LMFDB - Embedded newform 425.2.c.a.424.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(424,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("425.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.c (of order $2$, degree $1$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			424.5
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	425.424
Dual form			425.2.c.a.424.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.48119i q^{2} +1.67513 q^{3} -0.193937 q^{4} +2.48119i q^{6} +1.28726 q^{7} +2.67513i q^{8} -0.193937 q^{9} -0.481194i q^{11} -0.324869 q^{12} +2.15633i q^{13} +1.90668i q^{14} -4.35026 q^{16} +(3.67513 - 1.86907i) q^{17} -0.287258i q^{18} -3.35026 q^{19} +2.15633 q^{21} +0.712742 q^{22} +8.24965 q^{23} +4.48119i q^{24} -3.19394 q^{26} -5.35026 q^{27} -0.249646 q^{28} -0.649738i q^{29} +1.83146i q^{31} -1.09332i q^{32} -0.806063i q^{33} +(2.76845 + 5.44358i) q^{34} +0.0376114 q^{36} -4.31265 q^{37} -4.96239i q^{38} +3.61213i q^{39} -11.2750i q^{41} +3.19394i q^{42} -8.15633i q^{43} +0.0933212i q^{44} +12.2193i q^{46} -6.54420i q^{47} -7.28726 q^{48} -5.34297 q^{49} +(6.15633 - 3.13093i) q^{51} -0.418190i q^{52} +8.57452i q^{53} -7.92478i q^{54} +3.44358i q^{56} -5.61213 q^{57} +0.962389 q^{58} -4.96239 q^{59} +2.83638i q^{61} -2.71274 q^{62} -0.249646 q^{63} -7.08110 q^{64} +1.19394 q^{66} +4.93207i q^{67} +(-0.712742 + 0.362481i) q^{68} +13.8192 q^{69} -14.5320i q^{71} -0.518806i q^{72} -13.3503 q^{73} -6.38787i q^{74} +0.649738 q^{76} -0.619421i q^{77} -5.35026 q^{78} -9.05571i q^{79} -8.38058 q^{81} +16.7005 q^{82} +13.4314i q^{83} -0.418190 q^{84} +12.0811 q^{86} -1.08840i q^{87} +1.28726 q^{88} +16.7816 q^{89} +2.77575i q^{91} -1.59991 q^{92} +3.06793i q^{93} +9.69323 q^{94} -1.83146i q^{96} +3.66291 q^{97} -7.91397i q^{98} +0.0933212i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} - 4 q^{7} - 2 q^{9} - 12 q^{12} - 6 q^{16} + 12 q^{17} - 8 q^{21} + 16 q^{22} + 16 q^{23} - 20 q^{26} - 12 q^{27} + 32 q^{28} - 6 q^{34} + 22 q^{36} + 16 q^{37} - 32 q^{48} + 14 q^{49} + 16 q^{51}+ \cdots - 40 q^{97}+O(q^{100}) $ 6 * q - 2 * q^4 - 4 * q^7 - 2 * q^9 - 12 * q^12 - 6 * q^16 + 12 * q^17 - 8 * q^21 + 16 * q^22 + 16 * q^23 - 20 * q^26 - 12 * q^27 + 32 * q^28 - 6 * q^34 + 22 * q^36 + 16 * q^37 - 32 * q^48 + 14 * q^49 + 16 * q^51 - 32 * q^57 - 16 * q^58 - 8 * q^59 - 28 * q^62 + 32 * q^63 + 22 * q^64 + 8 * q^66 - 16 * q^68 - 60 * q^73 + 24 * q^76 - 12 * q^78 - 26 * q^81 + 60 * q^82 + 8 * q^86 - 4 * q^88 - 4 * q^89 + 44 * q^92 - 8 * q^94 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.48119i			1.04736i	0.851914	+	0.523681i	$0.175442\pi$
$2$			1.48119i			1.04736i	−0.851914	+	0.523681i	$0.824558\pi$
$3$	1.67513			0.967137			0.483569	−	0.875306i	$-0.339340\pi$
$3$	1.67513			0.967137			0.483569	+	0.875306i	$0.339340\pi$
$4$	−0.193937			−0.0969683
$5$		0			0
$5$		0			0
$6$			2.48119i			1.01294i
$7$	1.28726			0.486538			0.243269	−	0.969959i	$-0.421780\pi$
$7$	1.28726			0.486538			0.243269	+	0.969959i	$0.421780\pi$
$8$			2.67513i			0.945802i
$9$	−0.193937			−0.0646455
$10$		0			0
$11$		−	0.481194i		−	0.145086i	−0.997365	−	0.0725428i	$-0.976889\pi$
$11$		−	0.481194i		−	0.145086i	0.997365	−	0.0725428i	$-0.0231114\pi$
$12$	−0.324869			−0.0937816
$13$			2.15633i			0.598057i	0.954244	+	0.299028i	$0.0966626\pi$
$13$			2.15633i			0.598057i	−0.954244	+	0.299028i	$0.903337\pi$
$14$			1.90668i			0.509581i
$15$		0			0
$16$	−4.35026			−1.08757
$17$	3.67513	−	1.86907i	0.891350	−	0.453315i
$17$	3.67513	−	1.86907i	0.891350	−	0.453315i
$18$		−	0.287258i		−	0.0677073i
$19$	−3.35026			−0.768603			−0.384301	−	0.923208i	$-0.625558\pi$
$19$	−3.35026			−0.768603			−0.384301	+	0.923208i	$0.625558\pi$
$20$		0			0
$21$	2.15633			0.470549
$22$	0.712742			0.151957
$23$	8.24965			1.72017			0.860085	−	0.510151i	$-0.170410\pi$
$23$	8.24965			1.72017			0.860085	+	0.510151i	$0.170410\pi$
$24$			4.48119i			0.914720i
$25$		0			0
$26$	−3.19394			−0.626382
$27$	−5.35026			−1.02966
$28$	−0.249646			−0.0471787
$29$		−	0.649738i		−	0.120653i	−0.998179	−	0.0603267i	$-0.980786\pi$
$29$		−	0.649738i		−	0.120653i	0.998179	−	0.0603267i	$-0.0192142\pi$
$30$		0			0
$31$			1.83146i			0.328939i	0.986382	+	0.164470i	$0.0525912\pi$
$31$			1.83146i			0.328939i	−0.986382	+	0.164470i	$0.947409\pi$
$32$		−	1.09332i		−	0.193274i
$33$		−	0.806063i		−	0.140318i
$34$	2.76845	+	5.44358i	0.474786	+	0.933567i
$35$		0			0
$36$	0.0376114			0.00626857
$37$	−4.31265			−0.708995			−0.354498	−	0.935057i	$-0.615348\pi$
$37$	−4.31265			−0.708995			−0.354498	+	0.935057i	$0.615348\pi$
$38$		−	4.96239i		−	0.805006i
$39$			3.61213i			0.578403i
$40$		0			0
$41$		−	11.2750i		−	1.76087i	−0.474171	−	0.880433i	$-0.657252\pi$
$41$		−	11.2750i		−	1.76087i	0.474171	−	0.880433i	$-0.342748\pi$
$42$			3.19394i			0.492835i
$43$		−	8.15633i		−	1.24383i	−0.783086	−	0.621914i	$-0.786355\pi$
$43$		−	8.15633i		−	1.24383i	0.783086	−	0.621914i	$-0.213645\pi$
$44$			0.0933212i			0.0140687i
$45$		0			0
$46$			12.2193i			1.80164i
$47$		−	6.54420i		−	0.954569i	−0.878749	−	0.477285i	$-0.841621\pi$
$47$		−	6.54420i		−	0.954569i	0.878749	−	0.477285i	$-0.158379\pi$
$48$	−7.28726			−1.05183
$49$	−5.34297			−0.763281
$50$		0			0
$51$	6.15633	−	3.13093i	0.862058	−	0.438418i
$52$		−	0.418190i		−	0.0579926i
$53$			8.57452i			1.17780i	0.808206	+	0.588900i	$0.200439\pi$
$53$			8.57452i			1.17780i	−0.808206	+	0.588900i	$0.799561\pi$
$54$		−	7.92478i		−	1.07843i
$55$		0			0
$56$			3.44358i			0.460168i
$57$	−5.61213			−0.743344
$58$	0.962389			0.126368
$59$	−4.96239			−0.646048			−0.323024	−	0.946391i	$-0.604699\pi$
$59$	−4.96239			−0.646048			−0.323024	+	0.946391i	$0.604699\pi$
$60$		0			0
$61$			2.83638i			0.363161i	0.983376	+	0.181581i	$0.0581213\pi$
$61$			2.83638i			0.363161i	−0.983376	+	0.181581i	$0.941879\pi$
$62$	−2.71274			−0.344519
$63$	−0.249646			−0.0314525
$64$	−7.08110			−0.885138
$65$		0			0
$66$	1.19394			0.146963
$67$			4.93207i			0.602548i	0.953538	+	0.301274i	$0.0974120\pi$
$67$			4.93207i			0.602548i	−0.953538	+	0.301274i	$0.902588\pi$
$68$	−0.712742	+	0.362481i	−0.0864327	+	0.0439572i
$69$	13.8192			1.66364
$70$		0			0
$71$		−	14.5320i		−	1.72463i	−0.506373	−	0.862314i	$-0.669014\pi$
$71$		−	14.5320i		−	1.72463i	0.506373	−	0.862314i	$-0.330986\pi$
$72$		−	0.518806i		−	0.0611418i
$73$	−13.3503			−1.56253			−0.781265	−	0.624200i	$-0.785425\pi$
$73$	−13.3503			−1.56253			−0.781265	+	0.624200i	$0.785425\pi$
$74$		−	6.38787i		−	0.742575i
$75$		0			0
$76$	0.649738			0.0745301
$77$		−	0.619421i		−	0.0705896i
$78$	−5.35026			−0.605798
$79$		−	9.05571i		−	1.01885i	−0.860516	−	0.509423i	$-0.829859\pi$
$79$		−	9.05571i		−	1.01885i	0.860516	−	0.509423i	$-0.170141\pi$
$80$		0			0
$81$	−8.38058			−0.931175
$82$	16.7005			1.84426
$83$			13.4314i			1.47428i	0.675738	+	0.737142i	$0.263825\pi$
$83$			13.4314i			1.47428i	−0.675738	+	0.737142i	$0.736175\pi$
$84$	−0.418190			−0.0456283
$85$		0			0
$86$	12.0811			1.30274
$87$		−	1.08840i		−	0.116688i
$88$	1.28726			0.137222
$89$	16.7816			1.77885			0.889424	−	0.457082i	$-0.151106\pi$
$89$	16.7816			1.77885			0.889424	+	0.457082i	$0.151106\pi$
$90$		0			0
$91$			2.77575i			0.290977i
$92$	−1.59991			−0.166802
$93$			3.06793i			0.318129i
$94$	9.69323			0.999780
$95$		0			0
$96$		−	1.83146i		−	0.186922i
$97$	3.66291			0.371912			0.185956	−	0.982558i	$-0.440462\pi$
$97$	3.66291			0.371912			0.185956	+	0.982558i	$0.440462\pi$
$98$		−	7.91397i		−	0.799432i
$99$			0.0933212i			0.00937913i
$100$		0			0
$101$	6.85685			0.682282			0.341141	−	0.940012i	$-0.389187\pi$
$101$	6.85685			0.682282			0.341141	+	0.940012i	$0.389187\pi$
$102$	4.63752	+	9.11871i	0.459183	+	0.902887i
$103$		−	7.04349i		−	0.694016i	−0.937862	−	0.347008i	$-0.887198\pi$
$103$		−	7.04349i		−	0.694016i	0.937862	−	0.347008i	$-0.112802\pi$
$104$	−5.76845			−0.565643
$105$		0			0
$106$	−12.7005			−1.23358
$107$	5.86177			0.566679			0.283340	−	0.959020i	$-0.408558\pi$
$107$	5.86177			0.566679			0.283340	+	0.959020i	$0.408558\pi$
$108$	1.03761			0.0998442
$109$		−	12.7005i		−	1.21649i	−0.793750	−	0.608245i	$-0.791874\pi$
$109$		−	12.7005i		−	1.21649i	0.793750	−	0.608245i	$-0.208126\pi$
$110$		0			0
$111$	−7.22425			−0.685696
$112$	−5.59991			−0.529142
$113$	4.88717			0.459746			0.229873	−	0.973221i	$-0.426169\pi$
$113$	4.88717			0.459746			0.229873	+	0.973221i	$0.426169\pi$
$114$		−	8.31265i		−	0.778551i
$115$		0			0
$116$			0.126008i			0.0116995i
$117$		−	0.418190i		−	0.0386617i
$118$		−	7.35026i		−	0.676646i
$119$	4.73084	−	2.40597i	0.433675	−	0.220555i
$120$		0			0
$121$	10.7685			0.978950
$122$	−4.20123			−0.380362
$123$		−	18.8872i		−	1.70300i
$124$		−	0.355186i		−	0.0318967i
$125$		0			0
$126$		−	0.369775i		−	0.0329422i
$127$			1.76845i			0.156925i	0.996917	+	0.0784624i	$0.0250010\pi$
$127$			1.76845i			0.156925i	−0.996917	+	0.0784624i	$0.974999\pi$
$128$		−	12.6751i		−	1.12033i
$129$		−	13.6629i		−	1.20295i
$130$		0			0
$131$			11.1065i			0.970379i	0.874409	+	0.485189i	$0.161249\pi$
$131$			11.1065i			0.970379i	−0.874409	+	0.485189i	$0.838751\pi$
$132$			0.156325i			0.0136064i
$133$	−4.31265			−0.373954
$134$	−7.30536			−0.631087
$135$		0			0
$136$	5.00000	+	9.83146i	0.428746	+	0.843040i
$137$			11.7685i			1.00545i	0.864447	+	0.502723i	$0.167669\pi$
$137$			11.7685i			1.00545i	−0.864447	+	0.502723i	$0.832331\pi$
$138$			20.4690i			1.74243i
$139$			11.7054i			0.992843i	0.868082	+	0.496422i	$0.165353\pi$
$139$			11.7054i			0.992843i	−0.868082	+	0.496422i	$0.834647\pi$
$140$		0			0
$141$		−	10.9624i		−	0.923200i
$142$	21.5247			1.80631
$143$	1.03761			0.0867694
$144$	0.843675			0.0703062
$145$		0			0
$146$		−	19.7743i		−	1.63654i
$147$	−8.95017			−0.738198
$148$	0.836381			0.0687501
$149$	−17.1998			−1.40906			−0.704532	−	0.709672i	$-0.748843\pi$
$149$	−17.1998			−1.40906			−0.704532	+	0.709672i	$0.748843\pi$
$150$		0			0
$151$	−13.5877			−1.10575			−0.552875	−	0.833264i	$-0.686469\pi$
$151$	−13.5877			−1.10575			−0.552875	+	0.833264i	$0.686469\pi$
$152$		−	8.96239i		−	0.726946i
$153$	−0.712742	+	0.362481i	−0.0576218	+	0.0293048i
$154$	0.917483			0.0739329
$155$		0			0
$156$		−	0.700523i		−	0.0560868i
$157$		−	8.57452i		−	0.684321i	−0.939642	−	0.342160i	$-0.888841\pi$
$157$		−	8.57452i		−	0.684321i	0.939642	−	0.342160i	$-0.111159\pi$
$158$	13.4133			1.06710
$159$			14.3634i			1.13909i
$160$		0			0
$161$	10.6194			0.836928
$162$		−	12.4133i		−	0.975278i
$163$	14.3757			1.12599			0.562994	−	0.826461i	$-0.309649\pi$
$163$	14.3757			1.12599			0.562994	+	0.826461i	$0.309649\pi$
$164$			2.18664i			0.170748i
$165$		0			0
$166$	−19.8945			−1.54411
$167$	−7.54912			−0.584169			−0.292084	−	0.956393i	$-0.594349\pi$
$167$	−7.54912			−0.584169			−0.292084	+	0.956393i	$0.594349\pi$
$168$			5.76845i			0.445046i
$169$	8.35026			0.642328
$170$		0			0
$171$	0.649738			0.0496867
$172$			1.58181i			0.120612i
$173$	−11.8496			−0.900905			−0.450452	−	0.892800i	$-0.648737\pi$
$173$	−11.8496			−0.900905			−0.450452	+	0.892800i	$0.648737\pi$
$174$	1.61213			0.122215
$175$		0			0
$176$			2.09332i			0.157790i
$177$	−8.31265			−0.624817
$178$			24.8568i			1.86310i
$179$	3.22425			0.240992			0.120496	−	0.992714i	$-0.461551\pi$
$179$	3.22425			0.240992			0.120496	+	0.992714i	$0.461551\pi$
$180$		0			0
$181$			6.88717i			0.511919i	0.966688	+	0.255960i	$0.0823914\pi$
$181$			6.88717i			0.511919i	−0.966688	+	0.255960i	$0.917609\pi$
$182$	−4.11142			−0.304759
$183$			4.75131i			0.351227i
$184$			22.0689i			1.62694i
$185$		0			0
$186$	−4.54420			−0.333197
$187$	−0.899385	−	1.76845i	−0.0657695	−	0.129322i
$188$			1.26916i			0.0925630i
$189$	−6.88717			−0.500968
$190$		0			0
$191$	7.19982			0.520960			0.260480	−	0.965479i	$-0.416119\pi$
$191$	7.19982			0.520960			0.260480	+	0.965479i	$0.416119\pi$
$192$	−11.8618			−0.856050
$193$	−20.1114			−1.44765			−0.723826	−	0.689983i	$-0.757618\pi$
$193$	−20.1114			−1.44765			−0.723826	+	0.689983i	$0.757618\pi$
$194$			5.42548i			0.389527i
$195$		0			0
$196$	1.03620			0.0740141
$197$	−3.16362			−0.225399			−0.112699	−	0.993629i	$-0.535950\pi$
$197$	−3.16362			−0.225399			−0.112699	+	0.993629i	$0.535950\pi$
$198$	−0.138227			−0.00982335
$199$			21.4944i			1.52370i	0.647756	+	0.761848i	$0.275708\pi$
$199$			21.4944i			1.52370i	−0.647756	+	0.761848i	$0.724292\pi$
$200$		0			0
$201$			8.26187i			0.582747i
$202$			10.1563i			0.714597i
$203$		−	0.836381i		−	0.0587024i
$204$	−1.19394	+	0.607202i	−0.0835923	+	0.0425127i
$205$		0			0
$206$	10.4328			0.726886
$207$	−1.59991			−0.111201
$208$		−	9.38058i		−	0.650426i
$209$			1.61213i			0.111513i
$210$		0			0
$211$			20.8691i			1.43669i	0.695689	+	0.718343i	$0.255099\pi$
$211$			20.8691i			1.43669i	−0.695689	+	0.718343i	$0.744901\pi$
$212$		−	1.66291i		−	0.114209i
$213$		−	24.3430i		−	1.66795i
$214$			8.68243i			0.593518i
$215$		0			0
$216$		−	14.3127i		−	0.973853i
$217$			2.35756i			0.160041i
$218$	18.8119			1.27411
$219$	−22.3634			−1.51118
$220$		0			0
$221$	4.03032	+	7.92478i	0.271108	+	0.533078i
$222$		−	10.7005i		−	0.718172i
$223$			24.3430i			1.63013i	0.579373	+	0.815063i	$0.303298\pi$
$223$			24.3430i			1.63013i	−0.579373	+	0.815063i	$0.696702\pi$
$224$		−	1.40739i		−	0.0940349i
$225$		0			0
$226$			7.23884i			0.481521i
$227$	−11.2120			−0.744169			−0.372084	−	0.928199i	$-0.621357\pi$
$227$	−11.2120			−0.744169			−0.372084	+	0.928199i	$0.621357\pi$
$228$	1.08840			0.0720808
$229$	−12.1563			−0.803313			−0.401656	−	0.915790i	$-0.631565\pi$
$229$	−12.1563			−0.803313			−0.401656	+	0.915790i	$0.631565\pi$
$230$		0			0
$231$		−	1.03761i		−	0.0682698i
$232$	1.73813			0.114114
$233$	11.9756			0.784545			0.392273	−	0.919849i	$-0.371689\pi$
$233$	11.9756			0.784545			0.392273	+	0.919849i	$0.371689\pi$
$234$	0.619421			0.0404928
$235$		0			0
$236$	0.962389			0.0626462
$237$		−	15.1695i		−	0.985365i
$238$	3.56371	+	7.00729i	0.231001	+	0.454215i
$239$	8.83638			0.571578			0.285789	−	0.958293i	$-0.407744\pi$
$239$	8.83638			0.571578			0.285789	+	0.958293i	$0.407744\pi$
$240$		0			0
$241$		−	0.261865i		−	0.0168682i	−0.999964	−	0.00843411i	$-0.997315\pi$
$241$		−	0.261865i		−	0.0168682i	0.999964	−	0.00843411i	$-0.00268469\pi$
$242$			15.9502i			1.02532i
$243$	2.01222			0.129084
$244$		−	0.550078i		−	0.0352151i
$245$		0			0
$246$	27.9756			1.78366
$247$		−	7.22425i		−	0.459668i
$248$	−4.89938			−0.311111
$249$			22.4993i			1.42583i
$250$		0			0
$251$	−23.6629			−1.49359			−0.746795	−	0.665054i	$-0.768408\pi$
$251$	−23.6629			−1.49359			−0.746795	+	0.665054i	$0.768408\pi$
$252$	0.0484156			0.00304989
$253$		−	3.96968i		−	0.249572i
$254$	−2.61942			−0.164357
$255$		0			0
$256$	4.61213			0.288258
$257$			19.2447i			1.20045i	0.799830	+	0.600226i	$0.204923\pi$
$257$			19.2447i			1.20045i	−0.799830	+	0.600226i	$0.795077\pi$
$258$	20.2374			1.25993
$259$	−5.55149			−0.344953
$260$		0			0
$261$			0.126008i			0.00779970i
$262$	−16.4509			−1.01634
$263$			17.2447i			1.06336i	0.846947	+	0.531678i	$0.178438\pi$
$263$			17.2447i			1.06336i	−0.846947	+	0.531678i	$0.821562\pi$
$264$	2.15633			0.132713
$265$		0			0
$266$		−	6.38787i		−	0.391666i
$267$	28.1114			1.72039
$268$		−	0.956509i		−	0.0584281i
$269$		−	26.6253i		−	1.62337i	−0.584093	−	0.811687i	$-0.698550\pi$
$269$		−	26.6253i		−	1.62337i	0.584093	−	0.811687i	$-0.301450\pi$
$270$		0			0
$271$	−6.70052			−0.407028			−0.203514	−	0.979072i	$-0.565236\pi$
$271$	−6.70052			−0.407028			−0.203514	+	0.979072i	$0.565236\pi$
$272$	−15.9878	+	8.13093i	−0.969402	+	0.493010i
$273$			4.64974i			0.281415i
$274$	−17.4314			−1.05307
$275$		0			0
$276$	−2.68006			−0.161320
$277$	16.7005			1.00344			0.501719	−	0.865031i	$-0.332701\pi$
$277$	16.7005			1.00344			0.501719	+	0.865031i	$0.332701\pi$
$278$	−17.3380			−1.03987
$279$		−	0.355186i		−	0.0212644i
$280$		0			0
$281$	−28.4241			−1.69564			−0.847819	−	0.530286i	$-0.822085\pi$
$281$	−28.4241			−1.69564			−0.847819	+	0.530286i	$0.822085\pi$
$282$	16.2374			0.966925
$283$	10.0630			0.598183			0.299092	−	0.954224i	$-0.403316\pi$
$283$	10.0630			0.598183			0.299092	+	0.954224i	$0.403316\pi$
$284$			2.81828i			0.167234i
$285$		0			0
$286$			1.53690i			0.0908790i
$287$		−	14.5139i		−	0.856727i
$288$			0.212035i			0.0124943i
$289$	10.0132	−	13.7381i	0.589010	−	0.808126i
$290$		0			0
$291$	6.13586			0.359690
$292$	2.58910			0.151516
$293$		−	14.3127i		−	0.836154i	−0.908412	−	0.418077i	$-0.862704\pi$
$293$		−	14.3127i		−	0.836154i	0.908412	−	0.418077i	$-0.137296\pi$
$294$		−	13.2569i		−	0.773160i
$295$		0			0
$296$		−	11.5369i		−	0.670569i
$297$			2.57452i			0.149389i
$298$		−	25.4763i		−	1.47580i
$299$			17.7889i			1.02876i
$300$		0			0
$301$		−	10.4993i		−	0.605169i
$302$		−	20.1260i		−	1.15812i
$303$	11.4861			0.659860
$304$	14.5745			0.835906
$305$		0			0
$306$	−0.536904	−	1.05571i	−0.0306928	−	0.0603509i
$307$			29.2809i			1.67115i	0.549376	+	0.835575i	$0.314865\pi$
$307$			29.2809i			1.67115i	−0.549376	+	0.835575i	$0.685135\pi$
$308$			0.120128i			0.00684495i
$309$		−	11.7988i		−	0.671209i
$310$		0			0
$311$			4.54183i			0.257543i	0.991674	+	0.128772i	$0.0411035\pi$
$311$			4.54183i			0.257543i	−0.991674	+	0.128772i	$0.958897\pi$
$312$	−9.66291			−0.547055
$313$	−0.826531			−0.0467183			−0.0233592	−	0.999727i	$-0.507436\pi$
$313$	−0.826531			−0.0467183			−0.0233592	+	0.999727i	$0.507436\pi$
$314$	12.7005			0.716732
$315$		0			0
$316$			1.75623i			0.0987958i
$317$	32.2374			1.81063			0.905317	−	0.424736i	$-0.139633\pi$
$317$	32.2374			1.81063			0.905317	+	0.424736i	$0.139633\pi$
$318$	−21.2750			−1.19304
$319$	−0.312650			−0.0175051
$320$		0			0
$321$	9.81924			0.548056
$322$			15.7294i			0.876567i
$323$	−12.3127	+	6.26187i	−0.685094	+	0.348419i
$324$	1.62530			0.0902945
$325$		0			0
$326$			21.2931i			1.17932i
$327$		−	21.2750i		−	1.17651i
$328$	30.1622			1.66543
$329$		−	8.42407i		−	0.464434i
$330$		0			0
$331$	−6.82653			−0.375220			−0.187610	−	0.982244i	$-0.560074\pi$
$331$	−6.82653			−0.375220			−0.187610	+	0.982244i	$0.560074\pi$
$332$		−	2.60483i		−	0.142959i
$333$	0.836381			0.0458334
$334$		−	11.1817i		−	0.611836i
$335$		0			0
$336$	−9.38058			−0.511753
$337$	−18.0508			−0.983289			−0.491644	−	0.870796i	$-0.663604\pi$
$337$	−18.0508			−0.983289			−0.491644	+	0.870796i	$0.663604\pi$
$338$			12.3684i			0.672750i
$339$	8.18664			0.444637
$340$		0			0
$341$	0.881286			0.0477243
$342$			0.962389i			0.0520400i
$343$	−15.8886			−0.857903
$344$	21.8192			1.17641
$345$		0			0
$346$		−	17.5515i		−	0.943574i
$347$	18.3512			0.985145			0.492572	−	0.870271i	$-0.336057\pi$
$347$	18.3512			0.985145			0.492572	+	0.870271i	$0.336057\pi$
$348$			0.211080i			0.0113151i
$349$	13.6023			0.728113			0.364057	−	0.931377i	$-0.381391\pi$
$349$	13.6023			0.728113			0.364057	+	0.931377i	$0.381391\pi$
$350$		0			0
$351$		−	11.5369i		−	0.615794i
$352$	−0.526100			−0.0280412
$353$		−	27.4010i		−	1.45841i	−0.684295	−	0.729205i	$-0.739890\pi$
$353$		−	27.4010i		−	1.45841i	0.684295	−	0.729205i	$-0.260110\pi$
$354$		−	12.3127i		−	0.654410i
$355$		0			0
$356$	−3.25457			−0.172492
$357$	7.92478	−	4.03032i	0.419424	−	0.213307i
$358$			4.77575i			0.252406i
$359$	9.08840			0.479667			0.239834	−	0.970814i	$-0.422907\pi$
$359$	9.08840			0.479667			0.239834	+	0.970814i	$0.422907\pi$
$360$		0			0
$361$	−7.77575			−0.409250
$362$	−10.2012			−0.536165
$363$	18.0386			0.946779
$364$		−	0.538319i		−	0.0282156i
$365$		0			0
$366$	−7.03761			−0.367862
$367$	12.7635			0.666251			0.333125	−	0.942883i	$-0.391897\pi$
$367$	12.7635			0.666251			0.333125	+	0.942883i	$0.391897\pi$
$368$	−35.8881			−1.87080
$369$			2.18664i			0.113832i
$370$		0			0
$371$			11.0376i			0.573044i
$372$		−	0.594984i		−	0.0308485i
$373$		−	10.0957i		−	0.522735i	−0.965239	−	0.261368i	$-0.915827\pi$
$373$		−	10.0957i		−	0.522735i	0.965239	−	0.261368i	$-0.0841735\pi$
$374$	2.61942	−	1.33216i	0.135447	−	0.0688845i
$375$		0			0
$376$	17.5066			0.902833
$377$	1.40105			0.0721576
$378$		−	10.2012i		−	0.524695i
$379$		−	9.18172i		−	0.471633i	−0.971798	−	0.235817i	$-0.924224\pi$
$379$		−	9.18172i		−	0.471633i	0.971798	−	0.235817i	$-0.0757765\pi$
$380$		0			0
$381$			2.96239i			0.151768i
$382$			10.6643i			0.545634i
$383$			1.83383i			0.0937041i	0.998902	+	0.0468521i	$0.0149189\pi$
$383$			1.83383i			0.0937041i	−0.998902	+	0.0468521i	$0.985081\pi$
$384$		−	21.2325i		−	1.08352i
$385$		0			0
$386$		−	29.7889i		−	1.51622i
$387$			1.58181i			0.0804079i
$388$	−0.710373			−0.0360637
$389$	−11.6570			−0.591035			−0.295518	−	0.955337i	$-0.595492\pi$
$389$	−11.6570			−0.591035			−0.295518	+	0.955337i	$0.595492\pi$
$390$		0			0
$391$	30.3185	−	15.4191i	1.53327	−	0.779780i
$392$		−	14.2931i		−	0.721912i
$393$			18.6048i			0.938490i
$394$		−	4.68594i		−	0.236074i
$395$		0			0
$396$		−	0.0180984i		−	0.000909478i
$397$	9.37470			0.470503			0.235251	−	0.971935i	$-0.424409\pi$
$397$	9.37470			0.470503			0.235251	+	0.971935i	$0.424409\pi$
$398$	−31.8373			−1.59586
$399$	−7.22425			−0.361665
$400$		0			0
$401$			7.93937i			0.396473i	0.980154	+	0.198237i	$0.0635214\pi$
$401$			7.93937i			0.396473i	−0.980154	+	0.198237i	$0.936479\pi$
$402$	−12.2374			−0.610347
$403$	−3.94921			−0.196724
$404$	−1.32979			−0.0661597
$405$		0			0
$406$	1.23884			0.0614827
$407$			2.07522i			0.102865i
$408$	8.37565	+	16.4690i	0.414657	+	0.815336i
$409$	−9.07381			−0.448671			−0.224335	−	0.974512i	$-0.572021\pi$
$409$	−9.07381			−0.448671			−0.224335	+	0.974512i	$0.572021\pi$
$410$		0			0
$411$			19.7137i			0.972405i
$412$			1.36599i			0.0672975i
$413$	−6.38787			−0.314327
$414$		−	2.36977i		−	0.116468i
$415$		0			0
$416$	2.35756			0.115589
$417$			19.6082i			0.960216i
$418$	−2.38787			−0.116795
$419$			8.99508i			0.439438i	0.975563	+	0.219719i	$0.0705141\pi$
$419$			8.99508i			0.439438i	−0.975563	+	0.219719i	$0.929486\pi$
$420$		0			0
$421$	16.9076			0.824028			0.412014	−	0.911178i	$-0.364826\pi$
$421$	16.9076			0.824028			0.412014	+	0.911178i	$0.364826\pi$
$422$	−30.9111			−1.50473
$423$			1.26916i			0.0617086i
$424$	−22.9380			−1.11397
$425$		0			0
$426$	36.0567			1.74695
$427$			3.65115i			0.176692i
$428$	−1.13681			−0.0549499
$429$	1.73813			0.0839179
$430$		0			0
$431$			14.6678i			0.706525i	0.935524	+	0.353262i	$0.114928\pi$
$431$			14.6678i			0.706525i	−0.935524	+	0.353262i	$0.885072\pi$
$432$	23.2750			1.11982
$433$			6.68006i			0.321023i	0.987034	+	0.160511i	$0.0513144\pi$
$433$			6.68006i			0.321023i	−0.987034	+	0.160511i	$0.948686\pi$
$434$	−3.49200			−0.167621
$435$		0			0
$436$			2.46310i			0.117961i
$437$	−27.6385			−1.32213
$438$		−	33.1246i		−	1.58275i
$439$		−	9.56959i		−	0.456732i	−0.973575	−	0.228366i	$-0.926662\pi$
$439$		−	9.56959i		−	0.456732i	0.973575	−	0.228366i	$-0.0733382\pi$
$440$		0			0
$441$	1.03620			0.0493427
$442$	−11.7381	+	5.96968i	−0.558326	+	0.283949i
$443$			14.7915i			0.702764i	0.936232	+	0.351382i	$0.114288\pi$
$443$			14.7915i			0.702764i	−0.936232	+	0.351382i	$0.885712\pi$
$444$	1.40105			0.0664907
$445$		0			0
$446$	−36.0567			−1.70733
$447$	−28.8119			−1.36276
$448$	−9.11520			−0.430653
$449$		−	10.9018i		−	0.514486i	−0.966347	−	0.257243i	$-0.917186\pi$
$449$		−	10.9018i		−	0.514486i	0.966347	−	0.257243i	$-0.0828140\pi$
$450$		0			0
$451$	−5.42548			−0.255476
$452$	−0.947800			−0.0445808
$453$	−22.7612			−1.06941
$454$		−	16.6072i		−	0.779415i
$455$		0			0
$456$		−	15.0132i		−	0.703056i
$457$			7.61801i			0.356355i	0.983998	+	0.178178i	$0.0570202\pi$
$457$			7.61801i			0.356355i	−0.983998	+	0.178178i	$0.942980\pi$
$458$		−	18.0059i		−	0.841360i
$459$	−19.6629	+	10.0000i	−0.917786	+	0.466760i
$460$		0			0
$461$	4.57452			0.213056			0.106528	−	0.994310i	$-0.466027\pi$
$461$	4.57452			0.213056			0.106528	+	0.994310i	$0.466027\pi$
$462$	1.53690			0.0715032
$463$		−	2.56864i		−	0.119375i	−0.998217	−	0.0596873i	$-0.980990\pi$
$463$		−	2.56864i		−	0.119375i	0.998217	−	0.0596873i	$-0.0190104\pi$
$464$			2.82653i			0.131218i
$465$		0			0
$466$			17.7381i			0.821703i
$467$			1.55737i			0.0720666i	0.999351	+	0.0360333i	$0.0114722\pi$
$467$			1.55737i			0.0720666i	−0.999351	+	0.0360333i	$0.988528\pi$
$468$			0.0811024i			0.00374896i
$469$			6.34885i			0.293163i
$470$		0			0
$471$		−	14.3634i		−	0.661832i
$472$		−	13.2750i		−	0.611033i
$473$	−3.92478			−0.180461
$474$	22.4690			1.03203
$475$		0			0
$476$	−0.917483	+	0.466606i	−0.0420528	+	0.0213868i
$477$		−	1.66291i		−	0.0761395i
$478$			13.0884i			0.598649i
$479$			20.4060i			0.932373i	0.884687	+	0.466186i	$0.154372\pi$
$479$			20.4060i			0.932373i	−0.884687	+	0.466186i	$0.845628\pi$
$480$		0			0
$481$		−	9.29948i		−	0.424020i
$482$	0.387873			0.0176671
$483$	17.7889			0.809424
$484$	−2.08840			−0.0949271
$485$		0			0
$486$			2.98049i			0.135198i
$487$	−0.162664			−0.00737103			−0.00368551	−	0.999993i	$-0.501173\pi$
$487$	−0.162664			−0.00737103			−0.00368551	+	0.999993i	$0.501173\pi$
$488$	−7.58769			−0.343479
$489$	24.0811			1.08899
$490$		0			0
$491$	12.8364			0.579298			0.289649	−	0.957133i	$-0.406461\pi$
$491$	12.8364			0.579298			0.289649	+	0.957133i	$0.406461\pi$
$492$			3.66291i			0.165137i
$493$	−1.21440	−	2.38787i	−0.0546940	−	0.107544i
$494$	10.7005			0.481439
$495$		0			0
$496$		−	7.96731i		−	0.357743i
$497$		−	18.7064i		−	0.839097i
$498$	−33.3258			−1.49337
$499$			17.7416i			0.794225i	0.917770	+	0.397113i	$0.129988\pi$
$499$			17.7416i			0.794225i	−0.917770	+	0.397113i	$0.870012\pi$
$500$		0			0
$501$	−12.6458			−0.564971
$502$		−	35.0494i		−	1.56433i
$503$	−11.2120			−0.499920			−0.249960	−	0.968256i	$-0.580417\pi$
$503$	−11.2120			−0.499920			−0.249960	+	0.968256i	$0.580417\pi$
$504$		−	0.667837i		−	0.0297478i
$505$		0			0
$506$	5.87987			0.261392
$507$	13.9878			0.621219
$508$		−	0.342968i		−	0.0152167i
$509$	6.37328			0.282491			0.141245	−	0.989975i	$-0.454889\pi$
$509$	6.37328			0.282491			0.141245	+	0.989975i	$0.454889\pi$
$510$		0			0
$511$	−17.1852			−0.760230
$512$		−	18.5188i		−	0.818423i
$513$	17.9248			0.791398
$514$	−28.5052			−1.25731
$515$		0			0
$516$			2.64974i			0.116648i
$517$	−3.14903			−0.138494
$518$		−	8.22284i		−	0.361291i
$519$	−19.8496			−0.871299
$520$		0			0
$521$		−	0.986826i		−	0.0432336i	−0.999766	−	0.0216168i	$-0.993119\pi$
$521$		−	0.986826i		−	0.0432336i	0.999766	−	0.0216168i	$-0.00688138\pi$
$522$	−0.186642			−0.00816911
$523$		−	8.99271i		−	0.393224i	−0.980481	−	0.196612i	$-0.937006\pi$
$523$		−	8.99271i		−	0.393224i	0.980481	−	0.196612i	$-0.0629939\pi$
$524$		−	2.15396i		−	0.0940960i
$525$		0			0
$526$	−25.5428			−1.11372
$527$	3.42311	+	6.73084i	0.149113	+	0.293200i
$528$			3.50659i			0.152605i
$529$	45.0567			1.95899
$530$		0			0
$531$	0.962389			0.0417641
$532$	0.836381			0.0362617
$533$	24.3127			1.05310
$534$			41.6385i			1.80187i
$535$		0			0
$536$	−13.1939			−0.569891
$537$	5.40105			0.233072
$538$	39.4372			1.70026
$539$			2.57101i			0.110741i
$540$		0			0
$541$		−	37.3766i		−	1.60695i	−0.595341	−	0.803473i	$-0.702983\pi$
$541$		−	37.3766i		−	1.60695i	0.595341	−	0.803473i	$-0.297017\pi$
$542$		−	9.92478i		−	0.426306i
$543$			11.5369i			0.495096i
$544$	−2.04349	−	4.01810i	−0.0876140	−	0.172275i
$545$		0			0
$546$	−6.88717			−0.294743
$547$	22.1744			0.948110			0.474055	−	0.880495i	$-0.342790\pi$
$547$	22.1744			0.948110			0.474055	+	0.880495i	$0.342790\pi$
$548$		−	2.28233i		−	0.0974964i
$549$		−	0.550078i		−	0.0234768i
$550$		0			0
$551$			2.17679i			0.0927345i
$552$			36.9683i			1.57347i
$553$		−	11.6570i		−	0.495707i
$554$			24.7367i			1.05096i
$555$		0			0
$556$		−	2.27011i		−	0.0962743i
$557$			1.16950i			0.0495533i	0.999693	+	0.0247766i	$0.00788745\pi$
$557$			1.16950i			0.0495533i	−0.999693	+	0.0247766i	$0.992113\pi$
$558$	0.526100			0.0222716
$559$	17.5877			0.743880
$560$		0			0
$561$	−1.50659	−	2.96239i	−0.0636081	−	0.125072i
$562$		−	42.1016i		−	1.77595i
$563$			11.1333i			0.469213i	0.972090	+	0.234606i	$0.0753801\pi$
$563$			11.1333i			0.469213i	−0.972090	+	0.234606i	$0.924620\pi$
$564$			2.12601i			0.0895211i
$565$		0			0
$566$			14.9053i			0.626515i
$567$	−10.7880			−0.453052
$568$	38.8749			1.63116
$569$	−16.7005			−0.700122			−0.350061	−	0.936727i	$-0.613839\pi$
$569$	−16.7005			−0.700122			−0.350061	+	0.936727i	$0.613839\pi$
$570$		0			0
$571$			37.2833i			1.56026i	0.625619	+	0.780129i	$0.284846\pi$
$571$			37.2833i			1.56026i	−0.625619	+	0.780129i	$0.715154\pi$
$572$	−0.201231			−0.00841388
$573$	12.0606			0.503840
$574$	21.4979			0.897304
$575$		0			0
$576$	1.37328			0.0572202
$577$		−	1.63259i		−	0.0679658i	−0.999422	−	0.0339829i	$-0.989181\pi$
$577$		−	1.63259i		−	0.0679658i	0.999422	−	0.0339829i	$-0.0108192\pi$
$578$	20.3488	+	14.8315i	0.846400	+	0.616907i
$579$	−33.6893			−1.40008
$580$		0			0
$581$			17.2896i			0.717295i
$582$			9.08840i			0.376726i
$583$	4.12601			0.170882
$584$		−	35.7137i		−	1.47784i
$585$		0			0
$586$	21.1998			0.875756
$587$			23.0435i			0.951107i	0.879687	+	0.475553i	$0.157752\pi$
$587$			23.0435i			0.951107i	−0.879687	+	0.475553i	$0.842248\pi$
$588$	1.73577			0.0715818
$589$		−	6.13586i		−	0.252824i
$590$		0			0
$591$	−5.29948			−0.217991
$592$	18.7612			0.771079
$593$		−	44.2130i		−	1.81561i	−0.419393	−	0.907805i	$-0.637757\pi$
$593$		−	44.2130i		−	1.81561i	0.419393	−	0.907805i	$-0.362243\pi$
$594$	−3.81336			−0.156464
$595$		0			0
$596$	3.33567			0.136635
$597$			36.0059i			1.47362i
$598$	−26.3488			−1.07748
$599$	−15.4518			−0.631345			−0.315672	−	0.948868i	$-0.602230\pi$
$599$	−15.4518			−0.631345			−0.315672	+	0.948868i	$0.602230\pi$
$600$		0			0
$601$		−	43.0640i		−	1.75662i	−0.478096	−	0.878308i	$-0.658673\pi$
$601$		−	43.0640i		−	1.75662i	0.478096	−	0.878308i	$-0.341327\pi$
$602$	15.5515			0.633832
$603$		−	0.956509i		−	0.0389521i
$604$	2.63515			0.107223
$605$		0			0
$606$			17.0132i			0.691113i
$607$	−41.5002			−1.68444			−0.842222	−	0.539132i	$-0.818753\pi$
$607$	−41.5002			−1.68444			−0.842222	+	0.539132i	$0.818753\pi$
$608$			3.66291i			0.148551i
$609$		−	1.40105i		−	0.0567733i
$610$		0			0
$611$	14.1114			0.570887
$612$	0.138227	−	0.0702982i	0.00558749	−	0.00284164i
$613$			27.7137i			1.11935i	0.828714	+	0.559673i	$0.189073\pi$
$613$			27.7137i			1.11935i	−0.828714	+	0.559673i	$0.810927\pi$
$614$	−43.3707			−1.75030
$615$		0			0
$616$	1.65703			0.0667637
$617$	29.6629			1.19418			0.597092	−	0.802173i	$-0.296323\pi$
$617$	29.6629			1.19418			0.597092	+	0.802173i	$0.296323\pi$
$618$	17.4763			0.702999
$619$		−	26.4422i		−	1.06280i	−0.847121	−	0.531400i	$-0.821666\pi$
$619$		−	26.4422i		−	1.06280i	0.847121	−	0.531400i	$-0.178334\pi$
$620$		0			0
$621$	−44.1378			−1.77119
$622$	−6.72733			−0.269741
$623$	21.6023			0.865477
$624$		−	15.7137i		−	0.629051i
$625$		0			0
$626$		−	1.22425i		−	0.0489310i
$627$			2.70052i			0.107849i
$628$			1.66291i			0.0663574i
$629$	−15.8496	+	8.06063i	−0.631963	+	0.321399i
$630$		0			0
$631$	37.7499			1.50280			0.751400	−	0.659847i	$-0.229379\pi$
$631$	37.7499			1.50280			0.751400	+	0.659847i	$0.229379\pi$
$632$	24.2252			0.963627
$633$			34.9584i			1.38947i
$634$			47.7499i			1.89639i
$635$		0			0
$636$		−	2.78560i		−	0.110456i
$637$		−	11.5212i		−	0.456486i
$638$		−	0.463096i		−	0.0183341i
$639$			2.81828i			0.111490i
$640$		0			0
$641$			46.3488i			1.83067i	0.402694	+	0.915335i	$0.368074\pi$
$641$			46.3488i			1.83067i	−0.402694	+	0.915335i	$0.631926\pi$
$642$			14.5442i			0.574014i
$643$	−34.9502			−1.37830			−0.689150	−	0.724619i	$-0.742016\pi$
$643$	−34.9502			−1.37830			−0.689150	+	0.724619i	$0.742016\pi$
$644$	−2.05949			−0.0811554
$645$		0			0
$646$	−9.27504	−	18.2374i	−0.364922	−	0.717542i
$647$			36.5296i			1.43613i	0.695978	+	0.718064i	$0.254971\pi$
$647$			36.5296i			1.43613i	−0.695978	+	0.718064i	$0.745029\pi$
$648$		−	22.4191i		−	0.880707i
$649$			2.38787i			0.0937322i
$650$		0			0
$651$			3.94921i			0.154782i
$652$	−2.78797			−0.109185
$653$	−0.926192			−0.0362447			−0.0181223	−	0.999836i	$-0.505769\pi$
$653$	−0.926192			−0.0362447			−0.0181223	+	0.999836i	$0.505769\pi$
$654$	31.5125			1.23223
$655$		0			0
$656$			49.0494i			1.91506i
$657$	2.58910			0.101011
$658$	12.4777			0.486431
$659$	24.0118			0.935365			0.467683	−	0.883896i	$-0.345089\pi$
$659$	24.0118			0.935365			0.467683	+	0.883896i	$0.345089\pi$
$660$		0			0
$661$	−20.9478			−0.814775			−0.407387	−	0.913255i	$-0.633560\pi$
$661$	−20.9478			−0.814775			−0.407387	+	0.913255i	$0.633560\pi$
$662$		−	10.1114i		−	0.392991i
$663$	6.75131	+	13.2750i	0.262199	+	0.515560i
$664$	−35.9307			−1.39438
$665$		0			0
$666$			1.23884i			0.0480042i
$667$		−	5.36011i		−	0.207544i
$668$	1.46405			0.0566458
$669$			40.7777i			1.57656i
$670$		0			0
$671$	1.36485			0.0526895
$672$		−	2.35756i		−	0.0909447i
$673$	0.513881			0.0198087			0.00990433	−	0.999951i	$-0.496847\pi$
$673$	0.513881			0.0198087			0.00990433	+	0.999951i	$0.496847\pi$
$674$		−	26.7367i		−	1.02986i
$675$		0			0
$676$	−1.61942			−0.0622854
$677$	3.67276			0.141156			0.0705778	−	0.997506i	$-0.477516\pi$
$677$	3.67276			0.141156			0.0705778	+	0.997506i	$0.477516\pi$
$678$			12.1260i			0.465697i
$679$	4.71511			0.180949
$680$		0			0
$681$	−18.7816			−0.719713
$682$			1.30536i			0.0499847i
$683$	10.5115			0.402212			0.201106	−	0.979570i	$-0.435546\pi$
$683$	10.5115			0.402212			0.201106	+	0.979570i	$0.435546\pi$
$684$	−0.126008			−0.00481804
$685$		0			0
$686$		−	23.5341i		−	0.898535i
$687$	−20.3634			−0.776914
$688$			35.4821i			1.35274i
$689$	−18.4894			−0.704392
$690$		0			0
$691$			25.5940i			0.973643i	0.873502	+	0.486821i	$0.161844\pi$
$691$			25.5940i			0.973643i	−0.873502	+	0.486821i	$0.838156\pi$
$692$	2.29806			0.0873592
$693$			0.120128i			0.00456330i
$694$			27.1817i			1.03180i
$695$		0			0
$696$	2.91160			0.110364
$697$	−21.0738	−	41.4372i	−0.798227	−	1.56955i
$698$			20.1476i			0.762599i
$699$	20.0606			0.758763
$700$		0			0
$701$	30.8324			1.16452			0.582262	−	0.813001i	$-0.302168\pi$
$701$	30.8324			1.16452			0.582262	+	0.813001i	$0.302168\pi$
$702$	17.0884			0.644960
$703$	14.4485			0.544936
$704$			3.40739i			0.128421i
$705$		0			0
$706$	40.5863			1.52748
$707$	8.82653			0.331956
$708$	1.61213			0.0605874
$709$		−	28.1866i		−	1.05857i	−0.848444	−	0.529286i	$-0.822460\pi$
$709$		−	28.1866i		−	1.05857i	0.848444	−	0.529286i	$-0.177540\pi$
$710$		0			0
$711$			1.75623i			0.0658639i
$712$			44.8930i			1.68244i
$713$			15.1089i			0.565831i
$714$	5.96968	+	11.7381i	0.223410	+	0.439289i
$715$		0			0
$716$	−0.625301			−0.0233686
$717$	14.8021			0.552794
$718$			13.4617i			0.502385i
$719$		−	17.7200i		−	0.660846i	−0.943833	−	0.330423i	$-0.892809\pi$
$719$		−	17.7200i		−	0.660846i	0.943833	−	0.330423i	$-0.107191\pi$
$720$		0			0
$721$		−	9.06679i		−	0.337665i
$722$		−	11.5174i		−	0.428633i
$723$		−	0.438658i		−	0.0163139i
$724$		−	1.33567i		−	0.0496399i
$725$		0			0
$726$			26.7186i			0.991621i
$727$		−	9.68338i		−	0.359137i	−0.983746	−	0.179568i	$-0.942530\pi$
$727$		−	9.68338i		−	0.359137i	0.983746	−	0.179568i	$-0.0574701\pi$
$728$	−7.42548			−0.275207
$729$	28.5125			1.05602
$730$		0			0
$731$	−15.2447	−	29.9756i	−0.563846	−	1.10869i
$732$		−	0.921452i		−	0.0340579i
$733$		−	32.7123i		−	1.20826i	−0.796887	−	0.604128i	$-0.793522\pi$
$733$		−	32.7123i		−	1.20826i	0.796887	−	0.604128i	$-0.206478\pi$
$734$			18.9053i			0.697806i
$735$		0			0
$736$		−	9.01951i		−	0.332464i
$737$	2.37328			0.0874211
$738$	−3.23884			−0.119223
$739$	−1.42548			−0.0524373			−0.0262186	−	0.999656i	$-0.508347\pi$
$739$	−1.42548			−0.0524373			−0.0262186	+	0.999656i	$0.508347\pi$
$740$		0			0
$741$		−	12.1016i		−	0.444562i
$742$	−16.3488			−0.600185
$743$	16.8143			0.616857			0.308429	−	0.951247i	$-0.400197\pi$
$743$	16.8143			0.616857			0.308429	+	0.951247i	$0.400197\pi$
$744$	−8.20711			−0.300887
$745$		0			0
$746$	14.9537			0.547493
$747$		−	2.60483i		−	0.0953058i
$748$	0.174424	+	0.342968i	0.00637756	+	0.0125401i
$749$	7.54561			0.275711
$750$		0			0
$751$		−	44.0835i		−	1.60863i	−0.594204	−	0.804314i	$-0.702533\pi$
$751$		−	44.0835i		−	1.60863i	0.594204	−	0.804314i	$-0.297467\pi$
$752$			28.4690i			1.03816i
$753$	−39.6385			−1.44451
$754$			2.07522i			0.0755752i
$755$		0			0
$756$	1.33567			0.0485780
$757$		−	39.8094i		−	1.44690i	−0.690378	−	0.723448i	$-0.742556\pi$
$757$		−	39.8094i		−	1.44690i	0.690378	−	0.723448i	$-0.257444\pi$
$758$	13.5999			0.493971
$759$		−	6.64974i		−	0.241370i
$760$		0			0
$761$	2.81591			0.102077			0.0510384	−	0.998697i	$-0.483747\pi$
$761$	2.81591			0.102077			0.0510384	+	0.998697i	$0.483747\pi$
$762$	−4.38787			−0.158956
$763$		−	16.3488i		−	0.591868i
$764$	−1.39631			−0.0505166
$765$		0			0
$766$	−2.71625			−0.0981422
$767$		−	10.7005i		−	0.386374i
$768$	7.72592			0.278785
$769$	−36.0665			−1.30059			−0.650296	−	0.759681i	$-0.725355\pi$
$769$	−36.0665			−1.30059			−0.650296	+	0.759681i	$0.725355\pi$
$770$		0			0
$771$			32.2374i			1.16100i
$772$	3.90034			0.140376
$773$		−	11.6180i		−	0.417871i	−0.977929	−	0.208935i	$-0.933000\pi$
$773$		−	11.6180i		−	0.417871i	0.977929	−	0.208935i	$-0.0669998\pi$
$774$	−2.34297			−0.0842162
$775$		0			0
$776$			9.79877i			0.351755i
$777$	−9.29948			−0.333617
$778$		−	17.2663i		−	0.619028i
$779$			37.7743i			1.35341i
$780$		0			0
$781$	−6.99271			−0.250219
$782$	22.8388	+	44.9076i	0.816712	+	1.60589i
$783$			3.47627i			0.124232i
$784$	23.2433			0.830118
$785$		0			0
$786$	−27.5574			−0.982939
$787$	−28.4626			−1.01458			−0.507292	−	0.861774i	$-0.669353\pi$
$787$	−28.4626			−1.01458			−0.507292	+	0.861774i	$0.669353\pi$
$788$	0.613541			0.0218565
$789$			28.8872i			1.02841i
$790$		0			0
$791$	6.29104			0.223684
$792$	−0.249646			−0.00887080
$793$	−6.11616			−0.217191
$794$			13.8858i			0.492787i
$795$		0			0
$796$		−	4.16854i		−	0.147750i
$797$		−	50.5355i		−	1.79006i	−0.446007	−	0.895029i	$-0.647154\pi$
$797$		−	50.5355i		−	1.79006i	0.446007	−	0.895029i	$-0.352846\pi$
$798$		−	10.7005i		−	0.378794i
$799$	−12.2315	−	24.0508i	−0.432721	−	0.850856i
$800$		0			0
$801$	−3.25457			−0.114995
$802$	−11.7597			−0.415251
$803$			6.42407i			0.226701i
$804$		−	1.60228i		−	0.0565080i
$805$		0			0
$806$		−	5.84955i		−	0.206042i
$807$		−	44.6009i		−	1.57002i
$808$			18.3430i			0.645303i
$809$		−	2.50914i		−	0.0882167i	−0.999027	−	0.0441084i	$-0.985955\pi$
$809$		−	2.50914i		−	0.0882167i	0.999027	−	0.0441084i	$-0.0140447\pi$
$810$		0			0
$811$		−	18.0933i		−	0.635342i	−0.948201	−	0.317671i	$-0.897099\pi$
$811$		−	18.0933i		−	0.635342i	0.948201	−	0.317671i	$-0.102901\pi$
$812$			0.162205i			0.00569227i
$813$	−11.2243			−0.393652
$814$	−3.07381			−0.107737
$815$		0			0
$816$	−26.7816	+	13.6204i	−0.937544	+	0.476809i
$817$			27.3258i			0.956010i
$818$		−	13.4401i		−	0.469921i
$819$		−	0.538319i		−	0.0188104i
$820$		0			0
$821$			7.02776i			0.245271i	0.992452	+	0.122635i	$0.0391345\pi$
$821$			7.02776i			0.245271i	−0.992452	+	0.122635i	$0.960865\pi$
$822$	−29.1998			−1.01846
$823$	−28.5379			−0.994767			−0.497384	−	0.867531i	$-0.665706\pi$
$823$	−28.5379			−0.994767			−0.497384	+	0.867531i	$0.665706\pi$
$824$	18.8423			0.656401
$825$		0			0
$826$		−	9.46168i		−	0.329214i
$827$	−26.3004			−0.914556			−0.457278	−	0.889324i	$-0.651175\pi$
$827$	−26.3004			−0.914556			−0.457278	+	0.889324i	$0.651175\pi$
$828$	0.310281			0.0107830
$829$	27.2506			0.946453			0.473226	−	0.880941i	$-0.343089\pi$
$829$	27.2506			0.946453			0.473226	+	0.880941i	$0.343089\pi$
$830$		0			0
$831$	27.9756			0.970462
$832$		−	15.2692i		−	0.529363i
$833$	−19.6361	+	9.98637i	−0.680351	+	0.346007i
$834$	−29.0435			−1.00569
$835$		0			0
$836$		−	0.312650i		−	0.0108132i
$837$		−	9.79877i		−	0.338695i
$838$	−13.3235			−0.460251
$839$		−	38.6580i		−	1.33462i	−0.744779	−	0.667311i	$-0.767445\pi$
$839$		−	38.6580i		−	1.33462i	0.744779	−	0.667311i	$-0.232555\pi$
$840$		0			0
$841$	28.5778			0.985443
$842$			25.0435i			0.863056i
$843$	−47.6140			−1.63991
$844$		−	4.04728i		−	0.139313i
$845$		0			0
$846$	−1.87987			−0.0646313
$847$	13.8618			0.476296
$848$		−	37.3014i		−	1.28093i
$849$	16.8568			0.578526
$850$		0			0
$851$	−35.5778			−1.21959
$852$			4.72099i			0.161739i
$853$	−5.46168			−0.187004			−0.0935022	−	0.995619i	$-0.529806\pi$
$853$	−5.46168			−0.187004			−0.0935022	+	0.995619i	$0.529806\pi$
$854$	−5.40807			−0.185060
$855$		0			0
$856$			15.6810i			0.535966i
$857$	−8.30280			−0.283618			−0.141809	−	0.989894i	$-0.545292\pi$
$857$	−8.30280			−0.283618			−0.141809	+	0.989894i	$0.545292\pi$
$858$			2.57452i			0.0878925i
$859$	−10.7612			−0.367166			−0.183583	−	0.983004i	$-0.558770\pi$
$859$	−10.7612			−0.367166			−0.183583	+	0.983004i	$0.558770\pi$
$860$		0			0
$861$		−	24.3127i		−	0.828573i
$862$	−21.7259			−0.739988
$863$		−	43.7342i		−	1.48873i	−0.667774	−	0.744364i	$-0.732753\pi$
$863$		−	43.7342i		−	1.48873i	0.667774	−	0.744364i	$-0.267247\pi$
$864$			5.84955i			0.199006i
$865$		0			0
$866$	−9.89446			−0.336227
$867$	16.7734	−	23.0132i	0.569654	−	0.781568i
$868$		−	0.457216i		−	0.0155189i
$869$	−4.35756			−0.147820
$870$		0			0
$871$	−10.6351			−0.360358
$872$	33.9756			1.15056
$873$	−0.710373			−0.0240425
$874$		−	40.9380i		−	1.38475i
$875$		0			0
$876$	4.33709			0.146537
$877$	−43.5633			−1.47103			−0.735513	−	0.677510i	$-0.763059\pi$
$877$	−43.5633			−1.47103			−0.735513	+	0.677510i	$0.763059\pi$
$878$	14.1744			0.478364
$879$		−	23.9756i		−	0.808676i
$880$		0			0
$881$		−	43.4372i		−	1.46344i	−0.681606	−	0.731719i	$-0.738718\pi$
$881$		−	43.4372i		−	1.46344i	0.681606	−	0.731719i	$-0.261282\pi$
$882$			1.53481i			0.0516797i
$883$			6.56864i			0.221052i	0.993873	+	0.110526i	$0.0352536\pi$
$883$			6.56864i			0.221052i	−0.993873	+	0.110526i	$0.964746\pi$
$884$	−0.781626	−	1.53690i	−0.0262889	−	0.0516917i
$885$		0			0
$886$	−21.9090			−0.736049
$887$	−21.4396			−0.719872			−0.359936	−	0.932977i	$-0.617201\pi$
$887$	−21.4396			−0.719872			−0.359936	+	0.932977i	$0.617201\pi$
$888$		−	19.3258i		−	0.648532i
$889$			2.27645i			0.0763498i
$890$		0			0
$891$			4.03269i			0.135100i
$892$		−	4.72099i		−	0.158070i
$893$			21.9248i			0.733685i
$894$		−	42.6761i		−	1.42730i
$895$		0			0
$896$		−	16.3162i		−	0.545085i
$897$			29.7988i			0.994952i
$898$	16.1476			0.538853
$899$	1.18997			0.0396876
$900$		0			0
$901$	16.0263	+	31.5125i	0.533915	+	1.04983i
$902$		−	8.03620i		−	0.267576i
$903$		−	17.5877i		−	0.585282i
$904$			13.0738i			0.434828i
$905$		0			0
$906$		−	33.7137i		−	1.12006i
$907$	21.2628			0.706020			0.353010	−	0.935619i	$-0.385158\pi$
$907$	21.2628			0.706020			0.353010	+	0.935619i	$0.385158\pi$
$908$	2.17442			0.0721608
$909$	−1.32979			−0.0441065
$910$		0			0
$911$		−	48.6678i		−	1.61244i	−0.591618	−	0.806219i	$-0.701510\pi$
$911$		−	48.6678i		−	1.61244i	0.591618	−	0.806219i	$-0.298490\pi$
$912$	24.4142			0.808436
$913$	6.46310			0.213897
$914$	−11.2837			−0.373233
$915$		0			0
$916$	2.35756			0.0778958
$917$			14.2969i			0.472126i
$918$	−14.8119	−	29.1246i	−0.488867	−	0.961255i
$919$	−4.55993			−0.150418			−0.0752091	−	0.997168i	$-0.523962\pi$
$919$	−4.55993			−0.150418			−0.0752091	+	0.997168i	$0.523962\pi$
$920$		0			0
$921$			49.0494i			1.61623i
$922$			6.77575i			0.223147i
$923$	31.3357			1.03143
$924$			0.201231i			0.00662001i
$925$		0			0
$926$	3.80465			0.125029
$927$			1.36599i			0.0448650i
$928$	−0.710373			−0.0233191
$929$			23.3963i			0.767608i	0.923415	+	0.383804i	$0.125386\pi$
$929$			23.3963i			0.767608i	−0.923415	+	0.383804i	$0.874614\pi$
$930$		0			0
$931$	17.9003			0.586660
$932$	−2.32250			−0.0760760
$933$			7.60816i			0.249080i
$934$	−2.30677			−0.0754798
$935$		0			0
$936$	1.11871			0.0365663
$937$		−	30.3898i		−	0.992791i	−0.868097	−	0.496395i	$-0.834657\pi$
$937$		−	30.3898i		−	0.992791i	0.868097	−	0.496395i	$-0.165343\pi$
$938$	−9.40388			−0.307047
$939$	−1.38455			−0.0451830
$940$		0			0
$941$			25.9610i			0.846304i	0.906059	+	0.423152i	$0.139076\pi$
$941$			25.9610i			0.846304i	−0.906059	+	0.423152i	$0.860924\pi$
$942$	21.2750			0.693178
$943$		−	93.0151i		−	3.02899i
$944$	21.5877			0.702619
$945$		0			0
$946$		−	5.81336i		−	0.189009i
$947$	16.8289			0.546866			0.273433	−	0.961891i	$-0.411841\pi$
$947$	16.8289			0.546866			0.273433	+	0.961891i	$0.411841\pi$
$948$			2.94192i			0.0955491i
$949$		−	28.7875i		−	0.934482i
$950$		0			0
$951$	54.0019			1.75113
$952$	6.43629	+	12.6556i	0.208601	+	0.410171i
$953$			12.7553i			0.413184i	0.978427	+	0.206592i	$0.0662373\pi$
$953$			12.7553i			0.413184i	−0.978427	+	0.206592i	$0.933763\pi$
$954$	2.46310			0.0797457
$955$		0			0
$956$	−1.71370			−0.0554249
$957$	−0.523730			−0.0169298
$958$	−30.2252			−0.976532
$959$			15.1490i			0.489188i
$960$		0			0
$961$	27.6458			0.891799
$962$	13.7743			0.444102
$963$	−1.13681			−0.0366333
$964$			0.0507852i			0.00163568i
$965$		0			0
$966$			26.3488i			0.847760i
$967$			42.5560i			1.36851i	0.729244	+	0.684254i	$0.239872\pi$
$967$			42.5560i			1.36851i	−0.729244	+	0.684254i	$0.760128\pi$
$968$			28.8070i			0.925893i
$969$	−20.6253	+	10.4894i	−0.662580	+	0.336969i
$970$		0			0
$971$	−18.4485			−0.592041			−0.296020	−	0.955182i	$-0.595660\pi$
$971$	−18.4485			−0.592041			−0.296020	+	0.955182i	$0.595660\pi$
$972$	−0.390243			−0.0125170
$973$			15.0679i			0.483056i
$974$		−	0.240938i		−	0.00772014i
$975$		0			0
$976$		−	12.3390i		−	0.394962i
$977$			24.8383i			0.794647i	0.917679	+	0.397324i	$0.130061\pi$
$977$			24.8383i			0.794647i	−0.917679	+	0.397324i	$0.869939\pi$
$978$			35.6688i			1.14056i
$979$		−	8.07522i		−	0.258085i
$980$		0			0
$981$			2.46310i			0.0786406i
$982$			19.0132i			0.606735i
$983$	4.32487			0.137942			0.0689710	−	0.997619i	$-0.478028\pi$
$983$	4.32487			0.137942			0.0689710	+	0.997619i	$0.478028\pi$
$984$	50.5256			1.61070
$985$		0			0
$986$	3.53690	−	1.79877i	0.112638	−	0.0572845i
$987$		−	14.1114i		−	0.449171i
$988$			1.40105i			0.0445732i
$989$		−	67.2868i		−	2.13960i
$990$		0			0
$991$		−	31.8432i		−	1.01153i	−0.862670	−	0.505767i	$-0.831210\pi$
$991$		−	31.8432i		−	1.01153i	0.862670	−	0.505767i	$-0.168790\pi$
$992$	2.00237			0.0635753
$993$	−11.4353			−0.362889
$994$	27.7078			0.878839
$995$		0			0
$996$		−	4.36344i		−	0.138261i
$997$	−29.0278			−0.919318			−0.459659	−	0.888095i	$-0.652028\pi$
$997$	−29.0278			−0.919318			−0.459659	+	0.888095i	$0.652028\pi$
$998$	−26.2788			−0.831842
$999$	23.0738			0.730023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.c.a.424.5		6
5.2	odd	4		425.2.d.c.101.1		6
5.3	odd	4		85.2.d.a.16.6	yes	6
5.4	even	2		425.2.c.b.424.2		6
15.8	even	4		765.2.g.b.271.2		6
17.16	even	2		425.2.c.b.424.5		6
20.3	even	4		1360.2.c.f.1121.2		6
85.13	odd	4		1445.2.a.k.1.1		3
85.33	odd	4		85.2.d.a.16.5	✓	6
85.38	odd	4		1445.2.a.j.1.1		3
85.47	odd	4		7225.2.a.r.1.3		3
85.67	odd	4		425.2.d.c.101.2		6
85.72	odd	4		7225.2.a.q.1.3		3
85.84	even	2	inner	425.2.c.a.424.2		6
255.203	even	4		765.2.g.b.271.1		6
340.203	even	4		1360.2.c.f.1121.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.d.a.16.5	✓	6	85.33	odd	4
85.2.d.a.16.6	yes	6	5.3	odd	4
425.2.c.a.424.2		6	85.84	even	2	inner
425.2.c.a.424.5		6	1.1	even	1	trivial
425.2.c.b.424.2		6	5.4	even	2
425.2.c.b.424.5		6	17.16	even	2
425.2.d.c.101.1		6	5.2	odd	4
425.2.d.c.101.2		6	85.67	odd	4
765.2.g.b.271.1		6	255.203	even	4
765.2.g.b.271.2		6	15.8	even	4
1360.2.c.f.1121.2		6	20.3	even	4
1360.2.c.f.1121.5		6	340.203	even	4
1445.2.a.j.1.1		3	85.38	odd	4
1445.2.a.k.1.1		3	85.13	odd	4
7225.2.a.q.1.3		3	85.72	odd	4
7225.2.a.r.1.3		3	85.47	odd	4

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.48119i q^{2} +1.67513 q^{3} -0.193937 q^{4} +2.48119i q^{6} +1.28726 q^{7} +2.67513i q^{8} -0.193937 q^{9} -0.481194i q^{11} -0.324869 q^{12} +2.15633i q^{13} +1.90668i q^{14} -4.35026 q^{16} +(3.67513 - 1.86907i) q^{17} -0.287258i q^{18} -3.35026 q^{19} +2.15633 q^{21} +0.712742 q^{22} +8.24965 q^{23} +4.48119i q^{24} -3.19394 q^{26} -5.35026 q^{27} -0.249646 q^{28} -0.649738i q^{29} +1.83146i q^{31} -1.09332i q^{32} -0.806063i q^{33} +(2.76845 + 5.44358i) q^{34} +0.0376114 q^{36} -4.31265 q^{37} -4.96239i q^{38} +3.61213i q^{39} -11.2750i q^{41} +3.19394i q^{42} -8.15633i q^{43} +0.0933212i q^{44} +12.2193i q^{46} -6.54420i q^{47} -7.28726 q^{48} -5.34297 q^{49} +(6.15633 - 3.13093i) q^{51} -0.418190i q^{52} +8.57452i q^{53} -7.92478i q^{54} +3.44358i q^{56} -5.61213 q^{57} +0.962389 q^{58} -4.96239 q^{59} +2.83638i q^{61} -2.71274 q^{62} -0.249646 q^{63} -7.08110 q^{64} +1.19394 q^{66} +4.93207i q^{67} +(-0.712742 + 0.362481i) q^{68} +13.8192 q^{69} -14.5320i q^{71} -0.518806i q^{72} -13.3503 q^{73} -6.38787i q^{74} +0.649738 q^{76} -0.619421i q^{77} -5.35026 q^{78} -9.05571i q^{79} -8.38058 q^{81} +16.7005 q^{82} +13.4314i q^{83} -0.418190 q^{84} +12.0811 q^{86} -1.08840i q^{87} +1.28726 q^{88} +16.7816 q^{89} +2.77575i q^{91} -1.59991 q^{92} +3.06793i q^{93} +9.69323 q^{94} -1.83146i q^{96} +3.66291 q^{97} -7.91397i q^{98} +0.0933212i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} - 4 q^{7} - 2 q^{9} - 12 q^{12} - 6 q^{16} + 12 q^{17} - 8 q^{21} + 16 q^{22} + 16 q^{23} - 20 q^{26} - 12 q^{27} + 32 q^{28} - 6 q^{34} + 22 q^{36} + 16 q^{37} - 32 q^{48} + 14 q^{49} + 16 q^{51}+ \cdots - 40 q^{97}+O(q^{100}) \) 6 * q - 2 * q^4 - 4 * q^7 - 2 * q^9 - 12 * q^12 - 6 * q^16 + 12 * q^17 - 8 * q^21 + 16 * q^22 + 16 * q^23 - 20 * q^26 - 12 * q^27 + 32 * q^28 - 6 * q^34 + 22 * q^36 + 16 * q^37 - 32 * q^48 + 14 * q^49 + 16 * q^51 - 32 * q^57 - 16 * q^58 - 8 * q^59 - 28 * q^62 + 32 * q^63 + 22 * q^64 + 8 * q^66 - 16 * q^68 - 60 * q^73 + 24 * q^76 - 12 * q^78 - 26 * q^81 + 60 * q^82 + 8 * q^86 - 4 * q^88 - 4 * q^89 + 44 * q^92 - 8 * q^94 - 40 * q^97

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