LMFDB - Embedded newform 1600.2.q.g.849.1

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			849.1
Root			$1.21331 - 0.726558i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.g.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82762 + 1.82762i) q^{3} -4.50961 q^{7} -3.68037i q^{9} +O(q^{10})$	$q+(-1.82762 + 1.82762i) q^{3} -4.50961 q^{7} -3.68037i q^{9} +(1.64080 - 1.64080i) q^{11} +(1.51857 - 1.51857i) q^{13} +1.45616i q^{17} +(-2.67964 - 2.67964i) q^{19} +(8.24183 - 8.24183i) q^{21} +2.37423 q^{23} +(1.24345 + 1.24345i) q^{27} +(-0.924966 - 0.924966i) q^{29} +7.20435 q^{31} +5.99752i q^{33} +(-5.21123 - 5.21123i) q^{37} +5.55074i q^{39} +6.41166i q^{41} +(7.65800 + 7.65800i) q^{43} +2.51027i q^{47} +13.3366 q^{49} +(-2.66130 - 2.66130i) q^{51} +(-1.50312 - 1.50312i) q^{53} +9.79472 q^{57} +(-5.31807 + 5.31807i) q^{59} +(-1.02169 - 1.02169i) q^{61} +16.5970i q^{63} +(5.22745 - 5.22745i) q^{67} +(-4.33918 + 4.33918i) q^{69} -1.92097i q^{71} +1.39412 q^{73} +(-7.39938 + 7.39938i) q^{77} +5.06317 q^{79} +6.49599 q^{81} +(2.44974 - 2.44974i) q^{83} +3.38097 q^{87} +9.36007i q^{89} +(-6.84817 + 6.84817i) q^{91} +(-13.1668 + 13.1668i) q^{93} +18.6313i q^{97} +(-6.03876 - 6.03876i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−1.82762	+	1.82762i	−1.05518	+	1.05518i	−0.0567890	+	0.998386i	$0.518086\pi$
$3$	−1.82762	+	1.82762i	−1.05518	+	1.05518i	−0.998386	+	0.0567890i	$0.981914\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.50961			−1.70447			−0.852236	−	0.523158i	$-0.824754\pi$
$7$	−4.50961			−1.70447			−0.852236	+	0.523158i	$0.824754\pi$
$8$		0			0
$9$		−	3.68037i		−	1.22679i
$10$		0			0
$11$	1.64080	−	1.64080i	0.494721	−	0.494721i	−0.415069	−	0.909790i	$-0.636243\pi$
$11$	1.64080	−	1.64080i	0.494721	−	0.494721i	0.909790	+	0.415069i	$0.136243\pi$
$12$		0			0
$13$	1.51857	−	1.51857i	0.421176	−	0.421176i	−0.464432	−	0.885609i	$-0.653742\pi$
$13$	1.51857	−	1.51857i	0.421176	−	0.421176i	0.885609	+	0.464432i	$0.153742\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			1.45616i			0.353170i	0.984285	+	0.176585i	$0.0565051\pi$
$17$			1.45616i			0.353170i	−0.984285	+	0.176585i	$0.943495\pi$
$18$		0			0
$19$	−2.67964	−	2.67964i	−0.614752	−	0.614752i	0.329428	−	0.944181i	$-0.393144\pi$
$19$	−2.67964	−	2.67964i	−0.614752	−	0.614752i	−0.944181	+	0.329428i	$0.893144\pi$
$20$		0			0
$21$	8.24183	−	8.24183i	1.79852	−	1.79852i
$22$		0			0
$23$	2.37423			0.495061			0.247530	−	0.968880i	$-0.420381\pi$
$23$	2.37423			0.495061			0.247530	+	0.968880i	$0.420381\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.24345	+	1.24345i	0.239303	+	0.239303i
$28$		0			0
$29$	−0.924966	−	0.924966i	−0.171762	−	0.171762i	0.615991	−	0.787753i	$-0.288756\pi$
$29$	−0.924966	−	0.924966i	−0.171762	−	0.171762i	−0.787753	+	0.615991i	$0.788756\pi$
$30$		0			0
$31$	7.20435			1.29394			0.646970	−	0.762515i	$-0.276036\pi$
$31$	7.20435			1.29394			0.646970	+	0.762515i	$0.276036\pi$
$32$		0			0
$33$			5.99752i			1.04403i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.21123	−	5.21123i	−0.856720	−	0.856720i	0.134230	−	0.990950i	$-0.457144\pi$
$37$	−5.21123	−	5.21123i	−0.856720	−	0.856720i	−0.990950	+	0.134230i	$0.957144\pi$
$38$		0			0
$39$			5.55074i			0.888830i
$40$		0			0
$41$			6.41166i			1.00133i	0.865640	+	0.500667i	$0.166912\pi$
$41$			6.41166i			1.00133i	−0.865640	+	0.500667i	$0.833088\pi$
$42$		0			0
$43$	7.65800	+	7.65800i	1.16783	+	1.16783i	0.982716	+	0.185118i	$0.0592669\pi$
$43$	7.65800	+	7.65800i	1.16783	+	1.16783i	0.185118	+	0.982716i	$0.440733\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			2.51027i			0.366161i	0.983098	+	0.183081i	$0.0586069\pi$
$47$			2.51027i			0.366161i	−0.983098	+	0.183081i	$0.941393\pi$
$48$		0			0
$49$	13.3366			1.90522
$50$		0			0
$51$	−2.66130	−	2.66130i	−0.372657	−	0.372657i
$52$		0			0
$53$	−1.50312	−	1.50312i	−0.206470	−	0.206470i	0.596295	−	0.802765i	$-0.296639\pi$
$53$	−1.50312	−	1.50312i	−0.206470	−	0.206470i	−0.802765	+	0.596295i	$0.796639\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	9.79472			1.29734
$58$		0			0
$59$	−5.31807	+	5.31807i	−0.692353	+	0.692353i	−0.962749	−	0.270396i	$-0.912845\pi$
$59$	−5.31807	+	5.31807i	−0.692353	+	0.692353i	0.270396	+	0.962749i	$0.412845\pi$
$60$		0			0
$61$	−1.02169	−	1.02169i	−0.130815	−	0.130815i	0.638668	−	0.769483i	$-0.279486\pi$
$61$	−1.02169	−	1.02169i	−0.130815	−	0.130815i	−0.769483	+	0.638668i	$0.779486\pi$
$62$		0			0
$63$			16.5970i			2.09103i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.22745	−	5.22745i	0.638635	−	0.638635i	−0.311584	−	0.950219i	$-0.600859\pi$
$67$	5.22745	−	5.22745i	0.638635	−	0.638635i	0.950219	+	0.311584i	$0.100859\pi$
$68$		0			0
$69$	−4.33918	+	4.33918i	−0.522376	+	0.522376i
$70$		0			0
$71$		−	1.92097i		−	0.227978i	−0.993482	−	0.113989i	$-0.963637\pi$
$71$		−	1.92097i		−	0.227978i	0.993482	−	0.113989i	$-0.0363628\pi$
$72$		0			0
$73$	1.39412			0.163169			0.0815847	−	0.996666i	$-0.474002\pi$
$73$	1.39412			0.163169			0.0815847	+	0.996666i	$0.474002\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.39938	+	7.39938i	−0.843237	+	0.843237i
$78$		0			0
$79$	5.06317			0.569651			0.284825	−	0.958579i	$-0.408064\pi$
$79$	5.06317			0.569651			0.284825	+	0.958579i	$0.408064\pi$
$80$		0			0
$81$	6.49599			0.721777
$82$		0			0
$83$	2.44974	−	2.44974i	0.268894	−	0.268894i	−0.559761	−	0.828654i	$-0.689107\pi$
$83$	2.44974	−	2.44974i	0.268894	−	0.268894i	0.828654	+	0.559761i	$0.189107\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.38097			0.362478
$88$		0			0
$89$			9.36007i			0.992165i	0.868275	+	0.496083i	$0.165229\pi$
$89$			9.36007i			0.992165i	−0.868275	+	0.496083i	$0.834771\pi$
$90$		0			0
$91$	−6.84817	+	6.84817i	−0.717883	+	0.717883i
$92$		0			0
$93$	−13.1668	+	13.1668i	−1.36533	+	1.36533i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			18.6313i			1.89172i	0.324579	+	0.945859i	$0.394777\pi$
$97$			18.6313i			1.89172i	−0.324579	+	0.945859i	$0.605223\pi$
$98$		0			0
$99$	−6.03876	−	6.03876i	−0.606918	−	0.606918i
$100$		0			0
$101$	−4.84108	+	4.84108i	−0.481705	+	0.481705i	−0.905676	−	0.423971i	$-0.860636\pi$
$101$	−4.84108	+	4.84108i	−0.481705	+	0.481705i	0.423971	+	0.905676i	$0.360636\pi$
$102$		0			0
$103$	−9.12540			−0.899153			−0.449576	−	0.893242i	$-0.648425\pi$
$103$	−9.12540			−0.899153			−0.449576	+	0.893242i	$0.648425\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.1505	+	10.1505i	0.981290	+	0.981290i	0.999828	−	0.0185385i	$-0.00590132\pi$
$107$	10.1505	+	10.1505i	0.981290	+	0.981290i	−0.0185385	+	0.999828i	$0.505901\pi$
$108$		0			0
$109$	−1.35489	−	1.35489i	−0.129775	−	0.129775i	0.639236	−	0.769011i	$-0.279251\pi$
$109$	−1.35489	−	1.35489i	−0.129775	−	0.129775i	−0.769011	+	0.639236i	$0.779251\pi$
$110$		0			0
$111$	19.0483			1.80798
$112$		0			0
$113$			2.56039i			0.240861i	0.992722	+	0.120431i	$0.0384275\pi$
$113$			2.56039i			0.240861i	−0.992722	+	0.120431i	$0.961572\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.58891	−	5.58891i	−0.516695	−	0.516695i
$118$		0			0
$119$		−	6.56670i		−	0.601969i
$120$		0			0
$121$			5.61553i			0.510503i
$122$		0			0
$123$	−11.7181	−	11.7181i	−1.05658	−	1.05658i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	13.7354i		−	1.21882i	−0.792856	−	0.609409i	$-0.791407\pi$
$127$		−	13.7354i		−	1.21882i	0.792856	−	0.609409i	$-0.208593\pi$
$128$		0			0
$129$	−27.9918			−2.46454
$130$		0			0
$131$	−5.20726	−	5.20726i	−0.454960	−	0.454960i	0.442037	−	0.896997i	$-0.354256\pi$
$131$	−5.20726	−	5.20726i	−0.454960	−	0.454960i	−0.896997	+	0.442037i	$0.854256\pi$
$132$		0			0
$133$	12.0841	+	12.0841i	1.04783	+	1.04783i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	22.7563			1.94420			0.972102	−	0.234559i	$-0.0753645\pi$
$137$	22.7563			1.94420			0.972102	+	0.234559i	$0.0753645\pi$
$138$		0			0
$139$	6.28085	−	6.28085i	0.532734	−	0.532734i	−0.388651	−	0.921385i	$-0.627059\pi$
$139$	6.28085	−	6.28085i	0.532734	−	0.532734i	0.921385	+	0.388651i	$0.127059\pi$
$140$		0			0
$141$	−4.58782	−	4.58782i	−0.386364	−	0.386364i
$142$		0			0
$143$		−	4.98336i		−	0.416729i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−24.3741	+	24.3741i	−2.01034	+	2.01034i
$148$		0			0
$149$	12.9574	−	12.9574i	1.06151	−	1.06151i	0.0635329	−	0.997980i	$-0.479763\pi$
$149$	12.9574	−	12.9574i	1.06151	−	1.06151i	0.997980	−	0.0635329i	$-0.0202368\pi$
$150$		0			0
$151$			14.3417i			1.16711i	0.812073	+	0.583555i	$0.198339\pi$
$151$			14.3417i			1.16711i	−0.812073	+	0.583555i	$0.801661\pi$
$152$		0			0
$153$	5.35920			0.433266
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.10564	−	2.10564i	0.168049	−	0.168049i	−0.618073	−	0.786121i	$-0.712086\pi$
$157$	2.10564	−	2.10564i	0.168049	−	0.168049i	0.786121	+	0.618073i	$0.212086\pi$
$158$		0			0
$159$	5.49426			0.435723
$160$		0			0
$161$	−10.7068			−0.843817
$162$		0			0
$163$	5.34004	−	5.34004i	0.418265	−	0.418265i	−0.466341	−	0.884605i	$-0.654428\pi$
$163$	5.34004	−	5.34004i	0.418265	−	0.418265i	0.884605	+	0.466341i	$0.154428\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	16.0686			1.24343			0.621714	−	0.783245i	$-0.286437\pi$
$167$	16.0686			1.24343			0.621714	+	0.783245i	$0.286437\pi$
$168$		0			0
$169$			8.38787i			0.645221i
$170$		0			0
$171$	−9.86207	+	9.86207i	−0.754171	+	0.754171i
$172$		0			0
$173$	17.1133	−	17.1133i	1.30110	−	1.30110i	0.373453	−	0.927649i	$-0.378174\pi$
$173$	17.1133	−	17.1133i	1.30110	−	1.30110i	0.927649	−	0.373453i	$-0.121826\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	19.4388i		−	1.46111i
$178$		0			0
$179$	1.04482	+	1.04482i	0.0780933	+	0.0780933i	0.745075	−	0.666981i	$-0.232414\pi$
$179$	1.04482	+	1.04482i	0.0780933	+	0.0780933i	−0.666981	+	0.745075i	$0.732414\pi$
$180$		0			0
$181$	11.9886	−	11.9886i	0.891104	−	0.891104i	−0.103523	−	0.994627i	$-0.533012\pi$
$181$	11.9886	−	11.9886i	0.891104	−	0.891104i	0.994627	+	0.103523i	$0.0330115\pi$
$182$		0			0
$183$	3.73453			0.276065
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.38927	+	2.38927i	0.174721	+	0.174721i
$188$		0			0
$189$	−5.60748	−	5.60748i	−0.407884	−	0.407884i
$190$		0			0
$191$	−0.0667471			−0.00482965			−0.00241483	−	0.999997i	$-0.500769\pi$
$191$	−0.0667471			−0.00482965			−0.00241483	+	0.999997i	$0.500769\pi$
$192$		0			0
$193$			1.09895i			0.0791039i	0.999218	+	0.0395520i	$0.0125931\pi$
$193$			1.09895i			0.0791039i	−0.999218	+	0.0395520i	$0.987407\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.9289	+	11.9289i	0.849899	+	0.849899i	0.990120	−	0.140222i	$-0.0447815\pi$
$197$	11.9289	+	11.9289i	0.849899	+	0.849899i	−0.140222	+	0.990120i	$0.544782\pi$
$198$		0			0
$199$			11.0397i			0.782584i	0.920267	+	0.391292i	$0.127972\pi$
$199$			11.0397i			0.782584i	−0.920267	+	0.391292i	$0.872028\pi$
$200$		0			0
$201$			19.1076i			1.34774i
$202$		0			0
$203$	4.17123	+	4.17123i	0.292763	+	0.292763i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	8.73803i		−	0.607335i
$208$		0			0
$209$	−8.79353			−0.608261
$210$		0			0
$211$	8.59737	+	8.59737i	0.591868	+	0.591868i	0.938136	−	0.346268i	$-0.112551\pi$
$211$	8.59737	+	8.59737i	0.591868	+	0.591868i	−0.346268	+	0.938136i	$0.612551\pi$
$212$		0			0
$213$	3.51080	+	3.51080i	0.240556	+	0.240556i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−32.4888			−2.20548
$218$		0			0
$219$	−2.54792	+	2.54792i	−0.172172	+	0.172172i
$220$		0			0
$221$	2.21128	+	2.21128i	0.148747	+	0.148747i
$222$		0			0
$223$		−	21.4238i		−	1.43465i	−0.696741	−	0.717323i	$-0.745367\pi$
$223$		−	21.4238i		−	1.43465i	0.696741	−	0.717323i	$-0.254633\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.06331	+	8.06331i	−0.535181	+	0.535181i	−0.922110	−	0.386929i	$-0.873536\pi$
$227$	−8.06331	+	8.06331i	−0.535181	+	0.535181i	0.386929	+	0.922110i	$0.373536\pi$
$228$		0			0
$229$	−4.63169	+	4.63169i	−0.306071	+	0.306071i	−0.843383	−	0.537313i	$-0.819440\pi$
$229$	−4.63169	+	4.63169i	−0.306071	+	0.306071i	0.537313	+	0.843383i	$0.319440\pi$
$230$		0			0
$231$		−	27.0465i		−	1.77953i
$232$		0			0
$233$	−26.0672			−1.70772			−0.853860	−	0.520502i	$-0.825745\pi$
$233$	−26.0672			−1.70772			−0.853860	+	0.520502i	$0.825745\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.25353	+	9.25353i	−0.601081	+	0.601081i
$238$		0			0
$239$	5.12209			0.331320			0.165660	−	0.986183i	$-0.447025\pi$
$239$	5.12209			0.331320			0.165660	+	0.986183i	$0.447025\pi$
$240$		0			0
$241$	11.4987			0.740695			0.370347	−	0.928893i	$-0.379239\pi$
$241$	11.4987			0.740695			0.370347	+	0.928893i	$0.379239\pi$
$242$		0			0
$243$	−15.6025	+	15.6025i	−1.00090	+	1.00090i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.13847			−0.517838
$248$		0			0
$249$			8.95437i			0.567460i
$250$		0			0
$251$	19.8270	−	19.8270i	1.25147	−	1.25147i	0.296408	−	0.955061i	$-0.404211\pi$
$251$	19.8270	−	19.8270i	1.25147	−	1.25147i	0.955061	−	0.296408i	$-0.0957889\pi$
$252$		0			0
$253$	3.89564	−	3.89564i	0.244917	−	0.244917i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	24.2494i		−	1.51264i	−0.654203	−	0.756319i	$-0.726996\pi$
$257$		−	24.2494i		−	1.51264i	0.654203	−	0.756319i	$-0.273004\pi$
$258$		0			0
$259$	23.5006	+	23.5006i	1.46026	+	1.46026i
$260$		0			0
$261$	−3.40422	+	3.40422i	−0.210716	+	0.210716i
$262$		0			0
$263$	22.5680			1.39160			0.695802	−	0.718234i	$-0.255049\pi$
$263$	22.5680			1.39160			0.695802	+	0.718234i	$0.255049\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−17.1066	−	17.1066i	−1.04691	−	1.04691i
$268$		0			0
$269$	5.10558	+	5.10558i	0.311293	+	0.311293i	0.845410	−	0.534117i	$-0.179356\pi$
$269$	5.10558	+	5.10558i	0.311293	+	0.311293i	−0.534117	+	0.845410i	$0.679356\pi$
$270$		0			0
$271$	−6.67920			−0.405733			−0.202866	−	0.979206i	$-0.565026\pi$
$271$	−6.67920			−0.405733			−0.202866	+	0.979206i	$0.565026\pi$
$272$		0			0
$273$		−	25.0317i		−	1.51498i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.8524	−	11.8524i	−0.712141	−	0.712141i	0.254842	−	0.966983i	$-0.417977\pi$
$277$	−11.8524	−	11.8524i	−0.712141	−	0.712141i	−0.966983	+	0.254842i	$0.917977\pi$
$278$		0			0
$279$		−	26.5147i		−	1.58739i
$280$		0			0
$281$		−	0.477460i		−	0.0284829i	−0.999899	−	0.0142414i	$-0.995467\pi$
$281$		−	0.477460i		−	0.0284829i	0.999899	−	0.0142414i	$-0.00453334\pi$
$282$		0			0
$283$	−0.482914	−	0.482914i	−0.0287063	−	0.0287063i	0.692608	−	0.721314i	$-0.256462\pi$
$283$	−0.482914	−	0.482914i	−0.0287063	−	0.0287063i	−0.721314	+	0.692608i	$0.756462\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	28.9141i		−	1.70674i
$288$		0			0
$289$	14.8796			0.875271
$290$		0			0
$291$	−34.0508	−	34.0508i	−1.99609	−	1.99609i
$292$		0			0
$293$	−7.46638	−	7.46638i	−0.436190	−	0.436190i	0.454537	−	0.890728i	$-0.349805\pi$
$293$	−7.46638	−	7.46638i	−0.436190	−	0.436190i	−0.890728	+	0.454537i	$0.849805\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.08052			0.236776
$298$		0			0
$299$	3.60544	−	3.60544i	0.208508	−	0.208508i
$300$		0			0
$301$	−34.5346	−	34.5346i	−1.99054	−	1.99054i
$302$		0			0
$303$		−	17.6953i		−	1.01657i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.39349	−	2.39349i	0.136604	−	0.136604i	−0.635498	−	0.772102i	$-0.719205\pi$
$307$	2.39349	−	2.39349i	0.136604	−	0.136604i	0.772102	+	0.635498i	$0.219205\pi$
$308$		0			0
$309$	16.6777	−	16.6777i	0.948764	−	0.948764i
$310$		0			0
$311$			20.4404i			1.15907i	0.814948	+	0.579534i	$0.196765\pi$
$311$			20.4404i			1.15907i	−0.814948	+	0.579534i	$0.803235\pi$
$312$		0			0
$313$	2.46975			0.139598			0.0697992	−	0.997561i	$-0.477764\pi$
$313$	2.46975			0.139598			0.0697992	+	0.997561i	$0.477764\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.2241	−	16.2241i	0.911234	−	0.911234i	−0.0851350	−	0.996369i	$-0.527132\pi$
$317$	16.2241	−	16.2241i	0.911234	−	0.911234i	0.996369	+	0.0851350i	$0.0271322\pi$
$318$		0			0
$319$	−3.03537			−0.169948
$320$		0			0
$321$	−37.1026			−2.07086
$322$		0			0
$323$	3.90198	−	3.90198i	0.217112	−	0.217112i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.95246			0.273871
$328$		0			0
$329$		−	11.3204i		−	0.624111i
$330$		0			0
$331$	−3.42340	+	3.42340i	−0.188167	+	0.188167i	−0.794903	−	0.606736i	$-0.792479\pi$
$331$	−3.42340	+	3.42340i	−0.188167	+	0.188167i	0.606736	+	0.794903i	$0.292479\pi$
$332$		0			0
$333$	−19.1792	+	19.1792i	−1.05102	+	1.05102i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	5.40017i		−	0.294166i	−0.989124	−	0.147083i	$-0.953012\pi$
$337$		−	5.40017i		−	0.294166i	0.989124	−	0.147083i	$-0.0469884\pi$
$338$		0			0
$339$	−4.67941	−	4.67941i	−0.254151	−	0.254151i
$340$		0			0
$341$	11.8209	−	11.8209i	0.640139	−	0.640139i
$342$		0			0
$343$	−28.5754			−1.54292
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.07531	+	4.07531i	0.218774	+	0.218774i	0.807982	−	0.589208i	$-0.200560\pi$
$347$	4.07531	+	4.07531i	0.218774	+	0.218774i	−0.589208	+	0.807982i	$0.700560\pi$
$348$		0			0
$349$	−1.55681	−	1.55681i	−0.0833339	−	0.0833339i	0.664211	−	0.747545i	$-0.268768\pi$
$349$	−1.55681	−	1.55681i	−0.0833339	−	0.0833339i	−0.747545	+	0.664211i	$0.768768\pi$
$350$		0			0
$351$	3.77655			0.201577
$352$		0			0
$353$		−	1.34919i		−	0.0718103i	−0.999355	−	0.0359052i	$-0.988569\pi$
$353$		−	1.34919i		−	0.0718103i	0.999355	−	0.0359052i	$-0.0114314\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	12.0014	+	12.0014i	0.635182	+	0.635182i
$358$		0			0
$359$		−	23.2192i		−	1.22546i	−0.790291	−	0.612732i	$-0.790071\pi$
$359$		−	23.2192i		−	1.22546i	0.790291	−	0.612732i	$-0.209929\pi$
$360$		0			0
$361$		−	4.63903i		−	0.244159i
$362$		0			0
$363$	−10.2630	−	10.2630i	−0.538670	−	0.538670i
$364$		0			0
$365$		0			0
$366$		0			0
$367$			5.16452i			0.269586i	0.990874	+	0.134793i	$0.0430369\pi$
$367$			5.16452i			0.269586i	−0.990874	+	0.134793i	$0.956963\pi$
$368$		0			0
$369$	23.5973			1.22843
$370$		0			0
$371$	6.77849	+	6.77849i	0.351922	+	0.351922i
$372$		0			0
$373$	−18.5056	−	18.5056i	−0.958185	−	0.958185i	0.0409750	−	0.999160i	$-0.486954\pi$
$373$	−18.5056	−	18.5056i	−0.958185	−	0.958185i	−0.999160	+	0.0409750i	$0.986954\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.80926			−0.144684
$378$		0			0
$379$	−13.5254	+	13.5254i	−0.694754	+	0.694754i	−0.963274	−	0.268520i	$-0.913465\pi$
$379$	−13.5254	+	13.5254i	−0.694754	+	0.694754i	0.268520	+	0.963274i	$0.413465\pi$
$380$		0			0
$381$	25.1030	+	25.1030i	1.28607	+	1.28607i
$382$		0			0
$383$			21.9051i			1.11930i	0.828729	+	0.559650i	$0.189064\pi$
$383$			21.9051i			1.11930i	−0.828729	+	0.559650i	$0.810936\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	28.1843	−	28.1843i	1.43269	−	1.43269i
$388$		0			0
$389$	−4.48844	+	4.48844i	−0.227573	+	0.227573i	−0.811678	−	0.584105i	$-0.801446\pi$
$389$	−4.48844	+	4.48844i	−0.227573	+	0.227573i	0.584105	+	0.811678i	$0.301446\pi$
$390$		0			0
$391$			3.45725i			0.174841i
$392$		0			0
$393$	19.0337			0.960126
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−11.7892	+	11.7892i	−0.591682	+	0.591682i	−0.938086	−	0.346404i	$-0.887403\pi$
$397$	−11.7892	+	11.7892i	−0.591682	+	0.591682i	0.346404	+	0.938086i	$0.387403\pi$
$398$		0			0
$399$	−44.1703			−2.21128
$400$		0			0
$401$	24.9259			1.24474			0.622371	−	0.782722i	$-0.286170\pi$
$401$	24.9259			1.24474			0.622371	+	0.782722i	$0.286170\pi$
$402$		0			0
$403$	10.9403	−	10.9403i	0.544977	−	0.544977i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.1012			−0.847675
$408$		0			0
$409$		−	21.5355i		−	1.06486i	−0.846474	−	0.532430i	$-0.821279\pi$
$409$		−	21.5355i		−	1.06486i	0.846474	−	0.532430i	$-0.178721\pi$
$410$		0			0
$411$	−41.5898	+	41.5898i	−2.05148	+	2.05148i
$412$		0			0
$413$	23.9824	−	23.9824i	1.18010	−	1.18010i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			22.9580i			1.12426i
$418$		0			0
$419$	−17.2979	−	17.2979i	−0.845060	−	0.845060i	0.144452	−	0.989512i	$-0.453858\pi$
$419$	−17.2979	−	17.2979i	−0.845060	−	0.845060i	−0.989512	+	0.144452i	$0.953858\pi$
$420$		0			0
$421$	−19.4330	+	19.4330i	−0.947105	+	0.947105i	−0.998670	−	0.0515648i	$-0.983579\pi$
$421$	−19.4330	+	19.4330i	−0.947105	+	0.947105i	0.0515648	+	0.998670i	$0.483579\pi$
$422$		0			0
$423$	9.23874			0.449203
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4.60744	+	4.60744i	0.222970	+	0.222970i
$428$		0			0
$429$	9.10767	+	9.10767i	0.439723	+	0.439723i
$430$		0			0
$431$	−28.3769			−1.36687			−0.683433	−	0.730013i	$-0.739514\pi$
$431$	−28.3769			−1.36687			−0.683433	+	0.730013i	$0.739514\pi$
$432$		0			0
$433$		−	9.04007i		−	0.434438i	−0.976123	−	0.217219i	$-0.930301\pi$
$433$		−	9.04007i		−	0.434438i	0.976123	−	0.217219i	$-0.0696986\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.36208	−	6.36208i	−0.304340	−	0.304340i
$438$		0			0
$439$			28.2949i			1.35044i	0.737615	+	0.675221i	$0.235952\pi$
$439$			28.2949i			1.35044i	−0.737615	+	0.675221i	$0.764048\pi$
$440$		0			0
$441$		−	49.0834i		−	2.33731i
$442$		0			0
$443$	−13.1232	−	13.1232i	−0.623504	−	0.623504i	0.322922	−	0.946426i	$-0.395335\pi$
$443$	−13.1232	−	13.1232i	−0.623504	−	0.623504i	−0.946426	+	0.322922i	$0.895335\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			47.3624i			2.24016i
$448$		0			0
$449$	14.3902			0.679116			0.339558	−	0.940585i	$-0.389723\pi$
$449$	14.3902			0.679116			0.339558	+	0.940585i	$0.389723\pi$
$450$		0			0
$451$	10.5203	+	10.5203i	0.495380	+	0.495380i
$452$		0			0
$453$	−26.2111	−	26.2111i	−1.23151	−	1.23151i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.54538			0.212624			0.106312	−	0.994333i	$-0.466096\pi$
$457$	4.54538			0.212624			0.106312	+	0.994333i	$0.466096\pi$
$458$		0			0
$459$	−1.81066	+	1.81066i	−0.0845146	+	0.0845146i
$460$		0			0
$461$	19.8046	+	19.8046i	0.922393	+	0.922393i	0.997198	−	0.0748050i	$-0.0238334\pi$
$461$	19.8046	+	19.8046i	0.922393	+	0.922393i	−0.0748050	+	0.997198i	$0.523833\pi$
$462$		0			0
$463$		−	14.5997i		−	0.678506i	−0.940695	−	0.339253i	$-0.889826\pi$
$463$		−	14.5997i		−	0.678506i	0.940695	−	0.339253i	$-0.110174\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.8105	−	19.8105i	0.916722	−	0.916722i	−0.0800671	−	0.996789i	$-0.525513\pi$
$467$	19.8105	−	19.8105i	0.916722	−	0.916722i	0.996789	+	0.0800671i	$0.0255135\pi$
$468$		0			0
$469$	−23.5738	+	23.5738i	−1.08853	+	1.08853i
$470$		0			0
$471$			7.69661i			0.354641i
$472$		0			0
$473$	25.1306			1.15550
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.53204	+	5.53204i	−0.253295	+	0.253295i
$478$		0			0
$479$	21.0378			0.961243			0.480621	−	0.876928i	$-0.340411\pi$
$479$	21.0378			0.961243			0.480621	+	0.876928i	$0.340411\pi$
$480$		0			0
$481$	−15.8273			−0.721661
$482$		0			0
$483$	19.5680	−	19.5680i	0.890375	−	0.890375i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	10.2724			0.465485			0.232743	−	0.972538i	$-0.425230\pi$
$487$	10.2724			0.465485			0.232743	+	0.972538i	$0.425230\pi$
$488$		0			0
$489$			19.5191i			0.882685i
$490$		0			0
$491$	5.95681	−	5.95681i	0.268827	−	0.268827i	−0.559801	−	0.828627i	$-0.689122\pi$
$491$	5.95681	−	5.95681i	0.268827	−	0.268827i	0.828627	+	0.559801i	$0.189122\pi$
$492$		0			0
$493$	1.34690	−	1.34690i	0.0606612	−	0.0606612i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			8.66284i			0.388581i
$498$		0			0
$499$	−2.81466	−	2.81466i	−0.126002	−	0.126002i	0.641294	−	0.767295i	$-0.278398\pi$
$499$	−2.81466	−	2.81466i	−0.126002	−	0.126002i	−0.767295	+	0.641294i	$0.778398\pi$
$500$		0			0
$501$	−29.3673	+	29.3673i	−1.31203	+	1.31203i
$502$		0			0
$503$	5.49759			0.245125			0.122563	−	0.992461i	$-0.460889\pi$
$503$	5.49759			0.245125			0.122563	+	0.992461i	$0.460889\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−15.3298	−	15.3298i	−0.680821	−	0.680821i
$508$		0			0
$509$	4.37578	+	4.37578i	0.193953	+	0.193953i	0.797402	−	0.603449i	$-0.206207\pi$
$509$	4.37578	+	4.37578i	0.193953	+	0.193953i	−0.603449	+	0.797402i	$0.706207\pi$
$510$		0			0
$511$	−6.28693			−0.278118
$512$		0			0
$513$		−	6.66402i		−	0.294224i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.11887	+	4.11887i	0.181148	+	0.181148i
$518$		0			0
$519$			62.5532i			2.74578i
$520$		0			0
$521$			33.8729i			1.48400i	0.670401	+	0.741999i	$0.266122\pi$
$521$			33.8729i			1.48400i	−0.670401	+	0.741999i	$0.733878\pi$
$522$		0			0
$523$	27.8060	+	27.8060i	1.21587	+	1.21587i	0.969065	+	0.246804i	$0.0793803\pi$
$523$	27.8060	+	27.8060i	1.21587	+	1.21587i	0.246804	+	0.969065i	$0.420620\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			10.4907i			0.456981i
$528$		0			0
$529$	−17.3630			−0.754915
$530$		0			0
$531$	19.5724	+	19.5724i	0.849372	+	0.849372i
$532$		0			0
$533$	9.73658	+	9.73658i	0.421738	+	0.421738i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.81905			−0.164804
$538$		0			0
$539$	21.8827	−	21.8827i	0.942553	−	0.942553i
$540$		0			0
$541$	3.03066	+	3.03066i	0.130298	+	0.130298i	0.769248	−	0.638950i	$-0.220631\pi$
$541$	3.03066	+	3.03066i	0.130298	+	0.130298i	−0.638950	+	0.769248i	$0.720631\pi$
$542$		0			0
$543$			43.8211i			1.88054i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−18.4783	+	18.4783i	−0.790074	+	0.790074i	−0.981506	−	0.191432i	$-0.938687\pi$
$547$	−18.4783	+	18.4783i	−0.790074	+	0.790074i	0.191432	+	0.981506i	$0.438687\pi$
$548$		0			0
$549$	−3.76021	+	3.76021i	−0.160482	+	0.160482i
$550$		0			0
$551$			4.95716i			0.211182i
$552$		0			0
$553$	−22.8329			−0.970953
$554$		0			0
$555$		0			0
$556$		0			0
$557$	30.2060	−	30.2060i	1.27987	−	1.27987i	0.339127	−	0.940741i	$-0.389868\pi$
$557$	30.2060	−	30.2060i	1.27987	−	1.27987i	0.940741	−	0.339127i	$-0.110132\pi$
$558$		0			0
$559$	23.2585			0.983729
$560$		0			0
$561$	−8.73334			−0.368722
$562$		0			0
$563$	−2.86747	+	2.86747i	−0.120850	+	0.120850i	−0.764945	−	0.644095i	$-0.777234\pi$
$563$	−2.86747	+	2.86747i	−0.120850	+	0.120850i	0.644095	+	0.764945i	$0.277234\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−29.2944			−1.23025
$568$		0			0
$569$		−	35.8628i		−	1.50345i	−0.659479	−	0.751723i	$-0.729223\pi$
$569$		−	35.8628i		−	1.50345i	0.659479	−	0.751723i	$-0.270777\pi$
$570$		0			0
$571$	17.6509	−	17.6509i	0.738667	−	0.738667i	−0.233653	−	0.972320i	$-0.575068\pi$
$571$	17.6509	−	17.6509i	0.738667	−	0.738667i	0.972320	+	0.233653i	$0.0750679\pi$
$572$		0			0
$573$	0.121988	−	0.121988i	0.00509613	−	0.00509613i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			36.1387i			1.50448i	0.658892	+	0.752238i	$0.271025\pi$
$577$			36.1387i			1.50448i	−0.658892	+	0.752238i	$0.728975\pi$
$578$		0			0
$579$	−2.00845	−	2.00845i	−0.0834685	−	0.0834685i
$580$		0			0
$581$	−11.0474	+	11.0474i	−0.458322	+	0.458322i
$582$		0			0
$583$	−4.93265			−0.204290
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.4005	+	11.4005i	0.470550	+	0.470550i	0.902093	−	0.431542i	$-0.142030\pi$
$587$	11.4005	+	11.4005i	0.470550	+	0.470550i	−0.431542	+	0.902093i	$0.642030\pi$
$588$		0			0
$589$	−19.3051	−	19.3051i	−0.795453	−	0.795453i
$590$		0			0
$591$	−43.6029			−1.79358
$592$		0			0
$593$			35.0454i			1.43914i	0.694418	+	0.719572i	$0.255662\pi$
$593$			35.0454i			1.43914i	−0.694418	+	0.719572i	$0.744338\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−20.1764	−	20.1764i	−0.825764	−	0.825764i
$598$		0			0
$599$			18.2753i			0.746707i	0.927689	+	0.373354i	$0.121792\pi$
$599$			18.2753i			0.746707i	−0.927689	+	0.373354i	$0.878208\pi$
$600$		0			0
$601$		−	0.480142i		−	0.0195854i	−0.999952	−	0.00979269i	$-0.996883\pi$
$601$		−	0.480142i		−	0.0195854i	0.999952	−	0.00979269i	$-0.00311716\pi$
$602$		0			0
$603$	−19.2389	−	19.2389i	−0.783470	−	0.783470i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			38.6107i			1.56716i	0.621290	+	0.783581i	$0.286609\pi$
$607$			38.6107i			1.56716i	−0.621290	+	0.783581i	$0.713391\pi$
$608$		0			0
$609$	−15.2468			−0.617833
$610$		0			0
$611$	3.81204	+	3.81204i	0.154218	+	0.154218i
$612$		0			0
$613$	5.53592	+	5.53592i	0.223594	+	0.223594i	0.810010	−	0.586416i	$-0.199462\pi$
$613$	5.53592	+	5.53592i	0.223594	+	0.223594i	−0.586416	+	0.810010i	$0.699462\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	31.8836			1.28358			0.641792	−	0.766879i	$-0.278191\pi$
$617$	31.8836			1.28358			0.641792	+	0.766879i	$0.278191\pi$
$618$		0			0
$619$	−29.4054	+	29.4054i	−1.18190	+	1.18190i	−0.202650	+	0.979251i	$0.564955\pi$
$619$	−29.4054	+	29.4054i	−1.18190	+	1.18190i	−0.979251	+	0.202650i	$0.935045\pi$
$620$		0			0
$621$	2.95224	+	2.95224i	0.118469	+	0.118469i
$622$		0			0
$623$		−	42.2102i		−	1.69112i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	16.0712	−	16.0712i	0.641822	−	0.641822i
$628$		0			0
$629$	7.58837	−	7.58837i	0.302568	−	0.302568i
$630$		0			0
$631$		−	30.7381i		−	1.22367i	−0.790987	−	0.611833i	$-0.790432\pi$
$631$		−	30.7381i		−	1.22367i	0.790987	−	0.611833i	$-0.209568\pi$
$632$		0			0
$633$	−31.4254			−1.24905
$634$		0			0
$635$		0			0
$636$		0			0
$637$	20.2525	−	20.2525i	0.802435	−	0.802435i
$638$		0			0
$639$	−7.06989			−0.279681
$640$		0			0
$641$	13.6348			0.538540			0.269270	−	0.963065i	$-0.413218\pi$
$641$	13.6348			0.538540			0.269270	+	0.963065i	$0.413218\pi$
$642$		0			0
$643$	−14.9224	+	14.9224i	−0.588480	+	0.588480i	−0.937220	−	0.348740i	$-0.886610\pi$
$643$	−14.9224	+	14.9224i	−0.588480	+	0.588480i	0.348740	+	0.937220i	$0.386610\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.87972			0.191841			0.0959207	−	0.995389i	$-0.469420\pi$
$647$	4.87972			0.191841			0.0959207	+	0.995389i	$0.469420\pi$
$648$		0			0
$649$			17.4518i			0.685043i
$650$		0			0
$651$	59.3771	−	59.3771i	2.32717	−	2.32717i
$652$		0			0
$653$	−10.2913	+	10.2913i	−0.402731	+	0.402731i	−0.879194	−	0.476463i	$-0.841919\pi$
$653$	−10.2913	+	10.2913i	−0.402731	+	0.402731i	0.476463	+	0.879194i	$0.341919\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	5.13088i		−	0.200174i
$658$		0			0
$659$	−21.9025	−	21.9025i	−0.853201	−	0.853201i	0.137325	−	0.990526i	$-0.456149\pi$
$659$	−21.9025	−	21.9025i	−0.853201	−	0.853201i	−0.990526	+	0.137325i	$0.956149\pi$
$660$		0			0
$661$	5.40595	−	5.40595i	0.210267	−	0.210267i	−0.594114	−	0.804381i	$-0.702497\pi$
$661$	5.40595	−	5.40595i	0.210267	−	0.210267i	0.804381	+	0.594114i	$0.202497\pi$
$662$		0			0
$663$	−8.08276			−0.313908
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.19608	−	2.19608i	−0.0850326	−	0.0850326i
$668$		0			0
$669$	39.1546	+	39.1546i	1.51380	+	1.51380i
$670$		0			0
$671$	−3.35280			−0.129433
$672$		0			0
$673$		−	35.3820i		−	1.36388i	−0.731410	−	0.681938i	$-0.761138\pi$
$673$		−	35.3820i		−	1.36388i	0.731410	−	0.681938i	$-0.238862\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.17061	+	5.17061i	0.198723	+	0.198723i	0.799452	−	0.600730i	$-0.205123\pi$
$677$	5.17061	+	5.17061i	0.198723	+	0.198723i	−0.600730	+	0.799452i	$0.705123\pi$
$678$		0			0
$679$		−	84.0196i		−	3.22438i
$680$		0			0
$681$		−	29.4733i		−	1.12942i
$682$		0			0
$683$	26.5989	+	26.5989i	1.01778	+	1.01778i	0.999839	+	0.0179409i	$0.00571108\pi$
$683$	26.5989	+	26.5989i	1.01778	+	1.01778i	0.0179409	+	0.999839i	$0.494289\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	16.9299i		−	0.645916i
$688$		0			0
$689$	−4.56520			−0.173920
$690$		0			0
$691$	21.7989	+	21.7989i	0.829270	+	0.829270i	0.987416	−	0.158146i	$-0.0505516\pi$
$691$	21.7989	+	21.7989i	0.829270	+	0.829270i	−0.158146	+	0.987416i	$0.550552\pi$
$692$		0			0
$693$	27.2324	+	27.2324i	1.03447	+	1.03447i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−9.33640			−0.353641
$698$		0			0
$699$	47.6409	−	47.6409i	1.80194	−	1.80194i
$700$		0			0
$701$	−15.2175	−	15.2175i	−0.574756	−	0.574756i	0.358698	−	0.933454i	$-0.383221\pi$
$701$	−15.2175	−	15.2175i	−0.574756	−	0.574756i	−0.933454	+	0.358698i	$0.883221\pi$
$702$		0			0
$703$			27.9285i			1.05334i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	21.8313	−	21.8313i	0.821052	−	0.821052i
$708$		0			0
$709$	−4.87350	+	4.87350i	−0.183028	+	0.183028i	−0.792674	−	0.609646i	$-0.791312\pi$
$709$	−4.87350	+	4.87350i	−0.183028	+	0.183028i	0.609646	+	0.792674i	$0.291312\pi$
$710$		0			0
$711$		−	18.6343i		−	0.698842i
$712$		0			0
$713$	17.1048			0.640579
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−9.36121	+	9.36121i	−0.349601	+	0.349601i
$718$		0			0
$719$	9.27351			0.345843			0.172922	−	0.984936i	$-0.444679\pi$
$719$	9.27351			0.345843			0.172922	+	0.984936i	$0.444679\pi$
$720$		0			0
$721$	41.1520			1.53258
$722$		0			0
$723$	−21.0152	+	21.0152i	−0.781563	+	0.781563i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	10.6056			0.393341			0.196670	−	0.980470i	$-0.436987\pi$
$727$	10.6056			0.393341			0.196670	+	0.980470i	$0.436987\pi$
$728$		0			0
$729$		−	37.5430i		−	1.39048i
$730$		0			0
$731$	−11.1513	+	11.1513i	−0.412445	+	0.412445i
$732$		0			0
$733$	−29.6530	+	29.6530i	−1.09526	+	1.09526i	−0.100301	+	0.994957i	$0.531981\pi$
$733$	−29.6530	+	29.6530i	−1.09526	+	1.09526i	−0.994957	+	0.100301i	$0.968019\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	17.1544i		−	0.631892i
$738$		0			0
$739$	30.8751	+	30.8751i	1.13576	+	1.13576i	0.989202	+	0.146559i	$0.0468197\pi$
$739$	30.8751	+	30.8751i	1.13576	+	1.13576i	0.146559	+	0.989202i	$0.453180\pi$
$740$		0			0
$741$	14.8740	−	14.8740i	0.546410	−	0.546410i
$742$		0			0
$743$	−22.3956			−0.821617			−0.410808	−	0.911722i	$-0.634753\pi$
$743$	−22.3956			−0.821617			−0.410808	+	0.911722i	$0.634753\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−9.01594	−	9.01594i	−0.329876	−	0.329876i
$748$		0			0
$749$	−45.7749	−	45.7749i	−1.67258	−	1.67258i
$750$		0			0
$751$	−20.6448			−0.753341			−0.376670	−	0.926347i	$-0.622931\pi$
$751$	−20.6448			−0.753341			−0.376670	+	0.926347i	$0.622931\pi$
$752$		0			0
$753$			72.4724i			2.64104i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	24.1323	+	24.1323i	0.877104	+	0.877104i	0.993234	−	0.116130i	$-0.0370490\pi$
$757$	24.1323	+	24.1323i	0.877104	+	0.877104i	−0.116130	+	0.993234i	$0.537049\pi$
$758$		0			0
$759$			14.2395i			0.516860i
$760$		0			0
$761$		−	50.1874i		−	1.81929i	−0.415383	−	0.909647i	$-0.636352\pi$
$761$		−	50.1874i		−	1.81929i	0.415383	−	0.909647i	$-0.363648\pi$
$762$		0			0
$763$	6.11004	+	6.11004i	0.221198	+	0.221198i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			16.1517i			0.583206i
$768$		0			0
$769$	28.6887			1.03454			0.517270	−	0.855822i	$-0.326948\pi$
$769$	28.6887			1.03454			0.517270	+	0.855822i	$0.326948\pi$
$770$		0			0
$771$	44.3187	+	44.3187i	1.59610	+	1.59610i
$772$		0			0
$773$	37.5957	+	37.5957i	1.35222	+	1.35222i	0.883171	+	0.469052i	$0.155404\pi$
$773$	37.5957	+	37.5957i	1.35222	+	1.35222i	0.469052	+	0.883171i	$0.344596\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−85.9001			−3.08165
$778$		0			0
$779$	17.1810	−	17.1810i	0.615572	−	0.615572i
$780$		0			0
$781$	−3.15194	−	3.15194i	−0.112785	−	0.112785i
$782$		0			0
$783$		−	2.30030i		−	0.0822061i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.13285	+	3.13285i	−0.111674	+	0.111674i	−0.760736	−	0.649062i	$-0.775162\pi$
$787$	−3.13285	+	3.13285i	−0.111674	+	0.111674i	0.649062	+	0.760736i	$0.275162\pi$
$788$		0			0
$789$	−41.2457	+	41.2457i	−1.46839	+	1.46839i
$790$		0			0
$791$		−	11.5463i		−	0.410541i
$792$		0			0
$793$	−3.10304			−0.110192
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.0562195	+	0.0562195i	−0.00199140	+	0.00199140i	−0.708102	−	0.706110i	$-0.750448\pi$
$797$	−0.0562195	+	0.0562195i	−0.00199140	+	0.00199140i	0.706110	+	0.708102i	$0.250448\pi$
$798$		0			0
$799$	−3.65536			−0.129317
$800$		0			0
$801$	34.4485			1.21718
$802$		0			0
$803$	2.28748	−	2.28748i	0.0807233	−	0.0807233i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−18.6621			−0.656937
$808$		0			0
$809$		−	3.59856i		−	0.126518i	−0.997997	−	0.0632592i	$-0.979851\pi$
$809$		−	3.59856i		−	0.126518i	0.997997	−	0.0632592i	$-0.0201495\pi$
$810$		0			0
$811$	7.36274	−	7.36274i	0.258541	−	0.258541i	−0.565920	−	0.824460i	$-0.691479\pi$
$811$	7.36274	−	7.36274i	0.258541	−	0.258541i	0.824460	+	0.565920i	$0.191479\pi$
$812$		0			0
$813$	12.2070	−	12.2070i	0.428119	−	0.428119i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	41.0414i		−	1.43586i
$818$		0			0
$819$	25.2038	+	25.2038i	0.880691	+	0.880691i
$820$		0			0
$821$	14.7799	−	14.7799i	0.515824	−	0.515824i	−0.400481	−	0.916305i	$-0.631157\pi$
$821$	14.7799	−	14.7799i	0.515824	−	0.515824i	0.916305	+	0.400481i	$0.131157\pi$
$822$		0			0
$823$	−52.7544			−1.83890			−0.919452	−	0.393203i	$-0.871367\pi$
$823$	−52.7544			−1.83890			−0.919452	+	0.393203i	$0.871367\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.8883	−	16.8883i	−0.587265	−	0.587265i	0.349625	−	0.936890i	$-0.386309\pi$
$827$	−16.8883	−	16.8883i	−0.587265	−	0.587265i	−0.936890	+	0.349625i	$0.886309\pi$
$828$		0			0
$829$	8.55974	+	8.55974i	0.297292	+	0.297292i	0.839952	−	0.542660i	$-0.182583\pi$
$829$	8.55974	+	8.55974i	0.297292	+	0.297292i	−0.542660	+	0.839952i	$0.682583\pi$
$830$		0			0
$831$	43.3232			1.50287
$832$		0			0
$833$			19.4201i			0.672868i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	8.95827	+	8.95827i	0.309643	+	0.309643i
$838$		0			0
$839$			17.5407i			0.605572i	0.953059	+	0.302786i	$0.0979168\pi$
$839$			17.5407i			0.605572i	−0.953059	+	0.302786i	$0.902083\pi$
$840$		0			0
$841$		−	27.2889i		−	0.940996i
$842$		0			0
$843$	0.872614	+	0.872614i	0.0300544	+	0.0300544i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	25.3238i		−	0.870137i
$848$		0			0
$849$	1.76516			0.0605803
$850$		0			0
$851$	−12.3726	−	12.3726i	−0.424129	−	0.424129i
$852$		0			0
$853$	15.3577	+	15.3577i	0.525839	+	0.525839i	0.919329	−	0.393490i	$-0.128732\pi$
$853$	15.3577	+	15.3577i	0.525839	+	0.525839i	−0.393490	+	0.919329i	$0.628732\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.9553			−0.613341			−0.306671	−	0.951816i	$-0.599215\pi$
$857$	−17.9553			−0.613341			−0.306671	+	0.951816i	$0.599215\pi$
$858$		0			0
$859$	−33.3048	+	33.3048i	−1.13634	+	1.13634i	−0.147245	+	0.989100i	$0.547040\pi$
$859$	−33.3048	+	33.3048i	−1.13634	+	1.13634i	−0.989100	+	0.147245i	$0.952960\pi$
$860$		0			0
$861$	52.8439	+	52.8439i	1.80091	+	1.80091i
$862$		0			0
$863$		−	32.3557i		−	1.10140i	−0.834703	−	0.550701i	$-0.814361\pi$
$863$		−	32.3557i		−	1.10140i	0.834703	−	0.550701i	$-0.185639\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−27.1942	+	27.1942i	−0.923564	+	0.923564i
$868$		0			0
$869$	8.30766	−	8.30766i	0.281818	−	0.281818i
$870$		0			0
$871$		−	15.8765i		−	0.537956i
$872$		0			0
$873$	68.5699			2.32074
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−26.2297	+	26.2297i	−0.885714	+	0.885714i	−0.994108	−	0.108394i	$-0.965429\pi$
$877$	−26.2297	+	26.2297i	−0.885714	+	0.885714i	0.108394	+	0.994108i	$0.465429\pi$
$878$		0			0
$879$	27.2914			0.920515
$880$		0			0
$881$	−47.3359			−1.59479			−0.797394	−	0.603459i	$-0.793789\pi$
$881$	−47.3359			−1.59479			−0.797394	+	0.603459i	$0.793789\pi$
$882$		0			0
$883$	−8.08371	+	8.08371i	−0.272039	+	0.272039i	−0.829920	−	0.557882i	$-0.811614\pi$
$883$	−8.08371	+	8.08371i	−0.272039	+	0.272039i	0.557882	+	0.829920i	$0.311614\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.9255			0.433994			0.216997	−	0.976172i	$-0.430374\pi$
$887$	12.9255			0.433994			0.216997	+	0.976172i	$0.430374\pi$
$888$		0			0
$889$			61.9412i			2.07744i
$890$		0			0
$891$	10.6586	−	10.6586i	0.357078	−	0.357078i
$892$		0			0
$893$	6.72664	−	6.72664i	0.225098	−	0.225098i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			13.1787i			0.440025i
$898$		0			0
$899$	−6.66378	−	6.66378i	−0.222250	−	0.222250i
$900$		0			0
$901$	2.18878	−	2.18878i	0.0729190	−	0.0729190i
$902$		0			0
$903$	126.232			4.20074
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−16.4991	−	16.4991i	−0.547844	−	0.547844i	0.377973	−	0.925817i	$-0.376621\pi$
$907$	−16.4991	−	16.4991i	−0.547844	−	0.547844i	−0.925817	+	0.377973i	$0.876621\pi$
$908$		0			0
$909$	17.8169	+	17.8169i	0.590951	+	0.590951i
$910$		0			0
$911$	26.6745			0.883765			0.441883	−	0.897073i	$-0.354311\pi$
$911$	26.6745			0.883765			0.441883	+	0.897073i	$0.354311\pi$
$912$		0			0
$913$		−	8.03908i		−	0.266055i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	23.4827	+	23.4827i	0.775467	+	0.775467i
$918$		0			0
$919$		−	57.7425i		−	1.90475i	−0.304932	−	0.952374i	$-0.598634\pi$
$919$		−	57.7425i		−	1.90475i	0.304932	−	0.952374i	$-0.401366\pi$
$920$		0			0
$921$			8.74878i			0.288282i
$922$		0			0
$923$	−2.91714	−	2.91714i	−0.0960188	−	0.0960188i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			33.5848i			1.10307i
$928$		0			0
$929$	−42.5386			−1.39565			−0.697823	−	0.716270i	$-0.745848\pi$
$929$	−42.5386			−1.39565			−0.697823	+	0.716270i	$0.745848\pi$
$930$		0			0
$931$	−35.7372	−	35.7372i	−1.17124	−	1.17124i
$932$		0			0
$933$	−37.3572	−	37.3572i	−1.22302	−	1.22302i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−16.6795			−0.544894			−0.272447	−	0.962171i	$-0.587833\pi$
$937$	−16.6795			−0.544894			−0.272447	+	0.962171i	$0.587833\pi$
$938$		0			0
$939$	−4.51376	+	4.51376i	−0.147301	+	0.147301i
$940$		0			0
$941$	9.63152	+	9.63152i	0.313979	+	0.313979i	0.846449	−	0.532470i	$-0.178736\pi$
$941$	9.63152	+	9.63152i	0.313979	+	0.313979i	−0.532470	+	0.846449i	$0.678736\pi$
$942$		0			0
$943$			15.2227i			0.495721i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.44034	+	3.44034i	−0.111796	+	0.111796i	−0.760792	−	0.648996i	$-0.775189\pi$
$947$	−3.44034	+	3.44034i	−0.111796	+	0.111796i	0.648996	+	0.760792i	$0.275189\pi$
$948$		0			0
$949$	2.11707	−	2.11707i	0.0687231	−	0.0687231i
$950$		0			0
$951$			59.3028i			1.92302i
$952$		0			0
$953$	−17.6965			−0.573247			−0.286623	−	0.958043i	$-0.592533\pi$
$953$	−17.6965			−0.573247			−0.286623	+	0.958043i	$0.592533\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	5.54750	−	5.54750i	0.179325	−	0.179325i
$958$		0			0
$959$	−102.622			−3.31384
$960$		0			0
$961$	20.9027			0.674281
$962$		0			0
$963$	37.3577	−	37.3577i	1.20384	−	1.20384i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	15.0023			0.482442			0.241221	−	0.970470i	$-0.422452\pi$
$967$	15.0023			0.482442			0.241221	+	0.970470i	$0.422452\pi$
$968$		0			0
$969$			14.2627i			0.458183i
$970$		0			0
$971$	14.3135	−	14.3135i	0.459340	−	0.459340i	−0.439098	−	0.898439i	$-0.644702\pi$
$971$	14.3135	−	14.3135i	0.459340	−	0.459340i	0.898439	+	0.439098i	$0.144702\pi$
$972$		0			0
$973$	−28.3241	+	28.3241i	−0.908030	+	0.908030i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			48.1433i			1.54024i	0.637900	+	0.770120i	$0.279804\pi$
$977$			48.1433i			1.54024i	−0.637900	+	0.770120i	$0.720196\pi$
$978$		0			0
$979$	15.3580	+	15.3580i	0.490845	+	0.490845i
$980$		0			0
$981$	−4.98651	+	4.98651i	−0.159207	+	0.159207i
$982$		0			0
$983$	0.791292			0.0252383			0.0126191	−	0.999920i	$-0.495983\pi$
$983$	0.791292			0.0252383			0.0126191	+	0.999920i	$0.495983\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	20.6893	+	20.6893i	0.658547	+	0.658547i
$988$		0			0
$989$	18.1818	+	18.1818i	0.578149	+	0.578149i
$990$		0			0
$991$	60.2424			1.91366			0.956832	−	0.290643i	$-0.0938690\pi$
$991$	60.2424			1.91366			0.956832	+	0.290643i	$0.0938690\pi$
$992$		0			0
$993$		−	12.5133i		−	0.397099i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.15773	+	1.15773i	0.0366655	+	0.0366655i	0.725202	−	0.688536i	$-0.241746\pi$
$997$	1.15773	+	1.15773i	0.0366655	+	0.0366655i	−0.688536	+	0.725202i	$0.741746\pi$
$998$		0			0
$999$		−	12.9598i		−	0.410031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.g.849.1		16
4.3	odd	2		400.2.q.h.349.1		16
5.2	odd	4		1600.2.l.i.401.8		16
5.3	odd	4		320.2.l.a.81.1		16
5.4	even	2		1600.2.q.h.849.8		16
15.8	even	4		2880.2.t.c.721.8		16
16.5	even	4		1600.2.q.h.49.8		16
16.11	odd	4		400.2.q.g.149.8		16
20.3	even	4		80.2.l.a.61.3	yes	16
20.7	even	4		400.2.l.h.301.6		16
20.19	odd	2		400.2.q.g.349.8		16
40.3	even	4		640.2.l.b.161.1		16
40.13	odd	4		640.2.l.a.161.8		16
60.23	odd	4		720.2.t.c.541.6		16
80.3	even	4		640.2.l.b.481.1		16
80.13	odd	4		640.2.l.a.481.8		16
80.27	even	4		400.2.l.h.101.6		16
80.37	odd	4		1600.2.l.i.1201.8		16
80.43	even	4		80.2.l.a.21.3	✓	16
80.53	odd	4		320.2.l.a.241.1		16
80.59	odd	4		400.2.q.h.149.1		16
80.69	even	4	inner	1600.2.q.g.49.1		16
160.43	even	8		5120.2.a.v.1.7		8
160.53	odd	8		5120.2.a.t.1.2		8
160.123	even	8		5120.2.a.s.1.2		8
160.133	odd	8		5120.2.a.u.1.7		8
240.53	even	4		2880.2.t.c.2161.5		16
240.203	odd	4		720.2.t.c.181.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.3	✓	16	80.43	even	4
80.2.l.a.61.3	yes	16	20.3	even	4
320.2.l.a.81.1		16	5.3	odd	4
320.2.l.a.241.1		16	80.53	odd	4
400.2.l.h.101.6		16	80.27	even	4
400.2.l.h.301.6		16	20.7	even	4
400.2.q.g.149.8		16	16.11	odd	4
400.2.q.g.349.8		16	20.19	odd	2
400.2.q.h.149.1		16	80.59	odd	4
400.2.q.h.349.1		16	4.3	odd	2
640.2.l.a.161.8		16	40.13	odd	4
640.2.l.a.481.8		16	80.13	odd	4
640.2.l.b.161.1		16	40.3	even	4
640.2.l.b.481.1		16	80.3	even	4
720.2.t.c.181.6		16	240.203	odd	4
720.2.t.c.541.6		16	60.23	odd	4
1600.2.l.i.401.8		16	5.2	odd	4
1600.2.l.i.1201.8		16	80.37	odd	4
1600.2.q.g.49.1		16	80.69	even	4	inner
1600.2.q.g.849.1		16	1.1	even	1	trivial
1600.2.q.h.49.8		16	16.5	even	4
1600.2.q.h.849.8		16	5.4	even	2
2880.2.t.c.721.8		16	15.8	even	4
2880.2.t.c.2161.5		16	240.53	even	4
5120.2.a.s.1.2		8	160.123	even	8
5120.2.a.t.1.2		8	160.53	odd	8
5120.2.a.u.1.7		8	160.133	odd	8
5120.2.a.v.1.7		8	160.43	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)

\(f(q)\)	\(=\)	\(q+(-1.82762 + 1.82762i) q^{3} -4.50961 q^{7} -3.68037i q^{9} +O(q^{10})\)	\(q+(-1.82762 + 1.82762i) q^{3} -4.50961 q^{7} -3.68037i q^{9} +(1.64080 - 1.64080i) q^{11} +(1.51857 - 1.51857i) q^{13} +1.45616i q^{17} +(-2.67964 - 2.67964i) q^{19} +(8.24183 - 8.24183i) q^{21} +2.37423 q^{23} +(1.24345 + 1.24345i) q^{27} +(-0.924966 - 0.924966i) q^{29} +7.20435 q^{31} +5.99752i q^{33} +(-5.21123 - 5.21123i) q^{37} +5.55074i q^{39} +6.41166i q^{41} +(7.65800 + 7.65800i) q^{43} +2.51027i q^{47} +13.3366 q^{49} +(-2.66130 - 2.66130i) q^{51} +(-1.50312 - 1.50312i) q^{53} +9.79472 q^{57} +(-5.31807 + 5.31807i) q^{59} +(-1.02169 - 1.02169i) q^{61} +16.5970i q^{63} +(5.22745 - 5.22745i) q^{67} +(-4.33918 + 4.33918i) q^{69} -1.92097i q^{71} +1.39412 q^{73} +(-7.39938 + 7.39938i) q^{77} +5.06317 q^{79} +6.49599 q^{81} +(2.44974 - 2.44974i) q^{83} +3.38097 q^{87} +9.36007i q^{89} +(-6.84817 + 6.84817i) q^{91} +(-13.1668 + 13.1668i) q^{93} +18.6313i q^{97} +(-6.03876 - 6.03876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 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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