LMFDB - Embedded newform 1600.2.q.h.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(49,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1600.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.7
Root			$-1.39563 - 0.228522i$ of defining polynomial
Character	$\chi$	$=$	1600.49
Dual form			1600.2.q.h.849.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42313 + 1.42313i) q^{3} +0.690576 q^{7} +1.05061i q^{9} +O(q^{10})$	$q+(1.42313 + 1.42313i) q^{3} +0.690576 q^{7} +1.05061i q^{9} +(3.06057 + 3.06057i) q^{11} +(2.33686 + 2.33686i) q^{13} -5.28770i q^{17} +(5.38887 - 5.38887i) q^{19} +(0.982780 + 0.982780i) q^{21} -1.60841 q^{23} +(2.77424 - 2.77424i) q^{27} +(-1.70319 + 1.70319i) q^{29} +4.69807 q^{31} +8.71119i q^{33} +(-7.89871 + 7.89871i) q^{37} +6.65131i q^{39} +5.49891i q^{41} +(0.256166 - 0.256166i) q^{43} +4.60743i q^{47} -6.52310 q^{49} +(7.52510 - 7.52510i) q^{51} +(-4.99318 + 4.99318i) q^{53} +15.3382 q^{57} +(1.46478 + 1.46478i) q^{59} +(9.33004 - 9.33004i) q^{61} +0.725523i q^{63} +(1.94797 + 1.94797i) q^{67} +(-2.28897 - 2.28897i) q^{69} -2.32246i q^{71} +1.29733 q^{73} +(2.11356 + 2.11356i) q^{77} -5.01968 q^{79} +11.0480 q^{81} +(7.30477 + 7.30477i) q^{83} -4.84772 q^{87} +1.81564i q^{89} +(1.61378 + 1.61378i) q^{91} +(6.68597 + 6.68597i) q^{93} +5.27038i q^{97} +(-3.21546 + 3.21546i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^7 + 8 * q^11 - 8 * q^19 + 24 * q^23 + 24 * q^27 + 16 * q^29 + 16 * q^37 - 8 * q^43 + 16 * q^49 + 32 * q^51 + 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^69 + 16 * q^77 + 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.42313	+	1.42313i	0.821645	+	0.821645i	0.986344	−	0.164699i	$-0.0526652\pi$
$3$	1.42313	+	1.42313i	0.821645	+	0.821645i	−0.164699	+	0.986344i	$0.552665\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.690576			0.261013			0.130507	−	0.991447i	$-0.458340\pi$
$7$	0.690576			0.261013			0.130507	+	0.991447i	$0.458340\pi$
$8$		0			0
$9$			1.05061i			0.350202i
$10$		0			0
$11$	3.06057	+	3.06057i	0.922797	+	0.922797i	0.997226	−	0.0744292i	$-0.0237135\pi$
$11$	3.06057	+	3.06057i	0.922797	+	0.922797i	−0.0744292	+	0.997226i	$0.523713\pi$
$12$		0			0
$13$	2.33686	+	2.33686i	0.648128	+	0.648128i	0.952540	−	0.304413i	$-0.0984601\pi$
$13$	2.33686	+	2.33686i	0.648128	+	0.648128i	−0.304413	+	0.952540i	$0.598460\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	5.28770i		−	1.28246i	−0.767350	−	0.641228i	$-0.778425\pi$
$17$		−	5.28770i		−	1.28246i	0.767350	−	0.641228i	$-0.221575\pi$
$18$		0			0
$19$	5.38887	−	5.38887i	1.23629	−	1.23629i	0.274787	−	0.961505i	$-0.411393\pi$
$19$	5.38887	−	5.38887i	1.23629	−	1.23629i	0.961505	−	0.274787i	$-0.0886075\pi$
$20$		0			0
$21$	0.982780	+	0.982780i	0.214460	+	0.214460i
$22$		0			0
$23$	−1.60841			−0.335376			−0.167688	−	0.985840i	$-0.553630\pi$
$23$	−1.60841			−0.335376			−0.167688	+	0.985840i	$0.553630\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.77424	−	2.77424i	0.533903	−	0.533903i
$28$		0			0
$29$	−1.70319	+	1.70319i	−0.316274	+	0.316274i	−0.847334	−	0.531060i	$-0.821794\pi$
$29$	−1.70319	+	1.70319i	−0.316274	+	0.316274i	0.531060	+	0.847334i	$0.321794\pi$
$30$		0			0
$31$	4.69807			0.843798			0.421899	−	0.906643i	$-0.361364\pi$
$31$	4.69807			0.843798			0.421899	+	0.906643i	$0.361364\pi$
$32$		0			0
$33$			8.71119i			1.51642i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.89871	+	7.89871i	−1.29854	+	1.29854i	−0.369185	+	0.929356i	$0.620363\pi$
$37$	−7.89871	+	7.89871i	−1.29854	+	1.29854i	−0.929356	+	0.369185i	$0.879637\pi$
$38$		0			0
$39$			6.65131i			1.06506i
$40$		0			0
$41$			5.49891i			0.858785i	0.903118	+	0.429392i	$0.141272\pi$
$41$			5.49891i			0.858785i	−0.903118	+	0.429392i	$0.858728\pi$
$42$		0			0
$43$	0.256166	−	0.256166i	0.0390650	−	0.0390650i	−0.687304	−	0.726369i	$-0.741206\pi$
$43$	0.256166	−	0.256166i	0.0390650	−	0.0390650i	0.726369	+	0.687304i	$0.241206\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			4.60743i			0.672063i	0.941851	+	0.336032i	$0.109085\pi$
$47$			4.60743i			0.672063i	−0.941851	+	0.336032i	$0.890915\pi$
$48$		0			0
$49$	−6.52310			−0.931872
$50$		0			0
$51$	7.52510	−	7.52510i	1.05372	−	1.05372i
$52$		0			0
$53$	−4.99318	+	4.99318i	−0.685866	+	0.685866i	−0.961316	−	0.275449i	$-0.911173\pi$
$53$	−4.99318	+	4.99318i	−0.685866	+	0.685866i	0.275449	+	0.961316i	$0.411173\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	15.3382			2.03159
$58$		0			0
$59$	1.46478	+	1.46478i	0.190698	+	0.190698i	0.795998	−	0.605300i	$-0.206947\pi$
$59$	1.46478	+	1.46478i	0.190698	+	0.190698i	−0.605300	+	0.795998i	$0.706947\pi$
$60$		0			0
$61$	9.33004	−	9.33004i	1.19459	−	1.19459i	0.218825	−	0.975764i	$-0.429778\pi$
$61$	9.33004	−	9.33004i	1.19459	−	1.19459i	0.975764	−	0.218825i	$-0.0702224\pi$
$62$		0			0
$63$			0.725523i			0.0914074i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.94797	+	1.94797i	0.237982	+	0.237982i	0.816014	−	0.578032i	$-0.196179\pi$
$67$	1.94797	+	1.94797i	0.237982	+	0.237982i	−0.578032	+	0.816014i	$0.696179\pi$
$68$		0			0
$69$	−2.28897	−	2.28897i	−0.275560	−	0.275560i
$70$		0			0
$71$		−	2.32246i		−	0.275625i	−0.990458	−	0.137813i	$-0.955993\pi$
$71$		−	2.32246i		−	0.275625i	0.990458	−	0.137813i	$-0.0440072\pi$
$72$		0			0
$73$	1.29733			0.151841			0.0759206	−	0.997114i	$-0.475810\pi$
$73$	1.29733			0.151841			0.0759206	+	0.997114i	$0.475810\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.11356	+	2.11356i	0.240862	+	0.240862i
$78$		0			0
$79$	−5.01968			−0.564758			−0.282379	−	0.959303i	$-0.591124\pi$
$79$	−5.01968			−0.564758			−0.282379	+	0.959303i	$0.591124\pi$
$80$		0			0
$81$	11.0480			1.22756
$82$		0			0
$83$	7.30477	+	7.30477i	0.801802	+	0.801802i	0.983377	−	0.181575i	$-0.0581194\pi$
$83$	7.30477	+	7.30477i	0.801802	+	0.801802i	−0.181575	+	0.983377i	$0.558119\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.84772			−0.519730
$88$		0			0
$89$			1.81564i			0.192458i	0.995359	+	0.0962290i	$0.0306781\pi$
$89$			1.81564i			0.192458i	−0.995359	+	0.0962290i	$0.969322\pi$
$90$		0			0
$91$	1.61378	+	1.61378i	0.169170	+	0.169170i
$92$		0			0
$93$	6.68597	+	6.68597i	0.693303	+	0.693303i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			5.27038i			0.535126i	0.963540	+	0.267563i	$0.0862183\pi$
$97$			5.27038i			0.535126i	−0.963540	+	0.267563i	$0.913782\pi$
$98$		0			0
$99$	−3.21546	+	3.21546i	−0.323165	+	0.323165i
$100$		0			0
$101$	−13.4502	−	13.4502i	−1.33834	−	1.33834i	−0.897667	−	0.440675i	$-0.854739\pi$
$101$	−13.4502	−	13.4502i	−1.33834	−	1.33834i	−0.440675	−	0.897667i	$-0.645261\pi$
$102$		0			0
$103$	−2.64310			−0.260432			−0.130216	−	0.991486i	$-0.541567\pi$
$103$	−2.64310			−0.260432			−0.130216	+	0.991486i	$0.541567\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.28120	+	6.28120i	−0.607227	+	0.607227i	−0.942220	−	0.334994i	$-0.891266\pi$
$107$	−6.28120	+	6.28120i	−0.607227	+	0.607227i	0.334994	+	0.942220i	$0.391266\pi$
$108$		0			0
$109$	6.89216	−	6.89216i	0.660149	−	0.660149i	−0.295266	−	0.955415i	$-0.595408\pi$
$109$	6.89216	−	6.89216i	0.660149	−	0.660149i	0.955415	+	0.295266i	$0.0954083\pi$
$110$		0			0
$111$	−22.4818			−2.13388
$112$		0			0
$113$		−	6.46108i		−	0.607807i	−0.952703	−	0.303904i	$-0.901710\pi$
$113$		−	6.46108i		−	0.607807i	0.952703	−	0.303904i	$-0.0982901\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.45512	+	2.45512i	−0.226976	+	0.226976i
$118$		0			0
$119$		−	3.65156i		−	0.334738i
$120$		0			0
$121$			7.73420i			0.703109i
$122$		0			0
$123$	−7.82566	+	7.82566i	−0.705616	+	0.705616i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			16.6123i			1.47411i	0.675834	+	0.737054i	$0.263784\pi$
$127$			16.6123i			1.47411i	−0.675834	+	0.737054i	$0.736216\pi$
$128$		0			0
$129$	0.729117			0.0641951
$130$		0			0
$131$	11.7719	−	11.7719i	1.02851	−	1.02851i	0.0289318	−	0.999581i	$-0.490789\pi$
$131$	11.7719	−	11.7719i	1.02851	−	1.02851i	0.999581	−	0.0289318i	$-0.00921056\pi$
$132$		0			0
$133$	3.72143	−	3.72143i	0.322689	−	0.322689i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.41495			−0.718937			−0.359469	−	0.933157i	$-0.617042\pi$
$137$	−8.41495			−0.718937			−0.359469	+	0.933157i	$0.617042\pi$
$138$		0			0
$139$	−1.51845	−	1.51845i	−0.128793	−	0.128793i	0.639772	−	0.768565i	$-0.279029\pi$
$139$	−1.51845	−	1.51845i	−0.128793	−	0.128793i	−0.768565	+	0.639772i	$0.779029\pi$
$140$		0			0
$141$	−6.55698	+	6.55698i	−0.552198	+	0.552198i
$142$		0			0
$143$			14.3042i			1.19618i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−9.28324	−	9.28324i	−0.765668	−	0.765668i
$148$		0			0
$149$	2.61440	+	2.61440i	0.214180	+	0.214180i	0.806040	−	0.591860i	$-0.201606\pi$
$149$	2.61440	+	2.61440i	0.214180	+	0.214180i	−0.591860	+	0.806040i	$0.701606\pi$
$150$		0			0
$151$			12.7143i			1.03467i	0.855782	+	0.517337i	$0.173077\pi$
$151$			12.7143i			1.03467i	−0.855782	+	0.517337i	$0.826923\pi$
$152$		0			0
$153$	5.55529			0.449119
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.17831	−	7.17831i	−0.572891	−	0.572891i	0.360044	−	0.932935i	$-0.382762\pi$
$157$	−7.17831	−	7.17831i	−0.572891	−	0.572891i	−0.932935	+	0.360044i	$0.882762\pi$
$158$		0			0
$159$	−14.2119			−1.12708
$160$		0			0
$161$	−1.11073			−0.0875376
$162$		0			0
$163$	−7.05476	−	7.05476i	−0.552572	−	0.552572i	0.374611	−	0.927182i	$-0.377776\pi$
$163$	−7.05476	−	7.05476i	−0.552572	−	0.552572i	−0.927182	+	0.374611i	$0.877776\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.90586			0.302244			0.151122	−	0.988515i	$-0.451711\pi$
$167$	3.90586			0.302244			0.151122	+	0.988515i	$0.451711\pi$
$168$		0			0
$169$		−	2.07819i		−	0.159861i
$170$		0			0
$171$	5.66158	+	5.66158i	0.432952	+	0.432952i
$172$		0			0
$173$	−8.20139	−	8.20139i	−0.623540	−	0.623540i	0.322895	−	0.946435i	$-0.395344\pi$
$173$	−8.20139	−	8.20139i	−0.623540	−	0.623540i	−0.946435	+	0.322895i	$0.895344\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			4.16914i			0.313372i
$178$		0			0
$179$	−3.10363	+	3.10363i	−0.231976	+	0.231976i	−0.813517	−	0.581541i	$-0.802450\pi$
$179$	−3.10363	+	3.10363i	−0.231976	+	0.231976i	0.581541	+	0.813517i	$0.302450\pi$
$180$		0			0
$181$	−1.91041	−	1.91041i	−0.141999	−	0.141999i	0.632534	−	0.774533i	$-0.282015\pi$
$181$	−1.91041	−	1.91041i	−0.141999	−	0.141999i	−0.774533	+	0.632534i	$0.782015\pi$
$182$		0			0
$183$	26.5557			1.96306
$184$		0			0
$185$		0			0
$186$		0			0
$187$	16.1834	−	16.1834i	1.18345	−	1.18345i
$188$		0			0
$189$	1.91583	−	1.91583i	0.139356	−	0.139356i
$190$		0			0
$191$	−5.61041			−0.405955			−0.202977	−	0.979183i	$-0.565062\pi$
$191$	−5.61041			−0.405955			−0.202977	+	0.979183i	$0.565062\pi$
$192$		0			0
$193$		−	3.90696i		−	0.281229i	−0.990064	−	0.140615i	$-0.955092\pi$
$193$		−	3.90696i		−	0.281229i	0.990064	−	0.140615i	$-0.0449079\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.608436	+	0.608436i	−0.0433493	+	0.0433493i	−0.728449	−	0.685100i	$-0.759759\pi$
$197$	−0.608436	+	0.608436i	−0.0433493	+	0.0433493i	0.685100	+	0.728449i	$0.259759\pi$
$198$		0			0
$199$		−	15.5282i		−	1.10076i	−0.834913	−	0.550382i	$-0.814482\pi$
$199$		−	15.5282i		−	1.10076i	0.834913	−	0.550382i	$-0.185518\pi$
$200$		0			0
$201$			5.54443i			0.391074i
$202$		0			0
$203$	−1.17618	+	1.17618i	−0.0825517	+	0.0825517i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	1.68980i		−	0.117449i
$208$		0			0
$209$	32.9861			2.28169
$210$		0			0
$211$	−2.14501	+	2.14501i	−0.147669	+	0.147669i	−0.777076	−	0.629407i	$-0.783298\pi$
$211$	−2.14501	+	2.14501i	−0.147669	+	0.147669i	0.629407	+	0.777076i	$0.283298\pi$
$212$		0			0
$213$	3.30516	−	3.30516i	0.226466	−	0.226466i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.24437			0.220242
$218$		0			0
$219$	1.84627	+	1.84627i	0.124760	+	0.124760i
$220$		0			0
$221$	12.3566	−	12.3566i	0.831196	−	0.831196i
$222$		0			0
$223$		−	2.34794i		−	0.157230i	−0.996905	−	0.0786148i	$-0.974950\pi$
$223$		−	2.34794i		−	0.157230i	0.996905	−	0.0786148i	$-0.0250497\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.1881	−	13.1881i	−0.875325	−	0.875325i	0.117722	−	0.993047i	$-0.462441\pi$
$227$	−13.1881	−	13.1881i	−0.875325	−	0.875325i	−0.993047	+	0.117722i	$0.962441\pi$
$228$		0			0
$229$	−9.37860	−	9.37860i	−0.619755	−	0.619755i	0.325713	−	0.945469i	$-0.394396\pi$
$229$	−9.37860	−	9.37860i	−0.619755	−	0.619755i	−0.945469	+	0.325713i	$0.894396\pi$
$230$		0			0
$231$			6.01574i			0.395807i
$232$		0			0
$233$	−16.3435			−1.07070			−0.535350	−	0.844630i	$-0.679820\pi$
$233$	−16.3435			−1.07070			−0.535350	+	0.844630i	$0.679820\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−7.14367	−	7.14367i	−0.464031	−	0.464031i
$238$		0			0
$239$	19.3818			1.25371			0.626854	−	0.779137i	$-0.284342\pi$
$239$	19.3818			1.25371			0.626854	+	0.779137i	$0.284342\pi$
$240$		0			0
$241$	7.15965			0.461193			0.230597	−	0.973049i	$-0.425932\pi$
$241$	7.15965			0.461193			0.230597	+	0.973049i	$0.425932\pi$
$242$		0			0
$243$	7.40009	+	7.40009i	0.474716	+	0.474716i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	25.1861			1.60255
$248$		0			0
$249$			20.7913i			1.31759i
$250$		0			0
$251$	−10.4372	−	10.4372i	−0.658787	−	0.658787i	0.296306	−	0.955093i	$-0.404245\pi$
$251$	−10.4372	−	10.4372i	−0.658787	−	0.658787i	−0.955093	+	0.296306i	$0.904245\pi$
$252$		0			0
$253$	−4.92264	−	4.92264i	−0.309484	−	0.309484i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			5.72152i			0.356899i	0.983949	+	0.178449i	$0.0571081\pi$
$257$			5.72152i			0.356899i	−0.983949	+	0.178449i	$0.942892\pi$
$258$		0			0
$259$	−5.45466	+	5.45466i	−0.338936	+	0.338936i
$260$		0			0
$261$	−1.78938	−	1.78938i	−0.110760	−	0.110760i
$262$		0			0
$263$	−27.1378			−1.67339			−0.836695	−	0.547669i	$-0.815515\pi$
$263$	−27.1378			−1.67339			−0.836695	+	0.547669i	$0.815515\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.58390	+	2.58390i	−0.158132	+	0.158132i
$268$		0			0
$269$	−13.0770	+	13.0770i	−0.797320	+	0.797320i	−0.982672	−	0.185352i	$-0.940657\pi$
$269$	−13.0770	+	13.0770i	−0.797320	+	0.797320i	0.185352	+	0.982672i	$0.440657\pi$
$270$		0			0
$271$	−6.55264			−0.398044			−0.199022	−	0.979995i	$-0.563777\pi$
$271$	−6.55264			−0.398044			−0.199022	+	0.979995i	$0.563777\pi$
$272$		0			0
$273$			4.59324i			0.277995i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.2851	−	10.2851i	0.617973	−	0.617973i	−0.327038	−	0.945011i	$-0.606051\pi$
$277$	10.2851	−	10.2851i	0.617973	−	0.617973i	0.945011	+	0.327038i	$0.106051\pi$
$278$		0			0
$279$			4.93582i			0.295500i
$280$		0			0
$281$			29.9714i			1.78794i	0.448124	+	0.893971i	$0.352092\pi$
$281$			29.9714i			1.78794i	−0.448124	+	0.893971i	$0.647908\pi$
$282$		0			0
$283$	19.1176	−	19.1176i	1.13642	−	1.13642i	0.147334	−	0.989087i	$-0.452931\pi$
$283$	19.1176	−	19.1176i	1.13642	−	1.13642i	0.989087	−	0.147334i	$-0.0470691\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			3.79741i			0.224154i
$288$		0			0
$289$	−10.9598			−0.644695
$290$		0			0
$291$	−7.50044	+	7.50044i	−0.439684	+	0.439684i
$292$		0			0
$293$	7.27952	−	7.27952i	0.425274	−	0.425274i	−0.461741	−	0.887015i	$-0.652775\pi$
$293$	7.27952	−	7.27952i	0.425274	−	0.425274i	0.887015	+	0.461741i	$0.152775\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	16.9815			0.985369
$298$		0			0
$299$	−3.75862	−	3.75862i	−0.217366	−	0.217366i
$300$		0			0
$301$	0.176902	−	0.176902i	0.0101965	−	0.0101965i
$302$		0			0
$303$		−	38.2827i		−	2.19928i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.03304	−	7.03304i	−0.401397	−	0.401397i	0.477328	−	0.878725i	$-0.341605\pi$
$307$	−7.03304	−	7.03304i	−0.401397	−	0.401397i	−0.878725	+	0.477328i	$0.841605\pi$
$308$		0			0
$309$	−3.76147	−	3.76147i	−0.213983	−	0.213983i
$310$		0			0
$311$		−	14.2833i		−	0.809929i	−0.914332	−	0.404964i	$-0.867284\pi$
$311$		−	14.2833i		−	0.809929i	0.914332	−	0.404964i	$-0.132716\pi$
$312$		0			0
$313$	−18.4579			−1.04330			−0.521652	−	0.853158i	$-0.674684\pi$
$313$	−18.4579			−1.04330			−0.521652	+	0.853158i	$0.674684\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.21807	−	7.21807i	−0.405407	−	0.405407i	0.474726	−	0.880133i	$-0.342547\pi$
$317$	−7.21807	−	7.21807i	−0.405407	−	0.405407i	−0.880133	+	0.474726i	$0.842547\pi$
$318$		0			0
$319$	−10.4255			−0.583714
$320$		0			0
$321$	−17.8780			−0.997850
$322$		0			0
$323$	−28.4948	−	28.4948i	−1.58549	−	1.58549i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	19.6169			1.08482
$328$		0			0
$329$			3.18178i			0.175417i
$330$		0			0
$331$	15.4847	+	15.4847i	0.851116	+	0.851116i	0.990271	−	0.139155i	$-0.0444385\pi$
$331$	15.4847	+	15.4847i	0.851116	+	0.851116i	−0.139155	+	0.990271i	$0.544439\pi$
$332$		0			0
$333$	−8.29844	−	8.29844i	−0.454752	−	0.454752i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	26.0210i		−	1.41746i	−0.705482	−	0.708728i	$-0.749269\pi$
$337$		−	26.0210i		−	1.41746i	0.705482	−	0.708728i	$-0.250731\pi$
$338$		0			0
$339$	9.19497	−	9.19497i	0.499402	−	0.499402i
$340$		0			0
$341$	14.3788	+	14.3788i	0.778654	+	0.778654i
$342$		0			0
$343$	−9.33873			−0.504244
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.8554	+	12.8554i	−0.690115	+	0.690115i	−0.962257	−	0.272142i	$-0.912268\pi$
$347$	−12.8554	+	12.8554i	−0.690115	+	0.690115i	0.272142	+	0.962257i	$0.412268\pi$
$348$		0			0
$349$	20.0227	−	20.0227i	1.07179	−	1.07179i	0.0745736	−	0.997216i	$-0.476240\pi$
$349$	20.0227	−	20.0227i	1.07179	−	1.07179i	0.997216	−	0.0745736i	$-0.0237596\pi$
$350$		0			0
$351$	12.9660			0.692075
$352$		0			0
$353$		−	13.7062i		−	0.729510i	−0.931104	−	0.364755i	$-0.881153\pi$
$353$		−	13.7062i		−	0.729510i	0.931104	−	0.364755i	$-0.118847\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.19665	−	5.19665i	0.275036	−	0.275036i
$358$		0			0
$359$			32.3506i			1.70740i	0.520764	+	0.853700i	$0.325647\pi$
$359$			32.3506i			1.70740i	−0.520764	+	0.853700i	$0.674353\pi$
$360$		0			0
$361$		−	39.0799i		−	2.05684i
$362$		0			0
$363$	−11.0068	+	11.0068i	−0.577706	+	0.577706i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	16.3714i		−	0.854582i	−0.904114	−	0.427291i	$-0.859468\pi$
$367$		−	16.3714i		−	0.854582i	0.904114	−	0.427291i	$-0.140532\pi$
$368$		0			0
$369$	−5.77718			−0.300748
$370$		0			0
$371$	−3.44817	+	3.44817i	−0.179020	+	0.179020i
$372$		0			0
$373$	15.5321	−	15.5321i	0.804222	−	0.804222i	−0.179530	−	0.983752i	$-0.557458\pi$
$373$	15.5321	−	15.5321i	0.804222	−	0.804222i	0.983752	+	0.179530i	$0.0574578\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.96022			−0.409972
$378$		0			0
$379$	24.9538	+	24.9538i	1.28179	+	1.28179i	0.939647	+	0.342145i	$0.111153\pi$
$379$	24.9538	+	24.9538i	1.28179	+	1.28179i	0.342145	+	0.939647i	$0.388847\pi$
$380$		0			0
$381$	−23.6416	+	23.6416i	−1.21119	+	1.21119i
$382$		0			0
$383$			6.24887i			0.319302i	0.987174	+	0.159651i	$0.0510369\pi$
$383$			6.24887i			0.319302i	−0.987174	+	0.159651i	$0.948963\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.269130	+	0.269130i	0.0136806	+	0.0136806i
$388$		0			0
$389$	−2.10802	−	2.10802i	−0.106881	−	0.106881i	0.651644	−	0.758525i	$-0.274080\pi$
$389$	−2.10802	−	2.10802i	−0.106881	−	0.106881i	−0.758525	+	0.651644i	$0.774080\pi$
$390$		0			0
$391$			8.50478i			0.430105i
$392$		0			0
$393$	33.5058			1.69015
$394$		0			0
$395$		0			0
$396$		0			0
$397$	23.4977	+	23.4977i	1.17932	+	1.17932i	0.979919	+	0.199397i	$0.0638983\pi$
$397$	23.4977	+	23.4977i	1.17932	+	1.17932i	0.199397	+	0.979919i	$0.436102\pi$
$398$		0			0
$399$	10.5922			0.530271
$400$		0			0
$401$	−20.9893			−1.04816			−0.524078	−	0.851670i	$-0.675590\pi$
$401$	−20.9893			−1.04816			−0.524078	+	0.851670i	$0.675590\pi$
$402$		0			0
$403$	10.9787	+	10.9787i	0.546889	+	0.546889i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−48.3492			−2.39658
$408$		0			0
$409$		−	18.4025i		−	0.909944i	−0.890506	−	0.454972i	$-0.849649\pi$
$409$		−	18.4025i		−	0.909944i	0.890506	−	0.454972i	$-0.150351\pi$
$410$		0			0
$411$	−11.9756	−	11.9756i	−0.590711	−	0.590711i
$412$		0			0
$413$	1.01154	+	1.01154i	0.0497746	+	0.0497746i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	4.32190i		−	0.211644i
$418$		0			0
$419$	14.9331	−	14.9331i	0.729530	−	0.729530i	−0.240996	−	0.970526i	$-0.577474\pi$
$419$	14.9331	−	14.9331i	0.729530	−	0.729530i	0.970526	+	0.240996i	$0.0774740\pi$
$420$		0			0
$421$	−16.2680	−	16.2680i	−0.792854	−	0.792854i	0.189103	−	0.981957i	$-0.439442\pi$
$421$	−16.2680	−	16.2680i	−0.792854	−	0.792854i	−0.981957	+	0.189103i	$0.939442\pi$
$422$		0			0
$423$	−4.84060			−0.235358
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.44310	−	6.44310i	0.311804	−	0.311804i
$428$		0			0
$429$	−20.3568	+	20.3568i	−0.982836	+	0.982836i
$430$		0			0
$431$	−7.05425			−0.339791			−0.169896	−	0.985462i	$-0.554343\pi$
$431$	−7.05425			−0.339791			−0.169896	+	0.985462i	$0.554343\pi$
$432$		0			0
$433$			14.3192i			0.688139i	0.938944	+	0.344069i	$0.111806\pi$
$433$			14.3192i			0.688139i	−0.938944	+	0.344069i	$0.888194\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.66750	+	8.66750i	−0.414623	+	0.414623i
$438$		0			0
$439$		−	25.9047i		−	1.23637i	−0.786034	−	0.618183i	$-0.787869\pi$
$439$		−	25.9047i		−	1.23637i	0.786034	−	0.618183i	$-0.212131\pi$
$440$		0			0
$441$		−	6.85321i		−	0.326344i
$442$		0			0
$443$	11.1389	−	11.1389i	0.529224	−	0.529224i	−0.391117	−	0.920341i	$-0.627911\pi$
$443$	11.1389	−	11.1389i	0.529224	−	0.529224i	0.920341	+	0.391117i	$0.127911\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			7.44127i			0.351960i
$448$		0			0
$449$	−12.6659			−0.597740			−0.298870	−	0.954294i	$-0.596610\pi$
$449$	−12.6659			−0.597740			−0.298870	+	0.954294i	$0.596610\pi$
$450$		0			0
$451$	−16.8298	+	16.8298i	−0.792484	+	0.792484i
$452$		0			0
$453$	−18.0941	+	18.0941i	−0.850135	+	0.850135i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.9442			−0.792617			−0.396308	−	0.918117i	$-0.629709\pi$
$457$	−16.9442			−0.792617			−0.396308	+	0.918117i	$0.629709\pi$
$458$		0			0
$459$	−14.6694	−	14.6694i	−0.684708	−	0.684708i
$460$		0			0
$461$	−13.1888	+	13.1888i	−0.614264	+	0.614264i	−0.944054	−	0.329790i	$-0.893022\pi$
$461$	−13.1888	+	13.1888i	−0.614264	+	0.614264i	0.329790	+	0.944054i	$0.393022\pi$
$462$		0			0
$463$		−	14.0955i		−	0.655074i	−0.944838	−	0.327537i	$-0.893781\pi$
$463$		−	14.0955i		−	0.655074i	0.944838	−	0.327537i	$-0.106219\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.0918	+	12.0918i	0.559540	+	0.559540i	0.929177	−	0.369636i	$-0.120518\pi$
$467$	12.0918	+	12.0918i	0.559540	+	0.559540i	−0.369636	+	0.929177i	$0.620518\pi$
$468$		0			0
$469$	1.34522	+	1.34522i	0.0621165	+	0.0621165i
$470$		0			0
$471$		−	20.4313i		−	0.941427i
$472$		0			0
$473$	1.56803			0.0720981
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.24587	−	5.24587i	−0.240192	−	0.240192i
$478$		0			0
$479$	14.2523			0.651202			0.325601	−	0.945507i	$-0.394433\pi$
$479$	14.2523			0.651202			0.325601	+	0.945507i	$0.394433\pi$
$480$		0			0
$481$	−36.9163			−1.68324
$482$		0			0
$483$	−1.58071	−	1.58071i	−0.0719248	−	0.0719248i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−26.0424			−1.18010			−0.590048	−	0.807368i	$-0.700891\pi$
$487$	−26.0424			−1.18010			−0.590048	+	0.807368i	$0.700891\pi$
$488$		0			0
$489$		−	20.0797i		−	0.908036i
$490$		0			0
$491$	−3.46798	−	3.46798i	−0.156508	−	0.156508i	0.624509	−	0.781017i	$-0.285299\pi$
$491$	−3.46798	−	3.46798i	−0.156508	−	0.156508i	−0.781017	+	0.624509i	$0.785299\pi$
$492$		0			0
$493$	9.00595	+	9.00595i	0.405608	+	0.405608i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	1.60383i		−	0.0719418i
$498$		0			0
$499$	−5.30274	+	5.30274i	−0.237383	+	0.237383i	−0.815766	−	0.578383i	$-0.803684\pi$
$499$	−5.30274	+	5.30274i	−0.237383	+	0.237383i	0.578383	+	0.815766i	$0.303684\pi$
$500$		0			0
$501$	5.55855	+	5.55855i	0.248338	+	0.248338i
$502$		0			0
$503$	28.8492			1.28632			0.643161	−	0.765731i	$-0.277622\pi$
$503$	28.8492			1.28632			0.643161	+	0.765731i	$0.277622\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.95754	−	2.95754i	0.131349	−	0.131349i
$508$		0			0
$509$	−12.9968	+	12.9968i	−0.576072	+	0.576072i	−0.933819	−	0.357747i	$-0.883545\pi$
$509$	−12.9968	+	12.9968i	−0.576072	+	0.576072i	0.357747	+	0.933819i	$0.383545\pi$
$510$		0			0
$511$	0.895906			0.0396326
$512$		0			0
$513$		−	29.9001i		−	1.32012i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−14.1014	+	14.1014i	−0.620178	+	0.620178i
$518$		0			0
$519$		−	23.3433i		−	1.02466i
$520$		0			0
$521$		−	13.9833i		−	0.612618i	−0.951932	−	0.306309i	$-0.900906\pi$
$521$		−	13.9833i		−	0.612618i	0.951932	−	0.306309i	$-0.0990941\pi$
$522$		0			0
$523$	6.30689	−	6.30689i	0.275781	−	0.275781i	−0.555641	−	0.831422i	$-0.687527\pi$
$523$	6.30689	−	6.30689i	0.275781	−	0.275781i	0.831422	+	0.555641i	$0.187527\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	24.8420i		−	1.08213i
$528$		0			0
$529$	−20.4130			−0.887523
$530$		0			0
$531$	−1.53890	+	1.53890i	−0.0667827	+	0.0667827i
$532$		0			0
$533$	−12.8502	+	12.8502i	−0.556602	+	0.556602i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.83375			−0.381204
$538$		0			0
$539$	−19.9644	−	19.9644i	−0.859929	−	0.859929i
$540$		0			0
$541$	3.89317	−	3.89317i	0.167381	−	0.167381i	−0.618446	−	0.785827i	$-0.712238\pi$
$541$	3.89317	−	3.89317i	0.167381	−	0.167381i	0.785827	+	0.618446i	$0.212238\pi$
$542$		0			0
$543$		−	5.43752i		−	0.233346i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	27.8376	+	27.8376i	1.19025	+	1.19025i	0.976997	+	0.213251i	$0.0684053\pi$
$547$	27.8376	+	27.8376i	1.19025	+	1.19025i	0.213251	+	0.976997i	$0.431595\pi$
$548$		0			0
$549$	9.80220	+	9.80220i	0.418348	+	0.418348i
$550$		0			0
$551$			18.3565i			0.782014i
$552$		0			0
$553$	−3.46647			−0.147409
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.50454	+	1.50454i	0.0637492	+	0.0637492i	0.738263	−	0.674513i	$-0.235647\pi$
$557$	1.50454	+	1.50454i	0.0637492	+	0.0637492i	−0.674513	+	0.738263i	$0.735647\pi$
$558$		0			0
$559$	1.19725			0.0506382
$560$		0			0
$561$	46.0622			1.94475
$562$		0			0
$563$	−6.66663	−	6.66663i	−0.280965	−	0.280965i	0.552529	−	0.833494i	$-0.313663\pi$
$563$	−6.66663	−	6.66663i	−0.280965	−	0.280965i	−0.833494	+	0.552529i	$0.813663\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	7.62952			0.320410
$568$		0			0
$569$		−	8.38187i		−	0.351386i	−0.984445	−	0.175693i	$-0.943783\pi$
$569$		−	8.38187i		−	0.351386i	0.984445	−	0.175693i	$-0.0562167\pi$
$570$		0			0
$571$	−28.4129	−	28.4129i	−1.18904	−	1.18904i	−0.977333	−	0.211708i	$-0.932097\pi$
$571$	−28.4129	−	28.4129i	−1.18904	−	1.18904i	−0.211708	−	0.977333i	$-0.567903\pi$
$572$		0			0
$573$	−7.98435	−	7.98435i	−0.333551	−	0.333551i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			23.2045i			0.966014i	0.875616	+	0.483007i	$0.160455\pi$
$577$			23.2045i			0.966014i	−0.875616	+	0.483007i	$0.839545\pi$
$578$		0			0
$579$	5.56012	−	5.56012i	0.231071	−	0.231071i
$580$		0			0
$581$	5.04450	+	5.04450i	0.209281	+	0.209281i
$582$		0			0
$583$	−30.5640			−1.26583
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.0197	+	11.0197i	−0.454832	+	0.454832i	−0.896955	−	0.442123i	$-0.854226\pi$
$587$	−11.0197	+	11.0197i	−0.454832	+	0.454832i	0.442123	+	0.896955i	$0.354226\pi$
$588$		0			0
$589$	25.3173	−	25.3173i	1.04318	−	1.04318i
$590$		0			0
$591$	−1.73177			−0.0712354
$592$		0			0
$593$			6.98847i			0.286982i	0.989652	+	0.143491i	$0.0458328\pi$
$593$			6.98847i			0.286982i	−0.989652	+	0.143491i	$0.954167\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	22.0987	−	22.0987i	0.904438	−	0.904438i
$598$		0			0
$599$			39.9642i			1.63289i	0.577420	+	0.816447i	$0.304059\pi$
$599$			39.9642i			1.63289i	−0.577420	+	0.816447i	$0.695941\pi$
$600$		0			0
$601$			21.0830i			0.859993i	0.902831	+	0.429997i	$0.141485\pi$
$601$			21.0830i			0.859993i	−0.902831	+	0.429997i	$0.858515\pi$
$602$		0			0
$603$	−2.04655	+	2.04655i	−0.0833418	+	0.0833418i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	22.3189i		−	0.905897i	−0.891537	−	0.452949i	$-0.850372\pi$
$607$		−	22.3189i		−	0.905897i	0.891537	−	0.452949i	$-0.149628\pi$
$608$		0			0
$609$	−3.34772			−0.135656
$610$		0			0
$611$	−10.7669	+	10.7669i	−0.435583	+	0.435583i
$612$		0			0
$613$	−10.6045	+	10.6045i	−0.428312	+	0.428312i	−0.888053	−	0.459741i	$-0.847942\pi$
$613$	−10.6045	+	10.6045i	−0.428312	+	0.428312i	0.459741	+	0.888053i	$0.347942\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−33.7636			−1.35927			−0.679635	−	0.733550i	$-0.737862\pi$
$617$	−33.7636			−1.35927			−0.679635	+	0.733550i	$0.737862\pi$
$618$		0			0
$619$	4.86777	+	4.86777i	0.195652	+	0.195652i	0.798133	−	0.602481i	$-0.205821\pi$
$619$	4.86777	+	4.86777i	0.195652	+	0.195652i	−0.602481	+	0.798133i	$0.705821\pi$
$620$		0			0
$621$	−4.46211	+	4.46211i	−0.179058	+	0.179058i
$622$		0			0
$623$			1.25384i			0.0502341i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	46.9435	+	46.9435i	1.87474	+	1.87474i
$628$		0			0
$629$	41.7661	+	41.7661i	1.66532	+	1.66532i
$630$		0			0
$631$		−	16.1348i		−	0.642315i	−0.947026	−	0.321157i	$-0.895928\pi$
$631$		−	16.1348i		−	0.642315i	0.947026	−	0.321157i	$-0.104072\pi$
$632$		0			0
$633$	−6.10526			−0.242662
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−15.2436	−	15.2436i	−0.603972	−	0.603972i
$638$		0			0
$639$	2.43999			0.0965245
$640$		0			0
$641$	20.3125			0.802296			0.401148	−	0.916013i	$-0.368611\pi$
$641$	20.3125			0.802296			0.401148	+	0.916013i	$0.368611\pi$
$642$		0			0
$643$	7.78443	+	7.78443i	0.306988	+	0.306988i	0.843740	−	0.536752i	$-0.180349\pi$
$643$	7.78443	+	7.78443i	0.306988	+	0.306988i	−0.536752	+	0.843740i	$0.680349\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.7693			−0.855840			−0.427920	−	0.903817i	$-0.640754\pi$
$647$	−21.7693			−0.855840			−0.427920	+	0.903817i	$0.640754\pi$
$648$		0			0
$649$			8.96611i			0.351951i
$650$		0			0
$651$	4.61717	+	4.61717i	0.180961	+	0.180961i
$652$		0			0
$653$	26.3118	+	26.3118i	1.02966	+	1.02966i	0.999546	+	0.0301152i	$0.00958743\pi$
$653$	26.3118	+	26.3118i	1.02966	+	1.02966i	0.0301152	+	0.999546i	$0.490413\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			1.36298i			0.0531751i
$658$		0			0
$659$	−20.2389	+	20.2389i	−0.788397	+	0.788397i	−0.981231	−	0.192835i	$-0.938232\pi$
$659$	−20.2389	+	20.2389i	−0.788397	+	0.788397i	0.192835	+	0.981231i	$0.438232\pi$
$660$		0			0
$661$	6.81905	+	6.81905i	0.265230	+	0.265230i	0.827175	−	0.561945i	$-0.189947\pi$
$661$	6.81905	+	6.81905i	0.265230	+	0.265230i	−0.561945	+	0.827175i	$0.689947\pi$
$662$		0			0
$663$	35.1702			1.36590
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.73942	−	2.73942i	0.106071	−	0.106071i
$668$		0			0
$669$	3.34143	−	3.34143i	0.129187	−	0.129187i
$670$		0			0
$671$	57.1105			2.20473
$672$		0			0
$673$			8.19512i			0.315899i	0.987447	+	0.157949i	$0.0504883\pi$
$673$			8.19512i			0.315899i	−0.987447	+	0.157949i	$0.949512\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.8834	+	12.8834i	−0.495151	+	0.495151i	−0.909925	−	0.414774i	$-0.863861\pi$
$677$	−12.8834	+	12.8834i	−0.495151	+	0.495151i	0.414774	+	0.909925i	$0.363861\pi$
$678$		0			0
$679$			3.63960i			0.139675i
$680$		0			0
$681$		−	37.5368i		−	1.43841i
$682$		0			0
$683$	−15.0673	+	15.0673i	−0.576535	+	0.576535i	−0.933947	−	0.357412i	$-0.883659\pi$
$683$	−15.0673	+	15.0673i	−0.576535	+	0.576535i	0.357412	+	0.933947i	$0.383659\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	26.6940i		−	1.01844i
$688$		0			0
$689$	−23.3367			−0.889058
$690$		0			0
$691$	5.23733	−	5.23733i	0.199237	−	0.199237i	−0.600436	−	0.799673i	$-0.705006\pi$
$691$	5.23733	−	5.23733i	0.199237	−	0.199237i	0.799673	+	0.600436i	$0.205006\pi$
$692$		0			0
$693$	−2.22052	+	2.22052i	−0.0843504	+	0.0843504i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	29.0766			1.10135
$698$		0			0
$699$	−23.2590	−	23.2590i	−0.879736	−	0.879736i
$700$		0			0
$701$	21.7664	−	21.7664i	0.822106	−	0.822106i	−0.164303	−	0.986410i	$-0.552538\pi$
$701$	21.7664	−	21.7664i	0.822106	−	0.822106i	0.986410	+	0.164303i	$0.0525376\pi$
$702$		0			0
$703$			85.1304i			3.21075i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.28836	−	9.28836i	−0.349325	−	0.349325i
$708$		0			0
$709$	23.9643	+	23.9643i	0.899997	+	0.899997i	0.995435	−	0.0954387i	$-0.0304254\pi$
$709$	23.9643	+	23.9643i	0.899997	+	0.899997i	−0.0954387	+	0.995435i	$0.530425\pi$
$710$		0			0
$711$		−	5.27371i		−	0.197779i
$712$		0			0
$713$	−7.55640			−0.282990
$714$		0			0
$715$		0			0
$716$		0			0
$717$	27.5829	+	27.5829i	1.03010	+	1.03010i
$718$		0			0
$719$	−44.4408			−1.65736			−0.828681	−	0.559721i	$-0.810908\pi$
$719$	−44.4408			−1.65736			−0.828681	+	0.559721i	$0.810908\pi$
$720$		0			0
$721$	−1.82526			−0.0679762
$722$		0			0
$723$	10.1891	+	10.1891i	0.378937	+	0.378937i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	46.6543			1.73031			0.865155	−	0.501504i	$-0.167220\pi$
$727$	46.6543			1.73031			0.865155	+	0.501504i	$0.167220\pi$
$728$		0			0
$729$		−	12.0815i		−	0.447464i
$730$		0			0
$731$	−1.35453	−	1.35453i	−0.0500992	−	0.0500992i
$732$		0			0
$733$	−19.4202	−	19.4202i	−0.717303	−	0.717303i	0.250749	−	0.968052i	$-0.419323\pi$
$733$	−19.4202	−	19.4202i	−0.717303	−	0.717303i	−0.968052	+	0.250749i	$0.919323\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			11.9238i			0.439219i
$738$		0			0
$739$	−20.5243	+	20.5243i	−0.754999	+	0.754999i	−0.975408	−	0.220409i	$-0.929261\pi$
$739$	−20.5243	+	20.5243i	−0.754999	+	0.754999i	0.220409	+	0.975408i	$0.429261\pi$
$740$		0			0
$741$	35.8431	+	35.8431i	1.31673	+	1.31673i
$742$		0			0
$743$	12.9245			0.474154			0.237077	−	0.971491i	$-0.423811\pi$
$743$	12.9245			0.474154			0.237077	+	0.971491i	$0.423811\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−7.67443	+	7.67443i	−0.280793	+	0.280793i
$748$		0			0
$749$	−4.33765	+	4.33765i	−0.158494	+	0.158494i
$750$		0			0
$751$	52.2694			1.90734			0.953668	−	0.300861i	$-0.0972740\pi$
$751$	52.2694			1.90734			0.953668	+	0.300861i	$0.0972740\pi$
$752$		0			0
$753$		−	29.7069i		−	1.08258i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	34.4514	−	34.4514i	1.25216	−	1.25216i	0.297407	−	0.954751i	$-0.403878\pi$
$757$	34.4514	−	34.4514i	1.25216	−	1.25216i	0.954751	−	0.297407i	$-0.0961218\pi$
$758$		0			0
$759$		−	14.0111i		−	0.508572i
$760$		0			0
$761$		−	47.7467i		−	1.73082i	−0.501067	−	0.865408i	$-0.667059\pi$
$761$		−	47.7467i		−	1.73082i	0.501067	−	0.865408i	$-0.332941\pi$
$762$		0			0
$763$	4.75956	−	4.75956i	0.172308	−	0.172308i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			6.84595i			0.247193i
$768$		0			0
$769$	17.9108			0.645882			0.322941	−	0.946419i	$-0.395329\pi$
$769$	17.9108			0.645882			0.322941	+	0.946419i	$0.395329\pi$
$770$		0			0
$771$	−8.14247	+	8.14247i	−0.293244	+	0.293244i
$772$		0			0
$773$	3.73170	−	3.73170i	0.134220	−	0.134220i	−0.636805	−	0.771025i	$-0.719744\pi$
$773$	3.73170	−	3.73170i	0.134220	−	0.134220i	0.771025	+	0.636805i	$0.219744\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−15.5254			−0.556971
$778$		0			0
$779$	29.6329	+	29.6329i	1.06171	+	1.06171i
$780$		0			0
$781$	7.10805	−	7.10805i	0.254346	−	0.254346i
$782$		0			0
$783$			9.45012i			0.337720i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−2.40160	−	2.40160i	−0.0856076	−	0.0856076i	0.663006	−	0.748614i	$-0.269280\pi$
$787$	−2.40160	−	2.40160i	−0.0856076	−	0.0856076i	−0.748614	+	0.663006i	$0.769280\pi$
$788$		0			0
$789$	−38.6207	−	38.6207i	−1.37493	−	1.37493i
$790$		0			0
$791$		−	4.46187i		−	0.158646i
$792$		0			0
$793$	43.6060			1.54849
$794$		0			0
$795$		0			0
$796$		0			0
$797$	35.4972	+	35.4972i	1.25738	+	1.25738i	0.952341	+	0.305035i	$0.0986682\pi$
$797$	35.4972	+	35.4972i	1.25738	+	1.25738i	0.305035	+	0.952341i	$0.401332\pi$
$798$		0			0
$799$	24.3627			0.861892
$800$		0			0
$801$	−1.90753			−0.0673992
$802$		0			0
$803$	3.97058	+	3.97058i	0.140119	+	0.140119i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−37.2206			−1.31023
$808$		0			0
$809$			11.9182i			0.419021i	0.977806	+	0.209510i	$0.0671870\pi$
$809$			11.9182i			0.419021i	−0.977806	+	0.209510i	$0.932813\pi$
$810$		0			0
$811$	22.1494	+	22.1494i	0.777772	+	0.777772i	0.979452	−	0.201680i	$-0.0646400\pi$
$811$	22.1494	+	22.1494i	0.777772	+	0.777772i	−0.201680	+	0.979452i	$0.564640\pi$
$812$		0			0
$813$	−9.32527	−	9.32527i	−0.327051	−	0.327051i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	2.76090i		−	0.0965915i
$818$		0			0
$819$	−1.69545	+	1.69545i	−0.0592436	+	0.0592436i
$820$		0			0
$821$	13.3909	+	13.3909i	0.467344	+	0.467344i	0.901053	−	0.433709i	$-0.142795\pi$
$821$	13.3909	+	13.3909i	0.467344	+	0.467344i	−0.433709	+	0.901053i	$0.642795\pi$
$822$		0			0
$823$	−43.9496			−1.53199			−0.765994	−	0.642848i	$-0.777753\pi$
$823$	−43.9496			−1.53199			−0.765994	+	0.642848i	$0.777753\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.79096	−	1.79096i	0.0622777	−	0.0622777i	−0.675282	−	0.737560i	$-0.735978\pi$
$827$	1.79096	−	1.79096i	0.0622777	−	0.0622777i	0.737560	+	0.675282i	$0.235978\pi$
$828$		0			0
$829$	−13.4979	+	13.4979i	−0.468801	+	0.468801i	−0.901526	−	0.432725i	$-0.857552\pi$
$829$	−13.4979	+	13.4979i	−0.468801	+	0.468801i	0.432725	+	0.901526i	$0.357552\pi$
$830$		0			0
$831$	29.2742			1.01551
$832$		0			0
$833$			34.4923i			1.19509i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	13.0336	−	13.0336i	0.450507	−	0.450507i
$838$		0			0
$839$		−	14.5332i		−	0.501741i	−0.968021	−	0.250870i	$-0.919283\pi$
$839$		−	14.5332i		−	0.501741i	0.968021	−	0.250870i	$-0.0807168\pi$
$840$		0			0
$841$			23.1983i			0.799941i
$842$		0			0
$843$	−42.6532	+	42.6532i	−1.46905	+	1.46905i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			5.34105i			0.183521i
$848$		0			0
$849$	54.4136			1.86747
$850$		0			0
$851$	12.7043	−	12.7043i	0.435499	−	0.435499i
$852$		0			0
$853$	11.5836	−	11.5836i	0.396615	−	0.396615i	−0.480423	−	0.877037i	$-0.659517\pi$
$853$	11.5836	−	11.5836i	0.396615	−	0.396615i	0.877037	+	0.480423i	$0.159517\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.6443			−0.534399			−0.267200	−	0.963641i	$-0.586098\pi$
$857$	−15.6443			−0.534399			−0.267200	+	0.963641i	$0.586098\pi$
$858$		0			0
$859$	12.0947	+	12.0947i	0.412665	+	0.412665i	0.882666	−	0.470001i	$-0.155746\pi$
$859$	12.0947	+	12.0947i	0.412665	+	0.412665i	−0.470001	+	0.882666i	$0.655746\pi$
$860$		0			0
$861$	−5.40422	+	5.40422i	−0.184175	+	0.184175i
$862$		0			0
$863$		−	9.28120i		−	0.315936i	−0.987444	−	0.157968i	$-0.949506\pi$
$863$		−	9.28120i		−	0.315936i	0.987444	−	0.157968i	$-0.0504942\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.5973	−	15.5973i	−0.529711	−	0.529711i
$868$		0			0
$869$	−15.3631	−	15.3631i	−0.521157	−	0.521157i
$870$		0			0
$871$			9.10425i			0.308486i
$872$		0			0
$873$	−5.53709			−0.187402
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.97610	−	2.97610i	−0.100496	−	0.100496i	0.655071	−	0.755567i	$-0.272639\pi$
$877$	−2.97610	−	2.97610i	−0.100496	−	0.100496i	−0.755567	+	0.655071i	$0.772639\pi$
$878$		0			0
$879$	20.7194			0.698849
$880$		0			0
$881$	29.3318			0.988214			0.494107	−	0.869401i	$-0.335495\pi$
$881$	29.3318			0.988214			0.494107	+	0.869401i	$0.335495\pi$
$882$		0			0
$883$	35.5597	+	35.5597i	1.19668	+	1.19668i	0.975155	+	0.221525i	$0.0711033\pi$
$883$	35.5597	+	35.5597i	1.19668	+	1.19668i	0.221525	+	0.975155i	$0.428897\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.51671			0.151656			0.0758282	−	0.997121i	$-0.475840\pi$
$887$	4.51671			0.151656			0.0758282	+	0.997121i	$0.475840\pi$
$888$		0			0
$889$			11.4721i			0.384762i
$890$		0			0
$891$	33.8133	+	33.8133i	1.13279	+	1.13279i
$892$		0			0
$893$	24.8289	+	24.8289i	0.830867	+	0.830867i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	10.6980i		−	0.357196i
$898$		0			0
$899$	−8.00169	+	8.00169i	−0.266871	+	0.266871i
$900$		0			0
$901$	26.4025	+	26.4025i	0.879594	+	0.879594i
$902$		0			0
$903$	0.503511			0.0167558
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−5.06769	+	5.06769i	−0.168270	+	0.168270i	−0.786218	−	0.617949i	$-0.787964\pi$
$907$	−5.06769	+	5.06769i	−0.168270	+	0.168270i	0.617949	+	0.786218i	$0.287964\pi$
$908$		0			0
$909$	14.1308	−	14.1308i	0.468690	−	0.468690i
$910$		0			0
$911$	−36.7140			−1.21639			−0.608194	−	0.793788i	$-0.708106\pi$
$911$	−36.7140			−1.21639			−0.608194	+	0.793788i	$0.708106\pi$
$912$		0			0
$913$			44.7135i			1.47980i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.12937	−	8.12937i	0.268456	−	0.268456i
$918$		0			0
$919$		−	21.5651i		−	0.711365i	−0.934607	−	0.355683i	$-0.884248\pi$
$919$		−	21.5651i		−	0.711365i	0.934607	−	0.355683i	$-0.115752\pi$
$920$		0			0
$921$		−	20.0179i		−	0.659612i
$922$		0			0
$923$	5.42725	−	5.42725i	0.178640	−	0.178640i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		−	2.77685i		−	0.0912038i
$928$		0			0
$929$	45.6603			1.49807			0.749033	−	0.662532i	$-0.230518\pi$
$929$	45.6603			1.49807			0.749033	+	0.662532i	$0.230518\pi$
$930$		0			0
$931$	−35.1522	+	35.1522i	−1.15207	+	1.15207i
$932$		0			0
$933$	20.3269	−	20.3269i	0.665474	−	0.665474i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.29807			−0.0750746			−0.0375373	−	0.999295i	$-0.511951\pi$
$937$	−2.29807			−0.0750746			−0.0375373	+	0.999295i	$0.511951\pi$
$938$		0			0
$939$	−26.2681	−	26.2681i	−0.857226	−	0.857226i
$940$		0			0
$941$	−24.1999	+	24.1999i	−0.788894	+	0.788894i	−0.981313	−	0.192419i	$-0.938367\pi$
$941$	−24.1999	+	24.1999i	−0.788894	+	0.788894i	0.192419	+	0.981313i	$0.438367\pi$
$942$		0			0
$943$		−	8.84448i		−	0.288016i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.5182	−	24.5182i	−0.796733	−	0.796733i	0.185846	−	0.982579i	$-0.440498\pi$
$947$	−24.5182	−	24.5182i	−0.796733	−	0.796733i	−0.982579	+	0.185846i	$0.940498\pi$
$948$		0			0
$949$	3.03168	+	3.03168i	0.0984125	+	0.0984125i
$950$		0			0
$951$		−	20.5445i		−	0.666202i
$952$		0			0
$953$	−32.3462			−1.04780			−0.523898	−	0.851781i	$-0.675523\pi$
$953$	−32.3462			−1.04780			−0.523898	+	0.851781i	$0.675523\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−14.8368	−	14.8368i	−0.479605	−	0.479605i
$958$		0			0
$959$	−5.81116			−0.187652
$960$		0			0
$961$	−8.92816			−0.288005
$962$		0			0
$963$	−6.59907	−	6.59907i	−0.212652	−	0.212652i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	14.6983			0.472665			0.236333	−	0.971672i	$-0.424054\pi$
$967$	14.6983			0.472665			0.236333	+	0.971672i	$0.424054\pi$
$968$		0			0
$969$		−	81.1036i		−	2.60542i
$970$		0			0
$971$	−29.1065	−	29.1065i	−0.934073	−	0.934073i	0.0638845	−	0.997957i	$-0.479651\pi$
$971$	−29.1065	−	29.1065i	−0.934073	−	0.934073i	−0.997957	+	0.0638845i	$0.979651\pi$
$972$		0			0
$973$	−1.04860	−	1.04860i	−0.0336167	−	0.0336167i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			17.3533i			0.555180i	0.960700	+	0.277590i	$0.0895357\pi$
$977$			17.3533i			0.555180i	−0.960700	+	0.277590i	$0.910464\pi$
$978$		0			0
$979$	−5.55691	+	5.55691i	−0.177600	+	0.177600i
$980$		0			0
$981$	7.24094	+	7.24094i	0.231186	+	0.231186i
$982$		0			0
$983$	27.5174			0.877668			0.438834	−	0.898568i	$-0.355392\pi$
$983$	27.5174			0.877668			0.438834	+	0.898568i	$0.355392\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.52809	+	4.52809i	−0.144131	+	0.144131i
$988$		0			0
$989$	−0.412020	+	0.412020i	−0.0131015	+	0.0131015i
$990$		0			0
$991$	−6.96363			−0.221207			−0.110604	−	0.993865i	$-0.535278\pi$
$991$	−6.96363			−0.221207			−0.110604	+	0.993865i	$0.535278\pi$
$992$		0			0
$993$			44.0735i			1.39863i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	15.7051	−	15.7051i	0.497385	−	0.497385i	−0.413238	−	0.910623i	$-0.635602\pi$
$997$	15.7051	−	15.7051i	0.497385	−	0.497385i	0.910623	+	0.413238i	$0.135602\pi$
$998$		0			0
$999$			43.8259i			1.38659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.h.49.7		16
4.3	odd	2		400.2.q.g.149.1		16
5.2	odd	4		1600.2.l.i.1201.7		16
5.3	odd	4		320.2.l.a.241.2		16
5.4	even	2		1600.2.q.g.49.2		16
15.8	even	4		2880.2.t.c.2161.2		16
16.3	odd	4		400.2.q.h.349.8		16
16.13	even	4		1600.2.q.g.849.2		16
20.3	even	4		80.2.l.a.21.5	✓	16
20.7	even	4		400.2.l.h.101.4		16
20.19	odd	2		400.2.q.h.149.8		16
40.3	even	4		640.2.l.b.481.2		16
40.13	odd	4		640.2.l.a.481.7		16
60.23	odd	4		720.2.t.c.181.4		16
80.3	even	4		80.2.l.a.61.5	yes	16
80.13	odd	4		320.2.l.a.81.2		16
80.19	odd	4		400.2.q.g.349.1		16
80.29	even	4	inner	1600.2.q.h.849.7		16
80.43	even	4		640.2.l.b.161.2		16
80.53	odd	4		640.2.l.a.161.7		16
80.67	even	4		400.2.l.h.301.4		16
80.77	odd	4		1600.2.l.i.401.7		16
160.3	even	8		5120.2.a.s.1.7		8
160.13	odd	8		5120.2.a.t.1.7		8
160.83	even	8		5120.2.a.v.1.2		8
160.93	odd	8		5120.2.a.u.1.2		8
240.83	odd	4		720.2.t.c.541.4		16
240.173	even	4		2880.2.t.c.721.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.5	✓	16	20.3	even	4
80.2.l.a.61.5	yes	16	80.3	even	4
320.2.l.a.81.2		16	80.13	odd	4
320.2.l.a.241.2		16	5.3	odd	4
400.2.l.h.101.4		16	20.7	even	4
400.2.l.h.301.4		16	80.67	even	4
400.2.q.g.149.1		16	4.3	odd	2
400.2.q.g.349.1		16	80.19	odd	4
400.2.q.h.149.8		16	20.19	odd	2
400.2.q.h.349.8		16	16.3	odd	4
640.2.l.a.161.7		16	80.53	odd	4
640.2.l.a.481.7		16	40.13	odd	4
640.2.l.b.161.2		16	80.43	even	4
640.2.l.b.481.2		16	40.3	even	4
720.2.t.c.181.4		16	60.23	odd	4
720.2.t.c.541.4		16	240.83	odd	4
1600.2.l.i.401.7		16	80.77	odd	4
1600.2.l.i.1201.7		16	5.2	odd	4
1600.2.q.g.49.2		16	5.4	even	2
1600.2.q.g.849.2		16	16.13	even	4
1600.2.q.h.49.7		16	1.1	even	1	trivial
1600.2.q.h.849.7		16	80.29	even	4	inner
2880.2.t.c.721.3		16	240.173	even	4
2880.2.t.c.2161.2		16	15.8	even	4
5120.2.a.s.1.7		8	160.3	even	8
5120.2.a.t.1.7		8	160.13	odd	8
5120.2.a.u.1.2		8	160.93	odd	8
5120.2.a.v.1.2		8	160.83	even	8

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.42313 + 1.42313i) q^{3} +0.690576 q^{7} +1.05061i q^{9} +O(q^{10})\)	\(q+(1.42313 + 1.42313i) q^{3} +0.690576 q^{7} +1.05061i q^{9} +(3.06057 + 3.06057i) q^{11} +(2.33686 + 2.33686i) q^{13} -5.28770i q^{17} +(5.38887 - 5.38887i) q^{19} +(0.982780 + 0.982780i) q^{21} -1.60841 q^{23} +(2.77424 - 2.77424i) q^{27} +(-1.70319 + 1.70319i) q^{29} +4.69807 q^{31} +8.71119i q^{33} +(-7.89871 + 7.89871i) q^{37} +6.65131i q^{39} +5.49891i q^{41} +(0.256166 - 0.256166i) q^{43} +4.60743i q^{47} -6.52310 q^{49} +(7.52510 - 7.52510i) q^{51} +(-4.99318 + 4.99318i) q^{53} +15.3382 q^{57} +(1.46478 + 1.46478i) q^{59} +(9.33004 - 9.33004i) q^{61} +0.725523i q^{63} +(1.94797 + 1.94797i) q^{67} +(-2.28897 - 2.28897i) q^{69} -2.32246i q^{71} +1.29733 q^{73} +(2.11356 + 2.11356i) q^{77} -5.01968 q^{79} +11.0480 q^{81} +(7.30477 + 7.30477i) q^{83} -4.84772 q^{87} +1.81564i q^{89} +(1.61378 + 1.61378i) q^{91} +(6.68597 + 6.68597i) q^{93} +5.27038i q^{97} +(-3.21546 + 3.21546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^7 + 8 * q^11 - 8 * q^19 + 24 * q^23 + 24 * q^27 + 16 * q^29 + 16 * q^37 - 8 * q^43 + 16 * q^49 + 32 * q^51 + 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^69 + 16 * q^77 + 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 - 8 * q^99

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