LMFDB - Embedded newform 864.2.bn.a.683.41

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			683.41
Character	$\chi$	$=$	864.683
Dual form			864.2.bn.a.611.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31237 + 0.526966i) q^{2} +(1.44461 + 1.38314i) q^{4} +(-0.197197 - 1.49786i) q^{5} +(-0.749169 - 2.79594i) q^{7} +(1.16699 + 2.57646i) q^{8} +O(q^{10})$	\(q+(1.31237 + 0.526966i) q^{2} +(1.44461 + 1.38314i) q^{4} +(-0.197197 - 1.49786i) q^{5} +(-0.749169 - 2.79594i) q^{7} +(1.16699 + 2.57646i) q^{8} +(0.530525 - 2.06965i) q^{10} +(2.13008 - 1.63447i) q^{11} +(3.66441 - 4.77555i) q^{13} +(0.490179 - 4.06408i) q^{14} +(0.173820 + 3.99622i) q^{16} -6.71770 q^{17} +(0.341097 - 0.141287i) q^{19} +(1.78688 - 2.43658i) q^{20} +(3.65676 - 1.02254i) q^{22} +(1.19267 + 0.319575i) q^{23} +(2.62494 - 0.703350i) q^{25} +(7.32561 - 4.33626i) q^{26} +(2.78493 - 5.07526i) q^{28} +(4.33716 + 0.570998i) q^{29} +(-2.61091 + 1.50741i) q^{31} +(-1.87776 + 5.33611i) q^{32} +(-8.81608 - 3.54000i) q^{34} +(-4.04018 + 1.67350i) q^{35} +(-1.12563 + 2.71752i) q^{37} +(0.522098 - 0.00567395i) q^{38} +(3.62904 - 2.25606i) q^{40} +(0.617779 - 2.30558i) q^{41} +(4.06261 + 5.29450i) q^{43} +(5.33785 + 0.585034i) q^{44} +(1.39681 + 1.04790i) q^{46} +(7.66225 + 4.42380i) q^{47} +(-1.19384 + 0.689264i) q^{49} +(3.81552 + 0.460199i) q^{50} +(11.8989 - 1.83042i) q^{52} +(4.18058 - 10.0928i) q^{53} +(-2.86824 - 2.86824i) q^{55} +(6.32934 - 5.19305i) q^{56} +(5.39105 + 3.03489i) q^{58} +(-11.3742 + 1.49744i) q^{59} +(-0.560911 + 4.26054i) q^{61} +(-4.22082 + 0.602414i) q^{62} +(-5.27625 + 6.01342i) q^{64} +(-7.87571 - 4.54704i) q^{65} +(-9.36140 + 12.2000i) q^{67} +(-9.70448 - 9.29155i) q^{68} +(-6.18408 + 0.0672062i) q^{70} +(0.817505 + 0.817505i) q^{71} +(-5.70168 + 5.70168i) q^{73} +(-2.90928 + 2.97321i) q^{74} +(0.688174 + 0.267681i) q^{76} +(-6.16566 - 4.73108i) q^{77} +(-1.89149 + 3.27615i) q^{79} +(5.95149 - 1.04840i) q^{80} +(2.02572 - 2.70022i) q^{82} +(0.820020 + 0.107958i) q^{83} +(1.32471 + 10.0622i) q^{85} +(2.54162 + 9.08918i) q^{86} +(6.69693 + 3.58064i) q^{88} +(4.98702 - 4.98702i) q^{89} +(-16.0974 - 6.66777i) q^{91} +(1.28093 + 2.11130i) q^{92} +(7.72449 + 9.84340i) q^{94} +(-0.278891 - 0.483053i) q^{95} +(9.22126 - 15.9717i) q^{97} +(-1.92997 + 0.275454i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.31237	+	0.526966i	0.927984	+	0.372621i
$2$	1.31237	+	0.526966i	0.927984	+	0.372621i
$3$		0			0
$3$		0			0
$4$	1.44461	+	1.38314i	0.722307	+	0.691572i
$5$	−0.197197	−	1.49786i	−0.0881890	−	0.669862i	−0.977253	−	0.212078i	$-0.931977\pi$
$5$	−0.197197	−	1.49786i	−0.0881890	−	0.669862i	0.889064	−	0.457784i	$-0.151357\pi$
$6$		0			0
$7$	−0.749169	−	2.79594i	−0.283159	−	1.05677i	−0.950174	−	0.311721i	$-0.899095\pi$
$7$	−0.749169	−	2.79594i	−0.283159	−	1.05677i	0.667014	−	0.745045i	$-0.267572\pi$
$8$	1.16699	+	2.57646i	0.412595	+	0.910915i
$9$		0			0
$10$	0.530525	−	2.06965i	0.167767	−	0.654482i
$11$	2.13008	−	1.63447i	0.642243	−	0.492811i	−0.235542	−	0.971864i	$-0.575687\pi$
$11$	2.13008	−	1.63447i	0.642243	−	0.492811i	0.877786	+	0.479053i	$0.159020\pi$
$12$		0			0
$13$	3.66441	−	4.77555i	1.01632	−	1.32450i	0.0713167	−	0.997454i	$-0.477280\pi$
$13$	3.66441	−	4.77555i	1.01632	−	1.32450i	0.945008	−	0.327047i	$-0.106053\pi$
$14$	0.490179	−	4.06408i	0.131006	−	1.08617i
$15$		0			0
$16$	0.173820	+	3.99622i	0.0434550	+	0.999055i
$17$	−6.71770			−1.62928			−0.814641	−	0.579966i	$-0.803066\pi$
$17$	−6.71770			−1.62928			−0.814641	+	0.579966i	$0.803066\pi$
$18$		0			0
$19$	0.341097	−	0.141287i	0.0782530	−	0.0324134i	−0.343214	−	0.939257i	$-0.611515\pi$
$19$	0.341097	−	0.141287i	0.0782530	−	0.0324134i	0.421467	+	0.906844i	$0.361515\pi$
$20$	1.78688	−	2.43658i	0.399559	−	0.544835i
$21$		0			0
$22$	3.65676	−	1.02254i	0.779623	−	0.218007i
$23$	1.19267	+	0.319575i	0.248689	+	0.0666359i	0.381010	−	0.924571i	$-0.375576\pi$
$23$	1.19267	+	0.319575i	0.248689	+	0.0666359i	−0.132321	+	0.991207i	$0.542243\pi$
$24$		0			0
$25$	2.62494	−	0.703350i	0.524988	−	0.140670i
$26$	7.32561	−	4.33626i	1.43667	−	0.850411i
$27$		0			0
$28$	2.78493	−	5.07526i	0.526302	−	0.959134i
$29$	4.33716	+	0.570998i	0.805391	+	0.106032i	0.521970	−	0.852964i	$-0.325197\pi$
$29$	4.33716	+	0.570998i	0.805391	+	0.106032i	0.283421	+	0.958996i	$0.408531\pi$
$30$		0			0
$31$	−2.61091	+	1.50741i	−0.468933	+	0.270739i	−0.715793	−	0.698312i	$-0.753935\pi$
$31$	−2.61091	+	1.50741i	−0.468933	+	0.270739i	0.246860	+	0.969051i	$0.420601\pi$
$32$	−1.87776	+	5.33611i	−0.331944	+	0.943299i
$33$		0			0
$34$	−8.81608	−	3.54000i	−1.51195	−	0.607104i
$35$	−4.04018	+	1.67350i	−0.682916	+	0.282873i
$36$		0			0
$37$	−1.12563	+	2.71752i	−0.185053	+	0.446757i	−0.988995	−	0.147951i	$-0.952732\pi$
$37$	−1.12563	+	2.71752i	−0.185053	+	0.446757i	0.803942	+	0.594708i	$0.202732\pi$
$38$	0.522098	−	0.00567395i	0.0846954	−	0.000920437i
$39$		0			0
$40$	3.62904	−	2.25606i	0.573801	−	0.356714i
$41$	0.617779	−	2.30558i	0.0964809	−	0.360071i	−0.900759	−	0.434319i	$-0.856989\pi$
$41$	0.617779	−	2.30558i	0.0964809	−	0.360071i	0.997240	+	0.0742479i	$0.0236556\pi$
$42$		0			0
$43$	4.06261	+	5.29450i	0.619542	+	0.807403i	0.992731	−	0.120352i	$-0.0384024\pi$
$43$	4.06261	+	5.29450i	0.619542	+	0.807403i	−0.373189	+	0.927755i	$0.621736\pi$
$44$	5.33785	+	0.585034i	0.804711	+	0.0881972i
$45$		0			0
$46$	1.39681	+	1.04790i	0.205949	+	0.154504i
$47$	7.66225	+	4.42380i	1.11765	+	0.645278i	0.940801	−	0.338959i	$-0.110075\pi$
$47$	7.66225	+	4.42380i	1.11765	+	0.645278i	0.176853	+	0.984237i	$0.443408\pi$
$48$		0			0
$49$	−1.19384	+	0.689264i	−0.170549	+	0.0984662i
$50$	3.81552	+	0.460199i	0.539597	+	0.0650820i
$51$		0			0
$52$	11.8989	−	1.83042i	1.65009	−	0.253834i
$53$	4.18058	−	10.0928i	0.574247	−	1.38636i	−0.323661	−	0.946173i	$-0.604914\pi$
$53$	4.18058	−	10.0928i	0.574247	−	1.38636i	0.897909	−	0.440182i	$-0.145086\pi$
$54$		0			0
$55$	−2.86824	−	2.86824i	−0.386754	−	0.386754i
$56$	6.32934	−	5.19305i	0.845793	−	0.693950i
$57$		0			0
$58$	5.39105	+	3.03489i	0.707880	+	0.398501i
$59$	−11.3742	+	1.49744i	−1.48079	+	0.194949i	−0.827203	−	0.561903i	$-0.810069\pi$
$59$	−11.3742	+	1.49744i	−1.48079	+	0.194949i	−0.653585	+	0.756853i	$0.726736\pi$
$60$		0			0
$61$	−0.560911	+	4.26054i	−0.0718173	+	0.545506i	0.917280	+	0.398243i	$0.130380\pi$
$61$	−0.560911	+	4.26054i	−0.0718173	+	0.545506i	−0.989097	+	0.147264i	$0.952953\pi$
$62$	−4.22082	+	0.602414i	−0.536045	+	0.0765067i
$63$		0			0
$64$	−5.27625	+	6.01342i	−0.659531	+	0.751677i
$65$	−7.87571	−	4.54704i	−0.976861	−	0.563991i
$66$		0			0
$67$	−9.36140	+	12.2000i	−1.14368	+	1.49047i	−0.299744	+	0.954020i	$0.596901\pi$
$67$	−9.36140	+	12.2000i	−1.14368	+	1.49047i	−0.843933	+	0.536449i	$0.819765\pi$
$68$	−9.70448	−	9.29155i	−1.17684	−	1.12677i
$69$		0			0
$70$	−6.18408	+	0.0672062i	−0.739139	+	0.00803267i
$71$	0.817505	+	0.817505i	0.0970199	+	0.0970199i	0.753951	−	0.656931i	$-0.228146\pi$
$71$	0.817505	+	0.817505i	0.0970199	+	0.0970199i	−0.656931	+	0.753951i	$0.728146\pi$
$72$		0			0
$73$	−5.70168	+	5.70168i	−0.667331	+	0.667331i	−0.957097	−	0.289767i	$-0.906422\pi$
$73$	−5.70168	+	5.70168i	−0.667331	+	0.667331i	0.289767	+	0.957097i	$0.406422\pi$
$74$	−2.90928	+	2.97321i	−0.338197	+	0.345629i
$75$		0			0
$76$	0.688174	+	0.267681i	0.0789389	+	0.0307051i
$77$	−6.16566	−	4.73108i	−0.702643	−	0.539157i
$78$		0			0
$79$	−1.89149	+	3.27615i	−0.212809	+	0.368596i	−0.952593	−	0.304249i	$-0.901595\pi$
$79$	−1.89149	+	3.27615i	−0.212809	+	0.368596i	0.739784	+	0.672845i	$0.234928\pi$
$80$	5.95149	−	1.04840i	0.665397	−	0.117215i
$81$		0			0
$82$	2.02572	−	2.70022i	0.223703	−	0.298190i
$83$	0.820020	+	0.107958i	0.0900089	+	0.0118499i	0.175396	−	0.984498i	$-0.443879\pi$
$83$	0.820020	+	0.107958i	0.0900089	+	0.0118499i	−0.0853872	+	0.996348i	$0.527213\pi$
$84$		0			0
$85$	1.32471	+	10.0622i	0.143685	+	1.09139i
$86$	2.54162	+	9.08918i	0.274070	+	0.980111i
$87$		0			0
$88$	6.69693	+	3.58064i	0.713895	+	0.381698i
$89$	4.98702	−	4.98702i	0.528623	−	0.528623i	−0.391539	−	0.920162i	$-0.628057\pi$
$89$	4.98702	−	4.98702i	0.528623	−	0.528623i	0.920162	+	0.391539i	$0.128057\pi$
$90$		0			0
$91$	−16.0974	−	6.66777i	−1.68747	−	0.698972i
$92$	1.28093	+	2.11130i	0.133546	+	0.220118i
$93$		0			0
$94$	7.72449	+	9.84340i	0.796721	+	1.01527i
$95$	−0.278891	−	0.483053i	−0.0286136	−	0.0495602i
$96$		0			0
$97$	9.22126	−	15.9717i	0.936277	−	1.62168i	0.163937	−	0.986471i	$-0.447581\pi$
$97$	9.22126	−	15.9717i	0.936277	−	1.62168i	0.772340	−	0.635209i	$-0.219086\pi$
$98$	−1.92997	+	0.275454i	−0.194957	+	0.0278251i
$99$		0			0
$100$	4.76486	+	2.61460i	0.476486	+	0.261460i
$101$	−13.6386	+	10.4653i	−1.35710	+	1.04134i	−0.363119	+	0.931743i	$0.618288\pi$
$101$	−13.6386	+	10.4653i	−1.35710	+	1.04134i	−0.993977	+	0.109593i	$0.965045\pi$
$102$		0			0
$103$	5.40564	+	1.44844i	0.532634	+	0.142719i	0.515104	−	0.857128i	$-0.327753\pi$
$103$	5.40564	+	1.44844i	0.532634	+	0.142719i	0.0175296	+	0.999846i	$0.494420\pi$
$104$	16.5804	+	3.86815i	1.62584	+	0.379304i
$105$		0			0
$106$	10.8050	−	11.0425i	1.04948	−	1.07254i
$107$	−8.60194	−	3.56304i	−0.831581	−	0.344452i	−0.0740527	−	0.997254i	$-0.523593\pi$
$107$	−8.60194	−	3.56304i	−0.831581	−	0.344452i	−0.757528	+	0.652802i	$0.773593\pi$
$108$		0			0
$109$	6.93523	+	16.7431i	0.664275	+	1.60370i	0.791037	+	0.611768i	$0.209541\pi$
$109$	6.93523	+	16.7431i	0.664275	+	1.60370i	−0.126762	+	0.991933i	$0.540459\pi$
$110$	−2.25272	−	5.27566i	−0.214789	−	0.503014i
$111$		0			0
$112$	11.0430	−	3.47984i	1.04346	−	0.328814i
$113$	−2.16349	−	3.74728i	−0.203524	−	0.352514i	0.746137	−	0.665792i	$-0.231906\pi$
$113$	−2.16349	−	3.74728i	−0.203524	−	0.352514i	−0.949662	+	0.313278i	$0.898573\pi$
$114$		0			0
$115$	0.243487	−	1.84947i	0.0227053	−	0.172464i
$116$	5.47575	+	6.82379i	0.508411	+	0.633573i
$117$		0			0
$118$	−15.7162	−	4.02860i	−1.44679	−	0.370863i
$119$	5.03269	+	18.7823i	0.461346	+	1.72177i
$120$		0			0
$121$	−0.981254	+	3.66209i	−0.0892049	+	0.332917i
$122$	−2.98128	+	5.29581i	−0.269912	+	0.479460i
$123$		0			0
$124$	−5.85672	−	1.43364i	−0.525949	−	0.128745i
$125$	−4.46190	−	10.7720i	−0.399085	−	0.963476i
$126$		0			0
$127$		−	8.32807i		−	0.738997i	−0.929231	−	0.369498i	$-0.879529\pi$
$127$		−	8.32807i		−	0.738997i	0.929231	−	0.369498i	$-0.120471\pi$
$128$	−10.0932	+	5.11141i	−0.892125	+	0.451789i
$129$		0			0
$130$	−7.93968	−	10.1176i	−0.696356	−	0.887374i
$131$	−1.19309	−	0.915491i	−0.104241	−	0.0799868i	0.555326	−	0.831633i	$-0.312594\pi$
$131$	−1.19309	−	0.915491i	−0.104241	−	0.0799868i	−0.659567	+	0.751646i	$0.729260\pi$
$132$		0			0
$133$	−0.650569	−	0.847838i	−0.0564115	−	0.0735169i
$134$	−18.7146	+	11.0778i	−1.61669	+	0.956972i
$135$		0			0
$136$	−7.83951	−	17.3079i	−0.672233	−	1.48414i
$137$	9.35926	−	2.50781i	0.799616	−	0.214256i	0.164201	−	0.986427i	$-0.447496\pi$
$137$	9.35926	−	2.50781i	0.799616	−	0.214256i	0.635415	+	0.772171i	$0.280829\pi$
$138$		0			0
$139$	−10.9662	+	1.44372i	−0.930139	+	0.122455i	−0.580344	−	0.814371i	$-0.697082\pi$
$139$	−10.9662	+	1.44372i	−0.930139	+	0.122455i	−0.349795	+	0.936826i	$0.613749\pi$
$140$	−8.15120	−	3.17060i	−0.688902	−	0.267965i
$141$		0			0
$142$	0.642069	+	1.50366i	0.0538812	+	0.126185i
$143$		−	16.1617i		−	1.35151i
$144$		0			0
$145$		−	6.60905i		−	0.548852i
$146$	−10.4873	+	4.47810i	−0.867933	+	0.370610i
$147$		0			0
$148$	−5.38483	+	2.36885i	−0.442630	+	0.194719i
$149$	10.2630	−	1.35115i	0.840780	−	0.110691i	0.302179	−	0.953251i	$-0.402286\pi$
$149$	10.2630	−	1.35115i	0.840780	−	0.110691i	0.538602	+	0.842561i	$0.318953\pi$
$150$		0			0
$151$	1.45821	−	0.390726i	0.118668	−	0.0317969i	−0.198997	−	0.980000i	$-0.563768\pi$
$151$	1.45821	−	0.390726i	0.118668	−	0.0317969i	0.317664	+	0.948203i	$0.397102\pi$
$152$	0.762077	+	0.713940i	0.0618126	+	0.0579082i
$153$		0			0
$154$	−5.59850	−	9.45801i	−0.451140	−	0.762148i
$155$	2.77275	+	3.61351i	0.222712	+	0.290244i
$156$		0			0
$157$	−5.10990	−	3.92096i	−0.407814	−	0.312927i	0.384404	−	0.923165i	$-0.374407\pi$
$157$	−5.10990	−	3.92096i	−0.407814	−	0.312927i	−0.792218	+	0.610238i	$0.791074\pi$
$158$	−4.20875	+	3.30276i	−0.334830	+	0.262754i
$159$		0			0
$160$	8.36301	+	1.76035i	0.661154	+	0.139168i
$161$		−	3.57405i		−	0.281674i
$162$		0			0
$163$	5.12528	+	12.3735i	0.401443	+	0.969168i	0.987316	+	0.158766i	$0.0507515\pi$
$163$	5.12528	+	12.3735i	0.401443	+	0.969168i	−0.585874	+	0.810403i	$0.699248\pi$
$164$	4.08141	−	2.47620i	0.318704	−	0.193359i
$165$		0			0
$166$	1.01928	+	0.573803i	0.0791113	+	0.0445357i
$167$	−6.18025	+	23.0650i	−0.478242	+	1.78482i	0.130493	+	0.991449i	$0.458344\pi$
$167$	−6.18025	+	23.0650i	−0.478242	+	1.78482i	−0.608735	+	0.793374i	$0.708323\pi$
$168$		0			0
$169$	−6.01336	−	22.4422i	−0.462566	−	1.72632i
$170$	−3.56391	+	13.9033i	−0.273339	+	1.06634i
$171$		0			0
$172$	−1.45415	+	13.2677i	−0.110878	+	1.01165i
$173$	1.44523	−	10.9776i	0.109879	−	0.834615i	−0.844403	−	0.535708i	$-0.820045\pi$
$173$	1.44523	−	10.9776i	0.109879	−	0.834615i	0.954282	−	0.298907i	$-0.0966220\pi$
$174$		0			0
$175$	−3.93305	−	6.81224i	−0.297311	−	0.514957i
$176$	6.90195	+	8.22817i	0.520254	+	0.620222i
$177$		0			0
$178$	9.17279	−	3.91681i	0.687530	−	0.293578i
$179$	5.35065	+	12.9176i	0.399927	+	0.965508i	0.987683	+	0.156470i	$0.0500115\pi$
$179$	5.35065	+	12.9176i	0.399927	+	0.965508i	−0.587756	+	0.809038i	$0.699988\pi$
$180$		0			0
$181$	−12.7259	−	5.27125i	−0.945910	−	0.391809i	−0.144218	−	0.989546i	$-0.546067\pi$
$181$	−12.7259	−	5.27125i	−0.945910	−	0.391809i	−0.801692	+	0.597737i	$0.796067\pi$
$182$	−17.6120	−	17.2334i	−1.30549	−	1.27742i
$183$		0			0
$184$	0.568467	+	3.44580i	0.0419080	+	0.254028i
$185$	4.29243	+	1.15015i	0.315586	+	0.0845609i
$186$		0			0
$187$	−14.3092	+	10.9799i	−1.04639	+	0.802927i
$188$	4.95024	+	16.9887i	0.361033	+	1.23903i
$189$		0			0
$190$	−0.111455	−	0.780909i	−0.00808577	−	0.0566531i
$191$	−0.945335	+	1.63737i	−0.0684020	+	0.118476i	−0.898198	−	0.439591i	$-0.855123\pi$
$191$	−0.945335	+	1.63737i	−0.0684020	+	0.118476i	0.829796	+	0.558067i	$0.188457\pi$
$192$		0			0
$193$	−5.79542	−	10.0380i	−0.417164	−	0.722549i	0.578489	−	0.815690i	$-0.303642\pi$
$193$	−5.79542	−	10.0380i	−0.417164	−	0.722549i	−0.995653	+	0.0931413i	$0.970309\pi$
$194$	20.5182	−	16.1014i	1.47312	−	1.15602i
$195$		0			0
$196$	−2.67799	−	0.655533i	−0.191285	−	0.0468238i
$197$	2.20122	+	0.911774i	0.156830	+	0.0649612i	0.459718	−	0.888065i	$-0.347951\pi$
$197$	2.20122	+	0.911774i	0.156830	+	0.0649612i	−0.302887	+	0.953026i	$0.597951\pi$
$198$		0			0
$199$	−12.7954	+	12.7954i	−0.907044	+	0.907044i	−0.996033	−	0.0889888i	$-0.971636\pi$
$199$	−12.7954	+	12.7954i	−0.907044	+	0.907044i	0.0889888	+	0.996033i	$0.471636\pi$
$200$	4.87544	+	5.94223i	0.344746	+	0.420179i
$201$		0			0
$202$	−23.4138	+	6.54721i	−1.64739	+	0.460660i
$203$	−1.65279	−	12.5542i	−0.116003	−	0.881133i
$204$		0			0
$205$	−3.57526	−	0.470692i	−0.249707	−	0.0328745i
$206$	6.33091	+	4.74947i	0.441095	+	0.330911i
$207$		0			0
$208$	19.7211	+	13.8137i	1.36741	+	0.957809i
$209$	0.495635	−	0.858464i	0.0342838	−	0.0593812i
$210$		0			0
$211$	14.1770	+	10.8784i	0.975985	+	0.748899i	0.967969	−	0.251069i	$-0.0807820\pi$
$211$	14.1770	+	10.8784i	0.975985	+	0.748899i	0.00801522	+	0.999968i	$0.497449\pi$
$212$	19.9992	−	8.79788i	1.37355	−	0.604241i
$213$		0			0
$214$	−9.41131	−	9.20895i	−0.643344	−	0.629511i
$215$	7.12927	−	7.12927i	0.486212	−	0.486212i
$216$		0			0
$217$	6.17064	+	6.17064i	0.418890	+	0.418890i
$218$	0.278513	+	25.6278i	0.0188633	+	1.73573i
$219$		0			0
$220$	−0.176309	−	8.11070i	−0.0118867	−	0.546824i
$221$	−24.6164	+	32.0807i	−1.65588	+	2.15798i
$222$		0			0
$223$	8.05899	+	4.65286i	0.539670	+	0.311579i	0.744945	−	0.667126i	$-0.232476\pi$
$223$	8.05899	+	4.65286i	0.539670	+	0.311579i	−0.205275	+	0.978704i	$0.565809\pi$
$224$	16.3262	+	1.25244i	1.09084	+	0.0836823i
$225$		0			0
$226$	−0.864609	−	6.05789i	−0.0575129	−	0.402965i
$227$	1.57212	−	11.9414i	0.104345	−	0.792579i	−0.856627	−	0.515935i	$-0.827444\pi$
$227$	1.57212	−	11.9414i	0.104345	−	0.792579i	0.960973	−	0.276644i	$-0.0892222\pi$
$228$		0			0
$229$	18.3804	−	2.41983i	1.21461	−	0.159907i	0.504134	−	0.863625i	$-0.331812\pi$
$229$	18.3804	−	2.41983i	1.21461	−	0.159907i	0.710479	+	0.703718i	$0.248478\pi$
$230$	1.29415	−	2.29887i	0.0853337	−	0.151583i
$231$		0			0
$232$	3.59029	+	11.8409i	0.235714	+	0.777390i
$233$	−0.300490	−	0.300490i	−0.0196857	−	0.0196857i	0.697195	−	0.716881i	$-0.254431\pi$
$233$	−0.300490	−	0.300490i	−0.0196857	−	0.0196857i	−0.716881	+	0.697195i	$0.754431\pi$
$234$		0			0
$235$	5.11526	−	12.3493i	0.333683	−	0.805581i
$236$	−18.5024	−	13.5689i	−1.20441	−	0.883259i
$237$		0			0
$238$	−3.29287	+	27.3013i	−0.213445	+	1.76968i
$239$	4.28925	−	2.47640i	0.277448	−	0.160185i	−0.354819	−	0.934935i	$-0.615458\pi$
$239$	4.28925	−	2.47640i	0.277448	−	0.160185i	0.632268	+	0.774750i	$0.282124\pi$
$240$		0			0
$241$	−15.3413	−	8.85732i	−0.988222	−	0.570550i	−0.0834799	−	0.996509i	$-0.526603\pi$
$241$	−15.3413	−	8.85732i	−0.988222	−	0.570550i	−0.904742	+	0.425959i	$0.859937\pi$
$242$	−3.21756	+	4.28892i	−0.206833	+	0.275702i
$243$		0			0
$244$	−6.70325	+	5.37902i	−0.429131	+	0.344356i
$245$	1.26784	+	1.65228i	0.0809993	+	0.105560i
$246$		0			0
$247$	0.575196	−	2.14666i	0.0365988	−	0.136589i
$248$	−6.93069	−	4.96776i	−0.440099	−	0.315453i
$249$		0			0
$250$	−0.179186	−	16.4881i	−0.0113327	−	1.04280i
$251$	−8.48175	+	20.4768i	−0.535363	+	1.29248i	0.392566	+	0.919724i	$0.371588\pi$
$251$	−8.48175	+	20.4768i	−0.535363	+	1.29248i	−0.927929	+	0.372757i	$0.878412\pi$
$252$		0			0
$253$	3.06282	−	1.26866i	0.192558	−	0.0797600i
$254$	4.38861	−	10.9295i	0.275366	−	0.685777i
$255$		0			0
$256$	−15.9396	+	1.38925i	−0.996223	+	0.0868280i
$257$	−5.85009	+	3.37755i	−0.364919	+	0.210686i	−0.671236	−	0.741244i	$-0.734236\pi$
$257$	−5.85009	+	3.37755i	−0.364919	+	0.210686i	0.306318	+	0.951929i	$0.400903\pi$
$258$		0			0
$259$	8.44131	+	1.11132i	0.524517	+	0.0690540i
$260$	−5.08814	−	17.4620i	−0.315553	−	1.08295i
$261$		0			0
$262$	−1.08334	−	1.83018i	−0.0669290	−	0.113069i
$263$	0.344402	−	0.0922822i	0.0212367	−	0.00569036i	−0.248185	−	0.968713i	$-0.579834\pi$
$263$	0.344402	−	0.0922822i	0.0212367	−	0.00569036i	0.269422	+	0.963022i	$0.413167\pi$
$264$		0			0
$265$	−15.9420	−	4.27165i	−0.979309	−	0.262405i
$266$	−0.407004	−	1.45550i	−0.0249550	−	0.0892425i
$267$		0			0
$268$	−30.3980	+	4.67614i	−1.85685	+	0.285641i
$269$	1.23156	−	0.510127i	0.0750893	−	0.0311030i	−0.344823	−	0.938668i	$-0.612061\pi$
$269$	1.23156	−	0.510127i	0.0750893	−	0.0311030i	0.419912	+	0.907565i	$0.362061\pi$
$270$		0			0
$271$	6.71395			0.407843			0.203922	−	0.978987i	$-0.434631\pi$
$271$	6.71395			0.407843			0.203922	+	0.978987i	$0.434631\pi$
$272$	−1.16767	−	26.8454i	−0.0708005	−	1.62774i
$273$		0			0
$274$	13.6043	+	1.64085i	0.821867	+	0.0991273i
$275$	4.44173	−	5.78857i	0.267846	−	0.349064i
$276$		0			0
$277$	13.2460	−	10.1640i	0.795874	−	0.610696i	−0.128706	−	0.991683i	$-0.541082\pi$
$277$	13.2460	−	10.1640i	0.795874	−	0.610696i	0.924580	+	0.380987i	$0.124416\pi$
$278$	−15.1524	−	3.88410i	−0.908783	−	0.232953i
$279$		0			0
$280$	−9.02657	−	8.45639i	−0.539440	−	0.505366i
$281$	0.259775	+	0.969494i	0.0154969	+	0.0578351i	0.973241	−	0.229785i	$-0.0738025\pi$
$281$	0.259775	+	0.969494i	0.0154969	+	0.0578351i	−0.957744	+	0.287621i	$0.907136\pi$
$282$		0			0
$283$	1.71165	+	13.0012i	0.101747	+	0.772844i	0.963913	+	0.266218i	$0.0857741\pi$
$283$	1.71165	+	13.0012i	0.101747	+	0.772844i	−0.862166	+	0.506626i	$0.830893\pi$
$284$	0.0502514	+	2.31171i	0.00298187	+	0.137175i
$285$		0			0
$286$	8.51665	−	21.2100i	0.503600	−	1.25418i
$287$	−6.90909			−0.407831
$288$		0			0
$289$	28.1275			1.65456
$290$	3.48274	−	8.67350i	0.204514	−	0.509325i
$291$		0			0
$292$	−16.1230	+	0.350478i	−0.943525	+	0.0205102i
$293$	3.29546	+	25.0315i	0.192523	+	1.46236i	0.765845	+	0.643025i	$0.222321\pi$
$293$	3.29546	+	25.0315i	0.192523	+	1.46236i	−0.573322	+	0.819330i	$0.694346\pi$
$294$		0			0
$295$	4.48589	+	16.7416i	0.261179	+	0.974732i
$296$	−8.31518	+	0.271184i	−0.483310	+	0.0157622i
$297$		0			0
$298$	14.1809	+	3.63506i	0.821476	+	0.210573i
$299$	5.89658	−	4.52460i	0.341008	−	0.261665i
$300$		0			0
$301$	11.7595	−	15.3253i	0.677806	−	0.883335i
$302$	2.11961	+	0.255651i	0.121970	+	0.0147110i
$303$		0			0
$304$	0.623903	+	1.33854i	0.0357833	+	0.0767705i
$305$	6.49229			0.371748
$306$		0			0
$307$	18.4151	−	7.62778i	1.05101	−	0.435341i	0.210755	−	0.977539i	$-0.432408\pi$
$307$	18.4151	−	7.62778i	1.05101	−	0.435341i	0.840251	+	0.542198i	$0.182408\pi$
$308$	−2.36324	−	15.3626i	−0.134658	−	0.875365i
$309$		0			0
$310$	1.73466	+	6.20340i	0.0985222	+	0.352329i
$311$	12.5177	+	3.35412i	0.709815	+	0.190194i	0.595623	−	0.803264i	$-0.296905\pi$
$311$	12.5177	+	3.35412i	0.709815	+	0.190194i	0.114192	+	0.993459i	$0.463572\pi$
$312$		0			0
$313$	−0.820365	+	0.219816i	−0.0463698	+	0.0124247i	−0.281929	−	0.959435i	$-0.590974\pi$
$313$	−0.820365	+	0.219816i	−0.0463698	+	0.0124247i	0.235560	+	0.971860i	$0.424308\pi$
$314$	−4.63985	−	7.83849i	−0.261842	−	0.442351i
$315$		0			0
$316$	−7.26386	+	2.11657i	−0.408624	+	0.119067i
$317$	−2.77277	−	0.365042i	−0.155734	−	0.0205028i	0.0522559	−	0.998634i	$-0.483359\pi$
$317$	−2.77277	−	0.365042i	−0.155734	−	0.0205028i	−0.207990	+	0.978131i	$0.566692\pi$
$318$		0			0
$319$	10.1718	−	5.87268i	0.569510	−	0.328807i
$320$	10.0477	+	6.71724i	0.561683	+	0.375505i
$321$		0			0
$322$	1.88340	−	4.69046i	0.104958	−	0.261389i
$323$	−2.29139	+	0.949123i	−0.127496	+	0.0528106i
$324$		0			0
$325$	6.25997	−	15.1129i	0.347241	−	0.838313i
$326$	0.205826	+	18.9394i	0.0113997	+	1.04896i
$327$		0			0
$328$	6.66118	−	1.09892i	0.367802	−	0.0606777i
$329$	6.62836	−	24.7374i	0.365433	−	1.36382i
$330$		0			0
$331$	−10.2094	−	13.3052i	−0.561160	−	0.731318i	0.423482	−	0.905905i	$-0.360808\pi$
$331$	−10.2094	−	13.3052i	−0.561160	−	0.731318i	−0.984642	+	0.174587i	$0.944141\pi$
$332$	1.03529	+	1.29016i	0.0568190	+	0.0708069i
$333$		0			0
$334$	−20.2652	+	27.0130i	−1.10886	+	1.47808i
$335$	20.1199	+	11.6162i	1.09927	+	0.634663i
$336$		0			0
$337$	19.1018	−	11.0284i	1.04054	−	0.600755i	0.120553	−	0.992707i	$-0.461533\pi$
$337$	19.1018	−	11.0284i	1.04054	−	0.600755i	0.919986	+	0.391952i	$0.128200\pi$
$338$	3.93452	−	32.6212i	0.214009	−	1.77436i
$339$		0			0
$340$	−12.0037	+	16.3682i	−0.650993	+	0.887690i
$341$	−3.09763	+	7.47835i	−0.167746	+	0.404975i
$342$		0			0
$343$	−11.5059	−	11.5059i	−0.621258	−	0.621258i
$344$	−8.89999	+	16.6458i	−0.479856	+	0.897480i
$345$		0			0
$346$	7.68152	−	13.6451i	0.412961	−	0.733566i
$347$	1.18577	−	0.156110i	0.0636556	−	0.00838042i	−0.0986311	−	0.995124i	$-0.531446\pi$
$347$	1.18577	−	0.156110i	0.0636556	−	0.00838042i	0.162287	+	0.986744i	$0.448113\pi$
$348$		0			0
$349$	−4.01337	+	30.4846i	−0.214831	+	1.63180i	0.455850	+	0.890056i	$0.349335\pi$
$349$	−4.01337	+	30.4846i	−0.214831	+	1.63180i	−0.670681	+	0.741746i	$0.733998\pi$
$350$	−1.57179	−	11.0127i	−0.0840155	−	0.588656i
$351$		0			0
$352$	4.72192	+	14.4355i	0.251679	+	0.769413i
$353$	20.2790	+	11.7081i	1.07934	+	0.623159i	0.930719	−	0.365735i	$-0.119182\pi$
$353$	20.2790	+	11.7081i	1.07934	+	0.623159i	0.148624	+	0.988894i	$0.452516\pi$
$354$		0			0
$355$	1.06330	−	1.38571i	0.0564339	−	0.0735461i
$356$	14.1021	−	0.306548i	0.747409	−	0.0162470i
$357$		0			0
$358$	0.214877	+	19.7723i	0.0113566	+	1.04500i
$359$	7.96377	+	7.96377i	0.420312	+	0.420312i	0.885311	−	0.464999i	$-0.153945\pi$
$359$	7.96377	+	7.96377i	0.420312	+	0.420312i	−0.464999	+	0.885311i	$0.653945\pi$
$360$		0			0
$361$	−13.3386	+	13.3386i	−0.702034	+	0.702034i
$362$	−13.9233	−	13.6239i	−0.731793	−	0.716058i
$363$		0			0
$364$	−14.0321	−	31.8974i	−0.735480	−	1.67188i
$365$	9.66465	+	7.41594i	0.505871	+	0.388168i
$366$		0			0
$367$	6.43555	−	11.1467i	0.335933	−	0.581853i	−0.647731	−	0.761870i	$-0.724282\pi$
$367$	6.43555	−	11.1467i	0.335933	−	0.581853i	0.983664	+	0.180016i	$0.0576151\pi$
$368$	−1.06978	+	4.82172i	−0.0557662	+	0.251349i
$369$		0			0
$370$	5.02715	+	3.77138i	0.261349	+	0.196065i
$371$	−31.3509	−	4.12742i	−1.62766	−	0.214285i
$372$		0			0
$373$	0.540152	+	4.10286i	0.0279680	+	0.212438i	0.999723	−	0.0235559i	$-0.00749878\pi$
$373$	0.540152	+	4.10286i	0.0279680	+	0.212438i	−0.971755	+	0.235994i	$0.924165\pi$
$374$	−24.5650	+	6.86913i	−1.27022	+	0.355194i
$375$		0			0
$376$	−2.45593	+	24.9040i	−0.126655	+	1.28433i
$377$	18.6200	−	18.6200i	0.958978	−	0.958978i
$378$		0			0
$379$	−33.8399	−	14.0169i	−1.73824	−	0.720001i	−0.998911	−	0.0466541i	$-0.985144\pi$
$379$	−33.8399	−	14.0169i	−1.73824	−	0.720001i	−0.739326	−	0.673347i	$-0.764856\pi$
$380$	0.265243	−	1.08357i	0.0136067	−	0.0555861i
$381$		0			0
$382$	−2.10346	+	1.65067i	−0.107623	+	0.0844556i
$383$	−11.3036	−	19.5784i	−0.577587	−	1.00041i	−0.995755	−	0.0920401i	$-0.970661\pi$
$383$	−11.3036	−	19.5784i	−0.577587	−	1.00041i	0.418169	−	0.908369i	$-0.362672\pi$
$384$		0			0
$385$	−5.87063	+	10.1682i	−0.299195	+	0.518221i
$386$	−2.31606	−	16.2275i	−0.117884	−	0.825957i
$387$		0			0
$388$	35.4123	−	10.3186i	1.79779	−	0.523847i
$389$	24.3441	−	18.6799i	1.23429	−	0.947107i	0.234606	−	0.972091i	$-0.424620\pi$
$389$	24.3441	−	18.6799i	1.23429	−	0.947107i	0.999688	+	0.0249836i	$0.00795335\pi$
$390$		0			0
$391$	−8.01199	−	2.14681i	−0.405184	−	0.108569i
$392$	−3.16906	−	2.27151i	−0.160062	−	0.114729i
$393$		0			0
$394$	2.40833	+	2.35655i	0.121330	+	0.118721i
$395$	5.28020	+	2.18713i	0.265676	+	0.110047i
$396$		0			0
$397$	0.613871	+	1.48201i	0.0308093	+	0.0743802i	0.938535	−	0.345183i	$-0.112183\pi$
$397$	0.613871	+	1.48201i	0.0308093	+	0.0743802i	−0.907726	+	0.419563i	$0.862183\pi$
$398$	−23.5351	+	10.0495i	−1.17971	+	0.503738i
$399$		0			0
$400$	3.26701	+	10.3676i	0.163351	+	0.518379i
$401$	−11.8405	−	20.5083i	−0.591285	−	1.02413i	−0.994060	−	0.108836i	$-0.965288\pi$
$401$	−11.8405	−	20.5083i	−0.591285	−	1.02413i	0.402775	−	0.915299i	$-0.368046\pi$
$402$		0			0
$403$	−2.36873	+	17.9923i	−0.117995	+	0.896261i
$404$	−34.1776	−	3.74590i	−1.70040	−	0.186365i
$405$		0			0
$406$	4.44657	−	17.3467i	0.220679	−	0.860902i
$407$	2.04401	+	7.62835i	0.101318	+	0.378123i
$408$		0			0
$409$	4.56941	−	17.0533i	0.225943	−	0.843230i	−0.756082	−	0.654477i	$-0.772889\pi$
$409$	4.56941	−	17.0533i	0.225943	−	0.843230i	0.982025	−	0.188753i	$-0.0604445\pi$
$410$	−4.44401	−	2.50176i	−0.219474	−	0.123553i
$411$		0			0
$412$	5.80567	+	9.56922i	0.286025	+	0.471442i
$413$	12.7079	+	30.6796i	0.625315	+	1.50964i
$414$		0			0
$415$		−	1.24956i		−	0.0613386i
$416$	18.6020	+	28.5210i	0.912038	+	1.39836i
$417$		0			0
$418$	1.10284	−	0.865438i	0.0539415	−	0.0423299i
$419$	−5.25357	−	4.03121i	−0.256654	−	0.196937i	0.472418	−	0.881375i	$-0.343381\pi$
$419$	−5.25357	−	4.03121i	−0.256654	−	0.196937i	−0.729072	+	0.684437i	$0.760048\pi$
$420$		0			0
$421$	4.80144	+	6.25736i	0.234008	+	0.304965i	0.895566	−	0.444929i	$-0.146771\pi$
$421$	4.80144	+	6.25736i	0.234008	+	0.304965i	−0.661558	+	0.749894i	$0.730104\pi$
$422$	12.8729	+	21.7472i	0.626642	+	1.05864i
$423$		0			0
$424$	30.8824	−	1.00717i	1.49978	−	0.0489126i
$425$	−17.6335	+	4.72489i	−0.855353	+	0.229191i
$426$		0			0
$427$	12.3324	−	1.62359i	0.596808	−	0.0785713i
$428$	−7.49829	−	17.0450i	−0.362443	−	0.823899i
$429$		0			0
$430$	13.1131	−	5.59933i	0.632370	−	0.270024i
$431$			10.7560i			0.518098i	0.965864	+	0.259049i	$0.0834091\pi$
$431$			10.7560i			0.518098i	−0.965864	+	0.259049i	$0.916591\pi$
$432$		0			0
$433$		−	16.4622i		−	0.791122i	−0.918440	−	0.395561i	$-0.870550\pi$
$433$		−	16.4622i		−	0.791122i	0.918440	−	0.395561i	$-0.129450\pi$
$434$	4.84643	+	11.3499i	0.232636	+	0.544810i
$435$		0			0
$436$	−13.1394	+	33.7798i	−0.629265	+	1.61776i
$437$	0.451967	−	0.0595026i	0.0216205	−	0.00284640i
$438$		0			0
$439$	38.2364	−	10.2454i	1.82492	−	0.488987i	0.827548	−	0.561395i	$-0.189735\pi$
$439$	38.2364	−	10.2454i	1.82492	−	0.488987i	0.997375	+	0.0724081i	$0.0230684\pi$
$440$	4.04268	−	10.7371i	0.192727	−	0.511873i
$441$		0			0
$442$	−49.2112	+	29.1297i	−2.34074	+	1.38556i
$443$	−4.24156	−	5.52771i	−0.201523	−	0.262629i	0.681649	−	0.731679i	$-0.261263\pi$
$443$	−4.24156	−	5.52771i	−0.201523	−	0.262629i	−0.883172	+	0.469050i	$0.844596\pi$
$444$		0			0
$445$	−8.45327	−	6.48642i	−0.400723	−	0.307486i
$446$	8.12445	+	10.3531i	0.384704	+	0.490232i
$447$		0			0
$448$	20.7659	+	10.2470i	0.981099	+	0.484125i
$449$		−	16.3082i		−	0.769630i	−0.922994	−	0.384815i	$-0.874265\pi$
$449$		−	16.3082i		−	0.769630i	0.922994	−	0.384815i	$-0.125735\pi$
$450$		0			0
$451$	−2.45248	−	5.92081i	−0.115483	−	0.278800i
$452$	2.05762	−	8.40580i	0.0967822	−	0.395375i
$453$		0			0
$454$	8.35591	−	14.8431i	0.392162	−	0.696619i
$455$	−6.81301	+	25.4265i	−0.319399	+	1.19201i
$456$		0			0
$457$	8.15093	+	30.4197i	0.381284	+	1.42297i	0.843942	+	0.536435i	$0.180229\pi$
$457$	8.15093	+	30.4197i	0.381284	+	1.42297i	−0.462657	+	0.886537i	$0.653104\pi$
$458$	25.3970	+	6.51015i	1.18673	+	0.304199i
$459$		0			0
$460$	2.90983	−	2.33499i	0.135671	−	0.108869i
$461$	−0.241886	+	1.83731i	−0.0112657	+	0.0855718i	−0.996154	−	0.0876187i	$-0.972074\pi$
$461$	−0.241886	+	1.83731i	−0.0112657	+	0.0855718i	0.984888	+	0.173191i	$0.0554076\pi$
$462$		0			0
$463$	8.53857	+	14.7892i	0.396821	+	0.687314i	0.993332	−	0.115291i	$-0.0367800\pi$
$463$	8.53857	+	14.7892i	0.396821	+	0.687314i	−0.596511	+	0.802605i	$0.703447\pi$
$464$	−1.52795	+	17.4315i	−0.0709332	+	0.809237i
$465$		0			0
$466$	−0.236005	−	0.552700i	−0.0109327	−	0.0256033i
$467$	−5.81612	−	14.0414i	−0.269138	−	0.649757i	0.730305	−	0.683121i	$-0.239378\pi$
$467$	−5.81612	−	14.0414i	−0.269138	−	0.649757i	−0.999443	+	0.0333642i	$0.989378\pi$
$468$		0			0
$469$	41.1238	+	17.0340i	1.89892	+	0.786558i
$470$	13.2208	−	13.5113i	0.609828	−	0.623229i
$471$		0			0
$472$	−17.1316	−	27.5575i	−0.788548	−	1.26844i
$473$	17.3074	+	4.63750i	0.795794	+	0.213232i
$474$		0			0
$475$	0.795984	−	0.610780i	0.0365223	−	0.0280245i
$476$	−18.7083	+	34.0941i	−0.857494	+	1.56270i
$477$		0			0
$478$	6.93405	−	0.989657i	0.317156	−	0.0452659i
$479$	10.6471	−	18.4413i	0.486478	−	0.842605i	−0.513401	−	0.858149i	$-0.671615\pi$
$479$	10.6471	−	18.4413i	0.486478	−	0.842605i	0.999879	+	0.0155436i	$0.00494787\pi$
$480$		0			0
$481$	8.85288	+	15.3336i	0.403656	+	0.699153i
$482$	−15.4660	−	19.7084i	−0.704455	−	0.897694i
$483$		0			0
$484$	−6.48273	+	3.93309i	−0.294670	+	0.178777i
$485$	−25.7417	−	10.6626i	−1.16887	−	0.484162i
$486$		0			0
$487$	7.52400	−	7.52400i	0.340945	−	0.340945i	−0.515778	−	0.856723i	$-0.672497\pi$
$487$	7.52400	−	7.52400i	0.340945	−	0.340945i	0.856723	+	0.515778i	$0.172497\pi$
$488$	−11.6317	+	3.52686i	−0.526541	+	0.159654i
$489$		0			0
$490$	0.793176	+	2.83651i	0.0358320	+	0.128140i
$491$	3.26915	+	24.8317i	0.147535	+	1.12064i	0.891695	+	0.452637i	$0.149517\pi$
$491$	3.26915	+	24.8317i	0.147535	+	1.12064i	−0.744160	+	0.668001i	$0.767150\pi$
$492$		0			0
$493$	−29.1357	−	3.83579i	−1.31221	−	0.172755i
$494$	1.88608	−	2.51410i	0.0848589	−	0.113115i
$495$		0			0
$496$	−6.47777	−	10.1718i	−0.290860	−	0.456725i
$497$	1.67324	−	2.89814i	0.0750552	−	0.129999i
$498$		0			0
$499$	−27.8158	−	21.3438i	−1.24521	−	0.955479i	−0.245303	−	0.969447i	$-0.578887\pi$
$499$	−27.8158	−	21.3438i	−1.24521	−	0.955479i	−0.999902	+	0.0139671i	$0.995554\pi$
$500$	8.45349	−	21.7328i	0.378052	−	0.971922i
$501$		0			0
$502$	−21.9217	+	22.4034i	−0.978414	+	0.999914i
$503$	25.7127	−	25.7127i	1.14647	−	1.14647i	0.159233	−	0.987241i	$-0.449098\pi$
$503$	25.7127	−	25.7127i	1.14647	−	1.14647i	0.987241	−	0.159233i	$-0.0509021\pi$
$504$		0			0
$505$	18.3650	+	18.3650i	0.817232	+	0.817232i
$506$	4.68808	−	0.0509482i	0.208410	−	0.00226492i
$507$		0			0
$508$	11.5189	−	12.0309i	0.511070	−	0.533783i
$509$	−17.7383	+	23.1170i	−0.786235	+	1.02464i	0.212635	+	0.977132i	$0.431795\pi$
$509$	−17.7383	+	23.1170i	−0.786235	+	1.02464i	−0.998871	+	0.0475101i	$0.984871\pi$
$510$		0			0
$511$	20.2131	+	11.6700i	0.894173	+	0.516251i
$512$	−21.6507	−	6.57641i	−0.956833	−	0.290639i
$513$		0			0
$514$	−9.45732	+	1.34979i	−0.417144	+	0.0595367i
$515$	1.10358	−	8.38251i	0.0486295	−	0.369378i
$516$		0			0
$517$	23.5518	−	3.10065i	1.03581	−	0.136366i
$518$	10.4925	+	5.90674i	0.461013	+	0.259527i
$519$		0			0
$520$	2.52435	−	25.5978i	0.110700	−	1.12254i
$521$	21.3132	+	21.3132i	0.933748	+	0.933748i	0.997938	−	0.0641895i	$-0.0204462\pi$
$521$	21.3132	+	21.3132i	0.933748	+	0.933748i	−0.0641895	+	0.997938i	$0.520446\pi$
$522$		0			0
$523$	7.46445	−	18.0208i	0.326398	−	0.787994i	−0.672456	−	0.740137i	$-0.734761\pi$
$523$	7.46445	−	18.0208i	0.326398	−	0.787994i	0.998854	−	0.0478571i	$-0.0152392\pi$
$524$	−0.457300	−	2.97275i	−0.0199772	−	0.129865i
$525$		0			0
$526$	0.500611	+	0.0603798i	0.0218277	+	0.00263269i
$527$	17.5393	−	10.1263i	0.764024	−	0.441109i
$528$		0			0
$529$	−18.5983	−	10.7377i	−0.808620	−	0.466857i
$530$	−18.6707	−	14.0069i	−0.811005	−	0.608419i
$531$		0			0
$532$	0.232862	−	2.12463i	0.0100958	−	0.0921144i
$533$	−8.74664	−	11.3988i	−0.378859	−	0.493738i
$534$		0			0
$535$	−3.64065	+	13.5871i	−0.157399	+	0.587422i
$536$	−42.3575	−	9.88189i	−1.82956	−	0.426833i
$537$		0			0
$538$	1.88507	−	0.0204862i	0.0812712	−	0.000883224i
$539$	−1.41639	+	3.41948i	−0.0610084	+	0.147287i
$540$		0			0
$541$	−18.4185	+	7.62921i	−0.791875	+	0.328005i	−0.741697	−	0.670735i	$-0.765979\pi$
$541$	−18.4185	+	7.62921i	−0.791875	+	0.328005i	−0.0501777	+	0.998740i	$0.515979\pi$
$542$	8.81116	+	3.53802i	0.378472	+	0.151971i
$543$		0			0
$544$	12.6142	−	35.8464i	0.540829	−	1.53690i
$545$	23.7112	−	13.6897i	1.01568	−	0.586401i
$546$		0			0
$547$	−27.2337	−	3.58538i	−1.16443	−	0.153300i	−0.476564	−	0.879140i	$-0.658118\pi$
$547$	−27.2337	−	3.58538i	−1.16443	−	0.153300i	−0.687864	+	0.725840i	$0.741451\pi$
$548$	16.9892	+	9.32240i	0.725742	+	0.398233i
$549$		0			0
$550$	8.87955	−	5.25609i	0.378625	−	0.224121i
$551$	1.56007	−	0.418019i	0.0664611	−	0.0178082i
$552$		0			0
$553$	10.5770	+	2.83409i	0.449778	+	0.120518i
$554$	22.7397	−	6.35872i	0.966116	−	0.270156i
$555$		0			0
$556$	−17.8388	−	13.0822i	−0.756533	−	0.554808i
$557$	−14.5523	+	6.02776i	−0.616600	+	0.255404i	−0.669048	−	0.743219i	$-0.733298\pi$
$557$	−14.5523	+	6.02776i	−0.616600	+	0.255404i	0.0524474	+	0.998624i	$0.483298\pi$
$558$		0			0
$559$	40.1712			1.69906
$560$	−7.38994	−	15.8546i	−0.312282	−	0.669978i
$561$		0			0
$562$	−0.169970	+	1.40922i	−0.00716974	+	0.0594445i
$563$	3.28829	−	4.28538i	0.138585	−	0.180607i	−0.718905	−	0.695109i	$-0.755356\pi$
$563$	3.28829	−	4.28538i	0.138585	−	0.180607i	0.857490	+	0.514501i	$0.172023\pi$
$564$		0			0
$565$	−5.18626	+	3.97956i	−0.218187	+	0.167421i
$566$	−4.60490	+	17.9644i	−0.193558	+	0.755099i
$567$		0			0
$568$	−1.15224	+	3.06029i	−0.0483470	+	0.128407i
$569$	7.19831	+	26.8644i	0.301769	+	1.12622i	0.935691	+	0.352820i	$0.114777\pi$
$569$	7.19831	+	26.8644i	0.301769	+	1.12622i	−0.633923	+	0.773396i	$0.718556\pi$
$570$		0			0
$571$	1.49888	+	11.3851i	0.0627262	+	0.476453i	0.993762	+	0.111524i	$0.0355732\pi$
$571$	1.49888	+	11.3851i	0.0627262	+	0.476453i	−0.931036	+	0.364928i	$0.881093\pi$
$572$	22.3539	−	23.3474i	0.934665	−	0.976203i
$573$		0			0
$574$	−9.06726	−	3.64085i	−0.378460	−	0.151966i
$575$	3.35546			0.139932
$576$		0			0
$577$	−46.3559			−1.92982			−0.964912	−	0.262575i	$-0.915428\pi$
$577$	−46.3559			−1.92982			−0.964912	+	0.262575i	$0.915428\pi$
$578$	36.9136	+	14.8222i	1.53540	+	0.616523i
$579$		0			0
$580$	9.14127	−	9.54752i	0.379571	−	0.396439i
$581$	−0.312491	−	2.37360i	−0.0129643	−	0.0984737i
$582$		0			0
$583$	−7.59141	−	28.3315i	−0.314404	−	1.17337i
$584$	−21.3439	−	8.03629i	−0.883218	−	0.332544i
$585$		0			0
$586$	−8.86589	+	34.5871i	−0.366246	+	1.42878i
$587$	14.5445	−	11.1604i	0.600315	−	0.460638i	−0.263352	−	0.964700i	$-0.584828\pi$
$587$	14.5445	−	11.1604i	0.600315	−	0.460638i	0.863668	+	0.504062i	$0.168162\pi$
$588$		0			0
$589$	−0.677596	+	0.883060i	−0.0279198	+	0.0363858i
$590$	−2.93510	+	24.3350i	−0.120836	+	1.00186i
$591$		0			0
$592$	−11.0555	−	4.02592i	−0.454377	−	0.165464i
$593$	−27.7849			−1.14099			−0.570494	−	0.821302i	$-0.693248\pi$
$593$	−27.7849			−1.14099			−0.570494	+	0.821302i	$0.693248\pi$
$594$		0			0
$595$	27.1407	−	11.2421i	1.11266	−	0.460879i
$596$	16.6950	+	12.2434i	0.683852	+	0.501508i
$597$		0			0
$598$	10.1228	−	2.83064i	0.413951	−	0.115754i
$599$	−42.3837	−	11.3567i	−1.73175	−	0.464021i	−0.751165	−	0.660114i	$-0.770508\pi$
$599$	−42.3837	−	11.3567i	−1.73175	−	0.464021i	−0.980585	+	0.196093i	$0.937175\pi$
$600$		0			0
$601$	−5.48542	+	1.46981i	−0.223755	+	0.0599549i	−0.368955	−	0.929447i	$-0.620284\pi$
$601$	−5.48542	+	1.46981i	−0.223755	+	0.0599549i	0.145200	+	0.989402i	$0.453618\pi$
$602$	23.5087	−	13.9155i	0.958142	−	0.567155i
$603$		0			0
$604$	2.64698	+	1.45247i	0.107704	+	0.0591001i
$605$	5.67879	+	0.747626i	0.230875	+	0.0303953i
$606$		0			0
$607$	27.8576	−	16.0836i	1.13070	−	0.652812i	0.186592	−	0.982438i	$-0.440256\pi$
$607$	27.8576	−	16.0836i	1.13070	−	0.652812i	0.944112	+	0.329626i	$0.106923\pi$
$608$	0.113425	+	2.08543i	0.00460001	+	0.0845754i
$609$		0			0
$610$	8.52027	+	3.42122i	0.344976	+	0.138521i
$611$	49.2038	−	20.3809i	1.99057	−	0.824522i
$612$		0			0
$613$	5.12670	−	12.3769i	0.207065	−	0.499900i	−0.785893	−	0.618362i	$-0.787796\pi$
$613$	5.12670	−	12.3769i	0.207065	−	0.499900i	0.992959	+	0.118462i	$0.0377964\pi$
$614$	28.1869	−	0.306325i	1.13753	−	0.0123623i
$615$		0			0
$616$	4.99413	−	21.4067i	0.201219	−	0.862501i
$617$	−3.09919	+	11.5664i	−0.124769	+	0.465644i	−0.999831	−	0.0183662i	$-0.994154\pi$
$617$	−3.09919	+	11.5664i	−0.124769	+	0.465644i	0.875062	+	0.484010i	$0.160820\pi$
$618$		0			0
$619$	6.66924	+	8.69152i	0.268059	+	0.349342i	0.907916	−	0.419153i	$-0.137673\pi$
$619$	6.66924	+	8.69152i	0.268059	+	0.349342i	−0.639856	+	0.768494i	$0.721006\pi$
$620$	−0.992464	+	9.05524i	−0.0398583	+	0.363667i
$621$		0			0
$622$	14.6604	+	10.9982i	0.587827	+	0.440990i
$623$	−17.6795	−	10.2073i	−0.708315	−	0.408946i
$624$		0			0
$625$	−3.48775	+	2.01365i	−0.139510	+	0.0805462i
$626$	−1.19246	−	0.143825i	−0.0476601	−	0.00574840i
$627$		0			0
$628$	−1.95857	−	12.7320i	−0.0781556	−	0.508063i
$629$	7.56167	−	18.2555i	0.301503	−	0.727893i
$630$		0			0
$631$	1.47868	+	1.47868i	0.0588652	+	0.0588652i	0.735927	−	0.677061i	$-0.236747\pi$
$631$	1.47868	+	1.47868i	0.0588652	+	0.0588652i	−0.677061	+	0.735927i	$0.736747\pi$
$632$	−10.6482	−	1.05008i	−0.423563	−	0.0417701i
$633$		0			0
$634$	−3.44652	−	1.94022i	−0.136879	−	0.0770561i
$635$	−12.4743	+	1.64227i	−0.495026	+	0.0651714i
$636$		0			0
$637$	−1.08310	+	8.22699i	−0.0429141	+	0.325965i
$638$	16.4438	−	2.34693i	0.651017	−	0.0929159i
$639$		0			0
$640$	9.64651	+	14.1103i	0.381312	+	0.557758i
$641$	6.23393	+	3.59916i	0.246226	+	0.142158i	0.618035	−	0.786151i	$-0.287929\pi$
$641$	6.23393	+	3.59916i	0.246226	+	0.142158i	−0.371809	+	0.928309i	$0.621262\pi$
$642$		0			0
$643$	−19.9523	+	26.0024i	−0.786842	+	1.02543i	0.211997	+	0.977270i	$0.432003\pi$
$643$	−19.9523	+	26.0024i	−0.786842	+	1.02543i	−0.998840	+	0.0481624i	$0.984663\pi$
$644$	4.94342	−	5.16312i	0.194798	−	0.203455i
$645$		0			0
$646$	−3.50729	+	0.0381159i	−0.137993	+	0.00149965i
$647$	0.529459	+	0.529459i	0.0208152	+	0.0208152i	0.717438	−	0.696623i	$-0.245315\pi$
$647$	0.529459	+	0.529459i	0.0208152	+	0.0208152i	−0.696623	+	0.717438i	$0.745315\pi$
$648$		0			0
$649$	−21.7803	+	21.7803i	−0.854953	+	0.854953i
$650$	16.1794	−	16.5349i	0.634607	−	0.648552i
$651$		0			0
$652$	−9.71032	+	24.9640i	−0.380285	+	0.977664i
$653$	−4.40157	−	3.37745i	−0.172247	−	0.132170i	0.519040	−	0.854750i	$-0.326289\pi$
$653$	−4.40157	−	3.37745i	−0.172247	−	0.132170i	−0.691287	+	0.722580i	$0.742956\pi$
$654$		0			0
$655$	−1.13600	+	1.96761i	−0.0443873	+	0.0768810i
$656$	9.32100	+	2.06802i	0.363924	+	0.0807428i
$657$		0			0
$658$	21.7346	−	28.9716i	0.847302	−	1.12943i
$659$	22.0134	+	2.89813i	0.857522	+	0.112895i	0.546450	−	0.837492i	$-0.315979\pi$
$659$	22.0134	+	2.89813i	0.857522	+	0.112895i	0.311072	+	0.950386i	$0.399312\pi$
$660$		0			0
$661$	2.51759	+	19.1230i	0.0979228	+	0.743798i	0.968012	+	0.250904i	$0.0807277\pi$
$661$	2.51759	+	19.1230i	0.0979228	+	0.743798i	−0.870089	+	0.492894i	$0.835939\pi$
$662$	−6.38713	−	22.8413i	−0.248243	−	0.887751i
$663$		0			0
$664$	0.678810	+	2.23873i	0.0263429	+	0.0868796i
$665$	−1.14165	+	1.14165i	−0.0442713	+	0.0442713i
$666$		0			0
$667$	4.99032	+	2.06706i	0.193226	+	0.0800368i
$668$	−40.8303	+	24.7718i	−1.57977	+	0.958451i
$669$		0			0
$670$	20.2834	+	25.8473i	0.783614	+	0.998567i
$671$	5.76893	+	9.99208i	0.222707	+	0.385740i
$672$		0			0
$673$	−9.38576	+	16.2566i	−0.361794	+	0.626646i	−0.988256	−	0.152806i	$-0.951169\pi$
$673$	−9.38576	+	16.2566i	−0.361794	+	0.626646i	0.626462	+	0.779452i	$0.284502\pi$
$674$	30.8801	−	4.40734i	1.18946	−	0.169764i
$675$		0			0
$676$	22.3538	−	40.7376i	0.859760	−	1.56683i
$677$	19.3164	−	14.8220i	0.742391	−	0.569656i	−0.166823	−	0.985987i	$-0.553351\pi$
$677$	19.3164	−	14.8220i	0.742391	−	0.569656i	0.909213	+	0.416330i	$0.136684\pi$
$678$		0			0
$679$	−51.5642	−	13.8166i	−1.97885	−	0.530232i
$680$	−24.3788	+	15.1555i	−0.934883	+	0.581188i
$681$		0			0
$682$	−8.00607	+	8.18199i	−0.306568	+	0.313305i
$683$	−22.4745	−	9.30925i	−0.859963	−	0.356208i	−0.0912701	−	0.995826i	$-0.529093\pi$
$683$	−22.4745	−	9.30925i	−0.859963	−	0.356208i	−0.768693	+	0.639618i	$0.779093\pi$
$684$		0			0
$685$	−5.60195	−	13.5243i	−0.214040	−	0.516737i
$686$	−9.03671	−	21.1631i	−0.345023	−	0.808011i
$687$		0			0
$688$	−20.4518	+	17.1554i	−0.779718	+	0.654043i
$689$	−32.8794	−	56.9488i	−1.25261	−	2.16958i
$690$		0			0
$691$	−2.51606	+	19.1114i	−0.0957156	+	0.727032i	0.874541	+	0.484952i	$0.161163\pi$
$691$	−2.51606	+	19.1114i	−0.0957156	+	0.727032i	−0.970256	+	0.242080i	$0.922170\pi$
$692$	17.2715	−	13.8595i	0.656563	−	0.526859i
$693$		0			0
$694$	1.63843	+	0.419988i	0.0621941	+	0.0159425i
$695$	4.32499	+	16.1411i	0.164056	+	0.612266i
$696$		0			0
$697$	−4.15005	+	15.4882i	−0.157194	+	0.586658i
$698$	−21.3313	+	37.8921i	−0.807403	+	1.43424i
$699$		0			0
$700$	3.74058	−	15.2810i	0.141381	−	0.577569i
$701$	−5.75157	−	13.8855i	−0.217234	−	0.524449i	0.777268	−	0.629170i	$-0.216605\pi$
$701$	−5.75157	−	13.8855i	−0.217234	−	0.524449i	−0.994502	+	0.104721i	$0.966605\pi$
$702$		0			0
$703$			1.08597i			0.0409583i
$704$	−1.41010	+	21.4329i	−0.0531451	+	0.807784i
$705$		0			0
$706$	20.4438	+	26.0517i	0.769411	+	0.980468i
$707$	39.4780	+	30.2925i	1.48472	+	1.13927i
$708$		0			0
$709$	−17.5709	−	22.8988i	−0.659887	−	0.859982i	0.336778	−	0.941584i	$-0.390663\pi$
$709$	−17.5709	−	22.8988i	−0.659887	−	0.859982i	−0.996665	+	0.0816022i	$0.973996\pi$
$710$	2.12566	−	1.25825i	0.0797746	−	0.0472211i
$711$		0			0
$712$	18.6687	+	7.02902i	0.699638	+	0.263424i
$713$	−3.59568	+	0.963460i	−0.134659	+	0.0360819i
$714$		0			0
$715$	−24.2079	+	3.18703i	−0.905324	+	0.119188i
$716$	−10.1373	+	26.0617i	−0.378849	+	0.973972i
$717$		0			0
$718$	6.25475	+	14.6480i	0.233425	+	0.546659i
$719$		−	49.7852i		−	1.85668i	−0.371738	−	0.928338i	$-0.621238\pi$
$719$		−	49.7852i		−	1.85668i	0.371738	−	0.928338i	$-0.378762\pi$
$720$		0			0
$721$		−	16.1990i		−	0.603281i
$722$	−24.5342	+	10.4762i	−0.913069	+	0.389883i
$723$		0			0
$724$	−11.0931	−	25.2167i	−0.412273	−	0.937171i
$725$	11.7864	−	1.55171i	0.437736	−	0.0576290i
$726$		0			0
$727$	33.6064	−	9.00482i	1.24639	−	0.333970i	0.425451	−	0.904981i	$-0.360115\pi$
$727$	33.6064	−	9.00482i	1.24639	−	0.333970i	0.820942	+	0.571011i	$0.193449\pi$
$728$	−1.60638	−	49.2555i	−0.0595363	−	1.82553i
$729$		0			0
$730$	8.77562	+	14.8254i	0.324800	+	0.548712i
$731$	−27.2914	−	35.5668i	−1.00941	−	1.31549i
$732$		0			0
$733$	3.73562	+	2.86644i	0.137978	+	0.105875i	0.675445	−	0.737411i	$-0.263952\pi$
$733$	3.73562	+	2.86644i	0.137978	+	0.105875i	−0.537466	+	0.843285i	$0.680618\pi$
$734$	14.3197	−	11.2372i	0.528551	−	0.414774i
$735$		0			0
$736$	−3.94483	+	5.76413i	−0.145408	+	0.212469i
$737$			41.2879i			1.52086i
$738$		0			0
$739$	4.38631	+	10.5895i	0.161353	+	0.389541i	0.983792	−	0.179312i	$-0.0573873\pi$
$739$	4.38631	+	10.5895i	0.161353	+	0.389541i	−0.822439	+	0.568853i	$0.807387\pi$
$740$	4.61007	+	7.59858i	0.169470	+	0.279329i
$741$		0			0
$742$	−38.9688	−	21.9375i	−1.43059	−	0.805352i
$743$	4.70334	−	17.5531i	0.172549	−	0.643961i	−0.824407	−	0.565997i	$-0.808491\pi$
$743$	4.70334	−	17.5531i	0.172549	−	0.643961i	0.996956	−	0.0779643i	$-0.0248420\pi$
$744$		0			0
$745$	−4.04767	−	15.1061i	−0.148295	−	0.553445i
$746$	−1.45319	+	5.66910i	−0.0532050	+	0.207560i
$747$		0			0
$748$	−35.8581	−	3.93008i	−1.31110	−	0.143698i
$749$	−3.51773	+	26.7198i	−0.128535	+	0.976321i
$750$		0			0
$751$	−20.2013	−	34.9897i	−0.737156	−	1.27679i	−0.953771	−	0.300535i	$-0.902835\pi$
$751$	−20.2013	−	34.9897i	−0.737156	−	1.27679i	0.216615	−	0.976257i	$-0.430498\pi$
$752$	−16.3466	+	31.3890i	−0.596101	+	1.14464i
$753$		0			0
$754$	34.2483	−	14.6242i	1.24725	−	0.532580i
$755$	−0.872807	−	2.10714i	−0.0317647	−	0.0766867i
$756$		0			0
$757$	−3.73933	−	1.54888i	−0.135908	−	0.0562950i	0.313693	−	0.949525i	$-0.398434\pi$
$757$	−3.73933	−	1.54888i	−0.135908	−	0.0562950i	−0.449601	+	0.893230i	$0.648434\pi$
$758$	−37.0239	−	36.2278i	−1.34477	−	1.31585i
$759$		0			0
$760$	0.919101	−	1.28227i	0.0333393	−	0.0465128i
$761$	−31.8176	−	8.52550i	−1.15339	−	0.309049i	−0.369065	−	0.929403i	$-0.620322\pi$
$761$	−31.8176	−	8.52550i	−1.15339	−	0.309049i	−0.784322	+	0.620354i	$0.786989\pi$
$762$		0			0
$763$	41.6171	−	31.9339i	1.50664	−	1.15609i
$764$	−3.63036	+	1.05783i	−0.131342	+	0.0382709i
$765$		0			0
$766$	−4.51732	−	31.6507i	−0.163217	−	1.14358i
$767$	−34.5285	+	59.8051i	−1.24675	+	2.15944i
$768$		0			0
$769$	−15.5674	−	26.9636i	−0.561376	−	0.972331i	−0.997377	−	0.0723849i	$-0.976939\pi$
$769$	−15.5674	−	26.9636i	−0.561376	−	0.972331i	0.436001	−	0.899946i	$-0.356394\pi$
$770$	−13.0627	+	10.2508i	−0.470748	+	0.369414i
$771$		0			0
$772$	5.51181	−	22.5169i	0.198375	−	0.810401i
$773$	−3.37470	−	1.39785i	−0.121380	−	0.0502771i	0.321167	−	0.947023i	$-0.395925\pi$
$773$	−3.37470	−	1.39785i	−0.121380	−	0.0502771i	−0.442547	+	0.896745i	$0.645925\pi$
$774$		0			0
$775$	−5.79324	+	5.79324i	−0.208099	+	0.208099i
$776$	51.9115	+	5.11931i	1.86352	+	0.183772i
$777$		0			0
$778$	41.7920	−	11.6863i	1.49832	−	0.418976i
$779$	−0.115026	−	0.873711i	−0.00412124	−	0.0313039i
$780$		0			0
$781$	3.07754	+	0.405165i	0.110123	+	0.0144980i
$782$	−9.38338	−	7.03944i	−0.335549	−	0.251730i
$783$		0			0
$784$	−2.96196	−	4.65104i	−0.105784	−	0.166109i
$785$	−4.86539	+	8.42710i	−0.173653	+	0.300776i
$786$		0			0
$787$	−29.9603	−	22.9894i	−1.06797	−	0.819482i	−0.0837594	−	0.996486i	$-0.526693\pi$
$787$	−29.9603	−	22.9894i	−1.06797	−	0.819482i	−0.984210	+	0.177004i	$0.943359\pi$
$788$	1.91879	+	4.36176i	0.0683542	+	0.155381i
$789$		0			0
$790$	5.77702	+	5.65281i	0.205537	+	0.201118i
$791$	−8.85634	+	8.85634i	−0.314895	+	0.314895i
$792$		0			0
$793$	18.2910	+	18.2910i	0.649534	+	0.649534i
$794$	0.0246525	+	2.26844i	0.000874884	+	0.0805038i
$795$		0			0
$796$	−36.1824	+	0.786525i	−1.28245	+	0.0278776i
$797$	−3.65925	+	4.76883i	−0.129617	+	0.168921i	−0.853653	−	0.520842i	$-0.825618\pi$
$797$	−3.65925	+	4.76883i	−0.129617	+	0.168921i	0.724036	+	0.689762i	$0.242285\pi$
$798$		0			0
$799$	−51.4727	−	29.7178i	−1.82097	−	1.05134i
$800$	−1.17584	+	15.3277i	−0.0415723	+	0.541915i
$801$		0			0
$802$	−4.73187	−	33.1539i	−0.167088	−	1.17071i
$803$	−2.82582	+	21.4642i	−0.0997210	+	0.757456i
$804$		0			0
$805$	−5.35341	+	0.704790i	−0.188683	+	0.0248406i
$806$	−12.5900	+	22.3643i	−0.443463	+	0.787748i
$807$		0			0
$808$	−42.8796	−	22.9264i	−1.50850	−	0.806549i
$809$	18.3151	+	18.3151i	0.643923	+	0.643923i	0.951518	−	0.307595i	$-0.0995240\pi$
$809$	18.3151	+	18.3151i	0.643923	+	0.643923i	−0.307595	+	0.951518i	$0.599524\pi$
$810$		0			0
$811$	−15.6806	+	37.8562i	−0.550619	+	1.32931i	0.366396	+	0.930459i	$0.380591\pi$
$811$	−15.6806	+	37.8562i	−0.550619	+	1.32931i	−0.917015	+	0.398852i	$0.869409\pi$
$812$	14.9766	−	20.4220i	0.525577	−	0.716673i
$813$		0			0
$814$	−1.33739	+	11.0883i	−0.0468754	+	0.388645i
$815$	17.5231	−	10.1170i	0.613806	−	0.354381i
$816$		0			0
$817$	2.13379	+	1.23194i	0.0746517	+	0.0431002i
$818$	14.9832	−	19.9722i	0.523876	−	0.698312i
$819$		0			0
$820$	−4.51383	−	5.62507i	−0.157630	−	0.196436i
$821$	16.5609	+	21.5826i	0.577980	+	0.753238i	0.987250	−	0.159175i	$-0.0508835\pi$
$821$	16.5609	+	21.5826i	0.577980	+	0.753238i	−0.409271	+	0.912413i	$0.634217\pi$
$822$		0			0
$823$	−6.05090	+	22.5823i	−0.210921	+	0.787168i	0.776642	+	0.629943i	$0.216922\pi$
$823$	−6.05090	+	22.5823i	−0.210921	+	0.787168i	−0.987563	+	0.157225i	$0.949745\pi$
$824$	2.57652	+	15.6177i	0.0897572	+	0.544069i
$825$		0			0
$826$	0.510338	+	46.9595i	0.0177569	+	1.63393i
$827$	−20.6338	+	49.8145i	−0.717508	+	1.73222i	−0.0371828	+	0.999308i	$0.511838\pi$
$827$	−20.6338	+	49.8145i	−0.717508	+	1.73222i	−0.680326	+	0.732910i	$0.738162\pi$
$828$		0			0
$829$	−30.6520	+	12.6965i	−1.06459	+	0.440967i	−0.845078	−	0.534644i	$-0.820446\pi$
$829$	−30.6520	+	12.6965i	−1.06459	+	0.440967i	−0.219510	+	0.975610i	$0.570446\pi$
$830$	0.658476	−	1.63988i	0.0228561	−	0.0569212i
$831$		0			0
$832$	9.38304	+	47.2327i	0.325299	+	1.63750i
$833$	8.01985	−	4.63027i	0.277872	−	0.160429i
$834$		0			0
$835$	35.7668	+	4.70879i	1.23776	+	0.162954i
$836$	1.90338	−	0.554615i	0.0658298	−	0.0191818i
$837$		0			0
$838$	−4.77031	−	8.05888i	−0.164788	−	0.278389i
$839$	−0.215035	+	0.0576185i	−0.00742384	+	0.00198921i	−0.262529	−	0.964924i	$-0.584557\pi$
$839$	−0.215035	+	0.0576185i	−0.00742384	+	0.00198921i	0.255105	+	0.966913i	$0.417890\pi$
$840$		0			0
$841$	−9.52692	−	2.55273i	−0.328514	−	0.0880252i
$842$	3.00384	+	10.7421i	0.103519	+	0.370199i
$843$		0			0
$844$	5.43390	+	35.3239i	0.187042	+	1.21590i
$845$	−32.4293	+	13.4327i	−1.11560	+	0.462098i
$846$		0			0
$847$	10.9741			0.377075
$848$	41.0598	+	14.9522i	1.41000	+	0.513460i
$849$		0			0
$850$	−25.6315	−	3.09148i	−0.879155	−	0.106037i
$851$	−2.21096	+	2.88138i	−0.0757907	+	0.0987724i
$852$		0			0
$853$	−1.65665	+	1.27119i	−0.0567227	+	0.0435248i	−0.636734	−	0.771084i	$-0.719715\pi$
$853$	−1.65665	+	1.27119i	−0.0567227	+	0.0435248i	0.580011	+	0.814609i	$0.303048\pi$
$854$	17.0403	+	4.36802i	0.583105	+	0.149470i
$855$		0			0
$856$	−0.858396	−	26.3206i	−0.0293394	−	0.899619i
$857$	4.58621	+	17.1160i	0.156662	+	0.584671i	0.998957	+	0.0456543i	$0.0145373\pi$
$857$	4.58621	+	17.1160i	0.156662	+	0.584671i	−0.842295	+	0.539016i	$0.818796\pi$
$858$		0			0
$859$	−2.94144	−	22.3425i	−0.100361	−	0.762316i	−0.965430	−	0.260663i	$-0.916059\pi$
$859$	−2.94144	−	22.3425i	−0.100361	−	0.762316i	0.865069	−	0.501653i	$-0.167274\pi$
$860$	20.1598	−	0.438231i	0.687445	−	0.0149435i
$861$		0			0
$862$	−5.66804	+	14.1158i	−0.193054	+	0.480787i
$863$	−22.6224			−0.770076			−0.385038	−	0.922901i	$-0.625812\pi$
$863$	−22.6224			−0.770076			−0.385038	+	0.922901i	$0.625812\pi$
$864$		0			0
$865$	−16.7279			−0.568767
$866$	8.67501	−	21.6044i	0.294789	−	0.734148i
$867$		0			0
$868$	0.379304	+	17.4491i	0.0128744	+	0.592260i
$869$	1.32575	+	10.0700i	0.0449729	+	0.341603i
$870$		0			0
$871$	23.9578	+	89.4117i	0.811779	+	3.02960i
$872$	−35.0446	+	37.4075i	−1.18676	+	1.26678i
$873$		0			0
$874$	0.624503	+	0.160082i	0.0211241	+	0.00541486i
$875$	−26.7751	+	20.5453i	−0.905164	+	0.694556i
$876$		0			0
$877$	15.7128	−	20.4773i	0.530583	−	0.691469i	−0.448765	−	0.893650i	$-0.648136\pi$
$877$	15.7128	−	20.4773i	0.530583	−	0.691469i	0.979348	+	0.202180i	$0.0648027\pi$
$878$	55.5792	+	6.70353i	1.87571	+	0.226233i
$879$		0			0
$880$	10.9636	−	11.9607i	0.369582	−	0.403195i
$881$	−18.9952			−0.639965			−0.319983	−	0.947423i	$-0.603677\pi$
$881$	−18.9952			−0.639965			−0.319983	+	0.947423i	$0.603677\pi$
$882$		0			0
$883$	14.4411	−	5.98171i	0.485983	−	0.201301i	−0.126219	−	0.992002i	$-0.540284\pi$
$883$	14.4411	−	5.98171i	0.485983	−	0.201301i	0.612202	+	0.790702i	$0.290284\pi$
$884$	−79.9335	+	12.2962i	−2.68845	+	0.413566i
$885$		0			0
$886$	−2.65357	−	9.48954i	−0.0891485	−	0.318807i
$887$	−14.6087	−	3.91440i	−0.490513	−	0.131433i	0.00508051	−	0.999987i	$-0.498383\pi$
$887$	−14.6087	−	3.91440i	−0.490513	−	0.131433i	−0.495594	+	0.868554i	$0.665049\pi$
$888$		0			0
$889$	−23.2848	+	6.23914i	−0.780946	+	0.209254i
$890$	−7.67567	−	12.9672i	−0.257289	−	0.434660i
$891$		0			0
$892$	5.20655	+	17.8683i	0.174328	+	0.598276i
$893$	3.23860	+	0.426369i	0.108375	+	0.0142679i
$894$		0			0
$895$	18.2936	−	10.5618i	0.611488	−	0.353043i
$896$	21.8527	+	24.3908i	0.730048	+	0.814839i
$897$		0			0
$898$	8.59385	−	21.4023i	0.286780	−	0.714204i
$899$	−12.1847	+	5.04705i	−0.406381	+	0.168329i
$900$		0			0
$901$	−28.0839	+	67.8005i	−0.935610	+	2.25876i
$902$	−0.0984894	−	9.06266i	−0.00327934	−	0.301753i
$903$		0			0
$904$	7.12992	−	9.94720i	0.237138	−	0.330839i
$905$	−5.38607	+	20.1011i	−0.179039	+	0.668183i
$906$		0			0
$907$	−23.0574	−	30.0490i	−0.765608	−	0.997759i	−0.999674	−	0.0255388i	$-0.991870\pi$
$907$	−23.0574	−	30.0490i	−0.765608	−	0.997759i	0.234066	−	0.972221i	$-0.424797\pi$
$908$	18.7878	−	15.0763i	0.623495	−	0.500323i
$909$		0			0
$910$	−22.3401	+	29.7787i	−0.740566	+	0.987154i
$911$	−43.3076	−	25.0037i	−1.43484	−	0.828408i	−0.437360	−	0.899287i	$-0.644086\pi$
$911$	−43.3076	−	25.0037i	−1.43484	−	0.828408i	−0.997485	+	0.0708784i	$0.977420\pi$
$912$		0			0
$913$	1.92316	−	1.11034i	0.0636474	−	0.0367468i
$914$	−5.33312	+	44.2170i	−0.176404	+	1.46257i
$915$		0			0
$916$	29.8996	+	21.9271i	0.987911	+	0.724491i
$917$	−1.66583	+	4.02167i	−0.0550105	+	0.132807i
$918$		0			0
$919$	−15.4201	−	15.4201i	−0.508662	−	0.508662i	0.405454	−	0.914116i	$-0.367114\pi$
$919$	−15.4201	−	15.4201i	−0.508662	−	0.508662i	−0.914116	+	0.405454i	$0.867114\pi$
$920$	5.04922	−	1.53098i	0.166468	−	0.0504750i
$921$		0			0
$922$	−1.28564	+	2.28375i	−0.0423403	+	0.0752114i
$923$	6.89971	−	0.908364i	0.227107	−	0.0298992i
$924$		0			0
$925$	−1.04335	+	7.92504i	−0.0343052	+	0.260574i
$926$	3.41232	+	23.9084i	0.112136	+	0.785680i
$927$		0			0
$928$	−11.1910	+	22.0714i	−0.367364	+	0.724528i
$929$	−40.7702	−	23.5387i	−1.33763	−	0.772279i	−0.351171	−	0.936311i	$-0.614216\pi$
$929$	−40.7702	−	23.5387i	−1.33763	−	0.772279i	−0.986455	+	0.164033i	$0.947550\pi$
$930$		0			0
$931$	−0.309831	+	0.403780i	−0.0101543	+	0.0132333i
$932$	−0.0184709	−	0.849712i	−0.000605033	−	0.0278332i
$933$		0			0
$934$	−0.233570	−	21.4923i	−0.00764265	−	0.703250i
$935$	19.2680	+	19.2680i	0.630131	+	0.630131i
$936$		0			0
$937$	12.8628	−	12.8628i	0.420211	−	0.420211i	−0.465066	−	0.885276i	$-0.653969\pi$
$937$	12.8628	−	12.8628i	0.420211	−	0.420211i	0.885276	+	0.465066i	$0.153969\pi$
$938$	44.9931	+	44.0257i	1.46908	+	1.43749i
$939$		0			0
$940$	24.4705	−	10.7649i	0.798139	−	0.351111i
$941$	8.62323	+	6.61683i	0.281109	+	0.215703i	0.739686	−	0.672952i	$-0.234974\pi$
$941$	8.62323	+	6.61683i	0.281109	+	0.215703i	−0.458577	+	0.888655i	$0.651641\pi$
$942$		0			0
$943$	1.47361	−	2.55237i	0.0479874	−	0.0831166i
$944$	−7.96114	−	45.1933i	−0.259113	−	1.47092i
$945$		0			0
$946$	20.2698	+	15.2065i	0.659029	+	0.494406i
$947$	−5.41366	−	0.712722i	−0.175920	−	0.0231603i	0.0420513	−	0.999115i	$-0.486611\pi$
$947$	−5.41366	−	0.712722i	−0.175920	−	0.0231603i	−0.217972	+	0.975955i	$0.569944\pi$
$948$		0			0
$949$	6.33537	+	48.1219i	0.205655	+	1.56210i
$950$	1.36648	−	0.382111i	0.0443346	−	0.0123973i
$951$		0			0
$952$	−42.5186	+	34.8853i	−1.37803	+	1.13064i
$953$	−18.9942	+	18.9942i	−0.615284	+	0.615284i	−0.944318	−	0.329034i	$-0.893277\pi$
$953$	−18.9942	+	18.9942i	−0.615284	+	0.615284i	0.329034	+	0.944318i	$0.393277\pi$
$954$		0			0
$955$	2.63896	+	1.09309i	0.0853948	+	0.0353717i
$956$	9.62153	+	2.35521i	0.311182	+	0.0761730i
$957$		0			0
$958$	23.6908	−	18.5911i	0.765417	−	0.600652i
$959$	−14.0234	−	24.2892i	−0.452838	−	0.784338i
$960$		0			0
$961$	−10.9554	+	18.9754i	−0.353401	+	0.612109i
$962$	3.53792	+	24.7885i	0.114067	+	0.799214i
$963$		0			0
$964$	−9.91135	−	34.0147i	−0.319223	−	1.09554i
$965$	−13.8926	+	10.6602i	−0.447219	+	0.343163i
$966$		0			0
$967$	−32.3658	−	8.67240i	−1.04081	−	0.278885i	−0.302364	−	0.953193i	$-0.597776\pi$
$967$	−32.3658	−	8.67240i	−1.04081	−	0.278885i	−0.738451	+	0.674307i	$0.764442\pi$
$968$	−10.5803	+	1.74548i	−0.340065	+	0.0561018i
$969$		0			0
$970$	−28.1638	−	27.5582i	−0.904284	−	0.884841i
$971$	−23.0011	−	9.52735i	−0.738139	−	0.305747i	−0.0182473	−	0.999834i	$-0.505809\pi$
$971$	−23.0011	−	9.52735i	−0.738139	−	0.305747i	−0.719892	+	0.694086i	$0.755809\pi$
$972$		0			0
$973$	12.2521	+	29.5792i	0.392784	+	0.948265i
$974$	13.8391	−	5.90936i	0.443435	−	0.189348i
$975$		0			0
$976$	−17.1236	−	1.50096i	−0.548112	−	0.0480444i
$977$	18.0375	+	31.2419i	0.577071	+	0.999517i	0.995813	+	0.0914117i	$0.0291379\pi$
$977$	18.0375	+	31.2419i	0.577071	+	0.999517i	−0.418742	+	0.908105i	$0.637529\pi$
$978$		0			0
$979$	2.47163	−	18.7739i	0.0789936	−	0.600016i
$980$	−0.453805	+	4.14052i	−0.0144963	+	0.132264i
$981$		0			0
$982$	−8.79512	+	34.3110i	−0.280663	+	1.09491i
$983$	−11.0916	−	41.3945i	−0.353768	−	1.32028i	−0.882028	−	0.471197i	$-0.843822\pi$
$983$	−11.0916	−	41.3945i	−0.353768	−	1.32028i	0.528260	−	0.849083i	$-0.322845\pi$
$984$		0			0
$985$	0.931634	−	3.47691i	0.0296843	−	0.110783i
$986$	−36.2155	−	20.3875i	−1.15333	−	0.649270i
$987$		0			0
$988$	3.80008	−	2.30552i	0.120897	−	0.0733482i
$989$	3.15336	+	7.61289i	0.100271	+	0.242076i
$990$		0			0
$991$		−	9.65591i		−	0.306730i	−0.988170	−	0.153365i	$-0.950989\pi$
$991$		−	9.65591i		−	0.306730i	0.988170	−	0.153365i	$-0.0490110\pi$
$992$	−3.14105	−	16.7626i	−0.0997283	−	0.532214i
$993$		0			0
$994$	3.72313	−	2.92168i	0.118091	−	0.0926702i
$995$	21.6889	+	16.6425i	0.687586	+	0.527603i
$996$		0			0
$997$	−8.88320	−	11.5768i	−0.281334	−	0.366641i	0.631216	−	0.775607i	$-0.282556\pi$
$997$	−8.88320	−	11.5768i	−0.281334	−	0.366641i	−0.912550	+	0.408966i	$0.865890\pi$
$998$	−25.2571	−	42.6689i	−0.799498	−	1.35066i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.683.41		368
3.2	odd	2		288.2.bf.a.11.6	✓	368
9.4	even	3		288.2.bf.a.203.10	yes	368
9.5	odd	6	inner	864.2.bn.a.395.37		368
32.3	odd	8	inner	864.2.bn.a.35.37		368
96.35	even	8		288.2.bf.a.227.10	yes	368
288.67	odd	24		288.2.bf.a.131.6	yes	368
288.131	even	24	inner	864.2.bn.a.611.41		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.6	✓	368	3.2	odd	2
288.2.bf.a.131.6	yes	368	288.67	odd	24
288.2.bf.a.203.10	yes	368	9.4	even	3
288.2.bf.a.227.10	yes	368	96.35	even	8
864.2.bn.a.35.37		368	32.3	odd	8	inner
864.2.bn.a.395.37		368	9.5	odd	6	inner
864.2.bn.a.611.41		368	288.131	even	24	inner
864.2.bn.a.683.41		368	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.31237 + 0.526966i) q^{2} +(1.44461 + 1.38314i) q^{4} +(-0.197197 - 1.49786i) q^{5} +(-0.749169 - 2.79594i) q^{7} +(1.16699 + 2.57646i) q^{8} +O(q^{10})\)	\(q+(1.31237 + 0.526966i) q^{2} +(1.44461 + 1.38314i) q^{4} +(-0.197197 - 1.49786i) q^{5} +(-0.749169 - 2.79594i) q^{7} +(1.16699 + 2.57646i) q^{8} +(0.530525 - 2.06965i) q^{10} +(2.13008 - 1.63447i) q^{11} +(3.66441 - 4.77555i) q^{13} +(0.490179 - 4.06408i) q^{14} +(0.173820 + 3.99622i) q^{16} -6.71770 q^{17} +(0.341097 - 0.141287i) q^{19} +(1.78688 - 2.43658i) q^{20} +(3.65676 - 1.02254i) q^{22} +(1.19267 + 0.319575i) q^{23} +(2.62494 - 0.703350i) q^{25} +(7.32561 - 4.33626i) q^{26} +(2.78493 - 5.07526i) q^{28} +(4.33716 + 0.570998i) q^{29} +(-2.61091 + 1.50741i) q^{31} +(-1.87776 + 5.33611i) q^{32} +(-8.81608 - 3.54000i) q^{34} +(-4.04018 + 1.67350i) q^{35} +(-1.12563 + 2.71752i) q^{37} +(0.522098 - 0.00567395i) q^{38} +(3.62904 - 2.25606i) q^{40} +(0.617779 - 2.30558i) q^{41} +(4.06261 + 5.29450i) q^{43} +(5.33785 + 0.585034i) q^{44} +(1.39681 + 1.04790i) q^{46} +(7.66225 + 4.42380i) q^{47} +(-1.19384 + 0.689264i) q^{49} +(3.81552 + 0.460199i) q^{50} +(11.8989 - 1.83042i) q^{52} +(4.18058 - 10.0928i) q^{53} +(-2.86824 - 2.86824i) q^{55} +(6.32934 - 5.19305i) q^{56} +(5.39105 + 3.03489i) q^{58} +(-11.3742 + 1.49744i) q^{59} +(-0.560911 + 4.26054i) q^{61} +(-4.22082 + 0.602414i) q^{62} +(-5.27625 + 6.01342i) q^{64} +(-7.87571 - 4.54704i) q^{65} +(-9.36140 + 12.2000i) q^{67} +(-9.70448 - 9.29155i) q^{68} +(-6.18408 + 0.0672062i) q^{70} +(0.817505 + 0.817505i) q^{71} +(-5.70168 + 5.70168i) q^{73} +(-2.90928 + 2.97321i) q^{74} +(0.688174 + 0.267681i) q^{76} +(-6.16566 - 4.73108i) q^{77} +(-1.89149 + 3.27615i) q^{79} +(5.95149 - 1.04840i) q^{80} +(2.02572 - 2.70022i) q^{82} +(0.820020 + 0.107958i) q^{83} +(1.32471 + 10.0622i) q^{85} +(2.54162 + 9.08918i) q^{86} +(6.69693 + 3.58064i) q^{88} +(4.98702 - 4.98702i) q^{89} +(-16.0974 - 6.66777i) q^{91} +(1.28093 + 2.11130i) q^{92} +(7.72449 + 9.84340i) q^{94} +(-0.278891 - 0.483053i) q^{95} +(9.22126 - 15.9717i) q^{97} +(-1.92997 + 0.275454i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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