LMFDB - Embedded newform 1950.2.bc.g.751.1

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			751.1
Root			$1.33404 - 1.33404i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.g.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-4.02239 - 2.32233i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-4.02239 - 2.32233i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.81062 - 2.20006i) q^{11} +1.00000 q^{12} +(3.35432 - 1.32233i) q^{13} +4.64466 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-6.96699 - 4.02239i) q^{19} -4.64466i q^{21} +(-2.20006 + 3.81062i) q^{22} +(0.488292 + 0.845746i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-2.24376 + 2.82233i) q^{26} -1.00000 q^{27} +(-4.02239 + 2.32233i) q^{28} +(2.15637 + 3.73494i) q^{29} +6.44069i q^{31} +(0.866025 + 0.500000i) q^{32} +(3.81062 + 2.20006i) q^{33} -4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(-3.28745 + 1.89801i) q^{37} +8.04479 q^{38} +(2.82233 + 2.24376i) q^{39} +(-6.31274 + 3.64466i) q^{41} +(2.32233 + 4.02239i) q^{42} +(-0.358228 + 0.620469i) q^{43} -4.40013i q^{44} +(-0.845746 - 0.488292i) q^{46} -9.75342i q^{47} +(0.500000 - 0.866025i) q^{48} +(7.28643 + 12.6205i) q^{49} -4.00000 q^{51} +(0.531987 - 3.56609i) q^{52} -13.5089 q^{53} +(0.866025 - 0.500000i) q^{54} +(2.32233 - 4.02239i) q^{56} -8.04479i q^{57} +(-3.73494 - 2.15637i) q^{58} +(-1.88842 - 1.09028i) q^{59} +(-3.73205 + 6.46410i) q^{61} +(-3.22034 - 5.57780i) q^{62} +(4.02239 - 2.32233i) q^{63} -1.00000 q^{64} -4.40013 q^{66} +(1.58068 - 0.912609i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-0.488292 + 0.845746i) q^{69} +(-6.88764 - 3.97658i) q^{71} +(-0.866025 - 0.500000i) q^{72} +4.36112i q^{73} +(1.89801 - 3.28745i) q^{74} +(-6.96699 + 4.02239i) q^{76} -20.4371 q^{77} +(-3.56609 - 0.531987i) q^{78} -14.9340 q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.64466 - 6.31274i) q^{82} -3.51093i q^{83} +(-4.02239 - 2.32233i) q^{84} -0.716456i q^{86} +(-2.15637 + 3.73494i) q^{87} +(2.20006 + 3.81062i) q^{88} +(7.07780 - 4.08637i) q^{89} +(-16.5633 - 2.47090i) q^{91} +0.976584 q^{92} +(-5.57780 + 3.22034i) q^{93} +(4.87671 + 8.44671i) q^{94} +1.00000i q^{96} +(-11.9730 - 6.91261i) q^{97} +(-12.6205 - 7.28643i) q^{98} +4.40013i 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 $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.866025	+	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
$7$	−4.02239	−	2.32233i	−1.52032	−	0.877758i	−0.999713	−	0.0239629i	$-0.992372\pi$
$7$	−4.02239	−	2.32233i	−1.52032	−	0.877758i	−0.520609	−	0.853795i	$-0.674295\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.81062	−	2.20006i	1.14895	−	0.663344i	0.200316	−	0.979731i	$-0.435803\pi$
$11$	3.81062	−	2.20006i	1.14895	−	0.663344i	0.948630	+	0.316387i	$0.102470\pi$
$12$	1.00000			0.288675
$13$	3.35432	−	1.32233i	0.930320	−	0.366748i
$13$	3.35432	−	1.32233i	0.930320	−	0.366748i
$14$	4.64466			1.24134
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−6.96699	−	4.02239i	−1.59834	−	0.922800i	−0.991808	−	0.127739i	$-0.959228\pi$
$19$	−6.96699	−	4.02239i	−1.59834	−	0.922800i	−0.606529	−	0.795061i	$-0.707439\pi$
$20$		0			0
$21$		−	4.64466i		−	1.01355i
$22$	−2.20006	+	3.81062i	−0.469055	+	0.812427i
$23$	0.488292	+	0.845746i	0.101816	+	0.176350i	0.912433	−	0.409226i	$-0.134201\pi$
$23$	0.488292	+	0.845746i	0.101816	+	0.176350i	−0.810617	+	0.585577i	$0.800868\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	−2.24376	+	2.82233i	−0.440037	+	0.553504i
$27$	−1.00000			−0.192450
$28$	−4.02239	+	2.32233i	−0.760161	+	0.438879i
$29$	2.15637	+	3.73494i	0.400427	+	0.693561i	0.993777	−	0.111384i	$-0.0355283\pi$
$29$	2.15637	+	3.73494i	0.400427	+	0.693561i	−0.593350	+	0.804945i	$0.702195\pi$
$30$		0			0
$31$			6.44069i			1.15678i	0.815760	+	0.578391i	$0.196319\pi$
$31$			6.44069i			1.15678i	−0.815760	+	0.578391i	$0.803681\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.81062	+	2.20006i	0.663344	+	0.382982i
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−3.28745	+	1.89801i	−0.540454	+	0.312031i	−0.745263	−	0.666771i	$-0.767676\pi$
$37$	−3.28745	+	1.89801i	−0.540454	+	0.312031i	0.204809	+	0.978802i	$0.434343\pi$
$38$	8.04479			1.30504
$39$	2.82233	+	2.24376i	0.451934	+	0.359289i
$40$		0			0
$41$	−6.31274	+	3.64466i	−0.985884	+	0.569200i	−0.904041	−	0.427445i	$-0.859414\pi$
$41$	−6.31274	+	3.64466i	−0.985884	+	0.569200i	−0.0818424	+	0.996645i	$0.526080\pi$
$42$	2.32233	+	4.02239i	0.358343	+	0.620669i
$43$	−0.358228	+	0.620469i	−0.0546293	+	0.0946207i	−0.892047	−	0.451943i	$-0.850731\pi$
$43$	−0.358228	+	0.620469i	−0.0546293	+	0.0946207i	0.837418	+	0.546564i	$0.184064\pi$
$44$		−	4.40013i		−	0.663344i
$45$		0			0
$46$	−0.845746	−	0.488292i	−0.124698	−	0.0719947i
$47$		−	9.75342i		−	1.42268i	−0.702847	−	0.711341i	$-0.748088\pi$
$47$		−	9.75342i		−	1.42268i	0.702847	−	0.711341i	$-0.251912\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	7.28643	+	12.6205i	1.04092	+	1.80292i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	0.531987	−	3.56609i	0.0737734	−	0.494528i
$53$	−13.5089			−1.85559			−0.927794	−	0.373092i	$-0.878297\pi$
$53$	−13.5089			−1.85559			−0.927794	+	0.373092i	$0.878297\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	2.32233	−	4.02239i	0.310334	−	0.537515i
$57$		−	8.04479i		−	1.06556i
$58$	−3.73494	−	2.15637i	−0.490421	−	0.283145i
$59$	−1.88842	−	1.09028i	−0.245851	−	0.141942i	0.372012	−	0.928228i	$-0.378668\pi$
$59$	−1.88842	−	1.09028i	−0.245851	−	0.141942i	−0.617863	+	0.786286i	$0.712001\pi$
$60$		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	$0.325247\pi$
$62$	−3.22034	−	5.57780i	−0.408984	−	0.708381i
$63$	4.02239	−	2.32233i	0.506774	−	0.292586i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−4.40013			−0.541618
$67$	1.58068	−	0.912609i	0.193111	−	0.111493i	−0.400327	−	0.916372i	$-0.631103\pi$
$67$	1.58068	−	0.912609i	0.193111	−	0.111493i	0.593438	+	0.804879i	$0.297770\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$	−0.488292	+	0.845746i	−0.0587834	+	0.101816i
$70$		0			0
$71$	−6.88764	−	3.97658i	−0.817413	−	0.471934i	0.0321105	−	0.999484i	$-0.489777\pi$
$71$	−6.88764	−	3.97658i	−0.817413	−	0.471934i	−0.849524	+	0.527551i	$0.823110\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			4.36112i			0.510430i	0.966884	+	0.255215i	$0.0821463\pi$
$73$			4.36112i			0.510430i	−0.966884	+	0.255215i	$0.917854\pi$
$74$	1.89801	−	3.28745i	0.220640	−	0.382159i
$75$		0			0
$76$	−6.96699	+	4.02239i	−0.799168	+	0.461400i
$77$	−20.4371			−2.32902
$78$	−3.56609	−	0.531987i	−0.403780	−	0.0602357i
$79$	−14.9340			−1.68020			−0.840102	−	0.542429i	$-0.817505\pi$
$79$	−14.9340			−1.68020			−0.840102	+	0.542429i	$0.817505\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.64466	−	6.31274i	0.402485	−	0.697125i
$83$		−	3.51093i		−	0.385375i	−0.981260	−	0.192688i	$-0.938280\pi$
$83$		−	3.51093i		−	0.385375i	0.981260	−	0.192688i	$-0.0617204\pi$
$84$	−4.02239	−	2.32233i	−0.438879	−	0.253387i
$85$		0			0
$86$		−	0.716456i		−	0.0772575i
$87$	−2.15637	+	3.73494i	−0.231187	+	0.400427i
$88$	2.20006	+	3.81062i	0.234528	+	0.406214i
$89$	7.07780	−	4.08637i	0.750245	−	0.433154i	−0.0755374	−	0.997143i	$-0.524067\pi$
$89$	7.07780	−	4.08637i	0.750245	−	0.433154i	0.825782	+	0.563989i	$0.190734\pi$
$90$		0			0
$91$	−16.5633	−	2.47090i	−1.73630	−	0.259021i
$92$	0.976584			0.101816
$93$	−5.57780	+	3.22034i	−0.578391	+	0.333934i
$94$	4.87671	+	8.44671i	0.502994	+	0.871212i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−11.9730	−	6.91261i	−1.21567	−	0.701869i	−0.251683	−	0.967810i	$-0.580984\pi$
$97$	−11.9730	−	6.91261i	−1.21567	−	0.701869i	−0.963989	+	0.265941i	$0.914318\pi$
$98$	−12.6205	−	7.28643i	−1.27486	−	0.736041i
$99$			4.40013i			0.442229i
$100$		0			0
$101$	−3.40013	−	5.88919i	−0.338325	−	0.585997i	0.645793	−	0.763513i	$-0.276527\pi$
$101$	−3.40013	−	5.88919i	−0.338325	−	0.585997i	−0.984118	+	0.177516i	$0.943194\pi$
$102$	3.46410	−	2.00000i	0.342997	−	0.198030i
$103$	5.29137			0.521374			0.260687	−	0.965423i	$-0.416051\pi$
$103$	5.29137			0.521374			0.260687	+	0.965423i	$0.416051\pi$
$104$	1.32233	+	3.35432i	0.129665	+	0.328918i
$105$		0			0
$106$	11.6990	−	6.75444i	1.13631	−	0.656050i
$107$	8.46410	+	14.6603i	0.818256	+	1.41726i	0.906966	+	0.421203i	$0.138392\pi$
$107$	8.46410	+	14.6603i	0.818256	+	1.41726i	−0.0887109	+	0.996057i	$0.528275\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			12.8003i			1.22604i	0.790067	+	0.613021i	$0.210046\pi$
$109$			12.8003i			1.22604i	−0.790067	+	0.613021i	$0.789954\pi$
$110$		0			0
$111$	−3.28745	−	1.89801i	−0.312031	−	0.180151i
$112$			4.64466i			0.438879i
$113$	6.53308	−	11.3156i	0.614580	−	1.06448i	−0.375878	−	0.926669i	$-0.622659\pi$
$113$	6.53308	−	11.3156i	0.614580	−	1.06448i	0.990458	−	0.137815i	$-0.0440079\pi$
$114$	4.02239	+	6.96699i	0.376732	+	0.652518i
$115$		0			0
$116$	4.31274			0.400427
$117$	−0.531987	+	3.56609i	−0.0491823	+	0.329685i
$118$	2.18056			0.200737
$119$	16.0896	−	9.28932i	1.47493	−	0.851550i
$120$		0			0
$121$	4.18056	−	7.24094i	0.380051	−	0.658267i
$122$		−	7.46410i		−	0.675768i
$123$	−6.31274	−	3.64466i	−0.569200	−	0.328628i
$124$	5.57780	+	3.22034i	0.500901	+	0.289195i
$125$		0			0
$126$	−2.32233	+	4.02239i	−0.206890	+	0.358343i
$127$	−6.10978	−	10.5825i	−0.542156	−	0.939041i	−0.998780	−	0.0493816i	$-0.984275\pi$
$127$	−6.10978	−	10.5825i	−0.542156	−	0.939041i	0.456624	−	0.889660i	$-0.349058\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−0.716456			−0.0630805
$130$		0			0
$131$	−0.378757			−0.0330921			−0.0165461	−	0.999863i	$-0.505267\pi$
$131$	−0.378757			−0.0330921			−0.0165461	+	0.999863i	$0.505267\pi$
$132$	3.81062	−	2.20006i	0.331672	−	0.191491i
$133$	18.6826	+	32.3593i	1.61999	+	2.80591i
$134$	−0.912609	+	1.58068i	−0.0788374	+	0.136550i
$135$		0			0
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	1.08457	+	0.626177i	0.0926612	+	0.0534979i	0.545615	−	0.838036i	$-0.316296\pi$
$137$	1.08457	+	0.626177i	0.0926612	+	0.0534979i	−0.452953	+	0.891534i	$0.649630\pi$
$138$		−	0.976584i		−	0.0831323i
$139$	−1.67767	+	2.90581i	−0.142298	+	0.246468i	−0.928362	−	0.371678i	$-0.878783\pi$
$139$	−1.67767	+	2.90581i	−0.142298	+	0.246468i	0.786064	+	0.618146i	$0.212116\pi$
$140$		0			0
$141$	8.44671	−	4.87671i	0.711341	−	0.410693i
$142$	7.95317			0.667415
$143$	9.87282	−	12.4186i	0.825607	−	1.03850i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−2.18056	−	3.77684i	−0.180464	−	0.312573i
$147$	−7.28643	+	12.6205i	−0.600975	+	1.04092i
$148$			3.79603i			0.312031i
$149$	−4.00077	−	2.30985i	−0.327756	−	0.189230i	0.327088	−	0.944994i	$-0.393933\pi$
$149$	−4.00077	−	2.30985i	−0.327756	−	0.189230i	−0.654844	+	0.755764i	$0.727266\pi$
$150$		0			0
$151$			11.2425i			0.914901i	0.889235	+	0.457450i	$0.151237\pi$
$151$			11.2425i			0.914901i	−0.889235	+	0.457450i	$0.848763\pi$
$152$	4.02239	−	6.96699i	0.326259	−	0.565097i
$153$	−2.00000	−	3.46410i	−0.161690	−	0.280056i
$154$	17.6990	−	10.2185i	1.42623	−	0.823434i
$155$		0			0
$156$	3.35432	−	1.32233i	0.268560	−	0.105871i
$157$	1.50311			0.119961			0.0599807	−	0.998200i	$-0.480896\pi$
$157$	1.50311			0.119961			0.0599807	+	0.998200i	$0.480896\pi$
$158$	12.9332	−	7.46699i	1.02891	−	0.594042i
$159$	−6.75444	−	11.6990i	−0.535662	−	0.927794i
$160$		0			0
$161$		−	4.53590i		−	0.357479i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	0.152706	+	0.0881650i	0.0119609	+	0.00690561i	0.505969	−	0.862552i	$-0.331135\pi$
$163$	0.152706	+	0.0881650i	0.0119609	+	0.00690561i	−0.494008	+	0.869458i	$0.664469\pi$
$164$			7.28932i			0.569200i
$165$		0			0
$166$	1.75547	+	3.04056i	0.136251	+	0.235993i
$167$	−7.51851	+	4.34081i	−0.581800	+	0.335902i	−0.761848	−	0.647756i	$-0.775708\pi$
$167$	−7.51851	+	4.34081i	−0.581800	+	0.335902i	0.180049	+	0.983658i	$0.442374\pi$
$168$	4.64466			0.358343
$169$	9.50289	−	8.87103i	0.730991	−	0.682387i
$170$		0			0
$171$	6.96699	−	4.02239i	0.532779	−	0.307600i
$172$	0.358228	+	0.620469i	0.0273146	+	0.0473103i
$173$	−0.890216	+	1.54190i	−0.0676818	+	0.117228i	−0.897880	−	0.440239i	$-0.854894\pi$
$173$	−0.890216	+	1.54190i	−0.0676818	+	0.117228i	0.830199	+	0.557468i	$0.188227\pi$
$174$		−	4.31274i		−	0.326948i
$175$		0			0
$176$	−3.81062	−	2.20006i	−0.287236	−	0.165836i
$177$		−	2.18056i		−	0.163901i
$178$	−4.08637	+	7.07780i	−0.306286	+	0.530503i
$179$	−8.70786	−	15.0825i	−0.650856	−	1.12732i	−0.982916	−	0.184057i	$-0.941077\pi$
$179$	−8.70786	−	15.0825i	−0.650856	−	1.12732i	0.332059	−	0.943258i	$-0.392257\pi$
$180$		0			0
$181$	−10.3611			−0.770136			−0.385068	−	0.922888i	$-0.625822\pi$
$181$	−10.3611			−0.770136			−0.385068	+	0.922888i	$0.625822\pi$
$182$	15.5797	−	6.14177i	1.15484	−	0.455258i
$183$	−7.46410			−0.551762
$184$	−0.845746	+	0.488292i	−0.0623492	+	0.0359973i
$185$		0			0
$186$	3.22034	−	5.57780i	0.236127	−	0.408984i
$187$			17.6005i			1.28708i
$188$	−8.44671	−	4.87671i	−0.616040	−	0.355671i
$189$	4.02239	+	2.32233i	0.292586	+	0.168925i
$190$		0			0
$191$	0.448507	−	0.776837i	0.0324528	−	0.0562100i	−0.849343	−	0.527842i	$-0.823001\pi$
$191$	0.448507	−	0.776837i	0.0324528	−	0.0562100i	0.881796	+	0.471632i	$0.156335\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−17.5494	+	10.1322i	−1.26324	+	0.729330i	−0.973699	−	0.227837i	$-0.926835\pi$
$193$	−17.5494	+	10.1322i	−1.26324	+	0.729330i	−0.289537	+	0.957167i	$0.593501\pi$
$194$	13.8252			0.992593
$195$		0			0
$196$	14.5729			1.04092
$197$	−7.95060	+	4.59028i	−0.566457	+	0.327044i	−0.755733	−	0.654880i	$-0.772719\pi$
$197$	−7.95060	+	4.59028i	−0.566457	+	0.327044i	0.189276	+	0.981924i	$0.439386\pi$
$198$	−2.20006	−	3.81062i	−0.156352	−	0.270809i
$199$	−8.10876	+	14.0448i	−0.574815	+	0.995609i	0.421247	+	0.906946i	$0.361593\pi$
$199$	−8.10876	+	14.0448i	−0.574815	+	0.995609i	−0.996062	+	0.0886625i	$0.971741\pi$
$200$		0			0
$201$	1.58068	+	0.912609i	0.111493	+	0.0643705i
$202$	5.88919	+	3.40013i	0.414362	+	0.239232i
$203$		−	20.0312i		−	1.40591i
$204$	−2.00000	+	3.46410i	−0.140028	+	0.242536i
$205$		0			0
$206$	−4.58246	+	2.64568i	−0.319275	+	0.184333i
$207$	−0.976584			−0.0678773
$208$	−2.82233	−	2.24376i	−0.195693	−	0.155577i
$209$	−35.3981			−2.44854
$210$		0			0
$211$	0.809848	+	1.40270i	0.0557522	+	0.0965657i	0.892555	−	0.450939i	$-0.148911\pi$
$211$	0.809848	+	1.40270i	0.0557522	+	0.0965657i	−0.836802	+	0.547505i	$0.815578\pi$
$212$	−6.75444	+	11.6990i	−0.463897	+	0.803493i
$213$		−	7.95317i		−	0.544942i
$214$	−14.6603	−	8.46410i	−1.00215	−	0.578594i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	14.9574	−	25.9070i	1.01537	−	1.75868i
$218$	−6.40013	−	11.0853i	−0.433471	−	0.750794i
$219$	−3.77684	+	2.18056i	−0.255215	+	0.147348i
$220$		0			0
$221$	−2.12795	+	14.2644i	−0.143141	+	0.959524i
$222$	3.79603			0.254773
$223$	−1.93705	+	1.11836i	−0.129714	+	0.0748906i	−0.563453	−	0.826148i	$-0.690527\pi$
$223$	−1.93705	+	1.11836i	−0.129714	+	0.0748906i	0.433739	+	0.901039i	$0.357194\pi$
$224$	−2.32233	−	4.02239i	−0.155167	−	0.268757i
$225$		0			0
$226$			13.0662i			0.869148i
$227$	13.2679	+	7.66025i	0.880625	+	0.508429i	0.870864	−	0.491523i	$-0.163560\pi$
$227$	13.2679	+	7.66025i	0.880625	+	0.508429i	0.00976038	+	0.999952i	$0.496893\pi$
$228$	−6.96699	−	4.02239i	−0.461400	−	0.266389i
$229$		−	10.1279i		−	0.669274i	−0.942347	−	0.334637i	$-0.891386\pi$
$229$		−	10.1279i		−	0.669274i	0.942347	−	0.334637i	$-0.108614\pi$
$230$		0			0
$231$	−10.2185	−	17.6990i	−0.672331	−	1.16451i
$232$	−3.73494	+	2.15637i	−0.245211	+	0.141572i
$233$	−20.7519			−1.35950			−0.679750	−	0.733444i	$-0.737912\pi$
$233$	−20.7519			−1.35950			−0.679750	+	0.733444i	$0.737912\pi$
$234$	−1.32233	−	3.35432i	−0.0864434	−	0.219279i
$235$		0			0
$236$	−1.88842	+	1.09028i	−0.122926	+	0.0709711i
$237$	−7.46699	−	12.9332i	−0.485033	−	0.840102i
$238$	−9.28932	+	16.0896i	−0.602137	+	1.04293i
$239$		−	24.3539i		−	1.57532i	−0.616107	−	0.787662i	$-0.711291\pi$
$239$		−	24.3539i		−	1.57532i	0.616107	−	0.787662i	$-0.288709\pi$
$240$		0			0
$241$	−17.2066	−	9.93423i	−1.10837	−	0.639920i	−0.169966	−	0.985450i	$-0.554366\pi$
$241$	−17.2066	−	9.93423i	−1.10837	−	0.639920i	−0.938408	+	0.345530i	$0.887699\pi$
$242$			8.36112i			0.537473i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.73205	+	6.46410i	0.238920	+	0.413822i
$245$		0			0
$246$	7.28932			0.464750
$247$	−28.6884	−	4.27973i	−1.82540	−	0.272312i
$248$	−6.44069			−0.408984
$249$	3.04056	−	1.75547i	0.192688	−	0.111248i
$250$		0			0
$251$	6.78566	−	11.7531i	0.428307	−	0.741849i	−0.568416	−	0.822741i	$-0.692444\pi$
$251$	6.78566	−	11.7531i	0.428307	−	0.741849i	0.996723	+	0.0808920i	$0.0257769\pi$
$252$		−	4.64466i		−	0.292586i
$253$	3.72139	+	2.14855i	0.233962	+	0.135078i
$254$	10.5825	+	6.10978i	0.664002	+	0.383362i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.331150	−	0.573569i	−0.0206566	−	0.0357783i	0.855512	−	0.517782i	$-0.173242\pi$
$257$	−0.331150	−	0.573569i	−0.0206566	−	0.0357783i	−0.876169	+	0.482004i	$0.839909\pi$
$258$	0.620469	−	0.358228i	0.0386287	−	0.0223023i
$259$	17.6312			1.09555
$260$		0			0
$261$	−4.31274			−0.266952
$262$	0.328013	−	0.189378i	0.0202647	−	0.0116998i
$263$	15.3749	+	26.6301i	0.948058	+	1.64208i	0.749510	+	0.661993i	$0.230289\pi$
$263$	15.3749	+	26.6301i	0.948058	+	1.64208i	0.198548	+	0.980091i	$0.436377\pi$
$264$	−2.20006	+	3.81062i	−0.135405	+	0.234528i
$265$		0			0
$266$	−32.3593	−	18.6826i	−1.98408	−	1.14551i
$267$	7.07780	+	4.08637i	0.433154	+	0.250082i
$268$		−	1.82522i		−	0.111493i
$269$	1.87205	−	3.24249i	0.114141	−	0.197698i	−0.803295	−	0.595581i	$-0.796922\pi$
$269$	1.87205	−	3.24249i	0.114141	−	0.197698i	0.917436	+	0.397883i	$0.130255\pi$
$270$		0			0
$271$	24.0419	−	13.8806i	1.46044	−	0.843186i	0.461410	−	0.887187i	$-0.347344\pi$
$271$	24.0419	−	13.8806i	1.46044	−	0.843186i	0.999031	+	0.0440009i	$0.0140104\pi$
$272$	4.00000			0.242536
$273$	−6.14177	−	15.5797i	−0.371717	−	0.942924i
$274$	−1.25235			−0.0756575
$275$		0			0
$276$	0.488292	+	0.845746i	0.0293917	+	0.0509079i
$277$	−5.99609	+	10.3855i	−0.360270	+	0.624006i	−0.988005	−	0.154421i	$-0.950649\pi$
$277$	−5.99609	+	10.3855i	−0.360270	+	0.624006i	0.627735	+	0.778427i	$0.283982\pi$
$278$		−	3.35534i		−	0.201240i
$279$	−5.57780	−	3.22034i	−0.333934	−	0.192797i
$280$		0			0
$281$			3.63888i			0.217078i	0.994092	+	0.108539i	$0.0346172\pi$
$281$			3.63888i			0.217078i	−0.994092	+	0.108539i	$0.965383\pi$
$282$	−4.87671	+	8.44671i	−0.290404	+	0.502994i
$283$	−2.42220	−	4.19538i	−0.143985	−	0.249389i	0.785009	−	0.619485i	$-0.212658\pi$
$283$	−2.42220	−	4.19538i	−0.143985	−	0.249389i	−0.928994	+	0.370095i	$0.879325\pi$
$284$	−6.88764	+	3.97658i	−0.408707	+	0.235967i
$285$		0			0
$286$	−2.34081	+	15.6912i	−0.138415	+	0.927843i
$287$	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
$291$		−	13.8252i		−	0.810449i
$292$	3.77684	+	2.18056i	0.221023	+	0.127608i
$293$	−3.20500	−	1.85041i	−0.187238	−	0.108102i	0.403451	−	0.915001i	$-0.367811\pi$
$293$	−3.20500	−	1.85041i	−0.187238	−	0.108102i	−0.590689	+	0.806899i	$0.701144\pi$
$294$		−	14.5729i		−	0.849907i
$295$		0			0
$296$	−1.89801	−	3.28745i	−0.110320	−	0.191079i
$297$	−3.81062	+	2.20006i	−0.221115	+	0.127661i
$298$	4.61970			0.267612
$299$	2.75624	+	2.19122i	0.159398	+	0.126721i
$300$		0			0
$301$	2.88187	−	1.66385i	0.166108	−	0.0959026i
$302$	−5.62124	−	9.73628i	−0.323466	−	0.560260i
$303$	3.40013	−	5.88919i	0.195332	−	0.338325i
$304$			8.04479i			0.461400i
$305$		0			0
$306$	3.46410	+	2.00000i	0.198030	+	0.114332i
$307$			7.11454i			0.406048i	0.979174	+	0.203024i	$0.0650770\pi$
$307$			7.11454i			0.406048i	−0.979174	+	0.203024i	$0.934923\pi$
$308$	−10.2185	+	17.6990i	−0.582256	+	1.00850i
$309$	2.64568	+	4.58246i	0.150508	+	0.260687i
$310$		0			0
$311$	−19.9148			−1.12926			−0.564632	−	0.825343i	$-0.690982\pi$
$311$	−19.9148			−1.12926			−0.564632	+	0.825343i	$0.690982\pi$
$312$	−2.24376	+	2.82233i	−0.127028	+	0.159783i
$313$	−6.13950			−0.347025			−0.173513	−	0.984832i	$-0.555512\pi$
$313$	−6.13950			−0.347025			−0.173513	+	0.984832i	$0.555512\pi$
$314$	−1.30173	+	0.751556i	−0.0734611	+	0.0424128i
$315$		0			0
$316$	−7.46699	+	12.9332i	−0.420051	+	0.727550i
$317$		−	7.85286i		−	0.441061i	−0.975380	−	0.220530i	$-0.929221\pi$
$317$		−	7.85286i		−	0.441061i	0.975380	−	0.220530i	$-0.0707788\pi$
$318$	11.6990	+	6.75444i	0.656050	+	0.378770i
$319$	16.4342	+	9.48829i	0.920139	+	0.531242i
$320$		0			0
$321$	−8.46410	+	14.6603i	−0.472420	+	0.818256i
$322$	2.26795	+	3.92820i	0.126388	+	0.218910i
$323$	27.8680	−	16.0896i	1.55061	−	0.895248i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−0.176330			−0.00976601
$327$	−11.0853	+	6.40013i	−0.613021	+	0.353928i
$328$	−3.64466	−	6.31274i	−0.201243	−	0.348563i
$329$	−22.6507	+	39.2321i	−1.24877	+	2.16294i
$330$		0			0
$331$	27.7093	+	15.9980i	1.52304	+	0.879327i	0.999629	+	0.0272463i	$0.00867385\pi$
$331$	27.7093	+	15.9980i	1.52304	+	0.879327i	0.523410	+	0.852081i	$0.324659\pi$
$332$	−3.04056	−	1.75547i	−0.166872	−	0.0963438i
$333$		−	3.79603i		−	0.208021i
$334$	4.34081	−	7.51851i	0.237519	−	0.411394i
$335$		0			0
$336$	−4.02239	+	2.32233i	−0.219440	+	0.126693i
$337$	35.6432			1.94161			0.970806	−	0.239867i	$-0.0771039\pi$
$337$	35.6432			1.94161			0.970806	+	0.239867i	$0.0771039\pi$
$338$	−3.79423	+	12.4340i	−0.206379	+	0.676319i
$339$	13.0662			0.709656
$340$		0			0
$341$	14.1699	+	24.5430i	0.767344	+	1.32908i
$342$	−4.02239	+	6.96699i	−0.217506	+	0.376732i
$343$		−	35.1734i		−	1.89918i
$344$	−0.620469	−	0.358228i	−0.0334535	−	0.0193144i
$345$		0			0
$346$		−	1.78043i		−	0.0957166i
$347$	−3.44851	+	5.97299i	−0.185126	+	0.320647i	−0.943619	−	0.331034i	$-0.892603\pi$
$347$	−3.44851	+	5.97299i	−0.185126	+	0.320647i	0.758493	+	0.651681i	$0.225936\pi$
$348$	2.15637	+	3.73494i	0.115593	+	0.200214i
$349$	16.7321	−	9.66025i	0.895646	−	0.517102i	0.0198610	−	0.999803i	$-0.493678\pi$
$349$	16.7321	−	9.66025i	0.895646	−	0.517102i	0.875785	+	0.482701i	$0.160344\pi$
$350$		0			0
$351$	−3.35432	+	1.32233i	−0.179040	+	0.0705807i
$352$	4.40013			0.234528
$353$	23.7441	−	13.7086i	1.26377	−	0.729637i	0.289967	−	0.957037i	$-0.406356\pi$
$353$	23.7441	−	13.7086i	1.26377	−	0.729637i	0.973802	+	0.227400i	$0.0730224\pi$
$354$	1.09028	+	1.88842i	0.0579477	+	0.100368i
$355$		0			0
$356$		−	8.17274i		−	0.433154i
$357$	16.0896	+	9.28932i	0.851550	+	0.491643i
$358$	15.0825	+	8.70786i	0.797133	+	0.460225i
$359$			14.3611i			0.757951i	0.925407	+	0.378975i	$0.123723\pi$
$359$			14.3611i			0.757951i	−0.925407	+	0.378975i	$0.876277\pi$
$360$		0			0
$361$	22.8593	+	39.5935i	1.20312	+	2.08387i
$362$	8.97299	−	5.18056i	0.471610	−	0.272284i
$363$	8.36112			0.438845
$364$	−10.4215	+	13.1088i	−0.546235	+	0.687086i
$365$		0			0
$366$	6.46410	−	3.73205i	0.337884	−	0.195077i
$367$	−6.88764	−	11.9298i	−0.359532	−	0.622728i	0.628351	−	0.777930i	$-0.283730\pi$
$367$	−6.88764	−	11.9298i	−0.359532	−	0.622728i	−0.987883	+	0.155202i	$0.950397\pi$
$368$	0.488292	−	0.845746i	0.0254540	−	0.0440876i
$369$		−	7.28932i		−	0.379467i
$370$		0			0
$371$	54.3381	+	31.3721i	2.82109	+	1.62876i
$372$			6.44069i			0.333934i
$373$	−16.7313	+	28.9795i	−0.866316	+	1.50050i	−0.000581860		1.00000i	$0.500185\pi$
$373$	−16.7313	+	28.9795i	−0.866316	+	1.50050i	−0.865734	+	0.500504i	$0.833148\pi$
$374$	−8.80025	−	15.2425i	−0.455050	−	0.788170i
$375$		0			0
$376$	9.75342			0.502994
$377$	12.1720	+	9.67674i	0.626888	+	0.498377i
$378$	−4.64466			−0.238896
$379$	−28.9052	+	16.6884i	−1.48476	+	0.857227i	−0.999850	−	0.0173371i	$-0.994481\pi$
$379$	−28.9052	+	16.6884i	−1.48476	+	0.857227i	−0.484910	+	0.874564i	$0.661148\pi$
$380$		0			0
$381$	6.10978	−	10.5825i	0.313014	−	0.542156i
$382$			0.897014i			0.0458952i
$383$	−6.34829	−	3.66519i	−0.324383	−	0.187282i	0.328962	−	0.944343i	$-0.393301\pi$
$383$	−6.34829	−	3.66519i	−0.324383	−	0.187282i	−0.653344	+	0.757061i	$0.726635\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	10.1322	−	17.5494i	0.515714	−	0.893243i
$387$	−0.358228	−	0.620469i	−0.0182098	−	0.0315402i
$388$	−11.9730	+	6.91261i	−0.607836	+	0.350935i
$389$	−32.6198			−1.65389			−0.826946	−	0.562282i	$-0.809924\pi$
$389$	−32.6198			−1.65389			−0.826946	+	0.562282i	$0.809924\pi$
$390$		0			0
$391$	−3.90633			−0.197552
$392$	−12.6205	+	7.28643i	−0.637430	+	0.368020i
$393$	−0.189378	−	0.328013i	−0.00955288	−	0.0165461i
$394$	4.59028	−	7.95060i	0.231255	−	0.400545i
$395$		0			0
$396$	3.81062	+	2.20006i	0.191491	+	0.110557i
$397$	−12.5299	−	7.23416i	−0.628860	−	0.363072i	0.151451	−	0.988465i	$-0.451606\pi$
$397$	−12.5299	−	7.23416i	−0.628860	−	0.363072i	−0.780310	+	0.625392i	$0.784939\pi$
$398$		−	16.2175i		−	0.812911i
$399$	−18.6826	+	32.3593i	−0.935302	+	1.61999i
$400$		0			0
$401$	−6.31096	+	3.64364i	−0.315154	+	0.181955i	−0.649231	−	0.760592i	$-0.724909\pi$
$401$	−6.31096	+	3.64364i	−0.315154	+	0.181955i	0.334076	+	0.942546i	$0.391576\pi$
$402$	−1.82522			−0.0910336
$403$	8.51671	+	21.6041i	0.424248	+	1.07618i
$404$	−6.80025			−0.338325
$405$		0			0
$406$	10.0156	+	17.3475i	0.497066	+	0.860943i
$407$	−8.35150	+	14.4652i	−0.413968	+	0.717014i
$408$		−	4.00000i		−	0.198030i
$409$	−21.2840	−	12.2883i	−1.05242	−	0.607617i	−0.129097	−	0.991632i	$-0.541208\pi$
$409$	−21.2840	−	12.2883i	−1.05242	−	0.607617i	−0.923327	+	0.384015i	$0.874541\pi$
$410$		0			0
$411$			1.25235i			0.0617741i
$412$	2.64568	−	4.58246i	0.130343	−	0.225761i
$413$	5.06397	+	8.77106i	0.249182	+	0.431596i
$414$	0.845746	−	0.488292i	0.0415662	−	0.0239982i
$415$		0			0
$416$	3.56609	+	0.531987i	0.174842	+	0.0260828i
$417$	−3.35534			−0.164312
$418$	30.6556	−	17.6990i	1.49942	−	0.865688i
$419$	−7.77684	−	13.4699i	−0.379923	−	0.658047i	0.611127	−	0.791532i	$-0.290716\pi$
$419$	−7.77684	−	13.4699i	−0.379923	−	0.658047i	−0.991051	+	0.133486i	$0.957383\pi$
$420$		0			0
$421$		−	22.3143i		−	1.08753i	−0.839237	−	0.543766i	$-0.816998\pi$
$421$		−	22.3143i		−	1.08753i	0.839237	−	0.543766i	$-0.183002\pi$
$422$	−1.40270	−	0.809848i	−0.0682822	−	0.0394228i
$423$	8.44671	+	4.87671i	0.410693	+	0.237114i
$424$		−	13.5089i		−	0.656050i
$425$		0			0
$426$	3.97658	+	6.88764i	0.192666	+	0.333707i
$427$	30.0236	−	17.3341i	1.45294	−	0.838856i
$428$	16.9282			0.818256
$429$	15.6912	+	2.34081i	0.757580	+	0.113015i
$430$		0			0
$431$	21.0135	−	12.1322i	1.01219	−	0.584386i	0.100356	−	0.994952i	$-0.468002\pi$
$431$	21.0135	−	12.1322i	1.01219	−	0.584386i	0.911831	+	0.410565i	$0.134669\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	11.5494	−	20.0042i	0.555031	−	0.961342i	−0.442870	−	0.896586i	$-0.646040\pi$
$433$	11.5494	−	20.0042i	0.555031	−	0.961342i	0.997901	−	0.0647561i	$-0.0206269\pi$
$434$			29.9148i			1.43596i
$435$		0			0
$436$	11.0853	+	6.40013i	0.530892	+	0.306510i
$437$		−	7.85641i		−	0.375823i
$438$	2.18056	−	3.77684i	0.104191	−	0.180464i
$439$	−19.9980	−	34.6375i	−0.954450	−	1.65316i	−0.735621	−	0.677393i	$-0.763110\pi$
$439$	−19.9980	−	34.6375i	−0.954450	−	1.65316i	−0.218829	−	0.975763i	$-0.570224\pi$
$440$		0			0
$441$	−14.5729			−0.693946
$442$	−5.28932	−	13.4173i	−0.251587	−	0.638194i
$443$	15.6036			0.741350			0.370675	−	0.928763i	$-0.379126\pi$
$443$	15.6036			0.741350			0.370675	+	0.928763i	$0.379126\pi$
$444$	−3.28745	+	1.89801i	−0.156016	+	0.0900757i
$445$		0			0
$446$	1.11836	−	1.93705i	0.0529557	−	0.0917219i
$447$		−	4.61970i		−	0.218504i
$448$	4.02239	+	2.32233i	0.190040	+	0.109720i
$449$	23.3863	+	13.5021i	1.10367	+	0.637203i	0.937182	−	0.348841i	$-0.113425\pi$
$449$	23.3863	+	13.5021i	1.10367	+	0.637203i	0.166486	+	0.986044i	$0.446758\pi$
$450$		0			0
$451$	−16.0370	+	27.7768i	−0.755151	+	1.30796i
$452$	−6.53308	−	11.3156i	−0.307290	−	0.532242i
$453$	−9.73628	+	5.62124i	−0.457450	+	0.264109i
$454$	−15.3205			−0.719027
$455$		0			0
$456$	8.04479			0.376732
$457$	−15.4039	+	8.89342i	−0.720562	+	0.416017i	−0.814959	−	0.579518i	$-0.803241\pi$
$457$	−15.4039	+	8.89342i	−0.720562	+	0.416017i	0.0943975	+	0.995535i	$0.469908\pi$
$458$	5.06397	+	8.77106i	0.236624	+	0.409845i
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		0			0
$461$	21.6205	+	12.4826i	1.00697	+	0.581372i	0.910302	−	0.413945i	$-0.135849\pi$
$461$	21.6205	+	12.4826i	1.00697	+	0.581372i	0.0966638	+	0.995317i	$0.469183\pi$
$462$	17.6990	+	10.2185i	0.823434	+	0.475410i
$463$		−	15.6389i		−	0.726801i	−0.931633	−	0.363400i	$-0.881616\pi$
$463$		−	15.6389i		−	0.726801i	0.931633	−	0.363400i	$-0.118384\pi$
$464$	2.15637	−	3.73494i	0.100107	−	0.173390i
$465$		0			0
$466$	17.9716	−	10.3759i	0.832521	−	0.480656i
$467$	2.43914			0.112870			0.0564349	−	0.998406i	$-0.482027\pi$
$467$	2.43914			0.112870			0.0564349	+	0.998406i	$0.482027\pi$
$468$	2.82233	+	2.24376i	0.130462	+	0.103718i
$469$	−8.47751			−0.391455
$470$		0			0
$471$	0.751556	+	1.30173i	0.0346299	+	0.0599807i
$472$	1.09028	−	1.88842i	0.0501842	−	0.0869215i
$473$			3.15250i			0.144952i
$474$	12.9332	+	7.46699i	0.594042	+	0.342970i
$475$		0			0
$476$		−	18.5786i		−	0.851550i
$477$	6.75444	−	11.6990i	0.309265	−	0.535662i
$478$	12.1770	+	21.0911i	0.556961	+	0.964685i
$479$	12.2857	−	7.09317i	0.561349	−	0.324095i	−0.192338	−	0.981329i	$-0.561607\pi$
$479$	12.2857	−	7.09317i	0.561349	−	0.324095i	0.753687	+	0.657234i	$0.228274\pi$
$480$		0			0
$481$	−8.51737	+	10.7136i	−0.388358	+	0.488500i
$482$	19.8685			0.904983
$483$	3.92820	−	2.26795i	0.178739	−	0.103195i
$484$	−4.18056	−	7.24094i	−0.190025	−	0.329134i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−4.99115	−	2.88164i	−0.226171	−	0.130580i	0.382633	−	0.923900i	$-0.375017\pi$
$487$	−4.99115	−	2.88164i	−0.226171	−	0.130580i	−0.608804	+	0.793320i	$0.708351\pi$
$488$	−6.46410	−	3.73205i	−0.292616	−	0.168942i
$489$			0.176330i			0.00797392i
$490$		0			0
$491$	−0.537671	−	0.931273i	−0.0242647	−	0.0420278i	0.853638	−	0.520867i	$-0.174391\pi$
$491$	−0.537671	−	0.931273i	−0.0242647	−	0.0420278i	−0.877903	+	0.478839i	$0.841058\pi$
$492$	−6.31274	+	3.64466i	−0.284600	+	0.164314i
$493$	−17.2509			−0.776943
$494$	26.9848	−	10.6379i	1.21410	−	0.478620i
$495$		0			0
$496$	5.57780	−	3.22034i	0.250450	−	0.144598i
$497$	18.4699	+	31.9908i	0.828487	+	1.43498i
$498$	−1.75547	+	3.04056i	−0.0786644	+	0.136251i
$499$			14.7534i			0.660454i	0.943902	+	0.330227i	$0.107125\pi$
$499$			14.7534i			0.660454i	−0.943902	+	0.330227i	$0.892875\pi$
$500$		0			0
$501$	−7.51851	−	4.34081i	−0.335902	−	0.193933i
$502$			13.5713i			0.605717i
$503$	−13.3309	+	23.0898i	−0.594395	+	1.02952i	0.399236	+	0.916848i	$0.369275\pi$
$503$	−13.3309	+	23.0898i	−0.594395	+	1.02952i	−0.993632	+	0.112675i	$0.964058\pi$
$504$	2.32233	+	4.02239i	0.103445	+	0.179172i
$505$		0			0
$506$	−4.29709			−0.191029
$507$	12.4340	+	3.79423i	0.552212	+	0.168508i
$508$	−12.2196			−0.542156
$509$	12.2807	−	7.09028i	0.544333	−	0.314271i	−0.202500	−	0.979282i	$-0.564907\pi$
$509$	12.2807	−	7.09028i	0.544333	−	0.314271i	0.746833	+	0.665011i	$0.231573\pi$
$510$		0			0
$511$	10.1279	−	17.5421i	0.448034	−	0.776018i
$512$		−	1.00000i		−	0.0441942i
$513$	6.96699	+	4.02239i	0.307600	+	0.177593i
$514$	0.573569	+	0.331150i	0.0252990	+	0.0146064i
$515$		0			0
$516$	−0.358228	+	0.620469i	−0.0157701	+	0.0273146i
$517$	−21.4581	−	37.1666i	−0.943728	−	1.63459i
$518$	−15.2691	+	8.81562i	−0.670886	+	0.387336i
$519$	−1.78043			−0.0781523
$520$		0			0
$521$	23.7476			1.04040			0.520202	−	0.854043i	$-0.325857\pi$
$521$	23.7476			1.04040			0.520202	+	0.854043i	$0.325857\pi$
$522$	3.73494	−	2.15637i	0.163474	−	0.0943817i
$523$	6.92532	+	11.9950i	0.302823	+	0.524505i	0.976774	−	0.214271i	$-0.0687376\pi$
$523$	6.92532	+	11.9950i	0.302823	+	0.524505i	−0.673951	+	0.738776i	$0.735404\pi$
$524$	−0.189378	+	0.328013i	−0.00827303	+	0.0143293i
$525$		0			0
$526$	−26.6301	−	15.3749i	−1.16113	−	0.670378i
$527$	−22.3112	−	12.8814i	−0.971891	−	0.561121i
$528$		−	4.40013i		−	0.191491i
$529$	11.0231	−	19.0926i	0.479267	−	0.830115i
$530$		0			0
$531$	1.88842	−	1.09028i	0.0819504	−	0.0473141i
$532$	37.3653			1.61999
$533$	−16.3555	+	20.5729i	−0.708434	+	0.891110i
$534$	−8.17274			−0.353669
$535$		0			0
$536$	0.912609	+	1.58068i	0.0394187	+	0.0682752i
$537$	8.70786	−	15.0825i	0.375772	−	0.650856i
$538$			3.74410i			0.161420i
$539$	55.5317	+	32.0612i	2.39192	+	1.38097i
$540$		0			0
$541$			14.8898i			0.640164i	0.947390	+	0.320082i	$0.103710\pi$
$541$			14.8898i			0.640164i	−0.947390	+	0.320082i	$0.896290\pi$
$542$	−13.8806	+	24.0419i	−0.596223	+	1.03269i
$543$	−5.18056	−	8.97299i	−0.222319	−	0.385068i
$544$	−3.46410	+	2.00000i	−0.148522	+	0.0857493i
$545$		0			0
$546$	13.1088	+	10.4215i	0.561003	+	0.445999i
$547$	22.2019			0.949284			0.474642	−	0.880179i	$-0.342578\pi$
$547$	22.2019			0.949284			0.474642	+	0.880179i	$0.342578\pi$
$548$	1.08457	−	0.626177i	0.0463306	−	0.0267490i
$549$	−3.73205	−	6.46410i	−0.159280	−	0.275881i
$550$		0			0
$551$		−	34.6950i		−	1.47806i
$552$	−0.845746	−	0.488292i	−0.0359973	−	0.0207831i
$553$	60.0703	+	34.6816i	2.55445	+	1.47481i
$554$		−	11.9922i		−	0.509499i
$555$		0			0
$556$	1.67767	+	2.90581i	0.0711491	+	0.123234i
$557$	−1.64518	+	0.949847i	−0.0697087	+	0.0402463i	−0.534449	−	0.845201i	$-0.679481\pi$
$557$	−1.64518	+	0.949847i	−0.0697087	+	0.0402463i	0.464741	+	0.885447i	$0.346148\pi$
$558$	6.44069			0.272656
$559$	−0.381146	+	2.55495i	−0.0161207	+	0.108063i
$560$		0			0
$561$	−15.2425	+	8.80025i	−0.643538	+	0.371547i
$562$	−1.81944	−	3.15137i	−0.0767485	−	0.132932i
$563$	0.860000	−	1.48956i	0.0362447	−	0.0627777i	−0.847334	−	0.531060i	$-0.821794\pi$
$563$	0.860000	−	1.48956i	0.0362447	−	0.0627777i	0.883579	+	0.468283i	$0.155127\pi$
$564$		−	9.75342i		−	0.410693i
$565$		0			0
$566$	4.19538	+	2.42220i	0.176345	+	0.101813i
$567$			4.64466i			0.195057i
$568$	3.97658	−	6.88764i	0.166854	−	0.288999i
$569$	−0.300960	−	0.521278i	−0.0126169	−	0.0218531i	0.859648	−	0.510887i	$-0.170683\pi$
$569$	−0.300960	−	0.521278i	−0.0126169	−	0.0218531i	−0.872265	+	0.489034i	$0.837350\pi$
$570$		0			0
$571$	11.9808			0.501381			0.250691	−	0.968067i	$-0.419342\pi$
$571$	11.9808			0.501381			0.250691	+	0.968067i	$0.419342\pi$
$572$	−5.81842	−	14.7594i	−0.243280	−	0.617122i
$573$	0.897014			0.0374733
$574$	−29.3205	+	16.9282i	−1.22381	+	0.706570i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			43.0293i			1.79133i	0.444725	+	0.895667i	$0.353301\pi$
$577$			43.0293i			1.79133i	−0.444725	+	0.895667i	$0.646699\pi$
$578$	−0.866025	−	0.500000i	−0.0360219	−	0.0207973i
$579$	−17.5494	−	10.1322i	−0.729330	−	0.421079i
$580$		0			0
$581$	−8.15355	+	14.1224i	−0.338266	+	0.585894i
$582$	6.91261	+	11.9730i	0.286537	+	0.496296i
$583$	−51.4773	+	29.7204i	−2.13197	+	1.23089i
$584$	−4.36112			−0.180464
$585$		0			0
$586$	3.70081			0.152879
$587$	15.5147	−	8.95740i	0.640359	−	0.369711i	−0.144394	−	0.989520i	$-0.546123\pi$
$587$	15.5147	−	8.95740i	0.640359	−	0.369711i	0.784753	+	0.619809i	$0.212790\pi$
$588$	7.28643	+	12.6205i	0.300487	+	0.520459i
$589$	25.9070	−	44.8722i	1.06748	−	1.84893i
$590$		0			0
$591$	−7.95060	−	4.59028i	−0.327044	−	0.188819i
$592$	3.28745	+	1.89801i	0.135114	+	0.0780078i
$593$		−	0.669624i		−	0.0274981i	−0.999905	−	0.0137491i	$-0.995623\pi$
$593$		−	0.669624i		−	0.0274981i	0.999905	−	0.0137491i	$-0.00437660\pi$
$594$	2.20006	−	3.81062i	0.0902697	−	0.156352i
$595$		0			0
$596$	−4.00077	+	2.30985i	−0.163878	+	0.0946151i
$597$	−16.2175			−0.663739
$598$	−3.48258	−	0.519530i	−0.142413	−	0.0212452i
$599$	1.29241			0.0528066			0.0264033	−	0.999651i	$-0.491595\pi$
$599$	1.29241			0.0528066			0.0264033	+	0.999651i	$0.491595\pi$
$600$		0			0
$601$	5.73671	+	9.93627i	0.234005	+	0.405309i	0.958983	−	0.283463i	$-0.0914834\pi$
$601$	5.73671	+	9.93627i	0.234005	+	0.405309i	−0.724978	+	0.688772i	$0.758150\pi$
$602$	−1.66385	+	2.88187i	−0.0678134	+	0.117456i
$603$			1.82522i			0.0743286i
$604$	9.73628	+	5.62124i	0.396164	+	0.228725i
$605$		0			0
$606$			6.80025i			0.276241i
$607$	−12.0672	+	20.9010i	−0.489792	+	0.848344i	−0.999931	−	0.0117477i	$-0.996261\pi$
$607$	−12.0672	+	20.9010i	−0.489792	+	0.848344i	0.510139	+	0.860092i	$0.329594\pi$
$608$	−4.02239	−	6.96699i	−0.163130	−	0.282549i
$609$	17.3475	−	10.0156i	0.702957	−	0.405852i
$610$		0			0
$611$	−12.8972	−	32.7161i	−0.521766	−	1.32355i
$612$	−4.00000			−0.161690
$613$	−25.0716	+	14.4751i	−1.01263	+	0.584644i	−0.911961	−	0.410276i	$-0.865432\pi$
$613$	−25.0716	+	14.4751i	−1.01263	+	0.584644i	−0.100671	+	0.994920i	$0.532099\pi$
$614$	−3.55727	−	6.16137i	−0.143560	−	0.248653i
$615$		0			0
$616$		−	20.4371i		−	0.823434i
$617$	0.728597	+	0.420655i	0.0293322	+	0.0169349i	0.514594	−	0.857434i	$-0.327943\pi$
$617$	0.728597	+	0.420655i	0.0293322	+	0.0169349i	−0.485262	+	0.874369i	$0.661276\pi$
$618$	−4.58246	−	2.64568i	−0.184333	−	0.106425i
$619$		−	6.25076i		−	0.251239i	−0.992078	−	0.125620i	$-0.959908\pi$
$619$		−	6.25076i		−	0.251239i	0.992078	−	0.125620i	$-0.0400919\pi$
$620$		0			0
$621$	−0.488292	−	0.845746i	−0.0195945	−	0.0339386i
$622$	17.2467	−	9.95740i	0.691530	−	0.399255i
$623$	−37.9596			−1.52082
$624$	0.531987	−	3.56609i	0.0212965	−	0.142758i
$625$		0			0
$626$	5.31696	−	3.06975i	0.212509	−	0.122692i
$627$	−17.6990	−	30.6556i	−0.706832	−	1.22427i
$628$	0.751556	−	1.30173i	0.0299904	−	0.0519448i
$629$		−	15.1841i		−	0.605430i
$630$		0			0
$631$	2.61970	+	1.51248i	0.104288	+	0.0602110i	0.551237	−	0.834349i	$-0.314156\pi$
$631$	2.61970	+	1.51248i	0.104288	+	0.0602110i	−0.446949	+	0.894560i	$0.647489\pi$
$632$		−	14.9340i		−	0.594042i
$633$	−0.809848	+	1.40270i	−0.0321886	+	0.0557522i
$634$	3.92643	+	6.80078i	0.155938	+	0.270093i
$635$		0			0
$636$	−13.5089			−0.535662
$637$	41.1294	+	32.6980i	1.62961	+	1.29554i
$638$	−18.9766			−0.751290
$639$	6.88764	−	3.97658i	0.272471	−	0.157311i
$640$		0			0
$641$	0.386305	−	0.669099i	0.0152581	−	0.0264278i	−0.858296	−	0.513156i	$-0.828476\pi$
$641$	0.386305	−	0.669099i	0.0152581	−	0.0264278i	0.873554	+	0.486728i	$0.161810\pi$
$642$		−	16.9282i		−	0.668103i
$643$	−16.7788	−	9.68726i	−0.661693	−	0.382028i	0.131229	−	0.991352i	$-0.458108\pi$
$643$	−16.7788	−	9.68726i	−0.661693	−	0.382028i	−0.792922	+	0.609324i	$0.791441\pi$
$644$	−3.92820	−	2.26795i	−0.154793	−	0.0893697i
$645$		0			0
$646$	−16.0896	+	27.8680i	−0.633036	+	1.09645i
$647$	13.5953	+	23.5477i	0.534485	+	0.925755i	0.999188	+	0.0402882i	$0.0128276\pi$
$647$	13.5953	+	23.5477i	0.534485	+	0.925755i	−0.464703	+	0.885466i	$0.653839\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−9.59473			−0.376626
$650$		0			0
$651$	29.9148			1.17245
$652$	0.152706	−	0.0881650i	0.00598044	−	0.00345281i
$653$	7.89799	+	13.6797i	0.309072	+	0.535329i	0.978160	−	0.207855i	$-0.0666482\pi$
$653$	7.89799	+	13.6797i	0.309072	+	0.535329i	−0.669088	+	0.743184i	$0.733315\pi$
$654$	6.40013	−	11.0853i	0.250265	−	0.433471i
$655$		0			0
$656$	6.31274	+	3.64466i	0.246471	+	0.142300i
$657$	−3.77684	−	2.18056i	−0.147348	−	0.0850717i
$658$		−	45.3013i		−	1.76603i
$659$	−15.2381	+	26.3932i	−0.593593	+	1.02813i	0.400151	+	0.916449i	$0.368958\pi$
$659$	−15.2381	+	26.3932i	−0.593593	+	1.02813i	−0.993744	+	0.111684i	$0.964376\pi$
$660$		0			0
$661$	−24.1514	+	13.9438i	−0.939379	+	0.542351i	−0.889766	−	0.456418i	$-0.849132\pi$
$661$	−24.1514	+	13.9438i	−0.939379	+	0.542351i	−0.0496136	+	0.998768i	$0.515799\pi$
$662$	−31.9959			−1.24356
$663$	−13.4173	+	5.28932i	−0.521084	+	0.205420i
$664$	3.51093			0.136251
$665$		0			0
$666$	1.89801	+	3.28745i	0.0735465	+	0.127386i
$667$	−2.10587	+	3.64748i	−0.0815397	+	0.141231i
$668$			8.68162i			0.335902i
$669$	−1.93705	−	1.11836i	−0.0748906	−	0.0432381i
$670$		0			0
$671$			32.8430i			1.26789i
$672$	2.32233	−	4.02239i	0.0895858	−	0.155167i
$673$	0.489066	+	0.847086i	0.0188521	+	0.0326528i	0.875298	−	0.483585i	$-0.160666\pi$
$673$	0.489066	+	0.847086i	0.0188521	+	0.0326528i	−0.856445	+	0.516238i	$0.827332\pi$
$674$	−30.8680	+	17.8216i	−1.18899	+	0.686463i
$675$		0			0
$676$	−2.93109	−	12.6653i	−0.112734	−	0.487125i
$677$	19.1926			0.737630			0.368815	−	0.929503i	$-0.379764\pi$
$677$	19.1926			0.737630			0.368815	+	0.929503i	$0.379764\pi$
$678$	−11.3156	+	6.53308i	−0.434574	+	0.250901i
$679$	32.1067	+	55.6105i	1.23214	+	2.13413i
$680$		0			0
$681$			15.3205i			0.587083i
$682$	−24.5430	−	14.1699i	−0.939801	−	0.542594i
$683$	1.30851	+	0.755467i	0.0500687	+	0.0289071i	0.524825	−	0.851210i	$-0.324131\pi$
$683$	1.30851	+	0.755467i	0.0500687	+	0.0289071i	−0.474757	+	0.880117i	$0.657464\pi$
$684$		−	8.04479i		−	0.307600i
$685$		0			0
$686$	17.5867	+	30.4610i	0.671463	+	1.16301i
$687$	8.77106	−	5.06397i	0.334637	−	0.193203i
$688$	0.716456			0.0273146
$689$	−45.3131	+	17.8632i	−1.72629	+	0.680534i
$690$		0			0
$691$	28.6798	−	16.5583i	1.09103	−	0.629907i	0.157180	−	0.987570i	$-0.449760\pi$
$691$	28.6798	−	16.5583i	1.09103	−	0.629907i	0.933851	+	0.357663i	$0.116426\pi$
$692$	0.890216	+	1.54190i	0.0338409	+	0.0586142i
$693$	10.2185	−	17.6990i	0.388170	−	0.672331i
$694$		−	6.89701i		−	0.261807i
$695$		0			0
$696$	−3.73494	−	2.15637i	−0.141572	−	0.0817369i
$697$		−	29.1573i		−	1.10441i
$698$	−9.66025	+	16.7321i	−0.365646	+	0.633317i
$699$	−10.3759	−	17.9716i	−0.392454	−	0.679750i
$700$		0			0
$701$	27.8695			1.05262			0.526308	−	0.850294i	$-0.323576\pi$
$701$	27.8695			1.05262			0.526308	+	0.850294i	$0.323576\pi$
$702$	2.24376	−	2.82233i	0.0846852	−	0.106522i
$703$	30.5382			1.15177
$704$	−3.81062	+	2.20006i	−0.143618	+	0.0829180i
$705$		0			0
$706$	−13.7086	+	23.7441i	−0.515931	+	0.893619i
$707$			31.5849i			1.18787i
$708$	−1.88842	−	1.09028i	−0.0709711	−	0.0409752i
$709$	−9.57491	−	5.52808i	−0.359593	−	0.207611i	0.309309	−	0.950962i	$-0.399902\pi$
$709$	−9.57491	−	5.52808i	−0.359593	−	0.207611i	−0.668902	+	0.743350i	$0.733236\pi$
$710$		0			0
$711$	7.46699	−	12.9332i	0.280034	−	0.485033i
$712$	4.08637	+	7.07780i	0.153143	+	0.265252i
$713$	−5.44719	+	3.14493i	−0.203999	+	0.117779i
$714$	−18.5786			−0.695288
$715$		0			0
$716$	−17.4157			−0.650856
$717$	21.0911	−	12.1770i	0.787662	−	0.454757i
$718$	−7.18056	−	12.4371i	−0.267976	−	0.464148i
$719$	5.85641	−	10.1436i	0.218407	−	0.378292i	−0.735914	−	0.677075i	$-0.763247\pi$
$719$	5.85641	−	10.1436i	0.218407	−	0.378292i	0.954321	+	0.298783i	$0.0965806\pi$
$720$		0			0
$721$	−21.2840	−	12.2883i	−0.792656	−	0.457640i
$722$	−39.5935	−	22.8593i	−1.47352	−	0.850735i
$723$		−	19.8685i		−	0.738916i
$724$	−5.18056	+	8.97299i	−0.192534	+	0.333479i
$725$		0			0
$726$	−7.24094	+	4.18056i	−0.268736	+	0.155155i
$727$	19.4152			0.720071			0.360035	−	0.932939i	$-0.382765\pi$
$727$	19.4152			0.720071			0.360035	+	0.932939i	$0.382765\pi$
$728$	2.47090	−	16.5633i	0.0915777	−	0.613876i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−1.43291	−	2.48188i	−0.0529982	−	0.0917956i
$732$	−3.73205	+	6.46410i	−0.137941	+	0.238920i
$733$		−	11.9340i		−	0.440792i	−0.975411	−	0.220396i	$-0.929265\pi$
$733$		−	11.9340i		−	0.440792i	0.975411	−	0.220396i	$-0.0707349\pi$
$734$	11.9298	+	6.88764i	0.440335	+	0.254228i
$735$		0			0
$736$			0.976584i			0.0359973i
$737$	4.01559	−	6.95521i	0.147916	−	0.256199i
$738$	3.64466	+	6.31274i	0.134162	+	0.232375i
$739$	17.2017	−	9.93141i	0.632775	−	0.365333i	−0.149051	−	0.988830i	$-0.547622\pi$
$739$	17.2017	−	9.93141i	0.632775	−	0.365333i	0.781826	+	0.623497i	$0.214289\pi$
$740$		0			0
$741$	−10.6379	−	26.9848i	−0.390792	−	0.991310i
$742$	−62.7442			−2.30341
$743$	−14.2787	+	8.24383i	−0.523836	+	0.302437i	−0.738503	−	0.674251i	$-0.764467\pi$
$743$	−14.2787	+	8.24383i	−0.523836	+	0.302437i	0.214667	+	0.976687i	$0.431133\pi$
$744$	−3.22034	−	5.57780i	−0.118063	−	0.204492i
$745$		0			0
$746$		−	33.4627i		−	1.22516i
$747$	3.04056	+	1.75547i	0.111248	+	0.0642292i
$748$	15.2425	+	8.80025i	0.557320	+	0.321769i
$749$		−	78.6257i		−	2.87292i
$750$		0			0
$751$	−23.3312	−	40.4109i	−0.851368	−	1.47461i	−0.879974	−	0.475022i	$-0.842440\pi$
$751$	−23.3312	−	40.4109i	−0.851368	−	1.47461i	0.0286056	−	0.999591i	$-0.490893\pi$
$752$	−8.44671	+	4.87671i	−0.308020	+	0.177835i
$753$	13.5713			0.494566
$754$	−15.3796	−	2.29432i	−0.560092	−	0.0835542i
$755$		0			0
$756$	4.02239	−	2.32233i	0.146293	−	0.0844623i
$757$	1.31799	+	2.28282i	0.0479030	+	0.0829705i	0.888983	−	0.457941i	$-0.151413\pi$
$757$	1.31799	+	2.28282i	0.0479030	+	0.0829705i	−0.841080	+	0.540911i	$0.818079\pi$
$758$	16.6884	−	28.9052i	0.606151	−	1.04988i
$759$			4.29709i			0.155975i
$760$		0			0
$761$	0.0693410	+	0.0400340i	0.00251361	+	0.00145123i	0.501256	−	0.865299i	$-0.332871\pi$
$761$	0.0693410	+	0.0400340i	0.00251361	+	0.00145123i	−0.498743	+	0.866750i	$0.666205\pi$
$762$			12.2196i			0.442668i
$763$	29.7264	−	51.4877i	1.07617	−	1.86398i
$764$	−0.448507	−	0.776837i	−0.0162264	−	0.0281050i
$765$		0			0
$766$	7.33038			0.264857
$767$	−7.77606	−	1.16003i	−0.280777	−	0.0418862i
$768$	−1.00000			−0.0360844
$769$	4.92177	−	2.84159i	0.177484	−	0.102470i	−0.408626	−	0.912702i	$-0.633992\pi$
$769$	4.92177	−	2.84159i	0.177484	−	0.102470i	0.586110	+	0.810232i	$0.300659\pi$
$770$		0			0
$771$	0.331150	−	0.573569i	0.0119261	−	0.0206566i
$772$			20.2644i			0.729330i
$773$	6.57184	+	3.79425i	0.236373	+	0.136470i	0.613508	−	0.789688i	$-0.289758\pi$
$773$	6.57184	+	3.79425i	0.236373	+	0.136470i	−0.377136	+	0.926158i	$0.623091\pi$
$774$	0.620469	+	0.358228i	0.0223023	+	0.0128762i
$775$		0			0
$776$	6.91261	−	11.9730i	0.248148	−	0.429805i
$777$	8.81562	+	15.2691i	0.316259	+	0.547776i
$778$	28.2496	−	16.3099i	1.01280	−	0.584739i
$779$	58.6410			2.10103
$780$		0			0
$781$	−34.9949			−1.25222
$782$	3.38298	−	1.95317i	0.120975	−	0.0698451i
$783$	−2.15637	−	3.73494i	−0.0770623	−	0.133476i
$784$	7.28643	−	12.6205i	0.260230	−	0.450731i
$785$		0			0
$786$	0.328013	+	0.189378i	0.0116998	+	0.00675490i
$787$	4.10169	+	2.36811i	0.146210	+	0.0844142i	0.571320	−	0.820727i	$-0.306431\pi$
$787$	4.10169	+	2.36811i	0.146210	+	0.0844142i	−0.425111	+	0.905141i	$0.639765\pi$
$788$			9.18056i			0.327044i
$789$	−15.3749	+	26.6301i	−0.547361	+	0.948058i
$790$		0			0
$791$	−52.5572	+	30.3439i	−1.86872	+	1.07891i
$792$	−4.40013			−0.156352
$793$	−3.97081	+	26.6176i	−0.141008	+	0.945220i
$794$	14.4683			0.513462
$795$		0			0
$796$	8.10876	+	14.0448i	0.287407	+	0.497804i
$797$	20.5318	−	35.5621i	0.727274	−	1.25968i	−0.230757	−	0.973011i	$-0.574120\pi$
$797$	20.5318	−	35.5621i	0.727274	−	1.25968i	0.958031	−	0.286664i	$-0.0925463\pi$
$798$		−	37.3653i		−	1.32272i
$799$	33.7868	+	19.5068i	1.19529	+	0.690102i
$800$		0			0
$801$			8.17274i			0.288769i
$802$	3.64364	−	6.31096i	0.128661	−	0.222848i
$803$	9.59473	+	16.6186i	0.338591	+	0.586456i
$804$	1.58068	−	0.912609i	0.0557465	−	0.0321852i
$805$		0			0
$806$	−18.1777	−	14.4513i	−0.640284	−	0.509027i
$807$	3.74410			0.131799
$808$	5.88919	−	3.40013i	0.207181	−	0.119616i
$809$	13.8003	+	23.9027i	0.485191	+	0.840376i	0.999855	−	0.0170163i	$-0.00541671\pi$
$809$	13.8003	+	23.9027i	0.485191	+	0.840376i	−0.514664	+	0.857392i	$0.672083\pi$
$810$		0			0
$811$			10.6930i			0.375482i	0.982219	+	0.187741i	$0.0601165\pi$
$811$			10.6930i			0.375482i	−0.982219	+	0.187741i	$0.939883\pi$
$812$	−17.3475	−	10.0156i	−0.608779	−	0.351478i
$813$	24.0419	+	13.8806i	0.843186	+	0.486814i
$814$		−	16.7030i		−	0.585440i
$815$		0			0
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	4.99154	−	2.88187i	0.174632	−	0.100824i
$818$	24.5766			0.859300
$819$	10.4215	−	13.1088i	0.364157	−	0.458057i
$820$		0			0
$821$	15.2105	−	8.78177i	0.530849	−	0.306486i	−0.210513	−	0.977591i	$-0.567513\pi$
$821$	15.2105	−	8.78177i	0.530849	−	0.306486i	0.741362	+	0.671105i	$0.234180\pi$
$822$	−0.626177	−	1.08457i	−0.0218404	−	0.0378288i
$823$	19.3565	−	33.5264i	0.674725	−	1.16866i	−0.301824	−	0.953364i	$-0.597596\pi$
$823$	19.3565	−	33.5264i	0.674725	−	1.16866i	0.976549	−	0.215295i	$-0.0690712\pi$
$824$			5.29137i			0.184333i
$825$		0			0
$826$	−8.77106	−	5.06397i	−0.305184	−	0.176198i
$827$		−	28.4703i		−	0.990010i	−0.868890	−	0.495005i	$-0.835166\pi$
$827$		−	28.4703i		−	0.990010i	0.868890	−	0.495005i	$-0.164834\pi$
$828$	−0.488292	+	0.845746i	−0.0169693	+	0.0293917i
$829$	4.14354	+	7.17683i	0.143911	+	0.249262i	0.928966	−	0.370165i	$-0.120699\pi$
$829$	4.14354	+	7.17683i	0.143911	+	0.249262i	−0.785055	+	0.619426i	$0.787365\pi$
$830$		0			0
$831$	−11.9922			−0.416004
$832$	−3.35432	+	1.32233i	−0.116290	+	0.0458435i
$833$	−58.2915			−2.01968
$834$	2.90581	−	1.67767i	0.100620	−	0.0580930i
$835$		0			0
$836$	−17.6990	+	30.6556i	−0.612134	+	1.06025i
$837$		−	6.44069i		−	0.222623i
$838$	13.4699	+	7.77684i	0.465309	+	0.268646i
$839$	−36.8606	−	21.2815i	−1.27257	−	0.734719i	−0.297099	−	0.954847i	$-0.596019\pi$
$839$	−36.8606	−	21.2815i	−1.27257	−	0.734719i	−0.975471	+	0.220128i	$0.929353\pi$
$840$		0			0
$841$	5.20016	−	9.00693i	0.179316	−	0.310584i
$842$	11.1571	+	19.3247i	0.384500	+	0.665974i
$843$	−3.15137	+	1.81944i	−0.108539	+	0.0626649i
$844$	1.61970			0.0557522
$845$		0			0
$846$	−9.75342			−0.335330
$847$	−33.6317	+	19.4173i	−1.15560	+	0.667185i
$848$	6.75444	+	11.6990i	0.231949	+	0.401747i
$849$	2.42220	−	4.19538i	0.0831298	−	0.143985i
$850$		0			0
$851$	−3.21047	−	1.85357i	−0.110054	−	0.0635395i
$852$	−6.88764	−	3.97658i	−0.235967	−	0.136236i
$853$		−	28.1380i		−	0.963425i	−0.876329	−	0.481713i	$-0.840015\pi$
$853$		−	28.1380i		−	0.963425i	0.876329	−	0.481713i	$-0.159985\pi$
$854$	−17.3341	+	30.0236i	−0.593161	+	1.02738i
$855$		0			0
$856$	−14.6603	+	8.46410i	−0.501077	+	0.289297i
$857$	10.3355			0.353053			0.176526	−	0.984296i	$-0.443514\pi$
$857$	10.3355			0.353053			0.176526	+	0.984296i	$0.443514\pi$
$858$	−14.7594	+	5.81842i	−0.503878	+	0.198638i
$859$	0.380304			0.0129758			0.00648791	−	0.999979i	$-0.497935\pi$
$859$	0.380304			0.0129758			0.00648791	+	0.999979i	$0.497935\pi$
$860$		0			0
$861$	16.9282	+	29.3205i	0.576912	+	0.999240i
$862$	−12.1322	+	21.0135i	−0.413224	+	0.715724i
$863$		−	47.1484i		−	1.60495i	−0.596685	−	0.802475i	$-0.703516\pi$
$863$		−	47.1484i		−	1.60495i	0.596685	−	0.802475i	$-0.296484\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$			23.0989i			0.784932i
$867$	−0.500000	+	0.866025i	−0.0169809	+	0.0294118i
$868$	−14.9574	−	25.9070i	−0.507687	−	0.879340i
$869$	−56.9077	+	32.8557i	−1.93046	+	1.11455i
$870$		0			0
$871$	4.09535	−	5.15137i	0.138766	−	0.174547i
$872$	−12.8003			−0.433471
$873$	11.9730	−	6.91261i	0.405224	−	0.233956i
$874$	3.92820	+	6.80385i	0.132873	+	0.230144i
$875$		0			0
$876$			4.36112i			0.147348i
$877$	−34.6767	−	20.0206i	−1.17095	−	0.676047i	−0.217045	−	0.976162i	$-0.569642\pi$
$877$	−34.6767	−	20.0206i	−1.17095	−	0.676047i	−0.953903	+	0.300114i	$0.902975\pi$
$878$	34.6375	+	19.9980i	1.16896	+	0.674898i
$879$		−	3.70081i		−	0.124825i
$880$		0			0
$881$	−7.72246	−	13.3757i	−0.260176	−	0.450638i	0.706112	−	0.708100i	$-0.250447\pi$
$881$	−7.72246	−	13.3757i	−0.260176	−	0.450638i	−0.966289	+	0.257461i	$0.917114\pi$
$882$	12.6205	−	7.28643i	0.424953	−	0.245347i
$883$	6.02142			0.202637			0.101318	−	0.994854i	$-0.467694\pi$
$883$	6.02142			0.202637			0.101318	+	0.994854i	$0.467694\pi$
$884$	11.2893	+	8.97504i	0.379701	+	0.301863i
$885$		0			0
$886$	−13.5131	+	7.80180i	−0.453982	+	0.262107i
$887$	−24.5690	−	42.5548i	−0.824947	−	1.42885i	−0.901960	−	0.431820i	$-0.857872\pi$
$887$	−24.5690	−	42.5548i	−0.824947	−	1.42885i	0.0770129	−	0.997030i	$-0.475462\pi$
$888$	1.89801	−	3.28745i	0.0636931	−	0.110320i
$889$			56.7557i			1.90353i
$890$		0			0
$891$	−3.81062	−	2.20006i	−0.127661	−	0.0737049i
$892$			2.23671i			0.0748906i
$893$	−39.2321	+	67.9520i	−1.31285	+	2.27393i
$894$	2.30985	+	4.00077i	0.0772529	+	0.133806i
$895$		0			0
$896$	−4.64466			−0.155167
$897$	−0.519530	+	3.48258i	−0.0173466	+	0.116280i
$898$	−27.0042			−0.901141
$899$	−24.0556	+	13.8885i	−0.802298	+	0.463207i
$900$		0			0
$901$	27.0178	−	46.7962i	0.900093	−	1.55901i
$902$		−	32.0739i		−	1.06795i
$903$	2.88187	+	1.66385i	0.0959026	+	0.0553694i
$904$	11.3156	+	6.53308i	0.376352	+	0.217287i
$905$		0			0
$906$	5.62124	−	9.73628i	0.186753	−	0.323466i
$907$	−8.18345	−	14.1741i	−0.271727	−	0.470645i	0.697577	−	0.716510i	$-0.254261\pi$
$907$	−8.18345	−	14.1741i	−0.271727	−	0.470645i	−0.969304	+	0.245865i	$0.920928\pi$
$908$	13.2679	−	7.66025i	0.440312	−	0.254214i
$909$	6.80025			0.225550
$910$		0			0
$911$	−10.4819			−0.347280			−0.173640	−	0.984809i	$-0.555553\pi$
$911$	−10.4819			−0.347280			−0.173640	+	0.984809i	$0.555553\pi$
$912$	−6.96699	+	4.02239i	−0.230700	+	0.133195i
$913$	−7.72428	−	13.3788i	−0.255636	−	0.442775i
$914$	8.89342	−	15.4039i	0.294168	−	0.509514i
$915$		0			0
$916$	−8.77106	−	5.06397i	−0.289804	−	0.167318i
$917$	1.52351	+	0.879598i	0.0503107	+	0.0290469i
$918$			4.00000i			0.132020i
$919$	−1.60565	+	2.78107i	−0.0529655	+	0.0917389i	−0.891293	−	0.453429i	$-0.850201\pi$
$919$	−1.60565	+	2.78107i	−0.0529655	+	0.0917389i	0.838327	+	0.545168i	$0.183534\pi$
$920$		0			0
$921$	−6.16137	+	3.55727i	−0.203024	+	0.117216i
$922$	−24.9652			−0.822184
$923$	−28.3617	−	4.23098i	−0.933537	−	0.139265i
$924$	−20.4371			−0.672331
$925$		0			0
$926$	7.81944	+	13.5437i	0.256963	+	0.445073i
$927$	−2.64568	+	4.58246i	−0.0868956	+	0.150508i
$928$			4.31274i			0.141572i
$929$	40.2518	+	23.2394i	1.32062	+	0.762460i	0.983827	−	0.179120i	$-0.0573249\pi$
$929$	40.2518	+	23.2394i	1.32062	+	0.762460i	0.336792	+	0.941579i	$0.390658\pi$
$930$		0			0
$931$		−	117.236i		−	3.84224i
$932$	−10.3759	+	17.9716i	−0.339875	+	0.588681i
$933$	−9.95740	−	17.2467i	−0.325990	−	0.564632i
$934$	−2.11236	+	1.21957i	−0.0691184	+	0.0399055i
$935$		0			0
$936$	−3.56609	−	0.531987i	−0.116561	−	0.0173886i
$937$	27.7627			0.906969			0.453485	−	0.891264i	$-0.350181\pi$
$937$	27.7627			0.906969			0.453485	+	0.891264i	$0.350181\pi$
$938$	7.34174	−	4.23876i	0.239716	−	0.138400i
$939$	−3.06975	−	5.31696i	−0.100178	−	0.173513i
$940$		0			0
$941$		−	20.7962i		−	0.677935i	−0.940798	−	0.338968i	$-0.889922\pi$
$941$		−	20.7962i		−	0.677935i	0.940798	−	0.338968i	$-0.110078\pi$
$942$	−1.30173	−	0.751556i	−0.0424128	−	0.0244870i
$943$	−6.16491	−	3.55931i	−0.200757	−	0.115907i
$944$			2.18056i			0.0709711i
$945$		0			0
$946$	−1.57625	−	2.73014i	−0.0512483	−	0.0887646i
$947$	−7.84554	+	4.52962i	−0.254946	+	0.147193i	−0.622027	−	0.782996i	$-0.713691\pi$
$947$	−7.84554	+	4.52962i	−0.254946	+	0.147193i	0.367081	+	0.930189i	$0.380357\pi$
$948$	−14.9340			−0.485033
$949$	5.76683	+	14.6286i	0.187199	+	0.474863i
$950$		0			0
$951$	6.80078	−	3.92643i	0.220530	−	0.127323i
$952$	9.28932	+	16.0896i	0.301069	+	0.521466i
$953$	7.63811	−	13.2296i	0.247423	−	0.428549i	−0.715387	−	0.698728i	$-0.753750\pi$
$953$	7.63811	−	13.2296i	0.247423	−	0.428549i	0.962810	+	0.270180i	$0.0870831\pi$
$954$			13.5089i			0.437366i
$955$		0			0
$956$	−21.0911	−	12.1770i	−0.682136	−	0.393831i
$957$			18.9766i			0.613426i
$958$	−7.09317	+	12.2857i	−0.229170	+	0.396934i
$959$	−2.90838	−	5.03746i	−0.0939165	−	0.162668i
$960$		0			0
$961$	−10.4824			−0.338143
$962$	2.01944	−	13.5370i	0.0651093	−	0.436449i
$963$	−16.9282			−0.545504
$964$	−17.2066	+	9.93423i	−0.554187	+	0.319960i
$965$		0			0
$966$	−2.26795	+	3.92820i	−0.0729701	+	0.126388i
$967$		−	46.3036i		−	1.48902i	−0.667610	−	0.744511i	$-0.732683\pi$
$967$		−	46.3036i		−	1.48902i	0.667610	−	0.744511i	$-0.267317\pi$
$968$	7.24094	+	4.18056i	0.232733	+	0.134368i
$969$	27.8680	+	16.0896i	0.895248	+	0.516872i
$970$		0			0
$971$	−5.98258	+	10.3621i	−0.191990	+	0.332537i	−0.945910	−	0.324430i	$-0.894828\pi$
$971$	−5.98258	+	10.3621i	−0.191990	+	0.332537i	0.753919	+	0.656967i	$0.228161\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	13.4965	−	7.79221i	0.432678	−	0.249807i
$974$	5.76329			0.184668
$975$		0			0
$976$	7.46410			0.238920
$977$	−1.52780	+	0.882077i	−0.0488787	+	0.0282201i	−0.524240	−	0.851570i	$-0.675651\pi$
$977$	−1.52780	+	0.882077i	−0.0488787	+	0.0282201i	0.475362	+	0.879791i	$0.342317\pi$
$978$	−0.0881650	−	0.152706i	−0.00281921	−	0.00488301i
$979$	17.9805	−	31.1432i	0.574660	−	0.995341i
$980$		0			0
$981$	−11.0853	−	6.40013i	−0.353928	−	0.204340i
$982$	0.931273	+	0.537671i	0.0297181	+	0.0171578i
$983$		−	54.2821i		−	1.73133i	−0.500623	−	0.865666i	$-0.666896\pi$
$983$		−	54.2821i		−	1.73133i	0.500623	−	0.865666i	$-0.333104\pi$
$984$	3.64466	−	6.31274i	0.116188	−	0.201243i
$985$		0			0
$986$	14.9398	−	8.62547i	0.475779	−	0.274691i
$987$	−45.3013			−1.44196
$988$	−18.0506	+	22.7050i	−0.574265	+	0.722344i
$989$	−0.699680			−0.0222485
$990$		0			0
$991$	8.73917	+	15.1367i	0.277609	+	0.480833i	0.970790	−	0.239931i	$-0.0771248\pi$
$991$	8.73917	+	15.1367i	0.277609	+	0.480833i	−0.693181	+	0.720763i	$0.743791\pi$
$992$	−3.22034	+	5.57780i	−0.102246	+	0.177095i
$993$			31.9959i			1.01536i
$994$	−31.9908	−	18.4699i	−1.01469	−	0.585829i
$995$		0			0
$996$		−	3.51093i		−	0.111248i
$997$	−10.6457	+	18.4389i	−0.337152	+	0.583965i	−0.983896	−	0.178743i	$-0.942797\pi$
$997$	−10.6457	+	18.4389i	−0.337152	+	0.583965i	0.646744	+	0.762707i	$0.276130\pi$
$998$	−7.37671	−	12.7768i	−0.233506	−	0.404444i
$999$	3.28745	−	1.89801i	0.104010	−	0.0600505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.g.751.1		8
5.2	odd	4		1950.2.y.j.49.4		8
5.3	odd	4		1950.2.y.k.49.1		8
5.4	even	2		390.2.bb.c.361.4	yes	8
13.4	even	6	inner	1950.2.bc.g.901.1		8
15.14	odd	2		1170.2.bs.f.361.2		8
65.4	even	6		390.2.bb.c.121.4	✓	8
65.17	odd	12		1950.2.y.k.199.1		8
65.24	odd	12		5070.2.a.bz.1.1		4
65.29	even	6		5070.2.b.ba.1351.5		8
65.43	odd	12		1950.2.y.j.199.4		8
65.49	even	6		5070.2.b.ba.1351.4		8
65.54	odd	12		5070.2.a.ca.1.4		4
195.134	odd	6		1170.2.bs.f.901.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.4	✓	8	65.4	even	6
390.2.bb.c.361.4	yes	8	5.4	even	2
1170.2.bs.f.361.2		8	15.14	odd	2
1170.2.bs.f.901.2		8	195.134	odd	6
1950.2.y.j.49.4		8	5.2	odd	4
1950.2.y.j.199.4		8	65.43	odd	12
1950.2.y.k.49.1		8	5.3	odd	4
1950.2.y.k.199.1		8	65.17	odd	12
1950.2.bc.g.751.1		8	1.1	even	1	trivial
1950.2.bc.g.901.1		8	13.4	even	6	inner
5070.2.a.bz.1.1		4	65.24	odd	12
5070.2.a.ca.1.4		4	65.54	odd	12
5070.2.b.ba.1351.4		8	65.49	even	6
5070.2.b.ba.1351.5		8	65.29	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-4.02239 - 2.32233i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-4.02239 - 2.32233i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.81062 - 2.20006i) q^{11} +1.00000 q^{12} +(3.35432 - 1.32233i) q^{13} +4.64466 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-6.96699 - 4.02239i) q^{19} -4.64466i q^{21} +(-2.20006 + 3.81062i) q^{22} +(0.488292 + 0.845746i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-2.24376 + 2.82233i) q^{26} -1.00000 q^{27} +(-4.02239 + 2.32233i) q^{28} +(2.15637 + 3.73494i) q^{29} +6.44069i q^{31} +(0.866025 + 0.500000i) q^{32} +(3.81062 + 2.20006i) q^{33} -4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(-3.28745 + 1.89801i) q^{37} +8.04479 q^{38} +(2.82233 + 2.24376i) q^{39} +(-6.31274 + 3.64466i) q^{41} +(2.32233 + 4.02239i) q^{42} +(-0.358228 + 0.620469i) q^{43} -4.40013i q^{44} +(-0.845746 - 0.488292i) q^{46} -9.75342i q^{47} +(0.500000 - 0.866025i) q^{48} +(7.28643 + 12.6205i) q^{49} -4.00000 q^{51} +(0.531987 - 3.56609i) q^{52} -13.5089 q^{53} +(0.866025 - 0.500000i) q^{54} +(2.32233 - 4.02239i) q^{56} -8.04479i q^{57} +(-3.73494 - 2.15637i) q^{58} +(-1.88842 - 1.09028i) q^{59} +(-3.73205 + 6.46410i) q^{61} +(-3.22034 - 5.57780i) q^{62} +(4.02239 - 2.32233i) q^{63} -1.00000 q^{64} -4.40013 q^{66} +(1.58068 - 0.912609i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-0.488292 + 0.845746i) q^{69} +(-6.88764 - 3.97658i) q^{71} +(-0.866025 - 0.500000i) q^{72} +4.36112i q^{73} +(1.89801 - 3.28745i) q^{74} +(-6.96699 + 4.02239i) q^{76} -20.4371 q^{77} +(-3.56609 - 0.531987i) q^{78} -14.9340 q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.64466 - 6.31274i) q^{82} -3.51093i q^{83} +(-4.02239 - 2.32233i) q^{84} -0.716456i q^{86} +(-2.15637 + 3.73494i) q^{87} +(2.20006 + 3.81062i) q^{88} +(7.07780 - 4.08637i) q^{89} +(-16.5633 - 2.47090i) q^{91} +0.976584 q^{92} +(-5.57780 + 3.22034i) q^{93} +(4.87671 + 8.44671i) q^{94} +1.00000i q^{96} +(-11.9730 - 6.91261i) q^{97} +(-12.6205 - 7.28643i) q^{98} +4.40013i 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

L-functions

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