LMFDB - Embedded newform 180.3.c.a.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, 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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.2
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.3.c.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618034 + 1.90211i) q^{2} +(-3.23607 - 2.35114i) q^{4} +2.23607 q^{5} +5.25731i q^{7} +(6.47214 - 4.70228i) q^{8} +O(q^{10})$	\(q+(-0.618034 + 1.90211i) q^{2} +(-3.23607 - 2.35114i) q^{4} +2.23607 q^{5} +5.25731i q^{7} +(6.47214 - 4.70228i) q^{8} +(-1.38197 + 4.25325i) q^{10} +19.9192i q^{11} -8.47214 q^{13} +(-10.0000 - 3.24920i) q^{14} +(4.94427 + 15.2169i) q^{16} -11.8885 q^{17} +15.2169i q^{19} +(-7.23607 - 5.25731i) q^{20} +(-37.8885 - 12.3107i) q^{22} -0.555029i q^{23} +5.00000 q^{25} +(5.23607 - 16.1150i) q^{26} +(12.3607 - 17.0130i) q^{28} +10.9443 q^{29} +8.29451i q^{31} -32.0000 q^{32} +(7.34752 - 22.6134i) q^{34} +11.7557i q^{35} -18.3607 q^{37} +(-28.9443 - 9.40456i) q^{38} +(14.4721 - 10.5146i) q^{40} +14.5836 q^{41} -22.2703i q^{43} +(46.8328 - 64.4598i) q^{44} +(1.05573 + 0.343027i) q^{46} +53.3902i q^{47} +21.3607 q^{49} +(-3.09017 + 9.51057i) q^{50} +(27.4164 + 19.9192i) q^{52} +66.3607 q^{53} +44.5407i q^{55} +(24.7214 + 34.0260i) q^{56} +(-6.76393 + 20.8172i) q^{58} +17.4370i q^{59} +90.1378 q^{61} +(-15.7771 - 5.12629i) q^{62} +(19.7771 - 60.8676i) q^{64} -18.9443 q^{65} -50.2220i q^{67} +(38.4721 + 27.9516i) q^{68} +(-22.3607 - 7.26543i) q^{70} -80.7868i q^{71} -5.55418 q^{73} +(11.3475 - 34.9241i) q^{74} +(35.7771 - 49.2429i) q^{76} -104.721 q^{77} +13.8448i q^{79} +(11.0557 + 34.0260i) q^{80} +(-9.01316 + 27.7396i) q^{82} -76.2155i q^{83} -26.5836 q^{85} +(42.3607 + 13.7638i) q^{86} +(93.6656 + 128.920i) q^{88} +111.443 q^{89} -44.5407i q^{91} +(-1.30495 + 1.79611i) q^{92} +(-101.554 - 32.9970i) q^{94} +34.0260i q^{95} -92.8328 q^{97} +(-13.2016 + 40.6304i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8	$ 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 10 q^{10} - 16 q^{13} - 40 q^{14} - 16 q^{16} + 24 q^{17} - 20 q^{20} - 80 q^{22} + 20 q^{25} + 12 q^{26} - 40 q^{28} + 8 q^{29} - 128 q^{32} + 92 q^{34} + 16 q^{37} - 80 q^{38} + 40 q^{40} + 112 q^{41} + 80 q^{44} + 40 q^{46} - 4 q^{49} + 10 q^{50} + 56 q^{52} + 176 q^{53} - 80 q^{56} - 36 q^{58} + 128 q^{61} + 80 q^{62} - 64 q^{64} - 40 q^{65} + 136 q^{68} + 264 q^{73} + 108 q^{74} - 240 q^{77} + 80 q^{80} + 116 q^{82} - 160 q^{85} + 80 q^{86} + 160 q^{88} + 88 q^{89} + 120 q^{92} - 120 q^{94} - 264 q^{97} - 102 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 10 * q^10 - 16 * q^13 - 40 * q^14 - 16 * q^16 + 24 * q^17 - 20 * q^20 - 80 * q^22 + 20 * q^25 + 12 * q^26 - 40 * q^28 + 8 * q^29 - 128 * q^32 + 92 * q^34 + 16 * q^37 - 80 * q^38 + 40 * q^40 + 112 * q^41 + 80 * q^44 + 40 * q^46 - 4 * q^49 + 10 * q^50 + 56 * q^52 + 176 * q^53 - 80 * q^56 - 36 * q^58 + 128 * q^61 + 80 * q^62 - 64 * q^64 - 40 * q^65 + 136 * q^68 + 264 * q^73 + 108 * q^74 - 240 * q^77 + 80 * q^80 + 116 * q^82 - 160 * q^85 + 80 * q^86 + 160 * q^88 + 88 * q^89 + 120 * q^92 - 120 * q^94 - 264 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.618034	+	1.90211i	−0.309017	+	0.951057i
$2$	−0.618034	+	1.90211i	−0.309017	+	0.951057i
$3$		0			0
$3$		0			0
$4$	−3.23607	−	2.35114i	−0.809017	−	0.587785i
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$		0			0
$7$			5.25731i			0.751044i	0.926813	+	0.375522i	$0.122537\pi$
$7$			5.25731i			0.751044i	−0.926813	+	0.375522i	$0.877463\pi$
$8$	6.47214	−	4.70228i	0.809017	−	0.587785i
$9$		0			0
$10$	−1.38197	+	4.25325i	−0.138197	+	0.425325i
$11$			19.9192i			1.81084i	0.424522	+	0.905418i	$0.360442\pi$
$11$			19.9192i			1.81084i	−0.424522	+	0.905418i	$0.639558\pi$
$12$		0			0
$13$	−8.47214			−0.651703			−0.325851	−	0.945421i	$-0.605651\pi$
$13$	−8.47214			−0.651703			−0.325851	+	0.945421i	$0.605651\pi$
$14$	−10.0000	−	3.24920i	−0.714286	−	0.232085i
$15$		0			0
$16$	4.94427	+	15.2169i	0.309017	+	0.951057i
$17$	−11.8885			−0.699326			−0.349663	−	0.936876i	$-0.613704\pi$
$17$	−11.8885			−0.699326			−0.349663	+	0.936876i	$0.613704\pi$
$18$		0			0
$19$			15.2169i			0.800890i	0.916321	+	0.400445i	$0.131144\pi$
$19$			15.2169i			0.800890i	−0.916321	+	0.400445i	$0.868856\pi$
$20$	−7.23607	−	5.25731i	−0.361803	−	0.262866i
$21$		0			0
$22$	−37.8885	−	12.3107i	−1.72221	−	0.559579i
$23$		−	0.555029i		−	0.0241317i	−0.999927	−	0.0120659i	$-0.996159\pi$
$23$		−	0.555029i		−	0.0241317i	0.999927	−	0.0120659i	$-0.00384077\pi$
$24$		0			0
$25$	5.00000			0.200000
$26$	5.23607	−	16.1150i	0.201387	−	0.619806i
$27$		0			0
$28$	12.3607	−	17.0130i	0.441453	−	0.607608i
$29$	10.9443			0.377389			0.188694	−	0.982036i	$-0.439574\pi$
$29$	10.9443			0.377389			0.188694	+	0.982036i	$0.439574\pi$
$30$		0			0
$31$			8.29451i			0.267565i	0.991011	+	0.133782i	$0.0427123\pi$
$31$			8.29451i			0.267565i	−0.991011	+	0.133782i	$0.957288\pi$
$32$	−32.0000			−1.00000
$33$		0			0
$34$	7.34752	−	22.6134i	0.216104	−	0.665099i
$35$			11.7557i			0.335877i
$36$		0			0
$37$	−18.3607			−0.496235			−0.248117	−	0.968730i	$-0.579812\pi$
$37$	−18.3607			−0.496235			−0.248117	+	0.968730i	$0.579812\pi$
$38$	−28.9443	−	9.40456i	−0.761691	−	0.247489i
$39$		0			0
$40$	14.4721	−	10.5146i	0.361803	−	0.262866i
$41$	14.5836			0.355697			0.177849	−	0.984058i	$-0.443086\pi$
$41$	14.5836			0.355697			0.177849	+	0.984058i	$0.443086\pi$
$42$		0			0
$43$		−	22.2703i		−	0.517915i	−0.965889	−	0.258957i	$-0.916621\pi$
$43$		−	22.2703i		−	0.517915i	0.965889	−	0.258957i	$-0.0833789\pi$
$44$	46.8328	−	64.4598i	1.06438	−	1.46500i
$45$		0			0
$46$	1.05573	+	0.343027i	0.0229506	+	0.00745711i
$47$			53.3902i			1.13596i	0.823042	+	0.567981i	$0.192275\pi$
$47$			53.3902i			1.13596i	−0.823042	+	0.567981i	$0.807725\pi$
$48$		0			0
$49$	21.3607			0.435932
$50$	−3.09017	+	9.51057i	−0.0618034	+	0.190211i
$51$		0			0
$52$	27.4164	+	19.9192i	0.527239	+	0.383061i
$53$	66.3607			1.25209			0.626044	−	0.779788i	$-0.284673\pi$
$53$	66.3607			1.25209			0.626044	+	0.779788i	$0.284673\pi$
$54$		0			0
$55$			44.5407i			0.809830i
$56$	24.7214	+	34.0260i	0.441453	+	0.607608i
$57$		0			0
$58$	−6.76393	+	20.8172i	−0.116620	+	0.358918i
$59$			17.4370i			0.295543i	0.989022	+	0.147771i	$0.0472100\pi$
$59$			17.4370i			0.295543i	−0.989022	+	0.147771i	$0.952790\pi$
$60$		0			0
$61$	90.1378			1.47767			0.738834	−	0.673887i	$-0.235377\pi$
$61$	90.1378			1.47767			0.738834	+	0.673887i	$0.235377\pi$
$62$	−15.7771	−	5.12629i	−0.254469	−	0.0826820i
$63$		0			0
$64$	19.7771	−	60.8676i	0.309017	−	0.951057i
$65$	−18.9443			−0.291450
$66$		0			0
$67$		−	50.2220i		−	0.749582i	−0.927109	−	0.374791i	$-0.877715\pi$
$67$		−	50.2220i		−	0.749582i	0.927109	−	0.374791i	$-0.122285\pi$
$68$	38.4721	+	27.9516i	0.565767	+	0.411054i
$69$		0			0
$70$	−22.3607	−	7.26543i	−0.319438	−	0.103792i
$71$		−	80.7868i		−	1.13784i	−0.822392	−	0.568921i	$-0.807361\pi$
$71$		−	80.7868i		−	1.13784i	0.822392	−	0.568921i	$-0.192639\pi$
$72$		0			0
$73$	−5.55418			−0.0760846			−0.0380423	−	0.999276i	$-0.512112\pi$
$73$	−5.55418			−0.0760846			−0.0380423	+	0.999276i	$0.512112\pi$
$74$	11.3475	−	34.9241i	0.153345	−	0.471947i
$75$		0			0
$76$	35.7771	−	49.2429i	0.470751	−	0.647933i
$77$	−104.721			−1.36002
$78$		0			0
$79$			13.8448i			0.175251i	0.996154	+	0.0876253i	$0.0279278\pi$
$79$			13.8448i			0.175251i	−0.996154	+	0.0876253i	$0.972072\pi$
$80$	11.0557	+	34.0260i	0.138197	+	0.425325i
$81$		0			0
$82$	−9.01316	+	27.7396i	−0.109917	+	0.338288i
$83$		−	76.2155i		−	0.918260i	−0.888369	−	0.459130i	$-0.848161\pi$
$83$		−	76.2155i		−	0.918260i	0.888369	−	0.459130i	$-0.151839\pi$
$84$		0			0
$85$	−26.5836			−0.312748
$86$	42.3607	+	13.7638i	0.492566	+	0.160044i
$87$		0			0
$88$	93.6656	+	128.920i	1.06438	+	1.46500i
$89$	111.443			1.25217			0.626083	−	0.779757i	$-0.284657\pi$
$89$	111.443			1.25217			0.626083	+	0.779757i	$0.284657\pi$
$90$		0			0
$91$		−	44.5407i		−	0.489458i
$92$	−1.30495	+	1.79611i	−0.0141843	+	0.0195230i
$93$		0			0
$94$	−101.554	−	32.9970i	−1.08036	−	0.351031i
$95$			34.0260i			0.358169i
$96$		0			0
$97$	−92.8328			−0.957039			−0.478520	−	0.878077i	$-0.658826\pi$
$97$	−92.8328			−0.957039			−0.478520	+	0.878077i	$0.658826\pi$
$98$	−13.2016	+	40.6304i	−0.134710	+	0.414596i
$99$		0			0
$100$	−16.1803	−	11.7557i	−0.161803	−	0.117557i
$101$	−64.1115			−0.634767			−0.317383	−	0.948297i	$-0.602804\pi$
$101$	−64.1115			−0.634767			−0.317383	+	0.948297i	$0.602804\pi$
$102$		0			0
$103$		−	137.769i		−	1.33757i	−0.743458	−	0.668783i	$-0.766816\pi$
$103$		−	137.769i		−	1.33757i	0.743458	−	0.668783i	$-0.233184\pi$
$104$	−54.8328	+	39.8384i	−0.527239	+	0.383061i
$105$		0			0
$106$	−41.0132	+	126.226i	−0.386917	+	1.19081i
$107$		−	51.3320i		−	0.479739i	−0.970805	−	0.239869i	$-0.922895\pi$
$107$		−	51.3320i		−	0.479739i	0.970805	−	0.239869i	$-0.0771046\pi$
$108$		0			0
$109$	133.469			1.22449			0.612243	−	0.790669i	$-0.290267\pi$
$109$	133.469			1.22449			0.612243	+	0.790669i	$0.290267\pi$
$110$	−84.7214	−	27.5276i	−0.770194	−	0.250251i
$111$		0			0
$112$	−80.0000	+	25.9936i	−0.714286	+	0.232085i
$113$	−170.721			−1.51081			−0.755404	−	0.655259i	$-0.772559\pi$
$113$	−170.721			−1.51081			−0.755404	+	0.655259i	$0.772559\pi$
$114$		0			0
$115$		−	1.24108i		−	0.0107920i
$116$	−35.4164	−	25.7315i	−0.305314	−	0.221824i
$117$		0			0
$118$	−33.1672	−	10.7767i	−0.281078	−	0.0913277i
$119$		−	62.5018i		−	0.525225i
$120$		0			0
$121$	−275.774			−2.27912
$122$	−55.7082	+	171.452i	−0.456625	+	1.40535i
$123$		0			0
$124$	19.5016	−	26.8416i	0.157271	−	0.216464i
$125$	11.1803			0.0894427
$126$		0			0
$127$			198.637i			1.56407i	0.623235	+	0.782035i	$0.285818\pi$
$127$			198.637i			1.56407i	−0.623235	+	0.782035i	$0.714182\pi$
$128$	103.554	+	75.2365i	0.809017	+	0.587785i
$129$		0			0
$130$	11.7082	−	36.0341i	0.0900631	−	0.277186i
$131$			7.77041i			0.0593161i	0.999560	+	0.0296580i	$0.00944183\pi$
$131$			7.77041i			0.0593161i	−0.999560	+	0.0296580i	$0.990558\pi$
$132$		0			0
$133$	−80.0000			−0.601504
$134$	95.5279	+	31.0389i	0.712895	+	0.231633i
$135$		0			0
$136$	−76.9443	+	55.9033i	−0.565767	+	0.411054i
$137$	−0.832816			−0.00607895			−0.00303947	−	0.999995i	$-0.500967\pi$
$137$	−0.832816			−0.00607895			−0.00303947	+	0.999995i	$0.500967\pi$
$138$		0			0
$139$			237.658i			1.70977i	0.518817	+	0.854885i	$0.326373\pi$
$139$			237.658i			1.70977i	−0.518817	+	0.854885i	$0.673627\pi$
$140$	27.6393	−	38.0423i	0.197424	−	0.271730i
$141$		0			0
$142$	153.666	+	49.9290i	1.08215	+	0.351613i
$143$		−	168.758i		−	1.18013i
$144$		0			0
$145$	24.4721			0.168773
$146$	3.43267	−	10.5647i	0.0235114	−	0.0723607i
$147$		0			0
$148$	59.4164	+	43.1685i	0.401462	+	0.291679i
$149$	36.9706			0.248125			0.124062	−	0.992274i	$-0.460408\pi$
$149$	36.9706			0.248125			0.124062	+	0.992274i	$0.460408\pi$
$150$		0			0
$151$		−	282.723i		−	1.87234i	−0.351552	−	0.936168i	$-0.614346\pi$
$151$		−	282.723i		−	1.87234i	0.351552	−	0.936168i	$-0.385654\pi$
$152$	71.5542	+	98.4859i	0.470751	+	0.647933i
$153$		0			0
$154$	64.7214	−	199.192i	0.420269	−	1.29345i
$155$			18.5471i			0.119659i
$156$		0			0
$157$	204.748			1.30413			0.652063	−	0.758165i	$-0.273904\pi$
$157$	204.748			1.30413			0.652063	+	0.758165i	$0.273904\pi$
$158$	−26.3344	−	8.55656i	−0.166673	−	0.0541554i
$159$		0			0
$160$	−71.5542			−0.447214
$161$	2.91796			0.0181240
$162$		0			0
$163$		−	107.235i		−	0.657885i	−0.944350	−	0.328943i	$-0.893308\pi$
$163$		−	107.235i		−	0.657885i	0.944350	−	0.328943i	$-0.106692\pi$
$164$	−47.1935	−	34.2881i	−0.287765	−	0.209074i
$165$		0			0
$166$	144.971	+	47.1038i	0.873317	+	0.283758i
$167$			33.2090i			0.198856i	0.995045	+	0.0994280i	$0.0317013\pi$
$167$			33.2090i			0.198856i	−0.995045	+	0.0994280i	$0.968299\pi$
$168$		0			0
$169$	−97.2229			−0.575284
$170$	16.4296	−	50.5650i	0.0966445	−	0.297441i
$171$		0			0
$172$	−52.3607	+	72.0683i	−0.304423	+	0.419002i
$173$	226.361			1.30844			0.654222	−	0.756303i	$-0.272996\pi$
$173$	226.361			1.30844			0.654222	+	0.756303i	$0.272996\pi$
$174$		0			0
$175$			26.2866i			0.150209i
$176$	−303.108	+	98.4859i	−1.72221	+	0.559579i
$177$		0			0
$178$	−68.8754	+	211.977i	−0.386940	+	1.19088i
$179$			224.337i			1.25328i	0.779308	+	0.626641i	$0.215571\pi$
$179$			224.337i			1.25328i	−0.779308	+	0.626641i	$0.784429\pi$
$180$		0			0
$181$	86.2229			0.476370			0.238185	−	0.971220i	$-0.423448\pi$
$181$	86.2229			0.476370			0.238185	+	0.971220i	$0.423448\pi$
$182$	84.7214	+	27.5276i	0.465502	+	0.151251i
$183$		0			0
$184$	−2.60990	−	3.59222i	−0.0141843	−	0.0195230i
$185$	−41.0557			−0.221923
$186$		0			0
$187$		−	236.810i		−	1.26636i
$188$	125.528	−	172.774i	0.667701	−	0.919012i
$189$		0			0
$190$	−64.7214	−	21.0292i	−0.340639	−	0.110680i
$191$		−	31.0198i		−	0.162407i	−0.996698	−	0.0812036i	$-0.974124\pi$
$191$		−	31.0198i		−	0.162407i	0.996698	−	0.0812036i	$-0.0258764\pi$
$192$		0			0
$193$	110.223			0.571103			0.285552	−	0.958363i	$-0.407823\pi$
$193$	110.223			0.571103			0.285552	+	0.958363i	$0.407823\pi$
$194$	57.3738	−	176.579i	0.295741	−	0.910198i
$195$		0			0
$196$	−69.1246	−	50.2220i	−0.352677	−	0.256235i
$197$	172.525			0.875760			0.437880	−	0.899033i	$-0.355729\pi$
$197$	172.525			0.875760			0.437880	+	0.899033i	$0.355729\pi$
$198$		0			0
$199$			272.208i			1.36788i	0.729538	+	0.683940i	$0.239735\pi$
$199$			272.208i			1.36788i	−0.729538	+	0.683940i	$0.760265\pi$
$200$	32.3607	−	23.5114i	0.161803	−	0.117557i
$201$		0			0
$202$	39.6231	−	121.947i	0.196154	−	0.603699i
$203$			57.5374i			0.283436i
$204$		0			0
$205$	32.6099			0.159073
$206$	262.053	+	85.1461i	1.27210	+	0.413330i
$207$		0			0
$208$	−41.8885	−	128.920i	−0.201387	−	0.619806i
$209$	−303.108			−1.45028
$210$		0			0
$211$			205.266i			0.972826i	0.873729	+	0.486413i	$0.161695\pi$
$211$			205.266i			0.972826i	−0.873729	+	0.486413i	$0.838305\pi$
$212$	−214.748	−	156.023i	−1.01296	−	0.735959i
$213$		0			0
$214$	97.6393	+	31.7249i	0.456259	+	0.148247i
$215$		−	49.7980i		−	0.231618i
$216$		0			0
$217$	−43.6068			−0.200953
$218$	−82.4884	+	253.873i	−0.378387	+	1.16456i
$219$		0			0
$220$	104.721	−	144.137i	0.476006	−	0.655166i
$221$	100.721			0.455753
$222$		0			0
$223$		−	235.731i		−	1.05709i	−0.848905	−	0.528545i	$-0.822738\pi$
$223$		−	235.731i		−	1.05709i	0.848905	−	0.528545i	$-0.177262\pi$
$224$		−	168.234i		−	0.751044i
$225$		0			0
$226$	105.512	−	324.731i	0.466865	−	1.43686i
$227$		−	58.5165i		−	0.257782i	−0.991659	−	0.128891i	$-0.958858\pi$
$227$		−	58.5165i		−	0.257782i	0.991659	−	0.128891i	$-0.0411417\pi$
$228$		0			0
$229$	162.721			0.710574			0.355287	−	0.934757i	$-0.384383\pi$
$229$	162.721			0.710574			0.355287	+	0.934757i	$0.384383\pi$
$230$	2.36068	+	0.767031i	0.0102638	+	0.00333492i
$231$		0			0
$232$	70.8328	−	51.4631i	0.305314	−	0.221824i
$233$	−319.050			−1.36931			−0.684656	−	0.728867i	$-0.740047\pi$
$233$	−319.050			−1.36931			−0.684656	+	0.728867i	$0.740047\pi$
$234$		0			0
$235$			119.384i			0.508017i
$236$	40.9969	−	56.4274i	0.173716	−	0.239099i
$237$		0			0
$238$	118.885	+	38.6282i	0.499519	+	0.162303i
$239$			236.810i			0.990837i	0.868654	+	0.495419i	$0.164985\pi$
$239$			236.810i			0.990837i	−0.868654	+	0.495419i	$0.835015\pi$
$240$		0			0
$241$	−0.917961			−0.00380897			−0.00190448	−	0.999998i	$-0.500606\pi$
$241$	−0.917961			−0.00380897			−0.00190448	+	0.999998i	$0.500606\pi$
$242$	170.438	−	524.553i	0.704288	−	2.16758i
$243$		0			0
$244$	−291.692	−	211.927i	−1.19546	−	0.868552i
$245$	47.7639			0.194955
$246$		0			0
$247$		−	128.920i		−	0.521942i
$248$	39.0031	+	53.6832i	0.157271	+	0.216464i
$249$		0			0
$250$	−6.90983	+	21.2663i	−0.0276393	+	0.0850651i
$251$		−	136.690i		−	0.544582i	−0.962215	−	0.272291i	$-0.912219\pi$
$251$		−	136.690i		−	0.544582i	0.962215	−	0.272291i	$-0.0877813\pi$
$252$		0			0
$253$	11.0557			0.0436985
$254$	−377.830	−	122.764i	−1.48752	−	0.483324i
$255$		0			0
$256$	−207.108	+	150.473i	−0.809017	+	0.587785i
$257$	274.944			1.06982			0.534911	−	0.844908i	$-0.320345\pi$
$257$	274.944			1.06982			0.534911	+	0.844908i	$0.320345\pi$
$258$		0			0
$259$		−	96.5278i		−	0.372694i
$260$	61.3050	+	44.5407i	0.235788	+	0.171310i
$261$		0			0
$262$	−14.7802	−	4.80238i	−0.0564130	−	0.0183297i
$263$			406.385i			1.54519i	0.634899	+	0.772596i	$0.281042\pi$
$263$			406.385i			1.54519i	−0.634899	+	0.772596i	$0.718958\pi$
$264$		0			0
$265$	148.387			0.559951
$266$	49.4427	−	152.169i	0.185875	−	0.572064i
$267$		0			0
$268$	−118.079	+	162.522i	−0.440593	+	0.606424i
$269$	348.525			1.29563			0.647816	−	0.761797i	$-0.275683\pi$
$269$	348.525			1.29563			0.647816	+	0.761797i	$0.275683\pi$
$270$		0			0
$271$			247.849i			0.914571i	0.889320	+	0.457286i	$0.151178\pi$
$271$			247.849i			0.914571i	−0.889320	+	0.457286i	$0.848822\pi$
$272$	−58.7802	−	180.907i	−0.216104	−	0.665099i
$273$		0			0
$274$	0.514708	−	1.58411i	0.00187850	−	0.00578142i
$275$			99.5959i			0.362167i
$276$		0			0
$277$	−54.7539			−0.197667			−0.0988337	−	0.995104i	$-0.531511\pi$
$277$	−54.7539			−0.197667			−0.0988337	+	0.995104i	$0.531511\pi$
$278$	−452.053	−	146.881i	−1.62609	−	0.528348i
$279$		0			0
$280$	55.2786	+	76.0845i	0.197424	+	0.271730i
$281$	50.3607			0.179220			0.0896098	−	0.995977i	$-0.471438\pi$
$281$	50.3607			0.179220			0.0896098	+	0.995977i	$0.471438\pi$
$282$		0			0
$283$			147.336i			0.520621i	0.965525	+	0.260310i	$0.0838249\pi$
$283$			147.336i			0.520621i	−0.965525	+	0.260310i	$0.916175\pi$
$284$	−189.941	+	261.432i	−0.668807	+	0.920534i
$285$		0			0
$286$	320.997	+	104.298i	1.12237	+	0.364679i
$287$			76.6705i			0.267145i
$288$		0			0
$289$	−147.663			−0.510943
$290$	−15.1246	+	46.5488i	−0.0521538	+	0.160513i
$291$		0			0
$292$	17.9737	+	13.0586i	0.0615537	+	0.0447214i
$293$	−178.859			−0.610441			−0.305220	−	0.952282i	$-0.598730\pi$
$293$	−178.859			−0.610441			−0.305220	+	0.952282i	$0.598730\pi$
$294$		0			0
$295$			38.9904i			0.132171i
$296$	−118.833	+	86.3371i	−0.401462	+	0.291679i
$297$		0			0
$298$	−22.8491	+	70.3222i	−0.0766748	+	0.235981i
$299$			4.70228i			0.0157267i
$300$		0			0
$301$	117.082			0.388977
$302$	537.771	+	174.732i	1.78070	+	0.578584i
$303$		0			0
$304$	−231.554	+	75.2365i	−0.761691	+	0.247489i
$305$	201.554			0.660833
$306$		0			0
$307$			284.550i			0.926873i	0.886130	+	0.463436i	$0.153384\pi$
$307$			284.550i			0.926873i	−0.886130	+	0.463436i	$0.846616\pi$
$308$	338.885	+	246.215i	1.10028	+	0.799398i
$309$		0			0
$310$	−35.2786	−	11.4627i	−0.113802	−	0.0369765i
$311$			282.199i			0.907392i	0.891157	+	0.453696i	$0.149895\pi$
$311$			282.199i			0.907392i	−0.891157	+	0.453696i	$0.850105\pi$
$312$		0			0
$313$	−567.548			−1.81325			−0.906626	−	0.421935i	$-0.861351\pi$
$313$	−567.548			−1.81325			−0.906626	+	0.421935i	$0.861351\pi$
$314$	−126.541	+	389.453i	−0.402997	+	1.24030i
$315$		0			0
$316$	32.5511	−	44.8027i	0.103010	−	0.141781i
$317$	−161.141			−0.508331			−0.254165	−	0.967161i	$-0.581801\pi$
$317$	−161.141			−0.508331			−0.254165	+	0.967161i	$0.581801\pi$
$318$		0			0
$319$			218.001i			0.683389i
$320$	44.2229	−	136.104i	0.138197	−	0.425325i
$321$		0			0
$322$	−1.80340	+	5.55029i	−0.00560062	+	0.0172369i
$323$		−	180.907i		−	0.560083i
$324$		0			0
$325$	−42.3607			−0.130341
$326$	203.974	+	66.2751i	0.625686	+	0.203298i
$327$		0			0
$328$	94.3870	−	68.5762i	0.287765	−	0.209074i
$329$	−280.689			−0.853158
$330$		0			0
$331$		−	331.966i		−	1.00292i	−0.865181	−	0.501459i	$-0.832797\pi$
$331$		−	331.966i		−	1.00292i	0.865181	−	0.501459i	$-0.167203\pi$
$332$	−179.193	+	246.639i	−0.539739	+	0.742888i
$333$		0			0
$334$	−63.1672	−	20.5243i	−0.189123	−	0.0614499i
$335$		−	112.300i		−	0.335223i
$336$		0			0
$337$	−269.108			−0.798541			−0.399271	−	0.916833i	$-0.630737\pi$
$337$	−269.108			−0.798541			−0.399271	+	0.916833i	$0.630737\pi$
$338$	60.0871	−	184.929i	0.177772	−	0.547127i
$339$		0			0
$340$	86.0263	+	62.5018i	0.253019	+	0.183829i
$341$	−165.220			−0.484516
$342$		0			0
$343$			369.908i			1.07845i
$344$	−104.721	−	144.137i	−0.304423	−	0.419002i
$345$		0			0
$346$	−139.899	+	430.564i	−0.404331	+	1.24440i
$347$		−	503.075i		−	1.44978i	−0.688863	−	0.724892i	$-0.741890\pi$
$347$		−	503.075i		−	1.44978i	0.688863	−	0.724892i	$-0.258110\pi$
$348$		0			0
$349$	−0.504658			−0.00144601			−0.000723006	−	1.00000i	$-0.500230\pi$
$349$	−0.504658			−0.00144601			−0.000723006		1.00000i	$0.500230\pi$
$350$	−50.0000	−	16.2460i	−0.142857	−	0.0464171i
$351$		0			0
$352$		−	637.414i		−	1.81084i
$353$	335.994			0.951824			0.475912	−	0.879493i	$-0.342118\pi$
$353$	335.994			0.951824			0.475912	+	0.879493i	$0.342118\pi$
$354$		0			0
$355$		−	180.645i		−	0.508859i
$356$	−360.636	−	262.018i	−1.01302	−	0.736004i
$357$		0			0
$358$	−426.715	−	138.648i	−1.19194	−	0.387285i
$359$			98.4859i			0.274334i	0.990548	+	0.137167i	$0.0437997\pi$
$359$			98.4859i			0.274334i	−0.990548	+	0.137167i	$0.956200\pi$
$360$		0			0
$361$	129.446			0.358576
$362$	−53.2887	+	164.006i	−0.147206	+	0.453054i
$363$		0			0
$364$	−104.721	+	144.137i	−0.287696	+	0.395980i
$365$	−12.4195			−0.0340261
$366$		0			0
$367$		−	498.473i		−	1.35824i	−0.734029	−	0.679118i	$-0.762362\pi$
$367$		−	498.473i		−	1.35824i	0.734029	−	0.679118i	$-0.237638\pi$
$368$	8.44582	−	2.74421i	0.0229506	−	0.00745711i
$369$		0			0
$370$	25.3738	−	78.0926i	0.0685779	−	0.211061i
$371$			348.879i			0.940374i
$372$		0			0
$373$	600.354			1.60953			0.804765	−	0.593594i	$-0.202291\pi$
$373$	600.354			1.60953			0.804765	+	0.593594i	$0.202291\pi$
$374$	450.440	+	146.357i	1.20438	+	0.391328i
$375$		0			0
$376$	251.056	+	345.549i	0.667701	+	0.919012i
$377$	−92.7214			−0.245945
$378$		0			0
$379$		−	303.490i		−	0.800765i	−0.916348	−	0.400383i	$-0.868877\pi$
$379$		−	303.490i		−	0.800765i	0.916348	−	0.400383i	$-0.131123\pi$
$380$	80.0000	−	110.111i	0.210526	−	0.289765i
$381$		0			0
$382$	59.0031	+	19.1713i	0.154458	+	0.0501866i
$383$		−	332.583i		−	0.868362i	−0.900826	−	0.434181i	$-0.857038\pi$
$383$		−	332.583i		−	0.868362i	0.900826	−	0.434181i	$-0.142962\pi$
$384$		0			0
$385$	−234.164			−0.608218
$386$	−68.1215	+	209.656i	−0.176481	+	0.543151i
$387$		0			0
$388$	300.413	+	218.263i	0.774261	+	0.562534i
$389$	−392.354			−1.00862			−0.504312	−	0.863522i	$-0.668254\pi$
$389$	−392.354			−1.00862			−0.504312	+	0.863522i	$0.668254\pi$
$390$		0			0
$391$			6.59849i			0.0168759i
$392$	138.249	−	100.444i	0.352677	−	0.256235i
$393$		0			0
$394$	−106.626	+	328.162i	−0.270625	+	0.832897i
$395$			30.9579i			0.0783744i
$396$		0			0
$397$	334.190			0.841789			0.420895	−	0.907110i	$-0.361716\pi$
$397$	334.190			0.841789			0.420895	+	0.907110i	$0.361716\pi$
$398$	−517.771	−	168.234i	−1.30093	−	0.422698i
$399$		0			0
$400$	24.7214	+	76.0845i	0.0618034	+	0.190211i
$401$	−121.003			−0.301753			−0.150877	−	0.988553i	$-0.548210\pi$
$401$	−121.003			−0.301753			−0.150877	+	0.988553i	$0.548210\pi$
$402$		0			0
$403$		−	70.2722i		−	0.174373i
$404$	207.469	+	150.735i	0.513537	+	0.373107i
$405$		0			0
$406$	−109.443	−	35.5601i	−0.269563	−	0.0875864i
$407$		−	365.730i		−	0.898599i
$408$		0			0
$409$	−607.410			−1.48511			−0.742555	−	0.669785i	$-0.766386\pi$
$409$	−607.410			−1.48511			−0.742555	+	0.669785i	$0.766386\pi$
$410$	−20.1540	+	62.0277i	−0.0491562	+	0.151287i
$411$		0			0
$412$	−323.915	+	445.831i	−0.786201	+	1.08211i
$413$	−91.6718			−0.221966
$414$		0			0
$415$		−	170.423i		−	0.410658i
$416$	271.108			0.651703
$417$		0			0
$418$	187.331	−	576.546i	0.448161	−	1.37930i
$419$		−	466.760i		−	1.11398i	−0.830518	−	0.556992i	$-0.811955\pi$
$419$		−	466.760i		−	1.11398i	0.830518	−	0.556992i	$-0.188045\pi$
$420$		0			0
$421$	−73.0883			−0.173606			−0.0868031	−	0.996225i	$-0.527665\pi$
$421$	−73.0883			−0.173606			−0.0868031	+	0.996225i	$0.527665\pi$
$422$	−390.440	−	126.862i	−0.925212	−	0.300620i
$423$		0			0
$424$	429.495	−	312.047i	1.01296	−	0.735959i
$425$	−59.4427			−0.139865
$426$		0			0
$427$			473.882i			1.10979i
$428$	−120.689	+	166.114i	−0.281983	+	0.388117i
$429$		0			0
$430$	94.7214	+	30.7768i	0.220282	+	0.0715740i
$431$		−	463.630i		−	1.07571i	−0.843038	−	0.537853i	$-0.819235\pi$
$431$		−	463.630i		−	1.07571i	0.843038	−	0.537853i	$-0.180765\pi$
$432$		0			0
$433$	−99.8359			−0.230568			−0.115284	−	0.993333i	$-0.536778\pi$
$433$	−99.8359			−0.230568			−0.115284	+	0.993333i	$0.536778\pi$
$434$	26.9505	−	82.9451i	0.0620979	−	0.191118i
$435$		0			0
$436$	−431.915	−	313.805i	−0.990630	−	0.719735i
$437$	8.44582			0.0193268
$438$		0			0
$439$		−	374.086i		−	0.852133i	−0.904692	−	0.426066i	$-0.859899\pi$
$439$		−	374.086i		−	0.852133i	0.904692	−	0.426066i	$-0.140101\pi$
$440$	209.443	+	288.273i	0.476006	+	0.655166i
$441$		0			0
$442$	−62.2492	+	191.583i	−0.140835	+	0.433447i
$443$		−	290.100i		−	0.654854i	−0.944877	−	0.327427i	$-0.893818\pi$
$443$		−	290.100i		−	0.654854i	0.944877	−	0.327427i	$-0.106182\pi$
$444$		0			0
$445$	249.193			0.559985
$446$	448.387	+	145.690i	1.00535	+	0.326659i
$447$		0			0
$448$	320.000	+	103.974i	0.714286	+	0.232085i
$449$	−299.921			−0.667976			−0.333988	−	0.942577i	$-0.608394\pi$
$449$	−299.921			−0.667976			−0.333988	+	0.942577i	$0.608394\pi$
$450$		0			0
$451$			290.493i			0.644109i
$452$	552.466	+	401.390i	1.22227	+	0.888031i
$453$		0			0
$454$	111.305	+	36.1652i	0.245165	+	0.0796590i
$455$		−	99.5959i		−	0.218892i
$456$		0			0
$457$	822.328			1.79941			0.899703	−	0.436503i	$-0.143783\pi$
$457$	822.328			1.79941			0.899703	+	0.436503i	$0.143783\pi$
$458$	−100.567	+	309.514i	−0.219579	+	0.675796i
$459$		0			0
$460$	−2.91796	+	4.01623i	−0.00634339	+	0.00873093i
$461$	456.885			0.991075			0.495537	−	0.868587i	$-0.334971\pi$
$461$	456.885			0.991075			0.495537	+	0.868587i	$0.334971\pi$
$462$		0			0
$463$		−	400.249i		−	0.864469i	−0.901761	−	0.432234i	$-0.857725\pi$
$463$		−	400.249i		−	0.864469i	0.901761	−	0.432234i	$-0.142275\pi$
$464$	54.1115	+	166.538i	0.116620	+	0.358918i
$465$		0			0
$466$	197.183	−	606.868i	0.423140	−	1.30229i
$467$			913.145i			1.95534i	0.210139	+	0.977672i	$0.432608\pi$
$467$			913.145i			1.95534i	−0.210139	+	0.977672i	$0.567392\pi$
$468$		0			0
$469$	264.033			0.562969
$470$	−227.082	−	73.7834i	−0.483153	−	0.156986i
$471$		0			0
$472$	81.9938	+	112.855i	0.173716	+	0.239099i
$473$	443.607			0.937858
$474$		0			0
$475$			76.0845i			0.160178i
$476$	−146.950	+	202.260i	−0.308720	+	0.424916i
$477$		0			0
$478$	−450.440	−	146.357i	−0.942342	−	0.306186i
$479$		−	526.131i		−	1.09840i	−0.835692	−	0.549198i	$-0.814933\pi$
$479$		−	526.131i		−	1.09840i	0.835692	−	0.549198i	$-0.185067\pi$
$480$		0			0
$481$	155.554			0.323397
$482$	0.567331	−	1.74606i	0.00117704	−	0.00362254i
$483$		0			0
$484$	892.423	+	648.384i	1.84385	+	1.33964i
$485$	−207.580			−0.428001
$486$		0			0
$487$		−	443.541i		−	0.910762i	−0.890297	−	0.455381i	$-0.849503\pi$
$487$		−	443.541i		−	0.910762i	0.890297	−	0.455381i	$-0.150497\pi$
$488$	583.384	−	423.853i	1.19546	−	0.868552i
$489$		0			0
$490$	−29.5197	+	90.8524i	−0.0602444	+	0.185413i
$491$		−	287.163i		−	0.584854i	−0.956288	−	0.292427i	$-0.905537\pi$
$491$		−	287.163i		−	0.584854i	0.956288	−	0.292427i	$-0.0944628\pi$
$492$		0			0
$493$	−130.111			−0.263918
$494$	245.220	+	79.6767i	0.496396	+	0.161289i
$495$		0			0
$496$	−126.217	+	41.0103i	−0.254469	+	0.0826820i
$497$	424.721			0.854570
$498$		0			0
$499$		−	810.936i		−	1.62512i	−0.582876	−	0.812561i	$-0.698073\pi$
$499$		−	810.936i		−	1.62512i	0.582876	−	0.812561i	$-0.301927\pi$
$500$	−36.1803	−	26.2866i	−0.0723607	−	0.0525731i
$501$		0			0
$502$	260.000	+	84.4791i	0.517928	+	0.168285i
$503$			642.471i			1.27728i	0.769506	+	0.638639i	$0.220502\pi$
$503$			642.471i			1.27728i	−0.769506	+	0.638639i	$0.779498\pi$
$504$		0			0
$505$	−143.358			−0.283876
$506$	−6.83282	+	21.0292i	−0.0135036	+	0.0415598i
$507$		0			0
$508$	467.023	−	642.802i	0.919337	−	1.26536i
$509$	915.050			1.79774			0.898870	−	0.438216i	$-0.144389\pi$
$509$	915.050			1.79774			0.898870	+	0.438216i	$0.144389\pi$
$510$		0			0
$511$		−	29.2000i		−	0.0571429i
$512$	−158.217	−	486.941i	−0.309017	−	0.951057i
$513$		0			0
$514$	−169.925	+	522.975i	−0.330593	+	1.01746i
$515$		−	308.061i		−	0.598177i
$516$		0			0
$517$	−1063.49			−2.05704
$518$	183.607	+	59.6575i	0.354453	+	0.115169i
$519$		0			0
$520$	−122.610	+	89.0813i	−0.235788	+	0.171310i
$521$	−1006.98			−1.93279			−0.966396	−	0.257058i	$-0.917247\pi$
$521$	−1006.98			−1.93279			−0.966396	+	0.257058i	$0.917247\pi$
$522$		0			0
$523$			774.173i			1.48025i	0.672467	+	0.740127i	$0.265235\pi$
$523$			774.173i			1.48025i	−0.672467	+	0.740127i	$0.734765\pi$
$524$	18.2693	−	25.1456i	0.0348651	−	0.0479877i
$525$		0			0
$526$	−772.991	−	251.160i	−1.46956	−	0.477490i
$527$		−	98.6096i		−	0.187115i
$528$		0			0
$529$	528.692			0.999418
$530$	−91.7082	+	282.249i	−0.173034	+	0.532545i
$531$		0			0
$532$	258.885	+	188.091i	0.486627	+	0.353555i
$533$	−123.554			−0.231809
$534$		0			0
$535$		−	114.782i		−	0.214546i
$536$	−236.158	−	325.043i	−0.440593	−	0.606424i
$537$		0			0
$538$	−215.400	+	662.933i	−0.400372	+	1.23222i
$539$			425.487i			0.789401i
$540$		0			0
$541$	−259.115			−0.478955			−0.239477	−	0.970902i	$-0.576976\pi$
$541$	−259.115			−0.478955			−0.239477	+	0.970902i	$0.576976\pi$
$542$	−471.437	−	153.179i	−0.869809	−	0.282618i
$543$		0			0
$544$	380.433			0.699326
$545$	298.446			0.547607
$546$		0			0
$547$			149.818i			0.273890i	0.990579	+	0.136945i	$0.0437284\pi$
$547$			149.818i			0.273890i	−0.990579	+	0.136945i	$0.956272\pi$
$548$	2.69505	+	1.95807i	0.00491797	+	0.00357312i
$549$		0			0
$550$	−189.443	−	61.5537i	−0.344441	−	0.111916i
$551$			166.538i			0.302247i
$552$		0			0
$553$	−72.7864			−0.131621
$554$	33.8398	−	104.148i	0.0610826	−	0.187993i
$555$		0			0
$556$	558.768	−	769.078i	1.00498	−	1.38323i
$557$	−511.698			−0.918668			−0.459334	−	0.888264i	$-0.651912\pi$
$557$	−511.698			−0.918668			−0.459334	+	0.888264i	$0.651912\pi$
$558$		0			0
$559$			188.677i			0.337526i
$560$	−178.885	+	58.1234i	−0.319438	+	0.103792i
$561$		0			0
$562$	−31.1246	+	95.7917i	−0.0553819	+	0.170448i
$563$			490.726i			0.871627i	0.900037	+	0.435814i	$0.143539\pi$
$563$			490.726i			0.871627i	−0.900037	+	0.435814i	$0.856461\pi$
$564$		0			0
$565$	−381.745			−0.675654
$566$	−280.249	−	91.0585i	−0.495140	−	0.160881i
$567$		0			0
$568$	−379.882	−	522.863i	−0.668807	−	0.920534i
$569$	232.748			0.409047			0.204523	−	0.978862i	$-0.434436\pi$
$569$	232.748			0.409047			0.204523	+	0.978862i	$0.434436\pi$
$570$		0			0
$571$			210.755i			0.369098i	0.982823	+	0.184549i	$0.0590824\pi$
$571$			210.755i			0.369098i	−0.982823	+	0.184549i	$0.940918\pi$
$572$	−396.774	+	546.113i	−0.693661	+	0.954742i
$573$		0			0
$574$	−145.836	−	47.3850i	−0.254070	−	0.0825522i
$575$		−	2.77515i		−	0.00482634i
$576$		0			0
$577$	341.712			0.592222			0.296111	−	0.955154i	$-0.404310\pi$
$577$	341.712			0.592222			0.296111	+	0.955154i	$0.404310\pi$
$578$	91.2605	−	280.871i	0.157890	−	0.485936i
$579$		0			0
$580$	−79.1935	−	57.5374i	−0.136541	−	0.0992025i
$581$	400.689			0.689654
$582$		0			0
$583$			1321.85i			2.26733i
$584$	−35.9474	+	26.1173i	−0.0615537	+	0.0447214i
$585$		0			0
$586$	110.541	−	340.210i	0.188637	−	0.580564i
$587$			618.412i			1.05351i	0.850016	+	0.526756i	$0.176592\pi$
$587$			618.412i			1.05351i	−0.850016	+	0.526756i	$0.823408\pi$
$588$		0			0
$589$	−126.217			−0.214290
$590$	−74.1641	−	24.0974i	−0.125702	−	0.0408430i
$591$		0			0
$592$	−90.7802	−	279.393i	−0.153345	−	0.471947i
$593$	−120.663			−0.203478			−0.101739	−	0.994811i	$-0.532441\pi$
$593$	−120.663			−0.203478			−0.101739	+	0.994811i	$0.532441\pi$
$594$		0			0
$595$		−	139.758i		−	0.234888i
$596$	−119.639	−	86.9231i	−0.200737	−	0.145844i
$597$		0			0
$598$	−8.94427	−	2.90617i	−0.0149570	−	0.00485982i
$599$		−	849.927i		−	1.41891i	−0.704751	−	0.709455i	$-0.748941\pi$
$599$		−	849.927i		−	1.41891i	0.704751	−	0.709455i	$-0.251059\pi$
$600$		0			0
$601$	−11.3576			−0.0188978			−0.00944890	−	0.999955i	$-0.503008\pi$
$601$	−11.3576			−0.0188978			−0.00944890	+	0.999955i	$0.503008\pi$
$602$	−72.3607	+	222.703i	−0.120200	+	0.369939i
$603$		0			0
$604$	−664.721	+	914.910i	−1.10053	+	1.51475i
$605$	−616.649			−1.01926
$606$		0			0
$607$			1115.12i			1.83710i	0.395305	+	0.918550i	$0.370639\pi$
$607$			1115.12i			1.83710i	−0.395305	+	0.918550i	$0.629361\pi$
$608$		−	486.941i		−	0.800890i
$609$		0			0
$610$	−124.567	+	383.379i	−0.204209	+	0.628490i
$611$		−	452.329i		−	0.740309i
$612$		0			0
$613$	499.475			0.814805			0.407402	−	0.913249i	$-0.366435\pi$
$613$	499.475			0.814805			0.407402	+	0.913249i	$0.366435\pi$
$614$	−541.246	−	175.862i	−0.881508	−	0.286419i
$615$		0			0
$616$	−677.771	+	492.429i	−1.10028	+	0.799398i
$617$	−545.935			−0.884822			−0.442411	−	0.896813i	$-0.645877\pi$
$617$	−545.935			−0.884822			−0.442411	+	0.896813i	$0.645877\pi$
$618$		0			0
$619$		−	455.011i		−	0.735075i	−0.930009	−	0.367537i	$-0.880201\pi$
$619$		−	455.011i		−	0.735075i	0.930009	−	0.367537i	$-0.119799\pi$
$620$	43.6068	−	60.0196i	0.0703335	−	0.0968058i
$621$		0			0
$622$	−536.774	−	174.408i	−0.862981	−	0.280399i
$623$			585.889i			0.940432i
$624$		0			0
$625$	25.0000			0.0400000
$626$	350.764	−	1079.54i	0.560326	−	1.72451i
$627$		0			0
$628$	−662.577	−	481.391i	−1.05506	−	0.766546i
$629$	218.282			0.347030
$630$		0			0
$631$		−	267.706i		−	0.424257i	−0.977242	−	0.212128i	$-0.931960\pi$
$631$		−	267.706i		−	0.424257i	0.977242	−	0.212128i	$-0.0680395\pi$
$632$	65.1021	+	89.6054i	0.103010	+	0.141781i
$633$		0			0
$634$	99.5905	−	306.508i	0.157083	−	0.483451i
$635$			444.165i			0.699473i
$636$		0			0
$637$	−180.971			−0.284098
$638$	−414.663	−	134.732i	−0.649941	−	0.211179i
$639$		0			0
$640$	231.554	+	168.234i	0.361803	+	0.262866i
$641$	418.571			0.652997			0.326499	−	0.945198i	$-0.394131\pi$
$641$	418.571			0.652997			0.326499	+	0.945198i	$0.394131\pi$
$642$		0			0
$643$		−	439.339i		−	0.683265i	−0.939834	−	0.341633i	$-0.889020\pi$
$643$		−	439.339i		−	0.683265i	0.939834	−	0.341633i	$-0.110980\pi$
$644$	−9.44272	−	6.86054i	−0.0146626	−	0.0106530i
$645$		0			0
$646$	344.105	+	111.807i	0.532671	+	0.173075i
$647$			419.644i			0.648600i	0.945954	+	0.324300i	$0.105129\pi$
$647$			419.644i			0.648600i	−0.945954	+	0.324300i	$0.894871\pi$
$648$		0			0
$649$	−347.331			−0.535179
$650$	26.1803	−	80.5748i	0.0402774	−	0.123961i
$651$		0			0
$652$	−252.125	+	347.021i	−0.386695	+	0.532240i
$653$	370.085			0.566746			0.283373	−	0.959010i	$-0.408547\pi$
$653$	370.085			0.566746			0.283373	+	0.959010i	$0.408547\pi$
$654$		0			0
$655$			17.3752i			0.0265270i
$656$	72.1052	+	221.917i	0.109917	+	0.338288i
$657$		0			0
$658$	173.475	−	533.902i	0.263640	−	0.811401i
$659$		−	322.823i		−	0.489868i	−0.969540	−	0.244934i	$-0.921234\pi$
$659$		−	322.823i		−	0.489868i	0.969540	−	0.244934i	$-0.0787664\pi$
$660$		0			0
$661$	−812.735			−1.22955			−0.614777	−	0.788701i	$-0.710754\pi$
$661$	−812.735			−1.22955			−0.614777	+	0.788701i	$0.710754\pi$
$662$	631.437	+	205.166i	0.953832	+	0.309919i
$663$		0			0
$664$	−358.387	−	493.277i	−0.539739	−	0.742888i
$665$	−178.885			−0.269001
$666$		0			0
$667$		−	6.07439i		−	0.00910703i
$668$	78.0789	−	107.466i	0.116885	−	0.160878i
$669$		0			0
$670$	213.607	+	69.4051i	0.318816	+	0.103590i
$671$			1795.47i			2.67581i
$672$		0			0
$673$	467.378			0.694469			0.347235	−	0.937778i	$-0.387121\pi$
$673$	467.378			0.694469			0.347235	+	0.937778i	$0.387121\pi$
$674$	166.318	−	511.875i	0.246763	−	0.759458i
$675$		0			0
$676$	314.620	+	228.585i	0.465414	+	0.338143i
$677$	−548.237			−0.809803			−0.404902	−	0.914360i	$-0.632694\pi$
$677$	−548.237			−0.809803			−0.404902	+	0.914360i	$0.632694\pi$
$678$		0			0
$679$		−	488.051i		−	0.718779i
$680$	−172.053	+	125.004i	−0.253019	+	0.183829i
$681$		0			0
$682$	102.111	−	314.267i	0.149724	−	0.460802i
$683$			23.9663i			0.0350898i	0.999846	+	0.0175449i	$0.00558500\pi$
$683$			23.9663i			0.0350898i	−0.999846	+	0.0175449i	$0.994415\pi$
$684$		0			0
$685$	−1.86223			−0.00271859
$686$	−703.607	−	228.616i	−1.02567	−	0.333259i
$687$		0			0
$688$	338.885	−	110.111i	0.492566	−	0.160044i
$689$	−562.217			−0.815989
$690$		0			0
$691$			186.981i			0.270595i	0.990805	+	0.135298i	$0.0431990\pi$
$691$			186.981i			0.270595i	−0.990805	+	0.135298i	$0.956801\pi$
$692$	−732.519	−	532.206i	−1.05855	−	0.769084i
$693$		0			0
$694$	956.906	+	310.917i	1.37883	+	0.448008i
$695$			531.420i			0.764633i
$696$		0			0
$697$	−173.378			−0.248748
$698$	0.311896	−	0.959917i	0.000446842	−	0.00137524i
$699$		0			0
$700$	61.8034	−	85.0651i	0.0882906	−	0.121522i
$701$	706.636			1.00804			0.504020	−	0.863692i	$-0.331854\pi$
$701$	706.636			1.00804			0.504020	+	0.863692i	$0.331854\pi$
$702$		0			0
$703$		−	279.393i		−	0.397429i
$704$	1212.43	+	393.943i	1.72221	+	0.559579i
$705$		0			0
$706$	−207.656	+	639.098i	−0.294130	+	0.905238i
$707$		−	337.054i		−	0.476738i
$708$		0			0
$709$	−188.597			−0.266005			−0.133002	−	0.991116i	$-0.542462\pi$
$709$	−188.597			−0.266005			−0.133002	+	0.991116i	$0.542462\pi$
$710$	343.607	+	111.645i	0.483953	+	0.157246i
$711$		0			0
$712$	721.272	−	524.035i	1.01302	−	0.736004i
$713$	4.60369			0.00645679
$714$		0			0
$715$		−	377.354i		−	0.527769i
$716$	527.449	−	725.971i	0.736661	−	1.01393i
$717$		0			0
$718$	−187.331	−	60.8676i	−0.260907	−	0.0847738i
$719$			156.085i			0.217086i	0.994092	+	0.108543i	$0.0346186\pi$
$719$			156.085i			0.217086i	−0.994092	+	0.108543i	$0.965381\pi$
$720$		0			0
$721$	724.296			1.00457
$722$	−80.0019	+	246.221i	−0.110806	+	0.341026i
$723$		0			0
$724$	−279.023	−	202.722i	−0.385391	−	0.280003i
$725$	54.7214			0.0754777
$726$		0			0
$727$			715.164i			0.983719i	0.870675	+	0.491859i	$0.163683\pi$
$727$			715.164i			0.983719i	−0.870675	+	0.491859i	$0.836317\pi$
$728$	−209.443	−	288.273i	−0.287696	−	0.395980i
$729$		0			0
$730$	7.67568	−	23.6233i	0.0105146	−	0.0323607i
$731$			264.762i			0.362191i
$732$		0			0
$733$	1233.29			1.68252			0.841259	−	0.540632i	$-0.181815\pi$
$733$	1233.29			1.68252			0.841259	+	0.540632i	$0.181815\pi$
$734$	948.152	+	308.073i	1.29176	+	0.419718i
$735$		0			0
$736$			17.7609i			0.0241317i
$737$	1000.38			1.35737
$738$		0			0
$739$		−	8.55656i		−	0.0115786i	−0.999983	−	0.00578928i	$-0.998157\pi$
$739$		−	8.55656i		−	0.0115786i	0.999983	−	0.00578928i	$-0.00184280\pi$
$740$	132.859	+	96.5278i	0.179539	+	0.130443i
$741$		0			0
$742$	−663.607	−	215.619i	−0.894349	−	0.290592i
$743$		−	1010.56i		−	1.36011i	−0.733163	−	0.680053i	$-0.761957\pi$
$743$		−	1010.56i		−	1.36011i	0.733163	−	0.680053i	$-0.238043\pi$
$744$		0			0
$745$	82.6687			0.110965
$746$	−371.039	+	1141.94i	−0.497372	+	1.53075i
$747$		0			0
$748$	−556.774	+	766.334i	−0.744350	+	1.02451i
$749$	269.868			0.360305
$750$		0			0
$751$			1104.31i			1.47046i	0.677820	+	0.735228i	$0.262925\pi$
$751$			1104.31i			1.47046i	−0.677820	+	0.735228i	$0.737075\pi$
$752$	−812.433	+	263.976i	−1.08036	+	0.351031i
$753$		0			0
$754$	57.3050	−	176.367i	0.0760013	−	0.233908i
$755$		−	632.188i		−	0.837335i
$756$		0			0
$757$	−875.633			−1.15671			−0.578357	−	0.815783i	$-0.696306\pi$
$757$	−875.633			−1.15671			−0.578357	+	0.815783i	$0.696306\pi$
$758$	577.272	+	187.567i	0.761573	+	0.247450i
$759$		0			0
$760$	160.000	+	220.221i	0.210526	+	0.289765i
$761$	647.207			0.850470			0.425235	−	0.905083i	$-0.360192\pi$
$761$	647.207			0.850470			0.425235	+	0.905083i	$0.360192\pi$
$762$		0			0
$763$			701.688i			0.919644i
$764$	−72.9318	+	100.382i	−0.0954605	+	0.131390i
$765$		0			0
$766$	632.610	+	205.547i	0.825861	+	0.268339i
$767$		−	147.729i		−	0.192606i
$768$		0			0
$769$	631.430			0.821106			0.410553	−	0.911837i	$-0.365336\pi$
$769$	631.430			0.821106			0.410553	+	0.911837i	$0.365336\pi$
$770$	144.721	−	445.407i	0.187950	−	0.578450i
$771$		0			0
$772$	−356.689	−	259.150i	−0.462032	−	0.335686i
$773$	421.522			0.545306			0.272653	−	0.962112i	$-0.412099\pi$
$773$	421.522			0.545306			0.272653	+	0.962112i	$0.412099\pi$
$774$		0			0
$775$			41.4725i			0.0535129i
$776$	−600.827	+	436.526i	−0.774261	+	0.562534i
$777$		0			0
$778$	242.488	−	746.303i	0.311682	−	0.959258i
$779$			221.917i			0.284874i
$780$		0			0
$781$	1609.21			2.06044
$782$	−12.5511	−	4.07809i	−0.0160500	−	0.00521495i
$783$		0			0
$784$	105.613	+	325.043i	0.134710	+	0.414596i
$785$	457.830			0.583223
$786$		0			0
$787$		−	838.633i		−	1.06561i	−0.846239	−	0.532804i	$-0.821138\pi$
$787$		−	838.633i		−	1.06561i	0.846239	−	0.532804i	$-0.178862\pi$
$788$	−558.302	−	405.630i	−0.708505	−	0.514759i
$789$		0			0
$790$	−58.8854	−	19.1330i	−0.0745385	−	0.0242190i
$791$		−	897.535i		−	1.13468i
$792$		0			0
$793$	−763.659			−0.963001
$794$	−206.541	+	635.668i	−0.260127	+	0.800589i
$795$		0			0
$796$	640.000	−	880.884i	0.804020	−	1.10664i
$797$	−1213.57			−1.52268			−0.761339	−	0.648354i	$-0.775458\pi$
$797$	−1213.57			−1.52268			−0.761339	+	0.648354i	$0.775458\pi$
$798$		0			0
$799$		−	634.732i		−	0.794408i
$800$	−160.000			−0.200000
$801$		0			0
$802$	74.7840	−	230.162i	0.0932469	−	0.286985i
$803$		−	110.635i		−	0.137777i
$804$		0			0
$805$	6.52476			0.00810529
$806$	133.666	+	43.4306i	0.165838	+	0.0538841i
$807$		0			0
$808$	−414.938	+	301.470i	−0.513537	+	0.373107i
$809$	229.214			0.283330			0.141665	−	0.989915i	$-0.454754\pi$
$809$	229.214			0.283330			0.141665	+	0.989915i	$0.454754\pi$
$810$		0			0
$811$		−	454.225i		−	0.560080i	−0.959988	−	0.280040i	$-0.909652\pi$
$811$		−	454.225i		−	0.560080i	0.959988	−	0.280040i	$-0.0903478\pi$
$812$	135.279	−	186.195i	0.166599	−	0.229304i
$813$		0			0
$814$	695.659	+	226.033i	0.854618	+	0.277682i
$815$		−	239.785i		−	0.294215i
$816$		0			0
$817$	338.885			0.414792
$818$	375.400	−	1155.36i	0.458924	−	1.41242i
$819$		0			0
$820$	−105.528	−	76.6705i	−0.128693	−	0.0935006i
$821$	−1130.90			−1.37747			−0.688733	−	0.725015i	$-0.741833\pi$
$821$	−1130.90			−1.37747			−0.688733	+	0.725015i	$0.741833\pi$
$822$		0			0
$823$		−	780.148i		−	0.947931i	−0.880543	−	0.473966i	$-0.842822\pi$
$823$		−	780.148i		−	0.947931i	0.880543	−	0.473966i	$-0.157178\pi$
$824$	−647.830	−	891.661i	−0.786201	−	1.08211i
$825$		0			0
$826$	56.6563	−	174.370i	0.0685912	−	0.211102i
$827$			209.175i			0.252932i	0.991971	+	0.126466i	$0.0403635\pi$
$827$			209.175i			0.252932i	−0.991971	+	0.126466i	$0.959636\pi$
$828$		0			0
$829$	−508.525			−0.613419			−0.306710	−	0.951803i	$-0.599228\pi$
$829$	−508.525			−0.613419			−0.306710	+	0.951803i	$0.599228\pi$
$830$	324.164	+	105.327i	0.390559	+	0.126900i
$831$		0			0
$832$	−167.554	+	515.679i	−0.201387	+	0.619806i
$833$	−253.947			−0.304859
$834$		0			0
$835$			74.2575i			0.0889311i
$836$	980.879	+	712.650i	1.17330	+	0.852453i
$837$		0			0
$838$	887.830	+	288.473i	1.05946	+	0.344240i
$839$		−	274.028i		−	0.326613i	−0.986575	−	0.163306i	$-0.947784\pi$
$839$		−	274.028i		−	0.326613i	0.986575	−	0.163306i	$-0.0522159\pi$
$840$		0			0
$841$	−721.223			−0.857578
$842$	45.1710	−	139.022i	0.0536473	−	0.165109i
$843$		0			0
$844$	482.610	−	664.256i	0.571813	−	0.787033i
$845$	−217.397			−0.257275
$846$		0			0
$847$		−	1449.83i		−	1.71172i
$848$	328.105	+	1009.80i	0.386917	+	1.19081i
$849$		0			0
$850$	36.7376	−	113.067i	0.0432207	−	0.133020i
$851$			10.1907i			0.0119750i
$852$		0			0
$853$	−1583.28			−1.85613			−0.928066	−	0.372416i	$-0.878529\pi$
$853$	−1583.28			−1.85613			−0.928066	+	0.372416i	$0.878529\pi$
$854$	−901.378	−	292.875i	−1.05548	−	0.342945i
$855$		0			0
$856$	−241.378	−	332.228i	−0.281983	−	0.388117i
$857$	1007.38			1.17547			0.587735	−	0.809054i	$-0.300020\pi$
$857$	1007.38			1.17547			0.587735	+	0.809054i	$0.300020\pi$
$858$		0			0
$859$			76.6086i			0.0891835i	0.999005	+	0.0445917i	$0.0141987\pi$
$859$			76.6086i			0.0891835i	−0.999005	+	0.0445917i	$0.985801\pi$
$860$	−117.082	+	161.150i	−0.136142	+	0.187383i
$861$		0			0
$862$	881.876	+	286.539i	1.02306	+	0.332412i
$863$		−	255.450i		−	0.296002i	−0.988987	−	0.148001i	$-0.952716\pi$
$863$		−	255.450i		−	0.296002i	0.988987	−	0.148001i	$-0.0472839\pi$
$864$		0			0
$865$	506.158			0.585154
$866$	61.7020	−	189.899i	0.0712494	−	0.219283i
$867$		0			0
$868$	141.115	+	102.526i	0.162574	+	0.118117i
$869$	−275.777			−0.317350
$870$		0			0
$871$			425.487i			0.488504i
$872$	863.830	−	627.609i	0.990630	−	0.719735i
$873$		0			0
$874$	−5.21981	+	16.0649i	−0.00597232	+	0.0183809i
$875$			58.7785i			0.0671755i
$876$		0			0
$877$	601.522			0.685886			0.342943	−	0.939356i	$-0.388576\pi$
$877$	601.522			0.685886			0.342943	+	0.939356i	$0.388576\pi$
$878$	711.554	+	231.198i	0.810426	+	0.263323i
$879$		0			0
$880$	−677.771	+	220.221i	−0.770194	+	0.250251i
$881$	−237.850			−0.269977			−0.134989	−	0.990847i	$-0.543100\pi$
$881$	−237.850			−0.269977			−0.134989	+	0.990847i	$0.543100\pi$
$882$		0			0
$883$			1.30294i			0.00147559i	1.00000		0.000737794i	$0.000234847\pi$
$883$			1.30294i			0.00147559i	−1.00000		0.000737794i	$0.999765\pi$
$884$	−325.941	−	236.810i	−0.368712	−	0.267885i
$885$		0			0
$886$	551.803	+	179.292i	0.622803	+	0.202361i
$887$		−	536.353i		−	0.604682i	−0.953200	−	0.302341i	$-0.902232\pi$
$887$		−	536.353i		−	0.604682i	0.953200	−	0.302341i	$-0.0977682\pi$
$888$		0			0
$889$	−1044.30			−1.17469
$890$	−154.010	+	473.994i	−0.173045	+	0.532578i
$891$		0			0
$892$	−554.237	+	762.842i	−0.621342	+	0.855203i
$893$	−812.433			−0.909780
$894$		0			0
$895$			501.634i			0.560485i
$896$	−395.542	+	544.417i	−0.441453	+	0.607608i
$897$		0			0
$898$	185.361	−	570.484i	0.206416	−	0.635283i
$899$			90.7773i			0.100976i
$900$		0			0
$901$	−788.932			−0.875618
$902$	−552.551	−	179.535i	−0.612584	−	0.199041i
$903$		0			0
$904$	−1104.93	+	802.780i	−1.22227	+	0.888031i
$905$	192.800			0.213039
$906$		0			0
$907$		−	332.159i		−	0.366217i	−0.983093	−	0.183108i	$-0.941384\pi$
$907$		−	332.159i		−	0.366217i	0.983093	−	0.183108i	$-0.0586159\pi$
$908$	−137.580	+	189.363i	−0.151520	+	0.208550i
$909$		0			0
$910$	189.443	+	61.5537i	0.208179	+	0.0676414i
$911$		−	1450.06i		−	1.59172i	−0.605478	−	0.795862i	$-0.707018\pi$
$911$		−	1450.06i		−	1.59172i	0.605478	−	0.795862i	$-0.292982\pi$
$912$		0			0
$913$	1518.15			1.66282
$914$	−508.227	+	1564.16i	−0.556047	+	1.71134i
$915$		0			0
$916$	−526.577	−	382.581i	−0.574866	−	0.417665i
$917$	−40.8514			−0.0445490
$918$		0			0
$919$		−	814.405i		−	0.886186i	−0.896476	−	0.443093i	$-0.853881\pi$
$919$		−	814.405i		−	0.886186i	0.896476	−	0.443093i	$-0.146119\pi$
$920$	−5.83592	−	8.03246i	−0.00634339	−	0.00873093i
$921$		0			0
$922$	−282.371	+	869.048i	−0.306259	+	0.942568i
$923$			684.437i			0.741535i
$924$		0			0
$925$	−91.8034			−0.0992469
$926$	761.319	+	247.367i	0.822159	+	0.267136i
$927$		0			0
$928$	−350.217			−0.377389
$929$	−400.039			−0.430612			−0.215306	−	0.976547i	$-0.569075\pi$
$929$	−400.039			−0.430612			−0.215306	+	0.976547i	$0.569075\pi$
$930$		0			0
$931$			325.043i			0.349134i
$932$	1032.47	+	750.130i	1.10780	+	0.804861i
$933$		0			0
$934$	−1736.91	−	564.355i	−1.85964	−	0.604234i
$935$		−	529.524i		−	0.566335i
$936$		0			0
$937$	249.279			0.266039			0.133020	−	0.991113i	$-0.457533\pi$
$937$	249.279			0.266039			0.133020	+	0.991113i	$0.457533\pi$
$938$	−163.181	+	502.220i	−0.173967	+	0.535415i
$939$		0			0
$940$	280.689	−	386.335i	0.298605	−	0.410995i
$941$	−724.229			−0.769638			−0.384819	−	0.922992i	$-0.625736\pi$
$941$	−724.229			−0.769638			−0.384819	+	0.922992i	$0.625736\pi$
$942$		0			0
$943$		−	8.09432i		−	0.00858358i
$944$	−265.337	+	86.2134i	−0.281078	+	0.0913277i
$945$		0			0
$946$	−274.164	+	843.790i	−0.289814	+	0.891956i
$947$		−	1141.54i		−	1.20542i	−0.797959	−	0.602712i	$-0.794087\pi$
$947$		−	1141.54i		−	1.20542i	0.797959	−	0.602712i	$-0.205913\pi$
$948$		0			0
$949$	47.0557			0.0495845
$950$	−144.721	−	47.0228i	−0.152338	−	0.0494977i
$951$		0			0
$952$	−293.901	−	404.520i	−0.308720	−	0.424916i
$953$	−1295.33			−1.35921			−0.679604	−	0.733579i	$-0.737848\pi$
$953$	−1295.33			−1.35921			−0.679604	+	0.733579i	$0.737848\pi$
$954$		0			0
$955$		−	69.3623i		−	0.0726307i
$956$	556.774	−	766.334i	0.582400	−	0.801604i
$957$		0			0
$958$	1000.76	+	325.167i	1.04464	+	0.339423i
$959$		−	4.37837i		−	0.00456556i
$960$		0			0
$961$	892.201			0.928409
$962$	−96.1378	+	295.882i	−0.0999353	+	0.307569i
$963$		0			0
$964$	2.97058	+	2.15825i	0.00308152	+	0.00223885i
$965$	246.466			0.255405
$966$		0			0
$967$			398.477i			0.412075i	0.978544	+	0.206037i	$0.0660569\pi$
$967$			398.477i			0.412075i	−0.978544	+	0.206037i	$0.933943\pi$
$968$	−1784.85	+	1296.77i	−1.84385	+	1.33964i
$969$		0			0
$970$	128.292	−	394.842i	0.132260	−	0.407053i
$971$		−	928.093i		−	0.955811i	−0.878411	−	0.477906i	$-0.841396\pi$
$971$		−	928.093i		−	0.955811i	0.878411	−	0.477906i	$-0.158604\pi$
$972$		0			0
$973$	−1249.44			−1.28411
$974$	843.666	+	274.124i	0.866186	+	0.281441i
$975$		0			0
$976$	445.666	+	1371.62i	0.456625	+	1.40535i
$977$	1378.05			1.41049			0.705247	−	0.708962i	$-0.250836\pi$
$977$	1378.05			1.41049			0.705247	+	0.708962i	$0.250836\pi$
$978$		0			0
$979$			2219.85i			2.26747i
$980$	−154.567	−	112.300i	−0.157722	−	0.114592i
$981$		0			0
$982$	546.217	+	177.477i	0.556229	+	0.180730i
$983$			311.291i			0.316675i	0.987385	+	0.158337i	$0.0506134\pi$
$983$			311.291i			0.316675i	−0.987385	+	0.158337i	$0.949387\pi$
$984$		0			0
$985$	385.777			0.391652
$986$	80.4133	−	247.487i	0.0815551	−	0.251001i
$987$		0			0
$988$	−303.108	+	417.193i	−0.306790	+	0.422260i
$989$	−12.3607			−0.0124982
$990$		0			0
$991$		−	961.147i		−	0.969876i	−0.874549	−	0.484938i	$-0.838842\pi$
$991$		−	961.147i		−	0.969876i	0.874549	−	0.484938i	$-0.161158\pi$
$992$		−	265.424i		−	0.267565i
$993$		0			0
$994$	−262.492	+	807.868i	−0.264077	+	0.812745i
$995$			608.676i			0.611735i
$996$		0			0
$997$	−1089.68			−1.09296			−0.546479	−	0.837473i	$-0.684032\pi$
$997$	−1089.68			−1.09296			−0.546479	+	0.837473i	$0.684032\pi$
$998$	1542.49	+	501.186i	1.54558	+	0.502190i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.c.a.91.2		4
3.2	odd	2		20.3.b.a.11.3	✓	4
4.3	odd	2	inner	180.3.c.a.91.1		4
5.2	odd	4		900.3.f.e.199.1		8
5.3	odd	4		900.3.f.e.199.8		8
5.4	even	2		900.3.c.k.451.3		4
8.3	odd	2		2880.3.e.e.2431.1		4
8.5	even	2		2880.3.e.e.2431.2		4
12.11	even	2		20.3.b.a.11.4	yes	4
15.2	even	4		100.3.d.b.99.8		8
15.8	even	4		100.3.d.b.99.1		8
15.14	odd	2		100.3.b.f.51.2		4
20.3	even	4		900.3.f.e.199.2		8
20.7	even	4		900.3.f.e.199.7		8
20.19	odd	2		900.3.c.k.451.4		4
24.5	odd	2		320.3.b.c.191.2		4
24.11	even	2		320.3.b.c.191.3		4
48.5	odd	4		1280.3.g.e.1151.5		8
48.11	even	4		1280.3.g.e.1151.3		8
48.29	odd	4		1280.3.g.e.1151.4		8
48.35	even	4		1280.3.g.e.1151.6		8
60.23	odd	4		100.3.d.b.99.7		8
60.47	odd	4		100.3.d.b.99.2		8
60.59	even	2		100.3.b.f.51.1		4
120.29	odd	2		1600.3.b.s.1151.3		4
120.53	even	4		1600.3.h.n.1599.6		8
120.59	even	2		1600.3.b.s.1151.2		4
120.77	even	4		1600.3.h.n.1599.4		8
120.83	odd	4		1600.3.h.n.1599.3		8
120.107	odd	4		1600.3.h.n.1599.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.b.a.11.3	✓	4	3.2	odd	2
20.3.b.a.11.4	yes	4	12.11	even	2
100.3.b.f.51.1		4	60.59	even	2
100.3.b.f.51.2		4	15.14	odd	2
100.3.d.b.99.1		8	15.8	even	4
100.3.d.b.99.2		8	60.47	odd	4
100.3.d.b.99.7		8	60.23	odd	4
100.3.d.b.99.8		8	15.2	even	4
180.3.c.a.91.1		4	4.3	odd	2	inner
180.3.c.a.91.2		4	1.1	even	1	trivial
320.3.b.c.191.2		4	24.5	odd	2
320.3.b.c.191.3		4	24.11	even	2
900.3.c.k.451.3		4	5.4	even	2
900.3.c.k.451.4		4	20.19	odd	2
900.3.f.e.199.1		8	5.2	odd	4
900.3.f.e.199.2		8	20.3	even	4
900.3.f.e.199.7		8	20.7	even	4
900.3.f.e.199.8		8	5.3	odd	4
1280.3.g.e.1151.3		8	48.11	even	4
1280.3.g.e.1151.4		8	48.29	odd	4
1280.3.g.e.1151.5		8	48.5	odd	4
1280.3.g.e.1151.6		8	48.35	even	4
1600.3.b.s.1151.2		4	120.59	even	2
1600.3.b.s.1151.3		4	120.29	odd	2
1600.3.h.n.1599.3		8	120.83	odd	4
1600.3.h.n.1599.4		8	120.77	even	4
1600.3.h.n.1599.5		8	120.107	odd	4
1600.3.h.n.1599.6		8	120.53	even	4
2880.3.e.e.2431.1		4	8.3	odd	2
2880.3.e.e.2431.2		4	8.5	even	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.618034 + 1.90211i) q^{2} +(-3.23607 - 2.35114i) q^{4} +2.23607 q^{5} +5.25731i q^{7} +(6.47214 - 4.70228i) q^{8} +O(q^{10})\)	\(q+(-0.618034 + 1.90211i) q^{2} +(-3.23607 - 2.35114i) q^{4} +2.23607 q^{5} +5.25731i q^{7} +(6.47214 - 4.70228i) q^{8} +(-1.38197 + 4.25325i) q^{10} +19.9192i q^{11} -8.47214 q^{13} +(-10.0000 - 3.24920i) q^{14} +(4.94427 + 15.2169i) q^{16} -11.8885 q^{17} +15.2169i q^{19} +(-7.23607 - 5.25731i) q^{20} +(-37.8885 - 12.3107i) q^{22} -0.555029i q^{23} +5.00000 q^{25} +(5.23607 - 16.1150i) q^{26} +(12.3607 - 17.0130i) q^{28} +10.9443 q^{29} +8.29451i q^{31} -32.0000 q^{32} +(7.34752 - 22.6134i) q^{34} +11.7557i q^{35} -18.3607 q^{37} +(-28.9443 - 9.40456i) q^{38} +(14.4721 - 10.5146i) q^{40} +14.5836 q^{41} -22.2703i q^{43} +(46.8328 - 64.4598i) q^{44} +(1.05573 + 0.343027i) q^{46} +53.3902i q^{47} +21.3607 q^{49} +(-3.09017 + 9.51057i) q^{50} +(27.4164 + 19.9192i) q^{52} +66.3607 q^{53} +44.5407i q^{55} +(24.7214 + 34.0260i) q^{56} +(-6.76393 + 20.8172i) q^{58} +17.4370i q^{59} +90.1378 q^{61} +(-15.7771 - 5.12629i) q^{62} +(19.7771 - 60.8676i) q^{64} -18.9443 q^{65} -50.2220i q^{67} +(38.4721 + 27.9516i) q^{68} +(-22.3607 - 7.26543i) q^{70} -80.7868i q^{71} -5.55418 q^{73} +(11.3475 - 34.9241i) q^{74} +(35.7771 - 49.2429i) q^{76} -104.721 q^{77} +13.8448i q^{79} +(11.0557 + 34.0260i) q^{80} +(-9.01316 + 27.7396i) q^{82} -76.2155i q^{83} -26.5836 q^{85} +(42.3607 + 13.7638i) q^{86} +(93.6656 + 128.920i) q^{88} +111.443 q^{89} -44.5407i q^{91} +(-1.30495 + 1.79611i) q^{92} +(-101.554 - 32.9970i) q^{94} +34.0260i q^{95} -92.8328 q^{97} +(-13.2016 + 40.6304i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8	\( 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 10 q^{10} - 16 q^{13} - 40 q^{14} - 16 q^{16} + 24 q^{17} - 20 q^{20} - 80 q^{22} + 20 q^{25} + 12 q^{26} - 40 q^{28} + 8 q^{29} - 128 q^{32} + 92 q^{34} + 16 q^{37} - 80 q^{38} + 40 q^{40} + 112 q^{41} + 80 q^{44} + 40 q^{46} - 4 q^{49} + 10 q^{50} + 56 q^{52} + 176 q^{53} - 80 q^{56} - 36 q^{58} + 128 q^{61} + 80 q^{62} - 64 q^{64} - 40 q^{65} + 136 q^{68} + 264 q^{73} + 108 q^{74} - 240 q^{77} + 80 q^{80} + 116 q^{82} - 160 q^{85} + 80 q^{86} + 160 q^{88} + 88 q^{89} + 120 q^{92} - 120 q^{94} - 264 q^{97} - 102 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 10 * q^10 - 16 * q^13 - 40 * q^14 - 16 * q^16 + 24 * q^17 - 20 * q^20 - 80 * q^22 + 20 * q^25 + 12 * q^26 - 40 * q^28 + 8 * q^29 - 128 * q^32 + 92 * q^34 + 16 * q^37 - 80 * q^38 + 40 * q^40 + 112 * q^41 + 80 * q^44 + 40 * q^46 - 4 * q^49 + 10 * q^50 + 56 * q^52 + 176 * q^53 - 80 * q^56 - 36 * q^58 + 128 * q^61 + 80 * q^62 - 64 * q^64 - 40 * q^65 + 136 * q^68 + 264 * q^73 + 108 * q^74 - 240 * q^77 + 80 * q^80 + 116 * q^82 - 160 * q^85 + 80 * q^86 + 160 * q^88 + 88 * q^89 + 120 * q^92 - 120 * q^94 - 264 * q^97 - 102 * q^98

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