LMFDB - Embedded newform 1600.2.s.d.207.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(207,1600)]

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([2, 1, 1]))

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.s (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:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			207.8
Root			$1.41303 + 0.0578659i$ of defining polynomial
Character	$\chi$	$=$	1600.207
Dual form			1600.2.s.d.943.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.96251 q^{3} +(-1.60205 - 1.60205i) q^{7} +0.851447 q^{9} +O(q^{10})$	$q+1.96251 q^{3} +(-1.60205 - 1.60205i) q^{7} +0.851447 q^{9} +(-0.754587 + 0.754587i) q^{11} -5.94580i q^{13} +(-1.95574 - 1.95574i) q^{17} +(-0.780680 + 0.780680i) q^{19} +(-3.14404 - 3.14404i) q^{21} +(4.93121 - 4.93121i) q^{23} -4.21656 q^{27} +(-1.44802 - 1.44802i) q^{29} +3.60859i q^{31} +(-1.48089 + 1.48089i) q^{33} -10.2364i q^{37} -11.6687i q^{39} -6.93334i q^{41} +9.91344i q^{43} +(0.104270 - 0.104270i) q^{47} -1.86688i q^{49} +(-3.83816 - 3.83816i) q^{51} +4.03213 q^{53} +(-1.53209 + 1.53209i) q^{57} +(3.46736 + 3.46736i) q^{59} +(0.680578 - 0.680578i) q^{61} +(-1.36406 - 1.36406i) q^{63} -9.04721i q^{67} +(9.67754 - 9.67754i) q^{69} +3.64007 q^{71} +(2.94030 + 2.94030i) q^{73} +2.41777 q^{77} -10.7140 q^{79} -10.8294 q^{81} -4.23845 q^{83} +(-2.84176 - 2.84176i) q^{87} +0.0426256 q^{89} +(-9.52546 + 9.52546i) q^{91} +7.08189i q^{93} +(1.91173 + 1.91173i) q^{97} +(-0.642491 + 0.642491i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q + 2 * q^7 + 10 * q^9	$ 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.96251			1.13306			0.566528	−	0.824043i	$-0.308286\pi$
$3$	1.96251			1.13306			0.566528	+	0.824043i	$0.308286\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.60205	−	1.60205i	−0.605517	−	0.605517i	0.336254	−	0.941771i	$-0.390840\pi$
$7$	−1.60205	−	1.60205i	−0.605517	−	0.605517i	−0.941771	+	0.336254i	$0.890840\pi$
$8$		0			0
$9$	0.851447			0.283816
$10$		0			0
$11$	−0.754587	+	0.754587i	−0.227517	+	0.227517i	−0.811654	−	0.584138i	$-0.801433\pi$
$11$	−0.754587	+	0.754587i	−0.227517	+	0.227517i	0.584138	+	0.811654i	$0.301433\pi$
$12$		0			0
$13$		−	5.94580i		−	1.64907i	−0.565812	−	0.824534i	$-0.691437\pi$
$13$		−	5.94580i		−	1.64907i	0.565812	−	0.824534i	$-0.308563\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.95574	−	1.95574i	−0.474336	−	0.474336i	0.428978	−	0.903315i	$-0.358874\pi$
$17$	−1.95574	−	1.95574i	−0.474336	−	0.474336i	−0.903315	+	0.428978i	$0.858874\pi$
$18$		0			0
$19$	−0.780680	+	0.780680i	−0.179100	+	0.179100i	−0.790964	−	0.611863i	$-0.790420\pi$
$19$	−0.780680	+	0.780680i	−0.179100	+	0.179100i	0.611863	+	0.790964i	$0.290420\pi$
$20$		0			0
$21$	−3.14404	−	3.14404i	−0.686085	−	0.686085i
$22$		0			0
$23$	4.93121	−	4.93121i	1.02823	−	1.02823i	0.0286378	−	0.999590i	$-0.490883\pi$
$23$	4.93121	−	4.93121i	1.02823	−	1.02823i	0.999590	−	0.0286378i	$-0.00911693\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.21656			−0.811477
$28$		0			0
$29$	−1.44802	−	1.44802i	−0.268891	−	0.268891i	0.559762	−	0.828653i	$-0.310892\pi$
$29$	−1.44802	−	1.44802i	−0.268891	−	0.268891i	−0.828653	+	0.559762i	$0.810892\pi$
$30$		0			0
$31$			3.60859i			0.648121i	0.946036	+	0.324061i	$0.105048\pi$
$31$			3.60859i			0.648121i	−0.946036	+	0.324061i	$0.894952\pi$
$32$		0			0
$33$	−1.48089	+	1.48089i	−0.257789	+	0.257789i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	10.2364i		−	1.68285i	−0.540371	−	0.841427i	$-0.681716\pi$
$37$		−	10.2364i		−	1.68285i	0.540371	−	0.841427i	$-0.318284\pi$
$38$		0			0
$39$		−	11.6687i		−	1.86849i
$40$		0			0
$41$		−	6.93334i		−	1.08281i	−0.840763	−	0.541403i	$-0.817893\pi$
$41$		−	6.93334i		−	1.08281i	0.840763	−	0.541403i	$-0.182107\pi$
$42$		0			0
$43$			9.91344i			1.51179i	0.654695	+	0.755893i	$0.272797\pi$
$43$			9.91344i			1.51179i	−0.654695	+	0.755893i	$0.727203\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.104270	−	0.104270i	0.0152093	−	0.0152093i	−0.699461	−	0.714671i	$-0.746577\pi$
$47$	0.104270	−	0.104270i	0.0152093	−	0.0152093i	0.714671	+	0.699461i	$0.246577\pi$
$48$		0			0
$49$		−	1.86688i		−	0.266698i
$50$		0			0
$51$	−3.83816	−	3.83816i	−0.537450	−	0.537450i
$52$		0			0
$53$	4.03213			0.553856			0.276928	−	0.960891i	$-0.410684\pi$
$53$	4.03213			0.553856			0.276928	+	0.960891i	$0.410684\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.53209	+	1.53209i	−0.202931	+	0.202931i
$58$		0			0
$59$	3.46736	+	3.46736i	0.451412	+	0.451412i	0.895823	−	0.444411i	$-0.146587\pi$
$59$	3.46736	+	3.46736i	0.451412	+	0.451412i	−0.444411	+	0.895823i	$0.646587\pi$
$60$		0			0
$61$	0.680578	−	0.680578i	0.0871391	−	0.0871391i	−0.662194	−	0.749333i	$-0.730374\pi$
$61$	0.680578	−	0.680578i	0.0871391	−	0.0871391i	0.749333	+	0.662194i	$0.230374\pi$
$62$		0			0
$63$	−1.36406	−	1.36406i	−0.171855	−	0.171855i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	9.04721i		−	1.10529i	−0.833416	−	0.552646i	$-0.813618\pi$
$67$		−	9.04721i		−	1.10529i	0.833416	−	0.552646i	$-0.186382\pi$
$68$		0			0
$69$	9.67754	−	9.67754i	1.16504	−	1.16504i
$70$		0			0
$71$	3.64007			0.431997			0.215998	−	0.976394i	$-0.430699\pi$
$71$	3.64007			0.431997			0.215998	+	0.976394i	$0.430699\pi$
$72$		0			0
$73$	2.94030	+	2.94030i	0.344136	+	0.344136i	0.857920	−	0.513784i	$-0.171757\pi$
$73$	2.94030	+	2.94030i	0.344136	+	0.344136i	−0.513784	+	0.857920i	$0.671757\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.41777			0.275530
$78$		0			0
$79$	−10.7140			−1.20542			−0.602711	−	0.797960i	$-0.705913\pi$
$79$	−10.7140			−1.20542			−0.602711	+	0.797960i	$0.705913\pi$
$80$		0			0
$81$	−10.8294			−1.20326
$82$		0			0
$83$	−4.23845			−0.465230			−0.232615	−	0.972569i	$-0.574728\pi$
$83$	−4.23845			−0.465230			−0.232615	+	0.972569i	$0.574728\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.84176	−	2.84176i	−0.304668	−	0.304668i
$88$		0			0
$89$	0.0426256			0.00451831			0.00225915	−	0.999997i	$-0.499281\pi$
$89$	0.0426256			0.00451831			0.00225915	+	0.999997i	$0.499281\pi$
$90$		0			0
$91$	−9.52546	+	9.52546i	−0.998539	+	0.998539i
$92$		0			0
$93$			7.08189i			0.734358i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.91173	+	1.91173i	0.194106	+	0.194106i	0.797468	−	0.603362i	$-0.206172\pi$
$97$	1.91173	+	1.91173i	0.194106	+	0.194106i	−0.603362	+	0.797468i	$0.706172\pi$
$98$		0			0
$99$	−0.642491	+	0.642491i	−0.0645728	+	0.0645728i
$100$		0			0
$101$	4.96537	+	4.96537i	0.494073	+	0.494073i	0.909587	−	0.415514i	$-0.136398\pi$
$101$	4.96537	+	4.96537i	0.494073	+	0.494073i	−0.415514	+	0.909587i	$0.636398\pi$
$102$		0			0
$103$	0.442220	−	0.442220i	0.0435733	−	0.0435733i	−0.684984	−	0.728558i	$-0.740191\pi$
$103$	0.442220	−	0.442220i	0.0435733	−	0.0435733i	0.728558	+	0.684984i	$0.240191\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	17.5924			1.70072			0.850359	−	0.526204i	$-0.176385\pi$
$107$	17.5924			1.70072			0.850359	+	0.526204i	$0.176385\pi$
$108$		0			0
$109$	0.345161	+	0.345161i	0.0330605	+	0.0330605i	0.723444	−	0.690383i	$-0.242558\pi$
$109$	0.345161	+	0.345161i	0.0330605	+	0.0330605i	−0.690383	+	0.723444i	$0.742558\pi$
$110$		0			0
$111$		−	20.0890i		−	1.90677i
$112$		0			0
$113$	5.43662	−	5.43662i	0.511435	−	0.511435i	−0.403531	−	0.914966i	$-0.632217\pi$
$113$	5.43662	−	5.43662i	0.511435	−	0.511435i	0.914966	+	0.403531i	$0.132217\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	5.06253i		−	0.468031i
$118$		0			0
$119$			6.26638i			0.574438i
$120$		0			0
$121$			9.86120i			0.896472i
$122$		0			0
$123$		−	13.6067i		−	1.22688i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.27150	+	6.27150i	−0.556505	+	0.556505i	−0.928311	−	0.371805i	$-0.878739\pi$
$127$	−6.27150	+	6.27150i	−0.556505	+	0.556505i	0.371805	+	0.928311i	$0.378739\pi$
$128$		0			0
$129$			19.4552i			1.71294i
$130$		0			0
$131$	−1.61521	−	1.61521i	−0.141122	−	0.141122i	0.633017	−	0.774138i	$-0.281816\pi$
$131$	−1.61521	−	1.61521i	−0.141122	−	0.141122i	−0.774138	+	0.633017i	$0.781816\pi$
$132$		0			0
$133$	2.50138			0.216897
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.83585	+	6.83585i	−0.584026	+	0.584026i	−0.936007	−	0.351981i	$-0.885508\pi$
$137$	−6.83585	+	6.83585i	−0.584026	+	0.584026i	0.351981	+	0.936007i	$0.385508\pi$
$138$		0			0
$139$	13.7427	+	13.7427i	1.16564	+	1.16564i	0.983220	+	0.182423i	$0.0583940\pi$
$139$	13.7427	+	13.7427i	1.16564	+	1.16564i	0.182423	+	0.983220i	$0.441606\pi$
$140$		0			0
$141$	0.204631	−	0.204631i	0.0172330	−	0.0172330i
$142$		0			0
$143$	4.48662	+	4.48662i	0.375190	+	0.375190i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	3.66378i		−	0.302184i
$148$		0			0
$149$	−1.73811	+	1.73811i	−0.142391	+	0.142391i	−0.774709	−	0.632318i	$-0.782104\pi$
$149$	−1.73811	+	1.73811i	−0.142391	+	0.142391i	0.632318	+	0.774709i	$0.282104\pi$
$150$		0			0
$151$	−5.83522			−0.474864			−0.237432	−	0.971404i	$-0.576306\pi$
$151$	−5.83522			−0.474864			−0.237432	+	0.971404i	$0.576306\pi$
$152$		0			0
$153$	−1.66521	−	1.66521i	−0.134624	−	0.134624i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.14732			−0.251183			−0.125592	−	0.992082i	$-0.540083\pi$
$157$	−3.14732			−0.251183			−0.125592	+	0.992082i	$0.540083\pi$
$158$		0			0
$159$	7.91310			0.627550
$160$		0			0
$161$	−15.8001			−1.24522
$162$		0			0
$163$	7.82117			0.612601			0.306301	−	0.951935i	$-0.400909\pi$
$163$	7.82117			0.612601			0.306301	+	0.951935i	$0.400909\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.88460	−	9.88460i	−0.764893	−	0.764893i	0.212309	−	0.977203i	$-0.431902\pi$
$167$	−9.88460	−	9.88460i	−0.764893	−	0.764893i	−0.977203	+	0.212309i	$0.931902\pi$
$168$		0			0
$169$	−22.3525			−1.71942
$170$		0			0
$171$	−0.664708	+	0.664708i	−0.0508315	+	0.0508315i
$172$		0			0
$173$			3.49245i			0.265526i	0.991148	+	0.132763i	$0.0423849\pi$
$173$			3.49245i			0.265526i	−0.991148	+	0.132763i	$0.957615\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.80473	+	6.80473i	0.511475	+	0.511475i
$178$		0			0
$179$	13.0809	−	13.0809i	0.977713	−	0.977713i	−0.0220444	−	0.999757i	$-0.507018\pi$
$179$	13.0809	−	13.0809i	0.977713	−	0.977713i	0.999757	+	0.0220444i	$0.00701753\pi$
$180$		0			0
$181$	13.6393	+	13.6393i	1.01380	+	1.01380i	0.999903	+	0.0138952i	$0.00442312\pi$
$181$	13.6393	+	13.6393i	1.01380	+	1.01380i	0.0138952	+	0.999903i	$0.495577\pi$
$182$		0			0
$183$	1.33564	−	1.33564i	0.0987335	−	0.0987335i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.95155			0.215839
$188$		0			0
$189$	6.75513	+	6.75513i	0.491363	+	0.491363i
$190$		0			0
$191$		−	2.92523i		−	0.211662i	−0.994384	−	0.105831i	$-0.966250\pi$
$191$		−	2.92523i		−	0.211662i	0.994384	−	0.105831i	$-0.0337503\pi$
$192$		0			0
$193$	−0.0830702	+	0.0830702i	−0.00597953	+	0.00597953i	−0.710090	−	0.704111i	$-0.751346\pi$
$193$	−0.0830702	+	0.0830702i	−0.00597953	+	0.00597953i	0.704111	+	0.710090i	$0.251346\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	7.80487i		−	0.556074i	−0.960570	−	0.278037i	$-0.910316\pi$
$197$		−	7.80487i		−	0.556074i	0.960570	−	0.278037i	$-0.0896838\pi$
$198$		0			0
$199$		−	10.9740i		−	0.777924i	−0.921254	−	0.388962i	$-0.872834\pi$
$199$		−	10.9740i		−	0.777924i	0.921254	−	0.388962i	$-0.127166\pi$
$200$		0			0
$201$		−	17.7552i		−	1.25236i
$202$		0			0
$203$			4.63960i			0.325636i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.19866	−	4.19866i	0.291827	−	0.291827i
$208$		0			0
$209$		−	1.17818i		−	0.0814966i
$210$		0			0
$211$	8.92204	+	8.92204i	0.614218	+	0.614218i	0.944042	−	0.329824i	$-0.106989\pi$
$211$	8.92204	+	8.92204i	0.614218	+	0.614218i	−0.329824	+	0.944042i	$0.606989\pi$
$212$		0			0
$213$	7.14367			0.489477
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.78113	−	5.78113i	0.392449	−	0.392449i
$218$		0			0
$219$	5.77037	+	5.77037i	0.389926	+	0.389926i
$220$		0			0
$221$	−11.6284	+	11.6284i	−0.782213	+	0.782213i
$222$		0			0
$223$	−13.1678	−	13.1678i	−0.881784	−	0.881784i	0.111931	−	0.993716i	$-0.464296\pi$
$223$	−13.1678	−	13.1678i	−0.881784	−	0.881784i	−0.993716	+	0.111931i	$0.964296\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			19.3432i			1.28385i	0.766766	+	0.641927i	$0.221865\pi$
$227$			19.3432i			1.28385i	−0.766766	+	0.641927i	$0.778135\pi$
$228$		0			0
$229$	13.2143	−	13.2143i	0.873223	−	0.873223i	−0.119599	−	0.992822i	$-0.538161\pi$
$229$	13.2143	−	13.2143i	0.873223	−	0.873223i	0.992822	+	0.119599i	$0.0381610\pi$
$230$		0			0
$231$	4.74490			0.312191
$232$		0			0
$233$	−20.6884	−	20.6884i	−1.35534	−	1.35534i	−0.879570	−	0.475769i	$-0.842170\pi$
$233$	−20.6884	−	20.6884i	−1.35534	−	1.35534i	−0.475769	−	0.879570i	$-0.657830\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−21.0264			−1.36581
$238$		0			0
$239$	−14.1053			−0.912395			−0.456198	−	0.889878i	$-0.650789\pi$
$239$	−14.1053			−0.912395			−0.456198	+	0.889878i	$0.650789\pi$
$240$		0			0
$241$	12.8011			0.824592			0.412296	−	0.911050i	$-0.364727\pi$
$241$	12.8011			0.824592			0.412296	+	0.911050i	$0.364727\pi$
$242$		0			0
$243$	−8.60310			−0.551889
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.64177	+	4.64177i	0.295349	+	0.295349i
$248$		0			0
$249$	−8.31800			−0.527132
$250$		0			0
$251$	6.84118	−	6.84118i	0.431812	−	0.431812i	−0.457433	−	0.889244i	$-0.651231\pi$
$251$	6.84118	−	6.84118i	0.431812	−	0.431812i	0.889244	+	0.457433i	$0.151231\pi$
$252$		0			0
$253$			7.44205i			0.467878i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.66524	+	6.66524i	0.415766	+	0.415766i	0.883742	−	0.467975i	$-0.155016\pi$
$257$	6.66524	+	6.66524i	0.415766	+	0.415766i	−0.467975	+	0.883742i	$0.655016\pi$
$258$		0			0
$259$	−16.3992	+	16.3992i	−1.01900	+	1.01900i
$260$		0			0
$261$	−1.23291	−	1.23291i	−0.0763154	−	0.0763154i
$262$		0			0
$263$	−7.32015	+	7.32015i	−0.451380	+	0.451380i	−0.895812	−	0.444432i	$-0.853405\pi$
$263$	−7.32015	+	7.32015i	−0.451380	+	0.451380i	0.444432	+	0.895812i	$0.353405\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.0836533			0.00511950
$268$		0			0
$269$	−15.9801	−	15.9801i	−0.974321	−	0.974321i	0.0253576	−	0.999678i	$-0.491928\pi$
$269$	−15.9801	−	15.9801i	−0.974321	−	0.974321i	−0.999678	+	0.0253576i	$0.991928\pi$
$270$		0			0
$271$			3.59684i			0.218492i	0.994015	+	0.109246i	$0.0348437\pi$
$271$			3.59684i			0.218492i	−0.994015	+	0.109246i	$0.965156\pi$
$272$		0			0
$273$	−18.6938	+	18.6938i	−1.13140	+	1.13140i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			20.9416i			1.25826i	0.777300	+	0.629131i	$0.216589\pi$
$277$			20.9416i			1.25826i	−0.777300	+	0.629131i	$0.783411\pi$
$278$		0			0
$279$			3.07252i			0.183947i
$280$		0			0
$281$		−	3.26699i		−	0.194892i	−0.995241	−	0.0974462i	$-0.968933\pi$
$281$		−	3.26699i		−	0.194892i	0.995241	−	0.0974462i	$-0.0310674\pi$
$282$		0			0
$283$		0	0.000151619i		0	9.01279e-6i	−1.00000		4.50640e-6i	$-0.999999\pi$
$283$		0	0.000151619i		0	9.01279e-6i	1.00000		4.50640e-6i	$-1.43443e-6\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.1075	+	11.1075i	−0.655657	+	0.655657i
$288$		0			0
$289$		−	9.35017i		−	0.550010i
$290$		0			0
$291$	3.75178	+	3.75178i	0.219933	+	0.219933i
$292$		0			0
$293$	11.0593			0.646091			0.323045	−	0.946384i	$-0.395293\pi$
$293$	11.0593			0.646091			0.323045	+	0.946384i	$0.395293\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.18176	−	3.18176i	0.184624	−	0.184624i
$298$		0			0
$299$	−29.3200	−	29.3200i	−1.69562	−	1.69562i
$300$		0			0
$301$	15.8818	−	15.8818i	0.915413	−	0.915413i
$302$		0			0
$303$	9.74459	+	9.74459i	0.559812	+	0.559812i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			15.1317i			0.863613i	0.901966	+	0.431806i	$0.142124\pi$
$307$			15.1317i			0.863613i	−0.901966	+	0.431806i	$0.857876\pi$
$308$		0			0
$309$	0.867862	−	0.867862i	0.0493709	−	0.0493709i
$310$		0			0
$311$	27.1556			1.53985			0.769925	−	0.638134i	$-0.220293\pi$
$311$	27.1556			1.53985			0.769925	+	0.638134i	$0.220293\pi$
$312$		0			0
$313$	13.6695	+	13.6695i	0.772646	+	0.772646i	0.978568	−	0.205922i	$-0.0660194\pi$
$313$	13.6695	+	13.6695i	0.772646	+	0.772646i	−0.205922	+	0.978568i	$0.566019\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.8314			1.45084			0.725419	−	0.688307i	$-0.241646\pi$
$317$	25.8314			1.45084			0.725419	+	0.688307i	$0.241646\pi$
$318$		0			0
$319$	2.18532			0.122354
$320$		0			0
$321$	34.5252			1.92701
$322$		0			0
$323$	3.05361			0.169908
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.677383	+	0.677383i	0.0374594	+	0.0374594i
$328$		0			0
$329$	−0.334091			−0.0184190
$330$		0			0
$331$	13.6207	−	13.6207i	0.748659	−	0.748659i	−0.225568	−	0.974227i	$-0.572424\pi$
$331$	13.6207	−	13.6207i	0.748659	−	0.748659i	0.974227	+	0.225568i	$0.0724239\pi$
$332$		0			0
$333$		−	8.71576i		−	0.477621i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−16.0911	−	16.0911i	−0.876536	−	0.876536i	0.116638	−	0.993174i	$-0.462788\pi$
$337$	−16.0911	−	16.0911i	−0.876536	−	0.876536i	−0.993174	+	0.116638i	$0.962788\pi$
$338$		0			0
$339$	10.6694	−	10.6694i	0.579484	−	0.579484i
$340$		0			0
$341$	−2.72299	−	2.72299i	−0.147458	−	0.147458i
$342$		0			0
$343$	−14.2052	+	14.2052i	−0.767007	+	0.767007i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.57562			0.299315			0.149658	−	0.988738i	$-0.452183\pi$
$347$	5.57562			0.299315			0.149658	+	0.988738i	$0.452183\pi$
$348$		0			0
$349$	15.0811	+	15.0811i	0.807273	+	0.807273i	0.984220	−	0.176947i	$-0.0566222\pi$
$349$	15.0811	+	15.0811i	0.807273	+	0.807273i	−0.176947	+	0.984220i	$0.556622\pi$
$350$		0			0
$351$			25.0708i			1.33818i
$352$		0			0
$353$	−2.57880	+	2.57880i	−0.137256	+	0.137256i	−0.772397	−	0.635141i	$-0.780942\pi$
$353$	−2.57880	+	2.57880i	−0.137256	+	0.137256i	0.635141	+	0.772397i	$0.280942\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			12.2978i			0.650870i
$358$		0			0
$359$			5.77227i			0.304649i	0.988331	+	0.152324i	$0.0486758\pi$
$359$			5.77227i			0.304649i	−0.988331	+	0.152324i	$0.951324\pi$
$360$		0			0
$361$			17.7811i			0.935846i
$362$		0			0
$363$			19.3527i			1.01575i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.30496	−	8.30496i	0.433516	−	0.433516i	−0.456307	−	0.889822i	$-0.650828\pi$
$367$	8.30496	−	8.30496i	0.433516	−	0.433516i	0.889822	+	0.456307i	$0.150828\pi$
$368$		0			0
$369$		−	5.90337i		−	0.307317i
$370$		0			0
$371$	−6.45967	−	6.45967i	−0.335369	−	0.335369i
$372$		0			0
$373$	−16.0484			−0.830953			−0.415477	−	0.909604i	$-0.636385\pi$
$373$	−16.0484			−0.830953			−0.415477	+	0.909604i	$0.636385\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.60964	+	8.60964i	−0.443419	+	0.443419i
$378$		0			0
$379$	8.91367	+	8.91367i	0.457865	+	0.457865i	0.897954	−	0.440089i	$-0.145053\pi$
$379$	8.91367	+	8.91367i	0.457865	+	0.457865i	−0.440089	+	0.897954i	$0.645053\pi$
$380$		0			0
$381$	−12.3079	+	12.3079i	−0.630552	+	0.630552i
$382$		0			0
$383$	−24.8928	−	24.8928i	−1.27196	−	1.27196i	−0.945057	−	0.326904i	$-0.893995\pi$
$383$	−24.8928	−	24.8928i	−1.27196	−	1.27196i	−0.326904	−	0.945057i	$-0.606005\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			8.44078i			0.429069i
$388$		0			0
$389$	−16.5819	+	16.5819i	−0.840738	+	0.840738i	−0.988955	−	0.148217i	$-0.952647\pi$
$389$	−16.5819	+	16.5819i	−0.840738	+	0.840738i	0.148217	+	0.988955i	$0.452647\pi$
$390$		0			0
$391$	−19.2883			−0.975452
$392$		0			0
$393$	−3.16987	−	3.16987i	−0.159899	−	0.159899i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	8.62531			0.432892			0.216446	−	0.976295i	$-0.430553\pi$
$397$	8.62531			0.432892			0.216446	+	0.976295i	$0.430553\pi$
$398$		0			0
$399$	4.90897			0.245756
$400$		0			0
$401$	19.7107			0.984307			0.492153	−	0.870508i	$-0.336210\pi$
$401$	19.7107			0.984307			0.492153	+	0.870508i	$0.336210\pi$
$402$		0			0
$403$	21.4559			1.06880
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.72426	+	7.72426i	0.382877	+	0.382877i
$408$		0			0
$409$	26.7930			1.32483			0.662414	−	0.749138i	$-0.269532\pi$
$409$	26.7930			1.32483			0.662414	+	0.749138i	$0.269532\pi$
$410$		0			0
$411$	−13.4154	+	13.4154i	−0.661734	+	0.661734i
$412$		0			0
$413$		−	11.1098i		−	0.546675i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	26.9702	+	26.9702i	1.32074	+	1.32074i
$418$		0			0
$419$	−11.0752	+	11.0752i	−0.541061	+	0.541061i	−0.923840	−	0.382779i	$-0.874967\pi$
$419$	−11.0752	+	11.0752i	−0.541061	+	0.541061i	0.382779	+	0.923840i	$0.374967\pi$
$420$		0			0
$421$	−0.243092	−	0.243092i	−0.0118476	−	0.0118476i	0.701158	−	0.713006i	$-0.252667\pi$
$421$	−0.243092	−	0.243092i	−0.0118476	−	0.0118476i	−0.713006	+	0.701158i	$0.752667\pi$
$422$		0			0
$423$	0.0887804	−	0.0887804i	0.00431665	−	0.00431665i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.18064			−0.105528
$428$		0			0
$429$	8.80505	+	8.80505i	0.425112	+	0.425112i
$430$		0			0
$431$			20.7024i			0.997200i	0.866832	+	0.498600i	$0.166152\pi$
$431$			20.7024i			0.997200i	−0.866832	+	0.498600i	$0.833848\pi$
$432$		0			0
$433$	5.68221	−	5.68221i	0.273069	−	0.273069i	−0.557265	−	0.830335i	$-0.688149\pi$
$433$	5.68221	−	5.68221i	0.273069	−	0.273069i	0.830335	+	0.557265i	$0.188149\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			7.69939i			0.368312i
$438$		0			0
$439$			18.7902i			0.896808i	0.893831	+	0.448404i	$0.148007\pi$
$439$			18.7902i			0.896808i	−0.893831	+	0.448404i	$0.851993\pi$
$440$		0			0
$441$		−	1.58955i		−	0.0756930i
$442$		0			0
$443$		−	12.1641i		−	0.577934i	−0.957339	−	0.288967i	$-0.906688\pi$
$443$		−	12.1641i		−	0.577934i	0.957339	−	0.288967i	$-0.0933119\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−3.41105	+	3.41105i	−0.161337	+	0.161337i
$448$		0			0
$449$			27.2708i			1.28699i	0.765452	+	0.643493i	$0.222516\pi$
$449$			27.2708i			1.28699i	−0.765452	+	0.643493i	$0.777484\pi$
$450$		0			0
$451$	5.23181	+	5.23181i	0.246356	+	0.246356i
$452$		0			0
$453$	−11.4517			−0.538047
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.7514	+	19.7514i	−0.923933	+	0.923933i	−0.997305	−	0.0733714i	$-0.976624\pi$
$457$	−19.7514	+	19.7514i	−0.923933	+	0.923933i	0.0733714	+	0.997305i	$0.476624\pi$
$458$		0			0
$459$	8.24649	+	8.24649i	0.384913	+	0.384913i
$460$		0			0
$461$	12.9262	−	12.9262i	0.602035	−	0.602035i	−0.338818	−	0.940852i	$-0.610027\pi$
$461$	12.9262	−	12.9262i	0.602035	−	0.602035i	0.940852	+	0.338818i	$0.110027\pi$
$462$		0			0
$463$	14.5647	+	14.5647i	0.676879	+	0.676879i	0.959293	−	0.282414i	$-0.0911351\pi$
$463$	14.5647	+	14.5647i	0.676879	+	0.676879i	−0.282414	+	0.959293i	$0.591135\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	42.3556i		−	1.95998i	−0.199040	−	0.979991i	$-0.563782\pi$
$467$		−	42.3556i		−	1.95998i	0.199040	−	0.979991i	$-0.436218\pi$
$468$		0			0
$469$	−14.4941	+	14.4941i	−0.669274	+	0.669274i
$470$		0			0
$471$	−6.17665			−0.284605
$472$		0			0
$473$	−7.48056	−	7.48056i	−0.343956	−	0.343956i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.43315			0.157193
$478$		0			0
$479$	−27.0905			−1.23780			−0.618899	−	0.785470i	$-0.712421\pi$
$479$	−27.0905			−1.23780			−0.618899	+	0.785470i	$0.712421\pi$
$480$		0			0
$481$	−60.8636			−2.77514
$482$		0			0
$483$	−31.0078			−1.41090
$484$		0			0
$485$		0			0
$486$		0			0
$487$	21.9674	+	21.9674i	0.995436	+	0.995436i	0.999990	−	0.00455390i	$-0.00144956\pi$
$487$	21.9674	+	21.9674i	0.995436	+	0.995436i	−0.00455390	+	0.999990i	$0.501450\pi$
$488$		0			0
$489$	15.3491			0.694111
$490$		0			0
$491$	6.11955	−	6.11955i	0.276171	−	0.276171i	−0.555407	−	0.831579i	$-0.687438\pi$
$491$	6.11955	−	6.11955i	0.276171	−	0.276171i	0.831579	+	0.555407i	$0.187438\pi$
$492$		0			0
$493$			5.66390i			0.255089i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.83157	−	5.83157i	−0.261581	−	0.261581i
$498$		0			0
$499$	−15.4115	+	15.4115i	−0.689914	+	0.689914i	−0.962213	−	0.272298i	$-0.912216\pi$
$499$	−15.4115	+	15.4115i	−0.689914	+	0.689914i	0.272298	+	0.962213i	$0.412216\pi$
$500$		0			0
$501$	−19.3986	−	19.3986i	−0.866667	−	0.866667i
$502$		0			0
$503$	26.4312	−	26.4312i	1.17851	−	1.17851i	0.198387	−	0.980124i	$-0.436430\pi$
$503$	26.4312	−	26.4312i	1.17851	−	1.17851i	0.980124	−	0.198387i	$-0.0635704\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−43.8671			−1.94820
$508$		0			0
$509$	−0.233714	−	0.233714i	−0.0103592	−	0.0103592i	0.701908	−	0.712267i	$-0.252332\pi$
$509$	−0.233714	−	0.233714i	−0.0103592	−	0.0103592i	−0.712267	+	0.701908i	$0.752332\pi$
$510$		0			0
$511$		−	9.42101i		−	0.416761i
$512$		0			0
$513$	3.29178	−	3.29178i	0.145336	−	0.145336i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			0.157362i			0.00692075i
$518$		0			0
$519$			6.85397i			0.300856i
$520$		0			0
$521$		−	4.50147i		−	0.197213i	−0.995127	−	0.0986064i	$-0.968562\pi$
$521$		−	4.50147i		−	0.197213i	0.995127	−	0.0986064i	$-0.0314385\pi$
$522$		0			0
$523$			12.6042i			0.551141i	0.961281	+	0.275571i	$0.0888668\pi$
$523$			12.6042i			0.551141i	−0.961281	+	0.275571i	$0.911133\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.05746	−	7.05746i	0.307428	−	0.307428i
$528$		0			0
$529$		−	25.6336i		−	1.11450i
$530$		0			0
$531$	2.95227	+	2.95227i	0.128118	+	0.128118i
$532$		0			0
$533$	−41.2242			−1.78562
$534$		0			0
$535$		0			0
$536$		0			0
$537$	25.6714	−	25.6714i	1.10780	−	1.10780i
$538$		0			0
$539$	1.40873	+	1.40873i	0.0606782	+	0.0606782i
$540$		0			0
$541$	14.5013	−	14.5013i	0.623459	−	0.623459i	−0.322955	−	0.946414i	$-0.604676\pi$
$541$	14.5013	−	14.5013i	0.623459	−	0.623459i	0.946414	+	0.322955i	$0.104676\pi$
$542$		0			0
$543$	26.7672	+	26.7672i	1.14869	+	1.14869i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			30.2936i			1.29526i	0.761955	+	0.647630i	$0.224240\pi$
$547$			30.2936i			1.29526i	−0.761955	+	0.647630i	$0.775760\pi$
$548$		0			0
$549$	0.579476	−	0.579476i	0.0247314	−	0.0247314i
$550$		0			0
$551$	2.26088			0.0963169
$552$		0			0
$553$	17.1644	+	17.1644i	0.729904	+	0.729904i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.72758			0.412171			0.206085	−	0.978534i	$-0.433928\pi$
$557$	9.72758			0.412171			0.206085	+	0.978534i	$0.433928\pi$
$558$		0			0
$559$	58.9433			2.49304
$560$		0			0
$561$	5.79245			0.244557
$562$		0			0
$563$	−17.7853			−0.749562			−0.374781	−	0.927113i	$-0.622282\pi$
$563$	−17.7853			−0.749562			−0.374781	+	0.927113i	$0.622282\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	17.3492	+	17.3492i	0.728597	+	0.728597i
$568$		0			0
$569$	15.7897			0.661938			0.330969	−	0.943642i	$-0.392624\pi$
$569$	15.7897			0.661938			0.330969	+	0.943642i	$0.392624\pi$
$570$		0			0
$571$	−23.3108	+	23.3108i	−0.975528	+	0.975528i	−0.999708	−	0.0241793i	$-0.992303\pi$
$571$	−23.3108	+	23.3108i	−0.975528	+	0.975528i	0.0241793	+	0.999708i	$0.492303\pi$
$572$		0			0
$573$		−	5.74079i		−	0.239825i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−25.7383	−	25.7383i	−1.07150	−	1.07150i	−0.997239	−	0.0742597i	$-0.976341\pi$
$577$	−25.7383	−	25.7383i	−1.07150	−	1.07150i	−0.0742597	−	0.997239i	$-0.523659\pi$
$578$		0			0
$579$	−0.163026	+	0.163026i	−0.00677514	+	0.00677514i
$580$		0			0
$581$	6.79020	+	6.79020i	0.281705	+	0.281705i
$582$		0			0
$583$	−3.04260	+	3.04260i	−0.126011	+	0.126011i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.1327			0.954790			0.477395	−	0.878689i	$-0.341581\pi$
$587$	23.1327			0.954790			0.477395	+	0.878689i	$0.341581\pi$
$588$		0			0
$589$	−2.81715	−	2.81715i	−0.116079	−	0.116079i
$590$		0			0
$591$		−	15.3171i		−	0.630063i
$592$		0			0
$593$	25.5047	−	25.5047i	1.04735	−	1.04735i	0.0485322	−	0.998822i	$-0.484546\pi$
$593$	25.5047	−	25.5047i	1.04735	−	1.04735i	0.998822	−	0.0485322i	$-0.0154543\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	21.5365i		−	0.881432i
$598$		0			0
$599$		−	11.0699i		−	0.452304i	−0.974092	−	0.226152i	$-0.927385\pi$
$599$		−	11.0699i		−	0.452304i	0.974092	−	0.226152i	$-0.0726146\pi$
$600$		0			0
$601$			13.7579i			0.561197i	0.959825	+	0.280599i	$0.0905330\pi$
$601$			13.7579i			0.561197i	−0.959825	+	0.280599i	$0.909467\pi$
$602$		0			0
$603$		−	7.70322i		−	0.313700i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−18.4675	+	18.4675i	−0.749573	+	0.749573i	−0.974399	−	0.224826i	$-0.927819\pi$
$607$	−18.4675	+	18.4675i	−0.749573	+	0.749573i	0.224826	+	0.974399i	$0.427819\pi$
$608$		0			0
$609$			9.10526i			0.368964i
$610$		0			0
$611$	−0.619968	−	0.619968i	−0.0250812	−	0.0250812i
$612$		0			0
$613$	11.6810			0.471790			0.235895	−	0.971779i	$-0.424198\pi$
$613$	11.6810			0.471790			0.235895	+	0.971779i	$0.424198\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	29.1000	−	29.1000i	1.17152	−	1.17152i	0.189677	−	0.981847i	$-0.439256\pi$
$617$	29.1000	−	29.1000i	1.17152	−	1.17152i	0.981847	−	0.189677i	$-0.0607441\pi$
$618$		0			0
$619$	−4.23279	−	4.23279i	−0.170130	−	0.170130i	0.616906	−	0.787036i	$-0.288386\pi$
$619$	−4.23279	−	4.23279i	−0.170130	−	0.170130i	−0.787036	+	0.616906i	$0.788386\pi$
$620$		0			0
$621$	−20.7927	+	20.7927i	−0.834383	+	0.834383i
$622$		0			0
$623$	−0.0682883	−	0.0682883i	−0.00273591	−	0.00273591i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		−	2.31220i		−	0.0923402i
$628$		0			0
$629$	−20.0197	+	20.0197i	−0.798239	+	0.798239i
$630$		0			0
$631$	1.33886			0.0532991			0.0266496	−	0.999645i	$-0.491516\pi$
$631$	1.33886			0.0532991			0.0266496	+	0.999645i	$0.491516\pi$
$632$		0			0
$633$	17.5096	+	17.5096i	0.695944	+	0.695944i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−11.1001			−0.439803
$638$		0			0
$639$	3.09933			0.122608
$640$		0			0
$641$	24.5069			0.967965			0.483982	−	0.875078i	$-0.339190\pi$
$641$	24.5069			0.967965			0.483982	+	0.875078i	$0.339190\pi$
$642$		0			0
$643$	−10.8979			−0.429771			−0.214885	−	0.976639i	$-0.568938\pi$
$643$	−10.8979			−0.429771			−0.214885	+	0.976639i	$0.568938\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.6612	−	11.6612i	−0.458448	−	0.458448i	0.439698	−	0.898146i	$-0.355085\pi$
$647$	−11.6612	−	11.6612i	−0.458448	−	0.458448i	−0.898146	+	0.439698i	$0.855085\pi$
$648$		0			0
$649$	−5.23285			−0.205407
$650$		0			0
$651$	11.3455	−	11.3455i	0.444666	−	0.444666i
$652$		0			0
$653$			5.28393i			0.206776i	0.994641	+	0.103388i	$0.0329684\pi$
$653$			5.28393i			0.206776i	−0.994641	+	0.103388i	$0.967032\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.50351	+	2.50351i	0.0976713	+	0.0976713i
$658$		0			0
$659$	16.2902	−	16.2902i	0.634578	−	0.634578i	−0.314635	−	0.949213i	$-0.601882\pi$
$659$	16.2902	−	16.2902i	0.634578	−	0.634578i	0.949213	+	0.314635i	$0.101882\pi$
$660$		0			0
$661$	−12.7924	−	12.7924i	−0.497566	−	0.497566i	0.413114	−	0.910679i	$-0.364441\pi$
$661$	−12.7924	−	12.7924i	−0.497566	−	0.497566i	−0.910679	+	0.413114i	$0.864441\pi$
$662$		0			0
$663$	−22.8209	+	22.8209i	−0.886291	+	0.886291i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−14.2810			−0.552962
$668$		0			0
$669$	−25.8420	−	25.8420i	−0.999111	−	0.999111i
$670$		0			0
$671$			1.02711i			0.0396512i
$672$		0			0
$673$	−11.9553	+	11.9553i	−0.460841	+	0.460841i	−0.898931	−	0.438090i	$-0.855655\pi$
$673$	−11.9553	+	11.9553i	−0.460841	+	0.460841i	0.438090	+	0.898931i	$0.355655\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			3.18699i			0.122486i	0.998123	+	0.0612430i	$0.0195065\pi$
$677$			3.18699i			0.122486i	−0.998123	+	0.0612430i	$0.980494\pi$
$678$		0			0
$679$		−	6.12535i		−	0.235069i
$680$		0			0
$681$			37.9613i			1.45468i
$682$		0			0
$683$		−	35.1661i		−	1.34559i	−0.739827	−	0.672797i	$-0.765093\pi$
$683$		−	35.1661i		−	1.34559i	0.739827	−	0.672797i	$-0.234907\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	25.9331	−	25.9331i	0.989410	−	0.989410i
$688$		0			0
$689$		−	23.9743i		−	0.913346i
$690$		0			0
$691$	−2.90121	−	2.90121i	−0.110367	−	0.110367i	0.649767	−	0.760134i	$-0.274867\pi$
$691$	−2.90121	−	2.90121i	−0.110367	−	0.110367i	−0.760134	+	0.649767i	$0.774867\pi$
$692$		0			0
$693$	2.05860			0.0781999
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−13.5598	+	13.5598i	−0.513614	+	0.513614i
$698$		0			0
$699$	−40.6011	−	40.6011i	−1.53568	−	1.53568i
$700$		0			0
$701$	15.7397	−	15.7397i	0.594481	−	0.594481i	−0.344358	−	0.938839i	$-0.611903\pi$
$701$	15.7397	−	15.7397i	0.594481	−	0.594481i	0.938839	+	0.344358i	$0.111903\pi$
$702$		0			0
$703$	7.99136	+	7.99136i	0.301400	+	0.301400i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	15.9095i		−	0.598339i
$708$		0			0
$709$	1.95755	−	1.95755i	0.0735172	−	0.0735172i	−0.669392	−	0.742909i	$-0.733445\pi$
$709$	1.95755	−	1.95755i	0.0735172	−	0.0735172i	0.742909	+	0.669392i	$0.233445\pi$
$710$		0			0
$711$	−9.12243			−0.342118
$712$		0			0
$713$	17.7947	+	17.7947i	0.666416	+	0.666416i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−27.6818			−1.03379
$718$		0			0
$719$	−0.0658604			−0.00245618			−0.00122809	−	0.999999i	$-0.500391\pi$
$719$	−0.0658604			−0.00245618			−0.00122809	+	0.999999i	$0.500391\pi$
$720$		0			0
$721$	−1.41692			−0.0527687
$722$		0			0
$723$	25.1223			0.934309
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−16.2286	−	16.2286i	−0.601885	−	0.601885i	0.338927	−	0.940813i	$-0.389936\pi$
$727$	−16.2286	−	16.2286i	−0.601885	−	0.601885i	−0.940813	+	0.338927i	$0.889936\pi$
$728$		0			0
$729$	15.6045			0.577943
$730$		0			0
$731$	19.3881	−	19.3881i	0.717095	−	0.717095i
$732$		0			0
$733$		−	0.669106i		−	0.0247140i	−0.999924	−	0.0123570i	$-0.996067\pi$
$733$		−	0.669106i		−	0.0247140i	0.999924	−	0.0123570i	$-0.00393345\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.82691	+	6.82691i	0.251472	+	0.251472i
$738$		0			0
$739$	23.4183	−	23.4183i	0.861454	−	0.861454i	−0.130053	−	0.991507i	$-0.541515\pi$
$739$	23.4183	−	23.4183i	0.861454	−	0.861454i	0.991507	+	0.130053i	$0.0415147\pi$
$740$		0			0
$741$	9.10952	+	9.10952i	0.334647	+	0.334647i
$742$		0			0
$743$	30.0968	−	30.0968i	1.10414	−	1.10414i	0.110238	−	0.993905i	$-0.464839\pi$
$743$	30.0968	−	30.0968i	1.10414	−	1.10414i	0.993905	−	0.110238i	$-0.0351614\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.60882			−0.132040
$748$		0			0
$749$	−28.1838	−	28.1838i	−1.02981	−	1.02981i
$750$		0			0
$751$		−	53.2724i		−	1.94394i	−0.235107	−	0.971970i	$-0.575544\pi$
$751$		−	53.2724i		−	1.94394i	0.235107	−	0.971970i	$-0.424456\pi$
$752$		0			0
$753$	13.4259	−	13.4259i	0.489267	−	0.489267i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			27.1717i			0.987574i	0.869583	+	0.493787i	$0.164388\pi$
$757$			27.1717i			0.987574i	−0.869583	+	0.493787i	$0.835612\pi$
$758$		0			0
$759$			14.6051i			0.530132i
$760$		0			0
$761$		−	12.9068i		−	0.467870i	−0.972252	−	0.233935i	$-0.924840\pi$
$761$		−	12.9068i		−	0.467870i	0.972252	−	0.233935i	$-0.0751604\pi$
$762$		0			0
$763$		−	1.10593i		−	0.0400374i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	20.6162	−	20.6162i	0.744409	−	0.744409i
$768$		0			0
$769$		−	34.4858i		−	1.24359i	−0.783180	−	0.621795i	$-0.786404\pi$
$769$		−	34.4858i		−	1.24359i	0.783180	−	0.621795i	$-0.213596\pi$
$770$		0			0
$771$	13.0806	+	13.0806i	0.471087	+	0.471087i
$772$		0			0
$773$	−26.6789			−0.959574			−0.479787	−	0.877385i	$-0.659286\pi$
$773$	−26.6789			−0.959574			−0.479787	+	0.877385i	$0.659286\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−32.1836	+	32.1836i	−1.15458	+	1.15458i
$778$		0			0
$779$	5.41272	+	5.41272i	0.193931	+	0.193931i
$780$		0			0
$781$	−2.74675	+	2.74675i	−0.0982864	+	0.0982864i
$782$		0			0
$783$	6.10566	+	6.10566i	0.218199	+	0.218199i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	33.2611i		−	1.18563i	−0.805338	−	0.592815i	$-0.798016\pi$
$787$		−	33.2611i		−	1.18563i	0.805338	−	0.592815i	$-0.201984\pi$
$788$		0			0
$789$	−14.3659	+	14.3659i	−0.511439	+	0.511439i
$790$		0			0
$791$	−17.4195			−0.619365
$792$		0			0
$793$	−4.04658	−	4.04658i	−0.143698	−	0.143698i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.9072			−0.563461			−0.281730	−	0.959494i	$-0.590908\pi$
$797$	−15.9072			−0.563461			−0.281730	+	0.959494i	$0.590908\pi$
$798$		0			0
$799$	−0.407850			−0.0144287
$800$		0			0
$801$	0.0362935			0.00128237
$802$		0			0
$803$	−4.43743			−0.156593
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−31.3610	−	31.3610i	−1.10396	−	1.10396i
$808$		0			0
$809$	−12.4922			−0.439204			−0.219602	−	0.975590i	$-0.570476\pi$
$809$	−12.4922			−0.439204			−0.219602	+	0.975590i	$0.570476\pi$
$810$		0			0
$811$	35.4886	−	35.4886i	1.24617	−	1.24617i	0.288777	−	0.957396i	$-0.406751\pi$
$811$	35.4886	−	35.4886i	1.24617	−	1.24617i	0.957396	−	0.288777i	$-0.0932487\pi$
$812$		0			0
$813$			7.05884i			0.247564i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−7.73923	−	7.73923i	−0.270761	−	0.270761i
$818$		0			0
$819$	−8.11042	+	8.11042i	−0.283401	+	0.283401i
$820$		0			0
$821$	−15.9683	−	15.9683i	−0.557299	−	0.557299i	0.371239	−	0.928537i	$-0.378933\pi$
$821$	−15.9683	−	15.9683i	−0.557299	−	0.557299i	−0.928537	+	0.371239i	$0.878933\pi$
$822$		0			0
$823$	−21.7278	+	21.7278i	−0.757384	+	0.757384i	−0.975846	−	0.218462i	$-0.929896\pi$
$823$	−21.7278	+	21.7278i	−0.757384	+	0.757384i	0.218462	+	0.975846i	$0.429896\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−39.2381			−1.36444			−0.682221	−	0.731146i	$-0.738986\pi$
$827$	−39.2381			−1.36444			−0.682221	+	0.731146i	$0.738986\pi$
$828$		0			0
$829$	18.6072	+	18.6072i	0.646254	+	0.646254i	0.952086	−	0.305831i	$-0.0989344\pi$
$829$	18.6072	+	18.6072i	0.646254	+	0.646254i	−0.305831	+	0.952086i	$0.598934\pi$
$830$		0			0
$831$			41.0982i			1.42568i
$832$		0			0
$833$	−3.65114	+	3.65114i	−0.126504	+	0.126504i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	15.2158i		−	0.525935i
$838$		0			0
$839$		−	12.5955i		−	0.434845i	−0.976078	−	0.217422i	$-0.930235\pi$
$839$		−	12.5955i		−	0.434845i	0.976078	−	0.217422i	$-0.0697649\pi$
$840$		0			0
$841$		−	24.8065i		−	0.855396i
$842$		0			0
$843$		−	6.41151i		−	0.220824i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	15.7981	−	15.7981i	0.542829	−	0.542829i
$848$		0			0
$849$		0	0.000297553i		0	1.02120e-5i
$850$		0			0
$851$	−50.4778	−	50.4778i	−1.73036	−	1.73036i
$852$		0			0
$853$	43.6914			1.49597			0.747983	−	0.663718i	$-0.231022\pi$
$853$	43.6914			1.49597			0.747983	+	0.663718i	$0.231022\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.9373	−	28.9373i	0.988478	−	0.988478i	−0.0114561	−	0.999934i	$-0.503647\pi$
$857$	28.9373	−	28.9373i	0.988478	−	0.988478i	0.999934	+	0.0114561i	$0.00364668\pi$
$858$		0			0
$859$	−28.1247	−	28.1247i	−0.959602	−	0.959602i	0.0396134	−	0.999215i	$-0.487387\pi$
$859$	−28.1247	−	28.1247i	−0.959602	−	0.959602i	−0.999215	+	0.0396134i	$0.987387\pi$
$860$		0			0
$861$	−21.7987	+	21.7987i	−0.742896	+	0.742896i
$862$		0			0
$863$	−22.2144	−	22.2144i	−0.756186	−	0.756186i	0.219440	−	0.975626i	$-0.429577\pi$
$863$	−22.2144	−	22.2144i	−0.756186	−	0.756186i	−0.975626	+	0.219440i	$0.929577\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	18.3498i		−	0.623192i
$868$		0			0
$869$	8.08466	−	8.08466i	0.274253	−	0.274253i
$870$		0			0
$871$	−53.7929			−1.82270
$872$		0			0
$873$	1.62773	+	1.62773i	0.0550904	+	0.0550904i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.13889			0.173528			0.0867640	−	0.996229i	$-0.472347\pi$
$877$	5.13889			0.173528			0.0867640	+	0.996229i	$0.472347\pi$
$878$		0			0
$879$	21.7040			0.732057
$880$		0			0
$881$	−4.34528			−0.146396			−0.0731982	−	0.997317i	$-0.523321\pi$
$881$	−4.34528			−0.146396			−0.0731982	+	0.997317i	$0.523321\pi$
$882$		0			0
$883$	35.4317			1.19237			0.596186	−	0.802846i	$-0.296682\pi$
$883$	35.4317			1.19237			0.596186	+	0.802846i	$0.296682\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	37.4644	+	37.4644i	1.25793	+	1.25793i	0.952078	+	0.305855i	$0.0989422\pi$
$887$	37.4644	+	37.4644i	1.25793	+	1.25793i	0.305855	+	0.952078i	$0.401058\pi$
$888$		0			0
$889$	20.0945			0.673947
$890$		0			0
$891$	8.17171	−	8.17171i	0.273763	−	0.273763i
$892$		0			0
$893$			0.162803i			0.00544799i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−57.5407	−	57.5407i	−1.92123	−	1.92123i
$898$		0			0
$899$	5.22531	−	5.22531i	0.174274	−	0.174274i
$900$		0			0
$901$	−7.88580	−	7.88580i	−0.262714	−	0.262714i
$902$		0			0
$903$	31.1682	−	31.1682i	1.03721	−	1.03721i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.181405			0.00602345			0.00301173	−	0.999995i	$-0.499041\pi$
$907$	0.181405			0.00602345			0.00301173	+	0.999995i	$0.499041\pi$
$908$		0			0
$909$	4.22775	+	4.22775i	0.140226	+	0.140226i
$910$		0			0
$911$			23.4249i			0.776101i	0.921638	+	0.388050i	$0.126851\pi$
$911$			23.4249i			0.776101i	−0.921638	+	0.388050i	$0.873149\pi$
$912$		0			0
$913$	3.19828	−	3.19828i	0.105848	−	0.105848i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			5.17529i			0.170903i
$918$		0			0
$919$			3.05885i			0.100902i	0.998727	+	0.0504511i	$0.0160659\pi$
$919$			3.05885i			0.100902i	−0.998727	+	0.0504511i	$0.983934\pi$
$920$		0			0
$921$			29.6962i			0.978522i
$922$		0			0
$923$		−	21.6431i		−	0.712392i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.376527	−	0.376527i	0.0123668	−	0.0123668i
$928$		0			0
$929$		−	59.9772i		−	1.96779i	−0.178752	−	0.983894i	$-0.557206\pi$
$929$		−	59.9772i		−	1.96779i	0.178752	−	0.983894i	$-0.442794\pi$
$930$		0			0
$931$	1.45744	+	1.45744i	0.0477657	+	0.0477657i
$932$		0			0
$933$	53.2931			1.74474
$934$		0			0
$935$		0			0
$936$		0			0
$937$	23.7463	−	23.7463i	0.775759	−	0.775759i	−0.203347	−	0.979107i	$-0.565182\pi$
$937$	23.7463	−	23.7463i	0.775759	−	0.775759i	0.979107	+	0.203347i	$0.0651821\pi$
$938$		0			0
$939$	26.8266	+	26.8266i	0.875451	+	0.875451i
$940$		0			0
$941$	−35.2727	+	35.2727i	−1.14986	+	1.14986i	−0.163278	+	0.986580i	$0.552207\pi$
$941$	−35.2727	+	35.2727i	−1.14986	+	1.14986i	−0.986580	+	0.163278i	$0.947793\pi$
$942$		0			0
$943$	−34.1897	−	34.1897i	−1.11337	−	1.11337i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	19.9140i		−	0.647118i	−0.946208	−	0.323559i	$-0.895121\pi$
$947$		−	19.9140i		−	0.647118i	0.946208	−	0.323559i	$-0.104879\pi$
$948$		0			0
$949$	17.4824	−	17.4824i	0.567504	−	0.567504i
$950$		0			0
$951$	50.6945			1.64388
$952$		0			0
$953$	−23.1060	−	23.1060i	−0.748477	−	0.748477i	0.225716	−	0.974193i	$-0.427528\pi$
$953$	−23.1060	−	23.1060i	−0.748477	−	0.748477i	−0.974193	+	0.225716i	$0.927528\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	4.28871			0.138634
$958$		0			0
$959$	21.9027			0.707276
$960$		0			0
$961$	17.9781			0.579939
$962$		0			0
$963$	14.9790			0.482690
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−41.7332	−	41.7332i	−1.34205	−	1.34205i	−0.894018	−	0.448030i	$-0.852126\pi$
$967$	−41.7332	−	41.7332i	−1.34205	−	1.34205i	−0.448030	−	0.894018i	$-0.647874\pi$
$968$		0			0
$969$	5.99275			0.192515
$970$		0			0
$971$	−33.5030	+	33.5030i	−1.07516	+	1.07516i	−0.0782268	+	0.996936i	$0.524926\pi$
$971$	−33.5030	+	33.5030i	−1.07516	+	1.07516i	−0.996936	+	0.0782268i	$0.975074\pi$
$972$		0			0
$973$		−	44.0330i		−	1.41163i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.16848	−	9.16848i	−0.293326	−	0.293326i	0.545067	−	0.838393i	$-0.316504\pi$
$977$	−9.16848	−	9.16848i	−0.293326	−	0.293326i	−0.838393	+	0.545067i	$0.816504\pi$
$978$		0			0
$979$	−0.0321648	+	0.0321648i	−0.00102799	+	0.00102799i
$980$		0			0
$981$	0.293887	+	0.293887i	0.00938308	+	0.00938308i
$982$		0			0
$983$	−39.1183	+	39.1183i	−1.24768	+	1.24768i	−0.290936	+	0.956742i	$0.593967\pi$
$983$	−39.1183	+	39.1183i	−1.24768	+	1.24768i	−0.956742	+	0.290936i	$0.906033\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.655657			−0.0208698
$988$		0			0
$989$	48.8852	+	48.8852i	1.55446	+	1.55446i
$990$		0			0
$991$			12.9925i			0.412722i	0.978476	+	0.206361i	$0.0661621\pi$
$991$			12.9925i			0.412722i	−0.978476	+	0.206361i	$0.933838\pi$
$992$		0			0
$993$	26.7307	−	26.7307i	0.848273	−	0.848273i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			8.89509i			0.281710i	0.990030	+	0.140855i	$0.0449852\pi$
$997$			8.89509i			0.281710i	−0.990030	+	0.140855i	$0.955015\pi$
$998$		0			0
$999$			43.1624i			1.36560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.d.207.8		18
4.3	odd	2		400.2.s.d.107.4		18
5.2	odd	4		320.2.j.b.143.2		18
5.3	odd	4		1600.2.j.d.143.8		18
5.4	even	2		320.2.s.b.207.2		18
16.3	odd	4		1600.2.j.d.1007.2		18
16.13	even	4		400.2.j.d.307.1		18
20.3	even	4		400.2.j.d.43.1		18
20.7	even	4		80.2.j.b.43.9	✓	18
20.19	odd	2		80.2.s.b.27.6	yes	18
40.19	odd	2		640.2.s.d.287.2		18
40.27	even	4		640.2.j.d.543.2		18
40.29	even	2		640.2.s.c.287.8		18
40.37	odd	4		640.2.j.c.543.8		18
60.47	odd	4		720.2.bd.g.523.1		18
60.59	even	2		720.2.z.g.667.4		18
80.3	even	4	inner	1600.2.s.d.943.8		18
80.13	odd	4		400.2.s.d.243.4		18
80.19	odd	4		320.2.j.b.47.8		18
80.27	even	4		640.2.s.c.223.8		18
80.29	even	4		80.2.j.b.67.9	yes	18
80.37	odd	4		640.2.s.d.223.2		18
80.59	odd	4		640.2.j.c.607.2		18
80.67	even	4		320.2.s.b.303.2		18
80.69	even	4		640.2.j.d.607.8		18
80.77	odd	4		80.2.s.b.3.6	yes	18
240.29	odd	4		720.2.bd.g.307.1		18
240.77	even	4		720.2.z.g.163.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.9	✓	18	20.7	even	4
80.2.j.b.67.9	yes	18	80.29	even	4
80.2.s.b.3.6	yes	18	80.77	odd	4
80.2.s.b.27.6	yes	18	20.19	odd	2
320.2.j.b.47.8		18	80.19	odd	4
320.2.j.b.143.2		18	5.2	odd	4
320.2.s.b.207.2		18	5.4	even	2
320.2.s.b.303.2		18	80.67	even	4
400.2.j.d.43.1		18	20.3	even	4
400.2.j.d.307.1		18	16.13	even	4
400.2.s.d.107.4		18	4.3	odd	2
400.2.s.d.243.4		18	80.13	odd	4
640.2.j.c.543.8		18	40.37	odd	4
640.2.j.c.607.2		18	80.59	odd	4
640.2.j.d.543.2		18	40.27	even	4
640.2.j.d.607.8		18	80.69	even	4
640.2.s.c.223.8		18	80.27	even	4
640.2.s.c.287.8		18	40.29	even	2
640.2.s.d.223.2		18	80.37	odd	4
640.2.s.d.287.2		18	40.19	odd	2
720.2.z.g.163.4		18	240.77	even	4
720.2.z.g.667.4		18	60.59	even	2
720.2.bd.g.307.1		18	240.29	odd	4
720.2.bd.g.523.1		18	60.47	odd	4
1600.2.j.d.143.8		18	5.3	odd	4
1600.2.j.d.1007.2		18	16.3	odd	4
1600.2.s.d.207.8		18	1.1	even	1	trivial
1600.2.s.d.943.8		18	80.3	even	4	inner

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.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.96251 q^{3} +(-1.60205 - 1.60205i) q^{7} +0.851447 q^{9} +O(q^{10})\)	\(q+1.96251 q^{3} +(-1.60205 - 1.60205i) q^{7} +0.851447 q^{9} +(-0.754587 + 0.754587i) q^{11} -5.94580i q^{13} +(-1.95574 - 1.95574i) q^{17} +(-0.780680 + 0.780680i) q^{19} +(-3.14404 - 3.14404i) q^{21} +(4.93121 - 4.93121i) q^{23} -4.21656 q^{27} +(-1.44802 - 1.44802i) q^{29} +3.60859i q^{31} +(-1.48089 + 1.48089i) q^{33} -10.2364i q^{37} -11.6687i q^{39} -6.93334i q^{41} +9.91344i q^{43} +(0.104270 - 0.104270i) q^{47} -1.86688i q^{49} +(-3.83816 - 3.83816i) q^{51} +4.03213 q^{53} +(-1.53209 + 1.53209i) q^{57} +(3.46736 + 3.46736i) q^{59} +(0.680578 - 0.680578i) q^{61} +(-1.36406 - 1.36406i) q^{63} -9.04721i q^{67} +(9.67754 - 9.67754i) q^{69} +3.64007 q^{71} +(2.94030 + 2.94030i) q^{73} +2.41777 q^{77} -10.7140 q^{79} -10.8294 q^{81} -4.23845 q^{83} +(-2.84176 - 2.84176i) q^{87} +0.0426256 q^{89} +(-9.52546 + 9.52546i) q^{91} +7.08189i q^{93} +(1.91173 + 1.91173i) q^{97} +(-0.642491 + 0.642491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^7 + 10 * q^9	\( 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

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