LMFDB - Embedded newform 450.3.g.b.343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,3,Mod(307,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, 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("450.307");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.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:	$12.2616118962$
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			343.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	450.343
Dual form			450.3.g.b.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.285714	+	0.285714i	−0.835383	−	0.549669i	$-0.814754\pi$
$7$	−2.00000	+	2.00000i	−0.285714	+	0.285714i	0.549669	+	0.835383i	$0.314754\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$	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	0.582245	−	0.813014i	$-0.302175\pi$
$13$	−3.00000	−	3.00000i	−0.230769	−	0.230769i	−0.813014	+	0.582245i	$0.802175\pi$
$14$		−	4.00000i		−	0.285714i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	7.00000	−	7.00000i	0.411765	−	0.411765i	−0.470588	−	0.882353i	$-0.655958\pi$
$17$	7.00000	−	7.00000i	0.411765	−	0.411765i	0.882353	+	0.470588i	$0.155958\pi$
$18$		0			0
$19$			20.0000i			1.05263i	0.850289	+	0.526316i	$0.176427\pi$
$19$			20.0000i			1.05263i	−0.850289	+	0.526316i	$0.823573\pi$
$20$		0			0
$21$		0			0
$22$	−8.00000	+	8.00000i	−0.363636	+	0.363636i
$23$	−2.00000	−	2.00000i	−0.0869565	−	0.0869565i	0.662291	−	0.749247i	$-0.269584\pi$
$23$	−2.00000	−	2.00000i	−0.0869565	−	0.0869565i	−0.749247	+	0.662291i	$0.769584\pi$
$24$		0			0
$25$		0			0
$26$	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
$35$		0			0
$36$		0			0
$37$	3.00000	−	3.00000i	0.0810811	−	0.0810811i	−0.665403	−	0.746484i	$-0.731740\pi$
$37$	3.00000	−	3.00000i	0.0810811	−	0.0810811i	0.746484	+	0.665403i	$0.231740\pi$
$38$	−20.0000	−	20.0000i	−0.526316	−	0.526316i
$39$		0			0
$40$		0			0
$41$	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	0.999736	−	0.0229915i	$-0.00731906\pi$
$43$	42.0000	+	42.0000i	0.976744	+	0.976744i	−0.0229915	+	0.999736i	$0.507319\pi$
$44$		−	16.0000i		−	0.363636i
$45$		0			0
$46$	4.00000			0.0869565
$47$	−18.0000	+	18.0000i	−0.382979	+	0.382979i	−0.872174	−	0.489195i	$-0.837290\pi$
$47$	−18.0000	+	18.0000i	−0.382979	+	0.382979i	0.489195	+	0.872174i	$0.337290\pi$
$48$		0			0
$49$			41.0000i			0.836735i
$50$		0			0
$51$		0			0
$52$	−6.00000	+	6.00000i	−0.115385	+	0.115385i
$53$	53.0000	+	53.0000i	1.00000	+	1.00000i	1.00000			$0$
$53$	53.0000	+	53.0000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$54$		0			0
$55$		0			0
$56$	−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
$65$		0			0
$66$		0			0
$67$	−62.0000	+	62.0000i	−0.925373	+	0.925373i	−0.997403	−	0.0720294i	$-0.977052\pi$
$67$	−62.0000	+	62.0000i	−0.925373	+	0.925373i	0.0720294	+	0.997403i	$0.477052\pi$
$68$	−14.0000	−	14.0000i	−0.205882	−	0.205882i
$69$		0			0
$70$		0			0
$71$	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	0.951496	−	0.307661i	$-0.0995461\pi$
$73$	47.0000	+	47.0000i	0.643836	+	0.643836i	−0.307661	+	0.951496i	$0.599546\pi$
$74$			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			$\pi$
$80$		0			0
$81$		0			0
$82$	−8.00000	+	8.00000i	−0.0975610	+	0.0975610i
$83$	18.0000	+	18.0000i	0.216867	+	0.216867i	0.807177	−	0.590310i	$-0.200994\pi$
$83$	18.0000	+	18.0000i	0.216867	+	0.216867i	−0.590310	+	0.807177i	$0.700994\pi$
$84$		0			0
$85$		0			0
$86$	−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
$95$		0			0
$96$		0			0
$97$	63.0000	−	63.0000i	0.649485	−	0.649485i	−0.303384	−	0.952868i	$-0.598116\pi$
$97$	63.0000	−	63.0000i	0.649485	−	0.649485i	0.952868	+	0.303384i	$0.0981164\pi$
$98$	−41.0000	−	41.0000i	−0.418367	−	0.418367i
$99$		0			0
$100$		0			0
$101$	−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	$-0.949422\pi$
$103$	−118.000	−	118.000i	−1.14563	−	1.14563i	−0.158229	−	0.987403i	$-0.550578\pi$
$104$		−	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	$-0.362305\pi$
$107$	142.000	−	142.000i	1.32710	−	1.32710i	0.907886	−	0.419217i	$-0.137695\pi$
$108$		0			0
$109$			10.0000i			0.0917431i	0.998947	+	0.0458716i	$0.0146065\pi$
$109$			10.0000i			0.0917431i	−0.998947	+	0.0458716i	$0.985394\pi$
$110$		0			0
$111$		0			0
$112$	8.00000	−	8.00000i	0.0714286	−	0.0714286i
$113$	23.0000	+	23.0000i	0.203540	+	0.203540i	0.801515	−	0.597975i	$-0.204028\pi$
$113$	23.0000	+	23.0000i	0.203540	+	0.203540i	−0.597975	+	0.801515i	$0.704028\pi$
$114$		0			0
$115$		0			0
$116$	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
$125$		0			0
$126$		0			0
$127$	118.000	−	118.000i	0.929134	−	0.929134i	−0.0685161	−	0.997650i	$-0.521826\pi$
$127$	118.000	−	118.000i	0.929134	−	0.929134i	0.997650	+	0.0685161i	$0.0218265\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$	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	−0.898607	−	0.438753i	$-0.855420\pi$
$137$	−63.0000	+	63.0000i	−0.459854	+	0.459854i	0.438753	+	0.898607i	$0.355420\pi$
$138$		0			0
$139$		−	140.000i		−	1.00719i	−0.863939	−	0.503597i	$-0.832010\pi$
$139$		−	140.000i		−	1.00719i	0.863939	−	0.503597i	$-0.167990\pi$
$140$		0			0
$141$		0			0
$142$	−28.0000	+	28.0000i	−0.197183	+	0.197183i
$143$	−24.0000	−	24.0000i	−0.167832	−	0.167832i
$144$		0			0
$145$		0			0
$146$	−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
$155$		0			0
$156$		0			0
$157$	−27.0000	+	27.0000i	−0.171975	+	0.171975i	−0.787846	−	0.615872i	$-0.788804\pi$
$157$	−27.0000	+	27.0000i	−0.171975	+	0.171975i	0.615872	+	0.787846i	$0.288804\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.00000			0.0496894
$162$		0			0
$163$	82.0000	+	82.0000i	0.503067	+	0.503067i	0.912390	−	0.409322i	$-0.134235\pi$
$163$	82.0000	+	82.0000i	0.503067	+	0.503067i	−0.409322	+	0.912390i	$0.634235\pi$
$164$		−	16.0000i		−	0.0975610i
$165$		0			0
$166$	−36.0000			−0.216867
$167$	62.0000	−	62.0000i	0.371257	−	0.371257i	−0.496678	−	0.867935i	$-0.665447\pi$
$167$	62.0000	−	62.0000i	0.371257	−	0.371257i	0.867935	+	0.496678i	$0.165447\pi$
$168$		0			0
$169$		−	151.000i		−	0.893491i
$170$		0			0
$171$		0			0
$172$	84.0000	−	84.0000i	0.488372	−	0.488372i
$173$	−107.000	−	107.000i	−0.618497	−	0.618497i	0.326649	−	0.945146i	$-0.394081\pi$
$173$	−107.000	−	107.000i	−0.618497	−	0.618497i	−0.945146	+	0.326649i	$0.894081\pi$
$174$		0			0
$175$		0			0
$176$	−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
$185$		0			0
$186$		0			0
$187$	56.0000	−	56.0000i	0.299465	−	0.299465i
$188$	36.0000	+	36.0000i	0.191489	+	0.191489i
$189$		0			0
$190$		0			0
$191$	−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	0.839184	−	0.543847i	$-0.183033\pi$
$193$	57.0000	+	57.0000i	0.295337	+	0.295337i	−0.543847	+	0.839184i	$0.683033\pi$
$194$			126.000i			0.649485i
$195$		0			0
$196$	82.0000			0.418367
$197$	−3.00000	+	3.00000i	−0.0152284	+	0.0152284i	−0.714680	−	0.699452i	$-0.753428\pi$
$197$	−3.00000	+	3.00000i	−0.0152284	+	0.0152284i	0.699452	+	0.714680i	$0.253428\pi$
$198$		0			0
$199$			120.000i			0.603015i	0.953464	+	0.301508i	$0.0974898\pi$
$199$			120.000i			0.603015i	−0.953464	+	0.301508i	$0.902510\pi$
$200$		0			0
$201$		0			0
$202$	62.0000	−	62.0000i	0.306931	−	0.306931i
$203$	−80.0000	−	80.0000i	−0.394089	−	0.394089i
$204$		0			0
$205$		0			0
$206$	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
$215$		0			0
$216$		0			0
$217$	−104.000	+	104.000i	−0.479263	+	0.479263i
$218$	−10.0000	−	10.0000i	−0.0458716	−	0.0458716i
$219$		0			0
$220$		0			0
$221$	−42.0000			−0.190045
$222$		0			0
$223$	−138.000	−	138.000i	−0.618834	−	0.618834i	0.326398	−	0.945232i	$-0.394165\pi$
$223$	−138.000	−	138.000i	−0.618834	−	0.618834i	−0.945232	+	0.326398i	$0.894165\pi$
$224$			16.0000i			0.0714286i
$225$		0			0
$226$	−46.0000			−0.203540
$227$	2.00000	−	2.00000i	0.00881057	−	0.00881057i	−0.702688	−	0.711498i	$-0.748017\pi$
$227$	2.00000	−	2.00000i	0.00881057	−	0.00881057i	0.711498	+	0.702688i	$0.248017\pi$
$228$		0			0
$229$		−	120.000i		−	0.524017i	−0.965066	−	0.262009i	$-0.915615\pi$
$229$		−	120.000i		−	0.524017i	0.965066	−	0.262009i	$-0.0843849\pi$
$230$		0			0
$231$		0			0
$232$	−80.0000	+	80.0000i	−0.344828	+	0.344828i
$233$	183.000	+	183.000i	0.785408	+	0.785408i	0.980738	−	0.195330i	$-0.0625777\pi$
$233$	183.000	+	183.000i	0.785408	+	0.785408i	−0.195330	+	0.980738i	$0.562578\pi$
$234$		0			0
$235$		0			0
$236$	−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
$245$		0			0
$246$		0			0
$247$	60.0000	−	60.0000i	0.242915	−	0.242915i
$248$	104.000	+	104.000i	0.419355	+	0.419355i
$249$		0			0
$250$		0			0
$251$	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	$0.580277\pi$
$257$	−313.000	+	313.000i	−1.21790	+	1.21790i	−0.968366	+	0.249532i	$0.919723\pi$
$258$		0			0
$259$			12.0000i			0.0463320i
$260$		0			0
$261$		0			0
$262$	−128.000	+	128.000i	−0.488550	+	0.488550i
$263$	−262.000	−	262.000i	−0.996198	−	0.996198i	0.00379508	−	0.999993i	$-0.498792\pi$
$263$	−262.000	−	262.000i	−0.996198	−	0.996198i	−0.999993	+	0.00379508i	$0.998792\pi$
$264$		0			0
$265$		0			0
$266$	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
$275$		0			0
$276$		0			0
$277$	−267.000	+	267.000i	−0.963899	+	0.963899i	−0.999371	−	0.0354718i	$-0.988707\pi$
$277$	−267.000	+	267.000i	−0.963899	+	0.963899i	0.0354718	+	0.999371i	$0.488707\pi$
$278$	140.000	+	140.000i	0.503597	+	0.503597i
$279$		0			0
$280$		0			0
$281$	−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	0.997431	−	0.0716358i	$-0.0228219\pi$
$283$	262.000	+	262.000i	0.925795	+	0.925795i	−0.0716358	+	0.997431i	$0.522822\pi$
$284$		−	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
$290$		0			0
$291$		0			0
$292$	94.0000	−	94.0000i	0.321918	−	0.321918i
$293$	243.000	+	243.000i	0.829352	+	0.829352i	0.987427	−	0.158075i	$-0.0505289\pi$
$293$	243.000	+	243.000i	0.829352	+	0.829352i	−0.158075	+	0.987427i	$0.550529\pi$
$294$		0			0
$295$		0			0
$296$	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
$305$		0			0
$306$		0			0
$307$	18.0000	−	18.0000i	0.0586319	−	0.0586319i	−0.677183	−	0.735815i	$-0.736799\pi$
$307$	18.0000	−	18.0000i	0.0586319	−	0.0586319i	0.735815	+	0.677183i	$0.236799\pi$
$308$	32.0000	+	32.0000i	0.103896	+	0.103896i
$309$		0			0
$310$		0			0
$311$	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	0.351517	−	0.936182i	$-0.385666\pi$
$313$	−183.000	−	183.000i	−0.584665	−	0.584665i	−0.936182	+	0.351517i	$0.885666\pi$
$314$		−	54.0000i		−	0.171975i
$315$		0			0
$316$		0			0
$317$	−213.000	+	213.000i	−0.671924	+	0.671924i	−0.958159	−	0.286235i	$-0.907596\pi$
$317$	−213.000	+	213.000i	−0.671924	+	0.671924i	0.286235	+	0.958159i	$0.407596\pi$
$318$		0			0
$319$			320.000i			1.00313i
$320$		0			0
$321$		0			0
$322$	−8.00000	+	8.00000i	−0.0248447	+	0.0248447i
$323$	140.000	+	140.000i	0.433437	+	0.433437i
$324$		0			0
$325$		0			0
$326$	−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
$335$		0			0
$336$		0			0
$337$	−417.000	+	417.000i	−1.23739	+	1.23739i	−0.276324	+	0.961064i	$0.589116\pi$
$337$	−417.000	+	417.000i	−1.23739	+	1.23739i	−0.961064	+	0.276324i	$0.910884\pi$
$338$	151.000	+	151.000i	0.446746	+	0.446746i
$339$		0			0
$340$		0			0
$341$	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	−0.353356	−	0.935489i	$-0.614960\pi$
$347$	202.000	−	202.000i	0.582133	−	0.582133i	0.935489	+	0.353356i	$0.114960\pi$
$348$		0			0
$349$			440.000i			1.26074i	0.776293	+	0.630372i	$0.217098\pi$
$349$			440.000i			1.26074i	−0.776293	+	0.630372i	$0.782902\pi$
$350$		0			0
$351$		0			0
$352$	32.0000	−	32.0000i	0.0909091	−	0.0909091i
$353$	−447.000	−	447.000i	−1.26629	−	1.26629i	−0.947991	−	0.318298i	$-0.896889\pi$
$353$	−447.000	−	447.000i	−1.26629	−	1.26629i	−0.318298	−	0.947991i	$-0.603111\pi$
$354$		0			0
$355$		0			0
$356$	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
$365$		0			0
$366$		0			0
$367$	118.000	−	118.000i	0.321526	−	0.321526i	−0.527826	−	0.849352i	$-0.676993\pi$
$367$	118.000	−	118.000i	0.321526	−	0.321526i	0.849352	+	0.527826i	$0.176993\pi$
$368$	8.00000	+	8.00000i	0.0217391	+	0.0217391i
$369$		0			0
$370$		0			0
$371$	−212.000			−0.571429
$372$		0			0
$373$	107.000	+	107.000i	0.286863	+	0.286863i	0.835839	−	0.548975i	$-0.184982\pi$
$373$	107.000	+	107.000i	0.286863	+	0.286863i	−0.548975	+	0.835839i	$0.684982\pi$
$374$			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	$-0.148059\pi$
$380$		0			0
$381$		0			0
$382$	212.000	−	212.000i	0.554974	−	0.554974i
$383$	−342.000	−	342.000i	−0.892950	−	0.892950i	0.101849	−	0.994800i	$-0.467524\pi$
$383$	−342.000	−	342.000i	−0.892950	−	0.892950i	−0.994800	+	0.101849i	$0.967524\pi$
$384$		0			0
$385$		0			0
$386$	−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	−0.171570	−	0.985172i	$-0.554884\pi$
$397$	323.000	−	323.000i	0.813602	−	0.813602i	0.985172	+	0.171570i	$0.0548839\pi$
$398$	−120.000	−	120.000i	−0.301508	−	0.301508i
$399$		0			0
$400$		0			0
$401$	−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	$0.941298\pi$
$410$		0			0
$411$		0			0
$412$	−236.000	+	236.000i	−0.572816	+	0.572816i
$413$	40.0000	+	40.0000i	0.0968523	+	0.0968523i
$414$		0			0
$415$		0			0
$416$	−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
$425$		0			0
$426$		0			0
$427$	96.0000	−	96.0000i	0.224824	−	0.224824i
$428$	−284.000	−	284.000i	−0.663551	−	0.663551i
$429$		0			0
$430$		0			0
$431$	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	0.989830	−	0.142255i	$-0.0454353\pi$
$433$	367.000	+	367.000i	0.847575	+	0.847575i	−0.142255	+	0.989830i	$0.545435\pi$
$434$		−	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	$-0.220161\pi$
$440$		0			0
$441$		0			0
$442$	42.0000	−	42.0000i	0.0950226	−	0.0950226i
$443$	378.000	+	378.000i	0.853273	+	0.853273i	0.990535	−	0.137262i	$-0.0438301\pi$
$443$	378.000	+	378.000i	0.853273	+	0.853273i	−0.137262	+	0.990535i	$0.543830\pi$
$444$		0			0
$445$		0			0
$446$	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
$455$		0			0
$456$		0			0
$457$	393.000	−	393.000i	0.859956	−	0.859956i	−0.131376	−	0.991333i	$-0.541940\pi$
$457$	393.000	−	393.000i	0.859956	−	0.859956i	0.991333	+	0.131376i	$0.0419396\pi$
$458$	120.000	+	120.000i	0.262009	+	0.262009i
$459$		0			0
$460$		0			0
$461$	−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	0.339995	−	0.940427i	$-0.389575\pi$
$463$	−278.000	−	278.000i	−0.600432	−	0.600432i	−0.940427	+	0.339995i	$0.889575\pi$
$464$		−	160.000i		−	0.344828i
$465$		0			0
$466$	−366.000			−0.785408
$467$	−38.0000	+	38.0000i	−0.0813704	+	0.0813704i	−0.746621	−	0.665250i	$-0.768325\pi$
$467$	−38.0000	+	38.0000i	−0.0813704	+	0.0813704i	0.665250	+	0.746621i	$0.268325\pi$
$468$		0			0
$469$		−	248.000i		−	0.528785i
$470$		0			0
$471$		0			0
$472$	40.0000	−	40.0000i	0.0847458	−	0.0847458i
$473$	336.000	+	336.000i	0.710359	+	0.710359i
$474$		0			0
$475$		0			0
$476$	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
$485$		0			0
$486$		0			0
$487$	−522.000	+	522.000i	−1.07187	+	1.07187i	−0.0746595	+	0.997209i	$0.523787\pi$
$487$	−522.000	+	522.000i	−1.07187	+	1.07187i	−0.997209	+	0.0746595i	$0.976213\pi$
$488$	−96.0000	−	96.0000i	−0.196721	−	0.196721i
$489$		0			0
$490$		0			0
$491$	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	$-0.124338\pi$
$500$		0			0
$501$		0			0
$502$	−48.0000	+	48.0000i	−0.0956175	+	0.0956175i
$503$	−42.0000	−	42.0000i	−0.0834990	−	0.0834990i	0.664124	−	0.747623i	$-0.268805\pi$
$503$	−42.0000	−	42.0000i	−0.0834990	−	0.0834990i	−0.747623	+	0.664124i	$0.768805\pi$
$504$		0			0
$505$		0			0
$506$	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
$515$		0			0
$516$		0			0
$517$	−144.000	+	144.000i	−0.278530	+	0.278530i
$518$	−12.0000	−	12.0000i	−0.0231660	−	0.0231660i
$519$		0			0
$520$		0			0
$521$	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	0.416039	−	0.909347i	$-0.363418\pi$
$523$	−258.000	−	258.000i	−0.493308	−	0.493308i	−0.909347	+	0.416039i	$0.863418\pi$
$524$		−	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
$530$		0			0
$531$		0			0
$532$	−80.0000	+	80.0000i	−0.150376	+	0.150376i
$533$	−24.0000	−	24.0000i	−0.0450281	−	0.0450281i
$534$		0			0
$535$		0			0
$536$	−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
$545$		0			0
$546$		0			0
$547$	558.000	−	558.000i	1.02011	−	1.02011i	0.0203161	−	0.999794i	$-0.493533\pi$
$547$	558.000	−	558.000i	1.02011	−	1.02011i	0.999794	−	0.0203161i	$-0.00646725\pi$
$548$	126.000	+	126.000i	0.229927	+	0.229927i
$549$		0			0
$550$		0			0
$551$	−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	−0.709795	−	0.704409i	$-0.751212\pi$
$557$	−3.00000	+	3.00000i	−0.00538600	+	0.00538600i	0.704409	+	0.709795i	$0.251212\pi$
$558$		0			0
$559$		−	252.000i		−	0.450805i
$560$		0			0
$561$		0			0
$562$	312.000	−	312.000i	0.555160	−	0.555160i
$563$	−42.0000	−	42.0000i	−0.0746004	−	0.0746004i	0.668822	−	0.743422i	$-0.266799\pi$
$563$	−42.0000	−	42.0000i	−0.0746004	−	0.0746004i	−0.743422	+	0.668822i	$0.766799\pi$
$564$		0			0
$565$		0			0
$566$	−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
$575$		0			0
$576$		0			0
$577$	473.000	−	473.000i	0.819757	−	0.819757i	−0.166315	−	0.986073i	$-0.553187\pi$
$577$	473.000	−	473.000i	0.819757	−	0.819757i	0.986073	+	0.166315i	$0.0531869\pi$
$578$	−191.000	−	191.000i	−0.330450	−	0.330450i
$579$		0			0
$580$		0			0
$581$	−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	−0.855353	−	0.518045i	$-0.826660\pi$
$587$	−198.000	+	198.000i	−0.337308	+	0.337308i	0.518045	+	0.855353i	$0.326660\pi$
$588$		0			0
$589$			1040.00i			1.76570i
$590$		0			0
$591$		0			0
$592$	−12.0000	+	12.0000i	−0.0202703	+	0.0202703i
$593$	−47.0000	−	47.0000i	−0.0792580	−	0.0792580i	0.666366	−	0.745624i	$-0.267849\pi$
$593$	−47.0000	−	47.0000i	−0.0792580	−	0.0792580i	−0.745624	+	0.666366i	$0.767849\pi$
$594$		0			0
$595$		0			0
$596$	−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
$605$		0			0
$606$		0			0
$607$	−462.000	+	462.000i	−0.761120	+	0.761120i	−0.976525	−	0.215405i	$-0.930893\pi$
$607$	−462.000	+	462.000i	−0.761120	+	0.761120i	0.215405	+	0.976525i	$0.430893\pi$
$608$	80.0000	+	80.0000i	0.131579	+	0.131579i
$609$		0			0
$610$		0			0
$611$	108.000			0.176759
$612$		0			0
$613$	−723.000	−	723.000i	−1.17945	−	1.17945i	−0.979886	−	0.199560i	$-0.936049\pi$
$613$	−723.000	−	723.000i	−1.17945	−	1.17945i	−0.199560	−	0.979886i	$-0.563951\pi$
$614$			36.0000i			0.0586319i
$615$		0			0
$616$	−64.0000			−0.103896
$617$	327.000	−	327.000i	0.529984	−	0.529984i	−0.390584	−	0.920567i	$-0.627727\pi$
$617$	327.000	−	327.000i	0.529984	−	0.529984i	0.920567	+	0.390584i	$0.127727\pi$
$618$		0			0
$619$			660.000i			1.06624i	0.846041	+	0.533118i	$0.178980\pi$
$619$			660.000i			1.06624i	−0.846041	+	0.533118i	$0.821020\pi$
$620$		0			0
$621$		0			0
$622$	−388.000	+	388.000i	−0.623794	+	0.623794i
$623$	−160.000	−	160.000i	−0.256822	−	0.256822i
$624$		0			0
$625$		0			0
$626$	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
$635$		0			0
$636$		0			0
$637$	123.000	−	123.000i	0.193093	−	0.193093i
$638$	−320.000	−	320.000i	−0.501567	−	0.501567i
$639$		0			0
$640$		0			0
$641$	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	0.921132	−	0.389250i	$-0.127266\pi$
$643$	342.000	+	342.000i	0.531882	+	0.531882i	−0.389250	+	0.921132i	$0.627266\pi$
$644$		−	16.0000i		−	0.0248447i
$645$		0			0
$646$	−280.000			−0.433437
$647$	−118.000	+	118.000i	−0.182380	+	0.182380i	−0.792392	−	0.610012i	$-0.791165\pi$
$647$	−118.000	+	118.000i	−0.182380	+	0.182380i	0.610012	+	0.792392i	$0.291165\pi$
$648$		0			0
$649$		−	160.000i		−	0.246533i
$650$		0			0
$651$		0			0
$652$	164.000	−	164.000i	0.251534	−	0.251534i
$653$	453.000	+	453.000i	0.693721	+	0.693721i	0.963049	−	0.269327i	$-0.0868014\pi$
$653$	453.000	+	453.000i	0.693721	+	0.693721i	−0.269327	+	0.963049i	$0.586801\pi$
$654$		0			0
$655$		0			0
$656$	−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
$665$		0			0
$666$		0			0
$667$	80.0000	−	80.0000i	0.119940	−	0.119940i
$668$	−124.000	−	124.000i	−0.185629	−	0.185629i
$669$		0			0
$670$		0			0
$671$	−384.000			−0.572280
$672$		0			0
$673$	−193.000	−	193.000i	−0.286776	−	0.286776i	0.549028	−	0.835804i	$-0.314998\pi$
$673$	−193.000	−	193.000i	−0.286776	−	0.286776i	−0.835804	+	0.549028i	$0.814998\pi$
$674$		−	834.000i		−	1.23739i
$675$		0			0
$676$	−302.000			−0.446746
$677$	157.000	−	157.000i	0.231905	−	0.231905i	−0.581582	−	0.813488i	$-0.697566\pi$
$677$	157.000	−	157.000i	0.231905	−	0.231905i	0.813488	+	0.581582i	$0.197566\pi$
$678$		0			0
$679$			252.000i			0.371134i
$680$		0			0
$681$		0			0
$682$	−416.000	+	416.000i	−0.609971	+	0.609971i
$683$	438.000	+	438.000i	0.641288	+	0.641288i	0.950872	−	0.309584i	$-0.100190\pi$
$683$	438.000	+	438.000i	0.641288	+	0.641288i	−0.309584	+	0.950872i	$0.600190\pi$
$684$		0			0
$685$		0			0
$686$	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
$695$		0			0
$696$		0			0
$697$	56.0000	−	56.0000i	0.0803443	−	0.0803443i
$698$	−440.000	−	440.000i	−0.630372	−	0.630372i
$699$		0			0
$700$		0			0
$701$	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	$-0.180053\pi$
$710$		0			0
$711$		0			0
$712$	−160.000	+	160.000i	−0.224719	+	0.224719i
$713$	−104.000	−	104.000i	−0.145863	−	0.145863i
$714$		0			0
$715$		0			0
$716$	−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
$725$		0			0
$726$		0			0
$727$	558.000	−	558.000i	0.767538	−	0.767538i	−0.210135	−	0.977672i	$-0.567390\pi$
$727$	558.000	−	558.000i	0.767538	−	0.767538i	0.977672	+	0.210135i	$0.0673902\pi$
$728$	24.0000	+	24.0000i	0.0329670	+	0.0329670i
$729$		0			0
$730$		0			0
$731$	588.000			0.804378
$732$		0			0
$733$	827.000	+	827.000i	1.12824	+	1.12824i	0.990463	+	0.137777i	$0.0439957\pi$
$733$	827.000	+	827.000i	1.12824	+	1.12824i	0.137777	+	0.990463i	$0.456004\pi$
$734$			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	$0.842950\pi$
$740$		0			0
$741$		0			0
$742$	212.000	−	212.000i	0.285714	−	0.285714i
$743$	−382.000	−	382.000i	−0.514132	−	0.514132i	0.401658	−	0.915790i	$-0.368434\pi$
$743$	−382.000	−	382.000i	−0.514132	−	0.514132i	−0.915790	+	0.401658i	$0.868434\pi$
$744$		0			0
$745$		0			0
$746$	−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
$755$		0			0
$756$		0			0
$757$	−987.000	+	987.000i	−1.30383	+	1.30383i	−0.378043	+	0.925788i	$0.623403\pi$
$757$	−987.000	+	987.000i	−1.30383	+	1.30383i	−0.925788	+	0.378043i	$0.876597\pi$
$758$	340.000	+	340.000i	0.448549	+	0.448549i
$759$		0			0
$760$		0			0
$761$	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	$-0.0165646\pi$
$770$		0			0
$771$		0			0
$772$	114.000	−	114.000i	0.147668	−	0.147668i
$773$	243.000	+	243.000i	0.314360	+	0.314360i	0.846596	−	0.532236i	$-0.178648\pi$
$773$	243.000	+	243.000i	0.314360	+	0.314360i	−0.532236	+	0.846596i	$0.678648\pi$
$774$		0			0
$775$		0			0
$776$	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
$785$		0			0
$786$		0			0
$787$	−262.000	+	262.000i	−0.332910	+	0.332910i	−0.853690	−	0.520781i	$-0.825641\pi$
$787$	−262.000	+	262.000i	−0.332910	+	0.332910i	0.520781	+	0.853690i	$0.325641\pi$
$788$	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	−0.519478	−	0.854484i	$-0.673873\pi$
$797$	267.000	−	267.000i	0.335006	−	0.335006i	0.854484	+	0.519478i	$0.173873\pi$
$798$		0			0
$799$			252.000i			0.315394i
$800$		0			0
$801$		0			0
$802$	642.000	−	642.000i	0.800499	−	0.800499i
$803$	376.000	+	376.000i	0.468244	+	0.468244i
$804$		0			0
$805$		0			0
$806$	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
$815$		0			0
$816$		0			0
$817$	−840.000	+	840.000i	−1.02815	+	1.02815i
$818$	−150.000	−	150.000i	−0.183374	−	0.183374i
$819$		0			0
$820$		0			0
$821$	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	0.960645	−	0.277778i	$-0.0895979\pi$
$823$	562.000	+	562.000i	0.682868	+	0.682868i	−0.277778	+	0.960645i	$0.589598\pi$
$824$		−	472.000i		−	0.572816i
$825$		0			0
$826$	−80.0000			−0.0968523
$827$	762.000	−	762.000i	0.921403	−	0.921403i	−0.0757260	−	0.997129i	$-0.524127\pi$
$827$	762.000	−	762.000i	0.921403	−	0.921403i	0.997129	+	0.0757260i	$0.0241274\pi$
$828$		0			0
$829$		−	170.000i		−	0.205066i	−0.994730	−	0.102533i	$-0.967305\pi$
$829$		−	170.000i		−	0.205066i	0.994730	−	0.102533i	$-0.0326948\pi$
$830$		0			0
$831$		0			0
$832$	24.0000	−	24.0000i	0.0288462	−	0.0288462i
$833$	287.000	+	287.000i	0.344538	+	0.344538i
$834$		0			0
$835$		0			0
$836$	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
$845$		0			0
$846$		0			0
$847$	114.000	−	114.000i	0.134593	−	0.134593i
$848$	−212.000	−	212.000i	−0.250000	−	0.250000i
$849$		0			0
$850$		0			0
$851$	−12.0000			−0.0141011
$852$		0			0
$853$	−1123.00	−	1123.00i	−1.31653	−	1.31653i	−0.916504	−	0.400026i	$-0.869001\pi$
$853$	−1123.00	−	1123.00i	−1.31653	−	1.31653i	−0.400026	−	0.916504i	$-0.630999\pi$
$854$			192.000i			0.224824i
$855$		0			0
$856$	568.000			0.663551
$857$	417.000	−	417.000i	0.486581	−	0.486581i	−0.420644	−	0.907226i	$-0.638196\pi$
$857$	417.000	−	417.000i	0.486581	−	0.486581i	0.907226	+	0.420644i	$0.138196\pi$
$858$		0			0
$859$			1300.00i			1.51339i	0.653769	+	0.756694i	$0.273187\pi$
$859$			1300.00i			1.51339i	−0.653769	+	0.756694i	$0.726813\pi$
$860$		0			0
$861$		0			0
$862$	−788.000	+	788.000i	−0.914153	+	0.914153i
$863$	−242.000	−	242.000i	−0.280417	−	0.280417i	0.552858	−	0.833275i	$-0.313537\pi$
$863$	−242.000	−	242.000i	−0.280417	−	0.280417i	−0.833275	+	0.552858i	$0.813537\pi$
$864$		0			0
$865$		0			0
$866$	−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
$875$		0			0
$876$		0			0
$877$	453.000	−	453.000i	0.516534	−	0.516534i	−0.399987	−	0.916521i	$-0.630985\pi$
$877$	453.000	−	453.000i	0.516534	−	0.516534i	0.916521	+	0.399987i	$0.130985\pi$
$878$	560.000	+	560.000i	0.637813	+	0.637813i
$879$		0			0
$880$		0			0
$881$	−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	0.637125	−	0.770760i	$-0.280123\pi$
$883$	−118.000	−	118.000i	−0.133635	−	0.133635i	−0.770760	+	0.637125i	$0.780123\pi$
$884$			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	$0.624390\pi$
$887$	−1158.00	+	1158.00i	−1.30552	+	1.30552i	−0.924611	+	0.380914i	$0.875610\pi$
$888$		0			0
$889$			472.000i			0.530934i
$890$		0			0
$891$		0			0
$892$	−276.000	+	276.000i	−0.309417	+	0.309417i
$893$	−360.000	−	360.000i	−0.403135	−	0.403135i
$894$		0			0
$895$		0			0
$896$	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
$905$		0			0
$906$		0			0
$907$	−142.000	+	142.000i	−0.156560	+	0.156560i	−0.781040	−	0.624480i	$-0.785311\pi$
$907$	−142.000	+	142.000i	−0.156560	+	0.156560i	0.624480	+	0.781040i	$0.285311\pi$
$908$	−4.00000	−	4.00000i	−0.00440529	−	0.00440529i
$909$		0			0
$910$		0			0
$911$	−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	$-0.166867\pi$
$920$		0			0
$921$		0			0
$922$	622.000	−	622.000i	0.674620	−	0.674620i
$923$	−84.0000	−	84.0000i	−0.0910076	−	0.0910076i
$924$		0			0
$925$		0			0
$926$	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
$935$		0			0
$936$		0			0
$937$	233.000	−	233.000i	0.248666	−	0.248666i	−0.571757	−	0.820423i	$-0.693738\pi$
$937$	233.000	−	233.000i	0.248666	−	0.248666i	0.820423	+	0.571757i	$0.193738\pi$
$938$	248.000	+	248.000i	0.264392	+	0.264392i
$939$		0			0
$940$		0			0
$941$	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	−0.673614	−	0.739084i	$-0.735259\pi$
$947$	62.0000	−	62.0000i	0.0654699	−	0.0654699i	0.739084	+	0.673614i	$0.235259\pi$
$948$		0			0
$949$		−	282.000i		−	0.297155i
$950$		0			0
$951$		0			0
$952$	−56.0000	+	56.0000i	−0.0588235	+	0.0588235i
$953$	−1017.00	−	1017.00i	−1.06716	−	1.06716i	−0.997576	−	0.0695800i	$-0.977834\pi$
$953$	−1017.00	−	1017.00i	−1.06716	−	1.06716i	−0.0695800	−	0.997576i	$-0.522166\pi$
$954$		0			0
$955$		0			0
$956$	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
$965$		0			0
$966$		0			0
$967$	−502.000	+	502.000i	−0.519131	+	0.519131i	−0.917309	−	0.398177i	$-0.869643\pi$
$967$	−502.000	+	502.000i	−0.519131	+	0.519131i	0.398177	+	0.917309i	$0.369643\pi$
$968$	−114.000	−	114.000i	−0.117769	−	0.117769i
$969$		0			0
$970$		0			0
$971$	−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	−0.983320	−	0.181887i	$-0.941780\pi$
$977$	−783.000	+	783.000i	−0.801433	+	0.801433i	0.181887	+	0.983320i	$0.441780\pi$
$978$		0			0
$979$			640.000i			0.653728i
$980$		0			0
$981$		0			0
$982$	−328.000	+	328.000i	−0.334012	+	0.334012i
$983$	1058.00	+	1058.00i	1.07630	+	1.07630i	0.996838	+	0.0794589i	$0.0253192\pi$
$983$	1058.00	+	1058.00i	1.07630	+	1.07630i	0.0794589	+	0.996838i	$0.474681\pi$
$984$		0			0
$985$		0			0
$986$	−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
$995$		0			0
$996$		0			0
$997$	773.000	−	773.000i	0.775326	−	0.775326i	−0.203706	−	0.979032i	$-0.565299\pi$
$997$	773.000	−	773.000i	0.775326	−	0.775326i	0.979032	+	0.203706i	$0.0652987\pi$
$998$	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	450.3.g.b.343.1		2
3.2	odd	2		50.3.c.c.43.1		2
5.2	odd	4	inner	450.3.g.b.307.1		2
5.3	odd	4		90.3.g.b.37.1		2
5.4	even	2		90.3.g.b.73.1		2
12.11	even	2		400.3.p.b.193.1		2
15.2	even	4		50.3.c.c.7.1		2
15.8	even	4		10.3.c.a.7.1	yes	2
15.14	odd	2		10.3.c.a.3.1	✓	2
20.3	even	4		720.3.bh.c.577.1		2
20.19	odd	2		720.3.bh.c.433.1		2
60.23	odd	4		80.3.p.c.17.1		2
60.47	odd	4		400.3.p.b.257.1		2
60.59	even	2		80.3.p.c.33.1		2
105.83	odd	4		490.3.f.b.197.1		2
105.104	even	2		490.3.f.b.393.1		2
120.29	odd	2		320.3.p.h.193.1		2
120.53	even	4		320.3.p.h.257.1		2
120.59	even	2		320.3.p.a.193.1		2
120.83	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	15.14	odd	2
10.3.c.a.7.1	yes	2	15.8	even	4
50.3.c.c.7.1		2	15.2	even	4
50.3.c.c.43.1		2	3.2	odd	2
80.3.p.c.17.1		2	60.23	odd	4
80.3.p.c.33.1		2	60.59	even	2
90.3.g.b.37.1		2	5.3	odd	4
90.3.g.b.73.1		2	5.4	even	2
320.3.p.a.193.1		2	120.59	even	2
320.3.p.a.257.1		2	120.83	odd	4
320.3.p.h.193.1		2	120.29	odd	2
320.3.p.h.257.1		2	120.53	even	4
400.3.p.b.193.1		2	12.11	even	2
400.3.p.b.257.1		2	60.47	odd	4
450.3.g.b.307.1		2	5.2	odd	4	inner
450.3.g.b.343.1		2	1.1	even	1	trivial
490.3.f.b.197.1		2	105.83	odd	4
490.3.f.b.393.1		2	105.104	even	2
720.3.bh.c.433.1		2	20.19	odd	2
720.3.bh.c.577.1		2	20.3	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.g (of order \(4\), degree \(2\), minimal)

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

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