LMFDB - Embedded newform 10.32.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,32,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 32, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 32 $
Character orbit:	$[\chi]$	$=$	10.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:	$60.8771328190$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 17573188320 $ x^2 - x - 17573188320
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$132564.$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-32768.0 q^{2} -2.68139e7 q^{3} +1.07374e9 q^{4} +3.05176e10 q^{5} +8.78637e11 q^{6} +7.28747e11 q^{7} -3.51844e13 q^{8} +1.01311e14 q^{9} -1.00000e15 q^{10} -3.37576e15 q^{11} -2.87912e16 q^{12} -1.37589e17 q^{13} -2.38796e16 q^{14} -8.18295e17 q^{15} +1.15292e18 q^{16} +2.39641e18 q^{17} -3.31975e18 q^{18} +9.48888e18 q^{19} +3.27680e19 q^{20} -1.95405e19 q^{21} +1.10617e20 q^{22} +1.89426e21 q^{23} +9.43430e20 q^{24} +9.31323e20 q^{25} +4.50853e21 q^{26} +1.38457e22 q^{27} +7.82486e20 q^{28} +5.03519e21 q^{29} +2.68139e22 q^{30} -8.54182e22 q^{31} -3.77789e22 q^{32} +9.05173e22 q^{33} -7.85254e22 q^{34} +2.22396e22 q^{35} +1.08782e23 q^{36} +1.26772e24 q^{37} -3.10932e23 q^{38} +3.68931e24 q^{39} -1.07374e24 q^{40} +8.53929e24 q^{41} +6.40304e23 q^{42} +2.40945e25 q^{43} -3.62470e24 q^{44} +3.09176e24 q^{45} -6.20710e25 q^{46} -3.96314e25 q^{47} -3.09143e25 q^{48} -1.57244e26 q^{49} -3.05176e25 q^{50} -6.42569e25 q^{51} -1.47736e26 q^{52} +7.23147e25 q^{53} -4.53695e26 q^{54} -1.03020e26 q^{55} -2.56405e25 q^{56} -2.54434e26 q^{57} -1.64993e26 q^{58} -1.71371e27 q^{59} -8.78637e26 q^{60} +2.02558e27 q^{61} +2.79898e27 q^{62} +7.38299e25 q^{63} +1.23794e27 q^{64} -4.19890e27 q^{65} -2.96607e27 q^{66} -2.22923e28 q^{67} +2.57312e27 q^{68} -5.07923e28 q^{69} -7.28747e26 q^{70} -8.76737e28 q^{71} -3.56456e27 q^{72} -6.23103e28 q^{73} -4.15405e28 q^{74} -2.49724e28 q^{75} +1.01886e28 q^{76} -2.46008e27 q^{77} -1.20891e29 q^{78} +1.07042e29 q^{79} +3.51844e28 q^{80} -4.33834e29 q^{81} -2.79815e29 q^{82} -5.93551e28 q^{83} -2.09815e28 q^{84} +7.31325e28 q^{85} -7.89527e29 q^{86} -1.35013e29 q^{87} +1.18774e29 q^{88} +1.10405e30 q^{89} -1.01311e29 q^{90} -1.00268e29 q^{91} +2.03394e30 q^{92} +2.29039e30 q^{93} +1.29864e30 q^{94} +2.89578e29 q^{95} +1.01300e30 q^{96} +5.31660e30 q^{97} +5.15258e30 q^{98} -3.42001e29 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 65536 q^{2} - 5904756 q^{3} + 2147483648 q^{4} + 61035156250 q^{5} + 193487044608 q^{6} + 18016565093212 q^{7} - 70368744177664 q^{8} - 79171117705926 q^{9} - 20\!\cdots\!00 q^{10} - 17\!\cdots\!76 q^{11}+ \cdots + 21\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 65536 * q^2 - 5904756 * q^3 + 2147483648 * q^4 + 61035156250 * q^5 + 193487044608 * q^6 + 18016565093212 * q^7 - 70368744177664 * q^8 - 79171117705926 * q^9 - 2000000000000000 * q^10 - 17416121431336176 * q^11 - 6340183477714944 * q^12 - 25489812233411396 * q^13 - 590366804974370816 * q^14 - 180198852539062500 * q^15 + 2305843009213693952 * q^16 - 16396230747963647148 * q^17 + 2594279184987783168 * q^18 - 107880416928265082840 * q^19 + 65536000000000000000 * q^20 + 341932614252792754464 * q^21 + 570691467062023815168 * q^22 - 577071154821832133436 * q^23 + 207755132197763284992 * q^24 + 1862645149230957031250 * q^25 + 835250167264424624128 * q^26 - 2843043459520171719240 * q^27 + 19345139465400182898688 * q^28 + 67048805832697356280140 * q^29 + 5904756000000000000000 * q^30 + 56909800035573417801064 * q^31 - 75557863725914323419136 * q^32 - 203054257469968728424272 * q^33 + 537271689149272789745664 * q^34 + 549821932776245117187500 * q^35 - 85009340333679678849024 * q^36 + 2801153390572259937695932 * q^37 + 3535025501905390234501120 * q^38 + 6033212900355351396566088 * q^39 - 2147483648000000000000000 * q^40 + 1893631200697714321546884 * q^41 - 11204447903835512978276352 * q^42 + 25327635900154956194956684 * q^43 - 18700417992688396375425024 * q^44 - 2416110769834167480468750 * q^45 + 18909467601201795348430848 * q^46 - 204836832883272087160299828 * q^47 - 6807720171856307322617856 * q^48 - 16151031643901179650461214 * q^49 - 61035156250000000000000000 * q^50 - 457194512783561777077087656 * q^51 - 27369477480920666083426304 * q^52 + 93384041038067791074445644 * q^53 + 93160848081556986896056320 * q^54 - 531497846415288574218750000 * q^55 - 633901530002233193224208384 * q^56 - 2708523042419370548680789680 * q^57 - 2197055269525826970587627520 * q^58 + 401993734479158802793910280 * q^59 - 193487044608000000000000000 * q^60 - 523487156255386223571641876 * q^61 - 1864820327565669754505265152 * q^62 - 3046308524664113764706112756 * q^63 + 2475880078570760549798248448 * q^64 - 777887336224713012695312500 * q^65 + 6653681908775935293006544896 * q^66 + 3525975420949577285673481252 * q^67 - 17605318710043370774385917952 * q^68 - 102465607127544429209145592992 * q^69 - 18016565093212000000000000000 * q^70 - 155367638238255137782572480456 * q^71 + 2785586064054015716524818432 * q^72 - 121161803322719279904680358236 * q^73 - 91788194302271813638420299776 * q^74 - 5499232560396194458007812500 * q^75 - 115835715646435827204132700160 * q^76 - 245187227911068920618395555056 * q^77 - 197696320318844154562677571584 * q^78 - 106325261485679876782031095760 * q^79 + 70368744177664000000000000000 * q^80 - 671301359934033052744190089758 * q^81 - 62050507184462702888448294912 * q^82 - 165992230806613806640311266676 * q^83 + 367147348912882089272159502336 * q^84 - 500373252806507786499023437500 * q^85 - 829935973176277604596340621312 * q^86 + 1161637435058040293762416972680 * q^87 + 612775296784413372429927186432 * q^88 + 596773808150426638152387464820 * q^89 + 79171117705926000000000000000 * q^90 + 1837690480870898595062956149224 * q^91 - 619625434356180429977382027264 * q^92 + 5266346212626013088658434510208 * q^93 + 6712093339919059752068704763904 * q^94 - 3292249051765902186279296875000 * q^95 + 223075374591387478347541905408 * q^96 + 8308055695022791533341129836372 * q^97 + 529237004907353854786313060352 * q^98 + 2192029238850361923111708294288 * q^99

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 $

$2$	−32768.0	−0.707107
$2$	−32768.0	−0.707107
$3$	−2.68139e7	−1.07890	−0.539449	−	0.842018i	$-0.681367\pi$
$3$	−2.68139e7	−1.07890	−0.539449	+	0.842018i	$0.681367\pi$
$4$	1.07374e9	0.500000
$5$	3.05176e10	0.447214
$5$	3.05176e10	0.447214
$6$	8.78637e11	0.762896
$7$	7.28747e11	0.0580172	0.0290086	−	0.999579i	$-0.490765\pi$
$7$	7.28747e11	0.0580172	0.0290086	+	0.999579i	$0.490765\pi$
$8$	−3.51844e13	−0.353553
$9$	1.01311e14	0.164020
$10$	−1.00000e15	−0.316228
$11$	−3.37576e15	−0.243661	−0.121830	−	0.992551i	$-0.538876\pi$
$11$	−3.37576e15	−0.243661	−0.121830	+	0.992551i	$0.538876\pi$
$12$	−2.87912e16	−0.539449
$13$	−1.37589e17	−0.745527	−0.372763	−	0.927926i	$-0.621590\pi$
$13$	−1.37589e17	−0.745527	−0.372763	+	0.927926i	$0.621590\pi$
$14$	−2.38796e16	−0.0410244
$15$	−8.18295e17	−0.482498
$16$	1.15292e18	0.250000
$17$	2.39641e18	0.203050	0.101525	−	0.994833i	$-0.467628\pi$
$17$	2.39641e18	0.203050	0.101525	+	0.994833i	$0.467628\pi$
$18$	−3.31975e18	−0.115980
$19$	9.48888e18	0.143395	0.0716975	−	0.997426i	$-0.477158\pi$
$19$	9.48888e18	0.143395	0.0716975	+	0.997426i	$0.477158\pi$
$20$	3.27680e19	0.223607
$21$	−1.95405e19	−0.0625947
$22$	1.10617e20	0.172294
$23$	1.89426e21	1.48135	0.740674	−	0.671865i	$-0.234506\pi$
$23$	1.89426e21	1.48135	0.740674	+	0.671865i	$0.234506\pi$
$24$	9.43430e20	0.381448
$25$	9.31323e20	0.200000
$26$	4.50853e21	0.527167
$27$	1.38457e22	0.901937
$28$	7.82486e20	0.0290086
$29$	5.03519e21	0.108354	0.0541772	−	0.998531i	$-0.482746\pi$
$29$	5.03519e21	0.108354	0.0541772	+	0.998531i	$0.482746\pi$
$30$	2.68139e22	0.341177
$31$	−8.54182e22	−0.653799	−0.326899	−	0.945059i	$-0.606004\pi$
$31$	−8.54182e22	−0.653799	−0.326899	+	0.945059i	$0.606004\pi$
$32$	−3.77789e22	−0.176777
$33$	9.05173e22	0.262885
$34$	−7.85254e22	−0.143578
$35$	2.22396e22	0.0259461
$36$	1.08782e23	0.0820100
$37$	1.26772e24	0.625022	0.312511	−	0.949914i	$-0.398830\pi$
$37$	1.26772e24	0.625022	0.312511	+	0.949914i	$0.398830\pi$
$38$	−3.10932e23	−0.101396
$39$	3.68931e24	0.804347
$40$	−1.07374e24	−0.158114
$41$	8.53929e24	0.857574	0.428787	−	0.903406i	$-0.358941\pi$
$41$	8.53929e24	0.857574	0.428787	+	0.903406i	$0.358941\pi$
$42$	6.40304e23	0.0442611
$43$	2.40945e25	1.15653	0.578264	−	0.815850i	$-0.303730\pi$
$43$	2.40945e25	1.15653	0.578264	+	0.815850i	$0.303730\pi$
$44$	−3.62470e24	−0.121830
$45$	3.09176e24	0.0733520
$46$	−6.20710e25	−1.04747
$47$	−3.96314e25	−0.479207	−0.239603	−	0.970871i	$-0.577017\pi$
$47$	−3.96314e25	−0.479207	−0.239603	+	0.970871i	$0.577017\pi$
$48$	−3.09143e25	−0.269724
$49$	−1.57244e26	−0.996634
$50$	−3.05176e25	−0.141421
$51$	−6.42569e25	−0.219070
$52$	−1.47736e26	−0.372763
$53$	7.23147e25	0.135816	0.0679080	−	0.997692i	$-0.478368\pi$
$53$	7.23147e25	0.135816	0.0679080	+	0.997692i	$0.478368\pi$
$54$	−4.53695e26	−0.637766
$55$	−1.03020e26	−0.108968
$56$	−2.56405e25	−0.0205122
$57$	−2.54434e26	−0.154709
$58$	−1.64993e26	−0.0766182
$59$	−1.71371e27	−0.610563	−0.305281	−	0.952262i	$-0.598751\pi$
$59$	−1.71371e27	−0.610563	−0.305281	+	0.952262i	$0.598751\pi$
$60$	−8.78637e26	−0.241249
$61$	2.02558e27	0.430464	0.215232	−	0.976563i	$-0.430949\pi$
$61$	2.02558e27	0.430464	0.215232	+	0.976563i	$0.430949\pi$
$62$	2.79898e27	0.462305
$63$	7.38299e25	0.00951599
$64$	1.23794e27	0.125000
$65$	−4.19890e27	−0.333410
$66$	−2.96607e27	−0.185888
$67$	−2.22923e28	−1.10661	−0.553307	−	0.832978i	$-0.686634\pi$
$67$	−2.22923e28	−1.10661	−0.553307	+	0.832978i	$0.686634\pi$
$68$	2.57312e27	0.101525
$69$	−5.07923e28	−1.59822
$70$	−7.28747e26	−0.0183467
$71$	−8.76737e28	−1.77160	−0.885799	−	0.464069i	$-0.846389\pi$
$71$	−8.76737e28	−1.77160	−0.885799	+	0.464069i	$0.846389\pi$
$72$	−3.56456e27	−0.0579898
$73$	−6.23103e28	−0.818569	−0.409285	−	0.912407i	$-0.634222\pi$
$73$	−6.23103e28	−0.818569	−0.409285	+	0.912407i	$0.634222\pi$
$74$	−4.15405e28	−0.441958
$75$	−2.49724e28	−0.215780
$76$	1.01886e28	0.0716975
$77$	−2.46008e27	−0.0141365
$78$	−1.20891e29	−0.568759
$79$	1.07042e29	0.413367	0.206683	−	0.978408i	$-0.433733\pi$
$79$	1.07042e29	0.413367	0.206683	+	0.978408i	$0.433733\pi$
$80$	3.51844e28	0.111803
$81$	−4.33834e29	−1.13712
$82$	−2.79815e29	−0.606397
$83$	−5.93551e28	−0.106598	−0.0532988	−	0.998579i	$-0.516974\pi$
$83$	−5.93551e28	−0.106598	−0.0532988	+	0.998579i	$0.516974\pi$
$84$	−2.09815e28	−0.0312973
$85$	7.31325e28	0.0908065
$86$	−7.89527e29	−0.817789
$87$	−1.35013e29	−0.116903
$88$	1.18774e29	0.0861471
$89$	1.10405e30	0.672118	0.336059	−	0.941841i	$-0.390906\pi$
$89$	1.10405e30	0.672118	0.336059	+	0.941841i	$0.390906\pi$
$90$	−1.01311e29	−0.0518677
$91$	−1.00268e29	−0.0432534
$92$	2.03394e30	0.740674
$93$	2.29039e30	0.705382
$94$	1.29864e30	0.338850
$95$	2.89578e29	0.0641282
$96$	1.01300e30	0.190724
$97$	5.31660e30	0.852456	0.426228	−	0.904616i	$-0.359842\pi$
$97$	5.31660e30	0.852456	0.426228	+	0.904616i	$0.359842\pi$
$98$	5.15258e30	0.704727
$99$	−3.42001e29	−0.0399652
$100$	1.00000e30	0.100000
$101$	−6.37914e30	−0.546740	−0.273370	−	0.961909i	$-0.588138\pi$
$101$	−6.37914e30	−0.546740	−0.273370	+	0.961909i	$0.588138\pi$
$102$	2.10557e30	0.154906
$103$	1.27411e31	0.805803	0.402901	−	0.915243i	$-0.368002\pi$
$103$	1.27411e31	0.805803	0.402901	+	0.915243i	$0.368002\pi$
$104$	4.84100e30	0.263583
$105$	−5.96330e29	−0.0279932
$106$	−2.36961e30	−0.0960364
$107$	−1.47464e31	−0.516698	−0.258349	−	0.966052i	$-0.583178\pi$
$107$	−1.47464e31	−0.516698	−0.258349	+	0.966052i	$0.583178\pi$
$108$	1.48667e31	0.450968
$109$	−2.43352e31	−0.639917	−0.319958	−	0.947432i	$-0.603669\pi$
$109$	−2.43352e31	−0.639917	−0.319958	+	0.947432i	$0.603669\pi$
$110$	3.37576e30	0.0770523
$111$	−3.39924e31	−0.674335
$112$	8.40188e29	0.0145043
$113$	1.29196e32	1.94327	0.971633	−	0.236495i	$-0.0759987\pi$
$113$	1.29196e32	1.94327	0.971633	+	0.236495i	$0.0759987\pi$
$114$	8.33729e30	0.109396
$115$	5.78081e31	0.662479
$116$	5.40649e30	0.0541772
$117$	−1.39393e31	−0.122281
$118$	5.61548e31	0.431733
$119$	1.74637e30	0.0117804
$120$	2.87912e31	0.170589
$121$	−1.80548e32	−0.940629
$122$	−6.63742e31	−0.304384
$123$	−2.28971e32	−0.925235
$124$	−9.17171e31	−0.326899
$125$	2.84217e31	0.0894427
$126$	−2.41926e30	−0.00672882
$127$	−6.29352e32	−1.54859	−0.774294	−	0.632826i	$-0.781895\pi$
$127$	−6.29352e32	−1.54859	−0.774294	+	0.632826i	$0.781895\pi$
$128$	−4.05648e31	−0.0883883
$129$	−6.46066e32	−1.24778
$130$	1.37589e32	0.235756
$131$	−1.13960e33	−1.73400	−0.866999	−	0.498310i	$-0.833954\pi$
$131$	−1.13960e33	−1.73400	−0.866999	+	0.498310i	$0.833954\pi$
$132$	9.71922e31	0.131442
$133$	6.91499e30	0.00831939
$134$	7.30475e32	0.782494
$135$	4.22537e32	0.403358
$136$	−8.43160e31	−0.0717889
$137$	−1.23195e33	−0.936318	−0.468159	−	0.883644i	$-0.655083\pi$
$137$	−1.23195e33	−0.936318	−0.468159	+	0.883644i	$0.655083\pi$
$138$	1.66436e33	1.13011
$139$	−1.10200e33	−0.669042	−0.334521	−	0.942388i	$-0.608575\pi$
$139$	−1.10200e33	−0.669042	−0.334521	+	0.942388i	$0.608575\pi$
$140$	2.38796e31	0.0129730
$141$	1.06267e33	0.517015
$142$	2.87289e33	1.25271
$143$	4.64470e32	0.181656
$144$	1.16803e32	0.0410050
$145$	1.53662e32	0.0484576
$146$	2.04178e33	0.578816
$147$	4.21633e33	1.07527
$148$	1.36120e33	0.312511
$149$	−1.57024e33	−0.324772	−0.162386	−	0.986727i	$-0.551919\pi$
$149$	−1.57024e33	−0.324772	−0.162386	+	0.986727i	$0.551919\pi$
$150$	8.18295e32	0.152579
$151$	−1.72612e33	−0.290354	−0.145177	−	0.989406i	$-0.546375\pi$
$151$	−1.72612e33	−0.290354	−0.145177	+	0.989406i	$0.546375\pi$
$152$	−3.33860e32	−0.0506978
$153$	2.42782e32	0.0333042
$154$	8.06118e31	0.00999603
$155$	−2.60676e33	−0.292388
$156$	3.96136e33	0.402173
$157$	1.22917e34	1.13023	0.565114	−	0.825013i	$-0.308832\pi$
$157$	1.22917e34	1.13023	0.565114	+	0.825013i	$0.308832\pi$
$158$	−3.50756e33	−0.292294
$159$	−1.93904e33	−0.146531
$160$	−1.15292e33	−0.0790569
$161$	1.38043e33	0.0859437
$162$	1.42159e34	0.804063
$163$	−2.97139e34	−1.52775	−0.763874	−	0.645366i	$-0.776705\pi$
$163$	−2.97139e34	−1.52775	−0.763874	+	0.645366i	$0.776705\pi$
$164$	9.16899e33	0.428787
$165$	2.76237e33	0.117566
$166$	1.94495e33	0.0753759
$167$	−1.23629e32	−0.00436531	−0.00218265	−	0.999998i	$-0.500695\pi$
$167$	−1.23629e32	−0.00436531	−0.00218265	+	0.999998i	$0.500695\pi$
$168$	6.87521e32	0.0221306
$169$	−1.51291e34	−0.444190
$170$	−2.39641e33	−0.0642099
$171$	9.61326e32	0.0235197
$172$	2.58712e34	0.578264
$173$	−8.47230e34	−1.73096	−0.865479	−	0.500945i	$-0.832986\pi$
$173$	−8.47230e34	−1.73096	−0.865479	+	0.500945i	$0.832986\pi$
$174$	4.42411e33	0.0826632
$175$	6.78698e32	0.0116034
$176$	−3.89199e33	−0.0609152
$177$	4.59511e34	0.658735
$178$	−3.61776e34	−0.475259
$179$	−1.31638e35	−1.58547	−0.792736	−	0.609565i	$-0.791344\pi$
$179$	−1.31638e35	−1.58547	−0.792736	+	0.609565i	$0.791344\pi$
$180$	3.31975e33	0.0366760
$181$	7.25006e34	0.735062	0.367531	−	0.930011i	$-0.380203\pi$
$181$	7.25006e34	0.735062	0.367531	+	0.930011i	$0.380203\pi$
$182$	3.28558e33	0.0305848
$183$	−5.43136e34	−0.464426
$184$	−6.66482e34	−0.523736
$185$	3.86877e34	0.279519
$186$	−7.50516e34	−0.498780
$187$	−8.08970e33	−0.0494752
$188$	−4.25539e34	−0.239603
$189$	1.00900e34	0.0523279
$190$	−9.48888e33	−0.0453455
$191$	6.07467e34	0.267612	0.133806	−	0.991008i	$-0.457280\pi$
$191$	6.07467e34	0.267612	0.133806	+	0.991008i	$0.457280\pi$
$192$	−3.31940e34	−0.134862
$193$	3.30662e35	1.23950	0.619750	−	0.784799i	$-0.287234\pi$
$193$	3.30662e35	1.23950	0.619750	+	0.784799i	$0.287234\pi$
$194$	−1.74214e35	−0.602777
$195$	1.12589e35	0.359715
$196$	−1.68840e35	−0.498317
$197$	3.74089e35	1.02035	0.510174	−	0.860071i	$-0.329581\pi$
$197$	3.74089e35	1.02035	0.510174	+	0.860071i	$0.329581\pi$
$198$	1.12067e34	0.0282597
$199$	−1.54190e35	−0.359611	−0.179805	−	0.983702i	$-0.557547\pi$
$199$	−1.54190e35	−0.359611	−0.179805	+	0.983702i	$0.557547\pi$
$200$	−3.27680e34	−0.0707107
$201$	5.97744e35	1.19392
$202$	2.09032e35	0.386604
$203$	3.66938e33	0.00628643
$204$	−6.89954e34	−0.109535
$205$	2.60598e35	0.383519
$206$	−4.17499e35	−0.569789
$207$	1.91909e35	0.242971
$208$	−1.58630e35	−0.186382
$209$	−3.20322e34	−0.0349397
$210$	1.95405e34	0.0197942
$211$	−6.65945e35	−0.626701	−0.313350	−	0.949638i	$-0.601451\pi$
$211$	−6.65945e35	−0.626701	−0.313350	+	0.949638i	$0.601451\pi$
$212$	7.76473e34	0.0679080
$213$	2.35087e36	1.91137
$214$	4.83209e35	0.365361
$215$	7.35305e35	0.517215
$216$	−4.87152e35	−0.318883
$217$	−6.22482e34	−0.0379316
$218$	7.97415e35	0.452490
$219$	1.67078e36	0.883153
$220$	−1.10617e35	−0.0544842
$221$	−3.29720e35	−0.151379
$222$	1.11386e36	0.476827
$223$	−1.97136e36	−0.787117	−0.393559	−	0.919299i	$-0.628756\pi$
$223$	−1.97136e36	−0.787117	−0.393559	+	0.919299i	$0.628756\pi$
$224$	−2.75313e34	−0.0102561
$225$	9.43530e34	0.0328040
$226$	−4.23348e36	−1.37410
$227$	−5.24999e36	−1.59132	−0.795661	−	0.605743i	$-0.792876\pi$
$227$	−5.24999e36	−1.59132	−0.795661	+	0.605743i	$0.792876\pi$
$228$	−2.73196e35	−0.0773543
$229$	−5.83672e36	−1.54425	−0.772127	−	0.635468i	$-0.780807\pi$
$229$	−5.83672e36	−1.54425	−0.772127	+	0.635468i	$0.780807\pi$
$230$	−1.89426e36	−0.468443
$231$	6.59642e34	0.0152519
$232$	−1.77160e35	−0.0383091
$233$	−2.74902e36	−0.556110	−0.278055	−	0.960565i	$-0.589690\pi$
$233$	−2.74902e36	−0.556110	−0.278055	+	0.960565i	$0.589690\pi$
$234$	4.56763e35	0.0864659
$235$	−1.20946e36	−0.214308
$236$	−1.84008e36	−0.305281
$237$	−2.87022e36	−0.445980
$238$	−5.72252e34	−0.00832998
$239$	−6.06727e35	−0.0827610	−0.0413805	−	0.999143i	$-0.513176\pi$
$239$	−6.06727e35	−0.0827610	−0.0413805	+	0.999143i	$0.513176\pi$
$240$	−9.43430e35	−0.120624
$241$	9.96011e36	1.19399	0.596994	−	0.802246i	$-0.296362\pi$
$241$	9.96011e36	1.19399	0.596994	+	0.802246i	$0.296362\pi$
$242$	5.91619e36	0.665125
$243$	3.08065e36	0.324896
$244$	2.17495e36	0.215232
$245$	−4.79872e36	−0.445708
$246$	7.50293e36	0.654240
$247$	−1.30557e36	−0.106905
$248$	3.00538e36	0.231153
$249$	1.59154e36	0.115008
$250$	−9.31323e35	−0.0632456
$251$	2.33773e37	1.49228	0.746141	−	0.665788i	$-0.231905\pi$
$251$	2.33773e37	1.49228	0.746141	+	0.665788i	$0.231905\pi$
$252$	7.92743e34	0.00475799
$253$	−6.39456e36	−0.360946
$254$	2.06226e37	1.09502
$255$	−1.96097e36	−0.0979709
$256$	1.32923e36	0.0625000
$257$	−3.78920e37	−1.67720	−0.838599	−	0.544749i	$-0.816625\pi$
$257$	−3.78920e37	−1.67720	−0.838599	+	0.544749i	$0.816625\pi$
$258$	2.11703e37	0.882310
$259$	9.23845e35	0.0362621
$260$	−4.50853e36	−0.166705
$261$	5.10119e35	0.0177723
$262$	3.73425e37	1.22612
$263$	−1.23104e37	−0.381029	−0.190515	−	0.981684i	$-0.561016\pi$
$263$	−1.23104e37	−0.381029	−0.190515	+	0.981684i	$0.561016\pi$
$264$	−3.18480e36	−0.0929439
$265$	2.20687e36	0.0607387
$266$	−2.26590e35	−0.00588269
$267$	−2.96040e37	−0.725146
$268$	−2.39362e37	−0.553307
$269$	−8.37019e36	−0.182631	−0.0913156	−	0.995822i	$-0.529107\pi$
$269$	−8.37019e36	−0.182631	−0.0913156	+	0.995822i	$0.529107\pi$
$270$	−1.38457e37	−0.285217
$271$	6.44376e37	1.25347	0.626737	−	0.779231i	$-0.284390\pi$
$271$	6.44376e37	1.25347	0.626737	+	0.779231i	$0.284390\pi$
$272$	2.76287e36	0.0507624
$273$	2.68857e36	0.0466660
$274$	4.03685e37	0.662077
$275$	−3.14393e36	−0.0487321
$276$	−5.45379e37	−0.799111
$277$	3.75754e37	0.520556	0.260278	−	0.965534i	$-0.416186\pi$
$277$	3.75754e37	0.520556	0.260278	+	0.965534i	$0.416186\pi$
$278$	3.61104e37	0.473084
$279$	−8.65378e36	−0.107236
$280$	−7.82486e35	−0.00917333
$281$	−3.31550e37	−0.367791	−0.183896	−	0.982946i	$-0.558871\pi$
$281$	−3.31550e37	−0.367791	−0.183896	+	0.982946i	$0.558871\pi$
$282$	−3.48216e37	−0.365585
$283$	1.66415e38	1.65388	0.826938	−	0.562292i	$-0.190080\pi$
$283$	1.66415e38	1.65388	0.826938	+	0.562292i	$0.190080\pi$
$284$	−9.41390e37	−0.885799
$285$	−7.76470e36	−0.0691878
$286$	−1.52197e37	−0.128450
$287$	6.22298e36	0.0497541
$288$	−3.82741e36	−0.0289949
$289$	−1.33546e38	−0.958771
$290$	−5.03519e36	−0.0342647
$291$	−1.42559e38	−0.919713
$292$	−6.69052e37	−0.409285
$293$	5.69894e37	0.330633	0.165317	−	0.986241i	$-0.447135\pi$
$293$	5.69894e37	0.330633	0.165317	+	0.986241i	$0.447135\pi$
$294$	−1.38161e38	−0.760328
$295$	−5.22982e37	−0.273052
$296$	−4.46038e37	−0.220979
$297$	−4.67398e37	−0.219767
$298$	5.14536e37	0.229649
$299$	−2.60630e38	−1.10438
$300$	−2.68139e37	−0.107890
$301$	1.75588e37	0.0670986
$302$	5.65615e37	0.205311
$303$	1.71050e38	0.589877
$304$	1.09399e37	0.0358488
$305$	6.18158e37	0.192509
$306$	−7.95547e36	−0.0235496
$307$	3.60072e38	1.01331	0.506657	−	0.862147i	$-0.330881\pi$
$307$	3.60072e38	1.01331	0.506657	+	0.862147i	$0.330881\pi$
$308$	−2.64149e36	−0.00706826
$309$	−3.41637e38	−0.869379
$310$	8.54182e37	0.206749
$311$	2.32592e37	0.0535560	0.0267780	−	0.999641i	$-0.491475\pi$
$311$	2.32592e37	0.0535560	0.0267780	+	0.999641i	$0.491475\pi$
$312$	−1.29806e38	−0.284380
$313$	7.58763e38	1.58186	0.790932	−	0.611904i	$-0.209596\pi$
$313$	7.58763e38	1.58186	0.790932	+	0.611904i	$0.209596\pi$
$314$	−4.02773e38	−0.799191
$315$	2.25311e36	0.00425568
$316$	1.14936e38	0.206683
$317$	6.69462e38	1.14632	0.573162	−	0.819442i	$-0.305717\pi$
$317$	6.69462e38	1.14632	0.573162	+	0.819442i	$0.305717\pi$
$318$	6.35384e37	0.103613
$319$	−1.69976e37	−0.0264017
$320$	3.77789e37	0.0559017
$321$	3.95408e38	0.557464
$322$	−4.52340e37	−0.0607714
$323$	2.27392e37	0.0291163
$324$	−4.65825e38	−0.568559
$325$	−1.28140e38	−0.149105
$326$	9.73664e38	1.08028
$327$	6.52520e38	0.690405
$328$	−3.00449e38	−0.303198
$329$	−2.88813e37	−0.0278023
$330$	−9.05173e37	−0.0831315
$331$	1.26121e39	1.10523	0.552615	−	0.833437i	$-0.313630\pi$
$331$	1.26121e39	1.10523	0.552615	+	0.833437i	$0.313630\pi$
$332$	−6.37321e37	−0.0532988
$333$	1.28433e38	0.102516
$334$	4.05107e36	0.00308674
$335$	−6.80308e38	−0.494893
$336$	−2.25287e37	−0.0156487
$337$	1.05833e39	0.702036	0.351018	−	0.936369i	$-0.385836\pi$
$337$	1.05833e39	0.702036	0.351018	+	0.936369i	$0.385836\pi$
$338$	4.95750e38	0.314090
$339$	−3.46424e39	−2.09658
$340$	7.85254e37	0.0454033
$341$	2.88352e38	0.159305
$342$	−3.15007e37	−0.0166309
$343$	−2.29570e38	−0.115839
$344$	−8.47749e38	−0.408894
$345$	−1.55006e39	−0.714747
$346$	2.77620e39	1.22397
$347$	−5.76947e38	−0.243237	−0.121618	−	0.992577i	$-0.538808\pi$
$347$	−5.76947e38	−0.243237	−0.121618	+	0.992577i	$0.538808\pi$
$348$	−1.44969e38	−0.0584517
$349$	−2.40704e39	−0.928304	−0.464152	−	0.885756i	$-0.653641\pi$
$349$	−2.40704e39	−0.928304	−0.464152	+	0.885756i	$0.653641\pi$
$350$	−2.22396e37	−0.00820488
$351$	−1.90502e39	−0.672418
$352$	1.27533e38	0.0430735
$353$	3.14178e38	0.101547	0.0507736	−	0.998710i	$-0.483831\pi$
$353$	3.14178e38	0.101547	0.0507736	+	0.998710i	$0.483831\pi$
$354$	−1.50573e39	−0.465796
$355$	−2.67559e39	−0.792283
$356$	1.18547e39	0.336059
$357$	−4.68270e37	−0.0127098
$358$	4.31351e39	1.12110
$359$	−6.98872e39	−1.73954	−0.869768	−	0.493460i	$-0.835732\pi$
$359$	−6.98872e39	−1.73954	−0.869768	+	0.493460i	$0.835732\pi$
$360$	−1.08782e38	−0.0259338
$361$	−4.28883e39	−0.979438
$362$	−2.37570e39	−0.519767
$363$	4.84118e39	1.01484
$364$	−1.07662e38	−0.0216267
$365$	−1.90156e39	−0.366075
$366$	1.77975e39	0.328399
$367$	−2.43434e39	−0.430583	−0.215292	−	0.976550i	$-0.569070\pi$
$367$	−2.43434e39	−0.430583	−0.215292	+	0.976550i	$0.569070\pi$
$368$	2.18393e39	0.370337
$369$	8.65122e38	0.140659
$370$	−1.26772e39	−0.197649
$371$	5.26991e37	0.00787966
$372$	2.45929e39	0.352691
$373$	1.04824e40	1.44203	0.721017	−	0.692917i	$-0.243675\pi$
$373$	1.04824e40	1.44203	0.721017	+	0.692917i	$0.243675\pi$
$374$	2.65083e38	0.0349842
$375$	−7.62096e38	−0.0964995
$376$	1.39441e39	0.169425
$377$	−6.92789e38	−0.0807812
$378$	−3.30629e38	−0.0370014
$379$	6.74056e39	0.724083	0.362041	−	0.932162i	$-0.382080\pi$
$379$	6.74056e39	0.724083	0.362041	+	0.932162i	$0.382080\pi$
$380$	3.10932e38	0.0320641
$381$	1.68754e40	1.67077
$382$	−1.99055e39	−0.189230
$383$	1.08157e40	0.987358	0.493679	−	0.869644i	$-0.335652\pi$
$383$	1.08157e40	0.987358	0.493679	+	0.869644i	$0.335652\pi$
$384$	1.08770e39	0.0953620
$385$	−7.50756e37	−0.00632204
$386$	−1.08351e40	−0.876459
$387$	2.44103e39	0.189694
$388$	5.70865e39	0.426228
$389$	−2.00224e40	−1.43647	−0.718236	−	0.695800i	$-0.755050\pi$
$389$	−2.00224e40	−1.43647	−0.718236	+	0.695800i	$0.755050\pi$
$390$	−3.68931e39	−0.254357
$391$	4.53940e39	0.300787
$392$	5.53254e39	0.352363
$393$	3.05572e40	1.87081
$394$	−1.22581e40	−0.721495
$395$	3.26667e39	0.184863
$396$	−3.67221e38	−0.0199826
$397$	−2.20892e40	−1.15592	−0.577958	−	0.816066i	$-0.696150\pi$
$397$	−2.20892e40	−1.15592	−0.577958	+	0.816066i	$0.696150\pi$
$398$	5.05249e39	0.254283
$399$	−1.85418e38	−0.00897577
$400$	1.07374e39	0.0500000
$401$	−6.25993e39	−0.280435	−0.140217	−	0.990121i	$-0.544780\pi$
$401$	−6.25993e39	−0.280435	−0.140217	+	0.990121i	$0.544780\pi$
$402$	−1.95869e40	−0.844231
$403$	1.17526e40	0.487424
$404$	−6.84955e39	−0.273370
$405$	−1.32395e40	−0.508534
$406$	−1.20238e38	−0.00444518
$407$	−4.27951e39	−0.152293
$408$	2.26084e39	0.0774528
$409$	−3.54495e40	−1.16923	−0.584614	−	0.811311i	$-0.698754\pi$
$409$	−3.54495e40	−1.16923	−0.584614	+	0.811311i	$0.698754\pi$
$410$	−8.53929e39	−0.271189
$411$	3.30333e40	1.01019
$412$	1.36806e40	0.402901
$413$	−1.24886e39	−0.0354232
$414$	−6.28846e39	−0.171806
$415$	−1.81137e39	−0.0476719
$416$	5.19798e39	0.131792
$417$	2.95490e40	0.721828
$418$	1.04963e39	0.0247061
$419$	−2.98080e40	−0.676106	−0.338053	−	0.941127i	$-0.609768\pi$
$419$	−2.98080e40	−0.676106	−0.338053	+	0.941127i	$0.609768\pi$
$420$	−6.40304e38	−0.0139966
$421$	5.17658e40	1.09061	0.545307	−	0.838237i	$-0.316413\pi$
$421$	5.17658e40	1.09061	0.545307	+	0.838237i	$0.316413\pi$
$422$	2.18217e40	0.443144
$423$	−4.01509e39	−0.0785995
$424$	−2.54435e39	−0.0480182
$425$	2.23183e39	0.0406099
$426$	−7.70334e40	−1.35154
$427$	1.47613e39	0.0249743
$428$	−1.58338e40	−0.258349
$429$	−1.24542e40	−0.195988
$430$	−2.40945e40	−0.365726
$431$	3.26439e40	0.477973	0.238987	−	0.971023i	$-0.423185\pi$
$431$	3.26439e40	0.477973	0.238987	+	0.971023i	$0.423185\pi$
$432$	1.59630e40	0.225484
$433$	−1.01421e41	−1.38218	−0.691092	−	0.722767i	$-0.742870\pi$
$433$	−1.01421e41	−1.38218	−0.691092	+	0.722767i	$0.742870\pi$
$434$	2.03975e39	0.0268217
$435$	−4.12027e39	−0.0522808
$436$	−2.61297e40	−0.319958
$437$	1.79744e40	0.212418
$438$	−5.47482e40	−0.624483
$439$	−9.77448e40	−1.07620	−0.538101	−	0.842881i	$-0.680858\pi$
$439$	−9.77448e40	−1.07620	−0.538101	+	0.842881i	$0.680858\pi$
$440$	3.62470e39	0.0385261
$441$	−1.59305e40	−0.163468
$442$	1.08043e40	0.107041
$443$	−8.28639e40	−0.792698	−0.396349	−	0.918100i	$-0.629723\pi$
$443$	−8.28639e40	−0.792698	−0.396349	+	0.918100i	$0.629723\pi$
$444$	−3.64991e40	−0.337168
$445$	3.36931e40	0.300580
$446$	6.45974e40	0.556576
$447$	4.21042e40	0.350396
$448$	9.02145e38	0.00725215
$449$	1.71749e41	1.33375	0.666875	−	0.745169i	$-0.267631\pi$
$449$	1.71749e41	1.33375	0.666875	+	0.745169i	$0.267631\pi$
$450$	−3.09176e39	−0.0231959
$451$	−2.88266e40	−0.208957
$452$	1.38723e41	0.971633
$453$	4.62839e40	0.313262
$454$	1.72032e41	1.12523
$455$	−3.05993e39	−0.0193435
$456$	8.95209e39	0.0546978
$457$	1.56497e41	0.924281	0.462140	−	0.886807i	$-0.347082\pi$
$457$	1.56497e41	0.924281	0.462140	+	0.886807i	$0.347082\pi$
$458$	1.91258e41	1.09195
$459$	3.31799e40	0.183138
$460$	6.20710e40	0.331239
$461$	8.09856e40	0.417872	0.208936	−	0.977929i	$-0.433000\pi$
$461$	8.09856e40	0.417872	0.208936	+	0.977929i	$0.433000\pi$
$462$	−2.16152e39	−0.0107847
$463$	−5.84222e40	−0.281885	−0.140943	−	0.990018i	$-0.545013\pi$
$463$	−5.84222e40	−0.281885	−0.140943	+	0.990018i	$0.545013\pi$
$464$	5.80518e39	0.0270886
$465$	6.98972e40	0.315456
$466$	9.00799e40	0.393229
$467$	−1.90743e41	−0.805446	−0.402723	−	0.915322i	$-0.631936\pi$
$467$	−1.90743e41	−0.805446	−0.402723	+	0.915322i	$0.631936\pi$
$468$	−1.49672e40	−0.0611406
$469$	−1.62455e40	−0.0642027
$470$	3.96314e40	0.151538
$471$	−3.29587e41	−1.21940
$472$	6.02957e40	0.215867
$473$	−8.13372e40	−0.281800
$474$	9.40514e40	0.315356
$475$	8.83721e39	0.0286790
$476$	1.87515e39	0.00589019
$477$	7.32626e39	0.0222765
$478$	1.98812e40	0.0585209
$479$	−1.74507e41	−0.497294	−0.248647	−	0.968594i	$-0.579986\pi$
$479$	−1.74507e41	−0.497294	−0.248647	+	0.968594i	$0.579986\pi$
$480$	3.09143e40	0.0852943
$481$	−1.74424e41	−0.465971
$482$	−3.26373e41	−0.844277
$483$	−3.70148e40	−0.0927245
$484$	−1.93862e41	−0.470315
$485$	1.62250e41	0.381230
$486$	−1.00947e41	−0.229736
$487$	−5.84025e41	−1.28746	−0.643728	−	0.765254i	$-0.722613\pi$
$487$	−5.84025e41	−1.28746	−0.643728	+	0.765254i	$0.722613\pi$
$488$	−7.12687e40	−0.152192
$489$	7.96744e41	1.64828
$490$	1.57244e41	0.315163
$491$	−5.87015e41	−1.13995	−0.569975	−	0.821662i	$-0.693047\pi$
$491$	−5.87015e41	−1.13995	−0.569975	+	0.821662i	$0.693047\pi$
$492$	−2.45856e41	−0.462617
$493$	1.20664e40	0.0220013
$494$	4.27809e40	0.0755932
$495$	−1.04371e40	−0.0178730
$496$	−9.84805e40	−0.163450
$497$	−6.38920e40	−0.102783
$498$	−5.21516e40	−0.0813229
$499$	5.42200e41	0.819598	0.409799	−	0.912176i	$-0.365599\pi$
$499$	5.42200e41	0.819598	0.409799	+	0.912176i	$0.365599\pi$
$500$	3.05176e40	0.0447214
$501$	3.31497e39	0.00470972
$502$	−7.66026e41	−1.05520
$503$	−1.24021e42	−1.65651	−0.828253	−	0.560354i	$-0.810665\pi$
$503$	−1.24021e42	−1.65651	−0.828253	+	0.560354i	$0.810665\pi$
$504$	−2.59766e39	−0.00336441
$505$	−1.94676e41	−0.244510
$506$	2.09537e41	0.255228
$507$	4.05669e41	0.479235
$508$	−6.75761e41	−0.774294
$509$	9.96253e41	1.10725	0.553623	−	0.832768i	$-0.313245\pi$
$509$	9.96253e41	1.10725	0.553623	+	0.832768i	$0.313245\pi$
$510$	6.42569e40	0.0692759
$511$	−4.54084e40	−0.0474911
$512$	−4.35561e40	−0.0441942
$513$	1.31380e41	0.129333
$514$	1.24165e42	1.18596
$515$	3.88826e41	0.360366
$516$	−6.93708e41	−0.623888
$517$	1.33786e41	0.116764
$518$	−3.02725e40	−0.0256412
$519$	2.27175e42	1.86753
$520$	1.47736e41	0.117878
$521$	−4.81065e41	−0.372579	−0.186290	−	0.982495i	$-0.559646\pi$
$521$	−4.81065e41	−0.372579	−0.186290	+	0.982495i	$0.559646\pi$
$522$	−1.67156e40	−0.0125669
$523$	−4.21516e41	−0.307636	−0.153818	−	0.988099i	$-0.549157\pi$
$523$	−4.21516e41	−0.307636	−0.153818	+	0.988099i	$0.549157\pi$
$524$	−1.22364e42	−0.866999
$525$	−1.81985e40	−0.0125189
$526$	4.03388e41	0.269428
$527$	−2.04697e41	−0.132754
$528$	1.04359e41	0.0657212
$529$	1.95303e42	1.19439
$530$	−7.23147e40	−0.0429488
$531$	−1.73617e41	−0.100145
$532$	7.42492e39	0.00415969
$533$	−1.17492e42	−0.639345
$534$	9.70063e41	0.512756
$535$	−4.50024e41	−0.231074
$536$	7.84342e41	0.391247
$537$	3.52972e42	1.71056
$538$	2.74274e41	0.129140
$539$	5.30820e41	0.242841
$540$	4.53695e41	0.201679
$541$	3.12292e42	1.34897	0.674486	−	0.738288i	$-0.264365\pi$
$541$	3.12292e42	1.34897	0.674486	+	0.738288i	$0.264365\pi$
$542$	−2.11149e42	−0.886340
$543$	−1.94402e42	−0.793056
$544$	−9.05336e40	−0.0358944
$545$	−7.42650e41	−0.286180
$546$	−8.80991e40	−0.0329978
$547$	8.44341e41	0.307407	0.153704	−	0.988117i	$-0.450880\pi$
$547$	8.44341e41	0.307407	0.153704	+	0.988117i	$0.450880\pi$
$548$	−1.32279e42	−0.468159
$549$	2.05213e41	0.0706047
$550$	1.03020e41	0.0344588
$551$	4.77783e40	0.0155375
$552$	1.78710e42	0.565057
$553$	7.80068e40	0.0239824
$554$	−1.23127e42	−0.368089
$555$	−1.03737e42	−0.301572
$556$	−1.18327e42	−0.334521
$557$	−4.72577e42	−1.29932	−0.649662	−	0.760223i	$-0.725089\pi$
$557$	−4.72577e42	−1.29932	−0.649662	+	0.760223i	$0.725089\pi$
$558$	2.83567e41	0.0758273
$559$	−3.31514e42	−0.862223
$560$	2.56405e40	0.00648652
$561$	2.16916e41	0.0533787
$562$	1.08642e42	0.260068
$563$	−5.45592e42	−1.27054	−0.635269	−	0.772291i	$-0.719111\pi$
$563$	−5.45592e42	−1.27054	−0.635269	+	0.772291i	$0.719111\pi$
$564$	1.14104e42	0.258508
$565$	3.94274e42	0.869055
$566$	−5.45309e42	−1.16947
$567$	−3.16155e41	−0.0659724
$568$	3.08475e42	0.626354
$569$	−1.38927e42	−0.274503	−0.137251	−	0.990536i	$-0.543827\pi$
$569$	−1.38927e42	−0.274503	−0.137251	+	0.990536i	$0.543827\pi$
$570$	2.54434e41	0.0489232
$571$	7.44435e41	0.139305	0.0696526	−	0.997571i	$-0.477811\pi$
$571$	7.44435e41	0.139305	0.0696526	+	0.997571i	$0.477811\pi$
$572$	4.98720e41	0.0908278
$573$	−1.62885e42	−0.288726
$574$	−2.03915e41	−0.0351815
$575$	1.76416e42	0.296270
$576$	1.25417e41	0.0205025
$577$	3.47495e42	0.552998	0.276499	−	0.961014i	$-0.410826\pi$
$577$	3.47495e42	0.552998	0.276499	+	0.961014i	$0.410826\pi$
$578$	4.37604e42	0.677953
$579$	−8.86634e42	−1.33729
$580$	1.64993e41	0.0242288
$581$	−4.32549e40	−0.00618450
$582$	4.67136e42	0.650335
$583$	−2.44117e41	−0.0330930
$584$	2.19235e42	0.289408
$585$	−4.25394e41	−0.0546859
$586$	−1.86743e42	−0.233793
$587$	−1.21331e43	−1.47939	−0.739694	−	0.672944i	$-0.765030\pi$
$587$	−1.21331e43	−1.47939	−0.739694	+	0.672944i	$0.765030\pi$
$588$	4.52725e42	0.537633
$589$	−8.10523e41	−0.0937515
$590$	1.71371e42	0.193077
$591$	−1.00308e43	−1.10085
$592$	1.46158e42	0.156256
$593$	6.01048e42	0.625981	0.312991	−	0.949756i	$-0.398669\pi$
$593$	6.01048e42	0.625981	0.312991	+	0.949756i	$0.398669\pi$
$594$	1.53157e42	0.155398
$595$	5.32951e40	0.00526834
$596$	−1.68603e42	−0.162386
$597$	4.13442e42	0.387983
$598$	8.54031e42	0.780918
$599$	−1.66324e43	−1.48197	−0.740987	−	0.671520i	$-0.765642\pi$
$599$	−1.66324e43	−1.48197	−0.740987	+	0.671520i	$0.765642\pi$
$600$	8.78637e41	0.0762896
$601$	1.70666e43	1.44409	0.722043	−	0.691848i	$-0.243203\pi$
$601$	1.70666e43	1.44409	0.722043	+	0.691848i	$0.243203\pi$
$602$	−5.75366e41	−0.0474459
$603$	−2.25845e42	−0.181507
$604$	−1.85341e42	−0.145177
$605$	−5.50988e42	−0.420662
$606$	−5.60495e42	−0.417106
$607$	7.20634e42	0.522745	0.261373	−	0.965238i	$-0.415825\pi$
$607$	7.20634e42	0.522745	0.261373	+	0.965238i	$0.415825\pi$
$608$	−3.58480e41	−0.0253489
$609$	−9.83903e40	−0.00678241
$610$	−2.02558e42	−0.136125
$611$	5.45287e42	0.357261
$612$	2.60685e41	0.0166521
$613$	2.06526e43	1.28629	0.643144	−	0.765745i	$-0.277630\pi$
$613$	2.06526e43	1.28629	0.643144	+	0.765745i	$0.277630\pi$
$614$	−1.17988e43	−0.716522
$615$	−6.98765e42	−0.413778
$616$	8.65563e40	0.00499801
$617$	2.04236e43	1.15004	0.575018	−	0.818140i	$-0.304995\pi$
$617$	2.04236e43	1.15004	0.575018	+	0.818140i	$0.304995\pi$
$618$	1.11948e43	0.614744
$619$	−2.85830e42	−0.153074	−0.0765372	−	0.997067i	$-0.524386\pi$
$619$	−2.85830e42	−0.153074	−0.0765372	+	0.997067i	$0.524386\pi$
$620$	−2.79898e42	−0.146194
$621$	2.62273e43	1.33608
$622$	−7.62157e41	−0.0378698
$623$	8.04576e41	0.0389944
$624$	4.25348e42	0.201087
$625$	8.67362e41	0.0400000
$626$	−2.48632e43	−1.11855
$627$	8.58908e41	0.0376964
$628$	1.31981e43	0.565114
$629$	3.03796e42	0.126911
$630$	−7.38299e40	−0.00300922
$631$	3.58197e43	1.42451	0.712257	−	0.701919i	$-0.247673\pi$
$631$	3.58197e43	1.42451	0.712257	+	0.701919i	$0.247673\pi$
$632$	−3.76622e42	−0.146147
$633$	1.78566e43	0.676146
$634$	−2.19369e43	−0.810573
$635$	−1.92063e43	−0.692549
$636$	−2.08203e42	−0.0732657
$637$	2.16352e43	0.743017
$638$	5.56978e41	0.0186688
$639$	−8.88230e42	−0.290577
$640$	−1.23794e42	−0.0395285
$641$	2.02115e43	0.629941	0.314971	−	0.949101i	$-0.398005\pi$
$641$	2.02115e43	0.629941	0.314971	+	0.949101i	$0.398005\pi$
$642$	−1.29567e43	−0.394187
$643$	−1.67149e43	−0.496401	−0.248200	−	0.968709i	$-0.579839\pi$
$643$	−1.67149e43	−0.496401	−0.248200	+	0.968709i	$0.579839\pi$
$644$	1.48223e42	0.0429719
$645$	−1.97164e43	−0.558022
$646$	−7.45118e41	−0.0205883
$647$	−4.63260e43	−1.24971	−0.624853	−	0.780742i	$-0.714841\pi$
$647$	−4.63260e43	−1.24971	−0.624853	+	0.780742i	$0.714841\pi$
$648$	1.52642e43	0.402032
$649$	5.78507e42	0.148770
$650$	4.19890e42	0.105433
$651$	1.66912e42	0.0409243
$652$	−3.19050e43	−0.763874
$653$	−8.05067e43	−1.88225	−0.941126	−	0.338056i	$-0.890231\pi$
$653$	−8.05067e43	−1.88225	−0.941126	+	0.338056i	$0.890231\pi$
$654$	−2.13818e43	−0.488190
$655$	−3.47779e43	−0.775468
$656$	9.84513e42	0.214394
$657$	−6.31271e42	−0.134262
$658$	9.46382e41	0.0196592
$659$	−6.45090e43	−1.30887	−0.654435	−	0.756118i	$-0.727093\pi$
$659$	−6.45090e43	−1.30887	−0.654435	+	0.756118i	$0.727093\pi$
$660$	2.96607e42	0.0587829
$661$	−7.74577e42	−0.149948	−0.0749742	−	0.997185i	$-0.523887\pi$
$661$	−7.74577e42	−0.149948	−0.0749742	+	0.997185i	$0.523887\pi$
$662$	−4.13272e43	−0.781516
$663$	8.84108e42	0.163322
$664$	2.08837e42	0.0376880
$665$	2.11029e41	0.00372054
$666$	−4.20851e42	−0.0724899
$667$	9.53794e42	0.160511
$668$	−1.32746e41	−0.00218265
$669$	5.28597e43	0.849219
$670$	2.22923e43	0.349942
$671$	−6.83787e42	−0.104887
$672$	7.38220e41	0.0110653
$673$	4.06603e43	0.595576	0.297788	−	0.954632i	$-0.403751\pi$
$673$	4.06603e43	0.595576	0.297788	+	0.954632i	$0.403751\pi$
$674$	−3.46795e43	−0.496414
$675$	1.28948e43	0.180387
$676$	−1.62447e43	−0.222095
$677$	9.74695e42	0.130240	0.0651200	−	0.997877i	$-0.479257\pi$
$677$	9.74695e42	0.130240	0.0651200	+	0.997877i	$0.479257\pi$
$678$	1.13516e44	1.48251
$679$	3.87445e42	0.0494571
$680$	−2.57312e42	−0.0321050
$681$	1.40773e44	1.71687
$682$	−9.44871e42	−0.112646
$683$	1.36490e43	0.159067	0.0795337	−	0.996832i	$-0.474657\pi$
$683$	1.36490e43	0.159067	0.0795337	+	0.996832i	$0.474657\pi$
$684$	1.03222e42	0.0117598
$685$	−3.75961e43	−0.418734
$686$	7.52254e42	0.0819107
$687$	1.56505e44	1.66609
$688$	2.77790e43	0.289132
$689$	−9.94974e42	−0.101254
$690$	5.07923e43	0.505402
$691$	−1.10022e42	−0.0107046	−0.00535229	−	0.999986i	$-0.501704\pi$
$691$	−1.10022e42	−0.0107046	−0.00535229	+	0.999986i	$0.501704\pi$
$692$	−9.09706e43	−0.865479
$693$	−2.49232e41	−0.00231867
$694$	1.89054e43	0.171994
$695$	−3.36305e43	−0.299205
$696$	4.75035e42	0.0413316
$697$	2.04636e43	0.174130
$698$	7.88740e43	0.656410
$699$	7.37119e43	0.599986
$700$	7.28747e41	0.00580172
$701$	−2.42614e44	−1.88924	−0.944619	−	0.328169i	$-0.893568\pi$
$701$	−2.42614e44	−1.88924	−0.944619	+	0.328169i	$0.893568\pi$
$702$	6.24237e43	0.475471
$703$	1.20292e43	0.0896251
$704$	−4.17899e42	−0.0304576
$705$	3.24302e43	0.231216
$706$	−1.02950e43	−0.0718048
$707$	−4.64878e42	−0.0317204
$708$	4.93397e43	0.329367
$709$	−1.50345e44	−0.981909	−0.490954	−	0.871185i	$-0.663352\pi$
$709$	−1.50345e44	−0.981909	−0.490954	+	0.871185i	$0.663352\pi$
$710$	8.76737e43	0.560228
$711$	1.08445e43	0.0678004
$712$	−3.88454e43	−0.237629
$713$	−1.61804e44	−0.968503
$714$	1.53443e42	0.00898720
$715$	1.41745e43	0.0812388
$716$	−1.41345e44	−0.792736
$717$	1.62687e43	0.0892906
$718$	2.29006e44	1.23004
$719$	2.19794e43	0.115536	0.0577680	−	0.998330i	$-0.481602\pi$
$719$	2.19794e43	0.115536	0.0577680	+	0.998330i	$0.481602\pi$
$720$	3.56456e42	0.0183380
$721$	9.28501e42	0.0467505
$722$	1.40536e44	0.692567
$723$	−2.67069e44	−1.28819
$724$	7.78469e43	0.367531
$725$	4.68939e42	0.0216709
$726$	−1.58636e44	−0.717602
$727$	1.29172e43	0.0571987	0.0285993	−	0.999591i	$-0.490895\pi$
$727$	1.29172e43	0.0571987	0.0285993	+	0.999591i	$0.490895\pi$
$728$	3.52786e42	0.0152924
$729$	1.85363e44	0.786587
$730$	6.23103e43	0.258854
$731$	5.77401e43	0.234833
$732$	−5.83188e43	−0.232213
$733$	−3.65349e44	−1.42428	−0.712141	−	0.702037i	$-0.752274\pi$
$733$	−3.65349e44	−1.42428	−0.712141	+	0.702037i	$0.752274\pi$
$734$	7.97684e43	0.304468
$735$	1.28672e44	0.480874
$736$	−7.15629e43	−0.261868
$737$	7.52536e43	0.269638
$738$	−2.83483e43	−0.0994612
$739$	1.65100e44	0.567230	0.283615	−	0.958938i	$-0.408466\pi$
$739$	1.65100e44	0.567230	0.283615	+	0.958938i	$0.408466\pi$
$740$	4.15405e43	0.139759
$741$	3.50074e43	0.115339
$742$	−1.72684e42	−0.00557176
$743$	−5.25353e44	−1.66006	−0.830031	−	0.557717i	$-0.811677\pi$
$743$	−5.25353e44	−1.66006	−0.830031	+	0.557717i	$0.811677\pi$
$744$	−8.05860e43	−0.249390
$745$	−4.79199e43	−0.145243
$746$	−3.43489e44	−1.01967
$747$	−6.01331e42	−0.0174841
$748$	−8.68625e42	−0.0247376
$749$	−1.07464e43	−0.0299774
$750$	2.49724e43	0.0682355
$751$	2.28749e44	0.612265	0.306132	−	0.951989i	$-0.400965\pi$
$751$	2.28749e44	0.612265	0.306132	+	0.951989i	$0.400965\pi$
$752$	−4.56919e43	−0.119802
$753$	−6.26835e44	−1.61002
$754$	2.27013e43	0.0571209
$755$	−5.26770e43	−0.129850
$756$	1.08341e43	0.0261639
$757$	3.96084e43	0.0937134	0.0468567	−	0.998902i	$-0.485080\pi$
$757$	3.96084e43	0.0937134	0.0468567	+	0.998902i	$0.485080\pi$
$758$	−2.20875e44	−0.512004
$759$	1.71463e44	0.389424
$760$	−1.01886e43	−0.0226728
$761$	4.33856e44	0.945984	0.472992	−	0.881067i	$-0.343174\pi$
$761$	4.33856e44	0.945984	0.472992	+	0.881067i	$0.343174\pi$
$762$	−5.52972e44	−1.18141
$763$	−1.77342e43	−0.0371262
$764$	6.52262e43	0.133806
$765$	7.40911e42	0.0148941
$766$	−3.54410e44	−0.698168
$767$	2.35788e44	0.455191
$768$	−3.56418e43	−0.0674311
$769$	9.78759e44	1.81475	0.907377	−	0.420318i	$-0.138082\pi$
$769$	9.78759e44	1.81475	0.907377	+	0.420318i	$0.138082\pi$
$770$	2.46008e42	0.00447036
$771$	1.01603e45	1.80953
$772$	3.55046e44	0.619750
$773$	−4.51209e44	−0.771961	−0.385981	−	0.922507i	$-0.626137\pi$
$773$	−4.51209e44	−0.771961	−0.385981	+	0.922507i	$0.626137\pi$
$774$	−7.99876e43	−0.134134
$775$	−7.95519e43	−0.130760
$776$	−1.87061e44	−0.301389
$777$	−2.47719e43	−0.0391231
$778$	6.56094e44	1.01574
$779$	8.10283e43	0.122972
$780$	1.20891e44	0.179857
$781$	2.95966e44	0.431669
$782$	−1.48747e44	−0.212689
$783$	6.97157e43	0.0977289
$784$	−1.81290e44	−0.249159
$785$	3.75112e44	0.505453
$786$	−1.00130e45	−1.32286
$787$	2.01056e44	0.260441	0.130220	−	0.991485i	$-0.458431\pi$
$787$	2.01056e44	0.260441	0.130220	+	0.991485i	$0.458431\pi$
$788$	4.01675e44	0.510174
$789$	3.30090e44	0.411092
$790$	−1.07042e44	−0.130718
$791$	9.41509e43	0.112743
$792$	1.20331e43	0.0141298
$793$	−2.78698e44	−0.320922
$794$	7.23818e44	0.817357
$795$	−5.91747e43	−0.0655309
$796$	−1.65560e44	−0.179805
$797$	−1.47308e45	−1.56900	−0.784500	−	0.620129i	$-0.787080\pi$
$797$	−1.47308e45	−1.56900	−0.784500	+	0.620129i	$0.787080\pi$
$798$	6.07577e42	0.00634682
$799$	−9.49730e43	−0.0973027
$800$	−3.51844e43	−0.0353553
$801$	1.11853e44	0.110241
$802$	2.05125e44	0.198297
$803$	2.10345e44	0.199453
$804$	6.41823e44	0.596961
$805$	4.21275e43	0.0384352
$806$	−3.85111e44	−0.344661
$807$	2.24437e44	0.197040
$808$	2.24446e44	0.193302
$809$	1.82842e45	1.54481	0.772404	−	0.635131i	$-0.219054\pi$
$809$	1.82842e45	1.54481	0.772404	+	0.635131i	$0.219054\pi$
$810$	4.33834e44	0.359588
$811$	8.48526e44	0.689988	0.344994	−	0.938605i	$-0.387881\pi$
$811$	8.48526e44	0.689988	0.344994	+	0.938605i	$0.387881\pi$
$812$	3.93997e42	0.00314321
$813$	−1.72782e45	−1.35237
$814$	1.40231e44	0.107688
$815$	−9.06796e44	−0.683229
$816$	−7.40832e43	−0.0547674
$817$	2.28630e44	0.165840
$818$	1.16161e45	0.826769
$819$	−1.01582e43	−0.00709442
$820$	2.79815e44	0.191759
$821$	−2.50451e45	−1.68424	−0.842119	−	0.539291i	$-0.818692\pi$
$821$	−2.50451e45	−1.68424	−0.842119	+	0.539291i	$0.818692\pi$
$822$	−1.08244e45	−0.714313
$823$	1.83581e45	1.18886	0.594430	−	0.804148i	$-0.297378\pi$
$823$	1.83581e45	1.18886	0.594430	+	0.804148i	$0.297378\pi$
$824$	−4.48286e44	−0.284894
$825$	8.43008e43	0.0525770
$826$	4.09226e43	0.0250480
$827$	1.18525e43	0.00711988	0.00355994	−	0.999994i	$-0.498867\pi$
$827$	1.18525e43	0.00711988	0.00355994	+	0.999994i	$0.498867\pi$
$828$	2.06060e44	0.121485
$829$	−1.49150e45	−0.863034	−0.431517	−	0.902105i	$-0.642022\pi$
$829$	−1.49150e45	−0.863034	−0.431517	+	0.902105i	$0.642022\pi$
$830$	5.93551e43	0.0337091
$831$	−1.00754e45	−0.561626
$832$	−1.70328e44	−0.0931908
$833$	−3.76821e44	−0.202366
$834$	−9.68261e44	−0.510409
$835$	−3.77285e42	−0.00195222
$836$	−3.43943e43	−0.0174699
$837$	−1.18267e45	−0.589685
$838$	9.76747e44	0.478079
$839$	7.17066e44	0.344547	0.172274	−	0.985049i	$-0.444889\pi$
$839$	7.17066e44	0.344547	0.172274	+	0.985049i	$0.444889\pi$
$840$	2.09815e43	0.00989708
$841$	−2.13407e45	−0.988259
$842$	−1.69626e45	−0.771180
$843$	8.89015e44	0.396809
$844$	−7.15053e44	−0.313350
$845$	−4.61703e44	−0.198648
$846$	1.31567e44	0.0555782
$847$	−1.31574e44	−0.0545727
$848$	8.33732e43	0.0339540
$849$	−4.46224e45	−1.78436
$850$	−7.31325e43	−0.0287155
$851$	2.40138e45	0.925876
$852$	2.52423e45	0.955686
$853$	−2.17378e45	−0.808176	−0.404088	−	0.914720i	$-0.632411\pi$
$853$	−2.17378e45	−0.808176	−0.404088	+	0.914720i	$0.632411\pi$
$854$	−4.83700e43	−0.0176595
$855$	2.93373e43	0.0105183
$856$	5.18842e44	0.182680
$857$	1.46655e45	0.507102	0.253551	−	0.967322i	$-0.418401\pi$
$857$	1.46655e45	0.507102	0.253551	+	0.967322i	$0.418401\pi$
$858$	4.08100e44	0.138584
$859$	−3.71283e45	−1.23826	−0.619129	−	0.785290i	$-0.712514\pi$
$859$	−3.71283e45	−1.23826	−0.619129	+	0.785290i	$0.712514\pi$
$860$	7.89527e44	0.258608
$861$	−1.66862e44	−0.0536796
$862$	−1.06967e45	−0.337978
$863$	2.28506e45	0.709138	0.354569	−	0.935030i	$-0.384628\pi$
$863$	2.28506e45	0.709138	0.354569	+	0.935030i	$0.384628\pi$
$864$	−5.23075e44	−0.159441
$865$	−2.58554e45	−0.774108
$866$	3.32337e45	0.977352
$867$	3.58089e45	1.03442
$868$	−6.68385e43	−0.0189658
$869$	−3.61350e44	−0.100721
$870$	1.35013e44	0.0369681
$871$	3.06719e45	0.825010
$872$	8.56218e44	0.226245
$873$	5.38629e44	0.139820
$874$	−5.88984e44	−0.150202
$875$	2.07122e43	0.00518922
$876$	1.79399e45	0.441576
$877$	−1.08696e45	−0.262858	−0.131429	−	0.991326i	$-0.541957\pi$
$877$	−1.08696e45	−0.262858	−0.131429	+	0.991326i	$0.541957\pi$
$878$	3.20290e45	0.760989
$879$	−1.52811e45	−0.356719
$880$	−1.18774e44	−0.0272421
$881$	5.54107e45	1.24873	0.624363	−	0.781134i	$-0.285359\pi$
$881$	5.54107e45	1.24873	0.624363	+	0.781134i	$0.285359\pi$
$882$	5.22012e44	0.115589
$883$	2.97545e45	0.647384	0.323692	−	0.946162i	$-0.395076\pi$
$883$	2.97545e45	0.647384	0.323692	+	0.946162i	$0.395076\pi$
$884$	−3.54034e44	−0.0756894
$885$	1.40232e45	0.294595
$886$	2.71528e45	0.560522
$887$	9.12159e45	1.85035	0.925177	−	0.379537i	$-0.123917\pi$
$887$	9.12159e45	1.85035	0.925177	+	0.379537i	$0.123917\pi$
$888$	1.19600e45	0.238413
$889$	−4.58638e44	−0.0898448
$890$	−1.10405e45	−0.212542
$891$	1.46452e45	0.277071
$892$	−2.11673e45	−0.393559
$893$	−3.76058e44	−0.0687159
$894$	−1.37967e45	−0.247767
$895$	−4.01727e45	−0.709044
$896$	−2.95615e43	−0.00512805
$897$	6.98849e45	1.19152
$898$	−5.62786e45	−0.943104
$899$	−4.30097e44	−0.0708420
$900$	1.01311e44	0.0164020
$901$	1.73295e44	0.0275774
$902$	9.44590e44	0.147755
$903$	−4.70819e44	−0.0723925
$904$	−4.54567e45	−0.687048
$905$	2.21254e45	0.328730
$906$	−1.51663e45	−0.221510
$907$	−5.68239e45	−0.815865	−0.407932	−	0.913012i	$-0.633750\pi$
$907$	−5.68239e45	−0.815865	−0.407932	+	0.913012i	$0.633750\pi$
$908$	−5.63714e45	−0.795661
$909$	−6.46276e44	−0.0896763
$910$	1.00268e44	0.0136779
$911$	−2.79936e43	−0.00375426	−0.00187713	−	0.999998i	$-0.500598\pi$
$911$	−2.79936e43	−0.00375426	−0.00187713	+	0.999998i	$0.500598\pi$
$912$	−2.93342e44	−0.0386772
$913$	2.00369e44	0.0259737
$914$	−5.12808e45	−0.653565
$915$	−1.65752e45	−0.207698
$916$	−6.26713e45	−0.772127
$917$	−8.30482e44	−0.100602
$918$	−1.08724e45	−0.129498
$919$	−1.43630e46	−1.68211	−0.841055	−	0.540950i	$-0.818065\pi$
$919$	−1.43630e46	−1.68211	−0.841055	+	0.540950i	$0.818065\pi$
$920$	−2.03394e45	−0.234222
$921$	−9.65493e45	−1.09326
$922$	−2.65374e45	−0.295480
$923$	1.20630e46	1.32077
$924$	7.08285e43	0.00762593
$925$	1.18065e45	0.125004
$926$	1.91438e45	0.199323
$927$	1.29081e45	0.132168
$928$	−1.90224e44	−0.0191545
$929$	1.85223e46	1.83422	0.917108	−	0.398638i	$-0.130517\pi$
$929$	1.85223e46	1.83422	0.917108	+	0.398638i	$0.130517\pi$
$930$	−2.29039e45	−0.223061
$931$	−1.49207e45	−0.142912
$932$	−2.95174e45	−0.278055
$933$	−6.23669e44	−0.0577815
$934$	6.25026e45	0.569536
$935$	−2.46878e44	−0.0221260
$936$	4.90445e44	0.0432330
$937$	−7.97850e45	−0.691764	−0.345882	−	0.938278i	$-0.612420\pi$
$937$	−7.97850e45	−0.691764	−0.345882	+	0.938278i	$0.612420\pi$
$938$	5.32331e44	0.0453981
$939$	−2.03454e46	−1.70667
$940$	−1.29864e45	−0.107154
$941$	7.58451e45	0.615585	0.307793	−	0.951453i	$-0.400410\pi$
$941$	7.58451e45	0.615585	0.307793	+	0.951453i	$0.400410\pi$
$942$	1.07999e46	0.862246
$943$	1.61756e46	1.27037
$944$	−1.97577e45	−0.152641
$945$	3.07922e44	0.0234017
$946$	2.66526e45	0.199263
$947$	−1.64569e46	−1.21038	−0.605192	−	0.796079i	$-0.706904\pi$
$947$	−1.64569e46	−1.21038	−0.605192	+	0.796079i	$0.706904\pi$
$948$	−3.08188e45	−0.222990
$949$	8.57324e45	0.610265
$950$	−2.89578e44	−0.0202791
$951$	−1.79509e46	−1.23677
$952$	−6.14450e43	−0.00416499
$953$	1.88162e46	1.25485	0.627426	−	0.778676i	$-0.284109\pi$
$953$	1.88162e46	1.25485	0.627426	+	0.778676i	$0.284109\pi$
$954$	−2.40067e44	−0.0157519
$955$	1.85384e45	0.119680
$956$	−6.51468e44	−0.0413805
$957$	4.55772e44	0.0284848
$958$	5.71825e45	0.351640
$959$	−8.97778e44	−0.0543226
$960$	−1.01300e45	−0.0603122
$961$	−9.77291e45	−0.572547
$962$	5.71554e45	0.329491
$963$	−1.49397e45	−0.0847488
$964$	1.06946e46	0.596994
$965$	1.00910e46	0.554321
$966$	1.21290e45	0.0655661
$967$	−2.62276e46	−1.39524	−0.697619	−	0.716469i	$-0.745757\pi$
$967$	−2.62276e46	−1.39524	−0.697619	+	0.716469i	$0.745757\pi$
$968$	6.35246e45	0.332563
$969$	−6.09727e44	−0.0314135
$970$	−5.31660e45	−0.269570
$971$	1.34449e46	0.670904	0.335452	−	0.942057i	$-0.391111\pi$
$971$	1.34449e46	0.670904	0.335452	+	0.942057i	$0.391111\pi$
$972$	3.30782e45	0.162448
$973$	−8.03081e44	−0.0388160
$974$	1.91373e46	0.910369
$975$	3.43594e45	0.160869
$976$	2.33533e45	0.107616
$977$	−1.98144e46	−0.898699	−0.449350	−	0.893356i	$-0.648344\pi$
$977$	−1.98144e46	−0.898699	−0.449350	+	0.893356i	$0.648344\pi$
$978$	−2.61077e46	−1.16551
$979$	−3.72703e45	−0.163769
$980$	−5.15258e45	−0.222854
$981$	−2.46541e45	−0.104959
$982$	1.92353e46	0.806067
$983$	−5.61388e44	−0.0231571	−0.0115785	−	0.999933i	$-0.503686\pi$
$983$	−5.61388e44	−0.0231571	−0.0115785	+	0.999933i	$0.503686\pi$
$984$	8.05621e45	0.327120
$985$	1.14163e46	0.456313
$986$	−3.95390e44	−0.0155573
$987$	7.74419e44	0.0299958
$988$	−1.40185e45	−0.0534524
$989$	4.56411e46	1.71322
$990$	3.42001e44	0.0126381
$991$	9.54885e45	0.347384	0.173692	−	0.984800i	$-0.444430\pi$
$991$	9.54885e45	0.347384	0.173692	+	0.984800i	$0.444430\pi$
$992$	3.22701e45	0.115576
$993$	−3.38179e46	−1.19243
$994$	2.09361e45	0.0726787
$995$	−4.70550e45	−0.160823
$996$	1.70890e45	0.0575040
$997$	−4.00436e45	−0.132666	−0.0663328	−	0.997798i	$-0.521130\pi$
$997$	−4.00436e45	−0.132666	−0.0663328	+	0.997798i	$0.521130\pi$
$998$	−1.77668e46	−0.579543
$999$	1.75524e46	0.563731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.32.a.a.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.32.a.a.1.1	✓	2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-32768.0 q^{2} -2.68139e7 q^{3} +1.07374e9 q^{4} +3.05176e10 q^{5} +8.78637e11 q^{6} +7.28747e11 q^{7} -3.51844e13 q^{8} +1.01311e14 q^{9} -1.00000e15 q^{10} -3.37576e15 q^{11} -2.87912e16 q^{12} -1.37589e17 q^{13} -2.38796e16 q^{14} -8.18295e17 q^{15} +1.15292e18 q^{16} +2.39641e18 q^{17} -3.31975e18 q^{18} +9.48888e18 q^{19} +3.27680e19 q^{20} -1.95405e19 q^{21} +1.10617e20 q^{22} +1.89426e21 q^{23} +9.43430e20 q^{24} +9.31323e20 q^{25} +4.50853e21 q^{26} +1.38457e22 q^{27} +7.82486e20 q^{28} +5.03519e21 q^{29} +2.68139e22 q^{30} -8.54182e22 q^{31} -3.77789e22 q^{32} +9.05173e22 q^{33} -7.85254e22 q^{34} +2.22396e22 q^{35} +1.08782e23 q^{36} +1.26772e24 q^{37} -3.10932e23 q^{38} +3.68931e24 q^{39} -1.07374e24 q^{40} +8.53929e24 q^{41} +6.40304e23 q^{42} +2.40945e25 q^{43} -3.62470e24 q^{44} +3.09176e24 q^{45} -6.20710e25 q^{46} -3.96314e25 q^{47} -3.09143e25 q^{48} -1.57244e26 q^{49} -3.05176e25 q^{50} -6.42569e25 q^{51} -1.47736e26 q^{52} +7.23147e25 q^{53} -4.53695e26 q^{54} -1.03020e26 q^{55} -2.56405e25 q^{56} -2.54434e26 q^{57} -1.64993e26 q^{58} -1.71371e27 q^{59} -8.78637e26 q^{60} +2.02558e27 q^{61} +2.79898e27 q^{62} +7.38299e25 q^{63} +1.23794e27 q^{64} -4.19890e27 q^{65} -2.96607e27 q^{66} -2.22923e28 q^{67} +2.57312e27 q^{68} -5.07923e28 q^{69} -7.28747e26 q^{70} -8.76737e28 q^{71} -3.56456e27 q^{72} -6.23103e28 q^{73} -4.15405e28 q^{74} -2.49724e28 q^{75} +1.01886e28 q^{76} -2.46008e27 q^{77} -1.20891e29 q^{78} +1.07042e29 q^{79} +3.51844e28 q^{80} -4.33834e29 q^{81} -2.79815e29 q^{82} -5.93551e28 q^{83} -2.09815e28 q^{84} +7.31325e28 q^{85} -7.89527e29 q^{86} -1.35013e29 q^{87} +1.18774e29 q^{88} +1.10405e30 q^{89} -1.01311e29 q^{90} -1.00268e29 q^{91} +2.03394e30 q^{92} +2.29039e30 q^{93} +1.29864e30 q^{94} +2.89578e29 q^{95} +1.01300e30 q^{96} +5.31660e30 q^{97} +5.15258e30 q^{98} -3.42001e29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 65536 q^{2} - 5904756 q^{3} + 2147483648 q^{4} + 61035156250 q^{5} + 193487044608 q^{6} + 18016565093212 q^{7} - 70368744177664 q^{8} - 79171117705926 q^{9} - 20\!\cdots\!00 q^{10} - 17\!\cdots\!76 q^{11}+ \cdots + 21\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 65536 * q^2 - 5904756 * q^3 + 2147483648 * q^4 + 61035156250 * q^5 + 193487044608 * q^6 + 18016565093212 * q^7 - 70368744177664 * q^8 - 79171117705926 * q^9 - 2000000000000000 * q^10 - 17416121431336176 * q^11 - 6340183477714944 * q^12 - 25489812233411396 * q^13 - 590366804974370816 * q^14 - 180198852539062500 * q^15 + 2305843009213693952 * q^16 - 16396230747963647148 * q^17 + 2594279184987783168 * q^18 - 107880416928265082840 * q^19 + 65536000000000000000 * q^20 + 341932614252792754464 * q^21 + 570691467062023815168 * q^22 - 577071154821832133436 * q^23 + 207755132197763284992 * q^24 + 1862645149230957031250 * q^25 + 835250167264424624128 * q^26 - 2843043459520171719240 * q^27 + 19345139465400182898688 * q^28 + 67048805832697356280140 * q^29 + 5904756000000000000000 * q^30 + 56909800035573417801064 * q^31 - 75557863725914323419136 * q^32 - 203054257469968728424272 * q^33 + 537271689149272789745664 * q^34 + 549821932776245117187500 * q^35 - 85009340333679678849024 * q^36 + 2801153390572259937695932 * q^37 + 3535025501905390234501120 * q^38 + 6033212900355351396566088 * q^39 - 2147483648000000000000000 * q^40 + 1893631200697714321546884 * q^41 - 11204447903835512978276352 * q^42 + 25327635900154956194956684 * q^43 - 18700417992688396375425024 * q^44 - 2416110769834167480468750 * q^45 + 18909467601201795348430848 * q^46 - 204836832883272087160299828 * q^47 - 6807720171856307322617856 * q^48 - 16151031643901179650461214 * q^49 - 61035156250000000000000000 * q^50 - 457194512783561777077087656 * q^51 - 27369477480920666083426304 * q^52 + 93384041038067791074445644 * q^53 + 93160848081556986896056320 * q^54 - 531497846415288574218750000 * q^55 - 633901530002233193224208384 * q^56 - 2708523042419370548680789680 * q^57 - 2197055269525826970587627520 * q^58 + 401993734479158802793910280 * q^59 - 193487044608000000000000000 * q^60 - 523487156255386223571641876 * q^61 - 1864820327565669754505265152 * q^62 - 3046308524664113764706112756 * q^63 + 2475880078570760549798248448 * q^64 - 777887336224713012695312500 * q^65 + 6653681908775935293006544896 * q^66 + 3525975420949577285673481252 * q^67 - 17605318710043370774385917952 * q^68 - 102465607127544429209145592992 * q^69 - 18016565093212000000000000000 * q^70 - 155367638238255137782572480456 * q^71 + 2785586064054015716524818432 * q^72 - 121161803322719279904680358236 * q^73 - 91788194302271813638420299776 * q^74 - 5499232560396194458007812500 * q^75 - 115835715646435827204132700160 * q^76 - 245187227911068920618395555056 * q^77 - 197696320318844154562677571584 * q^78 - 106325261485679876782031095760 * q^79 + 70368744177664000000000000000 * q^80 - 671301359934033052744190089758 * q^81 - 62050507184462702888448294912 * q^82 - 165992230806613806640311266676 * q^83 + 367147348912882089272159502336 * q^84 - 500373252806507786499023437500 * q^85 - 829935973176277604596340621312 * q^86 + 1161637435058040293762416972680 * q^87 + 612775296784413372429927186432 * q^88 + 596773808150426638152387464820 * q^89 + 79171117705926000000000000000 * q^90 + 1837690480870898595062956149224 * q^91 - 619625434356180429977382027264 * q^92 + 5266346212626013088658434510208 * q^93 + 6712093339919059752068704763904 * q^94 - 3292249051765902186279296875000 * q^95 + 223075374591387478347541905408 * q^96 + 8308055695022791533341129836372 * q^97 + 529237004907353854786313060352 * q^98 + 2192029238850361923111708294288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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