LMFDB - Embedded newform 10.18.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,18,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, 18, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
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:	$18.3222087345$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2941}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 735 $ x^2 - x - 735
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-26.6155$ 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)

$f(q)$	$=$	\(q+256.000 q^{2} +21829.4 q^{3} +65536.0 q^{4} -390625. q^{5} +5.58834e6 q^{6} +1.53649e7 q^{7} +1.67772e7 q^{8} +3.47384e8 q^{9} -1.00000e8 q^{10} -1.15061e9 q^{11} +1.43061e9 q^{12} +4.71918e8 q^{13} +3.93342e9 q^{14} -8.52712e9 q^{15} +4.29497e9 q^{16} +1.89434e10 q^{17} +8.89303e10 q^{18} -7.11086e10 q^{19} -2.56000e10 q^{20} +3.35407e11 q^{21} -2.94556e11 q^{22} -6.03554e10 q^{23} +3.66237e11 q^{24} +1.52588e11 q^{25} +1.20811e11 q^{26} +4.76414e12 q^{27} +1.00695e12 q^{28} +1.95995e12 q^{29} -2.18294e12 q^{30} -2.11583e12 q^{31} +1.09951e12 q^{32} -2.51172e13 q^{33} +4.84950e12 q^{34} -6.00192e12 q^{35} +2.27662e13 q^{36} -3.79079e13 q^{37} -1.82038e13 q^{38} +1.03017e13 q^{39} -6.55360e12 q^{40} +7.71153e13 q^{41} +8.58642e13 q^{42} -9.99172e13 q^{43} -7.54065e13 q^{44} -1.35697e14 q^{45} -1.54510e13 q^{46} -2.88977e13 q^{47} +9.37567e13 q^{48} +3.44976e12 q^{49} +3.90625e13 q^{50} +4.13523e14 q^{51} +3.09276e13 q^{52} -1.47516e14 q^{53} +1.21962e15 q^{54} +4.49458e14 q^{55} +2.57780e14 q^{56} -1.55226e15 q^{57} +5.01748e14 q^{58} -3.95776e14 q^{59} -5.58834e14 q^{60} -2.00041e15 q^{61} -5.41653e14 q^{62} +5.33752e15 q^{63} +2.81475e14 q^{64} -1.84343e14 q^{65} -6.43000e15 q^{66} -3.33086e15 q^{67} +1.24147e15 q^{68} -1.31752e15 q^{69} -1.53649e15 q^{70} +2.99845e15 q^{71} +5.82814e15 q^{72} -1.02670e15 q^{73} -9.70443e15 q^{74} +3.33091e15 q^{75} -4.66017e15 q^{76} -1.76790e16 q^{77} +2.63723e15 q^{78} +4.95112e15 q^{79} -1.67772e15 q^{80} +5.91373e16 q^{81} +1.97415e16 q^{82} -3.56834e15 q^{83} +2.19812e16 q^{84} -7.39975e15 q^{85} -2.55788e16 q^{86} +4.27847e16 q^{87} -1.93041e16 q^{88} -3.06841e16 q^{89} -3.47384e16 q^{90} +7.25097e15 q^{91} -3.95545e15 q^{92} -4.61874e16 q^{93} -7.39781e15 q^{94} +2.77768e16 q^{95} +2.40017e16 q^{96} +3.74691e16 q^{97} +8.83140e14 q^{98} -3.99704e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 512 q^{2} + 17628 q^{3} + 131072 q^{4} - 781250 q^{5} + 4512768 q^{6} + 27684196 q^{7} + 33554432 q^{8} + 235896066 q^{9} - 200000000 q^{10} + 64515264 q^{11} + 1155268608 q^{12} + 2895838468 q^{13}+ \cdots - 53\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 512 * q^2 + 17628 * q^3 + 131072 * q^4 - 781250 * q^5 + 4512768 * q^6 + 27684196 * q^7 + 33554432 * q^8 + 235896066 * q^9 - 200000000 * q^10 + 64515264 * q^11 + 1155268608 * q^12 + 2895838468 * q^13 + 7087154176 * q^14 - 6885937500 * q^15 + 8589934592 * q^16 + 1580212596 * q^17 + 60389392896 * q^18 + 44213712760 * q^19 - 51200000000 * q^20 + 283648477944 * q^21 + 16515907584 * q^22 + 487549782828 * q^23 + 295748763648 * q^24 + 305175781250 * q^25 + 741334647808 * q^26 + 5775127941960 * q^27 + 1814311469056 * q^28 + 3987314863500 * q^29 - 1762800000000 * q^30 - 5492261339336 * q^31 + 2199023255552 * q^32 - 30222474885504 * q^33 + 404534424576 * q^34 - 10814139062500 * q^35 + 15459684581376 * q^36 - 62715287637884 * q^37 + 11318710466560 * q^38 + 117745895352 * q^39 - 13107200000000 * q^40 + 23411477277324 * q^41 + 72614010353664 * q^42 - 124856923191092 * q^43 + 4228072341504 * q^44 - 92146900781250 * q^45 + 124812744403968 * q^46 - 185946612123564 * q^47 + 75711683493888 * q^48 - 77415796886406 * q^49 + 78125000000000 * q^50 + 486473079414744 * q^51 + 189781669838848 * q^52 + 359339780647668 * q^53 + 1478432753141760 * q^54 - 25201275000000 * q^55 + 464463736078336 * q^56 - 2036779039451760 * q^57 + 1020752605056000 * q^58 + 902179170360600 * q^59 - 451276800000000 * q^60 - 1564422918967676 * q^61 - 1406018902870016 * q^62 + 3964069932109668 * q^63 + 562949953421312 * q^64 - 1131186901562500 * q^65 - 7736953570689024 * q^66 - 5839738931054684 * q^67 + 103560812691456 * q^68 - 3619512981398808 * q^69 - 2768419600000000 * q^70 - 67588560434136 * q^71 + 3957679252832256 * q^72 + 3533390699585668 * q^73 - 16055113635298304 * q^74 + 2689819335937500 * q^75 + 2897589879439360 * q^76 - 2709533546636928 * q^77 + 30142949210112 * q^78 + 19002656396552080 * q^79 - 3355443200000000 * q^80 + 69287326451135082 * q^81 + 5993338182994944 * q^82 + 21675087975118188 * q^83 + 18589186650537984 * q^84 - 617270545312500 * q^85 - 31963372336919552 * q^86 + 34266820308892200 * q^87 + 1082386519425024 * q^88 - 97499522192222220 * q^89 - 23589606600000000 * q^90 + 37111957465918664 * q^91 + 31952062567415808 * q^92 - 32001580397816304 * q^93 - 47602332703632384 * q^94 - 17270981546875000 * q^95 + 19382190974435328 * q^96 + 99889937855386756 * q^97 - 19818444002919936 * q^98 - 535176281294791488 * 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 $

$2$	256.000	0.707107
$2$	256.000	0.707107
$3$	21829.4	1.92093	0.960466	−	0.278398i	$-0.0898035\pi$
$3$	21829.4	1.92093	0.960466	+	0.278398i	$0.0898035\pi$
$4$	65536.0	0.500000
$5$	−390625.	−0.447214
$5$	−390625.	−0.447214
$6$	5.58834e6	1.35830
$7$	1.53649e7	1.00739	0.503694	−	0.863882i	$-0.331974\pi$
$7$	1.53649e7	1.00739	0.503694	+	0.863882i	$0.331974\pi$
$8$	1.67772e7	0.353553
$9$	3.47384e8	2.68998
$10$	−1.00000e8	−0.316228
$11$	−1.15061e9	−1.61842	−0.809209	−	0.587521i	$-0.800104\pi$
$11$	−1.15061e9	−1.61842	−0.809209	+	0.587521i	$0.800104\pi$
$12$	1.43061e9	0.960466
$13$	4.71918e8	0.160453	0.0802265	−	0.996777i	$-0.474436\pi$
$13$	4.71918e8	0.160453	0.0802265	+	0.996777i	$0.474436\pi$
$14$	3.93342e9	0.712330
$15$	−8.52712e9	−0.859067
$16$	4.29497e9	0.250000
$17$	1.89434e10	0.658630	0.329315	−	0.944220i	$-0.393182\pi$
$17$	1.89434e10	0.658630	0.329315	+	0.944220i	$0.393182\pi$
$18$	8.89303e10	1.90210
$19$	−7.11086e10	−0.960542	−0.480271	−	0.877120i	$-0.659462\pi$
$19$	−7.11086e10	−0.960542	−0.480271	+	0.877120i	$0.659462\pi$
$20$	−2.56000e10	−0.223607
$21$	3.35407e11	1.93512
$22$	−2.94556e11	−1.14439
$23$	−6.03554e10	−0.160705	−0.0803525	−	0.996767i	$-0.525605\pi$
$23$	−6.03554e10	−0.160705	−0.0803525	+	0.996767i	$0.525605\pi$
$24$	3.66237e11	0.679152
$25$	1.52588e11	0.200000
$26$	1.20811e11	0.113457
$27$	4.76414e12	3.24633
$28$	1.00695e12	0.503694
$29$	1.95995e12	0.727549	0.363775	−	0.931487i	$-0.381488\pi$
$29$	1.95995e12	0.727549	0.363775	+	0.931487i	$0.381488\pi$
$30$	−2.18294e12	−0.607452
$31$	−2.11583e12	−0.445561	−0.222780	−	0.974869i	$-0.571513\pi$
$31$	−2.11583e12	−0.445561	−0.222780	+	0.974869i	$0.571513\pi$
$32$	1.09951e12	0.176777
$33$	−2.51172e13	−3.10887
$34$	4.84950e12	0.465721
$35$	−6.00192e12	−0.450517
$36$	2.27662e13	1.34499
$37$	−3.79079e13	−1.77425	−0.887126	−	0.461526i	$-0.847302\pi$
$37$	−3.79079e13	−1.77425	−0.887126	+	0.461526i	$0.847302\pi$
$38$	−1.82038e13	−0.679206
$39$	1.03017e13	0.308219
$40$	−6.55360e12	−0.158114
$41$	7.71153e13	1.50827	0.754133	−	0.656722i	$-0.228057\pi$
$41$	7.71153e13	1.50827	0.754133	+	0.656722i	$0.228057\pi$
$42$	8.58642e13	1.36834
$43$	−9.99172e13	−1.30364	−0.651821	−	0.758373i	$-0.725995\pi$
$43$	−9.99172e13	−1.30364	−0.651821	+	0.758373i	$0.725995\pi$
$44$	−7.54065e13	−0.809209
$45$	−1.35697e14	−1.20299
$46$	−1.54510e13	−0.113636
$47$	−2.88977e13	−0.177024	−0.0885119	−	0.996075i	$-0.528211\pi$
$47$	−2.88977e13	−0.177024	−0.0885119	+	0.996075i	$0.528211\pi$
$48$	9.37567e13	0.480233
$49$	3.44976e12	0.0148294
$50$	3.90625e13	0.141421
$51$	4.13523e14	1.26518
$52$	3.09276e13	0.0802265
$53$	−1.47516e14	−0.325458	−0.162729	−	0.986671i	$-0.552030\pi$
$53$	−1.47516e14	−0.325458	−0.162729	+	0.986671i	$0.552030\pi$
$54$	1.21962e15	2.29550
$55$	4.49458e14	0.723779
$56$	2.57780e14	0.356165
$57$	−1.55226e15	−1.84513
$58$	5.01748e14	0.514455
$59$	−3.95776e14	−0.350919	−0.175460	−	0.984487i	$-0.556141\pi$
$59$	−3.95776e14	−0.350919	−0.175460	+	0.984487i	$0.556141\pi$
$60$	−5.58834e14	−0.429533
$61$	−2.00041e15	−1.33603	−0.668014	−	0.744148i	$-0.732856\pi$
$61$	−2.00041e15	−1.33603	−0.668014	+	0.744148i	$0.732856\pi$
$62$	−5.41653e14	−0.315059
$63$	5.33752e15	2.70985
$64$	2.81475e14	0.125000
$65$	−1.84343e14	−0.0717567
$66$	−6.43000e15	−2.19830
$67$	−3.33086e15	−1.00212	−0.501061	−	0.865412i	$-0.667057\pi$
$67$	−3.33086e15	−1.00212	−0.501061	+	0.865412i	$0.667057\pi$
$68$	1.24147e15	0.329315
$69$	−1.31752e15	−0.308703
$70$	−1.53649e15	−0.318564
$71$	2.99845e15	0.551062	0.275531	−	0.961292i	$-0.411146\pi$
$71$	2.99845e15	0.551062	0.275531	+	0.961292i	$0.411146\pi$
$72$	5.82814e15	0.951051
$73$	−1.02670e15	−0.149004	−0.0745021	−	0.997221i	$-0.523737\pi$
$73$	−1.02670e15	−0.149004	−0.0745021	+	0.997221i	$0.523737\pi$
$74$	−9.70443e15	−1.25459
$75$	3.33091e15	0.384186
$76$	−4.66017e15	−0.480271
$77$	−1.76790e16	−1.63037
$78$	2.63723e15	0.217944
$79$	4.95112e15	0.367175	0.183587	−	0.983003i	$-0.441229\pi$
$79$	4.95112e15	0.367175	0.183587	+	0.983003i	$0.441229\pi$
$80$	−1.67772e15	−0.111803
$81$	5.91373e16	3.54600
$82$	1.97415e16	1.06650
$83$	−3.56834e15	−0.173901	−0.0869506	−	0.996213i	$-0.527712\pi$
$83$	−3.56834e15	−0.173901	−0.0869506	+	0.996213i	$0.527712\pi$
$84$	2.19812e16	0.967561
$85$	−7.39975e15	−0.294548
$86$	−2.55788e16	−0.921814
$87$	4.27847e16	1.39757
$88$	−1.93041e16	−0.572197
$89$	−3.06841e16	−0.826224	−0.413112	−	0.910680i	$-0.635558\pi$
$89$	−3.06841e16	−0.826224	−0.413112	+	0.910680i	$0.635558\pi$
$90$	−3.47384e16	−0.850646
$91$	7.25097e15	0.161638
$92$	−3.95545e15	−0.0803525
$93$	−4.61874e16	−0.855892
$94$	−7.39781e15	−0.125175
$95$	2.77768e16	0.429567
$96$	2.40017e16	0.339576
$97$	3.74691e16	0.485415	0.242708	−	0.970099i	$-0.421964\pi$
$97$	3.74691e16	0.485415	0.242708	+	0.970099i	$0.421964\pi$
$98$	8.83140e14	0.0104860
$99$	−3.99704e17	−4.35351
$100$	1.00000e16	0.100000
$101$	1.64278e17	1.50955	0.754774	−	0.655985i	$-0.227746\pi$
$101$	1.64278e17	1.50955	0.754774	+	0.655985i	$0.227746\pi$
$102$	1.05862e17	0.894619
$103$	2.11450e17	1.64472	0.822359	−	0.568969i	$-0.192658\pi$
$103$	2.11450e17	1.64472	0.822359	+	0.568969i	$0.192658\pi$
$104$	7.91746e15	0.0567287
$105$	−1.31018e17	−0.865413
$106$	−3.77642e16	−0.230134
$107$	−1.95014e17	−1.09725	−0.548623	−	0.836070i	$-0.684848\pi$
$107$	−1.95014e17	−1.09725	−0.548623	+	0.836070i	$0.684848\pi$
$108$	3.12223e17	1.62317
$109$	1.33790e17	0.643129	0.321565	−	0.946888i	$-0.395791\pi$
$109$	1.33790e17	0.643129	0.321565	+	0.946888i	$0.395791\pi$
$110$	1.15061e17	0.511789
$111$	−8.27509e17	−3.40822
$112$	6.59918e16	0.251847
$113$	2.69841e17	0.954864	0.477432	−	0.878669i	$-0.341568\pi$
$113$	2.69841e17	0.954864	0.477432	+	0.878669i	$0.341568\pi$
$114$	−3.97379e17	−1.30471
$115$	2.35763e16	0.0718695
$116$	1.28447e17	0.363775
$117$	1.63937e17	0.431615
$118$	−1.01319e17	−0.248137
$119$	2.91063e17	0.663495
$120$	−1.43061e17	−0.303726
$121$	8.18459e17	1.61928
$122$	−5.12105e17	−0.944715
$123$	1.68338e18	2.89727
$124$	−1.38663e17	−0.222780
$125$	−5.96046e16	−0.0894427
$126$	1.36641e18	1.91615
$127$	4.12838e17	0.541312	0.270656	−	0.962676i	$-0.412759\pi$
$127$	4.12838e17	0.541312	0.270656	+	0.962676i	$0.412759\pi$
$128$	7.20576e16	0.0883883
$129$	−2.18114e18	−2.50421
$130$	−4.71918e16	−0.0507397
$131$	9.36308e16	0.0943220	0.0471610	−	0.998887i	$-0.484983\pi$
$131$	9.36308e16	0.0943220	0.0471610	+	0.998887i	$0.484983\pi$
$132$	−1.64608e18	−1.55444
$133$	−1.09258e18	−0.967638
$134$	−8.52701e17	−0.708608
$135$	−1.86099e18	−1.45180
$136$	3.17817e17	0.232861
$137$	1.56947e18	1.08051	0.540256	−	0.841501i	$-0.318328\pi$
$137$	1.56947e18	1.08051	0.540256	+	0.841501i	$0.318328\pi$
$138$	−3.37286e17	−0.218286
$139$	3.76763e17	0.229320	0.114660	−	0.993405i	$-0.463422\pi$
$139$	3.76763e17	0.229320	0.114660	+	0.993405i	$0.463422\pi$
$140$	−3.93342e17	−0.225259
$141$	−6.30821e17	−0.340050
$142$	7.67602e17	0.389659
$143$	−5.42994e17	−0.259680
$144$	1.49200e18	0.672494
$145$	−7.65606e17	−0.325370
$146$	−2.62835e17	−0.105362
$147$	7.53064e16	0.0284862
$148$	−2.48433e18	−0.887126
$149$	2.78279e18	0.938419	0.469210	−	0.883087i	$-0.344539\pi$
$149$	2.78279e18	0.938419	0.469210	+	0.883087i	$0.344539\pi$
$150$	8.52712e17	0.271661
$151$	2.92545e18	0.880822	0.440411	−	0.897796i	$-0.354833\pi$
$151$	2.92545e18	0.880822	0.440411	+	0.897796i	$0.354833\pi$
$152$	−1.19300e18	−0.339603
$153$	6.58062e18	1.77170
$154$	−4.52583e18	−1.15285
$155$	8.26497e17	0.199261
$156$	6.75132e17	0.154110
$157$	−4.82580e18	−1.04333	−0.521665	−	0.853150i	$-0.674689\pi$
$157$	−4.82580e18	−1.04333	−0.521665	+	0.853150i	$0.674689\pi$
$158$	1.26749e18	0.259632
$159$	−3.22020e18	−0.625183
$160$	−4.29497e17	−0.0790569
$161$	−9.27355e17	−0.161892
$162$	1.51392e19	2.50740
$163$	−4.37304e18	−0.687367	−0.343684	−	0.939085i	$-0.611675\pi$
$163$	−4.37304e18	−0.687367	−0.343684	+	0.939085i	$0.611675\pi$
$164$	5.05383e18	0.754133
$165$	9.81141e18	1.39033
$166$	−9.13495e17	−0.122967
$167$	−5.59866e15	−0.000716134 0	−0.000358067	−	1.00000i	$-0.500114\pi$
$167$	−5.59866e15	−0.000716134 0	−0.000358067		1.00000i	$0.500114\pi$
$168$	5.62720e18	0.684169
$169$	−8.42771e18	−0.974255
$170$	−1.89434e18	−0.208277
$171$	−2.47020e19	−2.58384
$172$	−6.54818e18	−0.651821
$173$	1.51898e19	1.43933	0.719664	−	0.694323i	$-0.244296\pi$
$173$	1.51898e19	1.43933	0.719664	+	0.694323i	$0.244296\pi$
$174$	1.09529e19	0.988233
$175$	2.34450e18	0.201477
$176$	−4.94184e18	−0.404605
$177$	−8.63957e18	−0.674092
$178$	−7.85512e18	−0.584229
$179$	−1.47005e19	−1.04251	−0.521256	−	0.853400i	$-0.674536\pi$
$179$	−1.47005e19	−1.04251	−0.521256	+	0.853400i	$0.674536\pi$
$180$	−8.89303e18	−0.601497
$181$	1.43306e19	0.924690	0.462345	−	0.886700i	$-0.347008\pi$
$181$	1.43306e19	0.924690	0.462345	+	0.886700i	$0.347008\pi$
$182$	1.85625e18	0.114296
$183$	−4.36679e19	−2.56642
$184$	−1.01260e18	−0.0568178
$185$	1.48078e19	0.793470
$186$	−1.18240e19	−0.605207
$187$	−2.17964e19	−1.06594
$188$	−1.89384e18	−0.0885119
$189$	7.32006e19	3.27031
$190$	7.11086e18	0.303750
$191$	4.75265e19	1.94157	0.970783	−	0.239957i	$-0.0771334\pi$
$191$	4.75265e19	1.94157	0.970783	+	0.239957i	$0.0771334\pi$
$192$	6.14444e18	0.240116
$193$	−1.41251e19	−0.528146	−0.264073	−	0.964503i	$-0.585066\pi$
$193$	−1.41251e19	−0.528146	−0.264073	+	0.964503i	$0.585066\pi$
$194$	9.59209e18	0.343240
$195$	−4.02410e18	−0.137840
$196$	2.26084e17	0.00741469
$197$	3.44120e19	1.08081	0.540403	−	0.841407i	$-0.318272\pi$
$197$	3.44120e19	1.08081	0.540403	+	0.841407i	$0.318272\pi$
$198$	−1.02324e20	−3.07840
$199$	6.74802e18	0.194502	0.0972512	−	0.995260i	$-0.468995\pi$
$199$	6.74802e18	0.194502	0.0972512	+	0.995260i	$0.468995\pi$
$200$	2.56000e18	0.0707107
$201$	−7.27109e19	−1.92501
$202$	4.20551e19	1.06741
$203$	3.01145e19	0.732924
$204$	2.71006e19	0.632591
$205$	−3.01232e19	−0.674517
$206$	5.41312e19	1.16299
$207$	−2.09665e19	−0.432293
$208$	2.02687e18	0.0401132
$209$	8.18183e19	1.55456
$210$	−3.35407e19	−0.611939
$211$	−4.48247e19	−0.785447	−0.392723	−	0.919657i	$-0.628467\pi$
$211$	−4.48247e19	−0.785447	−0.392723	+	0.919657i	$0.628467\pi$
$212$	−9.66763e18	−0.162729
$213$	6.54544e19	1.05855
$214$	−4.99236e19	−0.775870
$215$	3.90302e19	0.583007
$216$	7.99291e19	1.14775
$217$	−3.25096e19	−0.448852
$218$	3.42502e19	0.454761
$219$	−2.24123e19	−0.286227
$220$	2.94556e19	0.361889
$221$	8.93971e18	0.105679
$222$	−2.11842e20	−2.40997
$223$	1.02752e20	1.12512	0.562560	−	0.826757i	$-0.309817\pi$
$223$	1.02752e20	1.12512	0.562560	+	0.826757i	$0.309817\pi$
$224$	1.68939e19	0.178083
$225$	5.30066e19	0.537996
$226$	6.90793e19	0.675191
$227$	−4.88230e19	−0.459626	−0.229813	−	0.973235i	$-0.573811\pi$
$227$	−4.88230e19	−0.459626	−0.229813	+	0.973235i	$0.573811\pi$
$228$	−1.01729e20	−0.922567
$229$	−1.17440e19	−0.102616	−0.0513081	−	0.998683i	$-0.516339\pi$
$229$	−1.17440e19	−0.102616	−0.0513081	+	0.998683i	$0.516339\pi$
$230$	6.03554e18	0.0508194
$231$	−3.85923e20	−3.13184
$232$	3.28825e19	0.257228
$233$	−2.34893e20	−1.77152	−0.885759	−	0.464146i	$-0.846361\pi$
$233$	−2.34893e20	−1.77152	−0.885759	+	0.464146i	$0.846361\pi$
$234$	4.19678e19	0.305198
$235$	1.12882e19	0.0791674
$236$	−2.59376e19	−0.175460
$237$	1.08080e20	0.705318
$238$	7.45121e19	0.469162
$239$	−2.10348e20	−1.27808	−0.639038	−	0.769175i	$-0.720667\pi$
$239$	−2.10348e20	−1.27808	−0.639038	+	0.769175i	$0.720667\pi$
$240$	−3.66237e19	−0.214767
$241$	−2.95279e20	−1.67143	−0.835714	−	0.549164i	$-0.814946\pi$
$241$	−2.95279e20	−1.67143	−0.835714	+	0.549164i	$0.814946\pi$
$242$	2.09526e20	1.14500
$243$	6.75692e20	3.56530
$244$	−1.31099e20	−0.668014
$245$	−1.34756e18	−0.00663190
$246$	4.30946e20	2.04868
$247$	−3.35574e19	−0.154122
$248$	−3.54978e19	−0.157530
$249$	−7.78949e19	−0.334052
$250$	−1.52588e19	−0.0632456
$251$	3.61690e20	1.44914	0.724569	−	0.689203i	$-0.242039\pi$
$251$	3.61690e20	1.44914	0.724569	+	0.689203i	$0.242039\pi$
$252$	3.49800e20	1.35492
$253$	6.94456e19	0.260088
$254$	1.05687e20	0.382766
$255$	−1.61532e20	−0.565807
$256$	1.84467e19	0.0625000
$257$	2.83931e20	0.930640	0.465320	−	0.885143i	$-0.345939\pi$
$257$	2.83931e20	0.930640	0.465320	+	0.885143i	$0.345939\pi$
$258$	−5.58371e20	−1.77074
$259$	−5.82452e20	−1.78736
$260$	−1.20811e19	−0.0358784
$261$	6.80856e20	1.95709
$262$	2.39695e19	0.0666957
$263$	1.89218e20	0.509728	0.254864	−	0.966977i	$-0.417969\pi$
$263$	1.89218e20	0.509728	0.254864	+	0.966977i	$0.417969\pi$
$264$	−4.21397e20	−1.09915
$265$	5.76236e19	0.145549
$266$	−2.79700e20	−0.684223
$267$	−6.69816e20	−1.58712
$268$	−2.18291e20	−0.501061
$269$	2.43538e20	0.541592	0.270796	−	0.962637i	$-0.412713\pi$
$269$	2.43538e20	0.541592	0.270796	+	0.962637i	$0.412713\pi$
$270$	−4.76414e20	−1.02658
$271$	4.10787e20	0.857784	0.428892	−	0.903356i	$-0.358904\pi$
$271$	4.10787e20	0.857784	0.428892	+	0.903356i	$0.358904\pi$
$272$	8.13611e19	0.164657
$273$	1.58285e20	0.310496
$274$	4.01785e20	0.764037
$275$	−1.75569e20	−0.323684
$276$	−8.63453e19	−0.154352
$277$	3.28577e20	0.569586	0.284793	−	0.958589i	$-0.408075\pi$
$277$	3.28577e20	0.569586	0.284793	+	0.958589i	$0.408075\pi$
$278$	9.64513e19	0.162154
$279$	−7.35007e20	−1.19855
$280$	−1.00695e20	−0.159282
$281$	−7.77398e20	−1.19300	−0.596499	−	0.802614i	$-0.703442\pi$
$281$	−7.77398e20	−1.19300	−0.596499	+	0.802614i	$0.703442\pi$
$282$	−1.61490e20	−0.240452
$283$	−2.99751e20	−0.433088	−0.216544	−	0.976273i	$-0.569478\pi$
$283$	−2.99751e20	−0.433088	−0.216544	+	0.976273i	$0.569478\pi$
$284$	1.96506e20	0.275531
$285$	6.06351e20	0.825169
$286$	−1.39006e20	−0.183622
$287$	1.18487e21	1.51941
$288$	3.81953e20	0.475525
$289$	−4.68389e20	−0.566207
$290$	−1.95995e20	−0.230071
$291$	8.17929e20	0.932449
$292$	−6.72857e19	−0.0745021
$293$	2.44316e20	0.262771	0.131386	−	0.991331i	$-0.458057\pi$
$293$	2.44316e20	0.262771	0.131386	+	0.991331i	$0.458057\pi$
$294$	1.92784e19	0.0201428
$295$	1.54600e20	0.156936
$296$	−6.35990e20	−0.627293
$297$	−5.48168e21	−5.25392
$298$	7.12394e20	0.663563
$299$	−2.84828e19	−0.0257856
$300$	2.18294e20	0.192093
$301$	−1.53522e21	−1.31327
$302$	7.48914e20	0.622835
$303$	3.58609e21	2.89974
$304$	−3.05409e20	−0.240135
$305$	7.81411e20	0.597490
$306$	1.68464e21	1.25278
$307$	2.37158e21	1.71538	0.857692	−	0.514164i	$-0.171898\pi$
$307$	2.37158e21	1.71538	0.857692	+	0.514164i	$0.171898\pi$
$308$	−1.15861e21	−0.815187
$309$	4.61583e21	3.15939
$310$	2.11583e20	0.140899
$311$	3.83251e20	0.248325	0.124162	−	0.992262i	$-0.460376\pi$
$311$	3.83251e20	0.248325	0.124162	+	0.992262i	$0.460376\pi$
$312$	1.72834e20	0.108972
$313$	4.12820e20	0.253299	0.126650	−	0.991948i	$-0.459578\pi$
$313$	4.12820e20	0.253299	0.126650	+	0.991948i	$0.459578\pi$
$314$	−1.23540e21	−0.737746
$315$	−2.08497e21	−1.21188
$316$	3.24476e20	0.183587
$317$	−4.33728e20	−0.238899	−0.119449	−	0.992840i	$-0.538113\pi$
$317$	−4.33728e20	−0.238899	−0.119449	+	0.992840i	$0.538113\pi$
$318$	−8.24371e20	−0.442071
$319$	−2.25514e21	−1.17748
$320$	−1.09951e20	−0.0559017
$321$	−4.25705e21	−2.10774
$322$	−2.37403e20	−0.114475
$323$	−1.34704e21	−0.632641
$324$	3.87562e21	1.77300
$325$	7.20089e19	0.0320906
$326$	−1.11950e21	−0.486042
$327$	2.92056e21	1.23541
$328$	1.29378e21	0.533252
$329$	−4.44010e20	−0.178331
$330$	2.51172e21	0.983111
$331$	3.49674e20	0.133391	0.0666953	−	0.997773i	$-0.478754\pi$
$331$	3.49674e20	0.133391	0.0666953	+	0.997773i	$0.478754\pi$
$332$	−2.33855e20	−0.0869506
$333$	−1.31686e22	−4.77270
$334$	−1.43326e18	−0.000506383 0
$335$	1.30112e21	0.448163
$336$	1.44056e21	0.483781
$337$	5.76519e21	1.88782	0.943908	−	0.330209i	$-0.107119\pi$
$337$	5.76519e21	1.88782	0.943908	+	0.330209i	$0.107119\pi$
$338$	−2.15749e21	−0.688902
$339$	5.89048e21	1.83423
$340$	−4.84950e20	−0.147274
$341$	2.43450e21	0.721104
$342$	−6.32371e21	−1.82705
$343$	−3.52134e21	−0.992448
$344$	−1.67633e21	−0.460907
$345$	5.14658e20	0.138056
$346$	3.88858e21	1.01776
$347$	−4.09086e21	−1.04475	−0.522377	−	0.852715i	$-0.674955\pi$
$347$	−4.09086e21	−1.04475	−0.522377	+	0.852715i	$0.674955\pi$
$348$	2.80394e21	0.698786
$349$	−4.79307e20	−0.116573	−0.0582865	−	0.998300i	$-0.518564\pi$
$349$	−4.79307e20	−0.116573	−0.0582865	+	0.998300i	$0.518564\pi$
$350$	6.00192e20	0.142466
$351$	2.24828e21	0.520883
$352$	−1.26511e21	−0.286099
$353$	−3.84712e21	−0.849280	−0.424640	−	0.905362i	$-0.639599\pi$
$353$	−3.84712e21	−0.849280	−0.424640	+	0.905362i	$0.639599\pi$
$354$	−2.21173e21	−0.476655
$355$	−1.17127e21	−0.246442
$356$	−2.01091e21	−0.413112
$357$	6.35374e21	1.27453
$358$	−3.76332e21	−0.737167
$359$	−9.15897e21	−1.75204	−0.876019	−	0.482276i	$-0.839810\pi$
$359$	−9.15897e21	−1.75204	−0.876019	+	0.482276i	$0.839810\pi$
$360$	−2.27662e21	−0.425323
$361$	−4.23960e20	−0.0773595
$362$	3.66863e21	0.653854
$363$	1.78665e22	3.11052
$364$	4.75200e20	0.0808191
$365$	4.01054e20	0.0666367
$366$	−1.11790e22	−1.81473
$367$	2.75835e21	0.437510	0.218755	−	0.975780i	$-0.429800\pi$
$367$	2.75835e21	0.437510	0.218755	+	0.975780i	$0.429800\pi$
$368$	−2.59224e20	−0.0401762
$369$	2.67886e22	4.05720
$370$	3.79079e21	0.561068
$371$	−2.26657e21	−0.327862
$372$	−3.02694e21	−0.427946
$373$	−2.71586e21	−0.375303	−0.187652	−	0.982236i	$-0.560088\pi$
$373$	−2.71586e21	−0.375303	−0.187652	+	0.982236i	$0.560088\pi$
$374$	−5.57989e21	−0.753732
$375$	−1.30114e21	−0.171813
$376$	−4.84823e20	−0.0625873
$377$	9.24936e20	0.116737
$378$	1.87394e22	2.31246
$379$	−5.08917e21	−0.614065	−0.307032	−	0.951699i	$-0.599336\pi$
$379$	−5.08917e21	−0.614065	−0.307032	+	0.951699i	$0.599336\pi$
$380$	1.82038e21	0.214784
$381$	9.01202e21	1.03982
$382$	1.21668e22	1.37290
$383$	−7.65783e21	−0.845116	−0.422558	−	0.906336i	$-0.638868\pi$
$383$	−7.65783e21	−0.845116	−0.422558	+	0.906336i	$0.638868\pi$
$384$	1.57298e21	0.169788
$385$	6.90587e21	0.729126
$386$	−3.61603e21	−0.373456
$387$	−3.47097e22	−3.50677
$388$	2.45557e21	0.242708
$389$	−1.43205e22	−1.38480	−0.692401	−	0.721513i	$-0.743447\pi$
$389$	−1.43205e22	−1.38480	−0.692401	+	0.721513i	$0.743447\pi$
$390$	−1.03017e21	−0.0974674
$391$	−1.14333e21	−0.105845
$392$	5.78775e19	0.00524298
$393$	2.04391e21	0.181186
$394$	8.80948e21	0.764245
$395$	−1.93403e21	−0.164206
$396$	−2.61950e22	−2.17675
$397$	−1.12591e22	−0.915766	−0.457883	−	0.889012i	$-0.651392\pi$
$397$	−1.12591e22	−0.915766	−0.457883	+	0.889012i	$0.651392\pi$
$398$	1.72749e21	0.137534
$399$	−2.38503e22	−1.85877
$400$	6.55360e20	0.0500000
$401$	7.66443e21	0.572470	0.286235	−	0.958159i	$-0.407596\pi$
$401$	7.66443e21	0.572470	0.286235	+	0.958159i	$0.407596\pi$
$402$	−1.86140e22	−1.36119
$403$	−9.98499e20	−0.0714915
$404$	1.07661e22	0.754774
$405$	−2.31005e22	−1.58582
$406$	7.70931e21	0.518256
$407$	4.36173e22	2.87148
$408$	6.93776e21	0.447309
$409$	−5.89700e21	−0.372377	−0.186189	−	0.982514i	$-0.559614\pi$
$409$	−5.89700e21	−0.372377	−0.186189	+	0.982514i	$0.559614\pi$
$410$	−7.71153e21	−0.476955
$411$	3.42607e22	2.07559
$412$	1.38576e22	0.822359
$413$	−6.08106e21	−0.353512
$414$	−5.36742e21	−0.305677
$415$	1.39388e21	0.0777710
$416$	5.18879e20	0.0283643
$417$	8.22452e21	0.440508
$418$	2.09455e22	1.09924
$419$	2.21057e21	0.113680	0.0568400	−	0.998383i	$-0.481898\pi$
$419$	2.21057e21	0.113680	0.0568400	+	0.998383i	$0.481898\pi$
$420$	−8.58642e21	−0.432706
$421$	3.62617e21	0.179081	0.0895406	−	0.995983i	$-0.471460\pi$
$421$	3.62617e21	0.179081	0.0895406	+	0.995983i	$0.471460\pi$
$422$	−1.14751e22	−0.555395
$423$	−1.00386e22	−0.476190
$424$	−2.47491e21	−0.115067
$425$	2.89053e21	0.131726
$426$	1.67563e22	0.748509
$427$	−3.07361e22	−1.34590
$428$	−1.27805e22	−0.548623
$429$	−1.18532e22	−0.498828
$430$	9.99172e21	0.412248
$431$	3.75200e22	1.51777	0.758885	−	0.651225i	$-0.225744\pi$
$431$	3.75200e22	1.51777	0.758885	+	0.651225i	$0.225744\pi$
$432$	2.04618e22	0.811583
$433$	1.27233e22	0.494828	0.247414	−	0.968910i	$-0.420419\pi$
$433$	1.27233e22	0.494828	0.247414	+	0.968910i	$0.420419\pi$
$434$	−8.32245e21	−0.317386
$435$	−1.67128e22	−0.625013
$436$	8.76806e21	0.321565
$437$	4.29178e21	0.154364
$438$	−5.73754e21	−0.202393
$439$	−2.77606e22	−0.960461	−0.480231	−	0.877142i	$-0.659447\pi$
$439$	−2.77606e22	−0.960461	−0.480231	+	0.877142i	$0.659447\pi$
$440$	7.54065e21	0.255894
$441$	1.19839e21	0.0398907
$442$	2.28856e21	0.0747264
$443$	−2.37963e22	−0.762215	−0.381107	−	0.924531i	$-0.624457\pi$
$443$	−2.37963e22	−0.762215	−0.381107	+	0.924531i	$0.624457\pi$
$444$	−5.42316e22	−1.70411
$445$	1.19860e22	0.369499
$446$	2.63045e22	0.795579
$447$	6.07467e22	1.80264
$448$	4.32484e21	0.125923
$449$	3.33620e22	0.953144	0.476572	−	0.879135i	$-0.341879\pi$
$449$	3.33620e22	0.953144	0.476572	+	0.879135i	$0.341879\pi$
$450$	1.35697e22	0.380420
$451$	−8.87297e22	−2.44100
$452$	1.76843e22	0.477432
$453$	6.38609e22	1.69200
$454$	−1.24987e22	−0.325005
$455$	−2.83241e21	−0.0722868
$456$	−2.60426e22	−0.652354
$457$	1.34948e22	0.331801	0.165901	−	0.986142i	$-0.446947\pi$
$457$	1.34948e22	0.331801	0.165901	+	0.986142i	$0.446947\pi$
$458$	−3.00648e21	−0.0725606
$459$	9.02489e22	2.13813
$460$	1.54510e21	0.0359347
$461$	−1.45529e22	−0.332271	−0.166136	−	0.986103i	$-0.553129\pi$
$461$	−1.45529e22	−0.332271	−0.166136	+	0.986103i	$0.553129\pi$
$462$	−9.87964e22	−2.21454
$463$	−5.84077e22	−1.28538	−0.642690	−	0.766126i	$-0.722182\pi$
$463$	−5.84077e22	−1.28538	−0.642690	+	0.766126i	$0.722182\pi$
$464$	8.41793e21	0.181887
$465$	1.80420e22	0.382766
$466$	−6.01327e22	−1.25265
$467$	4.47563e22	0.915504	0.457752	−	0.889080i	$-0.348655\pi$
$467$	4.47563e22	0.915504	0.457752	+	0.889080i	$0.348655\pi$
$468$	1.07438e22	0.215807
$469$	−5.11784e22	−1.00953
$470$	2.88977e21	0.0559798
$471$	−1.05344e23	−2.00417
$472$	−6.64002e21	−0.124069
$473$	1.14966e23	2.10984
$474$	2.76685e22	0.498735
$475$	−1.08503e22	−0.192108
$476$	1.90751e22	0.331748
$477$	−5.12448e22	−0.875475
$478$	−5.38492e22	−0.903737
$479$	−3.08295e22	−0.508293	−0.254147	−	0.967166i	$-0.581795\pi$
$479$	−3.08295e22	−0.508293	−0.254147	+	0.967166i	$0.581795\pi$
$480$	−9.37567e21	−0.151863
$481$	−1.78894e22	−0.284684
$482$	−7.55915e22	−1.18188
$483$	−2.02436e22	−0.310984
$484$	5.36386e22	0.809639
$485$	−1.46364e22	−0.217084
$486$	1.72977e23	2.52104
$487$	−6.13205e22	−0.878233	−0.439116	−	0.898430i	$-0.644708\pi$
$487$	−6.13205e22	−0.878233	−0.439116	+	0.898430i	$0.644708\pi$
$488$	−3.35613e22	−0.472358
$489$	−9.54610e22	−1.32039
$490$	−3.44976e20	−0.00468946
$491$	5.21756e22	0.697067	0.348533	−	0.937296i	$-0.386680\pi$
$491$	5.21756e22	0.697067	0.348533	+	0.937296i	$0.386680\pi$
$492$	1.10322e23	1.44864
$493$	3.71281e22	0.479186
$494$	−8.59069e21	−0.108981
$495$	1.56134e23	1.94695
$496$	−9.08743e21	−0.111390
$497$	4.60708e22	0.555133
$498$	−1.99411e22	−0.236211
$499$	1.47068e23	1.71263	0.856314	−	0.516455i	$-0.172749\pi$
$499$	1.47068e23	1.71263	0.856314	+	0.516455i	$0.172749\pi$
$500$	−3.90625e21	−0.0447214
$501$	−1.22216e20	−0.00137564
$502$	9.25926e22	1.02469
$503$	−7.90275e22	−0.859905	−0.429953	−	0.902851i	$-0.641470\pi$
$503$	−7.90275e22	−0.859905	−0.429953	+	0.902851i	$0.641470\pi$
$504$	8.95488e22	0.958077
$505$	−6.41710e22	−0.675090
$506$	1.77781e22	0.183910
$507$	−1.83972e23	−1.87148
$508$	2.70557e22	0.270656
$509$	1.37816e23	1.35581	0.677905	−	0.735149i	$-0.262888\pi$
$509$	1.37816e23	1.35581	0.677905	+	0.735149i	$0.262888\pi$
$510$	−4.13523e22	−0.400086
$511$	−1.57751e22	−0.150105
$512$	4.72237e21	0.0441942
$513$	−3.38771e23	−3.11824
$514$	7.26864e22	0.658062
$515$	−8.25977e22	−0.735540
$516$	−1.42943e23	−1.25210
$517$	3.32500e22	0.286499
$518$	−1.49108e23	−1.26385
$519$	3.31584e23	2.76485
$520$	−3.09276e21	−0.0253698
$521$	1.81175e23	1.46210	0.731051	−	0.682323i	$-0.239030\pi$
$521$	1.81175e23	1.46210	0.731051	+	0.682323i	$0.239030\pi$
$522$	1.74299e23	1.38387
$523$	8.80774e22	0.688019	0.344009	−	0.938966i	$-0.388215\pi$
$523$	8.80774e22	0.688019	0.344009	+	0.938966i	$0.388215\pi$
$524$	6.13619e21	0.0471610
$525$	5.11791e22	0.387024
$526$	4.84398e22	0.360432
$527$	−4.00810e22	−0.293459
$528$	−1.07878e23	−0.777218
$529$	−1.37407e23	−0.974174
$530$	1.47516e22	0.102919
$531$	−1.37486e23	−0.943965
$532$	−7.16031e22	−0.483819
$533$	3.63921e22	0.242006
$534$	−1.71473e23	−1.12226
$535$	7.61774e22	0.490704
$536$	−5.58826e22	−0.354304
$537$	−3.20903e23	−2.00259
$538$	6.23457e22	0.382963
$539$	−3.96934e21	−0.0240001
$540$	−1.21962e23	−0.725902
$541$	1.23473e23	0.723429	0.361714	−	0.932289i	$-0.382192\pi$
$541$	1.23473e23	0.723429	0.361714	+	0.932289i	$0.382192\pi$
$542$	1.05161e23	0.606545
$543$	3.12829e23	1.77627
$544$	2.08284e22	0.116430
$545$	−5.22617e22	−0.287616
$546$	4.05209e22	0.219554
$547$	−2.14828e22	−0.114604	−0.0573018	−	0.998357i	$-0.518250\pi$
$547$	−2.14828e22	−0.114604	−0.0573018	+	0.998357i	$0.518250\pi$
$548$	1.02857e23	0.540256
$549$	−6.94911e23	−3.59389
$550$	−4.49458e22	−0.228879
$551$	−1.39369e23	−0.698842
$552$	−2.21044e22	−0.109143
$553$	7.60734e22	0.369887
$554$	8.41158e22	0.402758
$555$	3.23246e23	1.52420
$556$	2.46915e22	0.114660
$557$	3.09249e22	0.141429	0.0707146	−	0.997497i	$-0.477472\pi$
$557$	3.09249e22	0.141429	0.0707146	+	0.997497i	$0.477472\pi$
$558$	−1.88162e23	−0.847502
$559$	−4.71527e22	−0.209173
$560$	−2.57780e22	−0.112629
$561$	−4.75804e23	−2.04759
$562$	−1.99014e23	−0.843577
$563$	−6.71869e22	−0.280520	−0.140260	−	0.990115i	$-0.544794\pi$
$563$	−6.71869e22	−0.280520	−0.140260	+	0.990115i	$0.544794\pi$
$564$	−4.13415e22	−0.170025
$565$	−1.05407e23	−0.427028
$566$	−7.67363e22	−0.306239
$567$	9.08639e23	3.57220
$568$	5.03056e22	0.194830
$569$	2.77066e23	1.05713	0.528565	−	0.848893i	$-0.322730\pi$
$569$	2.77066e23	1.05713	0.528565	+	0.848893i	$0.322730\pi$
$570$	1.55226e23	0.583483
$571$	7.97807e22	0.295455	0.147727	−	0.989028i	$-0.452804\pi$
$571$	7.97807e22	0.295455	0.147727	+	0.989028i	$0.452804\pi$
$572$	−3.55856e22	−0.129840
$573$	1.03748e24	3.72962
$574$	3.03327e23	1.07438
$575$	−9.20950e21	−0.0321410
$576$	9.77799e22	0.336247
$577$	4.87229e22	0.165097	0.0825485	−	0.996587i	$-0.473694\pi$
$577$	4.87229e22	0.165097	0.0825485	+	0.996587i	$0.473694\pi$
$578$	−1.19908e23	−0.400369
$579$	−3.08343e23	−1.01453
$580$	−5.01748e22	−0.162685
$581$	−5.48272e22	−0.175186
$582$	2.09390e23	0.659341
$583$	1.69734e23	0.526728
$584$	−1.72251e22	−0.0526810
$585$	−6.40378e22	−0.193024
$586$	6.25450e22	0.185807
$587$	−4.71668e23	−1.38106	−0.690530	−	0.723303i	$-0.742623\pi$
$587$	−4.71668e23	−1.38106	−0.690530	+	0.723303i	$0.742623\pi$
$588$	4.93528e21	0.0142431
$589$	1.50454e23	0.427980
$590$	3.95776e22	0.110970
$591$	7.51195e23	2.07615
$592$	−1.62813e23	−0.443563
$593$	−3.16081e23	−0.848854	−0.424427	−	0.905462i	$-0.639524\pi$
$593$	−3.16081e23	−0.848854	−0.424427	+	0.905462i	$0.639524\pi$
$594$	−1.40331e24	−3.71508
$595$	−1.13696e23	−0.296724
$596$	1.82373e23	0.469210
$597$	1.47305e23	0.373626
$598$	−7.29159e21	−0.0182332
$599$	−4.03133e23	−0.993849	−0.496924	−	0.867794i	$-0.665537\pi$
$599$	−4.03133e23	−0.993849	−0.496924	+	0.867794i	$0.665537\pi$
$600$	5.58834e22	0.135830
$601$	−1.75215e23	−0.419894	−0.209947	−	0.977713i	$-0.567329\pi$
$601$	−1.75215e23	−0.419894	−0.209947	+	0.977713i	$0.567329\pi$
$602$	−3.93016e23	−0.928624
$603$	−1.15709e24	−2.69569
$604$	1.91722e23	0.440411
$605$	−3.19711e23	−0.724163
$606$	9.18039e23	2.05042
$607$	−5.38904e23	−1.18688	−0.593441	−	0.804877i	$-0.702231\pi$
$607$	−5.38904e23	−1.18688	−0.593441	+	0.804877i	$0.702231\pi$
$608$	−7.81847e22	−0.169801
$609$	6.57382e23	1.40790
$610$	2.00041e23	0.422489
$611$	−1.36373e22	−0.0284040
$612$	4.31268e23	0.885849
$613$	7.80727e23	1.58156	0.790779	−	0.612102i	$-0.209676\pi$
$613$	7.80727e23	1.58156	0.790779	+	0.612102i	$0.209676\pi$
$614$	6.07124e23	1.21296
$615$	−6.57572e23	−1.29570
$616$	−2.96605e23	−0.576424
$617$	−4.79487e22	−0.0919079	−0.0459539	−	0.998944i	$-0.514633\pi$
$617$	−4.79487e22	−0.0919079	−0.0459539	+	0.998944i	$0.514633\pi$
$618$	1.18165e24	2.23403
$619$	−7.24528e23	−1.35109	−0.675545	−	0.737319i	$-0.736092\pi$
$619$	−7.24528e23	−1.35109	−0.675545	+	0.737319i	$0.736092\pi$
$620$	5.41653e22	0.0996304
$621$	−2.87542e23	−0.521702
$622$	9.81123e22	0.175592
$623$	−4.71458e23	−0.832328
$624$	4.42454e22	0.0770548
$625$	2.32831e22	0.0400000
$626$	1.05682e23	0.179110
$627$	1.78605e24	2.98620
$628$	−3.16263e23	−0.521665
$629$	−7.18104e23	−1.16858
$630$	−5.33752e23	−0.856930
$631$	−5.16806e23	−0.818613	−0.409306	−	0.912397i	$-0.634229\pi$
$631$	−5.16806e23	−0.818613	−0.409306	+	0.912397i	$0.634229\pi$
$632$	8.30660e22	0.129816
$633$	−9.78499e23	−1.50879
$634$	−1.11034e23	−0.168927
$635$	−1.61265e23	−0.242082
$636$	−2.11039e23	−0.312591
$637$	1.62800e21	0.00237942
$638$	−5.77317e23	−0.832604
$639$	1.04161e24	1.48234
$640$	−2.81475e22	−0.0395285
$641$	8.96049e23	1.24176	0.620881	−	0.783905i	$-0.286775\pi$
$641$	8.96049e23	1.24176	0.620881	+	0.783905i	$0.286775\pi$
$642$	−1.08981e24	−1.49039
$643$	8.53474e23	1.15185	0.575927	−	0.817501i	$-0.304641\pi$
$643$	8.53474e23	1.15185	0.575927	+	0.817501i	$0.304641\pi$
$644$	−6.07751e22	−0.0809461
$645$	8.52007e23	1.11992
$646$	−3.44841e23	−0.447345
$647$	−1.37455e24	−1.75984	−0.879921	−	0.475119i	$-0.842405\pi$
$647$	−1.37455e24	−1.75984	−0.879921	+	0.475119i	$0.842405\pi$
$648$	9.92160e23	1.25370
$649$	4.55384e23	0.567934
$650$	1.84343e22	0.0226915
$651$	−7.09665e23	−0.862214
$652$	−2.86592e23	−0.343684
$653$	9.43977e22	0.111738	0.0558688	−	0.998438i	$-0.482207\pi$
$653$	9.43977e22	0.111738	0.0558688	+	0.998438i	$0.482207\pi$
$654$	7.47663e23	0.873565
$655$	−3.65745e22	−0.0421821
$656$	3.31208e23	0.377066
$657$	−3.56659e23	−0.400818
$658$	−1.13667e23	−0.126099
$659$	−4.47186e23	−0.489736	−0.244868	−	0.969556i	$-0.578745\pi$
$659$	−4.47186e23	−0.489736	−0.244868	+	0.969556i	$0.578745\pi$
$660$	6.43000e23	0.695165
$661$	1.38249e24	1.47554	0.737769	−	0.675054i	$-0.235879\pi$
$661$	1.38249e24	1.47554	0.737769	+	0.675054i	$0.235879\pi$
$662$	8.95165e22	0.0943214
$663$	1.95149e23	0.203002
$664$	−5.98668e22	−0.0614834
$665$	4.26788e23	0.432741
$666$	−3.37117e24	−3.37481
$667$	−1.18294e23	−0.116921
$668$	−3.66914e20	−0.000358067 0
$669$	2.24302e24	2.16128
$670$	3.33086e23	0.316899
$671$	2.30170e24	2.16225
$672$	3.68784e23	0.342084
$673$	5.98224e22	0.0547943	0.0273972	−	0.999625i	$-0.491278\pi$
$673$	5.98224e22	0.0547943	0.0273972	+	0.999625i	$0.491278\pi$
$674$	1.47589e24	1.33489
$675$	7.26951e23	0.649266
$676$	−5.52318e23	−0.487127
$677$	−9.03455e23	−0.786870	−0.393435	−	0.919352i	$-0.628713\pi$
$677$	−9.03455e23	−0.786870	−0.393435	+	0.919352i	$0.628713\pi$
$678$	1.50796e24	1.29700
$679$	5.75709e23	0.489001
$680$	−1.24147e23	−0.104138
$681$	−1.06578e24	−0.882910
$682$	6.23232e23	0.509897
$683$	2.90285e23	0.234557	0.117278	−	0.993099i	$-0.462583\pi$
$683$	2.90285e23	0.234557	0.117278	+	0.993099i	$0.462583\pi$
$684$	−1.61887e24	−1.29192
$685$	−6.13076e23	−0.483219
$686$	−9.01463e23	−0.701767
$687$	−2.56366e23	−0.197119
$688$	−4.29141e23	−0.325911
$689$	−6.96156e22	−0.0522207
$690$	1.31752e23	0.0976206
$691$	−1.83665e24	−1.34420	−0.672098	−	0.740462i	$-0.734607\pi$
$691$	−1.83665e24	−1.34420	−0.672098	+	0.740462i	$0.734607\pi$
$692$	9.95477e23	0.719664
$693$	−6.14142e24	−4.38567
$694$	−1.04726e24	−0.738753
$695$	−1.47173e23	−0.102555
$696$	7.17807e23	0.494117
$697$	1.46082e24	0.993388
$698$	−1.22703e23	−0.0824295
$699$	−5.12759e24	−3.40296
$700$	1.53649e23	0.100739
$701$	2.33493e23	0.151241	0.0756206	−	0.997137i	$-0.475906\pi$
$701$	2.33493e23	0.151241	0.0756206	+	0.997137i	$0.475906\pi$
$702$	5.75561e23	0.368320
$703$	2.69558e24	1.70424
$704$	−3.23868e23	−0.202302
$705$	2.46414e23	0.152075
$706$	−9.84863e23	−0.600532
$707$	2.52411e24	1.52070
$708$	−5.66203e23	−0.337046
$709$	3.27467e24	1.92608	0.963042	−	0.269351i	$-0.0868093\pi$
$709$	3.27467e24	1.92608	0.963042	+	0.269351i	$0.0868093\pi$
$710$	−2.99845e23	−0.174261
$711$	1.71994e24	0.987692
$712$	−5.14793e23	−0.292114
$713$	1.27702e23	0.0716038
$714$	1.62656e24	0.901228
$715$	2.12107e23	0.116132
$716$	−9.63411e23	−0.521256
$717$	−4.59178e24	−2.45510
$718$	−2.34470e24	−1.23888
$719$	3.32629e23	0.173686	0.0868428	−	0.996222i	$-0.472322\pi$
$719$	3.32629e23	0.173686	0.0868428	+	0.996222i	$0.472322\pi$
$720$	−5.82814e23	−0.300749
$721$	3.24891e24	1.65687
$722$	−1.08534e23	−0.0547014
$723$	−6.44578e24	−3.21070
$724$	9.39169e23	0.462345
$725$	2.99065e23	0.145510
$726$	4.57383e24	2.19947
$727$	3.34576e24	1.59020	0.795102	−	0.606476i	$-0.207417\pi$
$727$	3.34576e24	1.59020	0.795102	+	0.606476i	$0.207417\pi$
$728$	1.21651e23	0.0571478
$729$	7.11298e24	3.30269
$730$	1.02670e23	0.0471193
$731$	−1.89277e24	−0.858617
$732$	−2.86182e24	−1.28321
$733$	−4.10279e24	−1.81842	−0.909212	−	0.416333i	$-0.863315\pi$
$733$	−4.10279e24	−1.81842	−0.909212	+	0.416333i	$0.863315\pi$
$734$	7.06138e23	0.309366
$735$	−2.94166e22	−0.0127394
$736$	−6.63614e22	−0.0284089
$737$	3.83253e24	1.62185
$738$	6.85789e24	2.86887
$739$	−3.64889e24	−1.50898	−0.754490	−	0.656311i	$-0.772116\pi$
$739$	−3.64889e24	−1.50898	−0.754490	+	0.656311i	$0.772116\pi$
$740$	9.70443e23	0.396735
$741$	−7.32539e23	−0.296057
$742$	−5.80243e23	−0.231834
$743$	1.84119e24	0.727267	0.363634	−	0.931542i	$-0.381536\pi$
$743$	1.84119e24	0.727267	0.363634	+	0.931542i	$0.381536\pi$
$744$	−7.74897e23	−0.302603
$745$	−1.08703e24	−0.419674
$746$	−6.95261e23	−0.265380
$747$	−1.23959e24	−0.467790
$748$	−1.42845e24	−0.532969
$749$	−2.99638e24	−1.10535
$750$	−3.33091e23	−0.121490
$751$	−4.73106e24	−1.70616	−0.853078	−	0.521783i	$-0.825267\pi$
$751$	−4.73106e24	−1.70616	−0.853078	+	0.521783i	$0.825267\pi$
$752$	−1.24115e23	−0.0442559
$753$	7.89548e24	2.78369
$754$	2.36784e23	0.0825459
$755$	−1.14275e24	−0.393916
$756$	4.79728e24	1.63516
$757$	2.19059e24	0.738321	0.369160	−	0.929366i	$-0.379645\pi$
$757$	2.19059e24	0.738321	0.369160	+	0.929366i	$0.379645\pi$
$758$	−1.30283e24	−0.434209
$759$	1.51596e24	0.499611
$760$	4.66017e23	0.151875
$761$	−3.61511e24	−1.16507	−0.582534	−	0.812806i	$-0.697939\pi$
$761$	−3.61511e24	−1.16507	−0.582534	+	0.812806i	$0.697939\pi$
$762$	2.30708e24	0.735267
$763$	2.05567e24	0.647880
$764$	3.11470e24	0.970783
$765$	−2.57056e24	−0.792328
$766$	−1.96040e24	−0.597587
$767$	−1.86774e23	−0.0563061
$768$	4.02682e23	0.120058
$769$	−3.22044e24	−0.949601	−0.474800	−	0.880093i	$-0.657480\pi$
$769$	−3.22044e24	−0.949601	−0.474800	+	0.880093i	$0.657480\pi$
$770$	1.76790e24	0.515570
$771$	6.19806e24	1.78770
$772$	−9.25703e23	−0.264073
$773$	4.80504e24	1.35573	0.677863	−	0.735189i	$-0.262906\pi$
$773$	4.80504e24	1.35573	0.677863	+	0.735189i	$0.262906\pi$
$774$	−8.88567e24	−2.47966
$775$	−3.22850e23	−0.0891121
$776$	6.28627e23	0.171620
$777$	−1.27146e25	−3.43340
$778$	−3.66606e24	−0.979203
$779$	−5.48356e24	−1.44875
$780$	−2.63723e23	−0.0689199
$781$	−3.45004e24	−0.891848
$782$	−2.92693e23	−0.0748438
$783$	9.33749e24	2.36187
$784$	1.48166e22	0.00370734
$785$	1.88508e24	0.466592
$786$	5.23240e23	0.128118
$787$	8.96802e23	0.217226	0.108613	−	0.994084i	$-0.465359\pi$
$787$	8.96802e23	0.217226	0.108613	+	0.994084i	$0.465359\pi$
$788$	2.25523e24	0.540403
$789$	4.13052e24	0.979152
$790$	−4.95112e23	−0.116111
$791$	4.14608e24	0.961918
$792$	−6.70592e24	−1.53920
$793$	−9.44030e23	−0.214370
$794$	−2.88233e24	−0.647544
$795$	1.25789e24	0.279590
$796$	4.42238e23	0.0972512
$797$	−1.80946e24	−0.393688	−0.196844	−	0.980435i	$-0.563069\pi$
$797$	−1.80946e24	−0.393688	−0.196844	+	0.980435i	$0.563069\pi$
$798$	−6.10568e24	−1.31435
$799$	−5.47420e23	−0.116593
$800$	1.67772e23	0.0353553
$801$	−1.06592e25	−2.22252
$802$	1.96209e24	0.404797
$803$	1.18133e24	0.241151
$804$	−4.76518e24	−0.962505
$805$	3.62248e23	0.0724004
$806$	−2.55616e23	−0.0505521
$807$	5.31630e24	1.04036
$808$	2.75612e24	0.533706
$809$	−7.43901e23	−0.142545	−0.0712726	−	0.997457i	$-0.522706\pi$
$809$	−7.43901e23	−0.142545	−0.0712726	+	0.997457i	$0.522706\pi$
$810$	−5.91373e24	−1.12134
$811$	1.76744e24	0.331640	0.165820	−	0.986156i	$-0.446973\pi$
$811$	1.76744e24	0.331640	0.165820	+	0.986156i	$0.446973\pi$
$812$	1.97358e24	0.366462
$813$	8.96725e24	1.64774
$814$	1.11660e25	2.03045
$815$	1.70822e24	0.307400
$816$	1.77607e24	0.316296
$817$	7.10497e24	1.25220
$818$	−1.50963e24	−0.263310
$819$	2.51887e24	0.434803
$820$	−1.97415e24	−0.337258
$821$	4.58049e24	0.774453	0.387227	−	0.921985i	$-0.373433\pi$
$821$	4.58049e24	0.774453	0.387227	+	0.921985i	$0.373433\pi$
$822$	8.77075e24	1.46766
$823$	−7.92564e24	−1.31261	−0.656305	−	0.754496i	$-0.727882\pi$
$823$	−7.92564e24	−1.31261	−0.656305	+	0.754496i	$0.727882\pi$
$824$	3.54754e24	0.581495
$825$	−3.83258e24	−0.621774
$826$	−1.55675e24	−0.249971
$827$	6.56769e24	1.04380	0.521898	−	0.853008i	$-0.325224\pi$
$827$	6.56769e24	1.04380	0.521898	+	0.853008i	$0.325224\pi$
$828$	−1.37406e24	−0.216146
$829$	−1.03161e25	−1.60621	−0.803105	−	0.595838i	$-0.796820\pi$
$829$	−1.03161e25	−1.60621	−0.803105	+	0.595838i	$0.796820\pi$
$830$	3.56834e23	0.0549924
$831$	7.17266e24	1.09414
$832$	1.32833e23	0.0200566
$833$	6.53501e22	0.00976706
$834$	2.10548e24	0.311486
$835$	2.18698e21	0.000320265 0
$836$	5.36204e24	0.777279
$837$	−1.00801e25	−1.44644
$838$	5.65905e23	0.0803839
$839$	−2.05320e24	−0.288705	−0.144353	−	0.989526i	$-0.546110\pi$
$839$	−2.05320e24	−0.288705	−0.144353	+	0.989526i	$0.546110\pi$
$840$	−2.19812e24	−0.305970
$841$	−3.41573e24	−0.470672
$842$	9.28299e23	0.126630
$843$	−1.69702e25	−2.29167
$844$	−2.93763e24	−0.392723
$845$	3.29207e24	0.435700
$846$	−2.56988e24	−0.336717
$847$	1.25755e25	1.63124
$848$	−6.33578e23	−0.0813645
$849$	−6.54340e24	−0.831932
$850$	7.39975e23	0.0931443
$851$	2.28795e24	0.285131
$852$	4.28962e24	0.529276
$853$	−4.58487e24	−0.560093	−0.280047	−	0.959986i	$-0.590350\pi$
$853$	−4.58487e24	−0.560093	−0.280047	+	0.959986i	$0.590350\pi$
$854$	−7.86845e24	−0.951694
$855$	9.64921e24	1.15553
$856$	−3.27180e24	−0.387935
$857$	−1.47586e25	−1.73264	−0.866322	−	0.499485i	$-0.833522\pi$
$857$	−1.47586e25	−1.73264	−0.866322	+	0.499485i	$0.833522\pi$
$858$	−3.03443e24	−0.352724
$859$	7.38546e24	0.850033	0.425017	−	0.905186i	$-0.360268\pi$
$859$	7.38546e24	0.850033	0.425017	+	0.905186i	$0.360268\pi$
$860$	2.55788e24	0.291503
$861$	2.58650e25	2.91868
$862$	9.60512e24	1.07323
$863$	1.21992e24	0.134971	0.0674856	−	0.997720i	$-0.478502\pi$
$863$	1.21992e24	0.134971	0.0674856	+	0.997720i	$0.478502\pi$
$864$	5.23823e24	0.573876
$865$	−5.93351e24	−0.643687
$866$	3.25718e24	0.349896
$867$	−1.02247e25	−1.08765
$868$	−2.13055e24	−0.224426
$869$	−5.69681e24	−0.594243
$870$	−4.27847e24	−0.441951
$871$	−1.57189e24	−0.160794
$872$	2.24462e24	0.227381
$873$	1.30162e25	1.30576
$874$	1.09870e24	0.109152
$875$	−9.15820e23	−0.0901035
$876$	−1.46881e24	−0.143114
$877$	−7.86521e23	−0.0758951	−0.0379475	−	0.999280i	$-0.512082\pi$
$877$	−7.86521e23	−0.0758951	−0.0379475	+	0.999280i	$0.512082\pi$
$878$	−7.10670e24	−0.679149
$879$	5.33329e24	0.504765
$880$	1.93041e24	0.180945
$881$	−1.48916e25	−1.38244	−0.691218	−	0.722646i	$-0.742926\pi$
$881$	−1.48916e25	−1.38244	−0.691218	+	0.722646i	$0.742926\pi$
$882$	3.06789e23	0.0282070
$883$	2.17779e25	1.98313	0.991563	−	0.129627i	$-0.0413779\pi$
$883$	2.17779e25	1.98313	0.991563	+	0.129627i	$0.0413779\pi$
$884$	5.85873e23	0.0528395
$885$	3.37483e24	0.301463
$886$	−6.09185e24	−0.538967
$887$	−1.34341e25	−1.17722	−0.588609	−	0.808418i	$-0.700324\pi$
$887$	−1.34341e25	−1.17722	−0.588609	+	0.808418i	$0.700324\pi$
$888$	−1.38833e25	−1.20499
$889$	6.34322e24	0.545311
$890$	3.06841e24	0.261275
$891$	−6.80441e25	−5.73892
$892$	6.73395e24	0.562560
$893$	2.05487e24	0.170039
$894$	1.55512e25	1.27466
$895$	5.74238e24	0.466225
$896$	1.10716e24	0.0890413
$897$	−6.21763e23	−0.0495324
$898$	8.54068e24	0.673975
$899$	−4.14693e24	−0.324167
$900$	3.47384e24	0.268998
$901$	−2.79445e24	−0.214356
$902$	−2.27148e25	−1.72605
$903$	−3.35130e25	−2.52271
$904$	4.52718e24	0.337595
$905$	−5.59788e24	−0.413534
$906$	1.63484e25	1.19642
$907$	−2.23611e25	−1.62118	−0.810590	−	0.585614i	$-0.800853\pi$
$907$	−2.23611e25	−1.62118	−0.810590	+	0.585614i	$0.800853\pi$
$908$	−3.19966e24	−0.229813
$909$	5.70675e25	4.06065
$910$	−7.25097e23	−0.0511145
$911$	−2.25949e24	−0.157799	−0.0788994	−	0.996883i	$-0.525141\pi$
$911$	−2.25949e24	−0.157799	−0.0788994	+	0.996883i	$0.525141\pi$
$912$	−6.66691e24	−0.461284
$913$	4.10577e24	0.281445
$914$	3.45466e24	0.234619
$915$	1.70578e25	1.14774
$916$	−7.69658e23	−0.0513081
$917$	1.43863e24	0.0950187
$918$	2.31037e25	1.51189
$919$	−1.15664e25	−0.749923	−0.374962	−	0.927040i	$-0.622344\pi$
$919$	−1.15664e25	−0.749923	−0.374962	+	0.927040i	$0.622344\pi$
$920$	3.95545e23	0.0254097
$921$	5.17702e25	3.29513
$922$	−3.72555e24	−0.234951
$923$	1.41502e24	0.0884195
$924$	−2.52919e25	−1.56592
$925$	−5.78429e24	−0.354851
$926$	−1.49524e25	−0.908901
$927$	7.34544e25	4.42425
$928$	2.15499e24	0.128614
$929$	−3.15273e24	−0.186446	−0.0932229	−	0.995645i	$-0.529717\pi$
$929$	−3.15273e24	−0.186446	−0.0932229	+	0.995645i	$0.529717\pi$
$930$	4.61874e24	0.270657
$931$	−2.45308e23	−0.0142442
$932$	−1.53940e25	−0.885759
$933$	8.36616e24	0.477015
$934$	1.14576e25	0.647359
$935$	8.51424e24	0.476702
$936$	2.75040e24	0.152599
$937$	1.83098e25	1.00670	0.503348	−	0.864084i	$-0.332102\pi$
$937$	1.83098e25	1.00670	0.503348	+	0.864084i	$0.332102\pi$
$938$	−1.31017e25	−0.713843
$939$	9.01163e24	0.486570
$940$	7.39781e23	0.0395837
$941$	−7.12799e24	−0.377968	−0.188984	−	0.981980i	$-0.560519\pi$
$941$	−7.12799e24	−0.377968	−0.188984	+	0.981980i	$0.560519\pi$
$942$	−2.69682e25	−1.41716
$943$	−4.65432e24	−0.242386
$944$	−1.69984e24	−0.0877298
$945$	−2.85940e25	−1.46253
$946$	2.94313e25	1.49188
$947$	5.41921e24	0.272246	0.136123	−	0.990692i	$-0.456536\pi$
$947$	5.41921e24	0.272246	0.136123	+	0.990692i	$0.456536\pi$
$948$	7.08314e24	0.352659
$949$	−4.84517e23	−0.0239082
$950$	−2.77768e24	−0.135841
$951$	−9.46804e24	−0.458908
$952$	4.88323e24	0.234581
$953$	7.60605e24	0.362134	0.181067	−	0.983471i	$-0.442045\pi$
$953$	7.60605e24	0.362134	0.181067	+	0.983471i	$0.442045\pi$
$954$	−1.31187e25	−0.619054
$955$	−1.85650e25	−0.868295
$956$	−1.37854e25	−0.639038
$957$	−4.92285e25	−2.26186
$958$	−7.89235e24	−0.359418
$959$	2.41148e25	1.08849
$960$	−2.40017e24	−0.107383
$961$	−1.80734e25	−0.801476
$962$	−4.57969e24	−0.201302
$963$	−6.77449e25	−2.95157
$964$	−1.93514e25	−0.835714
$965$	5.51762e24	0.236194
$966$	−5.18237e24	−0.219899
$967$	3.18023e25	1.33762	0.668811	−	0.743433i	$-0.266804\pi$
$967$	3.18023e25	1.33762	0.668811	+	0.743433i	$0.266804\pi$
$968$	1.37315e25	0.572501
$969$	−2.94050e25	−1.21526
$970$	−3.74691e24	−0.153502
$971$	3.77342e25	1.53240	0.766198	−	0.642604i	$-0.222146\pi$
$971$	3.77342e25	1.53240	0.766198	+	0.642604i	$0.222146\pi$
$972$	4.42822e25	1.78265
$973$	5.78892e24	0.231014
$974$	−1.56981e25	−0.621004
$975$	1.57191e24	0.0616438
$976$	−8.59170e24	−0.334007
$977$	−2.38735e25	−0.920051	−0.460025	−	0.887906i	$-0.652160\pi$
$977$	−2.38735e25	−0.920051	−0.460025	+	0.887906i	$0.652160\pi$
$978$	−2.44380e25	−0.933654
$979$	3.53054e25	1.33718
$980$	−8.83140e22	−0.00331595
$981$	4.64765e25	1.73000
$982$	1.33569e25	0.492901
$983$	−1.84561e25	−0.675202	−0.337601	−	0.941289i	$-0.609616\pi$
$983$	−1.84561e25	−0.675202	−0.337601	+	0.941289i	$0.609616\pi$
$984$	2.82425e25	1.02434
$985$	−1.34422e25	−0.483351
$986$	9.50479e24	0.338835
$987$	−9.69250e24	−0.342563
$988$	−2.19922e24	−0.0770609
$989$	6.03054e24	0.209502
$990$	3.99704e25	1.37670
$991$	−3.80947e25	−1.30088	−0.650442	−	0.759556i	$-0.725416\pi$
$991$	−3.80947e25	−1.30088	−0.650442	+	0.759556i	$0.725416\pi$
$992$	−2.32638e24	−0.0787648
$993$	7.63318e24	0.256234
$994$	1.17941e25	0.392538
$995$	−2.63594e24	−0.0869842
$996$	−5.10492e24	−0.167026
$997$	−3.25991e25	−1.05754	−0.528770	−	0.848765i	$-0.677346\pi$
$997$	−3.25991e25	−1.05754	−0.528770	+	0.848765i	$0.677346\pi$
$998$	3.76494e25	1.21101
$999$	−1.80599e26	−5.75981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.18.a.d.1.2	✓	2
3.2	odd	2		90.18.a.j.1.2		2
4.3	odd	2		80.18.a.b.1.1		2
5.2	odd	4		50.18.b.f.49.3		4
5.3	odd	4		50.18.b.f.49.2		4
5.4	even	2		50.18.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.d.1.2	✓	2	1.1	even	1	trivial
50.18.a.c.1.1		2	5.4	even	2
50.18.b.f.49.2		4	5.3	odd	4
50.18.b.f.49.3		4	5.2	odd	4
80.18.a.b.1.1		2	4.3	odd	2
90.18.a.j.1.2		2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+256.000 q^{2} +21829.4 q^{3} +65536.0 q^{4} -390625. q^{5} +5.58834e6 q^{6} +1.53649e7 q^{7} +1.67772e7 q^{8} +3.47384e8 q^{9} -1.00000e8 q^{10} -1.15061e9 q^{11} +1.43061e9 q^{12} +4.71918e8 q^{13} +3.93342e9 q^{14} -8.52712e9 q^{15} +4.29497e9 q^{16} +1.89434e10 q^{17} +8.89303e10 q^{18} -7.11086e10 q^{19} -2.56000e10 q^{20} +3.35407e11 q^{21} -2.94556e11 q^{22} -6.03554e10 q^{23} +3.66237e11 q^{24} +1.52588e11 q^{25} +1.20811e11 q^{26} +4.76414e12 q^{27} +1.00695e12 q^{28} +1.95995e12 q^{29} -2.18294e12 q^{30} -2.11583e12 q^{31} +1.09951e12 q^{32} -2.51172e13 q^{33} +4.84950e12 q^{34} -6.00192e12 q^{35} +2.27662e13 q^{36} -3.79079e13 q^{37} -1.82038e13 q^{38} +1.03017e13 q^{39} -6.55360e12 q^{40} +7.71153e13 q^{41} +8.58642e13 q^{42} -9.99172e13 q^{43} -7.54065e13 q^{44} -1.35697e14 q^{45} -1.54510e13 q^{46} -2.88977e13 q^{47} +9.37567e13 q^{48} +3.44976e12 q^{49} +3.90625e13 q^{50} +4.13523e14 q^{51} +3.09276e13 q^{52} -1.47516e14 q^{53} +1.21962e15 q^{54} +4.49458e14 q^{55} +2.57780e14 q^{56} -1.55226e15 q^{57} +5.01748e14 q^{58} -3.95776e14 q^{59} -5.58834e14 q^{60} -2.00041e15 q^{61} -5.41653e14 q^{62} +5.33752e15 q^{63} +2.81475e14 q^{64} -1.84343e14 q^{65} -6.43000e15 q^{66} -3.33086e15 q^{67} +1.24147e15 q^{68} -1.31752e15 q^{69} -1.53649e15 q^{70} +2.99845e15 q^{71} +5.82814e15 q^{72} -1.02670e15 q^{73} -9.70443e15 q^{74} +3.33091e15 q^{75} -4.66017e15 q^{76} -1.76790e16 q^{77} +2.63723e15 q^{78} +4.95112e15 q^{79} -1.67772e15 q^{80} +5.91373e16 q^{81} +1.97415e16 q^{82} -3.56834e15 q^{83} +2.19812e16 q^{84} -7.39975e15 q^{85} -2.55788e16 q^{86} +4.27847e16 q^{87} -1.93041e16 q^{88} -3.06841e16 q^{89} -3.47384e16 q^{90} +7.25097e15 q^{91} -3.95545e15 q^{92} -4.61874e16 q^{93} -7.39781e15 q^{94} +2.77768e16 q^{95} +2.40017e16 q^{96} +3.74691e16 q^{97} +8.83140e14 q^{98} -3.99704e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 512 q^{2} + 17628 q^{3} + 131072 q^{4} - 781250 q^{5} + 4512768 q^{6} + 27684196 q^{7} + 33554432 q^{8} + 235896066 q^{9} - 200000000 q^{10} + 64515264 q^{11} + 1155268608 q^{12} + 2895838468 q^{13}+ \cdots - 53\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 512 * q^2 + 17628 * q^3 + 131072 * q^4 - 781250 * q^5 + 4512768 * q^6 + 27684196 * q^7 + 33554432 * q^8 + 235896066 * q^9 - 200000000 * q^10 + 64515264 * q^11 + 1155268608 * q^12 + 2895838468 * q^13 + 7087154176 * q^14 - 6885937500 * q^15 + 8589934592 * q^16 + 1580212596 * q^17 + 60389392896 * q^18 + 44213712760 * q^19 - 51200000000 * q^20 + 283648477944 * q^21 + 16515907584 * q^22 + 487549782828 * q^23 + 295748763648 * q^24 + 305175781250 * q^25 + 741334647808 * q^26 + 5775127941960 * q^27 + 1814311469056 * q^28 + 3987314863500 * q^29 - 1762800000000 * q^30 - 5492261339336 * q^31 + 2199023255552 * q^32 - 30222474885504 * q^33 + 404534424576 * q^34 - 10814139062500 * q^35 + 15459684581376 * q^36 - 62715287637884 * q^37 + 11318710466560 * q^38 + 117745895352 * q^39 - 13107200000000 * q^40 + 23411477277324 * q^41 + 72614010353664 * q^42 - 124856923191092 * q^43 + 4228072341504 * q^44 - 92146900781250 * q^45 + 124812744403968 * q^46 - 185946612123564 * q^47 + 75711683493888 * q^48 - 77415796886406 * q^49 + 78125000000000 * q^50 + 486473079414744 * q^51 + 189781669838848 * q^52 + 359339780647668 * q^53 + 1478432753141760 * q^54 - 25201275000000 * q^55 + 464463736078336 * q^56 - 2036779039451760 * q^57 + 1020752605056000 * q^58 + 902179170360600 * q^59 - 451276800000000 * q^60 - 1564422918967676 * q^61 - 1406018902870016 * q^62 + 3964069932109668 * q^63 + 562949953421312 * q^64 - 1131186901562500 * q^65 - 7736953570689024 * q^66 - 5839738931054684 * q^67 + 103560812691456 * q^68 - 3619512981398808 * q^69 - 2768419600000000 * q^70 - 67588560434136 * q^71 + 3957679252832256 * q^72 + 3533390699585668 * q^73 - 16055113635298304 * q^74 + 2689819335937500 * q^75 + 2897589879439360 * q^76 - 2709533546636928 * q^77 + 30142949210112 * q^78 + 19002656396552080 * q^79 - 3355443200000000 * q^80 + 69287326451135082 * q^81 + 5993338182994944 * q^82 + 21675087975118188 * q^83 + 18589186650537984 * q^84 - 617270545312500 * q^85 - 31963372336919552 * q^86 + 34266820308892200 * q^87 + 1082386519425024 * q^88 - 97499522192222220 * q^89 - 23589606600000000 * q^90 + 37111957465918664 * q^91 + 31952062567415808 * q^92 - 32001580397816304 * q^93 - 47602332703632384 * q^94 - 17270981546875000 * q^95 + 19382190974435328 * q^96 + 99889937855386756 * q^97 - 19818444002919936 * q^98 - 535176281294791488 * q^99

Introduction

L-functions

Modular forms

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