LMFDB - Embedded newform 90.3.g.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,3,Mod(37,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("90.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	90.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45232237924$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	90.73
Dual form			90.3.g.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} -5.00000i q^{5} +(2.00000 - 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} -5.00000i q^{5} +(2.00000 - 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-5.00000 - 5.00000i) q^{10} +8.00000 q^{11} +(3.00000 + 3.00000i) q^{13} -4.00000i q^{14} -4.00000 q^{16} +(-7.00000 + 7.00000i) q^{17} +20.0000i q^{19} -10.0000 q^{20} +(8.00000 - 8.00000i) q^{22} +(2.00000 + 2.00000i) q^{23} -25.0000 q^{25} +6.00000 q^{26} +(-4.00000 - 4.00000i) q^{28} +40.0000i q^{29} +52.0000 q^{31} +(-4.00000 + 4.00000i) q^{32} +14.0000i q^{34} +(-10.0000 - 10.0000i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(20.0000 + 20.0000i) q^{38} +(-10.0000 + 10.0000i) q^{40} +8.00000 q^{41} +(-42.0000 - 42.0000i) q^{43} -16.0000i q^{44} +4.00000 q^{46} +(18.0000 - 18.0000i) q^{47} +41.0000i q^{49} +(-25.0000 + 25.0000i) q^{50} +(6.00000 - 6.00000i) q^{52} +(-53.0000 - 53.0000i) q^{53} -40.0000i q^{55} -8.00000 q^{56} +(40.0000 + 40.0000i) q^{58} -20.0000i q^{59} -48.0000 q^{61} +(52.0000 - 52.0000i) q^{62} +8.00000i q^{64} +(15.0000 - 15.0000i) q^{65} +(62.0000 - 62.0000i) q^{67} +(14.0000 + 14.0000i) q^{68} -20.0000 q^{70} +28.0000 q^{71} +(-47.0000 - 47.0000i) q^{73} +6.00000i q^{74} +40.0000 q^{76} +(16.0000 - 16.0000i) q^{77} +20.0000i q^{80} +(8.00000 - 8.00000i) q^{82} +(-18.0000 - 18.0000i) q^{83} +(35.0000 + 35.0000i) q^{85} -84.0000 q^{86} +(-16.0000 - 16.0000i) q^{88} +80.0000i q^{89} +12.0000 q^{91} +(4.00000 - 4.00000i) q^{92} -36.0000i q^{94} +100.000 q^{95} +(-63.0000 + 63.0000i) q^{97} +(41.0000 + 41.0000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 4 * q^7 - 4 * q^8	$ 2 q + 2 q^{2} + 4 q^{7} - 4 q^{8} - 10 q^{10} + 16 q^{11} + 6 q^{13} - 8 q^{16} - 14 q^{17} - 20 q^{20} + 16 q^{22} + 4 q^{23} - 50 q^{25} + 12 q^{26} - 8 q^{28} + 104 q^{31} - 8 q^{32} - 20 q^{35} - 6 q^{37} + 40 q^{38} - 20 q^{40} + 16 q^{41} - 84 q^{43} + 8 q^{46} + 36 q^{47} - 50 q^{50} + 12 q^{52} - 106 q^{53} - 16 q^{56} + 80 q^{58} - 96 q^{61} + 104 q^{62} + 30 q^{65} + 124 q^{67} + 28 q^{68} - 40 q^{70} + 56 q^{71} - 94 q^{73} + 80 q^{76} + 32 q^{77} + 16 q^{82} - 36 q^{83} + 70 q^{85} - 168 q^{86} - 32 q^{88} + 24 q^{91} + 8 q^{92} + 200 q^{95} - 126 q^{97} + 82 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 4 * q^7 - 4 * q^8 - 10 * q^10 + 16 * q^11 + 6 * q^13 - 8 * q^16 - 14 * q^17 - 20 * q^20 + 16 * q^22 + 4 * q^23 - 50 * q^25 + 12 * q^26 - 8 * q^28 + 104 * q^31 - 8 * q^32 - 20 * q^35 - 6 * q^37 + 40 * q^38 - 20 * q^40 + 16 * q^41 - 84 * q^43 + 8 * q^46 + 36 * q^47 - 50 * q^50 + 12 * q^52 - 106 * q^53 - 16 * q^56 + 80 * q^58 - 96 * q^61 + 104 * q^62 + 30 * q^65 + 124 * q^67 + 28 * q^68 - 40 * q^70 + 56 * q^71 - 94 * q^73 + 80 * q^76 + 32 * q^77 + 16 * q^82 - 36 * q^83 + 70 * q^85 - 168 * q^86 - 32 * q^88 + 24 * q^91 + 8 * q^92 + 200 * q^95 - 126 * q^97 + 82 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$		−	5.00000i		−	1.00000i
$5$		−	5.00000i		−	1.00000i
$6$		0			0
$7$	2.00000	−	2.00000i	0.285714	−	0.285714i	−0.549669	−	0.835383i	$-0.685246\pi$
$7$	2.00000	−	2.00000i	0.285714	−	0.285714i	0.835383	+	0.549669i	$0.185246\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	−5.00000	−	5.00000i	−0.500000	−	0.500000i
$11$	8.00000			0.727273			0.363636	−	0.931541i	$-0.381535\pi$
$11$	8.00000			0.727273			0.363636	+	0.931541i	$0.381535\pi$
$12$		0			0
$13$	3.00000	+	3.00000i	0.230769	+	0.230769i	0.813014	−	0.582245i	$-0.197825\pi$
$13$	3.00000	+	3.00000i	0.230769	+	0.230769i	−0.582245	+	0.813014i	$0.697825\pi$
$14$		−	4.00000i		−	0.285714i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−7.00000	+	7.00000i	−0.411765	+	0.411765i	−0.882353	−	0.470588i	$-0.844042\pi$
$17$	−7.00000	+	7.00000i	−0.411765	+	0.411765i	0.470588	+	0.882353i	$0.344042\pi$
$18$		0			0
$19$			20.0000i			1.05263i	0.850289	+	0.526316i	$0.176427\pi$
$19$			20.0000i			1.05263i	−0.850289	+	0.526316i	$0.823573\pi$
$20$	−10.0000			−0.500000
$21$		0			0
$22$	8.00000	−	8.00000i	0.363636	−	0.363636i
$23$	2.00000	+	2.00000i	0.0869565	+	0.0869565i	0.749247	−	0.662291i	$-0.230416\pi$
$23$	2.00000	+	2.00000i	0.0869565	+	0.0869565i	−0.662291	+	0.749247i	$0.730416\pi$
$24$		0			0
$25$	−25.0000			−1.00000
$26$	6.00000			0.230769
$27$		0			0
$28$	−4.00000	−	4.00000i	−0.142857	−	0.142857i
$29$			40.0000i			1.37931i	0.724138	+	0.689655i	$0.242238\pi$
$29$			40.0000i			1.37931i	−0.724138	+	0.689655i	$0.757762\pi$
$30$		0			0
$31$	52.0000			1.67742			0.838710	−	0.544579i	$-0.183310\pi$
$31$	52.0000			1.67742			0.838710	+	0.544579i	$0.183310\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$			14.0000i			0.411765i
$35$	−10.0000	−	10.0000i	−0.285714	−	0.285714i
$36$		0			0
$37$	−3.00000	+	3.00000i	−0.0810811	+	0.0810811i	−0.746484	−	0.665403i	$-0.768260\pi$
$37$	−3.00000	+	3.00000i	−0.0810811	+	0.0810811i	0.665403	+	0.746484i	$0.268260\pi$
$38$	20.0000	+	20.0000i	0.526316	+	0.526316i
$39$		0			0
$40$	−10.0000	+	10.0000i	−0.250000	+	0.250000i
$41$	8.00000			0.195122			0.0975610	−	0.995230i	$-0.468896\pi$
$41$	8.00000			0.195122			0.0975610	+	0.995230i	$0.468896\pi$
$42$		0			0
$43$	−42.0000	−	42.0000i	−0.976744	−	0.976744i	0.0229915	−	0.999736i	$-0.492681\pi$
$43$	−42.0000	−	42.0000i	−0.976744	−	0.976744i	−0.999736	+	0.0229915i	$0.992681\pi$
$44$		−	16.0000i		−	0.363636i
$45$		0			0
$46$	4.00000			0.0869565
$47$	18.0000	−	18.0000i	0.382979	−	0.382979i	−0.489195	−	0.872174i	$-0.662710\pi$
$47$	18.0000	−	18.0000i	0.382979	−	0.382979i	0.872174	+	0.489195i	$0.162710\pi$
$48$		0			0
$49$			41.0000i			0.836735i
$50$	−25.0000	+	25.0000i	−0.500000	+	0.500000i
$51$		0			0
$52$	6.00000	−	6.00000i	0.115385	−	0.115385i
$53$	−53.0000	−	53.0000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$53$	−53.0000	−	53.0000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$54$		0			0
$55$		−	40.0000i		−	0.727273i
$56$	−8.00000			−0.142857
$57$		0			0
$58$	40.0000	+	40.0000i	0.689655	+	0.689655i
$59$		−	20.0000i		−	0.338983i	−0.985532	−	0.169492i	$-0.945787\pi$
$59$		−	20.0000i		−	0.338983i	0.985532	−	0.169492i	$-0.0542125\pi$
$60$		0			0
$61$	−48.0000			−0.786885			−0.393443	−	0.919349i	$-0.628716\pi$
$61$	−48.0000			−0.786885			−0.393443	+	0.919349i	$0.628716\pi$
$62$	52.0000	−	52.0000i	0.838710	−	0.838710i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	15.0000	−	15.0000i	0.230769	−	0.230769i
$66$		0			0
$67$	62.0000	−	62.0000i	0.925373	−	0.925373i	−0.0720294	−	0.997403i	$-0.522948\pi$
$67$	62.0000	−	62.0000i	0.925373	−	0.925373i	0.997403	+	0.0720294i	$0.0229475\pi$
$68$	14.0000	+	14.0000i	0.205882	+	0.205882i
$69$		0			0
$70$	−20.0000			−0.285714
$71$	28.0000			0.394366			0.197183	−	0.980367i	$-0.436821\pi$
$71$	28.0000			0.394366			0.197183	+	0.980367i	$0.436821\pi$
$72$		0			0
$73$	−47.0000	−	47.0000i	−0.643836	−	0.643836i	0.307661	−	0.951496i	$-0.400454\pi$
$73$	−47.0000	−	47.0000i	−0.643836	−	0.643836i	−0.951496	+	0.307661i	$0.900454\pi$
$74$			6.00000i			0.0810811i
$75$		0			0
$76$	40.0000			0.526316
$77$	16.0000	−	16.0000i	0.207792	−	0.207792i
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$			20.0000i			0.250000i
$81$		0			0
$82$	8.00000	−	8.00000i	0.0975610	−	0.0975610i
$83$	−18.0000	−	18.0000i	−0.216867	−	0.216867i	0.590310	−	0.807177i	$-0.299006\pi$
$83$	−18.0000	−	18.0000i	−0.216867	−	0.216867i	−0.807177	+	0.590310i	$0.799006\pi$
$84$		0			0
$85$	35.0000	+	35.0000i	0.411765	+	0.411765i
$86$	−84.0000			−0.976744
$87$		0			0
$88$	−16.0000	−	16.0000i	−0.181818	−	0.181818i
$89$			80.0000i			0.898876i	0.893311	+	0.449438i	$0.148376\pi$
$89$			80.0000i			0.898876i	−0.893311	+	0.449438i	$0.851624\pi$
$90$		0			0
$91$	12.0000			0.131868
$92$	4.00000	−	4.00000i	0.0434783	−	0.0434783i
$93$		0			0
$94$		−	36.0000i		−	0.382979i
$95$	100.000			1.05263
$96$		0			0
$97$	−63.0000	+	63.0000i	−0.649485	+	0.649485i	−0.952868	−	0.303384i	$-0.901884\pi$
$97$	−63.0000	+	63.0000i	−0.649485	+	0.649485i	0.303384	+	0.952868i	$0.401884\pi$
$98$	41.0000	+	41.0000i	0.418367	+	0.418367i
$99$		0			0
$100$			50.0000i			0.500000i
$101$	−62.0000			−0.613861			−0.306931	−	0.951732i	$-0.599302\pi$
$101$	−62.0000			−0.613861			−0.306931	+	0.951732i	$0.599302\pi$
$102$		0			0
$103$	118.000	+	118.000i	1.14563	+	1.14563i	0.987403	+	0.158229i	$0.0505783\pi$
$103$	118.000	+	118.000i	1.14563	+	1.14563i	0.158229	+	0.987403i	$0.449422\pi$
$104$		−	12.0000i		−	0.115385i
$105$		0			0
$106$	−106.000			−1.00000
$107$	−142.000	+	142.000i	−1.32710	+	1.32710i	−0.419217	+	0.907886i	$0.637695\pi$
$107$	−142.000	+	142.000i	−1.32710	+	1.32710i	−0.907886	+	0.419217i	$0.862305\pi$
$108$		0			0
$109$			10.0000i			0.0917431i	0.998947	+	0.0458716i	$0.0146065\pi$
$109$			10.0000i			0.0917431i	−0.998947	+	0.0458716i	$0.985394\pi$
$110$	−40.0000	−	40.0000i	−0.363636	−	0.363636i
$111$		0			0
$112$	−8.00000	+	8.00000i	−0.0714286	+	0.0714286i
$113$	−23.0000	−	23.0000i	−0.203540	−	0.203540i	0.597975	−	0.801515i	$-0.295972\pi$
$113$	−23.0000	−	23.0000i	−0.203540	−	0.203540i	−0.801515	+	0.597975i	$0.795972\pi$
$114$		0			0
$115$	10.0000	−	10.0000i	0.0869565	−	0.0869565i
$116$	80.0000			0.689655
$117$		0			0
$118$	−20.0000	−	20.0000i	−0.169492	−	0.169492i
$119$			28.0000i			0.235294i
$120$		0			0
$121$	−57.0000			−0.471074
$122$	−48.0000	+	48.0000i	−0.393443	+	0.393443i
$123$		0			0
$124$		−	104.000i		−	0.838710i
$125$			125.000i			1.00000i
$126$		0			0
$127$	−118.000	+	118.000i	−0.929134	+	0.929134i	−0.997650	−	0.0685161i	$-0.978174\pi$
$127$	−118.000	+	118.000i	−0.929134	+	0.929134i	0.0685161	+	0.997650i	$0.478174\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$		−	30.0000i		−	0.230769i
$131$	128.000			0.977099			0.488550	−	0.872536i	$-0.337526\pi$
$131$	128.000			0.977099			0.488550	+	0.872536i	$0.337526\pi$
$132$		0			0
$133$	40.0000	+	40.0000i	0.300752	+	0.300752i
$134$		−	124.000i		−	0.925373i
$135$		0			0
$136$	28.0000			0.205882
$137$	63.0000	−	63.0000i	0.459854	−	0.459854i	−0.438753	−	0.898607i	$-0.644580\pi$
$137$	63.0000	−	63.0000i	0.459854	−	0.459854i	0.898607	+	0.438753i	$0.144580\pi$
$138$		0			0
$139$		−	140.000i		−	1.00719i	−0.863939	−	0.503597i	$-0.832010\pi$
$139$		−	140.000i		−	1.00719i	0.863939	−	0.503597i	$-0.167990\pi$
$140$	−20.0000	+	20.0000i	−0.142857	+	0.142857i
$141$		0			0
$142$	28.0000	−	28.0000i	0.197183	−	0.197183i
$143$	24.0000	+	24.0000i	0.167832	+	0.167832i
$144$		0			0
$145$	200.000			1.37931
$146$	−94.0000			−0.643836
$147$		0			0
$148$	6.00000	+	6.00000i	0.0405405	+	0.0405405i
$149$		−	150.000i		−	1.00671i	−0.864079	−	0.503356i	$-0.832099\pi$
$149$		−	150.000i		−	1.00671i	0.864079	−	0.503356i	$-0.167901\pi$
$150$		0			0
$151$	52.0000			0.344371			0.172185	−	0.985065i	$-0.444917\pi$
$151$	52.0000			0.344371			0.172185	+	0.985065i	$0.444917\pi$
$152$	40.0000	−	40.0000i	0.263158	−	0.263158i
$153$		0			0
$154$		−	32.0000i		−	0.207792i
$155$		−	260.000i		−	1.67742i
$156$		0			0
$157$	27.0000	−	27.0000i	0.171975	−	0.171975i	−0.615872	−	0.787846i	$-0.711196\pi$
$157$	27.0000	−	27.0000i	0.171975	−	0.171975i	0.787846	+	0.615872i	$0.211196\pi$
$158$		0			0
$159$		0			0
$160$	20.0000	+	20.0000i	0.125000	+	0.125000i
$161$	8.00000			0.0496894
$162$		0			0
$163$	−82.0000	−	82.0000i	−0.503067	−	0.503067i	0.409322	−	0.912390i	$-0.365765\pi$
$163$	−82.0000	−	82.0000i	−0.503067	−	0.503067i	−0.912390	+	0.409322i	$0.865765\pi$
$164$		−	16.0000i		−	0.0975610i
$165$		0			0
$166$	−36.0000			−0.216867
$167$	−62.0000	+	62.0000i	−0.371257	+	0.371257i	−0.867935	−	0.496678i	$-0.834553\pi$
$167$	−62.0000	+	62.0000i	−0.371257	+	0.371257i	0.496678	+	0.867935i	$0.334553\pi$
$168$		0			0
$169$		−	151.000i		−	0.893491i
$170$	70.0000			0.411765
$171$		0			0
$172$	−84.0000	+	84.0000i	−0.488372	+	0.488372i
$173$	107.000	+	107.000i	0.618497	+	0.618497i	0.945146	−	0.326649i	$-0.105919\pi$
$173$	107.000	+	107.000i	0.618497	+	0.618497i	−0.326649	+	0.945146i	$0.605919\pi$
$174$		0			0
$175$	−50.0000	+	50.0000i	−0.285714	+	0.285714i
$176$	−32.0000			−0.181818
$177$		0			0
$178$	80.0000	+	80.0000i	0.449438	+	0.449438i
$179$		−	220.000i		−	1.22905i	−0.788897	−	0.614525i	$-0.789348\pi$
$179$		−	220.000i		−	1.22905i	0.788897	−	0.614525i	$-0.210652\pi$
$180$		0			0
$181$	2.00000			0.0110497			0.00552486	−	0.999985i	$-0.498241\pi$
$181$	2.00000			0.0110497			0.00552486	+	0.999985i	$0.498241\pi$
$182$	12.0000	−	12.0000i	0.0659341	−	0.0659341i
$183$		0			0
$184$		−	8.00000i		−	0.0434783i
$185$	15.0000	+	15.0000i	0.0810811	+	0.0810811i
$186$		0			0
$187$	−56.0000	+	56.0000i	−0.299465	+	0.299465i
$188$	−36.0000	−	36.0000i	−0.191489	−	0.191489i
$189$		0			0
$190$	100.000	−	100.000i	0.526316	−	0.526316i
$191$	−212.000			−1.10995			−0.554974	−	0.831868i	$-0.687272\pi$
$191$	−212.000			−1.10995			−0.554974	+	0.831868i	$0.687272\pi$
$192$		0			0
$193$	−57.0000	−	57.0000i	−0.295337	−	0.295337i	0.543847	−	0.839184i	$-0.316967\pi$
$193$	−57.0000	−	57.0000i	−0.295337	−	0.295337i	−0.839184	+	0.543847i	$0.816967\pi$
$194$			126.000i			0.649485i
$195$		0			0
$196$	82.0000			0.418367
$197$	3.00000	−	3.00000i	0.0152284	−	0.0152284i	−0.699452	−	0.714680i	$-0.746572\pi$
$197$	3.00000	−	3.00000i	0.0152284	−	0.0152284i	0.714680	+	0.699452i	$0.246572\pi$
$198$		0			0
$199$			120.000i			0.603015i	0.953464	+	0.301508i	$0.0974898\pi$
$199$			120.000i			0.603015i	−0.953464	+	0.301508i	$0.902510\pi$
$200$	50.0000	+	50.0000i	0.250000	+	0.250000i
$201$		0			0
$202$	−62.0000	+	62.0000i	−0.306931	+	0.306931i
$203$	80.0000	+	80.0000i	0.394089	+	0.394089i
$204$		0			0
$205$		−	40.0000i		−	0.195122i
$206$	236.000			1.14563
$207$		0			0
$208$	−12.0000	−	12.0000i	−0.0576923	−	0.0576923i
$209$			160.000i			0.765550i
$210$		0			0
$211$	−328.000			−1.55450			−0.777251	−	0.629190i	$-0.783387\pi$
$211$	−328.000			−1.55450			−0.777251	+	0.629190i	$0.783387\pi$
$212$	−106.000	+	106.000i	−0.500000	+	0.500000i
$213$		0			0
$214$			284.000i			1.32710i
$215$	−210.000	+	210.000i	−0.976744	+	0.976744i
$216$		0			0
$217$	104.000	−	104.000i	0.479263	−	0.479263i
$218$	10.0000	+	10.0000i	0.0458716	+	0.0458716i
$219$		0			0
$220$	−80.0000			−0.363636
$221$	−42.0000			−0.190045
$222$		0			0
$223$	138.000	+	138.000i	0.618834	+	0.618834i	0.945232	−	0.326398i	$-0.105835\pi$
$223$	138.000	+	138.000i	0.618834	+	0.618834i	−0.326398	+	0.945232i	$0.605835\pi$
$224$			16.0000i			0.0714286i
$225$		0			0
$226$	−46.0000			−0.203540
$227$	−2.00000	+	2.00000i	−0.00881057	+	0.00881057i	−0.711498	−	0.702688i	$-0.751983\pi$
$227$	−2.00000	+	2.00000i	−0.00881057	+	0.00881057i	0.702688	+	0.711498i	$0.251983\pi$
$228$		0			0
$229$		−	120.000i		−	0.524017i	−0.965066	−	0.262009i	$-0.915615\pi$
$229$		−	120.000i		−	0.524017i	0.965066	−	0.262009i	$-0.0843849\pi$
$230$		−	20.0000i		−	0.0869565i
$231$		0			0
$232$	80.0000	−	80.0000i	0.344828	−	0.344828i
$233$	−183.000	−	183.000i	−0.785408	−	0.785408i	0.195330	−	0.980738i	$-0.437422\pi$
$233$	−183.000	−	183.000i	−0.785408	−	0.785408i	−0.980738	+	0.195330i	$0.937422\pi$
$234$		0			0
$235$	−90.0000	−	90.0000i	−0.382979	−	0.382979i
$236$	−40.0000			−0.169492
$237$		0			0
$238$	28.0000	+	28.0000i	0.117647	+	0.117647i
$239$			120.000i			0.502092i	0.967975	+	0.251046i	$0.0807746\pi$
$239$			120.000i			0.502092i	−0.967975	+	0.251046i	$0.919225\pi$
$240$		0			0
$241$	232.000			0.962656			0.481328	−	0.876541i	$-0.340155\pi$
$241$	232.000			0.962656			0.481328	+	0.876541i	$0.340155\pi$
$242$	−57.0000	+	57.0000i	−0.235537	+	0.235537i
$243$		0			0
$244$			96.0000i			0.393443i
$245$	205.000			0.836735
$246$		0			0
$247$	−60.0000	+	60.0000i	−0.242915	+	0.242915i
$248$	−104.000	−	104.000i	−0.419355	−	0.419355i
$249$		0			0
$250$	125.000	+	125.000i	0.500000	+	0.500000i
$251$	48.0000			0.191235			0.0956175	−	0.995418i	$-0.469517\pi$
$251$	48.0000			0.191235			0.0956175	+	0.995418i	$0.469517\pi$
$252$		0			0
$253$	16.0000	+	16.0000i	0.0632411	+	0.0632411i
$254$			236.000i			0.929134i
$255$		0			0
$256$	16.0000			0.0625000
$257$	313.000	−	313.000i	1.21790	−	1.21790i	0.249532	−	0.968366i	$-0.419723\pi$
$257$	313.000	−	313.000i	1.21790	−	1.21790i	0.968366	−	0.249532i	$-0.0802769\pi$
$258$		0			0
$259$			12.0000i			0.0463320i
$260$	−30.0000	−	30.0000i	−0.115385	−	0.115385i
$261$		0			0
$262$	128.000	−	128.000i	0.488550	−	0.488550i
$263$	262.000	+	262.000i	0.996198	+	0.996198i	0.999993	−	0.00379508i	$-0.00120801\pi$
$263$	262.000	+	262.000i	0.996198	+	0.996198i	−0.00379508	+	0.999993i	$0.501208\pi$
$264$		0			0
$265$	−265.000	+	265.000i	−1.00000	+	1.00000i
$266$	80.0000			0.300752
$267$		0			0
$268$	−124.000	−	124.000i	−0.462687	−	0.462687i
$269$			10.0000i			0.0371747i	0.999827	+	0.0185874i	$0.00591688\pi$
$269$			10.0000i			0.0371747i	−0.999827	+	0.0185874i	$0.994083\pi$
$270$		0			0
$271$	252.000			0.929889			0.464945	−	0.885340i	$-0.346074\pi$
$271$	252.000			0.929889			0.464945	+	0.885340i	$0.346074\pi$
$272$	28.0000	−	28.0000i	0.102941	−	0.102941i
$273$		0			0
$274$		−	126.000i		−	0.459854i
$275$	−200.000			−0.727273
$276$		0			0
$277$	267.000	−	267.000i	0.963899	−	0.963899i	−0.0354718	−	0.999371i	$-0.511293\pi$
$277$	267.000	−	267.000i	0.963899	−	0.963899i	0.999371	+	0.0354718i	$0.0112934\pi$
$278$	−140.000	−	140.000i	−0.503597	−	0.503597i
$279$		0			0
$280$			40.0000i			0.142857i
$281$	−312.000			−1.11032			−0.555160	−	0.831743i	$-0.687343\pi$
$281$	−312.000			−1.11032			−0.555160	+	0.831743i	$0.687343\pi$
$282$		0			0
$283$	−262.000	−	262.000i	−0.925795	−	0.925795i	0.0716358	−	0.997431i	$-0.477178\pi$
$283$	−262.000	−	262.000i	−0.925795	−	0.925795i	−0.997431	+	0.0716358i	$0.977178\pi$
$284$		−	56.0000i		−	0.197183i
$285$		0			0
$286$	48.0000			0.167832
$287$	16.0000	−	16.0000i	0.0557491	−	0.0557491i
$288$		0			0
$289$			191.000i			0.660900i
$290$	200.000	−	200.000i	0.689655	−	0.689655i
$291$		0			0
$292$	−94.0000	+	94.0000i	−0.321918	+	0.321918i
$293$	−243.000	−	243.000i	−0.829352	−	0.829352i	0.158075	−	0.987427i	$-0.449471\pi$
$293$	−243.000	−	243.000i	−0.829352	−	0.829352i	−0.987427	+	0.158075i	$0.949471\pi$
$294$		0			0
$295$	−100.000			−0.338983
$296$	12.0000			0.0405405
$297$		0			0
$298$	−150.000	−	150.000i	−0.503356	−	0.503356i
$299$			12.0000i			0.0401338i
$300$		0			0
$301$	−168.000			−0.558140
$302$	52.0000	−	52.0000i	0.172185	−	0.172185i
$303$		0			0
$304$		−	80.0000i		−	0.263158i
$305$			240.000i			0.786885i
$306$		0			0
$307$	−18.0000	+	18.0000i	−0.0586319	+	0.0586319i	−0.735815	−	0.677183i	$-0.763201\pi$
$307$	−18.0000	+	18.0000i	−0.0586319	+	0.0586319i	0.677183	+	0.735815i	$0.263201\pi$
$308$	−32.0000	−	32.0000i	−0.103896	−	0.103896i
$309$		0			0
$310$	−260.000	−	260.000i	−0.838710	−	0.838710i
$311$	388.000			1.24759			0.623794	−	0.781589i	$-0.285590\pi$
$311$	388.000			1.24759			0.623794	+	0.781589i	$0.285590\pi$
$312$		0			0
$313$	183.000	+	183.000i	0.584665	+	0.584665i	0.936182	−	0.351517i	$-0.114334\pi$
$313$	183.000	+	183.000i	0.584665	+	0.584665i	−0.351517	+	0.936182i	$0.614334\pi$
$314$		−	54.0000i		−	0.171975i
$315$		0			0
$316$		0			0
$317$	213.000	−	213.000i	0.671924	−	0.671924i	−0.286235	−	0.958159i	$-0.592404\pi$
$317$	213.000	−	213.000i	0.671924	−	0.671924i	0.958159	+	0.286235i	$0.0924038\pi$
$318$		0			0
$319$			320.000i			1.00313i
$320$	40.0000			0.125000
$321$		0			0
$322$	8.00000	−	8.00000i	0.0248447	−	0.0248447i
$323$	−140.000	−	140.000i	−0.433437	−	0.433437i
$324$		0			0
$325$	−75.0000	−	75.0000i	−0.230769	−	0.230769i
$326$	−164.000			−0.503067
$327$		0			0
$328$	−16.0000	−	16.0000i	−0.0487805	−	0.0487805i
$329$		−	72.0000i		−	0.218845i
$330$		0			0
$331$	232.000			0.700906			0.350453	−	0.936580i	$-0.386028\pi$
$331$	232.000			0.700906			0.350453	+	0.936580i	$0.386028\pi$
$332$	−36.0000	+	36.0000i	−0.108434	+	0.108434i
$333$		0			0
$334$			124.000i			0.371257i
$335$	−310.000	−	310.000i	−0.925373	−	0.925373i
$336$		0			0
$337$	417.000	−	417.000i	1.23739	−	1.23739i	0.276324	−	0.961064i	$-0.410884\pi$
$337$	417.000	−	417.000i	1.23739	−	1.23739i	0.961064	−	0.276324i	$-0.0891164\pi$
$338$	−151.000	−	151.000i	−0.446746	−	0.446746i
$339$		0			0
$340$	70.0000	−	70.0000i	0.205882	−	0.205882i
$341$	416.000			1.21994
$342$		0			0
$343$	180.000	+	180.000i	0.524781	+	0.524781i
$344$			168.000i			0.488372i
$345$		0			0
$346$	214.000			0.618497
$347$	−202.000	+	202.000i	−0.582133	+	0.582133i	−0.935489	−	0.353356i	$-0.885040\pi$
$347$	−202.000	+	202.000i	−0.582133	+	0.582133i	0.353356	+	0.935489i	$0.385040\pi$
$348$		0			0
$349$			440.000i			1.26074i	0.776293	+	0.630372i	$0.217098\pi$
$349$			440.000i			1.26074i	−0.776293	+	0.630372i	$0.782902\pi$
$350$			100.000i			0.285714i
$351$		0			0
$352$	−32.0000	+	32.0000i	−0.0909091	+	0.0909091i
$353$	447.000	+	447.000i	1.26629	+	1.26629i	0.947991	+	0.318298i	$0.103111\pi$
$353$	447.000	+	447.000i	1.26629	+	1.26629i	0.318298	+	0.947991i	$0.396889\pi$
$354$		0			0
$355$		−	140.000i		−	0.394366i
$356$	160.000			0.449438
$357$		0			0
$358$	−220.000	−	220.000i	−0.614525	−	0.614525i
$359$		−	400.000i		−	1.11421i	−0.830443	−	0.557103i	$-0.811913\pi$
$359$		−	400.000i		−	1.11421i	0.830443	−	0.557103i	$-0.188087\pi$
$360$		0			0
$361$	−39.0000			−0.108033
$362$	2.00000	−	2.00000i	0.00552486	−	0.00552486i
$363$		0			0
$364$		−	24.0000i		−	0.0659341i
$365$	−235.000	+	235.000i	−0.643836	+	0.643836i
$366$		0			0
$367$	−118.000	+	118.000i	−0.321526	+	0.321526i	−0.849352	−	0.527826i	$-0.823007\pi$
$367$	−118.000	+	118.000i	−0.321526	+	0.321526i	0.527826	+	0.849352i	$0.323007\pi$
$368$	−8.00000	−	8.00000i	−0.0217391	−	0.0217391i
$369$		0			0
$370$	30.0000			0.0810811
$371$	−212.000			−0.571429
$372$		0			0
$373$	−107.000	−	107.000i	−0.286863	−	0.286863i	0.548975	−	0.835839i	$-0.315018\pi$
$373$	−107.000	−	107.000i	−0.286863	−	0.286863i	−0.835839	+	0.548975i	$0.815018\pi$
$374$			112.000i			0.299465i
$375$		0			0
$376$	−72.0000			−0.191489
$377$	−120.000	+	120.000i	−0.318302	+	0.318302i
$378$		0			0
$379$		−	340.000i		−	0.897098i	−0.893758	−	0.448549i	$-0.851941\pi$
$379$		−	340.000i		−	0.897098i	0.893758	−	0.448549i	$-0.148059\pi$
$380$		−	200.000i		−	0.526316i
$381$		0			0
$382$	−212.000	+	212.000i	−0.554974	+	0.554974i
$383$	342.000	+	342.000i	0.892950	+	0.892950i	0.994800	−	0.101849i	$-0.0324760\pi$
$383$	342.000	+	342.000i	0.892950	+	0.892950i	−0.101849	+	0.994800i	$0.532476\pi$
$384$		0			0
$385$	−80.0000	−	80.0000i	−0.207792	−	0.207792i
$386$	−114.000			−0.295337
$387$		0			0
$388$	126.000	+	126.000i	0.324742	+	0.324742i
$389$			390.000i			1.00257i	0.865282	+	0.501285i	$0.167139\pi$
$389$			390.000i			1.00257i	−0.865282	+	0.501285i	$0.832861\pi$
$390$		0			0
$391$	−28.0000			−0.0716113
$392$	82.0000	−	82.0000i	0.209184	−	0.209184i
$393$		0			0
$394$		−	6.00000i		−	0.0152284i
$395$		0			0
$396$		0			0
$397$	−323.000	+	323.000i	−0.813602	+	0.813602i	−0.985172	−	0.171570i	$-0.945116\pi$
$397$	−323.000	+	323.000i	−0.813602	+	0.813602i	0.171570	+	0.985172i	$0.445116\pi$
$398$	120.000	+	120.000i	0.301508	+	0.301508i
$399$		0			0
$400$	100.000			0.250000
$401$	−642.000			−1.60100			−0.800499	−	0.599334i	$-0.795432\pi$
$401$	−642.000			−1.60100			−0.800499	+	0.599334i	$0.795432\pi$
$402$		0			0
$403$	156.000	+	156.000i	0.387097	+	0.387097i
$404$			124.000i			0.306931i
$405$		0			0
$406$	160.000			0.394089
$407$	−24.0000	+	24.0000i	−0.0589681	+	0.0589681i
$408$		0			0
$409$			150.000i			0.366748i	0.983043	+	0.183374i	$0.0587020\pi$
$409$			150.000i			0.366748i	−0.983043	+	0.183374i	$0.941298\pi$
$410$	−40.0000	−	40.0000i	−0.0975610	−	0.0975610i
$411$		0			0
$412$	236.000	−	236.000i	0.572816	−	0.572816i
$413$	−40.0000	−	40.0000i	−0.0968523	−	0.0968523i
$414$		0			0
$415$	−90.0000	+	90.0000i	−0.216867	+	0.216867i
$416$	−24.0000			−0.0576923
$417$		0			0
$418$	160.000	+	160.000i	0.382775	+	0.382775i
$419$			300.000i			0.715990i	0.933723	+	0.357995i	$0.116540\pi$
$419$			300.000i			0.715990i	−0.933723	+	0.357995i	$0.883460\pi$
$420$		0			0
$421$	−208.000			−0.494062			−0.247031	−	0.969008i	$-0.579455\pi$
$421$	−208.000			−0.494062			−0.247031	+	0.969008i	$0.579455\pi$
$422$	−328.000	+	328.000i	−0.777251	+	0.777251i
$423$		0			0
$424$			212.000i			0.500000i
$425$	175.000	−	175.000i	0.411765	−	0.411765i
$426$		0			0
$427$	−96.0000	+	96.0000i	−0.224824	+	0.224824i
$428$	284.000	+	284.000i	0.663551	+	0.663551i
$429$		0			0
$430$			420.000i			0.976744i
$431$	788.000			1.82831			0.914153	−	0.405369i	$-0.132857\pi$
$431$	788.000			1.82831			0.914153	+	0.405369i	$0.132857\pi$
$432$		0			0
$433$	−367.000	−	367.000i	−0.847575	−	0.847575i	0.142255	−	0.989830i	$-0.454565\pi$
$433$	−367.000	−	367.000i	−0.847575	−	0.847575i	−0.989830	+	0.142255i	$0.954565\pi$
$434$		−	208.000i		−	0.479263i
$435$		0			0
$436$	20.0000			0.0458716
$437$	−40.0000	+	40.0000i	−0.0915332	+	0.0915332i
$438$		0			0
$439$		−	560.000i		−	1.27563i	−0.770191	−	0.637813i	$-0.779839\pi$
$439$		−	560.000i		−	1.27563i	0.770191	−	0.637813i	$-0.220161\pi$
$440$	−80.0000	+	80.0000i	−0.181818	+	0.181818i
$441$		0			0
$442$	−42.0000	+	42.0000i	−0.0950226	+	0.0950226i
$443$	−378.000	−	378.000i	−0.853273	−	0.853273i	0.137262	−	0.990535i	$-0.456170\pi$
$443$	−378.000	−	378.000i	−0.853273	−	0.853273i	−0.990535	+	0.137262i	$0.956170\pi$
$444$		0			0
$445$	400.000			0.898876
$446$	276.000			0.618834
$447$		0			0
$448$	16.0000	+	16.0000i	0.0357143	+	0.0357143i
$449$		−	410.000i		−	0.913140i	−0.889687	−	0.456570i	$-0.849078\pi$
$449$		−	410.000i		−	0.913140i	0.889687	−	0.456570i	$-0.150922\pi$
$450$		0			0
$451$	64.0000			0.141907
$452$	−46.0000	+	46.0000i	−0.101770	+	0.101770i
$453$		0			0
$454$			4.00000i			0.00881057i
$455$		−	60.0000i		−	0.131868i
$456$		0			0
$457$	−393.000	+	393.000i	−0.859956	+	0.859956i	−0.991333	−	0.131376i	$-0.958060\pi$
$457$	−393.000	+	393.000i	−0.859956	+	0.859956i	0.131376	+	0.991333i	$0.458060\pi$
$458$	−120.000	−	120.000i	−0.262009	−	0.262009i
$459$		0			0
$460$	−20.0000	−	20.0000i	−0.0434783	−	0.0434783i
$461$	−622.000			−1.34924			−0.674620	−	0.738165i	$-0.735693\pi$
$461$	−622.000			−1.34924			−0.674620	+	0.738165i	$0.735693\pi$
$462$		0			0
$463$	278.000	+	278.000i	0.600432	+	0.600432i	0.940427	−	0.339995i	$-0.110425\pi$
$463$	278.000	+	278.000i	0.600432	+	0.600432i	−0.339995	+	0.940427i	$0.610425\pi$
$464$		−	160.000i		−	0.344828i
$465$		0			0
$466$	−366.000			−0.785408
$467$	38.0000	−	38.0000i	0.0813704	−	0.0813704i	−0.665250	−	0.746621i	$-0.731675\pi$
$467$	38.0000	−	38.0000i	0.0813704	−	0.0813704i	0.746621	+	0.665250i	$0.231675\pi$
$468$		0			0
$469$		−	248.000i		−	0.528785i
$470$	−180.000			−0.382979
$471$		0			0
$472$	−40.0000	+	40.0000i	−0.0847458	+	0.0847458i
$473$	−336.000	−	336.000i	−0.710359	−	0.710359i
$474$		0			0
$475$		−	500.000i		−	1.05263i
$476$	56.0000			0.117647
$477$		0			0
$478$	120.000	+	120.000i	0.251046	+	0.251046i
$479$		−	440.000i		−	0.918580i	−0.888286	−	0.459290i	$-0.848104\pi$
$479$		−	440.000i		−	0.918580i	0.888286	−	0.459290i	$-0.151896\pi$
$480$		0			0
$481$	−18.0000			−0.0374220
$482$	232.000	−	232.000i	0.481328	−	0.481328i
$483$		0			0
$484$			114.000i			0.235537i
$485$	315.000	+	315.000i	0.649485	+	0.649485i
$486$		0			0
$487$	522.000	−	522.000i	1.07187	−	1.07187i	0.0746595	−	0.997209i	$-0.476213\pi$
$487$	522.000	−	522.000i	1.07187	−	1.07187i	0.997209	−	0.0746595i	$-0.0237870\pi$
$488$	96.0000	+	96.0000i	0.196721	+	0.196721i
$489$		0			0
$490$	205.000	−	205.000i	0.418367	−	0.418367i
$491$	328.000			0.668024			0.334012	−	0.942569i	$-0.391597\pi$
$491$	328.000			0.668024			0.334012	+	0.942569i	$0.391597\pi$
$492$		0			0
$493$	−280.000	−	280.000i	−0.567951	−	0.567951i
$494$			120.000i			0.242915i
$495$		0			0
$496$	−208.000			−0.419355
$497$	56.0000	−	56.0000i	0.112676	−	0.112676i
$498$		0			0
$499$		−	380.000i		−	0.761523i	−0.924673	−	0.380762i	$-0.875662\pi$
$499$		−	380.000i		−	0.761523i	0.924673	−	0.380762i	$-0.124338\pi$
$500$	250.000			0.500000
$501$		0			0
$502$	48.0000	−	48.0000i	0.0956175	−	0.0956175i
$503$	42.0000	+	42.0000i	0.0834990	+	0.0834990i	0.747623	−	0.664124i	$-0.231195\pi$
$503$	42.0000	+	42.0000i	0.0834990	+	0.0834990i	−0.664124	+	0.747623i	$0.731195\pi$
$504$		0			0
$505$			310.000i			0.613861i
$506$	32.0000			0.0632411
$507$		0			0
$508$	236.000	+	236.000i	0.464567	+	0.464567i
$509$		−	440.000i		−	0.864440i	−0.901768	−	0.432220i	$-0.857730\pi$
$509$		−	440.000i		−	0.864440i	0.901768	−	0.432220i	$-0.142270\pi$
$510$		0			0
$511$	−188.000			−0.367906
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	626.000i		−	1.21790i
$515$	590.000	−	590.000i	1.14563	−	1.14563i
$516$		0			0
$517$	144.000	−	144.000i	0.278530	−	0.278530i
$518$	12.0000	+	12.0000i	0.0231660	+	0.0231660i
$519$		0			0
$520$	−60.0000			−0.115385
$521$	258.000			0.495202			0.247601	−	0.968862i	$-0.420358\pi$
$521$	258.000			0.495202			0.247601	+	0.968862i	$0.420358\pi$
$522$		0			0
$523$	258.000	+	258.000i	0.493308	+	0.493308i	0.909347	−	0.416039i	$-0.136582\pi$
$523$	258.000	+	258.000i	0.493308	+	0.493308i	−0.416039	+	0.909347i	$0.636582\pi$
$524$		−	256.000i		−	0.488550i
$525$		0			0
$526$	524.000			0.996198
$527$	−364.000	+	364.000i	−0.690702	+	0.690702i
$528$		0			0
$529$		−	521.000i		−	0.984877i
$530$			530.000i			1.00000i
$531$		0			0
$532$	80.0000	−	80.0000i	0.150376	−	0.150376i
$533$	24.0000	+	24.0000i	0.0450281	+	0.0450281i
$534$		0			0
$535$	710.000	+	710.000i	1.32710	+	1.32710i
$536$	−248.000			−0.462687
$537$		0			0
$538$	10.0000	+	10.0000i	0.0185874	+	0.0185874i
$539$			328.000i			0.608534i
$540$		0			0
$541$	−338.000			−0.624769			−0.312384	−	0.949956i	$-0.601128\pi$
$541$	−338.000			−0.624769			−0.312384	+	0.949956i	$0.601128\pi$
$542$	252.000	−	252.000i	0.464945	−	0.464945i
$543$		0			0
$544$		−	56.0000i		−	0.102941i
$545$	50.0000			0.0917431
$546$		0			0
$547$	−558.000	+	558.000i	−1.02011	+	1.02011i	−0.0203161	+	0.999794i	$0.506467\pi$
$547$	−558.000	+	558.000i	−1.02011	+	1.02011i	−0.999794	+	0.0203161i	$0.993533\pi$
$548$	−126.000	−	126.000i	−0.229927	−	0.229927i
$549$		0			0
$550$	−200.000	+	200.000i	−0.363636	+	0.363636i
$551$	−800.000			−1.45191
$552$		0			0
$553$		0			0
$554$		−	534.000i		−	0.963899i
$555$		0			0
$556$	−280.000			−0.503597
$557$	3.00000	−	3.00000i	0.00538600	−	0.00538600i	−0.704409	−	0.709795i	$-0.748788\pi$
$557$	3.00000	−	3.00000i	0.00538600	−	0.00538600i	0.709795	+	0.704409i	$0.248788\pi$
$558$		0			0
$559$		−	252.000i		−	0.450805i
$560$	40.0000	+	40.0000i	0.0714286	+	0.0714286i
$561$		0			0
$562$	−312.000	+	312.000i	−0.555160	+	0.555160i
$563$	42.0000	+	42.0000i	0.0746004	+	0.0746004i	0.743422	−	0.668822i	$-0.233201\pi$
$563$	42.0000	+	42.0000i	0.0746004	+	0.0746004i	−0.668822	+	0.743422i	$0.733201\pi$
$564$		0			0
$565$	−115.000	+	115.000i	−0.203540	+	0.203540i
$566$	−524.000			−0.925795
$567$		0			0
$568$	−56.0000	−	56.0000i	−0.0985915	−	0.0985915i
$569$			950.000i			1.66960i	0.550557	+	0.834798i	$0.314416\pi$
$569$			950.000i			1.66960i	−0.550557	+	0.834798i	$0.685584\pi$
$570$		0			0
$571$	392.000			0.686515			0.343257	−	0.939241i	$-0.388470\pi$
$571$	392.000			0.686515			0.343257	+	0.939241i	$0.388470\pi$
$572$	48.0000	−	48.0000i	0.0839161	−	0.0839161i
$573$		0			0
$574$		−	32.0000i		−	0.0557491i
$575$	−50.0000	−	50.0000i	−0.0869565	−	0.0869565i
$576$		0			0
$577$	−473.000	+	473.000i	−0.819757	+	0.819757i	−0.986073	−	0.166315i	$-0.946813\pi$
$577$	−473.000	+	473.000i	−0.819757	+	0.819757i	0.166315	+	0.986073i	$0.446813\pi$
$578$	191.000	+	191.000i	0.330450	+	0.330450i
$579$		0			0
$580$		−	400.000i		−	0.689655i
$581$	−72.0000			−0.123924
$582$		0			0
$583$	−424.000	−	424.000i	−0.727273	−	0.727273i
$584$			188.000i			0.321918i
$585$		0			0
$586$	−486.000			−0.829352
$587$	198.000	−	198.000i	0.337308	−	0.337308i	−0.518045	−	0.855353i	$-0.673340\pi$
$587$	198.000	−	198.000i	0.337308	−	0.337308i	0.855353	+	0.518045i	$0.173340\pi$
$588$		0			0
$589$			1040.00i			1.76570i
$590$	−100.000	+	100.000i	−0.169492	+	0.169492i
$591$		0			0
$592$	12.0000	−	12.0000i	0.0202703	−	0.0202703i
$593$	47.0000	+	47.0000i	0.0792580	+	0.0792580i	0.745624	−	0.666366i	$-0.232151\pi$
$593$	47.0000	+	47.0000i	0.0792580	+	0.0792580i	−0.666366	+	0.745624i	$0.732151\pi$
$594$		0			0
$595$	140.000			0.235294
$596$	−300.000			−0.503356
$597$		0			0
$598$	12.0000	+	12.0000i	0.0200669	+	0.0200669i
$599$			520.000i			0.868114i	0.900886	+	0.434057i	$0.142918\pi$
$599$			520.000i			0.868114i	−0.900886	+	0.434057i	$0.857082\pi$
$600$		0			0
$601$	−328.000			−0.545757			−0.272879	−	0.962048i	$-0.587976\pi$
$601$	−328.000			−0.545757			−0.272879	+	0.962048i	$0.587976\pi$
$602$	−168.000	+	168.000i	−0.279070	+	0.279070i
$603$		0			0
$604$		−	104.000i		−	0.172185i
$605$			285.000i			0.471074i
$606$		0			0
$607$	462.000	−	462.000i	0.761120	−	0.761120i	−0.215405	−	0.976525i	$-0.569107\pi$
$607$	462.000	−	462.000i	0.761120	−	0.761120i	0.976525	+	0.215405i	$0.0691070\pi$
$608$	−80.0000	−	80.0000i	−0.131579	−	0.131579i
$609$		0			0
$610$	240.000	+	240.000i	0.393443	+	0.393443i
$611$	108.000			0.176759
$612$		0			0
$613$	723.000	+	723.000i	1.17945	+	1.17945i	0.979886	+	0.199560i	$0.0639512\pi$
$613$	723.000	+	723.000i	1.17945	+	1.17945i	0.199560	+	0.979886i	$0.436049\pi$
$614$			36.0000i			0.0586319i
$615$		0			0
$616$	−64.0000			−0.103896
$617$	−327.000	+	327.000i	−0.529984	+	0.529984i	−0.920567	−	0.390584i	$-0.872273\pi$
$617$	−327.000	+	327.000i	−0.529984	+	0.529984i	0.390584	+	0.920567i	$0.372273\pi$
$618$		0			0
$619$			660.000i			1.06624i	0.846041	+	0.533118i	$0.178980\pi$
$619$			660.000i			1.06624i	−0.846041	+	0.533118i	$0.821020\pi$
$620$	−520.000			−0.838710
$621$		0			0
$622$	388.000	−	388.000i	0.623794	−	0.623794i
$623$	160.000	+	160.000i	0.256822	+	0.256822i
$624$		0			0
$625$	625.000			1.00000
$626$	366.000			0.584665
$627$		0			0
$628$	−54.0000	−	54.0000i	−0.0859873	−	0.0859873i
$629$		−	42.0000i		−	0.0667727i
$630$		0			0
$631$	−548.000			−0.868463			−0.434231	−	0.900801i	$-0.642980\pi$
$631$	−548.000			−0.868463			−0.434231	+	0.900801i	$0.642980\pi$
$632$		0			0
$633$		0			0
$634$		−	426.000i		−	0.671924i
$635$	590.000	+	590.000i	0.929134	+	0.929134i
$636$		0			0
$637$	−123.000	+	123.000i	−0.193093	+	0.193093i
$638$	320.000	+	320.000i	0.501567	+	0.501567i
$639$		0			0
$640$	40.0000	−	40.0000i	0.0625000	−	0.0625000i
$641$	568.000			0.886115			0.443058	−	0.896493i	$-0.353894\pi$
$641$	568.000			0.886115			0.443058	+	0.896493i	$0.353894\pi$
$642$		0			0
$643$	−342.000	−	342.000i	−0.531882	−	0.531882i	0.389250	−	0.921132i	$-0.372734\pi$
$643$	−342.000	−	342.000i	−0.531882	−	0.531882i	−0.921132	+	0.389250i	$0.872734\pi$
$644$		−	16.0000i		−	0.0248447i
$645$		0			0
$646$	−280.000			−0.433437
$647$	118.000	−	118.000i	0.182380	−	0.182380i	−0.610012	−	0.792392i	$-0.708835\pi$
$647$	118.000	−	118.000i	0.182380	−	0.182380i	0.792392	+	0.610012i	$0.208835\pi$
$648$		0			0
$649$		−	160.000i		−	0.246533i
$650$	−150.000			−0.230769
$651$		0			0
$652$	−164.000	+	164.000i	−0.251534	+	0.251534i
$653$	−453.000	−	453.000i	−0.693721	−	0.693721i	0.269327	−	0.963049i	$-0.413199\pi$
$653$	−453.000	−	453.000i	−0.693721	−	0.693721i	−0.963049	+	0.269327i	$0.913199\pi$
$654$		0			0
$655$		−	640.000i		−	0.977099i
$656$	−32.0000			−0.0487805
$657$		0			0
$658$	−72.0000	−	72.0000i	−0.109422	−	0.109422i
$659$			140.000i			0.212443i	0.994342	+	0.106222i	$0.0338753\pi$
$659$			140.000i			0.212443i	−0.994342	+	0.106222i	$0.966125\pi$
$660$		0			0
$661$	512.000			0.774584			0.387292	−	0.921957i	$-0.373411\pi$
$661$	512.000			0.774584			0.387292	+	0.921957i	$0.373411\pi$
$662$	232.000	−	232.000i	0.350453	−	0.350453i
$663$		0			0
$664$			72.0000i			0.108434i
$665$	200.000	−	200.000i	0.300752	−	0.300752i
$666$		0			0
$667$	−80.0000	+	80.0000i	−0.119940	+	0.119940i
$668$	124.000	+	124.000i	0.185629	+	0.185629i
$669$		0			0
$670$	−620.000			−0.925373
$671$	−384.000			−0.572280
$672$		0			0
$673$	193.000	+	193.000i	0.286776	+	0.286776i	0.835804	−	0.549028i	$-0.185002\pi$
$673$	193.000	+	193.000i	0.286776	+	0.286776i	−0.549028	+	0.835804i	$0.685002\pi$
$674$		−	834.000i		−	1.23739i
$675$		0			0
$676$	−302.000			−0.446746
$677$	−157.000	+	157.000i	−0.231905	+	0.231905i	−0.813488	−	0.581582i	$-0.802434\pi$
$677$	−157.000	+	157.000i	−0.231905	+	0.231905i	0.581582	+	0.813488i	$0.302434\pi$
$678$		0			0
$679$			252.000i			0.371134i
$680$		−	140.000i		−	0.205882i
$681$		0			0
$682$	416.000	−	416.000i	0.609971	−	0.609971i
$683$	−438.000	−	438.000i	−0.641288	−	0.641288i	0.309584	−	0.950872i	$-0.399810\pi$
$683$	−438.000	−	438.000i	−0.641288	−	0.641288i	−0.950872	+	0.309584i	$0.899810\pi$
$684$		0			0
$685$	−315.000	−	315.000i	−0.459854	−	0.459854i
$686$	360.000			0.524781
$687$		0			0
$688$	168.000	+	168.000i	0.244186	+	0.244186i
$689$		−	318.000i		−	0.461538i
$690$		0			0
$691$	1032.00			1.49349			0.746744	−	0.665112i	$-0.231616\pi$
$691$	1032.00			1.49349			0.746744	+	0.665112i	$0.231616\pi$
$692$	214.000	−	214.000i	0.309249	−	0.309249i
$693$		0			0
$694$			404.000i			0.582133i
$695$	−700.000			−1.00719
$696$		0			0
$697$	−56.0000	+	56.0000i	−0.0803443	+	0.0803443i
$698$	440.000	+	440.000i	0.630372	+	0.630372i
$699$		0			0
$700$	100.000	+	100.000i	0.142857	+	0.142857i
$701$	128.000			0.182596			0.0912981	−	0.995824i	$-0.470898\pi$
$701$	128.000			0.182596			0.0912981	+	0.995824i	$0.470898\pi$
$702$		0			0
$703$	−60.0000	−	60.0000i	−0.0853485	−	0.0853485i
$704$			64.0000i			0.0909091i
$705$		0			0
$706$	894.000			1.26629
$707$	−124.000	+	124.000i	−0.175389	+	0.175389i
$708$		0			0
$709$		−	760.000i		−	1.07193i	−0.844239	−	0.535966i	$-0.819947\pi$
$709$		−	760.000i		−	1.07193i	0.844239	−	0.535966i	$-0.180053\pi$
$710$	−140.000	−	140.000i	−0.197183	−	0.197183i
$711$		0			0
$712$	160.000	−	160.000i	0.224719	−	0.224719i
$713$	104.000	+	104.000i	0.145863	+	0.145863i
$714$		0			0
$715$	120.000	−	120.000i	0.167832	−	0.167832i
$716$	−440.000			−0.614525
$717$		0			0
$718$	−400.000	−	400.000i	−0.557103	−	0.557103i
$719$		−	1160.00i		−	1.61335i	−0.590994	−	0.806676i	$-0.701264\pi$
$719$		−	1160.00i		−	1.61335i	0.590994	−	0.806676i	$-0.298736\pi$
$720$		0			0
$721$	472.000			0.654646
$722$	−39.0000	+	39.0000i	−0.0540166	+	0.0540166i
$723$		0			0
$724$		−	4.00000i		−	0.00552486i
$725$		−	1000.00i		−	1.37931i
$726$		0			0
$727$	−558.000	+	558.000i	−0.767538	+	0.767538i	−0.977672	−	0.210135i	$-0.932610\pi$
$727$	−558.000	+	558.000i	−0.767538	+	0.767538i	0.210135	+	0.977672i	$0.432610\pi$
$728$	−24.0000	−	24.0000i	−0.0329670	−	0.0329670i
$729$		0			0
$730$			470.000i			0.643836i
$731$	588.000			0.804378
$732$		0			0
$733$	−827.000	−	827.000i	−1.12824	−	1.12824i	−0.990463	−	0.137777i	$-0.956004\pi$
$733$	−827.000	−	827.000i	−1.12824	−	1.12824i	−0.137777	−	0.990463i	$-0.543996\pi$
$734$			236.000i			0.321526i
$735$		0			0
$736$	−16.0000			−0.0217391
$737$	496.000	−	496.000i	0.672999	−	0.672999i
$738$		0			0
$739$			700.000i			0.947226i	0.880733	+	0.473613i	$0.157050\pi$
$739$			700.000i			0.947226i	−0.880733	+	0.473613i	$0.842950\pi$
$740$	30.0000	−	30.0000i	0.0405405	−	0.0405405i
$741$		0			0
$742$	−212.000	+	212.000i	−0.285714	+	0.285714i
$743$	382.000	+	382.000i	0.514132	+	0.514132i	0.915790	−	0.401658i	$-0.131566\pi$
$743$	382.000	+	382.000i	0.514132	+	0.514132i	−0.401658	+	0.915790i	$0.631566\pi$
$744$		0			0
$745$	−750.000			−1.00671
$746$	−214.000			−0.286863
$747$		0			0
$748$	112.000	+	112.000i	0.149733	+	0.149733i
$749$			568.000i			0.758344i
$750$		0			0
$751$	−588.000			−0.782956			−0.391478	−	0.920187i	$-0.628036\pi$
$751$	−588.000			−0.782956			−0.391478	+	0.920187i	$0.628036\pi$
$752$	−72.0000	+	72.0000i	−0.0957447	+	0.0957447i
$753$		0			0
$754$			240.000i			0.318302i
$755$		−	260.000i		−	0.344371i
$756$		0			0
$757$	987.000	−	987.000i	1.30383	−	1.30383i	0.378043	−	0.925788i	$-0.376597\pi$
$757$	987.000	−	987.000i	1.30383	−	1.30383i	0.925788	−	0.378043i	$-0.123403\pi$
$758$	−340.000	−	340.000i	−0.448549	−	0.448549i
$759$		0			0
$760$	−200.000	−	200.000i	−0.263158	−	0.263158i
$761$	158.000			0.207622			0.103811	−	0.994597i	$-0.466896\pi$
$761$	158.000			0.207622			0.103811	+	0.994597i	$0.466896\pi$
$762$		0			0
$763$	20.0000	+	20.0000i	0.0262123	+	0.0262123i
$764$			424.000i			0.554974i
$765$		0			0
$766$	684.000			0.892950
$767$	60.0000	−	60.0000i	0.0782269	−	0.0782269i
$768$		0			0
$769$		−	80.0000i		−	0.104031i	−0.998646	−	0.0520156i	$-0.983435\pi$
$769$		−	80.0000i		−	0.104031i	0.998646	−	0.0520156i	$-0.0165646\pi$
$770$	−160.000			−0.207792
$771$		0			0
$772$	−114.000	+	114.000i	−0.147668	+	0.147668i
$773$	−243.000	−	243.000i	−0.314360	−	0.314360i	0.532236	−	0.846596i	$-0.321352\pi$
$773$	−243.000	−	243.000i	−0.314360	−	0.314360i	−0.846596	+	0.532236i	$0.821352\pi$
$774$		0			0
$775$	−1300.00			−1.67742
$776$	252.000			0.324742
$777$		0			0
$778$	390.000	+	390.000i	0.501285	+	0.501285i
$779$			160.000i			0.205392i
$780$		0			0
$781$	224.000			0.286812
$782$	−28.0000	+	28.0000i	−0.0358056	+	0.0358056i
$783$		0			0
$784$		−	164.000i		−	0.209184i
$785$	−135.000	−	135.000i	−0.171975	−	0.171975i
$786$		0			0
$787$	262.000	−	262.000i	0.332910	−	0.332910i	−0.520781	−	0.853690i	$-0.674359\pi$
$787$	262.000	−	262.000i	0.332910	−	0.332910i	0.853690	+	0.520781i	$0.174359\pi$
$788$	−6.00000	−	6.00000i	−0.00761421	−	0.00761421i
$789$		0			0
$790$		0			0
$791$	−92.0000			−0.116308
$792$		0			0
$793$	−144.000	−	144.000i	−0.181589	−	0.181589i
$794$			646.000i			0.813602i
$795$		0			0
$796$	240.000			0.301508
$797$	−267.000	+	267.000i	−0.335006	+	0.335006i	−0.854484	−	0.519478i	$-0.826127\pi$
$797$	−267.000	+	267.000i	−0.335006	+	0.335006i	0.519478	+	0.854484i	$0.326127\pi$
$798$		0			0
$799$			252.000i			0.315394i
$800$	100.000	−	100.000i	0.125000	−	0.125000i
$801$		0			0
$802$	−642.000	+	642.000i	−0.800499	+	0.800499i
$803$	−376.000	−	376.000i	−0.468244	−	0.468244i
$804$		0			0
$805$		−	40.0000i		−	0.0496894i
$806$	312.000			0.387097
$807$		0			0
$808$	124.000	+	124.000i	0.153465	+	0.153465i
$809$			560.000i			0.692213i	0.938195	+	0.346106i	$0.112496\pi$
$809$			560.000i			0.692213i	−0.938195	+	0.346106i	$0.887504\pi$
$810$		0			0
$811$	−208.000			−0.256473			−0.128237	−	0.991744i	$-0.540932\pi$
$811$	−208.000			−0.256473			−0.128237	+	0.991744i	$0.540932\pi$
$812$	160.000	−	160.000i	0.197044	−	0.197044i
$813$		0			0
$814$			48.0000i			0.0589681i
$815$	−410.000	+	410.000i	−0.503067	+	0.503067i
$816$		0			0
$817$	840.000	−	840.000i	1.02815	−	1.02815i
$818$	150.000	+	150.000i	0.183374	+	0.183374i
$819$		0			0
$820$	−80.0000			−0.0975610
$821$	1568.00			1.90987			0.954933	−	0.296821i	$-0.0959266\pi$
$821$	1568.00			1.90987			0.954933	+	0.296821i	$0.0959266\pi$
$822$		0			0
$823$	−562.000	−	562.000i	−0.682868	−	0.682868i	0.277778	−	0.960645i	$-0.410402\pi$
$823$	−562.000	−	562.000i	−0.682868	−	0.682868i	−0.960645	+	0.277778i	$0.910402\pi$
$824$		−	472.000i		−	0.572816i
$825$		0			0
$826$	−80.0000			−0.0968523
$827$	−762.000	+	762.000i	−0.921403	+	0.921403i	−0.997129	−	0.0757260i	$-0.975873\pi$
$827$	−762.000	+	762.000i	−0.921403	+	0.921403i	0.0757260	+	0.997129i	$0.475873\pi$
$828$		0			0
$829$		−	170.000i		−	0.205066i	−0.994730	−	0.102533i	$-0.967305\pi$
$829$		−	170.000i		−	0.205066i	0.994730	−	0.102533i	$-0.0326948\pi$
$830$			180.000i			0.216867i
$831$		0			0
$832$	−24.0000	+	24.0000i	−0.0288462	+	0.0288462i
$833$	−287.000	−	287.000i	−0.344538	−	0.344538i
$834$		0			0
$835$	310.000	+	310.000i	0.371257	+	0.371257i
$836$	320.000			0.382775
$837$		0			0
$838$	300.000	+	300.000i	0.357995	+	0.357995i
$839$		−	280.000i		−	0.333731i	−0.985980	−	0.166865i	$-0.946635\pi$
$839$		−	280.000i		−	0.333731i	0.985980	−	0.166865i	$-0.0533645\pi$
$840$		0			0
$841$	−759.000			−0.902497
$842$	−208.000	+	208.000i	−0.247031	+	0.247031i
$843$		0			0
$844$			656.000i			0.777251i
$845$	−755.000			−0.893491
$846$		0			0
$847$	−114.000	+	114.000i	−0.134593	+	0.134593i
$848$	212.000	+	212.000i	0.250000	+	0.250000i
$849$		0			0
$850$		−	350.000i		−	0.411765i
$851$	−12.0000			−0.0141011
$852$		0			0
$853$	1123.00	+	1123.00i	1.31653	+	1.31653i	0.916504	+	0.400026i	$0.130999\pi$
$853$	1123.00	+	1123.00i	1.31653	+	1.31653i	0.400026	+	0.916504i	$0.369001\pi$
$854$			192.000i			0.224824i
$855$		0			0
$856$	568.000			0.663551
$857$	−417.000	+	417.000i	−0.486581	+	0.486581i	−0.907226	−	0.420644i	$-0.861804\pi$
$857$	−417.000	+	417.000i	−0.486581	+	0.486581i	0.420644	+	0.907226i	$0.361804\pi$
$858$		0			0
$859$			1300.00i			1.51339i	0.653769	+	0.756694i	$0.273187\pi$
$859$			1300.00i			1.51339i	−0.653769	+	0.756694i	$0.726813\pi$
$860$	420.000	+	420.000i	0.488372	+	0.488372i
$861$		0			0
$862$	788.000	−	788.000i	0.914153	−	0.914153i
$863$	242.000	+	242.000i	0.280417	+	0.280417i	0.833275	−	0.552858i	$-0.186463\pi$
$863$	242.000	+	242.000i	0.280417	+	0.280417i	−0.552858	+	0.833275i	$0.686463\pi$
$864$		0			0
$865$	535.000	−	535.000i	0.618497	−	0.618497i
$866$	−734.000			−0.847575
$867$		0			0
$868$	−208.000	−	208.000i	−0.239631	−	0.239631i
$869$		0			0
$870$		0			0
$871$	372.000			0.427095
$872$	20.0000	−	20.0000i	0.0229358	−	0.0229358i
$873$		0			0
$874$			80.0000i			0.0915332i
$875$	250.000	+	250.000i	0.285714	+	0.285714i
$876$		0			0
$877$	−453.000	+	453.000i	−0.516534	+	0.516534i	−0.916521	−	0.399987i	$-0.869015\pi$
$877$	−453.000	+	453.000i	−0.516534	+	0.516534i	0.399987	+	0.916521i	$0.369015\pi$
$878$	−560.000	−	560.000i	−0.637813	−	0.637813i
$879$		0			0
$880$			160.000i			0.181818i
$881$	−712.000			−0.808173			−0.404086	−	0.914721i	$-0.632410\pi$
$881$	−712.000			−0.808173			−0.404086	+	0.914721i	$0.632410\pi$
$882$		0			0
$883$	118.000	+	118.000i	0.133635	+	0.133635i	0.770760	−	0.637125i	$-0.219877\pi$
$883$	118.000	+	118.000i	0.133635	+	0.133635i	−0.637125	+	0.770760i	$0.719877\pi$
$884$			84.0000i			0.0950226i
$885$		0			0
$886$	−756.000			−0.853273
$887$	1158.00	−	1158.00i	1.30552	−	1.30552i	0.380914	−	0.924611i	$-0.375610\pi$
$887$	1158.00	−	1158.00i	1.30552	−	1.30552i	0.924611	−	0.380914i	$-0.124390\pi$
$888$		0			0
$889$			472.000i			0.530934i
$890$	400.000	−	400.000i	0.449438	−	0.449438i
$891$		0			0
$892$	276.000	−	276.000i	0.309417	−	0.309417i
$893$	360.000	+	360.000i	0.403135	+	0.403135i
$894$		0			0
$895$	−1100.00			−1.22905
$896$	32.0000			0.0357143
$897$		0			0
$898$	−410.000	−	410.000i	−0.456570	−	0.456570i
$899$			2080.00i			2.31368i
$900$		0			0
$901$	742.000			0.823529
$902$	64.0000	−	64.0000i	0.0709534	−	0.0709534i
$903$		0			0
$904$			92.0000i			0.101770i
$905$		−	10.0000i		−	0.0110497i
$906$		0			0
$907$	142.000	−	142.000i	0.156560	−	0.156560i	−0.624480	−	0.781040i	$-0.714689\pi$
$907$	142.000	−	142.000i	0.156560	−	0.156560i	0.781040	+	0.624480i	$0.214689\pi$
$908$	4.00000	+	4.00000i	0.00440529	+	0.00440529i
$909$		0			0
$910$	−60.0000	−	60.0000i	−0.0659341	−	0.0659341i
$911$	−1172.00			−1.28650			−0.643249	−	0.765657i	$-0.722414\pi$
$911$	−1172.00			−1.28650			−0.643249	+	0.765657i	$0.722414\pi$
$912$		0			0
$913$	−144.000	−	144.000i	−0.157722	−	0.157722i
$914$			786.000i			0.859956i
$915$		0			0
$916$	−240.000			−0.262009
$917$	256.000	−	256.000i	0.279171	−	0.279171i
$918$		0			0
$919$		−	920.000i		−	1.00109i	−0.865711	−	0.500544i	$-0.833133\pi$
$919$		−	920.000i		−	1.00109i	0.865711	−	0.500544i	$-0.166867\pi$
$920$	−40.0000			−0.0434783
$921$		0			0
$922$	−622.000	+	622.000i	−0.674620	+	0.674620i
$923$	84.0000	+	84.0000i	0.0910076	+	0.0910076i
$924$		0			0
$925$	75.0000	−	75.0000i	0.0810811	−	0.0810811i
$926$	556.000			0.600432
$927$		0			0
$928$	−160.000	−	160.000i	−0.172414	−	0.172414i
$929$		−	1190.00i		−	1.28095i	−0.767980	−	0.640474i	$-0.778738\pi$
$929$		−	1190.00i		−	1.28095i	0.767980	−	0.640474i	$-0.221262\pi$
$930$		0			0
$931$	−820.000			−0.880773
$932$	−366.000	+	366.000i	−0.392704	+	0.392704i
$933$		0			0
$934$		−	76.0000i		−	0.0813704i
$935$	280.000	+	280.000i	0.299465	+	0.299465i
$936$		0			0
$937$	−233.000	+	233.000i	−0.248666	+	0.248666i	−0.820423	−	0.571757i	$-0.806262\pi$
$937$	−233.000	+	233.000i	−0.248666	+	0.248666i	0.571757	+	0.820423i	$0.306262\pi$
$938$	−248.000	−	248.000i	−0.264392	−	0.264392i
$939$		0			0
$940$	−180.000	+	180.000i	−0.191489	+	0.191489i
$941$	78.0000			0.0828905			0.0414453	−	0.999141i	$-0.486804\pi$
$941$	78.0000			0.0828905			0.0414453	+	0.999141i	$0.486804\pi$
$942$		0			0
$943$	16.0000	+	16.0000i	0.0169671	+	0.0169671i
$944$			80.0000i			0.0847458i
$945$		0			0
$946$	−672.000			−0.710359
$947$	−62.0000	+	62.0000i	−0.0654699	+	0.0654699i	−0.739084	−	0.673614i	$-0.764741\pi$
$947$	−62.0000	+	62.0000i	−0.0654699	+	0.0654699i	0.673614	+	0.739084i	$0.264741\pi$
$948$		0			0
$949$		−	282.000i		−	0.297155i
$950$	−500.000	−	500.000i	−0.526316	−	0.526316i
$951$		0			0
$952$	56.0000	−	56.0000i	0.0588235	−	0.0588235i
$953$	1017.00	+	1017.00i	1.06716	+	1.06716i	0.997576	+	0.0695800i	$0.0221659\pi$
$953$	1017.00	+	1017.00i	1.06716	+	1.06716i	0.0695800	+	0.997576i	$0.477834\pi$
$954$		0			0
$955$			1060.00i			1.10995i
$956$	240.000			0.251046
$957$		0			0
$958$	−440.000	−	440.000i	−0.459290	−	0.459290i
$959$		−	252.000i		−	0.262774i
$960$		0			0
$961$	1743.00			1.81374
$962$	−18.0000	+	18.0000i	−0.0187110	+	0.0187110i
$963$		0			0
$964$		−	464.000i		−	0.481328i
$965$	−285.000	+	285.000i	−0.295337	+	0.295337i
$966$		0			0
$967$	502.000	−	502.000i	0.519131	−	0.519131i	−0.398177	−	0.917309i	$-0.630357\pi$
$967$	502.000	−	502.000i	0.519131	−	0.519131i	0.917309	+	0.398177i	$0.130357\pi$
$968$	114.000	+	114.000i	0.117769	+	0.117769i
$969$		0			0
$970$	630.000			0.649485
$971$	−992.000			−1.02163			−0.510814	−	0.859691i	$-0.670656\pi$
$971$	−992.000			−1.02163			−0.510814	+	0.859691i	$0.670656\pi$
$972$		0			0
$973$	−280.000	−	280.000i	−0.287770	−	0.287770i
$974$		−	1044.00i		−	1.07187i
$975$		0			0
$976$	192.000			0.196721
$977$	783.000	−	783.000i	0.801433	−	0.801433i	−0.181887	−	0.983320i	$-0.558220\pi$
$977$	783.000	−	783.000i	0.801433	−	0.801433i	0.983320	+	0.181887i	$0.0582204\pi$
$978$		0			0
$979$			640.000i			0.653728i
$980$		−	410.000i		−	0.418367i
$981$		0			0
$982$	328.000	−	328.000i	0.334012	−	0.334012i
$983$	−1058.00	−	1058.00i	−1.07630	−	1.07630i	−0.996838	−	0.0794589i	$-0.974681\pi$
$983$	−1058.00	−	1058.00i	−1.07630	−	1.07630i	−0.0794589	−	0.996838i	$-0.525319\pi$
$984$		0			0
$985$	−15.0000	−	15.0000i	−0.0152284	−	0.0152284i
$986$	−560.000			−0.567951
$987$		0			0
$988$	120.000	+	120.000i	0.121457	+	0.121457i
$989$		−	168.000i		−	0.169869i
$990$		0			0
$991$	−68.0000			−0.0686176			−0.0343088	−	0.999411i	$-0.510923\pi$
$991$	−68.0000			−0.0686176			−0.0343088	+	0.999411i	$0.510923\pi$
$992$	−208.000	+	208.000i	−0.209677	+	0.209677i
$993$		0			0
$994$		−	112.000i		−	0.112676i
$995$	600.000			0.603015
$996$		0			0
$997$	−773.000	+	773.000i	−0.775326	+	0.775326i	−0.979032	−	0.203706i	$-0.934701\pi$
$997$	−773.000	+	773.000i	−0.775326	+	0.775326i	0.203706	+	0.979032i	$0.434701\pi$
$998$	−380.000	−	380.000i	−0.380762	−	0.380762i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.3.g.b.73.1		2
3.2	odd	2		10.3.c.a.3.1	✓	2
4.3	odd	2		720.3.bh.c.433.1		2
5.2	odd	4	inner	90.3.g.b.37.1		2
5.3	odd	4		450.3.g.b.307.1		2
5.4	even	2		450.3.g.b.343.1		2
12.11	even	2		80.3.p.c.33.1		2
15.2	even	4		10.3.c.a.7.1	yes	2
15.8	even	4		50.3.c.c.7.1		2
15.14	odd	2		50.3.c.c.43.1		2
20.7	even	4		720.3.bh.c.577.1		2
21.20	even	2		490.3.f.b.393.1		2
24.5	odd	2		320.3.p.h.193.1		2
24.11	even	2		320.3.p.a.193.1		2
60.23	odd	4		400.3.p.b.257.1		2
60.47	odd	4		80.3.p.c.17.1		2
60.59	even	2		400.3.p.b.193.1		2
105.62	odd	4		490.3.f.b.197.1		2
120.77	even	4		320.3.p.h.257.1		2
120.107	odd	4		320.3.p.a.257.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.3.c.a.3.1	✓	2	3.2	odd	2
10.3.c.a.7.1	yes	2	15.2	even	4
50.3.c.c.7.1		2	15.8	even	4
50.3.c.c.43.1		2	15.14	odd	2
80.3.p.c.17.1		2	60.47	odd	4
80.3.p.c.33.1		2	12.11	even	2
90.3.g.b.37.1		2	5.2	odd	4	inner
90.3.g.b.73.1		2	1.1	even	1	trivial
320.3.p.a.193.1		2	24.11	even	2
320.3.p.a.257.1		2	120.107	odd	4
320.3.p.h.193.1		2	24.5	odd	2
320.3.p.h.257.1		2	120.77	even	4
400.3.p.b.193.1		2	60.59	even	2
400.3.p.b.257.1		2	60.23	odd	4
450.3.g.b.307.1		2	5.3	odd	4
450.3.g.b.343.1		2	5.4	even	2
490.3.f.b.197.1		2	105.62	odd	4
490.3.f.b.393.1		2	21.20	even	2
720.3.bh.c.433.1		2	4.3	odd	2
720.3.bh.c.577.1		2	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	90.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} -5.00000i q^{5} +(2.00000 - 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} -5.00000i q^{5} +(2.00000 - 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-5.00000 - 5.00000i) q^{10} +8.00000 q^{11} +(3.00000 + 3.00000i) q^{13} -4.00000i q^{14} -4.00000 q^{16} +(-7.00000 + 7.00000i) q^{17} +20.0000i q^{19} -10.0000 q^{20} +(8.00000 - 8.00000i) q^{22} +(2.00000 + 2.00000i) q^{23} -25.0000 q^{25} +6.00000 q^{26} +(-4.00000 - 4.00000i) q^{28} +40.0000i q^{29} +52.0000 q^{31} +(-4.00000 + 4.00000i) q^{32} +14.0000i q^{34} +(-10.0000 - 10.0000i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(20.0000 + 20.0000i) q^{38} +(-10.0000 + 10.0000i) q^{40} +8.00000 q^{41} +(-42.0000 - 42.0000i) q^{43} -16.0000i q^{44} +4.00000 q^{46} +(18.0000 - 18.0000i) q^{47} +41.0000i q^{49} +(-25.0000 + 25.0000i) q^{50} +(6.00000 - 6.00000i) q^{52} +(-53.0000 - 53.0000i) q^{53} -40.0000i q^{55} -8.00000 q^{56} +(40.0000 + 40.0000i) q^{58} -20.0000i q^{59} -48.0000 q^{61} +(52.0000 - 52.0000i) q^{62} +8.00000i q^{64} +(15.0000 - 15.0000i) q^{65} +(62.0000 - 62.0000i) q^{67} +(14.0000 + 14.0000i) q^{68} -20.0000 q^{70} +28.0000 q^{71} +(-47.0000 - 47.0000i) q^{73} +6.00000i q^{74} +40.0000 q^{76} +(16.0000 - 16.0000i) q^{77} +20.0000i q^{80} +(8.00000 - 8.00000i) q^{82} +(-18.0000 - 18.0000i) q^{83} +(35.0000 + 35.0000i) q^{85} -84.0000 q^{86} +(-16.0000 - 16.0000i) q^{88} +80.0000i q^{89} +12.0000 q^{91} +(4.00000 - 4.00000i) q^{92} -36.0000i q^{94} +100.000 q^{95} +(-63.0000 + 63.0000i) q^{97} +(41.0000 + 41.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 4 * q^7 - 4 * q^8	\( 2 q + 2 q^{2} + 4 q^{7} - 4 q^{8} - 10 q^{10} + 16 q^{11} + 6 q^{13} - 8 q^{16} - 14 q^{17} - 20 q^{20} + 16 q^{22} + 4 q^{23} - 50 q^{25} + 12 q^{26} - 8 q^{28} + 104 q^{31} - 8 q^{32} - 20 q^{35} - 6 q^{37} + 40 q^{38} - 20 q^{40} + 16 q^{41} - 84 q^{43} + 8 q^{46} + 36 q^{47} - 50 q^{50} + 12 q^{52} - 106 q^{53} - 16 q^{56} + 80 q^{58} - 96 q^{61} + 104 q^{62} + 30 q^{65} + 124 q^{67} + 28 q^{68} - 40 q^{70} + 56 q^{71} - 94 q^{73} + 80 q^{76} + 32 q^{77} + 16 q^{82} - 36 q^{83} + 70 q^{85} - 168 q^{86} - 32 q^{88} + 24 q^{91} + 8 q^{92} + 200 q^{95} - 126 q^{97} + 82 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 4 * q^7 - 4 * q^8 - 10 * q^10 + 16 * q^11 + 6 * q^13 - 8 * q^16 - 14 * q^17 - 20 * q^20 + 16 * q^22 + 4 * q^23 - 50 * q^25 + 12 * q^26 - 8 * q^28 + 104 * q^31 - 8 * q^32 - 20 * q^35 - 6 * q^37 + 40 * q^38 - 20 * q^40 + 16 * q^41 - 84 * q^43 + 8 * q^46 + 36 * q^47 - 50 * q^50 + 12 * q^52 - 106 * q^53 - 16 * q^56 + 80 * q^58 - 96 * q^61 + 104 * q^62 + 30 * q^65 + 124 * q^67 + 28 * q^68 - 40 * q^70 + 56 * q^71 - 94 * q^73 + 80 * q^76 + 32 * q^77 + 16 * q^82 - 36 * q^83 + 70 * q^85 - 168 * q^86 - 32 * q^88 + 24 * q^91 + 8 * q^92 + 200 * q^95 - 126 * q^97 + 82 * q^98

Introduction

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