LMFDB - Embedded newform 1950.2.bc.g.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.17284886784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 $ x^8 - 2x^7 + 2x^6 + 30x^5 + 185x^4 + 36x^3 + 8x^2 + 208*x + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$-1.70006 - 1.70006i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.g.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.44460 - 0.834038i) q^{11} +1.00000 q^{12} +(2.24376 - 2.82233i) q^{13} -3.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(5.46699 - 3.15637i) q^{19} -3.64466i q^{21} +(0.834038 + 1.44460i) q^{22} +(-0.622266 + 1.07780i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.35432 + 1.32233i) q^{26} -1.00000 q^{27} +(3.15637 + 1.82233i) q^{28} +(-5.02239 + 8.69904i) q^{29} -4.21957i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.44460 + 0.834038i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-8.54267 - 4.93211i) q^{37} -6.31274 q^{38} +(-1.32233 - 3.35432i) q^{39} +(8.04479 + 4.64466i) q^{41} +(-1.82233 + 3.15637i) q^{42} +(3.78643 + 6.55829i) q^{43} -1.66808i q^{44} +(1.07780 - 0.622266i) q^{46} -6.82522i q^{47} +(0.500000 + 0.866025i) q^{48} +(3.14177 - 5.44171i) q^{49} -4.00000 q^{51} +(3.56609 + 0.531987i) q^{52} +0.848634 q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.82233 - 3.15637i) q^{56} -6.31274i q^{57} +(8.69904 - 5.02239i) q^{58} +(5.29034 - 3.05438i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(-2.10978 + 3.65425i) q^{62} +(-3.15637 - 1.82233i) q^{63} -1.00000 q^{64} +1.66808 q^{66} +(-12.7768 - 7.37671i) q^{67} +(2.00000 - 3.46410i) q^{68} +(0.622266 + 1.07780i) q^{69} +(-3.04056 + 1.75547i) q^{71} +(-0.866025 + 0.500000i) q^{72} +12.2175i q^{73} +(4.93211 + 8.54267i) q^{74} +(5.46699 + 3.15637i) q^{76} -6.07957 q^{77} +(-0.531987 + 3.56609i) q^{78} +9.93398 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.64466 - 8.04479i) q^{82} +7.95317i q^{83} +(3.15637 - 1.82233i) q^{84} -7.57286i q^{86} +(5.02239 + 8.69904i) q^{87} +(-0.834038 + 1.44460i) q^{88} +(5.15425 + 2.97581i) q^{89} +(1.93891 - 12.9972i) q^{91} -1.24453 q^{92} +(-3.65425 - 2.10978i) q^{93} +(-3.41261 + 5.91081i) q^{94} -1.00000i q^{96} +(2.38453 - 1.37671i) q^{97} +(-5.44171 + 3.14177i) q^{98} +1.66808i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} - 2 q^{22} - 4 q^{23} - 12 q^{26} - 8 q^{27} - 8 q^{29} + 6 q^{33} + 4 q^{36} - 30 q^{37} + 6 q^{39} + 2 q^{42} - 14 q^{43} - 6 q^{46} + 4 q^{48} + 14 q^{49} - 32 q^{51} + 6 q^{52} - 16 q^{53} + 2 q^{56} + 6 q^{58} + 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 4 q^{66} - 24 q^{67} + 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} - 6 q^{76} - 16 q^{77} - 6 q^{78} - 20 q^{79} - 4 q^{81} - 4 q^{82} + 8 q^{87} + 2 q^{88} + 42 q^{89} - 10 q^{91} - 8 q^{92} - 30 q^{93} - 8 q^{94} + 24 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 - 2 * q^22 - 4 * q^23 - 12 * q^26 - 8 * q^27 - 8 * q^29 + 6 * q^33 + 4 * q^36 - 30 * q^37 + 6 * q^39 + 2 * q^42 - 14 * q^43 - 6 * q^46 + 4 * q^48 + 14 * q^49 - 32 * q^51 + 6 * q^52 - 16 * q^53 + 2 * q^56 + 6 * q^58 + 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 4 * q^66 - 24 * q^67 + 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 - 6 * q^76 - 16 * q^77 - 6 * q^78 - 20 * q^79 - 4 * q^81 - 4 * q^82 + 8 * q^87 + 2 * q^88 + 42 * q^89 - 10 * q^91 - 8 * q^92 - 30 * q^93 - 8 * q^94 + 24 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	3.15637	−	1.82233i	1.19299	−	0.688776i	0.234010	−	0.972234i	$-0.424815\pi$
$7$	3.15637	−	1.82233i	1.19299	−	0.688776i	0.958985	+	0.283458i	$0.0914817\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.44460	−	0.834038i	−0.435562	−	0.251472i	0.266151	−	0.963931i	$-0.414248\pi$
$11$	−1.44460	−	0.834038i	−0.435562	−	0.251472i	−0.701713	+	0.712459i	$0.747581\pi$
$12$	1.00000			0.288675
$13$	2.24376	−	2.82233i	0.622307	−	0.782773i
$13$	2.24376	−	2.82233i	0.622307	−	0.782773i
$14$	−3.64466			−0.974076
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$			1.00000i			0.235702i
$19$	5.46699	−	3.15637i	1.25421	−	0.724120i	0.282270	−	0.959335i	$-0.408913\pi$
$19$	5.46699	−	3.15637i	1.25421	−	0.724120i	0.971943	+	0.235215i	$0.0755793\pi$
$20$		0			0
$21$		−	3.64466i		−	0.795330i
$22$	0.834038	+	1.44460i	0.177817	+	0.307989i
$23$	−0.622266	+	1.07780i	−0.129752	+	0.224736i	−0.923580	−	0.383405i	$-0.874751\pi$
$23$	−0.622266	+	1.07780i	−0.129752	+	0.224736i	0.793829	+	0.608141i	$0.208085\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	−3.35432	+	1.32233i	−0.657836	+	0.259330i
$27$	−1.00000			−0.192450
$28$	3.15637	+	1.82233i	0.596497	+	0.344388i
$29$	−5.02239	+	8.69904i	−0.932635	+	1.61537i	−0.153837	+	0.988096i	$0.549163\pi$
$29$	−5.02239	+	8.69904i	−0.932635	+	1.61537i	−0.778798	+	0.627275i	$0.784170\pi$
$30$		0			0
$31$		−	4.21957i		−	0.757857i	−0.925426	−	0.378928i	$-0.876293\pi$
$31$		−	4.21957i		−	0.757857i	0.925426	−	0.378928i	$-0.123707\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.44460	+	0.834038i	−0.251472	+	0.145187i
$34$			4.00000i			0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−8.54267	−	4.93211i	−1.40441	−	0.810835i	−0.409566	−	0.912281i	$-0.634320\pi$
$37$	−8.54267	−	4.93211i	−1.40441	−	0.810835i	−0.994841	+	0.101446i	$0.967653\pi$
$38$	−6.31274			−1.02406
$39$	−1.32233	−	3.35432i	−0.211742	−	0.537121i
$40$		0			0
$41$	8.04479	+	4.64466i	1.25638	+	0.725374i	0.972370	−	0.233446i	$-0.0750002\pi$
$41$	8.04479	+	4.64466i	1.25638	+	0.725374i	0.284015	+	0.958820i	$0.408334\pi$
$42$	−1.82233	+	3.15637i	−0.281192	+	0.487038i
$43$	3.78643	+	6.55829i	0.577425	+	1.00013i	0.995773	+	0.0918433i	$0.0292759\pi$
$43$	3.78643	+	6.55829i	0.577425	+	1.00013i	−0.418348	+	0.908287i	$0.637391\pi$
$44$		−	1.66808i		−	0.251472i
$45$		0			0
$46$	1.07780	−	0.622266i	0.158912	−	0.0917482i
$47$		−	6.82522i		−	0.995560i	−0.867303	−	0.497780i	$-0.834149\pi$
$47$		−	6.82522i		−	0.995560i	0.867303	−	0.497780i	$-0.165851\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	3.14177	−	5.44171i	0.448825	−	0.777387i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	3.56609	+	0.531987i	0.494528	+	0.0737734i
$53$	0.848634			0.116569			0.0582844	−	0.998300i	$-0.481437\pi$
$53$	0.848634			0.116569			0.0582844	+	0.998300i	$0.481437\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	−1.82233	−	3.15637i	−0.243519	−	0.421787i
$57$		−	6.31274i		−	0.836142i
$58$	8.69904	−	5.02239i	1.14224	−	0.659473i
$59$	5.29034	−	3.05438i	0.688744	−	0.397646i	−0.114397	−	0.993435i	$-0.536494\pi$
$59$	5.29034	−	3.05438i	0.688744	−	0.397646i	0.803141	+	0.595789i	$0.203160\pi$
$60$		0			0
$61$	−3.73205	−	6.46410i	−0.477840	−	0.827643i	0.521837	−	0.853045i	$-0.325247\pi$
$61$	−3.73205	−	6.46410i	−0.477840	−	0.827643i	−0.999677	+	0.0254017i	$0.991914\pi$
$62$	−2.10978	+	3.65425i	−0.267943	+	0.464091i
$63$	−3.15637	−	1.82233i	−0.397665	−	0.229592i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.66808			0.205326
$67$	−12.7768	−	7.37671i	−1.56094	−	0.901209i	−0.997162	−	0.0752814i	$-0.976014\pi$
$67$	−12.7768	−	7.37671i	−1.56094	−	0.901209i	−0.563777	−	0.825927i	$-0.690652\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	0.622266	+	1.07780i	0.0749121	+	0.129752i
$70$		0			0
$71$	−3.04056	+	1.75547i	−0.360848	+	0.208336i	−0.669453	−	0.742855i	$-0.733471\pi$
$71$	−3.04056	+	1.75547i	−0.360848	+	0.208336i	0.308605	+	0.951190i	$0.400138\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			12.2175i			1.42995i	0.699149	+	0.714976i	$0.253563\pi$
$73$			12.2175i			1.42995i	−0.699149	+	0.714976i	$0.746437\pi$
$74$	4.93211	+	8.54267i	0.573347	+	0.993065i
$75$		0			0
$76$	5.46699	+	3.15637i	0.627107	+	0.362060i
$77$	−6.07957			−0.692831
$78$	−0.531987	+	3.56609i	−0.0602357	+	0.403780i
$79$	9.93398			1.11766			0.558830	−	0.829282i	$-0.311250\pi$
$79$	9.93398			1.11766			0.558830	+	0.829282i	$0.311250\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.64466	−	8.04479i	−0.512917	−	0.888398i
$83$			7.95317i			0.872974i	0.899711	+	0.436487i	$0.143777\pi$
$83$			7.95317i			0.872974i	−0.899711	+	0.436487i	$0.856223\pi$
$84$	3.15637	−	1.82233i	0.344388	−	0.198832i
$85$		0			0
$86$		−	7.57286i		−	0.816603i
$87$	5.02239	+	8.69904i	0.538457	+	0.932635i
$88$	−0.834038	+	1.44460i	−0.0889087	+	0.153994i
$89$	5.15425	+	2.97581i	0.546350	+	0.315435i	0.747648	−	0.664095i	$-0.231183\pi$
$89$	5.15425	+	2.97581i	0.546350	+	0.315435i	−0.201299	+	0.979530i	$0.564516\pi$
$90$		0			0
$91$	1.93891	−	12.9972i	0.203253	−	1.36247i
$92$	−1.24453			−0.129752
$93$	−3.65425	−	2.10978i	−0.378928	−	0.218774i
$94$	−3.41261	+	5.91081i	−0.351984	+	0.609654i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	2.38453	−	1.37671i	0.242113	−	0.139784i	−0.374035	−	0.927415i	$-0.622026\pi$
$97$	2.38453	−	1.37671i	0.242113	−	0.139784i	0.616147	+	0.787631i	$0.288693\pi$
$98$	−5.44171	+	3.14177i	−0.549696	+	0.317367i
$99$			1.66808i			0.167648i
$100$		0			0
$101$	2.66808	−	4.62124i	0.265483	−	0.459831i	−0.702207	−	0.711973i	$-0.747802\pi$
$101$	2.66808	−	4.62124i	0.265483	−	0.459831i	0.967690	+	0.252142i	$0.0811351\pi$
$102$	3.46410	+	2.00000i	0.342997	+	0.198030i
$103$	7.51248			0.740227			0.370113	−	0.928987i	$-0.379319\pi$
$103$	7.51248			0.740227			0.370113	+	0.928987i	$0.379319\pi$
$104$	−2.82233	−	2.24376i	−0.276752	−	0.220019i
$105$		0			0
$106$	−0.734939	−	0.424317i	−0.0713835	−	0.0412133i
$107$	8.46410	−	14.6603i	0.818256	−	1.41726i	−0.0887109	−	0.996057i	$-0.528275\pi$
$107$	8.46410	−	14.6603i	0.818256	−	1.41726i	0.906966	−	0.421203i	$-0.138392\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$		−	0.663848i		−	0.0635851i	−0.999494	−	0.0317926i	$-0.989878\pi$
$109$		−	0.663848i		−	0.0635851i	0.999494	−	0.0317926i	$-0.0101216\pi$
$110$		0			0
$111$	−8.54267	+	4.93211i	−0.810835	+	0.468136i
$112$			3.64466i			0.344388i
$113$	−8.93500	−	15.4759i	−0.840534	−	1.45585i	−0.889444	−	0.457045i	$-0.848908\pi$
$113$	−8.93500	−	15.4759i	−0.840534	−	1.45585i	0.0489094	−	0.998803i	$-0.484425\pi$
$114$	−3.15637	+	5.46699i	−0.295621	+	0.512030i
$115$		0			0
$116$	−10.0448			−0.932635
$117$	−3.56609	−	0.531987i	−0.329685	−	0.0491823i
$118$	−6.10876			−0.562357
$119$	−12.6255	−	7.28932i	−1.15738	−	0.668211i
$120$		0			0
$121$	−4.10876	−	7.11658i	−0.373524	−	0.646962i
$122$			7.46410i			0.675768i
$123$	8.04479	−	4.64466i	0.725374	−	0.418795i
$124$	3.65425	−	2.10978i	0.328162	−	0.189464i
$125$		0			0
$126$	1.82233	+	3.15637i	0.162346	+	0.281192i
$127$	−7.22034	+	12.5060i	−0.640702	+	1.10973i	0.344575	+	0.938759i	$0.388023\pi$
$127$	−7.22034	+	12.5060i	−0.640702	+	1.10973i	−0.985276	+	0.170969i	$0.945310\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	7.57286			0.666753
$130$		0			0
$131$	−10.8892			−0.951393			−0.475697	−	0.879609i	$-0.657804\pi$
$131$	−10.8892			−0.951393			−0.475697	+	0.879609i	$0.657804\pi$
$132$	−1.44460	−	0.834038i	−0.125736	−	0.0725937i
$133$	11.5039	−	19.9253i	0.997513	−	1.72774i
$134$	7.37671	+	12.7768i	0.637251	+	1.10375i
$135$		0			0
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	−6.09419	+	3.51848i	−0.520662	+	0.300604i	−0.737205	−	0.675669i	$-0.763855\pi$
$137$	−6.09419	+	3.51848i	−0.520662	+	0.300604i	0.216544	+	0.976273i	$0.430522\pi$
$138$		−	1.24453i		−	0.105942i
$139$	−5.82233	−	10.0846i	−0.493844	−	0.855362i	0.506131	−	0.862456i	$-0.331075\pi$
$139$	−5.82233	−	10.0846i	−0.493844	−	0.855362i	−0.999975	+	0.00709431i	$0.997742\pi$
$140$		0			0
$141$	−5.91081	−	3.41261i	−0.497780	−	0.287394i
$142$	3.51093			0.294631
$143$	−5.59526	+	2.20575i	−0.467899	+	0.184454i
$144$	1.00000			0.0833333
$145$		0			0
$146$	6.10876	−	10.5807i	0.505565	−	0.875664i
$147$	−3.14177	−	5.44171i	−0.259129	−	0.448825i
$148$		−	9.86423i		−	0.810835i
$149$	−0.669099	+	0.386305i	−0.0548147	+	0.0316473i	−0.527157	−	0.849768i	$-0.676742\pi$
$149$	−0.669099	+	0.386305i	−0.0548147	+	0.0316473i	0.472342	+	0.881415i	$0.343409\pi$
$150$		0			0
$151$			9.77838i			0.795754i	0.917439	+	0.397877i	$0.130253\pi$
$151$			9.77838i			0.795754i	−0.917439	+	0.397877i	$0.869747\pi$
$152$	−3.15637	−	5.46699i	−0.256015	−	0.443431i
$153$	−2.00000	+	3.46410i	−0.161690	+	0.280056i
$154$	5.26506	+	3.03978i	0.424271	+	0.244953i
$155$		0			0
$156$	2.24376	−	2.82233i	0.179644	−	0.225967i
$157$	12.0135			0.958786			0.479393	−	0.877600i	$-0.340857\pi$
$157$	12.0135			0.958786			0.479393	+	0.877600i	$0.340857\pi$
$158$	−8.60308	−	4.96699i	−0.684424	−	0.395152i
$159$	0.424317	−	0.734939i	0.0336505	−	0.0582844i
$160$		0			0
$161$			4.53590i			0.357479i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	8.73960	−	5.04581i	0.684538	−	0.395218i	−0.117025	−	0.993129i	$-0.537336\pi$
$163$	8.73960	−	5.04581i	0.684538	−	0.395218i	0.801563	+	0.597911i	$0.204002\pi$
$164$			9.28932i			0.725374i
$165$		0			0
$166$	3.97658	−	6.88764i	0.308643	−	0.534585i
$167$	6.83902	+	3.94851i	0.529219	+	0.305545i	0.740698	−	0.671838i	$-0.234495\pi$
$167$	6.83902	+	3.94851i	0.529219	+	0.305545i	−0.211479	+	0.977382i	$0.567828\pi$
$168$	−3.64466			−0.281192
$169$	−2.93109	−	12.6653i	−0.225469	−	0.974250i
$170$		0			0
$171$	−5.46699	−	3.15637i	−0.418071	−	0.241373i
$172$	−3.78643	+	6.55829i	−0.288713	+	0.500065i
$173$	0.220343	+	0.381645i	0.0167523	+	0.0290159i	0.874280	−	0.485422i	$-0.161334\pi$
$173$	0.220343	+	0.381645i	0.0167523	+	0.0290159i	−0.857528	+	0.514438i	$0.828001\pi$
$174$		−	10.0448i		−	0.761493i
$175$		0			0
$176$	1.44460	−	0.834038i	0.108891	−	0.0628680i
$177$		−	6.10876i		−	0.459163i
$178$	−2.97581	−	5.15425i	−0.223046	−	0.386328i
$179$	−9.81842	+	17.0060i	−0.733863	+	1.27109i	0.221357	+	0.975193i	$0.428951\pi$
$179$	−9.81842	+	17.0060i	−0.733863	+	1.27109i	−0.955220	+	0.295895i	$0.904382\pi$
$180$		0			0
$181$	6.21752			0.462145			0.231072	−	0.972937i	$-0.425777\pi$
$181$	6.21752			0.462145			0.231072	+	0.972937i	$0.425777\pi$
$182$	−8.17774	+	10.2864i	−0.606174	+	0.762481i
$183$	−7.46410			−0.551762
$184$	1.07780	+	0.622266i	0.0794562	+	0.0458741i
$185$		0			0
$186$	2.10978	+	3.65425i	0.154697	+	0.267943i
$187$			6.67230i			0.487927i
$188$	5.91081	−	3.41261i	0.431090	−	0.248890i
$189$	−3.15637	+	1.82233i	−0.229592	+	0.132555i
$190$		0			0
$191$	−7.84081	−	13.5807i	−0.567341	−	0.982664i	−0.996828	−	0.0795905i	$-0.974639\pi$
$191$	−7.84081	−	13.5807i	−0.567341	−	0.982664i	0.429486	−	0.903073i	$-0.358695\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−7.03901	−	4.06397i	−0.506679	−	0.292531i	0.224788	−	0.974408i	$-0.427831\pi$
$193$	−7.03901	−	4.06397i	−0.506679	−	0.292531i	−0.731468	+	0.681876i	$0.761164\pi$
$194$	−2.75342			−0.197684
$195$		0			0
$196$	6.28354			0.448825
$197$	−0.771835	−	0.445619i	−0.0549910	−	0.0317491i	0.472252	−	0.881463i	$-0.343441\pi$
$197$	−0.771835	−	0.445619i	−0.0549910	−	0.0317491i	−0.527243	+	0.849714i	$0.676774\pi$
$198$	0.834038	−	1.44460i	0.0592725	−	0.102663i
$199$	0.180558	+	0.312736i	0.0127994	+	0.0221692i	0.872354	−	0.488874i	$-0.162592\pi$
$199$	0.180558	+	0.312736i	0.0127994	+	0.0221692i	−0.859555	+	0.511044i	$0.829259\pi$
$200$		0			0
$201$	−12.7768	+	7.37671i	−0.901209	+	0.520313i
$202$	−4.62124	+	2.66808i	−0.325150	+	0.187725i
$203$			36.6098i			2.56951i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$		0			0
$206$	−6.50600	−	3.75624i	−0.453295	−	0.261710i
$207$	1.24453			0.0865010
$208$	1.32233	+	3.35432i	0.0916871	+	0.232580i
$209$	−10.5301			−0.728384
$210$		0			0
$211$	−1.11370	+	1.92898i	−0.0766700	+	0.132796i	−0.901811	−	0.432130i	$-0.857762\pi$
$211$	−1.11370	+	1.92898i	−0.0766700	+	0.132796i	0.825141	+	0.564926i	$0.191095\pi$
$212$	0.424317	+	0.734939i	0.0291422	+	0.0504758i
$213$			3.51093i			0.240565i
$214$	−14.6603	+	8.46410i	−1.00215	+	0.578594i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−7.68945	−	13.3185i	−0.521994	−	0.904119i
$218$	−0.331924	+	0.574909i	−0.0224807	+	0.0389378i
$219$	10.5807	+	6.10876i	0.714976	+	0.412792i
$220$		0			0
$221$	−14.2644	−	2.12795i	−0.959524	−	0.143141i
$222$	9.86423			0.662044
$223$	−5.26872	−	3.04190i	−0.352820	−	0.203701i	0.313107	−	0.949718i	$-0.398630\pi$
$223$	−5.26872	−	3.04190i	−0.352820	−	0.203701i	−0.665927	+	0.746017i	$0.731964\pi$
$224$	1.82233	−	3.15637i	0.121760	−	0.210894i
$225$		0			0
$226$			17.8700i			1.18869i
$227$	13.2679	−	7.66025i	0.880625	−	0.508429i	0.00976038	−	0.999952i	$-0.496893\pi$
$227$	13.2679	−	7.66025i	0.880625	−	0.508429i	0.870864	+	0.491523i	$0.163560\pi$
$228$	5.46699	−	3.15637i	0.362060	−	0.209036i
$229$			22.2644i			1.47127i	0.677378	+	0.735635i	$0.263116\pi$
$229$			22.2644i			1.47127i	−0.677378	+	0.735635i	$0.736884\pi$
$230$		0			0
$231$	−3.03978	+	5.26506i	−0.200003	+	0.346416i
$232$	8.69904	+	5.02239i	0.571120	+	0.329736i
$233$	−10.8366			−0.709928			−0.354964	−	0.934880i	$-0.615507\pi$
$233$	−10.8366			−0.709928			−0.354964	+	0.934880i	$0.615507\pi$
$234$	2.82233	+	2.24376i	0.184501	+	0.146679i
$235$		0			0
$236$	5.29034	+	3.05438i	0.344372	+	0.198823i
$237$	4.96699	−	8.60308i	0.322641	−	0.558830i
$238$	7.28932	+	12.6255i	0.472496	+	0.818388i
$239$		−	16.4975i		−	1.06714i	−0.845757	−	0.533568i	$-0.820851\pi$
$239$		−	16.4975i		−	1.06714i	0.845757	−	0.533568i	$-0.179149\pi$
$240$		0			0
$241$	3.81428	−	2.20218i	0.245700	−	0.141855i	−0.372094	−	0.928195i	$-0.621360\pi$
$241$	3.81428	−	2.20218i	0.245700	−	0.141855i	0.617794	+	0.786340i	$0.288027\pi$
$242$			8.21752i			0.528242i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.73205	−	6.46410i	0.238920	−	0.413822i
$245$		0			0
$246$	−9.28932			−0.592265
$247$	3.35830	−	22.5118i	0.213683	−	1.43239i
$248$	−4.21957			−0.267943
$249$	6.88764	+	3.97658i	0.436487	+	0.252006i
$250$		0			0
$251$	5.97267	+	10.3450i	0.376992	+	0.652969i	0.990623	−	0.136624i	$-0.0436252\pi$
$251$	5.97267	+	10.3450i	0.376992	+	0.652969i	−0.613631	+	0.789593i	$0.710292\pi$
$252$		−	3.64466i		−	0.229592i
$253$	1.79785	−	1.03799i	0.113030	−	0.0652577i
$254$	12.5060	−	7.22034i	0.784696	−	0.453045i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.73103	+	16.8546i	−0.607005	+	1.05136i	0.384726	+	0.923031i	$0.374296\pi$
$257$	−9.73103	+	16.8546i	−0.607005	+	1.05136i	−0.991731	+	0.128333i	$0.959038\pi$
$258$	−6.55829	−	3.78643i	−0.408301	−	0.235733i
$259$	−35.9518			−2.23393
$260$		0			0
$261$	10.0448			0.621757
$262$	9.43032	+	5.44460i	0.582607	+	0.336368i
$263$	1.01739	−	1.76217i	0.0627350	−	0.108660i	−0.832952	−	0.553345i	$-0.813351\pi$
$263$	1.01739	−	1.76217i	0.0627350	−	0.108660i	0.895687	+	0.444685i	$0.146684\pi$
$264$	0.834038	+	1.44460i	0.0513315	+	0.0889087i
$265$		0			0
$266$	−19.9253	+	11.5039i	−1.22170	+	0.705349i
$267$	5.15425	−	2.97581i	0.315435	−	0.182117i
$268$		−	14.7534i		−	0.901209i
$269$	−10.2644	−	17.7784i	−0.625829	−	1.08397i	−0.988380	−	0.152003i	$-0.951428\pi$
$269$	−10.2644	−	17.7784i	−0.625829	−	1.08397i	0.362551	−	0.931964i	$-0.381906\pi$
$270$		0			0
$271$	22.1184	+	12.7700i	1.34359	+	0.775725i	0.987333	−	0.158662i	$-0.0507179\pi$
$271$	22.1184	+	12.7700i	1.34359	+	0.775725i	0.356261	+	0.934386i	$0.384051\pi$
$272$	4.00000			0.242536
$273$	−10.2864	−	8.17774i	−0.622563	−	0.494939i
$274$	7.03696			0.425119
$275$		0			0
$276$	−0.622266	+	1.07780i	−0.0374560	+	0.0648758i
$277$	−9.03019	−	15.6407i	−0.542572	−	0.939762i	−0.998755	−	0.0498760i	$-0.984117\pi$
$277$	−9.03019	−	15.6407i	−0.542572	−	0.939762i	0.456184	−	0.889886i	$-0.349216\pi$
$278$			11.6447i			0.698400i
$279$	−3.65425	+	2.10978i	−0.218774	+	0.126309i
$280$		0			0
$281$		−	20.2175i		−	1.20608i	−0.797712	−	0.603038i	$-0.793957\pi$
$281$		−	20.2175i		−	1.20608i	0.797712	−	0.603038i	$-0.206043\pi$
$282$	3.41261	+	5.91081i	0.203218	+	0.351984i
$283$	−4.34575	+	7.52705i	−0.258328	+	0.447437i	−0.965794	−	0.259310i	$-0.916505\pi$
$283$	−4.34575	+	7.52705i	−0.258328	+	0.447437i	0.707466	+	0.706747i	$0.249838\pi$
$284$	−3.04056	−	1.75547i	−0.180424	−	0.104168i
$285$		0			0
$286$	5.94851	+	0.887395i	0.351743	+	0.0524728i
$287$	33.8564			1.99848
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$		−	2.75342i		−	0.161408i
$292$	−10.5807	+	6.10876i	−0.619188	+	0.357488i
$293$	−6.53667	+	3.77395i	−0.381876	+	0.220476i	−0.678634	−	0.734476i	$-0.737428\pi$
$293$	−6.53667	+	3.77395i	−0.381876	+	0.220476i	0.296758	+	0.954953i	$0.404095\pi$
$294$			6.28354i			0.366464i
$295$		0			0
$296$	−4.93211	+	8.54267i	−0.286673	+	0.496533i
$297$	1.44460	+	0.834038i	0.0838240	+	0.0483958i
$298$	0.772609			0.0447560
$299$	1.64568	+	4.17456i	0.0951723	+	0.241421i
$300$		0			0
$301$	23.9027	+	13.8003i	1.37773	+	0.795433i
$302$	4.88919	−	8.46833i	0.281341	−	0.487298i
$303$	−2.66808	−	4.62124i	−0.153277	−	0.265483i
$304$			6.31274i			0.362060i
$305$		0			0
$306$	3.46410	−	2.00000i	0.198030	−	0.114332i
$307$			26.0427i			1.48634i	0.669104	+	0.743169i	$0.266678\pi$
$307$			26.0427i			1.48634i	−0.669104	+	0.743169i	$0.733322\pi$
$308$	−3.03978	−	5.26506i	−0.173208	−	0.300005i
$309$	3.75624	−	6.50600i	0.213685	−	0.370113i
$310$		0			0
$311$	25.3789			1.43910			0.719552	−	0.694438i	$-0.244347\pi$
$311$	25.3789			1.43910			0.719552	+	0.694438i	$0.244347\pi$
$312$	−3.35432	+	1.32233i	−0.189901	+	0.0748622i
$313$	31.4600			1.77822			0.889112	−	0.457689i	$-0.151323\pi$
$313$	31.4600			1.77822			0.889112	+	0.457689i	$0.151323\pi$
$314$	−10.4040	−	6.00677i	−0.587134	−	0.338982i
$315$		0			0
$316$	4.96699	+	8.60308i	0.279415	+	0.483961i
$317$		−	24.7093i		−	1.38781i	−0.720066	−	0.693905i	$-0.755889\pi$
$317$		−	24.7093i		−	1.38781i	0.720066	−	0.693905i	$-0.244111\pi$
$318$	−0.734939	+	0.424317i	−0.0412133	+	0.0237945i
$319$	14.5107	−	8.37773i	0.812441	−	0.469063i
$320$		0			0
$321$	−8.46410	−	14.6603i	−0.472420	−	0.818256i
$322$	2.26795	−	3.92820i	0.126388	−	0.218910i
$323$	−21.8680	−	12.6255i	−1.21677	−	0.702500i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−10.0916			−0.558923
$327$	−0.574909	−	0.331924i	−0.0317926	−	0.0183554i
$328$	4.64466	−	8.04479i	0.256458	−	0.444199i
$329$	−12.4378	−	21.5429i	−0.685718	−	1.18770i
$330$		0			0
$331$	−4.85286	+	2.80180i	−0.266737	+	0.154001i	−0.627404	−	0.778694i	$-0.715883\pi$
$331$	−4.85286	+	2.80180i	−0.266737	+	0.154001i	0.360667	+	0.932695i	$0.382549\pi$
$332$	−6.88764	+	3.97658i	−0.378009	+	0.218243i
$333$			9.86423i			0.540556i
$334$	−3.94851	−	6.83902i	−0.216053	−	0.374214i
$335$		0			0
$336$	3.15637	+	1.82233i	0.172194	+	0.0994162i
$337$	−21.7868			−1.18680			−0.593402	−	0.804906i	$-0.702216\pi$
$337$	−21.7868			−1.18680			−0.593402	+	0.804906i	$0.702216\pi$
$338$	−3.79423	+	12.4340i	−0.206379	+	0.676319i
$339$	−17.8700			−0.970565
$340$		0			0
$341$	−3.51928	+	6.09557i	−0.190580	+	0.330094i
$342$	3.15637	+	5.46699i	0.170677	+	0.295621i
$343$			2.61124i			0.140994i
$344$	6.55829	−	3.78643i	0.353599	−	0.204151i
$345$		0			0
$346$		−	0.440685i		−	0.0236914i
$347$	4.84081	+	8.38453i	0.259868	+	0.450105i	0.966206	−	0.257769i	$-0.0829875\pi$
$347$	4.84081	+	8.38453i	0.259868	+	0.450105i	−0.706338	+	0.707875i	$0.749654\pi$
$348$	−5.02239	+	8.69904i	−0.269229	+	0.466318i
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.875785	−	0.482701i	$-0.160344\pi$
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.0198610	+	0.999803i	$0.493678\pi$
$350$		0			0
$351$	−2.24376	+	2.82233i	−0.119763	+	0.150645i
$352$	−1.66808			−0.0889087
$353$	19.8970	+	11.4875i	1.05901	+	0.611419i	0.925158	−	0.379583i	$-0.123932\pi$
$353$	19.8970	+	11.4875i	1.05901	+	0.611419i	0.133851	+	0.991002i	$0.457266\pi$
$354$	−3.05438	+	5.29034i	−0.162338	+	0.281179i
$355$		0			0
$356$			5.95162i			0.315435i
$357$	−12.6255	+	7.28932i	−0.668211	+	0.385792i
$358$	17.0060	−	9.81842i	0.898795	−	0.518920i
$359$			2.21752i			0.117036i	0.998286	+	0.0585182i	$0.0186376\pi$
$359$			2.21752i			0.117036i	−0.998286	+	0.0585182i	$0.981362\pi$
$360$		0			0
$361$	10.4253	−	18.0572i	0.548701	−	0.950378i
$362$	−5.38453	−	3.10876i	−0.283005	−	0.163393i
$363$	−8.21752			−0.431308
$364$	12.2253	−	4.81944i	0.640782	−	0.252607i
$365$		0			0
$366$	6.46410	+	3.73205i	0.337884	+	0.195077i
$367$	−3.04056	+	5.26640i	−0.158716	+	0.274904i	−0.934406	−	0.356210i	$-0.884069\pi$
$367$	−3.04056	+	5.26640i	−0.158716	+	0.274904i	0.775690	+	0.631114i	$0.217402\pi$
$368$	−0.622266	−	1.07780i	−0.0324379	−	0.0561841i
$369$		−	9.28932i		−	0.483583i
$370$		0			0
$371$	2.67860	−	1.54649i	0.139066	−	0.0802898i
$372$		−	4.21957i		−	0.218774i
$373$	7.83904	+	13.5776i	0.405890	+	0.703022i	0.994425	−	0.105450i	$-0.0336282\pi$
$373$	7.83904	+	13.5776i	0.405890	+	0.703022i	−0.588535	+	0.808472i	$0.700295\pi$
$374$	3.33615	−	5.77838i	0.172508	−	0.298793i
$375$		0			0
$376$	−6.82522			−0.351984
$377$	13.2825	+	33.6934i	0.684085	+	1.73530i
$378$	3.64466			0.187461
$379$	26.6013	+	15.3583i	1.36642	+	0.788903i	0.990469	−	0.137737i	$-0.0439829\pi$
$379$	26.6013	+	15.3583i	1.36642	+	0.788903i	0.375951	+	0.926640i	$0.377316\pi$
$380$		0			0
$381$	7.22034	+	12.5060i	0.369909	+	0.640702i
$382$			15.6816i			0.802342i
$383$	−17.3741	+	10.0310i	−0.887777	+	0.512558i	−0.873215	−	0.487336i	$-0.837969\pi$
$383$	−17.3741	+	10.0310i	−0.887777	+	0.512558i	−0.0145623	+	0.999894i	$0.504635\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	4.06397	+	7.03901i	0.206851	+	0.358276i
$387$	3.78643	−	6.55829i	0.192475	−	0.333377i
$388$	2.38453	+	1.37671i	0.121056	+	0.0698919i
$389$	27.0314			1.37055			0.685273	−	0.728287i	$-0.259683\pi$
$389$	27.0314			1.37055			0.685273	+	0.728287i	$0.259683\pi$
$390$		0			0
$391$	4.97813			0.251755
$392$	−5.44171	−	3.14177i	−0.274848	−	0.158683i
$393$	−5.44460	+	9.43032i	−0.274644	+	0.475697i
$394$	0.445619	+	0.771835i	0.0224500	+	0.0388845i
$395$		0			0
$396$	−1.44460	+	0.834038i	−0.0725937	+	0.0419120i
$397$	3.23571	−	1.86814i	0.162396	−	0.0937592i	−0.416600	−	0.909090i	$-0.636778\pi$
$397$	3.23571	−	1.86814i	0.162396	−	0.0937592i	0.578995	+	0.815331i	$0.303445\pi$
$398$		−	0.361116i		−	0.0181011i
$399$	−11.5039	−	19.9253i	−0.575915	−	0.997513i
$400$		0			0
$401$	24.3276	+	14.0456i	1.21486	+	0.701402i	0.963815	−	0.266573i	$-0.0858912\pi$
$401$	24.3276	+	14.0456i	1.21486	+	0.701402i	0.251049	+	0.967974i	$0.419225\pi$
$402$	14.7534			0.735834
$403$	−11.9090	−	9.46770i	−0.593230	−	0.471620i
$404$	5.33615			0.265483
$405$		0			0
$406$	18.3049	−	31.7050i	0.908458	−	1.57349i
$407$	8.22714	+	14.2498i	0.407804	+	0.706338i
$408$			4.00000i			0.198030i
$409$	23.7122	−	13.6902i	1.17249	−	0.676938i	0.218225	−	0.975898i	$-0.429973\pi$
$409$	23.7122	−	13.6902i	1.17249	−	0.676938i	0.954265	+	0.298961i	$0.0966399\pi$
$410$		0			0
$411$			7.03696i			0.347108i
$412$	3.75624	+	6.50600i	0.185057	+	0.320528i
$413$	11.1322	−	19.2815i	0.547779	−	0.948780i
$414$	−1.07780	−	0.622266i	−0.0529708	−	0.0305827i
$415$		0			0
$416$	0.531987	−	3.56609i	0.0260828	−	0.174842i
$417$	−11.6447			−0.570241
$418$	9.11935	+	5.26506i	0.446042	+	0.257523i
$419$	6.58068	−	11.3981i	0.321487	−	0.556833i	−0.659308	−	0.751873i	$-0.729151\pi$
$419$	6.58068	−	11.3981i	0.321487	−	0.556833i	0.980795	+	0.195041i	$0.0624839\pi$
$420$		0			0
$421$			1.29341i			0.0630370i	0.999503	+	0.0315185i	$0.0100343\pi$
$421$			1.29341i			0.0630370i	−0.999503	+	0.0315185i	$0.989966\pi$
$422$	1.92898	−	1.11370i	0.0939011	−	0.0542138i
$423$	−5.91081	+	3.41261i	−0.287394	+	0.165927i
$424$		−	0.848634i		−	0.0412133i
$425$		0			0
$426$	1.75547	−	3.04056i	0.0850527	−	0.147316i
$427$	−23.5595	−	13.6021i	−1.14012	−	0.658250i
$428$	16.9282			0.818256
$429$	−0.887395	+	5.94851i	−0.0428439	+	0.287197i
$430$		0			0
$431$	10.5031	+	6.06397i	0.505917	+	0.292091i	0.731154	−	0.682213i	$-0.238982\pi$
$431$	10.5031	+	6.06397i	0.505917	+	0.292091i	−0.225237	+	0.974304i	$0.572316\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	1.03901	+	1.79962i	0.0499317	+	0.0864842i	0.889911	−	0.456134i	$-0.150766\pi$
$433$	1.03901	+	1.79962i	0.0499317	+	0.0864842i	−0.839979	+	0.542618i	$0.817433\pi$
$434$			15.3789i			0.738210i
$435$		0			0
$436$	0.574909	−	0.331924i	0.0275332	−	0.0158963i
$437$			7.85641i			0.375823i
$438$	−6.10876	−	10.5807i	−0.291888	−	0.505565i
$439$	−1.19820	+	2.07534i	−0.0571869	+	0.0990506i	−0.893202	−	0.449656i	$-0.851546\pi$
$439$	−1.19820	+	2.07534i	−0.0571869	+	0.0990506i	0.836015	+	0.548707i	$0.184880\pi$
$440$		0			0
$441$	−6.28354			−0.299216
$442$	11.2893	+	8.97504i	0.536978	+	0.426899i
$443$	−21.9959			−1.04506			−0.522529	−	0.852622i	$-0.675011\pi$
$443$	−21.9959			−1.04506			−0.522529	+	0.852622i	$0.675011\pi$
$444$	−8.54267	−	4.93211i	−0.405417	−	0.234068i
$445$		0			0
$446$	3.04190	+	5.26872i	0.144038	+	0.249481i
$447$			0.772609i			0.0365432i
$448$	−3.15637	+	1.82233i	−0.149124	+	0.0860970i
$449$	25.3098	−	14.6126i	1.19445	−	0.689613i	0.235134	−	0.971963i	$-0.424447\pi$
$449$	25.3098	−	14.6126i	1.19445	−	0.689613i	0.959312	+	0.282350i	$0.0911138\pi$
$450$		0			0
$451$	−7.74765	−	13.4193i	−0.364822	−	0.631891i
$452$	8.93500	−	15.4759i	0.420267	−	0.727924i
$453$	8.46833	+	4.88919i	0.397877	+	0.229714i
$454$	−15.3205			−0.719027
$455$		0			0
$456$	−6.31274			−0.295621
$457$	34.3321	+	19.8216i	1.60599	+	0.927216i	0.990256	+	0.139259i	$0.0444721\pi$
$457$	34.3321	+	19.8216i	1.60599	+	0.927216i	0.615730	+	0.787957i	$0.288861\pi$
$458$	11.1322	−	19.2815i	0.520172	−	0.900965i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	14.4417	−	8.33792i	0.672617	−	0.388336i	−0.124450	−	0.992226i	$-0.539717\pi$
$461$	14.4417	−	8.33792i	0.672617	−	0.388336i	0.797068	+	0.603890i	$0.206383\pi$
$462$	5.26506	−	3.03978i	0.244953	−	0.141424i
$463$			32.2175i			1.49728i	0.662979	+	0.748638i	$0.269292\pi$
$463$			32.2175i			1.49728i	−0.662979	+	0.748638i	$0.730708\pi$
$464$	−5.02239	−	8.69904i	−0.233159	−	0.403843i
$465$		0			0
$466$	9.38476	+	5.41829i	0.434740	+	0.250998i
$467$	6.88137			0.318432			0.159216	−	0.987244i	$-0.449103\pi$
$467$	6.88137			0.318432			0.159216	+	0.987244i	$0.449103\pi$
$468$	−1.32233	−	3.35432i	−0.0611247	−	0.155053i
$469$	−53.7712			−2.48292
$470$		0			0
$471$	6.00677	−	10.4040i	0.276778	−	0.479393i
$472$	−3.05438	−	5.29034i	−0.140589	−	0.243508i
$473$		−	12.6321i		−	0.580825i
$474$	−8.60308	+	4.96699i	−0.395152	+	0.228141i
$475$		0			0
$476$		−	14.5786i		−	0.668211i
$477$	−0.424317	−	0.734939i	−0.0194281	−	0.0336505i
$478$	−8.24876	+	14.2873i	−0.377290	+	0.653485i
$479$	−16.4293	−	9.48547i	−0.750675	−	0.433402i	0.0752629	−	0.997164i	$-0.476020\pi$
$479$	−16.4293	−	9.48547i	−0.750675	−	0.433402i	−0.825938	+	0.563761i	$0.809354\pi$
$480$		0			0
$481$	−33.0878	+	13.0438i	−1.50867	+	0.594744i
$482$	−4.40435			−0.200613
$483$	3.92820	+	2.26795i	0.178739	+	0.103195i
$484$	4.10876	−	7.11658i	0.186762	−	0.323481i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−1.65948	+	0.958101i	−0.0751982	+	0.0434157i	−0.537128	−	0.843501i	$-0.680491\pi$
$487$	−1.65948	+	0.958101i	−0.0751982	+	0.0434157i	0.461929	+	0.886917i	$0.347157\pi$
$488$	−6.46410	+	3.73205i	−0.292616	+	0.168942i
$489$		−	10.0916i		−	0.456359i
$490$		0			0
$491$	−16.8187	+	29.1309i	−0.759019	+	1.31466i	0.184332	+	0.982864i	$0.440988\pi$
$491$	−16.8187	+	29.1309i	−0.759019	+	1.31466i	−0.943351	+	0.331795i	$0.892346\pi$
$492$	8.04479	+	4.64466i	0.362687	+	0.209397i
$493$	40.1791			1.80958
$494$	−14.1643	+	17.8166i	−0.637280	+	0.801608i
$495$		0			0
$496$	3.65425	+	2.10978i	0.164081	+	0.0947321i
$497$	−6.39808	+	11.0818i	−0.286993	+	0.497087i
$498$	−3.97658	−	6.88764i	−0.178195	−	0.308643i
$499$			1.82522i			0.0817080i	0.999165	+	0.0408540i	$0.0130078\pi$
$499$			1.82522i			0.0817080i	−0.999165	+	0.0408540i	$0.986992\pi$
$500$		0			0
$501$	6.83902	−	3.94851i	0.305545	−	0.176406i
$502$		−	11.9453i		−	0.533147i
$503$	−9.99923	−	17.3192i	−0.445843	−	0.772224i	0.552267	−	0.833667i	$-0.313763\pi$
$503$	−9.99923	−	17.3192i	−0.445843	−	0.772224i	−0.998111	+	0.0614437i	$0.980430\pi$
$504$	−1.82233	+	3.15637i	−0.0811730	+	0.140596i
$505$		0			0
$506$	−2.07598			−0.0922884
$507$	−12.4340	−	3.79423i	−0.552212	−	0.168508i
$508$	−14.4407			−0.640702
$509$	5.10196	+	2.94562i	0.226141	+	0.130562i	0.608790	−	0.793331i	$-0.291655\pi$
$509$	5.10196	+	2.94562i	0.226141	+	0.130562i	−0.382650	+	0.923893i	$0.624988\pi$
$510$		0			0
$511$	22.2644	+	38.5630i	0.984917	+	1.70593i
$512$			1.00000i			0.0441942i
$513$	−5.46699	+	3.15637i	−0.241373	+	0.139357i
$514$	16.8546	−	9.73103i	0.743426	−	0.429217i
$515$		0			0
$516$	3.78643	+	6.55829i	0.166688	+	0.288713i
$517$	−5.69249	+	9.85968i	−0.250355	+	0.433628i
$518$	31.1351	+	17.9759i	1.36800	+	0.789815i
$519$	0.440685			0.0193439
$520$		0			0
$521$	32.0370			1.40356			0.701782	−	0.712391i	$-0.252388\pi$
$521$	32.0370			1.40356			0.701782	+	0.712391i	$0.252388\pi$
$522$	−8.69904	−	5.02239i	−0.380747	−	0.219824i
$523$	19.3593	−	33.5313i	0.846523	−	1.46622i	−0.0377693	−	0.999286i	$-0.512025\pi$
$523$	19.3593	−	33.5313i	0.846523	−	1.46622i	0.884292	−	0.466934i	$-0.154641\pi$
$524$	−5.44460	−	9.43032i	−0.237848	−	0.411965i
$525$		0			0
$526$	−1.76217	+	1.01739i	−0.0768344	+	0.0443604i
$527$	−14.6170	+	8.43914i	−0.636727	+	0.367615i
$528$		−	1.66808i		−	0.0725937i
$529$	10.7256	+	18.5772i	0.466329	+	0.807706i
$530$		0			0
$531$	−5.29034	−	3.05438i	−0.229581	−	0.132549i
$532$	23.0078			0.997513
$533$	31.1593	−	12.2835i	1.34966	−	0.532059i
$534$	−5.95162			−0.257552
$535$		0			0
$536$	−7.37671	+	12.7768i	−0.318625	+	0.551875i
$537$	9.81842	+	17.0060i	0.423696	+	0.733863i
$538$			20.5287i			0.885056i
$539$	−9.07718	+	5.24071i	−0.390982	+	0.225734i
$540$		0			0
$541$			25.9616i			1.11618i	0.829781	+	0.558089i	$0.188465\pi$
$541$			25.9616i			1.11618i	−0.829781	+	0.558089i	$0.811535\pi$
$542$	−12.7700	−	22.1184i	−0.548520	−	0.950065i
$543$	3.10876	−	5.38453i	0.133410	−	0.231072i
$544$	−3.46410	−	2.00000i	−0.148522	−	0.0857493i
$545$		0			0
$546$	4.81944	+	12.2253i	0.206253	+	0.523196i
$547$	17.7596			0.759348			0.379674	−	0.925120i	$-0.376036\pi$
$547$	17.7596			0.759348			0.379674	+	0.925120i	$0.376036\pi$
$548$	−6.09419	−	3.51848i	−0.260331	−	0.150302i
$549$	−3.73205	+	6.46410i	−0.159280	+	0.275881i
$550$		0			0
$551$			63.4101i			2.70136i
$552$	1.07780	−	0.622266i	0.0458741	−	0.0264854i
$553$	31.3553	−	18.1030i	1.33336	−	0.769817i
$554$			18.0604i			0.767312i
$555$		0			0
$556$	5.82233	−	10.0846i	0.246922	−	0.427681i
$557$	22.7074	+	13.1101i	0.962142	+	0.555493i	0.896832	−	0.442372i	$-0.145863\pi$
$557$	22.7074	+	13.1101i	0.962142	+	0.555493i	0.0653102	+	0.997865i	$0.479196\pi$
$558$	4.21957			0.178629
$559$	27.0055	+	4.02867i	1.14221	+	0.170394i
$560$		0			0
$561$	5.77838	+	3.33615i	0.243964	+	0.140852i
$562$	−10.1088	+	17.5089i	−0.426412	+	0.738568i
$563$	12.9964	+	22.5104i	0.547733	+	0.948702i	0.998429	+	0.0560243i	$0.0178424\pi$
$563$	12.9964	+	22.5104i	0.547733	+	0.948702i	−0.450696	+	0.892677i	$0.648824\pi$
$564$		−	6.82522i		−	0.287394i
$565$		0			0
$566$	7.52705	−	4.34575i	0.316386	−	0.182665i
$567$			3.64466i			0.153061i
$568$	1.75547	+	3.04056i	0.0736578	+	0.127579i
$569$	−12.7349	+	22.0576i	−0.533876	+	0.924701i	0.465340	+	0.885132i	$0.345932\pi$
$569$	−12.7349	+	22.0576i	−0.533876	+	0.924701i	−0.999217	+	0.0395693i	$0.987401\pi$
$570$		0			0
$571$	−8.44491			−0.353409			−0.176704	−	0.984264i	$-0.556544\pi$
$571$	−8.44491			−0.353409			−0.176704	+	0.984264i	$0.556544\pi$
$572$	−4.70786	−	3.74276i	−0.196846	−	0.156493i
$573$	−15.6816			−0.655109
$574$	−29.3205	−	16.9282i	−1.22381	−	0.706570i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			35.4216i			1.47462i	0.675554	+	0.737311i	$0.263905\pi$
$577$			35.4216i			1.47462i	−0.675554	+	0.737311i	$0.736095\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$	−7.03901	+	4.06397i	−0.292531	+	0.168893i
$580$		0			0
$581$	14.4933	+	25.1031i	0.601283	+	1.04145i
$582$	−1.37671	+	2.38453i	−0.0570665	+	0.0988420i
$583$	−1.22593	−	0.707793i	−0.0507730	−	0.0293138i
$584$	12.2175			0.505565
$585$		0			0
$586$	7.54790			0.311801
$587$	−23.7108	−	13.6894i	−0.978650	−	0.565024i	−0.0767878	−	0.997047i	$-0.524466\pi$
$587$	−23.7108	−	13.6894i	−0.978650	−	0.565024i	−0.901862	+	0.432024i	$0.857800\pi$
$588$	3.14177	−	5.44171i	0.129564	−	0.224412i
$589$	−13.3185	−	23.0683i	−0.548780	−	0.950514i
$590$		0			0
$591$	−0.771835	+	0.445619i	−0.0317491	+	0.0183303i
$592$	8.54267	−	4.93211i	0.351102	−	0.202709i
$593$		−	12.0619i		−	0.495324i	−0.968846	−	0.247662i	$-0.920338\pi$
$593$		−	12.0619i		−	0.495324i	0.968846	−	0.247662i	$-0.0796623\pi$
$594$	−0.834038	−	1.44460i	−0.0342210	−	0.0592725i
$595$		0			0
$596$	−0.669099	−	0.386305i	−0.0274074	−	0.0158237i
$597$	0.361116			0.0147795
$598$	0.662076	−	4.43811i	0.0270743	−	0.181488i
$599$	−28.6129			−1.16909			−0.584546	−	0.811360i	$-0.698727\pi$
$599$	−28.6129			−1.16909			−0.584546	+	0.811360i	$0.698727\pi$
$600$		0			0
$601$	9.58380	−	16.5996i	0.390931	−	0.677113i	−0.601641	−	0.798766i	$-0.705486\pi$
$601$	9.58380	−	16.5996i	0.390931	−	0.677113i	0.992573	+	0.121654i	$0.0388197\pi$
$602$	−13.8003	−	23.9027i	−0.562456	−	0.974203i
$603$			14.7534i			0.600806i
$604$	−8.46833	+	4.88919i	−0.344571	+	0.198938i
$605$		0			0
$606$			5.33615i			0.216766i
$607$	9.46910	+	16.4010i	0.384339	+	0.665695i	0.991677	−	0.128749i	$-0.0410960\pi$
$607$	9.46910	+	16.4010i	0.384339	+	0.665695i	−0.607338	+	0.794443i	$0.707763\pi$
$608$	3.15637	−	5.46699i	0.128008	−	0.221716i
$609$	31.7050	+	18.3049i	1.28475	+	0.741753i
$610$		0			0
$611$	−19.2630	−	15.3141i	−0.779298	−	0.619544i
$612$	−4.00000			−0.161690
$613$	15.5620	+	8.98472i	0.628543	+	0.362890i	0.780188	−	0.625546i	$-0.215124\pi$
$613$	15.5620	+	8.98472i	0.628543	+	0.362890i	−0.151645	+	0.988435i	$0.548457\pi$
$614$	13.0214	−	22.5537i	0.525500	−	0.910192i
$615$		0			0
$616$			6.07957i			0.244953i
$617$	15.6015	−	9.00755i	0.628094	−	0.362630i	−0.151920	−	0.988393i	$-0.548545\pi$
$617$	15.6015	−	9.00755i	0.628094	−	0.362630i	0.780014	+	0.625763i	$0.215212\pi$
$618$	−6.50600	+	3.75624i	−0.261710	+	0.151098i
$619$			25.0505i			1.00687i	0.864035	+	0.503433i	$0.167930\pi$
$619$			25.0505i			1.00687i	−0.864035	+	0.503433i	$0.832070\pi$
$620$		0			0
$621$	0.622266	−	1.07780i	0.0249707	−	0.0432505i
$622$	−21.9788	−	12.6894i	−0.881268	−	0.508800i
$623$	21.6916			0.869057
$624$	3.56609	+	0.531987i	0.142758	+	0.0212965i
$625$		0			0
$626$	−27.2452	−	15.7300i	−1.08894	−	0.628697i
$627$	−5.26506	+	9.11935i	−0.210266	+	0.364192i
$628$	6.00677	+	10.4040i	0.239696	+	0.415166i
$629$			39.4569i			1.57325i
$630$		0			0
$631$	−1.22739	+	0.708634i	−0.0488617	+	0.0282103i	−0.524232	−	0.851576i	$-0.675647\pi$
$631$	−1.22739	+	0.708634i	−0.0488617	+	0.0282103i	0.475370	+	0.879786i	$0.342314\pi$
$632$		−	9.93398i		−	0.395152i
$633$	1.11370	+	1.92898i	0.0442654	+	0.0766700i
$634$	−12.3546	+	21.3989i	−0.490665	+	0.849857i
$635$		0			0
$636$	0.848634			0.0336505
$637$	−8.30892	−	21.0770i	−0.329211	−	0.835101i
$638$	−16.7555			−0.663355
$639$	3.04056	+	1.75547i	0.120283	+	0.0694452i
$640$		0			0
$641$	2.30985	+	4.00077i	0.0912335	+	0.158021i	0.908030	−	0.418904i	$-0.137586\pi$
$641$	2.30985	+	4.00077i	0.0912335	+	0.158021i	−0.816797	+	0.576925i	$0.804252\pi$
$642$			16.9282i			0.668103i
$643$	−41.6468	+	24.0448i	−1.64239	+	0.948234i	−0.662408	+	0.749143i	$0.730465\pi$
$643$	−41.6468	+	24.0448i	−1.64239	+	0.948234i	−0.979981	+	0.199091i	$0.936201\pi$
$644$	−3.92820	+	2.26795i	−0.154793	+	0.0893697i
$645$		0			0
$646$	12.6255	+	21.8680i	0.496743	+	0.860383i
$647$	−1.87282	+	3.24383i	−0.0736283	+	0.127528i	−0.900489	−	0.434879i	$-0.856791\pi$
$647$	−1.87282	+	3.24383i	−0.0736283	+	0.127528i	0.826861	+	0.562407i	$0.190125\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−10.1899			−0.399988
$650$		0			0
$651$	−15.3789			−0.602746
$652$	8.73960	+	5.04581i	0.342269	+	0.197609i
$653$	21.1450	−	36.6241i	0.827466	−	1.43321i	−0.0725541	−	0.997364i	$-0.523115\pi$
$653$	21.1450	−	36.6241i	0.827466	−	1.43321i	0.900020	−	0.435849i	$-0.143552\pi$
$654$	0.331924	+	0.574909i	0.0129793	+	0.0224807i
$655$		0			0
$656$	−8.04479	+	4.64466i	−0.314096	+	0.181343i
$657$	10.5807	−	6.10876i	0.412792	−	0.238325i
$658$			24.8756i			0.969752i
$659$	14.5875	+	25.2663i	0.568248	+	0.984234i	0.996739	+	0.0806881i	$0.0257118\pi$
$659$	14.5875	+	25.2663i	0.568248	+	0.984234i	−0.428492	+	0.903546i	$0.640955\pi$
$660$		0			0
$661$	−38.5089	−	22.2331i	−1.49782	−	0.864768i	−0.497825	−	0.867277i	$-0.665868\pi$
$661$	−38.5089	−	22.2331i	−1.49782	−	0.864768i	−0.999997	+	0.00250931i	$0.999201\pi$
$662$	5.60360			0.217790
$663$	−8.97504	+	11.2893i	−0.348562	+	0.438441i
$664$	7.95317			0.308643
$665$		0			0
$666$	4.93211	−	8.54267i	0.191116	−	0.331022i
$667$	−6.25053	−	10.8262i	−0.242022	−	0.419194i
$668$			7.89701i			0.305545i
$669$	−5.26872	+	3.04190i	−0.203701	+	0.117607i
$670$		0			0
$671$			12.4507i			0.480654i
$672$	−1.82233	−	3.15637i	−0.0702979	−	0.121760i
$673$	−3.95317	+	6.84709i	−0.152383	+	0.263936i	−0.932103	−	0.362193i	$-0.882028\pi$
$673$	−3.95317	+	6.84709i	−0.152383	+	0.263936i	0.779720	+	0.626129i	$0.215362\pi$
$674$	18.8680	+	10.8934i	0.726767	+	0.419599i
$675$		0			0
$676$	9.50289	−	8.87103i	0.365496	−	0.341193i
$677$	7.05615			0.271190			0.135595	−	0.990764i	$-0.456705\pi$
$677$	7.05615			0.271190			0.135595	+	0.990764i	$0.456705\pi$
$678$	15.4759	+	8.93500i	0.594347	+	0.343147i
$679$	5.01764	−	8.69081i	0.192559	−	0.333523i
$680$		0			0
$681$		−	15.3205i		−	0.587083i
$682$	6.09557	−	3.51928i	0.233412	−	0.134760i
$683$	5.15559	−	2.97658i	0.197273	−	0.113896i	−0.398110	−	0.917338i	$-0.630334\pi$
$683$	5.15559	−	2.97658i	0.197273	−	0.113896i	0.595383	+	0.803442i	$0.297000\pi$
$684$		−	6.31274i		−	0.241373i
$685$		0			0
$686$	1.30562	−	2.26140i	0.0498488	−	0.0863406i
$687$	19.2815	+	11.1322i	0.735635	+	0.424719i
$688$	−7.57286			−0.288713
$689$	1.90413	−	2.39513i	0.0725416	−	0.0912470i
$690$		0			0
$691$	16.2458	+	9.37953i	0.618020	+	0.356814i	0.776098	−	0.630613i	$-0.217196\pi$
$691$	16.2458	+	9.37953i	0.618020	+	0.356814i	−0.158078	+	0.987427i	$0.550530\pi$
$692$	−0.220343	+	0.381645i	−0.00837617	+	0.0145080i
$693$	3.03978	+	5.26506i	0.115472	+	0.200003i
$694$		−	9.68162i		−	0.367509i
$695$		0			0
$696$	8.69904	−	5.02239i	0.329736	−	0.190373i
$697$		−	37.1573i		−	1.40743i
$698$	−9.66025	−	16.7321i	−0.365646	−	0.633317i
$699$	−5.41829	+	9.38476i	−0.204939	+	0.354964i
$700$		0			0
$701$	−28.5298			−1.07755			−0.538777	−	0.842448i	$-0.681113\pi$
$701$	−28.5298			−1.07755			−0.538777	+	0.842448i	$0.681113\pi$
$702$	3.35432	−	1.32233i	0.126601	−	0.0499081i
$703$	−62.2703			−2.34857
$704$	1.44460	+	0.834038i	0.0544453	+	0.0314340i
$705$		0			0
$706$	−11.4875	−	19.8970i	−0.432338	−	0.748832i
$707$		−	19.4485i		−	0.731435i
$708$	5.29034	−	3.05438i	0.198823	−	0.114791i
$709$	−20.0853	+	11.5963i	−0.754321	+	0.435507i	−0.827253	−	0.561830i	$-0.810098\pi$
$709$	−20.0853	+	11.5963i	−0.754321	+	0.435507i	0.0729321	+	0.997337i	$0.476764\pi$
$710$		0			0
$711$	−4.96699	−	8.60308i	−0.186277	−	0.322641i
$712$	2.97581	−	5.15425i	0.111523	−	0.193164i
$713$	4.54784	+	2.62570i	0.170318	+	0.0983331i
$714$	14.5786			0.545592
$715$		0			0
$716$	−19.6368			−0.733863
$717$	−14.2873	−	8.24876i	−0.533568	−	0.308056i
$718$	1.10876	−	1.92043i	0.0413786	−	0.0716698i
$719$	5.85641	+	10.1436i	0.218407	+	0.378292i	0.954321	−	0.298783i	$-0.0965806\pi$
$719$	5.85641	+	10.1436i	0.218407	+	0.378292i	−0.735914	+	0.677075i	$0.763247\pi$
$720$		0			0
$721$	23.7122	−	13.6902i	0.883087	−	0.509850i
$722$	−18.0572	+	10.4253i	−0.672019	+	0.387990i
$723$		−	4.40435i		−	0.163800i
$724$	3.10876	+	5.38453i	0.115536	+	0.200115i
$725$		0			0
$726$	7.11658	+	4.10876i	0.264121	+	0.152490i
$727$	−3.82677			−0.141927			−0.0709634	−	0.997479i	$-0.522607\pi$
$727$	−3.82677			−0.141927			−0.0709634	+	0.997479i	$0.522607\pi$
$728$	−12.9972	−	1.93891i	−0.481708	−	0.0718609i
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.1457	−	26.2332i	0.560185	−	0.970269i
$732$	−3.73205	−	6.46410i	−0.137941	−	0.238920i
$733$		−	12.9340i		−	0.477727i	−0.971053	−	0.238864i	$-0.923225\pi$
$733$		−	12.9340i		−	0.477727i	0.971053	−	0.238864i	$-0.0767749\pi$
$734$	5.26640	−	3.04056i	0.194386	−	0.112229i
$735$		0			0
$736$			1.24453i			0.0458741i
$737$	12.3049	+	21.3127i	0.453257	+	0.785065i
$738$	−4.64466	+	8.04479i	−0.170972	+	0.296133i
$739$	−30.6107	−	17.6731i	−1.12603	−	0.650115i	−0.183098	−	0.983095i	$-0.558612\pi$
$739$	−30.6107	−	17.6731i	−1.12603	−	0.650115i	−0.942934	+	0.332980i	$0.891946\pi$
$740$		0			0
$741$	−17.8166	−	14.1643i	−0.654510	−	0.520337i
$742$	−3.09298			−0.113547
$743$	32.1255	+	18.5477i	1.17857	+	0.680448i	0.955684	−	0.294396i	$-0.0951185\pi$
$743$	32.1255	+	18.5477i	1.17857	+	0.680448i	0.222887	+	0.974844i	$0.428452\pi$
$744$	−2.10978	+	3.65425i	−0.0773484	+	0.133971i
$745$		0			0
$746$		−	15.6781i		−	0.574015i
$747$	6.88764	−	3.97658i	0.252006	−	0.145496i
$748$	−5.77838	+	3.33615i	−0.211279	+	0.121982i
$749$		−	61.6975i		−	2.25438i
$750$		0			0
$751$	−4.82904	+	8.36414i	−0.176214	+	0.305212i	−0.940581	−	0.339570i	$-0.889718\pi$
$751$	−4.82904	+	8.36414i	−0.176214	+	0.305212i	0.764367	+	0.644782i	$0.223052\pi$
$752$	5.91081	+	3.41261i	0.215545	+	0.124445i
$753$	11.9453			0.435313
$754$	5.34370	−	35.8206i	0.194606	−	1.30451i
$755$		0			0
$756$	−3.15637	−	1.82233i	−0.114796	−	0.0662775i
$757$	−21.8443	+	37.8354i	−0.793943	+	1.37515i	0.129565	+	0.991571i	$0.458642\pi$
$757$	−21.8443	+	37.8354i	−0.793943	+	1.37515i	−0.923508	+	0.383579i	$0.874691\pi$
$758$	−15.3583	−	26.6013i	−0.557838	−	0.966204i
$759$		−	2.07598i		−	0.0753531i
$760$		0			0
$761$	34.5550	−	19.9503i	1.25262	−	0.723200i	0.280990	−	0.959711i	$-0.409337\pi$
$761$	34.5550	−	19.9503i	1.25262	−	0.723200i	0.971629	+	0.236511i	$0.0760040\pi$
$762$		−	14.4407i		−	0.523131i
$763$	−1.20975	−	2.09535i	−0.0437959	−	0.0758567i
$764$	7.84081	−	13.5807i	0.283671	−	0.491332i
$765$		0			0
$766$	20.0619			0.724867
$767$	3.24978	−	21.7844i	0.117343	−	0.786589i
$768$	−1.00000			−0.0360844
$769$	−15.2064	−	8.77941i	−0.548356	−	0.316594i	0.200103	−	0.979775i	$-0.435872\pi$
$769$	−15.2064	−	8.77941i	−0.548356	−	0.316594i	−0.748459	+	0.663181i	$0.769206\pi$
$770$		0			0
$771$	9.73103	+	16.8546i	0.350454	+	0.607005i
$772$		−	8.12795i		−	0.292531i
$773$	−11.1174	+	6.41861i	−0.399864	+	0.230861i	−0.686425	−	0.727201i	$-0.740821\pi$
$773$	−11.1174	+	6.41861i	−0.399864	+	0.230861i	0.286562	+	0.958062i	$0.407488\pi$
$774$	−6.55829	+	3.78643i	−0.235733	+	0.136100i
$775$		0			0
$776$	−1.37671	−	2.38453i	−0.0494210	−	0.0855997i
$777$	−17.9759	+	31.1351i	−0.644881	+	1.11697i
$778$	−23.4099	−	13.5157i	−0.839284	−	0.484561i
$779$	58.6410			2.10103
$780$		0			0
$781$	5.85651			0.209562
$782$	−4.31119	−	2.48907i	−0.154168	−	0.0890088i
$783$	5.02239	−	8.69904i	0.179486	−	0.310878i
$784$	3.14177	+	5.44171i	0.112206	+	0.194347i
$785$		0			0
$786$	9.43032	−	5.44460i	0.336368	−	0.194202i
$787$	6.02524	−	3.47867i	0.214777	−	0.124001i	−0.388753	−	0.921342i	$-0.627094\pi$
$787$	6.02524	−	3.47867i	0.214777	−	0.124001i	0.603529	+	0.797341i	$0.293761\pi$
$788$		−	0.891239i		−	0.0317491i
$789$	−1.01739	−	1.76217i	−0.0362201	−	0.0627350i
$790$		0			0
$791$	−56.4043	−	32.5650i	−2.00551	−	1.15788i
$792$	1.66808			0.0592725
$793$	−26.6176	−	3.97081i	−0.945220	−	0.141008i
$794$	−3.73628			−0.132596
$795$		0			0
$796$	−0.180558	+	0.312736i	−0.00639971	+	0.0110846i
$797$	−17.0677	−	29.5621i	−0.604569	−	1.04714i	−0.992119	−	0.125296i	$-0.960012\pi$
$797$	−17.0677	−	29.5621i	−0.604569	−	1.04714i	0.387550	−	0.921849i	$-0.373321\pi$
$798$			23.0078i			0.814466i
$799$	−23.6432	+	13.6504i	−0.836438	+	0.482918i
$800$		0			0
$801$		−	5.95162i		−	0.210290i
$802$	−14.0456	−	24.3276i	−0.495966	−	0.859038i
$803$	10.1899	−	17.6494i	0.359593	−	0.622833i
$804$	−12.7768	−	7.37671i	−0.450604	−	0.260157i
$805$		0			0
$806$	5.57966	+	14.1538i	0.196535	+	0.498545i
$807$	−20.5287			−0.722645
$808$	−4.62124	−	2.66808i	−0.162575	−	0.0938626i
$809$	1.66385	−	2.88187i	0.0584978	−	0.101321i	−0.835293	−	0.549804i	$-0.814702\pi$
$809$	1.66385	−	2.88187i	0.0584978	−	0.101321i	0.893791	+	0.448483i	$0.148036\pi$
$810$		0			0
$811$		−	20.6083i		−	0.723655i	−0.932245	−	0.361827i	$-0.882153\pi$
$811$		−	20.6083i		−	0.723655i	0.932245	−	0.361827i	$-0.117847\pi$
$812$	−31.7050	+	18.3049i	−1.11263	+	0.642377i
$813$	22.1184	−	12.7700i	0.775725	−	0.447865i
$814$		−	16.4543i		−	0.576722i
$815$		0			0
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$	41.4008	+	23.9027i	1.44843	+	0.836251i
$818$	−27.3804			−0.957335
$819$	−12.2253	+	4.81944i	−0.427188	+	0.168405i
$820$		0			0
$821$	1.36836	+	0.790025i	0.0477562	+	0.0275721i	0.523688	−	0.851910i	$-0.324556\pi$
$821$	1.36836	+	0.790025i	0.0477562	+	0.0275721i	−0.475932	+	0.879482i	$0.657889\pi$
$822$	3.51848	−	6.09419i	0.122721	−	0.212559i
$823$	−18.7584	−	32.4905i	−0.653878	−	1.13255i	−0.982174	−	0.187974i	$-0.939808\pi$
$823$	−18.7584	−	32.4905i	−0.653878	−	1.13255i	0.328296	−	0.944575i	$-0.393526\pi$
$824$		−	7.51248i		−	0.261710i
$825$		0			0
$826$	−19.2815	+	11.1322i	−0.670889	+	0.387338i
$827$			49.4912i			1.72098i	0.509469	+	0.860489i	$0.329842\pi$
$827$			49.4912i			1.72098i	−0.509469	+	0.860489i	$0.670158\pi$
$828$	0.622266	+	1.07780i	0.0216253	+	0.0374560i
$829$	24.5693	−	42.5552i	0.853326	−	1.47800i	−0.0248634	−	0.999691i	$-0.507915\pi$
$829$	24.5693	−	42.5552i	0.853326	−	1.47800i	0.878189	−	0.478313i	$-0.158752\pi$
$830$		0			0
$831$	−18.0604			−0.626508
$832$	−2.24376	+	2.82233i	−0.0777883	+	0.0978467i
$833$	−25.1342			−0.870848
$834$	10.0846	+	5.82233i	0.349200	+	0.201611i
$835$		0			0
$836$	−5.26506	−	9.11935i	−0.182096	−	0.315399i
$837$			4.21957i			0.145850i
$838$	−11.3981	+	6.58068i	−0.393740	+	0.227326i
$839$	−18.6560	+	10.7711i	−0.644078	+	0.371858i	−0.786184	−	0.617993i	$-0.787946\pi$
$839$	−18.6560	+	10.7711i	−0.644078	+	0.371858i	0.142106	+	0.989851i	$0.454613\pi$
$840$		0			0
$841$	−35.9489	−	62.2653i	−1.23962	−	2.14708i
$842$	0.646706	−	1.12013i	0.0222870	−	0.0386021i
$843$	−17.5089	−	10.1088i	−0.603038	−	0.348164i
$844$	−2.22739			−0.0766700
$845$		0			0
$846$	6.82522			0.234656
$847$	−25.9375	−	14.9750i	−0.891224	−	0.514548i
$848$	−0.424317	+	0.734939i	−0.0145711	+	0.0252379i
$849$	4.34575	+	7.52705i	0.149146	+	0.258328i
$850$		0			0
$851$	10.6316	−	6.13818i	0.364448	−	0.210414i
$852$	−3.04056	+	1.75547i	−0.104168	+	0.0601413i
$853$		−	2.79821i		−	0.0958088i	−0.998852	−	0.0479044i	$-0.984746\pi$
$853$		−	2.79821i		−	0.0958088i	0.998852	−	0.0479044i	$-0.0152543\pi$
$854$	13.6021	+	23.5595i	0.465453	+	0.806188i
$855$		0			0
$856$	−14.6603	−	8.46410i	−0.501077	−	0.289297i
$857$	48.9658			1.67264			0.836320	−	0.548242i	$-0.184703\pi$
$857$	48.9658			1.67264			0.836320	+	0.548242i	$0.184703\pi$
$858$	3.74276	−	4.70786i	0.127776	−	0.160724i
$859$	4.22739			0.144237			0.0721184	−	0.997396i	$-0.477024\pi$
$859$	4.22739			0.144237			0.0721184	+	0.997396i	$0.477024\pi$
$860$		0			0
$861$	16.9282	−	29.3205i	0.576912	−	0.999240i
$862$	−6.06397	−	10.5031i	−0.206540	−	0.357737i
$863$			19.0285i			0.647738i	0.946102	+	0.323869i	$0.104984\pi$
$863$			19.0285i			0.647738i	−0.946102	+	0.323869i	$0.895016\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$		−	2.07802i		−	0.0706141i
$867$	−0.500000	−	0.866025i	−0.0169809	−	0.0294118i
$868$	7.68945	−	13.3185i	0.260997	−	0.452060i
$869$	−14.3506	−	8.28532i	−0.486810	−	0.281060i
$870$		0			0
$871$	−49.4877	+	19.5089i	−1.67683	+	0.661033i
$872$	−0.663848			−0.0224807
$873$	−2.38453	−	1.37671i	−0.0807042	−	0.0465946i
$874$	3.92820	−	6.80385i	0.132873	−	0.230144i
$875$		0			0
$876$			12.2175i			0.412792i
$877$	−11.7323	+	6.77363i	−0.396171	+	0.228729i	−0.684830	−	0.728702i	$-0.740124\pi$
$877$	−11.7323	+	6.77363i	−0.396171	+	0.228729i	0.288660	+	0.957432i	$0.406790\pi$
$878$	2.07534	−	1.19820i	0.0700394	−	0.0404373i
$879$			7.54790i			0.254584i
$880$		0			0
$881$	2.49041	−	4.31351i	0.0839039	−	0.145326i	−0.821020	−	0.570900i	$-0.806594\pi$
$881$	2.49041	−	4.31351i	0.0839039	−	0.145326i	0.904924	+	0.425574i	$0.139928\pi$
$882$	5.44171	+	3.14177i	0.183232	+	0.105789i
$883$	−30.9829			−1.04266			−0.521330	−	0.853355i	$-0.674564\pi$
$883$	−30.9829			−1.04266			−0.521330	+	0.853355i	$0.674564\pi$
$884$	−5.28932	−	13.4173i	−0.177899	−	0.451272i
$885$		0			0
$886$	19.0490	+	10.9980i	0.639964	+	0.369483i
$887$	8.58826	−	14.8753i	0.288365	−	0.499464i	−0.685054	−	0.728492i	$-0.740222\pi$
$887$	8.58826	−	14.8753i	0.288365	−	0.499464i	0.973420	+	0.229028i	$0.0735549\pi$
$888$	4.93211	+	8.54267i	0.165511	+	0.286673i
$889$			52.6314i			1.76520i
$890$		0			0
$891$	1.44460	−	0.834038i	0.0483958	−	0.0279413i
$892$		−	6.08380i		−	0.203701i
$893$	−21.5429	−	37.3134i	−0.720906	−	1.24865i
$894$	0.386305	−	0.669099i	0.0129200	−	0.0223780i
$895$		0			0
$896$	3.64466			0.121760
$897$	4.43811	+	0.662076i	0.148184	+	0.0221061i
$898$	−29.2253			−0.975261
$899$	36.7062	+	21.1923i	1.22422	+	0.706804i
$900$		0			0
$901$	−1.69727	−	2.93975i	−0.0565442	−	0.0979374i
$902$			15.4953i			0.515937i
$903$	23.9027	−	13.8003i	0.795433	−	0.459244i
$904$	−15.4759	+	8.93500i	−0.514720	+	0.297174i
$905$		0			0
$906$	−4.88919	−	8.46833i	−0.162433	−	0.281341i
$907$	12.5399	−	21.7197i	0.416379	−	0.721190i	−0.579193	−	0.815190i	$-0.696632\pi$
$907$	12.5399	−	21.7197i	0.416379	−	0.721190i	0.995572	+	0.0940008i	$0.0299656\pi$
$908$	13.2679	+	7.66025i	0.440312	+	0.254214i
$909$	−5.33615			−0.176989
$910$		0			0
$911$	18.2332			0.604092			0.302046	−	0.953293i	$-0.402330\pi$
$911$	18.2332			0.604092			0.302046	+	0.953293i	$0.402330\pi$
$912$	5.46699	+	3.15637i	0.181030	+	0.104518i
$913$	6.63324	−	11.4891i	0.219528	−	0.380234i
$914$	−19.8216	−	34.3321i	−0.655641	−	1.13560i
$915$		0			0
$916$	−19.2815	+	11.1322i	−0.637079	+	0.367818i
$917$	−34.3703	+	19.8437i	−1.13501	+	0.655297i
$918$		−	4.00000i		−	0.132020i
$919$	17.1941	+	29.7811i	0.567181	+	0.982387i	0.996843	+	0.0793968i	$0.0252994\pi$
$919$	17.1941	+	29.7811i	0.567181	+	0.982387i	−0.429662	+	0.902990i	$0.641367\pi$
$920$		0			0
$921$	22.5537	+	13.0214i	0.743169	+	0.429069i
$922$	−16.6758			−0.549190
$923$	−1.86777	+	12.5203i	−0.0614785	+	0.412111i
$924$	−6.07957			−0.200003
$925$		0			0
$926$	16.1088	−	27.9012i	0.529367	−	0.916890i
$927$	−3.75624	−	6.50600i	−0.123371	−	0.213685i
$928$			10.0448i			0.329736i
$929$	26.9251	−	15.5452i	0.883384	−	0.510022i	0.0116114	−	0.999933i	$-0.496304\pi$
$929$	26.9251	−	15.5452i	0.883384	−	0.510022i	0.871773	+	0.489911i	$0.162971\pi$
$930$		0			0
$931$		−	39.6663i		−	1.30001i
$932$	−5.41829	−	9.38476i	−0.177482	−	0.307408i
$933$	12.6894	−	21.9788i	0.415434	−	0.719552i
$934$	−5.95944	−	3.44069i	−0.194999	−	0.112583i
$935$		0			0
$936$	−0.531987	+	3.56609i	−0.0173886	+	0.116561i
$937$	18.8783			0.616726			0.308363	−	0.951269i	$-0.400219\pi$
$937$	18.8783			0.616726			0.308363	+	0.951269i	$0.400219\pi$
$938$	46.5672	+	26.8856i	1.52047	+	0.877846i
$939$	15.7300	−	27.2452i	0.513329	−	0.889112i
$940$		0			0
$941$		−	28.9398i		−	0.943409i	−0.881757	−	0.471705i	$-0.843639\pi$
$941$		−	28.9398i		−	0.943409i	0.881757	−	0.471705i	$-0.156361\pi$
$942$	−10.4040	+	6.00677i	−0.338982	+	0.195711i
$943$	−10.0120	+	5.78043i	−0.326036	+	0.188237i
$944$			6.10876i			0.198823i
$945$		0			0
$946$	−6.31606	+	10.9397i	−0.205353	+	0.355681i
$947$	−6.81472	−	3.93448i	−0.221448	−	0.127853i	0.385172	−	0.922845i	$-0.374142\pi$
$947$	−6.81472	−	3.93448i	−0.221448	−	0.127853i	−0.606621	+	0.794991i	$0.707475\pi$
$948$	9.93398			0.322641
$949$	34.4819	+	27.4132i	1.11933	+	0.889869i
$950$		0			0
$951$	−21.3989	−	12.3546i	−0.693905	−	0.400626i
$952$	−7.28932	+	12.6255i	−0.236248	+	0.409194i
$953$	27.5484	+	47.7153i	0.892381	+	1.54565i	0.837013	+	0.547183i	$0.184300\pi$
$953$	27.5484	+	47.7153i	0.892381	+	1.54565i	0.0553681	+	0.998466i	$0.482367\pi$
$954$			0.848634i			0.0274755i
$955$		0			0
$956$	14.2873	−	8.24876i	0.462083	−	0.266784i
$957$		−	16.7555i		−	0.541627i
$958$	9.48547	+	16.4293i	0.306462	+	0.530807i
$959$	−12.8237	+	22.2112i	−0.414098	+	0.717239i
$960$		0			0
$961$	13.1952			0.425653
$962$	35.1767	+	5.24765i	1.13414	+	0.169191i
$963$	−16.9282			−0.545504
$964$	3.81428	+	2.20218i	0.122850	+	0.0709274i
$965$		0			0
$966$	−2.26795	−	3.92820i	−0.0729701	−	0.126388i
$967$		−	31.5523i		−	1.01465i	−0.861754	−	0.507326i	$-0.830634\pi$
$967$		−	31.5523i		−	1.01465i	0.861754	−	0.507326i	$-0.169366\pi$
$968$	−7.11658	+	4.10876i	−0.228736	+	0.132061i
$969$	−21.8680	+	12.6255i	−0.702500	+	0.405589i
$970$		0			0
$971$	−1.83792	−	3.18338i	−0.0589818	−	0.102159i	0.835027	−	0.550209i	$-0.185452\pi$
$971$	−1.83792	−	3.18338i	−0.0589818	−	0.102159i	−0.894009	+	0.448050i	$0.852119\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−36.7548	−	21.2204i	−1.17831	−	0.680295i
$974$	1.91620			0.0613991
$975$		0			0
$976$	7.46410			0.238920
$977$	−36.3908	−	21.0102i	−1.16424	−	0.672177i	−0.211927	−	0.977286i	$-0.567974\pi$
$977$	−36.3908	−	21.0102i	−1.16424	−	0.672177i	−0.952318	+	0.305109i	$0.901307\pi$
$978$	−5.04581	+	8.73960i	−0.161347	+	0.279462i
$979$	−4.96388	−	8.59769i	−0.158646	−	0.274783i
$980$		0			0
$981$	−0.574909	+	0.331924i	−0.0183554	+	0.0105975i
$982$	29.1309	−	16.8187i	0.929605	−	0.536707i
$983$			13.4307i			0.428372i	0.976793	+	0.214186i	$0.0687099\pi$
$983$			13.4307i			0.428372i	−0.976793	+	0.214186i	$0.931290\pi$
$984$	−4.64466	−	8.04479i	−0.148066	−	0.256458i
$985$		0			0
$986$	−34.7962	−	20.0896i	−1.10814	−	0.639782i
$987$	−24.8756			−0.791799
$988$	21.1749	−	8.34752i	0.673664	−	0.265570i
$989$	−9.42468			−0.299687
$990$		0			0
$991$	−21.8994	+	37.9309i	−0.695658	+	1.20492i	0.274300	+	0.961644i	$0.411554\pi$
$991$	−21.8994	+	37.9309i	−0.695658	+	1.20492i	−0.969958	+	0.243271i	$0.921780\pi$
$992$	−2.10978	−	3.65425i	−0.0669857	−	0.116023i
$993$			5.60360i			0.177825i
$994$	11.0818	−	6.39808i	0.351493	−	0.202935i
$995$		0			0
$996$			7.95317i			0.252006i
$997$	−11.7562	−	20.3624i	−0.372324	−	0.644884i	0.617599	−	0.786493i	$-0.288106\pi$
$997$	−11.7562	−	20.3624i	−0.372324	−	0.644884i	−0.989923	+	0.141609i	$0.954772\pi$
$998$	0.912609	−	1.58068i	0.0288881	−	0.0500357i
$999$	8.54267	+	4.93211i	0.270278	+	0.156045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.g.901.2		8
5.2	odd	4		1950.2.y.k.199.2		8
5.3	odd	4		1950.2.y.j.199.3		8
5.4	even	2		390.2.bb.c.121.3	✓	8
13.10	even	6	inner	1950.2.bc.g.751.2		8
15.14	odd	2		1170.2.bs.f.901.1		8
65.4	even	6		5070.2.b.ba.1351.8		8
65.9	even	6		5070.2.b.ba.1351.1		8
65.19	odd	12		5070.2.a.bz.1.4		4
65.23	odd	12		1950.2.y.k.49.2		8
65.49	even	6		390.2.bb.c.361.3	yes	8
65.59	odd	12		5070.2.a.ca.1.1		4
65.62	odd	12		1950.2.y.j.49.3		8
195.179	odd	6		1170.2.bs.f.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.3	✓	8	5.4	even	2
390.2.bb.c.361.3	yes	8	65.49	even	6
1170.2.bs.f.361.1		8	195.179	odd	6
1170.2.bs.f.901.1		8	15.14	odd	2
1950.2.y.j.49.3		8	65.62	odd	12
1950.2.y.j.199.3		8	5.3	odd	4
1950.2.y.k.49.2		8	65.23	odd	12
1950.2.y.k.199.2		8	5.2	odd	4
1950.2.bc.g.751.2		8	13.10	even	6	inner
1950.2.bc.g.901.2		8	1.1	even	1	trivial
5070.2.a.bz.1.4		4	65.19	odd	12
5070.2.a.ca.1.1		4	65.59	odd	12
5070.2.b.ba.1351.1		8	65.9	even	6
5070.2.b.ba.1351.8		8	65.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.44460 - 0.834038i) q^{11} +1.00000 q^{12} +(2.24376 - 2.82233i) q^{13} -3.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(5.46699 - 3.15637i) q^{19} -3.64466i q^{21} +(0.834038 + 1.44460i) q^{22} +(-0.622266 + 1.07780i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.35432 + 1.32233i) q^{26} -1.00000 q^{27} +(3.15637 + 1.82233i) q^{28} +(-5.02239 + 8.69904i) q^{29} -4.21957i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.44460 + 0.834038i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-8.54267 - 4.93211i) q^{37} -6.31274 q^{38} +(-1.32233 - 3.35432i) q^{39} +(8.04479 + 4.64466i) q^{41} +(-1.82233 + 3.15637i) q^{42} +(3.78643 + 6.55829i) q^{43} -1.66808i q^{44} +(1.07780 - 0.622266i) q^{46} -6.82522i q^{47} +(0.500000 + 0.866025i) q^{48} +(3.14177 - 5.44171i) q^{49} -4.00000 q^{51} +(3.56609 + 0.531987i) q^{52} +0.848634 q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.82233 - 3.15637i) q^{56} -6.31274i q^{57} +(8.69904 - 5.02239i) q^{58} +(5.29034 - 3.05438i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(-2.10978 + 3.65425i) q^{62} +(-3.15637 - 1.82233i) q^{63} -1.00000 q^{64} +1.66808 q^{66} +(-12.7768 - 7.37671i) q^{67} +(2.00000 - 3.46410i) q^{68} +(0.622266 + 1.07780i) q^{69} +(-3.04056 + 1.75547i) q^{71} +(-0.866025 + 0.500000i) q^{72} +12.2175i q^{73} +(4.93211 + 8.54267i) q^{74} +(5.46699 + 3.15637i) q^{76} -6.07957 q^{77} +(-0.531987 + 3.56609i) q^{78} +9.93398 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.64466 - 8.04479i) q^{82} +7.95317i q^{83} +(3.15637 - 1.82233i) q^{84} -7.57286i q^{86} +(5.02239 + 8.69904i) q^{87} +(-0.834038 + 1.44460i) q^{88} +(5.15425 + 2.97581i) q^{89} +(1.93891 - 12.9972i) q^{91} -1.24453 q^{92} +(-3.65425 - 2.10978i) q^{93} +(-3.41261 + 5.91081i) q^{94} -1.00000i q^{96} +(2.38453 - 1.37671i) q^{97} +(-5.44171 + 3.14177i) q^{98} +1.66808i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} - 2 q^{22} - 4 q^{23} - 12 q^{26} - 8 q^{27} - 8 q^{29} + 6 q^{33} + 4 q^{36} - 30 q^{37} + 6 q^{39} + 2 q^{42} - 14 q^{43} - 6 q^{46} + 4 q^{48} + 14 q^{49} - 32 q^{51} + 6 q^{52} - 16 q^{53} + 2 q^{56} + 6 q^{58} + 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 4 q^{66} - 24 q^{67} + 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} - 6 q^{76} - 16 q^{77} - 6 q^{78} - 20 q^{79} - 4 q^{81} - 4 q^{82} + 8 q^{87} + 2 q^{88} + 42 q^{89} - 10 q^{91} - 8 q^{92} - 30 q^{93} - 8 q^{94} + 24 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 - 2 * q^22 - 4 * q^23 - 12 * q^26 - 8 * q^27 - 8 * q^29 + 6 * q^33 + 4 * q^36 - 30 * q^37 + 6 * q^39 + 2 * q^42 - 14 * q^43 - 6 * q^46 + 4 * q^48 + 14 * q^49 - 32 * q^51 + 6 * q^52 - 16 * q^53 + 2 * q^56 + 6 * q^58 + 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 4 * q^66 - 24 * q^67 + 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 - 6 * q^76 - 16 * q^77 - 6 * q^78 - 20 * q^79 - 4 * q^81 - 4 * q^82 + 8 * q^87 + 2 * q^88 + 42 * q^89 - 10 * q^91 - 8 * q^92 - 30 * q^93 - 8 * q^94 + 24 * q^97 - 48 * q^98

Introduction

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