LMFDB - Embedded newform 21.30.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$111.883889004$
Analytic rank:	$1$
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} - 2 x^{6} - 2752306353 x^{5} - 358739735184 x^{4} + \cdots - 19\!\cdots\!04 $ x^7 - 2x^6 - 2752306353x^5 - 358739735184x^4 + 2112044285875555887x^3 - 87015327743334724410x^2 - 372546762120092709645386335x - 1910221430295883859730026686804
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{12}\cdot 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-37035.6$ 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)

$f(q)$	$=$	$q+37632.6 q^{2} -4.78297e6 q^{3} +8.79342e8 q^{4} +1.83976e10 q^{5} -1.79996e11 q^{6} -6.78223e11 q^{7} +1.28881e13 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q+37632.6 q^{2} -4.78297e6 q^{3} +8.79342e8 q^{4} +1.83976e10 q^{5} -1.79996e11 q^{6} -6.78223e11 q^{7} +1.28881e13 q^{8} +2.28768e13 q^{9} +6.92348e14 q^{10} -7.53994e14 q^{11} -4.20586e15 q^{12} -1.44227e16 q^{13} -2.55233e16 q^{14} -8.79950e16 q^{15} +1.29187e16 q^{16} -8.99872e17 q^{17} +8.60913e17 q^{18} +1.24939e18 q^{19} +1.61777e19 q^{20} +3.24392e18 q^{21} -2.83747e19 q^{22} -3.80568e19 q^{23} -6.16433e19 q^{24} +1.52206e20 q^{25} -5.42763e20 q^{26} -1.09419e20 q^{27} -5.96390e20 q^{28} -1.55071e21 q^{29} -3.31148e21 q^{30} -1.79680e20 q^{31} -6.43307e21 q^{32} +3.60633e21 q^{33} -3.38645e22 q^{34} -1.24776e22 q^{35} +2.01165e22 q^{36} +4.46221e22 q^{37} +4.70179e22 q^{38} +6.89832e22 q^{39} +2.37109e23 q^{40} -3.43321e23 q^{41} +1.22077e23 q^{42} +5.56573e23 q^{43} -6.63018e23 q^{44} +4.20877e23 q^{45} -1.43218e24 q^{46} +1.17621e24 q^{47} -6.17895e22 q^{48} +4.59987e23 q^{49} +5.72790e24 q^{50} +4.30406e24 q^{51} -1.26825e25 q^{52} +4.55961e24 q^{53} -4.11772e24 q^{54} -1.38716e25 q^{55} -8.74099e24 q^{56} -5.97581e24 q^{57} -5.83571e25 q^{58} +1.57929e25 q^{59} -7.73776e25 q^{60} -2.37660e25 q^{61} -6.76181e24 q^{62} -1.55156e25 q^{63} -2.49029e26 q^{64} -2.65342e26 q^{65} +1.35716e26 q^{66} -2.63221e26 q^{67} -7.91295e26 q^{68} +1.82025e26 q^{69} -4.69566e26 q^{70} -1.36949e27 q^{71} +2.94838e26 q^{72} +3.24441e26 q^{73} +1.67925e27 q^{74} -7.27995e26 q^{75} +1.09864e27 q^{76} +5.11376e26 q^{77} +2.59602e27 q^{78} +4.00843e27 q^{79} +2.37672e26 q^{80} +5.23348e26 q^{81} -1.29201e28 q^{82} -1.21477e28 q^{83} +2.85251e27 q^{84} -1.65554e28 q^{85} +2.09453e28 q^{86} +7.41698e27 q^{87} -9.71752e27 q^{88} -4.32540e27 q^{89} +1.58387e28 q^{90} +9.78179e27 q^{91} -3.34649e28 q^{92} +8.59402e26 q^{93} +4.42638e28 q^{94} +2.29858e28 q^{95} +3.07692e28 q^{96} +1.14699e29 q^{97} +1.73105e28 q^{98} -1.72490e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4177 q^{2} - 33480783 q^{3} + 1749008801 q^{4} - 1716792694 q^{5} - 19978461513 q^{6} - 4747561509943 q^{7} + 4282496015841 q^{8} + 160137547184727 q^{9}+O(q^{10}) $ 7 * q + 4177 * q^2 - 33480783 * q^3 + 1749008801 * q^4 - 1716792694 * q^5 - 19978461513 * q^6 - 4747561509943 * q^7 + 4282496015841 * q^8 + 160137547184727 * q^9	$ 7 q + 4177 q^{2} - 33480783 q^{3} + 1749008801 q^{4} - 1716792694 q^{5} - 19978461513 q^{6} - 4747561509943 q^{7} + 4282496015841 q^{8} + 160137547184727 q^{9} - 68989267066594 q^{10} + 2545492652300 q^{11} - 83\!\cdots\!69 q^{12}+ \cdots + 58\!\cdots\!00 q^{99}+O(q^{100}) $ 7 * q + 4177 * q^2 - 33480783 * q^3 + 1749008801 * q^4 - 1716792694 * q^5 - 19978461513 * q^6 - 4747561509943 * q^7 + 4282496015841 * q^8 + 160137547184727 * q^9 - 68989267066594 * q^10 + 2545492652300 * q^11 - 8365454875910169 * q^12 + 14913999229538746 * q^13 - 2832937775290273 * q^14 + 8211366234828486 * q^15 - 140832022360508287 * q^16 - 735563339328645834 * q^17 + 95556362084372097 * q^18 + 3231835378045104676 * q^19 + 24872044471029723934 * q^20 + 22707439527650560767 * q^21 - 17239876351747271380 * q^22 - 42184428229682843136 * q^23 - 20483045686391011929 * q^24 + 46804330940039088761 * q^25 - 675897714283725523994 * q^26 - 765932923920586514463 * q^27 - 1186218123454165144049 * q^28 - 2434304993428000346110 * q^29 + 329973525712240037586 * q^30 + 2199722846387345690880 * q^31 - 628893722935722970591 * q^32 - 12175012445678678700 * q^33 - 16286140216160397495774 * q^34 + 1164368416369392965206 * q^35 + 40011711342377185111761 * q^36 - 49022014961267638974534 * q^37 + 106333263742524376516156 * q^38 - 71333195980907706416874 * q^39 + 216038926502576778292062 * q^40 - 143191306451742660680690 * q^41 + 13549853558142341760537 * q^42 + 941039909393827256445716 * q^43 + 2764524465123176818801036 * q^44 - 39274710148831368854934 * q^45 + 3474443057659036283736168 * q^46 + 7006519280610369672608592 * q^47 + 673595197157617960964103 * q^48 + 3219905755813179726837607 * q^49 + 14679573416013792870926111 * q^50 + 3518176649545393836001146 * q^51 - 2546686232308412221676410 * q^52 - 10027193511015994202044662 * q^53 - 457043117602327124415993 * q^54 - 16298687268426081600331880 * q^55 - 2904487607327282801001009 * q^56 - 15457768426293016267063044 * q^57 - 48074139319095181887831538 * q^58 - 51309146879321339641894260 * q^59 - 118962217671556567654880046 * q^60 - 114001340360475297884404598 * q^61 - 123202320289320080578939968 * q^62 - 108608979330127274981177223 * q^63 - 502380072210108412189965887 * q^64 - 114667244579892903609270916 * q^65 + 82457794154240294845127220 * q^66 - 32181268110643474406964836 * q^67 + 390450998820575925888738594 * q^68 + 201766812505297918551350784 * q^69 + 46790112703505698996306306 * q^70 - 68692603646882069939817264 * q^71 + 97969772543591931935037201 * q^72 + 2610437603294481339652144758 * q^73 - 1970589544463881862899664826 * q^74 - 223863663951947820332111409 * q^75 - 495314146629295396545528580 * q^76 - 1726411848557457127402700 * q^77 + 3232797814589916385772058186 * q^78 + 11505613584082664484898031120 * q^79 + 242677199380181532889959454 * q^80 + 3663433431191523760494580647 * q^81 + 3166608206741095513542802234 * q^82 - 11108932922442693520275021468 * q^83 + 5673644511719444804866901481 * q^84 + 9256224639385320834953279412 * q^85 - 24087862070789790068131828852 * q^86 + 11643205320111329387433400590 * q^87 - 60048031588096637175274177716 * q^88 - 31316908572861218269624496914 * q^89 - 1578253144302347020332672834 * q^90 - 10115018385925386801026107354 * q^91 - 88556578633334432716269586104 * q^92 - 10521206182862436431762622720 * q^93 + 4915436657624620221918307680 * q^94 - 120026224917472203570811243048 * q^95 + 3007979181096151960924664679 * q^96 + 133134020386213024604639145390 * q^97 + 1921363763147378817000097777 * q^98 + 58232707102295304183060300 * 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 $

$2$	37632.6	1.62416	0.812081	−	0.583545i	$-0.198335\pi$
$2$	37632.6	1.62416	0.812081	+	0.583545i	$0.198335\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	8.79342e8	1.63790
$5$	1.83976e10	1.34802	0.674008	−	0.738724i	$-0.264571\pi$
$5$	1.83976e10	1.34802	0.674008	+	0.738724i	$0.264571\pi$
$6$	−1.79996e11	−0.937710
$7$	−6.78223e11	−0.377964
$7$	−6.78223e11	−0.377964
$8$	1.28881e13	1.03606
$9$	2.28768e13	0.333333
$10$	6.92348e14	2.18940
$11$	−7.53994e14	−0.598651	−0.299325	−	0.954151i	$-0.596762\pi$
$11$	−7.53994e14	−0.598651	−0.299325	+	0.954151i	$0.596762\pi$
$12$	−4.20586e15	−0.945643
$13$	−1.44227e16	−1.01594	−0.507969	−	0.861375i	$-0.669604\pi$
$13$	−1.44227e16	−1.01594	−0.507969	+	0.861375i	$0.669604\pi$
$14$	−2.55233e16	−0.613875
$15$	−8.79950e16	−0.778278
$16$	1.29187e16	0.0448206
$17$	−8.99872e17	−1.29620	−0.648099	−	0.761556i	$-0.724436\pi$
$17$	−8.99872e17	−1.29620	−0.648099	+	0.761556i	$0.724436\pi$
$18$	8.60913e17	0.541387
$19$	1.24939e18	0.358733	0.179367	−	0.983782i	$-0.442595\pi$
$19$	1.24939e18	0.358733	0.179367	+	0.983782i	$0.442595\pi$
$20$	1.61777e19	2.20792
$21$	3.24392e18	0.218218
$22$	−2.83747e19	−0.972306
$23$	−3.80568e19	−0.684508	−0.342254	−	0.939607i	$-0.611190\pi$
$23$	−3.80568e19	−0.684508	−0.342254	+	0.939607i	$0.611190\pi$
$24$	−6.16433e19	−0.598167
$25$	1.52206e20	0.817148
$26$	−5.42763e20	−1.65005
$27$	−1.09419e20	−0.192450
$28$	−5.96390e20	−0.619069
$29$	−1.55071e21	−0.967740	−0.483870	−	0.875140i	$-0.660769\pi$
$29$	−1.55071e21	−0.967740	−0.483870	+	0.875140i	$0.660769\pi$
$30$	−3.31148e21	−1.26405
$31$	−1.79680e20	−0.0426338	−0.0213169	−	0.999773i	$-0.506786\pi$
$31$	−1.79680e20	−0.0426338	−0.0213169	+	0.999773i	$0.506786\pi$
$32$	−6.43307e21	−0.963260
$33$	3.60633e21	0.345631
$34$	−3.38645e22	−2.10523
$35$	−1.24776e22	−0.509502
$36$	2.01165e22	0.545967
$37$	4.46221e22	0.814001	0.407001	−	0.913428i	$-0.366575\pi$
$37$	4.46221e22	0.814001	0.407001	+	0.913428i	$0.366575\pi$
$38$	4.70179e22	0.582641
$39$	6.89832e22	0.586552
$40$	2.37109e23	1.39662
$41$	−3.43321e23	−1.41363	−0.706813	−	0.707401i	$-0.749868\pi$
$41$	−3.43321e23	−1.41363	−0.706813	+	0.707401i	$0.749868\pi$
$42$	1.22077e23	0.354421
$43$	5.56573e23	1.14876	0.574381	−	0.818588i	$-0.305243\pi$
$43$	5.56573e23	1.14876	0.574381	+	0.818588i	$0.305243\pi$
$44$	−6.63018e23	−0.980532
$45$	4.20877e23	0.449339
$46$	−1.43218e24	−1.11175
$47$	1.17621e24	0.668445	0.334223	−	0.942494i	$-0.391526\pi$
$47$	1.17621e24	0.668445	0.334223	+	0.942494i	$0.391526\pi$
$48$	−6.17895e22	−0.0258772
$49$	4.59987e23	0.142857
$50$	5.72790e24	1.32718
$51$	4.30406e24	0.748360
$52$	−1.26825e25	−1.66401
$53$	4.55961e24	0.453866	0.226933	−	0.973910i	$-0.427130\pi$
$53$	4.55961e24	0.453866	0.226933	+	0.973910i	$0.427130\pi$
$54$	−4.11772e24	−0.312570
$55$	−1.38716e25	−0.806991
$56$	−8.74099e24	−0.391592
$57$	−5.97581e24	−0.207115
$58$	−5.83571e25	−1.57177
$59$	1.57929e25	0.331977	0.165989	−	0.986128i	$-0.446919\pi$
$59$	1.57929e25	0.331977	0.165989	+	0.986128i	$0.446919\pi$
$60$	−7.73776e25	−1.27474
$61$	−2.37660e25	−0.308088	−0.154044	−	0.988064i	$-0.549230\pi$
$61$	−2.37660e25	−0.308088	−0.154044	+	0.988064i	$0.549230\pi$
$62$	−6.76181e24	−0.0692442
$63$	−1.55156e25	−0.125988
$64$	−2.49029e26	−1.60931
$65$	−2.65342e26	−1.36950
$66$	1.35716e26	0.561361
$67$	−2.63221e26	−0.875459	−0.437730	−	0.899107i	$-0.644217\pi$
$67$	−2.63221e26	−0.875459	−0.437730	+	0.899107i	$0.644217\pi$
$68$	−7.91295e26	−2.12304
$69$	1.82025e26	0.395201
$70$	−4.69566e26	−0.827514
$71$	−1.36949e27	−1.96478	−0.982391	−	0.186837i	$-0.940176\pi$
$71$	−1.36949e27	−1.96478	−0.982391	+	0.186837i	$0.940176\pi$
$72$	2.94838e26	0.345352
$73$	3.24441e26	0.311139	0.155569	−	0.987825i	$-0.450279\pi$
$73$	3.24441e26	0.311139	0.155569	+	0.987825i	$0.450279\pi$
$74$	1.67925e27	1.32207
$75$	−7.27995e26	−0.471781
$76$	1.09864e27	0.587570
$77$	5.11376e26	0.226269
$78$	2.59602e27	0.952655
$79$	4.00843e27	1.22287	0.611437	−	0.791293i	$-0.290592\pi$
$79$	4.00843e27	1.22287	0.611437	+	0.791293i	$0.290592\pi$
$80$	2.37672e26	0.0604189
$81$	5.23348e26	0.111111
$82$	−1.29201e28	−2.29596
$83$	−1.21477e28	−1.81076	−0.905382	−	0.424597i	$-0.860416\pi$
$83$	−1.21477e28	−1.81076	−0.905382	+	0.424597i	$0.860416\pi$
$84$	2.85251e27	0.357419
$85$	−1.65554e28	−1.74730
$86$	2.09453e28	1.86577
$87$	7.41698e27	0.558725
$88$	−9.71752e27	−0.620236
$89$	−4.32540e27	−0.234353	−0.117177	−	0.993111i	$-0.537384\pi$
$89$	−4.32540e27	−0.234353	−0.117177	+	0.993111i	$0.537384\pi$
$90$	1.58387e28	0.729799
$91$	9.78179e27	0.383988
$92$	−3.34649e28	−1.12116
$93$	8.59402e26	0.0246146
$94$	4.42638e28	1.08566
$95$	2.29858e28	0.483578
$96$	3.07692e28	0.556138
$97$	1.14699e29	1.78390	0.891949	−	0.452136i	$-0.149338\pi$
$97$	1.14699e29	1.78390	0.891949	+	0.452136i	$0.149338\pi$
$98$	1.73105e28	0.232023
$99$	−1.72490e28	−0.199550
$100$	1.33841e29	1.33841
$101$	−8.18822e28	−0.708810	−0.354405	−	0.935092i	$-0.615317\pi$
$101$	−8.18822e28	−0.708810	−0.354405	+	0.935092i	$0.615317\pi$
$102$	1.61973e29	1.21546
$103$	−1.35407e29	−0.882065	−0.441033	−	0.897491i	$-0.645388\pi$
$103$	−1.35407e29	−0.882065	−0.441033	+	0.897491i	$0.645388\pi$
$104$	−1.85880e29	−1.05257
$105$	5.96802e28	0.294161
$106$	1.71590e29	0.737152
$107$	−1.56594e29	−0.587099	−0.293549	−	0.955944i	$-0.594836\pi$
$107$	−1.56594e29	−0.587099	−0.293549	+	0.955944i	$0.594836\pi$
$108$	−9.62167e28	−0.315214
$109$	−9.18239e28	−0.263191	−0.131596	−	0.991303i	$-0.542010\pi$
$109$	−9.18239e28	−0.263191	−0.131596	+	0.991303i	$0.542010\pi$
$110$	−5.22026e29	−1.31068
$111$	−2.13426e29	−0.469964
$112$	−8.76173e27	−0.0169406
$113$	−9.91018e29	−1.68440	−0.842198	−	0.539169i	$-0.818738\pi$
$113$	−9.91018e29	−1.68440	−0.842198	+	0.539169i	$0.818738\pi$
$114$	−2.24885e29	−0.336388
$115$	−7.00152e29	−0.922729
$116$	−1.36360e30	−1.58506
$117$	−3.29944e29	−0.338646
$118$	5.94328e29	0.539185
$119$	6.10314e29	0.489917
$120$	−1.13409e30	−0.806339
$121$	−1.01780e30	−0.641617
$122$	−8.94378e29	−0.500384
$123$	1.64209e30	0.816157
$124$	−1.58000e29	−0.0698300
$125$	−6.26599e29	−0.246487
$126$	−5.83891e29	−0.204625
$127$	−1.70832e30	−0.533847	−0.266923	−	0.963718i	$-0.586007\pi$
$127$	−1.70832e30	−0.533847	−0.266923	+	0.963718i	$0.586007\pi$
$128$	−5.91787e30	−1.65052
$129$	−2.66207e30	−0.663238
$130$	−9.98551e30	−2.22429
$131$	9.36226e30	1.86615	0.933076	−	0.359680i	$-0.117114\pi$
$131$	9.36226e30	1.86615	0.933076	+	0.359680i	$0.117114\pi$
$132$	3.17120e30	0.566110
$133$	−8.47367e29	−0.135588
$134$	−9.90569e30	−1.42189
$135$	−2.01304e30	−0.259426
$136$	−1.15976e31	−1.34293
$137$	1.06774e31	1.11178	0.555890	−	0.831256i	$-0.312378\pi$
$137$	1.06774e31	1.11178	0.555890	+	0.831256i	$0.312378\pi$
$138$	6.85006e30	0.641871
$139$	1.83910e31	1.55199	0.775996	−	0.630737i	$-0.217247\pi$
$139$	1.83910e31	1.55199	0.775996	+	0.630737i	$0.217247\pi$
$140$	−1.09721e31	−0.834515
$141$	−5.62577e30	−0.385927
$142$	−5.15377e31	−3.19112
$143$	1.08746e31	0.608192
$144$	2.95537e29	0.0149402
$145$	−2.85292e31	−1.30453
$146$	1.22096e31	0.505340
$147$	−2.20010e30	−0.0824786
$148$	3.92381e31	1.33325
$149$	6.29465e31	1.93986	0.969930	−	0.243384i	$-0.0782575\pi$
$149$	6.29465e31	1.93986	0.969930	+	0.243384i	$0.0782575\pi$
$150$	−2.73964e31	−0.766248
$151$	−4.03290e31	−1.02436	−0.512180	−	0.858878i	$-0.671162\pi$
$151$	−4.03290e31	−1.02436	−0.512180	+	0.858878i	$0.671162\pi$
$152$	1.61023e31	0.371668
$153$	−2.05862e31	−0.432066
$154$	1.92444e31	0.367497
$155$	−3.30566e30	−0.0574711
$156$	6.06598e31	0.960715
$157$	9.28989e31	1.34111	0.670557	−	0.741858i	$-0.266055\pi$
$157$	9.28989e31	1.34111	0.670557	+	0.741858i	$0.266055\pi$
$158$	1.50848e32	1.98615
$159$	−2.18085e31	−0.262040
$160$	−1.18353e32	−1.29849
$161$	2.58110e31	0.258720
$162$	1.96949e31	0.180462
$163$	−1.54823e32	−1.29753	−0.648763	−	0.760990i	$-0.724713\pi$
$163$	−1.54823e32	−1.29753	−0.648763	+	0.760990i	$0.724713\pi$
$164$	−3.01896e32	−2.31538
$165$	6.63476e31	0.465917
$166$	−4.57150e32	−2.94097
$167$	8.38512e31	0.494448	0.247224	−	0.968958i	$-0.420482\pi$
$167$	8.38512e31	0.494448	0.247224	+	0.968958i	$0.420482\pi$
$168$	4.18079e31	0.226086
$169$	6.47533e30	0.0321296
$170$	−6.23024e32	−2.83789
$171$	2.85821e31	0.119578
$172$	4.89418e32	1.88156
$173$	−4.43703e32	−1.56828	−0.784141	−	0.620583i	$-0.786896\pi$
$173$	−4.43703e32	−1.56828	−0.784141	+	0.620583i	$0.786896\pi$
$174$	2.79120e32	0.907460
$175$	−1.03229e32	−0.308853
$176$	−9.74058e30	−0.0268319
$177$	−7.55370e31	−0.191667
$178$	−1.62776e32	−0.380628
$179$	3.91124e32	0.843229	0.421614	−	0.906775i	$-0.361464\pi$
$179$	3.91124e32	0.843229	0.421614	+	0.906775i	$0.361464\pi$
$180$	3.70095e32	0.735973
$181$	3.00760e32	0.551926	0.275963	−	0.961168i	$-0.411003\pi$
$181$	3.00760e32	0.551926	0.275963	+	0.961168i	$0.411003\pi$
$182$	3.68114e32	0.623659
$183$	1.13672e32	0.177875
$184$	−4.90479e32	−0.709189
$185$	8.20938e32	1.09729
$186$	3.23415e31	0.0399782
$187$	6.78497e32	0.775970
$188$	1.03429e33	1.09485
$189$	7.42105e31	0.0727393
$190$	8.65014e32	0.785409
$191$	−3.30332e30	−0.00277950	−0.00138975	−	0.999999i	$-0.500442\pi$
$191$	−3.30332e30	−0.00277950	−0.00138975	+	0.999999i	$0.500442\pi$
$192$	1.19110e33	0.929136
$193$	4.91636e32	0.355682	0.177841	−	0.984059i	$-0.443089\pi$
$193$	4.91636e32	0.355682	0.177841	+	0.984059i	$0.443089\pi$
$194$	4.31643e33	2.89734
$195$	1.26912e33	0.790682
$196$	4.04485e32	0.233986
$197$	1.77496e33	0.953736	0.476868	−	0.878975i	$-0.341772\pi$
$197$	1.77496e33	0.953736	0.476868	+	0.878975i	$0.341772\pi$
$198$	−6.49123e32	−0.324102
$199$	−2.50153e33	−1.16101	−0.580505	−	0.814257i	$-0.697145\pi$
$199$	−2.50153e33	−1.16101	−0.580505	+	0.814257i	$0.697145\pi$
$200$	1.96164e33	0.846611
$201$	1.25898e33	0.505447
$202$	−3.08144e33	−1.15122
$203$	1.05172e33	0.365771
$204$	3.78474e33	1.22574
$205$	−6.31627e33	−1.90559
$206$	−5.09571e33	−1.43262
$207$	−8.70618e32	−0.228169
$208$	−1.86322e32	−0.0455349
$209$	−9.42034e32	−0.214756
$210$	2.24592e33	0.477766
$211$	−3.23082e33	−0.641531	−0.320766	−	0.947159i	$-0.603940\pi$
$211$	−3.23082e33	−0.641531	−0.320766	+	0.947159i	$0.603940\pi$
$212$	4.00946e33	0.743388
$213$	6.55025e33	1.13437
$214$	−5.89305e33	−0.953543
$215$	1.02396e34	1.54855
$216$	−1.41020e33	−0.199389
$217$	1.21863e32	0.0161141
$218$	−3.45557e33	−0.427465
$219$	−1.55179e33	−0.179636
$220$	−1.21979e34	−1.32177
$221$	1.29786e34	1.31686
$222$	−8.03178e33	−0.763297
$223$	−7.25354e33	−0.645847	−0.322923	−	0.946425i	$-0.604666\pi$
$223$	−7.25354e33	−0.645847	−0.322923	+	0.946425i	$0.604666\pi$
$224$	4.36306e33	0.364078
$225$	3.48198e33	0.272383
$226$	−3.72946e34	−2.73573
$227$	1.14536e34	0.788072	0.394036	−	0.919095i	$-0.371079\pi$
$227$	1.14536e34	0.788072	0.394036	+	0.919095i	$0.371079\pi$
$228$	−5.25478e33	−0.339234
$229$	4.28484e33	0.259609	0.129804	−	0.991540i	$-0.458565\pi$
$229$	4.28484e33	0.259609	0.129804	+	0.991540i	$0.458565\pi$
$230$	−2.63486e34	−1.49866
$231$	−2.44589e33	−0.130636
$232$	−1.99856e34	−1.00263
$233$	−1.68923e34	−0.796209	−0.398105	−	0.917340i	$-0.630332\pi$
$233$	−1.68923e34	−0.796209	−0.398105	+	0.917340i	$0.630332\pi$
$234$	−1.24167e34	−0.550016
$235$	2.16394e34	0.901075
$236$	1.38874e34	0.543746
$237$	−1.91722e34	−0.706027
$238$	2.29677e34	0.795704
$239$	−4.53503e34	−1.47846	−0.739232	−	0.673451i	$-0.764811\pi$
$239$	−4.53503e34	−1.47846	−0.739232	+	0.673451i	$0.764811\pi$
$240$	−1.13678e33	−0.0348829
$241$	5.76534e34	1.66563	0.832813	−	0.553554i	$-0.186729\pi$
$241$	5.76534e34	1.66563	0.832813	+	0.553554i	$0.186729\pi$
$242$	−3.83026e34	−1.04209
$243$	−2.50316e33	−0.0641500
$244$	−2.08985e34	−0.504617
$245$	8.46263e33	0.192574
$246$	6.17962e34	1.32557
$247$	−1.80196e34	−0.364451
$248$	−2.31572e33	−0.0441710
$249$	5.81021e34	1.04545
$250$	−2.35806e34	−0.400335
$251$	−2.98895e34	−0.478905	−0.239453	−	0.970908i	$-0.576968\pi$
$251$	−2.98895e34	−0.478905	−0.239453	+	0.970908i	$0.576968\pi$
$252$	−1.36435e34	−0.206356
$253$	2.86946e34	0.409782
$254$	−6.42887e34	−0.867053
$255$	7.91842e34	1.00880
$256$	−8.90087e34	−1.07140
$257$	7.99624e34	0.909610	0.454805	−	0.890591i	$-0.349709\pi$
$257$	7.99624e34	0.909610	0.454805	+	0.890591i	$0.349709\pi$
$258$	−1.00181e35	−1.07721
$259$	−3.02637e34	−0.307663
$260$	−2.33326e35	−2.24311
$261$	−3.54752e34	−0.322580
$262$	3.52326e35	3.03093
$263$	1.31157e35	1.06766	0.533830	−	0.845592i	$-0.320752\pi$
$263$	1.31157e35	1.06766	0.533830	+	0.845592i	$0.320752\pi$
$264$	4.64786e34	0.358093
$265$	8.38857e34	0.611819
$266$	−3.18886e34	−0.220218
$267$	2.06882e34	0.135304
$268$	−2.31461e35	−1.43392
$269$	1.28002e35	0.751291	0.375645	−	0.926763i	$-0.377421\pi$
$269$	1.28002e35	0.751291	0.375645	+	0.926763i	$0.377421\pi$
$270$	−7.57560e34	−0.421350
$271$	1.02152e35	0.538506	0.269253	−	0.963070i	$-0.413223\pi$
$271$	1.02152e35	0.538506	0.269253	+	0.963070i	$0.413223\pi$
$272$	−1.16251e34	−0.0580963
$273$	−4.67860e34	−0.221696
$274$	4.01820e35	1.80571
$275$	−1.14762e35	−0.489187
$276$	1.60062e35	0.647301
$277$	−2.61054e34	−0.100178	−0.0500891	−	0.998745i	$-0.515951\pi$
$277$	−2.61054e34	−0.100178	−0.0500891	+	0.998745i	$0.515951\pi$
$278$	6.92100e35	2.52069
$279$	−4.11049e33	−0.0142113
$280$	−1.60813e35	−0.527873
$281$	−2.45414e35	−0.764992	−0.382496	−	0.923957i	$-0.624935\pi$
$281$	−2.45414e35	−0.764992	−0.382496	+	0.923957i	$0.624935\pi$
$282$	−2.11713e35	−0.626808
$283$	−2.83579e35	−0.797573	−0.398786	−	0.917044i	$-0.630568\pi$
$283$	−2.83579e35	−0.797573	−0.398786	+	0.917044i	$0.630568\pi$
$284$	−1.20425e36	−3.21812
$285$	−1.09940e35	−0.279194
$286$	4.09240e35	0.987803
$287$	2.32848e35	0.534300
$288$	−1.47168e35	−0.321087
$289$	3.27800e35	0.680128
$290$	−1.07363e36	−2.11877
$291$	−5.48603e35	−1.02993
$292$	2.85295e35	0.509615
$293$	8.45957e35	1.43803	0.719014	−	0.694995i	$-0.244594\pi$
$293$	8.45957e35	1.43803	0.719014	+	0.694995i	$0.244594\pi$
$294$	−8.27955e34	−0.133959
$295$	2.90551e35	0.447511
$296$	5.75093e35	0.843351
$297$	8.25012e34	0.115210
$298$	2.36884e36	3.15065
$299$	5.48881e35	0.695418
$300$	−6.40157e35	−0.772730
$301$	−3.77481e35	−0.434191
$302$	−1.51769e36	−1.66373
$303$	3.91640e35	0.409232
$304$	1.61405e34	0.0160786
$305$	−4.37237e35	−0.415307
$306$	−7.74711e35	−0.701745
$307$	8.39049e35	0.724904	0.362452	−	0.932002i	$-0.381940\pi$
$307$	8.39049e35	0.724904	0.362452	+	0.932002i	$0.381940\pi$
$308$	4.49674e35	0.370606
$309$	6.47646e35	0.509261
$310$	−1.24401e35	−0.0933423
$311$	2.54688e36	1.82382	0.911911	−	0.410389i	$-0.134607\pi$
$311$	2.54688e36	1.82382	0.911911	+	0.410389i	$0.134607\pi$
$312$	8.89060e35	0.607701
$313$	−6.17027e35	−0.402635	−0.201317	−	0.979526i	$-0.564522\pi$
$313$	−6.17027e35	−0.402635	−0.201317	+	0.979526i	$0.564522\pi$
$314$	3.49603e36	2.17819
$315$	−2.85449e35	−0.169834
$316$	3.52478e36	2.00295
$317$	1.90938e36	1.03641	0.518206	−	0.855256i	$-0.326600\pi$
$317$	1.90938e36	1.03641	0.518206	+	0.855256i	$0.326600\pi$
$318$	−8.20710e35	−0.425595
$319$	1.16922e36	0.579338
$320$	−4.58152e36	−2.16938
$321$	7.48986e35	0.338962
$322$	9.71335e35	0.420203
$323$	−1.12429e36	−0.464989
$324$	4.60201e35	0.181989
$325$	−2.19521e36	−0.830172
$326$	−5.82641e36	−2.10739
$327$	4.39191e35	0.151953
$328$	−4.42474e36	−1.46459
$329$	−7.97732e35	−0.252649
$330$	2.49683e36	0.756724
$331$	−1.79539e36	−0.520778	−0.260389	−	0.965504i	$-0.583851\pi$
$331$	−1.79539e36	−0.520778	−0.260389	+	0.965504i	$0.583851\pi$
$332$	−1.06820e37	−2.96585
$333$	1.02081e36	0.271334
$334$	3.15554e36	0.803063
$335$	−4.84262e36	−1.18013
$336$	4.19071e34	0.00978065
$337$	3.91703e36	0.875636	0.437818	−	0.899064i	$-0.355751\pi$
$337$	3.91703e36	0.875636	0.437818	+	0.899064i	$0.355751\pi$
$338$	2.43684e35	0.0521836
$339$	4.74001e36	0.972486
$340$	−1.45579e37	−2.86190
$341$	1.35477e35	0.0255228
$342$	1.07562e36	0.194214
$343$	−3.11973e35	−0.0539949
$344$	7.17316e36	1.19018
$345$	3.34881e36	0.532738
$346$	−1.66977e37	−2.54714
$347$	−7.14627e36	−1.04545	−0.522724	−	0.852502i	$-0.675084\pi$
$347$	−7.14627e36	−1.04545	−0.522724	+	0.852502i	$0.675084\pi$
$348$	6.52206e36	0.915136
$349$	9.99316e36	1.34504	0.672518	−	0.740080i	$-0.265213\pi$
$349$	9.99316e36	1.34504	0.672518	+	0.740080i	$0.265213\pi$
$350$	−3.88479e36	−0.501627
$351$	1.57811e36	0.195517
$352$	4.85049e36	0.576657
$353$	−2.90465e36	−0.331406	−0.165703	−	0.986176i	$-0.552989\pi$
$353$	−2.90465e36	−0.331406	−0.165703	+	0.986176i	$0.552989\pi$
$354$	−2.84265e36	−0.311298
$355$	−2.51954e37	−2.64856
$356$	−3.80350e36	−0.383848
$357$	−2.91911e36	−0.282853
$358$	1.47190e37	1.36954
$359$	−1.60635e37	−1.43540	−0.717698	−	0.696355i	$-0.754804\pi$
$359$	−1.60635e37	−1.43540	−0.717698	+	0.696355i	$0.754804\pi$
$360$	5.42430e36	0.465540
$361$	−1.05688e37	−0.871310
$362$	1.13184e37	0.896417
$363$	4.86812e36	0.370438
$364$	8.60154e36	0.628935
$365$	5.96892e36	0.419420
$366$	4.27778e36	0.288897
$367$	−2.12923e37	−1.38218	−0.691089	−	0.722769i	$-0.742869\pi$
$367$	−2.12923e37	−1.38218	−0.691089	+	0.722769i	$0.742869\pi$
$368$	−4.91643e35	−0.0306801
$369$	−7.85408e36	−0.471208
$370$	3.08940e37	1.78217
$371$	−3.09243e36	−0.171545
$372$	7.55708e35	0.0403164
$373$	−2.76012e37	−1.41628	−0.708141	−	0.706071i	$-0.750466\pi$
$373$	−2.76012e37	−1.41628	−0.708141	+	0.706071i	$0.750466\pi$
$374$	2.55336e37	1.26030
$375$	2.99700e36	0.142310
$376$	1.51591e37	0.692546
$377$	2.23653e37	0.983163
$378$	2.79273e36	0.118140
$379$	−3.27017e37	−1.33138	−0.665690	−	0.746229i	$-0.731863\pi$
$379$	−3.27017e37	−1.33138	−0.665690	+	0.746229i	$0.731863\pi$
$380$	2.02124e37	0.792054
$381$	8.17086e36	0.308216
$382$	−1.24313e35	−0.00451436
$383$	−5.16579e37	−1.80615	−0.903077	−	0.429479i	$-0.858697\pi$
$383$	−5.16579e37	−1.80615	−0.903077	+	0.429479i	$0.858697\pi$
$384$	2.83050e37	0.952929
$385$	9.40807e36	0.305014
$386$	1.85015e37	0.577686
$387$	1.27326e37	0.382920
$388$	1.00860e38	2.92185
$389$	3.32852e37	0.928929	0.464464	−	0.885592i	$-0.346247\pi$
$389$	3.32852e37	0.928929	0.464464	+	0.885592i	$0.346247\pi$
$390$	4.77604e37	1.28419
$391$	3.42462e37	0.887258
$392$	5.92834e36	0.148008
$393$	−4.47794e37	−1.07742
$394$	6.67964e37	1.54902
$395$	7.37454e37	1.64845
$396$	−1.51677e37	−0.326844
$397$	7.30028e37	1.51662	0.758310	−	0.651894i	$-0.226025\pi$
$397$	7.30028e37	1.51662	0.758310	+	0.651894i	$0.226025\pi$
$398$	−9.41391e37	−1.88567
$399$	4.05293e36	0.0782820
$400$	1.96629e36	0.0366251
$401$	−6.99377e37	−1.25637	−0.628186	−	0.778064i	$-0.716202\pi$
$401$	−6.99377e37	−1.25637	−0.628186	+	0.778064i	$0.716202\pi$
$402$	4.73786e37	0.820927
$403$	2.59146e36	0.0433133
$404$	−7.20025e37	−1.16096
$405$	9.62832e36	0.149780
$406$	3.95791e37	0.594072
$407$	−3.36448e37	−0.487303
$408$	5.54710e37	0.775343
$409$	1.26721e37	0.170946	0.0854732	−	0.996340i	$-0.472760\pi$
$409$	1.26721e37	0.170946	0.0854732	+	0.996340i	$0.472760\pi$
$410$	−2.37698e38	−3.09499
$411$	−5.10698e37	−0.641886
$412$	−1.19069e38	−1.44474
$413$	−1.07111e37	−0.125476
$414$	−3.27636e37	−0.370584
$415$	−2.23488e38	−2.44094
$416$	9.27820e37	0.978612
$417$	−8.79634e37	−0.896044
$418$	−3.54512e37	−0.348799
$419$	3.39521e37	0.322674	0.161337	−	0.986899i	$-0.448419\pi$
$419$	3.39521e37	0.322674	0.161337	+	0.986899i	$0.448419\pi$
$420$	5.24793e37	0.481807
$421$	−5.17165e37	−0.458710	−0.229355	−	0.973343i	$-0.573662\pi$
$421$	−5.17165e37	−0.458710	−0.229355	+	0.973343i	$0.573662\pi$
$422$	−1.21584e38	−1.04195
$423$	2.69079e37	0.222815
$424$	5.87646e37	0.470231
$425$	−1.36966e38	−1.05919
$426$	2.46503e38	1.84240
$427$	1.61187e37	0.116446
$428$	−1.37700e38	−0.961610
$429$	−5.20129e37	−0.351140
$430$	3.85342e38	2.51509
$431$	−5.56569e37	−0.351236	−0.175618	−	0.984458i	$-0.556192\pi$
$431$	−5.56569e37	−0.351236	−0.175618	+	0.984458i	$0.556192\pi$
$432$	−1.41355e36	−0.00862573
$433$	2.74056e38	1.61721	0.808603	−	0.588354i	$-0.200224\pi$
$433$	2.74056e38	1.61721	0.808603	+	0.588354i	$0.200224\pi$
$434$	4.58601e36	0.0261718
$435$	1.36454e38	0.753170
$436$	−8.07446e37	−0.431081
$437$	−4.75479e37	−0.245556
$438$	−5.83980e37	−0.291758
$439$	1.81937e38	0.879399	0.439700	−	0.898145i	$-0.355085\pi$
$439$	1.81937e38	0.879399	0.439700	+	0.898145i	$0.355085\pi$
$440$	−1.78779e38	−0.836088
$441$	1.05230e37	0.0476190
$442$	4.88417e38	2.13879
$443$	−3.57438e38	−1.51477	−0.757385	−	0.652969i	$-0.773523\pi$
$443$	−3.57438e38	−1.51477	−0.757385	+	0.652969i	$0.773523\pi$
$444$	−1.87674e38	−0.769754
$445$	−7.95768e37	−0.315912
$446$	−2.72969e38	−1.04896
$447$	−3.01071e38	−1.11998
$448$	1.68897e38	0.608262
$449$	3.57893e38	1.24790	0.623952	−	0.781463i	$-0.285526\pi$
$449$	3.57893e38	1.24790	0.623952	+	0.781463i	$0.285526\pi$
$450$	1.31036e38	0.442394
$451$	2.58862e38	0.846268
$452$	−8.71443e38	−2.75887
$453$	1.92893e38	0.591414
$454$	4.31027e38	1.27996
$455$	1.79961e38	0.517623
$456$	−7.70166e37	−0.214582
$457$	3.17150e38	0.856013	0.428007	−	0.903776i	$-0.359216\pi$
$457$	3.17150e38	0.856013	0.428007	+	0.903776i	$0.359216\pi$
$458$	1.61250e38	0.421647
$459$	9.84630e37	0.249453
$460$	−6.15673e38	−1.51134
$461$	−1.80800e38	−0.430066	−0.215033	−	0.976607i	$-0.568986\pi$
$461$	−1.80800e38	−0.430066	−0.215033	+	0.976607i	$0.568986\pi$
$462$	−9.20454e37	−0.212175
$463$	5.44919e37	0.121733	0.0608664	−	0.998146i	$-0.480614\pi$
$463$	5.44919e37	0.121733	0.0608664	+	0.998146i	$0.480614\pi$
$464$	−2.00330e37	−0.0433747
$465$	1.58109e37	0.0331809
$466$	−6.35700e38	−1.29317
$467$	−6.25756e38	−1.23399	−0.616993	−	0.786969i	$-0.711649\pi$
$467$	−6.25756e38	−1.23399	−0.616993	+	0.786969i	$0.711649\pi$
$468$	−2.90134e38	−0.554669
$469$	1.78523e38	0.330892
$470$	8.14346e38	1.46349
$471$	−4.44333e38	−0.774292
$472$	2.03540e38	0.343947
$473$	−4.19653e38	−0.687707
$474$	−7.21500e38	−1.14670
$475$	1.90165e38	0.293138
$476$	5.36674e38	0.802435
$477$	1.04309e38	0.151289
$478$	−1.70665e39	−2.40126
$479$	−1.07051e39	−1.46126	−0.730629	−	0.682775i	$-0.760773\pi$
$479$	−1.07051e39	−1.46126	−0.730629	+	0.682775i	$0.760773\pi$
$480$	5.66078e38	0.749684
$481$	−6.43570e38	−0.826974
$482$	2.16965e39	2.70525
$483$	−1.23453e38	−0.149372
$484$	−8.94997e38	−1.05091
$485$	2.11018e39	2.40472
$486$	−9.42003e37	−0.104190
$487$	−1.11656e39	−1.19870	−0.599351	−	0.800486i	$-0.704575\pi$
$487$	−1.11656e39	−1.19870	−0.599351	+	0.800486i	$0.704575\pi$
$488$	−3.06299e38	−0.319196
$489$	7.40515e38	0.749127
$490$	3.18471e38	0.312771
$491$	−7.67288e38	−0.731605	−0.365803	−	0.930692i	$-0.619205\pi$
$491$	−7.67288e38	−0.731605	−0.365803	+	0.930692i	$0.619205\pi$
$492$	1.44396e39	1.33679
$493$	1.39544e39	1.25438
$494$	−6.78124e38	−0.591927
$495$	−3.17339e38	−0.268997
$496$	−2.32122e36	−0.00191087
$497$	9.28823e38	0.742618
$498$	2.18653e39	1.69797
$499$	1.53682e39	1.15922	0.579608	−	0.814896i	$-0.303206\pi$
$499$	1.53682e39	1.15922	0.579608	+	0.814896i	$0.303206\pi$
$500$	−5.50995e38	−0.403722
$501$	−4.01058e38	−0.285470
$502$	−1.12482e39	−0.777819
$503$	7.17483e38	0.482032	0.241016	−	0.970521i	$-0.422519\pi$
$503$	7.17483e38	0.482032	0.241016	+	0.970521i	$0.422519\pi$
$504$	−1.99966e38	−0.130531
$505$	−1.50643e39	−0.955487
$506$	1.07985e39	0.665552
$507$	−3.09713e37	−0.0185500
$508$	−1.50220e39	−0.874388
$509$	−3.42341e38	−0.193665	−0.0968326	−	0.995301i	$-0.530871\pi$
$509$	−3.42341e38	−0.193665	−0.0968326	+	0.995301i	$0.530871\pi$
$510$	2.97991e39	1.63846
$511$	−2.20043e38	−0.117599
$512$	−1.72494e38	−0.0896105
$513$	−1.36707e38	−0.0690382
$514$	3.00919e39	1.47735
$515$	−2.49115e39	−1.18904
$516$	−2.34087e39	−1.08632
$517$	−8.86854e38	−0.400165
$518$	−1.13890e39	−0.499695
$519$	2.12222e39	0.905448
$520$	−3.41975e39	−1.41888
$521$	−1.07899e39	−0.435382	−0.217691	−	0.976018i	$-0.569852\pi$
$521$	−1.07899e39	−0.435382	−0.217691	+	0.976018i	$0.569852\pi$
$522$	−1.33502e39	−0.523922
$523$	1.39520e39	0.532551	0.266275	−	0.963897i	$-0.414207\pi$
$523$	1.39520e39	0.532551	0.266275	+	0.963897i	$0.414207\pi$
$524$	8.23263e39	3.05657
$525$	4.93743e38	0.178316
$526$	4.93578e39	1.73405
$527$	1.61688e38	0.0552618
$528$	4.65889e37	0.0154914
$529$	−1.64274e39	−0.531448
$530$	3.15684e39	0.993693
$531$	3.61291e38	0.110659
$532$	−7.45125e38	−0.222081
$533$	4.95160e39	1.43616
$534$	7.78553e38	0.219755
$535$	−2.88095e39	−0.791419
$536$	−3.39241e39	−0.907025
$537$	−1.87073e39	−0.486838
$538$	4.81704e39	1.22022
$539$	−3.46827e38	−0.0855216
$540$	−1.77015e39	−0.424914
$541$	−6.98093e39	−1.63137	−0.815686	−	0.578494i	$-0.803640\pi$
$541$	−6.98093e39	−1.63137	−0.815686	+	0.578494i	$0.803640\pi$
$542$	3.84423e39	0.874620
$543$	−1.43853e39	−0.318654
$544$	5.78894e39	1.24858
$545$	−1.68933e39	−0.354786
$546$	−1.76068e39	−0.360070
$547$	1.26144e39	0.251218	0.125609	−	0.992080i	$-0.459912\pi$
$547$	1.26144e39	0.251218	0.125609	+	0.992080i	$0.459912\pi$
$548$	9.38911e39	1.82099
$549$	−5.43691e38	−0.102696
$550$	−4.31880e39	−0.794518
$551$	−1.93744e39	−0.347160
$552$	2.34595e39	0.409450
$553$	−2.71861e39	−0.462203
$554$	−9.82413e38	−0.162706
$555$	−3.92652e39	−0.633519
$556$	1.61719e40	2.54201
$557$	−1.15247e40	−1.76494	−0.882470	−	0.470369i	$-0.844121\pi$
$557$	−1.15247e40	−1.76494	−0.882470	+	0.470369i	$0.844121\pi$
$558$	−1.54688e38	−0.0230814
$559$	−8.02728e39	−1.16707
$560$	−1.61194e38	−0.0228362
$561$	−3.24523e39	−0.448006
$562$	−9.23555e39	−1.24247
$563$	1.83210e39	0.240203	0.120102	−	0.992762i	$-0.461678\pi$
$563$	1.83210e39	0.240203	0.120102	+	0.992762i	$0.461678\pi$
$564$	−4.94698e39	−0.632110
$565$	−1.82323e40	−2.27059
$566$	−1.06718e40	−1.29539
$567$	−3.54946e38	−0.0419961
$568$	−1.76501e40	−2.03562
$569$	7.53993e38	0.0847694	0.0423847	−	0.999101i	$-0.486504\pi$
$569$	7.53993e38	0.0847694	0.0423847	+	0.999101i	$0.486504\pi$
$570$	−4.13734e39	−0.453456
$571$	3.45477e39	0.369144	0.184572	−	0.982819i	$-0.440910\pi$
$571$	3.45477e39	0.369144	0.184572	+	0.982819i	$0.440910\pi$
$572$	9.56249e39	0.996159
$573$	1.57997e37	0.00160475
$574$	8.76268e39	0.867790
$575$	−5.79246e39	−0.559345
$576$	−5.69698e39	−0.536437
$577$	−3.81665e39	−0.350456	−0.175228	−	0.984528i	$-0.556066\pi$
$577$	−3.81665e39	−0.350456	−0.175228	+	0.984528i	$0.556066\pi$
$578$	1.23360e40	1.10464
$579$	−2.35148e39	−0.205353
$580$	−2.50869e40	−2.13669
$581$	8.23886e39	0.684405
$582$	−2.06453e40	−1.67278
$583$	−3.43792e39	−0.271707
$584$	4.18142e39	0.322357
$585$	−6.07017e39	−0.456500
$586$	3.18355e40	2.33559
$587$	−2.76727e40	−1.98061	−0.990307	−	0.138899i	$-0.955644\pi$
$587$	−2.76727e40	−1.98061	−0.990307	+	0.138899i	$0.955644\pi$
$588$	−1.93464e39	−0.135092
$589$	−2.24490e38	−0.0152942
$590$	1.09342e40	0.726830
$591$	−8.48958e39	−0.550640
$592$	5.76457e38	0.0364840
$593$	1.19086e39	0.0735473	0.0367737	−	0.999324i	$-0.488292\pi$
$593$	1.19086e39	0.0735473	0.0367737	+	0.999324i	$0.488292\pi$
$594$	3.10474e39	0.187120
$595$	1.12283e40	0.660416
$596$	5.53515e40	3.17730
$597$	1.19647e40	0.670310
$598$	2.06558e40	1.12947
$599$	2.46508e40	1.31565	0.657827	−	0.753169i	$-0.271476\pi$
$599$	2.46508e40	1.31565	0.657827	+	0.753169i	$0.271476\pi$
$600$	−9.38245e39	−0.488791
$601$	2.40286e40	1.22194	0.610969	−	0.791655i	$-0.290780\pi$
$601$	2.40286e40	1.22194	0.610969	+	0.791655i	$0.290780\pi$
$602$	−1.42056e40	−0.705196
$603$	−6.02165e39	−0.291820
$604$	−3.54630e40	−1.67780
$605$	−1.87251e40	−0.864910
$606$	1.47384e40	0.664658
$607$	2.23738e40	0.985152	0.492576	−	0.870269i	$-0.336055\pi$
$607$	2.23738e40	0.985152	0.492576	+	0.870269i	$0.336055\pi$
$608$	−8.03743e39	−0.345553
$609$	−5.03037e39	−0.211178
$610$	−1.64544e40	−0.674526
$611$	−1.69641e40	−0.679099
$612$	−1.81023e40	−0.707681
$613$	4.59145e40	1.75296	0.876482	−	0.481434i	$-0.159884\pi$
$613$	4.59145e40	1.75296	0.876482	+	0.481434i	$0.159884\pi$
$614$	3.15756e40	1.17736
$615$	3.02105e40	1.10019
$616$	6.59065e39	0.234427
$617$	−3.04832e39	−0.105907	−0.0529536	−	0.998597i	$-0.516864\pi$
$617$	−3.04832e39	−0.105907	−0.0529536	+	0.998597i	$0.516864\pi$
$618$	2.43726e40	0.827122
$619$	−1.47916e40	−0.490344	−0.245172	−	0.969480i	$-0.578844\pi$
$619$	−1.47916e40	−0.490344	−0.245172	+	0.969480i	$0.578844\pi$
$620$	−2.90681e39	−0.0941320
$621$	4.16414e39	0.131734
$622$	9.58456e40	2.96218
$623$	2.93359e39	0.0885772
$624$	8.91170e38	0.0262896
$625$	−3.98784e40	−1.14942
$626$	−2.32203e40	−0.653944
$627$	4.50572e39	0.123989
$628$	8.16899e40	2.19661
$629$	−4.01542e40	−1.05511
$630$	−1.07422e40	−0.275838
$631$	−9.86475e39	−0.247548	−0.123774	−	0.992310i	$-0.539500\pi$
$631$	−9.86475e39	−0.247548	−0.123774	+	0.992310i	$0.539500\pi$
$632$	5.16610e40	1.26697
$633$	1.54529e40	0.370388
$634$	7.18548e40	1.68330
$635$	−3.14290e40	−0.719634
$636$	−1.91771e40	−0.429195
$637$	−6.63423e39	−0.145134
$638$	4.40009e40	0.940939
$639$	−3.13296e40	−0.654927
$640$	−1.08874e41	−2.22493
$641$	−5.63189e39	−0.112516	−0.0562578	−	0.998416i	$-0.517917\pi$
$641$	−5.63189e39	−0.112516	−0.0562578	+	0.998416i	$0.517917\pi$
$642$	2.81863e40	0.550528
$643$	−5.70536e40	−1.08949	−0.544746	−	0.838601i	$-0.683374\pi$
$643$	−5.70536e40	−1.08949	−0.544746	+	0.838601i	$0.683374\pi$
$644$	2.26967e40	0.423758
$645$	−4.89757e40	−0.894055
$646$	−4.23101e40	−0.755218
$647$	−2.20096e40	−0.384150	−0.192075	−	0.981380i	$-0.561522\pi$
$647$	−2.20096e40	−0.384150	−0.192075	+	0.981380i	$0.561522\pi$
$648$	6.74494e39	0.115117
$649$	−1.19078e40	−0.198738
$650$	−8.26116e40	−1.34833
$651$	−5.82866e38	−0.00930346
$652$	−1.36143e41	−2.12522
$653$	7.34914e40	1.12201	0.561004	−	0.827813i	$-0.310415\pi$
$653$	7.34914e40	1.12201	0.561004	+	0.827813i	$0.310415\pi$
$654$	1.65279e40	0.246797
$655$	1.72243e41	2.51560
$656$	−4.43524e39	−0.0633595
$657$	7.42217e39	0.103713
$658$	−3.00207e40	−0.410342
$659$	6.24705e40	0.835289	0.417644	−	0.908611i	$-0.362856\pi$
$659$	6.24705e40	0.835289	0.417644	+	0.908611i	$0.362856\pi$
$660$	5.83423e40	0.763126
$661$	−8.78473e40	−1.12411	−0.562053	−	0.827101i	$-0.689988\pi$
$661$	−8.78473e40	−1.12411	−0.562053	+	0.827101i	$0.689988\pi$
$662$	−6.75652e40	−0.845828
$663$	−6.20760e40	−0.760287
$664$	−1.56561e41	−1.87605
$665$	−1.55895e40	−0.182775
$666$	3.84158e40	0.440690
$667$	5.90149e40	0.662426
$668$	7.37339e40	0.809857
$669$	3.46934e40	0.372880
$670$	−1.82241e41	−1.91673
$671$	1.79194e40	0.184437
$672$	−2.08684e40	−0.210201
$673$	1.11302e40	0.109720	0.0548599	−	0.998494i	$-0.482529\pi$
$673$	1.11302e40	0.109720	0.0548599	+	0.998494i	$0.482529\pi$
$674$	1.47408e41	1.42218
$675$	−1.66542e40	−0.157260
$676$	5.69403e39	0.0526251
$677$	4.44464e40	0.402069	0.201034	−	0.979584i	$-0.435570\pi$
$677$	4.44464e40	0.402069	0.201034	+	0.979584i	$0.435570\pi$
$678$	1.78379e41	1.57947
$679$	−7.77916e40	−0.674250
$680$	−2.13368e41	−1.81030
$681$	−5.47820e40	−0.454993
$682$	5.09836e39	0.0414531
$683$	4.93322e40	0.392672	0.196336	−	0.980537i	$-0.437096\pi$
$683$	4.93322e40	0.392672	0.196336	+	0.980537i	$0.437096\pi$
$684$	2.51334e40	0.195857
$685$	1.96439e41	1.49870
$686$	−1.17404e40	−0.0876965
$687$	−2.04942e40	−0.149885
$688$	7.19018e39	0.0514882
$689$	−6.57618e40	−0.461100
$690$	1.26024e41	0.865252
$691$	−2.13629e41	−1.43625	−0.718123	−	0.695916i	$-0.754999\pi$
$691$	−2.13629e41	−1.43625	−0.718123	+	0.695916i	$0.754999\pi$
$692$	−3.90167e41	−2.56869
$693$	1.16986e40	0.0754229
$694$	−2.68933e41	−1.69798
$695$	3.38349e41	2.09211
$696$	9.55906e40	0.578870
$697$	3.08945e41	1.83234
$698$	3.76069e41	2.18456
$699$	8.07952e40	0.459692
$700$	−9.07739e40	−0.505871
$701$	−2.00203e41	−1.09285	−0.546424	−	0.837508i	$-0.684011\pi$
$701$	−2.00203e41	−1.09285	−0.546424	+	0.837508i	$0.684011\pi$
$702$	5.93885e40	0.317552
$703$	5.57505e40	0.292009
$704$	1.87766e41	0.963415
$705$	−1.03501e41	−0.520236
$706$	−1.09309e41	−0.538257
$707$	5.55344e40	0.267905
$708$	−6.64229e40	−0.313932
$709$	1.78486e41	0.826484	0.413242	−	0.910621i	$-0.364396\pi$
$709$	1.78486e41	0.826484	0.413242	+	0.910621i	$0.364396\pi$
$710$	−9.48167e41	−4.30169
$711$	9.17001e40	0.407625
$712$	−5.57461e40	−0.242803
$713$	6.83803e39	0.0291832
$714$	−1.09854e41	−0.459400
$715$	2.00066e41	0.819853
$716$	3.43932e41	1.38113
$717$	2.16909e41	0.853591
$718$	−6.04513e41	−2.33131
$719$	−1.01535e41	−0.383748	−0.191874	−	0.981420i	$-0.561456\pi$
$719$	−1.01535e41	−0.383748	−0.191874	+	0.981420i	$0.561456\pi$
$720$	5.43717e39	0.0201396
$721$	9.18360e40	0.333389
$722$	−3.97733e41	−1.41515
$723$	−2.75754e41	−0.961650
$724$	2.64471e41	0.904000
$725$	−2.36026e41	−0.790787
$726$	1.83200e41	0.601651
$727$	2.76997e41	0.891714	0.445857	−	0.895104i	$-0.352899\pi$
$727$	2.76997e41	0.891714	0.445857	+	0.895104i	$0.352899\pi$
$728$	1.26068e41	0.397833
$729$	1.19725e40	0.0370370
$730$	2.24626e41	0.681207
$731$	−5.00845e41	−1.48902
$732$	9.99568e40	0.291341
$733$	6.55309e41	1.87257	0.936286	−	0.351238i	$-0.114239\pi$
$733$	6.55309e41	1.87257	0.936286	+	0.351238i	$0.114239\pi$
$734$	−8.01284e41	−2.24488
$735$	−4.04765e40	−0.111183
$736$	2.44822e41	0.659360
$737$	1.98467e41	0.524095
$738$	−2.95570e41	−0.765319
$739$	−1.86177e40	−0.0472697	−0.0236348	−	0.999721i	$-0.507524\pi$
$739$	−1.86177e40	−0.0472697	−0.0236348	+	0.999721i	$0.507524\pi$
$740$	7.21885e41	1.79725
$741$	8.61871e40	0.210416
$742$	−1.16376e41	−0.278617
$743$	−1.44243e41	−0.338656	−0.169328	−	0.985560i	$-0.554160\pi$
$743$	−1.44243e41	−0.338656	−0.169328	+	0.985560i	$0.554160\pi$
$744$	1.10760e40	0.0255021
$745$	1.15806e42	2.61496
$746$	−1.03870e42	−2.30027
$747$	−2.77901e41	−0.603588
$748$	5.96631e41	1.27096
$749$	1.06206e41	0.221902
$750$	1.12785e41	0.231134
$751$	2.58122e41	0.518855	0.259428	−	0.965763i	$-0.416466\pi$
$751$	2.58122e41	0.518855	0.259428	+	0.965763i	$0.416466\pi$
$752$	1.51950e40	0.0299601
$753$	1.42960e41	0.276496
$754$	8.41665e41	1.59682
$755$	−7.41956e41	−1.38085
$756$	6.52564e40	0.119140
$757$	−1.05631e42	−1.89191	−0.945957	−	0.324292i	$-0.894874\pi$
$757$	−1.05631e42	−1.89191	−0.945957	+	0.324292i	$0.894874\pi$
$758$	−1.23065e42	−2.16238
$759$	−1.37245e41	−0.236588
$760$	2.96242e41	0.501014
$761$	−1.36526e41	−0.226537	−0.113268	−	0.993564i	$-0.536132\pi$
$761$	−1.36526e41	−0.226537	−0.113268	+	0.993564i	$0.536132\pi$
$762$	3.07491e41	0.500593
$763$	6.22771e40	0.0994769
$764$	−2.90475e39	−0.00455255
$765$	−3.78735e41	−0.582432
$766$	−1.94402e42	−2.93349
$767$	−2.27776e41	−0.337268
$768$	4.25726e41	0.618575
$769$	9.74572e40	0.138957	0.0694787	−	0.997583i	$-0.477866\pi$
$769$	9.74572e40	0.138957	0.0694787	+	0.997583i	$0.477866\pi$
$770$	3.54050e41	0.495392
$771$	−3.82458e41	−0.525164
$772$	4.32316e41	0.582573
$773$	7.99226e41	1.05698	0.528490	−	0.848940i	$-0.322758\pi$
$773$	7.99226e41	1.05698	0.528490	+	0.848940i	$0.322758\pi$
$774$	4.79161e41	0.621925
$775$	−2.73482e40	−0.0348381
$776$	1.47825e42	1.84822
$777$	1.44751e41	0.177630
$778$	1.25261e42	1.50873
$779$	−4.28943e41	−0.507114
$780$	1.11599e42	1.29506
$781$	1.03259e42	1.17622
$782$	1.28878e42	1.44105
$783$	1.69677e41	0.186242
$784$	5.94241e39	0.00640294
$785$	1.70911e42	1.80784
$786$	−1.68517e42	−1.74991
$787$	5.36246e41	0.546676	0.273338	−	0.961918i	$-0.411872\pi$
$787$	5.36246e41	0.546676	0.273338	+	0.961918i	$0.411872\pi$
$788$	1.56080e42	1.56213
$789$	−6.27320e41	−0.616414
$790$	2.77523e42	2.67736
$791$	6.72131e41	0.636642
$792$	−2.22306e41	−0.206745
$793$	3.42770e41	0.312998
$794$	2.74728e42	2.46324
$795$	−4.01223e41	−0.353234
$796$	−2.19970e42	−1.90162
$797$	−1.83718e42	−1.55957	−0.779786	−	0.626046i	$-0.784672\pi$
$797$	−1.83718e42	−1.55957	−0.779786	+	0.626046i	$0.784672\pi$
$798$	1.52522e41	0.127143
$799$	−1.05844e42	−0.866437
$800$	−9.79150e41	−0.787126
$801$	−9.89512e40	−0.0781178
$802$	−2.63194e42	−2.04055
$803$	−2.44626e41	−0.186264
$804$	1.10707e42	0.827872
$805$	4.74860e41	0.348759
$806$	9.75233e40	0.0703478
$807$	−6.12229e41	−0.433758
$808$	−1.05530e42	−0.734367
$809$	2.46048e41	0.168177	0.0840885	−	0.996458i	$-0.473202\pi$
$809$	2.46048e41	0.168177	0.0840885	+	0.996458i	$0.473202\pi$
$810$	3.62339e41	0.243266
$811$	−9.21349e41	−0.607605	−0.303803	−	0.952735i	$-0.598256\pi$
$811$	−9.21349e41	−0.607605	−0.303803	+	0.952735i	$0.598256\pi$
$812$	9.24826e41	0.599097
$813$	−4.88588e41	−0.310906
$814$	−1.26614e42	−0.791458
$815$	−2.84837e42	−1.74909
$816$	5.56026e40	0.0335419
$817$	6.95379e41	0.412099
$818$	4.76883e41	0.277645
$819$	2.23776e41	0.127996
$820$	−5.55416e42	−3.12117
$821$	2.59098e41	0.143050	0.0715251	−	0.997439i	$-0.477213\pi$
$821$	2.59098e41	0.143050	0.0715251	+	0.997439i	$0.477213\pi$
$822$	−1.92189e42	−1.04253
$823$	−4.78816e41	−0.255194	−0.127597	−	0.991826i	$-0.540726\pi$
$823$	−4.78816e41	−0.255194	−0.127597	+	0.991826i	$0.540726\pi$
$824$	−1.74513e42	−0.913869
$825$	5.48904e41	0.282432
$826$	−4.03087e41	−0.203793
$827$	2.29219e42	1.13873	0.569366	−	0.822084i	$-0.307189\pi$
$827$	2.29219e42	1.13873	0.569366	+	0.822084i	$0.307189\pi$
$828$	−7.65571e41	−0.373719
$829$	−3.80834e40	−0.0182682	−0.00913409	−	0.999958i	$-0.502908\pi$
$829$	−3.80834e40	−0.0182682	−0.00913409	+	0.999958i	$0.502908\pi$
$830$	−8.41044e42	−3.96448
$831$	1.24861e41	0.0578379
$832$	3.59166e42	1.63496
$833$	−4.13929e41	−0.185171
$834$	−3.31029e42	−1.45532
$835$	1.54266e42	0.666524
$836$	−8.28370e41	−0.351749
$837$	1.96604e40	0.00820488
$838$	1.27771e42	0.524074
$839$	8.32992e41	0.335809	0.167905	−	0.985803i	$-0.446300\pi$
$839$	8.32992e41	0.335809	0.167905	+	0.985803i	$0.446300\pi$
$840$	7.69163e41	0.304768
$841$	−1.62996e41	−0.0634798
$842$	−1.94623e42	−0.745020
$843$	1.17381e42	0.441668
$844$	−2.84100e42	−1.05076
$845$	1.19130e41	0.0433112
$846$	1.01261e42	0.361888
$847$	6.90297e41	0.242508
$848$	5.89041e40	0.0203425
$849$	1.35635e42	0.460479
$850$	−5.15437e42	−1.72029
$851$	−1.69817e42	−0.557191
$852$	5.75991e42	1.85798
$853$	4.19029e42	1.32887	0.664437	−	0.747345i	$-0.268672\pi$
$853$	4.19029e42	1.32887	0.664437	+	0.747345i	$0.268672\pi$
$854$	6.06588e41	0.189127
$855$	5.25841e41	0.161193
$856$	−2.01820e42	−0.608267
$857$	3.67896e42	1.09019	0.545096	−	0.838374i	$-0.316493\pi$
$857$	3.67896e42	1.09019	0.545096	+	0.838374i	$0.316493\pi$
$858$	−1.95738e42	−0.570308
$859$	−5.80713e42	−1.66364	−0.831822	−	0.555042i	$-0.812702\pi$
$859$	−5.80713e42	−1.66364	−0.831822	+	0.555042i	$0.812702\pi$
$860$	9.00410e42	2.53637
$861$	−1.11371e42	−0.308478
$862$	−2.09451e42	−0.570464
$863$	5.44006e42	1.45696	0.728479	−	0.685068i	$-0.240227\pi$
$863$	5.44006e42	1.45696	0.728479	+	0.685068i	$0.240227\pi$
$864$	7.03900e41	0.185379
$865$	−8.16305e42	−2.11407
$866$	1.03135e43	2.62661
$867$	−1.56786e42	−0.392672
$868$	1.07159e41	0.0263933
$869$	−3.02233e42	−0.732075
$870$	5.13513e42	1.22327
$871$	3.79635e42	0.889412
$872$	−1.18343e42	−0.272681
$873$	2.62395e42	0.594633
$874$	−1.78935e42	−0.398823
$875$	4.24974e41	0.0931635
$876$	−1.36456e42	−0.294226
$877$	2.30331e42	0.488494	0.244247	−	0.969713i	$-0.421459\pi$
$877$	2.30331e42	0.488494	0.244247	+	0.969713i	$0.421459\pi$
$878$	6.84677e42	1.42829
$879$	−4.04618e42	−0.830246
$880$	−1.79203e41	−0.0361698
$881$	−5.51770e42	−1.09549	−0.547744	−	0.836646i	$-0.684513\pi$
$881$	−5.51770e42	−1.09549	−0.547744	+	0.836646i	$0.684513\pi$
$882$	3.96008e41	0.0773410
$883$	8.02607e42	1.54196	0.770979	−	0.636860i	$-0.219767\pi$
$883$	8.02607e42	1.54196	0.770979	+	0.636860i	$0.219767\pi$
$884$	1.14126e43	2.15688
$885$	−1.38970e42	−0.258370
$886$	−1.34513e43	−2.46023
$887$	−5.31205e42	−0.955806	−0.477903	−	0.878413i	$-0.658603\pi$
$887$	−5.31205e42	−0.955806	−0.477903	+	0.878413i	$0.658603\pi$
$888$	−2.75065e42	−0.486909
$889$	1.15863e42	0.201775
$890$	−2.99468e42	−0.513092
$891$	−3.94601e41	−0.0665168
$892$	−6.37834e42	−1.05783
$893$	1.46955e42	0.239793
$894$	−1.13301e43	−1.81903
$895$	7.19573e42	1.13669
$896$	4.01364e42	0.623838
$897$	−2.62528e42	−0.401500
$898$	1.34684e43	2.02680
$899$	2.78630e41	0.0412584
$900$	3.06185e42	0.446136
$901$	−4.10307e42	−0.588300
$902$	9.74164e42	1.37448
$903$	1.80548e42	0.250680
$904$	−1.27723e43	−1.74513
$905$	5.53325e42	0.744005
$906$	7.25905e42	0.960552
$907$	1.26266e43	1.64430	0.822149	−	0.569272i	$-0.192775\pi$
$907$	1.26266e43	1.64430	0.822149	+	0.569272i	$0.192775\pi$
$908$	1.00716e43	1.29078
$909$	−1.87320e42	−0.236270
$910$	6.77240e42	0.840703
$911$	−1.49765e43	−1.82976	−0.914882	−	0.403720i	$-0.867717\pi$
$911$	−1.49765e43	−1.82976	−0.914882	+	0.403720i	$0.867717\pi$
$912$	−7.71994e40	−0.00928300
$913$	9.15929e42	1.08402
$914$	1.19352e43	1.39030
$915$	2.09129e42	0.239778
$916$	3.76784e42	0.425214
$917$	−6.34970e42	−0.705339
$918$	3.70542e42	0.405153
$919$	1.52420e42	0.164046	0.0820230	−	0.996630i	$-0.473862\pi$
$919$	1.52420e42	0.164046	0.0820230	+	0.996630i	$0.473862\pi$
$920$	−9.02362e42	−0.955998
$921$	−4.01314e42	−0.418524
$922$	−6.80398e42	−0.698497
$923$	1.97518e43	1.99610
$924$	−2.15078e42	−0.213970
$925$	6.79174e42	0.665159
$926$	2.05067e42	0.197714
$927$	−3.09767e42	−0.294022
$928$	9.97580e42	0.932185
$929$	−9.80179e42	−0.901732	−0.450866	−	0.892592i	$-0.648885\pi$
$929$	−9.80179e42	−0.901732	−0.450866	+	0.892592i	$0.648885\pi$
$930$	5.95005e41	0.0538912
$931$	5.74704e41	0.0512476
$932$	−1.48541e43	−1.30411
$933$	−1.21816e43	−1.05298
$934$	−2.35488e43	−2.00419
$935$	1.24827e43	1.04602
$936$	−4.25235e42	−0.350856
$937$	6.83323e41	0.0555139	0.0277570	−	0.999615i	$-0.491164\pi$
$937$	6.83323e41	0.0555139	0.0277570	+	0.999615i	$0.491164\pi$
$938$	6.71827e42	0.537423
$939$	2.95122e42	0.232461
$940$	1.90284e43	1.47587
$941$	−7.97859e42	−0.609364	−0.304682	−	0.952454i	$-0.598550\pi$
$941$	−7.97859e42	−0.609364	−0.304682	+	0.952454i	$0.598550\pi$
$942$	−1.67214e43	−1.25758
$943$	1.30657e43	0.967638
$944$	2.04023e41	0.0148794
$945$	1.36529e42	0.0980538
$946$	−1.57926e43	−1.11695
$947$	−1.34448e43	−0.936439	−0.468219	−	0.883612i	$-0.655104\pi$
$947$	−1.34448e43	−0.936439	−0.468219	+	0.883612i	$0.655104\pi$
$948$	−1.68589e43	−1.15640
$949$	−4.67931e42	−0.316098
$950$	7.15639e42	0.476104
$951$	−9.13249e42	−0.598373
$952$	7.86577e42	0.507581
$953$	−2.50849e43	−1.59428	−0.797140	−	0.603794i	$-0.793655\pi$
$953$	−2.50849e43	−1.59428	−0.797140	+	0.603794i	$0.793655\pi$
$954$	3.92543e42	0.245717
$955$	−6.07731e40	−0.00374682
$956$	−3.98784e43	−2.42158
$957$	−5.59236e42	−0.334481
$958$	−4.02862e43	−2.37332
$959$	−7.24168e42	−0.420213
$960$	2.19133e43	1.25249
$961$	−1.77296e43	−0.998182
$962$	−2.42192e43	−1.34314
$963$	−3.58237e42	−0.195700
$964$	5.06970e43	2.72813
$965$	9.04489e42	0.479466
$966$	−4.64587e42	−0.242604
$967$	−1.01164e43	−0.520403	−0.260202	−	0.965554i	$-0.583789\pi$
$967$	−1.01164e43	−0.520403	−0.260202	+	0.965554i	$0.583789\pi$
$968$	−1.31175e43	−0.664751
$969$	5.37746e42	0.268462
$970$	7.94117e43	3.90566
$971$	1.70437e43	0.825819	0.412909	−	0.910772i	$-0.364513\pi$
$971$	1.70437e43	0.825819	0.412909	+	0.910772i	$0.364513\pi$
$972$	−2.20113e42	−0.105071
$973$	−1.24732e43	−0.586598
$974$	−4.20190e43	−1.94689
$975$	1.04996e43	0.479300
$976$	−3.07025e41	−0.0138087
$977$	−4.28138e42	−0.189720	−0.0948599	−	0.995491i	$-0.530240\pi$
$977$	−4.28138e42	−0.189720	−0.0948599	+	0.995491i	$0.530240\pi$
$978$	2.78675e43	1.21670
$979$	3.26132e42	0.140296
$980$	7.44154e42	0.315417
$981$	−2.10064e42	−0.0877304
$982$	−2.88751e43	−1.18825
$983$	−2.45500e43	−0.995463	−0.497732	−	0.867331i	$-0.665834\pi$
$983$	−2.45500e43	−0.995463	−0.497732	+	0.867331i	$0.665834\pi$
$984$	2.11634e43	0.845584
$985$	3.26549e43	1.28565
$986$	5.25139e43	2.03732
$987$	3.81553e42	0.145867
$988$	−1.58454e43	−0.596934
$989$	−2.11814e43	−0.786337
$990$	−1.19423e43	−0.436895
$991$	−2.21470e43	−0.798449	−0.399224	−	0.916853i	$-0.630721\pi$
$991$	−2.21470e43	−0.798449	−0.399224	+	0.916853i	$0.630721\pi$
$992$	1.15589e42	0.0410674
$993$	8.58730e42	0.300672
$994$	3.49540e43	1.20613
$995$	−4.60220e43	−1.56506
$996$	5.10916e43	1.71234
$997$	3.55798e43	1.17523	0.587616	−	0.809140i	$-0.300067\pi$
$997$	3.55798e43	1.17523	0.587616	+	0.809140i	$0.300067\pi$
$998$	5.78344e43	1.88275
$999$	−4.88250e42	−0.156655

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.b.1.7	✓	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q+37632.6 q^{2} -4.78297e6 q^{3} +8.79342e8 q^{4} +1.83976e10 q^{5} -1.79996e11 q^{6} -6.78223e11 q^{7} +1.28881e13 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q+37632.6 q^{2} -4.78297e6 q^{3} +8.79342e8 q^{4} +1.83976e10 q^{5} -1.79996e11 q^{6} -6.78223e11 q^{7} +1.28881e13 q^{8} +2.28768e13 q^{9} +6.92348e14 q^{10} -7.53994e14 q^{11} -4.20586e15 q^{12} -1.44227e16 q^{13} -2.55233e16 q^{14} -8.79950e16 q^{15} +1.29187e16 q^{16} -8.99872e17 q^{17} +8.60913e17 q^{18} +1.24939e18 q^{19} +1.61777e19 q^{20} +3.24392e18 q^{21} -2.83747e19 q^{22} -3.80568e19 q^{23} -6.16433e19 q^{24} +1.52206e20 q^{25} -5.42763e20 q^{26} -1.09419e20 q^{27} -5.96390e20 q^{28} -1.55071e21 q^{29} -3.31148e21 q^{30} -1.79680e20 q^{31} -6.43307e21 q^{32} +3.60633e21 q^{33} -3.38645e22 q^{34} -1.24776e22 q^{35} +2.01165e22 q^{36} +4.46221e22 q^{37} +4.70179e22 q^{38} +6.89832e22 q^{39} +2.37109e23 q^{40} -3.43321e23 q^{41} +1.22077e23 q^{42} +5.56573e23 q^{43} -6.63018e23 q^{44} +4.20877e23 q^{45} -1.43218e24 q^{46} +1.17621e24 q^{47} -6.17895e22 q^{48} +4.59987e23 q^{49} +5.72790e24 q^{50} +4.30406e24 q^{51} -1.26825e25 q^{52} +4.55961e24 q^{53} -4.11772e24 q^{54} -1.38716e25 q^{55} -8.74099e24 q^{56} -5.97581e24 q^{57} -5.83571e25 q^{58} +1.57929e25 q^{59} -7.73776e25 q^{60} -2.37660e25 q^{61} -6.76181e24 q^{62} -1.55156e25 q^{63} -2.49029e26 q^{64} -2.65342e26 q^{65} +1.35716e26 q^{66} -2.63221e26 q^{67} -7.91295e26 q^{68} +1.82025e26 q^{69} -4.69566e26 q^{70} -1.36949e27 q^{71} +2.94838e26 q^{72} +3.24441e26 q^{73} +1.67925e27 q^{74} -7.27995e26 q^{75} +1.09864e27 q^{76} +5.11376e26 q^{77} +2.59602e27 q^{78} +4.00843e27 q^{79} +2.37672e26 q^{80} +5.23348e26 q^{81} -1.29201e28 q^{82} -1.21477e28 q^{83} +2.85251e27 q^{84} -1.65554e28 q^{85} +2.09453e28 q^{86} +7.41698e27 q^{87} -9.71752e27 q^{88} -4.32540e27 q^{89} +1.58387e28 q^{90} +9.78179e27 q^{91} -3.34649e28 q^{92} +8.59402e26 q^{93} +4.42638e28 q^{94} +2.29858e28 q^{95} +3.07692e28 q^{96} +1.14699e29 q^{97} +1.73105e28 q^{98} -1.72490e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4177 q^{2} - 33480783 q^{3} + 1749008801 q^{4} - 1716792694 q^{5} - 19978461513 q^{6} - 4747561509943 q^{7} + 4282496015841 q^{8} + 160137547184727 q^{9}+O(q^{10}) \) 7 * q + 4177 * q^2 - 33480783 * q^3 + 1749008801 * q^4 - 1716792694 * q^5 - 19978461513 * q^6 - 4747561509943 * q^7 + 4282496015841 * q^8 + 160137547184727 * q^9	\( 7 q + 4177 q^{2} - 33480783 q^{3} + 1749008801 q^{4} - 1716792694 q^{5} - 19978461513 q^{6} - 4747561509943 q^{7} + 4282496015841 q^{8} + 160137547184727 q^{9} - 68989267066594 q^{10} + 2545492652300 q^{11} - 83\!\cdots\!69 q^{12}+ \cdots + 58\!\cdots\!00 q^{99}+O(q^{100}) \) 7 * q + 4177 * q^2 - 33480783 * q^3 + 1749008801 * q^4 - 1716792694 * q^5 - 19978461513 * q^6 - 4747561509943 * q^7 + 4282496015841 * q^8 + 160137547184727 * q^9 - 68989267066594 * q^10 + 2545492652300 * q^11 - 8365454875910169 * q^12 + 14913999229538746 * q^13 - 2832937775290273 * q^14 + 8211366234828486 * q^15 - 140832022360508287 * q^16 - 735563339328645834 * q^17 + 95556362084372097 * q^18 + 3231835378045104676 * q^19 + 24872044471029723934 * q^20 + 22707439527650560767 * q^21 - 17239876351747271380 * q^22 - 42184428229682843136 * q^23 - 20483045686391011929 * q^24 + 46804330940039088761 * q^25 - 675897714283725523994 * q^26 - 765932923920586514463 * q^27 - 1186218123454165144049 * q^28 - 2434304993428000346110 * q^29 + 329973525712240037586 * q^30 + 2199722846387345690880 * q^31 - 628893722935722970591 * q^32 - 12175012445678678700 * q^33 - 16286140216160397495774 * q^34 + 1164368416369392965206 * q^35 + 40011711342377185111761 * q^36 - 49022014961267638974534 * q^37 + 106333263742524376516156 * q^38 - 71333195980907706416874 * q^39 + 216038926502576778292062 * q^40 - 143191306451742660680690 * q^41 + 13549853558142341760537 * q^42 + 941039909393827256445716 * q^43 + 2764524465123176818801036 * q^44 - 39274710148831368854934 * q^45 + 3474443057659036283736168 * q^46 + 7006519280610369672608592 * q^47 + 673595197157617960964103 * q^48 + 3219905755813179726837607 * q^49 + 14679573416013792870926111 * q^50 + 3518176649545393836001146 * q^51 - 2546686232308412221676410 * q^52 - 10027193511015994202044662 * q^53 - 457043117602327124415993 * q^54 - 16298687268426081600331880 * q^55 - 2904487607327282801001009 * q^56 - 15457768426293016267063044 * q^57 - 48074139319095181887831538 * q^58 - 51309146879321339641894260 * q^59 - 118962217671556567654880046 * q^60 - 114001340360475297884404598 * q^61 - 123202320289320080578939968 * q^62 - 108608979330127274981177223 * q^63 - 502380072210108412189965887 * q^64 - 114667244579892903609270916 * q^65 + 82457794154240294845127220 * q^66 - 32181268110643474406964836 * q^67 + 390450998820575925888738594 * q^68 + 201766812505297918551350784 * q^69 + 46790112703505698996306306 * q^70 - 68692603646882069939817264 * q^71 + 97969772543591931935037201 * q^72 + 2610437603294481339652144758 * q^73 - 1970589544463881862899664826 * q^74 - 223863663951947820332111409 * q^75 - 495314146629295396545528580 * q^76 - 1726411848557457127402700 * q^77 + 3232797814589916385772058186 * q^78 + 11505613584082664484898031120 * q^79 + 242677199380181532889959454 * q^80 + 3663433431191523760494580647 * q^81 + 3166608206741095513542802234 * q^82 - 11108932922442693520275021468 * q^83 + 5673644511719444804866901481 * q^84 + 9256224639385320834953279412 * q^85 - 24087862070789790068131828852 * q^86 + 11643205320111329387433400590 * q^87 - 60048031588096637175274177716 * q^88 - 31316908572861218269624496914 * q^89 - 1578253144302347020332672834 * q^90 - 10115018385925386801026107354 * q^91 - 88556578633334432716269586104 * q^92 - 10521206182862436431762622720 * q^93 + 4915436657624620221918307680 * q^94 - 120026224917472203570811243048 * q^95 + 3007979181096151960924664679 * q^96 + 133134020386213024604639145390 * q^97 + 1921363763147378817000097777 * q^98 + 58232707102295304183060300 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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