LMFDB - Embedded newform 418.2.e.f.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(45,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("418.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.e (of order $3$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	418.45
Dual form			418.2.e.f.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.00000 + 1.73205i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.00000 + 1.73205i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +1.00000 q^{11} -2.00000 q^{12} +(2.00000 - 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-3.00000 + 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{18} +(-3.50000 - 2.59808i) q^{19} -3.00000 q^{20} +(-1.00000 - 1.73205i) q^{21} +(0.500000 + 0.866025i) q^{22} +(-1.00000 - 1.73205i) q^{24} +(-2.00000 + 3.46410i) q^{25} +4.00000 q^{26} +4.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -6.00000 q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(0.500000 - 4.33013i) q^{38} +8.00000 q^{39} +(-1.50000 - 2.59808i) q^{40} +(3.00000 + 5.19615i) q^{41} +(1.00000 - 1.73205i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-0.500000 + 0.866025i) q^{44} -3.00000 q^{45} +(-3.00000 + 5.19615i) q^{47} +(1.00000 - 1.73205i) q^{48} -6.00000 q^{49} -4.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(2.00000 + 3.46410i) q^{54} +(1.50000 + 2.59808i) q^{55} +1.00000 q^{56} +(1.00000 - 8.66025i) q^{57} +6.00000 q^{58} +(-3.00000 - 5.19615i) q^{60} +(2.00000 - 3.46410i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +12.0000 q^{65} +(-1.00000 + 1.73205i) q^{66} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{70} +(3.00000 + 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-0.500000 - 0.866025i) q^{74} -8.00000 q^{75} +(4.00000 - 1.73205i) q^{76} -1.00000 q^{77} +(4.00000 + 6.92820i) q^{78} +(-5.50000 - 9.52628i) q^{79} +(1.50000 - 2.59808i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-3.00000 + 5.19615i) q^{82} -3.00000 q^{83} +2.00000 q^{84} +(-2.00000 + 3.46410i) q^{86} +12.0000 q^{87} -1.00000 q^{88} +(9.00000 - 15.5885i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(-2.00000 + 3.46410i) q^{91} +(-4.00000 - 6.92820i) q^{93} -6.00000 q^{94} +(1.50000 - 12.9904i) q^{95} +2.00000 q^{96} +(9.50000 + 16.4545i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 4 q^{13} - q^{14} - 6 q^{15} - q^{16} - 2 q^{18} - 7 q^{19} - 6 q^{20} - 2 q^{21} + q^{22} - 2 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{27} + q^{28} + 6 q^{29} - 12 q^{30} - 8 q^{31} + q^{32} + 2 q^{33} - 3 q^{35} - q^{36} - 2 q^{37} + q^{38} + 16 q^{39} - 3 q^{40} + 6 q^{41} + 2 q^{42} + 4 q^{43} - q^{44} - 6 q^{45} - 6 q^{47} + 2 q^{48} - 12 q^{49} - 8 q^{50} + 4 q^{52} - 3 q^{53} + 4 q^{54} + 3 q^{55} + 2 q^{56} + 2 q^{57} + 12 q^{58} - 6 q^{60} + 4 q^{61} - 4 q^{62} + q^{63} + 2 q^{64} + 24 q^{65} - 2 q^{66} + 4 q^{67} + 3 q^{70} + 6 q^{71} + q^{72} - 2 q^{73} - q^{74} - 16 q^{75} + 8 q^{76} - 2 q^{77} + 8 q^{78} - 11 q^{79} + 3 q^{80} + 11 q^{81} - 6 q^{82} - 6 q^{83} + 4 q^{84} - 4 q^{86} + 24 q^{87} - 2 q^{88} + 18 q^{89} - 3 q^{90} - 4 q^{91} - 8 q^{93} - 12 q^{94} + 3 q^{95} + 4 q^{96} + 19 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 2 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 4 * q^13 - q^14 - 6 * q^15 - q^16 - 2 * q^18 - 7 * q^19 - 6 * q^20 - 2 * q^21 + q^22 - 2 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^27 + q^28 + 6 * q^29 - 12 * q^30 - 8 * q^31 + q^32 + 2 * q^33 - 3 * q^35 - q^36 - 2 * q^37 + q^38 + 16 * q^39 - 3 * q^40 + 6 * q^41 + 2 * q^42 + 4 * q^43 - q^44 - 6 * q^45 - 6 * q^47 + 2 * q^48 - 12 * q^49 - 8 * q^50 + 4 * q^52 - 3 * q^53 + 4 * q^54 + 3 * q^55 + 2 * q^56 + 2 * q^57 + 12 * q^58 - 6 * q^60 + 4 * q^61 - 4 * q^62 + q^63 + 2 * q^64 + 24 * q^65 - 2 * q^66 + 4 * q^67 + 3 * q^70 + 6 * q^71 + q^72 - 2 * q^73 - q^74 - 16 * q^75 + 8 * q^76 - 2 * q^77 + 8 * q^78 - 11 * q^79 + 3 * q^80 + 11 * q^81 - 6 * q^82 - 6 * q^83 + 4 * q^84 - 4 * q^86 + 24 * q^87 - 2 * q^88 + 18 * q^89 - 3 * q^90 - 4 * q^91 - 8 * q^93 - 12 * q^94 + 3 * q^95 + 4 * q^96 + 19 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	0.995782	+	0.0917517i	$0.0292466\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	−0.418432	+	0.908248i	$0.637420\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$	−1.00000	+	1.73205i	−0.408248	+	0.707107i
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$	−2.00000			−0.577350
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	−3.00000	+	5.19615i	−0.774597	+	1.34164i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−1.00000			−0.235702
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$	−3.00000			−0.670820
$21$	−1.00000	−	1.73205i	−0.218218	−	0.377964i
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	4.00000			0.784465
$27$	4.00000			0.769800
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$	−6.00000			−1.09545
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$		0			0
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	0.500000	−	4.33013i	0.0811107	−	0.702439i
$39$	8.00000			1.28103
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$	1.00000	−	1.73205i	0.154303	−	0.267261i
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−3.00000			−0.447214
$46$		0			0
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	1.00000	−	1.73205i	0.144338	−	0.250000i
$49$	−6.00000			−0.857143
$50$	−4.00000			−0.565685
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	1.00000			0.133631
$57$	1.00000	−	8.66025i	0.132453	−	1.14708i
$58$	6.00000			0.787839
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	12.0000			1.48842
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$		0			0
$69$		0			0
$70$	1.50000	−	2.59808i	0.179284	−	0.310530i
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	−8.00000			−0.923760
$76$	4.00000	−	1.73205i	0.458831	−	0.198680i
$77$	−1.00000			−0.113961
$78$	4.00000	+	6.92820i	0.452911	+	0.784465i
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$	2.00000			0.218218
$85$		0			0
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	12.0000			1.28654
$88$	−1.00000			−0.106600
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.217354	−	0.976093i	$-0.430258\pi$
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.736644	−	0.676280i	$-0.236409\pi$
$90$	−1.50000	−	2.59808i	−0.158114	−	0.273861i
$91$	−2.00000	+	3.46410i	−0.209657	+	0.363137i
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$	−6.00000			−0.618853
$95$	1.50000	−	12.9904i	0.153897	−	1.33278i
$96$	2.00000			0.204124
$97$	9.50000	+	16.4545i	0.964579	+	1.67070i	0.710742	+	0.703452i	$0.248359\pi$
$97$	9.50000	+	16.4545i	0.964579	+	1.67070i	0.253837	+	0.967247i	$0.418307\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	−0.500000	+	0.866025i	−0.0502519	+	0.0870388i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$	3.00000	−	5.19615i	0.292770	−	0.507093i
$106$	−3.00000			−0.291386
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$	−1.00000	−	1.73205i	−0.0949158	−	0.164399i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	8.00000	−	3.46410i	0.749269	−	0.324443i
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$		0			0
$119$		0			0
$120$	3.00000	−	5.19615i	0.273861	−	0.474342i
$121$	1.00000			0.0909091
$122$	4.00000			0.362143
$123$	−6.00000	+	10.3923i	−0.541002	+	0.937043i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	3.00000			0.268328
$126$	1.00000			0.0890871
$127$	8.00000	−	13.8564i	0.709885	−	1.22956i	−0.255014	−	0.966937i	$-0.582080\pi$
$127$	8.00000	−	13.8564i	0.709885	−	1.22956i	0.964899	−	0.262620i	$-0.0845865\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$	−2.00000			−0.174078
$133$	3.50000	+	2.59808i	0.303488	+	0.225282i
$134$	4.00000			0.345547
$135$	6.00000	+	10.3923i	0.516398	+	0.894427i
$136$		0			0
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	−0.344493	−	0.938789i	$-0.611949\pi$
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	0.985262	−	0.171054i	$-0.0547174\pi$
$138$		0			0
$139$	−8.50000	+	14.7224i	−0.720961	+	1.24874i	0.239655	+	0.970858i	$0.422966\pi$
$139$	−8.50000	+	14.7224i	−0.720961	+	1.24874i	−0.960615	+	0.277882i	$0.910368\pi$
$140$	3.00000			0.253546
$141$	−12.0000			−1.01058
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$	1.00000			0.0833333
$145$	18.0000			1.49482
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$	−6.00000	−	10.3923i	−0.494872	−	0.857143i
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	−4.00000	−	6.92820i	−0.326599	−	0.565685i
$151$	−19.0000			−1.54620			−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−19.0000			−1.54620			−0.773099	+	0.634285i	$0.781294\pi$
$152$	3.50000	+	2.59808i	0.283887	+	0.210732i
$153$		0			0
$154$	−0.500000	−	0.866025i	−0.0402911	−	0.0697863i
$155$	−6.00000	−	10.3923i	−0.481932	−	0.834730i
$156$	−4.00000	+	6.92820i	−0.320256	+	0.554700i
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	−0.975470	−	0.220131i	$-0.929352\pi$
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	0.297097	−	0.954847i	$-0.403982\pi$
$158$	5.50000	−	9.52628i	0.437557	−	0.757870i
$159$	−6.00000			−0.475831
$160$	3.00000			0.237171
$161$		0			0
$162$	−5.50000	+	9.52628i	−0.432121	+	0.748455i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−6.00000			−0.468521
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	−1.50000	−	2.59808i	−0.116423	−	0.201650i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$	1.00000	+	1.73205i	0.0771517	+	0.133631i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$	4.00000	−	1.73205i	0.305888	−	0.132453i
$172$	−4.00000			−0.304997
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	6.00000	+	10.3923i	0.454859	+	0.787839i
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$		0			0
$178$	18.0000			1.34916
$179$	−24.0000			−1.79384			−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000			−1.79384			−0.896922	+	0.442189i	$0.854202\pi$
$180$	1.50000	−	2.59808i	0.111803	−	0.193649i
$181$	−5.50000	+	9.52628i	−0.408812	+	0.708083i	−0.994757	−	0.102268i	$-0.967390\pi$
$181$	−5.50000	+	9.52628i	−0.408812	+	0.708083i	0.585945	+	0.810351i	$0.300723\pi$
$182$	−4.00000			−0.296500
$183$	8.00000			0.591377
$184$		0			0
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$		0			0
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	−4.00000			−0.290957
$190$	12.0000	−	5.19615i	0.870572	−	0.376969i
$191$	−6.00000			−0.434145			−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000			−0.434145			−0.217072	+	0.976156i	$0.569651\pi$
$192$	1.00000	+	1.73205i	0.0721688	+	0.125000i
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−9.50000	+	16.4545i	−0.682060	+	1.18136i
$195$	12.0000	+	20.7846i	0.859338	+	1.48842i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−1.00000			−0.0710669
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	8.00000			0.564276
$202$	12.0000			0.844317
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	−9.00000	+	15.5885i	−0.628587	+	1.08875i
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$		0			0
$208$	−4.00000			−0.277350
$209$	−3.50000	−	2.59808i	−0.242100	−	0.179713i
$210$	6.00000			0.414039
$211$	12.5000	+	21.6506i	0.860535	+	1.49049i	0.871413	+	0.490550i	$0.163204\pi$
$211$	12.5000	+	21.6506i	0.860535	+	1.49049i	−0.0108774	+	0.999941i	$0.503462\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−6.00000	+	10.3923i	−0.411113	+	0.712069i
$214$	−4.50000	−	7.79423i	−0.307614	−	0.532803i
$215$	−6.00000	+	10.3923i	−0.409197	+	0.708749i
$216$	−4.00000			−0.272166
$217$	4.00000			0.271538
$218$	−8.00000	+	13.8564i	−0.541828	+	0.938474i
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	−3.00000			−0.202260
$221$		0			0
$222$	1.00000	−	1.73205i	0.0671156	−	0.116248i
$223$	14.0000	+	24.2487i	0.937509	+	1.62381i	0.770097	+	0.637927i	$0.220208\pi$
$223$	14.0000	+	24.2487i	0.937509	+	1.62381i	0.167412	+	0.985887i	$0.446459\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−2.00000	−	3.46410i	−0.133333	−	0.230940i
$226$	−3.00000	−	5.19615i	−0.199557	−	0.345643i
$227$	27.0000			1.79205			0.896026	−	0.444001i	$-0.146441\pi$
$227$	27.0000			1.79205			0.896026	+	0.444001i	$0.146441\pi$
$228$	7.00000	+	5.19615i	0.463586	+	0.344124i
$229$	−25.0000			−1.65205			−0.826023	−	0.563636i	$-0.809402\pi$
$229$	−25.0000			−1.65205			−0.826023	+	0.563636i	$0.809402\pi$
$230$		0			0
$231$	−1.00000	−	1.73205i	−0.0657952	−	0.113961i
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$233$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$	−18.0000			−1.17419
$236$		0			0
$237$	11.0000	−	19.0526i	0.714527	−	1.23760i
$238$		0			0
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$	6.00000			0.387298
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	−5.00000	+	8.66025i	−0.320750	+	0.555556i
$244$	2.00000	+	3.46410i	0.128037	+	0.221766i
$245$	−9.00000	−	15.5885i	−0.574989	−	0.995910i
$246$	−12.0000			−0.765092
$247$	−16.0000	+	6.92820i	−1.01806	+	0.440831i
$248$	4.00000			0.254000
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−12.0000	+	20.7846i	−0.757433	+	1.31191i	0.186722	+	0.982413i	$0.440214\pi$
$251$	−12.0000	+	20.7846i	−0.757433	+	1.31191i	−0.944156	+	0.329500i	$0.893120\pi$
$252$	0.500000	+	0.866025i	0.0314970	+	0.0545545i
$253$		0			0
$254$	16.0000			1.00393
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	−0.690856	−	0.722993i	$-0.742766\pi$
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	0.971558	+	0.236802i	$0.0760993\pi$
$258$	−8.00000			−0.498058
$259$	1.00000			0.0621370
$260$	−6.00000	+	10.3923i	−0.372104	+	0.644503i
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$	−13.5000	−	23.3827i	−0.832446	−	1.44184i	−0.896093	−	0.443866i	$-0.853607\pi$
$263$	−13.5000	−	23.3827i	−0.832446	−	1.44184i	0.0636476	−	0.997972i	$-0.479727\pi$
$264$	−1.00000	−	1.73205i	−0.0615457	−	0.106600i
$265$	−9.00000			−0.552866
$266$	−0.500000	+	4.33013i	−0.0306570	+	0.265497i
$267$	36.0000			2.20316
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	0.816668	−	0.577108i	$-0.195819\pi$
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	−0.908124	+	0.418701i	$0.862486\pi$
$270$	−6.00000	+	10.3923i	−0.365148	+	0.632456i
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	0.952531	−	0.304443i	$-0.0984703\pi$
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	−0.739921	+	0.672694i	$0.765137\pi$
$272$		0			0
$273$	−8.00000			−0.484182
$274$	15.0000			0.906183
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	−28.0000			−1.68236			−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000			−1.68236			−0.841178	+	0.540758i	$0.818138\pi$
$278$	−17.0000			−1.01959
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	1.50000	+	2.59808i	0.0896421	+	0.155265i
$281$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$281$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$282$	−6.00000	−	10.3923i	−0.357295	−	0.618853i
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	0.991960	−	0.126550i	$-0.0403903\pi$
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	−0.605575	+	0.795788i	$0.707057\pi$
$284$	−6.00000			−0.356034
$285$	24.0000	−	10.3923i	1.42164	−	0.615587i
$286$	4.00000			0.236525
$287$	−3.00000	−	5.19615i	−0.177084	−	0.306719i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	9.00000	+	15.5885i	0.528498	+	0.915386i
$291$	−19.0000	+	32.9090i	−1.11380	+	1.92916i
$292$	2.00000			0.117041
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$	6.00000	−	10.3923i	0.349927	−	0.606092i
$295$		0			0
$296$	1.00000			0.0581238
$297$	4.00000			0.232104
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$		0			0
$300$	4.00000	−	6.92820i	0.230940	−	0.400000i
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	−9.50000	−	16.4545i	−0.546664	−	0.946849i
$303$	24.0000			1.37876
$304$	−0.500000	+	4.33013i	−0.0286770	+	0.248350i
$305$	12.0000			0.687118
$306$		0			0
$307$	−5.50000	−	9.52628i	−0.313902	−	0.543693i	0.665302	−	0.746575i	$-0.268303\pi$
$307$	−5.50000	−	9.52628i	−0.313902	−	0.543693i	−0.979203	+	0.202881i	$0.934970\pi$
$308$	0.500000	−	0.866025i	0.0284901	−	0.0493464i
$309$	−4.00000	−	6.92820i	−0.227552	−	0.394132i
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$	−8.00000			−0.452911
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	8.50000	−	14.7224i	0.479683	−	0.830835i
$315$	3.00000			0.169031
$316$	11.0000			0.618798
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$	−9.00000	−	15.5885i	−0.502331	−	0.870063i
$322$		0			0
$323$		0			0
$324$	−11.0000			−0.611111
$325$	8.00000	+	13.8564i	0.443760	+	0.768615i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$	−16.0000	+	27.7128i	−0.884802	+	1.53252i
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$	−6.00000			−0.330289
$331$	−16.0000			−0.879440			−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000			−0.879440			−0.439720	+	0.898135i	$0.644922\pi$
$332$	1.50000	−	2.59808i	0.0823232	−	0.142588i
$333$	0.500000	−	0.866025i	0.0273998	−	0.0474579i
$334$	−3.00000			−0.164153
$335$	12.0000			0.655630
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$	8.00000	+	13.8564i	0.435788	+	0.754807i	0.997360	−	0.0726214i	$-0.0231365\pi$
$337$	8.00000	+	13.8564i	0.435788	+	0.754807i	−0.561572	+	0.827428i	$0.689803\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$	−6.00000	−	10.3923i	−0.325875	−	0.564433i
$340$		0			0
$341$	−4.00000			−0.216612
$342$	3.50000	+	2.59808i	0.189258	+	0.140488i
$343$	13.0000			0.701934
$344$	−2.00000	−	3.46410i	−0.107833	−	0.186772i
$345$		0			0
$346$		0			0
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	0.822951	−	0.568112i	$-0.192326\pi$
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	−0.903475	+	0.428640i	$0.858993\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$	4.00000			0.213809
$351$	8.00000	−	13.8564i	0.427008	−	0.739600i
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	27.0000			1.43706			0.718532	−	0.695493i	$-0.244814\pi$
$353$	27.0000			1.43706			0.718532	+	0.695493i	$0.244814\pi$
$354$		0			0
$355$	−9.00000	+	15.5885i	−0.477670	+	0.827349i
$356$	9.00000	+	15.5885i	0.476999	+	0.826187i
$357$		0			0
$358$	−12.0000	−	20.7846i	−0.634220	−	1.09850i
$359$	1.50000	+	2.59808i	0.0791670	+	0.137121i	0.902891	−	0.429870i	$-0.141441\pi$
$359$	1.50000	+	2.59808i	0.0791670	+	0.137121i	−0.823724	+	0.566991i	$0.808107\pi$
$360$	3.00000			0.158114
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$	−11.0000			−0.578147
$363$	1.00000	+	1.73205i	0.0524864	+	0.0909091i
$364$	−2.00000	−	3.46410i	−0.104828	−	0.181568i
$365$	3.00000	−	5.19615i	0.157027	−	0.271979i
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$	1.50000	−	2.59808i	0.0779813	−	0.135068i
$371$	1.50000	−	2.59808i	0.0778761	−	0.134885i
$372$	8.00000			0.414781
$373$	32.0000			1.65690			0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000			1.65690			0.828449	+	0.560065i	$0.189224\pi$
$374$		0			0
$375$	3.00000	+	5.19615i	0.154919	+	0.268328i
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	−12.0000	−	20.7846i	−0.618031	−	1.07046i
$378$	−2.00000	−	3.46410i	−0.102869	−	0.178174i
$379$	32.0000			1.64373			0.821865	−	0.569683i	$-0.192934\pi$
$379$	32.0000			1.64373			0.821865	+	0.569683i	$0.192934\pi$
$380$	10.5000	+	7.79423i	0.538639	+	0.399835i
$381$	32.0000			1.63941
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$	−1.00000	+	1.73205i	−0.0510310	+	0.0883883i
$385$	−1.50000	−	2.59808i	−0.0764471	−	0.132410i
$386$	1.00000	−	1.73205i	0.0508987	−	0.0881591i
$387$	−4.00000			−0.203331
$388$	−19.0000			−0.964579
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	−0.957263	−	0.289220i	$-0.906604\pi$
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	0.729103	+	0.684403i	$0.239937\pi$
$390$	−12.0000	+	20.7846i	−0.607644	+	1.05247i
$391$		0			0
$392$	6.00000			0.303046
$393$		0			0
$394$	−6.00000	−	10.3923i	−0.302276	−	0.523557i
$395$	16.5000	−	28.5788i	0.830205	−	1.43796i
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	−2.50000	−	4.33013i	−0.125471	−	0.217323i	0.796446	−	0.604710i	$-0.206711\pi$
$397$	−2.50000	−	4.33013i	−0.125471	−	0.217323i	−0.921917	+	0.387387i	$0.873378\pi$
$398$	10.0000			0.501255
$399$	−1.00000	+	8.66025i	−0.0500626	+	0.433555i
$400$	4.00000			0.200000
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	0.948272	+	0.317460i	$0.102830\pi$
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	−0.199207	+	0.979957i	$0.563837\pi$
$402$	4.00000	+	6.92820i	0.199502	+	0.345547i
$403$	−8.00000	+	13.8564i	−0.398508	+	0.690237i
$404$	6.00000	+	10.3923i	0.298511	+	0.517036i
$405$	−16.5000	+	28.5788i	−0.819892	+	1.42009i
$406$	−6.00000			−0.297775
$407$	−1.00000			−0.0495682
$408$		0			0
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	0.911227	+	0.411905i	$0.135136\pi$
$410$	−18.0000			−0.888957
$411$	30.0000			1.47979
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$		0			0
$414$		0			0
$415$	−4.50000	−	7.79423i	−0.220896	−	0.382604i
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$	−34.0000			−1.66499
$418$	0.500000	−	4.33013i	0.0244558	−	0.211793i
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$	3.00000	+	5.19615i	0.146385	+	0.253546i
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	0.581086	−	0.813842i	$-0.302628\pi$
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	−0.995351	+	0.0963145i	$0.969295\pi$
$422$	−12.5000	+	21.6506i	−0.608490	+	1.05394i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$		0			0
$426$	−12.0000			−0.581402
$427$	−2.00000	+	3.46410i	−0.0967868	+	0.167640i
$428$	4.50000	−	7.79423i	0.217516	−	0.376748i
$429$	8.00000			0.386244
$430$	−12.0000			−0.578691
$431$	−7.50000	+	12.9904i	−0.361262	+	0.625725i	−0.988169	−	0.153370i	$-0.950987\pi$
$431$	−7.50000	+	12.9904i	−0.361262	+	0.625725i	0.626907	+	0.779094i	$0.284321\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	−7.00000	+	12.1244i	−0.336399	+	0.582659i	−0.983752	−	0.179530i	$-0.942542\pi$
$433$	−7.00000	+	12.1244i	−0.336399	+	0.582659i	0.647354	+	0.762190i	$0.275876\pi$
$434$	2.00000	+	3.46410i	0.0960031	+	0.166282i
$435$	18.0000	+	31.1769i	0.863034	+	1.49482i
$436$	−16.0000			−0.766261
$437$		0			0
$438$	4.00000			0.191127
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$	−1.50000	−	2.59808i	−0.0715097	−	0.123858i
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$		0			0
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$	2.00000			0.0949158
$445$	54.0000			2.55985
$446$	−14.0000	+	24.2487i	−0.662919	+	1.14821i
$447$	18.0000	−	31.1769i	0.851371	−	1.47462i
$448$	−1.00000			−0.0472456
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	2.00000	−	3.46410i	0.0942809	−	0.163299i
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	−19.0000	−	32.9090i	−0.892698	−	1.54620i
$454$	13.5000	+	23.3827i	0.633586	+	1.09740i
$455$	−12.0000			−0.562569
$456$	−1.00000	+	8.66025i	−0.0468293	+	0.405554i
$457$	−22.0000			−1.02912			−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000			−1.02912			−0.514558	+	0.857455i	$0.672044\pi$
$458$	−12.5000	−	21.6506i	−0.584087	−	1.01167i
$459$		0			0
$460$		0			0
$461$	3.00000	+	5.19615i	0.139724	+	0.242009i	0.927392	−	0.374091i	$-0.122045\pi$
$461$	3.00000	+	5.19615i	0.139724	+	0.242009i	−0.787668	+	0.616100i	$0.788712\pi$
$462$	1.00000	−	1.73205i	0.0465242	−	0.0805823i
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−6.00000			−0.278543
$465$	12.0000	−	20.7846i	0.556487	−	0.963863i
$466$		0			0
$467$	30.0000			1.38823			0.694117	−	0.719862i	$-0.255795\pi$
$467$	30.0000			1.38823			0.694117	+	0.719862i	$0.255795\pi$
$468$	−4.00000			−0.184900
$469$	−2.00000	+	3.46410i	−0.0923514	+	0.159957i
$470$	−9.00000	−	15.5885i	−0.415139	−	0.719042i
$471$	17.0000	−	29.4449i	0.783319	−	1.35675i
$472$		0			0
$473$	2.00000	+	3.46410i	0.0919601	+	0.159280i
$474$	22.0000			1.01049
$475$	16.0000	−	6.92820i	0.734130	−	0.317888i
$476$		0			0
$477$	−1.50000	−	2.59808i	−0.0686803	−	0.118958i
$478$	−7.50000	−	12.9904i	−0.343042	−	0.594166i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	3.00000	+	5.19615i	0.136931	+	0.237171i
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$	−2.00000			−0.0910975
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	−28.5000	+	49.3634i	−1.29412	+	2.24148i
$486$	−10.0000			−0.453609
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−2.00000	+	3.46410i	−0.0905357	+	0.156813i
$489$	−4.00000	−	6.92820i	−0.180886	−	0.313304i
$490$	9.00000	−	15.5885i	0.406579	−	0.704215i
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	0.949520	−	0.313707i	$-0.101571\pi$
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	−0.746438	+	0.665455i	$0.768237\pi$
$492$	−6.00000	−	10.3923i	−0.270501	−	0.468521i
$493$		0			0
$494$	−14.0000	−	10.3923i	−0.629890	−	0.467572i
$495$	−3.00000			−0.134840
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	3.00000	−	5.19615i	0.134433	−	0.232845i
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−6.00000			−0.268060
$502$	−24.0000			−1.07117
$503$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$503$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	36.0000			1.60198
$506$		0			0
$507$	3.00000	−	5.19615i	0.133235	−	0.230769i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	−0.748894	−	0.662690i	$-0.769415\pi$
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	0.948353	+	0.317217i	$0.102748\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$	−1.00000			−0.0441942
$513$	−14.0000	−	10.3923i	−0.618115	−	0.458831i
$514$	9.00000			0.396973
$515$	−6.00000	−	10.3923i	−0.264392	−	0.457940i
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	−3.00000	+	5.19615i	−0.131940	+	0.228527i
$518$	0.500000	+	0.866025i	0.0219687	+	0.0380510i
$519$		0			0
$520$	−12.0000			−0.526235
$521$	33.0000			1.44576			0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000			1.44576			0.722878	+	0.690976i	$0.242819\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	−0.854887	−	0.518815i	$-0.826373\pi$
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	0.876750	+	0.480946i	$0.159707\pi$
$524$		0			0
$525$	8.00000			0.349149
$526$	13.5000	−	23.3827i	0.588628	−	1.01953i
$527$		0			0
$528$	1.00000	−	1.73205i	0.0435194	−	0.0753778i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$		0			0
$532$	−4.00000	+	1.73205i	−0.173422	+	0.0750939i
$533$	24.0000			1.03956
$534$	18.0000	+	31.1769i	0.778936	+	1.34916i
$535$	−13.5000	−	23.3827i	−0.583656	−	1.01092i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	−24.0000	−	41.5692i	−1.03568	−	1.79384i
$538$	1.50000	−	2.59808i	0.0646696	−	0.112011i
$539$	−6.00000			−0.258438
$540$	−12.0000			−0.516398
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	0.0911008	+	0.995842i	$0.470961\pi$
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	−0.907975	+	0.419025i	$0.862372\pi$
$542$	−3.50000	+	6.06218i	−0.150338	+	0.260393i
$543$	−22.0000			−0.944110
$544$		0			0
$545$	−24.0000	+	41.5692i	−1.02805	+	1.78063i
$546$	−4.00000	−	6.92820i	−0.171184	−	0.296500i
$547$	9.50000	−	16.4545i	0.406191	−	0.703543i	−0.588269	−	0.808666i	$-0.700190\pi$
$547$	9.50000	−	16.4545i	0.406191	−	0.703543i	0.994459	+	0.105123i	$0.0335235\pi$
$548$	7.50000	+	12.9904i	0.320384	+	0.554922i
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$	−4.00000			−0.170561
$551$	−24.0000	+	10.3923i	−1.02243	+	0.442727i
$552$		0			0
$553$	5.50000	+	9.52628i	0.233884	+	0.405099i
$554$	−14.0000	−	24.2487i	−0.594803	−	1.03023i
$555$	3.00000	−	5.19615i	0.127343	−	0.220564i
$556$	−8.50000	−	14.7224i	−0.360480	−	0.624370i
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	−0.964686	−	0.263404i	$-0.915155\pi$
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	0.710457	+	0.703740i	$0.248488\pi$
$558$	4.00000			0.169334
$559$	16.0000			0.676728
$560$	−1.50000	+	2.59808i	−0.0633866	+	0.109789i
$561$		0			0
$562$		0			0
$563$	9.00000			0.379305			0.189652	−	0.981851i	$-0.439264\pi$
$563$	9.00000			0.379305			0.189652	+	0.981851i	$0.439264\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	−6.50000	+	11.2583i	−0.273215	+	0.473223i
$567$	−5.50000	−	9.52628i	−0.230978	−	0.400066i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−36.0000			−1.50920			−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000			−1.50920			−0.754599	+	0.656186i	$0.772169\pi$
$570$	21.0000	+	15.5885i	0.879593	+	0.652929i
$571$	−19.0000			−0.795125			−0.397563	−	0.917575i	$-0.630144\pi$
$571$	−19.0000			−0.795125			−0.397563	+	0.917575i	$0.630144\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$	−6.00000	−	10.3923i	−0.250654	−	0.434145i
$574$	3.00000	−	5.19615i	0.125218	−	0.216883i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	17.0000			0.707107
$579$	2.00000	−	3.46410i	0.0831172	−	0.143963i
$580$	−9.00000	+	15.5885i	−0.373705	+	0.647275i
$581$	3.00000			0.124461
$582$	−38.0000			−1.57515
$583$	−1.50000	+	2.59808i	−0.0621237	+	0.107601i
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$	−6.00000	+	10.3923i	−0.248069	+	0.429669i
$586$	15.0000	+	25.9808i	0.619644	+	1.07326i
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$	12.0000			0.494872
$589$	14.0000	+	10.3923i	0.576860	+	0.428207i
$590$		0			0
$591$	−12.0000	−	20.7846i	−0.493614	−	0.854965i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$	2.00000	+	3.46410i	0.0820610	+	0.142134i
$595$		0			0
$596$	18.0000			0.737309
$597$	20.0000			0.818546
$598$		0			0
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	0.219061	+	0.975711i	$0.429701\pi$
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	−0.954521	+	0.298143i	$0.903633\pi$
$600$	8.00000			0.326599
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	2.00000	−	3.46410i	0.0815139	−	0.141186i
$603$	2.00000	+	3.46410i	0.0814463	+	0.141069i
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$	1.50000	+	2.59808i	0.0609837	+	0.105627i
$606$	12.0000	+	20.7846i	0.487467	+	0.844317i
$607$	8.00000			0.324710			0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000			0.324710			0.162355	+	0.986732i	$0.448091\pi$
$608$	−4.00000	+	1.73205i	−0.162221	+	0.0702439i
$609$	−12.0000			−0.486265
$610$	6.00000	+	10.3923i	0.242933	+	0.420772i
$611$	12.0000	+	20.7846i	0.485468	+	0.840855i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	5.50000	−	9.52628i	0.221962	−	0.384449i
$615$	−36.0000			−1.45166
$616$	1.00000			0.0402911
$617$	−16.5000	+	28.5788i	−0.664265	+	1.15054i	0.315219	+	0.949019i	$0.397922\pi$
$617$	−16.5000	+	28.5788i	−0.664265	+	1.15054i	−0.979484	+	0.201522i	$0.935411\pi$
$618$	4.00000	−	6.92820i	0.160904	−	0.278693i
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$	12.0000			0.481932
$621$		0			0
$622$	−9.00000	−	15.5885i	−0.360867	−	0.625040i
$623$	−9.00000	+	15.5885i	−0.360577	+	0.624538i
$624$	−4.00000	−	6.92820i	−0.160128	−	0.277350i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	1.00000			0.0399680
$627$	1.00000	−	8.66025i	0.0399362	−	0.345857i
$628$	17.0000			0.678374
$629$		0			0
$630$	1.50000	+	2.59808i	0.0597614	+	0.103510i
$631$	8.00000	−	13.8564i	0.318475	−	0.551615i	−0.661695	−	0.749773i	$-0.730163\pi$
$631$	8.00000	−	13.8564i	0.318475	−	0.551615i	0.980170	+	0.198158i	$0.0634960\pi$
$632$	5.50000	+	9.52628i	0.218778	+	0.378935i
$633$	−25.0000	+	43.3013i	−0.993661	+	1.72107i
$634$	18.0000			0.714871
$635$	48.0000			1.90482
$636$	3.00000	−	5.19615i	0.118958	−	0.206041i
$637$	−12.0000	+	20.7846i	−0.475457	+	0.823516i
$638$	6.00000			0.237542
$639$	−6.00000			−0.237356
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$	9.00000	−	15.5885i	0.355202	−	0.615227i
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	0.694347	−	0.719640i	$-0.255693\pi$
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	−0.970400	+	0.241502i	$0.922360\pi$
$644$		0			0
$645$	−24.0000			−0.944999
$646$		0			0
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$	−5.50000	−	9.52628i	−0.216060	−	0.374228i
$649$		0			0
$650$	−8.00000	+	13.8564i	−0.313786	+	0.543493i
$651$	4.00000	+	6.92820i	0.156772	+	0.271538i
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$	−32.0000			−1.25130
$655$		0			0
$656$	3.00000	−	5.19615i	0.117130	−	0.202876i
$657$	2.00000			0.0780274
$658$	6.00000			0.233904
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	−20.5000	+	35.5070i	−0.797358	+	1.38106i	0.123974	+	0.992286i	$0.460436\pi$
$661$	−20.5000	+	35.5070i	−0.797358	+	1.38106i	−0.921331	+	0.388778i	$0.872897\pi$
$662$	−8.00000	−	13.8564i	−0.310929	−	0.538545i
$663$		0			0
$664$	3.00000			0.116423
$665$	−1.50000	+	12.9904i	−0.0581675	+	0.503745i
$666$	1.00000			0.0387492
$667$		0			0
$668$	−1.50000	−	2.59808i	−0.0580367	−	0.100523i
$669$	−28.0000	+	48.4974i	−1.08254	+	1.87502i
$670$	6.00000	+	10.3923i	0.231800	+	0.401490i
$671$	2.00000	−	3.46410i	0.0772091	−	0.133730i
$672$	−2.00000			−0.0771517
$673$	−10.0000			−0.385472			−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000			−0.385472			−0.192736	+	0.981251i	$0.561736\pi$
$674$	−8.00000	+	13.8564i	−0.308148	+	0.533729i
$675$	−8.00000	+	13.8564i	−0.307920	+	0.533333i
$676$	3.00000			0.115385
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$	6.00000	−	10.3923i	0.230429	−	0.399114i
$679$	−9.50000	−	16.4545i	−0.364577	−	0.631465i
$680$		0			0
$681$	27.0000	+	46.7654i	1.03464	+	1.79205i
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	42.0000			1.60709			0.803543	−	0.595247i	$-0.202946\pi$
$683$	42.0000			1.60709			0.803543	+	0.595247i	$0.202946\pi$
$684$	−0.500000	+	4.33013i	−0.0191180	+	0.165567i
$685$	45.0000			1.71936
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$	−25.0000	−	43.3013i	−0.953809	−	1.65205i
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$		0			0
$693$	0.500000	−	0.866025i	0.0189934	−	0.0328976i
$694$	1.50000	−	2.59808i	0.0569392	−	0.0986216i
$695$	−51.0000			−1.93454
$696$	−12.0000			−0.454859
$697$		0			0
$698$	−11.0000	−	19.0526i	−0.416356	−	0.721150i
$699$		0			0
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	−12.0000	−	20.7846i	−0.453234	−	0.785024i	0.545351	−	0.838208i	$-0.316396\pi$
$701$	−12.0000	−	20.7846i	−0.453234	−	0.785024i	−0.998585	+	0.0531839i	$0.983063\pi$
$702$	16.0000			0.603881
$703$	3.50000	+	2.59808i	0.132005	+	0.0979883i
$704$	1.00000			0.0376889
$705$	−18.0000	−	31.1769i	−0.677919	−	1.17419i
$706$	13.5000	+	23.3827i	0.508079	+	0.880019i
$707$	−6.00000	+	10.3923i	−0.225653	+	0.390843i
$708$		0			0
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	−0.529943	−	0.848034i	$-0.677787\pi$
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	0.999390	+	0.0349269i	$0.0111198\pi$
$710$	−18.0000			−0.675528
$711$	11.0000			0.412532
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$		0			0
$714$		0			0
$715$	12.0000			0.448775
$716$	12.0000	−	20.7846i	0.448461	−	0.776757i
$717$	−15.0000	−	25.9808i	−0.560185	−	0.970269i
$718$	−1.50000	+	2.59808i	−0.0559795	+	0.0969593i
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	0.977539	+	0.210752i	$0.0675914\pi$
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	−0.306253	+	0.951950i	$0.599075\pi$
$720$	1.50000	+	2.59808i	0.0559017	+	0.0968246i
$721$	4.00000			0.148968
$722$	−13.0000	+	13.8564i	−0.483810	+	0.515682i
$723$	−4.00000			−0.148762
$724$	−5.50000	−	9.52628i	−0.204406	−	0.354041i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	−25.0000	−	43.3013i	−0.927199	−	1.60596i	−0.787986	−	0.615693i	$-0.788876\pi$
$727$	−25.0000	−	43.3013i	−0.927199	−	1.60596i	−0.139212	−	0.990263i	$-0.544457\pi$
$728$	2.00000	−	3.46410i	0.0741249	−	0.128388i
$729$	13.0000			0.481481
$730$	6.00000			0.222070
$731$		0			0
$732$	−4.00000	+	6.92820i	−0.147844	+	0.256074i
$733$	−4.00000			−0.147743			−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000			−0.147743			−0.0738717	+	0.997268i	$0.523536\pi$
$734$	28.0000			1.03350
$735$	18.0000	−	31.1769i	0.663940	−	1.14998i
$736$		0			0
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$	−3.00000	−	5.19615i	−0.110432	−	0.191273i
$739$	26.0000	+	45.0333i	0.956425	+	1.65658i	0.731072	+	0.682300i	$0.239020\pi$
$739$	26.0000	+	45.0333i	0.956425	+	1.65658i	0.225354	+	0.974277i	$0.427646\pi$
$740$	3.00000			0.110282
$741$	−28.0000	−	20.7846i	−1.02861	−	0.763542i
$742$	3.00000			0.110133
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	0.991798	−	0.127815i	$-0.0407965\pi$
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	−0.606590	+	0.795015i	$0.707463\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$	27.0000	−	46.7654i	0.989203	−	1.71335i
$746$	16.0000	+	27.7128i	0.585802	+	1.01464i
$747$	1.50000	−	2.59808i	0.0548821	−	0.0950586i
$748$		0			0
$749$	9.00000			0.328853
$750$	−3.00000	+	5.19615i	−0.109545	+	0.189737i
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	−0.999570	−	0.0293387i	$-0.990660\pi$
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	0.525193	+	0.850983i	$0.323993\pi$
$752$	6.00000			0.218797
$753$	−48.0000			−1.74922
$754$	12.0000	−	20.7846i	0.437014	−	0.756931i
$755$	−28.5000	−	49.3634i	−1.03722	−	1.79652i
$756$	2.00000	−	3.46410i	0.0727393	−	0.125988i
$757$	11.0000	+	19.0526i	0.399802	+	0.692477i	0.993701	−	0.112062i	$-0.0357456\pi$
$757$	11.0000	+	19.0526i	0.399802	+	0.692477i	−0.593899	+	0.804539i	$0.702412\pi$
$758$	16.0000	+	27.7128i	0.581146	+	1.00657i
$759$		0			0
$760$	−1.50000	+	12.9904i	−0.0544107	+	0.471211i
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$	16.0000	+	27.7128i	0.579619	+	1.00393i
$763$	−8.00000	−	13.8564i	−0.289619	−	0.501636i
$764$	3.00000	−	5.19615i	0.108536	−	0.187990i
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$		0			0
$768$	−2.00000			−0.0721688
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	−0.761680	−	0.647954i	$-0.775625\pi$
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	0.941984	+	0.335657i	$0.108958\pi$
$770$	1.50000	−	2.59808i	0.0540562	−	0.0936282i
$771$	18.0000			0.648254
$772$	2.00000			0.0719816
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$	−2.00000	−	3.46410i	−0.0718885	−	0.124515i
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	−9.50000	−	16.4545i	−0.341030	−	0.590682i
$777$	1.00000	+	1.73205i	0.0358748	+	0.0621370i
$778$	−9.00000			−0.322666
$779$	3.00000	−	25.9808i	0.107486	−	0.930857i
$780$	−24.0000			−0.859338
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$		0			0
$783$	12.0000	−	20.7846i	0.428845	−	0.742781i
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	25.5000	−	44.1673i	0.910134	−	1.57640i
$786$		0			0
$787$	−31.0000			−1.10503			−0.552515	−	0.833503i	$-0.686332\pi$
$787$	−31.0000			−1.10503			−0.552515	+	0.833503i	$0.686332\pi$
$788$	6.00000	−	10.3923i	0.213741	−	0.370211i
$789$	27.0000	−	46.7654i	0.961225	−	1.66489i
$790$	33.0000			1.17409
$791$	6.00000			0.213335
$792$	0.500000	−	0.866025i	0.0177667	−	0.0307729i
$793$	−8.00000	−	13.8564i	−0.284088	−	0.492055i
$794$	2.50000	−	4.33013i	0.0887217	−	0.153670i
$795$	−9.00000	−	15.5885i	−0.319197	−	0.552866i
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$	−8.00000	+	3.46410i	−0.283197	+	0.122628i
$799$		0			0
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	−15.0000	+	25.9808i	−0.529668	+	0.917413i
$803$	−1.00000	−	1.73205i	−0.0352892	−	0.0611227i
$804$	−4.00000	+	6.92820i	−0.141069	+	0.244339i
$805$		0			0
$806$	−16.0000			−0.563576
$807$	3.00000	−	5.19615i	0.105605	−	0.182913i
$808$	−6.00000	+	10.3923i	−0.211079	+	0.365600i
$809$	−12.0000			−0.421898			−0.210949	−	0.977497i	$-0.567655\pi$
$809$	−12.0000			−0.421898			−0.210949	+	0.977497i	$0.567655\pi$
$810$	−33.0000			−1.15950
$811$	21.5000	−	37.2391i	0.754967	−	1.30764i	−0.190424	−	0.981702i	$-0.560986\pi$
$811$	21.5000	−	37.2391i	0.754967	−	1.30764i	0.945391	−	0.325939i	$-0.105681\pi$
$812$	−3.00000	−	5.19615i	−0.105279	−	0.182349i
$813$	−7.00000	+	12.1244i	−0.245501	+	0.425220i
$814$	−0.500000	−	0.866025i	−0.0175250	−	0.0303542i
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$		0			0
$817$	2.00000	−	17.3205i	0.0699711	−	0.605968i
$818$	4.00000			0.139857
$819$	−2.00000	−	3.46410i	−0.0698857	−	0.121046i
$820$	−9.00000	−	15.5885i	−0.314294	−	0.544373i
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	−0.995819	−	0.0913446i	$-0.970884\pi$
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	0.577016	+	0.816733i	$0.304217\pi$
$822$	15.0000	+	25.9808i	0.523185	+	0.906183i
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	4.00000			0.139347
$825$	−8.00000			−0.278524
$826$		0			0
$827$	6.00000	−	10.3923i	0.208640	−	0.361376i	−0.742646	−	0.669684i	$-0.766429\pi$
$827$	6.00000	−	10.3923i	0.208640	−	0.361376i	0.951286	+	0.308308i	$0.0997628\pi$
$828$		0			0
$829$	−10.0000			−0.347314			−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000			−0.347314			−0.173657	+	0.984806i	$0.555558\pi$
$830$	4.50000	−	7.79423i	0.156197	−	0.270542i
$831$	−28.0000	−	48.4974i	−0.971309	−	1.68236i
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$		0			0
$834$	−17.0000	−	29.4449i	−0.588662	−	1.01959i
$835$	−9.00000			−0.311458
$836$	4.00000	−	1.73205i	0.138343	−	0.0599042i
$837$	−16.0000			−0.553041
$838$	9.00000	+	15.5885i	0.310900	+	0.538494i
$839$	18.0000	+	31.1769i	0.621429	+	1.07635i	0.989220	+	0.146438i	$0.0467809\pi$
$839$	18.0000	+	31.1769i	0.621429	+	1.07635i	−0.367791	+	0.929909i	$0.619886\pi$
$840$	−3.00000	+	5.19615i	−0.103510	+	0.179284i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	8.50000	−	14.7224i	0.292929	−	0.507369i
$843$		0			0
$844$	−25.0000			−0.860535
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$	3.00000	−	5.19615i	0.103142	−	0.178647i
$847$	−1.00000			−0.0343604
$848$	3.00000			0.103020
$849$	−13.0000	+	22.5167i	−0.446159	+	0.772770i
$850$		0			0
$851$		0			0
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	0.552948	−	0.833215i	$-0.313503\pi$
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	−0.998060	+	0.0622597i	$0.980169\pi$
$854$	−4.00000			−0.136877
$855$	10.5000	+	7.79423i	0.359092	+	0.266557i
$856$	9.00000			0.307614
$857$	−24.0000	−	41.5692i	−0.819824	−	1.41998i	−0.905811	−	0.423681i	$-0.860738\pi$
$857$	−24.0000	−	41.5692i	−0.819824	−	1.41998i	0.0859870	−	0.996296i	$-0.472596\pi$
$858$	4.00000	+	6.92820i	0.136558	+	0.236525i
$859$	−1.00000	+	1.73205i	−0.0341196	+	0.0590968i	−0.882581	−	0.470160i	$-0.844196\pi$
$859$	−1.00000	+	1.73205i	−0.0341196	+	0.0590968i	0.848461	+	0.529257i	$0.177529\pi$
$860$	−6.00000	−	10.3923i	−0.204598	−	0.354375i
$861$	6.00000	−	10.3923i	0.204479	−	0.354169i
$862$	−15.0000			−0.510902
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$	2.00000	−	3.46410i	0.0680414	−	0.117851i
$865$		0			0
$866$	−14.0000			−0.475739
$867$	34.0000			1.15470
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	−5.50000	−	9.52628i	−0.186575	−	0.323157i
$870$	−18.0000	+	31.1769i	−0.610257	+	1.05700i
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	−8.00000	−	13.8564i	−0.270914	−	0.469237i
$873$	−19.0000			−0.643053
$874$		0			0
$875$	−3.00000			−0.101419
$876$	2.00000	+	3.46410i	0.0675737	+	0.117041i
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	0.646319	−	0.763067i	$-0.276307\pi$
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	−0.983995	+	0.178195i	$0.942974\pi$
$878$	17.5000	−	30.3109i	0.590596	−	1.02294i
$879$	30.0000	+	51.9615i	1.01187	+	1.75262i
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$	6.00000			0.202031
$883$	−7.00000	+	12.1244i	−0.235569	+	0.408017i	−0.959438	−	0.281920i	$-0.909029\pi$
$883$	−7.00000	+	12.1244i	−0.235569	+	0.408017i	0.723869	+	0.689937i	$0.242362\pi$
$884$		0			0
$885$		0			0
$886$	12.0000			0.403148
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	−0.443964	−	0.896045i	$-0.646428\pi$
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	0.997979	−	0.0635387i	$-0.0202386\pi$
$888$	1.00000	+	1.73205i	0.0335578	+	0.0581238i
$889$	−8.00000	+	13.8564i	−0.268311	+	0.464729i
$890$	27.0000	+	46.7654i	0.905042	+	1.56758i
$891$	5.50000	+	9.52628i	0.184257	+	0.319142i
$892$	−28.0000			−0.937509
$893$	24.0000	−	10.3923i	0.803129	−	0.347765i
$894$	36.0000			1.20402
$895$	−36.0000	−	62.3538i	−1.20335	−	2.08426i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	4.00000			0.133333
$901$		0			0
$902$	−3.00000	+	5.19615i	−0.0998891	+	0.173013i
$903$	4.00000	−	6.92820i	0.133112	−	0.230556i
$904$	6.00000			0.199557
$905$	−33.0000			−1.09696
$906$	19.0000	−	32.9090i	0.631233	−	1.09333i
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	−13.5000	+	23.3827i	−0.448013	+	0.775982i
$909$	6.00000	+	10.3923i	0.199007	+	0.344691i
$910$	−6.00000	−	10.3923i	−0.198898	−	0.344502i
$911$	42.0000			1.39152			0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000			1.39152			0.695761	+	0.718273i	$0.255067\pi$
$912$	−8.00000	+	3.46410i	−0.264906	+	0.114708i
$913$	−3.00000			−0.0992855
$914$	−11.0000	−	19.0526i	−0.363848	−	0.630203i
$915$	12.0000	+	20.7846i	0.396708	+	0.687118i
$916$	12.5000	−	21.6506i	0.413012	−	0.715357i
$917$		0			0
$918$		0			0
$919$	23.0000			0.758700			0.379350	−	0.925253i	$-0.376148\pi$
$919$	23.0000			0.758700			0.379350	+	0.925253i	$0.376148\pi$
$920$		0			0
$921$	11.0000	−	19.0526i	0.362462	−	0.627803i
$922$	−3.00000	+	5.19615i	−0.0987997	+	0.171126i
$923$	24.0000			0.789970
$924$	2.00000			0.0657952
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	−2.00000	−	3.46410i	−0.0657241	−	0.113837i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$	24.0000			0.786991
$931$	21.0000	+	15.5885i	0.688247	+	0.510891i
$932$		0			0
$933$	−18.0000	−	31.1769i	−0.589294	−	1.02069i
$934$	15.0000	+	25.9808i	0.490815	+	0.850117i
$935$		0			0
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	−25.0000	+	43.3013i	−0.816714	+	1.41459i	0.0913759	+	0.995816i	$0.470874\pi$
$937$	−25.0000	+	43.3013i	−0.816714	+	1.41459i	−0.908090	+	0.418774i	$0.862460\pi$
$938$	−4.00000			−0.130605
$939$	2.00000			0.0652675
$940$	9.00000	−	15.5885i	0.293548	−	0.508439i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$	34.0000			1.10778
$943$		0			0
$944$		0			0
$945$	−6.00000	−	10.3923i	−0.195180	−	0.338062i
$946$	−2.00000	+	3.46410i	−0.0650256	+	0.112628i
$947$	27.0000	+	46.7654i	0.877382	+	1.51967i	0.854203	+	0.519939i	$0.174045\pi$
$947$	27.0000	+	46.7654i	0.877382	+	1.51967i	0.0231788	+	0.999731i	$0.492621\pi$
$948$	11.0000	+	19.0526i	0.357263	+	0.618798i
$949$	−8.00000			−0.259691
$950$	14.0000	+	10.3923i	0.454220	+	0.337171i
$951$	36.0000			1.16738
$952$		0			0
$953$	−18.0000	−	31.1769i	−0.583077	−	1.00992i	−0.995112	−	0.0987513i	$-0.968515\pi$
$953$	−18.0000	−	31.1769i	−0.583077	−	1.00992i	0.412035	−	0.911168i	$-0.364818\pi$
$954$	1.50000	−	2.59808i	0.0485643	−	0.0841158i
$955$	−9.00000	−	15.5885i	−0.291233	−	0.504431i
$956$	7.50000	−	12.9904i	0.242567	−	0.420139i
$957$	12.0000			0.387905
$958$	24.0000			0.775405
$959$	−7.50000	+	12.9904i	−0.242188	+	0.419481i
$960$	−3.00000	+	5.19615i	−0.0968246	+	0.167705i
$961$	−15.0000			−0.483871
$962$	−4.00000			−0.128965
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$	−1.00000	−	1.73205i	−0.0322078	−	0.0557856i
$965$	3.00000	−	5.19615i	0.0965734	−	0.167270i
$966$		0			0
$967$	3.50000	+	6.06218i	0.112552	+	0.194946i	0.916799	−	0.399350i	$-0.130764\pi$
$967$	3.50000	+	6.06218i	0.112552	+	0.194946i	−0.804246	+	0.594296i	$0.797431\pi$
$968$	−1.00000			−0.0321412
$969$		0			0
$970$	−57.0000			−1.83016
$971$	15.0000	+	25.9808i	0.481373	+	0.833762i	0.999771	−	0.0213768i	$-0.00680496\pi$
$971$	15.0000	+	25.9808i	0.481373	+	0.833762i	−0.518399	+	0.855139i	$0.673472\pi$
$972$	−5.00000	−	8.66025i	−0.160375	−	0.277778i
$973$	8.50000	−	14.7224i	0.272497	−	0.471979i
$974$	1.00000	+	1.73205i	0.0320421	+	0.0554985i
$975$	−16.0000	+	27.7128i	−0.512410	+	0.887520i
$976$	−4.00000			−0.128037
$977$	57.0000			1.82359			0.911796	−	0.410644i	$-0.134696\pi$
$977$	57.0000			1.82359			0.911796	+	0.410644i	$0.134696\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$	18.0000			0.574989
$981$	−16.0000			−0.510841
$982$	−4.50000	+	7.79423i	−0.143601	+	0.248724i
$983$	21.0000	+	36.3731i	0.669796	+	1.16012i	0.977961	+	0.208788i	$0.0669518\pi$
$983$	21.0000	+	36.3731i	0.669796	+	1.16012i	−0.308165	+	0.951333i	$0.599715\pi$
$984$	6.00000	−	10.3923i	0.191273	−	0.331295i
$985$	−18.0000	−	31.1769i	−0.573528	−	0.993379i
$986$		0			0
$987$	12.0000			0.381964
$988$	2.00000	−	17.3205i	0.0636285	−	0.551039i
$989$		0			0
$990$	−1.50000	−	2.59808i	−0.0476731	−	0.0825723i
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	−0.992278	−	0.124033i	$-0.960417\pi$
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	0.388723	−	0.921355i	$-0.372916\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−16.0000	−	27.7128i	−0.507745	−	0.879440i
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$	30.0000			0.951064
$996$	6.00000			0.190117
$997$	−22.0000	+	38.1051i	−0.696747	+	1.20680i	0.272841	+	0.962059i	$0.412037\pi$
$997$	−22.0000	+	38.1051i	−0.696747	+	1.20680i	−0.969588	+	0.244742i	$0.921297\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$	−4.00000			−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.e.f.45.1	✓	2
19.7	even	3		7942.2.a.b.1.1		1
19.11	even	3	inner	418.2.e.f.353.1	yes	2
19.12	odd	6		7942.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.f.45.1	✓	2	1.1	even	1	trivial
418.2.e.f.353.1	yes	2	19.11	even	3	inner
7942.2.a.b.1.1		1	19.7	even	3
7942.2.a.r.1.1		1	19.12	odd	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.00000 + 1.73205i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.00000 + 1.73205i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +1.00000 q^{11} -2.00000 q^{12} +(2.00000 - 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-3.00000 + 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{18} +(-3.50000 - 2.59808i) q^{19} -3.00000 q^{20} +(-1.00000 - 1.73205i) q^{21} +(0.500000 + 0.866025i) q^{22} +(-1.00000 - 1.73205i) q^{24} +(-2.00000 + 3.46410i) q^{25} +4.00000 q^{26} +4.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -6.00000 q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(0.500000 - 4.33013i) q^{38} +8.00000 q^{39} +(-1.50000 - 2.59808i) q^{40} +(3.00000 + 5.19615i) q^{41} +(1.00000 - 1.73205i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-0.500000 + 0.866025i) q^{44} -3.00000 q^{45} +(-3.00000 + 5.19615i) q^{47} +(1.00000 - 1.73205i) q^{48} -6.00000 q^{49} -4.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(2.00000 + 3.46410i) q^{54} +(1.50000 + 2.59808i) q^{55} +1.00000 q^{56} +(1.00000 - 8.66025i) q^{57} +6.00000 q^{58} +(-3.00000 - 5.19615i) q^{60} +(2.00000 - 3.46410i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +12.0000 q^{65} +(-1.00000 + 1.73205i) q^{66} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{70} +(3.00000 + 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-0.500000 - 0.866025i) q^{74} -8.00000 q^{75} +(4.00000 - 1.73205i) q^{76} -1.00000 q^{77} +(4.00000 + 6.92820i) q^{78} +(-5.50000 - 9.52628i) q^{79} +(1.50000 - 2.59808i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-3.00000 + 5.19615i) q^{82} -3.00000 q^{83} +2.00000 q^{84} +(-2.00000 + 3.46410i) q^{86} +12.0000 q^{87} -1.00000 q^{88} +(9.00000 - 15.5885i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(-2.00000 + 3.46410i) q^{91} +(-4.00000 - 6.92820i) q^{93} -6.00000 q^{94} +(1.50000 - 12.9904i) q^{95} +2.00000 q^{96} +(9.50000 + 16.4545i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 4 q^{13} - q^{14} - 6 q^{15} - q^{16} - 2 q^{18} - 7 q^{19} - 6 q^{20} - 2 q^{21} + q^{22} - 2 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{27} + q^{28} + 6 q^{29} - 12 q^{30} - 8 q^{31} + q^{32} + 2 q^{33} - 3 q^{35} - q^{36} - 2 q^{37} + q^{38} + 16 q^{39} - 3 q^{40} + 6 q^{41} + 2 q^{42} + 4 q^{43} - q^{44} - 6 q^{45} - 6 q^{47} + 2 q^{48} - 12 q^{49} - 8 q^{50} + 4 q^{52} - 3 q^{53} + 4 q^{54} + 3 q^{55} + 2 q^{56} + 2 q^{57} + 12 q^{58} - 6 q^{60} + 4 q^{61} - 4 q^{62} + q^{63} + 2 q^{64} + 24 q^{65} - 2 q^{66} + 4 q^{67} + 3 q^{70} + 6 q^{71} + q^{72} - 2 q^{73} - q^{74} - 16 q^{75} + 8 q^{76} - 2 q^{77} + 8 q^{78} - 11 q^{79} + 3 q^{80} + 11 q^{81} - 6 q^{82} - 6 q^{83} + 4 q^{84} - 4 q^{86} + 24 q^{87} - 2 q^{88} + 18 q^{89} - 3 q^{90} - 4 q^{91} - 8 q^{93} - 12 q^{94} + 3 q^{95} + 4 q^{96} + 19 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 - q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 4 * q^13 - q^14 - 6 * q^15 - q^16 - 2 * q^18 - 7 * q^19 - 6 * q^20 - 2 * q^21 + q^22 - 2 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^27 + q^28 + 6 * q^29 - 12 * q^30 - 8 * q^31 + q^32 + 2 * q^33 - 3 * q^35 - q^36 - 2 * q^37 + q^38 + 16 * q^39 - 3 * q^40 + 6 * q^41 + 2 * q^42 + 4 * q^43 - q^44 - 6 * q^45 - 6 * q^47 + 2 * q^48 - 12 * q^49 - 8 * q^50 + 4 * q^52 - 3 * q^53 + 4 * q^54 + 3 * q^55 + 2 * q^56 + 2 * q^57 + 12 * q^58 - 6 * q^60 + 4 * q^61 - 4 * q^62 + q^63 + 2 * q^64 + 24 * q^65 - 2 * q^66 + 4 * q^67 + 3 * q^70 + 6 * q^71 + q^72 - 2 * q^73 - q^74 - 16 * q^75 + 8 * q^76 - 2 * q^77 + 8 * q^78 - 11 * q^79 + 3 * q^80 + 11 * q^81 - 6 * q^82 - 6 * q^83 + 4 * q^84 - 4 * q^86 + 24 * q^87 - 2 * q^88 + 18 * q^89 - 3 * q^90 - 4 * q^91 - 8 * q^93 - 12 * q^94 + 3 * q^95 + 4 * q^96 + 19 * q^97 - 6 * q^98 - q^99

Introduction

L-functions

Modular forms

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Database

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