LMFDB - Embedded newform 25.10.b.c.24.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,10,Mod(24,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			24.3
Root			$-6.48955i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.10.b.c.24.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-20.2014i q^{2} -30.5073i q^{3} +103.903 q^{4} -616.291 q^{6} -4010.25i q^{7} -12442.1i q^{8} +18752.3 q^{9} -42110.0 q^{11} -3169.79i q^{12} -123743. i q^{13} -81012.8 q^{14} -198150. q^{16} +319945. i q^{17} -378823. i q^{18} -1.08733e6 q^{19} -122342. q^{21} +850682. i q^{22} -1.50672e6i q^{23} -379575. q^{24} -2.49979e6 q^{26} -1.17256e6i q^{27} -416676. i q^{28} +2.62160e6 q^{29} +3.27023e6 q^{31} -2.36745e6i q^{32} +1.28466e6i q^{33} +6.46335e6 q^{34} +1.94841e6 q^{36} -2.51034e6i q^{37} +2.19655e7i q^{38} -3.77508e6 q^{39} +2.95349e7 q^{41} +2.47148e6i q^{42} +1.42413e7i q^{43} -4.37534e6 q^{44} -3.04378e7 q^{46} +1.35318e6i q^{47} +6.04503e6i q^{48} +2.42715e7 q^{49} +9.76067e6 q^{51} -1.28573e7i q^{52} -9.73342e7i q^{53} -2.36873e7 q^{54} -4.98960e7 q^{56} +3.31714e7i q^{57} -5.29599e7i q^{58} +7.48924e6 q^{59} -9.11752e7 q^{61} -6.60633e7i q^{62} -7.52015e7i q^{63} -1.49279e8 q^{64} +2.59520e7 q^{66} +2.94376e8i q^{67} +3.32432e7i q^{68} -4.59659e7 q^{69} +1.56193e8 q^{71} -2.33318e8i q^{72} +2.82539e8i q^{73} -5.07124e7 q^{74} -1.12976e8 q^{76} +1.68872e8i q^{77} +7.62619e7i q^{78} +5.55294e8 q^{79} +3.33330e8 q^{81} -5.96647e8i q^{82} -6.48378e6i q^{83} -1.27117e7 q^{84} +2.87694e8 q^{86} -7.99778e7i q^{87} +5.23937e8i q^{88} +5.99001e8 q^{89} -4.96242e8 q^{91} -1.56552e8i q^{92} -9.97660e7i q^{93} +2.73361e7 q^{94} -7.22244e7 q^{96} +9.25317e8i q^{97} -4.90319e8i q^{98} -7.89660e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	− 20.2014i	− 0.892785i	−0.894837	−	0.446393i	$-0.852709\pi$
$2$	− 20.2014i	− 0.892785i	0.894837	−	0.446393i	$-0.147291\pi$
$3$	− 30.5073i	− 0.217449i	−0.994072	−	0.108725i	$-0.965323\pi$
$3$	− 30.5073i	− 0.217449i	0.994072	−	0.108725i	$-0.0346767\pi$
$4$	103.903	0.202935
$5$	0	0
$5$	0	0
$6$	−616.291	−0.194136
$7$	− 4010.25i	− 0.631292i	−0.948877	−	0.315646i	$-0.897779\pi$
$7$	− 4010.25i	− 0.631292i	0.948877	−	0.315646i	$-0.102221\pi$
$8$	− 12442.1i	− 1.07396i
$9$	18752.3	0.952716
$10$	0	0
$11$	−42110.0	−0.867198	−0.433599	−	0.901106i	$-0.642757\pi$
$11$	−42110.0	−0.867198	−0.433599	+	0.901106i	$0.642757\pi$
$12$	− 3169.79i	− 0.0441281i
$13$	− 123743.i	− 1.20165i	−0.799382	−	0.600824i	$-0.794839\pi$
$13$	− 123743.i	− 1.20165i	0.799382	−	0.600824i	$-0.205161\pi$
$14$	−81012.8	−0.563608
$15$	0	0
$16$	−198150.	−0.755883
$17$	319945.i	0.929085i	0.885551	+	0.464543i	$0.153781\pi$
$17$	319945.i	0.929085i	−0.885551	+	0.464543i	$0.846219\pi$
$18$	− 378823.i	− 0.850570i
$19$	−1.08733e6	−1.91412	−0.957059	−	0.289893i	$-0.906380\pi$
$19$	−1.08733e6	−1.91412	−0.957059	+	0.289893i	$0.906380\pi$
$20$	0	0
$21$	−122342.	−0.137274
$22$	850682.i	0.774221i
$23$	− 1.50672e6i	− 1.12268i	−0.827585	−	0.561341i	$-0.810286\pi$
$23$	− 1.50672e6i	− 1.12268i	0.827585	−	0.561341i	$-0.189714\pi$
$24$	−379575.	−0.233532
$25$	0	0
$26$	−2.49979e6	−1.07281
$27$	− 1.17256e6i	− 0.424617i
$28$	− 416676.i	− 0.128111i
$29$	2.62160e6	0.688295	0.344148	−	0.938916i	$-0.388168\pi$
$29$	2.62160e6	0.688295	0.344148	+	0.938916i	$0.388168\pi$
$30$	0	0
$31$	3.27023e6	0.635991	0.317996	−	0.948092i	$-0.396990\pi$
$31$	3.27023e6	0.635991	0.317996	+	0.948092i	$0.396990\pi$
$32$	− 2.36745e6i	− 0.399122i
$33$	1.28466e6i	0.188572i
$34$	6.46335e6	0.829473
$35$	0	0
$36$	1.94841e6	0.193339
$37$	− 2.51034e6i	− 0.220204i	−0.993920	−	0.110102i	$-0.964882\pi$
$37$	− 2.51034e6i	− 0.220204i	0.993920	−	0.110102i	$-0.0351177\pi$
$38$	2.19655e7i	1.70890i
$39$	−3.77508e6	−0.261297
$40$	0	0
$41$	2.95349e7	1.63233	0.816165	−	0.577819i	$-0.196096\pi$
$41$	2.95349e7	1.63233	0.816165	+	0.577819i	$0.196096\pi$
$42$	2.47148e6i	0.122556i
$43$	1.42413e7i	0.635244i	0.948217	+	0.317622i	$0.102884\pi$
$43$	1.42413e7i	0.635244i	−0.948217	+	0.317622i	$0.897116\pi$
$44$	−4.37534e6	−0.175985
$45$	0	0
$46$	−3.04378e7	−1.00231
$47$	1.35318e6i	0.0404496i	0.999795	+	0.0202248i	$0.00643820\pi$
$47$	1.35318e6i	0.0404496i	−0.999795	+	0.0202248i	$0.993562\pi$
$48$	6.04503e6i	0.164366i
$49$	2.42715e7	0.601470
$50$	0	0
$51$	9.76067e6	0.202029
$52$	− 1.28573e7i	− 0.243856i
$53$	− 9.73342e7i	− 1.69443i	−0.531249	−	0.847216i	$-0.678277\pi$
$53$	− 9.73342e7i	− 1.69443i	0.531249	−	0.847216i	$-0.321723\pi$
$54$	−2.36873e7	−0.379092
$55$	0	0
$56$	−4.98960e7	−0.677984
$57$	3.31714e7i	0.416224i
$58$	− 5.29599e7i	− 0.614500i
$59$	7.48924e6	0.0804644	0.0402322	−	0.999190i	$-0.487190\pi$
$59$	7.48924e6	0.0804644	0.0402322	+	0.999190i	$0.487190\pi$
$60$	0	0
$61$	−9.11752e7	−0.843126	−0.421563	−	0.906799i	$-0.638518\pi$
$61$	−9.11752e7	−0.843126	−0.421563	+	0.906799i	$0.638518\pi$
$62$	− 6.60633e7i	− 0.567803i
$63$	− 7.52015e7i	− 0.601442i
$64$	−1.49279e8	−1.11221
$65$	0	0
$66$	2.59520e7	0.168354
$67$	2.94376e8i	1.78470i	0.451344	+	0.892350i	$0.350945\pi$
$67$	2.94376e8i	1.78470i	−0.451344	+	0.892350i	$0.649055\pi$
$68$	3.32432e7i	0.188544i
$69$	−4.59659e7	−0.244127
$70$	0	0
$71$	1.56193e8	0.729455	0.364728	−	0.931114i	$-0.381162\pi$
$71$	1.56193e8	0.729455	0.364728	+	0.931114i	$0.381162\pi$
$72$	− 2.33318e8i	− 1.02318i
$73$	2.82539e8i	1.16446i	0.813023	+	0.582232i	$0.197820\pi$
$73$	2.82539e8i	1.16446i	−0.813023	+	0.582232i	$0.802180\pi$
$74$	−5.07124e7	−0.196594
$75$	0	0
$76$	−1.12976e8	−0.388441
$77$	1.68872e8i	0.547455i
$78$	7.62619e7i	0.233282i
$79$	5.55294e8	1.60399	0.801994	−	0.597332i	$-0.203772\pi$
$79$	5.55294e8	1.60399	0.801994	+	0.597332i	$0.203772\pi$
$80$	0	0
$81$	3.33330e8	0.860383
$82$	− 5.96647e8i	− 1.45732i
$83$	− 6.48378e6i	− 0.0149960i	−0.999972	−	0.00749802i	$-0.997613\pi$
$83$	− 6.48378e6i	− 0.0149960i	0.999972	−	0.00749802i	$-0.00238672\pi$
$84$	−1.27117e7	−0.0278577
$85$	0	0
$86$	2.87694e8	0.567137
$87$	− 7.99778e7i	− 0.149669i
$88$	5.23937e8i	0.931338i
$89$	5.99001e8	1.01198	0.505990	−	0.862539i	$-0.331127\pi$
$89$	5.99001e8	1.01198	0.505990	+	0.862539i	$0.331127\pi$
$90$	0	0
$91$	−4.96242e8	−0.758591
$92$	− 1.56552e8i	− 0.227831i
$93$	− 9.97660e7i	− 0.138296i
$94$	2.73361e7	0.0361128
$95$	0	0
$96$	−7.22244e7	−0.0867887
$97$	9.25317e8i	1.06125i	0.847606	+	0.530625i	$0.178043\pi$
$97$	9.25317e8i	1.06125i	−0.847606	+	0.530625i	$0.821957\pi$
$98$	− 4.90319e8i	− 0.536984i
$99$	−7.89660e8	−0.826193
$100$	0	0
$101$	9.58959e8	0.916967	0.458483	−	0.888703i	$-0.348393\pi$
$101$	9.58959e8	0.916967	0.458483	+	0.888703i	$0.348393\pi$
$102$	− 1.97179e8i	− 0.180368i
$103$	− 1.60441e8i	− 0.140458i	−0.997531	−	0.0702292i	$-0.977627\pi$
$103$	− 1.60441e8i	− 0.140458i	0.997531	−	0.0702292i	$-0.0223731\pi$
$104$	−1.53963e9	−1.29052
$105$	0	0
$106$	−1.96629e9	−1.51276
$107$	9.60457e8i	0.708355i	0.935178	+	0.354178i	$0.115239\pi$
$107$	9.60457e8i	0.708355i	−0.935178	+	0.354178i	$0.884761\pi$
$108$	− 1.21832e8i	− 0.0861696i
$109$	−9.98912e8	−0.677810	−0.338905	−	0.940821i	$-0.610057\pi$
$109$	−9.98912e8	−0.677810	−0.338905	+	0.940821i	$0.610057\pi$
$110$	0	0
$111$	−7.65836e7	−0.0478831
$112$	7.94632e8i	0.477183i
$113$	− 2.50705e9i	− 1.44647i	−0.690601	−	0.723236i	$-0.742654\pi$
$113$	− 2.50705e9i	− 1.44647i	0.690601	−	0.723236i	$-0.257346\pi$
$114$	6.70109e8	0.371598
$115$	0	0
$116$	2.72391e8	0.139679
$117$	− 2.32047e9i	− 1.14483i
$118$	− 1.51293e8i	− 0.0718374i
$119$	1.28306e9	0.586524
$120$	0	0
$121$	−5.84695e8	−0.247968
$122$	1.84187e9i	0.752730i
$123$	− 9.01030e8i	− 0.354949i
$124$	3.39786e8	0.129065
$125$	0	0
$126$	−1.51918e9	−0.536958
$127$	− 2.47541e9i	− 0.844364i	−0.906511	−	0.422182i	$-0.861264\pi$
$127$	− 2.47541e9i	− 0.844364i	0.906511	−	0.422182i	$-0.138736\pi$
$128$	1.80351e9i	0.593845i
$129$	4.34463e8	0.138134
$130$	0	0
$131$	1.92402e9	0.570808	0.285404	−	0.958407i	$-0.407872\pi$
$131$	1.92402e9	0.570808	0.285404	+	0.958407i	$0.407872\pi$
$132$	1.33480e8i	0.0382678i
$133$	4.36045e9i	1.20837i
$134$	5.94680e9	1.59335
$135$	0	0
$136$	3.98079e9	0.997802
$137$	4.48594e8i	0.108796i	0.998519	+	0.0543978i	$0.0173239\pi$
$137$	4.48594e8i	0.108796i	−0.998519	+	0.0543978i	$0.982676\pi$
$138$	9.28577e8i	0.217953i
$139$	−4.48415e9	−1.01886	−0.509429	−	0.860513i	$-0.670143\pi$
$139$	−4.48415e9	−1.01886	−0.509429	+	0.860513i	$0.670143\pi$
$140$	0	0
$141$	4.12818e7	0.00879575
$142$	− 3.15532e9i	− 0.651247i
$143$	5.21084e9i	1.04207i
$144$	−3.71577e9	−0.720141
$145$	0	0
$146$	5.70769e9	1.03962
$147$	− 7.40458e8i	− 0.130789i
$148$	− 2.60831e8i	− 0.0446870i
$149$	2.20480e9	0.366463	0.183232	−	0.983070i	$-0.441344\pi$
$149$	2.20480e9	0.366463	0.183232	+	0.983070i	$0.441344\pi$
$150$	0	0
$151$	−3.21248e9	−0.502857	−0.251428	−	0.967876i	$-0.580900\pi$
$151$	−3.21248e9	−0.502857	−0.251428	+	0.967876i	$0.580900\pi$
$152$	1.35286e10i	2.05569i
$153$	5.99971e9i	0.885154i
$154$	3.41145e9	0.488760
$155$	0	0
$156$	−3.92241e8	−0.0530264
$157$	− 1.08870e10i	− 1.43007i	−0.699088	−	0.715036i	$-0.746410\pi$
$157$	− 1.08870e10i	− 1.43007i	0.699088	−	0.715036i	$-0.253590\pi$
$158$	− 1.12177e10i	− 1.43202i
$159$	−2.96940e9	−0.368453
$160$	0	0
$161$	−6.04232e9	−0.708740
$162$	− 6.73374e9i	− 0.768137i
$163$	− 1.19994e10i	− 1.33142i	−0.746212	−	0.665708i	$-0.768130\pi$
$163$	− 1.19994e10i	− 1.33142i	0.746212	−	0.665708i	$-0.231870\pi$
$164$	3.06875e9	0.331257
$165$	0	0
$166$	−1.30982e8	−0.0133882
$167$	9.68608e9i	0.963660i	0.876265	+	0.481830i	$0.160028\pi$
$167$	9.68608e9i	0.963660i	−0.876265	+	0.481830i	$0.839972\pi$
$168$	1.52219e9i	0.147427i
$169$	−4.70793e9	−0.443956
$170$	0	0
$171$	−2.03899e10	−1.82361
$172$	1.47971e9i	0.128913i
$173$	− 7.35665e9i	− 0.624414i	−0.950014	−	0.312207i	$-0.898932\pi$
$173$	− 7.35665e9i	− 0.624414i	0.950014	−	0.312207i	$-0.101068\pi$
$174$	−1.61567e9	−0.133623
$175$	0	0
$176$	8.34410e9	0.655500
$177$	− 2.28477e8i	− 0.0174969i
$178$	− 1.21007e10i	− 0.903481i
$179$	2.00351e9	0.145866	0.0729329	−	0.997337i	$-0.476764\pi$
$179$	2.00351e9	0.145866	0.0729329	+	0.997337i	$0.476764\pi$
$180$	0	0
$181$	5.63414e9	0.390188	0.195094	−	0.980785i	$-0.437499\pi$
$181$	5.63414e9	0.390188	0.195094	+	0.980785i	$0.437499\pi$
$182$	1.00248e10i	0.677258i
$183$	2.78151e9i	0.183337i
$184$	−1.87467e10	−1.20572
$185$	0	0
$186$	−2.01541e9	−0.123469
$187$	− 1.34729e10i	− 0.805701i
$188$	1.40599e8i	0.00820864i
$189$	−4.70225e9	−0.268057
$190$	0	0
$191$	9.16925e9	0.498521	0.249261	−	0.968436i	$-0.419812\pi$
$191$	9.16925e9	0.498521	0.249261	+	0.968436i	$0.419812\pi$
$192$	4.55409e9i	0.241850i
$193$	3.16327e10i	1.64107i	0.571594	+	0.820536i	$0.306325\pi$
$193$	3.16327e10i	1.64107i	−0.571594	+	0.820536i	$0.693675\pi$
$194$	1.86927e10	0.947469
$195$	0	0
$196$	2.52187e9	0.122059
$197$	2.59858e10i	1.22924i	0.788822	+	0.614621i	$0.210691\pi$
$197$	2.59858e10i	1.22924i	−0.788822	+	0.614621i	$0.789309\pi$
$198$	1.59522e10i	0.737613i
$199$	−1.05766e10	−0.478088	−0.239044	−	0.971009i	$-0.576834\pi$
$199$	−1.05766e10	−0.478088	−0.239044	+	0.971009i	$0.576834\pi$
$200$	0	0
$201$	8.98061e9	0.388082
$202$	− 1.93723e10i	− 0.818654i
$203$	− 1.05133e10i	− 0.434515i
$204$	1.01416e9	0.0409987
$205$	0	0
$206$	−3.24113e9	−0.125399
$207$	− 2.82544e10i	− 1.06960i
$208$	2.45198e10i	0.908304i
$209$	4.57873e10	1.65992
$210$	0	0
$211$	1.80228e10	0.625965	0.312983	−	0.949759i	$-0.398672\pi$
$211$	1.80228e10	0.625965	0.312983	+	0.949759i	$0.398672\pi$
$212$	− 1.01133e10i	− 0.343859i
$213$	− 4.76502e9i	− 0.158620i
$214$	1.94026e10	0.632409
$215$	0	0
$216$	−1.45891e10	−0.456023
$217$	− 1.31145e10i	− 0.401496i
$218$	2.01794e10i	0.605139i
$219$	8.61951e9	0.253212
$220$	0	0
$221$	3.95911e10	1.11643
$222$	1.54710e9i	0.0427493i
$223$	− 4.44522e10i	− 1.20371i	−0.798606	−	0.601855i	$-0.794429\pi$
$223$	− 4.44522e10i	− 1.20371i	0.798606	−	0.601855i	$-0.205571\pi$
$224$	−9.49405e9	−0.251962
$225$	0	0
$226$	−5.06460e10	−1.29139
$227$	5.59677e10i	1.39901i	0.714627	+	0.699505i	$0.246596\pi$
$227$	5.59677e10i	1.39901i	−0.714627	+	0.699505i	$0.753404\pi$
$228$	3.44660e9i	0.0844663i
$229$	1.47705e9	0.0354923	0.0177462	−	0.999843i	$-0.494351\pi$
$229$	1.47705e9	0.0354923	0.0177462	+	0.999843i	$0.494351\pi$
$230$	0	0
$231$	5.15182e9	0.119044
$232$	− 3.26182e10i	− 0.739203i
$233$	7.83279e9i	0.174106i	0.996204	+	0.0870532i	$0.0277450\pi$
$233$	7.83279e9i	0.174106i	−0.996204	+	0.0870532i	$0.972255\pi$
$234$	−4.68769e10	−1.02209
$235$	0	0
$236$	7.78152e8	0.0163290
$237$	− 1.69405e10i	− 0.348786i
$238$	− 2.59197e10i	− 0.523640i
$239$	−5.56371e10	−1.10300	−0.551498	−	0.834176i	$-0.685943\pi$
$239$	−5.56371e10	−1.10300	−0.551498	+	0.834176i	$0.685943\pi$
$240$	0	0
$241$	−1.16053e10	−0.221606	−0.110803	−	0.993842i	$-0.535342\pi$
$241$	−1.16053e10	−0.221606	−0.110803	+	0.993842i	$0.535342\pi$
$242$	1.18117e10i	0.221382i
$243$	− 3.32485e10i	− 0.611707i
$244$	−9.47334e9	−0.171100
$245$	0	0
$246$	−1.82021e10	−0.316893
$247$	1.34549e11i	2.30009i
$248$	− 4.06886e10i	− 0.683030i
$249$	−1.97803e8	−0.00326088
$250$	0	0
$251$	−3.45974e10	−0.550189	−0.275094	−	0.961417i	$-0.588709\pi$
$251$	−3.45974e10	−0.550189	−0.275094	+	0.961417i	$0.588709\pi$
$252$	− 7.81363e9i	− 0.122054i
$253$	6.34479e10i	0.973587i
$254$	−5.00067e10	−0.753836
$255$	0	0
$256$	−3.99972e10	−0.582036
$257$	− 3.67735e10i	− 0.525818i	−0.964821	−	0.262909i	$-0.915318\pi$
$257$	− 3.67735e10i	− 0.525818i	0.964821	−	0.262909i	$-0.0846820\pi$
$258$	− 8.77677e9i	− 0.123324i
$259$	−1.00671e10	−0.139013
$260$	0	0
$261$	4.91609e10	0.655750
$262$	− 3.88680e10i	− 0.509609i
$263$	− 1.33758e11i	− 1.72392i	−0.506974	−	0.861962i	$-0.669236\pi$
$263$	− 1.33758e11i	− 1.72392i	0.506974	−	0.861962i	$-0.330764\pi$
$264$	1.59839e10	0.202519
$265$	0	0
$266$	8.80873e10	1.07881
$267$	− 1.82739e10i	− 0.220055i
$268$	3.05864e10i	0.362178i
$269$	1.42461e11	1.65886	0.829429	−	0.558612i	$-0.188666\pi$
$269$	1.42461e11	1.65886	0.829429	+	0.558612i	$0.188666\pi$
$270$	0	0
$271$	−1.11046e11	−1.25067	−0.625333	−	0.780358i	$-0.715037\pi$
$271$	−1.11046e11	−1.25067	−0.625333	+	0.780358i	$0.715037\pi$
$272$	− 6.33972e10i	− 0.702279i
$273$	1.51390e10i	0.164955i
$274$	9.06224e9	0.0971310
$275$	0	0
$276$	−4.77598e9	−0.0495418
$277$	2.80726e10i	0.286500i	0.989687	+	0.143250i	$0.0457552\pi$
$277$	2.80726e10i	0.286500i	−0.989687	+	0.143250i	$0.954245\pi$
$278$	9.05861e10i	0.909620i
$279$	6.13244e10	0.605919
$280$	0	0
$281$	5.47143e10	0.523507	0.261753	−	0.965135i	$-0.415699\pi$
$281$	5.47143e10	0.523507	0.261753	+	0.965135i	$0.415699\pi$
$282$	− 8.33951e8i	− 0.00785271i
$283$	1.09950e11i	1.01895i	0.860484	+	0.509477i	$0.170161\pi$
$283$	1.09950e11i	1.01895i	−0.860484	+	0.509477i	$0.829839\pi$
$284$	1.62288e10	0.148032
$285$	0	0
$286$	1.05266e11	0.930341
$287$	− 1.18442e11i	− 1.03048i
$288$	− 4.43951e10i	− 0.380249i
$289$	1.62229e10	0.136801
$290$	0	0
$291$	2.82289e10	0.230768
$292$	2.93566e10i	0.236310i
$293$	2.30453e11i	1.82675i	0.407124	+	0.913373i	$0.366532\pi$
$293$	2.30453e11i	1.82675i	−0.407124	+	0.913373i	$0.633468\pi$
$294$	−1.49583e10	−0.116767
$295$	0	0
$296$	−3.12339e10	−0.236490
$297$	4.93764e10i	0.368227i
$298$	− 4.45400e10i	− 0.327173i
$299$	−1.86446e11	−1.34907
$300$	0	0
$301$	5.71111e10	0.401025
$302$	6.48966e10i	0.448943i
$303$	− 2.92552e10i	− 0.199394i
$304$	2.15454e11	1.44685
$305$	0	0
$306$	1.21203e11	0.790252
$307$	6.85036e10i	0.440140i	0.975484	+	0.220070i	$0.0706286\pi$
$307$	6.85036e10i	0.440140i	−0.975484	+	0.220070i	$0.929371\pi$
$308$	1.75462e10i	0.111098i
$309$	−4.89462e9	−0.0305426
$310$	0	0
$311$	−1.98797e11	−1.20500	−0.602502	−	0.798118i	$-0.705829\pi$
$311$	−1.98797e11	−1.20500	−0.602502	+	0.798118i	$0.705829\pi$
$312$	4.69699e10i	0.280624i
$313$	6.15202e10i	0.362300i	0.983455	+	0.181150i	$0.0579820\pi$
$313$	6.15202e10i	0.362300i	−0.983455	+	0.181150i	$0.942018\pi$
$314$	−2.19932e11	−1.27675
$315$	0	0
$316$	5.76965e10	0.325505
$317$	− 2.25932e11i	− 1.25664i	−0.777955	−	0.628320i	$-0.783743\pi$
$317$	− 2.25932e11i	− 1.25664i	0.777955	−	0.628320i	$-0.216257\pi$
$318$	5.99862e10i	0.328950i
$319$	−1.10395e11	−0.596888
$320$	0	0
$321$	2.93010e10	0.154031
$322$	1.22063e11i	0.632753i
$323$	− 3.47885e11i	− 1.77838i
$324$	3.46339e10	0.174602
$325$	0	0
$326$	−2.42404e11	−1.18867
$327$	3.04741e10i	0.147389i
$328$	− 3.67476e11i	− 1.75306i
$329$	5.42658e9	0.0255355
$330$	0	0
$331$	−8.38825e10	−0.384101	−0.192050	−	0.981385i	$-0.561514\pi$
$331$	−8.38825e10	−0.384101	−0.192050	+	0.981385i	$0.561514\pi$
$332$	− 6.73682e8i	− 0.00304322i
$333$	− 4.70746e10i	− 0.209791i
$334$	1.95673e11	0.860341
$335$	0	0
$336$	2.42421e10	0.103763
$337$	− 2.19457e11i	− 0.926862i	−0.886133	−	0.463431i	$-0.846618\pi$
$337$	− 2.19457e11i	− 0.926862i	0.886133	−	0.463431i	$-0.153382\pi$
$338$	9.51069e10i	0.396357i
$339$	−7.64834e10	−0.314535
$340$	0	0
$341$	−1.37710e11	−0.551530
$342$	4.11904e11i	1.62809i
$343$	− 2.59163e11i	− 1.01100i
$344$	1.77191e11	0.682228
$345$	0	0
$346$	−1.48615e11	−0.557467
$347$	− 1.85960e11i	− 0.688551i	−0.938869	−	0.344276i	$-0.888125\pi$
$347$	− 1.85960e11i	− 0.688551i	0.938869	−	0.344276i	$-0.111875\pi$
$348$	− 8.30990e9i	− 0.0303731i
$349$	−2.73237e11	−0.985881	−0.492940	−	0.870063i	$-0.664078\pi$
$349$	−2.73237e11	−0.985881	−0.492940	+	0.870063i	$0.664078\pi$
$350$	0	0
$351$	−1.45096e11	−0.510240
$352$	9.96932e10i	0.346117i
$353$	3.02861e11i	1.03814i	0.854731	+	0.519072i	$0.173722\pi$
$353$	3.02861e11i	1.03814i	−0.854731	+	0.519072i	$0.826278\pi$
$354$	−4.61555e9	−0.0156210
$355$	0	0
$356$	6.22378e10	0.205366
$357$	− 3.91427e10i	− 0.127539i
$358$	− 4.04738e10i	− 0.130227i
$359$	−2.47660e11	−0.786919	−0.393460	−	0.919342i	$-0.628722\pi$
$359$	−2.47660e11	−0.786919	−0.393460	+	0.919342i	$0.628722\pi$
$360$	0	0
$361$	8.59591e11	2.66385
$362$	− 1.13818e11i	− 0.348354i
$363$	1.78375e10i	0.0539205i
$364$	−5.15609e10	−0.153944
$365$	0	0
$366$	5.61904e10	0.163681
$367$	2.66354e11i	0.766412i	0.923663	+	0.383206i	$0.125180\pi$
$367$	2.66354e11i	0.766412i	−0.923663	+	0.383206i	$0.874820\pi$
$368$	2.98556e11i	0.848616i
$369$	5.53847e11	1.55515
$370$	0	0
$371$	−3.90335e11	−1.06968
$372$	− 1.03660e10i	− 0.0280651i
$373$	5.20850e11i	1.39323i	0.717445	+	0.696616i	$0.245312\pi$
$373$	5.20850e11i	1.39323i	−0.717445	+	0.696616i	$0.754688\pi$
$374$	−2.72172e11	−0.719318
$375$	0	0
$376$	1.68364e10	0.0434414
$377$	− 3.24405e11i	− 0.827088i
$378$	9.49921e10i	0.239318i
$379$	−3.28308e10	−0.0817344	−0.0408672	−	0.999165i	$-0.513012\pi$
$379$	−3.28308e10	−0.0817344	−0.0408672	+	0.999165i	$0.513012\pi$
$380$	0	0
$381$	−7.55180e10	−0.183607
$382$	− 1.85232e11i	− 0.445072i
$383$	7.15293e10i	0.169859i	0.996387	+	0.0849297i	$0.0270666\pi$
$383$	7.15293e10i	0.169859i	−0.996387	+	0.0849297i	$0.972933\pi$
$384$	5.50202e10	0.129131
$385$	0	0
$386$	6.39025e11	1.46513
$387$	2.67057e11i	0.605207i
$388$	9.61429e10i	0.215365i
$389$	2.02681e11	0.448787	0.224394	−	0.974499i	$-0.427960\pi$
$389$	2.02681e11	0.448787	0.224394	+	0.974499i	$0.427960\pi$
$390$	0	0
$391$	4.82067e11	1.04307
$392$	− 3.01989e11i	− 0.645956i
$393$	− 5.86968e10i	− 0.124122i
$394$	5.24949e11	1.09745
$395$	0	0
$396$	−8.20477e10	−0.167663
$397$	1.63266e10i	0.0329867i	0.999864	+	0.0164934i	$0.00525024\pi$
$397$	1.63266e10i	0.0329867i	−0.999864	+	0.0164934i	$0.994750\pi$
$398$	2.13663e11i	0.426830i
$399$	1.33026e11	0.262759
$400$	0	0
$401$	−8.20766e11	−1.58515	−0.792574	−	0.609776i	$-0.791259\pi$
$401$	−8.20766e11	−1.58515	−0.792574	+	0.609776i	$0.791259\pi$
$402$	− 1.81421e11i	− 0.346474i
$403$	− 4.04670e11i	− 0.764237i
$404$	9.96383e10	0.186085
$405$	0	0
$406$	−2.12383e11	−0.387929
$407$	1.05710e11i	0.190960i
$408$	− 1.21443e11i	− 0.216972i
$409$	4.24628e11	0.750332	0.375166	−	0.926958i	$-0.377586\pi$
$409$	4.24628e11	0.750332	0.375166	+	0.926958i	$0.377586\pi$
$410$	0	0
$411$	1.36854e10	0.0236575
$412$	− 1.66702e10i	− 0.0285039i
$413$	− 3.00337e10i	− 0.0507966i
$414$	−5.70780e11	−0.954920
$415$	0	0
$416$	−2.92956e11	−0.479603
$417$	1.36799e11i	0.221550i
$418$	− 9.24969e11i	− 1.48195i
$419$	1.26375e10	0.0200308	0.0100154	−	0.999950i	$-0.496812\pi$
$419$	1.26375e10	0.0200308	0.0100154	+	0.999950i	$0.496812\pi$
$420$	0	0
$421$	−3.04545e10	−0.0472479	−0.0236240	−	0.999721i	$-0.507520\pi$
$421$	−3.04545e10	−0.0472479	−0.0236240	+	0.999721i	$0.507520\pi$
$422$	− 3.64085e11i	− 0.558853i
$423$	2.53752e10i	0.0385370i
$424$	−1.21104e12	−1.81976
$425$	0	0
$426$	−9.62602e10	−0.141613
$427$	3.65635e11i	0.532259i
$428$	9.97940e10i	0.143750i
$429$	1.58969e11	0.226597
$430$	0	0
$431$	4.05830e11	0.566495	0.283248	−	0.959047i	$-0.408588\pi$
$431$	4.05830e11	0.566495	0.283248	+	0.959047i	$0.408588\pi$
$432$	2.32342e11i	0.320961i
$433$	− 1.36978e11i	− 0.187265i	−0.995607	−	0.0936324i	$-0.970152\pi$
$433$	− 1.36978e11i	− 0.187265i	0.995607	−	0.0936324i	$-0.0298478\pi$
$434$	−2.64931e11	−0.358450
$435$	0	0
$436$	−1.03790e11	−0.137551
$437$	1.63829e12i	2.14895i
$438$	− 1.74126e11i	− 0.226064i
$439$	−7.84981e11	−1.00872	−0.504358	−	0.863495i	$-0.668271\pi$
$439$	−7.84981e11	−1.00872	−0.504358	+	0.863495i	$0.668271\pi$
$440$	0	0
$441$	4.55146e11	0.573030
$442$	− 7.99797e11i	− 0.996734i
$443$	− 8.87799e11i	− 1.09521i	−0.836737	−	0.547605i	$-0.815540\pi$
$443$	− 8.87799e11i	− 1.09521i	0.836737	−	0.547605i	$-0.184460\pi$
$444$	−7.95724e9	−0.00971716
$445$	0	0
$446$	−8.97998e11	−1.07465
$447$	− 6.72624e10i	− 0.0796872i
$448$	5.98645e11i	0.702131i
$449$	−8.35477e11	−0.970122	−0.485061	−	0.874480i	$-0.661203\pi$
$449$	−8.35477e11	−0.970122	−0.485061	+	0.874480i	$0.661203\pi$
$450$	0	0
$451$	−1.24371e12	−1.41555
$452$	− 2.60489e11i	− 0.293540i
$453$	9.80041e10i	0.109346i
$454$	1.13063e12	1.24902
$455$	0	0
$456$	4.12722e11	0.447009
$457$	6.01172e11i	0.644727i	0.946616	+	0.322364i	$0.104477\pi$
$457$	6.01172e11i	0.644727i	−0.946616	+	0.322364i	$0.895523\pi$
$458$	− 2.98384e10i	− 0.0316870i
$459$	3.75154e11	0.394505
$460$	0	0
$461$	1.52807e12	1.57576	0.787879	−	0.615829i	$-0.211179\pi$
$461$	1.52807e12	1.57576	0.787879	+	0.615829i	$0.211179\pi$
$462$	− 1.04074e11i	− 0.106281i
$463$	7.80402e11i	0.789231i	0.918846	+	0.394615i	$0.129122\pi$
$463$	7.80402e11i	0.789231i	−0.918846	+	0.394615i	$0.870878\pi$
$464$	−5.19469e11	−0.520270
$465$	0	0
$466$	1.58234e11	0.155440
$467$	− 4.04751e11i	− 0.393788i	−0.980425	−	0.196894i	$-0.936915\pi$
$467$	− 4.04751e11i	− 0.393788i	0.980425	−	0.196894i	$-0.0630855\pi$
$468$	− 2.41103e11i	− 0.232326i
$469$	1.18052e12	1.12667
$470$	0	0
$471$	−3.32132e11	−0.310968
$472$	− 9.31820e10i	− 0.0864158i
$473$	− 5.99700e11i	− 0.550883i
$474$	−3.42223e11	−0.311391
$475$	0	0
$476$	1.33313e11	0.119026
$477$	− 1.82524e12i	− 1.61431i
$478$	1.12395e12i	0.984738i
$479$	2.06972e12	1.79640	0.898199	−	0.439588i	$-0.144876\pi$
$479$	2.06972e12	1.79640	0.898199	+	0.439588i	$0.144876\pi$
$480$	0	0
$481$	−3.10638e11	−0.264607
$482$	2.34444e11i	0.197846i
$483$	1.84335e11i	0.154115i
$484$	−6.07514e10	−0.0503213
$485$	0	0
$486$	−6.71666e11	−0.546123
$487$	− 2.41184e11i	− 0.194298i	−0.995270	−	0.0971490i	$-0.969028\pi$
$487$	− 2.41184e11i	− 0.194298i	0.995270	−	0.0971490i	$-0.0309723\pi$
$488$	1.13441e12i	0.905485i
$489$	−3.66068e11	−0.289516
$490$	0	0
$491$	2.27883e12	1.76948	0.884739	−	0.466088i	$-0.154337\pi$
$491$	2.27883e12	1.76948	0.884739	+	0.466088i	$0.154337\pi$
$492$	− 9.36194e10i	− 0.0720316i
$493$	8.38767e11i	0.639485i
$494$	2.71809e12	2.05349
$495$	0	0
$496$	−6.47997e11	−0.480735
$497$	− 6.26373e11i	− 0.460499i
$498$	3.99589e9i	0.00291127i
$499$	−9.88752e11	−0.713896	−0.356948	−	0.934124i	$-0.616183\pi$
$499$	−9.88752e11	−0.713896	−0.356948	+	0.934124i	$0.616183\pi$
$500$	0	0
$501$	2.95496e11	0.209547
$502$	6.98916e11i	0.491200i
$503$	− 1.22385e12i	− 0.852455i	−0.904616	−	0.426228i	$-0.859842\pi$
$503$	− 1.22385e12i	− 0.852455i	0.904616	−	0.426228i	$-0.140158\pi$
$504$	−9.35665e11	−0.645926
$505$	0	0
$506$	1.28174e12	0.869204
$507$	1.43626e11i	0.0965380i
$508$	− 2.57201e11i	− 0.171351i
$509$	−1.58447e12	−1.04629	−0.523146	−	0.852243i	$-0.675242\pi$
$509$	−1.58447e12	−1.04629	−0.523146	+	0.852243i	$0.675242\pi$
$510$	0	0
$511$	1.13305e12	0.735117
$512$	1.73140e12i	1.11348i
$513$	1.27495e12i	0.812767i
$514$	−7.42877e11	−0.469443
$515$	0	0
$516$	4.51418e10	0.0280321
$517$	− 5.69823e10i	− 0.0350778i
$518$	2.03369e11i	0.124109i
$519$	−2.24432e11	−0.135778
$520$	0	0
$521$	−2.71561e12	−1.61472	−0.807362	−	0.590057i	$-0.799105\pi$
$521$	−2.71561e12	−1.61472	−0.807362	+	0.590057i	$0.799105\pi$
$522$	− 9.93121e11i	− 0.585443i
$523$	2.16171e12i	1.26340i	0.775214	+	0.631698i	$0.217642\pi$
$523$	2.16171e12i	1.26340i	−0.775214	+	0.631698i	$0.782358\pi$
$524$	1.99911e11	0.115837
$525$	0	0
$526$	−2.70210e12	−1.53909
$527$	1.04630e12i	0.590890i
$528$	− 2.54556e11i	− 0.142538i
$529$	−4.69046e11	−0.260415
$530$	0	0
$531$	1.40441e11	0.0766597
$532$	4.53062e11i	0.245220i
$533$	− 3.65475e12i	− 1.96149i
$534$	−3.69159e11	−0.196462
$535$	0	0
$536$	3.66265e12	1.91670
$537$	− 6.11217e10i	− 0.0317184i
$538$	− 2.87791e12i	− 1.48100i
$539$	−1.02207e12	−0.521594
$540$	0	0
$541$	−2.29090e12	−1.14979	−0.574895	−	0.818227i	$-0.694957\pi$
$541$	−2.29090e12	−1.14979	−0.574895	+	0.818227i	$0.694957\pi$
$542$	2.24329e12i	1.11658i
$543$	− 1.71882e11i	− 0.0848462i
$544$	7.57453e11	0.370818
$545$	0	0
$546$	3.05830e11	0.147269
$547$	− 3.39447e12i	− 1.62117i	−0.585620	−	0.810586i	$-0.699149\pi$
$547$	− 3.39447e12i	− 1.62117i	0.585620	−	0.810586i	$-0.300851\pi$
$548$	4.66101e10i	0.0220784i
$549$	−1.70974e12	−0.803259
$550$	0	0
$551$	−2.85053e12	−1.31748
$552$	5.71913e11i	0.262183i
$553$	− 2.22687e12i	− 1.01259i
$554$	5.67107e11	0.255783
$555$	0	0
$556$	−4.65915e11	−0.206762
$557$	1.74706e12i	0.769060i	0.923113	+	0.384530i	$0.125636\pi$
$557$	1.74706e12i	0.769060i	−0.923113	+	0.384530i	$0.874364\pi$
$558$	− 1.23884e12i	− 0.540955i
$559$	1.76226e12	0.763340
$560$	0	0
$561$	−4.11022e11	−0.175199
$562$	− 1.10531e12i	− 0.467379i
$563$	2.58864e12i	1.08588i	0.839770	+	0.542942i	$0.182690\pi$
$563$	2.58864e12i	1.08588i	−0.839770	+	0.542942i	$0.817310\pi$
$564$	4.28929e9	0.00178496
$565$	0	0
$566$	2.22114e12	0.909707
$567$	− 1.33674e12i	− 0.543153i
$568$	− 1.94337e12i	− 0.783407i
$569$	1.99294e12	0.797055	0.398527	−	0.917156i	$-0.369521\pi$
$569$	1.99294e12	0.797055	0.398527	+	0.917156i	$0.369521\pi$
$570$	0	0
$571$	3.50761e10	0.0138086	0.00690428	−	0.999976i	$-0.497802\pi$
$571$	3.50761e10	0.0138086	0.00690428	+	0.999976i	$0.497802\pi$
$572$	5.41420e11i	0.211471i
$573$	− 2.79729e11i	− 0.108403i
$574$	−2.39270e12	−0.919995
$575$	0	0
$576$	−2.79932e12	−1.05962
$577$	− 7.75900e11i	− 0.291417i	−0.989328	−	0.145708i	$-0.953454\pi$
$577$	− 7.75900e11i	− 0.291417i	0.989328	−	0.145708i	$-0.0465461\pi$
$578$	− 3.27726e11i	− 0.122134i
$579$	9.65027e11	0.356850
$580$	0	0
$581$	−2.60016e10	−0.00946689
$582$	− 5.70265e11i	− 0.206027i
$583$	4.09874e12i	1.46941i
$584$	3.51538e12	1.25059
$585$	0	0
$586$	4.65548e12	1.63089
$587$	1.24477e12i	0.432730i	0.976313	+	0.216365i	$0.0694201\pi$
$587$	1.24477e12i	0.432730i	−0.976313	+	0.216365i	$0.930580\pi$
$588$	− 7.69355e10i	− 0.0265417i
$589$	−3.55581e12	−1.21736
$590$	0	0
$591$	7.92756e11	0.267298
$592$	4.97424e11i	0.166448i
$593$	2.57794e11i	0.0856103i	0.999083	+	0.0428052i	$0.0136295\pi$
$593$	2.57794e11i	0.0856103i	−0.999083	+	0.0428052i	$0.986371\pi$
$594$	9.97474e11	0.328747
$595$	0	0
$596$	2.29084e11	0.0743681
$597$	3.22664e11i	0.103960i
$598$	3.76648e12i	1.20443i
$599$	−2.32089e12	−0.736604	−0.368302	−	0.929706i	$-0.620061\pi$
$599$	−2.32089e12	−0.736604	−0.368302	+	0.929706i	$0.620061\pi$
$600$	0	0
$601$	1.78665e12	0.558605	0.279302	−	0.960203i	$-0.409897\pi$
$601$	1.78665e12	0.558605	0.279302	+	0.960203i	$0.409897\pi$
$602$	− 1.15373e12i	− 0.358029i
$603$	5.52022e12i	1.70031i
$604$	−3.33785e11	−0.102047
$605$	0	0
$606$	−5.90997e11	−0.178016
$607$	− 1.45787e12i	− 0.435883i	−0.975962	−	0.217941i	$-0.930066\pi$
$607$	− 1.45787e12i	− 0.435883i	0.975962	−	0.217941i	$-0.0699342\pi$
$608$	2.57419e12i	0.763966i
$609$	−3.20731e11	−0.0944851
$610$	0	0
$611$	1.67447e11	0.0486062
$612$	6.23386e11i	0.179629i
$613$	− 1.42075e12i	− 0.406394i	−0.979138	−	0.203197i	$-0.934867\pi$
$613$	− 1.42075e12i	− 0.406394i	0.979138	−	0.203197i	$-0.0651331\pi$
$614$	1.38387e12	0.392950
$615$	0	0
$616$	2.10112e12	0.587946
$617$	1.20441e12i	0.334573i	0.985908	+	0.167286i	$0.0535004\pi$
$617$	1.20441e12i	0.334573i	−0.985908	+	0.167286i	$0.946500\pi$
$618$	9.88782e10i	0.0272680i
$619$	4.91349e12	1.34519	0.672593	−	0.740013i	$-0.265181\pi$
$619$	4.91349e12	1.34519	0.672593	+	0.740013i	$0.265181\pi$
$620$	0	0
$621$	−1.76671e12	−0.476710
$622$	4.01598e12i	1.07581i
$623$	− 2.40214e12i	− 0.638856i
$624$	7.48032e11	0.197510
$625$	0	0
$626$	1.24280e12	0.323456
$627$	− 1.39685e12i	− 0.360948i
$628$	− 1.13118e12i	− 0.290211i
$629$	8.03171e11	0.204588
$630$	0	0
$631$	4.58663e12	1.15176	0.575879	−	0.817535i	$-0.304660\pi$
$631$	4.58663e12	1.15176	0.575879	+	0.817535i	$0.304660\pi$
$632$	− 6.90903e12i	− 1.72262i
$633$	− 5.49826e11i	− 0.136116i
$634$	−4.56414e12	−1.12191
$635$	0	0
$636$	−3.08529e11	−0.0747720
$637$	− 3.00344e12i	− 0.722755i
$638$	2.23014e12i	0.532893i
$639$	2.92898e12	0.694963
$640$	0	0
$641$	−2.30636e12	−0.539593	−0.269796	−	0.962917i	$-0.586956\pi$
$641$	−2.30636e12	−0.539593	−0.269796	+	0.962917i	$0.586956\pi$
$642$	− 5.91921e11i	− 0.137517i
$643$	− 2.59493e12i	− 0.598654i	−0.954151	−	0.299327i	$-0.903238\pi$
$643$	− 2.59493e12i	− 0.598654i	0.954151	−	0.299327i	$-0.0967622\pi$
$644$	−6.27813e11	−0.143828
$645$	0	0
$646$	−7.02777e12	−1.58771
$647$	5.14811e12i	1.15499i	0.816394	+	0.577495i	$0.195970\pi$
$647$	5.14811e12i	1.15499i	−0.816394	+	0.577495i	$0.804030\pi$
$648$	− 4.14733e12i	− 0.924019i
$649$	−3.15372e11	−0.0697786
$650$	0	0
$651$	−4.00087e11	−0.0873051
$652$	− 1.24676e12i	− 0.270191i
$653$	− 4.42559e12i	− 0.952492i	−0.879312	−	0.476246i	$-0.841997\pi$
$653$	− 4.42559e12i	− 0.952492i	0.879312	−	0.476246i	$-0.158003\pi$
$654$	6.15621e11	0.131587
$655$	0	0
$656$	−5.85234e12	−1.23385
$657$	5.29826e12i	1.10940i
$658$	− 1.09625e11i	− 0.0227977i
$659$	−1.09827e12	−0.226842	−0.113421	−	0.993547i	$-0.536181\pi$
$659$	−1.09827e12	−0.226842	−0.113421	+	0.993547i	$0.536181\pi$
$660$	0	0
$661$	7.99232e11	0.162842	0.0814209	−	0.996680i	$-0.474054\pi$
$661$	7.99232e11	0.162842	0.0814209	+	0.996680i	$0.474054\pi$
$662$	1.69455e12i	0.342919i
$663$	− 1.20782e12i	− 0.242768i
$664$	−8.06719e10	−0.0161052
$665$	0	0
$666$	−9.50974e11	−0.187299
$667$	− 3.95000e12i	− 0.772736i
$668$	1.00641e12i	0.195560i
$669$	−1.35612e12	−0.261746
$670$	0	0
$671$	3.83939e12	0.731157
$672$	2.89638e11i	0.0547891i
$673$	− 7.68445e12i	− 1.44393i	−0.691931	−	0.721963i	$-0.743240\pi$
$673$	− 7.68445e12i	− 1.44393i	0.691931	−	0.721963i	$-0.256760\pi$
$674$	−4.43334e12	−0.827488
$675$	0	0
$676$	−4.89167e11	−0.0900942
$677$	1.28854e12i	0.235749i	0.993029	+	0.117874i	$0.0376080\pi$
$677$	1.28854e12i	0.235749i	−0.993029	+	0.117874i	$0.962392\pi$
$678$	1.54507e12i	0.280812i
$679$	3.71076e12	0.669959
$680$	0	0
$681$	1.70742e12	0.304214
$682$	2.78193e12i	0.492398i
$683$	8.11444e11i	0.142681i	0.997452	+	0.0713404i	$0.0227277\pi$
$683$	8.11444e11i	0.142681i	−0.997452	+	0.0713404i	$0.977272\pi$
$684$	−2.11856e12	−0.370074
$685$	0	0
$686$	−5.23546e12	−0.902602
$687$	− 4.50607e10i	− 0.00771778i
$688$	− 2.82191e12i	− 0.480170i
$689$	−1.20445e13	−2.03611
$690$	0	0
$691$	2.26741e12	0.378338	0.189169	−	0.981945i	$-0.439421\pi$
$691$	2.26741e12	0.378338	0.189169	+	0.981945i	$0.439421\pi$
$692$	− 7.64375e11i	− 0.126715i
$693$	3.16673e12i	0.521569i
$694$	−3.75665e12	−0.614728
$695$	0	0
$696$	−9.95093e11	−0.160739
$697$	9.44955e12i	1.51657i
$698$	5.51977e12i	0.880180i
$699$	2.38957e11	0.0378594
$700$	0	0
$701$	−4.92113e12	−0.769721	−0.384861	−	0.922975i	$-0.625751\pi$
$701$	−4.92113e12	−0.769721	−0.384861	+	0.922975i	$0.625751\pi$
$702$	2.93115e12i	0.455534i
$703$	2.72956e12i	0.421496i
$704$	6.28612e12	0.964508
$705$	0	0
$706$	6.11822e12	0.926839
$707$	− 3.84566e12i	− 0.578874i
$708$	− 2.37393e10i	− 0.00355074i
$709$	6.12354e12	0.910112	0.455056	−	0.890463i	$-0.349619\pi$
$709$	6.12354e12	0.910112	0.455056	+	0.890463i	$0.349619\pi$
$710$	0	0
$711$	1.04130e13	1.52815
$712$	− 7.45283e12i	− 1.08683i
$713$	− 4.92732e12i	− 0.714016i
$714$	−7.90739e11	−0.113865
$715$	0	0
$716$	2.08170e11	0.0296012
$717$	1.69734e12i	0.239846i
$718$	5.00307e12i	0.702550i
$719$	2.30376e11	0.0321483	0.0160741	−	0.999871i	$-0.494883\pi$
$719$	2.30376e11	0.0321483	0.0160741	+	0.999871i	$0.494883\pi$
$720$	0	0
$721$	−6.43408e11	−0.0886702
$722$	− 1.73650e13i	− 2.37824i
$723$	3.54048e11i	0.0481880i
$724$	5.85402e11	0.0791827
$725$	0	0
$726$	3.60342e11	0.0481394
$727$	9.25894e12i	1.22930i	0.788801	+	0.614648i	$0.210702\pi$
$727$	9.25894e12i	1.22930i	−0.788801	+	0.614648i	$0.789298\pi$
$728$	6.17430e12i	0.814698i
$729$	5.54661e12	0.727368
$730$	0	0
$731$	−4.55643e12	−0.590196
$732$	2.89006e11i	0.0372055i
$733$	7.22531e12i	0.924461i	0.886760	+	0.462231i	$0.152951\pi$
$733$	7.22531e12i	0.924461i	−0.886760	+	0.462231i	$0.847049\pi$
$734$	5.38074e12	0.684241
$735$	0	0
$736$	−3.56707e12	−0.448086
$737$	− 1.23962e13i	− 1.54769i
$738$	− 1.11885e13i	− 1.38841i
$739$	1.24725e13	1.53834	0.769170	−	0.639044i	$-0.220670\pi$
$739$	1.24725e13	1.53834	0.769170	+	0.639044i	$0.220670\pi$
$740$	0	0
$741$	4.10474e12	0.500154
$742$	7.88531e12i	0.954996i
$743$	1.15645e13i	1.39212i	0.717986	+	0.696058i	$0.245064\pi$
$743$	1.15645e13i	1.39212i	−0.717986	+	0.696058i	$0.754936\pi$
$744$	−1.24130e12	−0.148525
$745$	0	0
$746$	1.05219e13	1.24386
$747$	− 1.21586e11i	− 0.0142870i
$748$	− 1.39987e12i	− 0.163505i
$749$	3.85167e12	0.447179
$750$	0	0
$751$	−3.70732e12	−0.425285	−0.212642	−	0.977130i	$-0.568207\pi$
$751$	−3.70732e12	−0.425285	−0.212642	+	0.977130i	$0.568207\pi$
$752$	− 2.68132e11i	− 0.0305752i
$753$	1.05547e12i	0.119638i
$754$	−6.55344e12	−0.738412
$755$	0	0
$756$	−4.88576e11	−0.0543982
$757$	− 4.86635e11i	− 0.0538607i	−0.999637	−	0.0269303i	$-0.991427\pi$
$757$	− 4.86635e11i	− 0.0538607i	0.999637	−	0.0269303i	$-0.00857323\pi$
$758$	6.63228e11i	0.0729712i
$759$	1.93562e12	0.211706
$760$	0	0
$761$	−4.28395e12	−0.463035	−0.231518	−	0.972831i	$-0.574369\pi$
$761$	−4.28395e12	−0.463035	−0.231518	+	0.972831i	$0.574369\pi$
$762$	1.52557e12i	0.163921i
$763$	4.00589e12i	0.427896i
$764$	9.52709e11	0.101167
$765$	0	0
$766$	1.44499e12	0.151648
$767$	− 9.26745e11i	− 0.0966899i
$768$	1.22021e12i	0.126563i
$769$	4.03625e12	0.416207	0.208103	−	0.978107i	$-0.433271\pi$
$769$	4.03625e12	0.416207	0.208103	+	0.978107i	$0.433271\pi$
$770$	0	0
$771$	−1.12186e12	−0.114339
$772$	3.28672e12i	0.333031i
$773$	− 1.21916e13i	− 1.22815i	−0.789247	−	0.614076i	$-0.789529\pi$
$773$	− 1.21916e13i	− 1.22815i	0.789247	−	0.614076i	$-0.210471\pi$
$774$	5.39492e12	0.540320
$775$	0	0
$776$	1.15129e13	1.13974
$777$	3.07120e11i	0.0302282i
$778$	− 4.09445e12i	− 0.400671i
$779$	−3.21141e13	−3.12447
$780$	0	0
$781$	−6.57728e12	−0.632582
$782$	− 9.73844e12i	− 0.931235i
$783$	− 3.07397e12i	− 0.292262i
$784$	−4.80940e12	−0.454641
$785$	0	0
$786$	−1.18576e12	−0.110814
$787$	− 1.20299e12i	− 0.111783i	−0.998437	−	0.0558913i	$-0.982200\pi$
$787$	− 1.20299e12i	− 0.111783i	0.998437	−	0.0558913i	$-0.0178000\pi$
$788$	2.69999e12i	0.249456i
$789$	−4.08059e12	−0.374866
$790$	0	0
$791$	−1.00539e13	−0.913147
$792$	9.82503e12i	0.887300i
$793$	1.12823e13i	1.01314i
$794$	3.29821e11	0.0294501
$795$	0	0
$796$	−1.09894e12	−0.0970208
$797$	1.72611e13i	1.51533i	0.652646	+	0.757663i	$0.273659\pi$
$797$	1.72611e13i	1.51533i	−0.652646	+	0.757663i	$0.726341\pi$
$798$	− 2.68731e12i	− 0.234587i
$799$	−4.32943e11	−0.0375811
$800$	0	0
$801$	1.12326e13	0.964130
$802$	1.65806e13i	1.41520i
$803$	− 1.18977e13i	− 1.00982i
$804$	9.33109e11	0.0787553
$805$	0	0
$806$	−8.17490e12	−0.682299
$807$	− 4.34609e12i	− 0.360718i
$808$	− 1.19315e13i	− 0.984788i
$809$	−7.44408e12	−0.611002	−0.305501	−	0.952192i	$-0.598824\pi$
$809$	−7.44408e12	−0.611002	−0.305501	+	0.952192i	$0.598824\pi$
$810$	0	0
$811$	−9.59955e12	−0.779214	−0.389607	−	0.920981i	$-0.627389\pi$
$811$	−9.59955e12	−0.779214	−0.389607	+	0.920981i	$0.627389\pi$
$812$	− 1.09235e12i	− 0.0881783i
$813$	3.38772e12i	0.271957i
$814$	2.13550e12	0.170486
$815$	0	0
$816$	−1.93408e12	−0.152710
$817$	− 1.54849e13i	− 1.21593i
$818$	− 8.57808e12i	− 0.669885i
$819$	−9.30568e12	−0.722721
$820$	0	0
$821$	−5.04043e12	−0.387189	−0.193595	−	0.981082i	$-0.562015\pi$
$821$	−5.04043e12	−0.387189	−0.193595	+	0.981082i	$0.562015\pi$
$822$	− 2.76464e11i	− 0.0211211i
$823$	− 1.62323e13i	− 1.23333i	−0.787225	−	0.616666i	$-0.788483\pi$
$823$	− 1.62323e13i	− 1.23333i	0.787225	−	0.616666i	$-0.211517\pi$
$824$	−1.99622e12	−0.150847
$825$	0	0
$826$	−6.06724e11	−0.0453504
$827$	− 1.74898e13i	− 1.30020i	−0.759850	−	0.650099i	$-0.774727\pi$
$827$	− 1.74898e13i	− 1.30020i	0.759850	−	0.650099i	$-0.225273\pi$
$828$	− 2.93571e12i	− 0.217058i
$829$	1.04102e13	0.765535	0.382768	−	0.923845i	$-0.374971\pi$
$829$	1.04102e13	0.765535	0.382768	+	0.923845i	$0.374971\pi$
$830$	0	0
$831$	8.56420e11	0.0622992
$832$	1.84722e13i	1.33649i
$833$	7.76555e12i	0.558817i
$834$	2.76354e12	0.197796
$835$	0	0
$836$	4.75742e12	0.336855
$837$	− 3.83454e12i	− 0.270053i
$838$	− 2.55296e11i	− 0.0178832i
$839$	2.66219e13	1.85485	0.927426	−	0.374006i	$-0.122016\pi$
$839$	2.66219e13	1.85485	0.927426	+	0.374006i	$0.122016\pi$
$840$	0	0
$841$	−7.63439e12	−0.526250
$842$	6.15225e11i	0.0421822i
$843$	− 1.66919e12i	− 0.113836i
$844$	1.87261e12	0.127030
$845$	0	0
$846$	5.12615e11	0.0344052
$847$	2.34477e12i	0.156540i
$848$	1.92868e13i	1.28079i
$849$	3.35427e12	0.221571
$850$	0	0
$851$	−3.78237e12	−0.247219
$852$	− 4.95098e11i	− 0.0321894i
$853$	7.30064e12i	0.472161i	0.971734	+	0.236080i	$0.0758629\pi$
$853$	7.30064e12i	0.472161i	−0.971734	+	0.236080i	$0.924137\pi$
$854$	7.38635e12	0.475192
$855$	0	0
$856$	1.19501e13	0.760747
$857$	− 1.18598e13i	− 0.751041i	−0.926814	−	0.375520i	$-0.877464\pi$
$857$	− 1.18598e13i	− 0.751041i	0.926814	−	0.375520i	$-0.122536\pi$
$858$	− 3.21139e12i	− 0.202302i
$859$	−1.67692e13	−1.05085	−0.525427	−	0.850839i	$-0.676094\pi$
$859$	−1.67692e13	−1.05085	−0.525427	+	0.850839i	$0.676094\pi$
$860$	0	0
$861$	−3.61336e12	−0.224077
$862$	− 8.19834e12i	− 0.505759i
$863$	− 6.71596e12i	− 0.412154i	−0.978536	−	0.206077i	$-0.933930\pi$
$863$	− 6.71596e12i	− 0.412154i	0.978536	−	0.206077i	$-0.0660698\pi$
$864$	−2.77597e12	−0.169474
$865$	0	0
$866$	−2.76716e12	−0.167187
$867$	− 4.94917e11i	− 0.0297472i
$868$	− 1.36263e12i	− 0.0814776i
$869$	−2.33834e13	−1.39098
$870$	0	0
$871$	3.64270e13	2.14458
$872$	1.24286e13i	0.727943i
$873$	1.73518e13i	1.01107i
$874$	3.30959e13	1.91855
$875$	0	0
$876$	8.95590e11	0.0513855
$877$	− 2.79757e13i	− 1.59692i	−0.602051	−	0.798458i	$-0.705649\pi$
$877$	− 2.79757e13i	− 1.59692i	0.602051	−	0.798458i	$-0.294351\pi$
$878$	1.58577e13i	0.900566i
$879$	7.03050e12	0.397225
$880$	0	0
$881$	2.06225e13	1.15332	0.576660	−	0.816984i	$-0.304356\pi$
$881$	2.06225e13	1.15332	0.576660	+	0.816984i	$0.304356\pi$
$882$	− 9.19460e12i	− 0.511593i
$883$	2.02048e13i	1.11849i	0.829003	+	0.559244i	$0.188909\pi$
$883$	2.02048e13i	1.11849i	−0.829003	+	0.559244i	$0.811091\pi$
$884$	4.11362e12	0.226563
$885$	0	0
$886$	−1.79348e13	−0.977788
$887$	3.19954e13i	1.73553i	0.496978	+	0.867763i	$0.334443\pi$
$887$	3.19954e13i	1.73553i	−0.496978	+	0.867763i	$0.665557\pi$
$888$	9.52862e11i	0.0514247i
$889$	−9.92701e12	−0.533041
$890$	0	0
$891$	−1.40365e13	−0.746122
$892$	− 4.61870e12i	− 0.244275i
$893$	− 1.47135e12i	− 0.0774254i
$894$	−1.35880e12	−0.0711436
$895$	0	0
$896$	7.23252e12	0.374890
$897$	5.68798e12i	0.293354i
$898$	1.68778e13i	0.866110i
$899$	8.57323e12	0.437750
$900$	0	0
$901$	3.11416e13	1.57427
$902$	2.51248e13i	1.26378i
$903$	− 1.74231e12i	− 0.0872026i
$904$	−3.11930e13	−1.55346
$905$	0	0
$906$	1.97982e12	0.0976223
$907$	2.40537e12i	0.118018i	0.998257	+	0.0590091i	$0.0187941\pi$
$907$	2.40537e12i	0.118018i	−0.998257	+	0.0590091i	$0.981206\pi$
$908$	5.81519e12i	0.283908i
$909$	1.79827e13	0.873609
$910$	0	0
$911$	−3.11773e13	−1.49970	−0.749852	−	0.661606i	$-0.769875\pi$
$911$	−3.11773e13	−1.49970	−0.749852	+	0.661606i	$0.769875\pi$
$912$	− 6.57292e12i	− 0.314616i
$913$	2.73032e11i	0.0130045i
$914$	1.21445e13	0.575603
$915$	0	0
$916$	1.53469e11	0.00720263
$917$	− 7.71582e12i	− 0.360346i
$918$	− 7.57865e12i	− 0.352208i
$919$	−3.42677e13	−1.58477	−0.792383	−	0.610024i	$-0.791160\pi$
$919$	−3.42677e13	−1.58477	−0.792383	+	0.610024i	$0.791160\pi$
$920$	0	0
$921$	2.08986e12	0.0957082
$922$	− 3.08692e13i	− 1.40681i
$923$	− 1.93278e13i	− 0.876548i
$924$	5.35288e11	0.0241581
$925$	0	0
$926$	1.57652e13	0.704614
$927$	− 3.00864e12i	− 0.133817i
$928$	− 6.20648e12i	− 0.274713i
$929$	2.52782e13	1.11346	0.556730	−	0.830693i	$-0.312056\pi$
$929$	2.52782e13	1.11346	0.556730	+	0.830693i	$0.312056\pi$
$930$	0	0
$931$	−2.63910e13	−1.15129
$932$	8.13848e11i	0.0353323i
$933$	6.06476e12i	0.262027i
$934$	−8.17655e12	−0.351568
$935$	0	0
$936$	−2.88716e13	−1.22950
$937$	2.72636e13i	1.15546i	0.816227	+	0.577731i	$0.196062\pi$
$937$	2.72636e13i	1.15546i	−0.816227	+	0.577731i	$0.803938\pi$
$938$	− 2.38482e13i	− 1.00587i
$939$	1.87682e12	0.0787819
$940$	0	0
$941$	1.57383e13	0.654340	0.327170	−	0.944966i	$-0.393905\pi$
$941$	1.57383e13	0.654340	0.327170	+	0.944966i	$0.393905\pi$
$942$	6.70953e12i	0.277628i
$943$	− 4.45008e13i	− 1.83259i
$944$	−1.48399e12	−0.0608217
$945$	0	0
$946$	−1.21148e13	−0.491820
$947$	− 9.71128e12i	− 0.392375i	−0.980566	−	0.196188i	$-0.937144\pi$
$947$	− 9.71128e12i	− 0.392375i	0.980566	−	0.196188i	$-0.0628562\pi$
$948$	− 1.76017e12i	− 0.0707809i
$949$	3.49624e13	1.39927
$950$	0	0
$951$	−6.89257e12	−0.273256
$952$	− 1.59640e13i	− 0.629905i
$953$	− 4.15385e12i	− 0.163130i	−0.996668	−	0.0815648i	$-0.974008\pi$
$953$	− 4.15385e12i	− 0.163130i	0.996668	−	0.0815648i	$-0.0259917\pi$
$954$	−3.68725e13	−1.44123
$955$	0	0
$956$	−5.78084e12	−0.223836
$957$	3.36787e12i	0.129793i
$958$	− 4.18114e13i	− 1.60380i
$959$	1.79897e12	0.0686818
$960$	0	0
$961$	−1.57452e13	−0.595515
$962$	6.27532e12i	0.236237i
$963$	1.80108e13i	0.674861i
$964$	−1.20582e12	−0.0449715
$965$	0	0
$966$	3.72383e12	0.137592
$967$	1.84544e13i	0.678706i	0.940659	+	0.339353i	$0.110208\pi$
$967$	1.84544e13i	0.678706i	−0.940659	+	0.339353i	$0.889792\pi$
$968$	7.27484e12i	0.266308i
$969$	−1.06130e13	−0.386707
$970$	0	0
$971$	−2.95973e12	−0.106848	−0.0534238	−	0.998572i	$-0.517013\pi$
$971$	−2.95973e12	−0.106848	−0.0534238	+	0.998572i	$0.517013\pi$
$972$	− 3.45460e12i	− 0.124137i
$973$	1.79826e13i	0.643197i
$974$	−4.87226e12	−0.173466
$975$	0	0
$976$	1.80664e13	0.637304
$977$	4.44178e13i	1.55967i	0.625988	+	0.779833i	$0.284696\pi$
$977$	4.44178e13i	1.55967i	−0.625988	+	0.779833i	$0.715304\pi$
$978$	7.39509e12i	0.258475i
$979$	−2.52239e13	−0.877588
$980$	0	0
$981$	−1.87319e13	−0.645761
$982$	− 4.60356e13i	− 1.57976i
$983$	− 4.57558e13i	− 1.56299i	−0.623914	−	0.781493i	$-0.714459\pi$
$983$	− 4.57558e13i	− 1.56299i	0.623914	−	0.781493i	$-0.285541\pi$
$984$	−1.12107e13	−0.381202
$985$	0	0
$986$	1.69443e13	0.570922
$987$	− 1.65550e11i	− 0.00555269i
$988$	1.39800e13i	0.466769i
$989$	2.14576e13	0.713177
$990$	0	0
$991$	1.30469e13	0.429710	0.214855	−	0.976646i	$-0.431072\pi$
$991$	1.30469e13	0.429710	0.214855	+	0.976646i	$0.431072\pi$
$992$	− 7.74210e12i	− 0.253838i
$993$	2.55903e12i	0.0835225i
$994$	−1.26536e13	−0.411127
$995$	0	0
$996$	−2.05522e10	−0.000661747 0
$997$	− 5.07578e12i	− 0.162695i	−0.996686	−	0.0813476i	$-0.974078\pi$
$997$	− 5.07578e12i	− 0.162695i	0.996686	−	0.0813476i	$-0.0259224\pi$
$998$	1.99742e13i	0.637356i
$999$	−2.94352e12	−0.0935022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.10.b.c.24.3		6
3.2	odd	2		225.10.b.m.199.4		6
4.3	odd	2		400.10.c.q.49.4		6
5.2	odd	4		25.10.a.c.1.3	✓	3
5.3	odd	4		25.10.a.d.1.1	yes	3
5.4	even	2	inner	25.10.b.c.24.4		6
15.2	even	4		225.10.a.p.1.1		3
15.8	even	4		225.10.a.m.1.3		3
15.14	odd	2		225.10.b.m.199.3		6
20.3	even	4		400.10.a.u.1.2		3
20.7	even	4		400.10.a.y.1.2		3
20.19	odd	2		400.10.c.q.49.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.10.a.c.1.3	✓	3	5.2	odd	4
25.10.a.d.1.1	yes	3	5.3	odd	4
25.10.b.c.24.3		6	1.1	even	1	trivial
25.10.b.c.24.4		6	5.4	even	2	inner
225.10.a.m.1.3		3	15.8	even	4
225.10.a.p.1.1		3	15.2	even	4
225.10.b.m.199.3		6	15.14	odd	2
225.10.b.m.199.4		6	3.2	odd	2
400.10.a.u.1.2		3	20.3	even	4
400.10.a.y.1.2		3	20.7	even	4
400.10.c.q.49.3		6	20.19	odd	2
400.10.c.q.49.4		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-20.2014i q^{2} -30.5073i q^{3} +103.903 q^{4} -616.291 q^{6} -4010.25i q^{7} -12442.1i q^{8} +18752.3 q^{9} -42110.0 q^{11} -3169.79i q^{12} -123743. i q^{13} -81012.8 q^{14} -198150. q^{16} +319945. i q^{17} -378823. i q^{18} -1.08733e6 q^{19} -122342. q^{21} +850682. i q^{22} -1.50672e6i q^{23} -379575. q^{24} -2.49979e6 q^{26} -1.17256e6i q^{27} -416676. i q^{28} +2.62160e6 q^{29} +3.27023e6 q^{31} -2.36745e6i q^{32} +1.28466e6i q^{33} +6.46335e6 q^{34} +1.94841e6 q^{36} -2.51034e6i q^{37} +2.19655e7i q^{38} -3.77508e6 q^{39} +2.95349e7 q^{41} +2.47148e6i q^{42} +1.42413e7i q^{43} -4.37534e6 q^{44} -3.04378e7 q^{46} +1.35318e6i q^{47} +6.04503e6i q^{48} +2.42715e7 q^{49} +9.76067e6 q^{51} -1.28573e7i q^{52} -9.73342e7i q^{53} -2.36873e7 q^{54} -4.98960e7 q^{56} +3.31714e7i q^{57} -5.29599e7i q^{58} +7.48924e6 q^{59} -9.11752e7 q^{61} -6.60633e7i q^{62} -7.52015e7i q^{63} -1.49279e8 q^{64} +2.59520e7 q^{66} +2.94376e8i q^{67} +3.32432e7i q^{68} -4.59659e7 q^{69} +1.56193e8 q^{71} -2.33318e8i q^{72} +2.82539e8i q^{73} -5.07124e7 q^{74} -1.12976e8 q^{76} +1.68872e8i q^{77} +7.62619e7i q^{78} +5.55294e8 q^{79} +3.33330e8 q^{81} -5.96647e8i q^{82} -6.48378e6i q^{83} -1.27117e7 q^{84} +2.87694e8 q^{86} -7.99778e7i q^{87} +5.23937e8i q^{88} +5.99001e8 q^{89} -4.96242e8 q^{91} -1.56552e8i q^{92} -9.97660e7i q^{93} +2.73361e7 q^{94} -7.22244e7 q^{96} +9.25317e8i q^{97} -4.90319e8i q^{98} -7.89660e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 682 q^{4} + 6842 q^{6} - 116468 q^{9} - 109398 q^{11} - 545844 q^{14} - 1398494 q^{16} - 1637690 q^{19} - 4750788 q^{21} - 5611470 q^{24} - 2560008 q^{26} - 4350960 q^{29} + 8548132 q^{31} + 13677926 q^{34}+ \cdots + 1784469044 q^{99}+O(q^{100}) \) 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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