LMFDB - Embedded newform 1600.2.q.e.849.2

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			849.2
Root			$1.35979 - 0.388551i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.e.49.2

$q$-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	−0.940426	−	0.339999i	$-0.889573\pi$
$3$	−1.03997	+	1.03997i	−0.600427	+	0.600427i	0.339999	+	0.940426i	$0.389573\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.49668			−0.565693			−0.282846	−	0.959165i	$-0.591279\pi$
$7$	−1.49668			−0.565693			−0.282846	+	0.959165i	$0.591279\pi$
$8$		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	−0.401019	−	0.916070i	$-0.631344\pi$
$13$	1.85704	−	1.85704i	0.515051	−	0.515051i	0.916070	+	0.401019i	$0.131344\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	6.50950i		−	1.57879i	−0.613888	−	0.789393i	$-0.710395\pi$
$17$		−	6.50950i		−	1.57879i	0.613888	−	0.789393i	$-0.289605\pi$
$18$		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	$-0.769906\pi$
$23$	−7.19295			−1.49983			−0.749917	+	0.661532i	$0.769906\pi$
$24$		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	0.528107	−	0.849178i	$-0.322902\pi$
$37$	−1.95300	−	1.95300i	−0.321071	−	0.321071i	−0.849178	+	0.528107i	$0.822902\pi$
$38$		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	0.998054	−	0.0623522i	$-0.0198602\pi$
$43$	6.13581	+	6.13581i	0.935702	+	0.935702i	−0.0623522	+	0.998054i	$0.519860\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	6.65476i		−	0.970697i	−0.874321	−	0.485348i	$-0.838693\pi$
$47$		−	6.65476i		−	0.970697i	0.874321	−	0.485348i	$-0.161307\pi$
$48$		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	0.970056	−	0.242882i	$-0.0780929\pi$
$53$	5.29390	+	5.29390i	0.727173	+	0.727173i	−0.242882	+	0.970056i	$0.578093\pi$
$54$		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	−0.202712	−	0.979238i	$-0.564976\pi$
$67$	6.35614	−	6.35614i	0.776526	−	0.776526i	0.979238	+	0.202712i	$0.0649756\pi$
$68$		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	$-0.545570\pi$
$73$	−2.43800			−0.285346			−0.142673	+	0.989770i	$0.545570\pi$
$74$		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	−0.535571	−	0.844490i	$-0.679904\pi$
$83$	2.81439	−	2.81439i	0.308919	−	0.308919i	0.844490	+	0.535571i	$0.179904\pi$
$84$		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	$-0.626975\pi$
$97$		−	18.1512i		−	1.84298i	0.388407	−	0.921488i	$-0.373025\pi$
$98$		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	$-0.514986\pi$
$103$	−0.955267			−0.0941253			−0.0470626	+	0.998892i	$0.514986\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.20266	+	7.20266i	0.696308	+	0.696308i	0.963612	−	0.267305i	$-0.0861330\pi$
$107$	7.20266	+	7.20266i	0.696308	+	0.696308i	−0.267305	+	0.963612i	$0.586133\pi$
$108$		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	$0.0291991\pi$
$113$			1.94751i			0.183206i	−0.995796	+	0.0916029i	$0.970801\pi$
$114$		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	$-0.981376\pi$
$127$		−	1.31796i		−	0.116950i	0.998289	−	0.0584750i	$-0.0186238\pi$
$128$		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	$-0.551288\pi$
$137$	−3.75559			−0.320862			−0.160431	+	0.987047i	$0.551288\pi$
$138$		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	−0.889470	−	0.456994i	$-0.848926\pi$
$157$	−5.41891	+	5.41891i	−0.432476	+	0.432476i	0.456994	+	0.889470i	$0.348926\pi$
$158$		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	−0.406608	−	0.913603i	$-0.633289\pi$
$163$	6.47288	−	6.47288i	0.506995	−	0.506995i	0.913603	+	0.406608i	$0.133289\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.29734			0.642068			0.321034	−	0.947068i	$-0.395970\pi$
$167$	8.29734			0.642068			0.321034	+	0.947068i	$0.395970\pi$
$168$		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	−0.996105	−	0.0881700i	$-0.971898\pi$
$173$	−11.9420	+	11.9420i	−0.907935	+	0.907935i	0.0881700	+	0.996105i	$0.471898\pi$
$174$		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	$-0.648512\pi$
$193$		−	24.8152i		−	1.78624i	0.449820	−	0.893119i	$-0.351488\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.81324	+	2.81324i	0.200435	+	0.200435i	0.800186	−	0.599751i	$-0.204734\pi$
$197$	2.81324	+	2.81324i	0.200435	+	0.200435i	−0.599751	+	0.800186i	$0.704734\pi$
$198$		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	$0.0850758\pi$
$223$			7.88779i			0.528205i	−0.964495	+	0.264103i	$0.914924\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.98838	−	5.98838i	0.397463	−	0.397463i	−0.479874	−	0.877337i	$-0.659318\pi$
$227$	5.98838	−	5.98838i	0.397463	−	0.397463i	0.877337	+	0.479874i	$0.159318\pi$
$228$		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	$-0.471946\pi$
$233$	2.68717			0.176042			0.0880212	+	0.996119i	$0.471946\pi$
$234$		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	$-0.955013\pi$
$257$		−	4.51630i		−	0.281719i	0.990030	−	0.140860i	$-0.0449866\pi$
$258$		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	$-0.714162\pi$
$263$	−20.2127			−1.24637			−0.623185	+	0.782075i	$0.714162\pi$
$264$		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	0.999300	−	0.0374115i	$-0.0119112\pi$
$277$	16.0090	+	16.0090i	0.961888	+	0.961888i	−0.0374115	+	0.999300i	$0.511911\pi$
$278$		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	0.633249	−	0.773949i	$-0.281721\pi$
$283$	−2.36694	−	2.36694i	−0.140700	−	0.140700i	−0.773949	+	0.633249i	$0.781721\pi$
$284$		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	$-0.958848\pi$
$293$	−19.1812	−	19.1812i	−1.12058	−	1.12058i	−0.128922	−	0.991655i	$-0.541152\pi$
$294$		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	$0.547447\pi$
$307$	−19.9292	+	19.9292i	−1.13742	+	1.13742i	−0.988911	+	0.148507i	$0.952553\pi$
$308$		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	$-0.498087\pi$
$313$	0.212621			0.0120180			0.00600902	+	0.999982i	$0.498087\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.21582	+	3.21582i	−0.180618	+	0.180618i	−0.791625	−	0.611007i	$-0.790765\pi$
$317$	−3.21582	+	3.21582i	−0.180618	+	0.180618i	0.611007	+	0.791625i	$0.290765\pi$
$318$		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	$0.0987847\pi$
$337$			11.2122i			0.610767i	−0.952229	+	0.305384i	$0.901215\pi$
$338$		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	0.739518	−	0.673137i	$-0.235054\pi$
$347$	1.23653	+	1.23653i	0.0663803	+	0.0663803i	−0.673137	+	0.739518i	$0.735054\pi$
$348$		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	$0.00634270\pi$
$353$			0.748709i			0.0398497i	−0.999801	+	0.0199249i	$0.993657\pi$
$354$		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	$0.180790\pi$
$367$			20.6101i			1.07584i	−0.842996	+	0.537920i	$0.819210\pi$
$368$		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	0.829660	−	0.558269i	$-0.188534\pi$
$373$	5.24143	+	5.24143i	0.271391	+	0.271391i	−0.558269	+	0.829660i	$0.688534\pi$
$374$		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	$-0.728164\pi$
$383$		−	29.5087i		−	1.50782i	0.656975	−	0.753912i	$-0.271836\pi$
$384$		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	$-0.465289\pi$
$397$	21.9750	−	21.9750i	1.10289	−	1.10289i	0.994060	−	0.108832i	$-0.0347111\pi$
$398$		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	$0.0944667\pi$
$433$			12.1705i			0.584877i	−0.956284	+	0.292439i	$0.905533\pi$
$434$		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	0.787920	−	0.615778i	$-0.211158\pi$
$443$	3.62318	+	3.62318i	0.172142	+	0.172142i	−0.615778	+	0.787920i	$0.711158\pi$
$444$		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	$-0.608586\pi$
$457$	−14.3039			−0.669108			−0.334554	+	0.942377i	$0.608586\pi$
$458$		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	$0.148446\pi$
$463$			19.3500i			0.899271i	−0.893212	+	0.449636i	$0.851554\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.1773	+	17.1773i	−0.794871	+	0.794871i	−0.982282	−	0.187410i	$-0.939991\pi$
$467$	−17.1773	+	17.1773i	−0.794871	+	0.794871i	0.187410	+	0.982282i	$0.439991\pi$
$468$		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	$-0.244808\pi$
$487$	31.7138			1.43709			0.718546	+	0.695480i	$0.244808\pi$
$488$		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	$-0.560238\pi$
$503$	−8.43795			−0.376230			−0.188115	+	0.982147i	$0.560238\pi$
$504$		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	0.893923	−	0.448220i	$-0.147942\pi$
$523$	10.1929	+	10.1929i	0.445703	+	0.445703i	−0.448220	+	0.893923i	$0.647942\pi$
$524$		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	−0.111935	−	0.993716i	$-0.535705\pi$
$547$	20.6231	−	20.6231i	0.881781	−	0.881781i	0.993716	+	0.111935i	$0.0357048\pi$
$548$		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	−0.679356	−	0.733809i	$-0.737741\pi$
$557$	1.28512	−	1.28512i	0.0544523	−	0.0544523i	0.733809	+	0.679356i	$0.237741\pi$
$558$		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	−0.997283	−	0.0736677i	$-0.976530\pi$
$563$	−21.9152	+	21.9152i	−0.923615	+	0.923615i	0.0736677	+	0.997283i	$0.476530\pi$
$564$		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	$-0.983847\pi$
$577$		−	2.43681i		−	0.101446i	0.998713	−	0.0507230i	$-0.0161526\pi$
$578$		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	0.698470	−	0.715639i	$-0.253865\pi$
$587$	−0.415982	−	0.415982i	−0.0171694	−	0.0171694i	−0.715639	+	0.698470i	$0.753865\pi$
$588$		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	$0.102021\pi$
$593$			15.3439i			0.630098i	−0.949075	+	0.315049i	$0.897979\pi$
$594$		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	$0.250588\pi$
$607$			34.9068i			1.41682i	−0.705800	+	0.708412i	$0.749412\pi$
$608$		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	0.710165	−	0.704035i	$-0.248620\pi$
$613$	0.151779	+	0.151779i	0.00613031	+	0.00613031i	−0.704035	+	0.710165i	$0.748620\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.288199			0.0116025			0.00580123	−	0.999983i	$-0.498153\pi$
$617$	0.288199			0.0116025			0.00580123	+	0.999983i	$0.498153\pi$
$618$		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	−0.583422	−	0.812169i	$-0.698287\pi$
$643$	5.80043	−	5.80043i	0.228747	−	0.228747i	0.812169	+	0.583422i	$0.198287\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	46.3186			1.82097			0.910485	−	0.413541i	$-0.135708\pi$
$647$	46.3186			1.82097			0.910485	+	0.413541i	$0.135708\pi$
$648$		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	−0.788343	−	0.615236i	$-0.789061\pi$
$653$	−4.42354	+	4.42354i	−0.173106	+	0.173106i	0.615236	+	0.788343i	$0.289061\pi$
$654$		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	$0.116436\pi$
$673$			18.5586i			0.715382i	−0.933840	+	0.357691i	$0.883564\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.71844	−	2.71844i	−0.104478	−	0.104478i	0.652935	−	0.757414i	$-0.273537\pi$
$677$	−2.71844	−	2.71844i	−0.104478	−	0.104478i	−0.757414	+	0.652935i	$0.773537\pi$
$678$		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	0.421999	−	0.906596i	$-0.361329\pi$
$683$	−12.6646	−	12.6646i	−0.484598	−	0.484598i	−0.906596	+	0.421999i	$0.861329\pi$
$684$		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	$-0.524430\pi$
$727$	−4.13463			−0.153345			−0.0766724	+	0.997056i	$0.524430\pi$
$728$		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	−0.967775	−	0.251817i	$-0.918972\pi$
$733$	−19.3838	+	19.3838i	−0.715957	+	0.715957i	0.251817	+	0.967775i	$0.418972\pi$
$734$		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	$-0.439215\pi$
$743$	10.3473			0.379604			0.189802	+	0.981822i	$0.439215\pi$
$744$		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	$-0.964164\pi$
$757$	−30.4305	−	30.4305i	−1.10601	−	1.10601i	−0.112345	−	0.993669i	$-0.535836\pi$
$758$		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	0.115527	−	0.993304i	$-0.463144\pi$
$773$	−24.4047	−	24.4047i	−0.877778	−	0.877778i	−0.993304	+	0.115527i	$0.963144\pi$
$774$		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	−0.943869	−	0.330320i	$-0.892843\pi$
$787$	−17.2122	+	17.2122i	−0.613549	+	0.613549i	0.330320	+	0.943869i	$0.392843\pi$
$788$		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	−0.248731	−	0.968573i	$-0.580014\pi$
$797$	20.3220	−	20.3220i	0.719841	−	0.719841i	0.968573	+	0.248731i	$0.0800136\pi$
$798$		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	$-0.296685\pi$
$823$	34.2064			1.19236			0.596179	+	0.802851i	$0.296685\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−31.3455	−	31.3455i	−1.08999	−	1.08999i	−0.995529	−	0.0944595i	$-0.969888\pi$
$827$	−31.3455	−	31.3455i	−1.08999	−	1.08999i	−0.0944595	−	0.995529i	$-0.530112\pi$
$828$		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	0.674267	−	0.738488i	$-0.264460\pi$
$853$	−1.87566	−	1.87566i	−0.0642212	−	0.0642212i	−0.738488	+	0.674267i	$0.764460\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.1714			0.791521			0.395760	−	0.918354i	$-0.370481\pi$
$857$	23.1714			0.791521			0.395760	+	0.918354i	$0.370481\pi$
$858$		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	$0.141568\pi$
$863$			25.2777i			0.860463i	−0.902719	+	0.430231i	$0.858432\pi$
$864$		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	−0.365651	−	0.930752i	$-0.619154\pi$
$877$	16.7350	−	16.7350i	0.565101	−	0.565101i	0.930752	+	0.365651i	$0.119154\pi$
$878$		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	−0.244198	−	0.969725i	$-0.578525\pi$
$883$	21.5593	−	21.5593i	0.725527	−	0.725527i	0.969725	+	0.244198i	$0.0785248\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−48.2072			−1.61864			−0.809320	−	0.587368i	$-0.800164\pi$
$887$	−48.2072			−1.61864			−0.809320	+	0.587368i	$0.800164\pi$
$888$		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	$0.0187607\pi$
$907$	31.8381	+	31.8381i	1.05717	+	1.05717i	0.0589044	+	0.998264i	$0.481239\pi$
$908$		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	$-0.600466\pi$
$937$	−19.0036			−0.620819			−0.310410	+	0.950603i	$0.600466\pi$
$938$		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	−0.768748	−	0.639552i	$-0.779120\pi$
$947$	−3.97577	+	3.97577i	−0.129195	+	0.129195i	0.639552	+	0.768748i	$0.279120\pi$
$948$		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	$-0.586632\pi$
$953$	−16.5970			−0.537628			−0.268814	+	0.963192i	$0.586632\pi$
$954$		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	$-0.544810\pi$
$967$	−8.72635			−0.280621			−0.140310	+	0.990108i	$0.544810\pi$
$968$		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	$0.132082\pi$
$977$			25.2020i			0.806284i	−0.915137	+	0.403142i	$0.867918\pi$
$978$		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	$-0.520327\pi$
$983$	−4.00157			−0.127630			−0.0638151	+	0.997962i	$0.520327\pi$
$984$		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	0.961521	−	0.274733i	$-0.0885895\pi$
$997$	21.6855	+	21.6855i	0.686787	+	0.686787i	−0.274733	+	0.961521i	$0.588590\pi$
$998$		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.e.849.2		12
4.3	odd	2		400.2.q.e.349.3		12
5.2	odd	4		1600.2.l.g.401.5		12
5.3	odd	4		1600.2.l.f.401.2		12
5.4	even	2		1600.2.q.f.849.5		12
16.5	even	4		1600.2.q.f.49.5		12
16.11	odd	4		400.2.q.f.149.4		12
20.3	even	4		400.2.l.g.301.6	yes	12
20.7	even	4		400.2.l.f.301.1	yes	12
20.19	odd	2		400.2.q.f.349.4		12
80.27	even	4		400.2.l.f.101.1	✓	12
80.37	odd	4		1600.2.l.g.1201.5		12
80.43	even	4		400.2.l.g.101.6	yes	12
80.53	odd	4		1600.2.l.f.1201.2		12
80.59	odd	4		400.2.q.e.149.3		12
80.69	even	4	inner	1600.2.q.e.49.2		12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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