LMFDB - Embedded newform 1050.3.p.f.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(451,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("1050.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 56 x^{10} + 300 x^{9} + 1007 x^{8} + 12456 x^{7} + 209990 x^{6} - 250384 x^{5} + \cdots + 6882692292 $ x^12 - 4x^11 + 56x^10 + 300x^9 + 1007x^8 + 12456x^7 + 209990x^6 - 250384x^5 + 4799806x^4 + 51487320x^3 - 123648876x^2 + 379489320*x + 6882692292
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$3.11049 + 6.59331i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.f.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-2.94762 - 6.34914i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-2.94762 - 6.34914i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-8.87118 - 15.3653i) q^{11} +(-3.00000 - 1.73205i) q^{12} -8.10715i q^{13} +(9.86035 + 0.879440i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(6.81875 - 3.93681i) q^{17} +(2.12132 + 3.67423i) q^{18} +(17.5951 + 10.1585i) q^{19} +(-9.91994 - 6.97100i) q^{21} +25.0915 q^{22} +(-16.2941 + 28.2223i) q^{23} +(4.24264 - 2.44949i) q^{24} +(9.92919 + 5.73262i) q^{26} -5.19615i q^{27} +(-8.04941 + 11.4546i) q^{28} -25.0915 q^{29} +(-46.0686 + 26.5977i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-26.6135 - 15.3653i) q^{33} +11.1350i q^{34} -6.00000 q^{36} +(-21.7817 + 37.7270i) q^{37} +(-24.8833 + 14.3664i) q^{38} +(-7.02100 - 12.1607i) q^{39} -70.3424i q^{41} +(15.5521 - 7.22016i) q^{42} +2.43179 q^{43} +(-17.7424 + 30.7307i) q^{44} +(-23.0434 - 39.9123i) q^{46} +(13.3264 + 7.69399i) q^{47} +6.92820i q^{48} +(-31.6231 + 37.4297i) q^{49} +(6.81875 - 11.8104i) q^{51} +(-14.0420 + 8.10715i) q^{52} +(25.4476 + 44.0765i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-8.33712 - 17.9581i) q^{56} +35.1902 q^{57} +(17.7424 - 30.7307i) q^{58} +(22.9688 - 13.2610i) q^{59} +(-28.7553 - 16.6019i) q^{61} -75.2297i q^{62} +(-20.9170 - 1.86557i) q^{63} +8.00000 q^{64} +(37.6372 - 21.7299i) q^{66} +(49.9171 + 86.4589i) q^{67} +(-13.6375 - 7.87362i) q^{68} +56.4445i q^{69} -97.0831 q^{71} +(4.24264 - 7.34847i) q^{72} +(-46.7957 + 27.0175i) q^{73} +(-30.8040 - 53.3541i) q^{74} -40.6342i q^{76} +(-71.4078 + 101.615i) q^{77} +19.8584 q^{78} +(37.3591 - 64.7079i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(86.1515 + 49.7396i) q^{82} -85.2206i q^{83} +(-2.15418 + 24.1528i) q^{84} +(-1.71954 + 2.97833i) q^{86} +(-37.6372 + 21.7299i) q^{87} +(-25.0915 - 43.4597i) q^{88} +(-115.343 - 66.5932i) q^{89} +(-51.4734 + 23.8968i) q^{91} +65.1765 q^{92} +(-46.0686 + 79.7931i) q^{93} +(-18.8464 + 10.8809i) q^{94} +(-8.48528 - 4.89898i) q^{96} -49.9973i q^{97} +(-23.4809 - 65.1970i) q^{98} -53.2271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−2.94762	−	6.34914i	−0.421088	−	0.907020i
$7$	−2.94762	−	6.34914i	−0.421088	−	0.907020i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−8.87118	−	15.3653i	−0.806471	−	1.39685i	−0.915293	−	0.402788i	$-0.868041\pi$
$11$	−8.87118	−	15.3653i	−0.806471	−	1.39685i	0.108822	−	0.994061i	$-0.465292\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$		−	8.10715i		−	0.623627i	−0.950143	−	0.311813i	$-0.899064\pi$
$13$		−	8.10715i		−	0.623627i	0.950143	−	0.311813i	$-0.100936\pi$
$14$	9.86035	+	0.879440i	0.704311	+	0.0628172i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	6.81875	−	3.93681i	0.401103	−	0.231577i	−0.285857	−	0.958272i	$-0.592278\pi$
$17$	6.81875	−	3.93681i	0.401103	−	0.231577i	0.686960	+	0.726695i	$0.258945\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	17.5951	+	10.1585i	0.926059	+	0.534660i	0.885563	−	0.464519i	$-0.153773\pi$
$19$	17.5951	+	10.1585i	0.926059	+	0.534660i	0.0404958	+	0.999180i	$0.487106\pi$
$20$		0			0
$21$	−9.91994	−	6.97100i	−0.472378	−	0.331952i
$22$	25.0915			1.14052
$23$	−16.2941	+	28.2223i	−0.708441	+	1.22706i	0.256995	+	0.966413i	$0.417268\pi$
$23$	−16.2941	+	28.2223i	−0.708441	+	1.22706i	−0.965435	+	0.260642i	$0.916066\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	9.92919	+	5.73262i	0.381892	+	0.220485i
$27$		−	5.19615i		−	0.192450i
$28$	−8.04941	+	11.4546i	−0.287479	+	0.409091i
$29$	−25.0915			−0.865224			−0.432612	−	0.901580i	$-0.642408\pi$
$29$	−25.0915			−0.865224			−0.432612	+	0.901580i	$0.642408\pi$
$30$		0			0
$31$	−46.0686	+	26.5977i	−1.48608	+	0.857991i	−0.999874	−	0.0158519i	$-0.994954\pi$
$31$	−46.0686	+	26.5977i	−1.48608	+	0.857991i	−0.486209	+	0.873843i	$0.661621\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	−26.6135	−	15.3653i	−0.806471	−	0.465616i
$34$			11.1350i			0.327499i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−21.7817	+	37.7270i	−0.588695	+	1.01965i	0.405709	+	0.914002i	$0.367025\pi$
$37$	−21.7817	+	37.7270i	−0.588695	+	1.01965i	−0.994404	+	0.105647i	$0.966309\pi$
$38$	−24.8833	+	14.3664i	−0.654822	+	0.378062i
$39$	−7.02100	−	12.1607i	−0.180026	−	0.311813i
$40$		0			0
$41$		−	70.3424i		−	1.71567i	−0.513927	−	0.857834i	$-0.671810\pi$
$41$		−	70.3424i		−	1.71567i	0.513927	−	0.857834i	$-0.328190\pi$
$42$	15.5521	−	7.22016i	0.370289	−	0.171908i
$43$	2.43179			0.0565533			0.0282767	−	0.999600i	$-0.490998\pi$
$43$	2.43179			0.0565533			0.0282767	+	0.999600i	$0.490998\pi$
$44$	−17.7424	+	30.7307i	−0.403236	+	0.698424i
$45$		0			0
$46$	−23.0434	−	39.9123i	−0.500943	−	0.867659i
$47$	13.3264	+	7.69399i	0.283540	+	0.163702i	0.635025	−	0.772492i	$-0.280990\pi$
$47$	13.3264	+	7.69399i	0.283540	+	0.163702i	−0.351485	+	0.936194i	$0.614323\pi$
$48$			6.92820i			0.144338i
$49$	−31.6231	+	37.4297i	−0.645370	+	0.763870i
$50$		0			0
$51$	6.81875	−	11.8104i	0.133701	−	0.231577i
$52$	−14.0420	+	8.10715i	−0.270038	+	0.155907i
$53$	25.4476	+	44.0765i	0.480143	+	0.831632i	0.999741	−	0.0227791i	$-0.00725145\pi$
$53$	25.4476	+	44.0765i	0.480143	+	0.831632i	−0.519598	+	0.854411i	$0.673918\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	−8.33712	−	17.9581i	−0.148877	−	0.320680i
$57$	35.1902			0.617372
$58$	17.7424	−	30.7307i	0.305903	−	0.529839i
$59$	22.9688	−	13.2610i	0.389302	−	0.224763i	−0.292556	−	0.956248i	$-0.594506\pi$
$59$	22.9688	−	13.2610i	0.389302	−	0.224763i	0.681858	+	0.731485i	$0.261172\pi$
$60$		0			0
$61$	−28.7553	−	16.6019i	−0.471399	−	0.272162i	0.245426	−	0.969415i	$-0.421072\pi$
$61$	−28.7553	−	16.6019i	−0.471399	−	0.272162i	−0.716825	+	0.697253i	$0.754405\pi$
$62$		−	75.2297i		−	1.21338i
$63$	−20.9170	−	1.86557i	−0.332015	−	0.0296123i
$64$	8.00000			0.125000
$65$		0			0
$66$	37.6372	−	21.7299i	0.570261	−	0.329240i
$67$	49.9171	+	86.4589i	0.745031	+	1.29043i	0.950180	+	0.311701i	$0.100899\pi$
$67$	49.9171	+	86.4589i	0.745031	+	1.29043i	−0.205149	+	0.978731i	$0.565768\pi$
$68$	−13.6375	−	7.87362i	−0.200552	−	0.115789i
$69$			56.4445i			0.818037i
$70$		0			0
$71$	−97.0831			−1.36737			−0.683684	−	0.729778i	$-0.739623\pi$
$71$	−97.0831			−1.36737			−0.683684	+	0.729778i	$0.739623\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	−46.7957	+	27.0175i	−0.641037	+	0.370103i	−0.785014	−	0.619478i	$-0.787344\pi$
$73$	−46.7957	+	27.0175i	−0.641037	+	0.370103i	0.143977	+	0.989581i	$0.454011\pi$
$74$	−30.8040	−	53.3541i	−0.416270	−	0.721001i
$75$		0			0
$76$		−	40.6342i		−	0.534660i
$77$	−71.4078	+	101.615i	−0.927374	+	1.31968i
$78$	19.8584			0.254595
$79$	37.3591	−	64.7079i	0.472900	−	0.819087i	−0.526619	−	0.850102i	$-0.676540\pi$
$79$	37.3591	−	64.7079i	0.472900	−	0.819087i	0.999519	+	0.0310142i	$0.00987372\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	86.1515	+	49.7396i	1.05063	+	0.606580i
$83$		−	85.2206i		−	1.02675i	−0.858163	−	0.513377i	$-0.828394\pi$
$83$		−	85.2206i		−	1.02675i	0.858163	−	0.513377i	$-0.171606\pi$
$84$	−2.15418	+	24.1528i	−0.0256450	+	0.287534i
$85$		0			0
$86$	−1.71954	+	2.97833i	−0.0199946	+	0.0346317i
$87$	−37.6372	+	21.7299i	−0.432612	+	0.249769i
$88$	−25.0915	−	43.4597i	−0.285131	−	0.493861i
$89$	−115.343	−	66.5932i	−1.29599	−	0.748238i	−0.316279	−	0.948666i	$-0.602433\pi$
$89$	−115.343	−	66.5932i	−1.29599	−	0.748238i	−0.979708	+	0.200428i	$0.935767\pi$
$90$		0			0
$91$	−51.4734	+	23.8968i	−0.565642	+	0.262602i
$92$	65.1765			0.708441
$93$	−46.0686	+	79.7931i	−0.495361	+	0.857991i
$94$	−18.8464	+	10.8809i	−0.200493	+	0.115755i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$		−	49.9973i		−	0.515436i	−0.966220	−	0.257718i	$-0.917029\pi$
$97$		−	49.9973i		−	0.515436i	0.966220	−	0.257718i	$-0.0829705\pi$
$98$	−23.4809	−	65.1970i	−0.239601	−	0.665276i
$99$	−53.2271			−0.537647
$100$		0			0
$101$	−142.296	+	82.1544i	−1.40887	+	0.813410i	−0.995279	−	0.0970542i	$-0.969058\pi$
$101$	−142.296	+	82.1544i	−1.40887	+	0.813410i	−0.413588	+	0.910464i	$0.635725\pi$
$102$	9.64318	+	16.7025i	0.0945409	+	0.163750i
$103$	84.3852	+	48.7198i	0.819274	+	0.473008i	0.850166	−	0.526515i	$-0.176502\pi$
$103$	84.3852	+	48.7198i	0.819274	+	0.473008i	−0.0308923	+	0.999523i	$0.509835\pi$
$104$		−	22.9305i		−	0.220485i
$105$		0			0
$106$	−71.9766			−0.679025
$107$	48.7339	−	84.4097i	0.455457	−	0.788875i	−0.543257	−	0.839567i	$-0.682809\pi$
$107$	48.7339	−	84.4097i	0.455457	−	0.788875i	0.998714	+	0.0506910i	$0.0161424\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	32.1284	+	55.6480i	0.294756	+	0.510532i	0.974928	−	0.222520i	$-0.0714284\pi$
$109$	32.1284	+	55.6480i	0.294756	+	0.510532i	−0.680172	+	0.733052i	$0.738095\pi$
$110$		0			0
$111$			75.4540i			0.679766i
$112$	27.8893	+	2.48743i	0.249012	+	0.0222092i
$113$	−43.4647			−0.384643			−0.192321	−	0.981332i	$-0.561602\pi$
$113$	−43.4647			−0.384643			−0.192321	+	0.981332i	$0.561602\pi$
$114$	−24.8833	+	43.0991i	−0.218274	+	0.378062i
$115$		0			0
$116$	25.0915	+	43.4597i	0.216306	+	0.374653i
$117$	−21.0630	−	12.1607i	−0.180026	−	0.103938i
$118$			37.5079i			0.317864i
$119$	−45.0944	−	31.6890i	−0.378945	−	0.266294i
$120$		0			0
$121$	−96.8957	+	167.828i	−0.800791	+	1.38701i
$122$	40.6662	−	23.4786i	0.333329	−	0.192448i
$123$	−60.9183	−	105.514i	−0.495271	−	0.857834i
$124$	92.1372	+	53.1954i	0.743042	+	0.428995i
$125$		0			0
$126$	17.0754	−	24.2988i	0.135519	−	0.192848i
$127$	186.018			1.46471			0.732354	−	0.680924i	$-0.238422\pi$
$127$	186.018			1.46471			0.732354	+	0.680924i	$0.238422\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	3.64769	−	2.10599i	0.0282767	−	0.0163255i
$130$		0			0
$131$	−78.0331	−	45.0524i	−0.595672	−	0.343912i	0.171665	−	0.985155i	$-0.445085\pi$
$131$	−78.0331	−	45.0524i	−0.595672	−	0.343912i	−0.767337	+	0.641244i	$0.778419\pi$
$132$			61.4613i			0.465616i
$133$	12.6343	−	141.657i	0.0949951	−	1.06509i
$134$	−141.187			−1.05363
$135$		0			0
$136$	19.2864	−	11.1350i	0.141811	−	0.0818749i
$137$	−5.41774	−	9.38380i	−0.0395456	−	0.0684949i	0.845575	−	0.533856i	$-0.179258\pi$
$137$	−5.41774	−	9.38380i	−0.0395456	−	0.0684949i	−0.885121	+	0.465361i	$0.845924\pi$
$138$	−69.1302	−	39.9123i	−0.500943	−	0.289220i
$139$		−	222.126i		−	1.59803i	−0.601314	−	0.799013i	$-0.705356\pi$
$139$		−	222.126i		−	1.59803i	0.601314	−	0.799013i	$-0.294644\pi$
$140$		0			0
$141$	26.6528			0.189027
$142$	68.6481	−	118.902i	0.483438	−	0.837338i
$143$	−124.569	+	71.9200i	−0.871112	+	0.502937i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$		−	76.4171i		−	0.523405i
$147$	−15.0196	+	83.5309i	−0.102174	+	0.568237i
$148$	87.1268			0.588695
$149$	4.33681	−	7.51157i	0.0291061	−	0.0504132i	−0.851105	−	0.524995i	$-0.824067\pi$
$149$	4.33681	−	7.51157i	0.0291061	−	0.0504132i	0.880212	+	0.474582i	$0.157401\pi$
$150$		0			0
$151$	−106.283	−	184.088i	−0.703861	−	1.21912i	−0.967101	−	0.254392i	$-0.918125\pi$
$151$	−106.283	−	184.088i	−0.703861	−	1.21912i	0.263240	−	0.964730i	$-0.415209\pi$
$152$	49.7665	+	28.7327i	0.327411	+	0.189031i
$153$		−	23.6209i		−	0.154385i
$154$	−73.9601	−	159.309i	−0.480260	−	1.03448i
$155$		0			0
$156$	−14.0420	+	24.3214i	−0.0900128	+	0.155907i
$157$	−113.829	+	65.7193i	−0.725027	+	0.418594i	−0.816600	−	0.577204i	$-0.804144\pi$
$157$	−113.829	+	65.7193i	−0.725027	+	0.418594i	0.0915732	+	0.995798i	$0.470810\pi$
$158$	52.8338	+	91.5108i	0.334391	+	0.579182i
$159$	76.3427	+	44.0765i	0.480143	+	0.277211i
$160$		0			0
$161$	227.216	+	20.2653i	1.41128	+	0.125871i
$162$	12.7279			0.0785674
$163$	−22.4281	+	38.8465i	−0.137595	+	0.238322i	−0.926586	−	0.376083i	$-0.877271\pi$
$163$	−22.4281	+	38.8465i	−0.137595	+	0.238322i	0.788990	+	0.614405i	$0.210604\pi$
$164$	−121.837	+	70.3424i	−0.742906	+	0.428917i
$165$		0			0
$166$	104.374	+	60.2601i	0.628756	+	0.363013i
$167$			139.845i			0.837398i	0.908125	+	0.418699i	$0.137514\pi$
$167$			139.845i			0.837398i	−0.908125	+	0.418699i	$0.862486\pi$
$168$	−28.0578	−	19.7170i	−0.167011	−	0.117363i
$169$	103.274			0.611090
$170$		0			0
$171$	52.7853	−	30.4756i	0.308686	−	0.178220i
$172$	−2.43179	−	4.21199i	−0.0141383	−	0.0244883i
$173$	−125.429	−	72.4165i	−0.725024	−	0.418593i	0.0915753	−	0.995798i	$-0.470810\pi$
$173$	−125.429	−	72.4165i	−0.725024	−	0.418593i	−0.816599	+	0.577206i	$0.804143\pi$
$174$		−	61.4613i		−	0.353226i
$175$		0			0
$176$	70.9695			0.403236
$177$	22.9688	−	39.7831i	0.129767	−	0.224763i
$178$	163.119	−	94.1770i	0.916401	−	0.529084i
$179$	16.2046	+	28.0672i	0.0905284	+	0.156800i	0.907734	−	0.419547i	$-0.137811\pi$
$179$	16.2046	+	28.0672i	0.0905284	+	0.156800i	−0.817205	+	0.576347i	$0.804478\pi$
$180$		0			0
$181$			119.139i			0.658227i	0.944290	+	0.329113i	$0.106750\pi$
$181$			119.139i			0.658227i	−0.944290	+	0.329113i	$0.893250\pi$
$182$	7.12975	−	79.9393i	0.0391745	−	0.439227i
$183$	−57.5107			−0.314266
$184$	−46.0868	+	79.8246i	−0.250472	+	0.433830i
$185$		0			0
$186$	−65.1508	−	112.845i	−0.350273	−	0.606691i
$187$	−120.981	−	69.8483i	−0.646956	−	0.373520i
$188$		−	30.7760i		−	0.163702i
$189$	−32.9911	+	15.3163i	−0.174556	+	0.0810384i
$190$		0			0
$191$	122.229	−	211.706i	0.639940	−	1.10841i	−0.345505	−	0.938417i	$-0.612292\pi$
$191$	122.229	−	211.706i	0.639940	−	1.10841i	0.985445	−	0.169992i	$-0.0543743\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	−127.781	−	221.323i	−0.662077	−	1.14675i	−0.980069	−	0.198657i	$-0.936342\pi$
$193$	−127.781	−	221.323i	−0.662077	−	1.14675i	0.317992	−	0.948093i	$-0.396991\pi$
$194$	61.2339	+	35.3534i	0.315639	+	0.182234i
$195$		0			0
$196$	96.4532	+	17.3432i	0.492108	+	0.0884856i
$197$	−351.495			−1.78424			−0.892118	−	0.451802i	$-0.850782\pi$
$197$	−351.495			−1.78424			−0.892118	+	0.451802i	$0.850782\pi$
$198$	37.6372	−	65.1896i	0.190087	−	0.329240i
$199$	266.168	−	153.672i	1.33753	−	0.772222i	0.351087	−	0.936343i	$-0.385812\pi$
$199$	266.168	−	153.672i	1.33753	−	0.772222i	0.986440	+	0.164121i	$0.0524787\pi$
$200$		0			0
$201$	149.751	+	86.4589i	0.745031	+	0.430144i
$202$		−	232.368i		−	1.15034i
$203$	73.9601	+	159.309i	0.364335	+	0.784775i
$204$	−27.2750			−0.133701
$205$		0			0
$206$	−119.339	+	68.9002i	−0.579314	+	0.334467i
$207$	48.8824	+	84.6668i	0.236147	+	0.409018i
$208$	28.0840	+	16.2143i	0.135019	+	0.0779533i
$209$		−	360.473i		−	1.72475i
$210$		0			0
$211$	−335.164			−1.58845			−0.794227	−	0.607621i	$-0.792124\pi$
$211$	−335.164			−1.58845			−0.794227	+	0.607621i	$0.792124\pi$
$212$	50.8952	−	88.1530i	0.240071	−	0.415816i
$213$	−145.625	+	84.0765i	−0.683684	+	0.394725i
$214$	68.9202	+	119.373i	0.322057	+	0.557819i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	304.665	+	214.096i	1.40399	+	0.986617i
$218$	−90.8728			−0.416847
$219$	−46.7957	+	81.0526i	−0.213679	+	0.370103i
$220$		0			0
$221$	−31.9163	−	55.2806i	−0.144418	−	0.250139i
$222$	−92.4119	−	53.3541i	−0.416270	−	0.240334i
$223$			50.9497i			0.228474i	0.993454	+	0.114237i	$0.0364423\pi$
$223$			50.9497i			0.228474i	−0.993454	+	0.114237i	$0.963558\pi$
$224$	−22.7672	+	32.3984i	−0.101639	+	0.144636i
$225$		0			0
$226$	30.7342	−	53.2331i	0.135992	−	0.235545i
$227$	−114.684	+	66.2128i	−0.505215	+	0.291686i	−0.730865	−	0.682522i	$-0.760883\pi$
$227$	−114.684	+	66.2128i	−0.505215	+	0.291686i	0.225649	+	0.974209i	$0.427550\pi$
$228$	−35.1902	−	60.9513i	−0.154343	−	0.267330i
$229$	159.636	+	92.1659i	0.697101	+	0.402471i	0.806267	−	0.591552i	$-0.201485\pi$
$229$	159.636	+	92.1659i	0.697101	+	0.402471i	−0.109166	+	0.994024i	$0.534818\pi$
$230$		0			0
$231$	−19.1101	+	214.264i	−0.0827278	+	0.927551i
$232$	−70.9695			−0.305903
$233$	−70.3332	+	121.821i	−0.301859	+	0.522836i	−0.976557	−	0.215258i	$-0.930941\pi$
$233$	−70.3332	+	121.821i	−0.301859	+	0.522836i	0.674698	+	0.738094i	$0.264274\pi$
$234$	29.7876	−	17.1979i	0.127297	−	0.0734951i
$235$		0			0
$236$	−45.9376	−	26.5221i	−0.194651	−	0.112382i
$237$		−	129.416i		−	0.546058i
$238$	70.6975	−	32.8217i	0.297048	−	0.137906i
$239$	−247.975			−1.03755			−0.518777	−	0.854910i	$-0.673612\pi$
$239$	−247.975			−1.03755			−0.518777	+	0.854910i	$0.673612\pi$
$240$		0			0
$241$	−189.530	+	109.425i	−0.786431	+	0.454046i	−0.838705	−	0.544587i	$-0.816687\pi$
$241$	−189.530	+	109.425i	−0.786431	+	0.454046i	0.0522735	+	0.998633i	$0.483353\pi$
$242$	−137.031	−	237.345i	−0.566245	−	0.980765i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			66.4076i			0.272162i
$245$		0			0
$246$	172.303			0.700419
$247$	82.3568	−	142.646i	0.333428	−	0.577515i
$248$	−130.302	+	75.2297i	−0.525410	+	0.303345i
$249$	−73.8032	−	127.831i	−0.296399	−	0.513377i
$250$		0			0
$251$			37.7083i			0.150232i	0.997175	+	0.0751161i	$0.0239327\pi$
$251$			37.7083i			0.150232i	−0.997175	+	0.0751161i	$0.976067\pi$
$252$	17.6857	+	38.0948i	0.0701814	+	0.151170i
$253$	578.193			2.28535
$254$	−131.534	+	227.824i	−0.517852	+	0.896946i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−16.5091	−	9.53153i	−0.0642377	−	0.0370877i	0.467537	−	0.883973i	$-0.345141\pi$
$257$	−16.5091	−	9.53153i	−0.0642377	−	0.0370877i	−0.531775	+	0.846886i	$0.678475\pi$
$258$			5.95665i			0.0230878i
$259$	303.738	+	27.0903i	1.17273	+	0.104596i
$260$		0			0
$261$	−37.6372	+	65.1896i	−0.144204	+	0.249769i
$262$	110.355	−	63.7137i	0.421204	−	0.243182i
$263$	−119.852	−	207.590i	−0.455712	−	0.789316i	0.543017	−	0.839722i	$-0.317282\pi$
$263$	−119.852	−	207.590i	−0.455712	−	0.789316i	−0.998729	+	0.0504060i	$0.983948\pi$
$264$	−75.2745	−	43.4597i	−0.285131	−	0.164620i
$265$		0			0
$266$	164.560	+	115.641i	0.618647	+	0.434739i
$267$	−230.686			−0.863991
$268$	99.8341	−	172.918i	0.372515	−	0.645216i
$269$	230.871	−	133.293i	0.858256	−	0.495514i	−0.00517171	−	0.999987i	$-0.501646\pi$
$269$	230.871	−	133.293i	0.858256	−	0.495514i	0.863428	+	0.504472i	$0.168313\pi$
$270$		0			0
$271$	316.324	+	182.630i	1.16725	+	0.673911i	0.953030	−	0.302875i	$-0.0979464\pi$
$271$	316.324	+	182.630i	1.16725	+	0.673911i	0.214218	+	0.976786i	$0.431280\pi$
$272$			31.4945i			0.115789i
$273$	−56.5149	+	80.4224i	−0.207014	+	0.294588i
$274$	15.3237			0.0559259
$275$		0			0
$276$	97.7648	−	56.4445i	0.354220	−	0.204509i
$277$	−212.467	−	368.004i	−0.767030	−	1.32853i	−0.939167	−	0.343461i	$-0.888401\pi$
$277$	−212.467	−	368.004i	−0.767030	−	1.32853i	0.172137	−	0.985073i	$-0.444933\pi$
$278$	272.047	+	157.066i	0.978587	+	0.564987i
$279$			159.586i			0.571994i
$280$		0			0
$281$	144.818			0.515368			0.257684	−	0.966229i	$-0.417041\pi$
$281$	144.818			0.515368			0.257684	+	0.966229i	$0.417041\pi$
$282$	−18.8464	+	32.6428i	−0.0668310	+	0.115755i
$283$	281.343	−	162.433i	0.994143	−	0.573969i	0.0876331	−	0.996153i	$-0.472070\pi$
$283$	281.343	−	162.433i	0.994143	−	0.573969i	0.906510	+	0.422184i	$0.138736\pi$
$284$	97.0831	+	168.153i	0.341842	+	0.592088i
$285$		0			0
$286$		−	203.420i		−	0.711260i
$287$	−446.614	+	207.342i	−1.55614	+	0.722447i
$288$	−16.9706			−0.0589256
$289$	−113.503	+	196.593i	−0.392744	+	0.680253i
$290$		0			0
$291$	−43.2989	−	74.9959i	−0.148793	−	0.257718i
$292$	93.5914	+	54.0350i	0.320519	+	0.185052i
$293$		−	171.836i		−	0.586470i	−0.956040	−	0.293235i	$-0.905268\pi$
$293$		−	171.836i		−	0.586470i	0.956040	−	0.293235i	$-0.0947319\pi$
$294$	−91.6835	−	77.4605i	−0.311849	−	0.263471i
$295$		0			0
$296$	−61.6080	+	106.708i	−0.208135	+	0.360500i
$297$	−79.8406	+	46.0960i	−0.268824	+	0.155205i
$298$	6.13317	+	10.6230i	0.0205811	+	0.0356475i
$299$	228.802	+	132.099i	0.765224	+	0.441802i
$300$		0			0
$301$	−7.16799	−	15.4398i	−0.0238139	−	0.0512950i
$302$	300.614			0.995410
$303$	−142.296	+	246.463i	−0.469622	+	0.813410i
$304$	−70.3805	+	40.6342i	−0.231515	+	0.133665i
$305$		0			0
$306$	28.9295	+	16.7025i	0.0945409	+	0.0545832i
$307$			114.101i			0.371663i	0.982582	+	0.185832i	$0.0594979\pi$
$307$			114.101i			0.371663i	−0.982582	+	0.185832i	$0.940502\pi$
$308$	247.411	+	22.0665i	0.803282	+	0.0716444i
$309$	168.770			0.546182
$310$		0			0
$311$	134.405	−	77.5988i	0.432171	−	0.249514i	−0.268100	−	0.963391i	$-0.586396\pi$
$311$	134.405	−	77.5988i	0.432171	−	0.249514i	0.700271	+	0.713877i	$0.253063\pi$
$312$	−19.8584	−	34.3957i	−0.0636486	−	0.110243i
$313$	368.143	+	212.548i	1.17618	+	0.679066i	0.955127	−	0.296197i	$-0.0957184\pi$
$313$	368.143	+	212.548i	1.17618	+	0.679066i	0.221050	+	0.975263i	$0.429052\pi$
$314$		−	185.882i		−	0.591982i
$315$		0			0
$316$	−149.437			−0.472900
$317$	7.19672	−	12.4651i	0.0227026	−	0.0393220i	−0.854451	−	0.519532i	$-0.826106\pi$
$317$	7.19672	−	12.4651i	0.0227026	−	0.0393220i	0.877153	+	0.480210i	$0.159440\pi$
$318$	−107.965	+	62.3336i	−0.339512	+	0.196018i
$319$	222.591	+	385.539i	0.697778	+	1.20859i
$320$		0			0
$321$		−	168.819i		−	0.525917i
$322$	−185.486	+	263.952i	−0.576043	+	0.819726i
$323$	159.969			0.495260
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−31.7181	−	54.9373i	−0.0972947	−	0.168519i
$327$	96.3851	+	55.6480i	0.294756	+	0.170177i
$328$		−	198.958i		−	0.606580i
$329$	9.56914	−	107.290i	0.0290855	−	0.326109i
$330$		0			0
$331$	42.5972	−	73.7805i	0.128692	−	0.222902i	−0.794478	−	0.607293i	$-0.792255\pi$
$331$	42.5972	−	73.7805i	0.128692	−	0.222902i	0.923170	+	0.384391i	$0.125589\pi$
$332$	−147.606	+	85.2206i	−0.444598	+	0.256689i
$333$	65.3451	+	113.181i	0.196232	+	0.339883i
$334$	−171.275	−	98.8857i	−0.512800	−	0.296065i
$335$		0			0
$336$	43.9881	−	20.4217i	0.130917	−	0.0607788i
$337$	122.057			0.362186			0.181093	−	0.983466i	$-0.442036\pi$
$337$	122.057			0.362186			0.181093	+	0.983466i	$0.442036\pi$
$338$	−73.0259	+	126.485i	−0.216053	+	0.374215i
$339$	−65.1970	+	37.6415i	−0.192321	+	0.111037i
$340$		0			0
$341$	817.366	+	471.906i	2.39697	+	1.38389i
$342$			86.1981i			0.252041i
$343$	330.859	+	90.4512i	0.964603	+	0.263706i
$344$	6.87815			0.0199946
$345$		0			0
$346$	177.383	−	102.412i	0.512669	−	0.295990i
$347$	−123.326	−	213.607i	−0.355406	−	0.615581i	0.631781	−	0.775147i	$-0.282324\pi$
$347$	−123.326	−	213.607i	−0.355406	−	0.615581i	−0.987187	+	0.159565i	$0.948991\pi$
$348$	75.2745	+	43.4597i	0.216306	+	0.124884i
$349$			265.448i			0.760596i	0.924864	+	0.380298i	$0.124179\pi$
$349$			265.448i			0.760596i	−0.924864	+	0.380298i	$0.875821\pi$
$350$		0			0
$351$	−42.1260			−0.120017
$352$	−50.1830	+	86.9195i	−0.142565	+	0.246930i
$353$	−243.873	+	140.800i	−0.690858	+	0.398867i	−0.803933	−	0.594720i	$-0.797263\pi$
$353$	−243.873	+	140.800i	−0.690858	+	0.398867i	0.113076	+	0.993586i	$0.463930\pi$
$354$	32.4828	+	56.2619i	0.0917593	+	0.158932i
$355$		0			0
$356$			266.373i			0.748238i
$357$	−95.0851	−	8.48060i	−0.266345	−	0.0237552i
$358$	−45.8335			−0.128026
$359$	−3.21594	+	5.57016i	−0.00895804	+	0.0155158i	−0.870470	−	0.492222i	$-0.836185\pi$
$359$	−3.21594	+	5.57016i	−0.00895804	+	0.0155158i	0.861512	+	0.507738i	$0.169518\pi$
$360$		0			0
$361$	25.8921	+	44.8463i	0.0717231	+	0.124228i
$362$	−145.915	−	84.2440i	−0.403080	−	0.232718i
$363$			335.657i			0.924674i
$364$	92.8638	+	65.2578i	0.255120	+	0.179280i
$365$		0			0
$366$	40.6662	−	70.4359i	0.111110	−	0.192448i
$367$	−216.948	+	125.255i	−0.591140	+	0.341295i	−0.765548	−	0.643379i	$-0.777532\pi$
$367$	−216.948	+	125.255i	−0.591140	+	0.341295i	0.174408	+	0.984673i	$0.444199\pi$
$368$	−65.1765	−	112.889i	−0.177110	−	0.306764i
$369$	−182.755	−	105.514i	−0.495271	−	0.285945i
$370$		0			0
$371$	204.838	−	291.491i	0.552124	−	0.785689i
$372$	184.274			0.495361
$373$	−211.379	+	366.119i	−0.566700	+	0.981552i	0.430190	+	0.902738i	$0.358447\pi$
$373$	−211.379	+	366.119i	−0.566700	+	0.981552i	−0.996889	+	0.0788140i	$0.974887\pi$
$374$	171.093	−	98.7804i	0.457467	−	0.264119i
$375$		0			0
$376$	37.6927	+	21.7619i	0.100247	+	0.0578774i
$377$			203.420i			0.539577i
$378$	4.56971	−	51.2359i	0.0120892	−	0.135545i
$379$	−510.205			−1.34619			−0.673093	−	0.739558i	$-0.735035\pi$
$379$	−510.205			−1.34619			−0.673093	+	0.739558i	$0.735035\pi$
$380$		0			0
$381$	279.027	−	161.096i	0.732354	−	0.422825i
$382$	172.857	+	299.398i	0.452506	+	0.783764i
$383$	232.862	+	134.443i	0.607995	+	0.351026i	0.772180	−	0.635404i	$-0.219166\pi$
$383$	232.862	+	134.443i	0.607995	+	0.351026i	−0.164185	+	0.986429i	$0.552500\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	361.419			0.936318
$387$	3.64769	−	6.31798i	0.00942555	−	0.0163255i
$388$	−86.5978	+	49.9973i	−0.223190	+	0.128859i
$389$	83.8883	+	145.299i	0.215651	+	0.373519i	0.953474	−	0.301476i	$-0.0974793\pi$
$389$	83.8883	+	145.299i	0.215651	+	0.373519i	−0.737823	+	0.674995i	$0.764146\pi$
$390$		0			0
$391$			256.588i			0.656234i
$392$	−89.4437	+	105.867i	−0.228173	+	0.270069i
$393$	−156.066			−0.397115
$394$	248.544	−	430.491i	0.630823	−	1.09262i
$395$		0			0
$396$	53.2271	+	92.1920i	0.134412	+	0.232808i
$397$	−314.858	−	181.784i	−0.793094	−	0.457893i	0.0479565	−	0.998849i	$-0.484729\pi$
$397$	−314.858	−	181.784i	−0.793094	−	0.457893i	−0.841051	+	0.540956i	$0.818062\pi$
$398$			434.650i			1.09209i
$399$	−103.727	−	223.428i	−0.259968	−	0.559969i
$400$		0			0
$401$	−139.416	+	241.475i	−0.347670	+	0.602182i	−0.985835	−	0.167717i	$-0.946360\pi$
$401$	−139.416	+	241.475i	−0.347670	+	0.602182i	0.638165	+	0.769900i	$0.279694\pi$
$402$	−211.780	+	122.271i	−0.526816	+	0.304158i
$403$	215.632	+	373.485i	0.535066	+	0.926761i
$404$	284.591	+	164.309i	0.704434	+	0.406705i
$405$		0			0
$406$	−247.411	−	22.0665i	−0.609387	−	0.0543509i
$407$	772.918			1.89906
$408$	19.2864	−	33.4049i	0.0472705	−	0.0818749i
$409$	337.862	−	195.065i	0.826068	−	0.476931i	−0.0264364	−	0.999650i	$-0.508416\pi$
$409$	337.862	−	195.065i	0.826068	−	0.476931i	0.852505	+	0.522720i	$0.175083\pi$
$410$		0			0
$411$	−16.2532	−	9.38380i	−0.0395456	−	0.0228316i
$412$		−	194.879i		−	0.473008i
$413$	−151.899	−	106.744i	−0.367795	−	0.258459i
$414$	−138.260			−0.333962
$415$		0			0
$416$	−39.7167	+	22.9305i	−0.0954729	+	0.0551213i
$417$	−192.366	−	333.188i	−0.461310	−	0.799013i
$418$	441.488	+	254.893i	1.05619	+	0.609792i
$419$			576.896i			1.37684i	0.725313	+	0.688419i	$0.241695\pi$
$419$			576.896i			1.37684i	−0.725313	+	0.688419i	$0.758305\pi$
$420$		0			0
$421$	649.851			1.54359			0.771795	−	0.635871i	$-0.219359\pi$
$421$	649.851			1.54359			0.771795	+	0.635871i	$0.219359\pi$
$422$	236.997	−	410.490i	0.561603	−	0.972725i
$423$	39.9792	−	23.0820i	0.0945134	−	0.0545673i
$424$	71.9766	+	124.667i	0.169756	+	0.294026i
$425$		0			0
$426$		−	237.804i		−	0.558226i
$427$	−20.6481	+	231.508i	−0.0483561	+	0.542172i
$428$	−194.936			−0.455457
$429$	−124.569	+	215.760i	−0.290371	+	0.502937i
$430$		0			0
$431$	−346.089	−	599.444i	−0.802991	−	1.39082i	−0.917639	−	0.397415i	$-0.869907\pi$
$431$	−346.089	−	599.444i	−0.802991	−	1.39082i	0.114648	−	0.993406i	$-0.463426\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$			116.563i			0.269200i	0.990900	+	0.134600i	$0.0429749\pi$
$433$			116.563i			0.269200i	−0.990900	+	0.134600i	$0.957025\pi$
$434$	−477.644	+	221.748i	−1.10056	+	0.510941i
$435$		0			0
$436$	64.2567	−	111.296i	0.147378	−	0.255266i
$437$	−573.394	+	331.049i	−1.31212	+	0.757550i
$438$	−66.1791	−	114.626i	−0.151094	−	0.261702i
$439$	152.664	+	88.1408i	0.347755	+	0.200776i	0.663696	−	0.748002i	$-0.268987\pi$
$439$	152.664	+	88.1408i	0.347755	+	0.200776i	−0.315941	+	0.948779i	$0.602320\pi$
$440$		0			0
$441$	49.8104	+	138.304i	0.112949	+	0.313614i
$442$	90.2729			0.204237
$443$	164.007	−	284.069i	0.370219	−	0.641239i	−0.619380	−	0.785092i	$-0.712616\pi$
$443$	164.007	−	284.069i	0.370219	−	0.641239i	0.989599	+	0.143853i	$0.0459492\pi$
$444$	130.690	−	75.4540i	0.294347	−	0.169942i
$445$		0			0
$446$	−62.4003	−	36.0268i	−0.139911	−	0.0807777i
$447$		−	15.0231i		−	0.0336088i
$448$	−23.5809	−	50.7931i	−0.0526360	−	0.113377i
$449$	−808.713			−1.80114			−0.900571	−	0.434709i	$-0.856851\pi$
$449$	−808.713			−1.80114			−0.900571	+	0.434709i	$0.856851\pi$
$450$		0			0
$451$	−1080.83	+	624.020i	−2.39653	+	1.38364i
$452$	43.4647	+	75.2830i	0.0961607	+	0.166555i
$453$	−318.849	−	184.088i	−0.703861	−	0.406374i
$454$		−	187.278i		−	0.412507i
$455$		0			0
$456$	99.5330			0.218274
$457$	168.446	−	291.757i	0.368591	−	0.638418i	−0.620755	−	0.784005i	$-0.713174\pi$
$457$	168.446	−	291.757i	0.368591	−	0.638418i	0.989345	+	0.145587i	$0.0465071\pi$
$458$	−225.760	+	130.342i	−0.492925	+	0.284590i
$459$	−20.4563	−	35.4313i	−0.0445670	−	0.0771924i
$460$		0			0
$461$		−	614.879i		−	1.33379i	−0.745150	−	0.666897i	$-0.767622\pi$
$461$		−	614.879i		−	1.33379i	0.745150	−	0.666897i	$-0.232378\pi$
$462$	−248.906	−	174.913i	−0.538758	−	0.378599i
$463$	818.194			1.76716			0.883578	−	0.468283i	$-0.155127\pi$
$463$	818.194			1.76716			0.883578	+	0.468283i	$0.155127\pi$
$464$	50.1830	−	86.9195i	0.108153	−	0.187326i
$465$		0			0
$466$	−99.4662	−	172.281i	−0.213447	−	0.369701i
$467$	460.542	+	265.894i	0.986172	+	0.569367i	0.904128	−	0.427262i	$-0.140522\pi$
$467$	460.542	+	265.894i	0.986172	+	0.569367i	0.0820440	+	0.996629i	$0.473855\pi$
$468$			48.6429i			0.103938i
$469$	401.803	−	571.778i	0.856723	−	1.21914i
$470$		0			0
$471$	−113.829	+	197.158i	−0.241676	+	0.418594i
$472$	64.9656	−	37.5079i	0.137639	−	0.0794659i
$473$	−21.5729	−	37.3653i	−0.0456086	−	0.0789964i
$474$	158.501	+	91.5108i	0.334391	+	0.193061i
$475$		0			0
$476$	−9.79255	+	109.795i	−0.0205726	+	0.230661i
$477$	152.685			0.320095
$478$	175.345	−	303.706i	0.366830	−	0.635369i
$479$	552.718	−	319.112i	1.15390	−	0.666204i	0.204065	−	0.978957i	$-0.434585\pi$
$479$	552.718	−	319.112i	1.15390	−	0.666204i	0.949834	+	0.312753i	$0.101251\pi$
$480$		0			0
$481$	305.858	+	176.587i	0.635880	+	0.367126i
$482$		−	309.501i		−	0.642118i
$483$	358.374	−	166.377i	0.741976	−	0.344466i
$484$	387.583			0.800791
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−194.425	−	336.754i	−0.399230	−	0.691486i	0.594402	−	0.804168i	$-0.297389\pi$
$487$	−194.425	−	336.754i	−0.399230	−	0.691486i	−0.993631	+	0.112683i	$0.964056\pi$
$488$	−81.3324	−	46.9573i	−0.166665	−	0.0962239i
$489$			77.6931i			0.158882i
$490$		0			0
$491$	695.908			1.41733			0.708664	−	0.705546i	$-0.249298\pi$
$491$	695.908			1.41733			0.708664	+	0.705546i	$0.249298\pi$
$492$	−121.837	+	211.027i	−0.247635	+	0.428917i
$493$	−171.093	+	98.7804i	−0.347044	+	0.200366i
$494$	116.470	+	201.732i	0.235769	+	0.408365i
$495$		0			0
$496$		−	212.782i		−	0.428995i
$497$	286.164	+	616.394i	0.575782	+	1.24023i
$498$	208.747			0.419171
$499$	265.395	−	459.678i	0.531854	−	0.921199i	−0.467454	−	0.884017i	$-0.654829\pi$
$499$	265.395	−	459.678i	0.531854	−	0.921199i	0.999309	−	0.0371815i	$-0.0118380\pi$
$500$		0			0
$501$	121.110	+	209.768i	0.241736	+	0.418699i
$502$	−46.1830	−	26.6638i	−0.0919980	−	0.0531151i
$503$		−	694.388i		−	1.38049i	−0.723574	−	0.690247i	$-0.757502\pi$
$503$		−	694.388i		−	1.38049i	0.723574	−	0.690247i	$-0.242498\pi$
$504$	−59.1621	−	5.27664i	−0.117385	−	0.0104695i
$505$		0			0
$506$	−408.844	+	708.139i	−0.807992	+	1.39948i
$507$	154.911	−	89.4381i	0.305545	−	0.176406i
$508$	−186.018	−	322.192i	−0.366177	−	0.634237i
$509$	−246.728	−	142.448i	−0.484730	−	0.279859i	0.237656	−	0.971349i	$-0.423621\pi$
$509$	−246.728	−	142.448i	−0.484730	−	0.279859i	−0.722386	+	0.691491i	$0.756954\pi$
$510$		0			0
$511$	309.474	+	217.475i	0.605624	+	0.425588i
$512$	22.6274			0.0441942
$513$	52.7853	−	91.4269i	0.102895	−	0.178220i
$514$	23.3474	−	13.4796i	0.0454229	−	0.0262250i
$515$		0			0
$516$	−7.29538	−	4.21199i	−0.0141383	−	0.00816277i
$517$		−	273.019i		−	0.528084i
$518$	−247.954	+	352.846i	−0.478676	+	0.681170i
$519$	−250.858			−0.483349
$520$		0			0
$521$	450.682	−	260.201i	0.865033	−	0.499427i	−0.000661748	−	1.00000i	$-0.500211\pi$
$521$	450.682	−	260.201i	0.865033	−	0.499427i	0.865694	+	0.500573i	$0.166877\pi$
$522$	−53.2271	−	92.1920i	−0.101968	−	0.176613i
$523$	−148.589	−	85.7878i	−0.284109	−	0.164030i	0.351173	−	0.936310i	$-0.385783\pi$
$523$	−148.589	−	85.7878i	−0.284109	−	0.164030i	−0.635282	+	0.772280i	$0.719116\pi$
$524$			180.210i			0.343912i
$525$		0			0
$526$	338.993			0.644473
$527$	−209.420	+	362.727i	−0.397382	+	0.688286i
$528$	106.454	−	61.4613i	0.201618	−	0.116404i
$529$	−266.498	−	461.587i	−0.503776	−	0.872566i
$530$		0			0
$531$		−	79.5663i		−	0.149842i
$532$	−257.992	+	119.774i	−0.484947	+	0.225139i
$533$	−570.276			−1.06994
$534$	163.119	−	282.531i	0.305467	−	0.529084i
$535$		0			0
$536$	141.187	+	244.543i	0.263408	+	0.456236i
$537$	48.6137	+	28.0672i	0.0905284	+	0.0522666i
$538$			377.011i			0.700763i
$539$	855.654	+	153.855i	1.58748	+	0.285444i
$540$		0			0
$541$	188.929	−	327.235i	0.349222	−	0.604871i	−0.636889	−	0.770955i	$-0.719779\pi$
$541$	188.929	−	327.235i	0.349222	−	0.604871i	0.986111	+	0.166085i	$0.0531125\pi$
$542$	−447.350	+	258.278i	−0.825369	+	0.476527i
$543$	103.177	+	178.709i	0.190014	+	0.329113i
$544$	−38.5727	−	22.2700i	−0.0709057	−	0.0409374i
$545$		0			0
$546$	−58.5349	−	126.084i	−0.107207	−	0.230922i
$547$	982.972			1.79702			0.898511	−	0.438950i	$-0.144650\pi$
$547$	982.972			1.79702			0.898511	+	0.438950i	$0.144650\pi$
$548$	−10.8355	+	18.7676i	−0.0197728	+	0.0342475i
$549$	−86.2660	+	49.8057i	−0.157133	+	0.0907208i
$550$		0			0
$551$	−441.488	−	254.893i	−0.801248	−	0.462601i
$552$			159.649i			0.289220i
$553$	−520.960	−	46.4642i	−0.942061	−	0.0840220i
$554$	600.948			1.08474
$555$		0			0
$556$	−384.733	+	222.126i	−0.691965	+	0.399506i
$557$	−180.216	−	312.143i	−0.323548	−	0.560401i	0.657670	−	0.753306i	$-0.271542\pi$
$557$	−180.216	−	312.143i	−0.323548	−	0.560401i	−0.981217	+	0.192905i	$0.938209\pi$
$558$	−195.452	−	112.845i	−0.350273	−	0.202230i
$559$		−	19.7149i		−	0.0352682i
$560$		0			0
$561$	−241.962			−0.431304
$562$	−102.402	+	177.366i	−0.182210	+	0.315597i
$563$	585.130	−	337.825i	1.03931	−	0.600044i	0.119670	−	0.992814i	$-0.461816\pi$
$563$	585.130	−	337.825i	1.03931	−	0.600044i	0.919637	+	0.392770i	$0.128483\pi$
$564$	−26.6528	−	46.1640i	−0.0472567	−	0.0818510i
$565$		0			0
$566$			459.430i			0.811715i
$567$	−36.2224	+	51.5455i	−0.0638842	+	0.0909092i
$568$	−274.593			−0.483438
$569$	−500.576	+	867.022i	−0.879746	+	1.52376i	−0.0281265	+	0.999604i	$0.508954\pi$
$569$	−500.576	+	867.022i	−0.879746	+	1.52376i	−0.851620	+	0.524160i	$0.824379\pi$
$570$		0			0
$571$	−363.407	−	629.439i	−0.636439	−	1.10235i	−0.986208	−	0.165509i	$-0.947073\pi$
$571$	−363.407	−	629.439i	−0.636439	−	1.10235i	0.349769	−	0.936836i	$-0.386260\pi$
$572$	249.138	+	143.840i	0.435556	+	0.251468i
$573$		−	423.412i		−	0.738940i
$574$	61.8619	−	693.601i	0.107773	−	1.20836i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	58.1213	−	33.5564i	0.100730	−	0.0581566i	−0.448789	−	0.893638i	$-0.648144\pi$
$577$	58.1213	−	33.5564i	0.100730	−	0.0581566i	0.549519	+	0.835481i	$0.314811\pi$
$578$	−160.518	−	278.025i	−0.277712	−	0.481011i
$579$	−383.342	−	221.323i	−0.662077	−	0.382250i
$580$		0			0
$581$	−541.078	+	251.198i	−0.931287	+	0.432354i
$582$	122.468			0.210426
$583$	451.500	−	782.021i	0.774443	−	1.34137i
$584$	−132.358	+	76.4171i	−0.226641	+	0.130851i
$585$		0			0
$586$	210.455	+	121.506i	0.359138	+	0.207349i
$587$		−	964.783i		−	1.64358i	−0.569788	−	0.821791i	$-0.692975\pi$
$587$		−	964.783i		−	1.64358i	0.569788	−	0.821791i	$-0.307025\pi$
$588$	159.699	−	57.5161i	0.271598	−	0.0978165i
$589$	−1080.78			−1.83493
$590$		0			0
$591$	−527.242	+	304.403i	−0.892118	+	0.515065i
$592$	−87.1268	−	150.908i	−0.147174	−	0.254912i
$593$	1.46699	+	0.846966i	0.00247384	+	0.00142827i	0.501236	−	0.865310i	$-0.332879\pi$
$593$	1.46699	+	0.846966i	0.00247384	+	0.00142827i	−0.498763	+	0.866739i	$0.666212\pi$
$594$		−	130.379i		−	0.219494i
$595$		0			0
$596$	−17.3472			−0.0291061
$597$	266.168	−	461.016i	0.445842	−	0.772222i
$598$	−323.575	+	186.816i	−0.541095	+	0.312402i
$599$	−46.3714	−	80.3177i	−0.0774147	−	0.134086i	0.824719	−	0.565543i	$-0.191333\pi$
$599$	−46.3714	−	80.3177i	−0.0774147	−	0.134086i	−0.902134	+	0.431456i	$0.858000\pi$
$600$		0			0
$601$		−	393.426i		−	0.654618i	−0.944917	−	0.327309i	$-0.893858\pi$
$601$		−	393.426i		−	0.654618i	0.944917	−	0.327309i	$-0.106142\pi$
$602$	23.9783	+	2.13862i	0.0398311	+	0.00355252i
$603$	299.502			0.496687
$604$	−212.566	+	368.175i	−0.351930	+	0.609561i
$605$		0			0
$606$	−201.236	−	348.552i	−0.332073	−	0.575168i
$607$	−257.278	−	148.539i	−0.423851	−	0.244711i	0.272872	−	0.962050i	$-0.412026\pi$
$607$	−257.278	−	148.539i	−0.423851	−	0.244711i	−0.696724	+	0.717340i	$0.745360\pi$
$608$		−	114.931i		−	0.189031i
$609$	248.906	+	174.913i	0.408713	+	0.287213i
$610$		0			0
$611$	62.3763	−	108.039i	0.102089	−	0.176823i
$612$	−40.9125	+	23.6209i	−0.0668505	+	0.0385962i
$613$	−505.823	−	876.111i	−0.825160	−	1.42922i	−0.901797	−	0.432160i	$-0.857752\pi$
$613$	−505.823	−	876.111i	−0.825160	−	1.42922i	0.0766368	−	0.997059i	$-0.475582\pi$
$614$	−139.744	−	80.6813i	−0.227596	−	0.131403i
$615$		0			0
$616$	−201.972	+	287.412i	−0.327876	+	0.466578i
$617$	−467.794			−0.758174			−0.379087	−	0.925361i	$-0.623762\pi$
$617$	−467.794			−0.758174			−0.379087	+	0.925361i	$0.623762\pi$
$618$	−119.339	+	206.701i	−0.193105	+	0.334467i
$619$	−919.996	+	531.160i	−1.48626	+	0.858094i	−0.999878	−	0.0156508i	$-0.995018\pi$
$619$	−919.996	+	531.160i	−1.48626	+	0.858094i	−0.486385	+	0.873745i	$0.661685\pi$
$620$		0			0
$621$	146.647	+	84.6668i	0.236147	+	0.136339i
$622$			219.483i			0.352866i
$623$	−82.8231	+	928.619i	−0.132942	+	1.49056i
$624$	56.1680			0.0900128
$625$		0			0
$626$	−520.633	+	300.588i	−0.831682	+	0.480172i
$627$	−312.179	−	540.710i	−0.497893	−	0.862376i
$628$	227.658	+	131.439i	0.362513	+	0.209297i
$629$			343.002i			0.545313i
$630$		0			0
$631$	−970.749			−1.53843			−0.769215	−	0.638990i	$-0.779352\pi$
$631$	−970.749			−1.53843			−0.769215	+	0.638990i	$0.779352\pi$
$632$	105.668	−	183.022i	0.167196	−	0.289591i
$633$	−502.746	+	290.260i	−0.794227	+	0.458547i
$634$	10.1777	+	17.6283i	0.0160531	+	0.0278049i
$635$		0			0
$636$		−	176.306i		−	0.277211i
$637$	303.448	+	256.373i	0.476370	+	0.402470i
$638$	−629.583			−0.986807
$639$	−145.625	+	252.229i	−0.227895	+	0.394725i
$640$		0			0
$641$	−523.506	−	906.739i	−0.816702	−	1.41457i	−0.908099	−	0.418755i	$-0.862467\pi$
$641$	−523.506	−	906.739i	−0.816702	−	1.41457i	0.0913975	−	0.995814i	$-0.470867\pi$
$642$	206.761	+	119.373i	0.322057	+	0.185940i
$643$			704.161i			1.09512i	0.836767	+	0.547559i	$0.184443\pi$
$643$			704.161i			1.09512i	−0.836767	+	0.547559i	$0.815557\pi$
$644$	−192.115	−	413.815i	−0.298316	−	0.642570i
$645$		0			0
$646$	−113.115	+	195.921i	−0.175101	+	0.303284i
$647$	326.037	−	188.237i	0.503921	−	0.290939i	−0.226411	−	0.974032i	$-0.572699\pi$
$647$	326.037	−	188.237i	0.503921	−	0.290939i	0.730331	+	0.683093i	$0.239366\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	−407.521	−	235.282i	−0.627921	−	0.362530i
$650$		0			0
$651$	642.410	+	57.2962i	0.986805	+	0.0880127i
$652$	89.7122			0.137595
$653$	−13.6120	+	23.5767i	−0.0208454	+	0.0361052i	−0.876260	−	0.481839i	$-0.839969\pi$
$653$	−13.6120	+	23.5767i	−0.0208454	+	0.0361052i	0.855415	+	0.517944i	$0.173302\pi$
$654$	−136.309	+	78.6981i	−0.208424	+	0.120334i
$655$		0			0
$656$	243.673	+	140.685i	0.371453	+	0.214459i
$657$			162.105i			0.246735i
$658$	124.636	+	87.5852i	0.189417	+	0.133108i
$659$	501.943			0.761674			0.380837	−	0.924642i	$-0.375636\pi$
$659$	501.943			0.761674			0.380837	+	0.924642i	$0.375636\pi$
$660$		0			0
$661$	−748.339	+	432.054i	−1.13213	+	0.653637i	−0.944470	−	0.328597i	$-0.893424\pi$
$661$	−748.339	+	432.054i	−1.13213	+	0.653637i	−0.187662	+	0.982234i	$0.560091\pi$
$662$	60.2415	+	104.341i	0.0909992	+	0.157615i
$663$	−95.7489	−	55.2806i	−0.144418	−	0.0833796i
$664$		−	241.040i		−	0.363013i
$665$		0			0
$666$	−184.824			−0.277513
$667$	408.844	−	708.139i	0.612960	−	1.06168i
$668$	242.219	−	139.845i	0.362604	−	0.209350i
$669$	44.1237	+	76.4245i	0.0659547	+	0.114237i
$670$		0			0
$671$			589.114i			0.877964i
$672$	−6.09294	+	68.3145i	−0.00906688	+	0.101659i
$673$	−726.018			−1.07878			−0.539389	−	0.842057i	$-0.681345\pi$
$673$	−726.018			−1.07878			−0.539389	+	0.842057i	$0.681345\pi$
$674$	−86.3071	+	149.488i	−0.128052	+	0.221793i
$675$		0			0
$676$	−103.274	−	178.876i	−0.152772	−	0.264610i
$677$	382.003	+	220.550i	0.564259	+	0.325775i	0.754853	−	0.655894i	$-0.227708\pi$
$677$	382.003	+	220.550i	0.564259	+	0.325775i	−0.190594	+	0.981669i	$0.561041\pi$
$678$		−	106.466i		−	0.157030i
$679$	−317.440	+	147.373i	−0.467510	+	0.217044i
$680$		0			0
$681$	−114.684	+	198.638i	−0.168405	+	0.291686i
$682$	−1155.93	+	667.376i	−1.69491	+	0.978557i
$683$	−594.725	−	1030.09i	−0.870754	−	1.50819i	−0.861218	−	0.508235i	$-0.830298\pi$
$683$	−594.725	−	1030.09i	−0.870754	−	1.50819i	−0.00953518	−	0.999955i	$-0.503035\pi$
$684$	−105.571	−	60.9513i	−0.154343	−	0.0891100i
$685$		0			0
$686$	−344.732	+	341.259i	−0.502525	+	0.497462i
$687$	319.272			0.464734
$688$	−4.86359	+	8.42398i	−0.00706917	+	0.0122442i
$689$	357.335	−	206.307i	0.518628	−	0.299430i
$690$		0			0
$691$	37.0369	+	21.3832i	0.0535989	+	0.0309453i	0.526560	−	0.850138i	$-0.323482\pi$
$691$	37.0369	+	21.3832i	0.0535989	+	0.0309453i	−0.472961	+	0.881083i	$0.656815\pi$
$692$			289.666i			0.418593i
$693$	156.893	+	337.946i	0.226397	+	0.487657i
$694$	348.818			0.502620
$695$		0			0
$696$	−106.454	+	61.4613i	−0.152951	+	0.0883065i
$697$	−276.925	−	479.648i	−0.397309	−	0.688160i
$698$	−325.106	−	187.700i	−0.465768	−	0.268911i
$699$			243.642i			0.348557i
$700$		0			0
$701$	368.695			0.525956			0.262978	−	0.964802i	$-0.415295\pi$
$701$	368.695			0.525956			0.262978	+	0.964802i	$0.415295\pi$
$702$	29.7876	−	51.5936i	0.0424324	−	0.0734951i
$703$	−766.503	+	442.541i	−1.09033	+	0.629503i
$704$	−70.9695	−	122.923i	−0.100809	−	0.174606i
$705$		0			0
$706$		−	398.243i		−	0.564083i
$707$	941.043	+	661.295i	1.33104	+	0.935353i
$708$	−91.8752			−0.129767
$709$	93.3436	−	161.676i	0.131655	−	0.228034i	−0.792660	−	0.609665i	$-0.791304\pi$
$709$	93.3436	−	161.676i	0.131655	−	0.228034i	0.924315	+	0.381631i	$0.124637\pi$
$710$		0			0
$711$	−112.077	−	194.124i	−0.157633	−	0.273029i
$712$	−326.239	−	188.354i	−0.458201	−	0.264542i
$713$		−	1733.55i		−	2.43134i
$714$	77.6219	−	110.458i	0.108714	−	0.154704i
$715$		0			0
$716$	32.4092	−	56.1343i	0.0452642	−	0.0783999i
$717$	−371.963	+	214.753i	−0.518777	+	0.299516i
$718$	−4.54802	−	7.87740i	−0.00633429	−	0.0109713i
$719$	−447.220	−	258.203i	−0.622003	−	0.359113i	0.155646	−	0.987813i	$-0.450254\pi$
$719$	−447.220	−	258.203i	−0.622003	−	0.359113i	−0.777648	+	0.628700i	$0.783588\pi$
$720$		0			0
$721$	60.5936	−	679.381i	0.0840411	−	0.942275i
$722$	−73.2338			−0.101432
$723$	−189.530	+	328.275i	−0.262144	+	0.454046i
$724$	206.355	−	119.139i	0.285020	−	0.164557i
$725$		0			0
$726$	−411.094	−	237.345i	−0.566245	−	0.326922i
$727$			986.117i			1.35642i	0.734868	+	0.678210i	$0.237244\pi$
$727$			986.117i			1.35642i	−0.734868	+	0.678210i	$0.762756\pi$
$728$	−145.589	+	67.5902i	−0.199985	+	0.0928437i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	16.5818	−	9.57351i	0.0226837	−	0.0130965i
$732$	57.5107	+	99.6114i	0.0785665	+	0.136081i
$733$	−1009.91	−	583.073i	−1.37778	−	0.795461i	−0.385887	−	0.922546i	$-0.626104\pi$
$733$	−1009.91	−	583.073i	−1.37778	−	0.795461i	−0.991892	+	0.127085i	$0.959438\pi$
$734$		−	354.275i		−	0.482664i
$735$		0			0
$736$	184.347			0.250472
$737$	885.647	−	1533.99i	1.20169	−	2.08139i
$738$	258.454	−	149.219i	0.350209	−	0.202193i
$739$	519.556	+	899.897i	0.703053	+	1.21772i	0.967390	+	0.253292i	$0.0815135\pi$
$739$	519.556	+	899.897i	0.703053	+	1.21772i	−0.264337	+	0.964430i	$0.585153\pi$
$740$		0			0
$741$		−	285.292i		−	0.385010i
$742$	212.159	+	456.989i	0.285929	+	0.615889i
$743$	320.811			0.431778			0.215889	−	0.976418i	$-0.430735\pi$
$743$	320.811			0.431778			0.215889	+	0.976418i	$0.430735\pi$
$744$	−130.302	+	225.689i	−0.175137	+	0.303345i
$745$		0			0
$746$	−298.935	−	517.771i	−0.400717	−	0.694062i
$747$	−221.410	−	127.831i	−0.296399	−	0.171126i
$748$			279.393i			0.373520i
$749$	−679.578	−	60.6112i	−0.907313	−	0.0809228i
$750$		0			0
$751$	560.762	−	971.268i	0.746687	−	1.29330i	−0.202715	−	0.979238i	$-0.564977\pi$
$751$	560.762	−	971.268i	0.746687	−	1.29330i	0.949402	−	0.314062i	$-0.101690\pi$
$752$	−53.3055	+	30.7760i	−0.0708850	+	0.0409255i
$753$	32.6563	+	56.5624i	0.0433683	+	0.0751161i
$754$	−249.138	−	143.840i	−0.330422	−	0.190769i
$755$		0			0
$756$	59.5196	+	41.8260i	0.0787297	+	0.0553254i
$757$	769.996			1.01717			0.508584	−	0.861012i	$-0.330169\pi$
$757$	769.996			1.01717			0.508584	+	0.861012i	$0.330169\pi$
$758$	360.769	−	624.871i	0.475949	−	0.824367i
$759$	867.289	−	500.730i	1.14267	−	0.659723i
$760$		0			0
$761$	−874.305	−	504.780i	−1.14889	−	0.663311i	−0.200273	−	0.979740i	$-0.564183\pi$
$761$	−874.305	−	504.780i	−1.14889	−	0.663311i	−0.948616	+	0.316429i	$0.897516\pi$
$762$			455.649i			0.597964i
$763$	258.615	−	368.016i	0.338944	−	0.482328i
$764$	−488.914			−0.639940
$765$		0			0
$766$	−329.317	+	190.131i	−0.429917	+	0.248213i
$767$	−107.509	−	186.211i	−0.140169	−	0.242779i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$			817.903i			1.06359i	0.846872	+	0.531797i	$0.178483\pi$
$769$			817.903i			1.06359i	−0.846872	+	0.531797i	$0.821517\pi$
$770$		0			0
$771$	−33.0182			−0.0428252
$772$	−255.562	+	442.646i	−0.331038	+	0.573375i
$773$	1112.36	−	642.220i	1.43901	−	0.830815i	0.441233	−	0.897393i	$-0.354541\pi$
$773$	1112.36	−	642.220i	1.43901	−	0.830815i	0.997781	+	0.0665776i	$0.0212080\pi$
$774$	5.15861	+	8.93498i	0.00666487	+	0.0115439i
$775$		0			0
$776$		−	141.414i		−	0.182234i
$777$	479.068	−	222.410i	0.616561	−	0.286241i
$778$	−237.272			−0.304977
$779$	714.576	−	1237.68i	0.917300	−	1.58881i
$780$		0			0
$781$	861.242	+	1491.71i	1.10274	+	1.91001i
$782$	−314.254	−	181.435i	−0.401860	−	0.232014i
$783$			130.379i			0.166512i
$784$	−66.4139	−	184.405i	−0.0847116	−	0.235210i
$785$		0			0
$786$	110.355	−	191.141i	0.140401	−	0.243182i
$787$	−694.748	+	401.113i	−0.882780	+	0.509673i	−0.871574	−	0.490264i	$-0.836900\pi$
$787$	−694.748	+	401.113i	−0.882780	+	0.509673i	−0.0112060	+	0.999937i	$0.503567\pi$
$788$	351.495	+	608.807i	0.446059	+	0.772597i
$789$	−359.556	−	207.590i	−0.455712	−	0.263105i
$790$		0			0
$791$	128.117	+	275.963i	0.161969	+	0.348879i
$792$	−150.549			−0.190087
$793$	−134.594	+	233.124i	−0.169728	+	0.293977i
$794$	445.277	−	257.081i	0.560802	−	0.323779i
$795$		0			0
$796$	−532.336	−	307.344i	−0.668764	−	0.386111i
$797$			1242.74i			1.55927i	0.626233	+	0.779636i	$0.284596\pi$
$797$			1242.74i			1.55927i	−0.626233	+	0.779636i	$0.715404\pi$
$798$	346.988	+	30.9477i	0.434822	+	0.0387816i
$799$	121.159			0.151638
$800$		0			0
$801$	−346.029	+	199.780i	−0.431996	+	0.249413i
$802$	−197.164	−	341.497i	−0.245840	−	0.425807i
$803$	830.267	+	479.355i	1.03396	+	0.596955i
$804$		−	345.836i		−	0.430144i
$805$		0			0
$806$	−609.898			−0.756697
$807$	230.871	−	399.880i	0.286085	−	0.495514i
$808$	−402.473	+	232.368i	−0.498110	+	0.287584i
$809$	−55.3589	−	95.8845i	−0.0684288	−	0.118522i	0.829781	−	0.558089i	$-0.188465\pi$
$809$	−55.3589	−	95.8845i	−0.0684288	−	0.118522i	−0.898210	+	0.439567i	$0.855132\pi$
$810$		0			0
$811$			437.207i			0.539096i	0.962987	+	0.269548i	$0.0868743\pi$
$811$			437.207i			0.539096i	−0.962987	+	0.269548i	$0.913126\pi$
$812$	201.972	−	287.412i	0.248734	−	0.353956i
$813$	632.649			0.778165
$814$	−546.535	+	946.627i	−0.671419	+	1.16293i
$815$		0			0
$816$	27.2750	+	47.2417i	0.0334253	+	0.0578943i
$817$	42.7877	+	24.7035i	0.0523717	+	0.0302368i
$818$			551.726i			0.674482i
$819$	−15.1245	+	169.577i	−0.0184670	+	0.207054i
$820$		0			0
$821$	340.004	−	588.903i	0.414133	−	0.717300i	−0.581204	−	0.813758i	$-0.697418\pi$
$821$	340.004	−	588.903i	0.414133	−	0.717300i	0.995337	+	0.0964580i	$0.0307513\pi$
$822$	22.9855	−	13.2707i	0.0279629	−	0.0161444i
$823$	251.176	+	435.049i	0.305195	+	0.528613i	0.977305	−	0.211838i	$-0.0679450\pi$
$823$	251.176	+	435.049i	0.305195	+	0.528613i	−0.672110	+	0.740452i	$0.734612\pi$
$824$	238.677	+	137.800i	0.289657	+	0.167234i
$825$		0			0
$826$	238.143	−	110.559i	0.288309	−	0.133849i
$827$	404.323			0.488904			0.244452	−	0.969661i	$-0.421392\pi$
$827$	404.323			0.488904			0.244452	+	0.969661i	$0.421392\pi$
$828$	97.7648	−	169.334i	0.118073	−	0.204509i
$829$	−587.862	+	339.402i	−0.709122	+	0.409412i	−0.810736	−	0.585412i	$-0.800933\pi$
$829$	−587.862	+	339.402i	−0.709122	+	0.409412i	0.101614	+	0.994824i	$0.467599\pi$
$830$		0			0
$831$	−637.402	−	368.004i	−0.767030	−	0.442845i
$832$		−	64.8572i		−	0.0779533i
$833$	−68.2768	+	379.718i	−0.0819650	+	0.455844i
$834$	544.094			0.652391
$835$		0			0
$836$	−624.358	+	360.473i	−0.746840	+	0.431188i
$837$	138.206	+	239.379i	0.165120	+	0.285997i
$838$	−706.550	−	407.927i	−0.843138	−	0.486786i
$839$			230.404i			0.274617i	0.990528	+	0.137309i	$0.0438452\pi$
$839$			230.404i			0.274617i	−0.990528	+	0.137309i	$0.956155\pi$
$840$		0			0
$841$	−211.417			−0.251388
$842$	−459.514	+	795.902i	−0.545742	+	0.945252i
$843$	217.228	−	125.416i	0.257684	−	0.148774i
$844$	335.164	+	580.521i	0.397113	+	0.687821i
$845$		0			0
$846$			65.2857i			0.0771698i
$847$	1351.18	+	120.511i	1.59525	+	0.142280i
$848$	−203.581			−0.240071
$849$	281.343	−	487.300i	0.331381	−	0.573969i
$850$		0			0
$851$	−709.828	−	1229.46i	−0.834111	−	1.44472i
$852$	291.249	+	168.153i	0.341842	+	0.197363i
$853$		−	234.440i		−	0.274842i	−0.990513	−	0.137421i	$-0.956119\pi$
$853$		−	234.440i		−	0.274842i	0.990513	−	0.137421i	$-0.0438813\pi$
$854$	−268.937	−	188.989i	−0.314915	−	0.221299i
$855$		0			0
$856$	137.840	−	238.747i	0.161029	−	0.278910i
$857$	−536.305	+	309.636i	−0.625794	+	0.361302i	−0.779121	−	0.626873i	$-0.784334\pi$
$857$	−536.305	+	309.636i	−0.625794	+	0.361302i	0.153327	+	0.988175i	$0.451001\pi$
$858$	−176.167	−	305.131i	−0.205323	−	0.355630i
$859$	−546.499	−	315.521i	−0.636204	−	0.367313i	0.146947	−	0.989144i	$-0.453055\pi$
$859$	−546.499	−	315.521i	−0.636204	−	0.367313i	−0.783151	+	0.621832i	$0.786389\pi$
$860$		0			0
$861$	−490.357	+	697.792i	−0.569520	+	0.810444i
$862$	978.888			1.13560
$863$	−637.108	+	1103.50i	−0.738247	+	1.27868i	0.215036	+	0.976606i	$0.431013\pi$
$863$	−637.108	+	1103.50i	−0.738247	+	1.27868i	−0.953284	+	0.302076i	$0.902320\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	−142.760	−	82.4228i	−0.164850	−	0.0951764i
$867$			393.186i			0.453502i
$868$	66.1600	−	741.791i	0.0762212	−	0.854598i
$869$	−1325.68			−1.52552
$870$		0			0
$871$	700.935	−	404.685i	0.804747	−	0.464621i
$872$	90.8728	+	157.396i	0.104212	+	0.180500i
$873$	−129.897	−	74.9959i	−0.148793	−	0.0859060i
$874$		−	936.349i		−	1.07134i
$875$		0			0
$876$	187.183			0.213679
$877$	−1.07486	+	1.86172i	−0.00122562	+	0.00212283i	−0.866638	−	0.498938i	$-0.833723\pi$
$877$	−1.07486	+	1.86172i	−0.00122562	+	0.00212283i	0.865412	+	0.501061i	$0.167057\pi$
$878$	−215.900	+	124.650i	−0.245900	+	0.141970i
$879$	−148.814	−	257.754i	−0.169299	−	0.293235i
$880$		0			0
$881$			839.378i			0.952756i	0.879241	+	0.476378i	$0.158051\pi$
$881$			839.378i			0.952756i	−0.879241	+	0.476378i	$0.841949\pi$
$882$	−204.608	−	36.7904i	−0.231982	−	0.0417125i
$883$	−1326.53			−1.50230			−0.751150	−	0.660131i	$-0.770501\pi$
$883$	−1326.53			−1.50230			−0.751150	+	0.660131i	$0.770501\pi$
$884$	−63.8326	+	110.561i	−0.0722088	+	0.125069i
$885$		0			0
$886$	231.941	+	401.734i	0.261785	+	0.453424i
$887$	880.761	+	508.507i	0.992966	+	0.573289i	0.906160	−	0.422936i	$-0.139001\pi$
$887$	880.761	+	508.507i	0.992966	+	0.573289i	0.0868064	+	0.996225i	$0.472334\pi$
$888$			213.416i			0.240334i
$889$	−548.309	−	1181.05i	−0.616771	−	1.32852i
$890$		0			0
$891$	−79.8406	+	138.288i	−0.0896079	+	0.155205i
$892$	88.2474	−	50.9497i	0.0989321	−	0.0571185i
$893$	156.320	+	270.753i	0.175050	+	0.303195i
$894$	18.3995	+	10.6230i	0.0205811	+	0.0118825i
$895$		0			0
$896$	78.8828	+	7.03552i	0.0880389	+	0.00785214i
$897$	457.604			0.510150
$898$	571.846	−	990.467i	0.636800	−	1.10297i
$899$	1155.93	−	667.376i	1.28579	−	0.742354i
$900$		0			0
$901$	347.042	+	200.365i	0.385174	+	0.222380i
$902$		−	1765.00i		−	1.95676i
$903$	−24.1232	−	16.9520i	−0.0267146	−	0.0187730i
$904$	−122.937			−0.135992
$905$		0			0
$906$	450.921	−	260.339i	0.497705	−	0.287350i
$907$	−309.272	−	535.675i	−0.340984	−	0.590601i	0.643632	−	0.765335i	$-0.277427\pi$
$907$	−309.272	−	535.675i	−0.340984	−	0.590601i	−0.984616	+	0.174734i	$0.944093\pi$
$908$	229.368	+	132.426i	0.252608	+	0.145843i
$909$			492.926i			0.542273i
$910$		0			0
$911$	821.498			0.901754			0.450877	−	0.892586i	$-0.351111\pi$
$911$	821.498			0.901754			0.450877	+	0.892586i	$0.351111\pi$
$912$	−70.3805	+	121.903i	−0.0771716	+	0.133665i
$913$	−1309.44	+	756.008i	−1.43422	+	0.828048i
$914$	238.218	+	412.607i	0.260633	+	0.451429i
$915$		0			0
$916$		−	368.664i		−	0.402471i
$917$	−56.0324	+	628.240i	−0.0611041	+	0.685104i
$918$	57.8591			0.0630273
$919$	−408.435	+	707.430i	−0.444434	+	0.769782i	−0.998013	−	0.0630149i	$-0.979928\pi$
$919$	−408.435	+	707.430i	−0.444434	+	0.769782i	0.553579	+	0.832797i	$0.313262\pi$
$920$		0			0
$921$	98.8141	+	171.151i	0.107290	+	0.185832i
$922$	753.069	+	434.785i	0.816778	+	0.471567i
$923$			787.067i			0.852727i
$924$	390.227	−	181.164i	0.422323	−	0.196065i
$925$		0			0
$926$	−578.550	+	1002.08i	−0.624784	+	1.08216i
$927$	253.156	−	146.159i	0.273091	−	0.157669i
$928$	70.9695	+	122.923i	0.0764757	+	0.132460i
$929$	109.848	+	63.4209i	0.118243	+	0.0682679i	0.557955	−	0.829871i	$-0.311586\pi$
$929$	109.848	+	63.4209i	0.118243	+	0.0682679i	−0.439712	+	0.898139i	$0.644919\pi$
$930$		0			0
$931$	−936.643	+	337.334i	−1.00606	+	0.362335i
$932$	281.333			0.301859
$933$	134.405	−	232.796i	0.144057	−	0.249514i
$934$	−651.305	+	376.031i	−0.697329	+	0.402603i
$935$		0			0
$936$	−59.5751	−	34.3957i	−0.0636486	−	0.0367476i
$937$		−	1128.69i		−	1.20458i	−0.798278	−	0.602289i	$-0.794255\pi$
$937$		−	1128.69i		−	1.20458i	0.798278	−	0.602289i	$-0.205745\pi$
$938$	416.165	+	896.414i	0.443672	+	0.955666i
$939$	736.287			0.784118
$940$		0			0
$941$	232.437	−	134.197i	0.247010	−	0.142611i	−0.371384	−	0.928479i	$-0.621117\pi$
$941$	232.437	−	134.197i	0.247010	−	0.142611i	0.618395	+	0.785868i	$0.287783\pi$
$942$	−160.979	−	278.823i	−0.170890	−	0.295991i
$943$	1985.22	+	1146.17i	2.10522	+	1.21545i
$944$			106.088i			0.112382i
$945$		0			0
$946$	61.0173			0.0645003
$947$	444.261	−	769.482i	0.469124	−	0.812547i	−0.530253	−	0.847840i	$-0.677903\pi$
$947$	444.261	−	769.482i	0.469124	−	0.812547i	0.999377	+	0.0352923i	$0.0112362\pi$
$948$	−224.155	+	129.416i	−0.236450	+	0.136515i
$949$	219.035	+	379.380i	0.230806	+	0.399768i
$950$		0			0
$951$		−	24.9302i		−	0.0262147i
$952$	−127.546	−	89.6301i	−0.133977	−	0.0941492i
$953$	−300.519			−0.315340			−0.157670	−	0.987492i	$-0.550398\pi$
$953$	−300.519			−0.315340			−0.157670	+	0.987492i	$0.550398\pi$
$954$	−107.965	+	187.001i	−0.113171	+	0.196018i
$955$		0			0
$956$	247.975	+	429.506i	0.259388	+	0.449274i
$957$	667.773	+	385.539i	0.697778	+	0.402862i
$958$			902.585i			0.942155i
$959$	−43.6096	+	62.0578i	−0.0454741	+	0.0647110i
$960$		0			0
$961$	934.376	−	1618.39i	0.972296	−	1.68407i
$962$	−432.549	+	249.732i	−0.449635	+	0.259597i
$963$	−146.202	−	253.229i	−0.151819	−	0.262958i
$964$	379.060	+	218.850i	0.393216	+	0.227023i
$965$		0			0
$966$	−49.6396	+	556.563i	−0.0513867	+	0.576152i
$967$	−391.420			−0.404778			−0.202389	−	0.979305i	$-0.564870\pi$
$967$	−391.420			−0.404778			−0.202389	+	0.979305i	$0.564870\pi$
$968$	−274.062	+	474.690i	−0.283122	+	0.490382i
$969$	239.954	−	138.537i	0.247630	−	0.142969i
$970$		0			0
$971$	−1370.55	−	791.285i	−1.41148	−	0.814918i	−0.415951	−	0.909387i	$-0.636551\pi$
$971$	−1370.55	−	791.285i	−1.41148	−	0.814918i	−0.995528	+	0.0944692i	$0.969885\pi$
$972$			31.1769i			0.0320750i
$973$	−1410.31	+	654.741i	−1.44944	+	0.672910i
$974$	549.916			0.564596
$975$		0			0
$976$	115.021	−	66.4076i	0.117850	−	0.0680406i
$977$	−425.703	−	737.340i	−0.435725	−	0.754698i	0.561630	−	0.827389i	$-0.310175\pi$
$977$	−425.703	−	737.340i	−0.435725	−	0.754698i	−0.997355	+	0.0726910i	$0.976841\pi$
$978$	−95.1542	−	54.9373i	−0.0972947	−	0.0561731i
$979$			2363.04i			2.41373i
$980$		0			0
$981$	192.770			0.196504
$982$	−492.082	+	852.310i	−0.501101	+	0.867933i
$983$	−196.599	+	113.507i	−0.199999	+	0.115470i	−0.596655	−	0.802498i	$-0.703504\pi$
$983$	−196.599	+	113.507i	−0.199999	+	0.115470i	0.396656	+	0.917967i	$0.370171\pi$
$984$	−172.303	−	298.437i	−0.175105	−	0.303290i
$985$		0			0
$986$		−	279.393i		−	0.283360i
$987$	−78.5621	−	169.222i	−0.0795969	−	0.171451i
$988$	−329.427			−0.333428
$989$	−39.6240	+	68.6307i	−0.0400647	+	0.0693940i
$990$		0			0
$991$	−276.368	−	478.683i	−0.278878	−	0.483031i	0.692228	−	0.721679i	$-0.256629\pi$
$991$	−276.368	−	478.683i	−0.278878	−	0.483031i	−0.971106	+	0.238648i	$0.923296\pi$
$992$	260.603	+	150.459i	0.262705	+	0.151673i
$993$		−	147.561i		−	0.148601i
$994$	−957.274	−	85.3788i	−0.963052	−	0.0858942i
$995$		0			0
$996$	−147.606	+	255.662i	−0.148199	+	0.256689i
$997$	233.746	−	134.953i	0.234449	−	0.135359i	−0.378174	−	0.925735i	$-0.623448\pi$
$997$	233.746	−	134.953i	0.234449	−	0.135359i	0.612623	+	0.790375i	$0.290114\pi$
$998$	375.326	+	650.083i	0.376078	+	0.651386i
$999$	196.035	+	113.181i	0.196232	+	0.113294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.f.901.1	yes	12
5.2	odd	4		1050.3.q.d.649.6		24
5.3	odd	4		1050.3.q.d.649.9		24
5.4	even	2		1050.3.p.e.901.6	yes	12
7.3	odd	6	inner	1050.3.p.f.451.1	yes	12
35.3	even	12		1050.3.q.d.199.6		24
35.17	even	12		1050.3.q.d.199.9		24
35.24	odd	6		1050.3.p.e.451.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.6	✓	12	35.24	odd	6
1050.3.p.e.901.6	yes	12	5.4	even	2
1050.3.p.f.451.1	yes	12	7.3	odd	6	inner
1050.3.p.f.901.1	yes	12	1.1	even	1	trivial
1050.3.q.d.199.6		24	35.3	even	12
1050.3.q.d.199.9		24	35.17	even	12
1050.3.q.d.649.6		24	5.2	odd	4
1050.3.q.d.649.9		24	5.3	odd	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-2.94762 - 6.34914i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-2.94762 - 6.34914i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-8.87118 - 15.3653i) q^{11} +(-3.00000 - 1.73205i) q^{12} -8.10715i q^{13} +(9.86035 + 0.879440i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(6.81875 - 3.93681i) q^{17} +(2.12132 + 3.67423i) q^{18} +(17.5951 + 10.1585i) q^{19} +(-9.91994 - 6.97100i) q^{21} +25.0915 q^{22} +(-16.2941 + 28.2223i) q^{23} +(4.24264 - 2.44949i) q^{24} +(9.92919 + 5.73262i) q^{26} -5.19615i q^{27} +(-8.04941 + 11.4546i) q^{28} -25.0915 q^{29} +(-46.0686 + 26.5977i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-26.6135 - 15.3653i) q^{33} +11.1350i q^{34} -6.00000 q^{36} +(-21.7817 + 37.7270i) q^{37} +(-24.8833 + 14.3664i) q^{38} +(-7.02100 - 12.1607i) q^{39} -70.3424i q^{41} +(15.5521 - 7.22016i) q^{42} +2.43179 q^{43} +(-17.7424 + 30.7307i) q^{44} +(-23.0434 - 39.9123i) q^{46} +(13.3264 + 7.69399i) q^{47} +6.92820i q^{48} +(-31.6231 + 37.4297i) q^{49} +(6.81875 - 11.8104i) q^{51} +(-14.0420 + 8.10715i) q^{52} +(25.4476 + 44.0765i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-8.33712 - 17.9581i) q^{56} +35.1902 q^{57} +(17.7424 - 30.7307i) q^{58} +(22.9688 - 13.2610i) q^{59} +(-28.7553 - 16.6019i) q^{61} -75.2297i q^{62} +(-20.9170 - 1.86557i) q^{63} +8.00000 q^{64} +(37.6372 - 21.7299i) q^{66} +(49.9171 + 86.4589i) q^{67} +(-13.6375 - 7.87362i) q^{68} +56.4445i q^{69} -97.0831 q^{71} +(4.24264 - 7.34847i) q^{72} +(-46.7957 + 27.0175i) q^{73} +(-30.8040 - 53.3541i) q^{74} -40.6342i q^{76} +(-71.4078 + 101.615i) q^{77} +19.8584 q^{78} +(37.3591 - 64.7079i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(86.1515 + 49.7396i) q^{82} -85.2206i q^{83} +(-2.15418 + 24.1528i) q^{84} +(-1.71954 + 2.97833i) q^{86} +(-37.6372 + 21.7299i) q^{87} +(-25.0915 - 43.4597i) q^{88} +(-115.343 - 66.5932i) q^{89} +(-51.4734 + 23.8968i) q^{91} +65.1765 q^{92} +(-46.0686 + 79.7931i) q^{93} +(-18.8464 + 10.8809i) q^{94} +(-8.48528 - 4.89898i) q^{96} -49.9973i q^{97} +(-23.4809 - 65.1970i) q^{98} -53.2271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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