LMFDB - Embedded newform 1170.2.e.g.469.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(469,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1170.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.e (of order $2$, degree $1$, 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:	$9.34249703649$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.2
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1170.469
Dual form			1170.2.e.g.469.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +3.70928i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +3.70928i q^{7} +1.00000i q^{8} +(2.17009 - 0.539189i) q^{10} -2.00000 q^{11} -1.00000i q^{13} +3.70928 q^{14} +1.00000 q^{16} -4.78765i q^{17} +0.630898 q^{19} +(-0.539189 - 2.17009i) q^{20} +2.00000i q^{22} +4.97107i q^{23} +(-4.41855 + 2.34017i) q^{25} -1.00000 q^{26} -3.70928i q^{28} -6.38962 q^{29} -3.07838 q^{31} -1.00000i q^{32} -4.78765 q^{34} +(-8.04945 + 2.00000i) q^{35} +10.6803i q^{37} -0.630898i q^{38} +(-2.17009 + 0.539189i) q^{40} -8.34017 q^{41} +11.0205i q^{43} +2.00000 q^{44} +4.97107 q^{46} -3.41855i q^{47} -6.75872 q^{49} +(2.34017 + 4.41855i) q^{50} +1.00000i q^{52} -13.1773i q^{53} +(-1.07838 - 4.34017i) q^{55} -3.70928 q^{56} +6.38962i q^{58} +7.26180 q^{59} -7.57531 q^{61} +3.07838i q^{62} -1.00000 q^{64} +(2.17009 - 0.539189i) q^{65} -0.156755i q^{67} +4.78765i q^{68} +(2.00000 + 8.04945i) q^{70} -7.60197 q^{71} +11.1278i q^{73} +10.6803 q^{74} -0.630898 q^{76} -7.41855i q^{77} +16.2823 q^{79} +(0.539189 + 2.17009i) q^{80} +8.34017i q^{82} +4.49693i q^{83} +(10.3896 - 2.58145i) q^{85} +11.0205 q^{86} -2.00000i q^{88} +4.73820 q^{89} +3.70928 q^{91} -4.97107i q^{92} -3.41855 q^{94} +(0.340173 + 1.36910i) q^{95} +11.7093i q^{97} +6.75872i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4}+O(q^{10}) $ 6 * q - 6 * q^4	$ 6 q - 6 q^{4} + 2 q^{10} - 12 q^{11} + 8 q^{14} + 6 q^{16} - 4 q^{19} + 2 q^{25} - 6 q^{26} + 20 q^{29} - 12 q^{31} - 8 q^{34} - 12 q^{35} - 2 q^{40} - 28 q^{41} + 12 q^{44} + 10 q^{49} - 8 q^{50} - 8 q^{56} + 28 q^{59} - 4 q^{61} - 6 q^{64} + 2 q^{65} + 12 q^{70} - 8 q^{71} + 20 q^{74} + 4 q^{76} + 16 q^{79} + 4 q^{85} + 44 q^{89} + 8 q^{91} + 8 q^{94} - 20 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^10 - 12 * q^11 + 8 * q^14 + 6 * q^16 - 4 * q^19 + 2 * q^25 - 6 * q^26 + 20 * q^29 - 12 * q^31 - 8 * q^34 - 12 * q^35 - 2 * q^40 - 28 * q^41 + 12 * q^44 + 10 * q^49 - 8 * q^50 - 8 * q^56 + 28 * q^59 - 4 * q^61 - 6 * q^64 + 2 * q^65 + 12 * q^70 - 8 * q^71 + 20 * q^74 + 4 * q^76 + 16 * q^79 + 4 * q^85 + 44 * q^89 + 8 * q^91 + 8 * q^94 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.539189	+	2.17009i	0.241133	+	0.970492i
$5$	0.539189	+	2.17009i	0.241133	+	0.970492i
$6$		0			0
$7$			3.70928i			1.40197i	0.713174	+	0.700987i	$0.247257\pi$
$7$			3.70928i			1.40197i	−0.713174	+	0.700987i	$0.752743\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.17009	−	0.539189i	0.686242	−	0.170506i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	3.70928			0.991346
$15$		0			0
$16$	1.00000			0.250000
$17$		−	4.78765i		−	1.16118i	−0.814197	−	0.580588i	$-0.802823\pi$
$17$		−	4.78765i		−	1.16118i	0.814197	−	0.580588i	$-0.197177\pi$
$18$		0			0
$19$	0.630898			0.144738			0.0723689	−	0.997378i	$-0.476944\pi$
$19$	0.630898			0.144738			0.0723689	+	0.997378i	$0.476944\pi$
$20$	−0.539189	−	2.17009i	−0.120566	−	0.485246i
$21$		0			0
$22$			2.00000i			0.426401i
$23$			4.97107i			1.03654i	0.855217	+	0.518270i	$0.173424\pi$
$23$			4.97107i			1.03654i	−0.855217	+	0.518270i	$0.826576\pi$
$24$		0			0
$25$	−4.41855	+	2.34017i	−0.883710	+	0.468035i
$26$	−1.00000			−0.196116
$27$		0			0
$28$		−	3.70928i		−	0.700987i
$29$	−6.38962			−1.18652			−0.593261	−	0.805010i	$-0.702160\pi$
$29$	−6.38962			−1.18652			−0.593261	+	0.805010i	$0.702160\pi$
$30$		0			0
$31$	−3.07838			−0.552893			−0.276446	−	0.961029i	$-0.589157\pi$
$31$	−3.07838			−0.552893			−0.276446	+	0.961029i	$0.589157\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−4.78765			−0.821076
$35$	−8.04945	+	2.00000i	−1.36061	+	0.338062i
$36$		0			0
$37$			10.6803i			1.75584i	0.478809	+	0.877919i	$0.341069\pi$
$37$			10.6803i			1.75584i	−0.478809	+	0.877919i	$0.658931\pi$
$38$		−	0.630898i		−	0.102345i
$39$		0			0
$40$	−2.17009	+	0.539189i	−0.343121	+	0.0852532i
$41$	−8.34017			−1.30252			−0.651258	−	0.758856i	$-0.725758\pi$
$41$	−8.34017			−1.30252			−0.651258	+	0.758856i	$0.725758\pi$
$42$		0			0
$43$			11.0205i			1.68061i	0.542111	+	0.840307i	$0.317625\pi$
$43$			11.0205i			1.68061i	−0.542111	+	0.840307i	$0.682375\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	4.97107			0.732944
$47$		−	3.41855i		−	0.498647i	−0.968420	−	0.249323i	$-0.919792\pi$
$47$		−	3.41855i		−	0.498647i	0.968420	−	0.249323i	$-0.0802082\pi$
$48$		0			0
$49$	−6.75872			−0.965532
$50$	2.34017	+	4.41855i	0.330950	+	0.624877i
$51$		0			0
$52$			1.00000i			0.138675i
$53$		−	13.1773i		−	1.81004i	−0.425371	−	0.905019i	$-0.639856\pi$
$53$		−	13.1773i		−	1.81004i	0.425371	−	0.905019i	$-0.360144\pi$
$54$		0			0
$55$	−1.07838	−	4.34017i	−0.145408	−	0.585229i
$56$	−3.70928			−0.495673
$57$		0			0
$58$			6.38962i			0.838998i
$59$	7.26180			0.945405			0.472703	−	0.881222i	$-0.343278\pi$
$59$	7.26180			0.945405			0.472703	+	0.881222i	$0.343278\pi$
$60$		0			0
$61$	−7.57531			−0.969919			−0.484959	−	0.874537i	$-0.661166\pi$
$61$	−7.57531			−0.969919			−0.484959	+	0.874537i	$0.661166\pi$
$62$			3.07838i			0.390954i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.17009	−	0.539189i	0.269166	−	0.0668781i
$66$		0			0
$67$		−	0.156755i		−	0.0191507i	−0.999954	−	0.00957537i	$-0.996952\pi$
$67$		−	0.156755i		−	0.0191507i	0.999954	−	0.00957537i	$-0.00304798\pi$
$68$			4.78765i			0.580588i
$69$		0			0
$70$	2.00000	+	8.04945i	0.239046	+	0.962093i
$71$	−7.60197			−0.902188			−0.451094	−	0.892477i	$-0.648966\pi$
$71$	−7.60197			−0.902188			−0.451094	+	0.892477i	$0.648966\pi$
$72$		0			0
$73$			11.1278i			1.30241i	0.758900	+	0.651207i	$0.225737\pi$
$73$			11.1278i			1.30241i	−0.758900	+	0.651207i	$0.774263\pi$
$74$	10.6803			1.24156
$75$		0			0
$76$	−0.630898			−0.0723689
$77$		−	7.41855i		−	0.845422i
$78$		0			0
$79$	16.2823			1.83190			0.915952	−	0.401288i	$-0.131438\pi$
$79$	16.2823			1.83190			0.915952	+	0.401288i	$0.131438\pi$
$80$	0.539189	+	2.17009i	0.0602831	+	0.242623i
$81$		0			0
$82$			8.34017i			0.921018i
$83$			4.49693i			0.493602i	0.969066	+	0.246801i	$0.0793794\pi$
$83$			4.49693i			0.493602i	−0.969066	+	0.246801i	$0.920621\pi$
$84$		0			0
$85$	10.3896	−	2.58145i	1.12691	−	0.279997i
$86$	11.0205			1.18837
$87$		0			0
$88$		−	2.00000i		−	0.213201i
$89$	4.73820			0.502249			0.251124	−	0.967955i	$-0.419200\pi$
$89$	4.73820			0.502249			0.251124	+	0.967955i	$0.419200\pi$
$90$		0			0
$91$	3.70928			0.388838
$92$		−	4.97107i		−	0.518270i
$93$		0			0
$94$	−3.41855			−0.352597
$95$	0.340173	+	1.36910i	0.0349010	+	0.140467i
$96$		0			0
$97$			11.7093i			1.18890i	0.804134	+	0.594448i	$0.202630\pi$
$97$			11.7093i			1.18890i	−0.804134	+	0.594448i	$0.797370\pi$
$98$			6.75872i			0.682734i
$99$		0			0
$100$	4.41855	−	2.34017i	0.441855	−	0.234017i
$101$	−11.8660			−1.18071			−0.590357	−	0.807142i	$-0.701013\pi$
$101$	−11.8660			−1.18071			−0.590357	+	0.807142i	$0.701013\pi$
$102$		0			0
$103$		−	14.5958i		−	1.43817i	−0.694922	−	0.719085i	$-0.744561\pi$
$103$		−	14.5958i		−	1.43817i	0.694922	−	0.719085i	$-0.255439\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	−13.1773			−1.27989
$107$			8.09890i			0.782950i	0.920189	+	0.391475i	$0.128035\pi$
$107$			8.09890i			0.782950i	−0.920189	+	0.391475i	$0.871965\pi$
$108$		0			0
$109$	9.12783			0.874287			0.437144	−	0.899392i	$-0.355990\pi$
$109$	9.12783			0.874287			0.437144	+	0.899392i	$0.355990\pi$
$110$	−4.34017	+	1.07838i	−0.413819	+	0.102819i
$111$		0			0
$112$			3.70928i			0.350494i
$113$		−	0.107307i		−	0.0100946i	−0.999987	−	0.00504730i	$-0.998393\pi$
$113$		−	0.107307i		−	0.0100946i	0.999987	−	0.00504730i	$-0.00160661\pi$
$114$		0			0
$115$	−10.7877	+	2.68035i	−1.00595	+	0.249944i
$116$	6.38962			0.593261
$117$		0			0
$118$		−	7.26180i		−	0.668502i
$119$	17.7587			1.62794
$120$		0			0
$121$	−7.00000			−0.636364
$122$			7.57531i			0.685836i
$123$		0			0
$124$	3.07838			0.276446
$125$	−7.46081	−	8.32684i	−0.667315	−	0.744775i
$126$		0			0
$127$		−	15.1773i		−	1.34677i	−0.739294	−	0.673383i	$-0.764841\pi$
$127$		−	15.1773i		−	1.34677i	0.739294	−	0.673383i	$-0.235159\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−0.539189	−	2.17009i	−0.0472900	−	0.190329i
$131$	11.9649			1.04538			0.522690	−	0.852523i	$-0.324928\pi$
$131$	11.9649			1.04538			0.522690	+	0.852523i	$0.324928\pi$
$132$		0			0
$133$			2.34017i			0.202919i
$134$	−0.156755			−0.0135416
$135$		0			0
$136$	4.78765			0.410538
$137$			22.0989i			1.88804i	0.329894	+	0.944018i	$0.392987\pi$
$137$			22.0989i			1.88804i	−0.329894	+	0.944018i	$0.607013\pi$
$138$		0			0
$139$	−2.52359			−0.214048			−0.107024	−	0.994256i	$-0.534132\pi$
$139$	−2.52359			−0.214048			−0.107024	+	0.994256i	$0.534132\pi$
$140$	8.04945	−	2.00000i	0.680303	−	0.169031i
$141$		0			0
$142$			7.60197i			0.637943i
$143$			2.00000i			0.167248i
$144$		0			0
$145$	−3.44521	−	13.8660i	−0.286109	−	1.15151i
$146$	11.1278			0.920945
$147$		0			0
$148$		−	10.6803i		−	0.877919i
$149$	15.2351			1.24811			0.624055	−	0.781380i	$-0.285484\pi$
$149$	15.2351			1.24811			0.624055	+	0.781380i	$0.285484\pi$
$150$		0			0
$151$	4.34017			0.353198			0.176599	−	0.984283i	$-0.443490\pi$
$151$	4.34017			0.353198			0.176599	+	0.984283i	$0.443490\pi$
$152$			0.630898i			0.0511726i
$153$		0			0
$154$	−7.41855			−0.597804
$155$	−1.65983	−	6.68035i	−0.133321	−	0.536578i
$156$		0			0
$157$			3.97334i			0.317107i	0.987350	+	0.158553i	$0.0506830\pi$
$157$			3.97334i			0.317107i	−0.987350	+	0.158553i	$0.949317\pi$
$158$		−	16.2823i		−	1.29535i
$159$		0			0
$160$	2.17009	−	0.539189i	0.171560	−	0.0426266i
$161$	−18.4391			−1.45320
$162$		0			0
$163$			1.63317i			0.127919i	0.997952	+	0.0639597i	$0.0203729\pi$
$163$			1.63317i			0.127919i	−0.997952	+	0.0639597i	$0.979627\pi$
$164$	8.34017			0.651258
$165$		0			0
$166$	4.49693			0.349029
$167$			2.15676i			0.166895i	0.996512	+	0.0834474i	$0.0265930\pi$
$167$			2.15676i			0.166895i	−0.996512	+	0.0834474i	$0.973407\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−2.58145	−	10.3896i	−0.197988	−	0.796848i
$171$		0			0
$172$		−	11.0205i		−	0.840307i
$173$			2.92162i			0.222127i	0.993813	+	0.111063i	$0.0354257\pi$
$173$			2.92162i			0.222127i	−0.993813	+	0.111063i	$0.964574\pi$
$174$		0			0
$175$	−8.68035	−	16.3896i	−0.656172	−	1.23894i
$176$	−2.00000			−0.150756
$177$		0			0
$178$		−	4.73820i		−	0.355143i
$179$	8.13397			0.607961			0.303981	−	0.952678i	$-0.401684\pi$
$179$	8.13397			0.607961			0.303981	+	0.952678i	$0.401684\pi$
$180$		0			0
$181$	−5.78539			−0.430024			−0.215012	−	0.976611i	$-0.568979\pi$
$181$	−5.78539			−0.430024			−0.215012	+	0.976611i	$0.568979\pi$
$182$		−	3.70928i		−	0.274950i
$183$		0			0
$184$	−4.97107			−0.366472
$185$	−23.1773	+	5.75872i	−1.70403	+	0.423390i
$186$		0			0
$187$			9.57531i			0.700216i
$188$			3.41855i			0.249323i
$189$		0			0
$190$	1.36910	−	0.340173i	0.0993251	−	0.0246787i
$191$	−4.89496			−0.354187			−0.177093	−	0.984194i	$-0.556669\pi$
$191$	−4.89496			−0.354187			−0.177093	+	0.984194i	$0.556669\pi$
$192$		0			0
$193$		−	3.12783i		−	0.225146i	−0.993643	−	0.112573i	$-0.964091\pi$
$193$		−	3.12783i		−	0.225146i	0.993643	−	0.112573i	$-0.0359092\pi$
$194$	11.7093			0.840677
$195$		0			0
$196$	6.75872			0.482766
$197$		−	4.83710i		−	0.344629i	−0.985042	−	0.172315i	$-0.944875\pi$
$197$		−	4.83710i		−	0.344629i	0.985042	−	0.172315i	$-0.0551246\pi$
$198$		0			0
$199$	−12.2823			−0.870670			−0.435335	−	0.900268i	$-0.643370\pi$
$199$	−12.2823			−0.870670			−0.435335	+	0.900268i	$0.643370\pi$
$200$	−2.34017	−	4.41855i	−0.165475	−	0.312439i
$201$		0			0
$202$			11.8660i			0.834891i
$203$		−	23.7009i		−	1.66347i
$204$		0			0
$205$	−4.49693	−	18.0989i	−0.314079	−	1.26408i
$206$	−14.5958			−1.01694
$207$		0			0
$208$		−	1.00000i		−	0.0693375i
$209$	−1.26180			−0.0872802
$210$		0			0
$211$	20.4124			1.40525			0.702624	−	0.711561i	$-0.252012\pi$
$211$	20.4124			1.40525			0.702624	+	0.711561i	$0.252012\pi$
$212$			13.1773i			0.905019i
$213$		0			0
$214$	8.09890			0.553629
$215$	−23.9155	+	5.94214i	−1.63102	+	0.405251i
$216$		0			0
$217$		−	11.4186i		−	0.775142i
$218$		−	9.12783i		−	0.618214i
$219$		0			0
$220$	1.07838	+	4.34017i	0.0727042	+	0.292614i
$221$	−4.78765			−0.322052
$222$		0			0
$223$		−	2.76099i		−	0.184890i	−0.995718	−	0.0924448i	$-0.970532\pi$
$223$		−	2.76099i		−	0.184890i	0.995718	−	0.0924448i	$-0.0294682\pi$
$224$	3.70928			0.247836
$225$		0			0
$226$	−0.107307			−0.00713797
$227$		−	4.36683i		−	0.289837i	−0.989444	−	0.144919i	$-0.953708\pi$
$227$		−	4.36683i		−	0.289837i	0.989444	−	0.144919i	$-0.0462920\pi$
$228$		0			0
$229$	20.6453			1.36428			0.682139	−	0.731222i	$-0.261050\pi$
$229$	20.6453			1.36428			0.682139	+	0.731222i	$0.261050\pi$
$230$	2.68035	+	10.7877i	0.176737	+	0.711317i
$231$		0			0
$232$		−	6.38962i		−	0.419499i
$233$			13.1545i			0.861779i	0.902405	+	0.430890i	$0.141800\pi$
$233$			13.1545i			0.861779i	−0.902405	+	0.430890i	$0.858200\pi$
$234$		0			0
$235$	7.41855	−	1.84324i	0.483933	−	0.120240i
$236$	−7.26180			−0.472703
$237$		0			0
$238$		−	17.7587i		−	1.15113i
$239$	7.31965			0.473469			0.236735	−	0.971574i	$-0.423923\pi$
$239$	7.31965			0.473469			0.236735	+	0.971574i	$0.423923\pi$
$240$		0			0
$241$	19.9421			1.28459			0.642293	−	0.766459i	$-0.277983\pi$
$241$	19.9421			1.28459			0.642293	+	0.766459i	$0.277983\pi$
$242$			7.00000i			0.449977i
$243$		0			0
$244$	7.57531			0.484959
$245$	−3.64423	−	14.6670i	−0.232821	−	0.937041i
$246$		0			0
$247$		−	0.630898i		−	0.0401431i
$248$		−	3.07838i		−	0.195477i
$249$		0			0
$250$	−8.32684	+	7.46081i	−0.526636	+	0.471863i
$251$	25.2267			1.59230			0.796148	−	0.605102i	$-0.206867\pi$
$251$	25.2267			1.59230			0.796148	+	0.605102i	$0.206867\pi$
$252$		0			0
$253$		−	9.94214i		−	0.625057i
$254$	−15.1773			−0.952307
$255$		0			0
$256$	1.00000			0.0625000
$257$			17.1545i			1.07007i	0.844831	+	0.535034i	$0.179701\pi$
$257$			17.1545i			1.07007i	−0.844831	+	0.535034i	$0.820299\pi$
$258$		0			0
$259$	−39.6163			−2.46164
$260$	−2.17009	+	0.539189i	−0.134583	+	0.0334391i
$261$		0			0
$262$		−	11.9649i		−	0.739196i
$263$			22.5464i			1.39027i	0.718880	+	0.695135i	$0.244655\pi$
$263$			22.5464i			1.39027i	−0.718880	+	0.695135i	$0.755345\pi$
$264$		0			0
$265$	28.5958	−	7.10504i	1.75663	−	0.436459i
$266$	2.34017			0.143485
$267$		0			0
$268$			0.156755i			0.00957537i
$269$	−7.96493			−0.485630			−0.242815	−	0.970073i	$-0.578071\pi$
$269$	−7.96493			−0.485630			−0.242815	+	0.970073i	$0.578071\pi$
$270$		0			0
$271$	14.8104			0.899670			0.449835	−	0.893112i	$-0.351483\pi$
$271$	14.8104			0.899670			0.449835	+	0.893112i	$0.351483\pi$
$272$		−	4.78765i		−	0.290294i
$273$		0			0
$274$	22.0989			1.33504
$275$	8.83710	−	4.68035i	0.532897	−	0.282235i
$276$		0			0
$277$		−	5.33403i		−	0.320491i	−0.987077	−	0.160245i	$-0.948771\pi$
$277$		−	5.33403i		−	0.320491i	0.987077	−	0.160245i	$-0.0512286\pi$
$278$			2.52359i			0.151355i
$279$		0			0
$280$	−2.00000	−	8.04945i	−0.119523	−	0.481047i
$281$	−20.6225			−1.23023			−0.615117	−	0.788436i	$-0.710891\pi$
$281$	−20.6225			−1.23023			−0.615117	+	0.788436i	$0.710891\pi$
$282$		0			0
$283$			29.1773i			1.73441i	0.497952	+	0.867204i	$0.334085\pi$
$283$			29.1773i			1.73441i	−0.497952	+	0.867204i	$0.665915\pi$
$284$	7.60197			0.451094
$285$		0			0
$286$	2.00000			0.118262
$287$		−	30.9360i		−	1.82609i
$288$		0			0
$289$	−5.92162			−0.348331
$290$	−13.8660	+	3.44521i	−0.814241	+	0.202310i
$291$		0			0
$292$		−	11.1278i		−	0.651207i
$293$		−	8.15676i		−	0.476523i	−0.971201	−	0.238261i	$-0.923423\pi$
$293$		−	8.15676i		−	0.476523i	0.971201	−	0.238261i	$-0.0765775\pi$
$294$		0			0
$295$	3.91548	+	15.7587i	0.227968	+	0.917508i
$296$	−10.6803			−0.620782
$297$		0			0
$298$		−	15.2351i		−	0.882548i
$299$	4.97107			0.287484
$300$		0			0
$301$	−40.8781			−2.35618
$302$		−	4.34017i		−	0.249749i
$303$		0			0
$304$	0.630898			0.0361845
$305$	−4.08452	−	16.4391i	−0.233879	−	0.941298i
$306$		0			0
$307$		−	21.1050i		−	1.20453i	−0.798297	−	0.602264i	$-0.794265\pi$
$307$		−	21.1050i		−	1.20453i	0.798297	−	0.602264i	$-0.205735\pi$
$308$			7.41855i			0.422711i
$309$		0			0
$310$	−6.68035	+	1.65983i	−0.379418	+	0.0942718i
$311$	−12.0989			−0.686065			−0.343033	−	0.939323i	$-0.611454\pi$
$311$	−12.0989			−0.686065			−0.343033	+	0.939323i	$0.611454\pi$
$312$		0			0
$313$			3.05172i			0.172493i	0.996274	+	0.0862466i	$0.0274873\pi$
$313$			3.05172i			0.172493i	−0.996274	+	0.0862466i	$0.972513\pi$
$314$	3.97334			0.224228
$315$		0			0
$316$	−16.2823			−0.915952
$317$		−	11.9733i		−	0.672490i	−0.941775	−	0.336245i	$-0.890843\pi$
$317$		−	11.9733i		−	0.672490i	0.941775	−	0.336245i	$-0.109157\pi$
$318$		0			0
$319$	12.7792			0.715500
$320$	−0.539189	−	2.17009i	−0.0301416	−	0.121312i
$321$		0			0
$322$			18.4391i			1.02757i
$323$		−	3.02052i		−	0.168066i
$324$		0			0
$325$	2.34017	+	4.41855i	0.129809	+	0.245097i
$326$	1.63317			0.0904526
$327$		0			0
$328$		−	8.34017i		−	0.460509i
$329$	12.6803			0.699090
$330$		0			0
$331$	2.37525			0.130555			0.0652776	−	0.997867i	$-0.479207\pi$
$331$	2.37525			0.130555			0.0652776	+	0.997867i	$0.479207\pi$
$332$		−	4.49693i		−	0.246801i
$333$		0			0
$334$	2.15676			0.118012
$335$	0.340173	−	0.0845208i	0.0185856	−	0.00461787i
$336$		0			0
$337$		−	19.1506i		−	1.04320i	−0.853190	−	0.521600i	$-0.825335\pi$
$337$		−	19.1506i		−	1.04320i	0.853190	−	0.521600i	$-0.174665\pi$
$338$			1.00000i			0.0543928i
$339$		0			0
$340$	−10.3896	+	2.58145i	−0.563456	+	0.139999i
$341$	6.15676			0.333407
$342$		0			0
$343$			0.894960i			0.0483233i
$344$	−11.0205			−0.594187
$345$		0			0
$346$	2.92162			0.157067
$347$			18.9360i			1.01654i	0.861198	+	0.508269i	$0.169714\pi$
$347$			18.9360i			1.01654i	−0.861198	+	0.508269i	$0.830286\pi$
$348$		0			0
$349$	10.2907			0.550850			0.275425	−	0.961323i	$-0.411181\pi$
$349$	10.2907			0.550850			0.275425	+	0.961323i	$0.411181\pi$
$350$	−16.3896	+	8.68035i	−0.876062	+	0.463984i
$351$		0			0
$352$			2.00000i			0.106600i
$353$		−	1.90110i		−	0.101186i	−0.998719	−	0.0505928i	$-0.983889\pi$
$353$		−	1.90110i		−	0.101186i	0.998719	−	0.0505928i	$-0.0161111\pi$
$354$		0			0
$355$	−4.09890	−	16.4969i	−0.217547	−	0.875566i
$356$	−4.73820			−0.251124
$357$		0			0
$358$		−	8.13397i		−	0.429894i
$359$	18.0722			0.953816			0.476908	−	0.878953i	$-0.341757\pi$
$359$	18.0722			0.953816			0.476908	+	0.878953i	$0.341757\pi$
$360$		0			0
$361$	−18.6020			−0.979051
$362$			5.78539i			0.304073i
$363$		0			0
$364$	−3.70928			−0.194419
$365$	−24.1483	+	6.00000i	−1.26398	+	0.314054i
$366$		0			0
$367$			3.54411i			0.185001i	0.995713	+	0.0925005i	$0.0294860\pi$
$367$			3.54411i			0.185001i	−0.995713	+	0.0925005i	$0.970514\pi$
$368$			4.97107i			0.259135i
$369$		0			0
$370$	5.75872	+	23.1773i	0.299382	+	1.20493i
$371$	48.8781			2.53763
$372$		0			0
$373$			0.822726i			0.0425991i	0.999773	+	0.0212996i	$0.00678037\pi$
$373$			0.822726i			0.0425991i	−0.999773	+	0.0212996i	$0.993220\pi$
$374$	9.57531			0.495127
$375$		0			0
$376$	3.41855			0.176298
$377$			6.38962i			0.329082i
$378$		0			0
$379$	−28.5152			−1.46473			−0.732363	−	0.680914i	$-0.761583\pi$
$379$	−28.5152			−1.46473			−0.732363	+	0.680914i	$0.761583\pi$
$380$	−0.340173	−	1.36910i	−0.0174505	−	0.0702335i
$381$		0			0
$382$			4.89496i			0.250448i
$383$		−	23.5174i		−	1.20169i	−0.799367	−	0.600843i	$-0.794832\pi$
$383$		−	23.5174i		−	1.20169i	0.799367	−	0.600843i	$-0.205168\pi$
$384$		0			0
$385$	16.0989	−	4.00000i	0.820476	−	0.203859i
$386$	−3.12783			−0.159202
$387$		0			0
$388$		−	11.7093i		−	0.594448i
$389$	3.55252			0.180120			0.0900600	−	0.995936i	$-0.471294\pi$
$389$	3.55252			0.180120			0.0900600	+	0.995936i	$0.471294\pi$
$390$		0			0
$391$	23.7998			1.20361
$392$		−	6.75872i		−	0.341367i
$393$		0			0
$394$	−4.83710			−0.243690
$395$	8.77924	+	35.3340i	0.441732	+	1.77785i
$396$		0			0
$397$		−	14.4657i		−	0.726014i	−0.931786	−	0.363007i	$-0.881750\pi$
$397$		−	14.4657i		−	0.726014i	0.931786	−	0.363007i	$-0.118250\pi$
$398$			12.2823i			0.615657i
$399$		0			0
$400$	−4.41855	+	2.34017i	−0.220928	+	0.117009i
$401$	−24.3402			−1.21549			−0.607745	−	0.794132i	$-0.707926\pi$
$401$	−24.3402			−1.21549			−0.607745	+	0.794132i	$0.707926\pi$
$402$		0			0
$403$			3.07838i			0.153345i
$404$	11.8660			0.590357
$405$		0			0
$406$	−23.7009			−1.17625
$407$		−	21.3607i		−	1.05881i
$408$		0			0
$409$	−16.8371			−0.832541			−0.416271	−	0.909241i	$-0.636663\pi$
$409$	−16.8371			−0.832541			−0.416271	+	0.909241i	$0.636663\pi$
$410$	−18.0989	+	4.49693i	−0.893841	+	0.222087i
$411$		0			0
$412$			14.5958i			0.719085i
$413$			26.9360i			1.32543i
$414$		0			0
$415$	−9.75872	+	2.42469i	−0.479037	+	0.119024i
$416$	−1.00000			−0.0490290
$417$		0			0
$418$			1.26180i			0.0617164i
$419$	24.5997			1.20177			0.600887	−	0.799334i	$-0.294814\pi$
$419$	24.5997			1.20177			0.600887	+	0.799334i	$0.294814\pi$
$420$		0			0
$421$	4.33176			0.211117			0.105559	−	0.994413i	$-0.466337\pi$
$421$	4.33176			0.211117			0.105559	+	0.994413i	$0.466337\pi$
$422$		−	20.4124i		−	0.993660i
$423$		0			0
$424$	13.1773			0.639945
$425$	11.2039	+	21.1545i	0.543471	+	1.02614i
$426$		0			0
$427$		−	28.0989i		−	1.35980i
$428$		−	8.09890i		−	0.391475i
$429$		0			0
$430$	5.94214	+	23.9155i	0.286555	+	1.15331i
$431$	2.52359			0.121557			0.0607785	−	0.998151i	$-0.480642\pi$
$431$	2.52359			0.121557			0.0607785	+	0.998151i	$0.480642\pi$
$432$		0			0
$433$		−	35.3484i		−	1.69874i	−0.527801	−	0.849368i	$-0.676983\pi$
$433$		−	35.3484i		−	1.69874i	0.527801	−	0.849368i	$-0.323017\pi$
$434$	−11.4186			−0.548108
$435$		0			0
$436$	−9.12783			−0.437144
$437$			3.13624i			0.150027i
$438$		0			0
$439$	14.5236			0.693173			0.346587	−	0.938018i	$-0.387341\pi$
$439$	14.5236			0.693173			0.346587	+	0.938018i	$0.387341\pi$
$440$	4.34017	−	1.07838i	0.206910	−	0.0514096i
$441$		0			0
$442$			4.78765i			0.227725i
$443$			20.0456i			0.952394i	0.879339	+	0.476197i	$0.157985\pi$
$443$			20.0456i			0.952394i	−0.879339	+	0.476197i	$0.842015\pi$
$444$		0			0
$445$	2.55479	+	10.2823i	0.121109	+	0.487428i
$446$	−2.76099			−0.130737
$447$		0			0
$448$		−	3.70928i		−	0.175247i
$449$	−19.0928			−0.901043			−0.450521	−	0.892766i	$-0.648762\pi$
$449$	−19.0928			−0.901043			−0.450521	+	0.892766i	$0.648762\pi$
$450$		0			0
$451$	16.6803			0.785447
$452$			0.107307i			0.00504730i
$453$		0			0
$454$	−4.36683			−0.204946
$455$	2.00000	+	8.04945i	0.0937614	+	0.377364i
$456$		0			0
$457$			23.2800i			1.08899i	0.838763	+	0.544497i	$0.183280\pi$
$457$			23.2800i			1.08899i	−0.838763	+	0.544497i	$0.816720\pi$
$458$		−	20.6453i		−	0.964690i
$459$		0			0
$460$	10.7877	−	2.68035i	0.502977	−	0.124972i
$461$	30.1711			1.40521			0.702605	−	0.711580i	$-0.252020\pi$
$461$	30.1711			1.40521			0.702605	+	0.711580i	$0.252020\pi$
$462$		0			0
$463$			24.0228i			1.11643i	0.829695	+	0.558217i	$0.188514\pi$
$463$			24.0228i			1.11643i	−0.829695	+	0.558217i	$0.811486\pi$
$464$	−6.38962			−0.296631
$465$		0			0
$466$	13.1545			0.609370
$467$			0.412408i			0.0190840i	0.999954	+	0.00954198i	$0.00303735\pi$
$467$			0.412408i			0.0190840i	−0.999954	+	0.00954198i	$0.996963\pi$
$468$		0			0
$469$	0.581449			0.0268488
$470$	−1.84324	−	7.41855i	−0.0850225	−	0.342192i
$471$		0			0
$472$			7.26180i			0.334251i
$473$		−	22.0410i		−	1.01345i
$474$		0			0
$475$	−2.78765	+	1.47641i	−0.127906	+	0.0677423i
$476$	−17.7587			−0.813970
$477$		0			0
$478$		−	7.31965i		−	0.334793i
$479$	40.5113			1.85101			0.925504	−	0.378737i	$-0.123641\pi$
$479$	40.5113			1.85101			0.925504	+	0.378737i	$0.123641\pi$
$480$		0			0
$481$	10.6803			0.486982
$482$		−	19.9421i		−	0.908340i
$483$		0			0
$484$	7.00000			0.318182
$485$	−25.4101	+	6.31351i	−1.15382	+	0.286682i
$486$		0			0
$487$		−	8.65756i		−	0.392311i	−0.980573	−	0.196156i	$-0.937154\pi$
$487$		−	8.65756i		−	0.392311i	0.980573	−	0.196156i	$-0.0628458\pi$
$488$		−	7.57531i		−	0.342918i
$489$		0			0
$490$	−14.6670	+	3.64423i	−0.662588	+	0.164629i
$491$	−39.6970			−1.79150			−0.895750	−	0.444558i	$-0.853361\pi$
$491$	−39.6970			−1.79150			−0.895750	+	0.444558i	$0.853361\pi$
$492$		0			0
$493$			30.5913i			1.37776i
$494$	−0.630898			−0.0283854
$495$		0			0
$496$	−3.07838			−0.138223
$497$		−	28.1978i		−	1.26484i
$498$		0			0
$499$	37.7770			1.69113			0.845565	−	0.533873i	$-0.179264\pi$
$499$	37.7770			1.69113			0.845565	+	0.533873i	$0.179264\pi$
$500$	7.46081	+	8.32684i	0.333658	+	0.372388i
$501$		0			0
$502$		−	25.2267i		−	1.12592i
$503$			2.54638i			0.113537i	0.998387	+	0.0567687i	$0.0180797\pi$
$503$			2.54638i			0.113537i	−0.998387	+	0.0567687i	$0.981920\pi$
$504$		0			0
$505$	−6.39803	−	25.7503i	−0.284709	−	1.14587i
$506$	−9.94214			−0.441982
$507$		0			0
$508$			15.1773i			0.673383i
$509$	−19.7009			−0.873225			−0.436613	−	0.899650i	$-0.643822\pi$
$509$	−19.7009			−0.873225			−0.436613	+	0.899650i	$0.643822\pi$
$510$		0			0
$511$	−41.2762			−1.82595
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	17.1545			0.756652
$515$	31.6742	−	7.86991i	1.39573	−	0.346790i
$516$		0			0
$517$			6.83710i			0.300695i
$518$			39.6163i			1.74064i
$519$		0			0
$520$	0.539189	+	2.17009i	0.0236450	+	0.0951646i
$521$	39.5174			1.73129			0.865645	−	0.500658i	$-0.166908\pi$
$521$	39.5174			1.73129			0.865645	+	0.500658i	$0.166908\pi$
$522$		0			0
$523$			19.6865i			0.860830i	0.902631	+	0.430415i	$0.141633\pi$
$523$			19.6865i			0.860830i	−0.902631	+	0.430415i	$0.858367\pi$
$524$	−11.9649			−0.522690
$525$		0			0
$526$	22.5464			0.983069
$527$			14.7382i			0.642006i
$528$		0			0
$529$	−1.71154			−0.0744149
$530$	−7.10504	−	28.5958i	−0.308623	−	1.24212i
$531$		0			0
$532$		−	2.34017i		−	0.101459i
$533$			8.34017i			0.361253i
$534$		0			0
$535$	−17.5753	+	4.36683i	−0.759847	+	0.188795i
$536$	0.156755			0.00677081
$537$		0			0
$538$			7.96493i			0.343392i
$539$	13.5174			0.582238
$540$		0			0
$541$	39.1689			1.68400			0.842000	−	0.539477i	$-0.181378\pi$
$541$	39.1689			1.68400			0.842000	+	0.539477i	$0.181378\pi$
$542$		−	14.8104i		−	0.636163i
$543$		0			0
$544$	−4.78765			−0.205269
$545$	4.92162	+	19.8082i	0.210819	+	0.848489i
$546$		0			0
$547$			46.1855i			1.97475i	0.158401	+	0.987375i	$0.449366\pi$
$547$			46.1855i			1.97475i	−0.158401	+	0.987375i	$0.550634\pi$
$548$		−	22.0989i		−	0.944018i
$549$		0			0
$550$	−4.68035	−	8.83710i	−0.199571	−	0.376815i
$551$	−4.03120			−0.171735
$552$		0			0
$553$			60.3956i			2.56828i
$554$	−5.33403			−0.226621
$555$		0			0
$556$	2.52359			0.107024
$557$		−	31.8576i		−	1.34985i	−0.737886	−	0.674925i	$-0.764176\pi$
$557$		−	31.8576i		−	1.34985i	0.737886	−	0.674925i	$-0.235824\pi$
$558$		0			0
$559$	11.0205			0.466118
$560$	−8.04945	+	2.00000i	−0.340151	+	0.0845154i
$561$		0			0
$562$			20.6225i			0.869907i
$563$			7.73206i			0.325868i	0.986637	+	0.162934i	$0.0520957\pi$
$563$			7.73206i			0.325868i	−0.986637	+	0.162934i	$0.947904\pi$
$564$		0			0
$565$	0.232866	−	0.0578588i	0.00979674	−	0.00243414i
$566$	29.1773			1.22641
$567$		0			0
$568$		−	7.60197i		−	0.318972i
$569$	30.7214			1.28791			0.643954	−	0.765064i	$-0.277293\pi$
$569$	30.7214			1.28791			0.643954	+	0.765064i	$0.277293\pi$
$570$		0			0
$571$	−46.5523			−1.94815			−0.974077	−	0.226215i	$-0.927365\pi$
$571$	−46.5523			−1.94815			−0.974077	+	0.226215i	$0.927365\pi$
$572$		−	2.00000i		−	0.0836242i
$573$		0			0
$574$	−30.9360			−1.29124
$575$	−11.6332	−	21.9649i	−0.485137	−	0.916001i
$576$		0			0
$577$			7.44134i			0.309787i	0.987931	+	0.154893i	$0.0495034\pi$
$577$			7.44134i			0.309787i	−0.987931	+	0.154893i	$0.950497\pi$
$578$			5.92162i			0.246307i
$579$		0			0
$580$	3.44521	+	13.8660i	0.143055	+	0.575756i
$581$	−16.6803			−0.692017
$582$		0			0
$583$			26.3545i			1.09149i
$584$	−11.1278			−0.460473
$585$		0			0
$586$	−8.15676			−0.336952
$587$			48.1445i			1.98713i	0.113242	+	0.993567i	$0.463877\pi$
$587$			48.1445i			1.98713i	−0.113242	+	0.993567i	$0.536123\pi$
$588$		0			0
$589$	−1.94214			−0.0800245
$590$	15.7587	−	3.91548i	0.648776	−	0.161198i
$591$		0			0
$592$			10.6803i			0.438960i
$593$		−	10.5814i		−	0.434528i	−0.976113	−	0.217264i	$-0.930287\pi$
$593$		−	10.5814i		−	0.434528i	0.976113	−	0.217264i	$-0.0697133\pi$
$594$		0			0
$595$	9.57531	+	38.5380i	0.392549	+	1.57990i
$596$	−15.2351			−0.624055
$597$		0			0
$598$		−	4.97107i		−	0.203282i
$599$	−4.68035			−0.191234			−0.0956169	−	0.995418i	$-0.530482\pi$
$599$	−4.68035			−0.191234			−0.0956169	+	0.995418i	$0.530482\pi$
$600$		0			0
$601$	−43.5897			−1.77806			−0.889030	−	0.457849i	$-0.848620\pi$
$601$	−43.5897			−1.77806			−0.889030	+	0.457849i	$0.848620\pi$
$602$			40.8781i			1.66607i
$603$		0			0
$604$	−4.34017			−0.176599
$605$	−3.77432	−	15.1906i	−0.153448	−	0.617586i
$606$		0			0
$607$		−	45.3340i		−	1.84005i	−0.391858	−	0.920026i	$-0.628168\pi$
$607$		−	45.3340i		−	1.84005i	0.391858	−	0.920026i	$-0.371832\pi$
$608$		−	0.630898i		−	0.0255863i
$609$		0			0
$610$	−16.4391	+	4.08452i	−0.665598	+	0.165377i
$611$	−3.41855			−0.138300
$612$		0			0
$613$			12.8904i			0.520639i	0.965522	+	0.260320i	$0.0838280\pi$
$613$			12.8904i			0.520639i	−0.965522	+	0.260320i	$0.916172\pi$
$614$	−21.1050			−0.851730
$615$		0			0
$616$	7.41855			0.298902
$617$		−	9.51745i		−	0.383158i	−0.981477	−	0.191579i	$-0.938639\pi$
$617$		−	9.51745i		−	0.383158i	0.981477	−	0.191579i	$-0.0613608\pi$
$618$		0			0
$619$	−18.6186			−0.748345			−0.374173	−	0.927359i	$-0.622073\pi$
$619$	−18.6186			−0.748345			−0.374173	+	0.927359i	$0.622073\pi$
$620$	1.65983	+	6.68035i	0.0666603	+	0.268289i
$621$		0			0
$622$			12.0989i			0.485122i
$623$			17.5753i			0.704140i
$624$		0			0
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$	3.05172			0.121971
$627$		0			0
$628$		−	3.97334i		−	0.158553i
$629$	51.1338			2.03884
$630$		0			0
$631$	31.1773			1.24115			0.620574	−	0.784148i	$-0.286900\pi$
$631$	31.1773			1.24115			0.620574	+	0.784148i	$0.286900\pi$
$632$			16.2823i			0.647676i
$633$		0			0
$634$	−11.9733			−0.475522
$635$	32.9360	−	8.18342i	1.30703	−	0.324749i
$636$		0			0
$637$			6.75872i			0.267790i
$638$		−	12.7792i		−	0.505935i
$639$		0			0
$640$	−2.17009	+	0.539189i	−0.0857802	+	0.0213133i
$641$	−16.4657			−0.650357			−0.325179	−	0.945653i	$-0.605424\pi$
$641$	−16.4657			−0.650357			−0.325179	+	0.945653i	$0.605424\pi$
$642$		0			0
$643$			15.1629i			0.597966i	0.954258	+	0.298983i	$0.0966474\pi$
$643$			15.1629i			0.597966i	−0.954258	+	0.298983i	$0.903353\pi$
$644$	18.4391			0.726601
$645$		0			0
$646$	−3.02052			−0.118841
$647$			48.4885i			1.90628i	0.302529	+	0.953140i	$0.402169\pi$
$647$			48.4885i			1.90628i	−0.302529	+	0.953140i	$0.597831\pi$
$648$		0			0
$649$	−14.5236			−0.570101
$650$	4.41855	−	2.34017i	0.173310	−	0.0917891i
$651$		0			0
$652$		−	1.63317i		−	0.0639597i
$653$			1.71315i			0.0670408i	0.999438	+	0.0335204i	$0.0106719\pi$
$653$			1.71315i			0.0670408i	−0.999438	+	0.0335204i	$0.989328\pi$
$654$		0			0
$655$	6.45136	+	25.9649i	0.252075	+	1.01453i
$656$	−8.34017			−0.325629
$657$		0			0
$658$		−	12.6803i		−	0.494331i
$659$	17.5936			0.685348			0.342674	−	0.939454i	$-0.388667\pi$
$659$	17.5936			0.685348			0.342674	+	0.939454i	$0.388667\pi$
$660$		0			0
$661$	−11.0166			−0.428498			−0.214249	−	0.976779i	$-0.568730\pi$
$661$	−11.0166			−0.428498			−0.214249	+	0.976779i	$0.568730\pi$
$662$		−	2.37525i		−	0.0923165i
$663$		0			0
$664$	−4.49693			−0.174515
$665$	−5.07838	+	1.26180i	−0.196931	+	0.0489303i
$666$		0			0
$667$		−	31.7633i		−	1.22988i
$668$		−	2.15676i		−	0.0834474i
$669$		0			0
$670$	−0.0845208	−	0.340173i	−0.00326532	−	0.0131420i
$671$	15.1506			0.584883
$672$		0			0
$673$		−	4.46573i		−	0.172141i	−0.996289	−	0.0860707i	$-0.972569\pi$
$673$		−	4.46573i		−	0.172141i	0.996289	−	0.0860707i	$-0.0274311\pi$
$674$	−19.1506			−0.737654
$675$		0			0
$676$	1.00000			0.0384615
$677$			26.0554i			1.00139i	0.865624	+	0.500695i	$0.166922\pi$
$677$			26.0554i			1.00139i	−0.865624	+	0.500695i	$0.833078\pi$
$678$		0			0
$679$	−43.4329			−1.66680
$680$	2.58145	+	10.3896i	0.0989941	+	0.398424i
$681$		0			0
$682$		−	6.15676i		−	0.235754i
$683$			25.0082i			0.956913i	0.878111	+	0.478457i	$0.158804\pi$
$683$			25.0082i			0.956913i	−0.878111	+	0.478457i	$0.841196\pi$
$684$		0			0
$685$	−47.9565	+	11.9155i	−1.83232	+	0.455267i
$686$	0.894960			0.0341697
$687$		0			0
$688$			11.0205i			0.420153i
$689$	−13.1773			−0.502014
$690$		0			0
$691$	−5.67808			−0.216004			−0.108002	−	0.994151i	$-0.534445\pi$
$691$	−5.67808			−0.216004			−0.108002	+	0.994151i	$0.534445\pi$
$692$		−	2.92162i		−	0.111063i
$693$		0			0
$694$	18.9360			0.718801
$695$	−1.36069	−	5.47641i	−0.0516140	−	0.207732i
$696$		0			0
$697$			39.9299i			1.51245i
$698$		−	10.2907i		−	0.389510i
$699$		0			0
$700$	8.68035	+	16.3896i	0.328086	+	0.619469i
$701$	15.6514			0.591146			0.295573	−	0.955320i	$-0.404489\pi$
$701$	15.6514			0.591146			0.295573	+	0.955320i	$0.404489\pi$
$702$		0			0
$703$			6.73820i			0.254136i
$704$	2.00000			0.0753778
$705$		0			0
$706$	−1.90110			−0.0715490
$707$		−	44.0144i		−	1.65533i
$708$		0			0
$709$	−6.50534			−0.244313			−0.122157	−	0.992511i	$-0.538981\pi$
$709$	−6.50534			−0.244313			−0.122157	+	0.992511i	$0.538981\pi$
$710$	−16.4969	+	4.09890i	−0.619119	+	0.153829i
$711$		0			0
$712$			4.73820i			0.177572i
$713$		−	15.3028i		−	0.573096i
$714$		0			0
$715$	−4.34017	+	1.07838i	−0.162313	+	0.0403290i
$716$	−8.13397			−0.303981
$717$		0			0
$718$		−	18.0722i		−	0.674450i
$719$	−24.2511			−0.904414			−0.452207	−	0.891913i	$-0.649363\pi$
$719$	−24.2511			−0.904414			−0.452207	+	0.891913i	$0.649363\pi$
$720$		0			0
$721$	54.1399			2.01628
$722$			18.6020i			0.692294i
$723$		0			0
$724$	5.78539			0.215012
$725$	28.2329	−	14.9528i	1.04854	−	0.555334i
$726$		0			0
$727$		−	8.28685i		−	0.307342i	−0.988122	−	0.153671i	$-0.950890\pi$
$727$		−	8.28685i		−	0.307342i	0.988122	−	0.153671i	$-0.0491096\pi$
$728$			3.70928i			0.137475i
$729$		0			0
$730$	6.00000	+	24.1483i	0.222070	+	0.893770i
$731$	52.7624			1.95149
$732$		0			0
$733$			24.2023i			0.893933i	0.894551	+	0.446967i	$0.147496\pi$
$733$			24.2023i			0.893933i	−0.894551	+	0.446967i	$0.852504\pi$
$734$	3.54411			0.130815
$735$		0			0
$736$	4.97107			0.183236
$737$			0.313511i			0.0115483i
$738$		0			0
$739$	38.4040			1.41271			0.706357	−	0.707856i	$-0.250337\pi$
$739$	38.4040			1.41271			0.706357	+	0.707856i	$0.250337\pi$
$740$	23.1773	−	5.75872i	0.852014	−	0.211695i
$741$		0			0
$742$		−	48.8781i		−	1.79437i
$743$		−	29.8888i		−	1.09651i	−0.836310	−	0.548257i	$-0.815291\pi$
$743$		−	29.8888i		−	1.09651i	0.836310	−	0.548257i	$-0.184709\pi$
$744$		0			0
$745$	8.21461	+	33.0616i	0.300960	+	1.21128i
$746$	0.822726			0.0301221
$747$		0			0
$748$		−	9.57531i		−	0.350108i
$749$	−30.0410			−1.09768
$750$		0			0
$751$	−14.9528			−0.545636			−0.272818	−	0.962066i	$-0.587956\pi$
$751$	−14.9528			−0.545636			−0.272818	+	0.962066i	$0.587956\pi$
$752$		−	3.41855i		−	0.124662i
$753$		0			0
$754$	6.38962			0.232696
$755$	2.34017	+	9.41855i	0.0851676	+	0.342776i
$756$		0			0
$757$		−	43.1917i		−	1.56983i	−0.619605	−	0.784914i	$-0.712707\pi$
$757$		−	43.1917i		−	1.56983i	0.619605	−	0.784914i	$-0.287293\pi$
$758$			28.5152i			1.03572i
$759$		0			0
$760$	−1.36910	+	0.340173i	−0.0496626	+	0.0123394i
$761$	−3.34632			−0.121304			−0.0606519	−	0.998159i	$-0.519318\pi$
$761$	−3.34632			−0.121304			−0.0606519	+	0.998159i	$0.519318\pi$
$762$		0			0
$763$			33.8576i			1.22573i
$764$	4.89496			0.177093
$765$		0			0
$766$	−23.5174			−0.849720
$767$		−	7.26180i		−	0.262208i
$768$		0			0
$769$	−35.5585			−1.28227			−0.641136	−	0.767427i	$-0.721537\pi$
$769$	−35.5585			−1.28227			−0.641136	+	0.767427i	$0.721537\pi$
$770$	−4.00000	−	16.0989i	−0.144150	−	0.580164i
$771$		0			0
$772$			3.12783i			0.112573i
$773$		−	40.2388i		−	1.44729i	−0.690172	−	0.723645i	$-0.742465\pi$
$773$		−	40.2388i		−	1.44729i	0.690172	−	0.723645i	$-0.257535\pi$
$774$		0			0
$775$	13.6020	−	7.20394i	0.488597	−	0.258773i
$776$	−11.7093			−0.420338
$777$		0			0
$778$		−	3.55252i		−	0.127364i
$779$	−5.26180			−0.188523
$780$		0			0
$781$	15.2039			0.544040
$782$		−	23.7998i		−	0.851078i
$783$		0			0
$784$	−6.75872			−0.241383
$785$	−8.62249	+	2.14238i	−0.307750	+	0.0764648i
$786$		0			0
$787$		−	19.4764i		−	0.694259i	−0.937817	−	0.347130i	$-0.887156\pi$
$787$		−	19.4764i		−	0.694259i	0.937817	−	0.347130i	$-0.112844\pi$
$788$			4.83710i			0.172315i
$789$		0			0
$790$	35.3340	−	8.77924i	1.25713	−	0.312351i
$791$	0.398032			0.0141524
$792$		0			0
$793$			7.57531i			0.269007i
$794$	−14.4657			−0.513370
$795$		0			0
$796$	12.2823			0.435335
$797$		−	11.2351i		−	0.397969i	−0.980003	−	0.198984i	$-0.936236\pi$
$797$		−	11.2351i		−	0.397969i	0.980003	−	0.198984i	$-0.0637643\pi$
$798$		0			0
$799$	−16.3668			−0.579017
$800$	2.34017	+	4.41855i	0.0827376	+	0.156219i
$801$		0			0
$802$			24.3402i			0.859481i
$803$		−	22.2557i		−	0.785385i
$804$		0			0
$805$	−9.94214	−	40.0144i	−0.350414	−	1.41032i
$806$	3.07838			0.108431
$807$		0			0
$808$		−	11.8660i		−	0.417446i
$809$	−25.9421			−0.912077			−0.456039	−	0.889960i	$-0.650732\pi$
$809$	−25.9421			−0.912077			−0.456039	+	0.889960i	$0.650732\pi$
$810$		0			0
$811$	15.0843			0.529683			0.264841	−	0.964292i	$-0.414680\pi$
$811$	15.0843			0.529683			0.264841	+	0.964292i	$0.414680\pi$
$812$			23.7009i			0.831737i
$813$		0			0
$814$	−21.3607			−0.748692
$815$	−3.54411	+	0.880584i	−0.124145	+	0.0308455i
$816$		0			0
$817$			6.95282i			0.243248i
$818$			16.8371i			0.588695i
$819$		0			0
$820$	4.49693	+	18.0989i	0.157040	+	0.632041i
$821$	−36.4268			−1.27130			−0.635652	−	0.771976i	$-0.719269\pi$
$821$	−36.4268			−1.27130			−0.635652	+	0.771976i	$0.719269\pi$
$822$		0			0
$823$			37.6020i			1.31072i	0.755316	+	0.655361i	$0.227484\pi$
$823$			37.6020i			1.31072i	−0.755316	+	0.655361i	$0.772516\pi$
$824$	14.5958			0.508470
$825$		0			0
$826$	26.9360			0.937223
$827$			44.4969i			1.54731i	0.633607	+	0.773655i	$0.281574\pi$
$827$			44.4969i			1.54731i	−0.633607	+	0.773655i	$0.718426\pi$
$828$		0			0
$829$	36.8371			1.27941			0.639703	−	0.768622i	$-0.279057\pi$
$829$	36.8371			1.27941			0.639703	+	0.768622i	$0.279057\pi$
$830$	2.42469	+	9.75872i	0.0841624	+	0.338730i
$831$		0			0
$832$			1.00000i			0.0346688i
$833$			32.3584i			1.12115i
$834$		0			0
$835$	−4.68035	+	1.16290i	−0.161970	+	0.0402438i
$836$	1.26180			0.0436401
$837$		0			0
$838$		−	24.5997i		−	0.849783i
$839$	−29.4764			−1.01764			−0.508819	−	0.860873i	$-0.669918\pi$
$839$	−29.4764			−1.01764			−0.508819	+	0.860873i	$0.669918\pi$
$840$		0			0
$841$	11.8273			0.407837
$842$		−	4.33176i		−	0.149282i
$843$		0			0
$844$	−20.4124			−0.702624
$845$	−0.539189	−	2.17009i	−0.0185487	−	0.0746532i
$846$		0			0
$847$		−	25.9649i		−	0.892165i
$848$		−	13.1773i		−	0.452509i
$849$		0			0
$850$	21.1545	−	11.2039i	0.725593	−	0.384292i
$851$	−53.0928			−1.82000
$852$		0			0
$853$		−	38.7792i		−	1.32778i	−0.747832	−	0.663888i	$-0.768905\pi$
$853$		−	38.7792i		−	1.32778i	0.747832	−	0.663888i	$-0.231095\pi$
$854$	−28.0989			−0.961524
$855$		0			0
$856$	−8.09890			−0.276815
$857$		−	38.0494i		−	1.29974i	−0.760044	−	0.649872i	$-0.774822\pi$
$857$		−	38.0494i		−	1.29974i	0.760044	−	0.649872i	$-0.225178\pi$
$858$		0			0
$859$	44.2434			1.50956			0.754782	−	0.655976i	$-0.227743\pi$
$859$	44.2434			1.50956			0.754782	+	0.655976i	$0.227743\pi$
$860$	23.9155	−	5.94214i	0.815511	−	0.202625i
$861$		0			0
$862$		−	2.52359i		−	0.0859538i
$863$		−	1.78992i		−	0.0609296i	−0.999536	−	0.0304648i	$-0.990301\pi$
$863$		−	1.78992i		−	0.0609296i	0.999536	−	0.0304648i	$-0.00969875\pi$
$864$		0			0
$865$	−6.34017	+	1.57531i	−0.215572	+	0.0535620i
$866$	−35.3484			−1.20119
$867$		0			0
$868$			11.4186i			0.387571i
$869$	−32.5646			−1.10468
$870$		0			0
$871$	−0.156755			−0.00531146
$872$			9.12783i			0.309107i
$873$		0			0
$874$	3.13624			0.106085
$875$	30.8865	−	27.6742i	1.04416	−	0.935559i
$876$		0			0
$877$			50.9770i			1.72137i	0.509136	+	0.860686i	$0.329965\pi$
$877$			50.9770i			1.72137i	−0.509136	+	0.860686i	$0.670035\pi$
$878$		−	14.5236i		−	0.490147i
$879$		0			0
$880$	−1.07838	−	4.34017i	−0.0363521	−	0.146307i
$881$	12.2679			0.413317			0.206659	−	0.978413i	$-0.433741\pi$
$881$	12.2679			0.413317			0.206659	+	0.978413i	$0.433741\pi$
$882$		0			0
$883$		−	13.6742i		−	0.460174i	−0.973170	−	0.230087i	$-0.926099\pi$
$883$		−	13.6742i		−	0.460174i	0.973170	−	0.230087i	$-0.0739010\pi$
$884$	4.78765			0.161026
$885$		0			0
$886$	20.0456			0.673444
$887$			39.9604i			1.34174i	0.741576	+	0.670869i	$0.234079\pi$
$887$			39.9604i			1.34174i	−0.741576	+	0.670869i	$0.765921\pi$
$888$		0			0
$889$	56.2967			1.88813
$890$	10.2823	−	2.55479i	0.344664	−	0.0856367i
$891$		0			0
$892$			2.76099i			0.0924448i
$893$		−	2.15676i		−	0.0721731i
$894$		0			0
$895$	4.38575	+	17.6514i	0.146599	+	0.590022i
$896$	−3.70928			−0.123918
$897$		0			0
$898$			19.0928i			0.637133i
$899$	19.6697			0.656020
$900$		0			0
$901$	−63.0882			−2.10177
$902$		−	16.6803i		−	0.555395i
$903$		0			0
$904$	0.107307			0.00356898
$905$	−3.11942	−	12.5548i	−0.103693	−	0.417335i
$906$		0			0
$907$		−	32.1834i		−	1.06863i	−0.845285	−	0.534316i	$-0.820569\pi$
$907$		−	32.1834i		−	1.06863i	0.845285	−	0.534316i	$-0.179431\pi$
$908$			4.36683i			0.144919i
$909$		0			0
$910$	8.04945	−	2.00000i	0.266837	−	0.0662994i
$911$	−29.5585			−0.979316			−0.489658	−	0.871914i	$-0.662878\pi$
$911$	−29.5585			−0.979316			−0.489658	+	0.871914i	$0.662878\pi$
$912$		0			0
$913$		−	8.99386i		−	0.297653i
$914$	23.2800			0.770036
$915$		0			0
$916$	−20.6453			−0.682139
$917$			44.3812i			1.46560i
$918$		0			0
$919$	2.83710			0.0935873			0.0467937	−	0.998905i	$-0.485100\pi$
$919$	2.83710			0.0935873			0.0467937	+	0.998905i	$0.485100\pi$
$920$	−2.68035	−	10.7877i	−0.0883684	−	0.355658i
$921$		0			0
$922$		−	30.1711i		−	0.993633i
$923$			7.60197i			0.250222i
$924$		0			0
$925$	−24.9939	−	47.1917i	−0.821793	−	1.55165i
$926$	24.0228			0.789438
$927$		0			0
$928$			6.38962i			0.209750i
$929$	−29.3028			−0.961395			−0.480697	−	0.876887i	$-0.659616\pi$
$929$	−29.3028			−0.961395			−0.480697	+	0.876887i	$0.659616\pi$
$930$		0			0
$931$	−4.26406			−0.139749
$932$		−	13.1545i		−	0.430890i
$933$		0			0
$934$	0.412408			0.0134944
$935$	−20.7792	+	5.16290i	−0.679554	+	0.168845i
$936$		0			0
$937$		−	7.30283i		−	0.238573i	−0.992860	−	0.119287i	$-0.961939\pi$
$937$		−	7.30283i		−	0.238573i	0.992860	−	0.119287i	$-0.0380607\pi$
$938$		−	0.581449i		−	0.0189850i
$939$		0			0
$940$	−7.41855	+	1.84324i	−0.241966	+	0.0601200i
$941$	−24.5503			−0.800315			−0.400158	−	0.916446i	$-0.631045\pi$
$941$	−24.5503			−0.800315			−0.400158	+	0.916446i	$0.631045\pi$
$942$		0			0
$943$		−	41.4596i		−	1.35011i
$944$	7.26180			0.236351
$945$		0			0
$946$	−22.0410			−0.716616
$947$		−	28.0677i		−	0.912078i	−0.889960	−	0.456039i	$-0.849268\pi$
$947$		−	28.0677i		−	0.912078i	0.889960	−	0.456039i	$-0.150732\pi$
$948$		0			0
$949$	11.1278			0.361225
$950$	1.47641	+	2.78765i	0.0479011	+	0.0904434i
$951$		0			0
$952$			17.7587i			0.575564i
$953$		−	35.4101i		−	1.14705i	−0.819189	−	0.573523i	$-0.805576\pi$
$953$		−	35.4101i		−	1.14705i	0.819189	−	0.573523i	$-0.194424\pi$
$954$		0			0
$955$	−2.63931	−	10.6225i	−0.0854060	−	0.343736i
$956$	−7.31965			−0.236735
$957$		0			0
$958$		−	40.5113i		−	1.30886i
$959$	−81.9709			−2.64698
$960$		0			0
$961$	−21.5236			−0.694309
$962$		−	10.6803i		−	0.344348i
$963$		0			0
$964$	−19.9421			−0.642293
$965$	6.78765	−	1.68649i	0.218502	−	0.0542900i
$966$		0			0
$967$		−	57.2222i		−	1.84014i	−0.391752	−	0.920071i	$-0.628131\pi$
$967$		−	57.2222i		−	1.84014i	0.391752	−	0.920071i	$-0.371869\pi$
$968$		−	7.00000i		−	0.224989i
$969$		0			0
$970$	6.31351	+	25.4101i	0.202715	+	0.815870i
$971$	31.1857			1.00080			0.500398	−	0.865795i	$-0.333187\pi$
$971$	31.1857			1.00080			0.500398	+	0.865795i	$0.333187\pi$
$972$		0			0
$973$		−	9.36069i		−	0.300090i
$974$	−8.65756			−0.277406
$975$		0			0
$976$	−7.57531			−0.242480
$977$			26.8326i			0.858450i	0.903198	+	0.429225i	$0.141213\pi$
$977$			26.8326i			0.858450i	−0.903198	+	0.429225i	$0.858787\pi$
$978$		0			0
$979$	−9.47641			−0.302867
$980$	3.64423	+	14.6670i	0.116411	+	0.468521i
$981$		0			0
$982$			39.6970i			1.26678i
$983$		−	17.9421i		−	0.572265i	−0.958190	−	0.286133i	$-0.907630\pi$
$983$		−	17.9421i		−	0.572265i	0.958190	−	0.286133i	$-0.0923698\pi$
$984$		0			0
$985$	10.4969	−	2.60811i	0.334460	−	0.0831013i
$986$	30.5913			0.974225
$987$		0			0
$988$			0.630898i			0.0200715i
$989$	−54.7838			−1.74202
$990$		0			0
$991$	−50.1543			−1.59320			−0.796602	−	0.604504i	$-0.793371\pi$
$991$	−50.1543			−1.59320			−0.796602	+	0.604504i	$0.793371\pi$
$992$			3.07838i			0.0977386i
$993$		0			0
$994$	−28.1978			−0.894380
$995$	−6.62249	−	26.6537i	−0.209947	−	0.844979i
$996$		0			0
$997$			12.8227i			0.406100i	0.979168	+	0.203050i	$0.0650854\pi$
$997$			12.8227i			0.406100i	−0.979168	+	0.203050i	$0.934915\pi$
$998$		−	37.7770i		−	1.19581i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.e.g.469.2	✓	6
3.2	odd	2		1170.2.e.h.469.5	yes	6
5.2	odd	4		5850.2.a.cr.1.1		3
5.3	odd	4		5850.2.a.cq.1.3		3
5.4	even	2	inner	1170.2.e.g.469.5	yes	6
15.2	even	4		5850.2.a.co.1.1		3
15.8	even	4		5850.2.a.ct.1.3		3
15.14	odd	2		1170.2.e.h.469.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.e.g.469.2	✓	6	1.1	even	1	trivial
1170.2.e.g.469.5	yes	6	5.4	even	2	inner
1170.2.e.h.469.2	yes	6	15.14	odd	2
1170.2.e.h.469.5	yes	6	3.2	odd	2
5850.2.a.co.1.1		3	15.2	even	4
5850.2.a.cq.1.3		3	5.3	odd	4
5850.2.a.cr.1.1		3	5.2	odd	4
5850.2.a.ct.1.3		3	15.8	even	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +3.70928i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.539189 + 2.17009i) q^{5} +3.70928i q^{7} +1.00000i q^{8} +(2.17009 - 0.539189i) q^{10} -2.00000 q^{11} -1.00000i q^{13} +3.70928 q^{14} +1.00000 q^{16} -4.78765i q^{17} +0.630898 q^{19} +(-0.539189 - 2.17009i) q^{20} +2.00000i q^{22} +4.97107i q^{23} +(-4.41855 + 2.34017i) q^{25} -1.00000 q^{26} -3.70928i q^{28} -6.38962 q^{29} -3.07838 q^{31} -1.00000i q^{32} -4.78765 q^{34} +(-8.04945 + 2.00000i) q^{35} +10.6803i q^{37} -0.630898i q^{38} +(-2.17009 + 0.539189i) q^{40} -8.34017 q^{41} +11.0205i q^{43} +2.00000 q^{44} +4.97107 q^{46} -3.41855i q^{47} -6.75872 q^{49} +(2.34017 + 4.41855i) q^{50} +1.00000i q^{52} -13.1773i q^{53} +(-1.07838 - 4.34017i) q^{55} -3.70928 q^{56} +6.38962i q^{58} +7.26180 q^{59} -7.57531 q^{61} +3.07838i q^{62} -1.00000 q^{64} +(2.17009 - 0.539189i) q^{65} -0.156755i q^{67} +4.78765i q^{68} +(2.00000 + 8.04945i) q^{70} -7.60197 q^{71} +11.1278i q^{73} +10.6803 q^{74} -0.630898 q^{76} -7.41855i q^{77} +16.2823 q^{79} +(0.539189 + 2.17009i) q^{80} +8.34017i q^{82} +4.49693i q^{83} +(10.3896 - 2.58145i) q^{85} +11.0205 q^{86} -2.00000i q^{88} +4.73820 q^{89} +3.70928 q^{91} -4.97107i q^{92} -3.41855 q^{94} +(0.340173 + 1.36910i) q^{95} +11.7093i q^{97} +6.75872i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4}+O(q^{10}) \) 6 * q - 6 * q^4	\( 6 q - 6 q^{4} + 2 q^{10} - 12 q^{11} + 8 q^{14} + 6 q^{16} - 4 q^{19} + 2 q^{25} - 6 q^{26} + 20 q^{29} - 12 q^{31} - 8 q^{34} - 12 q^{35} - 2 q^{40} - 28 q^{41} + 12 q^{44} + 10 q^{49} - 8 q^{50} - 8 q^{56} + 28 q^{59} - 4 q^{61} - 6 q^{64} + 2 q^{65} + 12 q^{70} - 8 q^{71} + 20 q^{74} + 4 q^{76} + 16 q^{79} + 4 q^{85} + 44 q^{89} + 8 q^{91} + 8 q^{94} - 20 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^10 - 12 * q^11 + 8 * q^14 + 6 * q^16 - 4 * q^19 + 2 * q^25 - 6 * q^26 + 20 * q^29 - 12 * q^31 - 8 * q^34 - 12 * q^35 - 2 * q^40 - 28 * q^41 + 12 * q^44 + 10 * q^49 - 8 * q^50 - 8 * q^56 + 28 * q^59 - 4 * q^61 - 6 * q^64 + 2 * q^65 + 12 * q^70 - 8 * q^71 + 20 * q^74 + 4 * q^76 + 16 * q^79 + 4 * q^85 + 44 * q^89 + 8 * q^91 + 8 * q^94 - 20 * q^95

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