LMFDB - Embedded newform 29.18.a.b.1.6

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			1.6
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)

$f(q)$	$=$	$q-332.840 q^{2} -18225.8 q^{3} -20289.6 q^{4} -318485. q^{5} +6.06628e6 q^{6} +9.82044e6 q^{7} +5.03792e7 q^{8} +2.03040e8 q^{9} +O(q^{10})$	\(q-332.840 q^{2} -18225.8 q^{3} -20289.6 q^{4} -318485. q^{5} +6.06628e6 q^{6} +9.82044e6 q^{7} +5.03792e7 q^{8} +2.03040e8 q^{9} +1.06005e8 q^{10} +9.36358e6 q^{11} +3.69795e8 q^{12} -3.20633e9 q^{13} -3.26863e9 q^{14} +5.80466e9 q^{15} -1.41088e10 q^{16} +8.46481e9 q^{17} -6.75799e10 q^{18} -7.69200e10 q^{19} +6.46194e9 q^{20} -1.78986e11 q^{21} -3.11657e9 q^{22} +1.60829e11 q^{23} -9.18202e11 q^{24} -6.61507e11 q^{25} +1.06720e12 q^{26} -1.34689e12 q^{27} -1.99253e11 q^{28} +5.00246e11 q^{29} -1.93202e12 q^{30} -4.63610e12 q^{31} -1.90733e12 q^{32} -1.70659e11 q^{33} -2.81742e12 q^{34} -3.12767e12 q^{35} -4.11961e12 q^{36} +4.51018e12 q^{37} +2.56020e13 q^{38} +5.84380e13 q^{39} -1.60450e13 q^{40} -1.95332e13 q^{41} +5.95735e13 q^{42} -2.62720e13 q^{43} -1.89983e11 q^{44} -6.46654e13 q^{45} -5.35304e13 q^{46} -2.05312e14 q^{47} +2.57145e14 q^{48} -1.36189e14 q^{49} +2.20176e14 q^{50} -1.54278e14 q^{51} +6.50552e13 q^{52} -1.23971e14 q^{53} +4.48300e14 q^{54} -2.98216e12 q^{55} +4.94746e14 q^{56} +1.40193e15 q^{57} -1.66502e14 q^{58} +6.96656e13 q^{59} -1.17774e14 q^{60} +2.14181e15 q^{61} +1.54308e15 q^{62} +1.99395e15 q^{63} +2.48410e15 q^{64} +1.02117e15 q^{65} +5.68021e13 q^{66} -1.15108e15 q^{67} -1.71748e14 q^{68} -2.93124e15 q^{69} +1.04101e15 q^{70} -2.06784e14 q^{71} +1.02290e16 q^{72} +2.75508e14 q^{73} -1.50117e15 q^{74} +1.20565e16 q^{75} +1.56068e15 q^{76} +9.19545e13 q^{77} -1.94505e16 q^{78} -1.64938e16 q^{79} +4.49345e15 q^{80} -1.67245e15 q^{81} +6.50144e15 q^{82} +1.11291e16 q^{83} +3.63155e15 q^{84} -2.69592e15 q^{85} +8.74436e15 q^{86} -9.11740e15 q^{87} +4.71729e14 q^{88} -6.18759e16 q^{89} +2.15232e16 q^{90} -3.14876e16 q^{91} -3.26316e15 q^{92} +8.44967e16 q^{93} +6.83361e16 q^{94} +2.44979e16 q^{95} +3.47626e16 q^{96} +1.57070e15 q^{97} +4.53293e16 q^{98} +1.90118e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−332.840	−0.919349	−0.459675	−	0.888087i	$-0.652034\pi$
$2$	−332.840	−0.919349	−0.459675	+	0.888087i	$0.652034\pi$
$3$	−18225.8	−1.60382	−0.801912	−	0.597443i	$-0.796183\pi$
$3$	−18225.8	−1.60382	−0.801912	+	0.597443i	$0.796183\pi$
$4$	−20289.6	−0.154797
$5$	−318485.	−0.364623	−0.182312	−	0.983241i	$-0.558358\pi$
$5$	−318485.	−0.364623	−0.182312	+	0.983241i	$0.558358\pi$
$6$	6.06628e6	1.47447
$7$	9.82044e6	0.643869	0.321935	−	0.946762i	$-0.395667\pi$
$7$	9.82044e6	0.643869	0.321935	+	0.946762i	$0.395667\pi$
$8$	5.03792e7	1.06166
$9$	2.03040e8	1.57225
$10$	1.06005e8	0.335216
$11$	9.36358e6	0.0131706	0.00658528	−	0.999978i	$-0.497904\pi$
$11$	9.36358e6	0.0131706	0.00658528	+	0.999978i	$0.497904\pi$
$12$	3.69795e8	0.248268
$13$	−3.20633e9	−1.09016	−0.545080	−	0.838384i	$-0.683501\pi$
$13$	−3.20633e9	−1.09016	−0.545080	+	0.838384i	$0.683501\pi$
$14$	−3.26863e9	−0.591940
$15$	5.80466e9	0.584791
$16$	−1.41088e10	−0.821240
$17$	8.46481e9	0.294307	0.147154	−	0.989114i	$-0.452989\pi$
$17$	8.46481e9	0.294307	0.147154	+	0.989114i	$0.452989\pi$
$18$	−6.75799e10	−1.44544
$19$	−7.69200e10	−1.03904	−0.519522	−	0.854457i	$-0.673890\pi$
$19$	−7.69200e10	−1.03904	−0.519522	+	0.854457i	$0.673890\pi$
$20$	6.46194e9	0.0564427
$21$	−1.78986e11	−1.03265
$22$	−3.11657e9	−0.0121083
$23$	1.60829e11	0.428231	0.214116	−	0.976808i	$-0.431313\pi$
$23$	1.60829e11	0.428231	0.214116	+	0.976808i	$0.431313\pi$
$24$	−9.18202e11	−1.70272
$25$	−6.61507e11	−0.867050
$26$	1.06720e12	1.00224
$27$	−1.34689e12	−0.917785
$28$	−1.99253e11	−0.0996692
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	−1.93202e12	−0.537627
$31$	−4.63610e12	−0.976289	−0.488144	−	0.872763i	$-0.662326\pi$
$31$	−4.63610e12	−0.976289	−0.488144	+	0.872763i	$0.662326\pi$
$32$	−1.90733e12	−0.306655
$33$	−1.70659e11	−0.0211232
$34$	−2.81742e12	−0.270571
$35$	−3.12767e12	−0.234770
$36$	−4.11961e12	−0.243380
$37$	4.51018e12	0.211096	0.105548	−	0.994414i	$-0.466340\pi$
$37$	4.51018e12	0.211096	0.105548	+	0.994414i	$0.466340\pi$
$38$	2.56020e13	0.955244
$39$	5.84380e13	1.74842
$40$	−1.60450e13	−0.387107
$41$	−1.95332e13	−0.382042	−0.191021	−	0.981586i	$-0.561180\pi$
$41$	−1.95332e13	−0.382042	−0.191021	+	0.981586i	$0.561180\pi$
$42$	5.95735e13	0.949368
$43$	−2.62720e13	−0.342776	−0.171388	−	0.985204i	$-0.554825\pi$
$43$	−2.62720e13	−0.342776	−0.171388	+	0.985204i	$0.554825\pi$
$44$	−1.89983e11	−0.00203877
$45$	−6.46654e13	−0.573278
$46$	−5.35304e13	−0.393694
$47$	−2.05312e14	−1.25772	−0.628859	−	0.777519i	$-0.716478\pi$
$47$	−2.05312e14	−1.25772	−0.628859	+	0.777519i	$0.716478\pi$
$48$	2.57145e14	1.31712
$49$	−1.36189e14	−0.585433
$50$	2.20176e14	0.797121
$51$	−1.54278e14	−0.472017
$52$	6.50552e13	0.168754
$53$	−1.23971e14	−0.273511	−0.136755	−	0.990605i	$-0.543667\pi$
$53$	−1.23971e14	−0.273511	−0.136755	+	0.990605i	$0.543667\pi$
$54$	4.48300e14	0.843765
$55$	−2.98216e12	−0.00480229
$56$	4.94746e14	0.683571
$57$	1.40193e15	1.66644
$58$	−1.66502e14	−0.170719
$59$	6.96656e13	0.0617698	0.0308849	−	0.999523i	$-0.490167\pi$
$59$	6.96656e13	0.0617698	0.0308849	+	0.999523i	$0.490167\pi$
$60$	−1.17774e14	−0.0905241
$61$	2.14181e15	1.43047	0.715233	−	0.698886i	$-0.246320\pi$
$61$	2.14181e15	1.43047	0.715233	+	0.698886i	$0.246320\pi$
$62$	1.54308e15	0.897550
$63$	1.99395e15	1.01232
$64$	2.48410e15	1.10316
$65$	1.02117e15	0.397497
$66$	5.68021e13	0.0194196
$67$	−1.15108e15	−0.346314	−0.173157	−	0.984894i	$-0.555397\pi$
$67$	−1.15108e15	−0.346314	−0.173157	+	0.984894i	$0.555397\pi$
$68$	−1.71748e14	−0.0455580
$69$	−2.93124e15	−0.686807
$70$	1.04101e15	0.215835
$71$	−2.06784e14	−0.0380033	−0.0190016	−	0.999819i	$-0.506049\pi$
$71$	−2.06784e14	−0.0380033	−0.0190016	+	0.999819i	$0.506049\pi$
$72$	1.02290e16	1.66920
$73$	2.75508e14	0.0399844	0.0199922	−	0.999800i	$-0.493636\pi$
$73$	2.75508e14	0.0399844	0.0199922	+	0.999800i	$0.493636\pi$
$74$	−1.50117e15	−0.194071
$75$	1.20565e16	1.39059
$76$	1.56068e15	0.160841
$77$	9.19545e13	0.00848011
$78$	−1.94505e16	−1.60741
$79$	−1.64938e16	−1.22318	−0.611591	−	0.791174i	$-0.709470\pi$
$79$	−1.64938e16	−1.22318	−0.611591	+	0.791174i	$0.709470\pi$
$80$	4.49345e15	0.299443
$81$	−1.67245e15	−0.100284
$82$	6.50144e15	0.351230
$83$	1.11291e16	0.542371	0.271185	−	0.962527i	$-0.412584\pi$
$83$	1.11291e16	0.542371	0.271185	+	0.962527i	$0.412584\pi$
$84$	3.63155e15	0.159852
$85$	−2.69592e15	−0.107311
$86$	8.74436e15	0.315131
$87$	−9.11740e15	−0.297822
$88$	4.71729e14	0.0139827
$89$	−6.18759e16	−1.66612	−0.833061	−	0.553182i	$-0.813414\pi$
$89$	−6.18759e16	−1.66612	−0.833061	+	0.553182i	$0.813414\pi$
$90$	2.15232e16	0.527043
$91$	−3.14876e16	−0.701920
$92$	−3.26316e15	−0.0662890
$93$	8.44967e16	1.56579
$94$	6.83361e16	1.15628
$95$	2.44979e16	0.378859
$96$	3.47626e16	0.491821
$97$	1.57070e15	0.0203485	0.0101743	−	0.999948i	$-0.496761\pi$
$97$	1.57070e15	0.0203485	0.0101743	+	0.999948i	$0.496761\pi$
$98$	4.53293e16	0.538217
$99$	1.90118e15	0.0207074
$100$	1.34217e16	0.134217
$101$	1.07285e17	0.985840	0.492920	−	0.870075i	$-0.335930\pi$
$101$	1.07285e17	0.985840	0.492920	+	0.870075i	$0.335930\pi$
$102$	5.13499e16	0.433948
$103$	−3.50328e15	−0.0272495	−0.0136248	−	0.999907i	$-0.504337\pi$
$103$	−3.50328e15	−0.0272495	−0.0136248	+	0.999907i	$0.504337\pi$
$104$	−1.61532e17	−1.15738
$105$	5.70043e16	0.376529
$106$	4.12624e16	0.251452
$107$	−3.49430e17	−1.96607	−0.983034	−	0.183422i	$-0.941283\pi$
$107$	−3.49430e17	−1.96607	−0.983034	+	0.183422i	$0.941283\pi$
$108$	2.73279e16	0.142071
$109$	−2.87690e17	−1.38293	−0.691464	−	0.722411i	$-0.743034\pi$
$109$	−2.87690e17	−1.38293	−0.691464	+	0.722411i	$0.743034\pi$
$110$	9.92583e14	0.00441498
$111$	−8.22018e16	−0.338560
$112$	−1.38555e17	−0.528771
$113$	−1.91324e17	−0.677023	−0.338511	−	0.940962i	$-0.609923\pi$
$113$	−1.91324e17	−0.677023	−0.338511	+	0.940962i	$0.609923\pi$
$114$	−4.66618e17	−1.53204
$115$	−5.12217e16	−0.156143
$116$	−1.01498e16	−0.0287451
$117$	−6.51015e17	−1.71400
$118$	−2.31875e16	−0.0567880
$119$	8.31281e16	0.189495
$120$	2.92434e17	0.620851
$121$	−5.05359e17	−0.999827
$122$	−7.12881e17	−1.31510
$123$	3.56009e17	0.612728
$124$	9.40646e16	0.151127
$125$	4.53665e17	0.680770
$126$	−6.63665e17	−0.930677
$127$	1.24826e18	1.63672	0.818359	−	0.574708i	$-0.194884\pi$
$127$	1.24826e18	1.63672	0.818359	+	0.574708i	$0.194884\pi$
$128$	−5.76812e17	−0.707537
$129$	4.78828e17	0.549753
$130$	−3.39886e17	−0.365439
$131$	7.84941e17	0.790735	0.395368	−	0.918523i	$-0.370617\pi$
$131$	7.84941e17	0.790735	0.395368	+	0.918523i	$0.370617\pi$
$132$	3.46260e15	0.00326982
$133$	−7.55388e17	−0.669008
$134$	3.83126e17	0.318384
$135$	4.28965e17	0.334646
$136$	4.26450e17	0.312455
$137$	−7.82588e17	−0.538776	−0.269388	−	0.963032i	$-0.586821\pi$
$137$	−7.82588e17	−0.538776	−0.269388	+	0.963032i	$0.586821\pi$
$138$	9.75635e17	0.631415
$139$	2.40417e18	1.46332	0.731661	−	0.681669i	$-0.238745\pi$
$139$	2.40417e18	1.46332	0.731661	+	0.681669i	$0.238745\pi$
$140$	6.34591e16	0.0363417
$141$	3.74199e18	2.01716
$142$	6.88259e16	0.0349383
$143$	−3.00227e16	−0.0143580
$144$	−2.86466e18	−1.29119
$145$	−1.59321e17	−0.0677088
$146$	−9.17002e16	−0.0367596
$147$	2.48216e18	0.938930
$148$	−9.15098e16	−0.0326771
$149$	2.84020e18	0.957779	0.478890	−	0.877875i	$-0.341039\pi$
$149$	2.84020e18	0.957779	0.478890	+	0.877875i	$0.341039\pi$
$150$	−4.01288e18	−1.27844
$151$	2.96188e18	0.891791	0.445895	−	0.895085i	$-0.352885\pi$
$151$	2.96188e18	0.891791	0.445895	+	0.895085i	$0.352885\pi$
$152$	−3.87517e18	−1.10311
$153$	1.71870e18	0.462724
$154$	−3.06061e16	−0.00779618
$155$	1.47653e18	0.355978
$156$	−1.18568e18	−0.270651
$157$	1.90893e18	0.412707	0.206354	−	0.978478i	$-0.433840\pi$
$157$	1.90893e18	0.412707	0.206354	+	0.978478i	$0.433840\pi$
$158$	5.48980e18	1.12453
$159$	2.25947e18	0.438663
$160$	6.07456e17	0.111814
$161$	1.57941e18	0.275725
$162$	5.56658e17	0.0921957
$163$	−7.02547e18	−1.10428	−0.552142	−	0.833750i	$-0.686189\pi$
$163$	−7.02547e18	−1.10428	−0.552142	+	0.833750i	$0.686189\pi$
$164$	3.96322e17	0.0591391
$165$	5.43524e16	0.00770202
$166$	−3.70421e18	−0.498628
$167$	4.80741e18	0.614923	0.307462	−	0.951560i	$-0.400520\pi$
$167$	4.80741e18	0.614923	0.307462	+	0.951560i	$0.400520\pi$
$168$	−9.01715e18	−1.09633
$169$	1.63015e18	0.188447
$170$	8.97308e17	0.0986566
$171$	−1.56179e19	−1.63363
$172$	5.33048e17	0.0530609
$173$	1.45503e19	1.37874	0.689369	−	0.724411i	$-0.257888\pi$
$173$	1.45503e19	1.37874	0.689369	+	0.724411i	$0.257888\pi$
$174$	3.03464e18	0.273803
$175$	−6.49629e18	−0.558267
$176$	−1.32109e17	−0.0108162
$177$	−1.26971e18	−0.0990679
$178$	2.05948e19	1.53175
$179$	1.08261e19	0.767751	0.383875	−	0.923385i	$-0.374589\pi$
$179$	1.08261e19	0.767751	0.383875	+	0.923385i	$0.374589\pi$
$180$	1.31203e18	0.0887420
$181$	1.14959e19	0.741777	0.370889	−	0.928677i	$-0.379053\pi$
$181$	1.14959e19	0.741777	0.370889	+	0.928677i	$0.379053\pi$
$182$	1.04803e19	0.645309
$183$	−3.90363e19	−2.29422
$184$	8.10244e18	0.454637
$185$	−1.43643e18	−0.0769704
$186$	−2.81239e19	−1.43951
$187$	7.92609e16	0.00387619
$188$	4.16571e18	0.194691
$189$	−1.32271e19	−0.590933
$190$	−8.15388e18	−0.348304
$191$	−6.91419e18	−0.282461	−0.141230	−	0.989977i	$-0.545106\pi$
$191$	−6.91419e18	−0.282461	−0.141230	+	0.989977i	$0.545106\pi$
$192$	−4.52748e19	−1.76928
$193$	1.71091e19	0.639721	0.319861	−	0.947465i	$-0.396364\pi$
$193$	1.71091e19	0.639721	0.319861	+	0.947465i	$0.396364\pi$
$194$	−5.22791e17	−0.0187074
$195$	−1.86117e19	−0.637516
$196$	2.76323e18	0.0906234
$197$	−1.88385e19	−0.591675	−0.295838	−	0.955238i	$-0.595599\pi$
$197$	−1.88385e19	−0.591675	−0.295838	+	0.955238i	$0.595599\pi$
$198$	−6.32790e17	−0.0190373
$199$	−2.19879e19	−0.633773	−0.316886	−	0.948464i	$-0.602637\pi$
$199$	−2.19879e19	−0.633773	−0.316886	+	0.948464i	$0.602637\pi$
$200$	−3.33262e19	−0.920514
$201$	2.09794e19	0.555427
$202$	−3.57087e19	−0.906331
$203$	4.91264e18	0.119563
$204$	3.13024e18	0.0730670
$205$	6.22105e18	0.139302
$206$	1.16603e18	0.0250518
$207$	3.26548e19	0.673285
$208$	4.52375e19	0.895283
$209$	−7.20246e17	−0.0136848
$210$	−1.89733e19	−0.346162
$211$	8.36965e19	1.46658	0.733291	−	0.679915i	$-0.237983\pi$
$211$	8.36965e19	1.46658	0.733291	+	0.679915i	$0.237983\pi$
$212$	2.51532e18	0.0423387
$213$	3.76881e18	0.0609505
$214$	1.16304e20	1.80750
$215$	8.36724e18	0.124984
$216$	−6.78553e19	−0.974377
$217$	−4.55285e19	−0.628602
$218$	9.57547e19	1.27139
$219$	−5.02137e18	−0.0641279
$220$	6.05069e16	0.000743382 0
$221$	−2.71410e19	−0.320842
$222$	2.73600e19	0.311255
$223$	−1.36177e20	−1.49112	−0.745558	−	0.666440i	$-0.767817\pi$
$223$	−1.36177e20	−1.49112	−0.745558	+	0.666440i	$0.767817\pi$
$224$	−1.87308e19	−0.197446
$225$	−1.34313e20	−1.36322
$226$	6.36803e19	0.622420
$227$	−1.32204e20	−1.24459	−0.622294	−	0.782784i	$-0.713799\pi$
$227$	−1.32204e20	−1.24459	−0.622294	+	0.782784i	$0.713799\pi$
$228$	−2.84446e19	−0.257961
$229$	9.74665e19	0.851635	0.425818	−	0.904809i	$-0.359986\pi$
$229$	9.74665e19	0.851635	0.425818	+	0.904809i	$0.359986\pi$
$230$	1.70486e19	0.143550
$231$	−1.67595e18	−0.0136006
$232$	2.52020e19	0.197146
$233$	−1.48581e20	−1.12057	−0.560283	−	0.828301i	$-0.689308\pi$
$233$	−1.48581e20	−1.12057	−0.560283	+	0.828301i	$0.689308\pi$
$234$	2.16684e20	1.57577
$235$	6.53890e19	0.458593
$236$	−1.41349e18	−0.00956181
$237$	3.00613e20	1.96177
$238$	−2.76684e19	−0.174212
$239$	1.89117e19	0.114908	0.0574538	−	0.998348i	$-0.481702\pi$
$239$	1.89117e19	0.114908	0.0574538	+	0.998348i	$0.481702\pi$
$240$	−8.18968e19	−0.480254
$241$	−4.04261e19	−0.228832	−0.114416	−	0.993433i	$-0.536500\pi$
$241$	−4.04261e19	−0.228832	−0.114416	+	0.993433i	$0.536500\pi$
$242$	1.68204e20	0.919190
$243$	2.04420e20	1.07862
$244$	−4.34565e19	−0.221433
$245$	4.33743e19	0.213462
$246$	−1.18494e20	−0.563311
$247$	2.46631e20	1.13272
$248$	−2.33563e20	−1.03649
$249$	−2.02837e20	−0.869866
$250$	−1.50998e20	−0.625865
$251$	2.84259e20	1.13890	0.569452	−	0.822025i	$-0.307156\pi$
$251$	2.84259e20	1.13890	0.569452	+	0.822025i	$0.307156\pi$
$252$	−4.04564e19	−0.156705
$253$	1.50594e18	0.00564004
$254$	−4.15471e20	−1.50471
$255$	4.91353e19	0.172108
$256$	−1.33611e20	−0.452690
$257$	2.56438e20	0.840524	0.420262	−	0.907403i	$-0.361938\pi$
$257$	2.56438e20	0.840524	0.420262	+	0.907403i	$0.361938\pi$
$258$	−1.59373e20	−0.505415
$259$	4.42920e19	0.135918
$260$	−2.07191e19	−0.0615316
$261$	1.01570e20	0.291959
$262$	−2.61260e20	−0.726962
$263$	2.38051e20	0.641277	0.320639	−	0.947202i	$-0.396103\pi$
$263$	2.38051e20	0.641277	0.320639	+	0.947202i	$0.396103\pi$
$264$	−8.59766e18	−0.0224257
$265$	3.94828e19	0.0997283
$266$	2.51423e20	0.615052
$267$	1.12774e21	2.67216
$268$	2.33550e19	0.0536085
$269$	4.64530e20	1.03305	0.516523	−	0.856273i	$-0.327226\pi$
$269$	4.64530e20	1.03305	0.516523	+	0.856273i	$0.327226\pi$
$270$	−1.42777e20	−0.307656
$271$	6.34118e20	1.32413	0.662066	−	0.749446i	$-0.269680\pi$
$271$	6.34118e20	1.32413	0.662066	+	0.749446i	$0.269680\pi$
$272$	−1.19428e20	−0.241697
$273$	5.73887e20	1.12576
$274$	2.60476e20	0.495323
$275$	−6.19407e18	−0.0114195
$276$	5.94737e19	0.106316
$277$	4.44454e19	0.0770458	0.0385229	−	0.999258i	$-0.487735\pi$
$277$	4.44454e19	0.0770458	0.0385229	+	0.999258i	$0.487735\pi$
$278$	−8.00205e20	−1.34530
$279$	−9.41315e20	−1.53497
$280$	−1.57569e20	−0.249246
$281$	−8.82170e20	−1.35378	−0.676891	−	0.736083i	$-0.736673\pi$
$281$	−8.82170e20	−1.35378	−0.676891	+	0.736083i	$0.736673\pi$
$282$	−1.24548e21	−1.85447
$283$	1.15837e21	1.67364	0.836822	−	0.547475i	$-0.184411\pi$
$283$	1.15837e21	1.67364	0.836822	+	0.547475i	$0.184411\pi$
$284$	4.19556e18	0.00588280
$285$	−4.46494e20	−0.607623
$286$	9.99276e18	0.0132000
$287$	−1.91825e20	−0.245985
$288$	−3.87265e20	−0.482138
$289$	−7.55587e20	−0.913383
$290$	5.30284e19	0.0622481
$291$	−2.86273e19	−0.0326354
$292$	−5.58996e18	−0.00618948
$293$	−1.59557e21	−1.71609	−0.858047	−	0.513571i	$-0.828322\pi$
$293$	−1.59557e21	−1.71609	−0.858047	+	0.513571i	$0.828322\pi$
$294$	−8.26164e20	−0.863205
$295$	−2.21875e19	−0.0225227
$296$	2.27219e20	0.224112
$297$	−1.26117e19	−0.0120877
$298$	−9.45331e20	−0.880533
$299$	−5.15672e20	−0.466840
$300$	−2.44622e20	−0.215260
$301$	−2.58002e20	−0.220703
$302$	−9.85831e20	−0.819867
$303$	−1.95535e21	−1.58111
$304$	1.08525e21	0.853304
$305$	−6.82136e20	−0.521582
$306$	−5.72051e20	−0.425405
$307$	1.77466e21	1.28362	0.641812	−	0.766862i	$-0.278183\pi$
$307$	1.77466e21	1.28362	0.641812	+	0.766862i	$0.278183\pi$
$308$	−1.86572e18	−0.00131270
$309$	6.38502e19	0.0437034
$310$	−4.91448e20	−0.327268
$311$	1.63898e21	1.06197	0.530984	−	0.847382i	$-0.321823\pi$
$311$	1.63898e21	1.06197	0.530984	+	0.847382i	$0.321823\pi$
$312$	2.94406e21	1.85623
$313$	−7.94089e19	−0.0487240	−0.0243620	−	0.999703i	$-0.507755\pi$
$313$	−7.94089e19	−0.0487240	−0.0243620	+	0.999703i	$0.507755\pi$
$314$	−6.35366e20	−0.379422
$315$	−6.35043e20	−0.369116
$316$	3.34653e20	0.189345
$317$	−2.25505e21	−1.24209	−0.621044	−	0.783776i	$-0.713291\pi$
$317$	−2.25505e21	−1.24209	−0.621044	+	0.783776i	$0.713291\pi$
$318$	−7.52041e20	−0.403284
$319$	4.68410e18	0.00244571
$320$	−7.91151e20	−0.402239
$321$	6.36866e21	3.15323
$322$	−5.25692e20	−0.253487
$323$	−6.51113e20	−0.305798
$324$	3.39333e19	0.0155236
$325$	2.12101e21	0.945222
$326$	2.33836e21	1.01522
$327$	5.24339e21	2.21797
$328$	−9.84068e20	−0.405600
$329$	−2.01626e21	−0.809806
$330$	−1.80906e19	−0.00708085
$331$	5.11331e21	1.95058	0.975290	−	0.220927i	$-0.0709084\pi$
$331$	5.11331e21	1.95058	0.975290	+	0.220927i	$0.0709084\pi$
$332$	−2.25805e20	−0.0839575
$333$	9.15749e20	0.331895
$334$	−1.60010e21	−0.565329
$335$	3.66602e20	0.126274
$336$	2.52527e21	0.848056
$337$	−1.78584e21	−0.584773	−0.292387	−	0.956300i	$-0.594449\pi$
$337$	−1.78584e21	−0.584773	−0.292387	+	0.956300i	$0.594449\pi$
$338$	−5.42578e20	−0.173249
$339$	3.48704e21	1.08582
$340$	5.46991e19	0.0166115
$341$	−4.34105e19	−0.0128583
$342$	5.19825e21	1.50188
$343$	−3.62197e21	−1.02081
$344$	−1.32356e21	−0.363913
$345$	9.33558e20	0.250426
$346$	−4.84294e21	−1.26754
$347$	−4.18884e21	−1.06978	−0.534889	−	0.844922i	$-0.679647\pi$
$347$	−4.18884e21	−1.06978	−0.534889	+	0.844922i	$0.679647\pi$
$348$	1.84988e20	0.0461021
$349$	2.00753e21	0.488254	0.244127	−	0.969743i	$-0.421499\pi$
$349$	2.00753e21	0.488254	0.244127	+	0.969743i	$0.421499\pi$
$350$	2.16222e21	0.513242
$351$	4.31858e21	1.00053
$352$	−1.78594e19	−0.00403882
$353$	−2.68437e21	−0.592595	−0.296298	−	0.955096i	$-0.595752\pi$
$353$	−2.68437e21	−0.592595	−0.296298	+	0.955096i	$0.595752\pi$
$354$	4.22611e20	0.0910780
$355$	6.58576e19	0.0138569
$356$	1.25544e21	0.257911
$357$	−1.51508e21	−0.303917
$358$	−3.60335e21	−0.705831
$359$	−9.74174e21	−1.86352	−0.931759	−	0.363077i	$-0.881726\pi$
$359$	−9.74174e21	−1.86352	−0.931759	+	0.363077i	$0.881726\pi$
$360$	−3.25779e21	−0.608628
$361$	4.36301e20	0.0796113
$362$	−3.82628e21	−0.681952
$363$	9.21059e21	1.60354
$364$	6.38871e20	0.108655
$365$	−8.77454e19	−0.0145792
$366$	1.29928e22	2.10919
$367$	3.91305e21	0.620660	0.310330	−	0.950629i	$-0.399560\pi$
$367$	3.91305e21	0.620660	0.310330	+	0.950629i	$0.399560\pi$
$368$	−2.26911e21	−0.351681
$369$	−3.96604e21	−0.600665
$370$	4.78100e20	0.0707627
$371$	−1.21745e21	−0.176105
$372$	−1.71440e21	−0.242381
$373$	2.02358e20	0.0279638	0.0139819	−	0.999902i	$-0.495549\pi$
$373$	2.02358e20	0.0279638	0.0139819	+	0.999902i	$0.495549\pi$
$374$	−2.63812e19	−0.00356357
$375$	−8.26842e21	−1.09183
$376$	−1.03435e22	−1.33527
$377$	−1.60396e21	−0.202437
$378$	4.40250e21	0.543274
$379$	1.06563e21	0.128579	0.0642897	−	0.997931i	$-0.479522\pi$
$379$	1.06563e21	0.128579	0.0642897	+	0.997931i	$0.479522\pi$
$380$	−4.97052e20	−0.0586464
$381$	−2.27506e22	−2.62501
$382$	2.30132e21	0.259680
$383$	8.39158e21	0.926092	0.463046	−	0.886334i	$-0.346756\pi$
$383$	8.39158e21	0.926092	0.463046	+	0.886334i	$0.346756\pi$
$384$	1.05129e22	1.13476
$385$	−2.92861e19	−0.00309205
$386$	−5.69460e21	−0.588127
$387$	−5.33427e21	−0.538930
$388$	−3.18688e19	−0.00314990
$389$	1.40638e22	1.35997	0.679985	−	0.733226i	$-0.261986\pi$
$389$	1.40638e22	1.35997	0.679985	+	0.733226i	$0.261986\pi$
$390$	6.19470e21	0.586099
$391$	1.36139e21	0.126032
$392$	−6.86111e21	−0.621531
$393$	−1.43062e22	−1.26820
$394$	6.27020e21	0.543956
$395$	5.25304e21	0.446001
$396$	−3.85743e19	−0.00320545
$397$	−7.22062e21	−0.587293	−0.293647	−	0.955914i	$-0.594869\pi$
$397$	−7.22062e21	−0.587293	−0.293647	+	0.955914i	$0.594869\pi$
$398$	7.31846e21	0.582658
$399$	1.37676e22	1.07297
$400$	9.33307e21	0.712056
$401$	−5.40980e21	−0.404067	−0.202034	−	0.979379i	$-0.564755\pi$
$401$	−5.40980e21	−0.404067	−0.202034	+	0.979379i	$0.564755\pi$
$402$	−6.98278e21	−0.510631
$403$	1.48649e22	1.06431
$404$	−2.17677e21	−0.152605
$405$	5.32650e20	0.0365658
$406$	−1.63512e21	−0.109921
$407$	4.22315e19	0.00278025
$408$	−7.77240e21	−0.501122
$409$	−2.89928e21	−0.183080	−0.0915402	−	0.995801i	$-0.529179\pi$
$409$	−2.89928e21	−0.183080	−0.0915402	+	0.995801i	$0.529179\pi$
$410$	−2.07061e21	−0.128067
$411$	1.42633e22	0.864101
$412$	7.10802e19	0.00421816
$413$	6.84147e20	0.0397717
$414$	−1.08688e22	−0.618984
$415$	−3.54445e21	−0.197761
$416$	6.11552e21	0.334303
$417$	−4.38180e22	−2.34691
$418$	2.39727e20	0.0125811
$419$	−1.52164e21	−0.0782513	−0.0391257	−	0.999234i	$-0.512457\pi$
$419$	−1.52164e21	−0.0782513	−0.0391257	+	0.999234i	$0.512457\pi$
$420$	−1.15659e21	−0.0582857
$421$	−1.72305e22	−0.850944	−0.425472	−	0.904971i	$-0.639892\pi$
$421$	−1.72305e22	−0.850944	−0.425472	+	0.904971i	$0.639892\pi$
$422$	−2.78575e22	−1.34830
$423$	−4.16867e22	−1.97745
$424$	−6.24554e21	−0.290376
$425$	−5.59952e21	−0.255179
$426$	−1.25441e21	−0.0560348
$427$	2.10335e22	0.921034
$428$	7.08980e21	0.304342
$429$	5.47189e20	0.0230277
$430$	−2.78495e21	−0.114904
$431$	1.14752e22	0.464198	0.232099	−	0.972692i	$-0.425441\pi$
$431$	1.14752e22	0.464198	0.232099	+	0.972692i	$0.425441\pi$
$432$	1.90030e22	0.753722
$433$	2.22821e22	0.866579	0.433289	−	0.901255i	$-0.357353\pi$
$433$	2.22821e22	0.866579	0.433289	+	0.901255i	$0.357353\pi$
$434$	1.51537e22	0.577905
$435$	2.90376e21	0.108593
$436$	5.83712e21	0.214074
$437$	−1.23710e22	−0.444951
$438$	1.67131e21	0.0589559
$439$	8.42409e21	0.291457	0.145729	−	0.989325i	$-0.453447\pi$
$439$	8.42409e21	0.291457	0.145729	+	0.989325i	$0.453447\pi$
$440$	−1.50239e20	−0.00509841
$441$	−2.76520e22	−0.920445
$442$	9.03360e21	0.294966
$443$	2.61533e22	0.837712	0.418856	−	0.908053i	$-0.362431\pi$
$443$	2.61533e22	0.837712	0.418856	+	0.908053i	$0.362431\pi$
$444$	1.66784e21	0.0524082
$445$	1.97066e22	0.607507
$446$	4.53251e22	1.37086
$447$	−5.17649e22	−1.53611
$448$	2.43950e22	0.710293
$449$	−2.97454e22	−0.849819	−0.424909	−	0.905236i	$-0.639694\pi$
$449$	−2.97454e22	−0.849819	−0.424909	+	0.905236i	$0.639694\pi$
$450$	4.47046e22	1.25327
$451$	−1.82901e20	−0.00503171
$452$	3.88189e21	0.104801
$453$	−5.39826e22	−1.43027
$454$	4.40028e22	1.14421
$455$	1.00283e22	0.255936
$456$	7.06281e22	1.76920
$457$	6.40802e22	1.57557	0.787783	−	0.615953i	$-0.211229\pi$
$457$	6.40802e22	1.57557	0.787783	+	0.615953i	$0.211229\pi$
$458$	−3.24407e22	−0.782950
$459$	−1.14012e22	−0.270111
$460$	1.03927e21	0.0241705
$461$	−5.46473e21	−0.124770	−0.0623851	−	0.998052i	$-0.519871\pi$
$461$	−5.46473e21	−0.124770	−0.0623851	+	0.998052i	$0.519871\pi$
$462$	5.57822e20	0.0125037
$463$	5.22777e22	1.15048	0.575239	−	0.817986i	$-0.304909\pi$
$463$	5.22777e22	1.15048	0.575239	+	0.817986i	$0.304909\pi$
$464$	−7.05788e21	−0.152501
$465$	−2.69110e22	−0.570925
$466$	4.94536e22	1.03019
$467$	9.48870e21	0.194095	0.0970473	−	0.995280i	$-0.469060\pi$
$467$	9.48870e21	0.194095	0.0970473	+	0.995280i	$0.469060\pi$
$468$	1.32088e22	0.265323
$469$	−1.13041e22	−0.222981
$470$	−2.17641e22	−0.421607
$471$	−3.47917e22	−0.661909
$472$	3.50970e21	0.0655787
$473$	−2.46000e20	−0.00451456
$474$	−1.00056e23	−1.80355
$475$	5.08831e22	0.900902
$476$	−1.68664e21	−0.0293334
$477$	−2.51711e22	−0.430027
$478$	−6.29458e21	−0.105640
$479$	2.56708e22	0.423240	0.211620	−	0.977352i	$-0.432126\pi$
$479$	2.56708e22	0.423240	0.211620	+	0.977352i	$0.432126\pi$
$480$	−1.10714e22	−0.179329
$481$	−1.44611e22	−0.230128
$482$	1.34554e22	0.210377
$483$	−2.87861e22	−0.442214
$484$	1.02535e22	0.154771
$485$	−5.00244e20	−0.00741954
$486$	−6.80390e22	−0.991630
$487$	−1.28868e23	−1.84565	−0.922825	−	0.385219i	$-0.874126\pi$
$487$	−1.28868e23	−1.84565	−0.922825	+	0.385219i	$0.874126\pi$
$488$	1.07903e23	1.51867
$489$	1.28045e23	1.77108
$490$	−1.44367e22	−0.196246
$491$	1.27346e23	1.70134	0.850670	−	0.525700i	$-0.176196\pi$
$491$	1.27346e23	1.70134	0.850670	+	0.525700i	$0.176196\pi$
$492$	−7.22329e21	−0.0948487
$493$	4.23449e21	0.0546515
$494$	−8.20887e22	−1.04137
$495$	−6.05499e20	−0.00755039
$496$	6.54098e22	0.801768
$497$	−2.03071e21	−0.0244691
$498$	6.75122e22	0.799711
$499$	−6.05712e22	−0.705362	−0.352681	−	0.935744i	$-0.614730\pi$
$499$	−6.05712e22	−0.705362	−0.352681	+	0.935744i	$0.614730\pi$
$500$	−9.20468e21	−0.105381
$501$	−8.76189e22	−0.986228
$502$	−9.46126e22	−1.04705
$503$	−8.97254e21	−0.0976309	−0.0488155	−	0.998808i	$-0.515545\pi$
$503$	−8.97254e21	−0.0976309	−0.0488155	+	0.998808i	$0.515545\pi$
$504$	1.00453e23	1.07474
$505$	−3.41686e22	−0.359460
$506$	−5.01236e20	−0.00518516
$507$	−2.97108e22	−0.302236
$508$	−2.53267e22	−0.253360
$509$	1.76507e22	0.173644	0.0868220	−	0.996224i	$-0.472329\pi$
$509$	1.76507e22	0.173644	0.0868220	+	0.996224i	$0.472329\pi$
$510$	−1.63542e22	−0.158228
$511$	2.70561e21	0.0257447
$512$	1.20075e23	1.12372
$513$	1.03603e23	0.953618
$514$	−8.53526e22	−0.772735
$515$	1.11574e21	0.00993581
$516$	−9.71524e21	−0.0851003
$517$	−1.92246e21	−0.0165648
$518$	−1.47421e22	−0.124956
$519$	−2.65192e23	−2.21125
$520$	5.14457e22	0.422008
$521$	7.01454e22	0.566081	0.283041	−	0.959108i	$-0.408657\pi$
$521$	7.01454e22	0.566081	0.283041	+	0.959108i	$0.408657\pi$
$522$	−3.38066e22	−0.268412
$523$	3.66650e22	0.286410	0.143205	−	0.989693i	$-0.454259\pi$
$523$	3.66650e22	0.286410	0.143205	+	0.989693i	$0.454259\pi$
$524$	−1.59261e22	−0.122404
$525$	1.18400e23	0.895361
$526$	−7.92328e22	−0.589557
$527$	−3.92437e22	−0.287329
$528$	2.40779e21	0.0173473
$529$	−1.15184e23	−0.816618
$530$	−1.31415e22	−0.0916851
$531$	1.41449e22	0.0971175
$532$	1.53265e22	0.103561
$533$	6.26300e22	0.416487
$534$	−3.75357e23	−2.45665
$535$	1.11288e23	0.716874
$536$	−5.79905e22	−0.367668
$537$	−1.97314e23	−1.23134
$538$	−1.54614e23	−0.949729
$539$	−1.27522e21	−0.00771047
$540$	−8.70354e21	−0.0518023
$541$	3.22978e23	1.89233	0.946165	−	0.323686i	$-0.104922\pi$
$541$	3.22978e23	1.89233	0.946165	+	0.323686i	$0.104922\pi$
$542$	−2.11060e23	−1.21734
$543$	−2.09521e23	−1.18968
$544$	−1.61452e22	−0.0902509
$545$	9.16251e22	0.504248
$546$	−1.91013e23	−1.03496
$547$	1.61822e23	0.863267	0.431633	−	0.902049i	$-0.357937\pi$
$547$	1.61822e23	0.863267	0.431633	+	0.902049i	$0.357937\pi$
$548$	1.58784e22	0.0834011
$549$	4.34874e23	2.24905
$550$	2.06163e21	0.0104985
$551$	−3.84790e22	−0.192946
$552$	−1.47674e23	−0.729157
$553$	−1.61977e23	−0.787569
$554$	−1.47932e22	−0.0708319
$555$	2.61801e22	0.123447
$556$	−4.87797e22	−0.226518
$557$	−1.97039e23	−0.901121	−0.450561	−	0.892746i	$-0.648776\pi$
$557$	−1.97039e23	−0.901121	−0.450561	+	0.892746i	$0.648776\pi$
$558$	3.13307e23	1.41117
$559$	8.42367e22	0.373681
$560$	4.41276e22	0.192802
$561$	−1.44459e21	−0.00621672
$562$	2.93621e23	1.24460
$563$	−4.24181e23	−1.77104	−0.885522	−	0.464597i	$-0.846199\pi$
$563$	−4.24181e23	−1.77104	−0.885522	+	0.464597i	$0.846199\pi$
$564$	−7.59234e22	−0.312251
$565$	6.09340e22	0.246858
$566$	−3.85552e23	−1.53866
$567$	−1.64242e22	−0.0645696
$568$	−1.04176e22	−0.0403466
$569$	3.39173e23	1.29410	0.647049	−	0.762449i	$-0.276003\pi$
$569$	3.39173e23	1.29410	0.647049	+	0.762449i	$0.276003\pi$
$570$	1.48611e23	0.558618
$571$	6.84513e22	0.253498	0.126749	−	0.991935i	$-0.459546\pi$
$571$	6.84513e22	0.253498	0.126749	+	0.991935i	$0.459546\pi$
$572$	6.09149e20	0.00222258
$573$	1.26017e23	0.453017
$574$	6.38470e22	0.226146
$575$	−1.06390e23	−0.371298
$576$	5.04373e23	1.73445
$577$	−1.80057e23	−0.610121	−0.305061	−	0.952333i	$-0.598677\pi$
$577$	−1.80057e23	−0.610121	−0.305061	+	0.952333i	$0.598677\pi$
$578$	2.51490e23	0.839718
$579$	−3.11828e23	−1.02600
$580$	3.23256e21	0.0104812
$581$	1.09293e23	0.349216
$582$	9.52829e21	0.0300033
$583$	−1.16081e21	−0.00360229
$584$	1.38799e22	0.0424499
$585$	2.07339e23	0.624965
$586$	5.31069e23	1.57769
$587$	8.40746e22	0.246173	0.123087	−	0.992396i	$-0.460721\pi$
$587$	8.40746e22	0.246173	0.123087	+	0.992396i	$0.460721\pi$
$588$	−5.03621e22	−0.145344
$589$	3.56609e23	1.01441
$590$	7.38488e21	0.0207062
$591$	3.43347e23	0.948942
$592$	−6.36333e22	−0.173360
$593$	−3.81961e23	−1.02578	−0.512890	−	0.858455i	$-0.671425\pi$
$593$	−3.81961e23	−1.02578	−0.512890	+	0.858455i	$0.671425\pi$
$594$	4.19769e21	0.0111128
$595$	−2.64751e22	−0.0690944
$596$	−5.76265e22	−0.148262
$597$	4.00748e23	1.01646
$598$	1.71636e23	0.429189
$599$	−3.18627e23	−0.785514	−0.392757	−	0.919642i	$-0.628479\pi$
$599$	−3.18627e23	−0.785514	−0.392757	+	0.919642i	$0.628479\pi$
$600$	6.07397e23	1.47634
$601$	5.82853e23	1.39677	0.698387	−	0.715720i	$-0.253901\pi$
$601$	5.82853e23	1.39677	0.698387	+	0.715720i	$0.253901\pi$
$602$	8.58735e22	0.202903
$603$	−2.33716e23	−0.544492
$604$	−6.00953e22	−0.138047
$605$	1.60950e23	0.364560
$606$	6.50820e23	1.45359
$607$	6.70463e23	1.47663	0.738313	−	0.674458i	$-0.235623\pi$
$607$	6.70463e23	1.47663	0.738313	+	0.674458i	$0.235623\pi$
$608$	1.46712e23	0.318628
$609$	−8.95369e22	−0.191759
$610$	2.27042e23	0.479515
$611$	6.58300e23	1.37111
$612$	−3.48717e22	−0.0716285
$613$	−9.15701e23	−1.85498	−0.927491	−	0.373845i	$-0.878039\pi$
$613$	−9.15701e23	−1.85498	−0.927491	+	0.373845i	$0.878039\pi$
$614$	−5.90676e23	−1.18010
$615$	−1.13384e23	−0.223415
$616$	4.63259e21	0.00900301
$617$	−9.04813e23	−1.73434	−0.867171	−	0.498010i	$-0.834064\pi$
$617$	−9.04813e23	−1.73434	−0.867171	+	0.498010i	$0.834064\pi$
$618$	−2.12519e22	−0.0401787
$619$	−6.78753e23	−1.26573	−0.632865	−	0.774262i	$-0.718121\pi$
$619$	−6.78753e23	−1.26573	−0.632865	+	0.774262i	$0.718121\pi$
$620$	−2.99582e22	−0.0551044
$621$	−2.16620e23	−0.393024
$622$	−5.45519e23	−0.976319
$623$	−6.07649e23	−1.07276
$624$	−8.24491e23	−1.43588
$625$	3.60204e23	0.618825
$626$	2.64305e22	0.0447943
$627$	1.31271e22	0.0219480
$628$	−3.87313e22	−0.0638860
$629$	3.81778e22	0.0621270
$630$	2.11368e23	0.339347
$631$	9.88826e23	1.56628	0.783141	−	0.621844i	$-0.213616\pi$
$631$	9.88826e23	1.56628	0.783141	+	0.621844i	$0.213616\pi$
$632$	−8.30945e23	−1.29861
$633$	−1.52544e24	−2.35214
$634$	7.50571e23	1.14191
$635$	−3.97553e23	−0.596785
$636$	−4.58437e22	−0.0679038
$637$	4.36669e23	0.638215
$638$	−1.55905e21	−0.00224846
$639$	−4.19855e22	−0.0597506
$640$	1.83706e23	0.257985
$641$	7.46475e23	1.03448	0.517240	−	0.855840i	$-0.326959\pi$
$641$	7.46475e23	1.03448	0.517240	+	0.855840i	$0.326959\pi$
$642$	−2.11974e24	−2.89892
$643$	−1.60985e23	−0.217266	−0.108633	−	0.994082i	$-0.534647\pi$
$643$	−1.60985e23	−0.217266	−0.108633	+	0.994082i	$0.534647\pi$
$644$	−3.20457e22	−0.0426815
$645$	−1.52500e23	−0.200453
$646$	2.16716e23	0.281135
$647$	1.47953e23	0.189425	0.0947124	−	0.995505i	$-0.469807\pi$
$647$	1.47953e23	0.189425	0.0947124	+	0.995505i	$0.469807\pi$
$648$	−8.42566e22	−0.106467
$649$	6.52320e20	0.000813543 0
$650$	−7.05957e23	−0.868989
$651$	8.29795e23	1.00817
$652$	1.42544e23	0.170940
$653$	−8.40989e23	−0.995470	−0.497735	−	0.867329i	$-0.665835\pi$
$653$	−8.40989e23	−0.995470	−0.497735	+	0.867329i	$0.665835\pi$
$654$	−1.74521e24	−2.03909
$655$	−2.49992e23	−0.288320
$656$	2.75591e23	0.313749
$657$	5.59393e22	0.0628654
$658$	6.71091e23	0.744494
$659$	1.54714e24	1.69435	0.847175	−	0.531314i	$-0.178302\pi$
$659$	1.54714e24	1.69435	0.847175	+	0.531314i	$0.178302\pi$
$660$	−1.10279e21	−0.00119225
$661$	−2.20956e23	−0.235827	−0.117914	−	0.993024i	$-0.537621\pi$
$661$	−2.20956e23	−0.235827	−0.117914	+	0.993024i	$0.537621\pi$
$662$	−1.70191e24	−1.79326
$663$	4.94667e23	0.514574
$664$	5.60675e23	0.575814
$665$	2.40580e23	0.243936
$666$	−3.04798e23	−0.305127
$667$	8.04542e22	0.0795205
$668$	−9.75404e22	−0.0951885
$669$	2.48193e24	2.39149
$670$	−1.22020e23	−0.116090
$671$	2.00550e22	0.0188400
$672$	3.41384e23	0.316668
$673$	1.15979e24	1.06231	0.531157	−	0.847273i	$-0.321757\pi$
$673$	1.15979e24	1.06231	0.531157	+	0.847273i	$0.321757\pi$
$674$	5.94398e23	0.537611
$675$	8.90978e23	0.795765
$676$	−3.30750e22	−0.0291711
$677$	−1.91800e24	−1.67050	−0.835248	−	0.549873i	$-0.814676\pi$
$677$	−1.91800e24	−1.67050	−0.835248	+	0.549873i	$0.814676\pi$
$678$	−1.16063e24	−0.998252
$679$	1.54249e22	0.0131018
$680$	−1.35818e23	−0.113928
$681$	2.40953e24	1.99610
$682$	1.44487e22	0.0118212
$683$	−2.26629e24	−1.83121	−0.915607	−	0.402075i	$-0.868289\pi$
$683$	−2.26629e24	−1.83121	−0.915607	+	0.402075i	$0.868289\pi$
$684$	3.16880e23	0.252882
$685$	2.49243e23	0.196450
$686$	1.20554e24	0.938482
$687$	−1.77641e24	−1.36587
$688$	3.70666e23	0.281502
$689$	3.97491e23	0.298170
$690$	−3.10725e23	−0.230229
$691$	−6.33975e23	−0.463990	−0.231995	−	0.972717i	$-0.574525\pi$
$691$	−6.33975e23	−0.463990	−0.231995	+	0.972717i	$0.574525\pi$
$692$	−2.95221e23	−0.213425
$693$	1.86705e22	0.0133328
$694$	1.39421e24	0.983499
$695$	−7.65694e23	−0.533561
$696$	−4.59327e23	−0.316187
$697$	−1.65345e23	−0.112438
$698$	−6.68185e23	−0.448876
$699$	2.70801e24	1.79719
$700$	1.31807e23	0.0864182
$701$	1.23966e24	0.802971	0.401485	−	0.915865i	$-0.368494\pi$
$701$	1.23966e24	0.802971	0.401485	+	0.915865i	$0.368494\pi$
$702$	−1.43740e24	−0.919838
$703$	−3.46923e23	−0.219338
$704$	2.32601e22	0.0145293
$705$	−1.19177e24	−0.735502
$706$	8.93467e23	0.544802
$707$	1.05358e24	0.634752
$708$	2.57620e22	0.0153354
$709$	1.92953e24	1.13490	0.567450	−	0.823408i	$-0.307930\pi$
$709$	1.92953e24	1.13490	0.567450	+	0.823408i	$0.307930\pi$
$710$	−2.19201e22	−0.0127393
$711$	−3.34891e24	−1.92315
$712$	−3.11726e24	−1.76886
$713$	−7.45620e23	−0.418077
$714$	5.04278e23	0.279406
$715$	9.56180e21	0.00523526
$716$	−2.19657e23	−0.118846
$717$	−3.44682e23	−0.184292
$718$	3.24244e24	1.71322
$719$	1.24227e24	0.648664	0.324332	−	0.945943i	$-0.394861\pi$
$719$	1.24227e24	0.648664	0.324332	+	0.945943i	$0.394861\pi$
$720$	9.12351e23	0.470799
$721$	−3.44038e22	−0.0175451
$722$	−1.45218e23	−0.0731905
$723$	7.36799e23	0.367006
$724$	−2.33246e23	−0.114825
$725$	−3.30916e23	−0.161007
$726$	−3.06565e24	−1.47422
$727$	2.83536e24	1.34761	0.673807	−	0.738907i	$-0.264658\pi$
$727$	2.83536e24	1.34761	0.673807	+	0.738907i	$0.264658\pi$
$728$	−1.58632e24	−0.745202
$729$	−3.50974e24	−1.62964
$730$	2.92052e22	0.0134034
$731$	−2.22387e23	−0.100882
$732$	7.92031e23	0.355139
$733$	3.76886e24	1.67042	0.835210	−	0.549931i	$-0.185346\pi$
$733$	3.76886e24	1.67042	0.835210	+	0.549931i	$0.185346\pi$
$734$	−1.30242e24	−0.570603
$735$	−7.90533e23	−0.342356
$736$	−3.06754e23	−0.131319
$737$	−1.07782e22	−0.00456115
$738$	1.32006e24	0.552221
$739$	−1.80876e24	−0.748001	−0.374000	−	0.927429i	$-0.622014\pi$
$739$	−1.80876e24	−0.748001	−0.374000	+	0.927429i	$0.622014\pi$
$740$	2.91445e22	0.0119148
$741$	−4.49505e24	−1.81669
$742$	4.05215e23	0.161902
$743$	2.01400e24	0.795526	0.397763	−	0.917488i	$-0.369787\pi$
$743$	2.01400e24	0.795526	0.397763	+	0.917488i	$0.369787\pi$
$744$	4.25687e24	1.66234
$745$	−9.04561e23	−0.349229
$746$	−6.73529e22	−0.0257085
$747$	2.25966e24	0.852741
$748$	−1.60817e21	−0.000600024 0
$749$	−3.43156e24	−1.26589
$750$	2.75206e24	1.00378
$751$	4.23140e24	1.52596	0.762982	−	0.646420i	$-0.223734\pi$
$751$	4.23140e24	1.52596	0.762982	+	0.646420i	$0.223734\pi$
$752$	2.89671e24	1.03289
$753$	−5.18085e24	−1.82660
$754$	5.33861e23	0.186111
$755$	−9.43314e23	−0.325168
$756$	2.68372e23	0.0914749
$757$	2.90411e24	0.978809	0.489404	−	0.872057i	$-0.337214\pi$
$757$	2.90411e24	0.978809	0.489404	+	0.872057i	$0.337214\pi$
$758$	−3.54683e23	−0.118209
$759$	−2.74469e22	−0.00904562
$760$	1.23418e24	0.402221
$761$	2.36377e23	0.0761792	0.0380896	−	0.999274i	$-0.487873\pi$
$761$	2.36377e23	0.0761792	0.0380896	+	0.999274i	$0.487873\pi$
$762$	7.57230e24	2.41330
$763$	−2.82524e24	−0.890425
$764$	1.40286e23	0.0437241
$765$	−5.47380e23	−0.168720
$766$	−2.79305e24	−0.851402
$767$	−2.23371e23	−0.0673390
$768$	2.43516e24	0.726035
$769$	6.49820e24	1.91610	0.958052	−	0.286594i	$-0.0925230\pi$
$769$	6.49820e24	1.91610	0.958052	+	0.286594i	$0.0925230\pi$
$770$	9.74760e21	0.00284267
$771$	−4.67378e24	−1.34805
$772$	−3.47137e23	−0.0990271
$773$	4.42844e24	1.24947	0.624734	−	0.780837i	$-0.285207\pi$
$773$	4.42844e24	1.24947	0.624734	+	0.780837i	$0.285207\pi$
$774$	1.77546e24	0.495464
$775$	3.06681e24	0.846491
$776$	7.91305e22	0.0216032
$777$	−8.07258e23	−0.217989
$778$	−4.68098e24	−1.25029
$779$	1.50250e24	0.396959
$780$	3.77623e23	0.0986857
$781$	−1.93624e21	−0.000500524 0
$782$	−4.53124e23	−0.115867
$783$	−6.73778e23	−0.170428
$784$	1.92147e24	0.480781
$785$	−6.07965e23	−0.150483
$786$	4.76167e24	1.16592
$787$	5.90703e24	1.43082	0.715408	−	0.698707i	$-0.246241\pi$
$787$	5.90703e24	1.43082	0.715408	+	0.698707i	$0.246241\pi$
$788$	3.82225e23	0.0915897
$789$	−4.33867e24	−1.02849
$790$	−1.74842e24	−0.410030
$791$	−1.87889e24	−0.435914
$792$	9.57801e22	0.0219842
$793$	−6.86736e24	−1.55944
$794$	2.40331e24	0.539927
$795$	−7.19607e23	−0.159947
$796$	4.46127e23	0.0981063
$797$	−3.76240e24	−0.818595	−0.409297	−	0.912401i	$-0.634226\pi$
$797$	−3.76240e24	−0.818595	−0.409297	+	0.912401i	$0.634226\pi$
$798$	−4.58240e24	−0.986434
$799$	−1.73793e24	−0.370156
$800$	1.26171e24	0.265885
$801$	−1.25633e25	−2.61956
$802$	1.80060e24	0.371479
$803$	2.57974e21	0.000526617 0
$804$	−4.25664e23	−0.0859786
$805$	−5.03020e23	−0.100536
$806$	−4.94762e24	−0.978472
$807$	−8.46644e24	−1.65682
$808$	5.40492e24	1.04663
$809$	−2.21471e24	−0.424379	−0.212190	−	0.977229i	$-0.568059\pi$
$809$	−2.21471e24	−0.424379	−0.212190	+	0.977229i	$0.568059\pi$
$810$	−1.77287e23	−0.0336167
$811$	−2.92354e24	−0.548569	−0.274284	−	0.961649i	$-0.588441\pi$
$811$	−2.92354e24	−0.548569	−0.274284	+	0.961649i	$0.588441\pi$
$812$	−9.96755e22	−0.0185081
$813$	−1.15573e25	−2.12367
$814$	−1.40563e22	−0.00255602
$815$	2.23751e24	0.402648
$816$	2.17668e24	0.387639
$817$	2.02084e24	0.356160
$818$	9.64996e23	0.168315
$819$	−6.39325e24	−1.10359
$820$	−1.26223e23	−0.0215635
$821$	−6.60841e24	−1.11733	−0.558663	−	0.829395i	$-0.688686\pi$
$821$	−6.60841e24	−1.11733	−0.558663	+	0.829395i	$0.688686\pi$
$822$	−4.74740e24	−0.794411
$823$	−9.19312e23	−0.152252	−0.0761262	−	0.997098i	$-0.524255\pi$
$823$	−9.19312e23	−0.152252	−0.0761262	+	0.997098i	$0.524255\pi$
$824$	−1.76493e23	−0.0289298
$825$	1.12892e23	0.0183149
$826$	−2.27711e23	−0.0365641
$827$	7.10161e24	1.12865	0.564326	−	0.825552i	$-0.309136\pi$
$827$	7.10161e24	1.12865	0.564326	+	0.825552i	$0.309136\pi$
$828$	−6.62553e23	−0.104223
$829$	5.68184e23	0.0884659	0.0442329	−	0.999021i	$-0.485916\pi$
$829$	5.68184e23	0.0884659	0.0442329	+	0.999021i	$0.485916\pi$
$830$	1.17974e24	0.181811
$831$	−8.10054e23	−0.123568
$832$	−7.96486e24	−1.20262
$833$	−1.15282e24	−0.172297
$834$	1.45844e25	2.15763
$835$	−1.53109e24	−0.224215
$836$	1.46135e22	0.00211837
$837$	6.24433e24	0.896023
$838$	5.06461e23	0.0719403
$839$	1.11695e25	1.57057	0.785286	−	0.619133i	$-0.212516\pi$
$839$	1.11695e25	1.57057	0.785286	+	0.619133i	$0.212516\pi$
$840$	2.87183e24	0.399746
$841$	2.50246e23	0.0344828
$842$	5.73501e24	0.782315
$843$	1.60783e25	2.17123
$844$	−1.69817e24	−0.227023
$845$	−5.19178e23	−0.0687122
$846$	1.38750e25	1.81796
$847$	−4.96285e24	−0.643757
$848$	1.74908e24	0.224618
$849$	−2.11123e25	−2.68423
$850$	1.86374e24	0.234599
$851$	7.25369e23	0.0903978
$852$	−7.64676e22	−0.00943498
$853$	−8.02812e24	−0.980725	−0.490362	−	0.871519i	$-0.663136\pi$
$853$	−8.02812e24	−0.980725	−0.490362	+	0.871519i	$0.663136\pi$
$854$	−7.00080e24	−0.846751
$855$	4.97406e24	0.595661
$856$	−1.76040e25	−2.08730
$857$	3.15264e24	0.370115	0.185058	−	0.982728i	$-0.440753\pi$
$857$	3.15264e24	0.370115	0.185058	+	0.982728i	$0.440753\pi$
$858$	−1.82126e23	−0.0211705
$859$	−2.60602e24	−0.299941	−0.149970	−	0.988691i	$-0.547918\pi$
$859$	−2.60602e24	−0.299941	−0.149970	+	0.988691i	$0.547918\pi$
$860$	−1.69768e23	−0.0193472
$861$	3.49617e24	0.394517
$862$	−3.81940e24	−0.426760
$863$	3.85035e24	0.425999	0.213000	−	0.977052i	$-0.431677\pi$
$863$	3.85035e24	0.425999	0.213000	+	0.977052i	$0.431677\pi$
$864$	2.56896e24	0.281444
$865$	−4.63407e24	−0.502720
$866$	−7.41636e24	−0.796688
$867$	1.37712e25	1.46490
$868$	9.23756e23	0.0973059
$869$	−1.54441e23	−0.0161100
$870$	−9.66487e23	−0.0998349
$871$	3.69075e24	0.377538
$872$	−1.44936e25	−1.46820
$873$	3.18915e23	0.0319929
$874$	4.11756e24	0.409065
$875$	4.45519e24	0.438327
$876$	1.01882e23	0.00992683
$877$	−1.23091e25	−1.18776	−0.593879	−	0.804554i	$-0.702404\pi$
$877$	−1.23091e25	−1.18776	−0.593879	+	0.804554i	$0.702404\pi$
$878$	−2.80387e24	−0.267951
$879$	2.90806e25	2.75231
$880$	4.20747e22	0.00394383
$881$	6.75609e24	0.627191	0.313596	−	0.949557i	$-0.398466\pi$
$881$	6.75609e24	0.627191	0.313596	+	0.949557i	$0.398466\pi$
$882$	9.20368e24	0.846210
$883$	−7.82807e24	−0.712834	−0.356417	−	0.934327i	$-0.616002\pi$
$883$	−7.82807e24	−0.712834	−0.356417	+	0.934327i	$0.616002\pi$
$884$	5.50679e23	0.0496655
$885$	4.04385e23	0.0361225
$886$	−8.70486e24	−0.770150
$887$	1.67016e25	1.46355	0.731776	−	0.681545i	$-0.238692\pi$
$887$	1.67016e25	1.46355	0.731776	+	0.681545i	$0.238692\pi$
$888$	−4.14126e24	−0.359437
$889$	1.22585e25	1.05383
$890$	−6.55913e24	−0.558511
$891$	−1.56601e22	−0.00132079
$892$	2.76297e24	0.230821
$893$	1.57926e25	1.30682
$894$	1.72294e25	1.41222
$895$	−3.44795e24	−0.279940
$896$	−5.66454e24	−0.455561
$897$	9.39854e24	0.748729
$898$	9.90046e24	0.781280
$899$	−2.31919e24	−0.181292
$900$	2.72515e24	0.211023
$901$	−1.04939e24	−0.0804962
$902$	6.08767e22	0.00462590
$903$	4.70231e24	0.353969
$904$	−9.63876e24	−0.718769
$905$	−3.66126e24	−0.270469
$906$	1.79676e25	1.31492
$907$	−1.60753e25	−1.16546	−0.582729	−	0.812667i	$-0.698015\pi$
$907$	−1.60753e25	−1.16546	−0.582729	+	0.812667i	$0.698015\pi$
$908$	2.68237e24	0.192659
$909$	2.17831e25	1.54999
$910$	−3.33783e24	−0.235295
$911$	5.48262e24	0.382897	0.191449	−	0.981503i	$-0.438681\pi$
$911$	5.48262e24	0.382897	0.191449	+	0.981503i	$0.438681\pi$
$912$	−1.97796e25	−1.36855
$913$	1.04208e23	0.00714332
$914$	−2.13285e25	−1.44849
$915$	1.24325e25	0.836525
$916$	−1.97756e24	−0.131831
$917$	7.70847e24	0.509130
$918$	3.79477e24	0.248326
$919$	3.41215e24	0.221231	0.110616	−	0.993863i	$-0.464718\pi$
$919$	3.41215e24	0.221231	0.110616	+	0.993863i	$0.464718\pi$
$920$	−2.58051e24	−0.165771
$921$	−3.23446e25	−2.05871
$922$	1.81888e24	0.114707
$923$	6.63018e23	0.0414296
$924$	3.40043e22	0.00210534
$925$	−2.98352e24	−0.183031
$926$	−1.74001e25	−1.05769
$927$	−7.11308e23	−0.0428430
$928$	−9.54134e23	−0.0569445
$929$	1.88183e25	1.11287	0.556437	−	0.830890i	$-0.312168\pi$
$929$	1.88183e25	1.11287	0.556437	+	0.830890i	$0.312168\pi$
$930$	8.95704e24	0.524879
$931$	1.04757e25	0.608290
$932$	3.01465e24	0.173461
$933$	−2.98718e25	−1.70321
$934$	−3.15822e24	−0.178441
$935$	−2.52434e22	−0.00141335
$936$	−3.27976e25	−1.81969
$937$	4.65832e24	0.256120	0.128060	−	0.991766i	$-0.459125\pi$
$937$	4.65832e24	0.256120	0.128060	+	0.991766i	$0.459125\pi$
$938$	3.76246e24	0.204997
$939$	1.44729e24	0.0781446
$940$	−1.32672e24	−0.0709890
$941$	6.56604e24	0.348170	0.174085	−	0.984731i	$-0.444303\pi$
$941$	6.56604e24	0.348170	0.174085	+	0.984731i	$0.444303\pi$
$942$	1.15801e25	0.608525
$943$	−3.14151e24	−0.163602
$944$	−9.82899e23	−0.0507279
$945$	4.21263e24	0.215468
$946$	8.18785e22	0.00415045
$947$	2.19819e25	1.10431	0.552153	−	0.833742i	$-0.313806\pi$
$947$	2.19819e25	1.10431	0.552153	+	0.833742i	$0.313806\pi$
$948$	−6.09933e24	−0.303676
$949$	−8.83371e23	−0.0435894
$950$	−1.69359e25	−0.828244
$951$	4.11001e25	1.99209
$952$	4.18793e24	0.201180
$953$	3.19472e25	1.52105	0.760525	−	0.649308i	$-0.224942\pi$
$953$	3.19472e25	1.52105	0.760525	+	0.649308i	$0.224942\pi$
$954$	8.37793e24	0.395344
$955$	2.20207e24	0.102992
$956$	−3.83711e23	−0.0177874
$957$	−8.53715e22	−0.00392249
$958$	−8.54426e24	−0.389106
$959$	−7.68536e24	−0.346901
$960$	1.44194e25	0.645120
$961$	−1.05671e24	−0.0468607
$962$	4.81325e24	0.211568
$963$	−7.09485e25	−3.09115
$964$	8.20230e23	0.0354226
$965$	−5.44901e24	−0.233257
$966$	9.58116e24	0.406549
$967$	−1.36577e25	−0.574449	−0.287224	−	0.957863i	$-0.592733\pi$
$967$	−1.36577e25	−0.574449	−0.287224	+	0.957863i	$0.592733\pi$
$968$	−2.54596e25	−1.06148
$969$	1.18671e25	0.490446
$970$	1.66501e23	0.00682115
$971$	−1.64712e25	−0.668903	−0.334451	−	0.942413i	$-0.608551\pi$
$971$	−1.64712e25	−0.668903	−0.334451	+	0.942413i	$0.608551\pi$
$972$	−4.14759e24	−0.166968
$973$	2.36100e25	0.942188
$974$	4.28925e25	1.69680
$975$	−3.86571e25	−1.51597
$976$	−3.02184e25	−1.17476
$977$	−9.34255e24	−0.360049	−0.180024	−	0.983662i	$-0.557618\pi$
$977$	−9.34255e24	−0.360049	−0.180024	+	0.983662i	$0.557618\pi$
$978$	−4.26185e25	−1.62824
$979$	−5.79380e23	−0.0219437
$980$	−8.80048e23	−0.0330434
$981$	−5.84127e25	−2.17431
$982$	−4.23857e25	−1.56413
$983$	1.14875e25	0.420262	0.210131	−	0.977673i	$-0.432611\pi$
$983$	1.14875e25	0.420262	0.210131	+	0.977673i	$0.432611\pi$
$984$	1.79355e25	0.650510
$985$	5.99978e24	0.215738
$986$	−1.40941e24	−0.0502438
$987$	3.67480e25	1.29879
$988$	−5.00405e24	−0.175343
$989$	−4.22530e24	−0.146788
$990$	2.01534e23	0.00694145
$991$	−5.37183e25	−1.83441	−0.917204	−	0.398418i	$-0.869559\pi$
$991$	−5.37183e25	−1.83441	−0.917204	+	0.398418i	$0.869559\pi$
$992$	8.84256e24	0.299384
$993$	−9.31942e25	−3.12839
$994$	6.75901e23	0.0224957
$995$	7.00284e24	0.231088
$996$	4.11548e24	0.134653
$997$	3.11554e25	1.01071	0.505353	−	0.862913i	$-0.331362\pi$
$997$	3.11554e25	1.01071	0.505353	+	0.862913i	$0.331362\pi$
$998$	2.01605e25	0.648473
$999$	−6.07473e24	−0.193741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.6	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-332.840 q^{2} -18225.8 q^{3} -20289.6 q^{4} -318485. q^{5} +6.06628e6 q^{6} +9.82044e6 q^{7} +5.03792e7 q^{8} +2.03040e8 q^{9} +O(q^{10})\)	\(q-332.840 q^{2} -18225.8 q^{3} -20289.6 q^{4} -318485. q^{5} +6.06628e6 q^{6} +9.82044e6 q^{7} +5.03792e7 q^{8} +2.03040e8 q^{9} +1.06005e8 q^{10} +9.36358e6 q^{11} +3.69795e8 q^{12} -3.20633e9 q^{13} -3.26863e9 q^{14} +5.80466e9 q^{15} -1.41088e10 q^{16} +8.46481e9 q^{17} -6.75799e10 q^{18} -7.69200e10 q^{19} +6.46194e9 q^{20} -1.78986e11 q^{21} -3.11657e9 q^{22} +1.60829e11 q^{23} -9.18202e11 q^{24} -6.61507e11 q^{25} +1.06720e12 q^{26} -1.34689e12 q^{27} -1.99253e11 q^{28} +5.00246e11 q^{29} -1.93202e12 q^{30} -4.63610e12 q^{31} -1.90733e12 q^{32} -1.70659e11 q^{33} -2.81742e12 q^{34} -3.12767e12 q^{35} -4.11961e12 q^{36} +4.51018e12 q^{37} +2.56020e13 q^{38} +5.84380e13 q^{39} -1.60450e13 q^{40} -1.95332e13 q^{41} +5.95735e13 q^{42} -2.62720e13 q^{43} -1.89983e11 q^{44} -6.46654e13 q^{45} -5.35304e13 q^{46} -2.05312e14 q^{47} +2.57145e14 q^{48} -1.36189e14 q^{49} +2.20176e14 q^{50} -1.54278e14 q^{51} +6.50552e13 q^{52} -1.23971e14 q^{53} +4.48300e14 q^{54} -2.98216e12 q^{55} +4.94746e14 q^{56} +1.40193e15 q^{57} -1.66502e14 q^{58} +6.96656e13 q^{59} -1.17774e14 q^{60} +2.14181e15 q^{61} +1.54308e15 q^{62} +1.99395e15 q^{63} +2.48410e15 q^{64} +1.02117e15 q^{65} +5.68021e13 q^{66} -1.15108e15 q^{67} -1.71748e14 q^{68} -2.93124e15 q^{69} +1.04101e15 q^{70} -2.06784e14 q^{71} +1.02290e16 q^{72} +2.75508e14 q^{73} -1.50117e15 q^{74} +1.20565e16 q^{75} +1.56068e15 q^{76} +9.19545e13 q^{77} -1.94505e16 q^{78} -1.64938e16 q^{79} +4.49345e15 q^{80} -1.67245e15 q^{81} +6.50144e15 q^{82} +1.11291e16 q^{83} +3.63155e15 q^{84} -2.69592e15 q^{85} +8.74436e15 q^{86} -9.11740e15 q^{87} +4.71729e14 q^{88} -6.18759e16 q^{89} +2.15232e16 q^{90} -3.14876e16 q^{91} -3.26316e15 q^{92} +8.44967e16 q^{93} +6.83361e16 q^{94} +2.44979e16 q^{95} +3.47626e16 q^{96} +1.57070e15 q^{97} +4.53293e16 q^{98} +1.90118e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 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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