LMFDB - Embedded newform 21.30.a.c.1.6

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			1.6
Root			$-13495.0$ 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)

$f(q)$	$=$	$q+35686.0 q^{2} -4.78297e6 q^{3} +7.36619e8 q^{4} -1.68211e10 q^{5} -1.70685e11 q^{6} +6.78223e11 q^{7} +7.12823e12 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q+35686.0 q^{2} -4.78297e6 q^{3} +7.36619e8 q^{4} -1.68211e10 q^{5} -1.70685e11 q^{6} +6.78223e11 q^{7} +7.12823e12 q^{8} +2.28768e13 q^{9} -6.00279e14 q^{10} -1.93651e15 q^{11} -3.52323e15 q^{12} -2.08320e16 q^{13} +2.42031e16 q^{14} +8.04549e16 q^{15} -1.41092e17 q^{16} +5.41261e17 q^{17} +8.16381e17 q^{18} +5.47941e18 q^{19} -1.23908e19 q^{20} -3.24392e18 q^{21} -6.91064e19 q^{22} +3.62573e19 q^{23} -3.40941e19 q^{24} +9.66858e19 q^{25} -7.43411e20 q^{26} -1.09419e20 q^{27} +4.99592e20 q^{28} +1.12792e21 q^{29} +2.87111e21 q^{30} +3.33644e21 q^{31} -8.86194e21 q^{32} +9.26229e21 q^{33} +1.93154e22 q^{34} -1.14085e22 q^{35} +1.68515e22 q^{36} -4.41363e22 q^{37} +1.95538e23 q^{38} +9.96388e22 q^{39} -1.19905e23 q^{40} -1.14696e23 q^{41} -1.15763e23 q^{42} +4.09568e22 q^{43} -1.42647e24 q^{44} -3.84813e23 q^{45} +1.29388e24 q^{46} -2.84804e24 q^{47} +6.74837e23 q^{48} +4.59987e23 q^{49} +3.45033e24 q^{50} -2.58883e24 q^{51} -1.53453e25 q^{52} +1.38463e25 q^{53} -3.90473e24 q^{54} +3.25744e25 q^{55} +4.83453e24 q^{56} -2.62078e25 q^{57} +4.02510e25 q^{58} +6.41898e25 q^{59} +5.92647e25 q^{60} +1.50726e26 q^{61} +1.19064e26 q^{62} +1.55156e25 q^{63} -2.40499e26 q^{64} +3.50418e26 q^{65} +3.30534e26 q^{66} -8.44985e25 q^{67} +3.98703e26 q^{68} -1.73418e26 q^{69} -4.07123e26 q^{70} +6.92427e26 q^{71} +1.63071e26 q^{72} -5.67464e26 q^{73} -1.57505e27 q^{74} -4.62445e26 q^{75} +4.03624e27 q^{76} -1.31339e27 q^{77} +3.55571e27 q^{78} -7.55696e26 q^{79} +2.37332e27 q^{80} +5.23348e26 q^{81} -4.09304e27 q^{82} +1.28423e28 q^{83} -2.38953e27 q^{84} -9.10462e27 q^{85} +1.46159e27 q^{86} -5.39481e27 q^{87} -1.38039e28 q^{88} +3.01287e28 q^{89} -1.37325e28 q^{90} -1.41287e28 q^{91} +2.67078e28 q^{92} -1.59581e28 q^{93} -1.01635e29 q^{94} -9.21698e28 q^{95} +4.23864e28 q^{96} +2.00179e28 q^{97} +1.64151e28 q^{98} -4.43012e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	35686.0	1.54015	0.770075	−	0.637954i	$-0.220219\pi$
$2$	35686.0	1.54015	0.770075	+	0.637954i	$0.220219\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	7.36619e8	1.37206
$5$	−1.68211e10	−1.23251	−0.616254	−	0.787547i	$-0.711351\pi$
$5$	−1.68211e10	−1.23251	−0.616254	+	0.787547i	$0.711351\pi$
$6$	−1.70685e11	−0.889206
$7$	6.78223e11	0.377964
$7$	6.78223e11	0.377964
$8$	7.12823e12	0.573029
$9$	2.28768e13	0.333333
$10$	−6.00279e14	−1.89825
$11$	−1.93651e15	−1.53754	−0.768771	−	0.639525i	$-0.779131\pi$
$11$	−1.93651e15	−1.53754	−0.768771	+	0.639525i	$0.779131\pi$
$12$	−3.52323e15	−0.792160
$13$	−2.08320e16	−1.46741	−0.733706	−	0.679467i	$-0.762211\pi$
$13$	−2.08320e16	−1.46741	−0.733706	+	0.679467i	$0.762211\pi$
$14$	2.42031e16	0.582122
$15$	8.04549e16	0.711589
$16$	−1.41092e17	−0.489510
$17$	5.41261e17	0.779646	0.389823	−	0.920890i	$-0.372536\pi$
$17$	5.41261e17	0.779646	0.389823	+	0.920890i	$0.372536\pi$
$18$	8.16381e17	0.513383
$19$	5.47941e18	1.57328	0.786641	−	0.617411i	$-0.211818\pi$
$19$	5.47941e18	1.57328	0.786641	+	0.617411i	$0.211818\pi$
$20$	−1.23908e19	−1.69108
$21$	−3.24392e18	−0.218218
$22$	−6.91064e19	−2.36804
$23$	3.62573e19	0.652142	0.326071	−	0.945345i	$-0.394275\pi$
$23$	3.62573e19	0.652142	0.326071	+	0.945345i	$0.394275\pi$
$24$	−3.40941e19	−0.330838
$25$	9.66858e19	0.519078
$26$	−7.43411e20	−2.26004
$27$	−1.09419e20	−0.192450
$28$	4.99592e20	0.518590
$29$	1.12792e21	0.703895	0.351948	−	0.936020i	$-0.385520\pi$
$29$	1.12792e21	0.703895	0.351948	+	0.936020i	$0.385520\pi$
$30$	2.87111e21	1.09595
$31$	3.33644e21	0.791661	0.395830	−	0.918324i	$-0.370457\pi$
$31$	3.33644e21	0.791661	0.395830	+	0.918324i	$0.370457\pi$
$32$	−8.86194e21	−1.32695
$33$	9.26229e21	0.887700
$34$	1.93154e22	1.20077
$35$	−1.14085e22	−0.465845
$36$	1.68515e22	0.457354
$37$	−4.41363e22	−0.805139	−0.402570	−	0.915389i	$-0.631883\pi$
$37$	−4.41363e22	−0.805139	−0.402570	+	0.915389i	$0.631883\pi$
$38$	1.95538e23	2.42309
$39$	9.96388e22	0.847211
$40$	−1.19905e23	−0.706263
$41$	−1.14696e23	−0.472261	−0.236130	−	0.971721i	$-0.575879\pi$
$41$	−1.14696e23	−0.472261	−0.236130	+	0.971721i	$0.575879\pi$
$42$	−1.15763e23	−0.336088
$43$	4.09568e22	0.0845344	0.0422672	−	0.999106i	$-0.486542\pi$
$43$	4.09568e22	0.0845344	0.0422672	+	0.999106i	$0.486542\pi$
$44$	−1.42647e24	−2.10960
$45$	−3.84813e23	−0.410836
$46$	1.29388e24	1.00440
$47$	−2.84804e24	−1.61856	−0.809278	−	0.587426i	$-0.800141\pi$
$47$	−2.84804e24	−1.61856	−0.809278	+	0.587426i	$0.800141\pi$
$48$	6.74837e23	0.282619
$49$	4.59987e23	0.142857
$50$	3.45033e24	0.799458
$51$	−2.58883e24	−0.450129
$52$	−1.53453e25	−2.01338
$53$	1.38463e25	1.37826	0.689132	−	0.724635i	$-0.257992\pi$
$53$	1.38463e25	1.37826	0.689132	+	0.724635i	$0.257992\pi$
$54$	−3.90473e24	−0.296402
$55$	3.25744e25	1.89503
$56$	4.83453e24	0.216585
$57$	−2.62078e25	−0.908335
$58$	4.02510e25	1.08410
$59$	6.41898e25	1.34931	0.674655	−	0.738133i	$-0.264293\pi$
$59$	6.41898e25	1.34931	0.674655	+	0.738133i	$0.264293\pi$
$60$	5.92647e25	0.976344
$61$	1.50726e26	1.95392	0.976960	−	0.213422i	$-0.0684609\pi$
$61$	1.50726e26	1.95392	0.976960	+	0.213422i	$0.0684609\pi$
$62$	1.19064e26	1.21928
$63$	1.55156e25	0.125988
$64$	−2.40499e26	−1.55419
$65$	3.50418e26	1.80860
$66$	3.30534e26	1.36719
$67$	−8.44985e25	−0.281038	−0.140519	−	0.990078i	$-0.544877\pi$
$67$	−8.44985e25	−0.281038	−0.140519	+	0.990078i	$0.544877\pi$
$68$	3.98703e26	1.06972
$69$	−1.73418e26	−0.376514
$70$	−4.07123e26	−0.717470
$71$	6.92427e26	0.993409	0.496705	−	0.867920i	$-0.334543\pi$
$71$	6.92427e26	0.993409	0.496705	+	0.867920i	$0.334543\pi$
$72$	1.63071e26	0.191010
$73$	−5.67464e26	−0.544198	−0.272099	−	0.962269i	$-0.587718\pi$
$73$	−5.67464e26	−0.544198	−0.272099	+	0.962269i	$0.587718\pi$
$74$	−1.57505e27	−1.24003
$75$	−4.62445e26	−0.299690
$76$	4.03624e27	2.15864
$77$	−1.31339e27	−0.581136
$78$	3.55571e27	1.30483
$79$	−7.55696e26	−0.230544	−0.115272	−	0.993334i	$-0.536774\pi$
$79$	−7.55696e26	−0.230544	−0.115272	+	0.993334i	$0.536774\pi$
$80$	2.37332e27	0.603326
$81$	5.23348e26	0.111111
$82$	−4.09304e27	−0.727352
$83$	1.28423e28	1.91430	0.957151	−	0.289590i	$-0.0935190\pi$
$83$	1.28423e28	1.91430	0.957151	+	0.289590i	$0.0935190\pi$
$84$	−2.38953e27	−0.299408
$85$	−9.10462e27	−0.960920
$86$	1.46159e27	0.130196
$87$	−5.39481e27	−0.406394
$88$	−1.38039e28	−0.881056
$89$	3.01287e28	1.63240	0.816198	−	0.577773i	$-0.196078\pi$
$89$	3.01287e28	1.63240	0.816198	+	0.577773i	$0.196078\pi$
$90$	−1.37325e28	−0.632749
$91$	−1.41287e28	−0.554630
$92$	2.67078e28	0.894778
$93$	−1.59581e28	−0.457066
$94$	−1.01635e29	−2.49282
$95$	−9.21698e28	−1.93908
$96$	4.23864e28	0.766114
$97$	2.00179e28	0.311335	0.155667	−	0.987810i	$-0.450247\pi$
$97$	2.00179e28	0.311335	0.155667	+	0.987810i	$0.450247\pi$
$98$	1.64151e28	0.220021
$99$	−4.43012e28	−0.512514
$100$	7.12206e28	0.712206
$101$	1.12243e29	0.971627	0.485813	−	0.874063i	$-0.338523\pi$
$101$	1.12243e29	0.971627	0.485813	+	0.874063i	$0.338523\pi$
$102$	−9.23851e28	−0.693265
$103$	−1.39691e29	−0.909974	−0.454987	−	0.890498i	$-0.650356\pi$
$103$	−1.39691e29	−0.909974	−0.454987	+	0.890498i	$0.650356\pi$
$104$	−1.48495e29	−0.840870
$105$	5.45664e28	0.268955
$106$	4.94118e29	2.12273
$107$	1.21754e29	0.456475	0.228238	−	0.973605i	$-0.426704\pi$
$107$	1.21754e29	0.456475	0.228238	+	0.973605i	$0.426704\pi$
$108$	−8.06002e28	−0.264053
$109$	2.60761e28	0.0747409	0.0373704	−	0.999301i	$-0.488102\pi$
$109$	2.60761e28	0.0747409	0.0373704	+	0.999301i	$0.488102\pi$
$110$	1.16245e30	2.91863
$111$	2.11103e29	0.464847
$112$	−9.56917e28	−0.185017
$113$	−6.95493e29	−1.18210	−0.591051	−	0.806634i	$-0.701287\pi$
$113$	−6.95493e29	−1.18210	−0.591051	+	0.806634i	$0.701287\pi$
$114$	−9.35253e29	−1.39897
$115$	−6.09889e29	−0.803771
$116$	8.30849e29	0.965787
$117$	−4.76569e29	−0.489138
$118$	2.29068e30	2.07814
$119$	3.67096e29	0.294678
$120$	5.73501e29	0.407761
$121$	2.16378e30	1.36403
$122$	5.37882e30	3.00933
$123$	5.48587e29	0.272660
$124$	2.45769e30	1.08621
$125$	1.50681e30	0.592741
$126$	5.53689e29	0.194041
$127$	−4.88350e30	−1.52608	−0.763040	−	0.646351i	$-0.776294\pi$
$127$	−4.88350e30	−1.52608	−0.763040	+	0.646351i	$0.776294\pi$
$128$	−3.82473e30	−1.06673
$129$	−1.95895e29	−0.0488060
$130$	1.25050e31	2.78551
$131$	−3.63959e30	−0.725468	−0.362734	−	0.931893i	$-0.618157\pi$
$131$	−3.63959e30	−0.725468	−0.362734	+	0.931893i	$0.618157\pi$
$132$	6.82278e30	1.21798
$133$	3.71626e30	0.594645
$134$	−3.01541e30	−0.432840
$135$	1.84055e30	0.237196
$136$	3.85823e30	0.446760
$137$	−6.75876e30	−0.703750	−0.351875	−	0.936047i	$-0.614456\pi$
$137$	−6.75876e30	−0.703750	−0.351875	+	0.936047i	$0.614456\pi$
$138$	−6.18858e30	−0.579888
$139$	−6.42873e30	−0.542513	−0.271257	−	0.962507i	$-0.587439\pi$
$139$	−6.42873e30	−0.542513	−0.271257	+	0.962507i	$0.587439\pi$
$140$	−8.40371e30	−0.639167
$141$	1.36221e31	0.934474
$142$	2.47100e31	1.53000
$143$	4.03415e31	2.25621
$144$	−3.22773e30	−0.163170
$145$	−1.89729e31	−0.867557
$146$	−2.02505e31	−0.838147
$147$	−2.20010e30	−0.0824786
$148$	−3.25117e31	−1.10470
$149$	−1.24360e29	−0.00383248	−0.00191624	−	0.999998i	$-0.500610\pi$
$149$	−1.24360e29	−0.00383248	−0.00191624	+	0.999998i	$0.500610\pi$
$150$	−1.65028e31	−0.461567
$151$	3.26985e31	0.830543	0.415272	−	0.909698i	$-0.363687\pi$
$151$	3.26985e31	0.830543	0.415272	+	0.909698i	$0.363687\pi$
$152$	3.90585e31	0.901536
$153$	1.23823e31	0.259882
$154$	−4.68696e31	−0.895036
$155$	−5.61227e31	−0.975729
$156$	7.33959e31	1.16243
$157$	1.45229e31	0.209657	0.104829	−	0.994490i	$-0.466571\pi$
$157$	1.45229e31	0.209657	0.104829	+	0.994490i	$0.466571\pi$
$158$	−2.69678e31	−0.355073
$159$	−6.62263e31	−0.795742
$160$	1.49068e32	1.63548
$161$	2.45905e31	0.246486
$162$	1.86762e31	0.171128
$163$	−1.07279e32	−0.899071	−0.449536	−	0.893262i	$-0.648411\pi$
$163$	−1.07279e32	−0.899071	−0.449536	+	0.893262i	$0.648411\pi$
$164$	−8.44872e31	−0.647970
$165$	−1.55802e32	−1.09410
$166$	4.58290e32	2.94831
$167$	1.23593e32	0.728795	0.364397	−	0.931244i	$-0.381275\pi$
$167$	1.23593e32	0.728795	0.364397	+	0.931244i	$0.381275\pi$
$168$	−2.31234e31	−0.125045
$169$	2.32434e32	1.15330
$170$	−3.24907e32	−1.47996
$171$	1.25351e32	0.524427
$172$	3.01696e31	0.115986
$173$	5.11503e31	0.180792	0.0903961	−	0.995906i	$-0.471187\pi$
$173$	5.11503e31	0.180792	0.0903961	+	0.995906i	$0.471187\pi$
$174$	−1.92519e32	−0.625908
$175$	6.55745e31	0.196193
$176$	2.73226e32	0.752642
$177$	−3.07018e32	−0.779024
$178$	1.07517e33	2.51413
$179$	5.69043e32	1.22681	0.613403	−	0.789770i	$-0.289800\pi$
$179$	5.69043e32	1.22681	0.613403	+	0.789770i	$0.289800\pi$
$180$	−2.83461e32	−0.563692
$181$	4.98136e31	0.0914131	0.0457066	−	0.998955i	$-0.485446\pi$
$181$	4.98136e31	0.0914131	0.0457066	+	0.998955i	$0.485446\pi$
$182$	−5.04198e32	−0.854213
$183$	−7.20920e32	−1.12810
$184$	2.58450e32	0.373696
$185$	7.42422e32	0.992341
$186$	−5.69481e32	−0.703949
$187$	−1.04816e33	−1.19874
$188$	−2.09793e33	−2.22076
$189$	−7.42105e31	−0.0727393
$190$	−3.28917e33	−2.98648
$191$	−2.11967e33	−1.78355	−0.891775	−	0.452479i	$-0.850540\pi$
$191$	−2.11967e33	−1.78355	−0.891775	+	0.452479i	$0.850540\pi$
$192$	1.15030e33	0.897311
$193$	−2.75018e33	−1.98967	−0.994834	−	0.101519i	$-0.967630\pi$
$193$	−2.75018e33	−1.98967	−0.994834	+	0.101519i	$0.967630\pi$
$194$	7.14357e32	0.479502
$195$	−1.67604e33	−1.04420
$196$	3.38835e32	0.196009
$197$	−3.09270e33	−1.66180	−0.830898	−	0.556424i	$-0.812173\pi$
$197$	−3.09270e33	−1.66180	−0.830898	+	0.556424i	$0.812173\pi$
$198$	−1.58093e33	−0.789348
$199$	2.49660e33	1.15872	0.579361	−	0.815071i	$-0.303302\pi$
$199$	2.49660e33	1.15872	0.579361	+	0.815071i	$0.303302\pi$
$200$	6.89198e32	0.297447
$201$	4.04154e32	0.162257
$202$	4.00550e33	1.49645
$203$	7.64983e32	0.266047
$204$	−1.90699e33	−0.617604
$205$	1.92931e33	0.582065
$206$	−4.98502e33	−1.40150
$207$	8.29451e32	0.217381
$208$	2.93922e33	0.718314
$209$	−1.06110e34	−2.41899
$210$	1.94726e33	0.414232
$211$	6.20204e33	1.23151	0.615756	−	0.787937i	$-0.288851\pi$
$211$	6.20204e33	1.23151	0.615756	+	0.787937i	$0.288851\pi$
$212$	1.01994e34	1.89106
$213$	−3.31186e33	−0.573545
$214$	4.34490e33	0.703040
$215$	−6.88940e32	−0.104189
$216$	−7.79963e32	−0.110279
$217$	2.26285e33	0.299220
$218$	9.30551e32	0.115112
$219$	2.71416e33	0.314193
$220$	2.39949e34	2.60010
$221$	−1.12755e34	−1.14406
$222$	7.53341e33	0.715934
$223$	−5.12417e33	−0.456250	−0.228125	−	0.973632i	$-0.573259\pi$
$223$	−5.12417e33	−0.456250	−0.228125	+	0.973632i	$0.573259\pi$
$224$	−6.01037e33	−0.501539
$225$	2.21186e33	0.173026
$226$	−2.48194e34	−1.82061
$227$	1.60738e34	1.10597	0.552984	−	0.833192i	$-0.313489\pi$
$227$	1.60738e34	1.10597	0.552984	+	0.833192i	$0.313489\pi$
$228$	−1.93052e34	−1.24629
$229$	2.40895e34	1.45953	0.729765	−	0.683699i	$-0.239630\pi$
$229$	2.40895e34	1.45953	0.729765	+	0.683699i	$0.239630\pi$
$230$	−2.17645e34	−1.23793
$231$	6.28190e33	0.335519
$232$	8.04008e33	0.403352
$233$	−7.09822e33	−0.334571	−0.167286	−	0.985908i	$-0.553500\pi$
$233$	−7.09822e33	−0.334571	−0.167286	+	0.985908i	$0.553500\pi$
$234$	−1.70068e34	−0.753345
$235$	4.79073e34	1.99489
$236$	4.72834e34	1.85133
$237$	3.61447e33	0.133105
$238$	1.31002e34	0.453849
$239$	8.03168e33	0.261841	0.130920	−	0.991393i	$-0.458207\pi$
$239$	8.03168e33	0.261841	0.130920	+	0.991393i	$0.458207\pi$
$240$	−1.13515e34	−0.348330
$241$	−1.17188e34	−0.338561	−0.169280	−	0.985568i	$-0.554144\pi$
$241$	−1.17188e34	−0.338561	−0.169280	+	0.985568i	$0.554144\pi$
$242$	7.72166e34	2.10082
$243$	−2.50316e33	−0.0641500
$244$	1.11028e35	2.68090
$245$	−7.73749e33	−0.176073
$246$	1.95769e34	0.419937
$247$	−1.14147e35	−2.30865
$248$	2.37829e34	0.453645
$249$	−6.14243e34	−1.10522
$250$	5.37722e34	0.912909
$251$	−7.06132e34	−1.13140	−0.565701	−	0.824611i	$-0.691394\pi$
$251$	−7.06132e34	−1.13140	−0.565701	+	0.824611i	$0.691394\pi$
$252$	1.14291e34	0.172863
$253$	−7.02128e34	−1.00269
$254$	−1.74273e35	−2.35039
$255$	4.35471e34	0.554787
$256$	−7.37240e33	−0.0887420
$257$	−5.86921e33	−0.0667650	−0.0333825	−	0.999443i	$-0.510628\pi$
$257$	−5.86921e33	−0.0667650	−0.0333825	+	0.999443i	$0.510628\pi$
$258$	−6.99072e33	−0.0751685
$259$	−2.99343e34	−0.304314
$260$	2.58124e35	2.48151
$261$	2.58032e34	0.234632
$262$	−1.29882e35	−1.11733
$263$	3.00834e34	0.244889	0.122444	−	0.992475i	$-0.460927\pi$
$263$	3.00834e34	0.244889	0.122444	+	0.992475i	$0.460927\pi$
$264$	6.60237e34	0.508678
$265$	−2.32910e35	−1.69872
$266$	1.32619e35	0.915842
$267$	−1.44105e35	−0.942464
$268$	−6.22433e34	−0.385601
$269$	3.05563e35	1.79346	0.896732	−	0.442575i	$-0.145935\pi$
$269$	3.05563e35	1.79346	0.896732	+	0.442575i	$0.145935\pi$
$270$	6.56819e34	0.365318
$271$	−1.78240e35	−0.939617	−0.469809	−	0.882768i	$-0.655677\pi$
$271$	−1.78240e35	−0.939617	−0.469809	+	0.882768i	$0.655677\pi$
$272$	−7.63674e34	−0.381645
$273$	6.75773e34	0.320216
$274$	−2.41193e35	−1.08388
$275$	−1.87233e35	−0.798104
$276$	−1.27743e35	−0.516600
$277$	−1.69520e35	−0.650524	−0.325262	−	0.945624i	$-0.605452\pi$
$277$	−1.69520e35	−0.650524	−0.325262	+	0.945624i	$0.605452\pi$
$278$	−2.29415e35	−0.835551
$279$	7.63271e34	0.263887
$280$	−8.13222e34	−0.266942
$281$	5.34319e35	1.66556	0.832778	−	0.553607i	$-0.186749\pi$
$281$	5.34319e35	1.66556	0.832778	+	0.553607i	$0.186749\pi$
$282$	4.86119e35	1.43923
$283$	−4.15752e35	−1.16931	−0.584657	−	0.811281i	$-0.698771\pi$
$283$	−4.15752e35	−1.16931	−0.584657	+	0.811281i	$0.698771\pi$
$284$	5.10055e35	1.36302
$285$	4.40846e35	1.11953
$286$	1.43963e36	3.47490
$287$	−7.77894e34	−0.178498
$288$	−2.02733e35	−0.442316
$289$	−1.89005e35	−0.392153
$290$	−6.77067e35	−1.33617
$291$	−9.57448e34	−0.179749
$292$	−4.18005e35	−0.746673
$293$	1.23655e35	0.210200	0.105100	−	0.994462i	$-0.466484\pi$
$293$	1.23655e35	0.210200	0.105100	+	0.994462i	$0.466484\pi$
$294$	−7.85128e34	−0.127029
$295$	−1.07974e36	−1.66304
$296$	−3.14614e35	−0.461368
$297$	2.11891e35	0.295900
$298$	−4.43791e33	−0.00590259
$299$	−7.55312e35	−0.956961
$300$	−3.40646e35	−0.411193
$301$	2.77779e34	0.0319510
$302$	1.16688e36	1.27916
$303$	−5.36855e35	−0.560969
$304$	−7.73099e35	−0.770138
$305$	−2.53539e36	−2.40822
$306$	4.41875e35	0.400257
$307$	−3.68905e35	−0.318719	−0.159359	−	0.987221i	$-0.550943\pi$
$307$	−3.68905e35	−0.318719	−0.159359	+	0.987221i	$0.550943\pi$
$308$	−9.67468e35	−0.797354
$309$	6.68138e35	0.525374
$310$	−2.00280e36	−1.50277
$311$	7.73177e35	0.553673	0.276836	−	0.960917i	$-0.410714\pi$
$311$	7.73177e35	0.553673	0.276836	+	0.960917i	$0.410714\pi$
$312$	7.10248e35	0.485477
$313$	1.47993e36	0.965710	0.482855	−	0.875700i	$-0.339600\pi$
$313$	1.47993e36	0.965710	0.482855	+	0.875700i	$0.339600\pi$
$314$	5.18266e35	0.322903
$315$	−2.60989e35	−0.155282
$316$	−5.56660e35	−0.316321
$317$	1.64009e36	0.890241	0.445121	−	0.895471i	$-0.353161\pi$
$317$	1.64009e36	0.890241	0.445121	+	0.895471i	$0.353161\pi$
$318$	−2.36335e36	−1.22556
$319$	−2.18424e36	−1.08227
$320$	4.04546e36	1.91555
$321$	−5.82344e35	−0.263546
$322$	8.77538e35	0.379626
$323$	2.96579e36	1.22660
$324$	3.85508e35	0.152451
$325$	−2.01416e36	−0.761702
$326$	−3.82835e36	−1.38470
$327$	−1.24721e35	−0.0431517
$328$	−8.17578e35	−0.270619
$329$	−1.93161e36	−0.611757
$330$	−5.55995e36	−1.68507
$331$	3.73549e36	1.08353	0.541765	−	0.840530i	$-0.317756\pi$
$331$	3.73549e36	1.08353	0.541765	+	0.840530i	$0.317756\pi$
$332$	9.45988e36	2.62654
$333$	−1.00970e36	−0.268380
$334$	4.41054e36	1.12245
$335$	1.42136e36	0.346381
$336$	4.57690e35	0.106820
$337$	7.29667e36	1.63114	0.815570	−	0.578658i	$-0.196423\pi$
$337$	7.29667e36	1.63114	0.815570	+	0.578658i	$0.196423\pi$
$338$	8.29464e36	1.77625
$339$	3.32652e36	0.682487
$340$	−6.70664e36	−1.31844
$341$	−6.46107e36	−1.21721
$342$	4.47329e36	0.807696
$343$	3.11973e35	0.0539949
$344$	2.91949e35	0.0484407
$345$	2.91708e36	0.464057
$346$	1.82535e36	0.278447
$347$	4.43396e35	0.0648655	0.0324328	−	0.999474i	$-0.489675\pi$
$347$	4.43396e35	0.0648655	0.0324328	+	0.999474i	$0.489675\pi$
$348$	−3.97393e36	−0.557597
$349$	−8.94111e36	−1.20344	−0.601718	−	0.798709i	$-0.705517\pi$
$349$	−8.94111e36	−1.20344	−0.601718	+	0.798709i	$0.705517\pi$
$350$	2.34009e36	0.302167
$351$	2.27942e36	0.282404
$352$	1.71613e37	2.04024
$353$	6.36294e36	0.725980	0.362990	−	0.931793i	$-0.381756\pi$
$353$	6.36294e36	0.725980	0.362990	+	0.931793i	$0.381756\pi$
$354$	−1.09562e37	−1.19981
$355$	−1.16474e37	−1.22439
$356$	2.21934e37	2.23975
$357$	−1.75581e36	−0.170133
$358$	2.03069e37	1.88947
$359$	8.89649e36	0.794967	0.397484	−	0.917609i	$-0.369884\pi$
$359$	8.89649e36	0.794967	0.397484	+	0.917609i	$0.369884\pi$
$360$	−2.74304e36	−0.235421
$361$	1.78941e37	1.47522
$362$	1.77765e36	0.140790
$363$	−1.03493e37	−0.787525
$364$	−1.04075e37	−0.760986
$365$	9.54539e36	0.670729
$366$	−2.57267e37	−1.73744
$367$	−1.15589e37	−0.750339	−0.375169	−	0.926956i	$-0.622415\pi$
$367$	−1.15589e37	−0.750339	−0.375169	+	0.926956i	$0.622415\pi$
$368$	−5.11561e36	−0.319230
$369$	−2.62387e36	−0.157420
$370$	2.64941e37	1.52835
$371$	9.39086e36	0.520935
$372$	−1.17550e37	−0.627122
$373$	1.65041e37	0.846863	0.423432	−	0.905928i	$-0.360825\pi$
$373$	1.65041e37	0.846863	0.423432	+	0.905928i	$0.360825\pi$
$374$	−3.74046e37	−1.84623
$375$	−7.20705e36	−0.342219
$376$	−2.03015e37	−0.927480
$377$	−2.34969e37	−1.03290
$378$	−2.64828e36	−0.112029
$379$	7.97974e36	0.324878	0.162439	−	0.986719i	$-0.448064\pi$
$379$	7.97974e36	0.324878	0.162439	+	0.986719i	$0.448064\pi$
$380$	−6.78941e37	−2.66054
$381$	2.33576e37	0.881083
$382$	−7.56427e37	−2.74693
$383$	2.31614e37	0.809810	0.404905	−	0.914359i	$-0.367305\pi$
$383$	2.31614e37	0.809810	0.404905	+	0.914359i	$0.367305\pi$
$384$	1.82936e37	0.615879
$385$	2.20927e37	0.716255
$386$	−9.81430e37	−3.06439
$387$	9.36961e35	0.0281781
$388$	1.47455e37	0.427170
$389$	2.15712e37	0.602011	0.301005	−	0.953622i	$-0.402678\pi$
$389$	2.15712e37	0.602011	0.301005	+	0.953622i	$0.402678\pi$
$390$	−5.98110e37	−1.60822
$391$	1.96247e37	0.508440
$392$	3.27889e36	0.0818613
$393$	1.74080e37	0.418849
$394$	−1.10366e38	−2.55942
$395$	1.27117e37	0.284148
$396$	−3.26332e37	−0.703200
$397$	6.58321e37	1.36765	0.683826	−	0.729645i	$-0.260315\pi$
$397$	6.58321e37	1.36765	0.683826	+	0.729645i	$0.260315\pi$
$398$	8.90937e37	1.78461
$399$	−1.77748e37	−0.343318
$400$	−1.36416e37	−0.254094
$401$	1.03068e37	0.185152	0.0925760	−	0.995706i	$-0.470490\pi$
$401$	1.03068e37	0.185152	0.0925760	+	0.995706i	$0.470490\pi$
$402$	1.44226e37	0.249900
$403$	−6.95048e37	−1.16169
$404$	8.26804e37	1.33313
$405$	−8.80330e36	−0.136945
$406$	2.72992e37	0.409753
$407$	8.54706e37	1.23793
$408$	−1.84538e37	−0.257937
$409$	1.13577e37	0.153216	0.0766078	−	0.997061i	$-0.475591\pi$
$409$	1.13577e37	0.153216	0.0766078	+	0.997061i	$0.475591\pi$
$410$	6.88495e37	0.896468
$411$	3.23269e37	0.406311
$412$	−1.02899e38	−1.24854
$413$	4.35350e37	0.509991
$414$	2.95998e37	0.334799
$415$	−2.16022e38	−2.35939
$416$	1.84612e38	1.94718
$417$	3.07484e37	0.313220
$418$	−3.78663e38	−3.72560
$419$	1.06180e38	1.00911	0.504557	−	0.863378i	$-0.331656\pi$
$419$	1.06180e38	1.00911	0.504557	+	0.863378i	$0.331656\pi$
$420$	4.01947e37	0.369023
$421$	1.93989e38	1.72063	0.860315	−	0.509763i	$-0.170267\pi$
$421$	1.93989e38	1.72063	0.860315	+	0.509763i	$0.170267\pi$
$422$	2.21326e38	1.89671
$423$	−6.51541e37	−0.539519
$424$	9.86993e37	0.789786
$425$	5.23322e37	0.404697
$426$	−1.18187e38	−0.883345
$427$	1.02226e38	0.738512
$428$	8.96861e37	0.626312
$429$	−1.92952e38	−1.30262
$430$	−2.45855e37	−0.160467
$431$	−1.79458e38	−1.13251	−0.566256	−	0.824230i	$-0.691609\pi$
$431$	−1.79458e38	−1.13251	−0.566256	+	0.824230i	$0.691609\pi$
$432$	1.54381e37	0.0942063
$433$	1.31854e38	0.778072	0.389036	−	0.921223i	$-0.372808\pi$
$433$	1.31854e38	0.778072	0.389036	+	0.921223i	$0.372808\pi$
$434$	8.07521e37	0.460843
$435$	9.07469e37	0.500884
$436$	1.92081e37	0.102549
$437$	1.98669e38	1.02600
$438$	9.68577e37	0.483904
$439$	−1.81501e38	−0.877292	−0.438646	−	0.898660i	$-0.644542\pi$
$439$	−1.81501e38	−0.877292	−0.438646	+	0.898660i	$0.644542\pi$
$440$	2.32197e38	1.08591
$441$	1.05230e37	0.0476190
$442$	−4.02379e38	−1.76203
$443$	−2.02487e37	−0.0858112	−0.0429056	−	0.999079i	$-0.513661\pi$
$443$	−2.02487e37	−0.0858112	−0.0429056	+	0.999079i	$0.513661\pi$
$444$	1.55502e38	0.637799
$445$	−5.06799e38	−2.01194
$446$	−1.82861e38	−0.702693
$447$	5.94810e35	0.00221268
$448$	−1.63112e38	−0.587428
$449$	−5.73495e36	−0.0199967	−0.00999833	−	0.999950i	$-0.503183\pi$
$449$	−5.73495e36	−0.0199967	−0.00999833	+	0.999950i	$0.503183\pi$
$450$	7.89325e37	0.266486
$451$	2.22110e38	0.726120
$452$	−5.12313e38	−1.62192
$453$	−1.56396e38	−0.479514
$454$	5.73609e38	1.70336
$455$	2.37661e38	0.683586
$456$	−1.86815e38	−0.520502
$457$	3.81130e38	1.02870	0.514350	−	0.857580i	$-0.328033\pi$
$457$	3.81130e38	1.02870	0.514350	+	0.857580i	$0.328033\pi$
$458$	8.59657e38	2.24789
$459$	−5.92242e37	−0.150043
$460$	−4.49256e38	−1.10282
$461$	−2.08022e38	−0.494819	−0.247410	−	0.968911i	$-0.579579\pi$
$461$	−2.08022e38	−0.494819	−0.247410	+	0.968911i	$0.579579\pi$
$462$	2.24176e38	0.516749
$463$	−4.84784e38	−1.08299	−0.541494	−	0.840705i	$-0.682141\pi$
$463$	−4.84784e38	−1.08299	−0.541494	+	0.840705i	$0.682141\pi$
$464$	−1.59140e38	−0.344564
$465$	2.68433e38	0.563337
$466$	−2.53307e38	−0.515289
$467$	−5.75180e38	−1.13425	−0.567126	−	0.823631i	$-0.691945\pi$
$467$	−5.75180e38	−1.13425	−0.567126	+	0.823631i	$0.691945\pi$
$468$	−3.51050e38	−0.671126
$469$	−5.73089e37	−0.106222
$470$	1.70962e39	3.07242
$471$	−6.94628e37	−0.121046
$472$	4.57559e38	0.773194
$473$	−7.93135e37	−0.129975
$474$	1.28986e38	0.205001
$475$	5.29781e38	0.816656
$476$	2.70410e38	0.404317
$477$	3.16758e38	0.459422
$478$	2.86619e38	0.403274
$479$	−3.43123e38	−0.468365	−0.234183	−	0.972193i	$-0.575241\pi$
$479$	−3.43123e38	−0.468365	−0.234183	+	0.972193i	$0.575241\pi$
$480$	−7.12986e38	−0.944242
$481$	9.19447e38	1.18147
$482$	−4.18198e38	−0.521435
$483$	−1.17616e38	−0.142309
$484$	1.59388e39	1.87154
$485$	−3.36723e38	−0.383723
$486$	−8.93276e37	−0.0988006
$487$	−8.22022e38	−0.882497	−0.441249	−	0.897385i	$-0.645464\pi$
$487$	−8.22022e38	−0.882497	−0.441249	+	0.897385i	$0.645464\pi$
$488$	1.07441e39	1.11965
$489$	5.13112e38	0.519079
$490$	−2.76120e38	−0.271178
$491$	−7.64669e38	−0.729108	−0.364554	−	0.931182i	$-0.618779\pi$
$491$	−7.64669e38	−0.729108	−0.364554	+	0.931182i	$0.618779\pi$
$492$	4.04100e38	0.374106
$493$	6.10500e38	0.548789
$494$	−4.07345e39	−3.55567
$495$	7.45197e38	0.631678
$496$	−4.70744e38	−0.387526
$497$	4.69620e38	0.375473
$498$	−2.19199e39	−1.70221
$499$	1.96264e39	1.48041	0.740205	−	0.672381i	$-0.234728\pi$
$499$	1.96264e39	1.48041	0.740205	+	0.672381i	$0.234728\pi$
$500$	1.10995e39	0.813276
$501$	−5.91142e38	−0.420770
$502$	−2.51990e39	−1.74253
$503$	2.04752e39	1.37560	0.687800	−	0.725900i	$-0.258577\pi$
$503$	2.04752e39	1.37560	0.687800	+	0.725900i	$0.258577\pi$
$504$	1.10598e38	0.0721949
$505$	−1.88805e39	−1.19754
$506$	−2.50561e39	−1.54430
$507$	−1.11172e39	−0.665858
$508$	−3.59728e39	−2.09388
$509$	−3.21667e39	−1.81970	−0.909848	−	0.414941i	$-0.863802\pi$
$509$	−3.21667e39	−1.81970	−0.909848	+	0.414941i	$0.863802\pi$
$510$	1.55402e39	0.854456
$511$	−3.84867e38	−0.205688
$512$	1.79029e39	0.930058
$513$	−5.99551e38	−0.302778
$514$	−2.09449e38	−0.102828
$515$	2.34976e39	1.12155
$516$	−1.44300e38	−0.0669648
$517$	5.51528e39	2.48860
$518$	−1.06823e39	−0.468689
$519$	−2.44650e38	−0.104380
$520$	2.49786e39	1.03638
$521$	1.62260e39	0.654732	0.327366	−	0.944898i	$-0.393839\pi$
$521$	1.62260e39	0.654732	0.327366	+	0.944898i	$0.393839\pi$
$522$	9.20814e38	0.361368
$523$	−1.40125e39	−0.534860	−0.267430	−	0.963577i	$-0.586174\pi$
$523$	−1.40125e39	−0.534860	−0.267430	+	0.963577i	$0.586174\pi$
$524$	−2.68099e39	−0.995386
$525$	−3.13641e38	−0.113272
$526$	1.07356e39	0.377165
$527$	1.80589e39	0.617215
$528$	−1.30683e39	−0.434538
$529$	−1.77647e39	−0.574711
$530$	−8.31162e39	−2.61629
$531$	1.46846e39	0.449770
$532$	2.73747e39	0.815889
$533$	2.38934e39	0.693001
$534$	−5.14252e39	−1.45154
$535$	−2.04803e39	−0.562610
$536$	−6.02325e38	−0.161043
$537$	−2.72171e39	−0.708297
$538$	1.09043e40	2.76220
$539$	−8.90771e38	−0.219649
$540$	1.35579e39	0.325448
$541$	−1.07372e39	−0.250917	−0.125459	−	0.992099i	$-0.540040\pi$
$541$	−1.07372e39	−0.250917	−0.125459	+	0.992099i	$0.540040\pi$
$542$	−6.36068e39	−1.44715
$543$	−2.38257e38	−0.0527774
$544$	−4.79662e39	−1.03455
$545$	−4.38629e38	−0.0921188
$546$	2.41156e39	0.493180
$547$	9.36992e39	1.86603	0.933017	−	0.359831i	$-0.117166\pi$
$547$	9.36992e39	1.86603	0.933017	+	0.359831i	$0.117166\pi$
$548$	−4.97863e39	−0.965588
$549$	3.44814e39	0.651307
$550$	−6.68161e39	−1.22920
$551$	6.18035e39	1.10743
$552$	−1.23616e39	−0.215754
$553$	−5.12530e38	−0.0871375
$554$	−6.04947e39	−1.00190
$555$	−3.55098e39	−0.572928
$556$	−4.73552e39	−0.744361
$557$	−1.81325e39	−0.277688	−0.138844	−	0.990314i	$-0.544339\pi$
$557$	−1.81325e39	−0.277688	−0.138844	+	0.990314i	$0.544339\pi$
$558$	2.72381e39	0.406425
$559$	−8.53212e38	−0.124047
$560$	1.60964e39	0.228036
$561$	5.01331e39	0.692091
$562$	1.90677e40	2.56521
$563$	3.48489e39	0.456896	0.228448	−	0.973556i	$-0.426635\pi$
$563$	3.48489e39	0.456896	0.228448	+	0.973556i	$0.426635\pi$
$564$	1.00343e40	1.28215
$565$	1.16990e40	1.45695
$566$	−1.48365e40	−1.80092
$567$	3.54946e38	0.0419961
$568$	4.93578e39	0.569252
$569$	7.82525e38	0.0879773	0.0439886	−	0.999032i	$-0.485993\pi$
$569$	7.82525e38	0.0879773	0.0439886	+	0.999032i	$0.485993\pi$
$570$	1.57320e40	1.72424
$571$	−4.23995e38	−0.0453041	−0.0226520	−	0.999743i	$-0.507211\pi$
$571$	−4.23995e38	−0.0453041	−0.0226520	+	0.999743i	$0.507211\pi$
$572$	2.97163e40	3.09565
$573$	1.01383e40	1.02973
$574$	−2.77599e39	−0.274913
$575$	3.50557e39	0.338512
$576$	−5.50184e39	−0.518063
$577$	9.48964e39	0.871366	0.435683	−	0.900100i	$-0.356507\pi$
$577$	9.48964e39	0.871366	0.435683	+	0.900100i	$0.356507\pi$
$578$	−6.74484e39	−0.603974
$579$	1.31540e40	1.14873
$580$	−1.39758e40	−1.19034
$581$	8.70994e39	0.723538
$582$	−3.41675e39	−0.276841
$583$	−2.68135e40	−2.11914
$584$	−4.04501e39	−0.311841
$585$	8.01643e39	0.602866
$586$	4.41277e39	0.323739
$587$	1.47731e40	1.05735	0.528676	−	0.848824i	$-0.322689\pi$
$587$	1.47731e40	1.05735	0.528676	+	0.848824i	$0.322689\pi$
$588$	−1.62064e39	−0.113166
$589$	1.82817e40	1.24551
$590$	−3.85317e40	−2.56132
$591$	1.47923e40	0.959439
$592$	6.22727e39	0.394124
$593$	7.66360e39	0.473304	0.236652	−	0.971594i	$-0.423950\pi$
$593$	7.66360e39	0.473304	0.236652	+	0.971594i	$0.423950\pi$
$594$	7.56156e39	0.455730
$595$	−6.17496e39	−0.363194
$596$	−9.16060e37	−0.00525839
$597$	−1.19412e40	−0.668989
$598$	−2.69541e40	−1.47386
$599$	6.62763e39	0.353728	0.176864	−	0.984235i	$-0.443405\pi$
$599$	6.62763e39	0.353728	0.176864	+	0.984235i	$0.443405\pi$
$600$	−3.29641e39	−0.171731
$601$	−1.95408e40	−0.993717	−0.496858	−	0.867832i	$-0.665513\pi$
$601$	−1.95408e40	−0.993717	−0.496858	+	0.867832i	$0.665513\pi$
$602$	9.91281e38	0.0492093
$603$	−1.93306e39	−0.0936792
$604$	2.40864e40	1.13956
$605$	−3.63972e40	−1.68118
$606$	−1.91582e40	−0.863976
$607$	−2.28808e40	−1.00748	−0.503739	−	0.863856i	$-0.668043\pi$
$607$	−2.28808e40	−1.00748	−0.503739	+	0.863856i	$0.668043\pi$
$608$	−4.85582e40	−2.08766
$609$	−3.65889e39	−0.153603
$610$	−9.04779e40	−3.70902
$611$	5.93305e40	2.37509
$612$	9.12105e39	0.356574
$613$	2.26370e40	0.864255	0.432128	−	0.901812i	$-0.357763\pi$
$613$	2.26370e40	0.864255	0.432128	+	0.901812i	$0.357763\pi$
$614$	−1.31647e40	−0.490875
$615$	−9.22785e39	−0.336056
$616$	−9.36213e39	−0.333008
$617$	−4.33106e40	−1.50473	−0.752367	−	0.658744i	$-0.771088\pi$
$617$	−4.33106e40	−1.50473	−0.752367	+	0.658744i	$0.771088\pi$
$618$	2.38432e40	0.809154
$619$	−3.33102e40	−1.10424	−0.552119	−	0.833766i	$-0.686180\pi$
$619$	−3.33102e40	−1.10424	−0.552119	+	0.833766i	$0.686180\pi$
$620$	−4.13411e40	−1.33876
$621$	−3.96724e39	−0.125505
$622$	2.75916e40	0.852739
$623$	2.04340e40	0.616987
$624$	−1.40582e40	−0.414718
$625$	−4.33555e40	−1.24964
$626$	5.28126e40	1.48734
$627$	5.07519e40	1.39660
$628$	1.06979e40	0.287662
$629$	−2.38893e40	−0.627723
$630$	−9.31367e39	−0.239157
$631$	5.83078e40	1.46319	0.731595	−	0.681739i	$-0.238776\pi$
$631$	5.83078e40	1.46319	0.731595	+	0.681739i	$0.238776\pi$
$632$	−5.38677e39	−0.132109
$633$	−2.96642e40	−0.711014
$634$	5.85281e40	1.37110
$635$	8.21460e40	1.88091
$636$	−4.87836e40	−1.09181
$637$	−9.58244e39	−0.209630
$638$	−7.79467e40	−1.66685
$639$	1.58405e40	0.331136
$640$	6.43363e40	1.31476
$641$	1.76817e39	0.0353250	0.0176625	−	0.999844i	$-0.494378\pi$
$641$	1.76817e39	0.0353250	0.0176625	+	0.999844i	$0.494378\pi$
$642$	−2.07815e40	−0.405901
$643$	5.75592e40	1.09915	0.549573	−	0.835446i	$-0.314790\pi$
$643$	5.75592e40	1.09915	0.549573	+	0.835446i	$0.314790\pi$
$644$	1.81139e40	0.338194
$645$	3.29518e39	0.0601538
$646$	1.05837e41	1.88915
$647$	−3.94361e40	−0.688307	−0.344154	−	0.938913i	$-0.611834\pi$
$647$	−3.94361e40	−0.688307	−0.344154	+	0.938913i	$0.611834\pi$
$648$	3.73054e39	0.0636699
$649$	−1.24304e41	−2.07462
$650$	−7.18772e40	−1.17313
$651$	−1.08232e40	−0.172755
$652$	−7.90237e40	−1.23358
$653$	4.69040e39	0.0716092	0.0358046	−	0.999359i	$-0.488601\pi$
$653$	4.69040e39	0.0716092	0.0358046	+	0.999359i	$0.488601\pi$
$654$	−4.45080e39	−0.0664600
$655$	6.12219e40	0.894145
$656$	1.61826e40	0.231176
$657$	−1.29818e40	−0.181399
$658$	−6.89314e40	−0.942197
$659$	7.95035e40	1.06304	0.531518	−	0.847047i	$-0.321622\pi$
$659$	7.95035e40	1.06304	0.531518	+	0.847047i	$0.321622\pi$
$660$	−1.14767e41	−1.50117
$661$	−2.25047e39	−0.0287973	−0.0143987	−	0.999896i	$-0.504583\pi$
$661$	−2.25047e39	−0.0287973	−0.0143987	+	0.999896i	$0.504583\pi$
$662$	1.33305e41	1.66880
$663$	5.39306e40	0.660524
$664$	9.15428e40	1.09695
$665$	−6.25117e40	−0.732905
$666$	−3.60320e40	−0.413345
$667$	4.08954e40	0.459039
$668$	9.10410e40	0.999950
$669$	2.45087e40	0.263416
$670$	5.07227e40	0.533479
$671$	−2.91884e41	−3.00423
$672$	2.87474e40	0.289564
$673$	1.65313e40	0.162963	0.0814813	−	0.996675i	$-0.474035\pi$
$673$	1.65313e40	0.162963	0.0814813	+	0.996675i	$0.474035\pi$
$674$	2.60389e41	2.51220
$675$	−1.05793e40	−0.0998966
$676$	1.71215e41	1.58240
$677$	1.43341e41	1.29668	0.648342	−	0.761349i	$-0.275463\pi$
$677$	1.43341e41	1.29668	0.648342	+	0.761349i	$0.275463\pi$
$678$	1.18710e41	1.05113
$679$	1.35766e40	0.117673
$680$	−6.48998e40	−0.550635
$681$	−7.68804e40	−0.638531
$682$	−2.30570e41	−1.87469
$683$	−1.93584e41	−1.54088	−0.770441	−	0.637511i	$-0.779964\pi$
$683$	−1.93584e41	−1.54088	−0.770441	+	0.637511i	$0.779964\pi$
$684$	9.23362e40	0.719546
$685$	1.13690e41	0.867379
$686$	1.11331e40	0.0831603
$687$	−1.15219e41	−0.842660
$688$	−5.77867e39	−0.0413805
$689$	−2.88445e41	−2.02248
$690$	1.04099e41	0.714717
$691$	1.32819e41	0.892954	0.446477	−	0.894795i	$-0.352679\pi$
$691$	1.32819e41	0.892954	0.446477	+	0.894795i	$0.352679\pi$
$692$	3.76783e40	0.248058
$693$	−3.00461e40	−0.193712
$694$	1.58230e40	0.0999026
$695$	1.08138e41	0.668652
$696$	−3.84555e40	−0.232876
$697$	−6.20804e40	−0.368196
$698$	−3.19072e41	−1.85347
$699$	3.39505e40	0.193165
$700$	4.83035e40	0.269189
$701$	2.74499e41	1.49841	0.749203	−	0.662341i	$-0.230437\pi$
$701$	2.74499e41	1.49841	0.749203	+	0.662341i	$0.230437\pi$
$702$	8.13432e40	0.434944
$703$	−2.41841e41	−1.26671
$704$	4.65730e41	2.38963
$705$	−2.29139e41	−1.15175
$706$	2.27068e41	1.11812
$707$	7.61258e40	0.367240
$708$	−2.26155e41	−1.06887
$709$	−1.61399e41	−0.747360	−0.373680	−	0.927558i	$-0.621904\pi$
$709$	−1.61399e41	−0.747360	−0.373680	+	0.927558i	$0.621904\pi$
$710$	−4.15649e41	−1.88574
$711$	−1.72879e40	−0.0768481
$712$	2.14764e41	0.935410
$713$	1.20970e41	0.516275
$714$	−6.26577e40	−0.262030
$715$	−6.78589e41	−2.78080
$716$	4.19168e41	1.68325
$717$	−3.84153e40	−0.151174
$718$	3.17480e41	1.22437
$719$	1.49929e41	0.566653	0.283326	−	0.959024i	$-0.408562\pi$
$719$	1.49929e41	0.566653	0.283326	+	0.959024i	$0.408562\pi$
$720$	5.42940e40	0.201109
$721$	−9.47418e40	−0.343938
$722$	6.38569e41	2.27205
$723$	5.60508e40	0.195468
$724$	3.66937e40	0.125424
$725$	1.09054e41	0.365376
$726$	−3.69325e41	−1.21291
$727$	−3.68979e41	−1.18783	−0.593913	−	0.804529i	$-0.702418\pi$
$727$	−3.68979e41	−1.18783	−0.593913	+	0.804529i	$0.702418\pi$
$728$	−1.00713e41	−0.317819
$729$	1.19725e40	0.0370370
$730$	3.40637e41	1.03302
$731$	2.21683e40	0.0659069
$732$	−5.31044e41	−1.54782
$733$	2.01815e41	0.576695	0.288348	−	0.957526i	$-0.406894\pi$
$733$	2.01815e41	0.576695	0.288348	+	0.957526i	$0.406894\pi$
$734$	−4.12490e41	−1.15563
$735$	3.70082e40	0.101656
$736$	−3.21310e41	−0.865358
$737$	1.63633e41	0.432107
$738$	−9.36355e40	−0.242451
$739$	−1.18629e41	−0.301195	−0.150597	−	0.988595i	$-0.548120\pi$
$739$	−1.18629e41	−0.301195	−0.150597	+	0.988595i	$0.548120\pi$
$740$	5.46883e41	1.36155
$741$	5.45962e41	1.33290
$742$	3.35122e41	0.802318
$743$	6.38101e41	1.49814	0.749069	−	0.662492i	$-0.230501\pi$
$743$	6.38101e41	1.49814	0.749069	+	0.662492i	$0.230501\pi$
$744$	−1.13753e41	−0.261912
$745$	2.09187e39	0.00472356
$746$	5.88965e41	1.30430
$747$	2.93791e41	0.638100
$748$	−7.72095e41	−1.64474
$749$	8.25762e40	0.172531
$750$	−2.57191e41	−0.527068
$751$	2.50976e41	0.504491	0.252246	−	0.967663i	$-0.418831\pi$
$751$	2.50976e41	0.504491	0.252246	+	0.967663i	$0.418831\pi$
$752$	4.01835e41	0.792300
$753$	3.37741e41	0.653215
$754$	−8.38509e41	−1.59083
$755$	−5.50026e41	−1.02365
$756$	−5.46649e40	−0.0998027
$757$	−8.02669e41	−1.43763	−0.718813	−	0.695203i	$-0.755314\pi$
$757$	−8.02669e41	−1.43763	−0.718813	+	0.695203i	$0.755314\pi$
$758$	2.84765e41	0.500361
$759$	3.35826e41	0.578906
$760$	−6.57007e41	−1.11115
$761$	7.75615e41	1.28697	0.643485	−	0.765459i	$-0.277488\pi$
$761$	7.75615e41	1.28697	0.643485	+	0.765459i	$0.277488\pi$
$762$	8.33541e41	1.35700
$763$	1.76854e40	0.0282494
$764$	−1.56139e42	−2.44714
$765$	−2.08284e41	−0.320307
$766$	8.26539e41	1.24723
$767$	−1.33720e42	−1.97999
$768$	3.52620e40	0.0512352
$769$	−2.42803e41	−0.346197	−0.173098	−	0.984905i	$-0.555378\pi$
$769$	−2.42803e41	−0.346197	−0.173098	+	0.984905i	$0.555378\pi$
$770$	7.88399e41	1.10314
$771$	2.80722e40	0.0385468
$772$	−2.02584e42	−2.72994
$773$	−1.04863e42	−1.38682	−0.693410	−	0.720543i	$-0.743893\pi$
$773$	−1.04863e42	−1.38682	−0.693410	+	0.720543i	$0.743893\pi$
$774$	3.34364e40	0.0433986
$775$	3.22587e41	0.410934
$776$	1.42692e41	0.178404
$777$	1.43175e41	0.175696
$778$	7.69788e41	0.927186
$779$	−6.28466e41	−0.742999
$780$	−1.23460e42	−1.43270
$781$	−1.34090e42	−1.52741
$782$	7.00326e41	0.783073
$783$	−1.23416e41	−0.135465
$784$	−6.49003e40	−0.0699300
$785$	−2.44292e41	−0.258404
$786$	6.21223e41	0.645090
$787$	3.16123e41	0.322272	0.161136	−	0.986932i	$-0.448484\pi$
$787$	3.16123e41	0.322272	0.161136	+	0.986932i	$0.448484\pi$
$788$	−2.27815e42	−2.28009
$789$	−1.43888e41	−0.141387
$790$	4.53628e41	0.437630
$791$	−4.71699e41	−0.446793
$792$	−3.15789e41	−0.293685
$793$	−3.13993e42	−2.86721
$794$	2.34929e42	2.10639
$795$	1.11400e42	0.980758
$796$	1.83905e42	1.58984
$797$	1.44249e42	1.22452	0.612260	−	0.790657i	$-0.290261\pi$
$797$	1.44249e42	1.22452	0.612260	+	0.790657i	$0.290261\pi$
$798$	−6.34310e41	−0.528761
$799$	−1.54154e42	−1.26190
$800$	−8.56823e41	−0.688789
$801$	6.89248e41	0.544132
$802$	3.67807e41	0.285162
$803$	1.09890e42	0.836727
$804$	2.97708e41	0.222627
$805$	−4.13641e41	−0.303797
$806$	−2.48035e42	−1.78918
$807$	−1.46150e42	−1.03546
$808$	8.00094e41	0.556770
$809$	6.45489e41	0.441200	0.220600	−	0.975364i	$-0.429199\pi$
$809$	6.45489e41	0.441200	0.220600	+	0.975364i	$0.429199\pi$
$810$	−3.14154e41	−0.210916
$811$	2.25112e42	1.48455	0.742276	−	0.670094i	$-0.233746\pi$
$811$	2.25112e42	1.48455	0.742276	+	0.670094i	$0.233746\pi$
$812$	5.63501e41	0.365033
$813$	8.52518e41	0.542488
$814$	3.05010e42	1.90660
$815$	1.80455e42	1.10811
$816$	3.65263e41	0.220343
$817$	2.24419e41	0.132996
$818$	4.05312e41	0.235975
$819$	−3.23220e41	−0.184877
$820$	1.42117e42	0.798629
$821$	1.76512e42	0.974538	0.487269	−	0.873252i	$-0.337993\pi$
$821$	1.76512e42	0.974538	0.487269	+	0.873252i	$0.337993\pi$
$822$	1.15362e42	0.625779
$823$	−6.67617e41	−0.355819	−0.177910	−	0.984047i	$-0.556933\pi$
$823$	−6.67617e41	−0.355819	−0.177910	+	0.984047i	$0.556933\pi$
$824$	−9.95750e41	−0.521442
$825$	8.95532e41	0.460785
$826$	1.55359e42	0.785462
$827$	2.59227e42	1.28781	0.643904	−	0.765107i	$-0.277314\pi$
$827$	2.59227e42	1.28781	0.643904	+	0.765107i	$0.277314\pi$
$828$	6.10990e41	0.298259
$829$	2.70438e42	1.29726	0.648630	−	0.761104i	$-0.275342\pi$
$829$	2.70438e42	1.29726	0.648630	+	0.761104i	$0.275342\pi$
$830$	−7.70896e42	−3.63382
$831$	8.10807e41	0.375580
$832$	5.01007e42	2.28064
$833$	2.48973e41	0.111378
$834$	1.09729e42	0.482406
$835$	−2.07897e42	−0.898246
$836$	−7.81624e42	−3.31900
$837$	−3.65070e41	−0.152355
$838$	3.78915e42	1.55419
$839$	3.47971e42	1.40280	0.701399	−	0.712769i	$-0.252559\pi$
$839$	3.47971e42	1.40280	0.701399	+	0.712769i	$0.252559\pi$
$840$	3.88962e41	0.154119
$841$	−1.29548e42	−0.504532
$842$	6.92270e42	2.65003
$843$	−2.55563e42	−0.961609
$844$	4.56854e42	1.68971
$845$	−3.90980e42	−1.42145
$846$	−2.32509e42	−0.830940
$847$	1.46752e42	0.515556
$848$	−1.95359e42	−0.674675
$849$	1.98853e42	0.675104
$850$	1.86753e42	0.623294
$851$	−1.60026e42	−0.525065
$852$	−2.43958e42	−0.786938
$853$	2.28652e41	0.0725127	0.0362563	−	0.999343i	$-0.488457\pi$
$853$	2.28652e41	0.0725127	0.0362563	+	0.999343i	$0.488457\pi$
$854$	3.64804e42	1.13742
$855$	−2.10855e42	−0.646361
$856$	8.67888e41	0.261574
$857$	−2.85302e42	−0.845440	−0.422720	−	0.906260i	$-0.638925\pi$
$857$	−2.85302e42	−0.845440	−0.422720	+	0.906260i	$0.638925\pi$
$858$	−6.88568e42	−2.00623
$859$	−2.96390e42	−0.849106	−0.424553	−	0.905403i	$-0.639569\pi$
$859$	−2.96390e42	−0.849106	−0.424553	+	0.905403i	$0.639569\pi$
$860$	−5.07487e41	−0.142954
$861$	3.72064e41	0.103056
$862$	−6.40414e42	−1.74424
$863$	1.94465e42	0.520817	0.260409	−	0.965498i	$-0.416143\pi$
$863$	1.94465e42	0.520817	0.260409	+	0.965498i	$0.416143\pi$
$864$	9.69664e41	0.255371
$865$	−8.60406e41	−0.222828
$866$	4.70535e42	1.19835
$867$	9.04006e41	0.226409
$868$	1.66686e42	0.410547
$869$	1.46342e42	0.354471
$870$	3.23839e42	0.771437
$871$	1.76027e42	0.412398
$872$	1.85876e41	0.0428287
$873$	4.57944e41	0.103778
$874$	7.08969e42	1.58020
$875$	1.02196e42	0.224035
$876$	1.99931e42	0.431092
$877$	−1.13279e42	−0.240245	−0.120122	−	0.992759i	$-0.538329\pi$
$877$	−1.13279e42	−0.240245	−0.120122	+	0.992759i	$0.538329\pi$
$878$	−6.47706e42	−1.35116
$879$	−5.91440e41	−0.121359
$880$	−4.59597e42	−0.927638
$881$	4.25984e42	0.845752	0.422876	−	0.906188i	$-0.361021\pi$
$881$	4.25984e42	0.845752	0.422876	+	0.906188i	$0.361021\pi$
$882$	3.75524e41	0.0733405
$883$	3.83672e42	0.737105	0.368553	−	0.929607i	$-0.379853\pi$
$883$	3.83672e42	0.737105	0.368553	+	0.929607i	$0.379853\pi$
$884$	−8.30579e42	−1.56972
$885$	5.16438e42	0.960154
$886$	−7.22597e41	−0.132162
$887$	−1.06341e43	−1.91341	−0.956705	−	0.291058i	$-0.905993\pi$
$887$	−1.06341e43	−1.91341	−0.956705	+	0.291058i	$0.905993\pi$
$888$	1.50479e42	0.266371
$889$	−3.31210e42	−0.576804
$890$	−1.80856e43	−3.09869
$891$	−1.01347e42	−0.170838
$892$	−3.77456e42	−0.626003
$893$	−1.56056e43	−2.54645
$894$	2.12264e40	0.00340786
$895$	−9.57194e42	−1.51205
$896$	−2.59402e42	−0.403188
$897$	3.61264e42	0.552502
$898$	−2.04657e41	−0.0307978
$899$	3.76325e42	0.557246
$900$	1.62930e42	0.237402
$901$	7.49444e42	1.07456
$902$	7.92622e42	1.11833
$903$	−1.32861e41	−0.0184469
$904$	−4.95763e42	−0.677379
$905$	−8.37921e41	−0.112668
$906$	−5.58114e42	−0.738524
$907$	−1.37246e43	−1.78728	−0.893641	−	0.448782i	$-0.851858\pi$
$907$	−1.37246e43	−1.78728	−0.893641	+	0.448782i	$0.851858\pi$
$908$	1.18403e43	1.51746
$909$	2.56776e42	0.323876
$910$	8.48118e42	1.05282
$911$	6.28747e42	0.768174	0.384087	−	0.923297i	$-0.374516\pi$
$911$	6.28747e42	0.768174	0.384087	+	0.923297i	$0.374516\pi$
$912$	3.69771e42	0.444639
$913$	−2.48693e43	−2.94332
$914$	1.36010e43	1.58435
$915$	1.21267e43	1.39039
$916$	1.77448e43	2.00256
$917$	−2.46845e42	−0.274201
$918$	−2.11348e42	−0.231088
$919$	1.77847e43	1.91413	0.957064	−	0.289875i	$-0.0936139\pi$
$919$	1.77847e43	1.91413	0.957064	+	0.289875i	$0.0936139\pi$
$920$	−4.34743e42	−0.460584
$921$	1.76446e42	0.184012
$922$	−7.42348e42	−0.762096
$923$	−1.44246e43	−1.45774
$924$	4.62737e42	0.460352
$925$	−4.26735e42	−0.417930
$926$	−1.73000e43	−1.66796
$927$	−3.19569e42	−0.303325
$928$	−9.99557e42	−0.934032
$929$	−6.67538e42	−0.614113	−0.307056	−	0.951691i	$-0.599344\pi$
$929$	−6.67538e42	−0.614113	−0.307056	+	0.951691i	$0.599344\pi$
$930$	9.57931e42	0.867624
$931$	2.52045e42	0.224755
$932$	−5.22868e42	−0.459052
$933$	−3.69808e42	−0.319663
$934$	−2.05259e43	−1.74692
$935$	1.76312e43	1.47745
$936$	−3.39709e42	−0.280290
$937$	6.50974e42	0.528858	0.264429	−	0.964405i	$-0.414816\pi$
$937$	6.50974e42	0.528858	0.264429	+	0.964405i	$0.414816\pi$
$938$	−2.04512e42	−0.163598
$939$	−7.07844e42	−0.557553
$940$	3.52895e43	2.73710
$941$	1.12055e43	0.855819	0.427910	−	0.903822i	$-0.359250\pi$
$941$	1.12055e43	0.855819	0.427910	+	0.903822i	$0.359250\pi$
$942$	−2.47885e42	−0.186428
$943$	−4.15856e42	−0.307981
$944$	−9.05664e42	−0.660501
$945$	1.24830e42	0.0896518
$946$	−2.83038e42	−0.200181
$947$	1.76995e43	1.23278	0.616391	−	0.787440i	$-0.288594\pi$
$947$	1.76995e43	1.23278	0.616391	+	0.787440i	$0.288594\pi$
$948$	2.66249e42	0.182628
$949$	1.18214e43	0.798563
$950$	1.89058e43	1.25777
$951$	−7.84449e42	−0.513981
$952$	2.61674e42	0.168859
$953$	−2.04676e43	−1.30083	−0.650414	−	0.759580i	$-0.725405\pi$
$953$	−2.04676e43	−1.30083	−0.650414	+	0.759580i	$0.725405\pi$
$954$	1.13038e43	0.707578
$955$	3.56553e43	2.19824
$956$	5.91629e42	0.359261
$957$	1.04471e43	0.624848
$958$	−1.22447e43	−0.721352
$959$	−4.58395e42	−0.265993
$960$	−1.93493e43	−1.10594
$961$	−6.63004e42	−0.373273
$962$	3.28114e43	1.81964
$963$	2.78533e42	0.152158
$964$	−8.63231e42	−0.464526
$965$	4.62612e43	2.45228
$966$	−4.19724e42	−0.219177
$967$	−1.80652e43	−0.929305	−0.464653	−	0.885493i	$-0.653821\pi$
$967$	−1.80652e43	−0.929305	−0.464653	+	0.885493i	$0.653821\pi$
$968$	1.54239e43	0.781631
$969$	−1.41853e43	−0.708179
$970$	−1.20163e43	−0.590990
$971$	3.30787e43	1.60277	0.801383	−	0.598152i	$-0.204098\pi$
$971$	3.30787e43	1.60277	0.801383	+	0.598152i	$0.204098\pi$
$972$	−1.84387e42	−0.0880177
$973$	−4.36011e42	−0.205051
$974$	−2.93347e43	−1.35918
$975$	9.63366e42	0.439769
$976$	−2.12663e43	−0.956464
$977$	1.46236e43	0.648013	0.324006	−	0.946055i	$-0.394970\pi$
$977$	1.46236e43	0.648013	0.324006	+	0.946055i	$0.394970\pi$
$978$	1.83109e43	0.799459
$979$	−5.83447e43	−2.50988
$980$	−5.69959e42	−0.241582
$981$	5.96537e41	0.0249136
$982$	−2.72880e43	−1.12294
$983$	2.75765e42	0.111818	0.0559091	−	0.998436i	$-0.482194\pi$
$983$	2.75765e42	0.111818	0.0559091	+	0.998436i	$0.482194\pi$
$984$	3.91045e42	0.156242
$985$	5.20228e43	2.04818
$986$	2.17863e43	0.845217
$987$	9.23883e42	0.353198
$988$	−8.40829e43	−3.16761
$989$	1.48498e42	0.0551284
$990$	2.65931e43	0.972878
$991$	3.83416e43	1.38230	0.691150	−	0.722712i	$-0.257105\pi$
$991$	3.83416e43	1.38230	0.691150	+	0.722712i	$0.257105\pi$
$992$	−2.95673e43	−1.05049
$993$	−1.78667e43	−0.625577
$994$	1.67589e43	0.578285
$995$	−4.19956e43	−1.42814
$996$	−4.52463e43	−1.51643
$997$	2.78711e43	0.920609	0.460304	−	0.887761i	$-0.347740\pi$
$997$	2.78711e43	0.920609	0.460304	+	0.887761i	$0.347740\pi$
$998$	7.00387e43	2.28005
$999$	4.82935e42	0.154949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.c.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+35686.0 q^{2} -4.78297e6 q^{3} +7.36619e8 q^{4} -1.68211e10 q^{5} -1.70685e11 q^{6} +6.78223e11 q^{7} +7.12823e12 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q+35686.0 q^{2} -4.78297e6 q^{3} +7.36619e8 q^{4} -1.68211e10 q^{5} -1.70685e11 q^{6} +6.78223e11 q^{7} +7.12823e12 q^{8} +2.28768e13 q^{9} -6.00279e14 q^{10} -1.93651e15 q^{11} -3.52323e15 q^{12} -2.08320e16 q^{13} +2.42031e16 q^{14} +8.04549e16 q^{15} -1.41092e17 q^{16} +5.41261e17 q^{17} +8.16381e17 q^{18} +5.47941e18 q^{19} -1.23908e19 q^{20} -3.24392e18 q^{21} -6.91064e19 q^{22} +3.62573e19 q^{23} -3.40941e19 q^{24} +9.66858e19 q^{25} -7.43411e20 q^{26} -1.09419e20 q^{27} +4.99592e20 q^{28} +1.12792e21 q^{29} +2.87111e21 q^{30} +3.33644e21 q^{31} -8.86194e21 q^{32} +9.26229e21 q^{33} +1.93154e22 q^{34} -1.14085e22 q^{35} +1.68515e22 q^{36} -4.41363e22 q^{37} +1.95538e23 q^{38} +9.96388e22 q^{39} -1.19905e23 q^{40} -1.14696e23 q^{41} -1.15763e23 q^{42} +4.09568e22 q^{43} -1.42647e24 q^{44} -3.84813e23 q^{45} +1.29388e24 q^{46} -2.84804e24 q^{47} +6.74837e23 q^{48} +4.59987e23 q^{49} +3.45033e24 q^{50} -2.58883e24 q^{51} -1.53453e25 q^{52} +1.38463e25 q^{53} -3.90473e24 q^{54} +3.25744e25 q^{55} +4.83453e24 q^{56} -2.62078e25 q^{57} +4.02510e25 q^{58} +6.41898e25 q^{59} +5.92647e25 q^{60} +1.50726e26 q^{61} +1.19064e26 q^{62} +1.55156e25 q^{63} -2.40499e26 q^{64} +3.50418e26 q^{65} +3.30534e26 q^{66} -8.44985e25 q^{67} +3.98703e26 q^{68} -1.73418e26 q^{69} -4.07123e26 q^{70} +6.92427e26 q^{71} +1.63071e26 q^{72} -5.67464e26 q^{73} -1.57505e27 q^{74} -4.62445e26 q^{75} +4.03624e27 q^{76} -1.31339e27 q^{77} +3.55571e27 q^{78} -7.55696e26 q^{79} +2.37332e27 q^{80} +5.23348e26 q^{81} -4.09304e27 q^{82} +1.28423e28 q^{83} -2.38953e27 q^{84} -9.10462e27 q^{85} +1.46159e27 q^{86} -5.39481e27 q^{87} -1.38039e28 q^{88} +3.01287e28 q^{89} -1.37325e28 q^{90} -1.41287e28 q^{91} +2.67078e28 q^{92} -1.59581e28 q^{93} -1.01635e29 q^{94} -9.21698e28 q^{95} +4.23864e28 q^{96} +2.00179e28 q^{97} +1.64151e28 q^{98} -4.43012e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9}+O(q^{10}) \) 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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