LMFDB - Embedded newform 5.26.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,26,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	5.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:	$19.7998389976$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 31823342x^{3} + 3040467992x^{2} + 155755658754016x - 41401144140044416 $ x^5 - x^4 - 31823342x^3 + 3040467992x^2 + 155755658754016*x - 41401144140044416
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 5^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-5113.32$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9306.64 q^{2} +770525. q^{3} +5.30591e7 q^{4} +2.44141e8 q^{5} +7.17100e9 q^{6} +2.22916e10 q^{7} +1.81523e11 q^{8} -2.53579e11 q^{9} +O(q^{10})$	\(q+9306.64 q^{2} +770525. q^{3} +5.30591e7 q^{4} +2.44141e8 q^{5} +7.17100e9 q^{6} +2.22916e10 q^{7} +1.81523e11 q^{8} -2.53579e11 q^{9} +2.27213e12 q^{10} +1.44598e13 q^{11} +4.08834e13 q^{12} -3.60229e13 q^{13} +2.07460e14 q^{14} +1.88117e14 q^{15} -9.10020e13 q^{16} -3.16000e14 q^{17} -2.35997e15 q^{18} -1.22595e16 q^{19} +1.29539e16 q^{20} +1.71763e16 q^{21} +1.34572e17 q^{22} +2.08778e17 q^{23} +1.39868e17 q^{24} +5.96046e16 q^{25} -3.35252e17 q^{26} -8.48247e17 q^{27} +1.18277e18 q^{28} +1.80715e18 q^{29} +1.75073e18 q^{30} -5.74938e18 q^{31} -6.93781e18 q^{32} +1.11416e19 q^{33} -2.94090e18 q^{34} +5.44229e18 q^{35} -1.34547e19 q^{36} -1.65359e19 q^{37} -1.14094e20 q^{38} -2.77566e19 q^{39} +4.43170e19 q^{40} -3.56102e19 q^{41} +1.59853e20 q^{42} -2.39694e20 q^{43} +7.67223e20 q^{44} -6.19090e19 q^{45} +1.94302e21 q^{46} -1.08949e21 q^{47} -7.01193e19 q^{48} -8.44153e20 q^{49} +5.54719e20 q^{50} -2.43486e20 q^{51} -1.91134e21 q^{52} -1.50948e21 q^{53} -7.89432e21 q^{54} +3.53022e21 q^{55} +4.04643e21 q^{56} -9.44622e21 q^{57} +1.68185e22 q^{58} -8.29010e21 q^{59} +9.98129e21 q^{60} +3.43835e22 q^{61} -5.35074e22 q^{62} -5.65269e21 q^{63} -6.15142e22 q^{64} -8.79466e21 q^{65} +1.03691e23 q^{66} +1.61232e22 q^{67} -1.67667e22 q^{68} +1.60869e23 q^{69} +5.06494e22 q^{70} +2.38697e23 q^{71} -4.60303e22 q^{72} -2.91525e23 q^{73} -1.53893e23 q^{74} +4.59269e22 q^{75} -6.50475e23 q^{76} +3.22332e23 q^{77} -2.58320e23 q^{78} -3.10353e23 q^{79} -2.22173e22 q^{80} -4.38741e23 q^{81} -3.31411e23 q^{82} +1.19782e24 q^{83} +9.11356e23 q^{84} -7.71485e22 q^{85} -2.23075e24 q^{86} +1.39246e24 q^{87} +2.62478e24 q^{88} +2.58927e24 q^{89} -5.76164e23 q^{90} -8.03009e23 q^{91} +1.10776e25 q^{92} -4.43004e24 q^{93} -1.01395e25 q^{94} -2.99303e24 q^{95} -5.34576e24 q^{96} +4.37733e24 q^{97} -7.85622e24 q^{98} -3.66670e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4602 q^{2} + 626204 q^{3} + 91050260 q^{4} + 1220703125 q^{5} + 5696574760 q^{6} + 55481235808 q^{7} - 325515457080 q^{8} + 277996846465 q^{9}+O(q^{10}) $ 5 * q - 4602 * q^2 + 626204 * q^3 + 91050260 * q^4 + 1220703125 * q^5 + 5696574760 * q^6 + 55481235808 * q^7 - 325515457080 * q^8 + 277996846465 * q^9	$ 5 q - 4602 q^{2} + 626204 q^{3} + 91050260 q^{4} + 1220703125 q^{5} + 5696574760 q^{6} + 55481235808 q^{7} - 325515457080 q^{8} + 277996846465 q^{9} - 1123535156250 q^{10} - 4144958451540 q^{11} - 26370992065712 q^{12} + 111211249076614 q^{13} - 445566653510880 q^{14} + 152881835937500 q^{15} + 30\!\cdots\!80 q^{16}+ \cdots - 22\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q - 4602 * q^2 + 626204 * q^3 + 91050260 * q^4 + 1220703125 * q^5 + 5696574760 * q^6 + 55481235808 * q^7 - 325515457080 * q^8 + 277996846465 * q^9 - 1123535156250 * q^10 - 4144958451540 * q^11 - 26370992065712 * q^12 + 111211249076614 * q^13 - 445566653510880 * q^14 + 152881835937500 * q^15 + 3044988017630480 * q^16 + 3179191896192378 * q^17 + 9100952570763854 * q^18 + 13473188050195300 * q^19 + 22229067382812500 * q^20 + 76768095576060960 * q^21 + 222905601184950696 * q^22 + 409020396998250624 * q^23 + 738233252736381600 * q^24 + 298023223876953125 * q^25 + 331732385439154260 * q^26 + 1707963140919696920 * q^27 + 6745183853862681376 * q^28 + 1510518246057732150 * q^29 + 1390765322265625000 * q^30 - 7800790900476562640 * q^31 - 26275496698670595552 * q^32 - 17083981126675017392 * q^33 - 30967164186095882580 * q^34 + 13545223585937500000 * q^35 - 127816747210020977020 * q^36 - 45693640863683938082 * q^37 - 107313021439059142920 * q^38 - 28513155461010121720 * q^39 - 79471547138671875000 * q^40 + 268182713424991346610 * q^41 + 472693454958668435136 * q^42 - 54212732396046197756 * q^43 + 1026843270980203159920 * q^44 + 67870323843994140625 * q^45 + 1806261760861861731360 * q^46 + 1313959570250307870888 * q^47 + 393501331052082428224 * q^48 + 2928508402086077906685 * q^49 - 274300575256347656250 * q^50 - 1679947779014963634440 * q^51 - 1533919945088032601192 * q^52 - 1722136215100242292146 * q^53 - 16134427338310747545200 * q^54 - 1011952746958007812500 * q^55 - 39415455111791618702400 * q^56 - 9510351594401743758160 * q^57 + 7814667131698315285620 * q^58 - 16547203533880040421300 * q^59 - 6438230484792968750000 * q^60 + 11587268554089248839510 * q^61 + 21314291783865447926496 * q^62 + 32595050340385317746784 * q^63 + 83981823170089659652160 * q^64 + 27151183856595214843750 * q^65 + 107686245599040557757920 * q^66 + 186273232047241909753228 * q^67 + 48790715540647305709416 * q^68 + 205103851249003209571680 * q^69 - 108780921267304687500000 * q^70 + 179635129178416728944760 * q^71 + 252302332499928005189160 * q^72 - 471333406608130631390126 * q^73 - 888672199125830235839580 * q^74 + 37324666976928710937500 * q^75 - 1191799860770260438242800 * q^76 - 286067188114809482097984 * q^77 - 1025178605609234961148112 * q^78 + 360282849255851991934000 * q^79 + 743405277741816406250000 * q^80 + 103584508446589901468605 * q^81 - 2050449668847875948936004 * q^82 + 1759227952818659145519084 * q^83 - 3837881595316615167665280 * q^84 + 776169896531342285156250 * q^85 - 565842386421331097744040 * q^86 + 8705381585373786685282760 * q^87 + 720634350501343968831840 * q^88 + 4092128669145981513024450 * q^89 + 2221912248721644042968750 * q^90 + 11972573281108721260967360 * q^91 + 6613215336376724900082528 * q^92 + 7392084747484240267531008 * q^93 - 17112742333122902932304880 * q^94 + 3289352551317211914062500 * q^95 - 10376386162767776801453440 * q^96 + 28613737566457196779163338 * q^97 - 56860534671603836155246314 * q^98 - 22864619024884333176273220 * 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 $

$2$	9306.64	1.60664	0.803319	−	0.595549i	$-0.203066\pi$
$2$	9306.64	1.60664	0.803319	+	0.595549i	$0.203066\pi$
$3$	770525.	0.837088	0.418544	−	0.908196i	$-0.362541\pi$
$3$	770525.	0.837088	0.418544	+	0.908196i	$0.362541\pi$
$4$	5.30591e7	1.58128
$5$	2.44141e8	0.447214
$5$	2.44141e8	0.447214
$6$	7.17100e9	1.34490
$7$	2.22916e10	0.608718	0.304359	−	0.952557i	$-0.401558\pi$
$7$	2.22916e10	0.608718	0.304359	+	0.952557i	$0.401558\pi$
$8$	1.81523e11	0.933912
$9$	−2.53579e11	−0.299283
$10$	2.27213e12	0.718510
$11$	1.44598e13	1.38916	0.694582	−	0.719414i	$-0.255589\pi$
$11$	1.44598e13	1.38916	0.694582	+	0.719414i	$0.255589\pi$
$12$	4.08834e13	1.32367
$13$	−3.60229e13	−0.428832	−0.214416	−	0.976742i	$-0.568785\pi$
$13$	−3.60229e13	−0.428832	−0.214416	+	0.976742i	$0.568785\pi$
$14$	2.07460e14	0.977989
$15$	1.88117e14	0.374357
$16$	−9.10020e13	−0.0808260
$17$	−3.16000e14	−0.131546	−0.0657728	−	0.997835i	$-0.520951\pi$
$17$	−3.16000e14	−0.131546	−0.0657728	+	0.997835i	$0.520951\pi$
$18$	−2.35997e15	−0.480839
$19$	−1.22595e16	−1.27072	−0.635362	−	0.772214i	$-0.719149\pi$
$19$	−1.22595e16	−1.27072	−0.635362	+	0.772214i	$0.719149\pi$
$20$	1.29539e16	0.707171
$21$	1.71763e16	0.509551
$22$	1.34572e17	2.23188
$23$	2.08778e17	1.98649	0.993245	−	0.116037i	$-0.0370190\pi$
$23$	2.08778e17	1.98649	0.993245	+	0.116037i	$0.0370190\pi$
$24$	1.39868e17	0.781767
$25$	5.96046e16	0.200000
$26$	−3.35252e17	−0.688977
$27$	−8.48247e17	−1.08761
$28$	1.18277e18	0.962555
$29$	1.80715e18	0.948463	0.474231	−	0.880400i	$-0.342726\pi$
$29$	1.80715e18	0.948463	0.474231	+	0.880400i	$0.342726\pi$
$30$	1.75073e18	0.601456
$31$	−5.74938e18	−1.31099	−0.655496	−	0.755199i	$-0.727540\pi$
$31$	−5.74938e18	−1.31099	−0.655496	+	0.755199i	$0.727540\pi$
$32$	−6.93781e18	−1.06377
$33$	1.11416e19	1.16285
$34$	−2.94090e18	−0.211346
$35$	5.44229e18	0.272227
$36$	−1.34547e19	−0.473251
$37$	−1.65359e19	−0.412958	−0.206479	−	0.978451i	$-0.566200\pi$
$37$	−1.65359e19	−0.412958	−0.206479	+	0.978451i	$0.566200\pi$
$38$	−1.14094e20	−2.04159
$39$	−2.77566e19	−0.358970
$40$	4.43170e19	0.417658
$41$	−3.56102e19	−0.246477	−0.123239	−	0.992377i	$-0.539328\pi$
$41$	−3.56102e19	−0.246477	−0.123239	+	0.992377i	$0.539328\pi$
$42$	1.59853e20	0.818663
$43$	−2.39694e20	−0.914749	−0.457374	−	0.889274i	$-0.651210\pi$
$43$	−2.39694e20	−0.914749	−0.457374	+	0.889274i	$0.651210\pi$
$44$	7.67223e20	2.19666
$45$	−6.19090e19	−0.133843
$46$	1.94302e21	3.19157
$47$	−1.08949e21	−1.36773	−0.683867	−	0.729606i	$-0.739703\pi$
$47$	−1.08949e21	−1.36773	−0.683867	+	0.729606i	$0.739703\pi$
$48$	−7.01193e19	−0.0676585
$49$	−8.44153e20	−0.629463
$50$	5.54719e20	0.321327
$51$	−2.43486e20	−0.110115
$52$	−1.91134e21	−0.678105
$53$	−1.50948e21	−0.422063	−0.211032	−	0.977479i	$-0.567682\pi$
$53$	−1.50948e21	−0.422063	−0.211032	+	0.977479i	$0.567682\pi$
$54$	−7.89432e21	−1.74740
$55$	3.53022e21	0.621253
$56$	4.04643e21	0.568489
$57$	−9.44622e21	−1.06371
$58$	1.68185e22	1.52384
$59$	−8.29010e21	−0.606610	−0.303305	−	0.952893i	$-0.598090\pi$
$59$	−8.29010e21	−0.606610	−0.303305	+	0.952893i	$0.598090\pi$
$60$	9.98129e21	0.591965
$61$	3.43835e22	1.65854	0.829272	−	0.558846i	$-0.188756\pi$
$61$	3.43835e22	1.65854	0.829272	+	0.558846i	$0.188756\pi$
$62$	−5.35074e22	−2.10629
$63$	−5.65269e21	−0.182179
$64$	−6.15142e22	−1.62827
$65$	−8.79466e21	−0.191779
$66$	1.03691e23	1.86828
$67$	1.61232e22	0.240723	0.120361	−	0.992730i	$-0.461595\pi$
$67$	1.61232e22	0.240723	0.120361	+	0.992730i	$0.461595\pi$
$68$	−1.67667e22	−0.208011
$69$	1.60869e23	1.66287
$70$	5.06494e22	0.437370
$71$	2.38697e23	1.72630	0.863151	−	0.504946i	$-0.168488\pi$
$71$	2.38697e23	1.72630	0.863151	+	0.504946i	$0.168488\pi$
$72$	−4.60303e22	−0.279504
$73$	−2.91525e23	−1.48984	−0.744921	−	0.667152i	$-0.767513\pi$
$73$	−2.91525e23	−1.48984	−0.744921	+	0.667152i	$0.767513\pi$
$74$	−1.53893e23	−0.663473
$75$	4.59269e22	0.167418
$76$	−6.50475e23	−2.00937
$77$	3.22332e23	0.845609
$78$	−2.58320e23	−0.576735
$79$	−3.10353e23	−0.590905	−0.295453	−	0.955357i	$-0.595470\pi$
$79$	−3.10353e23	−0.590905	−0.295453	+	0.955357i	$0.595470\pi$
$80$	−2.22173e22	−0.0361465
$81$	−4.38741e23	−0.611147
$82$	−3.31411e23	−0.395999
$83$	1.19782e24	1.23003	0.615013	−	0.788517i	$-0.289151\pi$
$83$	1.19782e24	1.23003	0.615013	+	0.788517i	$0.289151\pi$
$84$	9.11356e23	0.805744
$85$	−7.71485e22	−0.0588290
$86$	−2.23075e24	−1.46967
$87$	1.39246e24	0.793947
$88$	2.62478e24	1.29736
$89$	2.58927e24	1.11122	0.555612	−	0.831441i	$-0.312484\pi$
$89$	2.58927e24	1.11122	0.555612	+	0.831441i	$0.312484\pi$
$90$	−5.76164e23	−0.215038
$91$	−8.03009e23	−0.261038
$92$	1.10776e25	3.14120
$93$	−4.43004e24	−1.09742
$94$	−1.01395e25	−2.19745
$95$	−2.99303e24	−0.568285
$96$	−5.34576e24	−0.890469
$97$	4.37733e24	0.640564	0.320282	−	0.947322i	$-0.396222\pi$
$97$	4.37733e24	0.640564	0.320282	+	0.947322i	$0.396222\pi$
$98$	−7.85622e24	−1.01132
$99$	−3.66670e24	−0.415753
$100$	3.16257e24	0.316257
$101$	1.78402e25	1.57537	0.787687	−	0.616076i	$-0.211278\pi$
$101$	1.78402e25	1.57537	0.787687	+	0.616076i	$0.211278\pi$
$102$	−2.26604e24	−0.176915
$103$	7.35489e24	0.508289	0.254145	−	0.967166i	$-0.418206\pi$
$103$	7.35489e24	0.508289	0.254145	+	0.967166i	$0.418206\pi$
$104$	−6.53897e24	−0.400491
$105$	4.19342e24	0.227878
$106$	−1.40481e25	−0.678103
$107$	5.61984e23	0.0241227	0.0120614	−	0.999927i	$-0.496161\pi$
$107$	5.61984e23	0.0241227	0.0120614	+	0.999927i	$0.496161\pi$
$108$	−4.50072e25	−1.71983
$109$	2.51574e24	0.0856710	0.0428355	−	0.999082i	$-0.486361\pi$
$109$	2.51574e24	0.0856710	0.0428355	+	0.999082i	$0.486361\pi$
$110$	3.28545e25	0.998128
$111$	−1.27413e25	−0.345682
$112$	−2.02858e24	−0.0492002
$113$	6.47501e25	1.40527	0.702635	−	0.711550i	$-0.252007\pi$
$113$	6.47501e25	1.40527	0.702635	+	0.711550i	$0.252007\pi$
$114$	−8.79126e25	−1.70899
$115$	5.09711e25	0.888385
$116$	9.58859e25	1.49979
$117$	9.13466e24	0.128342
$118$	−7.71530e25	−0.974603
$119$	−7.04416e24	−0.0800741
$120$	3.41474e25	0.349617
$121$	1.00738e26	0.929775
$122$	3.19995e26	2.66468
$123$	−2.74386e25	−0.206323
$124$	−3.05057e26	−2.07305
$125$	1.45519e25	0.0894427
$126$	−5.26075e25	−0.292696
$127$	−2.48811e26	−1.25408	−0.627038	−	0.778989i	$-0.715733\pi$
$127$	−2.48811e26	−1.25408	−0.627038	+	0.778989i	$0.715733\pi$
$128$	−3.39696e26	−1.55226
$129$	−1.84690e26	−0.765726
$130$	−8.18487e25	−0.308120
$131$	−2.48984e26	−0.851688	−0.425844	−	0.904797i	$-0.640023\pi$
$131$	−2.48984e26	−0.851688	−0.425844	+	0.904797i	$0.640023\pi$
$132$	5.91165e26	1.83880
$133$	−2.73283e26	−0.773512
$134$	1.50053e26	0.386754
$135$	−2.07091e26	−0.486396
$136$	−5.73612e25	−0.122852
$137$	4.56320e26	0.891789	0.445895	−	0.895085i	$-0.352886\pi$
$137$	4.56320e26	0.891789	0.445895	+	0.895085i	$0.352886\pi$
$138$	1.49715e27	2.67163
$139$	−2.14159e26	−0.349181	−0.174590	−	0.984641i	$-0.555860\pi$
$139$	−2.14159e26	−0.349181	−0.174590	+	0.984641i	$0.555860\pi$
$140$	2.88763e26	0.430468
$141$	−8.39483e26	−1.14492
$142$	2.22146e27	2.77354
$143$	−5.20884e26	−0.595717
$144$	2.30762e25	0.0241898
$145$	4.41200e26	0.424165
$146$	−2.71312e27	−2.39364
$147$	−6.50441e26	−0.526916
$148$	−8.77378e26	−0.653003
$149$	1.08907e25	0.00745119	0.00372559	−	0.999993i	$-0.498814\pi$
$149$	1.08907e25	0.00745119	0.00372559	+	0.999993i	$0.498814\pi$
$150$	4.27425e26	0.268979
$151$	3.06427e27	1.77466	0.887330	−	0.461134i	$-0.152557\pi$
$151$	3.06427e27	1.77466	0.887330	+	0.461134i	$0.152557\pi$
$152$	−2.22537e27	−1.18674
$153$	8.01311e25	0.0393694
$154$	2.99983e27	1.35859
$155$	−1.40366e27	−0.586293
$156$	−1.47274e27	−0.567633
$157$	−4.87322e26	−0.173409	−0.0867043	−	0.996234i	$-0.527634\pi$
$157$	−4.87322e26	−0.173409	−0.0867043	+	0.996234i	$0.527634\pi$
$158$	−2.88835e27	−0.949370
$159$	−1.16309e27	−0.353304
$160$	−1.69380e27	−0.475732
$161$	4.65399e27	1.20921
$162$	−4.08320e27	−0.981891
$163$	1.64678e27	0.366682	0.183341	−	0.983049i	$-0.441309\pi$
$163$	1.64678e27	0.366682	0.183341	+	0.983049i	$0.441309\pi$
$164$	−1.88945e27	−0.389750
$165$	2.72013e27	0.520044
$166$	1.11476e28	1.97620
$167$	−4.79708e27	−0.788898	−0.394449	−	0.918918i	$-0.629065\pi$
$167$	−4.79708e27	−0.788898	−0.394449	+	0.918918i	$0.629065\pi$
$168$	3.11788e27	0.475875
$169$	−5.75876e27	−0.816103
$170$	−7.17994e26	−0.0945168
$171$	3.10874e27	0.380306
$172$	−1.27180e28	−1.44648
$173$	7.52503e25	0.00796034	0.00398017	−	0.999992i	$-0.498733\pi$
$173$	7.52503e25	0.00796034	0.00398017	+	0.999992i	$0.498733\pi$
$174$	1.29591e28	1.27558
$175$	1.32868e27	0.121744
$176$	−1.31587e27	−0.112281
$177$	−6.38774e27	−0.507787
$178$	2.40974e28	1.78534
$179$	1.80474e27	0.124667	0.0623336	−	0.998055i	$-0.480146\pi$
$179$	1.80474e27	0.124667	0.0623336	+	0.998055i	$0.480146\pi$
$180$	−3.28483e27	−0.211644
$181$	−2.03951e27	−0.122615	−0.0613075	−	0.998119i	$-0.519527\pi$
$181$	−2.03951e27	−0.122615	−0.0613075	+	0.998119i	$0.519527\pi$
$182$	−7.47331e27	−0.419393
$183$	2.64933e28	1.38835
$184$	3.78979e28	1.85521
$185$	−4.03708e27	−0.184680
$186$	−4.12288e28	−1.76315
$187$	−4.56930e27	−0.182738
$188$	−5.78076e28	−2.16278
$189$	−1.89088e28	−0.662051
$190$	−2.78551e28	−0.913028
$191$	5.41856e27	0.166329	0.0831643	−	0.996536i	$-0.473497\pi$
$191$	5.41856e27	0.166329	0.0831643	+	0.996536i	$0.473497\pi$
$192$	−4.73982e28	−1.36300
$193$	−5.98769e27	−0.161359	−0.0806795	−	0.996740i	$-0.525709\pi$
$193$	−5.98769e27	−0.161359	−0.0806795	+	0.996740i	$0.525709\pi$
$194$	4.07382e28	1.02915
$195$	−6.77651e27	−0.160536
$196$	−4.47899e28	−0.995359
$197$	7.60954e28	1.58683	0.793415	−	0.608681i	$-0.208301\pi$
$197$	7.60954e28	1.58683	0.793415	+	0.608681i	$0.208301\pi$
$198$	−3.41247e28	−0.667965
$199$	7.23513e28	1.32979	0.664895	−	0.746937i	$-0.268476\pi$
$199$	7.23513e28	1.32979	0.664895	+	0.746937i	$0.268476\pi$
$200$	1.08196e28	0.186782
$201$	1.24234e28	0.201506
$202$	1.66033e29	2.53105
$203$	4.02844e28	0.577346
$204$	−1.29192e28	−0.174123
$205$	−8.69390e27	−0.110228
$206$	6.84493e28	0.816636
$207$	−5.29417e28	−0.594523
$208$	3.27816e27	0.0346607
$209$	−1.77269e29	−1.76524
$210$	3.90267e28	0.366117
$211$	−2.76942e27	−0.0244826	−0.0122413	−	0.999925i	$-0.503897\pi$
$211$	−2.76942e27	−0.0244826	−0.0122413	+	0.999925i	$0.503897\pi$
$212$	−8.00914e28	−0.667402
$213$	1.83922e29	1.44507
$214$	5.23018e27	0.0387565
$215$	−5.85191e28	−0.409088
$216$	−1.53976e29	−1.01574
$217$	−1.28163e29	−0.798024
$218$	2.34130e28	0.137642
$219$	−2.24628e29	−1.24713
$220$	1.87310e29	0.982377
$221$	1.13833e28	0.0564109
$222$	−1.18579e29	−0.555386
$223$	−1.39341e29	−0.616977	−0.308489	−	0.951228i	$-0.599823\pi$
$223$	−1.39341e29	−0.616977	−0.308489	+	0.951228i	$0.599823\pi$
$224$	−1.54655e29	−0.647536
$225$	−1.51145e28	−0.0598566
$226$	6.02606e29	2.25776
$227$	4.12894e29	1.46391	0.731957	−	0.681351i	$-0.238607\pi$
$227$	4.12894e29	1.46391	0.731957	+	0.681351i	$0.238607\pi$
$228$	−5.01208e29	−1.68202
$229$	−2.70065e29	−0.858075	−0.429038	−	0.903287i	$-0.641147\pi$
$229$	−2.70065e29	−0.858075	−0.429038	+	0.903287i	$0.641147\pi$
$230$	4.74370e29	1.42731
$231$	2.48365e29	0.707849
$232$	3.28039e29	0.885780
$233$	−3.10072e29	−0.793439	−0.396720	−	0.917940i	$-0.629851\pi$
$233$	−3.10072e29	−0.793439	−0.396720	+	0.917940i	$0.629851\pi$
$234$	8.50130e28	0.206199
$235$	−2.65990e29	−0.611670
$236$	−4.39865e29	−0.959223
$237$	−2.39135e29	−0.494640
$238$	−6.55574e28	−0.128650
$239$	−8.54263e29	−1.59081	−0.795404	−	0.606080i	$-0.792741\pi$
$239$	−8.54263e29	−1.59081	−0.795404	+	0.606080i	$0.792741\pi$
$240$	−1.71190e28	−0.0302578
$241$	2.29408e29	0.384943	0.192471	−	0.981303i	$-0.438350\pi$
$241$	2.29408e29	0.384943	0.192471	+	0.981303i	$0.438350\pi$
$242$	9.37536e29	1.49381
$243$	3.80649e29	0.576031
$244$	1.82436e30	2.62263
$245$	−2.06092e29	−0.281504
$246$	−2.55361e29	−0.331486
$247$	4.41621e29	0.544927
$248$	−1.04364e30	−1.22435
$249$	9.22948e29	1.02964
$250$	1.35429e29	0.143702
$251$	−1.46552e30	−1.47934	−0.739671	−	0.672968i	$-0.765019\pi$
$251$	−1.46552e30	−1.47934	−0.739671	+	0.672968i	$0.765019\pi$
$252$	−2.99926e29	−0.288077
$253$	3.01888e30	2.75956
$254$	−2.31560e30	−2.01484
$255$	−5.94449e28	−0.0492450
$256$	−1.09735e30	−0.865658
$257$	5.30424e29	0.398528	0.199264	−	0.979946i	$-0.436145\pi$
$257$	5.30424e29	0.398528	0.199264	+	0.979946i	$0.436145\pi$
$258$	−1.71885e30	−1.23024
$259$	−3.68611e29	−0.251375
$260$	−4.66636e29	−0.303258
$261$	−4.58257e29	−0.283859
$262$	−2.31721e30	−1.36835
$263$	1.80670e30	1.01728	0.508639	−	0.860980i	$-0.330149\pi$
$263$	1.80670e30	1.01728	0.508639	+	0.860980i	$0.330149\pi$
$264$	2.02246e30	1.08600
$265$	−3.68524e29	−0.188753
$266$	−2.54335e30	−1.24275
$267$	1.99510e30	0.930193
$268$	8.55484e29	0.380651
$269$	−2.71112e30	−1.15145	−0.575726	−	0.817643i	$-0.695281\pi$
$269$	−2.71112e30	−1.15145	−0.575726	+	0.817643i	$0.695281\pi$
$270$	−1.92733e30	−0.781462
$271$	1.67482e30	0.648412	0.324206	−	0.945986i	$-0.394903\pi$
$271$	1.67482e30	0.648412	0.324206	+	0.945986i	$0.394903\pi$
$272$	2.87567e28	0.0106323
$273$	−6.18739e29	−0.218511
$274$	4.24680e30	1.43278
$275$	8.61871e29	0.277833
$276$	8.53554e30	2.62946
$277$	−3.03099e30	−0.892456	−0.446228	−	0.894919i	$-0.647233\pi$
$277$	−3.03099e30	−0.892456	−0.446228	+	0.894919i	$0.647233\pi$
$278$	−1.99310e30	−0.561007
$279$	1.45792e30	0.392357
$280$	9.87898e29	0.254236
$281$	6.28827e30	1.54775	0.773877	−	0.633336i	$-0.218315\pi$
$281$	6.28827e30	1.54775	0.773877	+	0.633336i	$0.218315\pi$
$282$	−7.81277e30	−1.83946
$283$	8.12659e27	0.00183053	0.000915267	−	1.00000i	$-0.499709\pi$
$283$	8.12659e27	0.00183053	0.000915267		1.00000i	$0.499709\pi$
$284$	1.26650e31	2.72977
$285$	−2.30621e30	−0.475705
$286$	−4.84768e30	−0.957102
$287$	−7.93809e29	−0.150035
$288$	1.75928e30	0.318368
$289$	−5.67077e30	−0.982696
$290$	4.10609e30	0.681480
$291$	3.37284e30	0.536209
$292$	−1.54681e31	−2.35586
$293$	−5.72991e30	−0.836185	−0.418093	−	0.908404i	$-0.637301\pi$
$293$	−5.72991e30	−0.836185	−0.418093	+	0.908404i	$0.637301\pi$
$294$	−6.05342e30	−0.846563
$295$	−2.02395e30	−0.271284
$296$	−3.00163e30	−0.385666
$297$	−1.22655e31	−1.51087
$298$	1.01355e29	0.0119714
$299$	−7.52078e30	−0.851870
$300$	2.43684e30	0.264735
$301$	−5.34317e30	−0.556824
$302$	2.85181e31	2.85124
$303$	1.37464e31	1.31873
$304$	1.11563e30	0.102708
$305$	8.39440e30	0.741723
$306$	7.45751e29	0.0632523
$307$	6.08937e30	0.495841	0.247921	−	0.968780i	$-0.420253\pi$
$307$	6.08937e30	0.495841	0.247921	+	0.968780i	$0.420253\pi$
$308$	1.71026e31	1.33715
$309$	5.66713e30	0.425483
$310$	−1.30633e31	−0.941960
$311$	−2.33429e30	−0.161678	−0.0808388	−	0.996727i	$-0.525760\pi$
$311$	−2.33429e30	−0.161678	−0.0808388	+	0.996727i	$0.525760\pi$
$312$	−5.03844e30	−0.335246
$313$	−2.02217e31	−1.29275	−0.646373	−	0.763022i	$-0.723715\pi$
$313$	−2.02217e31	−1.29275	−0.646373	+	0.763022i	$0.723715\pi$
$314$	−4.53533e30	−0.278605
$315$	−1.38005e30	−0.0814729
$316$	−1.64671e31	−0.934389
$317$	9.53583e30	0.520137	0.260069	−	0.965590i	$-0.416255\pi$
$317$	9.53583e30	0.520137	0.260069	+	0.965590i	$0.416255\pi$
$318$	−1.08245e31	−0.567632
$319$	2.61311e31	1.31757
$320$	−1.50181e31	−0.728183
$321$	4.33023e29	0.0201929
$322$	4.33130e31	1.94276
$323$	3.87399e30	0.167158
$324$	−2.32792e31	−0.966396
$325$	−2.14713e30	−0.0857663
$326$	1.53259e31	0.589125
$327$	1.93844e30	0.0717142
$328$	−6.46406e30	−0.230188
$329$	−2.42866e31	−0.832565
$330$	2.53152e31	0.835521
$331$	−1.42193e31	−0.451884	−0.225942	−	0.974141i	$-0.572546\pi$
$331$	−1.42193e31	−0.451884	−0.225942	+	0.974141i	$0.572546\pi$
$332$	6.35550e31	1.94502
$333$	4.19315e30	0.123591
$334$	−4.46447e31	−1.26747
$335$	3.93634e30	0.107654
$336$	−1.56307e30	−0.0411849
$337$	−1.41008e30	−0.0357988	−0.0178994	−	0.999840i	$-0.505698\pi$
$337$	−1.41008e30	−0.0357988	−0.0178994	+	0.999840i	$0.505698\pi$
$338$	−5.35947e31	−1.31118
$339$	4.98916e31	1.17634
$340$	−4.09343e30	−0.0930253
$341$	−8.31348e31	−1.82118
$342$	2.89319e31	0.611014
$343$	−4.87121e31	−0.991883
$344$	−4.35099e31	−0.854295
$345$	3.92746e31	0.743657
$346$	7.00327e29	0.0127894
$347$	−8.19556e31	−1.44364	−0.721822	−	0.692079i	$-0.756695\pi$
$347$	−8.19556e31	−1.44364	−0.721822	+	0.692079i	$0.756695\pi$
$348$	7.38825e31	1.25546
$349$	2.09125e30	0.0342837	0.0171418	−	0.999853i	$-0.494543\pi$
$349$	2.09125e30	0.0342837	0.0171418	+	0.999853i	$0.494543\pi$
$350$	1.23656e31	0.195598
$351$	3.05563e31	0.466404
$352$	−1.00319e32	−1.47775
$353$	1.15479e31	0.164180	0.0820898	−	0.996625i	$-0.473841\pi$
$353$	1.15479e31	0.164180	0.0820898	+	0.996625i	$0.473841\pi$
$354$	−5.94483e31	−0.815829
$355$	5.82755e31	0.772026
$356$	1.37384e32	1.75716
$357$	−5.42770e30	−0.0670291
$358$	1.67961e31	0.200295
$359$	6.94940e31	0.800325	0.400163	−	0.916444i	$-0.368954\pi$
$359$	6.94940e31	0.800325	0.400163	+	0.916444i	$0.368954\pi$
$360$	−1.12379e31	−0.124998
$361$	5.72178e31	0.614739
$362$	−1.89810e31	−0.196998
$363$	7.76215e31	0.778304
$364$	−4.26069e31	−0.412774
$365$	−7.11732e31	−0.666278
$366$	2.46564e32	2.23057
$367$	2.05325e32	1.79522	0.897608	−	0.440794i	$-0.145303\pi$
$367$	2.05325e32	1.79522	0.897608	+	0.440794i	$0.145303\pi$
$368$	−1.89992e31	−0.160560
$369$	9.03001e30	0.0737664
$370$	−3.75716e31	−0.296714
$371$	−3.36487e31	−0.256918
$372$	−2.35054e32	−1.73533
$373$	−1.09700e32	−0.783153	−0.391577	−	0.920146i	$-0.628070\pi$
$373$	−1.09700e32	−0.783153	−0.391577	+	0.920146i	$0.628070\pi$
$374$	−4.25248e31	−0.293594
$375$	1.12126e31	0.0748715
$376$	−1.97768e32	−1.27734
$377$	−6.50990e31	−0.406731
$378$	−1.75977e32	−1.06368
$379$	1.74988e32	1.02333	0.511667	−	0.859184i	$-0.329028\pi$
$379$	1.74988e32	1.02333	0.511667	+	0.859184i	$0.329028\pi$
$380$	−1.58807e32	−0.898620
$381$	−1.91716e32	−1.04977
$382$	5.04286e31	0.267230
$383$	1.47173e32	0.754819	0.377409	−	0.926047i	$-0.376815\pi$
$383$	1.47173e32	0.754819	0.377409	+	0.926047i	$0.376815\pi$
$384$	−2.61744e32	−1.29938
$385$	7.86943e31	0.378168
$386$	−5.57253e31	−0.259245
$387$	6.07815e31	0.273769
$388$	2.32257e32	1.01291
$389$	2.96744e32	1.25318	0.626588	−	0.779351i	$-0.284451\pi$
$389$	2.96744e32	1.25318	0.626588	+	0.779351i	$0.284451\pi$
$390$	−6.30665e31	−0.257924
$391$	−6.59739e31	−0.261314
$392$	−1.53233e32	−0.587863
$393$	−1.91849e32	−0.712938
$394$	7.08192e32	2.54946
$395$	−7.57699e31	−0.264261
$396$	−1.94552e32	−0.657424
$397$	−2.26952e32	−0.743109	−0.371554	−	0.928411i	$-0.621175\pi$
$397$	−2.26952e32	−0.743109	−0.371554	+	0.928411i	$0.621175\pi$
$398$	6.73348e32	2.13649
$399$	−2.10572e32	−0.647498
$400$	−5.42414e30	−0.0161652
$401$	−6.07194e32	−1.75397	−0.876986	−	0.480515i	$-0.840450\pi$
$401$	−6.07194e32	−1.75397	−0.876986	+	0.480515i	$0.840450\pi$
$402$	1.15620e32	0.323747
$403$	2.07109e32	0.562195
$404$	9.46587e32	2.49111
$405$	−1.07114e32	−0.273313
$406$	3.74912e32	0.927586
$407$	−2.39105e32	−0.573666
$408$	−4.41983e31	−0.102838
$409$	−3.27865e32	−0.739867	−0.369934	−	0.929058i	$-0.620620\pi$
$409$	−3.27865e32	−0.739867	−0.369934	+	0.929058i	$0.620620\pi$
$410$	−8.09110e31	−0.177096
$411$	3.51606e32	0.746507
$412$	3.90244e32	0.803749
$413$	−1.84800e32	−0.369255
$414$	−4.92709e32	−0.955183
$415$	2.92436e32	0.550084
$416$	2.49920e32	0.456178
$417$	−1.65015e32	−0.292295
$418$	−1.64978e33	−2.83611
$419$	−3.95380e32	−0.659689	−0.329844	−	0.944035i	$-0.606996\pi$
$419$	−3.95380e32	−0.659689	−0.329844	+	0.944035i	$0.606996\pi$
$420$	2.22499e32	0.360340
$421$	−7.69458e32	−1.20965	−0.604823	−	0.796360i	$-0.706756\pi$
$421$	−7.69458e32	−1.20965	−0.604823	+	0.796360i	$0.706756\pi$
$422$	−2.57740e31	−0.0393347
$423$	2.76273e32	0.409340
$424$	−2.74004e32	−0.394170
$425$	−1.88351e31	−0.0263091
$426$	1.71169e33	2.32170
$427$	7.66463e32	1.00958
$428$	2.98183e31	0.0381449
$429$	−4.01354e32	−0.498668
$430$	−5.44616e32	−0.657256
$431$	1.10896e33	1.30002	0.650010	−	0.759925i	$-0.274765\pi$
$431$	1.10896e33	1.30002	0.650010	+	0.759925i	$0.274765\pi$
$432$	7.71921e31	0.0879075
$433$	1.57788e33	1.74572	0.872862	−	0.487967i	$-0.162261\pi$
$433$	1.57788e33	1.74572	0.872862	+	0.487967i	$0.162261\pi$
$434$	−1.19277e33	−1.28213
$435$	3.39956e32	0.355064
$436$	1.33483e32	0.135470
$437$	−2.55950e33	−2.52428
$438$	−2.09053e33	−2.00369
$439$	−1.65106e32	−0.153800	−0.0769001	−	0.997039i	$-0.524502\pi$
$439$	−1.65106e32	−0.153800	−0.0769001	+	0.997039i	$0.524502\pi$
$440$	6.40815e32	0.580195
$441$	2.14059e32	0.188388
$442$	1.05940e32	0.0906319
$443$	1.71502e33	1.42634	0.713170	−	0.700992i	$-0.247259\pi$
$443$	1.71502e33	1.42634	0.713170	+	0.700992i	$0.247259\pi$
$444$	−6.76042e32	−0.546621
$445$	6.32146e32	0.496955
$446$	−1.29680e33	−0.991259
$447$	8.39152e30	0.00623730
$448$	−1.37125e33	−0.991155
$449$	−2.12622e33	−1.49461	−0.747305	−	0.664481i	$-0.768653\pi$
$449$	−2.12622e33	−1.49461	−0.747305	+	0.664481i	$0.768653\pi$
$450$	−1.40665e32	−0.0961679
$451$	−5.14916e32	−0.342397
$452$	3.43558e33	2.22213
$453$	2.36110e33	1.48555
$454$	3.84266e33	2.35198
$455$	−1.96047e32	−0.116740
$456$	−1.71470e33	−0.993410
$457$	3.00610e33	1.69454	0.847268	−	0.531165i	$-0.178246\pi$
$457$	3.00610e33	1.69454	0.847268	+	0.531165i	$0.178246\pi$
$458$	−2.51340e33	−1.37862
$459$	2.68046e32	0.143071
$460$	2.70448e33	1.40479
$461$	2.62147e32	0.132521	0.0662604	−	0.997802i	$-0.478893\pi$
$461$	2.62147e32	0.132521	0.0662604	+	0.997802i	$0.478893\pi$
$462$	2.31144e33	1.13726
$463$	1.49836e33	0.717552	0.358776	−	0.933424i	$-0.383194\pi$
$463$	1.49836e33	0.717552	0.358776	+	0.933424i	$0.383194\pi$
$464$	−1.64455e32	−0.0766604
$465$	−1.08155e33	−0.490779
$466$	−2.88573e33	−1.27477
$467$	−3.26675e32	−0.140493	−0.0702464	−	0.997530i	$-0.522379\pi$
$467$	−3.26675e32	−0.140493	−0.0702464	+	0.997530i	$0.522379\pi$
$468$	4.84677e32	0.202945
$469$	3.59413e32	0.146532
$470$	−2.47547e33	−0.982731
$471$	−3.75494e32	−0.145158
$472$	−1.50484e33	−0.566521
$473$	−3.46593e33	−1.27074
$474$	−2.22554e33	−0.794707
$475$	−7.30721e32	−0.254145
$476$	−3.73757e32	−0.126620
$477$	3.82772e32	0.126316
$478$	−7.95031e33	−2.55585
$479$	−2.81655e33	−0.882110	−0.441055	−	0.897480i	$-0.645396\pi$
$479$	−2.81655e33	−0.882110	−0.441055	+	0.897480i	$0.645396\pi$
$480$	−1.30512e33	−0.398230
$481$	5.95670e32	0.177089
$482$	2.13502e33	0.618463
$483$	3.58602e33	1.01222
$484$	5.34509e33	1.47024
$485$	1.06868e33	0.286469
$486$	3.54256e33	0.925473
$487$	−4.45254e33	−1.13369	−0.566846	−	0.823824i	$-0.691837\pi$
$487$	−4.45254e33	−1.13369	−0.566846	+	0.823824i	$0.691837\pi$
$488$	6.24138e33	1.54893
$489$	1.26888e33	0.306945
$490$	−1.91802e33	−0.452275
$491$	−4.83718e33	−1.11192	−0.555960	−	0.831209i	$-0.687649\pi$
$491$	−4.83718e33	−1.11192	−0.555960	+	0.831209i	$0.687649\pi$
$492$	−1.45587e33	−0.326255
$493$	−5.71062e32	−0.124766
$494$	4.11001e33	0.875500
$495$	−8.95191e32	−0.185930
$496$	5.23205e32	0.105962
$497$	5.32093e33	1.05083
$498$	8.58954e33	1.65426
$499$	4.14549e32	0.0778608	0.0389304	−	0.999242i	$-0.487605\pi$
$499$	4.14549e32	0.0778608	0.0389304	+	0.999242i	$0.487605\pi$
$500$	7.72111e32	0.141434
$501$	−3.69627e33	−0.660378
$502$	−1.36390e34	−2.37677
$503$	9.27814e33	1.57711	0.788553	−	0.614967i	$-0.210830\pi$
$503$	9.27814e33	1.57711	0.788553	+	0.614967i	$0.210830\pi$
$504$	−1.02609e33	−0.170139
$505$	4.35553e33	0.704529
$506$	2.80956e34	4.43361
$507$	−4.43727e33	−0.683151
$508$	−1.32017e34	−1.98305
$509$	−8.72441e33	−1.27869	−0.639343	−	0.768922i	$-0.720794\pi$
$509$	−8.72441e33	−1.27869	−0.639343	+	0.768922i	$0.720794\pi$
$510$	−5.53232e32	−0.0791189
$511$	−6.49857e33	−0.906894
$512$	1.18564e33	0.161465
$513$	1.03990e34	1.38206
$514$	4.93646e33	0.640290
$515$	1.79563e33	0.227314
$516$	−9.79951e33	−1.21083
$517$	−1.57539e34	−1.90001
$518$	−3.43053e33	−0.403868
$519$	5.79822e31	0.00666351
$520$	−1.59643e33	−0.179105
$521$	−2.94711e33	−0.322794	−0.161397	−	0.986890i	$-0.551600\pi$
$521$	−2.94711e33	−0.322794	−0.161397	+	0.986890i	$0.551600\pi$
$522$	−4.26483e33	−0.456058
$523$	−8.26051e33	−0.862453	−0.431227	−	0.902244i	$-0.641919\pi$
$523$	−8.26051e33	−0.862453	−0.431227	+	0.902244i	$0.641919\pi$
$524$	−1.32109e34	−1.34676
$525$	1.02378e33	0.101910
$526$	1.68143e34	1.63440
$527$	1.81681e33	0.172455
$528$	−1.01391e33	−0.0939887
$529$	3.25424e34	2.94614
$530$	−3.42972e33	−0.303257
$531$	2.10220e33	0.181548
$532$	−1.45001e34	−1.22314
$533$	1.28278e33	0.105697
$534$	1.85676e34	1.49448
$535$	1.37203e32	0.0107880
$536$	2.92673e33	0.224814
$537$	1.39060e33	0.104357
$538$	−2.52315e34	−1.84997
$539$	−1.22063e34	−0.874426
$540$	−1.09881e34	−0.769130
$541$	−1.11587e34	−0.763218	−0.381609	−	0.924324i	$-0.624630\pi$
$541$	−1.11587e34	−0.763218	−0.381609	+	0.924324i	$0.624630\pi$
$542$	1.55869e34	1.04176
$543$	−1.57149e33	−0.102640
$544$	2.19235e33	0.139934
$545$	6.14193e32	0.0383132
$546$	−5.75838e33	−0.351069
$547$	2.11032e34	1.25750	0.628749	−	0.777608i	$-0.283567\pi$
$547$	2.11032e34	1.25750	0.628749	+	0.777608i	$0.283567\pi$
$548$	2.42119e34	1.41017
$549$	−8.71893e33	−0.496374
$550$	8.02112e33	0.446376
$551$	−2.21547e34	−1.20523
$552$	2.92013e34	1.55297
$553$	−6.91828e33	−0.359695
$554$	−2.82083e34	−1.43385
$555$	−3.11067e33	−0.154594
$556$	−1.13631e34	−0.552154
$557$	3.99445e33	0.189787	0.0948936	−	0.995487i	$-0.469749\pi$
$557$	3.99445e33	0.189787	0.0948936	+	0.995487i	$0.469749\pi$
$558$	1.35684e34	0.630376
$559$	8.63448e33	0.392273
$560$	−4.95259e32	−0.0220030
$561$	−3.52076e33	−0.152968
$562$	5.85226e34	2.48668
$563$	7.65608e33	0.318164	0.159082	−	0.987265i	$-0.449147\pi$
$563$	7.65608e33	0.318164	0.159082	+	0.987265i	$0.449147\pi$
$564$	−4.45422e34	−1.81044
$565$	1.58081e34	0.628456
$566$	7.56312e31	0.00294101
$567$	−9.78024e33	−0.372016
$568$	4.33288e34	1.61221
$569$	3.48616e34	1.26895	0.634474	−	0.772944i	$-0.281217\pi$
$569$	3.48616e34	1.26895	0.634474	+	0.772944i	$0.281217\pi$
$570$	−2.14630e34	−0.764285
$571$	−2.99925e34	−1.04487	−0.522434	−	0.852680i	$-0.674976\pi$
$571$	−2.99925e34	−1.04487	−0.522434	+	0.852680i	$0.674976\pi$
$572$	−2.76376e34	−0.941998
$573$	4.17514e33	0.139232
$574$	−7.38770e33	−0.241052
$575$	1.24441e34	0.397298
$576$	1.55987e34	0.487313
$577$	−2.22570e34	−0.680409	−0.340204	−	0.940352i	$-0.610496\pi$
$577$	−2.22570e34	−0.680409	−0.340204	+	0.940352i	$0.610496\pi$
$578$	−5.27758e34	−1.57884
$579$	−4.61367e33	−0.135072
$580$	2.34096e34	0.670726
$581$	2.67013e34	0.748738
$582$	3.13898e34	0.861493
$583$	−2.18267e34	−0.586315
$584$	−5.29184e34	−1.39138
$585$	2.23014e33	0.0573963
$586$	−5.33262e34	−1.34345
$587$	−2.21711e34	−0.546779	−0.273389	−	0.961903i	$-0.588145\pi$
$587$	−2.21711e34	−0.546779	−0.273389	+	0.961903i	$0.588145\pi$
$588$	−3.45118e34	−0.833203
$589$	7.04843e34	1.66591
$590$	−1.88362e34	−0.435856
$591$	5.86334e34	1.32832
$592$	1.50480e33	0.0333777
$593$	−1.75924e34	−0.382069	−0.191034	−	0.981583i	$-0.561184\pi$
$593$	−1.75924e34	−0.382069	−0.191034	+	0.981583i	$0.561184\pi$
$594$	−1.14150e35	−2.42743
$595$	−1.71977e33	−0.0358102
$596$	5.77848e32	0.0117824
$597$	5.57485e34	1.11315
$598$	−6.99932e34	−1.36865
$599$	−8.14478e34	−1.55971	−0.779856	−	0.625959i	$-0.784708\pi$
$599$	−8.14478e34	−1.55971	−0.779856	+	0.625959i	$0.784708\pi$
$600$	8.33677e33	0.156353
$601$	6.30417e34	1.15797	0.578985	−	0.815338i	$-0.303449\pi$
$601$	6.30417e34	1.15797	0.578985	+	0.815338i	$0.303449\pi$
$602$	−4.97270e34	−0.894614
$603$	−4.08852e33	−0.0720443
$604$	1.62587e35	2.80624
$605$	2.45943e34	0.415808
$606$	1.27932e35	2.11872
$607$	−1.94077e34	−0.314859	−0.157429	−	0.987530i	$-0.550321\pi$
$607$	−1.94077e34	−0.314859	−0.157429	+	0.987530i	$0.550321\pi$
$608$	8.50538e34	1.35176
$609$	3.10401e34	0.483290
$610$	7.81237e34	1.19168
$611$	3.92468e34	0.586528
$612$	4.25168e33	0.0622541
$613$	−1.73385e34	−0.248746	−0.124373	−	0.992236i	$-0.539692\pi$
$613$	−1.73385e34	−0.248746	−0.124373	+	0.992236i	$0.539692\pi$
$614$	5.66716e34	0.796637
$615$	−6.69887e33	−0.0922705
$616$	5.85105e34	0.789724
$617$	−1.98613e34	−0.262689	−0.131345	−	0.991337i	$-0.541929\pi$
$617$	−1.98613e34	−0.262689	−0.131345	+	0.991337i	$0.541929\pi$
$618$	5.27419e34	0.683597
$619$	−9.11618e34	−1.15792	−0.578962	−	0.815355i	$-0.696542\pi$
$619$	−9.11618e34	−1.15792	−0.578962	+	0.815355i	$0.696542\pi$
$620$	−7.44767e34	−0.927096
$621$	−1.77095e35	−2.16054
$622$	−2.17244e34	−0.259757
$623$	5.77190e34	0.676422
$624$	2.52590e33	0.0290141
$625$	3.55271e33	0.0400000
$626$	−1.88196e35	−2.07697
$627$	−1.36590e35	−1.47766
$628$	−2.58569e34	−0.274208
$629$	5.22534e33	0.0543227
$630$	−1.28436e34	−0.130897
$631$	−4.67243e34	−0.466848	−0.233424	−	0.972375i	$-0.574993\pi$
$631$	−4.67243e34	−0.466848	−0.233424	+	0.972375i	$0.574993\pi$
$632$	−5.63361e34	−0.551853
$633$	−2.13391e33	−0.0204941
$634$	8.87465e34	0.835672
$635$	−6.07450e34	−0.560840
$636$	−6.17124e34	−0.558674
$637$	3.04088e34	0.269934
$638$	2.43192e35	2.11686
$639$	−6.05285e34	−0.516653
$640$	−8.29335e34	−0.694193
$641$	1.20388e35	0.988228	0.494114	−	0.869397i	$-0.335493\pi$
$641$	1.20388e35	0.988228	0.494114	+	0.869397i	$0.335493\pi$
$642$	4.02998e33	0.0324426
$643$	1.49643e34	0.118146	0.0590731	−	0.998254i	$-0.481185\pi$
$643$	1.49643e34	0.118146	0.0590731	+	0.998254i	$0.481185\pi$
$644$	2.46937e35	1.91211
$645$	−4.50905e34	−0.342443
$646$	3.60539e34	0.268562
$647$	1.05749e34	0.0772635	0.0386317	−	0.999254i	$-0.487700\pi$
$647$	1.05749e34	0.0772635	0.0386317	+	0.999254i	$0.487700\pi$
$648$	−7.96414e34	−0.570757
$649$	−1.19873e35	−0.842681
$650$	−1.99826e34	−0.137795
$651$	−9.87528e34	−0.668016
$652$	8.73764e34	0.579828
$653$	1.08968e35	0.709391	0.354696	−	0.934982i	$-0.384584\pi$
$653$	1.08968e35	0.709391	0.354696	+	0.934982i	$0.384584\pi$
$654$	1.80403e34	0.115219
$655$	−6.07872e34	−0.380887
$656$	3.24060e33	0.0199217
$657$	7.39247e34	0.445885
$658$	−2.26027e35	−1.33763
$659$	1.09264e35	0.634465	0.317233	−	0.948348i	$-0.397246\pi$
$659$	1.09264e35	0.634465	0.317233	+	0.948348i	$0.397246\pi$
$660$	1.44327e35	0.822336
$661$	−1.43992e35	−0.805044	−0.402522	−	0.915410i	$-0.631866\pi$
$661$	−1.43992e35	−0.805044	−0.402522	+	0.915410i	$0.631866\pi$
$662$	−1.32333e35	−0.726014
$663$	8.77109e33	0.0472209
$664$	2.17431e35	1.14874
$665$	−6.67195e34	−0.345925
$666$	3.90241e34	0.198566
$667$	3.77294e35	1.88411
$668$	−2.54529e35	−1.24747
$669$	−1.07366e35	−0.516465
$670$	3.66341e34	0.172962
$671$	4.97178e35	2.30399
$672$	−1.19166e35	−0.542045
$673$	−3.42777e35	−1.53046	−0.765232	−	0.643755i	$-0.777376\pi$
$673$	−3.42777e35	−1.53046	−0.765232	+	0.643755i	$0.777376\pi$
$674$	−1.31231e34	−0.0575157
$675$	−5.05594e34	−0.217523
$676$	−3.05554e35	−1.29049
$677$	1.46770e35	0.608524	0.304262	−	0.952588i	$-0.401590\pi$
$677$	1.46770e35	0.608524	0.304262	+	0.952588i	$0.401590\pi$
$678$	4.64323e35	1.88994
$679$	9.75777e34	0.389923
$680$	−1.40042e34	−0.0549411
$681$	3.18146e35	1.22543
$682$	−7.73706e35	−2.92598
$683$	2.69120e35	0.999278	0.499639	−	0.866234i	$-0.333466\pi$
$683$	2.69120e35	0.999278	0.499639	+	0.866234i	$0.333466\pi$
$684$	1.64947e35	0.601372
$685$	1.11406e35	0.398820
$686$	−4.53346e35	−1.59360
$687$	−2.08092e35	−0.718285
$688$	2.18126e34	0.0739355
$689$	5.43757e34	0.180994
$690$	3.65514e35	1.19479
$691$	3.83194e35	1.23011	0.615054	−	0.788485i	$-0.289134\pi$
$691$	3.83194e35	1.23011	0.615054	+	0.788485i	$0.289134\pi$
$692$	3.99271e33	0.0125876
$693$	−8.17367e34	−0.253076
$694$	−7.62731e35	−2.31941
$695$	−5.22848e34	−0.156158
$696$	2.52763e35	0.741477
$697$	1.12528e34	0.0324230
$698$	1.94625e34	0.0550814
$699$	−2.38918e35	−0.664179
$700$	7.04987e34	0.192511
$701$	−4.28405e35	−1.14916	−0.574578	−	0.818450i	$-0.694834\pi$
$701$	−4.28405e35	−1.14916	−0.574578	+	0.818450i	$0.694834\pi$
$702$	2.84377e35	0.749342
$703$	2.02721e35	0.524755
$704$	−8.89482e35	−2.26193
$705$	−2.04952e35	−0.512022
$706$	1.07472e35	0.263777
$707$	3.97688e35	0.958958
$708$	−3.38927e35	−0.802954
$709$	3.17775e35	0.739675	0.369838	−	0.929096i	$-0.379413\pi$
$709$	3.17775e35	0.739675	0.369838	+	0.929096i	$0.379413\pi$
$710$	5.42349e35	1.24037
$711$	7.86991e34	0.176848
$712$	4.70011e35	1.03779
$713$	−1.20034e36	−2.60427
$714$	−5.05137e34	−0.107691
$715$	−1.27169e35	−0.266413
$716$	9.57579e34	0.197134
$717$	−6.58231e35	−1.33165
$718$	6.46755e35	1.28583
$719$	−8.26528e35	−1.61490	−0.807452	−	0.589934i	$-0.799154\pi$
$719$	−8.26528e35	−1.61490	−0.807452	+	0.589934i	$0.799154\pi$
$720$	5.63384e33	0.0108180
$721$	1.63952e35	0.309405
$722$	5.32505e35	0.987663
$723$	1.76765e35	0.322231
$724$	−1.08214e35	−0.193889
$725$	1.07715e35	0.189693
$726$	7.22395e35	1.25045
$727$	6.73836e35	1.14650	0.573250	−	0.819380i	$-0.305682\pi$
$727$	6.73836e35	1.14650	0.573250	+	0.819380i	$0.305682\pi$
$728$	−1.45764e35	−0.243786
$729$	6.65040e35	1.09334
$730$	−6.62383e35	−1.07047
$731$	7.57435e34	0.120331
$732$	1.40571e36	2.19537
$733$	5.00441e35	0.768339	0.384170	−	0.923262i	$-0.374488\pi$
$733$	5.00441e35	0.768339	0.384170	+	0.923262i	$0.374488\pi$
$734$	1.91089e36	2.88426
$735$	−1.58799e35	−0.235644
$736$	−1.44846e36	−2.11317
$737$	2.33139e35	0.334403
$738$	8.40390e34	0.118516
$739$	−3.85575e35	−0.534630	−0.267315	−	0.963609i	$-0.586136\pi$
$739$	−3.85575e35	−0.534630	−0.267315	+	0.963609i	$0.586136\pi$
$740$	−2.14204e35	−0.292032
$741$	3.40280e35	0.456152
$742$	−3.13156e35	−0.412773
$743$	−3.73134e35	−0.483620	−0.241810	−	0.970324i	$-0.577741\pi$
$743$	−3.73134e35	−0.483620	−0.241810	+	0.970324i	$0.577741\pi$
$744$	−8.04153e35	−1.02489
$745$	2.65885e33	0.00333227
$746$	−1.02094e36	−1.25824
$747$	−3.03741e35	−0.368126
$748$	−2.42443e35	−0.288961
$749$	1.25275e34	0.0146839
$750$	1.04352e35	0.120291
$751$	−8.06594e35	−0.914441	−0.457221	−	0.889353i	$-0.651155\pi$
$751$	−8.06594e35	−0.914441	−0.457221	+	0.889353i	$0.651155\pi$
$752$	9.91462e34	0.110549
$753$	−1.12922e36	−1.23834
$754$	−6.05852e35	−0.653469
$755$	7.48113e35	0.793653
$756$	−1.00328e36	−1.04689
$757$	−7.38327e35	−0.757793	−0.378896	−	0.925439i	$-0.623696\pi$
$757$	−7.38327e35	−0.757793	−0.378896	+	0.925439i	$0.623696\pi$
$758$	1.62855e36	1.64413
$759$	2.32613e36	2.30999
$760$	−5.43303e35	−0.530728
$761$	−1.50315e36	−1.44442	−0.722211	−	0.691673i	$-0.756874\pi$
$761$	−1.50315e36	−1.44442	−0.722211	+	0.691673i	$0.756874\pi$
$762$	−1.78423e36	−1.68660
$763$	5.60798e34	0.0521495
$764$	2.87504e35	0.263013
$765$	1.95633e34	0.0176065
$766$	1.36968e36	1.21272
$767$	2.98634e35	0.260134
$768$	−8.45538e35	−0.724633
$769$	−1.45035e36	−1.22291	−0.611454	−	0.791280i	$-0.709415\pi$
$769$	−1.45035e36	−1.22291	−0.611454	+	0.791280i	$0.709415\pi$
$770$	7.32380e35	0.607578
$771$	4.08705e35	0.333603
$772$	−3.17701e35	−0.255154
$773$	−3.10612e34	−0.0245457	−0.0122728	−	0.999925i	$-0.503907\pi$
$773$	−3.10612e34	−0.0245457	−0.0122728	+	0.999925i	$0.503907\pi$
$774$	5.65671e35	0.439847
$775$	−3.42690e35	−0.262198
$776$	7.94584e35	0.598230
$777$	−2.84024e35	−0.210423
$778$	2.76169e36	2.01340
$779$	4.36562e35	0.313204
$780$	−3.59555e35	−0.253853
$781$	3.45150e36	2.39812
$782$	−6.13995e35	−0.419837
$783$	−1.53291e36	−1.03156
$784$	7.68195e34	0.0508769
$785$	−1.18975e35	−0.0775507
$786$	−1.78547e36	−1.14543
$787$	1.24926e36	0.788801	0.394400	−	0.918939i	$-0.370952\pi$
$787$	1.24926e36	0.788801	0.394400	+	0.918939i	$0.370952\pi$
$788$	4.03755e36	2.50923
$789$	1.39211e36	0.851551
$790$	−7.05163e35	−0.424571
$791$	1.44338e36	0.855413
$792$	−6.65589e35	−0.388277
$793$	−1.23859e36	−0.711236
$794$	−2.11216e36	−1.19391
$795$	−2.83957e35	−0.158003
$796$	3.83889e36	2.10278
$797$	−2.85096e36	−1.53731	−0.768655	−	0.639663i	$-0.779074\pi$
$797$	−2.85096e36	−1.53731	−0.768655	+	0.639663i	$0.779074\pi$
$798$	−1.95971e36	−1.04029
$799$	3.44281e35	0.179919
$800$	−4.13526e35	−0.212754
$801$	−6.56584e35	−0.332571
$802$	−5.65094e36	−2.81800
$803$	−4.21539e36	−2.06964
$804$	6.59172e35	0.318638
$805$	1.13623e36	0.540776
$806$	1.92749e36	0.903243
$807$	−2.08899e36	−0.963867
$808$	3.23841e36	1.47126
$809$	2.03075e36	0.908448	0.454224	−	0.890887i	$-0.349917\pi$
$809$	2.03075e36	0.908448	0.454224	+	0.890887i	$0.349917\pi$
$810$	−9.96876e35	−0.439115
$811$	1.33953e36	0.581022	0.290511	−	0.956872i	$-0.406175\pi$
$811$	1.33953e36	0.581022	0.290511	+	0.956872i	$0.406175\pi$
$812$	2.13745e36	0.912948
$813$	1.29049e36	0.542778
$814$	−2.22527e36	−0.921673
$815$	4.02045e35	0.163985
$816$	2.21577e34	0.00890017
$817$	2.93852e36	1.16239
$818$	−3.05132e36	−1.18870
$819$	2.03626e35	0.0781241
$820$	−4.61290e35	−0.174302
$821$	−4.10889e36	−1.52910	−0.764548	−	0.644567i	$-0.777038\pi$
$821$	−4.10889e36	−1.52910	−0.764548	+	0.644567i	$0.777038\pi$
$822$	3.27227e36	1.19937
$823$	4.90776e36	1.77168	0.885840	−	0.463990i	$-0.153583\pi$
$823$	4.90776e36	1.77168	0.885840	+	0.463990i	$0.153583\pi$
$824$	1.33508e36	0.474697
$825$	6.64093e35	0.232571
$826$	−1.71986e36	−0.593258
$827$	−5.80651e35	−0.197286	−0.0986429	−	0.995123i	$-0.531450\pi$
$827$	−5.80651e35	−0.197286	−0.0986429	+	0.995123i	$0.531450\pi$
$828$	−2.80904e36	−0.940109
$829$	−1.56689e36	−0.516543	−0.258272	−	0.966072i	$-0.583153\pi$
$829$	−1.56689e36	−0.516543	−0.258272	+	0.966072i	$0.583153\pi$
$830$	2.72159e36	0.883786
$831$	−2.33545e36	−0.747064
$832$	2.21592e36	0.698252
$833$	2.66753e35	0.0828030
$834$	−1.53573e36	−0.469612
$835$	−1.17116e36	−0.352806
$836$	−9.40574e36	−2.79135
$837$	4.87689e36	1.42585
$838$	−3.67965e36	−1.05988
$839$	−1.54768e36	−0.439195	−0.219598	−	0.975591i	$-0.570474\pi$
$839$	−1.54768e36	−0.439195	−0.219598	+	0.975591i	$0.570474\pi$
$840$	7.61201e35	0.212818
$841$	−3.64556e35	−0.100419
$842$	−7.16106e36	−1.94346
$843$	4.84527e36	1.29561
$844$	−1.46943e35	−0.0387139
$845$	−1.40595e36	−0.364973
$846$	2.57117e36	0.657661
$847$	2.24562e36	0.565971
$848$	1.37365e35	0.0341137
$849$	6.26175e33	0.00153232
$850$	−1.75291e35	−0.0422692
$851$	−3.45232e36	−0.820336
$852$	9.75872e36	2.28506
$853$	2.64390e36	0.610074	0.305037	−	0.952340i	$-0.401331\pi$
$853$	2.64390e36	0.610074	0.305037	+	0.952340i	$0.401331\pi$
$854$	7.13319e36	1.62204
$855$	7.58970e35	0.170078
$856$	1.02013e35	0.0225285
$857$	−1.26882e35	−0.0276146	−0.0138073	−	0.999905i	$-0.504395\pi$
$857$	−1.26882e35	−0.0276146	−0.0138073	+	0.999905i	$0.504395\pi$
$858$	−3.73526e36	−0.801179
$859$	3.89056e36	0.822427	0.411213	−	0.911539i	$-0.365105\pi$
$859$	3.89056e36	0.822427	0.411213	+	0.911539i	$0.365105\pi$
$860$	−3.10497e36	−0.646884
$861$	−6.11650e35	−0.125593
$862$	1.03207e37	2.08866
$863$	−3.85714e35	−0.0769361	−0.0384680	−	0.999260i	$-0.512248\pi$
$863$	−3.85714e35	−0.0769361	−0.0384680	+	0.999260i	$0.512248\pi$
$864$	5.88497e36	1.15697
$865$	1.83716e34	0.00355997
$866$	1.46848e37	2.80475
$867$	−4.36947e36	−0.822603
$868$	−6.80021e36	−1.26190
$869$	−4.48764e36	−0.820864
$870$	3.16384e36	0.570459
$871$	−5.80806e35	−0.103230
$872$	4.56663e35	0.0800092
$873$	−1.11000e36	−0.191710
$874$	−2.38204e37	−4.05560
$875$	3.24386e35	0.0544454
$876$	−1.19185e37	−1.97207
$877$	5.90524e36	0.963259	0.481629	−	0.876375i	$-0.340045\pi$
$877$	5.90524e36	0.963259	0.481629	+	0.876375i	$0.340045\pi$
$878$	−1.53658e36	−0.247101
$879$	−4.41504e36	−0.699961
$880$	−3.21257e35	−0.0502134
$881$	5.50635e36	0.848525	0.424263	−	0.905539i	$-0.360533\pi$
$881$	5.50635e36	0.848525	0.424263	+	0.905539i	$0.360533\pi$
$882$	1.99217e36	0.302670
$883$	1.09899e36	0.164622	0.0823108	−	0.996607i	$-0.473770\pi$
$883$	1.09899e36	0.164622	0.0823108	+	0.996607i	$0.473770\pi$
$884$	6.03985e35	0.0892016
$885$	−1.55951e36	−0.227089
$886$	1.59611e37	2.29161
$887$	−5.39216e36	−0.763339	−0.381670	−	0.924299i	$-0.624651\pi$
$887$	−5.39216e36	−0.763339	−0.381670	+	0.924299i	$0.624651\pi$
$888$	−2.31284e36	−0.322837
$889$	−5.54641e36	−0.763378
$890$	5.88315e36	0.798426
$891$	−6.34410e36	−0.848983
$892$	−7.39332e36	−0.975616
$893$	1.33566e37	1.73801
$894$	7.80969e34	0.0100211
$895$	4.40611e35	0.0557529
$896$	−7.57237e36	−0.944891
$897$	−5.79496e36	−0.713090
$898$	−1.97879e37	−2.40130
$899$	−1.03900e37	−1.24343
$900$	−8.01961e35	−0.0946503
$901$	4.76995e35	0.0555206
$902$	−4.79214e36	−0.550108
$903$	−4.11705e36	−0.466111
$904$	1.17536e37	1.31240
$905$	−4.97927e35	−0.0548351
$906$	2.19739e37	2.38674
$907$	−7.94948e36	−0.851624	−0.425812	−	0.904812i	$-0.640011\pi$
$907$	−7.94948e36	−0.851624	−0.425812	+	0.904812i	$0.640011\pi$
$908$	2.19078e37	2.31486
$909$	−4.52391e36	−0.471483
$910$	−1.82454e36	−0.187558
$911$	−9.52757e36	−0.966056	−0.483028	−	0.875605i	$-0.660463\pi$
$911$	−9.52757e36	−0.966056	−0.483028	+	0.875605i	$0.660463\pi$
$912$	8.59625e35	0.0859753
$913$	1.73202e37	1.70871
$914$	2.79767e37	2.72251
$915$	6.46810e36	0.620888
$916$	−1.43294e37	−1.35686
$917$	−5.55026e36	−0.518438
$918$	2.49461e36	0.229863
$919$	9.83660e35	0.0894131	0.0447066	−	0.999000i	$-0.485765\pi$
$919$	9.83660e35	0.0894131	0.0447066	+	0.999000i	$0.485765\pi$
$920$	9.25241e36	0.829673
$921$	4.69201e36	0.415063
$922$	2.43971e36	0.212913
$923$	−8.59854e36	−0.740293
$924$	1.31780e37	1.11931
$925$	−9.85615e35	−0.0825915
$926$	1.39447e37	1.15285
$927$	−1.86505e36	−0.152122
$928$	−1.25377e37	−1.00895
$929$	1.15035e37	0.913341	0.456671	−	0.889636i	$-0.349042\pi$
$929$	1.15035e37	0.913341	0.456671	+	0.889636i	$0.349042\pi$
$930$	−1.00656e37	−0.788504
$931$	1.03489e37	0.799873
$932$	−1.64521e37	−1.25465
$933$	−1.79863e36	−0.135338
$934$	−3.04024e36	−0.225721
$935$	−1.11555e36	−0.0817230
$936$	1.65815e36	0.119860
$937$	−2.46491e36	−0.175815	−0.0879076	−	0.996129i	$-0.528018\pi$
$937$	−2.46491e36	−0.175815	−0.0879076	+	0.996129i	$0.528018\pi$
$938$	3.34493e36	0.235424
$939$	−1.55813e37	−1.08214
$940$	−1.41132e37	−0.967223
$941$	−8.32049e36	−0.562702	−0.281351	−	0.959605i	$-0.590783\pi$
$941$	−8.32049e36	−0.562702	−0.281351	+	0.959605i	$0.590783\pi$
$942$	−3.49459e36	−0.233217
$943$	−7.43462e36	−0.489624
$944$	7.54416e35	0.0490299
$945$	−4.61640e36	−0.296078
$946$	−3.22561e37	−2.04161
$947$	2.59885e37	1.62333	0.811663	−	0.584126i	$-0.198563\pi$
$947$	2.59885e37	1.62333	0.811663	+	0.584126i	$0.198563\pi$
$948$	−1.26883e37	−0.782166
$949$	1.05016e37	0.638892
$950$	−6.80055e36	−0.408319
$951$	7.34760e36	0.435401
$952$	−1.27867e36	−0.0747822
$953$	3.40529e37	1.96559	0.982794	−	0.184707i	$-0.0591335\pi$
$953$	3.40529e37	1.96559	0.982794	+	0.184707i	$0.0591335\pi$
$954$	3.56232e36	0.202945
$955$	1.32289e36	0.0743844
$956$	−4.53264e37	−2.51552
$957$	2.01347e37	1.10292
$958$	−2.62126e37	−1.41723
$959$	1.01721e37	0.542848
$960$	−1.15718e37	−0.609553
$961$	1.38226e37	0.718698
$962$	5.54369e36	0.284518
$963$	−1.42507e35	−0.00721952
$964$	1.21722e37	0.608703
$965$	−1.46184e36	−0.0721619
$966$	3.33738e37	1.62627
$967$	−1.85686e37	−0.893197	−0.446599	−	0.894734i	$-0.647365\pi$
$967$	−1.85686e37	−0.893197	−0.446599	+	0.894734i	$0.647365\pi$
$968$	1.82863e37	0.868328
$969$	2.98501e36	0.139926
$970$	9.94585e36	0.460252
$971$	−1.16618e37	−0.532750	−0.266375	−	0.963869i	$-0.585826\pi$
$971$	−1.16618e37	−0.532750	−0.266375	+	0.963869i	$0.585826\pi$
$972$	2.01969e37	0.910868
$973$	−4.77394e36	−0.212553
$974$	−4.14381e37	−1.82143
$975$	−1.65442e36	−0.0717940
$976$	−3.12896e36	−0.134053
$977$	−1.47099e37	−0.622199	−0.311099	−	0.950377i	$-0.600697\pi$
$977$	−1.47099e37	−0.622199	−0.311099	+	0.950377i	$0.600697\pi$
$978$	1.18090e37	0.493149
$979$	3.74403e37	1.54367
$980$	−1.09350e37	−0.445138
$981$	−6.37938e35	−0.0256399
$982$	−4.50179e37	−1.78645
$983$	3.22525e37	1.26370	0.631850	−	0.775090i	$-0.282296\pi$
$983$	3.22525e37	1.26370	0.631850	+	0.775090i	$0.282296\pi$
$984$	−4.98072e36	−0.192688
$985$	1.85780e37	0.709652
$986$	−5.31466e36	−0.200454
$987$	−1.87134e37	−0.696930
$988$	2.34320e37	0.861684
$989$	−5.00428e37	−1.81714
$990$	−8.33121e36	−0.298723
$991$	−3.84340e37	−1.36080	−0.680400	−	0.732840i	$-0.738194\pi$
$991$	−3.84340e37	−1.36080	−0.680400	+	0.732840i	$0.738194\pi$
$992$	3.98881e37	1.39459
$993$	−1.09563e37	−0.378267
$994$	4.95200e37	1.68830
$995$	1.76639e37	0.594700
$996$	4.89708e37	1.62815
$997$	−2.10047e37	−0.689647	−0.344823	−	0.938668i	$-0.612061\pi$
$997$	−2.10047e37	−0.689647	−0.344823	+	0.938668i	$0.612061\pi$
$998$	3.85805e36	0.125094
$999$	1.40265e37	0.449139

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.a.b.1.5	✓	5
3.2	odd	2		45.26.a.f.1.1		5
5.2	odd	4		25.26.b.c.24.9		10
5.3	odd	4		25.26.b.c.24.2		10
5.4	even	2		25.26.a.c.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.a.b.1.5	✓	5	1.1	even	1	trivial
25.26.a.c.1.1		5	5.4	even	2
25.26.b.c.24.2		10	5.3	odd	4
25.26.b.c.24.9		10	5.2	odd	4
45.26.a.f.1.1		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+9306.64 q^{2} +770525. q^{3} +5.30591e7 q^{4} +2.44141e8 q^{5} +7.17100e9 q^{6} +2.22916e10 q^{7} +1.81523e11 q^{8} -2.53579e11 q^{9} +O(q^{10})\)	\(q+9306.64 q^{2} +770525. q^{3} +5.30591e7 q^{4} +2.44141e8 q^{5} +7.17100e9 q^{6} +2.22916e10 q^{7} +1.81523e11 q^{8} -2.53579e11 q^{9} +2.27213e12 q^{10} +1.44598e13 q^{11} +4.08834e13 q^{12} -3.60229e13 q^{13} +2.07460e14 q^{14} +1.88117e14 q^{15} -9.10020e13 q^{16} -3.16000e14 q^{17} -2.35997e15 q^{18} -1.22595e16 q^{19} +1.29539e16 q^{20} +1.71763e16 q^{21} +1.34572e17 q^{22} +2.08778e17 q^{23} +1.39868e17 q^{24} +5.96046e16 q^{25} -3.35252e17 q^{26} -8.48247e17 q^{27} +1.18277e18 q^{28} +1.80715e18 q^{29} +1.75073e18 q^{30} -5.74938e18 q^{31} -6.93781e18 q^{32} +1.11416e19 q^{33} -2.94090e18 q^{34} +5.44229e18 q^{35} -1.34547e19 q^{36} -1.65359e19 q^{37} -1.14094e20 q^{38} -2.77566e19 q^{39} +4.43170e19 q^{40} -3.56102e19 q^{41} +1.59853e20 q^{42} -2.39694e20 q^{43} +7.67223e20 q^{44} -6.19090e19 q^{45} +1.94302e21 q^{46} -1.08949e21 q^{47} -7.01193e19 q^{48} -8.44153e20 q^{49} +5.54719e20 q^{50} -2.43486e20 q^{51} -1.91134e21 q^{52} -1.50948e21 q^{53} -7.89432e21 q^{54} +3.53022e21 q^{55} +4.04643e21 q^{56} -9.44622e21 q^{57} +1.68185e22 q^{58} -8.29010e21 q^{59} +9.98129e21 q^{60} +3.43835e22 q^{61} -5.35074e22 q^{62} -5.65269e21 q^{63} -6.15142e22 q^{64} -8.79466e21 q^{65} +1.03691e23 q^{66} +1.61232e22 q^{67} -1.67667e22 q^{68} +1.60869e23 q^{69} +5.06494e22 q^{70} +2.38697e23 q^{71} -4.60303e22 q^{72} -2.91525e23 q^{73} -1.53893e23 q^{74} +4.59269e22 q^{75} -6.50475e23 q^{76} +3.22332e23 q^{77} -2.58320e23 q^{78} -3.10353e23 q^{79} -2.22173e22 q^{80} -4.38741e23 q^{81} -3.31411e23 q^{82} +1.19782e24 q^{83} +9.11356e23 q^{84} -7.71485e22 q^{85} -2.23075e24 q^{86} +1.39246e24 q^{87} +2.62478e24 q^{88} +2.58927e24 q^{89} -5.76164e23 q^{90} -8.03009e23 q^{91} +1.10776e25 q^{92} -4.43004e24 q^{93} -1.01395e25 q^{94} -2.99303e24 q^{95} -5.34576e24 q^{96} +4.37733e24 q^{97} -7.85622e24 q^{98} -3.66670e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4602 q^{2} + 626204 q^{3} + 91050260 q^{4} + 1220703125 q^{5} + 5696574760 q^{6} + 55481235808 q^{7} - 325515457080 q^{8} + 277996846465 q^{9}+O(q^{10}) \) 5 * q - 4602 * q^2 + 626204 * q^3 + 91050260 * q^4 + 1220703125 * q^5 + 5696574760 * q^6 + 55481235808 * q^7 - 325515457080 * q^8 + 277996846465 * q^9	\( 5 q - 4602 q^{2} + 626204 q^{3} + 91050260 q^{4} + 1220703125 q^{5} + 5696574760 q^{6} + 55481235808 q^{7} - 325515457080 q^{8} + 277996846465 q^{9} - 1123535156250 q^{10} - 4144958451540 q^{11} - 26370992065712 q^{12} + 111211249076614 q^{13} - 445566653510880 q^{14} + 152881835937500 q^{15} + 30\!\cdots\!80 q^{16}+ \cdots - 22\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q - 4602 * q^2 + 626204 * q^3 + 91050260 * q^4 + 1220703125 * q^5 + 5696574760 * q^6 + 55481235808 * q^7 - 325515457080 * q^8 + 277996846465 * q^9 - 1123535156250 * q^10 - 4144958451540 * q^11 - 26370992065712 * q^12 + 111211249076614 * q^13 - 445566653510880 * q^14 + 152881835937500 * q^15 + 3044988017630480 * q^16 + 3179191896192378 * q^17 + 9100952570763854 * q^18 + 13473188050195300 * q^19 + 22229067382812500 * q^20 + 76768095576060960 * q^21 + 222905601184950696 * q^22 + 409020396998250624 * q^23 + 738233252736381600 * q^24 + 298023223876953125 * q^25 + 331732385439154260 * q^26 + 1707963140919696920 * q^27 + 6745183853862681376 * q^28 + 1510518246057732150 * q^29 + 1390765322265625000 * q^30 - 7800790900476562640 * q^31 - 26275496698670595552 * q^32 - 17083981126675017392 * q^33 - 30967164186095882580 * q^34 + 13545223585937500000 * q^35 - 127816747210020977020 * q^36 - 45693640863683938082 * q^37 - 107313021439059142920 * q^38 - 28513155461010121720 * q^39 - 79471547138671875000 * q^40 + 268182713424991346610 * q^41 + 472693454958668435136 * q^42 - 54212732396046197756 * q^43 + 1026843270980203159920 * q^44 + 67870323843994140625 * q^45 + 1806261760861861731360 * q^46 + 1313959570250307870888 * q^47 + 393501331052082428224 * q^48 + 2928508402086077906685 * q^49 - 274300575256347656250 * q^50 - 1679947779014963634440 * q^51 - 1533919945088032601192 * q^52 - 1722136215100242292146 * q^53 - 16134427338310747545200 * q^54 - 1011952746958007812500 * q^55 - 39415455111791618702400 * q^56 - 9510351594401743758160 * q^57 + 7814667131698315285620 * q^58 - 16547203533880040421300 * q^59 - 6438230484792968750000 * q^60 + 11587268554089248839510 * q^61 + 21314291783865447926496 * q^62 + 32595050340385317746784 * q^63 + 83981823170089659652160 * q^64 + 27151183856595214843750 * q^65 + 107686245599040557757920 * q^66 + 186273232047241909753228 * q^67 + 48790715540647305709416 * q^68 + 205103851249003209571680 * q^69 - 108780921267304687500000 * q^70 + 179635129178416728944760 * q^71 + 252302332499928005189160 * q^72 - 471333406608130631390126 * q^73 - 888672199125830235839580 * q^74 + 37324666976928710937500 * q^75 - 1191799860770260438242800 * q^76 - 286067188114809482097984 * q^77 - 1025178605609234961148112 * q^78 + 360282849255851991934000 * q^79 + 743405277741816406250000 * q^80 + 103584508446589901468605 * q^81 - 2050449668847875948936004 * q^82 + 1759227952818659145519084 * q^83 - 3837881595316615167665280 * q^84 + 776169896531342285156250 * q^85 - 565842386421331097744040 * q^86 + 8705381585373786685282760 * q^87 + 720634350501343968831840 * q^88 + 4092128669145981513024450 * q^89 + 2221912248721644042968750 * q^90 + 11972573281108721260967360 * q^91 + 6613215336376724900082528 * q^92 + 7392084747484240267531008 * q^93 - 17112742333122902932304880 * q^94 + 3289352551317211914062500 * q^95 - 10376386162767776801453440 * q^96 + 28613737566457196779163338 * q^97 - 56860534671603836155246314 * q^98 - 22864619024884333176273220 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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