LMFDB - Embedded newform 74.3.d.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,3,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, 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:	$2.01635395627$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.3.d.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +4.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(-4.00000 + 4.00000i) q^{6} -4.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -7.00000 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +4.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(-4.00000 + 4.00000i) q^{6} -4.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -7.00000 q^{9} +6.00000 q^{10} +4.00000i q^{11} -8.00000 q^{12} +(3.00000 - 3.00000i) q^{13} +(-4.00000 - 4.00000i) q^{14} +(12.0000 + 12.0000i) q^{15} -4.00000 q^{16} +(23.0000 - 23.0000i) q^{17} +(-7.00000 - 7.00000i) q^{18} +(10.0000 - 10.0000i) q^{19} +(6.00000 + 6.00000i) q^{20} -16.0000i q^{21} +(-4.00000 + 4.00000i) q^{22} +(-10.0000 + 10.0000i) q^{23} +(-8.00000 - 8.00000i) q^{24} +7.00000i q^{25} +6.00000 q^{26} +8.00000i q^{27} -8.00000i q^{28} +(-19.0000 - 19.0000i) q^{29} +24.0000i q^{30} +(-18.0000 - 18.0000i) q^{31} +(-4.00000 - 4.00000i) q^{32} -16.0000 q^{33} +46.0000 q^{34} +(-12.0000 + 12.0000i) q^{35} -14.0000i q^{36} -37.0000i q^{37} +20.0000 q^{38} +(12.0000 + 12.0000i) q^{39} +12.0000i q^{40} +74.0000i q^{41} +(16.0000 - 16.0000i) q^{42} +(42.0000 - 42.0000i) q^{43} -8.00000 q^{44} +(-21.0000 + 21.0000i) q^{45} -20.0000 q^{46} -44.0000 q^{47} -16.0000i q^{48} -33.0000 q^{49} +(-7.00000 + 7.00000i) q^{50} +(92.0000 + 92.0000i) q^{51} +(6.00000 + 6.00000i) q^{52} -80.0000 q^{53} +(-8.00000 + 8.00000i) q^{54} +(12.0000 + 12.0000i) q^{55} +(8.00000 - 8.00000i) q^{56} +(40.0000 + 40.0000i) q^{57} -38.0000i q^{58} +(-54.0000 + 54.0000i) q^{59} +(-24.0000 + 24.0000i) q^{60} +(-3.00000 - 3.00000i) q^{61} -36.0000i q^{62} +28.0000 q^{63} -8.00000i q^{64} -18.0000i q^{65} +(-16.0000 - 16.0000i) q^{66} -12.0000i q^{67} +(46.0000 + 46.0000i) q^{68} +(-40.0000 - 40.0000i) q^{69} -24.0000 q^{70} +124.000 q^{71} +(14.0000 - 14.0000i) q^{72} -10.0000i q^{73} +(37.0000 - 37.0000i) q^{74} -28.0000 q^{75} +(20.0000 + 20.0000i) q^{76} -16.0000i q^{77} +24.0000i q^{78} +(14.0000 - 14.0000i) q^{79} +(-12.0000 + 12.0000i) q^{80} -95.0000 q^{81} +(-74.0000 + 74.0000i) q^{82} -64.0000 q^{83} +32.0000 q^{84} -138.000i q^{85} +84.0000 q^{86} +(76.0000 - 76.0000i) q^{87} +(-8.00000 - 8.00000i) q^{88} +(17.0000 + 17.0000i) q^{89} -42.0000 q^{90} +(-12.0000 + 12.0000i) q^{91} +(-20.0000 - 20.0000i) q^{92} +(72.0000 - 72.0000i) q^{93} +(-44.0000 - 44.0000i) q^{94} -60.0000i q^{95} +(16.0000 - 16.0000i) q^{96} +(129.000 - 129.000i) q^{97} +(-33.0000 - 33.0000i) q^{98} -28.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 6 q^{5} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 14 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 6 * q^5 - 8 * q^6 - 8 * q^7 - 4 * q^8 - 14 * q^9	$ 2 q + 2 q^{2} + 6 q^{5} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 14 q^{9} + 12 q^{10} - 16 q^{12} + 6 q^{13} - 8 q^{14} + 24 q^{15} - 8 q^{16} + 46 q^{17} - 14 q^{18} + 20 q^{19} + 12 q^{20} - 8 q^{22} - 20 q^{23} - 16 q^{24} + 12 q^{26} - 38 q^{29} - 36 q^{31} - 8 q^{32} - 32 q^{33} + 92 q^{34} - 24 q^{35} + 40 q^{38} + 24 q^{39} + 32 q^{42} + 84 q^{43} - 16 q^{44} - 42 q^{45} - 40 q^{46} - 88 q^{47} - 66 q^{49} - 14 q^{50} + 184 q^{51} + 12 q^{52} - 160 q^{53} - 16 q^{54} + 24 q^{55} + 16 q^{56} + 80 q^{57} - 108 q^{59} - 48 q^{60} - 6 q^{61} + 56 q^{63} - 32 q^{66} + 92 q^{68} - 80 q^{69} - 48 q^{70} + 248 q^{71} + 28 q^{72} + 74 q^{74} - 56 q^{75} + 40 q^{76} + 28 q^{79} - 24 q^{80} - 190 q^{81} - 148 q^{82} - 128 q^{83} + 64 q^{84} + 168 q^{86} + 152 q^{87} - 16 q^{88} + 34 q^{89} - 84 q^{90} - 24 q^{91} - 40 q^{92} + 144 q^{93} - 88 q^{94} + 32 q^{96} + 258 q^{97} - 66 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 6 * q^5 - 8 * q^6 - 8 * q^7 - 4 * q^8 - 14 * q^9 + 12 * q^10 - 16 * q^12 + 6 * q^13 - 8 * q^14 + 24 * q^15 - 8 * q^16 + 46 * q^17 - 14 * q^18 + 20 * q^19 + 12 * q^20 - 8 * q^22 - 20 * q^23 - 16 * q^24 + 12 * q^26 - 38 * q^29 - 36 * q^31 - 8 * q^32 - 32 * q^33 + 92 * q^34 - 24 * q^35 + 40 * q^38 + 24 * q^39 + 32 * q^42 + 84 * q^43 - 16 * q^44 - 42 * q^45 - 40 * q^46 - 88 * q^47 - 66 * q^49 - 14 * q^50 + 184 * q^51 + 12 * q^52 - 160 * q^53 - 16 * q^54 + 24 * q^55 + 16 * q^56 + 80 * q^57 - 108 * q^59 - 48 * q^60 - 6 * q^61 + 56 * q^63 - 32 * q^66 + 92 * q^68 - 80 * q^69 - 48 * q^70 + 248 * q^71 + 28 * q^72 + 74 * q^74 - 56 * q^75 + 40 * q^76 + 28 * q^79 - 24 * q^80 - 190 * q^81 - 148 * q^82 - 128 * q^83 + 64 * q^84 + 168 * q^86 + 152 * q^87 - 16 * q^88 + 34 * q^89 - 84 * q^90 - 24 * q^91 - 40 * q^92 + 144 * q^93 - 88 * q^94 + 32 * q^96 + 258 * q^97 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$			4.00000i			1.33333i	0.745356	+	0.666667i	$0.232280\pi$
$3$			4.00000i			1.33333i	−0.745356	+	0.666667i	$0.767720\pi$
$4$			2.00000i			0.500000i
$5$	3.00000	−	3.00000i	0.600000	−	0.600000i	−0.340312	−	0.940312i	$-0.610533\pi$
$5$	3.00000	−	3.00000i	0.600000	−	0.600000i	0.940312	+	0.340312i	$0.110533\pi$
$6$	−4.00000	+	4.00000i	−0.666667	+	0.666667i
$7$	−4.00000			−0.571429			−0.285714	−	0.958315i	$-0.592231\pi$
$7$	−4.00000			−0.571429			−0.285714	+	0.958315i	$0.592231\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−7.00000			−0.777778
$10$	6.00000			0.600000
$11$			4.00000i			0.363636i	0.983332	+	0.181818i	$0.0581982\pi$
$11$			4.00000i			0.363636i	−0.983332	+	0.181818i	$0.941802\pi$
$12$	−8.00000			−0.666667
$13$	3.00000	−	3.00000i	0.230769	−	0.230769i	−0.582245	−	0.813014i	$-0.697825\pi$
$13$	3.00000	−	3.00000i	0.230769	−	0.230769i	0.813014	+	0.582245i	$0.197825\pi$
$14$	−4.00000	−	4.00000i	−0.285714	−	0.285714i
$15$	12.0000	+	12.0000i	0.800000	+	0.800000i
$16$	−4.00000			−0.250000
$17$	23.0000	−	23.0000i	1.35294	−	1.35294i	0.470588	−	0.882353i	$-0.344042\pi$
$17$	23.0000	−	23.0000i	1.35294	−	1.35294i	0.882353	−	0.470588i	$-0.155958\pi$
$18$	−7.00000	−	7.00000i	−0.388889	−	0.388889i
$19$	10.0000	−	10.0000i	0.526316	−	0.526316i	−0.393156	−	0.919472i	$-0.628617\pi$
$19$	10.0000	−	10.0000i	0.526316	−	0.526316i	0.919472	+	0.393156i	$0.128617\pi$
$20$	6.00000	+	6.00000i	0.300000	+	0.300000i
$21$		−	16.0000i		−	0.761905i
$22$	−4.00000	+	4.00000i	−0.181818	+	0.181818i
$23$	−10.0000	+	10.0000i	−0.434783	+	0.434783i	−0.890252	−	0.455469i	$-0.849472\pi$
$23$	−10.0000	+	10.0000i	−0.434783	+	0.434783i	0.455469	+	0.890252i	$0.349472\pi$
$24$	−8.00000	−	8.00000i	−0.333333	−	0.333333i
$25$			7.00000i			0.280000i
$26$	6.00000			0.230769
$27$			8.00000i			0.296296i
$28$		−	8.00000i		−	0.285714i
$29$	−19.0000	−	19.0000i	−0.655172	−	0.655172i	0.299061	−	0.954234i	$-0.403326\pi$
$29$	−19.0000	−	19.0000i	−0.655172	−	0.655172i	−0.954234	+	0.299061i	$0.903326\pi$
$30$			24.0000i			0.800000i
$31$	−18.0000	−	18.0000i	−0.580645	−	0.580645i	0.354435	−	0.935081i	$-0.384673\pi$
$31$	−18.0000	−	18.0000i	−0.580645	−	0.580645i	−0.935081	+	0.354435i	$0.884673\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−16.0000			−0.484848
$34$	46.0000			1.35294
$35$	−12.0000	+	12.0000i	−0.342857	+	0.342857i
$36$		−	14.0000i		−	0.388889i
$37$		−	37.0000i		−	1.00000i
$37$		−	37.0000i		−	1.00000i
$38$	20.0000			0.526316
$39$	12.0000	+	12.0000i	0.307692	+	0.307692i
$40$			12.0000i			0.300000i
$41$			74.0000i			1.80488i	0.430818	+	0.902439i	$0.358225\pi$
$41$			74.0000i			1.80488i	−0.430818	+	0.902439i	$0.641775\pi$
$42$	16.0000	−	16.0000i	0.380952	−	0.380952i
$43$	42.0000	−	42.0000i	0.976744	−	0.976744i	−0.0229915	−	0.999736i	$-0.507319\pi$
$43$	42.0000	−	42.0000i	0.976744	−	0.976744i	0.999736	+	0.0229915i	$0.00731906\pi$
$44$	−8.00000			−0.181818
$45$	−21.0000	+	21.0000i	−0.466667	+	0.466667i
$46$	−20.0000			−0.434783
$47$	−44.0000			−0.936170			−0.468085	−	0.883683i	$-0.655056\pi$
$47$	−44.0000			−0.936170			−0.468085	+	0.883683i	$0.655056\pi$
$48$		−	16.0000i		−	0.333333i
$49$	−33.0000			−0.673469
$50$	−7.00000	+	7.00000i	−0.140000	+	0.140000i
$51$	92.0000	+	92.0000i	1.80392	+	1.80392i
$52$	6.00000	+	6.00000i	0.115385	+	0.115385i
$53$	−80.0000			−1.50943			−0.754717	−	0.656051i	$-0.772226\pi$
$53$	−80.0000			−1.50943			−0.754717	+	0.656051i	$0.772226\pi$
$54$	−8.00000	+	8.00000i	−0.148148	+	0.148148i
$55$	12.0000	+	12.0000i	0.218182	+	0.218182i
$56$	8.00000	−	8.00000i	0.142857	−	0.142857i
$57$	40.0000	+	40.0000i	0.701754	+	0.701754i
$58$		−	38.0000i		−	0.655172i
$59$	−54.0000	+	54.0000i	−0.915254	+	0.915254i	−0.996679	−	0.0814252i	$-0.974053\pi$
$59$	−54.0000	+	54.0000i	−0.915254	+	0.915254i	0.0814252	+	0.996679i	$0.474053\pi$
$60$	−24.0000	+	24.0000i	−0.400000	+	0.400000i
$61$	−3.00000	−	3.00000i	−0.0491803	−	0.0491803i	0.682089	−	0.731269i	$-0.261072\pi$
$61$	−3.00000	−	3.00000i	−0.0491803	−	0.0491803i	−0.731269	+	0.682089i	$0.761072\pi$
$62$		−	36.0000i		−	0.580645i
$63$	28.0000			0.444444
$64$		−	8.00000i		−	0.125000i
$65$		−	18.0000i		−	0.276923i
$66$	−16.0000	−	16.0000i	−0.242424	−	0.242424i
$67$		−	12.0000i		−	0.179104i	−0.995982	−	0.0895522i	$-0.971456\pi$
$67$		−	12.0000i		−	0.179104i	0.995982	−	0.0895522i	$-0.0285436\pi$
$68$	46.0000	+	46.0000i	0.676471	+	0.676471i
$69$	−40.0000	−	40.0000i	−0.579710	−	0.579710i
$70$	−24.0000			−0.342857
$71$	124.000			1.74648			0.873239	−	0.487291i	$-0.162015\pi$
$71$	124.000			1.74648			0.873239	+	0.487291i	$0.162015\pi$
$72$	14.0000	−	14.0000i	0.194444	−	0.194444i
$73$		−	10.0000i		−	0.136986i	−0.997652	−	0.0684932i	$-0.978181\pi$
$73$		−	10.0000i		−	0.136986i	0.997652	−	0.0684932i	$-0.0218191\pi$
$74$	37.0000	−	37.0000i	0.500000	−	0.500000i
$75$	−28.0000			−0.373333
$76$	20.0000	+	20.0000i	0.263158	+	0.263158i
$77$		−	16.0000i		−	0.207792i
$78$			24.0000i			0.307692i
$79$	14.0000	−	14.0000i	0.177215	−	0.177215i	−0.612926	−	0.790141i	$-0.710007\pi$
$79$	14.0000	−	14.0000i	0.177215	−	0.177215i	0.790141	+	0.612926i	$0.210007\pi$
$80$	−12.0000	+	12.0000i	−0.150000	+	0.150000i
$81$	−95.0000			−1.17284
$82$	−74.0000	+	74.0000i	−0.902439	+	0.902439i
$83$	−64.0000			−0.771084			−0.385542	−	0.922690i	$-0.625986\pi$
$83$	−64.0000			−0.771084			−0.385542	+	0.922690i	$0.625986\pi$
$84$	32.0000			0.380952
$85$		−	138.000i		−	1.62353i
$86$	84.0000			0.976744
$87$	76.0000	−	76.0000i	0.873563	−	0.873563i
$88$	−8.00000	−	8.00000i	−0.0909091	−	0.0909091i
$89$	17.0000	+	17.0000i	0.191011	+	0.191011i	0.796133	−	0.605122i	$-0.206876\pi$
$89$	17.0000	+	17.0000i	0.191011	+	0.191011i	−0.605122	+	0.796133i	$0.706876\pi$
$90$	−42.0000			−0.466667
$91$	−12.0000	+	12.0000i	−0.131868	+	0.131868i
$92$	−20.0000	−	20.0000i	−0.217391	−	0.217391i
$93$	72.0000	−	72.0000i	0.774194	−	0.774194i
$94$	−44.0000	−	44.0000i	−0.468085	−	0.468085i
$95$		−	60.0000i		−	0.631579i
$96$	16.0000	−	16.0000i	0.166667	−	0.166667i
$97$	129.000	−	129.000i	1.32990	−	1.32990i	0.424442	−	0.905455i	$-0.360470\pi$
$97$	129.000	−	129.000i	1.32990	−	1.32990i	0.905455	−	0.424442i	$-0.139530\pi$
$98$	−33.0000	−	33.0000i	−0.336735	−	0.336735i
$99$		−	28.0000i		−	0.282828i
$100$	−14.0000			−0.140000
$101$			118.000i			1.16832i	0.811640	+	0.584158i	$0.198575\pi$
$101$			118.000i			1.16832i	−0.811640	+	0.584158i	$0.801425\pi$
$102$			184.000i			1.80392i
$103$	−42.0000	−	42.0000i	−0.407767	−	0.407767i	0.473192	−	0.880959i	$-0.343102\pi$
$103$	−42.0000	−	42.0000i	−0.407767	−	0.407767i	−0.880959	+	0.473192i	$0.843102\pi$
$104$			12.0000i			0.115385i
$105$	−48.0000	−	48.0000i	−0.457143	−	0.457143i
$106$	−80.0000	−	80.0000i	−0.754717	−	0.754717i
$107$	−24.0000			−0.224299			−0.112150	−	0.993691i	$-0.535774\pi$
$107$	−24.0000			−0.224299			−0.112150	+	0.993691i	$0.535774\pi$
$108$	−16.0000			−0.148148
$109$	−91.0000	+	91.0000i	−0.834862	+	0.834862i	−0.988177	−	0.153315i	$-0.951005\pi$
$109$	−91.0000	+	91.0000i	−0.834862	+	0.834862i	0.153315	+	0.988177i	$0.451005\pi$
$110$			24.0000i			0.218182i
$111$	148.000			1.33333
$112$	16.0000			0.142857
$113$	7.00000	+	7.00000i	0.0619469	+	0.0619469i	0.737402	−	0.675455i	$-0.236053\pi$
$113$	7.00000	+	7.00000i	0.0619469	+	0.0619469i	−0.675455	+	0.737402i	$0.736053\pi$
$114$			80.0000i			0.701754i
$115$			60.0000i			0.521739i
$116$	38.0000	−	38.0000i	0.327586	−	0.327586i
$117$	−21.0000	+	21.0000i	−0.179487	+	0.179487i
$118$	−108.000			−0.915254
$119$	−92.0000	+	92.0000i	−0.773109	+	0.773109i
$120$	−48.0000			−0.400000
$121$	105.000			0.867769
$122$		−	6.00000i		−	0.0491803i
$123$	−296.000			−2.40650
$124$	36.0000	−	36.0000i	0.290323	−	0.290323i
$125$	96.0000	+	96.0000i	0.768000	+	0.768000i
$126$	28.0000	+	28.0000i	0.222222	+	0.222222i
$127$	76.0000			0.598425			0.299213	−	0.954186i	$-0.403276\pi$
$127$	76.0000			0.598425			0.299213	+	0.954186i	$0.403276\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	168.000	+	168.000i	1.30233	+	1.30233i
$130$	18.0000	−	18.0000i	0.138462	−	0.138462i
$131$	70.0000	+	70.0000i	0.534351	+	0.534351i	0.921864	−	0.387513i	$-0.126666\pi$
$131$	70.0000	+	70.0000i	0.534351	+	0.534351i	−0.387513	+	0.921864i	$0.626666\pi$
$132$		−	32.0000i		−	0.242424i
$133$	−40.0000	+	40.0000i	−0.300752	+	0.300752i
$134$	12.0000	−	12.0000i	0.0895522	−	0.0895522i
$135$	24.0000	+	24.0000i	0.177778	+	0.177778i
$136$			92.0000i			0.676471i
$137$	216.000			1.57664			0.788321	−	0.615264i	$-0.210951\pi$
$137$	216.000			1.57664			0.788321	+	0.615264i	$0.210951\pi$
$138$		−	80.0000i		−	0.579710i
$139$			180.000i			1.29496i	0.762081	+	0.647482i	$0.224178\pi$
$139$			180.000i			1.29496i	−0.762081	+	0.647482i	$0.775822\pi$
$140$	−24.0000	−	24.0000i	−0.171429	−	0.171429i
$141$		−	176.000i		−	1.24823i
$142$	124.000	+	124.000i	0.873239	+	0.873239i
$143$	12.0000	+	12.0000i	0.0839161	+	0.0839161i
$144$	28.0000			0.194444
$145$	−114.000			−0.786207
$146$	10.0000	−	10.0000i	0.0684932	−	0.0684932i
$147$		−	132.000i		−	0.897959i
$148$	74.0000			0.500000
$149$	−34.0000			−0.228188			−0.114094	−	0.993470i	$-0.536396\pi$
$149$	−34.0000			−0.228188			−0.114094	+	0.993470i	$0.536396\pi$
$150$	−28.0000	−	28.0000i	−0.186667	−	0.186667i
$151$		−	72.0000i		−	0.476821i	−0.971164	−	0.238411i	$-0.923374\pi$
$151$		−	72.0000i		−	0.476821i	0.971164	−	0.238411i	$-0.0766264\pi$
$152$			40.0000i			0.263158i
$153$	−161.000	+	161.000i	−1.05229	+	1.05229i
$154$	16.0000	−	16.0000i	0.103896	−	0.103896i
$155$	−108.000			−0.696774
$156$	−24.0000	+	24.0000i	−0.153846	+	0.153846i
$157$	−14.0000			−0.0891720			−0.0445860	−	0.999006i	$-0.514197\pi$
$157$	−14.0000			−0.0891720			−0.0445860	+	0.999006i	$0.514197\pi$
$158$	28.0000			0.177215
$159$		−	320.000i		−	2.01258i
$160$	−24.0000			−0.150000
$161$	40.0000	−	40.0000i	0.248447	−	0.248447i
$162$	−95.0000	−	95.0000i	−0.586420	−	0.586420i
$163$	−66.0000	−	66.0000i	−0.404908	−	0.404908i	0.475051	−	0.879959i	$-0.342430\pi$
$163$	−66.0000	−	66.0000i	−0.404908	−	0.404908i	−0.879959	+	0.475051i	$0.842430\pi$
$164$	−148.000			−0.902439
$165$	−48.0000	+	48.0000i	−0.290909	+	0.290909i
$166$	−64.0000	−	64.0000i	−0.385542	−	0.385542i
$167$	−230.000	+	230.000i	−1.37725	+	1.37725i	−0.528003	+	0.849242i	$0.677059\pi$
$167$	−230.000	+	230.000i	−1.37725	+	1.37725i	−0.849242	+	0.528003i	$0.822941\pi$
$168$	32.0000	+	32.0000i	0.190476	+	0.190476i
$169$			151.000i			0.893491i
$170$	138.000	−	138.000i	0.811765	−	0.811765i
$171$	−70.0000	+	70.0000i	−0.409357	+	0.409357i
$172$	84.0000	+	84.0000i	0.488372	+	0.488372i
$173$		−	88.0000i		−	0.508671i	−0.967116	−	0.254335i	$-0.918143\pi$
$173$		−	88.0000i		−	0.508671i	0.967116	−	0.254335i	$-0.0818567\pi$
$174$	152.000			0.873563
$175$		−	28.0000i		−	0.160000i
$176$		−	16.0000i		−	0.0909091i
$177$	−216.000	−	216.000i	−1.22034	−	1.22034i
$178$			34.0000i			0.191011i
$179$	−166.000	−	166.000i	−0.927374	−	0.927374i	0.0701614	−	0.997536i	$-0.477649\pi$
$179$	−166.000	−	166.000i	−0.927374	−	0.927374i	−0.997536	+	0.0701614i	$0.977649\pi$
$180$	−42.0000	−	42.0000i	−0.233333	−	0.233333i
$181$	304.000			1.67956			0.839779	−	0.542928i	$-0.182684\pi$
$181$	304.000			1.67956			0.839779	+	0.542928i	$0.182684\pi$
$182$	−24.0000			−0.131868
$183$	12.0000	−	12.0000i	0.0655738	−	0.0655738i
$184$		−	40.0000i		−	0.217391i
$185$	−111.000	−	111.000i	−0.600000	−	0.600000i
$186$	144.000			0.774194
$187$	92.0000	+	92.0000i	0.491979	+	0.491979i
$188$		−	88.0000i		−	0.468085i
$189$		−	32.0000i		−	0.169312i
$190$	60.0000	−	60.0000i	0.315789	−	0.315789i
$191$	186.000	−	186.000i	0.973822	−	0.973822i	−0.0258440	−	0.999666i	$-0.508227\pi$
$191$	186.000	−	186.000i	0.973822	−	0.973822i	0.999666	+	0.0258440i	$0.00822732\pi$
$192$	32.0000			0.166667
$193$	−9.00000	+	9.00000i	−0.0466321	+	0.0466321i	−0.730038	−	0.683406i	$-0.760498\pi$
$193$	−9.00000	+	9.00000i	−0.0466321	+	0.0466321i	0.683406	+	0.730038i	$0.260498\pi$
$194$	258.000			1.32990
$195$	72.0000			0.369231
$196$		−	66.0000i		−	0.336735i
$197$	34.0000			0.172589			0.0862944	−	0.996270i	$-0.472497\pi$
$197$	34.0000			0.172589			0.0862944	+	0.996270i	$0.472497\pi$
$198$	28.0000	−	28.0000i	0.141414	−	0.141414i
$199$	46.0000	+	46.0000i	0.231156	+	0.231156i	0.813175	−	0.582019i	$-0.197737\pi$
$199$	46.0000	+	46.0000i	0.231156	+	0.231156i	−0.582019	+	0.813175i	$0.697737\pi$
$200$	−14.0000	−	14.0000i	−0.0700000	−	0.0700000i
$201$	48.0000			0.238806
$202$	−118.000	+	118.000i	−0.584158	+	0.584158i
$203$	76.0000	+	76.0000i	0.374384	+	0.374384i
$204$	−184.000	+	184.000i	−0.901961	+	0.901961i
$205$	222.000	+	222.000i	1.08293	+	1.08293i
$206$		−	84.0000i		−	0.407767i
$207$	70.0000	−	70.0000i	0.338164	−	0.338164i
$208$	−12.0000	+	12.0000i	−0.0576923	+	0.0576923i
$209$	40.0000	+	40.0000i	0.191388	+	0.191388i
$210$		−	96.0000i		−	0.457143i
$211$	−208.000			−0.985782			−0.492891	−	0.870091i	$-0.664060\pi$
$211$	−208.000			−0.985782			−0.492891	+	0.870091i	$0.664060\pi$
$212$		−	160.000i		−	0.754717i
$213$			496.000i			2.32864i
$214$	−24.0000	−	24.0000i	−0.112150	−	0.112150i
$215$		−	252.000i		−	1.17209i
$216$	−16.0000	−	16.0000i	−0.0740741	−	0.0740741i
$217$	72.0000	+	72.0000i	0.331797	+	0.331797i
$218$	−182.000			−0.834862
$219$	40.0000			0.182648
$220$	−24.0000	+	24.0000i	−0.109091	+	0.109091i
$221$		−	138.000i		−	0.624434i
$222$	148.000	+	148.000i	0.666667	+	0.666667i
$223$	−124.000			−0.556054			−0.278027	−	0.960573i	$-0.589680\pi$
$223$	−124.000			−0.556054			−0.278027	+	0.960573i	$0.589680\pi$
$224$	16.0000	+	16.0000i	0.0714286	+	0.0714286i
$225$		−	49.0000i		−	0.217778i
$226$			14.0000i			0.0619469i
$227$	−90.0000	+	90.0000i	−0.396476	+	0.396476i	−0.876988	−	0.480512i	$-0.840451\pi$
$227$	−90.0000	+	90.0000i	−0.396476	+	0.396476i	0.480512	+	0.876988i	$0.340451\pi$
$228$	−80.0000	+	80.0000i	−0.350877	+	0.350877i
$229$	−2.00000			−0.00873362			−0.00436681	−	0.999990i	$-0.501390\pi$
$229$	−2.00000			−0.00873362			−0.00436681	+	0.999990i	$0.501390\pi$
$230$	−60.0000	+	60.0000i	−0.260870	+	0.260870i
$231$	64.0000			0.277056
$232$	76.0000			0.327586
$233$			42.0000i			0.180258i	0.995930	+	0.0901288i	$0.0287279\pi$
$233$			42.0000i			0.180258i	−0.995930	+	0.0901288i	$0.971272\pi$
$234$	−42.0000			−0.179487
$235$	−132.000	+	132.000i	−0.561702	+	0.561702i
$236$	−108.000	−	108.000i	−0.457627	−	0.457627i
$237$	56.0000	+	56.0000i	0.236287	+	0.236287i
$238$	−184.000			−0.773109
$239$	22.0000	−	22.0000i	0.0920502	−	0.0920502i	−0.659582	−	0.751632i	$-0.729267\pi$
$239$	22.0000	−	22.0000i	0.0920502	−	0.0920502i	0.751632	+	0.659582i	$0.229267\pi$
$240$	−48.0000	−	48.0000i	−0.200000	−	0.200000i
$241$	−175.000	+	175.000i	−0.726141	+	0.726141i	−0.969849	−	0.243708i	$-0.921636\pi$
$241$	−175.000	+	175.000i	−0.726141	+	0.726141i	0.243708	+	0.969849i	$0.421636\pi$
$242$	105.000	+	105.000i	0.433884	+	0.433884i
$243$		−	308.000i		−	1.26749i
$244$	6.00000	−	6.00000i	0.0245902	−	0.0245902i
$245$	−99.0000	+	99.0000i	−0.404082	+	0.404082i
$246$	−296.000	−	296.000i	−1.20325	−	1.20325i
$247$		−	60.0000i		−	0.242915i
$248$	72.0000			0.290323
$249$		−	256.000i		−	1.02811i
$250$			192.000i			0.768000i
$251$	−198.000	−	198.000i	−0.788845	−	0.788845i	0.192460	−	0.981305i	$-0.438353\pi$
$251$	−198.000	−	198.000i	−0.788845	−	0.788845i	−0.981305	+	0.192460i	$0.938353\pi$
$252$			56.0000i			0.222222i
$253$	−40.0000	−	40.0000i	−0.158103	−	0.158103i
$254$	76.0000	+	76.0000i	0.299213	+	0.299213i
$255$	552.000			2.16471
$256$	16.0000			0.0625000
$257$	−159.000	+	159.000i	−0.618677	+	0.618677i	−0.945192	−	0.326515i	$-0.894126\pi$
$257$	−159.000	+	159.000i	−0.618677	+	0.618677i	0.326515	+	0.945192i	$0.394126\pi$
$258$			336.000i			1.30233i
$259$			148.000i			0.571429i
$260$	36.0000			0.138462
$261$	133.000	+	133.000i	0.509579	+	0.509579i
$262$			140.000i			0.534351i
$263$		−	88.0000i		−	0.334601i	−0.985906	−	0.167300i	$-0.946495\pi$
$263$		−	88.0000i		−	0.334601i	0.985906	−	0.167300i	$-0.0535050\pi$
$264$	32.0000	−	32.0000i	0.121212	−	0.121212i
$265$	−240.000	+	240.000i	−0.905660	+	0.905660i
$266$	−80.0000			−0.300752
$267$	−68.0000	+	68.0000i	−0.254682	+	0.254682i
$268$	24.0000			0.0895522
$269$	178.000			0.661710			0.330855	−	0.943682i	$-0.392663\pi$
$269$	178.000			0.661710			0.330855	+	0.943682i	$0.392663\pi$
$270$			48.0000i			0.177778i
$271$	404.000			1.49077			0.745387	−	0.666631i	$-0.232265\pi$
$271$	404.000			1.49077			0.745387	+	0.666631i	$0.232265\pi$
$272$	−92.0000	+	92.0000i	−0.338235	+	0.338235i
$273$	−48.0000	−	48.0000i	−0.175824	−	0.175824i
$274$	216.000	+	216.000i	0.788321	+	0.788321i
$275$	−28.0000			−0.101818
$276$	80.0000	−	80.0000i	0.289855	−	0.289855i
$277$	−147.000	−	147.000i	−0.530686	−	0.530686i	0.390091	−	0.920776i	$-0.372444\pi$
$277$	−147.000	−	147.000i	−0.530686	−	0.530686i	−0.920776	+	0.390091i	$0.872444\pi$
$278$	−180.000	+	180.000i	−0.647482	+	0.647482i
$279$	126.000	+	126.000i	0.451613	+	0.451613i
$280$		−	48.0000i		−	0.171429i
$281$	135.000	−	135.000i	0.480427	−	0.480427i	−0.424841	−	0.905268i	$-0.639670\pi$
$281$	135.000	−	135.000i	0.480427	−	0.480427i	0.905268	+	0.424841i	$0.139670\pi$
$282$	176.000	−	176.000i	0.624113	−	0.624113i
$283$	−258.000	−	258.000i	−0.911661	−	0.911661i	0.0847421	−	0.996403i	$-0.472993\pi$
$283$	−258.000	−	258.000i	−0.911661	−	0.911661i	−0.996403	+	0.0847421i	$0.972993\pi$
$284$			248.000i			0.873239i
$285$	240.000			0.842105
$286$			24.0000i			0.0839161i
$287$		−	296.000i		−	1.03136i
$288$	28.0000	+	28.0000i	0.0972222	+	0.0972222i
$289$		−	769.000i		−	2.66090i
$290$	−114.000	−	114.000i	−0.393103	−	0.393103i
$291$	516.000	+	516.000i	1.77320	+	1.77320i
$292$	20.0000			0.0684932
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	132.000	−	132.000i	0.448980	−	0.448980i
$295$			324.000i			1.09831i
$296$	74.0000	+	74.0000i	0.250000	+	0.250000i
$297$	−32.0000			−0.107744
$298$	−34.0000	−	34.0000i	−0.114094	−	0.114094i
$299$			60.0000i			0.200669i
$300$		−	56.0000i		−	0.186667i
$301$	−168.000	+	168.000i	−0.558140	+	0.558140i
$302$	72.0000	−	72.0000i	0.238411	−	0.238411i
$303$	−472.000			−1.55776
$304$	−40.0000	+	40.0000i	−0.131579	+	0.131579i
$305$	−18.0000			−0.0590164
$306$	−322.000			−1.05229
$307$			364.000i			1.18567i	0.805325	+	0.592834i	$0.201991\pi$
$307$			364.000i			1.18567i	−0.805325	+	0.592834i	$0.798009\pi$
$308$	32.0000			0.103896
$309$	168.000	−	168.000i	0.543689	−	0.543689i
$310$	−108.000	−	108.000i	−0.348387	−	0.348387i
$311$	−238.000	−	238.000i	−0.765273	−	0.765273i	0.211997	−	0.977270i	$-0.432003\pi$
$311$	−238.000	−	238.000i	−0.765273	−	0.765273i	−0.977270	+	0.211997i	$0.932003\pi$
$312$	−48.0000			−0.153846
$313$	87.0000	−	87.0000i	0.277955	−	0.277955i	−0.554337	−	0.832292i	$-0.687028\pi$
$313$	87.0000	−	87.0000i	0.277955	−	0.277955i	0.832292	+	0.554337i	$0.187028\pi$
$314$	−14.0000	−	14.0000i	−0.0445860	−	0.0445860i
$315$	84.0000	−	84.0000i	0.266667	−	0.266667i
$316$	28.0000	+	28.0000i	0.0886076	+	0.0886076i
$317$			264.000i			0.832808i	0.909180	+	0.416404i	$0.136710\pi$
$317$			264.000i			0.832808i	−0.909180	+	0.416404i	$0.863290\pi$
$318$	320.000	−	320.000i	1.00629	−	1.00629i
$319$	76.0000	−	76.0000i	0.238245	−	0.238245i
$320$	−24.0000	−	24.0000i	−0.0750000	−	0.0750000i
$321$		−	96.0000i		−	0.299065i
$322$	80.0000			0.248447
$323$		−	460.000i		−	1.42415i
$324$		−	190.000i		−	0.586420i
$325$	21.0000	+	21.0000i	0.0646154	+	0.0646154i
$326$		−	132.000i		−	0.404908i
$327$	−364.000	−	364.000i	−1.11315	−	1.11315i
$328$	−148.000	−	148.000i	−0.451220	−	0.451220i
$329$	176.000			0.534954
$330$	−96.0000			−0.290909
$331$	−326.000	+	326.000i	−0.984894	+	0.984894i	−0.999888	−	0.0149933i	$-0.995227\pi$
$331$	−326.000	+	326.000i	−0.984894	+	0.984894i	0.0149933	+	0.999888i	$0.495227\pi$
$332$		−	128.000i		−	0.385542i
$333$			259.000i			0.777778i
$334$	−460.000			−1.37725
$335$	−36.0000	−	36.0000i	−0.107463	−	0.107463i
$336$			64.0000i			0.190476i
$337$		−	230.000i		−	0.682493i	−0.939974	−	0.341246i	$-0.889151\pi$
$337$		−	230.000i		−	0.682493i	0.939974	−	0.341246i	$-0.110849\pi$
$338$	−151.000	+	151.000i	−0.446746	+	0.446746i
$339$	−28.0000	+	28.0000i	−0.0825959	+	0.0825959i
$340$	276.000			0.811765
$341$	72.0000	−	72.0000i	0.211144	−	0.211144i
$342$	−140.000			−0.409357
$343$	328.000			0.956268
$344$			168.000i			0.488372i
$345$	−240.000			−0.695652
$346$	88.0000	−	88.0000i	0.254335	−	0.254335i
$347$	362.000	+	362.000i	1.04323	+	1.04323i	0.999022	+	0.0442052i	$0.0140755\pi$
$347$	362.000	+	362.000i	1.04323	+	1.04323i	0.0442052	+	0.999022i	$0.485924\pi$
$348$	152.000	+	152.000i	0.436782	+	0.436782i
$349$	−48.0000			−0.137536			−0.0687679	−	0.997633i	$-0.521907\pi$
$349$	−48.0000			−0.137536			−0.0687679	+	0.997633i	$0.521907\pi$
$350$	28.0000	−	28.0000i	0.0800000	−	0.0800000i
$351$	24.0000	+	24.0000i	0.0683761	+	0.0683761i
$352$	16.0000	−	16.0000i	0.0454545	−	0.0454545i
$353$	343.000	+	343.000i	0.971671	+	0.971671i	0.999610	−	0.0279383i	$-0.00889418\pi$
$353$	343.000	+	343.000i	0.971671	+	0.971671i	−0.0279383	+	0.999610i	$0.508894\pi$
$354$		−	432.000i		−	1.22034i
$355$	372.000	−	372.000i	1.04789	−	1.04789i
$356$	−34.0000	+	34.0000i	−0.0955056	+	0.0955056i
$357$	−368.000	−	368.000i	−1.03081	−	1.03081i
$358$		−	332.000i		−	0.927374i
$359$	−404.000			−1.12535			−0.562674	−	0.826679i	$-0.690227\pi$
$359$	−404.000			−1.12535			−0.562674	+	0.826679i	$0.690227\pi$
$360$		−	84.0000i		−	0.233333i
$361$			161.000i			0.445983i
$362$	304.000	+	304.000i	0.839779	+	0.839779i
$363$			420.000i			1.15702i
$364$	−24.0000	−	24.0000i	−0.0659341	−	0.0659341i
$365$	−30.0000	−	30.0000i	−0.0821918	−	0.0821918i
$366$	24.0000			0.0655738
$367$	492.000			1.34060			0.670300	−	0.742090i	$-0.266166\pi$
$367$	492.000			1.34060			0.670300	+	0.742090i	$0.266166\pi$
$368$	40.0000	−	40.0000i	0.108696	−	0.108696i
$369$		−	518.000i		−	1.40379i
$370$		−	222.000i		−	0.600000i
$371$	320.000			0.862534
$372$	144.000	+	144.000i	0.387097	+	0.387097i
$373$		−	488.000i		−	1.30831i	−0.756360	−	0.654155i	$-0.773024\pi$
$373$		−	488.000i		−	1.30831i	0.756360	−	0.654155i	$-0.226976\pi$
$374$			184.000i			0.491979i
$375$	−384.000	+	384.000i	−1.02400	+	1.02400i
$376$	88.0000	−	88.0000i	0.234043	−	0.234043i
$377$	−114.000			−0.302387
$378$	32.0000	−	32.0000i	0.0846561	−	0.0846561i
$379$	−440.000			−1.16095			−0.580475	−	0.814278i	$-0.697133\pi$
$379$	−440.000			−1.16095			−0.580475	+	0.814278i	$0.697133\pi$
$380$	120.000			0.315789
$381$			304.000i			0.797900i
$382$	372.000			0.973822
$383$	−450.000	+	450.000i	−1.17493	+	1.17493i	−0.193917	+	0.981018i	$0.562119\pi$
$383$	−450.000	+	450.000i	−1.17493	+	1.17493i	−0.981018	+	0.193917i	$0.937881\pi$
$384$	32.0000	+	32.0000i	0.0833333	+	0.0833333i
$385$	−48.0000	−	48.0000i	−0.124675	−	0.124675i
$386$	−18.0000			−0.0466321
$387$	−294.000	+	294.000i	−0.759690	+	0.759690i
$388$	258.000	+	258.000i	0.664948	+	0.664948i
$389$	21.0000	−	21.0000i	0.0539846	−	0.0539846i	−0.679599	−	0.733584i	$-0.737846\pi$
$389$	21.0000	−	21.0000i	0.0539846	−	0.0539846i	0.733584	+	0.679599i	$0.237846\pi$
$390$	72.0000	+	72.0000i	0.184615	+	0.184615i
$391$			460.000i			1.17647i
$392$	66.0000	−	66.0000i	0.168367	−	0.168367i
$393$	−280.000	+	280.000i	−0.712468	+	0.712468i
$394$	34.0000	+	34.0000i	0.0862944	+	0.0862944i
$395$		−	84.0000i		−	0.212658i
$396$	56.0000			0.141414
$397$		−	646.000i		−	1.62720i	−0.581422	−	0.813602i	$-0.697504\pi$
$397$		−	646.000i		−	1.62720i	0.581422	−	0.813602i	$-0.302496\pi$
$398$			92.0000i			0.231156i
$399$	−160.000	−	160.000i	−0.401003	−	0.401003i
$400$		−	28.0000i		−	0.0700000i
$401$	273.000	+	273.000i	0.680798	+	0.680798i	0.960180	−	0.279382i	$-0.0901296\pi$
$401$	273.000	+	273.000i	0.680798	+	0.680798i	−0.279382	+	0.960180i	$0.590130\pi$
$402$	48.0000	+	48.0000i	0.119403	+	0.119403i
$403$	−108.000			−0.267990
$404$	−236.000			−0.584158
$405$	−285.000	+	285.000i	−0.703704	+	0.703704i
$406$			152.000i			0.374384i
$407$	148.000			0.363636
$408$	−368.000			−0.901961
$409$	39.0000	+	39.0000i	0.0953545	+	0.0953545i	0.753175	−	0.657820i	$-0.228521\pi$
$409$	39.0000	+	39.0000i	0.0953545	+	0.0953545i	−0.657820	+	0.753175i	$0.728521\pi$
$410$			444.000i			1.08293i
$411$			864.000i			2.10219i
$412$	84.0000	−	84.0000i	0.203883	−	0.203883i
$413$	216.000	−	216.000i	0.523002	−	0.523002i
$414$	140.000			0.338164
$415$	−192.000	+	192.000i	−0.462651	+	0.462651i
$416$	−24.0000			−0.0576923
$417$	−720.000			−1.72662
$418$			80.0000i			0.191388i
$419$	464.000			1.10740			0.553699	−	0.832717i	$-0.313216\pi$
$419$	464.000			1.10740			0.553699	+	0.832717i	$0.313216\pi$
$420$	96.0000	−	96.0000i	0.228571	−	0.228571i
$421$	−469.000	−	469.000i	−1.11401	−	1.11401i	−0.992602	−	0.121412i	$-0.961258\pi$
$421$	−469.000	−	469.000i	−1.11401	−	1.11401i	−0.121412	−	0.992602i	$-0.538742\pi$
$422$	−208.000	−	208.000i	−0.492891	−	0.492891i
$423$	308.000			0.728132
$424$	160.000	−	160.000i	0.377358	−	0.377358i
$425$	161.000	+	161.000i	0.378824	+	0.378824i
$426$	−496.000	+	496.000i	−1.16432	+	1.16432i
$427$	12.0000	+	12.0000i	0.0281030	+	0.0281030i
$428$		−	48.0000i		−	0.112150i
$429$	−48.0000	+	48.0000i	−0.111888	+	0.111888i
$430$	252.000	−	252.000i	0.586047	−	0.586047i
$431$	450.000	+	450.000i	1.04408	+	1.04408i	0.998982	+	0.0451011i	$0.0143610\pi$
$431$	450.000	+	450.000i	1.04408	+	1.04408i	0.0451011	+	0.998982i	$0.485639\pi$
$432$		−	32.0000i		−	0.0740741i
$433$	200.000			0.461894			0.230947	−	0.972966i	$-0.425818\pi$
$433$	200.000			0.461894			0.230947	+	0.972966i	$0.425818\pi$
$434$			144.000i			0.331797i
$435$		−	456.000i		−	1.04828i
$436$	−182.000	−	182.000i	−0.417431	−	0.417431i
$437$			200.000i			0.457666i
$438$	40.0000	+	40.0000i	0.0913242	+	0.0913242i
$439$	246.000	+	246.000i	0.560364	+	0.560364i	0.929411	−	0.369046i	$-0.120316\pi$
$439$	246.000	+	246.000i	0.560364	+	0.560364i	−0.369046	+	0.929411i	$0.620316\pi$
$440$	−48.0000			−0.109091
$441$	231.000			0.523810
$442$	138.000	−	138.000i	0.312217	−	0.312217i
$443$		−	668.000i		−	1.50790i	−0.656931	−	0.753950i	$-0.728146\pi$
$443$		−	668.000i		−	1.50790i	0.656931	−	0.753950i	$-0.271854\pi$
$444$			296.000i			0.666667i
$445$	102.000			0.229213
$446$	−124.000	−	124.000i	−0.278027	−	0.278027i
$447$		−	136.000i		−	0.304251i
$448$			32.0000i			0.0714286i
$449$	199.000	−	199.000i	0.443207	−	0.443207i	−0.449881	−	0.893088i	$-0.648534\pi$
$449$	199.000	−	199.000i	0.443207	−	0.443207i	0.893088	+	0.449881i	$0.148534\pi$
$450$	49.0000	−	49.0000i	0.108889	−	0.108889i
$451$	−296.000			−0.656319
$452$	−14.0000	+	14.0000i	−0.0309735	+	0.0309735i
$453$	288.000			0.635762
$454$	−180.000			−0.396476
$455$			72.0000i			0.158242i
$456$	−160.000			−0.350877
$457$	−255.000	+	255.000i	−0.557987	+	0.557987i	−0.928734	−	0.370747i	$-0.879102\pi$
$457$	−255.000	+	255.000i	−0.557987	+	0.557987i	0.370747	+	0.928734i	$0.379102\pi$
$458$	−2.00000	−	2.00000i	−0.00436681	−	0.00436681i
$459$	184.000	+	184.000i	0.400871	+	0.400871i
$460$	−120.000			−0.260870
$461$	−555.000	+	555.000i	−1.20390	+	1.20390i	−0.230935	+	0.972969i	$0.574179\pi$
$461$	−555.000	+	555.000i	−1.20390	+	1.20390i	−0.972969	+	0.230935i	$0.925821\pi$
$462$	64.0000	+	64.0000i	0.138528	+	0.138528i
$463$	554.000	−	554.000i	1.19654	−	1.19654i	0.221350	−	0.975194i	$-0.428954\pi$
$463$	554.000	−	554.000i	1.19654	−	1.19654i	0.975194	−	0.221350i	$-0.0710463\pi$
$464$	76.0000	+	76.0000i	0.163793	+	0.163793i
$465$		−	432.000i		−	0.929032i
$466$	−42.0000	+	42.0000i	−0.0901288	+	0.0901288i
$467$	158.000	−	158.000i	0.338330	−	0.338330i	−0.517409	−	0.855738i	$-0.673103\pi$
$467$	158.000	−	158.000i	0.338330	−	0.338330i	0.855738	+	0.517409i	$0.173103\pi$
$468$	−42.0000	−	42.0000i	−0.0897436	−	0.0897436i
$469$			48.0000i			0.102345i
$470$	−264.000			−0.561702
$471$		−	56.0000i		−	0.118896i
$472$		−	216.000i		−	0.457627i
$473$	168.000	+	168.000i	0.355180	+	0.355180i
$474$			112.000i			0.236287i
$475$	70.0000	+	70.0000i	0.147368	+	0.147368i
$476$	−184.000	−	184.000i	−0.386555	−	0.386555i
$477$	560.000			1.17400
$478$	44.0000			0.0920502
$479$	290.000	−	290.000i	0.605428	−	0.605428i	−0.336320	−	0.941748i	$-0.609182\pi$
$479$	290.000	−	290.000i	0.605428	−	0.605428i	0.941748	+	0.336320i	$0.109182\pi$
$480$		−	96.0000i		−	0.200000i
$481$	−111.000	−	111.000i	−0.230769	−	0.230769i
$482$	−350.000			−0.726141
$483$	160.000	+	160.000i	0.331263	+	0.331263i
$484$			210.000i			0.433884i
$485$		−	774.000i		−	1.59588i
$486$	308.000	−	308.000i	0.633745	−	0.633745i
$487$	266.000	−	266.000i	0.546201	−	0.546201i	−0.379139	−	0.925340i	$-0.623780\pi$
$487$	266.000	−	266.000i	0.546201	−	0.546201i	0.925340	+	0.379139i	$0.123780\pi$
$488$	12.0000			0.0245902
$489$	264.000	−	264.000i	0.539877	−	0.539877i
$490$	−198.000			−0.404082
$491$	312.000			0.635438			0.317719	−	0.948185i	$-0.397083\pi$
$491$	312.000			0.635438			0.317719	+	0.948185i	$0.397083\pi$
$492$		−	592.000i		−	1.20325i
$493$	−874.000			−1.77282
$494$	60.0000	−	60.0000i	0.121457	−	0.121457i
$495$	−84.0000	−	84.0000i	−0.169697	−	0.169697i
$496$	72.0000	+	72.0000i	0.145161	+	0.145161i
$497$	−496.000			−0.997988
$498$	256.000	−	256.000i	0.514056	−	0.514056i
$499$	−210.000	−	210.000i	−0.420842	−	0.420842i	0.464652	−	0.885493i	$-0.346180\pi$
$499$	−210.000	−	210.000i	−0.420842	−	0.420842i	−0.885493	+	0.464652i	$0.846180\pi$
$500$	−192.000	+	192.000i	−0.384000	+	0.384000i
$501$	−920.000	−	920.000i	−1.83633	−	1.83633i
$502$		−	396.000i		−	0.788845i
$503$	298.000	−	298.000i	0.592445	−	0.592445i	−0.345846	−	0.938291i	$-0.612408\pi$
$503$	298.000	−	298.000i	0.592445	−	0.592445i	0.938291	+	0.345846i	$0.112408\pi$
$504$	−56.0000	+	56.0000i	−0.111111	+	0.111111i
$505$	354.000	+	354.000i	0.700990	+	0.700990i
$506$		−	80.0000i		−	0.158103i
$507$	−604.000			−1.19132
$508$			152.000i			0.299213i
$509$			808.000i			1.58743i	0.608292	+	0.793713i	$0.291855\pi$
$509$			808.000i			1.58743i	−0.608292	+	0.793713i	$0.708145\pi$
$510$	552.000	+	552.000i	1.08235	+	1.08235i
$511$			40.0000i			0.0782779i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	80.0000	+	80.0000i	0.155945	+	0.155945i
$514$	−318.000			−0.618677
$515$	−252.000			−0.489320
$516$	−336.000	+	336.000i	−0.651163	+	0.651163i
$517$		−	176.000i		−	0.340426i
$518$	−148.000	+	148.000i	−0.285714	+	0.285714i
$519$	352.000			0.678227
$520$	36.0000	+	36.0000i	0.0692308	+	0.0692308i
$521$		−	170.000i		−	0.326296i	−0.986602	−	0.163148i	$-0.947835\pi$
$521$		−	170.000i		−	0.326296i	0.986602	−	0.163148i	$-0.0521647\pi$
$522$			266.000i			0.509579i
$523$	654.000	−	654.000i	1.25048	−	1.25048i	0.294972	−	0.955506i	$-0.404690\pi$
$523$	654.000	−	654.000i	1.25048	−	1.25048i	0.955506	−	0.294972i	$-0.0953104\pi$
$524$	−140.000	+	140.000i	−0.267176	+	0.267176i
$525$	112.000			0.213333
$526$	88.0000	−	88.0000i	0.167300	−	0.167300i
$527$	−828.000			−1.57116
$528$	64.0000			0.121212
$529$			329.000i			0.621928i
$530$	−480.000			−0.905660
$531$	378.000	−	378.000i	0.711864	−	0.711864i
$532$	−80.0000	−	80.0000i	−0.150376	−	0.150376i
$533$	222.000	+	222.000i	0.416510	+	0.416510i
$534$	−136.000			−0.254682
$535$	−72.0000	+	72.0000i	−0.134579	+	0.134579i
$536$	24.0000	+	24.0000i	0.0447761	+	0.0447761i
$537$	664.000	−	664.000i	1.23650	−	1.23650i
$538$	178.000	+	178.000i	0.330855	+	0.330855i
$539$		−	132.000i		−	0.244898i
$540$	−48.0000	+	48.0000i	−0.0888889	+	0.0888889i
$541$	147.000	−	147.000i	0.271719	−	0.271719i	−0.558073	−	0.829792i	$-0.688459\pi$
$541$	147.000	−	147.000i	0.271719	−	0.271719i	0.829792	+	0.558073i	$0.188459\pi$
$542$	404.000	+	404.000i	0.745387	+	0.745387i
$543$			1216.00i			2.23941i
$544$	−184.000			−0.338235
$545$			546.000i			1.00183i
$546$		−	96.0000i		−	0.175824i
$547$	−294.000	−	294.000i	−0.537477	−	0.537477i	0.385310	−	0.922787i	$-0.374095\pi$
$547$	−294.000	−	294.000i	−0.537477	−	0.537477i	−0.922787	+	0.385310i	$0.874095\pi$
$548$			432.000i			0.788321i
$549$	21.0000	+	21.0000i	0.0382514	+	0.0382514i
$550$	−28.0000	−	28.0000i	−0.0509091	−	0.0509091i
$551$	−380.000			−0.689655
$552$	160.000			0.289855
$553$	−56.0000	+	56.0000i	−0.101266	+	0.101266i
$554$		−	294.000i		−	0.530686i
$555$	444.000	−	444.000i	0.800000	−	0.800000i
$556$	−360.000			−0.647482
$557$	−179.000	−	179.000i	−0.321364	−	0.321364i	0.527926	−	0.849290i	$-0.322970\pi$
$557$	−179.000	−	179.000i	−0.321364	−	0.321364i	−0.849290	+	0.527926i	$0.822970\pi$
$558$			252.000i			0.451613i
$559$		−	252.000i		−	0.450805i
$560$	48.0000	−	48.0000i	0.0857143	−	0.0857143i
$561$	−368.000	+	368.000i	−0.655971	+	0.655971i
$562$	270.000			0.480427
$563$	282.000	−	282.000i	0.500888	−	0.500888i	−0.410826	−	0.911714i	$-0.634760\pi$
$563$	282.000	−	282.000i	0.500888	−	0.500888i	0.911714	+	0.410826i	$0.134760\pi$
$564$	352.000			0.624113
$565$	42.0000			0.0743363
$566$		−	516.000i		−	0.911661i
$567$	380.000			0.670194
$568$	−248.000	+	248.000i	−0.436620	+	0.436620i
$569$	375.000	+	375.000i	0.659051	+	0.659051i	0.955156	−	0.296105i	$-0.0956877\pi$
$569$	375.000	+	375.000i	0.659051	+	0.659051i	−0.296105	+	0.955156i	$0.595688\pi$
$570$	240.000	+	240.000i	0.421053	+	0.421053i
$571$	−184.000			−0.322242			−0.161121	−	0.986935i	$-0.551511\pi$
$571$	−184.000			−0.322242			−0.161121	+	0.986935i	$0.551511\pi$
$572$	−24.0000	+	24.0000i	−0.0419580	+	0.0419580i
$573$	744.000	+	744.000i	1.29843	+	1.29843i
$574$	296.000	−	296.000i	0.515679	−	0.515679i
$575$	−70.0000	−	70.0000i	−0.121739	−	0.121739i
$576$			56.0000i			0.0972222i
$577$	−623.000	+	623.000i	−1.07972	+	1.07972i	−0.0831889	+	0.996534i	$0.526510\pi$
$577$	−623.000	+	623.000i	−1.07972	+	1.07972i	−0.996534	+	0.0831889i	$0.973490\pi$
$578$	769.000	−	769.000i	1.33045	−	1.33045i
$579$	−36.0000	−	36.0000i	−0.0621762	−	0.0621762i
$580$		−	228.000i		−	0.393103i
$581$	256.000			0.440620
$582$			1032.00i			1.77320i
$583$		−	320.000i		−	0.548885i
$584$	20.0000	+	20.0000i	0.0342466	+	0.0342466i
$585$			126.000i			0.215385i
$586$		0			0
$587$	−382.000	−	382.000i	−0.650767	−	0.650767i	0.302411	−	0.953178i	$-0.402208\pi$
$587$	−382.000	−	382.000i	−0.650767	−	0.650767i	−0.953178	+	0.302411i	$0.902208\pi$
$588$	264.000			0.448980
$589$	−360.000			−0.611205
$590$	−324.000	+	324.000i	−0.549153	+	0.549153i
$591$			136.000i			0.230118i
$592$			148.000i			0.250000i
$593$	734.000			1.23777			0.618887	−	0.785480i	$-0.287584\pi$
$593$	734.000			1.23777			0.618887	+	0.785480i	$0.287584\pi$
$594$	−32.0000	−	32.0000i	−0.0538721	−	0.0538721i
$595$			552.000i			0.927731i
$596$		−	68.0000i		−	0.114094i
$597$	−184.000	+	184.000i	−0.308208	+	0.308208i
$598$	−60.0000	+	60.0000i	−0.100334	+	0.100334i
$599$	−1004.00			−1.67613			−0.838063	−	0.545573i	$-0.816312\pi$
$599$	−1004.00			−1.67613			−0.838063	+	0.545573i	$0.816312\pi$
$600$	56.0000	−	56.0000i	0.0933333	−	0.0933333i
$601$	306.000			0.509151			0.254576	−	0.967053i	$-0.418064\pi$
$601$	306.000			0.509151			0.254576	+	0.967053i	$0.418064\pi$
$602$	−336.000			−0.558140
$603$			84.0000i			0.139303i
$604$	144.000			0.238411
$605$	315.000	−	315.000i	0.520661	−	0.520661i
$606$	−472.000	−	472.000i	−0.778878	−	0.778878i
$607$	298.000	+	298.000i	0.490939	+	0.490939i	0.908602	−	0.417663i	$-0.137151\pi$
$607$	298.000	+	298.000i	0.490939	+	0.490939i	−0.417663	+	0.908602i	$0.637151\pi$
$608$	−80.0000			−0.131579
$609$	−304.000	+	304.000i	−0.499179	+	0.499179i
$610$	−18.0000	−	18.0000i	−0.0295082	−	0.0295082i
$611$	−132.000	+	132.000i	−0.216039	+	0.216039i
$612$	−322.000	−	322.000i	−0.526144	−	0.526144i
$613$			470.000i			0.766721i	0.923599	+	0.383361i	$0.125233\pi$
$613$			470.000i			0.766721i	−0.923599	+	0.383361i	$0.874767\pi$
$614$	−364.000	+	364.000i	−0.592834	+	0.592834i
$615$	−888.000	+	888.000i	−1.44390	+	1.44390i
$616$	32.0000	+	32.0000i	0.0519481	+	0.0519481i
$617$			304.000i			0.492707i	0.969180	+	0.246353i	$0.0792324\pi$
$617$			304.000i			0.492707i	−0.969180	+	0.246353i	$0.920768\pi$
$618$	336.000			0.543689
$619$			956.000i			1.54443i	0.635363	+	0.772213i	$0.280850\pi$
$619$			956.000i			1.54443i	−0.635363	+	0.772213i	$0.719150\pi$
$620$		−	216.000i		−	0.348387i
$621$	−80.0000	−	80.0000i	−0.128824	−	0.128824i
$622$		−	476.000i		−	0.765273i
$623$	−68.0000	−	68.0000i	−0.109149	−	0.109149i
$624$	−48.0000	−	48.0000i	−0.0769231	−	0.0769231i
$625$	401.000			0.641600
$626$	174.000			0.277955
$627$	−160.000	+	160.000i	−0.255183	+	0.255183i
$628$		−	28.0000i		−	0.0445860i
$629$	−851.000	−	851.000i	−1.35294	−	1.35294i
$630$	168.000			0.266667
$631$	−362.000	−	362.000i	−0.573693	−	0.573693i	0.359466	−	0.933158i	$-0.382959\pi$
$631$	−362.000	−	362.000i	−0.573693	−	0.573693i	−0.933158	+	0.359466i	$0.882959\pi$
$632$			56.0000i			0.0886076i
$633$		−	832.000i		−	1.31438i
$634$	−264.000	+	264.000i	−0.416404	+	0.416404i
$635$	228.000	−	228.000i	0.359055	−	0.359055i
$636$	640.000			1.00629
$637$	−99.0000	+	99.0000i	−0.155416	+	0.155416i
$638$	152.000			0.238245
$639$	−868.000			−1.35837
$640$		−	48.0000i		−	0.0750000i
$641$	−398.000			−0.620905			−0.310452	−	0.950589i	$-0.600481\pi$
$641$	−398.000			−0.620905			−0.310452	+	0.950589i	$0.600481\pi$
$642$	96.0000	−	96.0000i	0.149533	−	0.149533i
$643$	218.000	+	218.000i	0.339036	+	0.339036i	0.856004	−	0.516969i	$-0.172940\pi$
$643$	218.000	+	218.000i	0.339036	+	0.339036i	−0.516969	+	0.856004i	$0.672940\pi$
$644$	80.0000	+	80.0000i	0.124224	+	0.124224i
$645$	1008.00			1.56279
$646$	460.000	−	460.000i	0.712074	−	0.712074i
$647$	−358.000	−	358.000i	−0.553323	−	0.553323i	0.374075	−	0.927398i	$-0.377960\pi$
$647$	−358.000	−	358.000i	−0.553323	−	0.553323i	−0.927398	+	0.374075i	$0.877960\pi$
$648$	190.000	−	190.000i	0.293210	−	0.293210i
$649$	−216.000	−	216.000i	−0.332820	−	0.332820i
$650$			42.0000i			0.0646154i
$651$	−288.000	+	288.000i	−0.442396	+	0.442396i
$652$	132.000	−	132.000i	0.202454	−	0.202454i
$653$	555.000	+	555.000i	0.849923	+	0.849923i	0.990123	−	0.140200i	$-0.0447745\pi$
$653$	555.000	+	555.000i	0.849923	+	0.849923i	−0.140200	+	0.990123i	$0.544774\pi$
$654$		−	728.000i		−	1.11315i
$655$	420.000			0.641221
$656$		−	296.000i		−	0.451220i
$657$			70.0000i			0.106545i
$658$	176.000	+	176.000i	0.267477	+	0.267477i
$659$			788.000i			1.19575i	0.801589	+	0.597876i	$0.203988\pi$
$659$			788.000i			1.19575i	−0.801589	+	0.597876i	$0.796012\pi$
$660$	−96.0000	−	96.0000i	−0.145455	−	0.145455i
$661$	−661.000	−	661.000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$661$	−661.000	−	661.000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$662$	−652.000			−0.984894
$663$	552.000			0.832579
$664$	128.000	−	128.000i	0.192771	−	0.192771i
$665$			240.000i			0.360902i
$666$	−259.000	+	259.000i	−0.388889	+	0.388889i
$667$	380.000			0.569715
$668$	−460.000	−	460.000i	−0.688623	−	0.688623i
$669$		−	496.000i		−	0.741405i
$670$		−	72.0000i		−	0.107463i
$671$	12.0000	−	12.0000i	0.0178838	−	0.0178838i
$672$	−64.0000	+	64.0000i	−0.0952381	+	0.0952381i
$673$	50.0000			0.0742942			0.0371471	−	0.999310i	$-0.488173\pi$
$673$	50.0000			0.0742942			0.0371471	+	0.999310i	$0.488173\pi$
$674$	230.000	−	230.000i	0.341246	−	0.341246i
$675$	−56.0000			−0.0829630
$676$	−302.000			−0.446746
$677$		−	296.000i		−	0.437223i	−0.975812	−	0.218612i	$-0.929847\pi$
$677$		−	296.000i		−	0.437223i	0.975812	−	0.218612i	$-0.0701527\pi$
$678$	−56.0000			−0.0825959
$679$	−516.000	+	516.000i	−0.759941	+	0.759941i
$680$	276.000	+	276.000i	0.405882	+	0.405882i
$681$	−360.000	−	360.000i	−0.528634	−	0.528634i
$682$	144.000			0.211144
$683$	6.00000	−	6.00000i	0.00878477	−	0.00878477i	−0.702701	−	0.711486i	$-0.748023\pi$
$683$	6.00000	−	6.00000i	0.00878477	−	0.00878477i	0.711486	+	0.702701i	$0.248023\pi$
$684$	−140.000	−	140.000i	−0.204678	−	0.204678i
$685$	648.000	−	648.000i	0.945985	−	0.945985i
$686$	328.000	+	328.000i	0.478134	+	0.478134i
$687$		−	8.00000i		−	0.0116448i
$688$	−168.000	+	168.000i	−0.244186	+	0.244186i
$689$	−240.000	+	240.000i	−0.348331	+	0.348331i
$690$	−240.000	−	240.000i	−0.347826	−	0.347826i
$691$		−	708.000i		−	1.02460i	−0.858806	−	0.512301i	$-0.828793\pi$
$691$		−	708.000i		−	1.02460i	0.858806	−	0.512301i	$-0.171207\pi$
$692$	176.000			0.254335
$693$			112.000i			0.161616i
$694$			724.000i			1.04323i
$695$	540.000	+	540.000i	0.776978	+	0.776978i
$696$			304.000i			0.436782i
$697$	1702.00	+	1702.00i	2.44189	+	2.44189i
$698$	−48.0000	−	48.0000i	−0.0687679	−	0.0687679i
$699$	−168.000			−0.240343
$700$	56.0000			0.0800000
$701$	291.000	−	291.000i	0.415121	−	0.415121i	−0.468397	−	0.883518i	$-0.655168\pi$
$701$	291.000	−	291.000i	0.415121	−	0.415121i	0.883518	+	0.468397i	$0.155168\pi$
$702$			48.0000i			0.0683761i
$703$	−370.000	−	370.000i	−0.526316	−	0.526316i
$704$	32.0000			0.0454545
$705$	−528.000	−	528.000i	−0.748936	−	0.748936i
$706$			686.000i			0.971671i
$707$		−	472.000i		−	0.667610i
$708$	432.000	−	432.000i	0.610169	−	0.610169i
$709$	−77.0000	+	77.0000i	−0.108604	+	0.108604i	−0.759320	−	0.650717i	$-0.774469\pi$
$709$	−77.0000	+	77.0000i	−0.108604	+	0.108604i	0.650717	+	0.759320i	$0.274469\pi$
$710$	744.000			1.04789
$711$	−98.0000	+	98.0000i	−0.137834	+	0.137834i
$712$	−68.0000			−0.0955056
$713$	360.000			0.504909
$714$		−	736.000i		−	1.03081i
$715$	72.0000			0.100699
$716$	332.000	−	332.000i	0.463687	−	0.463687i
$717$	88.0000	+	88.0000i	0.122734	+	0.122734i
$718$	−404.000	−	404.000i	−0.562674	−	0.562674i
$719$	−412.000			−0.573018			−0.286509	−	0.958078i	$-0.592495\pi$
$719$	−412.000			−0.573018			−0.286509	+	0.958078i	$0.592495\pi$
$720$	84.0000	−	84.0000i	0.116667	−	0.116667i
$721$	168.000	+	168.000i	0.233010	+	0.233010i
$722$	−161.000	+	161.000i	−0.222992	+	0.222992i
$723$	−700.000	−	700.000i	−0.968188	−	0.968188i
$724$			608.000i			0.839779i
$725$	133.000	−	133.000i	0.183448	−	0.183448i
$726$	−420.000	+	420.000i	−0.578512	+	0.578512i
$727$	−262.000	−	262.000i	−0.360385	−	0.360385i	0.503570	−	0.863955i	$-0.332020\pi$
$727$	−262.000	−	262.000i	−0.360385	−	0.360385i	−0.863955	+	0.503570i	$0.832020\pi$
$728$		−	48.0000i		−	0.0659341i
$729$	377.000			0.517147
$730$		−	60.0000i		−	0.0821918i
$731$		−	1932.00i		−	2.64295i
$732$	24.0000	+	24.0000i	0.0327869	+	0.0327869i
$733$			682.000i			0.930423i	0.885200	+	0.465211i	$0.154022\pi$
$733$			682.000i			0.930423i	−0.885200	+	0.465211i	$0.845978\pi$
$734$	492.000	+	492.000i	0.670300	+	0.670300i
$735$	−396.000	−	396.000i	−0.538776	−	0.538776i
$736$	80.0000			0.108696
$737$	48.0000			0.0651289
$738$	518.000	−	518.000i	0.701897	−	0.701897i
$739$			100.000i			0.135318i	0.997709	+	0.0676590i	$0.0215530\pi$
$739$			100.000i			0.135318i	−0.997709	+	0.0676590i	$0.978447\pi$
$740$	222.000	−	222.000i	0.300000	−	0.300000i
$741$	240.000			0.323887
$742$	320.000	+	320.000i	0.431267	+	0.431267i
$743$		−	800.000i		−	1.07672i	−0.842716	−	0.538358i	$-0.819045\pi$
$743$		−	800.000i		−	1.07672i	0.842716	−	0.538358i	$-0.180955\pi$
$744$			288.000i			0.387097i
$745$	−102.000	+	102.000i	−0.136913	+	0.136913i
$746$	488.000	−	488.000i	0.654155	−	0.654155i
$747$	448.000			0.599732
$748$	−184.000	+	184.000i	−0.245989	+	0.245989i
$749$	96.0000			0.128171
$750$	−768.000			−1.02400
$751$			536.000i			0.713715i	0.934159	+	0.356858i	$0.116152\pi$
$751$			536.000i			0.713715i	−0.934159	+	0.356858i	$0.883848\pi$
$752$	176.000			0.234043
$753$	792.000	−	792.000i	1.05179	−	1.05179i
$754$	−114.000	−	114.000i	−0.151194	−	0.151194i
$755$	−216.000	−	216.000i	−0.286093	−	0.286093i
$756$	64.0000			0.0846561
$757$	−157.000	+	157.000i	−0.207398	+	0.207398i	−0.803160	−	0.595763i	$-0.796850\pi$
$757$	−157.000	+	157.000i	−0.207398	+	0.207398i	0.595763	+	0.803160i	$0.296850\pi$
$758$	−440.000	−	440.000i	−0.580475	−	0.580475i
$759$	160.000	−	160.000i	0.210804	−	0.210804i
$760$	120.000	+	120.000i	0.157895	+	0.157895i
$761$			272.000i			0.357424i	0.983901	+	0.178712i	$0.0571931\pi$
$761$			272.000i			0.357424i	−0.983901	+	0.178712i	$0.942807\pi$
$762$	−304.000	+	304.000i	−0.398950	+	0.398950i
$763$	364.000	−	364.000i	0.477064	−	0.477064i
$764$	372.000	+	372.000i	0.486911	+	0.486911i
$765$			966.000i			1.26275i
$766$	−900.000			−1.17493
$767$			324.000i			0.422425i
$768$			64.0000i			0.0833333i
$769$	−761.000	−	761.000i	−0.989597	−	0.989597i	0.0103496	−	0.999946i	$-0.496706\pi$
$769$	−761.000	−	761.000i	−0.989597	−	0.989597i	−0.999946	+	0.0103496i	$0.996706\pi$
$770$		−	96.0000i		−	0.124675i
$771$	−636.000	−	636.000i	−0.824903	−	0.824903i
$772$	−18.0000	−	18.0000i	−0.0233161	−	0.0233161i
$773$	−1282.00			−1.65847			−0.829237	−	0.558898i	$-0.811225\pi$
$773$	−1282.00			−1.65847			−0.829237	+	0.558898i	$0.811225\pi$
$774$	−588.000			−0.759690
$775$	126.000	−	126.000i	0.162581	−	0.162581i
$776$			516.000i			0.664948i
$777$	−592.000			−0.761905
$778$	42.0000			0.0539846
$779$	740.000	+	740.000i	0.949936	+	0.949936i
$780$			144.000i			0.184615i
$781$			496.000i			0.635083i
$782$	−460.000	+	460.000i	−0.588235	+	0.588235i
$783$	152.000	−	152.000i	0.194125	−	0.194125i
$784$	132.000			0.168367
$785$	−42.0000	+	42.0000i	−0.0535032	+	0.0535032i
$786$	−560.000			−0.712468
$787$	−376.000			−0.477764			−0.238882	−	0.971049i	$-0.576781\pi$
$787$	−376.000			−0.477764			−0.238882	+	0.971049i	$0.576781\pi$
$788$			68.0000i			0.0862944i
$789$	352.000			0.446134
$790$	84.0000	−	84.0000i	0.106329	−	0.106329i
$791$	−28.0000	−	28.0000i	−0.0353982	−	0.0353982i
$792$	56.0000	+	56.0000i	0.0707071	+	0.0707071i
$793$	−18.0000			−0.0226986
$794$	646.000	−	646.000i	0.813602	−	0.813602i
$795$	−960.000	−	960.000i	−1.20755	−	1.20755i
$796$	−92.0000	+	92.0000i	−0.115578	+	0.115578i
$797$	−69.0000	−	69.0000i	−0.0865747	−	0.0865747i	0.662493	−	0.749068i	$-0.269498\pi$
$797$	−69.0000	−	69.0000i	−0.0865747	−	0.0865747i	−0.749068	+	0.662493i	$0.769498\pi$
$798$		−	320.000i		−	0.401003i
$799$	−1012.00	+	1012.00i	−1.26658	+	1.26658i
$800$	28.0000	−	28.0000i	0.0350000	−	0.0350000i
$801$	−119.000	−	119.000i	−0.148564	−	0.148564i
$802$			546.000i			0.680798i
$803$	40.0000			0.0498132
$804$			96.0000i			0.119403i
$805$		−	240.000i		−	0.298137i
$806$	−108.000	−	108.000i	−0.133995	−	0.133995i
$807$			712.000i			0.882280i
$808$	−236.000	−	236.000i	−0.292079	−	0.292079i
$809$	631.000	+	631.000i	0.779975	+	0.779975i	0.979826	−	0.199851i	$-0.0640458\pi$
$809$	631.000	+	631.000i	0.779975	+	0.779975i	−0.199851	+	0.979826i	$0.564046\pi$
$810$	−570.000			−0.703704
$811$	1184.00			1.45993			0.729963	−	0.683487i	$-0.239537\pi$
$811$	1184.00			1.45993			0.729963	+	0.683487i	$0.239537\pi$
$812$	−152.000	+	152.000i	−0.187192	+	0.187192i
$813$			1616.00i			1.98770i
$814$	148.000	+	148.000i	0.181818	+	0.181818i
$815$	−396.000			−0.485890
$816$	−368.000	−	368.000i	−0.450980	−	0.450980i
$817$		−	840.000i		−	1.02815i
$818$			78.0000i			0.0953545i
$819$	84.0000	−	84.0000i	0.102564	−	0.102564i
$820$	−444.000	+	444.000i	−0.541463	+	0.541463i
$821$	784.000			0.954933			0.477467	−	0.878650i	$-0.341555\pi$
$821$	784.000			0.954933			0.477467	+	0.878650i	$0.341555\pi$
$822$	−864.000	+	864.000i	−1.05109	+	1.05109i
$823$	1116.00			1.35601			0.678007	−	0.735055i	$-0.262844\pi$
$823$	1116.00			1.35601			0.678007	+	0.735055i	$0.262844\pi$
$824$	168.000			0.203883
$825$		−	112.000i		−	0.135758i
$826$	432.000			0.523002
$827$	382.000	−	382.000i	0.461911	−	0.461911i	−0.437371	−	0.899281i	$-0.644090\pi$
$827$	382.000	−	382.000i	0.461911	−	0.461911i	0.899281	+	0.437371i	$0.144090\pi$
$828$	140.000	+	140.000i	0.169082	+	0.169082i
$829$	603.000	+	603.000i	0.727382	+	0.727382i	0.970098	−	0.242715i	$-0.0780381\pi$
$829$	603.000	+	603.000i	0.727382	+	0.727382i	−0.242715	+	0.970098i	$0.578038\pi$
$830$	−384.000			−0.462651
$831$	588.000	−	588.000i	0.707581	−	0.707581i
$832$	−24.0000	−	24.0000i	−0.0288462	−	0.0288462i
$833$	−759.000	+	759.000i	−0.911164	+	0.911164i
$834$	−720.000	−	720.000i	−0.863309	−	0.863309i
$835$			1380.00i			1.65269i
$836$	−80.0000	+	80.0000i	−0.0956938	+	0.0956938i
$837$	144.000	−	144.000i	0.172043	−	0.172043i
$838$	464.000	+	464.000i	0.553699	+	0.553699i
$839$		−	48.0000i		−	0.0572110i	−0.999591	−	0.0286055i	$-0.990893\pi$
$839$		−	48.0000i		−	0.0572110i	0.999591	−	0.0286055i	$-0.00910665\pi$
$840$	192.000			0.228571
$841$		−	119.000i		−	0.141498i
$842$		−	938.000i		−	1.11401i
$843$	540.000	+	540.000i	0.640569	+	0.640569i
$844$		−	416.000i		−	0.492891i
$845$	453.000	+	453.000i	0.536095	+	0.536095i
$846$	308.000	+	308.000i	0.364066	+	0.364066i
$847$	−420.000			−0.495868
$848$	320.000			0.377358
$849$	1032.00	−	1032.00i	1.21555	−	1.21555i
$850$			322.000i			0.378824i
$851$	370.000	+	370.000i	0.434783	+	0.434783i
$852$	−992.000			−1.16432
$853$	−163.000	−	163.000i	−0.191090	−	0.191090i	0.605077	−	0.796167i	$-0.293142\pi$
$853$	−163.000	−	163.000i	−0.191090	−	0.191090i	−0.796167	+	0.605077i	$0.793142\pi$
$854$			24.0000i			0.0281030i
$855$			420.000i			0.491228i
$856$	48.0000	−	48.0000i	0.0560748	−	0.0560748i
$857$	−815.000	+	815.000i	−0.950992	+	0.950992i	−0.998854	−	0.0478621i	$-0.984759\pi$
$857$	−815.000	+	815.000i	−0.950992	+	0.950992i	0.0478621	+	0.998854i	$0.484759\pi$
$858$	−96.0000			−0.111888
$859$	962.000	−	962.000i	1.11991	−	1.11991i	0.128152	−	0.991754i	$-0.459095\pi$
$859$	962.000	−	962.000i	1.11991	−	1.11991i	0.991754	−	0.128152i	$-0.0409047\pi$
$860$	504.000			0.586047
$861$	1184.00			1.37515
$862$			900.000i			1.04408i
$863$	156.000			0.180765			0.0903824	−	0.995907i	$-0.471191\pi$
$863$	156.000			0.180765			0.0903824	+	0.995907i	$0.471191\pi$
$864$	32.0000	−	32.0000i	0.0370370	−	0.0370370i
$865$	−264.000	−	264.000i	−0.305202	−	0.305202i
$866$	200.000	+	200.000i	0.230947	+	0.230947i
$867$	3076.00			3.54787
$868$	−144.000	+	144.000i	−0.165899	+	0.165899i
$869$	56.0000	+	56.0000i	0.0644419	+	0.0644419i
$870$	456.000	−	456.000i	0.524138	−	0.524138i
$871$	−36.0000	−	36.0000i	−0.0413318	−	0.0413318i
$872$		−	364.000i		−	0.417431i
$873$	−903.000	+	903.000i	−1.03436	+	1.03436i
$874$	−200.000	+	200.000i	−0.228833	+	0.228833i
$875$	−384.000	−	384.000i	−0.438857	−	0.438857i
$876$			80.0000i			0.0913242i
$877$	210.000			0.239453			0.119726	−	0.992807i	$-0.461798\pi$
$877$	210.000			0.239453			0.119726	+	0.992807i	$0.461798\pi$
$878$			492.000i			0.560364i
$879$		0			0
$880$	−48.0000	−	48.0000i	−0.0545455	−	0.0545455i
$881$		−	720.000i		−	0.817253i	−0.912702	−	0.408627i	$-0.866008\pi$
$881$		−	720.000i		−	0.817253i	0.912702	−	0.408627i	$-0.133992\pi$
$882$	231.000	+	231.000i	0.261905	+	0.261905i
$883$	−294.000	−	294.000i	−0.332956	−	0.332956i	0.520752	−	0.853708i	$-0.325652\pi$
$883$	−294.000	−	294.000i	−0.332956	−	0.332956i	−0.853708	+	0.520752i	$0.825652\pi$
$884$	276.000			0.312217
$885$	−1296.00			−1.46441
$886$	668.000	−	668.000i	0.753950	−	0.753950i
$887$			904.000i			1.01917i	0.860422	+	0.509583i	$0.170200\pi$
$887$			904.000i			1.01917i	−0.860422	+	0.509583i	$0.829800\pi$
$888$	−296.000	+	296.000i	−0.333333	+	0.333333i
$889$	−304.000			−0.341957
$890$	102.000	+	102.000i	0.114607	+	0.114607i
$891$		−	380.000i		−	0.426487i
$892$		−	248.000i		−	0.278027i
$893$	−440.000	+	440.000i	−0.492721	+	0.492721i
$894$	136.000	−	136.000i	0.152125	−	0.152125i
$895$	−996.000			−1.11285
$896$	−32.0000	+	32.0000i	−0.0357143	+	0.0357143i
$897$	−240.000			−0.267559
$898$	398.000			0.443207
$899$			684.000i			0.760845i
$900$	98.0000			0.108889
$901$	−1840.00	+	1840.00i	−2.04218	+	2.04218i
$902$	−296.000	−	296.000i	−0.328160	−	0.328160i
$903$	−672.000	−	672.000i	−0.744186	−	0.744186i
$904$	−28.0000			−0.0309735
$905$	912.000	−	912.000i	1.00773	−	1.00773i
$906$	288.000	+	288.000i	0.317881	+	0.317881i
$907$	618.000	−	618.000i	0.681367	−	0.681367i	−0.278941	−	0.960308i	$-0.589983\pi$
$907$	618.000	−	618.000i	0.681367	−	0.681367i	0.960308	+	0.278941i	$0.0899834\pi$
$908$	−180.000	−	180.000i	−0.198238	−	0.198238i
$909$		−	826.000i		−	0.908691i
$910$	−72.0000	+	72.0000i	−0.0791209	+	0.0791209i
$911$	−882.000	+	882.000i	−0.968167	+	0.968167i	−0.999509	−	0.0313419i	$-0.990022\pi$
$911$	−882.000	+	882.000i	−0.968167	+	0.968167i	0.0313419	+	0.999509i	$0.490022\pi$
$912$	−160.000	−	160.000i	−0.175439	−	0.175439i
$913$		−	256.000i		−	0.280394i
$914$	−510.000			−0.557987
$915$		−	72.0000i		−	0.0786885i
$916$		−	4.00000i		−	0.00436681i
$917$	−280.000	−	280.000i	−0.305344	−	0.305344i
$918$			368.000i			0.400871i
$919$	−1218.00	−	1218.00i	−1.32535	−	1.32535i	−0.909374	−	0.415980i	$-0.863439\pi$
$919$	−1218.00	−	1218.00i	−1.32535	−	1.32535i	−0.415980	−	0.909374i	$-0.636561\pi$
$920$	−120.000	−	120.000i	−0.130435	−	0.130435i
$921$	−1456.00			−1.58089
$922$	−1110.00			−1.20390
$923$	372.000	−	372.000i	0.403034	−	0.403034i
$924$			128.000i			0.138528i
$925$	259.000			0.280000
$926$	1108.00			1.19654
$927$	294.000	+	294.000i	0.317152	+	0.317152i
$928$			152.000i			0.163793i
$929$		−	666.000i		−	0.716900i	−0.933549	−	0.358450i	$-0.883305\pi$
$929$		−	666.000i		−	0.716900i	0.933549	−	0.358450i	$-0.116695\pi$
$930$	432.000	−	432.000i	0.464516	−	0.464516i
$931$	−330.000	+	330.000i	−0.354458	+	0.354458i
$932$	−84.0000			−0.0901288
$933$	952.000	−	952.000i	1.02036	−	1.02036i
$934$	316.000			0.338330
$935$	552.000			0.590374
$936$		−	84.0000i		−	0.0897436i
$937$	−424.000			−0.452508			−0.226254	−	0.974068i	$-0.572648\pi$
$937$	−424.000			−0.452508			−0.226254	+	0.974068i	$0.572648\pi$
$938$	−48.0000	+	48.0000i	−0.0511727	+	0.0511727i
$939$	348.000	+	348.000i	0.370607	+	0.370607i
$940$	−264.000	−	264.000i	−0.280851	−	0.280851i
$941$	−912.000			−0.969182			−0.484591	−	0.874741i	$-0.661032\pi$
$941$	−912.000			−0.969182			−0.484591	+	0.874741i	$0.661032\pi$
$942$	56.0000	−	56.0000i	0.0594480	−	0.0594480i
$943$	−740.000	−	740.000i	−0.784730	−	0.784730i
$944$	216.000	−	216.000i	0.228814	−	0.228814i
$945$	−96.0000	−	96.0000i	−0.101587	−	0.101587i
$946$			336.000i			0.355180i
$947$	−134.000	+	134.000i	−0.141499	+	0.141499i	−0.774308	−	0.632809i	$-0.781902\pi$
$947$	−134.000	+	134.000i	−0.141499	+	0.141499i	0.632809	+	0.774308i	$0.281902\pi$
$948$	−112.000	+	112.000i	−0.118143	+	0.118143i
$949$	−30.0000	−	30.0000i	−0.0316122	−	0.0316122i
$950$			140.000i			0.147368i
$951$	−1056.00			−1.11041
$952$		−	368.000i		−	0.386555i
$953$		−	1264.00i		−	1.32634i	−0.748470	−	0.663169i	$-0.769211\pi$
$953$		−	1264.00i		−	1.32634i	0.748470	−	0.663169i	$-0.230789\pi$
$954$	560.000	+	560.000i	0.587002	+	0.587002i
$955$		−	1116.00i		−	1.16859i
$956$	44.0000	+	44.0000i	0.0460251	+	0.0460251i
$957$	304.000	+	304.000i	0.317659	+	0.317659i
$958$	580.000			0.605428
$959$	−864.000			−0.900938
$960$	96.0000	−	96.0000i	0.100000	−	0.100000i
$961$		−	313.000i		−	0.325702i
$962$		−	222.000i		−	0.230769i
$963$	168.000			0.174455
$964$	−350.000	−	350.000i	−0.363071	−	0.363071i
$965$			54.0000i			0.0559585i
$966$			320.000i			0.331263i
$967$	1006.00	−	1006.00i	1.04033	−	1.04033i	0.0411791	−	0.999152i	$-0.486889\pi$
$967$	1006.00	−	1006.00i	1.04033	−	1.04033i	0.999152	−	0.0411791i	$-0.0131114\pi$
$968$	−210.000	+	210.000i	−0.216942	+	0.216942i
$969$	1840.00			1.89886
$970$	774.000	−	774.000i	0.797938	−	0.797938i
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	616.000			0.633745
$973$		−	720.000i		−	0.739979i
$974$	532.000			0.546201
$975$	−84.0000	+	84.0000i	−0.0861538	+	0.0861538i
$976$	12.0000	+	12.0000i	0.0122951	+	0.0122951i
$977$	−921.000	−	921.000i	−0.942682	−	0.942682i	0.0557624	−	0.998444i	$-0.482241\pi$
$977$	−921.000	−	921.000i	−0.942682	−	0.942682i	−0.998444	+	0.0557624i	$0.982241\pi$
$978$	528.000			0.539877
$979$	−68.0000	+	68.0000i	−0.0694586	+	0.0694586i
$980$	−198.000	−	198.000i	−0.202041	−	0.202041i
$981$	637.000	−	637.000i	0.649337	−	0.649337i
$982$	312.000	+	312.000i	0.317719	+	0.317719i
$983$			1480.00i			1.50560i	0.658252	+	0.752798i	$0.271296\pi$
$983$			1480.00i			1.50560i	−0.658252	+	0.752798i	$0.728704\pi$
$984$	592.000	−	592.000i	0.601626	−	0.601626i
$985$	102.000	−	102.000i	0.103553	−	0.103553i
$986$	−874.000	−	874.000i	−0.886410	−	0.886410i
$987$			704.000i			0.713273i
$988$	120.000			0.121457
$989$			840.000i			0.849343i
$990$		−	168.000i		−	0.169697i
$991$	1038.00	+	1038.00i	1.04743	+	1.04743i	0.998818	+	0.0486090i	$0.0154788\pi$
$991$	1038.00	+	1038.00i	1.04743	+	1.04743i	0.0486090	+	0.998818i	$0.484521\pi$
$992$			144.000i			0.145161i
$993$	−1304.00	−	1304.00i	−1.31319	−	1.31319i
$994$	−496.000	−	496.000i	−0.498994	−	0.498994i
$995$	276.000			0.277387
$996$	512.000			0.514056
$997$	355.000	−	355.000i	0.356068	−	0.356068i	−0.506293	−	0.862361i	$-0.668985\pi$
$997$	355.000	−	355.000i	0.356068	−	0.356068i	0.862361	+	0.506293i	$0.168985\pi$
$998$		−	420.000i		−	0.420842i
$999$	296.000			0.296296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.3.d.b.31.1	✓	2
3.2	odd	2		666.3.i.a.253.1		2
4.3	odd	2		592.3.k.c.401.1		2
37.6	odd	4	inner	74.3.d.b.43.1	yes	2
111.80	even	4		666.3.i.a.487.1		2
148.43	even	4		592.3.k.c.561.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.3.d.b.31.1	✓	2	1.1	even	1	trivial
74.3.d.b.43.1	yes	2	37.6	odd	4	inner
592.3.k.c.401.1		2	4.3	odd	2
592.3.k.c.561.1		2	148.43	even	4
666.3.i.a.253.1		2	3.2	odd	2
666.3.i.a.487.1		2	111.80	even	4

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +4.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(-4.00000 + 4.00000i) q^{6} -4.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -7.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +4.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(-4.00000 + 4.00000i) q^{6} -4.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -7.00000 q^{9} +6.00000 q^{10} +4.00000i q^{11} -8.00000 q^{12} +(3.00000 - 3.00000i) q^{13} +(-4.00000 - 4.00000i) q^{14} +(12.0000 + 12.0000i) q^{15} -4.00000 q^{16} +(23.0000 - 23.0000i) q^{17} +(-7.00000 - 7.00000i) q^{18} +(10.0000 - 10.0000i) q^{19} +(6.00000 + 6.00000i) q^{20} -16.0000i q^{21} +(-4.00000 + 4.00000i) q^{22} +(-10.0000 + 10.0000i) q^{23} +(-8.00000 - 8.00000i) q^{24} +7.00000i q^{25} +6.00000 q^{26} +8.00000i q^{27} -8.00000i q^{28} +(-19.0000 - 19.0000i) q^{29} +24.0000i q^{30} +(-18.0000 - 18.0000i) q^{31} +(-4.00000 - 4.00000i) q^{32} -16.0000 q^{33} +46.0000 q^{34} +(-12.0000 + 12.0000i) q^{35} -14.0000i q^{36} -37.0000i q^{37} +20.0000 q^{38} +(12.0000 + 12.0000i) q^{39} +12.0000i q^{40} +74.0000i q^{41} +(16.0000 - 16.0000i) q^{42} +(42.0000 - 42.0000i) q^{43} -8.00000 q^{44} +(-21.0000 + 21.0000i) q^{45} -20.0000 q^{46} -44.0000 q^{47} -16.0000i q^{48} -33.0000 q^{49} +(-7.00000 + 7.00000i) q^{50} +(92.0000 + 92.0000i) q^{51} +(6.00000 + 6.00000i) q^{52} -80.0000 q^{53} +(-8.00000 + 8.00000i) q^{54} +(12.0000 + 12.0000i) q^{55} +(8.00000 - 8.00000i) q^{56} +(40.0000 + 40.0000i) q^{57} -38.0000i q^{58} +(-54.0000 + 54.0000i) q^{59} +(-24.0000 + 24.0000i) q^{60} +(-3.00000 - 3.00000i) q^{61} -36.0000i q^{62} +28.0000 q^{63} -8.00000i q^{64} -18.0000i q^{65} +(-16.0000 - 16.0000i) q^{66} -12.0000i q^{67} +(46.0000 + 46.0000i) q^{68} +(-40.0000 - 40.0000i) q^{69} -24.0000 q^{70} +124.000 q^{71} +(14.0000 - 14.0000i) q^{72} -10.0000i q^{73} +(37.0000 - 37.0000i) q^{74} -28.0000 q^{75} +(20.0000 + 20.0000i) q^{76} -16.0000i q^{77} +24.0000i q^{78} +(14.0000 - 14.0000i) q^{79} +(-12.0000 + 12.0000i) q^{80} -95.0000 q^{81} +(-74.0000 + 74.0000i) q^{82} -64.0000 q^{83} +32.0000 q^{84} -138.000i q^{85} +84.0000 q^{86} +(76.0000 - 76.0000i) q^{87} +(-8.00000 - 8.00000i) q^{88} +(17.0000 + 17.0000i) q^{89} -42.0000 q^{90} +(-12.0000 + 12.0000i) q^{91} +(-20.0000 - 20.0000i) q^{92} +(72.0000 - 72.0000i) q^{93} +(-44.0000 - 44.0000i) q^{94} -60.0000i q^{95} +(16.0000 - 16.0000i) q^{96} +(129.000 - 129.000i) q^{97} +(-33.0000 - 33.0000i) q^{98} -28.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 6 q^{5} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 14 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 6 * q^5 - 8 * q^6 - 8 * q^7 - 4 * q^8 - 14 * q^9	\( 2 q + 2 q^{2} + 6 q^{5} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 14 q^{9} + 12 q^{10} - 16 q^{12} + 6 q^{13} - 8 q^{14} + 24 q^{15} - 8 q^{16} + 46 q^{17} - 14 q^{18} + 20 q^{19} + 12 q^{20} - 8 q^{22} - 20 q^{23} - 16 q^{24} + 12 q^{26} - 38 q^{29} - 36 q^{31} - 8 q^{32} - 32 q^{33} + 92 q^{34} - 24 q^{35} + 40 q^{38} + 24 q^{39} + 32 q^{42} + 84 q^{43} - 16 q^{44} - 42 q^{45} - 40 q^{46} - 88 q^{47} - 66 q^{49} - 14 q^{50} + 184 q^{51} + 12 q^{52} - 160 q^{53} - 16 q^{54} + 24 q^{55} + 16 q^{56} + 80 q^{57} - 108 q^{59} - 48 q^{60} - 6 q^{61} + 56 q^{63} - 32 q^{66} + 92 q^{68} - 80 q^{69} - 48 q^{70} + 248 q^{71} + 28 q^{72} + 74 q^{74} - 56 q^{75} + 40 q^{76} + 28 q^{79} - 24 q^{80} - 190 q^{81} - 148 q^{82} - 128 q^{83} + 64 q^{84} + 168 q^{86} + 152 q^{87} - 16 q^{88} + 34 q^{89} - 84 q^{90} - 24 q^{91} - 40 q^{92} + 144 q^{93} - 88 q^{94} + 32 q^{96} + 258 q^{97} - 66 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 6 * q^5 - 8 * q^6 - 8 * q^7 - 4 * q^8 - 14 * q^9 + 12 * q^10 - 16 * q^12 + 6 * q^13 - 8 * q^14 + 24 * q^15 - 8 * q^16 + 46 * q^17 - 14 * q^18 + 20 * q^19 + 12 * q^20 - 8 * q^22 - 20 * q^23 - 16 * q^24 + 12 * q^26 - 38 * q^29 - 36 * q^31 - 8 * q^32 - 32 * q^33 + 92 * q^34 - 24 * q^35 + 40 * q^38 + 24 * q^39 + 32 * q^42 + 84 * q^43 - 16 * q^44 - 42 * q^45 - 40 * q^46 - 88 * q^47 - 66 * q^49 - 14 * q^50 + 184 * q^51 + 12 * q^52 - 160 * q^53 - 16 * q^54 + 24 * q^55 + 16 * q^56 + 80 * q^57 - 108 * q^59 - 48 * q^60 - 6 * q^61 + 56 * q^63 - 32 * q^66 + 92 * q^68 - 80 * q^69 - 48 * q^70 + 248 * q^71 + 28 * q^72 + 74 * q^74 - 56 * q^75 + 40 * q^76 + 28 * q^79 - 24 * q^80 - 190 * q^81 - 148 * q^82 - 128 * q^83 + 64 * q^84 + 168 * q^86 + 152 * q^87 - 16 * q^88 + 34 * q^89 - 84 * q^90 - 24 * q^91 - 40 * q^92 + 144 * q^93 - 88 * q^94 + 32 * q^96 + 258 * q^97 - 66 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more