LMFDB - Embedded newform 1600.2.q.f.849.5

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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			849.5
Root			$1.35979 - 0.388551i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.f.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03997 - 1.03997i) q^{3} +1.49668 q^{7} +0.836925i q^{9} +O(q^{10})$	$q+(1.03997 - 1.03997i) q^{3} +1.49668 q^{7} +0.836925i q^{9} +(-0.423260 + 0.423260i) q^{11} +(-1.85704 + 1.85704i) q^{13} +6.50950i q^{17} +(-1.75725 - 1.75725i) q^{19} +(1.55650 - 1.55650i) q^{21} +7.19295 q^{23} +(3.99029 + 3.99029i) q^{27} +(6.57892 + 6.57892i) q^{29} +6.75252 q^{31} +0.880355i q^{33} +(1.95300 + 1.95300i) q^{37} +3.86254i q^{39} -7.70745i q^{41} +(-6.13581 - 6.13581i) q^{43} +6.65476i q^{47} -4.75994 q^{49} +(6.76969 + 6.76969i) q^{51} +(-5.29390 - 5.29390i) q^{53} -3.65497 q^{57} +(5.91841 - 5.91841i) q^{59} +(-1.43686 - 1.43686i) q^{61} +1.25261i q^{63} +(-6.35614 + 6.35614i) q^{67} +(7.48045 - 7.48045i) q^{69} -4.08932i q^{71} +2.43800 q^{73} +(-0.633485 + 0.633485i) q^{77} +11.6722 q^{79} +5.78878 q^{81} +(-2.81439 + 2.81439i) q^{83} +13.6838 q^{87} -10.5543i q^{89} +(-2.77940 + 2.77940i) q^{91} +(7.02242 - 7.02242i) q^{93} +18.1512i q^{97} +(-0.354237 - 0.354237i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 12 q^{7}+O(q^{10}) $ 12 * q + 2 * q^3 - 12 * q^7	$ 12 q + 2 q^{3} - 12 q^{7} + 2 q^{11} + 4 q^{13} - 14 q^{19} - 20 q^{21} - 12 q^{23} - 10 q^{27} + 4 q^{31} - 8 q^{37} - 4 q^{49} - 10 q^{51} - 16 q^{53} - 16 q^{57} + 20 q^{59} + 4 q^{61} - 50 q^{67} + 40 q^{73} - 8 q^{77} + 12 q^{79} - 8 q^{81} - 2 q^{83} + 64 q^{87} + 44 q^{93} + 12 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 - 12 * q^7 + 2 * q^11 + 4 * q^13 - 14 * q^19 - 20 * q^21 - 12 * q^23 - 10 * q^27 + 4 * q^31 - 8 * q^37 - 4 * q^49 - 10 * q^51 - 16 * q^53 - 16 * q^57 + 20 * q^59 + 4 * q^61 - 50 * q^67 + 40 * q^73 - 8 * q^77 + 12 * q^79 - 8 * q^81 - 2 * q^83 + 64 * q^87 + 44 * q^93 + 12 * 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
$3$	1.03997	−	1.03997i	0.600427	−	0.600427i	−0.339999	−	0.940426i	$-0.610427\pi$
$3$	1.03997	−	1.03997i	0.600427	−	0.600427i	0.940426	+	0.339999i	$0.110427\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.49668			0.565693			0.282846	−	0.959165i	$-0.408721\pi$
$7$	1.49668			0.565693			0.282846	+	0.959165i	$0.408721\pi$
$8$		0			0
$9$			0.836925i			0.278975i
$10$		0			0
$11$	−0.423260	+	0.423260i	−0.127618	+	0.127618i	−0.768031	−	0.640413i	$-0.778763\pi$
$11$	−0.423260	+	0.423260i	−0.127618	+	0.127618i	0.640413	+	0.768031i	$0.278763\pi$
$12$		0			0
$13$	−1.85704	+	1.85704i	−0.515051	+	0.515051i	−0.916070	−	0.401019i	$-0.868656\pi$
$13$	−1.85704	+	1.85704i	−0.515051	+	0.515051i	0.401019	+	0.916070i	$0.368656\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			6.50950i			1.57879i	0.613888	+	0.789393i	$0.289605\pi$
$17$			6.50950i			1.57879i	−0.613888	+	0.789393i	$0.710395\pi$
$18$		0			0
$19$	−1.75725	−	1.75725i	−0.403141	−	0.403141i	0.476198	−	0.879338i	$-0.342015\pi$
$19$	−1.75725	−	1.75725i	−0.403141	−	0.403141i	−0.879338	+	0.476198i	$0.842015\pi$
$20$		0			0
$21$	1.55650	−	1.55650i	0.339657	−	0.339657i
$22$		0			0
$23$	7.19295			1.49983			0.749917	−	0.661532i	$-0.230094\pi$
$23$	7.19295			1.49983			0.749917	+	0.661532i	$0.230094\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.99029	+	3.99029i	0.767931	+	0.767931i
$28$		0			0
$29$	6.57892	+	6.57892i	1.22167	+	1.22167i	0.967036	+	0.254639i	$0.0819565\pi$
$29$	6.57892	+	6.57892i	1.22167	+	1.22167i	0.254639	+	0.967036i	$0.418043\pi$
$30$		0			0
$31$	6.75252			1.21279			0.606394	−	0.795164i	$-0.292615\pi$
$31$	6.75252			1.21279			0.606394	+	0.795164i	$0.292615\pi$
$32$		0			0
$33$			0.880355i			0.153250i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.95300	+	1.95300i	0.321071	+	0.321071i	0.849178	−	0.528107i	$-0.177098\pi$
$37$	1.95300	+	1.95300i	0.321071	+	0.321071i	−0.528107	+	0.849178i	$0.677098\pi$
$38$		0			0
$39$			3.86254i			0.618501i
$40$		0			0
$41$		−	7.70745i		−	1.20370i	−0.798609	−	0.601851i	$-0.794430\pi$
$41$		−	7.70745i		−	1.20370i	0.798609	−	0.601851i	$-0.205570\pi$
$42$		0			0
$43$	−6.13581	−	6.13581i	−0.935702	−	0.935702i	0.0623522	−	0.998054i	$-0.480140\pi$
$43$	−6.13581	−	6.13581i	−0.935702	−	0.935702i	−0.998054	+	0.0623522i	$0.980140\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			6.65476i			0.970697i	0.874321	+	0.485348i	$0.161307\pi$
$47$			6.65476i			0.970697i	−0.874321	+	0.485348i	$0.838693\pi$
$48$		0			0
$49$	−4.75994			−0.679992
$50$		0			0
$51$	6.76969	+	6.76969i	0.947946	+	0.947946i
$52$		0			0
$53$	−5.29390	−	5.29390i	−0.727173	−	0.727173i	0.242882	−	0.970056i	$-0.421907\pi$
$53$	−5.29390	−	5.29390i	−0.727173	−	0.727173i	−0.970056	+	0.242882i	$0.921907\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.65497			−0.484113
$58$		0			0
$59$	5.91841	−	5.91841i	0.770511	−	0.770511i	−0.207685	−	0.978196i	$-0.566593\pi$
$59$	5.91841	−	5.91841i	0.770511	−	0.770511i	0.978196	+	0.207685i	$0.0665929\pi$
$60$		0			0
$61$	−1.43686	−	1.43686i	−0.183971	−	0.183971i	0.609113	−	0.793084i	$-0.291526\pi$
$61$	−1.43686	−	1.43686i	−0.183971	−	0.183971i	−0.793084	+	0.609113i	$0.791526\pi$
$62$		0			0
$63$			1.25261i			0.157814i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.35614	+	6.35614i	−0.776526	+	0.776526i	−0.979238	−	0.202712i	$-0.935024\pi$
$67$	−6.35614	+	6.35614i	−0.776526	+	0.776526i	0.202712	+	0.979238i	$0.435024\pi$
$68$		0			0
$69$	7.48045	−	7.48045i	0.900540	−	0.900540i
$70$		0			0
$71$		−	4.08932i		−	0.485313i	−0.970112	−	0.242657i	$-0.921981\pi$
$71$		−	4.08932i		−	0.485313i	0.970112	−	0.242657i	$-0.0780188\pi$
$72$		0			0
$73$	2.43800			0.285346			0.142673	−	0.989770i	$-0.454430\pi$
$73$	2.43800			0.285346			0.142673	+	0.989770i	$0.454430\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.633485	+	0.633485i	−0.0721924	+	0.0721924i
$78$		0			0
$79$	11.6722			1.31323			0.656615	−	0.754226i	$-0.271988\pi$
$79$	11.6722			1.31323			0.656615	+	0.754226i	$0.271988\pi$
$80$		0			0
$81$	5.78878			0.643198
$82$		0			0
$83$	−2.81439	+	2.81439i	−0.308919	+	0.308919i	−0.844490	−	0.535571i	$-0.820096\pi$
$83$	−2.81439	+	2.81439i	−0.308919	+	0.308919i	0.535571	+	0.844490i	$0.320096\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	13.6838			1.46705
$88$		0			0
$89$		−	10.5543i		−	1.11876i	−0.828912	−	0.559379i	$-0.811040\pi$
$89$		−	10.5543i		−	1.11876i	0.828912	−	0.559379i	$-0.188960\pi$
$90$		0			0
$91$	−2.77940	+	2.77940i	−0.291360	+	0.291360i
$92$		0			0
$93$	7.02242	−	7.02242i	0.728191	−	0.728191i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			18.1512i			1.84298i	0.388407	+	0.921488i	$0.373025\pi$
$97$			18.1512i			1.84298i	−0.388407	+	0.921488i	$0.626975\pi$
$98$		0			0
$99$	−0.354237	−	0.354237i	−0.0356021	−	0.0356021i
$100$		0			0
$101$	−1.04036	+	1.04036i	−0.103520	+	0.103520i	−0.756970	−	0.653450i	$-0.773321\pi$
$101$	−1.04036	+	1.04036i	−0.103520	+	0.103520i	0.653450	+	0.756970i	$0.273321\pi$
$102$		0			0
$103$	0.955267			0.0941253			0.0470626	−	0.998892i	$-0.485014\pi$
$103$	0.955267			0.0941253			0.0470626	+	0.998892i	$0.485014\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.20266	−	7.20266i	−0.696308	−	0.696308i	0.267305	−	0.963612i	$-0.413867\pi$
$107$	−7.20266	−	7.20266i	−0.696308	−	0.696308i	−0.963612	+	0.267305i	$0.913867\pi$
$108$		0			0
$109$	5.67807	+	5.67807i	0.543861	+	0.543861i	0.924658	−	0.380798i	$-0.124351\pi$
$109$	5.67807	+	5.67807i	0.543861	+	0.543861i	−0.380798	+	0.924658i	$0.624351\pi$
$110$		0			0
$111$	4.06212			0.385560
$112$		0			0
$113$		−	1.94751i		−	0.183206i	−0.995796	−	0.0916029i	$-0.970801\pi$
$113$		−	1.94751i		−	0.183206i	0.995796	−	0.0916029i	$-0.0291991\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.55420	−	1.55420i	−0.143686	−	0.143686i
$118$		0			0
$119$			9.74266i			0.893108i
$120$		0			0
$121$			10.6417i			0.967427i
$122$		0			0
$123$	−8.01552	−	8.01552i	−0.722735	−	0.722735i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			1.31796i			0.116950i	0.998289	+	0.0584750i	$0.0186238\pi$
$127$			1.31796i			0.116950i	−0.998289	+	0.0584750i	$0.981376\pi$
$128$		0			0
$129$	−12.7621			−1.12364
$130$		0			0
$131$	−1.03026	−	1.03026i	−0.0900139	−	0.0900139i	0.660666	−	0.750680i	$-0.270274\pi$
$131$	−1.03026	−	1.03026i	−0.0900139	−	0.0900139i	−0.750680	+	0.660666i	$0.770274\pi$
$132$		0			0
$133$	−2.63004	−	2.63004i	−0.228054	−	0.228054i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.75559			0.320862			0.160431	−	0.987047i	$-0.448712\pi$
$137$	3.75559			0.320862			0.160431	+	0.987047i	$0.448712\pi$
$138$		0			0
$139$	12.9485	−	12.9485i	1.09828	−	1.09828i	0.103669	−	0.994612i	$-0.466942\pi$
$139$	12.9485	−	12.9485i	1.09828	−	1.09828i	0.994612	−	0.103669i	$-0.0330584\pi$
$140$		0			0
$141$	6.92075	+	6.92075i	0.582832	+	0.582832i
$142$		0			0
$143$		−	1.57202i		−	0.131459i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.95020	+	4.95020i	−0.408285	+	0.408285i
$148$		0			0
$149$	15.8472	−	15.8472i	1.29825	−	1.29825i	0.368709	−	0.929545i	$-0.379800\pi$
$149$	15.8472	−	15.8472i	1.29825	−	1.29825i	0.929545	−	0.368709i	$-0.120200\pi$
$150$		0			0
$151$		−	11.5316i		−	0.938424i	−0.883085	−	0.469212i	$-0.844538\pi$
$151$		−	11.5316i		−	0.938424i	0.883085	−	0.469212i	$-0.155462\pi$
$152$		0			0
$153$	−5.44797			−0.440442
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.41891	−	5.41891i	0.432476	−	0.432476i	−0.456994	−	0.889470i	$-0.651074\pi$
$157$	5.41891	−	5.41891i	0.432476	−	0.432476i	0.889470	+	0.456994i	$0.151074\pi$
$158$		0			0
$159$	−11.0110			−0.873229
$160$		0			0
$161$	10.7656			0.848445
$162$		0			0
$163$	−6.47288	+	6.47288i	−0.506995	+	0.506995i	−0.913603	−	0.406608i	$-0.866711\pi$
$163$	−6.47288	+	6.47288i	−0.506995	+	0.506995i	0.406608	+	0.913603i	$0.366711\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.29734			−0.642068			−0.321034	−	0.947068i	$-0.604030\pi$
$167$	−8.29734			−0.642068			−0.321034	+	0.947068i	$0.604030\pi$
$168$		0			0
$169$			6.10279i			0.469445i
$170$		0			0
$171$	1.47069	−	1.47069i	0.112466	−	0.112466i
$172$		0			0
$173$	11.9420	−	11.9420i	0.907935	−	0.907935i	−0.0881700	−	0.996105i	$-0.528102\pi$
$173$	11.9420	−	11.9420i	0.907935	−	0.907935i	0.996105	+	0.0881700i	$0.0281019\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	12.3099i		−	0.925271i
$178$		0			0
$179$	−10.8703	−	10.8703i	−0.812481	−	0.812481i	0.172524	−	0.985005i	$-0.444808\pi$
$179$	−10.8703	−	10.8703i	−0.812481	−	0.812481i	−0.985005	+	0.172524i	$0.944808\pi$
$180$		0			0
$181$	−4.09403	+	4.09403i	−0.304307	+	0.304307i	−0.842696	−	0.538389i	$-0.819033\pi$
$181$	−4.09403	+	4.09403i	−0.304307	+	0.304307i	0.538389	+	0.842696i	$0.319033\pi$
$182$		0			0
$183$	−2.98858			−0.220922
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.75521	−	2.75521i	−0.201481	−	0.201481i
$188$		0			0
$189$	5.97219	+	5.97219i	0.434413	+	0.434413i
$190$		0			0
$191$	−19.2542			−1.39319			−0.696594	−	0.717466i	$-0.745302\pi$
$191$	−19.2542			−1.39319			−0.696594	+	0.717466i	$0.745302\pi$
$192$		0			0
$193$			24.8152i			1.78624i	0.449820	+	0.893119i	$0.351488\pi$
$193$			24.8152i			1.78624i	−0.449820	+	0.893119i	$0.648512\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.81324	−	2.81324i	−0.200435	−	0.200435i	0.599751	−	0.800186i	$-0.295266\pi$
$197$	−2.81324	−	2.81324i	−0.200435	−	0.200435i	−0.800186	+	0.599751i	$0.795266\pi$
$198$		0			0
$199$			21.2194i			1.50420i	0.659048	+	0.752101i	$0.270959\pi$
$199$			21.2194i			1.50420i	−0.659048	+	0.752101i	$0.729041\pi$
$200$		0			0
$201$			13.2204i			0.932495i
$202$		0			0
$203$	9.84655	+	9.84655i	0.691092	+	0.691092i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			6.01996i			0.418416i
$208$		0			0
$209$	1.48755			0.102896
$210$		0			0
$211$	−15.5715	−	15.5715i	−1.07199	−	1.07199i	−0.997200	−	0.0747872i	$-0.976172\pi$
$211$	−15.5715	−	15.5715i	−1.07199	−	1.07199i	−0.0747872	−	0.997200i	$-0.523828\pi$
$212$		0			0
$213$	−4.25277	−	4.25277i	−0.291395	−	0.291395i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.1064			0.686065
$218$		0			0
$219$	2.53545	−	2.53545i	0.171330	−	0.171330i
$220$		0			0
$221$	−12.0884	−	12.0884i	−0.813155	−	0.813155i
$222$		0			0
$223$		−	7.88779i		−	0.528205i	−0.964495	−	0.264103i	$-0.914924\pi$
$223$		−	7.88779i		−	0.528205i	0.964495	−	0.264103i	$-0.0850758\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.98838	+	5.98838i	−0.397463	+	0.397463i	−0.877337	−	0.479874i	$-0.840682\pi$
$227$	−5.98838	+	5.98838i	−0.397463	+	0.397463i	0.479874	+	0.877337i	$0.340682\pi$
$228$		0			0
$229$	−19.4584	+	19.4584i	−1.28585	+	1.28585i	−0.348563	+	0.937286i	$0.613330\pi$
$229$	−19.4584	+	19.4584i	−1.28585	+	1.28585i	−0.937286	+	0.348563i	$0.886670\pi$
$230$		0			0
$231$			1.31761i			0.0866925i
$232$		0			0
$233$	−2.68717			−0.176042			−0.0880212	−	0.996119i	$-0.528054\pi$
$233$	−2.68717			−0.176042			−0.0880212	+	0.996119i	$0.528054\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	12.1388	−	12.1388i	0.788499	−	0.788499i
$238$		0			0
$239$	−12.6359			−0.817346			−0.408673	−	0.912681i	$-0.634008\pi$
$239$	−12.6359			−0.817346			−0.408673	+	0.912681i	$0.634008\pi$
$240$		0			0
$241$	7.53314			0.485252			0.242626	−	0.970120i	$-0.421991\pi$
$241$	7.53314			0.485252			0.242626	+	0.970120i	$0.421991\pi$
$242$		0			0
$243$	−5.95070	+	5.95070i	−0.381738	+	0.381738i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.52658			0.415276
$248$		0			0
$249$			5.85376i			0.370967i
$250$		0			0
$251$	9.95683	−	9.95683i	0.628470	−	0.628470i	−0.319213	−	0.947683i	$-0.603419\pi$
$251$	9.95683	−	9.95683i	0.628470	−	0.628470i	0.947683	+	0.319213i	$0.103419\pi$
$252$		0			0
$253$	−3.04449	+	3.04449i	−0.191405	+	0.191405i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			4.51630i			0.281719i	0.990030	+	0.140860i	$0.0449866\pi$
$257$			4.51630i			0.281719i	−0.990030	+	0.140860i	$0.955013\pi$
$258$		0			0
$259$	2.92302	+	2.92302i	0.181628	+	0.181628i
$260$		0			0
$261$	−5.50606	+	5.50606i	−0.340817	+	0.340817i
$262$		0			0
$263$	20.2127			1.24637			0.623185	−	0.782075i	$-0.285838\pi$
$263$	20.2127			1.24637			0.623185	+	0.782075i	$0.285838\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−10.9762	−	10.9762i	−0.671732	−	0.671732i
$268$		0			0
$269$	−16.9430	−	16.9430i	−1.03304	−	1.03304i	−0.999435	−	0.0335999i	$-0.989303\pi$
$269$	−16.9430	−	16.9430i	−1.03304	−	1.03304i	−0.0335999	−	0.999435i	$-0.510697\pi$
$270$		0			0
$271$	3.64054			0.221147			0.110573	−	0.993868i	$-0.464731\pi$
$271$	3.64054			0.221147			0.110573	+	0.993868i	$0.464731\pi$
$272$		0			0
$273$			5.78099i			0.349881i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−16.0090	−	16.0090i	−0.961888	−	0.961888i	0.0374115	−	0.999300i	$-0.488089\pi$
$277$	−16.0090	−	16.0090i	−0.961888	−	0.961888i	−0.999300	+	0.0374115i	$0.988089\pi$
$278$		0			0
$279$			5.65135i			0.338338i
$280$		0			0
$281$		−	5.51857i		−	0.329210i	−0.986360	−	0.164605i	$-0.947365\pi$
$281$		−	5.51857i		−	0.329210i	0.986360	−	0.164605i	$-0.0526350\pi$
$282$		0			0
$283$	2.36694	+	2.36694i	0.140700	+	0.140700i	0.773949	−	0.633249i	$-0.218279\pi$
$283$	2.36694	+	2.36694i	0.140700	+	0.140700i	−0.633249	+	0.773949i	$0.718279\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	11.5356i		−	0.680925i
$288$		0			0
$289$	−25.3736			−1.49257
$290$		0			0
$291$	18.8767	+	18.8767i	1.10657	+	1.10657i
$292$		0			0
$293$	19.1812	+	19.1812i	1.12058	+	1.12058i	0.991655	+	0.128922i	$0.0411517\pi$
$293$	19.1812	+	19.1812i	1.12058	+	1.12058i	0.128922	+	0.991655i	$0.458848\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.37786			−0.196003
$298$		0			0
$299$	−13.3576	+	13.3576i	−0.772491	+	0.772491i
$300$		0			0
$301$	−9.18335	−	9.18335i	−0.529320	−	0.529320i
$302$		0			0
$303$			2.16390i			0.124313i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	19.9292	−	19.9292i	1.13742	−	1.13742i	0.148507	−	0.988911i	$-0.452553\pi$
$307$	19.9292	−	19.9292i	1.13742	−	1.13742i	0.988911	−	0.148507i	$-0.0474469\pi$
$308$		0			0
$309$	0.993449	−	0.993449i	0.0565153	−	0.0565153i
$310$		0			0
$311$		−	5.73314i		−	0.325096i	−0.986701	−	0.162548i	$-0.948029\pi$
$311$		−	5.73314i		−	0.325096i	0.986701	−	0.162548i	$-0.0519713\pi$
$312$		0			0
$313$	−0.212621			−0.0120180			−0.00600902	−	0.999982i	$-0.501913\pi$
$313$	−0.212621			−0.0120180			−0.00600902	+	0.999982i	$0.501913\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.21582	−	3.21582i	0.180618	−	0.180618i	−0.611007	−	0.791625i	$-0.709235\pi$
$317$	3.21582	−	3.21582i	0.180618	−	0.180618i	0.791625	+	0.611007i	$0.209235\pi$
$318$		0			0
$319$	−5.56919			−0.311815
$320$		0			0
$321$	−14.9811			−0.836164
$322$		0			0
$323$	11.4388	−	11.4388i	0.636473	−	0.636473i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	11.8101			0.653097
$328$		0			0
$329$			9.96006i			0.549116i
$330$		0			0
$331$	−22.0295	+	22.0295i	−1.21085	+	1.21085i	−0.240106	+	0.970747i	$0.577182\pi$
$331$	−22.0295	+	22.0295i	−1.21085	+	1.21085i	−0.970747	+	0.240106i	$0.922818\pi$
$332$		0			0
$333$	−1.63451	+	1.63451i	−0.0895708	+	0.0895708i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	11.2122i		−	0.610767i	−0.952229	−	0.305384i	$-0.901215\pi$
$337$		−	11.2122i		−	0.610767i	0.952229	−	0.305384i	$-0.0987847\pi$
$338$		0			0
$339$	−2.02535	−	2.02535i	−0.110002	−	0.110002i
$340$		0			0
$341$	−2.85807	+	2.85807i	−0.154773	+	0.154773i
$342$		0			0
$343$	−17.6009			−0.950359
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.23653	−	1.23653i	−0.0663803	−	0.0663803i	0.673137	−	0.739518i	$-0.264946\pi$
$347$	−1.23653	−	1.23653i	−0.0663803	−	0.0663803i	−0.739518	+	0.673137i	$0.764946\pi$
$348$		0			0
$349$	5.61778	+	5.61778i	0.300713	+	0.300713i	0.841293	−	0.540580i	$-0.181795\pi$
$349$	5.61778	+	5.61778i	0.300713	+	0.300713i	−0.540580	+	0.841293i	$0.681795\pi$
$350$		0			0
$351$	−14.8203			−0.791047
$352$		0			0
$353$		−	0.748709i		−	0.0398497i	−0.999801	−	0.0199249i	$-0.993657\pi$
$353$		−	0.748709i		−	0.0398497i	0.999801	−	0.0199249i	$-0.00634270\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	10.1321	+	10.1321i	0.536246	+	0.536246i
$358$		0			0
$359$			2.69883i			0.142439i	0.997461	+	0.0712195i	$0.0226891\pi$
$359$			2.69883i			0.142439i	−0.997461	+	0.0712195i	$0.977311\pi$
$360$		0			0
$361$		−	12.8241i		−	0.674955i
$362$		0			0
$363$	11.0671	+	11.0671i	0.580870	+	0.580870i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	20.6101i		−	1.07584i	−0.842996	−	0.537920i	$-0.819210\pi$
$367$		−	20.6101i		−	1.07584i	0.842996	−	0.537920i	$-0.180790\pi$
$368$		0			0
$369$	6.45056			0.335802
$370$		0			0
$371$	−7.92329	−	7.92329i	−0.411357	−	0.411357i
$372$		0			0
$373$	−5.24143	−	5.24143i	−0.271391	−	0.271391i	0.558269	−	0.829660i	$-0.311466\pi$
$373$	−5.24143	−	5.24143i	−0.271391	−	0.271391i	−0.829660	+	0.558269i	$0.811466\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−24.4347			−1.25845
$378$		0			0
$379$	5.41344	−	5.41344i	0.278070	−	0.278070i	−0.554268	−	0.832338i	$-0.687002\pi$
$379$	5.41344	−	5.41344i	0.278070	−	0.278070i	0.832338	+	0.554268i	$0.187002\pi$
$380$		0			0
$381$	1.37064	+	1.37064i	0.0702199	+	0.0702199i
$382$		0			0
$383$			29.5087i			1.50782i	0.656975	+	0.753912i	$0.271836\pi$
$383$			29.5087i			1.50782i	−0.656975	+	0.753912i	$0.728164\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.13521	−	5.13521i	0.261037	−	0.261037i
$388$		0			0
$389$	−1.37884	+	1.37884i	−0.0699099	+	0.0699099i	−0.741197	−	0.671287i	$-0.765742\pi$
$389$	−1.37884	+	1.37884i	−0.0699099	+	0.0699099i	0.671287	+	0.741197i	$0.265742\pi$
$390$		0			0
$391$			46.8225i			2.36792i
$392$		0			0
$393$	−2.14287			−0.108094
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−21.9750	+	21.9750i	−1.10289	+	1.10289i	−0.108832	+	0.994060i	$0.534711\pi$
$397$	−21.9750	+	21.9750i	−1.10289	+	1.10289i	−0.994060	+	0.108832i	$0.965289\pi$
$398$		0			0
$399$	−5.47033			−0.273859
$400$		0			0
$401$	−31.4584			−1.57096			−0.785479	−	0.618889i	$-0.787583\pi$
$401$	−31.4584			−1.57096			−0.785479	+	0.618889i	$0.787583\pi$
$402$		0			0
$403$	−12.5397	+	12.5397i	−0.624648	+	0.624648i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.65325			−0.0819487
$408$		0			0
$409$		−	12.8017i		−	0.633003i	−0.948592	−	0.316502i	$-0.897492\pi$
$409$		−	12.8017i		−	0.633003i	0.948592	−	0.316502i	$-0.102508\pi$
$410$		0			0
$411$	3.90570	−	3.90570i	0.192654	−	0.192654i
$412$		0			0
$413$	8.85797	−	8.85797i	0.435872	−	0.435872i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	26.9322i		−	1.31888i
$418$		0			0
$419$	−11.4979	−	11.4979i	−0.561709	−	0.561709i	0.368084	−	0.929793i	$-0.380014\pi$
$419$	−11.4979	−	11.4979i	−0.561709	−	0.561709i	−0.929793	+	0.368084i	$0.880014\pi$
$420$		0			0
$421$	12.5714	−	12.5714i	0.612690	−	0.612690i	−0.330956	−	0.943646i	$-0.607371\pi$
$421$	12.5714	−	12.5714i	0.612690	−	0.612690i	0.943646	+	0.330956i	$0.107371\pi$
$422$		0			0
$423$	−5.56953			−0.270800
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.15052	−	2.15052i	−0.104071	−	0.104071i
$428$		0			0
$429$	−1.63486	−	1.63486i	−0.0789316	−	0.0789316i
$430$		0			0
$431$	15.2579			0.734946			0.367473	−	0.930034i	$-0.380223\pi$
$431$	15.2579			0.734946			0.367473	+	0.930034i	$0.380223\pi$
$432$		0			0
$433$		−	12.1705i		−	0.584877i	−0.956284	−	0.292439i	$-0.905533\pi$
$433$		−	12.1705i		−	0.584877i	0.956284	−	0.292439i	$-0.0944667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−12.6398	−	12.6398i	−0.604644	−	0.604644i
$438$		0			0
$439$		−	39.7535i		−	1.89733i	−0.316283	−	0.948665i	$-0.602435\pi$
$439$		−	39.7535i		−	1.89733i	0.316283	−	0.948665i	$-0.397565\pi$
$440$		0			0
$441$		−	3.98371i		−	0.189701i
$442$		0			0
$443$	−3.62318	−	3.62318i	−0.172142	−	0.172142i	0.615778	−	0.787920i	$-0.288842\pi$
$443$	−3.62318	−	3.62318i	−0.172142	−	0.172142i	−0.787920	+	0.615778i	$0.788842\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	32.9612i		−	1.55901i
$448$		0			0
$449$	5.38425			0.254098			0.127049	−	0.991896i	$-0.459449\pi$
$449$	5.38425			0.254098			0.127049	+	0.991896i	$0.459449\pi$
$450$		0			0
$451$	3.26225	+	3.26225i	0.153614	+	0.153614i
$452$		0			0
$453$	−11.9925	−	11.9925i	−0.563455	−	0.563455i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.3039			0.669108			0.334554	−	0.942377i	$-0.391414\pi$
$457$	14.3039			0.669108			0.334554	+	0.942377i	$0.391414\pi$
$458$		0			0
$459$	−25.9748	+	25.9748i	−1.21240	+	1.21240i
$460$		0			0
$461$	−4.50363	−	4.50363i	−0.209755	−	0.209755i	0.594408	−	0.804163i	$-0.297386\pi$
$461$	−4.50363	−	4.50363i	−0.209755	−	0.209755i	−0.804163	+	0.594408i	$0.797386\pi$
$462$		0			0
$463$		−	19.3500i		−	0.899271i	−0.893212	−	0.449636i	$-0.851554\pi$
$463$		−	19.3500i		−	0.899271i	0.893212	−	0.449636i	$-0.148446\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.1773	−	17.1773i	0.794871	−	0.794871i	−0.187410	−	0.982282i	$-0.560009\pi$
$467$	17.1773	−	17.1773i	0.794871	−	0.794871i	0.982282	+	0.187410i	$0.0600094\pi$
$468$		0			0
$469$	−9.51312	+	9.51312i	−0.439275	+	0.439275i
$470$		0			0
$471$		−	11.2710i		−	0.519341i
$472$		0			0
$473$	5.19408			0.238824
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.43060	−	4.43060i	0.202863	−	0.202863i
$478$		0			0
$479$	5.54474			0.253346			0.126673	−	0.991945i	$-0.459570\pi$
$479$	5.54474			0.253346			0.126673	+	0.991945i	$0.459570\pi$
$480$		0			0
$481$	−7.25361			−0.330736
$482$		0			0
$483$	11.1959	−	11.1959i	0.509429	−	0.509429i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−31.7138			−1.43709			−0.718546	−	0.695480i	$-0.755192\pi$
$487$	−31.7138			−1.43709			−0.718546	+	0.695480i	$0.755192\pi$
$488$		0			0
$489$			13.4632i			0.608827i
$490$		0			0
$491$	−7.39419	+	7.39419i	−0.333695	+	0.333695i	−0.853988	−	0.520293i	$-0.825823\pi$
$491$	−7.39419	+	7.39419i	−0.333695	+	0.333695i	0.520293	+	0.853988i	$0.325823\pi$
$492$		0			0
$493$	−42.8255	+	42.8255i	−1.92876	+	1.92876i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	6.12041i		−	0.274538i
$498$		0			0
$499$	14.0103	+	14.0103i	0.627189	+	0.627189i	0.947360	−	0.320171i	$-0.103740\pi$
$499$	14.0103	+	14.0103i	0.627189	+	0.627189i	−0.320171	+	0.947360i	$0.603740\pi$
$500$		0			0
$501$	−8.62899	+	8.62899i	−0.385515	+	0.385515i
$502$		0			0
$503$	8.43795			0.376230			0.188115	−	0.982147i	$-0.439762\pi$
$503$	8.43795			0.376230			0.188115	+	0.982147i	$0.439762\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.34671	+	6.34671i	0.281868	+	0.281868i
$508$		0			0
$509$	−2.09367	−	2.09367i	−0.0928004	−	0.0928004i	0.659183	−	0.751983i	$-0.270902\pi$
$509$	−2.09367	−	2.09367i	−0.0928004	−	0.0928004i	−0.751983	+	0.659183i	$0.770902\pi$
$510$		0			0
$511$	3.64891			0.161418
$512$		0			0
$513$		−	14.0239i		−	0.619169i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−2.81669	−	2.81669i	−0.123878	−	0.123878i
$518$		0			0
$519$		−	24.8387i		−	1.09030i
$520$		0			0
$521$		−	28.2558i		−	1.23791i	−0.785428	−	0.618954i	$-0.787557\pi$
$521$		−	28.2558i		−	1.23791i	0.785428	−	0.618954i	$-0.212443\pi$
$522$		0			0
$523$	−10.1929	−	10.1929i	−0.445703	−	0.445703i	0.448220	−	0.893923i	$-0.352058\pi$
$523$	−10.1929	−	10.1929i	−0.445703	−	0.445703i	−0.893923	+	0.448220i	$0.852058\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			43.9555i			1.91473i
$528$		0			0
$529$	28.7385			1.24950
$530$		0			0
$531$	4.95326	+	4.95326i	0.214953	+	0.214953i
$532$		0			0
$533$	14.3131	+	14.3131i	0.619967	+	0.619967i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−22.6095			−0.975671
$538$		0			0
$539$	2.01469	−	2.01469i	0.0867790	−	0.0867790i
$540$		0			0
$541$	3.86053	+	3.86053i	0.165977	+	0.165977i	0.785209	−	0.619231i	$-0.212556\pi$
$541$	3.86053	+	3.86053i	0.165977	+	0.165977i	−0.619231	+	0.785209i	$0.712556\pi$
$542$		0			0
$543$			8.51534i			0.365428i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−20.6231	+	20.6231i	−0.881781	+	0.881781i	−0.993716	−	0.111935i	$-0.964295\pi$
$547$	−20.6231	+	20.6231i	−0.881781	+	0.881781i	0.111935	+	0.993716i	$0.464295\pi$
$548$		0			0
$549$	1.20254	−	1.20254i	0.0513233	−	0.0513233i
$550$		0			0
$551$		−	23.1216i		−	0.985014i
$552$		0			0
$553$	17.4696			0.742884
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.28512	+	1.28512i	−0.0544523	+	0.0544523i	−0.733809	−	0.679356i	$-0.762259\pi$
$557$	−1.28512	+	1.28512i	−0.0544523	+	0.0544523i	0.679356	+	0.733809i	$0.262259\pi$
$558$		0			0
$559$	22.7889			0.963868
$560$		0			0
$561$	−5.73068			−0.241949
$562$		0			0
$563$	21.9152	−	21.9152i	0.923615	−	0.923615i	−0.0736677	−	0.997283i	$-0.523470\pi$
$563$	21.9152	−	21.9152i	0.923615	−	0.923615i	0.997283	+	0.0736677i	$0.0234704\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	8.66397			0.363852
$568$		0			0
$569$		−	35.6668i		−	1.49523i	−0.664132	−	0.747615i	$-0.731199\pi$
$569$		−	35.6668i		−	1.49523i	0.664132	−	0.747615i	$-0.268801\pi$
$570$		0			0
$571$	−5.60524	+	5.60524i	−0.234572	+	0.234572i	−0.814598	−	0.580026i	$-0.803042\pi$
$571$	−5.60524	+	5.60524i	−0.234572	+	0.234572i	0.580026	+	0.814598i	$0.303042\pi$
$572$		0			0
$573$	−20.0238	+	20.0238i	−0.836507	+	0.836507i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			2.43681i			0.101446i	0.998713	+	0.0507230i	$0.0161526\pi$
$577$			2.43681i			0.101446i	−0.998713	+	0.0507230i	$0.983847\pi$
$578$		0			0
$579$	25.8071	+	25.8071i	1.07251	+	1.07251i
$580$		0			0
$581$	−4.21225	+	4.21225i	−0.174753	+	0.174753i
$582$		0			0
$583$	4.48139			0.185600
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.415982	+	0.415982i	0.0171694	+	0.0171694i	0.715639	−	0.698470i	$-0.246135\pi$
$587$	0.415982	+	0.415982i	0.0171694	+	0.0171694i	−0.698470	+	0.715639i	$0.746135\pi$
$588$		0			0
$589$	−11.8659	−	11.8659i	−0.488924	−	0.488924i
$590$		0			0
$591$	−5.85136			−0.240693
$592$		0			0
$593$		−	15.3439i		−	0.630098i	−0.949075	−	0.315049i	$-0.897979\pi$
$593$		−	15.3439i		−	0.630098i	0.949075	−	0.315049i	$-0.102021\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	22.0675	+	22.0675i	0.903163	+	0.903163i
$598$		0			0
$599$		−	43.3487i		−	1.77118i	−0.464468	−	0.885590i	$-0.653754\pi$
$599$		−	43.3487i		−	1.77118i	0.464468	−	0.885590i	$-0.346246\pi$
$600$		0			0
$601$			38.7291i			1.57979i	0.613239	+	0.789897i	$0.289866\pi$
$601$			38.7291i			1.57979i	−0.613239	+	0.789897i	$0.710134\pi$
$602$		0			0
$603$	−5.31961	−	5.31961i	−0.216631	−	0.216631i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	34.9068i		−	1.41682i	−0.705800	−	0.708412i	$-0.749412\pi$
$607$		−	34.9068i		−	1.41682i	0.705800	−	0.708412i	$-0.250588\pi$
$608$		0			0
$609$	20.4802			0.829901
$610$		0			0
$611$	−12.3582	−	12.3582i	−0.499958	−	0.499958i
$612$		0			0
$613$	−0.151779	−	0.151779i	−0.00613031	−	0.00613031i	0.704035	−	0.710165i	$-0.251380\pi$
$613$	−0.151779	−	0.151779i	−0.00613031	−	0.00613031i	−0.710165	+	0.704035i	$0.751380\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.288199			−0.0116025			−0.00580123	−	0.999983i	$-0.501847\pi$
$617$	−0.288199			−0.0116025			−0.00580123	+	0.999983i	$0.501847\pi$
$618$		0			0
$619$	−11.5307	+	11.5307i	−0.463460	+	0.463460i	−0.899788	−	0.436328i	$-0.856279\pi$
$619$	−11.5307	+	11.5307i	−0.463460	+	0.463460i	0.436328	+	0.899788i	$0.356279\pi$
$620$		0			0
$621$	28.7019	+	28.7019i	1.15177	+	1.15177i
$622$		0			0
$623$		−	15.7965i		−	0.632873i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.54700	−	1.54700i	0.0617814	−	0.0617814i
$628$		0			0
$629$	−12.7131	+	12.7131i	−0.506903	+	0.506903i
$630$		0			0
$631$			14.2062i			0.565541i	0.959188	+	0.282771i	$0.0912536\pi$
$631$			14.2062i			0.565541i	−0.959188	+	0.282771i	$0.908746\pi$
$632$		0			0
$633$	−32.3878			−1.28730
$634$		0			0
$635$		0			0
$636$		0			0
$637$	8.83942	−	8.83942i	0.350230	−	0.350230i
$638$		0			0
$639$	3.42245			0.135390
$640$		0			0
$641$	19.7372			0.779572			0.389786	−	0.920905i	$-0.372549\pi$
$641$	19.7372			0.779572			0.389786	+	0.920905i	$0.372549\pi$
$642$		0			0
$643$	−5.80043	+	5.80043i	−0.228747	+	0.228747i	−0.812169	−	0.583422i	$-0.801713\pi$
$643$	−5.80043	+	5.80043i	−0.228747	+	0.228747i	0.583422	+	0.812169i	$0.301713\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−46.3186			−1.82097			−0.910485	−	0.413541i	$-0.864292\pi$
$647$	−46.3186			−1.82097			−0.910485	+	0.413541i	$0.864292\pi$
$648$		0			0
$649$			5.01005i			0.196662i
$650$		0			0
$651$	10.5103	−	10.5103i	0.411932	−	0.411932i
$652$		0			0
$653$	4.42354	−	4.42354i	0.173106	−	0.173106i	−0.615236	−	0.788343i	$-0.710939\pi$
$653$	4.42354	−	4.42354i	0.173106	−	0.173106i	0.788343	+	0.615236i	$0.210939\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			2.04042i			0.0796045i
$658$		0			0
$659$	−15.2461	−	15.2461i	−0.593905	−	0.593905i	0.344779	−	0.938684i	$-0.387954\pi$
$659$	−15.2461	−	15.2461i	−0.593905	−	0.593905i	−0.938684	+	0.344779i	$0.887954\pi$
$660$		0			0
$661$	19.1271	−	19.1271i	0.743958	−	0.743958i	−0.229379	−	0.973337i	$-0.573670\pi$
$661$	19.1271	−	19.1271i	0.743958	−	0.743958i	0.973337	+	0.229379i	$0.0736696\pi$
$662$		0			0
$663$	−25.1432			−0.976481
$664$		0			0
$665$		0			0
$666$		0			0
$667$	47.3218	+	47.3218i	1.83231	+	1.83231i
$668$		0			0
$669$	−8.20306	−	8.20306i	−0.317149	−	0.317149i
$670$		0			0
$671$	1.21633			0.0469559
$672$		0			0
$673$		−	18.5586i		−	0.715382i	−0.933840	−	0.357691i	$-0.883564\pi$
$673$		−	18.5586i		−	0.715382i	0.933840	−	0.357691i	$-0.116436\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.71844	+	2.71844i	0.104478	+	0.104478i	0.757414	−	0.652935i	$-0.226463\pi$
$677$	2.71844	+	2.71844i	0.104478	+	0.104478i	−0.652935	+	0.757414i	$0.726463\pi$
$678$		0			0
$679$			27.1666i			1.04256i
$680$		0			0
$681$			12.4555i			0.477295i
$682$		0			0
$683$	12.6646	+	12.6646i	0.484598	+	0.484598i	0.906596	−	0.421999i	$-0.138671\pi$
$683$	12.6646	+	12.6646i	0.484598	+	0.484598i	−0.421999	+	0.906596i	$0.638671\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			40.4723i			1.54412i
$688$		0			0
$689$	19.6620			0.749063
$690$		0			0
$691$	−26.8892	−	26.8892i	−1.02291	−	1.02291i	−0.999731	−	0.0231826i	$-0.992620\pi$
$691$	−26.8892	−	26.8892i	−1.02291	−	1.02291i	−0.0231826	−	0.999731i	$-0.507380\pi$
$692$		0			0
$693$	−0.530180	−	0.530180i	−0.0201399	−	0.0201399i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	50.1717			1.90039
$698$		0			0
$699$	−2.79458	+	2.79458i	−0.105701	+	0.105701i
$700$		0			0
$701$	25.3725	+	25.3725i	0.958305	+	0.958305i	0.999165	−	0.0408602i	$-0.0130098\pi$
$701$	25.3725	+	25.3725i	0.958305	+	0.958305i	−0.0408602	+	0.999165i	$0.513010\pi$
$702$		0			0
$703$		−	6.86382i		−	0.258874i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.55709	+	1.55709i	−0.0585606	+	0.0585606i
$708$		0			0
$709$	−16.1117	+	16.1117i	−0.605089	+	0.605089i	−0.941659	−	0.336570i	$-0.890733\pi$
$709$	−16.1117	+	16.1117i	−0.605089	+	0.605089i	0.336570	+	0.941659i	$0.390733\pi$
$710$		0			0
$711$			9.76879i			0.366358i
$712$		0			0
$713$	48.5705			1.81898
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−13.1409	+	13.1409i	−0.490757	+	0.490757i
$718$		0			0
$719$	29.1676			1.08777			0.543884	−	0.839160i	$-0.316953\pi$
$719$	29.1676			1.08777			0.543884	+	0.839160i	$0.316953\pi$
$720$		0			0
$721$	1.42973			0.0532460
$722$		0			0
$723$	7.83424	−	7.83424i	0.291358	−	0.291358i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	4.13463			0.153345			0.0766724	−	0.997056i	$-0.475570\pi$
$727$	4.13463			0.153345			0.0766724	+	0.997056i	$0.475570\pi$
$728$		0			0
$729$			29.7434i			1.10161i
$730$		0			0
$731$	39.9411	−	39.9411i	1.47727	−	1.47727i
$732$		0			0
$733$	19.3838	−	19.3838i	0.715957	−	0.715957i	−0.251817	−	0.967775i	$-0.581028\pi$
$733$	19.3838	−	19.3838i	0.715957	−	0.715957i	0.967775	+	0.251817i	$0.0810282\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	5.38060i		−	0.198197i
$738$		0			0
$739$	23.9820	+	23.9820i	0.882194	+	0.882194i	0.993757	−	0.111564i	$-0.0355859\pi$
$739$	23.9820	+	23.9820i	0.882194	+	0.882194i	−0.111564	+	0.993757i	$0.535586\pi$
$740$		0			0
$741$	6.78744	−	6.78744i	0.249343	−	0.249343i
$742$		0			0
$743$	−10.3473			−0.379604			−0.189802	−	0.981822i	$-0.560785\pi$
$743$	−10.3473			−0.379604			−0.189802	+	0.981822i	$0.560785\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.35543	−	2.35543i	−0.0861808	−	0.0861808i
$748$		0			0
$749$	−10.7801	−	10.7801i	−0.393896	−	0.393896i
$750$		0			0
$751$	37.0217			1.35094			0.675470	−	0.737387i	$-0.263941\pi$
$751$	37.0217			1.35094			0.675470	+	0.737387i	$0.263941\pi$
$752$		0			0
$753$		−	20.7096i		−	0.754700i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	30.4305	+	30.4305i	1.10601	+	1.10601i	0.993669	+	0.112345i	$0.0358361\pi$
$757$	30.4305	+	30.4305i	1.10601	+	1.10601i	0.112345	+	0.993669i	$0.464164\pi$
$758$		0			0
$759$			6.33235i			0.229850i
$760$		0			0
$761$		−	43.1054i		−	1.56257i	−0.624174	−	0.781285i	$-0.714564\pi$
$761$		−	43.1054i		−	1.56257i	0.624174	−	0.781285i	$-0.285436\pi$
$762$		0			0
$763$	8.49827	+	8.49827i	0.307658	+	0.307658i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			21.9815i			0.793705i
$768$		0			0
$769$	31.2507			1.12693			0.563465	−	0.826140i	$-0.309468\pi$
$769$	31.2507			1.12693			0.563465	+	0.826140i	$0.309468\pi$
$770$		0			0
$771$	4.69682	+	4.69682i	0.169152	+	0.169152i
$772$		0			0
$773$	24.4047	+	24.4047i	0.877778	+	0.877778i	0.993304	−	0.115527i	$-0.0368556\pi$
$773$	24.4047	+	24.4047i	0.877778	+	0.877778i	−0.115527	+	0.993304i	$0.536856\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	6.07970			0.218108
$778$		0			0
$779$	−13.5439	+	13.5439i	−0.485261	+	0.485261i
$780$		0			0
$781$	1.73085	+	1.73085i	0.0619345	+	0.0619345i
$782$		0			0
$783$			52.5036i			1.87632i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	17.2122	−	17.2122i	0.613549	−	0.613549i	−0.330320	−	0.943869i	$-0.607157\pi$
$787$	17.2122	−	17.2122i	0.613549	−	0.613549i	0.943869	+	0.330320i	$0.107157\pi$
$788$		0			0
$789$	21.0206	−	21.0206i	0.748354	−	0.748354i
$790$		0			0
$791$		−	2.91480i		−	0.103638i
$792$		0			0
$793$	5.33662			0.189509
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−20.3220	+	20.3220i	−0.719841	+	0.719841i	−0.968573	−	0.248731i	$-0.919986\pi$
$797$	−20.3220	+	20.3220i	−0.719841	+	0.719841i	0.248731	+	0.968573i	$0.419986\pi$
$798$		0			0
$799$	−43.3192			−1.53252
$800$		0			0
$801$	8.83319			0.312105
$802$		0			0
$803$	−1.03191	+	1.03191i	−0.0364153	+	0.0364153i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−35.2405			−1.24052
$808$		0			0
$809$		−	2.80407i		−	0.0985859i	−0.998784	−	0.0492930i	$-0.984303\pi$
$809$		−	2.80407i		−	0.0985859i	0.998784	−	0.0492930i	$-0.0156968\pi$
$810$		0			0
$811$	7.29902	−	7.29902i	0.256303	−	0.256303i	−0.567246	−	0.823549i	$-0.691991\pi$
$811$	7.29902	−	7.29902i	0.256303	−	0.256303i	0.823549	+	0.567246i	$0.191991\pi$
$812$		0			0
$813$	3.78605	−	3.78605i	0.132782	−	0.132782i
$814$		0			0
$815$		0			0
$816$		0			0
$817$			21.5643i			0.754439i
$818$		0			0
$819$	−2.32615	−	2.32615i	−0.0812823	−	0.0812823i
$820$		0			0
$821$	−10.0517	+	10.0517i	−0.350806	+	0.350806i	−0.860409	−	0.509603i	$-0.829792\pi$
$821$	−10.0517	+	10.0517i	−0.350806	+	0.350806i	0.509603	+	0.860409i	$0.329792\pi$
$822$		0			0
$823$	−34.2064			−1.19236			−0.596179	−	0.802851i	$-0.703315\pi$
$823$	−34.2064			−1.19236			−0.596179	+	0.802851i	$0.703315\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	31.3455	+	31.3455i	1.08999	+	1.08999i	0.995529	+	0.0944595i	$0.0301123\pi$
$827$	31.3455	+	31.3455i	1.08999	+	1.08999i	0.0944595	+	0.995529i	$0.469888\pi$
$828$		0			0
$829$	3.87895	+	3.87895i	0.134722	+	0.134722i	0.771252	−	0.636530i	$-0.219631\pi$
$829$	3.87895	+	3.87895i	0.134722	+	0.134722i	−0.636530	+	0.771252i	$0.719631\pi$
$830$		0			0
$831$	−33.2978			−1.15509
$832$		0			0
$833$		−	30.9849i		−	1.07356i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	26.9445	+	26.9445i	0.931338	+	0.931338i
$838$		0			0
$839$		−	32.9463i		−	1.13743i	−0.822533	−	0.568717i	$-0.807440\pi$
$839$		−	32.9463i		−	1.13743i	0.822533	−	0.568717i	$-0.192560\pi$
$840$		0			0
$841$			57.5644i			1.98498i
$842$		0			0
$843$	−5.73915	−	5.73915i	−0.197667	−	0.197667i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			15.9272i			0.547267i
$848$		0			0
$849$	4.92309			0.168960
$850$		0			0
$851$	14.0478	+	14.0478i	0.481553	+	0.481553i
$852$		0			0
$853$	1.87566	+	1.87566i	0.0642212	+	0.0642212i	0.738488	−	0.674267i	$-0.235540\pi$
$853$	1.87566	+	1.87566i	0.0642212	+	0.0642212i	−0.674267	+	0.738488i	$0.735540\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.1714			−0.791521			−0.395760	−	0.918354i	$-0.629519\pi$
$857$	−23.1714			−0.791521			−0.395760	+	0.918354i	$0.629519\pi$
$858$		0			0
$859$	−10.5073	+	10.5073i	−0.358506	+	0.358506i	−0.863262	−	0.504756i	$-0.831582\pi$
$859$	−10.5073	+	10.5073i	−0.358506	+	0.358506i	0.504756	+	0.863262i	$0.331582\pi$
$860$		0			0
$861$	−11.9967	−	11.9967i	−0.408846	−	0.408846i
$862$		0			0
$863$		−	25.2777i		−	0.860463i	−0.902719	−	0.430231i	$-0.858432\pi$
$863$		−	25.2777i		−	0.860463i	0.902719	−	0.430231i	$-0.141568\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−26.3878	+	26.3878i	−0.896177	+	0.896177i
$868$		0			0
$869$	−4.94039	+	4.94039i	−0.167591	+	0.167591i
$870$		0			0
$871$		−	23.6073i		−	0.799901i
$872$		0			0
$873$	−15.1912			−0.514144
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.7350	+	16.7350i	−0.565101	+	0.565101i	−0.930752	−	0.365651i	$-0.880846\pi$
$877$	−16.7350	+	16.7350i	−0.565101	+	0.565101i	0.365651	+	0.930752i	$0.380846\pi$
$878$		0			0
$879$	39.8957			1.34565
$880$		0			0
$881$	9.38791			0.316287			0.158143	−	0.987416i	$-0.449449\pi$
$881$	9.38791			0.316287			0.158143	+	0.987416i	$0.449449\pi$
$882$		0			0
$883$	−21.5593	+	21.5593i	−0.725527	+	0.725527i	−0.969725	−	0.244198i	$-0.921475\pi$
$883$	−21.5593	+	21.5593i	−0.725527	+	0.725527i	0.244198	+	0.969725i	$0.421475\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	48.2072			1.61864			0.809320	−	0.587368i	$-0.199836\pi$
$887$	48.2072			1.61864			0.809320	+	0.587368i	$0.199836\pi$
$888$		0			0
$889$			1.97256i			0.0661577i
$890$		0			0
$891$	−2.45016	+	2.45016i	−0.0820834	+	0.0820834i
$892$		0			0
$893$	11.6941	−	11.6941i	0.391327	−	0.391327i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			27.7830i			0.927648i
$898$		0			0
$899$	44.4243	+	44.4243i	1.48163	+	1.48163i
$900$		0			0
$901$	34.4607	−	34.4607i	1.14805	−	1.14805i
$902$		0			0
$903$	−19.1008			−0.635636
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−31.8381	−	31.8381i	−1.05717	−	1.05717i	−0.998264	−	0.0589044i	$-0.981239\pi$
$907$	−31.8381	−	31.8381i	−1.05717	−	1.05717i	−0.0589044	−	0.998264i	$-0.518761\pi$
$908$		0			0
$909$	−0.870707	−	0.870707i	−0.0288795	−	0.0288795i
$910$		0			0
$911$	−14.8669			−0.492561			−0.246281	−	0.969199i	$-0.579209\pi$
$911$	−14.8669			−0.492561			−0.246281	+	0.969199i	$0.579209\pi$
$912$		0			0
$913$		−	2.38244i		−	0.0788472i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.54197	−	1.54197i	−0.0509202	−	0.0509202i
$918$		0			0
$919$		−	5.27591i		−	0.174036i	−0.996207	−	0.0870181i	$-0.972266\pi$
$919$		−	5.27591i		−	0.174036i	0.996207	−	0.0870181i	$-0.0277338\pi$
$920$		0			0
$921$		−	41.4515i		−	1.36587i
$922$		0			0
$923$	7.59404	+	7.59404i	0.249961	+	0.249961i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			0.799487i			0.0262586i
$928$		0			0
$929$	9.13997			0.299873			0.149936	−	0.988696i	$-0.452093\pi$
$929$	9.13997			0.299873			0.149936	+	0.988696i	$0.452093\pi$
$930$		0			0
$931$	8.36441	+	8.36441i	0.274133	+	0.274133i
$932$		0			0
$933$	−5.96229	−	5.96229i	−0.195197	−	0.195197i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	19.0036			0.620819			0.310410	−	0.950603i	$-0.399534\pi$
$937$	19.0036			0.620819			0.310410	+	0.950603i	$0.399534\pi$
$938$		0			0
$939$	−0.221119	+	0.221119i	−0.00721596	+	0.00721596i
$940$		0			0
$941$	1.48322	+	1.48322i	0.0483517	+	0.0483517i	0.730869	−	0.682518i	$-0.239115\pi$
$941$	1.48322	+	1.48322i	0.0483517	+	0.0483517i	−0.682518	+	0.730869i	$0.739115\pi$
$942$		0			0
$943$		−	55.4393i		−	1.80535i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.97577	−	3.97577i	0.129195	−	0.129195i	−0.639552	−	0.768748i	$-0.720880\pi$
$947$	3.97577	−	3.97577i	0.129195	−	0.129195i	0.768748	+	0.639552i	$0.220880\pi$
$948$		0			0
$949$	−4.52747	+	4.52747i	−0.146968	+	0.146968i
$950$		0			0
$951$		−	6.68870i		−	0.216896i
$952$		0			0
$953$	16.5970			0.537628			0.268814	−	0.963192i	$-0.413368\pi$
$953$	16.5970			0.537628			0.268814	+	0.963192i	$0.413368\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−5.79179	+	5.79179i	−0.187222	+	0.187222i
$958$		0			0
$959$	5.62092			0.181509
$960$		0			0
$961$	14.5965			0.470855
$962$		0			0
$963$	6.02809	−	6.02809i	0.194252	−	0.194252i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	8.72635			0.280621			0.140310	−	0.990108i	$-0.455190\pi$
$967$	8.72635			0.280621			0.140310	+	0.990108i	$0.455190\pi$
$968$		0			0
$969$		−	23.7921i		−	0.764311i
$970$		0			0
$971$	14.5421	−	14.5421i	0.466677	−	0.466677i	−0.434159	−	0.900836i	$-0.642955\pi$
$971$	14.5421	−	14.5421i	0.466677	−	0.466677i	0.900836	+	0.434159i	$0.142955\pi$
$972$		0			0
$973$	19.3799	−	19.3799i	0.621289	−	0.621289i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	25.2020i		−	0.806284i	−0.915137	−	0.403142i	$-0.867918\pi$
$977$		−	25.2020i		−	0.806284i	0.915137	−	0.403142i	$-0.132082\pi$
$978$		0			0
$979$	4.46723	+	4.46723i	0.142773	+	0.142773i
$980$		0			0
$981$	−4.75212	+	4.75212i	−0.151724	+	0.151724i
$982$		0			0
$983$	4.00157			0.127630			0.0638151	−	0.997962i	$-0.479673\pi$
$983$	4.00157			0.127630			0.0638151	+	0.997962i	$0.479673\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	10.3582	+	10.3582i	0.329704	+	0.329704i
$988$		0			0
$989$	−44.1346	−	44.1346i	−1.40340	−	1.40340i
$990$		0			0
$991$	62.3391			1.98027			0.990134	−	0.140127i	$-0.0447510\pi$
$991$	62.3391			1.98027			0.990134	+	0.140127i	$0.0447510\pi$
$992$		0			0
$993$			45.8201i			1.45406i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−21.6855	−	21.6855i	−0.686787	−	0.686787i	0.274733	−	0.961521i	$-0.411410\pi$
$997$	−21.6855	−	21.6855i	−0.686787	−	0.686787i	−0.961521	+	0.274733i	$0.911410\pi$
$998$		0			0
$999$			15.5861i			0.493121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.f.849.5		12
4.3	odd	2		400.2.q.f.349.4		12
5.2	odd	4		1600.2.l.f.401.2		12
5.3	odd	4		1600.2.l.g.401.5		12
5.4	even	2		1600.2.q.e.849.2		12
16.5	even	4		1600.2.q.e.49.2		12
16.11	odd	4		400.2.q.e.149.3		12
20.3	even	4		400.2.l.f.301.1	yes	12
20.7	even	4		400.2.l.g.301.6	yes	12
20.19	odd	2		400.2.q.e.349.3		12
80.27	even	4		400.2.l.g.101.6	yes	12
80.37	odd	4		1600.2.l.f.1201.2		12
80.43	even	4		400.2.l.f.101.1	✓	12
80.53	odd	4		1600.2.l.g.1201.5		12
80.59	odd	4		400.2.q.f.149.4		12
80.69	even	4	inner	1600.2.q.f.49.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.1	✓	12	80.43	even	4
400.2.l.f.301.1	yes	12	20.3	even	4
400.2.l.g.101.6	yes	12	80.27	even	4
400.2.l.g.301.6	yes	12	20.7	even	4
400.2.q.e.149.3		12	16.11	odd	4
400.2.q.e.349.3		12	20.19	odd	2
400.2.q.f.149.4		12	80.59	odd	4
400.2.q.f.349.4		12	4.3	odd	2
1600.2.l.f.401.2		12	5.2	odd	4
1600.2.l.f.1201.2		12	80.37	odd	4
1600.2.l.g.401.5		12	5.3	odd	4
1600.2.l.g.1201.5		12	80.53	odd	4
1600.2.q.e.49.2		12	16.5	even	4
1600.2.q.e.849.2		12	5.4	even	2
1600.2.q.f.49.5		12	80.69	even	4	inner
1600.2.q.f.849.5		12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.03997 - 1.03997i) q^{3} +1.49668 q^{7} +0.836925i q^{9} +O(q^{10})\)	\(q+(1.03997 - 1.03997i) q^{3} +1.49668 q^{7} +0.836925i q^{9} +(-0.423260 + 0.423260i) q^{11} +(-1.85704 + 1.85704i) q^{13} +6.50950i q^{17} +(-1.75725 - 1.75725i) q^{19} +(1.55650 - 1.55650i) q^{21} +7.19295 q^{23} +(3.99029 + 3.99029i) q^{27} +(6.57892 + 6.57892i) q^{29} +6.75252 q^{31} +0.880355i q^{33} +(1.95300 + 1.95300i) q^{37} +3.86254i q^{39} -7.70745i q^{41} +(-6.13581 - 6.13581i) q^{43} +6.65476i q^{47} -4.75994 q^{49} +(6.76969 + 6.76969i) q^{51} +(-5.29390 - 5.29390i) q^{53} -3.65497 q^{57} +(5.91841 - 5.91841i) q^{59} +(-1.43686 - 1.43686i) q^{61} +1.25261i q^{63} +(-6.35614 + 6.35614i) q^{67} +(7.48045 - 7.48045i) q^{69} -4.08932i q^{71} +2.43800 q^{73} +(-0.633485 + 0.633485i) q^{77} +11.6722 q^{79} +5.78878 q^{81} +(-2.81439 + 2.81439i) q^{83} +13.6838 q^{87} -10.5543i q^{89} +(-2.77940 + 2.77940i) q^{91} +(7.02242 - 7.02242i) q^{93} +18.1512i q^{97} +(-0.354237 - 0.354237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 12 q^{7}+O(q^{10}) \) 12 * q + 2 * q^3 - 12 * q^7	\( 12 q + 2 q^{3} - 12 q^{7} + 2 q^{11} + 4 q^{13} - 14 q^{19} - 20 q^{21} - 12 q^{23} - 10 q^{27} + 4 q^{31} - 8 q^{37} - 4 q^{49} - 10 q^{51} - 16 q^{53} - 16 q^{57} + 20 q^{59} + 4 q^{61} - 50 q^{67} + 40 q^{73} - 8 q^{77} + 12 q^{79} - 8 q^{81} - 2 q^{83} + 64 q^{87} + 44 q^{93} + 12 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 - 12 * q^7 + 2 * q^11 + 4 * q^13 - 14 * q^19 - 20 * q^21 - 12 * q^23 - 10 * q^27 + 4 * q^31 - 8 * q^37 - 4 * q^49 - 10 * q^51 - 16 * q^53 - 16 * q^57 + 20 * q^59 + 4 * q^61 - 50 * q^67 + 40 * q^73 - 8 * q^77 + 12 * q^79 - 8 * q^81 - 2 * q^83 + 64 * q^87 + 44 * q^93 + 12 * q^99

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