LMFDB - Embedded newform 25.10.b.c.24.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,10,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, 10, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 10 $
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:	$12.8758959041$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 1305x^{4} + 433104x^{2} + 16000000 $ x^6 + 1305x^4 + 433104x^2 + 16000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.6
Root			$27.7229i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.10.b.c.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31.7828i q^{2} -268.664i q^{3} -498.143 q^{4} +8538.88 q^{6} -637.237i q^{7} +440.406i q^{8} -52497.3 q^{9} +O(q^{10})$	\(q+31.7828i q^{2} -268.664i q^{3} -498.143 q^{4} +8538.88 q^{6} -637.237i q^{7} +440.406i q^{8} -52497.3 q^{9} -49042.6 q^{11} +133833. i q^{12} +72726.2i q^{13} +20253.2 q^{14} -269047. q^{16} -67319.3i q^{17} -1.66851e6i q^{18} -341136. q^{19} -171203. q^{21} -1.55871e6i q^{22} -134355. i q^{23} +118321. q^{24} -2.31144e6 q^{26} +8.81603e6i q^{27} +317435. i q^{28} -4.45784e6 q^{29} +456520. q^{31} -8.32555e6i q^{32} +1.31760e7i q^{33} +2.13959e6 q^{34} +2.61512e7 q^{36} -1.30516e7i q^{37} -1.08422e7i q^{38} +1.95389e7 q^{39} -2.56667e7 q^{41} -5.44129e6i q^{42} +3.42710e6i q^{43} +2.44302e7 q^{44} +4.27016e6 q^{46} +3.39814e7i q^{47} +7.22831e7i q^{48} +3.99475e7 q^{49} -1.80863e7 q^{51} -3.62281e7i q^{52} -8.42456e7i q^{53} -2.80198e8 q^{54} +280643. q^{56} +9.16509e7i q^{57} -1.41682e8i q^{58} +7.46358e7 q^{59} +1.78017e8 q^{61} +1.45094e7i q^{62} +3.34533e7i q^{63} +1.26857e8 q^{64} -4.18769e8 q^{66} -6.94299e7i q^{67} +3.35347e7i q^{68} -3.60963e7 q^{69} -2.07860e8 q^{71} -2.31201e7i q^{72} -3.02516e8i q^{73} +4.14815e8 q^{74} +1.69935e8 q^{76} +3.12518e7i q^{77} +6.21000e8i q^{78} -3.72244e8 q^{79} +1.33524e9 q^{81} -8.15758e8i q^{82} +4.50079e8i q^{83} +8.52835e7 q^{84} -1.08923e8 q^{86} +1.19766e9i q^{87} -2.15987e7i q^{88} -5.82741e7 q^{89} +4.63438e7 q^{91} +6.69279e7i q^{92} -1.22650e8i q^{93} -1.08002e9 q^{94} -2.23678e9 q^{96} -7.85850e8i q^{97} +1.26964e9i q^{98} +2.57461e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 682 q^{4} + 6842 q^{6} - 116468 q^{9}+O(q^{10}) $ 6 * q - 682 * q^4 + 6842 * q^6 - 116468 * q^9	$ 6 q - 682 q^{4} + 6842 q^{6} - 116468 q^{9} - 109398 q^{11} - 545844 q^{14} - 1398494 q^{16} - 1637690 q^{19} - 4750788 q^{21} - 5611470 q^{24} - 2560008 q^{26} - 4350960 q^{29} + 8548132 q^{31} + 13677926 q^{34} + 53591596 q^{36} + 100828184 q^{39} + 11852622 q^{41} + 43991406 q^{44} + 28446492 q^{46} + 12907858 q^{49} - 51269398 q^{51} - 564500990 q^{54} - 339076260 q^{56} - 11341920 q^{59} + 250613852 q^{61} - 335084802 q^{64} - 1113831686 q^{66} + 628549884 q^{69} + 595101192 q^{71} + 503014716 q^{74} + 178829730 q^{76} + 620050340 q^{79} + 2797694726 q^{81} - 76534164 q^{84} + 67894392 q^{86} + 2207720070 q^{89} + 2366375312 q^{91} - 3455782264 q^{94} - 5134360898 q^{96} + 1784469044 q^{99}+O(q^{100}) $ 6 * q - 682 * q^4 + 6842 * q^6 - 116468 * q^9 - 109398 * q^11 - 545844 * q^14 - 1398494 * q^16 - 1637690 * q^19 - 4750788 * q^21 - 5611470 * q^24 - 2560008 * q^26 - 4350960 * q^29 + 8548132 * q^31 + 13677926 * q^34 + 53591596 * q^36 + 100828184 * q^39 + 11852622 * q^41 + 43991406 * q^44 + 28446492 * q^46 + 12907858 * q^49 - 51269398 * q^51 - 564500990 * q^54 - 339076260 * q^56 - 11341920 * q^59 + 250613852 * q^61 - 335084802 * q^64 - 1113831686 * q^66 + 628549884 * q^69 + 595101192 * q^71 + 503014716 * q^74 + 178829730 * q^76 + 620050340 * q^79 + 2797694726 * q^81 - 76534164 * q^84 + 67894392 * q^86 + 2207720070 * q^89 + 2366375312 * q^91 - 3455782264 * q^94 - 5134360898 * q^96 + 1784469044 * 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 $

$2$	31.7828i	1.40461i	0.711875	+	0.702306i	$0.247846\pi$
$2$	31.7828i	1.40461i	−0.711875	+	0.702306i	$0.752154\pi$
$3$	− 268.664i	− 1.91498i	−0.288470	−	0.957489i	$-0.593146\pi$
$3$	− 268.664i	− 1.91498i	0.288470	−	0.957489i	$-0.406854\pi$
$4$	−498.143	−0.972936
$5$	0	0
$5$	0	0
$6$	8538.88	2.68980
$7$	− 637.237i	− 0.100314i	−0.998741	−	0.0501568i	$-0.984028\pi$
$7$	− 637.237i	− 0.100314i	0.998741	−	0.0501568i	$-0.0159721\pi$
$8$	440.406i	0.0380144i
$9$	−52497.3	−2.66714
$10$	0	0
$11$	−49042.6	−1.00996	−0.504982	−	0.863130i	$-0.668501\pi$
$11$	−49042.6	−1.00996	−0.504982	+	0.863130i	$0.668501\pi$
$12$	133833.i	1.86315i
$13$	72726.2i	0.706229i	0.935580	+	0.353115i	$0.114877\pi$
$13$	72726.2i	0.706229i	−0.935580	+	0.353115i	$0.885123\pi$
$14$	20253.2	0.140902
$15$	0	0
$16$	−269047.	−1.02633
$17$	− 67319.3i	− 0.195488i	−0.995212	−	0.0977439i	$-0.968837\pi$
$17$	− 67319.3i	− 0.195488i	0.995212	−	0.0977439i	$-0.0311626\pi$
$18$	− 1.66851e6i	− 3.74630i
$19$	−341136.	−0.600532	−0.300266	−	0.953855i	$-0.597075\pi$
$19$	−341136.	−0.600532	−0.300266	+	0.953855i	$0.597075\pi$
$20$	0	0
$21$	−171203.	−0.192098
$22$	− 1.55871e6i	− 1.41861i
$23$	− 134355.i	− 0.100110i	−0.998746	−	0.0500550i	$-0.984060\pi$
$23$	− 134355.i	− 0.100110i	0.998746	−	0.0500550i	$-0.0159397\pi$
$24$	118321.	0.0727968
$25$	0	0
$26$	−2.31144e6	−0.991978
$27$	8.81603e6i	3.19254i
$28$	317435.i	0.0975988i
$29$	−4.45784e6	−1.17040	−0.585199	−	0.810890i	$-0.698984\pi$
$29$	−4.45784e6	−1.17040	−0.585199	+	0.810890i	$0.698984\pi$
$30$	0	0
$31$	456520.	0.0887834	0.0443917	−	0.999014i	$-0.485865\pi$
$31$	456520.	0.0887834	0.0443917	+	0.999014i	$0.485865\pi$
$32$	− 8.32555e6i	− 1.40358i
$33$	1.31760e7i	1.93406i
$34$	2.13959e6	0.274585
$35$	0	0
$36$	2.61512e7	2.59496
$37$	− 1.30516e7i	− 1.14487i	−0.819951	−	0.572433i	$-0.805999\pi$
$37$	− 1.30516e7i	− 1.14487i	0.819951	−	0.572433i	$-0.194001\pi$
$38$	− 1.08422e7i	− 0.843515i
$39$	1.95389e7	1.35241
$40$	0	0
$41$	−2.56667e7	−1.41854	−0.709272	−	0.704935i	$-0.750976\pi$
$41$	−2.56667e7	−1.41854	−0.709272	+	0.704935i	$0.750976\pi$
$42$	− 5.44129e6i	− 0.269824i
$43$	3.42710e6i	0.152869i	0.997075	+	0.0764344i	$0.0243536\pi$
$43$	3.42710e6i	0.152869i	−0.997075	+	0.0764344i	$0.975646\pi$
$44$	2.44302e7	0.982631
$45$	0	0
$46$	4.27016e6	0.140616
$47$	3.39814e7i	1.01578i	0.861421	+	0.507891i	$0.169575\pi$
$47$	3.39814e7i	1.01578i	−0.861421	+	0.507891i	$0.830425\pi$
$48$	7.22831e7i	1.96540i
$49$	3.99475e7	0.989937
$50$	0	0
$51$	−1.80863e7	−0.374355
$52$	− 3.62281e7i	− 0.687116i
$53$	− 8.42456e7i	− 1.46658i	−0.679916	−	0.733290i	$-0.737984\pi$
$53$	− 8.42456e7i	− 1.46658i	0.679916	−	0.733290i	$-0.262016\pi$
$54$	−2.80198e8	−4.48428
$55$	0	0
$56$	280643.	0.00381337
$57$	9.16509e7i	1.15001i
$58$	− 1.41682e8i	− 1.64396i
$59$	7.46358e7	0.801887	0.400944	−	0.916103i	$-0.368682\pi$
$59$	7.46358e7	0.801887	0.400944	+	0.916103i	$0.368682\pi$
$60$	0	0
$61$	1.78017e8	1.64618	0.823088	−	0.567913i	$-0.192249\pi$
$61$	1.78017e8	1.64618	0.823088	+	0.567913i	$0.192249\pi$
$62$	1.45094e7i	0.124706i
$63$	3.34533e7i	0.267551i
$64$	1.26857e8	0.945159
$65$	0	0
$66$	−4.18769e8	−2.71661
$67$	− 6.94299e7i	− 0.420930i	−0.977601	−	0.210465i	$-0.932502\pi$
$67$	− 6.94299e7i	− 0.420930i	0.977601	−	0.210465i	$-0.0674978\pi$
$68$	3.35347e7i	0.190197i
$69$	−3.60963e7	−0.191708
$70$	0	0
$71$	−2.07860e8	−0.970753	−0.485376	−	0.874305i	$-0.661317\pi$
$71$	−2.07860e8	−0.970753	−0.485376	+	0.874305i	$0.661317\pi$
$72$	− 2.31201e7i	− 0.101390i
$73$	− 3.02516e8i	− 1.24680i	−0.781905	−	0.623398i	$-0.785752\pi$
$73$	− 3.02516e8i	− 1.24680i	0.781905	−	0.623398i	$-0.214248\pi$
$74$	4.14815e8	1.60809
$75$	0	0
$76$	1.69935e8	0.584279
$77$	3.12518e7i	0.101313i
$78$	6.21000e8i	1.89962i
$79$	−3.72244e8	−1.07524	−0.537621	−	0.843187i	$-0.680677\pi$
$79$	−3.72244e8	−1.07524	−0.537621	+	0.843187i	$0.680677\pi$
$80$	0	0
$81$	1.33524e9	3.44650
$82$	− 8.15758e8i	− 1.99250i
$83$	4.50079e8i	1.04097i	0.853872	+	0.520484i	$0.174248\pi$
$83$	4.50079e8i	1.04097i	−0.853872	+	0.520484i	$0.825752\pi$
$84$	8.52835e7	0.186899
$85$	0	0
$86$	−1.08923e8	−0.214721
$87$	1.19766e9i	2.24129i
$88$	− 2.15987e7i	− 0.0383932i
$89$	−5.82741e7	−0.0984511	−0.0492255	−	0.998788i	$-0.515675\pi$
$89$	−5.82741e7	−0.0984511	−0.0492255	+	0.998788i	$0.515675\pi$
$90$	0	0
$91$	4.63438e7	0.0708444
$92$	6.69279e7i	0.0974006i
$93$	− 1.22650e8i	− 0.170018i
$94$	−1.08002e9	−1.42678
$95$	0	0
$96$	−2.23678e9	−2.68783
$97$	− 7.85850e8i	− 0.901295i	−0.892702	−	0.450647i	$-0.851193\pi$
$97$	− 7.85850e8i	− 0.901295i	0.892702	−	0.450647i	$-0.148807\pi$
$98$	1.26964e9i	1.39048i
$99$	2.57461e9	2.69372
$100$	0	0
$101$	−1.60460e8	−0.153433	−0.0767167	−	0.997053i	$-0.524444\pi$
$101$	−1.60460e8	−0.153433	−0.0767167	+	0.997053i	$0.524444\pi$
$102$	− 5.74832e8i	− 0.525823i
$103$	− 1.39454e9i	− 1.22085i	−0.792074	−	0.610425i	$-0.790999\pi$
$103$	− 1.39454e9i	− 1.22085i	0.792074	−	0.610425i	$-0.209001\pi$
$104$	−3.20291e7	−0.0268469
$105$	0	0
$106$	2.67756e9	2.05998
$107$	1.56463e9i	1.15394i	0.816764	+	0.576972i	$0.195766\pi$
$107$	1.56463e9i	1.15394i	−0.816764	+	0.576972i	$0.804234\pi$
$108$	− 4.39165e9i	− 3.10614i
$109$	−1.24703e9	−0.846172	−0.423086	−	0.906089i	$-0.639053\pi$
$109$	−1.24703e9	−0.846172	−0.423086	+	0.906089i	$0.639053\pi$
$110$	0	0
$111$	−3.50649e9	−2.19240
$112$	1.71447e8i	0.102955i
$113$	− 1.81056e9i	− 1.04463i	−0.852754	−	0.522313i	$-0.825069\pi$
$113$	− 1.81056e9i	− 1.04463i	0.852754	−	0.522313i	$-0.174931\pi$
$114$	−2.91292e9	−1.61531
$115$	0	0
$116$	2.22064e9	1.13872
$117$	− 3.81793e9i	− 1.88361i
$118$	2.37213e9i	1.12634i
$119$	−4.28984e7	−0.0196101
$120$	0	0
$121$	4.72275e7	0.0200291
$122$	5.65786e9i	2.31224i
$123$	6.89572e9i	2.71648i
$124$	−2.27412e8	−0.0863806
$125$	0	0
$126$	−1.06324e9	−0.375805
$127$	3.06491e9i	1.04545i	0.852503	+	0.522723i	$0.175084\pi$
$127$	3.06491e9i	1.04545i	−0.852503	+	0.522723i	$0.824916\pi$
$128$	− 2.30815e8i	− 0.0760010i
$129$	9.20739e8	0.292740
$130$	0	0
$131$	−1.83508e9	−0.544421	−0.272211	−	0.962238i	$-0.587755\pi$
$131$	−1.83508e9	−0.544421	−0.272211	+	0.962238i	$0.587755\pi$
$132$	− 6.56352e9i	− 1.88172i
$133$	2.17385e8i	0.0602416i
$134$	2.20667e9	0.591243
$135$	0	0
$136$	2.96478e7	0.00743136
$137$	4.62426e9i	1.12150i	0.827984	+	0.560751i	$0.189488\pi$
$137$	4.62426e9i	1.12150i	−0.827984	+	0.560751i	$0.810512\pi$
$138$	− 1.14724e9i	− 0.269276i
$139$	−2.57140e8	−0.0584255	−0.0292128	−	0.999573i	$-0.509300\pi$
$139$	−2.57140e8	−0.0584255	−0.0292128	+	0.999573i	$0.509300\pi$
$140$	0	0
$141$	9.12958e9	1.94520
$142$	− 6.60637e9i	− 1.36353i
$143$	− 3.56668e9i	− 0.713267i
$144$	1.41242e10	2.73737
$145$	0	0
$146$	9.61479e9	1.75127
$147$	− 1.07325e10i	− 1.89571i
$148$	6.50155e9i	1.11388i
$149$	−3.14809e9	−0.523250	−0.261625	−	0.965170i	$-0.584258\pi$
$149$	−3.14809e9	−0.523250	−0.261625	+	0.965170i	$0.584258\pi$
$150$	0	0
$151$	−1.02772e10	−1.60871	−0.804356	−	0.594147i	$-0.797490\pi$
$151$	−1.02772e10	−1.60871	−0.804356	+	0.594147i	$0.797490\pi$
$152$	− 1.50238e8i	− 0.0228289i
$153$	3.53408e9i	0.521393i
$154$	−9.93267e8	−0.142306
$155$	0	0
$156$	−9.73317e9	−1.31581
$157$	− 3.25077e9i	− 0.427009i	−0.976942	−	0.213505i	$-0.931512\pi$
$157$	− 3.25077e9i	− 0.427009i	0.976942	−	0.213505i	$-0.0684878\pi$
$158$	− 1.18309e10i	− 1.51030i
$159$	−2.26338e10	−2.80847
$160$	0	0
$161$	−8.56158e7	−0.0100424
$162$	4.24377e10i	4.84100i
$163$	3.40049e9i	0.377309i	0.982043	+	0.188655i	$0.0604127\pi$
$163$	3.40049e9i	0.377309i	−0.982043	+	0.188655i	$0.939587\pi$
$164$	1.27857e10	1.38015
$165$	0	0
$166$	−1.43047e10	−1.46216
$167$	− 5.27785e9i	− 0.525089i	−0.964920	−	0.262544i	$-0.915438\pi$
$167$	− 5.27785e9i	− 0.525089i	0.964920	−	0.262544i	$-0.0845616\pi$
$168$	− 7.53987e7i	− 0.00730251i
$169$	5.31540e9	0.501240
$170$	0	0
$171$	1.79087e10	1.60170
$172$	− 1.70719e9i	− 0.148732i
$173$	6.58861e9i	0.559224i	0.960113	+	0.279612i	$0.0902059\pi$
$173$	6.58861e9i	0.559224i	−0.960113	+	0.279612i	$0.909794\pi$
$174$	−3.80650e10	−3.14814
$175$	0	0
$176$	1.31947e10	1.03656
$177$	− 2.00520e10i	− 1.53560i
$178$	− 1.85211e9i	− 0.138286i
$179$	1.23663e10	0.900326	0.450163	−	0.892946i	$-0.351366\pi$
$179$	1.23663e10	0.900326	0.450163	+	0.892946i	$0.351366\pi$
$180$	0	0
$181$	−2.59914e10	−1.80002	−0.900009	−	0.435872i	$-0.856440\pi$
$181$	−2.59914e10	−1.80002	−0.900009	+	0.435872i	$0.856440\pi$
$182$	1.47293e9i	0.0995090i
$183$	− 4.78267e10i	− 3.15239i
$184$	5.91706e7	0.00380562
$185$	0	0
$186$	3.89817e9	0.238810
$187$	3.30151e9i	0.197436i
$188$	− 1.69276e10i	− 0.988292i
$189$	5.61790e9	0.320255
$190$	0	0
$191$	1.50506e10	0.818284	0.409142	−	0.912471i	$-0.365828\pi$
$191$	1.50506e10	0.818284	0.409142	+	0.912471i	$0.365828\pi$
$192$	− 3.40819e10i	− 1.80996i
$193$	1.40329e10i	0.728014i	0.931396	+	0.364007i	$0.118592\pi$
$193$	1.40329e10i	0.728014i	−0.931396	+	0.364007i	$0.881408\pi$
$194$	2.49765e10	1.26597
$195$	0	0
$196$	−1.98996e10	−0.963146
$197$	2.57285e10i	1.21707i	0.793526	+	0.608536i	$0.208243\pi$
$197$	2.57285e10i	1.21707i	−0.793526	+	0.608536i	$0.791757\pi$
$198$	8.18280e10i	3.78363i
$199$	2.94367e10	1.33061	0.665303	−	0.746573i	$-0.268302\pi$
$199$	2.94367e10	1.33061	0.665303	+	0.746573i	$0.268302\pi$
$200$	0	0
$201$	−1.86533e10	−0.806072
$202$	− 5.09985e9i	− 0.215515i
$203$	2.84070e9i	0.117407i
$204$	9.00956e9	0.364223
$205$	0	0
$206$	4.43222e10	1.71482
$207$	7.05326e9i	0.267007i
$208$	− 1.95667e10i	− 0.724825i
$209$	1.67302e10	0.606516
$210$	0	0
$211$	1.17275e10	0.407319	0.203659	−	0.979042i	$-0.434716\pi$
$211$	1.17275e10	0.407319	0.203659	+	0.979042i	$0.434716\pi$
$212$	4.19664e10i	1.42689i
$213$	5.58445e10i	1.85897i
$214$	−4.97283e10	−1.62084
$215$	0	0
$216$	−3.88263e9	−0.121363
$217$	− 2.90911e8i	− 0.00890619i
$218$	− 3.96341e10i	− 1.18854i
$219$	−8.12751e10	−2.38759
$220$	0	0
$221$	4.89588e9	0.138059
$222$	− 1.11446e11i	− 3.07947i
$223$	2.58340e10i	0.699550i	0.936834	+	0.349775i	$0.113742\pi$
$223$	2.58340e10i	0.699550i	−0.936834	+	0.349775i	$0.886258\pi$
$224$	−5.30535e9	−0.140799
$225$	0	0
$226$	5.75447e10	1.46729
$227$	2.50896e10i	0.627159i	0.949562	+	0.313580i	$0.101528\pi$
$227$	2.50896e10i	0.627159i	−0.949562	+	0.313580i	$0.898472\pi$
$228$	− 4.56553e10i	− 1.11888i
$229$	2.30463e10	0.553785	0.276892	−	0.960901i	$-0.410695\pi$
$229$	2.30463e10	0.553785	0.276892	+	0.960901i	$0.410695\pi$
$230$	0	0
$231$	8.39622e9	0.194013
$232$	− 1.96326e9i	− 0.0444920i
$233$	3.17197e10i	0.705062i	0.935800	+	0.352531i	$0.114679\pi$
$233$	3.17197e10i	0.705062i	−0.935800	+	0.352531i	$0.885321\pi$
$234$	1.21344e11	2.64575
$235$	0	0
$236$	−3.71793e10	−0.780185
$237$	1.00009e11i	2.05906i
$238$	− 1.36343e9i	− 0.0275446i
$239$	−2.23794e10	−0.443668	−0.221834	−	0.975084i	$-0.571204\pi$
$239$	−2.23794e10	−0.443668	−0.221834	+	0.975084i	$0.571204\pi$
$240$	0	0
$241$	−2.10823e10	−0.402569	−0.201285	−	0.979533i	$-0.564512\pi$
$241$	−2.10823e10	−0.402569	−0.201285	+	0.979533i	$0.564512\pi$
$242$	1.50102e9i	0.0281331i
$243$	− 1.85206e11i	− 3.40743i
$244$	−8.86778e10	−1.60162
$245$	0	0
$246$	−2.19165e11	−3.81560
$247$	− 2.48095e10i	− 0.424113i
$248$	2.01054e8i	0.00337505i
$249$	1.20920e11	1.99343
$250$	0	0
$251$	−7.96509e10	−1.26666	−0.633329	−	0.773883i	$-0.718312\pi$
$251$	−7.96509e10	−1.26666	−0.633329	+	0.773883i	$0.718312\pi$
$252$	− 1.66645e10i	− 0.260310i
$253$	6.58910e9i	0.101108i
$254$	−9.74114e10	−1.46845
$255$	0	0
$256$	7.22868e10	1.05191
$257$	3.30815e10i	0.473027i	0.971628	+	0.236514i	$0.0760048\pi$
$257$	3.30815e10i	0.473027i	−0.971628	+	0.236514i	$0.923995\pi$
$258$	2.92636e10i	0.411187i
$259$	−8.31695e9	−0.114846
$260$	0	0
$261$	2.34025e11	3.12162
$262$	− 5.83240e10i	− 0.764701i
$263$	6.05028e10i	0.779784i	0.920861	+	0.389892i	$0.127488\pi$
$263$	6.05028e10i	0.779784i	−0.920861	+	0.389892i	$0.872512\pi$
$264$	−5.80278e9	−0.0735222
$265$	0	0
$266$	−6.90908e9	−0.0846161
$267$	1.56562e10i	0.188532i
$268$	3.45860e10i	0.409538i
$269$	−2.61933e10	−0.305004	−0.152502	−	0.988303i	$-0.548733\pi$
$269$	−2.61933e10	−0.305004	−0.152502	+	0.988303i	$0.548733\pi$
$270$	0	0
$271$	5.42857e10	0.611398	0.305699	−	0.952128i	$-0.401110\pi$
$271$	5.42857e10	0.611398	0.305699	+	0.952128i	$0.401110\pi$
$272$	1.81120e10i	0.200635i
$273$	− 1.24509e10i	− 0.135666i
$274$	−1.46972e11	−1.57528
$275$	0	0
$276$	1.79811e10	0.186520
$277$	− 1.76561e11i	− 1.80192i	−0.433900	−	0.900961i	$-0.642863\pi$
$277$	− 1.76561e11i	− 1.80192i	0.433900	−	0.900961i	$-0.357137\pi$
$278$	− 8.17261e9i	− 0.0820652i
$279$	−2.39661e10	−0.236798
$280$	0	0
$281$	−7.91126e9	−0.0756950	−0.0378475	−	0.999284i	$-0.512050\pi$
$281$	−7.91126e9	−0.0756950	−0.0378475	+	0.999284i	$0.512050\pi$
$282$	2.90163e11i	2.73225i
$283$	− 1.34806e11i	− 1.24931i	−0.780899	−	0.624657i	$-0.785239\pi$
$283$	− 1.34806e11i	− 1.24931i	0.780899	−	0.624657i	$-0.214761\pi$
$284$	1.03544e11	0.944480
$285$	0	0
$286$	1.13359e11	1.00186
$287$	1.63558e10i	0.142299i
$288$	4.37069e11i	3.74356i
$289$	1.14056e11	0.961785
$290$	0	0
$291$	−2.11130e11	−1.72596
$292$	1.50696e11i	1.21305i
$293$	1.02784e11i	0.814741i	0.913263	+	0.407370i	$0.133554\pi$
$293$	1.02784e11i	0.814741i	−0.913263	+	0.407370i	$0.866446\pi$
$294$	3.41107e11	2.66273
$295$	0	0
$296$	5.74799e9	0.0435215
$297$	− 4.32361e11i	− 3.22435i
$298$	− 1.00055e11i	− 0.734964i
$299$	9.77110e9	0.0707006
$300$	0	0
$301$	2.18388e9	0.0153348
$302$	− 3.26638e11i	− 2.25962i
$303$	4.31098e10i	0.293822i
$304$	9.17815e10	0.616345
$305$	0	0
$306$	−1.12323e11	−0.732356
$307$	2.61472e11i	1.67998i	0.542606	+	0.839988i	$0.317438\pi$
$307$	2.61472e11i	1.67998i	−0.542606	+	0.839988i	$0.682562\pi$
$308$	− 1.55679e10i	− 0.0985713i
$309$	−3.74662e11	−2.33790
$310$	0	0
$311$	−8.24828e10	−0.499967	−0.249984	−	0.968250i	$-0.580425\pi$
$311$	−8.24828e10	−0.499967	−0.249984	+	0.968250i	$0.580425\pi$
$312$	8.60505e9i	0.0514112i
$313$	− 1.35766e11i	− 0.799540i	−0.916615	−	0.399770i	$-0.869090\pi$
$313$	− 1.35766e11i	− 0.799540i	0.916615	−	0.399770i	$-0.130910\pi$
$314$	1.03318e11	0.599783
$315$	0	0
$316$	1.85431e11	1.04614
$317$	9.06853e10i	0.504394i	0.967676	+	0.252197i	$0.0811531\pi$
$317$	9.06853e10i	0.504394i	−0.967676	+	0.252197i	$0.918847\pi$
$318$	− 7.19363e11i	− 3.94481i
$319$	2.18624e11	1.18206
$320$	0	0
$321$	4.20360e11	2.20978
$322$	− 2.72111e9i	− 0.0141057i
$323$	2.29650e10i	0.117397i
$324$	−6.65143e11	−3.35322
$325$	0	0
$326$	−1.08077e11	−0.529973
$327$	3.35033e11i	1.62040i
$328$	− 1.13038e10i	− 0.0539251i
$329$	2.16542e10	0.101897
$330$	0	0
$331$	−3.45169e11	−1.58054	−0.790271	−	0.612758i	$-0.790060\pi$
$331$	−3.45169e11	−1.58054	−0.790271	+	0.612758i	$0.790060\pi$
$332$	− 2.24204e11i	− 1.01279i
$333$	6.85173e11i	3.05352i
$334$	1.67745e11	0.737546
$335$	0	0
$336$	4.60615e10	0.197157
$337$	− 8.39418e10i	− 0.354523i	−0.984164	−	0.177261i	$-0.943276\pi$
$337$	− 8.39418e10i	− 0.354523i	0.984164	−	0.177261i	$-0.0567238\pi$
$338$	1.68938e11i	0.704048i
$339$	−4.86433e11	−2.00043
$340$	0	0
$341$	−2.23889e10	−0.0896681
$342$	5.69189e11i	2.24977i
$343$	− 5.11709e10i	− 0.199618i
$344$	−1.50932e9	−0.00581122
$345$	0	0
$346$	−2.09404e11	−0.785493
$347$	− 1.56153e11i	− 0.578188i	−0.957301	−	0.289094i	$-0.906646\pi$
$347$	− 1.56153e11i	− 0.578188i	0.957301	−	0.289094i	$-0.0933540\pi$
$348$	− 5.96607e11i	− 2.18063i
$349$	−6.31862e9	−0.0227986	−0.0113993	−	0.999935i	$-0.503629\pi$
$349$	−6.31862e9	−0.0227986	−0.0113993	+	0.999935i	$0.503629\pi$
$350$	0	0
$351$	−6.41156e11	−2.25466
$352$	4.08307e11i	1.41757i
$353$	− 2.83875e11i	− 0.973064i	−0.873663	−	0.486532i	$-0.838262\pi$
$353$	− 2.83875e11i	− 0.973064i	0.873663	−	0.486532i	$-0.161738\pi$
$354$	6.37307e11	2.15692
$355$	0	0
$356$	2.90288e10	0.0957866
$357$	1.15253e10i	0.0375529i
$358$	3.93034e11i	1.26461i
$359$	−6.00733e11	−1.90878	−0.954391	−	0.298558i	$-0.903494\pi$
$359$	−6.00733e11	−1.90878	−0.954391	+	0.298558i	$0.903494\pi$
$360$	0	0
$361$	−2.06314e11	−0.639361
$362$	− 8.26079e11i	− 2.52833i
$363$	− 1.26883e10i	− 0.0383552i
$364$	−2.30859e10	−0.0689271
$365$	0	0
$366$	1.52006e12	4.42789
$367$	− 4.97260e11i	− 1.43082i	−0.698702	−	0.715412i	$-0.746239\pi$
$367$	− 4.97260e11i	− 1.43082i	0.698702	−	0.715412i	$-0.253761\pi$
$368$	3.61477e10i	0.102746i
$369$	1.34743e12	3.78346
$370$	0	0
$371$	−5.36845e10	−0.147118
$372$	6.10974e10i	0.165417i
$373$	1.39183e11i	0.372303i	0.982521	+	0.186151i	$0.0596015\pi$
$373$	1.39183e11i	0.372303i	−0.982521	+	0.186151i	$0.940398\pi$
$374$	−1.04931e11	−0.277321
$375$	0	0
$376$	−1.49656e10	−0.0386144
$377$	− 3.24202e11i	− 0.826569i
$378$	1.78552e11i	0.449834i
$379$	5.65247e11	1.40722	0.703610	−	0.710587i	$-0.251570\pi$
$379$	5.65247e11	1.40722	0.703610	+	0.710587i	$0.251570\pi$
$380$	0	0
$381$	8.23432e11	2.00201
$382$	4.78350e11i	1.14937i
$383$	− 5.38864e11i	− 1.27963i	−0.768528	−	0.639816i	$-0.779011\pi$
$383$	− 5.38864e11i	− 1.27963i	0.768528	−	0.639816i	$-0.220989\pi$
$384$	−6.20117e10	−0.145540
$385$	0	0
$386$	−4.46004e11	−1.02258
$387$	− 1.79914e11i	− 0.407723i
$388$	3.91466e11i	0.876902i
$389$	−7.67552e11	−1.69955	−0.849776	−	0.527144i	$-0.823263\pi$
$389$	−7.67552e11	−1.69955	−0.849776	+	0.527144i	$0.823263\pi$
$390$	0	0
$391$	−9.04466e9	−0.0195703
$392$	1.75931e10i	0.0376319i
$393$	4.93021e11i	1.04255i
$394$	−8.17722e11	−1.70951
$395$	0	0
$396$	−1.28252e12	−2.62082
$397$	6.25258e11i	1.26329i	0.775259	+	0.631643i	$0.217619\pi$
$397$	6.25258e11i	1.26329i	−0.775259	+	0.631643i	$0.782381\pi$
$398$	9.35578e11i	1.86899i
$399$	5.84034e10	0.115361
$400$	0	0
$401$	−1.61329e11	−0.311574	−0.155787	−	0.987791i	$-0.549791\pi$
$401$	−1.61329e11	−0.311574	−0.155787	+	0.987791i	$0.549791\pi$
$402$	− 5.92853e11i	− 1.13222i
$403$	3.32009e10i	0.0627014i
$404$	7.99320e10	0.149281
$405$	0	0
$406$	−9.02853e10	−0.164911
$407$	6.40083e11i	1.15628i
$408$	− 7.96531e9i	− 0.0142309i
$409$	7.24004e11	1.27934	0.639670	−	0.768649i	$-0.279071\pi$
$409$	7.24004e11	1.27934	0.639670	+	0.768649i	$0.279071\pi$
$410$	0	0
$411$	1.24237e12	2.14765
$412$	6.94679e11i	1.18781i
$413$	− 4.75607e10i	− 0.0804403i
$414$	−2.24172e11	−0.375042
$415$	0	0
$416$	6.05486e11	0.991252
$417$	6.90842e10i	0.111884i
$418$	5.31731e11i	0.851920i
$419$	−2.80040e11	−0.443871	−0.221936	−	0.975061i	$-0.571237\pi$
$419$	−2.80040e11	−0.443871	−0.221936	+	0.975061i	$0.571237\pi$
$420$	0	0
$421$	−6.55915e10	−0.101760	−0.0508801	−	0.998705i	$-0.516203\pi$
$421$	−6.55915e10	−0.101760	−0.0508801	+	0.998705i	$0.516203\pi$
$422$	3.72732e11i	0.572125i
$423$	− 1.78393e12i	− 2.70924i
$424$	3.71023e10	0.0557512
$425$	0	0
$426$	−1.77489e12	−2.61113
$427$	− 1.13439e11i	− 0.165134i
$428$	− 7.79410e11i	− 1.12271i
$429$	−9.58239e11	−1.36589
$430$	0	0
$431$	1.00292e12	1.39997	0.699987	−	0.714156i	$-0.253189\pi$
$431$	1.00292e12	1.39997	0.699987	+	0.714156i	$0.253189\pi$
$432$	− 2.37192e12i	− 3.27660i
$433$	− 7.98482e11i	− 1.09162i	−0.837910	−	0.545808i	$-0.816223\pi$
$433$	− 7.98482e11i	− 1.09162i	0.837910	−	0.545808i	$-0.183777\pi$
$434$	9.24596e9	0.0125097
$435$	0	0
$436$	6.21201e11	0.823271
$437$	4.58332e10i	0.0601193i
$438$	− 2.58315e12i	− 3.35363i
$439$	−7.98379e11	−1.02593	−0.512966	−	0.858409i	$-0.671453\pi$
$439$	−7.98379e11	−1.02593	−0.512966	+	0.858409i	$0.671453\pi$
$440$	0	0
$441$	−2.09714e12	−2.64030
$442$	1.55604e11i	0.193920i
$443$	7.56642e11i	0.933413i	0.884412	+	0.466707i	$0.154560\pi$
$443$	7.56642e11i	0.933413i	−0.884412	+	0.466707i	$0.845440\pi$
$444$	1.74673e12	2.13306
$445$	0	0
$446$	−8.21074e11	−0.982597
$447$	8.45779e11i	1.00201i
$448$	− 8.08381e10i	− 0.0948124i
$449$	6.39419e11	0.742467	0.371234	−	0.928540i	$-0.378935\pi$
$449$	6.39419e11	0.742467	0.371234	+	0.928540i	$0.378935\pi$
$450$	0	0
$451$	1.25876e12	1.43268
$452$	9.01919e11i	1.01635i
$453$	2.76111e12i	3.08065i
$454$	−7.97418e11	−0.880916
$455$	0	0
$456$	−4.03636e10	−0.0437168
$457$	− 1.34276e12i	− 1.44005i	−0.693949	−	0.720024i	$-0.744131\pi$
$457$	− 1.34276e12i	− 1.44005i	0.693949	−	0.720024i	$-0.255869\pi$
$458$	7.32474e11i	0.777853i
$459$	5.93489e11	0.624102
$460$	0	0
$461$	3.47112e11	0.357945	0.178972	−	0.983854i	$-0.442723\pi$
$461$	3.47112e11	0.357945	0.178972	+	0.983854i	$0.442723\pi$
$462$	2.66855e11i	0.272513i
$463$	− 7.20214e11i	− 0.728362i	−0.931328	−	0.364181i	$-0.881349\pi$
$463$	− 7.20214e11i	− 0.728362i	0.931328	−	0.364181i	$-0.118651\pi$
$464$	1.19937e12	1.20122
$465$	0	0
$466$	−1.00814e12	−0.990339
$467$	− 7.31553e10i	− 0.0711737i	−0.999367	−	0.0355869i	$-0.988670\pi$
$467$	− 7.31553e10i	− 0.0711737i	0.999367	−	0.0355869i	$-0.0113300\pi$
$468$	1.90188e12i	1.83264i
$469$	−4.42433e10	−0.0422250
$470$	0	0
$471$	−8.73364e11	−0.817713
$472$	3.28701e10i	0.0304833i
$473$	− 1.68074e11i	− 0.154392i
$474$	−3.17855e12	−2.89219
$475$	0	0
$476$	2.13695e10	0.0190794
$477$	4.42267e12i	3.91158i
$478$	− 7.11279e11i	− 0.623181i
$479$	4.80307e10	0.0416878	0.0208439	−	0.999783i	$-0.493365\pi$
$479$	4.80307e10	0.0416878	0.0208439	+	0.999783i	$0.493365\pi$
$480$	0	0
$481$	9.49191e11	0.808539
$482$	− 6.70052e11i	− 0.565454i
$483$	2.30019e10i	0.0192310i
$484$	−2.35261e10	−0.0194870
$485$	0	0
$486$	5.88636e12	4.78612
$487$	− 1.24384e12i	− 1.00204i	−0.865435	−	0.501021i	$-0.832958\pi$
$487$	− 1.24384e12i	− 1.00204i	0.865435	−	0.501021i	$-0.167042\pi$
$488$	7.83997e10i	0.0625785i
$489$	9.13590e11	0.722539
$490$	0	0
$491$	−2.63145e11	−0.204328	−0.102164	−	0.994768i	$-0.532577\pi$
$491$	−2.63145e11	−0.204328	−0.102164	+	0.994768i	$0.532577\pi$
$492$	− 3.43506e12i	− 2.64296i
$493$	3.00099e11i	0.228798i
$494$	7.88515e11	0.595715
$495$	0	0
$496$	−1.22825e11	−0.0911212
$497$	1.32456e11i	0.0973798i
$498$	3.84317e12i	2.80000i
$499$	−3.75452e10	−0.0271083	−0.0135542	−	0.999908i	$-0.504315\pi$
$499$	−3.75452e10	−0.0271083	−0.0135542	+	0.999908i	$0.504315\pi$
$500$	0	0
$501$	−1.41797e12	−1.00553
$502$	− 2.53153e12i	− 1.77916i
$503$	2.86189e11i	0.199341i	0.995020	+	0.0996707i	$0.0317789\pi$
$503$	2.86189e11i	0.199341i	−0.995020	+	0.0996707i	$0.968221\pi$
$504$	−1.47330e10	−0.0101708
$505$	0	0
$506$	−2.09420e11	−0.142017
$507$	− 1.42806e12i	− 0.959864i
$508$	− 1.52677e12i	− 1.01715i
$509$	1.48505e12	0.980646	0.490323	−	0.871541i	$-0.336879\pi$
$509$	1.48505e12	0.980646	0.490323	+	0.871541i	$0.336879\pi$
$510$	0	0
$511$	−1.92774e11	−0.125071
$512$	2.17930e12i	1.40153i
$513$	− 3.00746e12i	− 1.91722i
$514$	−1.05142e12	−0.664420
$515$	0	0
$516$	−4.58660e11	−0.284818
$517$	− 1.66654e12i	− 1.02590i
$518$	− 2.64336e11i	− 0.161314i
$519$	1.77012e12	1.07090
$520$	0	0
$521$	−1.77521e12	−1.05556	−0.527778	−	0.849383i	$-0.676975\pi$
$521$	−1.77521e12	−1.05556	−0.527778	+	0.849383i	$0.676975\pi$
$522$	7.43795e12i	4.38466i
$523$	1.20614e12i	0.704922i	0.935826	+	0.352461i	$0.114655\pi$
$523$	1.20614e12i	0.704922i	−0.935826	+	0.352461i	$0.885345\pi$
$524$	9.14135e11	0.529687
$525$	0	0
$526$	−1.92294e12	−1.09529
$527$	− 3.07326e10i	− 0.0173561i
$528$	− 3.54495e12i	− 1.98499i
$529$	1.78310e12	0.989978
$530$	0	0
$531$	−3.91818e12	−2.13875
$532$	− 1.08289e11i	− 0.0586112i
$533$	− 1.86664e12i	− 1.00182i
$534$	−4.97596e11	−0.264814
$535$	0	0
$536$	3.05773e10	0.0160014
$537$	− 3.32237e12i	− 1.72410i
$538$	− 8.32495e11i	− 0.428412i
$539$	−1.95913e12	−0.999802
$540$	0	0
$541$	3.24195e12	1.62711	0.813557	−	0.581485i	$-0.197528\pi$
$541$	3.24195e12	1.62711	0.813557	+	0.581485i	$0.197528\pi$
$542$	1.72535e12i	0.858777i
$543$	6.98296e12i	3.44699i
$544$	−5.60471e11	−0.274383
$545$	0	0
$546$	3.95725e11	0.190558
$547$	− 9.33463e11i	− 0.445814i	−0.974840	−	0.222907i	$-0.928445\pi$
$547$	− 9.33463e11i	− 0.445814i	0.974840	−	0.222907i	$-0.0715547\pi$
$548$	− 2.30355e12i	− 1.09115i
$549$	−9.34540e12	−4.39059
$550$	0	0
$551$	1.52073e12	0.702861
$552$	− 1.58970e10i	− 0.00728769i
$553$	2.37208e11i	0.107861i
$554$	5.61160e12	2.53100
$555$	0	0
$556$	1.28092e11	0.0568443
$557$	1.31760e12i	0.580012i	0.957025	+	0.290006i	$0.0936572\pi$
$557$	1.31760e12i	0.580012i	−0.957025	+	0.290006i	$0.906343\pi$
$558$	− 7.61707e11i	− 0.332609i
$559$	−2.49240e11	−0.107960
$560$	0	0
$561$	8.86998e11	0.378085
$562$	− 2.51442e11i	− 0.106322i
$563$	− 4.33363e12i	− 1.81788i	−0.416931	−	0.908938i	$-0.636894\pi$
$563$	− 4.33363e12i	− 1.81788i	0.416931	−	0.908938i	$-0.363106\pi$
$564$	−4.54784e12	−1.89256
$565$	0	0
$566$	4.28452e12	1.75480
$567$	− 8.50868e11i	− 0.345731i
$568$	− 9.15429e10i	− 0.0369026i
$569$	−3.08940e12	−1.23558	−0.617788	−	0.786345i	$-0.711971\pi$
$569$	−3.08940e12	−1.23558	−0.617788	+	0.786345i	$0.711971\pi$
$570$	0	0
$571$	−7.43095e11	−0.292538	−0.146269	−	0.989245i	$-0.546726\pi$
$571$	−7.43095e11	−0.292538	−0.146269	+	0.989245i	$0.546726\pi$
$572$	1.77672e12i	0.693963i
$573$	− 4.04356e12i	− 1.56700i
$574$	−5.19832e11	−0.199875
$575$	0	0
$576$	−6.65966e12	−2.52087
$577$	2.25852e12i	0.848269i	0.905599	+	0.424134i	$0.139422\pi$
$577$	2.25852e12i	0.848269i	−0.905599	+	0.424134i	$0.860578\pi$
$578$	3.62501e12i	1.35093i
$579$	3.77013e12	1.39413
$580$	0	0
$581$	2.86807e11	0.104423
$582$	− 6.71028e12i	− 2.42430i
$583$	4.13162e12i	1.48119i
$584$	1.33230e11	0.0473962
$585$	0	0
$586$	−3.26674e12	−1.14440
$587$	4.75794e12i	1.65405i	0.562169	+	0.827023i	$0.309967\pi$
$587$	4.75794e12i	1.65405i	−0.562169	+	0.827023i	$0.690033\pi$
$588$	5.34630e12i	1.84440i
$589$	−1.55735e11	−0.0533173
$590$	0	0
$591$	6.91232e12	2.33067
$592$	3.51148e12i	1.17501i
$593$	− 2.01077e12i	− 0.667755i	−0.942616	−	0.333878i	$-0.891643\pi$
$593$	− 2.01077e12i	− 0.667755i	0.942616	−	0.333878i	$-0.108357\pi$
$594$	1.37416e13	4.52896
$595$	0	0
$596$	1.56820e12	0.509089
$597$	− 7.90857e12i	− 2.54808i
$598$	3.10552e11i	0.0993070i
$599$	3.29427e12	1.04554	0.522768	−	0.852475i	$-0.324899\pi$
$599$	3.29427e12	1.04554	0.522768	+	0.852475i	$0.324899\pi$
$600$	0	0
$601$	−1.98887e12	−0.621830	−0.310915	−	0.950438i	$-0.600635\pi$
$601$	−1.98887e12	−0.621830	−0.310915	+	0.950438i	$0.600635\pi$
$602$	6.94096e10i	0.0215395i
$603$	3.64488e12i	1.12268i
$604$	5.11952e12	1.56517
$605$	0	0
$606$	−1.37015e12	−0.412706
$607$	4.11631e12i	1.23072i	0.788246	+	0.615360i	$0.210989\pi$
$607$	4.11631e12i	1.23072i	−0.788246	+	0.615360i	$0.789011\pi$
$608$	2.84015e12i	0.842897i
$609$	7.63194e11	0.224832
$610$	0	0
$611$	−2.47134e12	−0.717376
$612$	− 1.76048e12i	− 0.507282i
$613$	2.06864e12i	0.591715i	0.955232	+	0.295858i	$0.0956054\pi$
$613$	2.06864e12i	0.591715i	−0.955232	+	0.295858i	$0.904395\pi$
$614$	−8.31031e12	−2.35971
$615$	0	0
$616$	−1.37635e10	−0.00385137
$617$	− 5.42058e12i	− 1.50578i	−0.658145	−	0.752891i	$-0.728659\pi$
$617$	− 5.42058e12i	− 1.50578i	0.658145	−	0.752891i	$-0.271341\pi$
$618$	− 1.19078e13i	− 3.28385i
$619$	−3.87240e12	−1.06016	−0.530081	−	0.847947i	$-0.677838\pi$
$619$	−3.87240e12	−1.06016	−0.530081	+	0.847947i	$0.677838\pi$
$620$	0	0
$621$	1.18447e12	0.319605
$622$	− 2.62153e12i	− 0.702260i
$623$	3.71344e10i	0.00987599i
$624$	−5.25688e12	−1.38802
$625$	0	0
$626$	4.31500e12	1.12304
$627$	− 4.49480e12i	− 1.16147i
$628$	1.61935e12i	0.415453i
$629$	−8.78623e11	−0.223807
$630$	0	0
$631$	−3.22937e12	−0.810933	−0.405467	−	0.914110i	$-0.632891\pi$
$631$	−3.22937e12	−0.810933	−0.405467	+	0.914110i	$0.632891\pi$
$632$	− 1.63939e11i	− 0.0408747i
$633$	− 3.15076e12i	− 0.780006i
$634$	−2.88223e12	−0.708478
$635$	0	0
$636$	1.12749e13	2.73246
$637$	2.90523e12i	0.699123i
$638$	6.94847e12i	1.66034i
$639$	1.09121e13	2.58913
$640$	0	0
$641$	1.10935e12	0.259543	0.129771	−	0.991544i	$-0.458576\pi$
$641$	1.10935e12	0.259543	0.129771	+	0.991544i	$0.458576\pi$
$642$	1.33602e13i	3.10388i
$643$	2.83993e12i	0.655177i	0.944821	+	0.327588i	$0.106236\pi$
$643$	2.83993e12i	0.655177i	−0.944821	+	0.327588i	$0.893764\pi$
$644$	4.26489e10	0.00977061
$645$	0	0
$646$	−7.29892e11	−0.164897
$647$	− 2.66962e12i	− 0.598935i	−0.954107	−	0.299467i	$-0.903191\pi$
$647$	− 2.66962e12i	− 0.598935i	0.954107	−	0.299467i	$-0.0968090\pi$
$648$	5.88050e11i	0.131017i
$649$	−3.66033e12	−0.809878
$650$	0	0
$651$	−7.81574e10	−0.0170552
$652$	− 1.69393e12i	− 0.367098i
$653$	− 4.72156e12i	− 1.01619i	−0.861300	−	0.508097i	$-0.830349\pi$
$653$	− 4.72156e12i	− 1.01619i	0.861300	−	0.508097i	$-0.169651\pi$
$654$	−1.06483e13	−2.27604
$655$	0	0
$656$	6.90554e12	1.45590
$657$	1.58813e13i	3.32538i
$658$	6.88231e11i	0.143126i
$659$	−4.01448e12	−0.829173	−0.414586	−	0.910010i	$-0.636074\pi$
$659$	−4.01448e12	−0.829173	−0.414586	+	0.910010i	$0.636074\pi$
$660$	0	0
$661$	−8.01591e12	−1.63323	−0.816613	−	0.577186i	$-0.804151\pi$
$661$	−8.01591e12	−1.63323	−0.816613	+	0.577186i	$0.804151\pi$
$662$	− 1.09704e13i	− 2.22005i
$663$	− 1.31535e12i	− 0.264380i
$664$	−1.98218e11	−0.0395718
$665$	0	0
$666$	−2.17767e13	−4.28901
$667$	5.98931e11i	0.117168i
$668$	2.62912e12i	0.510878i
$669$	6.94065e12	1.33962
$670$	0	0
$671$	−8.73040e12	−1.66258
$672$	1.42536e12i	0.269626i
$673$	− 3.55147e12i	− 0.667330i	−0.942692	−	0.333665i	$-0.891714\pi$
$673$	− 3.55147e12i	− 0.667330i	0.942692	−	0.333665i	$-0.108286\pi$
$674$	2.66790e12	0.497967
$675$	0	0
$676$	−2.64783e12	−0.487675
$677$	6.06872e12i	1.11032i	0.831744	+	0.555160i	$0.187343\pi$
$677$	6.06872e12i	1.11032i	−0.831744	+	0.555160i	$0.812657\pi$
$678$	− 1.54602e13i	− 2.80983i
$679$	−5.00773e11	−0.0904122
$680$	0	0
$681$	6.74068e12	1.20100
$682$	− 7.11581e11i	− 0.125949i
$683$	9.96514e11i	0.175223i	0.996155	+	0.0876113i	$0.0279233\pi$
$683$	9.96514e11i	0.175223i	−0.996155	+	0.0876113i	$0.972077\pi$
$684$	−8.92111e12	−1.55836
$685$	0	0
$686$	1.62635e12	0.280386
$687$	− 6.19170e12i	− 1.06049i
$688$	− 9.22050e11i	− 0.156894i
$689$	6.12686e12	1.03574
$690$	0	0
$691$	1.02702e13	1.71367	0.856835	−	0.515591i	$-0.172428\pi$
$691$	1.02702e13	1.71367	0.856835	+	0.515591i	$0.172428\pi$
$692$	− 3.28207e12i	− 0.544090i
$693$	− 1.64063e12i	− 0.270217i
$694$	4.96299e12	0.812130
$695$	0	0
$696$	−5.27457e11	−0.0852012
$697$	1.72786e12i	0.277308i
$698$	− 2.00823e11i	− 0.0320232i
$699$	8.52194e12	1.35018
$700$	0	0
$701$	−8.26127e12	−1.29216	−0.646079	−	0.763270i	$-0.723592\pi$
$701$	−8.26127e12	−1.29216	−0.646079	+	0.763270i	$0.723592\pi$
$702$	− 2.03777e13i	− 3.16693i
$703$	4.45236e12i	0.687529i
$704$	−6.22140e12	−0.954578
$705$	0	0
$706$	9.02234e12	1.36678
$707$	1.02251e11i	0.0153915i
$708$	9.98875e12i	1.49404i
$709$	8.11428e12	1.20598	0.602992	−	0.797747i	$-0.293975\pi$
$709$	8.11428e12	1.20598	0.602992	+	0.797747i	$0.293975\pi$
$710$	0	0
$711$	1.95418e13	2.86782
$712$	− 2.56643e10i	− 0.00374256i
$713$	− 6.13355e10i	− 0.00888810i
$714$	−3.66304e11	−0.0527473
$715$	0	0
$716$	−6.16017e12	−0.875960
$717$	6.01254e12i	0.849614i
$718$	− 1.90929e13i	− 2.68110i
$719$	−1.06399e13	−1.48476	−0.742380	−	0.669979i	$-0.766303\pi$
$719$	−1.06399e13	−1.48476	−0.742380	+	0.669979i	$0.766303\pi$
$720$	0	0
$721$	−8.88651e11	−0.122468
$722$	− 6.55723e12i	− 0.898055i
$723$	5.66405e12i	0.770911i
$724$	1.29475e13	1.75130
$725$	0	0
$726$	4.03270e11	0.0538742
$727$	1.35040e13i	1.79290i	0.443145	+	0.896450i	$0.353863\pi$
$727$	1.35040e13i	1.79290i	−0.443145	+	0.896450i	$0.646137\pi$
$728$	2.04101e10i	0.00269311i
$729$	−2.34766e13	−3.07866
$730$	0	0
$731$	2.30710e11	0.0298840
$732$	2.38245e13i	3.06708i
$733$	3.03764e12i	0.388659i	0.980936	+	0.194329i	$0.0622530\pi$
$733$	3.03764e12i	0.388659i	−0.980936	+	0.194329i	$0.937747\pi$
$734$	1.58043e13	2.00975
$735$	0	0
$736$	−1.11858e12	−0.140513
$737$	3.40502e12i	0.425124i
$738$	4.28251e13i	5.31429i
$739$	−7.29483e12	−0.899736	−0.449868	−	0.893095i	$-0.648529\pi$
$739$	−7.29483e12	−0.899736	−0.449868	+	0.893095i	$0.648529\pi$
$740$	0	0
$741$	−6.66542e12	−0.812168
$742$	− 1.70624e12i	− 0.206644i
$743$	− 1.18034e13i	− 1.42088i	−0.703756	−	0.710442i	$-0.748495\pi$
$743$	− 1.18034e13i	− 1.42088i	0.703756	−	0.710442i	$-0.251505\pi$
$744$	5.40160e10	0.00646315
$745$	0	0
$746$	−4.42362e12	−0.522941
$747$	− 2.36279e13i	− 2.77641i
$748$	− 1.64463e12i	− 0.192092i
$749$	9.97041e11	0.115756
$750$	0	0
$751$	1.20855e13	1.38639	0.693197	−	0.720748i	$-0.256202\pi$
$751$	1.20855e13	1.38639	0.693197	+	0.720748i	$0.256202\pi$
$752$	− 9.14258e12i	− 1.04253i
$753$	2.13993e13i	2.42562i
$754$	1.03040e13	1.16101
$755$	0	0
$756$	−2.79852e12	−0.311588
$757$	− 1.48077e13i	− 1.63891i	−0.573144	−	0.819455i	$-0.694276\pi$
$757$	− 1.48077e13i	− 1.63891i	0.573144	−	0.819455i	$-0.305724\pi$
$758$	1.79651e13i	1.97660i
$759$	1.77025e12	0.193619
$760$	0	0
$761$	−1.75185e13	−1.89350	−0.946749	−	0.321972i	$-0.895654\pi$
$761$	−1.75185e13	−1.89350	−0.946749	+	0.321972i	$0.895654\pi$
$762$	2.61709e13i	2.81204i
$763$	7.94656e11i	0.0848826i
$764$	−7.49736e12	−0.796138
$765$	0	0
$766$	1.71266e13	1.79739
$767$	5.42798e12i	0.566316i
$768$	− 1.94209e13i	− 2.01439i
$769$	−4.16729e12	−0.429720	−0.214860	−	0.976645i	$-0.568930\pi$
$769$	−4.16729e12	−0.429720	−0.214860	+	0.976645i	$0.568930\pi$
$770$	0	0
$771$	8.88781e12	0.905837
$772$	− 6.99039e12i	− 0.708311i
$773$	− 1.05896e13i	− 1.06677i	−0.845872	−	0.533386i	$-0.820919\pi$
$773$	− 1.05896e13i	− 1.06677i	0.845872	−	0.533386i	$-0.179081\pi$
$774$	5.71815e12	0.572692
$775$	0	0
$776$	3.46093e11	0.0342622
$777$	2.23446e12i	0.219927i
$778$	− 2.43949e13i	− 2.38721i
$779$	8.75583e12	0.851881
$780$	0	0
$781$	1.01940e13	0.980426
$782$	− 2.87464e11i	− 0.0274887i
$783$	− 3.93004e13i	− 3.73654i
$784$	−1.07478e13	−1.01600
$785$	0	0
$786$	−1.56696e13	−1.46439
$787$	− 2.50861e12i	− 0.233102i	−0.993185	−	0.116551i	$-0.962816\pi$
$787$	− 2.50861e12i	− 0.233102i	0.993185	−	0.116551i	$-0.0371839\pi$
$788$	− 1.28165e13i	− 1.18413i
$789$	1.62549e13	1.49327
$790$	0	0
$791$	−1.15376e12	−0.104790
$792$	1.13387e12i	0.102400i
$793$	1.29465e13i	1.16258i
$794$	−1.98724e13	−1.77443
$795$	0	0
$796$	−1.46637e13	−1.29460
$797$	− 1.85822e13i	− 1.63131i	−0.578541	−	0.815653i	$-0.696378\pi$
$797$	− 1.85822e13i	− 1.63131i	0.578541	−	0.815653i	$-0.303622\pi$
$798$	1.85622e12i	0.162038i
$799$	2.28760e12	0.198573
$800$	0	0
$801$	3.05923e12	0.262583
$802$	− 5.12746e12i	− 0.437641i
$803$	1.48362e13i	1.25922i
$804$	9.29202e12	0.784256
$805$	0	0
$806$	−1.05522e12	−0.0880712
$807$	7.03720e12i	0.584075i
$808$	− 7.06675e10i	− 0.00583268i
$809$	4.47333e12	0.367166	0.183583	−	0.983004i	$-0.441230\pi$
$809$	4.47333e12	0.367166	0.183583	+	0.983004i	$0.441230\pi$
$810$	0	0
$811$	−3.49582e12	−0.283763	−0.141881	−	0.989884i	$-0.545315\pi$
$811$	−3.49582e12	−0.283763	−0.141881	+	0.989884i	$0.545315\pi$
$812$	− 1.41508e12i	− 0.114229i
$813$	− 1.45846e13i	− 1.17081i
$814$	−2.03436e13	−1.62412
$815$	0	0
$816$	4.86605e12	0.384212
$817$	− 1.16911e12i	− 0.0918026i
$818$	2.30108e13i	1.79698i
$819$	−2.43293e12	−0.188952
$820$	0	0
$821$	−6.84197e12	−0.525578	−0.262789	−	0.964853i	$-0.584642\pi$
$821$	−6.84197e12	−0.525578	−0.262789	+	0.964853i	$0.584642\pi$
$822$	3.94860e13i	3.01662i
$823$	8.11058e12i	0.616244i	0.951347	+	0.308122i	$0.0997005\pi$
$823$	8.11058e12i	0.616244i	−0.951347	+	0.308122i	$0.900300\pi$
$824$	6.14163e11	0.0464099
$825$	0	0
$826$	1.51161e12	0.112987
$827$	5.06349e10i	0.00376422i	0.999998	+	0.00188211i	$0.000599095\pi$
$827$	5.06349e10i	0.00376422i	−0.999998	+	0.00188211i	$0.999401\pi$
$828$	− 3.51353e12i	− 0.259781i
$829$	1.50474e13	1.10654	0.553269	−	0.833002i	$-0.313380\pi$
$829$	1.50474e13	1.10654	0.553269	+	0.833002i	$0.313380\pi$
$830$	0	0
$831$	−4.74356e13	−3.45064
$832$	9.22584e12i	0.667499i
$833$	− 2.68924e12i	− 0.193521i
$834$	−2.19569e12	−0.157153
$835$	0	0
$836$	−8.33403e12	−0.590102
$837$	4.02469e12i	0.283444i
$838$	− 8.90044e12i	− 0.623467i
$839$	−2.68352e13	−1.86972	−0.934859	−	0.355020i	$-0.884474\pi$
$839$	−2.68352e13	−1.86972	−0.934859	+	0.355020i	$0.884474\pi$
$840$	0	0
$841$	5.36519e12	0.369831
$842$	− 2.08468e12i	− 0.142934i
$843$	2.12547e12i	0.144954i
$844$	−5.84197e12	−0.396295
$845$	0	0
$846$	5.66983e13	3.80543
$847$	− 3.00951e10i	− 0.00200919i
$848$	2.26660e13i	1.50520i
$849$	−3.62176e13	−2.39241
$850$	0	0
$851$	−1.75354e12	−0.114613
$852$	− 2.78186e13i	− 1.80866i
$853$	4.22107e12i	0.272993i	0.990641	+	0.136497i	$0.0435843\pi$
$853$	4.22107e12i	0.272993i	−0.990641	+	0.136497i	$0.956416\pi$
$854$	3.60540e12	0.231949
$855$	0	0
$856$	−6.89073e11	−0.0438665
$857$	7.57740e12i	0.479851i	0.970791	+	0.239926i	$0.0771230\pi$
$857$	7.57740e12i	0.479851i	−0.970791	+	0.239926i	$0.922877\pi$
$858$	− 3.04555e13i	− 1.91855i
$859$	−1.41463e13	−0.886486	−0.443243	−	0.896401i	$-0.646172\pi$
$859$	−1.41463e13	−0.886486	−0.443243	+	0.896401i	$0.646172\pi$
$860$	0	0
$861$	4.39421e12	0.272500
$862$	3.18757e13i	1.96642i
$863$	1.52498e13i	0.935868i	0.883763	+	0.467934i	$0.155002\pi$
$863$	1.52498e13i	0.935868i	−0.883763	+	0.467934i	$0.844998\pi$
$864$	7.33983e13	4.48099
$865$	0	0
$866$	2.53780e13	1.53330
$867$	− 3.06427e13i	− 1.84180i
$868$	1.44915e11i	0.00866515i
$869$	1.82558e13	1.08596
$870$	0	0
$871$	5.04937e12	0.297273
$872$	− 5.49201e11i	− 0.0321668i
$873$	4.12550e13i	2.40388i
$874$	−1.45671e12	−0.0844443
$875$	0	0
$876$	4.04867e13	2.32297
$877$	− 3.30350e12i	− 0.188572i	−0.995545	−	0.0942858i	$-0.969943\pi$
$877$	− 3.30350e12i	− 0.188572i	0.995545	−	0.0942858i	$-0.0300568\pi$
$878$	− 2.53747e13i	− 1.44104i
$879$	2.76142e13	1.56021
$880$	0	0
$881$	3.14728e13	1.76013	0.880063	−	0.474856i	$-0.157500\pi$
$881$	3.14728e13	1.76013	0.880063	+	0.474856i	$0.157500\pi$
$882$	− 6.66528e13i	− 3.70860i
$883$	1.10669e13i	0.612637i	0.951929	+	0.306318i	$0.0990973\pi$
$883$	1.10669e13i	0.612637i	−0.951929	+	0.306318i	$0.900903\pi$
$884$	−2.43885e12	−0.134323
$885$	0	0
$886$	−2.40482e13	−1.31108
$887$	6.92035e12i	0.375381i	0.982228	+	0.187690i	$0.0601001\pi$
$887$	6.92035e12i	0.375381i	−0.982228	+	0.187690i	$0.939900\pi$
$888$	− 1.54428e12i	− 0.0833426i
$889$	1.95308e12	0.104872
$890$	0	0
$891$	−6.54838e13	−3.48084
$892$	− 1.28690e13i	− 0.680618i
$893$	− 1.15923e13i	− 0.610010i
$894$	−2.68812e13	−1.40744
$895$	0	0
$896$	−1.47084e11	−0.00762394
$897$	− 2.62514e12i	− 0.135390i
$898$	2.03225e13i	1.04288i
$899$	−2.03509e12	−0.103912
$900$	0	0
$901$	−5.67136e12	−0.286699
$902$	4.00069e13i	2.01236i
$903$	− 5.86729e11i	− 0.0293659i
$904$	7.97383e11	0.0397108
$905$	0	0
$906$	−8.77557e13	−4.32712
$907$	2.00486e13i	0.983676i	0.870687	+	0.491838i	$0.163675\pi$
$907$	2.00486e13i	0.983676i	−0.870687	+	0.491838i	$0.836325\pi$
$908$	− 1.24982e13i	− 0.610186i
$909$	8.42371e12	0.409229
$910$	0	0
$911$	2.53798e13	1.22083	0.610416	−	0.792081i	$-0.291002\pi$
$911$	2.53798e13	1.22083	0.610416	+	0.792081i	$0.291002\pi$
$912$	− 2.46584e13i	− 1.18029i
$913$	− 2.20730e13i	− 1.05134i
$914$	4.26768e13	2.02271
$915$	0	0
$916$	−1.14803e13	−0.538797
$917$	1.16938e12i	0.0546129i
$918$	1.88627e13i	0.876622i
$919$	6.15926e12	0.284845	0.142423	−	0.989806i	$-0.454511\pi$
$919$	6.15926e12	0.284845	0.142423	+	0.989806i	$0.454511\pi$
$920$	0	0
$921$	7.02482e13	3.21712
$922$	1.10322e13i	0.502774i
$923$	− 1.51169e13i	− 0.685574i
$924$	−4.18252e12	−0.188762
$925$	0	0
$926$	2.28904e13	1.02307
$927$	7.32095e13i	3.25618i
$928$	3.71140e13i	1.64275i
$929$	−2.20000e13	−0.969061	−0.484531	−	0.874774i	$-0.661010\pi$
$929$	−2.20000e13	−0.969061	−0.484531	+	0.874774i	$0.661010\pi$
$930$	0	0
$931$	−1.36275e13	−0.594489
$932$	− 1.58010e13i	− 0.685980i
$933$	2.21601e13i	0.957426i
$934$	2.32508e12	0.0999715
$935$	0	0
$936$	1.68144e12	0.0716045
$937$	− 2.49274e12i	− 0.105645i	−0.998604	−	0.0528225i	$-0.983178\pi$
$937$	− 2.49274e12i	− 0.105645i	0.998604	−	0.0528225i	$-0.0168217\pi$
$938$	− 1.40617e12i	− 0.0593098i
$939$	−3.64753e13	−1.53110
$940$	0	0
$941$	−1.26366e13	−0.525382	−0.262691	−	0.964880i	$-0.584610\pi$
$941$	−1.26366e13	−0.525382	−0.262691	+	0.964880i	$0.584610\pi$
$942$	− 2.77579e13i	− 1.14857i
$943$	3.44844e12i	0.142010i
$944$	−2.00805e13	−0.823002
$945$	0	0
$946$	5.34185e12	0.216861
$947$	2.05809e13i	0.831551i	0.909467	+	0.415775i	$0.136490\pi$
$947$	2.05809e13i	0.831551i	−0.909467	+	0.415775i	$0.863510\pi$
$948$	− 4.98186e13i	− 2.00334i
$949$	2.20008e13	0.880524
$950$	0	0
$951$	2.43639e13	0.965904
$952$	− 1.88927e10i	0 0.000745466i
$953$	− 2.97887e13i	− 1.16986i	−0.811084	−	0.584929i	$-0.801122\pi$
$953$	− 2.97887e13i	− 1.16986i	0.811084	−	0.584929i	$-0.198878\pi$
$954$	−1.40565e14	−5.49425
$955$	0	0
$956$	1.11481e13	0.431660
$957$	− 5.87364e13i	− 2.26362i
$958$	1.52655e12i	0.0585553i
$959$	2.94675e12	0.112502
$960$	0	0
$961$	−2.62312e13	−0.992118
$962$	3.01679e13i	1.13568i
$963$	− 8.21389e13i	− 3.07773i
$964$	1.05020e13	0.391674
$965$	0	0
$966$	−7.31063e11	−0.0270121
$967$	− 1.74473e13i	− 0.641664i	−0.947136	−	0.320832i	$-0.896037\pi$
$967$	− 1.74473e13i	− 0.641664i	0.947136	−	0.320832i	$-0.103963\pi$
$968$	2.07993e10i	0 0.000761394i
$969$	6.16988e12	0.224812
$970$	0	0
$971$	−2.53844e13	−0.916390	−0.458195	−	0.888852i	$-0.651504\pi$
$971$	−2.53844e13	−0.916390	−0.458195	+	0.888852i	$0.651504\pi$
$972$	9.22592e13i	3.31521i
$973$	1.63859e11i	0.00586088i
$974$	3.95328e13	1.40748
$975$	0	0
$976$	−4.78948e13	−1.68952
$977$	− 3.23029e13i	− 1.13427i	−0.823625	−	0.567135i	$-0.808052\pi$
$977$	− 3.23029e13i	− 1.13427i	0.823625	−	0.567135i	$-0.191948\pi$
$978$	2.90364e13i	1.01489i
$979$	2.85791e12	0.0994321
$980$	0	0
$981$	6.54659e13	2.25686
$982$	− 8.36348e12i	− 0.287002i
$983$	− 1.78014e13i	− 0.608083i	−0.952659	−	0.304041i	$-0.901664\pi$
$983$	− 1.78014e13i	− 0.608083i	0.952659	−	0.304041i	$-0.0983361\pi$
$984$	−3.03692e12	−0.103265
$985$	0	0
$986$	−9.53796e12	−0.321373
$987$	− 5.81771e12i	− 0.195130i
$988$	1.23587e13i	0.412635i
$989$	4.60447e11	0.0153037
$990$	0	0
$991$	−3.38638e12	−0.111533	−0.0557666	−	0.998444i	$-0.517760\pi$
$991$	−3.38638e12	−0.111533	−0.0557666	+	0.998444i	$0.517760\pi$
$992$	− 3.80078e12i	− 0.124615i
$993$	9.27345e13i	3.02670i
$994$	−4.20982e12	−0.136781
$995$	0	0
$996$	−6.02355e13	−1.93948
$997$	− 4.17766e13i	− 1.33908i	−0.742778	−	0.669538i	$-0.766492\pi$
$997$	− 4.17766e13i	− 1.33908i	0.742778	−	0.669538i	$-0.233508\pi$
$998$	− 1.19329e12i	− 0.0380767i
$999$	1.15063e14	3.65503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.10.b.c.24.6		6
3.2	odd	2		225.10.b.m.199.1		6
4.3	odd	2		400.10.c.q.49.6		6
5.2	odd	4		25.10.a.c.1.1	✓	3
5.3	odd	4		25.10.a.d.1.3	yes	3
5.4	even	2	inner	25.10.b.c.24.1		6
15.2	even	4		225.10.a.p.1.3		3
15.8	even	4		225.10.a.m.1.1		3
15.14	odd	2		225.10.b.m.199.6		6
20.3	even	4		400.10.a.u.1.1		3
20.7	even	4		400.10.a.y.1.3		3
20.19	odd	2		400.10.c.q.49.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.10.a.c.1.1	✓	3	5.2	odd	4
25.10.a.d.1.3	yes	3	5.3	odd	4
25.10.b.c.24.1		6	5.4	even	2	inner
25.10.b.c.24.6		6	1.1	even	1	trivial
225.10.a.m.1.1		3	15.8	even	4
225.10.a.p.1.3		3	15.2	even	4
225.10.b.m.199.1		6	3.2	odd	2
225.10.b.m.199.6		6	15.14	odd	2
400.10.a.u.1.1		3	20.3	even	4
400.10.a.y.1.3		3	20.7	even	4
400.10.c.q.49.1		6	20.19	odd	2
400.10.c.q.49.6		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+31.7828i q^{2} -268.664i q^{3} -498.143 q^{4} +8538.88 q^{6} -637.237i q^{7} +440.406i q^{8} -52497.3 q^{9} +O(q^{10})\)	\(q+31.7828i q^{2} -268.664i q^{3} -498.143 q^{4} +8538.88 q^{6} -637.237i q^{7} +440.406i q^{8} -52497.3 q^{9} -49042.6 q^{11} +133833. i q^{12} +72726.2i q^{13} +20253.2 q^{14} -269047. q^{16} -67319.3i q^{17} -1.66851e6i q^{18} -341136. q^{19} -171203. q^{21} -1.55871e6i q^{22} -134355. i q^{23} +118321. q^{24} -2.31144e6 q^{26} +8.81603e6i q^{27} +317435. i q^{28} -4.45784e6 q^{29} +456520. q^{31} -8.32555e6i q^{32} +1.31760e7i q^{33} +2.13959e6 q^{34} +2.61512e7 q^{36} -1.30516e7i q^{37} -1.08422e7i q^{38} +1.95389e7 q^{39} -2.56667e7 q^{41} -5.44129e6i q^{42} +3.42710e6i q^{43} +2.44302e7 q^{44} +4.27016e6 q^{46} +3.39814e7i q^{47} +7.22831e7i q^{48} +3.99475e7 q^{49} -1.80863e7 q^{51} -3.62281e7i q^{52} -8.42456e7i q^{53} -2.80198e8 q^{54} +280643. q^{56} +9.16509e7i q^{57} -1.41682e8i q^{58} +7.46358e7 q^{59} +1.78017e8 q^{61} +1.45094e7i q^{62} +3.34533e7i q^{63} +1.26857e8 q^{64} -4.18769e8 q^{66} -6.94299e7i q^{67} +3.35347e7i q^{68} -3.60963e7 q^{69} -2.07860e8 q^{71} -2.31201e7i q^{72} -3.02516e8i q^{73} +4.14815e8 q^{74} +1.69935e8 q^{76} +3.12518e7i q^{77} +6.21000e8i q^{78} -3.72244e8 q^{79} +1.33524e9 q^{81} -8.15758e8i q^{82} +4.50079e8i q^{83} +8.52835e7 q^{84} -1.08923e8 q^{86} +1.19766e9i q^{87} -2.15987e7i q^{88} -5.82741e7 q^{89} +4.63438e7 q^{91} +6.69279e7i q^{92} -1.22650e8i q^{93} -1.08002e9 q^{94} -2.23678e9 q^{96} -7.85850e8i q^{97} +1.26964e9i q^{98} +2.57461e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 682 q^{4} + 6842 q^{6} - 116468 q^{9}+O(q^{10}) \) 6 * q - 682 * q^4 + 6842 * q^6 - 116468 * q^9	\( 6 q - 682 q^{4} + 6842 q^{6} - 116468 q^{9} - 109398 q^{11} - 545844 q^{14} - 1398494 q^{16} - 1637690 q^{19} - 4750788 q^{21} - 5611470 q^{24} - 2560008 q^{26} - 4350960 q^{29} + 8548132 q^{31} + 13677926 q^{34} + 53591596 q^{36} + 100828184 q^{39} + 11852622 q^{41} + 43991406 q^{44} + 28446492 q^{46} + 12907858 q^{49} - 51269398 q^{51} - 564500990 q^{54} - 339076260 q^{56} - 11341920 q^{59} + 250613852 q^{61} - 335084802 q^{64} - 1113831686 q^{66} + 628549884 q^{69} + 595101192 q^{71} + 503014716 q^{74} + 178829730 q^{76} + 620050340 q^{79} + 2797694726 q^{81} - 76534164 q^{84} + 67894392 q^{86} + 2207720070 q^{89} + 2366375312 q^{91} - 3455782264 q^{94} - 5134360898 q^{96} + 1784469044 q^{99}+O(q^{100}) \) 6 * q - 682 * q^4 + 6842 * q^6 - 116468 * q^9 - 109398 * q^11 - 545844 * q^14 - 1398494 * q^16 - 1637690 * q^19 - 4750788 * q^21 - 5611470 * q^24 - 2560008 * q^26 - 4350960 * q^29 + 8548132 * q^31 + 13677926 * q^34 + 53591596 * q^36 + 100828184 * q^39 + 11852622 * q^41 + 43991406 * q^44 + 28446492 * q^46 + 12907858 * q^49 - 51269398 * q^51 - 564500990 * q^54 - 339076260 * q^56 - 11341920 * q^59 + 250613852 * q^61 - 335084802 * q^64 - 1113831686 * q^66 + 628549884 * q^69 + 595101192 * q^71 + 503014716 * q^74 + 178829730 * q^76 + 620050340 * q^79 + 2797694726 * q^81 - 76534164 * q^84 + 67894392 * q^86 + 2207720070 * q^89 + 2366375312 * q^91 - 3455782264 * q^94 - 5134360898 * q^96 + 1784469044 * q^99

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