LMFDB - Embedded newform 21.30.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$111.883889004$
Analytic rank:	$1$
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			1.6
Root			$-34621.1$ 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)

$f(q)$	$=$	$q+35218.1 q^{2} -4.78297e6 q^{3} +7.03444e8 q^{4} -9.52746e9 q^{5} -1.68447e11 q^{6} -6.78223e11 q^{7} +5.86640e12 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q+35218.1 q^{2} -4.78297e6 q^{3} +7.03444e8 q^{4} -9.52746e9 q^{5} -1.68447e11 q^{6} -6.78223e11 q^{7} +5.86640e12 q^{8} +2.28768e13 q^{9} -3.35539e14 q^{10} +1.40596e15 q^{11} -3.36455e15 q^{12} +9.14643e15 q^{13} -2.38857e16 q^{14} +4.55696e16 q^{15} -1.71055e17 q^{16} +5.42423e17 q^{17} +8.05677e17 q^{18} +3.51069e17 q^{19} -6.70204e18 q^{20} +3.24392e18 q^{21} +4.95151e19 q^{22} +5.57573e19 q^{23} -2.80588e19 q^{24} -9.54919e19 q^{25} +3.22120e20 q^{26} -1.09419e20 q^{27} -4.77092e20 q^{28} -7.67421e20 q^{29} +1.60487e21 q^{30} -6.48726e21 q^{31} -9.17374e21 q^{32} -6.72465e21 q^{33} +1.91031e22 q^{34} +6.46175e21 q^{35} +1.60925e22 q^{36} -1.03434e23 q^{37} +1.23640e22 q^{38} -4.37471e22 q^{39} -5.58919e22 q^{40} +2.60697e23 q^{41} +1.14245e23 q^{42} -7.85743e23 q^{43} +9.89012e23 q^{44} -2.17958e23 q^{45} +1.96367e24 q^{46} +1.77189e24 q^{47} +8.18152e23 q^{48} +4.59987e23 q^{49} -3.36305e24 q^{50} -2.59439e24 q^{51} +6.43400e24 q^{52} -8.34786e24 q^{53} -3.85353e24 q^{54} -1.33952e25 q^{55} -3.97873e24 q^{56} -1.67915e24 q^{57} -2.70271e25 q^{58} -3.56475e25 q^{59} +3.20556e25 q^{60} -1.05730e26 q^{61} -2.28469e26 q^{62} -1.55156e25 q^{63} -2.31247e26 q^{64} -8.71423e25 q^{65} -2.36829e26 q^{66} -7.05323e25 q^{67} +3.81564e26 q^{68} -2.66685e26 q^{69} +2.27570e26 q^{70} +2.69926e26 q^{71} +1.34204e26 q^{72} +5.56345e26 q^{73} -3.64274e27 q^{74} +4.56735e26 q^{75} +2.46958e26 q^{76} -9.53552e26 q^{77} -1.54069e27 q^{78} -7.90005e26 q^{79} +1.62972e27 q^{80} +5.23348e26 q^{81} +9.18126e27 q^{82} -1.26338e27 q^{83} +2.28192e27 q^{84} -5.16791e27 q^{85} -2.76724e28 q^{86} +3.67055e27 q^{87} +8.24790e27 q^{88} -2.81819e27 q^{89} -7.67606e27 q^{90} -6.20332e27 q^{91} +3.92221e28 q^{92} +3.10284e28 q^{93} +6.24027e28 q^{94} -3.34480e27 q^{95} +4.38777e28 q^{96} +4.86677e28 q^{97} +1.61999e28 q^{98} +3.21638e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	35218.1	1.51996	0.759978	−	0.649949i	$-0.225210\pi$
$2$	35218.1	1.51996	0.759978	+	0.649949i	$0.225210\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	7.03444e8	1.31027
$5$	−9.52746e9	−0.698091	−0.349046	−	0.937106i	$-0.613494\pi$
$5$	−9.52746e9	−0.698091	−0.349046	+	0.937106i	$0.613494\pi$
$6$	−1.68447e11	−0.877547
$7$	−6.78223e11	−0.377964
$7$	−6.78223e11	−0.377964
$8$	5.86640e12	0.471592
$9$	2.28768e13	0.333333
$10$	−3.35539e14	−1.06107
$11$	1.40596e15	1.11629	0.558146	−	0.829743i	$-0.311513\pi$
$11$	1.40596e15	1.11629	0.558146	+	0.829743i	$0.311513\pi$
$12$	−3.36455e15	−0.756483
$13$	9.14643e15	0.644277	0.322139	−	0.946692i	$-0.395598\pi$
$13$	9.14643e15	0.644277	0.322139	+	0.946692i	$0.395598\pi$
$14$	−2.38857e16	−0.574489
$15$	4.55696e16	0.403043
$16$	−1.71055e17	−0.593467
$17$	5.42423e17	0.781319	0.390659	−	0.920535i	$-0.372247\pi$
$17$	5.42423e17	0.781319	0.390659	+	0.920535i	$0.372247\pi$
$18$	8.05677e17	0.506652
$19$	3.51069e17	0.100801	0.0504006	−	0.998729i	$-0.483950\pi$
$19$	3.51069e17	0.100801	0.0504006	+	0.998729i	$0.483950\pi$
$20$	−6.70204e18	−0.914686
$21$	3.24392e18	0.218218
$22$	4.95151e19	1.69672
$23$	5.57573e19	1.00288	0.501439	−	0.865193i	$-0.332804\pi$
$23$	5.57573e19	1.00288	0.501439	+	0.865193i	$0.332804\pi$
$24$	−2.80588e19	−0.272274
$25$	−9.54919e19	−0.512668
$26$	3.22120e20	0.979273
$27$	−1.09419e20	−0.192450
$28$	−4.77092e20	−0.495234
$29$	−7.67421e20	−0.478920	−0.239460	−	0.970906i	$-0.576970\pi$
$29$	−7.67421e20	−0.478920	−0.239460	+	0.970906i	$0.576970\pi$
$30$	1.60487e21	0.612608
$31$	−6.48726e21	−1.53928	−0.769639	−	0.638480i	$-0.779564\pi$
$31$	−6.48726e21	−1.53928	−0.769639	+	0.638480i	$0.779564\pi$
$32$	−9.17374e21	−1.37364
$33$	−6.72465e21	−0.644492
$34$	1.91031e22	1.18757
$35$	6.46175e21	0.263854
$36$	1.60925e22	0.436756
$37$	−1.03434e23	−1.88685	−0.943424	−	0.331588i	$-0.892416\pi$
$37$	−1.03434e23	−1.88685	−0.943424	+	0.331588i	$0.892416\pi$
$38$	1.23640e22	0.153213
$39$	−4.37471e22	−0.371974
$40$	−5.58919e22	−0.329214
$41$	2.60697e23	1.07342	0.536711	−	0.843766i	$-0.319667\pi$
$41$	2.60697e23	1.07342	0.536711	+	0.843766i	$0.319667\pi$
$42$	1.14245e23	0.331682
$43$	−7.85743e23	−1.62176	−0.810882	−	0.585210i	$-0.801012\pi$
$43$	−7.85743e23	−1.62176	−0.810882	+	0.585210i	$0.801012\pi$
$44$	9.89012e23	1.46264
$45$	−2.17958e23	−0.232697
$46$	1.96367e24	1.52433
$47$	1.77189e24	1.00697	0.503487	−	0.864003i	$-0.332050\pi$
$47$	1.77189e24	1.00697	0.503487	+	0.864003i	$0.332050\pi$
$48$	8.18152e23	0.342639
$49$	4.59987e23	0.142857
$50$	−3.36305e24	−0.779234
$51$	−2.59439e24	−0.451095
$52$	6.43400e24	0.844175
$53$	−8.34786e24	−0.830951	−0.415475	−	0.909604i	$-0.636385\pi$
$53$	−8.34786e24	−0.830951	−0.415475	+	0.909604i	$0.636385\pi$
$54$	−3.85353e24	−0.292516
$55$	−1.33952e25	−0.779274
$56$	−3.97873e24	−0.178245
$57$	−1.67915e24	−0.0581976
$58$	−2.70271e25	−0.727937
$59$	−3.56475e25	−0.749333	−0.374666	−	0.927160i	$-0.622243\pi$
$59$	−3.56475e25	−0.749333	−0.374666	+	0.927160i	$0.622243\pi$
$60$	3.20556e25	0.528094
$61$	−1.05730e26	−1.37062	−0.685308	−	0.728254i	$-0.740332\pi$
$61$	−1.05730e26	−1.37062	−0.685308	+	0.728254i	$0.740332\pi$
$62$	−2.28469e26	−2.33963
$63$	−1.55156e25	−0.125988
$64$	−2.31247e26	−1.49440
$65$	−8.71423e25	−0.449764
$66$	−2.36829e26	−0.979599
$67$	−7.05323e25	−0.234587	−0.117293	−	0.993097i	$-0.537422\pi$
$67$	−7.05323e25	−0.234587	−0.117293	+	0.993097i	$0.537422\pi$
$68$	3.81564e26	1.02374
$69$	−2.66685e26	−0.579011
$70$	2.27570e26	0.401046
$71$	2.69926e26	0.387256	0.193628	−	0.981075i	$-0.437975\pi$
$71$	2.69926e26	0.387256	0.193628	+	0.981075i	$0.437975\pi$
$72$	1.34204e26	0.157197
$73$	5.56345e26	0.533535	0.266767	−	0.963761i	$-0.414044\pi$
$73$	5.56345e26	0.533535	0.266767	+	0.963761i	$0.414044\pi$
$74$	−3.64274e27	−2.86793
$75$	4.56735e26	0.295989
$76$	2.46958e26	0.132076
$77$	−9.53552e26	−0.421919
$78$	−1.54069e27	−0.565384
$79$	−7.90005e26	−0.241011	−0.120505	−	0.992713i	$-0.538452\pi$
$79$	−7.90005e26	−0.241011	−0.120505	+	0.992713i	$0.538452\pi$
$80$	1.62972e27	0.414295
$81$	5.23348e26	0.111111
$82$	9.18126e27	1.63155
$83$	−1.26338e27	−0.188322	−0.0941610	−	0.995557i	$-0.530017\pi$
$83$	−1.26338e27	−0.188322	−0.0941610	+	0.995557i	$0.530017\pi$
$84$	2.28192e27	0.285924
$85$	−5.16791e27	−0.545432
$86$	−2.76724e28	−2.46501
$87$	3.67055e27	0.276504
$88$	8.24790e27	0.526435
$89$	−2.81819e27	−0.152692	−0.0763459	−	0.997081i	$-0.524325\pi$
$89$	−2.81819e27	−0.152692	−0.0763459	+	0.997081i	$0.524325\pi$
$90$	−7.67606e27	−0.353689
$91$	−6.20332e27	−0.243514
$92$	3.92221e28	1.31404
$93$	3.10284e28	0.888702
$94$	6.24027e28	1.53056
$95$	−3.34480e27	−0.0703684
$96$	4.38777e28	0.793070
$97$	4.86677e28	0.756921	0.378460	−	0.925618i	$-0.376454\pi$
$97$	4.86677e28	0.756921	0.378460	+	0.925618i	$0.376454\pi$
$98$	1.61999e28	0.217137
$99$	3.21638e28	0.372097
$100$	−6.71732e28	−0.671732
$101$	−1.31729e29	−1.14030	−0.570152	−	0.821539i	$-0.693116\pi$
$101$	−1.31729e29	−1.14030	−0.570152	+	0.821539i	$0.693116\pi$
$102$	−9.13695e28	−0.685644
$103$	1.79620e29	1.17008	0.585040	−	0.811004i	$-0.301079\pi$
$103$	1.79620e29	1.17008	0.585040	+	0.811004i	$0.301079\pi$
$104$	5.36566e28	0.303836
$105$	−3.09063e28	−0.152336
$106$	−2.93996e29	−1.26301
$107$	−1.49212e29	−0.559422	−0.279711	−	0.960084i	$-0.590239\pi$
$107$	−1.49212e29	−0.559422	−0.279711	+	0.960084i	$0.590239\pi$
$108$	−7.69702e28	−0.252161
$109$	−3.21604e28	−0.0921802	−0.0460901	−	0.998937i	$-0.514676\pi$
$109$	−3.21604e28	−0.0921802	−0.0460901	+	0.998937i	$0.514676\pi$
$110$	−4.71754e29	−1.18446
$111$	4.94720e29	1.08937
$112$	1.16014e29	0.224310
$113$	−5.09186e29	−0.865444	−0.432722	−	0.901527i	$-0.642447\pi$
$113$	−5.09186e29	−0.865444	−0.432722	+	0.901527i	$0.642447\pi$
$114$	−5.91366e28	−0.0884578
$115$	−5.31225e29	−0.700100
$116$	−5.39838e29	−0.627513
$117$	2.09241e29	0.214759
$118$	−1.25544e30	−1.13895
$119$	−3.67883e29	−0.295311
$120$	2.67329e29	0.190072
$121$	3.90405e29	0.246109
$122$	−3.72361e30	−2.08327
$123$	−1.24691e30	−0.619740
$124$	−4.56343e30	−2.01686
$125$	2.68442e30	1.05598
$126$	−5.46429e29	−0.191496
$127$	−3.77807e30	−1.18064	−0.590318	−	0.807171i	$-0.700998\pi$
$127$	−3.77807e30	−1.18064	−0.590318	+	0.807171i	$0.700998\pi$
$128$	−3.21897e30	−0.897786
$129$	3.75818e30	0.936326
$130$	−3.06899e30	−0.683622
$131$	−1.66099e29	−0.0331080	−0.0165540	−	0.999863i	$-0.505270\pi$
$131$	−1.66099e29	−0.0331080	−0.0165540	+	0.999863i	$0.505270\pi$
$132$	−4.73041e30	−0.844456
$133$	−2.38103e29	−0.0380993
$134$	−2.48401e30	−0.356562
$135$	1.04249e30	0.134348
$136$	3.18207e30	0.368464
$137$	3.46199e30	0.360477	0.180238	−	0.983623i	$-0.442313\pi$
$137$	3.46199e30	0.360477	0.180238	+	0.983623i	$0.442313\pi$
$138$	−9.39215e30	−0.880072
$139$	−1.27240e31	−1.07376	−0.536882	−	0.843658i	$-0.680398\pi$
$139$	−1.27240e31	−1.07376	−0.536882	+	0.843658i	$0.680398\pi$
$140$	4.54548e30	0.345719
$141$	−8.47491e30	−0.581377
$142$	9.50627e30	0.588612
$143$	1.28595e31	0.719202
$144$	−3.91320e30	−0.197822
$145$	7.31158e30	0.334330
$146$	1.95934e31	0.810950
$147$	−2.20010e30	−0.0824786
$148$	−7.27598e31	−2.47228
$149$	−3.16853e31	−0.976465	−0.488233	−	0.872714i	$-0.662358\pi$
$149$	−3.16853e31	−0.976465	−0.488233	+	0.872714i	$0.662358\pi$
$150$	1.60853e31	0.449891
$151$	6.63074e31	1.68421	0.842105	−	0.539314i	$-0.181316\pi$
$151$	6.63074e31	1.68421	0.842105	+	0.539314i	$0.181316\pi$
$152$	2.05951e30	0.0475370
$153$	1.24089e31	0.260440
$154$	−3.35823e31	−0.641298
$155$	6.18072e31	1.07456
$156$	−3.07736e31	−0.487385
$157$	−5.62437e31	−0.811950	−0.405975	−	0.913884i	$-0.633068\pi$
$157$	−5.62437e31	−0.811950	−0.405975	+	0.913884i	$0.633068\pi$
$158$	−2.78225e31	−0.366326
$159$	3.99276e31	0.479750
$160$	8.74025e31	0.958924
$161$	−3.78159e31	−0.379052
$162$	1.84313e31	0.168884
$163$	−2.23486e32	−1.87297	−0.936484	−	0.350710i	$-0.885940\pi$
$163$	−2.23486e32	−1.87297	−0.936484	+	0.350710i	$0.885940\pi$
$164$	1.83386e32	1.40647
$165$	6.40688e31	0.449914
$166$	−4.44938e31	−0.286241
$167$	−1.73308e32	−1.02195	−0.510976	−	0.859595i	$-0.670716\pi$
$167$	−1.73308e32	−1.02195	−0.510976	+	0.859595i	$0.670716\pi$
$168$	1.90301e31	0.102910
$169$	−1.17881e32	−0.584907
$170$	−1.82004e32	−0.829033
$171$	8.03134e30	0.0336004
$172$	−5.52726e32	−2.12494
$173$	3.02860e31	0.107047	0.0535234	−	0.998567i	$-0.482955\pi$
$173$	3.02860e31	0.107047	0.0535234	+	0.998567i	$0.482955\pi$
$174$	1.29270e32	0.420275
$175$	6.47648e31	0.193770
$176$	−2.40496e32	−0.662483
$177$	1.70501e32	0.432627
$178$	−9.92515e31	−0.232085
$179$	3.40097e31	0.0733219	0.0366609	−	0.999328i	$-0.488328\pi$
$179$	3.40097e31	0.0733219	0.0366609	+	0.999328i	$0.488328\pi$
$180$	−1.53321e32	−0.304895
$181$	−2.70474e32	−0.496348	−0.248174	−	0.968716i	$-0.579830\pi$
$181$	−2.70474e32	−0.496348	−0.248174	+	0.968716i	$0.579830\pi$
$182$	−2.18469e32	−0.370131
$183$	5.05703e32	0.791325
$184$	3.27094e32	0.472949
$185$	9.85461e32	1.31719
$186$	1.09276e33	1.35079
$187$	7.62623e32	0.872180
$188$	1.24643e33	1.31941
$189$	7.42105e31	0.0727393
$190$	−1.17798e32	−0.106957
$191$	1.31512e33	1.10657	0.553287	−	0.832990i	$-0.313373\pi$
$191$	1.31512e33	1.10657	0.553287	+	0.832990i	$0.313373\pi$
$192$	1.10605e33	0.862792
$193$	8.63298e32	0.624568	0.312284	−	0.949989i	$-0.398906\pi$
$193$	8.63298e32	0.624568	0.312284	+	0.949989i	$0.398906\pi$
$194$	1.71398e33	1.15049
$195$	4.16799e32	0.259672
$196$	3.23575e32	0.187181
$197$	9.91129e32	0.532562	0.266281	−	0.963895i	$-0.414205\pi$
$197$	9.91129e32	0.532562	0.266281	+	0.963895i	$0.414205\pi$
$198$	1.13275e33	0.565572
$199$	2.95420e33	1.37110	0.685552	−	0.728023i	$-0.259561\pi$
$199$	2.95420e33	1.37110	0.685552	+	0.728023i	$0.259561\pi$
$200$	−5.60194e32	−0.241770
$201$	3.37354e32	0.135439
$202$	−4.63924e33	−1.73321
$203$	5.20483e32	0.181015
$204$	−1.82501e33	−0.591054
$205$	−2.48378e33	−0.749346
$206$	6.32589e33	1.77847
$207$	1.27555e33	0.334292
$208$	−1.56455e33	−0.382358
$209$	4.93588e32	0.112524
$210$	−1.08846e33	−0.231544
$211$	−7.01380e33	−1.39270	−0.696351	−	0.717702i	$-0.745194\pi$
$211$	−7.01380e33	−1.39270	−0.696351	+	0.717702i	$0.745194\pi$
$212$	−5.87226e33	−1.08877
$213$	−1.29105e33	−0.223582
$214$	−5.25497e33	−0.850297
$215$	7.48613e33	1.13214
$216$	−6.41895e32	−0.0907580
$217$	4.39981e33	0.581792
$218$	−1.13263e33	−0.140110
$219$	−2.66098e33	−0.308037
$220$	−9.42278e33	−1.02106
$221$	4.96123e33	0.503386
$222$	1.74231e34	1.65580
$223$	−1.76490e34	−1.57144	−0.785721	−	0.618581i	$-0.787708\pi$
$223$	−1.76490e34	−1.57144	−0.785721	+	0.618581i	$0.787708\pi$
$224$	6.22184e33	0.519186
$225$	−2.18455e33	−0.170889
$226$	−1.79326e34	−1.31544
$227$	5.63016e33	0.387387	0.193694	−	0.981062i	$-0.437953\pi$
$227$	5.63016e33	0.387387	0.193694	+	0.981062i	$0.437953\pi$
$228$	−1.18119e33	−0.0762544
$229$	4.94363e33	0.299524	0.149762	−	0.988722i	$-0.452149\pi$
$229$	4.94363e33	0.299524	0.149762	+	0.988722i	$0.452149\pi$
$230$	−1.87087e34	−1.06412
$231$	4.56081e33	0.243595
$232$	−4.50200e33	−0.225855
$233$	−2.83722e34	−1.33731	−0.668656	−	0.743572i	$-0.733130\pi$
$233$	−2.83722e34	−1.33731	−0.668656	+	0.743572i	$0.733130\pi$
$234$	7.36907e33	0.326424
$235$	−1.68816e34	−0.702960
$236$	−2.50760e34	−0.981826
$237$	3.77857e33	0.139148
$238$	−1.29562e34	−0.448860
$239$	4.60666e34	1.50181	0.750907	−	0.660408i	$-0.229617\pi$
$239$	4.60666e34	1.50181	0.750907	+	0.660408i	$0.229617\pi$
$240$	−7.79492e33	−0.239193
$241$	−4.58843e33	−0.132561	−0.0662807	−	0.997801i	$-0.521113\pi$
$241$	−4.58843e33	−0.132561	−0.0662807	+	0.997801i	$0.521113\pi$
$242$	1.37493e34	0.374075
$243$	−2.50316e33	−0.0641500
$244$	−7.43751e34	−1.79587
$245$	−4.38251e33	−0.0997273
$246$	−4.39137e34	−0.941978
$247$	3.21103e33	0.0649439
$248$	−3.80569e34	−0.725911
$249$	6.04270e33	0.108728
$250$	9.45404e34	1.60504
$251$	1.87596e34	0.300576	0.150288	−	0.988642i	$-0.451980\pi$
$251$	1.87596e34	0.300576	0.150288	+	0.988642i	$0.451980\pi$
$252$	−1.09143e34	−0.165078
$253$	7.83923e34	1.11950
$254$	−1.33056e35	−1.79452
$255$	2.47180e34	0.314905
$256$	1.07837e34	0.129804
$257$	3.57174e34	0.406302	0.203151	−	0.979147i	$-0.434882\pi$
$257$	3.57174e34	0.406302	0.203151	+	0.979147i	$0.434882\pi$
$258$	1.32356e35	1.42317
$259$	7.01511e34	0.713162
$260$	−6.12997e34	−0.589312
$261$	−1.75561e34	−0.159640
$262$	−5.84970e33	−0.0503228
$263$	−8.99634e34	−0.732331	−0.366166	−	0.930550i	$-0.619330\pi$
$263$	−8.99634e34	−0.732331	−0.366166	+	0.930550i	$0.619330\pi$
$264$	−3.94494e34	−0.303937
$265$	7.95340e34	0.580079
$266$	−8.38555e33	−0.0579092
$267$	1.34793e34	0.0881567
$268$	−4.96155e34	−0.307371
$269$	2.88176e35	1.69142	0.845708	−	0.533647i	$-0.179179\pi$
$269$	2.88176e35	1.69142	0.845708	+	0.533647i	$0.179179\pi$
$270$	3.67144e34	0.204203
$271$	2.13695e35	1.12652	0.563261	−	0.826279i	$-0.309547\pi$
$271$	2.13695e35	1.12652	0.563261	+	0.826279i	$0.309547\pi$
$272$	−9.27843e34	−0.463687
$273$	2.96703e34	0.140593
$274$	1.21925e35	0.547909
$275$	−1.34258e35	−0.572288
$276$	−1.87598e35	−0.758660
$277$	4.27508e35	1.64054	0.820272	−	0.571974i	$-0.193822\pi$
$277$	4.27508e35	1.64054	0.820272	+	0.571974i	$0.193822\pi$
$278$	−4.48115e35	−1.63207
$279$	−1.48408e35	−0.513092
$280$	3.79072e34	0.124431
$281$	−3.27068e35	−1.01952	−0.509760	−	0.860317i	$-0.670266\pi$
$281$	−3.27068e35	−1.01952	−0.509760	+	0.860317i	$0.670266\pi$
$282$	−2.98470e35	−0.883668
$283$	−8.78173e34	−0.246988	−0.123494	−	0.992345i	$-0.539410\pi$
$283$	−8.78173e34	−0.246988	−0.123494	+	0.992345i	$0.539410\pi$
$284$	1.89878e35	0.507409
$285$	1.59981e34	0.0406272
$286$	4.52887e35	1.09316
$287$	−1.76811e35	−0.405715
$288$	−2.09866e35	−0.457879
$289$	−1.87746e35	−0.389541
$290$	2.57500e35	0.508167
$291$	−2.32776e35	−0.437008
$292$	3.91358e35	0.699073
$293$	4.02265e35	0.683805	0.341902	−	0.939735i	$-0.388929\pi$
$293$	4.02265e35	0.683805	0.341902	+	0.939735i	$0.388929\pi$
$294$	−7.74834e34	−0.125364
$295$	3.39630e35	0.523103
$296$	−6.06783e35	−0.889823
$297$	−1.53838e35	−0.214831
$298$	−1.11590e36	−1.48418
$299$	5.09980e35	0.646131
$300$	3.21288e35	0.387825
$301$	5.32909e35	0.612969
$302$	2.33522e36	2.55993
$303$	6.30055e35	0.658355
$304$	−6.00523e34	−0.0598222
$305$	1.00734e36	0.956815
$306$	4.37018e35	0.395857
$307$	1.65193e36	1.42720	0.713600	−	0.700553i	$-0.247063\pi$
$307$	1.65193e36	1.42720	0.713600	+	0.700553i	$0.247063\pi$
$308$	−6.70771e35	−0.552826
$309$	−8.59118e35	−0.675546
$310$	2.17673e36	1.63328
$311$	−2.53390e36	−1.81453	−0.907266	−	0.420558i	$-0.861834\pi$
$311$	−2.53390e36	−1.81453	−0.907266	+	0.420558i	$0.861834\pi$
$312$	−2.56638e35	−0.175420
$313$	1.31310e36	0.856850	0.428425	−	0.903577i	$-0.359069\pi$
$313$	1.31310e36	0.856850	0.428425	+	0.903577i	$0.359069\pi$
$314$	−1.98080e36	−1.23413
$315$	1.47824e35	0.0879512
$316$	−5.55724e35	−0.315789
$317$	1.30233e36	0.706906	0.353453	−	0.935452i	$-0.385007\pi$
$317$	1.30233e36	0.706906	0.353453	+	0.935452i	$0.385007\pi$
$318$	1.40617e36	0.729198
$319$	−1.07896e36	−0.534614
$320$	2.20320e36	1.04323
$321$	7.13677e35	0.322983
$322$	−1.33180e36	−0.576142
$323$	1.90428e35	0.0787579
$324$	3.68146e35	0.145585
$325$	−8.73410e35	−0.330301
$326$	−7.87076e36	−2.84683
$327$	1.53822e35	0.0532203
$328$	1.52935e36	0.506217
$329$	−1.20174e36	−0.380601
$330$	2.25638e36	0.683850
$331$	3.86912e36	1.12229	0.561147	−	0.827716i	$-0.310360\pi$
$331$	3.86912e36	1.12229	0.561147	+	0.827716i	$0.310360\pi$
$332$	−8.88716e35	−0.246752
$333$	−2.36623e36	−0.628950
$334$	−6.10359e36	−1.55332
$335$	6.71994e35	0.163763
$336$	−5.54890e35	−0.129505
$337$	3.81120e36	0.851977	0.425989	−	0.904728i	$-0.359926\pi$
$337$	3.81120e36	0.851977	0.425989	+	0.904728i	$0.359926\pi$
$338$	−4.15155e36	−0.889033
$339$	2.43542e36	0.499664
$340$	−3.63534e36	−0.714662
$341$	−9.12081e36	−1.71828
$342$	2.82849e35	0.0510711
$343$	−3.11973e35	−0.0539949
$344$	−4.60948e36	−0.764811
$345$	2.54083e36	0.404203
$346$	1.06662e36	0.162706
$347$	−8.02581e36	−1.17412	−0.587059	−	0.809544i	$-0.699714\pi$
$347$	−8.02581e36	−1.17412	−0.587059	+	0.809544i	$0.699714\pi$
$348$	2.58203e36	0.362295
$349$	−8.17829e36	−1.10076	−0.550382	−	0.834913i	$-0.685518\pi$
$349$	−8.17829e36	−1.10076	−0.550382	+	0.834913i	$0.685518\pi$
$350$	2.28089e36	0.294523
$351$	−1.00079e36	−0.123991
$352$	−1.28979e37	−1.53338
$353$	−2.40188e36	−0.274043	−0.137022	−	0.990568i	$-0.543753\pi$
$353$	−2.40188e36	−0.274043	−0.137022	+	0.990568i	$0.543753\pi$
$354$	6.00472e36	0.657575
$355$	−2.57171e36	−0.270340
$356$	−1.98244e36	−0.200067
$357$	1.75958e36	0.170498
$358$	1.19776e36	0.111446
$359$	1.65890e37	1.48235	0.741174	−	0.671313i	$-0.234269\pi$
$359$	1.65890e37	1.48235	0.741174	+	0.671313i	$0.234269\pi$
$360$	−1.27863e36	−0.109738
$361$	−1.20066e37	−0.989839
$362$	−9.52558e36	−0.754427
$363$	−1.86729e36	−0.142091
$364$	−4.36369e36	−0.319068
$365$	−5.30056e36	−0.372456
$366$	1.78099e37	1.20278
$367$	−2.09669e37	−1.36106	−0.680528	−	0.732722i	$-0.738249\pi$
$367$	−2.09669e37	−1.36106	−0.680528	+	0.732722i	$0.738249\pi$
$368$	−9.53758e36	−0.595175
$369$	5.96391e36	0.357807
$370$	3.47061e37	2.00208
$371$	5.66171e36	0.314070
$372$	2.18267e37	1.16444
$373$	−3.16876e37	−1.62596	−0.812982	−	0.582289i	$-0.802157\pi$
$373$	−3.16876e37	−1.62596	−0.812982	+	0.582289i	$0.802157\pi$
$374$	2.68581e37	1.32568
$375$	−1.28395e37	−0.609671
$376$	1.03946e37	0.474881
$377$	−7.01916e36	−0.308557
$378$	2.61355e36	0.110561
$379$	1.31244e37	0.534331	0.267165	−	0.963651i	$-0.413913\pi$
$379$	1.31244e37	0.534331	0.267165	+	0.963651i	$0.413913\pi$
$380$	−2.35288e36	−0.0922014
$381$	1.80704e37	0.681641
$382$	4.63160e37	1.68195
$383$	4.64213e37	1.62306	0.811531	−	0.584310i	$-0.198635\pi$
$383$	4.64213e37	1.62306	0.811531	+	0.584310i	$0.198635\pi$
$384$	1.53963e37	0.518337
$385$	9.08494e36	0.294538
$386$	3.04037e37	0.949316
$387$	−1.79753e37	−0.540588
$388$	3.42350e37	0.991768
$389$	−3.91096e37	−1.09147	−0.545737	−	0.837956i	$-0.683750\pi$
$389$	−3.91096e37	−1.09147	−0.545737	+	0.837956i	$0.683750\pi$
$390$	1.46789e37	0.394690
$391$	3.02440e37	0.783567
$392$	2.69846e36	0.0673703
$393$	7.94447e35	0.0191149
$394$	3.49057e37	0.809471
$395$	7.52674e36	0.168248
$396$	2.26254e37	0.487547
$397$	−6.60963e37	−1.37314	−0.686570	−	0.727064i	$-0.740884\pi$
$397$	−6.60963e37	−1.37314	−0.686570	+	0.727064i	$0.740884\pi$
$398$	1.04041e38	2.08402
$399$	1.13884e36	0.0219966
$400$	1.63344e37	0.304252
$401$	−7.86350e37	−1.41261	−0.706305	−	0.707907i	$-0.749639\pi$
$401$	−7.86350e37	−1.41261	−0.706305	+	0.707907i	$0.749639\pi$
$402$	1.18810e37	0.205861
$403$	−5.93353e37	−0.991722
$404$	−9.26639e37	−1.49410
$405$	−4.98618e36	−0.0775657
$406$	1.83304e37	0.275134
$407$	−1.45423e38	−2.10627
$408$	−1.52197e37	−0.212733
$409$	5.67006e37	0.764891	0.382446	−	0.923978i	$-0.375082\pi$
$409$	5.67006e37	0.764891	0.382446	+	0.923978i	$0.375082\pi$
$410$	−8.74741e37	−1.13897
$411$	−1.65586e37	−0.208121
$412$	1.26353e38	1.53312
$413$	2.41769e37	0.283221
$414$	4.49224e37	0.508110
$415$	1.20368e37	0.131466
$416$	−8.39070e37	−0.885003
$417$	6.08584e37	0.619937
$418$	1.73832e37	0.171031
$419$	−1.38394e38	−1.31527	−0.657633	−	0.753338i	$-0.728442\pi$
$419$	−1.38394e38	−1.31527	−0.657633	+	0.753338i	$0.728442\pi$
$420$	−2.17409e37	−0.199601
$421$	1.27597e38	1.13175	0.565875	−	0.824491i	$-0.308538\pi$
$421$	1.27597e38	1.13175	0.565875	+	0.824491i	$0.308538\pi$
$422$	−2.47013e38	−2.11684
$423$	4.05352e37	0.335658
$424$	−4.89719e37	−0.391870
$425$	−5.17970e37	−0.400558
$426$	−4.54682e37	−0.339835
$427$	7.17085e37	0.518044
$428$	−1.04962e38	−0.732992
$429$	−6.15065e37	−0.415231
$430$	2.63647e38	1.72080
$431$	−1.13614e38	−0.716985	−0.358492	−	0.933533i	$-0.616709\pi$
$431$	−1.13614e38	−0.716985	−0.358492	+	0.933533i	$0.616709\pi$
$432$	1.87167e37	0.114213
$433$	−8.21721e37	−0.484897	−0.242449	−	0.970164i	$-0.577951\pi$
$433$	−8.21721e37	−0.484897	−0.242449	+	0.970164i	$0.577951\pi$
$434$	1.54953e38	0.884299
$435$	−3.49710e37	−0.193025
$436$	−2.26231e37	−0.120781
$437$	1.95747e37	0.101091
$438$	−9.37148e37	−0.468202
$439$	7.47138e37	0.361131	0.180566	−	0.983563i	$-0.442207\pi$
$439$	7.47138e37	0.361131	0.180566	+	0.983563i	$0.442207\pi$
$440$	−7.85816e37	−0.367500
$441$	1.05230e37	0.0476190
$442$	1.74725e38	0.765125
$443$	−1.21667e38	−0.515607	−0.257803	−	0.966197i	$-0.582999\pi$
$443$	−1.21667e38	−0.515607	−0.257803	+	0.966197i	$0.582999\pi$
$444$	3.48008e38	1.42737
$445$	2.68502e37	0.106593
$446$	−6.21563e38	−2.38852
$447$	1.51550e38	0.563762
$448$	1.56837e38	0.564830
$449$	4.16639e38	1.45274	0.726370	−	0.687304i	$-0.241206\pi$
$449$	4.16639e38	1.45274	0.726370	+	0.687304i	$0.241206\pi$
$450$	−7.69357e37	−0.259745
$451$	3.66529e38	1.19825
$452$	−3.58184e38	−1.13396
$453$	−3.17146e38	−0.972379
$454$	1.98283e38	0.588812
$455$	5.91019e37	0.169995
$456$	−9.85058e36	−0.0274455
$457$	−1.07806e38	−0.290976	−0.145488	−	0.989360i	$-0.546475\pi$
$457$	−1.07806e38	−0.290976	−0.145488	+	0.989360i	$0.546475\pi$
$458$	1.74105e38	0.455263
$459$	−5.93513e37	−0.150365
$460$	−3.73687e38	−0.917318
$461$	1.31971e38	0.313918	0.156959	−	0.987605i	$-0.449831\pi$
$461$	1.31971e38	0.313918	0.156959	+	0.987605i	$0.449831\pi$
$462$	1.60623e38	0.370254
$463$	−4.62903e37	−0.103411	−0.0517054	−	0.998662i	$-0.516466\pi$
$463$	−4.62903e37	−0.103411	−0.0517054	+	0.998662i	$0.516466\pi$
$464$	1.31271e38	0.284223
$465$	−2.95622e38	−0.620395
$466$	−9.99217e38	−2.03266
$467$	4.84226e38	0.954889	0.477445	−	0.878662i	$-0.341563\pi$
$467$	4.84226e38	0.954889	0.477445	+	0.878662i	$0.341563\pi$
$468$	1.47189e38	0.281392
$469$	4.78366e37	0.0886655
$470$	−5.94540e38	−1.06847
$471$	2.69012e38	0.468779
$472$	−2.09122e38	−0.353379
$473$	−1.10472e39	−1.81036
$474$	1.33074e38	0.211498
$475$	−3.35243e37	−0.0516776
$476$	−2.58786e38	−0.386936
$477$	−1.90972e38	−0.276984
$478$	1.62238e39	2.28269
$479$	9.77903e38	1.33484	0.667422	−	0.744679i	$-0.267398\pi$
$479$	9.77903e38	1.33484	0.667422	+	0.744679i	$0.267398\pi$
$480$	−4.18044e38	−0.553635
$481$	−9.46049e38	−1.21565
$482$	−1.61596e38	−0.201487
$483$	1.80872e38	0.218846
$484$	2.74628e38	0.322468
$485$	−4.63679e38	−0.528400
$486$	−8.81564e37	−0.0975052
$487$	−1.65521e39	−1.77699	−0.888494	−	0.458889i	$-0.848247\pi$
$487$	−1.65521e39	−1.77699	−0.888494	+	0.458889i	$0.848247\pi$
$488$	−6.20254e38	−0.646371
$489$	1.06893e39	1.08136
$490$	−1.54344e38	−0.151581
$491$	1.10516e39	1.05376	0.526882	−	0.849938i	$-0.323361\pi$
$491$	1.10516e39	1.05376	0.526882	+	0.849938i	$0.323361\pi$
$492$	−8.77129e38	−0.812025
$493$	−4.16266e38	−0.374189
$494$	1.13086e38	0.0987119
$495$	−3.06439e38	−0.259758
$496$	1.10968e39	0.913511
$497$	−1.83070e38	−0.146369
$498$	2.12812e38	0.165261
$499$	−1.86431e38	−0.140624	−0.0703122	−	0.997525i	$-0.522400\pi$
$499$	−1.86431e38	−0.140624	−0.0703122	+	0.997525i	$0.522400\pi$
$500$	1.88834e39	1.38362
$501$	8.28928e38	0.590024
$502$	6.60677e38	0.456862
$503$	2.65419e39	1.78319	0.891593	−	0.452837i	$-0.149588\pi$
$503$	2.65419e39	1.78319	0.891593	+	0.452837i	$0.149588\pi$
$504$	−9.10205e37	−0.0594150
$505$	1.25504e39	0.796037
$506$	2.76083e39	1.70160
$507$	5.63821e38	0.337696
$508$	−2.65766e39	−1.54695
$509$	−2.39712e39	−1.35607	−0.678035	−	0.735030i	$-0.737168\pi$
$509$	−2.39712e39	−1.35607	−0.678035	+	0.735030i	$0.737168\pi$
$510$	8.70520e38	0.478642
$511$	−3.77326e38	−0.201657
$512$	2.10796e39	1.09508
$513$	−3.84136e37	−0.0193992
$514$	1.25790e39	0.617562
$515$	−1.71133e39	−0.816823
$516$	2.64367e39	1.22684
$517$	2.49120e39	1.12408
$518$	2.47059e39	1.08397
$519$	−1.44857e38	−0.0618035
$520$	−5.11211e38	−0.212105
$521$	−3.91627e39	−1.58025	−0.790125	−	0.612946i	$-0.789984\pi$
$521$	−3.91627e39	−1.58025	−0.790125	+	0.612946i	$0.789984\pi$
$522$	−6.18294e38	−0.242646
$523$	−5.19145e39	−1.98159	−0.990795	−	0.135367i	$-0.956779\pi$
$523$	−5.19145e39	−1.98159	−0.990795	+	0.135367i	$0.956779\pi$
$524$	−1.16841e38	−0.0433804
$525$	−3.09768e38	−0.111873
$526$	−3.16834e39	−1.11311
$527$	−3.51884e39	−1.20267
$528$	1.15029e39	0.382485
$529$	1.78132e37	0.00576282
$530$	2.80104e39	0.881695
$531$	−8.15500e38	−0.249778
$532$	−1.67492e38	−0.0499202
$533$	2.38445e39	0.691581
$534$	4.74717e38	0.133994
$535$	1.42161e39	0.390528
$536$	−4.13771e38	−0.110629
$537$	−1.62667e38	−0.0423324
$538$	1.01490e40	2.57088
$539$	6.46721e38	0.159470
$540$	7.33330e38	0.176031
$541$	2.30314e39	0.538219	0.269110	−	0.963110i	$-0.413271\pi$
$541$	2.30314e39	0.538219	0.269110	+	0.963110i	$0.413271\pi$
$542$	7.52593e39	1.71226
$543$	1.29367e39	0.286566
$544$	−4.97605e39	−1.07325
$545$	3.06408e38	0.0643502
$546$	1.04493e39	0.213695
$547$	−3.08885e39	−0.615150	−0.307575	−	0.951524i	$-0.599517\pi$
$547$	−3.08885e39	−0.615150	−0.307575	+	0.951524i	$0.599517\pi$
$548$	2.43531e39	0.472320
$549$	−2.41876e39	−0.456872
$550$	−4.72830e39	−0.869853
$551$	−2.69418e38	−0.0482757
$552$	−1.56448e39	−0.273057
$553$	5.35799e38	0.0910936
$554$	1.50560e40	2.49355
$555$	−4.71343e39	−0.760482
$556$	−8.95061e39	−1.40692
$557$	−1.61527e39	−0.247368	−0.123684	−	0.992322i	$-0.539471\pi$
$557$	−1.61527e39	−0.247368	−0.123684	+	0.992322i	$0.539471\pi$
$558$	−5.22664e39	−0.779878
$559$	−7.18674e39	−1.04487
$560$	−1.10532e39	−0.156589
$561$	−3.64760e39	−0.503554
$562$	−1.15187e40	−1.54963
$563$	−5.45333e39	−0.714974	−0.357487	−	0.933918i	$-0.616366\pi$
$563$	−5.45333e39	−0.714974	−0.357487	+	0.933918i	$0.616366\pi$
$564$	−5.96163e39	−0.761759
$565$	4.85125e39	0.604159
$566$	−3.09276e39	−0.375412
$567$	−3.54946e38	−0.0419961
$568$	1.58349e39	0.182627
$569$	−7.69438e39	−0.865059	−0.432530	−	0.901620i	$-0.642379\pi$
$569$	−7.69438e39	−0.865059	−0.432530	+	0.901620i	$0.642379\pi$
$570$	5.63422e38	0.0617516
$571$	−6.22587e39	−0.665237	−0.332619	−	0.943061i	$-0.607932\pi$
$571$	−6.22587e39	−0.665237	−0.332619	+	0.943061i	$0.607932\pi$
$572$	9.04593e39	0.942347
$573$	−6.29017e39	−0.638881
$574$	−6.22694e39	−0.616669
$575$	−5.32437e39	−0.514144
$576$	−5.29020e39	−0.498133
$577$	−5.53754e39	−0.508472	−0.254236	−	0.967142i	$-0.581824\pi$
$577$	−5.53754e39	−0.508472	−0.254236	+	0.967142i	$0.581824\pi$
$578$	−6.61207e39	−0.592085
$579$	−4.12913e39	−0.360595
$580$	5.14329e39	0.438061
$581$	8.56852e38	0.0711790
$582$	−8.19793e39	−0.664234
$583$	−1.17367e40	−0.927584
$584$	3.26374e39	0.251611
$585$	−1.99354e39	−0.149921
$586$	1.41670e40	1.03935
$587$	−1.68271e40	−1.20436	−0.602182	−	0.798359i	$-0.705702\pi$
$587$	−1.68271e40	−1.20436	−0.602182	+	0.798359i	$0.705702\pi$
$588$	−1.54765e39	−0.108069
$589$	−2.27748e39	−0.155161
$590$	1.19611e40	0.795093
$591$	−4.74054e39	−0.307475
$592$	1.76929e40	1.11978
$593$	2.17451e40	1.34298	0.671488	−	0.741016i	$-0.265656\pi$
$593$	2.17451e40	1.34298	0.671488	+	0.741016i	$0.265656\pi$
$594$	−5.41790e39	−0.326533
$595$	3.50500e39	0.206154
$596$	−2.22888e40	−1.27943
$597$	−1.41299e40	−0.791608
$598$	1.79605e40	0.982091
$599$	−1.07598e40	−0.574270	−0.287135	−	0.957890i	$-0.592703\pi$
$599$	−1.07598e40	−0.574270	−0.287135	+	0.957890i	$0.592703\pi$
$600$	2.67939e39	0.139586
$601$	2.37902e40	1.20982	0.604908	−	0.796296i	$-0.293210\pi$
$601$	2.37902e40	1.20982	0.604908	+	0.796296i	$0.293210\pi$
$602$	1.87680e40	0.931686
$603$	−1.61355e39	−0.0781956
$604$	4.66435e40	2.20676
$605$	−3.71957e39	−0.171807
$606$	2.21893e40	1.00067
$607$	9.97848e39	0.439368	0.219684	−	0.975571i	$-0.429497\pi$
$607$	9.97848e39	0.439368	0.219684	+	0.975571i	$0.429497\pi$
$608$	−3.22062e39	−0.138464
$609$	−2.48945e39	−0.104509
$610$	3.54766e40	1.45432
$611$	1.62065e40	0.648771
$612$	8.72896e39	0.341245
$613$	3.32472e40	1.26934	0.634670	−	0.772783i	$-0.281136\pi$
$613$	3.32472e40	1.26934	0.634670	+	0.772783i	$0.281136\pi$
$614$	5.81778e40	2.16928
$615$	1.18799e40	0.432635
$616$	−5.59392e39	−0.198974
$617$	−7.28536e39	−0.253114	−0.126557	−	0.991959i	$-0.540393\pi$
$617$	−7.28536e39	−0.253114	−0.126557	+	0.991959i	$0.540393\pi$
$618$	−3.02565e40	−1.02680
$619$	−3.81926e40	−1.26609	−0.633046	−	0.774115i	$-0.718195\pi$
$619$	−3.81926e40	−1.26609	−0.633046	+	0.774115i	$0.718195\pi$
$620$	4.34779e40	1.40796
$621$	−6.10090e39	−0.193004
$622$	−8.92393e40	−2.75801
$623$	1.91136e39	0.0577121
$624$	7.48317e39	0.220754
$625$	−7.78900e39	−0.224503
$626$	4.62449e40	1.30237
$627$	−2.36082e39	−0.0649655
$628$	−3.95643e40	−1.06387
$629$	−5.61048e40	−1.47423
$630$	5.20608e39	0.133682
$631$	−2.23810e40	−0.561633	−0.280817	−	0.959761i	$-0.590605\pi$
$631$	−2.23810e40	−0.561633	−0.280817	+	0.959761i	$0.590605\pi$
$632$	−4.63448e39	−0.113659
$633$	3.35468e40	0.804076
$634$	4.58656e40	1.07447
$635$	3.59954e40	0.824192
$636$	2.80868e40	0.628600
$637$	4.20723e39	0.0920396
$638$	−3.79990e40	−0.812591
$639$	6.17503e39	0.129085
$640$	3.06687e40	0.626737
$641$	3.31186e39	0.0661653	0.0330827	−	0.999453i	$-0.489468\pi$
$641$	3.31186e39	0.0661653	0.0330827	+	0.999453i	$0.489468\pi$
$642$	2.51344e40	0.490919
$643$	1.00244e41	1.91425	0.957126	−	0.289671i	$-0.0935458\pi$
$643$	1.00244e41	1.91425	0.957126	+	0.289671i	$0.0935458\pi$
$644$	−2.66013e40	−0.496659
$645$	−3.58059e40	−0.653641
$646$	6.70651e39	0.119709
$647$	−8.92540e40	−1.55781	−0.778907	−	0.627140i	$-0.784226\pi$
$647$	−8.92540e40	−1.55781	−0.778907	+	0.627140i	$0.784226\pi$
$648$	3.07016e39	0.0523991
$649$	−5.01188e40	−0.836474
$650$	−3.07598e40	−0.502043
$651$	−2.10442e40	−0.335898
$652$	−1.57210e41	−2.45409
$653$	8.37916e40	1.27926	0.639631	−	0.768682i	$-0.279087\pi$
$653$	8.37916e40	1.27926	0.639631	+	0.768682i	$0.279087\pi$
$654$	5.41733e39	0.0808925
$655$	1.58250e39	0.0231124
$656$	−4.45936e40	−0.637041
$657$	1.27274e40	0.177845
$658$	−4.23230e40	−0.578496
$659$	2.89809e40	0.387501	0.193751	−	0.981051i	$-0.437935\pi$
$659$	2.89809e40	0.387501	0.193751	+	0.981051i	$0.437935\pi$
$660$	4.50689e40	0.589508
$661$	−1.08221e40	−0.138481	−0.0692403	−	0.997600i	$-0.522058\pi$
$661$	−1.08221e40	−0.138481	−0.0692403	+	0.997600i	$0.522058\pi$
$662$	1.36263e41	1.70584
$663$	−2.37294e40	−0.290630
$664$	−7.41148e39	−0.0888112
$665$	2.26852e39	0.0265968
$666$	−8.33342e40	−0.955976
$667$	−4.27893e40	−0.480298
$668$	−1.21913e41	−1.33903
$669$	8.44144e40	0.907273
$670$	2.36664e40	0.248913
$671$	−1.48652e41	−1.53001
$672$	−2.97589e40	−0.299752
$673$	1.22089e41	1.20353	0.601767	−	0.798671i	$-0.294463\pi$
$673$	1.22089e41	1.20353	0.601767	+	0.798671i	$0.294463\pi$
$674$	1.34223e41	1.29497
$675$	1.04486e40	0.0986631
$676$	−8.29227e40	−0.766384
$677$	5.75052e40	0.520201	0.260101	−	0.965582i	$-0.416244\pi$
$677$	5.75052e40	0.520201	0.260101	+	0.965582i	$0.416244\pi$
$678$	8.57709e40	0.759468
$679$	−3.30075e40	−0.286089
$680$	−3.03170e40	−0.257221
$681$	−2.69289e40	−0.223658
$682$	−3.21218e41	−2.61172
$683$	9.14027e40	0.727543	0.363771	−	0.931488i	$-0.381489\pi$
$683$	9.14027e40	0.727543	0.363771	+	0.931488i	$0.381489\pi$
$684$	5.64960e39	0.0440255
$685$	−3.29839e40	−0.251646
$686$	−1.09871e40	−0.0820699
$687$	−2.36452e40	−0.172930
$688$	1.34405e41	0.962464
$689$	−7.63531e40	−0.535363
$690$	8.94834e40	0.614371
$691$	1.23816e41	0.832427	0.416214	−	0.909267i	$-0.363357\pi$
$691$	1.23816e41	0.832427	0.416214	+	0.909267i	$0.363357\pi$
$692$	2.13045e40	0.140260
$693$	−2.18142e40	−0.140640
$694$	−2.82654e41	−1.78461
$695$	1.21227e41	0.749585
$696$	2.15329e40	0.130397
$697$	1.41408e41	0.838684
$698$	−2.88024e41	−1.67311
$699$	1.35704e41	0.772098
$700$	4.55584e40	0.253891
$701$	2.83103e41	1.54537	0.772686	−	0.634789i	$-0.218913\pi$
$701$	2.83103e41	1.54537	0.772686	+	0.634789i	$0.218913\pi$
$702$	−3.52460e40	−0.188461
$703$	−3.63124e40	−0.190197
$704$	−3.25124e41	−1.66819
$705$	8.07444e40	0.405854
$706$	−8.45898e40	−0.416533
$707$	8.93415e40	0.430995
$708$	1.19938e41	0.566857
$709$	2.40547e41	1.11386	0.556929	−	0.830560i	$-0.311979\pi$
$709$	2.40547e41	1.11386	0.556929	+	0.830560i	$0.311979\pi$
$710$	−9.05707e40	−0.410905
$711$	−1.80728e40	−0.0803370
$712$	−1.65326e40	−0.0720083
$713$	−3.61712e41	−1.54371
$714$	6.19689e40	0.259149
$715$	−1.22518e41	−0.502069
$716$	2.39239e40	0.0960712
$717$	−2.20335e41	−0.867073
$718$	5.84232e41	2.25310
$719$	1.77527e41	0.670959	0.335480	−	0.942047i	$-0.391102\pi$
$719$	1.77527e41	0.670959	0.335480	+	0.942047i	$0.391102\pi$
$720$	3.72829e40	0.138098
$721$	−1.21823e41	−0.442249
$722$	−4.22849e41	−1.50451
$723$	2.19463e40	0.0765343
$724$	−1.90263e41	−0.650348
$725$	7.32825e40	0.245527
$726$	−6.57626e40	−0.215972
$727$	4.52015e41	1.45514	0.727568	−	0.686035i	$-0.240650\pi$
$727$	4.52015e41	1.45514	0.727568	+	0.686035i	$0.240650\pi$
$728$	−3.63911e40	−0.114839
$729$	1.19725e40	0.0370370
$730$	−1.86676e41	−0.566117
$731$	−4.26204e41	−1.26711
$732$	3.55734e41	1.03685
$733$	3.42642e41	0.979113	0.489556	−	0.871972i	$-0.337159\pi$
$733$	3.42642e41	0.979113	0.489556	+	0.871972i	$0.337159\pi$
$734$	−7.38414e41	−2.06874
$735$	2.09614e40	0.0575776
$736$	−5.11503e41	−1.37759
$737$	−9.91654e40	−0.261867
$738$	2.10038e41	0.543851
$739$	2.49138e41	0.632551	0.316276	−	0.948667i	$-0.397568\pi$
$739$	2.49138e41	0.632551	0.316276	+	0.948667i	$0.397568\pi$
$740$	6.93217e41	1.72587
$741$	−1.53583e40	−0.0374954
$742$	1.99395e41	0.477372
$743$	−1.34036e41	−0.314690	−0.157345	−	0.987544i	$-0.550294\pi$
$743$	−1.34036e41	−0.314690	−0.157345	+	0.987544i	$0.550294\pi$
$744$	1.82025e41	0.419105
$745$	3.01880e41	0.681662
$746$	−1.11598e42	−2.47139
$747$	−2.89020e40	−0.0627740
$748$	5.36462e41	1.14279
$749$	1.01199e41	0.211442
$750$	−4.52184e41	−0.926673
$751$	−4.15672e41	−0.835549	−0.417775	−	0.908551i	$-0.637190\pi$
$751$	−4.15672e41	−0.835549	−0.417775	+	0.908551i	$0.637190\pi$
$752$	−3.03092e41	−0.597607
$753$	−8.97265e40	−0.173538
$754$	−2.47202e41	−0.468993
$755$	−6.31741e41	−1.17573
$756$	5.22029e40	0.0953079
$757$	4.51792e41	0.809186	0.404593	−	0.914497i	$-0.367413\pi$
$757$	4.51792e41	0.809186	0.404593	+	0.914497i	$0.367413\pi$
$758$	4.62216e41	0.812159
$759$	−3.74948e41	−0.646346
$760$	−1.96219e40	−0.0331852
$761$	−4.47198e41	−0.742032	−0.371016	−	0.928626i	$-0.620991\pi$
$761$	−4.47198e41	−0.742032	−0.371016	+	0.928626i	$0.620991\pi$
$762$	6.36405e41	1.03606
$763$	2.18120e40	0.0348409
$764$	9.25112e41	1.44991
$765$	−1.18225e41	−0.181811
$766$	1.63487e42	2.46698
$767$	−3.26047e41	−0.482778
$768$	−5.15783e40	−0.0749426
$769$	8.15442e41	1.16268	0.581342	−	0.813660i	$-0.302528\pi$
$769$	8.15442e41	1.16268	0.581342	+	0.813660i	$0.302528\pi$
$770$	3.19954e41	0.447685
$771$	−1.70835e41	−0.234579
$772$	6.07282e41	0.818351
$773$	7.20992e41	0.953515	0.476758	−	0.879035i	$-0.341812\pi$
$773$	7.20992e41	0.953515	0.476758	+	0.879035i	$0.341812\pi$
$774$	−6.33055e41	−0.821670
$775$	6.19481e41	0.789139
$776$	2.85504e41	0.356958
$777$	−3.35531e41	−0.411744
$778$	−1.37736e42	−1.65899
$779$	9.15227e40	0.108202
$780$	2.93195e41	0.340239
$781$	3.79504e41	0.432291
$782$	1.06514e42	1.19099
$783$	8.39704e40	0.0921681
$784$	−7.86832e40	−0.0847811
$785$	5.35860e41	0.566815
$786$	2.79789e40	0.0290539
$787$	1.48247e42	1.51131	0.755655	−	0.654970i	$-0.227319\pi$
$787$	1.48247e42	1.51131	0.755655	+	0.654970i	$0.227319\pi$
$788$	6.97204e41	0.697798
$789$	4.30292e41	0.422812
$790$	2.65078e41	0.255729
$791$	3.45342e41	0.327107
$792$	1.88685e41	0.175478
$793$	−9.67051e41	−0.883056
$794$	−2.32779e42	−2.08711
$795$	−3.80408e41	−0.334909
$796$	2.07812e42	1.79651
$797$	1.46971e42	1.24763	0.623814	−	0.781573i	$-0.285582\pi$
$797$	1.46971e42	1.24763	0.623814	+	0.781573i	$0.285582\pi$
$798$	4.01078e40	0.0334339
$799$	9.61115e41	0.786768
$800$	8.76019e41	0.704220
$801$	−6.44712e40	−0.0508973
$802$	−2.76938e42	−2.14711
$803$	7.82197e41	0.595581
$804$	2.37310e41	0.177461
$805$	3.60289e41	0.264613
$806$	−2.08968e42	−1.50737
$807$	−1.37834e42	−0.976539
$808$	−7.72774e41	−0.537759
$809$	−2.36343e42	−1.61543	−0.807716	−	0.589571i	$-0.799297\pi$
$809$	−2.36343e42	−1.61543	−0.807716	+	0.589571i	$0.799297\pi$
$810$	−1.75604e41	−0.117896
$811$	3.21583e40	0.0212075	0.0106038	−	0.999944i	$-0.496625\pi$
$811$	3.21583e40	0.0212075	0.0106038	+	0.999944i	$0.496625\pi$
$812$	3.66131e41	0.237178
$813$	−1.02210e42	−0.650397
$814$	−5.12153e42	−3.20145
$815$	2.12926e42	1.30750
$816$	4.43784e41	0.267710
$817$	−2.75850e41	−0.163476
$818$	1.99689e42	1.16260
$819$	−1.41912e41	−0.0811713
$820$	−1.74720e42	−0.981843
$821$	−2.87979e42	−1.58996	−0.794978	−	0.606639i	$-0.792518\pi$
$821$	−2.87979e42	−1.58996	−0.794978	+	0.606639i	$0.792518\pi$
$822$	−5.83161e41	−0.316335
$823$	−9.54164e41	−0.508541	−0.254270	−	0.967133i	$-0.581835\pi$
$823$	−9.54164e41	−0.508541	−0.254270	+	0.967133i	$0.581835\pi$
$824$	1.05372e42	0.551801
$825$	6.42150e41	0.330411
$826$	8.51466e41	0.430484
$827$	−3.26563e42	−1.62232	−0.811160	−	0.584824i	$-0.801163\pi$
$827$	−3.26563e42	−1.62232	−0.811160	+	0.584824i	$0.801163\pi$
$828$	8.97276e41	0.438012
$829$	−1.06338e42	−0.510092	−0.255046	−	0.966929i	$-0.582091\pi$
$829$	−1.06338e42	−0.510092	−0.255046	+	0.966929i	$0.582091\pi$
$830$	4.23913e41	0.199823
$831$	−2.04476e42	−0.947168
$832$	−2.11509e42	−0.962808
$833$	2.49507e41	0.111617
$834$	2.14332e42	0.942278
$835$	1.65119e42	0.713416
$836$	3.47212e41	0.147436
$837$	7.09830e41	0.296234
$838$	−4.87397e42	−1.99915
$839$	−7.26597e41	−0.292917	−0.146459	−	0.989217i	$-0.546788\pi$
$839$	−7.26597e41	−0.292917	−0.146459	+	0.989217i	$0.546788\pi$
$840$	−1.81309e41	−0.0718405
$841$	−1.97875e42	−0.770636
$842$	4.49373e42	1.72021
$843$	1.56435e42	0.588620
$844$	−4.93382e42	−1.82481
$845$	1.12311e42	0.408318
$846$	1.42757e42	0.510186
$847$	−2.64782e41	−0.0930204
$848$	1.42795e42	0.493142
$849$	4.20027e41	0.142599
$850$	−1.82419e42	−0.608830
$851$	−5.76718e42	−1.89228
$852$	−9.08179e41	−0.292953
$853$	5.92391e42	1.87866	0.939329	−	0.343018i	$-0.111449\pi$
$853$	5.92391e42	1.87866	0.939329	+	0.343018i	$0.111449\pi$
$854$	2.52544e42	0.787404
$855$	−7.65183e40	−0.0234561
$856$	−8.75338e41	−0.263819
$857$	−2.55857e42	−0.758186	−0.379093	−	0.925359i	$-0.623764\pi$
$857$	−2.55857e42	−0.758186	−0.379093	+	0.925359i	$0.623764\pi$
$858$	−2.16614e42	−0.631134
$859$	9.52246e41	0.272802	0.136401	−	0.990654i	$-0.456446\pi$
$859$	9.52246e41	0.272802	0.136401	+	0.990654i	$0.456446\pi$
$860$	5.26608e42	1.48340
$861$	8.45680e41	0.234240
$862$	−4.00126e42	−1.08979
$863$	5.32293e42	1.42559	0.712794	−	0.701373i	$-0.247429\pi$
$863$	5.32293e42	1.42559	0.712794	+	0.701373i	$0.247429\pi$
$864$	1.00378e42	0.264357
$865$	−2.88549e41	−0.0747285
$866$	−2.89395e42	−0.737023
$867$	8.97985e41	0.224901
$868$	3.09502e42	0.762303
$869$	−1.11071e42	−0.269039
$870$	−1.23161e42	−0.293390
$871$	−6.45119e41	−0.151139
$872$	−1.88666e41	−0.0434715
$873$	1.11336e42	0.252307
$874$	6.89383e41	0.153654
$875$	−1.82064e42	−0.399123
$876$	−1.87185e42	−0.403610
$877$	5.71912e42	1.21293	0.606465	−	0.795110i	$-0.292587\pi$
$877$	5.71912e42	1.21293	0.606465	+	0.795110i	$0.292587\pi$
$878$	2.63128e42	0.548904
$879$	−1.92402e42	−0.394795
$880$	2.29132e42	0.462474
$881$	5.69039e42	1.12977	0.564886	−	0.825169i	$-0.308920\pi$
$881$	5.69039e42	1.12977	0.564886	+	0.825169i	$0.308920\pi$
$882$	3.70601e41	0.0723789
$883$	1.05261e42	0.202226	0.101113	−	0.994875i	$-0.467760\pi$
$883$	1.05261e42	0.202226	0.101113	+	0.994875i	$0.467760\pi$
$884$	3.48995e42	0.659570
$885$	−1.62444e42	−0.302013
$886$	−4.28488e42	−0.783699
$887$	3.37628e42	0.607499	0.303749	−	0.952752i	$-0.401761\pi$
$887$	3.37628e42	0.607499	0.303749	+	0.952752i	$0.401761\pi$
$888$	2.90222e42	0.513740
$889$	2.56237e42	0.446238
$890$	9.45615e41	0.162016
$891$	7.35804e41	0.124032
$892$	−1.24151e43	−2.05901
$893$	6.22057e41	0.101504
$894$	5.33730e42	0.856894
$895$	−3.24026e41	−0.0511854
$896$	2.18318e42	0.339331
$897$	−2.43922e42	−0.373044
$898$	1.46732e43	2.20810
$899$	4.97846e42	0.737190
$900$	−1.53671e42	−0.223911
$901$	−4.52807e42	−0.649237
$902$	1.29084e43	1.82129
$903$	−2.54889e42	−0.353898
$904$	−2.98709e42	−0.408137
$905$	2.57693e42	0.346496
$906$	−1.11693e43	−1.47797
$907$	3.64169e42	0.474239	0.237119	−	0.971481i	$-0.423797\pi$
$907$	3.64169e42	0.474239	0.237119	+	0.971481i	$0.423797\pi$
$908$	3.96050e42	0.507581
$909$	−3.01353e42	−0.380102
$910$	2.08146e42	0.258385
$911$	1.03602e43	1.26577	0.632883	−	0.774247i	$-0.281871\pi$
$911$	1.03602e43	1.26577	0.632883	+	0.774247i	$0.281871\pi$
$912$	2.87228e41	0.0345384
$913$	−1.77626e42	−0.210222
$914$	−3.79672e42	−0.442271
$915$	−4.81807e42	−0.552417
$916$	3.47756e42	0.392456
$917$	1.12652e41	0.0125137
$918$	−2.09024e42	−0.228548
$919$	−7.69888e41	−0.0828614	−0.0414307	−	0.999141i	$-0.513192\pi$
$919$	−7.69888e41	−0.0828614	−0.0414307	+	0.999141i	$0.513192\pi$
$920$	−3.11638e42	−0.330162
$921$	−7.90113e42	−0.823995
$922$	4.64778e42	0.477141
$923$	2.46886e42	0.249500
$924$	3.20828e42	0.319174
$925$	9.87708e42	0.967328
$926$	−1.63026e42	−0.157180
$927$	4.10914e42	0.390027
$928$	7.04012e42	0.657862
$929$	1.33803e42	0.123095	0.0615473	−	0.998104i	$-0.480396\pi$
$929$	1.33803e42	0.123095	0.0615473	+	0.998104i	$0.480396\pi$
$930$	−1.04112e43	−0.942974
$931$	1.61487e41	0.0144002
$932$	−1.99583e43	−1.75224
$933$	1.21196e43	1.04762
$934$	1.70535e43	1.45139
$935$	−7.26586e42	−0.608862
$936$	1.22749e42	0.101279
$937$	−1.15361e43	−0.937203	−0.468602	−	0.883410i	$-0.655242\pi$
$937$	−1.15361e43	−0.937203	−0.468602	+	0.883410i	$0.655242\pi$
$938$	1.68472e42	0.134768
$939$	−6.28052e42	−0.494703
$940$	−1.18753e43	−0.921066
$941$	−8.87945e42	−0.678167	−0.339084	−	0.940756i	$-0.610117\pi$
$941$	−8.87945e42	−0.678167	−0.339084	+	0.940756i	$0.610117\pi$
$942$	9.47409e42	0.712524
$943$	1.45358e43	1.07651
$944$	6.09769e42	0.444705
$945$	−7.07038e41	−0.0507787
$946$	−3.89061e43	−2.75167
$947$	−2.25139e43	−1.56811	−0.784054	−	0.620693i	$-0.786851\pi$
$947$	−2.25139e43	−1.56811	−0.784054	+	0.620693i	$0.786851\pi$
$948$	2.65801e42	0.182321
$949$	5.08857e42	0.343745
$950$	−1.18066e42	−0.0785477
$951$	−6.22900e42	−0.408132
$952$	−2.15815e42	−0.139266
$953$	−2.57845e43	−1.63875	−0.819374	−	0.573259i	$-0.805679\pi$
$953$	−2.57845e43	−1.63875	−0.819374	+	0.573259i	$0.805679\pi$
$954$	−6.72568e42	−0.421003
$955$	−1.25297e43	−0.772490
$956$	3.24053e43	1.96778
$957$	5.16064e42	0.308660
$958$	3.44399e43	2.02891
$959$	−2.34800e42	−0.136247
$960$	−1.05378e43	−0.602308
$961$	2.43227e43	1.36938
$962$	−3.33180e43	−1.84774
$963$	−3.41350e42	−0.186474
$964$	−3.22770e42	−0.173691
$965$	−8.22504e42	−0.436006
$966$	6.36997e42	0.332636
$967$	−3.04077e43	−1.56423	−0.782113	−	0.623136i	$-0.785858\pi$
$967$	−3.04077e43	−1.56423	−0.782113	+	0.623136i	$0.785858\pi$
$968$	2.29027e42	0.116063
$969$	−9.10811e41	−0.0454709
$970$	−1.63299e43	−0.803145
$971$	−7.47671e42	−0.362269	−0.181135	−	0.983458i	$-0.557977\pi$
$971$	−7.47671e42	−0.362269	−0.181135	+	0.983458i	$0.557977\pi$
$972$	−1.76083e42	−0.0840537
$973$	8.62970e42	0.405844
$974$	−5.82935e43	−2.70094
$975$	4.17749e42	0.190699
$976$	1.80857e43	0.813415
$977$	2.10224e43	0.931561	0.465781	−	0.884900i	$-0.345774\pi$
$977$	2.10224e43	0.931561	0.465781	+	0.884900i	$0.345774\pi$
$978$	3.76456e43	1.64362
$979$	−3.96226e42	−0.170449
$980$	−3.08285e42	−0.130669
$981$	−7.35728e41	−0.0307267
$982$	3.89217e43	1.60168
$983$	3.50297e43	1.42040	0.710199	−	0.704001i	$-0.248605\pi$
$983$	3.50297e43	1.42040	0.710199	+	0.704001i	$0.248605\pi$
$984$	−7.31484e42	−0.292265
$985$	−9.44295e42	−0.371777
$986$	−1.46601e43	−0.568751
$987$	5.74788e42	0.219740
$988$	2.25878e42	0.0850939
$989$	−4.38108e43	−1.62643
$990$	−1.07922e43	−0.394821
$991$	2.32558e43	0.838424	0.419212	−	0.907888i	$-0.362306\pi$
$991$	2.32558e43	0.838424	0.419212	+	0.907888i	$0.362306\pi$
$992$	5.95125e43	2.11441
$993$	−1.85059e43	−0.647956
$994$	−6.44737e42	−0.222474
$995$	−2.81461e43	−0.957156
$996$	4.25070e42	0.142462
$997$	−2.54526e43	−0.840721	−0.420361	−	0.907357i	$-0.638096\pi$
$997$	−2.54526e43	−0.840721	−0.420361	+	0.907357i	$0.638096\pi$
$998$	−6.56575e42	−0.213743
$999$	1.13176e43	0.363124

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.b.1.6	✓	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+35218.1 q^{2} -4.78297e6 q^{3} +7.03444e8 q^{4} -9.52746e9 q^{5} -1.68447e11 q^{6} -6.78223e11 q^{7} +5.86640e12 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q+35218.1 q^{2} -4.78297e6 q^{3} +7.03444e8 q^{4} -9.52746e9 q^{5} -1.68447e11 q^{6} -6.78223e11 q^{7} +5.86640e12 q^{8} +2.28768e13 q^{9} -3.35539e14 q^{10} +1.40596e15 q^{11} -3.36455e15 q^{12} +9.14643e15 q^{13} -2.38857e16 q^{14} +4.55696e16 q^{15} -1.71055e17 q^{16} +5.42423e17 q^{17} +8.05677e17 q^{18} +3.51069e17 q^{19} -6.70204e18 q^{20} +3.24392e18 q^{21} +4.95151e19 q^{22} +5.57573e19 q^{23} -2.80588e19 q^{24} -9.54919e19 q^{25} +3.22120e20 q^{26} -1.09419e20 q^{27} -4.77092e20 q^{28} -7.67421e20 q^{29} +1.60487e21 q^{30} -6.48726e21 q^{31} -9.17374e21 q^{32} -6.72465e21 q^{33} +1.91031e22 q^{34} +6.46175e21 q^{35} +1.60925e22 q^{36} -1.03434e23 q^{37} +1.23640e22 q^{38} -4.37471e22 q^{39} -5.58919e22 q^{40} +2.60697e23 q^{41} +1.14245e23 q^{42} -7.85743e23 q^{43} +9.89012e23 q^{44} -2.17958e23 q^{45} +1.96367e24 q^{46} +1.77189e24 q^{47} +8.18152e23 q^{48} +4.59987e23 q^{49} -3.36305e24 q^{50} -2.59439e24 q^{51} +6.43400e24 q^{52} -8.34786e24 q^{53} -3.85353e24 q^{54} -1.33952e25 q^{55} -3.97873e24 q^{56} -1.67915e24 q^{57} -2.70271e25 q^{58} -3.56475e25 q^{59} +3.20556e25 q^{60} -1.05730e26 q^{61} -2.28469e26 q^{62} -1.55156e25 q^{63} -2.31247e26 q^{64} -8.71423e25 q^{65} -2.36829e26 q^{66} -7.05323e25 q^{67} +3.81564e26 q^{68} -2.66685e26 q^{69} +2.27570e26 q^{70} +2.69926e26 q^{71} +1.34204e26 q^{72} +5.56345e26 q^{73} -3.64274e27 q^{74} +4.56735e26 q^{75} +2.46958e26 q^{76} -9.53552e26 q^{77} -1.54069e27 q^{78} -7.90005e26 q^{79} +1.62972e27 q^{80} +5.23348e26 q^{81} +9.18126e27 q^{82} -1.26338e27 q^{83} +2.28192e27 q^{84} -5.16791e27 q^{85} -2.76724e28 q^{86} +3.67055e27 q^{87} +8.24790e27 q^{88} -2.81819e27 q^{89} -7.67606e27 q^{90} -6.20332e27 q^{91} +3.92221e28 q^{92} +3.10284e28 q^{93} +6.24027e28 q^{94} -3.34480e27 q^{95} +4.38777e28 q^{96} +4.86677e28 q^{97} +1.61999e28 q^{98} +3.21638e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4177 q^{2} - 33480783 q^{3} + 1749008801 q^{4} - 1716792694 q^{5} - 19978461513 q^{6} - 4747561509943 q^{7} + 4282496015841 q^{8} + 160137547184727 q^{9}+O(q^{10}) \) 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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