LMFDB - Embedded newform 432.2.v.a.35.19

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			35.19
Character	$\chi$	$=$	432.35
Dual form			432.2.v.a.395.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26595 + 0.630383i) q^{2} +(1.20523 + 1.59606i) q^{4} +(-0.282421 + 1.05401i) q^{5} +(-1.93586 + 3.35301i) q^{7} +(0.519632 + 2.78028i) q^{8} +O(q^{10})$	\(q+(1.26595 + 0.630383i) q^{2} +(1.20523 + 1.59606i) q^{4} +(-0.282421 + 1.05401i) q^{5} +(-1.93586 + 3.35301i) q^{7} +(0.519632 + 2.78028i) q^{8} +(-1.02196 + 1.15629i) q^{10} +(-0.946349 - 3.53182i) q^{11} +(-1.03950 + 3.87946i) q^{13} +(-4.56438 + 3.02439i) q^{14} +(-1.09482 + 3.84726i) q^{16} -1.55026i q^{17} +(4.06175 - 4.06175i) q^{19} +(-2.02265 + 0.819569i) q^{20} +(1.02837 - 5.06766i) q^{22} +(3.86595 - 2.23201i) q^{23} +(3.29895 + 1.90465i) q^{25} +(-3.76149 + 4.25590i) q^{26} +(-7.68478 + 0.951413i) q^{28} +(1.14814 + 4.28493i) q^{29} +(-1.85935 + 1.07349i) q^{31} +(-3.81122 + 4.18026i) q^{32} +(0.977259 - 1.96255i) q^{34} +(-2.98738 - 2.98738i) q^{35} +(6.04318 - 6.04318i) q^{37} +(7.70240 - 2.58149i) q^{38} +(-3.07721 - 0.237514i) q^{40} +(1.59725 + 2.76652i) q^{41} +(5.51650 - 1.47814i) q^{43} +(4.49643 - 5.76711i) q^{44} +(6.30110 - 0.388570i) q^{46} +(0.0494357 - 0.0856252i) q^{47} +(-3.99512 - 6.91976i) q^{49} +(2.97563 + 4.49078i) q^{50} +(-7.44469 + 3.01656i) q^{52} +(-1.72094 - 1.72094i) q^{53} +3.98985 q^{55} +(-10.3283 - 3.63992i) q^{56} +(-1.24766 + 6.14826i) q^{58} +(-13.3806 - 3.58531i) q^{59} +(8.69586 - 2.33005i) q^{61} +(-3.03054 + 0.186885i) q^{62} +(-7.45997 + 2.88945i) q^{64} +(-3.79542 - 2.19129i) q^{65} +(-0.939315 - 0.251689i) q^{67} +(2.47431 - 1.86843i) q^{68} +(-1.89867 - 5.66506i) q^{70} -7.11471i q^{71} +10.4116i q^{73} +(11.4599 - 3.84082i) q^{74} +(11.3782 + 1.58744i) q^{76} +(13.6742 + 3.66400i) q^{77} +(-14.2402 - 8.22160i) q^{79} +(-3.74585 - 2.24050i) q^{80} +(0.278065 + 4.50914i) q^{82} +(15.0170 - 4.02380i) q^{83} +(1.63399 + 0.437828i) q^{85} +(7.91539 + 1.60626i) q^{86} +(9.32772 - 4.46637i) q^{88} -11.2398 q^{89} +(-10.9956 - 10.9956i) q^{91} +(8.22179 + 3.48020i) q^{92} +(0.116560 - 0.0772333i) q^{94} +(3.13400 + 5.42825i) q^{95} +(0.0532804 - 0.0922843i) q^{97} +(-0.695511 - 11.2785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.26595	+	0.630383i	0.895158	+	0.445748i
$2$	1.26595	+	0.630383i	0.895158	+	0.445748i
$3$		0			0
$3$		0			0
$4$	1.20523	+	1.59606i	0.602617	+	0.798030i
$5$	−0.282421	+	1.05401i	−0.126303	+	0.471368i	−0.999883	−	0.0153123i	$-0.995126\pi$
$5$	−0.282421	+	1.05401i	−0.126303	+	0.471368i	0.873580	+	0.486681i	$0.161792\pi$
$6$		0			0
$7$	−1.93586	+	3.35301i	−0.731687	+	1.26732i	0.224475	+	0.974480i	$0.427933\pi$
$7$	−1.93586	+	3.35301i	−0.731687	+	1.26732i	−0.956162	+	0.292839i	$0.905400\pi$
$8$	0.519632	+	2.78028i	0.183718	+	0.982979i
$9$		0			0
$10$	−1.02196	+	1.15629i	−0.323172	+	0.365650i
$11$	−0.946349	−	3.53182i	−0.285335	−	1.06488i	−0.948594	−	0.316495i	$-0.897494\pi$
$11$	−0.946349	−	3.53182i	−0.285335	−	1.06488i	0.663259	−	0.748390i	$-0.269173\pi$
$12$		0			0
$13$	−1.03950	+	3.87946i	−0.288305	+	1.07597i	0.658085	+	0.752943i	$0.271367\pi$
$13$	−1.03950	+	3.87946i	−0.288305	+	1.07597i	−0.946390	+	0.323025i	$0.895300\pi$
$14$	−4.56438	+	3.02439i	−1.21988	+	0.808303i
$15$		0			0
$16$	−1.09482	+	3.84726i	−0.273705	+	0.961814i
$17$		−	1.55026i		−	0.375994i	−0.982170	−	0.187997i	$-0.939800\pi$
$17$		−	1.55026i		−	0.375994i	0.982170	−	0.187997i	$-0.0601995\pi$
$18$		0			0
$19$	4.06175	−	4.06175i	0.931829	−	0.931829i	−0.0659916	−	0.997820i	$-0.521021\pi$
$19$	4.06175	−	4.06175i	0.931829	−	0.931829i	0.997820	+	0.0659916i	$0.0210211\pi$
$20$	−2.02265	+	0.819569i	−0.452278	+	0.183261i
$21$		0			0
$22$	1.02837	−	5.06766i	0.219250	−	1.08043i
$23$	3.86595	−	2.23201i	0.806106	−	0.465405i	−0.0394958	−	0.999220i	$-0.512575\pi$
$23$	3.86595	−	2.23201i	0.806106	−	0.465405i	0.845602	+	0.533814i	$0.179242\pi$
$24$		0			0
$25$	3.29895	+	1.90465i	0.659790	+	0.380930i
$26$	−3.76149	+	4.25590i	−0.737690	+	0.834651i
$27$		0			0
$28$	−7.68478	+	0.951413i	−1.45229	+	0.179800i
$29$	1.14814	+	4.28493i	0.213205	+	0.795691i	0.986791	+	0.162000i	$0.0517945\pi$
$29$	1.14814	+	4.28493i	0.213205	+	0.795691i	−0.773586	+	0.633691i	$0.781539\pi$
$30$		0			0
$31$	−1.85935	+	1.07349i	−0.333948	+	0.192805i	−0.657593	−	0.753374i	$-0.728425\pi$
$31$	−1.85935	+	1.07349i	−0.333948	+	0.192805i	0.323644	+	0.946179i	$0.395092\pi$
$32$	−3.81122	+	4.18026i	−0.673736	+	0.738972i
$33$		0			0
$34$	0.977259	−	1.96255i	0.167599	−	0.336574i
$35$	−2.98738	−	2.98738i	−0.504960	−	0.504960i
$36$		0			0
$37$	6.04318	−	6.04318i	0.993493	−	0.993493i	−0.00648560	−	0.999979i	$-0.502064\pi$
$37$	6.04318	−	6.04318i	0.993493	−	0.993493i	0.999979	+	0.00648560i	$0.00206445\pi$
$38$	7.70240	−	2.58149i	1.24949	−	0.418773i
$39$		0			0
$40$	−3.07721	−	0.237514i	−0.486549	−	0.0375543i
$41$	1.59725	+	2.76652i	0.249449	+	0.432058i	0.963373	−	0.268165i	$-0.0864173\pi$
$41$	1.59725	+	2.76652i	0.249449	+	0.432058i	−0.713924	+	0.700223i	$0.753084\pi$
$42$		0			0
$43$	5.51650	−	1.47814i	0.841259	−	0.225415i	0.187639	−	0.982238i	$-0.439916\pi$
$43$	5.51650	−	1.47814i	0.841259	−	0.225415i	0.653619	+	0.756823i	$0.273250\pi$
$44$	4.49643	−	5.76711i	0.677862	−	0.869424i
$45$		0			0
$46$	6.30110	−	0.388570i	0.929046	−	0.0572915i
$47$	0.0494357	−	0.0856252i	0.00721094	−	0.0124897i	−0.862397	−	0.506232i	$-0.831038\pi$
$47$	0.0494357	−	0.0856252i	0.00721094	−	0.0124897i	0.869608	+	0.493742i	$0.164371\pi$
$48$		0			0
$49$	−3.99512	−	6.91976i	−0.570732	−	0.988537i
$50$	2.97563	+	4.49078i	0.420818	+	0.635093i
$51$		0			0
$52$	−7.44469	+	3.01656i	−1.03239	+	0.418321i
$53$	−1.72094	−	1.72094i	−0.236389	−	0.236389i	0.578964	−	0.815353i	$-0.303457\pi$
$53$	−1.72094	−	1.72094i	−0.236389	−	0.236389i	−0.815353	+	0.578964i	$0.803457\pi$
$54$		0			0
$55$	3.98985			0.537991
$56$	−10.3283	−	3.63992i	−1.38017	−	0.486404i
$57$		0			0
$58$	−1.24766	+	6.14826i	−0.163826	+	0.807306i
$59$	−13.3806	−	3.58531i	−1.74200	−	0.466768i	−0.759112	−	0.650960i	$-0.774367\pi$
$59$	−13.3806	−	3.58531i	−1.74200	−	0.466768i	−0.982890	+	0.184192i	$0.941033\pi$
$60$		0			0
$61$	8.69586	−	2.33005i	1.11339	−	0.298332i	0.345184	−	0.938535i	$-0.387816\pi$
$61$	8.69586	−	2.33005i	1.11339	−	0.298332i	0.768206	+	0.640203i	$0.221150\pi$
$62$	−3.03054	+	0.186885i	−0.384879	+	0.0237344i
$63$		0			0
$64$	−7.45997	+	2.88945i	−0.932496	+	0.361181i
$65$	−3.79542	−	2.19129i	−0.470764	−	0.271796i
$66$		0			0
$67$	−0.939315	−	0.251689i	−0.114756	−	0.0307487i	0.200984	−	0.979594i	$-0.435586\pi$
$67$	−0.939315	−	0.251689i	−0.114756	−	0.0307487i	−0.315740	+	0.948846i	$0.602253\pi$
$68$	2.47431	−	1.86843i	0.300055	−	0.226581i
$69$		0			0
$70$	−1.89867	−	5.66506i	−0.226934	−	0.677104i
$71$		−	7.11471i		−	0.844361i	−0.906512	−	0.422180i	$-0.861265\pi$
$71$		−	7.11471i		−	0.844361i	0.906512	−	0.422180i	$-0.138735\pi$
$72$		0			0
$73$			10.4116i			1.21859i	0.792945	+	0.609293i	$0.208547\pi$
$73$			10.4116i			1.21859i	−0.792945	+	0.609293i	$0.791453\pi$
$74$	11.4599	−	3.84082i	1.33218	−	0.446486i
$75$		0			0
$76$	11.3782	+	1.58744i	1.30516	+	0.182091i
$77$	13.6742	+	3.66400i	1.55832	+	0.417552i
$78$		0			0
$79$	−14.2402	−	8.22160i	−1.60215	−	0.925003i	−0.991056	−	0.133446i	$-0.957396\pi$
$79$	−14.2402	−	8.22160i	−1.60215	−	0.925003i	−0.611095	−	0.791557i	$-0.709271\pi$
$80$	−3.74585	−	2.24050i	−0.418799	−	0.250495i
$81$		0			0
$82$	0.278065	+	4.50914i	0.0307072	+	0.497951i
$83$	15.0170	−	4.02380i	1.64833	−	0.441669i	0.689186	−	0.724584i	$-0.257968\pi$
$83$	15.0170	−	4.02380i	1.64833	−	0.441669i	0.959145	+	0.282915i	$0.0913015\pi$
$84$		0			0
$85$	1.63399	+	0.437828i	0.177232	+	0.0474891i
$86$	7.91539	+	1.60626i	0.853538	+	0.173208i
$87$		0			0
$88$	9.32772	−	4.46637i	0.994338	−	0.476116i
$89$	−11.2398			−1.19142			−0.595710	−	0.803200i	$-0.703129\pi$
$89$	−11.2398			−1.19142			−0.595710	+	0.803200i	$0.703129\pi$
$90$		0			0
$91$	−10.9956	−	10.9956i	−1.15265	−	1.15265i
$92$	8.22179	+	3.48020i	0.857181	+	0.362836i
$93$		0			0
$94$	0.116560	−	0.0772333i	0.0120222	−	0.00796601i
$95$	3.13400	+	5.42825i	0.321542	+	0.556927i
$96$		0			0
$97$	0.0532804	−	0.0922843i	0.00540980	−	0.00937005i	−0.863308	−	0.504678i	$-0.831611\pi$
$97$	0.0532804	−	0.0922843i	0.00540980	−	0.00937005i	0.868718	+	0.495308i	$0.164945\pi$
$98$	−0.695511	−	11.2785i	−0.0702572	−	1.13930i
$99$		0			0
$100$	0.936073	+	7.56087i	0.0936073	+	0.756087i
$101$	4.18366	−	1.12101i	0.416290	−	0.111545i	−0.0445936	−	0.999005i	$-0.514199\pi$
$101$	4.18366	−	1.12101i	0.416290	−	0.111545i	0.460883	+	0.887461i	$0.347533\pi$
$102$		0			0
$103$	−1.25063	−	2.16615i	−0.123228	−	0.213437i	0.797811	−	0.602908i	$-0.205991\pi$
$103$	−1.25063	−	2.16615i	−0.123228	−	0.213437i	−0.921039	+	0.389470i	$0.872658\pi$
$104$	−11.3262	−	0.874210i	−1.11062	−	0.0857233i
$105$		0			0
$106$	−1.09376	−	3.26346i	−0.106236	−	0.316975i
$107$	6.01074	−	6.01074i	0.581080	−	0.581080i	−0.354120	−	0.935200i	$-0.615220\pi$
$107$	6.01074	−	6.01074i	0.581080	−	0.581080i	0.935200	+	0.354120i	$0.115220\pi$
$108$		0			0
$109$	0.880973	+	0.880973i	0.0843819	+	0.0843819i	0.748038	−	0.663656i	$-0.230996\pi$
$109$	0.880973	+	0.880973i	0.0843819	+	0.0843819i	−0.663656	+	0.748038i	$0.730996\pi$
$110$	5.05093	+	2.51513i	0.481587	+	0.239809i
$111$		0			0
$112$	−10.7805	−	11.1187i	−1.01866	−	1.05062i
$113$	−2.13357	+	1.23182i	−0.200709	+	0.115880i	−0.596986	−	0.802251i	$-0.703635\pi$
$113$	−2.13357	+	1.23182i	−0.200709	+	0.115880i	0.396277	+	0.918131i	$0.370302\pi$
$114$		0			0
$115$	1.26073	+	4.70512i	0.117564	+	0.438755i
$116$	−5.45522	+	6.99685i	−0.506505	+	0.649641i
$117$		0			0
$118$	−14.6790	−	12.9737i	−1.35131	−	1.19433i
$119$	5.19805	+	3.00110i	0.476504	+	0.275110i
$120$		0			0
$121$	−2.05191	+	1.18467i	−0.186538	+	0.107698i
$122$	12.4773	+	2.53201i	1.12964	+	0.229237i
$123$		0			0
$124$	−3.95431	−	1.67382i	−0.355107	−	0.150313i
$125$	−6.79716	+	6.79716i	−0.607957	+	0.607957i
$126$		0			0
$127$			3.76697i			0.334264i	0.985934	+	0.167132i	$0.0534507\pi$
$127$			3.76697i			0.334264i	−0.985934	+	0.167132i	$0.946549\pi$
$128$	−11.2654	−	1.04475i	−0.995727	−	0.0923437i
$129$		0			0
$130$	−3.42344	−	5.16661i	−0.300256	−	0.453142i
$131$	−0.344757	+	1.28665i	−0.0301216	+	0.112415i	−0.979350	−	0.202173i	$-0.935200\pi$
$131$	−0.344757	+	1.28665i	−0.0301216	+	0.112415i	0.949228	+	0.314588i	$0.101866\pi$
$132$		0			0
$133$	5.75610	+	21.4821i	0.499117	+	1.86273i
$134$	−1.03046	−	0.910752i	−0.0890183	−	0.0786770i
$135$		0			0
$136$	4.31017	−	0.805566i	0.369594	−	0.0690767i
$137$	−5.59673	+	9.69382i	−0.478161	+	0.828199i	−0.999687	−	0.0250365i	$-0.992030\pi$
$137$	−5.59673	+	9.69382i	−0.478161	+	0.828199i	0.521526	+	0.853236i	$0.325363\pi$
$138$		0			0
$139$	0.808026	−	3.01559i	0.0685359	−	0.255779i	−0.923154	−	0.384430i	$-0.874398\pi$
$139$	0.808026	−	3.01559i	0.0685359	−	0.255779i	0.991690	+	0.128651i	$0.0410646\pi$
$140$	1.16755	−	8.36854i	0.0986757	−	0.707271i
$141$		0			0
$142$	4.48499	−	9.00683i	0.376372	−	0.755837i
$143$	14.6853			1.22805
$144$		0			0
$145$	−4.84062			−0.401992
$146$	−6.56330	+	13.1805i	−0.543182	+	1.09083i
$147$		0			0
$148$	16.9287	+	2.36183i	1.39153	+	0.194141i
$149$	3.87683	−	14.4685i	0.317602	−	1.18531i	−0.603941	−	0.797029i	$-0.706404\pi$
$149$	3.87683	−	14.4685i	0.317602	−	1.18531i	0.921543	−	0.388277i	$-0.126930\pi$
$150$		0			0
$151$	−0.301388	+	0.522019i	−0.0245266	+	0.0424813i	−0.878028	−	0.478609i	$-0.841141\pi$
$151$	−0.301388	+	0.522019i	−0.0245266	+	0.0424813i	0.853502	+	0.521090i	$0.174475\pi$
$152$	13.4034	+	9.18220i	1.08716	+	0.744775i
$153$		0			0
$154$	15.0011	+	13.2584i	1.20882	+	1.06840i
$155$	−0.606355	−	2.26295i	−0.0487036	−	0.181764i
$156$		0			0
$157$	−1.80210	+	6.72554i	−0.143823	+	0.536756i	0.855981	+	0.517006i	$0.172954\pi$
$157$	−1.80210	+	6.72554i	−0.143823	+	0.536756i	−0.999805	+	0.0197500i	$0.993713\pi$
$158$	−12.8446	−	19.3849i	−1.02186	−	1.54218i
$159$		0			0
$160$	−3.32967	−	5.19767i	−0.263233	−	0.410912i
$161$			17.2834i			1.36212i
$162$		0			0
$163$	7.73897	−	7.73897i	0.606163	−	0.606163i	−0.335778	−	0.941941i	$-0.608999\pi$
$163$	7.73897	−	7.73897i	0.606163	−	0.606163i	0.941941	+	0.335778i	$0.108999\pi$
$164$	−2.49047	+	5.88362i	−0.194473	+	0.459433i
$165$		0			0
$166$	21.5472	+	4.37256i	1.67239	+	0.339377i
$167$	−16.3533	+	9.44158i	−1.26546	+	0.730611i	−0.974125	−	0.226011i	$-0.927432\pi$
$167$	−16.3533	+	9.44158i	−1.26546	+	0.730611i	−0.291331	+	0.956622i	$0.594098\pi$
$168$		0			0
$169$	−2.71133	−	1.56539i	−0.208564	−	0.120414i
$170$	1.79255	+	1.58431i	0.137482	+	0.121511i
$171$		0			0
$172$	9.00789	+	7.02316i	0.686845	+	0.535511i
$173$	−4.38336	−	16.3589i	−0.333261	−	1.24375i	−0.905742	−	0.423829i	$-0.860686\pi$
$173$	−4.38336	−	16.3589i	−0.333261	−	1.24375i	0.572481	−	0.819918i	$-0.305981\pi$
$174$		0			0
$175$	−12.7726	+	7.37428i	−0.965519	+	0.557443i
$176$	14.6239	+	0.225858i	1.10232	+	0.0170247i
$177$		0			0
$178$	−14.2290	−	7.08539i	−1.06651	−	0.531073i
$179$	4.85114	+	4.85114i	0.362591	+	0.362591i	0.864766	−	0.502175i	$-0.167467\pi$
$179$	4.85114	+	4.85114i	0.362591	+	0.362591i	−0.502175	+	0.864766i	$0.667467\pi$
$180$		0			0
$181$	−1.98842	+	1.98842i	−0.147798	+	0.147798i	−0.777134	−	0.629336i	$-0.783327\pi$
$181$	−1.98842	+	1.98842i	−0.147798	+	0.147798i	0.629336	+	0.777134i	$0.283327\pi$
$182$	−6.98836	−	20.8512i	−0.518012	−	1.54559i
$183$		0			0
$184$	8.21448	+	9.58862i	0.605580	+	0.706882i
$185$	4.66286	+	8.07631i	0.342820	+	0.593782i
$186$		0			0
$187$	−5.47525	+	1.46709i	−0.400390	+	0.107284i
$188$	0.196245	−	0.0242960i	0.0143126	−	0.00177197i
$189$		0			0
$190$	0.545598	+	8.84749i	0.0395819	+	0.641864i
$191$	−10.1997	+	17.6664i	−0.738025	+	1.27830i	0.215358	+	0.976535i	$0.430908\pi$
$191$	−10.1997	+	17.6664i	−0.738025	+	1.27830i	−0.953383	+	0.301762i	$0.902425\pi$
$192$		0			0
$193$	−8.30403	−	14.3830i	−0.597737	−	1.03531i	−0.993154	−	0.116809i	$-0.962733\pi$
$193$	−8.30403	−	14.3830i	−0.597737	−	1.03531i	0.395417	−	0.918502i	$-0.370600\pi$
$194$	0.125624	−	0.0832398i	0.00901931	−	0.00597627i
$195$		0			0
$196$	6.22929	−	14.7164i	0.444949	−	1.05117i
$197$	2.03806	+	2.03806i	0.145206	+	0.145206i	0.775972	−	0.630767i	$-0.217260\pi$
$197$	2.03806	+	2.03806i	0.145206	+	0.145206i	−0.630767	+	0.775972i	$0.717260\pi$
$198$		0			0
$199$	−9.19698			−0.651956			−0.325978	−	0.945377i	$-0.605694\pi$
$199$	−9.19698			−0.651956			−0.325978	+	0.945377i	$0.605694\pi$
$200$	−3.58123	+	10.1617i	−0.253231	+	0.718543i
$201$		0			0
$202$	6.00295	+	1.21817i	0.422366	+	0.0857104i
$203$	−16.5901	−	4.44529i	−1.16439	−	0.311999i
$204$		0			0
$205$	−3.36704	+	0.902196i	−0.235164	+	0.0630121i
$206$	−0.217722	−	3.53061i	−0.0151694	−	0.245989i
$207$		0			0
$208$	−13.7872	−	8.24652i	−0.955971	−	0.571793i
$209$	−18.1892	−	10.5015i	−1.25817	−	0.726407i
$210$		0			0
$211$	−14.9104	−	3.99524i	−1.02648	−	0.275043i	−0.293978	−	0.955812i	$-0.594979\pi$
$211$	−14.9104	−	3.99524i	−1.02648	−	0.275043i	−0.732498	+	0.680769i	$0.761646\pi$
$212$	0.672586	−	4.82085i	0.0461934	−	0.331097i
$213$		0			0
$214$	11.3983	−	3.82020i	0.779174	−	0.261143i
$215$			6.23192i			0.425013i
$216$		0			0
$217$		−	8.31254i		−	0.564292i
$218$	0.559913	+	1.67061i	0.0379221	+	0.113148i
$219$		0			0
$220$	4.80871	+	6.36804i	0.324203	+	0.429333i
$221$	6.01418	+	1.61150i	0.404558	+	0.108401i
$222$		0			0
$223$	15.1760	+	8.76186i	1.01626	+	0.586738i	0.913018	−	0.407918i	$-0.133745\pi$
$223$	15.1760	+	8.76186i	1.01626	+	0.586738i	0.103241	+	0.994656i	$0.467079\pi$
$224$	−6.63845	−	20.8715i	−0.443550	−	1.39453i
$225$		0			0
$226$	−3.47750	+	0.214447i	−0.231320	+	0.0142648i
$227$	−19.5912	+	5.24944i	−1.30031	+	0.348418i	−0.841569	−	0.540150i	$-0.818367\pi$
$227$	−19.5912	+	5.24944i	−1.30031	+	0.348418i	−0.458745	+	0.888568i	$0.651701\pi$
$228$		0			0
$229$	15.0365	+	4.02901i	0.993638	+	0.266244i	0.718778	−	0.695240i	$-0.244702\pi$
$229$	15.0365	+	4.02901i	0.993638	+	0.266244i	0.274860	+	0.961484i	$0.411369\pi$
$230$	−1.37001	+	6.75117i	−0.0903357	+	0.445159i
$231$		0			0
$232$	−11.3167	+	5.41875i	−0.742979	+	0.355758i
$233$	27.1681			1.77984			0.889920	−	0.456116i	$-0.150760\pi$
$233$	27.1681			1.77984			0.889920	+	0.456116i	$0.150760\pi$
$234$		0			0
$235$	0.0762882	+	0.0762882i	0.00497649	+	0.00497649i
$236$	−10.4044	−	25.6773i	−0.677266	−	1.67145i
$237$		0			0
$238$	4.68861	+	7.07598i	0.303917	+	0.458668i
$239$	−2.48037	−	4.29612i	−0.160442	−	0.277893i	0.774586	−	0.632469i	$-0.217959\pi$
$239$	−2.48037	−	4.29612i	−0.160442	−	0.277893i	−0.935027	+	0.354576i	$0.884625\pi$
$240$		0			0
$241$	−4.93768	+	8.55231i	−0.318064	+	0.550903i	−0.980084	−	0.198583i	$-0.936366\pi$
$241$	−4.93768	+	8.55231i	−0.318064	+	0.550903i	0.662020	+	0.749486i	$0.269699\pi$
$242$	−3.34441	+	0.206240i	−0.214987	+	0.0132576i
$243$		0			0
$244$	14.1994	+	11.0709i	0.909026	+	0.708739i
$245$	8.42181	−	2.25662i	0.538050	−	0.144170i
$246$		0			0
$247$	11.5352	+	19.9796i	0.733968	+	1.27127i
$248$	−3.95079	−	4.61169i	−0.250876	−	0.292842i
$249$		0			0
$250$	−12.8897	+	4.32002i	−0.815213	+	0.273222i
$251$	−1.77292	+	1.77292i	−0.111906	+	0.111906i	−0.760842	−	0.648937i	$-0.775214\pi$
$251$	−1.77292	+	1.77292i	−0.111906	+	0.111906i	0.648937	+	0.760842i	$0.275214\pi$
$252$		0			0
$253$	−11.5416	−	11.5416i	−0.725613	−	0.725613i
$254$	−2.37463	+	4.76878i	−0.148998	+	0.299220i
$255$		0			0
$256$	−13.6027	−	8.42409i	−0.850172	−	0.526506i
$257$	−14.6473	+	8.45663i	−0.913674	+	0.527510i	−0.881612	−	0.471976i	$-0.843541\pi$
$257$	−14.6473	+	8.45663i	−0.913674	+	0.527510i	−0.0320628	+	0.999486i	$0.510208\pi$
$258$		0			0
$259$	8.56410	+	31.9616i	0.532147	+	1.98600i
$260$	−1.07695	−	8.69873i	−0.0667893	−	0.539472i
$261$		0			0
$262$	−1.24753	+	1.41150i	−0.0770724	+	0.0872028i
$263$	17.9408	+	10.3581i	1.10627	+	0.638708i	0.937862	−	0.347009i	$-0.112803\pi$
$263$	17.9408	+	10.3581i	1.10627	+	0.638708i	0.168413	+	0.985717i	$0.446136\pi$
$264$		0			0
$265$	2.29992	−	1.32786i	0.141283	−	0.0815696i
$266$	−6.25502	+	30.8237i	−0.383520	+	1.88992i
$267$		0			0
$268$	−0.730385	−	1.80255i	−0.0446153	−	0.110108i
$269$	−15.1523	+	15.1523i	−0.923853	+	0.923853i	−0.997299	−	0.0734463i	$-0.976600\pi$
$269$	−15.1523	+	15.1523i	−0.923853	+	0.923853i	0.0734463	+	0.997299i	$0.476600\pi$
$270$		0			0
$271$			20.0322i			1.21687i	0.793603	+	0.608436i	$0.208203\pi$
$271$			20.0322i			1.21687i	−0.793603	+	0.608436i	$0.791797\pi$
$272$	5.96426	+	1.69726i	0.361636	+	0.102911i
$273$		0			0
$274$	−13.1960	+	8.74377i	−0.797198	+	0.528230i
$275$	3.60493	−	13.4538i	0.217385	−	0.811293i
$276$		0			0
$277$	−7.20063	−	26.8731i	−0.432644	−	1.61465i	−0.746642	−	0.665226i	$-0.768335\pi$
$277$	−7.20063	−	26.8731i	−0.432644	−	1.61465i	0.313998	−	0.949424i	$-0.398331\pi$
$278$	2.92389	−	3.30821i	0.175364	−	0.198413i
$279$		0			0
$280$	6.75344	−	9.85811i	0.403595	−	0.589135i
$281$	8.83494	−	15.3026i	0.527048	−	0.912874i	−0.472455	−	0.881355i	$-0.656632\pi$
$281$	8.83494	−	15.3026i	0.527048	−	0.912874i	0.999503	−	0.0315195i	$-0.0100346\pi$
$282$		0			0
$283$	6.30060	−	23.5142i	0.374532	−	1.39777i	−0.479496	−	0.877544i	$-0.659180\pi$
$283$	6.30060	−	23.5142i	0.374532	−	1.39777i	0.854028	−	0.520228i	$-0.174153\pi$
$284$	11.3555	−	8.57490i	0.673826	−	0.508827i
$285$		0			0
$286$	18.5908	+	9.25736i	1.09930	+	0.547399i
$287$	−12.3682			−0.730074
$288$		0			0
$289$	14.5967			0.858629
$290$	−6.12797	−	3.05145i	−0.359847	−	0.179187i
$291$		0			0
$292$	−16.6175	+	12.5484i	−0.972468	+	0.734341i
$293$	1.34920	−	5.03527i	0.0788209	−	0.294164i	−0.915252	−	0.402883i	$-0.868008\pi$
$293$	1.34920	−	5.03527i	0.0788209	−	0.294164i	0.994073	+	0.108719i	$0.0346749\pi$
$294$		0			0
$295$	7.55792	−	13.0907i	0.440039	−	0.762170i
$296$	19.9420	+	13.6615i	1.15911	+	0.794061i
$297$		0			0
$298$	14.0286	−	15.8725i	0.812652	−	0.919467i
$299$	4.64033	+	17.3180i	0.268357	+	1.00152i
$300$		0			0
$301$	−5.72296	+	21.3584i	−0.329866	+	1.23108i
$302$	−0.710612	+	0.470857i	−0.0408911	+	0.0270948i
$303$		0			0
$304$	11.1797	+	20.0735i	0.641200	+	1.15129i
$305$			9.82358i			0.562497i
$306$		0			0
$307$	2.82663	−	2.82663i	0.161324	−	0.161324i	−0.621829	−	0.783153i	$-0.713610\pi$
$307$	2.82663	−	2.82663i	0.161324	−	0.161324i	0.783153	+	0.621829i	$0.213610\pi$
$308$	10.6327	+	26.2409i	0.605855	+	1.49521i
$309$		0			0
$310$	0.658912	−	3.24701i	0.0374237	−	0.184418i
$311$	2.51789	−	1.45371i	0.142777	−	0.0824322i	−0.426910	−	0.904294i	$-0.640398\pi$
$311$	2.51789	−	1.45371i	0.142777	−	0.0824322i	0.569687	+	0.821862i	$0.307065\pi$
$312$		0			0
$313$	−18.0136	−	10.4002i	−1.01819	−	0.587852i	−0.104611	−	0.994513i	$-0.533360\pi$
$313$	−18.0136	−	10.4002i	−1.01819	−	0.587852i	−0.913579	+	0.406661i	$0.866693\pi$
$314$	−6.52103	+	7.37815i	−0.368003	+	0.416373i
$315$		0			0
$316$	−4.04065	−	32.6372i	−0.227304	−	1.83599i
$317$	2.72034	+	10.1525i	0.152790	+	0.570219i	0.999284	+	0.0378219i	$0.0120419\pi$
$317$	2.72034	+	10.1525i	0.152790	+	0.570219i	−0.846495	+	0.532397i	$0.821291\pi$
$318$		0			0
$319$	14.0471	−	8.11008i	0.786485	−	0.454077i
$320$	−0.938658	−	8.67893i	−0.0524726	−	0.485167i
$321$		0			0
$322$	−10.8952	+	21.8799i	−0.607164	+	1.21932i
$323$	−6.29678	−	6.29678i	−0.350362	−	0.350362i
$324$		0			0
$325$	−10.8183	+	10.8183i	−0.600089	+	0.600089i
$326$	14.6756	−	4.91860i	0.812808	−	0.272416i
$327$		0			0
$328$	−6.86173	+	5.87838i	−0.378876	+	0.324579i
$329$	0.191401	+	0.331517i	0.0105523	+	0.0182771i
$330$		0			0
$331$	7.45721	−	1.99815i	0.409885	−	0.109828i	−0.0479837	−	0.998848i	$-0.515280\pi$
$331$	7.45721	−	1.99815i	0.409885	−	0.109828i	0.457869	+	0.889020i	$0.348613\pi$
$332$	24.5212	+	19.1184i	1.34578	+	1.04926i
$333$		0			0
$334$	−26.6542	+	1.64369i	−1.45845	+	0.0899384i
$335$	0.530565	−	0.918966i	0.0289879	−	0.0502085i
$336$		0			0
$337$	−15.1525	−	26.2448i	−0.825407	−	1.42965i	−0.901608	−	0.432554i	$-0.857613\pi$
$337$	−15.1525	−	26.2448i	−0.825407	−	1.42965i	0.0762015	−	0.997092i	$-0.475721\pi$
$338$	−2.44560	−	3.69087i	−0.133023	−	0.200757i
$339$		0			0
$340$	1.27055	+	3.13564i	0.0689051	+	0.170054i
$341$	5.55098	+	5.55098i	0.300602	+	0.300602i
$342$		0			0
$343$	3.83397			0.207015
$344$	6.97621	+	14.5694i	0.376132	+	0.785527i
$345$		0			0
$346$	4.76330	−	23.4727i	0.256076	−	1.26190i
$347$	27.6456	+	7.40762i	1.48409	+	0.397662i	0.907738	−	0.419537i	$-0.137808\pi$
$347$	27.6456	+	7.40762i	1.48409	+	0.397662i	0.576356	+	0.817199i	$0.304474\pi$
$348$		0			0
$349$	4.94221	−	1.32426i	0.264551	−	0.0708861i	−0.124105	−	0.992269i	$-0.539606\pi$
$349$	4.94221	−	1.32426i	0.264551	−	0.0708861i	0.388656	+	0.921383i	$0.372939\pi$
$350$	−20.8181	+	1.28379i	−1.11277	+	0.0686213i
$351$		0			0
$352$	18.3707	+	9.50458i	0.979161	+	0.506596i
$353$	−10.6375	−	6.14156i	−0.566176	−	0.326882i	0.189444	−	0.981891i	$-0.439331\pi$
$353$	−10.6375	−	6.14156i	−0.566176	−	0.326882i	−0.755621	+	0.655009i	$0.772665\pi$
$354$		0			0
$355$	7.49899	+	2.00935i	0.398005	+	0.106645i
$356$	−13.5466	−	17.9394i	−0.717970	−	0.950789i
$357$		0			0
$358$	3.08320	+	9.19935i	0.162952	+	0.486201i
$359$		−	8.35783i		−	0.441109i	−0.975375	−	0.220555i	$-0.929213\pi$
$359$		−	8.35783i		−	0.441109i	0.975375	−	0.220555i	$-0.0707867\pi$
$360$		0			0
$361$		−	13.9956i		−	0.736609i
$362$	−3.77069	+	1.26376i	−0.198183	+	0.0664219i
$363$		0			0
$364$	4.29734	−	30.8018i	0.225242	−	1.61445i
$365$	−10.9739	−	2.94046i	−0.574403	−	0.153911i
$366$		0			0
$367$	−5.59831	−	3.23218i	−0.292229	−	0.168719i	0.346718	−	0.937970i	$-0.387296\pi$
$367$	−5.59831	−	3.23218i	−0.292229	−	0.168719i	−0.638947	+	0.769251i	$0.720630\pi$
$368$	4.35459	+	17.3169i	0.226999	+	0.902707i
$369$		0			0
$370$	0.811757	+	13.1636i	0.0422012	+	0.684340i
$371$	9.10182	−	2.43882i	0.472543	−	0.126617i
$372$		0			0
$373$	11.5078	+	3.08351i	0.595853	+	0.159658i	0.544127	−	0.839003i	$-0.316861\pi$
$373$	11.5078	+	3.08351i	0.595853	+	0.159658i	0.0517262	+	0.998661i	$0.483528\pi$
$374$	−7.85620	−	1.59425i	−0.406234	−	0.0824368i
$375$		0			0
$376$	0.263751	+	0.0929518i	0.0136019	+	0.00479362i
$377$	−17.8167			−0.917607
$378$		0			0
$379$	7.76444	+	7.76444i	0.398833	+	0.398833i	0.877821	−	0.478988i	$-0.158996\pi$
$379$	7.76444	+	7.76444i	0.398833	+	0.398833i	−0.478988	+	0.877821i	$0.658996\pi$
$380$	−4.88661	+	11.5444i	−0.250678	+	0.592214i
$381$		0			0
$382$	−24.0489	+	15.9350i	−1.23045	+	0.815305i
$383$	2.86264	+	4.95824i	0.146274	+	0.253354i	0.929848	−	0.367945i	$-0.119939\pi$
$383$	2.86264	+	4.95824i	0.146274	+	0.253354i	−0.783573	+	0.621299i	$0.786605\pi$
$384$		0			0
$385$	−7.72380	+	13.3780i	−0.393641	+	0.681807i
$386$	−1.44565	−	23.4428i	−0.0735816	−	1.19321i
$387$		0			0
$388$	0.211507	−	0.0261856i	0.0107376	−	0.00132937i
$389$	−6.82104	+	1.82769i	−0.345841	+	0.0926677i	−0.427558	−	0.903988i	$-0.640626\pi$
$389$	−6.82104	+	1.82769i	−0.345841	+	0.0926677i	0.0817177	+	0.996656i	$0.473959\pi$
$390$		0			0
$391$	−3.46020	−	5.99324i	−0.174990	−	0.303091i
$392$	17.1629	−	14.7033i	0.866858	−	0.742629i
$393$		0			0
$394$	1.29531	+	3.86483i	0.0652569	+	0.194707i
$395$	12.6874	−	12.6874i	0.638373	−	0.638373i
$396$		0			0
$397$	−1.86429	−	1.86429i	−0.0935661	−	0.0935661i	0.658774	−	0.752340i	$-0.271075\pi$
$397$	−1.86429	−	1.86429i	−0.0935661	−	0.0935661i	−0.752340	+	0.658774i	$0.771075\pi$
$398$	−11.6429	−	5.79762i	−0.583604	−	0.290608i
$399$		0			0
$400$	−10.9394	+	10.6067i	−0.546971	+	0.530333i
$401$	34.3098	−	19.8088i	1.71335	−	0.989204i	0.783402	−	0.621516i	$-0.213483\pi$
$401$	34.3098	−	19.8088i	1.71335	−	0.989204i	0.929949	−	0.367688i	$-0.119851\pi$
$402$		0			0
$403$	−2.23179	−	8.32915i	−0.111173	−	0.414905i
$404$	6.83149	+	5.32630i	0.339879	+	0.264993i
$405$		0			0
$406$	−18.1999	−	16.0856i	−0.903245	−	0.798315i
$407$	−27.0624	−	15.6245i	−1.34143	−	0.774477i
$408$		0			0
$409$	−19.5426	+	11.2829i	−0.966317	+	0.557903i	−0.898111	−	0.439768i	$-0.855061\pi$
$409$	−19.5426	+	11.2829i	−0.966317	+	0.557903i	−0.0682056	+	0.997671i	$0.521727\pi$
$410$	−4.83122	−	0.980395i	−0.238597	−	0.0484182i
$411$		0			0
$412$	1.95001	−	4.60680i	0.0960701	−	0.226961i
$413$	37.9245	−	37.9245i	1.86614	−	1.86614i
$414$		0			0
$415$			16.9645i			0.832755i
$416$	−12.2554	−	19.1309i	−0.600870	−	0.937968i
$417$		0			0
$418$	−16.4065	−	24.7605i	−0.802470	−	1.21108i
$419$	0.145005	−	0.541167i	0.00708397	−	0.0264377i	−0.962293	−	0.272014i	$-0.912310\pi$
$419$	0.145005	−	0.541167i	0.00708397	−	0.0264377i	0.969377	+	0.245576i	$0.0789771\pi$
$420$		0			0
$421$	−5.65647	−	21.1102i	−0.275679	−	1.02885i	−0.955385	−	0.295364i	$-0.904559\pi$
$421$	−5.65647	−	21.1102i	−0.275679	−	1.02885i	0.679706	−	0.733485i	$-0.262108\pi$
$422$	−16.3573	−	14.4570i	−0.796259	−	0.703757i
$423$		0			0
$424$	3.89044	−	5.67895i	0.188936	−	0.275794i
$425$	2.95271	−	5.11424i	0.143227	−	0.248077i
$426$		0			0
$427$	−9.02130	+	33.6680i	−0.436571	+	1.62931i
$428$	16.8378	+	2.34915i	0.813888	+	0.113550i
$429$		0			0
$430$	−3.92849	+	7.88926i	−0.189449	+	0.380454i
$431$	−8.09784			−0.390059			−0.195030	−	0.980797i	$-0.562480\pi$
$431$	−8.09784			−0.390059			−0.195030	+	0.980797i	$0.562480\pi$
$432$		0			0
$433$	28.0379			1.34742			0.673708	−	0.738997i	$-0.264700\pi$
$433$	28.0379			1.34742			0.673708	+	0.738997i	$0.264700\pi$
$434$	5.24009	−	10.5232i	0.251532	−	0.505131i
$435$		0			0
$436$	−0.344307	+	2.46787i	−0.0164893	+	0.118189i
$437$	6.63666	−	24.7683i	0.317474	−	1.18483i
$438$		0			0
$439$	14.3003	−	24.7689i	0.682518	−	1.18216i	−0.291692	−	0.956512i	$-0.594218\pi$
$439$	14.3003	−	24.7689i	0.682518	−	1.18216i	0.974210	−	0.225644i	$-0.0724485\pi$
$440$	2.07325	+	11.0929i	0.0988385	+	0.528834i
$441$		0			0
$442$	6.59777	+	5.83130i	0.313824	+	0.277367i
$443$	1.74109	+	6.49785i	0.0827218	+	0.308722i	0.994873	−	0.101132i	$-0.0322464\pi$
$443$	1.74109	+	6.49785i	0.0827218	+	0.308722i	−0.912151	+	0.409854i	$0.865580\pi$
$444$		0			0
$445$	3.17437	−	11.8469i	0.150479	−	0.561597i
$446$	13.6886	+	20.6587i	0.648176	+	0.978219i
$447$		0			0
$448$	4.75311	−	30.6069i	0.224563	−	1.44604i
$449$		−	34.1293i		−	1.61066i	−0.592827	−	0.805330i	$-0.701988\pi$
$449$		−	34.1293i		−	1.61066i	0.592827	−	0.805330i	$-0.298012\pi$
$450$		0			0
$451$	8.25930	−	8.25930i	0.388915	−	0.388915i
$452$	−4.53751	−	1.92068i	−0.213426	−	0.0903411i
$453$		0			0
$454$	−28.1105	−	5.70444i	−1.31929	−	0.267723i
$455$	14.6948	−	8.48405i	0.688903	−	0.397739i
$456$		0			0
$457$	−0.228748	−	0.132067i	−0.0107004	−	0.00617786i	0.494640	−	0.869098i	$-0.335300\pi$
$457$	−0.228748	−	0.132067i	−0.0107004	−	0.00617786i	−0.505341	+	0.862920i	$0.668633\pi$
$458$	16.4955	+	14.5792i	0.770785	+	0.681243i
$459$		0			0
$460$	−5.99018	+	7.68298i	−0.279293	+	0.358221i
$461$	−5.93653	−	22.1554i	−0.276492	−	1.03188i	−0.954835	−	0.297136i	$-0.903968\pi$
$461$	−5.93653	−	22.1554i	−0.276492	−	1.03188i	0.678343	−	0.734745i	$-0.262698\pi$
$462$		0			0
$463$	25.1678	−	14.5306i	1.16964	−	0.675295i	0.216048	−	0.976383i	$-0.430683\pi$
$463$	25.1678	−	14.5306i	1.16964	−	0.675295i	0.953596	+	0.301088i	$0.0973498\pi$
$464$	−17.7422	−	0.274019i	−0.823662	−	0.0127210i
$465$		0			0
$466$	34.3933	+	17.1263i	1.59324	+	0.793360i
$467$	1.46976	+	1.46976i	0.0680123	+	0.0680123i	0.740295	−	0.672282i	$-0.234686\pi$
$467$	1.46976	+	1.46976i	0.0680123	+	0.0680123i	−0.672282	+	0.740295i	$0.734686\pi$
$468$		0			0
$469$	2.66230	−	2.66230i	0.122934	−	0.122934i
$470$	0.0484859	+	0.144667i	0.00223649	+	0.00667301i
$471$		0			0
$472$	3.01522	−	39.0648i	0.138787	−	1.79811i
$473$	−10.4411	−	18.0845i	−0.480081	−	0.831525i
$474$		0			0
$475$	21.1357	−	5.66329i	0.969772	−	0.259850i
$476$	1.47494	+	11.9134i	0.0676038	+	0.546051i
$477$		0			0
$478$	−0.431807	−	7.00224i	−0.0197504	−	0.320275i
$479$	−11.8147	+	20.4636i	−0.539826	+	0.935006i	0.459087	+	0.888391i	$0.348177\pi$
$479$	−11.8147	+	20.4636i	−0.539826	+	0.935006i	−0.998913	+	0.0466149i	$0.985157\pi$
$480$		0			0
$481$	17.1624	+	29.7262i	0.782539	+	1.35540i
$482$	−11.6421	+	7.71413i	−0.530281	+	0.351369i
$483$		0			0
$484$	−4.36385	−	1.84717i	−0.198357	−	0.0839623i
$485$	0.0822212	+	0.0822212i	0.00373347	+	0.00373347i
$486$		0			0
$487$	−8.44298			−0.382588			−0.191294	−	0.981533i	$-0.561268\pi$
$487$	−8.44298			−0.382588			−0.191294	+	0.981533i	$0.561268\pi$
$488$	10.9968	+	22.9662i	0.497804	+	1.03963i
$489$		0			0
$490$	12.0841	+	2.45221i	0.545903	+	0.110780i
$491$	−4.92678	−	1.32013i	−0.222342	−	0.0595765i	0.145928	−	0.989295i	$-0.453383\pi$
$491$	−4.92678	−	1.32013i	−0.222342	−	0.0595765i	−0.368270	+	0.929719i	$0.620050\pi$
$492$		0			0
$493$	6.64277	−	1.77992i	0.299175	−	0.0801638i
$494$	2.00816	+	32.5646i	0.0903516	+	1.46515i
$495$		0			0
$496$	−2.09436	−	8.32866i	−0.0940395	−	0.373968i
$497$	23.8557	+	13.7731i	1.07007	+	0.617808i
$498$		0			0
$499$	−19.9387	−	5.34256i	−0.892579	−	0.239166i	−0.216753	−	0.976227i	$-0.569546\pi$
$499$	−19.9387	−	5.34256i	−0.892579	−	0.239166i	−0.675827	+	0.737061i	$0.736213\pi$
$500$	−19.0409	−	2.65651i	−0.851533	−	0.118803i
$501$		0			0
$502$	−3.36204	+	1.12680i	−0.150055	+	0.0502916i
$503$		−	25.8852i		−	1.15417i	−0.816686	−	0.577083i	$-0.804191\pi$
$503$		−	25.8852i		−	1.15417i	0.816686	−	0.577083i	$-0.195809\pi$
$504$		0			0
$505$			4.72622i			0.210314i
$506$	−7.33540	−	21.8866i	−0.326098	−	0.972980i
$507$		0			0
$508$	−6.01231	+	4.54008i	−0.266753	+	0.201434i
$509$	−12.6568	−	3.39138i	−0.561003	−	0.150320i	−0.0328359	−	0.999461i	$-0.510454\pi$
$509$	−12.6568	−	3.39138i	−0.561003	−	0.150320i	−0.528167	+	0.849140i	$0.677121\pi$
$510$		0			0
$511$	−34.9102	−	20.1554i	−1.54434	−	0.891623i
$512$	−11.9099	−	19.2394i	−0.526349	−	0.850268i
$513$		0			0
$514$	−23.8736	+	1.47221i	−1.05302	+	0.0649366i
$515$	2.63635	−	0.706409i	0.116172	−	0.0311281i
$516$		0			0
$517$	−0.349196	−	0.0935669i	−0.0153576	−	0.00411507i
$518$	−9.30640	+	45.8603i	−0.408900	+	2.01499i
$519$		0			0
$520$	4.12018	−	11.6910i	0.180682	−	0.512685i
$521$	−15.9529			−0.698909			−0.349454	−	0.936953i	$-0.613633\pi$
$521$	−15.9529			−0.698909			−0.349454	+	0.936953i	$0.613633\pi$
$522$		0			0
$523$	8.00417	+	8.00417i	0.349998	+	0.349998i	0.860109	−	0.510111i	$-0.170396\pi$
$523$	8.00417	+	8.00417i	0.349998	+	0.349998i	−0.510111	+	0.860109i	$0.670396\pi$
$524$	−2.46908	+	1.00046i	−0.107862	+	0.0437054i
$525$		0			0
$526$	16.1824	+	24.4223i	0.705588	+	1.06486i
$527$	1.66420	+	2.88247i	0.0724936	+	0.125563i
$528$		0			0
$529$	−1.53630	+	2.66094i	−0.0667955	+	0.115693i
$530$	3.74863	−	0.231167i	0.162830	−	0.0100412i
$531$		0			0
$532$	−27.3492	+	35.0780i	−1.18574	+	1.52082i
$533$	−12.3929	+	3.32068i	−0.536798	+	0.143835i
$534$		0			0
$535$	4.63782	+	8.03294i	0.200511	+	0.347294i
$536$	0.211668	−	2.74235i	0.00914267	−	0.118451i
$537$		0			0
$538$	−28.7338	+	9.63024i	−1.23880	+	0.415189i
$539$	−20.6586	+	20.6586i	−0.889828	+	0.889828i
$540$		0			0
$541$	−16.5746	−	16.5746i	−0.712599	−	0.712599i	0.254479	−	0.967078i	$-0.418096\pi$
$541$	−16.5746	−	16.5746i	−0.712599	−	0.712599i	−0.967078	+	0.254479i	$0.918096\pi$
$542$	−12.6280	+	25.3597i	−0.542418	+	1.08929i
$543$		0			0
$544$	6.48050	+	5.90840i	0.277849	+	0.253321i
$545$	−1.17736	+	0.679750i	−0.0504326	+	0.0291173i
$546$		0			0
$547$	−0.996886	−	3.72043i	−0.0426238	−	0.159074i	0.941334	−	0.337477i	$-0.109574\pi$
$547$	−0.996886	−	3.72043i	−0.0426238	−	0.159074i	−0.983957	+	0.178403i	$0.942907\pi$
$548$	−22.2173	+	2.75061i	−0.949076	+	0.117500i
$549$		0			0
$550$	13.0447	−	14.7592i	0.556226	−	0.629336i
$551$	22.0678	+	12.7408i	0.940118	+	0.542778i
$552$		0			0
$553$	55.1343	−	31.8318i	2.34455	−	1.35362i
$554$	7.82475	−	38.5591i	0.332442	−	1.63822i
$555$		0			0
$556$	5.78693	−	2.34484i	0.245421	−	0.0994434i
$557$	−14.2615	+	14.2615i	−0.604278	+	0.604278i	−0.941445	−	0.337167i	$-0.890531\pi$
$557$	−14.2615	+	14.2615i	−0.604278	+	0.604278i	0.337167	+	0.941445i	$0.390531\pi$
$558$		0			0
$559$			22.9376i			0.970156i
$560$	14.7639	−	8.22258i	0.623887	−	0.347468i
$561$		0			0
$562$	20.8310	−	13.8028i	0.878704	−	0.582236i
$563$	−9.41300	+	35.1298i	−0.396711	+	1.48054i	0.422136	+	0.906532i	$0.361280\pi$
$563$	−9.41300	+	35.1298i	−0.396711	+	1.48054i	−0.818847	+	0.574012i	$0.805386\pi$
$564$		0			0
$565$	−0.695783	−	2.59670i	−0.0292718	−	0.109244i
$566$	22.7991	−	25.7958i	0.958319	−	1.08428i
$567$		0			0
$568$	19.7809	−	3.69703i	0.829989	−	0.155124i
$569$	12.2488	−	21.2155i	0.513496	−	0.889402i	−0.486381	−	0.873747i	$-0.661683\pi$
$569$	12.2488	−	21.2155i	0.513496	−	0.889402i	0.999877	−	0.0156550i	$-0.00498336\pi$
$570$		0			0
$571$	−2.12023	+	7.91280i	−0.0887288	+	0.331140i	−0.995994	−	0.0894183i	$-0.971499\pi$
$571$	−2.12023	+	7.91280i	−0.0887288	+	0.331140i	0.907265	+	0.420559i	$0.138166\pi$
$572$	17.6992	+	23.4386i	0.740042	+	0.980018i
$573$		0			0
$574$	−15.6575	−	7.79672i	−0.653532	−	0.325429i
$575$	17.0048			0.709147
$576$		0			0
$577$	−19.0192			−0.791779			−0.395889	−	0.918298i	$-0.629564\pi$
$577$	−19.0192			−0.791779			−0.395889	+	0.918298i	$0.629564\pi$
$578$	18.4786	+	9.20150i	0.768609	+	0.382732i
$579$		0			0
$580$	−5.83409	−	7.72593i	−0.242247	−	0.320802i
$581$	−15.5790	+	58.1417i	−0.646327	+	2.41213i
$582$		0			0
$583$	−4.44944	+	7.70665i	−0.184277	+	0.319177i
$584$	−28.9472	+	5.41020i	−1.19784	+	0.223876i
$585$		0			0
$586$	4.88216	−	5.52386i	0.201680	−	0.228189i
$587$	2.62450	+	9.79477i	0.108325	+	0.404274i	0.998701	−	0.0509516i	$-0.0162254\pi$
$587$	2.62450	+	9.79477i	0.108325	+	0.404274i	−0.890376	+	0.455225i	$0.849559\pi$
$588$		0			0
$589$	−3.19193	+	11.9124i	−0.131521	+	0.490844i
$590$	17.8201	−	11.8077i	0.733641	−	0.486117i
$591$		0			0
$592$	16.6335	+	29.8659i	0.683632	+	1.22748i
$593$			16.0166i			0.657724i	0.944378	+	0.328862i	$0.106665\pi$
$593$			16.0166i			0.657724i	−0.944378	+	0.328862i	$0.893335\pi$
$594$		0			0
$595$	−4.63123	+	4.63123i	−0.189862	+	0.189862i
$596$	27.7651	−	11.2503i	1.13730	−	0.460830i
$597$		0			0
$598$	−5.04254	+	24.8488i	−0.206205	+	1.01614i
$599$	−2.72485	+	1.57319i	−0.111334	+	0.0642790i	−0.554633	−	0.832095i	$-0.687141\pi$
$599$	−2.72485	+	1.57319i	−0.111334	+	0.0642790i	0.443299	+	0.896374i	$0.353808\pi$
$600$		0			0
$601$	−6.88132	−	3.97293i	−0.280695	−	0.162059i	0.353043	−	0.935607i	$-0.385147\pi$
$601$	−6.88132	−	3.97293i	−0.280695	−	0.162059i	−0.633738	+	0.773548i	$0.718480\pi$
$602$	−20.7089	+	23.4309i	−0.844032	+	0.954971i
$603$		0			0
$604$	−1.19642	+	0.148122i	−0.0486815	+	0.00602700i
$605$	−0.669154	−	2.49732i	−0.0272050	−	0.101530i
$606$		0			0
$607$	28.2159	−	16.2905i	1.14525	−	0.661209i	0.197523	−	0.980298i	$-0.436710\pi$
$607$	28.2159	−	16.2905i	1.14525	−	0.661209i	0.947725	+	0.319089i	$0.103377\pi$
$608$	1.49893	+	32.4594i	0.0607896	+	1.31640i
$609$		0			0
$610$	−6.19262	+	12.4361i	−0.250732	+	0.503524i
$611$	0.280791	+	0.280791i	0.0113596	+	0.0113596i
$612$		0			0
$613$	1.74081	−	1.74081i	0.0703105	−	0.0703105i	−0.671077	−	0.741388i	$-0.734168\pi$
$613$	1.74081	−	1.74081i	0.0703105	−	0.0703105i	0.741388	+	0.671077i	$0.234168\pi$
$614$	5.36021	−	1.79650i	0.216320	−	0.0725007i
$615$		0			0
$616$	−3.08140	+	39.9222i	−0.124153	+	1.60851i
$617$	8.76552	+	15.1823i	0.352887	+	0.611218i	0.986754	−	0.162224i	$-0.0518668\pi$
$617$	8.76552	+	15.1823i	0.352887	+	0.611218i	−0.633867	+	0.773442i	$0.718533\pi$
$618$		0			0
$619$	−12.3314	+	3.30420i	−0.495643	+	0.132807i	−0.497977	−	0.867190i	$-0.665924\pi$
$619$	−12.3314	+	3.30420i	−0.495643	+	0.132807i	0.00233438	+	0.999997i	$0.499257\pi$
$620$	2.88100	−	3.69516i	0.115704	−	0.148401i
$621$		0			0
$622$	4.10391	−	0.253076i	0.164552	−	0.0101474i
$623$	21.7588	−	37.6873i	0.871746	−	1.50991i
$624$		0			0
$625$	4.27862	+	7.41079i	0.171145	+	0.296432i
$626$	−16.2482	−	24.5215i	−0.649407	−	0.980077i
$627$		0			0
$628$	−12.9063	+	5.22959i	−0.515018	+	0.208683i
$629$	−9.36852	−	9.36852i	−0.373548	−	0.373548i
$630$		0			0
$631$	−24.1690			−0.962153			−0.481076	−	0.876679i	$-0.659754\pi$
$631$	−24.1690			−0.962153			−0.481076	+	0.876679i	$0.659754\pi$
$632$	15.4587	−	43.8641i	0.614915	−	1.74482i
$633$		0			0
$634$	−2.95613	+	14.5673i	−0.117403	+	0.578542i
$635$	−3.97043	−	1.06387i	−0.157562	−	0.0422185i
$636$		0			0
$637$	30.9979	−	8.30585i	1.22818	−	0.329090i
$638$	22.8953	−	1.41188i	0.906433	−	0.0558970i
$639$		0			0
$640$	4.28276	−	11.5788i	0.169291	−	0.457691i
$641$	19.3938	+	11.1970i	0.766010	+	0.442256i	0.831450	−	0.555600i	$-0.187511\pi$
$641$	19.3938	+	11.1970i	0.766010	+	0.442256i	−0.0654392	+	0.997857i	$0.520845\pi$
$642$		0			0
$643$	−3.74778	−	1.00422i	−0.147798	−	0.0396024i	0.184161	−	0.982896i	$-0.441043\pi$
$643$	−3.74778	−	1.00422i	−0.147798	−	0.0396024i	−0.331960	+	0.943294i	$0.607710\pi$
$644$	−27.5854	+	20.8306i	−1.08702	+	0.820840i
$645$		0			0
$646$	−4.00199	−	11.9408i	−0.157456	−	0.469803i
$647$			36.0008i			1.41534i	0.706544	+	0.707669i	$0.250253\pi$
$647$			36.0008i			1.41534i	−0.706544	+	0.707669i	$0.749747\pi$
$648$		0			0
$649$			50.6508i			1.98822i
$650$	−20.5150	+	6.87568i	−0.804664	+	0.269686i
$651$		0			0
$652$	21.6791	+	3.02459i	0.849021	+	0.118452i
$653$	−4.46647	−	1.19679i	−0.174786	−	0.0468339i	0.170364	−	0.985381i	$-0.445506\pi$
$653$	−4.46647	−	1.19679i	−0.174786	−	0.0468339i	−0.345151	+	0.938547i	$0.612172\pi$
$654$		0			0
$655$	−1.25878	−	0.726755i	−0.0491845	−	0.0283967i
$656$	−12.3922	+	3.11620i	−0.483834	+	0.121667i
$657$		0			0
$658$	0.0333211	+	0.540339i	0.00129899	+	0.0210646i
$659$	−35.4331	+	9.49427i	−1.38028	+	0.369844i	−0.871222	−	0.490889i	$-0.836672\pi$
$659$	−35.4331	+	9.49427i	−1.38028	+	0.369844i	−0.509056	+	0.860734i	$0.670005\pi$
$660$		0			0
$661$	−25.4912	−	6.83035i	−0.991493	−	0.265670i	−0.273616	−	0.961839i	$-0.588220\pi$
$661$	−25.4912	−	6.83035i	−0.991493	−	0.265670i	−0.717878	+	0.696169i	$0.754886\pi$
$662$	10.7000	+	2.17135i	0.415868	+	0.0843917i
$663$		0			0
$664$	18.9906	+	39.6607i	0.736979	+	1.53913i
$665$	−24.2680			−0.941072
$666$		0			0
$667$	14.0027	+	14.0027i	0.542185	+	0.542185i
$668$	−34.7789	−	14.7215i	−1.34564	−	0.569593i
$669$		0			0
$670$	1.25097	−	0.828902i	0.0483291	−	0.0320233i
$671$	−16.4586	−	28.5072i	−0.635378	−	1.10051i
$672$		0			0
$673$	−11.8530	+	20.5299i	−0.456898	+	0.791371i	−0.998795	−	0.0490741i	$-0.984373\pi$
$673$	−11.8530	+	20.5299i	−0.456898	+	0.791371i	0.541897	+	0.840445i	$0.317706\pi$
$674$	−2.63789	−	42.7763i	−0.101608	−	1.64768i
$675$		0			0
$676$	−0.769336	−	6.21410i	−0.0295898	−	0.239004i
$677$	0.592200	−	0.158680i	0.0227601	−	0.00609855i	−0.247421	−	0.968908i	$-0.579583\pi$
$677$	0.592200	−	0.158680i	0.0227601	−	0.00609855i	0.270181	+	0.962810i	$0.412916\pi$
$678$		0			0
$679$	0.206287	+	0.357299i	0.00791656	+	0.0137119i
$680$	−0.368209	+	4.77048i	−0.0141202	+	0.182940i
$681$		0			0
$682$	3.52799	+	10.5265i	0.135094	+	0.403080i
$683$	7.92296	−	7.92296i	0.303164	−	0.303164i	−0.539087	−	0.842250i	$-0.681230\pi$
$683$	7.92296	−	7.92296i	0.303164	−	0.303164i	0.842250	+	0.539087i	$0.181230\pi$
$684$		0			0
$685$	−8.63676	−	8.63676i	−0.329994	−	0.329994i
$686$	4.85360	+	2.41687i	0.185311	+	0.0922765i
$687$		0			0
$688$	−0.352777	+	22.8417i	−0.0134495	+	0.870831i
$689$	8.46522	−	4.88739i	0.322499	−	0.186195i
$690$		0			0
$691$	−2.72654	−	10.1756i	−0.103722	−	0.387097i	0.894475	−	0.447118i	$-0.147550\pi$
$691$	−2.72654	−	10.1756i	−0.103722	−	0.387097i	−0.998197	+	0.0600214i	$0.980883\pi$
$692$	20.8269	−	26.7125i	0.791719	−	1.01546i
$693$		0			0
$694$	30.3282	+	26.8050i	1.15124	+	1.01750i
$695$	2.95027	+	1.70334i	0.111910	+	0.0646112i
$696$		0			0
$697$	4.28883	−	2.47616i	0.162451	−	0.0937912i
$698$	7.09136	+	1.43904i	0.268412	+	0.0544686i
$699$		0			0
$700$	−27.1638	−	11.4981i	−1.02670	−	0.434589i
$701$	−17.1029	+	17.1029i	−0.645968	+	0.645968i	−0.952016	−	0.306048i	$-0.900993\pi$
$701$	−17.1029	+	17.1029i	−0.645968	+	0.645968i	0.306048	+	0.952016i	$0.400993\pi$
$702$		0			0
$703$		−	49.0918i		−	1.85153i
$704$	17.2648	+	23.6128i	0.650690	+	0.889943i
$705$		0			0
$706$	−9.59494	−	14.4806i	−0.361110	−	0.544983i
$707$	−4.34024	+	16.1980i	−0.163231	+	0.609188i
$708$		0			0
$709$	−0.358349	−	1.33738i	−0.0134581	−	0.0502263i	0.958870	−	0.283845i	$-0.0916100\pi$
$709$	−0.358349	−	1.33738i	−0.0134581	−	0.0502263i	−0.972328	+	0.233618i	$0.924943\pi$
$710$	8.22665	+	7.27096i	0.308741	+	0.272874i
$711$		0			0
$712$	−5.84057	−	31.2499i	−0.218885	−	1.17114i
$713$	−4.79209	+	8.30014i	−0.179465	+	0.310843i
$714$		0			0
$715$	−4.14744	+	15.4785i	−0.155106	+	0.578862i
$716$	−1.89595	+	13.5895i	−0.0708550	+	0.507862i
$717$		0			0
$718$	5.26863	−	10.5806i	0.196624	−	0.394863i
$719$	3.58660			0.133758			0.0668789	−	0.997761i	$-0.478696\pi$
$719$	3.58660			0.133758			0.0668789	+	0.997761i	$0.478696\pi$
$720$		0			0
$721$	9.68418			0.360658
$722$	8.82257	−	17.7176i	0.328342	−	0.659382i
$723$		0			0
$724$	−5.57014	−	0.777124i	−0.207013	−	0.0288816i
$725$	−4.37362	+	16.3226i	−0.162432	+	0.606205i
$726$		0			0
$727$	−19.8338	+	34.3531i	−0.735594	+	1.27409i	0.218869	+	0.975754i	$0.429763\pi$
$727$	−19.8338	+	34.3531i	−0.735594	+	1.27409i	−0.954462	+	0.298331i	$0.903570\pi$
$728$	24.8571	−	36.2844i	0.921266	−	1.34479i
$729$		0			0
$730$	−12.0388	−	10.6402i	−0.445576	−	0.393813i
$731$	−2.29151	−	8.55203i	−0.0847545	−	0.316308i
$732$		0			0
$733$	−1.99707	+	7.45317i	−0.0737635	+	0.275289i	−0.992950	−	0.118533i	$-0.962181\pi$
$733$	−1.99707	+	7.45317i	−0.0737635	+	0.275289i	0.919187	+	0.393822i	$0.128847\pi$
$734$	−5.04963	−	7.62084i	−0.186385	−	0.281290i
$735$		0			0
$736$	−5.40363	+	24.6673i	−0.199180	+	0.909250i
$737$			3.55568i			0.130975i
$738$		0			0
$739$	−3.67791	+	3.67791i	−0.135294	+	0.135294i	−0.771511	−	0.636216i	$-0.780499\pi$
$739$	−3.67791	+	3.67791i	−0.135294	+	0.135294i	0.636216	+	0.771511i	$0.280499\pi$
$740$	−7.27044	+	17.1761i	−0.267267	+	0.631404i
$741$		0			0
$742$	13.0598	+	2.65021i	0.479440	+	0.0972923i
$743$	−29.0142	+	16.7513i	−1.06443	+	0.614547i	−0.926654	−	0.375917i	$-0.877328\pi$
$743$	−29.0142	+	16.7513i	−1.06443	+	0.614547i	−0.137773	+	0.990464i	$0.543995\pi$
$744$		0			0
$745$	14.1551	+	8.17244i	0.518602	+	0.299415i
$746$	12.6245	+	11.1579i	0.462216	+	0.408520i
$747$		0			0
$748$	−8.94053	−	6.97065i	−0.326898	−	0.254872i
$749$	8.51811	+	31.7900i	0.311245	+	1.16158i
$750$		0			0
$751$	28.3480	−	16.3667i	1.03443	−	0.597231i	0.116182	−	0.993228i	$-0.462934\pi$
$751$	28.3480	−	16.3667i	1.03443	−	0.597231i	0.918252	+	0.395997i	$0.129601\pi$
$752$	0.275299	+	0.283936i	0.0100391	+	0.0103541i
$753$		0			0
$754$	−22.5550	−	11.2313i	−0.821404	−	0.409022i
$755$	−0.465095	−	0.465095i	−0.0169265	−	0.0169265i
$756$		0			0
$757$	−32.1096	+	32.1096i	−1.16704	+	1.16704i	−0.184143	+	0.982900i	$0.558951\pi$
$757$	−32.1096	+	32.1096i	−1.16704	+	1.16704i	−0.982900	+	0.184143i	$0.941049\pi$
$758$	4.93479	+	14.7239i	0.179240	+	0.534797i
$759$		0			0
$760$	−13.4636	+	11.5341i	−0.488374	+	0.418386i
$761$	−11.3534	−	19.6647i	−0.411562	−	0.712847i	0.583499	−	0.812114i	$-0.301683\pi$
$761$	−11.3534	−	19.6647i	−0.411562	−	0.712847i	−0.995061	+	0.0992676i	$0.968350\pi$
$762$		0			0
$763$	−4.65936	+	1.24847i	−0.168680	+	0.0451977i
$764$	−40.4897	+	5.01282i	−1.46487	+	0.181358i
$765$		0			0
$766$	0.498357	+	8.08142i	0.0180064	+	0.291994i
$767$	27.8182	−	48.1825i	1.00446	−	1.73977i
$768$		0			0
$769$	23.6477	+	40.9590i	0.852757	+	1.47702i	0.878710	+	0.477356i	$0.158405\pi$
$769$	23.6477	+	40.9590i	0.852757	+	1.47702i	−0.0259531	+	0.999663i	$0.508262\pi$
$770$	−18.2112	+	12.0669i	−0.656285	+	0.434860i
$771$		0			0
$772$	12.9478	−	30.5886i	0.466003	−	1.10091i
$773$	13.5761	+	13.5761i	0.488297	+	0.488297i	0.907768	−	0.419472i	$-0.137785\pi$
$773$	13.5761	+	13.5761i	0.488297	+	0.488297i	−0.419472	+	0.907768i	$0.637785\pi$
$774$		0			0
$775$	−8.17852			−0.293781
$776$	0.284263	+	0.100181i	0.0102044	+	0.00359628i
$777$		0			0
$778$	−9.78721	−	1.98611i	−0.350889	−	0.0712055i
$779$	17.7245	+	4.74927i	0.635047	+	0.170160i
$780$		0			0
$781$	−25.1279	+	6.73300i	−0.899147	+	0.240926i
$782$	−0.602386	−	9.76836i	−0.0215413	−	0.349316i
$783$		0			0
$784$	30.9960	−	7.79438i	1.10700	−	0.278371i
$785$	−6.57984	−	3.79887i	−0.234845	−	0.135588i
$786$		0			0
$787$	7.95128	+	2.13054i	0.283432	+	0.0759455i	0.397735	−	0.917501i	$-0.369797\pi$
$787$	7.95128	+	2.13054i	0.283432	+	0.0759455i	−0.114302	+	0.993446i	$0.536463\pi$
$788$	−0.796526	+	5.70920i	−0.0283750	+	0.203382i
$789$		0			0
$790$	24.0595	−	8.06364i	0.855998	−	0.286891i
$791$		−	9.53851i		−	0.339150i
$792$		0			0
$793$			36.1573i			1.28398i
$794$	−1.18487	−	3.53531i	−0.0420496	−	0.125463i
$795$		0			0
$796$	−11.0845	−	14.6789i	−0.392880	−	0.520281i
$797$	35.7427	+	9.57723i	1.26607	+	0.339243i	0.828525	−	0.559953i	$-0.189181\pi$
$797$	35.7427	+	9.57723i	1.26607	+	0.339243i	0.437547	+	0.899195i	$0.355847\pi$
$798$		0			0
$799$	−0.132742	−	0.0766384i	−0.00469606	−	0.00271127i
$800$	−20.5350	+	6.53142i	−0.726021	+	0.230921i
$801$		0			0
$802$	55.9215	−	3.44851i	1.97466	−	0.121771i
$803$	36.7719	−	9.85301i	1.29765	−	0.347705i
$804$		0			0
$805$	−18.2169	−	4.88121i	−0.642062	−	0.172040i
$806$	2.42523	−	11.9511i	0.0854251	−	0.420961i
$807$		0			0
$808$	5.29069	+	11.0493i	0.186126	+	0.388712i
$809$	42.6915			1.50095			0.750477	−	0.660897i	$-0.229824\pi$
$809$	42.6915			1.50095			0.750477	+	0.660897i	$0.229824\pi$
$810$		0			0
$811$	−21.6324	−	21.6324i	−0.759616	−	0.759616i	0.216637	−	0.976252i	$-0.430491\pi$
$811$	−21.6324	−	21.6324i	−0.759616	−	0.759616i	−0.976252	+	0.216637i	$0.930491\pi$
$812$	−12.9000	−	31.8364i	−0.452700	−	1.11724i
$813$		0			0
$814$	−24.4101	−	36.8394i	−0.855574	−	1.29122i
$815$	5.97131	+	10.3426i	0.209166	+	0.362286i
$816$		0			0
$817$	16.4028	−	28.4105i	0.573861	−	0.993957i
$818$	−31.8523	+	1.96424i	−1.11369	+	0.0686780i
$819$		0			0
$820$	−5.49803	−	4.28664i	−0.192000	−	0.149696i
$821$	−41.7600	+	11.1896i	−1.45744	+	0.390519i	−0.898603	−	0.438762i	$-0.855417\pi$
$821$	−41.7600	+	11.1896i	−1.45744	+	0.390519i	−0.558832	+	0.829281i	$0.688750\pi$
$822$		0			0
$823$	−7.47369	−	12.9448i	−0.260516	−	0.451227i	0.705863	−	0.708348i	$-0.250559\pi$
$823$	−7.47369	−	12.9448i	−0.260516	−	0.451227i	−0.966379	+	0.257121i	$0.917226\pi$
$824$	5.37266	−	4.60271i	0.187165	−	0.160343i
$825$		0			0
$826$	71.9174	−	24.1034i	2.50233	−	0.838665i
$827$	−3.17437	+	3.17437i	−0.110384	+	0.110384i	−0.760141	−	0.649758i	$-0.774870\pi$
$827$	−3.17437	+	3.17437i	−0.110384	+	0.110384i	0.649758	+	0.760141i	$0.274870\pi$
$828$		0			0
$829$	−6.24227	−	6.24227i	−0.216803	−	0.216803i	0.590347	−	0.807150i	$-0.298991\pi$
$829$	−6.24227	−	6.24227i	−0.216803	−	0.216803i	−0.807150	+	0.590347i	$0.798991\pi$
$830$	−10.6941	+	21.4761i	−0.371199	+	0.745448i
$831$		0			0
$832$	−3.45488	−	31.9442i	−0.119777	−	1.10747i
$833$	−10.7274	+	6.19349i	−0.371684	+	0.214592i
$834$		0			0
$835$	−5.33301	−	19.9031i	−0.184556	−	0.688774i
$836$	−5.16116	−	41.6879i	−0.178503	−	1.44181i
$837$		0			0
$838$	0.524711	−	0.593679i	0.0181258	−	0.0205083i
$839$	−8.61601	−	4.97446i	−0.297458	−	0.171737i	0.343842	−	0.939027i	$-0.388271\pi$
$839$	−8.61601	−	4.97446i	−0.297458	−	0.171737i	−0.641300	+	0.767290i	$0.721605\pi$
$840$		0			0
$841$	8.07235	−	4.66057i	0.278357	−	0.160709i
$842$	6.14674	−	30.2901i	0.211831	−	1.04387i
$843$		0			0
$844$	−11.5939	−	28.6131i	−0.399079	−	0.984905i
$845$	2.41567	−	2.41567i	0.0831016	−	0.0831016i
$846$		0			0
$847$		−	9.17346i		−	0.315204i
$848$	8.50500	−	4.73677i	0.292063	−	0.162661i
$849$		0			0
$850$	6.96189	−	4.61301i	0.238791	−	0.158225i
$851$	9.87421	−	36.8511i	0.338484	−	1.26324i
$852$		0			0
$853$	−5.53253	−	20.6477i	−0.189430	−	0.706963i	−0.993639	−	0.112616i	$-0.964077\pi$
$853$	−5.53253	−	20.6477i	−0.189430	−	0.706963i	0.804208	−	0.594347i	$-0.202590\pi$
$854$	−32.6442	+	36.9349i	−1.11706	+	1.26389i
$855$		0			0
$856$	19.8349	+	13.5882i	0.677944	+	0.464435i
$857$	−6.86646	+	11.8931i	−0.234554	+	0.406259i	−0.959143	−	0.282922i	$-0.908696\pi$
$857$	−6.86646	+	11.8931i	−0.234554	+	0.406259i	0.724589	+	0.689181i	$0.242030\pi$
$858$		0			0
$859$	−3.65143	+	13.6273i	−0.124585	+	0.464958i	−0.999825	−	0.0187321i	$-0.994037\pi$
$859$	−3.65143	+	13.6273i	−0.124585	+	0.464958i	0.875239	+	0.483690i	$0.160704\pi$
$860$	−9.94651	+	7.51092i	−0.339173	+	0.256120i
$861$		0			0
$862$	−10.2514	−	5.10474i	−0.349165	−	0.173868i
$863$	−30.6861			−1.04457			−0.522284	−	0.852772i	$-0.674920\pi$
$863$	−30.6861			−1.04457			−0.522284	+	0.852772i	$0.674920\pi$
$864$		0			0
$865$	18.4805			0.628355
$866$	35.4945	+	17.6746i	1.20615	+	0.600608i
$867$		0			0
$868$	13.2673	−	10.0186i	0.450322	−	0.340052i
$869$	−15.5610	+	58.0745i	−0.527871	+	1.97004i
$870$		0			0
$871$	1.95283	−	3.38240i	0.0661692	−	0.114608i
$872$	−1.99157	+	2.90714i	−0.0674432	+	0.0984481i
$873$		0			0
$874$	24.0152	−	27.1717i	0.812326	−	0.919098i
$875$	−9.63260	−	35.9493i	−0.325641	−	1.21531i
$876$		0			0
$877$	5.67328	−	21.1730i	0.191573	−	0.714960i	−0.801554	−	0.597922i	$-0.795993\pi$
$877$	5.67328	−	21.1730i	0.191573	−	0.714960i	0.993127	−	0.117038i	$-0.0373400\pi$
$878$	33.7174	−	22.3414i	1.13791	−	0.753986i
$879$		0			0
$880$	−4.36816	+	15.3500i	−0.147251	+	0.517447i
$881$		−	15.7695i		−	0.531287i	−0.964071	−	0.265644i	$-0.914416\pi$
$881$		−	15.7695i		−	0.531287i	0.964071	−	0.265644i	$-0.0855845\pi$
$882$		0			0
$883$	−32.1210	+	32.1210i	−1.08096	+	1.08096i	−0.0845378	+	0.996420i	$0.526941\pi$
$883$	−32.1210	+	32.1210i	−1.08096	+	1.08096i	−0.996420	+	0.0845378i	$0.973059\pi$
$884$	4.67646	+	11.5412i	0.157286	+	0.388174i
$885$		0			0
$886$	−1.89200	+	9.32347i	−0.0635631	+	0.313228i
$887$	−5.68281	+	3.28097i	−0.190810	+	0.110164i	−0.592362	−	0.805672i	$-0.701804\pi$
$887$	−5.68281	+	3.28097i	−0.190810	+	0.110164i	0.401552	+	0.915836i	$0.368471\pi$
$888$		0			0
$889$	−12.6307	−	7.29233i	−0.423620	−	0.244577i
$890$	11.4867	−	12.9965i	0.385034	−	0.435642i
$891$		0			0
$892$	4.30617	+	34.7819i	0.144181	+	1.16458i
$893$	−0.146992	−	0.548583i	−0.00491891	−	0.0183576i
$894$		0			0
$895$	−6.48322	+	3.74309i	−0.216710	+	0.125118i
$896$	25.3113	−	35.7504i	0.845590	−	1.19434i
$897$		0			0
$898$	21.5145	−	43.2058i	0.717948	−	1.44180i
$899$	−6.73464	−	6.73464i	−0.224613	−	0.224613i
$900$		0			0
$901$	−2.66790	+	2.66790i	−0.0888808	+	0.0888808i
$902$	15.6623	−	5.24930i	0.521499	−	0.174783i
$903$		0			0
$904$	−4.53347	−	5.29184i	−0.150781	−	0.176004i
$905$	−1.53424	−	2.65738i	−0.0509999	−	0.0883344i
$906$		0			0
$907$	−21.9728	+	5.88760i	−0.729596	+	0.195495i	−0.604449	−	0.796644i	$-0.706607\pi$
$907$	−21.9728	+	5.88760i	−0.729596	+	0.195495i	−0.125147	+	0.992138i	$0.539940\pi$
$908$	−31.9904	−	24.9419i	−1.06164	−	0.827727i
$909$		0			0
$910$	23.9510	−	1.47699i	0.793969	−	0.0489617i
$911$	−5.27703	+	9.14009i	−0.174836	+	0.302825i	−0.940104	−	0.340887i	$-0.889273\pi$
$911$	−5.27703	+	9.14009i	−0.174836	+	0.302825i	0.765269	+	0.643711i	$0.222606\pi$
$912$		0			0
$913$	−28.4227	−	49.2295i	−0.940653	−	1.62926i
$914$	−0.206329	−	0.311389i	−0.00682475	−	0.0102998i
$915$		0			0
$916$	11.6919	+	28.8550i	0.386312	+	0.953397i
$917$	−3.64675	−	3.64675i	−0.120426	−	0.120426i
$918$		0			0
$919$	−0.366138			−0.0120778			−0.00603890	−	0.999982i	$-0.501922\pi$
$919$	−0.366138			−0.0120778			−0.00603890	+	0.999982i	$0.501922\pi$
$920$	−12.4265	+	5.95013i	−0.409688	+	0.196170i
$921$		0			0
$922$	6.45109	−	31.7899i	0.212455	−	1.04694i
$923$	27.6012	+	7.39573i	0.908506	+	0.243433i
$924$		0			0
$925$	31.4463	−	8.42601i	1.03395	−	0.277046i
$926$	41.0208	−	2.52963i	1.34803	−	0.0831289i
$927$		0			0
$928$	−22.2880	−	11.5313i	−0.731638	−	0.378533i
$929$	40.6720	+	23.4820i	1.33440	+	0.770419i	0.985971	−	0.166915i	$-0.0533806\pi$
$929$	40.6720	+	23.4820i	1.33440	+	0.770419i	0.348433	+	0.937334i	$0.386714\pi$
$930$		0			0
$931$	−44.3335	−	11.8791i	−1.45297	−	0.389323i
$932$	32.7439	+	43.3619i	1.07256	+	1.42037i
$933$		0			0
$934$	0.934123	+	2.78714i	0.0305654	+	0.0911981i
$935$		−	6.18532i		−	0.202281i
$936$		0			0
$937$		−	52.8156i		−	1.72541i	−0.505706	−	0.862706i	$-0.668768\pi$
$937$		−	52.8156i		−	1.72541i	0.505706	−	0.862706i	$-0.331232\pi$
$938$	5.04859	−	1.69206i	0.164842	−	0.0552476i
$939$		0			0
$940$	−0.0298154	+	0.213706i	−0.000972471	+	0.00697031i
$941$	−53.1569	−	14.2433i	−1.73286	−	0.464320i	−0.752024	−	0.659135i	$-0.770922\pi$
$941$	−53.1569	−	14.2433i	−1.73286	−	0.464320i	−0.980840	+	0.194816i	$0.937589\pi$
$942$		0			0
$943$	12.3498	+	7.13015i	0.402164	+	0.232190i
$944$	28.4429	−	47.5532i	0.925738	−	1.54773i
$945$		0			0
$946$	−1.81769	−	29.4758i	−0.0590981	−	0.958342i
$947$	−18.7824	+	5.03273i	−0.610346	+	0.163542i	−0.550735	−	0.834680i	$-0.685653\pi$
$947$	−18.7824	+	5.03273i	−0.610346	+	0.163542i	−0.0596105	+	0.998222i	$0.518986\pi$
$948$		0			0
$949$	−40.3914	−	10.8228i	−1.31116	−	0.351324i
$950$	30.3267	+	6.15416i	0.983927	+	0.199667i
$951$		0			0
$952$	−5.64283	+	16.0115i	−0.182885	+	0.518936i
$953$	32.2129			1.04348			0.521739	−	0.853105i	$-0.325283\pi$
$953$	32.2129			1.04348			0.521739	+	0.853105i	$0.325283\pi$
$954$		0			0
$955$	−15.7400	−	15.7400i	−0.509334	−	0.509334i
$956$	3.86745	−	9.13665i	0.125082	−	0.295500i
$957$		0			0
$958$	−27.8566	+	18.4580i	−0.900007	+	0.596352i
$959$	−21.6690	−	37.5318i	−0.699729	−	1.21197i
$960$		0			0
$961$	−13.1952	+	22.8548i	−0.425652	+	0.737251i
$962$	2.98780	+	48.4506i	0.0963307	+	1.56211i
$963$		0			0
$964$	−19.6011	+	2.42671i	−0.631308	+	0.0781590i
$965$	17.5051	−	4.69047i	0.563508	−	0.150992i
$966$		0			0
$967$	−6.78008	−	11.7434i	−0.218033	−	0.377644i	0.736174	−	0.676793i	$-0.236631\pi$
$967$	−6.78008	−	11.7434i	−0.218033	−	0.377644i	−0.954206	+	0.299149i	$0.903297\pi$
$968$	−4.35997	−	5.08931i	−0.140135	−	0.163577i
$969$		0			0
$970$	0.0522567	+	0.155918i	0.00167786	+	0.00500623i
$971$	1.29201	−	1.29201i	0.0414626	−	0.0414626i	−0.686072	−	0.727534i	$-0.740666\pi$
$971$	1.29201	−	1.29201i	0.0414626	−	0.0414626i	0.727534	+	0.686072i	$0.240666\pi$
$972$		0			0
$973$	8.54709	+	8.54709i	0.274007	+	0.274007i
$974$	−10.6884	−	5.32231i	−0.342477	−	0.170538i
$975$		0			0
$976$	−0.556095	+	36.0062i	−0.0178002	+	1.15253i
$977$	30.8504	−	17.8115i	0.986993	−	0.569841i	0.0826189	−	0.996581i	$-0.473672\pi$
$977$	30.8504	−	17.8115i	0.986993	−	0.569841i	0.904374	+	0.426741i	$0.140338\pi$
$978$		0			0
$979$	10.6368	+	39.6971i	0.339954	+	1.26872i
$980$	13.7520	+	10.7220i	0.439290	+	0.342501i
$981$		0			0
$982$	−5.40485	−	4.77697i	−0.172476	−	0.152439i
$983$	−44.7746	−	25.8506i	−1.42809	−	0.824507i	−0.431118	−	0.902295i	$-0.641881\pi$
$983$	−44.7746	−	25.8506i	−1.42809	−	0.824507i	−0.996970	+	0.0777882i	$0.975214\pi$
$984$		0			0
$985$	−2.72373	+	1.57254i	−0.0867852	+	0.0501054i
$986$	9.53141	+	1.93420i	0.303542	+	0.0615975i
$987$		0			0
$988$	−17.9860	+	42.4910i	−0.572210	+	1.35182i
$989$	18.0273	−	18.0273i	0.573235	−	0.573235i
$990$		0			0
$991$			27.3724i			0.869513i	0.900548	+	0.434756i	$0.143166\pi$
$991$			27.3724i			0.869513i	−0.900548	+	0.434756i	$0.856834\pi$
$992$	2.59890	−	11.8639i	0.0825152	−	0.376678i
$993$		0			0
$994$	21.5177	+	32.4742i	0.682500	+	1.03002i
$995$	2.59742	−	9.69372i	0.0823439	−	0.307311i
$996$		0			0
$997$	13.9916	+	52.2174i	0.443119	+	1.65374i	0.720856	+	0.693085i	$0.243749\pi$
$997$	13.9916	+	52.2174i	0.443119	+	1.65374i	−0.277737	+	0.960657i	$0.589584\pi$
$998$	−21.8735	−	19.3324i	−0.692392	−	0.611957i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.35.19		88
3.2	odd	2		144.2.u.a.83.4	yes	88
4.3	odd	2		1728.2.z.a.1007.9		88
9.4	even	3		144.2.u.a.131.5	yes	88
9.5	odd	6	inner	432.2.v.a.179.18		88
12.11	even	2		576.2.y.a.47.13		88
16.5	even	4		1728.2.z.a.143.9		88
16.11	odd	4	inner	432.2.v.a.251.18		88
36.23	even	6		1728.2.z.a.1583.9		88
36.31	odd	6		576.2.y.a.239.21		88
48.5	odd	4		576.2.y.a.335.21		88
48.11	even	4		144.2.u.a.11.5	✓	88
144.5	odd	12		1728.2.z.a.719.9		88
144.59	even	12	inner	432.2.v.a.395.19		88
144.85	even	12		576.2.y.a.527.13		88
144.139	odd	12		144.2.u.a.59.4	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.5	✓	88	48.11	even	4
144.2.u.a.59.4	yes	88	144.139	odd	12
144.2.u.a.83.4	yes	88	3.2	odd	2
144.2.u.a.131.5	yes	88	9.4	even	3
432.2.v.a.35.19		88	1.1	even	1	trivial
432.2.v.a.179.18		88	9.5	odd	6	inner
432.2.v.a.251.18		88	16.11	odd	4	inner
432.2.v.a.395.19		88	144.59	even	12	inner
576.2.y.a.47.13		88	12.11	even	2
576.2.y.a.239.21		88	36.31	odd	6
576.2.y.a.335.21		88	48.5	odd	4
576.2.y.a.527.13		88	144.85	even	12
1728.2.z.a.143.9		88	16.5	even	4
1728.2.z.a.719.9		88	144.5	odd	12
1728.2.z.a.1007.9		88	4.3	odd	2
1728.2.z.a.1583.9		88	36.23	even	6

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)

\(f(q)\)	\(=\)	\(q+(1.26595 + 0.630383i) q^{2} +(1.20523 + 1.59606i) q^{4} +(-0.282421 + 1.05401i) q^{5} +(-1.93586 + 3.35301i) q^{7} +(0.519632 + 2.78028i) q^{8} +O(q^{10})\)	\(q+(1.26595 + 0.630383i) q^{2} +(1.20523 + 1.59606i) q^{4} +(-0.282421 + 1.05401i) q^{5} +(-1.93586 + 3.35301i) q^{7} +(0.519632 + 2.78028i) q^{8} +(-1.02196 + 1.15629i) q^{10} +(-0.946349 - 3.53182i) q^{11} +(-1.03950 + 3.87946i) q^{13} +(-4.56438 + 3.02439i) q^{14} +(-1.09482 + 3.84726i) q^{16} -1.55026i q^{17} +(4.06175 - 4.06175i) q^{19} +(-2.02265 + 0.819569i) q^{20} +(1.02837 - 5.06766i) q^{22} +(3.86595 - 2.23201i) q^{23} +(3.29895 + 1.90465i) q^{25} +(-3.76149 + 4.25590i) q^{26} +(-7.68478 + 0.951413i) q^{28} +(1.14814 + 4.28493i) q^{29} +(-1.85935 + 1.07349i) q^{31} +(-3.81122 + 4.18026i) q^{32} +(0.977259 - 1.96255i) q^{34} +(-2.98738 - 2.98738i) q^{35} +(6.04318 - 6.04318i) q^{37} +(7.70240 - 2.58149i) q^{38} +(-3.07721 - 0.237514i) q^{40} +(1.59725 + 2.76652i) q^{41} +(5.51650 - 1.47814i) q^{43} +(4.49643 - 5.76711i) q^{44} +(6.30110 - 0.388570i) q^{46} +(0.0494357 - 0.0856252i) q^{47} +(-3.99512 - 6.91976i) q^{49} +(2.97563 + 4.49078i) q^{50} +(-7.44469 + 3.01656i) q^{52} +(-1.72094 - 1.72094i) q^{53} +3.98985 q^{55} +(-10.3283 - 3.63992i) q^{56} +(-1.24766 + 6.14826i) q^{58} +(-13.3806 - 3.58531i) q^{59} +(8.69586 - 2.33005i) q^{61} +(-3.03054 + 0.186885i) q^{62} +(-7.45997 + 2.88945i) q^{64} +(-3.79542 - 2.19129i) q^{65} +(-0.939315 - 0.251689i) q^{67} +(2.47431 - 1.86843i) q^{68} +(-1.89867 - 5.66506i) q^{70} -7.11471i q^{71} +10.4116i q^{73} +(11.4599 - 3.84082i) q^{74} +(11.3782 + 1.58744i) q^{76} +(13.6742 + 3.66400i) q^{77} +(-14.2402 - 8.22160i) q^{79} +(-3.74585 - 2.24050i) q^{80} +(0.278065 + 4.50914i) q^{82} +(15.0170 - 4.02380i) q^{83} +(1.63399 + 0.437828i) q^{85} +(7.91539 + 1.60626i) q^{86} +(9.32772 - 4.46637i) q^{88} -11.2398 q^{89} +(-10.9956 - 10.9956i) q^{91} +(8.22179 + 3.48020i) q^{92} +(0.116560 - 0.0772333i) q^{94} +(3.13400 + 5.42825i) q^{95} +(0.0532804 - 0.0922843i) q^{97} +(-0.695511 - 11.2785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7}+O(q^{10}) \) 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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