LMFDB - Embedded newform 175.10.b.g.99.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,10,Mod(99,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("175.99");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.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:	$90.1312713287$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6045 x^{10} + 13278528 x^{8} + 12528585876 x^{6} + 4315564707360 x^{4} + 82968810446400 x^{2} + 360088576000000 $ x^12 + 6045x^10 + 13278528x^8 + 12528585876x^6 + 4315564707360x^4 + 82968810446400*x^2 + 360088576000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.9
Root			$28.3435i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.g.99.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+26.3435i q^{2} -1.97103i q^{3} -181.982 q^{4} +51.9238 q^{6} +2401.00i q^{7} +8693.85i q^{8} +19679.1 q^{9} -2245.43 q^{11} +358.691i q^{12} -123379. i q^{13} -63250.8 q^{14} -322201. q^{16} +18794.1i q^{17} +518417. i q^{18} -404776. q^{19} +4732.44 q^{21} -59152.4i q^{22} +1.75527e6i q^{23} +17135.8 q^{24} +3.25024e6 q^{26} -77583.8i q^{27} -436938. i q^{28} -3.94483e6 q^{29} +8.99428e6 q^{31} -4.03667e6i q^{32} +4425.79i q^{33} -495103. q^{34} -3.58124e6 q^{36} +1.04609e7i q^{37} -1.06632e7i q^{38} -243184. q^{39} +3.02704e6 q^{41} +124669. i q^{42} +1.60767e7i q^{43} +408626. q^{44} -4.62401e7 q^{46} +3.97557e7i q^{47} +635067. i q^{48} -5.76480e6 q^{49} +37043.7 q^{51} +2.24528e7i q^{52} +4.08073e7i q^{53} +2.04383e6 q^{54} -2.08739e7 q^{56} +797825. i q^{57} -1.03921e8i q^{58} -1.60585e8 q^{59} +1.49289e8 q^{61} +2.36941e8i q^{62} +4.72496e7i q^{63} -5.86269e7 q^{64} -116591. q^{66} -5.12683e7i q^{67} -3.42018e6i q^{68} +3.45969e6 q^{69} -3.35362e8 q^{71} +1.71087e8i q^{72} +1.35293e8i q^{73} -2.75578e8 q^{74} +7.36618e7 q^{76} -5.39127e6i q^{77} -6.40632e6i q^{78} -1.65365e8 q^{79} +3.87191e8 q^{81} +7.97429e7i q^{82} -1.61436e8i q^{83} -861217. q^{84} -4.23516e8 q^{86} +7.77536e6i q^{87} -1.95214e7i q^{88} -1.00313e9 q^{89} +2.96233e8 q^{91} -3.19428e8i q^{92} -1.77280e7i q^{93} -1.04731e9 q^{94} -7.95639e6 q^{96} +2.89165e8i q^{97} -1.51865e8i q^{98} -4.41880e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6018 q^{4} + 9776 q^{6} - 222180 q^{9} - 95592 q^{11} + 72030 q^{14} + 4742130 q^{16} - 722112 q^{19} + 595448 q^{21} - 9656152 q^{24} + 21695244 q^{26} - 32056368 q^{29} + 2725824 q^{31} + 18432588 q^{34}+ \cdots - 7143937568 q^{99}+O(q^{100}) $ 12 * q - 6018 * q^4 + 9776 * q^6 - 222180 * q^9 - 95592 * q^11 + 72030 * q^14 + 4742130 * q^16 - 722112 * q^19 + 595448 * q^21 - 9656152 * q^24 + 21695244 * q^26 - 32056368 * q^29 + 2725824 * q^31 + 18432588 * q^34 + 184639282 * q^36 + 40683736 * q^39 + 44905512 * q^41 + 188757456 * q^44 + 99179040 * q^46 - 69177612 * q^49 - 562676360 * q^51 + 580208616 * q^54 - 105840882 * q^56 - 240560784 * q^59 - 175387080 * q^61 - 1281294210 * q^64 - 2787941384 * q^66 - 2063267280 * q^69 + 507525024 * q^71 + 837612108 * q^74 - 1169438952 * q^76 - 1662159000 * q^79 + 3738629420 * q^81 - 2601032112 * q^84 + 1132399896 * q^86 - 1165159368 * q^89 - 490610736 * q^91 + 2231893320 * q^94 + 1978690504 * q^96 - 7143937568 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	26.3435i	1.16423i	0.813106	+	0.582115i	$0.197775\pi$
$2$	26.3435i	1.16423i	−0.813106	+	0.582115i	$0.802225\pi$
$3$	− 1.97103i	− 0.0140490i	−0.999975	−	0.00702452i	$-0.997764\pi$
$3$	− 1.97103i	− 0.0140490i	0.999975	−	0.00702452i	$-0.00223599\pi$
$4$	−181.982	−0.355433
$5$	0	0
$5$	0	0
$6$	51.9238	0.0163563
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	8693.85i	0.750425i
$9$	19679.1	0.999803
$10$	0	0
$11$	−2245.43	−0.0462415	−0.0231207	−	0.999733i	$-0.507360\pi$
$11$	−2245.43	−0.0462415	−0.0231207	+	0.999733i	$0.507360\pi$
$12$	358.691i	0.00499350i
$13$	− 123379.i	− 1.19811i	−0.800708	−	0.599055i	$-0.795543\pi$
$13$	− 123379.i	− 1.19811i	0.800708	−	0.599055i	$-0.204457\pi$
$14$	−63250.8	−0.440038
$15$	0	0
$16$	−322201.	−1.22910
$17$	18794.1i	0.0545760i	0.999628	+	0.0272880i	$0.00868711\pi$
$17$	18794.1i	0.0545760i	−0.999628	+	0.0272880i	$0.991313\pi$
$18$	518417.i	1.16400i
$19$	−404776.	−0.712564	−0.356282	−	0.934379i	$-0.615956\pi$
$19$	−404776.	−0.712564	−0.356282	+	0.934379i	$0.615956\pi$
$20$	0	0
$21$	4732.44	0.00531004
$22$	− 59152.4i	− 0.0538357i
$23$	1.75527e6i	1.30789i	0.756544	+	0.653943i	$0.226886\pi$
$23$	1.75527e6i	1.30789i	−0.756544	+	0.653943i	$0.773114\pi$
$24$	17135.8	0.0105428
$25$	0	0
$26$	3.25024e6	1.39488
$27$	− 77583.8i	− 0.0280953i
$28$	− 436938.i	− 0.134341i
$29$	−3.94483e6	−1.03571	−0.517854	−	0.855469i	$-0.673269\pi$
$29$	−3.94483e6	−1.03571	−0.517854	+	0.855469i	$0.673269\pi$
$30$	0	0
$31$	8.99428e6	1.74920	0.874599	−	0.484847i	$-0.161125\pi$
$31$	8.99428e6	1.74920	0.874599	+	0.484847i	$0.161125\pi$
$32$	− 4.03667e6i	− 0.680532i
$33$	4425.79i	0 0.000649648i
$34$	−495103.	−0.0635390
$35$	0	0
$36$	−3.58124e6	−0.355363
$37$	1.04609e7i	0.917618i	0.888535	+	0.458809i	$0.151724\pi$
$37$	1.04609e7i	0.917618i	−0.888535	+	0.458809i	$0.848276\pi$
$38$	− 1.06632e7i	− 0.829589i
$39$	−243184.	−0.0168323
$40$	0	0
$41$	3.02704e6	0.167298	0.0836489	−	0.996495i	$-0.473343\pi$
$41$	3.02704e6	0.167298	0.0836489	+	0.996495i	$0.473343\pi$
$42$	124669.i	0.00618211i
$43$	1.60767e7i	0.717114i	0.933508	+	0.358557i	$0.116731\pi$
$43$	1.60767e7i	0.717114i	−0.933508	+	0.358557i	$0.883269\pi$
$44$	408626.	0.0164357
$45$	0	0
$46$	−4.62401e7	−1.52268
$47$	3.97557e7i	1.18839i	0.804321	+	0.594196i	$0.202529\pi$
$47$	3.97557e7i	1.18839i	−0.804321	+	0.594196i	$0.797471\pi$
$48$	635067.i	0.0172677i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	37043.7	0.000766740 0
$52$	2.24528e7i	0.425848i
$53$	4.08073e7i	0.710389i	0.934792	+	0.355195i	$0.115585\pi$
$53$	4.08073e7i	0.710389i	−0.934792	+	0.355195i	$0.884415\pi$
$54$	2.04383e6	0.0327094
$55$	0	0
$56$	−2.08739e7	−0.283634
$57$	797825.i	0.0100108i
$58$	− 1.03921e8i	− 1.20580i
$59$	−1.60585e8	−1.72532	−0.862660	−	0.505784i	$-0.831203\pi$
$59$	−1.60585e8	−1.72532	−0.862660	+	0.505784i	$0.831203\pi$
$60$	0	0
$61$	1.49289e8	1.38052	0.690260	−	0.723561i	$-0.257496\pi$
$61$	1.49289e8	1.38052	0.690260	+	0.723561i	$0.257496\pi$
$62$	2.36941e8i	2.03647i
$63$	4.72496e7i	0.377890i
$64$	−5.86269e7	−0.436805
$65$	0	0
$66$	−116591.	−0.000756341 0
$67$	− 5.12683e7i	− 0.310822i	−0.987850	−	0.155411i	$-0.950330\pi$
$67$	− 5.12683e7i	− 0.310822i	0.987850	−	0.155411i	$-0.0496702\pi$
$68$	− 3.42018e6i	− 0.0193981i
$69$	3.45969e6	0.0183745
$70$	0	0
$71$	−3.35362e8	−1.56622	−0.783108	−	0.621886i	$-0.786367\pi$
$71$	−3.35362e8	−1.56622	−0.783108	+	0.621886i	$0.786367\pi$
$72$	1.71087e8i	0.750277i
$73$	1.35293e8i	0.557601i	0.960349	+	0.278801i	$0.0899368\pi$
$73$	1.35293e8i	0.557601i	−0.960349	+	0.278801i	$0.910063\pi$
$74$	−2.75578e8	−1.06832
$75$	0	0
$76$	7.36618e7	0.253269
$77$	− 5.39127e6i	− 0.0174776i
$78$	− 6.40632e6i	− 0.0195967i
$79$	−1.65365e8	−0.477665	−0.238832	−	0.971061i	$-0.576765\pi$
$79$	−1.65365e8	−0.477665	−0.238832	+	0.971061i	$0.576765\pi$
$80$	0	0
$81$	3.87191e8	0.999408
$82$	7.97429e7i	0.194773i
$83$	− 1.61436e8i	− 0.373379i	−0.982419	−	0.186690i	$-0.940224\pi$
$83$	− 1.61436e8i	− 0.373379i	0.982419	−	0.186690i	$-0.0597759\pi$
$84$	−861217.	−0.00188736
$85$	0	0
$86$	−4.23516e8	−0.834886
$87$	7.77536e6i	0.0145507i
$88$	− 1.95214e7i	− 0.0347007i
$89$	−1.00313e9	−1.69473	−0.847366	−	0.531009i	$-0.821813\pi$
$89$	−1.00313e9	−1.69473	−0.847366	+	0.531009i	$0.821813\pi$
$90$	0	0
$91$	2.96233e8	0.452843
$92$	− 3.19428e8i	− 0.464866i
$93$	− 1.77280e7i	− 0.0245746i
$94$	−1.04731e9	−1.38356
$95$	0	0
$96$	−7.95639e6	−0.00956082
$97$	2.89165e8i	0.331644i	0.986156	+	0.165822i	$0.0530278\pi$
$97$	2.89165e8i	0.331644i	−0.986156	+	0.165822i	$0.946972\pi$
$98$	− 1.51865e8i	− 0.166319i
$99$	−4.41880e7	−0.0462323
$100$	0	0
$101$	1.57210e8	0.150326	0.0751629	−	0.997171i	$-0.476052\pi$
$101$	1.57210e8	0.150326	0.0751629	+	0.997171i	$0.476052\pi$
$102$	975861.i	0 0.000892663i
$103$	5.15072e8i	0.450921i	0.974252	+	0.225461i	$0.0723887\pi$
$103$	5.15072e8i	0.450921i	−0.974252	+	0.225461i	$0.927611\pi$
$104$	1.07264e9	0.899092
$105$	0	0
$106$	−1.07501e9	−0.827057
$107$	2.36823e9i	1.74662i	0.487168	+	0.873308i	$0.338030\pi$
$107$	2.36823e9i	1.74662i	−0.487168	+	0.873308i	$0.661970\pi$
$108$	1.41188e7i	0.00998601i
$109$	−2.25821e8	−0.153231	−0.0766154	−	0.997061i	$-0.524411\pi$
$109$	−2.25821e8	−0.153231	−0.0766154	+	0.997061i	$0.524411\pi$
$110$	0	0
$111$	2.06188e7	0.0128917
$112$	− 7.73605e8i	− 0.464556i
$113$	− 2.93829e9i	− 1.69528i	−0.530572	−	0.847640i	$-0.678023\pi$
$113$	− 2.93829e9i	− 1.69528i	0.530572	−	0.847640i	$-0.321977\pi$
$114$	−2.10175e7	−0.0116549
$115$	0	0
$116$	7.17886e8	0.368125
$117$	− 2.42799e9i	− 1.19787i
$118$	− 4.23036e9i	− 2.00867i
$119$	−4.51246e7	−0.0206278
$120$	0	0
$121$	−2.35291e9	−0.997862
$122$	3.93279e9i	1.60724i
$123$	− 5.96637e6i	− 0.00235038i
$124$	−1.63679e9	−0.621723
$125$	0	0
$126$	−1.24472e9	−0.439951
$127$	− 3.08644e9i	− 1.05279i	−0.850241	−	0.526393i	$-0.823544\pi$
$127$	− 3.08644e9i	− 1.05279i	0.850241	−	0.526393i	$-0.176456\pi$
$128$	− 3.61122e9i	− 1.18907i
$129$	3.16876e7	0.0100748
$130$	0	0
$131$	−2.40858e9	−0.714561	−0.357281	−	0.933997i	$-0.616296\pi$
$131$	−2.40858e9	−0.714561	−0.357281	+	0.933997i	$0.616296\pi$
$132$	− 805413.i	0 0.000230906i
$133$	− 9.71868e8i	− 0.269324i
$134$	1.35059e9	0.361869
$135$	0	0
$136$	−1.63393e8	−0.0409551
$137$	− 5.47458e9i	− 1.32772i	−0.747855	−	0.663862i	$-0.768916\pi$
$137$	− 5.47458e9i	− 1.32772i	0.747855	−	0.663862i	$-0.231084\pi$
$138$	9.11405e7i	0.0213922i
$139$	−9.08897e8	−0.206513	−0.103257	−	0.994655i	$-0.532926\pi$
$139$	−9.08897e8	−0.206513	−0.103257	+	0.994655i	$0.532926\pi$
$140$	0	0
$141$	7.83596e7	0.0166958
$142$	− 8.83462e9i	− 1.82344i
$143$	2.77039e8i	0.0554024i
$144$	−6.34064e9	−1.22886
$145$	0	0
$146$	−3.56411e9	−0.649176
$147$	1.13626e7i	0.00200701i
$148$	− 1.90370e9i	− 0.326152i
$149$	−6.00080e9	−0.997403	−0.498702	−	0.866774i	$-0.666190\pi$
$149$	−6.00080e9	−0.997403	−0.498702	+	0.866774i	$0.666190\pi$
$150$	0	0
$151$	5.35390e9	0.838058	0.419029	−	0.907973i	$-0.362371\pi$
$151$	5.35390e9	0.838058	0.419029	+	0.907973i	$0.362371\pi$
$152$	− 3.51906e9i	− 0.534725i
$153$	3.69851e8i	0.0545652i
$154$	1.42025e8	0.0203480
$155$	0	0
$156$	4.42550e7	0.00598276
$157$	3.05256e8i	0.0400973i	0.999799	+	0.0200487i	$0.00638211\pi$
$157$	3.05256e8i	0.0400973i	−0.999799	+	0.0200487i	$0.993618\pi$
$158$	− 4.35631e9i	− 0.556112i
$159$	8.04323e7	0.00998030
$160$	0	0
$161$	−4.21441e9	−0.494334
$162$	1.02000e10i	1.16354i
$163$	9.53729e9i	1.05823i	0.848550	+	0.529116i	$0.177476\pi$
$163$	9.53729e9i	1.05823i	−0.848550	+	0.529116i	$0.822524\pi$
$164$	−5.50865e8	−0.0594632
$165$	0	0
$166$	4.25281e9	0.434700
$167$	7.59729e9i	0.755848i	0.925837	+	0.377924i	$0.123362\pi$
$167$	7.59729e9i	0.755848i	−0.925837	+	0.377924i	$0.876638\pi$
$168$	4.11431e7i	0.00398479i
$169$	−4.61792e9	−0.435468
$170$	0	0
$171$	−7.96564e9	−0.712423
$172$	− 2.92566e9i	− 0.254886i
$173$	− 1.61106e10i	− 1.36742i	−0.729751	−	0.683712i	$-0.760364\pi$
$173$	− 1.61106e10i	− 1.36742i	0.729751	−	0.683712i	$-0.239636\pi$
$174$	−2.04831e8	−0.0169404
$175$	0	0
$176$	7.23479e8	0.0568354
$177$	3.16516e8i	0.0242391i
$178$	− 2.64259e10i	− 1.97306i
$179$	−5.90583e9	−0.429974	−0.214987	−	0.976617i	$-0.568971\pi$
$179$	−5.90583e9	−0.429974	−0.214987	+	0.976617i	$0.568971\pi$
$180$	0	0
$181$	−4.57036e9	−0.316517	−0.158258	−	0.987398i	$-0.550588\pi$
$181$	−4.57036e9	−0.316517	−0.158258	+	0.987398i	$0.550588\pi$
$182$	7.80383e9i	0.527214i
$183$	− 2.94252e8i	− 0.0193950i
$184$	−1.52601e10	−0.981469
$185$	0	0
$186$	4.67018e8	0.0286105
$187$	− 4.22007e7i	− 0.00252367i
$188$	− 7.23481e9i	− 0.422393i
$189$	1.86279e8	0.0106190
$190$	0	0
$191$	1.08620e10	0.590555	0.295277	−	0.955412i	$-0.404588\pi$
$191$	1.08620e10	0.590555	0.295277	+	0.955412i	$0.404588\pi$
$192$	1.15555e8i	0.00613669i
$193$	3.53101e10i	1.83185i	0.401346	+	0.915926i	$0.368542\pi$
$193$	3.53101e10i	1.83185i	−0.401346	+	0.915926i	$0.631458\pi$
$194$	−7.61762e9	−0.386110
$195$	0	0
$196$	1.04909e9	0.0507761
$197$	1.34688e10i	0.637136i	0.947900	+	0.318568i	$0.103202\pi$
$197$	1.34688e10i	0.637136i	−0.947900	+	0.318568i	$0.896798\pi$
$198$	− 1.16407e9i	− 0.0538251i
$199$	2.38956e10	1.08014	0.540068	−	0.841621i	$-0.318399\pi$
$199$	2.38956e10	1.08014	0.540068	+	0.841621i	$0.318399\pi$
$200$	0	0
$201$	−1.01051e8	−0.00436676
$202$	4.14146e9i	0.175014i
$203$	− 9.47153e9i	− 0.391461i
$204$	−6.74127e6	−0.000272525 0
$205$	0	0
$206$	−1.35688e10	−0.524976
$207$	3.45422e10i	1.30763i
$208$	3.97529e10i	1.47260i
$209$	9.08895e8	0.0329500
$210$	0	0
$211$	−2.71767e10	−0.943898	−0.471949	−	0.881626i	$-0.656449\pi$
$211$	−2.71767e10	−0.943898	−0.471949	+	0.881626i	$0.656449\pi$
$212$	− 7.42618e9i	− 0.252496i
$213$	6.61008e8i	0.0220038i
$214$	−6.23876e10	−2.03346
$215$	0	0
$216$	6.74502e8	0.0210834
$217$	2.15953e10i	0.661135i
$218$	− 5.94893e9i	− 0.178396i
$219$	2.66667e8	0.00783377
$220$	0	0
$221$	2.31880e9	0.0653880
$222$	5.43171e8i	0.0150089i
$223$	− 2.65338e8i	− 0.00718502i	−0.999994	−	0.00359251i	$-0.998856\pi$
$223$	− 2.65338e8i	− 0.00718502i	0.999994	−	0.00359251i	$-0.00114353\pi$
$224$	9.69204e9	0.257217
$225$	0	0
$226$	7.74049e10	1.97370
$227$	2.92609e10i	0.731428i	0.930727	+	0.365714i	$0.119175\pi$
$227$	2.92609e10i	0.731428i	−0.930727	+	0.365714i	$0.880825\pi$
$228$	− 1.45189e8i	− 0.00355818i
$229$	3.93335e10	0.945156	0.472578	−	0.881289i	$-0.343324\pi$
$229$	3.93335e10	0.945156	0.472578	+	0.881289i	$0.343324\pi$
$230$	0	0
$231$	−1.06263e7	−0.000245544 0
$232$	− 3.42957e10i	− 0.777220i
$233$	4.02983e10i	0.895746i	0.894097	+	0.447873i	$0.147818\pi$
$233$	4.02983e10i	0.895746i	−0.894097	+	0.447873i	$0.852182\pi$
$234$	6.39619e10	1.39460
$235$	0	0
$236$	2.92234e10	0.613236
$237$	3.25940e8i	0.00671073i
$238$	− 1.18874e9i	− 0.0240155i
$239$	−3.54020e10	−0.701839	−0.350919	−	0.936406i	$-0.614131\pi$
$239$	−3.54020e10	−0.701839	−0.350919	+	0.936406i	$0.614131\pi$
$240$	0	0
$241$	3.42729e9	0.0654446	0.0327223	−	0.999464i	$-0.489582\pi$
$241$	3.42729e9	0.0654446	0.0327223	+	0.999464i	$0.489582\pi$
$242$	− 6.19838e10i	− 1.16174i
$243$	− 2.29025e9i	− 0.0421361i
$244$	−2.71678e10	−0.490683
$245$	0	0
$246$	1.57175e8	0.00273638
$247$	4.99410e10i	0.853730i
$248$	7.81949e10i	1.31264i
$249$	−3.18196e8	−0.00524563
$250$	0	0
$251$	−6.49927e10	−1.03355	−0.516776	−	0.856120i	$-0.672868\pi$
$251$	−6.49927e10	−1.03355	−0.516776	+	0.856120i	$0.672868\pi$
$252$	− 8.59855e9i	− 0.134315i
$253$	− 3.94134e9i	− 0.0604785i
$254$	8.13076e10	1.22569
$255$	0	0
$256$	6.51152e10	0.947551
$257$	− 7.71755e10i	− 1.10352i	−0.834003	−	0.551760i	$-0.813956\pi$
$257$	− 7.71755e10i	− 1.10352i	0.834003	−	0.551760i	$-0.186044\pi$
$258$	8.34762e8i	0.0117294i
$259$	−2.51167e10	−0.346827
$260$	0	0
$261$	−7.76307e10	−1.03550
$262$	− 6.34504e10i	− 0.831914i
$263$	5.32154e10i	0.685862i	0.939361	+	0.342931i	$0.111420\pi$
$263$	5.32154e10i	0.685862i	−0.939361	+	0.342931i	$0.888580\pi$
$264$	−3.84772e7	−0.000487512 0
$265$	0	0
$266$	2.56024e10	0.313555
$267$	1.97719e9i	0.0238094i
$268$	9.32989e9i	0.110476i
$269$	−2.15319e10	−0.250725	−0.125362	−	0.992111i	$-0.540009\pi$
$269$	−2.15319e10	−0.250725	−0.125362	+	0.992111i	$0.540009\pi$
$270$	0	0
$271$	4.81053e10	0.541790	0.270895	−	0.962609i	$-0.412680\pi$
$271$	4.81053e10	0.541790	0.270895	+	0.962609i	$0.412680\pi$
$272$	− 6.05548e9i	− 0.0670793i
$273$	− 5.83884e8i	− 0.00636202i
$274$	1.44220e11	1.54578
$275$	0	0
$276$	−6.29601e8	−0.00653092
$277$	− 6.60074e10i	− 0.673649i	−0.941568	−	0.336824i	$-0.890647\pi$
$277$	− 6.60074e10i	− 0.673649i	0.941568	−	0.336824i	$-0.109353\pi$
$278$	− 2.39436e10i	− 0.240429i
$279$	1.77000e11	1.74885
$280$	0	0
$281$	7.31129e10	0.699545	0.349772	−	0.936835i	$-0.386259\pi$
$281$	7.31129e10	0.699545	0.349772	+	0.936835i	$0.386259\pi$
$282$	2.06427e9i	0.0194377i
$283$	1.32293e11i	1.22602i	0.790073	+	0.613012i	$0.210042\pi$
$283$	1.32293e11i	1.22602i	−0.790073	+	0.613012i	$0.789958\pi$
$284$	6.10298e10	0.556685
$285$	0	0
$286$	−7.29818e9	−0.0645011
$287$	7.26792e9i	0.0632327i
$288$	− 7.94381e10i	− 0.680397i
$289$	1.18235e11	0.997021
$290$	0	0
$291$	5.69951e8	0.00465929
$292$	− 2.46209e10i	− 0.198190i
$293$	− 4.00575e10i	− 0.317526i	−0.987317	−	0.158763i	$-0.949249\pi$
$293$	− 4.00575e10i	− 0.317526i	0.987317	−	0.158763i	$-0.0507505\pi$
$294$	−2.99330e8	−0.00233662
$295$	0	0
$296$	−9.09456e10	−0.688603
$297$	1.74209e8i	0.00129917i
$298$	− 1.58082e11i	− 1.16121i
$299$	2.16564e11	1.56699
$300$	0	0
$301$	−3.86001e10	−0.271044
$302$	1.41041e11i	0.975693i
$303$	− 3.09865e8i	− 0.00211193i
$304$	1.30419e11	0.875812
$305$	0	0
$306$	−9.74319e9	−0.0635265
$307$	− 3.61839e10i	− 0.232484i	−0.993221	−	0.116242i	$-0.962915\pi$
$307$	− 3.61839e10i	− 0.232484i	0.993221	−	0.116242i	$-0.0370848\pi$
$308$	9.81112e8i	0.00621212i
$309$	1.01522e9	0.00633501
$310$	0	0
$311$	1.58042e11	0.957968	0.478984	−	0.877824i	$-0.341005\pi$
$311$	1.58042e11	0.957968	0.478984	+	0.877824i	$0.341005\pi$
$312$	− 2.11420e9i	− 0.0126314i
$313$	1.78114e11i	1.04894i	0.851430	+	0.524468i	$0.175736\pi$
$313$	1.78114e11i	1.04894i	−0.851430	+	0.524468i	$0.824264\pi$
$314$	−8.04151e9	−0.0466825
$315$	0	0
$316$	3.00935e10	0.169778
$317$	− 3.74923e10i	− 0.208533i	−0.994549	−	0.104267i	$-0.966751\pi$
$317$	− 3.74923e10i	− 0.208533i	0.994549	−	0.104267i	$-0.0332495\pi$
$318$	2.11887e9i	0.0116194i
$319$	8.85782e9	0.0478926
$320$	0	0
$321$	4.66785e9	0.0245383
$322$	− 1.11023e11i	− 0.575519i
$323$	− 7.60740e9i	− 0.0388888i
$324$	−7.04617e10	−0.355223
$325$	0	0
$326$	−2.51246e11	−1.23203
$327$	4.45100e8i	0.00215275i
$328$	2.63166e10i	0.125544i
$329$	−9.54535e10	−0.449170
$330$	0	0
$331$	1.08393e11	0.496335	0.248167	−	0.968717i	$-0.420172\pi$
$331$	1.08393e11	0.496335	0.248167	+	0.968717i	$0.420172\pi$
$332$	2.93785e10i	0.132711i
$333$	2.05862e11i	0.917437i
$334$	−2.00139e11	−0.879981
$335$	0	0
$336$	−1.52480e9	−0.00652657
$337$	− 3.53012e11i	− 1.49092i	−0.666548	−	0.745462i	$-0.732229\pi$
$337$	− 3.53012e11i	− 1.49092i	0.666548	−	0.745462i	$-0.267771\pi$
$338$	− 1.21652e11i	− 0.506986i
$339$	−5.79145e9	−0.0238171
$340$	0	0
$341$	−2.01960e10	−0.0808855
$342$	− 2.09843e11i	− 0.829425i
$343$	− 1.38413e10i	− 0.0539949i
$344$	−1.39768e11	−0.538140
$345$	0	0
$346$	4.24409e11	1.59200
$347$	4.58221e11i	1.69665i	0.529477	+	0.848324i	$0.322388\pi$
$347$	4.58221e11i	1.69665i	−0.529477	+	0.848324i	$0.677612\pi$
$348$	− 1.41497e9i	− 0.00517180i
$349$	−4.77589e11	−1.72322	−0.861608	−	0.507575i	$-0.830542\pi$
$349$	−4.77589e11	−1.72322	−0.861608	+	0.507575i	$0.830542\pi$
$350$	0	0
$351$	−9.57223e9	−0.0336613
$352$	9.06404e9i	0.0314688i
$353$	4.13087e11i	1.41597i	0.706226	+	0.707986i	$0.250396\pi$
$353$	4.13087e11i	1.41597i	−0.706226	+	0.707986i	$0.749604\pi$
$354$	−8.33816e9	−0.0282199
$355$	0	0
$356$	1.82551e11	0.602364
$357$	8.89419e7i	0 0.000289801i
$358$	− 1.55581e11i	− 0.500589i
$359$	1.83554e11	0.583230	0.291615	−	0.956536i	$-0.405807\pi$
$359$	1.83554e11	0.583230	0.291615	+	0.956536i	$0.405807\pi$
$360$	0	0
$361$	−1.58844e11	−0.492253
$362$	− 1.20399e11i	− 0.368498i
$363$	4.63764e9i	0.0140190i
$364$	−5.39091e10	−0.160955
$365$	0	0
$366$	7.75164e9	0.0225803
$367$	1.52885e11i	0.439915i	0.975509	+	0.219957i	$0.0705919\pi$
$367$	1.52885e11i	0.439915i	−0.975509	+	0.219957i	$0.929408\pi$
$368$	− 5.65552e11i	− 1.60752i
$369$	5.95694e10	0.167265
$370$	0	0
$371$	−9.79783e10	−0.268502
$372$	3.22617e9i	0.00873461i
$373$	3.94586e11i	1.05548i	0.849405	+	0.527742i	$0.176961\pi$
$373$	3.94586e11i	1.05548i	−0.849405	+	0.527742i	$0.823039\pi$
$374$	1.11172e9	0.00293814
$375$	0	0
$376$	−3.45630e11	−0.891798
$377$	4.86710e11i	1.24089i
$378$	4.90724e9i	0.0123630i
$379$	−7.26412e11	−1.80845	−0.904225	−	0.427057i	$-0.859550\pi$
$379$	−7.26412e11	−1.80845	−0.904225	+	0.427057i	$0.859550\pi$
$380$	0	0
$381$	−6.08345e9	−0.0147907
$382$	2.86144e11i	0.687542i
$383$	− 5.73936e11i	− 1.36292i	−0.731857	−	0.681458i	$-0.761346\pi$
$383$	− 5.73936e11i	− 1.36292i	0.731857	−	0.681458i	$-0.238654\pi$
$384$	−7.11780e9	−0.0167053
$385$	0	0
$386$	−9.30192e11	−2.13270
$387$	3.16375e11i	0.716972i
$388$	− 5.26227e10i	− 0.117877i
$389$	−2.27345e11	−0.503400	−0.251700	−	0.967805i	$-0.580990\pi$
$389$	−2.27345e11	−0.503400	−0.251700	+	0.967805i	$0.580990\pi$
$390$	0	0
$391$	−3.29888e10	−0.0713791
$392$	− 5.01183e10i	− 0.107204i
$393$	4.74737e9i	0.0100389i
$394$	−3.54817e11	−0.741773
$395$	0	0
$396$	8.04140e9	0.0164325
$397$	9.03630e11i	1.82572i	0.408277	+	0.912858i	$0.366130\pi$
$397$	9.03630e11i	1.82572i	−0.408277	+	0.912858i	$0.633870\pi$
$398$	6.29493e11i	1.25753i
$399$	−1.91558e9	−0.00378374
$400$	0	0
$401$	3.47203e11	0.670555	0.335277	−	0.942119i	$-0.391170\pi$
$401$	3.47203e11	0.670555	0.335277	+	0.942119i	$0.391170\pi$
$402$	− 2.66204e9i	− 0.00508391i
$403$	− 1.10971e12i	− 2.09573i
$404$	−2.86093e10	−0.0534307
$405$	0	0
$406$	2.49514e11	0.455750
$407$	− 2.34892e10i	− 0.0424320i
$408$	3.22052e8i	0 0.000575381i
$409$	1.06690e12	1.88524	0.942621	−	0.333866i	$-0.108353\pi$
$409$	1.06690e12	1.88524	0.942621	+	0.333866i	$0.108353\pi$
$410$	0	0
$411$	−1.07905e10	−0.0186533
$412$	− 9.37337e10i	− 0.160272i
$413$	− 3.85563e11i	− 0.652110i
$414$	−9.09965e11	−1.52238
$415$	0	0
$416$	−4.98041e11	−0.815352
$417$	1.79146e9i	0.00290132i
$418$	2.39435e10i	0.0383614i
$419$	−8.89018e11	−1.40912	−0.704559	−	0.709645i	$-0.748855\pi$
$419$	−8.89018e11	−1.40912	−0.704559	+	0.709645i	$0.748855\pi$
$420$	0	0
$421$	9.18431e11	1.42488	0.712438	−	0.701735i	$-0.247591\pi$
$421$	9.18431e11	1.42488	0.712438	+	0.701735i	$0.247591\pi$
$422$	− 7.15929e11i	− 1.09891i
$423$	7.82358e11i	1.18816i
$424$	−3.54773e11	−0.533094
$425$	0	0
$426$	−1.74133e10	−0.0256175
$427$	3.58442e11i	0.521788i
$428$	− 4.30975e11i	− 0.620805i
$429$	5.46051e8	0.000778351 0
$430$	0	0
$431$	−7.15695e11	−0.999034	−0.499517	−	0.866304i	$-0.666489\pi$
$431$	−7.15695e11	−0.999034	−0.499517	+	0.866304i	$0.666489\pi$
$432$	2.49976e10i	0.0345320i
$433$	− 1.30709e12i	− 1.78694i	−0.449119	−	0.893472i	$-0.648262\pi$
$433$	− 1.30709e12i	− 1.78694i	0.449119	−	0.893472i	$-0.351738\pi$
$434$	−5.68896e11	−0.769713
$435$	0	0
$436$	4.10954e10	0.0544633
$437$	− 7.10493e11i	− 0.931952i
$438$	7.02495e9i	0.00912031i
$439$	8.08851e11	1.03939	0.519695	−	0.854352i	$-0.326046\pi$
$439$	8.08851e11	1.03939	0.519695	+	0.854352i	$0.326046\pi$
$440$	0	0
$441$	−1.13446e11	−0.142829
$442$	6.10854e10i	0.0761267i
$443$	2.49522e11i	0.307816i	0.988085	+	0.153908i	$0.0491860\pi$
$443$	2.49522e11i	0.307816i	−0.988085	+	0.153908i	$0.950814\pi$
$444$	−3.75223e9	−0.00458212
$445$	0	0
$446$	6.98995e9	0.00836503
$447$	1.18277e10i	0.0140126i
$448$	− 1.40763e11i	− 0.165097i
$449$	−1.12524e12	−1.30658	−0.653291	−	0.757107i	$-0.726612\pi$
$449$	−1.12524e12	−1.30658	−0.653291	+	0.757107i	$0.726612\pi$
$450$	0	0
$451$	−6.79699e9	−0.00773610
$452$	5.34715e11i	0.602558i
$453$	− 1.05527e10i	− 0.0117739i
$454$	−7.70835e11	−0.851550
$455$	0	0
$456$	−6.93617e9	−0.00751238
$457$	− 7.92565e11i	− 0.849987i	−0.905196	−	0.424993i	$-0.860276\pi$
$457$	− 7.92565e11i	− 0.849987i	0.905196	−	0.424993i	$-0.139724\pi$
$458$	1.03618e12i	1.10038i
$459$	1.45812e9	0.00153333
$460$	0	0
$461$	8.54573e11	0.881241	0.440621	−	0.897693i	$-0.354758\pi$
$461$	8.54573e11	0.881241	0.440621	+	0.897693i	$0.354758\pi$
$462$	− 2.79935e8i	0 0.000285870i
$463$	− 1.55057e12i	− 1.56811i	−0.620690	−	0.784056i	$-0.713148\pi$
$463$	− 1.55057e12i	− 1.56811i	0.620690	−	0.784056i	$-0.286852\pi$
$464$	1.27103e12	1.27299
$465$	0	0
$466$	−1.06160e12	−1.04285
$467$	1.54154e11i	0.149979i	0.997184	+	0.0749893i	$0.0238923\pi$
$467$	1.54154e11i	0.149979i	−0.997184	+	0.0749893i	$0.976108\pi$
$468$	4.41850e11i	0.425764i
$469$	1.23095e11	0.117480
$470$	0	0
$471$	6.01667e8	0.000563329 0
$472$	− 1.39610e12i	− 1.29472i
$473$	− 3.60990e10i	− 0.0331604i
$474$	−8.58641e9	−0.00781284
$475$	0	0
$476$	8.21186e9	0.00733179
$477$	8.03052e11i	0.710249i
$478$	− 9.32614e11i	− 0.817102i
$479$	1.96197e12	1.70287	0.851437	−	0.524457i	$-0.175732\pi$
$479$	1.96197e12	1.70287	0.851437	+	0.524457i	$0.175732\pi$
$480$	0	0
$481$	1.29066e12	1.09941
$482$	9.02868e10i	0.0761926i
$483$	8.30672e9i	0.00694492i
$484$	4.28186e11	0.354673
$485$	0	0
$486$	6.03332e10	0.0490561
$487$	− 8.97598e11i	− 0.723106i	−0.932352	−	0.361553i	$-0.882247\pi$
$487$	− 8.97598e11i	− 0.723106i	0.932352	−	0.361553i	$-0.117753\pi$
$488$	1.29789e12i	1.03598i
$489$	1.87983e10	0.0148671
$490$	0	0
$491$	4.80068e11	0.372766	0.186383	−	0.982477i	$-0.440324\pi$
$491$	4.80068e11	0.372766	0.186383	+	0.982477i	$0.440324\pi$
$492$	1.08577e9i	0 0.000835401i
$493$	− 7.41395e10i	− 0.0565247i
$494$	−1.31562e12	−0.993939
$495$	0	0
$496$	−2.89797e12	−2.14994
$497$	− 8.05205e11i	− 0.591974i
$498$	− 8.38240e9i	− 0.00610712i
$499$	1.81750e12	1.31227	0.656133	−	0.754646i	$-0.272191\pi$
$499$	1.81750e12	1.31227	0.656133	+	0.754646i	$0.272191\pi$
$500$	0	0
$501$	1.49745e10	0.0106189
$502$	− 1.71214e12i	− 1.20329i
$503$	9.78467e11i	0.681538i	0.940147	+	0.340769i	$0.110687\pi$
$503$	9.78467e11i	0.681538i	−0.940147	+	0.340769i	$0.889313\pi$
$504$	−4.10780e11	−0.283578
$505$	0	0
$506$	1.03829e11	0.0704109
$507$	9.10205e9i	0.00611792i
$508$	5.61675e11i	0.374195i
$509$	−9.49400e11	−0.626930	−0.313465	−	0.949600i	$-0.601490\pi$
$509$	−9.49400e11	−0.626930	−0.313465	+	0.949600i	$0.601490\pi$
$510$	0	0
$511$	−3.24839e11	−0.210753
$512$	− 1.33578e11i	− 0.0859056i
$513$	3.14041e10i	0.0200197i
$514$	2.03308e12	1.28475
$515$	0	0
$516$	−5.76655e9	−0.00358090
$517$	− 8.92685e10i	− 0.0549529i
$518$	− 6.61662e11i	− 0.403787i
$519$	−3.17544e10	−0.0192110
$520$	0	0
$521$	3.20965e12	1.90848	0.954240	−	0.299042i	$-0.0966670\pi$
$521$	3.20965e12	1.90848	0.954240	+	0.299042i	$0.0966670\pi$
$522$	− 2.04507e12i	− 1.20556i
$523$	− 2.27961e12i	− 1.33230i	−0.745816	−	0.666152i	$-0.767940\pi$
$523$	− 2.27961e12i	− 1.33230i	0.745816	−	0.666152i	$-0.232060\pi$
$524$	4.38317e11	0.253979
$525$	0	0
$526$	−1.40188e12	−0.798501
$527$	1.69039e11i	0.0954642i
$528$	− 1.42600e9i	0 0.000798483i
$529$	−1.27983e12	−0.710564
$530$	0	0
$531$	−3.16016e12	−1.72498
$532$	1.76862e11i	0.0957265i
$533$	− 3.73473e11i	− 0.200441i
$534$	−5.20862e10	−0.0277196
$535$	0	0
$536$	4.45719e11	0.233249
$537$	1.16406e10i	0.00604073i
$538$	− 5.67226e11i	− 0.291901i
$539$	1.29444e10	0.00660592
$540$	0	0
$541$	2.51926e12	1.26440	0.632201	−	0.774804i	$-0.282152\pi$
$541$	2.51926e12	1.26440	0.632201	+	0.774804i	$0.282152\pi$
$542$	1.26726e12i	0.630769i
$543$	9.00830e9i	0.00444676i
$544$	7.58656e10	0.0371407
$545$	0	0
$546$	1.53816e10	0.00740685
$547$	2.15157e12i	1.02757i	0.857918	+	0.513787i	$0.171758\pi$
$547$	2.15157e12i	1.02757i	−0.857918	+	0.513787i	$0.828242\pi$
$548$	9.96272e11i	0.471917i
$549$	2.93787e12	1.38025
$550$	0	0
$551$	1.59677e12	0.738008
$552$	3.00780e10i	0.0137887i
$553$	− 3.97043e11i	− 0.180540i
$554$	1.73887e12	0.784282
$555$	0	0
$556$	1.65403e11	0.0734016
$557$	2.27895e12i	1.00320i	0.865100	+	0.501600i	$0.167255\pi$
$557$	2.27895e12i	1.00320i	−0.865100	+	0.501600i	$0.832745\pi$
$558$	4.66279e12i	2.03607i
$559$	1.98353e12	0.859181
$560$	0	0
$561$	−8.31788e7	−3.54552e−5 0
$562$	1.92605e12i	0.814431i
$563$	3.82145e12i	1.60303i	0.597978	+	0.801513i	$0.295971\pi$
$563$	3.82145e12i	1.60303i	−0.597978	+	0.801513i	$0.704029\pi$
$564$	−1.42600e10	−0.00593423
$565$	0	0
$566$	−3.48508e12	−1.42738
$567$	9.29646e11i	0.377741i
$568$	− 2.91559e12i	− 1.17533i
$569$	2.94845e12	1.17920	0.589601	−	0.807695i	$-0.299285\pi$
$569$	2.94845e12	1.17920	0.589601	+	0.807695i	$0.299285\pi$
$570$	0	0
$571$	2.99642e12	1.17962	0.589808	−	0.807544i	$-0.299203\pi$
$571$	2.99642e12	1.17962	0.589808	+	0.807544i	$0.299203\pi$
$572$	− 5.04160e10i	− 0.0196918i
$573$	− 2.14093e10i	− 0.00829673i
$574$	−1.91463e11	−0.0736174
$575$	0	0
$576$	−1.15373e12	−0.436718
$577$	1.87283e12i	0.703407i	0.936111	+	0.351703i	$0.114397\pi$
$577$	1.87283e12i	0.703407i	−0.936111	+	0.351703i	$0.885603\pi$
$578$	3.11472e12i	1.16076i
$579$	6.95971e10	0.0257358
$580$	0	0
$581$	3.87609e11	0.141124
$582$	1.50145e10i	0.00542448i
$583$	− 9.16297e10i	− 0.0328494i
$584$	−1.17622e12	−0.418438
$585$	0	0
$586$	1.05525e12	0.369673
$587$	1.94572e12i	0.676410i	0.941073	+	0.338205i	$0.109820\pi$
$587$	1.94572e12i	0.676410i	−0.941073	+	0.338205i	$0.890180\pi$
$588$	− 2.06778e9i	0 0.000713356i
$589$	−3.64067e12	−1.24642
$590$	0	0
$591$	2.65474e10	0.00895116
$592$	− 3.37052e12i	− 1.12784i
$593$	8.61235e11i	0.286006i	0.989722	+	0.143003i	$0.0456759\pi$
$593$	8.61235e11i	0.286006i	−0.989722	+	0.143003i	$0.954324\pi$
$594$	−4.58927e9	−0.00151253
$595$	0	0
$596$	1.09204e12	0.354510
$597$	− 4.70988e10i	− 0.0151749i
$598$	5.70507e12i	1.82434i
$599$	−2.81546e12	−0.893570	−0.446785	−	0.894641i	$-0.647431\pi$
$599$	−2.81546e12	−0.893570	−0.446785	+	0.894641i	$0.647431\pi$
$600$	0	0
$601$	4.79484e12	1.49913	0.749565	−	0.661931i	$-0.230263\pi$
$601$	4.79484e12	1.49913	0.749565	+	0.661931i	$0.230263\pi$
$602$	− 1.01686e12i	− 0.315557i
$603$	− 1.00891e12i	− 0.310761i
$604$	−9.74312e11	−0.297873
$605$	0	0
$606$	8.16293e9	0.00245878
$607$	− 7.43279e11i	− 0.222230i	−0.993808	−	0.111115i	$-0.964558\pi$
$607$	− 7.43279e11i	− 0.222230i	0.993808	−	0.111115i	$-0.0354422\pi$
$608$	1.63395e12i	0.484922i
$609$	−1.86686e10	−0.00549965
$610$	0	0
$611$	4.90503e12	1.42382
$612$	− 6.73061e10i	− 0.0193943i
$613$	6.45388e11i	0.184607i	0.995731	+	0.0923036i	$0.0294230\pi$
$613$	6.45388e11i	0.184607i	−0.995731	+	0.0923036i	$0.970577\pi$
$614$	9.53213e11	0.270665
$615$	0	0
$616$	4.68708e10	0.0131156
$617$	− 4.66543e12i	− 1.29601i	−0.761636	−	0.648005i	$-0.775604\pi$
$617$	− 4.66543e12i	− 1.29601i	0.761636	−	0.648005i	$-0.224396\pi$
$618$	2.67445e10i	0.00737542i
$619$	2.49665e12	0.683519	0.341759	−	0.939787i	$-0.388977\pi$
$619$	2.49665e12	0.683519	0.341759	+	0.939787i	$0.388977\pi$
$620$	0	0
$621$	1.36181e11	0.0367455
$622$	4.16338e12i	1.11530i
$623$	− 2.40851e12i	− 0.640549i
$624$	7.83541e10	0.0206886
$625$	0	0
$626$	−4.69215e12	−1.22120
$627$	− 1.79146e9i	0 0.000462916i
$628$	− 5.55509e10i	− 0.0142519i
$629$	−1.96604e11	−0.0500799
$630$	0	0
$631$	2.92442e12	0.734357	0.367179	−	0.930150i	$-0.380324\pi$
$631$	2.92442e12	0.734357	0.367179	+	0.930150i	$0.380324\pi$
$632$	− 1.43766e12i	− 0.358451i
$633$	5.35659e10i	0.0132609i
$634$	9.87678e11	0.242781
$635$	0	0
$636$	−1.46372e10	−0.00354733
$637$	7.11256e11i	0.171159i
$638$	2.33346e11i	0.0557581i
$639$	−6.59963e12	−1.56591
$640$	0	0
$641$	−4.23039e12	−0.989736	−0.494868	−	0.868968i	$-0.664784\pi$
$641$	−4.23039e12	−0.989736	−0.494868	+	0.868968i	$0.664784\pi$
$642$	1.22968e11i	0.0285682i
$643$	1.95718e12i	0.451524i	0.974183	+	0.225762i	$0.0724871\pi$
$643$	1.95718e12i	0.451524i	−0.974183	+	0.225762i	$0.927513\pi$
$644$	7.66946e11	0.175703
$645$	0	0
$646$	2.00406e11	0.0452756
$647$	4.71751e12i	1.05838i	0.848502	+	0.529192i	$0.177505\pi$
$647$	4.71751e12i	1.05838i	−0.848502	+	0.529192i	$0.822495\pi$
$648$	3.36618e12i	0.749980i
$649$	3.60580e11	0.0797813
$650$	0	0
$651$	4.25649e10	0.00928831
$652$	− 1.73561e12i	− 0.376130i
$653$	5.50754e12i	1.18536i	0.805440	+	0.592678i	$0.201929\pi$
$653$	5.50754e12i	1.18536i	−0.805440	+	0.592678i	$0.798071\pi$
$654$	−1.17255e10	−0.00250629
$655$	0	0
$656$	−9.75315e11	−0.205626
$657$	2.66245e12i	0.557491i
$658$	− 2.51458e12i	− 0.522937i
$659$	4.05044e12	0.836599	0.418300	−	0.908309i	$-0.362626\pi$
$659$	4.05044e12	0.836599	0.418300	+	0.908309i	$0.362626\pi$
$660$	0	0
$661$	−2.16897e12	−0.441923	−0.220962	−	0.975283i	$-0.570920\pi$
$661$	−2.16897e12	−0.441923	−0.220962	+	0.975283i	$0.570920\pi$
$662$	2.85545e12i	0.577848i
$663$	− 4.57042e9i	0 0.000918640i
$664$	1.40350e12	0.280193
$665$	0	0
$666$	−5.42312e12	−1.06811
$667$	− 6.92425e12i	− 1.35459i
$668$	− 1.38257e12i	− 0.268653i
$669$	−5.22989e8	−0.000100943 0
$670$	0	0
$671$	−3.35217e11	−0.0638373
$672$	− 1.91033e10i	− 0.00361365i
$673$	− 7.79666e12i	− 1.46501i	−0.680761	−	0.732505i	$-0.738351\pi$
$673$	− 7.79666e12i	− 1.46501i	0.680761	−	0.732505i	$-0.261649\pi$
$674$	9.29959e12	1.73578
$675$	0	0
$676$	8.40378e11	0.154780
$677$	3.98612e12i	0.729293i	0.931146	+	0.364646i	$0.118810\pi$
$677$	3.98612e12i	0.729293i	−0.931146	+	0.364646i	$0.881190\pi$
$678$	− 1.52567e11i	− 0.0277286i
$679$	−6.94284e11	−0.125350
$680$	0	0
$681$	5.76740e10	0.0102759
$682$	− 5.32034e11i	− 0.0941693i
$683$	− 7.20461e12i	− 1.26683i	−0.773814	−	0.633413i	$-0.781653\pi$
$683$	− 7.20461e12i	− 1.26683i	0.773814	−	0.633413i	$-0.218347\pi$
$684$	1.44960e12	0.253219
$685$	0	0
$686$	3.64628e11	0.0628625
$687$	− 7.75275e10i	− 0.0132785i
$688$	− 5.17992e12i	− 0.881405i
$689$	5.03477e12	0.851125
$690$	0	0
$691$	7.66976e12	1.27977	0.639883	−	0.768472i	$-0.278983\pi$
$691$	7.66976e12	1.27977	0.639883	+	0.768472i	$0.278983\pi$
$692$	2.93183e12i	0.486028i
$693$	− 1.06095e11i	− 0.0174742i
$694$	−1.20711e13	−1.97529
$695$	0	0
$696$	−6.75978e10	−0.0109192
$697$	5.68904e10i	0.00913044i
$698$	− 1.25814e13i	− 2.00622i
$699$	7.94290e10	0.0125844
$700$	0	0
$701$	−6.76464e11	−0.105807	−0.0529034	−	0.998600i	$-0.516848\pi$
$701$	−6.76464e11	−0.105807	−0.0529034	+	0.998600i	$0.516848\pi$
$702$	− 2.52166e11i	− 0.0391895i
$703$	− 4.23433e12i	− 0.653861i
$704$	1.31642e11	0.0201985
$705$	0	0
$706$	−1.08822e13	−1.64852
$707$	3.77461e11i	0.0568178i
$708$	− 5.76002e10i	− 0.00861538i
$709$	−1.19764e13	−1.77999	−0.889995	−	0.455970i	$-0.849292\pi$
$709$	−1.19764e13	−1.77999	−0.889995	+	0.455970i	$0.849292\pi$
$710$	0	0
$711$	−3.25425e12	−0.477570
$712$	− 8.72104e12i	− 1.27177i
$713$	1.57874e13i	2.28775i
$714$	−2.34304e9	−0.000337395 0
$715$	0	0
$716$	1.07475e12	0.152827
$717$	6.97783e10i	0.00986016i
$718$	4.83547e12i	0.679014i
$719$	9.56848e12	1.33525	0.667626	−	0.744497i	$-0.267311\pi$
$719$	9.56848e12	1.33525	0.667626	+	0.744497i	$0.267311\pi$
$720$	0	0
$721$	−1.23669e12	−0.170432
$722$	− 4.18451e12i	− 0.573096i
$723$	− 6.75527e9i	0 0.000919434i
$724$	8.31721e11	0.112500
$725$	0	0
$726$	−1.22172e11	−0.0163214
$727$	− 1.05787e13i	− 1.40451i	−0.711924	−	0.702257i	$-0.752176\pi$
$727$	− 1.05787e13i	− 1.40451i	0.711924	−	0.702257i	$-0.247824\pi$
$728$	2.57541e12i	0.339825i
$729$	7.61657e12	0.998816
$730$	0	0
$731$	−3.02147e11	−0.0391372
$732$	5.35485e10i	0.00689362i
$733$	− 5.59263e12i	− 0.715563i	−0.933805	−	0.357782i	$-0.883533\pi$
$733$	− 5.59263e12i	− 0.715563i	0.933805	−	0.357782i	$-0.116467\pi$
$734$	−4.02754e12	−0.512162
$735$	0	0
$736$	7.08546e12	0.890057
$737$	1.15119e11i	0.0143729i
$738$	1.56927e12i	0.194735i
$739$	7.75052e11	0.0955941	0.0477970	−	0.998857i	$-0.484780\pi$
$739$	7.75052e11	0.0955941	0.0477970	+	0.998857i	$0.484780\pi$
$740$	0	0
$741$	9.84350e10	0.0119941
$742$	− 2.58110e12i	− 0.312598i
$743$	2.61033e12i	0.314228i	0.987580	+	0.157114i	$0.0502191\pi$
$743$	2.61033e12i	0.314228i	−0.987580	+	0.157114i	$0.949781\pi$
$744$	1.54124e11	0.0184414
$745$	0	0
$746$	−1.03948e13	−1.22883
$747$	− 3.17693e12i	− 0.373306i
$748$	7.67976e9i	0 0.000896996i
$749$	−5.68613e12	−0.660159
$750$	0	0
$751$	1.00388e13	1.15160	0.575801	−	0.817590i	$-0.304690\pi$
$751$	1.00388e13	1.15160	0.575801	+	0.817590i	$0.304690\pi$
$752$	− 1.28093e13i	− 1.46065i
$753$	1.28102e11i	0.0145204i
$754$	−1.28217e13	−1.44468
$755$	0	0
$756$	−3.38993e10	−0.00377436
$757$	1.40463e12i	0.155464i	0.996974	+	0.0777320i	$0.0247678\pi$
$757$	1.40463e12i	0.155464i	−0.996974	+	0.0777320i	$0.975232\pi$
$758$	− 1.91363e13i	− 2.10545i
$759$	−7.76848e9	−0.000849666 0
$760$	0	0
$761$	−1.42436e13	−1.53954	−0.769769	−	0.638323i	$-0.779628\pi$
$761$	−1.42436e13	−1.53954	−0.769769	+	0.638323i	$0.779628\pi$
$762$	− 1.60260e11i	− 0.0172197i
$763$	− 5.42197e11i	− 0.0579158i
$764$	−1.97669e12	−0.209903
$765$	0	0
$766$	1.51195e13	1.58675
$767$	1.98128e13i	2.06712i
$768$	− 1.28344e11i	− 0.0133122i
$769$	1.29105e12	0.133129	0.0665647	−	0.997782i	$-0.478796\pi$
$769$	1.29105e12	0.133129	0.0665647	+	0.997782i	$0.478796\pi$
$770$	0	0
$771$	−1.52115e11	−0.0155034
$772$	− 6.42578e12i	− 0.651101i
$773$	− 8.58124e12i	− 0.864455i	−0.901765	−	0.432227i	$-0.857728\pi$
$773$	− 8.58124e12i	− 0.864455i	0.901765	−	0.432227i	$-0.142272\pi$
$774$	−8.33443e12	−0.834721
$775$	0	0
$776$	−2.51395e12	−0.248874
$777$	4.95056e10i	0.00487259i
$778$	− 5.98908e12i	− 0.586073i
$779$	−1.22527e12	−0.119210
$780$	0	0
$781$	7.53031e11	0.0724241
$782$	− 8.69041e11i	− 0.0831017i
$783$	3.06055e11i	0.0290985i
$784$	1.85743e12	0.175586
$785$	0	0
$786$	−1.25062e11	−0.0116876
$787$	3.12167e11i	0.0290068i	0.999895	+	0.0145034i	$0.00461674\pi$
$787$	3.12167e11i	0.0290068i	−0.999895	+	0.0145034i	$0.995383\pi$
$788$	− 2.45108e12i	− 0.226459i
$789$	1.04889e11	0.00963570
$790$	0	0
$791$	7.05483e12	0.640756
$792$	− 3.84164e11i	− 0.0346939i
$793$	− 1.84191e13i	− 1.65402i
$794$	−2.38048e13	−2.12555
$795$	0	0
$796$	−4.34855e12	−0.383916
$797$	8.61341e12i	0.756159i	0.925773	+	0.378079i	$0.123415\pi$
$797$	8.61341e12i	0.756159i	−0.925773	+	0.378079i	$0.876585\pi$
$798$	− 5.04631e10i	− 0.00440515i
$799$	−7.47173e11	−0.0648576
$800$	0	0
$801$	−1.97407e13	−1.69440
$802$	9.14656e12i	0.780680i
$803$	− 3.03791e11i	− 0.0257843i
$804$	1.83895e10	0.00155209
$805$	0	0
$806$	2.92336e13	2.43992
$807$	4.24400e10i	0.00352244i
$808$	1.36676e12i	0.112808i
$809$	2.01016e13	1.64992	0.824958	−	0.565193i	$-0.191198\pi$
$809$	2.01016e13	1.64992	0.824958	+	0.565193i	$0.191198\pi$
$810$	0	0
$811$	−1.62455e13	−1.31868	−0.659340	−	0.751845i	$-0.729164\pi$
$811$	−1.62455e13	−1.31868	−0.659340	+	0.751845i	$0.729164\pi$
$812$	1.72365e12i	0.139138i
$813$	− 9.48169e10i	− 0.00761164i
$814$	6.18789e11	0.0494006
$815$	0	0
$816$	−1.19355e10	−0.000942401 0
$817$	− 6.50745e12i	− 0.510989i
$818$	2.81058e13i	2.19486i
$819$	5.82961e12	0.452754
$820$	0	0
$821$	−8.24254e11	−0.0633165	−0.0316583	−	0.999499i	$-0.510079\pi$
$821$	−8.24254e11	−0.0633165	−0.0316583	+	0.999499i	$0.510079\pi$
$822$	− 2.84261e11i	− 0.0217167i
$823$	2.59567e13i	1.97220i	0.166159	+	0.986099i	$0.446864\pi$
$823$	2.59567e13i	1.97220i	−0.166159	+	0.986099i	$0.553136\pi$
$824$	−4.47796e12	−0.338382
$825$	0	0
$826$	1.01571e13	0.759206
$827$	1.31498e13i	0.977560i	0.872407	+	0.488780i	$0.162558\pi$
$827$	1.31498e13i	0.977560i	−0.872407	+	0.488780i	$0.837442\pi$
$828$	− 6.28605e12i	− 0.464774i
$829$	−1.78218e13	−1.31056	−0.655279	−	0.755387i	$-0.727449\pi$
$829$	−1.78218e13	−1.31056	−0.655279	+	0.755387i	$0.727449\pi$
$830$	0	0
$831$	−1.30102e11	−0.00946412
$832$	7.23334e12i	0.523340i
$833$	− 1.08344e11i	− 0.00779657i
$834$	−4.71934e10	−0.00337780
$835$	0	0
$836$	−1.65402e11	−0.0117115
$837$	− 6.97811e11i	− 0.0491443i
$838$	− 2.34199e13i	− 1.64054i
$839$	−1.79273e13	−1.24906	−0.624532	−	0.780999i	$-0.714710\pi$
$839$	−1.79273e13	−1.24906	−0.624532	+	0.780999i	$0.714710\pi$
$840$	0	0
$841$	1.05452e12	0.0726898
$842$	2.41947e13i	1.65888i
$843$	− 1.44107e11i	− 0.00982794i
$844$	4.94565e12	0.335492
$845$	0	0
$846$	−2.06101e13	−1.38329
$847$	− 5.64933e12i	− 0.377156i
$848$	− 1.31482e13i	− 0.873140i
$849$	2.60754e11	0.0172245
$850$	0	0
$851$	−1.83618e13	−1.20014
$852$	− 1.20291e11i	− 0.00782089i
$853$	1.65652e13i	1.07134i	0.844429	+	0.535668i	$0.179940\pi$
$853$	1.65652e13i	1.07134i	−0.844429	+	0.535668i	$0.820060\pi$
$854$	−9.44264e12	−0.607481
$855$	0	0
$856$	−2.05891e13	−1.31070
$857$	1.00056e13i	0.633619i	0.948489	+	0.316810i	$0.102612\pi$
$857$	1.00056e13i	0.633619i	−0.948489	+	0.316810i	$0.897388\pi$
$858$	1.43849e10i	0 0.000906180i
$859$	−4.82691e12	−0.302482	−0.151241	−	0.988497i	$-0.548327\pi$
$859$	−4.82691e12	−0.302482	−0.151241	+	0.988497i	$0.548327\pi$
$860$	0	0
$861$	1.43253e10	0.000888359 0
$862$	− 1.88539e13i	− 1.16311i
$863$	2.92326e12i	0.179398i	0.995969	+	0.0896992i	$0.0285906\pi$
$863$	2.92326e12i	0.179398i	−0.995969	+	0.0896992i	$0.971409\pi$
$864$	−3.13180e11	−0.0191198
$865$	0	0
$866$	3.44334e13	2.08042
$867$	− 2.33044e11i	− 0.0140072i
$868$	− 3.92994e12i	− 0.234989i
$869$	3.71316e11	0.0220879
$870$	0	0
$871$	−6.32544e12	−0.372399
$872$	− 1.96326e12i	− 0.114988i
$873$	5.69050e12i	0.331579i
$874$	1.87169e13	1.08501
$875$	0	0
$876$	−4.85285e10	−0.00278438
$877$	9.67239e12i	0.552123i	0.961140	+	0.276061i	$0.0890293\pi$
$877$	9.67239e12i	0.552123i	−0.961140	+	0.276061i	$0.910971\pi$
$878$	2.13080e13i	1.21009i
$879$	−7.89543e10	−0.00446094
$880$	0	0
$881$	1.87103e12	0.104638	0.0523191	−	0.998630i	$-0.483339\pi$
$881$	1.87103e12	0.104638	0.0523191	+	0.998630i	$0.483339\pi$
$882$	− 2.98857e12i	− 0.166286i
$883$	8.57451e12i	0.474664i	0.971429	+	0.237332i	$0.0762729\pi$
$883$	8.57451e12i	0.474664i	−0.971429	+	0.237332i	$0.923727\pi$
$884$	−4.21979e11	−0.0232411
$885$	0	0
$886$	−6.57328e12	−0.358369
$887$	1.80022e13i	0.976494i	0.872705	+	0.488247i	$0.162364\pi$
$887$	1.80022e13i	0.976494i	−0.872705	+	0.488247i	$0.837636\pi$
$888$	1.79256e11i	0.00967422i
$889$	7.41053e12	0.397916
$890$	0	0
$891$	−8.69409e11	−0.0462141
$892$	4.82867e10i	0.00255379i
$893$	− 1.60922e13i	− 0.846804i
$894$	−3.11584e11	−0.0163139
$895$	0	0
$896$	8.67053e12	0.449427
$897$	− 4.26854e11i	− 0.0220147i
$898$	− 2.96428e13i	− 1.52116i
$899$	−3.54809e13	−1.81166
$900$	0	0
$901$	−7.66937e11	−0.0387702
$902$	− 1.79057e11i	− 0.00900660i
$903$	7.60818e10i	0.00380790i
$904$	2.55450e13	1.27218
$905$	0	0
$906$	2.77995e11	0.0137076
$907$	− 2.53756e13i	− 1.24504i	−0.782604	−	0.622520i	$-0.786109\pi$
$907$	− 2.53756e13i	− 1.24504i	0.782604	−	0.622520i	$-0.213891\pi$
$908$	− 5.32495e12i	− 0.259973i
$909$	3.09375e12	0.150296
$910$	0	0
$911$	1.84038e13	0.885268	0.442634	−	0.896702i	$-0.354044\pi$
$911$	1.84038e13	0.885268	0.442634	+	0.896702i	$0.354044\pi$
$912$	− 2.57060e11i	− 0.0123043i
$913$	3.62494e11i	0.0172656i
$914$	2.08790e13	0.989581
$915$	0	0
$916$	−7.15798e12	−0.335939
$917$	− 5.78299e12i	− 0.270079i
$918$	3.84120e10i	0.00178515i
$919$	−7.61943e12	−0.352373	−0.176186	−	0.984357i	$-0.556376\pi$
$919$	−7.61943e12	−0.352373	−0.176186	+	0.984357i	$0.556376\pi$
$920$	0	0
$921$	−7.13195e10	−0.00326618
$922$	2.25125e13i	1.02597i
$923$	4.13767e13i	1.87650i
$924$	1.93380e9	8.72744e−5 0
$925$	0	0
$926$	4.08475e13	1.82564
$927$	1.01362e13i	0.450832i
$928$	1.59240e13i	0.704832i
$929$	3.02391e12	0.133198	0.0665991	−	0.997780i	$-0.478785\pi$
$929$	3.02391e12	0.133198	0.0665991	+	0.997780i	$0.478785\pi$
$930$	0	0
$931$	2.33345e12	0.101795
$932$	− 7.33355e12i	− 0.318378i
$933$	− 3.11505e11i	− 0.0134585i
$934$	−4.06097e12	−0.174610
$935$	0	0
$936$	2.11086e13	0.898914
$937$	1.00516e13i	0.425999i	0.977052	+	0.212999i	$0.0683233\pi$
$937$	1.00516e13i	0.425999i	−0.977052	+	0.212999i	$0.931677\pi$
$938$	3.24276e12i	0.136774i
$939$	3.51068e11	0.0147365
$940$	0	0
$941$	−1.52744e13	−0.635053	−0.317526	−	0.948249i	$-0.602852\pi$
$941$	−1.52744e13	−0.635053	−0.317526	+	0.948249i	$0.602852\pi$
$942$	1.58500e10i	0 0.000655845i
$943$	5.31328e12i	0.218806i
$944$	5.17405e13	2.12059
$945$	0	0
$946$	9.50974e11	0.0386063
$947$	− 4.29774e13i	− 1.73646i	−0.496162	−	0.868230i	$-0.665258\pi$
$947$	− 4.29774e13i	− 1.73646i	0.496162	−	0.868230i	$-0.334742\pi$
$948$	− 5.93151e10i	− 0.00238522i
$949$	1.66924e13	0.668068
$950$	0	0
$951$	−7.38982e10	−0.00292969
$952$	− 3.92307e11i	− 0.0154796i
$953$	1.01121e13i	0.397120i	0.980089	+	0.198560i	$0.0636265\pi$
$953$	1.01121e13i	0.397120i	−0.980089	+	0.198560i	$0.936373\pi$
$954$	−2.11552e13	−0.826894
$955$	0	0
$956$	6.44251e12	0.249457
$957$	− 1.74590e10i	0 0.000672846i
$958$	5.16852e13i	1.98254i
$959$	1.31445e13	0.501833
$960$	0	0
$961$	5.44575e13	2.05969
$962$	3.40005e13i	1.27996i
$963$	4.66047e13i	1.74627i
$964$	−6.23703e11	−0.0232612
$965$	0	0
$966$	−2.18828e11	−0.00808549
$967$	− 4.14688e13i	− 1.52511i	−0.646922	−	0.762556i	$-0.723944\pi$
$967$	− 4.14688e13i	− 1.52511i	0.646922	−	0.762556i	$-0.276056\pi$
$968$	− 2.04558e13i	− 0.748820i
$969$	−1.49944e10	−0.000546351 0
$970$	0	0
$971$	3.67205e12	0.132563	0.0662814	−	0.997801i	$-0.478886\pi$
$971$	3.67205e12	0.132563	0.0662814	+	0.997801i	$0.478886\pi$
$972$	4.16783e11i	0.0149765i
$973$	− 2.18226e12i	− 0.0780547i
$974$	2.36459e13	0.841862
$975$	0	0
$976$	−4.81010e13	−1.69680
$977$	− 8.95608e10i	− 0.00314480i	−0.999999	−	0.00157240i	$-0.999499\pi$
$977$	− 8.95608e10i	− 0.00314480i	0.999999	−	0.00157240i	$-0.000500510\pi$
$978$	4.95212e11i	0.0173088i
$979$	2.25245e12	0.0783669
$980$	0	0
$981$	−4.44397e12	−0.153200
$982$	1.26467e13i	0.433985i
$983$	− 4.67974e13i	− 1.59857i	−0.600953	−	0.799284i	$-0.705212\pi$
$983$	− 4.67974e13i	− 1.59857i	0.600953	−	0.799284i	$-0.294788\pi$
$984$	5.18707e10	0.00176378
$985$	0	0
$986$	1.95310e12	0.0658078
$987$	1.88141e11i	0.00631041i
$988$	− 9.08834e12i	− 0.303444i
$989$	−2.82190e13	−0.937902
$990$	0	0
$991$	−1.94121e12	−0.0639353	−0.0319677	−	0.999489i	$-0.510177\pi$
$991$	−1.94121e12	−0.0639353	−0.0319677	+	0.999489i	$0.510177\pi$
$992$	− 3.63070e13i	− 1.19038i
$993$	− 2.13645e11i	− 0.00697303i
$994$	2.12119e13	0.689194
$995$	0	0
$996$	5.79058e10	0.00186447
$997$	− 2.62275e13i	− 0.840677i	−0.907367	−	0.420338i	$-0.861911\pi$
$997$	− 2.62275e13i	− 0.840677i	0.907367	−	0.420338i	$-0.138089\pi$
$998$	4.78793e13i	1.52778i
$999$	8.11598e11	0.0257808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.g.99.9		12
5.2	odd	4		35.10.a.e.1.2	✓	6
5.3	odd	4		175.10.a.g.1.5		6
5.4	even	2	inner	175.10.b.g.99.4		12
15.2	even	4		315.10.a.l.1.5		6
35.27	even	4		245.10.a.g.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.e.1.2	✓	6	5.2	odd	4
175.10.a.g.1.5		6	5.3	odd	4
175.10.b.g.99.4		12	5.4	even	2	inner
175.10.b.g.99.9		12	1.1	even	1	trivial
245.10.a.g.1.2		6	35.27	even	4
315.10.a.l.1.5		6	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+26.3435i q^{2} -1.97103i q^{3} -181.982 q^{4} +51.9238 q^{6} +2401.00i q^{7} +8693.85i q^{8} +19679.1 q^{9} -2245.43 q^{11} +358.691i q^{12} -123379. i q^{13} -63250.8 q^{14} -322201. q^{16} +18794.1i q^{17} +518417. i q^{18} -404776. q^{19} +4732.44 q^{21} -59152.4i q^{22} +1.75527e6i q^{23} +17135.8 q^{24} +3.25024e6 q^{26} -77583.8i q^{27} -436938. i q^{28} -3.94483e6 q^{29} +8.99428e6 q^{31} -4.03667e6i q^{32} +4425.79i q^{33} -495103. q^{34} -3.58124e6 q^{36} +1.04609e7i q^{37} -1.06632e7i q^{38} -243184. q^{39} +3.02704e6 q^{41} +124669. i q^{42} +1.60767e7i q^{43} +408626. q^{44} -4.62401e7 q^{46} +3.97557e7i q^{47} +635067. i q^{48} -5.76480e6 q^{49} +37043.7 q^{51} +2.24528e7i q^{52} +4.08073e7i q^{53} +2.04383e6 q^{54} -2.08739e7 q^{56} +797825. i q^{57} -1.03921e8i q^{58} -1.60585e8 q^{59} +1.49289e8 q^{61} +2.36941e8i q^{62} +4.72496e7i q^{63} -5.86269e7 q^{64} -116591. q^{66} -5.12683e7i q^{67} -3.42018e6i q^{68} +3.45969e6 q^{69} -3.35362e8 q^{71} +1.71087e8i q^{72} +1.35293e8i q^{73} -2.75578e8 q^{74} +7.36618e7 q^{76} -5.39127e6i q^{77} -6.40632e6i q^{78} -1.65365e8 q^{79} +3.87191e8 q^{81} +7.97429e7i q^{82} -1.61436e8i q^{83} -861217. q^{84} -4.23516e8 q^{86} +7.77536e6i q^{87} -1.95214e7i q^{88} -1.00313e9 q^{89} +2.96233e8 q^{91} -3.19428e8i q^{92} -1.77280e7i q^{93} -1.04731e9 q^{94} -7.95639e6 q^{96} +2.89165e8i q^{97} -1.51865e8i q^{98} -4.41880e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6018 q^{4} + 9776 q^{6} - 222180 q^{9} - 95592 q^{11} + 72030 q^{14} + 4742130 q^{16} - 722112 q^{19} + 595448 q^{21} - 9656152 q^{24} + 21695244 q^{26} - 32056368 q^{29} + 2725824 q^{31} + 18432588 q^{34}+ \cdots - 7143937568 q^{99}+O(q^{100}) \) 12 * q - 6018 * q^4 + 9776 * q^6 - 222180 * q^9 - 95592 * q^11 + 72030 * q^14 + 4742130 * q^16 - 722112 * q^19 + 595448 * q^21 - 9656152 * q^24 + 21695244 * q^26 - 32056368 * q^29 + 2725824 * q^31 + 18432588 * q^34 + 184639282 * q^36 + 40683736 * q^39 + 44905512 * q^41 + 188757456 * q^44 + 99179040 * q^46 - 69177612 * q^49 - 562676360 * q^51 + 580208616 * q^54 - 105840882 * q^56 - 240560784 * q^59 - 175387080 * q^61 - 1281294210 * q^64 - 2787941384 * q^66 - 2063267280 * q^69 + 507525024 * q^71 + 837612108 * q^74 - 1169438952 * q^76 - 1662159000 * q^79 + 3738629420 * q^81 - 2601032112 * q^84 + 1132399896 * q^86 - 1165159368 * q^89 - 490610736 * q^91 + 2231893320 * q^94 + 1978690504 * q^96 - 7143937568 * q^99

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