LMFDB - Embedded newform 150.3.f.c.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(7,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, 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("150.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.f (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:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	150.7
Dual form			150.3.f.c.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(4.77526 + 4.77526i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(4.77526 + 4.77526i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +20.6969 q^{11} +(2.44949 + 2.44949i) q^{12} +(-8.32577 + 8.32577i) q^{13} +9.55051i q^{14} -4.00000 q^{16} +(-1.34847 - 1.34847i) q^{17} +(3.00000 - 3.00000i) q^{18} -33.6969i q^{19} +11.6969 q^{21} +(20.6969 + 20.6969i) q^{22} +(-16.0454 + 16.0454i) q^{23} +4.89898i q^{24} -16.6515 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-9.55051 + 9.55051i) q^{28} +8.69694i q^{29} -49.0908 q^{31} +(-4.00000 - 4.00000i) q^{32} +(25.3485 - 25.3485i) q^{33} -2.69694i q^{34} +6.00000 q^{36} +(-36.4949 - 36.4949i) q^{37} +(33.6969 - 33.6969i) q^{38} +20.3939i q^{39} +33.3031 q^{41} +(11.6969 + 11.6969i) q^{42} +(-24.1237 + 24.1237i) q^{43} +41.3939i q^{44} -32.0908 q^{46} +(-13.9546 - 13.9546i) q^{47} +(-4.89898 + 4.89898i) q^{48} -3.39388i q^{49} -3.30306 q^{51} +(-16.6515 - 16.6515i) q^{52} +(59.3939 - 59.3939i) q^{53} -7.34847i q^{54} -19.1010 q^{56} +(-41.2702 - 41.2702i) q^{57} +(-8.69694 + 8.69694i) q^{58} -30.0000i q^{59} -47.7878 q^{61} +(-49.0908 - 49.0908i) q^{62} +(14.3258 - 14.3258i) q^{63} -8.00000i q^{64} +50.6969 q^{66} +(17.0227 + 17.0227i) q^{67} +(2.69694 - 2.69694i) q^{68} +39.3031i q^{69} -9.30306 q^{71} +(6.00000 + 6.00000i) q^{72} +(22.2929 - 22.2929i) q^{73} -72.9898i q^{74} +67.3939 q^{76} +(98.8332 + 98.8332i) q^{77} +(-20.3939 + 20.3939i) q^{78} +27.3939i q^{79} -9.00000 q^{81} +(33.3031 + 33.3031i) q^{82} +(-63.4393 + 63.4393i) q^{83} +23.3939i q^{84} -48.2474 q^{86} +(10.6515 + 10.6515i) q^{87} +(-41.3939 + 41.3939i) q^{88} +17.3939i q^{89} -79.5153 q^{91} +(-32.0908 - 32.0908i) q^{92} +(-60.1237 + 60.1237i) q^{93} -27.9092i q^{94} -9.79796 q^{96} +(41.8763 + 41.8763i) q^{97} +(3.39388 - 3.39388i) q^{98} -62.0908i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 24 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 24 * q^7 - 8 * q^8	$ 4 q + 4 q^{2} + 24 q^{7} - 8 q^{8} + 24 q^{11} - 48 q^{13} - 16 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{21} + 24 q^{22} + 24 q^{23} - 96 q^{26} - 48 q^{28} - 20 q^{31} - 16 q^{32} + 72 q^{33} + 24 q^{36} - 48 q^{37} + 76 q^{38} + 192 q^{41} - 12 q^{42} - 72 q^{43} + 48 q^{46} - 144 q^{47} - 72 q^{51} - 96 q^{52} + 120 q^{53} - 96 q^{56} - 72 q^{57} + 24 q^{58} + 44 q^{61} - 20 q^{62} + 72 q^{63} + 144 q^{66} + 24 q^{67} - 48 q^{68} - 96 q^{71} + 24 q^{72} - 48 q^{73} + 152 q^{76} + 72 q^{77} + 36 q^{78} - 36 q^{81} + 192 q^{82} - 48 q^{83} - 144 q^{86} + 72 q^{87} - 48 q^{88} - 612 q^{91} + 48 q^{92} - 216 q^{93} + 192 q^{97} - 104 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 24 * q^7 - 8 * q^8 + 24 * q^11 - 48 * q^13 - 16 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^21 + 24 * q^22 + 24 * q^23 - 96 * q^26 - 48 * q^28 - 20 * q^31 - 16 * q^32 + 72 * q^33 + 24 * q^36 - 48 * q^37 + 76 * q^38 + 192 * q^41 - 12 * q^42 - 72 * q^43 + 48 * q^46 - 144 * q^47 - 72 * q^51 - 96 * q^52 + 120 * q^53 - 96 * q^56 - 72 * q^57 + 24 * q^58 + 44 * q^61 - 20 * q^62 + 72 * q^63 + 144 * q^66 + 24 * q^67 - 48 * q^68 - 96 * q^71 + 24 * q^72 - 48 * q^73 + 152 * q^76 + 72 * q^77 + 36 * q^78 - 36 * q^81 + 192 * q^82 - 48 * q^83 - 144 * q^86 + 72 * q^87 - 48 * q^88 - 612 * q^91 + 48 * q^92 - 216 * q^93 + 192 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	2.44949			0.408248
$7$	4.77526	+	4.77526i	0.682179	+	0.682179i	0.960491	−	0.278312i	$-0.0897748\pi$
$7$	4.77526	+	4.77526i	0.682179	+	0.682179i	−0.278312	+	0.960491i	$0.589775\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	20.6969			1.88154			0.940770	−	0.339046i	$-0.110104\pi$
$11$	20.6969			1.88154			0.940770	+	0.339046i	$0.110104\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−8.32577	+	8.32577i	−0.640443	+	0.640443i	−0.950664	−	0.310221i	$-0.899597\pi$
$13$	−8.32577	+	8.32577i	−0.640443	+	0.640443i	0.310221	+	0.950664i	$0.399597\pi$
$14$			9.55051i			0.682179i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−1.34847	−	1.34847i	−0.0793217	−	0.0793217i	0.666333	−	0.745654i	$-0.267863\pi$
$17$	−1.34847	−	1.34847i	−0.0793217	−	0.0793217i	−0.745654	+	0.666333i	$0.767863\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	33.6969i		−	1.77352i	−0.462227	−	0.886762i	$-0.652950\pi$
$19$		−	33.6969i		−	1.77352i	0.462227	−	0.886762i	$-0.347050\pi$
$20$		0			0
$21$	11.6969			0.556997
$22$	20.6969	+	20.6969i	0.940770	+	0.940770i
$23$	−16.0454	+	16.0454i	−0.697626	+	0.697626i	−0.963898	−	0.266272i	$-0.914208\pi$
$23$	−16.0454	+	16.0454i	−0.697626	+	0.697626i	0.266272	+	0.963898i	$0.414208\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	−16.6515			−0.640443
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−9.55051	+	9.55051i	−0.341090	+	0.341090i
$29$			8.69694i			0.299894i	0.988694	+	0.149947i	$0.0479104\pi$
$29$			8.69694i			0.299894i	−0.988694	+	0.149947i	$0.952090\pi$
$30$		0			0
$31$	−49.0908			−1.58357			−0.791787	−	0.610797i	$-0.790849\pi$
$31$	−49.0908			−1.58357			−0.791787	+	0.610797i	$0.790849\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	25.3485	−	25.3485i	0.768135	−	0.768135i
$34$		−	2.69694i		−	0.0793217i
$35$		0			0
$36$	6.00000			0.166667
$37$	−36.4949	−	36.4949i	−0.986349	−	0.986349i	0.0135595	−	0.999908i	$-0.495684\pi$
$37$	−36.4949	−	36.4949i	−0.986349	−	0.986349i	−0.999908	+	0.0135595i	$0.995684\pi$
$38$	33.6969	−	33.6969i	0.886762	−	0.886762i
$39$			20.3939i			0.522920i
$40$		0			0
$41$	33.3031			0.812270			0.406135	−	0.913813i	$-0.366876\pi$
$41$	33.3031			0.812270			0.406135	+	0.913813i	$0.366876\pi$
$42$	11.6969	+	11.6969i	0.278499	+	0.278499i
$43$	−24.1237	+	24.1237i	−0.561017	+	0.561017i	−0.929596	−	0.368579i	$-0.879844\pi$
$43$	−24.1237	+	24.1237i	−0.561017	+	0.561017i	0.368579	+	0.929596i	$0.379844\pi$
$44$			41.3939i			0.940770i
$45$		0			0
$46$	−32.0908			−0.697626
$47$	−13.9546	−	13.9546i	−0.296906	−	0.296906i	0.542895	−	0.839801i	$-0.317328\pi$
$47$	−13.9546	−	13.9546i	−0.296906	−	0.296906i	−0.839801	+	0.542895i	$0.817328\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$		−	3.39388i		−	0.0692628i
$50$		0			0
$51$	−3.30306			−0.0647659
$52$	−16.6515	−	16.6515i	−0.320222	−	0.320222i
$53$	59.3939	−	59.3939i	1.12064	−	1.12064i	0.128994	−	0.991645i	$-0.458825\pi$
$53$	59.3939	−	59.3939i	1.12064	−	1.12064i	0.991645	−	0.128994i	$-0.0411747\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−19.1010			−0.341090
$57$	−41.2702	−	41.2702i	−0.724038	−	0.724038i
$58$	−8.69694	+	8.69694i	−0.149947	+	0.149947i
$59$		−	30.0000i		−	0.508475i	−0.967142	−	0.254237i	$-0.918176\pi$
$59$		−	30.0000i		−	0.508475i	0.967142	−	0.254237i	$-0.0818244\pi$
$60$		0			0
$61$	−47.7878			−0.783406			−0.391703	−	0.920092i	$-0.628114\pi$
$61$	−47.7878			−0.783406			−0.391703	+	0.920092i	$0.628114\pi$
$62$	−49.0908	−	49.0908i	−0.791787	−	0.791787i
$63$	14.3258	−	14.3258i	0.227393	−	0.227393i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	50.6969			0.768135
$67$	17.0227	+	17.0227i	0.254070	+	0.254070i	0.822637	−	0.568567i	$-0.192502\pi$
$67$	17.0227	+	17.0227i	0.254070	+	0.254070i	−0.568567	+	0.822637i	$0.692502\pi$
$68$	2.69694	−	2.69694i	0.0396609	−	0.0396609i
$69$			39.3031i			0.569610i
$70$		0			0
$71$	−9.30306			−0.131029			−0.0655145	−	0.997852i	$-0.520869\pi$
$71$	−9.30306			−0.131029			−0.0655145	+	0.997852i	$0.520869\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	22.2929	−	22.2929i	0.305382	−	0.305382i	−0.537733	−	0.843115i	$-0.680719\pi$
$73$	22.2929	−	22.2929i	0.305382	−	0.305382i	0.843115	+	0.537733i	$0.180719\pi$
$74$		−	72.9898i		−	0.986349i
$75$		0			0
$76$	67.3939			0.886762
$77$	98.8332	+	98.8332i	1.28355	+	1.28355i
$78$	−20.3939	+	20.3939i	−0.261460	+	0.261460i
$79$			27.3939i			0.346758i	0.984855	+	0.173379i	$0.0554685\pi$
$79$			27.3939i			0.346758i	−0.984855	+	0.173379i	$0.944531\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	33.3031	+	33.3031i	0.406135	+	0.406135i
$83$	−63.4393	+	63.4393i	−0.764329	+	0.764329i	−0.977102	−	0.212773i	$-0.931751\pi$
$83$	−63.4393	+	63.4393i	−0.764329	+	0.764329i	0.212773	+	0.977102i	$0.431751\pi$
$84$			23.3939i			0.278499i
$85$		0			0
$86$	−48.2474			−0.561017
$87$	10.6515	+	10.6515i	0.122431	+	0.122431i
$88$	−41.3939	+	41.3939i	−0.470385	+	0.470385i
$89$			17.3939i			0.195437i	0.995214	+	0.0977184i	$0.0311545\pi$
$89$			17.3939i			0.195437i	−0.995214	+	0.0977184i	$0.968846\pi$
$90$		0			0
$91$	−79.5153			−0.873795
$92$	−32.0908	−	32.0908i	−0.348813	−	0.348813i
$93$	−60.1237	+	60.1237i	−0.646492	+	0.646492i
$94$		−	27.9092i		−	0.296906i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	41.8763	+	41.8763i	0.431714	+	0.431714i	0.889211	−	0.457497i	$-0.151254\pi$
$97$	41.8763	+	41.8763i	0.431714	+	0.431714i	−0.457497	+	0.889211i	$0.651254\pi$
$98$	3.39388	−	3.39388i	0.0346314	−	0.0346314i
$99$		−	62.0908i		−	0.627180i
$100$		0			0
$101$	162.879			1.61266			0.806330	−	0.591467i	$-0.201451\pi$
$101$	162.879			1.61266			0.806330	+	0.591467i	$0.201451\pi$
$102$	−3.30306	−	3.30306i	−0.0323830	−	0.0323830i
$103$	−36.9898	+	36.9898i	−0.359124	+	0.359124i	−0.863490	−	0.504366i	$-0.831726\pi$
$103$	−36.9898	+	36.9898i	−0.359124	+	0.359124i	0.504366	+	0.863490i	$0.331726\pi$
$104$		−	33.3031i		−	0.320222i
$105$		0			0
$106$	118.788			1.12064
$107$	134.091	+	134.091i	1.25319	+	1.25319i	0.954284	+	0.298901i	$0.0966201\pi$
$107$	134.091	+	134.091i	1.25319	+	1.25319i	0.298901	+	0.954284i	$0.403380\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			145.000i			1.33028i	0.746721	+	0.665138i	$0.231627\pi$
$109$			145.000i			1.33028i	−0.746721	+	0.665138i	$0.768373\pi$
$110$		0			0
$111$	−89.3939			−0.805350
$112$	−19.1010	−	19.1010i	−0.170545	−	0.170545i
$113$	−13.2122	+	13.2122i	−0.116923	+	0.116923i	−0.763147	−	0.646225i	$-0.776347\pi$
$113$	−13.2122	+	13.2122i	−0.116923	+	0.116923i	0.646225	+	0.763147i	$0.276347\pi$
$114$		−	82.5403i		−	0.724038i
$115$		0			0
$116$	−17.3939			−0.149947
$117$	24.9773	+	24.9773i	0.213481	+	0.213481i
$118$	30.0000	−	30.0000i	0.254237	−	0.254237i
$119$		−	12.8786i		−	0.108223i
$120$		0			0
$121$	307.363			2.54019
$122$	−47.7878	−	47.7878i	−0.391703	−	0.391703i
$123$	40.7878	−	40.7878i	0.331608	−	0.331608i
$124$		−	98.1816i		−	0.791787i
$125$		0			0
$126$	28.6515			0.227393
$127$	−50.6969	−	50.6969i	−0.399188	−	0.399188i	0.478758	−	0.877947i	$-0.341087\pi$
$127$	−50.6969	−	50.6969i	−0.399188	−	0.399188i	−0.877947	+	0.478758i	$0.841087\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			59.0908i			0.458068i
$130$		0			0
$131$	−156.272			−1.19292			−0.596460	−	0.802643i	$-0.703426\pi$
$131$	−156.272			−1.19292			−0.596460	+	0.802643i	$0.703426\pi$
$132$	50.6969	+	50.6969i	0.384068	+	0.384068i
$133$	160.911	−	160.911i	1.20986	−	1.20986i
$134$			34.0454i			0.254070i
$135$		0			0
$136$	5.39388			0.0396609
$137$	−91.3485	−	91.3485i	−0.666777	−	0.666777i	0.290191	−	0.956969i	$-0.406281\pi$
$137$	−91.3485	−	91.3485i	−0.666777	−	0.666777i	−0.956969	+	0.290191i	$0.906281\pi$
$138$	−39.3031	+	39.3031i	−0.284805	+	0.284805i
$139$		−	35.2122i		−	0.253326i	−0.991946	−	0.126663i	$-0.959573\pi$
$139$		−	35.2122i		−	0.253326i	0.991946	−	0.126663i	$-0.0404266\pi$
$140$		0			0
$141$	−34.1816			−0.242423
$142$	−9.30306	−	9.30306i	−0.0655145	−	0.0655145i
$143$	−172.318	+	172.318i	−1.20502	+	1.20502i
$144$			12.0000i			0.0833333i
$145$		0			0
$146$	44.5857			0.305382
$147$	−4.15663	−	4.15663i	−0.0282764	−	0.0282764i
$148$	72.9898	−	72.9898i	0.493174	−	0.493174i
$149$		−	4.78775i		−	0.0321326i	−0.999871	−	0.0160663i	$-0.994886\pi$
$149$		−	4.78775i		−	0.0321326i	0.999871	−	0.0160663i	$-0.00511428\pi$
$150$		0			0
$151$	37.8786			0.250851			0.125426	−	0.992103i	$-0.459970\pi$
$151$	37.8786			0.250851			0.125426	+	0.992103i	$0.459970\pi$
$152$	67.3939	+	67.3939i	0.443381	+	0.443381i
$153$	−4.04541	+	4.04541i	−0.0264406	+	0.0264406i
$154$			197.666i			1.28355i
$155$		0			0
$156$	−40.7878			−0.261460
$157$	−29.1339	−	29.1339i	−0.185566	−	0.185566i	0.608210	−	0.793776i	$-0.291888\pi$
$157$	−29.1339	−	29.1339i	−0.185566	−	0.185566i	−0.793776	+	0.608210i	$0.791888\pi$
$158$	−27.3939	+	27.3939i	−0.173379	+	0.173379i
$159$		−	145.485i		−	0.914998i
$160$		0			0
$161$	−153.242			−0.951813
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	193.856	−	193.856i	1.18930	−	1.18930i	0.212038	−	0.977261i	$-0.431990\pi$
$163$	193.856	−	193.856i	1.18930	−	1.18930i	0.977261	−	0.212038i	$-0.0680102\pi$
$164$			66.6061i			0.406135i
$165$		0			0
$166$	−126.879			−0.764329
$167$	−167.666	−	167.666i	−1.00399	−	1.00399i	−0.999992	−	0.00399795i	$-0.998727\pi$
$167$	−167.666	−	167.666i	−1.00399	−	1.00399i	−0.00399795	−	0.999992i	$-0.501273\pi$
$168$	−23.3939	+	23.3939i	−0.139249	+	0.139249i
$169$			30.3633i			0.179664i
$170$		0			0
$171$	−101.091			−0.591174
$172$	−48.2474	−	48.2474i	−0.280508	−	0.280508i
$173$	74.8332	−	74.8332i	0.432562	−	0.432562i	−0.456937	−	0.889499i	$-0.651054\pi$
$173$	74.8332	−	74.8332i	0.432562	−	0.432562i	0.889499	+	0.456937i	$0.151054\pi$
$174$			21.3031i			0.122431i
$175$		0			0
$176$	−82.7878			−0.470385
$177$	−36.7423	−	36.7423i	−0.207584	−	0.207584i
$178$	−17.3939	+	17.3939i	−0.0977184	+	0.0977184i
$179$			229.151i			1.28017i	0.768303	+	0.640087i	$0.221102\pi$
$179$			229.151i			1.28017i	−0.768303	+	0.640087i	$0.778898\pi$
$180$		0			0
$181$	−135.182			−0.746860			−0.373430	−	0.927658i	$-0.621818\pi$
$181$	−135.182			−0.746860			−0.373430	+	0.927658i	$0.621818\pi$
$182$	−79.5153	−	79.5153i	−0.436897	−	0.436897i
$183$	−58.5278	+	58.5278i	−0.319824	+	0.319824i
$184$		−	64.1816i		−	0.348813i
$185$		0			0
$186$	−120.247			−0.646492
$187$	−27.9092	−	27.9092i	−0.149247	−	0.149247i
$188$	27.9092	−	27.9092i	0.148453	−	0.148453i
$189$		−	35.0908i		−	0.185666i
$190$		0			0
$191$	−21.9092			−0.114708			−0.0573539	−	0.998354i	$-0.518266\pi$
$191$	−21.9092			−0.114708			−0.0573539	+	0.998354i	$0.518266\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−98.4870	+	98.4870i	−0.510295	+	0.510295i	−0.914617	−	0.404322i	$-0.867508\pi$
$193$	−98.4870	+	98.4870i	−0.510295	+	0.510295i	0.404322	+	0.914617i	$0.367508\pi$
$194$			83.7526i			0.431714i
$195$		0			0
$196$	6.78775			0.0346314
$197$	63.4393	+	63.4393i	0.322027	+	0.322027i	0.849544	−	0.527517i	$-0.176877\pi$
$197$	63.4393	+	63.4393i	0.322027	+	0.322027i	−0.527517	+	0.849544i	$0.676877\pi$
$198$	62.0908	−	62.0908i	0.313590	−	0.313590i
$199$		−	181.091i		−	0.910004i	−0.890490	−	0.455002i	$-0.849639\pi$
$199$		−	181.091i		−	0.910004i	0.890490	−	0.455002i	$-0.150361\pi$
$200$		0			0
$201$	41.6969			0.207447
$202$	162.879	+	162.879i	0.806330	+	0.806330i
$203$	−41.5301	+	41.5301i	−0.204582	+	0.204582i
$204$		−	6.60612i		−	0.0323830i
$205$		0			0
$206$	−73.9796			−0.359124
$207$	48.1362	+	48.1362i	0.232542	+	0.232542i
$208$	33.3031	−	33.3031i	0.160111	−	0.160111i
$209$		−	697.423i		−	3.33695i
$210$		0			0
$211$	28.7276			0.136150			0.0680748	−	0.997680i	$-0.478314\pi$
$211$	28.7276			0.136150			0.0680748	+	0.997680i	$0.478314\pi$
$212$	118.788	+	118.788i	0.560320	+	0.560320i
$213$	−11.3939	+	11.3939i	−0.0534924	+	0.0534924i
$214$			268.182i			1.25319i
$215$		0			0
$216$	14.6969			0.0680414
$217$	−234.421	−	234.421i	−1.08028	−	1.08028i
$218$	−145.000	+	145.000i	−0.665138	+	0.665138i
$219$		−	54.6061i		−	0.249343i
$220$		0			0
$221$	22.4541			0.101602
$222$	−89.3939	−	89.3939i	−0.402675	−	0.402675i
$223$	−33.1793	+	33.1793i	−0.148786	+	0.148786i	−0.777576	−	0.628789i	$-0.783551\pi$
$223$	−33.1793	+	33.1793i	−0.148786	+	0.148786i	0.628789	+	0.777576i	$0.283551\pi$
$224$		−	38.2020i		−	0.170545i
$225$		0			0
$226$	−26.4245			−0.116923
$227$	−252.879	−	252.879i	−1.11400	−	1.11400i	−0.992604	−	0.121399i	$-0.961262\pi$
$227$	−252.879	−	252.879i	−1.11400	−	1.11400i	−0.121399	−	0.992604i	$-0.538738\pi$
$228$	82.5403	−	82.5403i	0.362019	−	0.362019i
$229$			275.000i			1.20087i	0.799672	+	0.600437i	$0.205007\pi$
$229$			275.000i			1.20087i	−0.799672	+	0.600437i	$0.794993\pi$
$230$		0			0
$231$	242.091			1.04801
$232$	−17.3939	−	17.3939i	−0.0749736	−	0.0749736i
$233$	223.757	−	223.757i	0.960331	−	0.960331i	−0.0389116	−	0.999243i	$-0.512389\pi$
$233$	223.757	−	223.757i	0.960331	−	0.960331i	0.999243	+	0.0389116i	$0.0123891\pi$
$234$			49.9546i			0.213481i
$235$		0			0
$236$	60.0000			0.254237
$237$	33.5505	+	33.5505i	0.141563	+	0.141563i
$238$	12.8786	−	12.8786i	0.0541116	−	0.0541116i
$239$			305.666i			1.27894i	0.768817	+	0.639469i	$0.220846\pi$
$239$			305.666i			1.27894i	−0.768817	+	0.639469i	$0.779154\pi$
$240$		0			0
$241$	167.000			0.692946			0.346473	−	0.938060i	$-0.387379\pi$
$241$	167.000			0.692946			0.346473	+	0.938060i	$0.387379\pi$
$242$	307.363	+	307.363i	1.27010	+	1.27010i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		−	95.5755i		−	0.391703i
$245$		0			0
$246$	81.5755			0.331608
$247$	280.553	+	280.553i	1.13584	+	1.13584i
$248$	98.1816	−	98.1816i	0.395894	−	0.395894i
$249$			155.394i			0.624072i
$250$		0			0
$251$	261.576			1.04213			0.521067	−	0.853516i	$-0.325534\pi$
$251$	261.576			1.04213			0.521067	+	0.853516i	$0.325534\pi$
$252$	28.6515	+	28.6515i	0.113697	+	0.113697i
$253$	−332.091	+	332.091i	−1.31261	+	1.31261i
$254$		−	101.394i		−	0.399188i
$255$		0			0
$256$	16.0000			0.0625000
$257$	94.5153	+	94.5153i	0.367764	+	0.367764i	0.866661	−	0.498897i	$-0.166262\pi$
$257$	94.5153	+	94.5153i	0.367764	+	0.367764i	−0.498897	+	0.866661i	$0.666262\pi$
$258$	−59.0908	+	59.0908i	−0.229034	+	0.229034i
$259$		−	348.545i		−	1.34573i
$260$		0			0
$261$	26.0908			0.0999648
$262$	−156.272	−	156.272i	−0.596460	−	0.596460i
$263$	34.1816	−	34.1816i	0.129968	−	0.129968i	−0.639130	−	0.769098i	$-0.720706\pi$
$263$	34.1816	−	34.1816i	0.129968	−	0.129968i	0.769098	+	0.639130i	$0.220706\pi$
$264$			101.394i			0.384068i
$265$		0			0
$266$	321.823			1.20986
$267$	21.3031	+	21.3031i	0.0797867	+	0.0797867i
$268$	−34.0454	+	34.0454i	−0.127035	+	0.127035i
$269$			389.605i			1.44835i	0.689618	+	0.724173i	$0.257778\pi$
$269$			389.605i			1.44835i	−0.689618	+	0.724173i	$0.742222\pi$
$270$		0			0
$271$	156.788			0.578553			0.289276	−	0.957246i	$-0.406585\pi$
$271$	156.788			0.578553			0.289276	+	0.957246i	$0.406585\pi$
$272$	5.39388	+	5.39388i	0.0198304	+	0.0198304i
$273$	−97.3860	+	97.3860i	−0.356725	+	0.356725i
$274$		−	182.697i		−	0.666777i
$275$		0			0
$276$	−78.6061			−0.284805
$277$	285.588	+	285.588i	1.03100	+	1.03100i	0.999504	+	0.0314999i	$0.0100284\pi$
$277$	285.588	+	285.588i	1.03100	+	1.03100i	0.0314999	+	0.999504i	$0.489972\pi$
$278$	35.2122	−	35.2122i	0.126663	−	0.126663i
$279$			147.272i			0.527858i
$280$		0			0
$281$	−20.1520			−0.0717155			−0.0358577	−	0.999357i	$-0.511416\pi$
$281$	−20.1520			−0.0717155			−0.0358577	+	0.999357i	$0.511416\pi$
$282$	−34.1816	−	34.1816i	−0.121211	−	0.121211i
$283$	−170.573	+	170.573i	−0.602732	+	0.602732i	−0.941037	−	0.338304i	$-0.890147\pi$
$283$	−170.573	+	170.573i	−0.602732	+	0.602732i	0.338304	+	0.941037i	$0.390147\pi$
$284$		−	18.6061i		−	0.0655145i
$285$		0			0
$286$	−344.636			−1.20502
$287$	159.031	+	159.031i	0.554114	+	0.554114i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	285.363i		−	0.987416i
$290$		0			0
$291$	102.576			0.352493
$292$	44.5857	+	44.5857i	0.152691	+	0.152691i
$293$	259.621	−	259.621i	0.886078	−	0.886078i	−0.108066	−	0.994144i	$-0.534466\pi$
$293$	259.621	−	259.621i	0.886078	−	0.886078i	0.994144	+	0.108066i	$0.0344656\pi$
$294$		−	8.31327i		−	0.0282764i
$295$		0			0
$296$	145.980			0.493174
$297$	−76.0454	−	76.0454i	−0.256045	−	0.256045i
$298$	4.78775	−	4.78775i	0.0160663	−	0.0160663i
$299$		−	267.181i		−	0.893581i
$300$		0			0
$301$	−230.394			−0.765428
$302$	37.8786	+	37.8786i	0.125426	+	0.125426i
$303$	199.485	−	199.485i	0.658365	−	0.658365i
$304$			134.788i			0.443381i
$305$		0			0
$306$	−8.09082			−0.0264406
$307$	118.911	+	118.911i	0.387334	+	0.387334i	0.873735	−	0.486402i	$-0.161691\pi$
$307$	118.911	+	118.911i	0.387334	+	0.387334i	−0.486402	+	0.873735i	$0.661691\pi$
$308$	−197.666	+	197.666i	−0.641774	+	0.641774i
$309$			90.6061i			0.293224i
$310$		0			0
$311$	−52.7878			−0.169736			−0.0848678	−	0.996392i	$-0.527047\pi$
$311$	−52.7878			−0.169736			−0.0848678	+	0.996392i	$0.527047\pi$
$312$	−40.7878	−	40.7878i	−0.130730	−	0.130730i
$313$	−238.553	+	238.553i	−0.762150	+	0.762150i	−0.976711	−	0.214561i	$-0.931168\pi$
$313$	−238.553	+	238.553i	−0.762150	+	0.762150i	0.214561	+	0.976711i	$0.431168\pi$
$314$		−	58.2679i		−	0.185566i
$315$		0			0
$316$	−54.7878			−0.173379
$317$	−48.9398	−	48.9398i	−0.154384	−	0.154384i	0.625689	−	0.780073i	$-0.284818\pi$
$317$	−48.9398	−	48.9398i	−0.154384	−	0.154384i	−0.780073	+	0.625689i	$0.784818\pi$
$318$	145.485	−	145.485i	0.457499	−	0.457499i
$319$			180.000i			0.564263i
$320$		0			0
$321$	328.454			1.02322
$322$	−153.242	−	153.242i	−0.475906	−	0.475906i
$323$	−45.4393	+	45.4393i	−0.140679	+	0.140679i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	387.712			1.18930
$327$	177.588	+	177.588i	0.543083	+	0.543083i
$328$	−66.6061	+	66.6061i	−0.203067	+	0.203067i
$329$		−	133.273i		−	0.405087i
$330$		0			0
$331$	−291.939			−0.881990			−0.440995	−	0.897510i	$-0.645374\pi$
$331$	−291.939			−0.881990			−0.440995	+	0.897510i	$0.645374\pi$
$332$	−126.879	−	126.879i	−0.382164	−	0.382164i
$333$	−109.485	+	109.485i	−0.328783	+	0.328783i
$334$		−	335.333i		−	1.00399i
$335$		0			0
$336$	−46.7878			−0.139249
$337$	−266.462	−	266.462i	−0.790688	−	0.790688i	0.190918	−	0.981606i	$-0.438854\pi$
$337$	−266.462	−	266.462i	−0.790688	−	0.790688i	−0.981606	+	0.190918i	$0.938854\pi$
$338$	−30.3633	+	30.3633i	−0.0898321	+	0.0898321i
$339$			32.3633i			0.0954668i
$340$		0			0
$341$	−1016.03			−2.97956
$342$	−101.091	−	101.091i	−0.295587	−	0.295587i
$343$	250.194	−	250.194i	0.729429	−	0.729429i
$344$		−	96.4949i		−	0.280508i
$345$		0			0
$346$	149.666			0.432562
$347$	−141.773	−	141.773i	−0.408568	−	0.408568i	0.472671	−	0.881239i	$-0.343290\pi$
$347$	−141.773	−	141.773i	−0.408568	−	0.408568i	−0.881239	+	0.472671i	$0.843290\pi$
$348$	−21.3031	+	21.3031i	−0.0612157	+	0.0612157i
$349$		−	183.939i		−	0.527045i	−0.964653	−	0.263523i	$-0.915116\pi$
$349$		−	183.939i		−	0.527045i	0.964653	−	0.263523i	$-0.0848844\pi$
$350$		0			0
$351$	61.1816			0.174307
$352$	−82.7878	−	82.7878i	−0.235192	−	0.235192i
$353$	−54.7423	+	54.7423i	−0.155077	+	0.155077i	−0.780381	−	0.625304i	$-0.784975\pi$
$353$	−54.7423	+	54.7423i	−0.155077	+	0.155077i	0.625304	+	0.780381i	$0.284975\pi$
$354$		−	73.4847i		−	0.207584i
$355$		0			0
$356$	−34.7878			−0.0977184
$357$	−15.7730	−	15.7730i	−0.0441820	−	0.0441820i
$358$	−229.151	+	229.151i	−0.640087	+	0.640087i
$359$			648.272i			1.80577i	0.429879	+	0.902886i	$0.358556\pi$
$359$			648.272i			1.80577i	−0.429879	+	0.902886i	$0.641444\pi$
$360$		0			0
$361$	−774.484			−2.14538
$362$	−135.182	−	135.182i	−0.373430	−	0.373430i
$363$	376.442	−	376.442i	1.03703	−	1.03703i
$364$		−	159.031i		−	0.436897i
$365$		0			0
$366$	−117.056			−0.319824
$367$	−56.6594	−	56.6594i	−0.154385	−	0.154385i	0.625688	−	0.780073i	$-0.284818\pi$
$367$	−56.6594	−	56.6594i	−0.154385	−	0.154385i	−0.780073	+	0.625688i	$0.784818\pi$
$368$	64.1816	−	64.1816i	0.174407	−	0.174407i
$369$		−	99.9092i		−	0.270757i
$370$		0			0
$371$	567.242			1.52895
$372$	−120.247	−	120.247i	−0.323246	−	0.323246i
$373$	−155.815	+	155.815i	−0.417735	+	0.417735i	−0.884422	−	0.466688i	$-0.845447\pi$
$373$	−155.815	+	155.815i	−0.417735	+	0.417735i	0.466688	+	0.884422i	$0.345447\pi$
$374$		−	55.8184i		−	0.149247i
$375$		0			0
$376$	55.8184			0.148453
$377$	−72.4087	−	72.4087i	−0.192065	−	0.192065i
$378$	35.0908	−	35.0908i	0.0928328	−	0.0928328i
$379$			674.181i			1.77884i	0.457090	+	0.889420i	$0.348892\pi$
$379$			674.181i			1.77884i	−0.457090	+	0.889420i	$0.651108\pi$
$380$		0			0
$381$	−124.182			−0.325936
$382$	−21.9092	−	21.9092i	−0.0573539	−	0.0573539i
$383$	244.182	−	244.182i	0.637550	−	0.637550i	−0.312401	−	0.949950i	$-0.601133\pi$
$383$	244.182	−	244.182i	0.637550	−	0.637550i	0.949950	+	0.312401i	$0.101133\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−196.974			−0.510295
$387$	72.3712	+	72.3712i	0.187006	+	0.187006i
$388$	−83.7526	+	83.7526i	−0.215857	+	0.215857i
$389$			44.7582i			0.115060i	0.998344	+	0.0575298i	$0.0183224\pi$
$389$			44.7582i			0.115060i	−0.998344	+	0.0575298i	$0.981678\pi$
$390$		0			0
$391$	43.2735			0.110674
$392$	6.78775	+	6.78775i	0.0173157	+	0.0173157i
$393$	−191.394	+	191.394i	−0.487007	+	0.487007i
$394$			126.879i			0.322027i
$395$		0			0
$396$	124.182			0.313590
$397$	548.648	+	548.648i	1.38199	+	1.38199i	0.841090	+	0.540896i	$0.181915\pi$
$397$	548.648	+	548.648i	1.38199	+	1.38199i	0.540896	+	0.841090i	$0.318085\pi$
$398$	181.091	−	181.091i	0.455002	−	0.455002i
$399$		−	394.151i		−	0.987847i
$400$		0			0
$401$	273.303			0.681554			0.340777	−	0.940144i	$-0.389310\pi$
$401$	273.303			0.681554			0.340777	+	0.940144i	$0.389310\pi$
$402$	41.6969	+	41.6969i	0.103724	+	0.103724i
$403$	408.719	−	408.719i	1.01419	−	1.01419i
$404$			325.757i			0.806330i
$405$		0			0
$406$	−83.0602			−0.204582
$407$	−755.333	−	755.333i	−1.85585	−	1.85585i
$408$	6.60612	−	6.60612i	0.0161915	−	0.0161915i
$409$		−	197.182i		−	0.482107i	−0.970512	−	0.241053i	$-0.922507\pi$
$409$		−	197.182i		−	0.482107i	0.970512	−	0.241053i	$-0.0774929\pi$
$410$		0			0
$411$	−223.757			−0.544421
$412$	−73.9796	−	73.9796i	−0.179562	−	0.179562i
$413$	143.258	−	143.258i	0.346871	−	0.346871i
$414$			96.2724i			0.232542i
$415$		0			0
$416$	66.6061			0.160111
$417$	−43.1260	−	43.1260i	−0.103420	−	0.103420i
$418$	697.423	−	697.423i	1.66848	−	1.66848i
$419$			613.485i			1.46416i	0.681217	+	0.732082i	$0.261451\pi$
$419$			613.485i			1.46416i	−0.681217	+	0.732082i	$0.738549\pi$
$420$		0			0
$421$	128.120			0.304324			0.152162	−	0.988356i	$-0.451376\pi$
$421$	128.120			0.304324			0.152162	+	0.988356i	$0.451376\pi$
$422$	28.7276	+	28.7276i	0.0680748	+	0.0680748i
$423$	−41.8638	+	41.8638i	−0.0989687	+	0.0989687i
$424$			237.576i			0.560320i
$425$		0			0
$426$	−22.7878			−0.0534924
$427$	−228.199	−	228.199i	−0.534423	−	0.534423i
$428$	−268.182	+	268.182i	−0.626593	+	0.626593i
$429$			422.091i			0.983895i
$430$		0			0
$431$	−393.242			−0.912394			−0.456197	−	0.889879i	$-0.650789\pi$
$431$	−393.242			−0.912394			−0.456197	+	0.889879i	$0.650789\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	221.381	−	221.381i	0.511273	−	0.511273i	−0.403643	−	0.914917i	$-0.632256\pi$
$433$	221.381	−	221.381i	0.511273	−	0.511273i	0.914917	+	0.403643i	$0.132256\pi$
$434$		−	468.842i		−	1.08028i
$435$		0			0
$436$	−290.000			−0.665138
$437$	540.681	+	540.681i	1.23726	+	1.23726i
$438$	54.6061	−	54.6061i	0.124672	−	0.124672i
$439$		−	361.091i		−	0.822530i	−0.911516	−	0.411265i	$-0.865087\pi$
$439$		−	361.091i		−	0.822530i	0.911516	−	0.411265i	$-0.134913\pi$
$440$		0			0
$441$	−10.1816			−0.0230876
$442$	22.4541	+	22.4541i	0.0508011	+	0.0508011i
$443$	−440.636	+	440.636i	−0.994663	+	0.994663i	−0.999986	−	0.00532284i	$-0.998306\pi$
$443$	−440.636	+	440.636i	−0.994663	+	0.994663i	0.00532284	+	0.999986i	$0.498306\pi$
$444$		−	178.788i		−	0.402675i
$445$		0			0
$446$	−66.3587			−0.148786
$447$	−5.86378	−	5.86378i	−0.0131181	−	0.0131181i
$448$	38.2020	−	38.2020i	0.0852724	−	0.0852724i
$449$		−	280.849i		−	0.625499i	−0.949836	−	0.312749i	$-0.898750\pi$
$449$		−	280.849i		−	0.625499i	0.949836	−	0.312749i	$-0.101250\pi$
$450$		0			0
$451$	689.271			1.52832
$452$	−26.4245	−	26.4245i	−0.0584613	−	0.0584613i
$453$	46.3916	−	46.3916i	0.102410	−	0.102410i
$454$		−	505.757i		−	1.11400i
$455$		0			0
$456$	165.081			0.362019
$457$	−261.576	−	261.576i	−0.572375	−	0.572375i	0.360416	−	0.932792i	$-0.382635\pi$
$457$	−261.576	−	261.576i	−0.572375	−	0.572375i	−0.932792	+	0.360416i	$0.882635\pi$
$458$	−275.000	+	275.000i	−0.600437	+	0.600437i
$459$			9.90918i			0.0215886i
$460$		0			0
$461$	−9.30306			−0.0201802			−0.0100901	−	0.999949i	$-0.503212\pi$
$461$	−9.30306			−0.0201802			−0.0100901	+	0.999949i	$0.503212\pi$
$462$	242.091	+	242.091i	0.524006	+	0.524006i
$463$	−252.495	+	252.495i	−0.545345	+	0.545345i	−0.925091	−	0.379746i	$-0.876012\pi$
$463$	−252.495	+	252.495i	−0.545345	+	0.545345i	0.379746	+	0.925091i	$0.376012\pi$
$464$		−	34.7878i		−	0.0749736i
$465$		0			0
$466$	447.514			0.960331
$467$	366.470	+	366.470i	0.784732	+	0.784732i	0.980625	−	0.195893i	$-0.0627606\pi$
$467$	366.470	+	366.470i	0.784732	+	0.784732i	−0.195893	+	0.980625i	$0.562761\pi$
$468$	−49.9546	+	49.9546i	−0.106741	+	0.106741i
$469$			162.576i			0.346643i
$470$		0			0
$471$	−71.3633			−0.151514
$472$	60.0000	+	60.0000i	0.127119	+	0.127119i
$473$	−499.287	+	499.287i	−1.05558	+	1.05558i
$474$			67.1010i			0.141563i
$475$		0			0
$476$	25.7571			0.0541116
$477$	−178.182	−	178.182i	−0.373546	−	0.373546i
$478$	−305.666	+	305.666i	−0.639469	+	0.639469i
$479$		−	442.182i		−	0.923135i	−0.887105	−	0.461567i	$-0.847287\pi$
$479$		−	442.182i		−	0.923135i	0.887105	−	0.461567i	$-0.152713\pi$
$480$		0			0
$481$	607.696			1.26340
$482$	167.000	+	167.000i	0.346473	+	0.346473i
$483$	−187.682	+	187.682i	−0.388576	+	0.388576i
$484$			614.727i			1.27010i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	100.083	+	100.083i	0.205509	+	0.205509i	0.802355	−	0.596846i	$-0.203580\pi$
$487$	100.083	+	100.083i	0.205509	+	0.205509i	−0.596846	+	0.802355i	$0.703580\pi$
$488$	95.5755	−	95.5755i	0.195851	−	0.195851i
$489$		−	474.848i		−	0.971059i
$490$		0			0
$491$	286.788			0.584089			0.292045	−	0.956405i	$-0.405664\pi$
$491$	286.788			0.584089			0.292045	+	0.956405i	$0.405664\pi$
$492$	81.5755	+	81.5755i	0.165804	+	0.165804i
$493$	11.7276	−	11.7276i	0.0237881	−	0.0237881i
$494$			561.106i			1.13584i
$495$		0			0
$496$	196.363			0.395894
$497$	−44.4245	−	44.4245i	−0.0893853	−	0.0893853i
$498$	−155.394	+	155.394i	−0.312036	+	0.312036i
$499$			82.3643i			0.165059i	0.996589	+	0.0825294i	$0.0262998\pi$
$499$			82.3643i			0.165059i	−0.996589	+	0.0825294i	$0.973700\pi$
$500$		0			0
$501$	−410.697			−0.819754
$502$	261.576	+	261.576i	0.521067	+	0.521067i
$503$	219.848	−	219.848i	0.437073	−	0.437073i	−0.453952	−	0.891026i	$-0.649986\pi$
$503$	219.848	−	219.848i	0.437073	−	0.437073i	0.891026	+	0.453952i	$0.149986\pi$
$504$			57.3031i			0.113697i
$505$		0			0
$506$	−664.182			−1.31261
$507$	37.1872	+	37.1872i	0.0733476	+	0.0733476i
$508$	101.394	−	101.394i	0.199594	−	0.199594i
$509$		−	805.696i		−	1.58290i	−0.611234	−	0.791450i	$-0.709327\pi$
$509$		−	805.696i		−	1.58290i	0.611234	−	0.791450i	$-0.290673\pi$
$510$		0			0
$511$	212.908			0.416650
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−123.810	+	123.810i	−0.241346	+	0.241346i
$514$			189.031i			0.367764i
$515$		0			0
$516$	−118.182			−0.229034
$517$	−288.817	−	288.817i	−0.558641	−	0.558641i
$518$	348.545	−	348.545i	0.672867	−	0.672867i
$519$		−	183.303i		−	0.353185i
$520$		0			0
$521$	372.879			0.715698			0.357849	−	0.933779i	$-0.383510\pi$
$521$	372.879			0.715698			0.357849	+	0.933779i	$0.383510\pi$
$522$	26.0908	+	26.0908i	0.0499824	+	0.0499824i
$523$	56.1395	−	56.1395i	0.107341	−	0.107341i	−0.651396	−	0.758738i	$-0.725816\pi$
$523$	56.1395	−	56.1395i	0.107341	−	0.107341i	0.758738	+	0.651396i	$0.225816\pi$
$524$		−	312.545i		−	0.596460i
$525$		0			0
$526$	68.3633			0.129968
$527$	66.1975	+	66.1975i	0.125612	+	0.125612i
$528$	−101.394	+	101.394i	−0.192034	+	0.192034i
$529$			14.0898i			0.0266348i
$530$		0			0
$531$	−90.0000			−0.169492
$532$	321.823	+	321.823i	0.604930	+	0.604930i
$533$	−277.273	+	277.273i	−0.520213	+	0.520213i
$534$			42.6061i			0.0797867i
$535$		0			0
$536$	−68.0908			−0.127035
$537$	280.652	+	280.652i	0.522629	+	0.522629i
$538$	−389.605	+	389.605i	−0.724173	+	0.724173i
$539$		−	70.2429i		−	0.130321i
$540$		0			0
$541$	633.120			1.17028			0.585139	−	0.810933i	$-0.301040\pi$
$541$	633.120			1.17028			0.585139	+	0.810933i	$0.301040\pi$
$542$	156.788	+	156.788i	0.289276	+	0.289276i
$543$	−165.563	+	165.563i	−0.304904	+	0.304904i
$544$			10.7878i			0.0198304i
$545$		0			0
$546$	−194.772			−0.356725
$547$	32.0408	+	32.0408i	0.0585755	+	0.0585755i	0.735788	−	0.677212i	$-0.236812\pi$
$547$	32.0408	+	32.0408i	0.0585755	+	0.0585755i	−0.677212	+	0.735788i	$0.736812\pi$
$548$	182.697	−	182.697i	0.333389	−	0.333389i
$549$			143.363i			0.261135i
$550$		0			0
$551$	293.060			0.531870
$552$	−78.6061	−	78.6061i	−0.142402	−	0.142402i
$553$	−130.813	+	130.813i	−0.236551	+	0.236551i
$554$			571.176i			1.03100i
$555$		0			0
$556$	70.4245			0.126663
$557$	701.741	+	701.741i	1.25986	+	1.25986i	0.951160	+	0.308699i	$0.0998936\pi$
$557$	701.741	+	701.741i	1.25986	+	1.25986i	0.308699	+	0.951160i	$0.400106\pi$
$558$	−147.272	+	147.272i	−0.263929	+	0.263929i
$559$		−	401.697i		−	0.718599i
$560$		0			0
$561$	−68.3633			−0.121860
$562$	−20.1520	−	20.1520i	−0.0358577	−	0.0358577i
$563$	−265.621	+	265.621i	−0.471796	+	0.471796i	−0.902495	−	0.430700i	$-0.858267\pi$
$563$	−265.621	+	265.621i	−0.471796	+	0.471796i	0.430700	+	0.902495i	$0.358267\pi$
$564$		−	68.3633i		−	0.121211i
$565$		0			0
$566$	−341.146			−0.602732
$567$	−42.9773	−	42.9773i	−0.0757977	−	0.0757977i
$568$	18.6061	−	18.6061i	0.0327573	−	0.0327573i
$569$		−	946.999i		−	1.66432i	−0.554534	−	0.832161i	$-0.687104\pi$
$569$		−	946.999i		−	1.66432i	0.554534	−	0.832161i	$-0.312896\pi$
$570$		0			0
$571$	−337.334			−0.590777			−0.295389	−	0.955377i	$-0.595449\pi$
$571$	−337.334			−0.590777			−0.295389	+	0.955377i	$0.595449\pi$
$572$	−344.636	−	344.636i	−0.602510	−	0.602510i
$573$	−26.8332	+	26.8332i	−0.0468293	+	0.0468293i
$574$			318.061i			0.554114i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	−325.547	−	325.547i	−0.564207	−	0.564207i	0.366293	−	0.930500i	$-0.380627\pi$
$577$	−325.547	−	325.547i	−0.564207	−	0.564207i	−0.930500	+	0.366293i	$0.880627\pi$
$578$	285.363	−	285.363i	0.493708	−	0.493708i
$579$			241.243i			0.416654i
$580$		0			0
$581$	−605.878			−1.04282
$582$	102.576	+	102.576i	0.176247	+	0.176247i
$583$	1229.27	−	1229.27i	2.10853	−	2.10853i
$584$			89.1714i			0.152691i
$585$		0			0
$586$	519.242			0.886078
$587$	381.514	+	381.514i	0.649939	+	0.649939i	0.952978	−	0.303039i	$-0.0980012\pi$
$587$	381.514	+	381.514i	0.649939	+	0.649939i	−0.303039	+	0.952978i	$0.598001\pi$
$588$	8.31327	−	8.31327i	0.0141382	−	0.0141382i
$589$			1654.21i			2.80851i
$590$		0			0
$591$	155.394			0.262934
$592$	145.980	+	145.980i	0.246587	+	0.246587i
$593$	200.697	−	200.697i	0.338443	−	0.338443i	−0.517338	−	0.855781i	$-0.673077\pi$
$593$	200.697	−	200.697i	0.338443	−	0.338443i	0.855781	+	0.517338i	$0.173077\pi$
$594$		−	152.091i		−	0.256045i
$595$		0			0
$596$	9.57551			0.0160663
$597$	−221.790	−	221.790i	−0.371508	−	0.371508i
$598$	267.181	−	267.181i	0.446790	−	0.446790i
$599$		−	112.182i		−	0.187282i	−0.995606	−	0.0936408i	$-0.970149\pi$
$599$		−	112.182i		−	0.187282i	0.995606	−	0.0936408i	$-0.0298505\pi$
$600$		0			0
$601$	−59.5449			−0.0990764			−0.0495382	−	0.998772i	$-0.515775\pi$
$601$	−59.5449			−0.0990764			−0.0495382	+	0.998772i	$0.515775\pi$
$602$	−230.394	−	230.394i	−0.382714	−	0.382714i
$603$	51.0681	−	51.0681i	0.0846901	−	0.0846901i
$604$			75.7571i			0.125426i
$605$		0			0
$606$	398.969			0.658365
$607$	−406.070	−	406.070i	−0.668979	−	0.668979i	0.288500	−	0.957480i	$-0.406843\pi$
$607$	−406.070	−	406.070i	−0.668979	−	0.668979i	−0.957480	+	0.288500i	$0.906843\pi$
$608$	−134.788	+	134.788i	−0.221690	+	0.221690i
$609$			101.728i			0.167040i
$610$		0			0
$611$	232.365			0.380303
$612$	−8.09082	−	8.09082i	−0.0132203	−	0.0132203i
$613$	−81.7480	+	81.7480i	−0.133357	+	0.133357i	−0.770635	−	0.637277i	$-0.780061\pi$
$613$	−81.7480	+	81.7480i	−0.133357	+	0.133357i	0.637277	+	0.770635i	$0.280061\pi$
$614$			237.823i			0.387334i
$615$		0			0
$616$	−395.333			−0.641774
$617$	−734.636	−	734.636i	−1.19066	−	1.19066i	−0.976883	−	0.213775i	$-0.931424\pi$
$617$	−734.636	−	734.636i	−1.19066	−	1.19066i	−0.213775	−	0.976883i	$-0.568576\pi$
$618$	−90.6061	+	90.6061i	−0.146612	+	0.146612i
$619$		−	266.303i		−	0.430215i	−0.976590	−	0.215107i	$-0.930990\pi$
$619$		−	266.303i		−	0.430215i	0.976590	−	0.215107i	$-0.0690102\pi$
$620$		0			0
$621$	117.909			0.189870
$622$	−52.7878	−	52.7878i	−0.0848678	−	0.0848678i
$623$	−83.0602	+	83.0602i	−0.133323	+	0.133323i
$624$		−	81.5755i		−	0.130730i
$625$		0			0
$626$	−477.106			−0.762150
$627$	−854.166	−	854.166i	−1.36231	−	1.36231i
$628$	58.2679	−	58.2679i	0.0927832	−	0.0927832i
$629$			98.4245i			0.156478i
$630$		0			0
$631$	456.546			0.723528			0.361764	−	0.932270i	$-0.382175\pi$
$631$	456.546			0.723528			0.361764	+	0.932270i	$0.382175\pi$
$632$	−54.7878	−	54.7878i	−0.0866895	−	0.0866895i
$633$	35.1839	−	35.1839i	0.0555828	−	0.0555828i
$634$		−	97.8796i		−	0.154384i
$635$		0			0
$636$	290.969			0.457499
$637$	28.2566	+	28.2566i	0.0443589	+	0.0443589i
$638$	−180.000	+	180.000i	−0.282132	+	0.282132i
$639$			27.9092i			0.0436763i
$640$		0			0
$641$	538.120			0.839501			0.419751	−	0.907639i	$-0.362118\pi$
$641$	538.120			0.839501			0.419751	+	0.907639i	$0.362118\pi$
$642$	328.454	+	328.454i	0.511611	+	0.511611i
$643$	31.5459	−	31.5459i	0.0490605	−	0.0490605i	−0.682151	−	0.731211i	$-0.738955\pi$
$643$	31.5459	−	31.5459i	0.0490605	−	0.0490605i	0.731211	+	0.682151i	$0.238955\pi$
$644$		−	306.484i		−	0.475906i
$645$		0			0
$646$	−90.8786			−0.140679
$647$	−112.849	−	112.849i	−0.174419	−	0.174419i	0.614499	−	0.788918i	$-0.289358\pi$
$647$	−112.849	−	112.849i	−0.174419	−	0.174419i	−0.788918	+	0.614499i	$0.789358\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	620.908i		−	0.956715i
$650$		0			0
$651$	−574.212			−0.882046
$652$	387.712	+	387.712i	0.594650	+	0.594650i
$653$	491.803	−	491.803i	0.753143	−	0.753143i	−0.221921	−	0.975065i	$-0.571233\pi$
$653$	491.803	−	491.803i	0.753143	−	0.753143i	0.975065	+	0.221921i	$0.0712328\pi$
$654$			355.176i			0.543083i
$655$		0			0
$656$	−133.212			−0.203067
$657$	−66.8786	−	66.8786i	−0.101794	−	0.101794i
$658$	133.273	−	133.273i	0.202543	−	0.202543i
$659$			471.787i			0.715913i	0.933738	+	0.357957i	$0.116526\pi$
$659$			471.787i			0.715913i	−0.933738	+	0.357957i	$0.883474\pi$
$660$		0			0
$661$	−897.151			−1.35726			−0.678632	−	0.734479i	$-0.737427\pi$
$661$	−897.151			−1.35726			−0.678632	+	0.734479i	$0.737427\pi$
$662$	−291.939	−	291.939i	−0.440995	−	0.440995i
$663$	27.5005	−	27.5005i	0.0414789	−	0.0414789i
$664$		−	253.757i		−	0.382164i
$665$		0			0
$666$	−218.969			−0.328783
$667$	−139.546	−	139.546i	−0.209214	−	0.209214i
$668$	335.333	−	335.333i	0.501995	−	0.501995i
$669$			81.2724i			0.121483i
$670$		0			0
$671$	−989.060			−1.47401
$672$	−46.7878	−	46.7878i	−0.0696246	−	0.0696246i
$673$	−105.526	+	105.526i	−0.156799	+	0.156799i	−0.781146	−	0.624348i	$-0.785365\pi$
$673$	−105.526	+	105.526i	−0.156799	+	0.156799i	0.624348	+	0.781146i	$0.285365\pi$
$674$		−	532.924i		−	0.790688i
$675$		0			0
$676$	−60.7265			−0.0898321
$677$	−547.015	−	547.015i	−0.807998	−	0.807998i	0.176332	−	0.984331i	$-0.443577\pi$
$677$	−547.015	−	547.015i	−0.807998	−	0.807998i	−0.984331	+	0.176332i	$0.943577\pi$
$678$	−32.3633	+	32.3633i	−0.0477334	+	0.0477334i
$679$			399.940i			0.589013i
$680$		0			0
$681$	−619.423			−0.909579
$682$	−1016.03	−	1016.03i	−1.48978	−	1.48978i
$683$	−533.271	+	533.271i	−0.780778	+	0.780778i	−0.979962	−	0.199184i	$-0.936171\pi$
$683$	−533.271	+	533.271i	−0.780778	+	0.780778i	0.199184	+	0.979962i	$0.436171\pi$
$684$		−	202.182i		−	0.295587i
$685$		0			0
$686$	500.388			0.729429
$687$	336.805	+	336.805i	0.490254	+	0.490254i
$688$	96.4949	−	96.4949i	0.140254	−	0.140254i
$689$			988.999i			1.43541i
$690$		0			0
$691$	−1191.09			−1.72372			−0.861859	−	0.507147i	$-0.830700\pi$
$691$	−1191.09			−1.72372			−0.861859	+	0.507147i	$0.830700\pi$
$692$	149.666	+	149.666i	0.216281	+	0.216281i
$693$	296.499	−	296.499i	0.427849	−	0.427849i
$694$		−	283.546i		−	0.408568i
$695$		0			0
$696$	−42.6061			−0.0612157
$697$	−44.9082	−	44.9082i	−0.0644306	−	0.0644306i
$698$	183.939	−	183.939i	0.263523	−	0.263523i
$699$		−	548.091i		−	0.784107i
$700$		0			0
$701$	717.242			1.02317			0.511585	−	0.859233i	$-0.329059\pi$
$701$	717.242			1.02317			0.511585	+	0.859233i	$0.329059\pi$
$702$	61.1816	+	61.1816i	0.0871533	+	0.0871533i
$703$	−1229.77	+	1229.77i	−1.74931	+	1.74931i
$704$		−	165.576i		−	0.235192i
$705$		0			0
$706$	−109.485			−0.155077
$707$	777.787	+	777.787i	1.10012	+	1.10012i
$708$	73.4847	−	73.4847i	0.103792	−	0.103792i
$709$		−	148.514i		−	0.209470i	−0.994500	−	0.104735i	$-0.966601\pi$
$709$		−	148.514i		−	0.209470i	0.994500	−	0.104735i	$-0.0333994\pi$
$710$		0			0
$711$	82.1816			0.115586
$712$	−34.7878	−	34.7878i	−0.0488592	−	0.0488592i
$713$	787.682	−	787.682i	1.10474	−	1.10474i
$714$		−	31.5459i		−	0.0441820i
$715$		0			0
$716$	−458.302			−0.640087
$717$	374.363	+	374.363i	0.522124	+	0.522124i
$718$	−648.272	+	648.272i	−0.902886	+	0.902886i
$719$			43.4847i			0.0604794i	0.999543	+	0.0302397i	$0.00962706\pi$
$719$			43.4847i			0.0604794i	−0.999543	+	0.0302397i	$0.990373\pi$
$720$		0			0
$721$	−353.271			−0.489974
$722$	−774.484	−	774.484i	−1.07269	−	1.07269i
$723$	204.532	−	204.532i	0.282894	−	0.282894i
$724$		−	270.363i		−	0.373430i
$725$		0			0
$726$	752.883			1.03703
$727$	817.608	+	817.608i	1.12463	+	1.12463i	0.991036	+	0.133598i	$0.0426530\pi$
$727$	817.608	+	817.608i	1.12463	+	1.12463i	0.133598	+	0.991036i	$0.457347\pi$
$728$	159.031	−	159.031i	0.218449	−	0.218449i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	65.0602			0.0890016
$732$	−117.056	−	117.056i	−0.159912	−	0.159912i
$733$	842.030	−	842.030i	1.14874	−	1.14874i	0.161944	−	0.986800i	$-0.448223\pi$
$733$	842.030	−	842.030i	1.14874	−	1.14874i	0.986800	−	0.161944i	$-0.0517765\pi$
$734$		−	113.319i		−	0.154385i
$735$		0			0
$736$	128.363			0.174407
$737$	352.318	+	352.318i	0.478043	+	0.478043i
$738$	99.9092	−	99.9092i	0.135378	−	0.135378i
$739$		−	406.545i		−	0.550128i	−0.961426	−	0.275064i	$-0.911301\pi$
$739$		−	406.545i		−	0.550128i	0.961426	−	0.275064i	$-0.0886991\pi$
$740$		0			0
$741$	687.211			0.927411
$742$	567.242	+	567.242i	0.764477	+	0.764477i
$743$	−394.515	+	394.515i	−0.530976	+	0.530976i	−0.920863	−	0.389887i	$-0.872514\pi$
$743$	−394.515	+	394.515i	−0.530976	+	0.530976i	0.389887	+	0.920863i	$0.372514\pi$
$744$		−	240.495i		−	0.323246i
$745$		0			0
$746$	−311.630			−0.417735
$747$	190.318	+	190.318i	0.254776	+	0.254776i
$748$	55.8184	−	55.8184i	0.0746235	−	0.0746235i
$749$			1280.64i			1.70979i
$750$		0			0
$751$	−612.788			−0.815962			−0.407981	−	0.912990i	$-0.633767\pi$
$751$	−612.788			−0.815962			−0.407981	+	0.912990i	$0.633767\pi$
$752$	55.8184	+	55.8184i	0.0742266	+	0.0742266i
$753$	320.363	−	320.363i	0.425449	−	0.425449i
$754$		−	144.817i		−	0.192065i
$755$		0			0
$756$	70.1816			0.0928328
$757$	181.547	+	181.547i	0.239825	+	0.239825i	0.816777	−	0.576953i	$-0.195758\pi$
$757$	181.547	+	181.547i	0.239825	+	0.239825i	−0.576953	+	0.816777i	$0.695758\pi$
$758$	−674.181	+	674.181i	−0.889420	+	0.889420i
$759$			813.453i			1.07174i
$760$		0			0
$761$	497.271			0.653445			0.326722	−	0.945120i	$-0.394056\pi$
$761$	497.271			0.653445			0.326722	+	0.945120i	$0.394056\pi$
$762$	−124.182	−	124.182i	−0.162968	−	0.162968i
$763$	−692.412	+	692.412i	−0.907486	+	0.907486i
$764$		−	43.8184i		−	0.0573539i
$765$		0			0
$766$	488.363			0.637550
$767$	249.773	+	249.773i	0.325649	+	0.325649i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	220.271i		−	0.286439i	−0.989691	−	0.143219i	$-0.954255\pi$
$769$		−	220.271i		−	0.286439i	0.989691	−	0.143219i	$-0.0457455\pi$
$770$		0			0
$771$	231.514			0.300278
$772$	−196.974	−	196.974i	−0.255148	−	0.255148i
$773$	−917.605	+	917.605i	−1.18707	+	1.18707i	−0.209196	+	0.977874i	$0.567085\pi$
$773$	−917.605	+	917.605i	−1.18707	+	1.18707i	−0.977874	+	0.209196i	$0.932915\pi$
$774$			144.742i			0.187006i
$775$		0			0
$776$	−167.505			−0.215857
$777$	−426.879	−	426.879i	−0.549393	−	0.549393i
$778$	−44.7582	+	44.7582i	−0.0575298	+	0.0575298i
$779$		−	1122.21i		−	1.44058i
$780$		0			0
$781$	−192.545			−0.246536
$782$	43.2735	+	43.2735i	0.0553369	+	0.0553369i
$783$	31.9546	−	31.9546i	0.0408105	−	0.0408105i
$784$			13.5755i			0.0173157i
$785$		0			0
$786$	−382.788			−0.487007
$787$	−862.194	−	862.194i	−1.09555	−	1.09555i	−0.994925	−	0.100620i	$-0.967917\pi$
$787$	−862.194	−	862.194i	−1.09555	−	1.09555i	−0.100620	−	0.994925i	$-0.532083\pi$
$788$	−126.879	+	126.879i	−0.161013	+	0.161013i
$789$		−	83.7276i		−	0.106119i
$790$		0			0
$791$	−126.184			−0.159524
$792$	124.182	+	124.182i	0.156795	+	0.156795i
$793$	397.870	−	397.870i	0.501727	−	0.501727i
$794$			1097.30i			1.38199i
$795$		0			0
$796$	362.182			0.455002
$797$	175.818	+	175.818i	0.220600	+	0.220600i	0.808751	−	0.588151i	$-0.200144\pi$
$797$	175.818	+	175.818i	0.220600	+	0.220600i	−0.588151	+	0.808751i	$0.700144\pi$
$798$	394.151	−	394.151i	0.493924	−	0.493924i
$799$			37.6347i			0.0471022i
$800$		0			0
$801$	52.1816			0.0651456
$802$	273.303	+	273.303i	0.340777	+	0.340777i
$803$	461.394	−	461.394i	0.574588	−	0.574588i
$804$			83.3939i			0.103724i
$805$		0			0
$806$	817.437			1.01419
$807$	477.167	+	477.167i	0.591285	+	0.591285i
$808$	−325.757	+	325.757i	−0.403165	+	0.403165i
$809$			828.272i			1.02382i	0.859038	+	0.511911i	$0.171062\pi$
$809$			828.272i			1.02382i	−0.859038	+	0.511911i	$0.828938\pi$
$810$		0			0
$811$	−116.909			−0.144154			−0.0720772	−	0.997399i	$-0.522963\pi$
$811$	−116.909			−0.144154			−0.0720772	+	0.997399i	$0.522963\pi$
$812$	−83.0602	−	83.0602i	−0.102291	−	0.102291i
$813$	192.025	−	192.025i	0.236193	−	0.236193i
$814$		−	1510.67i		−	1.85585i
$815$		0			0
$816$	13.2122			0.0161915
$817$	812.896	+	812.896i	0.994976	+	0.994976i
$818$	197.182	−	197.182i	0.241053	−	0.241053i
$819$			238.546i			0.291265i
$820$		0			0
$821$	632.424			0.770310			0.385155	−	0.922852i	$-0.374148\pi$
$821$	632.424			0.770310			0.385155	+	0.922852i	$0.374148\pi$
$822$	−223.757	−	223.757i	−0.272211	−	0.272211i
$823$	−1028.81	+	1028.81i	−1.25007	+	1.25007i	−0.294385	+	0.955687i	$0.595115\pi$
$823$	−1028.81	+	1028.81i	−1.25007	+	1.25007i	−0.955687	+	0.294385i	$0.904885\pi$
$824$		−	147.959i		−	0.179562i
$825$		0			0
$826$	286.515			0.346871
$827$	−348.061	−	348.061i	−0.420872	−	0.420872i	0.464632	−	0.885504i	$-0.346187\pi$
$827$	−348.061	−	348.061i	−0.420872	−	0.420872i	−0.885504	+	0.464632i	$0.846187\pi$
$828$	−96.2724	+	96.2724i	−0.116271	+	0.116271i
$829$		−	901.392i		−	1.08732i	−0.839304	−	0.543662i	$-0.817037\pi$
$829$		−	901.392i		−	1.08732i	0.839304	−	0.543662i	$-0.182963\pi$
$830$		0			0
$831$	699.545			0.841811
$832$	66.6061	+	66.6061i	0.0800554	+	0.0800554i
$833$	−4.57654	+	4.57654i	−0.00549404	+	0.00549404i
$834$		−	86.2520i		−	0.103420i
$835$		0			0
$836$	1394.85			1.66848
$837$	180.371	+	180.371i	0.215497	+	0.215497i
$838$	−613.485	+	613.485i	−0.732082	+	0.732082i
$839$		−	99.1806i		−	0.118213i	−0.998252	−	0.0591064i	$-0.981175\pi$
$839$		−	99.1806i		−	0.118213i	0.998252	−	0.0591064i	$-0.0188251\pi$
$840$		0			0
$841$	765.363			0.910063
$842$	128.120	+	128.120i	0.152162	+	0.152162i
$843$	−24.6811	+	24.6811i	−0.0292777	+	0.0292777i
$844$			57.4551i			0.0680748i
$845$		0			0
$846$	−83.7276			−0.0989687
$847$	1467.74	+	1467.74i	1.73287	+	1.73287i
$848$	−237.576	+	237.576i	−0.280160	+	0.280160i
$849$			417.817i			0.492129i
$850$		0			0
$851$	1171.15			1.37621
$852$	−22.7878	−	22.7878i	−0.0267462	−	0.0267462i
$853$	662.612	−	662.612i	0.776802	−	0.776802i	−0.202484	−	0.979286i	$-0.564901\pi$
$853$	662.612	−	662.612i	0.776802	−	0.776802i	0.979286	+	0.202484i	$0.0649013\pi$
$854$		−	456.397i		−	0.534423i
$855$		0			0
$856$	−536.363			−0.626593
$857$	487.546	+	487.546i	0.568898	+	0.568898i	0.931820	−	0.362921i	$-0.118221\pi$
$857$	487.546	+	487.546i	0.568898	+	0.568898i	−0.362921	+	0.931820i	$0.618221\pi$
$858$	−422.091	+	422.091i	−0.491947	+	0.491947i
$859$			110.849i			0.129044i	0.997916	+	0.0645221i	$0.0205523\pi$
$859$			110.849i			0.129044i	−0.997916	+	0.0645221i	$0.979448\pi$
$860$		0			0
$861$	389.544			0.452432
$862$	−393.242	−	393.242i	−0.456197	−	0.456197i
$863$	917.271	−	917.271i	1.06289	−	1.06289i	0.0650018	−	0.997885i	$-0.479295\pi$
$863$	917.271	−	917.271i	1.06289	−	1.06289i	0.997885	−	0.0650018i	$-0.0207053\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	442.763			0.511273
$867$	−349.497	−	349.497i	−0.403111	−	0.403111i
$868$	468.842	−	468.842i	0.540141	−	0.540141i
$869$			566.969i			0.652439i
$870$		0			0
$871$	−283.454			−0.325435
$872$	−290.000	−	290.000i	−0.332569	−	0.332569i
$873$	125.629	−	125.629i	0.143905	−	0.143905i
$874$			1081.36i			1.23726i
$875$		0			0
$876$	109.212			0.124672
$877$	−53.7538	−	53.7538i	−0.0612928	−	0.0612928i	0.675796	−	0.737089i	$-0.263800\pi$
$877$	−53.7538	−	53.7538i	−0.0612928	−	0.0612928i	−0.737089	+	0.675796i	$0.763800\pi$
$878$	361.091	−	361.091i	0.411265	−	0.411265i
$879$		−	635.939i		−	0.723480i
$880$		0			0
$881$	648.545			0.736146			0.368073	−	0.929797i	$-0.380018\pi$
$881$	648.545			0.736146			0.368073	+	0.929797i	$0.380018\pi$
$882$	−10.1816	−	10.1816i	−0.0115438	−	0.0115438i
$883$	191.381	−	191.381i	0.216740	−	0.216740i	−0.590383	−	0.807123i	$-0.701023\pi$
$883$	191.381	−	191.381i	0.216740	−	0.216740i	0.807123	+	0.590383i	$0.201023\pi$
$884$			44.9082i			0.0508011i
$885$		0			0
$886$	−881.271			−0.994663
$887$	−468.347	−	468.347i	−0.528013	−	0.528013i	0.391967	−	0.919979i	$-0.371795\pi$
$887$	−468.347	−	468.347i	−0.528013	−	0.528013i	−0.919979	+	0.391967i	$0.871795\pi$
$888$	178.788	−	178.788i	0.201338	−	0.201338i
$889$		−	484.182i		−	0.544636i
$890$		0			0
$891$	−186.272			−0.209060
$892$	−66.3587	−	66.3587i	−0.0743931	−	0.0743931i
$893$	−470.227	+	470.227i	−0.526570	+	0.526570i
$894$		−	11.7276i		−	0.0131181i
$895$		0			0
$896$	76.4041			0.0852724
$897$	−327.228	−	327.228i	−0.364803	−	0.364803i
$898$	280.849	−	280.849i	0.312749	−	0.312749i
$899$		−	426.940i		−	0.474905i
$900$		0			0
$901$	−160.182			−0.177782
$902$	689.271	+	689.271i	0.764159	+	0.764159i
$903$	−282.174	+	282.174i	−0.312485	+	0.312485i
$904$		−	52.8490i		−	0.0584613i
$905$		0			0
$906$	92.7832			0.102410
$907$	−359.160	−	359.160i	−0.395987	−	0.395987i	0.480828	−	0.876815i	$-0.340336\pi$
$907$	−359.160	−	359.160i	−0.395987	−	0.395987i	−0.876815	+	0.480828i	$0.840336\pi$
$908$	505.757	−	505.757i	0.557001	−	0.557001i
$909$		−	488.636i		−	0.537553i
$910$		0			0
$911$	−1698.00			−1.86389			−0.931943	−	0.362605i	$-0.881887\pi$
$911$	−1698.00			−1.86389			−0.931943	+	0.362605i	$0.881887\pi$
$912$	165.081	+	165.081i	0.181009	+	0.181009i
$913$	−1313.00	+	1313.00i	−1.43811	+	1.43811i
$914$		−	523.151i		−	0.572375i
$915$		0			0
$916$	−550.000			−0.600437
$917$	−746.241	−	746.241i	−0.813785	−	0.813785i
$918$	−9.90918	+	9.90918i	−0.0107943	+	0.0107943i
$919$			316.728i			0.344644i	0.985041	+	0.172322i	$0.0551269\pi$
$919$			316.728i			0.344644i	−0.985041	+	0.172322i	$0.944873\pi$
$920$		0			0
$921$	291.272			0.316257
$922$	−9.30306	−	9.30306i	−0.0100901	−	0.0100901i
$923$	77.4551	−	77.4551i	0.0839167	−	0.0839167i
$924$			484.182i			0.524006i
$925$		0			0
$926$	−504.990			−0.545345
$927$	110.969	+	110.969i	0.119708	+	0.119708i
$928$	34.7878	−	34.7878i	0.0374868	−	0.0374868i
$929$		−	123.426i		−	0.132858i	−0.997791	−	0.0664292i	$-0.978839\pi$
$929$		−	123.426i		−	0.132858i	0.997791	−	0.0664292i	$-0.0211607\pi$
$930$		0			0
$931$	−114.363			−0.122839
$932$	447.514	+	447.514i	0.480166	+	0.480166i
$933$	−64.6515	+	64.6515i	−0.0692942	+	0.0692942i
$934$			732.940i			0.784732i
$935$		0			0
$936$	−99.9092			−0.106741
$937$	−261.513	−	261.513i	−0.279096	−	0.279096i	0.553652	−	0.832748i	$-0.313234\pi$
$937$	−261.513	−	261.513i	−0.279096	−	0.279096i	−0.832748	+	0.553652i	$0.813234\pi$
$938$	−162.576	+	162.576i	−0.173321	+	0.173321i
$939$			584.333i			0.622292i
$940$		0			0
$941$	−942.422			−1.00151			−0.500756	−	0.865589i	$-0.666945\pi$
$941$	−942.422			−1.00151			−0.500756	+	0.865589i	$0.666945\pi$
$942$	−71.3633	−	71.3633i	−0.0757572	−	0.0757572i
$943$	−534.361	+	534.361i	−0.566661	+	0.566661i
$944$			120.000i			0.127119i
$945$		0			0
$946$	−998.574			−1.05558
$947$	986.983	+	986.983i	1.04222	+	1.04222i	0.999069	+	0.0431523i	$0.0137401\pi$
$947$	986.983	+	986.983i	1.04222	+	1.04222i	0.0431523	+	0.999069i	$0.486260\pi$
$948$	−67.1010	+	67.1010i	−0.0707817	+	0.0707817i
$949$			371.210i			0.391159i
$950$		0			0
$951$	−119.878			−0.126054
$952$	25.7571	+	25.7571i	0.0270558	+	0.0270558i
$953$	112.454	−	112.454i	0.118000	−	0.118000i	−0.645641	−	0.763641i	$-0.723410\pi$
$953$	112.454	−	112.454i	0.118000	−	0.118000i	0.763641	+	0.645641i	$0.223410\pi$
$954$		−	356.363i		−	0.373546i
$955$		0			0
$956$	−611.333			−0.639469
$957$	220.454	+	220.454i	0.230360	+	0.230360i
$958$	442.182	−	442.182i	0.461567	−	0.461567i
$959$		−	872.424i		−	0.909723i
$960$		0			0
$961$	1448.91			1.50771
$962$	607.696	+	607.696i	0.631701	+	0.631701i
$963$	402.272	−	402.272i	0.417728	−	0.417728i
$964$			334.000i			0.346473i
$965$		0			0
$966$	−375.364			−0.388576
$967$	−700.009	−	700.009i	−0.723898	−	0.723898i	0.245499	−	0.969397i	$-0.421048\pi$
$967$	−700.009	−	700.009i	−0.723898	−	0.723898i	−0.969397	+	0.245499i	$0.921048\pi$
$968$	−614.727	+	614.727i	−0.635048	+	0.635048i
$969$			111.303i			0.114864i
$970$		0			0
$971$	−1450.18			−1.49349			−0.746746	−	0.665109i	$-0.768385\pi$
$971$	−1450.18			−1.49349			−0.746746	+	0.665109i	$0.768385\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	168.147	−	168.147i	0.172813	−	0.172813i
$974$			200.166i			0.205509i
$975$		0			0
$976$	191.151			0.195851
$977$	−1146.14	−	1146.14i	−1.17312	−	1.17312i	−0.981462	−	0.191656i	$-0.938614\pi$
$977$	−1146.14	−	1146.14i	−1.17312	−	1.17312i	−0.191656	−	0.981462i	$-0.561386\pi$
$978$	474.848	−	474.848i	0.485530	−	0.485530i
$979$			360.000i			0.367722i
$980$		0			0
$981$	435.000			0.443425
$982$	286.788	+	286.788i	0.292045	+	0.292045i
$983$	760.332	−	760.332i	0.773481	−	0.773481i	−0.205232	−	0.978713i	$-0.565795\pi$
$983$	760.332	−	760.332i	0.773481	−	0.773481i	0.978713	+	0.205232i	$0.0657950\pi$
$984$			163.151i			0.165804i
$985$		0			0
$986$	23.4551			0.0237881
$987$	−163.226	−	163.226i	−0.165376	−	0.165376i
$988$	−561.106	+	561.106i	−0.567921	+	0.567921i
$989$		−	774.150i		−	0.782760i
$990$		0			0
$991$	−222.605			−0.224627			−0.112313	−	0.993673i	$-0.535826\pi$
$991$	−222.605			−0.224627			−0.112313	+	0.993673i	$0.535826\pi$
$992$	196.363	+	196.363i	0.197947	+	0.197947i
$993$	−357.551	+	357.551i	−0.360071	+	0.360071i
$994$		−	88.8490i		−	0.0893853i
$995$		0			0
$996$	−310.788			−0.312036
$997$	−467.183	−	467.183i	−0.468588	−	0.468588i	0.432869	−	0.901457i	$-0.357501\pi$
$997$	−467.183	−	467.183i	−0.468588	−	0.468588i	−0.901457	+	0.432869i	$0.857501\pi$
$998$	−82.3643	+	82.3643i	−0.0825294	+	0.0825294i
$999$			268.182i			0.268450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.f.c.7.2	yes	4
3.2	odd	2		450.3.g.g.307.1		4
4.3	odd	2		1200.3.bg.a.1057.1		4
5.2	odd	4		150.3.f.a.43.1	yes	4
5.3	odd	4	inner	150.3.f.c.43.2	yes	4
5.4	even	2		150.3.f.a.7.1	✓	4
15.2	even	4		450.3.g.h.343.2		4
15.8	even	4		450.3.g.g.343.1		4
15.14	odd	2		450.3.g.h.307.2		4
20.3	even	4		1200.3.bg.a.193.1		4
20.7	even	4		1200.3.bg.p.193.2		4
20.19	odd	2		1200.3.bg.p.1057.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.f.a.7.1	✓	4	5.4	even	2
150.3.f.a.43.1	yes	4	5.2	odd	4
150.3.f.c.7.2	yes	4	1.1	even	1	trivial
150.3.f.c.43.2	yes	4	5.3	odd	4	inner
450.3.g.g.307.1		4	3.2	odd	2
450.3.g.g.343.1		4	15.8	even	4
450.3.g.h.307.2		4	15.14	odd	2
450.3.g.h.343.2		4	15.2	even	4
1200.3.bg.a.193.1		4	20.3	even	4
1200.3.bg.a.1057.1		4	4.3	odd	2
1200.3.bg.p.193.2		4	20.7	even	4
1200.3.bg.p.1057.2		4	20.19	odd	2

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(4.77526 + 4.77526i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(4.77526 + 4.77526i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +20.6969 q^{11} +(2.44949 + 2.44949i) q^{12} +(-8.32577 + 8.32577i) q^{13} +9.55051i q^{14} -4.00000 q^{16} +(-1.34847 - 1.34847i) q^{17} +(3.00000 - 3.00000i) q^{18} -33.6969i q^{19} +11.6969 q^{21} +(20.6969 + 20.6969i) q^{22} +(-16.0454 + 16.0454i) q^{23} +4.89898i q^{24} -16.6515 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-9.55051 + 9.55051i) q^{28} +8.69694i q^{29} -49.0908 q^{31} +(-4.00000 - 4.00000i) q^{32} +(25.3485 - 25.3485i) q^{33} -2.69694i q^{34} +6.00000 q^{36} +(-36.4949 - 36.4949i) q^{37} +(33.6969 - 33.6969i) q^{38} +20.3939i q^{39} +33.3031 q^{41} +(11.6969 + 11.6969i) q^{42} +(-24.1237 + 24.1237i) q^{43} +41.3939i q^{44} -32.0908 q^{46} +(-13.9546 - 13.9546i) q^{47} +(-4.89898 + 4.89898i) q^{48} -3.39388i q^{49} -3.30306 q^{51} +(-16.6515 - 16.6515i) q^{52} +(59.3939 - 59.3939i) q^{53} -7.34847i q^{54} -19.1010 q^{56} +(-41.2702 - 41.2702i) q^{57} +(-8.69694 + 8.69694i) q^{58} -30.0000i q^{59} -47.7878 q^{61} +(-49.0908 - 49.0908i) q^{62} +(14.3258 - 14.3258i) q^{63} -8.00000i q^{64} +50.6969 q^{66} +(17.0227 + 17.0227i) q^{67} +(2.69694 - 2.69694i) q^{68} +39.3031i q^{69} -9.30306 q^{71} +(6.00000 + 6.00000i) q^{72} +(22.2929 - 22.2929i) q^{73} -72.9898i q^{74} +67.3939 q^{76} +(98.8332 + 98.8332i) q^{77} +(-20.3939 + 20.3939i) q^{78} +27.3939i q^{79} -9.00000 q^{81} +(33.3031 + 33.3031i) q^{82} +(-63.4393 + 63.4393i) q^{83} +23.3939i q^{84} -48.2474 q^{86} +(10.6515 + 10.6515i) q^{87} +(-41.3939 + 41.3939i) q^{88} +17.3939i q^{89} -79.5153 q^{91} +(-32.0908 - 32.0908i) q^{92} +(-60.1237 + 60.1237i) q^{93} -27.9092i q^{94} -9.79796 q^{96} +(41.8763 + 41.8763i) q^{97} +(3.39388 - 3.39388i) q^{98} -62.0908i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 24 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 24 * q^7 - 8 * q^8	\( 4 q + 4 q^{2} + 24 q^{7} - 8 q^{8} + 24 q^{11} - 48 q^{13} - 16 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{21} + 24 q^{22} + 24 q^{23} - 96 q^{26} - 48 q^{28} - 20 q^{31} - 16 q^{32} + 72 q^{33} + 24 q^{36} - 48 q^{37} + 76 q^{38} + 192 q^{41} - 12 q^{42} - 72 q^{43} + 48 q^{46} - 144 q^{47} - 72 q^{51} - 96 q^{52} + 120 q^{53} - 96 q^{56} - 72 q^{57} + 24 q^{58} + 44 q^{61} - 20 q^{62} + 72 q^{63} + 144 q^{66} + 24 q^{67} - 48 q^{68} - 96 q^{71} + 24 q^{72} - 48 q^{73} + 152 q^{76} + 72 q^{77} + 36 q^{78} - 36 q^{81} + 192 q^{82} - 48 q^{83} - 144 q^{86} + 72 q^{87} - 48 q^{88} - 612 q^{91} + 48 q^{92} - 216 q^{93} + 192 q^{97} - 104 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 24 * q^7 - 8 * q^8 + 24 * q^11 - 48 * q^13 - 16 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^21 + 24 * q^22 + 24 * q^23 - 96 * q^26 - 48 * q^28 - 20 * q^31 - 16 * q^32 + 72 * q^33 + 24 * q^36 - 48 * q^37 + 76 * q^38 + 192 * q^41 - 12 * q^42 - 72 * q^43 + 48 * q^46 - 144 * q^47 - 72 * q^51 - 96 * q^52 + 120 * q^53 - 96 * q^56 - 72 * q^57 + 24 * q^58 + 44 * q^61 - 20 * q^62 + 72 * q^63 + 144 * q^66 + 24 * q^67 - 48 * q^68 - 96 * q^71 + 24 * q^72 - 48 * q^73 + 152 * q^76 + 72 * q^77 + 36 * q^78 - 36 * q^81 + 192 * q^82 - 48 * q^83 - 144 * q^86 + 72 * q^87 - 48 * q^88 - 612 * q^91 + 48 * q^92 - 216 * q^93 + 192 * q^97 - 104 * q^98

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