LMFDB - Embedded newform 864.2.bn.a.611.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			611.22
Character	$\chi$	$=$	864.611
Dual form			864.2.bn.a.683.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0101598 - 1.41418i) q^{2} +(-1.99979 - 0.0287354i) q^{4} +(-0.203653 + 1.54690i) q^{5} +(0.0488121 - 0.182169i) q^{7} +(-0.0609543 + 2.82777i) q^{8} +O(q^{10})$	\(q+(0.0101598 - 1.41418i) q^{2} +(-1.99979 - 0.0287354i) q^{4} +(-0.203653 + 1.54690i) q^{5} +(0.0488121 - 0.182169i) q^{7} +(-0.0609543 + 2.82777i) q^{8} +(2.18552 + 0.303717i) q^{10} +(1.65527 + 1.27014i) q^{11} +(-3.11766 - 4.06301i) q^{13} +(-0.257123 - 0.0708797i) q^{14} +(3.99835 + 0.114930i) q^{16} -6.30311 q^{17} +(-4.50721 - 1.86695i) q^{19} +(0.451715 - 3.08762i) q^{20} +(1.81302 - 2.32795i) q^{22} +(-4.54282 + 1.21725i) q^{23} +(2.47821 + 0.664034i) q^{25} +(-5.77750 + 4.36765i) q^{26} +(-0.102849 + 0.362898i) q^{28} +(-4.26178 + 0.561073i) q^{29} +(-5.30049 - 3.06024i) q^{31} +(0.203153 - 5.65321i) q^{32} +(-0.0640380 + 8.91371i) q^{34} +(0.271856 + 0.112607i) q^{35} +(1.61800 + 3.90619i) q^{37} +(-2.68599 + 6.35503i) q^{38} +(-4.36186 - 0.670174i) q^{40} +(-0.831961 - 3.10492i) q^{41} +(-4.52931 + 5.90271i) q^{43} +(-3.27371 - 2.58758i) q^{44} +(1.67525 + 6.43673i) q^{46} +(-1.00866 + 0.582347i) q^{47} +(6.03137 + 3.48222i) q^{49} +(0.964240 - 3.49788i) q^{50} +(6.11793 + 8.21478i) q^{52} +(3.04502 + 7.35132i) q^{53} +(-2.30187 + 2.30187i) q^{55} +(0.512157 + 0.149133i) q^{56} +(0.750159 + 6.03261i) q^{58} +(-9.10089 - 1.19815i) q^{59} +(-0.850975 - 6.46380i) q^{61} +(-4.38157 + 7.46474i) q^{62} +(-7.99257 - 0.344730i) q^{64} +(6.91999 - 3.99526i) q^{65} +(-1.34269 - 1.74983i) q^{67} +(12.6049 + 0.181122i) q^{68} +(0.162008 - 0.383309i) q^{70} +(5.65361 - 5.65361i) q^{71} +(6.45325 + 6.45325i) q^{73} +(5.54048 - 2.24845i) q^{74} +(8.95985 + 3.86303i) q^{76} +(0.312177 - 0.239542i) q^{77} +(-6.05908 - 10.4946i) q^{79} +(-0.992060 + 6.16163i) q^{80} +(-4.39936 + 1.14499i) q^{82} +(-10.6336 + 1.39993i) q^{83} +(1.28365 - 9.75027i) q^{85} +(8.30146 + 6.46522i) q^{86} +(-3.69255 + 4.60332i) q^{88} +(1.53722 + 1.53722i) q^{89} +(-0.892335 + 0.369617i) q^{91} +(9.11969 - 2.30370i) q^{92} +(0.813295 + 1.43233i) q^{94} +(3.80589 - 6.59199i) q^{95} +(4.59956 + 7.96668i) q^{97} +(4.98575 - 8.49405i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.0101598	−	1.41418i	0.00718403	−	0.999974i
$2$	0.0101598	−	1.41418i	0.00718403	−	0.999974i
$3$		0			0
$3$		0			0
$4$	−1.99979	−	0.0287354i	−0.999897	−	0.0143677i
$5$	−0.203653	+	1.54690i	−0.0910764	+	0.691794i	0.883611	+	0.468222i	$0.155105\pi$
$5$	−0.203653	+	1.54690i	−0.0910764	+	0.691794i	−0.974687	+	0.223572i	$0.928228\pi$
$6$		0			0
$7$	0.0488121	−	0.182169i	0.0184492	−	0.0688534i	−0.956088	−	0.293081i	$-0.905319\pi$
$7$	0.0488121	−	0.182169i	0.0184492	−	0.0688534i	0.974537	+	0.224228i	$0.0719860\pi$
$8$	−0.0609543	+	2.82777i	−0.0215506	+	0.999768i
$9$		0			0
$10$	2.18552	+	0.303717i	0.691122	+	0.0960439i
$11$	1.65527	+	1.27014i	0.499084	+	0.382961i	0.827405	−	0.561606i	$-0.189816\pi$
$11$	1.65527	+	1.27014i	0.499084	+	0.382961i	−0.328321	+	0.944566i	$0.606483\pi$
$12$		0			0
$13$	−3.11766	−	4.06301i	−0.864684	−	1.12688i	−0.990863	−	0.134870i	$-0.956938\pi$
$13$	−3.11766	−	4.06301i	−0.864684	−	1.12688i	0.126180	−	0.992007i	$-0.459728\pi$
$14$	−0.257123	−	0.0708797i	−0.0687191	−	0.0189434i
$15$		0			0
$16$	3.99835	+	0.114930i	0.999587	+	0.0287324i
$17$	−6.30311			−1.52873			−0.764364	−	0.644785i	$-0.776947\pi$
$17$	−6.30311			−1.52873			−0.764364	+	0.644785i	$0.776947\pi$
$18$		0			0
$19$	−4.50721	−	1.86695i	−1.03403	−	0.428307i	−0.199862	−	0.979824i	$-0.564049\pi$
$19$	−4.50721	−	1.86695i	−1.03403	−	0.428307i	−0.834164	+	0.551517i	$0.814049\pi$
$20$	0.451715	−	3.08762i	0.101006	−	0.690414i
$21$		0			0
$22$	1.81302	−	2.32795i	0.386536	−	0.496320i
$23$	−4.54282	+	1.21725i	−0.947244	+	0.253813i	−0.699193	−	0.714933i	$-0.746457\pi$
$23$	−4.54282	+	1.21725i	−0.947244	+	0.253813i	−0.248052	+	0.968747i	$0.579790\pi$
$24$		0			0
$25$	2.47821	+	0.664034i	0.495642	+	0.132807i
$26$	−5.77750	+	4.36765i	−1.13306	+	0.856566i
$27$		0			0
$28$	−0.102849	+	0.362898i	−0.0194366	+	0.0685813i
$29$	−4.26178	+	0.561073i	−0.791392	+	0.104189i	−0.515376	−	0.856964i	$-0.672348\pi$
$29$	−4.26178	+	0.561073i	−0.791392	+	0.104189i	−0.276016	+	0.961153i	$0.589014\pi$
$30$		0			0
$31$	−5.30049	−	3.06024i	−0.951997	−	0.549635i	−0.0582960	−	0.998299i	$-0.518567\pi$
$31$	−5.30049	−	3.06024i	−0.951997	−	0.549635i	−0.893701	+	0.448664i	$0.851900\pi$
$32$	0.203153	−	5.65321i	0.0359127	−	0.999355i
$33$		0			0
$34$	−0.0640380	+	8.91371i	−0.0109824	+	1.52869i
$35$	0.271856	+	0.112607i	0.0459521	+	0.0190340i
$36$		0			0
$37$	1.61800	+	3.90619i	0.265997	+	0.642173i	0.999288	−	0.0377422i	$-0.0120166\pi$
$37$	1.61800	+	3.90619i	0.265997	+	0.642173i	−0.733291	+	0.679915i	$0.762017\pi$
$38$	−2.68599	+	6.35503i	−0.435725	+	1.03092i
$39$		0			0
$40$	−4.36186	−	0.670174i	−0.689670	−	0.105964i
$41$	−0.831961	−	3.10492i	−0.129930	−	0.484907i	0.870037	−	0.492987i	$-0.164095\pi$
$41$	−0.831961	−	3.10492i	−0.129930	−	0.484907i	−0.999967	+	0.00807955i	$0.997428\pi$
$42$		0			0
$43$	−4.52931	+	5.90271i	−0.690713	+	0.900155i	−0.998686	−	0.0512401i	$-0.983683\pi$
$43$	−4.52931	+	5.90271i	−0.690713	+	0.900155i	0.307973	+	0.951395i	$0.400349\pi$
$44$	−3.27371	−	2.58758i	−0.493530	−	0.390092i
$45$		0			0
$46$	1.67525	+	6.43673i	0.247002	+	0.949043i
$47$	−1.00866	+	0.582347i	−0.147128	+	0.0849441i	−0.571757	−	0.820423i	$-0.693738\pi$
$47$	−1.00866	+	0.582347i	−0.147128	+	0.0849441i	0.424629	+	0.905367i	$0.360405\pi$
$48$		0			0
$49$	6.03137	+	3.48222i	0.861625	+	0.497459i
$50$	0.964240	−	3.49788i	0.136364	−	0.494675i
$51$		0			0
$52$	6.11793	+	8.21478i	0.848404	+	1.13918i
$53$	3.04502	+	7.35132i	0.418265	+	1.00978i	0.982850	+	0.184407i	$0.0590364\pi$
$53$	3.04502	+	7.35132i	0.418265	+	1.00978i	−0.564585	+	0.825375i	$0.690964\pi$
$54$		0			0
$55$	−2.30187	+	2.30187i	−0.310385	+	0.310385i
$56$	0.512157	+	0.149133i	0.0684399	+	0.0199288i
$57$		0			0
$58$	0.750159	+	6.03261i	0.0985006	+	0.792120i
$59$	−9.10089	−	1.19815i	−1.18483	−	0.155986i	−0.487755	−	0.872980i	$-0.662184\pi$
$59$	−9.10089	−	1.19815i	−1.18483	−	0.155986i	−0.697079	+	0.716994i	$0.745518\pi$
$60$		0			0
$61$	−0.850975	−	6.46380i	−0.108956	−	0.827605i	−0.955439	−	0.295189i	$-0.904618\pi$
$61$	−0.850975	−	6.46380i	−0.108956	−	0.827605i	0.846483	−	0.532416i	$-0.178716\pi$
$62$	−4.38157	+	7.46474i	−0.556460	+	0.948023i
$63$		0			0
$64$	−7.99257	−	0.344730i	−0.999071	−	0.0430912i
$65$	6.91999	−	3.99526i	0.858319	−	0.495551i
$66$		0			0
$67$	−1.34269	−	1.74983i	−0.164036	−	0.213776i	0.704102	−	0.710099i	$-0.251350\pi$
$67$	−1.34269	−	1.74983i	−0.164036	−	0.213776i	−0.868138	+	0.496323i	$0.834683\pi$
$68$	12.6049	+	0.181122i	1.52857	+	0.0219643i
$69$		0			0
$70$	0.162008	−	0.383309i	0.0193636	−	0.0458142i
$71$	5.65361	−	5.65361i	0.670960	−	0.670960i	−0.286977	−	0.957937i	$-0.592650\pi$
$71$	5.65361	−	5.65361i	0.670960	−	0.670960i	0.957937	+	0.286977i	$0.0926504\pi$
$72$		0			0
$73$	6.45325	+	6.45325i	0.755296	+	0.755296i	0.975462	−	0.220167i	$-0.0706601\pi$
$73$	6.45325	+	6.45325i	0.755296	+	0.755296i	−0.220167	+	0.975462i	$0.570660\pi$
$74$	5.54048	−	2.24845i	0.644067	−	0.261377i
$75$		0			0
$76$	8.95985	+	3.86303i	1.02776	+	0.443120i
$77$	0.312177	−	0.239542i	0.0355759	−	0.0272983i
$78$		0			0
$79$	−6.05908	−	10.4946i	−0.681700	−	1.18074i	−0.974462	−	0.224554i	$-0.927908\pi$
$79$	−6.05908	−	10.4946i	−0.681700	−	1.18074i	0.292762	−	0.956185i	$-0.405426\pi$
$80$	−0.992060	+	6.16163i	−0.110916	+	0.688891i
$81$		0			0
$82$	−4.39936	+	1.14499i	−0.485828	+	0.126444i
$83$	−10.6336	+	1.39993i	−1.16718	+	0.153663i	−0.689110	−	0.724657i	$-0.741998\pi$
$83$	−10.6336	+	1.39993i	−1.16718	+	0.153663i	−0.478074	+	0.878320i	$0.658665\pi$
$84$		0			0
$85$	1.28365	−	9.75027i	0.139231	−	1.05756i
$86$	8.30146	+	6.46522i	0.895170	+	0.697162i
$87$		0			0
$88$	−3.69255	+	4.60332i	−0.393627	+	0.490715i
$89$	1.53722	+	1.53722i	0.162945	+	0.162945i	0.783870	−	0.620925i	$-0.213243\pi$
$89$	1.53722	+	1.53722i	0.162945	+	0.162945i	−0.620925	+	0.783870i	$0.713243\pi$
$90$		0			0
$91$	−0.892335	+	0.369617i	−0.0935421	+	0.0387464i
$92$	9.11969	−	2.30370i	0.950793	−	0.240177i
$93$		0			0
$94$	0.813295	+	1.43233i	0.0838849	+	0.147734i
$95$	3.80589	−	6.59199i	0.390476	−	0.676324i
$96$		0			0
$97$	4.59956	+	7.96668i	0.467015	+	0.808893i	0.999290	−	0.0376780i	$-0.0119961\pi$
$97$	4.59956	+	7.96668i	0.467015	+	0.808893i	−0.532275	+	0.846571i	$0.678663\pi$
$98$	4.98575	−	8.49405i	0.503637	−	0.858029i
$99$		0			0
$100$	−4.93683	−	1.39914i	−0.493683	−	0.139914i
$101$	−10.4701	−	8.03397i	−1.04181	−	0.799410i	−0.0617475	−	0.998092i	$-0.519667\pi$
$101$	−10.4701	−	8.03397i	−1.04181	−	0.799410i	−0.980064	+	0.198682i	$0.936334\pi$
$102$		0			0
$103$	−4.69448	+	1.25788i	−0.462561	+	0.123943i	−0.482571	−	0.875857i	$-0.660297\pi$
$103$	−4.69448	+	1.25788i	−0.462561	+	0.123943i	0.0200099	+	0.999800i	$0.493630\pi$
$104$	11.6793	−	8.56837i	1.14525	−	0.840198i
$105$		0			0
$106$	10.4270	−	4.23151i	1.01276	−	0.411000i
$107$	11.1138	−	4.60349i	1.07441	−	0.445036i	0.225866	−	0.974158i	$-0.427479\pi$
$107$	11.1138	−	4.60349i	1.07441	−	0.445036i	0.848545	+	0.529122i	$0.177479\pi$
$108$		0			0
$109$	−2.59220	+	6.25812i	−0.248288	+	0.599419i	−0.998059	−	0.0622777i	$-0.980164\pi$
$109$	−2.59220	+	6.25812i	−0.248288	+	0.599419i	0.749771	+	0.661697i	$0.230164\pi$
$110$	3.23187	+	3.27864i	0.308147	+	0.312606i
$111$		0			0
$112$	0.216104	−	0.722766i	0.0204199	−	0.0682949i
$113$	−2.82489	+	4.89284i	−0.265743	+	0.460280i	−0.967758	−	0.251882i	$-0.918951\pi$
$113$	−2.82489	+	4.89284i	−0.265743	+	0.460280i	0.702015	+	0.712162i	$0.252284\pi$
$114$		0			0
$115$	−0.957796	−	7.27518i	−0.0893149	−	0.678414i
$116$	8.53879	−	0.999567i	0.792807	−	0.0928075i
$117$		0			0
$118$	−1.78687	+	12.8581i	−0.164494	+	1.18368i
$119$	−0.307668	+	1.14823i	−0.0282039	+	0.105258i
$120$		0			0
$121$	−1.72032	−	6.42033i	−0.156393	−	0.583667i
$122$	−9.14960	+	1.13776i	−0.828366	+	0.103008i
$123$		0			0
$124$	10.5120	+	6.27216i	0.944001	+	0.563257i
$125$	−4.51729	+	10.9057i	−0.404039	+	0.975436i
$126$		0			0
$127$		−	12.7548i		−	1.13181i	−0.824471	−	0.565904i	$-0.808527\pi$
$127$		−	12.7548i		−	1.13181i	0.824471	−	0.565904i	$-0.191473\pi$
$128$	−0.568711	+	11.2994i	−0.0502674	+	0.998736i
$129$		0			0
$130$	−5.57970	−	9.82668i	−0.489372	−	0.861857i
$131$	−14.2064	+	10.9010i	−1.24122	+	0.952424i	−0.999838	−	0.0180055i	$-0.994268\pi$
$131$	−14.2064	+	10.9010i	−1.24122	+	0.952424i	−0.241385	+	0.970429i	$0.577602\pi$
$132$		0			0
$133$	−0.560107	+	0.729945i	−0.0485674	+	0.0632943i
$134$	−2.48821	+	1.88103i	−0.214949	+	0.162496i
$135$		0			0
$136$	0.384202	−	17.8237i	0.0329450	−	1.52837i
$137$	10.3487	+	2.77292i	0.884146	+	0.236906i	0.672195	−	0.740374i	$-0.265352\pi$
$137$	10.3487	+	2.77292i	0.884146	+	0.236906i	0.211951	+	0.977280i	$0.432018\pi$
$138$		0			0
$139$	19.0533	+	2.50842i	1.61608	+	0.212761i	0.883673	−	0.468105i	$-0.155063\pi$
$139$	19.0533	+	2.50842i	1.61608	+	0.212761i	0.732408	+	0.680866i	$0.238397\pi$
$140$	−0.540421	−	0.233002i	−0.0456739	−	0.0196922i
$141$		0			0
$142$	−7.93777	−	8.05264i	−0.666123	−	0.675763i
$143$		−	10.6853i		−	0.893546i
$144$		0			0
$145$		−	6.70680i		−	0.556969i
$146$	9.19160	−	9.06047i	0.760702	−	0.749850i
$147$		0			0
$148$	−3.12341	−	7.85806i	−0.256743	−	0.645928i
$149$	−9.75031	−	1.28365i	−0.798776	−	0.105161i	−0.279921	−	0.960023i	$-0.590308\pi$
$149$	−9.75031	−	1.28365i	−0.798776	−	0.105161i	−0.518855	+	0.854862i	$0.673642\pi$
$150$		0			0
$151$	15.7125	+	4.21015i	1.27867	+	0.342617i	0.833345	−	0.552754i	$-0.186423\pi$
$151$	15.7125	+	4.21015i	1.27867	+	0.342617i	0.445321	+	0.895371i	$0.353090\pi$
$152$	5.55404	−	12.6316i	0.450492	−	1.02456i
$153$		0			0
$154$	−0.335583	−	0.443907i	−0.0270420	−	0.0357711i
$155$	5.81334	−	7.57609i	0.466939	−	0.608527i
$156$		0			0
$157$	15.1550	−	11.6288i	1.20950	−	0.928083i	0.210725	−	0.977545i	$-0.432418\pi$
$157$	15.1550	−	11.6288i	1.20950	−	0.928083i	0.998776	+	0.0494628i	$0.0157509\pi$
$158$	−14.9028	+	8.46199i	−1.18561	+	0.673200i
$159$		0			0
$160$	8.70356	+	1.46555i	0.688077	+	0.115862i
$161$			0.886979i			0.0699037i
$162$		0			0
$163$	−4.72964	+	11.4184i	−0.370454	+	0.894355i	0.623219	+	0.782047i	$0.285824\pi$
$163$	−4.72964	+	11.4184i	−0.370454	+	0.894355i	−0.993673	+	0.112308i	$0.964176\pi$
$164$	1.57453	+	6.23311i	0.122950	+	0.486724i
$165$		0			0
$166$	1.87172	+	15.0519i	0.145274	+	1.16826i
$167$	−1.70704	−	6.37075i	−0.132095	−	0.492983i	0.867898	−	0.496742i	$-0.165470\pi$
$167$	−1.70704	−	6.37075i	−0.132095	−	0.492983i	−0.999993	+	0.00375827i	$0.998804\pi$
$168$		0			0
$169$	−3.42363	+	12.7772i	−0.263356	+	0.982859i
$170$	−13.7756	−	1.91436i	−1.05654	−	0.146825i
$171$		0			0
$172$	9.22730	−	11.6741i	0.703575	−	0.890138i
$173$	2.41544	+	18.3471i	0.183642	+	1.39490i	0.796467	+	0.604682i	$0.206700\pi$
$173$	2.41544	+	18.3471i	0.183642	+	1.39490i	−0.612824	+	0.790219i	$0.709967\pi$
$174$		0			0
$175$	0.241933	−	0.419040i	0.0182884	−	0.0316765i
$176$	6.47239	+	5.26869i	0.487875	+	0.397142i
$177$		0			0
$178$	2.18952	−	2.15828i	0.164111	−	0.161770i
$179$	−0.357886	+	0.864013i	−0.0267496	+	0.0645793i	−0.936690	−	0.350160i	$-0.886127\pi$
$179$	−0.357886	+	0.864013i	−0.0267496	+	0.0645793i	0.909940	+	0.414739i	$0.136127\pi$
$180$		0			0
$181$	−10.8036	+	4.47498i	−0.803022	+	0.332622i	−0.746166	−	0.665760i	$-0.768107\pi$
$181$	−10.8036	+	4.47498i	−0.803022	+	0.332622i	−0.0568556	+	0.998382i	$0.518107\pi$
$182$	0.513638	+	1.26568i	0.0380734	+	0.0938181i
$183$		0			0
$184$	−3.16519	−	12.9203i	−0.233341	−	0.952494i
$185$	−6.37198	+	1.70737i	−0.468477	+	0.125528i
$186$		0			0
$187$	−10.4334	−	8.00581i	−0.762964	−	0.585443i
$188$	2.03384	−	1.13559i	0.148333	−	0.0828215i
$189$		0			0
$190$	−9.28357	−	5.44917i	−0.673501	−	0.395324i
$191$	−8.75611	−	15.1660i	−0.633570	−	1.09738i	−0.986816	−	0.161845i	$-0.948256\pi$
$191$	−8.75611	−	15.1660i	−0.633570	−	1.09738i	0.353246	−	0.935530i	$-0.385078\pi$
$192$		0			0
$193$	8.05348	−	13.9490i	0.579702	−	1.00407i	−0.415811	−	0.909451i	$-0.636502\pi$
$193$	8.05348	−	13.9490i	0.579702	−	1.00407i	0.995513	−	0.0946224i	$-0.0301644\pi$
$194$	11.3130	−	6.42366i	0.812228	−	0.461192i
$195$		0			0
$196$	−11.9614	−	7.13703i	−0.854389	−	0.509788i
$197$	18.5595	−	7.68761i	1.32231	−	0.547720i	0.393860	−	0.919171i	$-0.371140\pi$
$197$	18.5595	−	7.68761i	1.32231	−	0.547720i	0.928453	+	0.371451i	$0.121140\pi$
$198$		0			0
$199$	−13.9295	−	13.9295i	−0.987439	−	0.987439i	0.0124834	−	0.999922i	$-0.496026\pi$
$199$	−13.9295	−	13.9295i	−0.987439	−	0.987439i	−0.999922	+	0.0124834i	$0.996026\pi$
$200$	−2.02879	+	6.96733i	−0.143457	+	0.492665i
$201$		0			0
$202$	−11.4678	+	14.7249i	−0.806874	+	1.03604i
$203$	−0.105816	+	0.803751i	−0.00742682	+	0.0564123i
$204$		0			0
$205$	4.97243	−	0.654632i	0.347289	−	0.0457215i
$206$	1.73117	+	6.65161i	0.120617	+	0.463439i
$207$		0			0
$208$	−11.9985	−	16.6037i	−0.831949	−	1.15126i
$209$	−5.08939	−	8.81509i	−0.352041	−	0.609752i
$210$		0			0
$211$	−7.34706	+	5.63760i	−0.505792	+	0.388108i	−0.829900	−	0.557912i	$-0.811603\pi$
$211$	−7.34706	+	5.63760i	−0.505792	+	0.388108i	0.324108	+	0.946020i	$0.394936\pi$
$212$	−5.87817	−	14.7886i	−0.403714	−	1.01569i
$213$		0			0
$214$	−6.39723	−	15.7637i	−0.437306	−	1.07758i
$215$	−8.20848	−	8.20848i	−0.559814	−	0.559814i
$216$		0			0
$217$	−0.816209	+	0.816209i	−0.0554079	+	0.0554079i
$218$	8.82376	+	3.72941i	0.597620	+	0.252588i
$219$		0			0
$220$	4.66942	−	4.53713i	0.314812	−	0.305893i
$221$	19.6510	+	25.6096i	1.32187	+	1.72269i
$222$		0			0
$223$	−10.1056	+	5.83446i	−0.676720	+	0.390705i	−0.798618	−	0.601838i	$-0.794435\pi$
$223$	−10.1056	+	5.83446i	−0.676720	+	0.390705i	0.121898	+	0.992543i	$0.461102\pi$
$224$	−1.01992	−	0.312953i	−0.0681465	−	0.0209100i
$225$		0			0
$226$	6.89065	+	4.04460i	0.458359	+	0.269043i
$227$	−1.28541	−	9.76369i	−0.0853160	−	0.648039i	−0.979661	−	0.200661i	$-0.935691\pi$
$227$	−1.28541	−	9.76369i	−0.0853160	−	0.648039i	0.894345	−	0.447378i	$-0.147642\pi$
$228$		0			0
$229$	−20.4078	−	2.68673i	−1.34858	−	0.177544i	−0.578601	−	0.815611i	$-0.696401\pi$
$229$	−20.4078	−	2.68673i	−1.34858	−	0.177544i	−0.769981	+	0.638066i	$0.779734\pi$
$230$	−10.2981	+	1.28058i	−0.679038	+	0.0844389i
$231$		0			0
$232$	−1.32681	−	12.0855i	−0.0871096	−	0.793453i
$233$	6.59241	−	6.59241i	0.431883	−	0.431883i	−0.457385	−	0.889269i	$-0.651214\pi$
$233$	6.59241	−	6.59241i	0.431883	−	0.431883i	0.889269	+	0.457385i	$0.151214\pi$
$234$		0			0
$235$	−0.695416	−	1.67888i	−0.0453640	−	0.109518i
$236$	18.1655	+	2.65758i	1.18247	+	0.172994i
$237$		0			0
$238$	1.62068	+	0.446762i	0.105053	+	0.0289593i
$239$	2.57351	+	1.48582i	0.166466	+	0.0961094i	0.580919	−	0.813962i	$-0.302693\pi$
$239$	2.57351	+	1.48582i	0.166466	+	0.0961094i	−0.414452	+	0.910071i	$0.636027\pi$
$240$		0			0
$241$	12.7728	−	7.37437i	0.822768	−	0.475025i	−0.0286023	−	0.999591i	$-0.509106\pi$
$241$	12.7728	−	7.37437i	0.822768	−	0.475025i	0.851370	+	0.524566i	$0.175772\pi$
$242$	−9.09697	+	2.36761i	−0.584775	+	0.152196i
$243$		0			0
$244$	1.51604	+	12.9507i	0.0970542	+	0.829085i
$245$	−6.61494	+	8.62076i	−0.422613	+	0.550760i
$246$		0			0
$247$	6.46652	+	24.1334i	0.411455	+	1.53557i
$248$	8.97675	−	14.8020i	0.570024	−	0.939931i
$249$		0			0
$250$	15.3767	+	6.49905i	0.972508	+	0.411036i
$251$	−2.22936	−	5.38215i	−0.140716	−	0.339718i	0.837773	−	0.546019i	$-0.183857\pi$
$251$	−2.22936	−	5.38215i	−0.140716	−	0.339718i	−0.978489	+	0.206301i	$0.933857\pi$
$252$		0			0
$253$	−9.06569	−	3.75513i	−0.569955	−	0.236083i
$254$	−18.0376	−	0.129586i	−1.13178	−	0.00813094i
$255$		0			0
$256$	15.9736	+	0.919057i	0.998349	+	0.0574411i
$257$	25.6176	+	14.7904i	1.59798	+	0.922597i	0.991875	+	0.127216i	$0.0406041\pi$
$257$	25.6176	+	14.7904i	1.59798	+	0.922597i	0.606110	+	0.795381i	$0.292729\pi$
$258$		0			0
$259$	0.790564	−	0.104080i	0.0491233	−	0.00646720i
$260$	−13.9534	+	7.79084i	−0.865351	+	0.483168i
$261$		0			0
$262$	15.2716	+	20.2012i	0.943482	+	1.24803i
$263$	−8.81380	−	2.36165i	−0.543482	−	0.145626i	−0.0233752	−	0.999727i	$-0.507441\pi$
$263$	−8.81380	−	2.36165i	−0.543482	−	0.145626i	−0.520107	+	0.854101i	$0.674108\pi$
$264$		0			0
$265$	−11.9919	+	3.21321i	−0.736655	+	0.197386i
$266$	1.02658	+	0.799506i	0.0629437	+	0.0490209i
$267$		0			0
$268$	2.63483	+	3.53789i	0.160948	+	0.216111i
$269$	3.17330	+	1.31442i	0.193479	+	0.0801417i	0.477319	−	0.878730i	$-0.341608\pi$
$269$	3.17330	+	1.31442i	0.193479	+	0.0801417i	−0.283840	+	0.958872i	$0.591608\pi$
$270$		0			0
$271$	5.08474			0.308876			0.154438	−	0.988002i	$-0.450643\pi$
$271$	5.08474			0.308876			0.154438	+	0.988002i	$0.450643\pi$
$272$	−25.2020	−	0.724414i	−1.52810	−	0.0439240i
$273$		0			0
$274$	4.02654	−	14.6067i	0.243252	−	0.882422i
$275$	3.25870	+	4.24683i	0.196507	+	0.256093i
$276$		0			0
$277$	11.4093	+	8.75468i	0.685520	+	0.526018i	0.891774	−	0.452481i	$-0.149461\pi$
$277$	11.4093	+	8.75468i	0.685520	+	0.526018i	−0.206254	+	0.978498i	$0.566127\pi$
$278$	3.74092	−	26.9193i	0.224365	−	1.61451i
$279$		0			0
$280$	−0.334996	+	0.761883i	−0.0200199	+	0.0455312i
$281$	4.78849	−	17.8709i	0.285657	−	1.06609i	−0.662700	−	0.748885i	$-0.730590\pi$
$281$	4.78849	−	17.8709i	0.285657	−	1.06609i	0.948358	−	0.317203i	$-0.102744\pi$
$282$		0			0
$283$	−0.832867	+	6.32625i	−0.0495088	+	0.376057i	0.948697	+	0.316186i	$0.102402\pi$
$283$	−0.832867	+	6.32625i	−0.0495088	+	0.376057i	−0.998206	+	0.0598710i	$0.980931\pi$
$284$	−11.4685	+	11.1436i	−0.680531	+	0.661251i
$285$		0			0
$286$	−15.1109	−	0.108560i	−0.893523	−	0.00641926i
$287$	−0.606230			−0.0357846
$288$		0			0
$289$	22.7292			1.33701
$290$	−9.48460	−	0.0681394i	−0.556955	−	0.00400128i
$291$		0			0
$292$	−12.7197	−	13.0906i	−0.744366	−	0.766070i
$293$	0.611513	−	4.64490i	0.0357250	−	0.271358i	−0.964255	−	0.264977i	$-0.914636\pi$
$293$	0.611513	−	4.64490i	0.0357250	−	0.271358i	0.999980	−	0.00638086i	$-0.00203110\pi$
$294$		0			0
$295$	3.70685	−	13.8341i	0.215821	−	0.805455i
$296$	−11.1444	+	4.33722i	−0.647756	+	0.252096i
$297$		0			0
$298$	−1.91437	+	13.7756i	−0.110897	+	0.798000i
$299$	19.1087	+	14.6626i	1.10508	+	0.847960i
$300$		0			0
$301$	0.854207	+	1.11322i	0.0492356	+	0.0641651i
$302$	6.11354	−	22.1775i	0.351794	−	1.27617i
$303$		0			0
$304$	−17.8068	−	7.98272i	−1.02129	−	0.457841i
$305$	10.1721			0.582455
$306$		0			0
$307$	1.25336	+	0.519157i	0.0715328	+	0.0296299i	0.418163	−	0.908372i	$-0.362674\pi$
$307$	1.25336	+	0.519157i	0.0715328	+	0.0296299i	−0.346630	+	0.938002i	$0.612674\pi$
$308$	−0.631173	+	0.470064i	−0.0359644	+	0.0267844i
$309$		0			0
$310$	−10.6549	−	8.29807i	−0.605156	−	0.471298i
$311$	−12.0011	+	3.21569i	−0.680520	+	0.182345i	−0.582489	−	0.812839i	$-0.697921\pi$
$311$	−12.0011	+	3.21569i	−0.680520	+	0.182345i	−0.0980311	+	0.995183i	$0.531254\pi$
$312$		0			0
$313$	21.2727	+	5.69999i	1.20240	+	0.322183i	0.803776	−	0.594931i	$-0.202821\pi$
$313$	21.2727	+	5.69999i	1.20240	+	0.322183i	0.398625	+	0.917114i	$0.369487\pi$
$314$	−16.2913	−	21.5500i	−0.919370	−	1.21614i
$315$		0			0
$316$	11.8153	+	21.1612i	0.664665	+	1.19041i
$317$	−6.84125	+	0.900667i	−0.384243	+	0.0505865i	−0.320173	−	0.947359i	$-0.603741\pi$
$317$	−6.84125	+	0.900667i	−0.384243	+	0.0505865i	−0.0640693	+	0.997945i	$0.520408\pi$
$318$		0			0
$319$	−7.76705	−	4.48431i	−0.434871	−	0.251073i
$320$	2.16097	−	12.2935i	0.120802	−	0.687227i
$321$		0			0
$322$	1.25434	+	0.00901148i	0.0699019	+	0.000502190i
$323$	28.4095	+	11.7676i	1.58074	+	0.654766i
$324$		0			0
$325$	−5.02824	−	12.1392i	−0.278916	−	0.673364i
$326$	16.0995	+	6.80456i	0.891671	+	0.376870i
$327$		0			0
$328$	8.83071	−	2.16334i	0.487595	−	0.119450i
$329$	0.0568512	+	0.212171i	0.00313431	+	0.0116974i
$330$		0			0
$331$	−14.1278	+	18.4118i	−0.776536	+	1.01200i	0.222774	+	0.974870i	$0.428489\pi$
$331$	−14.1278	+	18.4118i	−0.776536	+	1.01200i	−0.999310	+	0.0371314i	$0.988178\pi$
$332$	21.3051	−	2.49402i	1.16927	−	0.136877i
$333$		0			0
$334$	−9.02671	+	2.34933i	−0.493920	+	0.128550i
$335$	2.98026	−	1.72065i	0.162829	−	0.0940092i
$336$		0			0
$337$	−28.0526	−	16.1962i	−1.52812	−	0.882261i	−0.999441	−	0.0334395i	$-0.989354\pi$
$337$	−28.0526	−	16.1962i	−1.52812	−	0.882261i	−0.528680	−	0.848821i	$-0.677313\pi$
$338$	18.0344	+	4.97144i	0.980942	+	0.270410i
$339$		0			0
$340$	−2.84721	+	19.4616i	−0.154411	+	1.05546i
$341$	−4.88685	−	11.7979i	−0.264638	−	0.638892i
$342$		0			0
$343$	1.86226	−	1.86226i	0.100552	−	0.100552i
$344$	−16.4154	−	13.1676i	−0.885061	−	0.709952i
$345$		0			0
$346$	25.9705	−	3.22945i	1.39618	−	0.173617i
$347$	20.8495	+	2.74489i	1.11926	+	0.147353i	0.667374	−	0.744723i	$-0.267418\pi$
$347$	20.8495	+	2.74489i	1.11926	+	0.147353i	0.451886	+	0.892076i	$0.350752\pi$
$348$		0			0
$349$	−2.00068	−	15.1966i	−0.107094	−	0.813457i	−0.957723	−	0.287692i	$-0.907112\pi$
$349$	−2.00068	−	15.1966i	−0.107094	−	0.813457i	0.850629	−	0.525766i	$-0.176221\pi$
$350$	−0.590139	−	0.346394i	−0.0315443	−	0.0185155i
$351$		0			0
$352$	7.51662	−	9.09957i	0.400637	−	0.485009i
$353$	29.1219	−	16.8135i	1.55000	−	0.894894i	0.551862	−	0.833935i	$-0.313917\pi$
$353$	29.1219	−	16.8135i	1.55000	−	0.894894i	0.998140	−	0.0609591i	$-0.0194159\pi$
$354$		0			0
$355$	7.59418	+	9.89693i	0.403057	+	0.525275i
$356$	−3.02995	−	3.11829i	−0.160587	−	0.165269i
$357$		0			0
$358$	1.21823	+	0.514892i	0.0643855	+	0.0272129i
$359$	−22.4302	+	22.4302i	−1.18382	+	1.18382i	−0.205071	+	0.978747i	$0.565743\pi$
$359$	−22.4302	+	22.4302i	−1.18382	+	1.18382i	−0.978747	+	0.205071i	$0.934257\pi$
$360$		0			0
$361$	3.39444	+	3.39444i	0.178655	+	0.178655i
$362$	6.21865	+	15.3236i	0.326845	+	0.805390i
$363$		0			0
$364$	1.79511	−	0.713517i	0.0940892	−	0.0373984i
$365$	−11.2967	+	8.66829i	−0.591298	+	0.453719i
$366$		0			0
$367$	−6.04156	−	10.4643i	−0.315367	−	0.546231i	0.664149	−	0.747601i	$-0.268794\pi$
$367$	−6.04156	−	10.4643i	−0.315367	−	0.546231i	−0.979515	+	0.201369i	$0.935461\pi$
$368$	−18.3037	+	4.34487i	−0.954146	+	0.226492i
$369$		0			0
$370$	2.34978	+	9.02846i	0.122159	+	0.469367i
$371$	1.48782	−	0.195875i	0.0772437	−	0.0101693i
$372$		0			0
$373$	−3.20529	+	24.3466i	−0.165964	+	1.26062i	0.682311	+	0.731062i	$0.260975\pi$
$373$	−3.20529	+	24.3466i	−0.165964	+	1.26062i	−0.848274	+	0.529557i	$0.822358\pi$
$374$	−11.4276	+	14.6733i	−0.590909	+	0.758738i
$375$		0			0
$376$	−1.58526	−	2.88774i	−0.0817537	−	0.148924i
$377$	15.5664	+	15.5664i	0.801712	+	0.801712i
$378$		0			0
$379$	12.0738	−	5.00114i	0.620191	−	0.256891i	−0.0503881	−	0.998730i	$-0.516046\pi$
$379$	12.0738	−	5.00114i	0.620191	−	0.256891i	0.670579	+	0.741838i	$0.266046\pi$
$380$	−7.80041	+	13.0733i	−0.400153	+	0.670644i
$381$		0			0
$382$	−21.5364	+	12.2286i	−1.10190	+	0.625670i
$383$	12.5301	−	21.7028i	0.640260	−	1.10896i	−0.345114	−	0.938561i	$-0.612160\pi$
$383$	12.5301	−	21.7028i	0.640260	−	1.10896i	0.985375	−	0.170403i	$-0.0545068\pi$
$384$		0			0
$385$	0.306971	+	0.531689i	0.0156447	+	0.0270974i
$386$	−19.6446	−	11.5308i	−0.999883	−	0.586900i
$387$		0			0
$388$	−8.96925	−	16.0639i	−0.455345	−	0.815520i
$389$	−21.5383	−	16.5269i	−1.09203	−	0.837947i	−0.104370	−	0.994539i	$-0.533283\pi$
$389$	−21.5383	−	16.5269i	−1.09203	−	0.837947i	−0.987663	+	0.156592i	$0.949949\pi$
$390$		0			0
$391$	28.6339	−	7.67243i	1.44808	−	0.388012i
$392$	−10.2145	+	16.8431i	−0.515912	+	0.850704i
$393$		0			0
$394$	−10.6831	−	26.3246i	−0.538206	−	1.32621i
$395$	17.4681	−	7.23552i	0.878915	−	0.364058i
$396$		0			0
$397$	−10.7365	+	25.9202i	−0.538849	+	1.30090i	0.386678	+	0.922215i	$0.373623\pi$
$397$	−10.7365	+	25.9202i	−0.538849	+	1.30090i	−0.925527	+	0.378682i	$0.876377\pi$
$398$	−19.8404	+	19.5573i	−0.994507	+	0.980319i
$399$		0			0
$400$	9.83243	+	2.93986i	0.491622	+	0.146993i
$401$	1.29812	−	2.24840i	0.0648248	−	0.112280i	−0.831791	−	0.555088i	$-0.812684\pi$
$401$	1.29812	−	2.24840i	0.0648248	−	0.112280i	0.896616	+	0.442808i	$0.146018\pi$
$402$		0			0
$403$	4.09134	+	31.0768i	0.203804	+	1.54804i
$404$	20.7071	+	16.3671i	1.03022	+	0.814296i
$405$		0			0
$406$	1.13557	+	0.157808i	0.0563575	+	0.00783189i
$407$	−2.28316	+	8.52089i	−0.113172	+	0.422365i
$408$		0			0
$409$	8.86816	+	33.0964i	0.438503	+	1.63651i	0.732543	+	0.680721i	$0.238333\pi$
$409$	8.86816	+	33.0964i	0.438503	+	1.63651i	−0.294041	+	0.955793i	$0.595000\pi$
$410$	−0.875247	−	7.03854i	−0.0432254	−	0.347609i
$411$		0			0
$412$	9.42414	−	2.38061i	0.464294	−	0.117284i
$413$	−0.662500	+	1.59942i	−0.0325995	+	0.0787021i
$414$		0			0
$415$		−	16.7341i		−	0.821446i
$416$	−23.6024	+	16.7994i	−1.15720	+	0.823657i
$417$		0			0
$418$	−12.5178	+	7.10775i	−0.612266	+	0.347651i
$419$	−10.5070	+	8.06231i	−0.513301	+	0.393870i	−0.832678	−	0.553758i	$-0.813193\pi$
$419$	−10.5070	+	8.06231i	−0.513301	+	0.393870i	0.319376	+	0.947628i	$0.396527\pi$
$420$		0			0
$421$	−9.87856	+	12.8740i	−0.481452	+	0.627440i	−0.969416	−	0.245423i	$-0.921073\pi$
$421$	−9.87856	+	12.8740i	−0.481452	+	0.627440i	0.487964	+	0.872864i	$0.337740\pi$
$422$	7.89792	+	10.4473i	0.384465	+	0.508568i
$423$		0			0
$424$	−20.9735	+	8.16252i	−1.01856	+	0.396407i
$425$	−15.6204	−	4.18548i	−0.757702	−	0.203026i
$426$		0			0
$427$	−1.21904	−	0.160490i	−0.0589936	−	0.00776665i
$428$	−22.3576	+	8.88666i	−1.08069	+	0.429553i
$429$		0			0
$430$	−11.6916	+	11.5249i	−0.563821	+	0.555778i
$431$			29.3391i			1.41321i	0.707606	+	0.706607i	$0.249775\pi$
$431$			29.3391i			1.41321i	−0.707606	+	0.706607i	$0.750225\pi$
$432$		0			0
$433$			28.9049i			1.38908i	0.719453	+	0.694541i	$0.244393\pi$
$433$			28.9049i			1.38908i	−0.719453	+	0.694541i	$0.755607\pi$
$434$	1.14597	+	1.16256i	0.0550084	+	0.0558045i
$435$		0			0
$436$	5.36369	−	12.4405i	0.256874	−	0.595790i
$437$	22.7480	+	2.99483i	1.08819	+	0.143262i
$438$		0			0
$439$	19.7355	+	5.28812i	0.941925	+	0.252388i	0.696932	−	0.717137i	$-0.254548\pi$
$439$	19.7355	+	5.28812i	0.941925	+	0.252388i	0.244993	+	0.969525i	$0.421214\pi$
$440$	−6.36886	−	6.64948i	−0.303624	−	0.317001i
$441$		0			0
$442$	36.4162	−	27.5297i	1.73214	−	1.30946i
$443$	−6.83229	+	8.90401i	−0.324612	+	0.423042i	−0.926942	−	0.375205i	$-0.877572\pi$
$443$	−6.83229	+	8.90401i	−0.324612	+	0.423042i	0.602330	+	0.798247i	$0.294239\pi$
$444$		0			0
$445$	−2.69098	+	2.06486i	−0.127565	+	0.0978838i
$446$	8.14830	+	14.3504i	0.385833	+	0.679510i
$447$		0			0
$448$	−0.452933	+	1.43917i	−0.0213991	+	0.0679945i
$449$		−	2.12286i		−	0.100184i	−0.998745	−	0.0500920i	$-0.984049\pi$
$449$		−	2.12286i		−	0.100184i	0.998745	−	0.0500920i	$-0.0159515\pi$
$450$		0			0
$451$	2.56655	−	6.19620i	0.120854	−	0.291768i
$452$	5.78979	−	9.70351i	0.272329	−	0.456415i
$453$		0			0
$454$	−13.8207	+	1.71861i	−0.648635	+	0.0806582i
$455$	−0.390034	−	1.45563i	−0.0182851	−	0.0682408i
$456$		0			0
$457$	−1.89176	+	7.06014i	−0.0884928	+	0.330260i	−0.995953	−	0.0898791i	$-0.971352\pi$
$457$	−1.89176	+	7.06014i	−0.0884928	+	0.330260i	0.907460	+	0.420139i	$0.138019\pi$
$458$	−4.00685	+	28.8329i	−0.187228	+	1.34727i
$459$		0			0
$460$	1.70634	+	14.5764i	0.0795585	+	0.679627i
$461$	0.134303	+	1.02013i	0.00625509	+	0.0475121i	0.994288	−	0.106733i	$-0.0340389\pi$
$461$	0.134303	+	1.02013i	0.00625509	+	0.0475121i	−0.988033	+	0.154245i	$0.950706\pi$
$462$		0			0
$463$	−13.0471	+	22.5983i	−0.606352	+	1.05023i	0.385485	+	0.922714i	$0.374034\pi$
$463$	−13.0471	+	22.5983i	−0.606352	+	1.05023i	−0.991836	+	0.127518i	$0.959299\pi$
$464$	−17.1045	+	1.75356i	−0.794059	+	0.0814071i
$465$		0			0
$466$	−9.25586	−	9.38982i	−0.428770	−	0.434975i
$467$	4.77434	−	11.5263i	0.220930	−	0.533372i	−0.774087	−	0.633079i	$-0.781791\pi$
$467$	4.77434	−	11.5263i	0.220930	−	0.533372i	0.995017	+	0.0997073i	$0.0317906\pi$
$468$		0			0
$469$	−0.384305	+	0.159184i	−0.0177456	+	0.00735045i
$470$	−2.38130	+	0.966385i	−0.109841	+	0.0445760i
$471$		0			0
$472$	3.94284	−	25.6622i	0.181484	−	1.18120i
$473$	−14.9945	+	4.01776i	−0.689448	+	0.184737i
$474$		0			0
$475$	−9.93010	−	7.61964i	−0.455624	−	0.349613i
$476$	0.648267	−	2.28739i	0.0297133	−	0.104842i
$477$		0			0
$478$	2.12735	−	3.62430i	0.0973028	−	0.165772i
$479$	−17.2030	−	29.7964i	−0.786023	−	1.36143i	−0.928386	−	0.371618i	$-0.878803\pi$
$479$	−17.2030	−	29.7964i	−0.786023	−	1.36143i	0.142362	−	0.989815i	$-0.454530\pi$
$480$		0			0
$481$	10.8265	−	18.7521i	0.493647	−	0.855022i
$482$	−10.2989	−	18.1379i	−0.469102	−	0.826159i
$483$		0			0
$484$	3.25580	+	12.8888i	0.147991	+	0.585853i
$485$	−13.2603	+	5.49262i	−0.602121	+	0.249407i
$486$		0			0
$487$	10.2955	+	10.2955i	0.466536	+	0.466536i	0.900790	−	0.434255i	$-0.142988\pi$
$487$	10.2955	+	10.2955i	0.466536	+	0.466536i	−0.434255	+	0.900790i	$0.642988\pi$
$488$	18.3300	−	2.01237i	0.829761	−	0.0910955i
$489$		0			0
$490$	12.1241	+	9.44228i	0.547710	+	0.426559i
$491$	−5.05925	+	38.4288i	−0.228321	+	1.73427i	0.366506	+	0.930416i	$0.380554\pi$
$491$	−5.05925	+	38.4288i	−0.228321	+	1.73427i	−0.594827	+	0.803854i	$0.702779\pi$
$492$		0			0
$493$	26.8624	−	3.53651i	1.20982	−	0.159276i
$494$	34.1946	−	8.89962i	1.53849	−	0.400413i
$495$		0			0
$496$	−20.8415	−	12.8451i	−0.935811	−	0.576762i
$497$	−0.753949	−	1.30588i	−0.0338192	−	0.0585766i
$498$		0			0
$499$	−24.8325	+	19.0546i	−1.11166	+	0.853003i	−0.990209	−	0.139595i	$-0.955420\pi$
$499$	−24.8325	+	19.0546i	−1.11166	+	0.853003i	−0.121447	+	0.992598i	$0.538753\pi$
$500$	9.34703	−	21.6793i	0.418012	−	0.969530i
$501$		0			0
$502$	−7.63396	+	3.09803i	−0.340720	+	0.138272i
$503$	−12.1484	−	12.1484i	−0.541668	−	0.541668i	0.382349	−	0.924018i	$-0.375115\pi$
$503$	−12.1484	−	12.1484i	−0.541668	−	0.541668i	−0.924018	+	0.382349i	$0.875115\pi$
$504$		0			0
$505$	14.5600	−	14.5600i	0.647911	−	0.647911i
$506$	−5.40253	+	12.7823i	−0.240172	+	0.568244i
$507$		0			0
$508$	−0.366515	+	25.5070i	−0.0162615	+	1.13169i
$509$	−19.8368	−	25.8519i	−0.879252	−	1.14586i	−0.988405	−	0.151839i	$-0.951481\pi$
$509$	−19.8368	−	25.8519i	−0.879252	−	1.14586i	0.109153	−	0.994025i	$-0.465186\pi$
$510$		0			0
$511$	1.49058	−	0.860586i	0.0659393	−	0.0380701i
$512$	1.46200	−	22.5801i	0.0646118	−	0.997910i
$513$		0			0
$514$	21.1764	−	36.0776i	0.934053	−	1.59132i
$515$	−0.989770	−	7.51805i	−0.0436145	−	0.331285i
$516$		0			0
$517$	−2.40926	−	0.317185i	−0.105959	−	0.0139498i
$518$	−0.139155	−	1.11905i	−0.00611413	−	0.0491685i
$519$		0			0
$520$	10.8759	+	19.8117i	0.476938	+	0.868799i
$521$	−17.0885	+	17.0885i	−0.748659	+	0.748659i	−0.974227	−	0.225568i	$-0.927576\pi$
$521$	−17.0885	+	17.0885i	−0.748659	+	0.748659i	0.225568	+	0.974227i	$0.427576\pi$
$522$		0			0
$523$	9.11458	+	22.0046i	0.398553	+	0.962192i	0.988010	+	0.154392i	$0.0493419\pi$
$523$	9.11458	+	22.0046i	0.398553	+	0.962192i	−0.589457	+	0.807800i	$0.700658\pi$
$524$	28.7232	−	21.3915i	1.25478	−	0.934492i
$525$		0			0
$526$	−3.42934	+	12.4403i	−0.149526	+	0.542422i
$527$	33.4096	+	19.2890i	1.45534	+	0.840243i
$528$		0			0
$529$	−0.763016	+	0.440528i	−0.0331746	+	0.0191534i
$530$	4.42222	+	16.9913i	0.192089	+	0.738054i
$531$		0			0
$532$	1.14107	−	1.44364i	0.0494718	−	0.0625899i
$533$	−10.0216	+	13.0604i	−0.434082	+	0.565707i
$534$		0			0
$535$	4.85777	+	18.1294i	0.210020	+	0.783804i
$536$	5.02997	−	3.69017i	0.217261	−	0.159391i
$537$		0			0
$538$	1.89107	−	4.47425i	0.0815296	−	0.192899i
$539$	5.56069	+	13.4247i	0.239516	+	0.578243i
$540$		0			0
$541$	17.1432	+	7.10093i	0.737042	+	0.305293i	0.719442	−	0.694552i	$-0.244397\pi$
$541$	17.1432	+	7.10093i	0.737042	+	0.305293i	0.0175999	+	0.999845i	$0.494397\pi$
$542$	0.0516597	−	7.19073i	0.00221898	−	0.308868i
$543$		0			0
$544$	−1.28050	+	35.6328i	−0.0549008	+	1.52774i
$545$	−9.15277	−	5.28435i	−0.392062	−	0.226357i
$546$		0			0
$547$	−30.6845	+	4.03969i	−1.31197	+	0.172725i	−0.753857	−	0.657038i	$-0.771809\pi$
$547$	−30.6845	+	4.03969i	−1.31197	+	0.172725i	−0.558116	+	0.829763i	$0.688476\pi$
$548$	−20.6155	−	5.84263i	−0.880651	−	0.249585i
$549$		0			0
$550$	6.03887	−	4.56524i	0.257498	−	0.194662i
$551$	20.2562	+	5.42764i	0.862944	+	0.231225i
$552$		0			0
$553$	−2.20755	+	0.591513i	−0.0938748	+	0.0251537i
$554$	12.4966	−	16.0459i	0.530929	−	0.681723i
$555$		0			0
$556$	−38.0306	−	5.56382i	−1.61286	−	0.235958i
$557$	12.1460	+	5.03103i	0.514641	+	0.213171i	0.624861	−	0.780736i	$-0.285156\pi$
$557$	12.1460	+	5.03103i	0.514641	+	0.213171i	−0.110220	+	0.993907i	$0.535156\pi$
$558$		0			0
$559$	38.1037			1.61161
$560$	1.07403	+	0.481485i	0.0453862	+	0.0203464i
$561$		0			0
$562$	−25.2240	−	6.95334i	−1.06401	−	0.293309i
$563$	−23.3154	−	30.3852i	−0.982626	−	1.28058i	−0.959753	−	0.280845i	$-0.909385\pi$
$563$	−23.3154	−	30.3852i	−0.982626	−	1.28058i	−0.0228732	−	0.999738i	$-0.507281\pi$
$564$		0			0
$565$	−6.99344	−	5.36625i	−0.294216	−	0.225760i
$566$	8.93798	+	1.24209i	0.375691	+	0.0522091i
$567$		0			0
$568$	15.6425	+	16.3317i	0.656345	+	0.685264i
$569$	−5.22209	+	19.4891i	−0.218921	+	0.817026i	0.765828	+	0.643046i	$0.222329\pi$
$569$	−5.22209	+	19.4891i	−0.218921	+	0.817026i	−0.984749	+	0.173980i	$0.944337\pi$
$570$		0			0
$571$	3.05077	−	23.1729i	0.127671	−	0.969756i	−0.800952	−	0.598729i	$-0.795673\pi$
$571$	3.05077	−	23.1729i	0.127671	−	0.969756i	0.928622	−	0.371026i	$-0.120994\pi$
$572$	−0.307045	+	21.3683i	−0.0128382	+	0.893454i
$573$		0			0
$574$	−0.00615915	+	0.857317i	−0.000257078	+	0.0357837i
$575$	−12.0664			−0.503202
$576$		0			0
$577$	−14.5094			−0.604036			−0.302018	−	0.953302i	$-0.597660\pi$
$577$	−14.5094			−0.604036			−0.302018	+	0.953302i	$0.597660\pi$
$578$	0.230923	−	32.1431i	0.00960512	−	1.33698i
$579$		0			0
$580$	−0.192722	+	13.4122i	−0.00800236	+	0.556912i
$581$	−0.264021	+	2.00544i	−0.0109534	+	0.0831996i
$582$		0			0
$583$	−4.29685	+	16.0361i	−0.177957	+	0.664145i
$584$	−18.6417	+	17.8550i	−0.771397	+	0.738843i
$585$		0			0
$586$	−6.56250	−	0.911979i	−0.271094	−	0.0376735i
$587$	0.367595	+	0.282066i	0.0151723	+	0.0116421i	0.616320	−	0.787496i	$-0.288623\pi$
$587$	0.367595	+	0.282066i	0.0151723	+	0.0116421i	−0.601147	+	0.799138i	$0.705290\pi$
$588$		0			0
$589$	18.1771	+	23.6889i	0.748976	+	0.976084i
$590$	−19.5263	−	5.38269i	−0.803883	−	0.221602i
$591$		0			0
$592$	6.02037	+	15.8042i	0.247436	+	0.649551i
$593$	−25.9623			−1.06614			−0.533072	−	0.846070i	$-0.678962\pi$
$593$	−25.9623			−1.06614			−0.533072	+	0.846070i	$0.678962\pi$
$594$		0			0
$595$	−1.71354	−	0.709771i	−0.0702483	−	0.0290978i
$596$	19.4617	+	2.84722i	0.797183	+	0.116627i
$597$		0			0
$598$	20.9297	−	26.8741i	0.855877	−	1.09896i
$599$	9.97403	−	2.67253i	0.407528	−	0.109197i	−0.0492307	−	0.998787i	$-0.515677\pi$
$599$	9.97403	−	2.67253i	0.407528	−	0.109197i	0.456759	+	0.889591i	$0.349010\pi$
$600$		0			0
$601$	−25.4003	−	6.80599i	−1.03610	−	0.277622i	−0.299604	−	0.954064i	$-0.596854\pi$
$601$	−25.4003	−	6.80599i	−1.03610	−	0.277622i	−0.736496	+	0.676442i	$0.763521\pi$
$602$	1.58297	−	1.19669i	0.0645172	−	0.0487734i
$603$		0			0
$604$	−31.3008	−	8.87094i	−1.27361	−	0.360953i
$605$	10.2820	−	1.35364i	0.418021	−	0.0550335i
$606$		0			0
$607$	1.14113	+	0.658834i	0.0463172	+	0.0267413i	0.522980	−	0.852345i	$-0.324820\pi$
$607$	1.14113	+	0.658834i	0.0463172	+	0.0267413i	−0.476663	+	0.879086i	$0.658154\pi$
$608$	−11.4699	+	25.1009i	−0.465166	+	1.01798i
$609$		0			0
$610$	0.103346	−	14.3852i	0.00418437	−	0.582440i
$611$	5.51073	+	2.28262i	0.222940	+	0.0923449i
$612$		0			0
$613$	−8.44938	−	20.3986i	−0.341267	−	0.823892i	−0.997588	−	0.0694101i	$-0.977888\pi$
$613$	−8.44938	−	20.3986i	−0.341267	−	0.823892i	0.656321	−	0.754482i	$-0.272112\pi$
$614$	0.746914	−	1.76719i	0.0301430	−	0.0713181i
$615$		0			0
$616$	0.658341	+	0.897366i	0.0265253	+	0.0361559i
$617$	−6.56520	−	24.5016i	−0.264305	−	0.986399i	−0.962674	−	0.270662i	$-0.912757\pi$
$617$	−6.56520	−	24.5016i	−0.264305	−	0.986399i	0.698370	−	0.715737i	$-0.253909\pi$
$618$		0			0
$619$	1.86123	−	2.42560i	0.0748092	−	0.0974933i	−0.754450	−	0.656358i	$-0.772096\pi$
$619$	1.86123	−	2.42560i	0.0748092	−	0.0974933i	0.829259	+	0.558865i	$0.188763\pi$
$620$	−11.8432	+	14.9836i	−0.475634	+	0.601755i
$621$		0			0
$622$	4.42562	+	17.0044i	0.177451	+	0.681813i
$623$	0.355069	−	0.204999i	0.0142255	−	0.00821311i
$624$		0			0
$625$	−4.84054	−	2.79469i	−0.193621	−	0.111787i
$626$	8.27692	−	30.0254i	0.330812	−	1.20006i
$627$		0			0
$628$	−30.6410	+	22.8198i	−1.22271	+	0.910609i
$629$	−10.1984	−	24.6211i	−0.406637	−	0.981708i
$630$		0			0
$631$	23.0221	−	23.0221i	0.916494	−	0.916494i	−0.0802781	−	0.996773i	$-0.525581\pi$
$631$	23.0221	−	23.0221i	0.916494	−	0.916494i	0.996773	+	0.0802781i	$0.0255808\pi$
$632$	30.0458	−	16.4940i	1.19516	−	0.656096i
$633$		0			0
$634$	1.20420	+	9.68389i	0.0478248	+	0.384596i
$635$	19.7304	+	2.59756i	0.782978	+	0.103081i
$636$		0			0
$637$	−4.65549	−	35.3619i	−0.184457	−	1.40109i
$638$	−6.42052	+	10.9384i	−0.254191	+	0.433056i
$639$		0			0
$640$	−17.3632	−	3.18090i	−0.686341	−	0.125736i
$641$	8.36589	−	4.83005i	0.330433	−	0.190776i	−0.325600	−	0.945507i	$-0.605566\pi$
$641$	8.36589	−	4.83005i	0.330433	−	0.190776i	0.656033	+	0.754732i	$0.272233\pi$
$642$		0			0
$643$	−1.71744	−	2.23821i	−0.0677291	−	0.0882663i	0.758260	−	0.651952i	$-0.226050\pi$
$643$	−1.71744	−	2.23821i	−0.0677291	−	0.0882663i	−0.825989	+	0.563686i	$0.809383\pi$
$644$	0.0254877	−	1.77377i	0.00100435	−	0.0698965i
$645$		0			0
$646$	16.9301	−	40.0564i	0.666105	−	1.57600i
$647$	−11.1956	+	11.1956i	−0.440143	+	0.440143i	−0.892060	−	0.451917i	$-0.850740\pi$
$647$	−11.1956	+	11.1956i	−0.440143	+	0.440143i	0.451917	+	0.892060i	$0.350740\pi$
$648$		0			0
$649$	−13.5426	−	13.5426i	−0.531595	−	0.531595i
$650$	−17.2181	+	6.98749i	−0.675350	+	0.274072i
$651$		0			0
$652$	9.78642	−	22.6985i	0.383266	−	0.888940i
$653$	−8.25434	+	6.33378i	−0.323017	+	0.247860i	−0.757522	−	0.652810i	$-0.773590\pi$
$653$	−8.25434	+	6.33378i	−0.323017	+	0.247860i	0.434505	+	0.900670i	$0.356923\pi$
$654$		0			0
$655$	−13.9695	−	24.1959i	−0.545835	−	0.945414i
$656$	−2.96962	−	12.5102i	−0.115944	−	0.488440i
$657$		0			0
$658$	0.300626	−	0.0782420i	0.0117196	−	0.00305019i
$659$	−7.18494	+	0.945916i	−0.279886	+	0.0368476i	−0.269162	−	0.963095i	$-0.586747\pi$
$659$	−7.18494	+	0.945916i	−0.279886	+	0.0368476i	−0.0107234	+	0.999943i	$0.503413\pi$
$660$		0			0
$661$	4.23505	−	32.1684i	0.164724	−	1.25121i	−0.686783	−	0.726863i	$-0.740978\pi$
$661$	4.23505	−	32.1684i	0.164724	−	1.25121i	0.851507	−	0.524343i	$-0.175689\pi$
$662$	25.8939	+	20.1663i	1.00640	+	0.783786i
$663$		0			0
$664$	−3.31053	−	30.1546i	−0.128473	−	1.17022i
$665$	−1.01508	−	1.01508i	−0.0393632	−	0.0393632i
$666$		0			0
$667$	18.6775	−	7.73649i	0.723197	−	0.299558i
$668$	3.23066	+	12.7892i	0.124998	+	0.494830i
$669$		0			0
$670$	−2.40303	−	4.23209i	−0.0928370	−	0.163500i
$671$	6.80131	−	11.7802i	0.262562	−	0.454770i
$672$		0			0
$673$	−3.04125	−	5.26761i	−0.117232	−	0.203051i	0.801438	−	0.598078i	$-0.204069\pi$
$673$	−3.04125	−	5.26761i	−0.117232	−	0.203051i	−0.918670	+	0.395027i	$0.870735\pi$
$674$	−23.1892	+	39.5067i	−0.893216	+	1.52174i
$675$		0			0
$676$	7.21372	−	25.4533i	0.277451	−	0.978974i
$677$	−30.0662	−	23.0706i	−1.15554	−	0.886675i	−0.160585	−	0.987022i	$-0.551338\pi$
$677$	−30.0662	−	23.0706i	−1.15554	−	0.886675i	−0.994953	+	0.100347i	$0.968005\pi$
$678$		0			0
$679$	1.67580	−	0.449028i	0.0643112	−	0.0172321i
$680$	27.4933	+	4.22418i	1.05432	+	0.161990i
$681$		0			0
$682$	−16.7340	+	6.79100i	−0.640776	+	0.260041i
$683$	−5.74522	+	2.37975i	−0.219835	+	0.0910585i	−0.489883	−	0.871788i	$-0.662960\pi$
$683$	−5.74522	+	2.37975i	−0.219835	+	0.0910585i	0.270048	+	0.962847i	$0.412960\pi$
$684$		0			0
$685$	−6.39696	+	15.4436i	−0.244415	+	0.590070i
$686$	−2.61464	−	2.65248i	−0.0998274	−	0.101272i
$687$		0			0
$688$	−18.7882	+	23.0805i	−0.716292	+	0.879937i
$689$	20.3752	−	35.2909i	0.776234	−	1.34448i
$690$		0			0
$691$	−0.757019	−	5.75013i	−0.0287984	−	0.218745i	0.970994	−	0.239102i	$-0.0768531\pi$
$691$	−0.757019	−	5.75013i	−0.0287984	−	0.218745i	−0.999793	+	0.0203569i	$0.993520\pi$
$692$	−4.30317	−	36.7598i	−0.163582	−	1.39740i
$693$		0			0
$694$	4.09358	−	29.4570i	0.155390	−	1.11817i
$695$	−7.76053	+	28.9627i	−0.294374	+	1.09862i
$696$		0			0
$697$	5.24394	+	19.5706i	0.198628	+	0.741291i
$698$	−21.5111	+	2.67492i	−0.814206	+	0.101247i
$699$		0			0
$700$	−0.495858	+	0.831042i	−0.0187417	+	0.0314104i
$701$	18.7779	−	45.3339i	0.709232	−	1.71224i	0.00732108	−	0.999973i	$-0.497670\pi$
$701$	18.7779	−	45.3339i	0.709232	−	1.71224i	0.701911	−	0.712265i	$-0.252330\pi$
$702$		0			0
$703$		−	20.6267i		−	0.777952i
$704$	−12.7920	−	10.7223i	−0.482118	−	0.404111i
$705$		0			0
$706$	−23.4814	−	41.3543i	−0.883736	−	1.55639i
$707$	−1.97461	+	1.51517i	−0.0742628	+	0.0569838i
$708$		0			0
$709$	−16.5758	+	21.6020i	−0.622516	+	0.811279i	−0.993069	−	0.117532i	$-0.962502\pi$
$709$	−16.5758	+	21.6020i	−0.622516	+	0.811279i	0.370553	+	0.928811i	$0.379168\pi$
$710$	14.0732	−	10.6390i	0.528157	−	0.399273i
$711$		0			0
$712$	−4.44060	+	4.25320i	−0.166419	+	0.159395i
$713$	27.8043	+	7.45013i	1.04128	+	0.279010i
$714$		0			0
$715$	16.5290	+	2.17609i	0.618150	+	0.0813810i
$716$	0.740525	−	1.71756i	0.0276747	−	0.0641884i
$717$		0			0
$718$	31.4923	+	31.9481i	1.17528	+	1.19229i
$719$		−	26.2968i		−	0.980706i	−0.871524	−	0.490353i	$-0.836868\pi$
$719$		−	26.2968i		−	0.980706i	0.871524	−	0.490353i	$-0.163132\pi$
$720$		0			0
$721$			0.916589i			0.0341356i
$722$	4.83483	−	4.76585i	0.179934	−	0.177367i
$723$		0			0
$724$	21.7335	−	8.63859i	0.807718	−	0.321051i
$725$	−10.9341	−	1.43951i	−0.406084	−	0.0534620i
$726$		0			0
$727$	−35.2544	−	9.44639i	−1.30751	−	0.350347i	−0.463228	−	0.886239i	$-0.653309\pi$
$727$	−35.2544	−	9.44639i	−1.30751	−	0.350347i	−0.844287	+	0.535892i	$0.819975\pi$
$728$	−0.990801	−	2.54585i	−0.0367215	−	0.0943554i
$729$		0			0
$730$	12.1437	+	16.0637i	0.449460	+	0.594543i
$731$	28.5487	−	37.2054i	1.05591	−	1.37609i
$732$		0			0
$733$	−38.2134	+	29.3221i	−1.41144	+	1.08304i	−0.427607	+	0.903965i	$0.640643\pi$
$733$	−38.2134	+	29.3221i	−1.41144	+	1.08304i	−0.983836	+	0.179073i	$0.942690\pi$
$734$	−14.8597	+	8.43752i	−0.548483	+	0.311434i
$735$		0			0
$736$	5.95845	+	25.9288i	0.219632	+	0.955749i
$737$		−	4.60186i		−	0.169512i
$738$		0			0
$739$	7.66115	−	18.4956i	0.281820	−	0.680373i	−0.718058	−	0.695983i	$-0.754969\pi$
$739$	7.66115	−	18.4956i	0.281820	−	0.680373i	0.999878	+	0.0156097i	$0.00496892\pi$
$740$	12.7917	−	3.23128i	0.470233	−	0.118784i
$741$		0			0
$742$	−0.261886	−	2.10603i	−0.00961414	−	0.0773147i
$743$	0.258745	+	0.965648i	0.00949242	+	0.0354262i	0.970510	−	0.241062i	$-0.0774959\pi$
$743$	0.258745	+	0.965648i	0.00949242	+	0.0354262i	−0.961017	+	0.276489i	$0.910829\pi$
$744$		0			0
$745$	3.97136	−	14.8213i	0.145499	−	0.543011i
$746$	34.3979	+	4.78021i	1.25939	+	0.175016i
$747$		0			0
$748$	20.6345	+	16.3098i	0.754474	+	0.596344i
$749$	−0.296126	−	2.24930i	−0.0108202	−	0.0821875i
$750$		0			0
$751$	17.0984	−	29.6154i	0.623931	−	1.08068i	−0.364815	−	0.931080i	$-0.618868\pi$
$751$	17.0984	−	29.6154i	0.623931	−	1.08068i	0.988746	−	0.149601i	$-0.0477988\pi$
$752$	−4.09988	+	2.21250i	−0.149507	+	0.0806817i
$753$		0			0
$754$	22.1718	−	21.8555i	0.807450	−	0.795931i
$755$	−9.71257	+	23.4482i	−0.353477	+	0.853368i
$756$		0			0
$757$	−41.7298	+	17.2851i	−1.51670	+	0.628236i	−0.976926	−	0.213576i	$-0.931489\pi$
$757$	−41.7298	+	17.2851i	−1.51670	+	0.628236i	−0.539770	+	0.841813i	$0.681489\pi$
$758$	−6.94983	−	17.1253i	−0.252429	−	0.622020i
$759$		0			0
$760$	18.4086	+	11.1640i	0.667752	+	0.404960i
$761$	−25.4127	+	6.80932i	−0.921210	+	0.246838i	−0.688103	−	0.725613i	$-0.741556\pi$
$761$	−25.4127	+	6.80932i	−0.921210	+	0.246838i	−0.233108	+	0.972451i	$0.574889\pi$
$762$		0			0
$763$	1.01351	+	0.777690i	0.0366914	+	0.0281543i
$764$	17.0746	+	30.5805i	0.617738	+	1.10636i
$765$		0			0
$766$	−30.5644	−	17.9403i	−1.10434	−	0.648211i
$767$	23.5054	+	40.7125i	0.848730	+	1.47004i
$768$		0			0
$769$	23.8544	−	41.3170i	0.860211	−	1.48993i	−0.0115146	−	0.999934i	$-0.503665\pi$
$769$	23.8544	−	41.3170i	0.860211	−	1.48993i	0.871725	−	0.489995i	$-0.163001\pi$
$770$	0.755022	−	0.428710i	0.0272091	−	0.0154496i
$771$		0			0
$772$	−16.5061	+	27.6638i	−0.594068	+	0.995641i
$773$	−0.388763	+	0.161031i	−0.0139828	+	0.00579188i	−0.389664	−	0.920957i	$-0.627409\pi$
$773$	−0.388763	+	0.161031i	−0.0139828	+	0.00579188i	0.375681	+	0.926749i	$0.377409\pi$
$774$		0			0
$775$	−11.1036	−	11.1036i	−0.398854	−	0.398854i
$776$	−22.8083	+	12.5209i	−0.818770	+	0.449474i
$777$		0			0
$778$	−23.5908	+	30.2910i	−0.845771	+	1.08599i
$779$	−2.04690	+	15.5478i	−0.0733379	+	0.557056i
$780$		0			0
$781$	16.5391	−	2.17742i	0.591817	−	0.0779142i
$782$	−10.5593	−	40.5714i	−0.377599	−	1.45083i
$783$		0			0
$784$	23.7153	+	14.6163i	0.846976	+	0.522011i
$785$	14.9023	+	25.8115i	0.531885	+	0.921252i
$786$		0			0
$787$	−0.546413	+	0.419278i	−0.0194775	+	0.0149456i	−0.618454	−	0.785821i	$-0.712241\pi$
$787$	−0.546413	+	0.419278i	−0.0194775	+	0.0149456i	0.598977	+	0.800766i	$0.295574\pi$
$788$	−37.3361	+	14.8403i	−1.33005	+	0.528664i
$789$		0			0
$790$	−10.0548	−	24.7765i	−0.357735	−	0.881507i
$791$	0.753437	+	0.753437i	0.0267891	+	0.0267891i
$792$		0			0
$793$	−23.6095	+	23.6095i	−0.838396	+	0.838396i
$794$	36.5467	+	15.4466i	1.29699	+	0.548181i
$795$		0			0
$796$	27.4559	+	28.2565i	0.973150	+	1.00152i
$797$	18.4239	+	24.0104i	0.652606	+	0.850493i	0.996060	−	0.0886763i	$-0.0282637\pi$
$797$	18.4239	+	24.0104i	0.652606	+	0.850493i	−0.343454	+	0.939169i	$0.611597\pi$
$798$		0			0
$799$	6.35766	−	3.67060i	0.224918	−	0.129856i
$800$	4.25738	−	13.8749i	0.150521	−	0.490553i
$801$		0			0
$802$	−3.16645	−	1.85861i	−0.111811	−	0.0656298i
$803$	2.48539	+	18.8784i	0.0877075	+	0.666205i
$804$		0			0
$805$	−1.37207	−	0.180636i	−0.0483589	−	0.00636658i
$806$	43.9896	−	5.47014i	1.54947	−	0.192677i
$807$		0			0
$808$	23.3564	−	29.1173i	0.821676	−	1.02434i
$809$	−1.16653	+	1.16653i	−0.0410129	+	0.0410129i	−0.727316	−	0.686303i	$-0.759232\pi$
$809$	−1.16653	+	1.16653i	−0.0410129	+	0.0410129i	0.686303	+	0.727316i	$0.259232\pi$
$810$		0			0
$811$	−13.7394	−	33.1698i	−0.482455	−	1.16475i	−0.958440	−	0.285296i	$-0.907908\pi$
$811$	−13.7394	−	33.1698i	−0.482455	−	1.16475i	0.475984	−	0.879454i	$-0.342092\pi$
$812$	0.234706	−	1.60430i	0.00823656	−	0.0562997i
$813$		0			0
$814$	12.0268	+	3.31537i	0.421541	+	0.116204i
$815$	−16.6998	−	9.64166i	−0.584970	−	0.337732i
$816$		0			0
$817$	31.4346	−	18.1488i	1.09976	−	0.634946i
$818$	46.8943	−	12.2049i	1.63962	−	0.426734i
$819$		0			0
$820$	−9.96264	+	1.16624i	−0.347910	+	0.0407270i
$821$	2.23519	−	2.91295i	0.0780086	−	0.101663i	−0.752719	−	0.658342i	$-0.771258\pi$
$821$	2.23519	−	2.91295i	0.0780086	−	0.101663i	0.830728	+	0.556679i	$0.187925\pi$
$822$		0			0
$823$	−4.38665	−	16.3712i	−0.152909	−	0.570664i	−0.999275	−	0.0380627i	$-0.987881\pi$
$823$	−4.38665	−	16.3712i	−0.152909	−	0.570664i	0.846366	−	0.532601i	$-0.178785\pi$
$824$	−3.27085	−	13.3516i	−0.113946	−	0.465124i
$825$		0			0
$826$	2.25513	+	0.953142i	0.0784659	+	0.0331640i
$827$	8.45934	+	20.4226i	0.294160	+	0.710165i	0.999998	+	0.00179202i	$0.000570419\pi$
$827$	8.45934	+	20.4226i	0.294160	+	0.710165i	−0.705838	+	0.708373i	$0.749430\pi$
$828$		0			0
$829$	10.1087	+	4.18714i	0.351088	+	0.145425i	0.551256	−	0.834336i	$-0.314149\pi$
$829$	10.1087	+	4.18714i	0.351088	+	0.145425i	−0.200168	+	0.979762i	$0.564149\pi$
$830$	−23.6650	−	0.170015i	−0.821425	−	0.00590129i
$831$		0			0
$832$	23.5175	+	33.5487i	0.815322	+	1.16309i
$833$	−38.0164	−	21.9488i	−1.31719	−	0.760480i
$834$		0			0
$835$	10.2025	−	1.34319i	0.353074	−	0.0464830i
$836$	9.92443	+	17.7746i	0.343244	+	0.614748i
$837$		0			0
$838$	11.2948	+	14.9407i	0.390172	+	0.516117i
$839$	42.9334	+	11.5040i	1.48222	+	0.397161i	0.907103	−	0.420908i	$-0.138288\pi$
$839$	42.9334	+	11.5040i	1.48222	+	0.397161i	0.575121	+	0.818069i	$0.304955\pi$
$840$		0			0
$841$	−10.1639	+	2.72341i	−0.350480	+	0.0939108i
$842$	18.1057	+	14.1008i	0.623965	+	0.485947i
$843$		0			0
$844$	14.8546	−	11.0629i	0.511316	−	0.380801i
$845$	−19.0677	−	7.89812i	−0.655950	−	0.271704i
$846$		0			0
$847$	−1.25356			−0.0430728
$848$	11.3302	+	29.7431i	0.389079	+	1.02138i
$849$		0			0
$850$	−6.07771	+	22.0475i	−0.208464	+	0.756224i
$851$	−12.1051	−	15.7756i	−0.414956	−	0.540781i
$852$		0			0
$853$	−10.9014	−	8.36493i	−0.373256	−	0.286410i	0.405050	−	0.914295i	$-0.367254\pi$
$853$	−10.9014	−	8.36493i	−0.373256	−	0.286410i	−0.778306	+	0.627885i	$0.783921\pi$
$854$	−0.239346	+	1.72231i	−0.00819026	+	0.0589363i
$855$		0			0
$856$	12.3402	+	31.7079i	0.421778	+	1.08375i
$857$	−10.8130	+	40.3548i	−0.369366	+	1.37849i	0.492038	+	0.870574i	$0.336252\pi$
$857$	−10.8130	+	40.3548i	−0.369366	+	1.37849i	−0.861404	+	0.507920i	$0.830415\pi$
$858$		0			0
$859$	−3.94314	+	29.9511i	−0.134538	+	1.02192i	0.782368	+	0.622817i	$0.214012\pi$
$859$	−3.94314	+	29.9511i	−0.134538	+	1.02192i	−0.916906	+	0.399103i	$0.869322\pi$
$860$	16.1794	+	16.6511i	0.551713	+	0.567799i
$861$		0			0
$862$	41.4907	+	0.298078i	1.41318	+	0.0101526i
$863$	−33.9351			−1.15516			−0.577582	−	0.816333i	$-0.696004\pi$
$863$	−33.9351			−1.15516			−0.577582	+	0.816333i	$0.696004\pi$
$864$		0			0
$865$	−28.8729			−0.981710
$866$	40.8767	+	0.293667i	1.38905	+	0.00997921i
$867$		0			0
$868$	1.65570	−	1.60880i	0.0561983	−	0.0546061i
$869$	3.30018	−	25.0674i	0.111951	−	0.850352i
$870$		0			0
$871$	−2.92353	+	10.9108i	−0.0990601	+	0.369697i
$872$	−17.5385	−	7.71160i	−0.593929	−	0.261148i
$873$		0			0
$874$	4.46634	−	32.1393i	0.151076	−	1.08713i
$875$	1.76618	+	1.35524i	0.0597079	+	0.0458155i
$876$		0			0
$877$	−12.7223	−	16.5800i	−0.429602	−	0.559868i	0.527524	−	0.849540i	$-0.323120\pi$
$877$	−12.7223	−	16.5800i	−0.429602	−	0.559868i	−0.957126	+	0.289672i	$0.906454\pi$
$878$	7.67884	−	27.8558i	0.259148	−	0.940088i
$879$		0			0
$880$	−9.46825	+	8.93914i	−0.319175	+	0.301338i
$881$	18.0274			0.607358			0.303679	−	0.952774i	$-0.401785\pi$
$881$	18.0274			0.607358			0.303679	+	0.952774i	$0.401785\pi$
$882$		0			0
$883$	36.9716	+	15.3141i	1.24419	+	0.515361i	0.905022	−	0.425364i	$-0.139854\pi$
$883$	36.9716	+	15.3141i	1.24419	+	0.515361i	0.339170	+	0.940725i	$0.389854\pi$
$884$	−38.5620	−	51.7786i	−1.29698	−	1.74150i
$885$		0			0
$886$	12.5224	+	9.75253i	0.420699	+	0.327643i
$887$	16.0326	−	4.29592i	0.538322	−	0.144243i	0.0205937	−	0.999788i	$-0.493444\pi$
$887$	16.0326	−	4.29592i	0.538322	−	0.144243i	0.517729	+	0.855545i	$0.326778\pi$
$888$		0			0
$889$	−2.32354	−	0.622590i	−0.0779289	−	0.0208810i
$890$	2.89274	+	3.82650i	0.0969649	+	0.128265i
$891$		0			0
$892$	20.3767	−	11.3773i	0.682264	−	0.380941i
$893$	5.63344	−	0.741656i	0.188516	−	0.0248186i
$894$		0			0
$895$	−1.26366	−	0.729572i	−0.0422393	−	0.0243869i
$896$	2.03064	+	0.655149i	0.0678390	+	0.0218870i
$897$		0			0
$898$	−3.00210	−	0.0215678i	−0.100181	−	0.000719725i
$899$	24.3065	+	10.0681i	0.810668	+	0.335790i
$900$		0			0
$901$	−19.1931	−	46.3362i	−0.639414	−	1.54368i
$902$	−8.73645	−	3.69251i	−0.290892	−	0.122947i
$903$		0			0
$904$	−13.6637	−	8.28637i	−0.454446	−	0.275600i
$905$	−4.72216	−	17.6233i	−0.156970	−	0.585819i
$906$		0			0
$907$	24.5675	−	32.0170i	0.815750	−	1.06311i	−0.181074	−	0.983469i	$-0.557957\pi$
$907$	24.5675	−	32.0170i	0.815750	−	1.06311i	0.996824	−	0.0796366i	$-0.0253760\pi$
$908$	2.29000	+	19.5623i	0.0759963	+	0.649198i
$909$		0			0
$910$	−2.06247	+	0.536788i	−0.0683704	+	0.0177943i
$911$	−12.5379	+	7.23877i	−0.415400	+	0.239831i	−0.693107	−	0.720834i	$-0.743759\pi$
$911$	−12.5379	+	7.23877i	−0.415400	+	0.239831i	0.277707	+	0.960666i	$0.410425\pi$
$912$		0			0
$913$	−19.3796	−	11.1888i	−0.641370	−	0.370295i
$914$	9.96507	+	2.74701i	0.329615	+	0.0908631i
$915$		0			0
$916$	40.7341	+	5.95933i	1.34589	+	0.196902i
$917$	1.29238	+	3.12008i	0.0426781	+	0.103034i
$918$		0			0
$919$	−29.1031	+	29.1031i	−0.960023	+	0.960023i	−0.999231	−	0.0392080i	$-0.987517\pi$
$919$	−29.1031	+	29.1031i	−0.960023	+	0.960023i	0.0392080	+	0.999231i	$0.487517\pi$
$920$	20.6309	−	2.26497i	0.680181	−	0.0746739i
$921$		0			0
$922$	1.44401	−	0.179563i	0.0475559	−	0.00591360i
$923$	−40.5967	−	5.34466i	−1.33626	−	0.175922i
$924$		0			0
$925$	1.41589	+	10.7548i	0.0465542	+	0.353614i
$926$	31.8254	+	18.6806i	1.04585	+	0.613881i
$927$		0			0
$928$	2.30607	+	24.2067i	0.0757005	+	0.794623i
$929$	29.1277	−	16.8169i	0.955650	−	0.551745i	0.0608185	−	0.998149i	$-0.480629\pi$
$929$	29.1277	−	16.8169i	0.955650	−	0.551745i	0.894831	+	0.446404i	$0.147296\pi$
$930$		0			0
$931$	−20.6836	−	26.9554i	−0.677877	−	0.883426i
$932$	−13.3729	+	12.9940i	−0.438044	+	0.425634i
$933$		0			0
$934$	−16.2517	−	6.86886i	−0.531771	−	0.224756i
$935$	14.5090	−	14.5090i	0.474494	−	0.474494i
$936$		0			0
$937$	−17.3037	−	17.3037i	−0.565288	−	0.565288i	0.365517	−	0.930805i	$-0.380892\pi$
$937$	−17.3037	−	17.3037i	−0.565288	−	0.565288i	−0.930805	+	0.365517i	$0.880892\pi$
$938$	0.221210	+	0.545093i	0.00722277	+	0.0177979i
$939$		0			0
$940$	1.34245	+	3.37740i	0.0437858	+	0.110159i
$941$	−16.1423	+	12.3864i	−0.526225	+	0.403787i	−0.837420	−	0.546559i	$-0.815937\pi$
$941$	−16.1423	+	12.3864i	−0.526225	+	0.403787i	0.311195	+	0.950346i	$0.399271\pi$
$942$		0			0
$943$	7.55890	+	13.0924i	0.246152	+	0.426347i
$944$	−36.2508	−	5.83660i	−1.17986	−	0.189965i
$945$		0			0
$946$	5.52949	+	21.2457i	0.179779	+	0.690757i
$947$	−9.51945	+	1.25326i	−0.309341	+	0.0407255i	−0.283598	−	0.958943i	$-0.591528\pi$
$947$	−9.51945	+	1.25326i	−0.309341	+	0.0407255i	−0.0257423	+	0.999669i	$0.508195\pi$
$948$		0			0
$949$	6.10060	−	46.3387i	0.198034	−	1.50422i
$950$	−10.8764	+	13.9655i	−0.352877	+	0.453101i
$951$		0			0
$952$	−3.22818	−	0.940003i	−0.104626	−	0.0304657i
$953$	−8.74554	−	8.74554i	−0.283296	−	0.283296i	0.551126	−	0.834422i	$-0.314198\pi$
$953$	−8.74554	−	8.74554i	−0.283296	−	0.283296i	−0.834422	+	0.551126i	$0.814198\pi$
$954$		0			0
$955$	25.2435	−	10.4562i	0.816861	−	0.338355i
$956$	−5.10379	−	3.04528i	−0.165068	−	0.0984912i
$957$		0			0
$958$	−42.3122	+	24.0253i	−1.36704	+	0.776223i
$959$	1.01028	−	1.74986i	0.0326236	−	0.0565058i
$960$		0			0
$961$	3.23015	+	5.59478i	0.104198	+	0.180477i
$962$	−26.4088	−	15.5011i	−0.851454	−	0.499777i
$963$		0			0
$964$	−25.7548	+	14.3802i	−0.829508	+	0.463155i
$965$	19.9376	+	15.2987i	0.641815	+	0.492482i
$966$		0			0
$967$	33.6256	−	9.00995i	1.08133	−	0.289740i	0.326187	−	0.945305i	$-0.394236\pi$
$967$	33.6256	−	9.00995i	1.08133	−	0.289740i	0.755139	+	0.655565i	$0.227569\pi$
$968$	18.2601	−	4.47333i	0.586902	−	0.143778i
$969$		0			0
$970$	7.63281	+	18.8083i	0.245075	+	0.603898i
$971$	−33.5566	+	13.8996i	−1.07688	+	0.446060i	−0.849415	−	0.527726i	$-0.823045\pi$
$971$	−33.5566	+	13.8996i	−1.07688	+	0.446060i	−0.227468	+	0.973785i	$0.573045\pi$
$972$		0			0
$973$	1.38699	−	3.34848i	0.0444648	−	0.107347i
$974$	14.6643	−	14.4551i	0.469875	−	0.463172i
$975$		0			0
$976$	−2.65961	−	25.9423i	−0.0851322	−	0.830394i
$977$	−0.540538	+	0.936239i	−0.0172933	+	0.0299530i	−0.874543	−	0.484949i	$-0.838838\pi$
$977$	−0.540538	+	0.936239i	−0.0172933	+	0.0299530i	0.857249	+	0.514902i	$0.172172\pi$
$978$		0			0
$979$	0.592041	+	4.49700i	0.0189217	+	0.143725i
$980$	13.4762	−	17.0497i	0.430483	−	0.544631i
$981$		0			0
$982$	54.2938	+	7.54511i	1.73258	+	0.240774i
$983$	−8.77327	+	32.7423i	−0.279824	+	1.04432i	0.672715	+	0.739901i	$0.265128\pi$
$983$	−8.77327	+	32.7423i	−0.279824	+	1.04432i	−0.952539	+	0.304416i	$0.901539\pi$
$984$		0			0
$985$	8.11224	+	30.2753i	0.258478	+	0.964652i
$986$	−4.72833	−	38.0242i	−0.150581	−	1.21094i
$987$		0			0
$988$	−12.2382	−	48.4476i	−0.389350	−	1.54132i
$989$	13.3908	−	32.3283i	0.425803	−	1.02798i
$990$		0			0
$991$			47.7127i			1.51564i	0.652461	+	0.757822i	$0.273736\pi$
$991$			47.7127i			1.51564i	−0.652461	+	0.757822i	$0.726264\pi$
$992$	−18.3770	+	29.3431i	−0.583470	+	0.931644i
$993$		0			0
$994$	−1.85440	+	1.05295i	−0.0588181	+	0.0333975i
$995$	24.3844	−	18.7108i	0.773036	−	0.593172i
$996$		0			0
$997$	11.3527	−	14.7952i	0.359544	−	0.468567i	−0.578199	−	0.815896i	$-0.696244\pi$
$997$	11.3527	−	14.7952i	0.359544	−	0.468567i	0.937744	+	0.347328i	$0.112911\pi$
$998$	26.6944	+	35.3111i	0.844995	+	1.11775i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.611.22		368
3.2	odd	2		288.2.bf.a.131.25	yes	368
9.2	odd	6	inner	864.2.bn.a.35.38		368
9.7	even	3		288.2.bf.a.227.9	yes	368
32.11	odd	8	inner	864.2.bn.a.395.38		368
96.11	even	8		288.2.bf.a.203.9	yes	368
288.11	even	24	inner	864.2.bn.a.683.22		368
288.43	odd	24		288.2.bf.a.11.25	✓	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.25	✓	368	288.43	odd	24
288.2.bf.a.131.25	yes	368	3.2	odd	2
288.2.bf.a.203.9	yes	368	96.11	even	8
288.2.bf.a.227.9	yes	368	9.7	even	3
864.2.bn.a.35.38		368	9.2	odd	6	inner
864.2.bn.a.395.38		368	32.11	odd	8	inner
864.2.bn.a.611.22		368	1.1	even	1	trivial
864.2.bn.a.683.22		368	288.11	even	24	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0101598 - 1.41418i) q^{2} +(-1.99979 - 0.0287354i) q^{4} +(-0.203653 + 1.54690i) q^{5} +(0.0488121 - 0.182169i) q^{7} +(-0.0609543 + 2.82777i) q^{8} +O(q^{10})\)	\(q+(0.0101598 - 1.41418i) q^{2} +(-1.99979 - 0.0287354i) q^{4} +(-0.203653 + 1.54690i) q^{5} +(0.0488121 - 0.182169i) q^{7} +(-0.0609543 + 2.82777i) q^{8} +(2.18552 + 0.303717i) q^{10} +(1.65527 + 1.27014i) q^{11} +(-3.11766 - 4.06301i) q^{13} +(-0.257123 - 0.0708797i) q^{14} +(3.99835 + 0.114930i) q^{16} -6.30311 q^{17} +(-4.50721 - 1.86695i) q^{19} +(0.451715 - 3.08762i) q^{20} +(1.81302 - 2.32795i) q^{22} +(-4.54282 + 1.21725i) q^{23} +(2.47821 + 0.664034i) q^{25} +(-5.77750 + 4.36765i) q^{26} +(-0.102849 + 0.362898i) q^{28} +(-4.26178 + 0.561073i) q^{29} +(-5.30049 - 3.06024i) q^{31} +(0.203153 - 5.65321i) q^{32} +(-0.0640380 + 8.91371i) q^{34} +(0.271856 + 0.112607i) q^{35} +(1.61800 + 3.90619i) q^{37} +(-2.68599 + 6.35503i) q^{38} +(-4.36186 - 0.670174i) q^{40} +(-0.831961 - 3.10492i) q^{41} +(-4.52931 + 5.90271i) q^{43} +(-3.27371 - 2.58758i) q^{44} +(1.67525 + 6.43673i) q^{46} +(-1.00866 + 0.582347i) q^{47} +(6.03137 + 3.48222i) q^{49} +(0.964240 - 3.49788i) q^{50} +(6.11793 + 8.21478i) q^{52} +(3.04502 + 7.35132i) q^{53} +(-2.30187 + 2.30187i) q^{55} +(0.512157 + 0.149133i) q^{56} +(0.750159 + 6.03261i) q^{58} +(-9.10089 - 1.19815i) q^{59} +(-0.850975 - 6.46380i) q^{61} +(-4.38157 + 7.46474i) q^{62} +(-7.99257 - 0.344730i) q^{64} +(6.91999 - 3.99526i) q^{65} +(-1.34269 - 1.74983i) q^{67} +(12.6049 + 0.181122i) q^{68} +(0.162008 - 0.383309i) q^{70} +(5.65361 - 5.65361i) q^{71} +(6.45325 + 6.45325i) q^{73} +(5.54048 - 2.24845i) q^{74} +(8.95985 + 3.86303i) q^{76} +(0.312177 - 0.239542i) q^{77} +(-6.05908 - 10.4946i) q^{79} +(-0.992060 + 6.16163i) q^{80} +(-4.39936 + 1.14499i) q^{82} +(-10.6336 + 1.39993i) q^{83} +(1.28365 - 9.75027i) q^{85} +(8.30146 + 6.46522i) q^{86} +(-3.69255 + 4.60332i) q^{88} +(1.53722 + 1.53722i) q^{89} +(-0.892335 + 0.369617i) q^{91} +(9.11969 - 2.30370i) q^{92} +(0.813295 + 1.43233i) q^{94} +(3.80589 - 6.59199i) q^{95} +(4.59956 + 7.96668i) q^{97} +(4.98575 - 8.49405i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

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