LMFDB - Embedded newform 882.2.z.a.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(37,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("882.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.z (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 294)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	882.235
Dual form			882.2.z.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988831 + 0.149042i) q^{2} +(0.955573 + 0.294755i) q^{4} +(0.0829648 + 1.10709i) q^{5} +(-2.15873 - 1.52966i) q^{7} +(0.900969 + 0.433884i) q^{8} +O(q^{10})$	\(q+(0.988831 + 0.149042i) q^{2} +(0.955573 + 0.294755i) q^{4} +(0.0829648 + 1.10709i) q^{5} +(-2.15873 - 1.52966i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.0829648 + 1.10709i) q^{10} +(0.896144 + 2.28334i) q^{11} +(1.75343 - 2.19874i) q^{13} +(-1.90664 - 1.83432i) q^{14} +(0.826239 + 0.563320i) q^{16} +(5.23495 + 4.85732i) q^{17} +(3.75130 + 6.49744i) q^{19} +(-0.247041 + 1.08236i) q^{20} +(0.545821 + 2.39140i) q^{22} +(1.89161 - 1.75516i) q^{23} +(3.72539 - 0.561513i) q^{25} +(2.06155 - 1.91284i) q^{26} +(-1.61195 - 2.09800i) q^{28} +(-1.31754 + 5.77251i) q^{29} +(4.79230 - 8.30051i) q^{31} +(0.733052 + 0.680173i) q^{32} +(4.45253 + 5.58330i) q^{34} +(1.51438 - 2.51682i) q^{35} +(-7.55789 + 2.33130i) q^{37} +(2.74101 + 6.98397i) q^{38} +(-0.405599 + 1.03345i) q^{40} +(1.70340 + 0.820316i) q^{41} +(-5.22216 + 2.51486i) q^{43} +(0.183305 + 2.44604i) q^{44} +(2.13207 - 1.45362i) q^{46} +(-9.22899 - 1.39105i) q^{47} +(2.32025 + 6.60427i) q^{49} +3.76747 q^{50} +(2.32362 - 1.58422i) q^{52} +(-9.41380 - 2.90377i) q^{53} +(-2.45351 + 1.18155i) q^{55} +(-1.28125 - 2.31482i) q^{56} +(-2.16317 + 5.51167i) q^{58} +(0.588835 - 7.85746i) q^{59} +(6.94339 - 2.14175i) q^{61} +(5.97590 - 7.49355i) q^{62} +(0.623490 + 0.781831i) q^{64} +(2.57967 + 1.75879i) q^{65} +(-0.0774217 + 0.134098i) q^{67} +(3.57065 + 6.18455i) q^{68} +(1.87257 - 2.26300i) q^{70} +(-2.31321 - 10.1348i) q^{71} +(2.08994 - 0.315008i) q^{73} +(-7.82094 + 1.17882i) q^{74} +(1.66949 + 7.31449i) q^{76} +(1.55820 - 6.29991i) q^{77} +(1.92214 + 3.32924i) q^{79} +(-0.555096 + 0.961455i) q^{80} +(1.56212 + 1.06503i) q^{82} +(-3.54971 - 4.45119i) q^{83} +(-4.94317 + 6.19854i) q^{85} +(-5.53865 + 1.70845i) q^{86} +(-0.183305 + 2.44604i) q^{88} +(4.86684 - 12.4005i) q^{89} +(-7.14852 + 2.06432i) q^{91} +(2.32491 - 1.11962i) q^{92} +(-8.91858 - 2.75102i) q^{94} +(-6.88202 + 4.69208i) q^{95} +8.21789 q^{97} +(1.31002 + 6.87632i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 2 q^{4} - q^{5} + 4 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 + 2 * q^4 - q^5 + 4 * q^8	$ 24 q - 2 q^{2} + 2 q^{4} - q^{5} + 4 q^{8} + q^{10} - 8 q^{11} - 2 q^{13} + 2 q^{16} - 9 q^{17} - 4 q^{19} - 5 q^{20} + 5 q^{22} + 38 q^{23} - 19 q^{25} + 20 q^{26} - 14 q^{28} + 14 q^{29} + 4 q^{31} - 2 q^{32} + 17 q^{34} - 42 q^{35} + 7 q^{37} + 18 q^{38} - 13 q^{40} - 2 q^{41} + 4 q^{43} + 6 q^{44} + 11 q^{46} + 8 q^{47} - 42 q^{49} + 4 q^{50} + 15 q^{52} + 10 q^{53} + 33 q^{55} + 7 q^{56} - 28 q^{58} - 14 q^{59} + 7 q^{61} + 8 q^{62} - 4 q^{64} - 23 q^{65} + 23 q^{67} - 9 q^{68} + 28 q^{70} - 36 q^{71} + 15 q^{73} + 14 q^{74} + q^{76} + 28 q^{77} + 38 q^{79} - 8 q^{80} - q^{82} - 27 q^{83} - 47 q^{85} - 26 q^{86} - 6 q^{88} + 121 q^{89} + 21 q^{91} + q^{92} - q^{94} - 44 q^{95} + 14 q^{97} + 21 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 2 * q^4 - q^5 + 4 * q^8 + q^10 - 8 * q^11 - 2 * q^13 + 2 * q^16 - 9 * q^17 - 4 * q^19 - 5 * q^20 + 5 * q^22 + 38 * q^23 - 19 * q^25 + 20 * q^26 - 14 * q^28 + 14 * q^29 + 4 * q^31 - 2 * q^32 + 17 * q^34 - 42 * q^35 + 7 * q^37 + 18 * q^38 - 13 * q^40 - 2 * q^41 + 4 * q^43 + 6 * q^44 + 11 * q^46 + 8 * q^47 - 42 * q^49 + 4 * q^50 + 15 * q^52 + 10 * q^53 + 33 * q^55 + 7 * q^56 - 28 * q^58 - 14 * q^59 + 7 * q^61 + 8 * q^62 - 4 * q^64 - 23 * q^65 + 23 * q^67 - 9 * q^68 + 28 * q^70 - 36 * q^71 + 15 * q^73 + 14 * q^74 + q^76 + 28 * q^77 + 38 * q^79 - 8 * q^80 - q^82 - 27 * q^83 - 47 * q^85 - 26 * q^86 - 6 * q^88 + 121 * q^89 + 21 * q^91 + q^92 - q^94 - 44 * q^95 + 14 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{17}{21}\right)$	$1$

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 $

$2$	0.988831	+	0.149042i	0.699209	+	0.105389i
$2$	0.988831	+	0.149042i	0.699209	+	0.105389i
$3$		0			0
$3$		0			0
$4$	0.955573	+	0.294755i	0.477786	+	0.147378i
$5$	0.0829648	+	1.10709i	0.0371030	+	0.495105i	0.984540	+	0.175162i	$0.0560448\pi$
$5$	0.0829648	+	1.10709i	0.0371030	+	0.495105i	−0.947437	+	0.319943i	$0.896336\pi$
$6$		0			0
$7$	−2.15873	−	1.52966i	−0.815924	−	0.578159i
$7$	−2.15873	−	1.52966i	−0.815924	−	0.578159i
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$		0			0
$10$	−0.0829648	+	1.10709i	−0.0262358	+	0.350092i
$11$	0.896144	+	2.28334i	0.270197	+	0.688452i	0.999989	+	0.00478172i	$0.00152208\pi$
$11$	0.896144	+	2.28334i	0.270197	+	0.688452i	−0.729791	+	0.683670i	$0.760383\pi$
$12$		0			0
$13$	1.75343	−	2.19874i	0.486315	−	0.609820i	−0.476766	−	0.879030i	$-0.658191\pi$
$13$	1.75343	−	2.19874i	0.486315	−	0.609820i	0.963081	+	0.269210i	$0.0867627\pi$
$14$	−1.90664	−	1.83432i	−0.509570	−	0.490243i
$15$		0			0
$16$	0.826239	+	0.563320i	0.206560	+	0.140830i
$17$	5.23495	+	4.85732i	1.26966	+	1.17807i	0.974934	+	0.222492i	$0.0714193\pi$
$17$	5.23495	+	4.85732i	1.26966	+	1.17807i	0.294727	+	0.955581i	$0.404771\pi$
$18$		0			0
$19$	3.75130	+	6.49744i	0.860607	+	1.49062i	0.871344	+	0.490673i	$0.163249\pi$
$19$	3.75130	+	6.49744i	0.860607	+	1.49062i	−0.0107369	+	0.999942i	$0.503418\pi$
$20$	−0.247041	+	1.08236i	−0.0552401	+	0.242023i
$21$		0			0
$22$	0.545821	+	2.39140i	0.116369	+	0.509848i
$23$	1.89161	−	1.75516i	0.394427	−	0.365975i	−0.457882	−	0.889013i	$-0.651392\pi$
$23$	1.89161	−	1.75516i	0.394427	−	0.365975i	0.852310	+	0.523038i	$0.175201\pi$
$24$		0			0
$25$	3.72539	−	0.561513i	0.745078	−	0.112303i
$26$	2.06155	−	1.91284i	0.404304	−	0.375139i
$27$		0			0
$28$	−1.61195	−	2.09800i	−0.304630	−	0.396485i
$29$	−1.31754	+	5.77251i	−0.244661	+	1.07193i	0.692057	+	0.721843i	$0.256705\pi$
$29$	−1.31754	+	5.77251i	−0.244661	+	1.07193i	−0.936718	+	0.350086i	$0.886153\pi$
$30$		0			0
$31$	4.79230	−	8.30051i	0.860723	−	1.49082i	−0.0105089	−	0.999945i	$-0.503345\pi$
$31$	4.79230	−	8.30051i	0.860723	−	1.49082i	0.871232	−	0.490871i	$-0.163322\pi$
$32$	0.733052	+	0.680173i	0.129586	+	0.120239i
$33$		0			0
$34$	4.45253	+	5.58330i	0.763603	+	0.957528i
$35$	1.51438	−	2.51682i	0.255976	−	0.425420i
$36$		0			0
$37$	−7.55789	+	2.33130i	−1.24251	+	0.383264i	−0.845215	−	0.534427i	$-0.820527\pi$
$37$	−7.55789	+	2.33130i	−1.24251	+	0.383264i	−0.397295	+	0.917691i	$0.630051\pi$
$38$	2.74101	+	6.98397i	0.444650	+	1.13295i
$39$		0			0
$40$	−0.405599	+	1.03345i	−0.0641308	+	0.163403i
$41$	1.70340	+	0.820316i	0.266027	+	0.128112i	0.562143	−	0.827040i	$-0.309977\pi$
$41$	1.70340	+	0.820316i	0.266027	+	0.128112i	−0.296116	+	0.955152i	$0.595691\pi$
$42$		0			0
$43$	−5.22216	+	2.51486i	−0.796372	+	0.383512i	−0.787396	−	0.616447i	$-0.788571\pi$
$43$	−5.22216	+	2.51486i	−0.796372	+	0.383512i	−0.00897563	+	0.999960i	$0.502857\pi$
$44$	0.183305	+	2.44604i	0.0276343	+	0.368754i
$45$		0			0
$46$	2.13207	−	1.45362i	0.314357	−	0.214325i
$47$	−9.22899	−	1.39105i	−1.34619	−	0.202905i	−0.563910	−	0.825836i	$-0.690703\pi$
$47$	−9.22899	−	1.39105i	−1.34619	−	0.202905i	−0.782276	+	0.622931i	$0.785942\pi$
$48$		0			0
$49$	2.32025	+	6.60427i	0.331465	+	0.943468i
$50$	3.76747			0.532801
$51$		0			0
$52$	2.32362	−	1.58422i	0.322228	−	0.219692i
$53$	−9.41380	−	2.90377i	−1.29308	−	0.398864i	−0.429500	−	0.903067i	$-0.641310\pi$
$53$	−9.41380	−	2.90377i	−1.29308	−	0.398864i	−0.863585	+	0.504203i	$0.831786\pi$
$54$		0			0
$55$	−2.45351	+	1.18155i	−0.330831	+	0.159320i
$56$	−1.28125	−	2.31482i	−0.171215	−	0.309331i
$57$		0			0
$58$	−2.16317	+	5.51167i	−0.284038	+	0.723717i
$59$	0.588835	−	7.85746i	0.0766598	−	1.02295i	−0.817711	−	0.575628i	$-0.804758\pi$
$59$	0.588835	−	7.85746i	0.0766598	−	1.02295i	0.894371	−	0.447325i	$-0.147623\pi$
$60$		0			0
$61$	6.94339	−	2.14175i	0.889010	−	0.274223i	0.183582	−	0.983004i	$-0.441231\pi$
$61$	6.94339	−	2.14175i	0.889010	−	0.274223i	0.705428	+	0.708781i	$0.250755\pi$
$62$	5.97590	−	7.49355i	0.758941	−	0.951681i
$63$		0			0
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	2.57967	+	1.75879i	0.319969	+	0.218151i
$66$		0			0
$67$	−0.0774217	+	0.134098i	−0.00945856	+	0.0163827i	−0.870716	−	0.491786i	$-0.836344\pi$
$67$	−0.0774217	+	0.134098i	−0.00945856	+	0.0163827i	0.861257	+	0.508169i	$0.169677\pi$
$68$	3.57065	+	6.18455i	0.433005	+	0.749987i
$69$		0			0
$70$	1.87257	−	2.26300i	0.223815	−	0.270480i
$71$	−2.31321	−	10.1348i	−0.274527	−	1.20278i	−0.904605	−	0.426250i	$-0.859834\pi$
$71$	−2.31321	−	10.1348i	−0.274527	−	1.20278i	0.630078	−	0.776531i	$-0.283023\pi$
$72$		0			0
$73$	2.08994	−	0.315008i	0.244609	−	0.0368689i	−0.0255933	−	0.999672i	$-0.508148\pi$
$73$	2.08994	−	0.315008i	0.244609	−	0.0368689i	0.270202	+	0.962804i	$0.412909\pi$
$74$	−7.82094	+	1.17882i	−0.909166	+	0.137035i
$75$		0			0
$76$	1.66949	+	7.31449i	0.191503	+	0.839030i
$77$	1.55820	−	6.29991i	0.177574	−	0.717942i
$78$		0			0
$79$	1.92214	+	3.32924i	0.216257	+	0.374569i	0.953661	−	0.300884i	$-0.0972817\pi$
$79$	1.92214	+	3.32924i	0.216257	+	0.374569i	−0.737403	+	0.675453i	$0.763948\pi$
$80$	−0.555096	+	0.961455i	−0.0620617	+	0.107494i
$81$		0			0
$82$	1.56212	+	1.06503i	0.172507	+	0.117613i
$83$	−3.54971	−	4.45119i	−0.389631	−	0.488582i	0.547870	−	0.836563i	$-0.315439\pi$
$83$	−3.54971	−	4.45119i	−0.389631	−	0.488582i	−0.937501	+	0.347981i	$0.886867\pi$
$84$		0			0
$85$	−4.94317	+	6.19854i	−0.536162	+	0.672326i
$86$	−5.53865	+	1.70845i	−0.597248	+	0.184227i
$87$		0			0
$88$	−0.183305	+	2.44604i	−0.0195404	+	0.260748i
$89$	4.86684	−	12.4005i	0.515884	−	1.31445i	−0.401286	−	0.915953i	$-0.631437\pi$
$89$	4.86684	−	12.4005i	0.515884	−	1.31445i	0.917169	−	0.398497i	$-0.130468\pi$
$90$		0			0
$91$	−7.14852	+	2.06432i	−0.749369	+	0.216399i
$92$	2.32491	−	1.11962i	0.242389	−	0.116728i
$93$		0			0
$94$	−8.91858	−	2.75102i	−0.919882	−	0.283746i
$95$	−6.88202	+	4.69208i	−0.706080	+	0.481397i
$96$		0			0
$97$	8.21789			0.834400			0.417200	−	0.908815i	$-0.363011\pi$
$97$	8.21789			0.834400			0.417200	+	0.908815i	$0.363011\pi$
$98$	1.31002	+	6.87632i	0.132332	+	0.694614i
$99$		0			0
$100$	3.72539	+	0.561513i	0.372539	+	0.0561513i
$101$	−5.80665	+	3.95891i	−0.577784	+	0.393926i	−0.816656	−	0.577125i	$-0.804175\pi$
$101$	−5.80665	+	3.95891i	−0.577784	+	0.393926i	0.238872	+	0.971051i	$0.423222\pi$
$102$		0			0
$103$	0.413381	+	5.51619i	0.0407317	+	0.543526i	0.979824	+	0.199862i	$0.0640493\pi$
$103$	0.413381	+	5.51619i	0.0407317	+	0.543526i	−0.939092	+	0.343665i	$0.888332\pi$
$104$	2.53379	−	1.22021i	0.248458	−	0.119651i
$105$		0			0
$106$	−8.87587	−	4.27439i	−0.862101	−	0.415166i
$107$	−0.312678	+	0.796691i	−0.0302277	+	0.0770190i	−0.945191	−	0.326519i	$-0.894124\pi$
$107$	−0.312678	+	0.796691i	−0.0302277	+	0.0770190i	0.914963	+	0.403538i	$0.132220\pi$
$108$		0			0
$109$	−6.44419	−	16.4195i	−0.617241	−	1.57271i	−0.806793	−	0.590834i	$-0.798799\pi$
$109$	−6.44419	−	16.4195i	−0.617241	−	1.57271i	0.189551	−	0.981871i	$-0.439297\pi$
$110$	−2.60220	+	0.802674i	−0.248110	+	0.0765319i
$111$		0			0
$112$	−0.921938	−	2.47993i	−0.0871149	−	0.234331i
$113$	8.33784	+	10.4553i	0.784358	+	0.983553i	0.999975	+	0.00707552i	$0.00225223\pi$
$113$	8.33784	+	10.4553i	0.784358	+	0.983553i	−0.215617	+	0.976478i	$0.569176\pi$
$114$		0			0
$115$	2.10005	+	1.94856i	0.195831	+	0.181704i
$116$	−2.96048	+	5.12770i	−0.274874	+	0.476095i
$117$		0			0
$118$	1.75335	−	7.68193i	0.161409	−	0.707179i
$119$	−3.87078	−	18.4934i	−0.354834	−	1.69529i
$120$		0			0
$121$	3.65302	−	3.38950i	0.332092	−	0.308137i
$122$	7.18505	−	1.08297i	0.650504	−	0.0980477i
$123$		0			0
$124$	7.02601	−	6.51919i	0.630955	−	0.585440i
$125$	2.16593	+	9.48954i	0.193726	+	0.848771i
$126$		0			0
$127$	−0.905000	+	3.96506i	−0.0803057	+	0.351842i	−0.999077	−	0.0429470i	$-0.986325\pi$
$127$	−0.905000	+	3.96506i	−0.0803057	+	0.351842i	0.918772	+	0.394789i	$0.129182\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	2.28872	+	2.12362i	0.200734	+	0.186254i
$131$	−6.35805	−	4.33485i	−0.555506	−	0.378737i	0.252784	−	0.967523i	$-0.418654\pi$
$131$	−6.35805	−	4.33485i	−0.555506	−	0.378737i	−0.808289	+	0.588785i	$0.799606\pi$
$132$		0			0
$133$	1.84085	−	19.7645i	0.159622	−	1.71380i
$134$	−0.0965432	+	0.121061i	−0.00834006	+	0.0104581i
$135$		0			0
$136$	2.60901	+	6.64766i	0.223721	+	0.570032i
$137$	−0.298165	+	3.97873i	−0.0254739	+	0.339926i	0.969876	+	0.243600i	$0.0783283\pi$
$137$	−0.298165	+	3.97873i	−0.0254739	+	0.339926i	−0.995350	+	0.0963262i	$0.969291\pi$
$138$		0			0
$139$	9.61286	+	4.62931i	0.815352	+	0.392653i	0.794601	−	0.607132i	$-0.207680\pi$
$139$	9.61286	+	4.62931i	0.815352	+	0.392653i	0.0207508	+	0.999785i	$0.493394\pi$
$140$	2.18894	−	1.95863i	0.184999	−	0.165535i
$141$		0			0
$142$	−0.776853	−	10.3664i	−0.0651921	−	0.869928i
$143$	6.59178	+	2.03330i	0.551233	+	0.170033i
$144$		0			0
$145$	−6.49999	−	0.979716i	−0.539795	−	0.0813610i
$146$	2.11355			0.174918
$147$		0			0
$148$	−7.90928			−0.650139
$149$	6.54521	+	0.986532i	0.536205	+	0.0808198i	0.411562	−	0.911382i	$-0.364983\pi$
$149$	6.54521	+	0.986532i	0.536205	+	0.0808198i	0.124643	+	0.992202i	$0.460222\pi$
$150$		0			0
$151$	−15.2987	−	4.71902i	−1.24499	−	0.384029i	−0.398863	−	0.917010i	$-0.630595\pi$
$151$	−15.2987	−	4.71902i	−1.24499	−	0.384029i	−0.846127	+	0.532982i	$0.821071\pi$
$152$	0.560670	+	7.48162i	0.0454763	+	0.606839i
$153$		0			0
$154$	2.47975	−	5.99731i	0.199824	−	0.483277i
$155$	9.58699	+	4.61685i	0.770046	+	0.370835i
$156$		0			0
$157$	0.791544	−	10.5624i	0.0631721	−	0.842973i	−0.872164	−	0.489213i	$-0.837284\pi$
$157$	0.791544	−	10.5624i	0.0631721	−	0.842973i	0.935336	−	0.353760i	$-0.115097\pi$
$158$	1.40447	+	3.57853i	0.111734	+	0.284693i
$159$		0			0
$160$	−0.692194	+	0.867984i	−0.0547227	+	0.0686201i
$161$	−6.76827	+	0.895386i	−0.533415	+	0.0705663i
$162$		0			0
$163$	−18.2155	−	12.4191i	−1.42675	−	0.972740i	−0.997581	−	0.0695139i	$-0.977855\pi$
$163$	−18.2155	−	12.4191i	−1.42675	−	0.972740i	−0.429166	−	0.903226i	$-0.641192\pi$
$164$	1.38593	+	1.28596i	0.108223	+	0.100416i
$165$		0			0
$166$	−2.84664	−	4.93053i	−0.220942	−	0.382684i
$167$	−0.0900139	+	0.394377i	−0.00696549	+	0.0305178i	−0.978291	−	0.207235i	$-0.933554\pi$
$167$	−0.0900139	+	0.394377i	−0.00696549	+	0.0305178i	0.971326	+	0.237753i	$0.0764107\pi$
$168$		0			0
$169$	1.13286	+	4.96339i	0.0871431	+	0.381799i
$170$	−5.81180	+	5.39256i	−0.445745	+	0.413591i
$171$		0			0
$172$	−5.73142	+	0.863873i	−0.437017	+	0.0658697i
$173$	−15.5826	+	14.4586i	−1.18472	+	1.09926i	−0.191688	+	0.981456i	$0.561396\pi$
$173$	−15.5826	+	14.4586i	−1.18472	+	1.09926i	−0.993036	+	0.117808i	$0.962413\pi$
$174$		0			0
$175$	−8.90105	−	4.48645i	−0.672856	−	0.339143i
$176$	−0.545821	+	2.39140i	−0.0411428	+	0.180258i
$177$		0			0
$178$	6.66068	−	11.5366i	0.499239	−	0.864707i
$179$	−10.8591	−	10.0758i	−0.811646	−	0.753097i	0.160610	−	0.987018i	$-0.448654\pi$
$179$	−10.8591	−	10.0758i	−0.811646	−	0.753097i	−0.972256	+	0.233921i	$0.924844\pi$
$180$		0			0
$181$	6.30962	+	7.91202i	0.468991	+	0.588096i	0.958924	−	0.283665i	$-0.0915502\pi$
$181$	6.30962	+	7.91202i	0.468991	+	0.588096i	−0.489933	+	0.871760i	$0.662979\pi$
$182$	−7.37635	+	0.975829i	−0.546772	+	0.0723333i
$183$		0			0
$184$	2.46581	−	0.760603i	0.181782	−	0.0560724i
$185$	−3.20800	−	8.17384i	−0.235857	−	0.600953i
$186$		0			0
$187$	−6.39964	+	16.3060i	−0.467988	+	1.19241i
$188$	−8.40895	−	4.04954i	−0.613286	−	0.295343i
$189$		0			0
$190$	−7.50447	+	3.61396i	−0.544431	+	0.262184i
$191$	0.367143	+	4.89918i	0.0265655	+	0.354492i	0.994608	+	0.103706i	$0.0330701\pi$
$191$	0.367143	+	4.89918i	0.0265655	+	0.354492i	−0.968042	+	0.250786i	$0.919311\pi$
$192$		0			0
$193$	−11.5189	+	7.85347i	−0.829151	+	0.565305i	−0.901850	−	0.432048i	$-0.857791\pi$
$193$	−11.5189	+	7.85347i	−0.829151	+	0.565305i	0.0726996	+	0.997354i	$0.476839\pi$
$194$	8.12610	+	1.22481i	0.583420	+	0.0879365i
$195$		0			0
$196$	0.270526	+	6.99477i	0.0193233	+	0.499626i
$197$	−12.4524			−0.887197			−0.443598	−	0.896226i	$-0.646298\pi$
$197$	−12.4524			−0.887197			−0.443598	+	0.896226i	$0.646298\pi$
$198$		0			0
$199$	12.1522	−	8.28521i	0.861444	−	0.587323i	−0.0499985	−	0.998749i	$-0.515922\pi$
$199$	12.1522	−	8.28521i	0.861444	−	0.587323i	0.911443	+	0.411426i	$0.134969\pi$
$200$	3.60009	+	1.11048i	0.254565	+	0.0785229i
$201$		0			0
$202$	−6.33184	+	3.04926i	−0.445507	+	0.214545i
$203$	11.6742	−	10.4459i	0.819369	−	0.733160i
$204$		0			0
$205$	−0.766840	+	1.95388i	−0.0535584	+	0.136465i
$206$	−0.413381	+	5.51619i	−0.0288016	+	0.384331i
$207$		0			0
$208$	2.68735	−	0.828937i	0.186334	−	0.0574764i
$209$	−11.4741	+	14.3881i	−0.793683	+	0.995247i
$210$		0			0
$211$	−10.2868	−	12.8992i	−0.708172	−	0.888019i	0.289432	−	0.957198i	$-0.406533\pi$
$211$	−10.2868	−	12.8992i	−0.708172	−	0.888019i	−0.997604	+	0.0691791i	$0.977962\pi$
$212$	−8.13967	−	5.54953i	−0.559035	−	0.381143i
$213$		0			0
$214$	−0.427926	+	0.741190i	−0.0292524	+	0.0506667i
$215$	−3.21743	−	5.57275i	−0.219427	−	0.380058i
$216$		0			0
$217$	−23.0423	+	10.5880i	−1.56421	+	0.718758i
$218$	−3.92501	−	17.1966i	−0.265835	−	1.16470i
$219$		0			0
$220$	−2.69277	+	0.405870i	−0.181547	+	0.0273638i
$221$	19.8591	−	2.99328i	1.33587	−	0.201350i
$222$		0			0
$223$	−1.96162	−	8.59441i	−0.131360	−	0.575524i	−0.997172	−	0.0751551i	$-0.976055\pi$
$223$	−1.96162	−	8.59441i	−0.131360	−	0.575524i	0.865812	−	0.500369i	$-0.166802\pi$
$224$	−0.542027	−	2.58963i	−0.0362157	−	0.173027i
$225$		0			0
$226$	6.68643	+	11.5812i	0.444774	+	0.770372i
$227$	10.3726	−	17.9659i	0.688456	−	1.19244i	−0.283882	−	0.958859i	$-0.591622\pi$
$227$	10.3726	−	17.9659i	0.688456	−	1.19244i	0.972337	−	0.233581i	$-0.0750444\pi$
$228$		0			0
$229$	1.39436	+	0.950661i	0.0921422	+	0.0628215i	0.608515	−	0.793543i	$-0.291766\pi$
$229$	1.39436	+	0.950661i	0.0921422	+	0.0628215i	−0.516373	+	0.856364i	$0.672718\pi$
$230$	1.78618	+	2.23979i	0.117777	+	0.147688i
$231$		0			0
$232$	−3.69166	+	4.62919i	−0.242369	+	0.303921i
$233$	8.52316	−	2.62905i	0.558371	−	0.172235i	−0.00270908	−	0.999996i	$-0.500862\pi$
$233$	8.52316	−	2.62905i	0.558371	−	0.172235i	0.561080	+	0.827762i	$0.310386\pi$
$234$		0			0
$235$	0.774330	−	10.3327i	0.0505117	−	0.674032i
$236$	2.87870	−	7.33481i	0.187387	−	0.477455i
$237$		0			0
$238$	−1.07125	−	18.8637i	−0.0694389	−	1.22275i
$239$	16.0232	−	7.71638i	1.03646	−	0.499131i	0.163302	−	0.986576i	$-0.447785\pi$
$239$	16.0232	−	7.71638i	1.03646	−	0.499131i	0.873154	+	0.487445i	$0.162071\pi$
$240$		0			0
$241$	16.3106	+	5.03116i	1.05066	+	0.324085i	0.771546	−	0.636173i	$-0.219484\pi$
$241$	16.3106	+	5.03116i	1.05066	+	0.324085i	0.279112	+	0.960258i	$0.409960\pi$
$242$	4.11740	−	2.80719i	0.264676	−	0.180453i
$243$		0			0
$244$	7.26621			0.465171
$245$	−7.11902	+	3.11665i	−0.454817	+	0.199115i
$246$		0			0
$247$	20.8638	+	3.14471i	1.32753	+	0.200093i
$248$	7.91917	−	5.39920i	0.502868	−	0.342850i
$249$		0			0
$250$	0.727392	+	9.70637i	0.0460043	+	0.613885i
$251$	−1.73431	+	0.835198i	−0.109468	+	0.0527172i	−0.487817	−	0.872946i	$-0.662207\pi$
$251$	−1.73431	+	0.835198i	−0.109468	+	0.0527172i	0.378348	+	0.925663i	$0.376492\pi$
$252$		0			0
$253$	5.70276	+	2.74631i	0.358530	+	0.172659i
$254$	−1.48585	+	3.78589i	−0.0932308	+	0.237548i
$255$		0			0
$256$	0.365341	+	0.930874i	0.0228338	+	0.0581796i
$257$	0.923604	−	0.284894i	0.0576128	−	0.0177712i	−0.265815	−	0.964024i	$-0.585641\pi$
$257$	0.923604	−	0.284894i	0.0576128	−	0.0177712i	0.323428	+	0.946253i	$0.395165\pi$
$258$		0			0
$259$	19.8816	+	6.52839i	1.23538	+	0.405654i
$260$	1.94665	+	2.44102i	0.120726	+	0.151386i
$261$		0			0
$262$	−5.64096	−	5.23405i	−0.348500	−	0.323361i
$263$	−5.36643	+	9.29493i	−0.330908	+	0.573150i	−0.982690	−	0.185257i	$-0.940688\pi$
$263$	−5.36643	+	9.29493i	−0.330908	+	0.573150i	0.651782	+	0.758406i	$0.274022\pi$
$264$		0			0
$265$	2.43372	−	10.6628i	0.149502	−	0.655012i
$266$	4.76603	−	19.2693i	0.292224	−	1.18148i
$267$		0			0
$268$	−0.113508	+	0.105320i	−0.00693362	+	0.00643346i
$269$	−2.13176	+	0.321311i	−0.129975	+	0.0195906i	−0.213708	−	0.976898i	$-0.568554\pi$
$269$	−2.13176	+	0.321311i	−0.129975	+	0.0195906i	0.0837323	+	0.996488i	$0.473316\pi$
$270$		0			0
$271$	−12.8115	+	11.8873i	−0.778242	+	0.722103i	−0.965555	−	0.260197i	$-0.916212\pi$
$271$	−12.8115	+	11.8873i	−0.778242	+	0.722103i	0.187314	+	0.982300i	$0.440022\pi$
$272$	1.58909	+	6.96226i	0.0963528	+	0.422149i
$273$		0			0
$274$	−0.887833	+	3.88985i	−0.0536360	+	0.234994i
$275$	4.62061	+	8.00313i	0.278633	+	0.482607i
$276$		0			0
$277$	−8.17162	−	7.58216i	−0.490985	−	0.455568i	0.395405	−	0.918507i	$-0.370604\pi$
$277$	−8.17162	−	7.58216i	−0.490985	−	0.455568i	−0.886390	+	0.462939i	$0.846795\pi$
$278$	8.81553	+	6.01032i	0.528720	+	0.360475i
$279$		0			0
$280$	2.45641	−	1.61051i	0.146799	−	0.0962464i
$281$	−9.33790	+	11.7094i	−0.557053	+	0.698522i	−0.978010	−	0.208559i	$-0.933123\pi$
$281$	−9.33790	+	11.7094i	−0.557053	+	0.698522i	0.420957	+	0.907080i	$0.361694\pi$
$282$		0			0
$283$	−5.57666	−	14.2091i	−0.331498	−	0.844643i	−0.995309	−	0.0967428i	$-0.969158\pi$
$283$	−5.57666	−	14.2091i	−0.331498	−	0.844643i	0.663812	−	0.747900i	$-0.268938\pi$
$284$	0.776853	−	10.3664i	0.0460977	−	0.615132i
$285$		0			0
$286$	6.21511	+	2.99304i	0.367507	+	0.176982i
$287$	−2.42238	−	4.37648i	−0.142989	−	0.258335i
$288$		0			0
$289$	2.54069	+	33.9032i	0.149453	+	1.99431i
$290$	−6.28137	−	1.93755i	−0.368855	−	0.113777i
$291$		0			0
$292$	2.08994	+	0.315008i	0.122304	+	0.0184344i
$293$	3.57910			0.209093			0.104547	−	0.994520i	$-0.466661\pi$
$293$	3.57910			0.209093			0.104547	+	0.994520i	$0.466661\pi$
$294$		0			0
$295$	8.74775			0.509314
$296$	−7.82094	−	1.17882i	−0.454583	−	0.0685174i
$297$		0			0
$298$	6.32507	+	1.95103i	0.366402	+	0.113020i
$299$	−0.542315	−	7.23670i	−0.0313629	−	0.418509i
$300$		0			0
$301$	15.1201	+	2.55924i	0.871510	+	0.147512i
$302$	−14.4245	−	6.94647i	−0.830036	−	0.399724i
$303$		0			0
$304$	−0.560670	+	7.48162i	−0.0321566	+	0.429100i
$305$	2.94717	+	7.50926i	0.168754	+	0.429979i
$306$		0			0
$307$	−4.38233	+	5.49527i	−0.250113	+	0.313631i	−0.891000	−	0.454004i	$-0.849995\pi$
$307$	−4.38233	+	5.49527i	−0.250113	+	0.313631i	0.640887	+	0.767635i	$0.278567\pi$
$308$	3.34591	−	5.56074i	0.190651	−	0.316852i
$309$		0			0
$310$	8.79181	+	5.99415i	0.499341	+	0.340445i
$311$	−10.7864	−	10.0083i	−0.611641	−	0.567520i	0.312334	−	0.949972i	$-0.398889\pi$
$311$	−10.7864	−	10.0083i	−0.611641	−	0.567520i	−0.923975	+	0.382452i	$0.875080\pi$
$312$		0			0
$313$	−13.7671	−	23.8454i	−0.778165	−	1.34782i	−0.932998	−	0.359880i	$-0.882817\pi$
$313$	−13.7671	−	23.8454i	−0.778165	−	1.34782i	0.154834	−	0.987941i	$-0.450516\pi$
$314$	2.35695	−	10.3265i	0.133010	−	0.582756i
$315$		0			0
$316$	0.855431	+	3.74789i	0.0481218	+	0.210835i
$317$	−3.44450	+	3.19603i	−0.193463	+	0.179507i	−0.770956	−	0.636888i	$-0.780221\pi$
$317$	−3.44450	+	3.19603i	−0.193463	+	0.179507i	0.577494	+	0.816395i	$0.304031\pi$
$318$		0			0
$319$	−14.3613	+	2.16462i	−0.804078	+	0.121195i
$320$	−0.813829	+	0.755123i	−0.0454944	+	0.0422127i
$321$		0			0
$322$	−6.82613	−	0.123374i	−0.380405	−	0.00687535i
$323$	−11.9223	+	52.2350i	−0.663375	+	2.90644i
$324$		0			0
$325$	5.29761	−	9.17573i	0.293859	−	0.508978i
$326$	−16.1611	−	14.9953i	−0.895078	−	0.830511i
$327$		0			0
$328$	1.17879	+	1.47816i	0.0650879	+	0.0816176i
$329$	17.7951	+	17.1202i	0.981075	+	0.943865i
$330$		0			0
$331$	13.3985	−	4.13290i	0.736449	−	0.227164i	0.0962325	−	0.995359i	$-0.469321\pi$
$331$	13.3985	−	4.13290i	0.736449	−	0.227164i	0.640217	+	0.768194i	$0.278845\pi$
$332$	−2.07999	−	5.29973i	−0.114154	−	0.290861i
$333$		0			0
$334$	−0.147787	+	0.376556i	−0.00808657	+	0.0206042i
$335$	−0.154882	−	0.0745872i	−0.00846210	−	0.00407513i
$336$		0			0
$337$	0.524871	−	0.252765i	0.0285915	−	0.0137690i	−0.419533	−	0.907740i	$-0.637806\pi$
$337$	0.524871	−	0.252765i	0.0285915	−	0.0137690i	0.448125	+	0.893971i	$0.352092\pi$
$338$	0.380453	+	5.07679i	0.0206939	+	0.276141i
$339$		0			0
$340$	−6.55061	+	4.46613i	−0.355257	+	0.242210i
$341$	23.2475	+	3.50399i	1.25892	+	0.189752i
$342$		0			0
$343$	5.09352	−	17.8061i	0.275024	−	0.961437i
$344$	−5.79616			−0.312508
$345$		0			0
$346$	−17.5635	+	11.9746i	−0.944220	+	0.643758i
$347$	−8.74461	−	2.69735i	−0.469435	−	0.144802i	0.0510073	−	0.998698i	$-0.483757\pi$
$347$	−8.74461	−	2.69735i	−0.469435	−	0.144802i	−0.520443	+	0.853897i	$0.674233\pi$
$348$		0			0
$349$	−1.69572	+	0.816617i	−0.0907700	+	0.0437125i	−0.478718	−	0.877969i	$-0.658898\pi$
$349$	−1.69572	+	0.816617i	−0.0907700	+	0.0437125i	0.387948	+	0.921681i	$0.373184\pi$
$350$	−8.13296	−	5.76297i	−0.434725	−	0.308044i
$351$		0			0
$352$	−0.896144	+	2.28334i	−0.0477646	+	0.121702i
$353$	2.42652	−	32.3797i	0.129151	−	1.72340i	−0.437311	−	0.899310i	$-0.644069\pi$
$353$	2.42652	−	32.3797i	0.129151	−	1.72340i	0.566462	−	0.824088i	$-0.308312\pi$
$354$		0			0
$355$	11.0282	−	3.40176i	0.585317	−	0.180546i
$356$	8.30573	−	10.4151i	0.440203	−	0.551997i
$357$		0			0
$358$	−9.23608	−	11.5817i	−0.488142	−	0.612111i
$359$	20.7800	+	14.1676i	1.09673	+	0.747735i	0.969733	−	0.244168i	$-0.0785150\pi$
$359$	20.7800	+	14.1676i	1.09673	+	0.747735i	0.126993	+	0.991904i	$0.459467\pi$
$360$		0			0
$361$	−18.6445	+	32.2932i	−0.981289	+	1.69964i
$362$	5.05992	+	8.76405i	0.265944	+	0.460628i
$363$		0			0
$364$	−7.43940	−	0.134458i	−0.389931	−	0.00704751i
$365$	0.522133	+	2.28761i	0.0273297	+	0.119739i
$366$		0			0
$367$	30.2467	−	4.55895i	1.57886	−	0.237975i	0.699679	−	0.714457i	$-0.253326\pi$
$367$	30.2467	−	4.55895i	1.57886	−	0.237975i	0.879184	+	0.476482i	$0.158088\pi$
$368$	2.55163	−	0.384597i	0.133013	−	0.0200485i
$369$		0			0
$370$	−1.95392	−	8.56067i	−0.101579	−	0.445048i
$371$	15.8801	+	20.6684i	0.824452	+	1.07305i
$372$		0			0
$373$	9.14041	+	15.8317i	0.473273	+	0.819732i	0.999532	−	0.0305919i	$-0.00973922\pi$
$373$	9.14041	+	15.8317i	0.473273	+	0.819732i	−0.526259	+	0.850324i	$0.676406\pi$
$374$	−8.75844	+	15.1701i	−0.452888	+	0.784426i
$375$		0			0
$376$	−7.71148	−	5.25760i	−0.397689	−	0.271140i
$377$	10.3820	+	13.0186i	0.534701	+	0.670494i
$378$		0			0
$379$	−7.90209	+	9.90891i	−0.405903	+	0.508986i	−0.942204	−	0.335041i	$-0.891250\pi$
$379$	−7.90209	+	9.90891i	−0.405903	+	0.508986i	0.536301	+	0.844027i	$0.319821\pi$
$380$	−7.95928	+	2.45511i	−0.408303	+	0.125945i
$381$		0			0
$382$	−0.367143	+	4.89918i	−0.0187847	+	0.250664i
$383$	3.16173	−	8.05595i	0.161557	−	0.411640i	−0.827057	−	0.562119i	$-0.809986\pi$
$383$	3.16173	−	8.05595i	0.161557	−	0.411640i	0.988613	+	0.150479i	$0.0480816\pi$
$384$		0			0
$385$	7.10384	+	1.20240i	0.362045	+	0.0612800i
$386$	−12.5608	+	6.04895i	−0.639327	+	0.307883i
$387$		0			0
$388$	7.85279	+	2.42227i	0.398665	+	0.122972i
$389$	−1.34991	+	0.920353i	−0.0684432	+	0.0466638i	−0.597058	−	0.802198i	$-0.703664\pi$
$389$	−1.34991	+	0.920353i	−0.0684432	+	0.0466638i	0.528615	+	0.848862i	$0.322712\pi$
$390$		0			0
$391$	18.4278			0.931935
$392$	−0.775012	+	6.95696i	−0.0391440	+	0.351380i
$393$		0			0
$394$	−12.3133	−	1.85593i	−0.620336	−	0.0935006i
$395$	−3.52629	+	2.40419i	−0.177427	+	0.120968i
$396$		0			0
$397$	2.17303	+	28.9971i	0.109061	+	1.45532i	0.736385	+	0.676563i	$0.236531\pi$
$397$	2.17303	+	28.9971i	0.109061	+	1.45532i	−0.627324	+	0.778759i	$0.715850\pi$
$398$	13.2513	−	6.38148i	0.664227	−	0.319875i
$399$		0			0
$400$	3.39437	+	1.63464i	0.169719	+	0.0817322i
$401$	13.7061	−	34.9226i	0.684451	−	1.74395i	0.0163665	−	0.999866i	$-0.494790\pi$
$401$	13.7061	−	34.9226i	0.684451	−	1.74395i	0.668084	−	0.744086i	$-0.267115\pi$
$402$		0			0
$403$	−9.84765	−	25.0914i	−0.490547	−	1.24989i
$404$	−6.71559	+	2.07149i	−0.334113	+	0.103060i
$405$		0			0
$406$	13.1007	−	8.58929i	0.650177	−	0.426279i
$407$	−12.0961	−	15.1680i	−0.599582	−	0.751852i
$408$		0			0
$409$	−0.884112	−	0.820336i	−0.0437165	−	0.0405630i	0.658012	−	0.753007i	$-0.271398\pi$
$409$	−0.884112	−	0.820336i	−0.0437165	−	0.0405630i	−0.701729	+	0.712444i	$0.747588\pi$
$410$	−1.04948	+	1.81776i	−0.0518303	+	0.0897728i
$411$		0			0
$412$	−1.23091	+	5.39297i	−0.0606426	+	0.265692i
$413$	−13.2904	+	16.0614i	−0.653978	+	0.790331i
$414$		0			0
$415$	4.63336	−	4.29913i	0.227443	−	0.211036i
$416$	2.78088	−	0.419150i	0.136344	−	0.0205505i
$417$		0			0
$418$	−13.4904	+	12.5173i	−0.659838	+	0.612240i
$419$	3.75160	+	16.4368i	0.183278	+	0.802992i	0.980056	+	0.198721i	$0.0636787\pi$
$419$	3.75160	+	16.4368i	0.183278	+	0.802992i	−0.796778	+	0.604272i	$0.793464\pi$
$420$		0			0
$421$	3.66576	−	16.0607i	0.178658	−	0.782753i	−0.803592	−	0.595180i	$-0.797081\pi$
$421$	3.66576	−	16.0607i	0.178658	−	0.782753i	0.982251	−	0.187573i	$-0.0600621\pi$
$422$	−8.24936	−	14.2883i	−0.401573	−	0.695544i
$423$		0			0
$424$	−7.22164	−	6.70070i	−0.350714	−	0.325415i
$425$	22.2297	+	15.1559i	1.07830	+	0.735171i
$426$		0			0
$427$	−18.2651	−	5.99759i	−0.883909	−	0.290244i
$428$	−0.533615	+	0.669133i	−0.0257933	+	0.0323437i
$429$		0			0
$430$	−2.35092	−	5.99004i	−0.113371	−	0.288865i
$431$	2.57822	−	34.4039i	0.124188	−	1.65718i	−0.492753	−	0.870169i	$-0.664009\pi$
$431$	2.57822	−	34.4039i	0.124188	−	1.65718i	0.616941	−	0.787009i	$-0.288372\pi$
$432$		0			0
$433$	−16.4970	−	7.94454i	−0.792796	−	0.381790i	−0.00676457	−	0.999977i	$-0.502153\pi$
$433$	−16.4970	−	7.94454i	−0.792796	−	0.381790i	−0.786031	+	0.618187i	$0.787868\pi$
$434$	−24.3630	+	7.03544i	−1.16946	+	0.337712i
$435$		0			0
$436$	−1.31815	−	17.5895i	−0.0631280	−	0.842385i
$437$	18.5000	+	5.70650i	0.884975	+	0.272979i
$438$		0			0
$439$	−7.83165	−	1.18043i	−0.373784	−	0.0563389i	−0.0405361	−	0.999178i	$-0.512907\pi$
$439$	−7.83165	−	1.18043i	−0.373784	−	0.0563389i	−0.333248	+	0.942839i	$0.608145\pi$
$440$	−2.72319			−0.129823
$441$		0			0
$442$	20.0834			0.955271
$443$	−32.1324	−	4.84318i	−1.52666	−	0.230106i	−0.668584	−	0.743637i	$-0.733099\pi$
$443$	−32.1324	−	4.84318i	−1.52666	−	0.230106i	−0.858071	+	0.513531i	$0.828337\pi$
$444$		0			0
$445$	14.1322	+	4.35921i	0.669932	+	0.206647i
$446$	−0.658778	−	8.79078i	−0.0311940	−	0.416255i
$447$		0			0
$448$	−0.150008	−	2.64150i	−0.00708720	−	0.124799i
$449$	−17.1470	−	8.25755i	−0.809216	−	0.389698i	−0.0169367	−	0.999857i	$-0.505391\pi$
$449$	−17.1470	−	8.25755i	−0.809216	−	0.389698i	−0.792279	+	0.610159i	$0.791106\pi$
$450$		0			0
$451$	−0.346563	+	4.62456i	−0.0163190	+	0.217762i
$452$	4.88565	+	12.4484i	0.229802	+	0.585525i
$453$		0			0
$454$	12.9345	−	16.2193i	0.607044	−	0.761209i
$455$	−2.87846	−	7.74278i	−0.134944	−	0.362987i
$456$		0			0
$457$	20.7034	+	14.1153i	0.968464	+	0.660287i	0.940669	−	0.339326i	$-0.110199\pi$
$457$	20.7034	+	14.1153i	0.968464	+	0.660287i	0.0277950	+	0.999614i	$0.491151\pi$
$458$	1.23710	+	1.14786i	0.0578060	+	0.0536361i
$459$		0			0
$460$	1.43240	+	2.48099i	0.0667861	+	0.115677i
$461$	−6.27621	+	27.4979i	−0.292312	+	1.28070i	0.588986	+	0.808143i	$0.299527\pi$
$461$	−6.27621	+	27.4979i	−0.292312	+	1.28070i	−0.881298	+	0.472560i	$0.843330\pi$
$462$		0			0
$463$	3.80824	+	16.6850i	0.176984	+	0.775417i	0.983012	+	0.183540i	$0.0587556\pi$
$463$	3.80824	+	16.6850i	0.176984	+	0.775417i	−0.806028	+	0.591877i	$0.798387\pi$
$464$	−4.34037	+	4.02728i	−0.201497	+	0.186962i
$465$		0			0
$466$	8.81980	−	1.32937i	0.408569	−	0.0615819i
$467$	−28.6108	+	26.5469i	−1.32395	+	1.22845i	−0.369801	+	0.929111i	$0.620574\pi$
$467$	−28.6108	+	26.5469i	−1.32395	+	1.22845i	−0.954148	+	0.299334i	$0.903235\pi$
$468$		0			0
$469$	0.372258	−	0.171053i	0.0171893	−	0.00789850i
$470$	2.30569	−	10.1019i	0.106354	−	0.465966i
$471$		0			0
$472$	3.93974	−	6.82384i	0.181341	−	0.314093i
$473$	−10.4221	−	9.67027i	−0.479208	−	0.444640i
$474$		0			0
$475$	17.6235	+	22.0991i	0.808620	+	1.01398i
$476$	1.75221	−	18.8127i	0.0803122	−	0.862279i
$477$		0			0
$478$	16.9943	−	5.24205i	0.777302	−	0.239766i
$479$	3.59410	+	9.15762i	0.164219	+	0.418422i	0.989169	−	0.146783i	$-0.0468920\pi$
$479$	3.59410	+	9.15762i	0.164219	+	0.418422i	−0.824950	+	0.565206i	$0.808797\pi$
$480$		0			0
$481$	−8.12635	+	20.7056i	−0.370530	+	0.944094i
$482$	15.3786	+	7.40593i	0.700475	+	0.337331i
$483$		0			0
$484$	4.48980	−	2.16217i	0.204082	−	0.0982806i
$485$	0.681796	+	9.09793i	0.0309588	+	0.413116i
$486$		0			0
$487$	32.4699	−	22.1376i	1.47135	−	1.00315i	0.479255	−	0.877676i	$-0.340907\pi$
$487$	32.4699	−	22.1376i	1.47135	−	1.00315i	0.992097	−	0.125475i	$-0.0400454\pi$
$488$	7.18505	+	1.08297i	0.325252	+	0.0490238i
$489$		0			0
$490$	−7.50401	+	2.02080i	−0.338997	+	0.0912905i
$491$	4.38795			0.198025			0.0990127	−	0.995086i	$-0.468432\pi$
$491$	4.38795			0.198025			0.0990127	+	0.995086i	$0.468432\pi$
$492$		0			0
$493$	−34.9362	+	23.8191i	−1.57345	+	1.07276i
$494$	20.1621	+	6.21918i	0.907135	+	0.279814i
$495$		0			0
$496$	8.63543	−	4.15861i	0.387742	−	0.186727i
$497$	−10.5093	+	25.4168i	−0.471405	+	1.14010i
$498$		0			0
$499$	−4.67159	+	11.9030i	−0.209129	+	0.532852i	−0.996497	−	0.0836317i	$-0.973348\pi$
$499$	−4.67159	+	11.9030i	−0.209129	+	0.532852i	0.787368	+	0.616484i	$0.211443\pi$
$500$	−0.727392	+	9.70637i	−0.0325299	+	0.434082i
$501$		0			0
$502$	−1.83941	+	0.567384i	−0.0820971	+	0.0253236i
$503$	6.82581	−	8.55929i	0.304348	−	0.381640i	−0.606014	−	0.795454i	$-0.707232\pi$
$503$	6.82581	−	8.55929i	0.304348	−	0.381640i	0.910361	+	0.413814i	$0.135804\pi$
$504$		0			0
$505$	−4.86461	−	6.10003i	−0.216472	−	0.271448i
$506$	5.22975	+	3.56558i	0.232491	+	0.158510i
$507$		0			0
$508$	−2.03352	+	3.52215i	−0.0902227	+	0.156270i
$509$	15.1279	+	26.2023i	0.670533	+	1.16140i	0.977753	+	0.209759i	$0.0672679\pi$
$509$	15.1279	+	26.2023i	0.670533	+	1.16140i	−0.307220	+	0.951639i	$0.599399\pi$
$510$		0			0
$511$	−4.99348	−	2.51689i	−0.220898	−	0.111341i
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$		0			0
$514$	0.955750	−	0.144056i	0.0421563	−	0.00635404i
$515$	−6.07261	+	0.915299i	−0.267591	+	0.0403329i
$516$		0			0
$517$	−5.09427	−	22.3195i	−0.224046	−	0.981609i
$518$	18.6865	+	9.41866i	0.821038	+	0.413832i
$519$		0			0
$520$	1.56109	+	2.70389i	0.0684584	+	0.118573i
$521$	16.5143	−	28.6037i	0.723507	−	1.25315i	−0.236079	−	0.971734i	$-0.575862\pi$
$521$	16.5143	−	28.6037i	0.723507	−	1.25315i	0.959586	−	0.281416i	$-0.0908042\pi$
$522$		0			0
$523$	−26.0027	−	17.7283i	−1.13702	−	0.775205i	−0.159738	−	0.987159i	$-0.551065\pi$
$523$	−26.0027	−	17.7283i	−1.13702	−	0.775205i	−0.977280	+	0.211954i	$0.932017\pi$
$524$	−4.79786	−	6.01633i	−0.209596	−	0.262825i
$525$		0			0
$526$	−6.69183	+	8.39128i	−0.291777	+	0.365877i
$527$	65.4057	−	20.1750i	2.84912	−	0.878837i
$528$		0			0
$529$	−1.22118	+	16.2956i	−0.0530949	+	0.708502i
$530$	3.99575	−	10.1810i	0.173564	−	0.442234i
$531$		0			0
$532$	7.58475	−	18.3438i	0.328841	−	0.795304i
$533$	4.79046	−	2.30697i	0.207498	−	0.0999258i
$534$		0			0
$535$	−0.907949	−	0.280065i	−0.0392540	−	0.0121083i
$536$	−0.127938	+	0.0872263i	−0.00552606	+	0.00376760i
$537$		0			0
$538$	−2.15583			−0.0929446
$539$	−13.0005	+	11.2163i	−0.559971	+	0.483120i
$540$		0			0
$541$	31.7454	+	4.78486i	1.36484	+	0.205717i	0.790281	−	0.612744i	$-0.209934\pi$
$541$	31.7454	+	4.78486i	1.36484	+	0.205717i	0.574562	+	0.818461i	$0.305172\pi$
$542$	−14.4401	+	9.84509i	−0.620255	+	0.422883i
$543$		0			0
$544$	0.533671	+	7.12134i	0.0228809	+	0.305325i
$545$	17.6432	−	8.49653i	0.755753	−	0.363951i
$546$		0			0
$547$	6.17146	+	2.97202i	0.263873	+	0.127074i	0.561143	−	0.827719i	$-0.310362\pi$
$547$	6.17146	+	2.97202i	0.263873	+	0.127074i	−0.297270	+	0.954793i	$0.596076\pi$
$548$	−1.45767	+	3.71408i	−0.0622685	+	0.158658i
$549$		0			0
$550$	3.37620	+	8.60241i	0.143961	+	0.366808i
$551$	−42.4490	+	13.0938i	−1.80839	+	0.557814i
$552$		0			0
$553$	0.943239	−	10.1272i	0.0401106	−	0.430651i
$554$	−6.95029	−	8.71539i	−0.295290	−	0.370281i
$555$		0			0
$556$	7.82127	+	7.25708i	0.331696	+	0.307769i
$557$	5.79956	−	10.0451i	0.245735	−	0.425626i	−0.716603	−	0.697481i	$-0.754304\pi$
$557$	5.79956	−	10.0451i	0.245735	−	0.425626i	0.962338	+	0.271856i	$0.0876373\pi$
$558$		0			0
$559$	−3.62720	+	15.8918i	−0.153414	+	0.672151i
$560$	2.66901	−	1.22641i	0.112786	−	0.0518254i
$561$		0			0
$562$	−10.9788	+	10.1868i	−0.463113	+	0.429706i
$563$	3.66347	−	0.552179i	0.154397	−	0.0232716i	−0.0713890	−	0.997449i	$-0.522743\pi$
$563$	3.66347	−	0.552179i	0.154397	−	0.0232716i	0.225786	+	0.974177i	$0.427505\pi$
$564$		0			0
$565$	−10.8832	+	10.0981i	−0.457860	+	0.424832i
$566$	−3.39661	−	14.8815i	−0.142770	−	0.625518i
$567$		0			0
$568$	2.31321	−	10.1348i	0.0970599	−	0.425247i
$569$	0.453693	+	0.785819i	0.0190198	+	0.0329432i	0.875379	−	0.483438i	$-0.160612\pi$
$569$	0.453693	+	0.785819i	0.0190198	+	0.0329432i	−0.856359	+	0.516381i	$0.827279\pi$
$570$		0			0
$571$	−15.1092	−	14.0193i	−0.632299	−	0.586688i	0.297515	−	0.954717i	$-0.403842\pi$
$571$	−15.1092	−	14.0193i	−0.632299	−	0.586688i	−0.929814	+	0.368029i	$0.880033\pi$
$572$	5.69961	+	3.88593i	0.238312	+	0.162479i
$573$		0			0
$574$	−1.74305	−	4.68863i	−0.0727534	−	0.195700i
$575$	6.06144	−	7.60080i	0.252779	−	0.316975i
$576$		0			0
$577$	6.66218	+	16.9750i	0.277350	+	0.706677i	0.999882	+	0.0153395i	$0.00488291\pi$
$577$	6.66218	+	16.9750i	0.277350	+	0.706677i	−0.722532	+	0.691337i	$0.757022\pi$
$578$	−2.54069	+	33.9032i	−0.105679	+	1.41019i
$579$		0			0
$580$	−5.92244	−	2.85210i	−0.245916	−	0.118427i
$581$	0.854038	+	15.0388i	0.0354314	+	0.623914i
$582$		0			0
$583$	−1.80583	−	24.0971i	−0.0747896	−	0.997998i
$584$	2.01965	+	0.622979i	0.0835736	+	0.0257790i
$585$		0			0
$586$	3.53912	+	0.533437i	0.146200	+	0.0220361i
$587$	37.1325			1.53262			0.766312	−	0.642468i	$-0.222090\pi$
$587$	37.1325			1.53262			0.766312	+	0.642468i	$0.222090\pi$
$588$		0			0
$589$	71.9095			2.96298
$590$	8.65005	+	1.30378i	0.356117	+	0.0536760i
$591$		0			0
$592$	−7.55789	−	2.33130i	−0.310627	−	0.0958159i
$593$	−1.50754	−	20.1167i	−0.0619071	−	0.826093i	−0.938592	−	0.345028i	$-0.887869\pi$
$593$	−1.50754	−	20.1167i	−0.0619071	−	0.826093i	0.876685	−	0.481064i	$-0.159750\pi$
$594$		0			0
$595$	20.1527	−	5.81960i	0.826179	−	0.238580i
$596$	5.96364	+	2.87194i	0.244280	+	0.117639i
$597$		0			0
$598$	0.542315	−	7.23670i	0.0221769	−	0.295931i
$599$	−15.8390	−	40.3570i	−0.647162	−	1.64894i	−0.755754	−	0.654856i	$-0.772729\pi$
$599$	−15.8390	−	40.3570i	−0.647162	−	1.64894i	0.108592	−	0.994086i	$-0.465366\pi$
$600$		0			0
$601$	−6.27570	+	7.86947i	−0.255991	+	0.321003i	−0.893175	−	0.449709i	$-0.851528\pi$
$601$	−6.27570	+	7.86947i	−0.255991	+	0.321003i	0.637184	+	0.770712i	$0.280099\pi$
$602$	14.5698	+	4.78420i	0.593822	+	0.194989i
$603$		0			0
$604$	−13.2281	−	9.01874i	−0.538242	−	0.366967i
$605$	4.05555	+	3.76300i	0.164882	+	0.152988i
$606$		0			0
$607$	20.1310	+	34.8680i	0.817093	+	1.41525i	0.907815	+	0.419371i	$0.137749\pi$
$607$	20.1310	+	34.8680i	0.817093	+	1.41525i	−0.0907216	+	0.995876i	$0.528917\pi$
$608$	−1.66949	+	7.31449i	−0.0677066	+	0.296642i
$609$		0			0
$610$	1.79505	+	7.86464i	0.0726795	+	0.318430i
$611$	−19.2410	+	17.8530i	−0.778406	+	0.722255i
$612$		0			0
$613$	−34.3924	+	5.18382i	−1.38910	+	0.209372i	−0.800634	−	0.599153i	$-0.795504\pi$
$613$	−34.3924	+	5.18382i	−1.38910	+	0.209372i	−0.588461	+	0.808526i	$0.700266\pi$
$614$	−5.15241	+	4.78074i	−0.207934	+	0.192935i
$615$		0			0
$616$	4.13732	−	4.99995i	0.166698	−	0.201454i
$617$	9.56905	−	41.9248i	0.385236	−	1.68783i	−0.295536	−	0.955332i	$-0.595498\pi$
$617$	9.56905	−	41.9248i	0.385236	−	1.68783i	0.680772	−	0.732496i	$-0.261645\pi$
$618$		0			0
$619$	−9.56757	+	16.5715i	−0.384553	+	0.666065i	−0.991707	−	0.128519i	$-0.958978\pi$
$619$	−9.56757	+	16.5715i	−0.384553	+	0.666065i	0.607154	+	0.794584i	$0.292311\pi$
$620$	7.80023	+	7.23756i	0.313265	+	0.290667i
$621$		0			0
$622$	−9.17427	−	11.5042i	−0.367855	−	0.461275i
$623$	−29.4748	+	19.3247i	−1.18088	+	0.774229i
$624$		0			0
$625$	7.67440	−	2.36724i	0.306976	−	0.0946896i
$626$	−10.0594	−	25.6309i	−0.402055	−	1.02442i
$627$		0			0
$628$	3.86970	−	9.85985i	0.154418	−	0.393451i
$629$	−50.8891	−	24.5069i	−2.02908	−	0.977153i
$630$		0			0
$631$	−33.2331	+	16.0042i	−1.32299	+	0.637117i	−0.956071	−	0.293136i	$-0.905301\pi$
$631$	−33.2331	+	16.0042i	−1.32299	+	0.637117i	−0.366917	+	0.930254i	$0.619587\pi$
$632$	0.287283	+	3.83352i	0.0114275	+	0.152489i
$633$		0			0
$634$	−3.88238	+	2.64696i	−0.154189	+	0.105124i
$635$	−4.46476	−	0.672954i	−0.177179	−	0.0267054i
$636$		0			0
$637$	18.5895	+	6.47853i	0.736541	+	0.256689i
$638$	−14.5235			−0.574991
$639$		0			0
$640$	−0.917284	+	0.625394i	−0.0362588	+	0.0247209i
$641$	28.6071	+	8.82411i	1.12991	+	0.348531i	0.802678	−	0.596412i	$-0.203408\pi$
$641$	28.6071	+	8.82411i	1.12991	+	0.348531i	0.327233	+	0.944944i	$0.393884\pi$
$642$		0			0
$643$	−0.598326	+	0.288139i	−0.0235957	+	0.0113631i	−0.445644	−	0.895210i	$-0.647025\pi$
$643$	−0.598326	+	0.288139i	−0.0235957	+	0.0113631i	0.422049	+	0.906573i	$0.361311\pi$
$644$	−6.73150	−	1.13938i	−0.265258	−	0.0448978i
$645$		0			0
$646$	−19.5744	+	49.8747i	−0.770143	+	1.96229i
$647$	−1.99857	+	26.6691i	−0.0785720	+	1.04847i	0.809002	+	0.587806i	$0.200008\pi$
$647$	−1.99857	+	26.6691i	−0.0785720	+	1.04847i	−0.887574	+	0.460665i	$0.847611\pi$
$648$		0			0
$649$	18.4689	−	5.69690i	0.724968	−	0.223623i
$650$	6.60601	−	8.28368i	0.259109	−	0.324913i
$651$		0			0
$652$	−13.7456	−	17.2365i	−0.538320	−	0.675032i
$653$	−29.5217	−	20.1275i	−1.15527	−	0.787652i	−0.174857	−	0.984594i	$-0.555946\pi$
$653$	−29.5217	−	20.1275i	−1.15527	−	0.787652i	−0.980415	+	0.196942i	$0.936899\pi$
$654$		0			0
$655$	4.27156	−	7.39857i	0.166904	−	0.289086i
$656$	0.945317	+	1.63734i	0.0369084	+	0.0639273i
$657$		0			0
$658$	15.0447	+	19.5812i	0.586504	+	0.763353i
$659$	−2.51175	−	11.0047i	−0.0978440	−	0.428682i	0.902152	−	0.431418i	$-0.141986\pi$
$659$	−2.51175	−	11.0047i	−0.0978440	−	0.428682i	−0.999996	+	0.00273531i	$0.999129\pi$
$660$		0			0
$661$	12.3978	−	1.86866i	0.482217	−	0.0726825i	0.0965647	−	0.995327i	$-0.469215\pi$
$661$	12.3978	−	1.86866i	0.482217	−	0.0726825i	0.385652	+	0.922644i	$0.373976\pi$
$662$	13.8648	−	2.08979i	0.538872	−	0.0812220i
$663$		0			0
$664$	−1.26688	−	5.55055i	−0.0491643	−	0.215403i
$665$	22.0337	+	0.398232i	0.854432	+	0.0154428i
$666$		0			0
$667$	7.63939	+	13.2318i	0.295798	+	0.512338i
$668$	−0.202260	+	0.350324i	−0.00782566	+	0.0135544i
$669$		0			0
$670$	−0.142035	−	0.0968381i	−0.00548730	−	0.00374118i
$671$	11.1126	+	13.9348i	0.428998	+	0.537946i
$672$		0			0
$673$	−18.8233	+	23.6037i	−0.725586	+	0.909857i	−0.998640	−	0.0521423i	$-0.983395\pi$
$673$	−18.8233	+	23.6037i	−0.725586	+	0.909857i	0.273053	+	0.961999i	$0.411966\pi$
$674$	0.556681	−	0.171713i	0.0214426	−	0.00661415i
$675$		0			0
$676$	−0.380453	+	5.07679i	−0.0146328	+	0.195261i
$677$	15.3346	−	39.0718i	0.589355	−	1.50165i	−0.255582	−	0.966787i	$-0.582267\pi$
$677$	15.3346	−	39.0718i	0.589355	−	1.50165i	0.844937	−	0.534865i	$-0.179638\pi$
$678$		0			0
$679$	−17.7402	−	12.5706i	−0.680807	−	0.482416i
$680$	−7.14309	+	3.43993i	−0.273925	+	0.131915i
$681$		0			0
$682$	22.4656	+	6.92971i	0.860251	+	0.265352i
$683$	20.8432	−	14.2106i	0.797542	−	0.543755i	−0.0945975	−	0.995516i	$-0.530156\pi$
$683$	20.8432	−	14.2106i	0.797542	−	0.543755i	0.892139	+	0.451761i	$0.149204\pi$
$684$		0			0
$685$	−4.42954			−0.169244
$686$	7.69049	−	16.8480i	0.293624	−	0.643261i
$687$		0			0
$688$	−5.73142	−	0.863873i	−0.218508	−	0.0329348i
$689$	−22.8911	+	15.6069i	−0.872081	+	0.594575i
$690$		0			0
$691$	0.186734	+	2.49180i	0.00710371	+	0.0947924i	0.999629	−	0.0272494i	$-0.00867483\pi$
$691$	0.186734	+	2.49180i	0.00710371	+	0.0947924i	−0.992525	+	0.122042i	$0.961056\pi$
$692$	−19.1521	+	9.22315i	−0.728052	+	0.350611i
$693$		0			0
$694$	−8.24492	−	3.97054i	−0.312973	−	0.150720i
$695$	−4.32752	+	11.0264i	−0.164152	+	0.418253i
$696$		0			0
$697$	4.93269	+	12.5683i	0.186839	+	0.476058i
$698$	−1.79849	+	0.554762i	−0.0680740	+	0.0209980i
$699$		0			0
$700$	−7.18320	−	6.91076i	−0.271499	−	0.261202i
$701$	20.6777	+	25.9290i	0.780986	+	0.979325i	0.999994	+	0.00360188i	$0.00114652\pi$
$701$	20.6777	+	25.9290i	0.780986	+	0.979325i	−0.219008	+	0.975723i	$0.570282\pi$
$702$		0			0
$703$	−43.4994	−	40.3616i	−1.64061	−	1.52226i
$704$	−1.22645	+	2.12427i	−0.0462235	+	0.0800615i
$705$		0			0
$706$	7.22537	−	31.6564i	0.271930	−	1.19140i
$707$	18.5908	+	0.336006i	0.699180	+	0.0126368i
$708$		0			0
$709$	2.45190	−	2.27503i	0.0920831	−	0.0854406i	−0.632788	−	0.774325i	$-0.718090\pi$
$709$	2.45190	−	2.27503i	0.0920831	−	0.0854406i	0.724871	+	0.688884i	$0.241899\pi$
$710$	11.4121	−	1.72009i	0.428287	−	0.0645538i
$711$		0			0
$712$	9.76524	−	9.06082i	0.365968	−	0.339569i
$713$	−5.50353	−	24.1126i	−0.206109	−	0.903022i
$714$		0			0
$715$	−1.70415	+	7.46638i	−0.0637317	+	0.279227i
$716$	−7.40676	−	12.8289i	−0.276804	−	0.479438i
$717$		0			0
$718$	18.4363	+	17.1064i	0.688038	+	0.638406i
$719$	1.34882	+	0.919608i	0.0503024	+	0.0342956i	0.588210	−	0.808708i	$-0.299833\pi$
$719$	1.34882	+	0.919608i	0.0503024	+	0.0342956i	−0.537908	+	0.843004i	$0.680785\pi$
$720$		0			0
$721$	7.54554	−	12.5403i	0.281011	−	0.467026i
$722$	−23.2493	+	29.1537i	−0.865249	+	1.08499i
$723$		0			0
$724$	3.69720	+	9.42030i	0.137405	+	0.350103i
$725$	−1.66701	+	22.2447i	−0.0619111	+	0.826147i
$726$		0			0
$727$	−23.4527	−	11.2942i	−0.869812	−	0.418880i	−0.0549193	−	0.998491i	$-0.517490\pi$
$727$	−23.4527	−	11.2942i	−0.869812	−	0.418880i	−0.814893	+	0.579611i	$0.803204\pi$
$728$	−7.33627	−	1.24174i	−0.271900	−	0.0460220i
$729$		0			0
$730$	0.175350	+	2.33988i	0.00648999	+	0.0866030i
$731$	−39.5532	−	12.2006i	−1.46293	−	0.451254i
$732$		0			0
$733$	6.32588	+	0.953473i	0.233652	+	0.0352173i	0.264824	−	0.964297i	$-0.414686\pi$
$733$	6.32588	+	0.953473i	0.233652	+	0.0352173i	−0.0311725	+	0.999514i	$0.509924\pi$
$734$	30.5883			1.12904
$735$		0			0
$736$	2.58046			0.0951169
$737$	−0.375572	−	0.0566084i	−0.0138344	−	0.00208520i
$738$		0			0
$739$	49.7132	+	15.3345i	1.82873	+	0.564088i	0.999990	+	0.00445210i	$0.00141715\pi$
$739$	49.7132	+	15.3345i	1.82873	+	0.564088i	0.828739	+	0.559636i	$0.189059\pi$
$740$	−0.656192	−	8.75627i	−0.0241221	−	0.321887i
$741$		0			0
$742$	12.6222	+	22.8044i	0.463377	+	0.837175i
$743$	0.613550	+	0.295470i	0.0225090	+	0.0108397i	0.445104	−	0.895479i	$-0.353167\pi$
$743$	0.613550	+	0.295470i	0.0225090	+	0.0108397i	−0.422595	+	0.906318i	$0.638881\pi$
$744$		0			0
$745$	−0.549156	+	7.32797i	−0.0201195	+	0.268476i
$746$	6.67874	+	17.0171i	0.244526	+	0.623042i
$747$		0			0
$748$	−10.9216	+	13.6953i	−0.399333	+	0.500748i
$749$	1.89366	−	1.24155i	0.0691928	−	0.0453652i
$750$		0			0
$751$	−28.0846	−	19.1478i	−1.02482	−	0.698712i	−0.0705065	−	0.997511i	$-0.522462\pi$
$751$	−28.0846	−	19.1478i	−1.02482	−	0.698712i	−0.954316	+	0.298799i	$0.903414\pi$
$752$	−6.84174	−	6.34821i	−0.249493	−	0.231495i
$753$		0			0
$754$	8.32573	+	14.4206i	0.303205	+	0.525167i
$755$	3.95512	−	17.3285i	0.143942	−	0.630649i
$756$		0			0
$757$	−1.62172	−	7.10524i	−0.0589426	−	0.258244i	0.936868	−	0.349683i	$-0.113711\pi$
$757$	−1.62172	−	7.10524i	−0.0589426	−	0.258244i	−0.995811	+	0.0914385i	$0.970854\pi$
$758$	−9.29067	+	8.62049i	−0.337452	+	0.313110i
$759$		0			0
$760$	−8.23630	+	1.24142i	−0.298762	+	0.0450311i
$761$	−24.1909	+	22.4459i	−0.876920	+	0.813663i	−0.983550	−	0.180636i	$-0.942184\pi$
$761$	−24.1909	+	22.4459i	−0.876920	+	0.813663i	0.106630	+	0.994299i	$0.465994\pi$
$762$		0			0
$763$	−11.2051	+	45.3028i	−0.405651	+	1.64007i
$764$	−1.09323	+	4.78974i	−0.0395516	+	0.173287i
$765$		0			0
$766$	4.32709	−	7.49474i	0.156344	−	0.270796i
$767$	−16.2440	−	15.0722i	−0.586537	−	0.544226i
$768$		0			0
$769$	−10.8866	−	13.6513i	−0.392579	−	0.492279i	0.545786	−	0.837925i	$-0.316231\pi$
$769$	−10.8866	−	13.6513i	−0.392579	−	0.492279i	−0.938365	+	0.345646i	$0.887660\pi$
$770$	6.84528	+	2.24774i	0.246687	+	0.0810030i
$771$		0			0
$772$	−13.3220	+	4.10930i	−0.479470	+	0.147897i
$773$	−0.959671	−	2.44520i	−0.0345170	−	0.0879478i	0.912576	−	0.408907i	$-0.134090\pi$
$773$	−0.959671	−	2.44520i	−0.0345170	−	0.0879478i	−0.947093	+	0.320959i	$0.895995\pi$
$774$		0			0
$775$	13.1924	−	33.6136i	0.473884	−	1.20744i
$776$	7.40406	+	3.56561i	0.265790	+	0.127998i
$777$		0			0
$778$	−1.47200	+	0.708880i	−0.0527739	+	0.0254146i
$779$	1.06002	+	14.1450i	0.0379792	+	0.506798i
$780$		0			0
$781$	21.0682	−	14.3641i	0.753881	−	0.513987i
$782$	18.2220	+	2.74653i	0.651618	+	0.0982155i
$783$		0			0
$784$	−1.80324	+	6.76375i	−0.0644013	+	0.241563i
$785$	11.7592			0.419704
$786$		0			0
$787$	0.848699	−	0.578633i	0.0302529	−	0.0206260i	−0.548099	−	0.836413i	$-0.684648\pi$
$787$	0.848699	−	0.578633i	0.0302529	−	0.0206260i	0.578352	+	0.815787i	$0.303696\pi$
$788$	−11.8992	−	3.67041i	−0.423891	−	0.130753i
$789$		0			0
$790$	−3.84523	+	1.85177i	−0.136807	+	0.0658829i
$791$	−2.00603	−	35.3243i	−0.0713263	−	1.25599i
$792$		0			0
$793$	7.46562	−	19.0221i	0.265112	−	0.675495i
$794$	−2.17303	+	28.9971i	−0.0771179	+	1.02907i
$795$		0			0
$796$	14.0544	−	4.33521i	0.498145	−	0.153657i
$797$	−4.44287	+	5.57119i	−0.157375	+	0.197342i	−0.854267	−	0.519834i	$-0.825994\pi$
$797$	−4.44287	+	5.57119i	−0.157375	+	0.197342i	0.696893	+	0.717175i	$0.254565\pi$
$798$		0			0
$799$	−41.5565	−	52.1102i	−1.47016	−	1.84353i
$800$	3.11283	+	2.12229i	0.110055	+	0.0750344i
$801$		0			0
$802$	18.7580	−	32.4898i	0.662367	−	1.14725i
$803$	2.59216	+	4.48974i	0.0914752	+	0.158440i
$804$		0			0
$805$	−1.55280	−	7.41879i	−0.0547290	−	0.261478i
$806$	−5.99798	−	26.2789i	−0.211270	−	0.925634i
$807$		0			0
$808$	−6.94932	+	1.04744i	−0.244476	+	0.0368489i
$809$	47.1247	−	7.10291i	1.65682	−	0.249725i	0.747027	−	0.664793i	$-0.231480\pi$
$809$	47.1247	−	7.10291i	1.65682	−	0.249725i	0.909790	+	0.415068i	$0.136242\pi$
$810$		0			0
$811$	−2.47996	−	10.8654i	−0.0870831	−	0.381536i	0.912540	−	0.408987i	$-0.134118\pi$
$811$	−2.47996	−	10.8654i	−0.0870831	−	0.381536i	−0.999623	+	0.0274513i	$0.991261\pi$
$812$	14.2346	−	6.54080i	0.499535	−	0.229537i
$813$		0			0
$814$	−9.70032	−	16.8015i	−0.339996	−	0.588891i
$815$	12.2378	−	21.1965i	0.428672	−	0.742481i
$816$		0			0
$817$	−35.9300	−	24.4967i	−1.25703	−	0.857030i
$818$	−0.751973	−	0.942944i	−0.0262921	−	0.0329693i
$819$		0			0
$820$	−1.30869	+	1.64104i	−0.0457013	+	0.0573076i
$821$	9.83768	−	3.03452i	0.343337	−	0.105906i	−0.118291	−	0.992979i	$-0.537742\pi$
$821$	9.83768	−	3.03452i	0.343337	−	0.105906i	0.461628	+	0.887073i	$0.347265\pi$
$822$		0			0
$823$	1.23089	−	16.4251i	0.0429061	−	0.572542i	−0.933777	−	0.357856i	$-0.883508\pi$
$823$	1.23089	−	16.4251i	0.0429061	−	0.572542i	0.976683	−	0.214687i	$-0.0688730\pi$
$824$	−2.02094	+	5.14927i	−0.0704028	+	0.179383i
$825$		0			0
$826$	−15.5358	+	13.9012i	−0.540560	+	0.483685i
$827$	−2.91100	+	1.40187i	−0.101225	+	0.0487476i	−0.483811	−	0.875172i	$-0.660748\pi$
$827$	−2.91100	+	1.40187i	−0.101225	+	0.0487476i	0.382586	+	0.923920i	$0.375034\pi$
$828$		0			0
$829$	−27.1786	−	8.38349i	−0.943952	−	0.291171i	−0.215684	−	0.976463i	$-0.569198\pi$
$829$	−27.1786	−	8.38349i	−0.943952	−	0.291171i	−0.728268	+	0.685292i	$0.759674\pi$
$830$	5.22236	−	3.56055i	0.181271	−	0.123588i
$831$		0			0
$832$	2.81229			0.0974986
$833$	−19.9327	+	45.8432i	−0.690627	+	1.58837i
$834$		0			0
$835$	−0.444078	−	0.0669340i	−0.0153680	−	0.00231635i
$836$	−15.2054	+	10.3668i	−0.525888	+	0.358544i
$837$		0			0
$838$	1.25992	+	16.8124i	0.0435231	+	0.580775i
$839$	15.6822	−	7.55214i	0.541409	−	0.260729i	−0.143131	−	0.989704i	$-0.545717\pi$
$839$	15.6822	−	7.55214i	0.541409	−	0.260729i	0.684541	+	0.728975i	$0.260003\pi$
$840$		0			0
$841$	−5.45787	−	2.62837i	−0.188203	−	0.0906336i
$842$	6.01855	−	15.3350i	0.207413	−	0.528479i
$843$		0			0
$844$	−6.02766	−	15.3582i	−0.207481	−	0.528652i
$845$	−5.40092	+	1.66596i	−0.185797	+	0.0573109i
$846$		0			0
$847$	−13.0707	+	1.72914i	−0.449114	+	0.0594141i
$848$	−6.14229	−	7.70219i	−0.210927	−	0.264494i
$849$		0			0
$850$	19.7225	+	18.2998i	0.676477	+	0.627679i
$851$	−10.2048	+	17.6752i	−0.349815	+	0.605898i
$852$		0			0
$853$	−3.31494	+	14.5237i	−0.113502	+	0.497283i	0.885938	+	0.463804i	$0.153516\pi$
$853$	−3.31494	+	14.5237i	−0.113502	+	0.497283i	−0.999439	+	0.0334787i	$0.989341\pi$
$854$	−17.1672	−	8.65287i	−0.587449	−	0.296095i
$855$		0			0
$856$	−0.627384	+	0.582128i	−0.0214436	+	0.0198967i
$857$	−26.2016	+	3.94925i	−0.895028	+	0.134904i	−0.580420	−	0.814318i	$-0.697111\pi$
$857$	−26.2016	+	3.94925i	−0.895028	+	0.134904i	−0.314609	+	0.949221i	$0.601873\pi$
$858$		0			0
$859$	22.3290	−	20.7182i	0.761854	−	0.706897i	−0.200200	−	0.979755i	$-0.564159\pi$
$859$	22.3290	−	20.7182i	0.761854	−	0.706897i	0.962054	+	0.272858i	$0.0879688\pi$
$860$	−1.43189	−	6.27352i	−0.0488270	−	0.213925i
$861$		0			0
$862$	7.67706	−	33.6354i	0.261482	−	1.14563i
$863$	6.75965	+	11.7081i	0.230101	+	0.398547i	0.957838	−	0.287310i	$-0.0927610\pi$
$863$	6.75965	+	11.7081i	0.230101	+	0.398547i	−0.727737	+	0.685857i	$0.759428\pi$
$864$		0			0
$865$	−17.2997	−	16.0518i	−0.588208	−	0.545777i
$866$	−15.1287	−	10.3146i	−0.514094	−	0.350503i
$867$		0			0
$868$	−25.1395	+	3.32574i	−0.853289	+	0.112883i
$869$	−5.87926	+	7.37236i	−0.199440	+	0.250090i
$870$		0			0
$871$	0.159093	+	0.405362i	0.00539066	+	0.0137352i
$872$	1.31815	−	17.5895i	0.0446382	−	0.595656i
$873$		0			0
$874$	17.4429	+	8.40004i	0.590014	+	0.284136i
$875$	9.84016	−	23.7985i	0.332658	−	0.804537i
$876$		0			0
$877$	−1.04781	−	13.9821i	−0.0353821	−	0.472141i	−0.986549	−	0.163465i	$-0.947733\pi$
$877$	−1.04781	−	13.9821i	−0.0353821	−	0.472141i	0.951167	−	0.308677i	$-0.0998861\pi$
$878$	−7.56824	−	2.33449i	−0.255416	−	0.0787853i
$879$		0			0
$880$	−2.69277	−	0.405870i	−0.0907733	−	0.0136819i
$881$	−57.1541			−1.92557			−0.962786	−	0.270266i	$-0.912888\pi$
$881$	−57.1541			−1.92557			−0.962786	+	0.270266i	$0.912888\pi$
$882$		0			0
$883$	16.4973			0.555179			0.277590	−	0.960700i	$-0.410464\pi$
$883$	16.4973			0.555179			0.277590	+	0.960700i	$0.410464\pi$
$884$	19.8591	+	2.99328i	0.667934	+	0.100675i
$885$		0			0
$886$	−31.0516	−	9.57816i	−1.04320	−	0.321785i
$887$	0.413071	+	5.51205i	0.0138696	+	0.185076i	0.999836	+	0.0181306i	$0.00577145\pi$
$887$	0.413071	+	5.51205i	0.0138696	+	0.185076i	−0.985966	+	0.166946i	$0.946610\pi$
$888$		0			0
$889$	8.01887	−	7.17516i	0.268944	−	0.240647i
$890$	13.3247	+	6.41682i	0.446644	+	0.215092i
$891$		0			0
$892$	0.658778	−	8.79078i	0.0220575	−	0.294337i
$893$	−25.5825	−	65.1830i	−0.856084	−	2.18127i
$894$		0			0
$895$	10.2538	−	12.8579i	0.342748	−	0.429792i
$896$	0.245362	−	2.63435i	0.00819697	−	0.0880074i
$897$		0			0
$898$	−15.7247	−	10.7209i	−0.524741	−	0.357763i
$899$	41.6008	+	38.5999i	1.38746	+	1.28738i
$900$		0			0
$901$	−35.1762	−	60.9269i	−1.17189	−	2.02977i
$902$	−1.03195	+	4.52126i	−0.0343601	+	0.150541i
$903$		0			0
$904$	2.97574	+	13.0376i	0.0989716	+	0.433623i
$905$	−8.23582	+	7.64173i	−0.273768	+	0.254020i
$906$		0			0
$907$	18.0329	−	2.71802i	0.598771	−	0.0902502i	0.157339	−	0.987545i	$-0.449709\pi$
$907$	18.0329	−	2.71802i	0.598771	−	0.0902502i	0.441432	+	0.897294i	$0.354470\pi$
$908$	15.2074	−	14.1104i	0.504674	−	0.468269i
$909$		0			0
$910$	−1.69231	−	8.08531i	−0.0560994	−	0.268026i
$911$	−4.60182	+	20.1619i	−0.152465	+	0.667993i	0.839699	+	0.543052i	$0.182731\pi$
$911$	−4.60182	+	20.1619i	−0.152465	+	0.667993i	−0.992164	+	0.124941i	$0.960126\pi$
$912$		0			0
$913$	6.98252	−	12.0941i	0.231088	−	0.400256i
$914$	18.3684	+	17.0434i	0.607572	+	0.563744i
$915$		0			0
$916$	1.05220	+	1.31942i	0.0347658	+	0.0435949i
$917$	7.09447	+	19.0835i	0.234280	+	0.630191i
$918$		0			0
$919$	−38.3618	+	11.8330i	−1.26544	+	0.390336i	−0.853604	−	0.520922i	$-0.825588\pi$
$919$	−38.3618	+	11.8330i	−1.26544	+	0.390336i	−0.411835	+	0.911259i	$0.635112\pi$
$920$	1.04663	+	2.66677i	0.0345064	+	0.0879208i
$921$		0			0
$922$	−10.3045	+	26.2553i	−0.339359	+	0.864673i
$923$	−26.3398	−	12.6846i	−0.866986	−	0.417519i
$924$		0			0
$925$	−26.8471	+	12.9289i	−0.882726	+	0.425098i
$926$	1.27894	+	17.0662i	0.0420284	+	0.560830i
$927$		0			0
$928$	−4.89213	+	3.33540i	−0.160592	+	0.109490i
$929$	−32.1796	−	4.85030i	−1.05578	−	0.159133i	−0.401863	−	0.915700i	$-0.631637\pi$
$929$	−32.1796	−	4.85030i	−1.05578	−	0.159133i	−0.653917	+	0.756567i	$0.726875\pi$
$930$		0			0
$931$	−34.2069	+	39.8503i	−1.12109	+	1.30604i
$932$	8.91942			0.292165
$933$		0			0
$934$	−32.2478	+	21.9862i	−1.05518	+	0.719411i
$935$	−18.5831	−	5.73214i	−0.607734	−	0.187461i
$936$		0			0
$937$	−8.00970	+	3.85727i	−0.261665	+	0.126011i	−0.560117	−	0.828413i	$-0.689244\pi$
$937$	−8.00970	+	3.85727i	−0.261665	+	0.126011i	0.298452	+	0.954425i	$0.403530\pi$
$938$	0.393594	−	0.113660i	0.0128513	−	0.00371114i
$939$		0			0
$940$	3.78555	−	9.64542i	0.123471	−	0.314599i
$941$	−0.841953	+	11.2351i	−0.0274469	+	0.366253i	0.966521	+	0.256586i	$0.0825977\pi$
$941$	−0.841953	+	11.2351i	−0.0274469	+	0.366253i	−0.993968	+	0.109667i	$0.965021\pi$
$942$		0			0
$943$	4.66195	−	1.43802i	0.151814	−	0.0468284i
$944$	4.91278	−	6.16043i	0.159897	−	0.200505i
$945$		0			0
$946$	−8.86439	−	11.1156i	−0.288206	−	0.361399i
$947$	24.3608	+	16.6089i	0.791620	+	0.539717i	0.890285	−	0.455404i	$-0.150505\pi$
$947$	24.3608	+	16.6089i	0.791620	+	0.539717i	−0.0986655	+	0.995121i	$0.531457\pi$
$948$		0			0
$949$	2.97195	−	5.14757i	0.0964737	−	0.167097i
$950$	14.1329	+	24.4789i	0.458532	+	0.794201i
$951$		0			0
$952$	4.53652	−	18.3414i	0.147030	−	0.594449i
$953$	−11.9858	−	52.5133i	−0.388259	−	1.70107i	−0.670651	−	0.741773i	$-0.733985\pi$
$953$	−11.9858	−	52.5133i	−0.388259	−	1.70107i	0.282393	−	0.959299i	$-0.408872\pi$
$954$		0			0
$955$	−5.39337	+	0.812919i	−0.174525	+	0.0263054i
$956$	17.5858	−	2.65063i	0.568765	−	0.0857276i
$957$		0			0
$958$	2.18909	+	9.59101i	0.0707261	+	0.309871i
$959$	6.72978	−	8.13292i	0.217316	−	0.262626i
$960$		0			0
$961$	−30.4323	−	52.7104i	−0.981689	−	1.70033i
$962$	−11.1216	+	19.2632i	−0.358575	+	0.621069i
$963$		0			0
$964$	14.1030	+	9.61527i	0.454228	+	0.309687i
$965$	−9.65016	−	12.1009i	−0.310650	−	0.389542i
$966$		0			0
$967$	−9.36942	+	11.7489i	−0.301300	+	0.377819i	−0.909316	−	0.416106i	$-0.863394\pi$
$967$	−9.36942	+	11.7489i	−0.301300	+	0.377819i	0.608016	+	0.793925i	$0.291966\pi$
$968$	4.76191	−	1.46885i	0.153053	−	0.0472107i
$969$		0			0
$970$	−0.681796	+	9.09793i	−0.0218911	+	0.292117i
$971$	−3.19052	+	8.12930i	−0.102389	+	0.260882i	−0.972884	−	0.231295i	$-0.925704\pi$
$971$	−3.19052	+	8.12930i	−0.102389	+	0.260882i	0.870495	+	0.492177i	$0.163799\pi$
$972$		0			0
$973$	−13.6703	−	24.6979i	−0.438250	−	0.791778i
$974$	35.4067	−	17.0510i	1.13450	−	0.546348i
$975$		0			0
$976$	6.94339	+	2.14175i	0.222252	+	0.0685558i
$977$	−43.4647	+	29.6338i	−1.39056	+	0.948068i	−0.390943	+	0.920415i	$0.627851\pi$
$977$	−43.4647	+	29.6338i	−1.39056	+	0.948068i	−0.999618	+	0.0276531i	$0.991197\pi$
$978$		0			0
$979$	32.6759			1.04433
$980$	−7.72139	+	0.879816i	−0.246651	+	0.0281047i
$981$		0			0
$982$	4.33894	+	0.653990i	0.138461	+	0.0208697i
$983$	2.32922	−	1.58804i	0.0742907	−	0.0506505i	−0.525605	−	0.850729i	$-0.676161\pi$
$983$	2.32922	−	1.58804i	0.0742907	−	0.0506505i	0.599896	+	0.800078i	$0.295209\pi$
$984$		0			0
$985$	−1.03311	−	13.7859i	−0.0329177	−	0.439256i
$986$	−38.0960	+	18.3461i	−1.21322	+	0.584258i
$987$		0			0
$988$	19.0100	+	9.15472i	0.604788	+	0.291250i
$989$	−5.46431	+	13.9228i	−0.173755	+	0.442720i
$990$		0			0
$991$	12.3434	+	31.4506i	0.392103	+	0.999061i	0.981542	+	0.191248i	$0.0612536\pi$
$991$	12.3434	+	31.4506i	0.392103	+	0.999061i	−0.589439	+	0.807813i	$0.700651\pi$
$992$	9.15879	−	2.82511i	0.290792	−	0.0896974i
$993$		0			0
$994$	−14.1801	+	23.5666i	−0.449765	+	0.747486i
$995$	10.1807	+	12.7661i	0.322749	+	0.404714i
$996$		0			0
$997$	−25.5048	−	23.6650i	−0.807746	−	0.749478i	0.163759	−	0.986500i	$-0.447638\pi$
$997$	−25.5048	−	23.6650i	−0.807746	−	0.749478i	−0.971504	+	0.237022i	$0.923829\pi$
$998$	−6.39346	+	11.0738i	−0.202381	+	0.350535i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.z.a.235.1		24
3.2	odd	2		294.2.m.b.235.2	✓	24
49.44	even	21	inner	882.2.z.a.289.1		24
147.44	odd	42		294.2.m.b.289.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.235.2	✓	24	3.2	odd	2
294.2.m.b.289.2	yes	24	147.44	odd	42
882.2.z.a.235.1		24	1.1	even	1	trivial
882.2.z.a.289.1		24	49.44	even	21	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.z (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988831 + 0.149042i) q^{2} +(0.955573 + 0.294755i) q^{4} +(0.0829648 + 1.10709i) q^{5} +(-2.15873 - 1.52966i) q^{7} +(0.900969 + 0.433884i) q^{8} +O(q^{10})\)	\(q+(0.988831 + 0.149042i) q^{2} +(0.955573 + 0.294755i) q^{4} +(0.0829648 + 1.10709i) q^{5} +(-2.15873 - 1.52966i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.0829648 + 1.10709i) q^{10} +(0.896144 + 2.28334i) q^{11} +(1.75343 - 2.19874i) q^{13} +(-1.90664 - 1.83432i) q^{14} +(0.826239 + 0.563320i) q^{16} +(5.23495 + 4.85732i) q^{17} +(3.75130 + 6.49744i) q^{19} +(-0.247041 + 1.08236i) q^{20} +(0.545821 + 2.39140i) q^{22} +(1.89161 - 1.75516i) q^{23} +(3.72539 - 0.561513i) q^{25} +(2.06155 - 1.91284i) q^{26} +(-1.61195 - 2.09800i) q^{28} +(-1.31754 + 5.77251i) q^{29} +(4.79230 - 8.30051i) q^{31} +(0.733052 + 0.680173i) q^{32} +(4.45253 + 5.58330i) q^{34} +(1.51438 - 2.51682i) q^{35} +(-7.55789 + 2.33130i) q^{37} +(2.74101 + 6.98397i) q^{38} +(-0.405599 + 1.03345i) q^{40} +(1.70340 + 0.820316i) q^{41} +(-5.22216 + 2.51486i) q^{43} +(0.183305 + 2.44604i) q^{44} +(2.13207 - 1.45362i) q^{46} +(-9.22899 - 1.39105i) q^{47} +(2.32025 + 6.60427i) q^{49} +3.76747 q^{50} +(2.32362 - 1.58422i) q^{52} +(-9.41380 - 2.90377i) q^{53} +(-2.45351 + 1.18155i) q^{55} +(-1.28125 - 2.31482i) q^{56} +(-2.16317 + 5.51167i) q^{58} +(0.588835 - 7.85746i) q^{59} +(6.94339 - 2.14175i) q^{61} +(5.97590 - 7.49355i) q^{62} +(0.623490 + 0.781831i) q^{64} +(2.57967 + 1.75879i) q^{65} +(-0.0774217 + 0.134098i) q^{67} +(3.57065 + 6.18455i) q^{68} +(1.87257 - 2.26300i) q^{70} +(-2.31321 - 10.1348i) q^{71} +(2.08994 - 0.315008i) q^{73} +(-7.82094 + 1.17882i) q^{74} +(1.66949 + 7.31449i) q^{76} +(1.55820 - 6.29991i) q^{77} +(1.92214 + 3.32924i) q^{79} +(-0.555096 + 0.961455i) q^{80} +(1.56212 + 1.06503i) q^{82} +(-3.54971 - 4.45119i) q^{83} +(-4.94317 + 6.19854i) q^{85} +(-5.53865 + 1.70845i) q^{86} +(-0.183305 + 2.44604i) q^{88} +(4.86684 - 12.4005i) q^{89} +(-7.14852 + 2.06432i) q^{91} +(2.32491 - 1.11962i) q^{92} +(-8.91858 - 2.75102i) q^{94} +(-6.88202 + 4.69208i) q^{95} +8.21789 q^{97} +(1.31002 + 6.87632i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{4} - q^{5} + 4 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 + 2 * q^4 - q^5 + 4 * q^8	\( 24 q - 2 q^{2} + 2 q^{4} - q^{5} + 4 q^{8} + q^{10} - 8 q^{11} - 2 q^{13} + 2 q^{16} - 9 q^{17} - 4 q^{19} - 5 q^{20} + 5 q^{22} + 38 q^{23} - 19 q^{25} + 20 q^{26} - 14 q^{28} + 14 q^{29} + 4 q^{31} - 2 q^{32} + 17 q^{34} - 42 q^{35} + 7 q^{37} + 18 q^{38} - 13 q^{40} - 2 q^{41} + 4 q^{43} + 6 q^{44} + 11 q^{46} + 8 q^{47} - 42 q^{49} + 4 q^{50} + 15 q^{52} + 10 q^{53} + 33 q^{55} + 7 q^{56} - 28 q^{58} - 14 q^{59} + 7 q^{61} + 8 q^{62} - 4 q^{64} - 23 q^{65} + 23 q^{67} - 9 q^{68} + 28 q^{70} - 36 q^{71} + 15 q^{73} + 14 q^{74} + q^{76} + 28 q^{77} + 38 q^{79} - 8 q^{80} - q^{82} - 27 q^{83} - 47 q^{85} - 26 q^{86} - 6 q^{88} + 121 q^{89} + 21 q^{91} + q^{92} - q^{94} - 44 q^{95} + 14 q^{97} + 21 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 2 * q^4 - q^5 + 4 * q^8 + q^10 - 8 * q^11 - 2 * q^13 + 2 * q^16 - 9 * q^17 - 4 * q^19 - 5 * q^20 + 5 * q^22 + 38 * q^23 - 19 * q^25 + 20 * q^26 - 14 * q^28 + 14 * q^29 + 4 * q^31 - 2 * q^32 + 17 * q^34 - 42 * q^35 + 7 * q^37 + 18 * q^38 - 13 * q^40 - 2 * q^41 + 4 * q^43 + 6 * q^44 + 11 * q^46 + 8 * q^47 - 42 * q^49 + 4 * q^50 + 15 * q^52 + 10 * q^53 + 33 * q^55 + 7 * q^56 - 28 * q^58 - 14 * q^59 + 7 * q^61 + 8 * q^62 - 4 * q^64 - 23 * q^65 + 23 * q^67 - 9 * q^68 + 28 * q^70 - 36 * q^71 + 15 * q^73 + 14 * q^74 + q^76 + 28 * q^77 + 38 * q^79 - 8 * q^80 - q^82 - 27 * q^83 - 47 * q^85 - 26 * q^86 - 6 * q^88 + 121 * q^89 + 21 * q^91 + q^92 - q^94 - 44 * q^95 + 14 * q^97 + 21 * q^98

Introduction

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