LMFDB - Embedded newform 3.30.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,30,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	3.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:	$15.9834127149$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 51006696x - 44860596480 $ x^3 - x^2 - 51006696*x - 44860596480
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-893.505$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9153.03 q^{2} +4.78297e6 q^{3} -4.53093e8 q^{4} +7.75011e7 q^{5} +4.37787e10 q^{6} +2.36726e12 q^{7} -9.06117e12 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q+9153.03 q^{2} +4.78297e6 q^{3} -4.53093e8 q^{4} +7.75011e7 q^{5} +4.37787e10 q^{6} +2.36726e12 q^{7} -9.06117e12 q^{8} +2.28768e13 q^{9} +7.09370e11 q^{10} +1.35102e15 q^{11} -2.16713e15 q^{12} -3.94372e15 q^{13} +2.16676e16 q^{14} +3.70685e14 q^{15} +1.60315e17 q^{16} +1.11421e18 q^{17} +2.09392e17 q^{18} +4.04379e18 q^{19} -3.51152e16 q^{20} +1.13225e19 q^{21} +1.23659e19 q^{22} +3.09684e19 q^{23} -4.33393e19 q^{24} -1.86259e20 q^{25} -3.60970e19 q^{26} +1.09419e20 q^{27} -1.07259e21 q^{28} -1.47473e21 q^{29} +3.39289e18 q^{30} +7.52674e20 q^{31} +6.33205e21 q^{32} +6.46187e21 q^{33} +1.01984e22 q^{34} +1.83466e20 q^{35} -1.03653e22 q^{36} -1.10676e21 q^{37} +3.70129e22 q^{38} -1.88627e22 q^{39} -7.02250e20 q^{40} -4.16650e23 q^{41} +1.03636e23 q^{42} +1.16313e23 q^{43} -6.12137e23 q^{44} +1.77298e21 q^{45} +2.83454e23 q^{46} +1.59110e24 q^{47} +7.66783e23 q^{48} +2.38403e24 q^{49} -1.70483e24 q^{50} +5.32924e24 q^{51} +1.78687e24 q^{52} -1.61284e25 q^{53} +1.00152e24 q^{54} +1.04705e23 q^{55} -2.14502e25 q^{56} +1.93413e25 q^{57} -1.34983e25 q^{58} -6.61892e25 q^{59} -1.67955e23 q^{60} +1.51472e26 q^{61} +6.88925e24 q^{62} +5.41554e25 q^{63} -2.81112e25 q^{64} -3.05643e23 q^{65} +5.91457e25 q^{66} +2.17774e26 q^{67} -5.04842e26 q^{68} +1.48121e26 q^{69} +1.67927e24 q^{70} +4.03644e26 q^{71} -2.07290e26 q^{72} -1.53956e27 q^{73} -1.01302e25 q^{74} -8.90869e26 q^{75} -1.83221e27 q^{76} +3.19821e27 q^{77} -1.72651e26 q^{78} +5.73849e27 q^{79} +1.24246e25 q^{80} +5.23348e26 q^{81} -3.81361e27 q^{82} +8.87856e27 q^{83} -5.13017e27 q^{84} +8.63527e25 q^{85} +1.06462e27 q^{86} -7.05361e27 q^{87} -1.22418e28 q^{88} -8.70301e26 q^{89} +1.62281e25 q^{90} -9.33584e27 q^{91} -1.40315e28 q^{92} +3.60002e27 q^{93} +1.45633e28 q^{94} +3.13398e26 q^{95} +3.02860e28 q^{96} +6.62073e27 q^{97} +2.18211e28 q^{98} +3.09069e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 11370 q^{2} + 14348907 q^{3} + 2104961700 q^{4} + 35492909586 q^{5} + 54382357530 q^{6} + 723913582632 q^{7} + 630313199016 q^{8} + 68630377364883 q^{9}+O(q^{10}) $ 3 * q + 11370 * q^2 + 14348907 * q^3 + 2104961700 * q^4 + 35492909586 * q^5 + 54382357530 * q^6 + 723913582632 * q^7 + 630313199016 * q^8 + 68630377364883 * q^9	$ 3 q + 11370 q^{2} + 14348907 q^{3} + 2104961700 q^{4} + 35492909586 q^{5} + 54382357530 q^{6} + 723913582632 q^{7} + 630313199016 q^{8} + 68630377364883 q^{9} - 334779369924996 q^{10} + 182675044475364 q^{11} + 10\!\cdots\!00 q^{12}+ \cdots + 41\!\cdots\!04 q^{99}+O(q^{100}) $ 3 * q + 11370 * q^2 + 14348907 * q^3 + 2104961700 * q^4 + 35492909586 * q^5 + 54382357530 * q^6 + 723913582632 * q^7 + 630313199016 * q^8 + 68630377364883 * q^9 - 334779369924996 * q^10 + 182675044475364 * q^11 + 10067966557287300 * q^12 + 9259572716201562 * q^13 - 120450158787784656 * q^14 + 169761486269640834 * q^15 + 1500169356985987344 * q^16 + 1072198906119498006 * q^17 + 260109130212906570 * q^18 + 3573738022673838588 * q^19 + 44431358843563300824 * q^20 + 3462456224407794408 * q^21 + 5937948604649594232 * q^22 + 2255441009197226856 * q^23 + 3014768491184358504 * q^24 + 107032338789541191021 * q^25 - 1497743341450819295124 * q^26 + 328256967394537077627 * q^27 - 3485513041911356199456 * q^28 + 975758353867945445466 * q^29 - 1601239348190788193124 * q^30 - 4310795768757336364368 * q^31 + 18876913054489573214112 * q^32 + 873729074799287275716 * q^33 + 67866341166487703151540 * q^34 - 14430259494134233374480 * q^35 + 48154771936541879993700 * q^36 - 27925678122459232189278 * q^37 - 142225433880276730339128 * q^38 + 44288249254837868797578 * q^39 - 108129617802599394192912 * q^40 - 69804619608851288718978 * q^41 - 576109375527051588323664 * q^42 - 693740310522122827674876 * q^43 - 2117857779499564977572688 * q^44 + 811963926221617750156146 * q^45 + 4620020103570468708081072 * q^46 + 1415959067390344943290608 * q^47 + 7175263529213910900744336 * q^48 + 2717825625267246250755723 * q^49 - 14651511011848257291000906 * q^50 + 5128294129803469258259814 * q^51 + 15401377033141462317909816 * q^52 + 2026116337260643996537026 * q^53 + 1244093906425295524206330 * q^54 - 20053964151511832211741864 * q^55 - 133879896037691995933089600 * q^56 + 17093078176570267077407772 * q^57 + 35308629357282460210284 * q^58 - 93305348607139212212742828 * q^59 + 212513811976639117378866456 * q^60 + 303096806772905191169090058 * q^61 - 362197525390562802152486496 * q^62 + 16560820785199524011837352 * q^63 + 265015022439684481406008896 * q^64 + 385927454665853764096033308 * q^65 + 28401024099632265074234808 * q^66 + 500799740942105395447763436 * q^67 - 430625977045044540127774200 * q^68 + 10787704428319050938215464 * q^69 - 2190923137138139447805738720 * q^70 + 231230996481801316056262776 * q^71 + 14419544235511560009518376 * q^72 + 63673289690883398415029886 * q^73 - 2938186329272588530875918756 * q^74 + 511932358427873040876521349 * q^75 - 2829633149821337155975657008 * q^76 + 4356628994062266983065035744 * q^77 - 7163659972115683713179943156 * q^78 + 7376231996756310126608131200 * q^79 + 22058960811505567152859842144 * q^80 + 1570042899082081611640534563 * q^81 - 12650067164628128121047255196 * q^82 + 27036927173545438643676286140 * q^83 - 16671100828557717449955864864 * q^84 - 6616892900361929463852172668 * q^85 - 21916001609490835312699050696 * q^86 + 4667021958041413159355068554 * q^87 - 21725279583477486875112151584 * q^88 - 18847541326307829508910067282 * q^89 - 7658678163976746013278105156 * q^90 + 36882675140537353230223738032 * q^91 - 41071545648724713668735716128 * q^92 - 20618402527297508353344848592 * q^93 - 60355386135226788370381393632 * q^94 + 10443256900314201021920744424 * q^95 + 90287689955318939506328058528 * q^96 - 25821730694946372903788747034 * q^97 + 252746844211061743934170389978 * q^98 + 4179019079163672261844080804 * 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 $

$2$	9153.03	0.395030	0.197515	−	0.980300i	$-0.436713\pi$
$2$	9153.03	0.395030	0.197515	+	0.980300i	$0.436713\pi$
$3$	4.78297e6	0.577350
$3$	4.78297e6	0.577350
$4$	−4.53093e8	−0.843951
$5$	7.75011e7	0.00567862	0.00283931	−	0.999996i	$-0.499096\pi$
$5$	7.75011e7	0.00567862	0.00283931	+	0.999996i	$0.499096\pi$
$6$	4.37787e10	0.228071
$7$	2.36726e12	1.31924	0.659622	−	0.751598i	$-0.270716\pi$
$7$	2.36726e12	1.31924	0.659622	+	0.751598i	$0.270716\pi$
$8$	−9.06117e12	−0.728416
$9$	2.28768e13	0.333333
$10$	7.09370e11	0.00224322
$11$	1.35102e15	1.07267	0.536336	−	0.844005i	$-0.319808\pi$
$11$	1.35102e15	1.07267	0.536336	+	0.844005i	$0.319808\pi$
$12$	−2.16713e15	−0.487256
$13$	−3.94372e15	−0.277797	−0.138899	−	0.990307i	$-0.544356\pi$
$13$	−3.94372e15	−0.277797	−0.138899	+	0.990307i	$0.544356\pi$
$14$	2.16676e16	0.521141
$15$	3.70685e14	0.00327855
$16$	1.60315e17	0.556205
$17$	1.11421e18	1.60494	0.802469	−	0.596693i	$-0.203519\pi$
$17$	1.11421e18	1.60494	0.802469	+	0.596693i	$0.203519\pi$
$18$	2.09392e17	0.131677
$19$	4.04379e18	1.16108	0.580539	−	0.814232i	$-0.302842\pi$
$19$	4.04379e18	1.16108	0.580539	+	0.814232i	$0.302842\pi$
$20$	−3.51152e16	−0.00479248
$21$	1.13225e19	0.761666
$22$	1.23659e19	0.423737
$23$	3.09684e19	0.557012	0.278506	−	0.960434i	$-0.410161\pi$
$23$	3.09684e19	0.557012	0.278506	+	0.960434i	$0.410161\pi$
$24$	−4.33393e19	−0.420551
$25$	−1.86259e20	−0.999968
$26$	−3.60970e19	−0.109738
$27$	1.09419e20	0.192450
$28$	−1.07259e21	−1.11338
$29$	−1.47473e21	−0.920328	−0.460164	−	0.887834i	$-0.652209\pi$
$29$	−1.47473e21	−0.920328	−0.460164	+	0.887834i	$0.652209\pi$
$30$	3.39289e18	0.00129513
$31$	7.52674e20	0.178592	0.0892961	−	0.996005i	$-0.471538\pi$
$31$	7.52674e20	0.178592	0.0892961	+	0.996005i	$0.471538\pi$
$32$	6.33205e21	0.948134
$33$	6.46187e21	0.619308
$34$	1.01984e22	0.633999
$35$	1.83466e20	0.00749148
$36$	−1.03653e22	−0.281317
$37$	−1.10676e21	−0.0201896	−0.0100948	−	0.999949i	$-0.503213\pi$
$37$	−1.10676e21	−0.0201896	−0.0100948	+	0.999949i	$0.503213\pi$
$38$	3.70129e22	0.458660
$39$	−1.88627e22	−0.160386
$40$	−7.02250e20	−0.00413640
$41$	−4.16650e23	−1.71556	−0.857780	−	0.514017i	$-0.828157\pi$
$41$	−4.16650e23	−1.71556	−0.857780	+	0.514017i	$0.828157\pi$
$42$	1.03636e23	0.300881
$43$	1.16313e23	0.240069	0.120035	−	0.992770i	$-0.461699\pi$
$43$	1.16313e23	0.240069	0.120035	+	0.992770i	$0.461699\pi$
$44$	−6.12137e23	−0.905283
$45$	1.77298e21	0.00189287
$46$	2.83454e23	0.220036
$47$	1.59110e24	0.904227	0.452113	−	0.891960i	$-0.350670\pi$
$47$	1.59110e24	0.904227	0.452113	+	0.891960i	$0.350670\pi$
$48$	7.66783e23	0.321125
$49$	2.38403e24	0.740404
$50$	−1.70483e24	−0.395017
$51$	5.32924e24	0.926612
$52$	1.78687e24	0.234447
$53$	−1.61284e25	−1.60543	−0.802715	−	0.596363i	$-0.796612\pi$
$53$	−1.61284e25	−1.60543	−0.802715	+	0.596363i	$0.796612\pi$
$54$	1.00152e24	0.0760235
$55$	1.04705e23	0.00609130
$56$	−2.14502e25	−0.960958
$57$	1.93413e25	0.670349
$58$	−1.34983e25	−0.363557
$59$	−6.61892e25	−1.39134	−0.695669	−	0.718362i	$-0.744892\pi$
$59$	−6.61892e25	−1.39134	−0.695669	+	0.718362i	$0.744892\pi$
$60$	−1.67955e23	−0.00276694
$61$	1.51472e26	1.96358	0.981790	−	0.189967i	$-0.0608381\pi$
$61$	1.51472e26	1.96358	0.981790	+	0.189967i	$0.0608381\pi$
$62$	6.88925e24	0.0705493
$63$	5.41554e25	0.439748
$64$	−2.81112e25	−0.181664
$65$	−3.05643e23	−0.00157751
$66$	5.91457e25	0.244645
$67$	2.17774e26	0.724303	0.362152	−	0.932119i	$-0.382042\pi$
$67$	2.17774e26	0.724303	0.362152	+	0.932119i	$0.382042\pi$
$68$	−5.04842e26	−1.35449
$69$	1.48121e26	0.321591
$70$	1.67927e24	0.00295936
$71$	4.03644e26	0.579098	0.289549	−	0.957163i	$-0.406495\pi$
$71$	4.03644e26	0.579098	0.289549	+	0.957163i	$0.406495\pi$
$72$	−2.07290e26	−0.242805
$73$	−1.53956e27	−1.47644	−0.738219	−	0.674561i	$-0.764333\pi$
$73$	−1.53956e27	−1.47644	−0.738219	+	0.674561i	$0.764333\pi$
$74$	−1.01302e25	−0.00797549
$75$	−8.90869e26	−0.577332
$76$	−1.83221e27	−0.979893
$77$	3.19821e27	1.41512
$78$	−1.72651e26	−0.0633574
$79$	5.73849e27	1.75067	0.875336	−	0.483515i	$-0.160640\pi$
$79$	5.73849e27	1.75067	0.875336	+	0.483515i	$0.160640\pi$
$80$	1.24246e25	0.00315848
$81$	5.23348e26	0.111111
$82$	−3.81361e27	−0.677697
$83$	8.87856e27	1.32346	0.661729	−	0.749743i	$-0.269823\pi$
$83$	8.87856e27	1.32346	0.661729	+	0.749743i	$0.269823\pi$
$84$	−5.13017e27	−0.642809
$85$	8.63527e25	0.00911384
$86$	1.06462e27	0.0948345
$87$	−7.05361e27	−0.531352
$88$	−1.22418e28	−0.781351
$89$	−8.70301e26	−0.0471536	−0.0235768	−	0.999722i	$-0.507505\pi$
$89$	−8.70301e26	−0.0471536	−0.0235768	+	0.999722i	$0.507505\pi$
$90$	1.62281e25	0.000747741 0
$91$	−9.33584e27	−0.366482
$92$	−1.40315e28	−0.470091
$93$	3.60002e27	0.103110
$94$	1.45633e28	0.357197
$95$	3.13398e26	0.00659332
$96$	3.02860e28	0.547405
$97$	6.62073e27	0.102971	0.0514856	−	0.998674i	$-0.483604\pi$
$97$	6.62073e27	0.102971	0.0514856	+	0.998674i	$0.483604\pi$
$98$	2.18211e28	0.292482
$99$	3.09069e28	0.357557
$100$	8.43924e28	0.843924
$101$	−1.56380e29	−1.35370	−0.676848	−	0.736122i	$-0.736655\pi$
$101$	−1.56380e29	−1.35370	−0.676848	+	0.736122i	$0.736655\pi$
$102$	4.87787e28	0.366039
$103$	9.92518e28	0.646545	0.323272	−	0.946306i	$-0.395217\pi$
$103$	9.92518e28	0.646545	0.323272	+	0.946306i	$0.395217\pi$
$104$	3.57347e28	0.202352
$105$	8.77510e26	0.00432521
$106$	−1.47624e29	−0.634192
$107$	−2.74064e29	−1.02751	−0.513757	−	0.857936i	$-0.671747\pi$
$107$	−2.74064e29	−1.02751	−0.513757	+	0.857936i	$0.671747\pi$
$108$	−4.95770e28	−0.162419
$109$	−6.74460e28	−0.193318	−0.0966589	−	0.995318i	$-0.530816\pi$
$109$	−6.74460e28	−0.193318	−0.0966589	+	0.995318i	$0.530816\pi$
$110$	9.58371e26	0.00240624
$111$	−5.29358e27	−0.0116565
$112$	3.79509e29	0.733771
$113$	−7.57991e29	−1.28833	−0.644165	−	0.764887i	$-0.722795\pi$
$113$	−7.57991e29	−1.28833	−0.644165	+	0.764887i	$0.722795\pi$
$114$	1.77032e29	0.264808
$115$	2.40008e27	0.00316306
$116$	6.68192e29	0.776712
$117$	−9.02198e28	−0.0925991
$118$	−6.05831e29	−0.549620
$119$	2.63763e30	2.11731
$120$	−3.35884e27	−0.00238815
$121$	2.38939e29	0.150626
$122$	1.38642e30	0.775673
$123$	−1.99283e30	−0.990479
$124$	−3.41031e29	−0.150723
$125$	−2.88709e28	−0.0113571
$126$	4.95686e29	0.173714
$127$	−5.24769e30	−1.63989	−0.819944	−	0.572443i	$-0.805996\pi$
$127$	−5.24769e30	−1.63989	−0.819944	+	0.572443i	$0.805996\pi$
$128$	−3.65680e30	−1.01990
$129$	5.56323e29	0.138604
$130$	−2.79756e27	−0.000623162 0
$131$	2.23400e30	0.445296	0.222648	−	0.974899i	$-0.428530\pi$
$131$	2.23400e30	0.445296	0.222648	+	0.974899i	$0.428530\pi$
$132$	−2.92783e30	−0.522666
$133$	9.57272e30	1.53174
$134$	1.99329e30	0.286121
$135$	8.48009e27	0.00109285
$136$	−1.00961e31	−1.16906
$137$	−1.88653e30	−0.196434	−0.0982169	−	0.995165i	$-0.531314\pi$
$137$	−1.88653e30	−0.196434	−0.0982169	+	0.995165i	$0.531314\pi$
$138$	1.35575e30	0.127038
$139$	1.55928e31	1.31586	0.657929	−	0.753080i	$-0.271433\pi$
$139$	1.55928e31	1.31586	0.657929	+	0.753080i	$0.271433\pi$
$140$	−8.31270e28	−0.00632245
$141$	7.61016e30	0.522056
$142$	3.69456e30	0.228761
$143$	−5.32804e30	−0.297985
$144$	3.66750e30	0.185402
$145$	−1.14293e29	−0.00522619
$146$	−1.40916e31	−0.583237
$147$	1.14028e31	0.427473
$148$	5.01464e29	0.0170390
$149$	−2.71650e31	−0.837161	−0.418581	−	0.908180i	$-0.637472\pi$
$149$	−2.71650e31	−0.837161	−0.418581	+	0.908180i	$0.637472\pi$
$150$	−8.15415e30	−0.228063
$151$	−3.09724e31	−0.786701	−0.393350	−	0.919389i	$-0.628684\pi$
$151$	−3.09724e31	−0.786701	−0.393350	+	0.919389i	$0.628684\pi$
$152$	−3.66415e31	−0.845748
$153$	2.54896e31	0.534980
$154$	2.92733e31	0.559013
$155$	5.83331e28	0.00101416
$156$	8.54656e30	0.135358
$157$	−1.22949e31	−0.177493	−0.0887465	−	0.996054i	$-0.528286\pi$
$157$	−1.22949e31	−0.177493	−0.0887465	+	0.996054i	$0.528286\pi$
$158$	5.25246e31	0.691568
$159$	−7.71416e31	−0.926895
$160$	4.90741e29	0.00538409
$161$	7.33103e31	0.734835
$162$	4.79022e30	0.0438922
$163$	4.96668e31	0.416242	0.208121	−	0.978103i	$-0.433265\pi$
$163$	4.96668e31	0.416242	0.208121	+	0.978103i	$0.433265\pi$
$164$	1.88781e32	1.44785
$165$	5.00802e29	0.00351681
$166$	8.12658e31	0.522806
$167$	−1.10300e32	−0.650409	−0.325204	−	0.945644i	$-0.605433\pi$
$167$	−1.10300e32	−0.650409	−0.325204	+	0.945644i	$0.605433\pi$
$168$	−1.02596e32	−0.554809
$169$	−1.85985e32	−0.922829
$170$	7.90388e29	0.00360024
$171$	9.25089e31	0.387026
$172$	−5.27007e31	−0.202607
$173$	−6.99192e31	−0.247131	−0.123566	−	0.992336i	$-0.539433\pi$
$173$	−6.99192e31	−0.247131	−0.123566	+	0.992336i	$0.539433\pi$
$174$	−6.45619e31	−0.209900
$175$	−4.40923e32	−1.31920
$176$	2.16589e32	0.596626
$177$	−3.16581e32	−0.803290
$178$	−7.96589e30	−0.0186271
$179$	2.53504e32	0.546533	0.273267	−	0.961938i	$-0.411896\pi$
$179$	2.53504e32	0.546533	0.273267	+	0.961938i	$0.411896\pi$
$180$	−8.03323e29	−0.00159749
$181$	3.91829e32	0.719047	0.359524	−	0.933136i	$-0.382939\pi$
$181$	3.91829e32	0.719047	0.359524	+	0.933136i	$0.382939\pi$
$182$	−8.54512e31	−0.144771
$183$	7.24484e32	1.13367
$184$	−2.80609e32	−0.405736
$185$	−8.57749e28	−0.000114649 0
$186$	3.29511e31	0.0407316
$187$	1.50532e33	1.72157
$188$	−7.20914e32	−0.763124
$189$	2.59024e32	0.253889
$190$	2.86854e30	0.00260456
$191$	−1.28910e33	−1.08468	−0.542340	−	0.840159i	$-0.682462\pi$
$191$	−1.28910e33	−1.08468	−0.542340	+	0.840159i	$0.682462\pi$
$192$	−1.34455e32	−0.104884
$193$	4.97838e32	0.360169	0.180085	−	0.983651i	$-0.442363\pi$
$193$	4.97838e32	0.360169	0.180085	+	0.983651i	$0.442363\pi$
$194$	6.05997e31	0.0406767
$195$	−1.46188e30	−0.000910773 0
$196$	−1.08019e33	−0.624865
$197$	−1.55767e33	−0.836982	−0.418491	−	0.908221i	$-0.637441\pi$
$197$	−1.55767e33	−0.836982	−0.418491	+	0.908221i	$0.637441\pi$
$198$	2.82892e32	0.141246
$199$	7.04836e32	0.327129	0.163564	−	0.986533i	$-0.447701\pi$
$199$	7.04836e32	0.327129	0.163564	+	0.986533i	$0.447701\pi$
$200$	1.68772e33	0.728392
$201$	1.04160e33	0.418177
$202$	−1.43135e33	−0.534751
$203$	−3.49108e33	−1.21414
$204$	−2.41464e33	−0.782015
$205$	−3.22909e31	−0.00974201
$206$	9.08454e32	0.255404
$207$	7.08457e32	0.185671
$208$	−6.32239e32	−0.154512
$209$	5.46323e33	1.24546
$210$	8.03187e30	0.00170859
$211$	1.94928e33	0.387060	0.193530	−	0.981094i	$-0.438006\pi$
$211$	1.94928e33	0.387060	0.193530	+	0.981094i	$0.438006\pi$
$212$	7.30766e33	1.35490
$213$	1.93062e33	0.334342
$214$	−2.50852e33	−0.405898
$215$	9.01440e30	0.00136326
$216$	−9.91464e32	−0.140184
$217$	1.78178e33	0.235607
$218$	−6.17335e32	−0.0763663
$219$	−7.36367e33	−0.852422
$220$	−4.74413e31	−0.00514076
$221$	−4.39414e33	−0.445848
$222$	−4.84523e31	−0.00460465
$223$	−1.28703e34	−1.14596	−0.572980	−	0.819569i	$-0.694213\pi$
$223$	−1.28703e34	−1.14596	−0.572980	+	0.819569i	$0.694213\pi$
$224$	1.49896e34	1.25082
$225$	−4.26100e33	−0.333323
$226$	−6.93792e33	−0.508928
$227$	−7.13668e33	−0.491045	−0.245523	−	0.969391i	$-0.578960\pi$
$227$	−7.13668e33	−0.491045	−0.245523	+	0.969391i	$0.578960\pi$
$228$	−8.76342e33	−0.565742
$229$	7.76578e33	0.470512	0.235256	−	0.971933i	$-0.424407\pi$
$229$	7.76578e33	0.470512	0.235256	+	0.971933i	$0.424407\pi$
$230$	2.19680e31	0.00124950
$231$	1.52970e34	0.817018
$232$	1.33628e34	0.670382
$233$	−4.12470e34	−1.94416	−0.972079	−	0.234655i	$-0.924604\pi$
$233$	−4.12470e34	−1.94416	−0.972079	+	0.234655i	$0.924604\pi$
$234$	−8.25784e32	−0.0365794
$235$	1.23312e32	0.00513476
$236$	2.99898e34	1.17422
$237$	2.74470e34	1.01075
$238$	2.41423e34	0.836399
$239$	−1.41693e34	−0.461933	−0.230967	−	0.972962i	$-0.574189\pi$
$239$	−1.41693e34	−0.461933	−0.230967	+	0.972962i	$0.574189\pi$
$240$	5.94265e31	0.00182355
$241$	4.46480e34	1.28990	0.644949	−	0.764226i	$-0.276879\pi$
$241$	4.46480e34	1.28990	0.644949	+	0.764226i	$0.276879\pi$
$242$	2.18701e33	0.0595016
$243$	2.50316e33	0.0641500
$244$	−6.86308e34	−1.65717
$245$	1.84765e32	0.00420447
$246$	−1.82404e34	−0.391269
$247$	−1.59476e34	−0.322544
$248$	−6.82011e33	−0.130089
$249$	4.24659e34	0.764099
$250$	−2.64257e32	−0.00448638
$251$	−6.47628e34	−1.03766	−0.518832	−	0.854876i	$-0.673633\pi$
$251$	−6.47628e34	−1.03766	−0.518832	+	0.854876i	$0.673633\pi$
$252$	−2.45374e34	−0.371126
$253$	4.18388e34	0.597491
$254$	−4.80323e34	−0.647805
$255$	4.13022e32	0.00526188
$256$	−1.83787e34	−0.221225
$257$	3.25353e34	0.370105	0.185052	−	0.982729i	$-0.440755\pi$
$257$	3.25353e34	0.370105	0.185052	+	0.982729i	$0.440755\pi$
$258$	5.09204e33	0.0547527
$259$	−2.61999e33	−0.0266350
$260$	1.38485e32	0.00133134
$261$	−3.37372e34	−0.306776
$262$	2.04478e34	0.175905
$263$	1.22094e35	0.993884	0.496942	−	0.867784i	$-0.334456\pi$
$263$	1.22094e35	0.993884	0.496942	+	0.867784i	$0.334456\pi$
$264$	−5.85521e34	−0.451113
$265$	−1.24997e33	−0.00911662
$266$	8.76194e34	0.605085
$267$	−4.16262e33	−0.0272241
$268$	−9.86717e34	−0.611277
$269$	1.59102e35	0.933832	0.466916	−	0.884302i	$-0.345365\pi$
$269$	1.59102e35	0.933832	0.466916	+	0.884302i	$0.345365\pi$
$270$	7.76185e31	0.000431709 0
$271$	1.27779e35	0.673603	0.336801	−	0.941576i	$-0.390655\pi$
$271$	1.27779e35	0.673603	0.336801	+	0.941576i	$0.390655\pi$
$272$	1.78625e35	0.892676
$273$	−4.46530e34	−0.211589
$274$	−1.72675e34	−0.0775972
$275$	−2.51638e35	−1.07264
$276$	−6.71124e34	−0.271407
$277$	−1.91741e35	−0.735797	−0.367899	−	0.929866i	$-0.619923\pi$
$277$	−1.91741e35	−0.735797	−0.367899	+	0.929866i	$0.619923\pi$
$278$	1.42721e35	0.519803
$279$	1.72188e34	0.0595307
$280$	−1.66241e33	−0.00545692
$281$	1.28520e35	0.400616	0.200308	−	0.979733i	$-0.435806\pi$
$281$	1.28520e35	0.400616	0.200308	+	0.979733i	$0.435806\pi$
$282$	6.96560e34	0.206228
$283$	−5.57469e35	−1.56790	−0.783949	−	0.620825i	$-0.786798\pi$
$283$	−5.57469e35	−1.56790	−0.783949	+	0.620825i	$0.786798\pi$
$284$	−1.82888e35	−0.488731
$285$	1.49897e33	0.00380666
$286$	−4.87677e34	−0.117713
$287$	−9.86322e35	−2.26324
$288$	1.44857e35	0.316045
$289$	7.59500e35	1.57583
$290$	−1.04613e33	−0.00206450
$291$	3.16667e34	0.0594504
$292$	6.97564e35	1.24604
$293$	6.37121e35	1.08303	0.541516	−	0.840690i	$-0.317851\pi$
$293$	6.37121e35	1.08303	0.541516	+	0.840690i	$0.317851\pi$
$294$	1.04370e35	0.168864
$295$	−5.12973e33	−0.00790088
$296$	1.00285e34	0.0147064
$297$	1.47827e35	0.206436
$298$	−2.48642e35	−0.330704
$299$	−1.22131e35	−0.154736
$300$	4.03646e35	0.487240
$301$	2.75344e35	0.316710
$302$	−2.83492e35	−0.310770
$303$	−7.47961e35	−0.781557
$304$	6.48281e35	0.645798
$305$	1.17392e34	0.0111504
$306$	2.33307e35	0.211333
$307$	−6.79434e35	−0.587004	−0.293502	−	0.955959i	$-0.594821\pi$
$307$	−6.79434e35	−0.587004	−0.293502	+	0.955959i	$0.594821\pi$
$308$	−1.44909e36	−1.19429
$309$	4.74718e35	0.373283
$310$	5.33924e32	0.000400622 0
$311$	−6.58635e35	−0.471649	−0.235825	−	0.971796i	$-0.575779\pi$
$311$	−6.58635e35	−0.471649	−0.235825	+	0.971796i	$0.575779\pi$
$312$	1.70918e35	0.116828
$313$	6.86536e35	0.447992	0.223996	−	0.974590i	$-0.428090\pi$
$313$	6.86536e35	0.447992	0.223996	+	0.974590i	$0.428090\pi$
$314$	−1.12536e35	−0.0701150
$315$	4.19710e33	0.00249716
$316$	−2.60007e36	−1.47748
$317$	2.16216e36	1.17362	0.586812	−	0.809723i	$-0.300383\pi$
$317$	2.16216e36	1.17362	0.586812	+	0.809723i	$0.300383\pi$
$318$	−7.06080e35	−0.366151
$319$	−1.99239e36	−0.987210
$320$	−2.17865e33	−0.00103160
$321$	−1.31084e36	−0.593235
$322$	6.71011e35	0.290282
$323$	4.50564e36	1.86346
$324$	−2.37125e35	−0.0937724
$325$	7.34552e35	0.277788
$326$	4.54601e35	0.164428
$327$	−3.22592e35	−0.111612
$328$	3.77534e36	1.24964
$329$	3.76654e36	1.19290
$330$	4.58386e33	0.00138925
$331$	−3.58505e36	−1.03989	−0.519947	−	0.854198i	$-0.674048\pi$
$331$	−3.58505e36	−1.03989	−0.519947	+	0.854198i	$0.674048\pi$
$332$	−4.02282e36	−1.11693
$333$	−2.53191e34	−0.00672986
$334$	−1.00958e36	−0.256931
$335$	1.68777e34	0.00411304
$336$	1.81518e36	0.423643
$337$	4.15405e36	0.928620	0.464310	−	0.885673i	$-0.346302\pi$
$337$	4.15405e36	0.928620	0.464310	+	0.885673i	$0.346302\pi$
$338$	−1.70233e36	−0.364545
$339$	−3.62545e36	−0.743817
$340$	−3.91258e34	−0.00769164
$341$	1.01688e36	0.191571
$342$	8.46737e35	0.152887
$343$	−1.97873e36	−0.342470
$344$	−1.05393e36	−0.174870
$345$	1.14795e34	0.00182619
$346$	−6.39972e35	−0.0976242
$347$	−6.00859e36	−0.879013	−0.439507	−	0.898239i	$-0.644847\pi$
$347$	−6.00859e36	−0.879013	−0.439507	+	0.898239i	$0.644847\pi$
$348$	3.19594e36	0.448435
$349$	−6.73640e36	−0.906690	−0.453345	−	0.891335i	$-0.649769\pi$
$349$	−6.73640e36	−0.906690	−0.453345	+	0.891335i	$0.649769\pi$
$350$	−4.03578e36	−0.521124
$351$	−4.31518e35	−0.0534621
$352$	8.55471e36	1.01704
$353$	−5.60149e36	−0.639103	−0.319551	−	0.947569i	$-0.603532\pi$
$353$	−5.60149e36	−0.639103	−0.319551	+	0.947569i	$0.603532\pi$
$354$	−2.89767e36	−0.317323
$355$	3.12828e34	0.00328848
$356$	3.94327e35	0.0397953
$357$	1.26157e37	1.22243
$358$	2.32033e36	0.215897
$359$	7.58784e36	0.678030	0.339015	−	0.940781i	$-0.389906\pi$
$359$	7.58784e36	0.678030	0.339015	+	0.940781i	$0.389906\pi$
$360$	−1.60652e34	−0.00137880
$361$	4.22241e36	0.348102
$362$	3.58642e36	0.284045
$363$	1.14284e36	0.0869637
$364$	4.23000e36	0.309293
$365$	−1.19318e35	−0.00838413
$366$	6.63123e36	0.447835
$367$	7.23638e36	0.469747	0.234873	−	0.972026i	$-0.424532\pi$
$367$	7.23638e36	0.469747	0.234873	+	0.972026i	$0.424532\pi$
$368$	4.96470e36	0.309813
$369$	−9.53163e36	−0.571853
$370$	−7.85100e32	−4.52898e−5 0
$371$	−3.81802e37	−2.11795
$372$	−1.63114e36	−0.0870201
$373$	−5.05729e36	−0.259502	−0.129751	−	0.991547i	$-0.541418\pi$
$373$	−5.05729e36	−0.259502	−0.129751	+	0.991547i	$0.541418\pi$
$374$	1.37782e37	0.680073
$375$	−1.38089e35	−0.00655700
$376$	−1.44172e37	−0.658653
$377$	5.81594e36	0.255665
$378$	2.37085e36	0.100294
$379$	−1.48001e37	−0.602556	−0.301278	−	0.953536i	$-0.597413\pi$
$379$	−1.48001e37	−0.602556	−0.301278	+	0.953536i	$0.597413\pi$
$380$	−1.41999e35	−0.00556444
$381$	−2.50995e37	−0.946790
$382$	−1.17991e37	−0.428481
$383$	2.89182e37	1.01109	0.505545	−	0.862800i	$-0.331292\pi$
$383$	2.89182e37	1.01109	0.505545	+	0.862800i	$0.331292\pi$
$384$	−1.74903e37	−0.588837
$385$	2.47865e35	0.00803591
$386$	4.55672e36	0.142278
$387$	2.66087e36	0.0800231
$388$	−2.99980e36	−0.0869026
$389$	5.63332e37	1.57215	0.786077	−	0.618128i	$-0.212109\pi$
$389$	5.63332e37	1.57215	0.786077	+	0.618128i	$0.212109\pi$
$390$	−1.33806e34	−0.000359783 0
$391$	3.45053e37	0.893970
$392$	−2.16021e37	−0.539322
$393$	1.06851e37	0.257092
$394$	−1.42574e37	−0.330633
$395$	4.44739e35	0.00994140
$396$	−1.40037e37	−0.301761
$397$	2.39301e37	0.497144	0.248572	−	0.968613i	$-0.420039\pi$
$397$	2.39301e37	0.497144	0.248572	+	0.968613i	$0.420039\pi$
$398$	6.45138e36	0.129226
$399$	4.57860e37	0.884353
$400$	−2.98601e37	−0.556188
$401$	−4.52973e37	−0.813728	−0.406864	−	0.913489i	$-0.633378\pi$
$401$	−4.52973e37	−0.813728	−0.406864	+	0.913489i	$0.633378\pi$
$402$	9.53383e36	0.165192
$403$	−2.96834e36	−0.0496124
$404$	7.08547e37	1.14245
$405$	4.05600e34	0.000630958 0
$406$	−3.19540e37	−0.479620
$407$	−1.49525e36	−0.0216568
$408$	−4.82891e37	−0.674959
$409$	6.90873e37	0.931988	0.465994	−	0.884788i	$-0.345697\pi$
$409$	6.90873e37	0.931988	0.465994	+	0.884788i	$0.345697\pi$
$410$	−2.95559e35	−0.00384839
$411$	−9.02323e36	−0.113411
$412$	−4.49703e37	−0.545652
$413$	−1.56687e38	−1.83551
$414$	6.48452e36	0.0733454
$415$	6.88099e35	0.00751542
$416$	−2.49719e37	−0.263389
$417$	7.45798e37	0.759711
$418$	5.00051e37	0.491992
$419$	−6.41032e37	−0.609223	−0.304612	−	0.952477i	$-0.598527\pi$
$419$	−6.41032e37	−0.609223	−0.304612	+	0.952477i	$0.598527\pi$
$420$	−3.97594e35	−0.00365027
$421$	−1.78026e38	−1.57904	−0.789522	−	0.613723i	$-0.789671\pi$
$421$	−1.78026e38	−1.57904	−0.789522	+	0.613723i	$0.789671\pi$
$422$	1.78418e37	0.152900
$423$	3.63992e37	0.301409
$424$	1.46142e38	1.16942
$425$	−2.07531e38	−1.60489
$426$	1.76710e37	0.132075
$427$	3.58573e38	2.59044
$428$	1.24177e38	0.867171
$429$	−2.54839e37	−0.172042
$430$	8.25091e34	0.000538529 0
$431$	8.75854e37	0.552728	0.276364	−	0.961053i	$-0.410870\pi$
$431$	8.75854e37	0.552728	0.276364	+	0.961053i	$0.410870\pi$
$432$	1.75415e37	0.107042
$433$	−2.34472e38	−1.38362	−0.691811	−	0.722079i	$-0.743187\pi$
$433$	−2.34472e38	−1.38362	−0.691811	+	0.722079i	$0.743187\pi$
$434$	1.63087e37	0.0930717
$435$	−5.46662e35	−0.00301734
$436$	3.05593e37	0.163151
$437$	1.25230e38	0.646734
$438$	−6.73998e37	−0.336732
$439$	−6.25702e37	−0.302435	−0.151217	−	0.988501i	$-0.548319\pi$
$439$	−6.25702e37	−0.302435	−0.151217	+	0.988501i	$0.548319\pi$
$440$	−9.48753e35	−0.00443700
$441$	5.45390e37	0.246801
$442$	−4.02197e37	−0.176123
$443$	3.01118e38	1.27609	0.638047	−	0.769997i	$-0.279743\pi$
$443$	3.01118e38	1.27609	0.638047	+	0.769997i	$0.279743\pi$
$444$	2.39849e36	0.00983749
$445$	−6.74493e34	−0.000267767 0
$446$	−1.17803e38	−0.452688
$447$	−1.29929e38	−0.483335
$448$	−6.65467e37	−0.239660
$449$	−2.69722e38	−0.940470	−0.470235	−	0.882541i	$-0.655831\pi$
$449$	−2.69722e38	−0.940470	−0.470235	+	0.882541i	$0.655831\pi$
$450$	−3.90010e37	−0.131672
$451$	−5.62902e38	−1.84023
$452$	3.43441e38	1.08729
$453$	−1.48140e38	−0.454202
$454$	−6.53223e37	−0.193978
$455$	−7.23538e35	−0.00208111
$456$	−1.75255e38	−0.488293
$457$	1.89912e37	0.0512587	0.0256294	−	0.999672i	$-0.491841\pi$
$457$	1.89912e37	0.0512587	0.0256294	+	0.999672i	$0.491841\pi$
$458$	7.10804e37	0.185866
$459$	1.21916e38	0.308871
$460$	−1.08746e36	−0.00266947
$461$	6.41964e37	0.152703	0.0763515	−	0.997081i	$-0.475673\pi$
$461$	6.41964e37	0.152703	0.0763515	+	0.997081i	$0.475673\pi$
$462$	1.40014e38	0.322746
$463$	8.08856e38	1.80695	0.903476	−	0.428638i	$-0.141006\pi$
$463$	8.08856e38	1.80695	0.903476	+	0.428638i	$0.141006\pi$
$464$	−2.36422e38	−0.511892
$465$	2.79005e35	0.000585524 0
$466$	−3.77535e38	−0.768000
$467$	5.94390e38	1.17213	0.586067	−	0.810263i	$-0.300676\pi$
$467$	5.94390e38	1.17213	0.586067	+	0.810263i	$0.300676\pi$
$468$	4.08779e37	0.0781491
$469$	5.15527e38	0.955533
$470$	1.12868e36	0.00202838
$471$	−5.88063e37	−0.102476
$472$	5.99751e38	1.01347
$473$	1.57141e38	0.257516
$474$	2.51223e38	0.399277
$475$	−7.53190e38	−1.16104
$476$	−1.19509e39	−1.78690
$477$	−3.68966e38	−0.535143
$478$	−1.29692e38	−0.182477
$479$	1.67063e38	0.228043	0.114021	−	0.993478i	$-0.463627\pi$
$479$	1.67063e38	0.228043	0.114021	+	0.993478i	$0.463627\pi$
$480$	2.34720e36	0.00310851
$481$	4.36474e36	0.00560861
$482$	4.08665e38	0.509548
$483$	3.50641e38	0.424257
$484$	−1.08261e38	−0.127121
$485$	5.13114e35	0.000584734 0
$486$	2.29115e37	0.0253412
$487$	8.91033e38	0.956586	0.478293	−	0.878200i	$-0.341256\pi$
$487$	8.91033e38	0.956586	0.478293	+	0.878200i	$0.341256\pi$
$488$	−1.37251e39	−1.43030
$489$	2.37555e38	0.240317
$490$	1.69116e36	0.00166089
$491$	−1.81901e39	−1.73442	−0.867209	−	0.497945i	$-0.834088\pi$
$491$	−1.81901e39	−1.73442	−0.867209	+	0.497945i	$0.834088\pi$
$492$	9.02936e38	0.835916
$493$	−1.64317e39	−1.47707
$494$	−1.45969e38	−0.127415
$495$	2.39532e36	0.00203043
$496$	1.20665e38	0.0993340
$497$	9.55531e38	0.763972
$498$	3.88692e38	0.301842
$499$	1.61372e39	1.21722	0.608610	−	0.793469i	$-0.291727\pi$
$499$	1.61372e39	1.21722	0.608610	+	0.793469i	$0.291727\pi$
$500$	1.30812e37	0.00958480
$501$	−5.27561e38	−0.375514
$502$	−5.92776e38	−0.409908
$503$	2.06862e38	0.138978	0.0694888	−	0.997583i	$-0.477863\pi$
$503$	2.06862e38	0.138978	0.0694888	+	0.997583i	$0.477863\pi$
$504$	−4.90711e38	−0.320319
$505$	−1.21196e37	−0.00768713
$506$	3.82952e38	0.236027
$507$	−8.89561e38	−0.532795
$508$	2.37769e39	1.38399
$509$	2.86738e39	1.62210	0.811048	−	0.584979i	$-0.198897\pi$
$509$	2.86738e39	1.62210	0.811048	+	0.584979i	$0.198897\pi$
$510$	3.78040e36	0.00207860
$511$	−3.64454e39	−1.94778
$512$	1.79501e39	0.932506
$513$	4.42467e38	0.223450
$514$	2.97797e38	0.146202
$515$	7.69212e36	0.00367148
$516$	−2.52066e38	−0.116975
$517$	2.14960e39	0.969939
$518$	−2.39808e37	−0.0105216
$519$	−3.34421e38	−0.142681
$520$	2.76948e36	0.00114908
$521$	−1.96494e39	−0.792869	−0.396434	−	0.918063i	$-0.629753\pi$
$521$	−1.96494e39	−0.792869	−0.396434	+	0.918063i	$0.629753\pi$
$522$	−3.08797e38	−0.121186
$523$	−1.93595e39	−0.738956	−0.369478	−	0.929239i	$-0.620464\pi$
$523$	−1.93595e39	−0.738956	−0.369478	+	0.929239i	$0.620464\pi$
$524$	−1.01221e39	−0.375808
$525$	−2.10892e39	−0.761641
$526$	1.11753e39	0.392614
$527$	8.38639e38	0.286630
$528$	1.03594e39	0.344462
$529$	−2.13202e39	−0.689738
$530$	−1.14410e37	−0.00360134
$531$	−1.51420e39	−0.463779
$532$	−4.33733e39	−1.29272
$533$	1.64315e39	0.476578
$534$	−3.81006e37	−0.0107543
$535$	−2.12403e37	−0.00583486
$536$	−1.97328e39	−0.527594
$537$	1.21250e39	0.315541
$538$	1.45627e39	0.368891
$539$	3.22087e39	0.794211
$540$	−3.84227e36	−0.000922313 0
$541$	−2.08297e39	−0.486769	−0.243384	−	0.969930i	$-0.578258\pi$
$541$	−2.08297e39	−0.486769	−0.243384	+	0.969930i	$0.578258\pi$
$542$	1.16956e39	0.266093
$543$	1.87411e39	0.415142
$544$	7.05524e39	1.52170
$545$	−5.22714e36	−0.00109778
$546$	−4.08710e38	−0.0835838
$547$	−6.68261e38	−0.133085	−0.0665426	−	0.997784i	$-0.521197\pi$
$547$	−6.68261e38	−0.133085	−0.0665426	+	0.997784i	$0.521197\pi$
$548$	8.54775e38	0.165781
$549$	3.46519e39	0.654527
$550$	−2.30325e39	−0.423724
$551$	−5.96351e39	−1.06857
$552$	−1.34215e39	−0.234252
$553$	1.35845e40	2.30956
$554$	−1.75501e39	−0.290662
$555$	−4.10259e35	−6.61926e−5 0
$556$	−7.06498e39	−1.11052
$557$	2.46363e39	0.377289	0.188645	−	0.982045i	$-0.439591\pi$
$557$	2.46363e39	0.377289	0.188645	+	0.982045i	$0.439591\pi$
$558$	1.57604e38	0.0235164
$559$	−4.58707e38	−0.0666906
$560$	2.94123e37	0.00416680
$561$	7.19990e39	0.993951
$562$	1.17634e39	0.158255
$563$	−7.87998e39	−1.03313	−0.516563	−	0.856249i	$-0.672789\pi$
$563$	−7.87998e39	−1.03313	−0.516563	+	0.856249i	$0.672789\pi$
$564$	−3.44811e39	−0.440590
$565$	−5.87452e37	−0.00731593
$566$	−5.10253e39	−0.619366
$567$	1.23890e39	0.146583
$568$	−3.65748e39	−0.421824
$569$	−1.44248e40	−1.62174	−0.810869	−	0.585228i	$-0.801005\pi$
$569$	−1.44248e40	−1.62174	−0.810869	+	0.585228i	$0.801005\pi$
$570$	1.37201e37	0.00150374
$571$	7.42805e39	0.793691	0.396845	−	0.917885i	$-0.370105\pi$
$571$	7.42805e39	0.793691	0.396845	+	0.917885i	$0.370105\pi$
$572$	2.41410e39	0.251485
$573$	−6.16571e39	−0.626241
$574$	−9.02783e39	−0.894048
$575$	−5.76812e39	−0.556994
$576$	−6.43094e38	−0.0605548
$577$	1.17690e40	1.08066	0.540331	−	0.841452i	$-0.318299\pi$
$577$	1.17690e40	1.08066	0.540331	+	0.841452i	$0.318299\pi$
$578$	6.95172e39	0.622499
$579$	2.38114e39	0.207944
$580$	5.17856e37	0.00441065
$581$	2.10179e40	1.74596
$582$	2.89846e38	0.0234847
$583$	−2.17897e40	−1.72210
$584$	1.39502e40	1.07546
$585$	−6.99213e36	−0.000525835 0
$586$	5.83159e39	0.427830
$587$	5.19285e39	0.371667	0.185833	−	0.982581i	$-0.440502\pi$
$587$	5.19285e39	0.371667	0.185833	+	0.982581i	$0.440502\pi$
$588$	−5.16651e39	−0.360766
$589$	3.04366e39	0.207359
$590$	−4.69526e37	−0.00312108
$591$	−7.45030e39	−0.483232
$592$	−1.77430e38	−0.0112296
$593$	1.59933e39	0.0987744	0.0493872	−	0.998780i	$-0.484273\pi$
$593$	1.59933e39	0.0987744	0.0493872	+	0.998780i	$0.484273\pi$
$594$	1.35306e39	0.0815483
$595$	2.04420e38	0.0120234
$596$	1.23083e40	0.706524
$597$	3.37121e39	0.188868
$598$	−1.11787e39	−0.0611255
$599$	−1.54240e40	−0.823205	−0.411602	−	0.911364i	$-0.635031\pi$
$599$	−1.54240e40	−0.823205	−0.411602	+	0.911364i	$0.635031\pi$
$600$	8.07231e39	0.420537
$601$	−1.57115e40	−0.798986	−0.399493	−	0.916736i	$-0.630814\pi$
$601$	−1.57115e40	−0.798986	−0.399493	+	0.916736i	$0.630814\pi$
$602$	2.52023e39	0.125110
$603$	4.98196e39	0.241434
$604$	1.40334e40	0.663937
$605$	1.85180e37	0.000855346 0
$606$	−6.84611e39	−0.308738
$607$	8.12340e39	0.357686	0.178843	−	0.983878i	$-0.442765\pi$
$607$	8.12340e39	0.357686	0.178843	+	0.983878i	$0.442765\pi$
$608$	2.56055e40	1.10086
$609$	−1.66977e40	−0.700982
$610$	1.07449e38	0.00440475
$611$	−6.27484e39	−0.251192
$612$	−1.15492e40	−0.451497
$613$	−4.31167e40	−1.64615	−0.823074	−	0.567934i	$-0.807743\pi$
$613$	−4.31167e40	−1.64615	−0.823074	+	0.567934i	$0.807743\pi$
$614$	−6.21888e39	−0.231884
$615$	−1.54446e38	−0.00562455
$616$	−2.89796e40	−1.03079
$617$	−3.43998e40	−1.19515	−0.597573	−	0.801815i	$-0.703868\pi$
$617$	−3.43998e40	−1.19515	−0.597573	+	0.801815i	$0.703868\pi$
$618$	4.34511e39	0.147458
$619$	3.54999e40	1.17683	0.588413	−	0.808561i	$-0.299753\pi$
$619$	3.54999e40	1.17683	0.588413	+	0.808561i	$0.299753\pi$
$620$	−2.64303e37	−0.000855900 0
$621$	3.38853e39	0.107197
$622$	−6.02850e39	−0.186315
$623$	−2.06023e39	−0.0622070
$624$	−3.02398e39	−0.0892078
$625$	3.46911e40	0.999903
$626$	6.28388e39	0.176970
$627$	2.61305e40	0.719064
$628$	5.57075e39	0.149795
$629$	−1.23316e39	−0.0324030
$630$	3.84162e37	0.000986453 0
$631$	6.42243e40	1.61166	0.805831	−	0.592146i	$-0.201719\pi$
$631$	6.42243e40	1.61166	0.805831	+	0.592146i	$0.201719\pi$
$632$	−5.19974e40	−1.27522
$633$	9.32334e39	0.223469
$634$	1.97903e40	0.463616
$635$	−4.06702e38	−0.00931230
$636$	3.49523e40	0.782254
$637$	−9.40197e39	−0.205682
$638$	−1.82364e40	−0.389978
$639$	9.23407e39	0.193033
$640$	−2.83406e38	−0.00579160
$641$	6.47463e40	1.29352	0.646760	−	0.762693i	$-0.276123\pi$
$641$	6.47463e40	1.29352	0.646760	+	0.762693i	$0.276123\pi$
$642$	−1.19982e40	−0.234346
$643$	−3.73592e40	−0.713408	−0.356704	−	0.934217i	$-0.616100\pi$
$643$	−3.73592e40	−0.713408	−0.356704	+	0.934217i	$0.616100\pi$
$644$	−3.32164e40	−0.620165
$645$	4.31156e37	0.000787080 0
$646$	4.12402e40	0.736122
$647$	−4.50264e39	−0.0785878	−0.0392939	−	0.999228i	$-0.512511\pi$
$647$	−4.50264e39	−0.0785878	−0.0392939	+	0.999228i	$0.512511\pi$
$648$	−4.74214e39	−0.0809351
$649$	−8.94227e40	−1.49245
$650$	6.72338e39	0.109735
$651$	8.52219e39	0.136028
$652$	−2.25037e40	−0.351288
$653$	−2.49574e40	−0.381029	−0.190514	−	0.981684i	$-0.561016\pi$
$653$	−2.49574e40	−0.381029	−0.190514	+	0.981684i	$0.561016\pi$
$654$	−2.95269e39	−0.0440901
$655$	1.73137e38	0.00252867
$656$	−6.67955e40	−0.954204
$657$	−3.52202e40	−0.492146
$658$	3.44753e40	0.471229
$659$	7.60511e40	1.01687	0.508437	−	0.861099i	$-0.330223\pi$
$659$	7.60511e40	1.01687	0.508437	+	0.861099i	$0.330223\pi$
$660$	−2.26910e38	−0.00296802
$661$	1.11173e40	0.142259	0.0711293	−	0.997467i	$-0.477340\pi$
$661$	1.11173e40	0.142259	0.0711293	+	0.997467i	$0.477340\pi$
$662$	−3.28141e40	−0.410789
$663$	−2.10171e40	−0.257410
$664$	−8.04502e40	−0.964028
$665$	7.41896e38	0.00869820
$666$	−2.31746e38	−0.00265850
$667$	−4.56701e40	−0.512634
$668$	4.99761e40	0.548913
$669$	−6.15584e40	−0.661620
$670$	1.54482e38	0.00162477
$671$	2.04641e41	2.10628
$672$	7.16949e40	0.722161
$673$	6.03608e40	0.595027	0.297513	−	0.954718i	$-0.403843\pi$
$673$	6.03608e40	0.595027	0.297513	+	0.954718i	$0.403843\pi$
$674$	3.80221e40	0.366833
$675$	−2.03802e40	−0.192444
$676$	8.42686e40	0.778823
$677$	−9.46933e40	−0.856611	−0.428306	−	0.903634i	$-0.640889\pi$
$677$	−9.46933e40	−0.856611	−0.428306	+	0.903634i	$0.640889\pi$
$678$	−3.31838e40	−0.293830
$679$	1.56730e40	0.135844
$680$	−7.82456e38	−0.00663866
$681$	−3.41345e40	−0.283505
$682$	9.30750e39	0.0756762
$683$	4.14072e40	0.329592	0.164796	−	0.986328i	$-0.447303\pi$
$683$	4.14072e40	0.329592	0.164796	+	0.986328i	$0.447303\pi$
$684$	−4.19152e40	−0.326631
$685$	−1.46208e38	−0.00111547
$686$	−1.81114e40	−0.135286
$687$	3.71435e40	0.271650
$688$	1.86468e40	0.133528
$689$	6.36060e40	0.445984
$690$	1.05072e38	0.000721401 0
$691$	3.25183e40	0.218623	0.109312	−	0.994008i	$-0.465135\pi$
$691$	3.25183e40	0.218623	0.109312	+	0.994008i	$0.465135\pi$
$692$	3.16799e40	0.208567
$693$	7.31649e40	0.471705
$694$	−5.49968e40	−0.347236
$695$	1.20846e39	0.00747226
$696$	6.39139e40	0.387045
$697$	−4.64237e41	−2.75337
$698$	−6.16584e40	−0.358170
$699$	−1.97283e41	−1.12246
$700$	1.99779e41	1.11334
$701$	2.94858e40	0.160954	0.0804769	−	0.996756i	$-0.474356\pi$
$701$	2.94858e40	0.160954	0.0804769	+	0.996756i	$0.474356\pi$
$702$	−3.94970e39	−0.0211191
$703$	−4.47549e39	−0.0234417
$704$	−3.79787e40	−0.194866
$705$	5.89796e38	0.00296456
$706$	−5.12706e40	−0.252465
$707$	−3.70193e41	−1.78586
$708$	1.43441e41	0.677937
$709$	2.50031e41	1.15777	0.578887	−	0.815407i	$-0.303487\pi$
$709$	2.50031e41	1.15777	0.578887	+	0.815407i	$0.303487\pi$
$710$	2.86333e38	0.00129905
$711$	1.31278e41	0.583557
$712$	7.88595e39	0.0343474
$713$	2.33091e40	0.0994780
$714$	1.15472e41	0.482895
$715$	−4.12929e38	−0.00169215
$716$	−1.14861e41	−0.461248
$717$	−6.77714e40	−0.266697
$718$	6.94517e40	0.267842
$719$	−3.90514e41	−1.47594	−0.737968	−	0.674836i	$-0.764215\pi$
$719$	−3.90514e41	−1.47594	−0.737968	+	0.674836i	$0.764215\pi$
$720$	2.84235e38	0.00105283
$721$	2.34955e41	0.852950
$722$	3.86479e40	0.137511
$723$	2.13550e41	0.744723
$724$	−1.77535e41	−0.606841
$725$	2.74682e41	0.920298
$726$	1.04604e40	0.0343533
$727$	4.02739e41	1.29651	0.648254	−	0.761424i	$-0.275500\pi$
$727$	4.02739e41	1.29651	0.648254	+	0.761424i	$0.275500\pi$
$728$	8.45936e40	0.266952
$729$	1.19725e40	0.0370370
$730$	−1.09212e39	−0.00331198
$731$	1.29598e41	0.385296
$732$	−3.28259e41	−0.956766
$733$	−3.78327e41	−1.08108	−0.540542	−	0.841317i	$-0.681781\pi$
$733$	−3.78327e41	−1.08108	−0.540542	+	0.841317i	$0.681781\pi$
$734$	6.62348e40	0.185564
$735$	8.83726e38	0.00242745
$736$	1.96093e41	0.528122
$737$	2.94216e41	0.776940
$738$	−8.72432e40	−0.225899
$739$	5.07223e41	1.28782	0.643909	−	0.765102i	$-0.277312\pi$
$739$	5.07223e41	1.28782	0.643909	+	0.765102i	$0.277312\pi$
$740$	3.88640e37	9.67582e−5 0
$741$	−7.62768e40	−0.186221
$742$	−3.49464e41	−0.836654
$743$	−1.98626e41	−0.466336	−0.233168	−	0.972436i	$-0.574909\pi$
$743$	−1.98626e41	−0.466336	−0.233168	+	0.972436i	$0.574909\pi$
$744$	−3.26204e40	−0.0751071
$745$	−2.10532e39	−0.00475392
$746$	−4.62895e40	−0.102511
$747$	2.03113e41	0.441153
$748$	−6.82050e41	−1.45292
$749$	−6.48782e41	−1.35554
$750$	−1.26393e39	−0.00259021
$751$	−8.88032e41	−1.78505	−0.892523	−	0.451002i	$-0.851067\pi$
$751$	−8.88032e41	−1.78505	−0.892523	+	0.451002i	$0.851067\pi$
$752$	2.55077e41	0.502936
$753$	−3.09758e41	−0.599095
$754$	5.32335e40	0.100995
$755$	−2.40040e39	−0.00446738
$756$	−1.17362e41	−0.214270
$757$	6.49700e41	1.16365	0.581825	−	0.813314i	$-0.302339\pi$
$757$	6.49700e41	1.16365	0.581825	+	0.813314i	$0.302339\pi$
$758$	−1.35466e41	−0.238027
$759$	2.00114e41	0.344962
$760$	−2.83975e39	−0.00480268
$761$	1.10949e42	1.84097	0.920483	−	0.390782i	$-0.127795\pi$
$761$	1.10949e42	1.84097	0.920483	+	0.390782i	$0.127795\pi$
$762$	−2.29737e41	−0.374010
$763$	−1.59662e41	−0.255033
$764$	5.84081e41	0.915418
$765$	1.97547e39	0.00303795
$766$	2.64689e41	0.399410
$767$	2.61032e41	0.386510
$768$	−8.79045e40	−0.127724
$769$	−2.07833e41	−0.296335	−0.148167	−	0.988962i	$-0.547337\pi$
$769$	−2.07833e41	−0.296335	−0.148167	+	0.988962i	$0.547337\pi$
$770$	2.26872e39	0.00317442
$771$	1.55615e41	0.213680
$772$	−2.25567e41	−0.303965
$773$	8.87060e41	1.17314	0.586570	−	0.809898i	$-0.300478\pi$
$773$	8.87060e41	1.17314	0.586570	+	0.809898i	$0.300478\pi$
$774$	2.43551e40	0.0316115
$775$	−1.40192e41	−0.178586
$776$	−5.99915e40	−0.0750058
$777$	−1.25313e40	−0.0153777
$778$	5.15619e41	0.621048
$779$	−1.68485e42	−1.99190
$780$	6.62368e38	0.000768648 0
$781$	5.45330e41	0.621183
$782$	3.15828e41	0.353145
$783$	−1.61364e41	−0.177117
$784$	3.82197e41	0.411817
$785$	−9.52871e38	−0.00100792
$786$	9.78014e40	0.101559
$787$	−3.90392e41	−0.397986	−0.198993	−	0.980001i	$-0.563767\pi$
$787$	−3.90392e41	−0.397986	−0.198993	+	0.980001i	$0.563767\pi$
$788$	7.05771e41	0.706372
$789$	5.83971e41	0.573819
$790$	4.07071e39	0.00392715
$791$	−1.79437e42	−1.69962
$792$	−2.80053e41	−0.260450
$793$	−5.97363e41	−0.545477
$794$	2.19033e41	0.196387
$795$	−5.97856e39	−0.00526348
$796$	−3.19356e41	−0.276081
$797$	−6.74054e41	−0.572201	−0.286101	−	0.958200i	$-0.592359\pi$
$797$	−6.74054e41	−0.572201	−0.286101	+	0.958200i	$0.592359\pi$
$798$	4.19081e41	0.349346
$799$	1.77282e42	1.45123
$800$	−1.17940e42	−0.948103
$801$	−1.99097e40	−0.0157179
$802$	−4.14608e41	−0.321447
$803$	−2.07997e42	−1.58373
$804$	−4.71944e41	−0.352921
$805$	5.68163e39	0.00417285
$806$	−2.71693e40	−0.0195984
$807$	7.60982e41	0.539148
$808$	1.41699e42	0.986054
$809$	−1.28154e41	−0.0875950	−0.0437975	−	0.999040i	$-0.513946\pi$
$809$	−1.28154e41	−0.0875950	−0.0437975	+	0.999040i	$0.513946\pi$
$810$	3.71247e38	0.000249247 0
$811$	−1.71105e42	−1.12839	−0.564197	−	0.825640i	$-0.690814\pi$
$811$	−1.71105e42	−1.12839	−0.564197	+	0.825640i	$0.690814\pi$
$812$	1.58179e42	1.02467
$813$	6.11162e41	0.388905
$814$	−1.36860e40	−0.00855508
$815$	3.84923e39	0.00236368
$816$	8.54359e41	0.515387
$817$	4.70346e41	0.278739
$818$	6.32358e41	0.368163
$819$	−2.13574e41	−0.122161
$820$	1.46308e40	0.00822179
$821$	1.40297e42	0.774589	0.387295	−	0.921956i	$-0.373410\pi$
$821$	1.40297e42	0.774589	0.387295	+	0.921956i	$0.373410\pi$
$822$	−8.25898e40	−0.0448008
$823$	9.20105e41	0.490388	0.245194	−	0.969474i	$-0.421148\pi$
$823$	9.20105e41	0.490388	0.245194	+	0.969474i	$0.421148\pi$
$824$	−8.99337e41	−0.470953
$825$	−1.20358e42	−0.619288
$826$	−1.43416e42	−0.725083
$827$	2.74691e42	1.36463	0.682313	−	0.731060i	$-0.260974\pi$
$827$	2.74691e42	1.36463	0.682313	+	0.731060i	$0.260974\pi$
$828$	−3.20997e41	−0.156697
$829$	3.75177e41	0.179968	0.0899840	−	0.995943i	$-0.471318\pi$
$829$	3.75177e41	0.179968	0.0899840	+	0.995943i	$0.471318\pi$
$830$	6.29819e39	0.00296881
$831$	−9.17091e41	−0.424813
$832$	1.10863e41	0.0504659
$833$	2.65632e42	1.18830
$834$	6.82631e41	0.300109
$835$	−8.54836e39	−0.00369342
$836$	−2.47535e42	−1.05110
$837$	8.23569e40	0.0343701
$838$	−5.86739e41	−0.240661
$839$	1.04224e42	0.420164	0.210082	−	0.977684i	$-0.432627\pi$
$839$	1.04224e42	0.420164	0.210082	+	0.977684i	$0.432627\pi$
$840$	−7.95127e39	−0.00315055
$841$	−3.92846e41	−0.152996
$842$	−1.62948e42	−0.623769
$843$	6.14706e41	0.231296
$844$	−8.83204e41	−0.326660
$845$	−1.44141e40	−0.00524039
$846$	3.33163e41	0.119066
$847$	5.65631e41	0.198712
$848$	−2.58563e42	−0.892948
$849$	−2.66636e42	−0.905226
$850$	−1.89954e42	−0.633978
$851$	−3.42744e40	−0.0112458
$852$	−8.74748e41	−0.282169
$853$	−5.07878e42	−1.61064	−0.805320	−	0.592840i	$-0.798007\pi$
$853$	−5.07878e42	−1.61064	−0.805320	+	0.592840i	$0.798007\pi$
$854$	3.28203e42	1.02330
$855$	7.16954e39	0.00219777
$856$	2.48334e42	0.748457
$857$	3.10571e42	0.920319	0.460159	−	0.887836i	$-0.347792\pi$
$857$	3.10571e42	0.920319	0.460159	+	0.887836i	$0.347792\pi$
$858$	−2.33254e41	−0.0679617
$859$	2.84385e42	0.814716	0.407358	−	0.913269i	$-0.366450\pi$
$859$	2.84385e42	0.814716	0.407358	+	0.913269i	$0.366450\pi$
$860$	−4.08436e39	−0.00115053
$861$	−4.71755e42	−1.30668
$862$	8.01672e41	0.218344
$863$	−2.10289e42	−0.563196	−0.281598	−	0.959533i	$-0.590864\pi$
$863$	−2.10289e42	−0.563196	−0.281598	+	0.959533i	$0.590864\pi$
$864$	6.92846e41	0.182468
$865$	−5.41881e39	−0.00140336
$866$	−2.14613e42	−0.546572
$867$	3.63266e42	0.909805
$868$	−8.07311e41	−0.198841
$869$	7.75280e42	1.87790
$870$	−5.00362e39	−0.00119194
$871$	−8.58839e41	−0.201209
$872$	6.11139e41	0.140816
$873$	1.51461e41	0.0343237
$874$	1.14623e42	0.255479
$875$	−6.83451e40	−0.0149827
$876$	3.33643e42	0.719402
$877$	3.91656e42	0.830636	0.415318	−	0.909676i	$-0.363670\pi$
$877$	3.91656e42	0.830636	0.415318	+	0.909676i	$0.363670\pi$
$878$	−5.72707e41	−0.119471
$879$	3.04733e42	0.625289
$880$	1.67859e40	0.00338801
$881$	−9.53085e42	−1.89226	−0.946130	−	0.323787i	$-0.895044\pi$
$881$	−9.53085e42	−1.89226	−0.946130	+	0.323787i	$0.895044\pi$
$882$	4.99197e41	0.0974939
$883$	6.67215e42	1.28185	0.640923	−	0.767605i	$-0.278552\pi$
$883$	6.67215e42	1.28185	0.640923	+	0.767605i	$0.278552\pi$
$884$	1.99096e42	0.376274
$885$	−2.45354e40	−0.00456158
$886$	2.75614e42	0.504095
$887$	−8.47040e42	−1.52409	−0.762047	−	0.647522i	$-0.775805\pi$
$887$	−8.47040e42	−1.52409	−0.762047	+	0.647522i	$0.775805\pi$
$888$	4.79661e40	0.00849075
$889$	−1.24227e43	−2.16341
$890$	−6.17365e38	−0.000105776 0
$891$	7.07052e41	0.119186
$892$	5.83146e42	0.967135
$893$	6.43406e42	1.04988
$894$	−1.18925e42	−0.190932
$895$	1.96469e40	0.00310355
$896$	−8.65660e42	−1.34549
$897$	−5.84147e41	−0.0893371
$898$	−2.46878e42	−0.371514
$899$	−1.10999e42	−0.164363
$900$	1.93063e42	0.281308
$901$	−1.79705e43	−2.57662
$902$	−5.15226e42	−0.726947
$903$	1.31696e42	0.182853
$904$	6.86829e42	0.938439
$905$	3.03672e40	0.00408320
$906$	−1.35593e42	−0.179423
$907$	8.56937e42	1.11595	0.557973	−	0.829859i	$-0.311579\pi$
$907$	8.56937e42	1.11595	0.557973	+	0.829859i	$0.311579\pi$
$908$	3.23358e42	0.414418
$909$	−3.57747e42	−0.451232
$910$	−6.62256e39	−0.000822102 0
$911$	2.70171e42	0.330082	0.165041	−	0.986287i	$-0.447224\pi$
$911$	2.70171e42	0.330082	0.165041	+	0.986287i	$0.447224\pi$
$912$	3.10071e42	0.372852
$913$	1.19951e43	1.41964
$914$	1.73827e41	0.0202487
$915$	5.61483e40	0.00643770
$916$	−3.51862e42	−0.397089
$917$	5.28846e42	0.587454
$918$	1.11590e42	0.122013
$919$	−2.67965e42	−0.288405	−0.144203	−	0.989548i	$-0.546062\pi$
$919$	−2.67965e42	−0.288405	−0.144203	+	0.989548i	$0.546062\pi$
$920$	−2.17475e40	−0.00230402
$921$	−3.24971e42	−0.338907
$922$	5.87592e41	0.0603222
$923$	−1.59186e42	−0.160872
$924$	−6.93095e42	−0.689523
$925$	2.06143e41	0.0201889
$926$	7.40348e42	0.713800
$927$	2.27056e42	0.215515
$928$	−9.33809e42	−0.872594
$929$	−6.28158e42	−0.577884	−0.288942	−	0.957347i	$-0.593304\pi$
$929$	−6.28158e42	−0.577884	−0.288942	+	0.957347i	$0.593304\pi$
$930$	2.55374e39	0.000231299 0
$931$	9.64052e42	0.859667
$932$	1.86887e43	1.64077
$933$	−3.15023e42	−0.272307
$934$	5.44047e42	0.463028
$935$	1.16664e41	0.00977616
$936$	8.17496e41	0.0674506
$937$	−7.16512e42	−0.582103	−0.291051	−	0.956707i	$-0.594005\pi$
$937$	−7.16512e42	−0.582103	−0.291051	+	0.956707i	$0.594005\pi$
$938$	4.71864e42	0.377464
$939$	3.28368e42	0.258648
$940$	−5.58717e40	−0.00433349
$941$	1.73896e43	1.32813	0.664063	−	0.747676i	$-0.268831\pi$
$941$	1.73896e43	1.32813	0.664063	+	0.747676i	$0.268831\pi$
$942$	−5.38256e41	−0.0404809
$943$	−1.29030e43	−0.955588
$944$	−1.06111e43	−0.773870
$945$	2.00746e40	0.00144174
$946$	1.43832e42	0.101726
$947$	−1.59126e43	−1.10833	−0.554163	−	0.832408i	$-0.686961\pi$
$947$	−1.59126e43	−1.10833	−0.554163	+	0.832408i	$0.686961\pi$
$948$	−1.24361e43	−0.853025
$949$	6.07160e42	0.410150
$950$	−6.89397e42	−0.458646
$951$	1.03415e43	0.677592
$952$	−2.39000e43	−1.54228
$953$	1.42741e43	0.907196	0.453598	−	0.891206i	$-0.350140\pi$
$953$	1.42741e43	0.907196	0.453598	+	0.891206i	$0.350140\pi$
$954$	−3.37716e42	−0.211397
$955$	−9.99065e40	−0.00615949
$956$	6.42002e42	0.389849
$957$	−9.52955e42	−0.569966
$958$	1.52914e42	0.0900836
$959$	−4.46592e42	−0.259144
$960$	−1.04204e40	−0.000595597 0
$961$	−1.71954e43	−0.968105
$962$	3.99506e40	0.00221557
$963$	−6.26971e42	−0.342504
$964$	−2.02297e43	−1.08861
$965$	3.85830e40	0.00204526
$966$	3.20942e42	0.167594
$967$	3.30294e43	1.69909	0.849545	−	0.527515i	$-0.176876\pi$
$967$	3.30294e43	1.69909	0.849545	+	0.527515i	$0.176876\pi$
$968$	−2.16506e42	−0.109718
$969$	2.15503e43	1.07587
$970$	4.69654e39	0.000230987 0
$971$	−8.82588e42	−0.427641	−0.213820	−	0.976873i	$-0.568591\pi$
$971$	−8.82588e42	−0.427641	−0.213820	+	0.976873i	$0.568591\pi$
$972$	−1.13416e42	−0.0541395
$973$	3.69123e43	1.73594
$974$	8.15565e42	0.377880
$975$	3.51334e42	0.160381
$976$	2.42832e43	1.09215
$977$	−2.37910e43	−1.05425	−0.527123	−	0.849789i	$-0.676729\pi$
$977$	−2.37910e43	−1.05425	−0.527123	+	0.849789i	$0.676729\pi$
$978$	2.17434e42	0.0949325
$979$	−1.17579e42	−0.0505803
$980$	−8.37158e40	−0.00354837
$981$	−1.54295e42	−0.0644393
$982$	−1.66495e43	−0.685146
$983$	−1.98553e43	−0.805099	−0.402550	−	0.915398i	$-0.631876\pi$
$983$	−1.98553e43	−0.805099	−0.402550	+	0.915398i	$0.631876\pi$
$984$	1.80573e43	0.721481
$985$	−1.20721e41	−0.00475290
$986$	−1.50399e43	−0.583487
$987$	1.80153e43	0.688719
$988$	7.22574e42	0.272212
$989$	3.60203e42	0.133721
$990$	2.19245e40	0.000802081 0
$991$	4.62689e43	1.66810	0.834049	−	0.551690i	$-0.186017\pi$
$991$	4.62689e43	1.66810	0.834049	+	0.551690i	$0.186017\pi$
$992$	4.76597e42	0.169329
$993$	−1.71472e43	−0.600383
$994$	8.74601e42	0.301792
$995$	5.46256e40	0.00185764
$996$	−1.92410e43	−0.644863
$997$	−1.00554e43	−0.332140	−0.166070	−	0.986114i	$-0.553108\pi$
$997$	−1.00554e43	−0.332140	−0.166070	+	0.986114i	$0.553108\pi$
$998$	1.47704e43	0.480839
$999$	−1.21100e41	−0.00388549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.30.a.b.1.2	✓	3
3.2	odd	2		9.30.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.30.a.b.1.2	✓	3	1.1	even	1	trivial
9.30.a.c.1.2		3	3.2	odd	2

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

\(f(q)\)	\(=\)	\(q+9153.03 q^{2} +4.78297e6 q^{3} -4.53093e8 q^{4} +7.75011e7 q^{5} +4.37787e10 q^{6} +2.36726e12 q^{7} -9.06117e12 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q+9153.03 q^{2} +4.78297e6 q^{3} -4.53093e8 q^{4} +7.75011e7 q^{5} +4.37787e10 q^{6} +2.36726e12 q^{7} -9.06117e12 q^{8} +2.28768e13 q^{9} +7.09370e11 q^{10} +1.35102e15 q^{11} -2.16713e15 q^{12} -3.94372e15 q^{13} +2.16676e16 q^{14} +3.70685e14 q^{15} +1.60315e17 q^{16} +1.11421e18 q^{17} +2.09392e17 q^{18} +4.04379e18 q^{19} -3.51152e16 q^{20} +1.13225e19 q^{21} +1.23659e19 q^{22} +3.09684e19 q^{23} -4.33393e19 q^{24} -1.86259e20 q^{25} -3.60970e19 q^{26} +1.09419e20 q^{27} -1.07259e21 q^{28} -1.47473e21 q^{29} +3.39289e18 q^{30} +7.52674e20 q^{31} +6.33205e21 q^{32} +6.46187e21 q^{33} +1.01984e22 q^{34} +1.83466e20 q^{35} -1.03653e22 q^{36} -1.10676e21 q^{37} +3.70129e22 q^{38} -1.88627e22 q^{39} -7.02250e20 q^{40} -4.16650e23 q^{41} +1.03636e23 q^{42} +1.16313e23 q^{43} -6.12137e23 q^{44} +1.77298e21 q^{45} +2.83454e23 q^{46} +1.59110e24 q^{47} +7.66783e23 q^{48} +2.38403e24 q^{49} -1.70483e24 q^{50} +5.32924e24 q^{51} +1.78687e24 q^{52} -1.61284e25 q^{53} +1.00152e24 q^{54} +1.04705e23 q^{55} -2.14502e25 q^{56} +1.93413e25 q^{57} -1.34983e25 q^{58} -6.61892e25 q^{59} -1.67955e23 q^{60} +1.51472e26 q^{61} +6.88925e24 q^{62} +5.41554e25 q^{63} -2.81112e25 q^{64} -3.05643e23 q^{65} +5.91457e25 q^{66} +2.17774e26 q^{67} -5.04842e26 q^{68} +1.48121e26 q^{69} +1.67927e24 q^{70} +4.03644e26 q^{71} -2.07290e26 q^{72} -1.53956e27 q^{73} -1.01302e25 q^{74} -8.90869e26 q^{75} -1.83221e27 q^{76} +3.19821e27 q^{77} -1.72651e26 q^{78} +5.73849e27 q^{79} +1.24246e25 q^{80} +5.23348e26 q^{81} -3.81361e27 q^{82} +8.87856e27 q^{83} -5.13017e27 q^{84} +8.63527e25 q^{85} +1.06462e27 q^{86} -7.05361e27 q^{87} -1.22418e28 q^{88} -8.70301e26 q^{89} +1.62281e25 q^{90} -9.33584e27 q^{91} -1.40315e28 q^{92} +3.60002e27 q^{93} +1.45633e28 q^{94} +3.13398e26 q^{95} +3.02860e28 q^{96} +6.62073e27 q^{97} +2.18211e28 q^{98} +3.09069e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 11370 q^{2} + 14348907 q^{3} + 2104961700 q^{4} + 35492909586 q^{5} + 54382357530 q^{6} + 723913582632 q^{7} + 630313199016 q^{8} + 68630377364883 q^{9}+O(q^{10}) \) 3 * q + 11370 * q^2 + 14348907 * q^3 + 2104961700 * q^4 + 35492909586 * q^5 + 54382357530 * q^6 + 723913582632 * q^7 + 630313199016 * q^8 + 68630377364883 * q^9	\( 3 q + 11370 q^{2} + 14348907 q^{3} + 2104961700 q^{4} + 35492909586 q^{5} + 54382357530 q^{6} + 723913582632 q^{7} + 630313199016 q^{8} + 68630377364883 q^{9} - 334779369924996 q^{10} + 182675044475364 q^{11} + 10\!\cdots\!00 q^{12}+ \cdots + 41\!\cdots\!04 q^{99}+O(q^{100}) \) 3 * q + 11370 * q^2 + 14348907 * q^3 + 2104961700 * q^4 + 35492909586 * q^5 + 54382357530 * q^6 + 723913582632 * q^7 + 630313199016 * q^8 + 68630377364883 * q^9 - 334779369924996 * q^10 + 182675044475364 * q^11 + 10067966557287300 * q^12 + 9259572716201562 * q^13 - 120450158787784656 * q^14 + 169761486269640834 * q^15 + 1500169356985987344 * q^16 + 1072198906119498006 * q^17 + 260109130212906570 * q^18 + 3573738022673838588 * q^19 + 44431358843563300824 * q^20 + 3462456224407794408 * q^21 + 5937948604649594232 * q^22 + 2255441009197226856 * q^23 + 3014768491184358504 * q^24 + 107032338789541191021 * q^25 - 1497743341450819295124 * q^26 + 328256967394537077627 * q^27 - 3485513041911356199456 * q^28 + 975758353867945445466 * q^29 - 1601239348190788193124 * q^30 - 4310795768757336364368 * q^31 + 18876913054489573214112 * q^32 + 873729074799287275716 * q^33 + 67866341166487703151540 * q^34 - 14430259494134233374480 * q^35 + 48154771936541879993700 * q^36 - 27925678122459232189278 * q^37 - 142225433880276730339128 * q^38 + 44288249254837868797578 * q^39 - 108129617802599394192912 * q^40 - 69804619608851288718978 * q^41 - 576109375527051588323664 * q^42 - 693740310522122827674876 * q^43 - 2117857779499564977572688 * q^44 + 811963926221617750156146 * q^45 + 4620020103570468708081072 * q^46 + 1415959067390344943290608 * q^47 + 7175263529213910900744336 * q^48 + 2717825625267246250755723 * q^49 - 14651511011848257291000906 * q^50 + 5128294129803469258259814 * q^51 + 15401377033141462317909816 * q^52 + 2026116337260643996537026 * q^53 + 1244093906425295524206330 * q^54 - 20053964151511832211741864 * q^55 - 133879896037691995933089600 * q^56 + 17093078176570267077407772 * q^57 + 35308629357282460210284 * q^58 - 93305348607139212212742828 * q^59 + 212513811976639117378866456 * q^60 + 303096806772905191169090058 * q^61 - 362197525390562802152486496 * q^62 + 16560820785199524011837352 * q^63 + 265015022439684481406008896 * q^64 + 385927454665853764096033308 * q^65 + 28401024099632265074234808 * q^66 + 500799740942105395447763436 * q^67 - 430625977045044540127774200 * q^68 + 10787704428319050938215464 * q^69 - 2190923137138139447805738720 * q^70 + 231230996481801316056262776 * q^71 + 14419544235511560009518376 * q^72 + 63673289690883398415029886 * q^73 - 2938186329272588530875918756 * q^74 + 511932358427873040876521349 * q^75 - 2829633149821337155975657008 * q^76 + 4356628994062266983065035744 * q^77 - 7163659972115683713179943156 * q^78 + 7376231996756310126608131200 * q^79 + 22058960811505567152859842144 * q^80 + 1570042899082081611640534563 * q^81 - 12650067164628128121047255196 * q^82 + 27036927173545438643676286140 * q^83 - 16671100828557717449955864864 * q^84 - 6616892900361929463852172668 * q^85 - 21916001609490835312699050696 * q^86 + 4667021958041413159355068554 * q^87 - 21725279583477486875112151584 * q^88 - 18847541326307829508910067282 * q^89 - 7658678163976746013278105156 * q^90 + 36882675140537353230223738032 * q^91 - 41071545648724713668735716128 * q^92 - 20618402527297508353344848592 * q^93 - 60355386135226788370381393632 * q^94 + 10443256900314201021920744424 * q^95 + 90287689955318939506328058528 * q^96 - 25821730694946372903788747034 * q^97 + 252746844211061743934170389978 * q^98 + 4179019079163672261844080804 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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