LMFDB - Embedded newform 25.26.b.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,26,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$98.9991949881$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.26.b.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-48.0000i q^{2} +195804. i q^{3} +3.35521e7 q^{4} +9.39859e6 q^{6} +3.90806e10i q^{7} -3.22111e9i q^{8} +8.08949e11 q^{9} +O(q^{10})$	\(q-48.0000i q^{2} +195804. i q^{3} +3.35521e7 q^{4} +9.39859e6 q^{6} +3.90806e10i q^{7} -3.22111e9i q^{8} +8.08949e11 q^{9} +8.41952e12 q^{11} +6.56964e12i q^{12} +8.16510e13i q^{13} +1.87587e12 q^{14} +1.12567e15 q^{16} -2.51990e15i q^{17} -3.88296e13i q^{18} +6.08206e15 q^{19} -7.65214e15 q^{21} -4.04137e14i q^{22} +9.49953e16i q^{23} +6.30707e14 q^{24} +3.91925e15 q^{26} +3.24298e17i q^{27} +1.31124e18i q^{28} +2.71247e17 q^{29} +4.29167e18 q^{31} -1.62115e17i q^{32} +1.64857e18i q^{33} -1.20955e17 q^{34} +2.71420e19 q^{36} +2.03015e19i q^{37} -2.91939e17i q^{38} -1.59876e19 q^{39} -1.83744e20 q^{41} +3.67303e17i q^{42} -3.00902e20i q^{43} +2.82493e20 q^{44} +4.55977e18 q^{46} -9.24361e20i q^{47} +2.20410e20i q^{48} -1.86224e20 q^{49} +4.93407e20 q^{51} +2.73957e21i q^{52} +9.90292e20i q^{53} +1.55663e19 q^{54} +1.25883e20 q^{56} +1.19089e21i q^{57} -1.30199e19i q^{58} -1.30526e22 q^{59} +9.01545e21 q^{61} -2.06000e20i q^{62} +3.16142e22i q^{63} +3.77634e22 q^{64} +7.91316e19 q^{66} -2.66891e22i q^{67} -8.45480e22i q^{68} -1.86005e22 q^{69} -1.92391e23 q^{71} -2.60572e21i q^{72} -4.24046e22i q^{73} +9.74471e20 q^{74} +2.04066e23 q^{76} +3.29040e23i q^{77} +7.67405e20i q^{78} +2.71681e23 q^{79} +6.21915e23 q^{81} +8.81972e21i q^{82} +9.31454e23i q^{83} -2.56745e23 q^{84} -1.44433e22 q^{86} +5.31112e22i q^{87} -2.71202e22i q^{88} +1.76364e24 q^{89} -3.19097e24 q^{91} +3.18729e24i q^{92} +8.40325e23i q^{93} -4.43693e22 q^{94} +3.17427e22 q^{96} +2.82924e24i q^{97} +8.93877e21i q^{98} +6.81096e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 67104256 q^{4} + 18797184 q^{6} + 1617898806054 q^{9}+O(q^{10}) $ 2 * q + 67104256 * q^4 + 18797184 * q^6 + 1617898806054 * q^9	$ 2 q + 67104256 q^{4} + 18797184 q^{6} + 1617898806054 q^{9} + 16839030598104 q^{11} + 3751737330432 q^{14} + 22\!\cdots\!12 q^{16}+ \cdots + 13\!\cdots\!08 q^{99}+O(q^{100}) $ 2 * q + 67104256 * q^4 + 18797184 * q^6 + 1617898806054 * q^9 + 16839030598104 * q^11 + 3751737330432 * q^14 + 2251335967834112 * q^16 + 12164112740617880 * q^19 - 15304274505164736 * q^21 + 1261414355927040 * q^24 + 7838500352190144 * q^26 + 542493918953474820 * q^29 + 8583332135043018304 * q^31 - 241910402779015488 * q^34 + 54283947831770982912 * q^36 - 31975202561671644912 * q^39 - 367488499148142449196 * q^41 + 564985310023501965312 * q^44 + 9119546908446760704 * q^46 - 372448914438786768114 * q^49 + 986813010536298929424 * q^51 + 31132610668192884480 * q^54 + 251766186268874833920 * q^56 - 26105138832908403675960 * q^59 + 18030902449402829235004 * q^61 + 75526736626474314366976 * q^64 + 158263178267095469568 * q^66 - 37200911726281448601792 * q^69 - 384781032372435274880496 * q^71 + 1948942506826476190272 * q^74 + 408131867679641908848640 * q^76 + 543362110051544554394720 * q^79 + 1243829527532757785952882 * q^81 - 513490977144423883358208 * q^84 - 28886575121816288232576 * q^86 + 3527271036099614633005260 * q^89 - 6381943226110274013676576 * q^91 - 88738660614211667394048 * q^94 + 63485430446375603011584 * q^96 + 13621923749889617558060808 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 48.0000i	− 0.00828641i	−0.999991	−	0.00414320i	$-0.998681\pi$
$2$	− 48.0000i	− 0.00828641i	0.999991	−	0.00414320i	$-0.00131883\pi$
$3$	195804.i	0.212719i	0.994328	+	0.106359i	$0.0339194\pi$
$3$	195804.i	0.212719i	−0.994328	+	0.106359i	$0.966081\pi$
$4$	3.35521e7	0.999931
$5$	0	0
$5$	0	0
$6$	9.39859e6	0.00176267
$7$	3.90806e10i	1.06718i	0.845745	+	0.533588i	$0.179157\pi$
$7$	3.90806e10i	1.06718i	−0.845745	+	0.533588i	$0.820843\pi$
$8$	− 3.22111e9i	− 0.0165722i
$9$	8.08949e11	0.954751
$10$	0	0
$11$	8.41952e12	0.808870	0.404435	−	0.914567i	$-0.367468\pi$
$11$	8.41952e12	0.808870	0.404435	+	0.914567i	$0.367468\pi$
$12$	6.56964e12i	0.212704i
$13$	8.16510e13i	0.972008i	0.873957	+	0.486004i	$0.161546\pi$
$13$	8.16510e13i	0.972008i	−0.873957	+	0.486004i	$0.838454\pi$
$14$	1.87587e12	0.00884305
$15$	0	0
$16$	1.12567e15	0.999794
$17$	− 2.51990e15i	− 1.04899i	−0.851413	−	0.524496i	$-0.824254\pi$
$17$	− 2.51990e15i	− 1.04899i	0.851413	−	0.524496i	$-0.175746\pi$
$18$	− 3.88296e13i	− 0.00791145i
$19$	6.08206e15	0.630421	0.315210	−	0.949022i	$-0.397925\pi$
$19$	6.08206e15	0.630421	0.315210	+	0.949022i	$0.397925\pi$
$20$	0	0
$21$	−7.65214e15	−0.227008
$22$	− 4.04137e14i	− 0.00670262i
$23$	9.49953e16i	0.903866i	0.892052	+	0.451933i	$0.149265\pi$
$23$	9.49953e16i	0.903866i	−0.892052	+	0.451933i	$0.850735\pi$
$24$	6.30707e14	0.00352523
$25$	0	0
$26$	3.91925e15	0.00805445
$27$	3.24298e17i	0.415812i
$28$	1.31124e18i	1.06710i
$29$	2.71247e17	0.142361	0.0711803	−	0.997463i	$-0.477323\pi$
$29$	2.71247e17	0.142361	0.0711803	+	0.997463i	$0.477323\pi$
$30$	0	0
$31$	4.29167e18	0.978599	0.489299	−	0.872116i	$-0.337253\pi$
$31$	4.29167e18	0.978599	0.489299	+	0.872116i	$0.337253\pi$
$32$	− 1.62115e17i	− 0.0248569i
$33$	1.64857e18i	0.172062i
$34$	−1.20955e17	−0.00869237
$35$	0	0
$36$	2.71420e19	0.954685
$37$	2.03015e19i	0.506998i	0.967336	+	0.253499i	$0.0815815\pi$
$37$	2.03015e19i	0.506998i	−0.967336	+	0.253499i	$0.918419\pi$
$38$	− 2.91939e17i	− 0.00522392i
$39$	−1.59876e19	−0.206764
$40$	0	0
$41$	−1.83744e20	−1.27179	−0.635895	−	0.771775i	$-0.719369\pi$
$41$	−1.83744e20	−1.27179	−0.635895	+	0.771775i	$0.719369\pi$
$42$	3.67303e17i	0.00188108i
$43$	− 3.00902e20i	− 1.14834i	−0.818737	−	0.574168i	$-0.805326\pi$
$43$	− 3.00902e20i	− 1.14834i	0.818737	−	0.574168i	$-0.194674\pi$
$44$	2.82493e20	0.808814
$45$	0	0
$46$	4.55977e18	0.00748980
$47$	− 9.24361e20i	− 1.16043i	−0.814464	−	0.580214i	$-0.802969\pi$
$47$	− 9.24361e20i	− 1.16043i	0.814464	−	0.580214i	$-0.197031\pi$
$48$	2.20410e20i	0.212675i
$49$	−1.86224e20	−0.138863
$50$	0	0
$51$	4.93407e20	0.223140
$52$	2.73957e21i	0.971941i
$53$	9.90292e20i	0.276895i	0.990370	+	0.138447i	$0.0442112\pi$
$53$	9.90292e20i	0.276895i	−0.990370	+	0.138447i	$0.955789\pi$
$54$	1.55663e19	0.00344559
$55$	0	0
$56$	1.25883e20	0.0176855
$57$	1.19089e21i	0.134102i
$58$	− 1.30199e19i	− 0.00117966i
$59$	−1.30526e22	−0.955093	−0.477547	−	0.878606i	$-0.658474\pi$
$59$	−1.30526e22	−0.955093	−0.477547	+	0.878606i	$0.658474\pi$
$60$	0	0
$61$	9.01545e21	0.434875	0.217438	−	0.976074i	$-0.430230\pi$
$61$	9.01545e21	0.434875	0.217438	+	0.976074i	$0.430230\pi$
$62$	− 2.06000e20i	− 0.00810907i
$63$	3.16142e22i	1.01889i
$64$	3.77634e22	0.999588
$65$	0	0
$66$	7.91316e19	0.00142577
$67$	− 2.66891e22i	− 0.398473i	−0.979951	−	0.199236i	$-0.936154\pi$
$67$	− 2.66891e22i	− 0.398473i	0.979951	−	0.199236i	$-0.0638461\pi$
$68$	− 8.45480e22i	− 1.04892i
$69$	−1.86005e22	−0.192269
$70$	0	0
$71$	−1.92391e23	−1.39141	−0.695704	−	0.718329i	$-0.744907\pi$
$71$	−1.92391e23	−1.39141	−0.695704	+	0.718329i	$0.744907\pi$
$72$	− 2.60572e21i	− 0.0158224i
$73$	− 4.24046e22i	− 0.216709i	−0.994112	−	0.108355i	$-0.965442\pi$
$73$	− 4.24046e22i	− 0.216709i	0.994112	−	0.108355i	$-0.0345582\pi$
$74$	9.74471e20	0.00420119
$75$	0	0
$76$	2.04066e23	0.630377
$77$	3.29040e23i	0.863206i
$78$	7.67405e20i	0.00171333i
$79$	2.71681e23	0.517274	0.258637	−	0.965975i	$-0.416727\pi$
$79$	2.71681e23	0.517274	0.258637	+	0.965975i	$0.416727\pi$
$80$	0	0
$81$	6.21915e23	0.866300
$82$	8.81972e21i	0.0105386i
$83$	9.31454e23i	0.956501i	0.878223	+	0.478251i	$0.158729\pi$
$83$	9.31454e23i	0.956501i	−0.878223	+	0.478251i	$0.841271\pi$
$84$	−2.56745e23	−0.226993
$85$	0	0
$86$	−1.44433e22	−0.00951558
$87$	5.31112e22i	0.0302828i
$88$	− 2.71202e22i	− 0.0134048i
$89$	1.76364e24	0.756892	0.378446	−	0.925623i	$-0.376459\pi$
$89$	1.76364e24	0.756892	0.378446	+	0.925623i	$0.376459\pi$
$90$	0	0
$91$	−3.19097e24	−1.03730
$92$	3.18729e24i	0.903804i
$93$	8.40325e23i	0.208166i
$94$	−4.43693e22	−0.00961578
$95$	0	0
$96$	3.17427e22	0.00528754
$97$	2.82924e24i	0.414022i	0.978339	+	0.207011i	$0.0663736\pi$
$97$	2.82924e24i	0.414022i	−0.978339	+	0.207011i	$0.933626\pi$
$98$	8.93877e21i	0.00115067i
$99$	6.81096e24	0.772269
$100$	0	0
$101$	1.86342e24	0.164549	0.0822744	−	0.996610i	$-0.473782\pi$
$101$	1.86342e24	0.164549	0.0822744	+	0.996610i	$0.473782\pi$
$102$	− 2.36835e22i	− 0.00184903i
$103$	− 4.85812e24i	− 0.335740i	−0.985809	−	0.167870i	$-0.946311\pi$
$103$	− 4.85812e24i	− 0.335740i	0.985809	−	0.167870i	$-0.0536889\pi$
$104$	2.63007e23	0.0161084
$105$	0	0
$106$	4.75340e22	0.00229446
$107$	3.58304e25i	1.53799i	0.639252	+	0.768997i	$0.279244\pi$
$107$	3.58304e25i	1.53799i	−0.639252	+	0.768997i	$0.720756\pi$
$108$	1.08809e25i	0.415784i
$109$	4.77795e25	1.62709	0.813543	−	0.581505i	$-0.197536\pi$
$109$	4.77795e25	1.62709	0.813543	+	0.581505i	$0.197536\pi$
$110$	0	0
$111$	−3.97511e24	−0.107848
$112$	4.39918e25i	1.06696i
$113$	7.46476e25i	1.62008i	0.586378	+	0.810038i	$0.300553\pi$
$113$	7.46476e25i	1.62008i	−0.586378	+	0.810038i	$0.699447\pi$
$114$	5.71628e22	0.00111123
$115$	0	0
$116$	9.10091e24	0.142351
$117$	6.60516e25i	0.928025i
$118$	6.26523e23i	0.00791429i
$119$	9.84792e25	1.11946
$120$	0	0
$121$	−3.74588e25	−0.345730
$122$	− 4.32742e23i	− 0.00360355i
$123$	− 3.59779e25i	− 0.270534i
$124$	1.43995e26	0.978532
$125$	0	0
$126$	1.51748e24	0.00844291
$127$	3.35905e26i	1.69305i	0.532350	+	0.846524i	$0.321309\pi$
$127$	3.35905e26i	1.69305i	−0.532350	+	0.846524i	$0.678691\pi$
$128$	− 7.25231e24i	− 0.0331399i
$129$	5.89178e25	0.244273
$130$	0	0
$131$	−1.74971e26	−0.598513	−0.299257	−	0.954173i	$-0.596739\pi$
$131$	−1.74971e26	−0.598513	−0.299257	+	0.954173i	$0.596739\pi$
$132$	5.53132e25i	0.172050i
$133$	2.37690e26i	0.672769i
$134$	−1.28108e24	−0.00330191
$135$	0	0
$136$	−8.11689e24	−0.0173841
$137$	6.18313e26i	1.20837i	0.796843	+	0.604187i	$0.206502\pi$
$137$	6.18313e26i	1.20837i	−0.796843	+	0.604187i	$0.793498\pi$
$138$	8.92822e23i	0.00159322i
$139$	4.84462e26	0.789905	0.394952	−	0.918702i	$-0.370761\pi$
$139$	4.84462e26	0.789905	0.394952	+	0.918702i	$0.370761\pi$
$140$	0	0
$141$	1.80994e26	0.246845
$142$	9.23474e24i	0.0115298i
$143$	6.87462e26i	0.786228i
$144$	9.10608e26	0.954554
$145$	0	0
$146$	−2.03542e24	−0.00179574
$147$	− 3.64635e25i	− 0.0295387i
$148$	6.81158e26i	0.506963i
$149$	−9.05569e26	−0.619574	−0.309787	−	0.950806i	$-0.600258\pi$
$149$	−9.05569e26	−0.619574	−0.309787	+	0.950806i	$0.600258\pi$
$150$	0	0
$151$	1.16190e27	0.672907	0.336454	−	0.941700i	$-0.390772\pi$
$151$	1.16190e27	0.672907	0.336454	+	0.941700i	$0.390772\pi$
$152$	− 1.95910e25i	− 0.0104475i
$153$	− 2.03847e27i	− 1.00152i
$154$	1.57939e25	0.00715287
$155$	0	0
$156$	−5.36418e26	−0.206750
$157$	− 3.41505e26i	− 0.121521i	−0.998152	−	0.0607605i	$-0.980647\pi$
$157$	− 3.41505e26i	− 0.121521i	0.998152	−	0.0607605i	$-0.0193526\pi$
$158$	− 1.30407e25i	− 0.00428634i
$159$	−1.93903e26	−0.0589008
$160$	0	0
$161$	−3.71247e27	−0.964583
$162$	− 2.98519e25i	− 0.00717851i
$163$	− 4.63202e27i	− 1.03140i	−0.856771	−	0.515698i	$-0.827533\pi$
$163$	− 4.63202e27i	− 1.03140i	0.856771	−	0.515698i	$-0.172467\pi$
$164$	−6.16501e27	−1.27170
$165$	0	0
$166$	4.47098e25	0.00792596
$167$	− 8.26470e27i	− 1.35916i	−0.733600	−	0.679581i	$-0.762162\pi$
$167$	− 8.26470e27i	− 1.35916i	0.733600	−	0.679581i	$-0.237838\pi$
$168$	2.46484e25i	0.00376204i
$169$	3.89517e26	0.0552004
$170$	0	0
$171$	4.92008e27	0.601895
$172$	− 1.00959e28i	− 1.14826i
$173$	6.02602e27i	0.637462i	0.947845	+	0.318731i	$0.103257\pi$
$173$	6.02602e27i	0.637462i	−0.947845	+	0.318731i	$0.896743\pi$
$174$	2.54934e24	0.000250935 0
$175$	0	0
$176$	9.47758e27	0.808703
$177$	− 2.55575e27i	− 0.203166i
$178$	− 8.46545e25i	− 0.00627191i
$179$	−2.41023e28	−1.66493	−0.832463	−	0.554081i	$-0.813070\pi$
$179$	−2.41023e28	−1.66493	−0.832463	+	0.554081i	$0.813070\pi$
$180$	0	0
$181$	−8.19193e27	−0.492498	−0.246249	−	0.969207i	$-0.579198\pi$
$181$	−8.19193e27	−0.492498	−0.246249	+	0.969207i	$0.579198\pi$
$182$	1.53167e26i	0.00859551i
$183$	1.76526e27i	0.0925061i
$184$	3.05991e26	0.0149791
$185$	0	0
$186$	4.03356e25	0.00172495
$187$	− 2.12163e28i	− 0.848497i
$188$	− 3.10143e28i	− 1.16035i
$189$	−1.26738e28	−0.443744
$190$	0	0
$191$	5.50602e27	0.169013	0.0845066	−	0.996423i	$-0.473069\pi$
$191$	5.50602e27	0.169013	0.0845066	+	0.996423i	$0.473069\pi$
$192$	7.39422e27i	0.212631i
$193$	− 2.08716e28i	− 0.562457i	−0.959641	−	0.281228i	$-0.909258\pi$
$193$	− 2.08716e28i	− 0.562457i	0.959641	−	0.281228i	$-0.0907419\pi$
$194$	1.35804e26	0.00343075
$195$	0	0
$196$	−6.24823e27	−0.138853
$197$	− 5.99370e28i	− 1.24988i	−0.780674	−	0.624938i	$-0.785124\pi$
$197$	− 5.99370e28i	− 1.24988i	0.780674	−	0.624938i	$-0.214876\pi$
$198$	− 3.26926e26i	− 0.00639933i
$199$	−2.24042e27	−0.0411782	−0.0205891	−	0.999788i	$-0.506554\pi$
$199$	−2.24042e27	−0.0411782	−0.0205891	+	0.999788i	$0.506554\pi$
$200$	0	0
$201$	5.22583e27	0.0847626
$202$	− 8.94444e25i	− 0.00136352i
$203$	1.06005e28i	0.151924i
$204$	1.65548e28	0.223125
$205$	0	0
$206$	−2.33190e26	−0.00278208
$207$	7.68464e28i	0.862967i
$208$	9.19120e28i	0.971808i
$209$	5.12080e28	0.509928
$210$	0	0
$211$	−7.52475e28	−0.665214	−0.332607	−	0.943066i	$-0.607928\pi$
$211$	−7.52475e28	−0.665214	−0.332607	+	0.943066i	$0.607928\pi$
$212$	3.32264e28i	0.276876i
$213$	− 3.76708e28i	− 0.295979i
$214$	1.71986e27	0.0127444
$215$	0	0
$216$	1.04460e27	0.00689094
$217$	1.67721e29i	1.04434i
$218$	− 2.29342e27i	− 0.0134827i
$219$	8.30299e27	0.0460981
$220$	0	0
$221$	2.05752e29	1.01963
$222$	1.90805e26i	0 0.000893673i
$223$	3.16696e29i	1.40227i	0.713029	+	0.701135i	$0.247323\pi$
$223$	3.16696e29i	1.40227i	−0.713029	+	0.701135i	$0.752677\pi$
$224$	6.33554e27	0.0265267
$225$	0	0
$226$	3.58308e27	0.0134246
$227$	3.85094e29i	1.36535i	0.730723	+	0.682674i	$0.239183\pi$
$227$	3.85094e29i	1.36535i	−0.730723	+	0.682674i	$0.760817\pi$
$228$	3.99569e28i	0.134093i
$229$	5.68261e29	1.80553	0.902765	−	0.430134i	$-0.141534\pi$
$229$	5.68261e29	1.80553	0.902765	+	0.430134i	$0.141534\pi$
$230$	0	0
$231$	−6.44273e28	−0.183620
$232$	− 8.73718e26i	− 0.00235924i
$233$	− 4.95586e29i	− 1.26815i	−0.773272	−	0.634075i	$-0.781381\pi$
$233$	− 4.95586e29i	− 1.26815i	0.773272	−	0.634075i	$-0.218619\pi$
$234$	3.17048e27	0.00769000
$235$	0	0
$236$	−4.37941e29	−0.955028
$237$	5.31962e28i	0.110034i
$238$	− 4.72700e27i	− 0.00927628i
$239$	1.44023e29	0.268200	0.134100	−	0.990968i	$-0.457186\pi$
$239$	1.44023e29	0.268200	0.134100	+	0.990968i	$0.457186\pi$
$240$	0	0
$241$	−3.19456e29	−0.536041	−0.268020	−	0.963413i	$-0.586369\pi$
$241$	−3.19456e29	−0.536041	−0.268020	+	0.963413i	$0.586369\pi$
$242$	1.79802e27i	0.00286486i
$243$	3.96547e29i	0.600090i
$244$	3.02488e29	0.434845
$245$	0	0
$246$	−1.72694e27	−0.00224175
$247$	4.96606e29i	0.612774i
$248$	− 1.38239e28i	− 0.0162176i
$249$	−1.82383e29	−0.203466
$250$	0	0
$251$	6.21677e29	0.627543	0.313771	−	0.949499i	$-0.398407\pi$
$251$	6.21677e29	0.627543	0.313771	+	0.949499i	$0.398407\pi$
$252$	1.06072e30i	1.01882i
$253$	7.99814e29i	0.731110i
$254$	1.61234e28	0.0140293
$255$	0	0
$256$	1.26678e30	0.999313
$257$	− 2.29446e30i	− 1.72392i	−0.506977	−	0.861960i	$-0.669237\pi$
$257$	− 2.29446e30i	− 1.72392i	0.506977	−	0.861960i	$-0.330763\pi$
$258$	− 2.82805e27i	− 0.00202414i
$259$	−7.93394e29	−0.541056
$260$	0	0
$261$	2.19425e29	0.135919
$262$	8.39859e27i	0.00495952i
$263$	− 7.73316e29i	− 0.435422i	−0.976013	−	0.217711i	$-0.930141\pi$
$263$	− 7.73316e29i	− 0.435422i	0.976013	−	0.217711i	$-0.0698590\pi$
$264$	5.31025e27	0.00285145
$265$	0	0
$266$	1.14091e28	0.00557484
$267$	3.45327e29i	0.161005i
$268$	− 8.95475e29i	− 0.398445i
$269$	−3.62259e30	−1.53856	−0.769282	−	0.638910i	$-0.779386\pi$
$269$	−3.62259e30	−1.53856	−0.769282	+	0.638910i	$0.779386\pi$
$270$	0	0
$271$	−3.62767e30	−1.40447	−0.702234	−	0.711946i	$-0.747814\pi$
$271$	−3.62767e30	−1.40447	−0.702234	+	0.711946i	$0.747814\pi$
$272$	− 2.83657e30i	− 1.04877i
$273$	− 6.24805e29i	− 0.220654i
$274$	2.96790e28	0.0100131
$275$	0	0
$276$	−6.24085e29	−0.192256
$277$	− 2.54808e30i	− 0.750266i	−0.926971	−	0.375133i	$-0.877597\pi$
$277$	− 2.54808e30i	− 0.750266i	0.926971	−	0.375133i	$-0.122403\pi$
$278$	− 2.32542e28i	− 0.00654547i
$279$	3.47174e30	0.934318
$280$	0	0
$281$	3.59817e30	0.885631	0.442816	−	0.896613i	$-0.353980\pi$
$281$	3.59817e30	0.885631	0.442816	+	0.896613i	$0.353980\pi$
$282$	− 8.68769e27i	− 0.00204546i
$283$	− 3.82265e30i	− 0.861061i	−0.902576	−	0.430530i	$-0.858327\pi$
$283$	− 3.82265e30i	− 0.861061i	0.902576	−	0.430530i	$-0.141673\pi$
$284$	−6.45511e30	−1.39131
$285$	0	0
$286$	3.29982e28	0.00651500
$287$	− 7.18084e30i	− 1.35722i
$288$	− 1.31143e29i	− 0.0237322i
$289$	−5.79269e29	−0.100382
$290$	0	0
$291$	−5.53977e29	−0.0880702
$292$	− 1.42276e30i	− 0.216694i
$293$	− 1.30007e29i	− 0.0189723i	−0.999955	−	0.00948615i	$-0.996980\pi$
$293$	− 1.30007e29i	− 0.0189723i	0.999955	−	0.00948615i	$-0.00301958\pi$
$294$	−1.75025e27	−0.000244770 0
$295$	0	0
$296$	6.53934e28	0.00840210
$297$	2.73043e30i	0.336338i
$298$	4.34673e28i	0.00513404i
$299$	−7.75646e30	−0.878565
$300$	0	0
$301$	1.17594e31	1.22548
$302$	− 5.57710e28i	− 0.00557599i
$303$	3.64866e29i	0.0350026i
$304$	6.84638e30	0.630291
$305$	0	0
$306$	−9.78466e28	−0.00829904
$307$	1.43602e31i	1.16931i	0.811281	+	0.584657i	$0.198771\pi$
$307$	1.43602e31i	1.16931i	−0.811281	+	0.584657i	$0.801229\pi$
$308$	1.10400e31i	0.863146i
$309$	9.51239e29	0.0714182
$310$	0	0
$311$	−2.24630e31	−1.55584	−0.777918	−	0.628366i	$-0.783724\pi$
$311$	−2.24630e31	−1.55584	−0.777918	+	0.628366i	$0.783724\pi$
$312$	5.14979e28i	0.00342655i
$313$	1.37956e30i	0.0881934i	0.999027	+	0.0440967i	$0.0140410\pi$
$313$	1.37956e30i	0.0881934i	−0.999027	+	0.0440967i	$0.985959\pi$
$314$	−1.63922e28	−0.00100697
$315$	0	0
$316$	9.11548e30	0.517239
$317$	− 1.02787e31i	− 0.560655i	−0.959904	−	0.280327i	$-0.909557\pi$
$317$	− 1.02787e31i	− 0.560655i	0.959904	−	0.280327i	$-0.0904430\pi$
$318$	9.30735e27i	0 0.000488076i
$319$	2.28377e30	0.115151
$320$	0	0
$321$	−7.01574e30	−0.327160
$322$	1.78199e29i	0.00799293i
$323$	− 1.53262e31i	− 0.661306i
$324$	2.08666e31	0.866240
$325$	0	0
$326$	−2.22337e29	−0.00854656
$327$	9.35542e30i	0.346112i
$328$	5.91861e29i	0.0210764i
$329$	3.61246e31	1.23838
$330$	0	0
$331$	−5.75356e30	−0.182847	−0.0914233	−	0.995812i	$-0.529142\pi$
$331$	−5.75356e30	−0.182847	−0.0914233	+	0.995812i	$0.529142\pi$
$332$	3.12523e31i	0.956435i
$333$	1.64229e31i	0.484057i
$334$	−3.96706e29	−0.0112626
$335$	0	0
$336$	−8.61377e30	−0.226961
$337$	6.69268e31i	1.69913i	0.527485	+	0.849564i	$0.323135\pi$
$337$	6.69268e31i	1.69913i	−0.527485	+	0.849564i	$0.676865\pi$
$338$	− 1.86968e28i	0 0.000457413i
$339$	−1.46163e31	−0.344621
$340$	0	0
$341$	3.61337e31	0.791559
$342$	− 2.36164e29i	− 0.00498754i
$343$	4.51320e31i	0.918984i
$344$	−9.69239e29	−0.0190305
$345$	0	0
$346$	2.89249e29	0.00528227
$347$	9.41781e29i	0.0165894i	0.999966	+	0.00829472i	$0.00264032\pi$
$347$	9.41781e29i	0.0165894i	−0.999966	+	0.00829472i	$0.997360\pi$
$348$	1.78200e30i	0.0302807i
$349$	3.39081e31	0.555886	0.277943	−	0.960598i	$-0.410347\pi$
$349$	3.39081e31	0.555886	0.277943	+	0.960598i	$0.410347\pi$
$350$	0	0
$351$	−2.64793e31	−0.404173
$352$	− 1.36493e30i	− 0.0201060i
$353$	− 1.30313e31i	− 0.185269i	−0.995700	−	0.0926346i	$-0.970471\pi$
$353$	− 1.30313e31i	− 0.185269i	0.995700	−	0.0926346i	$-0.0295289\pi$
$354$	−1.22676e29	−0.00168352
$355$	0	0
$356$	5.91737e31	0.756840
$357$	1.92826e31i	0.238130i
$358$	1.15691e30i	0.0137963i
$359$	1.30336e32	1.50101	0.750506	−	0.660864i	$-0.229810\pi$
$359$	1.30336e32	1.50101	0.750506	+	0.660864i	$0.229810\pi$
$360$	0	0
$361$	−5.60851e31	−0.602570
$362$	3.93213e29i	0.00408104i
$363$	− 7.33459e30i	− 0.0735433i
$364$	−1.07064e32	−1.03723
$365$	0	0
$366$	8.47325e28	0.000766543 0
$367$	− 2.06294e32i	− 1.80369i	−0.432061	−	0.901844i	$-0.642214\pi$
$367$	− 2.06294e32i	− 1.80369i	0.432061	−	0.901844i	$-0.357786\pi$
$368$	1.06933e32i	0.903680i
$369$	−1.48640e32	−1.21424
$370$	0	0
$371$	−3.87012e31	−0.295495
$372$	2.81947e31i	0.208152i
$373$	− 2.46051e32i	− 1.75657i	−0.478142	−	0.878283i	$-0.658689\pi$
$373$	− 2.46051e32i	− 1.75657i	0.478142	−	0.878283i	$-0.341311\pi$
$374$	−1.01838e30	−0.00703099
$375$	0	0
$376$	−2.97747e30	−0.0192309
$377$	2.21476e31i	0.138376i
$378$	6.08341e29i	0.00367705i
$379$	−7.12743e31	−0.416815	−0.208407	−	0.978042i	$-0.566828\pi$
$379$	−7.12743e31	−0.416815	−0.208407	+	0.978042i	$0.566828\pi$
$380$	0	0
$381$	−6.57715e31	−0.360143
$382$	− 2.64289e29i	− 0.00140051i
$383$	− 1.33051e32i	− 0.682393i	−0.939992	−	0.341196i	$-0.889168\pi$
$383$	− 1.33051e32i	− 0.682393i	0.939992	−	0.341196i	$-0.110832\pi$
$384$	1.42003e30	0.00704949
$385$	0	0
$386$	−1.00184e30	−0.00466075
$387$	− 2.43414e32i	− 1.09637i
$388$	9.49271e31i	0.413993i
$389$	−2.40509e32	−1.01569	−0.507844	−	0.861449i	$-0.669557\pi$
$389$	−2.40509e32	−1.01569	−0.507844	+	0.861449i	$0.669557\pi$
$390$	0	0
$391$	2.39379e32	0.948147
$392$	5.99850e29i	0.00230127i
$393$	− 3.42599e31i	− 0.127315i
$394$	−2.87698e30	−0.0103570
$395$	0	0
$396$	2.28522e32	0.772216
$397$	− 4.12137e32i	− 1.34946i	−0.738065	−	0.674730i	$-0.764260\pi$
$397$	− 4.12137e32i	− 1.34946i	0.738065	−	0.674730i	$-0.235740\pi$
$398$	1.07540e29i	0 0.000341219i
$399$	−4.65407e31	−0.143111
$400$	0	0
$401$	−7.16647e31	−0.207014	−0.103507	−	0.994629i	$-0.533006\pi$
$401$	−7.16647e31	−0.207014	−0.103507	+	0.994629i	$0.533006\pi$
$402$	− 2.50840e29i	0 0.000702377i
$403$	3.50419e32i	0.951206i
$404$	6.25219e31	0.164537
$405$	0	0
$406$	5.08824e29	0.00125890
$407$	1.70929e32i	0.410095i
$408$	− 1.58932e30i	− 0.00369793i
$409$	−1.34430e32	−0.303358	−0.151679	−	0.988430i	$-0.548468\pi$
$409$	−1.34430e32	−0.303358	−0.151679	+	0.988430i	$0.548468\pi$
$410$	0	0
$411$	−1.21068e32	−0.257044
$412$	− 1.63000e32i	− 0.335717i
$413$	− 5.10102e32i	− 1.01925i
$414$	3.68863e30	0.00715089
$415$	0	0
$416$	1.32368e31	0.0241612
$417$	9.48596e31i	0.168028i
$418$	− 2.45798e30i	− 0.00422547i
$419$	1.71876e32	0.286774	0.143387	−	0.989667i	$-0.454201\pi$
$419$	1.71876e32	0.286774	0.143387	+	0.989667i	$0.454201\pi$
$420$	0	0
$421$	−8.27664e32	−1.30115	−0.650576	−	0.759441i	$-0.725472\pi$
$421$	−8.27664e32	−1.30115	−0.650576	+	0.759441i	$0.725472\pi$
$422$	3.61188e30i	0.00551223i
$423$	− 7.47761e32i	− 1.10792i
$424$	3.18984e30	0.00458877
$425$	0	0
$426$	−1.80820e30	−0.00245260
$427$	3.52329e32i	0.464088i
$428$	1.20219e33i	1.53789i
$429$	−1.34608e32	−0.167245
$430$	0	0
$431$	−7.83836e31	−0.0918881	−0.0459441	−	0.998944i	$-0.514630\pi$
$431$	−7.83836e31	−0.0918881	−0.0459441	+	0.998944i	$0.514630\pi$
$432$	3.65052e32i	0.415727i
$433$	− 6.33273e32i	− 0.700635i	−0.936631	−	0.350318i	$-0.886074\pi$
$433$	− 6.33273e32i	− 0.700635i	0.936631	−	0.350318i	$-0.113926\pi$
$434$	8.05060e30	0.00865380
$435$	0	0
$436$	1.60310e33	1.62697
$437$	5.77767e32i	0.569816i
$438$	− 3.98543e29i	0 0.000381988i
$439$	1.48299e33	1.38144	0.690718	−	0.723124i	$-0.257295\pi$
$439$	1.48299e33	1.38144	0.690718	+	0.723124i	$0.257295\pi$
$440$	0	0
$441$	−1.50646e32	−0.132579
$442$	− 9.87612e30i	− 0.00844905i
$443$	1.20901e33i	1.00551i	0.864430	+	0.502753i	$0.167679\pi$
$443$	1.20901e33i	1.00551i	−0.864430	+	0.502753i	$0.832321\pi$
$444$	−1.33373e32	−0.107841
$445$	0	0
$446$	1.52014e31	0.0116198
$447$	− 1.77314e32i	− 0.131795i
$448$	1.47581e33i	1.06674i
$449$	9.48861e32	0.666996	0.333498	−	0.942751i	$-0.391771\pi$
$449$	9.48861e32	0.666996	0.333498	+	0.942751i	$0.391771\pi$
$450$	0	0
$451$	−1.54704e33	−1.02871
$452$	2.50459e33i	1.61996i
$453$	2.27504e32i	0.143140i
$454$	1.84845e31	0.0113138
$455$	0	0
$456$	3.83600e30	0.00222238
$457$	1.90644e33i	1.07466i	0.843373	+	0.537329i	$0.180567\pi$
$457$	1.90644e33i	1.07466i	−0.843373	+	0.537329i	$0.819433\pi$
$458$	− 2.72765e31i	− 0.0149614i
$459$	8.17199e32	0.436183
$460$	0	0
$461$	−4.56270e31	−0.0230653	−0.0115327	−	0.999933i	$-0.503671\pi$
$461$	−4.56270e31	−0.0230653	−0.0115327	+	0.999933i	$0.503671\pi$
$462$	3.09251e30i	0.00152155i
$463$	− 2.13521e33i	− 1.02254i	−0.859421	−	0.511269i	$-0.829176\pi$
$463$	− 2.13521e33i	− 1.02254i	0.859421	−	0.511269i	$-0.170824\pi$
$464$	3.05334e32	0.142331
$465$	0	0
$466$	−2.37882e31	−0.0105084
$467$	− 2.67225e33i	− 1.14926i	−0.818415	−	0.574628i	$-0.805147\pi$
$467$	− 2.67225e33i	− 1.14926i	0.818415	−	0.574628i	$-0.194853\pi$
$468$	2.21617e33i	0.927962i
$469$	1.04302e33	0.425240
$470$	0	0
$471$	6.68680e31	0.0258498
$472$	4.20438e31i	0.0158280i
$473$	− 2.53345e33i	− 0.928854i
$474$	2.55342e30	0.000911786 0
$475$	0	0
$476$	3.30419e33	1.11938
$477$	8.01096e32i	0.264366i
$478$	− 6.91313e30i	− 0.00222242i
$479$	−1.97240e33	−0.617733	−0.308867	−	0.951105i	$-0.599950\pi$
$479$	−1.97240e33	−0.617733	−0.308867	+	0.951105i	$0.599950\pi$
$480$	0	0
$481$	−1.65764e33	−0.492806
$482$	1.53339e31i	0.00444185i
$483$	− 7.26917e32i	− 0.205185i
$484$	−1.25682e33	−0.345706
$485$	0	0
$486$	1.90343e31	0.00497259
$487$	− 3.96366e32i	− 0.100922i	−0.998726	−	0.0504608i	$-0.983931\pi$
$487$	− 3.96366e32i	− 0.100922i	0.998726	−	0.0504608i	$-0.0160690\pi$
$488$	− 2.90398e31i	− 0.00720686i
$489$	9.06968e32	0.219397
$490$	0	0
$491$	−7.22626e33	−1.66110	−0.830548	−	0.556947i	$-0.811973\pi$
$491$	−7.22626e33	−1.66110	−0.830548	+	0.556947i	$0.811973\pi$
$492$	− 1.20713e33i	− 0.270515i
$493$	− 6.83515e32i	− 0.149335i
$494$	2.38371e31	0.00507769
$495$	0	0
$496$	4.83099e33	0.978397
$497$	− 7.51874e33i	− 1.48488i
$498$	8.75436e30i	0.00168600i
$499$	−8.19830e33	−1.53981	−0.769905	−	0.638159i	$-0.779696\pi$
$499$	−8.19830e33	−1.53981	−0.769905	+	0.638159i	$0.779696\pi$
$500$	0	0
$501$	1.61826e33	0.289119
$502$	− 2.98405e31i	− 0.00520008i
$503$	− 4.72562e33i	− 0.803265i	−0.915801	−	0.401633i	$-0.868443\pi$
$503$	− 4.72562e33i	− 0.803265i	0.915801	−	0.401633i	$-0.131557\pi$
$504$	1.01833e32	0.0168852
$505$	0	0
$506$	3.83911e31	0.00605827
$507$	7.62689e31i	0.0117422i
$508$	1.12703e34i	1.69293i
$509$	−1.96955e33	−0.288665	−0.144332	−	0.989529i	$-0.546103\pi$
$509$	−1.96955e33	−0.288665	−0.144332	+	0.989529i	$0.546103\pi$
$510$	0	0
$511$	1.65720e33	0.231267
$512$	− 3.04153e32i	− 0.0414207i
$513$	1.97240e33i	0.262137i
$514$	−1.10134e32	−0.0142851
$515$	0	0
$516$	1.97682e33	0.244256
$517$	− 7.78267e33i	− 0.938635i
$518$	3.80829e31i	0.00448341i
$519$	−1.17992e33	−0.135600
$520$	0	0
$521$	7.39782e33	0.810274	0.405137	−	0.914256i	$-0.367224\pi$
$521$	7.39782e33	0.810274	0.405137	+	0.914256i	$0.367224\pi$
$522$	− 1.05324e31i	− 0.00112628i
$523$	− 1.70332e34i	− 1.77838i	−0.457535	−	0.889191i	$-0.651268\pi$
$523$	− 1.70332e34i	− 1.77838i	0.457535	−	0.889191i	$-0.348732\pi$
$524$	−5.87063e33	−0.598472
$525$	0	0
$526$	−3.71192e31	−0.00360808
$527$	− 1.08146e34i	− 1.02654i
$528$	1.85575e33i	0.172026i
$529$	2.02166e33	0.183026
$530$	0	0
$531$	−1.05589e34	−0.911876
$532$	7.97502e33i	0.672723i
$533$	− 1.50029e34i	− 1.23619i
$534$	1.65757e31	0.00133415
$535$	0	0
$536$	−8.59686e31	−0.00660358
$537$	− 4.71932e33i	− 0.354161i
$538$	1.73884e32i	0.0127492i
$539$	−1.56792e33	−0.112322
$540$	0	0
$541$	−1.28681e34	−0.880134	−0.440067	−	0.897965i	$-0.645045\pi$
$541$	−1.28681e34	−0.880134	−0.440067	+	0.897965i	$0.645045\pi$
$542$	1.74128e32i	0.0116380i
$543$	− 1.60401e33i	− 0.104764i
$544$	−4.08513e32	−0.0260747
$545$	0	0
$546$	−2.99906e31	−0.00182843
$547$	2.06624e34i	1.23123i	0.788046	+	0.615616i	$0.211093\pi$
$547$	2.06624e34i	1.23123i	−0.788046	+	0.615616i	$0.788907\pi$
$548$	2.07457e34i	1.20829i
$549$	7.29304e33	0.415197
$550$	0	0
$551$	1.64974e33	0.0897471
$552$	5.99142e31i	0.00318633i
$553$	1.06175e34i	0.552022i
$554$	−1.22308e32	−0.00621701
$555$	0	0
$556$	1.62547e34	0.789851
$557$	− 3.28751e33i	− 0.156198i	−0.996946	−	0.0780992i	$-0.975115\pi$
$557$	− 3.28751e33i	− 0.156198i	0.996946	−	0.0780992i	$-0.0248851\pi$
$558$	− 1.66644e32i	− 0.00774214i
$559$	2.45689e34	1.11619
$560$	0	0
$561$	4.15424e33	0.180491
$562$	− 1.72712e32i	− 0.00733870i
$563$	1.80804e34i	0.751371i	0.926747	+	0.375685i	$0.122593\pi$
$563$	1.80804e34i	0.751371i	−0.926747	+	0.375685i	$0.877407\pi$
$564$	6.07272e33	0.246828
$565$	0	0
$566$	−1.83487e32	−0.00713510
$567$	2.43048e34i	0.924493i
$568$	6.19712e32i	0.0230587i
$569$	3.05967e33	0.111371	0.0556854	−	0.998448i	$-0.482266\pi$
$569$	3.05967e33	0.111371	0.0556854	+	0.998448i	$0.482266\pi$
$570$	0	0
$571$	−1.29884e34	−0.452486	−0.226243	−	0.974071i	$-0.572644\pi$
$571$	−1.29884e34	−0.452486	−0.226243	+	0.974071i	$0.572644\pi$
$572$	2.30658e34i	0.786174i
$573$	1.07810e33i	0.0359523i
$574$	−3.44680e32	−0.0112465
$575$	0	0
$576$	3.05487e34	0.954357
$577$	− 7.31490e31i	− 0.00223620i	−0.999999	−	0.00111810i	$-0.999644\pi$
$577$	− 7.31490e31i	− 0.00223620i	0.999999	−	0.00111810i	$-0.000355902\pi$
$578$	2.78049e31i	0 0.000831808i
$579$	4.08674e33	0.119645
$580$	0	0
$581$	−3.64018e34	−1.02075
$582$	2.65909e31i	0 0.000729786i
$583$	8.33778e33i	0.223972i
$584$	−1.36590e32	−0.00359136
$585$	0	0
$586$	−6.24031e30	−0.000157212 0
$587$	5.16226e34i	1.27310i	0.771234	+	0.636551i	$0.219640\pi$
$587$	5.16226e34i	1.27310i	−0.771234	+	0.636551i	$0.780360\pi$
$588$	− 1.22343e33i	− 0.0295367i
$589$	2.61022e34	0.616929
$590$	0	0
$591$	1.17359e34	0.265872
$592$	2.28527e34i	0.506894i
$593$	− 2.40705e34i	− 0.522758i	−0.965236	−	0.261379i	$-0.915823\pi$
$593$	− 2.40705e34i	− 0.522758i	0.965236	−	0.261379i	$-0.0841772\pi$
$594$	1.31061e32	0.00278703
$595$	0	0
$596$	−3.03838e34	−0.619531
$597$	− 4.38684e32i	− 0.00875937i
$598$	3.72310e32i	0.00728015i
$599$	8.30672e33	0.159072	0.0795361	−	0.996832i	$-0.474656\pi$
$599$	8.30672e33	0.159072	0.0795361	+	0.996832i	$0.474656\pi$
$600$	0	0
$601$	−3.00405e34	−0.551792	−0.275896	−	0.961187i	$-0.588975\pi$
$601$	−3.00405e34	−0.551792	−0.275896	+	0.961187i	$0.588975\pi$
$602$	− 5.64452e32i	− 0.0101548i
$603$	− 2.15901e34i	− 0.380442i
$604$	3.89841e34	0.672861
$605$	0	0
$606$	1.75136e31	0.000290046 0
$607$	− 1.00963e35i	− 1.63796i	−0.573825	−	0.818978i	$-0.694541\pi$
$607$	− 1.00963e35i	− 1.63796i	0.573825	−	0.818978i	$-0.305459\pi$
$608$	− 9.85991e32i	− 0.0156703i
$609$	−2.07562e33	−0.0323170
$610$	0	0
$611$	7.54750e34	1.12795
$612$	− 6.83951e34i	− 1.00146i
$613$	1.02453e33i	0.0146983i	0.999973	+	0.00734915i	$0.00233933\pi$
$613$	1.02453e33i	0.0146983i	−0.999973	+	0.00734915i	$0.997661\pi$
$614$	6.89290e32	0.00968941
$615$	0	0
$616$	1.05987e33	0.0143053
$617$	4.53271e34i	0.599505i	0.954017	+	0.299753i	$0.0969042\pi$
$617$	4.53271e34i	0.599505i	−0.954017	+	0.299753i	$0.903096\pi$
$618$	− 4.56595e31i	0 0.000591800i
$619$	−1.24784e35	−1.58499	−0.792496	−	0.609878i	$-0.791219\pi$
$619$	−1.24784e35	−1.58499	−0.792496	+	0.609878i	$0.791219\pi$
$620$	0	0
$621$	−3.08068e34	−0.375839
$622$	1.07823e33i	0.0128923i
$623$	6.89239e34i	0.807736i
$624$	−1.79967e34	−0.206722
$625$	0	0
$626$	6.62189e31	0.000730807 0
$627$	1.00267e34i	0.108471i
$628$	− 1.14582e34i	− 0.121513i
$629$	5.11577e34	0.531836
$630$	0	0
$631$	4.83338e34	0.482930	0.241465	−	0.970410i	$-0.422372\pi$
$631$	4.83338e34	0.482930	0.241465	+	0.970410i	$0.422372\pi$
$632$	− 8.75116e32i	− 0.00857239i
$633$	− 1.47338e34i	− 0.141503i
$634$	−4.93375e32	−0.00464581
$635$	0	0
$636$	−6.50586e33	−0.0588967
$637$	− 1.52054e34i	− 0.134976i
$638$	− 1.09621e32i	0 0.000954190i
$639$	−1.55634e35	−1.32845
$640$	0	0
$641$	8.30494e34	0.681728	0.340864	−	0.940113i	$-0.389280\pi$
$641$	8.30494e34	0.681728	0.340864	+	0.940113i	$0.389280\pi$
$642$	3.36756e32i	0.00271098i
$643$	− 5.25724e34i	− 0.415069i	−0.978228	−	0.207535i	$-0.933456\pi$
$643$	− 5.25724e34i	− 0.415069i	0.978228	−	0.207535i	$-0.0665440\pi$
$644$	−1.24561e35	−0.964517
$645$	0	0
$646$	−7.35656e32	−0.00547985
$647$	− 2.03021e35i	− 1.48333i	−0.670770	−	0.741665i	$-0.734036\pi$
$647$	− 2.03021e35i	− 1.48333i	0.670770	−	0.741665i	$-0.265964\pi$
$648$	− 2.00326e33i	− 0.0143565i
$649$	−1.09896e35	−0.772546
$650$	0	0
$651$	−3.28404e34	−0.222150
$652$	− 1.55414e35i	− 1.03132i
$653$	− 1.67657e35i	− 1.09146i	−0.837962	−	0.545728i	$-0.816253\pi$
$653$	− 1.67657e35i	− 1.09146i	0.837962	−	0.545728i	$-0.183747\pi$
$654$	4.49060e32	0.00286802
$655$	0	0
$656$	−2.06835e35	−1.27153
$657$	− 3.43032e34i	− 0.206903i
$658$	− 1.73398e33i	− 0.0102617i
$659$	2.92521e35	1.69859	0.849296	−	0.527917i	$-0.177027\pi$
$659$	2.92521e35	1.69859	0.849296	+	0.527917i	$0.177027\pi$
$660$	0	0
$661$	8.30227e34	0.464172	0.232086	−	0.972695i	$-0.425445\pi$
$661$	8.30227e34	0.464172	0.232086	+	0.972695i	$0.425445\pi$
$662$	2.76171e32i	0.00151514i
$663$	4.02872e34i	0.216894i
$664$	3.00032e33	0.0158514
$665$	0	0
$666$	7.88298e32	0.00401109
$667$	2.57672e34i	0.128675i
$668$	− 2.77298e35i	− 1.35907i
$669$	−6.20103e34	−0.298289
$670$	0	0
$671$	7.59057e34	0.351757
$672$	1.24052e33i	0.00564273i
$673$	3.23598e35i	1.44483i	0.691458	+	0.722417i	$0.256969\pi$
$673$	3.23598e35i	1.44483i	−0.691458	+	0.722417i	$0.743031\pi$
$674$	3.21249e33	0.0140797
$675$	0	0
$676$	1.30691e34	0.0551966
$677$	7.76333e34i	0.321877i	0.986964	+	0.160938i	$0.0514521\pi$
$677$	7.76333e34i	0.321877i	−0.986964	+	0.160938i	$0.948548\pi$
$678$	7.01582e32i	0.00285567i
$679$	−1.10568e35	−0.441834
$680$	0	0
$681$	−7.54029e34	−0.290435
$682$	− 1.73442e33i	− 0.00655918i
$683$	2.49909e35i	0.927945i	0.885850	+	0.463973i	$0.153576\pi$
$683$	2.49909e35i	0.927945i	−0.885850	+	0.463973i	$0.846424\pi$
$684$	1.65079e35	0.601853
$685$	0	0
$686$	2.16634e33	0.00761508
$687$	1.11268e35i	0.384070i
$688$	− 3.38716e35i	− 1.14810i
$689$	−8.08584e34	−0.269144
$690$	0	0
$691$	−8.56964e34	−0.275098	−0.137549	−	0.990495i	$-0.543922\pi$
$691$	−8.56964e34	−0.275098	−0.137549	+	0.990495i	$0.543922\pi$
$692$	2.02186e35i	0.637419i
$693$	2.66176e35i	0.824146i
$694$	4.52055e31	0.000137467 0
$695$	0	0
$696$	1.71077e32	0.000501854 0
$697$	4.63017e35i	1.33410i
$698$	− 1.62759e33i	− 0.00460630i
$699$	9.70378e34	0.269759
$700$	0	0
$701$	4.53464e35	1.21637	0.608187	−	0.793793i	$-0.291897\pi$
$701$	4.53464e35	1.21637	0.608187	+	0.793793i	$0.291897\pi$
$702$	1.27101e33i	0.00334914i
$703$	1.23475e35i	0.319622i
$704$	3.17949e35	0.808536
$705$	0	0
$706$	−6.25502e32	−0.00153522
$707$	7.28238e34i	0.175602i
$708$	− 8.57507e34i	− 0.203152i
$709$	4.93254e35	1.14813	0.574067	−	0.818808i	$-0.305365\pi$
$709$	4.93254e35	1.14813	0.574067	+	0.818808i	$0.305365\pi$
$710$	0	0
$711$	2.19776e35	0.493868
$712$	− 5.68087e33i	− 0.0125434i
$713$	4.07688e35i	0.884522i
$714$	9.25566e32	0.00197324
$715$	0	0
$716$	−8.08682e35	−1.66481
$717$	2.82004e34i	0.0570513i
$718$	− 6.25613e33i	− 0.0124380i
$719$	−2.13499e35	−0.417142	−0.208571	−	0.978007i	$-0.566881\pi$
$719$	−2.13499e35	−0.417142	−0.208571	+	0.978007i	$0.566881\pi$
$720$	0	0
$721$	1.89858e35	0.358293
$722$	2.69208e33i	0.00499314i
$723$	− 6.25508e34i	− 0.114026i
$724$	−2.74857e35	−0.492464
$725$	0	0
$726$	−3.52060e32	−0.000609409 0
$727$	5.12190e35i	0.871467i	0.900076	+	0.435734i	$0.143511\pi$
$727$	5.12190e35i	0.871467i	−0.900076	+	0.435734i	$0.856489\pi$
$728$	1.02785e34i	0.0171904i
$729$	4.49296e35	0.738649
$730$	0	0
$731$	−7.58243e35	−1.20459
$732$	5.92283e34i	0.0924998i
$733$	− 1.77366e35i	− 0.272315i	−0.990687	−	0.136157i	$-0.956525\pi$
$733$	− 1.77366e35i	− 0.272315i	0.990687	−	0.136157i	$-0.0434753\pi$
$734$	−9.90213e33	−0.0149461
$735$	0	0
$736$	1.54001e34	0.0224674
$737$	− 2.24709e35i	− 0.322312i
$738$	7.13471e33i	0.0100617i
$739$	1.13535e36	1.57425	0.787124	−	0.616794i	$-0.211569\pi$
$739$	1.13535e36	1.57425	0.787124	+	0.616794i	$0.211569\pi$
$740$	0	0
$741$	−9.72375e34	−0.130349
$742$	1.85766e33i	0.00244860i
$743$	− 4.03749e34i	− 0.0523301i	−0.999658	−	0.0261651i	$-0.991670\pi$
$743$	− 4.03749e34i	− 0.0523301i	0.999658	−	0.0261651i	$-0.00832954\pi$
$744$	2.70678e33	0.00344978
$745$	0	0
$746$	−1.18104e34	−0.0145556
$747$	7.53500e35i	0.913220i
$748$	− 7.11853e35i	− 0.848439i
$749$	−1.40027e36	−1.64131
$750$	0	0
$751$	7.72405e35	0.875681	0.437840	−	0.899053i	$-0.355744\pi$
$751$	7.72405e35	0.875681	0.437840	+	0.899053i	$0.355744\pi$
$752$	− 1.04052e36i	− 1.16019i
$753$	1.21727e35i	0.133490i
$754$	1.06308e33	0.00114664
$755$	0	0
$756$	−4.25232e35	−0.443714
$757$	3.31585e35i	0.340327i	0.985416	+	0.170163i	$0.0544296\pi$
$757$	3.31585e35i	0.340327i	−0.985416	+	0.170163i	$0.945570\pi$
$758$	3.42117e33i	0.00345390i
$759$	−1.56607e35	−0.155521
$760$	0	0
$761$	2.02230e36	1.94329	0.971646	−	0.236440i	$-0.0759807\pi$
$761$	2.02230e36	1.94329	0.971646	+	0.236440i	$0.0759807\pi$
$762$	3.15703e33i	0.00298429i
$763$	1.86725e36i	1.73639i
$764$	1.84739e35	0.169002
$765$	0	0
$766$	−6.38646e33	−0.00565458
$767$	− 1.06576e36i	− 0.928358i
$768$	2.48041e35i	0.212573i
$769$	−7.71193e35	−0.650255	−0.325128	−	0.945670i	$-0.605407\pi$
$769$	−7.71193e35	−0.650255	−0.325128	+	0.945670i	$0.605407\pi$
$770$	0	0
$771$	4.49265e35	0.366710
$772$	− 7.00286e35i	− 0.562418i
$773$	− 1.96060e36i	− 1.54934i	−0.632368	−	0.774668i	$-0.717917\pi$
$773$	− 1.96060e36i	− 1.54934i	0.632368	−	0.774668i	$-0.282083\pi$
$774$	−1.16839e34	−0.00908501
$775$	0	0
$776$	9.11331e33	0.00686127
$777$	− 1.55350e35i	− 0.115093i
$778$	1.15444e34i	0.00841641i
$779$	−1.11754e36	−0.801763
$780$	0	0
$781$	−1.61983e36	−1.12547
$782$	− 1.14902e34i	− 0.00785674i
$783$	8.79649e34i	0.0591953i
$784$	−2.09627e35	−0.138834
$785$	0	0
$786$	−1.64448e33	−0.00105498
$787$	− 8.92654e35i	− 0.563637i	−0.959468	−	0.281818i	$-0.909062\pi$
$787$	− 8.92654e35i	− 0.563637i	0.959468	−	0.281818i	$-0.0909375\pi$
$788$	− 2.01101e36i	− 1.24979i
$789$	1.51418e35	0.0926224
$790$	0	0
$791$	−2.91727e36	−1.72890
$792$	− 2.19389e34i	− 0.0127982i
$793$	7.36121e35i	0.422702i
$794$	−1.97826e34	−0.0111822
$795$	0	0
$796$	−7.51710e34	−0.0411753
$797$	− 2.35494e36i	− 1.26984i	−0.772577	−	0.634921i	$-0.781032\pi$
$797$	− 2.35494e36i	− 1.26984i	0.772577	−	0.634921i	$-0.218968\pi$
$798$	2.23396e33i	0.00118587i
$799$	−2.32930e36	−1.21728
$800$	0	0
$801$	1.42669e36	0.722643
$802$	3.43990e33i	0.00171541i
$803$	− 3.57026e35i	− 0.175289i
$804$	1.75338e35	0.0847568
$805$	0	0
$806$	1.68201e34	0.00788208
$807$	− 7.09317e35i	− 0.327281i
$808$	− 6.00231e33i	− 0.00272694i
$809$	1.29617e36	0.579834	0.289917	−	0.957052i	$-0.406372\pi$
$809$	1.29617e36	0.579834	0.289917	+	0.957052i	$0.406372\pi$
$810$	0	0
$811$	2.63606e36	1.14339	0.571695	−	0.820467i	$-0.306286\pi$
$811$	2.63606e36	1.14339	0.571695	+	0.820467i	$0.306286\pi$
$812$	3.55669e35i	0.151913i
$813$	− 7.10313e35i	− 0.298757i
$814$	8.20458e33	0.00339822
$815$	0	0
$816$	5.55412e35	0.223094
$817$	− 1.83010e36i	− 0.723935i
$818$	6.45265e33i	0.00251375i
$819$	−2.58133e36	−0.990366
$820$	0	0
$821$	−5.92271e35	−0.220410	−0.110205	−	0.993909i	$-0.535151\pi$
$821$	−5.92271e35	−0.220410	−0.110205	+	0.993909i	$0.535151\pi$
$822$	5.81127e33i	0.00212997i
$823$	− 4.76928e35i	− 0.172169i	−0.996288	−	0.0860845i	$-0.972564\pi$
$823$	− 4.76928e35i	− 0.172169i	0.996288	−	0.0860845i	$-0.0274355\pi$
$824$	−1.56486e34	−0.00556396
$825$	0	0
$826$	−2.44849e34	−0.00844594
$827$	4.17794e36i	1.41953i	0.704440	+	0.709763i	$0.251198\pi$
$827$	4.17794e36i	1.41953i	−0.704440	+	0.709763i	$0.748802\pi$
$828$	2.57836e36i	0.862908i
$829$	3.18023e36	1.04840	0.524199	−	0.851596i	$-0.324365\pi$
$829$	3.18023e36	1.04840	0.524199	+	0.851596i	$0.324365\pi$
$830$	0	0
$831$	4.98924e35	0.159596
$832$	3.08342e36i	0.971608i
$833$	4.69267e35i	0.145666i
$834$	4.55326e33	0.00139235
$835$	0	0
$836$	1.71814e36	0.509893
$837$	1.39178e36i	0.406913i
$838$	− 8.25006e33i	− 0.00237633i
$839$	3.57270e36	1.01384	0.506922	−	0.861992i	$-0.330783\pi$
$839$	3.57270e36	1.01384	0.506922	+	0.861992i	$0.330783\pi$
$840$	0	0
$841$	−3.55679e36	−0.979733
$842$	3.97279e34i	0.0107819i
$843$	7.04537e35i	0.188390i
$844$	−2.52471e36	−0.665168
$845$	0	0
$846$	−3.58925e34	−0.00918068
$847$	− 1.46391e36i	− 0.368954i
$848$	1.11474e36i	0.276838i
$849$	7.48489e35	0.183164
$850$	0	0
$851$	−1.92855e36	−0.458258
$852$	− 1.26394e36i	− 0.295958i
$853$	1.75466e36i	0.404884i	0.979294	+	0.202442i	$0.0648878\pi$
$853$	1.75466e36i	0.404884i	−0.979294	+	0.202442i	$0.935112\pi$
$854$	1.69118e34	0.00384562
$855$	0	0
$856$	1.15414e35	0.0254880
$857$	7.10324e36i	1.54595i	0.634435	+	0.772976i	$0.281233\pi$
$857$	7.10324e36i	1.54595i	−0.634435	+	0.772976i	$0.718767\pi$
$858$	6.46118e33i	0.00138586i
$859$	7.56695e36	1.59958	0.799791	−	0.600279i	$-0.204944\pi$
$859$	7.56695e36	1.59958	0.799791	+	0.600279i	$0.204944\pi$
$860$	0	0
$861$	1.40604e36	0.288707
$862$	3.76241e33i	0 0.000761423i
$863$	− 5.72195e36i	− 1.14132i	−0.821185	−	0.570662i	$-0.806687\pi$
$863$	− 5.72195e36i	− 1.14132i	0.821185	−	0.570662i	$-0.193313\pi$
$864$	5.25735e34	0.0103358
$865$	0	0
$866$	−3.03971e34	−0.00580575
$867$	− 1.13423e35i	− 0.0213532i
$868$	5.62739e36i	1.04426i
$869$	2.28742e36	0.418407
$870$	0	0
$871$	2.17919e36	0.387318
$872$	− 1.53903e35i	− 0.0269645i
$873$	2.28871e36i	0.395288i
$874$	2.77328e34	0.00472173
$875$	0	0
$876$	2.78583e35	0.0460949
$877$	3.21926e36i	0.525123i	0.964915	+	0.262561i	$0.0845672\pi$
$877$	3.21926e36i	0.525123i	−0.964915	+	0.262561i	$0.915433\pi$
$878$	− 7.11834e34i	− 0.0114471i
$879$	2.54558e34	0.00403576
$880$	0	0
$881$	−1.04633e37	−1.61238	−0.806191	−	0.591655i	$-0.798475\pi$
$881$	−1.04633e37	−1.61238	−0.806191	+	0.591655i	$0.798475\pi$
$882$	7.23102e33i	0.00109861i
$883$	− 4.11745e36i	− 0.616765i	−0.951263	−	0.308382i	$-0.900212\pi$
$883$	− 4.11745e36i	− 0.616765i	0.951263	−	0.308382i	$-0.0997876\pi$
$884$	6.90343e36	1.01956
$885$	0	0
$886$	5.80326e34	0.00833202
$887$	− 2.52904e36i	− 0.358022i	−0.983847	−	0.179011i	$-0.942710\pi$
$887$	− 2.52904e36i	− 0.358022i	0.983847	−	0.179011i	$-0.0572898\pi$
$888$	1.28043e34i	0.00178728i
$889$	−1.31273e37	−1.80678
$890$	0	0
$891$	5.23622e36	0.700723
$892$	1.06258e37i	1.40217i
$893$	− 5.62202e36i	− 0.731558i
$894$	−8.51107e33	−0.00109211
$895$	0	0
$896$	2.83425e35	0.0353661
$897$	− 1.51875e36i	− 0.186887i
$898$	− 4.55453e34i	− 0.00552700i
$899$	1.16410e36	0.139314
$900$	0	0
$901$	2.49544e36	0.290460
$902$	7.42578e34i	0.00852433i
$903$	2.30254e36i	0.260682i
$904$	2.40448e35	0.0268483
$905$	0	0
$906$	1.09202e34	0.00118612
$907$	− 4.93129e36i	− 0.528286i	−0.964484	−	0.264143i	$-0.914911\pi$
$907$	− 4.93129e36i	− 0.528286i	0.964484	−	0.264143i	$-0.0850891\pi$
$908$	1.29207e37i	1.36525i
$909$	1.50742e36	0.157103
$910$	0	0
$911$	−7.10548e36	−0.720466	−0.360233	−	0.932862i	$-0.617303\pi$
$911$	−7.10548e36	−0.720466	−0.360233	+	0.932862i	$0.617303\pi$
$912$	1.34055e36i	0.134075i
$913$	7.84240e36i	0.773685i
$914$	9.15090e34	0.00890505
$915$	0	0
$916$	1.90664e37	1.80541
$917$	− 6.83795e36i	− 0.638718i
$918$	− 3.92255e34i	− 0.00361439i
$919$	−2.64155e36	−0.240112	−0.120056	−	0.992767i	$-0.538307\pi$
$919$	−2.64155e36	−0.240112	−0.120056	+	0.992767i	$0.538307\pi$
$920$	0	0
$921$	−2.81179e36	−0.248735
$922$	2.19009e33i	0 0.000191129i
$923$	− 1.57089e37i	− 1.35246i
$924$	−2.16167e36	−0.183607
$925$	0	0
$926$	−1.02490e35	−0.00847316
$927$	− 3.92997e36i	− 0.320548i
$928$	− 4.39731e34i	− 0.00353865i
$929$	−5.01934e36	−0.398520	−0.199260	−	0.979947i	$-0.563854\pi$
$929$	−5.01934e36	−0.398520	−0.199260	+	0.979947i	$0.563854\pi$
$930$	0	0
$931$	−1.13263e36	−0.0875419
$932$	− 1.66280e37i	− 1.26806i
$933$	− 4.39835e36i	− 0.330955i
$934$	−1.28268e35	−0.00952320
$935$	0	0
$936$	2.12760e35	0.0153795
$937$	− 1.70189e37i	− 1.21391i	−0.794735	−	0.606956i	$-0.792390\pi$
$937$	− 1.70189e37i	− 1.21391i	0.794735	−	0.606956i	$-0.207610\pi$
$938$	− 5.00652e34i	− 0.00352371i
$939$	−2.70123e35	−0.0187604
$940$	0	0
$941$	−1.51254e37	−1.02291	−0.511455	−	0.859310i	$-0.670893\pi$
$941$	−1.51254e37	−1.02291	−0.511455	+	0.859310i	$0.670893\pi$
$942$	− 3.20967e33i	0 0.000214202i
$943$	− 1.74548e37i	− 1.14953i
$944$	−1.46929e37	−0.954897
$945$	0	0
$946$	−1.21605e35	−0.00769687
$947$	1.65329e36i	0.103270i	0.998666	+	0.0516351i	$0.0164433\pi$
$947$	1.65329e36i	0.103270i	−0.998666	+	0.0516351i	$0.983557\pi$
$948$	1.78485e36i	0.110026i
$949$	3.46238e36	0.210643
$950$	0	0
$951$	2.01260e36	0.119262
$952$	− 3.17213e35i	− 0.0185519i
$953$	− 2.77784e37i	− 1.60341i	−0.597718	−	0.801706i	$-0.703926\pi$
$953$	− 2.77784e37i	− 1.60341i	0.597718	−	0.801706i	$-0.296074\pi$
$954$	3.84526e34	0.00219064
$955$	0	0
$956$	4.83229e36	0.268182
$957$	4.47171e35i	0.0244948i
$958$	9.46752e34i	0.00511879i
$959$	−2.41640e37	−1.28955
$960$	0	0
$961$	−8.14395e35	−0.0423441
$962$	7.95666e34i	0.00408359i
$963$	2.89850e37i	1.46840i
$964$	−1.07184e37	−0.536004
$965$	0	0
$966$	−3.48920e34	−0.00170025
$967$	3.82441e36i	0.183965i	0.995761	+	0.0919823i	$0.0293203\pi$
$967$	3.82441e36i	0.183965i	−0.995761	+	0.0919823i	$0.970680\pi$
$968$	1.20659e35i	0.00572952i
$969$	3.00093e36	0.140672
$970$	0	0
$971$	−1.67087e37	−0.763311	−0.381655	−	0.924305i	$-0.624646\pi$
$971$	−1.67087e37	−0.763311	−0.381655	+	0.924305i	$0.624646\pi$
$972$	1.33050e37i	0.600049i
$973$	1.89331e37i	0.842967i
$974$	−1.90256e34	−0.000836277 0
$975$	0	0
$976$	1.01484e37	0.434786
$977$	− 3.54376e37i	− 1.49893i	−0.662043	−	0.749466i	$-0.730310\pi$
$977$	− 3.54376e37i	− 1.49893i	0.662043	−	0.749466i	$-0.269690\pi$
$978$	− 4.35345e34i	− 0.00181802i
$979$	1.48490e37	0.612227
$980$	0	0
$981$	3.86512e37	1.55346
$982$	3.46860e35i	0.0137645i
$983$	− 2.26759e37i	− 0.888476i	−0.895909	−	0.444238i	$-0.853475\pi$
$983$	− 2.26759e37i	− 0.888476i	0.895909	−	0.444238i	$-0.146525\pi$
$984$	−1.15889e35	−0.00448335
$985$	0	0
$986$	−3.28087e34	−0.00123745
$987$	7.07334e36i	0.263427i
$988$	1.66622e37i	0.612732i
$989$	2.85843e37	1.03794
$990$	0	0
$991$	−1.82706e36	−0.0646891	−0.0323445	−	0.999477i	$-0.510297\pi$
$991$	−1.82706e36	−0.0646891	−0.0323445	+	0.999477i	$0.510297\pi$
$992$	− 6.95742e35i	− 0.0243250i
$993$	− 1.12657e36i	− 0.0388949i
$994$	−3.60899e35	−0.0123043
$995$	0	0
$996$	−6.11932e36	−0.203452
$997$	2.34599e37i	0.770260i	0.922862	+	0.385130i	$0.125843\pi$
$997$	2.34599e37i	0.770260i	−0.922862	+	0.385130i	$0.874157\pi$
$998$	3.93518e35i	0.0127595i
$999$	−6.58373e36	−0.210816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.26.b.a.24.1		2
5.2	odd	4		25.26.a.a.1.1		1
5.3	odd	4		1.26.a.a.1.1	✓	1
5.4	even	2	inner	25.26.b.a.24.2		2
15.8	even	4		9.26.a.a.1.1		1
20.3	even	4		16.26.a.b.1.1		1
35.13	even	4		49.26.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.26.a.a.1.1	✓	1	5.3	odd	4
9.26.a.a.1.1		1	15.8	even	4
16.26.a.b.1.1		1	20.3	even	4
25.26.a.a.1.1		1	5.2	odd	4
25.26.b.a.24.1		2	1.1	even	1	trivial
25.26.b.a.24.2		2	5.4	even	2	inner
49.26.a.a.1.1		1	35.13	even	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-48.0000i q^{2} +195804. i q^{3} +3.35521e7 q^{4} +9.39859e6 q^{6} +3.90806e10i q^{7} -3.22111e9i q^{8} +8.08949e11 q^{9} +O(q^{10})\)	\(q-48.0000i q^{2} +195804. i q^{3} +3.35521e7 q^{4} +9.39859e6 q^{6} +3.90806e10i q^{7} -3.22111e9i q^{8} +8.08949e11 q^{9} +8.41952e12 q^{11} +6.56964e12i q^{12} +8.16510e13i q^{13} +1.87587e12 q^{14} +1.12567e15 q^{16} -2.51990e15i q^{17} -3.88296e13i q^{18} +6.08206e15 q^{19} -7.65214e15 q^{21} -4.04137e14i q^{22} +9.49953e16i q^{23} +6.30707e14 q^{24} +3.91925e15 q^{26} +3.24298e17i q^{27} +1.31124e18i q^{28} +2.71247e17 q^{29} +4.29167e18 q^{31} -1.62115e17i q^{32} +1.64857e18i q^{33} -1.20955e17 q^{34} +2.71420e19 q^{36} +2.03015e19i q^{37} -2.91939e17i q^{38} -1.59876e19 q^{39} -1.83744e20 q^{41} +3.67303e17i q^{42} -3.00902e20i q^{43} +2.82493e20 q^{44} +4.55977e18 q^{46} -9.24361e20i q^{47} +2.20410e20i q^{48} -1.86224e20 q^{49} +4.93407e20 q^{51} +2.73957e21i q^{52} +9.90292e20i q^{53} +1.55663e19 q^{54} +1.25883e20 q^{56} +1.19089e21i q^{57} -1.30199e19i q^{58} -1.30526e22 q^{59} +9.01545e21 q^{61} -2.06000e20i q^{62} +3.16142e22i q^{63} +3.77634e22 q^{64} +7.91316e19 q^{66} -2.66891e22i q^{67} -8.45480e22i q^{68} -1.86005e22 q^{69} -1.92391e23 q^{71} -2.60572e21i q^{72} -4.24046e22i q^{73} +9.74471e20 q^{74} +2.04066e23 q^{76} +3.29040e23i q^{77} +7.67405e20i q^{78} +2.71681e23 q^{79} +6.21915e23 q^{81} +8.81972e21i q^{82} +9.31454e23i q^{83} -2.56745e23 q^{84} -1.44433e22 q^{86} +5.31112e22i q^{87} -2.71202e22i q^{88} +1.76364e24 q^{89} -3.19097e24 q^{91} +3.18729e24i q^{92} +8.40325e23i q^{93} -4.43693e22 q^{94} +3.17427e22 q^{96} +2.82924e24i q^{97} +8.93877e21i q^{98} +6.81096e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 67104256 q^{4} + 18797184 q^{6} + 1617898806054 q^{9}+O(q^{10}) \) 2 * q + 67104256 * q^4 + 18797184 * q^6 + 1617898806054 * q^9	\( 2 q + 67104256 q^{4} + 18797184 q^{6} + 1617898806054 q^{9} + 16839030598104 q^{11} + 3751737330432 q^{14} + 22\!\cdots\!12 q^{16}+ \cdots + 13\!\cdots\!08 q^{99}+O(q^{100}) \) 2 * q + 67104256 * q^4 + 18797184 * q^6 + 1617898806054 * q^9 + 16839030598104 * q^11 + 3751737330432 * q^14 + 2251335967834112 * q^16 + 12164112740617880 * q^19 - 15304274505164736 * q^21 + 1261414355927040 * q^24 + 7838500352190144 * q^26 + 542493918953474820 * q^29 + 8583332135043018304 * q^31 - 241910402779015488 * q^34 + 54283947831770982912 * q^36 - 31975202561671644912 * q^39 - 367488499148142449196 * q^41 + 564985310023501965312 * q^44 + 9119546908446760704 * q^46 - 372448914438786768114 * q^49 + 986813010536298929424 * q^51 + 31132610668192884480 * q^54 + 251766186268874833920 * q^56 - 26105138832908403675960 * q^59 + 18030902449402829235004 * q^61 + 75526736626474314366976 * q^64 + 158263178267095469568 * q^66 - 37200911726281448601792 * q^69 - 384781032372435274880496 * q^71 + 1948942506826476190272 * q^74 + 408131867679641908848640 * q^76 + 543362110051544554394720 * q^79 + 1243829527532757785952882 * q^81 - 513490977144423883358208 * q^84 - 28886575121816288232576 * q^86 + 3527271036099614633005260 * q^89 - 6381943226110274013676576 * q^91 - 88738660614211667394048 * q^94 + 63485430446375603011584 * q^96 + 13621923749889617558060808 * q^99

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