LMFDB - Embedded newform 50.26.b.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, 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("50.49");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.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:	$197.998389976$
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 2)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.26.b.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4096.00i q^{2} -97956.0i q^{3} -1.67772e7 q^{4} -4.01228e8 q^{6} -4.08826e10i q^{7} +6.87195e10i q^{8} +8.37693e11 q^{9} +O(q^{10})$	\(q-4096.00i q^{2} -97956.0i q^{3} -1.67772e7 q^{4} -4.01228e8 q^{6} -4.08826e10i q^{7} +6.87195e10i q^{8} +8.37693e11 q^{9} -1.45062e13 q^{11} +1.64343e12i q^{12} -8.78440e13i q^{13} -1.67455e14 q^{14} +2.81475e14 q^{16} -2.65543e15i q^{17} -3.43119e15i q^{18} +1.39994e16 q^{19} -4.00470e15 q^{21} +5.94175e16i q^{22} -8.58528e16i q^{23} +6.73149e15 q^{24} -3.59809e17 q^{26} -1.65054e17i q^{27} +6.85897e17i q^{28} -2.08023e18 q^{29} +2.66353e18 q^{31} -1.15292e18i q^{32} +1.42097e18i q^{33} -1.08766e19 q^{34} -1.40542e19 q^{36} -5.13796e19i q^{37} -5.73416e19i q^{38} -8.60485e18 q^{39} +2.33560e20 q^{41} +1.64032e19i q^{42} +4.01336e19i q^{43} +2.43374e20 q^{44} -3.51653e20 q^{46} +2.79826e20i q^{47} -2.75722e19i q^{48} -3.30321e20 q^{49} -2.60115e20 q^{51} +1.47378e21i q^{52} -4.25070e20i q^{53} -6.76062e20 q^{54} +2.80943e21 q^{56} -1.37133e21i q^{57} +8.52062e21i q^{58} +8.33891e21 q^{59} +2.42979e22 q^{61} -1.09098e22i q^{62} -3.42471e22i q^{63} -4.72237e21 q^{64} +5.82030e21 q^{66} -1.24700e23i q^{67} +4.45507e22i q^{68} -8.40979e21 q^{69} -9.30490e22 q^{71} +5.75658e22i q^{72} -4.04218e22i q^{73} -2.10451e23 q^{74} -2.34871e23 q^{76} +5.93053e23i q^{77} +3.52454e22i q^{78} +8.05270e23 q^{79} +6.93600e23 q^{81} -9.56661e23i q^{82} -8.98335e21i q^{83} +6.71877e22 q^{84} +1.64387e23 q^{86} +2.03771e23i q^{87} -9.96860e23i q^{88} -3.55600e24 q^{89} -3.59129e24 q^{91} +1.44037e24i q^{92} -2.60909e23i q^{93} +1.14617e24 q^{94} -1.12936e23 q^{96} -8.66049e24i q^{97} +1.35300e24i q^{98} -1.21518e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 33554432 q^{4} - 802455552 q^{6} + 1675386463014 q^{9}+O(q^{10}) $ 2 * q - 33554432 * q^4 - 802455552 * q^6 + 1675386463014 * q^9	$ 2 q - 33554432 q^{4} - 802455552 q^{6} + 1675386463014 q^{9} - 29012444754216 q^{11} - 334910565318656 q^{14} + 562949953421312 q^{16} + 27\!\cdots\!80 q^{19}+ \cdots - 24\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 33554432 * q^4 - 802455552 * q^6 + 1675386463014 * q^9 - 29012444754216 * q^11 - 334910565318656 * q^14 + 562949953421312 * q^16 + 27998849408195480 * q^19 - 8009399252039616 * q^21 + 13462970126303232 * q^24 - 719617962287153152 * q^26 - 4160460859203053820 * q^29 + 5327064742605350464 * q^31 - 21753248717919338496 * q^34 - 28108320573461889024 * q^36 - 17209691678173919472 * q^39 + 467119614568450661844 * q^41 + 486748052329548742656 * q^44 - 703305979691298127872 * q^46 - 660642836998850133234 * q^49 - 520229792825319023856 * q^51 - 1352123033289508454400 * q^54 + 5618866895033200541696 * q^56 + 16677810543100138197960 * q^59 + 48595896938126376273724 * q^61 - 9444732965739290427392 * q^64 + 11640598685056952303616 * q^66 - 16819589977207226419392 * q^69 - 186097965393815479969776 * q^71 - 420901748574744053497856 * q^74 - 469742744272767738183680 * q^76 + 1610540227078311978788960 * q^79 + 1387199791368333628082802 * q^81 + 134375421281707078189056 * q^84 + 328774427400024995299328 * q^86 - 7112009273819794670044980 * q^89 - 7182587938399605028880416 * q^91 + 2292337828143166425268224 * q^94 - 225871157810536604762112 * q^96 - 24303528600077511402283512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

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 $

$2$	− 4096.00i	− 0.707107i
$2$	− 4096.00i	− 0.707107i
$3$	− 97956.0i	− 0.106418i	−0.998583	−	0.0532090i	$-0.983055\pi$
$3$	− 97956.0i	− 0.106418i	0.998583	−	0.0532090i	$-0.0169450\pi$
$4$	−1.67772e7	−0.500000
$5$	0	0
$5$	0	0
$6$	−4.01228e8	−0.0752489
$7$	− 4.08826e10i	− 1.11638i	−0.829712	−	0.558192i	$-0.811495\pi$
$7$	− 4.08826e10i	− 1.11638i	0.829712	−	0.558192i	$-0.188505\pi$
$8$	6.87195e10i	0.353553i
$9$	8.37693e11	0.988675
$10$	0	0
$11$	−1.45062e13	−1.39362	−0.696812	−	0.717254i	$-0.745399\pi$
$11$	−1.45062e13	−1.39362	−0.696812	+	0.717254i	$0.745399\pi$
$12$	1.64343e12i	0.0532090i
$13$	− 8.78440e13i	− 1.04573i	−0.852415	−	0.522866i	$-0.824863\pi$
$13$	− 8.78440e13i	− 1.04573i	0.852415	−	0.522866i	$-0.175137\pi$
$14$	−1.67455e14	−0.789402
$15$	0	0
$16$	2.81475e14	0.250000
$17$	− 2.65543e15i	− 1.10541i	−0.833378	−	0.552704i	$-0.813596\pi$
$17$	− 2.65543e15i	− 1.10541i	0.833378	−	0.552704i	$-0.186404\pi$
$18$	− 3.43119e15i	− 0.699099i
$19$	1.39994e16	1.45108	0.725538	−	0.688182i	$-0.241591\pi$
$19$	1.39994e16	1.45108	0.725538	+	0.688182i	$0.241591\pi$
$20$	0	0
$21$	−4.00470e15	−0.118803
$22$	5.94175e16i	0.985441i
$23$	− 8.58528e16i	− 0.816877i	−0.912786	−	0.408438i	$-0.866074\pi$
$23$	− 8.58528e16i	− 0.816877i	0.912786	−	0.408438i	$-0.133926\pi$
$24$	6.73149e15	0.0376245
$25$	0	0
$26$	−3.59809e17	−0.739444
$27$	− 1.65054e17i	− 0.211631i
$28$	6.85897e17i	0.558192i
$29$	−2.08023e18	−1.09178	−0.545892	−	0.837856i	$-0.683809\pi$
$29$	−2.08023e18	−1.09178	−0.545892	+	0.837856i	$0.683809\pi$
$30$	0	0
$31$	2.66353e18	0.607347	0.303673	−	0.952776i	$-0.401787\pi$
$31$	2.66353e18	0.607347	0.303673	+	0.952776i	$0.401787\pi$
$32$	− 1.15292e18i	− 0.176777i
$33$	1.42097e18i	0.148307i
$34$	−1.08766e19	−0.781642
$35$	0	0
$36$	−1.40542e19	−0.494338
$37$	− 5.13796e19i	− 1.28313i	−0.767070	−	0.641563i	$-0.778286\pi$
$37$	− 5.13796e19i	− 1.28313i	0.767070	−	0.641563i	$-0.221714\pi$
$38$	− 5.73416e19i	− 1.02607i
$39$	−8.60485e18	−0.111285
$40$	0	0
$41$	2.33560e20	1.61659	0.808295	−	0.588778i	$-0.200391\pi$
$41$	2.33560e20	1.61659	0.808295	+	0.588778i	$0.200391\pi$
$42$	1.64032e19i	0.0840067i
$43$	4.01336e19i	0.153162i	0.997063	+	0.0765812i	$0.0244005\pi$
$43$	4.01336e19i	0.153162i	−0.997063	+	0.0765812i	$0.975600\pi$
$44$	2.43374e20	0.696812
$45$	0	0
$46$	−3.51653e20	−0.577619
$47$	2.79826e20i	0.351290i	0.984454	+	0.175645i	$0.0562010\pi$
$47$	2.79826e20i	0.351290i	−0.984454	+	0.175645i	$0.943799\pi$
$48$	− 2.75722e19i	− 0.0266045i
$49$	−3.30321e20	−0.246312
$50$	0	0
$51$	−2.60115e20	−0.117635
$52$	1.47378e21i	0.522866i
$53$	− 4.25070e20i	− 0.118854i	−0.998233	−	0.0594268i	$-0.981073\pi$
$53$	− 4.25070e20i	− 0.118854i	0.998233	−	0.0594268i	$-0.0189273\pi$
$54$	−6.76062e20	−0.149646
$55$	0	0
$56$	2.80943e21	0.394701
$57$	− 1.37133e21i	− 0.154421i
$58$	8.52062e21i	0.772007i
$59$	8.33891e21	0.610181	0.305091	−	0.952323i	$-0.401313\pi$
$59$	8.33891e21	0.610181	0.305091	+	0.952323i	$0.401313\pi$
$60$	0	0
$61$	2.42979e22	1.17205	0.586026	−	0.810292i	$-0.300692\pi$
$61$	2.42979e22	1.17205	0.586026	+	0.810292i	$0.300692\pi$
$62$	− 1.09098e22i	− 0.429459i
$63$	− 3.42471e22i	− 1.10374i
$64$	−4.72237e21	−0.125000
$65$	0	0
$66$	5.82030e21	0.104869
$67$	− 1.24700e23i	− 1.86179i	−0.365282	−	0.930897i	$-0.619027\pi$
$67$	− 1.24700e23i	− 1.86179i	0.365282	−	0.930897i	$-0.380973\pi$
$68$	4.45507e22i	0.552704i
$69$	−8.40979e21	−0.0869304
$70$	0	0
$71$	−9.30490e22	−0.672949	−0.336475	−	0.941693i	$-0.609235\pi$
$71$	−9.30490e22	−0.672949	−0.336475	+	0.941693i	$0.609235\pi$
$72$	5.75658e22i	0.349549i
$73$	− 4.04218e22i	− 0.206576i	−0.994651	−	0.103288i	$-0.967064\pi$
$73$	− 4.04218e22i	− 0.206576i	0.994651	−	0.103288i	$-0.0329363\pi$
$74$	−2.10451e23	−0.907307
$75$	0	0
$76$	−2.34871e23	−0.725538
$77$	5.93053e23i	1.55582i
$78$	3.52454e22i	0.0786902i
$79$	8.05270e23	1.53321	0.766607	−	0.642116i	$-0.221943\pi$
$79$	8.05270e23	1.53321	0.766607	+	0.642116i	$0.221943\pi$
$80$	0	0
$81$	6.93600e23	0.966154
$82$	− 9.56661e23i	− 1.14310i
$83$	− 8.98335e21i	− 0.00922491i	−0.999989	−	0.00461245i	$-0.998532\pi$
$83$	− 8.98335e21i	− 0.00922491i	0.999989	−	0.00461245i	$-0.00146820\pi$
$84$	6.71877e22	0.0594017
$85$	0	0
$86$	1.64387e23	0.108302
$87$	2.03771e23i	0.116185i
$88$	− 9.96860e23i	− 0.492721i
$89$	−3.55600e24	−1.52611	−0.763057	−	0.646331i	$-0.776303\pi$
$89$	−3.55600e24	−1.52611	−0.763057	+	0.646331i	$0.776303\pi$
$90$	0	0
$91$	−3.59129e24	−1.16744
$92$	1.44037e24i	0.408438i
$93$	− 2.60909e23i	− 0.0646327i
$94$	1.14617e24	0.248399
$95$	0	0
$96$	−1.12936e23	−0.0188122
$97$	− 8.66049e24i	− 1.26735i	−0.773600	−	0.633674i	$-0.781546\pi$
$97$	− 8.66049e24i	− 1.26735i	0.773600	−	0.633674i	$-0.218454\pi$
$98$	1.35300e24i	0.174169i
$99$	−1.21518e25	−1.37784
$100$	0	0
$101$	7.28380e24	0.643193	0.321596	−	0.946877i	$-0.395781\pi$
$101$	7.28380e24	0.643193	0.321596	+	0.946877i	$0.395781\pi$
$102$	1.06543e24i	0.0831808i
$103$	− 1.52392e25i	− 1.05317i	−0.850123	−	0.526583i	$-0.823473\pi$
$103$	− 1.52392e25i	− 1.05317i	0.850123	−	0.526583i	$-0.176527\pi$
$104$	6.03659e24	0.369722
$105$	0	0
$106$	−1.74109e24	−0.0840422
$107$	− 6.27006e24i	− 0.269138i	−0.990904	−	0.134569i	$-0.957035\pi$
$107$	− 6.27006e24i	− 0.269138i	0.990904	−	0.134569i	$-0.0429650\pi$
$108$	2.76915e24i	0.105815i
$109$	1.66220e25	0.566047	0.283024	−	0.959113i	$-0.408663\pi$
$109$	1.66220e25	0.566047	0.283024	+	0.959113i	$0.408663\pi$
$110$	0	0
$111$	−5.03294e24	−0.136548
$112$	− 1.15074e25i	− 0.279096i
$113$	4.59044e25i	0.996263i	0.867102	+	0.498131i	$0.165980\pi$
$113$	4.59044e25i	0.996263i	−0.867102	+	0.498131i	$0.834020\pi$
$114$	−5.61696e24	−0.109192
$115$	0	0
$116$	3.49005e25	0.545892
$117$	− 7.35863e25i	− 1.03389i
$118$	− 3.41562e25i	− 0.431463i
$119$	−1.08561e26	−1.23406
$120$	0	0
$121$	1.02083e26	0.942189
$122$	− 9.95244e25i	− 0.828766i
$123$	− 2.28786e25i	− 0.172034i
$124$	−4.46867e25	−0.303673
$125$	0	0
$126$	−1.40276e26	−0.780463
$127$	− 3.66137e24i	− 0.0184543i	−0.999957	−	0.00922713i	$-0.997063\pi$
$127$	− 3.66137e24i	− 0.0184543i	0.999957	−	0.00922713i	$-0.00293713\pi$
$128$	1.93428e25i	0.0883883i
$129$	3.93133e24	0.0162993
$130$	0	0
$131$	−1.37888e26	−0.471667	−0.235833	−	0.971793i	$-0.575782\pi$
$131$	−1.37888e26	−0.471667	−0.235833	+	0.971793i	$0.575782\pi$
$132$	− 2.38399e25i	− 0.0741534i
$133$	− 5.72333e26i	− 1.61996i
$134$	−5.10772e26	−1.31649
$135$	0	0
$136$	1.82479e26	0.390821
$137$	− 4.32281e26i	− 0.844810i	−0.906407	−	0.422405i	$-0.861186\pi$
$137$	− 4.32281e26i	− 0.844810i	0.906407	−	0.422405i	$-0.138814\pi$
$138$	3.44465e25i	0.0614691i
$139$	4.00646e25	0.0653245	0.0326622	−	0.999466i	$-0.489601\pi$
$139$	4.00646e25	0.0653245	0.0326622	+	0.999466i	$0.489601\pi$
$140$	0	0
$141$	2.74107e25	0.0373836
$142$	3.81129e26i	0.475847i
$143$	1.27428e27i	1.45736i
$144$	2.35790e26	0.247169
$145$	0	0
$146$	−1.65568e26	−0.146071
$147$	3.23570e25i	0.0262121i
$148$	8.62007e26i	0.641563i
$149$	−1.12193e27	−0.767601	−0.383801	−	0.923416i	$-0.625385\pi$
$149$	−1.12193e27	−0.767601	−0.383801	+	0.923416i	$0.625385\pi$
$150$	0	0
$151$	−2.65183e26	−0.153580	−0.0767900	−	0.997047i	$-0.524467\pi$
$151$	−2.65183e26	−0.153580	−0.0767900	+	0.997047i	$0.524467\pi$
$152$	9.62033e26i	0.513033i
$153$	− 2.22443e27i	− 1.09289i
$154$	2.42914e27	1.10013
$155$	0	0
$156$	1.44365e26	0.0556424
$157$	− 8.32328e26i	− 0.296175i	−0.988974	−	0.148088i	$-0.952688\pi$
$157$	− 8.32328e26i	− 0.296175i	0.988974	−	0.148088i	$-0.0473117\pi$
$158$	− 3.29839e27i	− 1.08415i
$159$	−4.16382e25	−0.0126482
$160$	0	0
$161$	−3.50989e27	−0.911947
$162$	− 2.84099e27i	− 0.683174i
$163$	7.22281e27i	1.60828i	0.594442	+	0.804139i	$0.297373\pi$
$163$	7.22281e27i	1.60828i	−0.594442	+	0.804139i	$0.702627\pi$
$164$	−3.91848e27	−0.808295
$165$	0	0
$166$	−3.67958e25	−0.00652300
$167$	3.82503e27i	0.629041i	0.949251	+	0.314520i	$0.101844\pi$
$167$	3.82503e27i	0.629041i	−0.949251	+	0.314520i	$0.898156\pi$
$168$	− 2.75201e26i	− 0.0420033i
$169$	−6.60156e26	−0.0935542
$170$	0	0
$171$	1.17272e28	1.43464
$172$	− 6.73330e26i	− 0.0765812i
$173$	4.74370e27i	0.501812i	0.968012	+	0.250906i	$0.0807284\pi$
$173$	4.74370e27i	0.501812i	−0.968012	+	0.250906i	$0.919272\pi$
$174$	8.34646e26	0.0821555
$175$	0	0
$176$	−4.08314e27	−0.348406
$177$	− 8.16846e26i	− 0.0649343i
$178$	1.45654e28i	1.07913i
$179$	6.99171e27	0.482970	0.241485	−	0.970405i	$-0.422365\pi$
$179$	6.99171e27	0.482970	0.241485	+	0.970405i	$0.422365\pi$
$180$	0	0
$181$	−6.34714e27	−0.381589	−0.190794	−	0.981630i	$-0.561106\pi$
$181$	−6.34714e27	−0.381589	−0.190794	+	0.981630i	$0.561106\pi$
$182$	1.47099e28i	0.825503i
$183$	− 2.38013e27i	− 0.124727i
$184$	5.89976e27	0.288809
$185$	0	0
$186$	−1.06868e27	−0.0457022
$187$	3.85202e28i	1.54052i
$188$	− 4.69471e27i	− 0.175645i
$189$	−6.74785e27	−0.236261
$190$	0	0
$191$	−3.59244e28	−1.10274	−0.551369	−	0.834261i	$-0.685894\pi$
$191$	−3.59244e28	−1.10274	−0.551369	+	0.834261i	$0.685894\pi$
$192$	4.62584e26i	0.0133023i
$193$	3.76264e27i	0.101397i	0.998714	+	0.0506987i	$0.0161448\pi$
$193$	3.76264e27i	0.101397i	−0.998714	+	0.0506987i	$0.983855\pi$
$194$	−3.54734e28	−0.896150
$195$	0	0
$196$	5.54187e27	0.123156
$197$	− 1.84478e28i	− 0.384696i	−0.981327	−	0.192348i	$-0.938390\pi$
$197$	− 1.84478e28i	− 0.384696i	0.981327	−	0.192348i	$-0.0616102\pi$
$198$	4.97736e28i	0.974281i
$199$	−3.23533e28	−0.594641	−0.297321	−	0.954778i	$-0.596093\pi$
$199$	−3.23533e28	−0.594641	−0.297321	+	0.954778i	$0.596093\pi$
$200$	0	0
$201$	−1.22151e28	−0.198129
$202$	− 2.98345e28i	− 0.454806i
$203$	8.50453e28i	1.21885i
$204$	4.36400e27	0.0588177
$205$	0	0
$206$	−6.24198e28	−0.744701
$207$	− 7.19183e28i	− 0.807626i
$208$	− 2.47259e28i	− 0.261433i
$209$	−2.03079e29	−2.02226
$210$	0	0
$211$	7.34820e28	0.649607	0.324803	−	0.945782i	$-0.394702\pi$
$211$	7.34820e28	0.649607	0.324803	+	0.945782i	$0.394702\pi$
$212$	7.13150e27i	0.0594268i
$213$	9.11471e27i	0.0716140i
$214$	−2.56822e28	−0.190309
$215$	0	0
$216$	1.13424e28	0.0748228
$217$	− 1.08892e29i	− 0.678032i
$218$	− 6.80838e28i	− 0.400256i
$219$	−3.95956e27	−0.0219834
$220$	0	0
$221$	−2.33263e29	−1.15596
$222$	2.06149e28i	0.0965539i
$223$	3.83771e29i	1.69927i	0.527373	+	0.849634i	$0.323177\pi$
$223$	3.83771e29i	1.69927i	−0.527373	+	0.849634i	$0.676823\pi$
$224$	−4.71345e28	−0.197351
$225$	0	0
$226$	1.88024e29	0.704464
$227$	2.86396e28i	0.101541i	0.998710	+	0.0507707i	$0.0161678\pi$
$227$	2.86396e28i	0.101541i	−0.998710	+	0.0507707i	$0.983832\pi$
$228$	2.30071e28i	0.0772104i
$229$	−5.18014e29	−1.64588	−0.822939	−	0.568129i	$-0.807667\pi$
$229$	−5.18014e29	−1.64588	−0.822939	+	0.568129i	$0.807667\pi$
$230$	0	0
$231$	5.80931e28	0.165567
$232$	− 1.42952e29i	− 0.386004i
$233$	1.11488e29i	0.285285i	0.989774	+	0.142643i	$0.0455600\pi$
$233$	1.11488e29i	0.285285i	−0.989774	+	0.142643i	$0.954440\pi$
$234$	−3.01410e29	−0.731070
$235$	0	0
$236$	−1.39904e29	−0.305091
$237$	− 7.88810e28i	− 0.163162i
$238$	4.44665e29i	0.872612i
$239$	−9.81417e29	−1.82759	−0.913797	−	0.406170i	$-0.866864\pi$
$239$	−9.81417e29	−1.82759	−0.913797	+	0.406170i	$0.866864\pi$
$240$	0	0
$241$	−1.00294e30	−1.68292	−0.841459	−	0.540320i	$-0.818303\pi$
$241$	−1.00294e30	−1.68292	−0.841459	+	0.540320i	$0.818303\pi$
$242$	− 4.18134e29i	− 0.666228i
$243$	− 2.07791e29i	− 0.314447i
$244$	−4.07652e29	−0.586026
$245$	0	0
$246$	−9.37107e28	−0.121647
$247$	− 1.22977e30i	− 1.51744i
$248$	1.83037e29i	0.214730i
$249$	−8.79973e26	−0.000981697 0
$250$	0	0
$251$	1.14894e30	1.15978	0.579892	−	0.814694i	$-0.303095\pi$
$251$	1.14894e30	1.15978	0.579892	+	0.814694i	$0.303095\pi$
$252$	5.74571e29i	0.551870i
$253$	1.24540e30i	1.13842i
$254$	−1.49970e28	−0.0130491
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	1.28454e30i	0.965123i	0.875862	+	0.482562i	$0.160294\pi$
$257$	1.28454e30i	0.965123i	−0.875862	+	0.482562i	$0.839706\pi$
$258$	− 1.61027e28i	− 0.0115253i
$259$	−2.10053e30	−1.43246
$260$	0	0
$261$	−1.74259e30	−1.07942
$262$	5.64789e29i	0.333519i
$263$	2.47079e30i	1.39120i	0.718431	+	0.695598i	$0.244860\pi$
$263$	2.47079e30i	1.39120i	−0.718431	+	0.695598i	$0.755140\pi$
$264$	−9.76484e28	−0.0524344
$265$	0	0
$266$	−2.34428e30	−1.14548
$267$	3.48332e29i	0.162406i
$268$	2.09212e30i	0.930897i
$269$	−8.32933e29	−0.353758	−0.176879	−	0.984233i	$-0.556600\pi$
$269$	−8.32933e29	−0.353758	−0.176879	+	0.984233i	$0.556600\pi$
$270$	0	0
$271$	−3.89840e29	−0.150928	−0.0754641	−	0.997149i	$-0.524044\pi$
$271$	−3.89840e29	−0.150928	−0.0754641	+	0.997149i	$0.524044\pi$
$272$	− 7.47436e29i	− 0.276352i
$273$	3.51789e29i	0.124236i
$274$	−1.77062e30	−0.597371
$275$	0	0
$276$	1.41093e29	0.0434652
$277$	5.75822e30i	1.69548i	0.530416	+	0.847738i	$0.322036\pi$
$277$	5.75822e30i	1.69548i	−0.530416	+	0.847738i	$0.677964\pi$
$278$	− 1.64105e29i	− 0.0461914i
$279$	2.23122e30	0.600469
$280$	0	0
$281$	−7.34745e29	−0.180846	−0.0904228	−	0.995903i	$-0.528822\pi$
$281$	−7.34745e29	−0.180846	−0.0904228	+	0.995903i	$0.528822\pi$
$282$	− 1.12274e29i	− 0.0264342i
$283$	1.15692e30i	0.260600i	0.991475	+	0.130300i	$0.0415940\pi$
$283$	1.15692e30i	0.260600i	−0.991475	+	0.130300i	$0.958406\pi$
$284$	1.56110e30	0.336475
$285$	0	0
$286$	5.21947e30	1.03051
$287$	− 9.54854e30i	− 1.80473i
$288$	− 9.65795e29i	− 0.174775i
$289$	−1.28066e30	−0.221927
$290$	0	0
$291$	−8.48347e29	−0.134869
$292$	6.78165e29i	0.103288i
$293$	9.96443e29i	0.145414i	0.997353	+	0.0727072i	$0.0231639\pi$
$293$	9.96443e29i	0.145414i	−0.997353	+	0.0727072i	$0.976836\pi$
$294$	1.32534e29	0.0185347
$295$	0	0
$296$	3.53078e30	0.453653
$297$	2.39431e30i	0.294934i
$298$	4.59541e30i	0.542776i
$299$	−7.54165e30	−0.854233
$300$	0	0
$301$	1.64077e30	0.170988
$302$	1.08619e30i	0.108597i
$303$	− 7.13492e29i	− 0.0684473i
$304$	3.94049e30	0.362769
$305$	0	0
$306$	−9.11127e30	−0.772790
$307$	1.11603e31i	0.908755i	0.890809	+	0.454378i	$0.150138\pi$
$307$	1.11603e31i	0.908755i	−0.890809	+	0.454378i	$0.849862\pi$
$308$	− 9.94977e30i	− 0.777910i
$309$	−1.49277e30	−0.112076
$310$	0	0
$311$	−8.47315e30	−0.586867	−0.293434	−	0.955979i	$-0.594798\pi$
$311$	−8.47315e30	−0.586867	−0.293434	+	0.955979i	$0.594798\pi$
$312$	− 5.91321e29i	− 0.0393451i
$313$	1.15783e31i	0.740184i	0.928995	+	0.370092i	$0.120674\pi$
$313$	1.15783e31i	0.740184i	−0.928995	+	0.370092i	$0.879326\pi$
$314$	−3.40921e30	−0.209427
$315$	0	0
$316$	−1.35102e31	−0.766607
$317$	− 1.97191e31i	− 1.07559i	−0.843075	−	0.537796i	$-0.819257\pi$
$317$	− 1.97191e31i	− 1.07559i	0.843075	−	0.537796i	$-0.180743\pi$
$318$	1.70550e29i	0.00894361i
$319$	3.01763e31	1.52154
$320$	0	0
$321$	−6.14190e29	−0.0286411
$322$	1.43765e31i	0.644844i
$323$	− 3.71744e31i	− 1.60403i
$324$	−1.16367e31	−0.483077
$325$	0	0
$326$	2.95846e31	1.13722
$327$	− 1.62823e30i	− 0.0602376i
$328$	1.60501e31i	0.571551i
$329$	1.14400e31	0.392174
$330$	0	0
$331$	4.77112e31	1.51625	0.758124	−	0.652110i	$-0.226116\pi$
$331$	4.77112e31	1.51625	0.758124	+	0.652110i	$0.226116\pi$
$332$	1.50716e29i	0.00461245i
$333$	− 4.30403e31i	− 1.26859i
$334$	1.56673e31	0.444799
$335$	0	0
$336$	−1.12722e30	−0.0297008
$337$	− 3.28717e31i	− 0.834542i	−0.908782	−	0.417271i	$-0.862987\pi$
$337$	− 3.28717e31i	− 0.834542i	0.908782	−	0.417271i	$-0.137013\pi$
$338$	2.70400e30i	0.0661528i
$339$	4.49661e30	0.106020
$340$	0	0
$341$	−3.86378e31	−0.846413
$342$	− 4.80347e31i	− 1.01445i
$343$	− 4.13220e31i	− 0.841405i
$344$	−2.75796e30	−0.0541511
$345$	0	0
$346$	1.94302e31	0.354834
$347$	3.13233e31i	0.551759i	0.961192	+	0.275879i	$0.0889691\pi$
$347$	3.13233e31i	0.551759i	−0.961192	+	0.275879i	$0.911031\pi$
$348$	− 3.41871e30i	− 0.0580927i
$349$	−3.37807e31	−0.553796	−0.276898	−	0.960899i	$-0.589306\pi$
$349$	−3.37807e31	−0.553796	−0.276898	+	0.960899i	$0.589306\pi$
$350$	0	0
$351$	−1.44990e31	−0.221309
$352$	1.67245e31i	0.246360i
$353$	− 4.38482e31i	− 0.623401i	−0.950180	−	0.311701i	$-0.899101\pi$
$353$	− 4.38482e31i	− 0.623401i	0.950180	−	0.311701i	$-0.100899\pi$
$354$	−3.34580e30	−0.0459155
$355$	0	0
$356$	5.96599e31	0.763057
$357$	1.06342e31i	0.131326i
$358$	− 2.86380e31i	− 0.341512i
$359$	1.50427e32	1.73239	0.866193	−	0.499710i	$-0.166560\pi$
$359$	1.50427e32	1.73239	0.866193	+	0.499710i	$0.166560\pi$
$360$	0	0
$361$	1.02907e32	1.10562
$362$	2.59979e31i	0.269824i
$363$	− 9.99968e30i	− 0.100266i
$364$	6.02519e31	0.583719
$365$	0	0
$366$	−9.74901e30	−0.0881956
$367$	− 6.93296e31i	− 0.606168i	−0.952964	−	0.303084i	$-0.901984\pi$
$367$	− 6.93296e31i	− 0.606168i	0.952964	−	0.303084i	$-0.0980163\pi$
$368$	− 2.41654e31i	− 0.204219i
$369$	1.95651e32	1.59828
$370$	0	0
$371$	−1.73780e31	−0.132686
$372$	4.37733e30i	0.0323163i
$373$	− 6.14410e31i	− 0.438630i	−0.975654	−	0.219315i	$-0.929618\pi$
$373$	− 6.14410e31i	− 0.438630i	0.975654	−	0.219315i	$-0.0703822\pi$
$374$	1.57779e32	1.08931
$375$	0	0
$376$	−1.92295e31	−0.124200
$377$	1.82736e32i	1.14171i
$378$	2.76392e31i	0.167062i
$379$	−6.25980e31	−0.366075	−0.183038	−	0.983106i	$-0.558593\pi$
$379$	−6.25980e31	−0.366075	−0.183038	+	0.983106i	$0.558593\pi$
$380$	0	0
$381$	−3.58653e29	−0.00196387
$382$	1.47146e32i	0.779754i
$383$	− 1.95859e32i	− 1.00452i	−0.864716	−	0.502260i	$-0.832502\pi$
$383$	− 1.95859e32i	− 1.00452i	0.864716	−	0.502260i	$-0.167498\pi$
$384$	1.89474e30	0.00940612
$385$	0	0
$386$	1.54118e31	0.0716988
$387$	3.36196e31i	0.151428i
$388$	1.45299e32i	0.633674i
$389$	5.55896e31	0.234760	0.117380	−	0.993087i	$-0.462550\pi$
$389$	5.55896e31	0.234760	0.117380	+	0.993087i	$0.462550\pi$
$390$	0	0
$391$	−2.27976e32	−0.902982
$392$	− 2.26995e31i	− 0.0870845i
$393$	1.35070e31i	0.0501939i
$394$	−7.55624e31	−0.272021
$395$	0	0
$396$	2.03873e32	0.688921
$397$	− 4.00706e32i	− 1.31203i	−0.754746	−	0.656017i	$-0.772240\pi$
$397$	− 4.00706e32i	− 1.31203i	0.754746	−	0.656017i	$-0.227760\pi$
$398$	1.32519e32i	0.420475i
$399$	−5.60635e31	−0.172393
$400$	0	0
$401$	−2.79804e32	−0.808258	−0.404129	−	0.914702i	$-0.632425\pi$
$401$	−2.79804e32	−0.808258	−0.404129	+	0.914702i	$0.632425\pi$
$402$	5.00331e31i	0.140098i
$403$	− 2.33975e32i	− 0.635122i
$404$	−1.22202e32	−0.321596
$405$	0	0
$406$	3.48346e32	0.861856
$407$	7.45324e32i	1.78820i
$408$	− 1.78750e31i	− 0.0415904i
$409$	7.22159e32	1.62964	0.814820	−	0.579715i	$-0.196836\pi$
$409$	7.22159e32	1.62964	0.814820	+	0.579715i	$0.196836\pi$
$410$	0	0
$411$	−4.23445e31	−0.0899030
$412$	2.55672e32i	0.526583i
$413$	− 3.40916e32i	− 0.681196i
$414$	−2.94577e32	−0.571078
$415$	0	0
$416$	−1.01277e32	−0.184861
$417$	− 3.92457e30i	− 0.00695170i
$418$	8.31811e32i	1.42995i
$419$	−5.13071e32	−0.856057	−0.428028	−	0.903765i	$-0.640792\pi$
$419$	−5.13071e32	−0.856057	−0.428028	+	0.903765i	$0.640792\pi$
$420$	0	0
$421$	−1.30991e32	−0.205927	−0.102964	−	0.994685i	$-0.532833\pi$
$421$	−1.30991e32	−0.205927	−0.102964	+	0.994685i	$0.532833\pi$
$422$	− 3.00982e32i	− 0.459341i
$423$	2.34409e32i	0.347311i
$424$	2.92106e31	0.0420211
$425$	0	0
$426$	3.73338e31	0.0506387
$427$	− 9.93364e32i	− 1.30846i
$428$	1.05194e32i	0.134569i
$429$	1.24824e32	0.155089
$430$	0	0
$431$	4.25042e32	0.498271	0.249135	−	0.968469i	$-0.419854\pi$
$431$	4.25042e32	0.498271	0.249135	+	0.968469i	$0.419854\pi$
$432$	− 4.64586e31i	− 0.0529077i
$433$	− 2.18224e32i	− 0.241437i	−0.992687	−	0.120719i	$-0.961480\pi$
$433$	− 2.18224e32i	− 0.241437i	0.992687	−	0.120719i	$-0.0385199\pi$
$434$	−4.46023e32	−0.479441
$435$	0	0
$436$	−2.78871e32	−0.283024
$437$	− 1.20189e33i	− 1.18535i
$438$	1.62183e31i	0.0155446i
$439$	−1.96041e33	−1.82617	−0.913084	−	0.407771i	$-0.866306\pi$
$439$	−1.96041e33	−1.82617	−0.913084	+	0.407771i	$0.866306\pi$
$440$	0	0
$441$	−2.76708e32	−0.243523
$442$	9.55446e32i	0.817387i
$443$	1.81076e33i	1.50596i	0.658043	+	0.752980i	$0.271385\pi$
$443$	1.81076e33i	1.50596i	−0.658043	+	0.752980i	$0.728615\pi$
$444$	8.44387e31	0.0682739
$445$	0	0
$446$	1.57193e33	1.20156
$447$	1.09899e32i	0.0816866i
$448$	1.93063e32i	0.139548i
$449$	−1.96738e33	−1.38296	−0.691480	−	0.722396i	$-0.743041\pi$
$449$	−1.96738e33	−1.38296	−0.691480	+	0.722396i	$0.743041\pi$
$450$	0	0
$451$	−3.38807e33	−2.25292
$452$	− 7.70148e32i	− 0.498131i
$453$	2.59763e31i	0.0163437i
$454$	1.17308e32	0.0718006
$455$	0	0
$456$	9.42369e31	0.0545960
$457$	− 6.51681e32i	− 0.367352i	−0.982987	−	0.183676i	$-0.941200\pi$
$457$	− 6.51681e32i	− 0.367352i	0.982987	−	0.183676i	$-0.0587997\pi$
$458$	2.12178e33i	1.16381i
$459$	−4.38289e32	−0.233939
$460$	0	0
$461$	−3.73344e32	−0.188733	−0.0943666	−	0.995538i	$-0.530083\pi$
$461$	−3.73344e32	−0.188733	−0.0943666	+	0.995538i	$0.530083\pi$
$462$	− 2.37949e32i	− 0.117074i
$463$	− 3.92901e33i	− 1.88157i	−0.338999	−	0.940787i	$-0.610088\pi$
$463$	− 3.92901e33i	− 1.88157i	0.338999	−	0.940787i	$-0.389912\pi$
$464$	−5.85533e32	−0.272946
$465$	0	0
$466$	4.56655e32	0.201727
$467$	− 2.19321e33i	− 0.943235i	−0.881803	−	0.471618i	$-0.843670\pi$
$467$	− 2.19321e33i	− 0.943235i	0.881803	−	0.471618i	$-0.156330\pi$
$468$	1.23457e33i	0.516944i
$469$	−5.09807e33	−2.07848
$470$	0	0
$471$	−8.15315e31	−0.0315184
$472$	5.73045e32i	0.215732i
$473$	− 5.82187e32i	− 0.213451i
$474$	−3.23097e32	−0.115373
$475$	0	0
$476$	1.82135e33	0.617030
$477$	− 3.56079e32i	− 0.117508i
$478$	4.01989e33i	1.29230i
$479$	4.26617e33	1.33612	0.668058	−	0.744110i	$-0.267126\pi$
$479$	4.26617e33	1.33612	0.668058	+	0.744110i	$0.267126\pi$
$480$	0	0
$481$	−4.51339e33	−1.34180
$482$	4.10805e33i	1.19000i
$483$	3.43815e32i	0.0970477i
$484$	−1.71268e33	−0.471095
$485$	0	0
$486$	−8.51111e32	−0.222348
$487$	2.19049e33i	0.557737i	0.960329	+	0.278869i	$0.0899594\pi$
$487$	2.19049e33i	0.557737i	−0.960329	+	0.278869i	$0.910041\pi$
$488$	1.66974e33i	0.414383i
$489$	7.07517e32	0.171150
$490$	0	0
$491$	−1.06443e32	−0.0244681	−0.0122340	−	0.999925i	$-0.503894\pi$
$491$	−1.06443e32	−0.0244681	−0.0122340	+	0.999925i	$0.503894\pi$
$492$	3.83839e32i	0.0860172i
$493$	5.52390e33i	1.20687i
$494$	−5.03712e33	−1.07299
$495$	0	0
$496$	7.49718e32	0.151837
$497$	3.80409e33i	0.751269i
$498$	3.60437e30i	0 0.000694165i
$499$	3.46371e33	0.650555	0.325278	−	0.945619i	$-0.394542\pi$
$499$	3.46371e33	0.650555	0.325278	+	0.945619i	$0.394542\pi$
$500$	0	0
$501$	3.74684e32	0.0669413
$502$	− 4.70607e33i	− 0.820090i
$503$	− 1.02261e34i	− 1.73824i	−0.494599	−	0.869121i	$-0.664685\pi$
$503$	− 1.02261e34i	− 1.73824i	0.494599	−	0.869121i	$-0.335315\pi$
$504$	2.35344e33	0.390231
$505$	0	0
$506$	5.10116e33	0.804984
$507$	6.46663e31i	0.00995585i
$508$	6.14275e31i	0.00922713i
$509$	2.69685e33	0.395261	0.197630	−	0.980277i	$-0.436675\pi$
$509$	2.69685e33	0.395261	0.197630	+	0.980277i	$0.436675\pi$
$510$	0	0
$511$	−1.65255e33	−0.230618
$512$	− 3.24519e32i	− 0.0441942i
$513$	− 2.31066e33i	− 0.307093i
$514$	5.26147e33	0.682445
$515$	0	0
$516$	−6.59567e31	−0.00814963
$517$	− 4.05922e33i	− 0.489566i
$518$	8.60379e33i	1.01290i
$519$	4.64674e32	0.0534018
$520$	0	0
$521$	−9.39972e33	−1.02954	−0.514770	−	0.857328i	$-0.672123\pi$
$521$	−9.39972e33	−1.02954	−0.514770	+	0.857328i	$0.672123\pi$
$522$	7.13767e33i	0.763265i
$523$	4.23584e33i	0.442250i	0.975245	+	0.221125i	$0.0709729\pi$
$523$	4.23584e33i	0.442250i	−0.975245	+	0.221125i	$0.929027\pi$
$524$	2.31338e33	0.235833
$525$	0	0
$526$	1.01203e34	0.983724
$527$	− 7.07281e33i	− 0.671366i
$528$	3.99968e32i	0.0370767i
$529$	3.67507e33	0.332713
$530$	0	0
$531$	6.98544e33	0.603271
$532$	9.60216e33i	0.809979i
$533$	− 2.05168e34i	− 1.69052i
$534$	1.42677e33	0.114839
$535$	0	0
$536$	8.56932e33	0.658244
$537$	− 6.84880e32i	− 0.0513968i
$538$	3.41170e33i	0.250145i
$539$	4.79172e33	0.343267
$540$	0	0
$541$	3.36042e33	0.229841	0.114921	−	0.993375i	$-0.463339\pi$
$541$	3.36042e33	0.229841	0.114921	+	0.993375i	$0.463339\pi$
$542$	1.59678e33i	0.106722i
$543$	6.21740e32i	0.0406080i
$544$	−3.06150e33	−0.195410
$545$	0	0
$546$	1.44093e33	0.0878484
$547$	− 1.80091e33i	− 0.107313i	−0.998559	−	0.0536563i	$-0.982912\pi$
$547$	− 1.80091e33i	− 0.107313i	0.998559	−	0.0536563i	$-0.0170875\pi$
$548$	7.25247e33i	0.422405i
$549$	2.03542e34	1.15878
$550$	0	0
$551$	−2.91220e34	−1.58426
$552$	− 5.77917e32i	− 0.0307345i
$553$	− 3.29216e34i	− 1.71166i
$554$	2.35857e34	1.19888
$555$	0	0
$556$	−6.72172e32	−0.0326622
$557$	3.61276e34i	1.71652i	0.513214	+	0.858261i	$0.328455\pi$
$557$	3.61276e34i	1.71652i	−0.513214	+	0.858261i	$0.671545\pi$
$558$	− 9.13909e33i	− 0.424596i
$559$	3.52550e33	0.160167
$560$	0	0
$561$	3.77328e33	0.163940
$562$	3.00952e33i	0.127877i
$563$	− 2.65943e34i	− 1.10518i	−0.833452	−	0.552591i	$-0.813639\pi$
$563$	− 2.65943e34i	− 1.10518i	0.833452	−	0.552591i	$-0.186361\pi$
$564$	−4.59875e32	−0.0186918
$565$	0	0
$566$	4.73876e33	0.184272
$567$	− 2.83562e34i	− 1.07860i
$568$	− 6.39428e33i	− 0.237923i
$569$	−7.96966e33	−0.290093	−0.145046	−	0.989425i	$-0.546333\pi$
$569$	−7.96966e33	−0.290093	−0.145046	+	0.989425i	$0.546333\pi$
$570$	0	0
$571$	4.13744e34	1.44139	0.720693	−	0.693254i	$-0.243824\pi$
$571$	4.13744e34	1.44139	0.720693	+	0.693254i	$0.243824\pi$
$572$	− 2.13789e34i	− 0.728678i
$573$	3.51901e33i	0.117351i
$574$	−3.91108e34	−1.27614
$575$	0	0
$576$	−3.95589e33	−0.123584
$577$	− 3.07665e34i	− 0.940548i	−0.882520	−	0.470274i	$-0.844155\pi$
$577$	− 3.07665e34i	− 0.940548i	0.882520	−	0.470274i	$-0.155845\pi$
$578$	5.24558e33i	0.156926i
$579$	3.68573e32	0.0107905
$580$	0	0
$581$	−3.67263e32	−0.0102985
$582$	3.47483e33i	0.0953666i
$583$	6.16617e33i	0.165637i
$584$	2.77776e33	0.0730356
$585$	0	0
$586$	4.08143e33	0.102824
$587$	− 2.58213e34i	− 0.636798i	−0.947957	−	0.318399i	$-0.896855\pi$
$587$	− 2.58213e34i	− 0.636798i	0.947957	−	0.318399i	$-0.103145\pi$
$588$	− 5.42860e32i	− 0.0131060i
$589$	3.72879e34	0.881307
$590$	0	0
$591$	−1.80708e33	−0.0409386
$592$	− 1.44621e34i	− 0.320781i
$593$	− 4.00098e34i	− 0.868925i	−0.900690	−	0.434463i	$-0.856938\pi$
$593$	− 4.00098e34i	− 0.868925i	0.900690	−	0.434463i	$-0.143062\pi$
$594$	9.80710e33	0.208550
$595$	0	0
$596$	1.88228e34	0.383801
$597$	3.16920e33i	0.0632806i
$598$	3.08906e34i	0.604034i
$599$	2.84196e34	0.544230	0.272115	−	0.962265i	$-0.412277\pi$
$599$	2.84196e34	0.544230	0.272115	+	0.962265i	$0.412277\pi$
$600$	0	0
$601$	−1.02008e34	−0.187371	−0.0936856	−	0.995602i	$-0.529865\pi$
$601$	−1.02008e34	−0.187371	−0.0936856	+	0.995602i	$0.529865\pi$
$602$	− 6.72058e33i	− 0.120907i
$603$	− 1.04460e35i	− 1.84071i
$604$	4.44904e33	0.0767900
$605$	0	0
$606$	−2.92246e33	−0.0483996
$607$	7.37377e34i	1.19628i	0.801393	+	0.598138i	$0.204092\pi$
$607$	7.37377e34i	1.19628i	−0.801393	+	0.598138i	$0.795908\pi$
$608$	− 1.61402e34i	− 0.256516i
$609$	8.33070e33	0.129708
$610$	0	0
$611$	2.45811e34	0.367355
$612$	3.73198e34i	0.546445i
$613$	9.86145e34i	1.41477i	0.706830	+	0.707384i	$0.250125\pi$
$613$	9.86145e34i	1.41477i	−0.706830	+	0.707384i	$0.749875\pi$
$614$	4.57127e34	0.642587
$615$	0	0
$616$	−4.07543e34	−0.550065
$617$	− 6.22897e34i	− 0.823857i	−0.911216	−	0.411928i	$-0.864855\pi$
$617$	− 6.22897e34i	− 0.823857i	0.911216	−	0.411928i	$-0.135145\pi$
$618$	6.11440e33i	0.0792497i
$619$	1.66187e34	0.211089	0.105544	−	0.994415i	$-0.466341\pi$
$619$	1.66187e34	0.211089	0.105544	+	0.994415i	$0.466341\pi$
$620$	0	0
$621$	−1.41704e34	−0.172876
$622$	3.47060e34i	0.414978i
$623$	1.45379e35i	1.70373i
$624$	−2.42205e33	−0.0278212
$625$	0	0
$626$	4.74246e34	0.523389
$627$	1.98928e34i	0.215204i
$628$	1.39641e34i	0.148088i
$629$	−1.36435e35	−1.41838
$630$	0	0
$631$	−5.71133e34	−0.570650	−0.285325	−	0.958431i	$-0.592102\pi$
$631$	−5.71133e34	−0.570650	−0.285325	+	0.958431i	$0.592102\pi$
$632$	5.53377e34i	0.542073i
$633$	− 7.19801e33i	− 0.0691299i
$634$	−8.07696e34	−0.760558
$635$	0	0
$636$	6.98573e32	0.00632409
$637$	2.90168e34i	0.257576i
$638$	− 1.23602e35i	− 1.07589i
$639$	−7.79465e34	−0.665328
$640$	0	0
$641$	1.28313e34	0.105329	0.0526643	−	0.998612i	$-0.483229\pi$
$641$	1.28313e34	0.105329	0.0526643	+	0.998612i	$0.483229\pi$
$642$	2.51572e33i	0.0202523i
$643$	1.37614e35i	1.08649i	0.839574	+	0.543246i	$0.182805\pi$
$643$	1.37614e35i	1.08649i	−0.839574	+	0.543246i	$0.817195\pi$
$644$	5.88862e34	0.455974
$645$	0	0
$646$	−1.52266e35	−1.13422
$647$	9.39917e34i	0.686730i	0.939202	+	0.343365i	$0.111567\pi$
$647$	9.39917e34i	0.686730i	−0.939202	+	0.343365i	$0.888433\pi$
$648$	4.76638e34i	0.341587i
$649$	−1.20966e35	−0.850364
$650$	0	0
$651$	−1.06666e34	−0.0721549
$652$	− 1.21179e35i	− 0.804139i
$653$	1.48718e35i	0.968164i	0.875023	+	0.484082i	$0.160846\pi$
$653$	1.48718e35i	0.968164i	−0.875023	+	0.484082i	$0.839154\pi$
$654$	−6.66921e33	−0.0425944
$655$	0	0
$656$	6.57412e34	0.404148
$657$	− 3.38611e34i	− 0.204237i
$658$	− 4.68584e34i	− 0.277309i
$659$	1.21873e35	0.707683	0.353842	−	0.935305i	$-0.384875\pi$
$659$	1.21873e35	0.707683	0.353842	+	0.935305i	$0.384875\pi$
$660$	0	0
$661$	2.07522e35	1.16023	0.580117	−	0.814533i	$-0.303007\pi$
$661$	2.07522e35	1.16023	0.580117	+	0.814533i	$0.303007\pi$
$662$	− 1.95425e35i	− 1.07215i
$663$	2.28495e34i	0.123015i
$664$	6.17331e32	0.00326150
$665$	0	0
$666$	−1.76293e35	−0.897032
$667$	1.78594e35i	0.891852i
$668$	− 6.41733e34i	− 0.314520i
$669$	3.75927e34	0.180833
$670$	0	0
$671$	−3.52471e35	−1.63340
$672$	4.61710e33i	0.0210017i
$673$	2.63064e34i	0.117455i	0.998274	+	0.0587277i	$0.0187044\pi$
$673$	2.63064e34i	0.117455i	−0.998274	+	0.0587277i	$0.981296\pi$
$674$	−1.34642e35	−0.590110
$675$	0	0
$676$	1.10756e34	0.0467771
$677$	1.31255e35i	0.544198i	0.962269	+	0.272099i	$0.0877179\pi$
$677$	1.31255e35i	0.544198i	−0.962269	+	0.272099i	$0.912282\pi$
$678$	− 1.84181e34i	− 0.0749677i
$679$	−3.54064e35	−1.41485
$680$	0	0
$681$	2.80542e33	0.0108058
$682$	1.58260e35i	0.598505i
$683$	4.53998e35i	1.68576i	0.538104	+	0.842879i	$0.319141\pi$
$683$	4.53998e35i	1.68576i	−0.538104	+	0.842879i	$0.680859\pi$
$684$	−1.96750e35	−0.717321
$685$	0	0
$686$	−1.69255e35	−0.594963
$687$	5.07426e34i	0.175151i
$688$	1.12966e34i	0.0382906i
$689$	−3.73399e34	−0.124289
$690$	0	0
$691$	1.42914e35	0.458773	0.229387	−	0.973335i	$-0.426328\pi$
$691$	1.42914e35	0.458773	0.229387	+	0.973335i	$0.426328\pi$
$692$	− 7.95860e34i	− 0.250906i
$693$	4.96796e35i	1.53820i
$694$	1.28300e35	0.390152
$695$	0	0
$696$	−1.40030e34	−0.0410778
$697$	− 6.20201e35i	− 1.78699i
$698$	1.38366e35i	0.391593i
$699$	1.09209e34	0.0303595
$700$	0	0
$701$	4.38686e35	1.17673	0.588367	−	0.808594i	$-0.299771\pi$
$701$	4.38686e35	1.17673	0.588367	+	0.808594i	$0.299771\pi$
$702$	5.93879e34i	0.156489i
$703$	− 7.19285e35i	− 1.86191i
$704$	6.85037e34	0.174203
$705$	0	0
$706$	−1.79602e35	−0.440811
$707$	− 2.97781e35i	− 0.718050i
$708$	1.37044e34i	0.0324672i
$709$	−3.53471e35	−0.822766	−0.411383	−	0.911463i	$-0.634954\pi$
$709$	−3.53471e35	−0.822766	−0.411383	+	0.911463i	$0.634954\pi$
$710$	0	0
$711$	6.74569e35	1.51585
$712$	− 2.44367e35i	− 0.539563i
$713$	− 2.28672e35i	− 0.496127i
$714$	4.35576e34	0.0928617
$715$	0	0
$716$	−1.17301e35	−0.241485
$717$	9.61357e34i	0.194489i
$718$	− 6.16148e35i	− 1.22498i
$719$	−8.06410e35	−1.57560	−0.787798	−	0.615934i	$-0.788779\pi$
$719$	−8.06410e35	−1.57560	−0.787798	+	0.615934i	$0.788779\pi$
$720$	0	0
$721$	−6.23019e35	−1.17574
$722$	− 4.21509e35i	− 0.781793i
$723$	9.82443e34i	0.179093i
$724$	1.06487e35	0.190794
$725$	0	0
$726$	−4.09587e34	−0.0708987
$727$	− 4.49933e35i	− 0.765539i	−0.923844	−	0.382770i	$-0.874970\pi$
$727$	− 4.49933e35i	− 0.765539i	0.923844	−	0.382770i	$-0.125030\pi$
$728$	− 2.46792e35i	− 0.412751i
$729$	5.67325e35	0.932691
$730$	0	0
$731$	1.06572e35	0.169307
$732$	3.99320e34i	0.0623637i
$733$	1.09791e36i	1.68565i	0.538185	+	0.842827i	$0.319110\pi$
$733$	1.09791e36i	1.68565i	−0.538185	+	0.842827i	$0.680890\pi$
$734$	−2.83974e35	−0.428626
$735$	0	0
$736$	−9.89815e34	−0.144405
$737$	1.80893e36i	2.59464i
$738$	− 8.01388e35i	− 1.13016i
$739$	6.34879e35	0.880309	0.440155	−	0.897922i	$-0.354924\pi$
$739$	6.34879e35	0.880309	0.440155	+	0.897922i	$0.354924\pi$
$740$	0	0
$741$	−1.20463e35	−0.161483
$742$	7.11803e34i	0.0938234i
$743$	6.17895e35i	0.800856i	0.916328	+	0.400428i	$0.131139\pi$
$743$	6.17895e35i	0.800856i	−0.916328	+	0.400428i	$0.868861\pi$
$744$	1.79295e34	0.0228511
$745$	0	0
$746$	−2.51662e35	−0.310158
$747$	− 7.52529e33i	− 0.00912044i
$748$	− 6.46262e35i	− 0.770262i
$749$	−2.56337e35	−0.300461
$750$	0	0
$751$	6.31220e35	0.715619	0.357809	−	0.933795i	$-0.383524\pi$
$751$	6.31220e35	0.715619	0.357809	+	0.933795i	$0.383524\pi$
$752$	7.87641e34i	0.0878224i
$753$	− 1.12546e35i	− 0.123422i
$754$	7.48486e35	0.807312
$755$	0	0
$756$	1.13210e35	0.118131
$757$	2.78268e35i	0.285605i	0.989751	+	0.142802i	$0.0456113\pi$
$757$	2.78268e35i	0.285605i	−0.989751	+	0.142802i	$0.954389\pi$
$758$	2.56401e35i	0.258854i
$759$	1.21994e35	0.121148
$760$	0	0
$761$	2.91390e35	0.280005	0.140003	−	0.990151i	$-0.455289\pi$
$761$	2.91390e35	0.280005	0.140003	+	0.990151i	$0.455289\pi$
$762$	1.46904e33i	0.00138866i
$763$	− 6.79552e35i	− 0.631926i
$764$	6.02712e35	0.551369
$765$	0	0
$766$	−8.02238e35	−0.710303
$767$	− 7.32523e35i	− 0.638086i
$768$	− 7.76087e33i	− 0.00665113i
$769$	1.59678e36	1.34637	0.673187	−	0.739473i	$-0.264925\pi$
$769$	1.59678e36	1.34637	0.673187	+	0.739473i	$0.264925\pi$
$770$	0	0
$771$	1.25828e35	0.102707
$772$	− 6.31267e34i	− 0.0506987i
$773$	− 1.26764e36i	− 1.00173i	−0.865525	−	0.500866i	$-0.833015\pi$
$773$	− 1.26764e36i	− 1.00173i	0.865525	−	0.500866i	$-0.166985\pi$
$774$	1.37706e35	0.107076
$775$	0	0
$776$	5.95144e35	0.448075
$777$	2.05760e35i	0.152440i
$778$	− 2.27695e35i	− 0.166000i
$779$	3.26970e36	2.34580
$780$	0	0
$781$	1.34979e36	0.937838
$782$	9.33788e35i	0.638505i
$783$	3.43351e35i	0.231055i
$784$	−9.29772e34	−0.0615780
$785$	0	0
$786$	5.53245e34	0.0354924
$787$	1.69750e36i	1.07183i	0.844272	+	0.535915i	$0.180033\pi$
$787$	1.69750e36i	1.07183i	−0.844272	+	0.535915i	$0.819967\pi$
$788$	3.09503e35i	0.192348i
$789$	2.42028e35	0.148048
$790$	0	0
$791$	1.87669e36	1.11221
$792$	− 8.35063e35i	− 0.487141i
$793$	− 2.13443e36i	− 1.22565i
$794$	−1.64129e36	−0.927748
$795$	0	0
$796$	5.42798e35	0.297321
$797$	− 1.94040e36i	− 1.04631i	−0.852236	−	0.523157i	$-0.824754\pi$
$797$	− 1.94040e36i	− 1.04631i	0.852236	−	0.523157i	$-0.175246\pi$
$798$	2.29636e35i	0.121900i
$799$	7.43058e35	0.388319
$800$	0	0
$801$	−2.97884e36	−1.50883
$802$	1.14608e36i	0.571525i
$803$	5.86368e35i	0.287889i
$804$	2.04936e35	0.0990643
$805$	0	0
$806$	−9.58363e35	−0.449099
$807$	8.15908e34i	0.0376463i
$808$	5.00539e35i	0.227403i
$809$	−8.07086e35	−0.361047	−0.180523	−	0.983571i	$-0.557779\pi$
$809$	−8.07086e35	−0.361047	−0.180523	+	0.983571i	$0.557779\pi$
$810$	0	0
$811$	1.23381e36	0.535165	0.267583	−	0.963535i	$-0.413775\pi$
$811$	1.23381e36	0.535165	0.267583	+	0.963535i	$0.413775\pi$
$812$	− 1.42682e36i	− 0.609424i
$813$	3.81872e34i	0.0160615i
$814$	3.05285e36	1.26445
$815$	0	0
$816$	−7.32158e34	−0.0294088
$817$	5.61847e35i	0.222250i
$818$	− 2.95796e36i	− 1.15233i
$819$	−3.00840e36	−1.15422
$820$	0	0
$821$	−6.01008e34	−0.0223661	−0.0111831	−	0.999937i	$-0.503560\pi$
$821$	−6.01008e34	−0.0223661	−0.0111831	+	0.999937i	$0.503560\pi$
$822$	1.73443e35i	0.0635710i
$823$	− 1.64344e36i	− 0.593274i	−0.954990	−	0.296637i	$-0.904135\pi$
$823$	− 1.64344e36i	− 0.593274i	0.954990	−	0.296637i	$-0.0958652\pi$
$824$	1.04723e36	0.372351
$825$	0	0
$826$	−1.39639e36	−0.481679
$827$	4.86438e36i	1.65276i	0.563116	+	0.826378i	$0.309602\pi$
$827$	4.86438e36i	1.65276i	−0.563116	+	0.826378i	$0.690398\pi$
$828$	1.20659e36i	0.403813i
$829$	1.30083e36	0.428834	0.214417	−	0.976742i	$-0.431215\pi$
$829$	1.30083e36	0.428834	0.214417	+	0.976742i	$0.431215\pi$
$830$	0	0
$831$	5.64053e35	0.180429
$832$	4.14832e35i	0.130716i
$833$	8.77144e35i	0.272275i
$834$	−1.60750e34	−0.00491560
$835$	0	0
$836$	3.40710e36	1.01113
$837$	− 4.39627e35i	− 0.128533i
$838$	2.10154e36i	0.605323i
$839$	3.56272e36	1.01101	0.505506	−	0.862823i	$-0.331306\pi$
$839$	3.56272e36	1.01101	0.505506	+	0.862823i	$0.331306\pi$
$840$	0	0
$841$	6.96997e35	0.191991
$842$	5.36538e35i	0.145613i
$843$	7.19727e34i	0.0192452i
$844$	−1.23282e36	−0.324803
$845$	0	0
$846$	9.60138e35	0.245586
$847$	− 4.17344e36i	− 1.05184i
$848$	− 1.19647e35i	− 0.0297134i
$849$	1.13328e35	0.0277325
$850$	0	0
$851$	−4.41108e36	−1.04816
$852$	− 1.52919e35i	− 0.0358070i
$853$	2.91289e36i	0.672142i	0.941837	+	0.336071i	$0.109098\pi$
$853$	2.91289e36i	0.672142i	−0.941837	+	0.336071i	$0.890902\pi$
$854$	−4.06882e36	−0.925220
$855$	0	0
$856$	4.30876e35	0.0951546
$857$	− 6.85495e36i	− 1.49192i	−0.665993	−	0.745958i	$-0.731992\pi$
$857$	− 6.85495e36i	− 1.49192i	0.665993	−	0.745958i	$-0.268008\pi$
$858$	− 5.11278e35i	− 0.109665i
$859$	−6.94361e36	−1.46781	−0.733907	−	0.679250i	$-0.762305\pi$
$859$	−6.94361e36	−1.46781	−0.733907	+	0.679250i	$0.762305\pi$
$860$	0	0
$861$	−9.35337e35	−0.192056
$862$	− 1.74097e36i	− 0.352331i
$863$	5.37478e35i	0.107208i	0.998562	+	0.0536038i	$0.0170708\pi$
$863$	5.37478e35i	0.107208i	−0.998562	+	0.0536038i	$0.982929\pi$
$864$	−1.90294e35	−0.0374114
$865$	0	0
$866$	−8.93846e35	−0.170722
$867$	1.25448e35i	0.0236171i
$868$	1.82691e36i	0.339016i
$869$	−1.16814e37	−2.13673
$870$	0	0
$871$	−1.09542e37	−1.94694
$872$	1.14226e36i	0.200128i
$873$	− 7.25483e36i	− 1.25300i
$874$	−4.92294e36	−0.838169
$875$	0	0
$876$	6.64304e34	0.0109917
$877$	1.45532e36i	0.237391i	0.992931	+	0.118695i	$0.0378712\pi$
$877$	1.45532e36i	0.237391i	−0.992931	+	0.118695i	$0.962129\pi$
$878$	8.02985e36i	1.29130i
$879$	9.76076e34	0.0154747
$880$	0	0
$881$	7.73993e36	1.19272	0.596360	−	0.802717i	$-0.296613\pi$
$881$	7.73993e36	1.19272	0.596360	+	0.802717i	$0.296613\pi$
$882$	1.13340e36i	0.172197i
$883$	1.08821e35i	0.0163006i	0.999967	+	0.00815031i	$0.00259435\pi$
$883$	1.08821e35i	0.0163006i	−0.999967	+	0.00815031i	$0.997406\pi$
$884$	3.91351e36	0.577980
$885$	0	0
$886$	7.41686e36	1.06488
$887$	− 7.82913e36i	− 1.10833i	−0.832407	−	0.554164i	$-0.813038\pi$
$887$	− 7.82913e36i	− 1.10833i	0.832407	−	0.554164i	$-0.186962\pi$
$888$	− 3.45861e35i	− 0.0482769i
$889$	−1.49686e35	−0.0206020
$890$	0	0
$891$	−1.00615e37	−1.34646
$892$	− 6.43861e36i	− 0.849634i
$893$	3.91741e36i	0.509748i
$894$	4.50148e35	0.0577612
$895$	0	0
$896$	7.90785e35	0.0986753
$897$	7.38750e35i	0.0909059i
$898$	8.05840e36i	0.977900i
$899$	−5.54076e36	−0.663091
$900$	0	0
$901$	−1.12874e36	−0.131382
$902$	1.38775e37i	1.59305i
$903$	− 1.60723e35i	− 0.0181962i
$904$	−3.15453e36	−0.352232
$905$	0	0
$906$	1.06399e35	0.0115567
$907$	1.06412e36i	0.113999i	0.998374	+	0.0569993i	$0.0181533\pi$
$907$	1.06412e36i	0.113999i	−0.998374	+	0.0569993i	$0.981847\pi$
$908$	− 4.80492e35i	− 0.0507707i
$909$	6.10159e36	0.635909
$910$	0	0
$911$	7.34268e36	0.744517	0.372259	−	0.928129i	$-0.378583\pi$
$911$	7.34268e36	0.744517	0.372259	+	0.928129i	$0.378583\pi$
$912$	− 3.85994e35i	− 0.0386052i
$913$	1.30314e35i	0.0128561i
$914$	−2.66928e36	−0.259757
$915$	0	0
$916$	8.69083e36	0.822939
$917$	5.63723e36i	0.526561i
$918$	1.79523e36i	0.165420i
$919$	−5.22115e36	−0.474594	−0.237297	−	0.971437i	$-0.576262\pi$
$919$	−5.22115e36	−0.474594	−0.237297	+	0.971437i	$0.576262\pi$
$920$	0	0
$921$	1.09322e36	0.0967080
$922$	1.52922e36i	0.133454i
$923$	8.17379e36i	0.703724i
$924$	−9.74640e35	−0.0827836
$925$	0	0
$926$	−1.60932e37	−1.33047
$927$	− 1.27658e37i	− 1.04124i
$928$	2.39834e36i	0.193002i
$929$	1.16329e37	0.923618	0.461809	−	0.886979i	$-0.347201\pi$
$929$	1.16329e37	0.923618	0.461809	+	0.886979i	$0.347201\pi$
$930$	0	0
$931$	−4.62431e36	−0.357418
$932$	− 1.87046e36i	− 0.142643i
$933$	8.29996e35i	0.0624533i
$934$	−8.98341e36	−0.666968
$935$	0	0
$936$	5.05681e36	0.365535
$937$	5.72513e36i	0.408358i	0.978934	+	0.204179i	$0.0654524\pi$
$937$	5.72513e36i	0.408358i	−0.978934	+	0.204179i	$0.934548\pi$
$938$	2.08817e37i	1.46970i
$939$	1.13416e36	0.0787690
$940$	0	0
$941$	−2.32727e37	−1.57390	−0.786950	−	0.617016i	$-0.788341\pi$
$941$	−2.32727e37	−1.57390	−0.786950	+	0.617016i	$0.788341\pi$
$942$	3.33953e35i	0.0222869i
$943$	− 2.00518e37i	− 1.32055i
$944$	2.34719e36	0.152545
$945$	0	0
$946$	−2.38464e36	−0.150933
$947$	2.10624e37i	1.31563i	0.753180	+	0.657814i	$0.228519\pi$
$947$	2.10624e37i	1.31563i	−0.753180	+	0.657814i	$0.771481\pi$
$948$	1.32340e36i	0.0815809i
$949$	−3.55081e36	−0.216023
$950$	0	0
$951$	−1.93161e36	−0.114462
$952$	− 7.46024e36i	− 0.436306i
$953$	1.00956e36i	0.0582736i	0.999575	+	0.0291368i	$0.00927584\pi$
$953$	1.00956e36i	0.0582736i	−0.999575	+	0.0291368i	$0.990724\pi$
$954$	−1.45850e36	−0.0830905
$955$	0	0
$956$	1.64654e37	0.913797
$957$	− 2.95595e36i	− 0.161919i
$958$	− 1.74742e37i	− 0.944776i
$959$	−1.76728e37	−0.943131
$960$	0	0
$961$	−1.21384e37	−0.631130
$962$	1.84868e37i	0.948799i
$963$	− 5.25239e36i	− 0.266090i
$964$	1.68266e37	0.841459
$965$	0	0
$966$	1.40826e36	0.0686231
$967$	5.41536e36i	0.260493i	0.991482	+	0.130247i	$0.0415769\pi$
$967$	5.41536e36i	0.260493i	−0.991482	+	0.130247i	$0.958423\pi$
$968$	7.01512e36i	0.333114i
$969$	−3.64146e36	−0.170698
$970$	0	0
$971$	−5.44528e36	−0.248759	−0.124380	−	0.992235i	$-0.539694\pi$
$971$	−5.44528e36	−0.248759	−0.124380	+	0.992235i	$0.539694\pi$
$972$	3.48615e36i	0.157224i
$973$	− 1.63795e36i	− 0.0729271i
$974$	8.97226e36	0.394380
$975$	0	0
$976$	6.83926e36	0.293013
$977$	− 3.00155e37i	− 1.26959i	−0.772681	−	0.634794i	$-0.781085\pi$
$977$	− 3.00155e37i	− 1.26959i	0.772681	−	0.634794i	$-0.218915\pi$
$978$	− 2.89799e36i	− 0.121021i
$979$	5.15842e37	2.12683
$980$	0	0
$981$	1.39242e37	0.559637
$982$	4.35992e35i	0.0173015i
$983$	− 2.29888e36i	− 0.0900737i	−0.998985	−	0.0450368i	$-0.985659\pi$
$983$	− 2.29888e36i	− 0.0900737i	0.998985	−	0.0450368i	$-0.0143405\pi$
$984$	1.57220e36	0.0608233
$985$	0	0
$986$	2.26259e37	0.853383
$987$	− 1.12062e36i	− 0.0417344i
$988$	2.06320e37i	0.758718i
$989$	3.44558e36	0.125115
$990$	0	0
$991$	9.88586e36	0.350021	0.175010	−	0.984567i	$-0.444004\pi$
$991$	9.88586e36	0.350021	0.175010	+	0.984567i	$0.444004\pi$
$992$	− 3.07084e36i	− 0.107365i
$993$	− 4.67360e36i	− 0.161356i
$994$	1.55815e37	0.531228
$995$	0	0
$996$	1.47635e34	0.000490848 0
$997$	2.20132e37i	0.722759i	0.932419	+	0.361380i	$0.117694\pi$
$997$	2.20132e37i	0.722759i	−0.932419	+	0.361380i	$0.882306\pi$
$998$	− 1.41873e37i	− 0.460012i
$999$	−8.48041e36	−0.271549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.b.a.49.1		2
5.2	odd	4		50.26.a.b.1.1		1
5.3	odd	4		2.26.a.a.1.1	✓	1
5.4	even	2	inner	50.26.b.a.49.2		2
15.8	even	4		18.26.a.c.1.1		1
20.3	even	4		16.26.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.26.a.a.1.1	✓	1	5.3	odd	4
16.26.a.a.1.1		1	20.3	even	4
18.26.a.c.1.1		1	15.8	even	4
50.26.a.b.1.1		1	5.2	odd	4
50.26.b.a.49.1		2	1.1	even	1	trivial
50.26.b.a.49.2		2	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4096.00i q^{2} -97956.0i q^{3} -1.67772e7 q^{4} -4.01228e8 q^{6} -4.08826e10i q^{7} +6.87195e10i q^{8} +8.37693e11 q^{9} +O(q^{10})\)	\(q-4096.00i q^{2} -97956.0i q^{3} -1.67772e7 q^{4} -4.01228e8 q^{6} -4.08826e10i q^{7} +6.87195e10i q^{8} +8.37693e11 q^{9} -1.45062e13 q^{11} +1.64343e12i q^{12} -8.78440e13i q^{13} -1.67455e14 q^{14} +2.81475e14 q^{16} -2.65543e15i q^{17} -3.43119e15i q^{18} +1.39994e16 q^{19} -4.00470e15 q^{21} +5.94175e16i q^{22} -8.58528e16i q^{23} +6.73149e15 q^{24} -3.59809e17 q^{26} -1.65054e17i q^{27} +6.85897e17i q^{28} -2.08023e18 q^{29} +2.66353e18 q^{31} -1.15292e18i q^{32} +1.42097e18i q^{33} -1.08766e19 q^{34} -1.40542e19 q^{36} -5.13796e19i q^{37} -5.73416e19i q^{38} -8.60485e18 q^{39} +2.33560e20 q^{41} +1.64032e19i q^{42} +4.01336e19i q^{43} +2.43374e20 q^{44} -3.51653e20 q^{46} +2.79826e20i q^{47} -2.75722e19i q^{48} -3.30321e20 q^{49} -2.60115e20 q^{51} +1.47378e21i q^{52} -4.25070e20i q^{53} -6.76062e20 q^{54} +2.80943e21 q^{56} -1.37133e21i q^{57} +8.52062e21i q^{58} +8.33891e21 q^{59} +2.42979e22 q^{61} -1.09098e22i q^{62} -3.42471e22i q^{63} -4.72237e21 q^{64} +5.82030e21 q^{66} -1.24700e23i q^{67} +4.45507e22i q^{68} -8.40979e21 q^{69} -9.30490e22 q^{71} +5.75658e22i q^{72} -4.04218e22i q^{73} -2.10451e23 q^{74} -2.34871e23 q^{76} +5.93053e23i q^{77} +3.52454e22i q^{78} +8.05270e23 q^{79} +6.93600e23 q^{81} -9.56661e23i q^{82} -8.98335e21i q^{83} +6.71877e22 q^{84} +1.64387e23 q^{86} +2.03771e23i q^{87} -9.96860e23i q^{88} -3.55600e24 q^{89} -3.59129e24 q^{91} +1.44037e24i q^{92} -2.60909e23i q^{93} +1.14617e24 q^{94} -1.12936e23 q^{96} -8.66049e24i q^{97} +1.35300e24i q^{98} -1.21518e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 33554432 q^{4} - 802455552 q^{6} + 1675386463014 q^{9}+O(q^{10}) \) 2 * q - 33554432 * q^4 - 802455552 * q^6 + 1675386463014 * q^9	\( 2 q - 33554432 q^{4} - 802455552 q^{6} + 1675386463014 q^{9} - 29012444754216 q^{11} - 334910565318656 q^{14} + 562949953421312 q^{16} + 27\!\cdots\!80 q^{19}+ \cdots - 24\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 33554432 * q^4 - 802455552 * q^6 + 1675386463014 * q^9 - 29012444754216 * q^11 - 334910565318656 * q^14 + 562949953421312 * q^16 + 27998849408195480 * q^19 - 8009399252039616 * q^21 + 13462970126303232 * q^24 - 719617962287153152 * q^26 - 4160460859203053820 * q^29 + 5327064742605350464 * q^31 - 21753248717919338496 * q^34 - 28108320573461889024 * q^36 - 17209691678173919472 * q^39 + 467119614568450661844 * q^41 + 486748052329548742656 * q^44 - 703305979691298127872 * q^46 - 660642836998850133234 * q^49 - 520229792825319023856 * q^51 - 1352123033289508454400 * q^54 + 5618866895033200541696 * q^56 + 16677810543100138197960 * q^59 + 48595896938126376273724 * q^61 - 9444732965739290427392 * q^64 + 11640598685056952303616 * q^66 - 16819589977207226419392 * q^69 - 186097965393815479969776 * q^71 - 420901748574744053497856 * q^74 - 469742744272767738183680 * q^76 + 1610540227078311978788960 * q^79 + 1387199791368333628082802 * q^81 + 134375421281707078189056 * q^84 + 328774427400024995299328 * q^86 - 7112009273819794670044980 * q^89 - 7182587938399605028880416 * q^91 + 2292337828143166425268224 * q^94 - 225871157810536604762112 * q^96 - 24303528600077511402283512 * q^99

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