LMFDB - Embedded newform 14.14.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,14,Mod(1,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("14.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$15.0123300533$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{78985}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 19746 $ x^2 - x - 19746
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$141.021$ of defining polynomial
Character	$\chi$	$=$	14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+64.0000 q^{2} -852.214 q^{3} +4096.00 q^{4} +26804.3 q^{5} -54541.7 q^{6} -117649. q^{7} +262144. q^{8} -868055. q^{9} +O(q^{10})$	\(q+64.0000 q^{2} -852.214 q^{3} +4096.00 q^{4} +26804.3 q^{5} -54541.7 q^{6} -117649. q^{7} +262144. q^{8} -868055. q^{9} +1.71548e6 q^{10} +1.14061e7 q^{11} -3.49067e6 q^{12} +2.15572e7 q^{13} -7.52954e6 q^{14} -2.28430e7 q^{15} +1.67772e7 q^{16} +1.20207e8 q^{17} -5.55555e7 q^{18} -9.08000e7 q^{19} +1.09791e8 q^{20} +1.00262e8 q^{21} +7.29988e8 q^{22} +1.07647e9 q^{23} -2.23403e8 q^{24} -5.02231e8 q^{25} +1.37966e9 q^{26} +2.09847e9 q^{27} -4.81890e8 q^{28} -3.12433e9 q^{29} -1.46195e9 q^{30} -2.89958e9 q^{31} +1.07374e9 q^{32} -9.72040e9 q^{33} +7.69326e9 q^{34} -3.15350e9 q^{35} -3.55555e9 q^{36} -9.56536e9 q^{37} -5.81120e9 q^{38} -1.83713e10 q^{39} +7.02660e9 q^{40} -3.69673e9 q^{41} +6.41677e9 q^{42} -4.09888e10 q^{43} +4.67192e10 q^{44} -2.32676e10 q^{45} +6.88942e10 q^{46} +1.30557e11 q^{47} -1.42978e10 q^{48} +1.38413e10 q^{49} -3.21428e10 q^{50} -1.02442e11 q^{51} +8.82983e10 q^{52} -1.52597e11 q^{53} +1.34302e11 q^{54} +3.05732e11 q^{55} -3.08410e10 q^{56} +7.73810e10 q^{57} -1.99957e11 q^{58} -8.12315e10 q^{59} -9.35650e10 q^{60} +5.04475e10 q^{61} -1.85573e11 q^{62} +1.02126e11 q^{63} +6.87195e10 q^{64} +5.77826e11 q^{65} -6.22105e11 q^{66} -7.97676e11 q^{67} +4.92369e11 q^{68} -9.17384e11 q^{69} -2.01824e11 q^{70} +7.61441e11 q^{71} -2.27555e11 q^{72} +7.61569e10 q^{73} -6.12183e11 q^{74} +4.28008e11 q^{75} -3.71917e11 q^{76} -1.34191e12 q^{77} -1.17577e12 q^{78} -6.85675e11 q^{79} +4.49702e11 q^{80} -4.04386e11 q^{81} -2.36591e11 q^{82} +5.01959e12 q^{83} +4.10673e11 q^{84} +3.22207e12 q^{85} -2.62328e12 q^{86} +2.66260e12 q^{87} +2.99003e12 q^{88} +5.72955e12 q^{89} -1.48913e12 q^{90} -2.53618e12 q^{91} +4.40923e12 q^{92} +2.47106e12 q^{93} +8.35567e12 q^{94} -2.43383e12 q^{95} -9.15057e11 q^{96} -1.46130e13 q^{97} +8.85842e11 q^{98} -9.90109e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 128 q^{2} + 1106 q^{3} + 8192 q^{4} + 75530 q^{5} + 70784 q^{6} - 235298 q^{7} + 524288 q^{8} + 1372222 q^{9}+O(q^{10}) $ 2 * q + 128 * q^2 + 1106 * q^3 + 8192 * q^4 + 75530 * q^5 + 70784 * q^6 - 235298 * q^7 + 524288 * q^8 + 1372222 * q^9	\( 2 q + 128 q^{2} + 1106 q^{3} + 8192 q^{4} + 75530 q^{5} + 70784 q^{6} - 235298 q^{7} + 524288 q^{8} + 1372222 q^{9} + 4833920 q^{10} + 3335860 q^{11} + 4530176 q^{12} + 7998102 q^{13} - 15059072 q^{14} + 72572240 q^{15} + 33554432 q^{16} + 39024832 q^{17} + 87822208 q^{18} + 124092934 q^{19} + 309370880 q^{20} - 130119794 q^{21} + 213495040 q^{22} + 1900816000 q^{23} + 289931264 q^{24} + 651256570 q^{25} + 511878528 q^{26} + 3363388028 q^{27} - 963780608 q^{28} - 245135152 q^{29} + 4644623360 q^{30} - 11010560148 q^{31} + 2147483648 q^{32} - 25523571920 q^{33} + 2497589248 q^{34} - 8886028970 q^{35} + 5620621312 q^{36} - 39630491216 q^{37} + 7941947776 q^{38} - 44922928344 q^{39} + 19799736320 q^{40} - 2431027368 q^{41} - 8327666816 q^{42} + 17823138316 q^{43} + 13663682560 q^{44} + 85891353730 q^{45} + 121652224000 q^{46} + 64488311076 q^{47} + 18555600896 q^{48} + 27682574402 q^{49} + 41680420480 q^{50} - 261414624404 q^{51} + 32760225792 q^{52} - 126504176628 q^{53} + 215256833792 q^{54} - 87494006600 q^{55} - 61681958912 q^{56} + 498187264252 q^{57} - 15688649728 q^{58} + 341259961238 q^{59} + 297255895040 q^{60} + 447240700746 q^{61} - 704675849472 q^{62} - 161440546078 q^{63} + 137438953472 q^{64} - 82849532220 q^{65} - 1633508602880 q^{66} - 2071322290888 q^{67} + 159845711872 q^{68} + 696856132000 q^{69} - 568705854080 q^{70} + 650434465720 q^{71} + 359719763968 q^{72} - 1449809330116 q^{73} - 2536351437824 q^{74} + 2686782332710 q^{75} + 508284657664 q^{76} - 392460593140 q^{77} - 2875067414016 q^{78} + 1525152397656 q^{79} + 1267183124480 q^{80} - 1499135370722 q^{81} - 155585751552 q^{82} + 4257517639438 q^{83} - 532970676224 q^{84} - 733591000220 q^{85} + 1140680852224 q^{86} + 8300678039444 q^{87} + 874475683840 q^{88} + 12593651222628 q^{89} + 5497046638720 q^{90} - 940968702198 q^{91} + 7785742336000 q^{92} - 13411957732344 q^{93} + 4127251908864 q^{94} + 8036967852160 q^{95} + 1187558457344 q^{96} - 16541570007760 q^{97} + 1771684761728 q^{98} - 27980572324540 q^{99}+O(q^{100}) \) 2 * q + 128 * q^2 + 1106 * q^3 + 8192 * q^4 + 75530 * q^5 + 70784 * q^6 - 235298 * q^7 + 524288 * q^8 + 1372222 * q^9 + 4833920 * q^10 + 3335860 * q^11 + 4530176 * q^12 + 7998102 * q^13 - 15059072 * q^14 + 72572240 * q^15 + 33554432 * q^16 + 39024832 * q^17 + 87822208 * q^18 + 124092934 * q^19 + 309370880 * q^20 - 130119794 * q^21 + 213495040 * q^22 + 1900816000 * q^23 + 289931264 * q^24 + 651256570 * q^25 + 511878528 * q^26 + 3363388028 * q^27 - 963780608 * q^28 - 245135152 * q^29 + 4644623360 * q^30 - 11010560148 * q^31 + 2147483648 * q^32 - 25523571920 * q^33 + 2497589248 * q^34 - 8886028970 * q^35 + 5620621312 * q^36 - 39630491216 * q^37 + 7941947776 * q^38 - 44922928344 * q^39 + 19799736320 * q^40 - 2431027368 * q^41 - 8327666816 * q^42 + 17823138316 * q^43 + 13663682560 * q^44 + 85891353730 * q^45 + 121652224000 * q^46 + 64488311076 * q^47 + 18555600896 * q^48 + 27682574402 * q^49 + 41680420480 * q^50 - 261414624404 * q^51 + 32760225792 * q^52 - 126504176628 * q^53 + 215256833792 * q^54 - 87494006600 * q^55 - 61681958912 * q^56 + 498187264252 * q^57 - 15688649728 * q^58 + 341259961238 * q^59 + 297255895040 * q^60 + 447240700746 * q^61 - 704675849472 * q^62 - 161440546078 * q^63 + 137438953472 * q^64 - 82849532220 * q^65 - 1633508602880 * q^66 - 2071322290888 * q^67 + 159845711872 * q^68 + 696856132000 * q^69 - 568705854080 * q^70 + 650434465720 * q^71 + 359719763968 * q^72 - 1449809330116 * q^73 - 2536351437824 * q^74 + 2686782332710 * q^75 + 508284657664 * q^76 - 392460593140 * q^77 - 2875067414016 * q^78 + 1525152397656 * q^79 + 1267183124480 * q^80 - 1499135370722 * q^81 - 155585751552 * q^82 + 4257517639438 * q^83 - 532970676224 * q^84 - 733591000220 * q^85 + 1140680852224 * q^86 + 8300678039444 * q^87 + 874475683840 * q^88 + 12593651222628 * q^89 + 5497046638720 * q^90 - 940968702198 * q^91 + 7785742336000 * q^92 - 13411957732344 * q^93 + 4127251908864 * q^94 + 8036967852160 * q^95 + 1187558457344 * q^96 - 16541570007760 * q^97 + 1771684761728 * q^98 - 27980572324540 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	−852.214	−0.674932	−0.337466	−	0.941338i	$-0.609570\pi$
$3$	−852.214	−0.674932	−0.337466	+	0.941338i	$0.609570\pi$
$4$	4096.00	0.500000
$5$	26804.3	0.767185	0.383592	−	0.923502i	$-0.374687\pi$
$5$	26804.3	0.767185	0.383592	+	0.923502i	$0.374687\pi$
$6$	−54541.7	−0.477249
$7$	−117649.	−0.377964
$7$	−117649.	−0.377964
$8$	262144.	0.353553
$9$	−868055.	−0.544466
$10$	1.71548e6	0.542482
$11$	1.14061e7	1.94126	0.970629	−	0.240582i	$-0.0773383\pi$
$11$	1.14061e7	1.94126	0.970629	+	0.240582i	$0.0773383\pi$
$12$	−3.49067e6	−0.337466
$13$	2.15572e7	1.23868	0.619342	−	0.785121i	$-0.287399\pi$
$13$	2.15572e7	1.23868	0.619342	+	0.785121i	$0.287399\pi$
$14$	−7.52954e6	−0.267261
$15$	−2.28430e7	−0.517798
$16$	1.67772e7	0.250000
$17$	1.20207e8	1.20785	0.603924	−	0.797042i	$-0.293603\pi$
$17$	1.20207e8	1.20785	0.603924	+	0.797042i	$0.293603\pi$
$18$	−5.55555e7	−0.384996
$19$	−9.08000e7	−0.442779	−0.221390	−	0.975185i	$-0.571059\pi$
$19$	−9.08000e7	−0.442779	−0.221390	+	0.975185i	$0.571059\pi$
$20$	1.09791e8	0.383592
$21$	1.00262e8	0.255100
$22$	7.29988e8	1.37268
$23$	1.07647e9	1.51625	0.758127	−	0.652107i	$-0.226115\pi$
$23$	1.07647e9	1.51625	0.758127	+	0.652107i	$0.226115\pi$
$24$	−2.23403e8	−0.238625
$25$	−5.02231e8	−0.411427
$26$	1.37966e9	0.875882
$27$	2.09847e9	1.04241
$28$	−4.81890e8	−0.188982
$29$	−3.12433e9	−0.975372	−0.487686	−	0.873019i	$-0.662159\pi$
$29$	−3.12433e9	−0.975372	−0.487686	+	0.873019i	$0.662159\pi$
$30$	−1.46195e9	−0.366138
$31$	−2.89958e9	−0.586793	−0.293396	−	0.955991i	$-0.594786\pi$
$31$	−2.89958e9	−0.586793	−0.293396	+	0.955991i	$0.594786\pi$
$32$	1.07374e9	0.176777
$33$	−9.72040e9	−1.31022
$34$	7.69326e9	0.854078
$35$	−3.15350e9	−0.289969
$36$	−3.55555e9	−0.272233
$37$	−9.56536e9	−0.612901	−0.306450	−	0.951887i	$-0.599141\pi$
$37$	−9.56536e9	−0.612901	−0.306450	+	0.951887i	$0.599141\pi$
$38$	−5.81120e9	−0.313092
$39$	−1.83713e10	−0.836028
$40$	7.02660e9	0.271241
$41$	−3.69673e9	−0.121541	−0.0607705	−	0.998152i	$-0.519356\pi$
$41$	−3.69673e9	−0.121541	−0.0607705	+	0.998152i	$0.519356\pi$
$42$	6.41677e9	0.180383
$43$	−4.09888e10	−0.988827	−0.494413	−	0.869227i	$-0.664617\pi$
$43$	−4.09888e10	−0.988827	−0.494413	+	0.869227i	$0.664617\pi$
$44$	4.67192e10	0.970629
$45$	−2.32676e10	−0.417706
$46$	6.88942e10	1.07215
$47$	1.30557e11	1.76671	0.883355	−	0.468705i	$-0.155279\pi$
$47$	1.30557e11	1.76671	0.883355	+	0.468705i	$0.155279\pi$
$48$	−1.42978e10	−0.168733
$49$	1.38413e10	0.142857
$50$	−3.21428e10	−0.290923
$51$	−1.02442e11	−0.815216
$52$	8.82983e10	0.619342
$53$	−1.52597e11	−0.945698	−0.472849	−	0.881143i	$-0.656774\pi$
$53$	−1.52597e11	−0.945698	−0.472849	+	0.881143i	$0.656774\pi$
$54$	1.34302e11	0.737095
$55$	3.05732e11	1.48930
$56$	−3.08410e10	−0.133631
$57$	7.73810e10	0.298846
$58$	−1.99957e11	−0.689692
$59$	−8.12315e10	−0.250718	−0.125359	−	0.992111i	$-0.540008\pi$
$59$	−8.12315e10	−0.250718	−0.125359	+	0.992111i	$0.540008\pi$
$60$	−9.35650e10	−0.258899
$61$	5.04475e10	0.125371	0.0626853	−	0.998033i	$-0.480034\pi$
$61$	5.04475e10	0.125371	0.0626853	+	0.998033i	$0.480034\pi$
$62$	−1.85573e11	−0.414925
$63$	1.02126e11	0.205789
$64$	6.87195e10	0.125000
$65$	5.77826e11	0.950299
$66$	−6.22105e11	−0.926464
$67$	−7.97676e11	−1.07731	−0.538654	−	0.842527i	$-0.681067\pi$
$67$	−7.97676e11	−1.07731	−0.538654	+	0.842527i	$0.681067\pi$
$68$	4.92369e11	0.603924
$69$	−9.17384e11	−1.02337
$70$	−2.01824e11	−0.205039
$71$	7.61441e11	0.705435	0.352718	−	0.935730i	$-0.385258\pi$
$71$	7.61441e11	0.705435	0.352718	+	0.935730i	$0.385258\pi$
$72$	−2.27555e11	−0.192498
$73$	7.61569e10	0.0588994	0.0294497	−	0.999566i	$-0.490625\pi$
$73$	7.61569e10	0.0588994	0.0294497	+	0.999566i	$0.490625\pi$
$74$	−6.12183e11	−0.433386
$75$	4.28008e11	0.277686
$76$	−3.71917e11	−0.221390
$77$	−1.34191e12	−0.733726
$78$	−1.17577e12	−0.591161
$79$	−6.85675e11	−0.317353	−0.158676	−	0.987331i	$-0.550723\pi$
$79$	−6.85675e11	−0.317353	−0.158676	+	0.987331i	$0.550723\pi$
$80$	4.49702e11	0.191796
$81$	−4.04386e11	−0.159090
$82$	−2.36591e11	−0.0859424
$83$	5.01959e12	1.68524	0.842619	−	0.538511i	$-0.181013\pi$
$83$	5.01959e12	1.68524	0.842619	+	0.538511i	$0.181013\pi$
$84$	4.10673e11	0.127550
$85$	3.22207e12	0.926643
$86$	−2.62328e12	−0.699206
$87$	2.66260e12	0.658310
$88$	2.99003e12	0.686338
$89$	5.72955e12	1.22204	0.611020	−	0.791615i	$-0.290760\pi$
$89$	5.72955e12	1.22204	0.611020	+	0.791615i	$0.290760\pi$
$90$	−1.48913e12	−0.295363
$91$	−2.53618e12	−0.468178
$92$	4.40923e12	0.758127
$93$	2.47106e12	0.396045
$94$	8.35567e12	1.24925
$95$	−2.43383e12	−0.339694
$96$	−9.15057e11	−0.119312
$97$	−1.46130e13	−1.78124	−0.890619	−	0.454751i	$-0.849728\pi$
$97$	−1.46130e13	−1.78124	−0.890619	+	0.454751i	$0.849728\pi$
$98$	8.85842e11	0.101015
$99$	−9.90109e12	−1.05695
$100$	−2.05714e12	−0.205714
$101$	−2.92067e12	−0.273775	−0.136888	−	0.990587i	$-0.543710\pi$
$101$	−2.92067e12	−0.273775	−0.136888	+	0.990587i	$0.543710\pi$
$102$	−6.55630e12	−0.576445
$103$	−1.20131e13	−0.991316	−0.495658	−	0.868518i	$-0.665073\pi$
$103$	−1.20131e13	−0.991316	−0.495658	+	0.868518i	$0.665073\pi$
$104$	5.65109e12	0.437941
$105$	2.68746e12	0.195709
$106$	−9.76620e12	−0.668710
$107$	−6.14020e11	−0.0395538	−0.0197769	−	0.999804i	$-0.506296\pi$
$107$	−6.14020e11	−0.0395538	−0.0197769	+	0.999804i	$0.506296\pi$
$108$	8.59534e12	0.521205
$109$	−1.04627e13	−0.597544	−0.298772	−	0.954325i	$-0.596577\pi$
$109$	−1.04627e13	−0.597544	−0.298772	+	0.954325i	$0.596577\pi$
$110$	1.95668e13	1.05310
$111$	8.15173e12	0.413667
$112$	−1.97382e12	−0.0944911
$113$	−3.15876e13	−1.42727	−0.713635	−	0.700517i	$-0.752953\pi$
$113$	−3.15876e13	−1.42727	−0.713635	+	0.700517i	$0.752953\pi$
$114$	4.95238e12	0.211316
$115$	2.88541e13	1.16325
$116$	−1.27973e13	−0.487686
$117$	−1.87128e13	−0.674422
$118$	−5.19881e12	−0.177285
$119$	−1.41423e13	−0.456524
$120$	−5.98816e12	−0.183069
$121$	9.55755e13	2.76848
$122$	3.22864e12	0.0886504
$123$	3.15040e12	0.0820319
$124$	−1.18767e13	−0.293396
$125$	−4.61821e13	−1.08283
$126$	6.53605e12	0.145515
$127$	−4.40206e12	−0.0930962	−0.0465481	−	0.998916i	$-0.514822\pi$
$127$	−4.40206e12	−0.0930962	−0.0465481	+	0.998916i	$0.514822\pi$
$128$	4.39805e12	0.0883883
$129$	3.49312e13	0.667391
$130$	3.69809e13	0.671963
$131$	8.52074e13	1.47304	0.736519	−	0.676417i	$-0.236468\pi$
$131$	8.52074e13	1.47304	0.736519	+	0.676417i	$0.236468\pi$
$132$	−3.98148e13	−0.655109
$133$	1.06825e13	0.167355
$134$	−5.10513e13	−0.761772
$135$	5.62481e13	0.799721
$136$	3.15116e13	0.427039
$137$	−8.91713e13	−1.15224	−0.576118	−	0.817367i	$-0.695433\pi$
$137$	−8.91713e13	−1.15224	−0.576118	+	0.817367i	$0.695433\pi$
$138$	−5.87126e13	−0.723631
$139$	3.76770e13	0.443077	0.221539	−	0.975152i	$-0.428892\pi$
$139$	3.76770e13	0.443077	0.221539	+	0.975152i	$0.428892\pi$
$140$	−1.29167e13	−0.144984
$141$	−1.11263e14	−1.19241
$142$	4.87323e13	0.498818
$143$	2.45883e14	2.40460
$144$	−1.45635e13	−0.136117
$145$	−8.37456e13	−0.748290
$146$	4.87404e12	0.0416481
$147$	−1.17957e13	−0.0964189
$148$	−3.91797e13	−0.306450
$149$	−1.68810e14	−1.26382	−0.631912	−	0.775041i	$-0.717729\pi$
$149$	−1.68810e14	−1.26382	−0.631912	+	0.775041i	$0.717729\pi$
$150$	2.73925e13	0.196353
$151$	−2.58599e13	−0.177532	−0.0887662	−	0.996052i	$-0.528292\pi$
$151$	−2.58599e13	−0.177532	−0.0887662	+	0.996052i	$0.528292\pi$
$152$	−2.38027e13	−0.156546
$153$	−1.04346e14	−0.657633
$154$	−8.58823e13	−0.518823
$155$	−7.77214e13	−0.450178
$156$	−7.52490e13	−0.418014
$157$	2.64179e14	1.40783	0.703916	−	0.710283i	$-0.251433\pi$
$157$	2.64179e14	1.40783	0.703916	+	0.710283i	$0.251433\pi$
$158$	−4.38832e13	−0.224402
$159$	1.30045e14	0.638282
$160$	2.87809e13	0.135620
$161$	−1.26646e14	−0.573090
$162$	−2.58807e13	−0.112494
$163$	1.45635e14	0.608201	0.304100	−	0.952640i	$-0.401644\pi$
$163$	1.45635e14	0.608201	0.304100	+	0.952640i	$0.401644\pi$
$164$	−1.51418e13	−0.0607705
$165$	−2.60549e14	−1.00518
$166$	3.21254e14	1.19164
$167$	−5.17769e14	−1.84705	−0.923526	−	0.383536i	$-0.874706\pi$
$167$	−5.17769e14	−1.84705	−0.923526	+	0.383536i	$0.874706\pi$
$168$	2.62831e13	0.0901916
$169$	1.61837e14	0.534337
$170$	2.06213e14	0.655236
$171$	7.88194e13	0.241079
$172$	−1.67890e14	−0.494413
$173$	−1.63525e14	−0.463751	−0.231875	−	0.972746i	$-0.574486\pi$
$173$	−1.63525e14	−0.463751	−0.231875	+	0.972746i	$0.574486\pi$
$174$	1.70406e14	0.465495
$175$	5.90869e13	0.155505
$176$	1.91362e14	0.485314
$177$	6.92266e13	0.169218
$178$	3.66691e14	0.864113
$179$	7.46916e13	0.169718	0.0848588	−	0.996393i	$-0.472956\pi$
$179$	7.46916e13	0.169718	0.0848588	+	0.996393i	$0.472956\pi$
$180$	−9.53043e13	−0.208853
$181$	2.98361e14	0.630712	0.315356	−	0.948973i	$-0.397876\pi$
$181$	2.98361e14	0.630712	0.315356	+	0.948973i	$0.397876\pi$
$182$	−1.62316e14	−0.331052
$183$	−4.29920e13	−0.0846167
$184$	2.82191e14	0.536077
$185$	−2.56393e14	−0.470208
$186$	1.58148e14	0.280046
$187$	1.37109e15	2.34475
$188$	5.34763e14	0.883355
$189$	−2.46883e14	−0.393994
$190$	−1.55765e14	−0.240200
$191$	2.17202e14	0.323704	0.161852	−	0.986815i	$-0.448253\pi$
$191$	2.17202e14	0.323704	0.161852	+	0.986815i	$0.448253\pi$
$192$	−5.85637e13	−0.0843665
$193$	−6.48314e14	−0.902948	−0.451474	−	0.892284i	$-0.649102\pi$
$193$	−6.48314e14	−0.902948	−0.451474	+	0.892284i	$0.649102\pi$
$194$	−9.35229e14	−1.25953
$195$	−4.92431e14	−0.641388
$196$	5.66939e13	0.0714286
$197$	−9.05035e14	−1.10315	−0.551576	−	0.834125i	$-0.685973\pi$
$197$	−9.05035e14	−1.10315	−0.551576	+	0.834125i	$0.685973\pi$
$198$	−6.33670e14	−0.747376
$199$	−1.08905e14	−0.124309	−0.0621545	−	0.998067i	$-0.519797\pi$
$199$	−1.08905e14	−0.124309	−0.0621545	+	0.998067i	$0.519797\pi$
$200$	−1.31657e14	−0.145462
$201$	6.79790e14	0.727111
$202$	−1.86923e14	−0.193588
$203$	3.67574e14	0.368656
$204$	−4.19603e14	−0.407608
$205$	−9.90884e13	−0.0932444
$206$	−7.68837e14	−0.700966
$207$	−9.34437e14	−0.825549
$208$	3.61670e14	0.309671
$209$	−1.03567e15	−0.859549
$210$	1.71997e14	0.138387
$211$	1.72683e15	1.34715	0.673573	−	0.739121i	$-0.264759\pi$
$211$	1.72683e15	1.34715	0.673573	+	0.739121i	$0.264759\pi$
$212$	−6.25037e14	−0.472849
$213$	−6.48911e14	−0.476121
$214$	−3.92973e13	−0.0279687
$215$	−1.09868e15	−0.758613
$216$	5.50102e14	0.368548
$217$	3.41133e14	0.221787
$218$	−6.69610e14	−0.422527
$219$	−6.49019e13	−0.0397531
$220$	1.25228e15	0.744652
$221$	2.59133e15	1.49614
$222$	5.21711e14	0.292506
$223$	1.86709e15	1.01668	0.508338	−	0.861158i	$-0.330260\pi$
$223$	1.86709e15	1.01668	0.508338	+	0.861158i	$0.330260\pi$
$224$	−1.26325e14	−0.0668153
$225$	4.35964e14	0.224008
$226$	−2.02160e15	−1.00923
$227$	5.16507e14	0.250558	0.125279	−	0.992122i	$-0.460017\pi$
$227$	5.16507e14	0.250558	0.125279	+	0.992122i	$0.460017\pi$
$228$	3.16953e14	0.149423
$229$	−2.19098e15	−1.00394	−0.501971	−	0.864884i	$-0.667392\pi$
$229$	−2.19098e15	−1.00394	−0.501971	+	0.864884i	$0.667392\pi$
$230$	1.84666e15	0.822540
$231$	1.14360e15	0.495216
$232$	−8.19025e14	−0.344846
$233$	3.19057e15	1.30634	0.653168	−	0.757213i	$-0.273440\pi$
$233$	3.19057e15	1.30634	0.653168	+	0.757213i	$0.273440\pi$
$234$	−1.19762e15	−0.476888
$235$	3.49950e15	1.35539
$236$	−3.32724e14	−0.125359
$237$	5.84342e14	0.214192
$238$	−9.05104e14	−0.322811
$239$	2.32284e14	0.0806181	0.0403090	−	0.999187i	$-0.487166\pi$
$239$	2.32284e14	0.0806181	0.0403090	+	0.999187i	$0.487166\pi$
$240$	−3.83242e14	−0.129449
$241$	−5.87566e15	−1.93173	−0.965864	−	0.259050i	$-0.916591\pi$
$241$	−5.87566e15	−1.93173	−0.965864	+	0.259050i	$0.916591\pi$
$242$	6.11683e15	1.95761
$243$	−3.00102e15	−0.935035
$244$	2.06633e14	0.0626853
$245$	3.71006e14	0.109598
$246$	2.01626e14	0.0580053
$247$	−1.95739e15	−0.548464
$248$	−7.60109e14	−0.207463
$249$	−4.27777e15	−1.13742
$250$	−2.95565e15	−0.765673
$251$	−5.22828e15	−1.31971	−0.659857	−	0.751391i	$-0.729383\pi$
$251$	−5.22828e15	−1.31971	−0.659857	+	0.751391i	$0.729383\pi$
$252$	4.18307e14	0.102894
$253$	1.22783e16	2.94344
$254$	−2.81732e14	−0.0658289
$255$	−2.74590e15	−0.625421
$256$	2.81475e14	0.0625000
$257$	9.20659e13	0.0199312	0.00996560	−	0.999950i	$-0.496828\pi$
$257$	9.20659e13	0.0199312	0.00996560	+	0.999950i	$0.496828\pi$
$258$	2.23560e15	0.471917
$259$	1.12536e15	0.231655
$260$	2.36678e15	0.475150
$261$	2.71209e15	0.531057
$262$	5.45328e15	1.04160
$263$	−4.34970e15	−0.810489	−0.405245	−	0.914208i	$-0.632814\pi$
$263$	−4.34970e15	−0.810489	−0.405245	+	0.914208i	$0.632814\pi$
$264$	−2.54814e15	−0.463232
$265$	−4.09026e15	−0.725525
$266$	6.83682e14	0.118338
$267$	−4.88280e15	−0.824794
$268$	−3.26728e15	−0.538654
$269$	−7.52778e15	−1.21137	−0.605686	−	0.795704i	$-0.707101\pi$
$269$	−7.52778e15	−1.21137	−0.605686	+	0.795704i	$0.707101\pi$
$270$	3.59988e15	0.565488
$271$	−6.44262e14	−0.0988011	−0.0494006	−	0.998779i	$-0.515731\pi$
$271$	−6.44262e14	−0.0988011	−0.0494006	+	0.998779i	$0.515731\pi$
$272$	2.01674e15	0.301962
$273$	2.16137e15	0.315989
$274$	−5.70696e15	−0.814753
$275$	−5.72847e15	−0.798687
$276$	−3.75761e15	−0.511685
$277$	4.54380e14	0.0604367	0.0302184	−	0.999543i	$-0.490380\pi$
$277$	4.54380e14	0.0604367	0.0302184	+	0.999543i	$0.490380\pi$
$278$	2.41132e15	0.313303
$279$	2.51700e15	0.319489
$280$	−8.26672e14	−0.102519
$281$	8.82158e15	1.06894	0.534472	−	0.845186i	$-0.320510\pi$
$281$	8.82158e15	1.06894	0.534472	+	0.845186i	$0.320510\pi$
$282$	−7.12081e15	−0.843161
$283$	−9.99098e15	−1.15610	−0.578051	−	0.816001i	$-0.696187\pi$
$283$	−9.99098e15	−1.15610	−0.578051	+	0.816001i	$0.696187\pi$
$284$	3.11886e15	0.352718
$285$	2.07415e15	0.229270
$286$	1.57365e16	1.70031
$287$	4.34917e14	0.0459382
$288$	−9.32067e14	−0.0962490
$289$	4.54519e15	0.458898
$290$	−5.35972e15	−0.529121
$291$	1.24534e16	1.20221
$292$	3.11939e14	0.0294497
$293$	−6.88295e15	−0.635528	−0.317764	−	0.948170i	$-0.602932\pi$
$293$	−6.88295e15	−0.635528	−0.317764	+	0.948170i	$0.602932\pi$
$294$	−7.54927e14	−0.0681785
$295$	−2.17736e15	−0.192347
$296$	−2.50750e15	−0.216693
$297$	2.39353e16	2.02359
$298$	−1.08038e16	−0.893658
$299$	2.32057e16	1.87816
$300$	1.75312e15	0.138843
$301$	4.82229e15	0.373741
$302$	−1.65504e15	−0.125534
$303$	2.48904e15	0.184780
$304$	−1.52337e15	−0.110695
$305$	1.35221e15	0.0961824
$306$	−6.67817e15	−0.465017
$307$	−8.49115e15	−0.578852	−0.289426	−	0.957200i	$-0.593464\pi$
$307$	−8.49115e15	−0.578852	−0.289426	+	0.957200i	$0.593464\pi$
$308$	−5.49647e15	−0.366863
$309$	1.02377e16	0.669071
$310$	−4.97417e15	−0.318324
$311$	−2.21013e16	−1.38508	−0.692542	−	0.721378i	$-0.743509\pi$
$311$	−2.21013e16	−1.38508	−0.692542	+	0.721378i	$0.743509\pi$
$312$	−4.81593e15	−0.295580
$313$	1.52609e16	0.917366	0.458683	−	0.888600i	$-0.348321\pi$
$313$	1.52609e16	0.917366	0.458683	+	0.888600i	$0.348321\pi$
$314$	1.69075e16	0.995488
$315$	2.73741e15	0.157878
$316$	−2.80852e15	−0.158676
$317$	1.04548e16	0.578669	0.289334	−	0.957228i	$-0.406566\pi$
$317$	1.04548e16	0.578669	0.289334	+	0.957228i	$0.406566\pi$
$318$	8.32289e15	0.451334
$319$	−3.56363e16	−1.89345
$320$	1.84198e15	0.0958981
$321$	5.23276e14	0.0266961
$322$	−8.10534e15	−0.405236
$323$	−1.09148e16	−0.534811
$324$	−1.65636e15	−0.0795451
$325$	−1.08267e16	−0.509628
$326$	9.32065e15	0.430063
$327$	8.91642e15	0.403302
$328$	−9.69076e14	−0.0429712
$329$	−1.53599e16	−0.667753
$330$	−1.66751e16	−0.710769
$331$	4.82090e15	0.201486	0.100743	−	0.994912i	$-0.467878\pi$
$331$	4.82090e15	0.201486	0.100743	+	0.994912i	$0.467878\pi$
$332$	2.05603e16	0.842619
$333$	8.30326e15	0.333704
$334$	−3.31372e16	−1.30606
$335$	−2.13812e16	−0.826495
$336$	1.68212e15	0.0637751
$337$	−2.36422e16	−0.879210	−0.439605	−	0.898191i	$-0.644882\pi$
$337$	−2.36422e16	−0.879210	−0.439605	+	0.898191i	$0.644882\pi$
$338$	1.03576e16	0.377834
$339$	2.69194e16	0.963311
$340$	1.31976e16	0.463322
$341$	−3.30728e16	−1.13912
$342$	5.04444e15	0.170468
$343$	−1.62841e15	−0.0539949
$344$	−1.07450e16	−0.349603
$345$	−2.45899e16	−0.785113
$346$	−1.04656e16	−0.327921
$347$	−4.45624e16	−1.37034	−0.685168	−	0.728385i	$-0.740271\pi$
$347$	−4.45624e16	−1.37034	−0.685168	+	0.728385i	$0.740271\pi$
$348$	1.09060e16	0.329155
$349$	−1.66642e16	−0.493649	−0.246825	−	0.969060i	$-0.579387\pi$
$349$	−1.66642e16	−0.493649	−0.246825	+	0.969060i	$0.579387\pi$
$350$	3.78156e15	0.109959
$351$	4.52372e16	1.29122
$352$	1.22472e16	0.343169
$353$	6.90833e16	1.90037	0.950184	−	0.311689i	$-0.100895\pi$
$353$	6.90833e16	1.90037	0.950184	+	0.311689i	$0.100895\pi$
$354$	4.43050e15	0.119655
$355$	2.04099e16	0.541199
$356$	2.34682e16	0.611020
$357$	1.20522e16	0.308123
$358$	4.78026e15	0.120008
$359$	7.57849e16	1.86839	0.934197	−	0.356757i	$-0.116118\pi$
$359$	7.57849e16	1.86839	0.934197	+	0.356757i	$0.116118\pi$
$360$	−6.09947e15	−0.147681
$361$	−3.38083e16	−0.803946
$362$	1.90951e16	0.445981
$363$	−8.14507e16	−1.86854
$364$	−1.03882e16	−0.234089
$365$	2.04133e15	0.0451867
$366$	−2.75149e15	−0.0598330
$367$	6.26257e16	1.33790	0.668949	−	0.743308i	$-0.266744\pi$
$367$	6.26257e16	1.33790	0.668949	+	0.743308i	$0.266744\pi$
$368$	1.80602e16	0.379064
$369$	3.20897e15	0.0661750
$370$	−1.64092e16	−0.332487
$371$	1.79529e16	0.357440
$372$	1.01215e16	0.198023
$373$	3.78732e15	0.0728156	0.0364078	−	0.999337i	$-0.488408\pi$
$373$	3.78732e15	0.0728156	0.0364078	+	0.999337i	$0.488408\pi$
$374$	8.77498e16	1.65799
$375$	3.93570e16	0.730834
$376$	3.42248e16	0.624626
$377$	−6.73518e16	−1.20818
$378$	−1.58005e16	−0.278596
$379$	−6.21401e16	−1.07700	−0.538502	−	0.842624i	$-0.681009\pi$
$379$	−6.21401e16	−1.07700	−0.538502	+	0.842624i	$0.681009\pi$
$380$	−9.96898e15	−0.169847
$381$	3.75150e15	0.0628336
$382$	1.39010e16	0.228893
$383$	−8.20104e16	−1.32763	−0.663815	−	0.747897i	$-0.731064\pi$
$383$	−8.20104e16	−1.32763	−0.663815	+	0.747897i	$0.731064\pi$
$384$	−3.74807e15	−0.0596562
$385$	−3.59690e16	−0.562904
$386$	−4.14921e16	−0.638480
$387$	3.55805e16	0.538383
$388$	−5.98547e16	−0.890619
$389$	3.05248e16	0.446664	0.223332	−	0.974742i	$-0.428307\pi$
$389$	3.05248e16	0.446664	0.223332	+	0.974742i	$0.428307\pi$
$390$	−3.15156e16	−0.453530
$391$	1.29400e17	1.83141
$392$	3.62841e15	0.0505076
$393$	−7.26149e16	−0.994201
$394$	−5.79223e16	−0.780046
$395$	−1.83791e16	−0.243468
$396$	−4.05549e16	−0.528475
$397$	2.31781e16	0.297126	0.148563	−	0.988903i	$-0.452535\pi$
$397$	2.31781e16	0.297126	0.148563	+	0.988903i	$0.452535\pi$
$398$	−6.96992e15	−0.0878997
$399$	−9.10380e15	−0.112953
$400$	−8.42603e15	−0.102857
$401$	3.75848e16	0.451412	0.225706	−	0.974195i	$-0.427531\pi$
$401$	3.75848e16	0.451412	0.225706	+	0.974195i	$0.427531\pi$
$402$	4.35066e16	0.514145
$403$	−6.25069e16	−0.726851
$404$	−1.19631e16	−0.136888
$405$	−1.08393e16	−0.122052
$406$	2.35248e16	0.260679
$407$	−1.09103e17	−1.18980
$408$	−2.68546e16	−0.288222
$409$	6.43385e15	0.0679625	0.0339812	−	0.999422i	$-0.489181\pi$
$409$	6.43385e15	0.0679625	0.0339812	+	0.999422i	$0.489181\pi$
$410$	−6.34166e15	−0.0659337
$411$	7.59930e16	0.777681
$412$	−4.92055e16	−0.495658
$413$	9.55680e15	0.0947627
$414$	−5.98040e16	−0.583752
$415$	1.34547e17	1.29289
$416$	2.31469e16	0.218970
$417$	−3.21088e16	−0.299047
$418$	−6.62829e16	−0.607793
$419$	1.76217e17	1.59095	0.795474	−	0.605988i	$-0.207222\pi$
$419$	1.76217e17	1.59095	0.795474	+	0.605988i	$0.207222\pi$
$420$	1.10078e16	0.0978546
$421$	2.13231e17	1.86646	0.933228	−	0.359286i	$-0.116980\pi$
$421$	2.13231e17	1.86646	0.933228	+	0.359286i	$0.116980\pi$
$422$	1.10517e17	0.952576
$423$	−1.13331e17	−0.961914
$424$	−4.00024e16	−0.334355
$425$	−6.03718e16	−0.496942
$426$	−4.15303e16	−0.336669
$427$	−5.93510e15	−0.0473856
$428$	−2.51502e15	−0.0197769
$429$	−2.09545e17	−1.62295
$430$	−7.03153e16	−0.536420
$431$	1.99789e16	0.150131	0.0750653	−	0.997179i	$-0.476083\pi$
$431$	1.99789e16	0.150131	0.0750653	+	0.997179i	$0.476083\pi$
$432$	3.52065e16	0.260603
$433$	−1.04879e17	−0.764747	−0.382373	−	0.924008i	$-0.624893\pi$
$433$	−1.04879e17	−0.764747	−0.382373	+	0.924008i	$0.624893\pi$
$434$	2.18325e16	0.156827
$435$	7.13691e16	0.505045
$436$	−4.28551e16	−0.298772
$437$	−9.77437e16	−0.671366
$438$	−4.15372e15	−0.0281097
$439$	1.56129e17	1.04103	0.520517	−	0.853851i	$-0.325739\pi$
$439$	1.56129e17	1.04103	0.520517	+	0.853851i	$0.325739\pi$
$440$	8.01458e16	0.526548
$441$	−1.20150e16	−0.0777809
$442$	1.65845e17	1.05793
$443$	−1.28332e17	−0.806697	−0.403349	−	0.915046i	$-0.632154\pi$
$443$	−1.28332e17	−0.806697	−0.403349	+	0.915046i	$0.632154\pi$
$444$	3.33895e16	0.206833
$445$	1.53577e17	0.937530
$446$	1.19493e17	0.718899
$447$	1.43862e17	0.852995
$448$	−8.08478e15	−0.0472456
$449$	1.39530e16	0.0803648	0.0401824	−	0.999192i	$-0.487206\pi$
$449$	1.39530e16	0.0803648	0.0401824	+	0.999192i	$0.487206\pi$
$450$	2.79017e16	0.158398
$451$	−4.21651e16	−0.235942
$452$	−1.29383e17	−0.713635
$453$	2.20382e16	0.119822
$454$	3.30565e16	0.177171
$455$	−6.79807e16	−0.359179
$456$	2.02850e16	0.105658
$457$	−5.68782e15	−0.0292072	−0.0146036	−	0.999893i	$-0.504649\pi$
$457$	−5.68782e15	−0.0292072	−0.0146036	+	0.999893i	$0.504649\pi$
$458$	−1.40223e17	−0.709894
$459$	2.52251e17	1.25907
$460$	1.18187e17	0.581624
$461$	4.65199e16	0.225727	0.112863	−	0.993611i	$-0.463998\pi$
$461$	4.65199e16	0.225727	0.112863	+	0.993611i	$0.463998\pi$
$462$	7.31901e16	0.350170
$463$	−1.57068e17	−0.740987	−0.370493	−	0.928835i	$-0.620811\pi$
$463$	−1.57068e17	−0.740987	−0.370493	+	0.928835i	$0.620811\pi$
$464$	−5.24176e16	−0.243843
$465$	6.62352e16	0.303840
$466$	2.04197e17	0.923719
$467$	−1.59143e17	−0.709952	−0.354976	−	0.934875i	$-0.615511\pi$
$467$	−1.59143e17	−0.709952	−0.354976	+	0.934875i	$0.615511\pi$
$468$	−7.66478e16	−0.337211
$469$	9.38458e16	0.407184
$470$	2.23968e17	0.958407
$471$	−2.25137e17	−0.950192
$472$	−2.12943e16	−0.0886424
$473$	−4.67521e17	−1.91957
$474$	3.73979e16	0.151456
$475$	4.56026e16	0.182172
$476$	−5.79267e16	−0.228262
$477$	1.32463e17	0.514901
$478$	1.48662e16	0.0570056
$479$	−2.13853e17	−0.808973	−0.404486	−	0.914544i	$-0.632550\pi$
$479$	−2.13853e17	−0.808973	−0.404486	+	0.914544i	$0.632550\pi$
$480$	−2.45275e16	−0.0915346
$481$	−2.06202e17	−0.759190
$482$	−3.76042e17	−1.36594
$483$	1.07929e17	0.386797
$484$	3.91477e17	1.38424
$485$	−3.91691e17	−1.36654
$486$	−1.92065e17	−0.661170
$487$	4.49629e17	1.52727	0.763635	−	0.645648i	$-0.223413\pi$
$487$	4.49629e17	1.52727	0.763635	+	0.645648i	$0.223413\pi$
$488$	1.32245e16	0.0443252
$489$	−1.24112e17	−0.410494
$490$	2.37444e16	0.0774974
$491$	2.67159e17	0.860478	0.430239	−	0.902715i	$-0.358429\pi$
$491$	2.67159e17	0.860478	0.430239	+	0.902715i	$0.358429\pi$
$492$	1.29041e16	0.0410160
$493$	−3.75567e17	−1.17810
$494$	−1.25273e17	−0.387822
$495$	−2.65392e17	−0.810876
$496$	−4.86470e16	−0.146698
$497$	−8.95828e16	−0.266630
$498$	−2.73777e17	−0.804278
$499$	−1.50253e17	−0.435682	−0.217841	−	0.975984i	$-0.569901\pi$
$499$	−1.50253e17	−0.435682	−0.217841	+	0.975984i	$0.569901\pi$
$500$	−1.89162e17	−0.541413
$501$	4.41250e17	1.24663
$502$	−3.34610e17	−0.933179
$503$	1.58615e17	0.436668	0.218334	−	0.975874i	$-0.429938\pi$
$503$	1.58615e17	0.436668	0.218334	+	0.975874i	$0.429938\pi$
$504$	2.67717e16	0.0727574
$505$	−7.82867e16	−0.210036
$506$	7.85812e17	2.08133
$507$	−1.37920e17	−0.360642
$508$	−1.80308e16	−0.0465481
$509$	1.19995e17	0.305842	0.152921	−	0.988238i	$-0.451132\pi$
$509$	1.19995e17	0.305842	0.152921	+	0.988238i	$0.451132\pi$
$510$	−1.75737e17	−0.442240
$511$	−8.95978e15	−0.0222619
$512$	1.80144e16	0.0441942
$513$	−1.90541e17	−0.461558
$514$	5.89221e15	0.0140935
$515$	−3.22002e17	−0.760523
$516$	1.43078e17	0.333696
$517$	1.48914e18	3.42964
$518$	7.20227e16	0.163805
$519$	1.39358e17	0.313000
$520$	1.51474e17	0.335982
$521$	7.87870e17	1.72588	0.862938	−	0.505310i	$-0.168622\pi$
$521$	7.87870e17	1.72588	0.862938	+	0.505310i	$0.168622\pi$
$522$	1.73574e17	0.375514
$523$	−1.88103e17	−0.401916	−0.200958	−	0.979600i	$-0.564405\pi$
$523$	−1.88103e17	−0.401916	−0.200958	+	0.979600i	$0.564405\pi$
$524$	3.49010e17	0.736519
$525$	−5.03547e16	−0.104955
$526$	−2.78381e17	−0.573102
$527$	−3.48551e17	−0.708757
$528$	−1.63081e17	−0.327554
$529$	6.54757e17	1.29903
$530$	−2.61777e17	−0.513024
$531$	7.05134e16	0.136508
$532$	4.37556e16	0.0836775
$533$	−7.96911e16	−0.150551
$534$	−3.12499e17	−0.583218
$535$	−1.64584e16	−0.0303450
$536$	−2.09106e17	−0.380886
$537$	−6.36531e16	−0.114548
$538$	−4.81778e17	−0.856569
$539$	1.57875e17	0.277323
$540$	2.30392e17	0.399861
$541$	9.96930e17	1.70955	0.854776	−	0.518997i	$-0.173694\pi$
$541$	9.96930e17	1.70955	0.854776	+	0.518997i	$0.173694\pi$
$542$	−4.12328e16	−0.0698630
$543$	−2.54267e17	−0.425688
$544$	1.29072e17	0.213519
$545$	−2.80445e17	−0.458427
$546$	1.38328e17	0.223438
$547$	−7.63720e17	−1.21904	−0.609518	−	0.792772i	$-0.708637\pi$
$547$	−7.63720e17	−1.21904	−0.609518	+	0.792772i	$0.708637\pi$
$548$	−3.65245e17	−0.576118
$549$	−4.37912e16	−0.0682601
$550$	−3.66622e17	−0.564757
$551$	2.83689e17	0.431875
$552$	−2.40487e17	−0.361816
$553$	8.06690e16	0.119948
$554$	2.90803e16	0.0427352
$555$	2.18502e17	0.317359
$556$	1.54325e17	0.221539
$557$	1.02768e18	1.45814	0.729070	−	0.684439i	$-0.239953\pi$
$557$	1.02768e18	1.45814	0.729070	+	0.684439i	$0.239953\pi$
$558$	1.61088e17	0.225913
$559$	−8.83603e17	−1.22484
$560$	−5.29070e16	−0.0724922
$561$	−1.16846e18	−1.58254
$562$	5.64581e17	0.755858
$563$	4.83398e17	0.639736	0.319868	−	0.947462i	$-0.396361\pi$
$563$	4.83398e17	0.639736	0.319868	+	0.947462i	$0.396361\pi$
$564$	−4.55732e17	−0.596205
$565$	−8.46684e17	−1.09498
$566$	−6.39423e17	−0.817488
$567$	4.75756e16	0.0601304
$568$	1.99607e17	0.249409
$569$	5.48445e17	0.677491	0.338745	−	0.940878i	$-0.389997\pi$
$569$	5.48445e17	0.677491	0.338745	+	0.940878i	$0.389997\pi$
$570$	1.32745e17	0.162119
$571$	−7.84138e17	−0.946799	−0.473400	−	0.880848i	$-0.656973\pi$
$571$	−7.84138e17	−0.946799	−0.473400	+	0.880848i	$0.656973\pi$
$572$	1.00714e18	1.20230
$573$	−1.85103e17	−0.218478
$574$	2.78347e16	0.0324832
$575$	−5.40638e17	−0.623829
$576$	−5.96523e16	−0.0680583
$577$	−7.13128e17	−0.804497	−0.402249	−	0.915530i	$-0.631771\pi$
$577$	−7.13128e17	−0.804497	−0.402249	+	0.915530i	$0.631771\pi$
$578$	2.90892e17	0.324490
$579$	5.52502e17	0.609429
$580$	−3.43022e17	−0.374145
$581$	−5.90550e17	−0.636960
$582$	7.97015e17	0.850094
$583$	−1.74053e18	−1.83584
$584$	1.99641e16	0.0208241
$585$	−5.01585e17	−0.517406
$586$	−4.40509e17	−0.449386
$587$	−2.10123e17	−0.211995	−0.105998	−	0.994366i	$-0.533804\pi$
$587$	−2.10123e17	−0.211995	−0.105998	+	0.994366i	$0.533804\pi$
$588$	−4.83153e16	−0.0482095
$589$	2.63282e17	0.259820
$590$	−1.39351e17	−0.136010
$591$	7.71283e17	0.744552
$592$	−1.60480e17	−0.153225
$593$	2.10743e17	0.199020	0.0995100	−	0.995037i	$-0.468272\pi$
$593$	2.10743e17	0.199020	0.0995100	+	0.995037i	$0.468272\pi$
$594$	1.53186e18	1.43089
$595$	−3.79074e17	−0.350238
$596$	−6.91444e17	−0.631912
$597$	9.28103e16	0.0839002
$598$	1.48517e18	1.32806
$599$	−3.51847e17	−0.311229	−0.155614	−	0.987818i	$-0.549736\pi$
$599$	−3.51847e17	−0.311229	−0.155614	+	0.987818i	$0.549736\pi$
$600$	1.12200e17	0.0981767
$601$	5.54098e17	0.479626	0.239813	−	0.970819i	$-0.422914\pi$
$601$	5.54098e17	0.479626	0.239813	+	0.970819i	$0.422914\pi$
$602$	3.08627e17	0.264275
$603$	6.92427e17	0.586558
$604$	−1.05922e17	−0.0887662
$605$	2.56184e18	2.12394
$606$	1.59298e17	0.130659
$607$	−2.39029e17	−0.193966	−0.0969828	−	0.995286i	$-0.530919\pi$
$607$	−2.39029e17	−0.193966	−0.0969828	+	0.995286i	$0.530919\pi$
$608$	−9.74958e16	−0.0782731
$609$	−3.13252e17	−0.248818
$610$	8.65415e16	0.0680112
$611$	2.81445e18	2.18839
$612$	−4.27403e17	−0.328816
$613$	−2.47689e18	−1.88544	−0.942720	−	0.333584i	$-0.891742\pi$
$613$	−2.47689e18	−1.88544	−0.942720	+	0.333584i	$0.891742\pi$
$614$	−5.43434e17	−0.409310
$615$	8.44445e16	0.0629337
$616$	−3.51774e17	−0.259411
$617$	1.67255e17	0.122047	0.0610234	−	0.998136i	$-0.480564\pi$
$617$	1.67255e17	0.122047	0.0610234	+	0.998136i	$0.480564\pi$
$618$	6.55213e17	0.473105
$619$	−1.09640e18	−0.783396	−0.391698	−	0.920094i	$-0.628112\pi$
$619$	−1.09640e18	−0.783396	−0.391698	+	0.920094i	$0.628112\pi$
$620$	−3.18347e17	−0.225089
$621$	2.25895e18	1.58056
$622$	−1.41449e18	−0.979402
$623$	−6.74076e17	−0.461888
$624$	−3.08220e17	−0.209007
$625$	−6.24806e17	−0.419300
$626$	9.76699e17	0.648676
$627$	8.82612e17	0.580137
$628$	1.08208e18	0.703916
$629$	−1.14983e18	−0.740291
$630$	1.75195e17	0.111637
$631$	1.43818e18	0.907032	0.453516	−	0.891248i	$-0.350169\pi$
$631$	1.43818e18	0.907032	0.453516	+	0.891248i	$0.350169\pi$
$632$	−1.79746e17	−0.112201
$633$	−1.47163e18	−0.909232
$634$	6.69107e17	0.409181
$635$	−1.17994e17	−0.0714220
$636$	5.32665e17	0.319141
$637$	2.98379e17	0.176955
$638$	−2.28072e18	−1.33887
$639$	−6.60973e17	−0.384086
$640$	1.17887e17	0.0678102
$641$	−2.46842e18	−1.40554	−0.702768	−	0.711419i	$-0.748053\pi$
$641$	−2.46842e18	−1.40554	−0.702768	+	0.711419i	$0.748053\pi$
$642$	3.34897e16	0.0188770
$643$	5.03149e17	0.280753	0.140377	−	0.990098i	$-0.455169\pi$
$643$	5.03149e17	0.280753	0.140377	+	0.990098i	$0.455169\pi$
$644$	−5.18742e17	−0.286545
$645$	9.36308e17	0.512012
$646$	−6.98548e17	−0.378168
$647$	2.95986e18	1.58633	0.793165	−	0.609007i	$-0.208432\pi$
$647$	2.95986e18	1.58633	0.793165	+	0.609007i	$0.208432\pi$
$648$	−1.06007e17	−0.0562469
$649$	−9.26531e17	−0.486709
$650$	−6.92908e17	−0.360362
$651$	−2.90718e17	−0.149691
$652$	5.96522e17	0.304100
$653$	3.12926e18	1.57945	0.789725	−	0.613461i	$-0.210223\pi$
$653$	3.12926e18	1.57945	0.789725	+	0.613461i	$0.210223\pi$
$654$	5.70651e17	0.285177
$655$	2.28393e18	1.13009
$656$	−6.20208e16	−0.0303852
$657$	−6.61084e16	−0.0320687
$658$	−9.83036e17	−0.472173
$659$	−1.76569e18	−0.839767	−0.419884	−	0.907578i	$-0.637929\pi$
$659$	−1.76569e18	−0.839767	−0.419884	+	0.907578i	$0.637929\pi$
$660$	−1.06721e18	−0.502590
$661$	1.67354e18	0.780415	0.390207	−	0.920727i	$-0.372403\pi$
$661$	1.67354e18	0.780415	0.390207	+	0.920727i	$0.372403\pi$
$662$	3.08537e17	0.142472
$663$	−2.20837e18	−1.00979
$664$	1.31586e18	0.595821
$665$	2.86338e17	0.128392
$666$	5.31409e17	0.235964
$667$	−3.36326e18	−1.47891
$668$	−2.12078e18	−0.923526
$669$	−1.59116e18	−0.686188
$670$	−1.36839e18	−0.584420
$671$	5.75407e17	0.243377
$672$	1.07656e17	0.0450958
$673$	−4.28042e18	−1.77578	−0.887888	−	0.460059i	$-0.847828\pi$
$673$	−4.28042e18	−1.77578	−0.887888	+	0.460059i	$0.847828\pi$
$674$	−1.51310e18	−0.621695
$675$	−1.05392e18	−0.428876
$676$	6.62886e17	0.267169
$677$	4.46185e18	1.78110	0.890550	−	0.454885i	$-0.150320\pi$
$677$	4.46185e18	1.78110	0.890550	+	0.454885i	$0.150320\pi$
$678$	1.72284e18	0.681164
$679$	1.71920e18	0.673245
$680$	8.44647e17	0.327618
$681$	−4.40174e17	−0.169110
$682$	−2.11666e18	−0.805477
$683$	1.70016e18	0.640847	0.320424	−	0.947274i	$-0.396175\pi$
$683$	1.70016e18	0.640847	0.320424	+	0.947274i	$0.396175\pi$
$684$	3.22844e17	0.120539
$685$	−2.39018e18	−0.883978
$686$	−1.04218e17	−0.0381802
$687$	1.86719e18	0.677593
$688$	−6.87678e17	−0.247207
$689$	−3.28956e18	−1.17142
$690$	−1.57375e18	−0.555159
$691$	2.06120e18	0.720297	0.360149	−	0.932895i	$-0.382726\pi$
$691$	2.06120e18	0.720297	0.360149	+	0.932895i	$0.382726\pi$
$692$	−6.69798e17	−0.231875
$693$	1.16485e18	0.399489
$694$	−2.85199e18	−0.968974
$695$	1.00991e18	0.339922
$696$	6.97984e17	0.232748
$697$	−4.44374e17	−0.146803
$698$	−1.06651e18	−0.349063
$699$	−2.71905e18	−0.881689
$700$	2.42020e17	0.0777525
$701$	−5.26995e17	−0.167741	−0.0838705	−	0.996477i	$-0.526728\pi$
$701$	−5.26995e17	−0.167741	−0.0838705	+	0.996477i	$0.526728\pi$
$702$	2.89518e18	0.913028
$703$	8.68535e17	0.271380
$704$	7.83818e17	0.242657
$705$	−2.98232e18	−0.914798
$706$	4.42133e18	1.34376
$707$	3.43614e17	0.103477
$708$	2.83552e17	0.0846090
$709$	4.21726e18	1.24689	0.623447	−	0.781865i	$-0.285732\pi$
$709$	4.21726e18	1.24689	0.623447	+	0.781865i	$0.285732\pi$
$710$	1.30624e18	0.382686
$711$	5.95204e17	0.172788
$712$	1.50197e18	0.432056
$713$	−3.12132e18	−0.889727
$714$	7.71342e17	0.217876
$715$	6.59072e18	1.84478
$716$	3.05937e17	0.0848588
$717$	−1.97955e17	−0.0544118
$718$	4.85023e18	1.32115
$719$	−2.07601e17	−0.0560391	−0.0280196	−	0.999607i	$-0.508920\pi$
$719$	−2.07601e17	−0.0560391	−0.0280196	+	0.999607i	$0.508920\pi$
$720$	−3.90366e17	−0.104427
$721$	1.41333e18	0.374682
$722$	−2.16373e18	−0.568476
$723$	5.00732e18	1.30379
$724$	1.22209e18	0.315356
$725$	1.56914e18	0.401295
$726$	−5.21285e18	−1.32126
$727$	6.87549e17	0.172715	0.0863574	−	0.996264i	$-0.472477\pi$
$727$	6.87549e17	0.172715	0.0863574	+	0.996264i	$0.472477\pi$
$728$	−6.64845e17	−0.165526
$729$	3.20223e18	0.790176
$730$	1.30645e17	0.0319518
$731$	−4.92715e18	−1.19435
$732$	−1.76095e17	−0.0423083
$733$	−8.30226e17	−0.197706	−0.0988531	−	0.995102i	$-0.531517\pi$
$733$	−8.30226e17	−0.197706	−0.0988531	+	0.995102i	$0.531517\pi$
$734$	4.00805e18	0.946037
$735$	−3.16177e17	−0.0739711
$736$	1.15585e18	0.268038
$737$	−9.09834e18	−2.09133
$738$	2.05374e17	0.0467928
$739$	−1.49877e18	−0.338490	−0.169245	−	0.985574i	$-0.554133\pi$
$739$	−1.49877e18	−0.338490	−0.169245	+	0.985574i	$0.554133\pi$
$740$	−1.05019e18	−0.235104
$741$	1.66812e18	0.370176
$742$	1.14898e18	0.252748
$743$	3.97076e18	0.865857	0.432929	−	0.901428i	$-0.357480\pi$
$743$	3.97076e18	0.865857	0.432929	+	0.901428i	$0.357480\pi$
$744$	6.47775e17	0.140023
$745$	−4.52483e18	−0.969586
$746$	2.42388e17	0.0514884
$747$	−4.35728e18	−0.917555
$748$	5.61599e18	1.17237
$749$	7.22388e16	0.0149499
$750$	2.51885e18	0.516778
$751$	−1.95181e18	−0.396989	−0.198495	−	0.980102i	$-0.563605\pi$
$751$	−1.95181e18	−0.396989	−0.198495	+	0.980102i	$0.563605\pi$
$752$	2.19039e18	0.441677
$753$	4.45561e18	0.890718
$754$	−4.31052e18	−0.854310
$755$	−6.93159e17	−0.136200
$756$	−1.01123e18	−0.196997
$757$	−8.10690e18	−1.56578	−0.782892	−	0.622158i	$-0.786256\pi$
$757$	−8.10690e18	−1.56578	−0.782892	+	0.622158i	$0.786256\pi$
$758$	−3.97697e18	−0.761556
$759$	−1.04637e19	−1.98662
$760$	−6.38015e17	−0.120100
$761$	−1.33164e18	−0.248534	−0.124267	−	0.992249i	$-0.539658\pi$
$761$	−1.33164e18	−0.248534	−0.124267	+	0.992249i	$0.539658\pi$
$762$	2.40096e17	0.0444301
$763$	1.23092e18	0.225850
$764$	8.89661e17	0.161852
$765$	−2.79694e18	−0.504526
$766$	−5.24867e18	−0.938776
$767$	−1.75112e18	−0.310561
$768$	−2.39877e17	−0.0421833
$769$	−6.25218e17	−0.109021	−0.0545105	−	0.998513i	$-0.517360\pi$
$769$	−6.25218e17	−0.109021	−0.0545105	+	0.998513i	$0.517360\pi$
$770$	−2.30202e18	−0.398033
$771$	−7.84598e16	−0.0134522
$772$	−2.65549e18	−0.451474
$773$	7.95600e18	1.34131	0.670653	−	0.741771i	$-0.266014\pi$
$773$	7.95600e18	1.34131	0.670653	+	0.741771i	$0.266014\pi$
$774$	2.27715e18	0.380694
$775$	1.45626e18	0.241423
$776$	−3.83070e18	−0.629763
$777$	−9.59043e17	−0.156351
$778$	1.95359e18	0.315839
$779$	3.35663e17	0.0538158
$780$	−2.01700e18	−0.320694
$781$	8.68505e18	1.36943
$782$	8.28158e18	1.29500
$783$	−6.55632e18	−1.01674
$784$	2.32218e17	0.0357143
$785$	7.08115e18	1.08007
$786$	−4.64736e18	−0.703007
$787$	−3.64558e18	−0.546928	−0.273464	−	0.961882i	$-0.588170\pi$
$787$	−3.64558e18	−0.546928	−0.273464	+	0.961882i	$0.588170\pi$
$788$	−3.70702e18	−0.551576
$789$	3.70688e18	0.547025
$790$	−1.17626e18	−0.172158
$791$	3.71625e18	0.539458
$792$	−2.59551e18	−0.373688
$793$	1.08751e18	0.155295
$794$	1.48340e18	0.210100
$795$	3.48577e18	0.489680
$796$	−4.46075e17	−0.0621545
$797$	−2.55224e18	−0.352730	−0.176365	−	0.984325i	$-0.556434\pi$
$797$	−2.55224e18	−0.352730	−0.176365	+	0.984325i	$0.556434\pi$
$798$	−5.82643e17	−0.0798700
$799$	1.56939e19	2.13392
$800$	−5.39266e17	−0.0727308
$801$	−4.97356e18	−0.665359
$802$	2.40542e18	0.319197
$803$	8.68650e17	0.114339
$804$	2.78442e18	0.363555
$805$	−3.39466e18	−0.439666
$806$	−4.00044e18	−0.513961
$807$	6.41528e18	0.817594
$808$	−7.65637e17	−0.0967941
$809$	−1.10314e19	−1.38345	−0.691726	−	0.722160i	$-0.743149\pi$
$809$	−1.10314e19	−1.38345	−0.691726	+	0.722160i	$0.743149\pi$
$810$	−6.93715e17	−0.0863035
$811$	1.32107e19	1.63039	0.815193	−	0.579189i	$-0.196631\pi$
$811$	1.32107e19	1.63039	0.815193	+	0.579189i	$0.196631\pi$
$812$	1.50558e18	0.184328
$813$	5.49049e17	0.0666841
$814$	−6.98260e18	−0.841315
$815$	3.90366e18	0.466602
$816$	−1.71869e18	−0.203804
$817$	3.72178e18	0.437832
$818$	4.11766e17	0.0480567
$819$	2.20155e18	0.254907
$820$	−4.05866e17	−0.0466222
$821$	4.12625e18	0.470246	0.235123	−	0.971966i	$-0.424451\pi$
$821$	4.12625e18	0.470246	0.235123	+	0.971966i	$0.424451\pi$
$822$	4.86355e18	0.549903
$823$	−5.57025e18	−0.624851	−0.312425	−	0.949942i	$-0.601141\pi$
$823$	−5.57025e18	−0.624851	−0.312425	+	0.949942i	$0.601141\pi$
$824$	−3.14915e18	−0.350483
$825$	4.88188e18	0.539059
$826$	6.11635e17	0.0670073
$827$	−9.63092e18	−1.04684	−0.523422	−	0.852074i	$-0.675345\pi$
$827$	−9.63092e18	−1.04684	−0.523422	+	0.852074i	$0.675345\pi$
$828$	−3.82746e18	−0.412775
$829$	1.65767e19	1.77375	0.886876	−	0.462008i	$-0.152871\pi$
$829$	1.65767e19	1.77375	0.886876	+	0.462008i	$0.152871\pi$
$830$	8.61100e18	0.914210
$831$	−3.87229e17	−0.0407907
$832$	1.48140e18	0.154835
$833$	1.66382e18	0.172550
$834$	−2.05496e18	−0.211458
$835$	−1.38785e19	−1.41703
$836$	−4.24211e18	−0.429775
$837$	−6.08470e18	−0.611679
$838$	1.12779e19	1.12497
$839$	−1.73527e18	−0.171757	−0.0858784	−	0.996306i	$-0.527370\pi$
$839$	−1.73527e18	−0.171757	−0.0858784	+	0.996306i	$0.527370\pi$
$840$	7.04501e17	0.0691937
$841$	−4.99183e17	−0.0486503
$842$	1.36468e19	1.31978
$843$	−7.51787e18	−0.721465
$844$	7.07311e18	0.673573
$845$	4.33795e18	0.409936
$846$	−7.25318e18	−0.680176
$847$	−1.12444e19	−1.04639
$848$	−2.56015e18	−0.236425
$849$	8.51445e18	0.780291
$850$	−3.86379e18	−0.351391
$851$	−1.02968e19	−0.929313
$852$	−2.65794e18	−0.238061
$853$	5.04408e18	0.448346	0.224173	−	0.974549i	$-0.428032\pi$
$853$	5.04408e18	0.448346	0.224173	+	0.974549i	$0.428032\pi$
$854$	−3.79846e17	−0.0335067
$855$	2.11270e18	0.184952
$856$	−1.60962e17	−0.0139844
$857$	1.79237e18	0.154544	0.0772722	−	0.997010i	$-0.475379\pi$
$857$	1.79237e18	0.154544	0.0772722	+	0.997010i	$0.475379\pi$
$858$	−1.34108e19	−1.14760
$859$	5.54351e18	0.470792	0.235396	−	0.971899i	$-0.424361\pi$
$859$	5.54351e18	0.470792	0.235396	+	0.971899i	$0.424361\pi$
$860$	−4.50018e18	−0.379306
$861$	−3.70642e17	−0.0310052
$862$	1.27865e18	0.106158
$863$	4.20289e18	0.346320	0.173160	−	0.984894i	$-0.444602\pi$
$863$	4.20289e18	0.346320	0.173160	+	0.984894i	$0.444602\pi$
$864$	2.25322e18	0.184274
$865$	−4.38318e18	−0.355782
$866$	−6.71226e18	−0.540758
$867$	−3.87348e18	−0.309725
$868$	1.39728e18	0.110893
$869$	−7.82085e18	−0.616063
$870$	4.56763e18	0.357121
$871$	−1.71957e19	−1.33445
$872$	−2.74272e18	−0.211264
$873$	1.26849e19	0.969824
$874$	−6.25560e18	−0.474728
$875$	5.43328e18	0.409270
$876$	−2.65838e17	−0.0198765
$877$	1.24227e19	0.921973	0.460987	−	0.887407i	$-0.347496\pi$
$877$	1.24227e19	0.921973	0.460987	+	0.887407i	$0.347496\pi$
$878$	9.99227e18	0.736122
$879$	5.86574e18	0.428939
$880$	5.12933e18	0.372326
$881$	−1.28270e19	−0.924235	−0.462118	−	0.886819i	$-0.652910\pi$
$881$	−1.28270e19	−0.924235	−0.462118	+	0.886819i	$0.652910\pi$
$882$	−7.68960e17	−0.0549994
$883$	−1.89764e19	−1.34731	−0.673656	−	0.739045i	$-0.735277\pi$
$883$	−1.89764e19	−1.34731	−0.673656	+	0.739045i	$0.735277\pi$
$884$	1.06141e19	0.748071
$885$	1.85557e18	0.129821
$886$	−8.21325e18	−0.570421
$887$	−2.03084e19	−1.40014	−0.700070	−	0.714075i	$-0.746848\pi$
$887$	−2.03084e19	−1.40014	−0.700070	+	0.714075i	$0.746848\pi$
$888$	2.13693e18	0.146253
$889$	5.17898e17	0.0351871
$890$	9.82891e18	0.662934
$891$	−4.61245e18	−0.308835
$892$	7.64758e18	0.508338
$893$	−1.18546e19	−0.782263
$894$	9.20715e18	0.603159
$895$	2.00206e18	0.130205
$896$	−5.17426e17	−0.0334077
$897$	−1.97762e19	−1.26763
$898$	8.92991e17	0.0568265
$899$	9.05926e18	0.572341
$900$	1.78571e18	0.112004
$901$	−1.83432e19	−1.14226
$902$	−2.69857e18	−0.166836
$903$	−4.10962e18	−0.252250
$904$	−8.28049e18	−0.504616
$905$	7.99736e18	0.483873
$906$	1.41044e18	0.0847272
$907$	1.88777e19	1.12590	0.562952	−	0.826490i	$-0.309666\pi$
$907$	1.88777e19	1.12590	0.562952	+	0.826490i	$0.309666\pi$
$908$	2.11561e18	0.125279
$909$	2.53531e18	0.149061
$910$	−4.35076e18	−0.253978
$911$	−1.55318e19	−0.900229	−0.450114	−	0.892971i	$-0.648617\pi$
$911$	−1.55318e19	−0.900229	−0.450114	+	0.892971i	$0.648617\pi$
$912$	1.29824e18	0.0747116
$913$	5.72538e19	3.27148
$914$	−3.64021e17	−0.0206526
$915$	−1.15237e18	−0.0649166
$916$	−8.97427e18	−0.501971
$917$	−1.00246e19	−0.556756
$918$	1.61441e19	0.890300
$919$	−2.81182e19	−1.53970	−0.769852	−	0.638223i	$-0.779670\pi$
$919$	−2.81182e19	−1.53970	−0.769852	+	0.638223i	$0.779670\pi$
$920$	7.56394e18	0.411270
$921$	7.23628e18	0.390686
$922$	2.97727e18	0.159613
$923$	1.64145e19	0.873811
$924$	4.68417e18	0.247608
$925$	4.80402e18	0.252164
$926$	−1.00523e19	−0.523957
$927$	1.04280e19	0.539738
$928$	−3.35473e18	−0.172423
$929$	−1.72749e19	−0.881684	−0.440842	−	0.897585i	$-0.645320\pi$
$929$	−1.72749e19	−0.881684	−0.440842	+	0.897585i	$0.645320\pi$
$930$	4.23906e18	0.214847
$931$	−1.25679e18	−0.0632542
$932$	1.30686e19	0.653168
$933$	1.88351e19	0.934838
$934$	−1.01852e19	−0.502012
$935$	3.67512e19	1.79885
$936$	−4.90546e18	−0.238444
$937$	−1.34607e19	−0.649773	−0.324886	−	0.945753i	$-0.605326\pi$
$937$	−1.34607e19	−0.649773	−0.324886	+	0.945753i	$0.605326\pi$
$938$	6.00613e18	0.287923
$939$	−1.30056e19	−0.619160
$940$	1.43340e19	0.677696
$941$	2.16052e19	1.01444	0.507220	−	0.861817i	$-0.330673\pi$
$941$	2.16052e19	1.01444	0.507220	+	0.861817i	$0.330673\pi$
$942$	−1.44088e19	−0.671887
$943$	−3.97943e18	−0.184287
$944$	−1.36284e18	−0.0626796
$945$	−6.61754e18	−0.302266
$946$	−2.99213e19	−1.35734
$947$	−3.98223e18	−0.179412	−0.0897060	−	0.995968i	$-0.528593\pi$
$947$	−3.98223e18	−0.179412	−0.0897060	+	0.995968i	$0.528593\pi$
$948$	2.39346e18	0.107096
$949$	1.64173e18	0.0729577
$950$	2.91856e18	0.128815
$951$	−8.90971e18	−0.390562
$952$	−3.70731e18	−0.161406
$953$	1.63506e19	0.707016	0.353508	−	0.935431i	$-0.384989\pi$
$953$	1.63506e19	0.707016	0.353508	+	0.935431i	$0.384989\pi$
$954$	8.47760e18	0.364090
$955$	5.82196e18	0.248341
$956$	9.51434e17	0.0403090
$957$	3.03697e19	1.27795
$958$	−1.36866e19	−0.572030
$959$	1.04909e19	0.435504
$960$	−1.56976e18	−0.0647247
$961$	−1.60100e19	−0.655674
$962$	−1.31970e19	−0.536829
$963$	5.33003e17	0.0215357
$964$	−2.40667e19	−0.965864
$965$	−1.73776e19	−0.692728
$966$	6.90748e18	0.273507
$967$	8.27701e18	0.325538	0.162769	−	0.986664i	$-0.447957\pi$
$967$	8.27701e18	0.325538	0.162769	+	0.986664i	$0.447957\pi$
$968$	2.50545e19	0.978806
$969$	9.30175e18	0.360961
$970$	−2.50682e19	−0.966289
$971$	3.36787e19	1.28953	0.644764	−	0.764382i	$-0.276956\pi$
$971$	3.36787e19	1.28953	0.644764	+	0.764382i	$0.276956\pi$
$972$	−1.22922e19	−0.467518
$973$	−4.43266e18	−0.167467
$974$	2.87762e19	1.07994
$975$	9.22665e18	0.343965
$976$	8.46369e17	0.0313427
$977$	−3.81035e19	−1.40168	−0.700842	−	0.713316i	$-0.747192\pi$
$977$	−3.81035e19	−1.40168	−0.700842	+	0.713316i	$0.747192\pi$
$978$	−7.94319e18	−0.290263
$979$	6.53516e19	2.37229
$980$	1.51964e18	0.0547989
$981$	9.08217e18	0.325343
$982$	1.70982e19	0.608450
$983$	−2.44161e19	−0.863135	−0.431568	−	0.902081i	$-0.642039\pi$
$983$	−2.44161e19	−0.863135	−0.431568	+	0.902081i	$0.642039\pi$
$984$	8.25859e17	0.0290027
$985$	−2.42589e19	−0.846321
$986$	−2.40363e19	−0.833043
$987$	1.30899e19	0.450688
$988$	−8.01748e18	−0.274232
$989$	−4.41233e19	−1.49931
$990$	−1.69851e19	−0.573376
$991$	−1.52017e19	−0.509816	−0.254908	−	0.966965i	$-0.582045\pi$
$991$	−1.52017e19	−0.509816	−0.254908	+	0.966965i	$0.582045\pi$
$992$	−3.11340e18	−0.103731
$993$	−4.10843e18	−0.135990
$994$	−5.73330e18	−0.188536
$995$	−2.91912e18	−0.0953680
$996$	−1.75217e19	−0.568711
$997$	−5.99514e19	−1.93322	−0.966608	−	0.256259i	$-0.917510\pi$
$997$	−5.99514e19	−1.93322	−0.966608	+	0.256259i	$0.917510\pi$
$998$	−9.61619e18	−0.308074
$999$	−2.00726e19	−0.638894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.14.a.d.1.1	✓	2
3.2	odd	2		126.14.a.g.1.2		2
4.3	odd	2		112.14.a.c.1.2		2
7.2	even	3		98.14.c.i.67.2		4
7.3	odd	6		98.14.c.k.79.1		4
7.4	even	3		98.14.c.i.79.2		4
7.5	odd	6		98.14.c.k.67.1		4
7.6	odd	2		98.14.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.a.d.1.1	✓	2	1.1	even	1	trivial
98.14.a.f.1.2		2	7.6	odd	2
98.14.c.i.67.2		4	7.2	even	3
98.14.c.i.79.2		4	7.4	even	3
98.14.c.k.67.1		4	7.5	odd	6
98.14.c.k.79.1		4	7.3	odd	6
112.14.a.c.1.2		2	4.3	odd	2
126.14.a.g.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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q+64.0000 q^{2} -852.214 q^{3} +4096.00 q^{4} +26804.3 q^{5} -54541.7 q^{6} -117649. q^{7} +262144. q^{8} -868055. q^{9} +O(q^{10})\)	\(q+64.0000 q^{2} -852.214 q^{3} +4096.00 q^{4} +26804.3 q^{5} -54541.7 q^{6} -117649. q^{7} +262144. q^{8} -868055. q^{9} +1.71548e6 q^{10} +1.14061e7 q^{11} -3.49067e6 q^{12} +2.15572e7 q^{13} -7.52954e6 q^{14} -2.28430e7 q^{15} +1.67772e7 q^{16} +1.20207e8 q^{17} -5.55555e7 q^{18} -9.08000e7 q^{19} +1.09791e8 q^{20} +1.00262e8 q^{21} +7.29988e8 q^{22} +1.07647e9 q^{23} -2.23403e8 q^{24} -5.02231e8 q^{25} +1.37966e9 q^{26} +2.09847e9 q^{27} -4.81890e8 q^{28} -3.12433e9 q^{29} -1.46195e9 q^{30} -2.89958e9 q^{31} +1.07374e9 q^{32} -9.72040e9 q^{33} +7.69326e9 q^{34} -3.15350e9 q^{35} -3.55555e9 q^{36} -9.56536e9 q^{37} -5.81120e9 q^{38} -1.83713e10 q^{39} +7.02660e9 q^{40} -3.69673e9 q^{41} +6.41677e9 q^{42} -4.09888e10 q^{43} +4.67192e10 q^{44} -2.32676e10 q^{45} +6.88942e10 q^{46} +1.30557e11 q^{47} -1.42978e10 q^{48} +1.38413e10 q^{49} -3.21428e10 q^{50} -1.02442e11 q^{51} +8.82983e10 q^{52} -1.52597e11 q^{53} +1.34302e11 q^{54} +3.05732e11 q^{55} -3.08410e10 q^{56} +7.73810e10 q^{57} -1.99957e11 q^{58} -8.12315e10 q^{59} -9.35650e10 q^{60} +5.04475e10 q^{61} -1.85573e11 q^{62} +1.02126e11 q^{63} +6.87195e10 q^{64} +5.77826e11 q^{65} -6.22105e11 q^{66} -7.97676e11 q^{67} +4.92369e11 q^{68} -9.17384e11 q^{69} -2.01824e11 q^{70} +7.61441e11 q^{71} -2.27555e11 q^{72} +7.61569e10 q^{73} -6.12183e11 q^{74} +4.28008e11 q^{75} -3.71917e11 q^{76} -1.34191e12 q^{77} -1.17577e12 q^{78} -6.85675e11 q^{79} +4.49702e11 q^{80} -4.04386e11 q^{81} -2.36591e11 q^{82} +5.01959e12 q^{83} +4.10673e11 q^{84} +3.22207e12 q^{85} -2.62328e12 q^{86} +2.66260e12 q^{87} +2.99003e12 q^{88} +5.72955e12 q^{89} -1.48913e12 q^{90} -2.53618e12 q^{91} +4.40923e12 q^{92} +2.47106e12 q^{93} +8.35567e12 q^{94} -2.43383e12 q^{95} -9.15057e11 q^{96} -1.46130e13 q^{97} +8.85842e11 q^{98} -9.90109e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 128 q^{2} + 1106 q^{3} + 8192 q^{4} + 75530 q^{5} + 70784 q^{6} - 235298 q^{7} + 524288 q^{8} + 1372222 q^{9}+O(q^{10}) \) 2 * q + 128 * q^2 + 1106 * q^3 + 8192 * q^4 + 75530 * q^5 + 70784 * q^6 - 235298 * q^7 + 524288 * q^8 + 1372222 * q^9	\( 2 q + 128 q^{2} + 1106 q^{3} + 8192 q^{4} + 75530 q^{5} + 70784 q^{6} - 235298 q^{7} + 524288 q^{8} + 1372222 q^{9} + 4833920 q^{10} + 3335860 q^{11} + 4530176 q^{12} + 7998102 q^{13} - 15059072 q^{14} + 72572240 q^{15} + 33554432 q^{16} + 39024832 q^{17} + 87822208 q^{18} + 124092934 q^{19} + 309370880 q^{20} - 130119794 q^{21} + 213495040 q^{22} + 1900816000 q^{23} + 289931264 q^{24} + 651256570 q^{25} + 511878528 q^{26} + 3363388028 q^{27} - 963780608 q^{28} - 245135152 q^{29} + 4644623360 q^{30} - 11010560148 q^{31} + 2147483648 q^{32} - 25523571920 q^{33} + 2497589248 q^{34} - 8886028970 q^{35} + 5620621312 q^{36} - 39630491216 q^{37} + 7941947776 q^{38} - 44922928344 q^{39} + 19799736320 q^{40} - 2431027368 q^{41} - 8327666816 q^{42} + 17823138316 q^{43} + 13663682560 q^{44} + 85891353730 q^{45} + 121652224000 q^{46} + 64488311076 q^{47} + 18555600896 q^{48} + 27682574402 q^{49} + 41680420480 q^{50} - 261414624404 q^{51} + 32760225792 q^{52} - 126504176628 q^{53} + 215256833792 q^{54} - 87494006600 q^{55} - 61681958912 q^{56} + 498187264252 q^{57} - 15688649728 q^{58} + 341259961238 q^{59} + 297255895040 q^{60} + 447240700746 q^{61} - 704675849472 q^{62} - 161440546078 q^{63} + 137438953472 q^{64} - 82849532220 q^{65} - 1633508602880 q^{66} - 2071322290888 q^{67} + 159845711872 q^{68} + 696856132000 q^{69} - 568705854080 q^{70} + 650434465720 q^{71} + 359719763968 q^{72} - 1449809330116 q^{73} - 2536351437824 q^{74} + 2686782332710 q^{75} + 508284657664 q^{76} - 392460593140 q^{77} - 2875067414016 q^{78} + 1525152397656 q^{79} + 1267183124480 q^{80} - 1499135370722 q^{81} - 155585751552 q^{82} + 4257517639438 q^{83} - 532970676224 q^{84} - 733591000220 q^{85} + 1140680852224 q^{86} + 8300678039444 q^{87} + 874475683840 q^{88} + 12593651222628 q^{89} + 5497046638720 q^{90} - 940968702198 q^{91} + 7785742336000 q^{92} - 13411957732344 q^{93} + 4127251908864 q^{94} + 8036967852160 q^{95} + 1187558457344 q^{96} - 16541570007760 q^{97} + 1771684761728 q^{98} - 27980572324540 q^{99}+O(q^{100}) \) 2 * q + 128 * q^2 + 1106 * q^3 + 8192 * q^4 + 75530 * q^5 + 70784 * q^6 - 235298 * q^7 + 524288 * q^8 + 1372222 * q^9 + 4833920 * q^10 + 3335860 * q^11 + 4530176 * q^12 + 7998102 * q^13 - 15059072 * q^14 + 72572240 * q^15 + 33554432 * q^16 + 39024832 * q^17 + 87822208 * q^18 + 124092934 * q^19 + 309370880 * q^20 - 130119794 * q^21 + 213495040 * q^22 + 1900816000 * q^23 + 289931264 * q^24 + 651256570 * q^25 + 511878528 * q^26 + 3363388028 * q^27 - 963780608 * q^28 - 245135152 * q^29 + 4644623360 * q^30 - 11010560148 * q^31 + 2147483648 * q^32 - 25523571920 * q^33 + 2497589248 * q^34 - 8886028970 * q^35 + 5620621312 * q^36 - 39630491216 * q^37 + 7941947776 * q^38 - 44922928344 * q^39 + 19799736320 * q^40 - 2431027368 * q^41 - 8327666816 * q^42 + 17823138316 * q^43 + 13663682560 * q^44 + 85891353730 * q^45 + 121652224000 * q^46 + 64488311076 * q^47 + 18555600896 * q^48 + 27682574402 * q^49 + 41680420480 * q^50 - 261414624404 * q^51 + 32760225792 * q^52 - 126504176628 * q^53 + 215256833792 * q^54 - 87494006600 * q^55 - 61681958912 * q^56 + 498187264252 * q^57 - 15688649728 * q^58 + 341259961238 * q^59 + 297255895040 * q^60 + 447240700746 * q^61 - 704675849472 * q^62 - 161440546078 * q^63 + 137438953472 * q^64 - 82849532220 * q^65 - 1633508602880 * q^66 - 2071322290888 * q^67 + 159845711872 * q^68 + 696856132000 * q^69 - 568705854080 * q^70 + 650434465720 * q^71 + 359719763968 * q^72 - 1449809330116 * q^73 - 2536351437824 * q^74 + 2686782332710 * q^75 + 508284657664 * q^76 - 392460593140 * q^77 - 2875067414016 * q^78 + 1525152397656 * q^79 + 1267183124480 * q^80 - 1499135370722 * q^81 - 155585751552 * q^82 + 4257517639438 * q^83 - 532970676224 * q^84 - 733591000220 * q^85 + 1140680852224 * q^86 + 8300678039444 * q^87 + 874475683840 * q^88 + 12593651222628 * q^89 + 5497046638720 * q^90 - 940968702198 * q^91 + 7785742336000 * q^92 - 13411957732344 * q^93 + 4127251908864 * q^94 + 8036967852160 * q^95 + 1187558457344 * q^96 - 16541570007760 * q^97 + 1771684761728 * q^98 - 27980572324540 * q^99

Introduction

L-functions

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