LMFDB - Embedded newform 10.26.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, 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("10.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	10.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:	$39.5996779952$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{95351}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 95351 $ x^2 - 95351
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-308.790$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4096.00 q^{2} -715531. q^{3} +1.67772e7 q^{4} -2.44141e8 q^{5} -2.93082e9 q^{6} -6.40133e10 q^{7} +6.87195e10 q^{8} -3.35303e11 q^{9} -1.00000e12 q^{10} +1.40584e13 q^{11} -1.20046e13 q^{12} +1.57637e13 q^{13} -2.62199e14 q^{14} +1.74690e14 q^{15} +2.81475e14 q^{16} -1.00698e15 q^{17} -1.37340e15 q^{18} -8.66632e15 q^{19} -4.09600e15 q^{20} +4.58035e16 q^{21} +5.75832e16 q^{22} +1.43338e17 q^{23} -4.91709e16 q^{24} +5.96046e16 q^{25} +6.45682e16 q^{26} +8.46182e17 q^{27} -1.07397e18 q^{28} -3.60779e17 q^{29} +7.15531e17 q^{30} +8.72952e17 q^{31} +1.15292e18 q^{32} -1.00592e19 q^{33} -4.12457e18 q^{34} +1.56283e19 q^{35} -5.62546e18 q^{36} +7.37033e19 q^{37} -3.54972e19 q^{38} -1.12794e19 q^{39} -1.67772e19 q^{40} -6.57824e19 q^{41} +1.87611e20 q^{42} +4.50969e20 q^{43} +2.35861e20 q^{44} +8.18612e19 q^{45} +5.87113e20 q^{46} -5.55700e20 q^{47} -2.01404e20 q^{48} +2.75664e21 q^{49} +2.44141e20 q^{50} +7.20523e20 q^{51} +2.64471e20 q^{52} +4.75642e21 q^{53} +3.46596e21 q^{54} -3.43223e21 q^{55} -4.39896e21 q^{56} +6.20102e21 q^{57} -1.47775e21 q^{58} -1.95774e22 q^{59} +2.93082e21 q^{60} -2.95892e21 q^{61} +3.57561e21 q^{62} +2.14639e22 q^{63} +4.72237e21 q^{64} -3.84856e21 q^{65} -4.12026e22 q^{66} +4.26809e22 q^{67} -1.68942e22 q^{68} -1.02563e23 q^{69} +6.40133e22 q^{70} -1.93990e23 q^{71} -2.30419e22 q^{72} -2.11325e22 q^{73} +3.01889e23 q^{74} -4.26490e22 q^{75} -1.45397e23 q^{76} -8.99925e23 q^{77} -4.62006e22 q^{78} -4.99401e23 q^{79} -6.87195e22 q^{80} -3.21371e23 q^{81} -2.69445e23 q^{82} +1.79998e24 q^{83} +7.68456e23 q^{84} +2.45844e23 q^{85} +1.84717e24 q^{86} +2.58149e23 q^{87} +9.66086e23 q^{88} +2.07122e24 q^{89} +3.35303e23 q^{90} -1.00909e24 q^{91} +2.40482e24 q^{92} -6.24624e23 q^{93} -2.27615e24 q^{94} +2.11580e24 q^{95} -8.24952e23 q^{96} -3.44576e24 q^{97} +1.12912e25 q^{98} -4.71383e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8192 q^{2} - 97092 q^{3} + 33554432 q^{4} - 488281250 q^{5} - 397688832 q^{6} - 16137160124 q^{7} + 137438953472 q^{8} - 800124539454 q^{9} - 2000000000000 q^{10} + 14416600801344 q^{11} - 1628933455872 q^{12}+ \cdots - 48\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 8192 * q^2 - 97092 * q^3 + 33554432 * q^4 - 488281250 * q^5 - 397688832 * q^6 - 16137160124 * q^7 + 137438953472 * q^8 - 800124539454 * q^9 - 2000000000000 * q^10 + 14416600801344 * q^11 - 1628933455872 * q^12 + 93404548866628 * q^13 - 66097807867904 * q^14 + 23704101562500 * q^15 + 562949953421312 * q^16 + 499266882181236 * q^17 - 3277310113603584 * q^18 - 3830204591906120 * q^19 - 8192000000000000 * q^20 + 75412053748282104 * q^21 + 59050396882305024 * q^22 + 169271186050723788 * q^23 - 6672111435251712 * q^24 + 119209289550781250 * q^25 + 382585032157708288 * q^26 + 34721228182863240 * q^27 - 270736621026934784 * q^28 + 569443622853716940 * q^29 + 97092000000000000 * q^30 + 3982769593868414584 * q^31 + 2305843009213693952 * q^32 - 9837705729224836224 * q^33 + 2044997149414342656 * q^34 + 3939736358398437500 * q^35 - 13423862225320280064 * q^36 + 28241444663789328196 * q^37 - 15688518008447467520 * q^38 + 36736718047624459512 * q^39 - 33554432000000000000 * q^40 + 36676428854020432524 * q^41 + 308887772152963497984 * q^42 + 909017314298263251628 * q^43 + 241870425629921378304 * q^44 + 195342905140136718750 * q^45 + 693334778063764635648 * q^46 + 954929084389204818996 * q^47 - 27328968438791012352 * q^48 + 3707694774551412650874 * q^49 + 488281250000000000000 * q^50 + 1652042752773544110744 * q^51 + 1567068291717973147648 * q^52 + 2753692919774994609588 * q^53 + 142218150637007831040 * q^54 - 3519677930015625000000 * q^55 - 1108937199726324875264 * q^56 + 9191867441696689119120 * q^57 + 2332441079208824586240 * q^58 + 458866752134906177880 * q^59 + 397688832000000000000 * q^60 - 26987853585082462424636 * q^61 + 16313424256485026136064 * q^62 - 789976870259963054652 * q^63 + 9444732965739290427392 * q^64 - 22803844938141601562500 * q^65 - 40295242666904929173504 * q^66 - 14159647018044347838524 * q^67 + 8376308324001147518976 * q^68 - 86524983849189139233048 * q^69 + 16137160124000000000000 * q^70 - 173327708998984655450136 * q^71 - 54984139674911867142144 * q^72 - 341978509295241035156732 * q^73 + 115676957342881088290816 * q^74 - 5787134170532226562500 * q^75 - 64260169762600826961920 * q^76 - 882775887628764911584128 * q^77 + 150473597123069786161152 * q^78 - 927961875376490258946800 * q^79 - 137438953472000000000000 * q^80 - 429372483438817686010518 * q^81 + 150226652586067691618304 * q^82 + 681902409230287477811148 * q^83 + 1265204314738538487742464 * q^84 - 121891328657528320312500 * q^85 + 3723334919365686278668288 * q^86 + 833435461987898381769960 * q^87 + 990701263380157965533184 * q^88 + 3822788098104790038225780 * q^89 + 800124539454000000000000 * q^90 + 2708056932935479178393864 * q^91 + 2839899250949179947614208 * q^92 + 1298609917529886715704336 * q^93 + 3911389529658182938607616 * q^94 + 935108542945830078125000 * q^95 - 111939454725287986593792 * q^96 - 16314734149871901683914364 * q^97 + 15186717796562586217979904 * q^98 - 4880327126898398506596288 * q^99

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 $

$2$	4096.00	0.707107
$2$	4096.00	0.707107
$3$	−715531.	−0.777344	−0.388672	−	0.921376i	$-0.627066\pi$
$3$	−715531.	−0.777344	−0.388672	+	0.921376i	$0.627066\pi$
$4$	1.67772e7	0.500000
$5$	−2.44141e8	−0.447214
$5$	−2.44141e8	−0.447214
$6$	−2.93082e9	−0.549665
$7$	−6.40133e10	−1.74801	−0.874007	−	0.485914i	$-0.838487\pi$
$7$	−6.40133e10	−1.74801	−0.874007	+	0.485914i	$0.838487\pi$
$8$	6.87195e10	0.353553
$9$	−3.35303e11	−0.395737
$10$	−1.00000e12	−0.316228
$11$	1.40584e13	1.35060	0.675301	−	0.737542i	$-0.264014\pi$
$11$	1.40584e13	1.35060	0.675301	+	0.737542i	$0.264014\pi$
$12$	−1.20046e13	−0.388672
$13$	1.57637e13	0.187658	0.0938289	−	0.995588i	$-0.470089\pi$
$13$	1.57637e13	0.187658	0.0938289	+	0.995588i	$0.470089\pi$
$14$	−2.62199e14	−1.23603
$15$	1.74690e14	0.347639
$16$	2.81475e14	0.250000
$17$	−1.00698e15	−0.419187	−0.209593	−	0.977789i	$-0.567214\pi$
$17$	−1.00698e15	−0.419187	−0.209593	+	0.977789i	$0.567214\pi$
$18$	−1.37340e15	−0.279828
$19$	−8.66632e15	−0.898286	−0.449143	−	0.893460i	$-0.648271\pi$
$19$	−8.66632e15	−0.898286	−0.449143	+	0.893460i	$0.648271\pi$
$20$	−4.09600e15	−0.223607
$21$	4.58035e16	1.35881
$22$	5.75832e16	0.955020
$23$	1.43338e17	1.36384	0.681921	−	0.731426i	$-0.261145\pi$
$23$	1.43338e17	1.36384	0.681921	+	0.731426i	$0.261145\pi$
$24$	−4.91709e16	−0.274832
$25$	5.96046e16	0.200000
$26$	6.45682e16	0.132694
$27$	8.46182e17	1.08497
$28$	−1.07397e18	−0.874007
$29$	−3.60779e17	−0.189351	−0.0946753	−	0.995508i	$-0.530181\pi$
$29$	−3.60779e17	−0.189351	−0.0946753	+	0.995508i	$0.530181\pi$
$30$	7.15531e17	0.245818
$31$	8.72952e17	0.199053	0.0995266	−	0.995035i	$-0.468267\pi$
$31$	8.72952e17	0.199053	0.0995266	+	0.995035i	$0.468267\pi$
$32$	1.15292e18	0.176777
$33$	−1.00592e19	−1.04988
$34$	−4.12457e18	−0.296410
$35$	1.56283e19	0.781736
$36$	−5.62546e18	−0.197868
$37$	7.37033e19	1.84063	0.920313	−	0.391183i	$-0.127934\pi$
$37$	7.37033e19	1.84063	0.920313	+	0.391183i	$0.127934\pi$
$38$	−3.54972e19	−0.635184
$39$	−1.12794e19	−0.145875
$40$	−1.67772e19	−0.158114
$41$	−6.57824e19	−0.455315	−0.227657	−	0.973741i	$-0.573107\pi$
$41$	−6.57824e19	−0.455315	−0.227657	+	0.973741i	$0.573107\pi$
$42$	1.87611e20	0.960822
$43$	4.50969e20	1.72104	0.860519	−	0.509418i	$-0.170139\pi$
$43$	4.50969e20	1.72104	0.860519	+	0.509418i	$0.170139\pi$
$44$	2.35861e20	0.675301
$45$	8.18612e19	0.176979
$46$	5.87113e20	0.964382
$47$	−5.55700e20	−0.697617	−0.348809	−	0.937194i	$-0.613414\pi$
$47$	−5.55700e20	−0.697617	−0.348809	+	0.937194i	$0.613414\pi$
$48$	−2.01404e20	−0.194336
$49$	2.75664e21	2.05555
$50$	2.44141e20	0.141421
$51$	7.20523e20	0.325852
$52$	2.64471e20	0.0938289
$53$	4.75642e21	1.32994	0.664969	−	0.746871i	$-0.268445\pi$
$53$	4.75642e21	1.32994	0.664969	+	0.746871i	$0.268445\pi$
$54$	3.46596e21	0.767188
$55$	−3.43223e21	−0.604008
$56$	−4.39896e21	−0.618016
$57$	6.20102e21	0.698277
$58$	−1.47775e21	−0.133891
$59$	−1.95774e22	−1.43253	−0.716265	−	0.697828i	$-0.754150\pi$
$59$	−1.95774e22	−1.43253	−0.716265	+	0.697828i	$0.754150\pi$
$60$	2.93082e21	0.173819
$61$	−2.95892e21	−0.142728	−0.0713641	−	0.997450i	$-0.522735\pi$
$61$	−2.95892e21	−0.142728	−0.0713641	+	0.997450i	$0.522735\pi$
$62$	3.57561e21	0.140752
$63$	2.14639e22	0.691753
$64$	4.72237e21	0.125000
$65$	−3.84856e21	−0.0839231
$66$	−4.12026e22	−0.742379
$67$	4.26809e22	0.637234	0.318617	−	0.947884i	$-0.396782\pi$
$67$	4.26809e22	0.637234	0.318617	+	0.947884i	$0.396782\pi$
$68$	−1.68942e22	−0.209593
$69$	−1.02563e23	−1.06017
$70$	6.40133e22	0.552771
$71$	−1.93990e23	−1.40297	−0.701486	−	0.712683i	$-0.747480\pi$
$71$	−1.93990e23	−1.40297	−0.701486	+	0.712683i	$0.747480\pi$
$72$	−2.30419e22	−0.139914
$73$	−2.11325e22	−0.107998	−0.0539990	−	0.998541i	$-0.517197\pi$
$73$	−2.11325e22	−0.107998	−0.0539990	+	0.998541i	$0.517197\pi$
$74$	3.01889e23	1.30152
$75$	−4.26490e22	−0.155469
$76$	−1.45397e23	−0.449143
$77$	−8.99925e23	−2.36087
$78$	−4.62006e22	−0.103149
$79$	−4.99401e23	−0.950848	−0.475424	−	0.879757i	$-0.657705\pi$
$79$	−4.99401e23	−0.950848	−0.475424	+	0.879757i	$0.657705\pi$
$80$	−6.87195e22	−0.111803
$81$	−3.21371e23	−0.447656
$82$	−2.69445e23	−0.321956
$83$	1.79998e24	1.84838	0.924189	−	0.381937i	$-0.124743\pi$
$83$	1.79998e24	1.84838	0.924189	+	0.381937i	$0.124743\pi$
$84$	7.68456e23	0.679404
$85$	2.45844e23	0.187466
$86$	1.84717e24	1.21696
$87$	2.58149e23	0.147190
$88$	9.66086e23	0.477510
$89$	2.07122e24	0.888898	0.444449	−	0.895804i	$-0.353400\pi$
$89$	2.07122e24	0.888898	0.444449	+	0.895804i	$0.353400\pi$
$90$	3.35303e23	0.125143
$91$	−1.00909e24	−0.328029
$92$	2.40482e24	0.681921
$93$	−6.24624e23	−0.154733
$94$	−2.27615e24	−0.493290
$95$	2.11580e24	0.401726
$96$	−8.24952e23	−0.137416
$97$	−3.44576e24	−0.504242	−0.252121	−	0.967696i	$-0.581128\pi$
$97$	−3.44576e24	−0.504242	−0.252121	+	0.967696i	$0.581128\pi$
$98$	1.12912e25	1.45349
$99$	−4.71383e24	−0.534483
$100$	1.00000e24	0.100000
$101$	1.35804e24	0.119921	0.0599607	−	0.998201i	$-0.480902\pi$
$101$	1.35804e24	0.119921	0.0599607	+	0.998201i	$0.480902\pi$
$102$	2.95126e24	0.230412
$103$	−1.81348e25	−1.25328	−0.626639	−	0.779310i	$-0.715570\pi$
$103$	−1.81348e25	−1.25328	−0.626639	+	0.779310i	$0.715570\pi$
$104$	1.08327e24	0.0663471
$105$	−1.11825e25	−0.607677
$106$	1.94823e25	0.940409
$107$	−4.09213e25	−1.75652	−0.878259	−	0.478186i	$-0.841295\pi$
$107$	−4.09213e25	−1.75652	−0.878259	+	0.478186i	$0.841295\pi$
$108$	1.41966e25	0.542484
$109$	4.31829e25	1.47055	0.735277	−	0.677767i	$-0.237052\pi$
$109$	4.31829e25	1.47055	0.735277	+	0.677767i	$0.237052\pi$
$110$	−1.40584e25	−0.427098
$111$	−5.27370e25	−1.43080
$112$	−1.80181e25	−0.437003
$113$	−2.61097e25	−0.566659	−0.283329	−	0.959023i	$-0.591439\pi$
$113$	−2.61097e25	−0.566659	−0.283329	+	0.959023i	$0.591439\pi$
$114$	2.53994e25	0.493756
$115$	−3.49947e25	−0.609929
$116$	−6.05287e24	−0.0946753
$117$	−5.28563e24	−0.0742631
$118$	−8.01888e25	−1.01295
$119$	6.44599e25	0.732744
$120$	1.20046e25	0.122909
$121$	8.92916e25	0.824126
$122$	−1.21197e25	−0.100924
$123$	4.70694e25	0.353936
$124$	1.46457e25	0.0995266
$125$	−1.45519e25	−0.0894427
$126$	8.79160e25	0.489144
$127$	3.07316e25	0.154895	0.0774477	−	0.996996i	$-0.475323\pi$
$127$	3.07316e25	0.154895	0.0774477	+	0.996996i	$0.475323\pi$
$128$	1.93428e25	0.0883883
$129$	−3.22682e26	−1.33784
$130$	−1.57637e25	−0.0593426
$131$	1.55205e26	0.530902	0.265451	−	0.964124i	$-0.414479\pi$
$131$	1.55205e26	0.530902	0.265451	+	0.964124i	$0.414479\pi$
$132$	−1.68766e26	−0.524941
$133$	5.54760e26	1.57022
$134$	1.74821e26	0.450593
$135$	−2.06587e26	−0.485212
$136$	−6.91988e25	−0.148205
$137$	4.44205e26	0.868112	0.434056	−	0.900886i	$-0.357082\pi$
$137$	4.44205e26	0.868112	0.434056	+	0.900886i	$0.357082\pi$
$138$	−4.20098e26	−0.749656
$139$	9.86493e26	1.60845	0.804227	−	0.594322i	$-0.202579\pi$
$139$	9.86493e26	1.60845	0.804227	+	0.594322i	$0.202579\pi$
$140$	2.62199e26	0.390868
$141$	3.97621e26	0.542288
$142$	−7.94582e26	−0.992051
$143$	2.21613e26	0.253451
$144$	−9.43795e25	−0.0989342
$145$	8.80809e25	0.0846801
$146$	−8.65589e25	−0.0763661
$147$	−1.97246e27	−1.59787
$148$	1.23654e27	0.920313
$149$	1.38635e27	0.948518	0.474259	−	0.880385i	$-0.342716\pi$
$149$	1.38635e27	0.948518	0.474259	+	0.880385i	$0.342716\pi$
$150$	−1.74690e26	−0.109933
$151$	−9.02182e26	−0.522495	−0.261248	−	0.965272i	$-0.584134\pi$
$151$	−9.02182e26	−0.522495	−0.261248	+	0.965272i	$0.584134\pi$
$152$	−5.95545e26	−0.317592
$153$	3.37642e26	0.165888
$154$	−3.68609e27	−1.66939
$155$	−2.13123e26	−0.0890193
$156$	−1.89238e26	−0.0729373
$157$	2.62328e27	0.933466	0.466733	−	0.884398i	$-0.345431\pi$
$157$	2.62328e27	0.933466	0.466733	+	0.884398i	$0.345431\pi$
$158$	−2.04555e27	−0.672351
$159$	−3.40337e27	−1.03382
$160$	−2.81475e26	−0.0790569
$161$	−9.17555e27	−2.38401
$162$	−1.31634e27	−0.316540
$163$	1.18488e27	0.263834	0.131917	−	0.991261i	$-0.457887\pi$
$163$	1.18488e27	0.263834	0.131917	+	0.991261i	$0.457887\pi$
$164$	−1.10365e27	−0.227657
$165$	2.45587e27	0.469521
$166$	7.37270e27	1.30700
$167$	7.47611e27	1.22948	0.614738	−	0.788732i	$-0.289262\pi$
$167$	7.47611e27	1.22948	0.614738	+	0.788732i	$0.289262\pi$
$168$	3.14760e27	0.480411
$169$	−6.80792e27	−0.964785
$170$	1.00698e27	0.132558
$171$	2.90585e27	0.355485
$172$	7.56600e27	0.860519
$173$	−3.35797e27	−0.355223	−0.177611	−	0.984101i	$-0.556837\pi$
$173$	−3.35797e27	−0.355223	−0.177611	+	0.984101i	$0.556837\pi$
$174$	1.05738e27	0.104079
$175$	−3.81549e27	−0.349603
$176$	3.95709e27	0.337651
$177$	1.40082e28	1.11357
$178$	8.48373e27	0.628546
$179$	6.30645e27	0.435634	0.217817	−	0.975990i	$-0.430106\pi$
$179$	6.30645e27	0.435634	0.217817	+	0.975990i	$0.430106\pi$
$180$	1.37340e27	0.0884894
$181$	1.20387e28	0.723764	0.361882	−	0.932224i	$-0.382134\pi$
$181$	1.20387e28	0.723764	0.361882	+	0.932224i	$0.382134\pi$
$182$	−4.13322e27	−0.231951
$183$	2.11720e27	0.110949
$184$	9.85012e27	0.482191
$185$	−1.79940e28	−0.823153
$186$	−2.55846e27	−0.109413
$187$	−1.41565e28	−0.566154
$188$	−9.32310e27	−0.348809
$189$	−5.41669e28	−1.89654
$190$	8.66632e27	0.284063
$191$	2.13809e28	0.656309	0.328155	−	0.944624i	$-0.393573\pi$
$191$	2.13809e28	0.656309	0.328155	+	0.944624i	$0.393573\pi$
$192$	−3.37900e27	−0.0971680
$193$	2.97996e27	0.0803054	0.0401527	−	0.999194i	$-0.487216\pi$
$193$	2.97996e27	0.0803054	0.0401527	+	0.999194i	$0.487216\pi$
$194$	−1.41138e28	−0.356553
$195$	2.75377e27	0.0652371
$196$	4.62487e28	1.02778
$197$	4.10890e28	0.856836	0.428418	−	0.903581i	$-0.359071\pi$
$197$	4.10890e28	0.856836	0.428418	+	0.903581i	$0.359071\pi$
$198$	−1.93078e28	−0.377937
$199$	−5.34406e28	−0.982218	−0.491109	−	0.871098i	$-0.663408\pi$
$199$	−5.34406e28	−0.982218	−0.491109	+	0.871098i	$0.663408\pi$
$200$	4.09600e27	0.0707107
$201$	−3.05396e28	−0.495350
$202$	5.56255e27	0.0847973
$203$	2.30947e28	0.330987
$204$	1.20884e28	0.162926
$205$	1.60602e28	0.203623
$206$	−7.42801e28	−0.886202
$207$	−4.80618e28	−0.539722
$208$	4.43709e27	0.0469145
$209$	−1.21835e29	−1.21323
$210$	−4.58035e28	−0.429693
$211$	4.77946e28	0.422521	0.211260	−	0.977430i	$-0.432243\pi$
$211$	4.77946e28	0.422521	0.211260	+	0.977430i	$0.432243\pi$
$212$	7.97994e28	0.664969
$213$	1.38806e29	1.09059
$214$	−1.67614e29	−1.24205
$215$	−1.10100e29	−0.769672
$216$	5.81492e28	0.383594
$217$	−5.58805e28	−0.347948
$218$	1.76877e29	1.03984
$219$	1.51210e28	0.0839516
$220$	−5.75832e28	−0.302004
$221$	−1.58737e28	−0.0786637
$222$	−2.16011e29	−1.01173
$223$	4.45198e29	1.97125	0.985627	−	0.168934i	$-0.0540324\pi$
$223$	4.45198e29	1.97125	0.985627	+	0.168934i	$0.0540324\pi$
$224$	−7.38023e28	−0.309008
$225$	−1.99856e28	−0.0791474
$226$	−1.06945e29	−0.400688
$227$	−2.11324e29	−0.749248	−0.374624	−	0.927177i	$-0.622228\pi$
$227$	−2.11324e29	−0.749248	−0.374624	+	0.927177i	$0.622228\pi$
$228$	1.04036e29	0.349138
$229$	4.64740e29	1.47661	0.738307	−	0.674465i	$-0.235626\pi$
$229$	4.64740e29	1.47661	0.738307	+	0.674465i	$0.235626\pi$
$230$	−1.43338e29	−0.431285
$231$	6.43925e29	1.83521
$232$	−2.47926e28	−0.0669455
$233$	5.21268e29	1.33386	0.666932	−	0.745118i	$-0.267607\pi$
$233$	5.21268e29	1.33386	0.666932	+	0.745118i	$0.267607\pi$
$234$	−2.16499e28	−0.0525120
$235$	1.35669e29	0.311984
$236$	−3.28453e29	−0.716265
$237$	3.57337e29	0.739135
$238$	2.64028e29	0.518128
$239$	−9.68016e29	−1.80264	−0.901319	−	0.433155i	$-0.857400\pi$
$239$	−9.68016e29	−1.80264	−0.901319	+	0.433155i	$0.857400\pi$
$240$	4.91709e28	0.0869097
$241$	−1.30231e29	−0.218525	−0.109263	−	0.994013i	$-0.534849\pi$
$241$	−1.30231e29	−0.218525	−0.109263	+	0.994013i	$0.534849\pi$
$242$	3.65738e29	0.582745
$243$	−4.87009e29	−0.736985
$244$	−4.96424e28	−0.0713641
$245$	−6.73007e29	−0.919271
$246$	1.92796e29	0.250271
$247$	−1.36613e29	−0.168570
$248$	5.99888e28	0.0703759
$249$	−1.28794e30	−1.43682
$250$	−5.96046e28	−0.0632456
$251$	1.40543e30	1.41869	0.709345	−	0.704862i	$-0.248991\pi$
$251$	1.40543e30	1.41869	0.709345	+	0.704862i	$0.248991\pi$
$252$	3.60104e29	0.345877
$253$	2.01511e30	1.84201
$254$	1.25877e29	0.109528
$255$	−1.75909e29	−0.145725
$256$	7.92282e28	0.0625000
$257$	−1.02386e30	−0.769263	−0.384632	−	0.923070i	$-0.625671\pi$
$257$	−1.02386e30	−0.769263	−0.384632	+	0.923070i	$0.625671\pi$
$258$	−1.32171e30	−0.945995
$259$	−4.71799e30	−3.21744
$260$	−6.45682e28	−0.0419616
$261$	1.20970e29	0.0749330
$262$	6.35719e29	0.375404
$263$	−9.94329e29	−0.559865	−0.279933	−	0.960020i	$-0.590312\pi$
$263$	−9.94329e29	−0.559865	−0.279933	+	0.960020i	$0.590312\pi$
$264$	−6.91265e29	−0.371189
$265$	−1.16123e30	−0.594767
$266$	2.27230e30	1.11031
$267$	−1.48203e30	−0.690979
$268$	7.16067e29	0.318617
$269$	9.41553e29	0.399891	0.199945	−	0.979807i	$-0.435924\pi$
$269$	9.41553e29	0.399891	0.199945	+	0.979807i	$0.435924\pi$
$270$	−8.46182e29	−0.343097
$271$	−2.84694e29	−0.110220	−0.0551101	−	0.998480i	$-0.517551\pi$
$271$	−2.84694e29	−0.110220	−0.0551101	+	0.998480i	$0.517551\pi$
$272$	−2.83438e29	−0.104797
$273$	7.22034e29	0.254991
$274$	1.81946e30	0.613848
$275$	8.37946e29	0.270120
$276$	−1.72072e30	−0.530087
$277$	5.74193e30	1.69068	0.845339	−	0.534230i	$-0.179398\pi$
$277$	5.74193e30	1.69068	0.845339	+	0.534230i	$0.179398\pi$
$278$	4.04067e30	1.13735
$279$	−2.92704e29	−0.0787726
$280$	1.07397e30	0.276385
$281$	7.10013e29	0.174758	0.0873790	−	0.996175i	$-0.472151\pi$
$281$	7.10013e29	0.174758	0.0873790	+	0.996175i	$0.472151\pi$
$282$	1.62865e30	0.383456
$283$	4.98063e30	1.12190	0.560950	−	0.827850i	$-0.310436\pi$
$283$	4.98063e30	1.12190	0.560950	+	0.827850i	$0.310436\pi$
$284$	−3.25461e30	−0.701486
$285$	−1.51392e30	−0.312279
$286$	9.07726e29	0.179217
$287$	4.21095e30	0.795896
$288$	−3.86578e29	−0.0699571
$289$	−4.75663e30	−0.824283
$290$	3.60779e29	0.0598779
$291$	2.46555e30	0.391969
$292$	−3.54545e29	−0.0539990
$293$	−4.89769e30	−0.714736	−0.357368	−	0.933964i	$-0.616326\pi$
$293$	−4.89769e30	−0.714736	−0.357368	+	0.933964i	$0.616326\pi$
$294$	−8.07920e30	−1.12987
$295$	4.77963e30	0.640647
$296$	5.06485e30	0.650759
$297$	1.18960e31	1.46536
$298$	5.67850e30	0.670704
$299$	2.25954e30	0.255936
$300$	−7.15531e29	−0.0777344
$301$	−2.88680e31	−3.00840
$302$	−3.69534e30	−0.369460
$303$	−9.71724e29	−0.0932202
$304$	−2.43935e30	−0.224572
$305$	7.22391e29	0.0638300
$306$	1.38298e30	0.117300
$307$	−2.34261e31	−1.90752	−0.953762	−	0.300563i	$-0.902825\pi$
$307$	−2.34261e31	−1.90752	−0.953762	+	0.300563i	$0.902825\pi$
$308$	−1.50982e31	−1.18044
$309$	1.29760e31	0.974228
$310$	−8.72952e29	−0.0629461
$311$	1.34425e31	0.931054	0.465527	−	0.885034i	$-0.345865\pi$
$311$	1.34425e31	0.931054	0.465527	+	0.885034i	$0.345865\pi$
$312$	−7.75117e29	−0.0515745
$313$	2.25707e31	1.44292	0.721458	−	0.692458i	$-0.243472\pi$
$313$	2.25707e31	1.44292	0.721458	+	0.692458i	$0.243472\pi$
$314$	1.07449e31	0.660060
$315$	−5.24020e30	−0.309362
$316$	−8.37856e30	−0.475424
$317$	4.83401e29	0.0263674	0.0131837	−	0.999913i	$-0.495803\pi$
$317$	4.83401e29	0.0263674	0.0131837	+	0.999913i	$0.495803\pi$
$318$	−1.39402e31	−0.731021
$319$	−5.07198e30	−0.255737
$320$	−1.15292e30	−0.0559017
$321$	2.92805e31	1.36542
$322$	−3.75831e31	−1.68575
$323$	8.72677e30	0.376550
$324$	−5.39171e30	−0.223828
$325$	9.39591e29	0.0375316
$326$	4.85329e30	0.186559
$327$	−3.08987e31	−1.14313
$328$	−4.52053e30	−0.160978
$329$	3.55722e31	1.21944
$330$	1.00592e31	0.332002
$331$	−4.89856e31	−1.55675	−0.778375	−	0.627800i	$-0.783956\pi$
$331$	−4.89856e31	−1.55675	−0.778375	+	0.627800i	$0.783956\pi$
$332$	3.01986e31	0.924189
$333$	−2.47130e31	−0.728403
$334$	3.06221e31	0.869370
$335$	−1.04202e31	−0.284980
$336$	1.28926e31	0.339702
$337$	3.74477e31	0.950718	0.475359	−	0.879792i	$-0.342318\pi$
$337$	3.74477e31	0.950718	0.475359	+	0.879792i	$0.342318\pi$
$338$	−2.78852e31	−0.682206
$339$	1.86823e31	0.440489
$340$	4.12457e30	0.0937330
$341$	1.22723e31	0.268842
$342$	1.19023e31	0.251366
$343$	−9.06152e31	−1.84512
$344$	3.09903e31	0.608479
$345$	2.50398e31	0.474124
$346$	−1.37543e31	−0.251181
$347$	1.26433e31	0.222711	0.111356	−	0.993781i	$-0.464481\pi$
$347$	1.26433e31	0.222711	0.111356	+	0.993781i	$0.464481\pi$
$348$	4.33102e30	0.0735952
$349$	5.64423e31	0.925308	0.462654	−	0.886539i	$-0.346897\pi$
$349$	5.64423e31	0.925308	0.462654	+	0.886539i	$0.346897\pi$
$350$	−1.56283e31	−0.247206
$351$	1.33390e31	0.203603
$352$	1.62082e31	0.238755
$353$	−1.66522e31	−0.236749	−0.118374	−	0.992969i	$-0.537768\pi$
$353$	−1.66522e31	−0.236749	−0.118374	+	0.992969i	$0.537768\pi$
$354$	5.73776e31	0.787412
$355$	4.73608e31	0.627428
$356$	3.47494e31	0.444449
$357$	−4.61231e31	−0.569594
$358$	2.58312e31	0.308040
$359$	1.12363e32	1.29403	0.647014	−	0.762478i	$-0.276018\pi$
$359$	1.12363e32	1.29403	0.647014	+	0.762478i	$0.276018\pi$
$360$	5.62546e30	0.0625715
$361$	−1.79714e31	−0.193082
$362$	4.93104e31	0.511778
$363$	−6.38910e31	−0.640629
$364$	−1.69297e31	−0.164014
$365$	5.15931e30	0.0482982
$366$	8.67204e30	0.0784527
$367$	−1.62554e32	−1.42126	−0.710629	−	0.703567i	$-0.751590\pi$
$367$	−1.62554e32	−1.42126	−0.710629	+	0.703567i	$0.751590\pi$
$368$	4.03461e31	0.340960
$369$	2.20571e31	0.180185
$370$	−7.37033e31	−0.582057
$371$	−3.04474e32	−2.32475
$372$	−1.04795e31	−0.0773663
$373$	8.65344e31	0.617772	0.308886	−	0.951099i	$-0.400044\pi$
$373$	8.65344e31	0.617772	0.308886	+	0.951099i	$0.400044\pi$
$374$	−5.79849e31	−0.400332
$375$	1.04124e31	0.0695277
$376$	−3.81874e31	−0.246645
$377$	−5.68722e30	−0.0355331
$378$	−2.21868e32	−1.34105
$379$	−1.30491e32	−0.763117	−0.381558	−	0.924345i	$-0.624612\pi$
$379$	−1.30491e32	−0.763117	−0.381558	+	0.924345i	$0.624612\pi$
$380$	3.54972e31	0.200863
$381$	−2.19894e31	−0.120407
$382$	8.75761e31	0.464081
$383$	−3.19017e31	−0.163617	−0.0818087	−	0.996648i	$-0.526070\pi$
$383$	−3.19017e31	−0.163617	−0.0818087	+	0.996648i	$0.526070\pi$
$384$	−1.38404e31	−0.0687081
$385$	2.19708e32	1.05581
$386$	1.22059e31	0.0567845
$387$	−1.51211e32	−0.681078
$388$	−5.78103e31	−0.252121
$389$	1.71823e32	0.725622	0.362811	−	0.931863i	$-0.381817\pi$
$389$	1.71823e32	0.725622	0.362811	+	0.931863i	$0.381817\pi$
$390$	1.12794e31	0.0461296
$391$	−1.44338e32	−0.571704
$392$	1.89435e32	0.726747
$393$	−1.11054e32	−0.412693
$394$	1.68301e32	0.605874
$395$	1.21924e32	0.425232
$396$	−7.90849e31	−0.267241
$397$	1.44908e32	0.474471	0.237236	−	0.971452i	$-0.423759\pi$
$397$	1.44908e32	0.474471	0.237236	+	0.971452i	$0.423759\pi$
$398$	−2.18893e32	−0.694533
$399$	−3.96948e32	−1.22060
$400$	1.67772e31	0.0500000
$401$	6.47108e32	1.86927	0.934635	−	0.355609i	$-0.115726\pi$
$401$	6.47108e32	1.86927	0.934635	+	0.355609i	$0.115726\pi$
$402$	−1.25090e32	−0.350265
$403$	1.37610e31	0.0373539
$404$	2.27842e31	0.0599607
$405$	7.84597e31	0.200198
$406$	9.45958e31	0.234043
$407$	1.03615e33	2.48595
$408$	4.95140e31	0.115206
$409$	−1.49705e32	−0.337828	−0.168914	−	0.985631i	$-0.554026\pi$
$409$	−1.49705e32	−0.337828	−0.168914	+	0.985631i	$0.554026\pi$
$410$	6.57824e31	0.143983
$411$	−3.17842e32	−0.674822
$412$	−3.04251e32	−0.626639
$413$	1.25321e33	2.50408
$414$	−1.96861e32	−0.381641
$415$	−4.39447e32	−0.826619
$416$	1.81743e31	0.0331735
$417$	−7.05867e32	−1.25032
$418$	−4.99035e32	−0.857881
$419$	6.23538e32	1.04037	0.520185	−	0.854054i	$-0.325863\pi$
$419$	6.23538e32	1.04037	0.520185	+	0.854054i	$0.325863\pi$
$420$	−1.87611e32	−0.303839
$421$	4.35871e32	0.685223	0.342611	−	0.939477i	$-0.388689\pi$
$421$	4.35871e32	0.685223	0.342611	+	0.939477i	$0.388689\pi$
$422$	1.95767e32	0.298767
$423$	1.86328e32	0.276073
$424$	3.26859e32	0.470204
$425$	−6.00204e31	−0.0838373
$426$	5.68548e32	0.771165
$427$	1.89410e32	0.249491
$428$	−6.86546e32	−0.878259
$429$	−1.58571e32	−0.197019
$430$	−4.50969e32	−0.544240
$431$	−9.60606e32	−1.12611	−0.563053	−	0.826420i	$-0.690373\pi$
$431$	−9.60606e32	−1.12611	−0.563053	+	0.826420i	$0.690373\pi$
$432$	2.38179e32	0.271242
$433$	6.50298e32	0.719472	0.359736	−	0.933054i	$-0.382867\pi$
$433$	6.50298e32	0.719472	0.359736	+	0.933054i	$0.382867\pi$
$434$	−2.28887e32	−0.246036
$435$	−6.30246e31	−0.0658256
$436$	7.24489e32	0.735277
$437$	−1.24221e33	−1.22512
$438$	6.19356e31	0.0593627
$439$	−1.26999e33	−1.18303	−0.591515	−	0.806294i	$-0.701470\pi$
$439$	−1.26999e33	−1.18303	−0.591515	+	0.806294i	$0.701470\pi$
$440$	−2.35861e32	−0.213549
$441$	−9.24309e32	−0.813458
$442$	−6.50186e31	−0.0556236
$443$	3.57910e32	0.297665	0.148832	−	0.988862i	$-0.452449\pi$
$443$	3.57910e32	0.297665	0.148832	+	0.988862i	$0.452449\pi$
$444$	−8.84781e32	−0.715399
$445$	−5.05670e32	−0.397527
$446$	1.82353e33	1.39389
$447$	−9.91980e32	−0.737325
$448$	−3.02294e32	−0.218502
$449$	−2.89265e32	−0.203337	−0.101669	−	0.994818i	$-0.532418\pi$
$449$	−2.89265e32	−0.203337	−0.101669	+	0.994818i	$0.532418\pi$
$450$	−8.18612e31	−0.0559656
$451$	−9.24796e32	−0.614949
$452$	−4.38048e32	−0.283329
$453$	6.45540e32	0.406158
$454$	−8.65583e32	−0.529798
$455$	2.46359e32	0.146699
$456$	4.26131e32	0.246878
$457$	2.55962e33	1.44285	0.721427	−	0.692491i	$-0.243487\pi$
$457$	2.55962e33	1.44285	0.721427	+	0.692491i	$0.243487\pi$
$458$	1.90358e33	1.04412
$459$	−8.52085e32	−0.454804
$460$	−5.87113e32	−0.304964
$461$	−7.93005e31	−0.0400880	−0.0200440	−	0.999799i	$-0.506381\pi$
$461$	−7.93005e31	−0.0400880	−0.0200440	+	0.999799i	$0.506381\pi$
$462$	2.63752e33	1.29769
$463$	3.30952e32	0.158490	0.0792452	−	0.996855i	$-0.474749\pi$
$463$	3.30952e32	0.158490	0.0792452	+	0.996855i	$0.474749\pi$
$464$	−1.01550e32	−0.0473376
$465$	1.52496e32	0.0691986
$466$	2.13511e33	0.943185
$467$	−2.96201e33	−1.27387	−0.636936	−	0.770917i	$-0.719798\pi$
$467$	−2.96201e33	−1.27387	−0.636936	+	0.770917i	$0.719798\pi$
$468$	−8.86781e31	−0.0371316
$469$	−2.73215e33	−1.11389
$470$	5.55700e32	0.220606
$471$	−1.87704e33	−0.725624
$472$	−1.34535e33	−0.506476
$473$	6.33990e33	2.32444
$474$	1.46365e33	0.522648
$475$	−5.16553e32	−0.179657
$476$	1.08146e33	0.366372
$477$	−1.59484e33	−0.526306
$478$	−3.96499e33	−1.27466
$479$	1.66525e33	0.521537	0.260769	−	0.965401i	$-0.416024\pi$
$479$	1.66525e33	0.521537	0.260769	+	0.965401i	$0.416024\pi$
$480$	2.01404e32	0.0614544
$481$	1.16184e33	0.345408
$482$	−5.33427e32	−0.154521
$483$	6.56540e33	1.85320
$484$	1.49806e33	0.412063
$485$	8.41251e32	0.225504
$486$	−1.99479e33	−0.521127
$487$	−6.03193e33	−1.53583	−0.767917	−	0.640549i	$-0.778707\pi$
$487$	−6.03193e33	−1.53583	−0.767917	+	0.640549i	$0.778707\pi$
$488$	−2.03335e32	−0.0504620
$489$	−8.47822e32	−0.205090
$490$	−2.75664e33	−0.650023
$491$	2.62144e33	0.602590	0.301295	−	0.953531i	$-0.402581\pi$
$491$	2.62144e33	0.602590	0.301295	+	0.953531i	$0.402581\pi$
$492$	7.89693e32	0.176968
$493$	3.63296e32	0.0793732
$494$	−5.59568e32	−0.119197
$495$	1.15084e33	0.239028
$496$	2.45714e32	0.0497633
$497$	1.24179e34	2.45242
$498$	−5.27540e33	−1.01599
$499$	−8.04276e33	−1.51060	−0.755298	−	0.655382i	$-0.772508\pi$
$499$	−8.04276e33	−1.51060	−0.755298	+	0.655382i	$0.772508\pi$
$500$	−2.44141e32	−0.0447214
$501$	−5.34939e33	−0.955725
$502$	5.75664e33	1.00316
$503$	8.35523e33	1.42023	0.710115	−	0.704086i	$-0.248643\pi$
$503$	8.35523e33	1.42023	0.710115	+	0.704086i	$0.248643\pi$
$504$	1.47499e33	0.244572
$505$	−3.31554e32	−0.0536305
$506$	8.25387e33	1.30250
$507$	4.87128e33	0.749969
$508$	5.15590e32	0.0774477
$509$	−7.38135e33	−1.08184	−0.540920	−	0.841074i	$-0.681924\pi$
$509$	−7.38135e33	−1.08184	−0.540920	+	0.841074i	$0.681924\pi$
$510$	−7.20523e32	−0.103043
$511$	1.35276e33	0.188782
$512$	3.24519e32	0.0441942
$513$	−7.33328e33	−0.974611
$514$	−4.19371e33	−0.543951
$515$	4.42744e33	0.560483
$516$	−5.41371e33	−0.668919
$517$	−7.81225e33	−0.942203
$518$	−1.93249e34	−2.27507
$519$	2.40274e33	0.276130
$520$	−2.64471e32	−0.0296713
$521$	−1.16894e34	−1.28032	−0.640161	−	0.768241i	$-0.721133\pi$
$521$	−1.16894e34	−1.28032	−0.640161	+	0.768241i	$0.721133\pi$
$522$	4.95495e32	0.0529856
$523$	−1.32178e34	−1.38003	−0.690014	−	0.723796i	$-0.742396\pi$
$523$	−1.32178e34	−1.38003	−0.690014	+	0.723796i	$0.742396\pi$
$524$	2.60391e33	0.265451
$525$	2.73010e33	0.271761
$526$	−4.07277e33	−0.395884
$527$	−8.79041e32	−0.0834404
$528$	−2.83142e33	−0.262470
$529$	9.50007e33	0.860064
$530$	−4.75642e33	−0.420563
$531$	6.56435e33	0.566905
$532$	9.30733e33	0.785108
$533$	−1.03698e33	−0.0854434
$534$	−6.07037e33	−0.488596
$535$	9.99056e33	0.785539
$536$	2.93301e33	0.225296
$537$	−4.51247e33	−0.338638
$538$	3.85660e33	0.282765
$539$	3.87539e34	2.77623
$540$	−3.46596e33	−0.242606
$541$	−1.02274e34	−0.699522	−0.349761	−	0.936839i	$-0.613737\pi$
$541$	−1.02274e34	−0.699522	−0.349761	+	0.936839i	$0.613737\pi$
$542$	−1.16610e33	−0.0779375
$543$	−8.61406e33	−0.562613
$544$	−1.16096e33	−0.0741024
$545$	−1.05427e34	−0.657651
$546$	2.95745e33	0.180306
$547$	−9.41592e33	−0.561075	−0.280538	−	0.959843i	$-0.590513\pi$
$547$	−9.41592e33	−0.561075	−0.280538	+	0.959843i	$0.590513\pi$
$548$	7.45252e33	0.434056
$549$	9.92134e32	0.0564828
$550$	3.43223e33	0.191004
$551$	3.12663e33	0.170091
$552$	−7.04807e33	−0.374828
$553$	3.19683e34	1.66209
$554$	2.35190e34	1.19549
$555$	1.28753e34	0.639873
$556$	1.65506e34	0.804227
$557$	−1.93891e34	−0.921227	−0.460614	−	0.887601i	$-0.652371\pi$
$557$	−1.93891e34	−0.921227	−0.460614	+	0.887601i	$0.652371\pi$
$558$	−1.19891e33	−0.0557007
$559$	7.10894e33	0.322966
$560$	4.39896e33	0.195434
$561$	1.01294e34	0.440097
$562$	2.90821e33	0.123573
$563$	−2.14770e34	−0.892520	−0.446260	−	0.894903i	$-0.647244\pi$
$563$	−2.14770e34	−0.892520	−0.446260	+	0.894903i	$0.647244\pi$
$564$	6.67097e33	0.271144
$565$	6.37444e33	0.253418
$566$	2.04007e34	0.793303
$567$	2.05720e34	0.782508
$568$	−1.33309e34	−0.496026
$569$	−1.35765e33	−0.0494180	−0.0247090	−	0.999695i	$-0.507866\pi$
$569$	−1.35765e33	−0.0494180	−0.0247090	+	0.999695i	$0.507866\pi$
$570$	−6.20102e33	−0.220815
$571$	−1.57397e34	−0.548334	−0.274167	−	0.961682i	$-0.588402\pi$
$571$	−1.57397e34	−0.548334	−0.274167	+	0.961682i	$0.588402\pi$
$572$	3.71804e33	0.126726
$573$	−1.52987e34	−0.510178
$574$	1.72481e34	0.562784
$575$	8.54362e33	0.272768
$576$	−1.58343e33	−0.0494671
$577$	−5.82494e34	−1.78071	−0.890356	−	0.455266i	$-0.849544\pi$
$577$	−5.82494e34	−1.78071	−0.890356	+	0.455266i	$0.849544\pi$
$578$	−1.94831e34	−0.582856
$579$	−2.13226e33	−0.0624249
$580$	1.47775e33	0.0423401
$581$	−1.15222e35	−3.23099
$582$	1.00989e34	0.277164
$583$	6.68676e34	1.79622
$584$	−1.45222e33	−0.0381831
$585$	1.29044e33	0.0332115
$586$	−2.00609e34	−0.505395
$587$	4.94816e33	0.122030	0.0610151	−	0.998137i	$-0.480566\pi$
$587$	4.94816e33	0.122030	0.0610151	+	0.998137i	$0.480566\pi$
$588$	−3.30924e34	−0.798935
$589$	−7.56528e33	−0.178807
$590$	1.95774e34	0.453006
$591$	−2.94005e34	−0.666056
$592$	2.07456e34	0.460156
$593$	−5.71306e34	−1.24075	−0.620376	−	0.784304i	$-0.713020\pi$
$593$	−5.71306e34	−1.24075	−0.620376	+	0.784304i	$0.713020\pi$
$594$	4.87259e34	1.03617
$595$	−1.57373e34	−0.327693
$596$	2.32592e34	0.474259
$597$	3.82384e34	0.763521
$598$	9.25509e33	0.180974
$599$	4.92727e34	0.943564	0.471782	−	0.881715i	$-0.343611\pi$
$599$	4.92727e34	0.943564	0.471782	+	0.881715i	$0.343611\pi$
$600$	−2.93082e33	−0.0549665
$601$	7.24167e34	1.33017	0.665086	−	0.746767i	$-0.268395\pi$
$601$	7.24167e34	1.33017	0.665086	+	0.746767i	$0.268395\pi$
$602$	−1.18243e35	−2.12726
$603$	−1.43111e34	−0.252177
$604$	−1.51361e34	−0.261248
$605$	−2.17997e34	−0.368560
$606$	−3.98018e33	−0.0659166
$607$	−2.52292e34	−0.409304	−0.204652	−	0.978835i	$-0.565606\pi$
$607$	−2.52292e34	−0.409304	−0.204652	+	0.978835i	$0.565606\pi$
$608$	−9.99158e33	−0.158796
$609$	−1.65250e34	−0.257291
$610$	2.95892e33	0.0451346
$611$	−8.75990e33	−0.130913
$612$	5.66470e33	0.0829438
$613$	8.87757e34	1.27362	0.636808	−	0.771023i	$-0.280255\pi$
$613$	8.87757e34	1.27362	0.636808	+	0.771023i	$0.280255\pi$
$614$	−9.59532e34	−1.34882
$615$	−1.14916e34	−0.158285
$616$	−6.18424e34	−0.834694
$617$	3.04657e34	0.402946	0.201473	−	0.979494i	$-0.435427\pi$
$617$	3.04657e34	0.402946	0.201473	+	0.979494i	$0.435427\pi$
$618$	5.31498e34	0.688883
$619$	8.61565e34	1.09435	0.547173	−	0.837019i	$-0.315704\pi$
$619$	8.61565e34	1.09435	0.547173	+	0.837019i	$0.315704\pi$
$620$	−3.57561e33	−0.0445096
$621$	1.21290e35	1.47972
$622$	5.50605e34	0.658355
$623$	−1.32586e35	−1.55381
$624$	−3.17488e33	−0.0364687
$625$	3.55271e33	0.0400000
$626$	9.24496e34	1.02030
$627$	8.71765e34	0.943094
$628$	4.40113e34	0.466733
$629$	−7.42174e34	−0.771566
$630$	−2.14639e34	−0.218752
$631$	−3.11716e34	−0.311452	−0.155726	−	0.987800i	$-0.549772\pi$
$631$	−3.11716e34	−0.311452	−0.155726	+	0.987800i	$0.549772\pi$
$632$	−3.43186e34	−0.336175
$633$	−3.41985e34	−0.328444
$634$	1.98001e33	0.0186446
$635$	−7.50283e33	−0.0692713
$636$	−5.70990e34	−0.516910
$637$	4.34548e34	0.385741
$638$	−2.07748e34	−0.180834
$639$	6.50454e34	0.555208
$640$	−4.72237e33	−0.0395285
$641$	1.40132e35	1.15030	0.575150	−	0.818048i	$-0.304944\pi$
$641$	1.40132e35	1.15030	0.575150	+	0.818048i	$0.304944\pi$
$642$	1.19933e35	0.965496
$643$	2.61025e34	0.206085	0.103042	−	0.994677i	$-0.467142\pi$
$643$	2.61025e34	0.206085	0.103042	+	0.994677i	$0.467142\pi$
$644$	−1.53940e35	−1.19201
$645$	7.87799e34	0.598300
$646$	3.57449e34	0.266261
$647$	1.90009e35	1.38826	0.694131	−	0.719848i	$-0.255789\pi$
$647$	1.90009e35	1.38826	0.694131	+	0.719848i	$0.255789\pi$
$648$	−2.20844e34	−0.158270
$649$	−2.75226e35	−1.93478
$650$	3.84856e33	0.0265388
$651$	3.99843e34	0.270475
$652$	1.98791e34	0.131917
$653$	1.69030e35	1.10040	0.550198	−	0.835034i	$-0.314552\pi$
$653$	1.69030e35	1.10040	0.550198	+	0.835034i	$0.314552\pi$
$654$	−1.26561e35	−0.808312
$655$	−3.78918e34	−0.237426
$656$	−1.85161e34	−0.113829
$657$	7.08581e33	0.0427388
$658$	1.45704e35	0.862277
$659$	−2.20649e35	−1.28125	−0.640627	−	0.767853i	$-0.721325\pi$
$659$	−2.20649e35	−1.28125	−0.640627	+	0.767853i	$0.721325\pi$
$660$	4.12026e34	0.234761
$661$	9.29705e34	0.519789	0.259894	−	0.965637i	$-0.416312\pi$
$661$	9.29705e34	0.519789	0.259894	+	0.965637i	$0.416312\pi$
$662$	−2.00645e35	−1.10079
$663$	1.13581e34	0.0611487
$664$	1.23693e35	0.653500
$665$	−1.35439e35	−0.702222
$666$	−1.01224e35	−0.515059
$667$	−5.17134e34	−0.258244
$668$	1.25428e35	0.614738
$669$	−3.18553e35	−1.53234
$670$	−4.26809e34	−0.201511
$671$	−4.15976e34	−0.192769
$672$	5.28079e34	0.240205
$673$	−1.44593e35	−0.645593	−0.322796	−	0.946468i	$-0.604623\pi$
$673$	−1.44593e35	−0.645593	−0.322796	+	0.946468i	$0.604623\pi$
$674$	1.53386e35	0.672259
$675$	5.04364e34	0.216993
$676$	−1.14218e35	−0.482392
$677$	−2.51992e35	−1.04479	−0.522394	−	0.852704i	$-0.674961\pi$
$677$	−2.51992e35	−1.04479	−0.522394	+	0.852704i	$0.674961\pi$
$678$	7.65228e34	0.311472
$679$	2.20575e35	0.881422
$680$	1.68942e34	0.0662792
$681$	1.51209e35	0.582423
$682$	5.02674e34	0.190100
$683$	1.41934e35	0.527022	0.263511	−	0.964656i	$-0.415119\pi$
$683$	1.41934e35	0.527022	0.263511	+	0.964656i	$0.415119\pi$
$684$	4.87520e34	0.177742
$685$	−1.08448e35	−0.388232
$686$	−3.71160e35	−1.30470
$687$	−3.32536e35	−1.14784
$688$	1.26936e35	0.430260
$689$	7.49788e34	0.249573
$690$	1.02563e35	0.335256
$691$	4.26858e34	0.137028	0.0685138	−	0.997650i	$-0.478174\pi$
$691$	4.26858e34	0.137028	0.0685138	+	0.997650i	$0.478174\pi$
$692$	−5.63374e34	−0.177611
$693$	3.01748e35	0.934284
$694$	5.17870e34	0.157481
$695$	−2.40843e35	−0.719323
$696$	1.77399e34	0.0520397
$697$	6.62413e34	0.190862
$698$	2.31187e35	0.654292
$699$	−3.72984e35	−1.03687
$700$	−6.40133e34	−0.174801
$701$	−7.85276e34	−0.210643	−0.105322	−	0.994438i	$-0.533587\pi$
$701$	−7.85276e34	−0.210643	−0.105322	+	0.994438i	$0.533587\pi$
$702$	5.46364e34	0.143969
$703$	−6.38736e35	−1.65341
$704$	6.63889e34	0.168825
$705$	−9.70754e34	−0.242519
$706$	−6.82074e34	−0.167407
$707$	−8.69330e34	−0.209624
$708$	2.35019e35	0.556784
$709$	−3.06083e35	−0.712461	−0.356231	−	0.934398i	$-0.615938\pi$
$709$	−3.06083e35	−0.712461	−0.356231	+	0.934398i	$0.615938\pi$
$710$	1.93990e35	0.443659
$711$	1.67451e35	0.376285
$712$	1.42333e35	0.314273
$713$	1.25127e35	0.271477
$714$	−1.88920e35	−0.402764
$715$	−5.41047e34	−0.113347
$716$	1.05805e35	0.217817
$717$	6.92646e35	1.40127
$718$	4.60240e35	0.915016
$719$	2.20247e35	0.430327	0.215163	−	0.976578i	$-0.430972\pi$
$719$	2.20247e35	0.430327	0.215163	+	0.976578i	$0.430972\pi$
$720$	2.30419e34	0.0442447
$721$	1.16087e36	2.19075
$722$	−7.36109e34	−0.136530
$723$	9.31844e34	0.169869
$724$	2.01976e35	0.361882
$725$	−2.15041e34	−0.0378701
$726$	−2.61697e35	−0.452993
$727$	8.70105e33	0.0148044	0.00740221	−	0.999973i	$-0.497644\pi$
$727$	8.70105e33	0.0148044	0.00740221	+	0.999973i	$0.497644\pi$
$728$	−6.93440e34	−0.115976
$729$	6.20764e35	1.02055
$730$	2.11325e34	0.0341520
$731$	−4.54115e35	−0.721437
$732$	3.55207e34	0.0554744
$733$	−1.92172e35	−0.295046	−0.147523	−	0.989059i	$-0.547130\pi$
$733$	−1.92172e35	−0.295046	−0.147523	+	0.989059i	$0.547130\pi$
$734$	−6.65823e35	−1.00498
$735$	4.81558e35	0.714589
$736$	1.65258e35	0.241095
$737$	6.00026e35	0.860650
$738$	9.03457e34	0.127410
$739$	9.08434e35	1.25961	0.629807	−	0.776751i	$-0.283134\pi$
$739$	9.08434e35	1.25961	0.629807	+	0.776751i	$0.283134\pi$
$740$	−3.01889e35	−0.411576
$741$	9.77512e34	0.131037
$742$	−1.24713e36	−1.64385
$743$	−9.13810e35	−1.18439	−0.592197	−	0.805794i	$-0.701739\pi$
$743$	−9.13810e35	−1.18439	−0.592197	+	0.805794i	$0.701739\pi$
$744$	−4.29239e34	−0.0547063
$745$	−3.38465e35	−0.424190
$746$	3.54445e35	0.436831
$747$	−6.03538e35	−0.731471
$748$	−2.37506e35	−0.283077
$749$	2.61951e36	3.07042
$750$	4.26490e34	0.0491635
$751$	3.01650e35	0.341982	0.170991	−	0.985273i	$-0.445303\pi$
$751$	3.01650e35	0.341982	0.170991	+	0.985273i	$0.445303\pi$
$752$	−1.56416e35	−0.174404
$753$	−1.00563e36	−1.10281
$754$	−2.32949e34	−0.0251257
$755$	2.20259e35	0.233667
$756$	−9.08770e35	−0.948269
$757$	−1.11391e36	−1.14328	−0.571640	−	0.820504i	$-0.693693\pi$
$757$	−1.11391e36	−1.14328	−0.571640	+	0.820504i	$0.693693\pi$
$758$	−5.34492e35	−0.539605
$759$	−1.44187e36	−1.43187
$760$	1.45397e35	0.142031
$761$	−8.13224e35	−0.781451	−0.390726	−	0.920507i	$-0.627776\pi$
$761$	−8.13224e35	−0.781451	−0.390726	+	0.920507i	$0.627776\pi$
$762$	−9.00686e34	−0.0851405
$763$	−2.76428e36	−2.57055
$764$	3.58712e35	0.328155
$765$	−8.24322e34	−0.0741872
$766$	−1.30669e35	−0.115695
$767$	−3.08612e35	−0.268826
$768$	−5.66902e34	−0.0485840
$769$	−9.19378e35	−0.775202	−0.387601	−	0.921827i	$-0.626696\pi$
$769$	−9.19378e35	−0.775202	−0.387601	+	0.921827i	$0.626696\pi$
$770$	8.99925e35	0.746573
$771$	7.32601e35	0.597982
$772$	4.99955e34	0.0401527
$773$	1.53774e36	1.21518	0.607590	−	0.794251i	$-0.292136\pi$
$773$	1.53774e36	1.21518	0.607590	+	0.794251i	$0.292136\pi$
$774$	−6.19361e35	−0.481595
$775$	5.20320e34	0.0398106
$776$	−2.36791e35	−0.178276
$777$	3.37587e36	2.50106
$778$	7.03786e35	0.513093
$779$	5.70091e35	0.409003
$780$	4.62006e34	0.0326186
$781$	−2.72718e36	−1.89486
$782$	−5.91209e35	−0.404256
$783$	−3.05285e35	−0.205439
$784$	7.75924e35	0.513888
$785$	−6.40449e35	−0.417459
$786$	−4.54877e35	−0.291818
$787$	1.78317e36	1.12592	0.562960	−	0.826484i	$-0.309663\pi$
$787$	1.78317e36	1.12592	0.562960	+	0.826484i	$0.309663\pi$
$788$	6.89359e35	0.428418
$789$	7.11474e35	0.435208
$790$	4.99401e35	0.300684
$791$	1.67137e36	0.990527
$792$	−3.23932e35	−0.188968
$793$	−4.66435e34	−0.0267841
$794$	5.93542e35	0.335502
$795$	8.30900e35	0.462338
$796$	−8.96584e35	−0.491109
$797$	4.10600e35	0.221406	0.110703	−	0.993854i	$-0.464690\pi$
$797$	4.10600e35	0.221406	0.110703	+	0.993854i	$0.464690\pi$
$798$	−1.62590e36	−0.863093
$799$	5.59576e35	0.292432
$800$	6.87195e34	0.0353553
$801$	−6.94488e35	−0.351770
$802$	2.65055e36	1.32177
$803$	−2.97090e35	−0.145862
$804$	−5.12369e35	−0.247675
$805$	2.24013e36	1.06616
$806$	5.63649e34	0.0264132
$807$	−6.73711e35	−0.310853
$808$	9.33241e34	0.0423986
$809$	−2.45266e36	−1.09719	−0.548593	−	0.836090i	$-0.684836\pi$
$809$	−2.45266e36	−1.09719	−0.548593	+	0.836090i	$0.684836\pi$
$810$	3.21371e35	0.141561
$811$	−3.62915e36	−1.57414	−0.787072	−	0.616861i	$-0.788404\pi$
$811$	−3.62915e36	−1.57414	−0.787072	+	0.616861i	$0.788404\pi$
$812$	3.87464e35	0.165494
$813$	2.03707e35	0.0856790
$814$	4.24407e36	1.75783
$815$	−2.89279e35	−0.117990
$816$	2.02809e35	0.0814630
$817$	−3.90824e36	−1.54599
$818$	−6.13193e35	−0.238880
$819$	3.38351e35	0.129813
$820$	2.69445e35	0.101811
$821$	4.84702e36	1.80379	0.901894	−	0.431957i	$-0.142177\pi$
$821$	4.84702e36	1.80379	0.901894	+	0.431957i	$0.142177\pi$
$822$	−1.30188e36	−0.477171
$823$	3.60517e36	1.30145	0.650726	−	0.759312i	$-0.274465\pi$
$823$	3.60517e36	1.30145	0.650726	+	0.759312i	$0.274465\pi$
$824$	−1.24621e36	−0.443101
$825$	−5.99577e35	−0.209976
$826$	5.13315e36	1.77065
$827$	−1.03992e36	−0.353331	−0.176665	−	0.984271i	$-0.556531\pi$
$827$	−1.03992e36	−0.353331	−0.176665	+	0.984271i	$0.556531\pi$
$828$	−8.06343e35	−0.269861
$829$	3.59238e36	1.18427	0.592134	−	0.805839i	$-0.298286\pi$
$829$	3.59238e36	1.18427	0.592134	+	0.805839i	$0.298286\pi$
$830$	−1.79998e36	−0.584508
$831$	−4.10853e36	−1.31424
$832$	7.44421e34	0.0234572
$833$	−2.77587e36	−0.861660
$834$	−2.89123e36	−0.884111
$835$	−1.82522e36	−0.549838
$836$	−2.04405e36	−0.606613
$837$	7.38676e35	0.215966
$838$	2.55401e36	0.735652
$839$	4.65321e36	1.32047	0.660234	−	0.751060i	$-0.270457\pi$
$839$	4.65321e36	1.32047	0.660234	+	0.751060i	$0.270457\pi$
$840$	−7.68456e35	−0.214846
$841$	−3.50020e36	−0.964146
$842$	1.78533e36	0.484526
$843$	−5.08037e35	−0.135847
$844$	8.01860e35	0.211260
$845$	1.66209e36	0.431465
$846$	7.63200e35	0.195213
$847$	−5.71585e36	−1.44058
$848$	1.33881e36	0.332485
$849$	−3.56380e36	−0.872102
$850$	−2.45844e35	−0.0592820
$851$	1.05645e37	2.51032
$852$	2.32877e36	0.545296
$853$	−5.05930e36	−1.16742	−0.583710	−	0.811962i	$-0.698400\pi$
$853$	−5.05930e36	−1.16742	−0.583710	+	0.811962i	$0.698400\pi$
$854$	7.75823e35	0.176417
$855$	−7.09435e35	−0.158978
$856$	−2.81209e36	−0.621023
$857$	−2.18945e36	−0.476513	−0.238257	−	0.971202i	$-0.576576\pi$
$857$	−2.18945e36	−0.476513	−0.238257	+	0.971202i	$0.576576\pi$
$858$	−6.49506e35	−0.139313
$859$	−5.91491e36	−1.25035	−0.625177	−	0.780483i	$-0.714973\pi$
$859$	−5.91491e36	−1.25035	−0.625177	+	0.780483i	$0.714973\pi$
$860$	−1.84717e36	−0.384836
$861$	−3.01307e36	−0.618685
$862$	−3.93464e36	−0.796278
$863$	3.85509e36	0.768952	0.384476	−	0.923135i	$-0.374382\pi$
$863$	3.85509e36	0.768952	0.384476	+	0.923135i	$0.374382\pi$
$864$	9.75581e35	0.191797
$865$	8.19818e35	0.158861
$866$	2.66362e36	0.508744
$867$	3.40352e36	0.640751
$868$	−9.37520e35	−0.173974
$869$	−7.02078e36	−1.28422
$870$	−2.58149e35	−0.0465457
$871$	6.72810e35	0.119582
$872$	2.96751e36	0.519919
$873$	1.15538e36	0.199547
$874$	−5.08811e36	−0.866291
$875$	9.31516e35	0.156347
$876$	2.53688e35	0.0419758
$877$	−5.04839e36	−0.823489	−0.411744	−	0.911299i	$-0.635080\pi$
$877$	−5.04839e36	−0.823489	−0.411744	+	0.911299i	$0.635080\pi$
$878$	−5.20190e36	−0.836528
$879$	3.50445e36	0.555596
$880$	−9.66086e35	−0.151002
$881$	7.50642e36	1.15673	0.578367	−	0.815776i	$-0.303690\pi$
$881$	7.50642e36	1.15673	0.578367	+	0.815776i	$0.303690\pi$
$882$	−3.78597e36	−0.575201
$883$	1.15945e37	1.73677	0.868384	−	0.495893i	$-0.165159\pi$
$883$	1.15945e37	1.73677	0.868384	+	0.495893i	$0.165159\pi$
$884$	−2.66316e35	−0.0393318
$885$	−3.41997e36	−0.498003
$886$	1.46600e36	0.210481
$887$	1.11924e37	1.58445	0.792226	−	0.610228i	$-0.208922\pi$
$887$	1.11924e37	1.58445	0.792226	+	0.610228i	$0.208922\pi$
$888$	−3.62406e36	−0.505864
$889$	−1.96723e36	−0.270759
$890$	−2.07122e36	−0.281094
$891$	−4.51796e36	−0.604604
$892$	7.46919e36	0.985627
$893$	4.81587e36	0.626660
$894$	−4.06315e36	−0.521367
$895$	−1.53966e36	−0.194822
$896$	−1.23820e36	−0.154504
$897$	−1.61677e36	−0.198950
$898$	−1.18483e36	−0.143781
$899$	−3.14943e35	−0.0376908
$900$	−3.35303e35	−0.0395737
$901$	−4.78960e36	−0.557493
$902$	−3.78796e36	−0.434835
$903$	2.06560e37	2.33856
$904$	−1.79425e36	−0.200344
$905$	−2.93913e36	−0.323677
$906$	2.64413e36	0.287197
$907$	1.70146e36	0.182276	0.0911381	−	0.995838i	$-0.470950\pi$
$907$	1.70146e36	0.182276	0.0911381	+	0.995838i	$0.470950\pi$
$908$	−3.54543e36	−0.374624
$909$	−4.55357e35	−0.0474573
$910$	1.00909e36	0.103732
$911$	−1.90683e36	−0.193344	−0.0966721	−	0.995316i	$-0.530820\pi$
$911$	−1.90683e36	−0.193344	−0.0966721	+	0.995316i	$0.530820\pi$
$912$	1.74543e36	0.174569
$913$	2.53048e37	2.49642
$914$	1.04842e37	1.02025
$915$	−5.16894e35	−0.0496178
$916$	7.79705e36	0.738307
$917$	−9.93518e36	−0.928024
$918$	−3.49014e36	−0.321595
$919$	−1.39528e37	−1.26829	−0.634145	−	0.773214i	$-0.718648\pi$
$919$	−1.39528e37	−1.26829	−0.634145	+	0.773214i	$0.718648\pi$
$920$	−2.40482e36	−0.215642
$921$	1.67621e37	1.48280
$922$	−3.24815e35	−0.0283465
$923$	−3.05800e36	−0.263279
$924$	1.08033e37	0.917604
$925$	4.39306e36	0.368125
$926$	1.35558e36	0.112070
$927$	6.08066e36	0.495968
$928$	−4.15950e35	−0.0334728
$929$	3.87552e36	0.307704	0.153852	−	0.988094i	$-0.450832\pi$
$929$	3.87552e36	0.307704	0.153852	+	0.988094i	$0.450832\pi$
$930$	6.24624e35	0.0489308
$931$	−2.38899e37	−1.84647
$932$	8.74542e36	0.666932
$933$	−9.61853e36	−0.723749
$934$	−1.21324e37	−0.900763
$935$	3.45617e36	0.253192
$936$	−3.63226e35	−0.0262560
$937$	−7.59791e36	−0.541938	−0.270969	−	0.962588i	$-0.587344\pi$
$937$	−7.59791e36	−0.541938	−0.270969	+	0.962588i	$0.587344\pi$
$938$	−1.11909e37	−0.787642
$939$	−1.61500e37	−1.12164
$940$	2.27615e36	0.155992
$941$	−2.56881e37	−1.73725	−0.868624	−	0.495472i	$-0.834995\pi$
$941$	−2.56881e37	−1.73725	−0.868624	+	0.495472i	$0.834995\pi$
$942$	−7.68835e36	−0.513094
$943$	−9.42913e36	−0.620977
$944$	−5.51053e36	−0.358133
$945$	1.32243e37	0.848157
$946$	2.59682e37	1.64363
$947$	1.90718e37	1.19129	0.595645	−	0.803247i	$-0.296896\pi$
$947$	1.90718e37	1.19129	0.595645	+	0.803247i	$0.296896\pi$
$948$	5.99512e36	0.369568
$949$	−3.33127e35	−0.0202667
$950$	−2.11580e36	−0.127037
$951$	−3.45889e35	−0.0204965
$952$	4.42965e36	0.259064
$953$	−1.68185e36	−0.0970791	−0.0485396	−	0.998821i	$-0.515457\pi$
$953$	−1.68185e36	−0.0970791	−0.0485396	+	0.998821i	$0.515457\pi$
$954$	−6.53247e36	−0.372154
$955$	−5.21994e36	−0.293510
$956$	−1.62406e37	−0.901319
$957$	3.62916e36	0.198796
$958$	6.82086e36	0.368783
$959$	−2.84350e37	−1.51747
$960$	8.24952e35	0.0434548
$961$	−1.84707e37	−0.960378
$962$	4.75889e36	0.244240
$963$	1.37211e37	0.695119
$964$	−2.18492e36	−0.109263
$965$	−7.27530e35	−0.0359137
$966$	2.68919e37	1.31041
$967$	−4.14643e36	−0.199454	−0.0997271	−	0.995015i	$-0.531797\pi$
$967$	−4.14643e36	−0.199454	−0.0997271	+	0.995015i	$0.531797\pi$
$968$	6.13607e36	0.291373
$969$	−6.24428e36	−0.292708
$970$	3.44576e36	0.159455
$971$	2.14239e37	0.978720	0.489360	−	0.872082i	$-0.337230\pi$
$971$	2.14239e37	0.978720	0.489360	+	0.872082i	$0.337230\pi$
$972$	−8.17066e36	−0.368493
$973$	−6.31487e37	−2.81160
$974$	−2.47068e37	−1.08600
$975$	−6.72307e35	−0.0291749
$976$	−8.32861e35	−0.0356820
$977$	−1.15529e37	−0.488660	−0.244330	−	0.969692i	$-0.578568\pi$
$977$	−1.15529e37	−0.488660	−0.244330	+	0.969692i	$0.578568\pi$
$978$	−3.47268e36	−0.145020
$979$	2.91181e37	1.20055
$980$	−1.12912e37	−0.459635
$981$	−1.44794e37	−0.581952
$982$	1.07374e37	0.426096
$983$	−5.38686e36	−0.211065	−0.105533	−	0.994416i	$-0.533655\pi$
$983$	−5.38686e36	−0.211065	−0.105533	+	0.994416i	$0.533655\pi$
$984$	3.23458e36	0.125135
$985$	−1.00315e37	−0.383189
$986$	1.48806e36	0.0561254
$987$	−2.54530e37	−0.947927
$988$	−2.29199e36	−0.0842852
$989$	6.46410e37	2.34722
$990$	4.71383e36	0.169018
$991$	3.50366e37	1.24051	0.620256	−	0.784399i	$-0.287029\pi$
$991$	3.50366e37	1.24051	0.620256	+	0.784399i	$0.287029\pi$
$992$	1.00644e36	0.0351880
$993$	3.50508e37	1.21013
$994$	5.08638e37	1.73412
$995$	1.30470e37	0.439261
$996$	−2.16080e37	−0.718412
$997$	4.42953e37	1.45435	0.727174	−	0.686453i	$-0.240833\pi$
$997$	4.42953e37	1.45435	0.727174	+	0.686453i	$0.240833\pi$
$998$	−3.29431e37	−1.06815
$999$	6.23664e37	1.99702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.a.d.1.1	✓	2
5.2	odd	4		50.26.b.d.49.4		4
5.3	odd	4		50.26.b.d.49.1		4
5.4	even	2		50.26.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.d.1.1	✓	2	1.1	even	1	trivial
50.26.a.d.1.2		2	5.4	even	2
50.26.b.d.49.1		4	5.3	odd	4
50.26.b.d.49.4		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+4096.00 q^{2} -715531. q^{3} +1.67772e7 q^{4} -2.44141e8 q^{5} -2.93082e9 q^{6} -6.40133e10 q^{7} +6.87195e10 q^{8} -3.35303e11 q^{9} -1.00000e12 q^{10} +1.40584e13 q^{11} -1.20046e13 q^{12} +1.57637e13 q^{13} -2.62199e14 q^{14} +1.74690e14 q^{15} +2.81475e14 q^{16} -1.00698e15 q^{17} -1.37340e15 q^{18} -8.66632e15 q^{19} -4.09600e15 q^{20} +4.58035e16 q^{21} +5.75832e16 q^{22} +1.43338e17 q^{23} -4.91709e16 q^{24} +5.96046e16 q^{25} +6.45682e16 q^{26} +8.46182e17 q^{27} -1.07397e18 q^{28} -3.60779e17 q^{29} +7.15531e17 q^{30} +8.72952e17 q^{31} +1.15292e18 q^{32} -1.00592e19 q^{33} -4.12457e18 q^{34} +1.56283e19 q^{35} -5.62546e18 q^{36} +7.37033e19 q^{37} -3.54972e19 q^{38} -1.12794e19 q^{39} -1.67772e19 q^{40} -6.57824e19 q^{41} +1.87611e20 q^{42} +4.50969e20 q^{43} +2.35861e20 q^{44} +8.18612e19 q^{45} +5.87113e20 q^{46} -5.55700e20 q^{47} -2.01404e20 q^{48} +2.75664e21 q^{49} +2.44141e20 q^{50} +7.20523e20 q^{51} +2.64471e20 q^{52} +4.75642e21 q^{53} +3.46596e21 q^{54} -3.43223e21 q^{55} -4.39896e21 q^{56} +6.20102e21 q^{57} -1.47775e21 q^{58} -1.95774e22 q^{59} +2.93082e21 q^{60} -2.95892e21 q^{61} +3.57561e21 q^{62} +2.14639e22 q^{63} +4.72237e21 q^{64} -3.84856e21 q^{65} -4.12026e22 q^{66} +4.26809e22 q^{67} -1.68942e22 q^{68} -1.02563e23 q^{69} +6.40133e22 q^{70} -1.93990e23 q^{71} -2.30419e22 q^{72} -2.11325e22 q^{73} +3.01889e23 q^{74} -4.26490e22 q^{75} -1.45397e23 q^{76} -8.99925e23 q^{77} -4.62006e22 q^{78} -4.99401e23 q^{79} -6.87195e22 q^{80} -3.21371e23 q^{81} -2.69445e23 q^{82} +1.79998e24 q^{83} +7.68456e23 q^{84} +2.45844e23 q^{85} +1.84717e24 q^{86} +2.58149e23 q^{87} +9.66086e23 q^{88} +2.07122e24 q^{89} +3.35303e23 q^{90} -1.00909e24 q^{91} +2.40482e24 q^{92} -6.24624e23 q^{93} -2.27615e24 q^{94} +2.11580e24 q^{95} -8.24952e23 q^{96} -3.44576e24 q^{97} +1.12912e25 q^{98} -4.71383e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8192 q^{2} - 97092 q^{3} + 33554432 q^{4} - 488281250 q^{5} - 397688832 q^{6} - 16137160124 q^{7} + 137438953472 q^{8} - 800124539454 q^{9} - 2000000000000 q^{10} + 14416600801344 q^{11} - 1628933455872 q^{12}+ \cdots - 48\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 8192 * q^2 - 97092 * q^3 + 33554432 * q^4 - 488281250 * q^5 - 397688832 * q^6 - 16137160124 * q^7 + 137438953472 * q^8 - 800124539454 * q^9 - 2000000000000 * q^10 + 14416600801344 * q^11 - 1628933455872 * q^12 + 93404548866628 * q^13 - 66097807867904 * q^14 + 23704101562500 * q^15 + 562949953421312 * q^16 + 499266882181236 * q^17 - 3277310113603584 * q^18 - 3830204591906120 * q^19 - 8192000000000000 * q^20 + 75412053748282104 * q^21 + 59050396882305024 * q^22 + 169271186050723788 * q^23 - 6672111435251712 * q^24 + 119209289550781250 * q^25 + 382585032157708288 * q^26 + 34721228182863240 * q^27 - 270736621026934784 * q^28 + 569443622853716940 * q^29 + 97092000000000000 * q^30 + 3982769593868414584 * q^31 + 2305843009213693952 * q^32 - 9837705729224836224 * q^33 + 2044997149414342656 * q^34 + 3939736358398437500 * q^35 - 13423862225320280064 * q^36 + 28241444663789328196 * q^37 - 15688518008447467520 * q^38 + 36736718047624459512 * q^39 - 33554432000000000000 * q^40 + 36676428854020432524 * q^41 + 308887772152963497984 * q^42 + 909017314298263251628 * q^43 + 241870425629921378304 * q^44 + 195342905140136718750 * q^45 + 693334778063764635648 * q^46 + 954929084389204818996 * q^47 - 27328968438791012352 * q^48 + 3707694774551412650874 * q^49 + 488281250000000000000 * q^50 + 1652042752773544110744 * q^51 + 1567068291717973147648 * q^52 + 2753692919774994609588 * q^53 + 142218150637007831040 * q^54 - 3519677930015625000000 * q^55 - 1108937199726324875264 * q^56 + 9191867441696689119120 * q^57 + 2332441079208824586240 * q^58 + 458866752134906177880 * q^59 + 397688832000000000000 * q^60 - 26987853585082462424636 * q^61 + 16313424256485026136064 * q^62 - 789976870259963054652 * q^63 + 9444732965739290427392 * q^64 - 22803844938141601562500 * q^65 - 40295242666904929173504 * q^66 - 14159647018044347838524 * q^67 + 8376308324001147518976 * q^68 - 86524983849189139233048 * q^69 + 16137160124000000000000 * q^70 - 173327708998984655450136 * q^71 - 54984139674911867142144 * q^72 - 341978509295241035156732 * q^73 + 115676957342881088290816 * q^74 - 5787134170532226562500 * q^75 - 64260169762600826961920 * q^76 - 882775887628764911584128 * q^77 + 150473597123069786161152 * q^78 - 927961875376490258946800 * q^79 - 137438953472000000000000 * q^80 - 429372483438817686010518 * q^81 + 150226652586067691618304 * q^82 + 681902409230287477811148 * q^83 + 1265204314738538487742464 * q^84 - 121891328657528320312500 * q^85 + 3723334919365686278668288 * q^86 + 833435461987898381769960 * q^87 + 990701263380157965533184 * q^88 + 3822788098104790038225780 * q^89 + 800124539454000000000000 * q^90 + 2708056932935479178393864 * q^91 + 2839899250949179947614208 * q^92 + 1298609917529886715704336 * q^93 + 3911389529658182938607616 * q^94 + 935108542945830078125000 * q^95 - 111939454725287986593792 * q^96 - 16314734149871901683914364 * q^97 + 15186717796562586217979904 * q^98 - 4880327126898398506596288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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