LMFDB - Embedded newform 960.2.o.e.959.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(959,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, 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("960.959");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.o (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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 480)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			959.18
Character	$\chi$	$=$	960.959
Dual form			960.2.o.e.959.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16422 - 1.28241i) q^{3} +(2.19399 + 0.431733i) q^{5} +4.22289 q^{7} +(-0.289169 - 2.98603i) q^{9} +O(q^{10})$	\(q+(1.16422 - 1.28241i) q^{3} +(2.19399 + 0.431733i) q^{5} +4.22289 q^{7} +(-0.289169 - 2.98603i) q^{9} -2.42945 q^{11} -5.33021i q^{13} +(3.10796 - 2.31097i) q^{15} -3.57009 q^{17} -0.578337i q^{19} +(4.91638 - 5.41549i) q^{21} +5.39325i q^{23} +(4.62721 + 1.89444i) q^{25} +(-4.16598 - 3.10557i) q^{27} -5.10860i q^{29} +7.83276i q^{31} +(-2.82843 + 3.11556i) q^{33} +(9.26498 + 1.82316i) q^{35} +7.77246i q^{37} +(-6.83553 - 6.20555i) q^{39} +0.613779i q^{41} -2.32845 q^{43} +(0.654735 - 6.67618i) q^{45} +3.38272i q^{47} +10.8328 q^{49} +(-4.15639 + 4.57834i) q^{51} -1.26887 q^{53} +(-5.33021 - 1.04888i) q^{55} +(-0.741667 - 0.673313i) q^{57} -7.78774 q^{59} +6.67609 q^{61} +(-1.22113 - 12.6097i) q^{63} +(2.30123 - 11.6944i) q^{65} -0.113805 q^{67} +(6.91638 + 6.27895i) q^{69} +8.31277 q^{71} -13.1027i q^{73} +(7.81656 - 3.72845i) q^{75} -10.2593 q^{77} +3.42166i q^{79} +(-8.83276 + 1.72693i) q^{81} +5.68395i q^{83} +(-7.83276 - 1.54133i) q^{85} +(-6.55133 - 5.94755i) q^{87} -4.85891i q^{89} -22.5089i q^{91} +(10.0448 + 9.11908i) q^{93} +(0.249687 - 1.26887i) q^{95} +9.31379i q^{97} +(0.702522 + 7.25443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 8 q^{21} + 8 q^{25} + 24 q^{45} + 40 q^{49} - 32 q^{61} + 56 q^{69} + 8 q^{81} + 32 q^{85}+O(q^{100}) $ 24 * q + 8 * q^21 + 8 * q^25 + 24 * q^45 + 40 * q^49 - 32 * q^61 + 56 * q^69 + 8 * q^81 + 32 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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
$3$	1.16422	−	1.28241i	0.672165	−	0.740402i
$3$	1.16422	−	1.28241i	0.672165	−	0.740402i
$4$		0			0
$5$	2.19399	+	0.431733i	0.981184	+	0.193077i
$5$	2.19399	+	0.431733i	0.981184	+	0.193077i
$6$		0			0
$7$	4.22289			1.59610			0.798050	−	0.602591i	$-0.205865\pi$
$7$	4.22289			1.59610			0.798050	+	0.602591i	$0.205865\pi$
$8$		0			0
$9$	−0.289169	−	2.98603i	−0.0963895	−	0.995344i
$10$		0			0
$11$	−2.42945			−0.732508			−0.366254	−	0.930515i	$-0.619360\pi$
$11$	−2.42945			−0.732508			−0.366254	+	0.930515i	$0.619360\pi$
$12$		0			0
$13$		−	5.33021i		−	1.47833i	−0.673523	−	0.739167i	$-0.735220\pi$
$13$		−	5.33021i		−	1.47833i	0.673523	−	0.739167i	$-0.264780\pi$
$14$		0			0
$15$	3.10796	−	2.31097i	0.802471	−	0.596691i
$16$		0			0
$17$	−3.57009			−0.865875			−0.432938	−	0.901424i	$-0.642523\pi$
$17$	−3.57009			−0.865875			−0.432938	+	0.901424i	$0.642523\pi$
$18$		0			0
$19$		−	0.578337i		−	0.132680i	−0.997797	−	0.0663398i	$-0.978868\pi$
$19$		−	0.578337i		−	0.132680i	0.997797	−	0.0663398i	$-0.0211321\pi$
$20$		0			0
$21$	4.91638	−	5.41549i	1.07284	−	1.18176i
$22$		0			0
$23$			5.39325i			1.12457i	0.826943	+	0.562286i	$0.190078\pi$
$23$			5.39325i			1.12457i	−0.826943	+	0.562286i	$0.809922\pi$
$24$		0			0
$25$	4.62721	+	1.89444i	0.925443	+	0.378888i
$26$		0			0
$27$	−4.16598	−	3.10557i	−0.801744	−	0.597668i
$28$		0			0
$29$		−	5.10860i		−	0.948642i	−0.880352	−	0.474321i	$-0.842694\pi$
$29$		−	5.10860i		−	0.948642i	0.880352	−	0.474321i	$-0.157306\pi$
$30$		0			0
$31$			7.83276i			1.40681i	0.710791	+	0.703403i	$0.248337\pi$
$31$			7.83276i			1.40681i	−0.710791	+	0.703403i	$0.751663\pi$
$32$		0			0
$33$	−2.82843	+	3.11556i	−0.492366	+	0.542350i
$34$		0			0
$35$	9.26498	+	1.82316i	1.56607	+	0.308170i
$36$		0			0
$37$			7.77246i			1.27778i	0.769296	+	0.638892i	$0.220607\pi$
$37$			7.77246i			1.27778i	−0.769296	+	0.638892i	$0.779393\pi$
$38$		0			0
$39$	−6.83553	−	6.20555i	−1.09456	−	0.993683i
$40$		0			0
$41$			0.613779i			0.0958562i	0.998851	+	0.0479281i	$0.0152618\pi$
$41$			0.613779i			0.0958562i	−0.998851	+	0.0479281i	$0.984738\pi$
$42$		0			0
$43$	−2.32845			−0.355085			−0.177542	−	0.984113i	$-0.556815\pi$
$43$	−2.32845			−0.355085			−0.177542	+	0.984113i	$0.556815\pi$
$44$		0			0
$45$	0.654735	−	6.67618i	0.0976021	−	0.995226i
$46$		0			0
$47$			3.38272i			0.493420i	0.969089	+	0.246710i	$0.0793496\pi$
$47$			3.38272i			0.493420i	−0.969089	+	0.246710i	$0.920650\pi$
$48$		0			0
$49$	10.8328			1.54754
$50$		0			0
$51$	−4.15639	+	4.57834i	−0.582011	+	0.641095i
$52$		0			0
$53$	−1.26887			−0.174292			−0.0871462	−	0.996196i	$-0.527775\pi$
$53$	−1.26887			−0.174292			−0.0871462	+	0.996196i	$0.527775\pi$
$54$		0			0
$55$	−5.33021	−	1.04888i	−0.718725	−	0.141430i
$56$		0			0
$57$	−0.741667	−	0.673313i	−0.0982362	−	0.0891825i
$58$		0			0
$59$	−7.78774			−1.01388			−0.506939	−	0.861982i	$-0.669223\pi$
$59$	−7.78774			−1.01388			−0.506939	+	0.861982i	$0.669223\pi$
$60$		0			0
$61$	6.67609			0.854786			0.427393	−	0.904066i	$-0.359432\pi$
$61$	6.67609			0.854786			0.427393	+	0.904066i	$0.359432\pi$
$62$		0			0
$63$	−1.22113	−	12.6097i	−0.153847	−	1.58867i
$64$		0			0
$65$	2.30123	−	11.6944i	0.285432	−	1.45052i
$66$		0			0
$67$	−0.113805			−0.0139035			−0.00695174	−	0.999976i	$-0.502213\pi$
$67$	−0.113805			−0.0139035			−0.00695174	+	0.999976i	$0.502213\pi$
$68$		0			0
$69$	6.91638	+	6.27895i	0.832634	+	0.755897i
$70$		0			0
$71$	8.31277			0.986545			0.493272	−	0.869875i	$-0.335801\pi$
$71$	8.31277			0.986545			0.493272	+	0.869875i	$0.335801\pi$
$72$		0			0
$73$		−	13.1027i		−	1.53355i	−0.641915	−	0.766775i	$-0.721860\pi$
$73$		−	13.1027i		−	1.53355i	0.641915	−	0.766775i	$-0.278140\pi$
$74$		0			0
$75$	7.81656	−	3.72845i	0.902579	−	0.430524i
$76$		0			0
$77$	−10.2593			−1.16916
$78$		0			0
$79$			3.42166i			0.384967i	0.981300	+	0.192484i	$0.0616542\pi$
$79$			3.42166i			0.384967i	−0.981300	+	0.192484i	$0.938346\pi$
$80$		0			0
$81$	−8.83276	+	1.72693i	−0.981418	+	0.191881i
$82$		0			0
$83$			5.68395i			0.623894i	0.950099	+	0.311947i	$0.100981\pi$
$83$			5.68395i			0.623894i	−0.950099	+	0.311947i	$0.899019\pi$
$84$		0			0
$85$	−7.83276	−	1.54133i	−0.849582	−	0.167180i
$86$		0			0
$87$	−6.55133	−	5.94755i	−0.702377	−	0.637644i
$88$		0			0
$89$		−	4.85891i		−	0.515043i	−0.966273	−	0.257522i	$-0.917094\pi$
$89$		−	4.85891i		−	0.515043i	0.966273	−	0.257522i	$-0.0829059\pi$
$90$		0			0
$91$		−	22.5089i		−	2.35957i
$92$		0			0
$93$	10.0448	+	9.11908i	1.04160	+	0.945605i
$94$		0			0
$95$	0.249687	−	1.26887i	0.0256174	−	0.130183i
$96$		0			0
$97$			9.31379i			0.945672i	0.881151	+	0.472836i	$0.156770\pi$
$97$			9.31379i			0.945672i	−0.881151	+	0.472836i	$0.843230\pi$
$98$		0			0
$99$	0.702522	+	7.25443i	0.0706061	+	0.729097i
$100$		0			0
$101$		−	13.4214i		−	1.33548i	−0.744396	−	0.667738i	$-0.767263\pi$
$101$		−	13.4214i		−	1.33548i	0.744396	−	0.667738i	$-0.232737\pi$
$102$		0			0
$103$	−1.78063			−0.175451			−0.0877256	−	0.996145i	$-0.527960\pi$
$103$	−1.78063			−0.175451			−0.0877256	+	0.996145i	$0.527960\pi$
$104$		0			0
$105$	13.1246	−	9.75897i	1.28083	−	0.952378i
$106$		0			0
$107$			16.9977i			1.64323i	0.570046	+	0.821613i	$0.306925\pi$
$107$			16.9977i			1.64323i	−0.570046	+	0.821613i	$0.693075\pi$
$108$		0			0
$109$	−7.83276			−0.750243			−0.375121	−	0.926976i	$-0.622399\pi$
$109$	−7.83276			−0.750243			−0.375121	+	0.926976i	$0.622399\pi$
$110$		0			0
$111$	9.96750	+	9.04888i	0.946074	+	0.858881i
$112$		0			0
$113$	18.0029			1.69357			0.846786	−	0.531933i	$-0.178534\pi$
$113$	18.0029			1.69357			0.846786	+	0.531933i	$0.178534\pi$
$114$		0			0
$115$	−2.32845	+	11.8328i	−0.217129	+	1.10341i
$116$		0			0
$117$	−15.9162	+	1.54133i	−1.47145	+	0.142496i
$118$		0			0
$119$	−15.0761			−1.38202
$120$		0			0
$121$	−5.09775			−0.463432
$122$		0			0
$123$	0.787118	+	0.714576i	0.0709721	+	0.0644311i
$124$		0			0
$125$	9.33418	+	6.15411i	0.834875	+	0.550440i
$126$		0			0
$127$	−8.01176			−0.710929			−0.355465	−	0.934690i	$-0.615677\pi$
$127$	−8.01176			−0.710929			−0.355465	+	0.934690i	$0.615677\pi$
$128$		0			0
$129$	−2.71083	+	2.98603i	−0.238675	+	0.262905i
$130$		0			0
$131$	7.78774			0.680418			0.340209	−	0.940350i	$-0.389502\pi$
$131$	7.78774			0.680418			0.340209	+	0.940350i	$0.389502\pi$
$132$		0			0
$133$		−	2.44225i		−	0.211770i
$134$		0			0
$135$	−7.79936	−	8.61220i	−0.671262	−	0.741220i
$136$		0			0
$137$	−15.4652			−1.32128			−0.660640	−	0.750703i	$-0.729715\pi$
$137$	−15.4652			−1.32128			−0.660640	+	0.750703i	$0.729715\pi$
$138$		0			0
$139$		−	0.578337i		−	0.0490539i	−0.999699	−	0.0245270i	$-0.992192\pi$
$139$		−	0.578337i		−	0.0490539i	0.999699	−	0.0245270i	$-0.00780796\pi$
$140$		0			0
$141$	4.33804	+	3.93824i	0.365329	+	0.331660i
$142$		0			0
$143$			12.9495i			1.08289i
$144$		0			0
$145$	2.20555	−	11.2082i	0.183161	−	0.930792i
$146$		0			0
$147$	12.6118	−	13.8921i	1.04020	−	1.14580i
$148$		0			0
$149$			15.9396i			1.30582i	0.757435	+	0.652910i	$0.226452\pi$
$149$			15.9396i			1.30582i	−0.757435	+	0.652910i	$0.773548\pi$
$150$		0			0
$151$		−	12.5783i		−	1.02361i	−0.859101	−	0.511805i	$-0.828977\pi$
$151$		−	12.5783i		−	1.02361i	0.859101	−	0.511805i	$-0.171023\pi$
$152$		0			0
$153$	1.03236	+	10.6604i	0.0834613	+	0.861843i
$154$		0			0
$155$	−3.38166	+	17.1850i	−0.271622	+	1.38033i
$156$		0			0
$157$			10.8551i			0.866332i	0.901314	+	0.433166i	$0.142604\pi$
$157$			10.8551i			0.866332i	−0.901314	+	0.433166i	$0.857396\pi$
$158$		0			0
$159$	−1.47725	+	1.62721i	−0.117153	+	0.129046i
$160$		0			0
$161$			22.7751i			1.79493i
$162$		0			0
$163$	9.19998			0.720598			0.360299	−	0.932837i	$-0.382675\pi$
$163$	9.19998			0.720598			0.360299	+	0.932837i	$0.382675\pi$
$164$		0			0
$165$	−7.55064	+	5.61440i	−0.587817	+	0.437081i
$166$		0			0
$167$			1.74693i			0.135182i	0.997713	+	0.0675909i	$0.0215313\pi$
$167$			1.74693i			0.135182i	−0.997713	+	0.0675909i	$0.978469\pi$
$168$		0			0
$169$	−15.4111			−1.18547
$170$		0			0
$171$	−1.72693	+	0.167237i	−0.132062	+	0.0127889i
$172$		0			0
$173$	−8.56151			−0.650919			−0.325460	−	0.945556i	$-0.605519\pi$
$173$	−8.56151			−0.650919			−0.325460	+	0.945556i	$0.605519\pi$
$174$		0			0
$175$	19.5402	+	8.00000i	1.47710	+	0.604743i
$176$		0			0
$177$	−9.06666	+	9.98710i	−0.681492	+	0.750676i
$178$		0			0
$179$	11.2416			0.840237			0.420118	−	0.907469i	$-0.361989\pi$
$179$	11.2416			0.840237			0.420118	+	0.907469i	$0.361989\pi$
$180$		0			0
$181$	−0.843326			−0.0626839			−0.0313420	−	0.999509i	$-0.509978\pi$
$181$	−0.843326			−0.0626839			−0.0313420	+	0.999509i	$0.509978\pi$
$182$		0			0
$183$	7.77246	−	8.56151i	0.574557	−	0.632885i
$184$		0			0
$185$	−3.35563	+	17.0527i	−0.246711	+	1.25374i
$186$		0			0
$187$	8.67338			0.634260
$188$		0			0
$189$	−17.5925	−	13.1145i	−1.27966	−	0.953938i
$190$		0			0
$191$	18.5300			1.34078			0.670391	−	0.742008i	$-0.266127\pi$
$191$	18.5300			1.34078			0.670391	+	0.742008i	$0.266127\pi$
$192$		0			0
$193$		−	2.44225i		−	0.175797i	−0.996129	−	0.0878986i	$-0.971985\pi$
$193$		−	2.44225i		−	0.175797i	0.996129	−	0.0878986i	$-0.0280151\pi$
$194$		0			0
$195$	−12.3180	−	16.5661i	−0.882108	−	1.18632i
$196$		0			0
$197$	5.44239			0.387754			0.193877	−	0.981026i	$-0.437894\pi$
$197$	5.44239			0.387754			0.193877	+	0.981026i	$0.437894\pi$
$198$		0			0
$199$		−	6.67609i		−	0.473255i	−0.971600	−	0.236628i	$-0.923958\pi$
$199$		−	6.67609i		−	0.473255i	0.971600	−	0.236628i	$-0.0760422\pi$
$200$		0			0
$201$	−0.132494	+	0.145945i	−0.00934543	+	0.0102942i
$202$		0			0
$203$		−	21.5730i		−	1.51413i
$204$		0			0
$205$	−0.264989	+	1.34663i	−0.0185076	+	0.0940525i
$206$		0			0
$207$	16.1044	−	1.55956i	1.11933	−	0.108397i
$208$		0			0
$209$			1.40504i			0.0971889i
$210$		0			0
$211$		−	8.57834i		−	0.590557i	−0.955411	−	0.295279i	$-0.904588\pi$
$211$		−	8.57834i		−	0.590557i	0.955411	−	0.295279i	$-0.0954124\pi$
$212$		0			0
$213$	9.67792	−	10.6604i	0.663120	−	0.730439i
$214$		0			0
$215$	−5.10860	−	1.00527i	−0.348403	−	0.0685587i
$216$		0			0
$217$			33.0769i			2.24540i
$218$		0			0
$219$	−16.8030	−	15.2544i	−1.13544	−	1.03080i
$220$		0			0
$221$			19.0293i			1.28005i
$222$		0			0
$223$	3.12726			0.209417			0.104708	−	0.994503i	$-0.466609\pi$
$223$	3.12726			0.209417			0.104708	+	0.994503i	$0.466609\pi$
$224$		0			0
$225$	4.31881	−	14.3648i	0.287921	−	0.957654i
$226$		0			0
$227$		−	0.929043i		−	0.0616627i	−0.999525	−	0.0308314i	$-0.990185\pi$
$227$		−	0.929043i		−	0.0616627i	0.999525	−	0.0308314i	$-0.00981548\pi$
$228$		0			0
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$		0			0
$231$	−11.9441	+	13.1567i	−0.785866	+	0.865646i
$232$		0			0
$233$	6.10783			0.400137			0.200069	−	0.979782i	$-0.435883\pi$
$233$	6.10783			0.400137			0.200069	+	0.979782i	$0.435883\pi$
$234$		0			0
$235$	−1.46043	+	7.42166i	−0.0952681	+	0.484136i
$236$		0			0
$237$	4.38799	+	3.98358i	0.285030	+	0.258761i
$238$		0			0
$239$	15.0761			0.975192			0.487596	−	0.873069i	$-0.337874\pi$
$239$	15.0761			0.975192			0.487596	+	0.873069i	$0.337874\pi$
$240$		0			0
$241$	−25.4005			−1.63619			−0.818096	−	0.575081i	$-0.804970\pi$
$241$	−25.4005			−1.63619			−0.818096	+	0.575081i	$0.804970\pi$
$242$		0			0
$243$	−8.06867	+	13.3378i	−0.517605	+	0.855620i
$244$		0			0
$245$	23.7670	+	4.67686i	1.51842	+	0.298794i
$246$		0			0
$247$	−3.08266			−0.196145
$248$		0			0
$249$	7.28917	+	6.61738i	0.461932	+	0.419360i
$250$		0			0
$251$	−22.8638			−1.44315			−0.721576	−	0.692335i	$-0.756582\pi$
$251$	−22.8638			−1.44315			−0.721576	+	0.692335i	$0.756582\pi$
$252$		0			0
$253$		−	13.1027i		−	0.823757i
$254$		0			0
$255$	−11.0957	+	8.25039i	−0.694840	+	0.516660i
$256$		0			0
$257$	−13.8294			−0.862654			−0.431327	−	0.902196i	$-0.641955\pi$
$257$	−13.8294			−0.862654			−0.431327	+	0.902196i	$0.641955\pi$
$258$		0			0
$259$			32.8222i			2.03947i
$260$		0			0
$261$	−15.2544	+	1.47725i	−0.944225	+	0.0914392i
$262$		0			0
$263$			26.9663i			1.66281i	0.555666	+	0.831406i	$0.312463\pi$
$263$			26.9663i			1.66281i	−0.555666	+	0.831406i	$0.687537\pi$
$264$		0			0
$265$	−2.78389	−	0.547812i	−0.171013	−	0.0336518i
$266$		0			0
$267$	−6.23113	−	5.65685i	−0.381339	−	0.346194i
$268$		0			0
$269$			7.94868i			0.484640i	0.970196	+	0.242320i	$0.0779083\pi$
$269$			7.94868i			0.484640i	−0.970196	+	0.242320i	$0.922092\pi$
$270$		0			0
$271$		−	12.5783i		−	0.764080i	−0.924146	−	0.382040i	$-0.875222\pi$
$271$		−	12.5783i		−	0.764080i	0.924146	−	0.382040i	$-0.124778\pi$
$272$		0			0
$273$	−28.8657	−	26.2053i	−1.74703	−	1.58602i
$274$		0			0
$275$	−11.2416	−	4.60245i	−0.677894	−	0.277538i
$276$		0			0
$277$		−	4.68980i		−	0.281783i	−0.990025	−	0.140891i	$-0.955003\pi$
$277$		−	4.68980i		−	0.281783i	0.990025	−	0.140891i	$-0.0449969\pi$
$278$		0			0
$279$	23.3889	−	2.26499i	1.40026	−	0.135601i
$280$		0			0
$281$		−	15.6899i		−	0.935980i	−0.883734	−	0.467990i	$-0.844978\pi$
$281$		−	15.6899i		−	0.935980i	0.883734	−	0.467990i	$-0.155022\pi$
$282$		0			0
$283$	−24.5173			−1.45740			−0.728701	−	0.684832i	$-0.759875\pi$
$283$	−24.5173			−1.45740			−0.728701	+	0.684832i	$0.759875\pi$
$284$		0			0
$285$	−1.33652	−	1.79745i	−0.0791687	−	0.106472i
$286$		0			0
$287$			2.59192i			0.152996i
$288$		0			0
$289$	−4.25443			−0.250260
$290$		0			0
$291$	11.9441	+	10.8433i	0.700177	+	0.635647i
$292$		0			0
$293$	8.99044			0.525227			0.262614	−	0.964901i	$-0.415416\pi$
$293$	8.99044			0.525227			0.262614	+	0.964901i	$0.415416\pi$
$294$		0			0
$295$	−17.0862	−	3.36222i	−0.994800	−	0.195756i
$296$		0			0
$297$	10.1211	+	7.54485i	0.587284	+	0.437796i
$298$		0			0
$299$	28.7472			1.66249
$300$		0			0
$301$	−9.83276			−0.566751
$302$		0			0
$303$	−17.2117	−	15.6255i	−0.988789	−	0.897660i
$304$		0			0
$305$	14.6473	+	2.88229i	0.838702	+	0.165039i
$306$		0			0
$307$	−29.8804			−1.70536			−0.852682	−	0.522430i	$-0.825026\pi$
$307$	−29.8804			−1.70536			−0.852682	+	0.522430i	$0.825026\pi$
$308$		0			0
$309$	−2.07306	+	2.28351i	−0.117932	+	0.129904i
$310$		0			0
$311$	−32.2010			−1.82595			−0.912976	−	0.408013i	$-0.866222\pi$
$311$	−32.2010			−1.82595			−0.912976	+	0.408013i	$0.866222\pi$
$312$		0			0
$313$			8.67338i			0.490248i	0.969492	+	0.245124i	$0.0788288\pi$
$313$			8.67338i			0.490248i	−0.969492	+	0.245124i	$0.921171\pi$
$314$		0			0
$315$	2.76487	−	28.1927i	0.155783	−	1.58848i
$316$		0			0
$317$	−23.4233			−1.31558			−0.657791	−	0.753201i	$-0.728509\pi$
$317$	−23.4233			−1.31558			−0.657791	+	0.753201i	$0.728509\pi$
$318$		0			0
$319$			12.4111i			0.694888i
$320$		0			0
$321$	21.7980	+	19.7891i	1.21665	+	1.10452i
$322$		0			0
$323$			2.06472i			0.114884i
$324$		0			0
$325$	10.0978	−	24.6640i	0.560122	−	1.36811i
$326$		0			0
$327$	−9.11908	+	10.0448i	−0.504287	+	0.555481i
$328$		0			0
$329$			14.2848i			0.787548i
$330$		0			0
$331$			22.7527i			1.25060i	0.780384	+	0.625301i	$0.215024\pi$
$331$			22.7527i			1.25060i	−0.780384	+	0.625301i	$0.784976\pi$
$332$		0			0
$333$	23.2088	−	2.24755i	1.27183	−	0.123165i
$334$		0			0
$335$	−0.249687	−	0.0491334i	−0.0136419	−	0.00268444i
$336$		0			0
$337$		−	14.4493i		−	0.787103i	−0.919303	−	0.393552i	$-0.871246\pi$
$337$		−	14.4493i		−	0.787103i	0.919303	−	0.393552i	$-0.128754\pi$
$338$		0			0
$339$	20.9594	−	23.0872i	1.13836	−	1.25392i
$340$		0			0
$341$		−	19.0293i		−	1.03050i
$342$		0			0
$343$	16.1853			0.873925
$344$		0			0
$345$	12.4637	+	16.7620i	0.671021	+	0.902436i
$346$		0			0
$347$		−	5.83640i		−	0.313314i	−0.987653	−	0.156657i	$-0.949928\pi$
$347$		−	5.83640i		−	0.313314i	0.987653	−	0.156657i	$-0.0500717\pi$
$348$		0			0
$349$	31.9789			1.71179			0.855895	−	0.517150i	$-0.173007\pi$
$349$	31.9789			1.71179			0.855895	+	0.517150i	$0.173007\pi$
$350$		0			0
$351$	−16.5533	+	22.2056i	−0.883552	+	1.18524i
$352$		0			0
$353$	18.0029			0.958199			0.479099	−	0.877761i	$-0.340963\pi$
$353$	18.0029			0.958199			0.479099	+	0.877761i	$0.340963\pi$
$354$		0			0
$355$	18.2382	+	3.58890i	0.967982	+	0.190479i
$356$		0			0
$357$	−17.5519	+	19.3338i	−0.928948	+	1.02325i
$358$		0			0
$359$	13.6711			0.721531			0.360765	−	0.932657i	$-0.382516\pi$
$359$	13.6711			0.721531			0.360765	+	0.932657i	$0.382516\pi$
$360$		0			0
$361$	18.6655			0.982396
$362$		0			0
$363$	−5.93492	+	6.53743i	−0.311503	+	0.343126i
$364$		0			0
$365$	5.65685	−	28.7472i	0.296093	−	1.50469i
$366$		0			0
$367$	−4.45050			−0.232314			−0.116157	−	0.993231i	$-0.537058\pi$
$367$	−4.45050			−0.232314			−0.116157	+	0.993231i	$0.537058\pi$
$368$		0			0
$369$	1.83276	−	0.177486i	0.0954098	−	0.00923953i
$370$		0			0
$371$	−5.35828			−0.278188
$372$		0			0
$373$			15.3502i			0.794804i	0.917645	+	0.397402i	$0.130088\pi$
$373$			15.3502i			0.794804i	−0.917645	+	0.397402i	$0.869912\pi$
$374$		0			0
$375$	18.7592	−	4.80553i	0.968720	−	0.248156i
$376$		0			0
$377$	−27.2299			−1.40241
$378$		0			0
$379$		−	12.7738i		−	0.656148i	−0.944652	−	0.328074i	$-0.893600\pi$
$379$		−	12.7738i		−	0.656148i	0.944652	−	0.328074i	$-0.106400\pi$
$380$		0			0
$381$	−9.32748	+	10.2744i	−0.477861	+	0.526373i
$382$		0			0
$383$		−	30.6668i		−	1.56700i	−0.621392	−	0.783499i	$-0.713433\pi$
$383$		−	30.6668i		−	1.56700i	0.621392	−	0.783499i	$-0.286567\pi$
$384$		0			0
$385$	−22.5089	−	4.42928i	−1.14716	−	0.225737i
$386$		0			0
$387$	0.673313	+	6.95281i	0.0342264	+	0.353431i
$388$		0			0
$389$		−	14.5345i		−	0.736930i	−0.929642	−	0.368465i	$-0.879884\pi$
$389$		−	14.5345i		−	0.736930i	0.929642	−	0.368465i	$-0.120116\pi$
$390$		0			0
$391$		−	19.2544i		−	0.973738i
$392$		0			0
$393$	9.06666	−	9.98710i	0.457353	−	0.503783i
$394$		0			0
$395$	−1.47725	+	7.50711i	−0.0743283	+	0.377723i
$396$		0			0
$397$			28.4529i			1.42801i	0.700141	+	0.714005i	$0.253120\pi$
$397$			28.4529i			1.42801i	−0.700141	+	0.714005i	$0.746880\pi$
$398$		0			0
$399$	−3.13198	−	2.84333i	−0.156795	−	0.142344i
$400$		0			0
$401$		−	31.7016i		−	1.58310i	−0.611101	−	0.791552i	$-0.709273\pi$
$401$		−	31.7016i		−	1.58310i	0.611101	−	0.791552i	$-0.290727\pi$
$402$		0			0
$403$	41.7502			2.07973
$404$		0			0
$405$	−20.1246	−	0.0245181i	−0.999999	−	0.00121832i
$406$		0			0
$407$		−	18.8828i		−	0.935987i
$408$		0			0
$409$	3.83276			0.189518			0.0947590	−	0.995500i	$-0.469792\pi$
$409$	3.83276			0.189518			0.0947590	+	0.995500i	$0.469792\pi$
$410$		0			0
$411$	−18.0049	+	19.8328i	−0.888118	+	0.978278i
$412$		0			0
$413$	−32.8867			−1.61825
$414$		0			0
$415$	−2.45395	+	12.4705i	−0.120460	+	0.612155i
$416$		0			0
$417$	−0.741667	−	0.673313i	−0.0363196	−	0.0329723i
$418$		0			0
$419$	−14.1961			−0.693525			−0.346762	−	0.937953i	$-0.612719\pi$
$419$	−14.1961			−0.693525			−0.346762	+	0.937953i	$0.612719\pi$
$420$		0			0
$421$	24.9894			1.21791			0.608955	−	0.793205i	$-0.291589\pi$
$421$	24.9894			1.21791			0.608955	+	0.793205i	$0.291589\pi$
$422$		0			0
$423$	10.1009	−	0.978176i	0.491123	−	0.0475605i
$424$		0			0
$425$	−16.5196	−	6.76333i	−0.801318	−	0.328070i
$426$		0			0
$427$	28.1924			1.36432
$428$		0			0
$429$	16.6066	+	15.0761i	0.801774	+	0.727881i
$430$		0			0
$431$	−22.8895			−1.10255			−0.551274	−	0.834324i	$-0.685858\pi$
$431$	−22.8895			−1.10255			−0.551274	+	0.834324i	$0.685858\pi$
$432$		0			0
$433$			16.8915i			0.811756i	0.913927	+	0.405878i	$0.133034\pi$
$433$			16.8915i			0.811756i	−0.913927	+	0.405878i	$0.866966\pi$
$434$		0			0
$435$	−11.8058	−	15.8773i	−0.566046	−	0.761258i
$436$		0			0
$437$	3.11912			0.149208
$438$		0			0
$439$		−	0.989437i		−	0.0472233i	−0.999721	−	0.0236116i	$-0.992483\pi$
$439$		−	0.989437i		−	0.0472233i	0.999721	−	0.0236116i	$-0.00751651\pi$
$440$		0			0
$441$	−3.13249	−	32.3470i	−0.149166	−	1.54033i
$442$		0			0
$443$		−	14.4599i		−	0.687011i	−0.939151	−	0.343506i	$-0.888386\pi$
$443$		−	14.4599i		−	0.687011i	0.939151	−	0.343506i	$-0.111614\pi$
$444$		0			0
$445$	2.09775	−	10.6604i	0.0994430	−	0.505352i
$446$		0			0
$447$	20.4411	+	18.5572i	0.966832	+	0.877726i
$448$		0			0
$449$		−	25.9071i		−	1.22263i	−0.791387	−	0.611315i	$-0.790641\pi$
$449$		−	25.9071i		−	1.22263i	0.791387	−	0.611315i	$-0.209359\pi$
$450$		0			0
$451$		−	1.49115i		−	0.0702154i
$452$		0			0
$453$	−16.1306	−	14.6440i	−0.757883	−	0.688035i
$454$		0			0
$455$	9.71782	−	49.3843i	0.455578	−	2.31517i
$456$		0			0
$457$		−	39.5590i		−	1.85049i	−0.379368	−	0.925246i	$-0.623859\pi$
$457$		−	39.5590i		−	1.85049i	0.379368	−	0.925246i	$-0.376141\pi$
$458$		0			0
$459$	14.8730	+	11.0872i	0.694210	+	0.517506i
$460$		0			0
$461$			11.5170i			0.536398i	0.963364	+	0.268199i	$0.0864285\pi$
$461$			11.5170i			0.536398i	−0.963364	+	0.268199i	$0.913572\pi$
$462$		0			0
$463$	−37.0721			−1.72289			−0.861444	−	0.507852i	$-0.830440\pi$
$463$	−37.0721			−1.72289			−0.861444	+	0.507852i	$0.830440\pi$
$464$		0			0
$465$	18.1013	+	24.3439i	0.839428	+	1.12892i
$466$		0			0
$467$			16.4163i			0.759654i	0.925057	+	0.379827i	$0.124017\pi$
$467$			16.4163i			0.759654i	−0.925057	+	0.379827i	$0.875983\pi$
$468$		0			0
$469$	−0.480585			−0.0221914
$470$		0			0
$471$	13.9207	+	12.6378i	0.641434	+	0.582318i
$472$		0			0
$473$	5.65685			0.260102
$474$		0			0
$475$	1.09562	−	2.67609i	0.0502707	−	0.122787i
$476$		0			0
$477$	0.366917	+	3.78888i	0.0168000	+	0.173481i
$478$		0			0
$479$	18.5300			0.846656			0.423328	−	0.905977i	$-0.360862\pi$
$479$	18.5300			0.846656			0.423328	+	0.905977i	$0.360862\pi$
$480$		0			0
$481$	41.4288			1.88899
$482$		0			0
$483$	29.2071	+	26.5153i	1.32897	+	1.20649i
$484$		0			0
$485$	−4.02107	+	20.4344i	−0.182587	+	0.927878i
$486$		0			0
$487$	21.9824			0.996120			0.498060	−	0.867143i	$-0.334046\pi$
$487$	21.9824			0.996120			0.498060	+	0.867143i	$0.334046\pi$
$488$		0			0
$489$	10.7108	−	11.7982i	0.484361	−	0.533532i
$490$		0			0
$491$	42.7988			1.93148			0.965742	−	0.259502i	$-0.0835586\pi$
$491$	42.7988			1.93148			0.965742	+	0.259502i	$0.0835586\pi$
$492$		0			0
$493$			18.2382i			0.821406i
$494$		0			0
$495$	−1.59065	+	16.2195i	−0.0714943	+	0.729011i
$496$		0			0
$497$	35.1039			1.57462
$498$		0			0
$499$		−	23.0872i		−	1.03352i	−0.856129	−	0.516762i	$-0.827137\pi$
$499$		−	23.0872i		−	1.03352i	0.856129	−	0.516762i	$-0.172863\pi$
$500$		0			0
$501$	2.24029	+	2.03382i	0.100089	+	0.0908645i
$502$		0			0
$503$			33.5793i			1.49723i	0.663008	+	0.748613i	$0.269280\pi$
$503$			33.5793i			1.49723i	−0.663008	+	0.748613i	$0.730720\pi$
$504$		0			0
$505$	5.79445	−	29.4464i	0.257850	−	1.31035i
$506$		0			0
$507$	−17.9420	+	19.7634i	−0.796830	+	0.877724i
$508$		0			0
$509$		−	34.3551i		−	1.52276i	−0.648303	−	0.761382i	$-0.724521\pi$
$509$		−	34.3551i		−	1.52276i	0.648303	−	0.761382i	$-0.275479\pi$
$510$		0			0
$511$		−	55.3311i		−	2.44770i
$512$		0			0
$513$	−1.79607	+	2.40934i	−0.0792983	+	0.106375i
$514$		0			0
$515$	−3.90670	−	0.768759i	−0.172150	−	0.0338756i
$516$		0			0
$517$		−	8.21816i		−	0.361434i
$518$		0			0
$519$	−9.96750	+	10.9794i	−0.437525	+	0.481942i
$520$		0			0
$521$		−	10.2172i		−	0.447623i	−0.974632	−	0.223812i	$-0.928150\pi$
$521$		−	10.2172i		−	0.447623i	0.974632	−	0.223812i	$-0.0718500\pi$
$522$		0			0
$523$	−9.65520			−0.422192			−0.211096	−	0.977465i	$-0.567703\pi$
$523$	−9.65520			−0.422192			−0.211096	+	0.977465i	$0.567703\pi$
$524$		0			0
$525$	33.0085	−	15.7448i	1.44061	−	0.687160i
$526$		0			0
$527$		−	27.9637i		−	1.21812i
$528$		0			0
$529$	−6.08719			−0.264660
$530$		0			0
$531$	2.25197	+	23.2544i	0.0977271	+	1.00916i
$532$		0			0
$533$	3.27157			0.141707
$534$		0			0
$535$	−7.33845	+	37.2927i	−0.317269	+	1.61231i
$536$		0			0
$537$	13.0877	−	14.4164i	0.564777	−	0.622113i
$538$		0			0
$539$	−26.3177			−1.13358
$540$		0			0
$541$	−22.8222			−0.981203			−0.490602	−	0.871384i	$-0.663223\pi$
$541$	−22.8222			−0.981203			−0.490602	+	0.871384i	$0.663223\pi$
$542$		0			0
$543$	−0.981820	+	1.08149i	−0.0421339	+	0.0464113i
$544$		0			0
$545$	−17.1850	−	3.38166i	−0.736126	−	0.144855i
$546$		0			0
$547$	−12.9889			−0.555364			−0.277682	−	0.960673i	$-0.589566\pi$
$547$	−12.9889			−0.555364			−0.277682	+	0.960673i	$0.589566\pi$
$548$		0			0
$549$	−1.93051	−	19.9350i	−0.0823924	−	0.850805i
$550$		0			0
$551$	−2.95449			−0.125866
$552$		0			0
$553$			14.4493i			0.614446i
$554$		0			0
$555$	17.9619	+	24.1565i	0.762442	+	1.02539i
$556$		0			0
$557$	14.0659			0.595992			0.297996	−	0.954567i	$-0.403682\pi$
$557$	14.0659			0.595992			0.297996	+	0.954567i	$0.403682\pi$
$558$		0			0
$559$			12.4111i			0.524934i
$560$		0			0
$561$	10.0978	−	11.1229i	0.426327	−	0.469608i
$562$		0			0
$563$		−	20.7964i		−	0.876465i	−0.898862	−	0.438232i	$-0.855605\pi$
$563$		−	20.7964i		−	0.876465i	0.898862	−	0.438232i	$-0.144395\pi$
$564$		0			0
$565$	39.4983	+	7.77246i	1.66171	+	0.326990i
$566$		0			0
$567$	−37.2997	+	7.29264i	−1.56644	+	0.306262i
$568$		0			0
$569$			25.7296i			1.07864i	0.842101	+	0.539320i	$0.181319\pi$
$569$			25.7296i			1.07864i	−0.842101	+	0.539320i	$0.818681\pi$
$570$		0			0
$571$		−	41.4005i		−	1.73256i	−0.499560	−	0.866279i	$-0.666505\pi$
$571$		−	41.4005i		−	1.73256i	0.499560	−	0.866279i	$-0.333495\pi$
$572$		0			0
$573$	21.5730	−	23.7631i	0.901226	−	0.992717i
$574$		0			0
$575$	−10.2172	+	24.9557i	−0.426086	+	1.04073i
$576$		0			0
$577$			22.0270i			0.916998i	0.888695	+	0.458499i	$0.151613\pi$
$577$			22.0270i			0.916998i	−0.888695	+	0.458499i	$0.848387\pi$
$578$		0			0
$579$	−3.13198	−	2.84333i	−0.130160	−	0.118165i
$580$		0			0
$581$			24.0027i			0.995798i
$582$		0			0
$583$	3.08266			0.127671
$584$		0			0
$585$	−35.5854	−	3.48987i	−1.47127	−	0.144288i
$586$		0			0
$587$		−	23.5565i		−	0.972279i	−0.873881	−	0.486140i	$-0.838405\pi$
$587$		−	23.5565i		−	0.972279i	0.873881	−	0.486140i	$-0.161595\pi$
$588$		0			0
$589$	4.52998			0.186654
$590$		0			0
$591$	6.33615	−	6.97939i	0.260635	−	0.287094i
$592$		0			0
$593$	21.2745			0.873639			0.436819	−	0.899549i	$-0.356105\pi$
$593$	21.2745			0.873639			0.436819	+	0.899549i	$0.356105\pi$
$594$		0			0
$595$	−33.0769	−	6.50885i	−1.35602	−	0.266837i
$596$		0			0
$597$	−8.56151	−	7.77246i	−0.350399	−	0.318106i
$598$		0			0
$599$	3.30946			0.135221			0.0676105	−	0.997712i	$-0.478462\pi$
$599$	3.30946			0.135221			0.0676105	+	0.997712i	$0.478462\pi$
$600$		0			0
$601$	9.51941			0.388305			0.194153	−	0.980971i	$-0.437804\pi$
$601$	9.51941			0.388305			0.194153	+	0.980971i	$0.437804\pi$
$602$		0			0
$603$	0.0329088	+	0.339825i	0.00134015	+	0.0138387i
$604$		0			0
$605$	−11.1844	−	2.20087i	−0.454712	−	0.0894780i
$606$		0			0
$607$	20.6358			0.837582			0.418791	−	0.908083i	$-0.362454\pi$
$607$	20.6358			0.837582			0.418791	+	0.908083i	$0.362454\pi$
$608$		0			0
$609$	−27.6655	−	25.1158i	−1.12106	−	1.01774i
$610$		0			0
$611$	18.0306			0.729440
$612$		0			0
$613$			2.63695i			0.106506i	0.998581	+	0.0532528i	$0.0169589\pi$
$613$			2.63695i			0.106506i	−0.998581	+	0.0532528i	$0.983041\pi$
$614$		0			0
$615$	1.41843	+	1.90760i	0.0571965	+	0.0769218i
$616$		0			0
$617$	−5.20588			−0.209581			−0.104790	−	0.994494i	$-0.533417\pi$
$617$	−5.20588			−0.209581			−0.104790	+	0.994494i	$0.533417\pi$
$618$		0			0
$619$			45.9305i			1.84610i	0.384676	+	0.923052i	$0.374313\pi$
$619$			45.9305i			1.84610i	−0.384676	+	0.923052i	$0.625687\pi$
$620$		0			0
$621$	16.7491	−	22.4682i	0.672120	−	0.901618i
$622$		0			0
$623$		−	20.5186i		−	0.822061i
$624$		0			0
$625$	17.8222	+	17.5319i	0.712888	+	0.701278i
$626$		0			0
$627$	1.80185	+	1.63578i	0.0719588	+	0.0653269i
$628$		0			0
$629$		−	27.7484i		−	1.10640i
$630$		0			0
$631$		−	12.3627i		−	0.492153i	−0.969250	−	0.246076i	$-0.920859\pi$
$631$		−	12.3627i		−	0.492153i	0.969250	−	0.246076i	$-0.0791414\pi$
$632$		0			0
$633$	−11.0010	−	9.98710i	−0.437249	−	0.396952i
$634$		0			0
$635$	−17.5778	−	3.45894i	−0.697552	−	0.137264i
$636$		0			0
$637$		−	57.7409i		−	2.28778i
$638$		0			0
$639$	−2.40379	−	24.8222i	−0.0950926	−	0.981951i
$640$		0			0
$641$			25.9071i			1.02327i	0.859204	+	0.511634i	$0.170960\pi$
$641$			25.9071i			1.02327i	−0.859204	+	0.511634i	$0.829040\pi$
$642$		0			0
$643$	−30.5866			−1.20622			−0.603109	−	0.797659i	$-0.706072\pi$
$643$	−30.5866			−1.20622			−0.603109	+	0.797659i	$0.706072\pi$
$644$		0			0
$645$	−7.23671	+	5.38098i	−0.284945	+	0.211876i
$646$		0			0
$647$		−	6.97486i		−	0.274210i	−0.990557	−	0.137105i	$-0.956220\pi$
$647$		−	6.97486i		−	0.274210i	0.990557	−	0.137105i	$-0.0437798\pi$
$648$		0			0
$649$	18.9200			0.742673
$650$		0			0
$651$	42.4182	+	38.5089i	1.66250	+	1.50928i
$652$		0			0
$653$	−7.50711			−0.293776			−0.146888	−	0.989153i	$-0.546926\pi$
$653$	−7.50711			−0.293776			−0.146888	+	0.989153i	$0.546926\pi$
$654$		0			0
$655$	17.0862	+	3.36222i	0.667615	+	0.131373i
$656$		0			0
$657$	−39.1250	+	3.78888i	−1.52641	+	0.147818i
$658$		0			0
$659$	−36.5349			−1.42320			−0.711599	−	0.702586i	$-0.752029\pi$
$659$	−36.5349			−1.42320			−0.711599	+	0.702586i	$0.752029\pi$
$660$		0			0
$661$	−30.3416			−1.18015			−0.590076	−	0.807348i	$-0.700902\pi$
$661$	−30.3416			−1.18015			−0.590076	+	0.807348i	$0.700902\pi$
$662$		0			0
$663$	24.4035	+	22.1544i	0.947753	+	0.860406i
$664$		0			0
$665$	1.05440	−	5.35828i	0.0408879	−	0.207785i
$666$		0			0
$667$	27.5520			1.06682
$668$		0			0
$669$	3.64083	−	4.01044i	0.140763	−	0.155053i
$670$		0			0
$671$	−16.2193			−0.626137
$672$		0			0
$673$		−	4.42928i		−	0.170736i	−0.996349	−	0.0853682i	$-0.972793\pi$
$673$		−	4.42928i		−	0.170736i	0.996349	−	0.0853682i	$-0.0272066\pi$
$674$		0			0
$675$	−13.3936	−	22.2623i	−0.515519	−	0.856878i
$676$		0			0
$677$	22.5213			0.865564			0.432782	−	0.901498i	$-0.357532\pi$
$677$	22.5213			0.865564			0.432782	+	0.901498i	$0.357532\pi$
$678$		0			0
$679$			39.3311i			1.50939i
$680$		0			0
$681$	−1.19142	−	1.08161i	−0.0456552	−	0.0414475i
$682$		0			0
$683$		−	31.1256i		−	1.19099i	−0.803360	−	0.595494i	$-0.796956\pi$
$683$		−	31.1256i		−	1.19099i	0.803360	−	0.595494i	$-0.203044\pi$
$684$		0			0
$685$	−33.9305	−	6.67683i	−1.29642	−	0.255109i
$686$		0			0
$687$	−6.98534	+	7.69448i	−0.266507	+	0.293563i
$688$		0			0
$689$			6.76333i			0.257662i
$690$		0			0
$691$		−	36.7738i		−	1.39894i	−0.714661	−	0.699471i	$-0.753419\pi$
$691$		−	36.7738i		−	1.39894i	0.714661	−	0.699471i	$-0.246581\pi$
$692$		0			0
$693$	2.96667	+	30.6346i	0.112694	+	1.16371i
$694$		0			0
$695$	0.249687	−	1.26887i	0.00947118	−	0.0481309i
$696$		0			0
$697$		−	2.19125i		−	0.0829995i
$698$		0			0
$699$	7.11088	−	7.83276i	0.268958	−	0.296262i
$700$		0			0
$701$			12.3082i			0.464875i	0.972611	+	0.232437i	$0.0746701\pi$
$701$			12.3082i			0.464875i	−0.972611	+	0.232437i	$0.925330\pi$
$702$		0			0
$703$	4.49510			0.169536
$704$		0			0
$705$	7.81737	+	10.5133i	0.294419	+	0.395956i
$706$		0			0
$707$		−	56.6769i		−	2.13155i
$708$		0			0
$709$	−16.8433			−0.632564			−0.316282	−	0.948665i	$-0.602435\pi$
$709$	−16.8433			−0.632564			−0.316282	+	0.948665i	$0.602435\pi$
$710$		0			0
$711$	10.2172	−	0.989437i	0.383175	−	0.0371068i
$712$		0			0
$713$	−42.2441			−1.58205
$714$		0			0
$715$	−5.59073	+	28.4111i	−0.209081	+	1.06251i
$716$		0			0
$717$	17.5519	−	19.3338i	0.655489	−	0.722034i
$718$		0			0
$719$	−44.3226			−1.65296			−0.826478	−	0.562970i	$-0.809659\pi$
$719$	−44.3226			−1.65296			−0.826478	+	0.562970i	$0.809659\pi$
$720$		0			0
$721$	−7.51941			−0.280038
$722$		0			0
$723$	−29.5719	+	32.5740i	−1.09979	+	1.21144i
$724$		0			0
$725$	9.67792	−	23.6386i	0.359429	−	0.877914i
$726$		0			0
$727$	−27.7350			−1.02863			−0.514316	−	0.857601i	$-0.671954\pi$
$727$	−27.7350			−1.02863			−0.514316	+	0.857601i	$0.671954\pi$
$728$		0			0
$729$	7.71083	+	25.8755i	0.285586	+	0.958353i
$730$		0			0
$731$	8.31277			0.307459
$732$		0			0
$733$			15.7396i			0.581356i	0.956821	+	0.290678i	$0.0938808\pi$
$733$			15.7396i			0.581356i	−0.956821	+	0.290678i	$0.906119\pi$
$734$		0			0
$735$	33.6678	−	25.0342i	1.24185	−	0.923401i
$736$		0			0
$737$	0.276484			0.0101844
$738$		0			0
$739$		−	27.7139i		−	1.01947i	−0.860331	−	0.509736i	$-0.829743\pi$
$739$		−	27.7139i		−	1.01947i	0.860331	−	0.509736i	$-0.170257\pi$
$740$		0			0
$741$	−3.58890	+	3.95324i	−0.131842	+	0.145226i
$742$		0			0
$743$		−	31.1398i		−	1.14241i	−0.820808	−	0.571204i	$-0.806476\pi$
$743$		−	31.1398i		−	1.14241i	0.820808	−	0.571204i	$-0.193524\pi$
$744$		0			0
$745$	−6.88164	+	34.9713i	−0.252124	+	1.28125i
$746$		0			0
$747$	16.9724	−	1.64362i	0.620989	−	0.0601369i
$748$		0			0
$749$			71.7792i			2.62275i
$750$		0			0
$751$			2.14611i			0.0783127i	0.999233	+	0.0391564i	$0.0124670\pi$
$751$			2.14611i			0.0783127i	−0.999233	+	0.0391564i	$0.987533\pi$
$752$		0			0
$753$	−26.6186	+	29.3209i	−0.970036	+	1.06851i
$754$		0			0
$755$	5.43048	−	27.5968i	0.197636	−	1.00435i
$756$		0			0
$757$			15.3502i			0.557913i	0.960304	+	0.278957i	$0.0899885\pi$
$757$			15.3502i			0.557913i	−0.960304	+	0.278957i	$0.910011\pi$
$758$		0			0
$759$	−16.8030	−	15.2544i	−0.609911	−	0.553701i
$760$		0			0
$761$		−	13.6711i		−	0.495575i	−0.968814	−	0.247788i	$-0.920296\pi$
$761$		−	13.6711i		−	0.495575i	0.968814	−	0.247788i	$-0.0797035\pi$
$762$		0			0
$763$	−33.0769			−1.19746
$764$		0			0
$765$	−2.33746	+	23.8346i	−0.0845112	+	0.861741i
$766$		0			0
$767$			41.5102i			1.49885i
$768$		0			0
$769$	10.7456			0.387495			0.193748	−	0.981051i	$-0.437936\pi$
$769$	10.7456			0.387495			0.193748	+	0.981051i	$0.437936\pi$
$770$		0			0
$771$	−16.1005	+	17.7350i	−0.579846	+	0.638711i
$772$		0			0
$773$	11.3757			0.409156			0.204578	−	0.978850i	$-0.434418\pi$
$773$	11.3757			0.409156			0.204578	+	0.978850i	$0.434418\pi$
$774$		0			0
$775$	−14.8387	+	36.2439i	−0.533022	+	1.30192i
$776$		0			0
$777$	42.0916	+	38.2124i	1.51003	+	1.37086i
$778$		0			0
$779$	0.354971			0.0127182
$780$		0			0
$781$	−20.1955			−0.722652
$782$		0			0
$783$	−15.8651	+	21.2823i	−0.566973	+	0.760568i
$784$		0			0
$785$	−4.68651	+	23.8160i	−0.167269	+	0.850031i
$786$		0			0
$787$	−7.85335			−0.279942			−0.139971	−	0.990156i	$-0.544701\pi$
$787$	−7.85335			−0.279942			−0.139971	+	0.990156i	$0.544701\pi$
$788$		0			0
$789$	34.5819	+	31.3948i	1.23115	+	1.11768i
$790$		0			0
$791$	76.0243			2.70311
$792$		0			0
$793$		−	35.5849i		−	1.26366i
$794$		0			0
$795$	−3.94359	+	2.93232i	−0.139865	+	0.103999i
$796$		0			0
$797$	17.6140			0.623919			0.311959	−	0.950095i	$-0.399015\pi$
$797$	17.6140			0.623919			0.311959	+	0.950095i	$0.399015\pi$
$798$		0			0
$799$		−	12.0766i		−	0.427240i
$800$		0			0
$801$	−14.5089	+	1.40504i	−0.512645	+	0.0496448i
$802$		0			0
$803$			31.8323i			1.12334i
$804$		0			0
$805$	−9.83276	+	49.9684i	−0.346559	+	1.76115i
$806$		0			0
$807$	10.1935	+	9.25404i	0.358828	+	0.325758i
$808$		0			0
$809$			0.499375i			0.0175571i	0.999961	+	0.00877854i	$0.00279433\pi$
$809$			0.499375i			0.0175571i	−0.999961	+	0.00877854i	$0.997206\pi$
$810$		0			0
$811$			11.6172i			0.407934i	0.978978	+	0.203967i	$0.0653835\pi$
$811$			11.6172i			0.407934i	−0.978978	+	0.203967i	$0.934616\pi$
$812$		0			0
$813$	−16.1306	−	14.6440i	−0.565726	−	0.513587i
$814$		0			0
$815$	20.1847	+	3.97194i	0.707039	+	0.139131i
$816$		0			0
$817$			1.34663i			0.0471125i
$818$		0			0
$819$	−67.2121	+	6.50885i	−2.34858	+	0.227438i
$820$		0			0
$821$			11.2581i			0.392912i	0.980513	+	0.196456i	$0.0629433\pi$
$821$			11.2581i			0.392912i	−0.980513	+	0.196456i	$0.937057\pi$
$822$		0			0
$823$	43.0523			1.50071			0.750354	−	0.661036i	$-0.229883\pi$
$823$	43.0523			1.50071			0.750354	+	0.661036i	$0.229883\pi$
$824$		0			0
$825$	−18.9900	+	9.05810i	−0.661146	+	0.315363i
$826$		0			0
$827$			51.5202i			1.79153i	0.444526	+	0.895766i	$0.353372\pi$
$827$			51.5202i			1.79153i	−0.444526	+	0.895766i	$0.646628\pi$
$828$		0			0
$829$	2.48059			0.0861543			0.0430771	−	0.999072i	$-0.486284\pi$
$829$	2.48059			0.0861543			0.0430771	+	0.999072i	$0.486284\pi$
$830$		0			0
$831$	−6.01426	−	5.45998i	−0.208633	−	0.189404i
$832$		0			0
$833$	−38.6740			−1.33997
$834$		0			0
$835$	−0.754210	+	3.83276i	−0.0261005	+	0.132638i
$836$		0			0
$837$	24.3252	−	32.6312i	0.840803	−	1.12790i
$838$		0			0
$839$	−3.95324			−0.136481			−0.0682405	−	0.997669i	$-0.521739\pi$
$839$	−3.95324			−0.136481			−0.0682405	+	0.997669i	$0.521739\pi$
$840$		0			0
$841$	2.90225			0.100078
$842$		0			0
$843$	−20.1209	−	18.2665i	−0.693001	−	0.629132i
$844$		0			0
$845$	−33.8119	−	6.65348i	−1.16316	−	0.228887i
$846$		0			0
$847$	−21.5272			−0.739684
$848$		0			0
$849$	−28.5436	+	31.4413i	−0.979614	+	1.07906i
$850$		0			0
$851$	−41.9188			−1.43696
$852$		0			0
$853$		−	28.4529i		−	0.974208i	−0.873344	−	0.487104i	$-0.838053\pi$
$853$		−	28.4529i		−	0.974208i	0.873344	−	0.487104i	$-0.161947\pi$
$854$		0			0
$855$	−3.86108	−	0.378657i	−0.132046	−	0.0129498i
$856$		0			0
$857$	27.6808			0.945560			0.472780	−	0.881181i	$-0.343251\pi$
$857$	27.6808			0.945560			0.472780	+	0.881181i	$0.343251\pi$
$858$		0			0
$859$		−	18.8917i		−	0.644576i	−0.946642	−	0.322288i	$-0.895548\pi$
$859$		−	18.8917i		−	0.644576i	0.946642	−	0.322288i	$-0.104452\pi$
$860$		0			0
$861$	3.32391	+	3.01757i	0.113279	+	0.102839i
$862$		0			0
$863$		−	5.82219i		−	0.198190i	−0.995078	−	0.0990948i	$-0.968405\pi$
$863$		−	5.82219i		−	0.198190i	0.995078	−	0.0990948i	$-0.0315947\pi$
$864$		0			0
$865$	−18.7839	−	3.69629i	−0.638671	−	0.125677i
$866$		0			0
$867$	−4.95310	+	5.45593i	−0.168216	+	0.185293i
$868$		0			0
$869$		−	8.31277i		−	0.281992i
$870$		0			0
$871$			0.606604i			0.0205540i
$872$		0			0
$873$	27.8113	−	2.69325i	0.941268	−	0.0911528i
$874$		0			0
$875$	39.4172	+	25.9881i	1.33254	+	0.878558i
$876$		0			0
$877$		−	33.9778i		−	1.14735i	−0.819084	−	0.573674i	$-0.805518\pi$
$877$		−	33.9778i		−	1.14735i	0.819084	−	0.573674i	$-0.194482\pi$
$878$		0			0
$879$	10.4669	−	11.5295i	0.353039	−	0.388879i
$880$		0			0
$881$		−	5.79458i		−	0.195224i	−0.995225	−	0.0976121i	$-0.968880\pi$
$881$		−	5.79458i		−	0.195224i	0.995225	−	0.0976121i	$-0.0311205\pi$
$882$		0			0
$883$	55.4453			1.86588			0.932942	−	0.360027i	$-0.117233\pi$
$883$	55.4453			1.86588			0.932942	+	0.360027i	$0.117233\pi$
$884$		0			0
$885$	−24.2040	+	17.9972i	−0.813607	+	0.604971i
$886$		0			0
$887$		−	49.1749i		−	1.65113i	−0.564307	−	0.825565i	$-0.690857\pi$
$887$		−	49.1749i		−	1.65113i	0.564307	−	0.825565i	$-0.309143\pi$
$888$		0			0
$889$	−33.8328			−1.13471
$890$		0			0
$891$	21.4588	−	4.19550i	0.718897	−	0.140555i
$892$		0			0
$893$	1.95635			0.0654668
$894$		0			0
$895$	24.6640	+	4.85337i	0.824427	+	0.162230i
$896$		0			0
$897$	33.4681	−	36.8657i	1.11747	−	1.23091i
$898$		0			0
$899$	40.0144			1.33456
$900$		0			0
$901$	4.52998			0.150915
$902$		0			0
$903$	−11.4475	+	12.6097i	−0.380950	+	0.419623i
$904$		0			0
$905$	−1.85025	−	0.364092i	−0.0615044	−	0.0121028i
$906$		0			0
$907$	−11.4804			−0.381202			−0.190601	−	0.981668i	$-0.561044\pi$
$907$	−11.4804			−0.381202			−0.190601	+	0.981668i	$0.561044\pi$
$908$		0			0
$909$	−40.0766	+	3.88104i	−1.32926	+	0.128726i
$910$		0			0
$911$	−26.6983			−0.884555			−0.442278	−	0.896878i	$-0.645829\pi$
$911$	−26.6983			−0.884555			−0.442278	+	0.896878i	$0.645829\pi$
$912$		0			0
$913$		−	13.8089i		−	0.457007i
$914$		0			0
$915$	20.7490	−	15.4283i	0.685941	−	0.510043i
$916$		0			0
$917$	32.8867			1.08602
$918$		0			0
$919$			38.1260i			1.25766i	0.777542	+	0.628831i	$0.216466\pi$
$919$			38.1260i			1.25766i	−0.777542	+	0.628831i	$0.783534\pi$
$920$		0			0
$921$	−34.7875	+	38.3190i	−1.14629	+	1.26265i
$922$		0			0
$923$		−	44.3088i		−	1.45844i
$924$		0			0
$925$	−14.7244	+	35.9648i	−0.484137	+	1.18252i
$926$		0			0
$927$	0.514903	+	5.31703i	0.0169116	+	0.174634i
$928$		0			0
$929$		−	4.24513i		−	0.139278i	−0.997572	−	0.0696391i	$-0.977815\pi$
$929$		−	4.24513i		−	0.139278i	0.997572	−	0.0696391i	$-0.0221848\pi$
$930$		0			0
$931$		−	6.26499i		−	0.205327i
$932$		0			0
$933$	−37.4892	+	41.2950i	−1.22734	+	1.35194i
$934$		0			0
$935$	19.0293	+	3.74459i	0.622326	+	0.122461i
$936$		0			0
$937$		−	4.81869i		−	0.157420i	−0.996898	−	0.0787098i	$-0.974920\pi$
$937$		−	4.81869i		−	0.157420i	0.996898	−	0.0787098i	$-0.0250800\pi$
$938$		0			0
$939$	11.1229	+	10.0978i	0.362981	+	0.329528i
$940$		0			0
$941$		−	40.2641i		−	1.31257i	−0.754512	−	0.656286i	$-0.772126\pi$
$941$		−	40.2641i		−	1.31257i	0.754512	−	0.656286i	$-0.227874\pi$
$942$		0			0
$943$	−3.31027			−0.107797
$944$		0			0
$945$	−32.9358	−	36.3683i	−1.07140	−	1.18306i
$946$		0			0
$947$			6.05870i			0.196881i	0.995143	+	0.0984406i	$0.0313854\pi$
$947$			6.05870i			0.196881i	−0.995143	+	0.0984406i	$0.968615\pi$
$948$		0			0
$949$	−69.8399			−2.26710
$950$		0			0
$951$	−27.2699	+	30.0383i	−0.884287	+	0.974059i
$952$		0			0
$953$	16.3671			0.530184			0.265092	−	0.964223i	$-0.414598\pi$
$953$	16.3671			0.530184			0.265092	+	0.964223i	$0.414598\pi$
$954$		0			0
$955$	40.6546	+	8.00000i	1.31555	+	0.258874i
$956$		0			0
$957$	15.9162	+	14.4493i	0.514496	+	0.467079i
$958$		0			0
$959$	−65.3077			−2.10890
$960$		0			0
$961$	−30.3522			−0.979103
$962$		0			0
$963$	50.7555	−	4.91519i	1.63557	−	0.158390i
$964$		0			0
$965$	1.05440	−	5.35828i	0.0339424	−	0.172489i
$966$		0			0
$967$	12.8304			0.412599			0.206300	−	0.978489i	$-0.433858\pi$
$967$	12.8304			0.412599			0.206300	+	0.978489i	$0.433858\pi$
$968$		0			0
$969$	2.64782	+	2.40379i	0.0850603	+	0.0772209i
$970$		0			0
$971$	−4.88457			−0.156753			−0.0783767	−	0.996924i	$-0.524974\pi$
$971$	−4.88457			−0.156753			−0.0783767	+	0.996924i	$0.524974\pi$
$972$		0			0
$973$		−	2.44225i		−	0.0782950i
$974$		0			0
$975$	−19.8734	−	41.6639i	−0.636458	−	1.33431i
$976$		0			0
$977$	60.0946			1.92260			0.961298	−	0.275512i	$-0.0888475\pi$
$977$	60.0946			1.92260			0.961298	+	0.275512i	$0.0888475\pi$
$978$		0			0
$979$			11.8045i			0.377273i
$980$		0			0
$981$	2.26499	+	23.3889i	0.0723155	+	0.746749i
$982$		0			0
$983$			13.1690i			0.420026i	0.977699	+	0.210013i	$0.0673507\pi$
$983$			13.1690i			0.420026i	−0.977699	+	0.210013i	$0.932649\pi$
$984$		0			0
$985$	11.9406	+	2.34966i	0.380458	+	0.0748664i
$986$		0			0
$987$	18.3191	+	16.6307i	0.583102	+	0.529362i
$988$		0			0
$989$		−	12.5579i		−	0.399318i
$990$		0			0
$991$			26.7527i			0.849828i	0.905234	+	0.424914i	$0.139696\pi$
$991$			26.7527i			0.849828i	−0.905234	+	0.424914i	$0.860304\pi$
$992$		0			0
$993$	29.1784	+	26.4892i	0.925948	+	0.840611i
$994$		0			0
$995$	2.88229	−	14.6473i	0.0913747	−	0.464350i
$996$		0			0
$997$			3.13896i			0.0994118i	0.998764	+	0.0497059i	$0.0158284\pi$
$997$			3.13896i			0.0994118i	−0.998764	+	0.0497059i	$0.984172\pi$
$998$		0			0
$999$	24.1379	−	32.3799i	0.763690	−	1.02446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.o.e.959.18		24
3.2	odd	2	inner	960.2.o.e.959.19		24
4.3	odd	2	inner	960.2.o.e.959.8		24
5.4	even	2	inner	960.2.o.e.959.7		24
8.3	odd	2		480.2.o.a.479.17	yes	24
8.5	even	2		480.2.o.a.479.7	yes	24
12.11	even	2	inner	960.2.o.e.959.5		24
15.14	odd	2	inner	960.2.o.e.959.6		24
20.19	odd	2	inner	960.2.o.e.959.17		24
24.5	odd	2		480.2.o.a.479.6	yes	24
24.11	even	2		480.2.o.a.479.20	yes	24
40.3	even	4		2400.2.h.h.1151.20		24
40.13	odd	4		2400.2.h.h.1151.5		24
40.19	odd	2		480.2.o.a.479.8	yes	24
40.27	even	4		2400.2.h.h.1151.6		24
40.29	even	2		480.2.o.a.479.18	yes	24
40.37	odd	4		2400.2.h.h.1151.19		24
60.59	even	2	inner	960.2.o.e.959.20		24
120.29	odd	2		480.2.o.a.479.19	yes	24
120.53	even	4		2400.2.h.h.1151.18		24
120.59	even	2		480.2.o.a.479.5	✓	24
120.77	even	4		2400.2.h.h.1151.8		24
120.83	odd	4		2400.2.h.h.1151.7		24
120.107	odd	4		2400.2.h.h.1151.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.2.o.a.479.5	✓	24	120.59	even	2
480.2.o.a.479.6	yes	24	24.5	odd	2
480.2.o.a.479.7	yes	24	8.5	even	2
480.2.o.a.479.8	yes	24	40.19	odd	2
480.2.o.a.479.17	yes	24	8.3	odd	2
480.2.o.a.479.18	yes	24	40.29	even	2
480.2.o.a.479.19	yes	24	120.29	odd	2
480.2.o.a.479.20	yes	24	24.11	even	2
960.2.o.e.959.5		24	12.11	even	2	inner
960.2.o.e.959.6		24	15.14	odd	2	inner
960.2.o.e.959.7		24	5.4	even	2	inner
960.2.o.e.959.8		24	4.3	odd	2	inner
960.2.o.e.959.17		24	20.19	odd	2	inner
960.2.o.e.959.18		24	1.1	even	1	trivial
960.2.o.e.959.19		24	3.2	odd	2	inner
960.2.o.e.959.20		24	60.59	even	2	inner
2400.2.h.h.1151.5		24	40.13	odd	4
2400.2.h.h.1151.6		24	40.27	even	4
2400.2.h.h.1151.7		24	120.83	odd	4
2400.2.h.h.1151.8		24	120.77	even	4
2400.2.h.h.1151.17		24	120.107	odd	4
2400.2.h.h.1151.18		24	120.53	even	4
2400.2.h.h.1151.19		24	40.37	odd	4
2400.2.h.h.1151.20		24	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.o (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16422 - 1.28241i) q^{3} +(2.19399 + 0.431733i) q^{5} +4.22289 q^{7} +(-0.289169 - 2.98603i) q^{9} +O(q^{10})\)	\(q+(1.16422 - 1.28241i) q^{3} +(2.19399 + 0.431733i) q^{5} +4.22289 q^{7} +(-0.289169 - 2.98603i) q^{9} -2.42945 q^{11} -5.33021i q^{13} +(3.10796 - 2.31097i) q^{15} -3.57009 q^{17} -0.578337i q^{19} +(4.91638 - 5.41549i) q^{21} +5.39325i q^{23} +(4.62721 + 1.89444i) q^{25} +(-4.16598 - 3.10557i) q^{27} -5.10860i q^{29} +7.83276i q^{31} +(-2.82843 + 3.11556i) q^{33} +(9.26498 + 1.82316i) q^{35} +7.77246i q^{37} +(-6.83553 - 6.20555i) q^{39} +0.613779i q^{41} -2.32845 q^{43} +(0.654735 - 6.67618i) q^{45} +3.38272i q^{47} +10.8328 q^{49} +(-4.15639 + 4.57834i) q^{51} -1.26887 q^{53} +(-5.33021 - 1.04888i) q^{55} +(-0.741667 - 0.673313i) q^{57} -7.78774 q^{59} +6.67609 q^{61} +(-1.22113 - 12.6097i) q^{63} +(2.30123 - 11.6944i) q^{65} -0.113805 q^{67} +(6.91638 + 6.27895i) q^{69} +8.31277 q^{71} -13.1027i q^{73} +(7.81656 - 3.72845i) q^{75} -10.2593 q^{77} +3.42166i q^{79} +(-8.83276 + 1.72693i) q^{81} +5.68395i q^{83} +(-7.83276 - 1.54133i) q^{85} +(-6.55133 - 5.94755i) q^{87} -4.85891i q^{89} -22.5089i q^{91} +(10.0448 + 9.11908i) q^{93} +(0.249687 - 1.26887i) q^{95} +9.31379i q^{97} +(0.702522 + 7.25443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 8 q^{21} + 8 q^{25} + 24 q^{45} + 40 q^{49} - 32 q^{61} + 56 q^{69} + 8 q^{81} + 32 q^{85}+O(q^{100}) \) 24 * q + 8 * q^21 + 8 * q^25 + 24 * q^45 + 40 * q^49 - 32 * q^61 + 56 * q^69 + 8 * q^81 + 32 * q^85

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