LMFDB - Embedded newform 1170.2.e.h.469.3

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			469.3
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	1170.469
Dual form			1170.2.e.h.469.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} +0.903212i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} +0.903212i q^{7} +1.00000i q^{8} +(0.311108 - 2.21432i) q^{10} +2.00000 q^{11} +1.00000i q^{13} +0.903212 q^{14} +1.00000 q^{16} +5.33185i q^{17} +1.52543 q^{19} +(-2.21432 - 0.311108i) q^{20} -2.00000i q^{22} +2.14764i q^{23} +(4.80642 + 1.37778i) q^{25} +1.00000 q^{26} -0.903212i q^{28} -5.65878 q^{29} +2.42864 q^{31} -1.00000i q^{32} +5.33185 q^{34} +(-0.280996 + 2.00000i) q^{35} -3.24443i q^{37} -1.52543i q^{38} +(-0.311108 + 2.21432i) q^{40} +4.62222 q^{41} +0.133353i q^{43} -2.00000 q^{44} +2.14764 q^{46} +5.80642i q^{47} +6.18421 q^{49} +(1.37778 - 4.80642i) q^{50} -1.00000i q^{52} +8.99063i q^{53} +(4.42864 + 0.622216i) q^{55} -0.903212 q^{56} +5.65878i q^{58} -9.05086 q^{59} +12.6637 q^{61} -2.42864i q^{62} -1.00000 q^{64} +(-0.311108 + 2.21432i) q^{65} -10.8573i q^{67} -5.33185i q^{68} +(2.00000 + 0.280996i) q^{70} +5.67307 q^{71} +2.70964i q^{73} -3.24443 q^{74} -1.52543 q^{76} +1.80642i q^{77} +6.91750 q^{79} +(2.21432 + 0.311108i) q^{80} -4.62222i q^{82} -10.2351i q^{83} +(-1.65878 + 11.8064i) q^{85} +0.133353 q^{86} +2.00000i q^{88} -2.94914 q^{89} -0.903212 q^{91} -2.14764i q^{92} +5.80642 q^{94} +(3.37778 + 0.474572i) q^{95} -7.09679i q^{97} -6.18421i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$6$		0			0
$7$			0.903212i			0.341382i	0.985325	+	0.170691i	$0.0546000\pi$
$7$			0.903212i			0.341382i	−0.985325	+	0.170691i	$0.945400\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.311108	−	2.21432i	0.0983809	−	0.700229i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	0.903212			0.241394
$15$		0			0
$16$	1.00000			0.250000
$17$			5.33185i			1.29316i	0.762845	+	0.646582i	$0.223802\pi$
$17$			5.33185i			1.29316i	−0.762845	+	0.646582i	$0.776198\pi$
$18$		0			0
$19$	1.52543			0.349957			0.174979	−	0.984572i	$-0.444014\pi$
$19$	1.52543			0.349957			0.174979	+	0.984572i	$0.444014\pi$
$20$	−2.21432	−	0.311108i	−0.495137	−	0.0695658i
$21$		0			0
$22$		−	2.00000i		−	0.426401i
$23$			2.14764i			0.447815i	0.974610	+	0.223907i	$0.0718813\pi$
$23$			2.14764i			0.447815i	−0.974610	+	0.223907i	$0.928119\pi$
$24$		0			0
$25$	4.80642	+	1.37778i	0.961285	+	0.275557i
$26$	1.00000			0.196116
$27$		0			0
$28$		−	0.903212i		−	0.170691i
$29$	−5.65878			−1.05081			−0.525405	−	0.850853i	$-0.676086\pi$
$29$	−5.65878			−1.05081			−0.525405	+	0.850853i	$0.676086\pi$
$30$		0			0
$31$	2.42864			0.436197			0.218098	−	0.975927i	$-0.430015\pi$
$31$	2.42864			0.436197			0.218098	+	0.975927i	$0.430015\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	5.33185			0.914405
$35$	−0.280996	+	2.00000i	−0.0474970	+	0.338062i
$36$		0			0
$37$		−	3.24443i		−	0.533381i	−0.963782	−	0.266691i	$-0.914070\pi$
$37$		−	3.24443i		−	0.533381i	0.963782	−	0.266691i	$-0.0859302\pi$
$38$		−	1.52543i		−	0.247457i
$39$		0			0
$40$	−0.311108	+	2.21432i	−0.0491905	+	0.350115i
$41$	4.62222			0.721869			0.360934	−	0.932591i	$-0.382458\pi$
$41$	4.62222			0.721869			0.360934	+	0.932591i	$0.382458\pi$
$42$		0			0
$43$			0.133353i			0.0203362i	0.999948	+	0.0101681i	$0.00323666\pi$
$43$			0.133353i			0.0203362i	−0.999948	+	0.0101681i	$0.996763\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	2.14764			0.316653
$47$			5.80642i			0.846954i	0.905907	+	0.423477i	$0.139191\pi$
$47$			5.80642i			0.846954i	−0.905907	+	0.423477i	$0.860809\pi$
$48$		0			0
$49$	6.18421			0.883458
$50$	1.37778	−	4.80642i	0.194848	−	0.679731i
$51$		0			0
$52$		−	1.00000i		−	0.138675i
$53$			8.99063i			1.23496i	0.786587	+	0.617479i	$0.211846\pi$
$53$			8.99063i			1.23496i	−0.786587	+	0.617479i	$0.788154\pi$
$54$		0			0
$55$	4.42864	+	0.622216i	0.597158	+	0.0838995i
$56$	−0.903212			−0.120697
$57$		0			0
$58$			5.65878i			0.743034i
$59$	−9.05086			−1.17832			−0.589160	−	0.808016i	$-0.700541\pi$
$59$	−9.05086			−1.17832			−0.589160	+	0.808016i	$0.700541\pi$
$60$		0			0
$61$	12.6637			1.62142			0.810710	−	0.585447i	$-0.199081\pi$
$61$	12.6637			1.62142			0.810710	+	0.585447i	$0.199081\pi$
$62$		−	2.42864i		−	0.308438i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.311108	+	2.21432i	−0.0385882	+	0.274653i
$66$		0			0
$67$		−	10.8573i		−	1.32643i	−0.748430	−	0.663214i	$-0.769192\pi$
$67$		−	10.8573i		−	1.32643i	0.748430	−	0.663214i	$-0.230808\pi$
$68$		−	5.33185i		−	0.646582i
$69$		0			0
$70$	2.00000	+	0.280996i	0.239046	+	0.0335855i
$71$	5.67307			0.673270			0.336635	−	0.941635i	$-0.390711\pi$
$71$	5.67307			0.673270			0.336635	+	0.941635i	$0.390711\pi$
$72$		0			0
$73$			2.70964i			0.317139i	0.987348	+	0.158569i	$0.0506882\pi$
$73$			2.70964i			0.317139i	−0.987348	+	0.158569i	$0.949312\pi$
$74$	−3.24443			−0.377157
$75$		0			0
$76$	−1.52543			−0.174979
$77$			1.80642i			0.205861i
$78$		0			0
$79$	6.91750			0.778280			0.389140	−	0.921179i	$-0.372772\pi$
$79$	6.91750			0.778280			0.389140	+	0.921179i	$0.372772\pi$
$80$	2.21432	+	0.311108i	0.247568	+	0.0347829i
$81$		0			0
$82$		−	4.62222i		−	0.510438i
$83$		−	10.2351i		−	1.12344i	−0.827326	−	0.561722i	$-0.810139\pi$
$83$		−	10.2351i		−	1.12344i	0.827326	−	0.561722i	$-0.189861\pi$
$84$		0			0
$85$	−1.65878	+	11.8064i	−0.179920	+	1.28059i
$86$	0.133353			0.0143798
$87$		0			0
$88$			2.00000i			0.213201i
$89$	−2.94914			−0.312609			−0.156304	−	0.987709i	$-0.549958\pi$
$89$	−2.94914			−0.312609			−0.156304	+	0.987709i	$0.549958\pi$
$90$		0			0
$91$	−0.903212			−0.0946823
$92$		−	2.14764i		−	0.223907i
$93$		0			0
$94$	5.80642			0.598887
$95$	3.37778	+	0.474572i	0.346553	+	0.0486901i
$96$		0			0
$97$		−	7.09679i		−	0.720570i	−0.932842	−	0.360285i	$-0.882680\pi$
$97$		−	7.09679i		−	0.720570i	0.932842	−	0.360285i	$-0.117320\pi$
$98$		−	6.18421i		−	0.624699i
$99$		0			0
$100$	−4.80642	−	1.37778i	−0.480642	−	0.137778i
$101$	−3.76049			−0.374183			−0.187091	−	0.982343i	$-0.559906\pi$
$101$	−3.76049			−0.374183			−0.187091	+	0.982343i	$0.559906\pi$
$102$		0			0
$103$		−	16.7971i		−	1.65506i	−0.561419	−	0.827532i	$-0.689744\pi$
$103$		−	16.7971i		−	1.65506i	0.561419	−	0.827532i	$-0.310256\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	8.99063			0.873247
$107$		−	8.56199i		−	0.827719i	−0.910341	−	0.413860i	$-0.864180\pi$
$107$		−	8.56199i		−	0.827719i	0.910341	−	0.413860i	$-0.135820\pi$
$108$		0			0
$109$	−4.70964			−0.451101			−0.225551	−	0.974231i	$-0.572418\pi$
$109$	−4.70964			−0.451101			−0.225551	+	0.974231i	$0.572418\pi$
$110$	0.622216	−	4.42864i	0.0593259	−	0.422254i
$111$		0			0
$112$			0.903212i			0.0853455i
$113$			2.57628i			0.242356i	0.992631	+	0.121178i	$0.0386672\pi$
$113$			2.57628i			0.242356i	−0.992631	+	0.121178i	$0.961333\pi$
$114$		0			0
$115$	−0.668149	+	4.75557i	−0.0623052	+	0.443459i
$116$	5.65878			0.525405
$117$		0			0
$118$			9.05086i			0.833199i
$119$	−4.81579			−0.441463
$120$		0			0
$121$	−7.00000			−0.636364
$122$		−	12.6637i		−	1.14652i
$123$		0			0
$124$	−2.42864			−0.218098
$125$	10.2143	+	4.54617i	0.913597	+	0.406622i
$126$		0			0
$127$		−	6.99063i		−	0.620318i	−0.950685	−	0.310159i	$-0.899618\pi$
$127$		−	6.99063i		−	0.620318i	0.950685	−	0.310159i	$-0.100382\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	2.21432	+	0.311108i	0.194209	+	0.0272860i
$131$	20.3225			1.77558			0.887792	−	0.460245i	$-0.152239\pi$
$131$	20.3225			1.77558			0.887792	+	0.460245i	$0.152239\pi$
$132$		0			0
$133$			1.37778i			0.119469i
$134$	−10.8573			−0.937926
$135$		0			0
$136$	−5.33185			−0.457202
$137$			5.43801i			0.464600i	0.972644	+	0.232300i	$0.0746252\pi$
$137$			5.43801i			0.464600i	−0.972644	+	0.232300i	$0.925375\pi$
$138$		0			0
$139$	−6.10171			−0.517540			−0.258770	−	0.965939i	$-0.583317\pi$
$139$	−6.10171			−0.517540			−0.258770	+	0.965939i	$0.583317\pi$
$140$	0.280996	−	2.00000i	0.0237485	−	0.169031i
$141$		0			0
$142$		−	5.67307i		−	0.476074i
$143$			2.00000i			0.167248i
$144$		0			0
$145$	−12.5303	−	1.76049i	−1.04059	−	0.146201i
$146$	2.70964			0.224251
$147$		0			0
$148$			3.24443i			0.266691i
$149$	1.28592			0.105347			0.0526733	−	0.998612i	$-0.483226\pi$
$149$	1.28592			0.105347			0.0526733	+	0.998612i	$0.483226\pi$
$150$		0			0
$151$	0.622216			0.0506352			0.0253176	−	0.999679i	$-0.491940\pi$
$151$	0.622216			0.0506352			0.0253176	+	0.999679i	$0.491940\pi$
$152$			1.52543i			0.123729i
$153$		0			0
$154$	1.80642			0.145566
$155$	5.37778	+	0.755569i	0.431954	+	0.0606887i
$156$		0			0
$157$			14.3368i			1.14420i	0.820184	+	0.572100i	$0.193871\pi$
$157$			14.3368i			1.14420i	−0.820184	+	0.572100i	$0.806129\pi$
$158$		−	6.91750i		−	0.550327i
$159$		0			0
$160$	0.311108	−	2.21432i	0.0245952	−	0.175057i
$161$	−1.93978			−0.152876
$162$		0			0
$163$			12.9590i			1.01503i	0.861644	+	0.507513i	$0.169435\pi$
$163$			12.9590i			1.01503i	−0.861644	+	0.507513i	$0.830565\pi$
$164$	−4.62222			−0.360934
$165$		0			0
$166$	−10.2351			−0.794395
$167$		−	8.85728i		−	0.685397i	−0.939445	−	0.342698i	$-0.888659\pi$
$167$		−	8.85728i		−	0.685397i	0.939445	−	0.342698i	$-0.111341\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	11.8064	+	1.65878i	0.905511	+	0.127223i
$171$		0			0
$172$		−	0.133353i		−	0.0101681i
$173$			8.42864i			0.640818i	0.947279	+	0.320409i	$0.103820\pi$
$173$			8.42864i			0.640818i	−0.947279	+	0.320409i	$0.896180\pi$
$174$		0			0
$175$	−1.24443	+	4.34122i	−0.0940702	+	0.328165i
$176$	2.00000			0.150756
$177$		0			0
$178$			2.94914i			0.221048i
$179$	−23.7605			−1.77594			−0.887971	−	0.459899i	$-0.847886\pi$
$179$	−23.7605			−1.77594			−0.887971	+	0.459899i	$0.847886\pi$
$180$		0			0
$181$	−11.1526			−0.828964			−0.414482	−	0.910058i	$-0.636037\pi$
$181$	−11.1526			−0.828964			−0.414482	+	0.910058i	$0.636037\pi$
$182$			0.903212i			0.0669505i
$183$		0			0
$184$	−2.14764			−0.158326
$185$	1.00937	−	7.18421i	0.0742102	−	0.528193i
$186$		0			0
$187$			10.6637i			0.779807i
$188$		−	5.80642i		−	0.423477i
$189$		0			0
$190$	0.474572	−	3.37778i	0.0344291	−	0.245050i
$191$	−7.90813			−0.572213			−0.286106	−	0.958198i	$-0.592361\pi$
$191$	−7.90813			−0.572213			−0.286106	+	0.958198i	$0.592361\pi$
$192$		0			0
$193$		−	10.7096i		−	0.770896i	−0.922729	−	0.385448i	$-0.874047\pi$
$193$		−	10.7096i		−	0.770896i	0.922729	−	0.385448i	$-0.125953\pi$
$194$	−7.09679			−0.509520
$195$		0			0
$196$	−6.18421			−0.441729
$197$			13.6128i			0.969875i	0.874549	+	0.484938i	$0.161158\pi$
$197$			13.6128i			0.969875i	−0.874549	+	0.484938i	$0.838842\pi$
$198$		0			0
$199$	−2.91750			−0.206816			−0.103408	−	0.994639i	$-0.532975\pi$
$199$	−2.91750			−0.206816			−0.103408	+	0.994639i	$0.532975\pi$
$200$	−1.37778	+	4.80642i	−0.0974241	+	0.339865i
$201$		0			0
$202$			3.76049i			0.264587i
$203$		−	5.11108i		−	0.358727i
$204$		0			0
$205$	10.2351	+	1.43801i	0.714848	+	0.100435i
$206$	−16.7971			−1.17031
$207$		0			0
$208$			1.00000i			0.0693375i
$209$	3.05086			0.211032
$210$		0			0
$211$	−18.2766			−1.25821			−0.629105	−	0.777320i	$-0.716578\pi$
$211$	−18.2766			−1.25821			−0.629105	+	0.777320i	$0.716578\pi$
$212$		−	8.99063i		−	0.617479i
$213$		0			0
$214$	−8.56199			−0.585286
$215$	−0.0414872	+	0.295286i	−0.00282940	+	0.0201384i
$216$		0			0
$217$			2.19358i			0.148910i
$218$			4.70964i			0.318977i
$219$		0			0
$220$	−4.42864	−	0.622216i	−0.298579	−	0.0419498i
$221$	−5.33185			−0.358659
$222$		0			0
$223$		−	25.6686i		−	1.71890i	−0.511221	−	0.859449i	$-0.670807\pi$
$223$		−	25.6686i		−	1.71890i	0.511221	−	0.859449i	$-0.329193\pi$
$224$	0.903212			0.0603484
$225$		0			0
$226$	2.57628			0.171372
$227$		−	18.9590i		−	1.25835i	−0.777263	−	0.629176i	$-0.783392\pi$
$227$		−	18.9590i		−	1.25835i	0.777263	−	0.629176i	$-0.216608\pi$
$228$		0			0
$229$	−19.0781			−1.26071			−0.630357	−	0.776306i	$-0.717091\pi$
$229$	−19.0781			−1.26071			−0.630357	+	0.776306i	$0.717091\pi$
$230$	4.75557	+	0.668149i	0.313573	+	0.0440564i
$231$		0			0
$232$		−	5.65878i		−	0.371517i
$233$			17.6271i			1.15479i	0.816464	+	0.577396i	$0.195931\pi$
$233$			17.6271i			1.15479i	−0.816464	+	0.577396i	$0.804069\pi$
$234$		0			0
$235$	−1.80642	+	12.8573i	−0.117838	+	0.838716i
$236$	9.05086			0.589160
$237$		0			0
$238$			4.81579i			0.312161i
$239$	−14.7556			−0.954458			−0.477229	−	0.878779i	$-0.658359\pi$
$239$	−14.7556			−0.954458			−0.477229	+	0.878779i	$0.658359\pi$
$240$		0			0
$241$	14.2953			0.920840			0.460420	−	0.887701i	$-0.347699\pi$
$241$	14.2953			0.920840			0.460420	+	0.887701i	$0.347699\pi$
$242$			7.00000i			0.449977i
$243$		0			0
$244$	−12.6637			−0.810710
$245$	13.6938	+	1.92396i	0.874866	+	0.122917i
$246$		0			0
$247$			1.52543i			0.0970606i
$248$			2.42864i			0.154219i
$249$		0			0
$250$	4.54617	−	10.2143i	0.287525	−	0.646010i
$251$	5.27163			0.332742			0.166371	−	0.986063i	$-0.446795\pi$
$251$	5.27163			0.332742			0.166371	+	0.986063i	$0.446795\pi$
$252$		0			0
$253$			4.29529i			0.270042i
$254$	−6.99063			−0.438631
$255$		0			0
$256$	1.00000			0.0625000
$257$			21.6271i			1.34906i	0.738246	+	0.674532i	$0.235654\pi$
$257$			21.6271i			1.34906i	−0.738246	+	0.674532i	$0.764346\pi$
$258$		0			0
$259$	2.93041			0.182087
$260$	0.311108	−	2.21432i	0.0192941	−	0.137326i
$261$		0			0
$262$		−	20.3225i		−	1.25553i
$263$		−	0.516060i		−	0.0318216i	−0.999873	−	0.0159108i	$-0.994935\pi$
$263$		−	0.516060i		−	0.0318216i	0.999873	−	0.0159108i	$-0.00506478\pi$
$264$		0			0
$265$	−2.79706	+	19.9081i	−0.171822	+	1.22295i
$266$	1.37778			0.0844774
$267$		0			0
$268$			10.8573i			0.663214i
$269$	−24.3225			−1.48297			−0.741484	−	0.670971i	$-0.765878\pi$
$269$	−24.3225			−1.48297			−0.741484	+	0.670971i	$0.765878\pi$
$270$		0			0
$271$	−21.9496			−1.33334			−0.666672	−	0.745351i	$-0.732282\pi$
$271$	−21.9496			−1.33334			−0.666672	+	0.745351i	$0.732282\pi$
$272$			5.33185i			0.323291i
$273$		0			0
$274$	5.43801			0.328522
$275$	9.61285	+	2.75557i	0.579677	+	0.166167i
$276$		0			0
$277$		−	27.8479i		−	1.67322i	−0.547800	−	0.836609i	$-0.684534\pi$
$277$		−	27.8479i		−	1.67322i	0.547800	−	0.836609i	$-0.315466\pi$
$278$			6.10171i			0.365956i
$279$		0			0
$280$	−2.00000	−	0.280996i	−0.119523	−	0.0167927i
$281$	7.53972			0.449782			0.224891	−	0.974384i	$-0.427797\pi$
$281$	7.53972			0.449782			0.224891	+	0.974384i	$0.427797\pi$
$282$		0			0
$283$		−	7.00937i		−	0.416664i	−0.978058	−	0.208332i	$-0.933197\pi$
$283$		−	7.00937i		−	0.416664i	0.978058	−	0.208332i	$-0.0668034\pi$
$284$	−5.67307			−0.336635
$285$		0			0
$286$	2.00000			0.118262
$287$			4.17484i			0.246433i
$288$		0			0
$289$	−11.4286			−0.672273
$290$	−1.76049	+	12.5303i	−0.103380	+	0.735807i
$291$		0			0
$292$		−	2.70964i		−	0.158569i
$293$			2.85728i			0.166924i	0.996511	+	0.0834620i	$0.0265977\pi$
$293$			2.85728i			0.166924i	−0.996511	+	0.0834620i	$0.973402\pi$
$294$		0			0
$295$	−20.0415	−	2.81579i	−1.16686	−	0.163942i
$296$	3.24443			0.188579
$297$		0			0
$298$		−	1.28592i		−	0.0744913i
$299$	−2.14764			−0.124201
$300$		0			0
$301$	−0.120446			−0.00694240
$302$		−	0.622216i		−	0.0358045i
$303$		0			0
$304$	1.52543			0.0874893
$305$	28.0415	+	3.93978i	1.60565	+	0.225591i
$306$		0			0
$307$			33.9081i			1.93524i	0.252413	+	0.967620i	$0.418776\pi$
$307$			33.9081i			1.93524i	−0.252413	+	0.967620i	$0.581224\pi$
$308$		−	1.80642i		−	0.102931i
$309$		0			0
$310$	0.755569	−	5.37778i	0.0429134	−	0.305438i
$311$	−4.56199			−0.258687			−0.129343	−	0.991600i	$-0.541287\pi$
$311$	−4.56199			−0.258687			−0.129343	+	0.991600i	$0.541287\pi$
$312$		0			0
$313$			20.7654i			1.17373i	0.809685	+	0.586865i	$0.199638\pi$
$313$			20.7654i			1.17373i	−0.809685	+	0.586865i	$0.800362\pi$
$314$	14.3368			0.809071
$315$		0			0
$316$	−6.91750			−0.389140
$317$			6.33677i			0.355909i	0.984039	+	0.177954i	$0.0569479\pi$
$317$			6.33677i			0.355909i	−0.984039	+	0.177954i	$0.943052\pi$
$318$		0			0
$319$	−11.3176			−0.633662
$320$	−2.21432	−	0.311108i	−0.123784	−	0.0173915i
$321$		0			0
$322$			1.93978i			0.108100i
$323$			8.13335i			0.452552i
$324$		0			0
$325$	−1.37778	+	4.80642i	−0.0764257	+	0.266612i
$326$	12.9590			0.717732
$327$		0			0
$328$			4.62222i			0.255219i
$329$	−5.24443			−0.289135
$330$		0			0
$331$	30.9447			1.70087			0.850437	−	0.526077i	$-0.176337\pi$
$331$	30.9447			1.70087			0.850437	+	0.526077i	$0.176337\pi$
$332$			10.2351i			0.561722i
$333$		0			0
$334$	−8.85728			−0.484649
$335$	3.37778	−	24.0415i	0.184548	−	1.31353i
$336$		0			0
$337$		−	21.3274i		−	1.16178i	−0.813983	−	0.580889i	$-0.802705\pi$
$337$		−	21.3274i		−	1.16178i	0.813983	−	0.580889i	$-0.197295\pi$
$338$			1.00000i			0.0543928i
$339$		0			0
$340$	1.65878	−	11.8064i	0.0899600	−	0.640293i
$341$	4.85728			0.263036
$342$		0			0
$343$			11.9081i			0.642979i
$344$	−0.133353			−0.00718992
$345$		0			0
$346$	8.42864			0.453126
$347$		−	16.1748i		−	0.868311i	−0.900838	−	0.434155i	$-0.857047\pi$
$347$		−	16.1748i		−	0.868311i	0.900838	−	0.434155i	$-0.142953\pi$
$348$		0			0
$349$	14.9032			0.797751			0.398875	−	0.917005i	$-0.369401\pi$
$349$	14.9032			0.797751			0.398875	+	0.917005i	$0.369401\pi$
$350$	4.34122	+	1.24443i	0.232048	+	0.0665176i
$351$		0			0
$352$		−	2.00000i		−	0.106600i
$353$		−	18.5620i		−	0.987955i	−0.869475	−	0.493978i	$-0.835542\pi$
$353$		−	18.5620i		−	0.987955i	0.869475	−	0.493978i	$-0.164458\pi$
$354$		0			0
$355$	12.5620	+	1.76494i	0.666721	+	0.0936731i
$356$	2.94914			0.156304
$357$		0			0
$358$			23.7605i			1.25578i
$359$	16.8988			0.891883			0.445941	−	0.895062i	$-0.352869\pi$
$359$	16.8988			0.891883			0.445941	+	0.895062i	$0.352869\pi$
$360$		0			0
$361$	−16.6731			−0.877530
$362$			11.1526i			0.586166i
$363$		0			0
$364$	0.903212			0.0473412
$365$	−0.842989	+	6.00000i	−0.0441241	+	0.314054i
$366$		0			0
$367$			4.03164i			0.210450i	0.994448	+	0.105225i	$0.0335563\pi$
$367$			4.03164i			0.210450i	−0.994448	+	0.105225i	$0.966444\pi$
$368$			2.14764i			0.111954i
$369$		0			0
$370$	−7.18421	−	1.00937i	−0.373489	−	0.0524745i
$371$	−8.12045			−0.421593
$372$		0			0
$373$		−	22.9906i		−	1.19041i	−0.803574	−	0.595205i	$-0.797071\pi$
$373$		−	22.9906i		−	1.19041i	0.803574	−	0.595205i	$-0.202929\pi$
$374$	10.6637			0.551407
$375$		0			0
$376$	−5.80642			−0.299443
$377$		−	5.65878i		−	0.291442i
$378$		0			0
$379$	−18.1160			−0.930556			−0.465278	−	0.885164i	$-0.654046\pi$
$379$	−18.1160			−0.930556			−0.465278	+	0.885164i	$0.654046\pi$
$380$	−3.37778	−	0.474572i	−0.173277	−	0.0243451i
$381$		0			0
$382$			7.90813i			0.404615i
$383$			2.36842i			0.121020i	0.998168	+	0.0605102i	$0.0192728\pi$
$383$			2.36842i			0.121020i	−0.998168	+	0.0605102i	$0.980727\pi$
$384$		0			0
$385$	−0.561993	+	4.00000i	−0.0286418	+	0.203859i
$386$	−10.7096			−0.545106
$387$		0			0
$388$			7.09679i			0.360285i
$389$	−9.95407			−0.504691			−0.252346	−	0.967637i	$-0.581202\pi$
$389$	−9.95407			−0.504691			−0.252346	+	0.967637i	$0.581202\pi$
$390$		0			0
$391$	−11.4509			−0.579098
$392$			6.18421i			0.312350i
$393$		0			0
$394$	13.6128			0.685805
$395$	15.3176	+	2.15209i	0.770710	+	0.108283i
$396$		0			0
$397$			12.3970i			0.622187i	0.950379	+	0.311094i	$0.100695\pi$
$397$			12.3970i			0.622187i	−0.950379	+	0.311094i	$0.899305\pi$
$398$			2.91750i			0.146241i
$399$		0			0
$400$	4.80642	+	1.37778i	0.240321	+	0.0688892i
$401$	20.6222			1.02982			0.514912	−	0.857243i	$-0.327825\pi$
$401$	20.6222			1.02982			0.514912	+	0.857243i	$0.327825\pi$
$402$		0			0
$403$			2.42864i			0.120979i
$404$	3.76049			0.187091
$405$		0			0
$406$	−5.11108			−0.253659
$407$		−	6.48886i		−	0.321641i
$408$		0			0
$409$	1.61285			0.0797502			0.0398751	−	0.999205i	$-0.487304\pi$
$409$	1.61285			0.0797502			0.0398751	+	0.999205i	$0.487304\pi$
$410$	1.43801	−	10.2351i	0.0710181	−	0.505474i
$411$		0			0
$412$			16.7971i			0.827532i
$413$		−	8.17484i		−	0.402258i
$414$		0			0
$415$	3.18421	−	22.6637i	0.156307	−	1.11252i
$416$	1.00000			0.0490290
$417$		0			0
$418$		−	3.05086i		−	0.149222i
$419$	−38.1575			−1.86412			−0.932058	−	0.362310i	$-0.881988\pi$
$419$	−38.1575			−1.86412			−0.932058	+	0.362310i	$0.881988\pi$
$420$		0			0
$421$	−13.3635			−0.651297			−0.325648	−	0.945491i	$-0.605583\pi$
$421$	−13.3635			−0.651297			−0.325648	+	0.945491i	$0.605583\pi$
$422$			18.2766i			0.889689i
$423$		0			0
$424$	−8.99063			−0.436624
$425$	−7.34614	+	25.6271i	−0.356340	+	1.24310i
$426$		0			0
$427$			11.4380i			0.553524i
$428$			8.56199i			0.413860i
$429$		0			0
$430$	0.295286	+	0.0414872i	0.0142400	+	0.00200069i
$431$	−6.10171			−0.293909			−0.146955	−	0.989143i	$-0.546947\pi$
$431$	−6.10171			−0.293909			−0.146955	+	0.989143i	$0.546947\pi$
$432$		0			0
$433$		−	38.4514i		−	1.84786i	−0.382567	−	0.923928i	$-0.624960\pi$
$433$		−	38.4514i		−	1.84786i	0.382567	−	0.923928i	$-0.375040\pi$
$434$	2.19358			0.105295
$435$		0			0
$436$	4.70964			0.225551
$437$			3.27607i			0.156716i
$438$		0			0
$439$	18.1017			0.863947			0.431974	−	0.901886i	$-0.357817\pi$
$439$	18.1017			0.863947			0.431974	+	0.901886i	$0.357817\pi$
$440$	−0.622216	+	4.42864i	−0.0296630	+	0.211127i
$441$		0			0
$442$			5.33185i			0.253610i
$443$		−	33.2355i		−	1.57907i	−0.613707	−	0.789534i	$-0.710322\pi$
$443$		−	33.2355i		−	1.57907i	0.613707	−	0.789534i	$-0.289678\pi$
$444$		0			0
$445$	−6.53035	−	0.917502i	−0.309568	−	0.0434938i
$446$	−25.6686			−1.21544
$447$		0			0
$448$		−	0.903212i		−	0.0426728i
$449$	−27.0321			−1.27572			−0.637862	−	0.770150i	$-0.720181\pi$
$449$	−27.0321			−1.27572			−0.637862	+	0.770150i	$0.720181\pi$
$450$		0			0
$451$	9.24443			0.435303
$452$		−	2.57628i		−	0.121178i
$453$		0			0
$454$	−18.9590			−0.889789
$455$	−2.00000	−	0.280996i	−0.0937614	−	0.0131733i
$456$		0			0
$457$		−	29.4019i		−	1.37536i	−0.726012	−	0.687682i	$-0.758628\pi$
$457$		−	29.4019i		−	1.37536i	0.726012	−	0.687682i	$-0.241372\pi$
$458$			19.0781i			0.891459i
$459$		0			0
$460$	0.668149	−	4.75557i	0.0311526	−	0.221730i
$461$	21.4608			0.999527			0.499764	−	0.866162i	$-0.333420\pi$
$461$	21.4608			0.999527			0.499764	+	0.866162i	$0.333420\pi$
$462$		0			0
$463$			2.61777i			0.121658i	0.998148	+	0.0608290i	$0.0193744\pi$
$463$			2.61777i			0.121658i	−0.998148	+	0.0608290i	$0.980626\pi$
$464$	−5.65878			−0.262702
$465$		0			0
$466$	17.6271			0.816561
$467$		−	38.2766i		−	1.77123i	−0.464423	−	0.885614i	$-0.653738\pi$
$467$		−	38.2766i		−	1.77123i	0.464423	−	0.885614i	$-0.346262\pi$
$468$		0			0
$469$	9.80642			0.452819
$470$	12.8573	+	1.80642i	0.593062	+	0.0833241i
$471$		0			0
$472$		−	9.05086i		−	0.416599i
$473$			0.266706i			0.0122632i
$474$		0			0
$475$	7.33185	+	2.10171i	0.336408	+	0.0964331i
$476$	4.81579			0.220731
$477$		0			0
$478$			14.7556i			0.674904i
$479$	14.8385			0.677990			0.338995	−	0.940788i	$-0.389913\pi$
$479$	14.8385			0.677990			0.338995	+	0.940788i	$0.389913\pi$
$480$		0			0
$481$	3.24443			0.147933
$482$		−	14.2953i		−	0.651132i
$483$		0			0
$484$	7.00000			0.318182
$485$	2.20787	−	15.7146i	0.100254	−	0.713561i
$486$		0			0
$487$			27.8622i			1.26256i	0.775556	+	0.631278i	$0.217469\pi$
$487$			27.8622i			1.26256i	−0.775556	+	0.631278i	$0.782531\pi$
$488$			12.6637i			0.573259i
$489$		0			0
$490$	1.92396	−	13.6938i	0.0869155	−	0.618623i
$491$	−23.8435			−1.07604			−0.538020	−	0.842932i	$-0.680828\pi$
$491$	−23.8435			−1.07604			−0.538020	+	0.842932i	$0.680828\pi$
$492$		0			0
$493$		−	30.1718i		−	1.35887i
$494$	1.52543			0.0686322
$495$		0			0
$496$	2.42864			0.109049
$497$			5.12399i			0.229842i
$498$		0			0
$499$	29.1669			1.30569			0.652844	−	0.757492i	$-0.273576\pi$
$499$	29.1669			1.30569			0.652844	+	0.757492i	$0.273576\pi$
$500$	−10.2143	−	4.54617i	−0.456798	−	0.203311i
$501$		0			0
$502$		−	5.27163i		−	0.235284i
$503$		−	20.5161i		−	0.914766i	−0.889270	−	0.457383i	$-0.848787\pi$
$503$		−	20.5161i		−	0.914766i	0.889270	−	0.457383i	$-0.151213\pi$
$504$		0			0
$505$	−8.32693	−	1.16992i	−0.370543	−	0.0520607i
$506$	4.29529			0.190949
$507$		0			0
$508$			6.99063i			0.310159i
$509$	1.11108			0.0492477			0.0246238	−	0.999697i	$-0.492161\pi$
$509$	1.11108			0.0492477			0.0246238	+	0.999697i	$0.492161\pi$
$510$		0			0
$511$	−2.44738			−0.108266
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	21.6271			0.953932
$515$	5.22570	−	37.1941i	0.230272	−	1.63897i
$516$		0			0
$517$			11.6128i			0.510732i
$518$		−	2.93041i		−	0.128755i
$519$		0			0
$520$	−2.21432	−	0.311108i	−0.0971043	−	0.0136430i
$521$	−13.6316			−0.597211			−0.298605	−	0.954377i	$-0.596521\pi$
$521$	−13.6316			−0.597211			−0.298605	+	0.954377i	$0.596521\pi$
$522$		0			0
$523$		−	41.7146i		−	1.82405i	−0.410134	−	0.912025i	$-0.634518\pi$
$523$		−	41.7146i		−	1.82405i	0.410134	−	0.912025i	$-0.365482\pi$
$524$	−20.3225			−0.887792
$525$		0			0
$526$	−0.516060			−0.0225013
$527$			12.9491i			0.564074i
$528$		0			0
$529$	18.3876			0.799462
$530$	19.9081	+	2.79706i	0.864754	+	0.121496i
$531$		0			0
$532$		−	1.37778i		−	0.0597345i
$533$			4.62222i			0.200210i
$534$		0			0
$535$	2.66370	−	18.9590i	0.115162	−	0.819669i
$536$	10.8573			0.468963
$537$		0			0
$538$			24.3225i			1.04862i
$539$	12.3684			0.532745
$540$		0			0
$541$	3.02366			0.129997			0.0649986	−	0.997885i	$-0.479296\pi$
$541$	3.02366			0.129997			0.0649986	+	0.997885i	$0.479296\pi$
$542$			21.9496i			0.942817i
$543$		0			0
$544$	5.33185			0.228601
$545$	−10.4286	−	1.46520i	−0.446714	−	0.0627625i
$546$		0			0
$547$			46.0642i			1.96956i	0.173792	+	0.984782i	$0.444398\pi$
$547$			46.0642i			1.96956i	−0.173792	+	0.984782i	$0.555602\pi$
$548$		−	5.43801i		−	0.232300i
$549$		0			0
$550$	2.75557	−	9.61285i	0.117498	−	0.409893i
$551$	−8.63206			−0.367738
$552$		0			0
$553$			6.24797i			0.265691i
$554$	−27.8479			−1.18314
$555$		0			0
$556$	6.10171			0.258770
$557$		−	2.25380i		−	0.0954965i	−0.998859	−	0.0477483i	$-0.984795\pi$
$557$		−	2.25380i		−	0.0954965i	0.998859	−	0.0477483i	$-0.0152045\pi$
$558$		0			0
$559$	−0.133353			−0.00564023
$560$	−0.280996	+	2.00000i	−0.0118743	+	0.0845154i
$561$		0			0
$562$		−	7.53972i		−	0.318044i
$563$		−	23.5210i		−	0.991291i	−0.868525	−	0.495646i	$-0.834931\pi$
$563$		−	23.5210i		−	0.991291i	0.868525	−	0.495646i	$-0.165069\pi$
$564$		0			0
$565$	−0.801502	+	5.70471i	−0.0337194	+	0.239999i
$566$	−7.00937			−0.294626
$567$		0			0
$568$			5.67307i			0.238037i
$569$	−0.977725			−0.0409884			−0.0204942	−	0.999790i	$-0.506524\pi$
$569$	−0.977725			−0.0409884			−0.0204942	+	0.999790i	$0.506524\pi$
$570$		0			0
$571$	31.1052			1.30171			0.650857	−	0.759200i	$-0.274410\pi$
$571$	31.1052			1.30171			0.650857	+	0.759200i	$0.274410\pi$
$572$		−	2.00000i		−	0.0836242i
$573$		0			0
$574$	4.17484			0.174254
$575$	−2.95899	+	10.3225i	−0.123398	+	0.430477i
$576$		0			0
$577$			28.4242i			1.18331i	0.806190	+	0.591657i	$0.201526\pi$
$577$			28.4242i			1.18331i	−0.806190	+	0.591657i	$0.798474\pi$
$578$			11.4286i			0.475369i
$579$		0			0
$580$	12.5303	+	1.76049i	0.520294	+	0.0731004i
$581$	9.24443			0.383524
$582$		0			0
$583$			17.9813i			0.744708i
$584$	−2.70964			−0.112126
$585$		0			0
$586$	2.85728			0.118033
$587$		−	21.7975i		−	0.899680i	−0.893109	−	0.449840i	$-0.851481\pi$
$587$		−	21.7975i		−	0.899680i	0.893109	−	0.449840i	$-0.148519\pi$
$588$		0			0
$589$	3.70471			0.152650
$590$	−2.81579	+	20.0415i	−0.115924	+	0.825095i
$591$		0			0
$592$		−	3.24443i		−	0.133345i
$593$		−	19.8064i		−	0.813352i	−0.913572	−	0.406676i	$-0.866688\pi$
$593$		−	19.8064i		−	0.813352i	0.913572	−	0.406676i	$-0.133312\pi$
$594$		0			0
$595$	−10.6637	−	1.49823i	−0.437169	−	0.0614215i
$596$	−1.28592			−0.0526733
$597$		0			0
$598$			2.14764i			0.0878237i
$599$	−2.75557			−0.112589			−0.0562947	−	0.998414i	$-0.517929\pi$
$599$	−2.75557			−0.112589			−0.0562947	+	0.998414i	$0.517929\pi$
$600$		0			0
$601$	17.2672			0.704343			0.352172	−	0.935935i	$-0.385443\pi$
$601$	17.2672			0.704343			0.352172	+	0.935935i	$0.385443\pi$
$602$			0.120446i			0.00490902i
$603$		0			0
$604$	−0.622216			−0.0253176
$605$	−15.5002	−	2.17775i	−0.630174	−	0.0885383i
$606$		0			0
$607$			12.1521i			0.493238i	0.969113	+	0.246619i	$0.0793196\pi$
$607$			12.1521i			0.493238i	−0.969113	+	0.246619i	$0.920680\pi$
$608$		−	1.52543i		−	0.0618643i
$609$		0			0
$610$	3.93978	−	28.0415i	0.159517	−	1.13537i
$611$	−5.80642			−0.234903
$612$		0			0
$613$		−	31.0607i		−	1.25453i	−0.778806	−	0.627265i	$-0.784174\pi$
$613$		−	31.0607i		−	1.25453i	0.778806	−	0.627265i	$-0.215826\pi$
$614$	33.9081			1.36842
$615$		0			0
$616$	−1.80642			−0.0727829
$617$			16.3684i			0.658968i	0.944161	+	0.329484i	$0.106875\pi$
$617$			16.3684i			0.658968i	−0.944161	+	0.329484i	$0.893125\pi$
$618$		0			0
$619$	39.4148			1.58422			0.792108	−	0.610381i	$-0.208984\pi$
$619$	39.4148			1.58422			0.792108	+	0.610381i	$0.208984\pi$
$620$	−5.37778	−	0.755569i	−0.215977	−	0.0303444i
$621$		0			0
$622$			4.56199i			0.182919i
$623$		−	2.66370i		−	0.106719i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	20.7654			0.829953
$627$		0			0
$628$		−	14.3368i		−	0.572100i
$629$	17.2988			0.689749
$630$		0			0
$631$	9.00937			0.358657			0.179329	−	0.983789i	$-0.442607\pi$
$631$	9.00937			0.358657			0.179329	+	0.983789i	$0.442607\pi$
$632$			6.91750i			0.275163i
$633$		0			0
$634$	6.33677			0.251665
$635$	2.17484	−	15.4795i	0.0863059	−	0.614285i
$636$		0			0
$637$			6.18421i			0.245027i
$638$			11.3176i			0.448067i
$639$		0			0
$640$	−0.311108	+	2.21432i	−0.0122976	+	0.0875287i
$641$	14.3970			0.568647			0.284324	−	0.958728i	$-0.408231\pi$
$641$	14.3970			0.568647			0.284324	+	0.958728i	$0.408231\pi$
$642$		0			0
$643$		−	33.6128i		−	1.32556i	−0.748814	−	0.662781i	$-0.769376\pi$
$643$		−	33.6128i		−	1.32556i	0.748814	−	0.662781i	$-0.230624\pi$
$644$	1.93978			0.0764379
$645$		0			0
$646$	8.13335			0.320002
$647$			19.7792i			0.777602i	0.921322	+	0.388801i	$0.127111\pi$
$647$			19.7792i			0.777602i	−0.921322	+	0.388801i	$0.872889\pi$
$648$		0			0
$649$	−18.1017			−0.710554
$650$	4.80642	+	1.37778i	0.188523	+	0.0540411i
$651$		0			0
$652$		−	12.9590i		−	0.507513i
$653$			42.0513i			1.64560i	0.568334	+	0.822798i	$0.307588\pi$
$653$			42.0513i			1.64560i	−0.568334	+	0.822798i	$0.692412\pi$
$654$		0			0
$655$	45.0005	+	6.32248i	1.75831	+	0.247040i
$656$	4.62222			0.180467
$657$		0			0
$658$			5.24443i			0.204449i
$659$	−1.68736			−0.0657302			−0.0328651	−	0.999460i	$-0.510463\pi$
$659$	−1.68736			−0.0657302			−0.0328651	+	0.999460i	$0.510463\pi$
$660$		0			0
$661$	45.0879			1.75372			0.876858	−	0.480750i	$-0.159635\pi$
$661$	45.0879			1.75372			0.876858	+	0.480750i	$0.159635\pi$
$662$		−	30.9447i		−	1.20270i
$663$		0			0
$664$	10.2351			0.397197
$665$	−0.428639	+	3.05086i	−0.0166219	+	0.118307i
$666$		0			0
$667$		−	12.1530i		−	0.470568i
$668$			8.85728i			0.342698i
$669$		0			0
$670$	−24.0415	−	3.37778i	−0.928804	−	0.130495i
$671$	25.3274			0.977754
$672$		0			0
$673$			2.39700i			0.0923974i	0.998932	+	0.0461987i	$0.0147107\pi$
$673$			2.39700i			0.0923974i	−0.998932	+	0.0461987i	$0.985289\pi$
$674$	−21.3274			−0.821501
$675$		0			0
$676$	1.00000			0.0384615
$677$		−	36.8702i		−	1.41704i	−0.705693	−	0.708518i	$-0.749364\pi$
$677$		−	36.8702i		−	1.41704i	0.705693	−	0.708518i	$-0.250636\pi$
$678$		0			0
$679$	6.40990			0.245990
$680$	−11.8064	−	1.65878i	−0.452756	−	0.0636113i
$681$		0			0
$682$		−	4.85728i		−	0.185995i
$683$		−	45.0736i		−	1.72469i	−0.506318	−	0.862347i	$-0.668994\pi$
$683$		−	45.0736i		−	1.72469i	0.506318	−	0.862347i	$-0.331006\pi$
$684$		0			0
$685$	−1.69181	+	12.0415i	−0.0646406	+	0.460082i
$686$	11.9081			0.454655
$687$		0			0
$688$			0.133353i			0.00508404i
$689$	−8.99063			−0.342516
$690$		0			0
$691$	−13.7288			−0.522270			−0.261135	−	0.965302i	$-0.584097\pi$
$691$	−13.7288			−0.522270			−0.261135	+	0.965302i	$0.584097\pi$
$692$		−	8.42864i		−	0.320409i
$693$		0			0
$694$	−16.1748			−0.613989
$695$	−13.5111	−	1.89829i	−0.512507	−	0.0720062i
$696$		0			0
$697$			24.6450i			0.933495i
$698$		−	14.9032i		−	0.564095i
$699$		0			0
$700$	1.24443	−	4.34122i	0.0470351	−	0.164083i
$701$	−5.39207			−0.203656			−0.101828	−	0.994802i	$-0.532469\pi$
$701$	−5.39207			−0.203656			−0.101828	+	0.994802i	$0.532469\pi$
$702$		0			0
$703$		−	4.94914i		−	0.186661i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	−18.5620			−0.698590
$707$		−	3.39652i		−	0.127739i
$708$		0			0
$709$	−5.75065			−0.215970			−0.107985	−	0.994153i	$-0.534440\pi$
$709$	−5.75065			−0.215970			−0.107985	+	0.994153i	$0.534440\pi$
$710$	1.76494	−	12.5620i	0.0662369	−	0.471443i
$711$		0			0
$712$		−	2.94914i		−	0.110524i
$713$			5.21585i			0.195335i
$714$		0			0
$715$	−0.622216	+	4.42864i	−0.0232695	+	0.165622i
$716$	23.7605			0.887971
$717$		0			0
$718$		−	16.8988i		−	0.630656i
$719$	27.5496			1.02743			0.513713	−	0.857962i	$-0.328270\pi$
$719$	27.5496			1.02743			0.513713	+	0.857962i	$0.328270\pi$
$720$		0			0
$721$	15.1713			0.565009
$722$			16.6731i			0.620507i
$723$		0			0
$724$	11.1526			0.414482
$725$	−27.1985	−	7.79658i	−1.01013	−	0.289558i
$726$		0			0
$727$		−	32.0513i		−	1.18872i	−0.804200	−	0.594359i	$-0.797406\pi$
$727$		−	32.0513i		−	1.18872i	0.804200	−	0.594359i	$-0.202594\pi$
$728$		−	0.903212i		−	0.0334753i
$729$		0			0
$730$	6.00000	+	0.842989i	0.222070	+	0.0312004i
$731$	−0.711019			−0.0262980
$732$		0			0
$733$			40.0928i			1.48086i	0.672132	+	0.740431i	$0.265379\pi$
$733$			40.0928i			1.48086i	−0.672132	+	0.740431i	$0.734621\pi$
$734$	4.03164			0.148811
$735$		0			0
$736$	2.14764			0.0791632
$737$		−	21.7146i		−	0.799866i
$738$		0			0
$739$	−14.2623			−0.524646			−0.262323	−	0.964980i	$-0.584489\pi$
$739$	−14.2623			−0.524646			−0.262323	+	0.964980i	$0.584489\pi$
$740$	−1.00937	+	7.18421i	−0.0371051	+	0.264097i
$741$		0			0
$742$			8.12045i			0.298111i
$743$			12.3783i			0.454114i	0.973881	+	0.227057i	$0.0729104\pi$
$743$			12.3783i			0.454114i	−0.973881	+	0.227057i	$0.927090\pi$
$744$		0			0
$745$	2.84743	+	0.400059i	0.104322	+	0.0146570i
$746$	−22.9906			−0.841747
$747$		0			0
$748$		−	10.6637i		−	0.389904i
$749$	7.73329			0.282568
$750$		0			0
$751$	−7.79658			−0.284501			−0.142251	−	0.989831i	$-0.545434\pi$
$751$	−7.79658			−0.284501			−0.142251	+	0.989831i	$0.545434\pi$
$752$			5.80642i			0.211738i
$753$		0			0
$754$	−5.65878			−0.206081
$755$	1.37778	+	0.193576i	0.0501427	+	0.00704496i
$756$		0			0
$757$		−	19.5941i		−	0.712160i	−0.934455	−	0.356080i	$-0.884113\pi$
$757$		−	19.5941i		−	0.712160i	0.934455	−	0.356080i	$-0.115887\pi$
$758$			18.1160i			0.658003i
$759$		0			0
$760$	−0.474572	+	3.37778i	−0.0172146	+	0.122525i
$761$	29.0923			1.05460			0.527298	−	0.849680i	$-0.323205\pi$
$761$	29.0923			1.05460			0.527298	+	0.849680i	$0.323205\pi$
$762$		0			0
$763$		−	4.25380i		−	0.153998i
$764$	7.90813			0.286106
$765$		0			0
$766$	2.36842			0.0855744
$767$		−	9.05086i		−	0.326807i
$768$		0			0
$769$	12.6351			0.455634			0.227817	−	0.973704i	$-0.426841\pi$
$769$	12.6351			0.455634			0.227817	+	0.973704i	$0.426841\pi$
$770$	4.00000	+	0.561993i	0.144150	+	0.0202528i
$771$		0			0
$772$			10.7096i			0.385448i
$773$			15.3907i			0.553565i	0.960933	+	0.276782i	$0.0892681\pi$
$773$			15.3907i			0.553565i	−0.960933	+	0.276782i	$0.910732\pi$
$774$		0			0
$775$	11.6731	+	3.34614i	0.419309	+	0.120197i
$776$	7.09679			0.254760
$777$		0			0
$778$			9.95407i			0.356871i
$779$	7.05086			0.252623
$780$		0			0
$781$	11.3461			0.405997
$782$			11.4509i			0.409484i
$783$		0			0
$784$	6.18421			0.220865
$785$	−4.46028	+	31.7462i	−0.159194	+	1.13307i
$786$		0			0
$787$			15.8983i			0.566713i	0.959015	+	0.283356i	$0.0914479\pi$
$787$			15.8983i			0.566713i	−0.959015	+	0.283356i	$0.908552\pi$
$788$		−	13.6128i		−	0.484938i
$789$		0			0
$790$	2.15209	−	15.3176i	0.0765679	−	0.544974i
$791$	−2.32693			−0.0827361
$792$		0			0
$793$			12.6637i			0.449701i
$794$	12.3970			0.439953
$795$		0			0
$796$	2.91750			0.103408
$797$			5.28592i			0.187237i	0.995608	+	0.0936184i	$0.0298434\pi$
$797$			5.28592i			0.187237i	−0.995608	+	0.0936184i	$0.970157\pi$
$798$		0			0
$799$	−30.9590			−1.09525
$800$	1.37778	−	4.80642i	0.0487120	−	0.169933i
$801$		0			0
$802$		−	20.6222i		−	0.728196i
$803$			5.41927i			0.191242i
$804$		0			0
$805$	−4.29529	−	0.603480i	−0.151389	−	0.0212699i
$806$	2.42864			0.0855452
$807$		0			0
$808$		−	3.76049i		−	0.132294i
$809$	20.2953			0.713544			0.356772	−	0.934191i	$-0.383877\pi$
$809$	20.2953			0.713544			0.356772	+	0.934191i	$0.383877\pi$
$810$		0			0
$811$	−45.0178			−1.58079			−0.790395	−	0.612598i	$-0.790125\pi$
$811$	−45.0178			−1.58079			−0.790395	+	0.612598i	$0.790125\pi$
$812$			5.11108i			0.179364i
$813$		0			0
$814$	−6.48886			−0.227435
$815$	−4.03164	+	28.6953i	−0.141222	+	1.00515i
$816$		0			0
$817$			0.203420i			0.00711678i
$818$		−	1.61285i		−	0.0563919i
$819$		0			0
$820$	−10.2351	−	1.43801i	−0.357424	−	0.0502174i
$821$	−42.8800			−1.49652			−0.748262	−	0.663404i	$-0.769111\pi$
$821$	−42.8800			−1.49652			−0.748262	+	0.663404i	$0.769111\pi$
$822$		0			0
$823$		−	35.6731i		−	1.24349i	−0.783222	−	0.621743i	$-0.786425\pi$
$823$		−	35.6731i		−	1.24349i	0.783222	−	0.621743i	$-0.213575\pi$
$824$	16.7971			0.585153
$825$		0			0
$826$	−8.17484			−0.284439
$827$			29.7649i			1.03503i	0.855675	+	0.517514i	$0.173143\pi$
$827$			29.7649i			1.03503i	−0.855675	+	0.517514i	$0.826857\pi$
$828$		0			0
$829$	18.3872			0.638612			0.319306	−	0.947652i	$-0.396550\pi$
$829$	18.3872			0.638612			0.319306	+	0.947652i	$0.396550\pi$
$830$	−22.6637	−	3.18421i	−0.786669	−	0.110525i
$831$		0			0
$832$		−	1.00000i		−	0.0346688i
$833$			32.9733i			1.14246i
$834$		0			0
$835$	2.75557	−	19.6128i	0.0953604	−	0.678731i
$836$	−3.05086			−0.105516
$837$		0			0
$838$			38.1575i			1.31813i
$839$	25.8983			0.894108			0.447054	−	0.894507i	$-0.352473\pi$
$839$	25.8983			0.894108			0.447054	+	0.894507i	$0.352473\pi$
$840$		0			0
$841$	3.02180			0.104200
$842$			13.3635i			0.460536i
$843$		0			0
$844$	18.2766			0.629105
$845$	−2.21432	−	0.311108i	−0.0761749	−	0.0107024i
$846$		0			0
$847$		−	6.32248i		−	0.217243i
$848$			8.99063i			0.308740i
$849$		0			0
$850$	25.6271	+	7.34614i	0.879004	+	0.251971i
$851$	6.96788			0.238856
$852$		0			0
$853$			14.6824i			0.502717i	0.967894	+	0.251359i	$0.0808773\pi$
$853$			14.6824i			0.502717i	−0.967894	+	0.251359i	$0.919123\pi$
$854$	11.4380			0.391401
$855$		0			0
$856$	8.56199			0.292643
$857$		−	29.7190i		−	1.01518i	−0.861598	−	0.507591i	$-0.830536\pi$
$857$		−	29.7190i		−	1.01518i	0.861598	−	0.507591i	$-0.169464\pi$
$858$		0			0
$859$	−42.3595			−1.44529			−0.722644	−	0.691220i	$-0.757073\pi$
$859$	−42.3595			−1.44529			−0.722644	+	0.691220i	$0.757073\pi$
$860$	0.0414872	−	0.295286i	0.00141470	−	0.0100692i
$861$		0			0
$862$			6.10171i			0.207825i
$863$			23.8163i			0.810715i	0.914158	+	0.405358i	$0.132853\pi$
$863$			23.8163i			0.810715i	−0.914158	+	0.405358i	$0.867147\pi$
$864$		0			0
$865$	−2.62222	+	18.6637i	−0.0891580	+	0.634585i
$866$	−38.4514			−1.30663
$867$		0			0
$868$		−	2.19358i		−	0.0744548i
$869$	13.8350			0.469320
$870$		0			0
$871$	10.8573			0.367885
$872$		−	4.70964i		−	0.159488i
$873$		0			0
$874$	3.27607			0.110815
$875$	−4.10616	+	9.22570i	−0.138813	+	0.311885i
$876$		0			0
$877$			6.44155i			0.217516i	0.994068	+	0.108758i	$0.0346873\pi$
$877$			6.44155i			0.217516i	−0.994068	+	0.108758i	$0.965313\pi$
$878$		−	18.1017i		−	0.610903i
$879$		0			0
$880$	4.42864	+	0.622216i	0.149289	+	0.0209749i
$881$	−43.5210			−1.46626			−0.733130	−	0.680089i	$-0.761941\pi$
$881$	−43.5210			−1.46626			−0.733130	+	0.680089i	$0.761941\pi$
$882$		0			0
$883$		−	23.2257i		−	0.781607i	−0.920474	−	0.390803i	$-0.872197\pi$
$883$		−	23.2257i		−	0.781607i	0.920474	−	0.390803i	$-0.127803\pi$
$884$	5.33185			0.179330
$885$		0			0
$886$	−33.2355			−1.11657
$887$			38.6464i			1.29762i	0.760952	+	0.648809i	$0.224732\pi$
$887$			38.6464i			1.29762i	−0.760952	+	0.648809i	$0.775268\pi$
$888$		0			0
$889$	6.31402			0.211766
$890$	−0.917502	+	6.53035i	−0.0307547	+	0.218898i
$891$		0			0
$892$			25.6686i			0.859449i
$893$			8.85728i			0.296398i
$894$		0			0
$895$	−52.6133	−	7.39207i	−1.75867	−	0.247090i
$896$	−0.903212			−0.0301742
$897$		0			0
$898$			27.0321i			0.902074i
$899$	−13.7431			−0.458359
$900$		0			0
$901$	−47.9367			−1.59700
$902$		−	9.24443i		−	0.307806i
$903$		0			0
$904$	−2.57628			−0.0856859
$905$	−24.6953	−	3.46965i	−0.820901	−	0.115335i
$906$		0			0
$907$			39.4795i			1.31090i	0.755241	+	0.655448i	$0.227520\pi$
$907$			39.4795i			1.31090i	−0.755241	+	0.655448i	$0.772480\pi$
$908$			18.9590i			0.629176i
$909$		0			0
$910$	−0.280996	+	2.00000i	−0.00931494	+	0.0662994i
$911$	−18.6351			−0.617409			−0.308705	−	0.951158i	$-0.599895\pi$
$911$	−18.6351			−0.617409			−0.308705	+	0.951158i	$0.599895\pi$
$912$		0			0
$913$		−	20.4701i		−	0.677462i
$914$	−29.4019			−0.972529
$915$		0			0
$916$	19.0781			0.630357
$917$			18.3555i			0.606152i
$918$		0			0
$919$	−15.6128			−0.515020			−0.257510	−	0.966276i	$-0.582902\pi$
$919$	−15.6128			−0.515020			−0.257510	+	0.966276i	$0.582902\pi$
$920$	−4.75557	−	0.668149i	−0.156786	−	0.0220282i
$921$		0			0
$922$		−	21.4608i		−	0.706772i
$923$			5.67307i			0.186731i
$924$		0			0
$925$	4.47013	−	15.5941i	0.146977	−	0.512731i
$926$	2.61777			0.0860253
$927$		0			0
$928$			5.65878i			0.185759i
$929$	8.78415			0.288199			0.144099	−	0.989563i	$-0.453972\pi$
$929$	8.78415			0.288199			0.144099	+	0.989563i	$0.453972\pi$
$930$		0			0
$931$	9.43356			0.309172
$932$		−	17.6271i		−	0.577396i
$933$		0			0
$934$	−38.2766			−1.25245
$935$	−3.31756	+	23.6128i	−0.108496	+	0.772223i
$936$		0			0
$937$		−	13.2159i		−	0.431743i	−0.976422	−	0.215872i	$-0.930741\pi$
$937$		−	13.2159i		−	0.431743i	0.976422	−	0.215872i	$-0.0692592\pi$
$938$		−	9.80642i		−	0.320191i
$939$		0			0
$940$	1.80642	−	12.8573i	0.0589190	−	0.419358i
$941$	46.4385			1.51385			0.756926	−	0.653501i	$-0.226700\pi$
$941$	46.4385			1.51385			0.756926	+	0.653501i	$0.226700\pi$
$942$		0			0
$943$			9.92687i			0.323263i
$944$	−9.05086			−0.294580
$945$		0			0
$946$	0.266706			0.00867137
$947$		−	24.0701i		−	0.782172i	−0.920354	−	0.391086i	$-0.872099\pi$
$947$		−	24.0701i		−	0.782172i	0.920354	−	0.391086i	$-0.127901\pi$
$948$		0			0
$949$	−2.70964			−0.0879585
$950$	2.10171	−	7.33185i	0.0681885	−	0.237877i
$951$		0			0
$952$		−	4.81579i		−	0.156081i
$953$		−	12.2079i		−	0.395452i	−0.980257	−	0.197726i	$-0.936644\pi$
$953$		−	12.2079i		−	0.395452i	0.980257	−	0.197726i	$-0.0633556\pi$
$954$		0			0
$955$	−17.5111	−	2.46028i	−0.566647	−	0.0796129i
$956$	14.7556			0.477229
$957$		0			0
$958$		−	14.8385i		−	0.479412i
$959$	−4.91167			−0.158606
$960$		0			0
$961$	−25.1017			−0.809733
$962$		−	3.24443i		−	0.104605i
$963$		0			0
$964$	−14.2953			−0.460420
$965$	3.33185	−	23.7146i	0.107256	−	0.763399i
$966$		0			0
$967$			57.6972i			1.85542i	0.373305	+	0.927709i	$0.378224\pi$
$967$			57.6972i			1.85542i	−0.373305	+	0.927709i	$0.621776\pi$
$968$		−	7.00000i		−	0.224989i
$969$		0			0
$970$	−15.7146	−	2.20787i	−0.504564	−	0.0708903i
$971$	−22.9951			−0.737947			−0.368974	−	0.929440i	$-0.620291\pi$
$971$	−22.9951			−0.737947			−0.368974	+	0.929440i	$0.620291\pi$
$972$		0			0
$973$		−	5.51114i		−	0.176679i
$974$	27.8622			0.892763
$975$		0			0
$976$	12.6637			0.405355
$977$			39.3560i			1.25911i	0.776956	+	0.629555i	$0.216763\pi$
$977$			39.3560i			1.25911i	−0.776956	+	0.629555i	$0.783237\pi$
$978$		0			0
$979$	−5.89829			−0.188510
$980$	−13.6938	−	1.92396i	−0.437433	−	0.0614585i
$981$		0			0
$982$			23.8435i			0.760876i
$983$		−	12.2953i		−	0.392159i	−0.980588	−	0.196079i	$-0.937179\pi$
$983$		−	12.2953i		−	0.392159i	0.980588	−	0.196079i	$-0.0628210\pi$
$984$		0			0
$985$	−4.23506	+	30.1432i	−0.134940	+	0.960442i
$986$	−30.1718			−0.960865
$987$		0			0
$988$		−	1.52543i		−	0.0485303i
$989$	−0.286395			−0.00910683
$990$		0			0
$991$	29.4322			0.934944			0.467472	−	0.884008i	$-0.345165\pi$
$991$	29.4322			0.934944			0.467472	+	0.884008i	$0.345165\pi$
$992$		−	2.42864i		−	0.0771094i
$993$		0			0
$994$	5.12399			0.162523
$995$	−6.46028	−	0.907658i	−0.204805	−	0.0287747i
$996$		0			0
$997$		−	34.9906i		−	1.10816i	−0.832462	−	0.554082i	$-0.813069\pi$
$997$		−	34.9906i		−	1.10816i	0.832462	−	0.554082i	$-0.186931\pi$
$998$		−	29.1669i		−	0.923261i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.e.h.469.3	yes	6
3.2	odd	2		1170.2.e.g.469.4	yes	6
5.2	odd	4		5850.2.a.ct.1.1		3
5.3	odd	4		5850.2.a.co.1.3		3
5.4	even	2	inner	1170.2.e.h.469.6	yes	6
15.2	even	4		5850.2.a.cq.1.1		3
15.8	even	4		5850.2.a.cr.1.3		3
15.14	odd	2		1170.2.e.g.469.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.e.g.469.1	✓	6	15.14	odd	2
1170.2.e.g.469.4	yes	6	3.2	odd	2
1170.2.e.h.469.3	yes	6	1.1	even	1	trivial
1170.2.e.h.469.6	yes	6	5.4	even	2	inner
5850.2.a.co.1.3		3	5.3	odd	4
5850.2.a.cq.1.1		3	15.2	even	4
5850.2.a.cr.1.3		3	15.8	even	4
5850.2.a.ct.1.1		3	5.2	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} +0.903212i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} +0.903212i q^{7} +1.00000i q^{8} +(0.311108 - 2.21432i) q^{10} +2.00000 q^{11} +1.00000i q^{13} +0.903212 q^{14} +1.00000 q^{16} +5.33185i q^{17} +1.52543 q^{19} +(-2.21432 - 0.311108i) q^{20} -2.00000i q^{22} +2.14764i q^{23} +(4.80642 + 1.37778i) q^{25} +1.00000 q^{26} -0.903212i q^{28} -5.65878 q^{29} +2.42864 q^{31} -1.00000i q^{32} +5.33185 q^{34} +(-0.280996 + 2.00000i) q^{35} -3.24443i q^{37} -1.52543i q^{38} +(-0.311108 + 2.21432i) q^{40} +4.62222 q^{41} +0.133353i q^{43} -2.00000 q^{44} +2.14764 q^{46} +5.80642i q^{47} +6.18421 q^{49} +(1.37778 - 4.80642i) q^{50} -1.00000i q^{52} +8.99063i q^{53} +(4.42864 + 0.622216i) q^{55} -0.903212 q^{56} +5.65878i q^{58} -9.05086 q^{59} +12.6637 q^{61} -2.42864i q^{62} -1.00000 q^{64} +(-0.311108 + 2.21432i) q^{65} -10.8573i q^{67} -5.33185i q^{68} +(2.00000 + 0.280996i) q^{70} +5.67307 q^{71} +2.70964i q^{73} -3.24443 q^{74} -1.52543 q^{76} +1.80642i q^{77} +6.91750 q^{79} +(2.21432 + 0.311108i) q^{80} -4.62222i q^{82} -10.2351i q^{83} +(-1.65878 + 11.8064i) q^{85} +0.133353 q^{86} +2.00000i q^{88} -2.94914 q^{89} -0.903212 q^{91} -2.14764i q^{92} +5.80642 q^{94} +(3.37778 + 0.474572i) q^{95} -7.09679i q^{97} -6.18421i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4}+O(q^{10}) \) 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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