LMFDB - Embedded newform 21.30.a.c.1.3

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			1.3
Root			$7115.98$ 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)

$f(q)$	$=$	$q-5535.95 q^{2} -4.78297e6 q^{3} -5.06224e8 q^{4} -9.04739e9 q^{5} +2.64783e10 q^{6} +6.78223e11 q^{7} +5.77452e12 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q-5535.95 q^{2} -4.78297e6 q^{3} -5.06224e8 q^{4} -9.04739e9 q^{5} +2.64783e10 q^{6} +6.78223e11 q^{7} +5.77452e12 q^{8} +2.28768e13 q^{9} +5.00859e13 q^{10} -1.24835e15 q^{11} +2.42125e15 q^{12} -2.11453e15 q^{13} -3.75461e15 q^{14} +4.32734e16 q^{15} +2.39810e17 q^{16} +2.87237e17 q^{17} -1.26645e17 q^{18} -1.38973e18 q^{19} +4.58001e18 q^{20} -3.24392e18 q^{21} +6.91080e18 q^{22} -6.33379e19 q^{23} -2.76194e19 q^{24} -1.04409e20 q^{25} +1.17059e19 q^{26} -1.09419e20 q^{27} -3.43333e20 q^{28} +8.68489e19 q^{29} -2.39559e20 q^{30} -8.17902e21 q^{31} -4.42775e21 q^{32} +5.97082e21 q^{33} -1.59013e21 q^{34} -6.13615e21 q^{35} -1.15808e22 q^{36} -4.04940e21 q^{37} +7.69350e21 q^{38} +1.01137e22 q^{39} -5.22444e22 q^{40} -1.80143e23 q^{41} +1.79582e22 q^{42} -3.59182e23 q^{43} +6.31945e23 q^{44} -2.06975e23 q^{45} +3.50636e23 q^{46} -2.81426e23 q^{47} -1.14700e24 q^{48} +4.59987e23 q^{49} +5.78004e23 q^{50} -1.37385e24 q^{51} +1.07043e24 q^{52} -1.29050e25 q^{53} +6.05738e23 q^{54} +1.12943e25 q^{55} +3.91641e24 q^{56} +6.64705e24 q^{57} -4.80791e23 q^{58} +1.72595e25 q^{59} -2.19060e25 q^{60} -7.74557e25 q^{61} +4.52787e25 q^{62} +1.55156e25 q^{63} -1.04235e26 q^{64} +1.91310e25 q^{65} -3.30541e25 q^{66} +9.27862e25 q^{67} -1.45407e26 q^{68} +3.02943e26 q^{69} +3.39694e25 q^{70} +4.90313e26 q^{71} +1.32103e26 q^{72} -1.35108e27 q^{73} +2.24173e25 q^{74} +4.99386e26 q^{75} +7.03517e26 q^{76} -8.46659e26 q^{77} -5.59891e25 q^{78} +9.34764e26 q^{79} -2.16965e27 q^{80} +5.23348e26 q^{81} +9.97262e26 q^{82} -2.31835e27 q^{83} +1.64215e27 q^{84} -2.59875e27 q^{85} +1.98841e27 q^{86} -4.15396e26 q^{87} -7.20862e27 q^{88} -2.85779e28 q^{89} +1.14581e27 q^{90} -1.43412e27 q^{91} +3.20632e28 q^{92} +3.91200e28 q^{93} +1.55796e27 q^{94} +1.25735e28 q^{95} +2.11778e28 q^{96} +9.87228e28 q^{97} -2.54646e27 q^{98} -2.85582e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5535.95	−0.238923	−0.119461	−	0.992839i	$-0.538117\pi$
$2$	−5535.95	−0.238923	−0.119461	+	0.992839i	$0.538117\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	−5.06224e8	−0.942916
$5$	−9.04739e9	−0.662916	−0.331458	−	0.943470i	$-0.607541\pi$
$5$	−9.04739e9	−0.662916	−0.331458	+	0.943470i	$0.607541\pi$
$6$	2.64783e10	0.137942
$7$	6.78223e11	0.377964
$7$	6.78223e11	0.377964
$8$	5.77452e12	0.464207
$9$	2.28768e13	0.333333
$10$	5.00859e13	0.158386
$11$	−1.24835e15	−0.991157	−0.495578	−	0.868563i	$-0.665044\pi$
$11$	−1.24835e15	−0.991157	−0.495578	+	0.868563i	$0.665044\pi$
$12$	2.42125e15	0.544393
$13$	−2.11453e15	−0.148948	−0.0744741	−	0.997223i	$-0.523728\pi$
$13$	−2.11453e15	−0.148948	−0.0744741	+	0.997223i	$0.523728\pi$
$14$	−3.75461e15	−0.0903043
$15$	4.32734e16	0.382735
$16$	2.39810e17	0.832007
$17$	2.87237e17	0.413744	0.206872	−	0.978368i	$-0.433672\pi$
$17$	2.87237e17	0.413744	0.206872	+	0.978368i	$0.433672\pi$
$18$	−1.26645e17	−0.0796409
$19$	−1.38973e18	−0.399029	−0.199514	−	0.979895i	$-0.563936\pi$
$19$	−1.38973e18	−0.399029	−0.199514	+	0.979895i	$0.563936\pi$
$20$	4.58001e18	0.625074
$21$	−3.24392e18	−0.218218
$22$	6.91080e18	0.236810
$23$	−6.33379e19	−1.13923	−0.569614	−	0.821913i	$-0.692907\pi$
$23$	−6.33379e19	−1.13923	−0.569614	+	0.821913i	$0.692907\pi$
$24$	−2.76194e19	−0.268010
$25$	−1.04409e20	−0.560542
$26$	1.17059e19	0.0355871
$27$	−1.09419e20	−0.192450
$28$	−3.43333e20	−0.356389
$29$	8.68489e19	0.0541992	0.0270996	−	0.999633i	$-0.491373\pi$
$29$	8.68489e19	0.0541992	0.0270996	+	0.999633i	$0.491373\pi$
$30$	−2.39559e20	−0.0914440
$31$	−8.17902e21	−1.94069	−0.970346	−	0.241719i	$-0.922289\pi$
$31$	−8.17902e21	−1.94069	−0.970346	+	0.241719i	$0.922289\pi$
$32$	−4.42775e21	−0.662992
$33$	5.97082e21	0.572244
$34$	−1.59013e21	−0.0988528
$35$	−6.13615e21	−0.250559
$36$	−1.15808e22	−0.314305
$37$	−4.04940e21	−0.0738695	−0.0369348	−	0.999318i	$-0.511759\pi$
$37$	−4.04940e21	−0.0738695	−0.0369348	+	0.999318i	$0.511759\pi$
$38$	7.69350e21	0.0953370
$39$	1.01137e22	0.0859953
$40$	−5.22444e22	−0.307730
$41$	−1.80143e23	−0.741739	−0.370870	−	0.928685i	$-0.620940\pi$
$41$	−1.80143e23	−0.741739	−0.370870	+	0.928685i	$0.620940\pi$
$42$	1.79582e22	0.0521372
$43$	−3.59182e23	−0.741347	−0.370673	−	0.928763i	$-0.620873\pi$
$43$	−3.59182e23	−0.741347	−0.370673	+	0.928763i	$0.620873\pi$
$44$	6.31945e23	0.934577
$45$	−2.06975e23	−0.220972
$46$	3.50636e23	0.272187
$47$	−2.81426e23	−0.159936	−0.0799679	−	0.996797i	$-0.525482\pi$
$47$	−2.81426e23	−0.159936	−0.0799679	+	0.996797i	$0.525482\pi$
$48$	−1.14700e24	−0.480359
$49$	4.59987e23	0.142857
$50$	5.78004e23	0.133926
$51$	−1.37385e24	−0.238875
$52$	1.07043e24	0.140446
$53$	−1.29050e25	−1.28457	−0.642287	−	0.766464i	$-0.722014\pi$
$53$	−1.29050e25	−1.28457	−0.642287	+	0.766464i	$0.722014\pi$
$54$	6.05738e23	0.0459807
$55$	1.12943e25	0.657053
$56$	3.91641e24	0.175454
$57$	6.64705e24	0.230379
$58$	−4.80791e23	−0.0129494
$59$	1.72595e25	0.362806	0.181403	−	0.983409i	$-0.441936\pi$
$59$	1.72595e25	0.362806	0.181403	+	0.983409i	$0.441936\pi$
$60$	−2.19060e25	−0.360887
$61$	−7.74557e25	−1.00409	−0.502043	−	0.864843i	$-0.667418\pi$
$61$	−7.74557e25	−1.00409	−0.502043	+	0.864843i	$0.667418\pi$
$62$	4.52787e25	0.463675
$63$	1.55156e25	0.125988
$64$	−1.04235e26	−0.673603
$65$	1.91310e25	0.0987401
$66$	−3.30541e25	−0.136722
$67$	9.27862e25	0.308602	0.154301	−	0.988024i	$-0.450687\pi$
$67$	9.27862e25	0.308602	0.154301	+	0.988024i	$0.450687\pi$
$68$	−1.45407e26	−0.390126
$69$	3.02943e26	0.657733
$70$	3.39694e25	0.0598641
$71$	4.90313e26	0.703441	0.351720	−	0.936105i	$-0.385597\pi$
$71$	4.90313e26	0.703441	0.351720	+	0.936105i	$0.385597\pi$
$72$	1.32103e26	0.154736
$73$	−1.35108e27	−1.29569	−0.647845	−	0.761773i	$-0.724329\pi$
$73$	−1.35108e27	−1.29569	−0.647845	+	0.761773i	$0.724329\pi$
$74$	2.24173e25	0.0176491
$75$	4.99386e26	0.323629
$76$	7.03517e26	0.376251
$77$	−8.46659e26	−0.374622
$78$	−5.59891e25	−0.0205462
$79$	9.34764e26	0.285173	0.142587	−	0.989782i	$-0.454458\pi$
$79$	9.34764e26	0.285173	0.142587	+	0.989782i	$0.454458\pi$
$80$	−2.16965e27	−0.551550
$81$	5.23348e26	0.111111
$82$	9.97262e26	0.177218
$83$	−2.31835e27	−0.345578	−0.172789	−	0.984959i	$-0.555278\pi$
$83$	−2.31835e27	−0.345578	−0.172789	+	0.984959i	$0.555278\pi$
$84$	1.64215e27	0.205761
$85$	−2.59875e27	−0.274277
$86$	1.98841e27	0.177125
$87$	−4.15396e26	−0.0312920
$88$	−7.20862e27	−0.460101
$89$	−2.85779e28	−1.54837	−0.774187	−	0.632957i	$-0.781841\pi$
$89$	−2.85779e28	−1.54837	−0.774187	+	0.632957i	$0.781841\pi$
$90$	1.14581e27	0.0527952
$91$	−1.43412e27	−0.0562971
$92$	3.20632e28	1.07420
$93$	3.91200e28	1.12046
$94$	1.55796e27	0.0382123
$95$	1.25735e28	0.264523
$96$	2.11778e28	0.382778
$97$	9.87228e28	1.53542	0.767710	−	0.640798i	$-0.221396\pi$
$97$	9.87228e28	1.53542	0.767710	+	0.640798i	$0.221396\pi$
$98$	−2.54646e27	−0.0341318
$99$	−2.85582e28	−0.330386
$100$	5.28544e28	0.528544
$101$	4.15884e28	0.360008	0.180004	−	0.983666i	$-0.442389\pi$
$101$	4.15884e28	0.360008	0.180004	+	0.983666i	$0.442389\pi$
$102$	7.60555e27	0.0570727
$103$	1.20371e29	0.784117	0.392058	−	0.919940i	$-0.371763\pi$
$103$	1.20371e29	0.784117	0.392058	+	0.919940i	$0.371763\pi$
$104$	−1.22104e28	−0.0691427
$105$	2.93490e28	0.144660
$106$	7.14417e28	0.306914
$107$	−3.57961e28	−0.134206	−0.0671028	−	0.997746i	$-0.521376\pi$
$107$	−3.57961e28	−0.134206	−0.0671028	+	0.997746i	$0.521376\pi$
$108$	5.53905e28	0.181464
$109$	−2.02154e29	−0.579425	−0.289713	−	0.957114i	$-0.593560\pi$
$109$	−2.02154e29	−0.579425	−0.289713	+	0.957114i	$0.593560\pi$
$110$	−6.25247e28	−0.156985
$111$	1.93681e28	0.0426486
$112$	1.62644e29	0.314469
$113$	−6.56137e29	−1.11521	−0.557605	−	0.830106i	$-0.688280\pi$
$113$	−6.56137e29	−1.11521	−0.557605	+	0.830106i	$0.688280\pi$
$114$	−3.67978e28	−0.0550429
$115$	5.73043e29	0.755212
$116$	−4.39650e28	−0.0511053
$117$	−4.83737e28	−0.0496494
$118$	−9.55478e28	−0.0866826
$119$	1.94811e29	0.156381
$120$	2.49883e29	0.177668
$121$	−2.79330e28	−0.0176088
$122$	4.28791e29	0.239899
$123$	8.61618e29	0.428243
$124$	4.14042e30	1.82991
$125$	2.62984e30	1.03451
$126$	−8.58934e28	−0.0301014
$127$	2.55053e30	0.797032	0.398516	−	0.917161i	$-0.369525\pi$
$127$	2.55053e30	0.797032	0.398516	+	0.917161i	$0.369525\pi$
$128$	2.95417e30	0.823931
$129$	1.71795e30	0.428017
$130$	−1.05908e29	−0.0235913
$131$	3.16433e30	0.630736	0.315368	−	0.948970i	$-0.397872\pi$
$131$	3.16433e30	0.630736	0.315368	+	0.948970i	$0.397872\pi$
$132$	−3.02257e30	−0.539578
$133$	−9.42549e29	−0.150819
$134$	−5.13660e29	−0.0737320
$135$	9.89957e29	0.127578
$136$	1.65866e30	0.192063
$137$	1.46613e31	1.52659	0.763297	−	0.646047i	$-0.223579\pi$
$137$	1.46613e31	1.52659	0.763297	+	0.646047i	$0.223579\pi$
$138$	−1.67708e30	−0.157147
$139$	7.90680e30	0.667246	0.333623	−	0.942707i	$-0.391729\pi$
$139$	7.90680e30	0.667246	0.333623	+	0.942707i	$0.391729\pi$
$140$	3.10627e30	0.236256
$141$	1.34605e30	0.0923390
$142$	−2.71435e30	−0.168068
$143$	2.63967e30	0.147631
$144$	5.48607e30	0.277336
$145$	−7.85756e29	−0.0359295
$146$	7.47953e30	0.309569
$147$	−2.20010e30	−0.0824786
$148$	2.04990e30	0.0696528
$149$	5.61696e31	1.73101	0.865507	−	0.500897i	$-0.166997\pi$
$149$	5.61696e31	1.73101	0.865507	+	0.500897i	$0.166997\pi$
$150$	−2.76458e30	−0.0773224
$151$	−4.37841e31	−1.11212	−0.556059	−	0.831143i	$-0.687687\pi$
$151$	−4.37841e31	−1.11212	−0.556059	+	0.831143i	$0.687687\pi$
$152$	−8.02505e30	−0.185232
$153$	6.57107e30	0.137915
$154$	4.68706e30	0.0895057
$155$	7.39988e31	1.28652
$156$	−5.11982e30	−0.0810863
$157$	1.69283e31	0.244381	0.122190	−	0.992507i	$-0.461008\pi$
$157$	1.69283e31	0.244381	0.122190	+	0.992507i	$0.461008\pi$
$158$	−5.17481e30	−0.0681344
$159$	6.17244e31	0.741650
$160$	4.00596e31	0.439508
$161$	−4.29573e31	−0.430587
$162$	−2.89723e30	−0.0265470
$163$	1.08839e32	0.912143	0.456072	−	0.889943i	$-0.349256\pi$
$163$	1.08839e32	0.912143	0.456072	+	0.889943i	$0.349256\pi$
$164$	9.11927e31	0.699398
$165$	−5.40203e31	−0.379350
$166$	1.28343e31	0.0825664
$167$	−2.58367e32	−1.52352	−0.761760	−	0.647859i	$-0.775665\pi$
$167$	−2.58367e32	−1.52352	−0.761760	+	0.647859i	$0.775665\pi$
$168$	−1.87321e31	−0.101298
$169$	−1.97067e32	−0.977814
$170$	1.43866e31	0.0655311
$171$	−3.17926e31	−0.133010
$172$	1.81826e32	0.699028
$173$	−2.63980e32	−0.933044	−0.466522	−	0.884510i	$-0.654493\pi$
$173$	−2.63980e32	−0.933044	−0.466522	+	0.884510i	$0.654493\pi$
$174$	2.29961e30	0.00747635
$175$	−7.08127e31	−0.211865
$176$	−2.99366e32	−0.824649
$177$	−8.25517e31	−0.209466
$178$	1.58206e32	0.369941
$179$	−3.49027e32	−0.752471	−0.376236	−	0.926524i	$-0.622782\pi$
$179$	−3.49027e32	−0.752471	−0.376236	+	0.926524i	$0.622782\pi$
$180$	1.04776e32	0.208358
$181$	−2.50109e32	−0.458976	−0.229488	−	0.973312i	$-0.573705\pi$
$181$	−2.50109e32	−0.458976	−0.229488	+	0.973312i	$0.573705\pi$
$182$	7.93924e30	0.0134507
$183$	3.70468e32	0.579709
$184$	−3.65746e32	−0.528837
$185$	3.66365e31	0.0489693
$186$	−2.16566e32	−0.267703
$187$	−3.58573e32	−0.410085
$188$	1.42465e32	0.150806
$189$	−7.42105e31	−0.0727393
$190$	−6.96061e31	−0.0632004
$191$	2.14301e32	0.180318	0.0901592	−	0.995927i	$-0.471262\pi$
$191$	2.14301e32	0.180318	0.0901592	+	0.995927i	$0.471262\pi$
$192$	4.98553e32	0.388905
$193$	−2.12887e33	−1.54017	−0.770085	−	0.637942i	$-0.779786\pi$
$193$	−2.12887e33	−1.54017	−0.770085	+	0.637942i	$0.779786\pi$
$194$	−5.46524e32	−0.366847
$195$	−9.15029e31	−0.0570076
$196$	−2.32856e32	−0.134702
$197$	−1.54356e33	−0.829399	−0.414699	−	0.909959i	$-0.636113\pi$
$197$	−1.54356e33	−0.829399	−0.414699	+	0.909959i	$0.636113\pi$
$198$	1.58097e32	0.0789366
$199$	−1.40108e33	−0.650269	−0.325134	−	0.945668i	$-0.605410\pi$
$199$	−1.40108e33	−0.650269	−0.325134	+	0.945668i	$0.605410\pi$
$200$	−6.02913e32	−0.260207
$201$	−4.43794e32	−0.178171
$202$	−2.30232e32	−0.0860142
$203$	5.89029e31	0.0204854
$204$	6.95475e32	0.225239
$205$	1.62982e33	0.491711
$206$	−6.66366e32	−0.187343
$207$	−1.44897e33	−0.379742
$208$	−5.07085e32	−0.123926
$209$	1.73487e33	0.395500
$210$	−1.62475e32	−0.0345626
$211$	−2.68715e33	−0.533575	−0.266788	−	0.963755i	$-0.585962\pi$
$211$	−2.68715e33	−0.533575	−0.266788	+	0.963755i	$0.585962\pi$
$212$	6.53284e33	1.21125
$213$	−2.34515e33	−0.406132
$214$	1.98165e32	0.0320648
$215$	3.24966e33	0.491451
$216$	−6.31842e32	−0.0893366
$217$	−5.54720e33	−0.733513
$218$	1.11911e33	0.138438
$219$	6.46219e33	0.748066
$220$	−5.71745e33	−0.619546
$221$	−6.07372e32	−0.0616264
$222$	−1.07221e32	−0.0101897
$223$	1.51324e34	1.34737	0.673687	−	0.739017i	$-0.264710\pi$
$223$	1.51324e34	1.34737	0.673687	+	0.739017i	$0.264710\pi$
$224$	−3.00300e33	−0.250587
$225$	−2.38855e33	−0.186847
$226$	3.63234e33	0.266449
$227$	9.63124e32	0.0662685	0.0331343	−	0.999451i	$-0.489451\pi$
$227$	9.63124e32	0.0662685	0.0331343	+	0.999451i	$0.489451\pi$
$228$	−3.36490e33	−0.217228
$229$	−5.81973e33	−0.352605	−0.176302	−	0.984336i	$-0.556414\pi$
$229$	−5.81973e33	−0.352605	−0.176302	+	0.984336i	$0.556414\pi$
$230$	−3.17234e33	−0.180437
$231$	4.04955e33	0.216288
$232$	5.01511e32	0.0251596
$233$	2.19613e34	1.03514	0.517568	−	0.855642i	$-0.326838\pi$
$233$	2.19613e34	1.03514	0.517568	+	0.855642i	$0.326838\pi$
$234$	2.67794e32	0.0118624
$235$	2.54617e33	0.106024
$236$	−8.73719e33	−0.342096
$237$	−4.47095e33	−0.164645
$238$	−1.07846e33	−0.0373628
$239$	4.65678e34	1.51816	0.759078	−	0.651000i	$-0.225650\pi$
$239$	4.65678e34	1.51816	0.759078	+	0.651000i	$0.225650\pi$
$240$	1.03774e34	0.318438
$241$	1.81067e34	0.523108	0.261554	−	0.965189i	$-0.415765\pi$
$241$	1.81067e34	0.523108	0.261554	+	0.965189i	$0.415765\pi$
$242$	1.54635e32	0.00420713
$243$	−2.50316e33	−0.0641500
$244$	3.92099e34	0.946768
$245$	−4.16168e33	−0.0947023
$246$	−4.76987e33	−0.102317
$247$	2.93863e33	0.0594346
$248$	−4.72299e34	−0.900882
$249$	1.10886e34	0.199520
$250$	−1.45587e34	−0.247167
$251$	2.31905e34	0.371571	0.185785	−	0.982590i	$-0.440517\pi$
$251$	2.31905e34	0.371571	0.185785	+	0.982590i	$0.440517\pi$
$252$	−7.85436e33	−0.118796
$253$	7.90679e34	1.12915
$254$	−1.41196e34	−0.190429
$255$	1.24297e34	0.158354
$256$	3.96066e34	0.476747
$257$	1.30670e35	1.48643	0.743217	−	0.669051i	$-0.233299\pi$
$257$	1.30670e35	1.48643	0.743217	+	0.669051i	$0.233299\pi$
$258$	−9.51051e33	−0.102263
$259$	−2.74639e33	−0.0279201
$260$	−9.68457e33	−0.0931037
$261$	1.98682e33	0.0180664
$262$	−1.75175e34	−0.150697
$263$	−1.07351e35	−0.873876	−0.436938	−	0.899492i	$-0.643937\pi$
$263$	−1.07351e35	−0.873876	−0.436938	+	0.899492i	$0.643937\pi$
$264$	3.44786e34	0.265640
$265$	1.16757e35	0.851565
$266$	5.21791e33	0.0360340
$267$	1.36687e35	0.893954
$268$	−4.69706e34	−0.290986
$269$	−2.03586e35	−1.19492	−0.597461	−	0.801898i	$-0.703824\pi$
$269$	−2.03586e35	−1.19492	−0.597461	+	0.801898i	$0.703824\pi$
$270$	−5.48035e33	−0.0304813
$271$	−3.00634e35	−1.58483	−0.792417	−	0.609979i	$-0.791178\pi$
$271$	−3.00634e35	−1.58483	−0.792417	+	0.609979i	$0.791178\pi$
$272$	6.88823e34	0.344238
$273$	6.85937e33	0.0325032
$274$	−8.11641e34	−0.364738
$275$	1.30339e35	0.555585
$276$	−1.53357e35	−0.620187
$277$	2.24974e34	0.0863327	0.0431664	−	0.999068i	$-0.486255\pi$
$277$	2.24974e34	0.0863327	0.0431664	+	0.999068i	$0.486255\pi$
$278$	−4.37717e34	−0.159420
$279$	−1.87110e35	−0.646898
$280$	−3.54333e34	−0.116311
$281$	9.27463e34	0.289105	0.144552	−	0.989497i	$-0.453826\pi$
$281$	9.27463e34	0.289105	0.144552	+	0.989497i	$0.453826\pi$
$282$	−7.45168e33	−0.0220619
$283$	−4.79513e35	−1.34864	−0.674321	−	0.738438i	$-0.735564\pi$
$283$	−4.79513e35	−1.34864	−0.674321	+	0.738438i	$0.735564\pi$
$284$	−2.48208e35	−0.663286
$285$	−6.01385e34	−0.152722
$286$	−1.46131e34	−0.0352724
$287$	−1.22177e35	−0.280351
$288$	−1.01293e35	−0.220997
$289$	−3.99463e35	−0.828816
$290$	4.34991e33	0.00858438
$291$	−4.72188e35	−0.886475
$292$	6.83951e35	1.22173
$293$	−1.67571e35	−0.284852	−0.142426	−	0.989805i	$-0.545490\pi$
$293$	−1.67571e35	−0.284852	−0.142426	+	0.989805i	$0.545490\pi$
$294$	1.21797e34	0.0197060
$295$	−1.56154e35	−0.240510
$296$	−2.33833e34	−0.0342907
$297$	1.36593e35	0.190748
$298$	−3.10952e35	−0.413578
$299$	1.33930e35	0.169686
$300$	−2.52801e35	−0.305155
$301$	−2.43605e35	−0.280203
$302$	2.42387e35	0.265710
$303$	−1.98916e35	−0.207851
$304$	−3.33271e35	−0.331995
$305$	7.00772e35	0.665624
$306$	−3.63771e34	−0.0329509
$307$	4.89947e35	0.423295	0.211647	−	0.977346i	$-0.432117\pi$
$307$	4.89947e35	0.423295	0.211647	+	0.977346i	$0.432117\pi$
$308$	4.28599e35	0.353237
$309$	−5.75729e35	−0.452710
$310$	−4.09654e35	−0.307378
$311$	1.81936e36	1.30284	0.651422	−	0.758715i	$-0.274173\pi$
$311$	1.81936e36	1.30284	0.651422	+	0.758715i	$0.274173\pi$
$312$	5.84020e34	0.0399196
$313$	1.80176e36	1.17572	0.587861	−	0.808962i	$-0.299970\pi$
$313$	1.80176e36	1.17572	0.587861	+	0.808962i	$0.299970\pi$
$314$	−9.37140e34	−0.0583881
$315$	−1.40375e35	−0.0835196
$316$	−4.73200e35	−0.268895
$317$	−1.49880e36	−0.813550	−0.406775	−	0.913528i	$-0.633347\pi$
$317$	−1.49880e36	−0.813550	−0.406775	+	0.913528i	$0.633347\pi$
$318$	−3.41703e35	−0.177197
$319$	−1.08418e35	−0.0537199
$320$	9.43055e35	0.446542
$321$	1.71212e35	0.0774837
$322$	2.37809e35	0.102877
$323$	−3.99183e35	−0.165096
$324$	−2.64931e35	−0.104768
$325$	2.20776e35	0.0834918
$326$	−6.02526e35	−0.217932
$327$	9.66895e35	0.334531
$328$	−1.04024e36	−0.344320
$329$	−1.90870e35	−0.0604500
$330$	2.99054e35	0.0906353
$331$	−4.70250e36	−1.36403	−0.682014	−	0.731339i	$-0.738896\pi$
$331$	−4.70250e36	−1.36403	−0.682014	+	0.731339i	$0.738896\pi$
$332$	1.17360e36	0.325851
$333$	−9.26372e34	−0.0246232
$334$	1.43031e36	0.364004
$335$	−8.39473e35	−0.204577
$336$	−7.77923e35	−0.181559
$337$	4.96865e36	1.11072	0.555361	−	0.831610i	$-0.312580\pi$
$337$	4.96865e36	1.11072	0.555361	+	0.831610i	$0.312580\pi$
$338$	1.09095e36	0.233622
$339$	3.13828e36	0.643867
$340$	1.31555e36	0.258621
$341$	1.02103e37	1.92353
$342$	1.76003e35	0.0317790
$343$	3.11973e35	0.0539949
$344$	−2.07410e36	−0.344138
$345$	−2.74085e36	−0.436022
$346$	1.46138e36	0.222925
$347$	7.24582e36	1.06001	0.530005	−	0.847994i	$-0.322190\pi$
$347$	7.24582e36	1.06001	0.530005	+	0.847994i	$0.322190\pi$
$348$	2.10283e35	0.0295057
$349$	−8.08673e36	−1.08844	−0.544220	−	0.838943i	$-0.683174\pi$
$349$	−8.08673e36	−1.08844	−0.544220	+	0.838943i	$0.683174\pi$
$350$	3.92016e35	0.0506194
$351$	2.31370e35	0.0286651
$352$	5.52738e36	0.657129
$353$	1.00665e37	1.14854	0.574271	−	0.818665i	$-0.305286\pi$
$353$	1.00665e37	1.14854	0.574271	+	0.818665i	$0.305286\pi$
$354$	4.57002e35	0.0500462
$355$	−4.43606e36	−0.466322
$356$	1.44668e37	1.45999
$357$	−9.31775e35	−0.0902863
$358$	1.93219e36	0.179782
$359$	3.26792e36	0.292013	0.146006	−	0.989284i	$-0.453358\pi$
$359$	3.26792e36	0.292013	0.146006	+	0.989284i	$0.453358\pi$
$360$	−1.19518e36	−0.102577
$361$	−1.01985e37	−0.840776
$362$	1.38459e36	0.109660
$363$	1.33602e35	0.0101664
$364$	7.25988e35	0.0530835
$365$	1.22238e37	0.858933
$366$	−2.05089e36	−0.138506
$367$	−4.81021e36	−0.312252	−0.156126	−	0.987737i	$-0.549901\pi$
$367$	−4.81021e36	−0.312252	−0.156126	+	0.987737i	$0.549901\pi$
$368$	−1.51890e37	−0.947844
$369$	−4.12109e36	−0.247246
$370$	−2.02818e35	−0.0116999
$371$	−8.75250e36	−0.485524
$372$	−1.98035e37	−1.05650
$373$	−1.18259e37	−0.606815	−0.303408	−	0.952861i	$-0.598124\pi$
$373$	−1.18259e37	−0.606815	−0.303408	+	0.952861i	$0.598124\pi$
$374$	1.98504e36	0.0979786
$375$	−1.25784e37	−0.597274
$376$	−1.62510e36	−0.0742432
$377$	−1.83645e35	−0.00807288
$378$	4.10826e35	0.0173791
$379$	−1.08737e37	−0.442697	−0.221349	−	0.975195i	$-0.571046\pi$
$379$	−1.08737e37	−0.442697	−0.221349	+	0.975195i	$0.571046\pi$
$380$	−6.36499e36	−0.249423
$381$	−1.21991e37	−0.460167
$382$	−1.18636e36	−0.0430822
$383$	2.43617e37	0.851777	0.425888	−	0.904776i	$-0.359962\pi$
$383$	2.43617e37	0.851777	0.425888	+	0.904776i	$0.359962\pi$
$384$	−1.41297e37	−0.475697
$385$	7.66006e36	0.248343
$386$	1.17853e37	0.367981
$387$	−8.21692e36	−0.247116
$388$	−4.99758e37	−1.44777
$389$	6.58058e37	1.83652	0.918258	−	0.395982i	$-0.129596\pi$
$389$	6.58058e37	1.83652	0.918258	+	0.395982i	$0.129596\pi$
$390$	5.06556e35	0.0136204
$391$	−1.81930e37	−0.471348
$392$	2.65620e36	0.0663152
$393$	−1.51349e37	−0.364155
$394$	8.54507e36	0.198162
$395$	−8.45718e36	−0.189046
$396$	1.44569e37	0.311526
$397$	−3.07186e37	−0.638174	−0.319087	−	0.947725i	$-0.603376\pi$
$397$	−3.07186e37	−0.638174	−0.319087	+	0.947725i	$0.603376\pi$
$398$	7.75630e36	0.155364
$399$	4.50818e36	0.0870752
$400$	−2.50383e37	−0.466375
$401$	5.07278e37	0.911281	0.455641	−	0.890164i	$-0.349410\pi$
$401$	5.07278e37	0.911281	0.455641	+	0.890164i	$0.349410\pi$
$402$	2.45682e36	0.0425692
$403$	1.72948e37	0.289063
$404$	−2.10531e37	−0.339458
$405$	−4.73493e36	−0.0736573
$406$	−3.26084e35	−0.00489442
$407$	5.05506e36	0.0732163
$408$	−7.93331e36	−0.110887
$409$	−1.01286e38	−1.36635	−0.683175	−	0.730255i	$-0.739401\pi$
$409$	−1.01286e38	−1.36635	−0.683175	+	0.730255i	$0.739401\pi$
$410$	−9.02262e36	−0.117481
$411$	−7.01245e37	−0.881380
$412$	−6.09345e37	−0.739356
$413$	1.17058e37	0.137128
$414$	8.02142e36	0.0907290
$415$	2.09750e37	0.229089
$416$	9.36261e36	0.0987514
$417$	−3.78180e37	−0.385235
$418$	−9.60417e36	−0.0944939
$419$	4.89280e37	0.465001	0.232501	−	0.972596i	$-0.425309\pi$
$419$	4.89280e37	0.465001	0.232501	+	0.972596i	$0.425309\pi$
$420$	−1.48572e37	−0.136402
$421$	5.75047e37	0.510050	0.255025	−	0.966934i	$-0.417916\pi$
$421$	5.75047e37	0.510050	0.255025	+	0.966934i	$0.417916\pi$
$422$	1.48759e37	0.127483
$423$	−6.43813e36	−0.0533119
$424$	−7.45205e37	−0.596308
$425$	−2.99902e37	−0.231921
$426$	1.29827e37	0.0970341
$427$	−5.25322e37	−0.379509
$428$	1.81208e37	0.126545
$429$	−1.26255e37	−0.0852348
$430$	−1.79899e37	−0.117419
$431$	6.28909e37	0.396887	0.198444	−	0.980112i	$-0.436411\pi$
$431$	6.28909e37	0.396887	0.198444	+	0.980112i	$0.436411\pi$
$432$	−2.62397e37	−0.160120
$433$	2.51448e38	1.48379	0.741897	−	0.670513i	$-0.233926\pi$
$433$	2.51448e38	1.48379	0.741897	+	0.670513i	$0.233926\pi$
$434$	3.07090e37	0.175253
$435$	3.75825e36	0.0207439
$436$	1.02335e38	0.546349
$437$	8.80229e37	0.454585
$438$	−3.57744e37	−0.178730
$439$	−1.28096e38	−0.619157	−0.309578	−	0.950874i	$-0.600188\pi$
$439$	−1.28096e38	−0.619157	−0.309578	+	0.950874i	$0.600188\pi$
$440$	6.52193e37	0.305009
$441$	1.05230e37	0.0476190
$442$	3.36238e36	0.0147239
$443$	4.14024e38	1.75457	0.877287	−	0.479966i	$-0.159351\pi$
$443$	4.14024e38	1.75457	0.877287	+	0.479966i	$0.159351\pi$
$444$	−9.80462e36	−0.0402140
$445$	2.58556e38	1.02644
$446$	−8.37724e37	−0.321918
$447$	−2.68657e38	−0.999401
$448$	−7.06946e37	−0.254598
$449$	2.01183e38	0.701486	0.350743	−	0.936472i	$-0.385929\pi$
$449$	2.01183e38	0.701486	0.350743	+	0.936472i	$0.385929\pi$
$450$	1.32229e37	0.0446421
$451$	2.24881e38	0.735179
$452$	3.32152e38	1.05155
$453$	2.09418e38	0.642082
$454$	−5.33181e36	−0.0158331
$455$	1.29751e37	0.0373203
$456$	3.83836e37	0.106944
$457$	3.37067e38	0.909768	0.454884	−	0.890551i	$-0.349681\pi$
$457$	3.37067e38	0.909768	0.454884	+	0.890551i	$0.349681\pi$
$458$	3.22177e37	0.0842453
$459$	−3.14292e37	−0.0796251
$460$	−2.90088e38	−0.712101
$461$	−1.68871e38	−0.401691	−0.200845	−	0.979623i	$-0.564369\pi$
$461$	−1.68871e38	−0.401691	−0.200845	+	0.979623i	$0.564369\pi$
$462$	−2.24181e37	−0.0516761
$463$	−6.22210e38	−1.38999	−0.694997	−	0.719013i	$-0.744594\pi$
$463$	−6.22210e38	−1.38999	−0.694997	+	0.719013i	$0.744594\pi$
$464$	2.08272e37	0.0450941
$465$	−3.53934e38	−0.742770
$466$	−1.21577e38	−0.247317
$467$	5.54524e38	1.09352	0.546759	−	0.837290i	$-0.315861\pi$
$467$	5.54524e38	1.09352	0.546759	+	0.837290i	$0.315861\pi$
$468$	2.44879e37	0.0468152
$469$	6.29297e37	0.116641
$470$	−1.40955e37	−0.0253315
$471$	−8.09673e37	−0.141093
$472$	9.96655e37	0.168417
$473$	4.48384e38	0.734791
$474$	2.47509e37	0.0393374
$475$	1.45101e38	0.223673
$476$	−9.86181e37	−0.147454
$477$	−2.95226e38	−0.428192
$478$	−2.57797e38	−0.362722
$479$	1.22738e39	1.67538	0.837690	−	0.546146i	$-0.183905\pi$
$479$	1.22738e39	1.67538	0.837690	+	0.546146i	$0.183905\pi$
$480$	−1.91604e38	−0.253750
$481$	8.56257e36	0.0110027
$482$	−1.00238e38	−0.124982
$483$	2.05463e38	0.248600
$484$	1.41403e37	0.0166036
$485$	−8.93184e38	−1.01785
$486$	1.38573e37	0.0153269
$487$	2.01564e38	0.216393	0.108196	−	0.994130i	$-0.465492\pi$
$487$	2.01564e38	0.216393	0.108196	+	0.994130i	$0.465492\pi$
$488$	−4.47270e38	−0.466103
$489$	−5.20572e38	−0.526626
$490$	2.30389e37	0.0226265
$491$	−8.88073e38	−0.846773	−0.423386	−	0.905949i	$-0.639159\pi$
$491$	−8.88073e38	−0.846773	−0.423386	+	0.905949i	$0.639159\pi$
$492$	−4.36172e38	−0.403797
$493$	2.49462e37	0.0224246
$494$	−1.62681e37	−0.0142003
$495$	2.58378e38	0.219018
$496$	−1.96141e39	−1.61467
$497$	3.32542e38	0.265876
$498$	−6.13859e37	−0.0476698
$499$	−3.66155e38	−0.276189	−0.138095	−	0.990419i	$-0.544098\pi$
$499$	−3.66155e38	−0.276189	−0.138095	+	0.990419i	$0.544098\pi$
$500$	−1.33129e39	−0.975455
$501$	1.23576e39	0.879605
$502$	−1.28382e38	−0.0887767
$503$	3.45235e38	0.231942	0.115971	−	0.993253i	$-0.463002\pi$
$503$	3.45235e38	0.231942	0.115971	+	0.993253i	$0.463002\pi$
$504$	8.95950e37	0.0584845
$505$	−3.76267e38	−0.238655
$506$	−4.37716e38	−0.269780
$507$	9.42565e38	0.564541
$508$	−1.29114e39	−0.751534
$509$	1.56018e39	0.882604	0.441302	−	0.897359i	$-0.354517\pi$
$509$	1.56018e39	0.882604	0.441302	+	0.897359i	$0.354517\pi$
$510$	−6.88104e37	−0.0378344
$511$	−9.16336e38	−0.489724
$512$	−1.80527e39	−0.937836
$513$	1.52063e38	0.0767932
$514$	−7.23382e38	−0.355143
$515$	−1.08904e39	−0.519804
$516$	−8.69670e38	−0.403584
$517$	3.51318e38	0.158521
$518$	1.52039e37	0.00667073
$519$	1.26261e39	0.538693
$520$	1.10472e38	0.0458358
$521$	−2.67068e39	−1.07764	−0.538822	−	0.842420i	$-0.681130\pi$
$521$	−2.67068e39	−1.07764	−0.538822	+	0.842420i	$0.681130\pi$
$522$	−1.09990e37	−0.00431648
$523$	2.52431e39	0.963537	0.481768	−	0.876299i	$-0.339995\pi$
$523$	2.52431e39	0.963537	0.481768	+	0.876299i	$0.339995\pi$
$524$	−1.60186e39	−0.594731
$525$	3.38695e38	0.122320
$526$	5.94292e38	0.208789
$527$	−2.34932e39	−0.802950
$528$	1.43186e39	0.476111
$529$	9.20636e38	0.297838
$530$	−6.46361e38	−0.203458
$531$	3.94842e38	0.120935
$532$	4.77141e38	0.142209
$533$	3.80918e38	0.110481
$534$	−7.56694e38	−0.213586
$535$	3.23861e38	0.0889671
$536$	5.35796e38	0.143255
$537$	1.66938e39	0.434439
$538$	1.12704e39	0.285494
$539$	−5.74224e38	−0.141594
$540$	−5.01140e38	−0.120296
$541$	8.06290e39	1.88422	0.942109	−	0.335307i	$-0.108840\pi$
$541$	8.06290e39	1.88422	0.942109	+	0.335307i	$0.108840\pi$
$542$	1.66430e39	0.378653
$543$	1.19626e39	0.264990
$544$	−1.27181e39	−0.274309
$545$	1.82896e39	0.384110
$546$	−3.79731e37	−0.00776574
$547$	5.06738e39	1.00918	0.504588	−	0.863360i	$-0.331644\pi$
$547$	5.06738e39	1.00918	0.504588	+	0.863360i	$0.331644\pi$
$548$	−7.42190e39	−1.43945
$549$	−1.77194e39	−0.334695
$550$	−7.21551e38	−0.132742
$551$	−1.20697e38	−0.0216271
$552$	1.74935e39	0.305324
$553$	6.33978e38	0.107785
$554$	−1.24544e38	−0.0206268
$555$	−1.75231e38	−0.0282724
$556$	−4.00261e39	−0.629157
$557$	2.71730e39	0.416137	0.208069	−	0.978114i	$-0.433282\pi$
$557$	2.71730e39	0.416137	0.208069	+	0.978114i	$0.433282\pi$
$558$	1.03583e39	0.154558
$559$	7.59500e38	0.110422
$560$	−1.47151e39	−0.208466
$561$	1.71504e39	0.236763
$562$	−5.13439e38	−0.0690736
$563$	2.23651e39	0.293224	0.146612	−	0.989194i	$-0.453163\pi$
$563$	2.23651e39	0.293224	0.146612	+	0.989194i	$0.453163\pi$
$564$	−6.81405e38	−0.0870679
$565$	5.93633e39	0.739291
$566$	2.65456e39	0.322221
$567$	3.54946e38	0.0419961
$568$	2.83133e39	0.326542
$569$	−5.94014e39	−0.667834	−0.333917	−	0.942602i	$-0.608371\pi$
$569$	−5.94014e39	−0.667834	−0.333917	+	0.942602i	$0.608371\pi$
$570$	3.32924e38	0.0364888
$571$	−3.55877e39	−0.380256	−0.190128	−	0.981759i	$-0.560890\pi$
$571$	−3.55877e39	−0.380256	−0.190128	+	0.981759i	$0.560890\pi$
$572$	−1.33627e39	−0.139204
$573$	−1.02499e39	−0.104107
$574$	6.76366e38	0.0669822
$575$	6.61306e39	0.638585
$576$	−2.38456e39	−0.224534
$577$	−8.65228e39	−0.794477	−0.397239	−	0.917715i	$-0.630031\pi$
$577$	−8.65228e39	−0.794477	−0.397239	+	0.917715i	$0.630031\pi$
$578$	2.21141e39	0.198023
$579$	1.01823e40	0.889217
$580$	3.97769e38	0.0338785
$581$	−1.57236e39	−0.130616
$582$	2.61401e39	0.211799
$583$	1.61100e40	1.27321
$584$	−7.80186e39	−0.601467
$585$	4.37656e38	0.0329134
$586$	9.27667e38	0.0680576
$587$	6.19077e39	0.443090	0.221545	−	0.975150i	$-0.428890\pi$
$587$	6.19077e39	0.443090	0.221545	+	0.975150i	$0.428890\pi$
$588$	1.11374e39	0.0777704
$589$	1.13667e40	0.774393
$590$	8.64459e38	0.0574633
$591$	7.38280e39	0.478853
$592$	−9.71084e38	−0.0614599
$593$	−1.01522e40	−0.627000	−0.313500	−	0.949588i	$-0.601501\pi$
$593$	−1.01522e40	−0.627000	−0.313500	+	0.949588i	$0.601501\pi$
$594$	−7.56173e38	−0.0455741
$595$	−1.76253e39	−0.103667
$596$	−2.84344e40	−1.63220
$597$	6.70132e39	0.375433
$598$	−7.41430e38	−0.0405418
$599$	9.91544e38	0.0529204	0.0264602	−	0.999650i	$-0.491576\pi$
$599$	9.91544e38	0.0529204	0.0264602	+	0.999650i	$0.491576\pi$
$600$	2.88371e39	0.150231
$601$	1.89981e40	0.966119	0.483059	−	0.875588i	$-0.339526\pi$
$601$	1.89981e40	0.966119	0.483059	+	0.875588i	$0.339526\pi$
$602$	1.34859e39	0.0669468
$603$	2.12265e39	0.102867
$604$	2.21646e40	1.04863
$605$	2.52720e38	0.0116731
$606$	1.10119e39	0.0496603
$607$	−6.33125e39	−0.278775	−0.139387	−	0.990238i	$-0.544513\pi$
$607$	−6.33125e39	−0.278775	−0.139387	+	0.990238i	$0.544513\pi$
$608$	6.15339e39	0.264553
$609$	−2.81731e38	−0.0118272
$610$	−3.87944e39	−0.159033
$611$	5.95084e38	0.0238221
$612$	−3.32643e39	−0.130042
$613$	−2.43587e40	−0.929986	−0.464993	−	0.885314i	$-0.653943\pi$
$613$	−2.43587e40	−0.929986	−0.464993	+	0.885314i	$0.653943\pi$
$614$	−2.71232e39	−0.101135
$615$	−7.79540e39	−0.283889
$616$	−4.88905e39	−0.173902
$617$	−5.30801e40	−1.84415	−0.922076	−	0.387009i	$-0.873508\pi$
$617$	−5.30801e40	−1.84415	−0.922076	+	0.387009i	$0.873508\pi$
$618$	3.18721e39	0.108163
$619$	−5.97026e39	−0.197915	−0.0989575	−	0.995092i	$-0.531551\pi$
$619$	−5.97026e39	−0.197915	−0.0989575	+	0.995092i	$0.531551\pi$
$620$	−3.74600e40	−1.21308
$621$	6.93037e39	0.219244
$622$	−1.00719e40	−0.311279
$623$	−1.93822e40	−0.585230
$624$	2.42537e39	0.0715486
$625$	−4.34547e39	−0.125250
$626$	−9.97447e39	−0.280907
$627$	−8.29785e39	−0.228342
$628$	−8.56949e39	−0.230431
$629$	−1.16314e39	−0.0305631
$630$	7.77112e38	0.0199547
$631$	2.28016e40	0.572189	0.286095	−	0.958201i	$-0.407643\pi$
$631$	2.28016e40	0.572189	0.286095	+	0.958201i	$0.407643\pi$
$632$	5.39782e39	0.132379
$633$	1.28525e40	0.308060
$634$	8.29728e39	0.194375
$635$	−2.30756e40	−0.528365
$636$	−3.12464e40	−0.699313
$637$	−9.72655e38	−0.0212783
$638$	6.00195e38	0.0128349
$639$	1.12168e40	0.234480
$640$	−2.67275e40	−0.546197
$641$	−1.73379e40	−0.346382	−0.173191	−	0.984888i	$-0.555408\pi$
$641$	−1.73379e40	−0.346382	−0.173191	+	0.984888i	$0.555408\pi$
$642$	−9.47819e38	−0.0185126
$643$	3.52355e40	0.672855	0.336428	−	0.941709i	$-0.390781\pi$
$643$	3.52355e40	0.672855	0.336428	+	0.941709i	$0.390781\pi$
$644$	2.17460e40	0.406008
$645$	−1.55430e40	−0.283739
$646$	2.20986e39	0.0394451
$647$	2.78855e40	0.486705	0.243352	−	0.969938i	$-0.421753\pi$
$647$	2.78855e40	0.486705	0.243352	+	0.969938i	$0.421753\pi$
$648$	3.02208e39	0.0515785
$649$	−2.15459e40	−0.359598
$650$	−1.22221e39	−0.0199481
$651$	2.65321e40	0.423494
$652$	−5.50968e40	−0.860075
$653$	−6.27863e40	−0.958570	−0.479285	−	0.877659i	$-0.659104\pi$
$653$	−6.27863e40	−0.958570	−0.479285	+	0.877659i	$0.659104\pi$
$654$	−5.35268e39	−0.0799271
$655$	−2.86289e40	−0.418125
$656$	−4.32000e40	−0.617132
$657$	−3.09085e40	−0.431896
$658$	1.05665e39	0.0144429
$659$	8.27991e40	1.10710	0.553550	−	0.832816i	$-0.313273\pi$
$659$	8.27991e40	1.10710	0.553550	+	0.832816i	$0.313273\pi$
$660$	2.73464e40	0.357695
$661$	3.57059e40	0.456898	0.228449	−	0.973556i	$-0.426635\pi$
$661$	3.57059e40	0.456898	0.228449	+	0.973556i	$0.426635\pi$
$662$	2.60328e40	0.325897
$663$	2.90504e39	0.0355800
$664$	−1.33874e40	−0.160420
$665$	8.52762e39	0.0999802
$666$	5.12835e38	0.00588303
$667$	−5.50083e39	−0.0617453
$668$	1.30792e41	1.43655
$669$	−7.23779e40	−0.777907
$670$	4.64728e39	0.0488781
$671$	9.66917e40	0.995206
$672$	1.43633e40	0.144677
$673$	−4.67319e40	−0.460675	−0.230338	−	0.973111i	$-0.573983\pi$
$673$	−4.67319e40	−0.460675	−0.230338	+	0.973111i	$0.573983\pi$
$674$	−2.75062e40	−0.265376
$675$	1.14243e40	0.107876
$676$	9.97600e40	0.921997
$677$	1.56096e41	1.41207	0.706035	−	0.708176i	$-0.250482\pi$
$677$	1.56096e41	1.41207	0.706035	+	0.708176i	$0.250482\pi$
$678$	−1.73734e40	−0.153834
$679$	6.69560e40	0.580334
$680$	−1.50065e40	−0.127321
$681$	−4.60659e39	−0.0382602
$682$	−5.65236e40	−0.459575
$683$	2.15335e41	1.71401	0.857007	−	0.515305i	$-0.172321\pi$
$683$	2.15335e41	1.71401	0.857007	+	0.515305i	$0.172321\pi$
$684$	1.60942e40	0.125417
$685$	−1.32646e41	−1.01200
$686$	−1.72707e39	−0.0129006
$687$	2.78356e40	0.203577
$688$	−8.61352e40	−0.616805
$689$	2.72881e40	0.191335
$690$	1.51732e40	0.104175
$691$	2.46242e39	0.0165551	0.00827754	−	0.999966i	$-0.497365\pi$
$691$	2.46242e39	0.0165551	0.00827754	+	0.999966i	$0.497365\pi$
$692$	1.33633e41	0.879782
$693$	−1.93689e40	−0.124874
$694$	−4.01125e40	−0.253260
$695$	−7.15359e40	−0.442328
$696$	−2.39871e39	−0.0145259
$697$	−5.17438e40	−0.306890
$698$	4.47677e40	0.260053
$699$	−1.05040e41	−0.597636
$700$	3.58471e40	0.199771
$701$	−2.97668e41	−1.62488	−0.812440	−	0.583044i	$-0.801861\pi$
$701$	−2.97668e41	−1.62488	−0.812440	+	0.583044i	$0.801861\pi$
$702$	−1.28085e39	−0.00684874
$703$	5.62758e39	0.0294761
$704$	1.30122e41	0.667646
$705$	−1.21783e40	−0.0612130
$706$	−5.57279e40	−0.274413
$707$	2.82062e40	0.136070
$708$	4.17897e40	0.197509
$709$	3.29376e41	1.52518	0.762591	−	0.646881i	$-0.223927\pi$
$709$	3.29376e41	1.52518	0.762591	+	0.646881i	$0.223927\pi$
$710$	2.45578e40	0.111415
$711$	2.13844e40	0.0950578
$712$	−1.65024e41	−0.718765
$713$	5.18042e41	2.21089
$714$	5.15826e39	0.0215714
$715$	−2.38822e40	−0.0978669
$716$	1.76686e41	0.709517
$717$	−2.22732e41	−0.876508
$718$	−1.80910e40	−0.0697685
$719$	−2.16273e40	−0.0817398	−0.0408699	−	0.999164i	$-0.513013\pi$
$719$	−2.16273e40	−0.0817398	−0.0408699	+	0.999164i	$0.513013\pi$
$720$	−4.96347e40	−0.183850
$721$	8.16381e40	0.296368
$722$	5.64582e40	0.200880
$723$	−8.66037e40	−0.302017
$724$	1.26611e41	0.432775
$725$	−9.06782e39	−0.0303810
$726$	−7.39617e38	−0.00242899
$727$	4.57705e40	0.147346	0.0736728	−	0.997282i	$-0.476528\pi$
$727$	4.57705e40	0.147346	0.0736728	+	0.997282i	$0.476528\pi$
$728$	−8.28138e39	−0.0261335
$729$	1.19725e40	0.0370370
$730$	−6.76703e40	−0.205219
$731$	−1.03170e41	−0.306728
$732$	−1.87540e41	−0.546617
$733$	5.99238e41	1.71235	0.856173	−	0.516690i	$-0.172836\pi$
$733$	5.99238e41	1.71235	0.856173	+	0.516690i	$0.172836\pi$
$734$	2.66291e40	0.0746042
$735$	1.99052e40	0.0546764
$736$	2.80444e41	0.755298
$737$	−1.15830e41	−0.305873
$738$	2.28142e40	0.0590727
$739$	−7.18829e41	−1.82508	−0.912539	−	0.408989i	$-0.865881\pi$
$739$	−7.18829e41	−1.82508	−0.912539	+	0.408989i	$0.865881\pi$
$740$	−1.85463e40	−0.0461739
$741$	−1.40554e40	−0.0343146
$742$	4.84534e40	0.116003
$743$	−5.15743e41	−1.21086	−0.605432	−	0.795897i	$-0.707000\pi$
$743$	−5.15743e41	−1.21086	−0.605432	+	0.795897i	$0.707000\pi$
$744$	2.25899e41	0.520125
$745$	−5.08189e41	−1.14752
$746$	6.54676e40	0.144982
$747$	−5.30364e40	−0.115193
$748$	1.81518e41	0.386676
$749$	−2.42777e40	−0.0507250
$750$	6.96336e40	0.142702
$751$	−7.33148e41	−1.47371	−0.736856	−	0.676050i	$-0.763690\pi$
$751$	−7.33148e41	−1.47371	−0.736856	+	0.676050i	$0.763690\pi$
$752$	−6.74887e40	−0.133068
$753$	−1.10920e41	−0.214527
$754$	1.01665e39	0.00192879
$755$	3.96132e41	0.737241
$756$	3.75671e40	0.0685870
$757$	−7.09215e41	−1.27025	−0.635123	−	0.772411i	$-0.719051\pi$
$757$	−7.09215e41	−1.27025	−0.635123	+	0.772411i	$0.719051\pi$
$758$	6.01960e40	0.105770
$759$	−3.78179e41	−0.651916
$760$	7.26058e40	0.122793
$761$	−6.02240e41	−0.999291	−0.499645	−	0.866230i	$-0.666536\pi$
$761$	−6.02240e41	−0.999291	−0.499645	+	0.866230i	$0.666536\pi$
$762$	6.75335e40	0.109944
$763$	−1.37105e41	−0.219002
$764$	−1.08484e41	−0.170025
$765$	−5.94511e40	−0.0914258
$766$	−1.34865e41	−0.203509
$767$	−3.64958e40	−0.0540393
$768$	−1.89437e41	−0.275250
$769$	−1.33915e42	−1.90940	−0.954702	−	0.297564i	$-0.903826\pi$
$769$	−1.33915e42	−1.90940	−0.954702	+	0.297564i	$0.903826\pi$
$770$	−4.24057e40	−0.0593347
$771$	−6.24990e41	−0.858193
$772$	1.07769e42	1.45225
$773$	−3.82444e41	−0.505784	−0.252892	−	0.967495i	$-0.581382\pi$
$773$	−3.82444e41	−0.505784	−0.252892	+	0.967495i	$0.581382\pi$
$774$	4.54885e40	0.0590415
$775$	8.53965e41	1.08784
$776$	5.70077e41	0.712752
$777$	1.31359e40	0.0161197
$778$	−3.64298e41	−0.438785
$779$	2.50351e41	0.295975
$780$	4.63210e40	0.0537534
$781$	−6.12082e41	−0.697220
$782$	1.00716e41	0.112616
$783$	−9.50292e39	−0.0104307
$784$	1.10309e41	0.118858
$785$	−1.53157e41	−0.162004
$786$	8.37859e40	0.0870050
$787$	2.74922e41	0.280269	0.140135	−	0.990132i	$-0.455247\pi$
$787$	2.74922e41	0.280269	0.140135	+	0.990132i	$0.455247\pi$
$788$	7.81387e41	0.782053
$789$	5.13459e41	0.504532
$790$	4.68185e40	0.0451674
$791$	−4.45007e41	−0.421510
$792$	−1.64910e41	−0.153367
$793$	1.63782e41	0.149557
$794$	1.70057e41	0.152474
$795$	−5.58445e41	−0.491651
$796$	7.09260e41	0.613149
$797$	1.82608e42	1.55015	0.775077	−	0.631867i	$-0.217711\pi$
$797$	1.82608e42	1.55015	0.775077	+	0.631867i	$0.217711\pi$
$798$	−2.49571e40	−0.0208042
$799$	−8.08361e40	−0.0661725
$800$	4.62297e41	0.371635
$801$	−6.53771e41	−0.516124
$802$	−2.80827e41	−0.217726
$803$	1.68662e42	1.28423
$804$	2.24659e41	0.168001
$805$	3.88651e41	0.285443
$806$	−9.57431e40	−0.0690636
$807$	9.73744e41	0.689888
$808$	2.40153e41	0.167118
$809$	−2.50270e42	−1.71063	−0.855313	−	0.518112i	$-0.826635\pi$
$809$	−2.50270e42	−1.71063	−0.855313	+	0.518112i	$0.826635\pi$
$810$	2.62124e40	0.0175984
$811$	5.09209e41	0.335810	0.167905	−	0.985803i	$-0.446300\pi$
$811$	5.09209e41	0.335810	0.167905	+	0.985803i	$0.446300\pi$
$812$	−2.98181e40	−0.0193160
$813$	1.43792e42	0.915005
$814$	−2.79846e40	−0.0174930
$815$	−9.84707e41	−0.604674
$816$	−3.29462e41	−0.198746
$817$	4.99167e41	0.295819
$818$	5.60715e41	0.326452
$819$	−3.28081e40	−0.0187657
$820$	−8.25056e41	−0.463642
$821$	4.69986e41	0.259483	0.129742	−	0.991548i	$-0.458585\pi$
$821$	4.69986e41	0.259483	0.129742	+	0.991548i	$0.458585\pi$
$822$	3.88206e41	0.210582
$823$	1.33862e42	0.713444	0.356722	−	0.934211i	$-0.383894\pi$
$823$	1.33862e42	0.713444	0.356722	+	0.934211i	$0.383894\pi$
$824$	6.95083e41	0.363992
$825$	−6.23408e41	−0.320767
$826$	−6.48028e40	−0.0327629
$827$	−2.74761e42	−1.36497	−0.682487	−	0.730898i	$-0.739102\pi$
$827$	−2.74761e42	−1.36497	−0.682487	+	0.730898i	$0.739102\pi$
$828$	7.33503e41	0.358065
$829$	−8.99169e41	−0.431321	−0.215661	−	0.976468i	$-0.569190\pi$
$829$	−8.99169e41	−0.431321	−0.215661	+	0.976468i	$0.569190\pi$
$830$	−1.16117e41	−0.0547346
$831$	−1.07604e41	−0.0498442
$832$	2.20408e41	0.100332
$833$	1.32125e41	0.0591063
$834$	2.09358e41	0.0920413
$835$	2.33755e42	1.00997
$836$	−8.78235e41	−0.372923
$837$	8.94940e41	0.373486
$838$	−2.70863e41	−0.111099
$839$	1.00595e41	0.0405535	0.0202767	−	0.999794i	$-0.493545\pi$
$839$	1.00595e41	0.0405535	0.0202767	+	0.999794i	$0.493545\pi$
$840$	1.69477e41	0.0671522
$841$	−2.56014e42	−0.997062
$842$	−3.18343e41	−0.121863
$843$	−4.43603e41	−0.166915
$844$	1.36030e42	0.503116
$845$	1.78294e42	0.648209
$846$	3.56412e40	0.0127374
$847$	−1.89448e40	−0.00665549
$848$	−3.09475e42	−1.06877
$849$	2.29350e42	0.778639
$850$	1.66024e41	0.0554112
$851$	2.56480e41	0.0841542
$852$	1.18717e42	0.382948
$853$	6.23073e42	1.97596	0.987980	−	0.154583i	$-0.0494035\pi$
$853$	6.23073e42	1.97596	0.987980	+	0.154583i	$0.0494035\pi$
$854$	2.90816e41	0.0906732
$855$	2.87641e41	0.0881742
$856$	−2.06705e41	−0.0622991
$857$	−5.02683e42	−1.48961	−0.744805	−	0.667282i	$-0.767458\pi$
$857$	−5.02683e42	−1.48961	−0.744805	+	0.667282i	$0.767458\pi$
$858$	6.98940e40	0.0203645
$859$	6.33334e42	1.81440	0.907198	−	0.420704i	$-0.138217\pi$
$859$	6.33334e42	1.81440	0.907198	+	0.420704i	$0.138217\pi$
$860$	−1.64506e42	−0.463397
$861$	5.84369e41	0.161861
$862$	−3.48161e41	−0.0948254
$863$	−1.90075e42	−0.509061	−0.254530	−	0.967065i	$-0.581921\pi$
$863$	−1.90075e42	−0.509061	−0.254530	+	0.967065i	$0.581921\pi$
$864$	4.84480e41	0.127593
$865$	2.38833e42	0.618530
$866$	−1.39200e42	−0.354512
$867$	1.91062e42	0.478517
$868$	2.80813e42	0.691641
$869$	−1.16691e42	−0.282652
$870$	−2.08055e40	−0.00495620
$871$	−1.96199e41	−0.0459657
$872$	−1.16734e42	−0.268973
$873$	2.25846e42	0.511807
$874$	−4.87290e41	−0.108611
$875$	1.78362e42	0.391007
$876$	−3.27132e42	−0.705364
$877$	−8.61192e42	−1.82644	−0.913221	−	0.407466i	$-0.866413\pi$
$877$	−8.61192e42	−1.82644	−0.913221	+	0.407466i	$0.866413\pi$
$878$	7.09134e41	0.147931
$879$	8.01489e41	0.164459
$880$	2.70848e42	0.546673
$881$	−3.10903e42	−0.617269	−0.308635	−	0.951181i	$-0.599872\pi$
$881$	−3.10903e42	−0.617269	−0.308635	+	0.951181i	$0.599872\pi$
$882$	−5.82549e40	−0.0113773
$883$	−8.83285e42	−1.69696	−0.848478	−	0.529231i	$-0.822481\pi$
$883$	−8.83285e42	−1.69696	−0.848478	+	0.529231i	$0.822481\pi$
$884$	3.07466e41	0.0581085
$885$	7.46878e41	0.138858
$886$	−2.29202e42	−0.419207
$887$	−5.14326e41	−0.0925435	−0.0462718	−	0.998929i	$-0.514734\pi$
$887$	−5.14326e41	−0.0925435	−0.0462718	+	0.998929i	$0.514734\pi$
$888$	1.11842e41	0.0197978
$889$	1.72983e42	0.301250
$890$	−1.43135e42	−0.245240
$891$	−6.53321e41	−0.110129
$892$	−7.66040e42	−1.27046
$893$	3.91108e41	0.0638190
$894$	1.48727e42	0.238780
$895$	3.15778e42	0.498825
$896$	2.00359e42	0.311417
$897$	−6.40583e41	−0.0979682
$898$	−1.11374e42	−0.167601
$899$	−7.10339e41	−0.105184
$900$	1.20914e42	0.176181
$901$	−3.70681e42	−0.531485
$902$	−1.24493e42	−0.175651
$903$	1.16516e42	0.161775
$904$	−3.78888e42	−0.517688
$905$	2.26283e42	0.304262
$906$	−1.15933e42	−0.153408
$907$	−1.71576e42	−0.223435	−0.111717	−	0.993740i	$-0.535635\pi$
$907$	−1.71576e42	−0.223435	−0.111717	+	0.993740i	$0.535635\pi$
$908$	−4.87557e41	−0.0624857
$909$	9.51410e41	0.120003
$910$	−7.18294e40	−0.00891666
$911$	−1.59686e43	−1.95097	−0.975485	−	0.220066i	$-0.929373\pi$
$911$	−1.59686e43	−1.95097	−0.975485	+	0.220066i	$0.929373\pi$
$912$	1.59403e42	0.191677
$913$	2.89411e42	0.342522
$914$	−1.86598e42	−0.217364
$915$	−3.35177e42	−0.384298
$916$	2.94609e42	0.332477
$917$	2.14612e42	0.238396
$918$	1.73991e41	0.0190242
$919$	7.19852e42	0.774762	0.387381	−	0.921920i	$-0.373380\pi$
$919$	7.19852e42	0.774762	0.387381	+	0.921920i	$0.373380\pi$
$920$	3.30905e42	0.350574
$921$	−2.34340e42	−0.244389
$922$	9.34862e41	0.0959730
$923$	−1.03678e42	−0.104776
$924$	−2.04998e42	−0.203941
$925$	4.22794e41	0.0414070
$926$	3.44452e42	0.332101
$927$	2.75369e42	0.261372
$928$	−3.84545e41	−0.0359337
$929$	5.68901e42	0.523370	0.261685	−	0.965153i	$-0.415722\pi$
$929$	5.68901e42	0.523370	0.261685	+	0.965153i	$0.415722\pi$
$930$	1.95936e42	0.177465
$931$	−6.39259e41	−0.0570041
$932$	−1.11173e43	−0.976046
$933$	−8.70194e42	−0.752198
$934$	−3.06982e42	−0.261266
$935$	3.24415e42	0.271852
$936$	−2.79335e41	−0.0230476
$937$	1.96772e42	0.159860	0.0799299	−	0.996800i	$-0.474530\pi$
$937$	1.96772e42	0.159860	0.0799299	+	0.996800i	$0.474530\pi$
$938$	−3.48376e41	−0.0278681
$939$	−8.61778e42	−0.678804
$940$	−1.28893e42	−0.0999717
$941$	−2.06091e43	−1.57402	−0.787010	−	0.616940i	$-0.788372\pi$
$941$	−2.06091e43	−1.57402	−0.787010	+	0.616940i	$0.788372\pi$
$942$	4.48231e41	0.0337104
$943$	1.14099e43	0.845009
$944$	4.13900e42	0.301857
$945$	6.71412e41	0.0482200
$946$	−2.48223e42	−0.175558
$947$	2.18350e43	1.52082	0.760412	−	0.649441i	$-0.224997\pi$
$947$	2.18350e43	1.52082	0.760412	+	0.649441i	$0.224997\pi$
$948$	2.26330e42	0.155246
$949$	2.85691e42	0.192991
$950$	−8.03272e41	−0.0534405
$951$	7.16871e42	0.469703
$952$	1.12494e42	0.0725929
$953$	−8.07701e42	−0.513338	−0.256669	−	0.966499i	$-0.582625\pi$
$953$	−8.07701e42	−0.513338	−0.256669	+	0.966499i	$0.582625\pi$
$954$	1.63436e42	0.102305
$955$	−1.93886e42	−0.119536
$956$	−2.35738e43	−1.43149
$957$	5.18559e41	0.0310152
$958$	−6.79470e42	−0.400286
$959$	9.94362e42	0.576999
$960$	−4.51060e42	−0.257811
$961$	4.91345e43	2.76629
$962$	−4.74020e40	−0.00262880
$963$	−8.18900e41	−0.0447352
$964$	−9.16604e42	−0.493247
$965$	1.92607e43	1.02100
$966$	−1.13743e42	−0.0593961
$967$	−2.47013e43	−1.27068	−0.635339	−	0.772234i	$-0.719139\pi$
$967$	−2.47013e43	−1.27068	−0.635339	+	0.772234i	$0.719139\pi$
$968$	−1.61299e41	−0.00817411
$969$	1.90928e42	0.0953181
$970$	4.94462e42	0.243188
$971$	2.86796e43	1.38962	0.694808	−	0.719195i	$-0.255489\pi$
$971$	2.86796e43	1.38962	0.694808	+	0.719195i	$0.255489\pi$
$972$	1.26716e42	0.0604881
$973$	5.36257e42	0.252195
$974$	−1.11585e42	−0.0517011
$975$	−1.05597e42	−0.0482040
$976$	−1.85746e43	−0.835405
$977$	1.76075e40	0.000780238 0	0.000390119	−	1.00000i	$-0.499876\pi$
$977$	1.76075e40	0.000780238 0	0.000390119		1.00000i	$0.499876\pi$
$978$	2.88186e42	0.125823
$979$	3.56752e43	1.53468
$980$	2.10674e42	0.0892963
$981$	−4.62463e42	−0.193142
$982$	4.91633e42	0.202313
$983$	1.18413e43	0.480145	0.240073	−	0.970755i	$-0.422829\pi$
$983$	1.18413e43	0.480145	0.240073	+	0.970755i	$0.422829\pi$
$984$	4.97543e42	0.198793
$985$	1.39652e43	0.549822
$986$	−1.38101e41	−0.00535775
$987$	9.12924e41	0.0349009
$988$	−1.48761e42	−0.0560419
$989$	2.27498e43	0.844563
$990$	−1.43037e42	−0.0523283
$991$	−2.66284e43	−0.960013	−0.480007	−	0.877265i	$-0.659366\pi$
$991$	−2.66284e43	−0.960013	−0.480007	+	0.877265i	$0.659366\pi$
$992$	3.62146e43	1.28666
$993$	2.24919e43	0.787522
$994$	−1.84093e42	−0.0635237
$995$	1.26761e43	0.431074
$996$	−5.61331e42	−0.188130
$997$	−2.85611e42	−0.0943399	−0.0471700	−	0.998887i	$-0.515020\pi$
$997$	−2.85611e42	−0.0943399	−0.0471700	+	0.998887i	$0.515020\pi$
$998$	2.02702e42	0.0659879
$999$	4.43081e41	0.0142162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.c.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.c.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-5535.95 q^{2} -4.78297e6 q^{3} -5.06224e8 q^{4} -9.04739e9 q^{5} +2.64783e10 q^{6} +6.78223e11 q^{7} +5.77452e12 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q-5535.95 q^{2} -4.78297e6 q^{3} -5.06224e8 q^{4} -9.04739e9 q^{5} +2.64783e10 q^{6} +6.78223e11 q^{7} +5.77452e12 q^{8} +2.28768e13 q^{9} +5.00859e13 q^{10} -1.24835e15 q^{11} +2.42125e15 q^{12} -2.11453e15 q^{13} -3.75461e15 q^{14} +4.32734e16 q^{15} +2.39810e17 q^{16} +2.87237e17 q^{17} -1.26645e17 q^{18} -1.38973e18 q^{19} +4.58001e18 q^{20} -3.24392e18 q^{21} +6.91080e18 q^{22} -6.33379e19 q^{23} -2.76194e19 q^{24} -1.04409e20 q^{25} +1.17059e19 q^{26} -1.09419e20 q^{27} -3.43333e20 q^{28} +8.68489e19 q^{29} -2.39559e20 q^{30} -8.17902e21 q^{31} -4.42775e21 q^{32} +5.97082e21 q^{33} -1.59013e21 q^{34} -6.13615e21 q^{35} -1.15808e22 q^{36} -4.04940e21 q^{37} +7.69350e21 q^{38} +1.01137e22 q^{39} -5.22444e22 q^{40} -1.80143e23 q^{41} +1.79582e22 q^{42} -3.59182e23 q^{43} +6.31945e23 q^{44} -2.06975e23 q^{45} +3.50636e23 q^{46} -2.81426e23 q^{47} -1.14700e24 q^{48} +4.59987e23 q^{49} +5.78004e23 q^{50} -1.37385e24 q^{51} +1.07043e24 q^{52} -1.29050e25 q^{53} +6.05738e23 q^{54} +1.12943e25 q^{55} +3.91641e24 q^{56} +6.64705e24 q^{57} -4.80791e23 q^{58} +1.72595e25 q^{59} -2.19060e25 q^{60} -7.74557e25 q^{61} +4.52787e25 q^{62} +1.55156e25 q^{63} -1.04235e26 q^{64} +1.91310e25 q^{65} -3.30541e25 q^{66} +9.27862e25 q^{67} -1.45407e26 q^{68} +3.02943e26 q^{69} +3.39694e25 q^{70} +4.90313e26 q^{71} +1.32103e26 q^{72} -1.35108e27 q^{73} +2.24173e25 q^{74} +4.99386e26 q^{75} +7.03517e26 q^{76} -8.46659e26 q^{77} -5.59891e25 q^{78} +9.34764e26 q^{79} -2.16965e27 q^{80} +5.23348e26 q^{81} +9.97262e26 q^{82} -2.31835e27 q^{83} +1.64215e27 q^{84} -2.59875e27 q^{85} +1.98841e27 q^{86} -4.15396e26 q^{87} -7.20862e27 q^{88} -2.85779e28 q^{89} +1.14581e27 q^{90} -1.43412e27 q^{91} +3.20632e28 q^{92} +3.91200e28 q^{93} +1.55796e27 q^{94} +1.25735e28 q^{95} +2.11778e28 q^{96} +9.87228e28 q^{97} -2.54646e27 q^{98} -2.85582e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 60870 q^{2} - 33480783 q^{3} + 2201135476 q^{4} - 2861618502 q^{5} - 291139323030 q^{6} + 4747561509943 q^{7} + 9964333994280 q^{8} + 160137547184727 q^{9}+O(q^{10}) \) 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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