LMFDB - Embedded newform 100.3.b.f.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,3,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	100.b (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:	$2.72480264360$
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:	$\Z[a_1, a_2, a_3]$
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			51.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.3.b.f.51.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618034 - 1.90211i) q^{2} +2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} +(4.47214 - 1.45309i) q^{6} +5.25731i q^{7} +(6.47214 + 4.70228i) q^{8} +3.47214 q^{9} +O(q^{10})$	\(q+(-0.618034 - 1.90211i) q^{2} +2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} +(4.47214 - 1.45309i) q^{6} +5.25731i q^{7} +(6.47214 + 4.70228i) q^{8} +3.47214 q^{9} +19.9192i q^{11} +(-5.52786 - 7.60845i) q^{12} +8.47214 q^{13} +(10.0000 - 3.24920i) q^{14} +(4.94427 - 15.2169i) q^{16} -11.8885 q^{17} +(-2.14590 - 6.60440i) q^{18} -15.2169i q^{19} -12.3607 q^{21} +(37.8885 - 12.3107i) q^{22} +0.555029i q^{23} +(-11.0557 + 15.2169i) q^{24} +(-5.23607 - 16.1150i) q^{26} +29.3238i q^{27} +(-12.3607 - 17.0130i) q^{28} -10.9443 q^{29} -8.29451i q^{31} -32.0000 q^{32} -46.8328 q^{33} +(7.34752 + 22.6134i) q^{34} +(-11.2361 + 8.16348i) q^{36} +18.3607 q^{37} +(-28.9443 + 9.40456i) q^{38} +19.9192i q^{39} -14.5836 q^{41} +(7.63932 + 23.5114i) q^{42} -22.2703i q^{43} +(-46.8328 - 64.4598i) q^{44} +(1.05573 - 0.343027i) q^{46} -53.3902i q^{47} +(35.7771 + 11.6247i) q^{48} +21.3607 q^{49} -27.9516i q^{51} +(-27.4164 + 19.9192i) q^{52} +66.3607 q^{53} +(55.7771 - 18.1231i) q^{54} +(-24.7214 + 34.0260i) q^{56} +35.7771 q^{57} +(6.76393 + 20.8172i) q^{58} +17.4370i q^{59} +90.1378 q^{61} +(-15.7771 + 5.12629i) q^{62} +18.2541i q^{63} +(19.7771 + 60.8676i) q^{64} +(28.9443 + 89.0813i) q^{66} -50.2220i q^{67} +(38.4721 - 27.9516i) q^{68} -1.30495 q^{69} -80.7868i q^{71} +(22.4721 + 16.3270i) q^{72} +5.55418 q^{73} +(-11.3475 - 34.9241i) q^{74} +(35.7771 + 49.2429i) q^{76} -104.721 q^{77} +(37.8885 - 12.3107i) q^{78} -13.8448i q^{79} -37.6950 q^{81} +(9.01316 + 27.7396i) q^{82} +76.2155i q^{83} +(40.0000 - 29.0617i) q^{84} +(-42.3607 + 13.7638i) q^{86} -25.7315i q^{87} +(-93.6656 + 128.920i) q^{88} -111.443 q^{89} +44.5407i q^{91} +(-1.30495 - 1.79611i) q^{92} +19.5016 q^{93} +(-101.554 + 32.9970i) q^{94} -75.2365i q^{96} +92.8328 q^{97} +(-13.2016 - 40.6304i) q^{98} +69.1621i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^9	$ 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{9} - 40 q^{12} + 16 q^{13} + 40 q^{14} - 16 q^{16} + 24 q^{17} - 22 q^{18} + 40 q^{21} + 80 q^{22} - 80 q^{24} - 12 q^{26} + 40 q^{28} - 8 q^{29} - 128 q^{32} - 80 q^{33} + 92 q^{34} - 36 q^{36} - 16 q^{37} - 80 q^{38} - 112 q^{41} + 120 q^{42} - 80 q^{44} + 40 q^{46} - 4 q^{49} - 56 q^{52} + 176 q^{53} + 80 q^{54} + 80 q^{56} + 36 q^{58} + 128 q^{61} + 80 q^{62} - 64 q^{64} + 80 q^{66} + 136 q^{68} + 120 q^{69} + 72 q^{72} - 264 q^{73} - 108 q^{74} - 240 q^{77} + 80 q^{78} - 276 q^{81} - 116 q^{82} + 160 q^{84} - 80 q^{86} - 160 q^{88} - 88 q^{89} + 120 q^{92} + 400 q^{93} - 120 q^{94} + 264 q^{97} - 102 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^9 - 40 * q^12 + 16 * q^13 + 40 * q^14 - 16 * q^16 + 24 * q^17 - 22 * q^18 + 40 * q^21 + 80 * q^22 - 80 * q^24 - 12 * q^26 + 40 * q^28 - 8 * q^29 - 128 * q^32 - 80 * q^33 + 92 * q^34 - 36 * q^36 - 16 * q^37 - 80 * q^38 - 112 * q^41 + 120 * q^42 - 80 * q^44 + 40 * q^46 - 4 * q^49 - 56 * q^52 + 176 * q^53 + 80 * q^54 + 80 * q^56 + 36 * q^58 + 128 * q^61 + 80 * q^62 - 64 * q^64 + 80 * q^66 + 136 * q^68 + 120 * q^69 + 72 * q^72 - 264 * q^73 - 108 * q^74 - 240 * q^77 + 80 * q^78 - 276 * q^81 - 116 * q^82 + 160 * q^84 - 80 * q^86 - 160 * q^88 - 88 * q^89 + 120 * q^92 + 400 * q^93 - 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 $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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
$3$			2.35114i			0.783714i	0.920026	+	0.391857i	$0.128167\pi$
$3$			2.35114i			0.783714i	−0.920026	+	0.391857i	$0.871833\pi$
$4$	−3.23607	+	2.35114i	−0.809017	+	0.587785i
$5$		0			0
$5$		0			0
$6$	4.47214	−	1.45309i	0.745356	−	0.242181i
$7$			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
$9$	3.47214			0.385793
$10$		0			0
$11$			19.9192i			1.81084i	0.424522	+	0.905418i	$0.360442\pi$
$11$			19.9192i			1.81084i	−0.424522	+	0.905418i	$0.639558\pi$
$12$	−5.52786	−	7.60845i	−0.460655	−	0.634038i
$13$	8.47214			0.651703			0.325851	−	0.945421i	$-0.394349\pi$
$13$	8.47214			0.651703			0.325851	+	0.945421i	$0.394349\pi$
$14$	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	$0.613704\pi$
$18$	−2.14590	−	6.60440i	−0.119217	−	0.366911i
$19$		−	15.2169i		−	0.800890i	−0.916321	−	0.400445i	$-0.868856\pi$
$19$		−	15.2169i		−	0.800890i	0.916321	−	0.400445i	$-0.131144\pi$
$20$		0			0
$21$	−12.3607			−0.588604
$22$	37.8885	−	12.3107i	1.72221	−	0.559579i
$23$			0.555029i			0.0241317i	0.999927	+	0.0120659i	$0.00384077\pi$
$23$			0.555029i			0.0241317i	−0.999927	+	0.0120659i	$0.996159\pi$
$24$	−11.0557	+	15.2169i	−0.460655	+	0.634038i
$25$		0			0
$26$	−5.23607	−	16.1150i	−0.201387	−	0.619806i
$27$			29.3238i			1.08606i
$28$	−12.3607	−	17.0130i	−0.441453	−	0.607608i
$29$	−10.9443			−0.377389			−0.188694	−	0.982036i	$-0.560426\pi$
$29$	−10.9443			−0.377389			−0.188694	+	0.982036i	$0.560426\pi$
$30$		0			0
$31$		−	8.29451i		−	0.267565i	−0.991011	−	0.133782i	$-0.957288\pi$
$31$		−	8.29451i		−	0.267565i	0.991011	−	0.133782i	$-0.0427123\pi$
$32$	−32.0000			−1.00000
$33$	−46.8328			−1.41918
$34$	7.34752	+	22.6134i	0.216104	+	0.665099i
$35$		0			0
$36$	−11.2361	+	8.16348i	−0.312113	+	0.226763i
$37$	18.3607			0.496235			0.248117	−	0.968730i	$-0.420188\pi$
$37$	18.3607			0.496235			0.248117	+	0.968730i	$0.420188\pi$
$38$	−28.9443	+	9.40456i	−0.761691	+	0.247489i
$39$			19.9192i			0.510748i
$40$		0			0
$41$	−14.5836			−0.355697			−0.177849	−	0.984058i	$-0.556914\pi$
$41$	−14.5836			−0.355697			−0.177849	+	0.984058i	$0.556914\pi$
$42$	7.63932	+	23.5114i	0.181889	+	0.559795i
$43$		−	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	$-0.807725\pi$
$47$		−	53.3902i		−	1.13596i	0.823042	−	0.567981i	$-0.192275\pi$
$48$	35.7771	+	11.6247i	0.745356	+	0.242181i
$49$	21.3607			0.435932
$50$		0			0
$51$		−	27.9516i		−	0.548071i
$52$	−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	$0.284673\pi$
$54$	55.7771	−	18.1231i	1.03291	−	0.335612i
$55$		0			0
$56$	−24.7214	+	34.0260i	−0.441453	+	0.607608i
$57$	35.7771			0.627668
$58$	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
$63$			18.2541i			0.289748i
$64$	19.7771	+	60.8676i	0.309017	+	0.951057i
$65$		0			0
$66$	28.9443	+	89.0813i	0.438550	+	1.34972i
$67$		−	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
$69$	−1.30495			−0.0189123
$70$		0			0
$71$		−	80.7868i		−	1.13784i	−0.822392	−	0.568921i	$-0.807361\pi$
$71$		−	80.7868i		−	1.13784i	0.822392	−	0.568921i	$-0.192639\pi$
$72$	22.4721	+	16.3270i	0.312113	+	0.226763i
$73$	5.55418			0.0760846			0.0380423	−	0.999276i	$-0.487888\pi$
$73$	5.55418			0.0760846			0.0380423	+	0.999276i	$0.487888\pi$
$74$	−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
$78$	37.8885	−	12.3107i	0.485751	−	0.157830i
$79$		−	13.8448i		−	0.175251i	−0.996154	−	0.0876253i	$-0.972072\pi$
$79$		−	13.8448i		−	0.175251i	0.996154	−	0.0876253i	$-0.0279278\pi$
$80$		0			0
$81$	−37.6950			−0.465371
$82$	9.01316	+	27.7396i	0.109917	+	0.338288i
$83$			76.2155i			0.918260i	0.888369	+	0.459130i	$0.151839\pi$
$83$			76.2155i			0.918260i	−0.888369	+	0.459130i	$0.848161\pi$
$84$	40.0000	−	29.0617i	0.476190	−	0.345973i
$85$		0			0
$86$	−42.3607	+	13.7638i	−0.492566	+	0.160044i
$87$		−	25.7315i		−	0.295765i
$88$	−93.6656	+	128.920i	−1.06438	+	1.46500i
$89$	−111.443			−1.25217			−0.626083	−	0.779757i	$-0.715343\pi$
$89$	−111.443			−1.25217			−0.626083	+	0.779757i	$0.715343\pi$
$90$		0			0
$91$			44.5407i			0.489458i
$92$	−1.30495	−	1.79611i	−0.0141843	−	0.0195230i
$93$	19.5016			0.209694
$94$	−101.554	+	32.9970i	−1.08036	+	0.351031i
$95$		0			0
$96$		−	75.2365i		−	0.783714i
$97$	92.8328			0.957039			0.478520	−	0.878077i	$-0.341174\pi$
$97$	92.8328			0.957039			0.478520	+	0.878077i	$0.341174\pi$
$98$	−13.2016	−	40.6304i	−0.134710	−	0.414596i
$99$			69.1621i			0.698607i
$100$		0			0
$101$	64.1115			0.634767			0.317383	−	0.948297i	$-0.397196\pi$
$101$	64.1115			0.634767			0.317383	+	0.948297i	$0.397196\pi$
$102$	−53.1672	+	17.2751i	−0.521247	+	0.169363i
$103$		−	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	$0.0771046\pi$
$107$			51.3320i			0.479739i	−0.970805	+	0.239869i	$0.922895\pi$
$108$	−68.9443	−	94.8936i	−0.638373	−	0.878645i
$109$	133.469			1.22449			0.612243	−	0.790669i	$-0.290267\pi$
$109$	133.469			1.22449			0.612243	+	0.790669i	$0.290267\pi$
$110$		0			0
$111$			43.1685i			0.388906i
$112$	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	$0.772559\pi$
$114$	−22.1115	−	68.0521i	−0.193960	−	0.596948i
$115$		0			0
$116$	35.4164	−	25.7315i	0.305314	−	0.221824i
$117$	29.4164			0.251422
$118$	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
$123$		−	34.2881i		−	0.278765i
$124$	19.5016	+	26.8416i	0.157271	+	0.216464i
$125$		0			0
$126$	34.7214	−	11.2817i	0.275566	−	0.0895369i
$127$			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
$129$	52.3607			0.405897
$130$		0			0
$131$			7.77041i			0.0593161i	0.999560	+	0.0296580i	$0.00944183\pi$
$131$			7.77041i			0.0593161i	−0.999560	+	0.0296580i	$0.990558\pi$
$132$	151.554	−	110.111i	1.14814	−	0.834171i
$133$	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	$0.500967\pi$
$138$	0.806504	+	2.48217i	0.00584424	+	0.0179867i
$139$		−	237.658i		−	1.70977i	−0.518817	−	0.854885i	$-0.673627\pi$
$139$		−	237.658i		−	1.70977i	0.518817	−	0.854885i	$-0.326373\pi$
$140$		0			0
$141$	125.528			0.890269
$142$	−153.666	+	49.9290i	−1.08215	+	0.351613i
$143$			168.758i			1.18013i
$144$	17.1672	−	52.8352i	0.119217	−	0.366911i
$145$		0			0
$146$	−3.43267	−	10.5647i	−0.0235114	−	0.0723607i
$147$			50.2220i			0.341646i
$148$	−59.4164	+	43.1685i	−0.401462	+	0.291679i
$149$	−36.9706			−0.248125			−0.124062	−	0.992274i	$-0.539592\pi$
$149$	−36.9706			−0.248125			−0.124062	+	0.992274i	$0.539592\pi$
$150$		0			0
$151$			282.723i			1.87234i	0.351552	+	0.936168i	$0.385654\pi$
$151$			282.723i			1.87234i	−0.351552	+	0.936168i	$0.614346\pi$
$152$	71.5542	−	98.4859i	0.470751	−	0.647933i
$153$	−41.2786			−0.269795
$154$	64.7214	+	199.192i	0.420269	+	1.29345i
$155$		0			0
$156$	−46.8328	−	64.4598i	−0.300210	−	0.413204i
$157$	−204.748			−1.30413			−0.652063	−	0.758165i	$-0.726096\pi$
$157$	−204.748			−1.30413			−0.652063	+	0.758165i	$0.726096\pi$
$158$	−26.3344	+	8.55656i	−0.166673	+	0.0541554i
$159$			156.023i			0.981279i
$160$		0			0
$161$	−2.91796			−0.0181240
$162$	23.2968	+	71.7002i	0.143808	+	0.442594i
$163$		−	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	$-0.968299\pi$
$167$		−	33.2090i		−	0.198856i	0.995045	−	0.0994280i	$-0.0317013\pi$
$168$	−80.0000	−	58.1234i	−0.476190	−	0.345973i
$169$	−97.2229			−0.575284
$170$		0			0
$171$		−	52.8352i		−	0.308978i
$172$	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	$0.272996\pi$
$174$	−48.9443	+	15.9030i	−0.281289	+	0.0913963i
$175$		0			0
$176$	303.108	+	98.4859i	1.72221	+	0.559579i
$177$	−40.9969			−0.231621
$178$	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
$183$			211.927i			1.15807i
$184$	−2.60990	+	3.59222i	−0.0141843	+	0.0195230i
$185$		0			0
$186$	−12.0526	−	37.0942i	−0.0647990	−	0.199431i
$187$		−	236.810i		−	1.26636i
$188$	125.528	+	172.774i	0.667701	+	0.919012i
$189$	−154.164			−0.815683
$190$		0			0
$191$		−	31.0198i		−	0.162407i	−0.996698	−	0.0812036i	$-0.974124\pi$
$191$		−	31.0198i		−	0.162407i	0.996698	−	0.0812036i	$-0.0258764\pi$
$192$	−143.108	+	46.4987i	−0.745356	+	0.242181i
$193$	−110.223			−0.571103			−0.285552	−	0.958363i	$-0.592177\pi$
$193$	−110.223			−0.571103			−0.285552	+	0.958363i	$0.592177\pi$
$194$	−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	$0.355729\pi$
$198$	131.554	−	42.7445i	0.664415	−	0.215882i
$199$		−	272.208i		−	1.36788i	−0.729538	−	0.683940i	$-0.760265\pi$
$199$		−	272.208i		−	1.36788i	0.729538	−	0.683940i	$-0.239735\pi$
$200$		0			0
$201$	118.079			0.587457
$202$	−39.6231	−	121.947i	−0.196154	−	0.603699i
$203$		−	57.5374i		−	0.283436i
$204$	65.7183	+	90.4534i	0.322148	+	0.443399i
$205$		0			0
$206$	−262.053	+	85.1461i	−1.27210	+	0.413330i
$207$			1.92714i			0.00930984i
$208$	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	$-0.838305\pi$
$211$		−	205.266i		−	0.972826i	0.873729	−	0.486413i	$-0.161695\pi$
$212$	−214.748	+	156.023i	−1.01296	+	0.735959i
$213$	189.941			0.891743
$214$	97.6393	−	31.7249i	0.456259	−	0.148247i
$215$		0			0
$216$	−137.889	+	189.787i	−0.638373	+	0.878645i
$217$	43.6068			0.200953
$218$	−82.4884	−	253.873i	−0.378387	−	1.16456i
$219$			13.0586i			0.0596285i
$220$		0			0
$221$	−100.721			−0.455753
$222$	82.1115	−	26.6796i	0.369871	−	0.120179i
$223$		−	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	$0.0411417\pi$
$227$			58.5165i			0.257782i	−0.991659	+	0.128891i	$0.958858\pi$
$228$	−115.777	+	84.1170i	−0.507794	+	0.368934i
$229$	162.721			0.710574			0.355287	−	0.934757i	$-0.384383\pi$
$229$	162.721			0.710574			0.355287	+	0.934757i	$0.384383\pi$
$230$		0			0
$231$		−	246.215i		−	1.06586i
$232$	−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	$0.740047\pi$
$234$	−18.1803	−	55.9533i	−0.0776938	−	0.239117i
$235$		0			0
$236$	−40.9969	−	56.4274i	−0.173716	−	0.239099i
$237$	32.5511			0.137346
$238$	−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
$243$			175.287i			0.721347i
$244$	−291.692	+	211.927i	−1.19546	+	0.868552i
$245$		0			0
$246$	−65.2198	+	21.1912i	−0.265121	+	0.0861431i
$247$		−	128.920i		−	0.521942i
$248$	39.0031	−	53.6832i	0.157271	−	0.216464i
$249$	−179.193			−0.719653
$250$		0			0
$251$		−	136.690i		−	0.544582i	−0.962215	−	0.272291i	$-0.912219\pi$
$251$		−	136.690i		−	0.544582i	0.962215	−	0.272291i	$-0.0877813\pi$
$252$	−42.9180	−	59.0715i	−0.170309	−	0.234411i
$253$	−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	$0.320345\pi$
$258$	−32.3607	−	99.5959i	−0.125429	−	0.386031i
$259$			96.5278i			0.372694i
$260$		0			0
$261$	−38.0000			−0.145594
$262$	14.7802	−	4.80238i	0.0564130	−	0.0183297i
$263$		−	406.385i		−	1.54519i	−0.634899	−	0.772596i	$-0.718958\pi$
$263$		−	406.385i		−	1.54519i	0.634899	−	0.772596i	$-0.281042\pi$
$264$	−303.108	−	220.221i	−1.14814	−	0.834171i
$265$		0			0
$266$	−49.4427	−	152.169i	−0.185875	−	0.572064i
$267$		−	262.018i		−	0.981339i
$268$	118.079	+	162.522i	0.440593	+	0.606424i
$269$	−348.525			−1.29563			−0.647816	−	0.761797i	$-0.724317\pi$
$269$	−348.525			−1.29563			−0.647816	+	0.761797i	$0.724317\pi$
$270$		0			0
$271$		−	247.849i		−	0.914571i	−0.889320	−	0.457286i	$-0.848822\pi$
$271$		−	247.849i		−	0.914571i	0.889320	−	0.457286i	$-0.151178\pi$
$272$	−58.7802	+	180.907i	−0.216104	+	0.665099i
$273$	−104.721			−0.383595
$274$	0.514708	+	1.58411i	0.00187850	+	0.00578142i
$275$		0			0
$276$	4.22291	−	3.06813i	0.0153004	−	0.0111164i
$277$	54.7539			0.197667			0.0988337	−	0.995104i	$-0.468489\pi$
$277$	54.7539			0.197667			0.0988337	+	0.995104i	$0.468489\pi$
$278$	−452.053	+	146.881i	−1.62609	+	0.528348i
$279$		−	28.7997i		−	0.103225i
$280$		0			0
$281$	−50.3607			−0.179220			−0.0896098	−	0.995977i	$-0.528562\pi$
$281$	−50.3607			−0.179220			−0.0896098	+	0.995977i	$0.528562\pi$
$282$	−77.5805	−	238.768i	−0.275108	−	0.846696i
$283$			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
$288$	−111.108			−0.385793
$289$	−147.663			−0.510943
$290$		0			0
$291$			218.263i			0.750045i
$292$	−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	$0.598730\pi$
$294$	95.5279	−	31.0389i	0.324925	−	0.105574i
$295$		0			0
$296$	118.833	+	86.3371i	0.401462	+	0.291679i
$297$	−584.105			−1.96668
$298$	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
$303$			150.735i			0.497475i
$304$	−231.554	−	75.2365i	−0.761691	−	0.247489i
$305$		0			0
$306$	25.5116	+	78.5166i	0.0833713	+	0.256590i
$307$			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
$309$	323.915			1.04827
$310$		0			0
$311$			282.199i			0.907392i	0.891157	+	0.453696i	$0.149895\pi$
$311$			282.199i			0.907392i	−0.891157	+	0.453696i	$0.850105\pi$
$312$	−93.6656	+	128.920i	−0.300210	+	0.413204i
$313$	567.548			1.81325			0.906626	−	0.421935i	$-0.138649\pi$
$313$	567.548			1.81325			0.906626	+	0.421935i	$0.138649\pi$
$314$	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	$0.581801\pi$
$318$	296.774	−	96.4277i	0.933252	−	0.303232i
$319$		−	218.001i		−	0.683389i
$320$		0			0
$321$	−120.689			−0.375978
$322$	1.80340	+	5.55029i	0.00560062	+	0.0172369i
$323$			180.907i			0.560083i
$324$	121.984	−	88.6264i	0.376493	−	0.273538i
$325$		0			0
$326$	−203.974	+	66.2751i	−0.625686	+	0.203298i
$327$			313.805i			0.959647i
$328$	−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	$0.167203\pi$
$331$			331.966i			1.00292i	−0.865181	+	0.501459i	$0.832797\pi$
$332$	−179.193	−	246.639i	−0.539739	−	0.742888i
$333$	63.7508			0.191444
$334$	−63.1672	+	20.5243i	−0.189123	+	0.0614499i
$335$		0			0
$336$	−61.1146	+	188.091i	−0.181889	+	0.559795i
$337$	269.108			0.798541			0.399271	−	0.916833i	$-0.369263\pi$
$337$	269.108			0.798541			0.399271	+	0.916833i	$0.369263\pi$
$338$	60.0871	+	184.929i	0.177772	+	0.547127i
$339$		−	401.390i		−	1.18404i
$340$		0			0
$341$	165.220			0.484516
$342$	−100.498	+	32.6539i	−0.293855	+	0.0954793i
$343$			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	$0.258110\pi$
$347$			503.075i			1.44978i	−0.688863	+	0.724892i	$0.741890\pi$
$348$	60.4984	+	83.2690i	0.173846	+	0.239279i
$349$	−0.504658			−0.00144601			−0.000723006	−	1.00000i	$-0.500230\pi$
$349$	−0.504658			−0.00144601			−0.000723006		1.00000i	$0.500230\pi$
$350$		0			0
$351$			248.435i			0.707791i
$352$		−	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	$0.342118\pi$
$354$	25.3375	+	77.9807i	0.0715748	+	0.220285i
$355$		0			0
$356$	360.636	−	262.018i	1.01302	−	0.736004i
$357$	146.950			0.411626
$358$	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
$363$		−	648.384i		−	1.78618i
$364$	−104.721	−	144.137i	−0.287696	−	0.395980i
$365$		0			0
$366$	403.108	−	130.978i	1.10139	−	0.357863i
$367$		−	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
$369$	−50.6362			−0.137226
$370$		0			0
$371$			348.879i			0.940374i
$372$	−63.1084	+	45.8509i	−0.169646	+	0.123255i
$373$	−600.354			−1.60953			−0.804765	−	0.593594i	$-0.797709\pi$
$373$	−600.354			−1.60953			−0.804765	+	0.593594i	$0.797709\pi$
$374$	−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
$378$	95.2786	+	293.238i	0.252060	+	0.775761i
$379$			303.490i			0.800765i	0.916348	+	0.400383i	$0.131123\pi$
$379$			303.490i			0.800765i	−0.916348	+	0.400383i	$0.868877\pi$
$380$		0			0
$381$	−467.023			−1.22578
$382$	−59.0031	+	19.1713i	−0.154458	+	0.0501866i
$383$			332.583i			0.868362i	0.900826	+	0.434181i	$0.142962\pi$
$383$			332.583i			0.868362i	−0.900826	+	0.434181i	$0.857038\pi$
$384$	176.892	+	243.470i	0.460655	+	0.634038i
$385$		0			0
$386$	68.1215	+	209.656i	0.176481	+	0.543151i
$387$		−	77.3256i		−	0.199808i
$388$	−300.413	+	218.263i	−0.774261	+	0.562534i
$389$	392.354			1.00862			0.504312	−	0.863522i	$-0.331746\pi$
$389$	392.354			1.00862			0.504312	+	0.863522i	$0.331746\pi$
$390$		0			0
$391$		−	6.59849i		−	0.0168759i
$392$	138.249	+	100.444i	0.352677	+	0.256235i
$393$	−18.2693			−0.0464868
$394$	−106.626	−	328.162i	−0.270625	−	0.832897i
$395$		0			0
$396$	−162.610	−	223.813i	−0.410631	−	0.565185i
$397$	−334.190			−0.841789			−0.420895	−	0.907110i	$-0.638284\pi$
$397$	−334.190			−0.841789			−0.420895	+	0.907110i	$0.638284\pi$
$398$	−517.771	+	168.234i	−1.30093	+	0.422698i
$399$			188.091i			0.471407i
$400$		0			0
$401$	121.003			0.301753			0.150877	−	0.988553i	$-0.451790\pi$
$401$	121.003			0.301753			0.150877	+	0.988553i	$0.451790\pi$
$402$	−72.9768	−	224.599i	−0.181534	−	0.558705i
$403$		−	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
$408$	131.437	−	180.907i	0.322148	−	0.443399i
$409$	−607.410			−1.48511			−0.742555	−	0.669785i	$-0.766386\pi$
$409$	−607.410			−1.48511			−0.742555	+	0.669785i	$0.766386\pi$
$410$		0			0
$411$		−	1.95807i		−	0.00476415i
$412$	323.915	+	445.831i	0.786201	+	1.08211i
$413$	−91.6718			−0.221966
$414$	3.66563	−	1.19104i	0.00885418	−	0.00287690i
$415$		0			0
$416$	−271.108			−0.651703
$417$	558.768			1.33997
$418$	−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
$423$		−	185.378i		−	0.438246i
$424$	429.495	+	312.047i	1.01296	+	0.735959i
$425$		0			0
$426$	−117.390	−	361.290i	−0.275564	−	0.848098i
$427$			473.882i			1.10979i
$428$	−120.689	−	166.114i	−0.281983	−	0.388117i
$429$	−396.774			−0.924881
$430$		0			0
$431$		−	463.630i		−	1.07571i	−0.843038	−	0.537853i	$-0.819235\pi$
$431$		−	463.630i		−	1.07571i	0.843038	−	0.537853i	$-0.180765\pi$
$432$	446.217	+	144.985i	1.03291	+	0.335612i
$433$	99.8359			0.230568			0.115284	−	0.993333i	$-0.463222\pi$
$433$	99.8359			0.230568			0.115284	+	0.993333i	$0.463222\pi$
$434$	−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
$438$	24.8390	−	8.07069i	0.0567101	−	0.0184262i
$439$			374.086i			0.852133i	0.904692	+	0.426066i	$0.140101\pi$
$439$			374.086i			0.852133i	−0.904692	+	0.426066i	$0.859899\pi$
$440$		0			0
$441$	74.1672			0.168180
$442$	62.2492	+	191.583i	0.140835	+	0.433447i
$443$			290.100i			0.654854i	0.944877	+	0.327427i	$0.106182\pi$
$443$			290.100i			0.654854i	−0.944877	+	0.327427i	$0.893818\pi$
$444$	−101.495	−	139.696i	−0.228593	−	0.314631i
$445$		0			0
$446$	−448.387	+	145.690i	−1.00535	+	0.326659i
$447$		−	86.9231i		−	0.194459i
$448$	−320.000	+	103.974i	−0.714286	+	0.232085i
$449$	299.921			0.667976			0.333988	−	0.942577i	$-0.391606\pi$
$449$	299.921			0.667976			0.333988	+	0.942577i	$0.391606\pi$
$450$		0			0
$451$		−	290.493i		−	0.644109i
$452$	552.466	−	401.390i	1.22227	−	0.888031i
$453$	−664.721			−1.46738
$454$	111.305	−	36.1652i	0.245165	−	0.0796590i
$455$		0			0
$456$	231.554	+	168.234i	0.507794	+	0.368934i
$457$	−822.328			−1.79941			−0.899703	−	0.436503i	$-0.856217\pi$
$457$	−822.328			−1.79941			−0.899703	+	0.436503i	$0.856217\pi$
$458$	−100.567	−	309.514i	−0.219579	−	0.675796i
$459$		−	348.617i		−	0.759513i
$460$		0			0
$461$	−456.885			−0.991075			−0.495537	−	0.868587i	$-0.665029\pi$
$461$	−456.885			−0.991075			−0.495537	+	0.868587i	$0.665029\pi$
$462$	−468.328	+	152.169i	−1.01370	+	0.329370i
$463$		−	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	$-0.567392\pi$
$467$		−	913.145i		−	1.95534i	0.210139	−	0.977672i	$-0.432608\pi$
$468$	−95.1935	+	69.1621i	−0.203405	+	0.147782i
$469$	264.033			0.562969
$470$		0			0
$471$		−	481.391i		−	1.02206i
$472$	−81.9938	+	112.855i	−0.173716	+	0.239099i
$473$	443.607			0.937858
$474$	−20.1177	−	61.9158i	−0.0424423	−	0.130624i
$475$		0			0
$476$	146.950	+	202.260i	0.308720	+	0.424916i
$477$	230.413			0.483047
$478$	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
$483$		−	6.86054i		−	0.0142040i
$484$	892.423	−	648.384i	1.84385	−	1.33964i
$485$		0			0
$486$	333.416	−	108.334i	0.686042	−	0.222909i
$487$		−	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
$489$	252.125			0.515594
$490$		0			0
$491$		−	287.163i		−	0.584854i	−0.956288	−	0.292427i	$-0.905537\pi$
$491$		−	287.163i		−	0.584854i	0.956288	−	0.292427i	$-0.0944628\pi$
$492$	80.6161	+	110.959i	0.163854	+	0.225526i
$493$	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
$498$	110.748	+	340.846i	0.222385	+	0.684430i
$499$			810.936i			1.62512i	0.582876	+	0.812561i	$0.301927\pi$
$499$			810.936i			1.62512i	−0.582876	+	0.812561i	$0.698073\pi$
$500$		0			0
$501$	78.0789			0.155846
$502$	−260.000	+	84.4791i	−0.517928	+	0.168285i
$503$		−	642.471i		−	1.27728i	−0.769506	−	0.638639i	$-0.779498\pi$
$503$		−	642.471i		−	1.27728i	0.769506	−	0.638639i	$-0.220502\pi$
$504$	−85.8359	+	118.143i	−0.170309	+	0.234411i
$505$		0			0
$506$	6.83282	+	21.0292i	0.0135036	+	0.0415598i
$507$		−	228.585i		−	0.450858i
$508$	−467.023	−	642.802i	−0.919337	−	1.26536i
$509$	−915.050			−1.79774			−0.898870	−	0.438216i	$-0.855611\pi$
$509$	−915.050			−1.79774			−0.898870	+	0.438216i	$0.855611\pi$
$510$		0			0
$511$			29.2000i			0.0571429i
$512$	−158.217	+	486.941i	−0.309017	+	0.951057i
$513$	446.217			0.869818
$514$	−169.925	−	522.975i	−0.330593	−	1.01746i
$515$		0			0
$516$	−169.443	+	123.107i	−0.328377	+	0.238580i
$517$	1063.49			2.05704
$518$	183.607	−	59.6575i	0.354453	−	0.115169i
$519$			532.206i			1.02544i
$520$		0			0
$521$	1006.98			1.93279			0.966396	−	0.257058i	$-0.0827533\pi$
$521$	1006.98			1.93279			0.966396	+	0.257058i	$0.0827533\pi$
$522$	23.4853	+	72.2803i	0.0449910	+	0.138468i
$523$			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
$528$	−231.554	+	712.650i	−0.438550	+	1.34972i
$529$	528.692			0.999418
$530$		0			0
$531$			60.5437i			0.114018i
$532$	−258.885	+	188.091i	−0.486627	+	0.353555i
$533$	−123.554			−0.231809
$534$	−498.387	+	161.936i	−0.933309	+	0.303250i
$535$		0			0
$536$	236.158	−	325.043i	0.440593	−	0.606424i
$537$	−527.449			−0.982214
$538$	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
$543$			202.722i			0.373337i
$544$	380.433			0.699326
$545$		0			0
$546$	64.7214	+	199.192i	0.118537	+	0.364820i
$547$			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
$549$	312.971			0.570074
$550$		0			0
$551$			166.538i			0.302247i
$552$	−8.44582	−	6.13625i	−0.0153004	−	0.0111164i
$553$	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	$0.651912\pi$
$558$	−54.7802	+	17.7992i	−0.0981724	+	0.0318981i
$559$		−	188.677i		−	0.337526i
$560$		0			0
$561$	556.774			0.992467
$562$	31.1246	+	95.7917i	0.0553819	+	0.170448i
$563$		−	490.726i		−	0.871627i	−0.900037	−	0.435814i	$-0.856461\pi$
$563$		−	490.726i		−	0.871627i	0.900037	−	0.435814i	$-0.143539\pi$
$564$	−406.217	+	295.134i	−0.720242	+	0.523287i
$565$		0			0
$566$	280.249	−	91.0585i	0.495140	−	0.160881i
$567$		−	198.175i		−	0.349514i
$568$	379.882	−	522.863i	0.668807	−	0.920534i
$569$	−232.748			−0.409047			−0.204523	−	0.978862i	$-0.565564\pi$
$569$	−232.748			−0.409047			−0.204523	+	0.978862i	$0.565564\pi$
$570$		0			0
$571$		−	210.755i		−	0.369098i	−0.982823	−	0.184549i	$-0.940918\pi$
$571$		−	210.755i		−	0.369098i	0.982823	−	0.184549i	$-0.0590824\pi$
$572$	−396.774	−	546.113i	−0.693661	−	0.954742i
$573$	72.9318			0.127281
$574$	−145.836	+	47.3850i	−0.254070	+	0.0825522i
$575$		0			0
$576$	68.6687	+	211.341i	0.119217	+	0.366911i
$577$	−341.712			−0.592222			−0.296111	−	0.955154i	$-0.595690\pi$
$577$	−341.712			−0.592222			−0.296111	+	0.955154i	$0.595690\pi$
$578$	91.2605	+	280.871i	0.157890	+	0.485936i
$579$		−	259.150i		−	0.447581i
$580$		0			0
$581$	−400.689			−0.689654
$582$	415.161	−	134.894i	0.713335	−	0.231777i
$583$			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	$-0.823408\pi$
$587$		−	618.412i		−	1.05351i	0.850016	−	0.526756i	$-0.176592\pi$
$588$	−118.079	−	162.522i	−0.200815	−	0.276397i
$589$	−126.217			−0.214290
$590$		0			0
$591$			405.630i			0.686345i
$592$	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	$0.532441\pi$
$594$	360.997	+	1111.03i	0.607739	+	1.87043i
$595$		0			0
$596$	119.639	−	86.9231i	0.200737	−	0.145844i
$597$	640.000			1.07203
$598$	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
$603$		−	174.378i		−	0.289183i
$604$	−664.721	−	914.910i	−1.10053	−	1.51475i
$605$		0			0
$606$	286.715	−	93.1594i	0.473127	−	0.153728i
$607$			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
$609$	135.279			0.222132
$610$		0			0
$611$		−	452.329i		−	0.740309i
$612$	133.580	−	97.0519i	0.218269	−	0.158582i
$613$	−499.475			−0.814805			−0.407402	−	0.913249i	$-0.633565\pi$
$613$	−499.475			−0.814805			−0.407402	+	0.913249i	$0.633565\pi$
$614$	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	$0.645877\pi$
$618$	−200.190	−	616.123i	−0.323933	−	0.996962i
$619$			455.011i			0.735075i	0.930009	+	0.367537i	$0.119799\pi$
$619$			455.011i			0.735075i	−0.930009	+	0.367537i	$0.880201\pi$
$620$		0			0
$621$	−16.2755			−0.0262086
$622$	536.774	−	174.408i	0.862981	−	0.280399i
$623$		−	585.889i		−	0.940432i
$624$	303.108	+	98.4859i	0.485751	+	0.157830i
$625$		0			0
$626$	−350.764	−	1079.54i	−0.560326	−	1.72451i
$627$			712.650i			1.13660i
$628$	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	$0.0680395\pi$
$631$			267.706i			0.424257i	−0.977242	+	0.212128i	$0.931960\pi$
$632$	65.1021	−	89.6054i	0.103010	−	0.141781i
$633$	482.610			0.762417
$634$	99.5905	+	306.508i	0.157083	+	0.483451i
$635$		0			0
$636$	−366.833	−	504.902i	−0.576781	−	0.793871i
$637$	180.971			0.284098
$638$	−414.663	+	134.732i	−0.649941	+	0.211179i
$639$		−	280.503i		−	0.438971i
$640$		0			0
$641$	−418.571			−0.652997			−0.326499	−	0.945198i	$-0.605869\pi$
$641$	−418.571			−0.652997			−0.326499	+	0.945198i	$0.605869\pi$
$642$	74.5898	+	229.564i	0.116183	+	0.357576i
$643$		−	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	$-0.894871\pi$
$647$		−	419.644i		−	0.648600i	0.945954	−	0.324300i	$-0.105129\pi$
$648$	−243.967	−	177.253i	−0.376493	−	0.273538i
$649$	−347.331			−0.535179
$650$		0			0
$651$			102.526i			0.157490i
$652$	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	$0.408547\pi$
$654$	596.892	−	193.942i	0.912678	−	0.296547i
$655$		0			0
$656$	−72.1052	+	221.917i	−0.109917	+	0.338288i
$657$	19.2849			0.0293529
$658$	−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
$663$		−	236.810i		−	0.357180i
$664$	−358.387	+	493.277i	−0.539739	+	0.742888i
$665$		0			0
$666$	−39.4001	−	121.261i	−0.0591594	−	0.182074i
$667$		−	6.07439i		−	0.00910703i
$668$	78.0789	+	107.466i	0.116885	+	0.160878i
$669$	554.237			0.828456
$670$		0			0
$671$			1795.47i			2.67581i
$672$	395.542			0.588604
$673$	−467.378			−0.694469			−0.347235	−	0.937778i	$-0.612879\pi$
$673$	−467.378			−0.694469			−0.347235	+	0.937778i	$0.612879\pi$
$674$	−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	$0.632694\pi$
$678$	−763.489	+	248.073i	−1.12609	+	0.365889i
$679$			488.051i			0.718779i
$680$		0			0
$681$	−137.580			−0.202027
$682$	−102.111	−	314.267i	−0.149724	−	0.460802i
$683$		−	23.9663i		−	0.0350898i	−0.999846	−	0.0175449i	$-0.994415\pi$
$683$		−	23.9663i		−	0.0350898i	0.999846	−	0.0175449i	$-0.00558500\pi$
$684$	124.223	+	170.978i	0.181612	+	0.249968i
$685$		0			0
$686$	703.607	−	228.616i	1.02567	−	0.333259i
$687$			382.581i			0.556886i
$688$	−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	$-0.956801\pi$
$691$		−	186.981i		−	0.270595i	0.990805	−	0.135298i	$-0.0431990\pi$
$692$	−732.519	+	532.206i	−1.05855	+	0.769084i
$693$	−363.607			−0.524685
$694$	956.906	−	310.917i	1.37883	−	0.448008i
$695$		0			0
$696$	120.997	−	166.538i	0.173846	−	0.239279i
$697$	173.378			0.248748
$698$	0.311896	+	0.959917i	0.000446842	+	0.00137524i
$699$		−	750.130i		−	1.07315i
$700$		0			0
$701$	−706.636			−1.00804			−0.504020	−	0.863692i	$-0.668146\pi$
$701$	−706.636			−1.00804			−0.504020	+	0.863692i	$0.668146\pi$
$702$	472.551	−	153.541i	0.673150	−	0.218720i
$703$		−	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
$708$	132.669	−	96.3895i	0.187385	−	0.136143i
$709$	−188.597			−0.266005			−0.133002	−	0.991116i	$-0.542462\pi$
$709$	−188.597			−0.266005			−0.133002	+	0.991116i	$0.542462\pi$
$710$		0			0
$711$		−	48.0710i		−	0.0676104i
$712$	−721.272	−	524.035i	−1.01302	−	0.736004i
$713$	4.60369			0.00645679
$714$	−90.8204	−	279.516i	−0.127199	−	0.391480i
$715$		0			0
$716$	−527.449	−	725.971i	−0.736661	−	1.01393i
$717$	−556.774			−0.776533
$718$	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
$723$		−	2.15825i		−	0.00298514i
$724$	−279.023	+	202.722i	−0.385391	+	0.280003i
$725$		0			0
$726$	−1233.30	+	400.723i	−1.69876	+	0.551960i
$727$			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
$729$	−751.381			−1.03070
$730$		0			0
$731$			264.762i			0.362191i
$732$	−498.269	−	685.809i	−0.680696	−	0.936897i
$733$	−1233.29			−1.68252			−0.841259	−	0.540632i	$-0.818185\pi$
$733$	−1233.29			−1.68252			−0.841259	+	0.540632i	$0.818185\pi$
$734$	−948.152	+	308.073i	−1.29176	+	0.419718i
$735$		0			0
$736$		−	17.7609i		−	0.0241317i
$737$	1000.38			1.35737
$738$	31.2949	+	96.3158i	0.0424050	+	0.130509i
$739$			8.55656i			0.0115786i	0.999983	+	0.00578928i	$0.00184280\pi$
$739$			8.55656i			0.0115786i	−0.999983	+	0.00578928i	$0.998157\pi$
$740$		0			0
$741$	303.108			0.409053
$742$	663.607	−	215.619i	0.894349	−	0.290592i
$743$			1010.56i			1.36011i	0.733163	+	0.680053i	$0.238043\pi$
$743$			1010.56i			1.36011i	−0.733163	+	0.680053i	$0.761957\pi$
$744$	126.217	+	91.7018i	0.169646	+	0.123255i
$745$		0			0
$746$	371.039	+	1141.94i	0.497372	+	1.53075i
$747$			264.631i			0.354258i
$748$	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	$-0.737075\pi$
$751$		−	1104.31i		−	1.47046i	0.677820	−	0.735228i	$-0.262925\pi$
$752$	−812.433	−	263.976i	−1.08036	−	0.351031i
$753$	321.378			0.426796
$754$	57.3050	+	176.367i	0.0760013	+	0.233908i
$755$		0			0
$756$	498.885	−	362.461i	0.659901	−	0.479446i
$757$	875.633			1.15671			0.578357	−	0.815783i	$-0.303694\pi$
$757$	875.633			1.15671			0.578357	+	0.815783i	$0.303694\pi$
$758$	577.272	−	187.567i	0.761573	−	0.247450i
$759$		−	25.9936i		−	0.0342471i
$760$		0			0
$761$	−647.207			−0.850470			−0.425235	−	0.905083i	$-0.639808\pi$
$761$	−647.207			−0.850470			−0.425235	+	0.905083i	$0.639808\pi$
$762$	288.636	+	888.331i	0.378788	+	1.16579i
$763$			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
$768$	353.783	−	486.941i	0.460655	−	0.634038i
$769$	631.430			0.821106			0.410553	−	0.911837i	$-0.365336\pi$
$769$	631.430			0.821106			0.410553	+	0.911837i	$0.365336\pi$
$770$		0			0
$771$			646.433i			0.838434i
$772$	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	$0.412099\pi$
$774$	−147.082	+	47.7899i	−0.190028	+	0.0617440i
$775$		0			0
$776$	600.827	+	436.526i	0.774261	+	0.562534i
$777$	−226.950			−0.292086
$778$	−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
$783$		−	320.927i		−	0.409869i
$784$	105.613	−	325.043i	0.134710	−	0.414596i
$785$		0			0
$786$	11.2911	+	34.7503i	0.0143652	+	0.0442116i
$787$		−	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
$789$	955.469			1.21099
$790$		0			0
$791$		−	897.535i		−	1.13468i
$792$	−325.220	+	447.627i	−0.410631	+	0.565185i
$793$	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	$0.775458\pi$
$798$	357.771	−	116.247i	0.448334	−	0.145673i
$799$			634.732i			0.794408i
$800$		0			0
$801$	−386.944			−0.483076
$802$	−74.7840	−	230.162i	−0.0932469	−	0.286985i
$803$			110.635i			0.137777i
$804$	−382.111	+	277.620i	−0.475263	+	0.345299i
$805$		0			0
$806$	−133.666	+	43.4306i	−0.165838	+	0.0538841i
$807$		−	819.431i		−	1.01540i
$808$	414.938	+	301.470i	0.513537	+	0.373107i
$809$	−229.214			−0.283330			−0.141665	−	0.989915i	$-0.545246\pi$
$809$	−229.214			−0.283330			−0.141665	+	0.989915i	$0.545246\pi$
$810$		0			0
$811$			454.225i			0.560080i	0.959988	+	0.280040i	$0.0903478\pi$
$811$			454.225i			0.560080i	−0.959988	+	0.280040i	$0.909652\pi$
$812$	135.279	+	186.195i	0.166599	+	0.229304i
$813$	582.728			0.716762
$814$	695.659	−	226.033i	0.854618	−	0.277682i
$815$		0			0
$816$	−425.337	−	138.201i	−0.521247	−	0.169363i
$817$	−338.885			−0.414792
$818$	375.400	+	1155.36i	0.458924	+	1.41242i
$819$			154.651i			0.188829i
$820$		0			0
$821$	1130.90			1.37747			0.688733	−	0.725015i	$-0.258167\pi$
$821$	1130.90			1.37747			0.688733	+	0.725015i	$0.258167\pi$
$822$	−3.72447	+	1.21015i	−0.00453098	+	0.00147220i
$823$		−	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	$-0.959636\pi$
$827$		−	209.175i		−	0.252932i	0.991971	−	0.126466i	$-0.0403635\pi$
$828$	−4.53097	−	6.23634i	−0.00547219	−	0.00753182i
$829$	−508.525			−0.613419			−0.306710	−	0.951803i	$-0.599228\pi$
$829$	−508.525			−0.613419			−0.306710	+	0.951803i	$0.599228\pi$
$830$		0			0
$831$			128.734i			0.154915i
$832$	167.554	+	515.679i	0.201387	+	0.619806i
$833$	−253.947			−0.304859
$834$	−345.337	−	1062.84i	−0.414074	−	1.27439i
$835$		0			0
$836$	−980.879	+	712.650i	−1.17330	+	0.852453i
$837$	243.226			0.290593
$838$	−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
$843$		−	118.405i		−	0.140457i
$844$	482.610	+	664.256i	0.571813	+	0.787033i
$845$		0			0
$846$	−352.610	+	114.570i	−0.416797	+	0.135425i
$847$		−	1449.83i		−	1.71172i
$848$	328.105	−	1009.80i	0.386917	−	1.19081i
$849$	−346.407			−0.408018
$850$		0			0
$851$			10.1907i			0.0119750i
$852$	−614.663	+	446.578i	−0.721435	+	0.524153i
$853$	1583.28			1.85613			0.928066	−	0.372416i	$-0.121471\pi$
$853$	1583.28			1.85613			0.928066	+	0.372416i	$0.121471\pi$
$854$	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	$0.300020\pi$
$858$	245.220	+	754.709i	0.285804	+	0.879614i
$859$		−	76.6086i		−	0.0891835i	−0.999005	−	0.0445917i	$-0.985801\pi$
$859$		−	76.6086i		−	0.0891835i	0.999005	−	0.0445917i	$-0.0141987\pi$
$860$		0			0
$861$	180.263			0.209365
$862$	−881.876	+	286.539i	−1.02306	+	0.332412i
$863$			255.450i			0.296002i	0.988987	+	0.148001i	$0.0472839\pi$
$863$			255.450i			0.296002i	−0.988987	+	0.148001i	$0.952716\pi$
$864$		−	938.360i		−	1.08606i
$865$		0			0
$866$	−61.7020	−	189.899i	−0.0712494	−	0.219283i
$867$		−	347.175i		−	0.400433i
$868$	−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
$873$	322.328			0.369219
$874$	−5.21981	−	16.0649i	−0.00597232	−	0.0183809i
$875$		0			0
$876$	−30.7027	−	42.2587i	−0.0350488	−	0.0482405i
$877$	−601.522			−0.685886			−0.342943	−	0.939356i	$-0.611424\pi$
$877$	−601.522			−0.685886			−0.342943	+	0.939356i	$0.611424\pi$
$878$	711.554	−	231.198i	0.810426	−	0.263323i
$879$		−	420.523i		−	0.478411i
$880$		0			0
$881$	237.850			0.269977			0.134989	−	0.990847i	$-0.456900\pi$
$881$	237.850			0.269977			0.134989	+	0.990847i	$0.456900\pi$
$882$	−45.8378	−	141.074i	−0.0519703	−	0.159948i
$883$			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	$0.0977682\pi$
$887$			536.353i			0.604682i	−0.953200	+	0.302341i	$0.902232\pi$
$888$	−202.991	+	279.393i	−0.228593	+	0.314631i
$889$	−1044.30			−1.17469
$890$		0			0
$891$		−	750.855i		−	0.842710i
$892$	554.237	+	762.842i	0.621342	+	0.855203i
$893$	−812.433			−0.909780
$894$	−165.337	+	53.7214i	−0.184941	+	0.0600911i
$895$		0			0
$896$	395.542	+	544.417i	0.441453	+	0.607608i
$897$	−11.0557			−0.0123252
$898$	−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
$903$			275.276i			0.304846i
$904$	−1104.93	−	802.780i	−1.22227	−	0.888031i
$905$		0			0
$906$	410.820	+	1264.38i	0.453444	+	1.39556i
$907$		−	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
$909$	222.604			0.244889
$910$		0			0
$911$		−	1450.06i		−	1.59172i	−0.605478	−	0.795862i	$-0.707018\pi$
$911$		−	1450.06i		−	1.59172i	0.605478	−	0.795862i	$-0.292982\pi$
$912$	176.892	−	544.417i	0.193960	−	0.596948i
$913$	−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
$918$	−663.108	+	215.457i	−0.722340	+	0.234703i
$919$			814.405i			0.886186i	0.896476	+	0.443093i	$0.146119\pi$
$919$			814.405i			0.886186i	−0.896476	+	0.443093i	$0.853881\pi$
$920$		0			0
$921$	−669.017			−0.726403
$922$	282.371	+	869.048i	0.306259	+	0.942568i
$923$		−	684.437i		−	0.741535i
$924$	578.885	+	796.767i	0.626499	+	0.862302i
$925$		0			0
$926$	−761.319	+	247.367i	−0.822159	+	0.267136i
$927$		−	478.353i		−	0.516023i
$928$	350.217			0.377389
$929$	400.039			0.430612			0.215306	−	0.976547i	$-0.430925\pi$
$929$	400.039			0.430612			0.215306	+	0.976547i	$0.430925\pi$
$930$		0			0
$931$		−	325.043i		−	0.349134i
$932$	1032.47	−	750.130i	1.10780	−	0.804861i
$933$	−663.489			−0.711135
$934$	−1736.91	+	564.355i	−1.85964	+	0.604234i
$935$		0			0
$936$	190.387	+	138.324i	0.203405	+	0.147782i
$937$	−249.279			−0.266039			−0.133020	−	0.991113i	$-0.542467\pi$
$937$	−249.279			−0.266039			−0.133020	+	0.991113i	$0.542467\pi$
$938$	−163.181	−	502.220i	−0.173967	−	0.535415i
$939$			1334.39i			1.42107i
$940$		0			0
$941$	724.229			0.769638			0.384819	−	0.922992i	$-0.374264\pi$
$941$	724.229			0.769638			0.384819	+	0.922992i	$0.374264\pi$
$942$	−915.659	+	297.516i	−0.972038	+	0.315834i
$943$		−	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	$0.205913\pi$
$947$			1141.54i			1.20542i	−0.797959	+	0.602712i	$0.794087\pi$
$948$	−105.337	+	76.5322i	−0.111115	+	0.0807301i
$949$	47.0557			0.0495845
$950$		0			0
$951$		−	378.865i		−	0.398386i
$952$	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	$0.737848\pi$
$954$	−142.403	−	438.272i	−0.149270	−	0.459405i
$955$		0			0
$956$	−556.774	−	766.334i	−0.582400	−	0.801604i
$957$	512.551			0.535581
$958$	−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
$963$			178.232i			0.185080i
$964$	2.97058	−	2.15825i	0.00308152	−	0.00223885i
$965$		0			0
$966$	−13.0495	+	4.24005i	−0.0135088	+	0.00438928i
$967$			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
$969$	−425.337			−0.438945
$970$		0			0
$971$		−	928.093i		−	0.955811i	−0.878411	−	0.477906i	$-0.841396\pi$
$971$		−	928.093i		−	0.955811i	0.878411	−	0.477906i	$-0.158604\pi$
$972$	−412.125	−	567.242i	−0.423997	−	0.583582i
$973$	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	$0.250836\pi$
$978$	−155.822	−	479.571i	−0.159327	−	0.490359i
$979$		−	2219.85i		−	2.26747i
$980$		0			0
$981$	463.423			0.472398
$982$	−546.217	+	177.477i	−0.556229	+	0.180730i
$983$		−	311.291i		−	0.316675i	−0.987385	−	0.158337i	$-0.949387\pi$
$983$		−	311.291i		−	0.316675i	0.987385	−	0.158337i	$-0.0506134\pi$
$984$	161.232	−	221.917i	0.163854	−	0.225526i
$985$		0			0
$986$	−80.4133	−	247.487i	−0.0815551	−	0.251001i
$987$			659.939i			0.668631i
$988$	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	$0.161158\pi$
$991$			961.147i			0.969876i	−0.874549	+	0.484938i	$0.838842\pi$
$992$			265.424i			0.267565i
$993$	−780.498			−0.786000
$994$	−262.492	−	807.868i	−0.264077	−	0.812745i
$995$		0			0
$996$	579.882	−	421.309i	0.582211	−	0.423001i
$997$	1089.68			1.09296			0.546479	−	0.837473i	$-0.315968\pi$
$997$	1089.68			1.09296			0.546479	+	0.837473i	$0.315968\pi$
$998$	1542.49	−	501.186i	1.54558	−	0.502190i
$999$			538.404i			0.538943i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.b.a.11.3	✓	4	20.19	odd	2
20.3.b.a.11.4	yes	4	5.4	even	2
100.3.b.f.51.1		4	1.1	even	1	trivial
100.3.b.f.51.2		4	4.3	odd	2	inner
100.3.d.b.99.1		8	20.7	even	4
100.3.d.b.99.2		8	5.3	odd	4
100.3.d.b.99.7		8	5.2	odd	4
100.3.d.b.99.8		8	20.3	even	4
180.3.c.a.91.1		4	15.14	odd	2
180.3.c.a.91.2		4	60.59	even	2
320.3.b.c.191.2		4	40.19	odd	2
320.3.b.c.191.3		4	40.29	even	2
900.3.c.k.451.3		4	12.11	even	2
900.3.c.k.451.4		4	3.2	odd	2
900.3.f.e.199.1		8	60.23	odd	4
900.3.f.e.199.2		8	15.2	even	4
900.3.f.e.199.7		8	15.8	even	4
900.3.f.e.199.8		8	60.47	odd	4
1280.3.g.e.1151.3		8	80.69	even	4
1280.3.g.e.1151.4		8	80.19	odd	4
1280.3.g.e.1151.5		8	80.59	odd	4
1280.3.g.e.1151.6		8	80.29	even	4
1600.3.b.s.1151.2		4	8.5	even	2
1600.3.b.s.1151.3		4	8.3	odd	2
1600.3.h.n.1599.3		8	40.37	odd	4
1600.3.h.n.1599.4		8	40.3	even	4
1600.3.h.n.1599.5		8	40.13	odd	4
1600.3.h.n.1599.6		8	40.27	even	4
2880.3.e.e.2431.1		4	120.29	odd	2
2880.3.e.e.2431.2		4	120.59	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.618034 - 1.90211i) q^{2} +2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} +(4.47214 - 1.45309i) q^{6} +5.25731i q^{7} +(6.47214 + 4.70228i) q^{8} +3.47214 q^{9} +O(q^{10})\)	\(q+(-0.618034 - 1.90211i) q^{2} +2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} +(4.47214 - 1.45309i) q^{6} +5.25731i q^{7} +(6.47214 + 4.70228i) q^{8} +3.47214 q^{9} +19.9192i q^{11} +(-5.52786 - 7.60845i) q^{12} +8.47214 q^{13} +(10.0000 - 3.24920i) q^{14} +(4.94427 - 15.2169i) q^{16} -11.8885 q^{17} +(-2.14590 - 6.60440i) q^{18} -15.2169i q^{19} -12.3607 q^{21} +(37.8885 - 12.3107i) q^{22} +0.555029i q^{23} +(-11.0557 + 15.2169i) q^{24} +(-5.23607 - 16.1150i) q^{26} +29.3238i q^{27} +(-12.3607 - 17.0130i) q^{28} -10.9443 q^{29} -8.29451i q^{31} -32.0000 q^{32} -46.8328 q^{33} +(7.34752 + 22.6134i) q^{34} +(-11.2361 + 8.16348i) q^{36} +18.3607 q^{37} +(-28.9443 + 9.40456i) q^{38} +19.9192i q^{39} -14.5836 q^{41} +(7.63932 + 23.5114i) q^{42} -22.2703i q^{43} +(-46.8328 - 64.4598i) q^{44} +(1.05573 - 0.343027i) q^{46} -53.3902i q^{47} +(35.7771 + 11.6247i) q^{48} +21.3607 q^{49} -27.9516i q^{51} +(-27.4164 + 19.9192i) q^{52} +66.3607 q^{53} +(55.7771 - 18.1231i) q^{54} +(-24.7214 + 34.0260i) q^{56} +35.7771 q^{57} +(6.76393 + 20.8172i) q^{58} +17.4370i q^{59} +90.1378 q^{61} +(-15.7771 + 5.12629i) q^{62} +18.2541i q^{63} +(19.7771 + 60.8676i) q^{64} +(28.9443 + 89.0813i) q^{66} -50.2220i q^{67} +(38.4721 - 27.9516i) q^{68} -1.30495 q^{69} -80.7868i q^{71} +(22.4721 + 16.3270i) q^{72} +5.55418 q^{73} +(-11.3475 - 34.9241i) q^{74} +(35.7771 + 49.2429i) q^{76} -104.721 q^{77} +(37.8885 - 12.3107i) q^{78} -13.8448i q^{79} -37.6950 q^{81} +(9.01316 + 27.7396i) q^{82} +76.2155i q^{83} +(40.0000 - 29.0617i) q^{84} +(-42.3607 + 13.7638i) q^{86} -25.7315i q^{87} +(-93.6656 + 128.920i) q^{88} -111.443 q^{89} +44.5407i q^{91} +(-1.30495 - 1.79611i) q^{92} +19.5016 q^{93} +(-101.554 + 32.9970i) q^{94} -75.2365i q^{96} +92.8328 q^{97} +(-13.2016 - 40.6304i) q^{98} +69.1621i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^9	\( 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{9} - 40 q^{12} + 16 q^{13} + 40 q^{14} - 16 q^{16} + 24 q^{17} - 22 q^{18} + 40 q^{21} + 80 q^{22} - 80 q^{24} - 12 q^{26} + 40 q^{28} - 8 q^{29} - 128 q^{32} - 80 q^{33} + 92 q^{34} - 36 q^{36} - 16 q^{37} - 80 q^{38} - 112 q^{41} + 120 q^{42} - 80 q^{44} + 40 q^{46} - 4 q^{49} - 56 q^{52} + 176 q^{53} + 80 q^{54} + 80 q^{56} + 36 q^{58} + 128 q^{61} + 80 q^{62} - 64 q^{64} + 80 q^{66} + 136 q^{68} + 120 q^{69} + 72 q^{72} - 264 q^{73} - 108 q^{74} - 240 q^{77} + 80 q^{78} - 276 q^{81} - 116 q^{82} + 160 q^{84} - 80 q^{86} - 160 q^{88} - 88 q^{89} + 120 q^{92} + 400 q^{93} - 120 q^{94} + 264 q^{97} - 102 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^9 - 40 * q^12 + 16 * q^13 + 40 * q^14 - 16 * q^16 + 24 * q^17 - 22 * q^18 + 40 * q^21 + 80 * q^22 - 80 * q^24 - 12 * q^26 + 40 * q^28 - 8 * q^29 - 128 * q^32 - 80 * q^33 + 92 * q^34 - 36 * q^36 - 16 * q^37 - 80 * q^38 - 112 * q^41 + 120 * q^42 - 80 * q^44 + 40 * q^46 - 4 * q^49 - 56 * q^52 + 176 * q^53 + 80 * q^54 + 80 * q^56 + 36 * q^58 + 128 * q^61 + 80 * q^62 - 64 * q^64 + 80 * q^66 + 136 * q^68 + 120 * q^69 + 72 * q^72 - 264 * q^73 - 108 * q^74 - 240 * q^77 + 80 * q^78 - 276 * q^81 - 116 * q^82 + 160 * q^84 - 80 * q^86 - 160 * q^88 - 88 * q^89 + 120 * q^92 + 400 * q^93 - 120 * q^94 + 264 * q^97 - 102 * q^98

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