LMFDB - Embedded newform 432.2.v.a.251.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(35,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("432.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			251.13
Character	$\chi$	$=$	432.251
Dual form			432.2.v.a.179.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.354608 - 1.36903i) q^{2} +(-1.74851 - 0.970941i) q^{4} +(-1.76649 - 0.473330i) q^{5} +(1.40613 - 2.43549i) q^{7} +(-1.94929 + 2.04946i) q^{8} +O(q^{10})$	\(q+(0.354608 - 1.36903i) q^{2} +(-1.74851 - 0.970941i) q^{4} +(-1.76649 - 0.473330i) q^{5} +(1.40613 - 2.43549i) q^{7} +(-1.94929 + 2.04946i) q^{8} +(-1.27442 + 2.25054i) q^{10} +(-5.79446 + 1.55262i) q^{11} +(-1.10810 - 0.296913i) q^{13} +(-2.83565 - 2.78869i) q^{14} +(2.11455 + 3.39539i) q^{16} -0.699378i q^{17} +(-2.01481 - 2.01481i) q^{19} +(2.62914 + 2.54278i) q^{20} +(0.0708264 + 8.48338i) q^{22} +(4.91498 - 2.83767i) q^{23} +(-1.43368 - 0.827735i) q^{25} +(-0.799424 + 1.41173i) q^{26} +(-4.82335 + 2.89320i) q^{28} +(-5.41802 + 1.45175i) q^{29} +(-5.15522 + 2.97637i) q^{31} +(5.39824 - 1.69085i) q^{32} +(-0.957472 - 0.248005i) q^{34} +(-3.63671 + 3.63671i) q^{35} +(3.48490 + 3.48490i) q^{37} +(-3.47280 + 2.04387i) q^{38} +(4.41347 - 2.69770i) q^{40} +(-1.55998 - 2.70196i) q^{41} +(-1.90129 - 7.09570i) q^{43} +(11.6392 + 2.91131i) q^{44} +(-2.14197 - 7.73504i) q^{46} +(2.83634 - 4.91269i) q^{47} +(-0.454420 - 0.787079i) q^{49} +(-1.64159 + 1.66923i) q^{50} +(1.64923 + 1.59505i) q^{52} +(4.45605 - 4.45605i) q^{53} +10.9708 q^{55} +(2.25049 + 7.62929i) q^{56} +(0.0662251 + 7.93225i) q^{58} +(3.65938 - 13.6570i) q^{59} +(3.54643 + 13.2354i) q^{61} +(2.24666 + 8.11312i) q^{62} +(-0.400567 - 7.98997i) q^{64} +(1.81690 + 1.04899i) q^{65} +(3.45542 - 12.8958i) q^{67} +(-0.679055 + 1.22287i) q^{68} +(3.68917 + 6.26839i) q^{70} -7.21910i q^{71} -3.75535i q^{73} +(6.00671 - 3.53517i) q^{74} +(1.56664 + 5.47916i) q^{76} +(-4.36638 + 16.2956i) q^{77} +(-2.96345 - 1.71095i) q^{79} +(-2.12818 - 6.99881i) q^{80} +(-4.25226 + 1.17752i) q^{82} +(-0.308735 - 1.15222i) q^{83} +(-0.331036 + 1.23544i) q^{85} +(-10.3885 + 0.0867317i) q^{86} +(8.11303 - 14.9020i) q^{88} -0.391835 q^{89} +(-2.28126 + 2.28126i) q^{91} +(-11.3491 + 0.189517i) q^{92} +(-5.71984 - 5.62513i) q^{94} +(2.60547 + 4.51280i) q^{95} +(-0.875387 + 1.51622i) q^{97} +(-1.23868 + 0.343012i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.354608	−	1.36903i	0.250746	−	0.968053i
$2$	0.354608	−	1.36903i	0.250746	−	0.968053i
$3$		0			0
$3$		0			0
$4$	−1.74851	−	0.970941i	−0.874253	−	0.485471i
$5$	−1.76649	−	0.473330i	−0.789999	−	0.211679i	−0.158810	−	0.987309i	$-0.550766\pi$
$5$	−1.76649	−	0.473330i	−0.789999	−	0.211679i	−0.631188	+	0.775630i	$0.717432\pi$
$6$		0			0
$7$	1.40613	−	2.43549i	0.531468	−	0.920530i	−0.467857	−	0.883804i	$-0.654974\pi$
$7$	1.40613	−	2.43549i	0.531468	−	0.920530i	0.999325	−	0.0367260i	$-0.0116929\pi$
$8$	−1.94929	+	2.04946i	−0.689177	+	0.724593i
$9$		0			0
$10$	−1.27442	+	2.25054i	−0.403006	+	0.711683i
$11$	−5.79446	+	1.55262i	−1.74710	+	0.468133i	−0.984002	−	0.178156i	$-0.942987\pi$
$11$	−5.79446	+	1.55262i	−1.74710	+	0.468133i	−0.763093	+	0.646288i	$0.776320\pi$
$12$		0			0
$13$	−1.10810	−	0.296913i	−0.307330	−	0.0823489i	0.101858	−	0.994799i	$-0.467521\pi$
$13$	−1.10810	−	0.296913i	−0.307330	−	0.0823489i	−0.409188	+	0.912450i	$0.634188\pi$
$14$	−2.83565	−	2.78869i	−0.757858	−	0.745309i
$15$		0			0
$16$	2.11455	+	3.39539i	0.528636	+	0.848848i
$17$		−	0.699378i		−	0.169624i	−0.996397	−	0.0848120i	$-0.972971\pi$
$17$		−	0.699378i		−	0.169624i	0.996397	−	0.0848120i	$-0.0270290\pi$
$18$		0			0
$19$	−2.01481	−	2.01481i	−0.462228	−	0.462228i	0.437157	−	0.899385i	$-0.355985\pi$
$19$	−2.01481	−	2.01481i	−0.462228	−	0.462228i	−0.899385	+	0.437157i	$0.855985\pi$
$20$	2.62914	+	2.54278i	0.587894	+	0.568583i
$21$		0			0
$22$	0.0708264	+	8.48338i	0.0151002	+	1.80866i
$23$	4.91498	−	2.83767i	1.02485	−	0.591695i	0.109341	−	0.994004i	$-0.465126\pi$
$23$	4.91498	−	2.83767i	1.02485	−	0.591695i	0.915504	+	0.402310i	$0.131792\pi$
$24$		0			0
$25$	−1.43368	−	0.827735i	−0.286736	−	0.165547i
$26$	−0.799424	+	1.41173i	−0.156780	+	0.276863i
$27$		0			0
$28$	−4.82335	+	2.89320i	−0.911528	+	0.546764i
$29$	−5.41802	+	1.45175i	−1.00610	+	0.269584i	−0.723999	−	0.689801i	$-0.757698\pi$
$29$	−5.41802	+	1.45175i	−1.00610	+	0.269584i	−0.282101	+	0.959385i	$0.591031\pi$
$30$		0			0
$31$	−5.15522	+	2.97637i	−0.925905	+	0.534572i	−0.885514	−	0.464612i	$-0.846194\pi$
$31$	−5.15522	+	2.97637i	−0.925905	+	0.534572i	−0.0403909	+	0.999184i	$0.512860\pi$
$32$	5.39824	−	1.69085i	0.954284	−	0.298903i
$33$		0			0
$34$	−0.957472	−	0.248005i	−0.164205	−	0.0425325i
$35$	−3.63671	+	3.63671i	−0.614717	+	0.614717i
$36$		0			0
$37$	3.48490	+	3.48490i	0.572913	+	0.572913i	0.932941	−	0.360028i	$-0.117233\pi$
$37$	3.48490	+	3.48490i	0.572913	+	0.572913i	−0.360028	+	0.932941i	$0.617233\pi$
$38$	−3.47280	+	2.04387i	−0.563363	+	0.331559i
$39$		0			0
$40$	4.41347	−	2.69770i	0.697830	−	0.426543i
$41$	−1.55998	−	2.70196i	−0.243628	−	0.421975i	0.718117	−	0.695922i	$-0.245004\pi$
$41$	−1.55998	−	2.70196i	−0.243628	−	0.421975i	−0.961745	+	0.273947i	$0.911671\pi$
$42$		0			0
$43$	−1.90129	−	7.09570i	−0.289944	−	1.08208i	−0.945151	−	0.326635i	$-0.894085\pi$
$43$	−1.90129	−	7.09570i	−0.289944	−	1.08208i	0.655207	−	0.755450i	$-0.272581\pi$
$44$	11.6392	+	2.91131i	1.75467	+	0.438897i
$45$		0			0
$46$	−2.14197	−	7.73504i	−0.315816	−	1.14047i
$47$	2.83634	−	4.91269i	0.413723	−	0.716589i	−0.581570	−	0.813496i	$-0.697562\pi$
$47$	2.83634	−	4.91269i	0.413723	−	0.716589i	0.995293	+	0.0969068i	$0.0308949\pi$
$48$		0			0
$49$	−0.454420	−	0.787079i	−0.0649172	−	0.112440i
$50$	−1.64159	+	1.66923i	−0.232156	+	0.236065i
$51$		0			0
$52$	1.64923	+	1.59505i	0.228706	+	0.221194i
$53$	4.45605	−	4.45605i	0.612086	−	0.612086i	−0.331403	−	0.943489i	$-0.607522\pi$
$53$	4.45605	−	4.45605i	0.612086	−	0.612086i	0.943489	+	0.331403i	$0.107522\pi$
$54$		0			0
$55$	10.9708			1.47930
$56$	2.25049	+	7.62929i	0.300734	+	1.01951i
$57$		0			0
$58$	0.0662251	+	7.93225i	0.00869578	+	1.04156i
$59$	3.65938	−	13.6570i	0.476411	−	1.77799i	−0.139552	−	0.990215i	$-0.544566\pi$
$59$	3.65938	−	13.6570i	0.476411	−	1.77799i	0.615963	−	0.787775i	$-0.288767\pi$
$60$		0			0
$61$	3.54643	+	13.2354i	0.454074	+	1.69463i	0.690797	+	0.723048i	$0.257260\pi$
$61$	3.54643	+	13.2354i	0.454074	+	1.69463i	−0.236724	+	0.971577i	$0.576074\pi$
$62$	2.24666	+	8.11312i	0.285327	+	1.03037i
$63$		0			0
$64$	−0.400567	−	7.98997i	−0.0500709	−	0.998746i
$65$	1.81690	+	1.04899i	0.225359	+	0.130111i
$66$		0			0
$67$	3.45542	−	12.8958i	0.422146	−	1.57547i	−0.347930	−	0.937520i	$-0.613115\pi$
$67$	3.45542	−	12.8958i	0.422146	−	1.57547i	0.770077	−	0.637952i	$-0.220218\pi$
$68$	−0.679055	+	1.22287i	−0.0823475	+	0.148294i
$69$		0			0
$70$	3.68917	+	6.26839i	0.440940	+	0.749216i
$71$		−	7.21910i		−	0.856749i	−0.903601	−	0.428375i	$-0.859086\pi$
$71$		−	7.21910i		−	0.856749i	0.903601	−	0.428375i	$-0.140914\pi$
$72$		0			0
$73$		−	3.75535i		−	0.439531i	−0.975553	−	0.219765i	$-0.929471\pi$
$73$		−	3.75535i		−	0.439531i	0.975553	−	0.219765i	$-0.0705292\pi$
$74$	6.00671	−	3.53517i	0.698266	−	0.410955i
$75$		0			0
$76$	1.56664	+	5.47916i	0.179706	+	0.628502i
$77$	−4.36638	+	16.2956i	−0.497596	+	1.85705i
$78$		0			0
$79$	−2.96345	−	1.71095i	−0.333415	−	0.192497i	0.323942	−	0.946077i	$-0.394992\pi$
$79$	−2.96345	−	1.71095i	−0.333415	−	0.192497i	−0.657356	+	0.753580i	$0.728325\pi$
$80$	−2.12818	−	6.99881i	−0.237938	−	0.782490i
$81$		0			0
$82$	−4.25226	+	1.17752i	−0.469583	+	0.130036i
$83$	−0.308735	−	1.15222i	−0.0338881	−	0.126472i	0.946910	−	0.321500i	$-0.104187\pi$
$83$	−0.308735	−	1.15222i	−0.0338881	−	0.126472i	−0.980798	+	0.195028i	$0.937520\pi$
$84$		0			0
$85$	−0.331036	+	1.23544i	−0.0359059	+	0.134003i
$86$	−10.3885	+	0.0867317i	−1.12022	+	0.00935252i
$87$		0			0
$88$	8.11303	−	14.9020i	0.864852	−	1.58856i
$89$	−0.391835			−0.0415344			−0.0207672	−	0.999784i	$-0.506611\pi$
$89$	−0.391835			−0.0415344			−0.0207672	+	0.999784i	$0.506611\pi$
$90$		0			0
$91$	−2.28126	+	2.28126i	−0.239141	+	0.239141i
$92$	−11.3491	+	0.189517i	−1.18322	+	0.0197585i
$93$		0			0
$94$	−5.71984	−	5.62513i	−0.589957	−	0.580188i
$95$	2.60547	+	4.51280i	0.267315	+	0.463004i
$96$		0			0
$97$	−0.875387	+	1.51622i	−0.0888821	+	0.153948i	−0.907039	−	0.421047i	$-0.861663\pi$
$97$	−0.875387	+	1.51622i	−0.0888821	+	0.153948i	0.818157	+	0.574995i	$0.194996\pi$
$98$	−1.23868	+	0.343012i	−0.125125	+	0.0346494i
$99$		0			0
$100$	1.70311	+	2.83932i	0.170311	+	0.283932i
$101$	0.218761	+	0.816427i	0.0217675	+	0.0812375i	0.975955	−	0.217971i	$-0.0699439\pi$
$101$	0.218761	+	0.816427i	0.0217675	+	0.0812375i	−0.954188	+	0.299209i	$0.903277\pi$
$102$		0			0
$103$	−5.30341	−	9.18577i	−0.522560	−	0.905101i	−0.999655	−	0.0262492i	$-0.991644\pi$
$103$	−5.30341	−	9.18577i	−0.522560	−	0.905101i	0.477095	−	0.878852i	$-0.341690\pi$
$104$	2.76851	−	1.69223i	0.271474	−	0.165937i
$105$		0			0
$106$	−4.52033	−	7.68064i	−0.439054	−	0.746010i
$107$	6.39894	+	6.39894i	0.618609	+	0.618609i	0.945174	−	0.326566i	$-0.105891\pi$
$107$	6.39894	+	6.39894i	0.618609	+	0.618609i	−0.326566	+	0.945174i	$0.605891\pi$
$108$		0			0
$109$	1.52592	−	1.52592i	0.146157	−	0.146157i	−0.630242	−	0.776399i	$-0.717044\pi$
$109$	1.52592	−	1.52592i	0.146157	−	0.146157i	0.776399	+	0.630242i	$0.217044\pi$
$110$	3.89032	−	15.0193i	0.370928	−	1.43204i
$111$		0			0
$112$	11.2428	−	0.375588i	1.06234	−	0.0354897i
$113$	−5.75213	+	3.32099i	−0.541115	+	0.312413i	−0.745531	−	0.666471i	$-0.767804\pi$
$113$	−5.75213	+	3.32099i	−0.541115	+	0.312413i	0.204416	+	0.978884i	$0.434471\pi$
$114$		0			0
$115$	−10.0254	+	2.68630i	−0.934876	+	0.250499i
$116$	10.8830	+	2.72218i	1.01046	+	0.252748i
$117$		0			0
$118$	−17.3992	−	9.85270i	−1.60173	−	0.907015i
$119$	−1.70333	−	0.983418i	−0.156144	−	0.0901498i
$120$		0			0
$121$	21.6389	−	12.4932i	1.96717	−	1.13575i
$122$	19.3774	−	0.161779i	1.75434	−	0.0146467i
$123$		0			0
$124$	11.9038	−	0.198780i	1.06899	−	0.0178510i
$125$	8.60659	+	8.60659i	0.769797	+	0.769797i
$126$		0			0
$127$			13.8224i			1.22654i	0.789874	+	0.613270i	$0.210146\pi$
$127$			13.8224i			1.22654i	−0.789874	+	0.613270i	$0.789854\pi$
$128$	−11.0806	−	2.28492i	−0.979394	−	0.201960i
$129$		0			0
$130$	2.08039	−	2.11542i	0.182462	−	0.185535i
$131$	−8.97914	−	2.40595i	−0.784511	−	0.210209i	−0.155739	−	0.987798i	$-0.549776\pi$
$131$	−8.97914	−	2.40595i	−0.784511	−	0.210209i	−0.628773	+	0.777589i	$0.716442\pi$
$132$		0			0
$133$	−7.74013	+	2.07396i	−0.671154	+	0.179835i
$134$	−16.4295	−	9.30354i	−1.41929	−	0.803703i
$135$		0			0
$136$	1.43335	+	1.36329i	0.122908	+	0.116901i
$137$	−5.96603	+	10.3335i	−0.509712	+	0.882848i	0.490224	+	0.871596i	$0.336915\pi$
$137$	−5.96603	+	10.3335i	−0.509712	+	0.882848i	−0.999937	+	0.0112514i	$0.996419\pi$
$138$		0			0
$139$	1.20712	+	0.323448i	0.102387	+	0.0274345i	0.309649	−	0.950851i	$-0.399789\pi$
$139$	1.20712	+	0.323448i	0.102387	+	0.0274345i	−0.207262	+	0.978286i	$0.566455\pi$
$140$	9.88985	−	2.82778i	0.835845	−	0.238991i
$141$		0			0
$142$	−9.88319	−	2.55995i	−0.829379	−	0.214826i
$143$	6.88181			0.575486
$144$		0			0
$145$	10.2580			0.851884
$146$	−5.14120	−	1.33168i	−0.425489	−	0.110211i
$147$		0			0
$148$	−2.70973	−	9.47699i	−0.222739	−	0.779004i
$149$	3.47417	+	0.930902i	0.284615	+	0.0762625i	0.398302	−	0.917254i	$-0.369599\pi$
$149$	3.47417	+	0.930902i	0.284615	+	0.0762625i	−0.113687	+	0.993517i	$0.536266\pi$
$150$		0			0
$151$	−5.43126	+	9.40721i	−0.441989	+	0.765548i	−0.997837	−	0.0657361i	$-0.979060\pi$
$151$	−5.43126	+	9.40721i	−0.441989	+	0.765548i	0.555848	+	0.831284i	$0.312394\pi$
$152$	8.05669	−	0.201830i	0.653484	−	0.0163705i
$153$		0			0
$154$	20.7608	+	11.7563i	1.67295	+	0.947347i
$155$	10.5155	−	2.81761i	0.844621	−	0.226316i
$156$		0			0
$157$	−9.52986	−	2.55352i	−0.760565	−	0.203793i	−0.142366	−	0.989814i	$-0.545471\pi$
$157$	−9.52986	−	2.55352i	−0.760565	−	0.203793i	−0.618199	+	0.786021i	$0.712138\pi$
$158$	−3.39321	+	3.45035i	−0.269950	+	0.274495i
$159$		0			0
$160$	−10.3363	+	0.431720i	−0.817154	+	0.0341305i
$161$		−	15.9606i		−	1.25787i
$162$		0			0
$163$	−3.66703	−	3.66703i	−0.287224	−	0.287224i	0.548758	−	0.835981i	$-0.315101\pi$
$163$	−3.66703	−	3.66703i	−0.287224	−	0.287224i	−0.835981	+	0.548758i	$0.815101\pi$
$164$	0.104185	+	6.23904i	0.00813547	+	0.487187i
$165$		0			0
$166$	−1.68690	+	0.0140837i	−0.130929	+	0.00109311i
$167$	17.4253	−	10.0605i	1.34841	−	0.778505i	0.360385	−	0.932803i	$-0.382645\pi$
$167$	17.4253	−	10.0605i	1.34841	−	0.778505i	0.988024	+	0.154299i	$0.0493118\pi$
$168$		0			0
$169$	−10.1186	−	5.84198i	−0.778355	−	0.449383i
$170$	1.57398	+	0.891299i	0.120719	+	0.0683595i
$171$		0			0
$172$	−3.56510	+	14.2529i	−0.271836	+	1.08677i
$173$	10.1074	−	2.70826i	0.768450	−	0.205906i	0.146763	−	0.989172i	$-0.453114\pi$
$173$	10.1074	−	2.70826i	0.768450	−	0.205906i	0.621687	+	0.783266i	$0.286448\pi$
$174$		0			0
$175$	−4.03189	+	2.32781i	−0.304782	+	0.175966i
$176$	−17.5244	−	16.3914i	−1.32095	−	1.23555i
$177$		0			0
$178$	−0.138948	+	0.536435i	−0.0104146	+	0.0402075i
$179$	−12.4542	+	12.4542i	−0.930872	+	0.930872i	−0.997760	−	0.0668885i	$-0.978693\pi$
$179$	−12.4542	+	12.4542i	−0.930872	+	0.930872i	0.0668885	+	0.997760i	$0.478693\pi$
$180$		0			0
$181$	−9.12083	−	9.12083i	−0.677946	−	0.677946i	0.281589	−	0.959535i	$-0.409139\pi$
$181$	−9.12083	−	9.12083i	−0.677946	−	0.677946i	−0.959535	+	0.281589i	$0.909139\pi$
$182$	2.31417	+	3.93207i	0.171537	+	0.291465i
$183$		0			0
$184$	−3.76503	+	15.6045i	−0.277561	+	1.15038i
$185$	−4.50653	−	7.80554i	−0.331327	−	0.573875i
$186$		0			0
$187$	1.08587	+	4.05252i	0.0794066	+	0.296349i
$188$	−9.72929	+	5.83594i	−0.709582	+	0.425630i
$189$		0			0
$190$	7.10210	−	1.96670i	0.515240	−	0.142679i
$191$	−1.76985	+	3.06547i	−0.128062	+	0.221810i	−0.922926	−	0.384978i	$-0.874209\pi$
$191$	−1.76985	+	3.06547i	−0.128062	+	0.221810i	0.794864	+	0.606788i	$0.207542\pi$
$192$		0			0
$193$	7.43004	+	12.8692i	0.534826	+	0.926346i	0.999172	+	0.0406916i	$0.0129561\pi$
$193$	7.43004	+	12.8692i	0.534826	+	0.926346i	−0.464346	+	0.885654i	$0.653711\pi$
$194$	1.76533	+	1.73610i	0.126743	+	0.124644i
$195$		0			0
$196$	0.0303489	+	1.81743i	0.00216778	+	0.129816i
$197$	−11.9105	+	11.9105i	−0.848589	+	0.848589i	−0.989957	−	0.141368i	$-0.954850\pi$
$197$	−11.9105	+	11.9105i	−0.848589	+	0.848589i	0.141368	+	0.989957i	$0.454850\pi$
$198$		0			0
$199$	15.5983			1.10574			0.552868	−	0.833269i	$-0.313533\pi$
$199$	15.5983			1.10574			0.552868	+	0.833269i	$0.313533\pi$
$200$	4.49106	−	1.32478i	0.317566	−	0.0936757i
$201$		0			0
$202$	1.19529	−	0.00997929i	0.0841003	−	0.000702140i
$203$	−4.08272	+	15.2369i	−0.286551	+	1.06942i
$204$		0			0
$205$	1.47677	+	5.51137i	0.103142	+	0.384931i
$206$	−14.4563	+	4.00319i	−1.00722	+	0.278916i
$207$		0			0
$208$	−1.33498	−	4.39026i	−0.0925643	−	0.304409i
$209$	14.8029	+	8.54648i	1.02394	+	0.591172i
$210$		0			0
$211$	−4.18049	+	15.6018i	−0.287797	+	1.07407i	0.658975	+	0.752165i	$0.270990\pi$
$211$	−4.18049	+	15.6018i	−0.287797	+	1.07407i	−0.946771	+	0.321907i	$0.895676\pi$
$212$	−12.1180	+	3.46487i	−0.832268	+	0.237968i
$213$		0			0
$214$	11.0295	−	6.49124i	0.753960	−	0.443732i
$215$			13.4344i			0.916220i
$216$		0			0
$217$			16.7407i			1.13643i
$218$	−1.54793	−	2.63014i	−0.104839	−	0.178136i
$219$		0			0
$220$	−19.1824	−	10.6520i	−1.29328	−	0.718155i
$221$	−0.207655	+	0.774977i	−0.0139684	+	0.0521306i
$222$		0			0
$223$	13.9254	+	8.03982i	0.932512	+	0.538386i	0.887605	−	0.460605i	$-0.152368\pi$
$223$	13.9254	+	8.03982i	0.932512	+	0.538386i	0.0449068	+	0.998991i	$0.485701\pi$
$224$	3.47259	−	15.5249i	0.232023	−	1.03730i
$225$		0			0
$226$	2.50680	+	9.05251i	0.166750	+	0.602164i
$227$	−2.85895	−	10.6697i	−0.189755	−	0.708176i	−0.993562	−	0.113286i	$-0.963862\pi$
$227$	−2.85895	−	10.6697i	−0.189755	−	0.708176i	0.803807	−	0.594890i	$-0.202804\pi$
$228$		0			0
$229$	0.104652	−	0.390566i	0.00691559	−	0.0258093i	−0.962382	−	0.271701i	$-0.912414\pi$
$229$	0.104652	−	0.390566i	0.00691559	−	0.0258093i	0.969297	+	0.245891i	$0.0790806\pi$
$230$	0.122542	+	14.6777i	0.00808018	+	0.967821i
$231$		0			0
$232$	7.58596	−	13.9339i	0.498043	−	0.914805i
$233$	−11.6252			−0.761590			−0.380795	−	0.924659i	$-0.624350\pi$
$233$	−11.6252			−0.761590			−0.380795	+	0.924659i	$0.624350\pi$
$234$		0			0
$235$	−7.33569	+	7.33569i	−0.478528	+	0.478528i
$236$	−19.6586	+	20.3263i	−1.27967	+	1.32313i
$237$		0			0
$238$	−1.95035	+	1.98319i	−0.126422	+	0.128551i
$239$	1.55685	+	2.69654i	0.100704	+	0.174425i	0.911975	−	0.410246i	$-0.134557\pi$
$239$	1.55685	+	2.69654i	0.100704	+	0.174425i	−0.811271	+	0.584671i	$0.801224\pi$
$240$		0			0
$241$	−7.16669	+	12.4131i	−0.461647	+	0.799596i	−0.999043	−	0.0437337i	$-0.986075\pi$
$241$	−7.16669	+	12.4131i	−0.461647	+	0.799596i	0.537396	+	0.843330i	$0.319408\pi$
$242$	−9.43029	−	34.0545i	−0.606202	−	2.18911i
$243$		0			0
$244$	6.64989	−	26.5856i	0.425716	−	1.70197i
$245$	0.430181	+	1.60546i	0.0274833	+	0.102569i
$246$		0			0
$247$	1.63437	+	2.83082i	0.103993	+	0.180121i
$248$	3.94905	−	16.3672i	0.250765	−	1.03932i
$249$		0			0
$250$	14.8347	−	8.73075i	0.938228	−	0.552181i
$251$	−3.06176	−	3.06176i	−0.193257	−	0.193257i	0.603845	−	0.797102i	$-0.293635\pi$
$251$	−3.06176	−	3.06176i	−0.193257	−	0.193257i	−0.797102	+	0.603845i	$0.793635\pi$
$252$		0			0
$253$	−24.0739	+	24.0739i	−1.51351	+	1.51351i
$254$	18.9233	+	4.90154i	1.18735	+	0.307550i
$255$		0			0
$256$	−7.05739	+	14.3594i	−0.441087	+	0.897464i
$257$	−2.78074	+	1.60546i	−0.173458	+	0.100146i	−0.584215	−	0.811599i	$-0.698598\pi$
$257$	−2.78074	+	1.60546i	−0.173458	+	0.100146i	0.410757	+	0.911745i	$0.365264\pi$
$258$		0			0
$259$	13.3877	−	3.58722i	0.831870	−	0.222899i
$260$	−2.15836	−	3.59827i	−0.133856	−	0.223155i
$261$		0			0
$262$	−6.47791	+	11.4396i	−0.400207	+	0.706739i
$263$	−2.63762	−	1.52283i	−0.162643	−	0.0939018i	0.416469	−	0.909150i	$-0.363267\pi$
$263$	−2.63762	−	1.52283i	−0.162643	−	0.0939018i	−0.579112	+	0.815248i	$0.696601\pi$
$264$		0			0
$265$	−9.98076	+	5.76240i	−0.613113	+	0.353981i
$266$	0.0946086	+	11.3319i	0.00580082	+	0.694806i
$267$		0			0
$268$	−18.5629	+	19.1934i	−1.13391	+	1.17242i
$269$	1.99648	+	1.99648i	0.121727	+	0.121727i	0.765346	−	0.643619i	$-0.222568\pi$
$269$	1.99648	+	1.99648i	0.121727	+	0.121727i	−0.643619	+	0.765346i	$0.722568\pi$
$270$		0			0
$271$		−	13.9357i		−	0.846534i	−0.906005	−	0.423267i	$-0.860883\pi$
$271$		−	13.9357i		−	0.846534i	0.906005	−	0.423267i	$-0.139117\pi$
$272$	2.37466	−	1.47887i	0.143985	−	0.0896695i
$273$		0			0
$274$	12.0313	+	11.8320i	0.726835	+	0.714799i
$275$	9.59256	+	2.57032i	0.578453	+	0.154996i
$276$		0			0
$277$	30.2253	−	8.09885i	1.81606	−	0.486613i	0.819774	−	0.572686i	$-0.194099\pi$
$277$	30.2253	−	8.09885i	1.81606	−	0.486613i	0.996289	+	0.0860738i	$0.0274321\pi$
$278$	0.870867	−	1.53790i	0.0522311	−	0.0922368i
$279$		0			0
$280$	−0.364301	−	14.5423i	−0.0217712	−	0.869068i
$281$	11.3745	−	19.7012i	0.678544	−	1.17527i	−0.296875	−	0.954916i	$-0.595944\pi$
$281$	11.3745	−	19.7012i	0.678544	−	1.17527i	0.975419	−	0.220357i	$-0.0707222\pi$
$282$		0			0
$283$	−2.36412	−	0.633463i	−0.140532	−	0.0376555i	0.187867	−	0.982194i	$-0.439843\pi$
$283$	−2.36412	−	0.633463i	−0.140532	−	0.0376555i	−0.328399	+	0.944539i	$0.606509\pi$
$284$	−7.00932	+	12.6226i	−0.415927	+	0.749016i
$285$		0			0
$286$	2.44035	−	9.42143i	0.144301	−	0.557101i
$287$	−8.77415			−0.517921
$288$		0			0
$289$	16.5109			0.971228
$290$	3.63759	−	14.0436i	0.213606	−	0.824668i
$291$		0			0
$292$	−3.64623	+	6.56626i	−0.213379	+	0.384261i
$293$	−7.53030	−	2.01774i	−0.439925	−	0.117877i	0.0320565	−	0.999486i	$-0.489794\pi$
$293$	−7.53030	−	2.01774i	−0.439925	−	0.117877i	−0.471981	+	0.881609i	$0.656461\pi$
$294$		0			0
$295$	−12.9285	+	22.3929i	−0.752728	+	1.30376i
$296$	−13.9352	+	0.349094i	−0.809968	+	0.0202907i
$297$		0			0
$298$	2.50641	−	4.42616i	0.145192	−	0.256400i
$299$	−6.28881	+	1.68508i	−0.363691	+	0.0974508i
$300$		0			0
$301$	−19.9550	−	5.34693i	−1.15019	−	0.308192i
$302$	10.9528	+	10.7714i	0.630264	+	0.619827i
$303$		0			0
$304$	2.58066	−	11.1015i	0.148011	−	0.636712i
$305$		−	25.0589i		−	1.43487i
$306$		0			0
$307$	−24.0831	−	24.0831i	−1.37450	−	1.37450i	−0.853652	−	0.520843i	$-0.825618\pi$
$307$	−24.0831	−	24.0831i	−1.37450	−	1.37450i	−0.520843	−	0.853652i	$-0.674382\pi$
$308$	23.4567	−	24.2534i	1.33657	−	1.38197i
$309$		0			0
$310$	−0.128532	−	15.3952i	−0.00730011	−	0.874386i
$311$	−9.09165	+	5.24907i	−0.515540	+	0.297647i	−0.735108	−	0.677950i	$-0.762869\pi$
$311$	−9.09165	+	5.24907i	−0.515540	+	0.297647i	0.219568	+	0.975597i	$0.429535\pi$
$312$		0			0
$313$	−19.1380	−	11.0493i	−1.08174	−	0.624544i	−0.150376	−	0.988629i	$-0.548048\pi$
$313$	−19.1380	−	11.0493i	−1.08174	−	0.624544i	−0.931366	+	0.364085i	$0.881382\pi$
$314$	−6.87522	+	12.1412i	−0.387991	+	0.685167i
$315$		0			0
$316$	3.52038	+	5.86895i	0.198037	+	0.330154i
$317$	21.3323	−	5.71597i	1.19814	−	0.321041i	0.396042	−	0.918232i	$-0.370383\pi$
$317$	21.3323	−	5.71597i	1.19814	−	0.321041i	0.802099	+	0.597192i	$0.203717\pi$
$318$		0			0
$319$	29.1405	−	16.8243i	1.63155	−	0.941978i
$320$	−3.07429	+	14.3038i	−0.171858	+	0.799607i
$321$		0			0
$322$	−21.8505	−	5.65974i	−1.21768	−	0.315405i
$323$	−1.40911	+	1.40911i	−0.0784050	+	0.0784050i
$324$		0			0
$325$	1.34289	+	1.34289i	0.0744900	+	0.0744900i
$326$	−6.32064	+	3.71992i	−0.350068	+	0.206028i
$327$		0			0
$328$	8.57840	+	2.06978i	0.473663	+	0.114285i
$329$	−7.97655	−	13.8158i	−0.439761	−	0.761689i
$330$		0			0
$331$	−0.848686	−	3.16734i	−0.0466480	−	0.174093i	0.938672	−	0.344812i	$-0.112057\pi$
$331$	−0.848686	−	3.16734i	−0.0466480	−	0.174093i	−0.985320	+	0.170720i	$0.945391\pi$
$332$	−0.578908	+	2.31442i	−0.0317717	+	0.127020i
$333$		0			0
$334$	−7.59401	−	27.4233i	−0.415525	−	1.50054i
$335$	−12.2079	+	21.1447i	−0.666990	+	1.15526i
$336$		0			0
$337$	−11.5710	−	20.0416i	−0.630315	−	1.09174i	−0.987487	−	0.157699i	$-0.949593\pi$
$337$	−11.5710	−	20.0416i	−0.630315	−	1.09174i	0.357172	−	0.934038i	$-0.383741\pi$
$338$	−11.5860	+	11.7811i	−0.630196	+	0.640808i
$339$		0			0
$340$	1.77836	−	1.83877i	0.0964453	−	0.0997210i
$341$	25.2506	−	25.2506i	1.36739	−	1.36739i
$342$		0			0
$343$	17.1300			0.924931
$344$	18.2485	+	9.93494i	0.983894	+	0.535656i
$345$		0			0
$346$	−0.123544	−	14.7977i	−0.00664175	−	0.795530i
$347$	−2.03374	+	7.59002i	−0.109177	+	0.407454i	−0.998785	−	0.0492700i	$-0.984311\pi$
$347$	−2.03374	+	7.59002i	−0.109177	+	0.407454i	0.889609	+	0.456724i	$0.150977\pi$
$348$		0			0
$349$	−5.62138	−	20.9793i	−0.300905	−	1.12299i	−0.936413	−	0.350900i	$-0.885876\pi$
$349$	−5.62138	−	20.9793i	−0.300905	−	1.12299i	0.635508	−	0.772095i	$-0.280791\pi$
$350$	1.75711	+	6.34525i	0.0939216	+	0.339168i
$351$		0			0
$352$	−28.6547	+	18.1790i	−1.52730	+	0.968943i
$353$	0.108858	+	0.0628489i	0.00579390	+	0.00334511i	0.502894	−	0.864348i	$-0.332269\pi$
$353$	0.108858	+	0.0628489i	0.00579390	+	0.00334511i	−0.497100	+	0.867693i	$0.665602\pi$
$354$		0			0
$355$	−3.41701	+	12.7525i	−0.181356	+	0.676831i
$356$	0.685126	+	0.380449i	0.0363116	+	0.0201638i
$357$		0			0
$358$	12.6339	+	21.4666i	0.667721	+	1.13455i
$359$			4.07414i			0.215025i	0.994204	+	0.107512i	$0.0342886\pi$
$359$			4.07414i			0.215025i	−0.994204	+	0.107512i	$0.965711\pi$
$360$		0			0
$361$		−	10.8811i		−	0.572691i
$362$	−15.7210	+	9.25240i	−0.826280	+	0.486295i
$363$		0			0
$364$	6.20377	−	1.77383i	0.325166	−	0.0929738i
$365$	−1.77752	+	6.63379i	−0.0930396	+	0.347229i
$366$		0			0
$367$	−4.96310	−	2.86545i	−0.259072	−	0.149575i	0.364839	−	0.931071i	$-0.381124\pi$
$367$	−4.96310	−	2.86545i	−0.259072	−	0.149575i	−0.623911	+	0.781495i	$0.714457\pi$
$368$	20.0280	+	10.6879i	1.04403	+	0.557147i
$369$		0			0
$370$	−12.2841	+	3.40168i	−0.638620	+	0.176845i
$371$	−4.58689	−	17.1185i	−0.238139	−	0.888748i
$372$		0			0
$373$	−5.28955	+	19.7409i	−0.273882	+	1.02214i	0.682704	+	0.730695i	$0.260804\pi$
$373$	−5.28955	+	19.7409i	−0.273882	+	1.02214i	−0.956587	+	0.291448i	$0.905863\pi$
$374$	5.93309	−	0.0495344i	0.306793	−	0.00256136i
$375$		0			0
$376$	4.53951	+	15.3892i	0.234108	+	0.793637i
$377$	6.43473			0.331405
$378$		0			0
$379$	−2.85273	+	2.85273i	−0.146535	+	0.146535i	−0.776568	−	0.630033i	$-0.783041\pi$
$379$	−2.85273	+	2.85273i	−0.146535	+	0.146535i	0.630033	+	0.776568i	$0.283041\pi$
$380$	−0.174009	−	10.4204i	−0.00892647	−	0.534556i
$381$		0			0
$382$	3.56913	+	3.51003i	0.182612	+	0.179589i
$383$	7.78731	+	13.4880i	0.397913	+	0.689206i	0.993468	−	0.114109i	$-0.0364012\pi$
$383$	7.78731	+	13.4880i	0.397913	+	0.689206i	−0.595555	+	0.803314i	$0.703068\pi$
$384$		0			0
$385$	15.4263	−	26.7192i	0.786200	−	1.36174i
$386$	20.2531	−	5.60845i	1.03086	−	0.285462i
$387$		0			0
$388$	3.00278	−	1.80116i	0.152443	−	0.0914401i
$389$	7.22357	+	26.9587i	0.366250	+	1.36686i	0.865719	+	0.500531i	$0.166862\pi$
$389$	7.22357	+	26.9587i	0.366250	+	1.36686i	−0.499469	+	0.866332i	$0.666471\pi$
$390$		0			0
$391$	−1.98460	−	3.43743i	−0.100366	−	0.173838i
$392$	2.49888	+	0.602926i	0.126213	+	0.0304524i
$393$		0			0
$394$	12.0823	+	20.5295i	0.608699	+	1.03426i
$395$	4.42507	+	4.42507i	0.222649	+	0.222649i
$396$		0			0
$397$	27.4204	−	27.4204i	1.37619	−	1.37619i	0.525230	−	0.850961i	$-0.323979\pi$
$397$	27.4204	−	27.4204i	1.37619	−	1.37619i	0.850961	−	0.525230i	$-0.176021\pi$
$398$	5.53130	−	21.3546i	0.277259	−	1.07041i
$399$		0			0
$400$	−0.221094	−	6.61819i	−0.0110547	−	0.330910i
$401$	14.6316	−	8.44757i	0.730669	−	0.421852i	−0.0879981	−	0.996121i	$-0.528047\pi$
$401$	14.6316	−	8.44757i	0.730669	−	0.421852i	0.818667	+	0.574269i	$0.194714\pi$
$402$		0			0
$403$	6.59620	−	1.76745i	0.328580	−	0.0880428i
$404$	0.410198	−	1.63993i	0.0204081	−	0.0815896i
$405$		0			0
$406$	19.4121	+	10.9925i	0.963405	+	0.545549i
$407$	−25.6038	−	14.7824i	−1.26913	−	0.732735i
$408$		0			0
$409$	14.9737	−	8.64508i	0.740402	−	0.427471i	−0.0818133	−	0.996648i	$-0.526071\pi$
$409$	14.9737	−	8.64508i	0.740402	−	0.427471i	0.822216	+	0.569176i	$0.192738\pi$
$410$	8.06893	−	0.0673662i	0.398496	−	0.00332698i
$411$		0			0
$412$	0.354194	+	21.2107i	0.0174499	+	1.04497i
$413$	−28.1160	−	28.1160i	−1.38350	−	1.38350i
$414$		0			0
$415$			2.18151i			0.107086i
$416$	−6.48380	+	0.270812i	−0.317895	+	0.0132777i
$417$		0			0
$418$	16.9497	−	17.2351i	0.829035	−	0.842995i
$419$	−2.94162	−	0.788205i	−0.143708	−	0.0385063i	0.186248	−	0.982503i	$-0.440367\pi$
$419$	−2.94162	−	0.788205i	−0.143708	−	0.0385063i	−0.329956	+	0.943996i	$0.607034\pi$
$420$		0			0
$421$	8.89561	−	2.38357i	0.433546	−	0.116168i	−0.0354445	−	0.999372i	$-0.511285\pi$
$421$	8.89561	−	2.38357i	0.433546	−	0.116168i	0.468990	+	0.883203i	$0.344618\pi$
$422$	19.8769	+	11.2558i	0.967595	+	0.547922i
$423$		0			0
$424$	0.446378	+	17.8186i	0.0216780	+	0.865349i
$425$	−0.578900	+	1.00268i	−0.0280808	+	0.0486373i
$426$		0			0
$427$	37.2216	+	9.97350i	1.80128	+	0.482651i
$428$	−4.97559	−	17.4016i	−0.240504	−	0.841137i
$429$		0			0
$430$	18.3922	+	4.76396i	0.886950	+	0.229739i
$431$	7.28002			0.350666			0.175333	−	0.984509i	$-0.443900\pi$
$431$	7.28002			0.350666			0.175333	+	0.984509i	$0.443900\pi$
$432$		0			0
$433$	−19.9763			−0.960002			−0.480001	−	0.877268i	$-0.659364\pi$
$433$	−19.9763			−0.960002			−0.480001	+	0.877268i	$0.659364\pi$
$434$	22.9186	+	5.93638i	1.10013	+	0.284956i
$435$		0			0
$436$	−4.14966	+	1.18650i	−0.198733	+	0.0568232i
$437$	−15.6201	−	4.18539i	−0.747210	−	0.200214i
$438$		0			0
$439$	15.3133	−	26.5235i	0.730866	−	1.26590i	−0.225647	−	0.974209i	$-0.572450\pi$
$439$	15.3133	−	26.5235i	0.730866	−	1.26590i	0.956513	−	0.291688i	$-0.0942170\pi$
$440$	−21.3852	+	22.4841i	−1.01950	+	1.07189i
$441$		0			0
$442$	0.987334	+	0.559099i	0.0469627	+	0.0265937i
$443$	−28.7698	+	7.70884i	−1.36689	+	0.366258i	−0.866343	−	0.499450i	$-0.833536\pi$
$443$	−28.7698	+	7.70884i	−1.36689	+	0.366258i	−0.500550	+	0.865708i	$0.666869\pi$
$444$		0			0
$445$	0.692173	+	0.185467i	0.0328121	+	0.00879199i
$446$	15.9448	−	16.2133i	0.755010	−	0.767723i
$447$		0			0
$448$	−20.0228	−	10.2594i	−0.945987	−	0.484710i
$449$			26.8028i			1.26490i	0.774599	+	0.632452i	$0.217952\pi$
$449$			26.8028i			1.26490i	−0.774599	+	0.632452i	$0.782048\pi$
$450$		0			0
$451$	13.2344	+	13.2344i	0.623181	+	0.623181i
$452$	13.2821	−	0.221796i	0.624739	−	0.0104324i
$453$		0			0
$454$	−15.6211	+	0.130418i	−0.733132	+	0.00612080i
$455$	5.10961	−	2.95004i	0.239542	−	0.138300i
$456$		0			0
$457$	3.25342	+	1.87837i	0.152189	+	0.0878662i	0.574161	−	0.818743i	$-0.305329\pi$
$457$	3.25342	+	1.87837i	0.152189	+	0.0878662i	−0.421972	+	0.906609i	$0.638662\pi$
$458$	−0.497588	−	0.281770i	−0.0232507	−	0.0131662i
$459$		0			0
$460$	20.1378	+	5.03708i	0.938928	+	0.234855i
$461$	−3.92641	+	1.05208i	−0.182871	+	0.0490002i	−0.349092	−	0.937088i	$-0.613510\pi$
$461$	−3.92641	+	1.05208i	−0.182871	+	0.0490002i	0.166221	+	0.986088i	$0.446843\pi$
$462$		0			0
$463$	−20.2888	+	11.7137i	−0.942899	+	0.544383i	−0.890868	−	0.454263i	$-0.849903\pi$
$463$	−20.2888	+	11.7137i	−0.942899	+	0.544383i	−0.0520310	+	0.998645i	$0.516569\pi$
$464$	−16.3859	−	15.3265i	−0.760697	−	0.711515i
$465$		0			0
$466$	−4.12238	+	15.9153i	−0.190966	+	0.737260i
$467$	13.2570	−	13.2570i	0.613463	−	0.613463i	−0.330384	−	0.943847i	$-0.607178\pi$
$467$	13.2570	−	13.2570i	0.613463	−	0.613463i	0.943847	+	0.330384i	$0.107178\pi$
$468$		0			0
$469$	−26.5489	−	26.5489i	−1.22591	−	1.22591i
$470$	7.44151	+	12.6441i	0.343251	+	0.583229i
$471$		0			0
$472$	20.8563	+	34.1211i	0.959988	+	1.57055i
$473$	22.0339	+	38.1638i	1.01312	+	1.75477i
$474$		0			0
$475$	1.22086	+	4.55631i	0.0560169	+	0.209058i
$476$	2.02344	+	3.37335i	0.0927443	+	0.154617i
$477$		0			0
$478$	4.24372	−	1.17516i	0.194103	−	0.0537506i
$479$	17.6429	−	30.5584i	0.806124	−	1.39625i	−0.109405	−	0.993997i	$-0.534895\pi$
$479$	17.6429	−	30.5584i	0.806124	−	1.39625i	0.915529	−	0.402251i	$-0.131772\pi$
$480$		0			0
$481$	−2.82689	−	4.89631i	−0.128895	−	0.223252i
$482$	14.4525	+	14.2132i	0.658295	+	0.647394i
$483$		0			0
$484$	−49.9658	+	0.834372i	−2.27117	+	0.0379260i
$485$	2.26403	−	2.26403i	0.102804	−	0.102804i
$486$		0			0
$487$	−12.1433			−0.550266			−0.275133	−	0.961406i	$-0.588722\pi$
$487$	−12.1433			−0.550266			−0.275133	+	0.961406i	$0.588722\pi$
$488$	−34.0385	−	18.5314i	−1.54085	−	0.838878i
$489$		0			0
$490$	2.35047	−	0.0196237i	0.106183	−	0.000886509i
$491$	0.200028	−	0.746514i	0.00902713	−	0.0336897i	−0.961265	−	0.275625i	$-0.911115\pi$
$491$	0.200028	−	0.746514i	0.00902713	−	0.0336897i	0.970293	+	0.241935i	$0.0777820\pi$
$492$		0			0
$493$	1.01532	+	3.78924i	0.0457279	+	0.170659i
$494$	4.45505	−	1.23368i	0.200442	−	0.0555059i
$495$		0			0
$496$	−21.0069	−	11.2103i	−0.943237	−	0.503359i
$497$	−17.5821	−	10.1510i	−0.788664	−	0.455335i
$498$		0			0
$499$	−0.210439	+	0.785369i	−0.00942054	+	0.0351579i	−0.970476	−	0.241197i	$-0.922460\pi$
$499$	−0.210439	+	0.785369i	−0.00942054	+	0.0351579i	0.961056	+	0.276355i	$0.0891266\pi$
$500$	−6.69218	−	23.4052i	−0.299283	−	1.04671i
$501$		0			0
$502$	−5.27738	+	3.10593i	−0.235541	+	0.138624i
$503$			5.40486i			0.240991i	0.992714	+	0.120495i	$0.0384483\pi$
$503$			5.40486i			0.240991i	−0.992714	+	0.120495i	$0.961552\pi$
$504$		0			0
$505$		−	1.54576i		−	0.0687852i
$506$	24.4211	+	41.4947i	1.08565	+	1.84467i
$507$		0			0
$508$	13.4207	−	24.1685i	0.595449	−	1.07231i
$509$	7.42301	−	27.7030i	0.329019	−	1.22792i	−0.581191	−	0.813768i	$-0.697413\pi$
$509$	7.42301	−	27.7030i	0.329019	−	1.22792i	0.910210	−	0.414148i	$-0.135920\pi$
$510$		0			0
$511$	−9.14614	−	5.28052i	−0.404601	−	0.233597i
$512$	17.1559	+	14.7538i	0.758192	+	0.652031i
$513$		0			0
$514$	1.21186	+	4.37624i	0.0534528	+	0.193028i
$515$	5.02052	+	18.7368i	0.221231	+	0.825644i
$516$		0			0
$517$	−8.80753	+	32.8701i	−0.387355	+	1.44563i
$518$	−0.163639	−	19.6002i	−0.00718989	−	0.861185i
$519$		0			0
$520$	−5.69152	+	1.67889i	−0.249590	+	0.0736241i
$521$	−12.8208			−0.561689			−0.280845	−	0.959753i	$-0.590615\pi$
$521$	−12.8208			−0.561689			−0.280845	+	0.959753i	$0.590615\pi$
$522$		0			0
$523$	−2.08204	+	2.08204i	−0.0910411	+	0.0910411i	−0.751161	−	0.660120i	$-0.770506\pi$
$523$	−2.08204	+	2.08204i	−0.0910411	+	0.0910411i	0.660120	+	0.751161i	$0.270506\pi$
$524$	13.3640	+	12.9250i	0.583811	+	0.564633i
$525$		0			0
$526$	−3.02013	+	3.07098i	−0.131684	+	0.133901i
$527$	2.08161	+	3.60545i	0.0906762	+	0.157056i
$528$		0			0
$529$	4.60471	−	7.97560i	0.200205	−	0.346765i
$530$	4.34965	+	15.7074i	0.188937	+	0.682285i
$531$		0			0
$532$	15.5474	+	3.88888i	0.674063	+	0.168604i
$533$	0.926356	+	3.45721i	0.0401249	+	0.149748i
$534$		0			0
$535$	−8.27485	−	14.3325i	−0.357753	−	0.619647i
$536$	19.6938	+	32.2193i	0.850643	+	1.39166i
$537$		0			0
$538$	3.44121	−	2.02528i	0.148361	−	0.0873158i
$539$	3.85515	+	3.85515i	0.166053	+	0.166053i
$540$		0			0
$541$	22.7002	−	22.7002i	0.975956	−	0.975956i	−0.0237613	−	0.999718i	$-0.507564\pi$
$541$	22.7002	−	22.7002i	0.975956	−	0.975956i	0.999718	+	0.0237613i	$0.00756417\pi$
$542$	−19.0785	−	4.94172i	−0.819490	−	0.212265i
$543$		0			0
$544$	−1.18254	−	3.77541i	−0.0507011	−	0.161869i
$545$	−3.41779	+	1.97326i	−0.146402	+	0.0845253i
$546$		0			0
$547$	19.9084	−	5.33444i	0.851222	−	0.228084i	0.193271	−	0.981145i	$-0.438090\pi$
$547$	19.9084	−	5.33444i	0.851222	−	0.228084i	0.657951	+	0.753061i	$0.271424\pi$
$548$	20.4648	−	12.2755i	0.874214	−	0.524382i
$549$		0			0
$550$	6.92045	−	12.2211i	0.295089	−	0.521109i
$551$	13.8413	+	7.99125i	0.589657	+	0.340439i
$552$		0			0
$553$	−8.33402	+	4.81165i	−0.354399	+	0.204612i
$554$	−0.369448	−	44.2514i	−0.0156963	−	1.88006i
$555$		0			0
$556$	−1.79661	−	1.73760i	−0.0761934	−	0.0736905i
$557$	−10.7551	−	10.7551i	−0.455708	−	0.455708i	0.441535	−	0.897244i	$-0.354434\pi$
$557$	−10.7551	−	10.7551i	−0.455708	−	0.455708i	−0.897244	+	0.441535i	$0.854434\pi$
$558$		0			0
$559$			8.42723i			0.356434i
$560$	−20.0381	−	4.65807i	−0.846763	−	0.196840i
$561$		0			0
$562$	−22.9381	−	22.5582i	−0.967585	−	0.951562i
$563$	20.7659	+	5.56420i	0.875177	+	0.234503i	0.668325	−	0.743869i	$-0.267012\pi$
$563$	20.7659	+	5.56420i	0.875177	+	0.234503i	0.206852	+	0.978372i	$0.433678\pi$
$564$		0			0
$565$	11.7330	−	3.14385i	0.493611	−	0.132263i
$566$	−1.70557	+	3.01192i	−0.0716904	+	0.126601i
$567$		0			0
$568$	14.7953	+	14.0721i	0.620795	+	0.590452i
$569$	1.88272	−	3.26097i	0.0789277	−	0.136707i	−0.823860	−	0.566794i	$-0.808184\pi$
$569$	1.88272	−	3.26097i	0.0789277	−	0.136707i	0.902788	+	0.430087i	$0.141517\pi$
$570$		0			0
$571$	16.3264	+	4.37466i	0.683241	+	0.183074i	0.583712	−	0.811961i	$-0.301600\pi$
$571$	16.3264	+	4.37466i	0.683241	+	0.183074i	0.0995287	+	0.995035i	$0.468266\pi$
$572$	−12.0329	−	6.68183i	−0.503120	−	0.279381i
$573$		0			0
$574$	−3.11139	+	12.0121i	−0.129867	+	0.501375i
$575$	−9.39535			−0.391813
$576$		0			0
$577$	−9.76787			−0.406642			−0.203321	−	0.979112i	$-0.565173\pi$
$577$	−9.76787			−0.406642			−0.203321	+	0.979112i	$0.565173\pi$
$578$	5.85489	−	22.6039i	0.243531	−	0.940200i
$579$		0			0
$580$	−17.9362	−	9.95995i	−0.744762	−	0.413565i
$581$	−3.24034	−	0.868246i	−0.134432	−	0.0360209i
$582$		0			0
$583$	−18.9019	+	32.7390i	−0.782835	+	1.35591i
$584$	7.69644	+	7.32026i	0.318481	+	0.302914i
$585$		0			0
$586$	−5.43266	+	9.59372i	−0.224421	+	0.396313i
$587$	22.1733	−	5.94132i	0.915190	−	0.245224i	0.229662	−	0.973271i	$-0.426238\pi$
$587$	22.1733	−	5.94132i	0.915190	−	0.245224i	0.685528	+	0.728046i	$0.259571\pi$
$588$		0			0
$589$	16.3836	+	4.38996i	0.675073	+	0.180885i
$590$	26.0720	+	25.6403i	1.07337	+	1.05559i
$591$		0			0
$592$	−4.46362	+	19.2016i	−0.183454	+	0.789180i
$593$			1.37926i			0.0566394i	0.999599	+	0.0283197i	$0.00901564\pi$
$593$			1.37926i			0.0566394i	−0.999599	+	0.0283197i	$0.990984\pi$
$594$		0			0
$595$	2.54344	+	2.54344i	0.104271	+	0.104271i
$596$	−5.17076	−	5.00091i	−0.211803	−	0.204845i
$597$		0			0
$598$	0.0768689	+	9.20714i	0.00314340	+	0.376508i
$599$	−26.6820	+	15.4049i	−1.09020	+	0.629425i	−0.933629	−	0.358242i	$-0.883376\pi$
$599$	−26.6820	+	15.4049i	−1.09020	+	0.629425i	−0.156568	+	0.987667i	$0.550043\pi$
$600$		0			0
$601$	−2.43951	−	1.40845i	−0.0995098	−	0.0574520i	0.449419	−	0.893321i	$-0.351631\pi$
$601$	−2.43951	−	1.40845i	−0.0995098	−	0.0574520i	−0.548929	+	0.835869i	$0.684964\pi$
$602$	−14.3963	+	25.4230i	−0.586751	+	1.03616i
$603$		0			0
$604$	18.6304	−	11.1751i	0.758062	−	0.454710i
$605$	−44.1382	+	11.8268i	−1.79447	+	0.480828i
$606$		0			0
$607$	−26.2297	+	15.1437i	−1.06463	+	0.614666i	−0.926710	−	0.375777i	$-0.877376\pi$
$607$	−26.2297	+	15.1437i	−1.06463	+	0.614666i	−0.137922	+	0.990443i	$0.544042\pi$
$608$	−14.2831	−	7.46968i	−0.579258	−	0.302935i
$609$		0			0
$610$	−34.3065	−	8.88610i	−1.38903	−	0.359788i
$611$	−4.60158	+	4.60158i	−0.186160	+	0.186160i
$612$		0			0
$613$	3.66344	+	3.66344i	0.147965	+	0.147965i	0.777208	−	0.629243i	$-0.216635\pi$
$613$	3.66344	+	3.66344i	0.147965	+	0.147965i	−0.629243	+	0.777208i	$0.716635\pi$
$614$	−41.5107	+	24.4305i	−1.67523	+	0.985935i
$615$		0			0
$616$	−24.8858	−	40.7134i	−1.00268	−	1.64039i
$617$	−13.2053	−	22.8722i	−0.531624	−	0.920799i	−0.999319	−	0.0369091i	$-0.988249\pi$
$617$	−13.2053	−	22.8722i	−0.531624	−	0.920799i	0.467695	−	0.883890i	$-0.345085\pi$
$618$		0			0
$619$	−12.6542	−	47.2262i	−0.508617	−	1.89818i	−0.433858	−	0.900981i	$-0.642848\pi$
$619$	−12.6542	−	47.2262i	−0.508617	−	1.89818i	−0.0747583	−	0.997202i	$-0.523819\pi$
$620$	−21.1221	−	5.28329i	−0.848282	−	0.212182i
$621$		0			0
$622$	3.96218	+	14.3081i	0.158869	+	0.573704i
$623$	−0.550972	+	0.954312i	−0.0220742	+	0.0382337i
$624$		0			0
$625$	−6.99103	−	12.1088i	−0.279641	−	0.484353i
$626$	−21.9134	+	22.2823i	−0.875834	+	0.890582i
$627$		0			0
$628$	14.1837	+	13.7178i	0.565991	+	0.547399i
$629$	2.43726	−	2.43726i	0.0971799	−	0.0971799i
$630$		0			0
$631$	−36.5500			−1.45503			−0.727516	−	0.686090i	$-0.759325\pi$
$631$	−36.5500			−1.45503			−0.727516	+	0.686090i	$0.759325\pi$
$632$	9.28314	−	2.73834i	0.369264	−	0.108926i
$633$		0			0
$634$	−0.260747	−	31.2315i	−0.0103556	−	1.24036i
$635$	6.54255	−	24.4171i	0.259633	−	0.968964i
$636$		0			0
$637$	0.269847	+	1.00708i	0.0106917	+	0.0399020i
$638$	−12.6995	−	45.8603i	−0.502779	−	1.81563i
$639$		0			0
$640$	18.4922	+	9.28105i	0.730969	+	0.366866i
$641$	5.95425	+	3.43769i	0.235179	+	0.135780i	0.612959	−	0.790115i	$-0.289979\pi$
$641$	5.95425	+	3.43769i	0.235179	+	0.135780i	−0.377780	+	0.925895i	$0.623312\pi$
$642$		0			0
$643$	−7.59808	+	28.3564i	−0.299639	+	1.11827i	0.637823	+	0.770183i	$0.279835\pi$
$643$	−7.59808	+	28.3564i	−0.299639	+	1.11827i	−0.937463	+	0.348086i	$0.886832\pi$
$644$	−15.4968	+	27.9071i	−0.610658	+	1.09969i
$645$		0			0
$646$	1.42944	+	2.42880i	0.0562405	+	0.0955599i
$647$		−	1.90726i		−	0.0749821i	−0.999297	−	0.0374911i	$-0.988063\pi$
$647$		−	1.90726i		−	0.0749821i	0.999297	−	0.0374911i	$-0.0119366\pi$
$648$		0			0
$649$			84.8166i			3.32934i
$650$	2.31466	−	1.36226i	0.0907884	−	0.0534322i
$651$		0			0
$652$	2.85135	+	9.97229i	0.111667	+	0.390545i
$653$	5.94070	−	22.1710i	0.232478	−	0.867618i	−0.746792	−	0.665057i	$-0.768407\pi$
$653$	5.94070	−	22.1710i	0.232478	−	0.867618i	0.979270	−	0.202560i	$-0.0649263\pi$
$654$		0			0
$655$	14.7228	+	8.50019i	0.575266	+	0.332130i
$656$	5.87558	−	11.0102i	0.229403	−	0.429874i
$657$		0			0
$658$	−21.7428	+	6.02097i	−0.847624	+	0.234722i
$659$	3.86006	+	14.4059i	0.150366	+	0.561175i	0.999458	+	0.0329291i	$0.0104835\pi$
$659$	3.86006	+	14.4059i	0.150366	+	0.561175i	−0.849091	+	0.528246i	$0.822850\pi$
$660$		0			0
$661$	9.76236	−	36.4336i	0.379712	−	1.41710i	−0.466625	−	0.884455i	$-0.654530\pi$
$661$	9.76236	−	36.4336i	0.379712	−	1.41710i	0.846337	−	0.532648i	$-0.178803\pi$
$662$	−4.63715	+	0.0387148i	−0.180228	+	0.00150469i
$663$		0			0
$664$	2.96323	+	1.61326i	0.114996	+	0.0626065i
$665$	14.6545			0.568278
$666$		0			0
$667$	−22.5099	+	22.5099i	−0.871586	+	0.871586i
$668$	−40.2364	+	0.671901i	−1.55679	+	0.0259966i
$669$		0			0
$670$	24.6188	+	24.2112i	0.951109	+	0.935359i
$671$	−41.0993	−	71.1860i	−1.58662	−	2.74811i
$672$		0			0
$673$	−11.2966	+	19.5664i	−0.435454	+	0.754228i	−0.997333	−	0.0729916i	$-0.976745\pi$
$673$	−11.2966	+	19.5664i	−0.435454	+	0.754228i	0.561879	+	0.827220i	$0.310079\pi$
$674$	−31.5409	+	8.73421i	−1.21491	+	0.336429i
$675$		0			0
$676$	12.0202	+	20.0393i	0.462317	+	0.770743i
$677$	−8.14191	−	30.3860i	−0.312919	−	1.16783i	−0.925911	−	0.377741i	$-0.876701\pi$
$677$	−8.14191	−	30.3860i	−0.312919	−	1.16783i	0.612992	−	0.790089i	$-0.289966\pi$
$678$		0			0
$679$	2.46182	+	4.26400i	0.0944760	+	0.163637i
$680$	−1.88671	−	3.08668i	−0.0723520	−	0.118369i
$681$		0			0
$682$	−25.6148	−	43.5229i	−0.980841	−	1.66658i
$683$	−24.1502	−	24.1502i	−0.924081	−	0.924081i	0.0732336	−	0.997315i	$-0.476668\pi$
$683$	−24.1502	−	24.1502i	−0.924081	−	0.924081i	−0.997315	+	0.0732336i	$0.976668\pi$
$684$		0			0
$685$	15.4301	−	15.4301i	0.589553	−	0.589553i
$686$	6.07443	−	23.4515i	0.231923	−	0.895382i
$687$		0			0
$688$	20.0723	−	21.4598i	0.765251	−	0.818148i
$689$	−6.26079	+	3.61467i	−0.238517	+	0.137708i
$690$		0			0
$691$	39.9843	−	10.7138i	1.52108	−	0.407571i	0.600980	−	0.799264i	$-0.294777\pi$
$691$	39.9843	−	10.7138i	1.52108	−	0.407571i	0.920096	+	0.391693i	$0.128111\pi$
$692$	−20.3024	−	5.07826i	−0.771781	−	0.193046i
$693$		0			0
$694$	9.66981	+	5.47574i	0.367061	+	0.207856i
$695$	−1.97928	−	1.14273i	−0.0750782	−	0.0433464i
$696$		0			0
$697$	−1.88969	+	1.09101i	−0.0715772	+	0.0413251i
$698$	−30.7147	+	0.256432i	−1.16257	+	0.00970610i
$699$		0			0
$700$	9.30995	−	0.155465i	0.351883	−	0.00587604i
$701$	21.1814	+	21.1814i	0.800009	+	0.800009i	0.983097	−	0.183088i	$-0.0586092\pi$
$701$	21.1814	+	21.1814i	0.800009	+	0.800009i	−0.183088	+	0.983097i	$0.558609\pi$
$702$		0			0
$703$		−	14.0428i		−	0.529633i
$704$	14.7265	+	45.6756i	0.555024	+	1.72146i
$705$		0			0
$706$	0.124644	−	0.126743i	0.00469104	−	0.00477003i
$707$	2.29601	+	0.615214i	0.0863503	+	0.0231375i
$708$		0			0
$709$	−15.8532	+	4.24787i	−0.595381	+	0.159532i	−0.543911	−	0.839143i	$-0.683057\pi$
$709$	−15.8532	+	4.24787i	−0.595381	+	0.159532i	−0.0514698	+	0.998675i	$0.516391\pi$
$710$	16.2469	+	9.20014i	0.609734	+	0.345275i
$711$		0			0
$712$	0.763799	−	0.803050i	0.0286246	−	0.0300956i
$713$	−16.8919	+	29.2576i	−0.632606	+	1.09571i
$714$		0			0
$715$	−12.1566	−	3.25736i	−0.454633	−	0.121819i
$716$	33.8686	−	9.68396i	1.26573	−	0.361906i
$717$		0			0
$718$	5.57764	+	1.44472i	0.208156	+	0.0539166i
$719$	23.3461			0.870664			0.435332	−	0.900270i	$-0.356631\pi$
$719$	23.3461			0.870664			0.435332	+	0.900270i	$0.356631\pi$
$720$		0			0
$721$	−29.8292			−1.11090
$722$	−14.8966	−	3.85854i	−0.554395	−	0.143600i
$723$		0			0
$724$	7.09203	+	24.8036i	0.263573	+	0.921819i
$725$	8.96937	+	2.40334i	0.333114	+	0.0892576i
$726$		0			0
$727$	−2.90255	+	5.02736i	−0.107650	+	0.186454i	−0.914818	−	0.403867i	$-0.867666\pi$
$727$	−2.90255	+	5.02736i	−0.107650	+	0.186454i	0.807168	+	0.590322i	$0.200999\pi$
$728$	−0.228521	−	9.12218i	−0.00846956	−	0.338090i
$729$		0			0
$730$	8.45156	+	4.78588i	0.312806	+	0.177133i
$731$	−4.96258	+	1.32972i	−0.183548	+	0.0491814i
$732$		0			0
$733$	0.898647	+	0.240792i	0.0331923	+	0.00889384i	0.275377	−	0.961336i	$-0.411197\pi$
$733$	0.898647	+	0.240792i	0.0331923	+	0.00889384i	−0.242185	+	0.970230i	$0.577864\pi$
$734$	−5.68285	+	5.77854i	−0.209758	+	0.213290i
$735$		0			0
$736$	21.7342	−	23.6289i	0.801134	−	0.870973i
$737$			80.0891i			2.95012i
$738$		0			0
$739$	5.91328	+	5.91328i	0.217523	+	0.217523i	0.807454	−	0.589931i	$-0.200845\pi$
$739$	5.91328	+	5.91328i	0.217523	+	0.217523i	−0.589931	+	0.807454i	$0.700845\pi$
$740$	0.300974	+	18.0236i	0.0110640	+	0.662561i
$741$		0			0
$742$	−25.0624	+	0.209242i	−0.920068	+	0.00768150i
$743$	−20.3899	+	11.7721i	−0.748032	+	0.431876i	−0.824982	−	0.565158i	$-0.808815\pi$
$743$	−20.3899	+	11.7721i	−0.748032	+	0.431876i	0.0769504	+	0.997035i	$0.475482\pi$
$744$		0			0
$745$	−5.69647	−	3.28886i	−0.208703	−	0.120494i
$746$	25.1502	+	14.2418i	0.920814	+	0.521431i
$747$		0			0
$748$	2.03611	−	8.14017i	0.0744475	−	0.297634i
$749$	24.5823	−	6.58682i	0.898219	−	0.240677i
$750$		0			0
$751$	13.0649	−	7.54301i	0.476744	−	0.275248i	−0.242315	−	0.970198i	$-0.577907\pi$
$751$	13.0649	−	7.54301i	0.476744	−	0.275248i	0.719059	+	0.694949i	$0.244573\pi$
$752$	22.6781	−	0.757607i	0.826985	−	0.0276271i
$753$		0			0
$754$	2.28181	−	8.80936i	0.0830985	−	0.320818i
$755$	14.0470	−	14.0470i	0.511222	−	0.511222i
$756$		0			0
$757$	4.48920	+	4.48920i	0.163163	+	0.163163i	0.783966	−	0.620803i	$-0.213193\pi$
$757$	4.48920	+	4.48920i	0.163163	+	0.163163i	−0.620803	+	0.783966i	$0.713193\pi$
$758$	2.89388	+	4.91709i	0.105111	+	0.178597i
$759$		0			0
$760$	−14.3276	−	3.45694i	−0.519717	−	0.125396i
$761$	19.0628	+	33.0177i	0.691025	+	1.19689i	0.971502	+	0.237030i	$0.0761739\pi$
$761$	19.0628	+	33.0177i	0.691025	+	1.19689i	−0.280477	+	0.959861i	$0.590493\pi$
$762$		0			0
$763$	−1.57072	−	5.86202i	−0.0568640	−	0.212219i
$764$	6.07099	−	3.64157i	0.219641	−	0.131747i
$765$		0			0
$766$	21.2270	−	5.87813i	0.766963	−	0.212385i
$767$	−8.10989	+	14.0467i	−0.292831	+	0.507198i
$768$		0			0
$769$	17.5683	+	30.4291i	0.633528	+	1.09730i	0.986825	+	0.161791i	$0.0517271\pi$
$769$	17.5683	+	30.4291i	0.633528	+	1.09730i	−0.353297	+	0.935511i	$0.614940\pi$
$770$	−31.1092	−	30.5940i	−1.12110	−	1.10253i
$771$		0			0
$772$	−0.496223	−	29.7160i	−0.0178595	−	1.06950i
$773$	−23.4773	+	23.4773i	−0.844420	+	0.844420i	−0.989430	−	0.145010i	$-0.953678\pi$
$773$	−23.4773	+	23.4773i	−0.844420	+	0.844420i	0.145010	+	0.989430i	$0.453678\pi$
$774$		0			0
$775$	9.85458			0.353987
$776$	−1.40104	−	4.74961i	−0.0502944	−	0.170501i
$777$		0			0
$778$	39.4690	−	0.329520i	1.41503	−	0.0118139i
$779$	−2.30087	+	8.58698i	−0.0824374	+	0.307660i
$780$		0			0
$781$	11.2085	+	41.8308i	0.401073	+	1.49682i
$782$	−5.40972	+	1.49805i	−0.193451	+	0.0535700i
$783$		0			0
$784$	1.71155	−	3.20725i	0.0611268	−	0.114545i
$785$	15.6257	+	9.02153i	0.557707	+	0.321992i
$786$		0			0
$787$	0.0559379	−	0.208763i	0.00199397	−	0.00744160i	−0.964922	−	0.262538i	$-0.915441\pi$
$787$	0.0559379	−	0.208763i	0.00199397	−	0.00744160i	0.966916	+	0.255096i	$0.0821072\pi$
$788$	32.3900	−	9.26119i	1.15385	−	0.329916i
$789$		0			0
$790$	7.62723	−	4.48890i	0.271365	−	0.159708i
$791$			18.6790i			0.664150i
$792$		0			0
$793$		−	15.7191i		−	0.558202i
$794$	−27.8159	−	47.2629i	−0.987151	−	1.67730i
$795$		0			0
$796$	−27.2738	−	15.1451i	−0.966693	−	0.536803i
$797$	0.791183	−	2.95273i	0.0280251	−	0.104591i	−0.950497	−	0.310735i	$-0.899425\pi$
$797$	0.791183	−	2.95273i	0.0280251	−	0.104591i	0.978522	+	0.206144i	$0.0660915\pi$
$798$		0			0
$799$	−3.43583	−	1.98367i	−0.121551	−	0.0701774i
$800$	−9.13893	−	2.04418i	−0.323110	−	0.0722727i
$801$		0			0
$802$	−6.37652	−	23.0268i	−0.225163	−	0.813103i
$803$	5.83064	+	21.7602i	0.205759	+	0.767902i
$804$		0			0
$805$	−7.55460	+	28.1942i	−0.266265	+	0.993714i
$806$	−0.0806262	−	9.65717i	−0.00283994	−	0.340159i
$807$		0			0
$808$	−2.09966	−	1.14311i	−0.0738658	−	0.0402144i
$809$	42.5506			1.49600			0.748000	−	0.663699i	$-0.231014\pi$
$809$	42.5506			1.49600			0.748000	+	0.663699i	$0.231014\pi$
$810$		0			0
$811$	15.1448	−	15.1448i	0.531806	−	0.531806i	−0.389304	−	0.921109i	$-0.627284\pi$
$811$	15.1448	−	15.1448i	0.531806	−	0.531806i	0.921109	+	0.389304i	$0.127284\pi$
$812$	21.9328	−	22.6777i	0.769690	−	0.795833i
$813$		0			0
$814$	−29.3169	+	29.8105i	−1.02756	+	1.04486i
$815$	4.74206	+	8.21348i	0.166107	+	0.287706i
$816$		0			0
$817$	−10.4657	+	18.1272i	−0.366150	+	0.634190i
$818$	−6.52560	−	23.5651i	−0.228162	−	0.823935i
$819$		0			0
$820$	2.76908	−	11.0705i	0.0967006	−	0.386599i
$821$	−7.15352	−	26.6973i	−0.249660	−	0.931742i	−0.970984	−	0.239145i	$-0.923133\pi$
$821$	−7.15352	−	26.6973i	−0.249660	−	0.931742i	0.721324	−	0.692598i	$-0.243534\pi$
$822$		0			0
$823$	−10.1921	−	17.6532i	−0.355273	−	0.615350i	0.631892	−	0.775057i	$-0.282279\pi$
$823$	−10.1921	−	17.6532i	−0.355273	−	0.615350i	−0.987165	+	0.159706i	$0.948945\pi$
$824$	29.1637	+	7.03658i	1.01597	+	0.245131i
$825$		0			0
$826$	−48.4618	+	28.5215i	−1.68620	+	0.992391i
$827$	8.34698	+	8.34698i	0.290253	+	0.290253i	0.837180	−	0.546927i	$-0.184203\pi$
$827$	8.34698	+	8.34698i	0.290253	+	0.290253i	−0.546927	+	0.837180i	$0.684203\pi$
$828$		0			0
$829$	−2.48126	+	2.48126i	−0.0861778	+	0.0861778i	−0.748882	−	0.662704i	$-0.769409\pi$
$829$	−2.48126	+	2.48126i	−0.0861778	+	0.0861778i	0.662704	+	0.748882i	$0.269409\pi$
$830$	2.98656	+	0.773582i	0.103665	+	0.0268514i
$831$		0			0
$832$	−1.92846	+	8.97258i	−0.0668573	+	0.311068i
$833$	−0.550465	+	0.317811i	−0.0190725	+	0.0110115i
$834$		0			0
$835$	−35.5435	+	9.52386i	−1.23004	+	0.329587i
$836$	−17.5849	−	29.3164i	−0.608186	−	1.01393i
$837$		0			0
$838$	−2.12220	+	3.74767i	−0.0733103	+	0.129461i
$839$	17.7430	+	10.2439i	0.612558	+	0.353660i	0.773966	−	0.633227i	$-0.218270\pi$
$839$	17.7430	+	10.2439i	0.612558	+	0.353660i	−0.161408	+	0.986888i	$0.551604\pi$
$840$		0			0
$841$	2.13260	−	1.23126i	0.0735380	−	0.0424572i
$842$	−0.108732	−	13.0236i	−0.00374716	−	0.448824i
$843$		0			0
$844$	22.4580	−	23.2208i	0.773038	−	0.799294i
$845$	15.1092	+	15.1092i	0.519774	+	0.519774i
$846$		0			0
$847$		−	70.2684i		−	2.41445i
$848$	24.5526	+	5.70753i	0.843139	+	0.195997i
$849$		0			0
$850$	1.16743	+	1.14809i	0.0400424	+	0.0393793i
$851$	27.0172	+	7.23923i	0.926137	+	0.248158i
$852$		0			0
$853$	−15.1632	+	4.06296i	−0.519177	+	0.139113i	−0.508886	−	0.860834i	$-0.669942\pi$
$853$	−15.1632	+	4.06296i	−0.519177	+	0.139113i	−0.0102909	+	0.999947i	$0.503276\pi$
$854$	26.8531	−	47.4209i	0.918896	−	1.62271i
$855$		0			0
$856$	−25.5877	+	0.641003i	−0.874570	+	0.0219090i
$857$	0.102894	−	0.178217i	0.00351478	−	0.00608778i	−0.864263	−	0.503041i	$-0.832215\pi$
$857$	0.102894	−	0.178217i	0.00351478	−	0.00608778i	0.867777	+	0.496953i	$0.165548\pi$
$858$		0			0
$859$	2.73650	+	0.733242i	0.0933681	+	0.0250179i	0.305201	−	0.952288i	$-0.401276\pi$
$859$	2.73650	+	0.733242i	0.0933681	+	0.0250179i	−0.211833	+	0.977306i	$0.567943\pi$
$860$	13.0440	−	23.4902i	0.444798	−	0.801008i
$861$		0			0
$862$	2.58155	−	9.96659i	0.0879281	−	0.339463i
$863$	−26.9928			−0.918846			−0.459423	−	0.888218i	$-0.651944\pi$
$863$	−26.9928			−0.918846			−0.459423	+	0.888218i	$0.651944\pi$
$864$		0			0
$865$	−19.1365			−0.650660
$866$	−7.08378	+	27.3483i	−0.240717	+	0.929333i
$867$		0			0
$868$	16.2542	−	29.2712i	0.551704	−	0.993528i
$869$	19.8281	+	5.31292i	0.672621	+	0.180228i
$870$		0			0
$871$	−7.65786	+	13.2638i	−0.259477	+	0.449427i
$872$	0.152857	+	6.10177i	0.00517638	+	0.206632i
$873$		0			0
$874$	−11.2689	+	19.9002i	−0.381178	+	0.673136i
$875$	33.0633	−	8.85929i	1.11774	−	0.299499i
$876$		0			0
$877$	52.0038	+	13.9344i	1.75604	+	0.470531i	0.985900	−	0.167338i	$-0.0535171\pi$
$877$	52.0038	+	13.9344i	1.75604	+	0.470531i	0.770145	+	0.637869i	$0.220184\pi$
$878$	−30.8813	−	30.3699i	−1.04219	−	1.02494i
$879$		0			0
$880$	23.1982	+	37.2500i	0.782010	+	1.25570i
$881$		−	27.9049i		−	0.940139i	−0.882629	−	0.470069i	$-0.844229\pi$
$881$		−	27.9049i		−	0.940139i	0.882629	−	0.470069i	$-0.155771\pi$
$882$		0			0
$883$	3.83601	+	3.83601i	0.129092	+	0.129092i	0.768701	−	0.639609i	$-0.220904\pi$
$883$	3.83601	+	3.83601i	0.129092	+	0.129092i	−0.639609	+	0.768701i	$0.720904\pi$
$884$	1.11554	−	1.15343i	0.0375198	−	0.0387941i
$885$		0			0
$886$	0.351656	+	42.1204i	0.0118141	+	1.41506i
$887$	44.3036	−	25.5787i	1.48757	−	0.858849i	0.487671	−	0.873028i	$-0.337847\pi$
$887$	44.3036	−	25.5787i	1.48757	−	0.858849i	0.999899	+	0.0141788i	$0.00451340\pi$
$888$		0			0
$889$	33.6644	+	19.4361i	1.12907	+	0.651867i
$890$	0.499361	−	0.881840i	0.0167386	−	0.0295593i
$891$		0			0
$892$	−16.5424	−	27.5784i	−0.553881	−	0.923393i
$893$	−15.6128	+	4.18343i	−0.522462	+	0.139993i
$894$		0			0
$895$	27.8952	−	16.1053i	0.932434	−	0.538341i
$896$	−21.1457	+	23.7738i	−0.706427	+	0.794226i
$897$		0			0
$898$	36.6940	+	9.50451i	1.22449	+	0.317170i
$899$	23.6101	−	23.6101i	0.787442	−	0.787442i
$900$		0			0
$901$	−3.11647	−	3.11647i	−0.103825	−	0.103825i
$902$	22.8113	−	13.4253i	0.759533	−	0.447012i
$903$		0			0
$904$	4.40631	−	18.2623i	0.146552	−	0.607396i
$905$	11.7947	+	20.4290i	0.392069	+	0.679084i
$906$		0			0
$907$	2.67896	+	9.99802i	0.0889535	+	0.331979i	0.996033	−	0.0889794i	$-0.0283605\pi$
$907$	2.67896	+	9.99802i	0.0889535	+	0.331979i	−0.907080	+	0.420958i	$0.861694\pi$
$908$	−5.36081	+	21.4320i	−0.177905	+	0.711246i
$909$		0			0
$910$	−2.22679	−	8.04134i	−0.0738173	−	0.266568i
$911$	−5.69107	+	9.85722i	−0.188553	+	0.326584i	−0.944768	−	0.327739i	$-0.893713\pi$
$911$	−5.69107	+	9.85722i	−0.188553	+	0.326584i	0.756215	+	0.654324i	$0.227047\pi$
$912$		0			0
$913$	3.57791	+	6.19712i	0.118411	+	0.205095i
$914$	3.72524	−	3.78796i	0.123220	−	0.125295i
$915$		0			0
$916$	−0.562201	+	0.581296i	−0.0185756	+	0.0192066i
$917$	−18.4856	+	18.4856i	−0.610447	+	0.610447i
$918$		0			0
$919$	11.8316			0.390288			0.195144	−	0.980775i	$-0.437483\pi$
$919$	11.8316			0.390288			0.195144	+	0.980775i	$0.437483\pi$
$920$	14.0369	−	25.7831i	0.462785	−	0.850043i
$921$		0			0
$922$	0.0479930	+	5.74846i	0.00158056	+	0.189315i
$923$	−2.14345	+	7.99945i	−0.0705524	+	0.263305i
$924$		0			0
$925$	−2.11165	−	7.88080i	−0.0694307	−	0.259119i
$926$	8.84192	+	31.9298i	0.290563	+	1.04928i
$927$		0			0
$928$	−26.7931	+	16.9980i	−0.879526	+	0.557986i
$929$	−35.7139	−	20.6194i	−1.17174	−	0.676502i	−0.217647	−	0.976027i	$-0.569838\pi$
$929$	−35.7139	−	20.6194i	−1.17174	−	0.676502i	−0.954088	+	0.299525i	$0.903172\pi$
$930$		0			0
$931$	−0.670242	+	2.50138i	−0.0219663	+	0.0819794i
$932$	20.3267	+	11.2874i	0.665823	+	0.369730i
$933$		0			0
$934$	−13.4483	−	22.8504i	−0.440041	−	0.747688i
$935$		−	7.67271i		−	0.250924i
$936$		0			0
$937$			15.6750i			0.512081i	0.966666	+	0.256041i	$0.0824181\pi$
$937$			15.6750i			0.512081i	−0.966666	+	0.256041i	$0.917582\pi$
$938$	−45.7607	+	26.9318i	−1.49414	+	0.879355i
$939$		0			0
$940$	19.9490	−	5.70397i	0.650666	−	0.186043i
$941$	−2.58237	+	9.63753i	−0.0841828	+	0.314174i	−0.995158	−	0.0982863i	$-0.968664\pi$
$941$	−2.58237	+	9.63753i	−0.0841828	+	0.314174i	0.910975	+	0.412461i	$0.135331\pi$
$942$		0			0
$943$	−15.3345	−	8.85340i	−0.499361	−	0.288306i
$944$	54.1088	−	16.4533i	1.76109	−	0.535509i
$945$		0			0
$946$	60.0609	−	16.6319i	1.95275	−	0.540750i
$947$	0.612832	+	2.28712i	0.0199144	+	0.0743214i	0.975168	−	0.221467i	$-0.0710844\pi$
$947$	0.612832	+	2.28712i	0.0199144	+	0.0743214i	−0.955254	+	0.295788i	$0.904418\pi$
$948$		0			0
$949$	−1.11501	+	4.16129i	−0.0361949	+	0.135081i
$950$	6.67067	−	0.0556924i	0.216425	−	0.00180690i
$951$		0			0
$952$	5.33575	−	1.57394i	0.172933	−	0.0510118i
$953$	43.1152			1.39664			0.698320	−	0.715786i	$-0.253931\pi$
$953$	43.1152			1.39664			0.698320	+	0.715786i	$0.253931\pi$
$954$		0			0
$955$	4.57740	−	4.57740i	0.148121	−	0.148121i
$956$	−0.103976	−	6.22652i	−0.00336282	−	0.201380i
$957$		0			0
$958$	−35.5791	−	34.9900i	−1.14951	−	1.13047i
$959$	16.7781	+	29.0605i	0.541792	+	0.938411i
$960$		0			0
$961$	2.21754	−	3.84089i	0.0715334	−	0.123900i
$962$	−7.70565	+	2.13383i	−0.248440	+	0.0687974i
$963$		0			0
$964$	24.5834	−	14.7459i	0.791777	−	0.474933i
$965$	−7.03372	−	26.2502i	−0.226423	−	0.845023i
$966$		0			0
$967$	−21.1271	−	36.5932i	−0.679401	−	1.17676i	−0.975162	−	0.221495i	$-0.928906\pi$
$967$	−21.1271	−	36.5932i	−0.679401	−	1.17676i	0.295761	−	0.955262i	$-0.404427\pi$
$968$	−16.5760	+	68.7008i	−0.532773	+	2.20813i
$969$		0			0
$970$	−2.29669	−	3.90238i	−0.0737423	−	0.125298i
$971$	11.0093	+	11.0093i	0.353305	+	0.353305i	0.861338	−	0.508033i	$-0.169627\pi$
$971$	11.0093	+	11.0093i	0.353305	+	0.353305i	−0.508033	+	0.861338i	$0.669627\pi$
$972$		0			0
$973$	2.48513	−	2.48513i	0.0796697	−	0.0796697i
$974$	−4.30612	+	16.6246i	−0.137977	+	0.532686i
$975$		0			0
$976$	−37.4405	+	40.0285i	−1.19844	+	1.28128i
$977$	−30.5197	+	17.6206i	−0.976413	+	0.563732i	−0.901185	−	0.433434i	$-0.857302\pi$
$977$	−30.5197	+	17.6206i	−0.976413	+	0.563732i	−0.0752275	+	0.997166i	$0.523968\pi$
$978$		0			0
$979$	2.27047	−	0.608371i	0.0725646	−	0.0194436i
$980$	0.806631	−	3.22483i	0.0257669	−	0.103013i
$981$		0			0
$982$	−0.951071	−	0.538565i	−0.0303499	−	0.0171863i
$983$	33.9109	+	19.5785i	1.08159	+	0.624456i	0.931325	−	0.364190i	$-0.118654\pi$
$983$	33.9109	+	19.5785i	1.08159	+	0.624456i	0.150264	+	0.988646i	$0.451987\pi$
$984$		0			0
$985$	26.6774	−	15.4022i	0.850013	−	0.490755i
$986$	5.54764	−	0.0463164i	0.176673	−	0.00147501i
$987$		0			0
$988$	−0.109153	−	6.53658i	−0.00347263	−	0.207956i
$989$	−29.4801	−	29.4801i	−0.937411	−	0.937411i
$990$		0			0
$991$			15.1164i			0.480188i	0.970750	+	0.240094i	$0.0771783\pi$
$991$			15.1164i			0.480188i	−0.970750	+	0.240094i	$0.922822\pi$
$992$	−22.7965	+	24.7839i	−0.723791	+	0.786888i
$993$		0			0
$994$	−20.1318	+	20.4708i	−0.638543	+	0.649295i
$995$	−27.5543	−	7.38315i	−0.873530	−	0.234062i
$996$		0			0
$997$	38.7668	−	10.3875i	1.22776	−	0.328976i	0.414051	−	0.910254i	$-0.364113\pi$
$997$	38.7668	−	10.3875i	1.22776	−	0.328976i	0.813706	+	0.581277i	$0.197447\pi$
$998$	1.00057	+	0.566596i	0.0316726	+	0.0179353i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.251.13		88
3.2	odd	2		144.2.u.a.11.10	✓	88
4.3	odd	2		1728.2.z.a.143.6		88
9.4	even	3		144.2.u.a.59.17	yes	88
9.5	odd	6	inner	432.2.v.a.395.6		88
12.11	even	2		576.2.y.a.335.16		88
16.3	odd	4	inner	432.2.v.a.35.6		88
16.13	even	4		1728.2.z.a.1007.6		88
36.23	even	6		1728.2.z.a.719.6		88
36.31	odd	6		576.2.y.a.527.18		88
48.29	odd	4		576.2.y.a.47.18		88
48.35	even	4		144.2.u.a.83.17	yes	88
144.13	even	12		576.2.y.a.239.16		88
144.67	odd	12		144.2.u.a.131.10	yes	88
144.77	odd	12		1728.2.z.a.1583.6		88
144.131	even	12	inner	432.2.v.a.179.13		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.10	✓	88	3.2	odd	2
144.2.u.a.59.17	yes	88	9.4	even	3
144.2.u.a.83.17	yes	88	48.35	even	4
144.2.u.a.131.10	yes	88	144.67	odd	12
432.2.v.a.35.6		88	16.3	odd	4	inner
432.2.v.a.179.13		88	144.131	even	12	inner
432.2.v.a.251.13		88	1.1	even	1	trivial
432.2.v.a.395.6		88	9.5	odd	6	inner
576.2.y.a.47.18		88	48.29	odd	4
576.2.y.a.239.16		88	144.13	even	12
576.2.y.a.335.16		88	12.11	even	2
576.2.y.a.527.18		88	36.31	odd	6
1728.2.z.a.143.6		88	4.3	odd	2
1728.2.z.a.719.6		88	36.23	even	6
1728.2.z.a.1007.6		88	16.13	even	4
1728.2.z.a.1583.6		88	144.77	odd	12

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.354608 - 1.36903i) q^{2} +(-1.74851 - 0.970941i) q^{4} +(-1.76649 - 0.473330i) q^{5} +(1.40613 - 2.43549i) q^{7} +(-1.94929 + 2.04946i) q^{8} +O(q^{10})\)	\(q+(0.354608 - 1.36903i) q^{2} +(-1.74851 - 0.970941i) q^{4} +(-1.76649 - 0.473330i) q^{5} +(1.40613 - 2.43549i) q^{7} +(-1.94929 + 2.04946i) q^{8} +(-1.27442 + 2.25054i) q^{10} +(-5.79446 + 1.55262i) q^{11} +(-1.10810 - 0.296913i) q^{13} +(-2.83565 - 2.78869i) q^{14} +(2.11455 + 3.39539i) q^{16} -0.699378i q^{17} +(-2.01481 - 2.01481i) q^{19} +(2.62914 + 2.54278i) q^{20} +(0.0708264 + 8.48338i) q^{22} +(4.91498 - 2.83767i) q^{23} +(-1.43368 - 0.827735i) q^{25} +(-0.799424 + 1.41173i) q^{26} +(-4.82335 + 2.89320i) q^{28} +(-5.41802 + 1.45175i) q^{29} +(-5.15522 + 2.97637i) q^{31} +(5.39824 - 1.69085i) q^{32} +(-0.957472 - 0.248005i) q^{34} +(-3.63671 + 3.63671i) q^{35} +(3.48490 + 3.48490i) q^{37} +(-3.47280 + 2.04387i) q^{38} +(4.41347 - 2.69770i) q^{40} +(-1.55998 - 2.70196i) q^{41} +(-1.90129 - 7.09570i) q^{43} +(11.6392 + 2.91131i) q^{44} +(-2.14197 - 7.73504i) q^{46} +(2.83634 - 4.91269i) q^{47} +(-0.454420 - 0.787079i) q^{49} +(-1.64159 + 1.66923i) q^{50} +(1.64923 + 1.59505i) q^{52} +(4.45605 - 4.45605i) q^{53} +10.9708 q^{55} +(2.25049 + 7.62929i) q^{56} +(0.0662251 + 7.93225i) q^{58} +(3.65938 - 13.6570i) q^{59} +(3.54643 + 13.2354i) q^{61} +(2.24666 + 8.11312i) q^{62} +(-0.400567 - 7.98997i) q^{64} +(1.81690 + 1.04899i) q^{65} +(3.45542 - 12.8958i) q^{67} +(-0.679055 + 1.22287i) q^{68} +(3.68917 + 6.26839i) q^{70} -7.21910i q^{71} -3.75535i q^{73} +(6.00671 - 3.53517i) q^{74} +(1.56664 + 5.47916i) q^{76} +(-4.36638 + 16.2956i) q^{77} +(-2.96345 - 1.71095i) q^{79} +(-2.12818 - 6.99881i) q^{80} +(-4.25226 + 1.17752i) q^{82} +(-0.308735 - 1.15222i) q^{83} +(-0.331036 + 1.23544i) q^{85} +(-10.3885 + 0.0867317i) q^{86} +(8.11303 - 14.9020i) q^{88} -0.391835 q^{89} +(-2.28126 + 2.28126i) q^{91} +(-11.3491 + 0.189517i) q^{92} +(-5.71984 - 5.62513i) q^{94} +(2.60547 + 4.51280i) q^{95} +(-0.875387 + 1.51622i) q^{97} +(-1.23868 + 0.343012i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 40 q^{46} - 24 q^{49} - 72 q^{50} - 2 q^{52} - 16 q^{55} - 36 q^{56} + 16 q^{58} + 42 q^{59} - 2 q^{61} - 44 q^{64} + 12 q^{65} - 2 q^{67} - 96 q^{68} - 16 q^{70} - 78 q^{74} - 14 q^{76} + 6 q^{77} - 36 q^{82} - 54 q^{83} + 8 q^{85} - 54 q^{86} + 22 q^{88} + 20 q^{91} - 108 q^{92} + 6 q^{94} - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

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