LMFDB - Embedded newform 29.18.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,18,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, 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("29.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	29.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:	$53.1344053299$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-275.201 q^{2} +7065.32 q^{3} -55336.6 q^{4} -620891. q^{5} -1.94438e6 q^{6} +2.72618e7 q^{7} +5.12998e7 q^{8} -7.92215e7 q^{9} +O(q^{10})$	\(q-275.201 q^{2} +7065.32 q^{3} -55336.6 q^{4} -620891. q^{5} -1.94438e6 q^{6} +2.72618e7 q^{7} +5.12998e7 q^{8} -7.92215e7 q^{9} +1.70870e8 q^{10} +6.43661e7 q^{11} -3.90970e8 q^{12} +5.86404e8 q^{13} -7.50246e9 q^{14} -4.38679e9 q^{15} -6.86466e9 q^{16} -3.10293e10 q^{17} +2.18018e10 q^{18} +5.29680e10 q^{19} +3.43580e10 q^{20} +1.92613e11 q^{21} -1.77136e10 q^{22} +1.60419e11 q^{23} +3.62449e11 q^{24} -3.77434e11 q^{25} -1.61379e11 q^{26} -1.47214e12 q^{27} -1.50857e12 q^{28} +5.00246e11 q^{29} +1.20725e12 q^{30} +7.27024e11 q^{31} -4.83480e12 q^{32} +4.54767e11 q^{33} +8.53929e12 q^{34} -1.69266e13 q^{35} +4.38384e12 q^{36} -9.77502e12 q^{37} -1.45768e13 q^{38} +4.14313e12 q^{39} -3.18515e13 q^{40} -6.44608e13 q^{41} -5.30073e13 q^{42} +1.42883e14 q^{43} -3.56180e12 q^{44} +4.91879e13 q^{45} -4.41474e13 q^{46} +1.73045e14 q^{47} -4.85010e13 q^{48} +5.10574e14 q^{49} +1.03870e14 q^{50} -2.19232e14 q^{51} -3.24496e13 q^{52} -8.85198e13 q^{53} +4.05134e14 q^{54} -3.99643e13 q^{55} +1.39852e15 q^{56} +3.74236e14 q^{57} -1.37668e14 q^{58} +4.51204e14 q^{59} +2.42750e14 q^{60} +1.64260e15 q^{61} -2.00078e14 q^{62} -2.15972e15 q^{63} +2.23031e15 q^{64} -3.64093e14 q^{65} -1.25152e14 q^{66} +7.01809e14 q^{67} +1.71706e15 q^{68} +1.13341e15 q^{69} +4.65821e15 q^{70} +4.44430e15 q^{71} -4.06404e15 q^{72} -8.65761e14 q^{73} +2.69009e15 q^{74} -2.66669e15 q^{75} -2.93107e15 q^{76} +1.75474e15 q^{77} -1.14019e15 q^{78} +1.17326e16 q^{79} +4.26220e15 q^{80} -1.70462e14 q^{81} +1.77397e16 q^{82} +1.52260e16 q^{83} -1.06585e16 q^{84} +1.92658e16 q^{85} -3.93214e16 q^{86} +3.53440e15 q^{87} +3.30197e15 q^{88} +5.11031e16 q^{89} -1.35365e16 q^{90} +1.59864e16 q^{91} -8.87702e15 q^{92} +5.13665e15 q^{93} -4.76222e16 q^{94} -3.28873e16 q^{95} -3.41594e16 q^{96} +7.79795e16 q^{97} -1.40510e17 q^{98} -5.09918e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) $ 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * 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 $

$2$	−275.201	−0.760142	−0.380071	−	0.924957i	$-0.624100\pi$
$2$	−275.201	−0.760142	−0.380071	+	0.924957i	$0.624100\pi$
$3$	7065.32	0.621729	0.310864	−	0.950454i	$-0.399382\pi$
$3$	7065.32	0.621729	0.310864	+	0.950454i	$0.399382\pi$
$4$	−55336.6	−0.422184
$5$	−620891.	−0.710837	−0.355419	−	0.934707i	$-0.615662\pi$
$5$	−620891.	−0.710837	−0.355419	+	0.934707i	$0.615662\pi$
$6$	−1.94438e6	−0.472602
$7$	2.72618e7	1.78740	0.893698	−	0.448668i	$-0.148102\pi$
$7$	2.72618e7	1.78740	0.893698	+	0.448668i	$0.148102\pi$
$8$	5.12998e7	1.08106
$9$	−7.92215e7	−0.613454
$10$	1.70870e8	0.540337
$11$	6.43661e7	0.0905357	0.0452678	−	0.998975i	$-0.485586\pi$
$11$	6.43661e7	0.0905357	0.0452678	+	0.998975i	$0.485586\pi$
$12$	−3.90970e8	−0.262484
$13$	5.86404e8	0.199379	0.0996893	−	0.995019i	$-0.468215\pi$
$13$	5.86404e8	0.199379	0.0996893	+	0.995019i	$0.468215\pi$
$14$	−7.50246e9	−1.35867
$15$	−4.38679e9	−0.441948
$16$	−6.86466e9	−0.399576
$17$	−3.10293e10	−1.07884	−0.539419	−	0.842037i	$-0.681356\pi$
$17$	−3.10293e10	−1.07884	−0.539419	+	0.842037i	$0.681356\pi$
$18$	2.18018e10	0.466312
$19$	5.29680e10	0.715497	0.357749	−	0.933818i	$-0.383544\pi$
$19$	5.29680e10	0.715497	0.357749	+	0.933818i	$0.383544\pi$
$20$	3.43580e10	0.300104
$21$	1.92613e11	1.11128
$22$	−1.77136e10	−0.0688199
$23$	1.60419e11	0.427138	0.213569	−	0.976928i	$-0.431491\pi$
$23$	1.60419e11	0.427138	0.213569	+	0.976928i	$0.431491\pi$
$24$	3.62449e11	0.672127
$25$	−3.77434e11	−0.494711
$26$	−1.61379e11	−0.151556
$27$	−1.47214e12	−1.00313
$28$	−1.50857e12	−0.754611
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	1.20725e12	0.335943
$31$	7.27024e11	0.153100	0.0765498	−	0.997066i	$-0.475610\pi$
$31$	7.27024e11	0.153100	0.0765498	+	0.997066i	$0.475610\pi$
$32$	−4.83480e12	−0.777328
$33$	4.54767e11	0.0562886
$34$	8.53929e12	0.820070
$35$	−1.69266e13	−1.27055
$36$	4.38384e12	0.258991
$37$	−9.77502e12	−0.457513	−0.228756	−	0.973484i	$-0.573466\pi$
$37$	−9.77502e12	−0.457513	−0.228756	+	0.973484i	$0.573466\pi$
$38$	−1.45768e13	−0.543879
$39$	4.14313e12	0.123959
$40$	−3.18515e13	−0.768459
$41$	−6.44608e13	−1.26076	−0.630380	−	0.776286i	$-0.717101\pi$
$41$	−6.44608e13	−1.26076	−0.630380	+	0.776286i	$0.717101\pi$
$42$	−5.30073e13	−0.844727
$43$	1.42883e14	1.86422	0.932110	−	0.362175i	$-0.117966\pi$
$43$	1.42883e14	1.86422	0.932110	+	0.362175i	$0.117966\pi$
$44$	−3.56180e12	−0.0382227
$45$	4.91879e13	0.436066
$46$	−4.41474e13	−0.324686
$47$	1.73045e14	1.06005	0.530027	−	0.847981i	$-0.322182\pi$
$47$	1.73045e14	1.06005	0.530027	+	0.847981i	$0.322182\pi$
$48$	−4.85010e13	−0.248428
$49$	5.10574e14	2.19479
$50$	1.03870e14	0.376050
$51$	−2.19232e14	−0.670745
$52$	−3.24496e13	−0.0841745
$53$	−8.85198e13	−0.195297	−0.0976485	−	0.995221i	$-0.531132\pi$
$53$	−8.85198e13	−0.195297	−0.0976485	+	0.995221i	$0.531132\pi$
$54$	4.05134e14	0.762521
$55$	−3.99643e13	−0.0643561
$56$	1.39852e15	1.93229
$57$	3.74236e14	0.444845
$58$	−1.37668e14	−0.141155
$59$	4.51204e14	0.400065	0.200033	−	0.979789i	$-0.435895\pi$
$59$	4.51204e14	0.400065	0.200033	+	0.979789i	$0.435895\pi$
$60$	2.42750e14	0.186583
$61$	1.64260e15	1.09705	0.548526	−	0.836133i	$-0.315189\pi$
$61$	1.64260e15	1.09705	0.548526	+	0.836133i	$0.315189\pi$
$62$	−2.00078e14	−0.116377
$63$	−2.15972e15	−1.09648
$64$	2.23031e15	0.990455
$65$	−3.64093e14	−0.141726
$66$	−1.25152e14	−0.0427873
$67$	7.01809e14	0.211146	0.105573	−	0.994412i	$-0.466332\pi$
$67$	7.01809e14	0.211146	0.105573	+	0.994412i	$0.466332\pi$
$68$	1.71706e15	0.455469
$69$	1.13341e15	0.265564
$70$	4.65821e15	0.965797
$71$	4.44430e15	0.816784	0.408392	−	0.912807i	$-0.366090\pi$
$71$	4.44430e15	0.816784	0.408392	+	0.912807i	$0.366090\pi$
$72$	−4.06404e15	−0.663181
$73$	−8.65761e14	−0.125648	−0.0628238	−	0.998025i	$-0.520011\pi$
$73$	−8.65761e14	−0.125648	−0.0628238	+	0.998025i	$0.520011\pi$
$74$	2.69009e15	0.347775
$75$	−2.66669e15	−0.307576
$76$	−2.93107e15	−0.302072
$77$	1.75474e15	0.161823
$78$	−1.14019e15	−0.0942267
$79$	1.17326e16	0.870090	0.435045	−	0.900409i	$-0.356732\pi$
$79$	1.17326e16	0.870090	0.435045	+	0.900409i	$0.356732\pi$
$80$	4.26220e15	0.284033
$81$	−1.70462e14	−0.0102213
$82$	1.77397e16	0.958357
$83$	1.52260e16	0.742032	0.371016	−	0.928626i	$-0.379009\pi$
$83$	1.52260e16	0.742032	0.371016	+	0.928626i	$0.379009\pi$
$84$	−1.06585e16	−0.469163
$85$	1.92658e16	0.766879
$86$	−3.93214e16	−1.41707
$87$	3.53440e15	0.115452
$88$	3.30197e15	0.0978747
$89$	5.11031e16	1.37604	0.688022	−	0.725690i	$-0.258479\pi$
$89$	5.11031e16	1.37604	0.688022	+	0.725690i	$0.258479\pi$
$90$	−1.35365e16	−0.331472
$91$	1.59864e16	0.356368
$92$	−8.87702e15	−0.180331
$93$	5.13665e15	0.0951865
$94$	−4.76222e16	−0.805792
$95$	−3.28873e16	−0.508602
$96$	−3.41594e16	−0.483287
$97$	7.79795e16	1.01023	0.505116	−	0.863052i	$-0.331450\pi$
$97$	7.79795e16	1.01023	0.505116	+	0.863052i	$0.331450\pi$
$98$	−1.40510e17	−1.66835
$99$	−5.09918e15	−0.0555394
$100$	2.08859e16	0.208859
$101$	−1.75244e16	−0.161031	−0.0805157	−	0.996753i	$-0.525657\pi$
$101$	−1.75244e16	−0.161031	−0.0805157	+	0.996753i	$0.525657\pi$
$102$	6.03328e16	0.509861
$103$	1.53601e16	0.119475	0.0597375	−	0.998214i	$-0.480974\pi$
$103$	1.53601e16	0.119475	0.0597375	+	0.998214i	$0.480974\pi$
$104$	3.00824e16	0.215540
$105$	−1.19592e17	−0.789936
$106$	2.43607e16	0.148453
$107$	8.04122e16	0.452439	0.226219	−	0.974076i	$-0.427363\pi$
$107$	8.04122e16	0.452439	0.226219	+	0.974076i	$0.427363\pi$
$108$	8.14632e16	0.423506
$109$	1.20639e17	0.579914	0.289957	−	0.957040i	$-0.406359\pi$
$109$	1.20639e17	0.579914	0.289957	+	0.957040i	$0.406359\pi$
$110$	1.09982e16	0.0489198
$111$	−6.90636e16	−0.284449
$112$	−1.87143e17	−0.714201
$113$	−3.07891e17	−1.08951	−0.544753	−	0.838596i	$-0.683377\pi$
$113$	−3.07891e17	−1.08951	−0.544753	+	0.838596i	$0.683377\pi$
$114$	−1.02990e17	−0.338145
$115$	−9.96025e16	−0.303626
$116$	−2.76819e16	−0.0783977
$117$	−4.64558e16	−0.122309
$118$	−1.24172e17	−0.304106
$119$	−8.45915e17	−1.92831
$120$	−2.25041e17	−0.477773
$121$	−5.01304e17	−0.991803
$122$	−4.52044e17	−0.833916
$123$	−4.55436e17	−0.783851
$124$	−4.02310e16	−0.0646363
$125$	7.08047e17	1.06250
$126$	5.94356e17	0.833484
$127$	7.36322e17	0.965464	0.482732	−	0.875768i	$-0.339645\pi$
$127$	7.36322e17	0.965464	0.482732	+	0.875768i	$0.339645\pi$
$128$	1.99254e16	0.0244412
$129$	1.00951e18	1.15904
$130$	1.00199e17	0.107732
$131$	−1.55798e18	−1.56948	−0.784739	−	0.619827i	$-0.787203\pi$
$131$	−1.55798e18	−1.56948	−0.784739	+	0.619827i	$0.787203\pi$
$132$	−2.51652e16	−0.0237642
$133$	1.44400e18	1.27888
$134$	−1.93138e17	−0.160501
$135$	9.14038e17	0.713062
$136$	−1.59180e18	−1.16629
$137$	2.05599e18	1.41546	0.707728	−	0.706485i	$-0.249720\pi$
$137$	2.05599e18	1.41546	0.707728	+	0.706485i	$0.249720\pi$
$138$	−3.11915e17	−0.201866
$139$	−3.10190e18	−1.88800	−0.943999	−	0.329948i	$-0.892969\pi$
$139$	−3.10190e18	−1.88800	−0.943999	+	0.329948i	$0.892969\pi$
$140$	9.36659e17	0.536406
$141$	1.22262e18	0.659066
$142$	−1.22307e18	−0.620872
$143$	3.77446e16	0.0180509
$144$	5.43829e17	0.245121
$145$	−3.10598e17	−0.131999
$146$	2.38258e17	0.0955099
$147$	3.60737e18	1.36456
$148$	5.40916e17	0.193155
$149$	1.10187e18	0.371577	0.185789	−	0.982590i	$-0.440516\pi$
$149$	1.10187e18	0.371577	0.185789	+	0.982590i	$0.440516\pi$
$150$	7.33876e17	0.233801
$151$	3.18251e18	0.958221	0.479111	−	0.877754i	$-0.340959\pi$
$151$	3.18251e18	0.958221	0.479111	+	0.877754i	$0.340959\pi$
$152$	2.71725e18	0.773497
$153$	2.45819e18	0.661817
$154$	−4.82905e17	−0.123009
$155$	−4.51402e17	−0.108829
$156$	−2.29266e17	−0.0523337
$157$	7.15203e18	1.54626	0.773129	−	0.634248i	$-0.218690\pi$
$157$	7.15203e18	1.54626	0.773129	+	0.634248i	$0.218690\pi$
$158$	−3.22882e18	−0.661392
$159$	−6.25420e17	−0.121422
$160$	3.00188e18	0.552553
$161$	4.37330e18	0.763465
$162$	4.69113e16	0.00776963
$163$	−3.36022e18	−0.528169	−0.264084	−	0.964500i	$-0.585070\pi$
$163$	−3.36022e18	−0.528169	−0.264084	+	0.964500i	$0.585070\pi$
$164$	3.56704e18	0.532274
$165$	−2.82361e17	−0.0400120
$166$	−4.19021e18	−0.564050
$167$	−5.61683e18	−0.718457	−0.359229	−	0.933250i	$-0.616960\pi$
$167$	−5.61683e18	−0.718457	−0.359229	+	0.933250i	$0.616960\pi$
$168$	9.88101e18	1.20136
$169$	−8.30655e18	−0.960248
$170$	−5.30197e18	−0.582937
$171$	−4.19620e18	−0.438924
$172$	−7.90663e18	−0.787045
$173$	1.01326e19	0.960129	0.480065	−	0.877233i	$-0.340613\pi$
$173$	1.01326e19	0.960129	0.480065	+	0.877233i	$0.340613\pi$
$174$	−9.72669e17	−0.0877600
$175$	−1.02895e19	−0.884244
$176$	−4.41852e17	−0.0361759
$177$	3.18790e18	0.248732
$178$	−1.40636e19	−1.04599
$179$	−9.96774e18	−0.706880	−0.353440	−	0.935457i	$-0.614988\pi$
$179$	−9.96774e18	−0.706880	−0.353440	+	0.935457i	$0.614988\pi$
$180$	−2.72189e18	−0.184100
$181$	4.00045e18	0.258132	0.129066	−	0.991636i	$-0.458802\pi$
$181$	4.00045e18	0.258132	0.129066	+	0.991636i	$0.458802\pi$
$182$	−4.39947e18	−0.270891
$183$	1.16055e19	0.682069
$184$	8.22944e18	0.461763
$185$	6.06922e18	0.325217
$186$	−1.41361e18	−0.0723552
$187$	−1.99724e18	−0.0976734
$188$	−9.57574e18	−0.447539
$189$	−4.01332e19	−1.79299
$190$	9.05062e18	0.386610
$191$	3.18928e18	0.130289	0.0651447	−	0.997876i	$-0.479249\pi$
$191$	3.18928e18	0.130289	0.0651447	+	0.997876i	$0.479249\pi$
$192$	1.57578e19	0.615794
$193$	−1.21602e19	−0.454679	−0.227340	−	0.973816i	$-0.573003\pi$
$193$	−1.21602e19	−0.454679	−0.227340	+	0.973816i	$0.573003\pi$
$194$	−2.14600e19	−0.767919
$195$	−2.57243e18	−0.0881149
$196$	−2.82534e19	−0.926605
$197$	2.52396e19	0.792721	0.396360	−	0.918095i	$-0.370273\pi$
$197$	2.52396e19	0.792721	0.396360	+	0.918095i	$0.370273\pi$
$198$	1.40330e18	0.0422178
$199$	4.17039e19	1.20206	0.601029	−	0.799228i	$-0.294758\pi$
$199$	4.17039e19	1.20206	0.601029	+	0.799228i	$0.294758\pi$
$200$	−1.93623e19	−0.534813
$201$	4.95850e18	0.131276
$202$	4.82272e18	0.122407
$203$	1.36376e19	0.331911
$204$	1.21315e19	0.283178
$205$	4.00231e19	0.896196
$206$	−4.22710e18	−0.0908179
$207$	−1.27086e19	−0.262029
$208$	−4.02546e18	−0.0796668
$209$	3.40935e18	0.0647780
$210$	3.29117e19	0.600463
$211$	−6.21552e19	−1.08912	−0.544561	−	0.838721i	$-0.683304\pi$
$211$	−6.21552e19	−1.08912	−0.544561	+	0.838721i	$0.683304\pi$
$212$	4.89838e18	0.0824513
$213$	3.14004e19	0.507818
$214$	−2.21295e19	−0.343918
$215$	−8.87144e19	−1.32516
$216$	−7.55205e19	−1.08445
$217$	1.98200e19	0.273650
$218$	−3.32000e19	−0.440817
$219$	−6.11688e18	−0.0781187
$220$	2.21149e18	0.0271701
$221$	−1.81957e19	−0.215097
$222$	1.90064e19	0.216221
$223$	1.25750e20	1.37694	0.688472	−	0.725263i	$-0.258282\pi$
$223$	1.25750e20	1.37694	0.688472	+	0.725263i	$0.258282\pi$
$224$	−1.31805e20	−1.38939
$225$	2.99009e19	0.303482
$226$	8.47318e19	0.828180
$227$	−1.65848e20	−1.56131	−0.780657	−	0.624960i	$-0.785115\pi$
$227$	−1.65848e20	−1.56131	−0.780657	+	0.624960i	$0.785115\pi$
$228$	−2.07089e19	−0.187807
$229$	−8.34006e19	−0.728731	−0.364366	−	0.931256i	$-0.618714\pi$
$229$	−8.34006e19	−0.728731	−0.364366	+	0.931256i	$0.618714\pi$
$230$	2.74107e19	0.230799
$231$	1.23978e19	0.100610
$232$	2.56625e19	0.200748
$233$	1.93098e20	1.45631	0.728154	−	0.685414i	$-0.240379\pi$
$233$	1.93098e20	1.45631	0.728154	+	0.685414i	$0.240379\pi$
$234$	1.27847e19	0.0929725
$235$	−1.07442e20	−0.753526
$236$	−2.49681e19	−0.168901
$237$	8.28946e19	0.540960
$238$	2.32796e20	1.46579
$239$	2.27368e20	1.38149	0.690745	−	0.723098i	$-0.257283\pi$
$239$	2.27368e20	1.38149	0.690745	+	0.723098i	$0.257283\pi$
$240$	3.01138e19	0.176592
$241$	1.33894e20	0.757909	0.378955	−	0.925415i	$-0.376284\pi$
$241$	1.33894e20	0.757909	0.378955	+	0.925415i	$0.376284\pi$
$242$	1.37959e20	0.753911
$243$	1.88908e20	0.996775
$244$	−9.08957e19	−0.463159
$245$	−3.17011e20	−1.56014
$246$	1.25336e20	0.595838
$247$	3.10606e19	0.142655
$248$	3.72962e19	0.165510
$249$	1.07577e20	0.461343
$250$	−1.94855e20	−0.807647
$251$	2.46785e19	0.0988762	0.0494381	−	0.998777i	$-0.484257\pi$
$251$	2.46785e19	0.0988762	0.0494381	+	0.998777i	$0.484257\pi$
$252$	1.19511e20	0.462919
$253$	1.03255e19	0.0386712
$254$	−2.02636e20	−0.733889
$255$	1.36119e20	0.476790
$256$	−2.97814e20	−1.00903
$257$	3.37458e20	1.10608	0.553042	−	0.833153i	$-0.313467\pi$
$257$	3.37458e20	1.10608	0.553042	+	0.833153i	$0.313467\pi$
$258$	−2.77818e20	−0.881034
$259$	−2.66485e20	−0.817757
$260$	2.01476e19	0.0598344
$261$	−3.96303e19	−0.113915
$262$	4.28756e20	1.19303
$263$	6.61383e20	1.78168	0.890839	−	0.454319i	$-0.150117\pi$
$263$	6.61383e20	1.78168	0.890839	+	0.454319i	$0.150117\pi$
$264$	2.33294e19	0.0608515
$265$	5.49611e19	0.138824
$266$	−3.97391e20	−0.972128
$267$	3.61060e20	0.855526
$268$	−3.88357e19	−0.0891426
$269$	−5.57024e20	−1.23874	−0.619369	−	0.785100i	$-0.712612\pi$
$269$	−5.57024e20	−1.23874	−0.619369	+	0.785100i	$0.712612\pi$
$270$	−2.51544e20	−0.542028
$271$	6.76253e20	1.41212	0.706058	−	0.708154i	$-0.250472\pi$
$271$	6.76253e20	1.41212	0.706058	+	0.708154i	$0.250472\pi$
$272$	2.13006e20	0.431078
$273$	1.12949e20	0.221564
$274$	−5.65810e20	−1.07595
$275$	−2.42940e19	−0.0447890
$276$	−6.27189e19	−0.112117
$277$	5.65903e20	0.980989	0.490494	−	0.871444i	$-0.336816\pi$
$277$	5.65903e20	0.980989	0.490494	+	0.871444i	$0.336816\pi$
$278$	8.53644e20	1.43515
$279$	−5.75959e19	−0.0939195
$280$	−8.68330e20	−1.37354
$281$	−1.15115e21	−1.76656	−0.883282	−	0.468842i	$-0.844671\pi$
$281$	−1.15115e21	−1.76656	−0.883282	+	0.468842i	$0.844671\pi$
$282$	−3.36466e20	−0.500984
$283$	−6.78475e20	−0.980278	−0.490139	−	0.871644i	$-0.663054\pi$
$283$	−6.78475e20	−0.980278	−0.490139	+	0.871644i	$0.663054\pi$
$284$	−2.45932e20	−0.344834
$285$	−2.32359e20	−0.316212
$286$	−1.03873e19	−0.0137212
$287$	−1.75732e21	−2.25348
$288$	3.83020e20	0.476854
$289$	1.35579e20	0.163893
$290$	8.54769e19	0.100338
$291$	5.50950e20	0.628090
$292$	4.79083e19	0.0530464
$293$	−3.70959e20	−0.398980	−0.199490	−	0.979900i	$-0.563929\pi$
$293$	−3.70959e20	−0.398980	−0.199490	+	0.979900i	$0.563929\pi$
$294$	−9.92751e20	−1.03726
$295$	−2.80148e20	−0.284381
$296$	−5.01457e20	−0.494600
$297$	−9.47560e19	−0.0908191
$298$	−3.03237e20	−0.282451
$299$	9.40702e19	0.0851622
$300$	1.47566e20	0.129854
$301$	3.89523e21	3.33210
$302$	−8.75829e20	−0.728384
$303$	−1.23815e20	−0.100118
$304$	−3.63607e20	−0.285896
$305$	−1.01987e21	−0.779826
$306$	−6.76496e20	−0.503075
$307$	5.52511e20	0.399636	0.199818	−	0.979833i	$-0.435965\pi$
$307$	5.52511e20	0.399636	0.199818	+	0.979833i	$0.435965\pi$
$308$	−9.71011e19	−0.0683192
$309$	1.08524e20	0.0742810
$310$	1.24226e20	0.0827254
$311$	−9.29008e20	−0.601944	−0.300972	−	0.953633i	$-0.597311\pi$
$311$	−9.29008e20	−0.601944	−0.300972	+	0.953633i	$0.597311\pi$
$312$	2.12542e20	0.134008
$313$	3.11081e21	1.90874	0.954371	−	0.298625i	$-0.0965278\pi$
$313$	3.11081e21	1.90874	0.954371	+	0.298625i	$0.0965278\pi$
$314$	−1.96824e21	−1.17538
$315$	1.34095e21	0.779422
$316$	−6.49242e20	−0.367339
$317$	−3.94921e20	−0.217524	−0.108762	−	0.994068i	$-0.534689\pi$
$317$	−3.94921e20	−0.217524	−0.108762	+	0.994068i	$0.534689\pi$
$318$	1.72116e20	0.0922977
$319$	3.21989e19	0.0168121
$320$	−1.38478e21	−0.704052
$321$	5.68137e20	0.281294
$322$	−1.20354e21	−0.580342
$323$	−1.64356e21	−0.771906
$324$	9.43279e18	0.00431527
$325$	−2.21329e20	−0.0986347
$326$	9.24734e20	0.401483
$327$	8.52355e20	0.360549
$328$	−3.30682e21	−1.36296
$329$	4.71753e21	1.89474
$330$	7.77059e19	0.0304148
$331$	3.35691e21	1.28056	0.640282	−	0.768140i	$-0.278817\pi$
$331$	3.35691e21	1.28056	0.640282	+	0.768140i	$0.278817\pi$
$332$	−8.42556e20	−0.313274
$333$	7.74392e20	0.280663
$334$	1.54575e21	0.546129
$335$	−4.35747e20	−0.150091
$336$	−1.32222e21	−0.444039
$337$	8.44884e20	0.276658	0.138329	−	0.990386i	$-0.455827\pi$
$337$	8.44884e20	0.276658	0.138329	+	0.990386i	$0.455827\pi$
$338$	2.28597e21	0.729925
$339$	−2.17535e21	−0.677378
$340$	−1.06610e21	−0.323764
$341$	4.67957e19	0.0138610
$342$	1.15480e21	0.333645
$343$	7.57725e21	2.13556
$344$	7.32984e21	2.01534
$345$	−7.03723e20	−0.188773
$346$	−2.78850e21	−0.729834
$347$	3.04981e21	0.778883	0.389441	−	0.921051i	$-0.372668\pi$
$347$	3.04981e21	0.778883	0.389441	+	0.921051i	$0.372668\pi$
$348$	−1.95581e20	−0.0487421
$349$	6.01583e21	1.46312	0.731559	−	0.681778i	$-0.238793\pi$
$349$	6.01583e21	1.46312	0.731559	+	0.681778i	$0.238793\pi$
$350$	2.83169e21	0.672151
$351$	−8.63269e20	−0.200003
$352$	−3.11198e20	−0.0703759
$353$	−2.35616e21	−0.520139	−0.260070	−	0.965590i	$-0.583745\pi$
$353$	−2.35616e21	−0.520139	−0.260070	+	0.965590i	$0.583745\pi$
$354$	−8.77312e20	−0.189072
$355$	−2.75942e21	−0.580601
$356$	−2.82787e21	−0.580945
$357$	−5.97666e21	−1.19889
$358$	2.74313e21	0.537329
$359$	3.40797e21	0.651918	0.325959	−	0.945384i	$-0.394313\pi$
$359$	3.40797e21	0.651918	0.325959	+	0.945384i	$0.394313\pi$
$360$	2.52333e21	0.471414
$361$	−2.67478e21	−0.488063
$362$	−1.10093e21	−0.196217
$363$	−3.54187e21	−0.616633
$364$	−8.84633e20	−0.150453
$365$	5.37543e20	0.0893149
$366$	−3.19383e21	−0.518469
$367$	−8.06166e21	−1.27868	−0.639342	−	0.768923i	$-0.720793\pi$
$367$	−8.06166e21	−1.27868	−0.639342	+	0.768923i	$0.720793\pi$
$368$	−1.10122e21	−0.170674
$369$	5.10668e21	0.773418
$370$	−1.67025e21	−0.247211
$371$	−2.41321e21	−0.349073
$372$	−2.84245e20	−0.0401862
$373$	−6.29484e21	−0.869880	−0.434940	−	0.900459i	$-0.643230\pi$
$373$	−6.29484e21	−0.869880	−0.434940	+	0.900459i	$0.643230\pi$
$374$	5.49641e20	0.0742456
$375$	5.00258e21	0.660584
$376$	8.87719e21	1.14598
$377$	2.93346e20	0.0370237
$378$	1.10447e22	1.36293
$379$	−8.95460e21	−1.08047	−0.540235	−	0.841514i	$-0.681665\pi$
$379$	−8.95460e21	−1.08047	−0.540235	+	0.841514i	$0.681665\pi$
$380$	1.81987e21	0.214724
$381$	5.20234e21	0.600256
$382$	−8.77693e20	−0.0990385
$383$	−1.43335e22	−1.58185	−0.790923	−	0.611916i	$-0.790399\pi$
$383$	−1.43335e22	−1.58185	−0.790923	+	0.611916i	$0.790399\pi$
$384$	1.40779e20	0.0151958
$385$	−1.08950e21	−0.115030
$386$	3.34651e21	0.345621
$387$	−1.13194e22	−1.14361
$388$	−4.31512e21	−0.426504
$389$	−1.73259e22	−1.67542	−0.837712	−	0.546113i	$-0.816107\pi$
$389$	−1.73259e22	−1.67542	−0.837712	+	0.546113i	$0.816107\pi$
$390$	7.07935e20	0.0669798
$391$	−4.97769e21	−0.460813
$392$	2.61923e22	2.37270
$393$	−1.10076e22	−0.975789
$394$	−6.94597e21	−0.602580
$395$	−7.28467e21	−0.618492
$396$	2.82171e20	0.0234479
$397$	1.60638e22	1.30656	0.653280	−	0.757116i	$-0.273392\pi$
$397$	1.60638e22	1.30656	0.653280	+	0.757116i	$0.273392\pi$
$398$	−1.14769e22	−0.913734
$399$	1.02023e22	0.795115
$400$	2.59096e21	0.197674
$401$	−6.15988e21	−0.460092	−0.230046	−	0.973180i	$-0.573888\pi$
$401$	−6.15988e21	−0.460092	−0.230046	+	0.973180i	$0.573888\pi$
$402$	−1.36458e21	−0.0997881
$403$	4.26330e20	0.0305248
$404$	9.69738e20	0.0679849
$405$	1.05838e20	0.00726567
$406$	−3.75308e21	−0.252300
$407$	−6.29181e20	−0.0414212
$408$	−1.12466e22	−0.725117
$409$	6.89638e21	0.435485	0.217743	−	0.976006i	$-0.430131\pi$
$409$	6.89638e21	0.435485	0.217743	+	0.976006i	$0.430131\pi$
$410$	−1.10144e22	−0.681236
$411$	1.45262e22	0.880029
$412$	−8.49974e20	−0.0504405
$413$	1.23006e22	0.715075
$414$	3.49742e21	0.199180
$415$	−9.45370e21	−0.527464
$416$	−2.83515e21	−0.154982
$417$	−2.19159e22	−1.17382
$418$	−9.38255e20	−0.0492405
$419$	−5.13587e21	−0.264116	−0.132058	−	0.991242i	$-0.542158\pi$
$419$	−5.13587e21	−0.264116	−0.132058	+	0.991242i	$0.542158\pi$
$420$	6.61779e21	0.333499
$421$	2.49739e22	1.23336	0.616678	−	0.787216i	$-0.288478\pi$
$421$	2.49739e22	1.23336	0.616678	+	0.787216i	$0.288478\pi$
$422$	1.71052e22	0.827888
$423$	−1.37089e22	−0.650294
$424$	−4.54104e21	−0.211128
$425$	1.17115e22	0.533713
$426$	−8.64141e21	−0.386014
$427$	4.47801e22	1.96087
$428$	−4.44973e21	−0.191013
$429$	2.66677e20	0.0112227
$430$	2.44143e22	1.00731
$431$	−2.73222e22	−1.10525	−0.552623	−	0.833432i	$-0.686373\pi$
$431$	−2.73222e22	−1.10525	−0.552623	+	0.833432i	$0.686373\pi$
$432$	1.01057e22	0.400827
$433$	−3.23696e22	−1.25890	−0.629449	−	0.777041i	$-0.716720\pi$
$433$	−3.23696e22	−1.25890	−0.629449	+	0.777041i	$0.716720\pi$
$434$	−5.45447e21	−0.208013
$435$	−2.19448e21	−0.0820676
$436$	−6.67577e21	−0.244831
$437$	8.49706e21	0.305616
$438$	1.68337e21	0.0593813
$439$	2.52322e22	0.872986	0.436493	−	0.899708i	$-0.356220\pi$
$439$	2.52322e22	0.872986	0.436493	+	0.899708i	$0.356220\pi$
$440$	−2.05016e21	−0.0695729
$441$	−4.04485e22	−1.34640
$442$	5.00748e21	0.163504
$443$	−5.07854e22	−1.62670	−0.813350	−	0.581775i	$-0.802358\pi$
$443$	−5.07854e22	−1.62670	−0.813350	+	0.581775i	$0.802358\pi$
$444$	3.82174e21	0.120090
$445$	−3.17295e22	−0.978143
$446$	−3.46065e22	−1.04667
$447$	7.78509e21	0.231020
$448$	6.08021e22	1.77034
$449$	−3.71727e22	−1.06201	−0.531007	−	0.847367i	$-0.678186\pi$
$449$	−3.71727e22	−1.06201	−0.531007	+	0.847367i	$0.678186\pi$
$450$	−8.22875e21	−0.230689
$451$	−4.14909e21	−0.114144
$452$	1.70376e22	0.459973
$453$	2.24854e22	0.595754
$454$	4.56415e22	1.18682
$455$	−9.92582e21	−0.253320
$456$	1.91982e22	0.480905
$457$	4.84965e22	1.19240	0.596201	−	0.802835i	$-0.296676\pi$
$457$	4.84965e22	1.19240	0.596201	+	0.802835i	$0.296676\pi$
$458$	2.29519e22	0.553939
$459$	4.56795e22	1.08222
$460$	5.51166e21	0.128186
$461$	1.78431e22	0.407393	0.203697	−	0.979034i	$-0.434704\pi$
$461$	1.78431e22	0.407393	0.203697	+	0.979034i	$0.434704\pi$
$462$	−3.41187e21	−0.0764779
$463$	−4.48460e21	−0.0986928	−0.0493464	−	0.998782i	$-0.515714\pi$
$463$	−4.48460e21	−0.0986928	−0.0493464	+	0.998782i	$0.515714\pi$
$464$	−3.43402e21	−0.0741994
$465$	−3.18930e21	−0.0676621
$466$	−5.31408e22	−1.10700
$467$	−1.51961e22	−0.310841	−0.155420	−	0.987848i	$-0.549673\pi$
$467$	−1.51961e22	−0.310841	−0.155420	+	0.987848i	$0.549673\pi$
$468$	2.57070e21	0.0516371
$469$	1.91326e22	0.377402
$470$	2.95682e22	0.572787
$471$	5.05313e22	0.961353
$472$	2.31467e22	0.432495
$473$	9.19680e21	0.168778
$474$	−2.28126e22	−0.411206
$475$	−1.99919e22	−0.353964
$476$	4.68100e22	0.814104
$477$	7.01267e21	0.119806
$478$	−6.25720e22	−1.05013
$479$	−1.74935e22	−0.288419	−0.144210	−	0.989547i	$-0.546064\pi$
$479$	−1.74935e22	−0.288419	−0.144210	+	0.989547i	$0.546064\pi$
$480$	2.12093e22	0.343538
$481$	−5.73211e21	−0.0912182
$482$	−3.68478e22	−0.576118
$483$	3.08987e22	0.474668
$484$	2.77404e22	0.418724
$485$	−4.84167e22	−0.718110
$486$	−5.19877e22	−0.757691
$487$	3.73949e22	0.535570	0.267785	−	0.963479i	$-0.413708\pi$
$487$	3.73949e22	0.535570	0.267785	+	0.963479i	$0.413708\pi$
$488$	8.42649e22	1.18598
$489$	−2.37410e22	−0.328378
$490$	8.72416e22	1.18592
$491$	−3.88156e22	−0.518577	−0.259289	−	0.965800i	$-0.583488\pi$
$491$	−3.88156e22	−0.518577	−0.259289	+	0.965800i	$0.583488\pi$
$492$	2.52022e22	0.330930
$493$	−1.55223e22	−0.200335
$494$	−8.54791e21	−0.108438
$495$	3.16603e21	0.0394795
$496$	−4.99077e21	−0.0611749
$497$	1.21160e23	1.45992
$498$	−2.96052e22	−0.350686
$499$	2.72246e22	0.317034	0.158517	−	0.987356i	$-0.449329\pi$
$499$	2.72246e22	0.317034	0.158517	+	0.987356i	$0.449329\pi$
$500$	−3.91809e22	−0.448569
$501$	−3.96846e22	−0.446685
$502$	−6.79154e21	−0.0751600
$503$	9.46361e21	0.102974	0.0514872	−	0.998674i	$-0.483604\pi$
$503$	9.46361e21	0.102974	0.0514872	+	0.998674i	$0.483604\pi$
$504$	−1.10793e23	−1.18537
$505$	1.08807e22	0.114467
$506$	−2.84159e21	−0.0293956
$507$	−5.86884e22	−0.597014
$508$	−4.07455e22	−0.407604
$509$	1.55676e23	1.53152	0.765758	−	0.643128i	$-0.222364\pi$
$509$	1.55676e23	1.53152	0.765758	+	0.643128i	$0.222364\pi$
$510$	−3.74601e22	−0.362428
$511$	−2.36022e22	−0.224582
$512$	7.93470e22	0.742568
$513$	−7.79764e22	−0.717737
$514$	−9.28687e22	−0.840781
$515$	−9.53693e21	−0.0849272
$516$	−5.58628e22	−0.489328
$517$	1.11383e22	0.0959727
$518$	7.33368e22	0.621611
$519$	7.15901e22	0.596940
$520$	−1.86779e22	−0.153214
$521$	−3.31513e22	−0.267534	−0.133767	−	0.991013i	$-0.542707\pi$
$521$	−3.31513e22	−0.267534	−0.133767	+	0.991013i	$0.542707\pi$
$522$	1.09063e22	0.0865919
$523$	−1.91253e23	−1.49397	−0.746987	−	0.664838i	$-0.768500\pi$
$523$	−1.91253e23	−1.49397	−0.746987	+	0.664838i	$0.768500\pi$
$524$	8.62131e22	0.662609
$525$	−7.26988e22	−0.549760
$526$	−1.82013e23	−1.35433
$527$	−2.25591e22	−0.165170
$528$	−3.12182e21	−0.0224916
$529$	−1.15316e23	−0.817553
$530$	−1.51253e22	−0.105526
$531$	−3.57451e22	−0.245421
$532$	−7.99061e22	−0.539922
$533$	−3.78000e22	−0.251369
$534$	−9.93639e22	−0.650321
$535$	−4.99272e22	−0.321610
$536$	3.60027e22	0.228262
$537$	−7.04252e22	−0.439488
$538$	1.53294e23	0.941617
$539$	3.28637e22	0.198706
$540$	−5.05797e22	−0.301044
$541$	−1.68705e22	−0.0988445	−0.0494222	−	0.998778i	$-0.515738\pi$
$541$	−1.68705e22	−0.0988445	−0.0494222	+	0.998778i	$0.515738\pi$
$542$	−1.86105e23	−1.07341
$543$	2.82645e22	0.160488
$544$	1.50021e23	0.838611
$545$	−7.49038e22	−0.412225
$546$	−3.10837e22	−0.168420
$547$	−3.33920e23	−1.78135	−0.890677	−	0.454637i	$-0.849769\pi$
$547$	−3.33920e23	−1.78135	−0.890677	+	0.454637i	$0.849769\pi$
$548$	−1.13771e23	−0.597583
$549$	−1.30129e23	−0.672991
$550$	6.68572e21	0.0340460
$551$	2.64971e22	0.132865
$552$	5.81436e22	0.287091
$553$	3.19852e23	1.55520
$554$	−1.55737e23	−0.745691
$555$	4.28810e22	0.202197
$556$	1.71648e23	0.797084
$557$	1.74292e23	0.797094	0.398547	−	0.917148i	$-0.369515\pi$
$557$	1.74292e23	0.797094	0.398547	+	0.917148i	$0.369515\pi$
$558$	1.58504e22	0.0713922
$559$	8.37869e22	0.371685
$560$	1.16195e23	0.507680
$561$	−1.41111e22	−0.0607263
$562$	3.16798e23	1.34284
$563$	1.22487e23	0.511409	0.255704	−	0.966755i	$-0.417693\pi$
$563$	1.22487e23	0.511409	0.255704	+	0.966755i	$0.417693\pi$
$564$	−6.76556e22	−0.278248
$565$	1.91167e23	0.774462
$566$	1.86717e23	0.745151
$567$	−4.64711e21	−0.0182695
$568$	2.27992e23	0.882994
$569$	−4.32759e23	−1.65117	−0.825584	−	0.564279i	$-0.809154\pi$
$569$	−4.32759e23	−1.65117	−0.825584	+	0.564279i	$0.809154\pi$
$570$	6.39455e22	0.240366
$571$	2.54448e23	0.942305	0.471153	−	0.882052i	$-0.343838\pi$
$571$	2.54448e23	0.942305	0.471153	+	0.882052i	$0.343838\pi$
$572$	−2.08865e21	−0.00762079
$573$	2.25333e22	0.0810047
$574$	4.83615e23	1.71296
$575$	−6.05475e22	−0.211310
$576$	−1.76688e23	−0.607598
$577$	2.06031e23	0.698134	0.349067	−	0.937098i	$-0.386499\pi$
$577$	2.06031e23	0.698134	0.349067	+	0.937098i	$0.386499\pi$
$578$	−3.73114e22	−0.124582
$579$	−8.59159e22	−0.282687
$580$	1.71874e22	0.0557280
$581$	4.15089e23	1.32631
$582$	−1.51622e23	−0.477437
$583$	−5.69768e21	−0.0176813
$584$	−4.44134e22	−0.135833
$585$	2.88440e22	0.0869421
$586$	1.02088e23	0.303281
$587$	1.82842e23	0.535368	0.267684	−	0.963507i	$-0.413742\pi$
$587$	1.82842e23	0.535368	0.267684	+	0.963507i	$0.413742\pi$
$588$	−1.99619e23	−0.576097
$589$	3.85090e22	0.109542
$590$	7.70970e22	0.216170
$591$	1.78326e23	0.492857
$592$	6.71022e22	0.182811
$593$	−1.91371e23	−0.513940	−0.256970	−	0.966419i	$-0.582724\pi$
$593$	−1.91371e23	−0.513940	−0.256970	+	0.966419i	$0.582724\pi$
$594$	2.60769e22	0.0690354
$595$	5.25221e23	1.37072
$596$	−6.09740e22	−0.156874
$597$	2.94651e23	0.747353
$598$	−2.58882e22	−0.0647353
$599$	−7.84490e23	−1.93401	−0.967007	−	0.254750i	$-0.918007\pi$
$599$	−7.84490e23	−1.93401	−0.967007	+	0.254750i	$0.918007\pi$
$600$	−1.36801e23	−0.332508
$601$	−8.14238e23	−1.95127	−0.975637	−	0.219391i	$-0.929593\pi$
$601$	−8.14238e23	−1.95127	−0.975637	+	0.219391i	$0.929593\pi$
$602$	−1.07197e24	−2.53287
$603$	−5.55984e22	−0.129528
$604$	−1.76109e23	−0.404546
$605$	3.11255e23	0.705011
$606$	3.40740e22	0.0761037
$607$	6.62130e23	1.45828	0.729138	−	0.684367i	$-0.239921\pi$
$607$	6.62130e23	1.45828	0.729138	+	0.684367i	$0.239921\pi$
$608$	−2.56090e23	−0.556176
$609$	9.63540e22	0.206359
$610$	2.80670e23	0.592778
$611$	1.01474e23	0.211352
$612$	−1.36028e23	−0.279409
$613$	7.28838e23	1.47644	0.738222	−	0.674557i	$-0.235665\pi$
$613$	7.28838e23	1.47644	0.738222	+	0.674557i	$0.235665\pi$
$614$	−1.52052e23	−0.303780
$615$	2.82776e23	0.557190
$616$	9.00176e22	0.174941
$617$	−1.98266e23	−0.380035	−0.190017	−	0.981781i	$-0.560854\pi$
$617$	−1.98266e23	−0.380035	−0.190017	+	0.981781i	$0.560854\pi$
$618$	−2.98658e22	−0.0564641
$619$	1.01053e24	1.88442	0.942212	−	0.335017i	$-0.108742\pi$
$619$	1.01053e24	1.88442	0.942212	+	0.335017i	$0.108742\pi$
$620$	2.49791e22	0.0459459
$621$	−2.36159e23	−0.428475
$622$	2.55664e23	0.457563
$623$	1.39316e24	2.45954
$624$	−2.84412e22	−0.0495312
$625$	−1.51661e23	−0.260551
$626$	−8.56098e23	−1.45091
$627$	2.40881e22	0.0402744
$628$	−3.95769e23	−0.652806
$629$	3.03312e23	0.493583
$630$	−3.69030e23	−0.592471
$631$	−7.58913e23	−1.20210	−0.601052	−	0.799210i	$-0.705252\pi$
$631$	−7.58913e23	−1.20210	−0.601052	+	0.799210i	$0.705252\pi$
$632$	6.01880e23	0.940621
$633$	−4.39146e23	−0.677139
$634$	1.08683e23	0.165349
$635$	−4.57175e23	−0.686287
$636$	3.46086e22	0.0512624
$637$	2.99403e23	0.437593
$638$	−8.86117e21	−0.0127795
$639$	−3.52084e23	−0.501059
$640$	−1.23715e22	−0.0173737
$641$	−8.99920e23	−1.24713	−0.623564	−	0.781772i	$-0.714316\pi$
$641$	−8.99920e23	−1.24713	−0.623564	+	0.781772i	$0.714316\pi$
$642$	−1.56352e23	−0.213823
$643$	−1.74644e23	−0.235700	−0.117850	−	0.993031i	$-0.537600\pi$
$643$	−1.74644e23	−0.235700	−0.117850	+	0.993031i	$0.537600\pi$
$644$	−2.42003e23	−0.322323
$645$	−6.26795e23	−0.823888
$646$	4.52309e23	0.586758
$647$	−1.05814e24	−1.35474	−0.677372	−	0.735641i	$-0.736881\pi$
$647$	−1.05814e24	−1.35474	−0.677372	+	0.735641i	$0.736881\pi$
$648$	−8.74467e21	−0.0110498
$649$	2.90423e22	0.0362202
$650$	6.09099e22	0.0749763
$651$	1.40034e23	0.170136
$652$	1.85943e23	0.222985
$653$	−9.92357e23	−1.17464	−0.587321	−	0.809354i	$-0.699817\pi$
$653$	−9.92357e23	−1.17464	−0.587321	+	0.809354i	$0.699817\pi$
$654$	−2.34569e23	−0.274069
$655$	9.67333e23	1.11564
$656$	4.42501e23	0.503770
$657$	6.85869e22	0.0770789
$658$	−1.29827e24	−1.44027
$659$	7.39660e23	0.810039	0.405020	−	0.914308i	$-0.367265\pi$
$659$	7.39660e23	0.810039	0.405020	+	0.914308i	$0.367265\pi$
$660$	1.56249e22	0.0168925
$661$	1.28597e23	0.137252	0.0686258	−	0.997642i	$-0.478139\pi$
$661$	1.28597e23	0.137252	0.0686258	+	0.997642i	$0.478139\pi$
$662$	−9.23824e23	−0.973411
$663$	−1.28558e23	−0.133732
$664$	7.81092e23	0.802183
$665$	−8.96568e23	−0.909074
$666$	−2.13113e23	−0.213344
$667$	8.02489e22	0.0793176
$668$	3.10816e23	0.303321
$669$	8.88463e23	0.856086
$670$	1.19918e23	0.114090
$671$	1.05728e23	0.0993224
$672$	−9.31247e23	−0.863825
$673$	−1.05495e24	−0.966283	−0.483142	−	0.875542i	$-0.660504\pi$
$673$	−1.05495e24	−0.966283	−0.483142	+	0.875542i	$0.660504\pi$
$674$	−2.32513e23	−0.210299
$675$	5.55636e23	0.496259
$676$	4.59656e23	0.405402
$677$	5.37510e23	0.468147	0.234074	−	0.972219i	$-0.424794\pi$
$677$	5.37510e23	0.468147	0.234074	+	0.972219i	$0.424794\pi$
$678$	5.98657e23	0.514903
$679$	2.12586e24	1.80568
$680$	9.88332e23	0.829043
$681$	−1.17177e24	−0.970714
$682$	−1.28782e22	−0.0105363
$683$	−2.85014e23	−0.230298	−0.115149	−	0.993348i	$-0.536735\pi$
$683$	−2.85014e23	−0.230298	−0.115149	+	0.993348i	$0.536735\pi$
$684$	2.32204e23	0.185307
$685$	−1.27655e24	−1.00616
$686$	−2.08526e24	−1.62333
$687$	−5.89251e23	−0.453073
$688$	−9.80840e23	−0.744898
$689$	−5.19083e22	−0.0389380
$690$	1.93665e23	0.143494
$691$	5.09992e23	0.373250	0.186625	−	0.982431i	$-0.440245\pi$
$691$	5.09992e23	0.373250	0.186625	+	0.982431i	$0.440245\pi$
$692$	−5.60704e23	−0.405352
$693$	−1.39013e23	−0.0992710
$694$	−8.39310e23	−0.592061
$695$	1.92594e24	1.34206
$696$	1.81314e23	0.124811
$697$	2.00017e24	1.36016
$698$	−1.65556e24	−1.11218
$699$	1.36430e24	0.905428
$700$	5.69387e23	0.373314
$701$	−1.64225e24	−1.06374	−0.531869	−	0.846826i	$-0.678510\pi$
$701$	−1.64225e24	−1.06374	−0.531869	+	0.846826i	$0.678510\pi$
$702$	2.37572e23	0.152030
$703$	−5.17764e23	−0.327349
$704$	1.43556e23	0.0896715
$705$	−7.59113e23	−0.468489
$706$	6.48417e23	0.395379
$707$	−4.77745e23	−0.287827
$708$	−1.76407e23	−0.105011
$709$	1.30885e24	0.769831	0.384916	−	0.922952i	$-0.374231\pi$
$709$	1.30885e24	0.769831	0.384916	+	0.922952i	$0.374231\pi$
$710$	7.59396e23	0.441339
$711$	−9.29475e23	−0.533760
$712$	2.62158e24	1.48759
$713$	1.16628e23	0.0653947
$714$	1.64478e24	0.911324
$715$	−2.34352e22	−0.0128312
$716$	5.51580e23	0.298434
$717$	1.60643e24	0.858912
$718$	−9.37876e23	−0.495550
$719$	8.51530e23	0.444636	0.222318	−	0.974974i	$-0.428638\pi$
$719$	8.51530e23	0.444636	0.222318	+	0.974974i	$0.428638\pi$
$720$	−3.37658e23	−0.174241
$721$	4.18743e23	0.213549
$722$	7.36101e23	0.370997
$723$	9.46005e23	0.471214
$724$	−2.21371e23	−0.108979
$725$	−1.88810e23	−0.0918655
$726$	9.74725e23	0.468728
$727$	−2.16935e24	−1.03107	−0.515533	−	0.856870i	$-0.672406\pi$
$727$	−2.16935e24	−1.03107	−0.515533	+	0.856870i	$0.672406\pi$
$728$	8.20099e23	0.385256
$729$	1.35671e24	0.629945
$730$	−1.47932e23	−0.0678920
$731$	−4.43355e24	−2.01119
$732$	−6.42207e23	−0.287959
$733$	4.75782e23	0.210874	0.105437	−	0.994426i	$-0.466376\pi$
$733$	4.75782e23	0.210874	0.105437	+	0.994426i	$0.466376\pi$
$734$	2.21858e24	0.971981
$735$	−2.23978e24	−0.969981
$736$	−7.75593e23	−0.332026
$737$	4.51728e22	0.0191163
$738$	−1.40536e24	−0.587908
$739$	4.65308e24	1.92426	0.962128	−	0.272598i	$-0.0878828\pi$
$739$	4.65308e24	1.92426	0.962128	+	0.272598i	$0.0878828\pi$
$740$	−3.35850e23	−0.137302
$741$	2.19453e23	0.0886926
$742$	6.64116e23	0.265345
$743$	−2.38022e24	−0.940181	−0.470091	−	0.882618i	$-0.655779\pi$
$743$	−2.38022e24	−0.940181	−0.470091	+	0.882618i	$0.655779\pi$
$744$	2.63509e23	0.102902
$745$	−6.84144e23	−0.264131
$746$	1.73234e24	0.661232
$747$	−1.20623e24	−0.455202
$748$	1.10520e23	0.0412362
$749$	2.19218e24	0.808687
$750$	−1.37671e24	−0.502138
$751$	1.21739e24	0.439025	0.219512	−	0.975610i	$-0.429553\pi$
$751$	1.21739e24	0.439025	0.219512	+	0.975610i	$0.429553\pi$
$752$	−1.18790e24	−0.423572
$753$	1.74361e23	0.0614742
$754$	−8.07292e22	−0.0281432
$755$	−1.97599e24	−0.681139
$756$	2.22083e24	0.756973
$757$	−1.14951e24	−0.387434	−0.193717	−	0.981057i	$-0.562054\pi$
$757$	−1.14951e24	−0.387434	−0.193717	+	0.981057i	$0.562054\pi$
$758$	2.46431e24	0.821310
$759$	7.29532e22	0.0240430
$760$	−1.68711e24	−0.549830
$761$	−4.49008e24	−1.44705	−0.723527	−	0.690296i	$-0.757480\pi$
$761$	−4.49008e24	−1.44705	−0.723527	+	0.690296i	$0.757480\pi$
$762$	−1.43169e24	−0.456280
$763$	3.28884e24	1.03654
$764$	−1.76484e23	−0.0550062
$765$	−1.52627e24	−0.470444
$766$	3.94460e24	1.20243
$767$	2.64588e23	0.0797644
$768$	−2.10415e24	−0.627345
$769$	1.28099e24	0.377720	0.188860	−	0.982004i	$-0.439521\pi$
$769$	1.28099e24	0.377720	0.188860	+	0.982004i	$0.439521\pi$
$770$	2.99831e23	0.0874390
$771$	2.38425e24	0.687684
$772$	6.72906e23	0.191958
$773$	2.30942e24	0.651594	0.325797	−	0.945440i	$-0.394367\pi$
$773$	2.30942e24	0.651594	0.325797	+	0.945440i	$0.394367\pi$
$774$	3.11510e24	0.869308
$775$	−2.74404e23	−0.0757400
$776$	4.00033e24	1.09212
$777$	−1.88280e24	−0.508423
$778$	4.76810e24	1.27356
$779$	−3.41436e24	−0.902071
$780$	1.42349e23	0.0372007
$781$	2.86063e23	0.0739481
$782$	1.36986e24	0.350283
$783$	−7.36433e23	−0.186277
$784$	−3.50492e24	−0.876984
$785$	−4.44063e24	−1.09914
$786$	3.02930e24	0.741738
$787$	3.75479e24	0.909495	0.454747	−	0.890620i	$-0.349730\pi$
$787$	3.75479e24	0.909495	0.454747	+	0.890620i	$0.349730\pi$
$788$	−1.39667e24	−0.334674
$789$	4.67288e24	1.10772
$790$	2.00475e24	0.470142
$791$	−8.39365e24	−1.94738
$792$	−2.61587e23	−0.0600415
$793$	9.63225e23	0.218729
$794$	−4.42077e24	−0.993171
$795$	3.88318e23	0.0863111
$796$	−2.30775e24	−0.507490
$797$	−2.11929e24	−0.461099	−0.230550	−	0.973061i	$-0.574052\pi$
$797$	−2.11929e24	−0.461099	−0.230550	+	0.973061i	$0.574052\pi$
$798$	−2.80769e24	−0.604400
$799$	−5.36948e24	−1.14363
$800$	1.82482e24	0.384552
$801$	−4.04847e24	−0.844139
$802$	1.69520e24	0.349735
$803$	−5.57257e22	−0.0113756
$804$	−2.74386e23	−0.0554225
$805$	−2.71534e24	−0.542700
$806$	−1.17326e23	−0.0232032
$807$	−3.93555e24	−0.770159
$808$	−8.98996e23	−0.174085
$809$	6.41483e24	1.22920	0.614601	−	0.788838i	$-0.289317\pi$
$809$	6.41483e24	1.22920	0.614601	+	0.788838i	$0.289317\pi$
$810$	−2.91268e22	−0.00552294
$811$	−7.63671e24	−1.43294	−0.716472	−	0.697616i	$-0.754244\pi$
$811$	−7.63671e24	−1.43294	−0.716472	+	0.697616i	$0.754244\pi$
$812$	−7.54658e23	−0.140128
$813$	4.77794e24	0.877953
$814$	1.73151e23	0.0314860
$815$	2.08633e24	0.375442
$816$	1.50495e24	0.268014
$817$	7.56820e24	1.33384
$818$	−1.89789e24	−0.331030
$819$	−1.26647e24	−0.218615
$820$	−2.21474e24	−0.378360
$821$	9.91280e24	1.67602	0.838010	−	0.545654i	$-0.183719\pi$
$821$	9.91280e24	1.67602	0.838010	+	0.545654i	$0.183719\pi$
$822$	−3.99763e24	−0.668947
$823$	−9.37680e24	−1.55295	−0.776473	−	0.630151i	$-0.782993\pi$
$823$	−9.37680e24	−1.55295	−0.776473	+	0.630151i	$0.782993\pi$
$824$	7.87968e23	0.129160
$825$	−1.71645e23	−0.0278466
$826$	−3.38514e24	−0.543559
$827$	6.91719e24	1.09934	0.549671	−	0.835381i	$-0.314753\pi$
$827$	6.91719e24	1.09934	0.549671	+	0.835381i	$0.314753\pi$
$828$	7.03251e23	0.110625
$829$	−9.17167e24	−1.42802	−0.714011	−	0.700135i	$-0.753123\pi$
$829$	−9.17167e24	−1.42802	−0.714011	+	0.700135i	$0.753123\pi$
$830$	2.60166e24	0.400948
$831$	3.99828e24	0.609909
$832$	1.30786e24	0.197475
$833$	−1.58428e25	−2.36782
$834$	6.03127e24	0.892272
$835$	3.48743e24	0.510706
$836$	−1.88662e23	−0.0273483
$837$	−1.07028e24	−0.153579
$838$	1.41339e24	0.200766
$839$	2.44624e24	0.343972	0.171986	−	0.985099i	$-0.444982\pi$
$839$	2.44624e24	0.343972	0.171986	+	0.985099i	$0.444982\pi$
$840$	−6.13503e24	−0.853970
$841$	2.50246e23	0.0344828
$842$	−6.87283e24	−0.937525
$843$	−8.13326e24	−1.09832
$844$	3.43946e24	0.459811
$845$	5.15746e24	0.682580
$846$	3.77270e24	0.494316
$847$	−1.36664e25	−1.77275
$848$	6.07658e23	0.0780360
$849$	−4.79364e24	−0.609467
$850$	−3.22302e24	−0.405698
$851$	−1.56810e24	−0.195421
$852$	−1.73759e24	−0.214393
$853$	−1.00896e25	−1.23256	−0.616281	−	0.787526i	$-0.711361\pi$
$853$	−1.00896e25	−1.23256	−0.616281	+	0.787526i	$0.711361\pi$
$854$	−1.23235e25	−1.49054
$855$	2.60538e24	0.312004
$856$	4.12513e24	0.489114
$857$	9.30465e24	1.09235	0.546177	−	0.837670i	$-0.316083\pi$
$857$	9.30465e24	1.09235	0.546177	+	0.837670i	$0.316083\pi$
$858$	−7.33898e22	−0.00853087
$859$	2.35972e24	0.271593	0.135796	−	0.990737i	$-0.456641\pi$
$859$	2.35972e24	0.271593	0.135796	+	0.990737i	$0.456641\pi$
$860$	4.90915e24	0.559461
$861$	−1.24160e25	−1.40105
$862$	7.51909e24	0.840143
$863$	1.26821e25	1.40313	0.701567	−	0.712603i	$-0.252484\pi$
$863$	1.26821e25	1.40313	0.701567	+	0.712603i	$0.252484\pi$
$864$	7.11751e24	0.779761
$865$	−6.29125e24	−0.682495
$866$	8.90815e24	0.956942
$867$	9.57908e23	0.101897
$868$	−1.09677e24	−0.115531
$869$	7.55183e23	0.0787742
$870$	6.03921e23	0.0623830
$871$	4.11544e23	0.0420980
$872$	6.18877e24	0.626923
$873$	−6.17765e24	−0.619730
$874$	−2.33840e24	−0.232312
$875$	1.93026e25	1.89910
$876$	3.38487e23	0.0329805
$877$	−6.95139e24	−0.670772	−0.335386	−	0.942081i	$-0.608867\pi$
$877$	−6.95139e24	−0.670772	−0.335386	+	0.942081i	$0.608867\pi$
$878$	−6.94393e24	−0.663593
$879$	−2.62094e24	−0.248057
$880$	2.74342e23	0.0257151
$881$	1.17883e25	1.09435	0.547175	−	0.837018i	$-0.315703\pi$
$881$	1.17883e25	1.09435	0.547175	+	0.837018i	$0.315703\pi$
$882$	1.11314e25	1.02345
$883$	−1.85904e24	−0.169286	−0.0846432	−	0.996411i	$-0.526975\pi$
$883$	−1.85904e24	−0.169286	−0.0846432	+	0.996411i	$0.526975\pi$
$884$	1.00689e24	0.0908107
$885$	−1.97934e24	−0.176808
$886$	1.39762e25	1.23652
$887$	5.22940e24	0.458249	0.229124	−	0.973397i	$-0.426414\pi$
$887$	5.22940e24	0.458249	0.229124	+	0.973397i	$0.426414\pi$
$888$	−3.54295e24	−0.307507
$889$	2.00734e25	1.72567
$890$	8.73197e24	0.743528
$891$	−1.09720e22	−0.000925391 0
$892$	−6.95857e24	−0.581325
$893$	9.16587e24	0.758466
$894$	−2.14246e24	−0.175608
$895$	6.18888e24	0.502477
$896$	5.43203e23	0.0436862
$897$	6.64635e23	0.0529478
$898$	1.02300e25	0.807281
$899$	3.63691e23	0.0284299
$900$	−1.65461e24	−0.128125
$901$	2.74671e24	0.210694
$902$	1.14183e24	0.0867655
$903$	2.75210e25	2.07166
$904$	−1.57947e25	−1.17782
$905$	−2.48385e24	−0.183490
$906$	−6.18801e24	−0.452857
$907$	1.94030e25	1.40672	0.703358	−	0.710835i	$-0.251683\pi$
$907$	1.94030e25	1.40672	0.703358	+	0.710835i	$0.251683\pi$
$908$	9.17745e24	0.659163
$909$	1.38831e24	0.0987853
$910$	2.73159e24	0.192559
$911$	1.64184e25	1.14664	0.573318	−	0.819333i	$-0.305656\pi$
$911$	1.64184e25	1.14664	0.573318	+	0.819333i	$0.305656\pi$
$912$	−2.56900e24	−0.177749
$913$	9.80041e23	0.0671804
$914$	−1.33463e25	−0.906395
$915$	−7.20573e24	−0.484840
$916$	4.61510e24	0.307659
$917$	−4.24732e25	−2.80528
$918$	−1.25710e25	−0.822637
$919$	−1.78581e25	−1.15785	−0.578927	−	0.815380i	$-0.696528\pi$
$919$	−1.78581e25	−1.15785	−0.578927	+	0.815380i	$0.696528\pi$
$920$	−5.10958e24	−0.328238
$921$	3.90367e24	0.248465
$922$	−4.91045e24	−0.309676
$923$	2.60616e24	0.162849
$924$	−6.86050e23	−0.0424760
$925$	3.68943e24	0.226336
$926$	1.23417e24	0.0750205
$927$	−1.21685e24	−0.0732923
$928$	−2.41859e24	−0.144346
$929$	−5.31955e24	−0.314588	−0.157294	−	0.987552i	$-0.550277\pi$
$929$	−5.31955e24	−0.314588	−0.157294	+	0.987552i	$0.550277\pi$
$930$	8.77698e23	0.0514328
$931$	2.70441e25	1.57036
$932$	−1.06854e25	−0.614830
$933$	−6.56374e24	−0.374246
$934$	4.18197e24	0.236283
$935$	1.24007e24	0.0694299
$936$	−2.38317e24	−0.132224
$937$	−2.50045e25	−1.37478	−0.687388	−	0.726290i	$-0.741243\pi$
$937$	−2.50045e25	−1.37478	−0.687388	+	0.726290i	$0.741243\pi$
$938$	−5.26530e24	−0.286879
$939$	2.19789e25	1.18672
$940$	5.94548e24	0.318127
$941$	−1.25452e25	−0.665220	−0.332610	−	0.943065i	$-0.607929\pi$
$941$	−1.25452e25	−0.665220	−0.332610	+	0.943065i	$0.607929\pi$
$942$	−1.39063e25	−0.730765
$943$	−1.03407e25	−0.538519
$944$	−3.09736e24	−0.159856
$945$	2.49183e25	1.27452
$946$	−2.53097e24	−0.128296
$947$	2.41151e25	1.21148	0.605738	−	0.795664i	$-0.292878\pi$
$947$	2.41151e25	1.21148	0.605738	+	0.795664i	$0.292878\pi$
$948$	−4.58710e24	−0.228385
$949$	−5.07686e23	−0.0250514
$950$	5.50180e24	0.269063
$951$	−2.79024e24	−0.135241
$952$	−4.33952e25	−2.08463
$953$	1.36562e25	0.650190	0.325095	−	0.945681i	$-0.394604\pi$
$953$	1.36562e25	0.650190	0.325095	+	0.945681i	$0.394604\pi$
$954$	−1.92989e24	−0.0910692
$955$	−1.98020e24	−0.0926146
$956$	−1.25818e25	−0.583244
$957$	2.27496e23	0.0104525
$958$	4.81422e24	0.219240
$959$	5.60500e25	2.52998
$960$	−9.78388e24	−0.437729
$961$	−2.20216e25	−0.976560
$962$	1.57748e24	0.0693388
$963$	−6.37037e24	−0.277550
$964$	−7.40925e24	−0.319977
$965$	7.55018e24	0.323203
$966$	−8.50336e24	−0.360815
$967$	2.51961e25	1.05976	0.529881	−	0.848072i	$-0.322237\pi$
$967$	2.51961e25	1.05976	0.529881	+	0.848072i	$0.322237\pi$
$968$	−2.57168e25	−1.07220
$969$	−1.16123e25	−0.479916
$970$	1.33243e25	0.545865
$971$	1.28706e25	0.522678	0.261339	−	0.965247i	$-0.415836\pi$
$971$	1.28706e25	0.522678	0.261339	+	0.965247i	$0.415836\pi$
$972$	−1.04535e25	−0.420823
$973$	−8.45633e25	−3.37460
$974$	−1.02911e25	−0.407109
$975$	−1.56376e24	−0.0613240
$976$	−1.12759e25	−0.438356
$977$	−3.80187e25	−1.46519	−0.732594	−	0.680666i	$-0.761691\pi$
$977$	−3.80187e25	−1.46519	−0.732594	+	0.680666i	$0.761691\pi$
$978$	6.53354e24	0.249613
$979$	3.28931e24	0.124581
$980$	1.75423e25	0.658665
$981$	−9.55723e24	−0.355750
$982$	1.06821e25	0.394192
$983$	−1.73844e25	−0.635997	−0.317998	−	0.948091i	$-0.603011\pi$
$983$	−1.73844e25	−0.635997	−0.317998	+	0.948091i	$0.603011\pi$
$984$	−2.33637e25	−0.847392
$985$	−1.56711e25	−0.563495
$986$	4.27175e24	0.152283
$987$	3.33308e25	1.17801
$988$	−1.71879e24	−0.0602266
$989$	2.29210e25	0.796280
$990$	−8.71295e23	−0.0300100
$991$	−9.50191e24	−0.324478	−0.162239	−	0.986752i	$-0.551871\pi$
$991$	−9.50191e24	−0.324478	−0.162239	+	0.986752i	$0.551871\pi$
$992$	−3.51502e24	−0.119009
$993$	2.37176e25	0.796164
$994$	−3.33432e25	−1.10974
$995$	−2.58935e25	−0.854467
$996$	−5.95292e24	−0.194772
$997$	1.19972e25	0.389198	0.194599	−	0.980883i	$-0.437659\pi$
$997$	1.19972e25	0.389198	0.194599	+	0.980883i	$0.437659\pi$
$998$	−7.49222e24	−0.240991
$999$	1.43902e25	0.458945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.7	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.7	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-275.201 q^{2} +7065.32 q^{3} -55336.6 q^{4} -620891. q^{5} -1.94438e6 q^{6} +2.72618e7 q^{7} +5.12998e7 q^{8} -7.92215e7 q^{9} +O(q^{10})\)	\(q-275.201 q^{2} +7065.32 q^{3} -55336.6 q^{4} -620891. q^{5} -1.94438e6 q^{6} +2.72618e7 q^{7} +5.12998e7 q^{8} -7.92215e7 q^{9} +1.70870e8 q^{10} +6.43661e7 q^{11} -3.90970e8 q^{12} +5.86404e8 q^{13} -7.50246e9 q^{14} -4.38679e9 q^{15} -6.86466e9 q^{16} -3.10293e10 q^{17} +2.18018e10 q^{18} +5.29680e10 q^{19} +3.43580e10 q^{20} +1.92613e11 q^{21} -1.77136e10 q^{22} +1.60419e11 q^{23} +3.62449e11 q^{24} -3.77434e11 q^{25} -1.61379e11 q^{26} -1.47214e12 q^{27} -1.50857e12 q^{28} +5.00246e11 q^{29} +1.20725e12 q^{30} +7.27024e11 q^{31} -4.83480e12 q^{32} +4.54767e11 q^{33} +8.53929e12 q^{34} -1.69266e13 q^{35} +4.38384e12 q^{36} -9.77502e12 q^{37} -1.45768e13 q^{38} +4.14313e12 q^{39} -3.18515e13 q^{40} -6.44608e13 q^{41} -5.30073e13 q^{42} +1.42883e14 q^{43} -3.56180e12 q^{44} +4.91879e13 q^{45} -4.41474e13 q^{46} +1.73045e14 q^{47} -4.85010e13 q^{48} +5.10574e14 q^{49} +1.03870e14 q^{50} -2.19232e14 q^{51} -3.24496e13 q^{52} -8.85198e13 q^{53} +4.05134e14 q^{54} -3.99643e13 q^{55} +1.39852e15 q^{56} +3.74236e14 q^{57} -1.37668e14 q^{58} +4.51204e14 q^{59} +2.42750e14 q^{60} +1.64260e15 q^{61} -2.00078e14 q^{62} -2.15972e15 q^{63} +2.23031e15 q^{64} -3.64093e14 q^{65} -1.25152e14 q^{66} +7.01809e14 q^{67} +1.71706e15 q^{68} +1.13341e15 q^{69} +4.65821e15 q^{70} +4.44430e15 q^{71} -4.06404e15 q^{72} -8.65761e14 q^{73} +2.69009e15 q^{74} -2.66669e15 q^{75} -2.93107e15 q^{76} +1.75474e15 q^{77} -1.14019e15 q^{78} +1.17326e16 q^{79} +4.26220e15 q^{80} -1.70462e14 q^{81} +1.77397e16 q^{82} +1.52260e16 q^{83} -1.06585e16 q^{84} +1.92658e16 q^{85} -3.93214e16 q^{86} +3.53440e15 q^{87} +3.30197e15 q^{88} +5.11031e16 q^{89} -1.35365e16 q^{90} +1.59864e16 q^{91} -8.87702e15 q^{92} +5.13665e15 q^{93} -4.76222e16 q^{94} -3.28873e16 q^{95} -3.41594e16 q^{96} +7.79795e16 q^{97} -1.40510e17 q^{98} -5.09918e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * q^99

Introduction

L-functions

Modular forms

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