LMFDB - Embedded newform 5.26.a.b.1.2

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			1.2
Root			$2350.27$ 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)

$f(q)$	$=$	$q-5620.55 q^{2} -161492. q^{3} -1.96387e6 q^{4} +2.44141e8 q^{5} +9.07675e8 q^{6} -4.86926e10 q^{7} +1.99632e11 q^{8} -8.21209e11 q^{9} +O(q^{10})$	\(q-5620.55 q^{2} -161492. q^{3} -1.96387e6 q^{4} +2.44141e8 q^{5} +9.07675e8 q^{6} -4.86926e10 q^{7} +1.99632e11 q^{8} -8.21209e11 q^{9} -1.37220e12 q^{10} -4.24041e12 q^{11} +3.17150e11 q^{12} -1.64670e14 q^{13} +2.73679e14 q^{14} -3.94268e13 q^{15} -1.05615e15 q^{16} +3.80397e15 q^{17} +4.61564e15 q^{18} +6.65988e15 q^{19} -4.79461e14 q^{20} +7.86348e15 q^{21} +2.38334e16 q^{22} +6.99884e16 q^{23} -3.22391e16 q^{24} +5.96046e16 q^{25} +9.25533e17 q^{26} +2.69450e17 q^{27} +9.56261e16 q^{28} +2.33329e18 q^{29} +2.21600e17 q^{30} -6.07465e18 q^{31} -7.62428e17 q^{32} +6.84794e17 q^{33} -2.13804e19 q^{34} -1.18878e19 q^{35} +1.61275e18 q^{36} -1.94537e18 q^{37} -3.74322e19 q^{38} +2.65929e19 q^{39} +4.87384e19 q^{40} +2.35963e19 q^{41} -4.41971e19 q^{42} +2.45267e20 q^{43} +8.32763e18 q^{44} -2.00490e20 q^{45} -3.93373e20 q^{46} +1.25013e21 q^{47} +1.70560e20 q^{48} +1.02990e21 q^{49} -3.35011e20 q^{50} -6.14312e20 q^{51} +3.23390e20 q^{52} +3.59462e20 q^{53} -1.51445e21 q^{54} -1.03526e21 q^{55} -9.72062e21 q^{56} -1.07552e21 q^{57} -1.31144e22 q^{58} +3.01921e21 q^{59} +7.74293e19 q^{60} -2.21901e22 q^{61} +3.41428e22 q^{62} +3.99868e22 q^{63} +3.97237e22 q^{64} -4.02025e22 q^{65} -3.84892e21 q^{66} +9.61859e22 q^{67} -7.47052e21 q^{68} -1.13026e22 q^{69} +6.68162e22 q^{70} -8.70609e22 q^{71} -1.63940e23 q^{72} -2.72860e22 q^{73} +1.09340e22 q^{74} -9.62569e21 q^{75} -1.30792e22 q^{76} +2.06477e23 q^{77} -1.49467e23 q^{78} -6.64384e23 q^{79} -2.57848e23 q^{80} +6.52287e23 q^{81} -1.32624e23 q^{82} +1.19385e23 q^{83} -1.54429e22 q^{84} +9.28704e23 q^{85} -1.37854e24 q^{86} -3.76808e23 q^{87} -8.46524e23 q^{88} +8.26026e23 q^{89} +1.12687e24 q^{90} +8.01819e24 q^{91} -1.37448e23 q^{92} +9.81009e23 q^{93} -7.02644e24 q^{94} +1.62595e24 q^{95} +1.23126e23 q^{96} +4.97990e24 q^{97} -5.78861e24 q^{98} +3.48226e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5620.55	−0.970295	−0.485147	−	0.874432i	$-0.661234\pi$
$2$	−5620.55	−0.970295	−0.485147	+	0.874432i	$0.661234\pi$
$3$	−161492.	−0.175443	−0.0877215	−	0.996145i	$-0.527959\pi$
$3$	−161492.	−0.175443	−0.0877215	+	0.996145i	$0.527959\pi$
$4$	−1.96387e6	−0.0585280
$5$	2.44141e8	0.447214
$5$	2.44141e8	0.447214
$6$	9.07675e8	0.170231
$7$	−4.86926e10	−1.32965	−0.664825	−	0.746999i	$-0.731494\pi$
$7$	−4.86926e10	−1.32965	−0.664825	+	0.746999i	$0.731494\pi$
$8$	1.99632e11	1.02708
$9$	−8.21209e11	−0.969220
$10$	−1.37220e12	−0.433929
$11$	−4.24041e12	−0.407380	−0.203690	−	0.979035i	$-0.565293\pi$
$11$	−4.24041e12	−0.407380	−0.203690	+	0.979035i	$0.565293\pi$
$12$	3.17150e11	0.0102683
$13$	−1.64670e14	−1.96030	−0.980148	−	0.198269i	$-0.936468\pi$
$13$	−1.64670e14	−1.96030	−0.980148	+	0.198269i	$0.936468\pi$
$14$	2.73679e14	1.29015
$15$	−3.94268e13	−0.0784605
$16$	−1.05615e15	−0.938046
$17$	3.80397e15	1.58353	0.791764	−	0.610827i	$-0.209163\pi$
$17$	3.80397e15	1.58353	0.791764	+	0.610827i	$0.209163\pi$
$18$	4.61564e15	0.940429
$19$	6.65988e15	0.690314	0.345157	−	0.938545i	$-0.387826\pi$
$19$	6.65988e15	0.690314	0.345157	+	0.938545i	$0.387826\pi$
$20$	−4.79461e14	−0.0261745
$21$	7.86348e15	0.233278
$22$	2.38334e16	0.395279
$23$	6.99884e16	0.665929	0.332964	−	0.942939i	$-0.391951\pi$
$23$	6.99884e16	0.665929	0.332964	+	0.942939i	$0.391951\pi$
$24$	−3.22391e16	−0.180195
$25$	5.96046e16	0.200000
$26$	9.25533e17	1.90206
$27$	2.69450e17	0.345486
$28$	9.56261e16	0.0778218
$29$	2.33329e18	1.22460	0.612299	−	0.790627i	$-0.290245\pi$
$29$	2.33329e18	1.22460	0.612299	+	0.790627i	$0.290245\pi$
$30$	2.21600e17	0.0761298
$31$	−6.07465e18	−1.38516	−0.692580	−	0.721341i	$-0.743526\pi$
$31$	−6.07465e18	−1.38516	−0.692580	+	0.721341i	$0.743526\pi$
$32$	−7.62428e17	−0.116903
$33$	6.84794e17	0.0714720
$34$	−2.13804e19	−1.53649
$35$	−1.18878e19	−0.594638
$36$	1.61275e18	0.0567265
$37$	−1.94537e18	−0.0485826	−0.0242913	−	0.999705i	$-0.507733\pi$
$37$	−1.94537e18	−0.0485826	−0.0242913	+	0.999705i	$0.507733\pi$
$38$	−3.74322e19	−0.669808
$39$	2.65929e19	0.343920
$40$	4.87384e19	0.459326
$41$	2.35963e19	0.163322	0.0816611	−	0.996660i	$-0.473977\pi$
$41$	2.35963e19	0.163322	0.0816611	+	0.996660i	$0.473977\pi$
$42$	−4.41971e19	−0.226348
$43$	2.45267e20	0.936017	0.468008	−	0.883724i	$-0.344972\pi$
$43$	2.45267e20	0.936017	0.468008	+	0.883724i	$0.344972\pi$
$44$	8.32763e18	0.0238431
$45$	−2.00490e20	−0.433448
$46$	−3.93373e20	−0.646147
$47$	1.25013e21	1.56940	0.784700	−	0.619876i	$-0.212817\pi$
$47$	1.25013e21	1.56940	0.784700	+	0.619876i	$0.212817\pi$
$48$	1.70560e20	0.164574
$49$	1.02990e21	0.767971
$50$	−3.35011e20	−0.194059
$51$	−6.14312e20	−0.277819
$52$	3.23390e20	0.114732
$53$	3.59462e20	0.100509	0.0502545	−	0.998736i	$-0.483997\pi$
$53$	3.59462e20	0.100509	0.0502545	+	0.998736i	$0.483997\pi$
$54$	−1.51445e21	−0.335223
$55$	−1.03526e21	−0.182186
$56$	−9.72062e21	−1.36566
$57$	−1.07552e21	−0.121111
$58$	−1.31144e22	−1.18822
$59$	3.01921e21	0.220924	0.110462	−	0.993880i	$-0.464767\pi$
$59$	3.01921e21	0.220924	0.110462	+	0.993880i	$0.464767\pi$
$60$	7.74293e19	0.00459214
$61$	−2.21901e22	−1.07037	−0.535187	−	0.844733i	$-0.679759\pi$
$61$	−2.21901e22	−1.07037	−0.535187	+	0.844733i	$0.679759\pi$
$62$	3.41428e22	1.34401
$63$	3.99868e22	1.28872
$64$	3.97237e22	1.05148
$65$	−4.02025e22	−0.876671
$66$	−3.84892e21	−0.0693489
$67$	9.61859e22	1.43607	0.718036	−	0.696006i	$-0.245041\pi$
$67$	9.61859e22	1.43607	0.718036	+	0.696006i	$0.245041\pi$
$68$	−7.47052e21	−0.0926807
$69$	−1.13026e22	−0.116833
$70$	6.68162e22	0.576974
$71$	−8.70609e22	−0.629642	−0.314821	−	0.949151i	$-0.601945\pi$
$71$	−8.70609e22	−0.629642	−0.314821	+	0.949151i	$0.601945\pi$
$72$	−1.63940e23	−0.995470
$73$	−2.72860e22	−0.139445	−0.0697227	−	0.997566i	$-0.522211\pi$
$73$	−2.72860e22	−0.139445	−0.0697227	+	0.997566i	$0.522211\pi$
$74$	1.09340e22	0.0471394
$75$	−9.62569e21	−0.0350886
$76$	−1.30792e22	−0.0404027
$77$	2.06477e23	0.541673
$78$	−1.49467e23	−0.333704
$79$	−6.64384e23	−1.26497	−0.632485	−	0.774572i	$-0.717965\pi$
$79$	−6.64384e23	−1.26497	−0.632485	+	0.774572i	$0.717965\pi$
$80$	−2.57848e23	−0.419507
$81$	6.52287e23	0.908607
$82$	−1.32624e23	−0.158471
$83$	1.19385e23	0.122595	0.0612977	−	0.998120i	$-0.480476\pi$
$83$	1.19385e23	0.122595	0.0612977	+	0.998120i	$0.480476\pi$
$84$	−1.54429e22	−0.0136533
$85$	9.28704e23	0.708175
$86$	−1.37854e24	−0.908212
$87$	−3.76808e23	−0.214847
$88$	−8.46524e23	−0.418413
$89$	8.26026e23	0.354502	0.177251	−	0.984166i	$-0.443280\pi$
$89$	8.26026e23	0.354502	0.177251	+	0.984166i	$0.443280\pi$
$90$	1.12687e24	0.420573
$91$	8.01819e24	2.60651
$92$	−1.37448e23	−0.0389755
$93$	9.81009e23	0.243017
$94$	−7.02644e24	−1.52278
$95$	1.62595e24	0.308718
$96$	1.23126e23	0.0205097
$97$	4.97990e24	0.728743	0.364371	−	0.931254i	$-0.381284\pi$
$97$	4.97990e24	0.728743	0.364371	+	0.931254i	$0.381284\pi$
$98$	−5.78861e24	−0.745158
$99$	3.48226e24	0.394841
$100$	−1.17056e23	−0.0117056
$101$	−1.95352e25	−1.72505	−0.862523	−	0.506017i	$-0.831117\pi$
$101$	−1.95352e25	−1.72505	−0.862523	+	0.506017i	$0.831117\pi$
$102$	3.45277e24	0.269566
$103$	−6.23086e24	−0.430608	−0.215304	−	0.976547i	$-0.569074\pi$
$103$	−6.23086e24	−0.430608	−0.215304	+	0.976547i	$0.569074\pi$
$104$	−3.28734e25	−2.01339
$105$	1.91980e24	0.104325
$106$	−2.02037e24	−0.0975233
$107$	2.95639e25	1.26901	0.634505	−	0.772919i	$-0.281204\pi$
$107$	2.95639e25	1.26901	0.634505	+	0.772919i	$0.281204\pi$
$108$	−5.29165e23	−0.0202206
$109$	1.51166e25	0.514781	0.257391	−	0.966307i	$-0.417137\pi$
$109$	1.51166e25	0.514781	0.257391	+	0.966307i	$0.417137\pi$
$110$	5.81871e24	0.176774
$111$	3.14162e23	0.00852348
$112$	5.14265e25	1.24727
$113$	−5.66481e24	−0.122943	−0.0614717	−	0.998109i	$-0.519579\pi$
$113$	−5.66481e24	−0.122943	−0.0614717	+	0.998109i	$0.519579\pi$
$114$	6.04501e24	0.117513
$115$	1.70870e25	0.297813
$116$	−4.58228e24	−0.0716732
$117$	1.35228e26	1.89996
$118$	−1.69696e25	−0.214361
$119$	−1.85225e26	−2.10554
$120$	−7.87087e24	−0.0805856
$121$	−9.03660e25	−0.834042
$122$	1.24720e26	1.03858
$123$	−3.81062e24	−0.0286537
$124$	1.19298e25	0.0810706
$125$	1.45519e25	0.0894427
$126$	−2.24748e26	−1.25044
$127$	9.15919e25	0.461648	0.230824	−	0.972996i	$-0.425858\pi$
$127$	9.15919e25	0.461648	0.230824	+	0.972996i	$0.425858\pi$
$128$	−1.97686e26	−0.903340
$129$	−3.96087e25	−0.164218
$130$	2.25960e26	0.850629
$131$	2.10046e26	0.718494	0.359247	−	0.933243i	$-0.383034\pi$
$131$	2.10046e26	0.718494	0.359247	+	0.933243i	$0.383034\pi$
$132$	−1.34485e24	−0.00418311
$133$	−3.24287e26	−0.917876
$134$	−5.40618e26	−1.39341
$135$	6.57836e25	0.154506
$136$	7.59396e26	1.62642
$137$	6.34597e25	0.124020	0.0620099	−	0.998076i	$-0.480249\pi$
$137$	6.34597e25	0.124020	0.0620099	+	0.998076i	$0.480249\pi$
$138$	6.35267e25	0.113362
$139$	−8.09159e26	−1.31932	−0.659658	−	0.751566i	$-0.729299\pi$
$139$	−8.09159e26	−1.31932	−0.659658	+	0.751566i	$0.729299\pi$
$140$	2.33462e25	0.0348030
$141$	−2.01887e26	−0.275340
$142$	4.89330e26	0.610939
$143$	6.98267e26	0.798585
$144$	8.67317e26	0.909173
$145$	5.69650e26	0.547656
$146$	1.53362e26	0.135303
$147$	−1.66321e26	−0.134735
$148$	3.82046e24	0.00284344
$149$	1.84364e26	0.126139	0.0630694	−	0.998009i	$-0.479911\pi$
$149$	1.84364e26	0.126139	0.0630694	+	0.998009i	$0.479911\pi$
$150$	5.41017e25	0.0340463
$151$	2.76612e26	0.160199	0.0800993	−	0.996787i	$-0.474476\pi$
$151$	2.76612e26	0.160199	0.0800993	+	0.996787i	$0.474476\pi$
$152$	1.32953e27	0.709010
$153$	−3.12386e27	−1.53479
$154$	−1.16051e27	−0.525582
$155$	−1.48307e27	−0.619462
$156$	−5.22250e25	−0.0201290
$157$	−3.84455e27	−1.36804	−0.684022	−	0.729462i	$-0.739771\pi$
$157$	−3.84455e27	−1.36804	−0.684022	+	0.729462i	$0.739771\pi$
$158$	3.73420e27	1.22739
$159$	−5.80504e25	−0.0176336
$160$	−1.86140e26	−0.0522804
$161$	−3.40792e27	−0.885453
$162$	−3.66621e27	−0.881616
$163$	1.68740e26	0.0375728	0.0187864	−	0.999824i	$-0.494020\pi$
$163$	1.68740e26	0.0375728	0.0187864	+	0.999824i	$0.494020\pi$
$164$	−4.63401e25	−0.00955892
$165$	1.67186e26	0.0319632
$166$	−6.71010e26	−0.118954
$167$	6.75927e27	1.11159	0.555794	−	0.831320i	$-0.312414\pi$
$167$	6.75927e27	1.11159	0.555794	+	0.831320i	$0.312414\pi$
$168$	1.56981e27	0.239596
$169$	2.00597e28	2.84276
$170$	−5.21983e27	−0.687139
$171$	−5.46915e27	−0.669066
$172$	−4.81673e26	−0.0547832
$173$	8.21719e27	0.869255	0.434627	−	0.900610i	$-0.356880\pi$
$173$	8.21719e27	0.869255	0.434627	+	0.900610i	$0.356880\pi$
$174$	2.11787e27	0.208465
$175$	−2.90231e27	−0.265930
$176$	4.47850e27	0.382141
$177$	−4.87579e26	−0.0387596
$178$	−4.64272e27	−0.343972
$179$	−5.13179e26	−0.0354491	−0.0177246	−	0.999843i	$-0.505642\pi$
$179$	−5.13179e26	−0.0354491	−0.0177246	+	0.999843i	$0.505642\pi$
$180$	3.93738e26	0.0253688
$181$	8.03481e27	0.483052	0.241526	−	0.970394i	$-0.422352\pi$
$181$	8.03481e27	0.483052	0.241526	+	0.970394i	$0.422352\pi$
$182$	−4.50666e28	−2.52908
$183$	3.58353e27	0.187790
$184$	1.39719e28	0.683965
$185$	−4.74944e26	−0.0217268
$186$	−5.51381e27	−0.235798
$187$	−1.61304e28	−0.645098
$188$	−2.45511e27	−0.0918538
$189$	−1.31202e28	−0.459376
$190$	−9.13872e27	−0.299547
$191$	3.88902e28	1.19378	0.596888	−	0.802325i	$-0.296404\pi$
$191$	3.88902e28	1.19378	0.596888	+	0.802325i	$0.296404\pi$
$192$	−6.41507e27	−0.184474
$193$	3.84513e28	1.03620	0.518101	−	0.855320i	$-0.326639\pi$
$193$	3.84513e28	1.03620	0.518101	+	0.855320i	$0.326639\pi$
$194$	−2.79898e28	−0.707095
$195$	6.49240e27	0.153806
$196$	−2.02260e27	−0.0449478
$197$	−5.83452e28	−1.21668	−0.608342	−	0.793675i	$-0.708165\pi$
$197$	−5.83452e28	−1.21668	−0.608342	+	0.793675i	$0.708165\pi$
$198$	−1.95722e28	−0.383112
$199$	6.90116e28	1.26841	0.634203	−	0.773166i	$-0.281328\pi$
$199$	6.90116e28	1.26841	0.634203	+	0.773166i	$0.281328\pi$
$200$	1.18990e28	0.205417
$201$	−1.55333e28	−0.251949
$202$	1.09799e29	1.67380
$203$	−1.13614e29	−1.62829
$204$	1.20643e27	0.0162602
$205$	5.76081e27	0.0730399
$206$	3.50208e28	0.417817
$207$	−5.74751e28	−0.645432
$208$	1.73915e29	1.83885
$209$	−2.82406e28	−0.281220
$210$	−1.07903e28	−0.101226
$211$	7.08178e28	0.626054	0.313027	−	0.949744i	$-0.398657\pi$
$211$	7.08178e28	0.626054	0.313027	+	0.949744i	$0.398657\pi$
$212$	−7.05938e26	−0.00588259
$213$	1.40597e28	0.110466
$214$	−1.66166e29	−1.23131
$215$	5.98797e28	0.418599
$216$	5.37908e28	0.354843
$217$	2.95790e29	1.84178
$218$	−8.49635e28	−0.499489
$219$	4.40648e27	0.0244647
$220$	2.03311e27	0.0106630
$221$	−6.26399e29	−3.10418
$222$	−1.76576e27	−0.00827029
$223$	−3.92731e29	−1.73894	−0.869470	−	0.493986i	$-0.835539\pi$
$223$	−3.92731e29	−1.73894	−0.869470	+	0.493986i	$0.835539\pi$
$224$	3.71246e28	0.155440
$225$	−4.89479e28	−0.193844
$226$	3.18394e28	0.119291
$227$	2.97533e29	1.05490	0.527451	−	0.849585i	$-0.323148\pi$
$227$	2.97533e29	1.05490	0.527451	+	0.849585i	$0.323148\pi$
$228$	2.11218e27	0.00708837
$229$	1.03207e28	0.0327918	0.0163959	−	0.999866i	$-0.494781\pi$
$229$	1.03207e28	0.0327918	0.0163959	+	0.999866i	$0.494781\pi$
$230$	−9.60383e28	−0.288966
$231$	−3.33444e28	−0.0950328
$232$	4.65800e29	1.25776
$233$	−4.90509e28	−0.125516	−0.0627579	−	0.998029i	$-0.519990\pi$
$233$	−4.90509e28	−0.125516	−0.0627579	+	0.998029i	$0.519990\pi$
$234$	−7.60056e29	−1.84352
$235$	3.05209e29	0.701857
$236$	−5.92934e27	−0.0129302
$237$	1.07293e29	0.221930
$238$	1.04107e30	2.04299
$239$	1.52453e29	0.283899	0.141949	−	0.989874i	$-0.454663\pi$
$239$	1.52453e29	0.283899	0.141949	+	0.989874i	$0.454663\pi$
$240$	4.16405e28	0.0735996
$241$	6.62123e29	1.11103	0.555515	−	0.831507i	$-0.312521\pi$
$241$	6.62123e29	1.11103	0.555515	+	0.831507i	$0.312521\pi$
$242$	5.07906e29	0.809266
$243$	−3.33641e29	−0.504895
$244$	4.35785e28	0.0626469
$245$	2.51441e29	0.343447
$246$	2.14178e28	0.0278026
$247$	−1.09668e30	−1.35322
$248$	−1.21270e30	−1.42268
$249$	−1.92798e28	−0.0215085
$250$	−8.17897e28	−0.0867858
$251$	7.12546e29	0.719269	0.359635	−	0.933093i	$-0.382901\pi$
$251$	7.12546e29	0.719269	0.359635	+	0.933093i	$0.382901\pi$
$252$	−7.85290e28	−0.0754264
$253$	−2.96780e29	−0.271286
$254$	−5.14797e29	−0.447934
$255$	−1.49979e29	−0.124244
$256$	−2.21802e29	−0.174971
$257$	−4.98457e29	−0.374510	−0.187255	−	0.982311i	$-0.559959\pi$
$257$	−4.98457e29	−0.374510	−0.187255	+	0.982311i	$0.559959\pi$
$258$	2.22623e29	0.159339
$259$	9.47251e28	0.0645979
$260$	7.89527e28	0.0513098
$261$	−1.91612e30	−1.18690
$262$	−1.18057e30	−0.697151
$263$	1.57317e30	0.885785	0.442893	−	0.896575i	$-0.353952\pi$
$263$	1.57317e30	0.885785	0.442893	+	0.896575i	$0.353952\pi$
$264$	1.36707e29	0.0734077
$265$	8.77593e28	0.0449490
$266$	1.82267e30	0.890610
$267$	−1.33397e29	−0.0621949
$268$	−1.88897e29	−0.0840504
$269$	2.26106e30	0.960302	0.480151	−	0.877186i	$-0.340582\pi$
$269$	2.26106e30	0.960302	0.480151	+	0.877186i	$0.340582\pi$
$270$	−3.69740e29	−0.149916
$271$	3.05368e30	1.18225	0.591123	−	0.806582i	$-0.298685\pi$
$271$	3.05368e30	1.18225	0.591123	+	0.806582i	$0.298685\pi$
$272$	−4.01755e30	−1.48542
$273$	−1.29488e30	−0.457294
$274$	−3.56678e29	−0.120336
$275$	−2.52748e29	−0.0814760
$276$	2.21968e28	0.00683798
$277$	9.07706e29	0.267269	0.133634	−	0.991031i	$-0.457335\pi$
$277$	9.07706e29	0.267269	0.133634	+	0.991031i	$0.457335\pi$
$278$	4.54791e30	1.28012
$279$	4.98855e30	1.34252
$280$	−2.37320e30	−0.610743
$281$	−3.78227e30	−0.930943	−0.465472	−	0.885063i	$-0.654115\pi$
$281$	−3.78227e30	−0.930943	−0.465472	+	0.885063i	$0.654115\pi$
$282$	1.13472e30	0.267161
$283$	6.20146e29	0.139689	0.0698447	−	0.997558i	$-0.477750\pi$
$283$	6.20146e29	0.139689	0.0698447	+	0.997558i	$0.477750\pi$
$284$	1.70977e29	0.0368517
$285$	−2.62578e29	−0.0541624
$286$	−3.92464e30	−0.774863
$287$	−1.14896e30	−0.217161
$288$	6.26112e29	0.113304
$289$	8.69958e30	1.50756
$290$	−3.20175e30	−0.531388
$291$	−8.04216e29	−0.127853
$292$	5.35862e28	0.00816146
$293$	2.11326e28	0.00308395	0.00154198	−	0.999999i	$-0.499509\pi$
$293$	2.11326e28	0.00308395	0.00154198	+	0.999999i	$0.499509\pi$
$294$	9.34817e29	0.130733
$295$	7.37111e29	0.0988002
$296$	−3.88359e29	−0.0498984
$297$	−1.14258e30	−0.140744
$298$	−1.03623e30	−0.122392
$299$	−1.15250e31	−1.30542
$300$	1.89036e28	0.00205367
$301$	−1.19427e31	−1.24458
$302$	−1.55471e30	−0.155440
$303$	3.15479e30	0.302647
$304$	−7.03381e30	−0.647546
$305$	−5.41750e30	−0.478686
$306$	1.75578e31	1.48920
$307$	−1.38036e31	−1.12399	−0.561997	−	0.827139i	$-0.689967\pi$
$307$	−1.38036e31	−1.12399	−0.561997	+	0.827139i	$0.689967\pi$
$308$	−4.05494e29	−0.0317030
$309$	1.00624e30	0.0755472
$310$	8.33566e30	0.601061
$311$	1.34528e31	0.931767	0.465884	−	0.884846i	$-0.345736\pi$
$311$	1.34528e31	0.931767	0.465884	+	0.884846i	$0.345736\pi$
$312$	5.30880e30	0.353235
$313$	−2.11936e31	−1.35488	−0.677440	−	0.735578i	$-0.736911\pi$
$313$	−2.11936e31	−1.35488	−0.677440	+	0.735578i	$0.736911\pi$
$314$	2.16085e31	1.32741
$315$	9.76240e30	0.576335
$316$	1.30477e30	0.0740362
$317$	1.89239e31	1.03221	0.516107	−	0.856524i	$-0.327381\pi$
$317$	1.89239e31	1.03221	0.516107	+	0.856524i	$0.327381\pi$
$318$	3.26275e29	0.0171098
$319$	−9.89410e30	−0.498876
$320$	9.69816e30	0.470235
$321$	−4.77435e30	−0.222639
$322$	1.91544e31	0.859150
$323$	2.53340e31	1.09313
$324$	−1.28101e30	−0.0531789
$325$	−9.81507e30	−0.392059
$326$	−9.48411e29	−0.0364567
$327$	−2.44121e30	−0.0903148
$328$	4.71058e30	0.167746
$329$	−6.08723e31	−2.08675
$330$	−9.39677e29	−0.0310138
$331$	8.28866e30	0.263411	0.131706	−	0.991289i	$-0.457955\pi$
$331$	8.28866e30	0.263411	0.131706	+	0.991289i	$0.457955\pi$
$332$	−2.34457e29	−0.00717527
$333$	1.59755e30	0.0470872
$334$	−3.79908e31	−1.07857
$335$	2.34829e31	0.642231
$336$	−8.30499e30	−0.218826
$337$	−1.73200e31	−0.439719	−0.219859	−	0.975532i	$-0.570560\pi$
$337$	−1.73200e31	−0.439719	−0.219859	+	0.975532i	$0.570560\pi$
$338$	−1.12746e32	−2.75831
$339$	9.14824e29	0.0215696
$340$	−1.82386e30	−0.0414481
$341$	2.57590e31	0.564286
$342$	3.07396e31	0.649191
$343$	1.51515e31	0.308517
$344$	4.89632e31	0.961368
$345$	−2.75942e30	−0.0522491
$346$	−4.61851e31	−0.843433
$347$	9.40631e31	1.65692	0.828459	−	0.560050i	$-0.189218\pi$
$347$	9.40631e31	1.65692	0.828459	+	0.560050i	$0.189218\pi$
$348$	7.40003e29	0.0125746
$349$	−6.50222e31	−1.06597	−0.532984	−	0.846126i	$-0.678929\pi$
$349$	−6.50222e31	−1.06597	−0.532984	+	0.846126i	$0.678929\pi$
$350$	1.63125e31	0.258031
$351$	−4.43701e31	−0.677254
$352$	3.23301e30	0.0476237
$353$	1.13991e32	1.62064	0.810320	−	0.585988i	$-0.199293\pi$
$353$	1.13991e32	1.62064	0.810320	+	0.585988i	$0.199293\pi$
$354$	2.74046e30	0.0376082
$355$	−2.12551e31	−0.281585
$356$	−1.62221e30	−0.0207483
$357$	2.99125e31	0.369402
$358$	2.88435e30	0.0343961
$359$	1.32386e32	1.52462	0.762312	−	0.647209i	$-0.224064\pi$
$359$	1.32386e32	1.52462	0.762312	+	0.647209i	$0.224064\pi$
$360$	−4.00244e31	−0.445188
$361$	−4.87225e31	−0.523467
$362$	−4.51601e31	−0.468703
$363$	1.45934e31	0.146327
$364$	−1.57467e31	−0.152554
$365$	−6.66162e30	−0.0623619
$366$	−2.01414e31	−0.182211
$367$	1.33755e32	1.16946	0.584728	−	0.811230i	$-0.301201\pi$
$367$	1.33755e32	1.16946	0.584728	+	0.811230i	$0.301201\pi$
$368$	−7.39180e31	−0.624672
$369$	−1.93775e31	−0.158295
$370$	2.66944e30	0.0210814
$371$	−1.75032e31	−0.133642
$372$	−1.92658e30	−0.0142233
$373$	−6.83031e31	−0.487618	−0.243809	−	0.969823i	$-0.578397\pi$
$373$	−6.83031e31	−0.487618	−0.243809	+	0.969823i	$0.578397\pi$
$374$	9.06618e31	0.625935
$375$	−2.35002e30	−0.0156921
$376$	2.49567e32	1.61191
$377$	−3.84221e32	−2.40057
$378$	7.37427e31	0.445730
$379$	2.65242e31	0.155115	0.0775573	−	0.996988i	$-0.475288\pi$
$379$	2.65242e31	0.155115	0.0775573	+	0.996988i	$0.475288\pi$
$380$	−3.19315e30	−0.0180686
$381$	−1.47914e31	−0.0809929
$382$	−2.18584e32	−1.15831
$383$	1.36025e32	0.697646	0.348823	−	0.937189i	$-0.386582\pi$
$383$	1.36025e32	0.697646	0.348823	+	0.937189i	$0.386582\pi$
$384$	3.19248e31	0.158485
$385$	5.04094e31	0.242244
$386$	−2.16117e32	−1.00542
$387$	−2.01415e32	−0.907206
$388$	−9.77990e30	−0.0426518
$389$	−1.35952e32	−0.574139	−0.287069	−	0.957910i	$-0.592681\pi$
$389$	−1.35952e32	−0.574139	−0.287069	+	0.957910i	$0.592681\pi$
$390$	−3.64908e31	−0.149237
$391$	2.66234e32	1.05452
$392$	2.05602e32	0.788771
$393$	−3.39208e31	−0.126055
$394$	3.27932e32	1.18054
$395$	−1.62203e32	−0.565712
$396$	−6.83873e30	−0.0231092
$397$	−4.64212e32	−1.51997	−0.759985	−	0.649941i	$-0.774794\pi$
$397$	−4.64212e32	−1.51997	−0.759985	+	0.649941i	$0.774794\pi$
$398$	−3.87883e32	−1.23073
$399$	5.23699e31	0.161035
$400$	−6.29512e31	−0.187609
$401$	2.01779e31	0.0582868	0.0291434	−	0.999575i	$-0.490722\pi$
$401$	2.01779e31	0.0582868	0.0291434	+	0.999575i	$0.490722\pi$
$402$	8.73056e31	0.244465
$403$	1.00031e33	2.71532
$404$	3.83647e31	0.100963
$405$	1.59250e32	0.406341
$406$	6.38572e32	1.57992
$407$	8.24917e30	0.0197916
$408$	−1.22637e32	−0.285344
$409$	−1.32920e32	−0.299950	−0.149975	−	0.988690i	$-0.547919\pi$
$409$	−1.32920e32	−0.299950	−0.149975	+	0.988690i	$0.547919\pi$
$410$	−3.23789e31	−0.0708702
$411$	−1.02482e31	−0.0217584
$412$	1.22366e31	0.0252026
$413$	−1.47013e32	−0.293752
$414$	3.23041e32	0.626259
$415$	2.91468e31	0.0548264
$416$	1.25549e32	0.229164
$417$	1.30673e32	0.231465
$418$	1.58728e32	0.272866
$419$	−5.32651e31	−0.0888724	−0.0444362	−	0.999012i	$-0.514149\pi$
$419$	−5.32651e31	−0.0888724	−0.0444362	+	0.999012i	$0.514149\pi$
$420$	−3.77023e30	−0.00610594
$421$	−1.17889e33	−1.85331	−0.926657	−	0.375909i	$-0.877331\pi$
$421$	−1.17889e33	−1.85331	−0.926657	+	0.375909i	$0.877331\pi$
$422$	−3.98035e32	−0.607457
$423$	−1.02662e33	−1.52109
$424$	7.17603e31	0.103231
$425$	2.26734e32	0.316706
$426$	−7.90231e31	−0.107185
$427$	1.08049e33	1.42322
$428$	−5.80598e31	−0.0742726
$429$	−1.12765e32	−0.140106
$430$	−3.36556e32	−0.406165
$431$	−1.10742e33	−1.29821	−0.649107	−	0.760697i	$-0.724857\pi$
$431$	−1.10742e33	−1.29821	−0.649107	+	0.760697i	$0.724857\pi$
$432$	−2.84578e32	−0.324082
$433$	2.95407e32	0.326831	0.163415	−	0.986557i	$-0.447749\pi$
$433$	2.95407e32	0.326831	0.163415	+	0.986557i	$0.447749\pi$
$434$	−1.66250e33	−1.78707
$435$	−9.19941e31	−0.0960825
$436$	−2.96871e31	−0.0301291
$437$	4.66114e32	0.459700
$438$	−2.47668e31	−0.0237380
$439$	3.23987e32	0.301802	0.150901	−	0.988549i	$-0.451783\pi$
$439$	3.23987e32	0.301802	0.150901	+	0.988549i	$0.451783\pi$
$440$	−2.06671e32	−0.187120
$441$	−8.45765e32	−0.744333
$442$	3.52070e33	3.01197
$443$	1.00161e33	0.833015	0.416508	−	0.909132i	$-0.363254\pi$
$443$	1.00161e33	0.833015	0.416508	+	0.909132i	$0.363254\pi$
$444$	−6.16975e29	−0.000498862 0
$445$	2.01667e32	0.158538
$446$	2.20736e33	1.68728
$447$	−2.97734e31	−0.0221302
$448$	−1.93425e33	−1.39810
$449$	1.14437e33	0.804429	0.402214	−	0.915545i	$-0.368241\pi$
$449$	1.14437e33	0.804429	0.402214	+	0.915545i	$0.368241\pi$
$450$	2.75114e32	0.188086
$451$	−1.00058e32	−0.0665342
$452$	1.11250e31	0.00719563
$453$	−4.46707e31	−0.0281057
$454$	−1.67230e33	−1.02357
$455$	1.95757e33	1.16567
$456$	−2.14708e32	−0.124391
$457$	−2.42221e33	−1.36540	−0.682699	−	0.730700i	$-0.739194\pi$
$457$	−2.42221e33	−1.36540	−0.682699	+	0.730700i	$0.739194\pi$
$458$	−5.80079e31	−0.0318177
$459$	1.02498e33	0.547087
$460$	−3.35567e31	−0.0174304
$461$	8.99670e32	0.454801	0.227401	−	0.973801i	$-0.426977\pi$
$461$	8.99670e32	0.454801	0.227401	+	0.973801i	$0.426977\pi$
$462$	1.87414e32	0.0922098
$463$	1.05191e33	0.503752	0.251876	−	0.967759i	$-0.418952\pi$
$463$	1.05191e33	0.503752	0.251876	+	0.967759i	$0.418952\pi$
$464$	−2.46429e33	−1.14873
$465$	2.39504e32	0.108680
$466$	2.75693e32	0.121787
$467$	1.96362e33	0.844494	0.422247	−	0.906481i	$-0.361241\pi$
$467$	1.96362e33	0.844494	0.422247	+	0.906481i	$0.361241\pi$
$468$	−2.65571e32	−0.111201
$469$	−4.68354e33	−1.90948
$470$	−1.71544e33	−0.681008
$471$	6.20865e32	0.240014
$472$	6.02732e32	0.226908
$473$	−1.04003e33	−0.381314
$474$	−6.03045e32	−0.215338
$475$	3.96960e32	0.138063
$476$	3.63759e32	0.123233
$477$	−2.95194e32	−0.0974153
$478$	−8.56872e32	−0.275465
$479$	5.97765e33	1.87213	0.936066	−	0.351824i	$-0.114438\pi$
$479$	5.97765e33	1.87213	0.936066	+	0.351824i	$0.114438\pi$
$480$	3.00601e31	0.00917223
$481$	3.20343e32	0.0952362
$482$	−3.72149e33	−1.07803
$483$	5.50352e32	0.155347
$484$	1.77467e32	0.0488148
$485$	1.21580e33	0.325904
$486$	1.87524e33	0.489897
$487$	−5.43009e33	−1.38260	−0.691298	−	0.722570i	$-0.742961\pi$
$487$	−5.43009e33	−1.38260	−0.691298	+	0.722570i	$0.742961\pi$
$488$	−4.42986e33	−1.09936
$489$	−2.72502e31	−0.00659188
$490$	−1.41324e33	−0.333245
$491$	−7.86842e33	−1.80871	−0.904355	−	0.426781i	$-0.859647\pi$
$491$	−7.86842e33	−1.80871	−0.904355	+	0.426781i	$0.859647\pi$
$492$	7.48357e30	0.00167705
$493$	8.87576e33	1.93918
$494$	6.16394e33	1.31302
$495$	8.50162e32	0.176578
$496$	6.41572e33	1.29934
$497$	4.23923e33	0.837205
$498$	1.08363e32	0.0208696
$499$	−8.74288e33	−1.64209	−0.821046	−	0.570862i	$-0.806609\pi$
$499$	−8.74288e33	−1.64209	−0.821046	+	0.570862i	$0.806609\pi$
$500$	−2.85781e31	−0.00523490
$501$	−1.09157e33	−0.195020
$502$	−4.00490e33	−0.697903
$503$	2.50553e32	0.0425892	0.0212946	−	0.999773i	$-0.493221\pi$
$503$	2.50553e32	0.0425892	0.0212946	+	0.999773i	$0.493221\pi$
$504$	7.98266e33	1.32363
$505$	−4.76934e33	−0.771464
$506$	1.66806e33	0.263227
$507$	−3.23948e33	−0.498742
$508$	−1.79875e32	−0.0270193
$509$	1.22617e34	1.79712	0.898560	−	0.438850i	$-0.144614\pi$
$509$	1.22617e34	1.79712	0.898560	+	0.438850i	$0.144614\pi$
$510$	8.42962e32	0.120554
$511$	1.32863e33	0.185414
$512$	7.87988e33	1.07311
$513$	1.79450e33	0.238494
$514$	2.80160e33	0.363385
$515$	−1.52120e33	−0.192574
$516$	7.77865e31	0.00961132
$517$	−5.30109e33	−0.639342
$518$	−5.32407e32	−0.0626790
$519$	−1.32701e33	−0.152505
$520$	−8.02573e33	−0.900415
$521$	−1.66039e34	−1.81860	−0.909302	−	0.416138i	$-0.863383\pi$
$521$	−1.66039e34	−1.81860	−0.909302	+	0.416138i	$0.863383\pi$
$522$	1.07696e34	1.15165
$523$	9.25313e33	0.966090	0.483045	−	0.875595i	$-0.339531\pi$
$523$	9.25313e33	0.966090	0.483045	+	0.875595i	$0.339531\pi$
$524$	−4.12504e32	−0.0420520
$525$	4.68700e32	0.0466556
$526$	−8.84207e33	−0.859473
$527$	−2.31078e34	−2.19344
$528$	−7.23243e32	−0.0670440
$529$	−6.14740e33	−0.556539
$530$	−4.93255e32	−0.0436138
$531$	−2.47940e33	−0.214124
$532$	6.36859e32	0.0537214
$533$	−3.88559e33	−0.320160
$534$	7.49764e32	0.0603474
$535$	7.21776e33	0.567518
$536$	1.92018e34	1.47497
$537$	8.28744e31	0.00621931
$538$	−1.27084e34	−0.931777
$539$	−4.36721e33	−0.312856
$540$	−1.29191e32	−0.00904292
$541$	6.19049e33	0.423408	0.211704	−	0.977334i	$-0.432099\pi$
$541$	6.19049e33	0.423408	0.211704	+	0.977334i	$0.432099\pi$
$542$	−1.71634e34	−1.14713
$543$	−1.29756e33	−0.0847481
$544$	−2.90025e33	−0.185118
$545$	3.69057e33	0.230217
$546$	7.27792e33	0.443710
$547$	1.47983e34	0.881802	0.440901	−	0.897556i	$-0.354659\pi$
$547$	1.47983e34	0.881802	0.440901	+	0.897556i	$0.354659\pi$
$548$	−1.24627e32	−0.00725862
$549$	1.82227e34	1.03743
$550$	1.42058e33	0.0790557
$551$	1.55394e34	0.845356
$552$	−2.25636e33	−0.119997
$553$	3.23506e34	1.68197
$554$	−5.10181e33	−0.259330
$555$	7.66998e31	0.00381181
$556$	1.58908e33	0.0772169
$557$	3.51384e34	1.66952	0.834760	−	0.550614i	$-0.185607\pi$
$557$	3.51384e34	1.66952	0.834760	+	0.550614i	$0.185607\pi$
$558$	−2.80384e34	−1.30264
$559$	−4.03880e34	−1.83487
$560$	1.25553e34	0.557798
$561$	2.60494e33	0.113178
$562$	2.12584e34	0.903289
$563$	1.42441e34	0.591945	0.295972	−	0.955197i	$-0.404356\pi$
$563$	1.42441e34	0.591945	0.295972	+	0.955197i	$0.404356\pi$
$564$	3.96481e32	0.0161151
$565$	−1.38301e33	−0.0549820
$566$	−3.48556e33	−0.135540
$567$	−3.17616e34	−1.20813
$568$	−1.73802e34	−0.646696
$569$	−1.27231e34	−0.463116	−0.231558	−	0.972821i	$-0.574382\pi$
$569$	−1.27231e34	−0.463116	−0.231558	+	0.972821i	$0.574382\pi$
$570$	1.47583e33	0.0525535
$571$	−6.11617e33	−0.213073	−0.106536	−	0.994309i	$-0.533976\pi$
$571$	−6.11617e33	−0.213073	−0.106536	+	0.994309i	$0.533976\pi$
$572$	−1.37131e33	−0.0467396
$573$	−6.28046e33	−0.209440
$574$	6.45781e33	0.210711
$575$	4.17163e33	0.133186
$576$	−3.26214e34	−1.01911
$577$	2.71759e34	0.830781	0.415391	−	0.909643i	$-0.363645\pi$
$577$	2.71759e34	0.830781	0.415391	+	0.909643i	$0.363645\pi$
$578$	−4.88964e34	−1.46278
$579$	−6.20958e33	−0.181794
$580$	−1.11872e33	−0.0320532
$581$	−5.81318e33	−0.163009
$582$	4.52014e33	0.124055
$583$	−1.52427e33	−0.0409453
$584$	−5.44717e33	−0.143222
$585$	3.30147e34	0.849687
$586$	−1.18777e32	−0.00299234
$587$	2.64497e34	0.652295	0.326147	−	0.945319i	$-0.394249\pi$
$587$	2.64497e34	0.652295	0.326147	+	0.945319i	$0.394249\pi$
$588$	3.26634e32	0.00788578
$589$	−4.04564e34	−0.956195
$590$	−4.14297e33	−0.0958654
$591$	9.42231e33	0.213459
$592$	2.05460e33	0.0455727
$593$	3.40641e34	0.739798	0.369899	−	0.929072i	$-0.379392\pi$
$593$	3.40641e34	0.739798	0.369899	+	0.929072i	$0.379392\pi$
$594$	6.42191e33	0.136563
$595$	−4.52210e34	−0.941626
$596$	−3.62068e32	−0.00738264
$597$	−1.11448e34	−0.222533
$598$	6.47766e34	1.26664
$599$	−1.28982e34	−0.246998	−0.123499	−	0.992345i	$-0.539412\pi$
$599$	−1.28982e34	−0.246998	−0.123499	+	0.992345i	$0.539412\pi$
$600$	−1.92160e33	−0.0360390
$601$	3.90337e34	0.716983	0.358492	−	0.933533i	$-0.383291\pi$
$601$	3.90337e34	0.716983	0.358492	+	0.933533i	$0.383291\pi$
$602$	6.71245e34	1.20760
$603$	−7.89887e34	−1.39187
$604$	−5.43230e32	−0.00937610
$605$	−2.20620e34	−0.372995
$606$	−1.77316e34	−0.293657
$607$	6.85577e34	1.11224	0.556119	−	0.831103i	$-0.312290\pi$
$607$	6.85577e34	1.11224	0.556119	+	0.831103i	$0.312290\pi$
$608$	−5.07768e33	−0.0806994
$609$	1.83478e34	0.285672
$610$	3.04493e34	0.464467
$611$	−2.05859e35	−3.07649
$612$	6.13486e33	0.0898280
$613$	9.89487e34	1.41956	0.709781	−	0.704422i	$-0.248794\pi$
$613$	9.89487e34	1.41956	0.709781	+	0.704422i	$0.248794\pi$
$614$	7.75840e34	1.09060
$615$	−9.30326e32	−0.0128143
$616$	4.12194e34	0.556344
$617$	−6.48873e34	−0.858213	−0.429106	−	0.903254i	$-0.641171\pi$
$617$	−6.48873e34	−0.858213	−0.429106	+	0.903254i	$0.641171\pi$
$618$	−5.65559e33	−0.0733031
$619$	1.17456e35	1.49191	0.745956	−	0.665995i	$-0.231993\pi$
$619$	1.17456e35	1.49191	0.745956	+	0.665995i	$0.231993\pi$
$620$	2.91256e33	0.0362559
$621$	1.88583e34	0.230069
$622$	−7.56121e34	−0.904089
$623$	−4.02214e34	−0.471364
$624$	−2.80860e34	−0.322613
$625$	3.55271e33	0.0400000
$626$	1.19120e35	1.31463
$627$	4.56065e33	0.0493381
$628$	7.55021e33	0.0800688
$629$	−7.40013e33	−0.0769319
$630$	−5.48701e34	−0.559215
$631$	1.37738e35	1.37622	0.688108	−	0.725609i	$-0.258442\pi$
$631$	1.37738e35	1.37622	0.688108	+	0.725609i	$0.258442\pi$
$632$	−1.32632e35	−1.29923
$633$	−1.14365e34	−0.109837
$634$	−1.06363e35	−1.00155
$635$	2.23613e34	0.206455
$636$	1.14004e32	0.00103206
$637$	−1.69594e35	−1.50545
$638$	5.56103e34	0.484057
$639$	7.14952e34	0.610262
$640$	−4.82632e34	−0.403986
$641$	5.95192e34	0.488576	0.244288	−	0.969703i	$-0.421446\pi$
$641$	5.95192e34	0.488576	0.244288	+	0.969703i	$0.421446\pi$
$642$	2.68345e34	0.216025
$643$	−1.30205e35	−1.02800	−0.513998	−	0.857791i	$-0.671836\pi$
$643$	−1.30205e35	−1.02800	−0.513998	+	0.857791i	$0.671836\pi$
$644$	6.69272e33	0.0518238
$645$	−9.67010e33	−0.0734403
$646$	−1.42391e35	−1.06066
$647$	−2.21950e35	−1.62163	−0.810816	−	0.585301i	$-0.800976\pi$
$647$	−2.21950e35	−1.62163	−0.810816	+	0.585301i	$0.800976\pi$
$648$	1.30218e35	0.933216
$649$	−1.28027e34	−0.0900000
$650$	5.51661e34	0.380413
$651$	−4.77679e34	−0.323127
$652$	−3.31384e32	−0.00219906
$653$	−2.16397e35	−1.40876	−0.704381	−	0.709823i	$-0.748775\pi$
$653$	−2.16397e35	−1.40876	−0.704381	+	0.709823i	$0.748775\pi$
$654$	1.37210e34	0.0876320
$655$	5.12808e34	0.321320
$656$	−2.49211e34	−0.153204
$657$	2.24075e34	0.135153
$658$	3.42136e35	2.02477
$659$	2.02567e35	1.17625	0.588126	−	0.808769i	$-0.299866\pi$
$659$	2.02567e35	1.17625	0.588126	+	0.808769i	$0.299866\pi$
$660$	−3.28332e32	−0.00187074
$661$	2.44349e35	1.36613	0.683065	−	0.730358i	$-0.260647\pi$
$661$	2.44349e35	1.36613	0.683065	+	0.730358i	$0.260647\pi$
$662$	−4.65868e34	−0.255587
$663$	1.01159e35	0.544607
$664$	2.38332e34	0.125916
$665$	−7.91716e34	−0.410487
$666$	−8.97913e33	−0.0456885
$667$	1.63303e35	0.815495
$668$	−1.32744e34	−0.0650590
$669$	6.34231e34	0.305085
$670$	−1.31987e35	−0.623154
$671$	9.40951e34	0.436049
$672$	−5.99534e33	−0.0272708
$673$	−1.46636e35	−0.654714	−0.327357	−	0.944901i	$-0.606158\pi$
$673$	−1.46636e35	−0.654714	−0.327357	+	0.944901i	$0.606158\pi$
$674$	9.73480e34	0.426657
$675$	1.60604e34	0.0690972
$676$	−3.93946e34	−0.166381
$677$	2.81475e35	1.16703	0.583514	−	0.812103i	$-0.301678\pi$
$677$	2.81475e35	1.16703	0.583514	+	0.812103i	$0.301678\pi$
$678$	−5.14181e33	−0.0209288
$679$	−2.42485e35	−0.968973
$680$	1.85399e35	0.727356
$681$	−4.80494e34	−0.185075
$682$	−1.44780e35	−0.547524
$683$	7.24197e34	0.268904	0.134452	−	0.990920i	$-0.457073\pi$
$683$	7.24197e34	0.268904	0.134452	+	0.990920i	$0.457073\pi$
$684$	1.07407e34	0.0391591
$685$	1.54931e34	0.0554633
$686$	−8.51598e34	−0.299353
$687$	−1.66671e33	−0.00575309
$688$	−2.59038e35	−0.878027
$689$	−5.91925e34	−0.197027
$690$	1.55095e34	0.0506971
$691$	−2.31151e35	−0.742027	−0.371014	−	0.928627i	$-0.620990\pi$
$691$	−2.31151e35	−0.742027	−0.371014	+	0.928627i	$0.620990\pi$
$692$	−1.61375e34	−0.0508757
$693$	−1.69561e35	−0.525000
$694$	−5.28686e35	−1.60770
$695$	−1.97548e35	−0.590016
$696$	−7.52230e34	−0.220666
$697$	8.97596e34	0.258625
$698$	3.65460e35	1.03430
$699$	7.92135e33	0.0220209
$700$	5.69976e33	0.0155644
$701$	−3.68827e35	−0.989344	−0.494672	−	0.869080i	$-0.664712\pi$
$701$	−3.68827e35	−0.989344	−0.494672	+	0.869080i	$0.664712\pi$
$702$	2.49385e35	0.657136
$703$	−1.29559e34	−0.0335372
$704$	−1.68445e35	−0.428350
$705$	−4.92889e34	−0.123136
$706$	−6.40692e35	−1.57250
$707$	9.51220e35	2.29371
$708$	9.57543e32	0.00226852
$709$	5.32208e35	1.23881	0.619403	−	0.785073i	$-0.287375\pi$
$709$	5.32208e35	1.23881	0.619403	+	0.785073i	$0.287375\pi$
$710$	1.19465e35	0.273220
$711$	5.45598e35	1.22603
$712$	1.64902e35	0.364104
$713$	−4.25155e35	−0.922418
$714$	−1.68124e35	−0.358429
$715$	1.70475e35	0.357138
$716$	1.00782e33	0.00207477
$717$	−2.46201e34	−0.0498081
$718$	−7.44085e35	−1.47934
$719$	9.03652e34	0.176559	0.0882796	−	0.996096i	$-0.471863\pi$
$719$	9.03652e34	0.176559	0.0882796	+	0.996096i	$0.471863\pi$
$720$	2.11747e35	0.406595
$721$	3.03397e35	0.572559
$722$	2.73847e35	0.507917
$723$	−1.06928e35	−0.194922
$724$	−1.57794e34	−0.0282720
$725$	1.39075e35	0.244919
$726$	−8.20229e34	−0.141980
$727$	−3.65394e35	−0.621700	−0.310850	−	0.950459i	$-0.600614\pi$
$727$	−3.65394e35	−0.621700	−0.310850	+	0.950459i	$0.600614\pi$
$728$	1.60069e36	2.67710
$729$	−4.98795e35	−0.820026
$730$	3.74420e34	0.0605094
$731$	9.32989e35	1.48221
$732$	−7.03759e33	−0.0109910
$733$	−7.53864e35	−1.15743	−0.578713	−	0.815531i	$-0.696445\pi$
$733$	−7.53864e35	−1.15743	−0.578713	+	0.815531i	$0.696445\pi$
$734$	−7.51775e35	−1.13472
$735$	−4.06058e34	−0.0602554
$736$	−5.33611e34	−0.0778488
$737$	−4.07868e35	−0.585027
$738$	1.08912e35	0.153593
$739$	−1.47048e34	−0.0203893	−0.0101947	−	0.999948i	$-0.503245\pi$
$739$	−1.47048e34	−0.0203893	−0.0101947	+	0.999948i	$0.503245\pi$
$740$	9.32729e32	0.00127163
$741$	1.77105e35	0.237413
$742$	9.83773e34	0.129672
$743$	1.19689e35	0.155130	0.0775648	−	0.996987i	$-0.475286\pi$
$743$	1.19689e35	0.155130	0.0775648	+	0.996987i	$0.475286\pi$
$744$	1.95841e35	0.249599
$745$	4.50108e34	0.0564109
$746$	3.83901e35	0.473134
$747$	−9.80402e34	−0.118822
$748$	3.16781e34	0.0377563
$749$	−1.43955e36	−1.68734
$750$	1.32084e34	0.0152260
$751$	1.31509e35	0.149092	0.0745461	−	0.997218i	$-0.476249\pi$
$751$	1.31509e35	0.149092	0.0745461	+	0.997218i	$0.476249\pi$
$752$	−1.32033e36	−1.47217
$753$	−1.15071e35	−0.126191
$754$	2.15953e36	2.32926
$755$	6.75322e34	0.0716430
$756$	2.57664e34	0.0268863
$757$	3.61675e35	0.371210	0.185605	−	0.982624i	$-0.440576\pi$
$757$	3.61675e35	0.371210	0.185605	+	0.982624i	$0.440576\pi$
$758$	−1.49081e35	−0.150507
$759$	4.79276e34	0.0475953
$760$	3.24592e35	0.317079
$761$	−1.16974e36	−1.12404	−0.562019	−	0.827125i	$-0.689975\pi$
$761$	−1.16974e36	−1.12404	−0.562019	+	0.827125i	$0.689975\pi$
$762$	8.31357e34	0.0785870
$763$	−7.36066e35	−0.684479
$764$	−7.63753e34	−0.0698693
$765$	−7.62660e35	−0.686378
$766$	−7.64536e35	−0.676922
$767$	−4.97172e35	−0.433076
$768$	3.58193e34	0.0306974
$769$	1.35769e35	0.114478	0.0572388	−	0.998361i	$-0.481770\pi$
$769$	1.35769e35	0.114478	0.0572388	+	0.998361i	$0.481770\pi$
$770$	−2.83328e35	−0.235048
$771$	8.04969e34	0.0657052
$772$	−7.55134e34	−0.0606468
$773$	1.44242e35	0.113985	0.0569926	−	0.998375i	$-0.481849\pi$
$773$	1.44242e35	0.113985	0.0569926	+	0.998375i	$0.481849\pi$
$774$	1.13207e36	0.880257
$775$	−3.62077e35	−0.277032
$776$	9.94150e35	0.748480
$777$	−1.52974e34	−0.0113332
$778$	7.64127e35	0.557084
$779$	1.57148e35	0.112744
$780$	−1.27503e34	−0.00900194
$781$	3.69174e35	0.256504
$782$	−1.49638e36	−1.02319
$783$	6.28703e35	0.423081
$784$	−1.08773e36	−0.720393
$785$	−9.38611e35	−0.611808
$786$	1.90654e35	0.122310
$787$	−2.06647e35	−0.130481	−0.0652403	−	0.997870i	$-0.520781\pi$
$787$	−2.06647e35	−0.130481	−0.0652403	+	0.997870i	$0.520781\pi$
$788$	1.14583e35	0.0712100
$789$	−2.54055e35	−0.155405
$790$	9.11670e35	0.548907
$791$	2.75835e35	0.163472
$792$	6.95173e35	0.405535
$793$	3.65403e36	2.09825
$794$	2.60913e36	1.47482
$795$	−1.41725e34	−0.00788599
$796$	−1.35530e35	−0.0742373
$797$	−7.82604e34	−0.0422001	−0.0211000	−	0.999777i	$-0.506717\pi$
$797$	−7.82604e34	−0.0422001	−0.0211000	+	0.999777i	$0.506717\pi$
$798$	−2.94347e35	−0.156251
$799$	4.75548e36	2.48519
$800$	−4.54442e34	−0.0233805
$801$	−6.78340e35	−0.343590
$802$	−1.13411e35	−0.0565554
$803$	1.15704e35	0.0568072
$804$	3.05054e34	0.0147461
$805$	−8.32011e35	−0.395987
$806$	−5.62229e36	−2.63466
$807$	−3.65143e35	−0.168478
$808$	−3.89986e36	−1.77177
$809$	2.42162e35	0.108330	0.0541652	−	0.998532i	$-0.482750\pi$
$809$	2.42162e35	0.108330	0.0541652	+	0.998532i	$0.482750\pi$
$810$	−8.95071e35	−0.394271
$811$	2.92932e36	1.27059	0.635297	−	0.772268i	$-0.280878\pi$
$811$	2.92932e36	1.27059	0.635297	+	0.772268i	$0.280878\pi$
$812$	2.23123e35	0.0953003
$813$	−4.93146e35	−0.207417
$814$	−4.63649e34	−0.0192037
$815$	4.11963e34	0.0168030
$816$	6.48804e35	0.260607
$817$	1.63345e36	0.646145
$818$	7.47083e35	0.291040
$819$	−6.58461e36	−2.52628
$820$	−1.13135e34	−0.00427488
$821$	−8.55168e35	−0.318245	−0.159123	−	0.987259i	$-0.550867\pi$
$821$	−8.55168e35	−0.318245	−0.159123	+	0.987259i	$0.550867\pi$
$822$	5.76008e34	0.0211121
$823$	−2.41450e36	−0.871625	−0.435812	−	0.900038i	$-0.643539\pi$
$823$	−2.41450e36	−0.871625	−0.435812	+	0.900038i	$0.643539\pi$
$824$	−1.24388e36	−0.442271
$825$	4.08169e34	0.0142944
$826$	8.26294e35	0.285026
$827$	−5.33865e35	−0.181390	−0.0906949	−	0.995879i	$-0.528909\pi$
$827$	−5.33865e35	−0.181390	−0.0906949	+	0.995879i	$0.528909\pi$
$828$	1.12874e35	0.0377758
$829$	1.79700e36	0.592401	0.296200	−	0.955126i	$-0.404280\pi$
$829$	1.79700e36	0.592401	0.296200	+	0.955126i	$0.404280\pi$
$830$	−1.63821e35	−0.0531977
$831$	−1.46588e35	−0.0468905
$832$	−6.54128e36	−2.06120
$833$	3.91772e36	1.21610
$834$	−7.34453e35	−0.224589
$835$	1.65021e36	0.497117
$836$	5.54610e34	0.0164592
$837$	−1.63681e36	−0.478553
$838$	2.99379e35	0.0862325
$839$	−1.16243e36	−0.329871	−0.164935	−	0.986304i	$-0.552742\pi$
$839$	−1.16243e36	−0.329871	−0.164935	+	0.986304i	$0.552742\pi$
$840$	3.83253e35	0.107151
$841$	1.81387e36	0.499638
$842$	6.62603e36	1.79826
$843$	6.10807e35	0.163328
$844$	−1.39077e35	−0.0366417
$845$	4.89738e36	1.27132
$846$	5.77018e36	1.47591
$847$	4.40015e36	1.10898
$848$	−3.79645e35	−0.0942821
$849$	−1.00149e35	−0.0245075
$850$	−1.27437e36	−0.307298
$851$	−1.36153e35	−0.0323526
$852$	−2.76114e34	−0.00646537
$853$	−6.50741e36	−1.50157	−0.750784	−	0.660547i	$-0.770324\pi$
$853$	−6.50741e36	−1.50157	−0.750784	+	0.660547i	$0.770324\pi$
$854$	−6.07296e36	−1.38095
$855$	−1.33524e36	−0.299215
$856$	5.90192e36	1.30338
$857$	−2.15753e36	−0.469565	−0.234783	−	0.972048i	$-0.575438\pi$
$857$	−2.15753e36	−0.469565	−0.234783	+	0.972048i	$0.575438\pi$
$858$	6.33800e35	0.135944
$859$	7.32557e34	0.0154856	0.00774278	−	0.999970i	$-0.497535\pi$
$859$	7.32557e34	0.0154856	0.00774278	+	0.999970i	$0.497535\pi$
$860$	−1.17596e35	−0.0244998
$861$	1.85549e35	0.0380995
$862$	6.22430e36	1.25965
$863$	2.45498e36	0.489681	0.244841	−	0.969563i	$-0.421264\pi$
$863$	2.45498e36	0.489681	0.244841	+	0.969563i	$0.421264\pi$
$864$	−2.05436e35	−0.0403882
$865$	2.00615e36	0.388742
$866$	−1.66035e36	−0.317122
$867$	−1.40491e36	−0.264491
$868$	−5.80895e35	−0.107796
$869$	2.81726e36	0.515323
$870$	5.17057e35	0.0932284
$871$	−1.58389e37	−2.81513
$872$	3.01776e36	0.528724
$873$	−4.08954e36	−0.706312
$874$	−2.61982e36	−0.446044
$875$	−7.08571e35	−0.118928
$876$	−8.65377e33	−0.00143187
$877$	3.31458e36	0.540671	0.270335	−	0.962766i	$-0.412865\pi$
$877$	3.31458e36	0.540671	0.270335	+	0.962766i	$0.412865\pi$
$878$	−1.82099e36	−0.292836
$879$	−3.41275e33	−0.000541058 0
$880$	1.09338e36	0.170899
$881$	3.67808e36	0.566790	0.283395	−	0.959003i	$-0.408539\pi$
$881$	3.67808e36	0.566790	0.283395	+	0.959003i	$0.408539\pi$
$882$	4.75366e36	0.722222
$883$	−3.81719e35	−0.0571788	−0.0285894	−	0.999591i	$-0.509102\pi$
$883$	−3.81719e35	−0.0571788	−0.0285894	+	0.999591i	$0.509102\pi$
$884$	1.23017e36	0.181682
$885$	−1.19038e35	−0.0173338
$886$	−5.62961e36	−0.808270
$887$	−6.11827e36	−0.866130	−0.433065	−	0.901363i	$-0.642568\pi$
$887$	−6.11827e36	−0.866130	−0.433065	+	0.901363i	$0.642568\pi$
$888$	6.27169e34	0.00875433
$889$	−4.45985e36	−0.613830
$890$	−1.13348e36	−0.153829
$891$	−2.76597e36	−0.370148
$892$	7.71274e35	0.101777
$893$	8.32575e36	1.08338
$894$	1.67343e35	0.0214728
$895$	−1.25288e35	−0.0158533
$896$	9.62584e36	1.20113
$897$	1.86119e36	0.229026
$898$	−6.43199e36	−0.780533
$899$	−1.41739e37	−1.69626
$900$	9.61274e34	0.0113453
$901$	1.36738e36	0.159159
$902$	5.62380e35	0.0645578
$903$	1.92865e36	0.218352
$904$	−1.13088e36	−0.126273
$905$	1.96162e36	0.216027
$906$	2.51074e35	0.0272709
$907$	4.97096e36	0.532537	0.266268	−	0.963899i	$-0.414209\pi$
$907$	4.97096e36	0.532537	0.266268	+	0.963899i	$0.414209\pi$
$908$	−5.84318e35	−0.0617413
$909$	1.60425e37	1.67195
$910$	−1.10026e37	−1.13104
$911$	−1.58272e37	−1.60481	−0.802407	−	0.596777i	$-0.796448\pi$
$911$	−1.58272e37	−1.60481	−0.802407	+	0.596777i	$0.796448\pi$
$912$	1.13591e36	0.113608
$913$	−5.06243e35	−0.0499429
$914$	1.36141e37	1.32484
$915$	8.74884e35	0.0839821
$916$	−2.02685e34	−0.00191924
$917$	−1.02277e37	−0.955346
$918$	−5.76094e36	−0.530835
$919$	1.93499e37	1.75888	0.879438	−	0.476014i	$-0.157919\pi$
$919$	1.93499e37	1.75888	0.879438	+	0.476014i	$0.157919\pi$
$920$	3.41112e36	0.305879
$921$	2.22918e36	0.197197
$922$	−5.05664e36	−0.441291
$923$	1.43363e37	1.23429
$924$	6.54842e34	0.00556208
$925$	−1.15953e35	−0.00971652
$926$	−5.91232e36	−0.488788
$927$	5.11683e36	0.417354
$928$	−1.77896e36	−0.143159
$929$	−4.88021e36	−0.387474	−0.193737	−	0.981054i	$-0.562061\pi$
$929$	−4.88021e36	−0.387474	−0.193737	+	0.981054i	$0.562061\pi$
$930$	−1.34614e36	−0.105452
$931$	6.85903e36	0.530141
$932$	9.63298e34	0.00734618
$933$	−2.17252e36	−0.163472
$934$	−1.10366e37	−0.819408
$935$	−3.93809e36	−0.288496
$936$	2.69959e37	1.95142
$937$	−6.46379e36	−0.461044	−0.230522	−	0.973067i	$-0.574043\pi$
$937$	−6.46379e36	−0.461044	−0.230522	+	0.973067i	$0.574043\pi$
$938$	2.63241e37	1.85275
$939$	3.42261e36	0.237704
$940$	−5.99391e35	−0.0410783
$941$	−8.45960e36	−0.572110	−0.286055	−	0.958213i	$-0.592344\pi$
$941$	−8.45960e36	−0.572110	−0.286055	+	0.958213i	$0.592344\pi$
$942$	−3.48960e36	−0.232884
$943$	1.65146e36	0.108761
$944$	−3.18873e36	−0.207237
$945$	−3.20317e36	−0.205439
$946$	5.84556e36	0.369987
$947$	−1.88534e37	−1.17765	−0.588825	−	0.808261i	$-0.700409\pi$
$947$	−1.88534e37	−1.17765	−0.588825	+	0.808261i	$0.700409\pi$
$948$	−2.10710e35	−0.0129891
$949$	4.49317e36	0.273354
$950$	−2.23113e36	−0.133962
$951$	−3.05606e36	−0.181095
$952$	−3.69770e37	−2.16257
$953$	7.82036e36	0.451404	0.225702	−	0.974196i	$-0.427532\pi$
$953$	7.82036e36	0.451404	0.225702	+	0.974196i	$0.427532\pi$
$954$	1.65915e36	0.0945215
$955$	9.49467e36	0.533873
$956$	−2.99399e35	−0.0166160
$957$	1.59782e36	0.0875244
$958$	−3.35977e37	−1.81652
$959$	−3.09002e36	−0.164903
$960$	−1.56618e36	−0.0824994
$961$	1.76685e37	0.918668
$962$	−1.80050e36	−0.0924072
$963$	−2.42782e37	−1.22995
$964$	−1.30033e36	−0.0650263
$965$	9.38752e36	0.463403
$966$	−3.09328e36	−0.150732
$967$	−3.49443e37	−1.68092	−0.840458	−	0.541877i	$-0.817714\pi$
$967$	−3.49443e37	−1.68092	−0.840458	+	0.541877i	$0.817714\pi$
$968$	−1.80400e37	−0.856631
$969$	−4.09125e36	−0.191782
$970$	−6.83344e36	−0.316223
$971$	−6.04598e36	−0.276202	−0.138101	−	0.990418i	$-0.544100\pi$
$971$	−6.04598e36	−0.276202	−0.138101	+	0.990418i	$0.544100\pi$
$972$	6.55228e35	0.0295505
$973$	3.94000e37	1.75423
$974$	3.05201e37	1.34153
$975$	1.58506e36	0.0687840
$976$	2.34360e37	1.00406
$977$	1.65765e37	0.701152	0.350576	−	0.936534i	$-0.385986\pi$
$977$	1.65765e37	0.701152	0.350576	+	0.936534i	$0.385986\pi$
$978$	1.53161e35	0.00639607
$979$	−3.50269e36	−0.144417
$980$	−4.93798e35	−0.0201013
$981$	−1.24139e37	−0.498936
$982$	4.42248e37	1.75498
$983$	1.44794e37	0.567324	0.283662	−	0.958924i	$-0.408451\pi$
$983$	1.44794e37	0.567324	0.283662	+	0.958924i	$0.408451\pi$
$984$	−7.60722e35	−0.0294298
$985$	−1.42444e37	−0.544117
$986$	−4.98866e37	−1.88158
$987$	9.83041e36	0.366106
$988$	2.15374e36	0.0792012
$989$	1.71658e37	0.623321
$990$	−4.77838e36	−0.171333
$991$	4.33483e37	1.53480	0.767400	−	0.641169i	$-0.221550\pi$
$991$	4.33483e37	1.53480	0.767400	+	0.641169i	$0.221550\pi$
$992$	4.63148e36	0.161929
$993$	−1.33856e36	−0.0462137
$994$	−2.38268e37	−0.812335
$995$	1.68485e37	0.567249
$996$	3.78631e34	0.00125885
$997$	3.63221e37	1.19256	0.596282	−	0.802775i	$-0.296644\pi$
$997$	3.63221e37	1.19256	0.596282	+	0.802775i	$0.296644\pi$
$998$	4.91398e37	1.59331
$999$	−5.24179e35	−0.0167846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.a.b.1.2	✓	5
3.2	odd	2		45.26.a.f.1.4		5
5.2	odd	4		25.26.b.c.24.3		10
5.3	odd	4		25.26.b.c.24.8		10
5.4	even	2		25.26.a.c.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.a.b.1.2	✓	5	1.1	even	1	trivial
25.26.a.c.1.4		5	5.4	even	2
25.26.b.c.24.3		10	5.2	odd	4
25.26.b.c.24.8		10	5.3	odd	4
45.26.a.f.1.4		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)

\(f(q)\)	\(=\)	\(q-5620.55 q^{2} -161492. q^{3} -1.96387e6 q^{4} +2.44141e8 q^{5} +9.07675e8 q^{6} -4.86926e10 q^{7} +1.99632e11 q^{8} -8.21209e11 q^{9} +O(q^{10})\)	\(q-5620.55 q^{2} -161492. q^{3} -1.96387e6 q^{4} +2.44141e8 q^{5} +9.07675e8 q^{6} -4.86926e10 q^{7} +1.99632e11 q^{8} -8.21209e11 q^{9} -1.37220e12 q^{10} -4.24041e12 q^{11} +3.17150e11 q^{12} -1.64670e14 q^{13} +2.73679e14 q^{14} -3.94268e13 q^{15} -1.05615e15 q^{16} +3.80397e15 q^{17} +4.61564e15 q^{18} +6.65988e15 q^{19} -4.79461e14 q^{20} +7.86348e15 q^{21} +2.38334e16 q^{22} +6.99884e16 q^{23} -3.22391e16 q^{24} +5.96046e16 q^{25} +9.25533e17 q^{26} +2.69450e17 q^{27} +9.56261e16 q^{28} +2.33329e18 q^{29} +2.21600e17 q^{30} -6.07465e18 q^{31} -7.62428e17 q^{32} +6.84794e17 q^{33} -2.13804e19 q^{34} -1.18878e19 q^{35} +1.61275e18 q^{36} -1.94537e18 q^{37} -3.74322e19 q^{38} +2.65929e19 q^{39} +4.87384e19 q^{40} +2.35963e19 q^{41} -4.41971e19 q^{42} +2.45267e20 q^{43} +8.32763e18 q^{44} -2.00490e20 q^{45} -3.93373e20 q^{46} +1.25013e21 q^{47} +1.70560e20 q^{48} +1.02990e21 q^{49} -3.35011e20 q^{50} -6.14312e20 q^{51} +3.23390e20 q^{52} +3.59462e20 q^{53} -1.51445e21 q^{54} -1.03526e21 q^{55} -9.72062e21 q^{56} -1.07552e21 q^{57} -1.31144e22 q^{58} +3.01921e21 q^{59} +7.74293e19 q^{60} -2.21901e22 q^{61} +3.41428e22 q^{62} +3.99868e22 q^{63} +3.97237e22 q^{64} -4.02025e22 q^{65} -3.84892e21 q^{66} +9.61859e22 q^{67} -7.47052e21 q^{68} -1.13026e22 q^{69} +6.68162e22 q^{70} -8.70609e22 q^{71} -1.63940e23 q^{72} -2.72860e22 q^{73} +1.09340e22 q^{74} -9.62569e21 q^{75} -1.30792e22 q^{76} +2.06477e23 q^{77} -1.49467e23 q^{78} -6.64384e23 q^{79} -2.57848e23 q^{80} +6.52287e23 q^{81} -1.32624e23 q^{82} +1.19385e23 q^{83} -1.54429e22 q^{84} +9.28704e23 q^{85} -1.37854e24 q^{86} -3.76808e23 q^{87} -8.46524e23 q^{88} +8.26026e23 q^{89} +1.12687e24 q^{90} +8.01819e24 q^{91} -1.37448e23 q^{92} +9.81009e23 q^{93} -7.02644e24 q^{94} +1.62595e24 q^{95} +1.23126e23 q^{96} +4.97990e24 q^{97} -5.78861e24 q^{98} +3.48226e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4602 q^{2} + 626204 q^{3} + 91050260 q^{4} + 1220703125 q^{5} + 5696574760 q^{6} + 55481235808 q^{7} - 325515457080 q^{8} + 277996846465 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

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