
$384$	−1.08187e37	−0.364228
$385$	−9.50216e36	−0.308064
$386$	−2.42702e37	−0.757805
$387$	−1.99782e37	−0.600825
$388$	9.52633e36	0.275972
$389$	−4.79896e36	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$389$	−4.79896e36	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$390$	−8.86370e36	−0.238330
$391$	3.22974e37	0.836766
$392$	−6.12514e36	−0.152921
$393$	2.84036e37	0.683409
$394$	−1.39950e37	−0.324547
$395$	2.40033e37	0.536553
$396$	−4.30950e36	−0.0928638
$397$	2.00819e37	0.417197	0.208599	−	0.978001i	$-0.433110\pi$
$397$	2.00819e37	0.417197	0.208599	+	0.978001i	$0.433110\pi$
$398$	−6.54529e36	−0.131107
$399$	1.21366e37	0.234418
$400$	2.91359e37	0.542699
$401$	5.79112e37	1.04033	0.520163	−	0.854067i	$-0.325871\pi$
$401$	5.79112e37	1.04033	0.520163	+	0.854067i	$0.325871\pi$
$402$	−3.21433e37	−0.556945
$403$	−6.56221e37	−1.09680
$404$	1.47776e37	0.238273
$405$	−3.92254e36	−0.0610196
$406$	−3.27641e37	−0.491780
$407$	1.32989e38	1.92617
$408$	−3.34096e37	−0.466980
$409$	−2.60563e37	−0.351500	−0.175750	−	0.984435i	$-0.556235\pi$
$409$	−2.60563e37	−0.351500	−0.175750	+	0.984435i	$0.556235\pi$
$410$	1.13811e37	0.148190
$411$	−7.32989e37	−0.921279
$412$	−1.73115e37	−0.210051
$413$	4.52827e37	0.530465
$414$	−2.94137e37	−0.332694
$415$	5.38110e36	0.0587725
$416$	−2.92657e37	−0.308678
$417$	1.70099e36	0.0173272
$418$	−1.46046e38	−1.43693
$419$	1.39557e38	1.32632	0.663158	−	0.748479i	$-0.269216\pi$
$419$	1.39557e38	1.32632	0.663158	+	0.748479i	$0.269216\pi$
$420$	−2.45022e36	−0.0224952
$421$	−1.56212e38	−1.38555	−0.692776	−	0.721153i	$-0.743612\pi$
$421$	−1.56212e38	−1.38555	−0.692776	+	0.721153i	$0.743612\pi$
$422$	6.36811e37	0.545733
$423$	7.11649e37	0.589292
$424$	−1.23955e38	−0.991878
$425$	6.82403e37	0.527717
$426$	1.09277e38	0.816753
$427$	6.76963e37	0.489059
$428$	8.65430e36	0.0604362
$429$	1.05857e38	0.714645
$430$	1.36688e38	0.892147
$431$	1.54546e38	0.975301	0.487650	−	0.873039i	$-0.337854\pi$
$431$	1.54546e38	0.975301	0.487650	+	0.873039i	$0.337854\pi$
$432$	2.45066e37	0.149544
$433$	−1.08440e38	−0.639903	−0.319952	−	0.947434i	$-0.603667\pi$
$433$	−1.08440e38	−0.639903	−0.319952	+	0.947434i	$0.603667\pi$
$434$	7.84987e37	0.447983
$435$	−8.29296e37	−0.457737
$436$	7.69865e36	0.0411018
$437$	2.30352e38	1.18963
$438$	−6.91861e37	−0.345656
$439$	−1.98487e38	−0.959395	−0.479698	−	0.877434i	$-0.659254\pi$
$439$	−1.98487e38	−0.959395	−0.479698	+	0.877434i	$0.659254\pi$
$440$	1.86561e38	0.872482
$441$	1.05230e37	0.0476190
$442$	1.29701e38	0.567964
$443$	−4.12888e38	−1.74976	−0.874880	−	0.484339i	$-0.839060\pi$
$443$	−4.12888e38	−1.74976	−0.874880	+	0.484339i	$0.839060\pi$
$444$	3.42924e37	0.140652
$445$	−8.93867e37	−0.354857
$446$	1.80883e37	0.0695091
$447$	−9.85692e37	−0.366676
$448$	1.16560e38	0.419777
$449$	7.09442e37	0.247369	0.123684	−	0.992322i	$-0.460529\pi$
$449$	7.09442e37	0.247369	0.123684	+	0.992322i	$0.460529\pi$
$450$	−6.21475e37	−0.209818
$451$	−1.35923e38	−0.444357
$452$	−8.21395e37	−0.260043
$453$	−1.49793e38	−0.459270
$454$	−1.06790e38	−0.317119
$455$	6.01866e37	0.173115
$456$	−2.38284e38	−0.663904
$457$	4.03215e38	1.08831	0.544154	−	0.838985i	$-0.316851\pi$
$457$	4.03215e38	1.08831	0.544154	+	0.838985i	$0.316851\pi$
$458$	5.56286e38	1.45462
$459$	5.73978e37	0.145416
$460$	−4.65050e37	−0.114159
$461$	4.71756e38	1.12216	0.561079	−	0.827762i	$-0.310386\pi$
$461$	4.71756e38	1.12216	0.561079	+	0.827762i	$0.310386\pi$
$462$	−1.26629e38	−0.291894
$463$	5.25235e38	1.17336	0.586678	−	0.809821i	$-0.300436\pi$
$463$	5.25235e38	1.17336	0.586678	+	0.809821i	$0.300436\pi$
$464$	5.18116e38	1.12180
$465$	1.98689e38	0.416971
$466$	−2.76064e38	−0.561583
$467$	1.94638e38	0.383824	0.191912	−	0.981412i	$-0.438531\pi$
$467$	1.94638e38	0.383824	0.191912	+	0.981412i	$0.438531\pi$
$468$	2.72963e37	0.0521843
$469$	2.18260e38	0.404547
$470$	−4.86897e38	−0.875021
$471$	−5.00642e38	−0.872417
$472$	−8.89059e38	−1.50235
$473$	−1.63243e39	−2.67515
$474$	3.19876e38	0.508388
$475$	4.86704e38	0.750253
$476$	3.58537e37	0.0536084
$477$	2.12955e38	0.308866
$478$	5.95348e38	0.837657
$479$	1.26476e39	1.72640	0.863200	−	0.504862i	$-0.168457\pi$
$479$	1.26476e39	1.72640	0.863200	+	0.504862i	$0.168457\pi$
$480$	8.86100e37	0.117351
$481$	−8.42349e38	−1.08240
$482$	4.31440e38	0.537946
$483$	1.99726e38	0.241658
$484$	−1.92269e38	−0.225762
$485$	7.08506e38	0.807399
$486$	−5.22731e37	−0.0578166
$487$	−6.30765e38	−0.677170	−0.338585	−	0.940936i	$-0.609948\pi$
$487$	−6.30765e38	−0.677170	−0.338585	+	0.940936i	$0.609948\pi$
$488$	−1.32912e39	−1.38508
$489$	−2.23141e38	−0.225736
$490$	−7.19966e37	−0.0707081
$491$	1.84947e39	1.76346	0.881729	−	0.471757i	$-0.156380\pi$
$491$	1.84947e39	1.76346	0.881729	+	0.471757i	$0.156380\pi$
$492$	−3.50489e37	−0.0324475
$493$	1.21350e39	1.09083
$494$	9.25056e38	0.807472
$495$	−3.20512e38	−0.271687
$496$	−1.24134e39	−1.02190
$497$	−7.42018e38	−0.593263
$498$	7.17105e37	0.0556874
$499$	−1.46464e39	−1.10477	−0.552386	−	0.833589i	$-0.686282\pi$
$499$	−1.46464e39	−1.10477	−0.552386	+	0.833589i	$0.686282\pi$
$500$	−2.38950e38	−0.175082
$501$	−4.90583e38	−0.349193
$502$	1.21800e39	0.842253
$503$	−2.14682e39	−1.44231	−0.721157	−	0.692771i	$-0.756390\pi$
$503$	−2.14682e39	−1.44231	−0.721157	+	0.692771i	$0.756390\pi$
$504$	−2.06604e38	−0.134864
$505$	1.09906e39	0.697105
$506$	−2.40341e39	−1.48131
$507$	2.93451e38	0.175760
$508$	−4.90816e38	−0.285690
$509$	−1.79503e39	−1.01546	−0.507731	−	0.861516i	$-0.669516\pi$
$509$	−1.79503e39	−1.01546	−0.507731	+	0.861516i	$0.669516\pi$
$510$	−3.92706e38	−0.215923
$511$	4.69789e38	0.251073
$512$	−2.15475e39	−1.11939
$513$	4.09374e38	0.206737
$514$	−1.34806e39	−0.661824
$515$	−1.28751e39	−0.614535
$516$	−4.20938e38	−0.195343
$517$	5.81492e39	2.62380
$518$	1.00764e39	0.442102
$519$	−1.79329e39	−0.765110
$520$	−1.18167e39	−0.490286
$521$	1.34078e37	0.00541016	0.00270508	−	0.999996i	$-0.499139\pi$
$521$	1.34078e37	0.00541016	0.00270508	+	0.999996i	$0.499139\pi$
$522$	−1.10515e39	−0.433709
$523$	−2.97328e38	−0.113491	−0.0567454	−	0.998389i	$-0.518072\pi$
$523$	−2.97328e38	−0.113491	−0.0567454	+	0.998389i	$0.518072\pi$
$524$	5.98458e38	0.222193
$525$	4.21996e38	0.152405
$526$	−5.22215e38	−0.183466
$527$	−2.90738e39	−0.993684
$528$	2.00245e39	0.665840
$529$	6.99724e38	0.226370
$530$	−1.45700e39	−0.458626
$531$	1.52741e39	0.467826
$532$	2.55716e38	0.0762149
$533$	8.60933e38	0.249704
$534$	−1.19120e39	−0.336230
$535$	6.43650e38	0.176815
$536$	−4.28522e39	−1.14573
$537$	3.26437e39	0.849517
$538$	3.34174e39	0.846505
$539$	8.59841e38	0.212022
$540$	−8.26472e37	−0.0198389
$541$	8.03740e36	0.00187826	0.000939129	−	1.00000i	$-0.499701\pi$
$541$	8.03740e36	0.00187826	0.000939129		1.00000i	$0.499701\pi$
$542$	−1.37489e39	−0.312807
$543$	−1.82881e39	−0.405107
$544$	−1.29662e39	−0.279658
$545$	5.72575e38	0.120249
$546$	8.02068e38	0.164028
$547$	2.88570e39	0.574691	0.287345	−	0.957827i	$-0.407227\pi$
$547$	2.88570e39	0.574691	0.287345	+	0.957827i	$0.407227\pi$
$548$	−1.54440e39	−0.299530
$549$	2.28343e39	0.431309
$550$	−5.07810e39	−0.934205
$551$	8.65492e39	1.55083
$552$	−3.92132e39	−0.684410
$553$	−2.17203e39	−0.369277
$554$	−7.28858e39	−1.20712
$555$	2.55044e39	0.411498
$556$	3.58396e37	0.00563350
$557$	4.07056e39	0.623381	0.311690	−	0.950184i	$-0.399105\pi$
$557$	4.07056e39	0.623381	0.311690	+	0.950184i	$0.399105\pi$
$558$	2.64780e39	0.395084
$559$	1.03398e40	1.50329
$560$	1.13852e39	0.161292
$561$	4.69000e39	0.647458
$562$	3.34051e39	0.449404
$563$	−1.46109e39	−0.191560	−0.0957799	−	0.995403i	$-0.530535\pi$
$563$	−1.46109e39	−0.191560	−0.0957799	+	0.995403i	$0.530535\pi$
$564$	1.49943e39	0.191593
$565$	−6.10900e39	−0.760795
$566$	−8.29537e39	−1.00693
$567$	3.54946e38	0.0419961
$568$	1.45684e40	1.68020
$569$	5.18249e39	0.582654	0.291327	−	0.956624i	$-0.405903\pi$
$569$	5.18249e39	0.582654	0.291327	+	0.956624i	$0.405903\pi$
$570$	−2.80086e39	−0.306977
$571$	1.24896e40	1.33452	0.667258	−	0.744827i	$-0.267468\pi$
$571$	1.24896e40	1.33452	0.667258	+	0.744827i	$0.267468\pi$
$572$	2.23040e39	0.232349
$573$	6.14256e39	0.623889
$574$	−1.02987e39	−0.101990
$575$	8.00944e39	0.773426
$576$	3.93163e39	0.370209
$577$	−1.20166e40	−1.10340	−0.551700	−	0.834043i	$-0.686021\pi$
$577$	−1.20166e40	−1.10340	−0.551700	+	0.834043i	$0.686021\pi$
$578$	−4.31849e39	−0.386704
$579$	5.55879e39	0.485446
$580$	−1.74731e39	−0.148821
$581$	−4.86931e38	−0.0404495
$582$	9.44180e39	0.765018
$583$	1.74006e40	1.37522
$584$	−9.22362e39	−0.711075
$585$	2.03012e39	0.152673
$586$	3.69248e39	0.270896
$587$	1.30946e40	0.937214	0.468607	−	0.883407i	$-0.344756\pi$
$587$	1.30946e40	0.937214	0.468607	+	0.883407i	$0.344756\pi$
$588$	2.21718e38	0.0154821
$589$	−2.07361e40	−1.41272
$590$	−1.04502e40	−0.694660
$591$	3.20538e39	0.207903
$592$	−1.59343e40	−1.00848
$593$	1.68004e40	1.03759	0.518795	−	0.854899i	$-0.326381\pi$
$593$	1.68004e40	1.03759	0.518795	+	0.854899i	$0.326381\pi$
$594$	−4.27126e39	−0.257426
$595$	2.66656e39	0.156840
$596$	−2.07684e39	−0.119215
$597$	1.49912e39	0.0839863
$598$	1.52232e40	0.832412
$599$	−1.04485e40	−0.557654	−0.278827	−	0.960341i	$-0.589946\pi$
$599$	−1.04485e40	−0.557654	−0.278827	+	0.960341i	$0.589946\pi$
$600$	−8.28526e39	−0.431632
$601$	−1.79999e40	−0.915358	−0.457679	−	0.889117i	$-0.651319\pi$
$601$	−1.79999e40	−0.915358	−0.457679	+	0.889117i	$0.651319\pi$
$602$	−1.23687e40	−0.614011
$603$	7.36203e39	0.356777
$604$	−3.15612e39	−0.149320
$605$	−1.42997e40	−0.660502
$606$	1.46465e40	0.660513
$607$	8.24979e39	0.363251	0.181626	−	0.983368i	$-0.441864\pi$
$607$	8.24979e39	0.363251	0.181626	+	0.983368i	$0.441864\pi$
$608$	−9.24775e39	−0.397589
$609$	7.50422e39	0.315032
$610$	−1.56228e40	−0.640438
$611$	−3.68316e40	−1.47443
$612$	1.20936e39	0.0472782
$613$	−1.37097e40	−0.523421	−0.261711	−	0.965146i	$-0.584287\pi$
$613$	−1.37097e40	−0.523421	−0.261711	+	0.965146i	$0.584287\pi$
$614$	−2.82156e40	−1.05208
$615$	−2.60671e39	−0.0949300
$616$	−1.68817e40	−0.600477
$617$	−3.86816e39	−0.134391	−0.0671954	−	0.997740i	$-0.521405\pi$
$617$	−3.86816e39	−0.134391	−0.0671954	+	0.997740i	$0.521405\pi$
$618$	−1.71578e40	−0.582277
$619$	1.57216e40	0.521175	0.260587	−	0.965450i	$-0.416084\pi$
$619$	1.57216e40	0.521175	0.260587	+	0.965450i	$0.416084\pi$
$620$	4.18634e39	0.135567
$621$	6.73685e39	0.213122
$622$	−2.44077e40	−0.754340
$623$	8.08852e39	0.244226
$624$	−1.26835e40	−0.374165
$625$	6.45929e39	0.186176
$626$	2.57105e40	0.724074
$627$	3.34501e40	0.920489
$628$	−1.05484e40	−0.283644
$629$	−3.73202e40	−0.980640
$630$	−2.42848e39	−0.0623586
$631$	−2.39390e38	−0.00600732	−0.00300366	−	0.999995i	$-0.500956\pi$
$631$	−2.39390e38	−0.00600732	−0.00300366	+	0.999995i	$0.500956\pi$
$632$	4.26446e40	1.04584
$633$	−1.45854e40	−0.349594
$634$	1.13264e40	0.265336
$635$	−3.65037e40	−0.835829
$636$	4.48692e39	0.100420
$637$	−5.44623e39	−0.119144
$638$	−9.03023e40	−1.93107
$639$	−2.50286e40	−0.523208
$640$	−1.69534e40	−0.346454
$641$	3.04687e40	0.608713	0.304356	−	0.952558i	$-0.401559\pi$
$641$	3.04687e40	0.608713	0.304356	+	0.952558i	$0.401559\pi$
$642$	8.57751e39	0.167534
$643$	−3.60085e40	−0.687617	−0.343808	−	0.939040i	$-0.611717\pi$
$643$	−3.60085e40	−0.687617	−0.343808	+	0.939040i	$0.611717\pi$
$644$	4.20819e39	0.0785689
$645$	−3.13066e40	−0.571506
$646$	4.09846e40	0.731558
$647$	−3.90406e40	−0.681403	−0.340701	−	0.940172i	$-0.610665\pi$
$647$	−3.90406e40	−0.681403	−0.340701	+	0.940172i	$0.610665\pi$
$648$	−6.96885e39	−0.118939
$649$	1.24805e41	2.08298
$650$	3.21647e40	0.524971
$651$	−1.79792e40	−0.286976
$652$	−4.70154e39	−0.0733921
$653$	4.57246e40	0.698086	0.349043	−	0.937107i	$-0.386507\pi$
$653$	4.57246e40	0.698086	0.349043	+	0.937107i	$0.386507\pi$
$654$	7.63034e39	0.113937
$655$	4.45094e40	0.650059
$656$	1.62858e40	0.232651
$657$	1.58462e40	0.221426
$658$	4.40589e40	0.602224
$659$	8.41440e39	0.112508	0.0562542	−	0.998416i	$-0.482084\pi$
$659$	8.41440e39	0.112508	0.0562542	+	0.998416i	$0.482084\pi$
$660$	−6.75314e39	−0.0883321
$661$	−1.25211e41	−1.60222	−0.801110	−	0.598517i	$-0.795757\pi$
$661$	−1.25211e41	−1.60222	−0.801110	+	0.598517i	$0.795757\pi$
$662$	7.83263e40	0.980543
$663$	−2.97065e40	−0.363835
$664$	9.56017e39	0.114559
$665$	1.90185e40	0.222978
$666$	3.39881e40	0.389898
$667$	1.42430e41	1.59873
$668$	−1.03365e40	−0.113531
$669$	−4.14290e39	−0.0445272
$670$	−5.03697e40	−0.529767
$671$	1.86580e41	1.92039
$672$	−8.01824e39	−0.0807652
$673$	−6.52790e40	−0.643510	−0.321755	−	0.946823i	$-0.604273\pi$
$673$	−6.52790e40	−0.643510	−0.321755	+	0.946823i	$0.604273\pi$
$674$	−9.58355e40	−0.924608
$675$	1.42341e40	0.134408
$676$	6.18296e39	0.0571438
$677$	−1.08438e40	−0.0980943	−0.0490472	−	0.998796i	$-0.515618\pi$
$677$	−1.08438e40	−0.0980943	−0.0490472	+	0.998796i	$0.515618\pi$
$678$	−8.14107e40	−0.720860
$679$	−6.41120e40	−0.555684
$680$	−5.23540e40	−0.444192
$681$	2.44591e40	0.203145
$682$	2.16353e41	1.75910
$683$	7.76700e40	0.618234	0.309117	−	0.951024i	$-0.399967\pi$
$683$	7.76700e40	0.618234	0.309117	+	0.951024i	$0.399967\pi$
$684$	8.62544e39	0.0672152
$685$	−1.14862e41	−0.876321
$686$	6.51490e39	0.0486641
$687$	−1.27411e41	−0.931822
$688$	1.95593e41	1.40062
$689$	−1.10216e41	−0.772794
$690$	−4.60924e40	−0.316459
$691$	1.88679e40	0.126850	0.0634252	−	0.997987i	$-0.479798\pi$
$691$	1.88679e40	0.126850	0.0634252	+	0.997987i	$0.479798\pi$
$692$	−3.77843e40	−0.248756
$693$	2.90028e40	0.186986
$694$	−1.24281e41	−0.784682
$695$	2.66551e39	0.0164817
$696$	−1.47334e41	−0.892216
$697$	3.81436e40	0.226228
$698$	2.89303e41	1.68054
$699$	6.32291e40	0.359748
$700$	8.89138e39	0.0495505
$701$	4.89077e39	0.0266972	0.0133486	−	0.999911i	$-0.495751\pi$
$701$	4.89077e39	0.0266972	0.0133486	+	0.999911i	$0.495751\pi$
$702$	2.70541e40	0.144659
$703$	−2.66176e41	−1.39417
$704$	3.21255e41	1.64834
$705$	1.11518e41	0.560535
$706$	2.27751e41	1.12148
$707$	−9.94533e40	−0.479775
$708$	3.21822e40	0.152102
$709$	−3.78526e41	−1.75277	−0.876386	−	0.481610i	$-0.840052\pi$
$709$	−3.78526e41	−1.75277	−0.876386	+	0.481610i	$0.840052\pi$
$710$	1.71241e41	0.776896
$711$	−7.32637e40	−0.325671
$712$	−1.58806e41	−0.691684
$713$	−3.41243e41	−1.45635
$714$	3.55356e40	0.148607
$715$	1.65882e41	0.679771
$716$	6.87797e40	0.276199
$717$	−1.36357e41	−0.536599
$718$	1.58465e41	0.611123
$719$	8.90637e40	0.336614	0.168307	−	0.985735i	$-0.446170\pi$
$719$	8.90637e40	0.336614	0.168307	+	0.985735i	$0.446170\pi$
$720$	3.84028e40	0.142246
$721$	1.16506e41	0.422947
$722$	3.90053e40	0.138782
$723$	−9.88161e40	−0.344606
$724$	−3.85326e40	−0.131710
$725$	3.00936e41	1.00826
$726$	−1.90563e41	−0.625831
$727$	−2.89312e41	−0.931358	−0.465679	−	0.884954i	$-0.654190\pi$
$727$	−2.89312e41	−0.931358	−0.465679	+	0.884954i	$0.654190\pi$
$728$	1.06929e41	0.337434
$729$	1.19725e40	0.0370370
$730$	−1.08417e41	−0.328788
$731$	4.58105e41	1.36196
$732$	4.81115e40	0.140229
$733$	2.26822e40	0.0648152	0.0324076	−	0.999475i	$-0.489683\pi$
$733$	2.26822e40	0.0648152	0.0324076	+	0.999475i	$0.489683\pi$
$734$	2.35319e41	0.659270
$735$	1.64899e40	0.0452953
$736$	−1.52185e41	−0.409869
$737$	6.01555e41	1.58854
$738$	−3.47379e40	−0.0899470
$739$	3.46093e41	0.878716	0.439358	−	0.898312i	$-0.355206\pi$
$739$	3.46093e41	0.878716	0.439358	+	0.898312i	$0.355206\pi$
$740$	5.37374e40	0.133788
$741$	−2.11873e41	−0.517263
$742$	1.31842e41	0.315645
$743$	−2.34110e40	−0.0549644	−0.0274822	−	0.999622i	$-0.508749\pi$
$743$	−2.34110e40	−0.0549644	−0.0274822	+	0.999622i	$0.508749\pi$
$744$	3.52995e41	0.812756
$745$	−1.54461e41	−0.348782
$746$	−6.85947e41	−1.51907
$747$	−1.64244e40	−0.0356731
$748$	9.88176e40	0.210504
$749$	−5.82433e40	−0.121691
$750$	−2.36830e41	−0.485342
$751$	−6.73727e41	−1.35427	−0.677134	−	0.735860i	$-0.736778\pi$
$751$	−6.73727e41	−1.35427	−0.677134	+	0.735860i	$0.736778\pi$
$752$	−6.96725e41	−1.37373
$753$	−2.78967e41	−0.539543
$754$	5.71974e41	1.08516
$755$	−2.34731e41	−0.436858
$756$	7.47866e39	0.0136539
$757$	−8.16891e41	−1.46310	−0.731549	−	0.681788i	$-0.761202\pi$
$757$	−8.16891e41	−1.46310	−0.731549	+	0.681788i	$0.761202\pi$
$758$	3.02707e41	0.531887
$759$	5.50472e41	0.948919
$760$	−3.73400e41	−0.631506
$761$	2.32824e40	0.0386322	0.0193161	−	0.999813i	$-0.493851\pi$
$761$	2.32824e40	0.0386322	0.0193161	+	0.999813i	$0.493851\pi$
$762$	−4.86461e41	−0.791955
$763$	−5.18118e40	−0.0827604
$764$	1.29423e41	0.202842
$765$	8.99445e40	0.138320
$766$	−7.87178e41	−1.18783
$767$	−7.90515e41	−1.17052
$768$	2.15385e41	0.312952
$769$	7.73435e41	1.10279	0.551394	−	0.834245i	$-0.314096\pi$
$769$	7.73435e41	1.10279	0.551394	+	0.834245i	$0.314096\pi$
$770$	−1.98432e41	−0.277650
$771$	3.08756e41	0.423962
$772$	1.17123e41	0.157830
$773$	−4.01238e41	−0.530640	−0.265320	−	0.964160i	$-0.585478\pi$
$773$	−4.01238e41	−0.530640	−0.265320	+	0.964160i	$0.585478\pi$
$774$	−4.17203e41	−0.541507
$775$	−7.21004e41	−0.918465
$776$	1.25875e42	1.57378
$777$	−2.30787e41	−0.283209
$778$	−1.00216e41	−0.120707
$779$	2.72048e41	0.321627
$780$	4.27744e40	0.0496377
$781$	−2.04510e42	−2.32957
$782$	6.74462e41	0.754153
$783$	2.53121e41	0.277832
$784$	−1.03023e41	−0.111008
$785$	−7.84524e41	−0.829844
$786$	5.93148e41	0.615937
$787$	−1.31316e42	−1.33870	−0.669352	−	0.742946i	$-0.733428\pi$
$787$	−1.31316e42	−1.33870	−0.669352	+	0.742946i	$0.733428\pi$
$788$	6.75368e40	0.0675944
$789$	1.19607e41	0.117528
$790$	5.01257e41	0.483579
$791$	5.52797e41	0.523609
$792$	−5.69428e41	−0.529571
$793$	−1.18180e42	−1.07915
$794$	4.19367e41	0.376008
$795$	3.33708e41	0.293794
$796$	3.15862e40	0.0273060
$797$	1.45661e42	1.23651	0.618253	−	0.785979i	$-0.287841\pi$
$797$	1.45661e42	1.23651	0.618253	+	0.785979i	$0.287841\pi$
$798$	2.53447e41	0.211274
$799$	−1.63182e42	−1.33581
$800$	−3.21549e41	−0.258489
$801$	2.72830e41	0.215387
$802$	1.20935e42	0.937615
$803$	1.29480e42	0.985890
$804$	1.55117e41	0.115997
$805$	3.12978e41	0.229865
$806$	−1.37038e42	−0.988513
$807$	−7.65384e41	−0.542267
$808$	1.95262e42	1.35879
$809$	−1.51641e42	−1.03648	−0.518242	−	0.855234i	$-0.673413\pi$
$809$	−1.51641e42	−1.03648	−0.518242	+	0.855234i	$0.673413\pi$
$810$	−8.19138e40	−0.0549952
$811$	1.87643e42	1.23745	0.618727	−	0.785606i	$-0.287649\pi$
$811$	1.87643e42	1.23745	0.618727	+	0.785606i	$0.287649\pi$
$812$	1.58113e41	0.102425
$813$	3.14901e41	0.200383
$814$	2.77718e42	1.73600
$815$	−3.49669e41	−0.214720
$816$	−5.61942e41	−0.338988
$817$	3.26730e42	1.93629
$818$	−5.44131e41	−0.316797
$819$	−1.83704e41	−0.105076
$820$	−5.49230e40	−0.0308641
$821$	−4.12509e40	−0.0227750	−0.0113875	−	0.999935i	$-0.503625\pi$
$821$	−4.12509e40	−0.0227750	−0.0113875	+	0.999935i	$0.503625\pi$
$822$	−1.53069e42	−0.830322
$823$	5.58620e41	0.297728	0.148864	−	0.988858i	$-0.452438\pi$
$823$	5.58620e41	0.297728	0.148864	+	0.988858i	$0.452438\pi$
$824$	−2.28742e42	−1.19785
$825$	1.16308e42	0.598448
$826$	9.45633e41	0.478092
$827$	−2.85723e41	−0.141943	−0.0709716	−	0.997478i	$-0.522610\pi$
$827$	−2.85723e41	−0.141943	−0.0709716	+	0.997478i	$0.522610\pi$
$828$	1.41944e41	0.0692912
$829$	2.60760e42	1.25084	0.625418	−	0.780290i	$-0.284928\pi$
$829$	2.60760e42	1.25084	0.625418	+	0.780290i	$0.284928\pi$
$830$	1.12373e41	0.0529699
$831$	1.66936e42	0.773278
$832$	−2.03483e42	−0.926275
$833$	−2.41295e41	−0.107943
$834$	3.55216e40	0.0156165
$835$	−7.68762e41	−0.332153
$836$	7.04789e41	0.299273
$837$	−6.06446e41	−0.253089
$838$	2.91435e42	1.19537
$839$	4.32393e42	1.74313	0.871567	−	0.490277i	$-0.163104\pi$
$839$	4.32393e42	1.74313	0.871567	+	0.490277i	$0.163104\pi$
$840$	−3.23756e41	−0.128283
$841$	2.78376e42	1.08415
$842$	−3.26215e42	−1.24876
$843$	−7.65104e41	−0.287886
$844$	−3.07312e41	−0.113662
$845$	4.59848e41	0.167183
$846$	1.48613e42	0.531112
$847$	1.29397e42	0.454583
$848$	−2.08489e42	−0.720018
$849$	1.89995e42	0.645032
$850$	1.42505e42	0.475616
$851$	−4.38032e42	−1.43723
$852$	−5.27349e41	−0.170108
$853$	−1.72043e42	−0.545603	−0.272802	−	0.962070i	$-0.587950\pi$
$853$	−1.72043e42	−0.545603	−0.272802	+	0.962070i	$0.587950\pi$
$854$	1.41369e42	0.440774
$855$	6.41504e41	0.196648
$856$	1.14352e42	0.344647
$857$	−2.82835e41	−0.0838129	−0.0419064	−	0.999122i	$-0.513343\pi$
$857$	−2.82835e41	−0.0838129	−0.0419064	+	0.999122i	$0.513343\pi$
$858$	2.21061e42	0.644089
$859$	−2.70090e42	−0.773761	−0.386880	−	0.922130i	$-0.626447\pi$
$859$	−2.70090e42	−0.773761	−0.386880	+	0.922130i	$0.626447\pi$
$860$	−6.59626e41	−0.185810
$861$	2.35879e41	0.0653346
$862$	3.22737e42	0.879010
$863$	2.78753e42	0.746557	0.373279	−	0.927719i	$-0.378234\pi$
$863$	2.78753e42	0.746557	0.373279	+	0.927719i	$0.378234\pi$
$864$	−2.70459e41	−0.0712282
$865$	−2.81015e42	−0.727773
$866$	−2.26454e42	−0.576726
$867$	9.89098e41	0.247721
$868$	−3.78818e41	−0.0933028
$869$	−5.98641e42	−1.45004
$870$	−1.73181e42	−0.412545
$871$	−3.81025e42	−0.892668
$872$	1.01725e42	0.234389
$873$	−2.16253e42	−0.490067
$874$	4.81041e42	1.07218
$875$	1.60813e42	0.352536
$876$	3.33877e41	0.0719909
$877$	4.15717e42	0.881666	0.440833	−	0.897589i	$-0.354683\pi$
$877$	4.15717e42	0.881666	0.440833	+	0.897589i	$0.354683\pi$
$878$	−4.14499e42	−0.864675
$879$	−8.45717e41	−0.173535
$880$	3.13791e42	0.633347
$881$	3.72860e41	0.0740278	0.0370139	−	0.999315i	$-0.488215\pi$
$881$	3.72860e41	0.0740278	0.0370139	+	0.999315i	$0.488215\pi$
$882$	2.19751e41	0.0429177
$883$	−7.55130e42	−1.45075	−0.725373	−	0.688356i	$-0.758333\pi$
$883$	−7.55130e42	−1.45075	−0.725373	+	0.688356i	$0.758333\pi$
$884$	−6.25910e41	−0.118292
$885$	2.39350e42	0.444996
$886$	−8.62230e42	−1.57701
$887$	2.86252e42	0.515058	0.257529	−	0.966271i	$-0.417092\pi$
$887$	2.86252e42	0.515058	0.257529	+	0.966271i	$0.417092\pi$
$888$	4.53116e42	0.802088
$889$	3.30318e42	0.575250
$890$	−1.86665e42	−0.319822
$891$	9.78280e41	0.164906
$892$	−8.72902e40	−0.0144769
$893$	−1.16385e43	−1.89912
$894$	−2.05841e42	−0.330474
$895$	5.11538e42	0.808061
$896$	1.53409e42	0.238444
$897$	−3.48668e42	−0.533239
$898$	1.48152e42	0.222946
$899$	−1.28214e43	−1.89854
$900$	2.99911e41	0.0436994
$901$	−4.88309e42	−0.700141
$902$	−2.83846e42	−0.400486
$903$	2.83291e42	0.393333
$904$	−1.08534e43	−1.48293
$905$	−2.86580e42	−0.385338
$906$	−3.12811e42	−0.413927
$907$	6.68953e42	0.871143	0.435572	−	0.900154i	$-0.356546\pi$
$907$	6.68953e42	0.871143	0.435572	+	0.900154i	$0.356546\pi$
$908$	5.15348e41	0.0660475
$909$	−3.35461e42	−0.423122
$910$	1.25687e42	0.156023
$911$	−9.11052e42	−1.11308	−0.556540	−	0.830821i	$-0.687872\pi$
$911$	−9.11052e42	−1.11308	−0.556540	+	0.830821i	$0.687872\pi$
$912$	−4.00789e42	−0.481938
$913$	−1.34205e42	−0.158833
$914$	8.42029e42	0.980861
$915$	3.57822e42	0.410262
$916$	−2.68452e42	−0.302958
$917$	−4.02761e42	−0.447396
$918$	1.19863e42	0.131059
$919$	7.03531e41	0.0757196	0.0378598	−	0.999283i	$-0.487946\pi$
$919$	7.03531e41	0.0757196	0.0378598	+	0.999283i	$0.487946\pi$
$920$	−6.14486e42	−0.651011
$921$	6.46244e42	0.673957
$922$	9.85162e42	1.01137
$923$	1.29537e43	1.30909
$924$	6.11085e41	0.0607937
$925$	−9.25506e42	−0.906409
$926$	1.09684e43	1.05751
$927$	3.92980e42	0.373004
$928$	−5.71800e42	−0.534317
$929$	6.00158e42	0.552125	0.276063	−	0.961140i	$-0.410970\pi$
$929$	6.00158e42	0.552125	0.276063	+	0.961140i	$0.410970\pi$
$930$	4.14920e42	0.375804
$931$	−1.72097e42	−0.153462
$932$	1.33223e42	0.116963
$933$	5.59029e42	0.483227
$934$	4.06460e42	0.345930
$935$	7.34941e42	0.615863
$936$	3.60675e42	0.297589
$937$	−1.84109e42	−0.149572	−0.0747860	−	0.997200i	$-0.523827\pi$
$937$	−1.84109e42	−0.149572	−0.0747860	+	0.997200i	$0.523827\pi$
$938$	4.55791e42	0.364606
$939$	−5.88868e42	−0.463839
$940$	2.34966e42	0.182243
$941$	7.92439e42	0.605224	0.302612	−	0.953114i	$-0.402141\pi$
$941$	7.92439e42	0.605224	0.302612	+	0.953114i	$0.402141\pi$
$942$	−1.04548e43	−0.786284
$943$	4.47696e42	0.331561
$944$	−1.49538e43	−1.09058
$945$	5.56214e41	0.0399467
$946$	−3.40899e43	−2.41104
$947$	8.46746e42	0.589764	0.294882	−	0.955534i	$-0.404720\pi$
$947$	8.46746e42	0.589764	0.294882	+	0.955534i	$0.404720\pi$
$948$	−1.54365e42	−0.105884
$949$	−8.20127e42	−0.554015
$950$	1.01638e43	0.676182
$951$	−2.59416e42	−0.169973
$952$	4.73747e42	0.305710
$953$	−2.82094e42	−0.179286	−0.0896430	−	0.995974i	$-0.528573\pi$
$953$	−2.82094e42	−0.179286	−0.0896430	+	0.995974i	$0.528573\pi$
$954$	4.44711e42	0.278372
$955$	9.62562e42	0.593444
$956$	−2.87302e42	−0.174461
$957$	2.06826e43	1.23704
$958$	2.64117e43	1.55595
$959$	1.03938e43	0.603118
$960$	6.16101e42	0.352143
$961$	1.29566e43	0.729458
$962$	−1.75907e43	−0.975537
$963$	−1.96457e42	−0.107322
$964$	−2.08204e42	−0.112040
$965$	8.71083e42	0.461757
$966$	4.17085e42	0.217799
$967$	−3.14881e43	−1.61980	−0.809902	−	0.586565i	$-0.800480\pi$
$967$	−3.14881e43	−1.61980	−0.809902	+	0.586565i	$0.800480\pi$
$968$	−2.54051e43	−1.28744
$969$	−9.38702e42	−0.468633
$970$	1.47956e43	0.727686
$971$	1.26507e43	0.612966	0.306483	−	0.951876i	$-0.400848\pi$
$971$	1.26507e43	0.612966	0.306483	+	0.951876i	$0.400848\pi$
$972$	2.52259e41	0.0120416
$973$	−2.41200e41	−0.0113433
$974$	−1.31722e43	−0.610313
$975$	−7.36692e42	−0.336294
$976$	−2.23555e43	−1.00545
$977$	3.07708e43	1.36354	0.681770	−	0.731567i	$-0.261211\pi$
$977$	3.07708e43	1.36354	0.681770	+	0.731567i	$0.261211\pi$
$978$	−4.65982e42	−0.203449
$979$	2.22930e43	0.959004
$980$	3.47440e41	0.0147266
$981$	−1.74764e42	−0.0729878
$982$	3.86222e43	1.58935
$983$	3.44195e43	1.39566	0.697829	−	0.716264i	$-0.254149\pi$
$983$	3.44195e43	1.39566	0.697829	+	0.716264i	$0.254149\pi$
$984$	−4.63113e42	−0.185037
$985$	5.02295e42	0.197758
$986$	2.53413e43	0.983135
$987$	−1.00911e43	−0.385782
$988$	−4.46413e42	−0.168175
$989$	5.37683e43	1.99609
$990$	−6.69322e42	−0.244864
$991$	3.77112e43	1.35957	0.679787	−	0.733410i	$-0.262072\pi$
$991$	3.77112e43	1.35957	0.679787	+	0.733410i	$0.262072\pi$
$992$	1.36996e43	0.486731
$993$	−1.79397e43	−0.628131
$994$	−1.54955e43	−0.534690
$995$	2.34917e42	0.0798878
$996$	−3.46060e41	−0.0115982
$997$	−5.93117e43	−1.95912	−0.979559	−	0.201157i	$-0.935530\pi$
$997$	−5.93117e43	−1.95912	−0.979559	+	0.201157i	$0.935530\pi$
$998$	−3.05859e43	−0.995699
$999$	−7.78456e42	−0.249767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.c.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+20882.9 q^{2} -4.78297e6 q^{3} -1.00776e8 q^{4} -7.49509e9 q^{5} -9.98822e10 q^{6} +6.78223e11 q^{7} -1.33159e13 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q+20882.9 q^{2} -4.78297e6 q^{3} -1.00776e8 q^{4} -7.49509e9 q^{5} -9.98822e10 q^{6} +6.78223e11 q^{7} -1.33159e13 q^{8} +2.28768e13 q^{9} -1.56519e14 q^{10} +1.86927e15 q^{11} +4.82010e14 q^{12} -1.18400e16 q^{13} +1.41632e16 q^{14} +3.58488e16 q^{15} -2.23971e17 q^{16} -5.24569e17 q^{17} +4.77733e17 q^{18} -3.74134e18 q^{19} +7.55328e17 q^{20} -3.24392e18 q^{21} +3.90358e19 q^{22} -6.15693e19 q^{23} +6.36896e19 q^{24} -1.30088e20 q^{25} -2.47253e20 q^{26} -1.09419e20 q^{27} -6.83489e19 q^{28} -2.31332e21 q^{29} +7.48625e20 q^{30} +5.54242e21 q^{31} +2.47177e21 q^{32} -8.94068e21 q^{33} -1.09545e22 q^{34} -5.08334e21 q^{35} -2.30544e21 q^{36} +7.11445e22 q^{37} -7.81300e22 q^{38} +5.66302e22 q^{39} +9.98039e22 q^{40} -7.27141e22 q^{41} -6.77424e22 q^{42} -8.73297e23 q^{43} -1.88379e23 q^{44} -1.71464e23 q^{45} -1.28574e24 q^{46} +3.11079e24 q^{47} +1.07124e24 q^{48} +4.59987e23 q^{49} -2.71662e24 q^{50} +2.50900e24 q^{51} +1.19319e24 q^{52} +9.30877e24 q^{53} -2.28498e24 q^{54} -1.40104e25 q^{55} -9.03116e24 q^{56} +1.78947e25 q^{57} -4.83088e25 q^{58} +6.67667e25 q^{59} -3.61271e24 q^{60} +9.98143e25 q^{61} +1.15742e26 q^{62} +1.55156e25 q^{63} +1.71861e26 q^{64} +8.87416e25 q^{65} -1.86707e26 q^{66} +3.21812e26 q^{67} +5.28642e25 q^{68} +2.94484e26 q^{69} -1.06155e26 q^{70} -1.09406e27 q^{71} -3.04625e26 q^{72} +6.92677e26 q^{73} +1.48570e27 q^{74} +6.22208e26 q^{75} +3.77039e26 q^{76} +1.26778e27 q^{77} +1.18260e27 q^{78} -3.20253e27 q^{79} +1.67868e27 q^{80} +5.23348e26 q^{81} -1.51848e27 q^{82} -7.17951e26 q^{83} +3.26910e26 q^{84} +3.93169e27 q^{85} -1.82370e28 q^{86} +1.10645e28 q^{87} -2.48911e28 q^{88} +1.19260e28 q^{89} -3.58065e27 q^{90} -8.03014e27 q^{91} +6.20473e27 q^{92} -2.65092e28 q^{93} +6.49622e28 q^{94} +2.80417e28 q^{95} -1.18224e28 q^{96} -9.45294e28 q^{97} +9.60584e27 q^{98} +4.27630e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9}+O(q^{10}) \) 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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