LMFDB - Embedded newform 1950.2.y.k.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

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.y (of order $6$, degree $2$, 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:	$15.5708283941$
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			49.2
Root			$1.33404 - 1.33404i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.k.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	1.82233	−	3.15637i	0.688776	−	1.19299i	−0.283458	−	0.958985i	$-0.591482\pi$
$7$	1.82233	−	3.15637i	0.688776	−	1.19299i	0.972234	−	0.234010i	$-0.0751849\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.44460	+	0.834038i	−0.435562	+	0.251472i	−0.701713	−	0.712459i	$-0.747581\pi$
$11$	−1.44460	+	0.834038i	−0.435562	+	0.251472i	0.266151	+	0.963931i	$0.414248\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−2.82233	+	2.24376i	−0.782773	+	0.622307i
$13$	−2.82233	+	2.24376i	−0.782773	+	0.622307i
$14$	3.64466			0.974076
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	0.857321	−	0.514782i	$-0.172127\pi$
$17$	3.46410	+	2.00000i	0.840168	+	0.485071i	−0.0171533	+	0.999853i	$0.505460\pi$
$18$	1.00000			0.235702
$19$	−5.46699	−	3.15637i	−1.25421	−	0.724120i	−0.282270	−	0.959335i	$-0.591087\pi$
$19$	−5.46699	−	3.15637i	−1.25421	−	0.724120i	−0.971943	+	0.235215i	$0.924421\pi$
$20$		0			0
$21$			3.64466i			0.795330i
$22$	−1.44460	−	0.834038i	−0.307989	−	0.177817i
$23$	1.07780	−	0.622266i	0.224736	−	0.129752i	−0.383405	−	0.923580i	$-0.625249\pi$
$23$	1.07780	−	0.622266i	0.224736	−	0.129752i	0.608141	+	0.793829i	$0.291915\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	−3.35432	−	1.32233i	−0.657836	−	0.259330i
$27$			1.00000i			0.192450i
$28$	1.82233	+	3.15637i	0.344388	+	0.596497i
$29$	5.02239	+	8.69904i	0.932635	+	1.61537i	0.778798	+	0.627275i	$0.215830\pi$
$29$	5.02239	+	8.69904i	0.932635	+	1.61537i	0.153837	+	0.988096i	$0.450837\pi$
$30$		0			0
$31$			4.21957i			0.757857i	0.925426	+	0.378928i	$0.123707\pi$
$31$			4.21957i			0.757857i	−0.925426	+	0.378928i	$0.876293\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.834038	−	1.44460i	0.145187	−	0.251472i
$34$			4.00000i			0.685994i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	4.93211	+	8.54267i	0.810835	+	1.40441i	0.912281	+	0.409566i	$0.134320\pi$
$37$	4.93211	+	8.54267i	0.810835	+	1.40441i	−0.101446	+	0.994841i	$0.532347\pi$
$38$		−	6.31274i		−	1.02406i
$39$	1.32233	−	3.35432i	0.211742	−	0.537121i
$40$		0			0
$41$	8.04479	−	4.64466i	1.25638	−	0.725374i	0.284015	−	0.958820i	$-0.408334\pi$
$41$	8.04479	−	4.64466i	1.25638	−	0.725374i	0.972370	+	0.233446i	$0.0750002\pi$
$42$	−3.15637	+	1.82233i	−0.487038	+	0.281192i
$43$	6.55829	+	3.78643i	1.00013	+	0.577425i	0.908287	−	0.418348i	$-0.137391\pi$
$43$	6.55829	+	3.78643i	1.00013	+	0.577425i	0.0918433	+	0.995773i	$0.470724\pi$
$44$		−	1.66808i		−	0.251472i
$45$		0			0
$46$	1.07780	+	0.622266i	0.158912	+	0.0917482i
$47$	6.82522			0.995560			0.497780	−	0.867303i	$-0.334149\pi$
$47$	6.82522			0.995560			0.497780	+	0.867303i	$0.334149\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−3.14177	−	5.44171i	−0.448825	−	0.777387i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	−0.531987	−	3.56609i	−0.0737734	−	0.494528i
$53$			0.848634i			0.116569i	0.998300	+	0.0582844i	$0.0185630\pi$
$53$			0.848634i			0.116569i	−0.998300	+	0.0582844i	$0.981437\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−1.82233	+	3.15637i	−0.243519	+	0.421787i
$57$	6.31274			0.836142
$58$	−5.02239	+	8.69904i	−0.659473	+	1.14224i
$59$	−5.29034	−	3.05438i	−0.688744	−	0.397646i	0.114397	−	0.993435i	$-0.463506\pi$
$59$	−5.29034	−	3.05438i	−0.688744	−	0.397646i	−0.803141	+	0.595789i	$0.796840\pi$
$60$		0			0
$61$	−3.73205	+	6.46410i	−0.477840	+	0.827643i	−0.999677	−	0.0254017i	$-0.991914\pi$
$61$	−3.73205	+	6.46410i	−0.477840	+	0.827643i	0.521837	+	0.853045i	$0.325247\pi$
$62$	−3.65425	+	2.10978i	−0.464091	+	0.267943i
$63$	−1.82233	−	3.15637i	−0.229592	−	0.397665i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.66808			0.205326
$67$	7.37671	+	12.7768i	0.901209	+	1.56094i	0.825927	+	0.563777i	$0.190652\pi$
$67$	7.37671	+	12.7768i	0.901209	+	1.56094i	0.0752814	+	0.997162i	$0.476014\pi$
$68$	−3.46410	+	2.00000i	−0.420084	+	0.242536i
$69$	−0.622266	+	1.07780i	−0.0749121	+	0.129752i
$70$		0			0
$71$	−3.04056	−	1.75547i	−0.360848	−	0.208336i	0.308605	−	0.951190i	$-0.400138\pi$
$71$	−3.04056	−	1.75547i	−0.360848	−	0.208336i	−0.669453	+	0.742855i	$0.733471\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	12.2175			1.42995			0.714976	−	0.699149i	$-0.246437\pi$
$73$	12.2175			1.42995			0.714976	+	0.699149i	$0.246437\pi$
$74$	−4.93211	+	8.54267i	−0.573347	+	0.993065i
$75$		0			0
$76$	5.46699	−	3.15637i	0.627107	−	0.362060i
$77$			6.07957i			0.692831i
$78$	3.56609	−	0.531987i	0.403780	−	0.0602357i
$79$	−9.93398			−1.11766			−0.558830	−	0.829282i	$-0.688750\pi$
$79$	−9.93398			−1.11766			−0.558830	+	0.829282i	$0.688750\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.04479	+	4.64466i	0.888398	+	0.512917i
$83$	7.95317			0.872974			0.436487	−	0.899711i	$-0.356223\pi$
$83$	7.95317			0.872974			0.436487	+	0.899711i	$0.356223\pi$
$84$	−3.15637	−	1.82233i	−0.344388	−	0.198832i
$85$		0			0
$86$			7.57286i			0.816603i
$87$	−8.69904	−	5.02239i	−0.932635	−	0.538457i
$88$	1.44460	−	0.834038i	0.153994	−	0.0889087i
$89$	−5.15425	+	2.97581i	−0.546350	+	0.315435i	−0.747648	−	0.664095i	$-0.768817\pi$
$89$	−5.15425	+	2.97581i	−0.546350	+	0.315435i	0.201299	+	0.979530i	$0.435484\pi$
$90$		0			0
$91$	1.93891	+	12.9972i	0.203253	+	1.36247i
$92$			1.24453i			0.129752i
$93$	−2.10978	−	3.65425i	−0.218774	−	0.378928i
$94$	3.41261	+	5.91081i	0.351984	+	0.609654i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	1.37671	−	2.38453i	0.139784	−	0.242113i	−0.787631	−	0.616147i	$-0.788693\pi$
$97$	1.37671	−	2.38453i	0.139784	−	0.242113i	0.927415	+	0.374035i	$0.122026\pi$
$98$	3.14177	−	5.44171i	0.317367	−	0.549696i
$99$			1.66808i			0.167648i
$100$		0			0
$101$	2.66808	+	4.62124i	0.265483	+	0.459831i	0.967690	−	0.252142i	$-0.0811351\pi$
$101$	2.66808	+	4.62124i	0.265483	+	0.459831i	−0.702207	+	0.711973i	$0.747802\pi$
$102$	−2.00000	−	3.46410i	−0.198030	−	0.342997i
$103$			7.51248i			0.740227i	0.928987	+	0.370113i	$0.120681\pi$
$103$			7.51248i			0.740227i	−0.928987	+	0.370113i	$0.879319\pi$
$104$	2.82233	−	2.24376i	0.276752	−	0.220019i
$105$		0			0
$106$	−0.734939	+	0.424317i	−0.0713835	+	0.0412133i
$107$	14.6603	−	8.46410i	1.41726	−	0.818256i	0.421203	−	0.906966i	$-0.361608\pi$
$107$	14.6603	−	8.46410i	1.41726	−	0.818256i	0.996057	+	0.0887109i	$0.0282747\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$		−	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
$112$	−3.64466			−0.344388
$113$	−15.4759	−	8.93500i	−1.45585	−	0.840534i	−0.457045	−	0.889444i	$-0.651092\pi$
$113$	−15.4759	−	8.93500i	−1.45585	−	0.840534i	−0.998803	+	0.0489094i	$0.984425\pi$
$114$	3.15637	+	5.46699i	0.295621	+	0.512030i
$115$		0			0
$116$	−10.0448			−0.932635
$117$	0.531987	+	3.56609i	0.0491823	+	0.329685i
$118$		−	6.10876i		−	0.562357i
$119$	12.6255	−	7.28932i	1.15738	−	0.668211i
$120$		0			0
$121$	−4.10876	+	7.11658i	−0.373524	+	0.646962i
$122$	−7.46410			−0.675768
$123$	−4.64466	+	8.04479i	−0.418795	+	0.725374i
$124$	−3.65425	−	2.10978i	−0.328162	−	0.189464i
$125$		0			0
$126$	1.82233	−	3.15637i	0.162346	−	0.281192i
$127$	−12.5060	+	7.22034i	−1.10973	+	0.640702i	−0.938759	−	0.344575i	$-0.888023\pi$
$127$	−12.5060	+	7.22034i	−1.10973	+	0.640702i	−0.170969	+	0.985276i	$0.554690\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−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	$0.657804\pi$
$132$	0.834038	+	1.44460i	0.0725937	+	0.125736i
$133$	−19.9253	+	11.5039i	−1.72774	+	0.997513i
$134$	−7.37671	+	12.7768i	−0.637251	+	1.10375i
$135$		0			0
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	−3.51848	+	6.09419i	−0.300604	+	0.520662i	−0.976273	−	0.216544i	$-0.930522\pi$
$137$	−3.51848	+	6.09419i	−0.300604	+	0.520662i	0.675669	+	0.737205i	$0.263855\pi$
$138$	−1.24453			−0.105942
$139$	5.82233	−	10.0846i	0.493844	−	0.855362i	−0.506131	−	0.862456i	$-0.668925\pi$
$139$	5.82233	−	10.0846i	0.493844	−	0.855362i	0.999975	+	0.00709431i	$0.00225821\pi$
$140$		0			0
$141$	−5.91081	+	3.41261i	−0.497780	+	0.287394i
$142$		−	3.51093i		−	0.294631i
$143$	2.20575	−	5.59526i	0.184454	−	0.467899i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	6.10876	+	10.5807i	0.505565	+	0.875664i
$147$	5.44171	+	3.14177i	0.448825	+	0.259129i
$148$	−9.86423			−0.810835
$149$	0.669099	+	0.386305i	0.0548147	+	0.0316473i	0.527157	−	0.849768i	$-0.323258\pi$
$149$	0.669099	+	0.386305i	0.0548147	+	0.0316473i	−0.472342	+	0.881415i	$0.656591\pi$
$150$		0			0
$151$		−	9.77838i		−	0.795754i	−0.917439	−	0.397877i	$-0.869747\pi$
$151$		−	9.77838i		−	0.795754i	0.917439	−	0.397877i	$-0.130253\pi$
$152$	5.46699	+	3.15637i	0.443431	+	0.256015i
$153$	3.46410	−	2.00000i	0.280056	−	0.161690i
$154$	−5.26506	+	3.03978i	−0.424271	+	0.244953i
$155$		0			0
$156$	2.24376	+	2.82233i	0.179644	+	0.225967i
$157$		−	12.0135i		−	0.958786i	−0.877600	−	0.479393i	$-0.840857\pi$
$157$		−	12.0135i		−	0.958786i	0.877600	−	0.479393i	$-0.159143\pi$
$158$	−4.96699	−	8.60308i	−0.395152	−	0.684424i
$159$	−0.424317	−	0.734939i	−0.0336505	−	0.0582844i
$160$		0			0
$161$		−	4.53590i		−	0.357479i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−5.04581	+	8.73960i	−0.395218	+	0.684538i	−0.993129	−	0.117025i	$-0.962664\pi$
$163$	−5.04581	+	8.73960i	−0.395218	+	0.684538i	0.597911	+	0.801563i	$0.295998\pi$
$164$			9.28932i			0.725374i
$165$		0			0
$166$	3.97658	+	6.88764i	0.308643	+	0.534585i
$167$	−3.94851	−	6.83902i	−0.305545	−	0.529219i	0.671838	−	0.740698i	$-0.265505\pi$
$167$	−3.94851	−	6.83902i	−0.305545	−	0.529219i	−0.977382	+	0.211479i	$0.932172\pi$
$168$		−	3.64466i		−	0.281192i
$169$	2.93109	−	12.6653i	0.225469	−	0.974250i
$170$		0			0
$171$	−5.46699	+	3.15637i	−0.418071	+	0.241373i
$172$	−6.55829	+	3.78643i	−0.500065	+	0.288713i
$173$	0.381645	+	0.220343i	0.0290159	+	0.0167523i	0.514438	−	0.857528i	$-0.328001\pi$
$173$	0.381645	+	0.220343i	0.0290159	+	0.0167523i	−0.485422	+	0.874280i	$0.661334\pi$
$174$		−	10.0448i		−	0.761493i
$175$		0			0
$176$	1.44460	+	0.834038i	0.108891	+	0.0628680i
$177$	6.10876			0.459163
$178$	−5.15425	−	2.97581i	−0.386328	−	0.223046i
$179$	9.81842	+	17.0060i	0.733863	+	1.27109i	0.955220	+	0.295895i	$0.0956180\pi$
$179$	9.81842	+	17.0060i	0.733863	+	1.27109i	−0.221357	+	0.975193i	$0.571049\pi$
$180$		0			0
$181$	6.21752			0.462145			0.231072	−	0.972937i	$-0.425777\pi$
$181$	6.21752			0.462145			0.231072	+	0.972937i	$0.425777\pi$
$182$	−10.2864	+	8.17774i	−0.762481	+	0.606174i
$183$		−	7.46410i		−	0.551762i
$184$	−1.07780	+	0.622266i	−0.0794562	+	0.0458741i
$185$		0			0
$186$	2.10978	−	3.65425i	0.154697	−	0.267943i
$187$	−6.67230			−0.487927
$188$	−3.41261	+	5.91081i	−0.248890	+	0.431090i
$189$	3.15637	+	1.82233i	0.229592	+	0.132555i
$190$		0			0
$191$	−7.84081	+	13.5807i	−0.567341	+	0.982664i	0.429486	+	0.903073i	$0.358695\pi$
$191$	−7.84081	+	13.5807i	−0.567341	+	0.982664i	−0.996828	+	0.0795905i	$0.974639\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−4.06397	−	7.03901i	−0.292531	−	0.506679i	0.681876	−	0.731468i	$-0.261164\pi$
$193$	−4.06397	−	7.03901i	−0.292531	−	0.506679i	−0.974408	+	0.224788i	$0.927831\pi$
$194$	2.75342			0.197684
$195$		0			0
$196$	6.28354			0.448825
$197$	0.445619	+	0.771835i	0.0317491	+	0.0549910i	0.881463	−	0.472252i	$-0.156559\pi$
$197$	0.445619	+	0.771835i	0.0317491	+	0.0549910i	−0.849714	+	0.527243i	$0.823226\pi$
$198$	−1.44460	+	0.834038i	−0.102663	+	0.0592725i
$199$	−0.180558	+	0.312736i	−0.0127994	+	0.0221692i	−0.872354	−	0.488874i	$-0.837408\pi$
$199$	−0.180558	+	0.312736i	−0.0127994	+	0.0221692i	0.859555	+	0.511044i	$0.170741\pi$
$200$		0			0
$201$	−12.7768	−	7.37671i	−0.901209	−	0.520313i
$202$	−2.66808	+	4.62124i	−0.187725	+	0.325150i
$203$	36.6098			2.56951
$204$	2.00000	−	3.46410i	0.140028	−	0.242536i
$205$		0			0
$206$	−6.50600	+	3.75624i	−0.453295	+	0.261710i
$207$		−	1.24453i		−	0.0865010i
$208$	3.35432	+	1.32233i	0.232580	+	0.0916871i
$209$	10.5301			0.728384
$210$		0			0
$211$	−1.11370	−	1.92898i	−0.0766700	−	0.132796i	0.825141	−	0.564926i	$-0.191095\pi$
$211$	−1.11370	−	1.92898i	−0.0766700	−	0.132796i	−0.901811	+	0.432130i	$0.857762\pi$
$212$	−0.734939	−	0.424317i	−0.0504758	−	0.0291422i
$213$	3.51093			0.240565
$214$	14.6603	+	8.46410i	1.00215	+	0.578594i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	13.3185	+	7.68945i	0.904119	+	0.521994i
$218$	0.574909	−	0.331924i	0.0389378	−	0.0224807i
$219$	−10.5807	+	6.10876i	−0.714976	+	0.412792i
$220$		0			0
$221$	−14.2644	+	2.12795i	−0.959524	+	0.143141i
$222$		−	9.86423i		−	0.662044i
$223$	−3.04190	−	5.26872i	−0.203701	−	0.352820i	0.746017	−	0.665927i	$-0.231964\pi$
$223$	−3.04190	−	5.26872i	−0.203701	−	0.352820i	−0.949718	+	0.313107i	$0.898630\pi$
$224$	−1.82233	−	3.15637i	−0.121760	−	0.210894i
$225$		0			0
$226$		−	17.8700i		−	1.18869i
$227$	7.66025	−	13.2679i	0.508429	−	0.880625i	−0.491523	−	0.870864i	$-0.663560\pi$
$227$	7.66025	−	13.2679i	0.508429	−	0.880625i	0.999952	−	0.00976038i	$-0.00310687\pi$
$228$	−3.15637	+	5.46699i	−0.209036	+	0.362060i
$229$			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
$232$	−5.02239	−	8.69904i	−0.329736	−	0.571120i
$233$		−	10.8366i		−	0.709928i	−0.934880	−	0.354964i	$-0.884493\pi$
$233$		−	10.8366i		−	0.709928i	0.934880	−	0.354964i	$-0.115507\pi$
$234$	−2.82233	+	2.24376i	−0.184501	+	0.146679i
$235$		0			0
$236$	5.29034	−	3.05438i	0.344372	−	0.198823i
$237$	8.60308	−	4.96699i	0.558830	−	0.322641i
$238$	12.6255	+	7.28932i	0.818388	+	0.472496i
$239$		−	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	0.617794	−	0.786340i	$-0.288027\pi$
$241$	3.81428	+	2.20218i	0.245700	+	0.141855i	−0.372094	+	0.928195i	$0.621360\pi$
$242$	−8.21752			−0.528242
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−3.73205	−	6.46410i	−0.238920	−	0.413822i
$245$		0			0
$246$	−9.28932			−0.592265
$247$	22.5118	−	3.35830i	1.43239	−	0.213683i
$248$		−	4.21957i		−	0.267943i
$249$	−6.88764	+	3.97658i	−0.436487	+	0.252006i
$250$		0			0
$251$	5.97267	−	10.3450i	0.376992	−	0.652969i	−0.613631	−	0.789593i	$-0.710292\pi$
$251$	5.97267	−	10.3450i	0.376992	−	0.652969i	0.990623	+	0.136624i	$0.0436252\pi$
$252$	3.64466			0.229592
$253$	−1.03799	+	1.79785i	−0.0652577	+	0.113030i
$254$	−12.5060	−	7.22034i	−0.784696	−	0.453045i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−16.8546	+	9.73103i	−1.05136	+	0.607005i	−0.923031	−	0.384726i	$-0.874296\pi$
$257$	−16.8546	+	9.73103i	−1.05136	+	0.607005i	−0.128333	+	0.991731i	$0.540962\pi$
$258$	−3.78643	−	6.55829i	−0.235733	−	0.408301i
$259$	35.9518			2.23393
$260$		0			0
$261$	10.0448			0.621757
$262$	−5.44460	−	9.43032i	−0.336368	−	0.582607i
$263$	−1.76217	+	1.01739i	−0.108660	+	0.0627350i	−0.553345	−	0.832952i	$-0.686649\pi$
$263$	−1.76217	+	1.01739i	−0.108660	+	0.0627350i	0.444685	+	0.895687i	$0.353316\pi$
$264$	−0.834038	+	1.44460i	−0.0513315	+	0.0889087i
$265$		0			0
$266$	−19.9253	−	11.5039i	−1.22170	−	0.705349i
$267$	2.97581	−	5.15425i	0.182117	−	0.315435i
$268$	−14.7534			−0.901209
$269$	10.2644	−	17.7784i	0.625829	−	1.08397i	−0.362551	−	0.931964i	$-0.618094\pi$
$269$	10.2644	−	17.7784i	0.625829	−	1.08397i	0.988380	−	0.152003i	$-0.0485725\pi$
$270$		0			0
$271$	22.1184	−	12.7700i	1.34359	−	0.775725i	0.356261	−	0.934386i	$-0.384051\pi$
$271$	22.1184	−	12.7700i	1.34359	−	0.775725i	0.987333	+	0.158662i	$0.0507179\pi$
$272$		−	4.00000i		−	0.242536i
$273$	−8.17774	−	10.2864i	−0.494939	−	0.622563i
$274$	−7.03696			−0.425119
$275$		0			0
$276$	−0.622266	−	1.07780i	−0.0374560	−	0.0648758i
$277$	15.6407	+	9.03019i	0.939762	+	0.542572i	0.889886	−	0.456184i	$-0.150784\pi$
$277$	15.6407	+	9.03019i	0.939762	+	0.542572i	0.0498760	+	0.998755i	$0.484117\pi$
$278$	11.6447			0.698400
$279$	3.65425	+	2.10978i	0.218774	+	0.126309i
$280$		0			0
$281$			20.2175i			1.20608i	0.797712	+	0.603038i	$0.206043\pi$
$281$			20.2175i			1.20608i	−0.797712	+	0.603038i	$0.793957\pi$
$282$	−5.91081	−	3.41261i	−0.351984	−	0.203218i
$283$	7.52705	−	4.34575i	0.447437	−	0.258328i	−0.259310	−	0.965794i	$-0.583495\pi$
$283$	7.52705	−	4.34575i	0.447437	−	0.258328i	0.706747	+	0.707466i	$0.250162\pi$
$284$	3.04056	−	1.75547i	0.180424	−	0.104168i
$285$		0			0
$286$	5.94851	−	0.887395i	0.351743	−	0.0524728i
$287$		−	33.8564i		−	1.99848i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$			2.75342i			0.161408i
$292$	−6.10876	+	10.5807i	−0.357488	+	0.619188i
$293$	3.77395	−	6.53667i	0.220476	−	0.381876i	−0.734476	−	0.678634i	$-0.762572\pi$
$293$	3.77395	−	6.53667i	0.220476	−	0.381876i	0.954953	+	0.296758i	$0.0959054\pi$
$294$			6.28354i			0.366464i
$295$		0			0
$296$	−4.93211	−	8.54267i	−0.286673	−	0.496533i
$297$	−0.834038	−	1.44460i	−0.0483958	−	0.0838240i
$298$			0.772609i			0.0447560i
$299$	−1.64568	+	4.17456i	−0.0951723	+	0.241421i
$300$		0			0
$301$	23.9027	−	13.8003i	1.37773	−	0.795433i
$302$	8.46833	−	4.88919i	0.487298	−	0.281341i
$303$	−4.62124	−	2.66808i	−0.265483	−	0.153277i
$304$			6.31274i			0.362060i
$305$		0			0
$306$	3.46410	+	2.00000i	0.198030	+	0.114332i
$307$	−26.0427			−1.48634			−0.743169	−	0.669104i	$-0.766678\pi$
$307$	−26.0427			−1.48634			−0.743169	+	0.669104i	$0.766678\pi$
$308$	−5.26506	−	3.03978i	−0.300005	−	0.173208i
$309$	−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	$0.244347\pi$
$312$	−1.32233	+	3.35432i	−0.0748622	+	0.189901i
$313$			31.4600i			1.77822i	0.457689	+	0.889112i	$0.348677\pi$
$313$			31.4600i			1.77822i	−0.457689	+	0.889112i	$0.651323\pi$
$314$	10.4040	−	6.00677i	0.587134	−	0.338982i
$315$		0			0
$316$	4.96699	−	8.60308i	0.279415	−	0.483961i
$317$	24.7093			1.38781			0.693905	−	0.720066i	$-0.255889\pi$
$317$	24.7093			1.38781			0.693905	+	0.720066i	$0.255889\pi$
$318$	0.424317	−	0.734939i	0.0237945	−	0.0412133i
$319$	−14.5107	−	8.37773i	−0.812441	−	0.469063i
$320$		0			0
$321$	−8.46410	+	14.6603i	−0.472420	+	0.818256i
$322$	3.92820	−	2.26795i	0.218910	−	0.126388i
$323$	−12.6255	−	21.8680i	−0.702500	−	1.21677i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−10.0916			−0.558923
$327$	0.331924	+	0.574909i	0.0183554	+	0.0317926i
$328$	−8.04479	+	4.64466i	−0.444199	+	0.256458i
$329$	12.4378	−	21.5429i	0.685718	−	1.18770i
$330$		0			0
$331$	−4.85286	−	2.80180i	−0.266737	−	0.154001i	0.360667	−	0.932695i	$-0.382549\pi$
$331$	−4.85286	−	2.80180i	−0.266737	−	0.154001i	−0.627404	+	0.778694i	$0.715883\pi$
$332$	−3.97658	+	6.88764i	−0.218243	+	0.378009i
$333$	9.86423			0.540556
$334$	3.94851	−	6.83902i	0.216053	−	0.374214i
$335$		0			0
$336$	3.15637	−	1.82233i	0.172194	−	0.0994162i
$337$			21.7868i			1.18680i	0.804906	+	0.593402i	$0.202216\pi$
$337$			21.7868i			1.18680i	−0.804906	+	0.593402i	$0.797784\pi$
$338$	12.4340	−	3.79423i	0.676319	−	0.206379i
$339$	17.8700			0.970565
$340$		0			0
$341$	−3.51928	−	6.09557i	−0.190580	−	0.330094i
$342$	−5.46699	−	3.15637i	−0.295621	−	0.170677i
$343$	2.61124			0.140994
$344$	−6.55829	−	3.78643i	−0.353599	−	0.204151i
$345$		0			0
$346$			0.440685i			0.0236914i
$347$	−8.38453	−	4.84081i	−0.450105	−	0.259868i	0.257769	−	0.966206i	$-0.417013\pi$
$347$	−8.38453	−	4.84081i	−0.450105	−	0.259868i	−0.707875	+	0.706338i	$0.750346\pi$
$348$	8.69904	−	5.02239i	0.466318	−	0.269229i
$349$	−16.7321	+	9.66025i	−0.895646	+	0.517102i	−0.875785	−	0.482701i	$-0.839656\pi$
$349$	−16.7321	+	9.66025i	−0.895646	+	0.517102i	−0.0198610	+	0.999803i	$0.506322\pi$
$350$		0			0
$351$	−2.24376	−	2.82233i	−0.119763	−	0.150645i
$352$			1.66808i			0.0889087i
$353$	11.4875	+	19.8970i	0.611419	+	1.05901i	0.991002	+	0.133851i	$0.0427343\pi$
$353$	11.4875	+	19.8970i	0.611419	+	1.05901i	−0.379583	+	0.925158i	$0.623932\pi$
$354$	3.05438	+	5.29034i	0.162338	+	0.281179i
$355$		0			0
$356$		−	5.95162i		−	0.315435i
$357$	−7.28932	+	12.6255i	−0.385792	+	0.668211i
$358$	−9.81842	+	17.0060i	−0.518920	+	0.898795i
$359$			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
$362$	3.10876	+	5.38453i	0.163393	+	0.283005i
$363$		−	8.21752i		−	0.431308i
$364$	−12.2253	−	4.81944i	−0.640782	−	0.252607i
$365$		0			0
$366$	6.46410	−	3.73205i	0.337884	−	0.195077i
$367$	−5.26640	+	3.04056i	−0.274904	+	0.158716i	−0.631114	−	0.775690i	$-0.717402\pi$
$367$	−5.26640	+	3.04056i	−0.274904	+	0.158716i	0.356210	+	0.934406i	$0.384069\pi$
$368$	−1.07780	−	0.622266i	−0.0561841	−	0.0324379i
$369$		−	9.28932i		−	0.483583i
$370$		0			0
$371$	2.67860	+	1.54649i	0.139066	+	0.0802898i
$372$	4.21957			0.218774
$373$	13.5776	+	7.83904i	0.703022	+	0.405890i	0.808472	−	0.588535i	$-0.200295\pi$
$373$	13.5776	+	7.83904i	0.703022	+	0.405890i	−0.105450	+	0.994425i	$0.533628\pi$
$374$	−3.33615	−	5.77838i	−0.172508	−	0.298793i
$375$		0			0
$376$	−6.82522			−0.351984
$377$	−33.6934	−	13.2825i	−1.73530	−	0.684085i
$378$			3.64466i			0.187461i
$379$	−26.6013	+	15.3583i	−1.36642	+	0.788903i	−0.990469	−	0.137737i	$-0.956017\pi$
$379$	−26.6013	+	15.3583i	−1.36642	+	0.788903i	−0.375951	+	0.926640i	$0.622684\pi$
$380$		0			0
$381$	7.22034	−	12.5060i	0.369909	−	0.640702i
$382$	−15.6816			−0.802342
$383$	10.0310	−	17.3741i	0.512558	−	0.887777i	−0.487336	−	0.873215i	$-0.662031\pi$
$383$	10.0310	−	17.3741i	0.512558	−	0.887777i	0.999894	−	0.0145623i	$-0.00463550\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	4.06397	−	7.03901i	0.206851	−	0.358276i
$387$	6.55829	−	3.78643i	0.333377	−	0.192475i
$388$	1.37671	+	2.38453i	0.0698919	+	0.121056i
$389$	−27.0314			−1.37055			−0.685273	−	0.728287i	$-0.740317\pi$
$389$	−27.0314			−1.37055			−0.685273	+	0.728287i	$0.740317\pi$
$390$		0			0
$391$	4.97813			0.251755
$392$	3.14177	+	5.44171i	0.158683	+	0.274848i
$393$	9.43032	−	5.44460i	0.475697	−	0.274644i
$394$	−0.445619	+	0.771835i	−0.0224500	+	0.0388845i
$395$		0			0
$396$	−1.44460	−	0.834038i	−0.0725937	−	0.0419120i
$397$	1.86814	−	3.23571i	0.0937592	−	0.162396i	−0.815331	−	0.578995i	$-0.803445\pi$
$397$	1.86814	−	3.23571i	0.0937592	−	0.162396i	0.909090	+	0.416600i	$0.136778\pi$
$398$	−0.361116			−0.0181011
$399$	11.5039	−	19.9253i	0.575915	−	0.997513i
$400$		0			0
$401$	24.3276	−	14.0456i	1.21486	−	0.701402i	0.251049	−	0.967974i	$-0.419225\pi$
$401$	24.3276	−	14.0456i	1.21486	−	0.701402i	0.963815	+	0.266573i	$0.0858912\pi$
$402$		−	14.7534i		−	0.735834i
$403$	−9.46770	−	11.9090i	−0.471620	−	0.593230i
$404$	−5.33615			−0.265483
$405$		0			0
$406$	18.3049	+	31.7050i	0.908458	+	1.57349i
$407$	−14.2498	−	8.22714i	−0.706338	−	0.407804i
$408$	4.00000			0.198030
$409$	−23.7122	−	13.6902i	−1.17249	−	0.676938i	−0.218225	−	0.975898i	$-0.570027\pi$
$409$	−23.7122	−	13.6902i	−1.17249	−	0.676938i	−0.954265	+	0.298961i	$0.903360\pi$
$410$		0			0
$411$		−	7.03696i		−	0.347108i
$412$	−6.50600	−	3.75624i	−0.320528	−	0.185057i
$413$	−19.2815	+	11.1322i	−0.948780	+	0.547779i
$414$	1.07780	−	0.622266i	0.0529708	−	0.0305827i
$415$		0			0
$416$	0.531987	+	3.56609i	0.0260828	+	0.174842i
$417$			11.6447i			0.570241i
$418$	5.26506	+	9.11935i	0.257523	+	0.446042i
$419$	−6.58068	−	11.3981i	−0.321487	−	0.556833i	0.659308	−	0.751873i	$-0.270849\pi$
$419$	−6.58068	−	11.3981i	−0.321487	−	0.556833i	−0.980795	+	0.195041i	$0.937516\pi$
$420$		0			0
$421$		−	1.29341i		−	0.0630370i	−0.999503	−	0.0315185i	$-0.989966\pi$
$421$		−	1.29341i		−	0.0630370i	0.999503	−	0.0315185i	$-0.0100343\pi$
$422$	1.11370	−	1.92898i	0.0542138	−	0.0939011i
$423$	3.41261	−	5.91081i	0.165927	−	0.287394i
$424$		−	0.848634i		−	0.0412133i
$425$		0			0
$426$	1.75547	+	3.04056i	0.0850527	+	0.147316i
$427$	13.6021	+	23.5595i	0.658250	+	1.14012i
$428$			16.9282i			0.818256i
$429$	0.887395	+	5.94851i	0.0428439	+	0.287197i
$430$		0			0
$431$	10.5031	−	6.06397i	0.505917	−	0.292091i	−0.225237	−	0.974304i	$-0.572316\pi$
$431$	10.5031	−	6.06397i	0.505917	−	0.292091i	0.731154	+	0.682213i	$0.238982\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	1.79962	+	1.03901i	0.0864842	+	0.0499317i	0.542618	−	0.839979i	$-0.317433\pi$
$433$	1.79962	+	1.03901i	0.0864842	+	0.0499317i	−0.456134	+	0.889911i	$0.650766\pi$
$434$			15.3789i			0.738210i
$435$		0			0
$436$	0.574909	+	0.331924i	0.0275332	+	0.0158963i
$437$	−7.85641			−0.375823
$438$	−10.5807	−	6.10876i	−0.505565	−	0.291888i
$439$	1.19820	+	2.07534i	0.0571869	+	0.0990506i	0.893202	−	0.449656i	$-0.148454\pi$
$439$	1.19820	+	2.07534i	0.0571869	+	0.0990506i	−0.836015	+	0.548707i	$0.815120\pi$
$440$		0			0
$441$	−6.28354			−0.299216
$442$	−8.97504	−	11.2893i	−0.426899	−	0.536978i
$443$		−	21.9959i		−	1.04506i	−0.852622	−	0.522529i	$-0.824989\pi$
$443$		−	21.9959i		−	1.04506i	0.852622	−	0.522529i	$-0.175011\pi$
$444$	8.54267	−	4.93211i	0.405417	−	0.234068i
$445$		0			0
$446$	3.04190	−	5.26872i	0.144038	−	0.249481i
$447$	−0.772609			−0.0365432
$448$	1.82233	−	3.15637i	0.0860970	−	0.149124i
$449$	−25.3098	−	14.6126i	−1.19445	−	0.689613i	−0.235134	−	0.971963i	$-0.575553\pi$
$449$	−25.3098	−	14.6126i	−1.19445	−	0.689613i	−0.959312	+	0.282350i	$0.908886\pi$
$450$		0			0
$451$	−7.74765	+	13.4193i	−0.364822	+	0.631891i
$452$	15.4759	−	8.93500i	0.727924	−	0.420267i
$453$	4.88919	+	8.46833i	0.229714	+	0.397877i
$454$	15.3205			0.719027
$455$		0			0
$456$	−6.31274			−0.295621
$457$	−19.8216	−	34.3321i	−0.927216	−	1.60599i	−0.787957	−	0.615730i	$-0.788861\pi$
$457$	−19.8216	−	34.3321i	−0.927216	−	1.60599i	−0.139259	−	0.990256i	$-0.544472\pi$
$458$	−19.2815	+	11.1322i	−0.900965	+	0.520172i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$		0			0
$461$	14.4417	+	8.33792i	0.672617	+	0.388336i	0.797068	−	0.603890i	$-0.206383\pi$
$461$	14.4417	+	8.33792i	0.672617	+	0.388336i	−0.124450	+	0.992226i	$0.539717\pi$
$462$	3.03978	−	5.26506i	0.141424	−	0.244953i
$463$	32.2175			1.49728			0.748638	−	0.662979i	$-0.230708\pi$
$463$	32.2175			1.49728			0.748638	+	0.662979i	$0.230708\pi$
$464$	5.02239	−	8.69904i	0.233159	−	0.403843i
$465$		0			0
$466$	9.38476	−	5.41829i	0.434740	−	0.250998i
$467$		−	6.88137i		−	0.318432i	−0.987244	−	0.159216i	$-0.949103\pi$
$467$		−	6.88137i		−	0.318432i	0.987244	−	0.159216i	$-0.0508966\pi$
$468$	−3.35432	−	1.32233i	−0.155053	−	0.0611247i
$469$	53.7712			2.48292
$470$		0			0
$471$	6.00677	+	10.4040i	0.276778	+	0.479393i
$472$	5.29034	+	3.05438i	0.243508	+	0.140589i
$473$	−12.6321			−0.580825
$474$	8.60308	+	4.96699i	0.395152	+	0.228141i
$475$		0			0
$476$			14.5786i			0.668211i
$477$	0.734939	+	0.424317i	0.0336505	+	0.0194281i
$478$	14.2873	−	8.24876i	0.653485	−	0.377290i
$479$	16.4293	−	9.48547i	0.750675	−	0.433402i	−0.0752629	−	0.997164i	$-0.523980\pi$
$479$	16.4293	−	9.48547i	0.750675	−	0.433402i	0.825938	+	0.563761i	$0.190646\pi$
$480$		0			0
$481$	−33.0878	−	13.0438i	−1.50867	−	0.594744i
$482$			4.40435i			0.200613i
$483$	2.26795	+	3.92820i	0.103195	+	0.178739i
$484$	−4.10876	−	7.11658i	−0.186762	−	0.323481i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−0.958101	+	1.65948i	−0.0434157	+	0.0751982i	−0.886917	−	0.461929i	$-0.847157\pi$
$487$	−0.958101	+	1.65948i	−0.0434157	+	0.0751982i	0.843501	+	0.537128i	$0.180491\pi$
$488$	3.73205	−	6.46410i	0.168942	−	0.292616i
$489$		−	10.0916i		−	0.456359i
$490$		0			0
$491$	−16.8187	−	29.1309i	−0.759019	−	1.31466i	−0.943351	−	0.331795i	$-0.892346\pi$
$491$	−16.8187	−	29.1309i	−0.759019	−	1.31466i	0.184332	−	0.982864i	$-0.440988\pi$
$492$	−4.64466	−	8.04479i	−0.209397	−	0.362687i
$493$			40.1791i			1.80958i
$494$	14.1643	+	17.8166i	0.637280	+	0.801608i
$495$		0			0
$496$	3.65425	−	2.10978i	0.164081	−	0.0947321i
$497$	−11.0818	+	6.39808i	−0.497087	+	0.286993i
$498$	−6.88764	−	3.97658i	−0.308643	−	0.178195i
$499$			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
$502$	11.9453			0.533147
$503$	−17.3192	−	9.99923i	−0.772224	−	0.445843i	0.0614437	−	0.998111i	$-0.480430\pi$
$503$	−17.3192	−	9.99923i	−0.772224	−	0.445843i	−0.833667	+	0.552267i	$0.813763\pi$
$504$	1.82233	+	3.15637i	0.0811730	+	0.140596i
$505$		0			0
$506$	−2.07598			−0.0922884
$507$	3.79423	+	12.4340i	0.168508	+	0.552212i
$508$		−	14.4407i		−	0.640702i
$509$	−5.10196	+	2.94562i	−0.226141	+	0.130562i	−0.608790	−	0.793331i	$-0.708345\pi$
$509$	−5.10196	+	2.94562i	−0.226141	+	0.130562i	0.382650	+	0.923893i	$0.375012\pi$
$510$		0			0
$511$	22.2644	−	38.5630i	0.984917	−	1.70593i
$512$	−1.00000			−0.0441942
$513$	3.15637	−	5.46699i	0.139357	−	0.241373i
$514$	−16.8546	−	9.73103i	−0.743426	−	0.429217i
$515$		0			0
$516$	3.78643	−	6.55829i	0.166688	−	0.288713i
$517$	−9.85968	+	5.69249i	−0.433628	+	0.250355i
$518$	17.9759	+	31.1351i	0.789815	+	1.36800i
$519$	−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	$0.252388\pi$
$522$	5.02239	+	8.69904i	0.219824	+	0.380747i
$523$	−33.5313	+	19.3593i	−1.46622	+	0.846523i	−0.999286	−	0.0377693i	$-0.987975\pi$
$523$	−33.5313	+	19.3593i	−1.46622	+	0.846523i	−0.466934	+	0.884292i	$0.654641\pi$
$524$	5.44460	−	9.43032i	0.237848	−	0.411965i
$525$		0			0
$526$	−1.76217	−	1.01739i	−0.0768344	−	0.0443604i
$527$	−8.43914	+	14.6170i	−0.367615	+	0.636727i
$528$	−1.66808			−0.0725937
$529$	−10.7256	+	18.5772i	−0.466329	+	0.807706i
$530$		0			0
$531$	−5.29034	+	3.05438i	−0.229581	+	0.132549i
$532$		−	23.0078i		−	0.997513i
$533$	−12.2835	+	31.1593i	−0.532059	+	1.34966i
$534$	5.95162			0.257552
$535$		0			0
$536$	−7.37671	−	12.7768i	−0.318625	−	0.551875i
$537$	−17.0060	−	9.81842i	−0.733863	−	0.423696i
$538$	20.5287			0.885056
$539$	9.07718	+	5.24071i	0.390982	+	0.225734i
$540$		0			0
$541$		−	25.9616i		−	1.11618i	−0.829781	−	0.558089i	$-0.811535\pi$
$541$		−	25.9616i		−	1.11618i	0.829781	−	0.558089i	$-0.188465\pi$
$542$	22.1184	+	12.7700i	0.950065	+	0.548520i
$543$	−5.38453	+	3.10876i	−0.231072	+	0.133410i
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$		0			0
$546$	4.81944	−	12.2253i	0.206253	−	0.523196i
$547$		−	17.7596i		−	0.759348i	−0.925120	−	0.379674i	$-0.876036\pi$
$547$		−	17.7596i		−	0.759348i	0.925120	−	0.379674i	$-0.123964\pi$
$548$	−3.51848	−	6.09419i	−0.150302	−	0.260331i
$549$	3.73205	+	6.46410i	0.159280	+	0.275881i
$550$		0			0
$551$		−	63.4101i		−	2.70136i
$552$	0.622266	−	1.07780i	0.0264854	−	0.0458741i
$553$	−18.1030	+	31.3553i	−0.769817	+	1.33336i
$554$			18.0604i			0.767312i
$555$		0			0
$556$	5.82233	+	10.0846i	0.246922	+	0.427681i
$557$	−13.1101	−	22.7074i	−0.555493	−	0.962142i	−0.997865	−	0.0653102i	$-0.979196\pi$
$557$	−13.1101	−	22.7074i	−0.555493	−	0.962142i	0.442372	−	0.896832i	$-0.354137\pi$
$558$			4.21957i			0.178629i
$559$	−27.0055	+	4.02867i	−1.14221	+	0.170394i
$560$		0			0
$561$	5.77838	−	3.33615i	0.243964	−	0.140852i
$562$	−17.5089	+	10.1088i	−0.738568	+	0.426412i
$563$	22.5104	+	12.9964i	0.948702	+	0.547733i	0.892677	−	0.450696i	$-0.148824\pi$
$563$	22.5104	+	12.9964i	0.948702	+	0.547733i	0.0560243	+	0.998429i	$0.482158\pi$
$564$		−	6.82522i		−	0.287394i
$565$		0			0
$566$	7.52705	+	4.34575i	0.316386	+	0.182665i
$567$	−3.64466			−0.153061
$568$	3.04056	+	1.75547i	0.127579	+	0.0736578i
$569$	12.7349	+	22.0576i	0.533876	+	0.924701i	0.999217	+	0.0395693i	$0.0125986\pi$
$569$	12.7349	+	22.0576i	0.533876	+	0.924701i	−0.465340	+	0.885132i	$0.654068\pi$
$570$		0			0
$571$	−8.44491			−0.353409			−0.176704	−	0.984264i	$-0.556544\pi$
$571$	−8.44491			−0.353409			−0.176704	+	0.984264i	$0.556544\pi$
$572$	3.74276	+	4.70786i	0.156493	+	0.196846i
$573$		−	15.6816i		−	0.655109i
$574$	29.3205	−	16.9282i	1.22381	−	0.706570i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−35.4216			−1.47462			−0.737311	−	0.675554i	$-0.763905\pi$
$577$	−35.4216			−1.47462			−0.737311	+	0.675554i	$0.763905\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$	7.03901	+	4.06397i	0.292531	+	0.168893i
$580$		0			0
$581$	14.4933	−	25.1031i	0.601283	−	1.04145i
$582$	−2.38453	+	1.37671i	−0.0988420	+	0.0570665i
$583$	−0.707793	−	1.22593i	−0.0293138	−	0.0507730i
$584$	−12.2175			−0.505565
$585$		0			0
$586$	7.54790			0.311801
$587$	13.6894	+	23.7108i	0.565024	+	0.978650i	0.997047	+	0.0767878i	$0.0244664\pi$
$587$	13.6894	+	23.7108i	0.565024	+	0.978650i	−0.432024	+	0.901862i	$0.642200\pi$
$588$	−5.44171	+	3.14177i	−0.224412	+	0.129564i
$589$	13.3185	−	23.0683i	0.548780	−	0.950514i
$590$		0			0
$591$	−0.771835	−	0.445619i	−0.0317491	−	0.0183303i
$592$	4.93211	−	8.54267i	0.202709	−	0.351102i
$593$	−12.0619			−0.495324			−0.247662	−	0.968846i	$-0.579662\pi$
$593$	−12.0619			−0.495324			−0.247662	+	0.968846i	$0.579662\pi$
$594$	0.834038	−	1.44460i	0.0342210	−	0.0592725i
$595$		0			0
$596$	−0.669099	+	0.386305i	−0.0274074	+	0.0158237i
$597$		−	0.361116i		−	0.0147795i
$598$	−4.43811	+	0.662076i	−0.181488	+	0.0270743i
$599$	28.6129			1.16909			0.584546	−	0.811360i	$-0.301273\pi$
$599$	28.6129			1.16909			0.584546	+	0.811360i	$0.301273\pi$
$600$		0			0
$601$	9.58380	+	16.5996i	0.390931	+	0.677113i	0.992573	−	0.121654i	$-0.0388197\pi$
$601$	9.58380	+	16.5996i	0.390931	+	0.677113i	−0.601641	+	0.798766i	$0.705486\pi$
$602$	23.9027	+	13.8003i	0.974203	+	0.562456i
$603$	14.7534			0.600806
$604$	8.46833	+	4.88919i	0.344571	+	0.198938i
$605$		0			0
$606$		−	5.33615i		−	0.216766i
$607$	−16.4010	−	9.46910i	−0.665695	−	0.384339i	0.128749	−	0.991677i	$-0.458904\pi$
$607$	−16.4010	−	9.46910i	−0.665695	−	0.384339i	−0.794443	+	0.607338i	$0.792237\pi$
$608$	−5.46699	+	3.15637i	−0.221716	+	0.128008i
$609$	−31.7050	+	18.3049i	−1.28475	+	0.741753i
$610$		0			0
$611$	−19.2630	+	15.3141i	−0.779298	+	0.619544i
$612$			4.00000i			0.161690i
$613$	8.98472	+	15.5620i	0.362890	+	0.628543i	0.988435	−	0.151645i	$-0.0484569\pi$
$613$	8.98472	+	15.5620i	0.362890	+	0.628543i	−0.625546	+	0.780188i	$0.715124\pi$
$614$	−13.0214	−	22.5537i	−0.525500	−	0.910192i
$615$		0			0
$616$		−	6.07957i		−	0.244953i
$617$	9.00755	−	15.6015i	0.362630	−	0.628094i	−0.625763	−	0.780014i	$-0.715212\pi$
$617$	9.00755	−	15.6015i	0.362630	−	0.628094i	0.988393	+	0.151920i	$0.0485455\pi$
$618$	3.75624	−	6.50600i	0.151098	−	0.261710i
$619$			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
$622$	12.6894	+	21.9788i	0.508800	+	0.881268i
$623$			21.6916i			0.869057i
$624$	−3.56609	+	0.531987i	−0.142758	+	0.0212965i
$625$		0			0
$626$	−27.2452	+	15.7300i	−1.08894	+	0.628697i
$627$	−9.11935	+	5.26506i	−0.364192	+	0.210266i
$628$	10.4040	+	6.00677i	0.415166	+	0.239696i
$629$			39.4569i			1.57325i
$630$		0			0
$631$	−1.22739	−	0.708634i	−0.0488617	−	0.0282103i	0.475370	−	0.879786i	$-0.342314\pi$
$631$	−1.22739	−	0.708634i	−0.0488617	−	0.0282103i	−0.524232	+	0.851576i	$0.675647\pi$
$632$	9.93398			0.395152
$633$	1.92898	+	1.11370i	0.0766700	+	0.0442654i
$634$	12.3546	+	21.3989i	0.490665	+	0.849857i
$635$		0			0
$636$	0.848634			0.0336505
$637$	21.0770	+	8.30892i	0.835101	+	0.329211i
$638$		−	16.7555i		−	0.663355i
$639$	−3.04056	+	1.75547i	−0.120283	+	0.0694452i
$640$		0			0
$641$	2.30985	−	4.00077i	0.0912335	−	0.158021i	−0.816797	−	0.576925i	$-0.804252\pi$
$641$	2.30985	−	4.00077i	0.0912335	−	0.158021i	0.908030	+	0.418904i	$0.137586\pi$
$642$	−16.9282			−0.668103
$643$	24.0448	−	41.6468i	0.948234	−	1.64239i	0.199091	−	0.979981i	$-0.436201\pi$
$643$	24.0448	−	41.6468i	0.948234	−	1.64239i	0.749143	−	0.662408i	$-0.230465\pi$
$644$	3.92820	+	2.26795i	0.154793	+	0.0893697i
$645$		0			0
$646$	12.6255	−	21.8680i	0.496743	−	0.860383i
$647$	−3.24383	+	1.87282i	−0.127528	+	0.0736283i	−0.562407	−	0.826861i	$-0.690125\pi$
$647$	−3.24383	+	1.87282i	−0.127528	+	0.0736283i	0.434879	+	0.900489i	$0.356791\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	10.1899			0.399988
$650$		0			0
$651$	−15.3789			−0.602746
$652$	−5.04581	−	8.73960i	−0.197609	−	0.342269i
$653$	−36.6241	+	21.1450i	−1.43321	+	0.827466i	−0.997364	−	0.0725541i	$-0.976885\pi$
$653$	−36.6241	+	21.1450i	−1.43321	+	0.827466i	−0.435849	+	0.900020i	$0.643552\pi$
$654$	−0.331924	+	0.574909i	−0.0129793	+	0.0224807i
$655$		0			0
$656$	−8.04479	−	4.64466i	−0.314096	−	0.181343i
$657$	6.10876	−	10.5807i	0.238325	−	0.412792i
$658$	24.8756			0.969752
$659$	−14.5875	+	25.2663i	−0.568248	+	0.984234i	0.428492	+	0.903546i	$0.359045\pi$
$659$	−14.5875	+	25.2663i	−0.568248	+	0.984234i	−0.996739	+	0.0806881i	$0.974288\pi$
$660$		0			0
$661$	−38.5089	+	22.2331i	−1.49782	+	0.864768i	−0.999997	−	0.00250931i	$-0.999201\pi$
$661$	−38.5089	+	22.2331i	−1.49782	+	0.864768i	−0.497825	+	0.867277i	$0.665868\pi$
$662$		−	5.60360i		−	0.217790i
$663$	11.2893	−	8.97504i	0.438441	−	0.348562i
$664$	−7.95317			−0.308643
$665$		0			0
$666$	4.93211	+	8.54267i	0.191116	+	0.331022i
$667$	10.8262	+	6.25053i	0.419194	+	0.242022i
$668$	7.89701			0.305545
$669$	5.26872	+	3.04190i	0.203701	+	0.117607i
$670$		0			0
$671$		−	12.4507i		−	0.480654i
$672$	3.15637	+	1.82233i	0.121760	+	0.0702979i
$673$	6.84709	−	3.95317i	0.263936	−	0.152383i	−0.362193	−	0.932103i	$-0.617972\pi$
$673$	6.84709	−	3.95317i	0.263936	−	0.152383i	0.626129	+	0.779720i	$0.284638\pi$
$674$	−18.8680	+	10.8934i	−0.726767	+	0.419599i
$675$		0			0
$676$	9.50289	+	8.87103i	0.365496	+	0.341193i
$677$		−	7.05615i		−	0.271190i	−0.990764	−	0.135595i	$-0.956705\pi$
$677$		−	7.05615i		−	0.271190i	0.990764	−	0.135595i	$-0.0432946\pi$
$678$	8.93500	+	15.4759i	0.343147	+	0.594347i
$679$	−5.01764	−	8.69081i	−0.192559	−	0.333523i
$680$		0			0
$681$			15.3205i			0.587083i
$682$	3.51928	−	6.09557i	0.134760	−	0.233412i
$683$	−2.97658	+	5.15559i	−0.113896	+	0.197273i	−0.917338	−	0.398110i	$-0.869666\pi$
$683$	−2.97658	+	5.15559i	−0.113896	+	0.197273i	0.803442	+	0.595383i	$0.203000\pi$
$684$		−	6.31274i		−	0.241373i
$685$		0			0
$686$	1.30562	+	2.26140i	0.0498488	+	0.0863406i
$687$	−11.1322	−	19.2815i	−0.424719	−	0.735635i
$688$		−	7.57286i		−	0.288713i
$689$	−1.90413	−	2.39513i	−0.0725416	−	0.0912470i
$690$		0			0
$691$	16.2458	−	9.37953i	0.618020	−	0.356814i	−0.158078	−	0.987427i	$-0.550530\pi$
$691$	16.2458	−	9.37953i	0.618020	−	0.356814i	0.776098	+	0.630613i	$0.217196\pi$
$692$	−0.381645	+	0.220343i	−0.0145080	+	0.00837617i
$693$	5.26506	+	3.03978i	0.200003	+	0.115472i
$694$		−	9.68162i		−	0.367509i
$695$		0			0
$696$	8.69904	+	5.02239i	0.329736	+	0.190373i
$697$	37.1573			1.40743
$698$	−16.7321	−	9.66025i	−0.633317	−	0.365646i
$699$	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	$0.681113\pi$
$702$	1.32233	−	3.35432i	0.0499081	−	0.126601i
$703$		−	62.2703i		−	2.34857i
$704$	−1.44460	+	0.834038i	−0.0544453	+	0.0314340i
$705$		0			0
$706$	−11.4875	+	19.8970i	−0.432338	+	0.748832i
$707$	19.4485			0.731435
$708$	−3.05438	+	5.29034i	−0.114791	+	0.198823i
$709$	20.0853	+	11.5963i	0.754321	+	0.435507i	0.827253	−	0.561830i	$-0.189902\pi$
$709$	20.0853	+	11.5963i	0.754321	+	0.435507i	−0.0729321	+	0.997337i	$0.523236\pi$
$710$		0			0
$711$	−4.96699	+	8.60308i	−0.186277	+	0.322641i
$712$	5.15425	−	2.97581i	0.193164	−	0.111523i
$713$	2.62570	+	4.54784i	0.0983331	+	0.170318i
$714$	−14.5786			−0.545592
$715$		0			0
$716$	−19.6368			−0.733863
$717$	8.24876	+	14.2873i	0.308056	+	0.533568i
$718$	−1.92043	+	1.10876i	−0.0716698	+	0.0413786i
$719$	−5.85641	+	10.1436i	−0.218407	+	0.378292i	−0.954321	−	0.298783i	$-0.903419\pi$
$719$	−5.85641	+	10.1436i	−0.218407	+	0.378292i	0.735914	+	0.677075i	$0.236753\pi$
$720$		0			0
$721$	23.7122	+	13.6902i	0.883087	+	0.509850i
$722$	−10.4253	+	18.0572i	−0.387990	+	0.672019i
$723$	−4.40435			−0.163800
$724$	−3.10876	+	5.38453i	−0.115536	+	0.200115i
$725$		0			0
$726$	7.11658	−	4.10876i	0.264121	−	0.152490i
$727$			3.82677i			0.141927i	0.997479	+	0.0709634i	$0.0226074\pi$
$727$			3.82677i			0.141927i	−0.997479	+	0.0709634i	$0.977393\pi$
$728$	−1.93891	−	12.9972i	−0.0718609	−	0.481708i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	15.1457	+	26.2332i	0.560185	+	0.970269i
$732$	6.46410	+	3.73205i	0.238920	+	0.137941i
$733$	−12.9340			−0.477727			−0.238864	−	0.971053i	$-0.576775\pi$
$733$	−12.9340			−0.477727			−0.238864	+	0.971053i	$0.576775\pi$
$734$	−5.26640	−	3.04056i	−0.194386	−	0.112229i
$735$		0			0
$736$		−	1.24453i		−	0.0458741i
$737$	−21.3127	−	12.3049i	−0.785065	−	0.453257i
$738$	8.04479	−	4.64466i	0.296133	−	0.170972i
$739$	30.6107	−	17.6731i	1.12603	−	0.650115i	0.183098	−	0.983095i	$-0.441388\pi$
$739$	30.6107	−	17.6731i	1.12603	−	0.650115i	0.942934	+	0.332980i	$0.108054\pi$
$740$		0			0
$741$	−17.8166	+	14.1643i	−0.654510	+	0.520337i
$742$			3.09298i			0.113547i
$743$	18.5477	+	32.1255i	0.680448	+	1.17857i	0.974844	+	0.222887i	$0.0715482\pi$
$743$	18.5477	+	32.1255i	0.680448	+	1.17857i	−0.294396	+	0.955684i	$0.595118\pi$
$744$	2.10978	+	3.65425i	0.0773484	+	0.133971i
$745$		0			0
$746$			15.6781i			0.574015i
$747$	3.97658	−	6.88764i	0.145496	−	0.252006i
$748$	3.33615	−	5.77838i	0.121982	−	0.211279i
$749$		−	61.6975i		−	2.25438i
$750$		0			0
$751$	−4.82904	−	8.36414i	−0.176214	−	0.305212i	0.764367	−	0.644782i	$-0.223052\pi$
$751$	−4.82904	−	8.36414i	−0.176214	−	0.305212i	−0.940581	+	0.339570i	$0.889718\pi$
$752$	−3.41261	−	5.91081i	−0.124445	−	0.215545i
$753$			11.9453i			0.435313i
$754$	−5.34370	−	35.8206i	−0.194606	−	1.30451i
$755$		0			0
$756$	−3.15637	+	1.82233i	−0.114796	+	0.0662775i
$757$	−37.8354	+	21.8443i	−1.37515	+	0.793943i	−0.991571	−	0.129565i	$-0.958642\pi$
$757$	−37.8354	+	21.8443i	−1.37515	+	0.793943i	−0.383579	+	0.923508i	$0.625309\pi$
$758$	−26.6013	−	15.3583i	−0.966204	−	0.557838i
$759$		−	2.07598i		−	0.0753531i
$760$		0			0
$761$	34.5550	+	19.9503i	1.25262	+	0.723200i	0.971629	−	0.236511i	$-0.0760040\pi$
$761$	34.5550	+	19.9503i	1.25262	+	0.723200i	0.280990	+	0.959711i	$0.409337\pi$
$762$	14.4407			0.523131
$763$	−2.09535	−	1.20975i	−0.0758567	−	0.0437959i
$764$	−7.84081	−	13.5807i	−0.283671	−	0.491332i
$765$		0			0
$766$	20.0619			0.724867
$767$	21.7844	−	3.24978i	0.786589	−	0.117343i
$768$		−	1.00000i		−	0.0360844i
$769$	15.2064	−	8.77941i	0.548356	−	0.316594i	−0.200103	−	0.979775i	$-0.564128\pi$
$769$	15.2064	−	8.77941i	0.548356	−	0.316594i	0.748459	+	0.663181i	$0.230794\pi$
$770$		0			0
$771$	9.73103	−	16.8546i	0.350454	−	0.607005i
$772$	8.12795			0.292531
$773$	6.41861	−	11.1174i	0.230861	−	0.399864i	−0.727201	−	0.686425i	$-0.759179\pi$
$773$	6.41861	−	11.1174i	0.230861	−	0.399864i	0.958062	+	0.286562i	$0.0925123\pi$
$774$	6.55829	+	3.78643i	0.235733	+	0.136100i
$775$		0			0
$776$	−1.37671	+	2.38453i	−0.0494210	+	0.0855997i
$777$	−31.1351	+	17.9759i	−1.11697	+	0.644881i
$778$	−13.5157	−	23.4099i	−0.484561	−	0.839284i
$779$	−58.6410			−2.10103
$780$		0			0
$781$	5.85651			0.209562
$782$	2.48907	+	4.31119i	0.0890088	+	0.154168i
$783$	−8.69904	+	5.02239i	−0.310878	+	0.179486i
$784$	−3.14177	+	5.44171i	−0.112206	+	0.194347i
$785$		0			0
$786$	9.43032	+	5.44460i	0.336368	+	0.194202i
$787$	3.47867	−	6.02524i	0.124001	−	0.214777i	−0.797341	−	0.603529i	$-0.793761\pi$
$787$	3.47867	−	6.02524i	0.124001	−	0.214777i	0.921342	+	0.388753i	$0.127094\pi$
$788$	−0.891239			−0.0317491
$789$	1.01739	−	1.76217i	0.0362201	−	0.0627350i
$790$		0			0
$791$	−56.4043	+	32.5650i	−2.00551	+	1.15788i
$792$		−	1.66808i		−	0.0592725i
$793$	−3.97081	−	26.6176i	−0.141008	−	0.945220i
$794$	3.73628			0.132596
$795$		0			0
$796$	−0.180558	−	0.312736i	−0.00639971	−	0.0110846i
$797$	29.5621	+	17.0677i	1.04714	+	0.604569i	0.921849	−	0.387550i	$-0.126679\pi$
$797$	29.5621	+	17.0677i	1.04714	+	0.604569i	0.125296	+	0.992119i	$0.460012\pi$
$798$	23.0078			0.814466
$799$	23.6432	+	13.6504i	0.836438	+	0.482918i
$800$		0			0
$801$			5.95162i			0.210290i
$802$	24.3276	+	14.0456i	0.859038	+	0.495966i
$803$	−17.6494	+	10.1899i	−0.622833	+	0.359593i
$804$	12.7768	−	7.37671i	0.450604	−	0.260157i
$805$		0			0
$806$	5.57966	−	14.1538i	0.196535	−	0.498545i
$807$			20.5287i			0.722645i
$808$	−2.66808	−	4.62124i	−0.0938626	−	0.162575i
$809$	−1.66385	−	2.88187i	−0.0584978	−	0.101321i	0.835293	−	0.549804i	$-0.185298\pi$
$809$	−1.66385	−	2.88187i	−0.0584978	−	0.101321i	−0.893791	+	0.448483i	$0.851964\pi$
$810$		0			0
$811$			20.6083i			0.723655i	0.932245	+	0.361827i	$0.117847\pi$
$811$			20.6083i			0.723655i	−0.932245	+	0.361827i	$0.882153\pi$
$812$	−18.3049	+	31.7050i	−0.642377	+	1.11263i
$813$	−12.7700	+	22.1184i	−0.447865	+	0.775725i
$814$		−	16.4543i		−	0.576722i
$815$		0			0
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	−23.9027	−	41.4008i	−0.836251	−	1.44843i
$818$		−	27.3804i		−	0.957335i
$819$	12.2253	+	4.81944i	0.427188	+	0.168405i
$820$		0			0
$821$	1.36836	−	0.790025i	0.0477562	−	0.0275721i	−0.475932	−	0.879482i	$-0.657889\pi$
$821$	1.36836	−	0.790025i	0.0477562	−	0.0275721i	0.523688	+	0.851910i	$0.324556\pi$
$822$	6.09419	−	3.51848i	0.212559	−	0.122721i
$823$	−32.4905	−	18.7584i	−1.13255	−	0.653878i	−0.187974	−	0.982174i	$-0.560192\pi$
$823$	−32.4905	−	18.7584i	−1.13255	−	0.653878i	−0.944575	+	0.328296i	$0.893526\pi$
$824$		−	7.51248i		−	0.261710i
$825$		0			0
$826$	−19.2815	−	11.1322i	−0.670889	−	0.387338i
$827$	−49.4912			−1.72098			−0.860489	−	0.509469i	$-0.829842\pi$
$827$	−49.4912			−1.72098			−0.860489	+	0.509469i	$0.829842\pi$
$828$	1.07780	+	0.622266i	0.0374560	+	0.0216253i
$829$	−24.5693	−	42.5552i	−0.853326	−	1.47800i	−0.878189	−	0.478313i	$-0.841248\pi$
$829$	−24.5693	−	42.5552i	−0.853326	−	1.47800i	0.0248634	−	0.999691i	$-0.492085\pi$
$830$		0			0
$831$	−18.0604			−0.626508
$832$	−2.82233	+	2.24376i	−0.0978467	+	0.0777883i
$833$		−	25.1342i		−	0.870848i
$834$	−10.0846	+	5.82233i	−0.349200	+	0.201611i
$835$		0			0
$836$	−5.26506	+	9.11935i	−0.182096	+	0.315399i
$837$	−4.21957			−0.145850
$838$	6.58068	−	11.3981i	0.227326	−	0.393740i
$839$	18.6560	+	10.7711i	0.644078	+	0.371858i	0.786184	−	0.617993i	$-0.212054\pi$
$839$	18.6560	+	10.7711i	0.644078	+	0.371858i	−0.142106	+	0.989851i	$0.545387\pi$
$840$		0			0
$841$	−35.9489	+	62.2653i	−1.23962	+	2.14708i
$842$	1.12013	−	0.646706i	0.0386021	−	0.0222870i
$843$	−10.1088	−	17.5089i	−0.348164	−	0.603038i
$844$	2.22739			0.0766700
$845$		0			0
$846$	6.82522			0.234656
$847$	14.9750	+	25.9375i	0.514548	+	0.891224i
$848$	0.734939	−	0.424317i	0.0252379	−	0.0145711i
$849$	−4.34575	+	7.52705i	−0.149146	+	0.258328i
$850$		0			0
$851$	10.6316	+	6.13818i	0.364448	+	0.210414i
$852$	−1.75547	+	3.04056i	−0.0601413	+	0.104168i
$853$	−2.79821			−0.0958088			−0.0479044	−	0.998852i	$-0.515254\pi$
$853$	−2.79821			−0.0958088			−0.0479044	+	0.998852i	$0.515254\pi$
$854$	−13.6021	+	23.5595i	−0.465453	+	0.806188i
$855$		0			0
$856$	−14.6603	+	8.46410i	−0.501077	+	0.289297i
$857$		−	48.9658i		−	1.67264i	−0.548242	−	0.836320i	$-0.684703\pi$
$857$		−	48.9658i		−	1.67264i	0.548242	−	0.836320i	$-0.315297\pi$
$858$	−4.70786	+	3.74276i	−0.160724	+	0.127776i
$859$	−4.22739			−0.144237			−0.0721184	−	0.997396i	$-0.522976\pi$
$859$	−4.22739			−0.144237			−0.0721184	+	0.997396i	$0.522976\pi$
$860$		0			0
$861$	16.9282	+	29.3205i	0.576912	+	0.999240i
$862$	10.5031	+	6.06397i	0.357737	+	0.206540i
$863$	19.0285			0.647738			0.323869	−	0.946102i	$-0.395016\pi$
$863$	19.0285			0.647738			0.323869	+	0.946102i	$0.395016\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$			2.07802i			0.0706141i
$867$	0.866025	+	0.500000i	0.0294118	+	0.0169809i
$868$	−13.3185	+	7.68945i	−0.452060	+	0.260997i
$869$	14.3506	−	8.28532i	0.486810	−	0.281060i
$870$		0			0
$871$	−49.4877	−	19.5089i	−1.67683	−	0.661033i
$872$			0.663848i			0.0224807i
$873$	−1.37671	−	2.38453i	−0.0465946	−	0.0807042i
$874$	−3.92820	−	6.80385i	−0.132873	−	0.230144i
$875$		0			0
$876$		−	12.2175i		−	0.412792i
$877$	−6.77363	+	11.7323i	−0.228729	+	0.396171i	−0.957432	−	0.288660i	$-0.906790\pi$
$877$	−6.77363	+	11.7323i	−0.228729	+	0.396171i	0.728702	+	0.684830i	$0.240124\pi$
$878$	−1.19820	+	2.07534i	−0.0404373	+	0.0700394i
$879$			7.54790i			0.254584i
$880$		0			0
$881$	2.49041	+	4.31351i	0.0839039	+	0.145326i	0.904924	−	0.425574i	$-0.139928\pi$
$881$	2.49041	+	4.31351i	0.0839039	+	0.145326i	−0.821020	+	0.570900i	$0.806594\pi$
$882$	−3.14177	−	5.44171i	−0.105789	−	0.183232i
$883$		−	30.9829i		−	1.04266i	−0.853355	−	0.521330i	$-0.825436\pi$
$883$		−	30.9829i		−	1.04266i	0.853355	−	0.521330i	$-0.174564\pi$
$884$	5.28932	−	13.4173i	0.177899	−	0.451272i
$885$		0			0
$886$	19.0490	−	10.9980i	0.639964	−	0.369483i
$887$	14.8753	−	8.58826i	0.499464	−	0.288365i	−0.229028	−	0.973420i	$-0.573555\pi$
$887$	14.8753	−	8.58826i	0.499464	−	0.288365i	0.728492	+	0.685054i	$0.240222\pi$
$888$	8.54267	+	4.93211i	0.286673	+	0.165511i
$889$			52.6314i			1.76520i
$890$		0			0
$891$	1.44460	+	0.834038i	0.0483958	+	0.0279413i
$892$	6.08380			0.203701
$893$	−37.3134	−	21.5429i	−1.24865	−	0.720906i
$894$	−0.386305	−	0.669099i	−0.0129200	−	0.0223780i
$895$		0			0
$896$	3.64466			0.121760
$897$	−0.662076	−	4.43811i	−0.0221061	−	0.148184i
$898$		−	29.2253i		−	0.975261i
$899$	−36.7062	+	21.1923i	−1.22422	+	0.706804i
$900$		0			0
$901$	−1.69727	+	2.93975i	−0.0565442	+	0.0979374i
$902$	−15.4953			−0.515937
$903$	−13.8003	+	23.9027i	−0.459244	+	0.795433i
$904$	15.4759	+	8.93500i	0.514720	+	0.297174i
$905$		0			0
$906$	−4.88919	+	8.46833i	−0.162433	+	0.281341i
$907$	21.7197	−	12.5399i	0.721190	−	0.416379i	−0.0940008	−	0.995572i	$-0.529966\pi$
$907$	21.7197	−	12.5399i	0.721190	−	0.416379i	0.815190	+	0.579193i	$0.196632\pi$
$908$	7.66025	+	13.2679i	0.254214	+	0.440312i
$909$	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	$0.402330\pi$
$912$	−3.15637	−	5.46699i	−0.104518	−	0.181030i
$913$	−11.4891	+	6.63324i	−0.380234	+	0.219528i
$914$	19.8216	−	34.3321i	0.655641	−	1.13560i
$915$		0			0
$916$	−19.2815	−	11.1322i	−0.637079	−	0.367818i
$917$	−19.8437	+	34.3703i	−0.655297	+	1.13501i
$918$	−4.00000			−0.132020
$919$	−17.1941	+	29.7811i	−0.567181	+	0.982387i	0.429662	+	0.902990i	$0.358633\pi$
$919$	−17.1941	+	29.7811i	−0.567181	+	0.982387i	−0.996843	+	0.0793968i	$0.974701\pi$
$920$		0			0
$921$	22.5537	−	13.0214i	0.743169	−	0.429069i
$922$			16.6758i			0.549190i
$923$	12.5203	−	1.86777i	0.412111	−	0.0614785i
$924$	6.07957			0.200003
$925$		0			0
$926$	16.1088	+	27.9012i	0.529367	+	0.916890i
$927$	6.50600	+	3.75624i	0.213685	+	0.123371i
$928$	10.0448			0.329736
$929$	−26.9251	−	15.5452i	−0.883384	−	0.510022i	−0.0116114	−	0.999933i	$-0.503696\pi$
$929$	−26.9251	−	15.5452i	−0.883384	−	0.510022i	−0.871773	+	0.489911i	$0.837029\pi$
$930$		0			0
$931$			39.6663i			1.30001i
$932$	9.38476	+	5.41829i	0.307408	+	0.177482i
$933$	−21.9788	+	12.6894i	−0.719552	+	0.415434i
$934$	5.95944	−	3.44069i	0.194999	−	0.112583i
$935$		0			0
$936$	−0.531987	−	3.56609i	−0.0173886	−	0.116561i
$937$		−	18.8783i		−	0.616726i	−0.951269	−	0.308363i	$-0.900219\pi$
$937$		−	18.8783i		−	0.616726i	0.951269	−	0.308363i	$-0.0997812\pi$
$938$	26.8856	+	46.5672i	0.877846	+	1.52047i
$939$	−15.7300	−	27.2452i	−0.513329	−	0.889112i
$940$		0			0
$941$			28.9398i			0.943409i	0.881757	+	0.471705i	$0.156361\pi$
$941$			28.9398i			0.943409i	−0.881757	+	0.471705i	$0.843639\pi$
$942$	−6.00677	+	10.4040i	−0.195711	+	0.338982i
$943$	5.78043	−	10.0120i	0.188237	−	0.326036i
$944$			6.10876i			0.198823i
$945$		0			0
$946$	−6.31606	−	10.9397i	−0.205353	−	0.355681i
$947$	3.93448	+	6.81472i	0.127853	+	0.221448i	0.922845	−	0.385172i	$-0.125858\pi$
$947$	3.93448	+	6.81472i	0.127853	+	0.221448i	−0.794991	+	0.606621i	$0.792525\pi$
$948$			9.93398i			0.322641i
$949$	−34.4819	+	27.4132i	−1.11933	+	0.889869i
$950$		0			0
$951$	−21.3989	+	12.3546i	−0.693905	+	0.400626i
$952$	−12.6255	+	7.28932i	−0.409194	+	0.236248i
$953$	47.7153	+	27.5484i	1.54565	+	0.892381i	0.998466	+	0.0553681i	$0.0176332\pi$
$953$	47.7153	+	27.5484i	1.54565	+	0.892381i	0.547183	+	0.837013i	$0.315700\pi$
$954$			0.848634i			0.0274755i
$955$		0			0
$956$	14.2873	+	8.24876i	0.462083	+	0.266784i
$957$	16.7555			0.541627
$958$	16.4293	+	9.48547i	0.530807	+	0.306462i
$959$	12.8237	+	22.2112i	0.414098	+	0.717239i
$960$		0			0
$961$	13.1952			0.425653
$962$	−5.24765	−	35.1767i	−0.169191	−	1.13414i
$963$		−	16.9282i		−	0.545504i
$964$	−3.81428	+	2.20218i	−0.122850	+	0.0709274i
$965$		0			0
$966$	−2.26795	+	3.92820i	−0.0729701	+	0.126388i
$967$	31.5523			1.01465			0.507326	−	0.861754i	$-0.330634\pi$
$967$	31.5523			1.01465			0.507326	+	0.861754i	$0.330634\pi$
$968$	4.10876	−	7.11658i	0.132061	−	0.228736i
$969$	21.8680	+	12.6255i	0.702500	+	0.405589i
$970$		0			0
$971$	−1.83792	+	3.18338i	−0.0589818	+	0.102159i	−0.894009	−	0.448050i	$-0.852119\pi$
$971$	−1.83792	+	3.18338i	−0.0589818	+	0.102159i	0.835027	+	0.550209i	$0.185452\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−21.2204	−	36.7548i	−0.680295	−	1.17831i
$974$	−1.91620			−0.0613991
$975$		0			0
$976$	7.46410			0.238920
$977$	21.0102	+	36.3908i	0.672177	+	1.16424i	0.977286	+	0.211927i	$0.0679738\pi$
$977$	21.0102	+	36.3908i	0.672177	+	1.16424i	−0.305109	+	0.952318i	$0.598693\pi$
$978$	8.73960	−	5.04581i	0.279462	−	0.161347i
$979$	4.96388	−	8.59769i	0.158646	−	0.274783i
$980$		0			0
$981$	−0.574909	−	0.331924i	−0.0183554	−	0.0105975i
$982$	16.8187	−	29.1309i	0.536707	−	0.929605i
$983$	13.4307			0.428372			0.214186	−	0.976793i	$-0.431290\pi$
$983$	13.4307			0.428372			0.214186	+	0.976793i	$0.431290\pi$
$984$	4.64466	−	8.04479i	0.148066	−	0.256458i
$985$		0			0
$986$	−34.7962	+	20.0896i	−1.10814	+	0.639782i
$987$			24.8756i			0.791799i
$988$	−8.34752	+	21.1749i	−0.265570	+	0.673664i
$989$	9.42468			0.299687
$990$		0			0
$991$	−21.8994	−	37.9309i	−0.695658	−	1.20492i	−0.969958	−	0.243271i	$-0.921780\pi$
$991$	−21.8994	−	37.9309i	−0.695658	−	1.20492i	0.274300	−	0.961644i	$-0.411554\pi$
$992$	3.65425	+	2.10978i	0.116023	+	0.0669857i
$993$	5.60360			0.177825
$994$	−11.0818	−	6.39808i	−0.351493	−	0.202935i
$995$		0			0
$996$		−	7.95317i		−	0.252006i
$997$	20.3624	+	11.7562i	0.644884	+	0.372324i	0.786493	−	0.617599i	$-0.211894\pi$
$997$	20.3624	+	11.7562i	0.644884	+	0.372324i	−0.141609	+	0.989923i	$0.545228\pi$
$998$	−1.58068	+	0.912609i	−0.0500357	+	0.0288881i
$999$	−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.y.k.49.2		8
5.2	odd	4		1950.2.bc.g.751.2		8
5.3	odd	4		390.2.bb.c.361.3	yes	8
5.4	even	2		1950.2.y.j.49.3		8
13.4	even	6		1950.2.y.j.199.3		8
15.8	even	4		1170.2.bs.f.361.1		8
65.3	odd	12		5070.2.b.ba.1351.8		8
65.4	even	6	inner	1950.2.y.k.199.2		8
65.17	odd	12		1950.2.bc.g.901.2		8
65.23	odd	12		5070.2.b.ba.1351.1		8
65.28	even	12		5070.2.a.ca.1.1		4
65.43	odd	12		390.2.bb.c.121.3	✓	8
65.63	even	12		5070.2.a.bz.1.4		4
195.173	even	12		1170.2.bs.f.901.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.3	✓	8	65.43	odd	12
390.2.bb.c.361.3	yes	8	5.3	odd	4
1170.2.bs.f.361.1		8	15.8	even	4
1170.2.bs.f.901.1		8	195.173	even	12
1950.2.y.j.49.3		8	5.4	even	2
1950.2.y.j.199.3		8	13.4	even	6
1950.2.y.k.49.2		8	1.1	even	1	trivial
1950.2.y.k.199.2		8	65.4	even	6	inner
1950.2.bc.g.751.2		8	5.2	odd	4
1950.2.bc.g.901.2		8	65.17	odd	12
5070.2.a.bz.1.4		4	65.63	even	12
5070.2.a.ca.1.1		4	65.28	even	12
5070.2.b.ba.1351.1		8	65.23	odd	12
5070.2.b.ba.1351.8		8	65.3	odd	12

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.y (of order \(6\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

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Database

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