LMFDB - Embedded newform 1500.2.i.a.557.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(557,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1500.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.i (of order $4$, degree $2$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.12
Character	$\chi$	$=$	1500.557
Dual form			1500.2.i.a.1193.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.858034 + 1.50459i) q^{3} +(3.42398 + 3.42398i) q^{7} +(-1.52756 + 2.58197i) q^{9} +O(q^{10})$	$q+(0.858034 + 1.50459i) q^{3} +(3.42398 + 3.42398i) q^{7} +(-1.52756 + 2.58197i) q^{9} -4.41615i q^{11} +(2.37783 - 2.37783i) q^{13} +(2.76118 - 2.76118i) q^{17} +5.73740i q^{19} +(-2.21378 + 8.08956i) q^{21} +(4.22136 + 4.22136i) q^{23} +(-5.19549 - 0.0829215i) q^{27} +9.67346 q^{29} -0.881652 q^{31} +(6.64447 - 3.78920i) q^{33} +(-4.89356 - 4.89356i) q^{37} +(5.61792 + 1.53739i) q^{39} -4.74193i q^{41} +(-2.35399 + 2.35399i) q^{43} +(-1.71773 + 1.71773i) q^{47} +16.4472i q^{49} +(6.52362 + 1.78525i) q^{51} +(-0.0871466 - 0.0871466i) q^{53} +(-8.63241 + 4.92288i) q^{57} -12.4145 q^{59} -8.20953 q^{61} +(-14.0709 + 3.61029i) q^{63} +(-5.36363 - 5.36363i) q^{67} +(-2.72933 + 9.97347i) q^{69} +5.14462i q^{71} +(-0.0238484 + 0.0238484i) q^{73} +(15.1208 - 15.1208i) q^{77} +10.1374i q^{79} +(-4.33314 - 7.88821i) q^{81} +(-3.11282 - 3.11282i) q^{83} +(8.30015 + 14.5545i) q^{87} +2.72207 q^{89} +16.2833 q^{91} +(-0.756487 - 1.32652i) q^{93} +(4.70234 + 4.70234i) q^{97} +(11.4024 + 6.74591i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 12 q^{21} - 32 q^{31} + 100 q^{51} + 48 q^{61} + 52 q^{81} + 232 q^{91}+O(q^{100}) $ 32 * q - 12 * q^21 - 32 * q^31 + 100 * q^51 + 48 * q^61 + 52 * q^81 + 232 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.858034	+	1.50459i	0.495386	+	0.868673i
$3$	0.858034	+	1.50459i	0.495386	+	0.868673i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.42398	+	3.42398i	1.29414	+	1.29414i	0.932201	+	0.361941i	$0.117886\pi$
$7$	3.42398	+	3.42398i	1.29414	+	1.29414i	0.361941	+	0.932201i	$0.382114\pi$
$8$		0			0
$9$	−1.52756	+	2.58197i	−0.509185	+	0.860657i
$10$		0			0
$11$		−	4.41615i		−	1.33152i	−0.746167	−	0.665759i	$-0.768108\pi$
$11$		−	4.41615i		−	1.33152i	0.746167	−	0.665759i	$-0.231892\pi$
$12$		0			0
$13$	2.37783	−	2.37783i	0.659493	−	0.659493i	−0.295767	−	0.955260i	$-0.595575\pi$
$13$	2.37783	−	2.37783i	0.659493	−	0.659493i	0.955260	+	0.295767i	$0.0955753\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.76118	−	2.76118i	0.669685	−	0.669685i	−0.287958	−	0.957643i	$-0.592976\pi$
$17$	2.76118	−	2.76118i	0.669685	−	0.669685i	0.957643	+	0.287958i	$0.0929765\pi$
$18$		0			0
$19$			5.73740i			1.31625i	0.752909	+	0.658125i	$0.228650\pi$
$19$			5.73740i			1.31625i	−0.752909	+	0.658125i	$0.771350\pi$
$20$		0			0
$21$	−2.21378	+	8.08956i	−0.483086	+	1.76529i
$22$		0			0
$23$	4.22136	+	4.22136i	0.880214	+	0.880214i	0.993556	−	0.113342i	$-0.0361555\pi$
$23$	4.22136	+	4.22136i	0.880214	+	0.880214i	−0.113342	+	0.993556i	$0.536155\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.19549	−	0.0829215i	−0.999873	−	0.0159583i
$28$		0			0
$29$	9.67346			1.79632			0.898158	−	0.439673i	$-0.144906\pi$
$29$	9.67346			1.79632			0.898158	+	0.439673i	$0.144906\pi$
$30$		0			0
$31$	−0.881652			−0.158349			−0.0791747	−	0.996861i	$-0.525228\pi$
$31$	−0.881652			−0.158349			−0.0791747	+	0.996861i	$0.525228\pi$
$32$		0			0
$33$	6.64447	−	3.78920i	1.15665	−	0.659615i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.89356	−	4.89356i	−0.804496	−	0.804496i	0.179298	−	0.983795i	$-0.442617\pi$
$37$	−4.89356	−	4.89356i	−0.804496	−	0.804496i	−0.983795	+	0.179298i	$0.942617\pi$
$38$		0			0
$39$	5.61792	+	1.53739i	0.899587	+	0.246180i
$40$		0			0
$41$		−	4.74193i		−	0.740565i	−0.928919	−	0.370283i	$-0.879261\pi$
$41$		−	4.74193i		−	0.740565i	0.928919	−	0.370283i	$-0.120739\pi$
$42$		0			0
$43$	−2.35399	+	2.35399i	−0.358980	+	0.358980i	−0.863437	−	0.504457i	$-0.831693\pi$
$43$	−2.35399	+	2.35399i	−0.358980	+	0.358980i	0.504457	+	0.863437i	$0.331693\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.71773	+	1.71773i	−0.250557	+	0.250557i	−0.821199	−	0.570642i	$-0.806694\pi$
$47$	−1.71773	+	1.71773i	−0.250557	+	0.250557i	0.570642	+	0.821199i	$0.306694\pi$
$48$		0			0
$49$			16.4472i			2.34961i
$50$		0			0
$51$	6.52362	+	1.78525i	0.913489	+	0.249985i
$52$		0			0
$53$	−0.0871466	−	0.0871466i	−0.0119705	−	0.0119705i	0.701096	−	0.713067i	$-0.252694\pi$
$53$	−0.0871466	−	0.0871466i	−0.0119705	−	0.0119705i	−0.713067	+	0.701096i	$0.752694\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.63241	+	4.92288i	−1.14339	+	0.652052i
$58$		0			0
$59$	−12.4145			−1.61623			−0.808117	−	0.589021i	$-0.799513\pi$
$59$	−12.4145			−1.61623			−0.808117	+	0.589021i	$0.799513\pi$
$60$		0			0
$61$	−8.20953			−1.05112			−0.525562	−	0.850756i	$-0.676145\pi$
$61$	−8.20953			−1.05112			−0.525562	+	0.850756i	$0.676145\pi$
$62$		0			0
$63$	−14.0709	+	3.61029i	−1.77277	+	0.454854i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.36363	−	5.36363i	−0.655272	−	0.655272i	0.298986	−	0.954258i	$-0.403352\pi$
$67$	−5.36363	−	5.36363i	−0.655272	−	0.655272i	−0.954258	+	0.298986i	$0.903352\pi$
$68$		0			0
$69$	−2.72933	+	9.97347i	−0.328573	+	1.20066i
$70$		0			0
$71$			5.14462i			0.610554i	0.952264	+	0.305277i	$0.0987491\pi$
$71$			5.14462i			0.610554i	−0.952264	+	0.305277i	$0.901251\pi$
$72$		0			0
$73$	−0.0238484	+	0.0238484i	−0.00279125	+	0.00279125i	−0.708501	−	0.705710i	$-0.750628\pi$
$73$	−0.0238484	+	0.0238484i	−0.00279125	+	0.00279125i	0.705710	+	0.708501i	$0.250628\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	15.1208	−	15.1208i	1.72317	−	1.72317i
$78$		0			0
$79$			10.1374i			1.14055i	0.821455	+	0.570274i	$0.193163\pi$
$79$			10.1374i			1.14055i	−0.821455	+	0.570274i	$0.806837\pi$
$80$		0			0
$81$	−4.33314	−	7.88821i	−0.481460	−	0.876468i
$82$		0			0
$83$	−3.11282	−	3.11282i	−0.341677	−	0.341677i	0.515321	−	0.856997i	$-0.327673\pi$
$83$	−3.11282	−	3.11282i	−0.341677	−	0.341677i	−0.856997	+	0.515321i	$0.827673\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	8.30015	+	14.5545i	0.889870	+	1.56041i
$88$		0			0
$89$	2.72207			0.288539			0.144269	−	0.989538i	$-0.453917\pi$
$89$	2.72207			0.288539			0.144269	+	0.989538i	$0.453917\pi$
$90$		0			0
$91$	16.2833			1.70695
$92$		0			0
$93$	−0.756487	−	1.32652i	−0.0784441	−	0.137554i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.70234	+	4.70234i	0.477451	+	0.477451i	0.904315	−	0.426865i	$-0.140382\pi$
$97$	4.70234	+	4.70234i	0.477451	+	0.477451i	−0.426865	+	0.904315i	$0.640382\pi$
$98$		0			0
$99$	11.4024	+	6.74591i	1.14598	+	0.677990i
$100$		0			0
$101$			0.314035i			0.0312477i	0.999878	+	0.0156238i	$0.00497342\pi$
$101$			0.314035i			0.0312477i	−0.999878	+	0.0156238i	$0.995027\pi$
$102$		0			0
$103$	4.58416	−	4.58416i	0.451691	−	0.451691i	−0.444224	−	0.895916i	$-0.646521\pi$
$103$	4.58416	−	4.58416i	0.451691	−	0.451691i	0.895916	+	0.444224i	$0.146521\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.228153	−	0.228153i	0.0220564	−	0.0220564i	−0.695993	−	0.718049i	$-0.745035\pi$
$107$	0.228153	−	0.228153i	0.0220564	−	0.0220564i	0.718049	+	0.695993i	$0.245035\pi$
$108$		0			0
$109$		−	7.32624i		−	0.701726i	−0.936427	−	0.350863i	$-0.885888\pi$
$109$		−	7.32624i		−	0.701726i	0.936427	−	0.350863i	$-0.114112\pi$
$110$		0			0
$111$	3.16394	−	11.5616i	0.300308	−	1.09738i
$112$		0			0
$113$	−12.2186	−	12.2186i	−1.14943	−	1.14943i	−0.986665	−	0.162764i	$-0.947959\pi$
$113$	−12.2186	−	12.2186i	−1.14943	−	1.14943i	−0.162764	−	0.986665i	$-0.552041\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.50722	+	9.77178i	0.231793	+	0.903401i
$118$		0			0
$119$	18.9084			1.73333
$120$		0			0
$121$	−8.50235			−0.772941
$122$		0			0
$123$	7.13464	−	4.06874i	0.643309	−	0.366866i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.90272	+	8.90272i	0.789988	+	0.789988i	0.981492	−	0.191504i	$-0.0613363\pi$
$127$	8.90272	+	8.90272i	0.789988	+	0.789988i	−0.191504	+	0.981492i	$0.561336\pi$
$128$		0			0
$129$	−5.56157	−	1.52197i	−0.489669	−	0.134002i
$130$		0			0
$131$			10.9218i			0.954242i	0.878838	+	0.477121i	$0.158320\pi$
$131$			10.9218i			0.954242i	−0.878838	+	0.477121i	$0.841680\pi$
$132$		0			0
$133$	−19.6447	+	19.6447i	−1.70341	+	1.70341i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.2902	−	10.2902i	0.879154	−	0.879154i	−0.114293	−	0.993447i	$-0.536460\pi$
$137$	10.2902	−	10.2902i	0.879154	−	0.879154i	0.993447	+	0.114293i	$0.0364604\pi$
$138$		0			0
$139$			8.54528i			0.724801i	0.932022	+	0.362401i	$0.118043\pi$
$139$			8.54528i			0.724801i	−0.932022	+	0.362401i	$0.881957\pi$
$140$		0			0
$141$	−4.05835	−	1.11060i	−0.341775	−	0.0935298i
$142$		0			0
$143$	−10.5009	−	10.5009i	−0.878126	−	0.878126i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−24.7463	+	14.1123i	−2.04104	+	1.16396i
$148$		0			0
$149$	−3.76458			−0.308406			−0.154203	−	0.988039i	$-0.549281\pi$
$149$	−3.76458			−0.308406			−0.154203	+	0.988039i	$0.549281\pi$
$150$		0			0
$151$	8.09283			0.658585			0.329293	−	0.944228i	$-0.393190\pi$
$151$	8.09283			0.658585			0.329293	+	0.944228i	$0.393190\pi$
$152$		0			0
$153$	2.91143	+	11.3471i	0.235375	+	0.917362i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.57865	−	1.57865i	−0.125990	−	0.125990i	0.641300	−	0.767290i	$-0.278395\pi$
$157$	−1.57865	−	1.57865i	−0.125990	−	0.125990i	−0.767290	+	0.641300i	$0.778395\pi$
$158$		0			0
$159$	0.0563448	−	0.205894i	0.00446843	−	0.0163285i
$160$		0			0
$161$			28.9077i			2.27824i
$162$		0			0
$163$	7.14261	−	7.14261i	0.559453	−	0.559453i	−0.369699	−	0.929152i	$-0.620539\pi$
$163$	7.14261	−	7.14261i	0.559453	−	0.559453i	0.929152	+	0.369699i	$0.120539\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.8531	−	13.8531i	1.07198	−	1.07198i	0.0747830	−	0.997200i	$-0.476174\pi$
$167$	13.8531	−	13.8531i	1.07198	−	1.07198i	0.997200	−	0.0747830i	$-0.0238264\pi$
$168$		0			0
$169$			1.69181i			0.130139i
$170$		0			0
$171$	−14.8138	−	8.76420i	−1.13284	−	0.670215i
$172$		0			0
$173$	6.01112	+	6.01112i	0.457017	+	0.457017i	0.897675	−	0.440658i	$-0.145255\pi$
$173$	6.01112	+	6.01112i	0.457017	+	0.457017i	−0.440658	+	0.897675i	$0.645255\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.6521	−	18.6787i	−0.800660	−	1.40398i
$178$		0			0
$179$	−18.5057			−1.38318			−0.691592	−	0.722288i	$-0.743090\pi$
$179$	−18.5057			−1.38318			−0.691592	+	0.722288i	$0.743090\pi$
$180$		0			0
$181$	−20.8738			−1.55154			−0.775768	−	0.631018i	$-0.782637\pi$
$181$	−20.8738			−1.55154			−0.775768	+	0.631018i	$0.782637\pi$
$182$		0			0
$183$	−7.04406	−	12.3519i	−0.520712	−	0.913082i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−12.1938	−	12.1938i	−0.891697	−	0.891697i
$188$		0			0
$189$	−17.5053	−	18.0732i	−1.27332	−	1.31463i
$190$		0			0
$191$		−	3.45054i		−	0.249673i	−0.992177	−	0.124836i	$-0.960159\pi$
$191$		−	3.45054i		−	0.249673i	0.992177	−	0.124836i	$-0.0398406\pi$
$192$		0			0
$193$	3.54216	−	3.54216i	0.254970	−	0.254970i	−0.568035	−	0.823005i	$-0.692296\pi$
$193$	3.54216	−	3.54216i	0.254970	−	0.254970i	0.823005	+	0.568035i	$0.192296\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.69706	+	7.69706i	−0.548393	+	0.548393i	−0.925976	−	0.377583i	$-0.876755\pi$
$197$	−7.69706	+	7.69706i	−0.548393	+	0.548393i	0.377583	+	0.925976i	$0.376755\pi$
$198$		0			0
$199$		−	8.66527i		−	0.614265i	−0.951667	−	0.307132i	$-0.900631\pi$
$199$		−	8.66527i		−	0.614265i	0.951667	−	0.307132i	$-0.0993694\pi$
$200$		0			0
$201$	3.46787	−	12.6722i	0.244605	−	0.893830i
$202$		0			0
$203$	33.1217	+	33.1217i	2.32469	+	2.32469i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−17.3478	+	4.45106i	−1.20575	+	0.309370i
$208$		0			0
$209$	25.3372			1.75261
$210$		0			0
$211$	18.2843			1.25874			0.629372	−	0.777104i	$-0.283312\pi$
$211$	18.2843			1.25874			0.629372	+	0.777104i	$0.283312\pi$
$212$		0			0
$213$	−7.74052	+	4.41426i	−0.530372	+	0.302460i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.01876	−	3.01876i	−0.204927	−	0.204927i
$218$		0			0
$219$	−0.0563448	−	0.0154193i	−0.00380743	−	0.00104194i
$220$		0			0
$221$		−	13.1313i		−	0.883304i
$222$		0			0
$223$	3.00054	−	3.00054i	0.200931	−	0.200931i	−0.599468	−	0.800399i	$-0.704621\pi$
$223$	3.00054	−	3.00054i	0.200931	−	0.200931i	0.800399	+	0.599468i	$0.204621\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.3714	−	15.3714i	1.02024	−	1.02024i	0.0204446	−	0.999791i	$-0.493492\pi$
$227$	15.3714	−	15.3714i	1.02024	−	1.02024i	0.999791	−	0.0204446i	$-0.00650819\pi$
$228$		0			0
$229$		−	16.1230i		−	1.06544i	−0.846291	−	0.532720i	$-0.821170\pi$
$229$		−	16.1230i		−	1.06544i	0.846291	−	0.532720i	$-0.178830\pi$
$230$		0			0
$231$	35.7247	+	9.77637i	2.35051	+	0.643238i
$232$		0			0
$233$	−1.63447	−	1.63447i	−0.107078	−	0.107078i	0.651538	−	0.758616i	$-0.274124\pi$
$233$	−1.63447	−	1.63447i	−0.107078	−	0.107078i	−0.758616	+	0.651538i	$0.774124\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−15.2526	+	8.69824i	−0.990763	+	0.565011i
$238$		0			0
$239$	−19.8668			−1.28508			−0.642538	−	0.766254i	$-0.722118\pi$
$239$	−19.8668			−1.28508			−0.642538	+	0.766254i	$0.722118\pi$
$240$		0			0
$241$	−4.54857			−0.292999			−0.146499	−	0.989211i	$-0.546801\pi$
$241$	−4.54857			−0.292999			−0.146499	+	0.989211i	$0.546801\pi$
$242$		0			0
$243$	8.15051	−	13.2879i	0.522855	−	0.852422i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.6426	+	13.6426i	0.868057	+	0.868057i
$248$		0			0
$249$	2.01260	−	7.35442i	0.127543	−	0.466067i
$250$		0			0
$251$		−	26.3680i		−	1.66433i	−0.554528	−	0.832165i	$-0.687101\pi$
$251$		−	26.3680i		−	1.66433i	0.554528	−	0.832165i	$-0.312899\pi$
$252$		0			0
$253$	18.6421	−	18.6421i	1.17202	−	1.17202i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.39871	+	4.39871i	−0.274384	+	0.274384i	−0.830862	−	0.556478i	$-0.812152\pi$
$257$	−4.39871	+	4.39871i	−0.274384	+	0.274384i	0.556478	+	0.830862i	$0.312152\pi$
$258$		0			0
$259$		−	33.5109i		−	2.08226i
$260$		0			0
$261$	−14.7768	+	24.9766i	−0.914658	+	1.54601i
$262$		0			0
$263$	−10.1674	−	10.1674i	−0.626948	−	0.626948i	0.320351	−	0.947299i	$-0.396199\pi$
$263$	−10.1674	−	10.1674i	−0.626948	−	0.626948i	−0.947299	+	0.320351i	$0.896199\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.33563	+	4.09558i	0.142938	+	0.250646i
$268$		0			0
$269$	−20.7849			−1.26727			−0.633637	−	0.773630i	$-0.718439\pi$
$269$	−20.7849			−1.26727			−0.633637	+	0.773630i	$0.718439\pi$
$270$		0			0
$271$	7.70922			0.468302			0.234151	−	0.972200i	$-0.424769\pi$
$271$	7.70922			0.468302			0.234151	+	0.972200i	$0.424769\pi$
$272$		0			0
$273$	13.9716	+	24.4996i	0.845601	+	1.48278i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.19159	−	2.19159i	−0.131680	−	0.131680i	0.638195	−	0.769875i	$-0.279681\pi$
$277$	−2.19159	−	2.19159i	−0.131680	−	0.131680i	−0.769875	+	0.638195i	$0.779681\pi$
$278$		0			0
$279$	1.34677	−	2.27640i	0.0806292	−	0.136284i
$280$		0			0
$281$		−	0.201346i		−	0.0120113i	−0.999982	−	0.00600564i	$-0.998088\pi$
$281$		−	0.201346i		−	0.0120113i	0.999982	−	0.00600564i	$-0.00191167\pi$
$282$		0			0
$283$	8.13301	−	8.13301i	0.483457	−	0.483457i	−0.422777	−	0.906234i	$-0.638944\pi$
$283$	8.13301	−	8.13301i	0.483457	−	0.483457i	0.906234	+	0.422777i	$0.138944\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.2363	−	16.2363i	0.958396	−	0.958396i
$288$		0			0
$289$			1.75176i			0.103045i
$290$		0			0
$291$	−3.04031	+	11.1098i	−0.178226	+	0.651271i
$292$		0			0
$293$	5.36318	+	5.36318i	0.313321	+	0.313321i	0.846195	−	0.532874i	$-0.178888\pi$
$293$	5.36318	+	5.36318i	0.313321	+	0.313321i	−0.532874	+	0.846195i	$0.678888\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.366193	+	22.9440i	−0.0212487	+	1.33135i
$298$		0			0
$299$	20.0754			1.16099
$300$		0			0
$301$	−16.1200			−0.929141
$302$		0			0
$303$	−0.472493	+	0.269453i	−0.0271440	+	0.0154797i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	10.6091	+	10.6091i	0.605493	+	0.605493i	0.941765	−	0.336272i	$-0.109166\pi$
$307$	10.6091	+	10.6091i	0.605493	+	0.605493i	−0.336272	+	0.941765i	$0.609166\pi$
$308$		0			0
$309$	10.8306	+	2.96390i	0.616133	+	0.168610i
$310$		0			0
$311$		−	22.8047i		−	1.29314i	−0.762856	−	0.646568i	$-0.776203\pi$
$311$		−	22.8047i		−	1.29314i	0.762856	−	0.646568i	$-0.223797\pi$
$312$		0			0
$313$	−8.55473	+	8.55473i	−0.483542	+	0.483542i	−0.906261	−	0.422719i	$-0.861076\pi$
$313$	−8.55473	+	8.55473i	−0.483542	+	0.483542i	0.422719	+	0.906261i	$0.361076\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.0447	−	11.0447i	0.620333	−	0.620333i	−0.325283	−	0.945617i	$-0.605460\pi$
$317$	11.0447	−	11.0447i	0.620333	−	0.620333i	0.945617	+	0.325283i	$0.105460\pi$
$318$		0			0
$319$		−	42.7194i		−	2.39183i
$320$		0			0
$321$	0.539038	+	0.147513i	0.0300862	+	0.00823335i
$322$		0			0
$323$	15.8420	+	15.8420i	0.881472	+	0.881472i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	11.0230	−	6.28616i	0.609571	−	0.347625i
$328$		0			0
$329$	−11.7630			−0.648513
$330$		0			0
$331$	−1.14324			−0.0628380			−0.0314190	−	0.999506i	$-0.510003\pi$
$331$	−1.14324			−0.0628380			−0.0314190	+	0.999506i	$0.510003\pi$
$332$		0			0
$333$	20.1102	−	5.15984i	1.10203	−	0.282757i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	19.4455	+	19.4455i	1.05926	+	1.05926i	0.998130	+	0.0611320i	$0.0194711\pi$
$337$	19.4455	+	19.4455i	1.05926	+	1.05926i	0.0611320	+	0.998130i	$0.480529\pi$
$338$		0			0
$339$	7.89996	−	28.8679i	0.429067	−	1.56789i
$340$		0			0
$341$			3.89350i			0.210845i
$342$		0			0
$343$	−32.3472	+	32.3472i	−1.74658	+	1.74658i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.41341	+	3.41341i	−0.183242	+	0.183242i	−0.792767	−	0.609525i	$-0.791360\pi$
$347$	−3.41341	+	3.41341i	−0.183242	+	0.183242i	0.609525	+	0.792767i	$0.291360\pi$
$348$		0			0
$349$		−	23.6765i		−	1.26737i	−0.773590	−	0.633686i	$-0.781541\pi$
$349$		−	23.6765i		−	1.26737i	0.773590	−	0.633686i	$-0.218459\pi$
$350$		0			0
$351$	−12.5512	+	12.1568i	−0.669933	+	0.648884i
$352$		0			0
$353$	−9.09843	−	9.09843i	−0.484261	−	0.484261i	0.422229	−	0.906489i	$-0.361248\pi$
$353$	−9.09843	−	9.09843i	−0.484261	−	0.484261i	−0.906489	+	0.422229i	$0.861248\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	16.2241	+	28.4494i	0.858669	+	1.50570i
$358$		0			0
$359$	−13.1167			−0.692275			−0.346137	−	0.938184i	$-0.612507\pi$
$359$	−13.1167			−0.692275			−0.346137	+	0.938184i	$0.612507\pi$
$360$		0			0
$361$	−13.9177			−0.732513
$362$		0			0
$363$	−7.29530	−	12.7925i	−0.382904	−	0.671433i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−13.7664	−	13.7664i	−0.718600	−	0.718600i	0.249719	−	0.968318i	$-0.419662\pi$
$367$	−13.7664	−	13.7664i	−0.718600	−	0.718600i	−0.968318	+	0.249719i	$0.919662\pi$
$368$		0			0
$369$	12.2435	+	7.24357i	0.637372	+	0.377085i
$370$		0			0
$371$		−	0.596776i		−	0.0309831i
$372$		0			0
$373$	8.30777	−	8.30777i	0.430160	−	0.430160i	−0.458523	−	0.888683i	$-0.651621\pi$
$373$	8.30777	−	8.30777i	0.430160	−	0.430160i	0.888683	+	0.458523i	$0.151621\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	23.0019	−	23.0019i	1.18466	−	1.18466i
$378$		0			0
$379$			2.77970i			0.142784i	0.997448	+	0.0713919i	$0.0227441\pi$
$379$			2.77970i			0.142784i	−0.997448	+	0.0713919i	$0.977256\pi$
$380$		0			0
$381$	−5.75607	+	21.0337i	−0.294892	+	1.07759i
$382$		0			0
$383$	−0.696749	−	0.696749i	−0.0356022	−	0.0356022i	0.689082	−	0.724684i	$-0.258014\pi$
$383$	−0.696749	−	0.696749i	−0.0356022	−	0.0356022i	−0.724684	+	0.689082i	$0.758014\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.48208	−	9.67377i	−0.126171	−	0.491745i
$388$		0			0
$389$	−7.01377			−0.355612			−0.177806	−	0.984066i	$-0.556900\pi$
$389$	−7.01377			−0.355612			−0.177806	+	0.984066i	$0.556900\pi$
$390$		0			0
$391$	23.3119			1.17893
$392$		0			0
$393$	−16.4328	+	9.37127i	−0.828924	+	0.472718i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−18.3572	−	18.3572i	−0.921324	−	0.921324i	0.0757992	−	0.997123i	$-0.475849\pi$
$397$	−18.3572	−	18.3572i	−0.921324	−	0.921324i	−0.997123	+	0.0757992i	$0.975849\pi$
$398$		0			0
$399$	−46.4130	−	12.7013i	−2.32356	−	0.635862i
$400$		0			0
$401$			22.9988i			1.14851i	0.818678	+	0.574253i	$0.194707\pi$
$401$			22.9988i			1.14851i	−0.818678	+	0.574253i	$0.805293\pi$
$402$		0			0
$403$	−2.09642	+	2.09642i	−0.104430	+	0.104430i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−21.6107	+	21.6107i	−1.07120	+	1.07120i
$408$		0			0
$409$			8.13216i			0.402109i	0.979580	+	0.201055i	$0.0644369\pi$
$409$			8.13216i			0.402109i	−0.979580	+	0.201055i	$0.935563\pi$
$410$		0			0
$411$	24.3119	+	6.65317i	1.19922	+	0.328177i
$412$		0			0
$413$	−42.5071	−	42.5071i	−2.09164	−	2.09164i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−12.8571	+	7.33214i	−0.629615	+	0.359056i
$418$		0			0
$419$	−19.0329			−0.929817			−0.464908	−	0.885359i	$-0.653913\pi$
$419$	−19.0329			−0.929817			−0.464908	+	0.885359i	$0.653913\pi$
$420$		0			0
$421$	36.5086			1.77932			0.889660	−	0.456623i	$-0.150941\pi$
$421$	36.5086			1.77932			0.889660	+	0.456623i	$0.150941\pi$
$422$		0			0
$423$	−1.81120	−	7.05907i	−0.0880637	−	0.343224i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−28.1093	−	28.1093i	−1.36030	−	1.36030i
$428$		0			0
$429$	6.78936	−	24.8095i	0.327793	−	1.19782i
$430$		0			0
$431$		−	28.7877i		−	1.38666i	−0.720622	−	0.693328i	$-0.756144\pi$
$431$		−	28.7877i		−	1.38666i	0.720622	−	0.693328i	$-0.243856\pi$
$432$		0			0
$433$	19.6350	−	19.6350i	0.943596	−	0.943596i	−0.0548962	−	0.998492i	$-0.517483\pi$
$433$	19.6350	−	19.6350i	0.943596	−	0.943596i	0.998492	+	0.0548962i	$0.0174828\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−24.2196	+	24.2196i	−1.15858	+	1.15858i
$438$		0			0
$439$			33.5692i			1.60217i	0.598550	+	0.801085i	$0.295744\pi$
$439$			33.5692i			1.60217i	−0.598550	+	0.801085i	$0.704256\pi$
$440$		0			0
$441$	−42.4663	−	25.1241i	−2.02221	−	1.19639i
$442$		0			0
$443$	−3.58770	−	3.58770i	−0.170457	−	0.170457i	0.616723	−	0.787180i	$-0.288460\pi$
$443$	−3.58770	−	3.58770i	−0.170457	−	0.170457i	−0.787180	+	0.616723i	$0.788460\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−3.23013	−	5.66413i	−0.152780	−	0.267904i
$448$		0			0
$449$	−14.7484			−0.696022			−0.348011	−	0.937491i	$-0.613143\pi$
$449$	−14.7484			−0.696022			−0.348011	+	0.937491i	$0.613143\pi$
$450$		0			0
$451$	−20.9411			−0.986076
$452$		0			0
$453$	6.94392	+	12.1764i	0.326254	+	0.572095i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.74860	−	2.74860i	−0.128574	−	0.128574i	0.639891	−	0.768466i	$-0.278979\pi$
$457$	−2.74860	−	2.74860i	−0.128574	−	0.128574i	−0.768466	+	0.639891i	$0.778979\pi$
$458$		0			0
$459$	−14.5746	+	14.1167i	−0.680286	+	0.658912i
$460$		0			0
$461$		−	35.4016i		−	1.64882i	−0.565996	−	0.824408i	$-0.691508\pi$
$461$		−	35.4016i		−	1.64882i	0.565996	−	0.824408i	$-0.308492\pi$
$462$		0			0
$463$	−18.1341	+	18.1341i	−0.842765	+	0.842765i	−0.989218	−	0.146453i	$-0.953214\pi$
$463$	−18.1341	+	18.1341i	−0.842765	+	0.842765i	0.146453	+	0.989218i	$0.453214\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	24.7235	−	24.7235i	1.14407	−	1.14407i	0.156368	−	0.987699i	$-0.450021\pi$
$467$	24.7235	−	24.7235i	1.14407	−	1.14407i	0.987699	−	0.156368i	$-0.0499787\pi$
$468$		0			0
$469$		−	36.7299i		−	1.69603i
$470$		0			0
$471$	1.02068	−	3.72975i	0.0470305	−	0.171858i
$472$		0			0
$473$	10.3955	+	10.3955i	0.477988	+	0.477988i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.358131	−	0.0918886i	0.0163977	−	0.00420729i
$478$		0			0
$479$	38.4729			1.75787			0.878937	−	0.476938i	$-0.158254\pi$
$479$	38.4729			1.75787			0.878937	+	0.476938i	$0.158254\pi$
$480$		0			0
$481$	−23.2722			−1.06112
$482$		0			0
$483$	−43.4941	+	24.8038i	−1.97905	+	1.12861i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−11.6381	−	11.6381i	−0.527372	−	0.527372i	0.392416	−	0.919788i	$-0.371639\pi$
$487$	−11.6381	−	11.6381i	−0.527372	−	0.527372i	−0.919788	+	0.392416i	$0.871639\pi$
$488$		0			0
$489$	16.8753	+	4.61807i	0.763126	+	0.208836i
$490$		0			0
$491$			26.3914i			1.19103i	0.803344	+	0.595515i	$0.203052\pi$
$491$			26.3914i			1.19103i	−0.803344	+	0.595515i	$0.796948\pi$
$492$		0			0
$493$	26.7102	−	26.7102i	1.20297	−	1.20297i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.6151	+	17.6151i	−0.790144	+	0.790144i
$498$		0			0
$499$		−	11.5453i		−	0.516838i	−0.966033	−	0.258419i	$-0.916799\pi$
$499$		−	11.5453i		−	0.516838i	0.966033	−	0.258419i	$-0.0832015\pi$
$500$		0			0
$501$	32.7295	+	8.95673i	1.46225	+	0.400157i
$502$		0			0
$503$	6.60909	+	6.60909i	0.294685	+	0.294685i	0.838928	−	0.544243i	$-0.183183\pi$
$503$	6.60909	+	6.60909i	0.294685	+	0.294685i	−0.544243	+	0.838928i	$0.683183\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.54547	+	1.45163i	−0.113048	+	0.0644690i
$508$		0			0
$509$	−0.302286			−0.0133986			−0.00669930	−	0.999978i	$-0.502132\pi$
$509$	−0.302286			−0.0133986			−0.00669930	+	0.999978i	$0.502132\pi$
$510$		0			0
$511$	−0.163313			−0.00722454
$512$		0			0
$513$	0.475754	−	29.8086i	0.0210050	−	1.31608i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	7.58576	+	7.58576i	0.333622	+	0.333622i
$518$		0			0
$519$	−3.88650	+	14.2020i	−0.170599	+	0.623399i
$520$		0			0
$521$			19.6062i			0.858961i	0.903076	+	0.429481i	$0.141303\pi$
$521$			19.6062i			0.858961i	−0.903076	+	0.429481i	$0.858697\pi$
$522$		0			0
$523$	−10.9098	+	10.9098i	−0.477051	+	0.477051i	−0.904187	−	0.427136i	$-0.859523\pi$
$523$	−10.9098	+	10.9098i	−0.477051	+	0.477051i	0.427136	+	0.904187i	$0.359523\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.43440	+	2.43440i	−0.106044	+	0.106044i
$528$		0			0
$529$			12.6398i			0.549555i
$530$		0			0
$531$	18.9639	−	32.0540i	0.822963	−	1.39102i
$532$		0			0
$533$	−11.2755	−	11.2755i	−0.488397	−	0.488397i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−15.8786	−	27.8435i	−0.685210	−	1.20154i
$538$		0			0
$539$	72.6334			3.12854
$540$		0			0
$541$	1.42388			0.0612175			0.0306087	−	0.999531i	$-0.490255\pi$
$541$	1.42388			0.0612175			0.0306087	+	0.999531i	$0.490255\pi$
$542$		0			0
$543$	−17.9104	−	31.4064i	−0.768609	−	1.34778i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	20.4348	+	20.4348i	0.873729	+	0.873729i	0.992877	−	0.119148i	$-0.0380162\pi$
$547$	20.4348	+	20.4348i	0.873729	+	0.873729i	−0.119148	+	0.992877i	$0.538016\pi$
$548$		0			0
$549$	12.5405	−	21.1968i	0.535217	−	0.904656i
$550$		0			0
$551$			55.5005i			2.36440i
$552$		0			0
$553$	−34.7103	+	34.7103i	−1.47603	+	1.47603i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.79018	+	2.79018i	−0.118224	+	0.118224i	−0.763743	−	0.645520i	$-0.776641\pi$
$557$	−2.79018	+	2.79018i	−0.118224	+	0.118224i	0.645520	+	0.763743i	$0.276641\pi$
$558$		0			0
$559$			11.1948i			0.473489i
$560$		0			0
$561$	7.88391	−	28.8093i	0.332859	−	1.21633i
$562$		0			0
$563$	27.2961	+	27.2961i	1.15039	+	1.15039i	0.986474	+	0.163920i	$0.0524138\pi$
$563$	27.2961	+	27.2961i	1.15039	+	1.15039i	0.163920	+	0.986474i	$0.447586\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	12.1725	−	41.8456i	0.511196	−	1.75735i
$568$		0			0
$569$	−10.4137			−0.436564			−0.218282	−	0.975886i	$-0.570045\pi$
$569$	−10.4137			−0.436564			−0.218282	+	0.975886i	$0.570045\pi$
$570$		0			0
$571$	34.7745			1.45527			0.727634	−	0.685966i	$-0.240620\pi$
$571$	34.7745			1.45527			0.727634	+	0.685966i	$0.240620\pi$
$572$		0			0
$573$	5.19164	−	2.96068i	0.216884	−	0.123684i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	20.3923	+	20.3923i	0.848943	+	0.848943i	0.990001	−	0.141059i	$-0.0450506\pi$
$577$	20.3923	+	20.3923i	0.848943	+	0.848943i	−0.141059	+	0.990001i	$0.545051\pi$
$578$		0			0
$579$	8.36877	+	2.29019i	0.347794	+	0.0951770i
$580$		0			0
$581$		−	21.3165i		−	0.884356i
$582$		0			0
$583$	−0.384852	+	0.384852i	−0.0159389	+	0.0159389i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.5126	−	19.5126i	0.805369	−	0.805369i	−0.178560	−	0.983929i	$-0.557144\pi$
$587$	19.5126	−	19.5126i	0.805369	−	0.805369i	0.983929	+	0.178560i	$0.0571438\pi$
$588$		0			0
$589$		−	5.05839i		−	0.208427i
$590$		0			0
$591$	−18.1852	−	4.97655i	−0.748040	−	0.204708i
$592$		0			0
$593$	−24.9428	−	24.9428i	−1.02428	−	1.02428i	−0.999698	−	0.0245811i	$-0.992175\pi$
$593$	−24.9428	−	24.9428i	−1.02428	−	1.02428i	−0.0245811	−	0.999698i	$-0.507825\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	13.0376	−	7.43510i	0.533595	−	0.304298i
$598$		0			0
$599$	−14.7602			−0.603085			−0.301542	−	0.953453i	$-0.597501\pi$
$599$	−14.7602			−0.603085			−0.301542	+	0.953453i	$0.597501\pi$
$600$		0			0
$601$	−24.3977			−0.995204			−0.497602	−	0.867405i	$-0.665786\pi$
$601$	−24.3977			−0.995204			−0.497602	+	0.867405i	$0.665786\pi$
$602$		0			0
$603$	22.0420	−	5.65549i	0.897619	−	0.230309i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.12386	−	4.12386i	−0.167382	−	0.167382i	0.618446	−	0.785828i	$-0.287763\pi$
$607$	−4.12386	−	4.12386i	−0.167382	−	0.167382i	−0.785828	+	0.618446i	$0.787763\pi$
$608$		0			0
$609$	−21.4149	+	78.2540i	−0.867776	+	3.17101i
$610$		0			0
$611$			8.16898i			0.330481i
$612$		0			0
$613$	−30.2152	+	30.2152i	−1.22038	+	1.22038i	−0.252885	+	0.967496i	$0.581379\pi$
$613$	−30.2152	+	30.2152i	−1.22038	+	1.22038i	−0.967496	+	0.252885i	$0.918621\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.7621	+	20.7621i	−0.835851	+	0.835851i	−0.988310	−	0.152459i	$-0.951281\pi$
$617$	−20.7621	+	20.7621i	−0.835851	+	0.835851i	0.152459	+	0.988310i	$0.451281\pi$
$618$		0			0
$619$			16.7853i			0.674657i	0.941387	+	0.337328i	$0.109523\pi$
$619$			16.7853i			0.674657i	−0.941387	+	0.337328i	$0.890477\pi$
$620$		0			0
$621$	−21.5820	−	22.2821i	−0.866056	−	0.894149i
$622$		0			0
$623$	9.32030	+	9.32030i	0.373410	+	0.373410i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	21.7402	+	38.1220i	0.868218	+	1.52244i
$628$		0			0
$629$	−27.0240			−1.07752
$630$		0			0
$631$	−7.79407			−0.310277			−0.155138	−	0.987893i	$-0.549582\pi$
$631$	−7.79407			−0.310277			−0.155138	+	0.987893i	$0.549582\pi$
$632$		0			0
$633$	15.6886	+	27.5103i	0.623564	+	1.09344i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	39.1088	+	39.1088i	1.54955	+	1.54955i
$638$		0			0
$639$	−13.2833	−	7.85870i	−0.525478	−	0.310885i
$640$		0			0
$641$			32.2410i			1.27344i	0.771093	+	0.636722i	$0.219710\pi$
$641$			32.2410i			1.27344i	−0.771093	+	0.636722i	$0.780290\pi$
$642$		0			0
$643$	25.7525	−	25.7525i	1.01558	−	1.01558i	0.0157009	−	0.999877i	$-0.495002\pi$
$643$	25.7525	−	25.7525i	1.01558	−	1.01558i	0.999877	−	0.0157009i	$-0.00499795\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−33.4842	+	33.4842i	−1.31640	+	1.31640i	−0.399793	+	0.916605i	$0.630918\pi$
$647$	−33.4842	+	33.4842i	−1.31640	+	1.31640i	−0.916605	+	0.399793i	$0.869082\pi$
$648$		0			0
$649$			54.8244i			2.15205i
$650$		0			0
$651$	1.95178	−	7.13217i	0.0764964	−	0.279532i
$652$		0			0
$653$	15.9175	+	15.9175i	0.622900	+	0.622900i	0.946272	−	0.323372i	$-0.104816\pi$
$653$	15.9175	+	15.9175i	0.622900	+	0.622900i	−0.323372	+	0.946272i	$0.604816\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.0251461	−	0.0980058i	−0.000981044	−	0.00382357i
$658$		0			0
$659$	−14.9498			−0.582361			−0.291180	−	0.956668i	$-0.594048\pi$
$659$	−14.9498			−0.582361			−0.291180	+	0.956668i	$0.594048\pi$
$660$		0			0
$661$	−27.6456			−1.07529			−0.537645	−	0.843171i	$-0.680686\pi$
$661$	−27.6456			−1.07529			−0.537645	+	0.843171i	$0.680686\pi$
$662$		0			0
$663$	19.7571	−	11.2671i	0.767302	−	0.437577i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	40.8351	+	40.8351i	1.58114	+	1.58114i
$668$		0			0
$669$	7.08913	+	1.94000i	0.274082	+	0.0750049i
$670$		0			0
$671$			36.2545i			1.39959i
$672$		0			0
$673$	31.1863	−	31.1863i	1.20214	−	1.20214i	0.228631	−	0.973513i	$-0.426575\pi$
$673$	31.1863	−	31.1863i	1.20214	−	1.20214i	0.973513	−	0.228631i	$-0.0734250\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.3236	−	18.3236i	0.704232	−	0.704232i	−0.261084	−	0.965316i	$-0.584080\pi$
$677$	18.3236	−	18.3236i	0.704232	−	0.704232i	0.965316	+	0.261084i	$0.0840801\pi$
$678$		0			0
$679$			32.2014i			1.23578i
$680$		0			0
$681$	36.3168	+	9.93841i	1.39166	+	0.380841i
$682$		0			0
$683$	−13.8198	−	13.8198i	−0.528799	−	0.528799i	0.391415	−	0.920214i	$-0.371986\pi$
$683$	−13.8198	−	13.8198i	−0.528799	−	0.528799i	−0.920214	+	0.391415i	$0.871986\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	24.2585	−	13.8341i	0.925519	−	0.527804i
$688$		0			0
$689$	−0.414440			−0.0157889
$690$		0			0
$691$	−16.7034			−0.635427			−0.317713	−	0.948187i	$-0.602915\pi$
$691$	−16.7034			−0.635427			−0.317713	+	0.948187i	$0.602915\pi$
$692$		0			0
$693$	15.9436	+	62.1393i	0.605646	+	2.36048i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−13.0933	−	13.0933i	−0.495945	−	0.495945i
$698$		0			0
$699$	1.05677	−	3.86164i	0.0399708	−	0.146060i
$700$		0			0
$701$		−	7.98664i		−	0.301651i	−0.988560	−	0.150826i	$-0.951807\pi$
$701$		−	7.98664i		−	0.301651i	0.988560	−	0.150826i	$-0.0481932\pi$
$702$		0			0
$703$	28.0763	−	28.0763i	1.05892	−	1.05892i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.07525	+	1.07525i	−0.0404389	+	0.0404389i
$708$		0			0
$709$		−	7.05933i		−	0.265119i	−0.991175	−	0.132559i	$-0.957680\pi$
$709$		−	7.05933i		−	0.265119i	0.991175	−	0.132559i	$-0.0423195\pi$
$710$		0			0
$711$	−26.1745	−	15.4855i	−0.981620	−	0.580750i
$712$		0			0
$713$	−3.72177	−	3.72177i	−0.139381	−	0.139381i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−17.0464	−	29.8913i	−0.636608	−	1.11631i
$718$		0			0
$719$	9.77889			0.364691			0.182345	−	0.983235i	$-0.441631\pi$
$719$	9.77889			0.364691			0.182345	+	0.983235i	$0.441631\pi$
$720$		0			0
$721$	31.3921			1.16910
$722$		0			0
$723$	−3.90282	−	6.84371i	−0.145148	−	0.254520i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−30.2965	−	30.2965i	−1.12364	−	1.12364i	−0.991190	−	0.132446i	$-0.957717\pi$
$727$	−30.2965	−	30.2965i	−1.12364	−	1.12364i	−0.132446	−	0.991190i	$-0.542283\pi$
$728$		0			0
$729$	26.9862	+	0.861636i	0.999491	+	0.0319124i
$730$		0			0
$731$			12.9996i			0.480806i
$732$		0			0
$733$	−2.93851	+	2.93851i	−0.108536	+	0.108536i	−0.759289	−	0.650753i	$-0.774453\pi$
$733$	−2.93851	+	2.93851i	−0.108536	+	0.108536i	0.650753	+	0.759289i	$0.274453\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−23.6866	+	23.6866i	−0.872507	+	0.872507i
$738$		0			0
$739$			53.1480i			1.95508i	0.210750	+	0.977540i	$0.432409\pi$
$739$			53.1480i			1.95508i	−0.210750	+	0.977540i	$0.567591\pi$
$740$		0			0
$741$	−8.82064	+	32.2322i	−0.324034	+	1.18408i
$742$		0			0
$743$	26.2120	+	26.2120i	0.961626	+	0.961626i	0.999290	−	0.0376646i	$-0.0119919\pi$
$743$	26.2120	+	26.2120i	0.961626	+	0.961626i	−0.0376646	+	0.999290i	$0.511992\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	12.7922	−	3.28220i	0.468043	−	0.120090i
$748$		0			0
$749$	1.56238			0.0570881
$750$		0			0
$751$	−19.3427			−0.705826			−0.352913	−	0.935656i	$-0.614809\pi$
$751$	−19.3427			−0.705826			−0.352913	+	0.935656i	$0.614809\pi$
$752$		0			0
$753$	39.6728	−	22.6246i	1.44576	−	0.824486i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−32.3784	−	32.3784i	−1.17681	−	1.17681i	−0.980552	−	0.196261i	$-0.937120\pi$
$757$	−32.3784	−	32.3784i	−1.17681	−	1.17681i	−0.196261	−	0.980552i	$-0.562880\pi$
$758$		0			0
$759$	44.0443	+	12.0531i	1.59871	+	0.437500i
$760$		0			0
$761$			6.06269i			0.219772i	0.993944	+	0.109886i	$0.0350487\pi$
$761$			6.06269i			0.219772i	−0.993944	+	0.109886i	$0.964951\pi$
$762$		0			0
$763$	25.0849	−	25.0849i	0.908133	−	0.908133i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−29.5197	+	29.5197i	−1.06589	+	1.06589i
$768$		0			0
$769$			18.4706i			0.666067i	0.942915	+	0.333034i	$0.108072\pi$
$769$			18.4706i			0.666067i	−0.942915	+	0.333034i	$0.891928\pi$
$770$		0			0
$771$	−10.3925	−	2.84399i	−0.374276	−	0.102424i
$772$		0			0
$773$	−11.8012	−	11.8012i	−0.424460	−	0.424460i	0.462276	−	0.886736i	$-0.347033\pi$
$773$	−11.8012	−	11.8012i	−0.424460	−	0.424460i	−0.886736	+	0.462276i	$0.847033\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	50.4200	−	28.7535i	1.80881	−	1.03152i
$778$		0			0
$779$	27.2063			0.974768
$780$		0			0
$781$	22.7194			0.812964
$782$		0			0
$783$	−50.2584	−	0.802138i	−1.79609	−	0.0286661i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	4.84195	+	4.84195i	0.172597	+	0.172597i	0.788119	−	0.615522i	$-0.211055\pi$
$787$	4.84195	+	4.84195i	0.172597	+	0.172597i	−0.615522	+	0.788119i	$0.711055\pi$
$788$		0			0
$789$	6.57375	−	24.0217i	0.234032	−	0.855195i
$790$		0			0
$791$		−	83.6724i		−	2.97505i
$792$		0			0
$793$	−19.5209	+	19.5209i	−0.693208	+	0.693208i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.4480	−	15.4480i	0.547195	−	0.547195i	−0.378433	−	0.925629i	$-0.623537\pi$
$797$	15.4480	−	15.4480i	0.547195	−	0.547195i	0.925629	+	0.378433i	$0.123537\pi$
$798$		0			0
$799$			9.48595i			0.335589i
$800$		0			0
$801$	−4.15811	+	7.02830i	−0.146920	+	0.248333i
$802$		0			0
$803$	0.105318	+	0.105318i	0.00371660	+	0.00371660i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−17.8341	−	31.2726i	−0.627790	−	1.10085i
$808$		0			0
$809$	24.0296			0.844834			0.422417	−	0.906401i	$-0.361182\pi$
$809$	24.0296			0.844834			0.422417	+	0.906401i	$0.361182\pi$
$810$		0			0
$811$	44.3486			1.55729			0.778645	−	0.627465i	$-0.215907\pi$
$811$	44.3486			1.55729			0.778645	+	0.627465i	$0.215907\pi$
$812$		0			0
$813$	6.61477	+	11.5992i	0.231990	+	0.406801i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−13.5058	−	13.5058i	−0.472507	−	0.472507i
$818$		0			0
$819$	−24.8737	+	42.0430i	−0.869156	+	1.46910i
$820$		0			0
$821$		−	43.0045i		−	1.50087i	−0.660945	−	0.750435i	$-0.729844\pi$
$821$		−	43.0045i		−	1.50087i	0.660945	−	0.750435i	$-0.270156\pi$
$822$		0			0
$823$	−9.90076	+	9.90076i	−0.345119	+	0.345119i	−0.858288	−	0.513169i	$-0.828471\pi$
$823$	−9.90076	+	9.90076i	−0.345119	+	0.345119i	0.513169	+	0.858288i	$0.328471\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−36.8550	+	36.8550i	−1.28157	+	1.28157i	−0.341799	+	0.939773i	$0.611036\pi$
$827$	−36.8550	+	36.8550i	−1.28157	+	1.28157i	−0.939773	+	0.341799i	$0.888964\pi$
$828$		0			0
$829$			27.9793i			0.971763i	0.874025	+	0.485881i	$0.161501\pi$
$829$			27.9793i			0.971763i	−0.874025	+	0.485881i	$0.838499\pi$
$830$		0			0
$831$	1.41698	−	5.17789i	0.0491544	−	0.179619i
$832$		0			0
$833$	45.4138	+	45.4138i	1.57350	+	1.57350i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	4.58061	+	0.0731079i	0.158329	+	0.00252698i
$838$		0			0
$839$	−42.4892			−1.46689			−0.733444	−	0.679749i	$-0.762089\pi$
$839$	−42.4892			−1.46689			−0.733444	+	0.679749i	$0.762089\pi$
$840$		0			0
$841$	64.5758			2.22675
$842$		0			0
$843$	0.302942	−	0.172761i	0.0104339	−	0.00595022i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−29.1118	−	29.1118i	−1.00029	−	1.00029i
$848$		0			0
$849$	19.2152	+	5.25842i	0.659464	+	0.180468i
$850$		0			0
$851$		−	41.3150i		−	1.41626i
$852$		0			0
$853$	−19.0417	+	19.0417i	−0.651976	+	0.651976i	−0.953469	−	0.301492i	$-0.902515\pi$
$853$	−19.0417	+	19.0417i	−0.651976	+	0.651976i	0.301492	+	0.953469i	$0.402515\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.99735	+	1.99735i	−0.0682280	+	0.0682280i	−0.740397	−	0.672169i	$-0.765363\pi$
$857$	−1.99735	+	1.99735i	−0.0682280	+	0.0682280i	0.672169	+	0.740397i	$0.265363\pi$
$858$		0			0
$859$		−	6.03280i		−	0.205836i	−0.994690	−	0.102918i	$-0.967182\pi$
$859$		−	6.03280i		−	0.205836i	0.994690	−	0.102918i	$-0.0328180\pi$
$860$		0			0
$861$	38.3601	+	10.4976i	1.30731	+	0.357757i
$862$		0			0
$863$	14.8790	+	14.8790i	0.506487	+	0.506487i	0.913446	−	0.406959i	$-0.133411\pi$
$863$	14.8790	+	14.8790i	0.506487	+	0.506487i	−0.406959	+	0.913446i	$0.633411\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.63568	+	1.50307i	−0.0895124	+	0.0510470i
$868$		0			0
$869$	44.7683			1.51866
$870$		0			0
$871$	−25.5077			−0.864294
$872$		0			0
$873$	−19.3244	+	4.95822i	−0.654032	+	0.167810i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−37.4705	−	37.4705i	−1.26529	−	1.26529i	−0.948494	−	0.316796i	$-0.897393\pi$
$877$	−37.4705	−	37.4705i	−1.26529	−	1.26529i	−0.316796	−	0.948494i	$-0.602607\pi$
$878$		0			0
$879$	−3.46758	+	12.6712i	−0.116958	+	0.427388i
$880$		0			0
$881$			43.2873i			1.45839i	0.684308	+	0.729193i	$0.260104\pi$
$881$			43.2873i			1.45839i	−0.684308	+	0.729193i	$0.739896\pi$
$882$		0			0
$883$	23.1543	−	23.1543i	0.779205	−	0.779205i	−0.200490	−	0.979696i	$-0.564254\pi$
$883$	23.1543	−	23.1543i	0.779205	−	0.779205i	0.979696	+	0.200490i	$0.0642536\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.91638	+	5.91638i	−0.198653	+	0.198653i	−0.799422	−	0.600770i	$-0.794861\pi$
$887$	−5.91638	+	5.91638i	−0.198653	+	0.198653i	0.600770	+	0.799422i	$0.294861\pi$
$888$		0			0
$889$			60.9654i			2.04471i
$890$		0			0
$891$	−34.8355	+	19.1358i	−1.16703	+	0.641073i
$892$		0			0
$893$	−9.85532	−	9.85532i	−0.329796	−	0.329796i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	17.2254	+	30.2051i	0.575138	+	1.00852i
$898$		0			0
$899$	−8.52862			−0.284445
$900$		0			0
$901$	−0.481255			−0.0160329
$902$		0			0
$903$	−13.8315	−	24.2539i	−0.460283	−	0.807120i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	28.1570	+	28.1570i	0.934936	+	0.934936i	0.998009	−	0.0630725i	$-0.0200899\pi$
$907$	28.1570	+	28.1570i	0.934936	+	0.934936i	−0.0630725	+	0.998009i	$0.520090\pi$
$908$		0			0
$909$	−0.810830	−	0.479706i	−0.0268935	−	0.0159109i
$910$		0			0
$911$			38.1427i			1.26372i	0.775081	+	0.631861i	$0.217709\pi$
$911$			38.1427i			1.26372i	−0.775081	+	0.631861i	$0.782291\pi$
$912$		0			0
$913$	−13.7467	+	13.7467i	−0.454949	+	0.454949i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−37.3960	+	37.3960i	−1.23492	+	1.23492i
$918$		0			0
$919$		−	39.5872i		−	1.30586i	−0.757417	−	0.652931i	$-0.773539\pi$
$919$		−	39.5872i		−	1.30586i	0.757417	−	0.652931i	$-0.226461\pi$
$920$		0			0
$921$	−6.85933	+	25.0652i	−0.226023	+	0.825928i
$922$		0			0
$923$	12.2331	+	12.2331i	0.402656	+	0.402656i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	4.83361	+	18.8387i	0.158756	+	0.618745i
$928$		0			0
$929$	−20.9401			−0.687021			−0.343510	−	0.939149i	$-0.611616\pi$
$929$	−20.9401			−0.687021			−0.343510	+	0.939149i	$0.611616\pi$
$930$		0			0
$931$	−94.3644			−3.09267
$932$		0			0
$933$	34.3117	−	19.5672i	1.12331	−	0.640602i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−34.0741	−	34.0741i	−1.11315	−	1.11315i	−0.992722	−	0.120432i	$-0.961572\pi$
$937$	−34.0741	−	34.0741i	−1.11315	−	1.11315i	−0.120432	−	0.992722i	$-0.538428\pi$
$938$		0			0
$939$	−20.2116	−	5.53108i	−0.659580	−	0.180500i
$940$		0			0
$941$			4.66054i			0.151929i	0.997111	+	0.0759646i	$0.0242036\pi$
$941$			4.66054i			0.151929i	−0.997111	+	0.0759646i	$0.975796\pi$
$942$		0			0
$943$	20.0174	−	20.0174i	0.651856	−	0.651856i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.26077	+	1.26077i	−0.0409696	+	0.0409696i	−0.727295	−	0.686325i	$-0.759223\pi$
$947$	−1.26077	+	1.26077i	−0.0409696	+	0.0409696i	0.686325	+	0.727295i	$0.259223\pi$
$948$		0			0
$949$			0.113415i			0.00368162i
$950$		0			0
$951$	26.0945	+	7.14099i	0.846171	+	0.231562i
$952$		0			0
$953$	−33.1756	−	33.1756i	−1.07466	−	1.07466i	−0.996978	−	0.0776838i	$-0.975248\pi$
$953$	−33.1756	−	33.1756i	−1.07466	−	1.07466i	−0.0776838	−	0.996978i	$-0.524752\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	64.2750	−	36.6547i	2.07772	−	1.18488i
$958$		0			0
$959$	70.4670			2.27550
$960$		0			0
$961$	−30.2227			−0.974925
$962$		0			0
$963$	0.240567	+	0.937599i	0.00775218	+	0.0302137i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	11.7229	+	11.7229i	0.376982	+	0.376982i	0.870012	−	0.493030i	$-0.164111\pi$
$967$	11.7229	+	11.7229i	0.376982	+	0.376982i	−0.493030	+	0.870012i	$0.664111\pi$
$968$		0			0
$969$	−10.2427	+	37.4286i	−0.329042	+	1.20238i
$970$		0			0
$971$		−	37.8141i		−	1.21351i	−0.794888	−	0.606756i	$-0.792470\pi$
$971$		−	37.8141i		−	1.21351i	0.794888	−	0.606756i	$-0.207530\pi$
$972$		0			0
$973$	−29.2588	+	29.2588i	−0.937995	+	0.937995i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.7028	+	11.7028i	−0.374407	+	0.374407i	−0.869079	−	0.494673i	$-0.835288\pi$
$977$	−11.7028	+	11.7028i	−0.374407	+	0.374407i	0.494673	+	0.869079i	$0.335288\pi$
$978$		0			0
$979$		−	12.0210i		−	0.384194i
$980$		0			0
$981$	18.9161	+	11.1912i	0.603946	+	0.357309i
$982$		0			0
$983$	−19.6784	−	19.6784i	−0.627644	−	0.627644i	0.319831	−	0.947475i	$-0.396374\pi$
$983$	−19.6784	−	19.6784i	−0.627644	−	0.627644i	−0.947475	+	0.319831i	$0.896374\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−10.0930	−	17.6984i	−0.321264	−	0.563346i
$988$		0			0
$989$	−19.8740			−0.631958
$990$		0			0
$991$	18.6286			0.591756			0.295878	−	0.955226i	$-0.404388\pi$
$991$	18.6286			0.591756			0.295878	+	0.955226i	$0.404388\pi$
$992$		0			0
$993$	−0.980936	−	1.72010i	−0.0311291	−	0.0545857i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	28.7625	+	28.7625i	0.910918	+	0.910918i	0.996344	−	0.0854267i	$-0.0272254\pi$
$997$	28.7625	+	28.7625i	0.910918	+	0.910918i	−0.0854267	+	0.996344i	$0.527225\pi$
$998$		0			0
$999$	25.0187	+	25.8302i	0.791556	+	0.817232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.i.a.557.12	yes	32
3.2	odd	2	inner	1500.2.i.a.557.4	✓	32
5.2	odd	4	inner	1500.2.i.a.1193.13	yes	32
5.3	odd	4	inner	1500.2.i.a.1193.4	yes	32
5.4	even	2	inner	1500.2.i.a.557.5	yes	32
15.2	even	4	inner	1500.2.i.a.1193.5	yes	32
15.8	even	4	inner	1500.2.i.a.1193.12	yes	32
15.14	odd	2	inner	1500.2.i.a.557.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1500.2.i.a.557.4	✓	32	3.2	odd	2	inner
1500.2.i.a.557.5	yes	32	5.4	even	2	inner
1500.2.i.a.557.12	yes	32	1.1	even	1	trivial
1500.2.i.a.557.13	yes	32	15.14	odd	2	inner
1500.2.i.a.1193.4	yes	32	5.3	odd	4	inner
1500.2.i.a.1193.5	yes	32	15.2	even	4	inner
1500.2.i.a.1193.12	yes	32	15.8	even	4	inner
1500.2.i.a.1193.13	yes	32	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.858034 + 1.50459i) q^{3} +(3.42398 + 3.42398i) q^{7} +(-1.52756 + 2.58197i) q^{9} +O(q^{10})\)	\(q+(0.858034 + 1.50459i) q^{3} +(3.42398 + 3.42398i) q^{7} +(-1.52756 + 2.58197i) q^{9} -4.41615i q^{11} +(2.37783 - 2.37783i) q^{13} +(2.76118 - 2.76118i) q^{17} +5.73740i q^{19} +(-2.21378 + 8.08956i) q^{21} +(4.22136 + 4.22136i) q^{23} +(-5.19549 - 0.0829215i) q^{27} +9.67346 q^{29} -0.881652 q^{31} +(6.64447 - 3.78920i) q^{33} +(-4.89356 - 4.89356i) q^{37} +(5.61792 + 1.53739i) q^{39} -4.74193i q^{41} +(-2.35399 + 2.35399i) q^{43} +(-1.71773 + 1.71773i) q^{47} +16.4472i q^{49} +(6.52362 + 1.78525i) q^{51} +(-0.0871466 - 0.0871466i) q^{53} +(-8.63241 + 4.92288i) q^{57} -12.4145 q^{59} -8.20953 q^{61} +(-14.0709 + 3.61029i) q^{63} +(-5.36363 - 5.36363i) q^{67} +(-2.72933 + 9.97347i) q^{69} +5.14462i q^{71} +(-0.0238484 + 0.0238484i) q^{73} +(15.1208 - 15.1208i) q^{77} +10.1374i q^{79} +(-4.33314 - 7.88821i) q^{81} +(-3.11282 - 3.11282i) q^{83} +(8.30015 + 14.5545i) q^{87} +2.72207 q^{89} +16.2833 q^{91} +(-0.756487 - 1.32652i) q^{93} +(4.70234 + 4.70234i) q^{97} +(11.4024 + 6.74591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 12 q^{21} - 32 q^{31} + 100 q^{51} + 48 q^{61} + 52 q^{81} + 232 q^{91}+O(q^{100}) \) 32 * q - 12 * q^21 - 32 * q^31 + 100 * q^51 + 48 * q^61 + 52 * q^81 + 232 * q^91

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