LMFDB - Embedded newform 392.3.k.a.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.6812263629$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.a.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +4.00000 q^{4} +(4.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{6} -8.00000 q^{8} +(4.00000 - 6.92820i) q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +4.00000 q^{4} +(4.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{6} -8.00000 q^{8} +(4.00000 - 6.92820i) q^{9} +(-9.00000 - 5.19615i) q^{10} +(-8.50000 - 14.7224i) q^{11} +(2.00000 + 3.46410i) q^{12} -13.8564i q^{13} +5.19615i q^{15} +16.0000 q^{16} +(-12.5000 - 21.6506i) q^{17} +(-8.00000 + 13.8564i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(18.0000 + 10.3923i) q^{20} +(17.0000 + 29.4449i) q^{22} +(4.50000 + 2.59808i) q^{23} +(-4.00000 - 6.92820i) q^{24} +(1.00000 + 1.73205i) q^{25} +27.7128i q^{26} +17.0000 q^{27} -13.8564i q^{29} -10.3923i q^{30} +(-28.5000 + 16.4545i) q^{31} -32.0000 q^{32} +(8.50000 - 14.7224i) q^{33} +(25.0000 + 43.3013i) q^{34} +(16.0000 - 27.7128i) q^{36} +(7.50000 + 4.33013i) q^{37} +(7.00000 - 12.1244i) q^{38} +(12.0000 - 6.92820i) q^{39} +(-36.0000 - 20.7846i) q^{40} -26.0000 q^{41} +14.0000 q^{43} +(-34.0000 - 58.8897i) q^{44} +(36.0000 - 20.7846i) q^{45} +(-9.00000 - 5.19615i) q^{46} +(43.5000 + 25.1147i) q^{47} +(8.00000 + 13.8564i) q^{48} +(-2.00000 - 3.46410i) q^{50} +(12.5000 - 21.6506i) q^{51} -55.4256i q^{52} +(79.5000 - 45.8993i) q^{53} -34.0000 q^{54} -88.3346i q^{55} -7.00000 q^{57} +27.7128i q^{58} +(-27.5000 - 47.6314i) q^{59} +20.7846i q^{60} +(-19.5000 - 11.2583i) q^{61} +(57.0000 - 32.9090i) q^{62} +64.0000 q^{64} +(36.0000 - 62.3538i) q^{65} +(-17.0000 + 29.4449i) q^{66} +(-8.50000 - 14.7224i) q^{67} +(-50.0000 - 86.6025i) q^{68} +5.19615i q^{69} +(-32.0000 + 55.4256i) q^{72} +(59.5000 + 103.057i) q^{73} +(-15.0000 - 8.66025i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(-14.0000 + 24.2487i) q^{76} +(-24.0000 + 13.8564i) q^{78} +(64.5000 + 37.2391i) q^{79} +(72.0000 + 41.5692i) q^{80} +(-27.5000 - 47.6314i) q^{81} +52.0000 q^{82} -110.000 q^{83} -129.904i q^{85} -28.0000 q^{86} +(12.0000 - 6.92820i) q^{87} +(68.0000 + 117.779i) q^{88} +(35.5000 - 61.4878i) q^{89} +(-72.0000 + 41.5692i) q^{90} +(18.0000 + 10.3923i) q^{92} +(-28.5000 - 16.4545i) q^{93} +(-87.0000 - 50.2295i) q^{94} +(-31.5000 + 18.1865i) q^{95} +(-16.0000 - 27.7128i) q^{96} +22.0000 q^{97} -136.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + q^{3} + 8 q^{4} + 9 q^{5} - 2 q^{6} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 + q^3 + 8 * q^4 + 9 * q^5 - 2 * q^6 - 16 * q^8 + 8 * q^9	$ 2 q - 4 q^{2} + q^{3} + 8 q^{4} + 9 q^{5} - 2 q^{6} - 16 q^{8} + 8 q^{9} - 18 q^{10} - 17 q^{11} + 4 q^{12} + 32 q^{16} - 25 q^{17} - 16 q^{18} - 7 q^{19} + 36 q^{20} + 34 q^{22} + 9 q^{23} - 8 q^{24} + 2 q^{25} + 34 q^{27} - 57 q^{31} - 64 q^{32} + 17 q^{33} + 50 q^{34} + 32 q^{36} + 15 q^{37} + 14 q^{38} + 24 q^{39} - 72 q^{40} - 52 q^{41} + 28 q^{43} - 68 q^{44} + 72 q^{45} - 18 q^{46} + 87 q^{47} + 16 q^{48} - 4 q^{50} + 25 q^{51} + 159 q^{53} - 68 q^{54} - 14 q^{57} - 55 q^{59} - 39 q^{61} + 114 q^{62} + 128 q^{64} + 72 q^{65} - 34 q^{66} - 17 q^{67} - 100 q^{68} - 64 q^{72} + 119 q^{73} - 30 q^{74} - 2 q^{75} - 28 q^{76} - 48 q^{78} + 129 q^{79} + 144 q^{80} - 55 q^{81} + 104 q^{82} - 220 q^{83} - 56 q^{86} + 24 q^{87} + 136 q^{88} + 71 q^{89} - 144 q^{90} + 36 q^{92} - 57 q^{93} - 174 q^{94} - 63 q^{95} - 32 q^{96} + 44 q^{97} - 272 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 + q^3 + 8 * q^4 + 9 * q^5 - 2 * q^6 - 16 * q^8 + 8 * q^9 - 18 * q^10 - 17 * q^11 + 4 * q^12 + 32 * q^16 - 25 * q^17 - 16 * q^18 - 7 * q^19 + 36 * q^20 + 34 * q^22 + 9 * q^23 - 8 * q^24 + 2 * q^25 + 34 * q^27 - 57 * q^31 - 64 * q^32 + 17 * q^33 + 50 * q^34 + 32 * q^36 + 15 * q^37 + 14 * q^38 + 24 * q^39 - 72 * q^40 - 52 * q^41 + 28 * q^43 - 68 * q^44 + 72 * q^45 - 18 * q^46 + 87 * q^47 + 16 * q^48 - 4 * q^50 + 25 * q^51 + 159 * q^53 - 68 * q^54 - 14 * q^57 - 55 * q^59 - 39 * q^61 + 114 * q^62 + 128 * q^64 + 72 * q^65 - 34 * q^66 - 17 * q^67 - 100 * q^68 - 64 * q^72 + 119 * q^73 - 30 * q^74 - 2 * q^75 - 28 * q^76 - 48 * q^78 + 129 * q^79 + 144 * q^80 - 55 * q^81 + 104 * q^82 - 220 * q^83 - 56 * q^86 + 24 * q^87 + 136 * q^88 + 71 * q^89 - 144 * q^90 + 36 * q^92 - 57 * q^93 - 174 * q^94 - 63 * q^95 - 32 * q^96 + 44 * q^97 - 272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.00000			−1.00000
$2$	−2.00000			−1.00000
$3$	0.500000	+	0.866025i	0.166667	+	0.288675i	0.937246	−	0.348669i	$-0.113366\pi$
$3$	0.500000	+	0.866025i	0.166667	+	0.288675i	−0.770579	+	0.637344i	$0.780033\pi$
$4$	4.00000			1.00000
$5$	4.50000	+	2.59808i	0.900000	+	0.519615i	0.877200	−	0.480125i	$-0.159409\pi$
$5$	4.50000	+	2.59808i	0.900000	+	0.519615i	0.0227998	+	0.999740i	$0.492742\pi$
$6$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$7$		0			0
$7$		0			0
$8$	−8.00000			−1.00000
$9$	4.00000	−	6.92820i	0.444444	−	0.769800i
$10$	−9.00000	−	5.19615i	−0.900000	−	0.519615i
$11$	−8.50000	−	14.7224i	−0.772727	−	1.33840i	−0.936063	−	0.351832i	$-0.885559\pi$
$11$	−8.50000	−	14.7224i	−0.772727	−	1.33840i	0.163336	−	0.986571i	$-0.447775\pi$
$12$	2.00000	+	3.46410i	0.166667	+	0.288675i
$13$		−	13.8564i		−	1.06588i	−0.846154	−	0.532939i	$-0.821088\pi$
$13$		−	13.8564i		−	1.06588i	0.846154	−	0.532939i	$-0.178912\pi$
$14$		0			0
$15$			5.19615i			0.346410i
$16$	16.0000			1.00000
$17$	−12.5000	−	21.6506i	−0.735294	−	1.27357i	−0.954594	−	0.297909i	$-0.903711\pi$
$17$	−12.5000	−	21.6506i	−0.735294	−	1.27357i	0.219300	−	0.975657i	$-0.429623\pi$
$18$	−8.00000	+	13.8564i	−0.444444	+	0.769800i
$19$	−3.50000	+	6.06218i	−0.184211	+	0.319062i	−0.943310	−	0.331912i	$-0.892306\pi$
$19$	−3.50000	+	6.06218i	−0.184211	+	0.319062i	0.759100	+	0.650974i	$0.225639\pi$
$20$	18.0000	+	10.3923i	0.900000	+	0.519615i
$21$		0			0
$22$	17.0000	+	29.4449i	0.772727	+	1.33840i
$23$	4.50000	+	2.59808i	0.195652	+	0.112960i	0.594626	−	0.804003i	$-0.297300\pi$
$23$	4.50000	+	2.59808i	0.195652	+	0.112960i	−0.398974	+	0.916962i	$0.630634\pi$
$24$	−4.00000	−	6.92820i	−0.166667	−	0.288675i
$25$	1.00000	+	1.73205i	0.0400000	+	0.0692820i
$26$			27.7128i			1.06588i
$27$	17.0000			0.629630
$28$		0			0
$29$		−	13.8564i		−	0.477807i	−0.971043	−	0.238904i	$-0.923212\pi$
$29$		−	13.8564i		−	0.477807i	0.971043	−	0.238904i	$-0.0767880\pi$
$30$		−	10.3923i		−	0.346410i
$31$	−28.5000	+	16.4545i	−0.919355	+	0.530790i	−0.883429	−	0.468565i	$-0.844771\pi$
$31$	−28.5000	+	16.4545i	−0.919355	+	0.530790i	−0.0359257	+	0.999354i	$0.511438\pi$
$32$	−32.0000			−1.00000
$33$	8.50000	−	14.7224i	0.257576	−	0.446134i
$34$	25.0000	+	43.3013i	0.735294	+	1.27357i
$35$		0			0
$36$	16.0000	−	27.7128i	0.444444	−	0.769800i
$37$	7.50000	+	4.33013i	0.202703	+	0.117030i	0.597916	−	0.801559i	$-0.295996\pi$
$37$	7.50000	+	4.33013i	0.202703	+	0.117030i	−0.395213	+	0.918590i	$0.629329\pi$
$38$	7.00000	−	12.1244i	0.184211	−	0.319062i
$39$	12.0000	−	6.92820i	0.307692	−	0.177646i
$40$	−36.0000	−	20.7846i	−0.900000	−	0.519615i
$41$	−26.0000			−0.634146			−0.317073	−	0.948401i	$-0.602700\pi$
$41$	−26.0000			−0.634146			−0.317073	+	0.948401i	$0.602700\pi$
$42$		0			0
$43$	14.0000			0.325581			0.162791	−	0.986661i	$-0.447950\pi$
$43$	14.0000			0.325581			0.162791	+	0.986661i	$0.447950\pi$
$44$	−34.0000	−	58.8897i	−0.772727	−	1.33840i
$45$	36.0000	−	20.7846i	0.800000	−	0.461880i
$46$	−9.00000	−	5.19615i	−0.195652	−	0.112960i
$47$	43.5000	+	25.1147i	0.925532	+	0.534356i	0.885396	−	0.464838i	$-0.153887\pi$
$47$	43.5000	+	25.1147i	0.925532	+	0.534356i	0.0401362	+	0.999194i	$0.487221\pi$
$48$	8.00000	+	13.8564i	0.166667	+	0.288675i
$49$		0			0
$50$	−2.00000	−	3.46410i	−0.0400000	−	0.0692820i
$51$	12.5000	−	21.6506i	0.245098	−	0.424522i
$52$		−	55.4256i		−	1.06588i
$53$	79.5000	−	45.8993i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$53$	79.5000	−	45.8993i	1.50000	−	0.866025i	1.00000			$0$
$54$	−34.0000			−0.629630
$55$		−	88.3346i		−	1.60608i
$56$		0			0
$57$	−7.00000			−0.122807
$58$			27.7128i			0.477807i
$59$	−27.5000	−	47.6314i	−0.466102	−	0.807312i	0.533149	−	0.846021i	$-0.321009\pi$
$59$	−27.5000	−	47.6314i	−0.466102	−	0.807312i	−0.999250	+	0.0387097i	$0.987675\pi$
$60$			20.7846i			0.346410i
$61$	−19.5000	−	11.2583i	−0.319672	−	0.184563i	0.331574	−	0.943429i	$-0.392420\pi$
$61$	−19.5000	−	11.2583i	−0.319672	−	0.184563i	−0.651246	+	0.758866i	$0.725754\pi$
$62$	57.0000	−	32.9090i	0.919355	−	0.530790i
$63$		0			0
$64$	64.0000			1.00000
$65$	36.0000	−	62.3538i	0.553846	−	0.959290i
$66$	−17.0000	+	29.4449i	−0.257576	+	0.446134i
$67$	−8.50000	−	14.7224i	−0.126866	−	0.219738i	0.795595	−	0.605829i	$-0.207158\pi$
$67$	−8.50000	−	14.7224i	−0.126866	−	0.219738i	−0.922461	+	0.386091i	$0.873825\pi$
$68$	−50.0000	−	86.6025i	−0.735294	−	1.27357i
$69$			5.19615i			0.0753066i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−32.0000	+	55.4256i	−0.444444	+	0.769800i
$73$	59.5000	+	103.057i	0.815068	+	1.41174i	0.909279	+	0.416188i	$0.136634\pi$
$73$	59.5000	+	103.057i	0.815068	+	1.41174i	−0.0942102	+	0.995552i	$0.530033\pi$
$74$	−15.0000	−	8.66025i	−0.202703	−	0.117030i
$75$	−1.00000	+	1.73205i	−0.0133333	+	0.0230940i
$76$	−14.0000	+	24.2487i	−0.184211	+	0.319062i
$77$		0			0
$78$	−24.0000	+	13.8564i	−0.307692	+	0.177646i
$79$	64.5000	+	37.2391i	0.816456	+	0.471381i	0.849193	−	0.528083i	$-0.177089\pi$
$79$	64.5000	+	37.2391i	0.816456	+	0.471381i	−0.0327370	+	0.999464i	$0.510422\pi$
$80$	72.0000	+	41.5692i	0.900000	+	0.519615i
$81$	−27.5000	−	47.6314i	−0.339506	−	0.588042i
$82$	52.0000			0.634146
$83$	−110.000			−1.32530			−0.662651	−	0.748929i	$-0.730569\pi$
$83$	−110.000			−1.32530			−0.662651	+	0.748929i	$0.730569\pi$
$84$		0			0
$85$		−	129.904i		−	1.52828i
$86$	−28.0000			−0.325581
$87$	12.0000	−	6.92820i	0.137931	−	0.0796345i
$88$	68.0000	+	117.779i	0.772727	+	1.33840i
$89$	35.5000	−	61.4878i	0.398876	−	0.690874i	−0.594711	−	0.803939i	$-0.702734\pi$
$89$	35.5000	−	61.4878i	0.398876	−	0.690874i	0.993588	+	0.113065i	$0.0360669\pi$
$90$	−72.0000	+	41.5692i	−0.800000	+	0.461880i
$91$		0			0
$92$	18.0000	+	10.3923i	0.195652	+	0.112960i
$93$	−28.5000	−	16.4545i	−0.306452	−	0.176930i
$94$	−87.0000	−	50.2295i	−0.925532	−	0.534356i
$95$	−31.5000	+	18.1865i	−0.331579	+	0.191437i
$96$	−16.0000	−	27.7128i	−0.166667	−	0.288675i
$97$	22.0000			0.226804			0.113402	−	0.993549i	$-0.463825\pi$
$97$	22.0000			0.226804			0.113402	+	0.993549i	$0.463825\pi$
$98$		0			0
$99$	−136.000			−1.37374
$100$	4.00000	+	6.92820i	0.0400000	+	0.0692820i
$101$	−67.5000	+	38.9711i	−0.668317	+	0.385853i	−0.795439	−	0.606034i	$-0.792759\pi$
$101$	−67.5000	+	38.9711i	−0.668317	+	0.385853i	0.127122	+	0.991887i	$0.459426\pi$
$102$	−25.0000	+	43.3013i	−0.245098	+	0.424522i
$103$	139.500	+	80.5404i	1.35437	+	0.781945i	0.988858	−	0.148862i	$-0.0475610\pi$
$103$	139.500	+	80.5404i	1.35437	+	0.781945i	0.365511	+	0.930807i	$0.380894\pi$
$104$			110.851i			1.06588i
$105$		0			0
$106$	−159.000	+	91.7987i	−1.50000	+	0.866025i
$107$	−32.5000	+	56.2917i	−0.303738	+	0.526090i	−0.976980	−	0.213333i	$-0.931568\pi$
$107$	−32.5000	+	56.2917i	−0.303738	+	0.526090i	0.673241	+	0.739423i	$0.264902\pi$
$108$	68.0000			0.629630
$109$	7.50000	−	4.33013i	0.0688073	−	0.0397259i	−0.465202	−	0.885205i	$-0.654018\pi$
$109$	7.50000	−	4.33013i	0.0688073	−	0.0397259i	0.534009	+	0.845479i	$0.320685\pi$
$110$			176.669i			1.60608i
$111$			8.66025i			0.0780203i
$112$		0			0
$113$	122.000			1.07965			0.539823	−	0.841779i	$-0.318491\pi$
$113$	122.000			1.07965			0.539823	+	0.841779i	$0.318491\pi$
$114$	14.0000			0.122807
$115$	13.5000	+	23.3827i	0.117391	+	0.203328i
$116$		−	55.4256i		−	0.477807i
$117$	−96.0000	−	55.4256i	−0.820513	−	0.473723i
$118$	55.0000	+	95.2628i	0.466102	+	0.807312i
$119$		0			0
$120$		−	41.5692i		−	0.346410i
$121$	−84.0000	+	145.492i	−0.694215	+	1.20242i
$122$	39.0000	+	22.5167i	0.319672	+	0.184563i
$123$	−13.0000	−	22.5167i	−0.105691	−	0.183062i
$124$	−114.000	+	65.8179i	−0.919355	+	0.530790i
$125$		−	119.512i		−	0.956092i
$126$		0			0
$127$			166.277i			1.30927i	0.755947	+	0.654633i	$0.227177\pi$
$127$			166.277i			1.30927i	−0.755947	+	0.654633i	$0.772823\pi$
$128$	−128.000			−1.00000
$129$	7.00000	+	12.1244i	0.0542636	+	0.0939873i
$130$	−72.0000	+	124.708i	−0.553846	+	0.959290i
$131$	8.50000	−	14.7224i	0.0648855	−	0.112385i	−0.831758	−	0.555139i	$-0.812665\pi$
$131$	8.50000	−	14.7224i	0.0648855	−	0.112385i	0.896643	+	0.442754i	$0.145998\pi$
$132$	34.0000	−	58.8897i	0.257576	−	0.446134i
$133$		0			0
$134$	17.0000	+	29.4449i	0.126866	+	0.219738i
$135$	76.5000	+	44.1673i	0.566667	+	0.327165i
$136$	100.000	+	173.205i	0.735294	+	1.27357i
$137$	72.5000	+	125.574i	0.529197	+	0.916596i	0.999420	+	0.0340486i	$0.0108401\pi$
$137$	72.5000	+	125.574i	0.529197	+	0.916596i	−0.470223	+	0.882548i	$0.655827\pi$
$138$		−	10.3923i		−	0.0753066i
$139$	82.0000			0.589928			0.294964	−	0.955508i	$-0.404692\pi$
$139$	82.0000			0.589928			0.294964	+	0.955508i	$0.404692\pi$
$140$		0			0
$141$			50.2295i			0.356237i
$142$		0			0
$143$	−204.000	+	117.779i	−1.42657	+	0.823633i
$144$	64.0000	−	110.851i	0.444444	−	0.769800i
$145$	36.0000	−	62.3538i	0.248276	−	0.430026i
$146$	−119.000	−	206.114i	−0.815068	−	1.41174i
$147$		0			0
$148$	30.0000	+	17.3205i	0.202703	+	0.117030i
$149$	−4.50000	−	2.59808i	−0.0302013	−	0.0174368i	0.484823	−	0.874612i	$-0.338884\pi$
$149$	−4.50000	−	2.59808i	−0.0302013	−	0.0174368i	−0.515025	+	0.857175i	$0.672217\pi$
$150$	2.00000	−	3.46410i	0.0133333	−	0.0230940i
$151$	−31.5000	+	18.1865i	−0.208609	+	0.120441i	−0.600665	−	0.799501i	$-0.705097\pi$
$151$	−31.5000	+	18.1865i	−0.208609	+	0.120441i	0.392056	+	0.919942i	$0.371764\pi$
$152$	28.0000	−	48.4974i	0.184211	−	0.319062i
$153$	−200.000			−1.30719
$154$		0			0
$155$	−171.000			−1.10323
$156$	48.0000	−	27.7128i	0.307692	−	0.177646i
$157$	268.500	−	155.019i	1.71019	−	0.987379i	0.775909	−	0.630845i	$-0.217292\pi$
$157$	268.500	−	155.019i	1.71019	−	0.987379i	0.934282	−	0.356534i	$-0.116042\pi$
$158$	−129.000	−	74.4782i	−0.816456	−	0.471381i
$159$	79.5000	+	45.8993i	0.500000	+	0.288675i
$160$	−144.000	−	83.1384i	−0.900000	−	0.519615i
$161$		0			0
$162$	55.0000	+	95.2628i	0.339506	+	0.588042i
$163$	−8.50000	+	14.7224i	−0.0521472	+	0.0903217i	−0.890921	−	0.454159i	$-0.849940\pi$
$163$	−8.50000	+	14.7224i	−0.0521472	+	0.0903217i	0.838773	+	0.544481i	$0.183273\pi$
$164$	−104.000			−0.634146
$165$	76.5000	−	44.1673i	0.463636	−	0.267681i
$166$	220.000			1.32530
$167$		−	13.8564i		−	0.0829725i	−0.999139	−	0.0414862i	$-0.986791\pi$
$167$		−	13.8564i		−	0.0829725i	0.999139	−	0.0414862i	$-0.0132093\pi$
$168$		0			0
$169$	−23.0000			−0.136095
$170$			259.808i			1.52828i
$171$	28.0000	+	48.4974i	0.163743	+	0.283611i
$172$	56.0000			0.325581
$173$	−91.5000	−	52.8275i	−0.528902	−	0.305362i	0.211667	−	0.977342i	$-0.432111\pi$
$173$	−91.5000	−	52.8275i	−0.528902	−	0.305362i	−0.740569	+	0.671980i	$0.765444\pi$
$174$	−24.0000	+	13.8564i	−0.137931	+	0.0796345i
$175$		0			0
$176$	−136.000	−	235.559i	−0.772727	−	1.33840i
$177$	27.5000	−	47.6314i	0.155367	−	0.269104i
$178$	−71.0000	+	122.976i	−0.398876	+	0.690874i
$179$	−44.5000	−	77.0763i	−0.248603	−	0.430594i	0.714535	−	0.699600i	$-0.246638\pi$
$179$	−44.5000	−	77.0763i	−0.248603	−	0.430594i	−0.963139	+	0.269006i	$0.913305\pi$
$180$	144.000	−	83.1384i	0.800000	−	0.461880i
$181$			249.415i			1.37799i	0.724768	+	0.688993i	$0.241947\pi$
$181$			249.415i			1.37799i	−0.724768	+	0.688993i	$0.758053\pi$
$182$		0			0
$183$		−	22.5167i		−	0.123042i
$184$	−36.0000	−	20.7846i	−0.195652	−	0.112960i
$185$	22.5000	+	38.9711i	0.121622	+	0.210655i
$186$	57.0000	+	32.9090i	0.306452	+	0.176930i
$187$	−212.500	+	368.061i	−1.13636	+	1.96824i
$188$	174.000	+	100.459i	0.925532	+	0.534356i
$189$		0			0
$190$	63.0000	−	36.3731i	0.331579	−	0.191437i
$191$	−187.500	−	108.253i	−0.981675	−	0.566771i	−0.0788999	−	0.996883i	$-0.525141\pi$
$191$	−187.500	−	108.253i	−0.981675	−	0.566771i	−0.902776	+	0.430112i	$0.858474\pi$
$192$	32.0000	+	55.4256i	0.166667	+	0.288675i
$193$	36.5000	+	63.2199i	0.189119	+	0.327564i	0.944957	−	0.327195i	$-0.106103\pi$
$193$	36.5000	+	63.2199i	0.189119	+	0.327564i	−0.755838	+	0.654759i	$0.772770\pi$
$194$	−44.0000			−0.226804
$195$	72.0000			0.369231
$196$		0			0
$197$		−	207.846i		−	1.05506i	−0.849538	−	0.527528i	$-0.823119\pi$
$197$		−	207.846i		−	1.05506i	0.849538	−	0.527528i	$-0.176881\pi$
$198$	272.000			1.37374
$199$	55.5000	−	32.0429i	0.278894	−	0.161020i	−0.354028	−	0.935235i	$-0.615188\pi$
$199$	55.5000	−	32.0429i	0.278894	−	0.161020i	0.632923	+	0.774215i	$0.281855\pi$
$200$	−8.00000	−	13.8564i	−0.0400000	−	0.0692820i
$201$	8.50000	−	14.7224i	0.0422886	−	0.0732459i
$202$	135.000	−	77.9423i	0.668317	−	0.385853i
$203$		0			0
$204$	50.0000	−	86.6025i	0.245098	−	0.424522i
$205$	−117.000	−	67.5500i	−0.570732	−	0.329512i
$206$	−279.000	−	161.081i	−1.35437	−	0.781945i
$207$	36.0000	−	20.7846i	0.173913	−	0.100409i
$208$		−	221.703i		−	1.06588i
$209$	119.000			0.569378
$210$		0			0
$211$	302.000			1.43128			0.715640	−	0.698470i	$-0.246135\pi$
$211$	302.000			1.43128			0.715640	+	0.698470i	$0.246135\pi$
$212$	318.000	−	183.597i	1.50000	−	0.866025i
$213$		0			0
$214$	65.0000	−	112.583i	0.303738	−	0.526090i
$215$	63.0000	+	36.3731i	0.293023	+	0.169177i
$216$	−136.000			−0.629630
$217$		0			0
$218$	−15.0000	+	8.66025i	−0.0688073	+	0.0397259i
$219$	−59.5000	+	103.057i	−0.271689	+	0.470580i
$220$		−	353.338i		−	1.60608i
$221$	−300.000	+	173.205i	−1.35747	+	0.783733i
$222$		−	17.3205i		−	0.0780203i
$223$			138.564i			0.621364i	0.950514	+	0.310682i	$0.100557\pi$
$223$			138.564i			0.621364i	−0.950514	+	0.310682i	$0.899443\pi$
$224$		0			0
$225$	16.0000			0.0711111
$226$	−244.000			−1.07965
$227$	−27.5000	−	47.6314i	−0.121145	−	0.209830i	0.799074	−	0.601232i	$-0.205323\pi$
$227$	−27.5000	−	47.6314i	−0.121145	−	0.209830i	−0.920220	+	0.391402i	$0.871990\pi$
$228$	−28.0000			−0.122807
$229$	−283.500	−	163.679i	−1.23799	−	0.714755i	−0.269308	−	0.963054i	$-0.586795\pi$
$229$	−283.500	−	163.679i	−1.23799	−	0.714755i	−0.968683	+	0.248300i	$0.920128\pi$
$230$	−27.0000	−	46.7654i	−0.117391	−	0.203328i
$231$		0			0
$232$			110.851i			0.477807i
$233$	192.500	−	333.420i	0.826180	−	1.43099i	−0.0748337	−	0.997196i	$-0.523843\pi$
$233$	192.500	−	333.420i	0.826180	−	1.43099i	0.901014	−	0.433790i	$-0.142824\pi$
$234$	192.000	+	110.851i	0.820513	+	0.473723i
$235$	130.500	+	226.033i	0.555319	+	0.961841i
$236$	−110.000	−	190.526i	−0.466102	−	0.807312i
$237$			74.4782i			0.314254i
$238$		0			0
$239$			429.549i			1.79727i	0.438693	+	0.898637i	$0.355442\pi$
$239$			429.549i			1.79727i	−0.438693	+	0.898637i	$0.644558\pi$
$240$			83.1384i			0.346410i
$241$	−72.5000	−	125.574i	−0.300830	−	0.521053i	0.675494	−	0.737365i	$-0.263930\pi$
$241$	−72.5000	−	125.574i	−0.300830	−	0.521053i	−0.976324	+	0.216313i	$0.930597\pi$
$242$	168.000	−	290.985i	0.694215	−	1.20242i
$243$	104.000	−	180.133i	0.427984	−	0.741289i
$244$	−78.0000	−	45.0333i	−0.319672	−	0.184563i
$245$		0			0
$246$	26.0000	+	45.0333i	0.105691	+	0.183062i
$247$	84.0000	+	48.4974i	0.340081	+	0.196346i
$248$	228.000	−	131.636i	0.919355	−	0.530790i
$249$	−55.0000	−	95.2628i	−0.220884	−	0.382582i
$250$			239.023i			0.956092i
$251$	58.0000			0.231076			0.115538	−	0.993303i	$-0.463141\pi$
$251$	58.0000			0.231076			0.115538	+	0.993303i	$0.463141\pi$
$252$		0			0
$253$		−	88.3346i		−	0.349149i
$254$		−	332.554i		−	1.30927i
$255$	112.500	−	64.9519i	0.441176	−	0.254713i
$256$	256.000			1.00000
$257$	59.5000	−	103.057i	0.231518	−	0.401000i	−0.726737	−	0.686915i	$-0.758964\pi$
$257$	59.5000	−	103.057i	0.231518	−	0.401000i	0.958255	+	0.285915i	$0.0922976\pi$
$258$	−14.0000	−	24.2487i	−0.0542636	−	0.0939873i
$259$		0			0
$260$	144.000	−	249.415i	0.553846	−	0.959290i
$261$	−96.0000	−	55.4256i	−0.367816	−	0.212359i
$262$	−17.0000	+	29.4449i	−0.0648855	+	0.112385i
$263$	−283.500	+	163.679i	−1.07795	+	0.622353i	−0.930342	−	0.366694i	$-0.880490\pi$
$263$	−283.500	+	163.679i	−1.07795	+	0.622353i	−0.147605	+	0.989046i	$0.547156\pi$
$264$	−68.0000	+	117.779i	−0.257576	+	0.446134i
$265$	477.000			1.80000
$266$		0			0
$267$	71.0000			0.265918
$268$	−34.0000	−	58.8897i	−0.126866	−	0.219738i
$269$	−115.500	+	66.6840i	−0.429368	+	0.247896i	−0.699077	−	0.715046i	$-0.746406\pi$
$269$	−115.500	+	66.6840i	−0.429368	+	0.247896i	0.269709	+	0.962942i	$0.413072\pi$
$270$	−153.000	−	88.3346i	−0.566667	−	0.327165i
$271$	−376.500	−	217.372i	−1.38930	−	0.802112i	−0.396063	−	0.918223i	$-0.629624\pi$
$271$	−376.500	−	217.372i	−1.38930	−	0.802112i	−0.993236	+	0.116111i	$0.962957\pi$
$272$	−200.000	−	346.410i	−0.735294	−	1.27357i
$273$		0			0
$274$	−145.000	−	251.147i	−0.529197	−	0.916596i
$275$	17.0000	−	29.4449i	0.0618182	−	0.107072i
$276$			20.7846i			0.0753066i
$277$	175.500	−	101.325i	0.633574	−	0.365794i	−0.148561	−	0.988903i	$-0.547464\pi$
$277$	175.500	−	101.325i	0.633574	−	0.365794i	0.782135	+	0.623109i	$0.214131\pi$
$278$	−164.000			−0.589928
$279$			263.272i			0.943626i
$280$		0			0
$281$	74.0000			0.263345			0.131673	−	0.991293i	$-0.457965\pi$
$281$	74.0000			0.263345			0.131673	+	0.991293i	$0.457965\pi$
$282$		−	100.459i		−	0.356237i
$283$	−231.500	−	400.970i	−0.818021	−	1.41685i	−0.907138	−	0.420833i	$-0.861738\pi$
$283$	−231.500	−	400.970i	−0.818021	−	1.41685i	0.0891169	−	0.996021i	$-0.471596\pi$
$284$		0			0
$285$	−31.5000	−	18.1865i	−0.110526	−	0.0638124i
$286$	408.000	−	235.559i	1.42657	−	0.823633i
$287$		0			0
$288$	−128.000	+	221.703i	−0.444444	+	0.769800i
$289$	−168.000	+	290.985i	−0.581315	+	1.00687i
$290$	−72.0000	+	124.708i	−0.248276	+	0.430026i
$291$	11.0000	+	19.0526i	0.0378007	+	0.0654727i
$292$	238.000	+	412.228i	0.815068	+	1.41174i
$293$			110.851i			0.378332i	0.981945	+	0.189166i	$0.0605784\pi$
$293$			110.851i			0.378332i	−0.981945	+	0.189166i	$0.939422\pi$
$294$		0			0
$295$		−	285.788i		−	0.968774i
$296$	−60.0000	−	34.6410i	−0.202703	−	0.117030i
$297$	−144.500	−	250.281i	−0.486532	−	0.842698i
$298$	9.00000	+	5.19615i	0.0302013	+	0.0174368i
$299$	36.0000	−	62.3538i	0.120401	−	0.208541i
$300$	−4.00000	+	6.92820i	−0.0133333	+	0.0230940i
$301$		0			0
$302$	63.0000	−	36.3731i	0.208609	−	0.120441i
$303$	−67.5000	−	38.9711i	−0.222772	−	0.128618i
$304$	−56.0000	+	96.9948i	−0.184211	+	0.319062i
$305$	−58.5000	−	101.325i	−0.191803	−	0.332213i
$306$	400.000			1.30719
$307$	274.000			0.892508			0.446254	−	0.894906i	$-0.352758\pi$
$307$	274.000			0.892508			0.446254	+	0.894906i	$0.352758\pi$
$308$		0			0
$309$			161.081i			0.521297i
$310$	342.000			1.10323
$311$	43.5000	−	25.1147i	0.139871	−	0.0807548i	−0.428431	−	0.903574i	$-0.640934\pi$
$311$	43.5000	−	25.1147i	0.139871	−	0.0807548i	0.568303	+	0.822820i	$0.307600\pi$
$312$	−96.0000	+	55.4256i	−0.307692	+	0.177646i
$313$	−204.500	+	354.204i	−0.653355	+	1.13164i	0.328949	+	0.944348i	$0.393306\pi$
$313$	−204.500	+	354.204i	−0.653355	+	1.13164i	−0.982304	+	0.187296i	$0.940028\pi$
$314$	−537.000	+	310.037i	−1.71019	+	0.987379i
$315$		0			0
$316$	258.000	+	148.956i	0.816456	+	0.471381i
$317$	163.500	+	94.3968i	0.515773	+	0.297782i	0.735203	−	0.677847i	$-0.237087\pi$
$317$	163.500	+	94.3968i	0.515773	+	0.297782i	−0.219431	+	0.975628i	$0.570420\pi$
$318$	−159.000	−	91.7987i	−0.500000	−	0.288675i
$319$	−204.000	+	117.779i	−0.639498	+	0.369215i
$320$	288.000	+	166.277i	0.900000	+	0.519615i
$321$	−65.0000			−0.202492
$322$		0			0
$323$	175.000			0.541796
$324$	−110.000	−	190.526i	−0.339506	−	0.588042i
$325$	24.0000	−	13.8564i	0.0738462	−	0.0426351i
$326$	17.0000	−	29.4449i	0.0521472	−	0.0903217i
$327$	7.50000	+	4.33013i	0.0229358	+	0.0132420i
$328$	208.000			0.634146
$329$		0			0
$330$	−153.000	+	88.3346i	−0.463636	+	0.267681i
$331$	147.500	−	255.477i	0.445619	−	0.771835i	−0.552476	−	0.833529i	$-0.686317\pi$
$331$	147.500	−	255.477i	0.445619	−	0.771835i	0.998095	+	0.0616936i	$0.0196502\pi$
$332$	−440.000			−1.32530
$333$	60.0000	−	34.6410i	0.180180	−	0.104027i
$334$			27.7128i			0.0829725i
$335$		−	88.3346i		−	0.263685i
$336$		0			0
$337$	26.0000			0.0771513			0.0385757	−	0.999256i	$-0.487718\pi$
$337$	26.0000			0.0771513			0.0385757	+	0.999256i	$0.487718\pi$
$338$	46.0000			0.136095
$339$	61.0000	+	105.655i	0.179941	+	0.311667i
$340$		−	519.615i		−	1.52828i
$341$	484.500	+	279.726i	1.42082	+	0.820311i
$342$	−56.0000	−	96.9948i	−0.163743	−	0.283611i
$343$		0			0
$344$	−112.000			−0.325581
$345$	−13.5000	+	23.3827i	−0.0391304	+	0.0677759i
$346$	183.000	+	105.655i	0.528902	+	0.305362i
$347$	−188.500	−	326.492i	−0.543228	−	0.940898i	−0.998716	−	0.0506562i	$-0.983869\pi$
$347$	−188.500	−	326.492i	−0.543228	−	0.940898i	0.455488	−	0.890242i	$-0.349465\pi$
$348$	48.0000	−	27.7128i	0.137931	−	0.0796345i
$349$			96.9948i			0.277922i	0.990298	+	0.138961i	$0.0443763\pi$
$349$			96.9948i			0.277922i	−0.990298	+	0.138961i	$0.955624\pi$
$350$		0			0
$351$		−	235.559i		−	0.671108i
$352$	272.000	+	471.118i	0.772727	+	1.33840i
$353$	251.500	+	435.611i	0.712465	+	1.23402i	0.963929	+	0.266158i	$0.0857544\pi$
$353$	251.500	+	435.611i	0.712465	+	1.23402i	−0.251465	+	0.967866i	$0.580912\pi$
$354$	−55.0000	+	95.2628i	−0.155367	+	0.269104i
$355$		0			0
$356$	142.000	−	245.951i	0.398876	−	0.690874i
$357$		0			0
$358$	89.0000	+	154.153i	0.248603	+	0.430594i
$359$	160.500	+	92.6647i	0.447075	+	0.258119i	0.706594	−	0.707619i	$-0.250231\pi$
$359$	160.500	+	92.6647i	0.447075	+	0.258119i	−0.259519	+	0.965738i	$0.583564\pi$
$360$	−288.000	+	166.277i	−0.800000	+	0.461880i
$361$	156.000	+	270.200i	0.432133	+	0.748476i
$362$		−	498.831i		−	1.37799i
$363$	−168.000			−0.462810
$364$		0			0
$365$			618.342i			1.69409i
$366$			45.0333i			0.123042i
$367$	−256.500	+	148.090i	−0.698910	+	0.403516i	−0.806941	−	0.590632i	$-0.798879\pi$
$367$	−256.500	+	148.090i	−0.698910	+	0.403516i	0.108031	+	0.994147i	$0.465545\pi$
$368$	72.0000	+	41.5692i	0.195652	+	0.112960i
$369$	−104.000	+	180.133i	−0.281843	+	0.488166i
$370$	−45.0000	−	77.9423i	−0.121622	−	0.210655i
$371$		0			0
$372$	−114.000	−	65.8179i	−0.306452	−	0.176930i
$373$	103.500	+	59.7558i	0.277480	+	0.160203i	0.632282	−	0.774738i	$-0.282118\pi$
$373$	103.500	+	59.7558i	0.277480	+	0.160203i	−0.354802	+	0.934941i	$0.615452\pi$
$374$	425.000	−	736.122i	1.13636	−	1.96824i
$375$	103.500	−	59.7558i	0.276000	−	0.159349i
$376$	−348.000	−	200.918i	−0.925532	−	0.534356i
$377$	−192.000			−0.509284
$378$		0			0
$379$	−634.000			−1.67282			−0.836412	−	0.548102i	$-0.815351\pi$
$379$	−634.000			−1.67282			−0.836412	+	0.548102i	$0.815351\pi$
$380$	−126.000	+	72.7461i	−0.331579	+	0.191437i
$381$	−144.000	+	83.1384i	−0.377953	+	0.218211i
$382$	375.000	+	216.506i	0.981675	+	0.566771i
$383$	211.500	+	122.110i	0.552219	+	0.318824i	0.750017	−	0.661419i	$-0.230045\pi$
$383$	211.500	+	122.110i	0.552219	+	0.318824i	−0.197797	+	0.980243i	$0.563379\pi$
$384$	−64.0000	−	110.851i	−0.166667	−	0.288675i
$385$		0			0
$386$	−73.0000	−	126.440i	−0.189119	−	0.327564i
$387$	56.0000	−	96.9948i	0.144703	−	0.250633i
$388$	88.0000			0.226804
$389$	−508.500	+	293.583i	−1.30720	+	0.754711i	−0.981628	−	0.190807i	$-0.938890\pi$
$389$	−508.500	+	293.583i	−1.30720	+	0.754711i	−0.325570	+	0.945518i	$0.605556\pi$
$390$	−144.000			−0.369231
$391$		−	129.904i		−	0.332235i
$392$		0			0
$393$	17.0000			0.0432570
$394$			415.692i			1.05506i
$395$	193.500	+	335.152i	0.489873	+	0.848486i
$396$	−544.000			−1.37374
$397$	208.500	+	120.378i	0.525189	+	0.303218i	0.739055	−	0.673645i	$-0.235272\pi$
$397$	208.500	+	120.378i	0.525189	+	0.303218i	−0.213866	+	0.976863i	$0.568606\pi$
$398$	−111.000	+	64.0859i	−0.278894	+	0.161020i
$399$		0			0
$400$	16.0000	+	27.7128i	0.0400000	+	0.0692820i
$401$	−59.5000	+	103.057i	−0.148379	+	0.257000i	−0.930629	−	0.365965i	$-0.880739\pi$
$401$	−59.5000	+	103.057i	−0.148379	+	0.257000i	0.782249	+	0.622965i	$0.214072\pi$
$402$	−17.0000	+	29.4449i	−0.0422886	+	0.0732459i
$403$	228.000	+	394.908i	0.565757	+	0.979920i
$404$	−270.000	+	155.885i	−0.668317	+	0.385853i
$405$		−	285.788i		−	0.705650i
$406$		0			0
$407$		−	147.224i		−	0.361731i
$408$	−100.000	+	173.205i	−0.245098	+	0.424522i
$409$	−72.5000	−	125.574i	−0.177262	−	0.307026i	0.763680	−	0.645595i	$-0.223391\pi$
$409$	−72.5000	−	125.574i	−0.177262	−	0.307026i	−0.940942	+	0.338569i	$0.890057\pi$
$410$	234.000	+	135.100i	0.570732	+	0.329512i
$411$	−72.5000	+	125.574i	−0.176399	+	0.305532i
$412$	558.000	+	322.161i	1.35437	+	0.781945i
$413$		0			0
$414$	−72.0000	+	41.5692i	−0.173913	+	0.100409i
$415$	−495.000	−	285.788i	−1.19277	−	0.688647i
$416$			443.405i			1.06588i
$417$	41.0000	+	71.0141i	0.0983213	+	0.170298i
$418$	−238.000			−0.569378
$419$	−302.000			−0.720764			−0.360382	−	0.932805i	$-0.617354\pi$
$419$	−302.000			−0.720764			−0.360382	+	0.932805i	$0.617354\pi$
$420$		0			0
$421$			401.836i			0.954479i	0.878773	+	0.477240i	$0.158363\pi$
$421$			401.836i			0.954479i	−0.878773	+	0.477240i	$0.841637\pi$
$422$	−604.000			−1.43128
$423$	348.000	−	200.918i	0.822695	−	0.474983i
$424$	−636.000	+	367.195i	−1.50000	+	0.866025i
$425$	25.0000	−	43.3013i	0.0588235	−	0.101885i
$426$		0			0
$427$		0			0
$428$	−130.000	+	225.167i	−0.303738	+	0.526090i
$429$	−204.000	−	117.779i	−0.475524	−	0.274544i
$430$	−126.000	−	72.7461i	−0.293023	−	0.169177i
$431$	700.500	−	404.434i	1.62529	−	0.938362i	0.639817	−	0.768527i	$-0.279010\pi$
$431$	700.500	−	404.434i	1.62529	−	0.938362i	0.985473	−	0.169835i	$-0.0543234\pi$
$432$	272.000			0.629630
$433$	−410.000			−0.946882			−0.473441	−	0.880825i	$-0.656988\pi$
$433$	−410.000			−0.946882			−0.473441	+	0.880825i	$0.656988\pi$
$434$		0			0
$435$	72.0000			0.165517
$436$	30.0000	−	17.3205i	0.0688073	−	0.0397259i
$437$	−31.5000	+	18.1865i	−0.0720824	+	0.0416168i
$438$	119.000	−	206.114i	0.271689	−	0.470580i
$439$	−424.500	−	245.085i	−0.966970	−	0.558281i	−0.0686591	−	0.997640i	$-0.521872\pi$
$439$	−424.500	−	245.085i	−0.966970	−	0.558281i	−0.898311	+	0.439360i	$0.855205\pi$
$440$			706.677i			1.60608i
$441$		0			0
$442$	600.000	−	346.410i	1.35747	−	0.783733i
$443$	−200.500	+	347.276i	−0.452596	+	0.783919i	−0.998546	−	0.0538983i	$-0.982835\pi$
$443$	−200.500	+	347.276i	−0.452596	+	0.783919i	0.545950	+	0.837817i	$0.316169\pi$
$444$			34.6410i			0.0780203i
$445$	319.500	−	184.463i	0.717978	−	0.414525i
$446$		−	277.128i		−	0.621364i
$447$		−	5.19615i		−	0.0116245i
$448$		0			0
$449$	−310.000			−0.690423			−0.345212	−	0.938525i	$-0.612193\pi$
$449$	−310.000			−0.690423			−0.345212	+	0.938525i	$0.612193\pi$
$450$	−32.0000			−0.0711111
$451$	221.000	+	382.783i	0.490022	+	0.848743i
$452$	488.000			1.07965
$453$	−31.5000	−	18.1865i	−0.0695364	−	0.0401469i
$454$	55.0000	+	95.2628i	0.121145	+	0.209830i
$455$		0			0
$456$	56.0000			0.122807
$457$	−83.5000	+	144.626i	−0.182713	+	0.316469i	−0.942804	−	0.333349i	$-0.891821\pi$
$457$	−83.5000	+	144.626i	−0.182713	+	0.316469i	0.760090	+	0.649818i	$0.225155\pi$
$458$	567.000	+	327.358i	1.23799	+	0.714755i
$459$	−212.500	−	368.061i	−0.462963	−	0.801875i
$460$	54.0000	+	93.5307i	0.117391	+	0.203328i
$461$			13.8564i			0.0300573i	0.999887	+	0.0150286i	$0.00478394\pi$
$461$			13.8564i			0.0300573i	−0.999887	+	0.0150286i	$0.995216\pi$
$462$		0			0
$463$		−	609.682i		−	1.31681i	−0.752665	−	0.658404i	$-0.771232\pi$
$463$		−	609.682i		−	1.31681i	0.752665	−	0.658404i	$-0.228768\pi$
$464$		−	221.703i		−	0.477807i
$465$	−85.5000	−	148.090i	−0.183871	−	0.318474i
$466$	−385.000	+	666.840i	−0.826180	+	1.43099i
$467$	392.500	−	679.830i	0.840471	−	1.45574i	−0.0490258	−	0.998798i	$-0.515612\pi$
$467$	392.500	−	679.830i	0.840471	−	1.45574i	0.889497	−	0.456941i	$-0.151055\pi$
$468$	−384.000	−	221.703i	−0.820513	−	0.473723i
$469$		0			0
$470$	−261.000	−	452.065i	−0.555319	−	0.961841i
$471$	268.500	+	155.019i	0.570064	+	0.329126i
$472$	220.000	+	381.051i	0.466102	+	0.807312i
$473$	−119.000	−	206.114i	−0.251586	−	0.435759i
$474$		−	148.956i		−	0.314254i
$475$	−14.0000			−0.0294737
$476$		0			0
$477$		−	734.390i		−	1.53960i
$478$		−	859.097i		−	1.79727i
$479$	535.500	−	309.171i	1.11795	−	0.645451i	0.177076	−	0.984197i	$-0.443336\pi$
$479$	535.500	−	309.171i	1.11795	−	0.645451i	0.940878	+	0.338746i	$0.110003\pi$
$480$		−	166.277i		−	0.346410i
$481$	60.0000	−	103.923i	0.124740	−	0.216056i
$482$	145.000	+	251.147i	0.300830	+	0.521053i
$483$		0			0
$484$	−336.000	+	581.969i	−0.694215	+	1.20242i
$485$	99.0000	+	57.1577i	0.204124	+	0.117851i
$486$	−208.000	+	360.267i	−0.427984	+	0.741289i
$487$	340.500	−	196.588i	0.699179	−	0.403671i	−0.107863	−	0.994166i	$-0.534401\pi$
$487$	340.500	−	196.588i	0.699179	−	0.403671i	0.807041	+	0.590495i	$0.201067\pi$
$488$	156.000	+	90.0666i	0.319672	+	0.184563i
$489$	−17.0000			−0.0347648
$490$		0			0
$491$	422.000			0.859470			0.429735	−	0.902955i	$-0.358607\pi$
$491$	422.000			0.859470			0.429735	+	0.902955i	$0.358607\pi$
$492$	−52.0000	−	90.0666i	−0.105691	−	0.183062i
$493$	−300.000	+	173.205i	−0.608519	+	0.351329i
$494$	−168.000	−	96.9948i	−0.340081	−	0.196346i
$495$	−612.000	−	353.338i	−1.23636	−	0.713815i
$496$	−456.000	+	263.272i	−0.919355	+	0.530790i
$497$		0			0
$498$	110.000	+	190.526i	0.220884	+	0.382582i
$499$	−32.5000	+	56.2917i	−0.0651303	+	0.112809i	−0.896752	−	0.442534i	$-0.854080\pi$
$499$	−32.5000	+	56.2917i	−0.0651303	+	0.112809i	0.831622	+	0.555343i	$0.187413\pi$
$500$		−	478.046i		−	0.956092i
$501$	12.0000	−	6.92820i	0.0239521	−	0.0138287i
$502$	−116.000			−0.231076
$503$		−	249.415i		−	0.495855i	−0.968779	−	0.247928i	$-0.920250\pi$
$503$		−	249.415i		−	0.495855i	0.968779	−	0.247928i	$-0.0797496\pi$
$504$		0			0
$505$	−405.000			−0.801980
$506$			176.669i			0.349149i
$507$	−11.5000	−	19.9186i	−0.0226824	−	0.0392871i
$508$			665.108i			1.30927i
$509$	472.500	+	272.798i	0.928291	+	0.535949i	0.886271	−	0.463168i	$-0.153287\pi$
$509$	472.500	+	272.798i	0.928291	+	0.535949i	0.0420202	+	0.999117i	$0.486621\pi$
$510$	−225.000	+	129.904i	−0.441176	+	0.254713i
$511$		0			0
$512$	−512.000			−1.00000
$513$	−59.5000	+	103.057i	−0.115984	+	0.200891i
$514$	−119.000	+	206.114i	−0.231518	+	0.401000i
$515$	418.500	+	724.863i	0.812621	+	1.40750i
$516$	28.0000	+	48.4974i	0.0542636	+	0.0939873i
$517$		−	853.901i		−	1.65165i
$518$		0			0
$519$		−	105.655i		−	0.203574i
$520$	−288.000	+	498.831i	−0.553846	+	0.959290i
$521$	−12.5000	−	21.6506i	−0.0239923	−	0.0415559i	0.853780	−	0.520634i	$-0.174304\pi$
$521$	−12.5000	−	21.6506i	−0.0239923	−	0.0415559i	−0.877772	+	0.479078i	$0.840971\pi$
$522$	192.000	+	110.851i	0.367816	+	0.212359i
$523$	296.500	−	513.553i	0.566922	−	0.981937i	−0.429946	−	0.902854i	$-0.641468\pi$
$523$	296.500	−	513.553i	0.566922	−	0.981937i	0.996868	−	0.0790826i	$-0.0251991\pi$
$524$	34.0000	−	58.8897i	0.0648855	−	0.112385i
$525$		0			0
$526$	567.000	−	327.358i	1.07795	−	0.622353i
$527$	712.500	+	411.362i	1.35199	+	0.780573i
$528$	136.000	−	235.559i	0.257576	−	0.446134i
$529$	−251.000	−	434.745i	−0.474480	−	0.821824i
$530$	−954.000			−1.80000
$531$	−440.000			−0.828625
$532$		0			0
$533$			360.267i			0.675922i
$534$	−142.000			−0.265918
$535$	−292.500	+	168.875i	−0.546729	+	0.315654i
$536$	68.0000	+	117.779i	0.126866	+	0.219738i
$537$	44.5000	−	77.0763i	0.0828678	−	0.143531i
$538$	231.000	−	133.368i	0.429368	−	0.247896i
$539$		0			0
$540$	306.000	+	176.669i	0.566667	+	0.327165i
$541$	655.500	+	378.453i	1.21165	+	0.699544i	0.963117	−	0.269081i	$-0.0867200\pi$
$541$	655.500	+	378.453i	1.21165	+	0.699544i	0.248528	+	0.968625i	$0.420053\pi$
$542$	753.000	+	434.745i	1.38930	+	0.802112i
$543$	−216.000	+	124.708i	−0.397790	+	0.229664i
$544$	400.000	+	692.820i	0.735294	+	1.27357i
$545$	45.0000			0.0825688
$546$		0			0
$547$	662.000			1.21024			0.605119	−	0.796135i	$-0.293126\pi$
$547$	662.000			1.21024			0.605119	+	0.796135i	$0.293126\pi$
$548$	290.000	+	502.295i	0.529197	+	0.916596i
$549$	−156.000	+	90.0666i	−0.284153	+	0.164056i
$550$	−34.0000	+	58.8897i	−0.0618182	+	0.107072i
$551$	84.0000	+	48.4974i	0.152450	+	0.0880171i
$552$		−	41.5692i		−	0.0753066i
$553$		0			0
$554$	−351.000	+	202.650i	−0.633574	+	0.365794i
$555$	−22.5000	+	38.9711i	−0.0405405	+	0.0702183i
$556$	328.000			0.589928
$557$	511.500	−	295.315i	0.918312	−	0.530188i	0.0352161	−	0.999380i	$-0.488788\pi$
$557$	511.500	−	295.315i	0.918312	−	0.530188i	0.883096	+	0.469192i	$0.155455\pi$
$558$		−	526.543i		−	0.943626i
$559$		−	193.990i		−	0.347030i
$560$		0			0
$561$	−425.000			−0.757576
$562$	−148.000			−0.263345
$563$	368.500	+	638.261i	0.654529	+	1.13368i	0.982012	+	0.188821i	$0.0604665\pi$
$563$	368.500	+	638.261i	0.654529	+	1.13368i	−0.327482	+	0.944857i	$0.606200\pi$
$564$			200.918i			0.356237i
$565$	549.000	+	316.965i	0.971681	+	0.561001i
$566$	463.000	+	801.940i	0.818021	+	1.41685i
$567$		0			0
$568$		0			0
$569$	60.5000	−	104.789i	0.106327	−	0.184164i	−0.807953	−	0.589247i	$-0.799424\pi$
$569$	60.5000	−	104.789i	0.106327	−	0.184164i	0.914280	+	0.405084i	$0.132758\pi$
$570$	63.0000	+	36.3731i	0.110526	+	0.0638124i
$571$	−368.500	−	638.261i	−0.645359	−	1.11779i	−0.984218	−	0.176958i	$-0.943374\pi$
$571$	−368.500	−	638.261i	−0.645359	−	1.11779i	0.338859	−	0.940837i	$-0.389959\pi$
$572$	−816.000	+	471.118i	−1.42657	+	0.823633i
$573$		−	216.506i		−	0.377847i
$574$		0			0
$575$			10.3923i			0.0180736i
$576$	256.000	−	443.405i	0.444444	−	0.769800i
$577$	23.5000	+	40.7032i	0.0407279	+	0.0705428i	0.885671	−	0.464314i	$-0.153699\pi$
$577$	23.5000	+	40.7032i	0.0407279	+	0.0705428i	−0.844943	+	0.534857i	$0.820366\pi$
$578$	336.000	−	581.969i	0.581315	−	1.00687i
$579$	−36.5000	+	63.2199i	−0.0630397	+	0.109188i
$580$	144.000	−	249.415i	0.248276	−	0.430026i
$581$		0			0
$582$	−22.0000	−	38.1051i	−0.0378007	−	0.0654727i
$583$	−1351.50	−	780.289i	−2.31818	−	1.33840i
$584$	−476.000	−	824.456i	−0.815068	−	1.41174i
$585$	−288.000	−	498.831i	−0.492308	−	0.852702i
$586$		−	221.703i		−	0.378332i
$587$	−446.000			−0.759796			−0.379898	−	0.925028i	$-0.624041\pi$
$587$	−446.000			−0.759796			−0.379898	+	0.925028i	$0.624041\pi$
$588$		0			0
$589$		−	230.363i		−	0.391108i
$590$			571.577i			0.968774i
$591$	180.000	−	103.923i	0.304569	−	0.175843i
$592$	120.000	+	69.2820i	0.202703	+	0.117030i
$593$	107.500	−	186.195i	0.181282	−	0.313989i	−0.761036	−	0.648710i	$-0.775309\pi$
$593$	107.500	−	186.195i	0.181282	−	0.313989i	0.942317	+	0.334721i	$0.108642\pi$
$594$	289.000	+	500.563i	0.486532	+	0.842698i
$595$		0			0
$596$	−18.0000	−	10.3923i	−0.0302013	−	0.0174368i
$597$	55.5000	+	32.0429i	0.0929648	+	0.0536733i
$598$	−72.0000	+	124.708i	−0.120401	+	0.208541i
$599$	244.500	−	141.162i	0.408180	−	0.235663i	−0.281827	−	0.959465i	$-0.590941\pi$
$599$	244.500	−	141.162i	0.408180	−	0.235663i	0.690008	+	0.723802i	$0.257607\pi$
$600$	8.00000	−	13.8564i	0.0133333	−	0.0230940i
$601$	−266.000			−0.442596			−0.221298	−	0.975206i	$-0.571029\pi$
$601$	−266.000			−0.442596			−0.221298	+	0.975206i	$0.571029\pi$
$602$		0			0
$603$	−136.000			−0.225539
$604$	−126.000	+	72.7461i	−0.208609	+	0.120441i
$605$	−756.000	+	436.477i	−1.24959	+	0.721449i
$606$	135.000	+	77.9423i	0.222772	+	0.128618i
$607$	571.500	+	329.956i	0.941516	+	0.543584i	0.890435	−	0.455110i	$-0.150400\pi$
$607$	571.500	+	329.956i	0.941516	+	0.543584i	0.0510805	+	0.998695i	$0.483733\pi$
$608$	112.000	−	193.990i	0.184211	−	0.319062i
$609$		0			0
$610$	117.000	+	202.650i	0.191803	+	0.332213i
$611$	348.000	−	602.754i	0.569558	−	0.986504i
$612$	−800.000			−1.30719
$613$	−604.500	+	349.008i	−0.986134	+	0.569345i	−0.904116	−	0.427286i	$-0.859470\pi$
$613$	−604.500	+	349.008i	−0.986134	+	0.569345i	−0.0820174	+	0.996631i	$0.526136\pi$
$614$	−548.000			−0.892508
$615$		−	135.100i		−	0.219675i
$616$		0			0
$617$	−118.000			−0.191248			−0.0956240	−	0.995418i	$-0.530485\pi$
$617$	−118.000			−0.191248			−0.0956240	+	0.995418i	$0.530485\pi$
$618$		−	322.161i		−	0.521297i
$619$	−459.500	−	795.877i	−0.742326	−	1.28575i	−0.951434	−	0.307854i	$-0.900389\pi$
$619$	−459.500	−	795.877i	−0.742326	−	1.28575i	0.209107	−	0.977893i	$-0.432944\pi$
$620$	−684.000			−1.10323
$621$	76.5000	+	44.1673i	0.123188	+	0.0711229i
$622$	−87.0000	+	50.2295i	−0.139871	+	0.0807548i
$623$		0			0
$624$	192.000	−	110.851i	0.307692	−	0.177646i
$625$	335.500	−	581.103i	0.536800	−	0.929765i
$626$	409.000	−	708.409i	0.653355	−	1.13164i
$627$	59.5000	+	103.057i	0.0948963	+	0.164365i
$628$	1074.00	−	620.074i	1.71019	−	0.987379i
$629$		−	216.506i		−	0.344207i
$630$		0			0
$631$			166.277i			0.263513i	0.991282	+	0.131757i	$0.0420617\pi$
$631$			166.277i			0.263513i	−0.991282	+	0.131757i	$0.957938\pi$
$632$	−516.000	−	297.913i	−0.816456	−	0.471381i
$633$	151.000	+	261.540i	0.238547	+	0.413175i
$634$	−327.000	−	188.794i	−0.515773	−	0.297782i
$635$	−432.000	+	748.246i	−0.680315	+	1.17834i
$636$	318.000	+	183.597i	0.500000	+	0.288675i
$637$		0			0
$638$	408.000	−	235.559i	0.639498	−	0.369215i
$639$		0			0
$640$	−576.000	−	332.554i	−0.900000	−	0.519615i
$641$	0.500000	+	0.866025i	0.000780031	+	0.00135105i	0.866415	−	0.499324i	$-0.166418\pi$
$641$	0.500000	+	0.866025i	0.000780031	+	0.00135105i	−0.865635	+	0.500675i	$0.833085\pi$
$642$	130.000			0.202492
$643$	514.000			0.799378			0.399689	−	0.916651i	$-0.369118\pi$
$643$	514.000			0.799378			0.399689	+	0.916651i	$0.369118\pi$
$644$		0			0
$645$			72.7461i			0.112785i
$646$	−350.000			−0.541796
$647$	−52.5000	+	30.3109i	−0.0811437	+	0.0468484i	−0.540023	−	0.841650i	$-0.681584\pi$
$647$	−52.5000	+	30.3109i	−0.0811437	+	0.0468484i	0.458879	+	0.888499i	$0.348251\pi$
$648$	220.000	+	381.051i	0.339506	+	0.588042i
$649$	−467.500	+	809.734i	−0.720339	+	1.24766i
$650$	−48.0000	+	27.7128i	−0.0738462	+	0.0426351i
$651$		0			0
$652$	−34.0000	+	58.8897i	−0.0521472	+	0.0903217i
$653$	283.500	+	163.679i	0.434150	+	0.250657i	0.701113	−	0.713050i	$-0.252687\pi$
$653$	283.500	+	163.679i	0.434150	+	0.250657i	−0.266963	+	0.963707i	$0.586020\pi$
$654$	−15.0000	−	8.66025i	−0.0229358	−	0.0132420i
$655$	76.5000	−	44.1673i	0.116794	−	0.0674310i
$656$	−416.000			−0.634146
$657$	952.000			1.44901
$658$		0			0
$659$	542.000			0.822458			0.411229	−	0.911532i	$-0.365100\pi$
$659$	542.000			0.822458			0.411229	+	0.911532i	$0.365100\pi$
$660$	306.000	−	176.669i	0.463636	−	0.267681i
$661$	1024.50	−	591.495i	1.54992	−	0.894849i	0.551778	−	0.833991i	$-0.313950\pi$
$661$	1024.50	−	591.495i	1.54992	−	0.894849i	0.998146	−	0.0608582i	$-0.0193837\pi$
$662$	−295.000	+	510.955i	−0.445619	+	0.771835i
$663$	−300.000	−	173.205i	−0.452489	−	0.261244i
$664$	880.000			1.32530
$665$		0			0
$666$	−120.000	+	69.2820i	−0.180180	+	0.104027i
$667$	36.0000	−	62.3538i	0.0539730	−	0.0934840i
$668$		−	55.4256i		−	0.0829725i
$669$	−120.000	+	69.2820i	−0.179372	+	0.103561i
$670$			176.669i			0.263685i
$671$			382.783i			0.570467i
$672$		0			0
$673$	218.000			0.323923			0.161961	−	0.986797i	$-0.448218\pi$
$673$	218.000			0.323923			0.161961	+	0.986797i	$0.448218\pi$
$674$	−52.0000			−0.0771513
$675$	17.0000	+	29.4449i	0.0251852	+	0.0436220i
$676$	−92.0000			−0.136095
$677$	556.500	+	321.295i	0.822009	+	0.474587i	0.851109	−	0.524989i	$-0.175931\pi$
$677$	556.500	+	321.295i	0.822009	+	0.474587i	−0.0290999	+	0.999577i	$0.509264\pi$
$678$	−122.000	−	211.310i	−0.179941	−	0.311667i
$679$		0			0
$680$			1039.23i			1.52828i
$681$	27.5000	−	47.6314i	0.0403818	−	0.0699433i
$682$	−969.000	−	559.452i	−1.42082	−	0.820311i
$683$	183.500	+	317.831i	0.268668	+	0.465346i	0.968518	−	0.248943i	$-0.0800833\pi$
$683$	183.500	+	317.831i	0.268668	+	0.465346i	−0.699850	+	0.714289i	$0.746750\pi$
$684$	112.000	+	193.990i	0.163743	+	0.283611i
$685$			753.442i			1.09992i
$686$		0			0
$687$		−	327.358i		−	0.476503i
$688$	224.000			0.325581
$689$	−636.000	−	1101.58i	−0.923077	−	1.59882i
$690$	27.0000	−	46.7654i	0.0391304	−	0.0677759i
$691$	248.500	−	430.415i	0.359624	−	0.622887i	−0.628274	−	0.777992i	$-0.716238\pi$
$691$	248.500	−	430.415i	0.359624	−	0.622887i	0.987898	+	0.155105i	$0.0495717\pi$
$692$	−366.000	−	211.310i	−0.528902	−	0.305362i
$693$		0			0
$694$	377.000	+	652.983i	0.543228	+	0.940898i
$695$	369.000	+	213.042i	0.530935	+	0.306536i
$696$	−96.0000	+	55.4256i	−0.137931	+	0.0796345i
$697$	325.000	+	562.917i	0.466284	+	0.807628i
$698$		−	193.990i		−	0.277922i
$699$	385.000			0.550787
$700$		0			0
$701$			332.554i			0.474399i	0.971461	+	0.237200i	$0.0762295\pi$
$701$			332.554i			0.474399i	−0.971461	+	0.237200i	$0.923770\pi$
$702$			471.118i			0.671108i
$703$	−52.5000	+	30.3109i	−0.0746799	+	0.0431165i
$704$	−544.000	−	942.236i	−0.772727	−	1.33840i
$705$	−130.500	+	226.033i	−0.185106	+	0.320614i
$706$	−503.000	−	871.222i	−0.712465	−	1.23402i
$707$		0			0
$708$	110.000	−	190.526i	0.155367	−	0.269104i
$709$	343.500	+	198.320i	0.484485	+	0.279718i	0.722284	−	0.691597i	$-0.243092\pi$
$709$	343.500	+	198.320i	0.484485	+	0.279718i	−0.237799	+	0.971314i	$0.576426\pi$
$710$		0			0
$711$	516.000	−	297.913i	0.725738	−	0.419005i
$712$	−284.000	+	491.902i	−0.398876	+	0.690874i
$713$	−171.000			−0.239832
$714$		0			0
$715$	−1224.00			−1.71189
$716$	−178.000	−	308.305i	−0.248603	−	0.430594i
$717$	−372.000	+	214.774i	−0.518828	+	0.299546i
$718$	−321.000	−	185.329i	−0.447075	−	0.258119i
$719$	55.5000	+	32.0429i	0.0771905	+	0.0445660i	0.538098	−	0.842882i	$-0.319143\pi$
$719$	55.5000	+	32.0429i	0.0771905	+	0.0445660i	−0.460908	+	0.887448i	$0.652476\pi$
$720$	576.000	−	332.554i	0.800000	−	0.461880i
$721$		0			0
$722$	−312.000	−	540.400i	−0.432133	−	0.748476i
$723$	72.5000	−	125.574i	0.100277	−	0.173684i
$724$			997.661i			1.37799i
$725$	24.0000	−	13.8564i	0.0331034	−	0.0191123i
$726$	336.000			0.462810
$727$			55.4256i			0.0762388i	0.999273	+	0.0381194i	$0.0121367\pi$
$727$			55.4256i			0.0762388i	−0.999273	+	0.0381194i	$0.987863\pi$
$728$		0			0
$729$	−287.000			−0.393690
$730$		−	1236.68i		−	1.69409i
$731$	−175.000	−	303.109i	−0.239398	−	0.414650i
$732$		−	90.0666i		−	0.123042i
$733$	−715.500	−	413.094i	−0.976126	−	0.563566i	−0.0750273	−	0.997181i	$-0.523904\pi$
$733$	−715.500	−	413.094i	−0.976126	−	0.563566i	−0.901098	+	0.433615i	$0.857238\pi$
$734$	513.000	−	296.181i	0.698910	−	0.403516i
$735$		0			0
$736$	−144.000	−	83.1384i	−0.195652	−	0.112960i
$737$	−144.500	+	250.281i	−0.196065	+	0.339595i
$738$	208.000	−	360.267i	0.281843	−	0.488166i
$739$	−356.500	−	617.476i	−0.482409	−	0.835556i	0.517387	−	0.855751i	$-0.326905\pi$
$739$	−356.500	−	617.476i	−0.482409	−	0.835556i	−0.999796	+	0.0201950i	$0.993571\pi$
$740$	90.0000	+	155.885i	0.121622	+	0.210655i
$741$			96.9948i			0.130897i
$742$		0			0
$743$			637.395i			0.857866i	0.903336	+	0.428933i	$0.141110\pi$
$743$			637.395i			0.857866i	−0.903336	+	0.428933i	$0.858890\pi$
$744$	228.000	+	131.636i	0.306452	+	0.176930i
$745$	−13.5000	−	23.3827i	−0.0181208	−	0.0313862i
$746$	−207.000	−	119.512i	−0.277480	−	0.160203i
$747$	−440.000	+	762.102i	−0.589023	+	1.02022i
$748$	−850.000	+	1472.24i	−1.13636	+	1.96824i
$749$		0			0
$750$	−207.000	+	119.512i	−0.276000	+	0.159349i
$751$	1012.50	+	584.567i	1.34820	+	0.778385i	0.987995	−	0.154487i	$-0.0493725\pi$
$751$	1012.50	+	584.567i	1.34820	+	0.778385i	0.360208	+	0.932872i	$0.382706\pi$
$752$	696.000	+	401.836i	0.925532	+	0.534356i
$753$	29.0000	+	50.2295i	0.0385126	+	0.0667058i
$754$	384.000			0.509284
$755$	−189.000			−0.250331
$756$		0			0
$757$			1039.23i			1.37283i	0.727211	+	0.686414i	$0.240816\pi$
$757$			1039.23i			1.37283i	−0.727211	+	0.686414i	$0.759184\pi$
$758$	1268.00			1.67282
$759$	76.5000	−	44.1673i	0.100791	−	0.0581914i
$760$	252.000	−	145.492i	0.331579	−	0.191437i
$761$	431.500	−	747.380i	0.567017	−	0.982102i	−0.429842	−	0.902904i	$-0.641431\pi$
$761$	431.500	−	747.380i	0.567017	−	0.982102i	0.996859	−	0.0791982i	$-0.0252360\pi$
$762$	288.000	−	166.277i	0.377953	−	0.218211i
$763$		0			0
$764$	−750.000	−	433.013i	−0.981675	−	0.566771i
$765$	−900.000	−	519.615i	−1.17647	−	0.679236i
$766$	−423.000	−	244.219i	−0.552219	−	0.318824i
$767$	−660.000	+	381.051i	−0.860495	+	0.496807i
$768$	128.000	+	221.703i	0.166667	+	0.288675i
$769$	−410.000			−0.533160			−0.266580	−	0.963813i	$-0.585894\pi$
$769$	−410.000			−0.533160			−0.266580	+	0.963813i	$0.585894\pi$
$770$		0			0
$771$	119.000			0.154345
$772$	146.000	+	252.879i	0.189119	+	0.327564i
$773$	−691.500	+	399.238i	−0.894567	+	0.516478i	−0.875433	−	0.483339i	$-0.839424\pi$
$773$	−691.500	+	399.238i	−0.894567	+	0.516478i	−0.0191332	+	0.999817i	$0.506091\pi$
$774$	−112.000	+	193.990i	−0.144703	+	0.250633i
$775$	−57.0000	−	32.9090i	−0.0735484	−	0.0424632i
$776$	−176.000			−0.226804
$777$		0			0
$778$	1017.00	−	587.165i	1.30720	−	0.754711i
$779$	91.0000	−	157.617i	0.116816	−	0.202332i
$780$	288.000			0.369231
$781$		0			0
$782$			259.808i			0.332235i
$783$		−	235.559i		−	0.300842i
$784$		0			0
$785$	1611.00			2.05223
$786$	−34.0000			−0.0432570
$787$	−15.5000	−	26.8468i	−0.0196950	−	0.0341128i	0.856010	−	0.516959i	$-0.172936\pi$
$787$	−15.5000	−	26.8468i	−0.0196950	−	0.0341128i	−0.875705	+	0.482847i	$0.839603\pi$
$788$		−	831.384i		−	1.05506i
$789$	−283.500	−	163.679i	−0.359316	−	0.207451i
$790$	−387.000	−	670.304i	−0.489873	−	0.848486i
$791$		0			0
$792$	1088.00			1.37374
$793$	−156.000	+	270.200i	−0.196721	+	0.340731i
$794$	−417.000	−	240.755i	−0.525189	−	0.303218i
$795$	238.500	+	413.094i	0.300000	+	0.519615i
$796$	222.000	−	128.172i	0.278894	−	0.161020i
$797$		−	595.825i		−	0.747585i	−0.927512	−	0.373793i	$-0.878057\pi$
$797$		−	595.825i		−	0.747585i	0.927512	−	0.373793i	$-0.121943\pi$
$798$		0			0
$799$		−	1255.74i		−	1.57164i
$800$	−32.0000	−	55.4256i	−0.0400000	−	0.0692820i
$801$	−284.000	−	491.902i	−0.354557	−	0.614110i
$802$	119.000	−	206.114i	0.148379	−	0.257000i
$803$	1011.50	−	1751.97i	1.25965	−	2.18178i
$804$	34.0000	−	58.8897i	0.0422886	−	0.0732459i
$805$		0			0
$806$	−456.000	−	789.815i	−0.565757	−	0.979920i
$807$	−115.500	−	66.6840i	−0.143123	−	0.0826319i
$808$	540.000	−	311.769i	0.668317	−	0.385853i
$809$	156.500	+	271.066i	0.193449	+	0.335063i	0.946391	−	0.323024i	$-0.104699\pi$
$809$	156.500	+	271.066i	0.193449	+	0.335063i	−0.752942	+	0.658087i	$0.771366\pi$
$810$			571.577i			0.705650i
$811$	1138.00			1.40321			0.701603	−	0.712568i	$-0.252468\pi$
$811$	1138.00			1.40321			0.701603	+	0.712568i	$0.252468\pi$
$812$		0			0
$813$		−	434.745i		−	0.534741i
$814$			294.449i			0.361731i
$815$	−76.5000	+	44.1673i	−0.0938650	+	0.0541930i
$816$	200.000	−	346.410i	0.245098	−	0.424522i
$817$	−49.0000	+	84.8705i	−0.0599755	+	0.103881i
$818$	145.000	+	251.147i	0.177262	+	0.307026i
$819$		0			0
$820$	−468.000	−	270.200i	−0.570732	−	0.329512i
$821$	−1060.50	−	612.280i	−1.29172	−	0.745773i	−0.312759	−	0.949833i	$-0.601253\pi$
$821$	−1060.50	−	612.280i	−1.29172	−	0.745773i	−0.978959	+	0.204059i	$0.934587\pi$
$822$	145.000	−	251.147i	0.176399	−	0.305532i
$823$	100.500	−	58.0237i	0.122114	−	0.0705027i	−0.437699	−	0.899122i	$-0.644206\pi$
$823$	100.500	−	58.0237i	0.122114	−	0.0705027i	0.559813	+	0.828619i	$0.310873\pi$
$824$	−1116.00	−	644.323i	−1.35437	−	0.781945i
$825$	34.0000			0.0412121
$826$		0			0
$827$	−754.000			−0.911729			−0.455865	−	0.890049i	$-0.650670\pi$
$827$	−754.000			−0.911729			−0.455865	+	0.890049i	$0.650670\pi$
$828$	144.000	−	83.1384i	0.173913	−	0.100409i
$829$	784.500	−	452.931i	0.946321	−	0.546359i	0.0543848	−	0.998520i	$-0.482680\pi$
$829$	784.500	−	452.931i	0.946321	−	0.546359i	0.891936	+	0.452161i	$0.149347\pi$
$830$	990.000	+	571.577i	1.19277	+	0.688647i
$831$	175.500	+	101.325i	0.211191	+	0.121931i
$832$		−	886.810i		−	1.06588i
$833$		0			0
$834$	−82.0000	−	142.028i	−0.0983213	−	0.170298i
$835$	36.0000	−	62.3538i	0.0431138	−	0.0746752i
$836$	476.000			0.569378
$837$	−484.500	+	279.726i	−0.578853	+	0.334201i
$838$	604.000			0.720764
$839$			1053.09i			1.25517i	0.778548	+	0.627585i	$0.215956\pi$
$839$			1053.09i			1.25517i	−0.778548	+	0.627585i	$0.784044\pi$
$840$		0			0
$841$	649.000			0.771700
$842$		−	803.672i		−	0.954479i
$843$	37.0000	+	64.0859i	0.0438909	+	0.0760212i
$844$	1208.00			1.43128
$845$	−103.500	−	59.7558i	−0.122485	−	0.0707169i
$846$	−696.000	+	401.836i	−0.822695	+	0.474983i
$847$		0			0
$848$	1272.00	−	734.390i	1.50000	−	0.866025i
$849$	231.500	−	400.970i	0.272674	−	0.472285i
$850$	−50.0000	+	86.6025i	−0.0588235	+	0.101885i
$851$	22.5000	+	38.9711i	0.0264395	+	0.0457945i
$852$		0			0
$853$			845.241i			0.990904i	0.868635	+	0.495452i	$0.164997\pi$
$853$			845.241i			0.990904i	−0.868635	+	0.495452i	$0.835003\pi$
$854$		0			0
$855$			290.985i			0.340333i
$856$	260.000	−	450.333i	0.303738	−	0.526090i
$857$	443.500	+	768.165i	0.517503	+	0.896341i	0.999793	+	0.0203300i	$0.00647167\pi$
$857$	443.500	+	768.165i	0.517503	+	0.896341i	−0.482290	+	0.876011i	$0.660195\pi$
$858$	408.000	+	235.559i	0.475524	+	0.274544i
$859$	−831.500	+	1440.20i	−0.967986	+	1.67660i	−0.266617	+	0.963803i	$0.585906\pi$
$859$	−831.500	+	1440.20i	−0.967986	+	1.67660i	−0.701369	+	0.712798i	$0.747427\pi$
$860$	252.000	+	145.492i	0.293023	+	0.169177i
$861$		0			0
$862$	−1401.00	+	808.868i	−1.62529	+	0.938362i
$863$	−487.500	−	281.458i	−0.564890	−	0.326139i	0.190216	−	0.981742i	$-0.439081\pi$
$863$	−487.500	−	281.458i	−0.564890	−	0.326139i	−0.755106	+	0.655603i	$0.772415\pi$
$864$	−544.000			−0.629630
$865$	−274.500	−	475.448i	−0.317341	−	0.549651i
$866$	820.000			0.946882
$867$	−336.000			−0.387543
$868$		0			0
$869$		−	1266.13i		−	1.45700i
$870$	−144.000			−0.165517
$871$	−204.000	+	117.779i	−0.234214	+	0.135223i
$872$	−60.0000	+	34.6410i	−0.0688073	+	0.0397259i
$873$	88.0000	−	152.420i	0.100802	−	0.174594i
$874$	63.0000	−	36.3731i	0.0720824	−	0.0416168i
$875$		0			0
$876$	−238.000	+	412.228i	−0.271689	+	0.470580i
$877$	103.500	+	59.7558i	0.118016	+	0.0681365i	0.557846	−	0.829944i	$-0.311628\pi$
$877$	103.500	+	59.7558i	0.118016	+	0.0681365i	−0.439830	+	0.898081i	$0.644961\pi$
$878$	849.000	+	490.170i	0.966970	+	0.558281i
$879$	−96.0000	+	55.4256i	−0.109215	+	0.0630553i
$880$		−	1413.35i		−	1.60608i
$881$	574.000			0.651532			0.325766	−	0.945450i	$-0.394378\pi$
$881$	574.000			0.651532			0.325766	+	0.945450i	$0.394378\pi$
$882$		0			0
$883$	1166.00			1.32050			0.660249	−	0.751047i	$-0.270451\pi$
$883$	1166.00			1.32050			0.660249	+	0.751047i	$0.270451\pi$
$884$	−1200.00	+	692.820i	−1.35747	+	0.783733i
$885$	247.500	−	142.894i	0.279661	−	0.161462i
$886$	401.000	−	694.552i	0.452596	−	0.783919i
$887$	−472.500	−	272.798i	−0.532694	−	0.307551i	0.209419	−	0.977826i	$-0.432843\pi$
$887$	−472.500	−	272.798i	−0.532694	−	0.307551i	−0.742113	+	0.670275i	$0.766176\pi$
$888$		−	69.2820i		−	0.0780203i
$889$		0			0
$890$	−639.000	+	368.927i	−0.717978	+	0.414525i
$891$	−467.500	+	809.734i	−0.524691	+	0.908792i
$892$			554.256i			0.621364i
$893$	−304.500	+	175.803i	−0.340985	+	0.196868i
$894$			10.3923i			0.0116245i
$895$		−	462.458i		−	0.516712i
$896$		0			0
$897$	72.0000			0.0802676
$898$	620.000			0.690423
$899$	228.000	+	394.908i	0.253615	+	0.439274i
$900$	64.0000			0.0711111
$901$	−1987.50	−	1147.48i	−2.20588	−	1.27357i
$902$	−442.000	−	765.566i	−0.490022	−	0.848743i
$903$		0			0
$904$	−976.000			−1.07965
$905$	−648.000	+	1122.37i	−0.716022	+	1.24019i
$906$	63.0000	+	36.3731i	0.0695364	+	0.0401469i
$907$	−260.500	−	451.199i	−0.287211	−	0.497463i	0.685932	−	0.727665i	$-0.259395\pi$
$907$	−260.500	−	451.199i	−0.287211	−	0.497463i	−0.973143	+	0.230202i	$0.926061\pi$
$908$	−110.000	−	190.526i	−0.121145	−	0.209830i
$909$			623.538i			0.685961i
$910$		0			0
$911$			1191.65i			1.30807i	0.756465	+	0.654035i	$0.226925\pi$
$911$			1191.65i			1.30807i	−0.756465	+	0.654035i	$0.773075\pi$
$912$	−112.000			−0.122807
$913$	935.000	+	1619.47i	1.02410	+	1.77379i
$914$	167.000	−	289.252i	0.182713	−	0.316469i
$915$	58.5000	−	101.325i	0.0639344	−	0.110738i
$916$	−1134.00	−	654.715i	−1.23799	−	0.714755i
$917$		0			0
$918$	425.000	+	736.122i	0.462963	+	0.801875i
$919$	−1207.50	−	697.150i	−1.31393	−	0.758597i	−0.331184	−	0.943566i	$-0.607448\pi$
$919$	−1207.50	−	697.150i	−1.31393	−	0.758597i	−0.982744	+	0.184969i	$0.940781\pi$
$920$	−108.000	−	187.061i	−0.117391	−	0.203328i
$921$	137.000	+	237.291i	0.148751	+	0.257645i
$922$		−	27.7128i		−	0.0300573i
$923$		0			0
$924$		0			0
$925$			17.3205i			0.0187249i
$926$			1219.36i			1.31681i
$927$	1116.00	−	644.323i	1.20388	−	0.695062i
$928$			443.405i			0.477807i
$929$	−480.500	+	832.250i	−0.517223	+	0.895856i	0.482577	+	0.875853i	$0.339701\pi$
$929$	−480.500	+	832.250i	−0.517223	+	0.895856i	−0.999800	+	0.0200027i	$0.993633\pi$
$930$	171.000	+	296.181i	0.183871	+	0.318474i
$931$		0			0
$932$	770.000	−	1333.68i	0.826180	−	1.43099i
$933$	43.5000	+	25.1147i	0.0466238	+	0.0269183i
$934$	−785.000	+	1359.66i	−0.840471	+	1.45574i
$935$	−1912.50	+	1104.18i	−2.04545	+	1.18094i
$936$	768.000	+	443.405i	0.820513	+	0.473723i
$937$	142.000			0.151547			0.0757737	−	0.997125i	$-0.475857\pi$
$937$	142.000			0.151547			0.0757737	+	0.997125i	$0.475857\pi$
$938$		0			0
$939$	−409.000			−0.435570
$940$	522.000	+	904.131i	0.555319	+	0.961841i
$941$	1060.50	−	612.280i	1.12699	−	0.650669i	0.183816	−	0.982961i	$-0.441155\pi$
$941$	1060.50	−	612.280i	1.12699	−	0.650669i	0.943177	+	0.332291i	$0.107822\pi$
$942$	−537.000	−	310.037i	−0.570064	−	0.329126i
$943$	−117.000	−	67.5500i	−0.124072	−	0.0716331i
$944$	−440.000	−	762.102i	−0.466102	−	0.807312i
$945$		0			0
$946$	238.000	+	412.228i	0.251586	+	0.435759i
$947$	87.5000	−	151.554i	0.0923970	−	0.160036i	−0.816122	−	0.577879i	$-0.803880\pi$
$947$	87.5000	−	151.554i	0.0923970	−	0.160036i	0.908519	+	0.417843i	$0.137214\pi$
$948$			297.913i			0.314254i
$949$	1428.00	−	824.456i	1.50474	−	0.868763i
$950$	28.0000			0.0294737
$951$			188.794i			0.198521i
$952$		0			0
$953$	−454.000			−0.476390			−0.238195	−	0.971217i	$-0.576556\pi$
$953$	−454.000			−0.476390			−0.238195	+	0.971217i	$0.576556\pi$
$954$			1468.78i			1.53960i
$955$	−562.500	−	974.279i	−0.589005	−	1.02019i
$956$			1718.19i			1.79727i
$957$	−204.000	−	117.779i	−0.213166	−	0.123072i
$958$	−1071.00	+	618.342i	−1.11795	+	0.645451i
$959$		0			0
$960$			332.554i			0.346410i
$961$	61.0000	−	105.655i	0.0634755	−	0.109943i
$962$	−120.000	+	207.846i	−0.124740	+	0.216056i
$963$	260.000	+	450.333i	0.269990	+	0.467636i
$964$	−290.000	−	502.295i	−0.300830	−	0.521053i
$965$			379.319i			0.393077i
$966$		0			0
$967$			720.533i			0.745122i	0.928008	+	0.372561i	$0.121520\pi$
$967$			720.533i			0.745122i	−0.928008	+	0.372561i	$0.878480\pi$
$968$	672.000	−	1163.94i	0.694215	−	1.20242i
$969$	87.5000	+	151.554i	0.0902993	+	0.156403i
$970$	−198.000	−	114.315i	−0.204124	−	0.117851i
$971$	−819.500	+	1419.42i	−0.843975	+	1.46181i	0.0425329	+	0.999095i	$0.486457\pi$
$971$	−819.500	+	1419.42i	−0.843975	+	1.46181i	−0.886508	+	0.462713i	$0.846876\pi$
$972$	416.000	−	720.533i	0.427984	−	0.741289i
$973$		0			0
$974$	−681.000	+	393.176i	−0.699179	+	0.403671i
$975$	24.0000	+	13.8564i	0.0246154	+	0.0142117i
$976$	−312.000	−	180.133i	−0.319672	−	0.184563i
$977$	396.500	+	686.758i	0.405834	+	0.702925i	0.994418	−	0.105511i	$-0.0336477\pi$
$977$	396.500	+	686.758i	0.405834	+	0.702925i	−0.588584	+	0.808436i	$0.700314\pi$
$978$	34.0000			0.0347648
$979$	−1207.00			−1.23289
$980$		0			0
$981$		−	69.2820i		−	0.0706239i
$982$	−844.000			−0.859470
$983$	−1336.50	+	771.629i	−1.35961	+	0.784973i	−0.989572	−	0.144042i	$-0.953990\pi$
$983$	−1336.50	+	771.629i	−1.35961	+	0.784973i	−0.370042	+	0.929015i	$0.620657\pi$
$984$	104.000	+	180.133i	0.105691	+	0.183062i
$985$	540.000	−	935.307i	0.548223	−	0.949551i
$986$	600.000	−	346.410i	0.608519	−	0.351329i
$987$		0			0
$988$	336.000	+	193.990i	0.340081	+	0.196346i
$989$	63.0000	+	36.3731i	0.0637007	+	0.0367776i
$990$	1224.00	+	706.677i	1.23636	+	0.713815i
$991$	−775.500	+	447.735i	−0.782543	+	0.451801i	−0.837331	−	0.546697i	$-0.815885\pi$
$991$	−775.500	+	447.735i	−0.782543	+	0.451801i	0.0547878	+	0.998498i	$0.482552\pi$
$992$	912.000	−	526.543i	0.919355	−	0.530790i
$993$	295.000			0.297080
$994$		0			0
$995$	333.000			0.334673
$996$	−220.000	−	381.051i	−0.220884	−	0.382582i
$997$	688.500	−	397.506i	0.690572	−	0.398702i	−0.113254	−	0.993566i	$-0.536128\pi$
$997$	688.500	−	397.506i	0.690572	−	0.398702i	0.803826	+	0.594864i	$0.202794\pi$
$998$	65.0000	−	112.583i	0.0651303	−	0.112809i
$999$	127.500	+	73.6122i	0.127628	+	0.0736858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.a.275.1		2
7.2	even	3		392.3.g.d.99.2		2
7.3	odd	6		56.3.k.b.11.1	yes	2
7.4	even	3		392.3.k.c.67.1		2
7.5	odd	6		392.3.g.e.99.2		2
7.6	odd	2		56.3.k.a.51.1	yes	2
8.3	odd	2		392.3.k.c.275.1		2
28.3	even	6		224.3.o.b.207.1		2
28.19	even	6		1568.3.g.c.687.2		2
28.23	odd	6		1568.3.g.f.687.1		2
28.27	even	2		224.3.o.a.79.1		2
56.3	even	6		56.3.k.a.11.1	✓	2
56.5	odd	6		1568.3.g.c.687.1		2
56.11	odd	6	inner	392.3.k.a.67.1		2
56.13	odd	2		224.3.o.b.79.1		2
56.19	even	6		392.3.g.e.99.1		2
56.27	even	2		56.3.k.b.51.1	yes	2
56.37	even	6		1568.3.g.f.687.2		2
56.45	odd	6		224.3.o.a.207.1		2
56.51	odd	6		392.3.g.d.99.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.a.11.1	✓	2	56.3	even	6
56.3.k.a.51.1	yes	2	7.6	odd	2
56.3.k.b.11.1	yes	2	7.3	odd	6
56.3.k.b.51.1	yes	2	56.27	even	2
224.3.o.a.79.1		2	28.27	even	2
224.3.o.a.207.1		2	56.45	odd	6
224.3.o.b.79.1		2	56.13	odd	2
224.3.o.b.207.1		2	28.3	even	6
392.3.g.d.99.1		2	56.51	odd	6
392.3.g.d.99.2		2	7.2	even	3
392.3.g.e.99.1		2	56.19	even	6
392.3.g.e.99.2		2	7.5	odd	6
392.3.k.a.67.1		2	56.11	odd	6	inner
392.3.k.a.275.1		2	1.1	even	1	trivial
392.3.k.c.67.1		2	7.4	even	3
392.3.k.c.275.1		2	8.3	odd	2
1568.3.g.c.687.1		2	56.5	odd	6
1568.3.g.c.687.2		2	28.19	even	6
1568.3.g.f.687.1		2	28.23	odd	6
1568.3.g.f.687.2		2	56.37	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +4.00000 q^{4} +(4.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{6} -8.00000 q^{8} +(4.00000 - 6.92820i) q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +4.00000 q^{4} +(4.50000 + 2.59808i) q^{5} +(-1.00000 - 1.73205i) q^{6} -8.00000 q^{8} +(4.00000 - 6.92820i) q^{9} +(-9.00000 - 5.19615i) q^{10} +(-8.50000 - 14.7224i) q^{11} +(2.00000 + 3.46410i) q^{12} -13.8564i q^{13} +5.19615i q^{15} +16.0000 q^{16} +(-12.5000 - 21.6506i) q^{17} +(-8.00000 + 13.8564i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(18.0000 + 10.3923i) q^{20} +(17.0000 + 29.4449i) q^{22} +(4.50000 + 2.59808i) q^{23} +(-4.00000 - 6.92820i) q^{24} +(1.00000 + 1.73205i) q^{25} +27.7128i q^{26} +17.0000 q^{27} -13.8564i q^{29} -10.3923i q^{30} +(-28.5000 + 16.4545i) q^{31} -32.0000 q^{32} +(8.50000 - 14.7224i) q^{33} +(25.0000 + 43.3013i) q^{34} +(16.0000 - 27.7128i) q^{36} +(7.50000 + 4.33013i) q^{37} +(7.00000 - 12.1244i) q^{38} +(12.0000 - 6.92820i) q^{39} +(-36.0000 - 20.7846i) q^{40} -26.0000 q^{41} +14.0000 q^{43} +(-34.0000 - 58.8897i) q^{44} +(36.0000 - 20.7846i) q^{45} +(-9.00000 - 5.19615i) q^{46} +(43.5000 + 25.1147i) q^{47} +(8.00000 + 13.8564i) q^{48} +(-2.00000 - 3.46410i) q^{50} +(12.5000 - 21.6506i) q^{51} -55.4256i q^{52} +(79.5000 - 45.8993i) q^{53} -34.0000 q^{54} -88.3346i q^{55} -7.00000 q^{57} +27.7128i q^{58} +(-27.5000 - 47.6314i) q^{59} +20.7846i q^{60} +(-19.5000 - 11.2583i) q^{61} +(57.0000 - 32.9090i) q^{62} +64.0000 q^{64} +(36.0000 - 62.3538i) q^{65} +(-17.0000 + 29.4449i) q^{66} +(-8.50000 - 14.7224i) q^{67} +(-50.0000 - 86.6025i) q^{68} +5.19615i q^{69} +(-32.0000 + 55.4256i) q^{72} +(59.5000 + 103.057i) q^{73} +(-15.0000 - 8.66025i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(-14.0000 + 24.2487i) q^{76} +(-24.0000 + 13.8564i) q^{78} +(64.5000 + 37.2391i) q^{79} +(72.0000 + 41.5692i) q^{80} +(-27.5000 - 47.6314i) q^{81} +52.0000 q^{82} -110.000 q^{83} -129.904i q^{85} -28.0000 q^{86} +(12.0000 - 6.92820i) q^{87} +(68.0000 + 117.779i) q^{88} +(35.5000 - 61.4878i) q^{89} +(-72.0000 + 41.5692i) q^{90} +(18.0000 + 10.3923i) q^{92} +(-28.5000 - 16.4545i) q^{93} +(-87.0000 - 50.2295i) q^{94} +(-31.5000 + 18.1865i) q^{95} +(-16.0000 - 27.7128i) q^{96} +22.0000 q^{97} -136.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + q^{3} + 8 q^{4} + 9 q^{5} - 2 q^{6} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 + q^3 + 8 * q^4 + 9 * q^5 - 2 * q^6 - 16 * q^8 + 8 * q^9	\( 2 q - 4 q^{2} + q^{3} + 8 q^{4} + 9 q^{5} - 2 q^{6} - 16 q^{8} + 8 q^{9} - 18 q^{10} - 17 q^{11} + 4 q^{12} + 32 q^{16} - 25 q^{17} - 16 q^{18} - 7 q^{19} + 36 q^{20} + 34 q^{22} + 9 q^{23} - 8 q^{24} + 2 q^{25} + 34 q^{27} - 57 q^{31} - 64 q^{32} + 17 q^{33} + 50 q^{34} + 32 q^{36} + 15 q^{37} + 14 q^{38} + 24 q^{39} - 72 q^{40} - 52 q^{41} + 28 q^{43} - 68 q^{44} + 72 q^{45} - 18 q^{46} + 87 q^{47} + 16 q^{48} - 4 q^{50} + 25 q^{51} + 159 q^{53} - 68 q^{54} - 14 q^{57} - 55 q^{59} - 39 q^{61} + 114 q^{62} + 128 q^{64} + 72 q^{65} - 34 q^{66} - 17 q^{67} - 100 q^{68} - 64 q^{72} + 119 q^{73} - 30 q^{74} - 2 q^{75} - 28 q^{76} - 48 q^{78} + 129 q^{79} + 144 q^{80} - 55 q^{81} + 104 q^{82} - 220 q^{83} - 56 q^{86} + 24 q^{87} + 136 q^{88} + 71 q^{89} - 144 q^{90} + 36 q^{92} - 57 q^{93} - 174 q^{94} - 63 q^{95} - 32 q^{96} + 44 q^{97} - 272 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + q^3 + 8 * q^4 + 9 * q^5 - 2 * q^6 - 16 * q^8 + 8 * q^9 - 18 * q^10 - 17 * q^11 + 4 * q^12 + 32 * q^16 - 25 * q^17 - 16 * q^18 - 7 * q^19 + 36 * q^20 + 34 * q^22 + 9 * q^23 - 8 * q^24 + 2 * q^25 + 34 * q^27 - 57 * q^31 - 64 * q^32 + 17 * q^33 + 50 * q^34 + 32 * q^36 + 15 * q^37 + 14 * q^38 + 24 * q^39 - 72 * q^40 - 52 * q^41 + 28 * q^43 - 68 * q^44 + 72 * q^45 - 18 * q^46 + 87 * q^47 + 16 * q^48 - 4 * q^50 + 25 * q^51 + 159 * q^53 - 68 * q^54 - 14 * q^57 - 55 * q^59 - 39 * q^61 + 114 * q^62 + 128 * q^64 + 72 * q^65 - 34 * q^66 - 17 * q^67 - 100 * q^68 - 64 * q^72 + 119 * q^73 - 30 * q^74 - 2 * q^75 - 28 * q^76 - 48 * q^78 + 129 * q^79 + 144 * q^80 - 55 * q^81 + 104 * q^82 - 220 * q^83 - 56 * q^86 + 24 * q^87 + 136 * q^88 + 71 * q^89 - 144 * q^90 + 36 * q^92 - 57 * q^93 - 174 * q^94 - 63 * q^95 - 32 * q^96 + 44 * q^97 - 272 * q^99

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