LMFDB - Embedded newform 21.30.a.b.1.2

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			1.2
Root			$27718.7$ 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)

$f(q)$	$=$	$q-27121.7 q^{2} -4.78297e6 q^{3} +1.98714e8 q^{4} -7.72707e9 q^{5} +1.29722e11 q^{6} -6.78223e11 q^{7} +9.17138e12 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q-27121.7 q^{2} -4.78297e6 q^{3} +1.98714e8 q^{4} -7.72707e9 q^{5} +1.29722e11 q^{6} -6.78223e11 q^{7} +9.17138e12 q^{8} +2.28768e13 q^{9} +2.09571e14 q^{10} -1.28657e14 q^{11} -9.50443e14 q^{12} -2.01529e16 q^{13} +1.83945e16 q^{14} +3.69583e16 q^{15} -3.55427e17 q^{16} -5.14803e17 q^{17} -6.20457e17 q^{18} +5.72683e18 q^{19} -1.53548e18 q^{20} +3.24392e18 q^{21} +3.48939e18 q^{22} -3.38443e19 q^{23} -4.38664e19 q^{24} -1.26557e20 q^{25} +5.46581e20 q^{26} -1.09419e20 q^{27} -1.34772e20 q^{28} +9.81008e20 q^{29} -1.00237e21 q^{30} -4.58953e21 q^{31} +4.71593e21 q^{32} +6.15362e20 q^{33} +1.39623e22 q^{34} +5.24068e21 q^{35} +4.54594e21 q^{36} +1.40492e21 q^{37} -1.55321e23 q^{38} +9.63908e22 q^{39} -7.08679e22 q^{40} +1.32210e23 q^{41} -8.79805e22 q^{42} +3.35474e23 q^{43} -2.55660e22 q^{44} -1.76771e23 q^{45} +9.17915e23 q^{46} +2.03677e24 q^{47} +1.70000e24 q^{48} +4.59987e23 q^{49} +3.43244e24 q^{50} +2.46229e24 q^{51} -4.00467e24 q^{52} +1.15740e25 q^{53} +2.96763e24 q^{54} +9.94141e23 q^{55} -6.22024e24 q^{56} -2.73913e25 q^{57} -2.66066e25 q^{58} -1.13823e25 q^{59} +7.34414e24 q^{60} +6.05775e25 q^{61} +1.24476e26 q^{62} -1.55156e25 q^{63} +6.29146e25 q^{64} +1.55723e26 q^{65} -1.66897e25 q^{66} +4.09640e26 q^{67} -1.02299e26 q^{68} +1.61876e26 q^{69} -1.42136e26 q^{70} -5.21530e26 q^{71} +2.09812e26 q^{72} +2.05559e27 q^{73} -3.81037e25 q^{74} +6.05318e26 q^{75} +1.13800e27 q^{76} +8.72581e25 q^{77} -2.61428e27 q^{78} +3.77681e26 q^{79} +2.74641e27 q^{80} +5.23348e26 q^{81} -3.58574e27 q^{82} +5.78546e27 q^{83} +6.44613e26 q^{84} +3.97792e27 q^{85} -9.09860e27 q^{86} -4.69213e27 q^{87} -1.17996e27 q^{88} -3.34627e28 q^{89} +4.79431e27 q^{90} +1.36682e28 q^{91} -6.72535e27 q^{92} +2.19516e28 q^{93} -5.52406e28 q^{94} -4.42516e28 q^{95} -2.25561e28 q^{96} -8.34065e28 q^{97} -1.24756e28 q^{98} -2.94326e27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−27121.7	−1.17053	−0.585264	−	0.810843i	$-0.699009\pi$
$2$	−27121.7	−1.17053	−0.585264	+	0.810843i	$0.699009\pi$
$3$	−4.78297e6	−0.577350
$3$	−4.78297e6	−0.577350
$4$	1.98714e8	0.370134
$5$	−7.72707e9	−0.566174	−0.283087	−	0.959094i	$-0.591358\pi$
$5$	−7.72707e9	−0.566174	−0.283087	+	0.959094i	$0.591358\pi$
$6$	1.29722e11	0.675804
$7$	−6.78223e11	−0.377964
$7$	−6.78223e11	−0.377964
$8$	9.17138e12	0.737275
$9$	2.28768e13	0.333333
$10$	2.09571e14	0.662722
$11$	−1.28657e14	−0.102150	−0.0510751	−	0.998695i	$-0.516265\pi$
$11$	−1.28657e14	−0.102150	−0.0510751	+	0.998695i	$0.516265\pi$
$12$	−9.50443e14	−0.213697
$13$	−2.01529e16	−1.41958	−0.709790	−	0.704414i	$-0.751210\pi$
$13$	−2.01529e16	−1.41958	−0.709790	+	0.704414i	$0.751210\pi$
$14$	1.83945e16	0.442418
$15$	3.69583e16	0.326881
$16$	−3.55427e17	−1.23313
$17$	−5.14803e17	−0.741535	−0.370768	−	0.928726i	$-0.620905\pi$
$17$	−5.14803e17	−0.741535	−0.370768	+	0.928726i	$0.620905\pi$
$18$	−6.20457e17	−0.390176
$19$	5.72683e18	1.64432	0.822162	−	0.569254i	$-0.192768\pi$
$19$	5.72683e18	1.64432	0.822162	+	0.569254i	$0.192768\pi$
$20$	−1.53548e18	−0.209560
$21$	3.24392e18	0.218218
$22$	3.48939e18	0.119570
$23$	−3.38443e19	−0.608741	−0.304370	−	0.952554i	$-0.598446\pi$
$23$	−3.38443e19	−0.608741	−0.304370	+	0.952554i	$0.598446\pi$
$24$	−4.38664e19	−0.425666
$25$	−1.26557e20	−0.679447
$26$	5.46581e20	1.66166
$27$	−1.09419e20	−0.192450
$28$	−1.34772e20	−0.139897
$29$	9.81008e20	0.612212	0.306106	−	0.951997i	$-0.400974\pi$
$29$	9.81008e20	0.612212	0.306106	+	0.951997i	$0.400974\pi$
$30$	−1.00237e21	−0.382623
$31$	−4.58953e21	−1.08899	−0.544495	−	0.838764i	$-0.683279\pi$
$31$	−4.58953e21	−1.08899	−0.544495	+	0.838764i	$0.683279\pi$
$32$	4.71593e21	0.706142
$33$	6.15362e20	0.0589765
$34$	1.39623e22	0.867987
$35$	5.24068e21	0.213994
$36$	4.54594e21	0.123378
$37$	1.40492e21	0.0256287	0.0128143	−	0.999918i	$-0.495921\pi$
$37$	1.40492e21	0.0256287	0.0128143	+	0.999918i	$0.495921\pi$
$38$	−1.55321e23	−1.92473
$39$	9.63908e22	0.819594
$40$	−7.08679e22	−0.417426
$41$	1.32210e23	0.544374	0.272187	−	0.962244i	$-0.412253\pi$
$41$	1.32210e23	0.544374	0.272187	+	0.962244i	$0.412253\pi$
$42$	−8.79805e22	−0.255430
$43$	3.35474e23	0.692414	0.346207	−	0.938158i	$-0.387470\pi$
$43$	3.35474e23	0.692414	0.346207	+	0.938158i	$0.387470\pi$
$44$	−2.55660e22	−0.0378093
$45$	−1.76771e23	−0.188725
$46$	9.17915e23	0.712548
$47$	2.03677e24	1.15751	0.578753	−	0.815503i	$-0.303540\pi$
$47$	2.03677e24	1.15751	0.578753	+	0.815503i	$0.303540\pi$
$48$	1.70000e24	0.711951
$49$	4.59987e23	0.142857
$50$	3.43244e24	0.795312
$51$	2.46229e24	0.428126
$52$	−4.00467e24	−0.525434
$53$	1.15740e25	1.15208	0.576041	−	0.817421i	$-0.304597\pi$
$53$	1.15740e25	1.15208	0.576041	+	0.817421i	$0.304597\pi$
$54$	2.96763e24	0.225268
$55$	9.94141e23	0.0578348
$56$	−6.22024e24	−0.278664
$57$	−2.73913e25	−0.949351
$58$	−2.66066e25	−0.716611
$59$	−1.13823e25	−0.239263	−0.119632	−	0.992818i	$-0.538171\pi$
$59$	−1.13823e25	−0.239263	−0.119632	+	0.992818i	$0.538171\pi$
$60$	7.34414e24	0.120990
$61$	6.05775e25	0.785287	0.392644	−	0.919691i	$-0.371561\pi$
$61$	6.05775e25	0.785287	0.392644	+	0.919691i	$0.371561\pi$
$62$	1.24476e26	1.27469
$63$	−1.55156e25	−0.125988
$64$	6.29146e25	0.406576
$65$	1.55723e26	0.803728
$66$	−1.66897e25	−0.0690336
$67$	4.09640e26	1.36244	0.681220	−	0.732079i	$-0.261450\pi$
$67$	4.09640e26	1.36244	0.681220	+	0.732079i	$0.261450\pi$
$68$	−1.02299e26	−0.274467
$69$	1.61876e26	0.351457
$70$	−1.42136e26	−0.250485
$71$	−5.21530e26	−0.748227	−0.374113	−	0.927383i	$-0.622053\pi$
$71$	−5.21530e26	−0.748227	−0.374113	+	0.927383i	$0.622053\pi$
$72$	2.09812e26	0.245758
$73$	2.05559e27	1.97131	0.985657	−	0.168759i	$-0.0539761\pi$
$73$	2.05559e27	1.97131	0.985657	+	0.168759i	$0.0539761\pi$
$74$	−3.81037e25	−0.0299990
$75$	6.05318e26	0.392279
$76$	1.13800e27	0.608620
$77$	8.72581e25	0.0386092
$78$	−2.61428e27	−0.959357
$79$	3.77681e26	0.115221	0.0576105	−	0.998339i	$-0.481652\pi$
$79$	3.77681e26	0.115221	0.0576105	+	0.998339i	$0.481652\pi$
$80$	2.74641e27	0.698169
$81$	5.23348e26	0.111111
$82$	−3.58574e27	−0.637204
$83$	5.78546e27	0.862394	0.431197	−	0.902258i	$-0.358091\pi$
$83$	5.78546e27	0.862394	0.431197	+	0.902258i	$0.358091\pi$
$84$	6.44613e26	0.0807698
$85$	3.97792e27	0.419838
$86$	−9.09860e27	−0.810489
$87$	−4.69213e27	−0.353461
$88$	−1.17996e27	−0.0753129
$89$	−3.34627e28	−1.81304	−0.906518	−	0.422167i	$-0.861270\pi$
$89$	−3.34627e28	−1.81304	−0.906518	+	0.422167i	$0.861270\pi$
$90$	4.79431e27	0.220907
$91$	1.36682e28	0.536550
$92$	−6.72535e27	−0.225316
$93$	2.19516e28	0.628728
$94$	−5.52406e28	−1.35489
$95$	−4.42516e28	−0.930973
$96$	−2.25561e28	−0.407691
$97$	−8.34065e28	−1.29721	−0.648604	−	0.761126i	$-0.724647\pi$
$97$	−8.34065e28	−1.29721	−0.648604	+	0.761126i	$0.724647\pi$
$98$	−1.24756e28	−0.167218
$99$	−2.94326e27	−0.0340501
$100$	−2.51486e28	−0.251486
$101$	−3.14689e27	−0.0272409	−0.0136205	−	0.999907i	$-0.504336\pi$
$101$	−3.14689e27	−0.0272409	−0.0136205	+	0.999907i	$0.504336\pi$
$102$	−6.67814e28	−0.501133
$103$	2.11501e29	1.37776	0.688879	−	0.724877i	$-0.258103\pi$
$103$	2.11501e29	1.37776	0.688879	+	0.724877i	$0.258103\pi$
$104$	−1.84830e29	−1.04662
$105$	−2.50660e28	−0.123549
$106$	−3.13906e29	−1.34854
$107$	1.15671e29	0.433670	0.216835	−	0.976208i	$-0.430427\pi$
$107$	1.15671e29	0.433670	0.216835	+	0.976208i	$0.430427\pi$
$108$	−2.17431e28	−0.0712323
$109$	−1.38170e29	−0.396032	−0.198016	−	0.980199i	$-0.563450\pi$
$109$	−1.38170e29	−0.396032	−0.198016	+	0.980199i	$0.563450\pi$
$110$	−2.69628e28	−0.0676972
$111$	−6.71968e27	−0.0147967
$112$	2.41059e29	0.466081
$113$	−4.17858e29	−0.710218	−0.355109	−	0.934825i	$-0.615556\pi$
$113$	−4.17858e29	−0.710218	−0.355109	+	0.934825i	$0.615556\pi$
$114$	7.42897e29	1.11124
$115$	2.61517e29	0.344653
$116$	1.94940e29	0.226600
$117$	−4.61034e29	−0.473193
$118$	3.08707e29	0.280064
$119$	3.49151e29	0.280274
$120$	3.38959e29	0.241001
$121$	−1.56976e30	−0.989565
$122$	−1.64296e30	−0.919200
$123$	−6.32354e29	−0.314294
$124$	−9.12004e29	−0.403072
$125$	2.41719e30	0.950859
$126$	4.20808e29	0.147473
$127$	1.49433e30	0.466974	0.233487	−	0.972360i	$-0.424986\pi$
$127$	1.49433e30	0.466974	0.233487	+	0.972360i	$0.424986\pi$
$128$	−4.23819e30	−1.18205
$129$	−1.60456e30	−0.399765
$130$	−4.22347e30	−0.940786
$131$	4.17150e30	0.831493	0.415746	−	0.909481i	$-0.363520\pi$
$131$	4.17150e30	0.831493	0.415746	+	0.909481i	$0.363520\pi$
$132$	1.22281e29	0.0218292
$133$	−3.88407e30	−0.621496
$134$	−1.11101e31	−1.59477
$135$	8.45488e29	0.108960
$136$	−4.72145e30	−0.546716
$137$	−9.65792e30	−1.00562	−0.502812	−	0.864396i	$-0.667701\pi$
$137$	−9.65792e30	−1.00562	−0.502812	+	0.864396i	$0.667701\pi$
$138$	−4.39036e30	−0.411389
$139$	−1.34902e31	−1.13843	−0.569213	−	0.822190i	$-0.692752\pi$
$139$	−1.34902e31	−1.13843	−0.569213	+	0.822190i	$0.692752\pi$
$140$	1.04140e30	0.0792063
$141$	−9.74181e30	−0.668286
$142$	1.41448e31	0.875820
$143$	2.59282e30	0.145010
$144$	−8.13103e30	−0.411045
$145$	−7.58032e30	−0.346618
$146$	−5.57511e31	−2.30748
$147$	−2.20010e30	−0.0824786
$148$	2.79177e29	0.00948603
$149$	−4.29614e31	−1.32397	−0.661983	−	0.749518i	$-0.730285\pi$
$149$	−4.29614e31	−1.32397	−0.661983	+	0.749518i	$0.730285\pi$
$150$	−1.64172e31	−0.459173
$151$	−6.31131e30	−0.160307	−0.0801537	−	0.996783i	$-0.525541\pi$
$151$	−6.31131e30	−0.160307	−0.0801537	+	0.996783i	$0.525541\pi$
$152$	5.25230e31	1.21232
$153$	−1.17770e31	−0.247178
$154$	−2.36659e30	−0.0451931
$155$	3.54636e31	0.616557
$156$	1.91542e31	0.303360
$157$	−2.43950e31	−0.352172	−0.176086	−	0.984375i	$-0.556344\pi$
$157$	−2.43950e31	−0.352172	−0.176086	+	0.984375i	$0.556344\pi$
$158$	−1.02433e31	−0.134869
$159$	−5.53581e31	−0.665155
$160$	−3.64403e31	−0.399799
$161$	2.29540e31	0.230082
$162$	−1.41941e31	−0.130059
$163$	2.34876e32	1.96842	0.984210	−	0.177004i	$-0.0566405\pi$
$163$	2.34876e32	1.96842	0.984210	+	0.177004i	$0.0566405\pi$
$164$	2.62719e31	0.201491
$165$	−4.75495e30	−0.0333909
$166$	−1.56911e32	−1.00946
$167$	−1.94407e32	−1.14637	−0.573183	−	0.819428i	$-0.694291\pi$
$167$	−1.94407e32	−1.14637	−0.573183	+	0.819428i	$0.694291\pi$
$168$	2.97512e31	0.160887
$169$	2.04602e32	1.01520
$170$	−1.07888e32	−0.491432
$171$	1.31012e32	0.548108
$172$	6.66633e31	0.256286
$173$	2.86279e32	1.01186	0.505932	−	0.862574i	$-0.331149\pi$
$173$	2.86279e32	1.01186	0.505932	+	0.862574i	$0.331149\pi$
$174$	1.27258e32	0.413735
$175$	8.58338e31	0.256807
$176$	4.57282e31	0.125965
$177$	5.44412e31	0.138139
$178$	9.07566e32	2.12221
$179$	2.44241e31	0.0526562	0.0263281	−	0.999653i	$-0.491619\pi$
$179$	2.44241e31	0.0526562	0.0263281	+	0.999653i	$0.491619\pi$
$180$	−3.51268e31	−0.0698533
$181$	3.31671e32	0.608651	0.304326	−	0.952568i	$-0.401569\pi$
$181$	3.31671e32	0.608651	0.304326	+	0.952568i	$0.401569\pi$
$182$	−3.70704e32	−0.628047
$183$	−2.89740e32	−0.453386
$184$	−3.10399e32	−0.448810
$185$	−1.08559e31	−0.0145103
$186$	−5.95364e32	−0.735944
$187$	6.62330e31	0.0757480
$188$	4.04735e32	0.428432
$189$	7.42105e31	0.0727393
$190$	1.20018e33	1.08973
$191$	8.00859e32	0.673864	0.336932	−	0.941529i	$-0.390611\pi$
$191$	8.00859e32	0.673864	0.336932	+	0.941529i	$0.390611\pi$
$192$	−3.00919e32	−0.234737
$193$	1.40571e33	1.01698	0.508492	−	0.861067i	$-0.330203\pi$
$193$	1.40571e33	1.01698	0.508492	+	0.861067i	$0.330203\pi$
$194$	2.26212e33	1.51842
$195$	−7.44819e32	−0.464033
$196$	9.14058e31	0.0528763
$197$	−3.01342e33	−1.61920	−0.809598	−	0.586985i	$-0.800315\pi$
$197$	−3.01342e33	−1.61920	−0.809598	+	0.586985i	$0.800315\pi$
$198$	7.98261e31	0.0398565
$199$	4.17526e33	1.93782	0.968912	−	0.247406i	$-0.0795782\pi$
$199$	4.17526e33	1.93782	0.968912	+	0.247406i	$0.0795782\pi$
$200$	−1.16070e33	−0.500940
$201$	−1.95929e33	−0.786605
$202$	8.53490e31	0.0318863
$203$	−6.65343e32	−0.231394
$204$	4.89291e32	0.158464
$205$	−1.02159e33	−0.308210
$206$	−5.73626e33	−1.61270
$207$	−7.74250e32	−0.202914
$208$	7.16289e33	1.75053
$209$	−7.36797e32	−0.167968
$210$	6.79832e32	0.144618
$211$	−3.62408e33	−0.719619	−0.359810	−	0.933026i	$-0.617158\pi$
$211$	−3.62408e33	−0.719619	−0.359810	+	0.933026i	$0.617158\pi$
$212$	2.29992e33	0.426425
$213$	2.49446e33	0.431989
$214$	−3.13719e33	−0.507623
$215$	−2.59223e33	−0.392027
$216$	−1.00352e33	−0.141889
$217$	3.11273e33	0.411599
$218$	3.74741e33	0.463566
$219$	−9.83184e33	−1.13814
$220$	1.97550e32	0.0214066
$221$	1.03748e34	1.05267
$222$	1.82249e32	0.0173200
$223$	1.48359e34	1.32097	0.660487	−	0.750837i	$-0.270350\pi$
$223$	1.48359e34	1.32097	0.660487	+	0.750837i	$0.270350\pi$
$224$	−3.19845e33	−0.266897
$225$	−2.89522e33	−0.226482
$226$	1.13330e34	0.831329
$227$	6.87537e33	0.473065	0.236533	−	0.971624i	$-0.423989\pi$
$227$	6.87537e33	0.473065	0.236533	+	0.971624i	$0.423989\pi$
$228$	−5.44303e33	−0.351387
$229$	2.00076e33	0.121222	0.0606110	−	0.998161i	$-0.480695\pi$
$229$	2.00076e33	0.121222	0.0606110	+	0.998161i	$0.480695\pi$
$230$	−7.09279e33	−0.403426
$231$	−4.17353e32	−0.0222910
$232$	8.99720e33	0.451369
$233$	−1.22972e34	−0.579623	−0.289812	−	0.957084i	$-0.593593\pi$
$233$	−1.22972e34	−0.579623	−0.289812	+	0.957084i	$0.593593\pi$
$234$	1.25040e34	0.553885
$235$	−1.57383e34	−0.655350
$236$	−2.26183e33	−0.0885595
$237$	−1.80643e33	−0.0665229
$238$	−9.46957e33	−0.328068
$239$	−6.01891e34	−1.96222	−0.981111	−	0.193444i	$-0.938034\pi$
$239$	−6.01891e34	−1.96222	−0.981111	+	0.193444i	$0.938034\pi$
$240$	−1.31360e34	−0.403088
$241$	−6.65109e33	−0.192152	−0.0960761	−	0.995374i	$-0.530629\pi$
$241$	−6.65109e33	−0.192152	−0.0960761	+	0.995374i	$0.530629\pi$
$242$	4.25744e34	1.15831
$243$	−2.50316e33	−0.0641500
$244$	1.20376e34	0.290661
$245$	−3.55435e33	−0.0808820
$246$	1.71505e34	0.367890
$247$	−1.15412e35	−2.33425
$248$	−4.20923e34	−0.802885
$249$	−2.76717e34	−0.497903
$250$	−6.55583e34	−1.11301
$251$	−1.05336e35	−1.68775	−0.843876	−	0.536538i	$-0.819732\pi$
$251$	−1.05336e35	−1.68775	−0.843876	+	0.536538i	$0.819732\pi$
$252$	−3.08316e33	−0.0466325
$253$	4.35431e33	0.0621830
$254$	−4.05287e34	−0.546606
$255$	−1.90263e34	−0.242393
$256$	8.11698e34	0.977046
$257$	1.60802e34	0.182920	0.0914598	−	0.995809i	$-0.470847\pi$
$257$	1.60802e34	0.182920	0.0914598	+	0.995809i	$0.470847\pi$
$258$	4.35183e34	0.467936
$259$	−9.52848e32	−0.00968672
$260$	3.09444e34	0.297487
$261$	2.24423e34	0.204071
$262$	−1.13138e35	−0.973285
$263$	−9.17583e34	−0.746943	−0.373471	−	0.927642i	$-0.621833\pi$
$263$	−9.17583e34	−0.746943	−0.373471	+	0.927642i	$0.621833\pi$
$264$	5.64372e33	0.0434819
$265$	−8.94331e34	−0.652279
$266$	1.05342e35	0.727478
$267$	1.60051e35	1.04676
$268$	8.14012e34	0.504285
$269$	3.55748e34	0.208802	0.104401	−	0.994535i	$-0.466708\pi$
$269$	3.55748e34	0.208802	0.104401	+	0.994535i	$0.466708\pi$
$270$	−2.29310e34	−0.127541
$271$	1.77418e35	0.935282	0.467641	−	0.883919i	$-0.345104\pi$
$271$	1.77418e35	0.935282	0.467641	+	0.883919i	$0.345104\pi$
$272$	1.82975e35	0.914413
$273$	−6.53745e34	−0.309778
$274$	2.61939e35	1.17711
$275$	1.62824e34	0.0694057
$276$	3.21671e34	0.130086
$277$	−3.64812e35	−1.39995	−0.699976	−	0.714167i	$-0.746806\pi$
$277$	−3.64812e35	−1.39995	−0.699976	+	0.714167i	$0.746806\pi$
$278$	3.65877e35	1.33256
$279$	−1.04994e35	−0.362997
$280$	4.80642e34	0.157772
$281$	4.84579e34	0.151051	0.0755253	−	0.997144i	$-0.475937\pi$
$281$	4.84579e34	0.151051	0.0755253	+	0.997144i	$0.475937\pi$
$282$	2.64214e35	0.782247
$283$	1.48796e35	0.418492	0.209246	−	0.977863i	$-0.432899\pi$
$283$	1.48796e35	0.418492	0.209246	+	0.977863i	$0.432899\pi$
$284$	−1.03635e35	−0.276944
$285$	2.11654e35	0.537497
$286$	−7.03215e34	−0.169739
$287$	−8.96676e34	−0.205754
$288$	1.07885e35	0.235381
$289$	−2.16946e35	−0.450125
$290$	2.05591e35	0.405726
$291$	3.98931e35	0.748944
$292$	4.08476e35	0.729650
$293$	6.37168e35	1.08311	0.541556	−	0.840665i	$-0.317835\pi$
$293$	6.37168e35	1.08311	0.541556	+	0.840665i	$0.317835\pi$
$294$	5.96704e34	0.0965435
$295$	8.79519e34	0.135465
$296$	1.28850e34	0.0188954
$297$	1.40775e34	0.0196588
$298$	1.16518e36	1.54974
$299$	6.82062e35	0.864156
$300$	1.20285e35	0.145196
$301$	−2.27526e35	−0.261708
$302$	1.71173e35	0.187644
$303$	1.50515e34	0.0157276
$304$	−2.03547e36	−2.02767
$305$	−4.68086e35	−0.444609
$306$	3.19413e35	0.289329
$307$	−4.63359e35	−0.400323	−0.200162	−	0.979763i	$-0.564147\pi$
$307$	−4.63359e35	−0.400323	−0.200162	+	0.979763i	$0.564147\pi$
$308$	1.73394e34	0.0142906
$309$	−1.01160e36	−0.795449
$310$	−9.61833e35	−0.721697
$311$	−1.56436e36	−1.12024	−0.560122	−	0.828410i	$-0.689246\pi$
$311$	−1.56436e36	−1.12024	−0.560122	+	0.828410i	$0.689246\pi$
$312$	8.84037e35	0.604267
$313$	−2.02025e36	−1.31829	−0.659146	−	0.752015i	$-0.729082\pi$
$313$	−2.02025e36	−1.31829	−0.659146	+	0.752015i	$0.729082\pi$
$314$	6.61632e35	0.412227
$315$	1.19890e35	0.0713312
$316$	7.50504e34	0.0426472
$317$	1.23793e36	0.671949	0.335975	−	0.941871i	$-0.390934\pi$
$317$	1.23793e36	0.671949	0.335975	+	0.941871i	$0.390934\pi$
$318$	1.50140e36	0.778582
$319$	−1.26214e35	−0.0625376
$320$	−4.86145e35	−0.230193
$321$	−5.53251e35	−0.250380
$322$	−6.22551e35	−0.269318
$323$	−2.94819e36	−1.21932
$324$	1.03997e35	0.0411260
$325$	2.55049e36	0.964529
$326$	−6.37022e36	−2.30409
$327$	6.60864e35	0.228649
$328$	1.21254e36	0.401353
$329$	−1.38139e36	−0.437496
$330$	1.28962e35	0.0390850
$331$	2.46422e36	0.714782	0.357391	−	0.933955i	$-0.383666\pi$
$331$	2.46422e36	0.714782	0.357391	+	0.933955i	$0.383666\pi$
$332$	1.14965e36	0.319201
$333$	3.21400e34	0.00854289
$334$	5.27264e36	1.34185
$335$	−3.16531e36	−0.771378
$336$	−1.15298e36	−0.269092
$337$	3.49419e36	0.781112	0.390556	−	0.920579i	$-0.372283\pi$
$337$	3.49419e36	0.781112	0.390556	+	0.920579i	$0.372283\pi$
$338$	−5.54916e36	−1.18832
$339$	1.99860e36	0.410045
$340$	7.90469e35	0.155396
$341$	5.90475e35	0.111241
$342$	−3.55325e36	−0.641575
$343$	−3.11973e35	−0.0539949
$344$	3.07676e36	0.510500
$345$	−1.25083e36	−0.198985
$346$	−7.76438e36	−1.18441
$347$	−3.37726e36	−0.494068	−0.247034	−	0.969007i	$-0.579456\pi$
$347$	−3.37726e36	−0.494068	−0.247034	+	0.969007i	$0.579456\pi$
$348$	−9.32393e35	−0.130828
$349$	6.12071e36	0.823821	0.411911	−	0.911224i	$-0.364862\pi$
$349$	6.12071e36	0.823821	0.411911	+	0.911224i	$0.364862\pi$
$350$	−2.32796e36	−0.300599
$351$	2.20511e36	0.273198
$352$	−6.06737e35	−0.0721326
$353$	−8.12860e36	−0.927433	−0.463716	−	0.885984i	$-0.653484\pi$
$353$	−8.12860e36	−0.927433	−0.463716	+	0.885984i	$0.653484\pi$
$354$	−1.47654e36	−0.161695
$355$	4.02990e36	0.423626
$356$	−6.64952e36	−0.671066
$357$	−1.66998e36	−0.161816
$358$	−6.62422e35	−0.0616355
$359$	−2.01875e36	−0.180390	−0.0901949	−	0.995924i	$-0.528749\pi$
$359$	−2.01875e36	−0.180390	−0.0901949	+	0.995924i	$0.528749\pi$
$360$	−1.62123e36	−0.139142
$361$	2.06668e37	1.70380
$362$	−8.99548e36	−0.712443
$363$	7.50810e36	0.571326
$364$	2.71606e36	0.198595
$365$	−1.58837e37	−1.11611
$366$	7.85824e36	0.530700
$367$	3.25910e36	0.211563	0.105782	−	0.994389i	$-0.466266\pi$
$367$	3.25910e36	0.211563	0.105782	+	0.994389i	$0.466266\pi$
$368$	1.20292e37	0.750659
$369$	3.02453e36	0.181458
$370$	2.94430e35	0.0169847
$371$	−7.84976e36	−0.435446
$372$	4.36209e36	0.232714
$373$	−3.61204e36	−0.185342	−0.0926711	−	0.995697i	$-0.529541\pi$
$373$	−3.61204e36	−0.185342	−0.0926711	+	0.995697i	$0.529541\pi$
$374$	−1.79635e36	−0.0886651
$375$	−1.15614e37	−0.548979
$376$	1.86800e37	0.853401
$377$	−1.97702e37	−0.869083
$378$	−2.01271e36	−0.0851433
$379$	1.30977e37	0.533244	0.266622	−	0.963801i	$-0.414092\pi$
$379$	1.30977e37	0.533244	0.266622	+	0.963801i	$0.414092\pi$
$380$	−8.79342e36	−0.344585
$381$	−7.14733e36	−0.269608
$382$	−2.17206e37	−0.788777
$383$	4.10337e36	0.143469	0.0717346	−	0.997424i	$-0.477147\pi$
$383$	4.10337e36	0.143469	0.0717346	+	0.997424i	$0.477147\pi$
$384$	2.02711e37	0.682457
$385$	−6.74250e35	−0.0218595
$386$	−3.81251e37	−1.19041
$387$	7.67456e36	0.230805
$388$	−1.65741e37	−0.480141
$389$	6.54540e37	1.82670	0.913349	−	0.407177i	$-0.133487\pi$
$389$	6.54540e37	1.82670	0.913349	+	0.407177i	$0.133487\pi$
$390$	2.02007e37	0.543163
$391$	1.74232e37	0.451403
$392$	4.21871e36	0.105325
$393$	−1.99522e37	−0.480063
$394$	8.17290e37	1.89531
$395$	−2.91836e36	−0.0652351
$396$	−5.84867e35	−0.0126031
$397$	1.54960e37	0.321926	0.160963	−	0.986960i	$-0.448540\pi$
$397$	1.54960e37	0.321926	0.160963	+	0.986960i	$0.448540\pi$
$398$	−1.13240e38	−2.26828
$399$	1.85774e37	0.358821
$400$	4.49817e37	0.837850
$401$	−1.93698e37	−0.347961	−0.173981	−	0.984749i	$-0.555663\pi$
$401$	−1.93698e37	−0.347961	−0.173981	+	0.984749i	$0.555663\pi$
$402$	5.31393e37	0.920743
$403$	9.24925e37	1.54591
$404$	−6.25332e35	−0.0100828
$405$	−4.04394e36	−0.0629082
$406$	1.80452e37	0.270853
$407$	−1.80752e35	−0.00261797
$408$	2.25826e37	0.315647
$409$	−9.92557e37	−1.33896	−0.669480	−	0.742830i	$-0.733483\pi$
$409$	−9.92557e37	−1.33896	−0.669480	+	0.742830i	$0.733483\pi$
$410$	2.77073e37	0.360768
$411$	4.61935e37	0.580597
$412$	4.20282e37	0.509955
$413$	7.71975e36	0.0904331
$414$	2.09989e37	0.237516
$415$	−4.47046e37	−0.488265
$416$	−9.50397e37	−1.00242
$417$	6.45233e37	0.657270
$418$	1.99832e37	0.196611
$419$	−7.05447e37	−0.670441	−0.335221	−	0.942140i	$-0.608811\pi$
$419$	−7.05447e37	−0.670441	−0.335221	+	0.942140i	$0.608811\pi$
$420$	−4.98097e36	−0.0457298
$421$	−2.18248e37	−0.193580	−0.0967899	−	0.995305i	$-0.530857\pi$
$421$	−2.18248e37	−0.193580	−0.0967899	+	0.995305i	$0.530857\pi$
$422$	9.82912e37	0.842334
$423$	4.65948e37	0.385835
$424$	1.06150e38	0.849402
$425$	6.51519e37	0.503834
$426$	−6.76540e37	−0.505655
$427$	−4.10850e37	−0.296811
$428$	2.29855e37	0.160516
$429$	−1.24014e37	−0.0837218
$430$	7.03055e37	0.458878
$431$	3.31301e37	0.209075	0.104537	−	0.994521i	$-0.466664\pi$
$431$	3.31301e37	0.209075	0.104537	+	0.994521i	$0.466664\pi$
$432$	3.88905e37	0.237317
$433$	−2.78444e38	−1.64310	−0.821550	−	0.570136i	$-0.806890\pi$
$433$	−2.78444e38	−1.64310	−0.821550	+	0.570136i	$0.806890\pi$
$434$	−8.44223e37	−0.481788
$435$	3.62564e37	0.200120
$436$	−2.74564e37	−0.146585
$437$	−1.93821e38	−1.00097
$438$	2.66656e38	1.33222
$439$	−1.58600e38	−0.766597	−0.383299	−	0.923624i	$-0.625212\pi$
$439$	−1.58600e38	−0.766597	−0.383299	+	0.923624i	$0.625212\pi$
$440$	9.11765e36	0.0426402
$441$	1.05230e37	0.0476190
$442$	−2.81382e38	−1.23218
$443$	−1.72162e38	−0.729596	−0.364798	−	0.931087i	$-0.618862\pi$
$443$	−1.72162e38	−0.729596	−0.364798	+	0.931087i	$0.618862\pi$
$444$	−1.33529e36	−0.00547676
$445$	2.58569e38	1.02649
$446$	−4.02375e38	−1.54624
$447$	2.05483e38	0.764393
$448$	−4.26701e37	−0.153671
$449$	−4.26922e38	−1.48859	−0.744297	−	0.667848i	$-0.767216\pi$
$449$	−4.26922e38	−1.48859	−0.744297	+	0.667848i	$0.767216\pi$
$450$	7.85231e37	0.265104
$451$	−1.70097e37	−0.0556079
$452$	−8.30343e37	−0.262876
$453$	3.01868e37	0.0925536
$454$	−1.86471e38	−0.553736
$455$	−1.05615e38	−0.303781
$456$	−2.51216e38	−0.699933
$457$	−2.13623e38	−0.576585	−0.288293	−	0.957542i	$-0.593088\pi$
$457$	−2.13623e38	−0.576585	−0.288293	+	0.957542i	$0.593088\pi$
$458$	−5.42640e37	−0.141894
$459$	5.63292e37	0.142709
$460$	5.19672e37	0.127568
$461$	−2.38382e38	−0.567034	−0.283517	−	0.958967i	$-0.591501\pi$
$461$	−2.38382e38	−0.567034	−0.283517	+	0.958967i	$0.591501\pi$
$462$	1.13193e37	0.0260922
$463$	−4.51465e38	−1.00855	−0.504277	−	0.863542i	$-0.668241\pi$
$463$	−4.51465e38	−1.00855	−0.504277	+	0.863542i	$0.668241\pi$
$464$	−3.48677e38	−0.754940
$465$	−1.69621e38	−0.355970
$466$	3.33521e38	0.678465
$467$	3.63117e38	0.716063	0.358032	−	0.933710i	$-0.383448\pi$
$467$	3.63117e38	0.716063	0.358032	+	0.933710i	$0.383448\pi$
$468$	−9.16140e37	−0.175145
$469$	−2.77827e38	−0.514954
$470$	4.26848e38	0.767104
$471$	1.16680e38	0.203327
$472$	−1.04391e38	−0.176403
$473$	−4.31610e37	−0.0707303
$474$	4.89935e37	0.0778669
$475$	−7.24770e38	−1.11723
$476$	6.93813e37	0.103739
$477$	2.64776e38	0.384027
$478$	1.63243e39	2.29683
$479$	−8.90605e37	−0.121568	−0.0607841	−	0.998151i	$-0.519360\pi$
$479$	−8.90605e37	−0.121568	−0.0607841	+	0.998151i	$0.519360\pi$
$480$	1.74293e38	0.230824
$481$	−2.83132e37	−0.0363819
$482$	1.80389e38	0.224919
$483$	−1.09788e38	−0.132838
$484$	−3.11933e38	−0.366272
$485$	6.44488e38	0.734446
$486$	6.78898e37	0.0750894
$487$	1.24014e39	1.33138	0.665688	−	0.746230i	$-0.268138\pi$
$487$	1.24014e39	1.33138	0.665688	+	0.746230i	$0.268138\pi$
$488$	5.55579e38	0.578973
$489$	−1.12340e39	−1.13647
$490$	9.63998e37	0.0946745
$491$	−1.64061e39	−1.56432	−0.782159	−	0.623079i	$-0.785881\pi$
$491$	−1.64061e39	−1.56432	−0.782159	+	0.623079i	$0.785881\pi$
$492$	−1.25658e38	−0.116331
$493$	−5.05026e38	−0.453977
$494$	3.13018e39	2.73230
$495$	2.27428e37	0.0192783
$496$	1.63124e39	1.34287
$497$	3.53714e38	0.282803
$498$	7.50502e38	0.582809
$499$	2.34310e39	1.76739	0.883697	−	0.468059i	$-0.155046\pi$
$499$	2.34310e39	1.76739	0.883697	+	0.468059i	$0.155046\pi$
$500$	4.80330e38	0.351945
$501$	9.29842e38	0.661854
$502$	2.85689e39	1.97556
$503$	−2.69883e39	−1.81317	−0.906587	−	0.422018i	$-0.861322\pi$
$503$	−2.69883e39	−1.81317	−0.906587	+	0.422018i	$0.861322\pi$
$504$	−1.42299e38	−0.0928880
$505$	2.43163e37	0.0154231
$506$	−1.18096e38	−0.0727869
$507$	−9.78607e38	−0.586129
$508$	2.96944e38	0.172843
$509$	3.54744e38	0.200681	0.100341	−	0.994953i	$-0.468007\pi$
$509$	3.54744e38	0.200681	0.100341	+	0.994953i	$0.468007\pi$
$510$	5.16024e38	0.283728
$511$	−1.39415e39	−0.745087
$512$	7.39008e37	0.0383914
$513$	−6.26624e38	−0.316450
$514$	−4.36121e38	−0.214112
$515$	−1.63428e39	−0.780050
$516$	−3.18849e38	−0.147967
$517$	−2.62045e38	−0.118240
$518$	2.58428e37	0.0113386
$519$	−1.36927e39	−0.584199
$520$	1.42820e39	0.592569
$521$	−2.06872e39	−0.834747	−0.417373	−	0.908735i	$-0.637049\pi$
$521$	−2.06872e39	−0.834747	−0.417373	+	0.908735i	$0.637049\pi$
$522$	−6.08673e38	−0.238870
$523$	−1.00945e39	−0.385309	−0.192655	−	0.981267i	$-0.561710\pi$
$523$	−1.00945e39	−0.385309	−0.192655	+	0.981267i	$0.561710\pi$
$524$	8.28936e38	0.307764
$525$	−4.10541e38	−0.148268
$526$	2.48864e39	0.874317
$527$	2.36270e39	0.807524
$528$	−2.18716e38	−0.0727259
$529$	−1.94562e39	−0.629435
$530$	2.42558e39	0.763510
$531$	−2.60391e38	−0.0797545
$532$	−7.71820e38	−0.230037
$533$	−2.66441e39	−0.772781
$534$	−4.34086e39	−1.22526
$535$	−8.93798e38	−0.245533
$536$	3.75696e39	1.00449
$537$	−1.16820e38	−0.0304011
$538$	−9.64847e38	−0.244408
$539$	−5.91805e37	−0.0145929
$540$	1.68010e38	0.0403298
$541$	−5.61765e39	−1.31279	−0.656394	−	0.754418i	$-0.727919\pi$
$541$	−5.61765e39	−1.31279	−0.656394	+	0.754418i	$0.727919\pi$
$542$	−4.81187e39	−1.09477
$543$	−1.58637e39	−0.351405
$544$	−2.42777e39	−0.523629
$545$	1.06765e39	0.224223
$546$	1.77307e39	0.362603
$547$	2.28943e39	0.455944	0.227972	−	0.973668i	$-0.426791\pi$
$547$	2.28943e39	0.455944	0.227972	+	0.973668i	$0.426791\pi$
$548$	−1.91917e39	−0.372215
$549$	1.38582e39	0.261762
$550$	−4.41607e38	−0.0812413
$551$	5.61807e39	1.00667
$552$	1.48463e39	0.259120
$553$	−2.56152e38	−0.0435495
$554$	9.89432e39	1.63868
$555$	5.19234e37	0.00837751
$556$	−2.68070e39	−0.421370
$557$	8.41513e39	1.28873	0.644363	−	0.764720i	$-0.277123\pi$
$557$	8.41513e39	1.28873	0.644363	+	0.764720i	$0.277123\pi$
$558$	2.84761e39	0.424897
$559$	−6.76078e39	−0.982936
$560$	−1.86268e39	−0.263883
$561$	−3.16791e38	−0.0437331
$562$	−1.31426e39	−0.176809
$563$	−4.57960e39	−0.600422	−0.300211	−	0.953873i	$-0.597057\pi$
$563$	−4.57960e39	−0.600422	−0.300211	+	0.953873i	$0.597057\pi$
$564$	−1.93584e39	−0.247355
$565$	3.22882e39	0.402107
$566$	−4.03559e39	−0.489857
$567$	−3.54946e38	−0.0419961
$568$	−4.78315e39	−0.551649
$569$	9.08689e39	1.02162	0.510808	−	0.859695i	$-0.329346\pi$
$569$	9.08689e39	1.02162	0.510808	+	0.859695i	$0.329346\pi$
$570$	−5.74042e39	−0.629155
$571$	−5.16716e39	−0.552114	−0.276057	−	0.961141i	$-0.589028\pi$
$571$	−5.16716e39	−0.552114	−0.276057	+	0.961141i	$0.589028\pi$
$572$	5.15229e38	0.0536732
$573$	−3.83049e39	−0.389056
$574$	2.43193e39	0.240840
$575$	4.28323e39	0.413607
$576$	1.43928e39	0.135525
$577$	−1.49445e39	−0.137225	−0.0686125	−	0.997643i	$-0.521857\pi$
$577$	−1.49445e39	−0.137225	−0.0686125	+	0.997643i	$0.521857\pi$
$578$	5.88394e39	0.526884
$579$	−6.72345e39	−0.587155
$580$	−1.50632e39	−0.128295
$581$	−3.92383e39	−0.325954
$582$	−1.08197e40	−0.876659
$583$	−1.48908e39	−0.117686
$584$	1.88526e40	1.45340
$585$	3.56244e39	0.267909
$586$	−1.72811e40	−1.26781
$587$	3.95117e39	0.282796	0.141398	−	0.989953i	$-0.454840\pi$
$587$	3.95117e39	0.282796	0.141398	+	0.989953i	$0.454840\pi$
$588$	−4.37191e38	−0.0305281
$589$	−2.62835e40	−1.79065
$590$	−2.38540e39	−0.158565
$591$	1.44131e40	0.934843
$592$	−4.99346e38	−0.0316036
$593$	2.05944e40	1.27191	0.635955	−	0.771726i	$-0.280606\pi$
$593$	2.05944e40	1.27191	0.635955	+	0.771726i	$0.280606\pi$
$594$	−3.81806e38	−0.0230112
$595$	−2.69792e39	−0.158684
$596$	−8.53703e39	−0.490045
$597$	−1.99702e40	−1.11880
$598$	−1.84987e40	−1.01152
$599$	−3.34427e40	−1.78489	−0.892447	−	0.451152i	$-0.851013\pi$
$599$	−3.34427e40	−1.78489	−0.892447	+	0.451152i	$0.851013\pi$
$600$	5.55160e39	0.289218
$601$	2.47553e40	1.25889	0.629445	−	0.777045i	$-0.283282\pi$
$601$	2.47553e40	1.25889	0.629445	+	0.777045i	$0.283282\pi$
$602$	6.17088e39	0.306336
$603$	9.37124e39	0.454147
$604$	−1.25415e39	−0.0593352
$605$	1.21296e40	0.560266
$606$	−4.08222e38	−0.0184095
$607$	−4.62007e39	−0.203429	−0.101714	−	0.994814i	$-0.532433\pi$
$607$	−4.62007e39	−0.203429	−0.101714	+	0.994814i	$0.532433\pi$
$608$	2.70073e40	1.16113
$609$	3.18231e39	0.133596
$610$	1.26953e40	0.520427
$611$	−4.10469e40	−1.64317
$612$	−2.34026e39	−0.0914891
$613$	−7.49964e39	−0.286328	−0.143164	−	0.989699i	$-0.545728\pi$
$613$	−7.49964e39	−0.286328	−0.143164	+	0.989699i	$0.545728\pi$
$614$	1.25671e40	0.468589
$615$	4.88625e39	0.177945
$616$	8.00277e38	0.0284656
$617$	2.49274e40	0.866049	0.433025	−	0.901382i	$-0.357446\pi$
$617$	2.49274e40	0.866049	0.433025	+	0.901382i	$0.357446\pi$
$618$	2.74364e40	0.931094
$619$	−3.84040e40	−1.27310	−0.636549	−	0.771236i	$-0.719639\pi$
$619$	−3.84040e40	−1.27310	−0.636549	+	0.771236i	$0.719639\pi$
$620$	7.04712e39	0.228209
$621$	3.70321e39	0.117152
$622$	4.24282e40	1.31128
$623$	2.26952e40	0.685263
$624$	−3.42599e40	−1.01067
$625$	4.89525e39	0.141096
$626$	5.47925e40	1.54310
$627$	3.52408e39	0.0969764
$628$	−4.84762e39	−0.130351
$629$	−7.23256e38	−0.0190046
$630$	−3.25161e39	−0.0834951
$631$	1.06781e40	0.267959	0.133980	−	0.990984i	$-0.457224\pi$
$631$	1.06781e40	0.267959	0.133980	+	0.990984i	$0.457224\pi$
$632$	3.46385e39	0.0849496
$633$	1.73339e40	0.415472
$634$	−3.35747e40	−0.786535
$635$	−1.15468e40	−0.264388
$636$	−1.10004e40	−0.246196
$637$	−9.27008e39	−0.202797
$638$	3.42312e39	0.0732020
$639$	−1.19309e40	−0.249409
$640$	3.27488e40	0.669246
$641$	−3.61973e40	−0.723160	−0.361580	−	0.932341i	$-0.617763\pi$
$641$	−3.61973e40	−0.723160	−0.361580	+	0.932341i	$0.617763\pi$
$642$	1.50051e40	0.293076
$643$	−1.17054e40	−0.223526	−0.111763	−	0.993735i	$-0.535650\pi$
$643$	−1.17054e40	−0.223526	−0.111763	+	0.993735i	$0.535650\pi$
$644$	4.56128e39	0.0851613
$645$	1.23985e40	0.226337
$646$	7.99599e40	1.42725
$647$	6.69632e40	1.16876	0.584378	−	0.811482i	$-0.301339\pi$
$647$	6.69632e40	1.16876	0.584378	+	0.811482i	$0.301339\pi$
$648$	4.79982e39	0.0819195
$649$	1.46441e39	0.0244408
$650$	−6.91736e40	−1.12901
$651$	−1.48881e40	−0.237637
$652$	4.66731e40	0.728579
$653$	1.21063e41	1.84829	0.924145	−	0.382042i	$-0.124779\pi$
$653$	1.21063e41	1.84829	0.924145	+	0.382042i	$0.124779\pi$
$654$	−1.79237e40	−0.267640
$655$	−3.22335e40	−0.470769
$656$	−4.69908e40	−0.671286
$657$	4.70254e40	0.657105
$658$	3.74655e40	0.512101
$659$	1.33354e40	0.178307	0.0891536	−	0.996018i	$-0.471584\pi$
$659$	1.33354e40	0.178307	0.0891536	+	0.996018i	$0.471584\pi$
$660$	−9.44875e38	−0.0123591
$661$	9.92249e40	1.26970	0.634848	−	0.772637i	$-0.281063\pi$
$661$	9.92249e40	1.26970	0.634848	+	0.772637i	$0.281063\pi$
$662$	−6.68338e40	−0.836672
$663$	−4.96223e40	−0.607758
$664$	5.30606e40	0.635822
$665$	3.00125e40	0.351875
$666$	−8.71691e38	−0.00999968
$667$	−3.32016e40	−0.372678
$668$	−3.86314e40	−0.424309
$669$	−7.09598e40	−0.762665
$670$	8.58486e40	0.902919
$671$	−7.79372e39	−0.0802173
$672$	1.52981e40	0.154093
$673$	−5.23649e40	−0.516205	−0.258102	−	0.966118i	$-0.583097\pi$
$673$	−5.23649e40	−0.516205	−0.258102	+	0.966118i	$0.583097\pi$
$674$	−9.47684e40	−0.914313
$675$	1.38477e40	0.130760
$676$	4.06574e40	0.375762
$677$	−2.15200e41	−1.94674	−0.973369	−	0.229246i	$-0.926374\pi$
$677$	−2.15200e41	−1.94674	−0.973369	+	0.229246i	$0.926374\pi$
$678$	−5.42055e40	−0.479968
$679$	5.65682e40	0.490299
$680$	3.64830e40	0.309536
$681$	−3.28847e40	−0.273124
$682$	−1.60147e40	−0.130210
$683$	−2.16639e41	−1.72439	−0.862196	−	0.506575i	$-0.830911\pi$
$683$	−2.16639e41	−1.72439	−0.862196	+	0.506575i	$0.830911\pi$
$684$	2.60338e40	0.202873
$685$	7.46274e40	0.569358
$686$	8.46124e39	0.0632025
$687$	−9.56959e39	−0.0699875
$688$	−1.19236e41	−0.853840
$689$	−2.33250e41	−1.63547
$690$	3.39246e40	0.232918
$691$	−2.08878e41	−1.40431	−0.702153	−	0.712026i	$-0.747778\pi$
$691$	−2.08878e41	−1.40431	−0.702153	+	0.712026i	$0.747778\pi$
$692$	5.68878e40	0.374525
$693$	1.99619e39	0.0128697
$694$	9.15968e40	0.578320
$695$	1.04240e41	0.644547
$696$	−4.30333e40	−0.260598
$697$	−6.80619e40	−0.403672
$698$	−1.66004e41	−0.964305
$699$	5.88172e40	0.334646
$700$	1.70564e40	0.0950529
$701$	−3.07757e41	−1.67995	−0.839977	−	0.542623i	$-0.817431\pi$
$701$	−3.07757e41	−1.67995	−0.839977	+	0.542623i	$0.817431\pi$
$702$	−5.98064e40	−0.319786
$703$	8.04573e39	0.0421418
$704$	−8.09440e39	−0.0415319
$705$	7.52757e40	0.378366
$706$	2.20461e41	1.08559
$707$	2.13430e39	0.0102961
$708$	1.08182e40	0.0511298
$709$	−5.30993e40	−0.245877	−0.122939	−	0.992414i	$-0.539232\pi$
$709$	−5.30993e40	−0.245877	−0.122939	+	0.992414i	$0.539232\pi$
$710$	−1.09298e41	−0.495866
$711$	8.64012e39	0.0384070
$712$	−3.06900e41	−1.33671
$713$	1.55330e41	0.662912
$714$	4.52927e40	0.189410
$715$	−2.00349e40	−0.0821011
$716$	4.85341e39	0.0194898
$717$	2.87883e41	1.13289
$718$	5.47518e40	0.211151
$719$	5.27461e41	1.99352	0.996761	−	0.0804171i	$-0.0256252\pi$
$719$	5.27461e41	1.99352	0.996761	+	0.0804171i	$0.0256252\pi$
$720$	6.28290e40	0.232723
$721$	−1.43445e41	−0.520743
$722$	−5.60518e41	−1.99435
$723$	3.18119e40	0.110939
$724$	6.59078e40	0.225282
$725$	−1.24153e41	−0.415966
$726$	−2.03632e41	−0.668752
$727$	−1.47566e40	−0.0475047	−0.0237524	−	0.999718i	$-0.507561\pi$
$727$	−1.47566e40	−0.0475047	−0.0237524	+	0.999718i	$0.507561\pi$
$728$	1.25356e41	0.395585
$729$	1.19725e40	0.0370370
$730$	4.30793e41	1.30643
$731$	−1.72703e41	−0.513449
$732$	−5.75755e40	−0.167813
$733$	3.74098e41	1.06900	0.534500	−	0.845169i	$-0.320500\pi$
$733$	3.74098e41	1.06900	0.534500	+	0.845169i	$0.320500\pi$
$734$	−8.83922e40	−0.247640
$735$	1.70003e40	0.0466972
$736$	−1.59607e41	−0.429858
$737$	−5.27030e40	−0.139174
$738$	−8.20303e40	−0.212401
$739$	−2.43704e41	−0.618754	−0.309377	−	0.950939i	$-0.600120\pi$
$739$	−2.43704e41	−0.618754	−0.309377	+	0.950939i	$0.600120\pi$
$740$	−2.15722e39	−0.00537074
$741$	5.52014e41	1.34768
$742$	2.12899e41	0.509702
$743$	5.61424e41	1.31811	0.659057	−	0.752093i	$-0.270956\pi$
$743$	5.61424e41	1.31811	0.659057	+	0.752093i	$0.270956\pi$
$744$	2.01326e41	0.463546
$745$	3.31965e41	0.749595
$746$	9.79645e40	0.216948
$747$	1.32353e41	0.287465
$748$	1.31614e40	0.0280369
$749$	−7.84508e40	−0.163912
$750$	3.13563e41	0.642594
$751$	−2.95743e41	−0.594477	−0.297238	−	0.954803i	$-0.596066\pi$
$751$	−2.95743e41	−0.594477	−0.297238	+	0.954803i	$0.596066\pi$
$752$	−7.23923e41	−1.42736
$753$	5.03820e41	0.974425
$754$	5.36201e41	1.01729
$755$	4.87679e40	0.0907619
$756$	1.47467e40	0.0269233
$757$	−1.20093e41	−0.215094	−0.107547	−	0.994200i	$-0.534300\pi$
$757$	−1.20093e41	−0.215094	−0.107547	+	0.994200i	$0.534300\pi$
$758$	−3.55231e41	−0.624177
$759$	−2.08265e40	−0.0359014
$760$	−4.05848e41	−0.686384
$761$	1.07697e42	1.78701	0.893505	−	0.449052i	$-0.148238\pi$
$761$	1.07697e42	1.78701	0.893505	+	0.449052i	$0.148238\pi$
$762$	1.93848e41	0.315583
$763$	9.37102e40	0.149686
$764$	1.59142e41	0.249420
$765$	9.10020e40	0.139946
$766$	−1.11290e41	−0.167935
$767$	2.29387e41	0.339653
$768$	−3.88233e41	−0.564098
$769$	6.03811e41	0.860932	0.430466	−	0.902607i	$-0.358349\pi$
$769$	6.03811e41	0.860932	0.430466	+	0.902607i	$0.358349\pi$
$770$	1.82868e40	0.0255871
$771$	−7.69109e40	−0.105609
$772$	2.79334e41	0.376420
$773$	1.18764e42	1.57066	0.785332	−	0.619075i	$-0.212492\pi$
$773$	1.18764e42	1.57066	0.785332	+	0.619075i	$0.212492\pi$
$774$	−2.08147e41	−0.270163
$775$	5.80837e41	0.739911
$776$	−7.64953e41	−0.956400
$777$	4.55744e39	0.00559263
$778$	−1.77522e42	−2.13820
$779$	7.57142e41	0.895126
$780$	−1.48006e41	−0.171754
$781$	6.70985e40	0.0764316
$782$	−4.72545e41	−0.528379
$783$	−1.07341e41	−0.117820
$784$	−1.63492e41	−0.176162
$785$	1.88502e41	0.199391
$786$	5.41136e41	0.561926
$787$	−1.56586e41	−0.159631	−0.0798157	−	0.996810i	$-0.525433\pi$
$787$	−1.56586e41	−0.159631	−0.0798157	+	0.996810i	$0.525433\pi$
$788$	−5.98809e41	−0.599319
$789$	4.38877e41	0.431247
$790$	7.91509e40	0.0763595
$791$	2.83401e41	0.268437
$792$	−2.69937e40	−0.0251043
$793$	−1.22081e42	−1.11478
$794$	−4.20276e41	−0.376823
$795$	4.27756e41	0.376593
$796$	8.29684e41	0.717254
$797$	−1.63322e41	−0.138643	−0.0693215	−	0.997594i	$-0.522083\pi$
$797$	−1.63322e41	−0.138643	−0.0693215	+	0.997594i	$0.522083\pi$
$798$	−5.03850e41	−0.420010
$799$	−1.04854e42	−0.858332
$800$	−5.96833e41	−0.479786
$801$	−7.65520e41	−0.604345
$802$	5.25340e41	0.407298
$803$	−2.64467e41	−0.201370
$804$	−3.89339e41	−0.291149
$805$	−1.77367e41	−0.130267
$806$	−2.50855e42	−1.80953
$807$	−1.70153e41	−0.120552
$808$	−2.88613e40	−0.0200841
$809$	−1.65799e41	−0.113326	−0.0566629	−	0.998393i	$-0.518046\pi$
$809$	−1.65799e41	−0.113326	−0.0566629	+	0.998393i	$0.518046\pi$
$810$	1.09678e41	0.0736357
$811$	−2.89591e42	−1.90977	−0.954887	−	0.296968i	$-0.904025\pi$
$811$	−2.89591e42	−1.90977	−0.954887	+	0.296968i	$0.904025\pi$
$812$	−1.32213e41	−0.0856469
$813$	−8.48584e41	−0.539985
$814$	4.90231e39	0.00306441
$815$	−1.81490e42	−1.11447
$816$	−8.75163e41	−0.527937
$817$	1.92120e42	1.13855
$818$	2.69198e42	1.56729
$819$	3.12684e41	0.178850
$820$	−2.03005e41	−0.114079
$821$	2.99741e42	1.65490	0.827448	−	0.561543i	$-0.189792\pi$
$821$	2.99741e42	1.65490	0.827448	+	0.561543i	$0.189792\pi$
$822$	−1.25285e42	−0.679605
$823$	3.03988e42	1.62016	0.810082	−	0.586316i	$-0.199422\pi$
$823$	3.03988e42	1.62016	0.810082	+	0.586316i	$0.199422\pi$
$824$	1.93976e42	1.01579
$825$	−7.78784e40	−0.0400714
$826$	−2.09372e41	−0.105854
$827$	1.43971e42	0.715227	0.357613	−	0.933870i	$-0.383591\pi$
$827$	1.43971e42	0.715227	0.357613	+	0.933870i	$0.383591\pi$
$828$	−1.53854e41	−0.0751052
$829$	−2.00139e42	−0.960042	−0.480021	−	0.877257i	$-0.659371\pi$
$829$	−2.00139e42	−0.960042	−0.480021	+	0.877257i	$0.659371\pi$
$830$	1.21246e42	0.571527
$831$	1.74489e42	0.808263
$832$	−1.26791e42	−0.577167
$833$	−2.36803e41	−0.105934
$834$	−1.74998e42	−0.769353
$835$	1.50220e42	0.649042
$836$	−1.46412e41	−0.0621707
$837$	5.02182e41	0.209576
$838$	1.91329e42	0.784770
$839$	−2.16003e42	−0.870784	−0.435392	−	0.900241i	$-0.643390\pi$
$839$	−2.16003e42	−0.870784	−0.435392	+	0.900241i	$0.643390\pi$
$840$	−2.29890e41	−0.0910898
$841$	−1.60531e42	−0.625197
$842$	5.91925e41	0.226590
$843$	−2.31772e41	−0.0872091
$844$	−7.20157e41	−0.266355
$845$	−1.58098e42	−0.574782
$846$	−1.26373e42	−0.451631
$847$	1.06465e42	0.374021
$848$	−4.11371e42	−1.42067
$849$	−7.11686e41	−0.241617
$850$	−1.76703e42	−0.589752
$851$	−4.75485e40	−0.0156012
$852$	4.95685e41	0.159894
$853$	4.22776e42	1.34076	0.670378	−	0.742020i	$-0.266132\pi$
$853$	4.22776e42	1.34076	0.670378	+	0.742020i	$0.266132\pi$
$854$	1.11429e42	0.347425
$855$	−1.01234e42	−0.310324
$856$	1.06086e42	0.319735
$857$	−5.04412e42	−1.49473	−0.747366	−	0.664413i	$-0.768682\pi$
$857$	−5.04412e42	−1.49473	−0.747366	+	0.664413i	$0.768682\pi$
$858$	3.36345e41	0.0979986
$859$	4.00905e42	1.14853	0.574263	−	0.818671i	$-0.305289\pi$
$859$	4.00905e42	1.14853	0.574263	+	0.818671i	$0.305289\pi$
$860$	−5.15112e41	−0.145102
$861$	4.28877e41	0.118792
$862$	−8.98543e41	−0.244728
$863$	4.24119e42	1.13588	0.567938	−	0.823071i	$-0.307741\pi$
$863$	4.24119e42	1.13588	0.567938	+	0.823071i	$0.307741\pi$
$864$	−5.16012e41	−0.135897
$865$	−2.21210e42	−0.572890
$866$	7.55188e42	1.92329
$867$	1.03765e42	0.259880
$868$	6.18542e41	0.152347
$869$	−4.85912e40	−0.0117699
$870$	−9.83335e41	−0.234246
$871$	−8.25544e42	−1.93409
$872$	−1.26721e42	−0.291985
$873$	−1.90807e42	−0.432403
$874$	5.25675e42	1.17166
$875$	−1.63940e42	−0.359391
$876$	−1.95373e42	−0.421264
$877$	−5.08572e42	−1.07860	−0.539298	−	0.842115i	$-0.681310\pi$
$877$	−5.08572e42	−1.07860	−0.539298	+	0.842115i	$0.681310\pi$
$878$	4.30149e42	0.897323
$879$	−3.04755e42	−0.625335
$880$	−3.53345e41	−0.0713181
$881$	6.52827e42	1.29613	0.648063	−	0.761586i	$-0.275579\pi$
$881$	6.52827e42	1.29613	0.648063	+	0.761586i	$0.275579\pi$
$882$	−2.85402e41	−0.0557394
$883$	−8.47972e42	−1.62911	−0.814557	−	0.580083i	$-0.803020\pi$
$883$	−8.47972e42	−1.62911	−0.814557	+	0.580083i	$0.803020\pi$
$884$	2.06162e42	0.389628
$885$	−4.20671e41	−0.0782106
$886$	4.66932e42	0.854013
$887$	−1.33228e41	−0.0239720	−0.0119860	−	0.999928i	$-0.503815\pi$
$887$	−1.33228e41	−0.0239720	−0.0119860	+	0.999928i	$0.503815\pi$
$888$	−6.16287e40	−0.0109093
$889$	−1.01349e42	−0.176500
$890$	−7.01282e42	−1.20154
$891$	−6.73323e40	−0.0113500
$892$	2.94811e42	0.488937
$893$	1.16642e43	1.90331
$894$	−5.57304e42	−0.894742
$895$	−1.88727e41	−0.0298125
$896$	2.87444e42	0.446773
$897$	−3.26228e42	−0.498920
$898$	1.15788e43	1.74244
$899$	−4.50237e42	−0.666692
$900$	−5.75320e41	−0.0838288
$901$	−5.95833e42	−0.854310
$902$	4.61331e41	0.0650906
$903$	1.08825e42	0.151097
$904$	−3.83234e42	−0.523626
$905$	−2.56285e42	−0.344602
$906$	−8.18717e41	−0.108336
$907$	4.40769e42	0.573992	0.286996	−	0.957932i	$-0.407343\pi$
$907$	4.40769e42	0.573992	0.286996	+	0.957932i	$0.407343\pi$
$908$	1.36623e42	0.175097
$909$	−7.19908e40	−0.00908031
$910$	2.86445e42	0.355584
$911$	−5.03128e42	−0.614698	−0.307349	−	0.951597i	$-0.599442\pi$
$911$	−5.03128e42	−0.614698	−0.307349	+	0.951597i	$0.599442\pi$
$912$	9.73559e42	1.17068
$913$	−7.44340e41	−0.0880937
$914$	5.79382e42	0.674908
$915$	2.23884e42	0.256695
$916$	3.97580e41	0.0448683
$917$	−2.82921e42	−0.314275
$918$	−1.52774e42	−0.167044
$919$	−4.59793e42	−0.494866	−0.247433	−	0.968905i	$-0.579587\pi$
$919$	−4.59793e42	−0.494866	−0.247433	+	0.968905i	$0.579587\pi$
$920$	2.39848e42	0.254104
$921$	2.21623e42	0.231127
$922$	6.46531e42	0.663729
$923$	1.05104e43	1.06217
$924$	−8.29339e40	−0.00825066
$925$	−1.77802e41	−0.0174133
$926$	1.22445e43	1.18054
$927$	4.83847e42	0.459252
$928$	4.62636e42	0.432309
$929$	1.65009e43	1.51803	0.759015	−	0.651073i	$-0.225681\pi$
$929$	1.65009e43	1.51803	0.759015	+	0.651073i	$0.225681\pi$
$930$	4.60042e42	0.416672
$931$	2.63427e42	0.234903
$932$	−2.44363e42	−0.214538
$933$	7.48231e42	0.646773
$934$	−9.84833e42	−0.838171
$935$	−5.11787e41	−0.0428865
$936$	−4.22832e42	−0.348874
$937$	2.50322e42	0.203364	0.101682	−	0.994817i	$-0.467578\pi$
$937$	2.50322e42	0.203364	0.101682	+	0.994817i	$0.467578\pi$
$938$	7.53514e42	0.602768
$939$	9.66278e42	0.761116
$940$	−3.12742e42	−0.242567
$941$	−2.69242e42	−0.205633	−0.102817	−	0.994700i	$-0.532785\pi$
$941$	−2.69242e42	−0.205633	−0.102817	+	0.994700i	$0.532785\pi$
$942$	−3.16457e42	−0.237999
$943$	−4.47455e42	−0.331382
$944$	4.04558e42	0.295044
$945$	−5.73430e41	−0.0411831
$946$	1.17060e42	0.0827917
$947$	6.85882e42	0.477721	0.238861	−	0.971054i	$-0.423226\pi$
$947$	6.85882e42	0.477721	0.238861	+	0.971054i	$0.423226\pi$
$948$	−3.58964e41	−0.0246224
$949$	−4.14262e43	−2.79844
$950$	1.96570e43	1.30775
$951$	−5.92098e42	−0.387950
$952$	3.20220e42	0.206639
$953$	−2.25688e43	−1.43437	−0.717186	−	0.696882i	$-0.754570\pi$
$953$	−2.25688e43	−1.43437	−0.717186	+	0.696882i	$0.754570\pi$
$954$	−7.18117e42	−0.449515
$955$	−6.18830e42	−0.381524
$956$	−1.19604e43	−0.726285
$957$	6.03676e41	0.0361061
$958$	2.41547e42	0.142299
$959$	6.55023e42	0.380090
$960$	2.32522e42	0.132902
$961$	3.30190e42	0.185898
$962$	7.67901e41	0.0425860
$963$	2.64618e42	0.144557
$964$	−1.32166e42	−0.0711221
$965$	−1.08620e43	−0.575789
$966$	2.97764e42	0.155491
$967$	−2.67002e43	−1.37351	−0.686754	−	0.726890i	$-0.740965\pi$
$967$	−2.67002e43	−1.37351	−0.686754	+	0.726890i	$0.740965\pi$
$968$	−1.43968e43	−0.729582
$969$	1.41011e43	0.703977
$970$	−1.74796e43	−0.859689
$971$	−2.72035e43	−1.31809	−0.659045	−	0.752103i	$-0.729039\pi$
$971$	−2.72035e43	−1.31809	−0.659045	+	0.752103i	$0.729039\pi$
$972$	−4.97412e41	−0.0237441
$973$	9.14938e42	0.430284
$974$	−3.36347e43	−1.55841
$975$	−1.21989e43	−0.556871
$976$	−2.15309e43	−0.968365
$977$	−2.43296e43	−1.07811	−0.539056	−	0.842270i	$-0.681219\pi$
$977$	−2.43296e43	−1.07811	−0.539056	+	0.842270i	$0.681219\pi$
$978$	3.04686e43	1.33027
$979$	4.30522e42	0.185202
$980$	−7.06299e41	−0.0299371
$981$	−3.16089e42	−0.132011
$982$	4.44962e43	1.83108
$983$	4.11738e42	0.166953	0.0834767	−	0.996510i	$-0.473398\pi$
$983$	4.11738e42	0.166953	0.0834767	+	0.996510i	$0.473398\pi$
$984$	−5.79956e42	−0.231721
$985$	2.32849e43	0.916746
$986$	1.36972e43	0.531392
$987$	6.60712e42	0.252589
$988$	−2.29341e43	−0.863984
$989$	−1.13539e43	−0.421500
$990$	−6.16822e41	−0.0225657
$991$	−3.11122e43	−1.12166	−0.560831	−	0.827930i	$-0.689518\pi$
$991$	−3.11122e43	−1.12166	−0.560831	+	0.827930i	$0.689518\pi$
$992$	−2.16439e43	−0.768982
$993$	−1.17863e43	−0.412680
$994$	−9.59330e42	−0.331029
$995$	−3.22625e43	−1.09714
$996$	−5.49875e42	−0.184291
$997$	2.72028e43	0.898532	0.449266	−	0.893398i	$-0.351686\pi$
$997$	2.72028e43	0.898532	0.449266	+	0.893398i	$0.351686\pi$
$998$	−6.35489e43	−2.06878
$999$	−1.53725e41	−0.00493224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.b.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-27121.7 q^{2} -4.78297e6 q^{3} +1.98714e8 q^{4} -7.72707e9 q^{5} +1.29722e11 q^{6} -6.78223e11 q^{7} +9.17138e12 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q-27121.7 q^{2} -4.78297e6 q^{3} +1.98714e8 q^{4} -7.72707e9 q^{5} +1.29722e11 q^{6} -6.78223e11 q^{7} +9.17138e12 q^{8} +2.28768e13 q^{9} +2.09571e14 q^{10} -1.28657e14 q^{11} -9.50443e14 q^{12} -2.01529e16 q^{13} +1.83945e16 q^{14} +3.69583e16 q^{15} -3.55427e17 q^{16} -5.14803e17 q^{17} -6.20457e17 q^{18} +5.72683e18 q^{19} -1.53548e18 q^{20} +3.24392e18 q^{21} +3.48939e18 q^{22} -3.38443e19 q^{23} -4.38664e19 q^{24} -1.26557e20 q^{25} +5.46581e20 q^{26} -1.09419e20 q^{27} -1.34772e20 q^{28} +9.81008e20 q^{29} -1.00237e21 q^{30} -4.58953e21 q^{31} +4.71593e21 q^{32} +6.15362e20 q^{33} +1.39623e22 q^{34} +5.24068e21 q^{35} +4.54594e21 q^{36} +1.40492e21 q^{37} -1.55321e23 q^{38} +9.63908e22 q^{39} -7.08679e22 q^{40} +1.32210e23 q^{41} -8.79805e22 q^{42} +3.35474e23 q^{43} -2.55660e22 q^{44} -1.76771e23 q^{45} +9.17915e23 q^{46} +2.03677e24 q^{47} +1.70000e24 q^{48} +4.59987e23 q^{49} +3.43244e24 q^{50} +2.46229e24 q^{51} -4.00467e24 q^{52} +1.15740e25 q^{53} +2.96763e24 q^{54} +9.94141e23 q^{55} -6.22024e24 q^{56} -2.73913e25 q^{57} -2.66066e25 q^{58} -1.13823e25 q^{59} +7.34414e24 q^{60} +6.05775e25 q^{61} +1.24476e26 q^{62} -1.55156e25 q^{63} +6.29146e25 q^{64} +1.55723e26 q^{65} -1.66897e25 q^{66} +4.09640e26 q^{67} -1.02299e26 q^{68} +1.61876e26 q^{69} -1.42136e26 q^{70} -5.21530e26 q^{71} +2.09812e26 q^{72} +2.05559e27 q^{73} -3.81037e25 q^{74} +6.05318e26 q^{75} +1.13800e27 q^{76} +8.72581e25 q^{77} -2.61428e27 q^{78} +3.77681e26 q^{79} +2.74641e27 q^{80} +5.23348e26 q^{81} -3.58574e27 q^{82} +5.78546e27 q^{83} +6.44613e26 q^{84} +3.97792e27 q^{85} -9.09860e27 q^{86} -4.69213e27 q^{87} -1.17996e27 q^{88} -3.34627e28 q^{89} +4.79431e27 q^{90} +1.36682e28 q^{91} -6.72535e27 q^{92} +2.19516e28 q^{93} -5.52406e28 q^{94} -4.42516e28 q^{95} -2.25561e28 q^{96} -8.34065e28 q^{97} -1.24756e28 q^{98} -2.94326e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4177 q^{2} - 33480783 q^{3} + 1749008801 q^{4} - 1716792694 q^{5} - 19978461513 q^{6} - 4747561509943 q^{7} + 4282496015841 q^{8} + 160137547184727 q^{9}+O(q^{10}) \) 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

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Groups

Database

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