LMFDB - Embedded newform 29.18.a.b.1.3

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			1.3
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)

$f(q)$	$=$	$q-645.655 q^{2} +14883.2 q^{3} +285798. q^{4} +954733. q^{5} -9.60943e6 q^{6} +1.80737e7 q^{7} -9.98999e7 q^{8} +9.23704e7 q^{9} +O(q^{10})$	\(q-645.655 q^{2} +14883.2 q^{3} +285798. q^{4} +954733. q^{5} -9.60943e6 q^{6} +1.80737e7 q^{7} -9.98999e7 q^{8} +9.23704e7 q^{9} -6.16428e8 q^{10} -1.63616e8 q^{11} +4.25360e9 q^{12} +4.33002e9 q^{13} -1.16694e10 q^{14} +1.42095e10 q^{15} +2.70407e10 q^{16} +5.11795e10 q^{17} -5.96394e10 q^{18} +8.96514e10 q^{19} +2.72861e11 q^{20} +2.68996e11 q^{21} +1.05639e11 q^{22} -2.78368e11 q^{23} -1.48683e12 q^{24} +1.48576e11 q^{25} -2.79570e12 q^{26} -5.47252e11 q^{27} +5.16545e12 q^{28} +5.00246e11 q^{29} -9.17444e12 q^{30} -2.36840e12 q^{31} -4.36488e12 q^{32} -2.43513e12 q^{33} -3.30443e13 q^{34} +1.72556e13 q^{35} +2.63993e13 q^{36} +3.03597e13 q^{37} -5.78839e13 q^{38} +6.44448e13 q^{39} -9.53777e13 q^{40} -8.45031e13 q^{41} -1.73678e14 q^{42} -1.94211e13 q^{43} -4.67611e13 q^{44} +8.81891e13 q^{45} +1.79730e14 q^{46} +9.65771e13 q^{47} +4.02453e14 q^{48} +9.40296e13 q^{49} -9.59287e13 q^{50} +7.61717e14 q^{51} +1.23751e15 q^{52} -5.94756e14 q^{53} +3.53336e14 q^{54} -1.56209e14 q^{55} -1.80556e15 q^{56} +1.33430e15 q^{57} -3.22987e14 q^{58} -1.80184e14 q^{59} +4.06106e15 q^{60} -1.33081e15 q^{61} +1.52917e15 q^{62} +1.66948e15 q^{63} -7.26069e14 q^{64} +4.13402e15 q^{65} +1.57226e15 q^{66} +2.44049e15 q^{67} +1.46270e16 q^{68} -4.14302e15 q^{69} -1.11412e16 q^{70} -5.66814e15 q^{71} -9.22780e15 q^{72} -1.53697e15 q^{73} -1.96019e16 q^{74} +2.21129e15 q^{75} +2.56222e16 q^{76} -2.95715e15 q^{77} -4.16091e16 q^{78} -1.72129e16 q^{79} +2.58166e16 q^{80} -2.00736e16 q^{81} +5.45599e16 q^{82} +8.38378e15 q^{83} +7.68785e16 q^{84} +4.88628e16 q^{85} +1.25393e16 q^{86} +7.44528e15 q^{87} +1.63452e16 q^{88} -3.85946e16 q^{89} -5.69397e16 q^{90} +7.82597e16 q^{91} -7.95573e16 q^{92} -3.52495e16 q^{93} -6.23555e16 q^{94} +8.55931e16 q^{95} -6.49636e16 q^{96} +8.15125e16 q^{97} -6.07107e16 q^{98} -1.51133e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−645.655	−1.78339	−0.891693	−	0.452640i	$-0.850482\pi$
$2$	−645.655	−1.78339	−0.891693	+	0.452640i	$0.850482\pi$
$3$	14883.2	1.30968	0.654842	−	0.755766i	$-0.272735\pi$
$3$	14883.2	1.30968	0.654842	+	0.755766i	$0.272735\pi$
$4$	285798.	2.18047
$5$	954733.	1.09304	0.546521	−	0.837445i	$-0.315952\pi$
$5$	954733.	1.09304	0.546521	+	0.837445i	$0.315952\pi$
$6$	−9.60943e6	−2.33567
$7$	1.80737e7	1.18499	0.592495	−	0.805574i	$-0.298143\pi$
$7$	1.80737e7	1.18499	0.592495	+	0.805574i	$0.298143\pi$
$8$	−9.98999e7	−2.10523
$9$	9.23704e7	0.715273
$10$	−6.16428e8	−1.94932
$11$	−1.63616e8	−0.230138	−0.115069	−	0.993358i	$-0.536709\pi$
$11$	−1.63616e8	−0.230138	−0.115069	+	0.993358i	$0.536709\pi$
$12$	4.25360e9	2.85573
$13$	4.33002e9	1.47222	0.736108	−	0.676864i	$-0.236661\pi$
$13$	4.33002e9	1.47222	0.736108	+	0.676864i	$0.236661\pi$
$14$	−1.16694e10	−2.11330
$15$	1.42095e10	1.43154
$16$	2.70407e10	1.57398
$17$	5.11795e10	1.77943	0.889714	−	0.456518i	$-0.150904\pi$
$17$	5.11795e10	1.77943	0.889714	+	0.456518i	$0.150904\pi$
$18$	−5.96394e10	−1.27561
$19$	8.96514e10	1.21102	0.605510	−	0.795838i	$-0.292969\pi$
$19$	8.96514e10	1.21102	0.605510	+	0.795838i	$0.292969\pi$
$20$	2.72861e11	2.38334
$21$	2.68996e11	1.55196
$22$	1.05639e11	0.410424
$23$	−2.78368e11	−0.741197	−0.370598	−	0.928793i	$-0.620847\pi$
$23$	−2.78368e11	−0.741197	−0.370598	+	0.928793i	$0.620847\pi$
$24$	−1.48683e12	−2.75719
$25$	1.48576e11	0.194741
$26$	−2.79570e12	−2.62553
$27$	−5.47252e11	−0.372903
$28$	5.16545e12	2.58383
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	−9.17444e12	−2.55299
$31$	−2.36840e12	−0.498748	−0.249374	−	0.968407i	$-0.580225\pi$
$31$	−2.36840e12	−0.498748	−0.249374	+	0.968407i	$0.580225\pi$
$32$	−4.36488e12	−0.701775
$33$	−2.43513e12	−0.301408
$34$	−3.30443e13	−3.17341
$35$	1.72556e13	1.29524
$36$	2.63993e13	1.55963
$37$	3.03597e13	1.42096	0.710482	−	0.703715i	$-0.248477\pi$
$37$	3.03597e13	1.42096	0.710482	+	0.703715i	$0.248477\pi$
$38$	−5.78839e13	−2.15972
$39$	6.44448e13	1.92814
$40$	−9.53777e13	−2.30111
$41$	−8.45031e13	−1.65276	−0.826380	−	0.563113i	$-0.809604\pi$
$41$	−8.45031e13	−1.65276	−0.826380	+	0.563113i	$0.809604\pi$
$42$	−1.73678e14	−2.76775
$43$	−1.94211e13	−0.253392	−0.126696	−	0.991942i	$-0.540437\pi$
$43$	−1.94211e13	−0.253392	−0.126696	+	0.991942i	$0.540437\pi$
$44$	−4.67611e13	−0.501808
$45$	8.81891e13	0.781823
$46$	1.79730e14	1.32184
$47$	9.65771e13	0.591619	0.295810	−	0.955247i	$-0.404411\pi$
$47$	9.65771e13	0.591619	0.295810	+	0.955247i	$0.404411\pi$
$48$	4.02453e14	2.06141
$49$	9.40296e13	0.404202
$50$	−9.59287e13	−0.347299
$51$	7.61717e14	2.33049
$52$	1.23751e15	3.21012
$53$	−5.94756e14	−1.31218	−0.656090	−	0.754682i	$-0.727791\pi$
$53$	−5.94756e14	−1.31218	−0.656090	+	0.754682i	$0.727791\pi$
$54$	3.53336e14	0.665030
$55$	−1.56209e14	−0.251550
$56$	−1.80556e15	−2.49468
$57$	1.33430e15	1.58605
$58$	−3.22987e14	−0.331167
$59$	−1.80184e14	−0.159763	−0.0798813	−	0.996804i	$-0.525454\pi$
$59$	−1.80184e14	−0.159763	−0.0798813	+	0.996804i	$0.525454\pi$
$60$	4.06106e15	3.12143
$61$	−1.33081e15	−0.888820	−0.444410	−	0.895824i	$-0.646587\pi$
$61$	−1.33081e15	−0.888820	−0.444410	+	0.895824i	$0.646587\pi$
$62$	1.52917e15	0.889461
$63$	1.66948e15	0.847591
$64$	−7.26069e14	−0.322439
$65$	4.13402e15	1.60920
$66$	1.57226e15	0.537526
$67$	2.44049e15	0.734245	0.367122	−	0.930173i	$-0.380343\pi$
$67$	2.44049e15	0.734245	0.367122	+	0.930173i	$0.380343\pi$
$68$	1.46270e16	3.87999
$69$	−4.14302e15	−0.970733
$70$	−1.11412e16	−2.30992
$71$	−5.66814e15	−1.04171	−0.520853	−	0.853647i	$-0.674386\pi$
$71$	−5.66814e15	−1.04171	−0.520853	+	0.853647i	$0.674386\pi$
$72$	−9.22780e15	−1.50582
$73$	−1.53697e15	−0.223060	−0.111530	−	0.993761i	$-0.535575\pi$
$73$	−1.53697e15	−0.223060	−0.111530	+	0.993761i	$0.535575\pi$
$74$	−1.96019e16	−2.53413
$75$	2.21129e15	0.255050
$76$	2.56222e16	2.64059
$77$	−2.95715e15	−0.272711
$78$	−4.16091e16	−3.43862
$79$	−1.72129e16	−1.27651	−0.638256	−	0.769824i	$-0.720344\pi$
$79$	−1.72129e16	−1.27651	−0.638256	+	0.769824i	$0.720344\pi$
$80$	2.58166e16	1.72042
$81$	−2.00736e16	−1.20366
$82$	5.45599e16	2.94751
$83$	8.38378e15	0.408579	0.204290	−	0.978911i	$-0.434512\pi$
$83$	8.38378e15	0.408579	0.204290	+	0.978911i	$0.434512\pi$
$84$	7.68785e16	3.38401
$85$	4.88628e16	1.94499
$86$	1.25393e16	0.451895
$87$	7.44528e15	0.243202
$88$	1.63452e16	0.484493
$89$	−3.85946e16	−1.03923	−0.519615	−	0.854400i	$-0.673925\pi$
$89$	−3.85946e16	−1.03923	−0.519615	+	0.854400i	$0.673925\pi$
$90$	−5.69397e16	−1.39429
$91$	7.82597e16	1.74456
$92$	−7.95573e16	−1.61616
$93$	−3.52495e16	−0.653202
$94$	−6.23555e16	−1.05509
$95$	8.55931e16	1.32370
$96$	−6.49636e16	−0.919104
$97$	8.15125e16	1.05600	0.528001	−	0.849244i	$-0.322942\pi$
$97$	8.15125e16	1.05600	0.528001	+	0.849244i	$0.322942\pi$
$98$	−6.07107e16	−0.720848
$99$	−1.51133e16	−0.164611
$100$	4.24627e16	0.424627
$101$	1.67885e17	1.54270	0.771349	−	0.636412i	$-0.219582\pi$
$101$	1.67885e17	1.54270	0.771349	+	0.636412i	$0.219582\pi$
$102$	−4.91806e17	−4.15616
$103$	1.21257e17	0.943169	0.471585	−	0.881821i	$-0.343682\pi$
$103$	1.21257e17	0.943169	0.471585	+	0.881821i	$0.343682\pi$
$104$	−4.32569e17	−3.09936
$105$	2.56819e17	1.69636
$106$	3.84007e17	2.34013
$107$	−9.11858e16	−0.513056	−0.256528	−	0.966537i	$-0.582579\pi$
$107$	−9.11858e16	−0.513056	−0.256528	+	0.966537i	$0.582579\pi$
$108$	−1.56404e17	−0.813103
$109$	−3.65713e17	−1.75799	−0.878994	−	0.476834i	$-0.841784\pi$
$109$	−3.65713e17	−1.75799	−0.878994	+	0.476834i	$0.841784\pi$
$110$	1.00857e17	0.448611
$111$	4.51851e17	1.86101
$112$	4.88727e17	1.86515
$113$	1.69688e15	0.00600459	0.00300230	−	0.999995i	$-0.499044\pi$
$113$	1.69688e15	0.00600459	0.00300230	+	0.999995i	$0.499044\pi$
$114$	−8.61499e17	−2.82855
$115$	−2.65768e17	−0.810159
$116$	1.42970e17	0.404903
$117$	3.99966e17	1.05304
$118$	1.16337e17	0.284918
$119$	9.25006e17	2.10860
$120$	−1.41953e18	−3.01373
$121$	−4.78677e17	−0.947037
$122$	8.59247e17	1.58511
$123$	−1.25768e18	−2.16459
$124$	−6.76886e17	−1.08750
$125$	−5.86553e17	−0.880182
$126$	−1.07791e18	−1.51158
$127$	1.08499e18	1.42264	0.711320	−	0.702868i	$-0.248098\pi$
$127$	1.08499e18	1.42264	0.711320	+	0.702868i	$0.248098\pi$
$128$	1.04090e18	1.27681
$129$	−2.89049e17	−0.331863
$130$	−2.66915e18	−2.86982
$131$	−5.51328e17	−0.555398	−0.277699	−	0.960668i	$-0.589572\pi$
$131$	−5.51328e17	−0.555398	−0.277699	+	0.960668i	$0.589572\pi$
$132$	−6.95957e17	−0.657210
$133$	1.62034e18	1.43505
$134$	−1.57571e18	−1.30944
$135$	−5.22480e17	−0.407598
$136$	−5.11283e18	−3.74611
$137$	2.01819e18	1.38943	0.694717	−	0.719283i	$-0.255530\pi$
$137$	2.01819e18	1.38943	0.694717	+	0.719283i	$0.255530\pi$
$138$	2.67496e18	1.73119
$139$	1.76829e18	1.07628	0.538142	−	0.842854i	$-0.319126\pi$
$139$	1.76829e18	1.07628	0.538142	+	0.842854i	$0.319126\pi$
$140$	4.93162e18	2.82424
$141$	1.43738e18	0.774834
$142$	3.65966e18	1.85776
$143$	−7.08460e17	−0.338812
$144$	2.49776e18	1.12582
$145$	4.77602e17	0.202973
$146$	9.92354e17	0.397803
$147$	1.39946e18	0.529376
$148$	8.67676e18	3.09837
$149$	−1.28596e17	−0.0433656	−0.0216828	−	0.999765i	$-0.506902\pi$
$149$	−1.28596e17	−0.0433656	−0.0216828	+	0.999765i	$0.506902\pi$
$150$	−1.42773e18	−0.454852
$151$	−1.87304e18	−0.563953	−0.281977	−	0.959421i	$-0.590990\pi$
$151$	−1.87304e18	−0.563953	−0.281977	+	0.959421i	$0.590990\pi$
$152$	−8.95616e18	−2.54948
$153$	4.72748e18	1.27278
$154$	1.90930e18	0.486349
$155$	−2.26119e18	−0.545153
$156$	1.84182e19	4.20425
$157$	−1.37344e18	−0.296935	−0.148468	−	0.988917i	$-0.547434\pi$
$157$	−1.37344e18	−0.296935	−0.148468	+	0.988917i	$0.547434\pi$
$158$	1.11136e19	2.27651
$159$	−8.85189e18	−1.71854
$160$	−4.16730e18	−0.767070
$161$	−5.03116e18	−0.878311
$162$	1.29606e19	2.14659
$163$	8.00163e18	1.25772	0.628860	−	0.777519i	$-0.283522\pi$
$163$	8.00163e18	1.25772	0.628860	+	0.777519i	$0.283522\pi$
$164$	−2.41509e19	−3.60379
$165$	−2.32490e18	−0.329451
$166$	−5.41303e18	−0.728655
$167$	9.77713e18	1.25061	0.625304	−	0.780381i	$-0.284975\pi$
$167$	9.77713e18	1.25061	0.625304	+	0.780381i	$0.284975\pi$
$168$	−2.68726e19	−3.26724
$169$	1.00987e19	1.16742
$170$	−3.15485e19	−3.46867
$171$	8.28114e18	0.866210
$172$	−5.55052e18	−0.552512
$173$	−1.06185e19	−1.00617	−0.503084	−	0.864238i	$-0.667801\pi$
$173$	−1.06185e19	−1.00617	−0.503084	+	0.864238i	$0.667801\pi$
$174$	−4.80708e18	−0.433724
$175$	2.68532e18	0.230766
$176$	−4.42429e18	−0.362231
$177$	−2.68173e18	−0.209238
$178$	2.49188e19	1.85335
$179$	−2.29142e19	−1.62500	−0.812501	−	0.582960i	$-0.801895\pi$
$179$	−2.29142e19	−1.62500	−0.812501	+	0.582960i	$0.801895\pi$
$180$	2.52043e19	1.70474
$181$	2.24468e19	1.44840	0.724198	−	0.689592i	$-0.242210\pi$
$181$	2.24468e19	1.44840	0.724198	+	0.689592i	$0.242210\pi$
$182$	−5.05288e19	−3.11123
$183$	−1.98068e19	−1.16407
$184$	2.78090e19	1.56039
$185$	2.89854e19	1.55317
$186$	2.27590e19	1.16491
$187$	−8.37378e18	−0.409513
$188$	2.76016e19	1.29001
$189$	−9.89090e18	−0.441886
$190$	−5.52636e19	−2.36066
$191$	8.15204e18	0.333029	0.166515	−	0.986039i	$-0.446749\pi$
$191$	8.15204e18	0.333029	0.166515	+	0.986039i	$0.446749\pi$
$192$	−1.08063e19	−0.422294
$193$	−5.90065e18	−0.220629	−0.110315	−	0.993897i	$-0.535186\pi$
$193$	−5.90065e18	−0.220629	−0.110315	+	0.993897i	$0.535186\pi$
$194$	−5.26290e19	−1.88326
$195$	6.15275e19	2.10754
$196$	2.68735e19	0.881349
$197$	−2.48407e18	−0.0780191	−0.0390095	−	0.999239i	$-0.512420\pi$
$197$	−2.48407e18	−0.0780191	−0.0390095	+	0.999239i	$0.512420\pi$
$198$	9.75796e18	0.293565
$199$	4.88334e19	1.40756	0.703778	−	0.710420i	$-0.251495\pi$
$199$	4.88334e19	1.40756	0.703778	+	0.710420i	$0.251495\pi$
$200$	−1.48427e19	−0.409976
$201$	3.63223e19	0.961628
$202$	−1.08396e20	−2.75123
$203$	9.04132e18	0.220047
$204$	2.17697e20	5.08156
$205$	−8.06779e19	−1.80654
$206$	−7.82901e19	−1.68204
$207$	−2.57130e19	−0.530158
$208$	1.17087e20	2.31723
$209$	−1.46684e19	−0.278701
$210$	−1.65817e20	−3.02527
$211$	−3.00726e19	−0.526952	−0.263476	−	0.964666i	$-0.584869\pi$
$211$	−3.00726e19	−0.526952	−0.263476	+	0.964666i	$0.584869\pi$
$212$	−1.69980e20	−2.86117
$213$	−8.43603e19	−1.36430
$214$	5.88746e19	0.914978
$215$	−1.85420e19	−0.276968
$216$	5.46704e19	0.785047
$217$	−4.28059e19	−0.591012
$218$	2.36125e20	3.13517
$219$	−2.28751e19	−0.292138
$220$	−4.46444e19	−0.548497
$221$	2.21609e20	2.61970
$222$	−2.91740e20	−3.31891
$223$	1.29928e20	1.42269	0.711347	−	0.702841i	$-0.248085\pi$
$223$	1.29928e20	1.42269	0.711347	+	0.702841i	$0.248085\pi$
$224$	−7.88898e19	−0.831597
$225$	1.37240e19	0.139293
$226$	−1.09560e18	−0.0107085
$227$	1.87841e19	0.176836	0.0884180	−	0.996083i	$-0.471819\pi$
$227$	1.87841e19	0.176836	0.0884180	+	0.996083i	$0.471819\pi$
$228$	3.81341e20	3.45834
$229$	7.75871e19	0.677935	0.338968	−	0.940798i	$-0.389922\pi$
$229$	7.75871e19	0.677935	0.338968	+	0.940798i	$0.389922\pi$
$230$	1.71594e20	1.44483
$231$	−4.40120e19	−0.357165
$232$	−4.99746e19	−0.390932
$233$	−1.91389e20	−1.44341	−0.721707	−	0.692199i	$-0.756642\pi$
$233$	−1.91389e20	−1.44341	−0.721707	+	0.692199i	$0.756642\pi$
$234$	−2.58240e20	−1.87797
$235$	9.22053e19	0.646665
$236$	−5.14964e19	−0.348357
$237$	−2.56184e20	−1.67183
$238$	−5.97235e20	−3.76046
$239$	−2.52552e20	−1.53451	−0.767253	−	0.641345i	$-0.778377\pi$
$239$	−2.52552e20	−1.53451	−0.767253	+	0.641345i	$0.778377\pi$
$240$	3.84235e20	2.25321
$241$	−1.27038e20	−0.719102	−0.359551	−	0.933125i	$-0.617070\pi$
$241$	−1.27038e20	−0.719102	−0.359551	+	0.933125i	$0.617070\pi$
$242$	3.09060e20	1.68893
$243$	−2.28088e20	−1.20351
$244$	−3.80345e20	−1.93804
$245$	8.97732e19	0.441809
$246$	8.12027e20	3.86031
$247$	3.88193e20	1.78288
$248$	2.36603e20	1.04998
$249$	1.24778e20	0.535110
$250$	3.78711e20	1.56970
$251$	−1.19032e20	−0.476912	−0.238456	−	0.971153i	$-0.576641\pi$
$251$	−1.19032e20	−0.476912	−0.238456	+	0.971153i	$0.576641\pi$
$252$	4.77135e20	1.84815
$253$	4.55455e19	0.170577
$254$	−7.00531e20	−2.53712
$255$	7.27236e20	2.54732
$256$	−5.76898e20	−1.95461
$257$	−5.11555e20	−1.67672	−0.838360	−	0.545117i	$-0.816485\pi$
$257$	−5.11555e20	−1.67672	−0.838360	+	0.545117i	$0.816485\pi$
$258$	1.86626e20	0.591840
$259$	5.48714e20	1.68383
$260$	1.18150e21	3.50880
$261$	4.62080e19	0.132823
$262$	3.55968e20	0.990490
$263$	−4.69281e20	−1.26418	−0.632091	−	0.774895i	$-0.717803\pi$
$263$	−4.69281e20	−1.26418	−0.632091	+	0.774895i	$0.717803\pi$
$264$	2.43269e20	0.634533
$265$	−5.67833e20	−1.43427
$266$	−1.04618e21	−2.55924
$267$	−5.74413e20	−1.36106
$268$	6.97487e20	1.60100
$269$	5.98639e20	1.33128	0.665642	−	0.746271i	$-0.268158\pi$
$269$	5.98639e20	1.33128	0.665642	+	0.746271i	$0.268158\pi$
$270$	3.37342e20	0.726906
$271$	1.92263e20	0.401474	0.200737	−	0.979645i	$-0.435666\pi$
$271$	1.92263e20	0.401474	0.200737	+	0.979645i	$0.435666\pi$
$272$	1.38393e21	2.80078
$273$	1.16476e21	2.28483
$274$	−1.30306e21	−2.47790
$275$	−2.43094e19	−0.0448173
$276$	−1.18407e21	−2.11665
$277$	−8.40638e20	−1.45724	−0.728620	−	0.684918i	$-0.759838\pi$
$277$	−8.40638e20	−1.45724	−0.728620	+	0.684918i	$0.759838\pi$
$278$	−1.14170e21	−1.91943
$279$	−2.18770e20	−0.356741
$280$	−1.72383e21	−2.72679
$281$	2.84695e20	0.436893	0.218447	−	0.975849i	$-0.429901\pi$
$281$	2.84695e20	0.436893	0.218447	+	0.975849i	$0.429901\pi$
$282$	−9.28051e20	−1.38183
$283$	8.90156e20	1.28612	0.643060	−	0.765816i	$-0.277664\pi$
$283$	8.90156e20	1.28612	0.643060	+	0.765816i	$0.277664\pi$
$284$	−1.61995e21	−2.27141
$285$	1.27390e21	1.73362
$286$	4.57421e20	0.604234
$287$	−1.52729e21	−1.95850
$288$	−4.03186e20	−0.501961
$289$	1.79210e21	2.16636
$290$	−3.08366e20	−0.361979
$291$	1.21317e21	1.38303
$292$	−4.39264e20	−0.486376
$293$	−5.73524e20	−0.616846	−0.308423	−	0.951249i	$-0.599801\pi$
$293$	−5.73524e20	−0.616846	−0.308423	+	0.951249i	$0.599801\pi$
$294$	−9.03571e20	−0.944083
$295$	−1.72028e20	−0.174627
$296$	−3.03293e21	−2.99146
$297$	8.95391e19	0.0858189
$298$	8.30289e19	0.0773377
$299$	−1.20534e21	−1.09120
$300$	6.31983e20	0.556128
$301$	−3.51012e20	−0.300266
$302$	1.20934e21	1.00575
$303$	2.49868e21	2.02045
$304$	2.42424e21	1.90612
$305$	−1.27057e21	−0.971518
$306$	−3.05232e21	−2.26985
$307$	8.21971e20	0.594539	0.297270	−	0.954794i	$-0.403924\pi$
$307$	8.21971e20	0.594539	0.297270	+	0.954794i	$0.403924\pi$
$308$	−8.45149e20	−0.594637
$309$	1.80469e21	1.23525
$310$	1.45995e21	0.972218
$311$	1.53791e21	0.996477	0.498239	−	0.867040i	$-0.333980\pi$
$311$	1.53791e21	0.996477	0.498239	+	0.867040i	$0.333980\pi$
$312$	−6.43802e21	−4.05918
$313$	1.42511e21	0.874421	0.437211	−	0.899359i	$-0.355966\pi$
$313$	1.42511e21	0.874421	0.437211	+	0.899359i	$0.355966\pi$
$314$	8.86767e20	0.529551
$315$	1.59391e21	0.926453
$316$	−4.91943e21	−2.78339
$317$	1.64676e21	0.907038	0.453519	−	0.891247i	$-0.350168\pi$
$317$	1.64676e21	0.907038	0.453519	+	0.891247i	$0.350168\pi$
$318$	5.71527e21	3.06483
$319$	−8.18482e19	−0.0427355
$320$	−6.93202e20	−0.352440
$321$	−1.35714e21	−0.671942
$322$	3.24839e21	1.56637
$323$	4.58831e21	2.15492
$324$	−5.73701e21	−2.62454
$325$	6.43337e20	0.286701
$326$	−5.16629e21	−2.24300
$327$	−5.44300e21	−2.30241
$328$	8.44185e21	3.47945
$329$	1.74551e21	0.701063
$330$	1.50108e21	0.587539
$331$	−4.54685e21	−1.73449	−0.867247	−	0.497878i	$-0.834113\pi$
$331$	−4.54685e21	−1.73449	−0.867247	+	0.497878i	$0.834113\pi$
$332$	2.39607e21	0.890894
$333$	2.80434e21	1.01638
$334$	−6.31265e21	−2.23032
$335$	2.33001e21	0.802560
$336$	7.27383e21	2.44275
$337$	5.00380e21	1.63850	0.819248	−	0.573439i	$-0.194391\pi$
$337$	5.00380e21	1.63850	0.819248	+	0.573439i	$0.194391\pi$
$338$	−6.52027e21	−2.08197
$339$	2.52550e19	0.00786412
$340$	1.39649e22	4.24099
$341$	3.87508e20	0.114781
$342$	−5.34676e21	−1.54479
$343$	−2.50504e21	−0.706015
$344$	1.94017e21	0.533448
$345$	−3.95548e21	−1.06105
$346$	6.85587e21	1.79439
$347$	−4.17722e21	−1.06681	−0.533404	−	0.845861i	$-0.679088\pi$
$347$	−4.17722e21	−1.06681	−0.533404	+	0.845861i	$0.679088\pi$
$348$	2.12785e21	0.530295
$349$	5.82193e21	1.41596	0.707979	−	0.706233i	$-0.249607\pi$
$349$	5.82193e21	1.41596	0.707979	+	0.706233i	$0.249607\pi$
$350$	−1.73379e21	−0.411546
$351$	−2.36962e21	−0.548994
$352$	7.14164e20	0.161505
$353$	−2.45544e21	−0.542057	−0.271028	−	0.962571i	$-0.587364\pi$
$353$	−2.45544e21	−0.542057	−0.271028	+	0.962571i	$0.587364\pi$
$354$	1.73147e21	0.373153
$355$	−5.41156e21	−1.13863
$356$	−1.10303e22	−2.26601
$357$	1.37671e22	2.76161
$358$	1.47947e22	2.89801
$359$	9.63080e20	0.184230	0.0921148	−	0.995748i	$-0.470637\pi$
$359$	9.63080e20	0.184230	0.0921148	+	0.995748i	$0.470637\pi$
$360$	−8.81008e21	−1.64592
$361$	2.55698e21	0.466569
$362$	−1.44929e22	−2.58305
$363$	−7.12426e21	−1.24032
$364$	2.23665e22	3.80396
$365$	−1.46740e21	−0.243814
$366$	1.27884e22	2.07599
$367$	−3.28839e21	−0.521581	−0.260791	−	0.965395i	$-0.583983\pi$
$367$	−3.28839e21	−0.521581	−0.260791	+	0.965395i	$0.583983\pi$
$368$	−7.52728e21	−1.16663
$369$	−7.80559e21	−1.18217
$370$	−1.87146e22	−2.76991
$371$	−1.07495e22	−1.55492
$372$	−1.00743e22	−1.42429
$373$	9.77462e21	1.35075	0.675375	−	0.737474i	$-0.263982\pi$
$373$	9.77462e21	1.35075	0.675375	+	0.737474i	$0.263982\pi$
$374$	5.40657e21	0.730321
$375$	−8.72981e21	−1.15276
$376$	−9.64804e21	−1.24550
$377$	2.16608e21	0.273384
$378$	6.38611e21	0.788054
$379$	−7.55961e21	−0.912149	−0.456075	−	0.889942i	$-0.650745\pi$
$379$	−7.55961e21	−0.912149	−0.456075	+	0.889942i	$0.650745\pi$
$380$	2.44624e22	2.88628
$381$	1.61482e22	1.86321
$382$	−5.26340e21	−0.593920
$383$	−9.38965e21	−1.03624	−0.518119	−	0.855308i	$-0.673368\pi$
$383$	−9.38965e21	−1.03624	−0.518119	+	0.855308i	$0.673368\pi$
$384$	1.54920e22	1.67222
$385$	−2.82329e21	−0.298084
$386$	3.80979e21	0.393467
$387$	−1.79394e21	−0.181244
$388$	2.32962e22	2.30258
$389$	3.43837e21	0.332492	0.166246	−	0.986084i	$-0.446835\pi$
$389$	3.43837e21	0.332492	0.166246	+	0.986084i	$0.446835\pi$
$390$	−3.97256e22	−3.75855
$391$	−1.42468e22	−1.31891
$392$	−9.39355e21	−0.850938
$393$	−8.20555e21	−0.727396
$394$	1.60385e21	0.139138
$395$	−1.64338e22	−1.39528
$396$	−4.31935e21	−0.358929
$397$	3.71243e21	0.301953	0.150976	−	0.988537i	$-0.451758\pi$
$397$	3.71243e21	0.301953	0.150976	+	0.988537i	$0.451758\pi$
$398$	−3.15295e22	−2.51022
$399$	2.41158e22	1.87946
$400$	4.01759e21	0.306518
$401$	−2.30999e21	−0.172538	−0.0862688	−	0.996272i	$-0.527494\pi$
$401$	−2.30999e21	−0.172538	−0.0862688	+	0.996272i	$0.527494\pi$
$402$	−2.34517e22	−1.71496
$403$	−1.02552e22	−0.734265
$404$	4.79814e22	3.36381
$405$	−1.91649e22	−1.31565
$406$	−5.83758e21	−0.392429
$407$	−4.96733e21	−0.327017
$408$	−7.60954e22	−4.90622
$409$	−3.38041e21	−0.213462	−0.106731	−	0.994288i	$-0.534038\pi$
$409$	−3.38041e21	−0.213462	−0.106731	+	0.994288i	$0.534038\pi$
$410$	5.20901e22	3.22175
$411$	3.00372e22	1.81972
$412$	3.46550e22	2.05655
$413$	−3.25660e21	−0.189317
$414$	1.66017e22	0.945476
$415$	8.00427e21	0.446594
$416$	−1.89001e22	−1.03317
$417$	2.63178e22	1.40959
$418$	9.47072e21	0.497032
$419$	−1.91876e22	−0.986739	−0.493369	−	0.869820i	$-0.664235\pi$
$419$	−1.91876e22	−0.986739	−0.493369	+	0.869820i	$0.664235\pi$
$420$	7.33985e22	3.69886
$421$	−3.06665e22	−1.51449	−0.757244	−	0.653132i	$-0.773455\pi$
$421$	−3.06665e22	−1.51449	−0.757244	+	0.653132i	$0.773455\pi$
$422$	1.94166e22	0.939759
$423$	8.92087e21	0.423169
$424$	5.94160e22	2.76245
$425$	7.60404e21	0.346528
$426$	5.44676e22	2.43308
$427$	−2.40528e22	−1.05324
$428$	−2.60608e22	−1.11870
$429$	−1.05442e22	−0.443737
$430$	1.19717e22	0.493941
$431$	2.41512e22	0.976971	0.488486	−	0.872572i	$-0.337549\pi$
$431$	2.41512e22	0.976971	0.488486	+	0.872572i	$0.337549\pi$
$432$	−1.47981e22	−0.586940
$433$	−3.26498e22	−1.26979	−0.634897	−	0.772597i	$-0.718958\pi$
$433$	−3.26498e22	−1.26979	−0.634897	+	0.772597i	$0.718958\pi$
$434$	2.76378e22	1.05400
$435$	7.10826e21	0.265830
$436$	−1.04520e23	−3.83324
$437$	−2.49561e22	−0.897604
$438$	1.47694e22	0.520996
$439$	−3.33883e22	−1.15517	−0.577586	−	0.816330i	$-0.696005\pi$
$439$	−3.33883e22	−1.15517	−0.577586	+	0.816330i	$0.696005\pi$
$440$	1.56053e22	0.529571
$441$	8.68556e21	0.289114
$442$	−1.43083e23	−4.67195
$443$	1.88444e22	0.603601	0.301800	−	0.953371i	$-0.402412\pi$
$443$	1.88444e22	0.603601	0.301800	+	0.953371i	$0.402412\pi$
$444$	1.29138e23	4.05788
$445$	−3.68476e22	−1.13592
$446$	−8.38887e22	−2.53722
$447$	−1.91393e21	−0.0567952
$448$	−1.31228e22	−0.382087
$449$	−3.26676e22	−0.933304	−0.466652	−	0.884441i	$-0.654540\pi$
$449$	−3.26676e22	−0.933304	−0.466652	+	0.884441i	$0.654540\pi$
$450$	−8.86098e21	−0.248414
$451$	1.38260e22	0.380362
$452$	4.84965e20	0.0130928
$453$	−2.78769e22	−0.738601
$454$	−1.21281e22	−0.315367
$455$	7.47172e22	1.90688
$456$	−1.33297e23	−3.33901
$457$	9.67539e21	0.237893	0.118946	−	0.992901i	$-0.462048\pi$
$457$	9.67539e21	0.237893	0.118946	+	0.992901i	$0.462048\pi$
$458$	−5.00945e22	−1.20902
$459$	−2.80081e22	−0.663554
$460$	−7.59559e22	−1.76653
$461$	1.83202e21	0.0418286	0.0209143	−	0.999781i	$-0.493342\pi$
$461$	1.83202e21	0.0418286	0.0209143	+	0.999781i	$0.493342\pi$
$462$	2.84165e22	0.636963
$463$	1.56727e22	0.344910	0.172455	−	0.985017i	$-0.444830\pi$
$463$	1.56727e22	0.344910	0.172455	+	0.985017i	$0.444830\pi$
$464$	1.35270e22	0.292280
$465$	−3.36539e22	−0.713978
$466$	1.23571e23	2.57417
$467$	5.80904e22	1.18826	0.594129	−	0.804370i	$-0.297497\pi$
$467$	5.80904e22	1.18826	0.594129	+	0.804370i	$0.297497\pi$
$468$	1.14310e23	2.29611
$469$	4.41087e22	0.870072
$470$	−5.95328e22	−1.15325
$471$	−2.04412e22	−0.388891
$472$	1.80004e22	0.336337
$473$	3.17760e21	0.0583149
$474$	1.65407e23	2.98152
$475$	1.33200e22	0.235836
$476$	2.64365e23	4.59775
$477$	−5.49378e22	−0.938567
$478$	1.63061e23	2.73662
$479$	8.51939e22	1.40461	0.702307	−	0.711875i	$-0.252154\pi$
$479$	8.51939e22	1.40461	0.702307	+	0.711875i	$0.252154\pi$
$480$	−6.20229e22	−1.00462
$481$	1.31458e23	2.09197
$482$	8.20230e22	1.28244
$483$	−7.48799e22	−1.15031
$484$	−1.36805e23	−2.06498
$485$	7.78227e22	1.15425
$486$	1.47266e23	2.14632
$487$	−4.47381e22	−0.640739	−0.320370	−	0.947293i	$-0.603807\pi$
$487$	−4.47381e22	−0.640739	−0.320370	+	0.947293i	$0.603807\pi$
$488$	1.32948e23	1.87117
$489$	1.19090e23	1.64722
$490$	−5.79625e22	−0.787917
$491$	2.24806e22	0.300341	0.150171	−	0.988660i	$-0.452018\pi$
$491$	2.24806e22	0.300341	0.150171	+	0.988660i	$0.452018\pi$
$492$	−3.59443e23	−4.71983
$493$	2.56024e22	0.330432
$494$	−2.50638e23	−3.17957
$495$	−1.44291e22	−0.179927
$496$	−6.40433e22	−0.785017
$497$	−1.02445e23	−1.23441
$498$	−8.05634e22	−0.954307
$499$	−1.50494e23	−1.75252	−0.876262	−	0.481836i	$-0.839970\pi$
$499$	−1.50494e23	−1.75252	−0.876262	+	0.481836i	$0.839970\pi$
$500$	−1.67636e23	−1.91921
$501$	1.45515e23	1.63790
$502$	7.68538e22	0.850518
$503$	−9.48795e22	−1.03239	−0.516196	−	0.856471i	$-0.672652\pi$
$503$	−9.48795e22	−1.03239	−0.516196	+	0.856471i	$0.672652\pi$
$504$	−1.66781e23	−1.78438
$505$	1.60286e23	1.68623
$506$	−2.94067e22	−0.304205
$507$	1.50301e23	1.52895
$508$	3.10089e23	3.10202
$509$	3.53997e22	0.348256	0.174128	−	0.984723i	$-0.444289\pi$
$509$	3.53997e22	0.348256	0.174128	+	0.984723i	$0.444289\pi$
$510$	−4.69544e23	−4.54286
$511$	−2.77789e22	−0.264324
$512$	2.36044e23	2.20901
$513$	−4.90619e22	−0.451593
$514$	3.30288e23	2.99024
$515$	1.15768e23	1.03092
$516$	−8.26097e22	−0.723617
$517$	−1.58015e22	−0.136154
$518$	−3.54280e23	−3.00292
$519$	−1.58037e23	−1.31776
$520$	−4.12988e23	−3.38773
$521$	5.25323e22	0.423942	0.211971	−	0.977276i	$-0.432012\pi$
$521$	5.25323e22	0.423942	0.211971	+	0.977276i	$0.432012\pi$
$522$	−2.98344e22	−0.236874
$523$	3.45072e22	0.269554	0.134777	−	0.990876i	$-0.456968\pi$
$523$	3.45072e22	0.269554	0.134777	+	0.990876i	$0.456968\pi$
$524$	−1.57569e23	−1.21103
$525$	3.99662e22	0.302231
$526$	3.02994e23	2.25452
$527$	−1.21214e23	−0.887486
$528$	−6.58477e22	−0.474408
$529$	−6.35611e22	−0.450628
$530$	3.66624e23	2.55786
$531$	−1.66437e22	−0.114274
$532$	4.63089e23	3.12907
$533$	−3.65900e23	−2.43322
$534$	3.70873e23	2.42730
$535$	−8.70581e22	−0.560792
$536$	−2.43804e23	−1.54576
$537$	−3.41037e23	−2.12824
$538$	−3.86514e23	−2.37419
$539$	−1.53847e22	−0.0930220
$540$	−1.49324e23	−0.888756
$541$	−2.71733e23	−1.59208	−0.796041	−	0.605242i	$-0.793076\pi$
$541$	−2.71733e23	−1.59208	−0.796041	+	0.605242i	$0.793076\pi$
$542$	−1.24136e23	−0.715983
$543$	3.34081e23	1.89694
$544$	−2.23393e23	−1.24876
$545$	−3.49159e23	−1.92155
$546$	−7.52032e23	−4.07473
$547$	7.86656e22	0.419655	0.209828	−	0.977738i	$-0.432710\pi$
$547$	7.86656e22	0.419655	0.209828	+	0.977738i	$0.432710\pi$
$548$	5.76796e23	3.02962
$549$	−1.22928e23	−0.635749
$550$	1.56955e22	0.0799265
$551$	4.48478e22	0.224881
$552$	4.13887e23	2.04362
$553$	−3.11102e23	−1.51265
$554$	5.42762e23	2.59882
$555$	4.31397e23	2.03417
$556$	5.05374e23	2.34680
$557$	3.77522e23	1.72652	0.863262	−	0.504756i	$-0.168417\pi$
$557$	3.77522e23	1.72652	0.863262	+	0.504756i	$0.168417\pi$
$558$	1.41250e23	0.636207
$559$	−8.40939e22	−0.373047
$560$	4.66603e23	2.03868
$561$	−1.24629e23	−0.536333
$562$	−1.83815e23	−0.779150
$563$	4.39470e23	1.83488	0.917440	−	0.397874i	$-0.130252\pi$
$563$	4.39470e23	1.83488	0.917440	+	0.397874i	$0.130252\pi$
$564$	4.10801e23	1.68950
$565$	1.62006e21	0.00656327
$566$	−5.74734e23	−2.29365
$567$	−3.62805e23	−1.42632
$568$	5.66247e23	2.19303
$569$	8.19442e22	0.312654	0.156327	−	0.987705i	$-0.450035\pi$
$569$	8.19442e22	0.312654	0.156327	+	0.987705i	$0.450035\pi$
$570$	−8.22501e23	−3.09172
$571$	−4.04798e23	−1.49910	−0.749551	−	0.661947i	$-0.769730\pi$
$571$	−4.04798e23	−1.49910	−0.749551	+	0.661947i	$0.769730\pi$
$572$	−2.02477e23	−0.738770
$573$	1.21329e23	0.436163
$574$	9.86101e23	3.49277
$575$	−4.13588e22	−0.144342
$576$	−6.70673e22	−0.230632
$577$	1.88491e23	0.638698	0.319349	−	0.947637i	$-0.396536\pi$
$577$	1.88491e23	0.638698	0.319349	+	0.947637i	$0.396536\pi$
$578$	−1.15708e24	−3.86347
$579$	−8.78208e22	−0.288955
$580$	1.36498e23	0.442576
$581$	1.51526e23	0.484162
$582$	−7.83289e23	−2.46648
$583$	9.73115e22	0.301982
$584$	1.53543e23	0.469594
$585$	3.81861e23	1.15101
$586$	3.70299e23	1.10007
$587$	7.10981e22	0.208178	0.104089	−	0.994568i	$-0.466807\pi$
$587$	7.10981e22	0.208178	0.104089	+	0.994568i	$0.466807\pi$
$588$	3.99965e23	1.15429
$589$	−2.12331e23	−0.603994
$590$	1.11071e23	0.311428
$591$	−3.69710e22	−0.102180
$592$	8.20948e23	2.23656
$593$	−1.17349e23	−0.315148	−0.157574	−	0.987507i	$-0.550367\pi$
$593$	−1.17349e23	−0.315148	−0.157574	+	0.987507i	$0.550367\pi$
$594$	−5.78114e22	−0.153048
$595$	8.83133e23	2.30479
$596$	−3.67526e22	−0.0945574
$597$	7.26799e23	1.84345
$598$	7.78235e23	1.94604
$599$	4.09095e23	1.00855	0.504273	−	0.863544i	$-0.331760\pi$
$599$	4.09095e23	1.00855	0.504273	+	0.863544i	$0.331760\pi$
$600$	−2.20907e23	−0.536939
$601$	−3.75264e23	−0.899299	−0.449649	−	0.893205i	$-0.648451\pi$
$601$	−3.75264e23	−0.899299	−0.449649	+	0.893205i	$0.648451\pi$
$602$	2.26633e23	0.535491
$603$	2.25429e23	0.525185
$604$	−5.35312e23	−1.22968
$605$	−4.57009e23	−1.03515
$606$	−1.61328e24	−3.60324
$607$	1.43973e23	0.317086	0.158543	−	0.987352i	$-0.449320\pi$
$607$	1.43973e23	0.317086	0.158543	+	0.987352i	$0.449320\pi$
$608$	−3.91318e23	−0.849864
$609$	1.34564e23	0.288192
$610$	8.20351e23	1.73259
$611$	4.18181e23	0.870992
$612$	1.35111e24	2.77525
$613$	5.25038e23	1.06360	0.531799	−	0.846871i	$-0.321516\pi$
$613$	5.25038e23	1.06360	0.531799	+	0.846871i	$0.321516\pi$
$614$	−5.30710e23	−1.06029
$615$	−1.20075e24	−2.36599
$616$	2.95419e23	0.574120
$617$	−3.49285e22	−0.0669508	−0.0334754	−	0.999440i	$-0.510658\pi$
$617$	−3.49285e22	−0.0669508	−0.0334754	+	0.999440i	$0.510658\pi$
$618$	−1.16521e24	−2.20294
$619$	−1.47469e23	−0.274998	−0.137499	−	0.990502i	$-0.543906\pi$
$619$	−1.47469e23	−0.274998	−0.137499	+	0.990502i	$0.543906\pi$
$620$	−6.46245e23	−1.18869
$621$	1.52338e23	0.276394
$622$	−9.92959e23	−1.77710
$623$	−6.97550e23	−1.23148
$624$	1.74263e24	3.03484
$625$	−6.73356e23	−1.15682
$626$	−9.20128e23	−1.55943
$627$	−2.18313e23	−0.365011
$628$	−3.92526e23	−0.647458
$629$	1.55380e24	2.52850
$630$	−1.02911e24	−1.65222
$631$	7.40740e23	1.17332	0.586660	−	0.809833i	$-0.300443\pi$
$631$	7.40740e23	1.17332	0.586660	+	0.809833i	$0.300443\pi$
$632$	1.71957e24	2.68736
$633$	−4.47578e23	−0.690140
$634$	−1.06324e24	−1.61760
$635$	1.03588e24	1.55501
$636$	−2.52986e24	−3.74723
$637$	4.07150e23	0.595072
$638$	5.28457e22	0.0762139
$639$	−5.23569e23	−0.745103
$640$	9.93786e23	1.39561
$641$	−3.50461e23	−0.485676	−0.242838	−	0.970067i	$-0.578078\pi$
$641$	−3.50461e23	−0.485676	−0.242838	+	0.970067i	$0.578078\pi$
$642$	8.76244e23	1.19833
$643$	−6.96395e23	−0.939858	−0.469929	−	0.882704i	$-0.655721\pi$
$643$	−6.96395e23	−0.939858	−0.469929	+	0.882704i	$0.655721\pi$
$644$	−1.43790e24	−1.91513
$645$	−2.75965e23	−0.362740
$646$	−2.96247e24	−3.84306
$647$	−2.63794e23	−0.337738	−0.168869	−	0.985639i	$-0.554011\pi$
$647$	−2.63794e23	−0.337738	−0.168869	+	0.985639i	$0.554011\pi$
$648$	2.00535e24	2.53398
$649$	2.94810e22	0.0367674
$650$	−4.15374e23	−0.511299
$651$	−6.37090e23	−0.774039
$652$	2.28685e24	2.74242
$653$	−1.64108e24	−1.94253	−0.971263	−	0.238007i	$-0.923506\pi$
$653$	−1.64108e24	−1.94253	−0.971263	+	0.238007i	$0.923506\pi$
$654$	3.51430e24	4.10608
$655$	−5.26371e23	−0.607074
$656$	−2.28502e24	−2.60140
$657$	−1.41971e23	−0.159549
$658$	−1.12700e24	−1.25027
$659$	5.73508e22	0.0628078	0.0314039	−	0.999507i	$-0.490002\pi$
$659$	5.73508e22	0.0628078	0.0314039	+	0.999507i	$0.490002\pi$
$660$	−6.64453e23	−0.718358
$661$	−1.04064e24	−1.11067	−0.555336	−	0.831626i	$-0.687410\pi$
$661$	−1.04064e24	−1.11067	−0.555336	+	0.831626i	$0.687410\pi$
$662$	2.93570e24	3.09327
$663$	3.29825e24	3.43099
$664$	−8.37539e23	−0.860154
$665$	1.54699e24	1.56857
$666$	−1.81064e24	−1.81259
$667$	−1.39253e23	−0.137637
$668$	2.79429e24	2.72691
$669$	1.93375e24	1.86328
$670$	−1.50439e24	−1.43128
$671$	2.17742e23	0.204551
$672$	−1.17414e24	−1.08913
$673$	−3.50405e23	−0.320953	−0.160477	−	0.987040i	$-0.551303\pi$
$673$	−3.50405e23	−0.320953	−0.160477	+	0.987040i	$0.551303\pi$
$674$	−3.23073e24	−2.92207
$675$	−8.13084e22	−0.0726195
$676$	2.88619e24	2.54553
$677$	−6.35949e23	−0.553884	−0.276942	−	0.960887i	$-0.589321\pi$
$677$	−6.35949e23	−0.553884	−0.276942	+	0.960887i	$0.589321\pi$
$678$	−1.63060e22	−0.0140248
$679$	1.47324e24	1.25135
$680$	−4.88139e24	−4.09466
$681$	2.79568e23	0.231599
$682$	−2.50197e23	−0.204698
$683$	−8.56675e23	−0.692214	−0.346107	−	0.938195i	$-0.612497\pi$
$683$	−8.56675e23	−0.692214	−0.346107	+	0.938195i	$0.612497\pi$
$684$	2.36674e24	1.88874
$685$	1.92684e24	1.51871
$686$	1.61739e24	1.25910
$687$	1.15475e24	0.887881
$688$	−5.25160e23	−0.398832
$689$	−2.57531e24	−1.93181
$690$	2.55388e24	1.89227
$691$	1.21066e24	0.886053	0.443027	−	0.896508i	$-0.353905\pi$
$691$	1.21066e24	0.886053	0.443027	+	0.896508i	$0.353905\pi$
$692$	−3.03474e24	−2.19392
$693$	−2.73153e23	−0.195063
$694$	2.69704e24	1.90253
$695$	1.68824e24	1.17642
$696$	−7.43783e23	−0.511997
$697$	−4.32483e24	−2.94097
$698$	−3.75896e24	−2.52520
$699$	−2.84848e24	−1.89042
$700$	7.67460e23	0.503179
$701$	8.06024e23	0.522089	0.261045	−	0.965327i	$-0.415933\pi$
$701$	8.06024e23	0.522089	0.261045	+	0.965327i	$0.415933\pi$
$702$	1.52995e24	0.979068
$703$	2.72179e24	1.72082
$704$	1.18796e23	0.0742054
$705$	1.37231e24	0.846927
$706$	1.58537e24	0.966697
$707$	3.03432e24	1.82808
$708$	−7.66433e23	−0.456238
$709$	−5.09200e22	−0.0299499	−0.0149749	−	0.999888i	$-0.504767\pi$
$709$	−5.09200e22	−0.0299499	−0.0149749	+	0.999888i	$0.504767\pi$
$710$	3.49400e24	2.03061
$711$	−1.58997e24	−0.913054
$712$	3.85560e24	2.18782
$713$	6.59289e23	0.369670
$714$	−8.88878e24	−4.92501
$715$	−6.76391e23	−0.370336
$716$	−6.54884e24	−3.54327
$717$	−3.75879e24	−2.00972
$718$	−6.21817e23	−0.328553
$719$	1.84407e24	0.962902	0.481451	−	0.876473i	$-0.340110\pi$
$719$	1.84407e24	0.962902	0.481451	+	0.876473i	$0.340110\pi$
$720$	2.38470e24	1.23057
$721$	2.19156e24	1.11765
$722$	−1.65093e24	−0.832074
$723$	−1.89074e24	−0.941796
$724$	6.41527e24	3.15818
$725$	7.43245e22	0.0361625
$726$	4.59981e24	2.21197
$727$	9.59151e23	0.455873	0.227937	−	0.973676i	$-0.426802\pi$
$727$	9.59151e23	0.455873	0.227937	+	0.973676i	$0.426802\pi$
$728$	−7.81814e24	−3.67271
$729$	−8.02377e23	−0.372559
$730$	9.47434e23	0.434815
$731$	−9.93963e23	−0.450892
$732$	−5.66076e24	−2.53823
$733$	−3.35057e24	−1.48503	−0.742514	−	0.669831i	$-0.766367\pi$
$733$	−3.35057e24	−1.48503	−0.742514	+	0.669831i	$0.766367\pi$
$734$	2.12317e24	0.930181
$735$	1.33612e24	0.578631
$736$	1.21505e24	0.520153
$737$	−3.99302e23	−0.168977
$738$	5.03972e24	2.10827
$739$	−8.18867e23	−0.338638	−0.169319	−	0.985561i	$-0.554157\pi$
$739$	−8.18867e23	−0.338638	−0.169319	+	0.985561i	$0.554157\pi$
$740$	8.28399e24	3.38665
$741$	5.77756e24	2.33502
$742$	6.94044e24	2.77303
$743$	−2.28443e24	−0.902347	−0.451173	−	0.892436i	$-0.648994\pi$
$743$	−2.28443e24	−0.902347	−0.451173	+	0.892436i	$0.648994\pi$
$744$	3.52142e24	1.37514
$745$	−1.22775e23	−0.0474004
$746$	−6.31103e24	−2.40891
$747$	7.74414e23	0.292245
$748$	−2.39321e24	−0.892931
$749$	−1.64807e24	−0.607967
$750$	5.63645e24	2.05582
$751$	3.36388e24	1.21311	0.606557	−	0.795040i	$-0.292550\pi$
$751$	3.36388e24	1.21311	0.606557	+	0.795040i	$0.292550\pi$
$752$	2.61151e24	0.931194
$753$	−1.77159e24	−0.624604
$754$	−1.39854e24	−0.487549
$755$	−1.78825e24	−0.616425
$756$	−2.82680e24	−0.963519
$757$	2.85798e24	0.963261	0.481631	−	0.876374i	$-0.340045\pi$
$757$	2.85798e24	0.963261	0.481631	+	0.876374i	$0.340045\pi$
$758$	4.88090e24	1.62671
$759$	6.77864e23	0.223402
$760$	−8.55074e24	−2.78669
$761$	−4.10866e24	−1.32413	−0.662065	−	0.749447i	$-0.730320\pi$
$761$	−4.10866e24	−1.32413	−0.662065	+	0.749447i	$0.730320\pi$
$762$	−1.04262e25	−3.32282
$763$	−6.60981e24	−2.08320
$764$	2.32984e24	0.726160
$765$	4.51348e24	1.39120
$766$	6.06248e24	1.84802
$767$	−7.80202e23	−0.235205
$768$	−8.58610e24	−2.55992
$769$	2.31222e24	0.681797	0.340898	−	0.940100i	$-0.389269\pi$
$769$	2.31222e24	0.681797	0.340898	+	0.940100i	$0.389269\pi$
$770$	1.82287e24	0.531600
$771$	−7.61359e24	−2.19597
$772$	−1.68640e24	−0.481075
$773$	2.16669e24	0.611323	0.305661	−	0.952140i	$-0.401122\pi$
$773$	2.16669e24	0.611323	0.305661	+	0.952140i	$0.401122\pi$
$774$	1.15826e24	0.323228
$775$	−3.51887e23	−0.0971268
$776$	−8.14309e24	−2.22313
$777$	8.16663e24	2.20528
$778$	−2.22000e24	−0.592961
$779$	−7.57582e24	−2.00153
$780$	1.75845e25	4.59542
$781$	9.27398e23	0.239735
$782$	9.19850e24	2.35212
$783$	−2.73761e23	−0.0692463
$784$	2.54263e24	0.636204
$785$	−1.31127e24	−0.324563
$786$	5.29795e24	1.29723
$787$	−4.02529e24	−0.975018	−0.487509	−	0.873118i	$-0.662094\pi$
$787$	−4.02529e24	−0.975018	−0.487509	+	0.873118i	$0.662094\pi$
$788$	−7.09943e23	−0.170118
$789$	−6.98442e24	−1.65568
$790$	1.06105e25	2.48833
$791$	3.06689e22	0.00711538
$792$	1.50981e24	0.346545
$793$	−5.76246e24	−1.30854
$794$	−2.39695e24	−0.538499
$795$	−8.45119e24	−1.87844
$796$	1.39565e25	3.06913
$797$	−5.44766e24	−1.18526	−0.592631	−	0.805474i	$-0.701911\pi$
$797$	−5.44766e24	−1.18526	−0.592631	+	0.805474i	$0.701911\pi$
$798$	−1.55705e25	−3.35180
$799$	4.94277e24	1.05274
$800$	−6.48516e23	−0.136665
$801$	−3.56500e24	−0.743333
$802$	1.49146e24	0.307701
$803$	2.51473e23	0.0513345
$804$	1.03809e25	2.09680
$805$	−4.80341e24	−0.960031
$806$	6.62135e24	1.30948
$807$	8.90968e24	1.74356
$808$	−1.67717e25	−3.24774
$809$	5.80752e23	0.111283	0.0556414	−	0.998451i	$-0.482280\pi$
$809$	5.80752e23	0.111283	0.0556414	+	0.998451i	$0.482280\pi$
$810$	1.23739e25	2.34631
$811$	3.19811e24	0.600090	0.300045	−	0.953925i	$-0.402998\pi$
$811$	3.19811e24	0.600090	0.300045	+	0.953925i	$0.402998\pi$
$812$	2.58400e24	0.479806
$813$	2.86150e24	0.525804
$814$	3.20718e24	0.583198
$815$	7.63942e24	1.37474
$816$	2.05974e25	3.66813
$817$	−1.74113e24	−0.306862
$818$	2.18258e24	0.380686
$819$	7.22889e24	1.24784
$820$	−2.30576e25	−3.93910
$821$	−7.56232e24	−1.27861	−0.639305	−	0.768953i	$-0.720778\pi$
$821$	−7.56232e24	−1.27861	−0.639305	+	0.768953i	$0.720778\pi$
$822$	−1.93937e25	−3.24526
$823$	−4.16723e24	−0.690158	−0.345079	−	0.938574i	$-0.612148\pi$
$823$	−4.16723e24	−0.690158	−0.345079	+	0.938574i	$0.612148\pi$
$824$	−1.21135e25	−1.98559
$825$	−3.61802e23	−0.0586965
$826$	2.10264e24	0.337625
$827$	−8.45598e24	−1.34390	−0.671950	−	0.740596i	$-0.734543\pi$
$827$	−8.45598e24	−1.34390	−0.671950	+	0.740596i	$0.734543\pi$
$828$	−7.34874e24	−1.15599
$829$	7.30805e24	1.13786	0.568929	−	0.822386i	$-0.307358\pi$
$829$	7.30805e24	1.13786	0.568929	+	0.822386i	$0.307358\pi$
$830$	−5.16800e24	−0.796450
$831$	−1.25114e25	−1.90852
$832$	−3.14390e24	−0.474701
$833$	4.81239e24	0.719248
$834$	−1.69922e25	−2.51385
$835$	9.33455e24	1.36697
$836$	−4.19220e24	−0.607699
$837$	1.29611e24	0.185985
$838$	1.23886e25	1.75974
$839$	8.35418e24	1.17470	0.587350	−	0.809333i	$-0.300171\pi$
$839$	8.35418e24	1.17470	0.587350	+	0.809333i	$0.300171\pi$
$840$	−2.56562e25	−3.57123
$841$	2.50246e23	0.0344828
$842$	1.98000e25	2.70092
$843$	4.23718e24	0.572192
$844$	−8.59471e24	−1.14900
$845$	9.64155e24	1.27604
$846$	−5.75980e24	−0.754674
$847$	−8.65148e24	−1.12223
$848$	−1.60826e25	−2.06534
$849$	1.32484e25	1.68441
$850$	−4.90959e24	−0.617994
$851$	−8.45119e24	−1.05321
$852$	−2.41100e25	−2.97482
$853$	−1.19530e25	−1.46020	−0.730098	−	0.683342i	$-0.760526\pi$
$853$	−1.19530e25	−1.46020	−0.730098	+	0.683342i	$0.760526\pi$
$854$	1.55298e25	1.87834
$855$	7.90627e24	0.946804
$856$	9.10945e24	1.08010
$857$	−5.32682e24	−0.625361	−0.312681	−	0.949858i	$-0.601227\pi$
$857$	−5.32682e24	−0.625361	−0.312681	+	0.949858i	$0.601227\pi$
$858$	6.80790e24	0.791355
$859$	3.60851e24	0.415323	0.207661	−	0.978201i	$-0.433415\pi$
$859$	3.60851e24	0.415323	0.207661	+	0.978201i	$0.433415\pi$
$860$	−5.29927e24	−0.603919
$861$	−2.27310e25	−2.56502
$862$	−1.55933e25	−1.74232
$863$	−1.28137e24	−0.141770	−0.0708848	−	0.997485i	$-0.522582\pi$
$863$	−1.28137e24	−0.141770	−0.0708848	+	0.997485i	$0.522582\pi$
$864$	2.38869e24	0.261694
$865$	−1.01378e25	−1.09978
$866$	2.10805e25	2.26453
$867$	2.66723e25	2.83725
$868$	−1.22339e25	−1.28868
$869$	2.81631e24	0.293773
$870$	−4.58948e24	−0.474078
$871$	1.05674e25	1.08097
$872$	3.65347e25	3.70097
$873$	7.52935e24	0.755329
$874$	1.61130e25	1.60077
$875$	−1.06012e25	−1.04301
$876$	−6.53768e24	−0.636999
$877$	−1.06601e25	−1.02864	−0.514322	−	0.857597i	$-0.671956\pi$
$877$	−1.06601e25	−1.02864	−0.514322	+	0.857597i	$0.671956\pi$
$878$	2.15574e25	2.06012
$879$	−8.53589e24	−0.807873
$880$	−4.22401e24	−0.395934
$881$	6.83036e24	0.634087	0.317043	−	0.948411i	$-0.397310\pi$
$881$	6.83036e24	0.634087	0.317043	+	0.948411i	$0.397310\pi$
$882$	−5.60787e24	−0.515603
$883$	5.77117e24	0.525530	0.262765	−	0.964860i	$-0.415366\pi$
$883$	5.77117e24	0.525530	0.262765	+	0.964860i	$0.415366\pi$
$884$	6.33354e25	5.71218
$885$	−2.56033e24	−0.228706
$886$	−1.21670e25	−1.07645
$887$	−5.24053e24	−0.459224	−0.229612	−	0.973282i	$-0.573746\pi$
$887$	−5.24053e24	−0.459224	−0.229612	+	0.973282i	$0.573746\pi$
$888$	−4.51398e25	−3.91787
$889$	1.96099e25	1.68581
$890$	2.37908e25	2.02579
$891$	3.28436e24	0.277007
$892$	3.71332e25	3.10214
$893$	8.65827e24	0.716463
$894$	1.23574e24	0.101288
$895$	−2.18769e25	−1.77620
$896$	1.88130e25	1.51301
$897$	−1.79394e25	−1.42913
$898$	2.10920e25	1.66444
$899$	−1.18479e24	−0.0926152
$900$	3.92230e24	0.303724
$901$	−3.04393e25	−2.33493
$902$	−8.92686e24	−0.678333
$903$	−5.22419e24	−0.393254
$904$	−1.69518e23	−0.0126411
$905$	2.14307e25	1.58316
$906$	1.79989e25	1.31721
$907$	1.51449e25	1.09801	0.549003	−	0.835820i	$-0.315008\pi$
$907$	1.51449e25	1.09801	0.549003	+	0.835820i	$0.315008\pi$
$908$	5.36847e24	0.385586
$909$	1.55076e25	1.10345
$910$	−4.82415e25	−3.40071
$911$	1.28115e25	0.894732	0.447366	−	0.894351i	$-0.352362\pi$
$911$	1.28115e25	0.894732	0.447366	+	0.894351i	$0.352362\pi$
$912$	3.60805e25	2.49641
$913$	−1.37172e24	−0.0940294
$914$	−6.24697e24	−0.424255
$915$	−1.89102e25	−1.27238
$916$	2.21743e25	1.47822
$917$	−9.96457e24	−0.658141
$918$	1.80836e25	1.18337
$919$	−3.21309e24	−0.208325	−0.104162	−	0.994560i	$-0.533216\pi$
$919$	−3.21309e24	−0.208325	−0.104162	+	0.994560i	$0.533216\pi$
$920$	2.65501e25	1.70557
$921$	1.22336e25	0.778659
$922$	−1.18285e24	−0.0745965
$923$	−2.45432e25	−1.53362
$924$	−1.25785e25	−0.778787
$925$	4.51072e24	0.276720
$926$	−1.01192e25	−0.615108
$927$	1.12005e25	0.674623
$928$	−2.18352e24	−0.130316
$929$	−1.54037e25	−0.910944	−0.455472	−	0.890250i	$-0.650529\pi$
$929$	−1.54037e25	−0.910944	−0.455472	+	0.890250i	$0.650529\pi$
$930$	2.17288e25	1.27330
$931$	8.42988e24	0.489496
$932$	−5.46986e25	−3.14732
$933$	2.28891e25	1.30507
$934$	−3.75064e25	−2.11912
$935$	−7.99473e24	−0.447615
$936$	−3.99566e25	−2.21689
$937$	−1.65163e25	−0.908083	−0.454042	−	0.890981i	$-0.650018\pi$
$937$	−1.65163e25	−0.908083	−0.454042	+	0.890981i	$0.650018\pi$
$938$	−2.84790e25	−1.55168
$939$	2.12102e25	1.14522
$940$	2.63521e25	1.41003
$941$	1.13211e25	0.600312	0.300156	−	0.953890i	$-0.402961\pi$
$941$	1.13211e25	0.600312	0.300156	+	0.953890i	$0.402961\pi$
$942$	1.31980e25	0.693544
$943$	2.35230e25	1.22502
$944$	−4.87231e24	−0.251462
$945$	−9.44317e24	−0.483000
$946$	−2.05163e24	−0.103998
$947$	2.69015e25	1.35145	0.675727	−	0.737152i	$-0.263830\pi$
$947$	2.69015e25	1.35145	0.675727	+	0.737152i	$0.263830\pi$
$948$	−7.32171e25	−3.64537
$949$	−6.65513e24	−0.328393
$950$	−8.60014e24	−0.420586
$951$	2.45090e25	1.18793
$952$	−9.24080e25	−4.43910
$953$	2.54029e25	1.20947	0.604733	−	0.796428i	$-0.293280\pi$
$953$	2.54029e25	1.20947	0.604733	+	0.796428i	$0.293280\pi$
$954$	3.54709e25	1.67383
$955$	7.78302e24	0.364015
$956$	−7.21789e25	−3.34594
$957$	−1.21817e24	−0.0559700
$958$	−5.50059e25	−2.50497
$959$	3.64763e25	1.64647
$960$	−1.03171e25	−0.461585
$961$	−1.69408e25	−0.751250
$962$	−8.48767e25	−3.73079
$963$	−8.42287e24	−0.366975
$964$	−3.63074e25	−1.56798
$965$	−5.63355e24	−0.241157
$966$	4.83466e25	2.05145
$967$	−1.75933e25	−0.739984	−0.369992	−	0.929035i	$-0.620640\pi$
$967$	−1.75933e25	−0.739984	−0.369992	+	0.929035i	$0.620640\pi$
$968$	4.78198e25	1.99373
$969$	6.82890e25	2.82227
$970$	−5.02466e25	−2.05848
$971$	−3.77277e24	−0.153214	−0.0766068	−	0.997061i	$-0.524409\pi$
$971$	−3.77277e24	−0.153214	−0.0766068	+	0.997061i	$0.524409\pi$
$972$	−6.51872e25	−2.62421
$973$	3.19596e25	1.27539
$974$	2.88854e25	1.14269
$975$	9.57493e24	0.375488
$976$	−3.59861e25	−1.39898
$977$	−8.08742e24	−0.311678	−0.155839	−	0.987782i	$-0.549808\pi$
$977$	−8.08742e24	−0.311678	−0.155839	+	0.987782i	$0.549808\pi$
$978$	−7.68912e25	−2.93762
$979$	6.31469e24	0.239166
$980$	2.56570e25	0.963352
$981$	−3.37811e25	−1.25744
$982$	−1.45147e25	−0.535625
$983$	3.50594e25	1.28262	0.641312	−	0.767280i	$-0.278390\pi$
$983$	3.50594e25	1.28262	0.641312	+	0.767280i	$0.278390\pi$
$984$	1.25642e26	4.55697
$985$	−2.37162e24	−0.0852781
$986$	−1.65303e25	−0.589287
$987$	2.59788e25	0.918171
$988$	1.10945e26	3.88752
$989$	5.40622e24	0.187813
$990$	9.31624e24	0.320879
$991$	−1.27204e25	−0.434386	−0.217193	−	0.976129i	$-0.569690\pi$
$991$	−1.27204e25	−0.434386	−0.217193	+	0.976129i	$0.569690\pi$
$992$	1.03378e25	0.350009
$993$	−6.76719e25	−2.27164
$994$	6.61438e25	2.20143
$995$	4.66229e25	1.53852
$996$	3.56613e25	1.16679
$997$	−7.57365e24	−0.245695	−0.122847	−	0.992426i	$-0.539203\pi$
$997$	−7.57365e24	−0.245695	−0.122847	+	0.992426i	$0.539203\pi$
$998$	9.71670e25	3.12543
$999$	−1.66144e25	−0.529881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.3	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-645.655 q^{2} +14883.2 q^{3} +285798. q^{4} +954733. q^{5} -9.60943e6 q^{6} +1.80737e7 q^{7} -9.98999e7 q^{8} +9.23704e7 q^{9} +O(q^{10})\)	\(q-645.655 q^{2} +14883.2 q^{3} +285798. q^{4} +954733. q^{5} -9.60943e6 q^{6} +1.80737e7 q^{7} -9.98999e7 q^{8} +9.23704e7 q^{9} -6.16428e8 q^{10} -1.63616e8 q^{11} +4.25360e9 q^{12} +4.33002e9 q^{13} -1.16694e10 q^{14} +1.42095e10 q^{15} +2.70407e10 q^{16} +5.11795e10 q^{17} -5.96394e10 q^{18} +8.96514e10 q^{19} +2.72861e11 q^{20} +2.68996e11 q^{21} +1.05639e11 q^{22} -2.78368e11 q^{23} -1.48683e12 q^{24} +1.48576e11 q^{25} -2.79570e12 q^{26} -5.47252e11 q^{27} +5.16545e12 q^{28} +5.00246e11 q^{29} -9.17444e12 q^{30} -2.36840e12 q^{31} -4.36488e12 q^{32} -2.43513e12 q^{33} -3.30443e13 q^{34} +1.72556e13 q^{35} +2.63993e13 q^{36} +3.03597e13 q^{37} -5.78839e13 q^{38} +6.44448e13 q^{39} -9.53777e13 q^{40} -8.45031e13 q^{41} -1.73678e14 q^{42} -1.94211e13 q^{43} -4.67611e13 q^{44} +8.81891e13 q^{45} +1.79730e14 q^{46} +9.65771e13 q^{47} +4.02453e14 q^{48} +9.40296e13 q^{49} -9.59287e13 q^{50} +7.61717e14 q^{51} +1.23751e15 q^{52} -5.94756e14 q^{53} +3.53336e14 q^{54} -1.56209e14 q^{55} -1.80556e15 q^{56} +1.33430e15 q^{57} -3.22987e14 q^{58} -1.80184e14 q^{59} +4.06106e15 q^{60} -1.33081e15 q^{61} +1.52917e15 q^{62} +1.66948e15 q^{63} -7.26069e14 q^{64} +4.13402e15 q^{65} +1.57226e15 q^{66} +2.44049e15 q^{67} +1.46270e16 q^{68} -4.14302e15 q^{69} -1.11412e16 q^{70} -5.66814e15 q^{71} -9.22780e15 q^{72} -1.53697e15 q^{73} -1.96019e16 q^{74} +2.21129e15 q^{75} +2.56222e16 q^{76} -2.95715e15 q^{77} -4.16091e16 q^{78} -1.72129e16 q^{79} +2.58166e16 q^{80} -2.00736e16 q^{81} +5.45599e16 q^{82} +8.38378e15 q^{83} +7.68785e16 q^{84} +4.88628e16 q^{85} +1.25393e16 q^{86} +7.44528e15 q^{87} +1.63452e16 q^{88} -3.85946e16 q^{89} -5.69397e16 q^{90} +7.82597e16 q^{91} -7.95573e16 q^{92} -3.52495e16 q^{93} -6.23555e16 q^{94} +8.55931e16 q^{95} -6.49636e16 q^{96} +8.15125e16 q^{97} -6.07107e16 q^{98} -1.51133e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 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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