LMFDB - Embedded newform 210.2.n.b.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(79,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("210.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.7652750400000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} - 14 x^{9} + 21 x^{8} - 108 x^{7} + 368 x^{6} - 216 x^{5} + 84 x^{4} + \cdots + 64 $ x^12 - 6x^11 + 18x^10 - 14x^9 + 21x^8 - 108x^7 + 368x^6 - 216x^5 + 84x^4 - 112x^3 + 288x^2 - 192*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.3
Root			$-0.685661 + 0.685661i$ of defining polynomial
Character	$\chi$	$=$	210.109
Dual form			210.2.n.b.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.20942 - 0.344208i) q^{5} +1.00000 q^{6} +(-2.51980 - 0.806615i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.20942 - 0.344208i) q^{5} +1.00000 q^{6} +(-2.51980 - 0.806615i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.74131 + 1.40280i) q^{10} +(2.39213 - 4.14329i) q^{11} +(-0.866025 + 0.500000i) q^{12} -3.17103i q^{13} +(2.58551 - 0.561349i) q^{14} +(-2.08551 - 0.806615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.52625 + 2.61323i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.58551 - 2.74619i) q^{19} +(0.806615 - 2.08551i) q^{20} +(1.77890 + 1.95845i) q^{21} +4.78426i q^{22} +(6.21029 - 3.58551i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.76304 - 1.52100i) q^{25} +(1.58551 + 2.74619i) q^{26} -1.00000i q^{27} +(-1.95845 + 1.77890i) q^{28} -2.38677 q^{29} +(2.20942 - 0.344208i) q^{30} +(-2.08551 + 3.61222i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.14329 + 2.39213i) q^{33} -5.22646 q^{34} +(-5.84492 - 0.914813i) q^{35} +1.00000 q^{36} +(-6.21029 + 3.58551i) q^{37} +(2.74619 + 1.58551i) q^{38} +(-1.58551 + 2.74619i) q^{39} +(0.344208 + 2.20942i) q^{40} -2.05543 q^{41} +(-2.51980 - 0.806615i) q^{42} -2.00000i q^{43} +(-2.39213 - 4.14329i) q^{44} +(1.40280 + 1.74131i) q^{45} +(-3.58551 + 6.21029i) q^{46} +(-9.97063 + 5.75654i) q^{47} +1.00000i q^{48} +(5.69874 + 4.06501i) q^{49} +(-3.36441 + 3.69874i) q^{50} +(-2.61323 - 4.52625i) q^{51} +(-2.74619 - 1.58551i) q^{52} +(7.02832 + 4.05780i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.85906 - 9.97764i) q^{55} +(0.806615 - 2.51980i) q^{56} +3.17103i q^{57} +(2.06700 - 1.19339i) q^{58} +(-5.36441 + 9.29144i) q^{59} +(-1.74131 + 1.40280i) q^{60} +(-3.55780 - 6.16229i) q^{61} -4.17103i q^{62} +(-0.561349 - 2.58551i) q^{63} -1.00000 q^{64} +(-1.09150 - 7.00613i) q^{65} +(2.39213 - 4.14329i) q^{66} +(8.28658 + 4.78426i) q^{67} +(4.52625 - 2.61323i) q^{68} -7.17103 q^{69} +(5.51926 - 2.13021i) q^{70} +6.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(3.58551 - 6.21029i) q^{74} +(-4.88541 - 1.06430i) q^{75} -3.17103 q^{76} +(-9.36972 + 8.51072i) q^{77} -3.17103i q^{78} +(6.08551 + 10.5404i) q^{79} +(-1.40280 - 1.74131i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.78005 - 1.02771i) q^{82} -3.39749i q^{83} +(2.58551 - 0.561349i) q^{84} +(10.8999 + 4.21574i) q^{85} +(1.00000 + 1.73205i) q^{86} +(2.06700 + 1.19339i) q^{87} +(4.14329 + 2.39213i) q^{88} +(4.78426 + 8.28658i) q^{89} +(-2.08551 - 0.806615i) q^{90} +(-2.55780 + 7.99035i) q^{91} -7.17103i q^{92} +(3.61222 - 2.08551i) q^{93} +(5.75654 - 9.97063i) q^{94} +(-4.44833 - 5.52173i) q^{95} +(-0.500000 - 0.866025i) q^{96} +1.27117i q^{97} +(-6.96776 - 0.671030i) q^{98} +4.78426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 12 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 12 * q^6 + 6 * q^9	$ 12 q + 6 q^{4} + 12 q^{6} + 6 q^{9} - 6 q^{11} + 6 q^{14} - 6 q^{16} + 6 q^{19} + 6 q^{21} + 6 q^{24} - 6 q^{26} - 48 q^{29} - 24 q^{34} - 30 q^{35} + 12 q^{36} + 6 q^{39} - 36 q^{41} + 6 q^{44} - 18 q^{46} + 24 q^{49} - 12 q^{51} + 6 q^{54} + 60 q^{55} - 24 q^{59} - 12 q^{61} - 12 q^{64} - 30 q^{65} - 6 q^{66} - 36 q^{69} - 30 q^{70} + 72 q^{71} + 18 q^{74} + 12 q^{76} + 48 q^{79} - 6 q^{81} + 6 q^{84} + 12 q^{86} - 12 q^{89} - 6 q^{94} - 6 q^{96} - 12 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 12 * q^6 + 6 * q^9 - 6 * q^11 + 6 * q^14 - 6 * q^16 + 6 * q^19 + 6 * q^21 + 6 * q^24 - 6 * q^26 - 48 * q^29 - 24 * q^34 - 30 * q^35 + 12 * q^36 + 6 * q^39 - 36 * q^41 + 6 * q^44 - 18 * q^46 + 24 * q^49 - 12 * q^51 + 6 * q^54 + 60 * q^55 - 24 * q^59 - 12 * q^61 - 12 * q^64 - 30 * q^65 - 6 * q^66 - 36 * q^69 - 30 * q^70 + 72 * q^71 + 18 * q^74 + 12 * q^76 + 48 * q^79 - 6 * q^81 + 6 * q^84 + 12 * q^86 - 12 * q^89 - 6 * q^94 - 6 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.20942	−	0.344208i	0.988081	−	0.153935i
$5$	2.20942	−	0.344208i	0.988081	−	0.153935i
$6$	1.00000			0.408248
$7$	−2.51980	−	0.806615i	−0.952393	−	0.304872i
$7$	−2.51980	−	0.806615i	−0.952393	−	0.304872i
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.74131	+	1.40280i	−0.550649	+	0.443605i
$11$	2.39213	−	4.14329i	0.721254	−	1.24925i	−0.239243	−	0.970960i	$-0.576899\pi$
$11$	2.39213	−	4.14329i	0.721254	−	1.24925i	0.960497	−	0.278289i	$-0.0897674\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$		−	3.17103i		−	0.879485i	−0.898124	−	0.439743i	$-0.855070\pi$
$13$		−	3.17103i		−	0.879485i	0.898124	−	0.439743i	$-0.144930\pi$
$14$	2.58551	−	0.561349i	0.691008	−	0.150027i
$15$	−2.08551	−	0.806615i	−0.538478	−	0.208267i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.52625	+	2.61323i	1.09778	+	0.633801i	0.935636	−	0.352966i	$-0.114827\pi$
$17$	4.52625	+	2.61323i	1.09778	+	0.633801i	0.162140	+	0.986768i	$0.448160\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−1.58551	−	2.74619i	−0.363742	−	0.630020i	0.624831	−	0.780760i	$-0.285168\pi$
$19$	−1.58551	−	2.74619i	−0.363742	−	0.630020i	−0.988573	+	0.150740i	$0.951834\pi$
$20$	0.806615	−	2.08551i	0.180365	−	0.466335i
$21$	1.77890	+	1.95845i	0.388188	+	0.427368i
$22$			4.78426i			1.02001i
$23$	6.21029	−	3.58551i	1.29494	−	0.747632i	0.315411	−	0.948955i	$-0.397858\pi$
$23$	6.21029	−	3.58551i	1.29494	−	0.747632i	0.979525	+	0.201324i	$0.0645243\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.76304	−	1.52100i	0.952608	−	0.304200i
$26$	1.58551	+	2.74619i	0.310945	+	0.538573i
$27$		−	1.00000i		−	0.192450i
$28$	−1.95845	+	1.77890i	−0.370112	+	0.336180i
$29$	−2.38677			−0.443212			−0.221606	−	0.975136i	$-0.571130\pi$
$29$	−2.38677			−0.443212			−0.221606	+	0.975136i	$0.571130\pi$
$30$	2.20942	−	0.344208i	0.403382	−	0.0628436i
$31$	−2.08551	+	3.61222i	−0.374570	+	0.648773i	−0.990263	−	0.139213i	$-0.955543\pi$
$31$	−2.08551	+	3.61222i	−0.374570	+	0.648773i	0.615693	+	0.787986i	$0.288876\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.14329	+	2.39213i	−0.721254	+	0.416416i
$34$	−5.22646			−0.896330
$35$	−5.84492	−	0.914813i	−0.987972	−	0.154632i
$36$	1.00000			0.166667
$37$	−6.21029	+	3.58551i	−1.02097	+	0.589455i	−0.914384	−	0.404849i	$-0.867324\pi$
$37$	−6.21029	+	3.58551i	−1.02097	+	0.589455i	−0.106582	+	0.994304i	$0.533991\pi$
$38$	2.74619	+	1.58551i	0.445491	+	0.257204i
$39$	−1.58551	+	2.74619i	−0.253886	+	0.439743i
$40$	0.344208	+	2.20942i	0.0544241	+	0.349339i
$41$	−2.05543			−0.321004			−0.160502	−	0.987035i	$-0.551311\pi$
$41$	−2.05543			−0.321004			−0.160502	+	0.987035i	$0.551311\pi$
$42$	−2.51980	−	0.806615i	−0.388813	−	0.124463i
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	−2.39213	−	4.14329i	−0.360627	−	0.624625i
$45$	1.40280	+	1.74131i	0.209117	+	0.259579i
$46$	−3.58551	+	6.21029i	−0.528655	+	0.915658i
$47$	−9.97063	+	5.75654i	−1.45437	+	0.839678i	−0.998725	−	0.0504854i	$-0.983923\pi$
$47$	−9.97063	+	5.75654i	−1.45437	+	0.839678i	−0.455641	+	0.890164i	$0.650590\pi$
$48$			1.00000i			0.144338i
$49$	5.69874	+	4.06501i	0.814106	+	0.580716i
$50$	−3.36441	+	3.69874i	−0.475800	+	0.523081i
$51$	−2.61323	−	4.52625i	−0.365925	−	0.633801i
$52$	−2.74619	−	1.58551i	−0.380828	−	0.219871i
$53$	7.02832	+	4.05780i	0.965413	+	0.557382i	0.897835	−	0.440332i	$-0.145139\pi$
$53$	7.02832	+	4.05780i	0.965413	+	0.557382i	0.0675785	+	0.997714i	$0.478473\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	3.85906	−	9.97764i	0.520355	−	1.34539i
$56$	0.806615	−	2.51980i	0.107788	−	0.336722i
$57$			3.17103i			0.420013i
$58$	2.06700	−	1.19339i	0.271411	−	0.156699i
$59$	−5.36441	+	9.29144i	−0.698387	+	1.20964i	0.270638	+	0.962681i	$0.412765\pi$
$59$	−5.36441	+	9.29144i	−0.698387	+	1.20964i	−0.969025	+	0.246961i	$0.920568\pi$
$60$	−1.74131	+	1.40280i	−0.224802	+	0.181101i
$61$	−3.55780	−	6.16229i	−0.455530	−	0.789000i	0.543189	−	0.839611i	$-0.317217\pi$
$61$	−3.55780	−	6.16229i	−0.455530	−	0.789000i	−0.998718	+	0.0506101i	$0.983883\pi$
$62$		−	4.17103i		−	0.529721i
$63$	−0.561349	−	2.58551i	−0.0707233	−	0.325744i
$64$	−1.00000			−0.125000
$65$	−1.09150	−	7.00613i	−0.135383	−	0.869003i
$66$	2.39213	−	4.14329i	0.294451	−	0.510004i
$67$	8.28658	+	4.78426i	1.01237	+	0.584490i	0.911884	−	0.410448i	$-0.134628\pi$
$67$	8.28658	+	4.78426i	1.01237	+	0.584490i	0.100483	+	0.994939i	$0.467961\pi$
$68$	4.52625	−	2.61323i	0.548888	−	0.316901i
$69$	−7.17103			−0.863291
$70$	5.51926	−	2.13021i	0.659677	−	0.254609i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	0.283387	−	0.959006i	$-0.408542\pi$
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	−0.688830	+	0.724923i	$0.741875\pi$
$74$	3.58551	−	6.21029i	0.416808	−	0.721932i
$75$	−4.88541	−	1.06430i	−0.564119	−	0.122894i
$76$	−3.17103			−0.363742
$77$	−9.36972	+	8.51072i	−1.06778	+	0.969886i
$78$		−	3.17103i		−	0.359048i
$79$	6.08551	+	10.5404i	0.684674	+	1.18589i	0.973539	+	0.228520i	$0.0733887\pi$
$79$	6.08551	+	10.5404i	0.684674	+	1.18589i	−0.288865	+	0.957370i	$0.593278\pi$
$80$	−1.40280	−	1.74131i	−0.156838	−	0.194684i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.78005	−	1.02771i	0.196574	−	0.113492i
$83$		−	3.39749i		−	0.372923i	−0.982462	−	0.186461i	$-0.940298\pi$
$83$		−	3.39749i		−	0.372923i	0.982462	−	0.186461i	$-0.0597019\pi$
$84$	2.58551	−	0.561349i	0.282103	−	0.0612482i
$85$	10.8999	+	4.21574i	1.18226	+	0.457261i
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	2.06700	+	1.19339i	0.221606	+	0.127944i
$88$	4.14329	+	2.39213i	0.441676	+	0.255002i
$89$	4.78426	+	8.28658i	0.507131	+	0.878376i	0.999966	+	0.00825326i	$0.00262713\pi$
$89$	4.78426	+	8.28658i	0.507131	+	0.878376i	−0.492835	+	0.870123i	$0.664040\pi$
$90$	−2.08551	−	0.806615i	−0.219833	−	0.0850247i
$91$	−2.55780	+	7.99035i	−0.268130	+	0.837616i
$92$		−	7.17103i		−	0.747632i
$93$	3.61222	−	2.08551i	0.374570	−	0.216258i
$94$	5.75654	−	9.97063i	0.593742	−	1.02839i
$95$	−4.44833	−	5.52173i	−0.456389	−	0.566518i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$			1.27117i			0.129068i	0.997916	+	0.0645339i	$0.0205561\pi$
$97$			1.27117i			0.129068i	−0.997916	+	0.0645339i	$0.979444\pi$
$98$	−6.96776	−	0.671030i	−0.703850	−	0.0677842i
$99$	4.78426			0.480836
$100$	1.06430	−	4.88541i	0.106430	−	0.488541i
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$	4.52625	+	2.61323i	0.448165	+	0.258748i
$103$	−9.72240	+	5.61323i	−0.957976	+	0.553088i	−0.895550	−	0.444962i	$-0.853217\pi$
$103$	−9.72240	+	5.61323i	−0.957976	+	0.553088i	−0.0624268	+	0.998050i	$0.519884\pi$
$104$	3.17103			0.310945
$105$	4.60444	+	3.71471i	0.449348	+	0.362519i
$106$	−8.11560			−0.788257
$107$	1.21026	−	0.698745i	0.117000	−	0.0675502i	−0.440358	−	0.897822i	$-0.645148\pi$
$107$	1.21026	−	0.698745i	0.117000	−	0.0675502i	0.557358	+	0.830272i	$0.311815\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	6.22646	−	10.7845i	0.596387	−	1.03297i	−0.396963	−	0.917835i	$-0.629936\pi$
$109$	6.22646	−	10.7845i	0.596387	−	1.03297i	0.993350	−	0.115137i	$-0.0367308\pi$
$110$	1.64678	+	10.5704i	0.157015	+	1.00785i
$111$	7.17103			0.680644
$112$	0.561349	+	2.58551i	0.0530425	+	0.244308i
$113$			6.34206i			0.596611i	0.954470	+	0.298305i	$0.0964214\pi$
$113$			6.34206i			0.596611i	−0.954470	+	0.298305i	$0.903579\pi$
$114$	−1.58551	−	2.74619i	−0.148497	−	0.257204i
$115$	12.4870	−	10.0595i	1.16442	−	0.938056i
$116$	−1.19339	+	2.06700i	−0.110803	+	0.191916i
$117$	2.74619	−	1.58551i	0.253886	−	0.146581i
$118$		−	10.7288i		−	0.987669i
$119$	−9.29735	−	10.2357i	−0.852287	−	0.938309i
$120$	0.806615	−	2.08551i	0.0736335	−	0.190381i
$121$	−5.94457	−	10.2963i	−0.540415	−	0.936027i
$122$	6.16229	+	3.55780i	0.557908	+	0.322108i
$123$	1.78005	+	1.02771i	0.160502	+	0.0926659i
$124$	2.08551	+	3.61222i	0.187285	+	0.324387i
$125$	10.0000	−	5.00000i	0.894427	−	0.447214i
$126$	1.77890	+	1.95845i	0.158477	+	0.174472i
$127$		−	18.0107i		−	1.59819i	−0.601203	−	0.799096i	$-0.705312\pi$
$127$		−	18.0107i		−	1.59819i	0.601203	−	0.799096i	$-0.294688\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−1.00000	+	1.73205i	−0.0880451	+	0.152499i
$130$	4.44833	+	5.52173i	0.390144	+	0.484288i
$131$	2.77890	+	4.81320i	0.242794	+	0.420531i	0.961509	−	0.274774i	$-0.0886029\pi$
$131$	2.77890	+	4.81320i	0.242794	+	0.420531i	−0.718715	+	0.695304i	$0.755270\pi$
$132$			4.78426i			0.416416i
$133$	1.78005	+	8.19874i	0.154350	+	0.710921i
$134$	−9.56852			−0.826594
$135$	−0.344208	−	2.20942i	−0.0296247	−	0.190156i
$136$	−2.61323	+	4.52625i	−0.224083	+	0.388122i
$137$	−12.8128	−	7.39749i	−1.09467	−	0.632010i	−0.159857	−	0.987140i	$-0.551103\pi$
$137$	−12.8128	−	7.39749i	−1.09467	−	0.632010i	−0.934817	+	0.355130i	$0.884437\pi$
$138$	6.21029	−	3.58551i	0.528655	−	0.305219i
$139$	−3.65794			−0.310262			−0.155131	−	0.987894i	$-0.549580\pi$
$139$	−3.65794			−0.310262			−0.155131	+	0.987894i	$0.549580\pi$
$140$	−3.71471	+	4.60444i	−0.313951	+	0.389147i
$141$	11.5131			0.969577
$142$	−5.19615	+	3.00000i	−0.436051	+	0.251754i
$143$	−13.1385	−	7.58551i	−1.09870	−	0.634333i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−5.27337	+	0.821546i	−0.437929	+	0.0682257i
$146$	4.00000			0.331042
$147$	−2.90275	−	6.36977i	−0.239415	−	0.525370i
$148$			7.17103i			0.589455i
$149$	11.1710	+	19.3488i	0.915166	+	1.58511i	0.806657	+	0.591019i	$0.201274\pi$
$149$	11.1710	+	19.3488i	0.915166	+	1.58511i	0.108509	+	0.994095i	$0.465392\pi$
$150$	4.76304	−	1.52100i	0.388901	−	0.124189i
$151$	−8.25654	+	14.3008i	−0.671908	+	1.16378i	0.305454	+	0.952207i	$0.401192\pi$
$151$	−8.25654	+	14.3008i	−0.671908	+	1.16378i	−0.977362	+	0.211572i	$0.932142\pi$
$152$	2.74619	−	1.58551i	0.222746	−	0.128602i
$153$			5.22646i			0.422534i
$154$	3.85906	−	12.0554i	0.310972	−	0.971448i
$155$	−3.36441	+	8.69874i	−0.270236	+	0.698700i
$156$	1.58551	+	2.74619i	0.126943	+	0.219871i
$157$	8.61225	+	4.97229i	0.687332	+	0.396832i	0.802612	−	0.596502i	$-0.203443\pi$
$157$	8.61225	+	4.97229i	0.687332	+	0.396832i	−0.115280	+	0.993333i	$0.536776\pi$
$158$	−10.5404	−	6.08551i	−0.838551	−	0.484138i
$159$	−4.05780	−	7.02832i	−0.321804	−	0.557382i
$160$	2.08551	+	0.806615i	0.164874	+	0.0637685i
$161$	−18.5408	+	4.02545i	−1.46122	+	0.317250i
$162$		−	1.00000i		−	0.0785674i
$163$	2.49796	−	1.44220i	0.195656	−	0.112962i	−0.398972	−	0.916963i	$-0.630633\pi$
$163$	2.49796	−	1.44220i	0.195656	−	0.112962i	0.594627	+	0.804001i	$0.297300\pi$
$164$	−1.02771	+	1.78005i	−0.0802511	+	0.138999i
$165$	−8.33086	+	6.71137i	−0.648557	+	0.522479i
$166$	1.69874	+	2.94231i	0.131848	+	0.228368i
$167$		−	4.05543i		−	0.313819i	−0.987613	−	0.156909i	$-0.949847\pi$
$167$		−	4.05543i		−	0.313819i	0.987613	−	0.156909i	$-0.0501530\pi$
$168$	−1.95845	+	1.77890i	−0.151097	+	0.137245i
$169$	2.94457			0.226505
$170$	−11.5474	+	1.79899i	−0.885647	+	0.137976i
$171$	1.58551	−	2.74619i	0.121247	−	0.210007i
$172$	−1.73205	−	1.00000i	−0.132068	−	0.0762493i
$173$	5.54039	−	3.19874i	0.421228	−	0.243196i	−0.274375	−	0.961623i	$-0.588471\pi$
$173$	5.54039	−	3.19874i	0.421228	−	0.243196i	0.695603	+	0.718427i	$0.255137\pi$
$174$	−2.38677			−0.180941
$175$	−13.2288	−	0.00933150i	−1.00000	−	0.000705395i
$176$	−4.78426			−0.360627
$177$	9.29144	−	5.36441i	0.698387	−	0.403214i
$178$	−8.28658	−	4.78426i	−0.621105	−	0.358595i
$179$	9.75654	−	16.8988i	0.729238	−	1.26308i	−0.227967	−	0.973669i	$-0.573208\pi$
$179$	9.75654	−	16.8988i	0.729238	−	1.26308i	0.957206	−	0.289409i	$-0.0934588\pi$
$180$	2.20942	−	0.344208i	0.164680	−	0.0256558i
$181$	−23.0262			−1.71152			−0.855761	−	0.517371i	$-0.826911\pi$
$181$	−23.0262			−1.71152			−0.855761	+	0.517371i	$0.826911\pi$
$182$	−1.78005	−	8.19874i	−0.131946	−	0.607731i
$183$			7.11560i			0.526000i
$184$	3.58551	+	6.21029i	0.264328	+	0.457829i
$185$	−12.4870	+	10.0595i	−0.918060	+	0.739591i
$186$	−2.08551	+	3.61222i	−0.152917	+	0.264861i
$187$	21.6547	−	12.5024i	1.58355	−	0.914264i
$188$			11.5131i			0.839678i
$189$	−0.806615	+	2.51980i	−0.0586726	+	0.183288i
$190$	6.61323	+	2.55780i	0.479774	+	0.185562i
$191$	5.11560	+	8.86048i	0.370152	+	0.641122i	0.989589	−	0.143925i	$-0.0459723\pi$
$191$	5.11560	+	8.86048i	0.370152	+	0.641122i	−0.619437	+	0.785047i	$0.712639\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	10.0574	+	5.80661i	0.723944	+	0.417969i	0.816203	−	0.577766i	$-0.196075\pi$
$193$	10.0574	+	5.80661i	0.723944	+	0.417969i	−0.0922586	+	0.995735i	$0.529409\pi$
$194$	−0.635585	−	1.10087i	−0.0456324	−	0.0790376i
$195$	−2.55780	+	6.61323i	−0.183168	+	0.473583i
$196$	6.36977	−	2.90275i	0.454984	−	0.207339i
$197$			2.39749i			0.170814i	0.996346	+	0.0854070i	$0.0272191\pi$
$197$			2.39749i			0.170814i	−0.996346	+	0.0854070i	$0.972781\pi$
$198$	−4.14329	+	2.39213i	−0.294451	+	0.170001i
$199$	−9.17103	+	15.8847i	−0.650117	+	1.12604i	0.332977	+	0.942935i	$0.391947\pi$
$199$	−9.17103	+	15.8847i	−0.650117	+	1.12604i	−0.983094	+	0.183101i	$0.941387\pi$
$200$	1.52100	+	4.76304i	0.107551	+	0.336798i
$201$	−4.78426	−	8.28658i	−0.337456	−	0.584490i
$202$			8.00000i			0.562878i
$203$	6.01417	+	1.92520i	0.422112	+	0.135123i
$204$	−5.22646			−0.365925
$205$	−4.54130	+	0.707496i	−0.317178	+	0.0494137i
$206$	5.61323	−	9.72240i	0.391092	−	0.677392i
$207$	6.21029	+	3.58551i	0.431645	+	0.249211i
$208$	−2.74619	+	1.58551i	−0.190414	+	0.109936i
$209$	−15.1710			−1.04940
$210$	−5.84492	−	0.914813i	−0.403338	−	0.0631281i
$211$	−2.82897			−0.194754			−0.0973772	−	0.995248i	$-0.531045\pi$
$211$	−2.82897			−0.194754			−0.0973772	+	0.995248i	$0.531045\pi$
$212$	7.02832	−	4.05780i	0.482707	−	0.278691i
$213$	−5.19615	−	3.00000i	−0.356034	−	0.205557i
$214$	−0.698745	+	1.21026i	−0.0477652	+	0.0827318i
$215$	−0.688417	−	4.41883i	−0.0469496	−	0.301362i
$216$	1.00000			0.0680414
$217$	8.16874	−	7.41984i	0.554530	−	0.503692i
$218$			12.4529i			0.843418i
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$	−6.71137	−	8.33086i	−0.452480	−	0.561667i
$221$	8.28663	−	14.3529i	0.557419	−	0.965478i
$222$	−6.21029	+	3.58551i	−0.416808	+	0.240644i
$223$			14.2973i			0.957421i	0.877973	+	0.478711i	$0.158896\pi$
$223$			14.2973i			0.957421i	−0.877973	+	0.478711i	$0.841104\pi$
$224$	−1.77890	−	1.95845i	−0.118858	−	0.130854i
$225$	3.69874	+	3.36441i	0.246583	+	0.224294i
$226$	−3.17103	−	5.49238i	−0.210934	−	0.365348i
$227$	9.57428	+	5.52771i	0.635467	+	0.366887i	0.782866	−	0.622190i	$-0.213757\pi$
$227$	9.57428	+	5.52771i	0.635467	+	0.366887i	−0.147399	+	0.989077i	$0.547090\pi$
$228$	2.74619	+	1.58551i	0.181871	+	0.105003i
$229$	−9.22646	−	15.9807i	−0.609702	−	1.05603i	−0.991289	−	0.131702i	$-0.957956\pi$
$229$	−9.22646	−	15.9807i	−0.609702	−	1.05603i	0.381588	−	0.924333i	$-0.375377\pi$
$230$	−5.78426	+	14.9553i	−0.381403	+	0.986123i
$231$	12.3698	−	2.68564i	0.813871	−	0.176702i
$232$		−	2.38677i		−	0.156699i
$233$	−7.89434	+	4.55780i	−0.517175	+	0.298591i	−0.735778	−	0.677223i	$-0.763183\pi$
$233$	−7.89434	+	4.55780i	−0.517175	+	0.298591i	0.218603	+	0.975814i	$0.429850\pi$
$234$	−1.58551	+	2.74619i	−0.103648	+	0.179524i
$235$	−20.0478	+	16.1506i	−1.30778	+	1.05355i
$236$	5.36441	+	9.29144i	0.349194	+	0.604821i
$237$		−	12.1710i		−	0.790593i
$238$	13.1696	+	4.21574i	0.853659	+	0.273266i
$239$	−13.1156			−0.848378			−0.424189	−	0.905574i	$-0.639441\pi$
$239$	−13.1156			−0.848378			−0.424189	+	0.905574i	$0.639441\pi$
$240$	0.344208	+	2.20942i	0.0222186	+	0.142617i
$241$	2.67103	−	4.62636i	0.172056	−	0.298010i	−0.767082	−	0.641549i	$-0.778292\pi$
$241$	2.67103	−	4.62636i	0.172056	−	0.298010i	0.939139	+	0.343539i	$0.111626\pi$
$242$	10.2963	+	5.94457i	0.661871	+	0.382131i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−7.11560			−0.455530
$245$	13.9901	+	7.01974i	0.893795	+	0.448475i
$246$	−2.05543			−0.131049
$247$	−8.70826	+	5.02771i	−0.554093	+	0.319906i
$248$	−3.61222	−	2.08551i	−0.229376	−	0.132430i
$249$	−1.69874	+	2.94231i	−0.107654	+	0.186461i
$250$	−6.16025	+	9.33013i	−0.389609	+	0.590089i
$251$	27.9213			1.76238			0.881188	−	0.472765i	$-0.156744\pi$
$251$	27.9213			1.76238			0.881188	+	0.472765i	$0.156744\pi$
$252$	−2.51980	−	0.806615i	−0.158732	−	0.0508120i
$253$		−	34.3081i		−	2.15693i
$254$	9.00536	+	15.5977i	0.565047	+	0.978689i
$255$	−7.33169	−	9.10087i	−0.459128	−	0.569918i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	18.3052	−	10.5685i	1.14185	−	0.659246i	0.194960	−	0.980811i	$-0.437542\pi$
$257$	18.3052	−	10.5685i	1.14185	−	0.659246i	0.946887	+	0.321565i	$0.104209\pi$
$258$		−	2.00000i		−	0.124515i
$259$	18.5408	−	4.02545i	1.15207	−	0.250129i
$260$	−6.61323	−	2.55780i	−0.410135	−	0.158628i
$261$	−1.19339	−	2.06700i	−0.0738687	−	0.127944i
$262$	−4.81320	−	2.77890i	−0.297360	−	0.171681i
$263$	−10.3149	−	5.95529i	−0.636042	−	0.367219i	0.147046	−	0.989130i	$-0.453023\pi$
$263$	−10.3149	−	5.95529i	−0.636042	−	0.367219i	−0.783088	+	0.621911i	$0.786357\pi$
$264$	−2.39213	−	4.14329i	−0.147225	−	0.255002i
$265$	16.9252	+	6.54616i	1.03971	+	0.402128i
$266$	−5.64094	−	6.21029i	−0.345869	−	0.380778i
$267$		−	9.56852i		−	0.585584i
$268$	8.28658	−	4.78426i	0.506183	−	0.292245i
$269$	−1.63559	+	2.83292i	−0.0997234	+	0.172726i	−0.911570	−	0.411145i	$-0.865129\pi$
$269$	−1.63559	+	2.83292i	−0.0997234	+	0.172726i	0.811847	+	0.583871i	$0.198462\pi$
$270$	1.40280	+	1.74131i	0.0853718	+	0.105973i
$271$	−0.311975	−	0.540356i	−0.0189511	−	0.0328243i	0.856394	−	0.516322i	$-0.172699\pi$
$271$	−0.311975	−	0.540356i	−0.0189511	−	0.0328243i	−0.875345	+	0.483498i	$0.839366\pi$
$272$		−	5.22646i		−	0.316901i
$273$	6.21029	−	5.64094i	0.375864	−	0.341406i
$274$	14.7950			0.893797
$275$	5.09187	−	23.3731i	0.307051	−	1.40945i
$276$	−3.58551	+	6.21029i	−0.215823	+	0.373816i
$277$	−24.9372	−	14.3975i	−1.49833	−	0.865061i	−0.498332	−	0.866986i	$-0.666054\pi$
$277$	−24.9372	−	14.3975i	−1.49833	−	0.865061i	−0.999998	+	0.00192499i	$0.999387\pi$
$278$	3.16787	−	1.82897i	0.189996	−	0.109694i
$279$	−4.17103			−0.249713
$280$	0.914813	−	5.84492i	0.0546705	−	0.349301i
$281$	2.82897			0.168762			0.0843811	−	0.996434i	$-0.473109\pi$
$281$	2.82897			0.168762			0.0843811	+	0.996434i	$0.473109\pi$
$282$	−9.97063	+	5.75654i	−0.593742	+	0.342797i
$283$	21.7693	+	12.5685i	1.29405	+	0.747121i	0.979370	−	0.202076i	$-0.0647689\pi$
$283$	21.7693	+	12.5685i	1.29405	+	0.747121i	0.314682	+	0.949197i	$0.398102\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	1.09150	+	7.00613i	0.0646546	+	0.415007i
$286$	15.1710			0.897082
$287$	5.17926	+	1.65794i	0.305722	+	0.0978651i
$288$			1.00000i			0.0589256i
$289$	5.15794	+	8.93381i	0.303408	+	0.525519i
$290$	4.15610	−	3.34816i	0.244054	−	0.196611i
$291$	0.635585	−	1.10087i	0.0372587	−	0.0645339i
$292$	−3.46410	+	2.00000i	−0.202721	+	0.117041i
$293$			10.2265i			0.597436i	0.954341	+	0.298718i	$0.0965590\pi$
$293$			10.2265i			0.597436i	−0.954341	+	0.298718i	$0.903441\pi$
$294$	5.69874	+	4.06501i	0.332358	+	0.237076i
$295$	−8.65403	+	22.3751i	−0.503857	+	1.30273i
$296$	−3.58551	−	6.21029i	−0.208404	−	0.360966i
$297$	−4.14329	−	2.39213i	−0.240418	−	0.138805i
$298$	−19.3488	−	11.1710i	−1.12085	−	0.647120i
$299$	−11.3698	−	19.6930i	−0.657531	−	1.13888i
$300$	−3.36441	+	3.69874i	−0.194245	+	0.213547i
$301$	−1.61323	+	5.03959i	−0.0929850	+	0.290477i
$302$		−	16.5131i		−	0.950222i
$303$	−6.92820	+	4.00000i	−0.398015	+	0.229794i
$304$	−1.58551	+	2.74619i	−0.0909355	+	0.157505i
$305$	−9.98177	−	12.3904i	−0.571555	−	0.709475i
$306$	−2.61323	−	4.52625i	−0.149388	−	0.258748i
$307$			23.4577i			1.33880i	0.742902	+	0.669400i	$0.233449\pi$
$307$			23.4577i			1.33880i	−0.742902	+	0.669400i	$0.766551\pi$
$308$	2.68564	+	12.3698i	0.153029	+	0.704833i
$309$	11.2265			0.638651
$310$	−1.43570	−	9.21554i	−0.0815425	−	0.523408i
$311$	2.82897	−	4.89992i	0.160416	−	0.277849i	−0.774602	−	0.632449i	$-0.782050\pi$
$311$	2.82897	−	4.89992i	0.160416	−	0.277849i	0.935018	+	0.354600i	$0.115383\pi$
$312$	−2.74619	−	1.58551i	−0.155473	−	0.0897621i
$313$	−14.1914	+	8.19339i	−0.802143	+	0.463118i	−0.844220	−	0.535997i	$-0.819936\pi$
$313$	−14.1914	+	8.19339i	−0.802143	+	0.463118i	0.0420769	+	0.999114i	$0.486603\pi$
$314$	−9.94457			−0.561205
$315$	−2.13021	−	5.51926i	−0.120024	−	0.310975i
$316$	12.1710			0.684674
$317$	−3.90845	+	2.25654i	−0.219520	+	0.126740i	−0.605728	−	0.795672i	$-0.707118\pi$
$317$	−3.90845	+	2.25654i	−0.219520	+	0.126740i	0.386208	+	0.922412i	$0.373785\pi$
$318$	7.02832	+	4.05780i	0.394128	+	0.227550i
$319$	−5.70946	+	9.88908i	−0.319669	+	0.553682i
$320$	−2.20942	+	0.344208i	−0.123510	+	0.0192418i
$321$	−1.39749			−0.0780003
$322$	14.0441	−	12.7565i	0.782646	−	0.710894i
$323$		−	16.5733i		−	0.922161i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−4.82313	−	15.1037i	−0.267539	−	0.837805i
$326$	−1.44220	+	2.49796i	−0.0798761	+	0.138349i
$327$	−10.7845	+	6.22646i	−0.596387	+	0.344324i
$328$		−	2.05543i		−	0.113492i
$329$	29.7673	−	6.46286i	1.64112	−	0.356309i
$330$	3.85906	−	9.97764i	0.212434	−	0.549251i
$331$	6.54080	+	11.3290i	0.359515	+	0.622698i	0.987880	−	0.155220i	$-0.0496088\pi$
$331$	6.54080	+	11.3290i	0.359515	+	0.622698i	−0.628365	+	0.777919i	$0.716275\pi$
$332$	−2.94231	−	1.69874i	−0.161480	−	0.0932307i
$333$	−6.21029	−	3.58551i	−0.340322	−	0.196485i
$334$	2.02771	+	3.51211i	0.110952	+	0.192174i
$335$	19.9553	+	7.71811i	1.09027	+	0.421685i
$336$	0.806615	−	2.51980i	0.0440045	−	0.137466i
$337$		−	20.2973i		−	1.10567i	−0.833292	−	0.552834i	$-0.813547\pi$
$337$		−	20.2973i		−	1.10567i	0.833292	−	0.552834i	$-0.186453\pi$
$338$	−2.55007	+	1.47229i	−0.138706	+	0.0800817i
$339$	3.17103	−	5.49238i	0.172227	−	0.298305i
$340$	9.10087	−	7.33169i	0.493564	−	0.397616i
$341$	9.97764	+	17.2818i	0.540320	+	0.935861i
$342$			3.17103i			0.171470i
$343$	−11.0808	−	14.8397i	−0.598306	−	0.801268i
$344$	2.00000			0.107833
$345$	−15.8438	+	2.46833i	−0.853001	+	0.132890i
$346$	−3.19874	+	5.54039i	−0.171966	+	0.297853i
$347$	12.5166	+	7.22646i	0.671926	+	0.387937i	0.796806	−	0.604235i	$-0.206521\pi$
$347$	12.5166	+	7.22646i	0.671926	+	0.387937i	−0.124880	+	0.992172i	$0.539855\pi$
$348$	2.06700	−	1.19339i	0.110803	−	0.0639722i
$349$	−13.8891			−0.743469			−0.371734	−	0.928339i	$-0.621237\pi$
$349$	−13.8891			−0.743469			−0.371734	+	0.928339i	$0.621237\pi$
$350$	11.4611	−	6.60630i	0.612622	−	0.353121i
$351$	−3.17103			−0.169257
$352$	4.14329	−	2.39213i	0.220838	−	0.127501i
$353$	5.58839	+	3.22646i	0.297440	+	0.171727i	0.641292	−	0.767297i	$-0.278399\pi$
$353$	5.58839	+	3.22646i	0.297440	+	0.171727i	−0.343852	+	0.939024i	$0.611732\pi$
$354$	−5.36441	+	9.29144i	−0.285115	+	0.493834i
$355$	13.2565	−	2.06525i	0.703582	−	0.109612i
$356$	9.56852			0.507131
$357$	2.93387	+	13.5131i	0.155277	+	0.715189i
$358$			19.5131i			1.03130i
$359$	3.61323	+	6.25830i	0.190699	+	0.330300i	0.945482	−	0.325674i	$-0.105591\pi$
$359$	3.61323	+	6.25830i	0.190699	+	0.330300i	−0.754783	+	0.655974i	$0.772258\pi$
$360$	−1.74131	+	1.40280i	−0.0917749	+	0.0739341i
$361$	4.47229	−	7.74622i	0.235383	−	0.407696i
$362$	19.9413	−	11.5131i	1.04809	−	0.605115i
$363$			11.8891i			0.624018i
$364$	5.64094	+	6.21029i	0.295666	+	0.325508i
$365$	−8.34206	−	3.22646i	−0.436643	−	0.168881i
$366$	−3.55780	−	6.16229i	−0.185969	−	0.322108i
$367$	−1.81878	−	1.05007i	−0.0949393	−	0.0548132i	0.451779	−	0.892130i	$-0.350790\pi$
$367$	−1.81878	−	1.05007i	−0.0949393	−	0.0548132i	−0.546718	+	0.837317i	$0.684123\pi$
$368$	−6.21029	−	3.58551i	−0.323734	−	0.186908i
$369$	−1.02771	−	1.78005i	−0.0535007	−	0.0926659i
$370$	5.78426	−	14.9553i	0.300709	−	0.777488i
$371$	−14.4368	−	15.8940i	−0.749523	−	0.825174i
$372$		−	4.17103i		−	0.216258i
$373$	−20.1333	+	11.6239i	−1.04246	+	0.601865i	−0.920529	−	0.390673i	$-0.872242\pi$
$373$	−20.1333	+	11.6239i	−1.04246	+	0.601865i	−0.121932	+	0.992538i	$0.538909\pi$
$374$	−12.5024	+	21.6547i	−0.646482	+	1.11974i
$375$	−11.1603	−	0.669873i	−0.576313	−	0.0345921i
$376$	−5.75654	−	9.97063i	−0.296871	−	0.514196i
$377$			7.56852i			0.389799i
$378$	−0.561349	−	2.58551i	−0.0288727	−	0.132985i
$379$	−2.16629			−0.111275			−0.0556374	−	0.998451i	$-0.517719\pi$
$379$	−2.16629			−0.111275			−0.0556374	+	0.998451i	$0.517719\pi$
$380$	−7.00613	+	1.09150i	−0.359407	+	0.0559925i
$381$	−9.00536	+	15.5977i	−0.461359	+	0.799096i
$382$	−8.86048	−	5.11560i	−0.453342	−	0.261737i
$383$	−6.97621	+	4.02771i	−0.356468	+	0.205807i	−0.667530	−	0.744583i	$-0.732648\pi$
$383$	−6.97621	+	4.02771i	−0.356468	+	0.205807i	0.311063	+	0.950389i	$0.399315\pi$
$384$	−1.00000			−0.0510310
$385$	−17.7721	+	22.0289i	−0.905753	+	1.12269i
$386$	−11.6132			−0.591098
$387$	1.73205	−	1.00000i	0.0880451	−	0.0508329i
$388$	1.10087	+	0.635585i	0.0558880	+	0.0322669i
$389$	5.94457	−	10.2963i	0.301402	−	0.522043i	−0.675052	−	0.737770i	$-0.735879\pi$
$389$	5.94457	−	10.2963i	0.301402	−	0.522043i	0.976454	+	0.215727i	$0.0692122\pi$
$390$	−1.09150	−	7.00613i	−0.0552700	−	0.354769i
$391$	37.4791			1.89540
$392$	−4.06501	+	5.69874i	−0.205314	+	0.287830i
$393$		−	5.55780i		−	0.280354i
$394$	−1.19874	−	2.07629i	−0.0603919	−	0.104602i
$395$	17.0735	+	21.1935i	0.859063	+	1.06636i
$396$	2.39213	−	4.14329i	0.120209	−	0.208208i
$397$	13.9524	−	8.05543i	0.700252	−	0.404290i	−0.107190	−	0.994239i	$-0.534185\pi$
$397$	13.9524	−	8.05543i	0.700252	−	0.404290i	0.807441	+	0.589948i	$0.200852\pi$
$398$		−	18.3421i		−	0.919404i
$399$	2.55780	−	7.99035i	0.128050	−	0.400018i
$400$	−3.69874	−	3.36441i	−0.184937	−	0.168221i
$401$	−12.4854	−	21.6253i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$401$	−12.4854	−	21.6253i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$402$	8.28658	+	4.78426i	0.413297	+	0.238617i
$403$	11.4545	+	6.61323i	0.570587	+	0.329428i
$404$	−4.00000	−	6.92820i	−0.199007	−	0.344691i
$405$	−0.806615	+	2.08551i	−0.0400810	+	0.103630i
$406$	−6.17103	+	1.33981i	−0.306263	+	0.0664937i
$407$			34.3081i			1.70059i
$408$	4.52625	−	2.61323i	0.224083	−	0.129374i
$409$	1.52771	−	2.64608i	0.0755406	−	0.130840i	−0.825781	−	0.563991i	$-0.809265\pi$
$409$	1.52771	−	2.64608i	0.0755406	−	0.130840i	0.901321	+	0.433151i	$0.142598\pi$
$410$	3.57913	−	2.88336i	0.176761	−	0.142399i
$411$	7.39749	+	12.8128i	0.364891	+	0.632010i
$412$			11.2265i			0.553088i
$413$	21.0118	−	19.0855i	1.03393	−	0.939137i
$414$	−7.17103			−0.352437
$415$	−1.16944	−	7.50647i	−0.0574058	−	0.368478i
$416$	1.58551	−	2.74619i	0.0777363	−	0.134643i
$417$	3.16787	+	1.82897i	0.155131	+	0.0895651i
$418$	13.1385	−	7.58551i	0.642625	−	0.371020i
$419$	20.1972			0.986698			0.493349	−	0.869831i	$-0.335773\pi$
$419$	20.1972			0.986698			0.493349	+	0.869831i	$0.335773\pi$
$420$	5.51926	−	2.13021i	0.269312	−	0.103944i
$421$	−30.3635			−1.47983			−0.739913	−	0.672702i	$-0.765133\pi$
$421$	−30.3635			−1.47983			−0.739913	+	0.672702i	$0.765133\pi$
$422$	2.44996	−	1.41449i	0.119262	−	0.0688561i
$423$	−9.97063	−	5.75654i	−0.484789	−	0.279893i
$424$	−4.05780	+	7.02832i	−0.197064	+	0.341325i
$425$	25.5334	+	5.56250i	1.23855	+	0.269821i
$426$	6.00000			0.290701
$427$	3.99434	+	18.3975i	0.193299	+	0.890317i
$428$		−	1.39749i		−	0.0675502i
$429$	7.58551	+	13.1385i	0.366232	+	0.634333i
$430$	2.80560	+	3.48261i	0.135298	+	0.167947i
$431$	−12.2866	+	21.2811i	−0.591826	+	1.02507i	0.402160	+	0.915569i	$0.368259\pi$
$431$	−12.2866	+	21.2811i	−0.591826	+	1.02507i	−0.993986	+	0.109504i	$0.965074\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$			4.68412i			0.225104i	0.993646	+	0.112552i	$0.0359026\pi$
$433$			4.68412i			0.225104i	−0.993646	+	0.112552i	$0.964097\pi$
$434$	−3.36441	+	10.5101i	−0.161497	+	0.504503i
$435$	4.97764	+	1.92520i	0.238660	+	0.0923065i
$436$	−6.22646	−	10.7845i	−0.298193	−	0.516486i
$437$	−19.6930	−	11.3698i	−0.942045	−	0.543890i
$438$	−3.46410	−	2.00000i	−0.165521	−	0.0955637i
$439$	−15.2565	−	26.4251i	−0.728155	−	1.26120i	−0.957662	−	0.287895i	$-0.907045\pi$
$439$	−15.2565	−	26.4251i	−0.728155	−	1.26120i	0.229507	−	0.973307i	$-0.426289\pi$
$440$	9.97764	+	3.85906i	0.475666	+	0.183973i
$441$	−0.671030	+	6.96776i	−0.0319538	+	0.331798i
$442$			16.5733i			0.788310i
$443$	−8.23447	+	4.75417i	−0.391232	+	0.225878i	−0.682694	−	0.730705i	$-0.739192\pi$
$443$	−8.23447	+	4.75417i	−0.391232	+	0.225878i	0.291462	+	0.956582i	$0.405858\pi$
$444$	3.58551	−	6.21029i	0.170161	−	0.294728i
$445$	13.4227	+	16.6617i	0.636299	+	0.789841i
$446$	−7.14867	−	12.3819i	−0.338500	−	0.586298i
$447$		−	22.3421i		−	1.05674i
$448$	2.51980	+	0.806615i	0.119049	+	0.0381090i
$449$	−17.6239			−0.831726			−0.415863	−	0.909427i	$-0.636520\pi$
$449$	−17.6239			−0.831726			−0.415863	+	0.909427i	$0.636520\pi$
$450$	−4.88541	−	1.06430i	−0.230301	−	0.0501714i
$451$	−4.91686	+	8.51624i	−0.231526	+	0.401014i
$452$	5.49238	+	3.17103i	0.258340	+	0.149153i
$453$	14.3008	−	8.25654i	0.671908	−	0.387926i
$454$	−11.0554			−0.518857
$455$	−2.90090	+	18.5344i	−0.135996	+	0.868907i
$456$	−3.17103			−0.148497
$457$	−0.334953	+	0.193385i	−0.0156684	+	0.00904617i	−0.507814	−	0.861467i	$-0.669546\pi$
$457$	−0.334953	+	0.193385i	−0.0156684	+	0.00904617i	0.492145	+	0.870513i	$0.336213\pi$
$458$	15.9807	+	9.22646i	0.746729	+	0.431124i
$459$	2.61323	−	4.52625i	0.121975	−	0.211267i
$460$	−2.46833	−	15.8438i	−0.115086	−	0.738721i
$461$	−37.3682			−1.74041			−0.870206	−	0.492688i	$-0.836014\pi$
$461$	−37.3682			−1.74041			−0.870206	+	0.492688i	$0.836014\pi$
$462$	−9.36972	+	8.51072i	−0.435919	+	0.395954i
$463$			24.3081i			1.12969i	0.825196	+	0.564846i	$0.191064\pi$
$463$			24.3081i			1.12969i	−0.825196	+	0.564846i	$0.808936\pi$
$464$	1.19339	+	2.06700i	0.0554015	+	0.0959582i
$465$	7.26304	−	5.85113i	0.336815	−	0.271339i
$466$	4.55780	−	7.89434i	0.211136	−	0.365698i
$467$	−24.7452	+	14.2866i	−1.14507	+	0.661106i	−0.947681	−	0.319219i	$-0.896579\pi$
$467$	−24.7452	+	14.2866i	−1.14507	+	0.661106i	−0.197389	+	0.980325i	$0.563246\pi$
$468$		−	3.17103i		−	0.146581i
$469$	−17.0214	−	18.7394i	−0.785977	−	0.865307i
$470$	9.28663	−	24.0107i	0.428360	−	1.10753i
$471$	−4.97229	−	8.61225i	−0.229111	−	0.396832i
$472$	−9.29144	−	5.36441i	−0.427673	−	0.246917i
$473$	−8.28658	−	4.78426i	−0.381017	−	0.219980i
$474$	6.08551	+	10.5404i	0.279517	+	0.484138i
$475$	−11.7288	−	10.6687i	−0.538156	−	0.489512i
$476$	−13.5131	+	2.93387i	−0.619371	+	0.134474i
$477$			8.11560i			0.371588i
$478$	11.3584	−	6.55780i	0.519523	−	0.299947i
$479$	−4.28189	+	7.41645i	−0.195645	+	0.338866i	−0.947112	−	0.320904i	$-0.896013\pi$
$479$	−4.28189	+	7.41645i	−0.195645	+	0.338866i	0.751467	+	0.659771i	$0.229347\pi$
$480$	−1.40280	−	1.74131i	−0.0640288	−	0.0794794i
$481$	11.3698	+	19.6930i	0.518417	+	0.897925i
$482$			5.34206i			0.243324i
$483$	18.0695	+	5.78426i	0.822192	+	0.263193i
$484$	−11.8891			−0.540415
$485$	0.437548	+	2.80854i	0.0198680	+	0.127529i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−27.5781	−	15.9222i	−1.24968	−	0.721504i	−0.278636	−	0.960397i	$-0.589882\pi$
$487$	−27.5781	−	15.9222i	−1.24968	−	0.721504i	−0.971046	+	0.238892i	$0.923216\pi$
$488$	6.16229	−	3.55780i	0.278954	−	0.161054i
$489$	−2.88440			−0.130437
$490$	−15.6257	+	0.915779i	−0.705896	+	0.0413707i
$491$	4.49763			0.202975			0.101488	−	0.994837i	$-0.467640\pi$
$491$	4.49763			0.202975			0.101488	+	0.994837i	$0.467640\pi$
$492$	1.78005	−	1.02771i	0.0802511	−	0.0463330i
$493$	−10.8031	−	6.23718i	−0.486548	−	0.280908i
$494$	5.02771	−	8.70826i	0.226208	−	0.391803i
$495$	10.5704	−	1.64678i	0.475105	−	0.0740174i
$496$	4.17103			0.187285
$497$	−15.1188	−	4.83969i	−0.678170	−	0.217090i
$498$		−	3.39749i		−	0.152245i
$499$	−0.171030	−	0.296232i	−0.00765634	−	0.0132612i	0.862172	−	0.506616i	$-0.169104\pi$
$499$	−0.171030	−	0.296232i	−0.00765634	−	0.0132612i	−0.869828	+	0.493355i	$0.835770\pi$
$500$	0.669873	−	11.1603i	0.0299576	−	0.499102i
$501$	−2.02771	+	3.51211i	−0.0905916	+	0.156909i
$502$	−24.1806	+	13.9606i	−1.07923	+	0.623094i
$503$		−	7.56852i		−	0.337464i	−0.985662	−	0.168732i	$-0.946033\pi$
$503$		−	7.56852i		−	0.337464i	0.985662	−	0.168732i	$-0.0539672\pi$
$504$	2.58551	−	0.561349i	0.115168	−	0.0250045i
$505$	6.45292	−	16.6841i	0.287151	−	0.742434i
$506$	17.1540	+	29.7117i	0.762590	+	1.32084i
$507$	−2.55007	−	1.47229i	−0.113253	−	0.0653865i
$508$	−15.5977	−	9.00536i	−0.692038	−	0.399548i
$509$	15.4800	+	26.8122i	0.686140	+	1.18843i	0.973077	+	0.230479i	$0.0740294\pi$
$509$	15.4800	+	26.8122i	0.686140	+	1.18843i	−0.286938	+	0.957949i	$0.592637\pi$
$510$	10.8999	+	4.21574i	0.482654	+	0.186676i
$511$	7.11560	+	7.83379i	0.314776	+	0.346546i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.74619	+	1.58551i	−0.121247	+	0.0700022i
$514$	−10.5685	+	18.3052i	−0.466157	+	0.807408i
$515$	−19.5487	+	15.7485i	−0.861419	+	0.693962i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$			55.0816i			2.42249i
$518$	−14.0441	+	12.7565i	−0.617062	+	0.560490i
$519$	−6.39749			−0.280819
$520$	7.00613	−	1.09150i	0.307239	−	0.0478652i
$521$	−2.42520	+	4.20058i	−0.106250	+	0.184031i	−0.914248	−	0.405154i	$-0.867218\pi$
$521$	−2.42520	+	4.20058i	−0.106250	+	0.184031i	0.807998	+	0.589185i	$0.200551\pi$
$522$	2.06700	+	1.19339i	0.0904703	+	0.0522330i
$523$	3.68289	−	2.12632i	0.161042	−	0.0929774i	−0.417313	−	0.908763i	$-0.637028\pi$
$523$	3.68289	−	2.12632i	0.161042	−	0.0929774i	0.578355	+	0.815785i	$0.303695\pi$
$524$	5.55780			0.242794
$525$	11.4518	+	6.62246i	0.499796	+	0.289028i
$526$	11.9106			0.519326
$527$	−18.8791	+	10.8999i	−0.822387	+	0.474805i
$528$	4.14329	+	2.39213i	0.180314	+	0.104104i
$529$	14.2118	−	24.6156i	0.617906	−	1.07024i
$530$	−17.9307	+	2.79346i	−0.778862	+	0.121340i
$531$	−10.7288			−0.465592
$532$	7.99035	+	2.55780i	0.346426	+	0.110895i
$533$			6.51783i			0.282319i
$534$	4.78426	+	8.28658i	0.207035	+	0.358595i
$535$	2.43346	−	1.96040i	0.105208	−	0.0847555i
$536$	−4.78426	+	8.28658i	−0.206649	+	0.357926i
$537$	−16.8988	+	9.75654i	−0.729238	+	0.421026i
$538$		−	3.27117i		−	0.141030i
$539$	30.4747	−	13.8875i	1.31264	−	0.598178i
$540$	−2.08551	−	0.806615i	−0.0897463	−	0.0347112i
$541$	−19.1817	−	33.2238i	−0.824688	−	1.42840i	−0.902158	−	0.431406i	$-0.858017\pi$
$541$	−19.1817	−	33.2238i	−0.824688	−	1.42840i	0.0774699	−	0.996995i	$-0.475316\pi$
$542$	0.540356	+	0.311975i	0.0232103	+	0.0134005i
$543$	19.9413	+	11.5131i	0.855761	+	0.494074i
$544$	2.61323	+	4.52625i	0.112041	+	0.194061i
$545$	10.0447	−	25.9707i	0.430268	−	1.11246i
$546$	−2.55780	+	7.99035i	−0.109464	+	0.341955i
$547$			1.44818i			0.0619197i	0.999521	+	0.0309598i	$0.00985640\pi$
$547$			1.44818i			0.0619197i	−0.999521	+	0.0309598i	$0.990144\pi$
$548$	−12.8128	+	7.39749i	−0.547337	+	0.316005i
$549$	3.55780	−	6.16229i	0.151843	−	0.263000i
$550$	7.27686	+	22.7876i	0.310286	+	0.971668i
$551$	3.78426	+	6.55453i	0.161215	+	0.279232i
$552$		−	7.17103i		−	0.305219i
$553$	−6.83220	−	31.4684i	−0.290535	−	1.33817i
$554$	28.7950			1.22338
$555$	15.8438	−	2.46833i	0.672531	−	0.104775i
$556$	−1.82897	+	3.16787i	−0.0775656	+	0.134348i
$557$	11.2769	+	6.51072i	0.477817	+	0.275868i	0.719506	−	0.694486i	$-0.244368\pi$
$557$	11.2769	+	6.51072i	0.477817	+	0.275868i	−0.241689	+	0.970354i	$0.577701\pi$
$558$	3.61222	−	2.08551i	0.152917	−	0.0882869i
$559$	−6.34206			−0.268241
$560$	2.13021	+	5.51926i	0.0900178	+	0.233231i
$561$	−25.0047			−1.05570
$562$	−2.44996	+	1.41449i	−0.103345	+	0.0596665i
$563$	−5.06660	−	2.92520i	−0.213532	−	0.123283i	0.389420	−	0.921060i	$-0.372676\pi$
$563$	−5.06660	−	2.92520i	−0.213532	−	0.123283i	−0.602952	+	0.797778i	$0.706009\pi$
$564$	5.75654	−	9.97063i	0.242394	−	0.419839i
$565$	2.18299	+	14.0123i	0.0918391	+	0.589500i
$566$	−25.1370			−1.05659
$567$	1.95845	−	1.77890i	0.0822470	−	0.0747068i
$568$			6.00000i			0.251754i
$569$	−20.3251	−	35.2040i	−0.852071	−	1.47583i	−0.879336	−	0.476202i	$-0.842013\pi$
$569$	−20.3251	−	35.2040i	−0.852071	−	1.47583i	0.0272649	−	0.999628i	$-0.491320\pi$
$570$	−4.44833	−	5.52173i	−0.186320	−	0.231280i
$571$	1.61323	−	2.79420i	0.0675116	−	0.116933i	−0.830294	−	0.557326i	$-0.811827\pi$
$571$	1.61323	−	2.79420i	0.0675116	−	0.116933i	0.897805	+	0.440393i	$0.145161\pi$
$572$	−13.1385	+	7.58551i	−0.549348	+	0.317166i
$573$		−	10.2312i		−	0.427415i
$574$	−5.31434	+	1.15381i	−0.221816	+	0.0481592i
$575$	24.1263	−	26.5238i	1.00614	−	1.10612i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	10.0759	+	5.81733i	0.419466	+	0.242179i	0.694849	−	0.719156i	$-0.255471\pi$
$577$	10.0759	+	5.81733i	0.419466	+	0.242179i	−0.275383	+	0.961335i	$0.588805\pi$
$578$	−8.93381	−	5.15794i	−0.371598	−	0.214542i
$579$	−5.80661	−	10.0574i	−0.241315	−	0.417969i
$580$	−1.92520	+	4.97764i	−0.0799398	+	0.206685i
$581$	−2.74047	+	8.56098i	−0.113694	+	0.355169i
$582$			1.27117i			0.0526917i
$583$	33.6253	−	19.4136i	1.39262	−	0.804028i
$584$	2.00000	−	3.46410i	0.0827606	−	0.143346i
$585$	5.52173	−	4.44833i	0.228296	−	0.183916i
$586$	−5.11323	−	8.85637i	−0.211226	−	0.365853i
$587$		−	28.9446i		−	1.19467i	−0.801992	−	0.597335i	$-0.796226\pi$
$587$		−	28.9446i		−	1.19467i	0.801992	−	0.597335i	$-0.203774\pi$
$588$	−6.96776	−	0.671030i	−0.287346	−	0.0276728i
$589$	13.2265			0.544987
$590$	−3.69295	−	23.7045i	−0.152036	−	0.975897i
$591$	1.19874	−	2.07629i	0.0493098	−	0.0854070i
$592$	6.21029	+	3.58551i	0.255242	+	0.147364i
$593$	−9.92262	+	5.72883i	−0.407473	+	0.235255i	−0.689704	−	0.724092i	$-0.742259\pi$
$593$	−9.92262	+	5.72883i	−0.407473	+	0.235255i	0.282230	+	0.959347i	$0.408926\pi$
$594$	4.78426			0.196301
$595$	−24.0649	−	19.4148i	−0.986567	−	0.795929i
$596$	22.3421			0.915166
$597$	15.8847	−	9.17103i	0.650117	−	0.375345i
$598$	19.6930	+	11.3698i	0.805308	+	0.464945i
$599$	−1.50237	+	2.60218i	−0.0613852	+	0.106322i	−0.895085	−	0.445896i	$-0.852885\pi$
$599$	−1.50237	+	2.60218i	−0.0613852	+	0.106322i	0.833700	+	0.552218i	$0.186218\pi$
$600$	1.06430	−	4.88541i	0.0434497	−	0.199446i
$601$	40.0816			1.63496			0.817481	−	0.575955i	$-0.195370\pi$
$601$	40.0816			1.63496			0.817481	+	0.575955i	$0.195370\pi$
$602$	−1.12270	−	5.17103i	−0.0457578	−	0.210755i
$603$			9.56852i			0.389660i
$604$	8.25654	+	14.3008i	0.335954	+	0.581889i
$605$	−16.6781	−	20.7026i	−0.678061	−	0.841682i
$606$	4.00000	−	6.92820i	0.162489	−	0.281439i
$607$	22.6220	−	13.0608i	0.918197	−	0.530121i	0.0351374	−	0.999382i	$-0.488813\pi$
$607$	22.6220	−	13.0608i	0.918197	−	0.530121i	0.883059	+	0.469261i	$0.155480\pi$
$608$		−	3.17103i		−	0.128602i
$609$	−4.24583	−	4.67436i	−0.172050	−	0.189415i
$610$	14.8397	+	5.73955i	0.600841	+	0.232388i
$611$	18.2542	+	31.6172i	0.738485	+	1.27909i
$612$	4.52625	+	2.61323i	0.182963	+	0.105634i
$613$	35.9514	+	20.7565i	1.45206	+	0.838349i	0.998598	−	0.0529254i	$-0.0168546\pi$
$613$	35.9514	+	20.7565i	1.45206	+	0.838349i	0.453464	+	0.891274i	$0.350188\pi$
$614$	−11.7288	−	20.3149i	−0.473337	−	0.819844i
$615$	4.28663	+	1.65794i	0.172854	+	0.0668546i
$616$	−8.51072	−	9.36972i	−0.342907	−	0.377517i
$617$			31.1156i			1.25267i	0.779555	+	0.626333i	$0.215445\pi$
$617$			31.1156i			1.25267i	−0.779555	+	0.626333i	$0.784555\pi$
$618$	−9.72240	+	5.61323i	−0.391092	+	0.225797i
$619$	16.4961	−	28.5721i	0.663034	−	1.14841i	−0.316780	−	0.948499i	$-0.602602\pi$
$619$	16.4961	−	28.5721i	0.663034	−	1.14841i	0.979814	−	0.199910i	$-0.0640649\pi$
$620$	5.85113	+	7.26304i	0.234987	+	0.291691i
$621$	−3.58551	−	6.21029i	−0.143882	−	0.249211i
$622$			5.65794i			0.226863i
$623$	−5.37128	−	24.7395i	−0.215196	−	0.991169i
$624$	3.17103			0.126943
$625$	20.3731	−	14.4892i	0.814925	−	0.579567i
$626$	8.19339	−	14.1914i	0.327474	−	0.567201i
$627$	13.1385	+	7.58551i	0.524701	+	0.302936i
$628$	8.61225	−	4.97229i	0.343666	−	0.198416i
$629$	−37.4791			−1.49439
$630$	4.60444	+	3.71471i	0.183445	+	0.147998i
$631$	47.6501			1.89692			0.948461	−	0.316894i	$-0.102640\pi$
$631$	47.6501			1.89692			0.948461	+	0.316894i	$0.102640\pi$
$632$	−10.5404	+	6.08551i	−0.419275	+	0.242069i
$633$	2.44996	+	1.41449i	0.0973772	+	0.0562207i
$634$	2.25654	−	3.90845i	0.0896188	−	0.155224i
$635$	−6.19944	−	39.7932i	−0.246017	−	1.57914i
$636$	−8.11560			−0.321804
$637$	12.8903	−	18.0709i	0.510731	−	0.715995i
$638$		−	11.4189i		−	0.452080i
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$	1.74131	−	1.40280i	0.0688312	−	0.0554506i
$641$	−5.14331	+	8.90848i	−0.203149	+	0.351864i	−0.949541	−	0.313642i	$-0.898451\pi$
$641$	−5.14331	+	8.90848i	−0.203149	+	0.351864i	0.746393	+	0.665506i	$0.231784\pi$
$642$	1.21026	−	0.698745i	0.0477652	−	0.0275773i
$643$		−	38.9368i		−	1.53552i	−0.640740	−	0.767758i	$-0.721372\pi$
$643$		−	38.9368i		−	1.53552i	0.640740	−	0.767758i	$-0.278628\pi$
$644$	−5.78426	+	18.0695i	−0.227932	+	0.712039i
$645$	−1.61323	+	4.17103i	−0.0635209	+	0.164234i
$646$	8.28663	+	14.3529i	0.326033	+	0.564706i
$647$	−29.3194	−	16.9276i	−1.15267	−	0.665492i	−0.203130	−	0.979152i	$-0.565111\pi$
$647$	−29.3194	−	16.9276i	−1.15267	−	0.665492i	−0.949535	+	0.313660i	$0.898445\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	25.6648	+	44.4527i	1.00743	+	1.74492i
$650$	11.7288	+	10.6687i	0.460043	+	0.418459i
$651$	−10.7843	+	2.34140i	−0.422668	+	0.0917668i
$652$		−	2.88440i		−	0.112962i
$653$	4.64493	−	2.68175i	0.181770	−	0.104945i	−0.406354	−	0.913716i	$-0.633200\pi$
$653$	4.64493	−	2.68175i	0.181770	−	0.104945i	0.588124	+	0.808771i	$0.299867\pi$
$654$	6.22646	−	10.7845i	0.243474	−	0.421709i
$655$	7.79649	+	9.67783i	0.304634	+	0.378144i
$656$	1.02771	+	1.78005i	0.0401255	+	0.0694995i
$657$		−	4.00000i		−	0.156055i
$658$	−22.5478	+	20.4806i	−0.879004	+	0.798418i
$659$	−23.2265			−0.904774			−0.452387	−	0.891822i	$-0.649427\pi$
$659$	−23.2265			−0.904774			−0.452387	+	0.891822i	$0.649427\pi$
$660$	1.64678	+	10.5704i	0.0641009	+	0.411453i
$661$	18.2973	−	31.6919i	0.711684	−	1.23267i	−0.252540	−	0.967586i	$-0.581266\pi$
$661$	18.2973	−	31.6919i	0.711684	−	1.23267i	0.964224	−	0.265087i	$-0.0854007\pi$
$662$	−11.3290	−	6.54080i	−0.440314	−	0.254216i
$663$	−14.3529	+	8.28663i	−0.557419	+	0.321826i
$664$	3.39749			0.131848
$665$	6.75496	+	17.5017i	0.261946	+	0.678688i
$666$	7.17103			0.277872
$667$	−14.8225	+	8.55780i	−0.573931	+	0.331359i
$668$	−3.51211	−	2.02771i	−0.135887	−	0.0784546i
$669$	7.14867	−	12.3819i	0.276384	−	0.478711i
$670$	−21.1408	+	3.29357i	−0.816742	+	0.127242i
$671$	−34.0429			−1.31421
$672$	0.561349	+	2.58551i	0.0216545	+	0.0997384i
$673$		−	17.7336i		−	0.683579i	−0.939777	−	0.341789i	$-0.888967\pi$
$673$		−	17.7336i		−	0.683579i	0.939777	−	0.341789i	$-0.111033\pi$
$674$	10.1487	+	17.5780i	0.390912	+	0.677080i
$675$	−1.52100	−	4.76304i	−0.0585433	−	0.183330i
$676$	1.47229	−	2.55007i	0.0566263	−	0.0980797i
$677$	−22.7128	+	13.1132i	−0.872923	+	0.503982i	−0.868319	−	0.496007i	$-0.834799\pi$
$677$	−22.7128	+	13.1132i	−0.872923	+	0.503982i	−0.00460456	+	0.999989i	$0.501466\pi$
$678$			6.34206i			0.243565i
$679$	1.02534	−	3.20309i	0.0393491	−	0.122923i
$680$	−4.21574	+	10.8999i	−0.161666	+	0.417991i
$681$	−5.52771	−	9.57428i	−0.211822	−	0.366887i
$682$	−17.2818	−	9.97764i	−0.661754	−	0.382064i
$683$	42.6246	+	24.6093i	1.63098	+	0.941650i	0.983790	+	0.179325i	$0.0573914\pi$
$683$	42.6246	+	24.6093i	1.63098	+	0.941650i	0.647195	+	0.762324i	$0.275942\pi$
$684$	−1.58551	−	2.74619i	−0.0606237	−	0.105003i
$685$	−30.8551	−	11.9339i	−1.17891	−	0.455969i
$686$	17.0161	+	7.31116i	0.649677	+	0.279141i
$687$			18.4529i			0.704023i
$688$	−1.73205	+	1.00000i	−0.0660338	+	0.0381246i
$689$	12.8674	−	22.2870i	0.490209	−	0.849067i
$690$	12.4870	−	10.0595i	0.475370	−	0.382960i
$691$	−4.45292	−	7.71268i	−0.169397	−	0.293404i	0.768811	−	0.639476i	$-0.220849\pi$
$691$	−4.45292	−	7.71268i	−0.169397	−	0.293404i	−0.938208	+	0.346072i	$0.887515\pi$
$692$		−	6.39749i		−	0.243196i
$693$	−12.0554	−	3.85906i	−0.457945	−	0.146593i
$694$	−14.4529			−0.548625
$695$	−8.08191	+	1.25909i	−0.306564	+	0.0477602i
$696$	−1.19339	+	2.06700i	−0.0452351	+	0.0783496i
$697$	−9.30338	−	5.37131i	−0.352391	−	0.203453i
$698$	12.0283	−	6.94457i	0.455280	−	0.262856i
$699$	9.11560			0.344784
$700$	−6.62246	+	11.4518i	−0.250305	+	0.432836i
$701$	11.9553			0.451545			0.225773	−	0.974180i	$-0.427509\pi$
$701$	11.9553			0.451545			0.225773	+	0.974180i	$0.427509\pi$
$702$	2.74619	−	1.58551i	0.103648	−	0.0598414i
$703$	19.6930	+	11.3698i	0.742737	+	0.428819i
$704$	−2.39213	+	4.14329i	−0.0901568	+	0.156156i
$705$	25.4372	−	3.96290i	0.958021	−	0.149252i
$706$	−6.45292			−0.242859
$707$	−15.6676	+	14.2312i	−0.589240	+	0.535219i
$708$		−	10.7288i		−	0.403214i
$709$	26.0816	+	45.1747i	0.979515	+	1.69657i	0.664149	+	0.747600i	$0.268794\pi$
$709$	26.0816	+	45.1747i	0.979515	+	1.69657i	0.315367	+	0.948970i	$0.397872\pi$
$710$	−10.4478	+	8.41681i	−0.392100	+	0.315877i
$711$	−6.08551	+	10.5404i	−0.228225	+	0.395297i
$712$	−8.28658	+	4.78426i	−0.310553	+	0.179298i
$713$			29.9106i			1.12016i
$714$	−9.29735	−	10.2357i	−0.347945	−	0.383063i
$715$	−31.6394	−	12.2372i	−1.18325	−	0.457645i
$716$	−9.75654	−	16.8988i	−0.364619	−	0.631539i
$717$	11.3584	+	6.55780i	0.424189	+	0.244906i
$718$	−6.25830	−	3.61323i	−0.233558	−	0.134845i
$719$	12.8951	+	22.3350i	0.480907	+	0.832955i	0.999760	−	0.0219083i	$-0.00697420\pi$
$719$	12.8951	+	22.3350i	0.480907	+	0.832955i	−0.518853	+	0.854863i	$0.673641\pi$
$720$	0.806615	−	2.08551i	0.0300608	−	0.0777226i
$721$	29.0262	−	6.30196i	1.08099	−	0.234697i
$722$			8.94457i			0.332882i
$723$	−4.62636	+	2.67103i	−0.172056	+	0.0993367i
$724$	−11.5131	+	19.9413i	−0.427881	+	0.741111i
$725$	−11.3683	+	3.63028i	−0.422207	+	0.134825i
$726$	−5.94457	−	10.2963i	−0.220624	−	0.382131i
$727$		−	34.6054i		−	1.28344i	−0.766937	−	0.641722i	$-0.778220\pi$
$727$		−	34.6054i		−	1.28344i	0.766937	−	0.641722i	$-0.221780\pi$
$728$	−7.99035	−	2.55780i	−0.296142	−	0.0947984i
$729$	−1.00000			−0.0370370
$730$	8.83767	−	1.37683i	0.327097	−	0.0509589i
$731$	5.22646	−	9.05249i	0.193308	−	0.334819i
$732$	6.16229	+	3.55780i	0.227765	+	0.131500i
$733$	−26.8215	+	15.4854i	−0.990673	+	0.571965i	−0.905475	−	0.424399i	$-0.860485\pi$
$733$	−26.8215	+	15.4854i	−0.990673	+	0.571965i	−0.0851976	+	0.996364i	$0.527152\pi$
$734$	2.10014			0.0775176
$735$	−8.60592	−	13.0743i	−0.317434	−	0.482254i
$736$	7.17103			0.264328
$737$	39.6452	−	22.8891i	1.46035	−	0.843132i
$738$	1.78005	+	1.02771i	0.0655247	+	0.0378307i
$739$	−1.08788	+	1.88427i	−0.0400185	+	0.0693141i	−0.885341	−	0.464942i	$-0.846075\pi$
$739$	−1.08788	+	1.88427i	−0.0400185	+	0.0693141i	0.845322	+	0.534257i	$0.179408\pi$
$740$	2.46833	+	15.8438i	0.0907376	+	0.582429i
$741$	10.0554			0.369395
$742$	20.4497	+	6.54616i	0.750731	+	0.240317i
$743$		−	31.9446i		−	1.17193i	−0.810335	−	0.585966i	$-0.800715\pi$
$743$		−	31.9446i		−	1.17193i	0.810335	−	0.585966i	$-0.199285\pi$
$744$	2.08551	+	3.61222i	0.0764587	+	0.132430i
$745$	31.3415	+	38.9044i	1.14826	+	1.42535i
$746$	11.6239	−	20.1333i	0.425583	−	0.737131i
$747$	2.94231	−	1.69874i	0.107654	−	0.0621538i
$748$		−	25.0047i		−	0.914264i
$749$	−3.61323	+	0.784479i	−0.132025	+	0.0286643i
$750$	10.0000	−	5.00000i	0.365148	−	0.182574i
$751$	2.80363	+	4.85602i	0.102306	+	0.177199i	0.912634	−	0.408777i	$-0.134045\pi$
$751$	2.80363	+	4.85602i	0.102306	+	0.177199i	−0.810329	+	0.585976i	$0.800711\pi$
$752$	9.97063	+	5.75654i	0.363591	+	0.209920i
$753$	−24.1806	−	13.9606i	−0.881188	−	0.508754i
$754$	−3.78426	−	6.55453i	−0.137815	−	0.238702i
$755$	−13.3197	+	34.4383i	−0.484754	+	1.25334i
$756$	1.77890	+	1.95845i	0.0646980	+	0.0712280i
$757$			24.2312i			0.880698i	0.897827	+	0.440349i	$0.145145\pi$
$757$			24.2312i			0.880698i	−0.897827	+	0.440349i	$0.854855\pi$
$758$	1.87606	−	1.08314i	0.0681416	−	0.0393416i
$759$	−17.1540	+	29.7117i	−0.622652	+	1.07846i
$760$	5.52173	−	4.44833i	0.200294	−	0.161358i
$761$	−19.9276	−	34.5156i	−0.722374	−	1.25119i	−0.960046	−	0.279843i	$-0.909718\pi$
$761$	−19.9276	−	34.5156i	−0.722374	−	1.25119i	0.237672	−	0.971346i	$-0.423616\pi$
$762$		−	18.0107i		−	0.652460i
$763$	−24.3884	+	22.1525i	−0.882919	+	0.801974i
$764$	10.2312			0.370152
$765$	1.79899	+	11.5474i	0.0650427	+	0.417498i
$766$	4.02771	−	6.97621i	0.145527	−	0.252061i
$767$	29.4634	+	17.0107i	1.06386	+	0.614221i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−29.7950			−1.07443			−0.537217	−	0.843444i	$-0.680524\pi$
$769$	−29.7950			−1.07443			−0.537217	+	0.843444i	$0.680524\pi$
$770$	4.37670	−	27.9636i	0.157725	−	1.00774i
$771$	−21.1370			−0.761232
$772$	10.0574	−	5.80661i	0.361972	−	0.208985i
$773$	−0.144011	−	0.0831449i	−0.00517972	−	0.00299051i	0.497408	−	0.867517i	$-0.334285\pi$
$773$	−0.144011	−	0.0831449i	−0.00517972	−	0.00299051i	−0.502588	+	0.864526i	$0.667619\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	−4.43921	+	20.3772i	−0.159461	+	0.731971i
$776$	−1.27117			−0.0456324
$777$	−18.0695	−	5.78426i	−0.648241	−	0.207509i
$778$			11.8891i			0.426246i
$779$	3.25891	+	5.64461i	0.116763	+	0.202239i
$780$	4.44833	+	5.52173i	0.159276	+	0.197710i
$781$	14.3528	−	24.8597i	0.513583	−	0.889552i
$782$	−32.4579	+	18.7395i	−1.16069	+	0.670125i
$783$			2.38677i			0.0852962i
$784$	0.671030	−	6.96776i	0.0239653	−	0.248849i
$785$	20.7395	+	8.02144i	0.740226	+	0.286297i
$786$	2.77890	+	4.81320i	0.0991201	+	0.171681i
$787$	−24.6410	−	14.2265i	−0.878355	−	0.507119i	−0.00823936	−	0.999966i	$-0.502623\pi$
$787$	−24.6410	−	14.2265i	−0.878355	−	0.507119i	−0.870116	+	0.492848i	$0.835956\pi$
$788$	2.07629	+	1.19874i	0.0739647	+	0.0427035i
$789$	5.95529	+	10.3149i	0.212014	+	0.367219i
$790$	−25.3829	−	9.81733i	−0.903082	−	0.349285i
$791$	5.11560	−	15.9807i	0.181890	−	0.568208i
$792$			4.78426i			0.170001i
$793$	−19.5408	+	11.2819i	−0.693914	+	0.400632i
$794$	−8.05543	+	13.9524i	−0.285877	+	0.495153i
$795$	−11.3846	−	14.1317i	−0.403769	−	0.501201i
$796$	9.17103	+	15.8847i	0.325059	+	0.563018i
$797$		−	36.6334i		−	1.29762i	−0.760949	−	0.648811i	$-0.775266\pi$
$797$		−	36.6334i		−	1.29762i	0.760949	−	0.648811i	$-0.224734\pi$
$798$	1.78005	+	8.19874i	0.0630132	+	0.290232i
$799$	−60.1727			−2.12876
$800$	4.88541	+	1.06430i	0.172725	+	0.0376286i
$801$	−4.78426	+	8.28658i	−0.169044	+	0.292792i
$802$	21.6253	+	12.4854i	0.763616	+	0.440874i
$803$	−16.5732	+	9.56852i	−0.584854	+	0.337666i
$804$	−9.56852			−0.337456
$805$	−39.5788	+	15.2758i	−1.39497	+	0.538401i
$806$	−13.2265			−0.465882
$807$	2.83292	−	1.63559i	0.0997234	−	0.0575753i
$808$	6.92820	+	4.00000i	0.243733	+	0.140720i
$809$	−10.1433	+	17.5687i	−0.356620	+	0.617684i	−0.987394	−	0.158283i	$-0.949404\pi$
$809$	−10.1433	+	17.5687i	−0.356620	+	0.617684i	0.630774	+	0.775967i	$0.282738\pi$
$810$	−0.344208	−	2.20942i	−0.0120943	−	0.0776310i
$811$	1.38079			0.0484861			0.0242431	−	0.999706i	$-0.492282\pi$
$811$	1.38079			0.0484861			0.0242431	+	0.999706i	$0.492282\pi$
$812$	4.67436	−	4.24583i	0.164038	−	0.148999i
$813$			0.623949i			0.0218829i
$814$	−17.1540	−	29.7117i	−0.601249	−	1.04139i
$815$	5.02262	−	4.04624i	0.175935	−	0.141734i
$816$	−2.61323	+	4.52625i	−0.0914813	+	0.158450i
$817$	−5.49238	+	3.17103i	−0.192154	+	0.110940i
$818$			3.05543i			0.106831i
$819$	−8.19874	+	1.78005i	−0.286487	+	0.0622001i
$820$	−1.65794	+	4.28663i	−0.0578978	+	0.149696i
$821$	8.70647	+	15.0801i	0.303858	+	0.526298i	0.977006	−	0.213210i	$-0.0683918\pi$
$821$	8.70647	+	15.0801i	0.303858	+	0.526298i	−0.673148	+	0.739507i	$0.735058\pi$
$822$	−12.8128	−	7.39749i	−0.446899	−	0.258017i
$823$	−17.8355	−	10.2973i	−0.621708	−	0.358943i	0.155826	−	0.987785i	$-0.450196\pi$
$823$	−17.8355	−	10.2973i	−0.621708	−	0.358943i	−0.777534	+	0.628842i	$0.783529\pi$
$824$	−5.61323	−	9.72240i	−0.195546	−	0.338696i
$825$	−16.0962	+	17.6958i	−0.560399	+	0.616087i
$826$	−8.65403	+	27.0345i	−0.301112	+	0.940649i
$827$		−	13.8504i		−	0.481626i	−0.970572	−	0.240813i	$-0.922586\pi$
$827$		−	13.8504i		−	0.481626i	0.970572	−	0.240813i	$-0.0774140\pi$
$828$	6.21029	−	3.58551i	0.215823	−	0.124605i
$829$	−0.613230	+	1.06215i	−0.0212984	+	0.0368898i	−0.876478	−	0.481442i	$-0.840113\pi$
$829$	−0.613230	+	1.06215i	−0.0212984	+	0.0368898i	0.855180	+	0.518331i	$0.173447\pi$
$830$	4.76600	+	5.91607i	0.165430	+	0.205350i
$831$	14.3975	+	24.9372i	0.499443	+	0.865061i
$832$			3.17103i			0.109936i
$833$	15.1711	+	33.2914i	0.525648	+	1.15348i
$834$	−3.65794			−0.126664
$835$	−1.39591	−	8.96013i	−0.0483076	−	0.310078i
$836$	−7.58551	+	13.1385i	−0.262351	+	0.454404i
$837$	3.61222	+	2.08551i	0.124857	+	0.0720859i
$838$	−17.4913	+	10.0986i	−0.604227	+	0.348850i
$839$	−29.9106			−1.03263			−0.516314	−	0.856399i	$-0.672696\pi$
$839$	−29.9106			−1.03263			−0.516314	+	0.856399i	$0.672696\pi$
$840$	−3.71471	+	4.60444i	−0.128170	+	0.158868i
$841$	−23.3033			−0.803563
$842$	26.2956	−	15.1817i	0.906205	−	0.523198i
$843$	−2.44996	−	1.41449i	−0.0843811	−	0.0487175i
$844$	−1.41449	+	2.44996i	−0.0486886	+	0.0843311i
$845$	6.50578	−	1.01355i	0.223806	−	0.0348670i
$846$	11.5131			0.395828
$847$	6.67396	+	30.7395i	0.229320	+	1.05622i
$848$		−	8.11560i		−	0.278691i
$849$	−12.5685	−	21.7693i	−0.431350	−	0.747121i
$850$	−24.8938	+	7.94944i	−0.853852	+	0.272664i
$851$	−25.7118	+	44.5342i	−0.881390	+	1.52661i
$852$	−5.19615	+	3.00000i	−0.178017	+	0.102778i
$853$		−	10.7181i		−	0.366981i	−0.983021	−	0.183491i	$-0.941260\pi$
$853$		−	10.7181i		−	0.366981i	0.983021	−	0.183491i	$-0.0587397\pi$
$854$	−12.6579	−	13.9355i	−0.433146	−	0.476864i
$855$	2.55780	−	6.61323i	0.0874749	−	0.226168i
$856$	0.698745	+	1.21026i	0.0238826	+	0.0413659i
$857$	34.3716	+	19.8444i	1.17411	+	0.677873i	0.954645	−	0.297747i	$-0.0962353\pi$
$857$	34.3716	+	19.8444i	1.17411	+	0.677873i	0.219465	+	0.975620i	$0.429569\pi$
$858$	−13.1385	−	7.58551i	−0.448541	−	0.258965i
$859$	5.50237	+	9.53038i	0.187738	+	0.325173i	0.944496	−	0.328523i	$-0.106551\pi$
$859$	5.50237	+	9.53038i	0.187738	+	0.325173i	−0.756757	+	0.653696i	$0.773218\pi$
$860$	−4.17103	−	1.61323i	−0.142231	−	0.0550107i
$861$	−3.65640	−	4.02545i	−0.124610	−	0.137187i
$862$		−	24.5733i		−	0.836969i
$863$	7.47266	−	4.31434i	0.254372	−	0.146862i	−0.367392	−	0.930066i	$-0.619749\pi$
$863$	7.47266	−	4.31434i	0.254372	−	0.146862i	0.621765	+	0.783204i	$0.286416\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	11.1400	−	8.97441i	0.378771	−	0.305139i
$866$	−2.34206	−	4.05657i	−0.0795864	−	0.137848i
$867$		−	10.3159i		−	0.350346i
$868$	−2.34140	−	10.7843i	−0.0794724	−	0.366042i
$869$	58.2294			1.97530
$870$	−5.27337	+	0.821546i	−0.178784	+	0.0278530i
$871$	15.1710	−	26.2770i	0.514051	−	0.890362i
$872$	10.7845	+	6.22646i	0.365211	+	0.210855i
$873$	−1.10087	+	0.635585i	−0.0372587	+	0.0215113i
$874$	22.7395			0.769177
$875$	−29.2310	+	4.53283i	−0.988189	+	0.153238i
$876$	4.00000			0.135147
$877$	33.5494	−	19.3698i	1.13288	−	0.654071i	0.188225	−	0.982126i	$-0.439726\pi$
$877$	33.5494	−	19.3698i	1.13288	−	0.654071i	0.944659	+	0.328055i	$0.106393\pi$
$878$	26.4251	+	15.2565i	0.891804	+	0.514883i
$879$	5.11323	−	8.85637i	0.172465	−	0.298718i
$880$	−10.5704	+	1.64678i	−0.356329	+	0.0555130i
$881$	−6.03399			−0.203290			−0.101645	−	0.994821i	$-0.532411\pi$
$881$	−6.03399			−0.203290			−0.101645	+	0.994821i	$0.532411\pi$
$882$	−2.90275	−	6.36977i	−0.0977408	−	0.214481i
$883$			7.77828i			0.261760i	0.991398	+	0.130880i	$0.0417803\pi$
$883$			7.77828i			0.261760i	−0.991398	+	0.130880i	$0.958220\pi$
$884$	−8.28663	−	14.3529i	−0.278710	−	0.482739i
$885$	18.6822	−	15.0504i	0.627995	−	0.505914i
$886$	4.75417	−	8.23447i	0.159720	−	0.276642i
$887$	21.5587	−	12.4469i	0.723871	−	0.417927i	−0.0923045	−	0.995731i	$-0.529423\pi$
$887$	21.5587	−	12.4469i	0.723871	−	0.417927i	0.816176	+	0.577803i	$0.196090\pi$
$888$			7.17103i			0.240644i
$889$	−14.5277	+	45.3833i	−0.487244	+	1.52211i
$890$	−19.9553	−	7.71811i	−0.668903	−	0.258712i
$891$	2.39213	+	4.14329i	0.0801394	+	0.138805i
$892$	12.3819	+	7.14867i	0.414576	+	0.239355i
$893$	31.6172	+	18.2542i	1.05803	+	0.610853i
$894$	11.1710	+	19.3488i	0.373615	+	0.647120i
$895$	15.7395	−	40.6948i	0.526115	−	1.36028i
$896$	−2.58551	+	0.561349i	−0.0863760	+	0.0187534i
$897$			22.7395i			0.759251i
$898$	15.2628	−	8.81197i	0.509326	−	0.294059i
$899$	4.97764	−	8.62153i	0.166014	−	0.287544i
$900$	4.76304	−	1.52100i	0.158768	−	0.0507000i
$901$	21.2079	+	36.7332i	0.706539	+	1.22376i
$902$		−	9.83371i		−	0.327427i
$903$	3.91689	−	3.55780i	0.130346	−	0.118396i
$904$	−6.34206			−0.210934
$905$	−50.8744	+	7.92580i	−1.69112	+	0.263463i
$906$	−8.25654	+	14.3008i	−0.274305	+	0.475111i
$907$	−40.4482	−	23.3528i	−1.34306	−	0.775416i	−0.355805	−	0.934560i	$-0.615793\pi$
$907$	−40.4482	−	23.3528i	−1.34306	−	0.775416i	−0.987255	+	0.159144i	$0.949127\pi$
$908$	9.57428	−	5.52771i	0.317734	−	0.183444i
$909$	8.00000			0.265343
$910$	−6.75496	−	17.5017i	−0.223925	−	0.580177i
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	2.74619	−	1.58551i	0.0909355	−	0.0525016i
$913$	−14.0768	−	8.12724i	−0.465874	−	0.268972i
$914$	0.193385	−	0.334953i	0.00639661	−	0.0110793i
$915$	2.44925	+	15.7213i	0.0809697	+	0.519731i
$916$	−18.4529			−0.609702
$917$	−3.11987	−	14.3698i	−0.103027	−	0.474532i
$918$			5.22646i			0.172499i
$919$	−17.1156	−	29.6451i	−0.564592	−	0.977901i	−0.997088	−	0.0762654i	$-0.975700\pi$
$919$	−17.1156	−	29.6451i	−0.564592	−	0.977901i	0.432496	−	0.901636i	$-0.357633\pi$
$920$	10.0595	+	12.4870i	0.331653	+	0.411683i
$921$	11.7288	−	20.3149i	0.386478	−	0.669400i
$922$	32.3618	−	18.6841i	1.06578	−	0.615329i
$923$		−	19.0262i		−	0.626254i
$924$	3.85906	−	12.0554i	0.126954	−	0.396592i
$925$	−24.1263	+	26.5238i	−0.793268	+	0.872097i
$926$	−12.1540	−	21.0514i	−0.399406	−	0.691792i
$927$	−9.72240	−	5.61323i	−0.319325	−	0.184363i
$928$	−2.06700	−	1.19339i	−0.0678527	−	0.0391748i
$929$	−13.8274	−	23.9498i	−0.453663	−	0.785768i	0.544947	−	0.838471i	$-0.316550\pi$
$929$	−13.8274	−	23.9498i	−0.453663	−	0.785768i	−0.998610	+	0.0527025i	$0.983216\pi$
$930$	−3.36441	+	8.69874i	−0.110324	+	0.285243i
$931$	2.12786	−	22.0950i	0.0697376	−	0.724134i
$932$			9.11560i			0.298591i
$933$	−4.89992	+	2.82897i	−0.160416	+	0.0926163i
$934$	14.2866	−	24.7452i	0.467473	−	0.809687i
$935$	43.5409	−	35.0767i	1.42394	−	1.14713i
$936$	1.58551	+	2.74619i	0.0518242	+	0.0897621i
$937$			38.8397i			1.26884i	0.772990	+	0.634419i	$0.218760\pi$
$937$			38.8397i			1.26884i	−0.772990	+	0.634419i	$0.781240\pi$
$938$	24.1107	+	7.71811i	0.787243	+	0.252005i
$939$	16.3868			0.534762
$940$	3.96290	+	25.4372i	0.129256	+	0.829670i
$941$	9.87750	−	17.1083i	0.321997	−	0.557716i	−0.658903	−	0.752228i	$-0.728979\pi$
$941$	9.87750	−	17.1083i	0.321997	−	0.557716i	0.980900	+	0.194512i	$0.0623124\pi$
$942$	8.61225	+	4.97229i	0.280602	+	0.162006i
$943$	−12.7648	+	7.36977i	−0.415680	+	0.239993i
$944$	10.7288			0.349194
$945$	−0.914813	+	5.84492i	−0.0297589	+	0.190135i
$946$	9.56852			0.311099
$947$	32.9543	−	19.0262i	1.07087	−	0.618268i	0.142452	−	0.989802i	$-0.454501\pi$
$947$	32.9543	−	19.0262i	1.07087	−	0.618268i	0.928419	+	0.371534i	$0.121168\pi$
$948$	−10.5404	−	6.08551i	−0.342337	−	0.197648i
$949$	−6.34206	+	10.9848i	−0.205872	+	0.356581i
$950$	15.4918	+	3.37492i	0.502620	+	0.109497i
$951$	4.51309			0.146347
$952$	10.2357	−	9.29735i	0.331742	−	0.301329i
$953$			52.5947i			1.70371i	0.523778	+	0.851855i	$0.324522\pi$
$953$			52.5947i			1.70371i	−0.523778	+	0.851855i	$0.675478\pi$
$954$	−4.05780	−	7.02832i	−0.131376	−	0.227550i
$955$	14.3523	+	17.8157i	0.464431	+	0.576501i
$956$	−6.55780	+	11.3584i	−0.212094	+	0.367358i
$957$	9.88908	−	5.70946i	0.319669	−	0.184561i
$958$		−	8.56378i		−	0.276683i
$959$	26.3188	+	28.9752i	0.849878	+	0.935657i
$960$	2.08551	+	0.806615i	0.0673097	+	0.0260334i
$961$	6.80126	+	11.7801i	0.219395	+	0.380004i
$962$	−19.6930	−	11.3698i	−0.634929	−	0.366576i
$963$	1.21026	+	0.698745i	0.0390001	+	0.0225167i
$964$	−2.67103	−	4.62636i	−0.0860281	−	0.149005i
$965$	24.2196	+	9.36740i	0.779655	+	0.301547i
$966$	−18.5408	+	4.02545i	−0.596541	+	0.129517i
$967$			4.61797i			0.148504i	0.997240	+	0.0742520i	$0.0236569\pi$
$967$			4.61797i			0.148504i	−0.997240	+	0.0742520i	$0.976343\pi$
$968$	10.2963	−	5.94457i	0.330936	−	0.191066i
$969$	−8.28663	+	14.3529i	−0.266205	+	0.461080i
$970$	−1.78320	−	2.21350i	−0.0572551	−	0.0710711i
$971$	−19.4523	−	33.6924i	−0.624254	−	1.08124i	−0.988685	−	0.150009i	$-0.952070\pi$
$971$	−19.4523	−	33.6924i	−0.624254	−	1.08124i	0.364431	−	0.931231i	$-0.381264\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	9.21726	+	2.95055i	0.295492	+	0.0945903i
$974$	31.8444			1.02036
$975$	−3.37492	+	15.4918i	−0.108084	+	0.496134i
$976$	−3.55780	+	6.16229i	−0.113882	+	0.197250i
$977$	−13.8750	−	8.01072i	−0.443900	−	0.256286i	0.261351	−	0.965244i	$-0.415832\pi$
$977$	−13.8750	−	8.01072i	−0.443900	−	0.256286i	−0.705250	+	0.708958i	$0.749165\pi$
$978$	2.49796	−	1.44220i	0.0798761	−	0.0461165i
$979$	45.7783			1.46308
$980$	13.0743	−	8.60592i	0.417644	−	0.274906i
$981$	12.4529			0.397591
$982$	−3.89506	+	2.24881i	−0.124296	+	0.0717626i
$983$	1.78005	+	1.02771i	0.0567749	+	0.0327790i	0.528119	−	0.849171i	$-0.322898\pi$
$983$	1.78005	+	1.02771i	0.0567749	+	0.0327790i	−0.471344	+	0.881950i	$0.656231\pi$
$984$	−1.02771	+	1.78005i	−0.0327624	+	0.0567461i
$985$	0.825236	+	5.29705i	0.0262942	+	0.168778i
$986$	12.4744			0.397264
$987$	−29.0106	−	9.28663i	−0.923419	−	0.295597i
$988$			10.0554i			0.319906i
$989$	−7.17103	−	12.4206i	−0.228025	−	0.394952i
$990$	−8.33086	+	6.71137i	−0.264772	+	0.213301i
$991$	13.5986	−	23.5535i	0.431974	−	0.748201i	−0.565069	−	0.825043i	$-0.691151\pi$
$991$	13.5986	−	23.5535i	0.431974	−	0.748201i	0.997043	+	0.0768427i	$0.0244839\pi$
$992$	−3.61222	+	2.08551i	−0.114688	+	0.0662152i
$993$		−	13.0816i		−	0.415132i
$994$	15.5131	−	3.36809i	0.492045	−	0.106829i
$995$	−14.7950	+	38.2526i	−0.469032	+	1.21269i
$996$	1.69874	+	2.94231i	0.0538268	+	0.0932307i
$997$	−15.9993	−	9.23718i	−0.506702	−	0.292544i	0.224775	−	0.974411i	$-0.427835\pi$
$997$	−15.9993	−	9.23718i	−0.506702	−	0.292544i	−0.731477	+	0.681866i	$0.761169\pi$
$998$	0.296232	+	0.171030i	0.00937707	+	0.00541385i
$999$	3.58551	+	6.21029i	0.113441	+	0.196485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.n.b.109.3	yes	12
3.2	odd	2		630.2.u.f.109.4		12
4.3	odd	2		1680.2.di.c.529.6		12
5.2	odd	4		1050.2.i.u.151.2		6
5.3	odd	4		1050.2.i.v.151.2		6
5.4	even	2	inner	210.2.n.b.109.4	yes	12
7.2	even	3	inner	210.2.n.b.79.4	yes	12
7.3	odd	6		1470.2.g.h.589.2		6
7.4	even	3		1470.2.g.i.589.2		6
7.5	odd	6		1470.2.n.j.79.6		12
7.6	odd	2		1470.2.n.j.949.1		12
15.14	odd	2		630.2.u.f.109.3		12
20.19	odd	2		1680.2.di.c.529.1		12
21.2	odd	6		630.2.u.f.289.3		12
28.23	odd	6		1680.2.di.c.289.1		12
35.2	odd	12		1050.2.i.u.751.2		6
35.3	even	12		7350.2.a.do.1.1		3
35.4	even	6		1470.2.g.i.589.5		6
35.9	even	6	inner	210.2.n.b.79.3	✓	12
35.17	even	12		7350.2.a.dp.1.1		3
35.18	odd	12		7350.2.a.dn.1.1		3
35.19	odd	6		1470.2.n.j.79.1		12
35.23	odd	12		1050.2.i.v.751.2		6
35.24	odd	6		1470.2.g.h.589.5		6
35.32	odd	12		7350.2.a.dq.1.1		3
35.34	odd	2		1470.2.n.j.949.6		12
105.44	odd	6		630.2.u.f.289.4		12
140.79	odd	6		1680.2.di.c.289.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.b.79.3	✓	12	35.9	even	6	inner
210.2.n.b.79.4	yes	12	7.2	even	3	inner
210.2.n.b.109.3	yes	12	1.1	even	1	trivial
210.2.n.b.109.4	yes	12	5.4	even	2	inner
630.2.u.f.109.3		12	15.14	odd	2
630.2.u.f.109.4		12	3.2	odd	2
630.2.u.f.289.3		12	21.2	odd	6
630.2.u.f.289.4		12	105.44	odd	6
1050.2.i.u.151.2		6	5.2	odd	4
1050.2.i.u.751.2		6	35.2	odd	12
1050.2.i.v.151.2		6	5.3	odd	4
1050.2.i.v.751.2		6	35.23	odd	12
1470.2.g.h.589.2		6	7.3	odd	6
1470.2.g.h.589.5		6	35.24	odd	6
1470.2.g.i.589.2		6	7.4	even	3
1470.2.g.i.589.5		6	35.4	even	6
1470.2.n.j.79.1		12	35.19	odd	6
1470.2.n.j.79.6		12	7.5	odd	6
1470.2.n.j.949.1		12	7.6	odd	2
1470.2.n.j.949.6		12	35.34	odd	2
1680.2.di.c.289.1		12	28.23	odd	6
1680.2.di.c.289.6		12	140.79	odd	6
1680.2.di.c.529.1		12	20.19	odd	2
1680.2.di.c.529.6		12	4.3	odd	2
7350.2.a.dn.1.1		3	35.18	odd	12
7350.2.a.do.1.1		3	35.3	even	12
7350.2.a.dp.1.1		3	35.17	even	12
7350.2.a.dq.1.1		3	35.32	odd	12

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.20942 - 0.344208i) q^{5} +1.00000 q^{6} +(-2.51980 - 0.806615i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.20942 - 0.344208i) q^{5} +1.00000 q^{6} +(-2.51980 - 0.806615i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.74131 + 1.40280i) q^{10} +(2.39213 - 4.14329i) q^{11} +(-0.866025 + 0.500000i) q^{12} -3.17103i q^{13} +(2.58551 - 0.561349i) q^{14} +(-2.08551 - 0.806615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.52625 + 2.61323i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.58551 - 2.74619i) q^{19} +(0.806615 - 2.08551i) q^{20} +(1.77890 + 1.95845i) q^{21} +4.78426i q^{22} +(6.21029 - 3.58551i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.76304 - 1.52100i) q^{25} +(1.58551 + 2.74619i) q^{26} -1.00000i q^{27} +(-1.95845 + 1.77890i) q^{28} -2.38677 q^{29} +(2.20942 - 0.344208i) q^{30} +(-2.08551 + 3.61222i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.14329 + 2.39213i) q^{33} -5.22646 q^{34} +(-5.84492 - 0.914813i) q^{35} +1.00000 q^{36} +(-6.21029 + 3.58551i) q^{37} +(2.74619 + 1.58551i) q^{38} +(-1.58551 + 2.74619i) q^{39} +(0.344208 + 2.20942i) q^{40} -2.05543 q^{41} +(-2.51980 - 0.806615i) q^{42} -2.00000i q^{43} +(-2.39213 - 4.14329i) q^{44} +(1.40280 + 1.74131i) q^{45} +(-3.58551 + 6.21029i) q^{46} +(-9.97063 + 5.75654i) q^{47} +1.00000i q^{48} +(5.69874 + 4.06501i) q^{49} +(-3.36441 + 3.69874i) q^{50} +(-2.61323 - 4.52625i) q^{51} +(-2.74619 - 1.58551i) q^{52} +(7.02832 + 4.05780i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.85906 - 9.97764i) q^{55} +(0.806615 - 2.51980i) q^{56} +3.17103i q^{57} +(2.06700 - 1.19339i) q^{58} +(-5.36441 + 9.29144i) q^{59} +(-1.74131 + 1.40280i) q^{60} +(-3.55780 - 6.16229i) q^{61} -4.17103i q^{62} +(-0.561349 - 2.58551i) q^{63} -1.00000 q^{64} +(-1.09150 - 7.00613i) q^{65} +(2.39213 - 4.14329i) q^{66} +(8.28658 + 4.78426i) q^{67} +(4.52625 - 2.61323i) q^{68} -7.17103 q^{69} +(5.51926 - 2.13021i) q^{70} +6.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(3.58551 - 6.21029i) q^{74} +(-4.88541 - 1.06430i) q^{75} -3.17103 q^{76} +(-9.36972 + 8.51072i) q^{77} -3.17103i q^{78} +(6.08551 + 10.5404i) q^{79} +(-1.40280 - 1.74131i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.78005 - 1.02771i) q^{82} -3.39749i q^{83} +(2.58551 - 0.561349i) q^{84} +(10.8999 + 4.21574i) q^{85} +(1.00000 + 1.73205i) q^{86} +(2.06700 + 1.19339i) q^{87} +(4.14329 + 2.39213i) q^{88} +(4.78426 + 8.28658i) q^{89} +(-2.08551 - 0.806615i) q^{90} +(-2.55780 + 7.99035i) q^{91} -7.17103i q^{92} +(3.61222 - 2.08551i) q^{93} +(5.75654 - 9.97063i) q^{94} +(-4.44833 - 5.52173i) q^{95} +(-0.500000 - 0.866025i) q^{96} +1.27117i q^{97} +(-6.96776 - 0.671030i) q^{98} +4.78426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 12 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 12 * q^6 + 6 * q^9	\( 12 q + 6 q^{4} + 12 q^{6} + 6 q^{9} - 6 q^{11} + 6 q^{14} - 6 q^{16} + 6 q^{19} + 6 q^{21} + 6 q^{24} - 6 q^{26} - 48 q^{29} - 24 q^{34} - 30 q^{35} + 12 q^{36} + 6 q^{39} - 36 q^{41} + 6 q^{44} - 18 q^{46} + 24 q^{49} - 12 q^{51} + 6 q^{54} + 60 q^{55} - 24 q^{59} - 12 q^{61} - 12 q^{64} - 30 q^{65} - 6 q^{66} - 36 q^{69} - 30 q^{70} + 72 q^{71} + 18 q^{74} + 12 q^{76} + 48 q^{79} - 6 q^{81} + 6 q^{84} + 12 q^{86} - 12 q^{89} - 6 q^{94} - 6 q^{96} - 12 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 12 * q^6 + 6 * q^9 - 6 * q^11 + 6 * q^14 - 6 * q^16 + 6 * q^19 + 6 * q^21 + 6 * q^24 - 6 * q^26 - 48 * q^29 - 24 * q^34 - 30 * q^35 + 12 * q^36 + 6 * q^39 - 36 * q^41 + 6 * q^44 - 18 * q^46 + 24 * q^49 - 12 * q^51 + 6 * q^54 + 60 * q^55 - 24 * q^59 - 12 * q^61 - 12 * q^64 - 30 * q^65 - 6 * q^66 - 36 * q^69 - 30 * q^70 + 72 * q^71 + 18 * q^74 + 12 * q^76 + 48 * q^79 - 6 * q^81 + 6 * q^84 + 12 * q^86 - 12 * q^89 - 6 * q^94 - 6 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more