LMFDB - Embedded newform 210.3.c.a.29.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(29,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("210.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.18
Character	$\chi$	$=$	210.29
Dual form			210.3.c.a.29.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-1.07726 + 2.79991i) q^{3} +2.00000 q^{4} +(2.52563 + 4.31523i) q^{5} +(-1.52347 + 3.95968i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-6.67904 - 6.03245i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-1.07726 + 2.79991i) q^{3} +2.00000 q^{4} +(2.52563 + 4.31523i) q^{5} +(-1.52347 + 3.95968i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-6.67904 - 6.03245i) q^{9} +(3.57177 + 6.10266i) q^{10} -5.98577i q^{11} +(-2.15451 + 5.59983i) q^{12} +19.0169i q^{13} +3.74166i q^{14} +(-14.8030 + 2.42293i) q^{15} +4.00000 q^{16} -2.02915 q^{17} +(-9.44559 - 8.53117i) q^{18} -21.1068 q^{19} +(5.05125 + 8.63046i) q^{20} +(-7.40788 - 2.85015i) q^{21} -8.46515i q^{22} +32.2716 q^{23} +(-3.04694 + 7.91935i) q^{24} +(-12.2424 + 21.7973i) q^{25} +26.8940i q^{26} +(24.0854 - 12.2023i) q^{27} +5.29150i q^{28} -12.2603i q^{29} +(-20.9346 + 3.42654i) q^{30} +39.3082 q^{31} +5.65685 q^{32} +(16.7596 + 6.44820i) q^{33} -2.86965 q^{34} +(-11.4170 + 6.68218i) q^{35} +(-13.3581 - 12.0649i) q^{36} +20.3241i q^{37} -29.8495 q^{38} +(-53.2458 - 20.4861i) q^{39} +(7.14355 + 12.2053i) q^{40} -34.7183i q^{41} +(-10.4763 - 4.03072i) q^{42} -40.3307i q^{43} -11.9715i q^{44} +(9.16264 - 44.0573i) q^{45} +45.6389 q^{46} +72.4398 q^{47} +(-4.30902 + 11.1997i) q^{48} -7.00000 q^{49} +(-17.3134 + 30.8261i) q^{50} +(2.18591 - 5.68144i) q^{51} +38.0339i q^{52} -57.5848 q^{53} +(34.0619 - 17.2566i) q^{54} +(25.8300 - 15.1178i) q^{55} +7.48331i q^{56} +(22.7374 - 59.0972i) q^{57} -17.3387i q^{58} -71.7934i q^{59} +(-29.6060 + 4.84586i) q^{60} +81.7294 q^{61} +55.5902 q^{62} +(15.9604 - 17.6711i) q^{63} +8.00000 q^{64} +(-82.0625 + 48.0297i) q^{65} +(23.7017 + 9.11913i) q^{66} -81.7131i q^{67} -4.05830 q^{68} +(-34.7647 + 90.3576i) q^{69} +(-16.1461 + 9.45003i) q^{70} +7.70229i q^{71} +(-18.8912 - 17.0623i) q^{72} +12.0694i q^{73} +28.7427i q^{74} +(-47.8424 - 57.7590i) q^{75} -42.2136 q^{76} +15.8369 q^{77} +(-75.3009 - 28.9717i) q^{78} +131.622 q^{79} +(10.1025 + 17.2609i) q^{80} +(8.21915 + 80.5819i) q^{81} -49.0991i q^{82} -115.864 q^{83} +(-14.8158 - 5.70030i) q^{84} +(-5.12487 - 8.75624i) q^{85} -57.0363i q^{86} +(34.3277 + 13.2075i) q^{87} -16.9303i q^{88} +101.939i q^{89} +(12.9579 - 62.3064i) q^{90} -50.3141 q^{91} +64.5431 q^{92} +(-42.3450 + 110.060i) q^{93} +102.445 q^{94} +(-53.3078 - 91.0806i) q^{95} +(-6.09388 + 15.8387i) q^{96} -8.19281i q^{97} -9.89949 q^{98} +(-36.1088 + 39.9792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) $ 24 * q + 48 * q^4 + 44 * q^9	$ 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) $ 24 * q + 48 * q^4 + 44 * q^9 + 16 * q^10 + 4 * q^15 + 96 * q^16 - 80 * q^19 - 28 * q^21 + 48 * q^25 - 56 * q^30 + 224 * q^31 + 128 * q^34 + 88 * q^36 - 92 * q^39 + 32 * q^40 - 72 * q^45 - 144 * q^46 - 168 * q^49 - 284 * q^51 - 144 * q^54 - 320 * q^55 + 8 * q^60 + 192 * q^64 + 224 * q^66 - 152 * q^69 - 56 * q^70 + 48 * q^75 - 160 * q^76 - 72 * q^79 - 212 * q^81 - 56 * q^84 - 64 * q^85 - 240 * q^90 + 168 * q^91 - 128 * q^94 - 876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	−1.07726	+	2.79991i	−0.359085	+	0.933305i
$3$	−1.07726	+	2.79991i	−0.359085	+	0.933305i
$4$	2.00000			0.500000
$5$	2.52563	+	4.31523i	0.505125	+	0.863046i
$5$	2.52563	+	4.31523i	0.505125	+	0.863046i
$6$	−1.52347	+	3.95968i	−0.253912	+	0.659946i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.82843			0.353553
$9$	−6.67904	−	6.03245i	−0.742116	−	0.670272i
$10$	3.57177	+	6.10266i	0.357177	+	0.610266i
$11$		−	5.98577i		−	0.544161i	−0.962275	−	0.272080i	$-0.912288\pi$
$11$		−	5.98577i		−	0.544161i	0.962275	−	0.272080i	$-0.0877116\pi$
$12$	−2.15451	+	5.59983i	−0.179543	+	0.466652i
$13$			19.0169i			1.46284i	0.681926	+	0.731421i	$0.261142\pi$
$13$			19.0169i			1.46284i	−0.681926	+	0.731421i	$0.738858\pi$
$14$			3.74166i			0.267261i
$15$	−14.8030	+	2.42293i	−0.986868	+	0.161529i
$16$	4.00000			0.250000
$17$	−2.02915			−0.119362			−0.0596809	−	0.998218i	$-0.519008\pi$
$17$	−2.02915			−0.119362			−0.0596809	+	0.998218i	$0.519008\pi$
$18$	−9.44559	−	8.53117i	−0.524755	−	0.473954i
$19$	−21.1068			−1.11088			−0.555442	−	0.831556i	$-0.687451\pi$
$19$	−21.1068			−1.11088			−0.555442	+	0.831556i	$0.687451\pi$
$20$	5.05125	+	8.63046i	0.252563	+	0.431523i
$21$	−7.40788	−	2.85015i	−0.352756	−	0.135721i
$22$		−	8.46515i		−	0.384780i
$23$	32.2716			1.40311			0.701555	−	0.712615i	$-0.252489\pi$
$23$	32.2716			1.40311			0.701555	+	0.712615i	$0.252489\pi$
$24$	−3.04694	+	7.91935i	−0.126956	+	0.329973i
$25$	−12.2424	+	21.7973i	−0.489697	+	0.871893i
$26$			26.8940i			1.03439i
$27$	24.0854	−	12.2023i	0.892051	−	0.451935i
$28$			5.29150i			0.188982i
$29$		−	12.2603i		−	0.422768i	−0.977403	−	0.211384i	$-0.932203\pi$
$29$		−	12.2603i		−	0.422768i	0.977403	−	0.211384i	$-0.0677971\pi$
$30$	−20.9346	+	3.42654i	−0.697821	+	0.114218i
$31$	39.3082			1.26801			0.634004	−	0.773330i	$-0.281410\pi$
$31$	39.3082			1.26801			0.634004	+	0.773330i	$0.281410\pi$
$32$	5.65685			0.176777
$33$	16.7596	+	6.44820i	0.507868	+	0.195400i
$34$	−2.86965			−0.0844015
$35$	−11.4170	+	6.68218i	−0.326201	+	0.190919i
$36$	−13.3581	−	12.0649i	−0.371058	−	0.335136i
$37$			20.3241i			0.549301i	0.961544	+	0.274650i	$0.0885621\pi$
$37$			20.3241i			0.549301i	−0.961544	+	0.274650i	$0.911438\pi$
$38$	−29.8495			−0.785513
$39$	−53.2458	−	20.4861i	−1.36528	−	0.525285i
$40$	7.14355	+	12.2053i	0.178589	+	0.305133i
$41$		−	34.7183i		−	0.846788i	−0.905946	−	0.423394i	$-0.860839\pi$
$41$		−	34.7183i		−	0.846788i	0.905946	−	0.423394i	$-0.139161\pi$
$42$	−10.4763	−	4.03072i	−0.249436	−	0.0959696i
$43$		−	40.3307i		−	0.937924i	−0.883218	−	0.468962i	$-0.844628\pi$
$43$		−	40.3307i		−	0.937924i	0.883218	−	0.468962i	$-0.155372\pi$
$44$		−	11.9715i		−	0.272080i
$45$	9.16264	−	44.0573i	0.203614	−	0.979051i
$46$	45.6389			0.992149
$47$	72.4398			1.54127			0.770636	−	0.637275i	$-0.219939\pi$
$47$	72.4398			1.54127			0.770636	+	0.637275i	$0.219939\pi$
$48$	−4.30902	+	11.1997i	−0.0897713	+	0.233326i
$49$	−7.00000			−0.142857
$50$	−17.3134	+	30.8261i	−0.346268	+	0.616521i
$51$	2.18591	−	5.68144i	0.0428610	−	0.111401i
$52$			38.0339i			0.731421i
$53$	−57.5848			−1.08651			−0.543253	−	0.839569i	$-0.682807\pi$
$53$	−57.5848			−1.08651			−0.543253	+	0.839569i	$0.682807\pi$
$54$	34.0619	−	17.2566i	0.630775	−	0.319566i
$55$	25.8300	−	15.1178i	0.469636	−	0.274869i
$56$			7.48331i			0.133631i
$57$	22.7374	−	59.0972i	0.398902	−	1.03679i
$58$		−	17.3387i		−	0.298942i
$59$		−	71.7934i		−	1.21684i	−0.793616	−	0.608419i	$-0.791804\pi$
$59$		−	71.7934i		−	1.21684i	0.793616	−	0.608419i	$-0.208196\pi$
$60$	−29.6060	+	4.84586i	−0.493434	+	0.0807643i
$61$	81.7294			1.33983			0.669913	−	0.742439i	$-0.266331\pi$
$61$	81.7294			1.33983			0.669913	+	0.742439i	$0.266331\pi$
$62$	55.5902			0.896617
$63$	15.9604	−	17.6711i	0.253339	−	0.280493i
$64$	8.00000			0.125000
$65$	−82.0625	+	48.0297i	−1.26250	+	0.738918i
$66$	23.7017	+	9.11913i	0.359117	+	0.138169i
$67$		−	81.7131i		−	1.21960i	−0.792556	−	0.609799i	$-0.791250\pi$
$67$		−	81.7131i		−	1.21960i	0.792556	−	0.609799i	$-0.208750\pi$
$68$	−4.05830			−0.0596809
$69$	−34.7647	+	90.3576i	−0.503836	+	1.30953i
$70$	−16.1461	+	9.45003i	−0.230659	+	0.135000i
$71$			7.70229i			0.108483i	0.998528	+	0.0542415i	$0.0172741\pi$
$71$			7.70229i			0.108483i	−0.998528	+	0.0542415i	$0.982726\pi$
$72$	−18.8912	−	17.0623i	−0.262377	−	0.236977i
$73$			12.0694i			0.165334i	0.996577	+	0.0826671i	$0.0263438\pi$
$73$			12.0694i			0.165334i	−0.996577	+	0.0826671i	$0.973656\pi$
$74$			28.7427i			0.388414i
$75$	−47.8424	−	57.7590i	−0.637899	−	0.770120i
$76$	−42.2136			−0.555442
$77$	15.8369			0.205673
$78$	−75.3009	−	28.9717i	−0.965397	−	0.371433i
$79$	131.622			1.66610			0.833049	−	0.553199i	$-0.186593\pi$
$79$	131.622			1.66610			0.833049	+	0.553199i	$0.186593\pi$
$80$	10.1025	+	17.2609i	0.126281	+	0.215762i
$81$	8.21915	+	80.5819i	0.101471	+	0.994838i
$82$		−	49.0991i		−	0.598769i
$83$	−115.864			−1.39596			−0.697978	−	0.716119i	$-0.745917\pi$
$83$	−115.864			−1.39596			−0.697978	+	0.716119i	$0.745917\pi$
$84$	−14.8158	−	5.70030i	−0.176378	−	0.0678607i
$85$	−5.12487	−	8.75624i	−0.0602926	−	0.103015i
$86$		−	57.0363i		−	0.663212i
$87$	34.3277	+	13.2075i	0.394572	+	0.151810i
$88$		−	16.9303i		−	0.192390i
$89$			101.939i			1.14538i	0.819771	+	0.572692i	$0.194101\pi$
$89$			101.939i			1.14538i	−0.819771	+	0.572692i	$0.805899\pi$
$90$	12.9579	−	62.3064i	0.143977	−	0.692294i
$91$	−50.3141			−0.552902
$92$	64.5431			0.701555
$93$	−42.3450	+	110.060i	−0.455323	+	1.18344i
$94$	102.445			1.08984
$95$	−53.3078	−	91.0806i	−0.561135	−	0.958743i
$96$	−6.09388	+	15.8387i	−0.0634779	+	0.164987i
$97$		−	8.19281i		−	0.0844619i	−0.999108	−	0.0422310i	$-0.986553\pi$
$97$		−	8.19281i		−	0.0844619i	0.999108	−	0.0422310i	$-0.0134465\pi$
$98$	−9.89949			−0.101015
$99$	−36.1088	+	39.9792i	−0.364736	+	0.403830i
$100$	−24.4848	+	43.5946i	−0.244848	+	0.435946i
$101$		−	136.484i		−	1.35133i	−0.737208	−	0.675665i	$-0.763856\pi$
$101$		−	136.484i		−	1.35133i	0.737208	−	0.675665i	$-0.236144\pi$
$102$	3.09135	−	8.03477i	0.0303073	−	0.0787723i
$103$			129.191i			1.25428i	0.778905	+	0.627142i	$0.215776\pi$
$103$			129.191i			1.25428i	−0.778905	+	0.627142i	$0.784224\pi$
$104$			53.7880i			0.517193i
$105$	−6.41047	−	39.1651i	−0.0610521	−	0.373001i
$106$	−81.4372			−0.768275
$107$	20.2629			0.189373			0.0946866	−	0.995507i	$-0.469815\pi$
$107$	20.2629			0.189373			0.0946866	+	0.995507i	$0.469815\pi$
$108$	48.1707	−	24.4045i	0.446025	−	0.225968i
$109$	−112.569			−1.03275			−0.516373	−	0.856364i	$-0.672718\pi$
$109$	−112.569			−1.03275			−0.516373	+	0.856364i	$0.672718\pi$
$110$	36.5291	−	21.3798i	0.332083	−	0.194362i
$111$	−56.9058	−	21.8943i	−0.512665	−	0.197246i
$112$			10.5830i			0.0944911i
$113$	6.53779			0.0578565			0.0289283	−	0.999581i	$-0.490791\pi$
$113$	6.53779			0.0578565			0.0289283	+	0.999581i	$0.490791\pi$
$114$	32.1555	−	83.5760i	0.282066	−	0.733123i
$115$	81.5059	+	139.259i	0.708747	+	1.21095i
$116$		−	24.5206i		−	0.211384i
$117$	114.719	−	127.015i	0.980502	−	1.08560i
$118$		−	101.531i		−	0.860434i
$119$		−	5.36862i		−	0.0451145i
$120$	−41.8693	+	6.85308i	−0.348911	+	0.0571090i
$121$	85.1706			0.703889
$122$	115.583			0.947400
$123$	97.2082	+	37.4005i	0.790311	+	0.304069i
$124$	78.6165			0.634004
$125$	−124.980	+	2.22300i	−0.999842	+	0.0177840i
$126$	22.5714	−	24.9907i	0.179138	−	0.198339i
$127$			15.0411i			0.118434i	0.998245	+	0.0592170i	$0.0188604\pi$
$127$			15.0411i			0.118434i	−0.998245	+	0.0592170i	$0.981140\pi$
$128$	11.3137			0.0883883
$129$	112.923	+	43.4465i	0.875369	+	0.336795i
$130$	−116.054	+	67.9242i	−0.892722	+	0.522494i
$131$		−	51.5923i		−	0.393834i	−0.980420	−	0.196917i	$-0.936907\pi$
$131$		−	51.5923i		−	0.393834i	0.980420	−	0.196917i	$-0.0630930\pi$
$132$	33.5193	+	12.8964i	0.253934	+	0.0977000i
$133$		−	55.8433i		−	0.419874i
$134$		−	115.560i		−	0.862386i
$135$	113.486	+	73.1156i	0.840638	+	0.541597i
$136$	−5.73930			−0.0422007
$137$	−47.5888			−0.347364			−0.173682	−	0.984802i	$-0.555566\pi$
$137$	−47.5888			−0.347364			−0.173682	+	0.984802i	$0.555566\pi$
$138$	−49.1647	+	127.785i	−0.356266	+	0.925978i
$139$	−117.730			−0.846975			−0.423488	−	0.905902i	$-0.639194\pi$
$139$	−117.730			−0.846975			−0.423488	+	0.905902i	$0.639194\pi$
$140$	−22.8341	+	13.3644i	−0.163100	+	0.0954597i
$141$	−78.0362	+	202.825i	−0.553448	+	1.43848i
$142$			10.8927i			0.0767091i
$143$	113.831			0.796021
$144$	−26.7162	−	24.1298i	−0.185529	−	0.167568i
$145$	52.9059	−	30.9649i	0.364869	−	0.213551i
$146$			17.0687i			0.116909i
$147$	7.54079	−	19.5994i	0.0512979	−	0.133329i
$148$			40.6483i			0.274650i
$149$			186.336i			1.25057i	0.780395	+	0.625287i	$0.215018\pi$
$149$			186.336i			1.25057i	−0.780395	+	0.625287i	$0.784982\pi$
$150$	−67.6594	−	81.6836i	−0.451062	−	0.544557i
$151$	−183.560			−1.21563			−0.607816	−	0.794078i	$-0.707954\pi$
$151$	−183.560			−1.21563			−0.607816	+	0.794078i	$0.707954\pi$
$152$	−59.6990			−0.392756
$153$	13.5528	+	12.2407i	0.0885802	+	0.0800048i
$154$	22.3967			0.145433
$155$	99.2779	+	169.624i	0.640503	+	1.09435i
$156$	−106.492	−	40.9722i	−0.682639	−	0.262642i
$157$			264.877i			1.68712i	0.537038	+	0.843558i	$0.319543\pi$
$157$			264.877i			1.68712i	−0.537038	+	0.843558i	$0.680457\pi$
$158$	186.141			1.17811
$159$	62.0335	−	161.232i	0.390148	−	1.01404i
$160$	14.2871	+	24.4106i	0.0892944	+	0.152566i
$161$			85.3825i			0.530326i
$162$	11.6236	+	113.960i	0.0717508	+	0.703457i
$163$		−	214.877i		−	1.31826i	−0.752027	−	0.659132i	$-0.770924\pi$
$163$		−	214.877i		−	1.31826i	0.752027	−	0.659132i	$-0.229076\pi$
$164$		−	69.4366i		−	0.423394i
$165$	14.5031	+	88.6074i	0.0878976	+	0.537015i
$166$	−163.857			−0.987090
$167$	−54.5954			−0.326919			−0.163459	−	0.986550i	$-0.552265\pi$
$167$	−54.5954			−0.326919			−0.163459	+	0.986550i	$0.552265\pi$
$168$	−20.9526	−	8.06144i	−0.124718	−	0.0479848i
$169$	−192.644			−1.13991
$170$	−7.24766	−	12.3832i	−0.0426333	−	0.0728424i
$171$	140.973	+	127.326i	0.824404	+	0.744594i
$172$		−	80.6615i		−	0.468962i
$173$	−310.651			−1.79567			−0.897834	−	0.440334i	$-0.854860\pi$
$173$	−310.651			−1.79567			−0.897834	+	0.440334i	$0.854860\pi$
$174$	48.5468	+	18.6782i	0.279004	+	0.107346i
$175$	−57.6703	−	32.3904i	−0.329544	−	0.185088i
$176$		−	23.9431i		−	0.136040i
$177$	201.015	+	77.3399i	1.13568	+	0.436949i
$178$			144.164i			0.809909i
$179$			162.922i			0.910181i	0.890445	+	0.455090i	$0.150393\pi$
$179$			162.922i			0.910181i	−0.890445	+	0.455090i	$0.849607\pi$
$180$	18.3253	−	88.1146i	0.101807	−	0.489526i
$181$	−51.5088			−0.284579			−0.142289	−	0.989825i	$-0.545446\pi$
$181$	−51.5088			−0.284579			−0.142289	+	0.989825i	$0.545446\pi$
$182$	−71.1549			−0.390961
$183$	−88.0435	+	228.835i	−0.481112	+	1.25047i
$184$	91.2777			0.496075
$185$	−87.7033	+	51.3311i	−0.474072	+	0.277466i
$186$	−59.8849	+	155.648i	−0.321962	+	0.836817i
$187$			12.1460i			0.0649519i
$188$	144.880			0.770636
$189$	32.2841	+	63.7239i	0.170815	+	0.337163i
$190$	−75.3887	−	128.807i	−0.396782	−	0.677934i
$191$		−	227.310i		−	1.19011i	−0.803687	−	0.595053i	$-0.797131\pi$
$191$		−	227.310i		−	1.19011i	0.803687	−	0.595053i	$-0.202869\pi$
$192$	−8.61805	+	22.3993i	−0.0448857	+	0.116663i
$193$		−	239.861i		−	1.24280i	−0.783493	−	0.621401i	$-0.786564\pi$
$193$		−	239.861i		−	1.24280i	0.783493	−	0.621401i	$-0.213436\pi$
$194$		−	11.5864i		−	0.0597236i
$195$	−46.0767	−	281.508i	−0.236291	−	1.44363i
$196$	−14.0000			−0.0714286
$197$	184.116			0.934599			0.467300	−	0.884099i	$-0.345227\pi$
$197$	184.116			0.934599			0.467300	+	0.884099i	$0.345227\pi$
$198$	−51.0656	+	56.5391i	−0.257907	+	0.285551i
$199$	−215.792			−1.08438			−0.542190	−	0.840256i	$-0.682405\pi$
$199$	−215.792			−1.08438			−0.542190	+	0.840256i	$0.682405\pi$
$200$	−34.6268	+	61.6521i	−0.173134	+	0.308261i
$201$	228.790	+	88.0259i	1.13826	+	0.437940i
$202$		−	193.018i		−	0.955535i
$203$	32.4377			0.159791
$204$	4.37182	−	11.3629i	0.0214305	−	0.0557004i
$205$	149.817	−	87.6854i	0.730817	−	0.427734i
$206$			182.704i			0.886913i
$207$	−215.543	−	194.676i	−1.04127	−	0.940466i
$208$			76.0678i			0.365710i
$209$			126.340i			0.604499i
$210$	−9.06578	−	55.3878i	−0.0431704	−	0.263752i
$211$	−122.387			−0.580031			−0.290015	−	0.957022i	$-0.593660\pi$
$211$	−122.387			−0.580031			−0.290015	+	0.957022i	$0.593660\pi$
$212$	−115.170			−0.543253
$213$	−21.5658	−	8.29734i	−0.101248	−	0.0389546i
$214$	28.6561			0.133907
$215$	174.036	−	101.860i	0.809472	−	0.473769i
$216$	68.1237	−	34.5132i	0.315388	−	0.159783i
$217$			104.000i			0.479262i
$218$	−159.197			−0.730262
$219$	−33.7933	−	13.0018i	−0.154307	−	0.0593690i
$220$	51.6599	−	30.2356i	0.234818	−	0.137435i
$221$		−	38.5882i		−	0.174607i
$222$	−80.4770	−	30.9632i	−0.362509	−	0.139474i
$223$		−	70.1315i		−	0.314491i	−0.987560	−	0.157245i	$-0.949739\pi$
$223$		−	70.1315i		−	0.314491i	0.987560	−	0.157245i	$-0.0502614\pi$
$224$			14.9666i			0.0668153i
$225$	213.259	−	71.7334i	0.947817	−	0.318815i
$226$	9.24583			0.0409108
$227$	31.4277			0.138448			0.0692240	−	0.997601i	$-0.477948\pi$
$227$	31.4277			0.138448			0.0692240	+	0.997601i	$0.477948\pi$
$228$	45.4748	−	118.194i	0.199451	−	0.518396i
$229$	35.7207			0.155986			0.0779928	−	0.996954i	$-0.475149\pi$
$229$	35.7207			0.155986			0.0779928	+	0.996954i	$0.475149\pi$
$230$	115.267	+	196.942i	0.501160	+	0.856271i
$231$	−17.0603	+	44.3418i	−0.0738543	+	0.191956i
$232$		−	34.6773i		−	0.149471i
$233$	324.542			1.39288			0.696442	−	0.717613i	$-0.254765\pi$
$233$	324.542			1.39288			0.696442	+	0.717613i	$0.254765\pi$
$234$	162.237	−	179.626i	0.693319	−	0.767633i
$235$	182.956	+	312.594i	0.778536	+	1.33019i
$236$		−	143.587i		−	0.608419i
$237$	−141.790	+	368.530i	−0.598271	+	1.55498i
$238$		−	7.59238i		−	0.0319008i
$239$		−	400.039i		−	1.67380i	−0.547353	−	0.836902i	$-0.684364\pi$
$239$		−	400.039i		−	1.67380i	0.547353	−	0.836902i	$-0.315636\pi$
$240$	−59.2121	+	9.69172i	−0.246717	+	0.0403822i
$241$	396.305			1.64442			0.822209	−	0.569185i	$-0.192741\pi$
$241$	396.305			1.64442			0.822209	+	0.569185i	$0.192741\pi$
$242$	120.449			0.497725
$243$	−234.477	−	63.7944i	−0.964924	−	0.262528i
$244$	163.459			0.669913
$245$	−17.6794	−	30.2066i	−0.0721607	−	0.123292i
$246$	137.473	+	52.8923i	0.558834	+	0.215009i
$247$		−	401.386i		−	1.62505i
$248$	111.180			0.448308
$249$	124.816	−	324.410i	0.501267	−	1.30285i
$250$	−176.749	+	3.14379i	−0.706995	+	0.0125752i
$251$		−	221.226i		−	0.881377i	−0.897660	−	0.440688i	$-0.854734\pi$
$251$		−	221.226i		−	0.881377i	0.897660	−	0.440688i	$-0.145266\pi$
$252$	31.9207	−	35.3422i	0.126669	−	0.140247i
$253$		−	193.170i		−	0.763518i
$254$			21.2714i			0.0837455i
$255$	30.0375	−	4.91649i	0.117794	−	0.0192803i
$256$	16.0000			0.0625000
$257$	−203.815			−0.793055			−0.396528	−	0.918023i	$-0.629785\pi$
$257$	−203.815			−0.793055			−0.396528	+	0.918023i	$0.629785\pi$
$258$	159.697	+	61.4426i	0.618979	+	0.238150i
$259$	−53.7726			−0.207616
$260$	−164.125	+	96.0594i	−0.631250	+	0.369459i
$261$	−73.9595	+	81.8869i	−0.283370	+	0.313743i
$262$		−	72.9625i		−	0.278483i
$263$	98.2019			0.373391			0.186696	−	0.982418i	$-0.440222\pi$
$263$	98.2019			0.373391			0.186696	+	0.982418i	$0.440222\pi$
$264$	47.4034	+	18.2383i	0.179558	+	0.0690844i
$265$	−145.438	−	248.492i	−0.548821	−	0.937704i
$266$		−	78.9743i		−	0.296896i
$267$	−285.421	−	109.815i	−1.06899	−	0.411290i
$268$		−	163.426i		−	0.609799i
$269$		−	308.644i		−	1.14738i	−0.819074	−	0.573688i	$-0.805512\pi$
$269$		−	308.644i		−	1.14738i	0.819074	−	0.573688i	$-0.194488\pi$
$270$	160.494	+	103.401i	0.594421	+	0.382967i
$271$	−398.841			−1.47174			−0.735870	−	0.677123i	$-0.763226\pi$
$271$	−398.841			−1.47174			−0.735870	+	0.677123i	$0.763226\pi$
$272$	−8.11660			−0.0298404
$273$	54.2012	−	140.875i	0.198539	−	0.516026i
$274$	−67.3007			−0.245623
$275$	130.474	+	73.2803i	0.474450	+	0.266474i
$276$	−69.5294	+	180.715i	−0.251918	+	0.654765i
$277$			79.7207i			0.287800i	0.989592	+	0.143900i	$0.0459644\pi$
$277$			79.7207i			0.287800i	−0.989592	+	0.143900i	$0.954036\pi$
$278$	−166.495			−0.598902
$279$	−262.541	−	237.125i	−0.941008	−	0.849910i
$280$	−32.2922	+	18.9001i	−0.115329	+	0.0675002i
$281$		−	210.169i		−	0.747934i	−0.927442	−	0.373967i	$-0.877997\pi$
$281$		−	210.169i		−	0.747934i	0.927442	−	0.373967i	$-0.122003\pi$
$282$	−110.360	+	286.838i	−0.391347	+	1.01716i
$283$		−	262.941i		−	0.929120i	−0.885542	−	0.464560i	$-0.846213\pi$
$283$		−	262.941i		−	0.929120i	0.885542	−	0.464560i	$-0.153787\pi$
$284$			15.4046i			0.0542415i
$285$	312.444	−	51.1403i	1.09630	−	0.179439i
$286$	160.981			0.562872
$287$	91.8560			0.320056
$288$	−37.7824	−	34.1247i	−0.131189	−	0.118488i
$289$	−284.883			−0.985753
$290$	74.8203	−	43.7910i	0.258001	−	0.151003i
$291$	22.9392	+	8.82575i	0.0788287	+	0.0303290i
$292$			24.1388i			0.0826671i
$293$	−357.570			−1.22037			−0.610187	−	0.792257i	$-0.708906\pi$
$293$	−357.570			−1.22037			−0.610187	+	0.792257i	$0.708906\pi$
$294$	10.6643	−	27.7177i	0.0362731	−	0.0942780i
$295$	309.805	−	181.323i	1.05019	−	0.614656i
$296$			57.4853i			0.194207i
$297$	−73.0398	−	144.169i	−0.245925	−	0.485419i
$298$			263.518i			0.884290i
$299$			613.706i			2.05253i
$300$	−95.6848	−	115.518i	−0.318949	−	0.385060i
$301$	106.705			0.354502
$302$	−259.593			−0.859581
$303$	382.145	+	147.029i	1.26120	+	0.485243i
$304$	−84.4271			−0.277721
$305$	206.418	+	352.681i	0.676780	+	1.15633i
$306$	19.1665	+	17.3110i	0.0626356	+	0.0565719i
$307$			293.405i			0.955717i	0.878437	+	0.477858i	$0.158587\pi$
$307$			293.405i			0.955717i	−0.878437	+	0.477858i	$0.841413\pi$
$308$	31.6737			0.102837
$309$	−361.725	−	139.172i	−1.17063	−	0.450395i
$310$	140.400	+	239.885i	0.452904	+	0.773822i
$311$		−	59.2465i		−	0.190503i	−0.995453	−	0.0952517i	$-0.969634\pi$
$311$		−	59.2465i		−	0.190503i	0.995453	−	0.0952517i	$-0.0303656\pi$
$312$	−150.602	−	57.9435i	−0.482698	−	0.185716i
$313$			450.587i			1.43957i	0.694195	+	0.719787i	$0.255761\pi$
$313$			450.587i			1.43957i	−0.694195	+	0.719787i	$0.744239\pi$
$314$			374.593i			1.19297i
$315$	116.565	+	24.2421i	0.370047	+	0.0769590i
$316$	263.243			0.833049
$317$	−277.454			−0.875249			−0.437624	−	0.899158i	$-0.644180\pi$
$317$	−277.454			−0.875249			−0.437624	+	0.899158i	$0.644180\pi$
$318$	87.7287	−	228.017i	0.275876	−	0.717035i
$319$	−73.3872			−0.230054
$320$	20.2050	+	34.5218i	0.0631407	+	0.107881i
$321$	−21.8284	+	56.7345i	−0.0680011	+	0.176743i
$322$			120.749i			0.374997i
$323$	42.8288			0.132597
$324$	16.4383	+	161.164i	0.0507355	+	0.497419i
$325$	−414.518	−	232.813i	−1.27544	−	0.716349i
$326$		−	303.882i		−	0.932153i
$327$	121.266	−	315.185i	0.370844	−	0.963867i
$328$		−	98.1982i		−	0.299385i
$329$			191.658i			0.582546i
$330$	20.5105	+	125.310i	0.0621530	+	0.379727i
$331$	275.898			0.833529			0.416764	−	0.909015i	$-0.363164\pi$
$331$	275.898			0.833529			0.416764	+	0.909015i	$0.363164\pi$
$332$	−231.729			−0.697978
$333$	122.604	−	135.746i	0.368181	−	0.407645i
$334$	−77.2096			−0.231166
$335$	352.611	−	206.377i	1.05257	−	0.616050i
$336$	−29.6315	−	11.4006i	−0.0881890	−	0.0339304i
$337$			102.798i			0.305038i	0.988301	+	0.152519i	$0.0487385\pi$
$337$			102.798i			0.305038i	−0.988301	+	0.152519i	$0.951261\pi$
$338$	−272.440			−0.806035
$339$	−7.04287	+	18.3053i	−0.0207754	+	0.0539978i
$340$	−10.2497	−	17.5125i	−0.0301463	−	0.0515073i
$341$		−	235.290i		−	0.690000i
$342$	199.366	+	180.066i	0.582941	+	0.526507i
$343$		−	18.5203i		−	0.0539949i
$344$		−	114.073i		−	0.331606i
$345$	−477.716	+	78.1917i	−1.38469	+	0.226643i
$346$	−439.326			−1.26973
$347$	−456.590			−1.31582			−0.657910	−	0.753096i	$-0.728559\pi$
$347$	−456.590			−1.31582			−0.657910	+	0.753096i	$0.728559\pi$
$348$	68.6555	+	26.4149i	0.197286	+	0.0759049i
$349$	570.605			1.63497			0.817486	−	0.575948i	$-0.195367\pi$
$349$	570.605			1.63497			0.817486	+	0.575948i	$0.195367\pi$
$350$	−81.5581	−	45.8070i	−0.233023	−	0.130877i
$351$	232.050	+	458.030i	0.661110	+	1.30493i
$352$		−	33.8606i		−	0.0961949i
$353$	−4.74525			−0.0134426			−0.00672132	−	0.999977i	$-0.502139\pi$
$353$	−4.74525			−0.0134426			−0.00672132	+	0.999977i	$0.502139\pi$
$354$	284.279	+	109.375i	0.803048	+	0.308969i
$355$	−33.2372	+	19.4531i	−0.0936258	+	0.0547975i
$356$			203.878i			0.572692i
$357$	15.0317	+	5.78338i	0.0421056	+	0.0161999i
$358$			230.407i			0.643595i
$359$			457.086i			1.27322i	0.771186	+	0.636610i	$0.219664\pi$
$359$			457.086i			1.27322i	−0.771186	+	0.636610i	$0.780336\pi$
$360$	25.9159	−	124.613i	0.0719885	−	0.346147i
$361$	84.4961			0.234061
$362$	−72.8444			−0.201228
$363$	−91.7505	+	238.470i	−0.252756	+	0.656943i
$364$	−100.628			−0.276451
$365$	−52.0822	+	30.4828i	−0.142691	+	0.0835144i
$366$	−124.512	+	323.622i	−0.340198	+	0.884213i
$367$			556.637i			1.51672i	0.651834	+	0.758361i	$0.274000\pi$
$367$			556.637i			1.51672i	−0.651834	+	0.758361i	$0.726000\pi$
$368$	129.086			0.350778
$369$	−209.436	+	231.885i	−0.567578	+	0.628414i
$370$	−124.031	+	72.5932i	−0.335219	+	0.196198i
$371$		−	152.355i		−	0.410660i
$372$	−84.6900	+	220.119i	−0.227661	+	0.591719i
$373$		−	77.2267i		−	0.207042i	−0.994627	−	0.103521i	$-0.966989\pi$
$373$		−	77.2267i		−	0.207042i	0.994627	−	0.103521i	$-0.0330109\pi$
$374$			17.1771i			0.0459280i
$375$	128.411	−	352.329i	0.342431	−	0.939543i
$376$	204.891			0.544922
$377$	233.153			0.618443
$378$	45.6566	+	90.1192i	0.120785	+	0.238411i
$379$	476.133			1.25629			0.628143	−	0.778098i	$-0.283815\pi$
$379$	476.133			1.25629			0.628143	+	0.778098i	$0.283815\pi$
$380$	−106.616	−	182.161i	−0.280568	−	0.479372i
$381$	−42.1138	−	16.2031i	−0.110535	−	0.0425279i
$382$		−	321.465i		−	0.841532i
$383$	600.374			1.56756			0.783778	−	0.621041i	$-0.213290\pi$
$383$	600.374			1.56756			0.783778	+	0.621041i	$0.213290\pi$
$384$	−12.1878	+	31.6774i	−0.0317390	+	0.0824933i
$385$	39.9980	+	68.3397i	0.103891	+	0.177506i
$386$		−	339.214i		−	0.878794i
$387$	−243.293	+	269.371i	−0.628664	+	0.696048i
$388$		−	16.3856i		−	0.0422310i
$389$		−	315.387i		−	0.810763i	−0.914148	−	0.405382i	$-0.867139\pi$
$389$		−	315.387i		−	0.810763i	0.914148	−	0.405382i	$-0.132861\pi$
$390$	−65.1623	−	398.113i	−0.167083	−	1.02080i
$391$	−65.4838			−0.167478
$392$	−19.7990			−0.0505076
$393$	144.454	+	55.5781i	0.367567	+	0.141420i
$394$	260.379			0.660861
$395$	332.427	+	567.978i	0.841588	+	1.43792i
$396$	−72.2176	+	79.9584i	−0.182368	+	0.201915i
$397$			291.527i			0.734325i	0.930157	+	0.367163i	$0.119671\pi$
$397$			291.527i			0.734325i	−0.930157	+	0.367163i	$0.880329\pi$
$398$	−305.176			−0.766773
$399$	156.356	+	60.1575i	0.391871	+	0.150771i
$400$	−48.9697	+	87.1893i	−0.122424	+	0.217973i
$401$		−	312.203i		−	0.778560i	−0.921119	−	0.389280i	$-0.872724\pi$
$401$		−	312.203i		−	0.778560i	0.921119	−	0.389280i	$-0.127276\pi$
$402$	323.557	+	124.487i	0.804869	+	0.309670i
$403$			747.522i			1.85489i
$404$		−	272.969i		−	0.675665i
$405$	−326.971	+	238.987i	−0.807336	+	0.590092i
$406$	45.8738			0.112990
$407$	121.655			0.298908
$408$	6.18269	−	16.0695i	0.0151537	−	0.0393861i
$409$	−602.689			−1.47357			−0.736784	−	0.676128i	$-0.763657\pi$
$409$	−602.689			−1.47357			−0.736784	+	0.676128i	$0.763657\pi$
$410$	211.874	−	124.006i	0.516765	−	0.302453i
$411$	51.2653	−	133.245i	0.124733	−	0.324196i
$412$			258.383i			0.627142i
$413$	189.948			0.459922
$414$	−304.824	−	275.314i	−0.736289	−	0.665010i
$415$	−292.630	−	499.981i	−0.705133	−	1.20477i
$416$			107.576i			0.258596i
$417$	126.825	−	329.633i	0.304136	−	0.790486i
$418$			178.672i			0.427445i
$419$			179.970i			0.429522i	0.976667	+	0.214761i	$0.0688972\pi$
$419$			179.970i			0.429522i	−0.976667	+	0.214761i	$0.931103\pi$
$420$	−12.8209	−	78.3302i	−0.0305261	−	0.186501i
$421$	454.959			1.08066			0.540331	−	0.841453i	$-0.318299\pi$
$421$	454.959			1.08066			0.540331	+	0.841453i	$0.318299\pi$
$422$	−173.081			−0.410144
$423$	−483.828	−	436.989i	−1.14380	−	1.03307i
$424$	−162.874			−0.384138
$425$	24.8417	−	44.2300i	0.0584511	−	0.104071i
$426$	−30.4986	−	11.7342i	−0.0715929	−	0.0275451i
$427$			216.236i			0.506407i
$428$	40.5259			0.0946866
$429$	−122.625	+	318.717i	−0.285839	+	0.742930i
$430$	246.125	−	144.052i	0.572383	−	0.335005i
$431$			280.437i			0.650665i	0.945600	+	0.325333i	$0.105476\pi$
$431$			280.437i			0.650665i	−0.945600	+	0.325333i	$0.894524\pi$
$432$	96.3415	−	48.8090i	0.223013	−	0.112984i
$433$			172.401i			0.398155i	0.979984	+	0.199077i	$0.0637945\pi$
$433$			172.401i			0.398155i	−0.979984	+	0.199077i	$0.936206\pi$
$434$			147.078i			0.338889i
$435$	29.7058	+	181.489i	0.0682892	+	0.417217i
$436$	−225.139			−0.516373
$437$	−681.149			−1.55869
$438$	−47.7909	−	18.3874i	−0.109112	−	0.0419803i
$439$	299.659			0.682594			0.341297	−	0.939955i	$-0.389134\pi$
$439$	299.659			0.682594			0.341297	+	0.939955i	$0.389134\pi$
$440$	73.0582	−	42.7596i	0.166041	−	0.0971810i
$441$	46.7533	+	42.2271i	0.106017	+	0.0957531i
$442$		−	54.5720i		−	0.123466i
$443$	389.448			0.879115			0.439558	−	0.898214i	$-0.355135\pi$
$443$	389.448			0.879115			0.439558	+	0.898214i	$0.355135\pi$
$444$	−113.812	−	43.7886i	−0.256332	−	0.0986229i
$445$	−439.891	+	257.460i	−0.988519	+	0.578562i
$446$		−	99.1809i		−	0.222379i
$447$	−521.724	−	200.731i	−1.16717	−	0.449063i
$448$			21.1660i			0.0472456i
$449$		−	614.023i		−	1.36753i	−0.729700	−	0.683767i	$-0.760340\pi$
$449$		−	614.023i		−	1.36753i	0.729700	−	0.683767i	$-0.239660\pi$
$450$	301.594	−	101.446i	0.670208	−	0.225436i
$451$	−207.816			−0.460788
$452$	13.0756			0.0289283
$453$	197.741	−	513.953i	0.436515	−	1.13455i
$454$	44.4455			0.0978975
$455$	−127.075	−	217.117i	−0.279285	−	0.477180i
$456$	64.3111	−	167.152i	0.141033	−	0.366562i
$457$		−	215.558i		−	0.471681i	−0.971792	−	0.235840i	$-0.924216\pi$
$457$		−	215.558i		−	0.471681i	0.971792	−	0.235840i	$-0.0757843\pi$
$458$	50.5167			0.110299
$459$	−48.8728	+	24.7602i	−0.106477	+	0.0539438i
$460$	163.012	+	278.518i	0.354373	+	0.605475i
$461$		−	369.603i		−	0.801743i	−0.916134	−	0.400871i	$-0.868707\pi$
$461$		−	369.603i		−	0.801743i	0.916134	−	0.400871i	$-0.131293\pi$
$462$	−24.1270	+	62.7088i	−0.0522229	+	0.135733i
$463$		−	0.675303i		−	0.00145854i	−1.00000		0.000729269i	$-0.999768\pi$
$463$		−	0.675303i		−	0.00145854i	1.00000		0.000729269i	$-0.000232133\pi$
$464$		−	49.0411i		−	0.105692i
$465$	−581.881	+	95.2411i	−1.25136	+	0.204820i
$466$	458.972			0.984918
$467$	−90.1341			−0.193007			−0.0965033	−	0.995333i	$-0.530766\pi$
$467$	−90.1341			−0.193007			−0.0965033	+	0.995333i	$0.530766\pi$
$468$	229.437	−	254.030i	0.490251	−	0.542799i
$469$	216.193			0.460965
$470$	258.739	+	442.075i	0.550508	+	0.940586i
$471$	−741.634	−	285.341i	−1.57459	−	0.605819i
$472$		−	203.063i		−	0.430217i
$473$	−241.410			−0.510381
$474$	−200.522	+	521.179i	−0.423042	+	1.09953i
$475$	258.398	−	460.071i	0.543996	−	0.968571i
$476$		−	10.7372i		−	0.0225572i
$477$	384.611	+	347.377i	0.806313	+	0.728254i
$478$		−	565.741i		−	1.18356i
$479$			422.277i			0.881579i	0.897610	+	0.440790i	$0.145302\pi$
$479$			422.277i			0.881579i	−0.897610	+	0.440790i	$0.854698\pi$
$480$	−83.7385	+	13.7062i	−0.174455	+	0.0285545i
$481$	−386.503			−0.803540
$482$	560.460			1.16278
$483$	−239.064	−	91.9788i	−0.494956	−	0.190432i
$484$	170.341			0.351945
$485$	35.3538	−	20.6920i	0.0728945	−	0.0426638i
$486$	−331.600	−	90.2189i	−0.682304	−	0.185636i
$487$			240.184i			0.493191i	0.969119	+	0.246595i	$0.0793119\pi$
$487$			240.184i			0.493191i	−0.969119	+	0.246595i	$0.920688\pi$
$488$	231.166			0.473700
$489$	601.637	+	231.478i	1.23034	+	0.473369i
$490$	−25.0024	−	42.7186i	−0.0510254	−	0.0871808i
$491$			961.188i			1.95761i	0.204788	+	0.978806i	$0.434349\pi$
$491$			961.188i			1.95761i	−0.204788	+	0.978806i	$0.565651\pi$
$492$	194.416	+	74.8010i	0.395155	+	0.152034i
$493$			24.8779i			0.0504624i
$494$		−	567.646i		−	1.14908i
$495$	−263.717	−	54.8454i	−0.532761	−	0.110799i
$496$	157.233			0.317002
$497$	−20.3783			−0.0410027
$498$	176.516	−	458.785i	0.354450	−	0.921256i
$499$	203.222			0.407259			0.203629	−	0.979048i	$-0.434726\pi$
$499$	203.222			0.407259			0.203629	+	0.979048i	$0.434726\pi$
$500$	−249.960	+	4.44599i	−0.499921	+	0.00889199i
$501$	58.8132	−	152.862i	0.117392	−	0.305115i
$502$		−	312.860i		−	0.623228i
$503$	−112.900			−0.224453			−0.112226	−	0.993683i	$-0.535798\pi$
$503$	−112.900			−0.224453			−0.112226	+	0.993683i	$0.535798\pi$
$504$	45.1427	−	49.9814i	0.0895689	−	0.0991694i
$505$	588.962	−	344.709i	1.16626	−	0.682591i
$506$		−	273.184i		−	0.539889i
$507$	207.527	−	539.387i	0.409323	−	1.06388i
$508$			30.0822i			0.0592170i
$509$			876.657i			1.72231i	0.508341	+	0.861156i	$0.330259\pi$
$509$			876.657i			1.72231i	−0.508341	+	0.861156i	$0.669741\pi$
$510$	42.4795	−	6.95296i	0.0832931	−	0.0136333i
$511$	−31.9326			−0.0624904
$512$	22.6274			0.0441942
$513$	−508.365	+	257.550i	−0.990964	+	0.502047i
$514$	−288.238			−0.560775
$515$	−557.490	+	326.289i	−1.08251	+	0.633571i
$516$	225.845	+	86.8930i	0.437684	+	0.168397i
$517$		−	433.608i		−	0.838700i
$518$	−76.0459			−0.146807
$519$	334.650	−	869.795i	0.644798	−	1.67591i
$520$	−232.108	+	135.848i	−0.446361	+	0.261247i
$521$		−	497.586i		−	0.955060i	−0.878616	−	0.477530i	$-0.841532\pi$
$521$		−	497.586i		−	0.955060i	0.878616	−	0.477530i	$-0.158468\pi$
$522$	−104.595	+	115.806i	−0.200373	+	0.221850i
$523$		−	519.528i		−	0.993362i	−0.867933	−	0.496681i	$-0.834552\pi$
$523$		−	519.528i		−	0.993362i	0.867933	−	0.496681i	$-0.165448\pi$
$524$		−	103.185i		−	0.196917i
$525$	152.816	−	126.579i	0.291078	−	0.241103i
$526$	138.878			0.264027
$527$	−79.7623			−0.151352
$528$	67.0385	+	25.7928i	0.126967	+	0.0488500i
$529$	512.453			0.968720
$530$	−205.680	−	351.420i	−0.388075	−	0.663057i
$531$	−433.090	+	479.511i	−0.815612	+	0.903034i
$532$		−	111.687i		−	0.209937i
$533$	660.236			1.23872
$534$	−403.646	−	155.301i	−0.755892	−	0.290826i
$535$	51.1766	+	87.4392i	0.0956572	+	0.163438i
$536$		−	231.120i		−	0.431193i
$537$	−456.169	−	175.509i	−0.849476	−	0.326832i
$538$		−	436.488i		−	0.811317i
$539$			41.9004i			0.0777372i
$540$	226.972	+	146.231i	0.420319	+	0.270798i
$541$	853.843			1.57827			0.789134	−	0.614220i	$-0.210529\pi$
$541$	853.843			1.57827			0.789134	+	0.614220i	$0.210529\pi$
$542$	−564.047			−1.04068
$543$	55.4881	−	144.220i	0.102188	−	0.265599i
$544$	−11.4786			−0.0211004
$545$	−284.308	−	485.763i	−0.521666	−	0.891308i
$546$	76.6520	−	199.228i	0.140388	−	0.364886i
$547$			468.232i			0.855999i	0.903779	+	0.428000i	$0.140782\pi$
$547$			468.232i			0.855999i	−0.903779	+	0.428000i	$0.859218\pi$
$548$	−95.1776			−0.173682
$549$	−545.874	−	493.028i	−0.994306	−	0.898048i
$550$	184.518	+	103.634i	0.335487	+	0.188425i
$551$			258.775i			0.469646i
$552$	−98.3295	+	255.570i	−0.178133	+	0.462989i
$553$			348.238i			0.629726i
$554$			112.742i			0.203506i
$555$	−49.2439	−	300.858i	−0.0887278	−	0.542087i
$556$	−235.459			−0.423488
$557$	260.390			0.467487			0.233744	−	0.972298i	$-0.424902\pi$
$557$	260.390			0.467487			0.233744	+	0.972298i	$0.424902\pi$
$558$	−371.289	−	335.345i	−0.665393	−	0.600977i
$559$	766.967			1.37203
$560$	−45.6681	+	26.7287i	−0.0815502	+	0.0477298i
$561$	−34.0078	−	13.0844i	−0.0606200	−	0.0233233i
$562$		−	297.224i		−	0.528869i
$563$	−62.6717			−0.111317			−0.0556587	−	0.998450i	$-0.517726\pi$
$563$	−62.6717			−0.111317			−0.0556587	+	0.998450i	$0.517726\pi$
$564$	−156.072	+	405.650i	−0.276724	+	0.719238i
$565$	16.5120	+	28.2121i	0.0292248	+	0.0499329i
$566$		−	371.855i		−	0.656987i
$567$	−213.200	+	21.7458i	−0.376014	+	0.0383524i
$568$			21.7854i			0.0383545i
$569$		−	221.137i		−	0.388641i	−0.980938	−	0.194320i	$-0.937750\pi$
$569$		−	221.137i		−	0.388641i	0.980938	−	0.194320i	$-0.0622501\pi$
$570$	441.863	−	72.3232i	0.775198	−	0.126883i
$571$	520.798			0.912080			0.456040	−	0.889959i	$-0.349267\pi$
$571$	520.798			0.912080			0.456040	+	0.889959i	$0.349267\pi$
$572$	227.662			0.398010
$573$	636.449	+	244.871i	1.11073	+	0.427349i
$574$	129.904			0.226314
$575$	−395.082	+	703.433i	−0.687099	+	1.22336i
$576$	−53.4323	−	48.2596i	−0.0927644	−	0.0837840i
$577$			78.8359i			0.136631i	0.997664	+	0.0683154i	$0.0217624\pi$
$577$			78.8359i			0.136631i	−0.997664	+	0.0683154i	$0.978238\pi$
$578$	−402.885			−0.697032
$579$	671.590	+	258.391i	1.15991	+	0.446272i
$580$	105.812	−	61.9298i	0.182434	−	0.106775i
$581$		−	306.548i		−	0.527622i
$582$	32.4409	+	12.4815i	0.0557403	+	0.0214459i
$583$			344.689i			0.591234i
$584$			34.1374i			0.0584544i
$585$	837.835	+	174.245i	1.43220	+	0.297855i
$586$	−505.680			−0.862935
$587$	146.455			0.249498			0.124749	−	0.992188i	$-0.460187\pi$
$587$	146.455			0.249498			0.124749	+	0.992188i	$0.460187\pi$
$588$	15.0816	−	39.1988i	0.0256489	−	0.0666646i
$589$	−829.670			−1.40861
$590$	438.131	−	256.430i	0.742595	−	0.434627i
$591$	−198.340	+	515.509i	−0.335601	+	0.872266i
$592$			81.2965i			0.137325i
$593$	−240.021			−0.404758			−0.202379	−	0.979307i	$-0.564867\pi$
$593$	−240.021			−0.404758			−0.202379	+	0.979307i	$0.564867\pi$
$594$	−103.294	−	203.886i	−0.173895	−	0.343243i
$595$	23.1668	−	13.5591i	0.0389359	−	0.0227885i
$596$			372.671i			0.625287i
$597$	232.463	−	604.198i	0.389385	−	1.01206i
$598$			867.912i			1.45136i
$599$		−	886.239i		−	1.47953i	−0.672865	−	0.739766i	$-0.734936\pi$
$599$		−	886.239i		−	1.47953i	0.672865	−	0.739766i	$-0.265064\pi$
$600$	−135.319	−	163.367i	−0.225531	−	0.272279i
$601$	−162.944			−0.271121			−0.135561	−	0.990769i	$-0.543284\pi$
$601$	−162.944			−0.271121			−0.135561	+	0.990769i	$0.543284\pi$
$602$	150.904			0.250671
$603$	−492.930	+	545.765i	−0.817463	+	0.905083i
$604$	−367.121			−0.607816
$605$	215.109	+	367.531i	0.355552	+	0.607489i
$606$	540.434	+	207.930i	0.891805	+	0.343119i
$607$		−	649.221i		−	1.06956i	−0.844992	−	0.534779i	$-0.820395\pi$
$607$		−	649.221i		−	1.06956i	0.844992	−	0.534779i	$-0.179605\pi$
$608$	−119.398			−0.196378
$609$	−34.9437	+	90.8227i	−0.0573787	+	0.149134i
$610$	291.919	+	498.767i	0.478556	+	0.817650i
$611$			1377.58i			2.25464i
$612$	27.1055	+	24.4815i	0.0442901	+	0.0400024i
$613$		−	109.849i		−	0.179199i	−0.995978	−	0.0895994i	$-0.971441\pi$
$613$		−	109.849i		−	0.179199i	0.995978	−	0.0895994i	$-0.0285587\pi$
$614$			414.937i			0.675794i
$615$	84.1200	+	513.936i	0.136780	+	0.835668i
$616$	44.7934			0.0727165
$617$	871.161			1.41193			0.705966	−	0.708246i	$-0.250513\pi$
$617$	871.161			1.41193			0.705966	+	0.708246i	$0.250513\pi$
$618$	−511.556	−	196.819i	−0.827760	−	0.318477i
$619$	−153.281			−0.247627			−0.123814	−	0.992305i	$-0.539513\pi$
$619$	−153.281			−0.247627			−0.123814	+	0.992305i	$0.539513\pi$
$620$	198.556	+	339.248i	0.320251	+	0.547174i
$621$	777.272	−	393.786i	1.25165	−	0.634115i
$622$		−	83.7873i		−	0.134706i
$623$	−269.706			−0.432914
$624$	−212.983	−	81.9444i	−0.341319	−	0.131321i
$625$	−325.246	−	533.704i	−0.520394	−	0.853926i
$626$			637.226i			1.01793i
$627$	−353.742	−	136.101i	−0.564182	−	0.217067i
$628$			529.755i			0.843558i
$629$		−	41.2407i		−	0.0655655i
$630$	164.847	+	34.2835i	0.261662	+	0.0544182i
$631$	−959.345			−1.52036			−0.760178	−	0.649715i	$-0.774888\pi$
$631$	−959.345			−1.52036			−0.760178	+	0.649715i	$0.774888\pi$
$632$	372.282			0.589055
$633$	131.842	−	342.672i	0.208281	−	0.541346i
$634$	−392.379			−0.618894
$635$	−64.9059	+	37.9882i	−0.102214	+	0.0598240i
$636$	124.067	−	322.465i	0.195074	−	0.507020i
$637$		−	133.119i		−	0.208977i
$638$	−103.785			−0.162673
$639$	46.4637	−	51.4439i	0.0727131	−	0.0805069i
$640$	28.5742	+	48.8213i	0.0446472	+	0.0762832i
$641$			733.758i			1.14471i	0.820007	+	0.572354i	$0.193970\pi$
$641$			733.758i			1.14471i	−0.820007	+	0.572354i	$0.806030\pi$
$642$	−30.8700	+	80.2346i	−0.0480840	+	0.124976i
$643$			164.305i			0.255529i	0.991805	+	0.127765i	$0.0407802\pi$
$643$			164.305i			0.255529i	−0.991805	+	0.127765i	$0.959220\pi$
$644$			170.765i			0.265163i
$645$	97.7185	+	597.017i	0.151502	+	0.925607i
$646$	60.5691			0.0937602
$647$	1171.84			1.81119			0.905594	−	0.424146i	$-0.139426\pi$
$647$	1171.84			1.81119			0.905594	+	0.424146i	$0.139426\pi$
$648$	23.2473	+	227.920i	0.0358754	+	0.351729i
$649$	−429.739			−0.662155
$650$	−586.217	−	329.248i	−0.901873	−	0.506535i
$651$	−291.191	−	112.034i	−0.447297	−	0.172096i
$652$		−	429.754i		−	0.659132i
$653$	−804.521			−1.23204			−0.616019	−	0.787731i	$-0.711256\pi$
$653$	−804.521			−1.23204			−0.616019	+	0.787731i	$0.711256\pi$
$654$	171.496	−	445.738i	0.262226	−	0.681557i
$655$	222.632	−	130.303i	0.339897	−	0.198936i
$656$		−	138.873i		−	0.211697i
$657$	72.8080	−	80.6119i	0.110819	−	0.122697i
$658$			271.045i			0.411922i
$659$		−	864.248i		−	1.31145i	−0.754999	−	0.655727i	$-0.772362\pi$
$659$		−	864.248i		−	1.31145i	0.754999	−	0.655727i	$-0.227638\pi$
$660$	29.0062	+	177.215i	0.0439488	+	0.268507i
$661$	−963.638			−1.45785			−0.728924	−	0.684595i	$-0.759979\pi$
$661$	−963.638			−1.45785			−0.728924	+	0.684595i	$0.759979\pi$
$662$	390.179			0.589394
$663$	108.044	+	41.5694i	0.162962	+	0.0626989i
$664$	−327.714			−0.493545
$665$	240.977	−	141.039i	0.362371	−	0.212089i
$666$	173.389	−	191.973i	0.260343	−	0.288248i
$667$		−	395.658i		−	0.593191i
$668$	−109.191			−0.163459
$669$	196.362	+	75.5496i	0.293516	+	0.112929i
$670$	498.667	−	291.861i	0.744279	−	0.435613i
$671$		−	489.213i		−	0.729081i
$672$	−41.9053	−	16.1229i	−0.0623590	−	0.0239924i
$673$			149.734i			0.222487i	0.993793	+	0.111244i	$0.0354834\pi$
$673$			149.734i			0.222487i	−0.993793	+	0.111244i	$0.964517\pi$
$674$			145.378i			0.215694i
$675$	−28.8870	+	674.382i	−0.0427955	+	0.999084i
$676$	−385.288			−0.569953
$677$	325.257			0.480439			0.240219	−	0.970719i	$-0.422781\pi$
$677$	325.257			0.480439			0.240219	+	0.970719i	$0.422781\pi$
$678$	−9.96012	+	25.8875i	−0.0146904	+	0.0381822i
$679$	21.6761			0.0319236
$680$	−14.4953	−	24.7664i	−0.0213167	−	0.0364212i
$681$	−33.8557	+	87.9949i	−0.0497146	+	0.129214i
$682$		−	332.750i		−	0.487904i
$683$	−551.573			−0.807575			−0.403787	−	0.914853i	$-0.632306\pi$
$683$	−551.573			−0.807575			−0.403787	+	0.914853i	$0.632306\pi$
$684$	281.946	+	254.651i	0.412202	+	0.372297i
$685$	−120.192	−	205.357i	−0.175462	−	0.299791i
$686$		−	26.1916i		−	0.0381802i
$687$	−38.4803	+	100.015i	−0.0560121	+	0.145582i
$688$		−	161.323i		−	0.234481i
$689$		−	1095.09i		−	1.58939i
$690$	−675.593	+	110.580i	−0.979120	+	0.160261i
$691$	−495.558			−0.717161			−0.358580	−	0.933499i	$-0.616739\pi$
$691$	−495.558			−0.717161			−0.358580	+	0.933499i	$0.616739\pi$
$692$	−621.301			−0.897834
$693$	−105.775	−	95.5350i	−0.152633	−	0.137857i
$694$	−645.715			−0.930426
$695$	−297.341	−	508.030i	−0.427829	−	0.730979i
$696$	97.0935	+	37.3563i	0.139502	+	0.0536729i
$697$			70.4486i			0.101074i
$698$	806.958			1.15610
$699$	−349.615	+	908.690i	−0.500164	+	1.29999i
$700$	−115.341	−	64.7808i	−0.164772	−	0.0925440i
$701$			377.346i			0.538297i	0.963099	+	0.269149i	$0.0867423\pi$
$701$			377.346i			0.538297i	−0.963099	+	0.269149i	$0.913258\pi$
$702$	328.168	+	647.752i	0.467475	+	0.922724i
$703$		−	428.977i		−	0.610209i
$704$		−	47.8861i		−	0.0680201i
$705$	−1072.33	+	175.517i	−1.52103	+	0.248960i
$706$	−6.71080			−0.00950539
$707$	361.104			0.510755
$708$	402.031	+	154.680i	0.567840	+	0.218474i
$709$	517.276			0.729585			0.364792	−	0.931089i	$-0.381140\pi$
$709$	517.276			0.729585			0.364792	+	0.931089i	$0.381140\pi$
$710$	−47.0044	+	27.5109i	−0.0662034	+	0.0387477i
$711$	−879.107	−	794.001i	−1.23644	−	1.11674i
$712$			288.327i			0.404954i
$713$	1268.54			1.77916
$714$	21.2580	+	8.17894i	0.0297731	+	0.0114551i
$715$	287.495	+	491.207i	0.402090	+	0.687003i
$716$			325.845i			0.455090i
$717$	1120.08	+	430.944i	1.56217	+	0.601038i
$718$			646.418i			0.900303i
$719$		−	1187.74i		−	1.65193i	−0.563720	−	0.825966i	$-0.690630\pi$
$719$		−	1187.74i		−	1.65193i	0.563720	−	0.825966i	$-0.309370\pi$
$720$	36.6506	−	176.229i	0.0509036	−	0.244763i
$721$	−341.808			−0.474075
$722$	119.496			0.165506
$723$	−426.922	+	1109.62i	−0.590487	+	1.53474i
$724$	−103.018			−0.142289
$725$	267.241	+	150.096i	0.368609	+	0.207028i
$726$	−129.755	+	337.248i	−0.178726	+	0.464529i
$727$			892.878i			1.22817i	0.789241	+	0.614084i	$0.210474\pi$
$727$			892.878i			1.22817i	−0.789241	+	0.614084i	$0.789526\pi$
$728$	−142.310			−0.195480
$729$	431.210	−	587.791i	0.591509	−	0.806298i
$730$	−73.6553	+	43.1091i	−0.100898	+	0.0590536i
$731$			81.8371i			0.111952i
$732$	−176.087	+	457.671i	−0.240556	+	0.625233i
$733$		−	868.737i		−	1.18518i	−0.805504	−	0.592590i	$-0.798106\pi$
$733$		−	868.737i		−	1.18518i	0.805504	−	0.592590i	$-0.201894\pi$
$734$			787.204i			1.07248i
$735$	103.621	−	16.9605i	0.140981	−	0.0230755i
$736$	182.555			0.248037
$737$	−489.116			−0.663657
$738$	−296.188	+	327.935i	−0.401338	+	0.444356i
$739$	−356.963			−0.483035			−0.241517	−	0.970396i	$-0.577645\pi$
$739$	−356.963			−0.483035			−0.241517	+	0.970396i	$0.577645\pi$
$740$	−175.407	+	102.662i	−0.237036	+	0.138733i
$741$	1123.85	+	432.396i	1.51666	+	0.583530i
$742$		−	215.463i		−	0.290381i
$743$	−982.069			−1.32176			−0.660881	−	0.750491i	$-0.729817\pi$
$743$	−982.069			−1.32176			−0.660881	+	0.750491i	$0.729817\pi$
$744$	−119.770	+	311.296i	−0.160981	+	0.418408i
$745$	−804.081	+	470.614i	−1.07930	+	0.631697i
$746$		−	109.215i		−	0.146401i
$747$	773.863	+	698.946i	1.03596	+	0.935670i
$748$			24.2920i			0.0324760i
$749$			53.6107i			0.0715763i
$750$	181.601	−	498.268i	0.242135	−	0.664357i
$751$	−710.167			−0.945628			−0.472814	−	0.881162i	$-0.656762\pi$
$751$	−710.167			−0.945628			−0.472814	+	0.881162i	$0.656762\pi$
$752$	289.759			0.385318
$753$	619.413	+	238.317i	0.822593	+	0.316489i
$754$	329.728			0.437305
$755$	−463.605	−	792.105i	−0.614046	−	1.04915i
$756$	64.5682	+	127.448i	0.0854077	+	0.168582i
$757$		−	346.357i		−	0.457540i	−0.973481	−	0.228770i	$-0.926530\pi$
$757$		−	346.357i		−	0.457540i	0.973481	−	0.228770i	$-0.0734703\pi$
$758$	673.353			0.888329
$759$	540.859	+	208.093i	0.712595	+	0.274168i
$760$	−150.777	−	257.615i	−0.198391	−	0.338967i
$761$		−	1138.06i		−	1.49548i	−0.663994	−	0.747738i	$-0.731140\pi$
$761$		−	1138.06i		−	1.49548i	0.663994	−	0.747738i	$-0.268860\pi$
$762$	−59.5580	−	22.9147i	−0.0781600	−	0.0300718i
$763$		−	297.830i		−	0.390341i
$764$		−	454.620i		−	0.595053i
$765$	−18.5924	+	89.3988i	−0.0243037	+	0.116861i
$766$	849.057			1.10843
$767$	1365.29			1.78004
$768$	−17.2361	+	44.7986i	−0.0224428	+	0.0583315i
$769$	−395.138			−0.513833			−0.256917	−	0.966434i	$-0.582707\pi$
$769$	−395.138			−0.513833			−0.256917	+	0.966434i	$0.582707\pi$
$770$	56.5657	+	96.6469i	0.0734619	+	0.125515i
$771$	219.561	−	570.665i	0.284774	−	0.740162i
$772$		−	479.722i		−	0.621401i
$773$	−1244.98			−1.61058			−0.805290	−	0.592881i	$-0.797990\pi$
$773$	−1244.98			−1.61058			−0.805290	+	0.592881i	$0.797990\pi$
$774$	−344.068	+	380.947i	−0.444533	+	0.492180i
$775$	−481.228	+	856.814i	−0.620939	+	1.10557i
$776$		−	23.1728i		−	0.0298618i
$777$	57.9268	−	150.559i	0.0745519	−	0.193769i
$778$		−	446.024i		−	0.573296i
$779$			732.791i			0.940682i
$780$	−92.1535	−	563.016i	−0.118145	−	0.721816i
$781$	46.1041			0.0590322
$782$	−92.6081			−0.118425
$783$	−149.603	−	295.293i	−0.191064	−	0.377131i
$784$	−28.0000			−0.0357143
$785$	−1143.01	+	668.981i	−1.45606	+	0.852205i
$786$	204.289	+	78.5992i	0.259909	+	0.0999990i
$787$		−	333.519i		−	0.423785i	−0.977293	−	0.211892i	$-0.932037\pi$
$787$		−	333.519i		−	0.423785i	0.977293	−	0.211892i	$-0.0679627\pi$
$788$	368.232			0.467300
$789$	−105.789	+	274.957i	−0.134079	+	0.348488i
$790$	470.123	+	803.242i	0.595093	+	1.01676i
$791$			17.2974i			0.0218677i
$792$	−102.131	+	113.078i	−0.128954	+	0.142775i
$793$			1554.24i			1.95995i
$794$			412.281i			0.519246i
$795$	852.429	−	139.524i	1.07224	−	0.175502i
$796$	−431.583			−0.542190
$797$	541.407			0.679306			0.339653	−	0.940551i	$-0.389690\pi$
$797$	541.407			0.679306			0.339653	+	0.940551i	$0.389690\pi$
$798$	221.121	+	85.0756i	0.277094	+	0.106611i
$799$	−146.991			−0.183969
$800$	−69.2536	+	123.304i	−0.0865670	+	0.154130i
$801$	614.943	−	680.856i	0.767719	−	0.850007i
$802$		−	441.521i		−	0.550525i
$803$	72.2446			0.0899683
$804$	457.579	+	176.052i	0.569128	+	0.218970i
$805$	−368.445	+	215.644i	−0.457696	+	0.267881i
$806$			1057.16i			1.31161i
$807$	864.176	+	332.488i	1.07085	+	0.412005i
$808$		−	386.036i		−	0.477768i
$809$			812.942i			1.00487i	0.864614	+	0.502436i	$0.167563\pi$
$809$			812.942i			1.00487i	−0.864614	+	0.502436i	$0.832437\pi$
$810$	−462.407	+	337.979i	−0.570873	+	0.417258i
$811$	−750.662			−0.925600			−0.462800	−	0.886463i	$-0.653155\pi$
$811$	−750.662			−0.925600			−0.462800	+	0.886463i	$0.653155\pi$
$812$	64.8753			0.0798957
$813$	429.654	−	1116.72i	0.528480	−	1.37358i
$814$	172.047			0.211360
$815$	927.244	−	542.699i	1.13772	−	0.665888i
$816$	8.74365	−	22.7258i	0.0107153	−	0.0278502i
$817$			851.252i			1.04192i
$818$	−852.331			−1.04197
$819$	336.050	+	303.517i	0.410317	+	0.370595i
$820$	299.635	−	175.371i	0.365408	−	0.213867i
$821$		−	1216.71i		−	1.48199i	−0.671513	−	0.740993i	$-0.734355\pi$
$821$		−	1216.71i		−	1.48199i	0.671513	−	0.740993i	$-0.265645\pi$
$822$	72.5001	−	188.436i	0.0881996	−	0.229241i
$823$		−	918.365i		−	1.11588i	−0.829883	−	0.557938i	$-0.811593\pi$
$823$		−	918.365i		−	1.11588i	0.829883	−	0.557938i	$-0.188407\pi$
$824$			365.408i			0.443457i
$825$	−345.732	+	286.373i	−0.419069	+	0.347119i
$826$	268.626			0.325214
$827$	−973.601			−1.17727			−0.588634	−	0.808400i	$-0.700334\pi$
$827$	−973.601			−1.17727			−0.588634	+	0.808400i	$0.700334\pi$
$828$	−431.086	−	389.353i	−0.520635	−	0.470233i
$829$	759.447			0.916100			0.458050	−	0.888926i	$-0.348548\pi$
$829$	759.447			0.916100			0.458050	+	0.888926i	$0.348548\pi$
$830$	−413.841	−	707.081i	−0.498604	−	0.851904i
$831$	−223.211	−	85.8796i	−0.268606	−	0.103345i
$832$			152.136i			0.182855i
$833$	14.2040			0.0170517
$834$	179.357	−	466.171i	0.215057	−	0.558958i
$835$	−137.888	−	235.592i	−0.165135	−	0.282146i
$836$			252.681i			0.302249i
$837$	946.753	−	479.649i	1.13113	−	0.573057i
$838$			254.515i			0.303718i
$839$			937.182i			1.11702i	0.829497	+	0.558512i	$0.188627\pi$
$839$			937.182i			1.11702i	−0.829497	+	0.558512i	$0.811373\pi$
$840$	−18.1316	−	110.776i	−0.0215852	−	0.131876i
$841$	690.685			0.821267
$842$	643.409			0.764144
$843$	588.456	+	226.406i	0.698050	+	0.268572i
$844$	−244.773			−0.290015
$845$	−486.547	−	831.304i	−0.575795	−	0.983791i
$846$	−684.237	−	617.996i	−0.808790	−	0.730492i
$847$			225.340i			0.266045i
$848$	−230.339			−0.271626
$849$	736.212	+	283.255i	0.867152	+	0.333633i
$850$	35.1315	−	62.5507i	0.0413311	−	0.0735890i
$851$			655.891i			0.770730i
$852$	−43.1315	−	16.5947i	−0.0506238	−	0.0194773i
$853$		−	465.533i		−	0.545760i	−0.962048	−	0.272880i	$-0.912024\pi$
$853$		−	465.533i		−	0.545760i	0.962048	−	0.272880i	$-0.0879762\pi$
$854$			305.803i			0.358084i
$855$	−193.394	+	929.908i	−0.226192	+	1.08761i
$856$	57.3122			0.0669535
$857$	−1612.01			−1.88099			−0.940494	−	0.339811i	$-0.889637\pi$
$857$	−1612.01			−1.88099			−0.940494	+	0.339811i	$0.889637\pi$
$858$	−173.418	+	450.734i	−0.202119	+	0.525331i
$859$	1111.27			1.29368			0.646842	−	0.762624i	$-0.276089\pi$
$859$	1111.27			1.29368			0.646842	+	0.762624i	$0.276089\pi$
$860$	348.073	−	203.721i	0.404736	−	0.236885i
$861$	−98.9524	+	257.189i	−0.114927	+	0.298709i
$862$			396.597i			0.460090i
$863$	681.862			0.790106			0.395053	−	0.918658i	$-0.370726\pi$
$863$	681.862			0.790106			0.395053	+	0.918658i	$0.370726\pi$
$864$	136.247	−	69.0264i	0.157694	−	0.0798916i
$865$	−784.587	−	1340.53i	−0.907037	−	1.54974i
$866$			243.812i			0.281538i
$867$	306.891	−	797.647i	0.353969	−	0.920008i
$868$			208.000i			0.239631i
$869$		−	787.857i		−	0.906625i
$870$	42.0104	+	256.665i	0.0482878	+	0.295017i
$871$	1553.93			1.78408
$872$	−318.394			−0.365131
$873$	−49.4227	+	54.7201i	−0.0566125	+	0.0626805i
$874$	−963.289			−1.10216
$875$	−5.88150	−	330.667i	−0.00672171	−	0.377905i
$876$	−67.5865	−	26.0036i	−0.0771536	−	0.0296845i
$877$		−	206.003i		−	0.234896i	−0.993079	−	0.117448i	$-0.962529\pi$
$877$		−	206.003i		−	0.234896i	0.993079	−	0.117448i	$-0.0374713\pi$
$878$	423.782			0.482667
$879$	385.194	−	1001.16i	0.438219	−	1.13898i
$880$	103.320	−	60.4712i	0.117409	−	0.0687173i
$881$			909.333i			1.03216i	0.856540	+	0.516080i	$0.172609\pi$
$881$			909.333i			1.03216i	−0.856540	+	0.516080i	$0.827391\pi$
$882$	66.1191	+	59.7182i	0.0749650	+	0.0677077i
$883$		−	776.956i		−	0.879905i	−0.898021	−	0.439952i	$-0.854995\pi$
$883$		−	776.956i		−	0.879905i	0.898021	−	0.439952i	$-0.145005\pi$
$884$		−	77.1764i		−	0.0873036i
$885$	173.951	+	1062.76i	0.196554	+	1.20086i
$886$	550.763			0.621628
$887$	−1228.23			−1.38470			−0.692350	−	0.721562i	$-0.743425\pi$
$887$	−1228.23			−1.38470			−0.692350	+	0.721562i	$0.743425\pi$
$888$	−160.954	−	61.9264i	−0.181254	−	0.0697369i
$889$	−39.7951			−0.0447638
$890$	−622.100	+	364.104i	−0.698988	+	0.409105i
$891$	482.345	−	49.1979i	0.541352	−	0.0552165i
$892$		−	140.263i		−	0.157245i
$893$	−1528.97			−1.71217
$894$	−737.829	−	283.877i	−0.825312	−	0.317535i
$895$	−703.047	+	411.481i	−0.785528	+	0.459755i
$896$			29.9333i			0.0334077i
$897$	−1718.32	−	661.119i	−1.91564	−	0.737033i
$898$		−	868.359i		−	0.966993i
$899$		−	481.930i		−	0.536074i
$900$	426.518	−	143.467i	0.473908	−	0.159407i
$901$	116.848			0.129687
$902$	−293.896			−0.325827
$903$	−114.949	+	298.765i	−0.127296	+	0.330858i
$904$	18.4917			0.0204554
$905$	−130.092	−	222.272i	−0.143748	−	0.245605i
$906$	279.649	−	726.840i	0.308663	−	0.802251i
$907$		−	254.429i		−	0.280517i	−0.990115	−	0.140259i	$-0.955207\pi$
$907$		−	254.429i		−	0.280517i	0.990115	−	0.140259i	$-0.0447934\pi$
$908$	62.8554			0.0692240
$909$	−823.335	+	911.585i	−0.905759	+	1.00284i
$910$	−179.711	−	307.050i	−0.197484	−	0.337417i
$911$		−	231.235i		−	0.253825i	−0.991914	−	0.126913i	$-0.959493\pi$
$911$		−	231.235i		−	0.253825i	0.991914	−	0.126913i	$-0.0405068\pi$
$912$	90.9496	−	236.389i	0.0997254	−	0.259198i
$913$			693.537i			0.759624i
$914$		−	304.845i		−	0.333529i
$915$	−1209.84	+	198.025i	−1.32223	+	0.216420i
$916$	71.4414			0.0779928
$917$	136.500			0.148855
$918$	−69.1166	+	35.0162i	−0.0752904	+	0.0381440i
$919$	279.584			0.304226			0.152113	−	0.988363i	$-0.451392\pi$
$919$	279.584			0.304226			0.152113	+	0.988363i	$0.451392\pi$
$920$	230.533	+	393.884i	0.250580	+	0.428135i
$921$	−821.509	−	316.072i	−0.891975	−	0.343184i
$922$		−	522.698i		−	0.566918i
$923$	−146.474			−0.158693
$924$	−34.1207	+	88.6836i	−0.0369271	+	0.0959780i
$925$	−443.011	−	248.817i	−0.478931	−	0.268991i
$926$		−	0.955022i		−	0.00103134i
$927$	779.340	−	862.874i	0.840712	−	0.930824i
$928$		−	69.3546i		−	0.0747356i
$929$			1522.35i			1.63870i	0.573294	+	0.819350i	$0.305665\pi$
$929$			1522.35i			1.63870i	−0.573294	+	0.819350i	$0.694335\pi$
$930$	−822.903	+	134.691i	−0.884842	+	0.144829i
$931$	147.747			0.158698
$932$	649.084			0.696442
$933$	165.885	+	63.8237i	0.177798	+	0.0684069i
$934$	−127.469			−0.136476
$935$	−52.4128	+	30.6763i	−0.0560565	+	0.0328089i
$936$	324.474	−	359.252i	0.346660	−	0.383817i
$937$		−	1402.37i		−	1.49666i	−0.663328	−	0.748329i	$-0.730856\pi$
$937$		−	1402.37i		−	1.49666i	0.663328	−	0.748329i	$-0.269144\pi$
$938$	305.742			0.325951
$939$	−1261.60	−	485.397i	−1.34356	−	0.516930i
$940$	365.912	+	625.189i	0.389268	+	0.665095i
$941$			569.377i			0.605077i	0.953137	+	0.302538i	$0.0978340\pi$
$941$			569.377i			0.605077i	−0.953137	+	0.302538i	$0.902166\pi$
$942$	−1048.83	−	403.533i	−1.11341	−	0.428379i
$943$		−	1120.41i		−	1.18814i
$944$		−	287.174i		−	0.304210i
$945$	−193.446	+	300.256i	−0.204704	+	0.317731i
$946$	−341.406			−0.360894
$947$	130.552			0.137858			0.0689290	−	0.997622i	$-0.478042\pi$
$947$	130.552			0.137858			0.0689290	+	0.997622i	$0.478042\pi$
$948$	−283.581	+	737.059i	−0.299136	+	0.777488i
$949$	−229.523			−0.241858
$950$	365.430	−	650.639i	0.384663	−	0.684883i
$951$	298.889	−	776.847i	0.314289	−	0.816874i
$952$		−	15.1848i		−	0.0159504i
$953$	154.008			0.161603			0.0808016	−	0.996730i	$-0.474252\pi$
$953$	154.008			0.161603			0.0808016	+	0.996730i	$0.474252\pi$
$954$	543.922	+	491.266i	0.570149	+	0.514953i
$955$	980.896	−	574.100i	1.02712	−	0.601152i
$956$		−	800.078i		−	0.836902i
$957$	79.0568	−	205.478i	0.0826090	−	0.214710i
$958$			597.189i			0.623371i
$959$		−	125.908i		−	0.131291i
$960$	−118.424	+	19.3834i	−0.123359	+	0.0201911i
$961$	584.137			0.607843
$962$	−546.597			−0.568189
$963$	−135.337	−	122.235i	−0.140537	−	0.126932i
$964$	792.610			0.822209
$965$	1035.05	−	605.799i	1.07260	−	0.627771i
$966$	−338.087	−	130.078i	−0.349987	−	0.134656i
$967$		−	614.131i		−	0.635089i	−0.948243	−	0.317544i	$-0.897142\pi$
$967$		−	614.131i		−	0.635089i	0.948243	−	0.317544i	$-0.102858\pi$
$968$	240.899			0.248862
$969$	−46.1376	+	119.917i	−0.0476136	+	0.123753i
$970$	49.9979	−	29.2629i	0.0515442	−	0.0301679i
$971$			288.285i			0.296895i	0.988920	+	0.148448i	$0.0474277\pi$
$971$			288.285i			0.296895i	−0.988920	+	0.148448i	$0.952572\pi$
$972$	−468.953	−	127.589i	−0.482462	−	0.131264i
$973$		−	311.483i		−	0.320127i
$974$			339.671i			0.348739i
$975$	1098.40	−	909.816i	1.12656	−	0.933145i
$976$	326.918			0.334957
$977$	480.732			0.492049			0.246025	−	0.969264i	$-0.420876\pi$
$977$	480.732			0.492049			0.246025	+	0.969264i	$0.420876\pi$
$978$	850.844	+	327.359i	0.869983	+	0.334723i
$979$	610.184			0.623273
$980$	−35.3588	−	60.4132i	−0.0360804	−	0.0616461i
$981$	751.855	+	679.069i	0.766417	+	0.692221i
$982$			1359.32i			1.38424i
$983$	1414.59			1.43905			0.719526	−	0.694465i	$-0.244359\pi$
$983$	1414.59			1.43905			0.719526	+	0.694465i	$0.244359\pi$
$984$	274.946	+	105.785i	0.279417	+	0.107505i
$985$	465.008	+	794.503i	0.472090	+	0.806602i
$986$			35.1827i			0.0356823i
$987$	−536.625	−	206.464i	−0.543693	−	0.209184i
$988$		−	802.773i		−	0.812523i
$989$		−	1301.54i		−	1.31601i
$990$	−372.952	−	77.5632i	−0.376719	−	0.0783466i
$991$	−549.944			−0.554939			−0.277469	−	0.960735i	$-0.589496\pi$
$991$	−549.944			−0.554939			−0.277469	+	0.960735i	$0.589496\pi$
$992$	222.361			0.224154
$993$	−297.213	+	772.491i	−0.299308	+	0.777937i
$994$	−28.8193			−0.0289933
$995$	−545.009	−	931.191i	−0.547748	−	0.935870i
$996$	249.631	−	648.821i	0.250634	−	0.651426i
$997$			524.552i			0.526130i	0.964778	+	0.263065i	$0.0847334\pi$
$997$			524.552i			0.526130i	−0.964778	+	0.263065i	$0.915267\pi$
$998$	287.399			0.287975
$999$	248.000	+	489.514i	0.248248	+	0.490004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.c.a.29.18	yes	24
3.2	odd	2	inner	210.3.c.a.29.8	yes	24
5.2	odd	4		1050.3.e.e.701.20		24
5.3	odd	4		1050.3.e.e.701.17		24
5.4	even	2	inner	210.3.c.a.29.7	✓	24
15.2	even	4		1050.3.e.e.701.18		24
15.8	even	4		1050.3.e.e.701.19		24
15.14	odd	2	inner	210.3.c.a.29.17	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.7	✓	24	5.4	even	2	inner
210.3.c.a.29.8	yes	24	3.2	odd	2	inner
210.3.c.a.29.17	yes	24	15.14	odd	2	inner
210.3.c.a.29.18	yes	24	1.1	even	1	trivial
1050.3.e.e.701.17		24	5.3	odd	4
1050.3.e.e.701.18		24	15.2	even	4
1050.3.e.e.701.19		24	15.8	even	4
1050.3.e.e.701.20		24	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-1.07726 + 2.79991i) q^{3} +2.00000 q^{4} +(2.52563 + 4.31523i) q^{5} +(-1.52347 + 3.95968i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-6.67904 - 6.03245i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-1.07726 + 2.79991i) q^{3} +2.00000 q^{4} +(2.52563 + 4.31523i) q^{5} +(-1.52347 + 3.95968i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-6.67904 - 6.03245i) q^{9} +(3.57177 + 6.10266i) q^{10} -5.98577i q^{11} +(-2.15451 + 5.59983i) q^{12} +19.0169i q^{13} +3.74166i q^{14} +(-14.8030 + 2.42293i) q^{15} +4.00000 q^{16} -2.02915 q^{17} +(-9.44559 - 8.53117i) q^{18} -21.1068 q^{19} +(5.05125 + 8.63046i) q^{20} +(-7.40788 - 2.85015i) q^{21} -8.46515i q^{22} +32.2716 q^{23} +(-3.04694 + 7.91935i) q^{24} +(-12.2424 + 21.7973i) q^{25} +26.8940i q^{26} +(24.0854 - 12.2023i) q^{27} +5.29150i q^{28} -12.2603i q^{29} +(-20.9346 + 3.42654i) q^{30} +39.3082 q^{31} +5.65685 q^{32} +(16.7596 + 6.44820i) q^{33} -2.86965 q^{34} +(-11.4170 + 6.68218i) q^{35} +(-13.3581 - 12.0649i) q^{36} +20.3241i q^{37} -29.8495 q^{38} +(-53.2458 - 20.4861i) q^{39} +(7.14355 + 12.2053i) q^{40} -34.7183i q^{41} +(-10.4763 - 4.03072i) q^{42} -40.3307i q^{43} -11.9715i q^{44} +(9.16264 - 44.0573i) q^{45} +45.6389 q^{46} +72.4398 q^{47} +(-4.30902 + 11.1997i) q^{48} -7.00000 q^{49} +(-17.3134 + 30.8261i) q^{50} +(2.18591 - 5.68144i) q^{51} +38.0339i q^{52} -57.5848 q^{53} +(34.0619 - 17.2566i) q^{54} +(25.8300 - 15.1178i) q^{55} +7.48331i q^{56} +(22.7374 - 59.0972i) q^{57} -17.3387i q^{58} -71.7934i q^{59} +(-29.6060 + 4.84586i) q^{60} +81.7294 q^{61} +55.5902 q^{62} +(15.9604 - 17.6711i) q^{63} +8.00000 q^{64} +(-82.0625 + 48.0297i) q^{65} +(23.7017 + 9.11913i) q^{66} -81.7131i q^{67} -4.05830 q^{68} +(-34.7647 + 90.3576i) q^{69} +(-16.1461 + 9.45003i) q^{70} +7.70229i q^{71} +(-18.8912 - 17.0623i) q^{72} +12.0694i q^{73} +28.7427i q^{74} +(-47.8424 - 57.7590i) q^{75} -42.2136 q^{76} +15.8369 q^{77} +(-75.3009 - 28.9717i) q^{78} +131.622 q^{79} +(10.1025 + 17.2609i) q^{80} +(8.21915 + 80.5819i) q^{81} -49.0991i q^{82} -115.864 q^{83} +(-14.8158 - 5.70030i) q^{84} +(-5.12487 - 8.75624i) q^{85} -57.0363i q^{86} +(34.3277 + 13.2075i) q^{87} -16.9303i q^{88} +101.939i q^{89} +(12.9579 - 62.3064i) q^{90} -50.3141 q^{91} +64.5431 q^{92} +(-42.3450 + 110.060i) q^{93} +102.445 q^{94} +(-53.3078 - 91.0806i) q^{95} +(-6.09388 + 15.8387i) q^{96} -8.19281i q^{97} -9.89949 q^{98} +(-36.1088 + 39.9792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) \) 24 * q + 48 * q^4 + 44 * q^9	\( 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) \) 24 * q + 48 * q^4 + 44 * q^9 + 16 * q^10 + 4 * q^15 + 96 * q^16 - 80 * q^19 - 28 * q^21 + 48 * q^25 - 56 * q^30 + 224 * q^31 + 128 * q^34 + 88 * q^36 - 92 * q^39 + 32 * q^40 - 72 * q^45 - 144 * q^46 - 168 * q^49 - 284 * q^51 - 144 * q^54 - 320 * q^55 + 8 * q^60 + 192 * q^64 + 224 * q^66 - 152 * q^69 - 56 * q^70 + 48 * q^75 - 160 * q^76 - 72 * q^79 - 212 * q^81 - 56 * q^84 - 64 * q^85 - 240 * q^90 + 168 * q^91 - 128 * q^94 - 876 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more