LMFDB - Embedded newform 2240.2.e.f.2239.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(2239,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2240.2239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.e (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 28x^{12} + 16x^{10} - 40x^{8} + 610x^{6} + 1625x^{4} - 524x^{2} + 1444 $ x^16 - 6x^14 + 28x^12 + 16x^10 - 40x^8 + 610x^6 + 1625x^4 - 524*x^2 + 1444
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2239.8
Root			$0.744612 - 0.556573i$ of defining polynomial
Character	$\chi$	$=$	2240.2239
Dual form			2240.2.e.f.2239.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.662153i q^{3} +(1.31119 + 1.81129i) q^{5} +(1.19935 - 2.35829i) q^{7} +2.56155 q^{9} +O(q^{10})$	\(q-0.662153i q^{3} +(1.31119 + 1.81129i) q^{5} +(1.19935 - 2.35829i) q^{7} +2.56155 q^{9} +3.09218i q^{11} -4.66988 q^{13} +(1.19935 - 0.868210i) q^{15} -2.04750 q^{17} +5.60083 q^{19} +(-1.56155 - 0.794156i) q^{21} +1.87285 q^{23} +(-1.56155 + 4.74990i) q^{25} -3.68260i q^{27} +3.56155 q^{29} +8.74599 q^{31} +2.04750 q^{33} +(5.84414 - 0.919799i) q^{35} -3.70861i q^{37} +3.09218i q^{39} +8.48528i q^{41} +4.27156 q^{43} +(3.35869 + 4.63972i) q^{45} -0.290319i q^{47} +(-4.12311 - 5.65685i) q^{49} +1.35576i q^{51} +9.49980i q^{53} +(-5.60083 + 4.05444i) q^{55} -3.70861i q^{57} -8.05650 q^{59} -6.45101i q^{61} +(3.07221 - 6.04090i) q^{63} +(-6.12311 - 8.45851i) q^{65} +2.39871 q^{67} -1.24012i q^{69} +9.65719i q^{71} -4.09499 q^{73} +(3.14516 + 1.03399i) q^{75} +(7.29226 + 3.70861i) q^{77} +1.35576i q^{79} +5.24621 q^{81} -12.4536i q^{83} +(-2.68466 - 3.70861i) q^{85} -2.35829i q^{87} -2.82843i q^{89} +(-5.60083 + 11.0129i) q^{91} -5.79119i q^{93} +(7.34376 + 10.1447i) q^{95} +6.14249 q^{97} +7.92077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^9	$ 16 q + 8 q^{9} + 8 q^{21} + 8 q^{25} + 24 q^{29} - 32 q^{65} - 48 q^{81} + 56 q^{85}+O(q^{100}) $ 16 * q + 8 * q^9 + 8 * q^21 + 8 * q^25 + 24 * q^29 - 32 * q^65 - 48 * q^81 + 56 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$		−	0.662153i		−	0.382294i	−0.981561	−	0.191147i	$-0.938779\pi$
$3$		−	0.662153i		−	0.382294i	0.981561	−	0.191147i	$-0.0612208\pi$
$4$		0			0
$5$	1.31119	+	1.81129i	0.586383	+	0.810034i
$5$	1.31119	+	1.81129i	0.586383	+	0.810034i
$6$		0			0
$7$	1.19935	−	2.35829i	0.453313	−	0.891352i
$7$	1.19935	−	2.35829i	0.453313	−	0.891352i
$8$		0			0
$9$	2.56155			0.853851
$10$		0			0
$11$			3.09218i			0.932326i	0.884699	+	0.466163i	$0.154364\pi$
$11$			3.09218i			0.932326i	−0.884699	+	0.466163i	$0.845636\pi$
$12$		0			0
$13$	−4.66988			−1.29519			−0.647596	−	0.761984i	$-0.724225\pi$
$13$	−4.66988			−1.29519			−0.647596	+	0.761984i	$0.724225\pi$
$14$		0			0
$15$	1.19935	−	0.868210i	0.309672	−	0.224171i
$16$		0			0
$17$	−2.04750			−0.496590			−0.248295	−	0.968684i	$-0.579870\pi$
$17$	−2.04750			−0.496590			−0.248295	+	0.968684i	$0.579870\pi$
$18$		0			0
$19$	5.60083			1.28492			0.642459	−	0.766320i	$-0.277914\pi$
$19$	5.60083			1.28492			0.642459	+	0.766320i	$0.277914\pi$
$20$		0			0
$21$	−1.56155	−	0.794156i	−0.340759	−	0.173299i
$22$		0			0
$23$	1.87285			0.390517			0.195258	−	0.980752i	$-0.437445\pi$
$23$	1.87285			0.390517			0.195258	+	0.980752i	$0.437445\pi$
$24$		0			0
$25$	−1.56155	+	4.74990i	−0.312311	+	0.949980i
$26$		0			0
$27$		−	3.68260i		−	0.708717i
$28$		0			0
$29$	3.56155			0.661364			0.330682	−	0.943742i	$-0.392721\pi$
$29$	3.56155			0.661364			0.330682	+	0.943742i	$0.392721\pi$
$30$		0			0
$31$	8.74599			1.57083			0.785414	−	0.618971i	$-0.212450\pi$
$31$	8.74599			1.57083			0.785414	+	0.618971i	$0.212450\pi$
$32$		0			0
$33$	2.04750			0.356423
$34$		0			0
$35$	5.84414	−	0.919799i	0.987840	−	0.155474i
$36$		0			0
$37$		−	3.70861i		−	0.609692i	−0.952402	−	0.304846i	$-0.901395\pi$
$37$		−	3.70861i		−	0.609692i	0.952402	−	0.304846i	$-0.0986050\pi$
$38$		0			0
$39$			3.09218i			0.495144i
$40$		0			0
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$		0			0
$43$	4.27156			0.651407			0.325703	−	0.945472i	$-0.394399\pi$
$43$	4.27156			0.651407			0.325703	+	0.945472i	$0.394399\pi$
$44$		0			0
$45$	3.35869	+	4.63972i	0.500683	+	0.691648i
$46$		0			0
$47$		−	0.290319i		−	0.0423474i	−0.999776	−	0.0211737i	$-0.993260\pi$
$47$		−	0.290319i		−	0.0423474i	0.999776	−	0.0211737i	$-0.00674031\pi$
$48$		0			0
$49$	−4.12311	−	5.65685i	−0.589015	−	0.808122i
$50$		0			0
$51$			1.35576i			0.189844i
$52$		0			0
$53$			9.49980i			1.30490i	0.757833	+	0.652449i	$0.226258\pi$
$53$			9.49980i			1.30490i	−0.757833	+	0.652449i	$0.773742\pi$
$54$		0			0
$55$	−5.60083	+	4.05444i	−0.755216	+	0.546700i
$56$		0			0
$57$		−	3.70861i		−	0.491217i
$58$		0			0
$59$	−8.05650			−1.04887			−0.524434	−	0.851451i	$-0.675723\pi$
$59$	−8.05650			−1.04887			−0.524434	+	0.851451i	$0.675723\pi$
$60$		0			0
$61$		−	6.45101i		−	0.825967i	−0.910738	−	0.412984i	$-0.864487\pi$
$61$		−	6.45101i		−	0.825967i	0.910738	−	0.412984i	$-0.135513\pi$
$62$		0			0
$63$	3.07221	−	6.04090i	0.387062	−	0.761081i
$64$		0			0
$65$	−6.12311	−	8.45851i	−0.759478	−	1.04915i
$66$		0			0
$67$	2.39871			0.293049			0.146524	−	0.989207i	$-0.453191\pi$
$67$	2.39871			0.293049			0.146524	+	0.989207i	$0.453191\pi$
$68$		0			0
$69$		−	1.24012i		−	0.149292i
$70$		0			0
$71$			9.65719i			1.14610i	0.819521	+	0.573049i	$0.194240\pi$
$71$			9.65719i			1.14610i	−0.819521	+	0.573049i	$0.805760\pi$
$72$		0			0
$73$	−4.09499			−0.479282			−0.239641	−	0.970862i	$-0.577030\pi$
$73$	−4.09499			−0.479282			−0.239641	+	0.970862i	$0.577030\pi$
$74$		0			0
$75$	3.14516	+	1.03399i	0.363172	+	0.119395i
$76$		0			0
$77$	7.29226	+	3.70861i	0.831030	+	0.422635i
$78$		0			0
$79$			1.35576i			0.152534i	0.997087	+	0.0762672i	$0.0243002\pi$
$79$			1.35576i			0.152534i	−0.997087	+	0.0762672i	$0.975700\pi$
$80$		0			0
$81$	5.24621			0.582912
$82$		0			0
$83$		−	12.4536i		−	1.36696i	−0.729968	−	0.683482i	$-0.760465\pi$
$83$		−	12.4536i		−	1.36696i	0.729968	−	0.683482i	$-0.239535\pi$
$84$		0			0
$85$	−2.68466	−	3.70861i	−0.291192	−	0.402255i
$86$		0			0
$87$		−	2.35829i		−	0.252836i
$88$		0			0
$89$		−	2.82843i		−	0.299813i	−0.988700	−	0.149906i	$-0.952103\pi$
$89$		−	2.82843i		−	0.299813i	0.988700	−	0.149906i	$-0.0478972\pi$
$90$		0			0
$91$	−5.60083	+	11.0129i	−0.587127	+	1.15447i
$92$		0			0
$93$		−	5.79119i		−	0.600518i
$94$		0			0
$95$	7.34376	+	10.1447i	0.753454	+	1.04083i
$96$		0			0
$97$	6.14249			0.623675			0.311837	−	0.950135i	$-0.399056\pi$
$97$	6.14249			0.623675			0.311837	+	0.950135i	$0.399056\pi$
$98$		0			0
$99$			7.92077i			0.796068i
$100$		0			0
$101$		−	2.38247i		−	0.237064i	−0.992950	−	0.118532i	$-0.962181\pi$
$101$		−	2.38247i		−	0.237064i	0.992950	−	0.118532i	$-0.0378189\pi$
$102$		0			0
$103$		−	1.03399i		−	0.101882i	−0.998702	−	0.0509409i	$-0.983778\pi$
$103$		−	1.03399i		−	0.101882i	0.998702	−	0.0509409i	$-0.0162220\pi$
$104$		0			0
$105$	−0.609048	−	3.86972i	−0.0594370	−	0.377646i
$106$		0			0
$107$	14.6875			1.41990			0.709948	−	0.704254i	$-0.248718\pi$
$107$	14.6875			1.41990			0.709948	+	0.704254i	$0.248718\pi$
$108$		0			0
$109$	−0.438447			−0.0419956			−0.0209978	−	0.999780i	$-0.506684\pi$
$109$	−0.438447			−0.0419956			−0.0209978	+	0.999780i	$0.506684\pi$
$110$		0			0
$111$	−2.45567			−0.233082
$112$		0			0
$113$			3.70861i			0.348877i	0.984668	+	0.174438i	$0.0558110\pi$
$113$			3.70861i			0.348877i	−0.984668	+	0.174438i	$0.944189\pi$
$114$		0			0
$115$	2.45567	+	3.39228i	0.228992	+	0.316332i
$116$		0			0
$117$	−11.9621			−1.10590
$118$		0			0
$119$	−2.45567	+	4.82860i	−0.225111	+	0.442637i
$120$		0			0
$121$	1.43845			0.130768
$122$		0			0
$123$	5.61856			0.506608
$124$		0			0
$125$	−10.6509	+	3.39960i	−0.952650	+	0.304070i
$126$		0			0
$127$	17.0862			1.51616			0.758079	−	0.652163i	$-0.226138\pi$
$127$	17.0862			1.51616			0.758079	+	0.652163i	$0.226138\pi$
$128$		0			0
$129$		−	2.82843i		−	0.249029i
$130$		0			0
$131$	−5.60083			−0.489347			−0.244673	−	0.969606i	$-0.578681\pi$
$131$	−5.60083			−0.489347			−0.244673	+	0.969606i	$0.578681\pi$
$132$		0			0
$133$	6.71737	−	13.2084i	0.582470	−	1.14531i
$134$		0			0
$135$	6.67026	−	4.82860i	0.574085	−	0.415579i
$136$		0			0
$137$			13.2084i			1.12847i	0.825614	+	0.564235i	$0.190829\pi$
$137$			13.2084i			1.12847i	−0.825614	+	0.564235i	$0.809171\pi$
$138$		0			0
$139$	14.3468			1.21688			0.608441	−	0.793599i	$-0.291795\pi$
$139$	14.3468			1.21688			0.608441	+	0.793599i	$0.291795\pi$
$140$		0			0
$141$	−0.192236			−0.0161892
$142$		0			0
$143$		−	14.4401i		−	1.20754i
$144$		0			0
$145$	4.66988	+	6.45101i	0.387812	+	0.535727i
$146$		0			0
$147$	−3.74571	+	2.73013i	−0.308941	+	0.225177i
$148$		0			0
$149$	2.00000			0.163846			0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000			0.163846			0.0819232	+	0.996639i	$0.473894\pi$
$150$		0			0
$151$		−	18.9337i		−	1.54080i	−0.637558	−	0.770402i	$-0.720055\pi$
$151$		−	18.9337i		−	1.54080i	0.637558	−	0.770402i	$-0.279945\pi$
$152$		0			0
$153$	−5.24477			−0.424014
$154$		0			0
$155$	11.4677	+	15.8415i	0.921106	+	1.27242i
$156$		0			0
$157$	2.62238			0.209289			0.104644	−	0.994510i	$-0.466630\pi$
$157$	2.62238			0.209289			0.104644	+	0.994510i	$0.466630\pi$
$158$		0			0
$159$	6.29033			0.498855
$160$		0			0
$161$	2.24621	−	4.41674i	0.177026	−	0.348088i
$162$		0			0
$163$	−15.7392			−1.23279			−0.616396	−	0.787436i	$-0.711408\pi$
$163$	−15.7392			−1.23279			−0.616396	+	0.787436i	$0.711408\pi$
$164$		0			0
$165$	2.68466	+	3.70861i	0.209000	+	0.288715i
$166$		0			0
$167$			8.39919i			0.649949i	0.945723	+	0.324974i	$0.105356\pi$
$167$			8.39919i			0.649949i	−0.945723	+	0.324974i	$0.894644\pi$
$168$		0			0
$169$	8.80776			0.677520
$170$		0			0
$171$	14.3468			1.09713
$172$		0			0
$173$	8.76487			0.666381			0.333190	−	0.942860i	$-0.391875\pi$
$173$	8.76487			0.666381			0.333190	+	0.942860i	$0.391875\pi$
$174$		0			0
$175$	9.32881	+	9.37941i	0.705192	+	0.709017i
$176$		0			0
$177$			5.33464i			0.400976i
$178$		0			0
$179$		−	1.73642i		−	0.129786i	−0.997892	−	0.0648931i	$-0.979329\pi$
$179$		−	1.73642i		−	0.129786i	0.997892	−	0.0648931i	$-0.0206706\pi$
$180$		0			0
$181$			9.27944i			0.689735i	0.938651	+	0.344868i	$0.112076\pi$
$181$			9.27944i			0.689735i	−0.938651	+	0.344868i	$0.887924\pi$
$182$		0			0
$183$	−4.27156			−0.315763
$184$		0			0
$185$	6.71737	−	4.86270i	0.493871	−	0.357513i
$186$		0			0
$187$		−	6.33122i		−	0.462984i
$188$		0			0
$189$	−8.68466	−	4.41674i	−0.631716	−	0.321270i
$190$		0			0
$191$			13.7245i			0.993067i	0.868018	+	0.496534i	$0.165394\pi$
$191$			13.7245i			0.993067i	−0.868018	+	0.496534i	$0.834606\pi$
$192$		0			0
$193$		−	3.70861i		−	0.266952i	−0.991052	−	0.133476i	$-0.957386\pi$
$193$		−	3.70861i		−	0.266952i	0.991052	−	0.133476i	$-0.0426138\pi$
$194$		0			0
$195$	−5.60083	+	4.05444i	−0.401084	+	0.290344i
$196$		0			0
$197$			11.1258i			0.792683i	0.918103	+	0.396341i	$0.129720\pi$
$197$			11.1258i			0.792683i	−0.918103	+	0.396341i	$0.870280\pi$
$198$		0			0
$199$	−6.29033			−0.445909			−0.222955	−	0.974829i	$-0.571570\pi$
$199$	−6.29033			−0.445909			−0.222955	+	0.974829i	$0.571570\pi$
$200$		0			0
$201$		−	1.58831i		−	0.112031i
$202$		0			0
$203$	4.27156	−	8.39919i	0.299805	−	0.589508i
$204$		0			0
$205$	−15.3693	+	11.1258i	−1.07344	+	0.777062i
$206$		0			0
$207$	4.79741			0.333443
$208$		0			0
$209$			17.3188i			1.19796i
$210$		0			0
$211$		−	25.1181i		−	1.72920i	−0.502461	−	0.864600i	$-0.667572\pi$
$211$		−	25.1181i		−	1.72920i	0.502461	−	0.864600i	$-0.332428\pi$
$212$		0			0
$213$	6.39454			0.438147
$214$		0			0
$215$	5.60083	+	7.73704i	0.381974	+	0.527662i
$216$		0			0
$217$	10.4895	−	20.6256i	0.712076	−	1.40016i
$218$		0			0
$219$			2.71151i			0.183227i
$220$		0			0
$221$	9.56155			0.643180
$222$		0			0
$223$		−	19.1567i		−	1.28283i	−0.767196	−	0.641413i	$-0.778349\pi$
$223$		−	19.1567i		−	1.28283i	0.767196	−	0.641413i	$-0.221651\pi$
$224$		0			0
$225$	−4.00000	+	12.1671i	−0.266667	+	0.811141i
$226$		0			0
$227$			14.0683i			0.933743i	0.884325	+	0.466871i	$0.154619\pi$
$227$			14.0683i			0.933743i	−0.884325	+	0.466871i	$0.845381\pi$
$228$		0			0
$229$			8.03932i			0.531253i	0.964076	+	0.265627i	$0.0855788\pi$
$229$			8.03932i			0.531253i	−0.964076	+	0.265627i	$0.914421\pi$
$230$		0			0
$231$	2.45567	−	4.82860i	0.161571	−	0.317698i
$232$		0			0
$233$		−	7.41722i		−	0.485918i	−0.970037	−	0.242959i	$-0.921882\pi$
$233$		−	7.41722i		−	0.485918i	0.970037	−	0.242959i	$-0.0781181\pi$
$234$		0			0
$235$	0.525853	−	0.380664i	0.0343029	−	0.0248318i
$236$		0			0
$237$	0.897718			0.0583131
$238$		0			0
$239$		−	3.09218i		−	0.200016i	−0.994987	−	0.100008i	$-0.968113\pi$
$239$		−	3.09218i		−	0.200016i	0.994987	−	0.100008i	$-0.0318869\pi$
$240$		0			0
$241$		−	18.9071i		−	1.21791i	−0.793204	−	0.608956i	$-0.791589\pi$
$241$		−	18.9071i		−	1.21791i	0.793204	−	0.608956i	$-0.208411\pi$
$242$		0			0
$243$		−	14.5216i		−	0.931561i
$244$		0			0
$245$	4.84003	−	14.8854i	0.309218	−	0.950991i
$246$		0			0
$247$	−26.1552			−1.66422
$248$		0			0
$249$	−8.24621			−0.522582
$250$		0			0
$251$	3.14516			0.198521			0.0992605	−	0.995061i	$-0.468352\pi$
$251$	3.14516			0.198521			0.0992605	+	0.995061i	$0.468352\pi$
$252$		0			0
$253$			5.79119i			0.364089i
$254$		0			0
$255$	−2.45567	+	1.77766i	−0.153780	+	0.111321i
$256$		0			0
$257$	−28.0193			−1.74779			−0.873897	−	0.486111i	$-0.838415\pi$
$257$	−28.0193			−1.74779			−0.873897	+	0.486111i	$0.838415\pi$
$258$		0			0
$259$	−8.74599	−	4.44793i	−0.543450	−	0.276381i
$260$		0			0
$261$	9.12311			0.564706
$262$		0			0
$263$	−11.9935			−0.739553			−0.369776	−	0.929121i	$-0.620566\pi$
$263$	−11.9935			−0.739553			−0.369776	+	0.929121i	$0.620566\pi$
$264$		0			0
$265$	−17.2069	+	12.4561i	−1.05701	+	0.765170i
$266$		0			0
$267$	−1.87285			−0.114617
$268$		0			0
$269$		−	16.5246i		−	1.00752i	−0.863843	−	0.503761i	$-0.831949\pi$
$269$		−	16.5246i		−	1.00752i	0.863843	−	0.503761i	$-0.168051\pi$
$270$		0			0
$271$	−8.74599			−0.531281			−0.265641	−	0.964072i	$-0.585583\pi$
$271$	−8.74599			−0.531281			−0.265641	+	0.964072i	$0.585583\pi$
$272$		0			0
$273$	7.29226	+	3.70861i	0.441348	+	0.224455i
$274$		0			0
$275$	−14.6875	−	4.82860i	−0.885691	−	0.291175i
$276$		0			0
$277$			2.08258i			0.125130i	0.998041	+	0.0625651i	$0.0199281\pi$
$277$			2.08258i			0.125130i	−0.998041	+	0.0625651i	$0.980072\pi$
$278$		0			0
$279$	22.4033			1.34125
$280$		0			0
$281$	−20.0540			−1.19632			−0.598160	−	0.801377i	$-0.704101\pi$
$281$	−20.0540			−1.19632			−0.598160	+	0.801377i	$0.704101\pi$
$282$		0			0
$283$		−	19.5285i		−	1.16085i	−0.814314	−	0.580425i	$-0.802887\pi$
$283$		−	19.5285i		−	1.16085i	0.814314	−	0.580425i	$-0.197113\pi$
$284$		0			0
$285$	6.71737	−	4.86270i	0.397903	−	0.288041i
$286$		0			0
$287$	20.0108	+	10.1768i	1.18120	+	0.600720i
$288$		0			0
$289$	−12.8078			−0.753398
$290$		0			0
$291$		−	4.06727i		−	0.238427i
$292$		0			0
$293$	−15.1594			−0.885622			−0.442811	−	0.896615i	$-0.646019\pi$
$293$	−15.1594			−0.885622			−0.442811	+	0.896615i	$0.646019\pi$
$294$		0			0
$295$	−10.5636	−	14.5927i	−0.615038	−	0.849618i
$296$		0			0
$297$	11.3873			0.660755
$298$		0			0
$299$	−8.74599			−0.505794
$300$		0			0
$301$	5.12311	−	10.0736i	0.295291	−	0.580632i
$302$		0			0
$303$	−1.57756			−0.0906284
$304$		0			0
$305$	11.6847	−	8.45851i	0.669062	−	0.484333i
$306$		0			0
$307$			26.1500i			1.49246i	0.665687	+	0.746231i	$0.268139\pi$
$307$			26.1500i			1.49246i	−0.665687	+	0.746231i	$0.731861\pi$
$308$		0			0
$309$	−0.684658			−0.0389489
$310$		0			0
$311$	−19.9477			−1.13113			−0.565564	−	0.824704i	$-0.691341\pi$
$311$	−19.9477			−1.13113			−0.565564	+	0.824704i	$0.691341\pi$
$312$		0			0
$313$	11.3873			0.643646			0.321823	−	0.946800i	$-0.395704\pi$
$313$	11.3873			0.643646			0.321823	+	0.946800i	$0.395704\pi$
$314$		0			0
$315$	14.9701	−	2.35611i	0.843468	−	0.132752i
$316$		0			0
$317$		−	31.7515i		−	1.78334i	−0.452686	−	0.891670i	$-0.649534\pi$
$317$		−	31.7515i		−	1.78334i	0.452686	−	0.891670i	$-0.350466\pi$
$318$		0			0
$319$			11.0129i			0.616607i
$320$		0			0
$321$		−	9.72540i		−	0.542819i
$322$		0			0
$323$	−11.4677			−0.638079
$324$		0			0
$325$	7.29226	−	22.1815i	0.404502	−	1.23041i
$326$		0			0
$327$			0.290319i			0.0160547i
$328$		0			0
$329$	−0.684658	−	0.348195i	−0.0377464	−	0.0191966i
$330$		0			0
$331$		−	1.73642i		−	0.0954423i	−0.998861	−	0.0477211i	$-0.984804\pi$
$331$		−	1.73642i		−	0.0954423i	0.998861	−	0.0477211i	$-0.0151959\pi$
$332$		0			0
$333$		−	9.49980i		−	0.520586i
$334$		0			0
$335$	3.14516	+	4.34475i	0.171839	+	0.237379i
$336$		0			0
$337$		−	5.33464i		−	0.290596i	−0.989388	−	0.145298i	$-0.953586\pi$
$337$		−	5.33464i		−	0.290596i	0.989388	−	0.145298i	$-0.0464141\pi$
$338$		0			0
$339$	2.45567			0.133374
$340$		0			0
$341$			27.0442i			1.46452i
$342$		0			0
$343$	−18.2856	+	2.93893i	−0.987329	+	0.158687i
$344$		0			0
$345$	2.24621	−	1.62603i	0.120932	−	0.0875425i
$346$		0			0
$347$	4.27156			0.229309			0.114655	−	0.993405i	$-0.463424\pi$
$347$	4.27156			0.229309			0.114655	+	0.993405i	$0.463424\pi$
$348$		0			0
$349$			36.3236i			1.94436i	0.234241	+	0.972179i	$0.424740\pi$
$349$			36.3236i			1.94436i	−0.234241	+	0.972179i	$0.575260\pi$
$350$		0			0
$351$			17.1973i			0.917924i
$352$		0			0
$353$	27.1216			1.44353			0.721767	−	0.692136i	$-0.243330\pi$
$353$	27.1216			1.44353			0.721767	+	0.692136i	$0.243330\pi$
$354$		0			0
$355$	−17.4920	+	12.6624i	−0.928378	+	0.672052i
$356$		0			0
$357$	3.19727	+	1.62603i	0.169218	+	0.0860586i
$358$		0			0
$359$		−	26.4738i		−	1.39724i	−0.715495	−	0.698618i	$-0.753799\pi$
$359$		−	26.4738i		−	1.39724i	0.715495	−	0.698618i	$-0.246201\pi$
$360$		0			0
$361$	12.3693			0.651017
$362$		0			0
$363$		−	0.952473i		−	0.0499919i
$364$		0			0
$365$	−5.36932	−	7.41722i	−0.281043	−	0.388235i
$366$		0			0
$367$			31.8191i			1.66094i	0.557061	+	0.830472i	$0.311929\pi$
$367$			31.8191i			1.66094i	−0.557061	+	0.830472i	$0.688071\pi$
$368$		0			0
$369$			21.7355i			1.13150i
$370$		0			0
$371$	22.4033	+	11.3936i	1.16312	+	0.591527i
$372$		0			0
$373$			22.7082i			1.17579i	0.808938	+	0.587893i	$0.200043\pi$
$373$			22.7082i			1.17579i	−0.808938	+	0.587893i	$0.799957\pi$
$374$		0			0
$375$	2.25106	+	7.05256i	0.116244	+	0.364193i
$376$		0			0
$377$	−16.6320			−0.856593
$378$		0			0
$379$			5.20926i			0.267582i	0.991010	+	0.133791i	$0.0427150\pi$
$379$			5.20926i			0.267582i	−0.991010	+	0.133791i	$0.957285\pi$
$380$		0			0
$381$		−	11.3137i		−	0.579619i
$382$		0			0
$383$		−	26.9752i		−	1.37837i	−0.724586	−	0.689185i	$-0.757969\pi$
$383$		−	26.9752i		−	1.37837i	0.724586	−	0.689185i	$-0.242031\pi$
$384$		0			0
$385$	2.84418	+	18.0711i	0.144953	+	0.920989i
$386$		0			0
$387$	10.9418			0.556204
$388$		0			0
$389$	−16.9309			−0.858429			−0.429215	−	0.903203i	$-0.641210\pi$
$389$	−16.9309			−0.858429			−0.429215	+	0.903203i	$0.641210\pi$
$390$		0			0
$391$	−3.83466			−0.193927
$392$		0			0
$393$			3.70861i			0.187075i
$394$		0			0
$395$	−2.45567	+	1.77766i	−0.123558	+	0.0894436i
$396$		0			0
$397$	−12.8599			−0.645418			−0.322709	−	0.946498i	$-0.604593\pi$
$397$	−12.8599			−0.645418			−0.322709	+	0.946498i	$0.604593\pi$
$398$		0			0
$399$	−8.74599	−	4.44793i	−0.437847	−	0.222675i
$400$		0			0
$401$	17.5616			0.876982			0.438491	−	0.898736i	$-0.355513\pi$
$401$	17.5616			0.876982			0.438491	+	0.898736i	$0.355513\pi$
$402$		0			0
$403$	−40.8427			−2.03452
$404$		0			0
$405$	6.87879	+	9.50242i	0.341810	+	0.472179i
$406$		0			0
$407$	11.4677			0.568432
$408$		0			0
$409$		−	4.76493i		−	0.235611i	−0.993037	−	0.117805i	$-0.962414\pi$
$409$		−	4.76493i		−	0.235611i	0.993037	−	0.117805i	$-0.0375859\pi$
$410$		0			0
$411$	8.74599			0.431408
$412$		0			0
$413$	−9.66259	+	18.9996i	−0.475465	+	0.934909i
$414$		0			0
$415$	22.5571	−	16.3291i	1.10729	−	0.801564i
$416$		0			0
$417$		−	9.49980i		−	0.465207i
$418$		0			0
$419$	−20.6372			−1.00819			−0.504095	−	0.863648i	$-0.668174\pi$
$419$	−20.6372			−1.00819			−0.504095	+	0.863648i	$0.668174\pi$
$420$		0			0
$421$	−8.43845			−0.411265			−0.205632	−	0.978629i	$-0.565925\pi$
$421$	−8.43845			−0.411265			−0.205632	+	0.978629i	$0.565925\pi$
$422$		0			0
$423$		−	0.743668i		−	0.0361584i
$424$		0			0
$425$	3.19727	−	9.72540i	0.155090	−	0.471751i
$426$		0			0
$427$	−15.2134	−	7.73704i	−0.736227	−	0.374421i
$428$		0			0
$429$	−9.56155			−0.461636
$430$		0			0
$431$		−	15.4609i		−	0.744724i	−0.928087	−	0.372362i	$-0.878548\pi$
$431$		−	15.4609i		−	0.744724i	0.928087	−	0.372362i	$-0.121452\pi$
$432$		0			0
$433$	−38.5088			−1.85062			−0.925308	−	0.379218i	$-0.876193\pi$
$433$	−38.5088			−1.85062			−0.925308	+	0.379218i	$0.876193\pi$
$434$		0			0
$435$	4.27156	−	3.09218i	0.204806	−	0.148258i
$436$		0			0
$437$	10.4895			0.501782
$438$		0			0
$439$	−23.7823			−1.13507			−0.567534	−	0.823350i	$-0.692102\pi$
$439$	−23.7823			−1.13507			−0.567534	+	0.823350i	$0.692102\pi$
$440$		0			0
$441$	−10.5616	−	14.4903i	−0.502931	−	0.690016i
$442$		0			0
$443$	−13.8664			−0.658812			−0.329406	−	0.944188i	$-0.606848\pi$
$443$	−13.8664			−0.658812			−0.329406	+	0.944188i	$0.606848\pi$
$444$		0			0
$445$	5.12311	−	3.70861i	0.242858	−	0.175805i
$446$		0			0
$447$		−	1.32431i		−	0.0626376i
$448$		0			0
$449$	18.6847			0.881784			0.440892	−	0.897560i	$-0.354662\pi$
$449$	18.6847			0.881784			0.440892	+	0.897560i	$0.354662\pi$
$450$		0			0
$451$	−26.2380			−1.23550
$452$		0			0
$453$	−12.5370			−0.589041
$454$		0			0
$455$	−27.2914	+	4.29535i	−1.27944	+	0.201369i
$456$		0			0
$457$			37.5427i			1.75617i	0.478504	+	0.878086i	$0.341179\pi$
$457$			37.5427i			1.75617i	−0.478504	+	0.878086i	$0.658821\pi$
$458$		0			0
$459$			7.54011i			0.351942i
$460$		0			0
$461$			19.7012i			0.917578i	0.888545	+	0.458789i	$0.151717\pi$
$461$			19.7012i			0.917578i	−0.888545	+	0.458789i	$0.848283\pi$
$462$		0			0
$463$	−27.2069			−1.26441			−0.632206	−	0.774800i	$-0.717850\pi$
$463$	−27.2069			−1.26441			−0.632206	+	0.774800i	$0.717850\pi$
$464$		0			0
$465$	10.4895	−	7.59336i	0.486440	−	0.352134i
$466$		0			0
$467$			31.0297i			1.43588i	0.696104	+	0.717941i	$0.254915\pi$
$467$			31.0297i			1.43588i	−0.696104	+	0.717941i	$0.745085\pi$
$468$		0			0
$469$	2.87689	−	5.65685i	0.132843	−	0.261209i
$470$		0			0
$471$		−	1.73642i		−	0.0800100i
$472$		0			0
$473$			13.2084i			0.607323i
$474$		0			0
$475$	−8.74599	+	26.6034i	−0.401294	+	1.22065i
$476$		0			0
$477$			24.3342i			1.11419i
$478$		0			0
$479$	3.83466			0.175210			0.0876050	−	0.996155i	$-0.472079\pi$
$479$	3.83466			0.175210			0.0876050	+	0.996155i	$0.472079\pi$
$480$		0			0
$481$			17.3188i			0.789667i
$482$		0			0
$483$	−2.92456	−	1.48734i	−0.133072	−	0.0676762i
$484$		0			0
$485$	8.05398	+	11.1258i	0.365712	+	0.505198i
$486$		0			0
$487$	−38.9699			−1.76589			−0.882947	−	0.469473i	$-0.844444\pi$
$487$	−38.9699			−1.76589			−0.882947	+	0.469473i	$0.844444\pi$
$488$		0			0
$489$			10.4218i			0.471290i
$490$		0			0
$491$			6.56502i			0.296275i	0.988967	+	0.148138i	$0.0473278\pi$
$491$			6.56502i			0.296275i	−0.988967	+	0.148138i	$0.952672\pi$
$492$		0			0
$493$	−7.29226			−0.328427
$494$		0			0
$495$	−14.3468	+	10.3857i	−0.644842	+	0.466800i
$496$		0			0
$497$	22.7745	+	11.5824i	1.02158	+	0.519541i
$498$		0			0
$499$		−	34.0139i		−	1.52267i	−0.648357	−	0.761336i	$-0.724544\pi$
$499$		−	34.0139i		−	1.52267i	0.648357	−	0.761336i	$-0.275456\pi$
$500$		0			0
$501$	5.56155			0.248472
$502$		0			0
$503$		−	7.81855i		−	0.348612i	−0.984692	−	0.174306i	$-0.944232\pi$
$503$		−	7.81855i		−	0.348612i	0.984692	−	0.174306i	$-0.0557682\pi$
$504$		0			0
$505$	4.31534	−	3.12387i	0.192030	−	0.139010i
$506$		0			0
$507$		−	5.83209i		−	0.259012i
$508$		0			0
$509$		−	1.14235i		−	0.0506338i	−0.999679	−	0.0253169i	$-0.991941\pi$
$509$		−	1.14235i		−	0.0506338i	0.999679	−	0.0253169i	$-0.00805948\pi$
$510$		0			0
$511$	−4.91134	+	9.65719i	−0.217265	+	0.427209i
$512$		0			0
$513$		−	20.6256i		−	0.910644i
$514$		0			0
$515$	1.87285	−	1.35576i	0.0825278	−	0.0597417i
$516$		0			0
$517$	0.897718			0.0394816
$518$		0			0
$519$		−	5.80369i		−	0.254754i
$520$		0			0
$521$			2.82843i			0.123916i	0.998079	+	0.0619578i	$0.0197344\pi$
$521$			2.82843i			0.123916i	−0.998079	+	0.0619578i	$0.980266\pi$
$522$		0			0
$523$		−	7.15640i		−	0.312927i	−0.987684	−	0.156464i	$-0.949991\pi$
$523$		−	7.15640i		−	0.312927i	0.987684	−	0.156464i	$-0.0500094\pi$
$524$		0			0
$525$	6.21061	−	6.17710i	0.271053	−	0.269591i
$526$		0			0
$527$	−17.9074			−0.780058
$528$		0			0
$529$	−19.4924			−0.847497
$530$		0			0
$531$	−20.6372			−0.895576
$532$		0			0
$533$		−	39.6252i		−	1.71636i
$534$		0			0
$535$	19.2582	+	26.6034i	0.832603	+	1.15016i
$536$		0			0
$537$	−1.14978			−0.0496165
$538$		0			0
$539$	17.4920	−	12.7494i	0.753433	−	0.549154i
$540$		0			0
$541$	23.5616			1.01299			0.506495	−	0.862243i	$-0.330941\pi$
$541$	23.5616			1.01299			0.506495	+	0.862243i	$0.330941\pi$
$542$		0			0
$543$	6.14441			0.263682
$544$		0			0
$545$	−0.574888	−	0.794156i	−0.0246255	−	0.0340179i
$546$		0			0
$547$	−37.3923			−1.59878			−0.799390	−	0.600812i	$-0.794844\pi$
$547$	−37.3923			−1.59878			−0.799390	+	0.600812i	$0.794844\pi$
$548$		0			0
$549$		−	16.5246i		−	0.705253i
$550$		0			0
$551$	19.9477			0.849799
$552$		0			0
$553$	3.19727	+	1.62603i	0.135962	+	0.0691458i
$554$		0			0
$555$	−3.21985	−	4.44793i	−0.136675	−	0.188804i
$556$		0			0
$557$		−	9.49980i		−	0.402519i	−0.979538	−	0.201260i	$-0.935496\pi$
$557$		−	9.49980i		−	0.402519i	0.979538	−	0.201260i	$-0.0645035\pi$
$558$		0			0
$559$	−19.9477			−0.843696
$560$		0			0
$561$	−4.19224			−0.176996
$562$		0			0
$563$		−	27.9277i		−	1.17701i	−0.808493	−	0.588506i	$-0.799716\pi$
$563$		−	27.9277i		−	1.17701i	0.808493	−	0.588506i	$-0.200284\pi$
$564$		0			0
$565$	−6.71737	+	4.86270i	−0.282602	+	0.204575i
$566$		0			0
$567$	6.29206	−	12.3721i	0.264242	−	0.519580i
$568$		0			0
$569$	13.8617			0.581114			0.290557	−	0.956858i	$-0.406159\pi$
$569$	13.8617			0.581114			0.290557	+	0.956858i	$0.406159\pi$
$570$		0			0
$571$		−	17.5780i		−	0.735615i	−0.929902	−	0.367807i	$-0.880109\pi$
$571$		−	17.5780i		−	0.735615i	0.929902	−	0.367807i	$-0.119891\pi$
$572$		0			0
$573$	9.08770			0.379644
$574$		0			0
$575$	−2.92456	+	8.89586i	−0.121963	+	0.370983i
$576$		0			0
$577$	18.9316			0.788132			0.394066	−	0.919082i	$-0.371068\pi$
$577$	18.9316			0.788132			0.394066	+	0.919082i	$0.371068\pi$
$578$		0			0
$579$	−2.45567			−0.102054
$580$		0			0
$581$	−29.3693	−	14.9363i	−1.21844	−	0.619662i
$582$		0			0
$583$	−29.3751			−1.21659
$584$		0			0
$585$	−15.6847	−	21.6669i	−0.648481	−	0.895817i
$586$		0			0
$587$		−	9.06134i		−	0.374002i	−0.982360	−	0.187001i	$-0.940123\pi$
$587$		−	9.06134i		−	0.374002i	0.982360	−	0.187001i	$-0.0598767\pi$
$588$		0			0
$589$	48.9848			2.01839
$590$		0			0
$591$	7.36701			0.303038
$592$		0			0
$593$	−31.2165			−1.28191			−0.640955	−	0.767579i	$-0.721461\pi$
$593$	−31.2165			−1.28191			−0.640955	+	0.767579i	$0.721461\pi$
$594$		0			0
$595$	−11.9658	+	1.88328i	−0.490552	+	0.0772071i
$596$		0			0
$597$			4.16516i			0.170469i
$598$		0			0
$599$		−	14.4858i		−	0.591873i	−0.955208	−	0.295937i	$-0.904368\pi$
$599$		−	14.4858i		−	0.591873i	0.955208	−	0.295937i	$-0.0956317\pi$
$600$		0			0
$601$			39.4024i			1.60726i	0.595130	+	0.803630i	$0.297101\pi$
$601$			39.4024i			1.60726i	−0.595130	+	0.803630i	$0.702899\pi$
$602$		0			0
$603$	6.14441			0.250220
$604$		0			0
$605$	1.88608	+	2.60545i	0.0766801	+	0.105926i
$606$		0			0
$607$			10.6302i			0.431466i	0.976452	+	0.215733i	$0.0692141\pi$
$607$			10.6302i			0.431466i	−0.976452	+	0.215733i	$0.930786\pi$
$608$		0			0
$609$	−5.56155	−	2.82843i	−0.225365	−	0.114614i
$610$		0			0
$611$			1.35576i			0.0548480i
$612$		0			0
$613$		−	13.6650i		−	0.551923i	−0.961169	−	0.275961i	$-0.911004\pi$
$613$		−	13.6650i		−	0.551923i	0.961169	−	0.275961i	$-0.0889962\pi$
$614$		0			0
$615$	7.36701	+	10.1768i	0.297066	+	0.410370i
$616$		0			0
$617$		−	35.9166i		−	1.44595i	−0.690875	−	0.722974i	$-0.742774\pi$
$617$		−	35.9166i		−	1.44595i	0.690875	−	0.722974i	$-0.257226\pi$
$618$		0			0
$619$	10.5122			0.422520			0.211260	−	0.977430i	$-0.432243\pi$
$619$	10.5122			0.422520			0.211260	+	0.977430i	$0.432243\pi$
$620$		0			0
$621$		−	6.89697i		−	0.276766i
$622$		0			0
$623$	−6.67026	−	3.39228i	−0.267238	−	0.135909i
$624$		0			0
$625$	−20.1231	−	14.8344i	−0.804924	−	0.593378i
$626$		0			0
$627$	11.4677			0.457975
$628$		0			0
$629$			7.59336i			0.302767i
$630$		0			0
$631$		−	32.2775i		−	1.28495i	−0.766308	−	0.642474i	$-0.777908\pi$
$631$		−	32.2775i		−	1.28495i	0.766308	−	0.642474i	$-0.222092\pi$
$632$		0			0
$633$	−16.6320			−0.661063
$634$		0			0
$635$	22.4033	+	30.9481i	0.889049	+	1.22814i
$636$		0			0
$637$	19.2544	+	26.4168i	0.762887	+	1.04667i
$638$		0			0
$639$			24.7374i			0.978597i
$640$		0			0
$641$	−17.8617			−0.705496			−0.352748	−	0.935718i	$-0.614753\pi$
$641$	−17.8617			−0.705496			−0.352748	+	0.935718i	$0.614753\pi$
$642$		0			0
$643$			0.499124i			0.0196835i	0.999952	+	0.00984176i	$0.00313278\pi$
$643$			0.499124i			0.0196835i	−0.999952	+	0.00984176i	$0.996867\pi$
$644$		0			0
$645$	5.12311	−	3.70861i	0.201722	−	0.146026i
$646$		0			0
$647$			5.87787i			0.231083i	0.993303	+	0.115541i	$0.0368603\pi$
$647$			5.87787i			0.231083i	−0.993303	+	0.115541i	$0.963140\pi$
$648$		0			0
$649$		−	24.9121i		−	0.977886i
$650$		0			0
$651$	−13.6573	−	6.94568i	−0.535273	−	0.272223i
$652$		0			0
$653$			11.1258i			0.435387i	0.976017	+	0.217694i	$0.0698534\pi$
$653$			11.1258i			0.435387i	−0.976017	+	0.217694i	$0.930147\pi$
$654$		0			0
$655$	−7.34376	−	10.1447i	−0.286945	−	0.396388i
$656$		0			0
$657$	−10.4895			−0.409236
$658$		0			0
$659$		−	19.6950i		−	0.767210i	−0.923497	−	0.383605i	$-0.874682\pi$
$659$		−	19.6950i		−	0.767210i	0.923497	−	0.383605i	$-0.125318\pi$
$660$		0			0
$661$		−	42.3286i		−	1.64639i	−0.567756	−	0.823197i	$-0.692188\pi$
$661$		−	42.3286i		−	1.64639i	0.567756	−	0.823197i	$-0.307812\pi$
$662$		0			0
$663$		−	6.33122i		−	0.245884i
$664$		0			0
$665$	32.7320	−	5.15164i	1.26929	−	0.199772i
$666$		0			0
$667$	6.67026			0.258274
$668$		0			0
$669$	−12.6847			−0.490417
$670$		0			0
$671$	19.9477			0.770071
$672$		0			0
$673$			5.79119i			0.223234i	0.993751	+	0.111617i	$0.0356030\pi$
$673$			5.79119i			0.223234i	−0.993751	+	0.111617i	$0.964397\pi$
$674$		0			0
$675$	17.4920	+	5.75058i	0.673267	+	0.221340i
$676$		0			0
$677$	6.46532			0.248482			0.124241	−	0.992252i	$-0.460350\pi$
$677$	6.46532			0.248482			0.124241	+	0.992252i	$0.460350\pi$
$678$		0			0
$679$	7.36701	−	14.4858i	0.282720	−	0.555914i
$680$		0			0
$681$	9.31534			0.356965
$682$		0			0
$683$	−5.32326			−0.203689			−0.101845	−	0.994800i	$-0.532474\pi$
$683$	−5.32326			−0.203689			−0.101845	+	0.994800i	$0.532474\pi$
$684$		0			0
$685$	−23.9243	+	17.3188i	−0.914100	+	0.661716i
$686$		0			0
$687$	5.32326			0.203095
$688$		0			0
$689$		−	44.3629i		−	1.69009i
$690$		0			0
$691$	12.9678			0.493320			0.246660	−	0.969102i	$-0.420667\pi$
$691$	12.9678			0.493320			0.246660	+	0.969102i	$0.420667\pi$
$692$		0			0
$693$	18.6795	+	9.49980i	0.709576	+	0.360868i
$694$		0			0
$695$	18.8114	+	25.9863i	0.713559	+	0.985716i
$696$		0			0
$697$		−	17.3736i		−	0.658071i
$698$		0			0
$699$	−4.91134			−0.185764
$700$		0			0
$701$	−47.6695			−1.80045			−0.900226	−	0.435423i	$-0.856599\pi$
$701$	−47.6695			−1.80045			−0.900226	+	0.435423i	$0.856599\pi$
$702$		0			0
$703$		−	20.7713i		−	0.783404i
$704$		0			0
$705$	−0.252058	−	0.348195i	−0.00949306	−	0.0131138i
$706$		0			0
$707$	−5.61856	−	2.85742i	−0.211308	−	0.107464i
$708$		0			0
$709$	−10.1922			−0.382777			−0.191389	−	0.981514i	$-0.561299\pi$
$709$	−10.1922			−0.382777			−0.191389	+	0.981514i	$0.561299\pi$
$710$		0			0
$711$			3.47284i			0.130242i
$712$		0			0
$713$	16.3800			0.613434
$714$		0			0
$715$	26.1552	−	18.9337i	0.978149	−	0.708081i
$716$		0			0
$717$	−2.04750			−0.0764651
$718$		0			0
$719$	36.0607			1.34484			0.672418	−	0.740172i	$-0.265256\pi$
$719$	36.0607			1.34484			0.672418	+	0.740172i	$0.265256\pi$
$720$		0			0
$721$	−2.43845	−	1.24012i	−0.0908125	−	0.0461843i
$722$		0			0
$723$	−12.5194			−0.465601
$724$		0			0
$725$	−5.56155	+	16.9170i	−0.206551	+	0.628282i
$726$		0			0
$727$		−	6.20393i		−	0.230091i	−0.993360	−	0.115045i	$-0.963299\pi$
$727$		−	6.20393i		−	0.230091i	0.993360	−	0.115045i	$-0.0367014\pi$
$728$		0			0
$729$	6.12311			0.226782
$730$		0			0
$731$	−8.74599			−0.323482
$732$		0			0
$733$	11.0644			0.408674			0.204337	−	0.978901i	$-0.434496\pi$
$733$	11.0644			0.408674			0.204337	+	0.978901i	$0.434496\pi$
$734$		0			0
$735$	−9.85640	−	3.20484i	−0.363559	−	0.118212i
$736$		0			0
$737$			7.41722i			0.273217i
$738$		0			0
$739$		−	14.6996i		−	0.540732i	−0.962758	−	0.270366i	$-0.912855\pi$
$739$		−	14.6996i		−	0.540732i	0.962758	−	0.270366i	$-0.0871447\pi$
$740$		0			0
$741$			17.3188i			0.636220i
$742$		0			0
$743$	−4.79741			−0.176000			−0.0880000	−	0.996120i	$-0.528048\pi$
$743$	−4.79741			−0.176000			−0.0880000	+	0.996120i	$0.528048\pi$
$744$		0			0
$745$	2.62238	+	3.62258i	0.0960767	+	0.132721i
$746$		0			0
$747$		−	31.9006i		−	1.16718i
$748$		0			0
$749$	17.6155	−	34.6375i	0.643657	−	1.26563i
$750$		0			0
$751$		−	24.3567i		−	0.888790i	−0.895831	−	0.444395i	$-0.853419\pi$
$751$		−	24.3567i		−	0.888790i	0.895831	−	0.444395i	$-0.146581\pi$
$752$		0			0
$753$		−	2.08258i		−	0.0758934i
$754$		0			0
$755$	34.2945	−	24.8257i	1.24810	−	0.903501i
$756$		0			0
$757$		−	28.4994i		−	1.03583i	−0.855433	−	0.517914i	$-0.826709\pi$
$757$		−	28.4994i		−	1.03583i	0.855433	−	0.517914i	$-0.173291\pi$
$758$		0			0
$759$	3.83466			0.139189
$760$		0			0
$761$			3.52482i			0.127775i	0.997957	+	0.0638873i	$0.0203498\pi$
$761$			3.52482i			0.127775i	−0.997957	+	0.0638873i	$0.979650\pi$
$762$		0			0
$763$	−0.525853	+	1.03399i	−0.0190372	+	0.0374329i
$764$		0			0
$765$	−6.87689	−	9.49980i	−0.248635	−	0.343466i
$766$		0			0
$767$	37.6229			1.35848
$768$		0			0
$769$			8.83348i			0.318543i	0.987235	+	0.159272i	$0.0509146\pi$
$769$			8.83348i			0.318543i	−0.987235	+	0.159272i	$0.949085\pi$
$770$		0			0
$771$			18.5531i			0.668172i
$772$		0			0
$773$	48.4234			1.74167			0.870835	−	0.491575i	$-0.163579\pi$
$773$	48.4234			1.74167			0.870835	+	0.491575i	$0.163579\pi$
$774$		0			0
$775$	−13.6573	+	41.5426i	−0.490586	+	1.49225i
$776$		0			0
$777$	−2.94521	+	5.79119i	−0.105659	+	0.207758i
$778$		0			0
$779$			47.5246i			1.70275i
$780$		0			0
$781$	−29.8617			−1.06854
$782$		0			0
$783$		−	13.1158i		−	0.468720i
$784$		0			0
$785$	3.43845	+	4.74990i	0.122723	+	0.169531i
$786$		0			0
$787$			37.4882i			1.33631i	0.744023	+	0.668154i	$0.232915\pi$
$787$			37.4882i			1.33631i	−0.744023	+	0.668154i	$0.767085\pi$
$788$		0			0
$789$			7.94156i			0.282727i
$790$		0			0
$791$	8.74599	+	4.44793i	0.310972	+	0.158150i
$792$		0			0
$793$			30.1254i			1.06979i
$794$		0			0
$795$	8.24782	+	11.3936i	0.292520	+	0.404090i
$796$		0			0
$797$	−47.2737			−1.67452			−0.837260	−	0.546805i	$-0.815844\pi$
$797$	−47.2737			−1.67452			−0.837260	+	0.546805i	$0.815844\pi$
$798$		0			0
$799$			0.594427i			0.0210293i
$800$		0			0
$801$		−	7.24517i		−	0.255995i
$802$		0			0
$803$		−	12.6624i		−	0.446847i
$804$		0			0
$805$	10.9452	−	1.72265i	0.385768	−	0.0607153i
$806$		0			0
$807$	−10.9418			−0.385170
$808$		0			0
$809$	10.0540			0.353479			0.176739	−	0.984258i	$-0.443445\pi$
$809$	10.0540			0.353479			0.176739	+	0.984258i	$0.443445\pi$
$810$		0			0
$811$	−3.14516			−0.110442			−0.0552208	−	0.998474i	$-0.517586\pi$
$811$	−3.14516			−0.110442			−0.0552208	+	0.998474i	$0.517586\pi$
$812$		0			0
$813$			5.79119i			0.203106i
$814$		0			0
$815$	−20.6372	−	28.5083i	−0.722888	−	0.998604i
$816$		0			0
$817$	23.9243			0.837005
$818$		0			0
$819$	−14.3468	+	28.2102i	−0.501319	+	0.985746i
$820$		0			0
$821$	7.06913			0.246714			0.123357	−	0.992362i	$-0.460634\pi$
$821$	7.06913			0.246714			0.123357	+	0.992362i	$0.460634\pi$
$822$		0			0
$823$	3.21985			0.112237			0.0561185	−	0.998424i	$-0.482128\pi$
$823$	3.21985			0.112237			0.0561185	+	0.998424i	$0.482128\pi$
$824$		0			0
$825$	−3.19727	+	9.72540i	−0.111315	+	0.338595i
$826$		0			0
$827$	2.39871			0.0834112			0.0417056	−	0.999130i	$-0.486721\pi$
$827$	2.39871			0.0834112			0.0417056	+	0.999130i	$0.486721\pi$
$828$		0			0
$829$			25.9018i			0.899607i	0.893128	+	0.449803i	$0.148506\pi$
$829$			25.9018i			0.899607i	−0.893128	+	0.449803i	$0.851494\pi$
$830$		0			0
$831$	1.37899			0.0478366
$832$		0			0
$833$	8.44204	+	11.5824i	0.292499	+	0.401306i
$834$		0			0
$835$	−15.2134	+	11.0129i	−0.526481	+	0.381119i
$836$		0			0
$837$		−	32.2080i		−	1.11327i
$838$		0			0
$839$	−47.2623			−1.63168			−0.815838	−	0.578280i	$-0.803724\pi$
$839$	−47.2623			−1.63168			−0.815838	+	0.578280i	$0.803724\pi$
$840$		0			0
$841$	−16.3153			−0.562598
$842$		0			0
$843$			13.2788i			0.457346i
$844$		0			0
$845$	11.5487	+	15.9534i	0.397286	+	0.548815i
$846$		0			0
$847$	1.72521	−	3.39228i	0.0592788	−	0.116560i
$848$		0			0
$849$	−12.9309			−0.443786
$850$		0			0
$851$		−	6.94568i		−	0.238095i
$852$		0			0
$853$	−45.2262			−1.54851			−0.774257	−	0.632871i	$-0.781876\pi$
$853$	−45.2262			−1.54851			−0.774257	+	0.632871i	$0.781876\pi$
$854$		0			0
$855$	18.8114	+	25.9863i	0.643338	+	0.888712i
$856$		0			0
$857$	−14.5845			−0.498198			−0.249099	−	0.968478i	$-0.580134\pi$
$857$	−14.5845			−0.498198			−0.249099	+	0.968478i	$0.580134\pi$
$858$		0			0
$859$	3.14516			0.107312			0.0536558	−	0.998559i	$-0.482913\pi$
$859$	3.14516			0.107312			0.0536558	+	0.998559i	$0.482913\pi$
$860$		0			0
$861$	6.73863	−	13.2502i	0.229652	−	0.451566i
$862$		0			0
$863$	28.8492			0.982038			0.491019	−	0.871149i	$-0.336625\pi$
$863$	28.8492			0.982038			0.491019	+	0.871149i	$0.336625\pi$
$864$		0			0
$865$	11.4924	+	15.8757i	0.390754	+	0.539791i
$866$		0			0
$867$			8.48071i			0.288020i
$868$		0			0
$869$	−4.19224			−0.142212
$870$		0			0
$871$	−11.2017			−0.379554
$872$		0			0
$873$	15.7343			0.532525
$874$		0			0
$875$	−4.75698	+	29.1954i	−0.160815	+	0.986985i
$876$		0			0
$877$			3.70861i			0.125231i	0.998038	+	0.0626154i	$0.0199442\pi$
$877$			3.70861i			0.125231i	−0.998038	+	0.0626154i	$0.980056\pi$
$878$		0			0
$879$			10.0379i			0.338569i
$880$		0			0
$881$			54.0883i			1.82228i	0.412095	+	0.911141i	$0.364797\pi$
$881$			54.0883i			1.82228i	−0.412095	+	0.911141i	$0.635203\pi$
$882$		0			0
$883$	−19.7155			−0.663479			−0.331740	−	0.943371i	$-0.607636\pi$
$883$	−19.7155			−0.663479			−0.331740	+	0.943371i	$0.607636\pi$
$884$		0			0
$885$	−9.66259	+	6.99474i	−0.324804	+	0.235125i
$886$		0			0
$887$		−	15.3110i		−	0.514095i	−0.966399	−	0.257047i	$-0.917250\pi$
$887$		−	15.3110i		−	0.514095i	0.966399	−	0.257047i	$-0.0827496\pi$
$888$		0			0
$889$	20.4924	−	40.2944i	0.687294	−	1.35143i
$890$		0			0
$891$			16.2222i			0.543464i
$892$		0			0
$893$		−	1.62603i		−	0.0544130i
$894$		0			0
$895$	3.14516	−	2.27678i	0.105131	−	0.0761044i
$896$		0			0
$897$			5.79119i			0.193362i
$898$		0			0
$899$	31.1493			1.03889
$900$		0			0
$901$		−	19.4508i		−	0.648000i
$902$		0			0
$903$	−6.67026	−	3.39228i	−0.221972	−	0.112888i
$904$		0			0
$905$	−16.8078	+	12.1671i	−0.558709	+	0.404449i
$906$		0			0
$907$	−2.62926			−0.0873033			−0.0436516	−	0.999047i	$-0.513899\pi$
$907$	−2.62926			−0.0873033			−0.0436516	+	0.999047i	$0.513899\pi$
$908$		0			0
$909$		−	6.10281i		−	0.202418i
$910$		0			0
$911$		−	40.3652i		−	1.33736i	−0.743551	−	0.668679i	$-0.766860\pi$
$911$		−	40.3652i		−	1.33736i	0.743551	−	0.668679i	$-0.233140\pi$
$912$		0			0
$913$	38.5088			1.27446
$914$		0			0
$915$	−5.60083	−	7.73704i	−0.185158	−	0.255779i
$916$		0			0
$917$	−6.71737	+	13.2084i	−0.221827	+	0.436180i
$918$		0			0
$919$			11.7743i			0.388398i	0.980962	+	0.194199i	$0.0622107\pi$
$919$			11.7743i			0.388398i	−0.980962	+	0.194199i	$0.937789\pi$
$920$		0			0
$921$	17.3153			0.570560
$922$		0			0
$923$		−	45.0979i		−	1.48442i
$924$		0			0
$925$	17.6155	+	5.79119i	0.579195	+	0.190413i
$926$		0			0
$927$		−	2.64861i		−	0.0869919i
$928$		0			0
$929$			17.6670i			0.579634i	0.957082	+	0.289817i	$0.0935944\pi$
$929$			17.6670i			0.579634i	−0.957082	+	0.289817i	$0.906406\pi$
$930$		0			0
$931$	−23.0928	−	31.6831i	−0.756837	−	1.03837i
$932$		0			0
$933$			13.2084i			0.432424i
$934$		0			0
$935$	11.4677	−	8.30144i	0.375033	−	0.271486i
$936$		0			0
$937$	−38.7609			−1.26626			−0.633131	−	0.774045i	$-0.718231\pi$
$937$	−38.7609			−1.26626			−0.633131	+	0.774045i	$0.718231\pi$
$938$		0			0
$939$		−	7.54011i		−	0.246062i
$940$		0			0
$941$			37.9119i			1.23589i	0.786220	+	0.617946i	$0.212035\pi$
$941$			37.9119i			1.23589i	−0.786220	+	0.617946i	$0.787965\pi$
$942$		0			0
$943$			15.8917i			0.517504i
$944$		0			0
$945$	−3.38725	−	21.5216i	−0.110187	−	0.700099i
$946$		0			0
$947$	41.5991			1.35179			0.675895	−	0.736998i	$-0.263757\pi$
$947$	41.5991			1.35179			0.675895	+	0.736998i	$0.263757\pi$
$948$		0			0
$949$	19.1231			0.620762
$950$		0			0
$951$	−21.0243			−0.681761
$952$		0			0
$953$		−	24.7908i		−	0.803053i	−0.915848	−	0.401526i	$-0.868480\pi$
$953$		−	24.7908i		−	0.803053i	0.915848	−	0.401526i	$-0.131520\pi$
$954$		0			0
$955$	−24.8590	+	17.9954i	−0.804418	+	0.582317i
$956$		0			0
$957$	7.29226			0.235725
$958$		0			0
$959$	31.1493	+	15.8415i	1.00586	+	0.511550i
$960$		0			0
$961$	45.4924			1.46750
$962$		0			0
$963$	37.6229			1.21238
$964$		0			0
$965$	6.71737	−	4.86270i	0.216240	−	0.156536i
$966$		0			0
$967$	−18.1379			−0.583277			−0.291638	−	0.956529i	$-0.594200\pi$
$967$	−18.1379			−0.583277			−0.291638	+	0.956529i	$0.594200\pi$
$968$		0			0
$969$			7.59336i			0.243934i
$970$		0			0
$971$	−32.9155			−1.05631			−0.528154	−	0.849148i	$-0.677116\pi$
$971$	−32.9155			−1.05631			−0.528154	+	0.849148i	$0.677116\pi$
$972$		0			0
$973$	17.2069	−	33.8340i	0.551628	−	1.08467i
$974$		0			0
$975$	−14.6875	−	4.82860i	−0.470377	−	0.154639i
$976$		0			0
$977$			5.79119i			0.185277i	0.995700	+	0.0926383i	$0.0295300\pi$
$977$			5.79119i			0.185277i	−0.995700	+	0.0926383i	$0.970470\pi$
$978$		0			0
$979$	8.74599			0.279523
$980$		0			0
$981$	−1.12311			−0.0358580
$982$		0			0
$983$		−	38.4406i		−	1.22607i	−0.790057	−	0.613033i	$-0.789949\pi$
$983$		−	38.4406i		−	1.22607i	0.790057	−	0.613033i	$-0.210051\pi$
$984$		0			0
$985$	−20.1521	+	14.5881i	−0.642100	+	0.464815i
$986$		0			0
$987$	−0.230559	+	0.453349i	−0.00733876	+	0.0144303i
$988$		0			0
$989$	8.00000			0.254385
$990$		0			0
$991$			50.2361i			1.59580i	0.602787	+	0.797902i	$0.294057\pi$
$991$			50.2361i			1.59580i	−0.602787	+	0.797902i	$0.705943\pi$
$992$		0			0
$993$	−1.14978			−0.0364871
$994$		0			0
$995$	−8.24782	−	11.3936i	−0.261474	−	0.361202i
$996$		0			0
$997$	26.7987			0.848724			0.424362	−	0.905493i	$-0.360498\pi$
$997$	26.7987			0.848724			0.424362	+	0.905493i	$0.360498\pi$
$998$		0			0
$999$	−13.6573			−0.432099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.e.f.2239.8		16
4.3	odd	2	inner	2240.2.e.f.2239.12		16
5.4	even	2	inner	2240.2.e.f.2239.10		16
7.6	odd	2	inner	2240.2.e.f.2239.9		16
8.3	odd	2		140.2.c.b.139.13	yes	16
8.5	even	2		140.2.c.b.139.2	yes	16
20.19	odd	2	inner	2240.2.e.f.2239.6		16
28.27	even	2	inner	2240.2.e.f.2239.5		16
35.34	odd	2	inner	2240.2.e.f.2239.7		16
40.3	even	4		700.2.g.l.251.6		16
40.13	odd	4		700.2.g.l.251.7		16
40.19	odd	2		140.2.c.b.139.4	yes	16
40.27	even	4		700.2.g.l.251.11		16
40.29	even	2		140.2.c.b.139.15	yes	16
40.37	odd	4		700.2.g.l.251.10		16
56.3	even	6		980.2.s.f.19.10		32
56.5	odd	6		980.2.s.f.619.8		32
56.11	odd	6		980.2.s.f.19.9		32
56.13	odd	2		140.2.c.b.139.1	✓	16
56.19	even	6		980.2.s.f.619.3		32
56.27	even	2		140.2.c.b.139.14	yes	16
56.37	even	6		980.2.s.f.619.7		32
56.45	odd	6		980.2.s.f.19.13		32
56.51	odd	6		980.2.s.f.619.4		32
56.53	even	6		980.2.s.f.19.14		32
140.139	even	2	inner	2240.2.e.f.2239.11		16
280.13	even	4		700.2.g.l.251.8		16
280.19	even	6		980.2.s.f.619.14		32
280.27	odd	4		700.2.g.l.251.12		16
280.59	even	6		980.2.s.f.19.7		32
280.69	odd	2		140.2.c.b.139.16	yes	16
280.83	odd	4		700.2.g.l.251.5		16
280.109	even	6		980.2.s.f.19.3		32
280.139	even	2		140.2.c.b.139.3	yes	16
280.149	even	6		980.2.s.f.619.10		32
280.179	odd	6		980.2.s.f.19.8		32
280.219	odd	6		980.2.s.f.619.13		32
280.229	odd	6		980.2.s.f.619.9		32
280.237	even	4		700.2.g.l.251.9		16
280.269	odd	6		980.2.s.f.19.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.1	✓	16	56.13	odd	2
140.2.c.b.139.2	yes	16	8.5	even	2
140.2.c.b.139.3	yes	16	280.139	even	2
140.2.c.b.139.4	yes	16	40.19	odd	2
140.2.c.b.139.13	yes	16	8.3	odd	2
140.2.c.b.139.14	yes	16	56.27	even	2
140.2.c.b.139.15	yes	16	40.29	even	2
140.2.c.b.139.16	yes	16	280.69	odd	2
700.2.g.l.251.5		16	280.83	odd	4
700.2.g.l.251.6		16	40.3	even	4
700.2.g.l.251.7		16	40.13	odd	4
700.2.g.l.251.8		16	280.13	even	4
700.2.g.l.251.9		16	280.237	even	4
700.2.g.l.251.10		16	40.37	odd	4
700.2.g.l.251.11		16	40.27	even	4
700.2.g.l.251.12		16	280.27	odd	4
980.2.s.f.19.3		32	280.109	even	6
980.2.s.f.19.4		32	280.269	odd	6
980.2.s.f.19.7		32	280.59	even	6
980.2.s.f.19.8		32	280.179	odd	6
980.2.s.f.19.9		32	56.11	odd	6
980.2.s.f.19.10		32	56.3	even	6
980.2.s.f.19.13		32	56.45	odd	6
980.2.s.f.19.14		32	56.53	even	6
980.2.s.f.619.3		32	56.19	even	6
980.2.s.f.619.4		32	56.51	odd	6
980.2.s.f.619.7		32	56.37	even	6
980.2.s.f.619.8		32	56.5	odd	6
980.2.s.f.619.9		32	280.229	odd	6
980.2.s.f.619.10		32	280.149	even	6
980.2.s.f.619.13		32	280.219	odd	6
980.2.s.f.619.14		32	280.19	even	6
2240.2.e.f.2239.5		16	28.27	even	2	inner
2240.2.e.f.2239.6		16	20.19	odd	2	inner
2240.2.e.f.2239.7		16	35.34	odd	2	inner
2240.2.e.f.2239.8		16	1.1	even	1	trivial
2240.2.e.f.2239.9		16	7.6	odd	2	inner
2240.2.e.f.2239.10		16	5.4	even	2	inner
2240.2.e.f.2239.11		16	140.139	even	2	inner
2240.2.e.f.2239.12		16	4.3	odd	2	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:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.662153i q^{3} +(1.31119 + 1.81129i) q^{5} +(1.19935 - 2.35829i) q^{7} +2.56155 q^{9} +O(q^{10})\)	\(q-0.662153i q^{3} +(1.31119 + 1.81129i) q^{5} +(1.19935 - 2.35829i) q^{7} +2.56155 q^{9} +3.09218i q^{11} -4.66988 q^{13} +(1.19935 - 0.868210i) q^{15} -2.04750 q^{17} +5.60083 q^{19} +(-1.56155 - 0.794156i) q^{21} +1.87285 q^{23} +(-1.56155 + 4.74990i) q^{25} -3.68260i q^{27} +3.56155 q^{29} +8.74599 q^{31} +2.04750 q^{33} +(5.84414 - 0.919799i) q^{35} -3.70861i q^{37} +3.09218i q^{39} +8.48528i q^{41} +4.27156 q^{43} +(3.35869 + 4.63972i) q^{45} -0.290319i q^{47} +(-4.12311 - 5.65685i) q^{49} +1.35576i q^{51} +9.49980i q^{53} +(-5.60083 + 4.05444i) q^{55} -3.70861i q^{57} -8.05650 q^{59} -6.45101i q^{61} +(3.07221 - 6.04090i) q^{63} +(-6.12311 - 8.45851i) q^{65} +2.39871 q^{67} -1.24012i q^{69} +9.65719i q^{71} -4.09499 q^{73} +(3.14516 + 1.03399i) q^{75} +(7.29226 + 3.70861i) q^{77} +1.35576i q^{79} +5.24621 q^{81} -12.4536i q^{83} +(-2.68466 - 3.70861i) q^{85} -2.35829i q^{87} -2.82843i q^{89} +(-5.60083 + 11.0129i) q^{91} -5.79119i q^{93} +(7.34376 + 10.1447i) q^{95} +6.14249 q^{97} +7.92077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^9	\( 16 q + 8 q^{9} + 8 q^{21} + 8 q^{25} + 24 q^{29} - 32 q^{65} - 48 q^{81} + 56 q^{85}+O(q^{100}) \) 16 * q + 8 * q^9 + 8 * q^21 + 8 * q^25 + 24 * q^29 - 32 * q^65 - 48 * q^81 + 56 * q^85

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