LMFDB - Embedded newform 483.2.i.g.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} + \cdots + 6400 $ x^16 - x^15 + 16x^14 - 7x^13 + 161x^12 - 50x^11 + 929x^10 - 47x^9 + 3741x^8 - 158x^7 + 8993x^6 + 265x^5 + 15176x^4 + 383x^3 + 12649x^2 + 2960x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$1.25839 - 2.17960i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.g.415.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25839 - 2.17960i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.16710 + 3.75353i) q^{4} +(-1.20917 - 2.09434i) q^{5} +2.51679 q^{6} +(-0.750699 + 2.53702i) q^{7} +5.87470 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.25839 - 2.17960i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.16710 + 3.75353i) q^{4} +(-1.20917 - 2.09434i) q^{5} +2.51679 q^{6} +(-0.750699 + 2.53702i) q^{7} +5.87470 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.04322 + 5.27101i) q^{10} +(-0.624198 + 1.08114i) q^{11} +(-2.16710 - 3.75353i) q^{12} +2.06826 q^{13} +(6.47435 - 1.55634i) q^{14} +2.41834 q^{15} +(-3.05847 - 5.29743i) q^{16} +(1.65514 - 2.86679i) q^{17} +(-1.25839 + 2.17960i) q^{18} +(1.80992 + 3.13487i) q^{19} +10.4816 q^{20} +(-1.82177 - 1.91863i) q^{21} +3.14194 q^{22} +(0.500000 + 0.866025i) q^{23} +(-2.93735 + 5.08764i) q^{24} +(-0.424185 + 0.734710i) q^{25} +(-2.60268 - 4.50798i) q^{26} +1.00000 q^{27} +(-7.89593 - 8.31575i) q^{28} +4.27807 q^{29} +(-3.04322 - 5.27101i) q^{30} +(3.98872 - 6.90866i) q^{31} +(-1.82281 + 3.15721i) q^{32} +(-0.624198 - 1.08114i) q^{33} -8.33126 q^{34} +(6.22111 - 1.49546i) q^{35} +4.33421 q^{36} +(-2.54588 - 4.40959i) q^{37} +(4.55517 - 7.88979i) q^{38} +(-1.03413 + 1.79117i) q^{39} +(-7.10351 - 12.3036i) q^{40} -0.885683 q^{41} +(-1.88935 + 6.38512i) q^{42} +9.94532 q^{43} +(-2.70540 - 4.68590i) q^{44} +(-1.20917 + 2.09434i) q^{45} +(1.25839 - 2.17960i) q^{46} +(2.84595 + 4.92934i) q^{47} +6.11694 q^{48} +(-5.87290 - 3.80907i) q^{49} +2.13516 q^{50} +(1.65514 + 2.86679i) q^{51} +(-4.48213 + 7.76328i) q^{52} +(1.47101 - 2.54786i) q^{53} +(-1.25839 - 2.17960i) q^{54} +3.01905 q^{55} +(-4.41013 + 14.9042i) q^{56} -3.61984 q^{57} +(-5.38350 - 9.32449i) q^{58} +(-1.01222 + 1.75322i) q^{59} +(-5.24079 + 9.07732i) q^{60} +(3.69246 + 6.39553i) q^{61} -20.0775 q^{62} +(2.57247 - 0.618384i) q^{63} -3.05862 q^{64} +(-2.50088 - 4.33165i) q^{65} +(-1.57097 + 2.72100i) q^{66} +(-4.14189 + 7.17396i) q^{67} +(7.17372 + 12.4252i) q^{68} -1.00000 q^{69} +(-11.0881 - 11.6776i) q^{70} -8.27631 q^{71} +(-2.93735 - 5.08764i) q^{72} +(5.99365 - 10.3813i) q^{73} +(-6.40743 + 11.0980i) q^{74} +(-0.424185 - 0.734710i) q^{75} -15.6891 q^{76} +(-2.27429 - 2.39521i) q^{77} +5.20537 q^{78} +(7.61124 + 13.1831i) q^{79} +(-7.39642 + 12.8110i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.11454 + 1.93043i) q^{82} +15.7586 q^{83} +(11.1496 - 2.68020i) q^{84} -8.00538 q^{85} +(-12.5151 - 21.6768i) q^{86} +(-2.13904 + 3.70492i) q^{87} +(-3.66698 + 6.35139i) q^{88} +(8.13322 + 14.0871i) q^{89} +6.08644 q^{90} +(-1.55264 + 5.24721i) q^{91} -4.33421 q^{92} +(3.98872 + 6.90866i) q^{93} +(7.16266 - 12.4061i) q^{94} +(4.37700 - 7.58118i) q^{95} +(-1.82281 - 3.15721i) q^{96} +16.6972 q^{97} +(-0.911833 + 17.5939i) q^{98} +1.24840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.25839	−	2.17960i	−0.889818	−	1.54121i	−0.840090	−	0.542447i	$-0.817498\pi$
$2$	−1.25839	−	2.17960i	−0.889818	−	1.54121i	−0.0497279	−	0.998763i	$-0.515835\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−2.16710	+	3.75353i	−1.08355	+	1.87677i
$5$	−1.20917	−	2.09434i	−0.540757	−	0.936619i	−0.998861	−	0.0477203i	$-0.984804\pi$
$5$	−1.20917	−	2.09434i	−0.540757	−	0.936619i	0.458103	−	0.888899i	$-0.348529\pi$
$6$	2.51679			1.02747
$7$	−0.750699	+	2.53702i	−0.283738	+	0.958902i
$7$	−0.750699	+	2.53702i	−0.283738	+	0.958902i
$8$	5.87470			2.07702
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−3.04322	+	5.27101i	−0.962351	+	1.66684i
$11$	−0.624198	+	1.08114i	−0.188203	+	0.325977i	−0.944651	−	0.328077i	$-0.893600\pi$
$11$	−0.624198	+	1.08114i	−0.188203	+	0.325977i	0.756448	+	0.654053i	$0.226933\pi$
$12$	−2.16710	−	3.75353i	−0.625589	−	1.08355i
$13$	2.06826			0.573632			0.286816	−	0.957986i	$-0.407403\pi$
$13$	2.06826			0.573632			0.286816	+	0.957986i	$0.407403\pi$
$14$	6.47435	−	1.55634i	1.73034	−	0.415949i
$15$	2.41834			0.624413
$16$	−3.05847	−	5.29743i	−0.764618	−	1.32436i
$17$	1.65514	−	2.86679i	0.401430	−	0.695298i	−0.592469	−	0.805594i	$-0.701847\pi$
$17$	1.65514	−	2.86679i	0.401430	−	0.695298i	0.993899	+	0.110296i	$0.0351799\pi$
$18$	−1.25839	+	2.17960i	−0.296606	+	0.513737i
$19$	1.80992	+	3.13487i	0.415224	+	0.719188i	0.995452	−	0.0952655i	$-0.0303700\pi$
$19$	1.80992	+	3.13487i	0.415224	+	0.719188i	−0.580228	+	0.814454i	$0.697037\pi$
$20$	10.4816			2.34375
$21$	−1.82177	−	1.91863i	−0.397543	−	0.418680i
$22$	3.14194			0.669865
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	−2.93735	+	5.08764i	−0.599584	+	1.03851i
$25$	−0.424185	+	0.734710i	−0.0848370	+	0.146942i
$26$	−2.60268	−	4.50798i	−0.510428	−	0.884088i
$27$	1.00000			0.192450
$28$	−7.89593	−	8.31575i	−1.49219	−	1.57153i
$29$	4.27807			0.794418			0.397209	−	0.917728i	$-0.369979\pi$
$29$	4.27807			0.794418			0.397209	+	0.917728i	$0.369979\pi$
$30$	−3.04322	−	5.27101i	−0.555614	−	0.962351i
$31$	3.98872	−	6.90866i	0.716395	−	1.24083i	−0.246024	−	0.969264i	$-0.579124\pi$
$31$	3.98872	−	6.90866i	0.716395	−	1.24083i	0.962419	−	0.271569i	$-0.0875425\pi$
$32$	−1.82281	+	3.15721i	−0.322231	+	0.558120i
$33$	−0.624198	−	1.08114i	−0.108659	−	0.188203i
$34$	−8.33126			−1.42880
$35$	6.22111	−	1.49546i	1.05156	−	0.252779i
$36$	4.33421			0.722368
$37$	−2.54588	−	4.40959i	−0.418540	−	0.724932i	0.577253	−	0.816565i	$-0.304125\pi$
$37$	−2.54588	−	4.40959i	−0.418540	−	0.724932i	−0.995793	+	0.0916333i	$0.970791\pi$
$38$	4.55517	−	7.88979i	0.738947	−	1.27989i
$39$	−1.03413	+	1.79117i	−0.165593	+	0.286816i
$40$	−7.10351	−	12.3036i	−1.12316	−	1.94538i
$41$	−0.885683			−0.138320			−0.0691602	−	0.997606i	$-0.522032\pi$
$41$	−0.885683			−0.138320			−0.0691602	+	0.997606i	$0.522032\pi$
$42$	−1.88935	+	6.38512i	−0.291533	+	0.985246i
$43$	9.94532			1.51665			0.758324	−	0.651878i	$-0.226019\pi$
$43$	9.94532			1.51665			0.758324	+	0.651878i	$0.226019\pi$
$44$	−2.70540	−	4.68590i	−0.407855	−	0.706426i
$45$	−1.20917	+	2.09434i	−0.180252	+	0.312206i
$46$	1.25839	−	2.17960i	0.185540	−	0.321364i
$47$	2.84595	+	4.92934i	0.415125	+	0.719018i	0.995442	−	0.0953732i	$-0.0304044\pi$
$47$	2.84595	+	4.92934i	0.415125	+	0.719018i	−0.580316	+	0.814391i	$0.697071\pi$
$48$	6.11694			0.882904
$49$	−5.87290	−	3.80907i	−0.838986	−	0.544153i
$50$	2.13516			0.301958
$51$	1.65514	+	2.86679i	0.231766	+	0.401430i
$52$	−4.48213	+	7.76328i	−0.621560	+	1.07657i
$53$	1.47101	−	2.54786i	0.202058	−	0.349975i	−0.747133	−	0.664674i	$-0.768570\pi$
$53$	1.47101	−	2.54786i	0.202058	−	0.349975i	0.949192	+	0.314699i	$0.101904\pi$
$54$	−1.25839	−	2.17960i	−0.171246	−	0.296606i
$55$	3.01905			0.407088
$56$	−4.41013	+	14.9042i	−0.589328	+	1.99166i
$57$	−3.61984			−0.479459
$58$	−5.38350	−	9.32449i	−0.706888	−	1.22437i
$59$	−1.01222	+	1.75322i	−0.131780	+	0.228249i	−0.924363	−	0.381515i	$-0.875403\pi$
$59$	−1.01222	+	1.75322i	−0.131780	+	0.228249i	0.792583	+	0.609764i	$0.208736\pi$
$60$	−5.24079	+	9.07732i	−0.676584	+	1.17188i
$61$	3.69246	+	6.39553i	0.472771	+	0.818863i	0.999514	−	0.0311612i	$-0.00992052\pi$
$61$	3.69246	+	6.39553i	0.472771	+	0.818863i	−0.526744	+	0.850024i	$0.676587\pi$
$62$	−20.0775			−2.54984
$63$	2.57247	−	0.618384i	0.324101	−	0.0779090i
$64$	−3.05862			−0.382328
$65$	−2.50088	−	4.33165i	−0.310196	−	0.537275i
$66$	−1.57097	+	2.72100i	−0.193373	+	0.334932i
$67$	−4.14189	+	7.17396i	−0.506012	+	0.876439i	0.493964	+	0.869483i	$0.335548\pi$
$67$	−4.14189	+	7.17396i	−0.506012	+	0.876439i	−0.999976	+	0.00695624i	$0.997786\pi$
$68$	7.17372	+	12.4252i	0.869941	+	1.50678i
$69$	−1.00000			−0.120386
$70$	−11.0881	−	11.6776i	−1.32528	−	1.39575i
$71$	−8.27631			−0.982218			−0.491109	−	0.871098i	$-0.663408\pi$
$71$	−8.27631			−0.982218			−0.491109	+	0.871098i	$0.663408\pi$
$72$	−2.93735	−	5.08764i	−0.346170	−	0.599584i
$73$	5.99365	−	10.3813i	0.701504	−	1.21504i	−0.266435	−	0.963853i	$-0.585846\pi$
$73$	5.99365	−	10.3813i	0.701504	−	1.21504i	0.967939	−	0.251187i	$-0.0808210\pi$
$74$	−6.40743	+	11.0980i	−0.744848	+	1.29011i
$75$	−0.424185	−	0.734710i	−0.0489807	−	0.0848370i
$76$	−15.6891			−1.79967
$77$	−2.27429	−	2.39521i	−0.259180	−	0.272960i
$78$	5.20537			0.589392
$79$	7.61124	+	13.1831i	0.856332	+	1.48321i	0.875404	+	0.483392i	$0.160596\pi$
$79$	7.61124	+	13.1831i	0.856332	+	1.48321i	−0.0190719	+	0.999818i	$0.506071\pi$
$80$	−7.39642	+	12.8110i	−0.826945	+	1.43231i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.11454	+	1.93043i	0.123080	+	0.213181i
$83$	15.7586			1.72973			0.864866	−	0.502003i	$-0.167403\pi$
$83$	15.7586			1.72973			0.864866	+	0.502003i	$0.167403\pi$
$84$	11.1496	−	2.68020i	1.21652	−	0.292434i
$85$	−8.00538			−0.868305
$86$	−12.5151	−	21.6768i	−1.34954	−	2.33747i
$87$	−2.13904	+	3.70492i	−0.229329	+	0.397209i
$88$	−3.66698	+	6.35139i	−0.390901	+	0.677060i
$89$	8.13322	+	14.0871i	0.862119	+	1.49323i	0.869879	+	0.493264i	$0.164196\pi$
$89$	8.13322	+	14.0871i	0.862119	+	1.49323i	−0.00776025	+	0.999970i	$0.502470\pi$
$90$	6.08644			0.641567
$91$	−1.55264	+	5.24721i	−0.162761	+	0.550057i
$92$	−4.33421			−0.451872
$93$	3.98872	+	6.90866i	0.413611	+	0.716395i
$94$	7.16266	−	12.4061i	0.738772	−	1.27959i
$95$	4.37700	−	7.58118i	0.449070	−	0.777813i
$96$	−1.82281	−	3.15721i	−0.186040	−	0.322231i
$97$	16.6972			1.69534			0.847671	−	0.530522i	$-0.178004\pi$
$97$	16.6972			1.69534			0.847671	+	0.530522i	$0.178004\pi$
$98$	−0.911833	+	17.5939i	−0.0921091	+	1.77725i
$99$	1.24840			0.125469
$100$	−1.83851	−	3.18439i	−0.183851	−	0.318439i
$101$	4.52907	−	7.84457i	0.450659	−	0.780564i	−0.547768	−	0.836630i	$-0.684522\pi$
$101$	4.52907	−	7.84457i	0.450659	−	0.780564i	0.998427	+	0.0560661i	$0.0178558\pi$
$102$	4.16563	−	7.21508i	0.412459	−	0.714400i
$103$	−3.85379	−	6.67496i	−0.379725	−	0.657703i	0.611297	−	0.791401i	$-0.290648\pi$
$103$	−3.85379	−	6.67496i	−0.379725	−	0.657703i	−0.991022	+	0.133698i	$0.957315\pi$
$104$	12.1504			1.19145
$105$	−1.81545	+	6.13537i	−0.177169	+	0.598751i
$106$	−7.40442			−0.719181
$107$	−7.40937	−	12.8334i	−0.716291	−	1.24065i	−0.962459	−	0.271425i	$-0.912505\pi$
$107$	−7.40937	−	12.8334i	−0.716291	−	1.24065i	0.246168	−	0.969227i	$-0.420828\pi$
$108$	−2.16710	+	3.75353i	−0.208530	+	0.361184i
$109$	2.02465	−	3.50679i	0.193926	−	0.335889i	−0.752622	−	0.658453i	$-0.771211\pi$
$109$	2.02465	−	3.50679i	0.193926	−	0.335889i	0.946548	+	0.322563i	$0.104545\pi$
$110$	−3.79915	−	6.58031i	−0.362234	−	0.627408i
$111$	5.09175			0.483288
$112$	15.7356	−	3.78262i	1.48688	−	0.357424i
$113$	3.97551			0.373984			0.186992	−	0.982361i	$-0.440126\pi$
$113$	3.97551			0.373984			0.186992	+	0.982361i	$0.440126\pi$
$114$	4.55517	+	7.88979i	0.426631	+	0.738947i
$115$	1.20917	−	2.09434i	0.112756	−	0.195299i
$116$	−9.27103	+	16.0579i	−0.860794	+	1.49094i
$117$	−1.03413	−	1.79117i	−0.0956054	−	0.165593i
$118$	5.09508			0.469040
$119$	6.03057	+	6.35121i	0.552821	+	0.582214i
$120$	14.2070			1.29692
$121$	4.72075	+	8.17659i	0.429159	+	0.743326i
$122$	9.29312	−	16.0962i	0.841360	−	1.45728i
$123$	0.442841	−	0.767024i	0.0399297	−	0.0691602i
$124$	17.2879	+	29.9436i	1.55250	+	2.68901i
$125$	−10.0401			−0.898010
$126$	−4.58501	−	4.82879i	−0.408465	−	0.430182i
$127$	4.89271			0.434158			0.217079	−	0.976154i	$-0.430347\pi$
$127$	4.89271			0.434158			0.217079	+	0.976154i	$0.430347\pi$
$128$	7.49457	+	12.9810i	0.662433	+	1.14737i
$129$	−4.97266	+	8.61290i	−0.437818	+	0.758324i
$130$	−6.29417	+	10.9018i	−0.552036	+	0.956154i
$131$	0.763003	+	1.32156i	0.0666639	+	0.115465i	0.897431	−	0.441155i	$-0.145431\pi$
$131$	0.763003	+	1.32156i	0.0666639	+	0.115465i	−0.830767	+	0.556620i	$0.812098\pi$
$132$	5.41081			0.470950
$133$	−9.31192	+	2.23845i	−0.807446	+	0.194098i
$134$	20.8485			1.80103
$135$	−1.20917	−	2.09434i	−0.104069	−	0.180252i
$136$	9.72344	−	16.8415i	0.833779	−	1.44415i
$137$	−7.04942	+	12.2100i	−0.602273	+	1.04317i	0.390203	+	0.920729i	$0.372405\pi$
$137$	−7.04942	+	12.2100i	−0.602273	+	1.04317i	−0.992476	+	0.122438i	$0.960929\pi$
$138$	1.25839	+	2.17960i	0.107121	+	0.185540i
$139$	2.76556			0.234572			0.117286	−	0.993098i	$-0.462581\pi$
$139$	2.76556			0.234572			0.117286	+	0.993098i	$0.462581\pi$
$140$	−7.86852	+	26.5920i	−0.665011	+	2.24743i
$141$	−5.69191			−0.479345
$142$	10.4148	+	18.0390i	0.873995	+	1.51380i
$143$	−1.29100	+	2.23608i	−0.107959	+	0.186991i
$144$	−3.05847	+	5.29743i	−0.254873	+	0.441452i
$145$	−5.17292	−	8.95976i	−0.429588	−	0.744068i
$146$	−30.1695			−2.49684
$147$	6.23520	−	3.18155i	0.514271	−	0.262410i
$148$	22.0687			1.81404
$149$	3.51575	+	6.08946i	0.288021	+	0.498868i	0.973337	−	0.229378i	$-0.0736692\pi$
$149$	3.51575	+	6.08946i	0.288021	+	0.498868i	−0.685316	+	0.728246i	$0.740336\pi$
$150$	−1.06758	+	1.84911i	−0.0871677	+	0.150979i
$151$	−11.5176	+	19.9490i	−0.937287	+	1.62343i	−0.166783	+	0.985994i	$0.553338\pi$
$151$	−11.5176	+	19.9490i	−0.937287	+	1.62343i	−0.770504	+	0.637435i	$0.779995\pi$
$152$	10.6327	+	18.4164i	0.862428	+	1.49377i
$153$	−3.31028			−0.267620
$154$	−2.35865	+	7.97116i	−0.190066	+	0.642335i
$155$	−19.2922			−1.54958
$156$	−4.48213	−	7.76328i	−0.358858	−	0.621560i
$157$	9.12339	−	15.8022i	0.728126	−	1.26115i	−0.229548	−	0.973297i	$-0.573725\pi$
$157$	9.12339	−	15.8022i	0.728126	−	1.26115i	0.957674	−	0.287854i	$-0.0929417\pi$
$158$	19.1559	−	33.1789i	1.52396	−	2.63957i
$159$	1.47101	+	2.54786i	0.116658	+	0.202058i
$160$	8.81637			0.696995
$161$	−2.57247	+	0.618384i	−0.202739	+	0.0487355i
$162$	2.51679			0.197737
$163$	−2.52697	−	4.37685i	−0.197928	−	0.342821i	0.749929	−	0.661519i	$-0.230088\pi$
$163$	−2.52697	−	4.37685i	−0.197928	−	0.342821i	−0.947856	+	0.318698i	$0.896755\pi$
$164$	1.91937	−	3.32444i	0.149877	−	0.259595i
$165$	−1.50952	+	2.61457i	−0.117516	+	0.203544i
$166$	−19.8305	−	34.3475i	−1.53915	−	2.66588i
$167$	19.3192			1.49497			0.747483	−	0.664281i	$-0.231262\pi$
$167$	19.3192			1.49497			0.747483	+	0.664281i	$0.231262\pi$
$168$	−10.7024	−	11.2714i	−0.825705	−	0.869606i
$169$	−8.72230			−0.670946
$170$	10.0739	+	17.4485i	0.772634	+	1.33824i
$171$	1.80992	−	3.13487i	0.138408	−	0.239729i
$172$	−21.5525	+	37.3301i	−1.64337	+	2.84639i
$173$	−4.72351	−	8.18136i	−0.359122	−	0.622017i	0.628692	−	0.777654i	$-0.283590\pi$
$173$	−4.72351	−	8.18136i	−0.359122	−	0.622017i	−0.987814	+	0.155637i	$0.950257\pi$
$174$	10.7670			0.816244
$175$	−1.54554	−	1.62771i	−0.116832	−	0.123043i
$176$	7.63636			0.575613
$177$	−1.01222	−	1.75322i	−0.0760832	−	0.131780i
$178$	20.4696	−	35.4543i	1.53426	−	2.65741i
$179$	8.13253	−	14.0859i	0.607854	−	1.05283i	−0.383740	−	0.923441i	$-0.625364\pi$
$179$	8.13253	−	14.0859i	0.607854	−	1.05283i	0.991594	−	0.129392i	$-0.0413026\pi$
$180$	−5.24079	−	9.07732i	−0.390626	−	0.676584i
$181$	−0.386268			−0.0287110			−0.0143555	−	0.999897i	$-0.504570\pi$
$181$	−0.386268			−0.0287110			−0.0143555	+	0.999897i	$0.504570\pi$
$182$	13.3906	−	3.21891i	0.992581	−	0.238602i
$183$	−7.38492			−0.545909
$184$	2.93735	+	5.08764i	0.216544	+	0.375066i
$185$	−6.15680	+	10.6639i	−0.452657	+	0.784025i
$186$	10.0387	−	17.3876i	0.736077	−	1.27492i
$187$	2.06627	+	3.57888i	0.151101	+	0.261714i
$188$	−24.6699			−1.79924
$189$	−0.750699	+	2.53702i	−0.0546053	+	0.184541i
$190$	−22.0319			−1.59836
$191$	−10.1987	−	17.6646i	−0.737950	−	1.27817i	−0.953417	−	0.301656i	$-0.902460\pi$
$191$	−10.1987	−	17.6646i	−0.737950	−	1.27817i	0.215466	−	0.976511i	$-0.430873\pi$
$192$	1.52931	−	2.64884i	0.110369	−	0.191164i
$193$	−12.5098	+	21.6675i	−0.900472	+	1.55966i	−0.0735890	+	0.997289i	$0.523445\pi$
$193$	−12.5098	+	21.6675i	−0.900472	+	1.55966i	−0.826883	+	0.562374i	$0.809888\pi$
$194$	−21.0116	−	36.3932i	−1.50855	−	2.61288i
$195$	5.00176			0.358183
$196$	27.0247	−	13.7895i	1.93033	−	0.984963i
$197$	−24.5131			−1.74649			−0.873243	−	0.487285i	$-0.837987\pi$
$197$	−24.5131			−1.74649			−0.873243	+	0.487285i	$0.837987\pi$
$198$	−1.57097	−	2.72100i	−0.111644	−	0.193373i
$199$	−6.90736	+	11.9639i	−0.489650	+	0.848098i	−0.999929	−	0.0119105i	$-0.996209\pi$
$199$	−6.90736	+	11.9639i	−0.489650	+	0.848098i	0.510279	+	0.860009i	$0.329542\pi$
$200$	−2.49196	+	4.31620i	−0.176208	+	0.305201i
$201$	−4.14189	−	7.17396i	−0.292146	−	0.506012i
$202$	−22.7974			−1.60402
$203$	−3.21155	+	10.8535i	−0.225406	+	0.761769i
$204$	−14.3474			−1.00452
$205$	1.07094	+	1.85492i	0.0747978	+	0.129554i
$206$	−9.69916	+	16.7994i	−0.675772	+	1.17047i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	−6.32571	−	10.9565i	−0.438609	−	0.759693i
$209$	−4.51899			−0.312585
$210$	15.6572	−	3.76376i	1.08045	−	0.259724i
$211$	−11.2182			−0.772296			−0.386148	−	0.922437i	$-0.626195\pi$
$211$	−11.2182			−0.772296			−0.386148	+	0.922437i	$0.626195\pi$
$212$	6.37565	+	11.0430i	0.437882	+	0.758433i
$213$	4.13816	−	7.16750i	0.283542	−	0.491109i
$214$	−18.6478	+	32.2989i	−1.27474	+	2.20791i
$215$	−12.0256	−	20.8289i	−0.820138	−	1.42052i
$216$	5.87470			0.399723
$217$	14.5331	+	15.3058i	0.986569	+	1.03902i
$218$	−10.1912			−0.690235
$219$	5.99365	+	10.3813i	0.405013	+	0.701504i
$220$	−6.54259	+	11.3321i	−0.441101	+	0.764010i
$221$	3.42326	−	5.92926i	0.230273	−	0.398845i
$222$	−6.40743	−	11.0980i	−0.430038	−	0.744848i
$223$	21.3084			1.42691			0.713457	−	0.700699i	$-0.247128\pi$
$223$	21.3084			1.42691			0.713457	+	0.700699i	$0.247128\pi$
$224$	−6.64150	−	6.99462i	−0.443754	−	0.467348i
$225$	0.848370			0.0565580
$226$	−5.00275	−	8.66502i	−0.332778	−	0.576388i
$227$	2.18050	−	3.77674i	0.144725	−	0.250671i	−0.784545	−	0.620071i	$-0.787104\pi$
$227$	2.18050	−	3.77674i	0.144725	−	0.250671i	0.929270	+	0.369401i	$0.120437\pi$
$228$	7.84456	−	13.5872i	0.519519	−	0.899833i
$229$	−5.11309	−	8.85614i	−0.337883	−	0.585230i	0.646152	−	0.763209i	$-0.276377\pi$
$229$	−5.11309	−	8.85614i	−0.337883	−	0.585230i	−0.984034	+	0.177979i	$0.943044\pi$
$230$	−6.08644			−0.401328
$231$	3.21146	−	0.771988i	0.211299	−	0.0507931i
$232$	25.1324			1.65002
$233$	−2.18315	−	3.78133i	−0.143023	−	0.247723i	0.785611	−	0.618721i	$-0.212349\pi$
$233$	−2.18315	−	3.78133i	−0.143023	−	0.247723i	−0.928634	+	0.370998i	$0.879016\pi$
$234$	−2.60268	+	4.50798i	−0.170143	+	0.294696i
$235$	6.88249	−	11.9208i	0.448964	−	0.777628i
$236$	−4.38717	−	7.59881i	−0.285581	−	0.494640i
$237$	−15.2225			−0.988807
$238$	6.25427	−	21.1365i	0.405404	−	1.37008i
$239$	−13.5057			−0.873613			−0.436807	−	0.899555i	$-0.643891\pi$
$239$	−13.5057			−0.873613			−0.436807	+	0.899555i	$0.643891\pi$
$240$	−7.39642	−	12.8110i	−0.477437	−	0.826945i
$241$	2.60192	−	4.50666i	0.167604	−	0.290299i	−0.769973	−	0.638077i	$-0.779730\pi$
$241$	2.60192	−	4.50666i	0.167604	−	0.290299i	0.937577	+	0.347778i	$0.113064\pi$
$242$	11.8811	−	20.5787i	0.763747	−	1.32285i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−32.0078			−2.04909
$245$	−0.876167	+	16.9057i	−0.0559762	+	1.08007i
$246$	−2.22907			−0.142120
$247$	3.74338	+	6.48373i	0.238186	+	0.412550i
$248$	23.4325	−	40.5863i	1.48797	−	2.57723i
$249$	−7.87930	+	13.6474i	−0.499331	+	0.864866i
$250$	12.6343	+	21.8833i	0.799065	+	1.38402i
$251$	−17.4948			−1.10426			−0.552130	−	0.833758i	$-0.686185\pi$
$251$	−17.4948			−1.10426			−0.552130	+	0.833758i	$0.686185\pi$
$252$	−3.25368	+	10.9960i	−0.204963	+	0.692680i
$253$	−1.24840			−0.0784860
$254$	−6.15696	−	10.6642i	−0.386322	−	0.669129i
$255$	4.00269	−	6.93286i	0.250658	−	0.434153i
$256$	15.8036	−	27.3727i	0.987726	−	1.71079i
$257$	−9.37661	−	16.2408i	−0.584897	−	1.01307i	−0.994888	−	0.100982i	$-0.967802\pi$
$257$	−9.37661	−	16.2408i	−0.584897	−	1.01307i	0.409992	−	0.912089i	$-0.365532\pi$
$258$	25.0302			1.55831
$259$	13.0984	−	3.14866i	0.813894	−	0.195648i
$260$	21.6787			1.34445
$261$	−2.13904	−	3.70492i	−0.132403	−	0.229329i
$262$	1.92032	−	3.32608i	0.118637	−	0.205486i
$263$	−0.362446	+	0.627776i	−0.0223494	+	0.0387103i	−0.876984	−	0.480520i	$-0.840448\pi$
$263$	−0.362446	+	0.627776i	−0.0223494	+	0.0387103i	0.854634	+	0.519230i	$0.173781\pi$
$264$	−3.66698	−	6.35139i	−0.225687	−	0.390901i
$265$	−7.11479			−0.437058
$266$	16.5970	+	17.4794i	1.01763	+	1.07173i
$267$	−16.2664			−0.995490
$268$	−17.9518	−	31.0934i	−1.09658	−	1.89933i
$269$	−5.83934	+	10.1140i	−0.356031	+	0.616664i	−0.987294	−	0.158905i	$-0.949204\pi$
$269$	−5.83934	+	10.1140i	−0.356031	+	0.616664i	0.631263	+	0.775569i	$0.282537\pi$
$270$	−3.04322	+	5.27101i	−0.185205	+	0.320784i
$271$	6.68064	+	11.5712i	0.405820	+	0.702900i	0.994417	−	0.105526i	$-0.0336527\pi$
$271$	6.68064	+	11.5712i	0.405820	+	0.702900i	−0.588597	+	0.808427i	$0.700319\pi$
$272$	−20.2488			−1.22776
$273$	−3.76790	−	3.96823i	−0.228043	−	0.240168i
$274$	35.4838			2.14365
$275$	−0.529551	−	0.917209i	−0.0319331	−	0.0553098i
$276$	2.16710	−	3.75353i	0.130444	−	0.225936i
$277$	10.2472	−	17.7487i	0.615696	−	1.06642i	−0.374566	−	0.927200i	$-0.622208\pi$
$277$	10.2472	−	17.7487i	0.615696	−	1.06642i	0.990262	−	0.139217i	$-0.0444584\pi$
$278$	−3.48016	−	6.02782i	−0.208726	−	0.361525i
$279$	−7.97744			−0.477597
$280$	36.5471	−	8.78539i	2.18411	−	0.525028i
$281$	−7.39242			−0.440995			−0.220497	−	0.975388i	$-0.570768\pi$
$281$	−7.39242			−0.440995			−0.220497	+	0.975388i	$0.570768\pi$
$282$	7.16266	+	12.4061i	0.426530	+	0.738772i
$283$	2.71862	−	4.70879i	0.161605	−	0.279909i	−0.773839	−	0.633382i	$-0.781666\pi$
$283$	2.71862	−	4.70879i	0.161605	−	0.279909i	0.935445	+	0.353473i	$0.114999\pi$
$284$	17.9356	−	31.0654i	1.06428	−	1.84339i
$285$	4.37700	+	7.58118i	0.259271	+	0.449070i
$286$	6.49836			0.384256
$287$	0.664881	−	2.24699i	0.0392467	−	0.132636i
$288$	3.64563			0.214821
$289$	3.02103	+	5.23257i	0.177708	+	0.307799i
$290$	−13.0191	+	22.5498i	−0.764510	+	1.32417i
$291$	−8.34859	+	14.4602i	−0.489403	+	0.847671i
$292$	25.9777	+	44.9947i	1.52023	+	2.63312i
$293$	22.0096			1.28582			0.642908	−	0.765943i	$-0.277728\pi$
$293$	22.0096			1.28582			0.642908	+	0.765943i	$0.277728\pi$
$294$	−14.7808	−	9.58661i	−0.862036	−	0.559103i
$295$	4.89579			0.285044
$296$	−14.9563	−	25.9050i	−0.869315	−	1.50570i
$297$	−0.624198	+	1.08114i	−0.0362196	+	0.0627343i
$298$	8.84839	−	15.3259i	0.512573	−	0.887803i
$299$	1.03413	+	1.79117i	0.0598053	+	0.103586i
$300$	3.67701			0.212292
$301$	−7.46594	+	25.2314i	−0.430330	+	1.45432i
$302$	57.9745			3.33606
$303$	4.52907	+	7.84457i	0.260188	+	0.450659i
$304$	11.0712	−	19.1758i	0.634975	−	1.09981i
$305$	8.92962	−	15.4666i	0.511309	−	0.885612i
$306$	4.16563	+	7.21508i	0.238133	+	0.412459i
$307$	−0.129089			−0.00736751			−0.00368375	−	0.999993i	$-0.501173\pi$
$307$	−0.129089			−0.00736751			−0.00368375	+	0.999993i	$0.501173\pi$
$308$	13.9191	−	3.34596i	0.793117	−	0.190654i
$309$	7.70758			0.438469
$310$	24.2771	+	42.0492i	1.37885	+	2.38823i
$311$	3.96738	−	6.87171i	0.224970	−	0.389659i	−0.731341	−	0.682012i	$-0.761105\pi$
$311$	3.96738	−	6.87171i	0.224970	−	0.389659i	0.956310	+	0.292354i	$0.0944384\pi$
$312$	−6.07520	+	10.5226i	−0.343941	+	0.595723i
$313$	4.84122	+	8.38524i	0.273642	+	0.473962i	0.969792	−	0.243935i	$-0.0784384\pi$
$313$	4.84122	+	8.38524i	0.273642	+	0.473962i	−0.696150	+	0.717897i	$0.745105\pi$
$314$	−45.9232			−2.59160
$315$	−4.40566	−	4.63991i	−0.248231	−	0.261429i
$316$	−65.9774			−3.71152
$317$	8.90270	+	15.4199i	0.500025	+	0.866069i	1.00000		2.92970e-5i	$9.32551e-6\pi$
$317$	8.90270	+	15.4199i	0.500025	+	0.866069i	−0.499975	+	0.866040i	$0.666657\pi$
$318$	3.70221	−	6.41242i	0.207610	−	0.359590i
$319$	−2.67037	+	4.62521i	−0.149512	+	0.258962i
$320$	3.69839	+	6.40581i	0.206747	+	0.358095i
$321$	14.8187			0.827102
$322$	4.58501	+	4.82879i	0.255512	+	0.269098i
$323$	11.9827			0.666733
$324$	−2.16710	−	3.75353i	−0.120395	−	0.208530i
$325$	−0.877325	+	1.51957i	−0.0486652	+	0.0842906i
$326$	−6.35985	+	11.0156i	−0.352240	+	0.610097i
$327$	2.02465	+	3.50679i	0.111963	+	0.193926i
$328$	−5.20312			−0.287294
$329$	−14.6423	+	3.51978i	−0.807254	+	0.194052i
$330$	7.59829			0.418272
$331$	−11.9088	−	20.6267i	−0.654568	−	1.13375i	−0.982002	−	0.188872i	$-0.939517\pi$
$331$	−11.9088	−	20.6267i	−0.654568	−	1.13375i	0.327433	−	0.944874i	$-0.393816\pi$
$332$	−34.1505	+	59.1505i	−1.87425	+	3.24630i
$333$	−2.54588	+	4.40959i	−0.139513	+	0.241644i
$334$	−24.3112	−	42.1082i	−1.33025	−	2.30406i
$335$	20.0330			1.09452
$336$	−4.59198	+	15.5188i	−0.250513	+	0.846619i
$337$	−4.59296			−0.250194			−0.125097	−	0.992144i	$-0.539924\pi$
$337$	−4.59296			−0.250194			−0.125097	+	0.992144i	$0.539924\pi$
$338$	10.9761	+	19.0111i	0.597020	+	1.03407i
$339$	−1.98775	+	3.44289i	−0.107960	+	0.186992i
$340$	17.3485	−	30.0485i	0.940854	−	1.62961i
$341$	4.97950	+	8.62475i	0.269655	+	0.467056i
$342$	−9.11035			−0.492631
$343$	14.0725	−	12.0402i	0.759841	−	0.650109i
$344$	58.4258			3.15011
$345$	1.20917	+	2.09434i	0.0650995	+	0.112756i
$346$	−11.8881	+	20.5907i	−0.639106	+	1.10696i
$347$	15.7541	−	27.2870i	0.845726	−	1.46484i	−0.0392631	−	0.999229i	$-0.512501\pi$
$347$	15.7541	−	27.2870i	0.845726	−	1.46484i	0.884989	−	0.465612i	$-0.154166\pi$
$348$	−9.27103	−	16.0579i	−0.496979	−	0.860794i
$349$	−31.4878			−1.68551			−0.842753	−	0.538300i	$-0.819067\pi$
$349$	−31.4878			−1.68551			−0.842753	+	0.538300i	$0.819067\pi$
$350$	−1.60287	+	5.41695i	−0.0856768	+	0.289548i
$351$	2.06826			0.110396
$352$	−2.27559	−	3.94144i	−0.121290	−	0.210080i
$353$	−17.4569	+	30.2363i	−0.929139	+	1.60932i	−0.144373	+	0.989523i	$0.546117\pi$
$353$	−17.4569	+	30.2363i	−0.929139	+	1.60932i	−0.784766	+	0.619793i	$0.787217\pi$
$354$	−2.54754	+	4.41247i	−0.135400	+	0.234520i
$355$	10.0075	+	17.3334i	0.531141	+	0.919964i
$356$	−70.5021			−3.73660
$357$	−8.51559	+	2.04702i	−0.450693	+	0.108340i
$358$	−40.9356			−2.16352
$359$	−8.06051	−	13.9612i	−0.425417	−	0.736844i	0.571042	−	0.820921i	$-0.306539\pi$
$359$	−8.06051	−	13.9612i	−0.425417	−	0.736844i	−0.996459	+	0.0840765i	$0.973206\pi$
$360$	−7.10351	+	12.3036i	−0.374388	+	0.648459i
$361$	2.94839	−	5.10677i	0.155179	−	0.268777i
$362$	0.486076	+	0.841909i	0.0255476	+	0.0442497i
$363$	−9.44151			−0.495551
$364$	−16.3308	−	17.1991i	−0.855969	−	0.901480i
$365$	−28.9894			−1.51737
$366$	9.29312	+	16.0962i	0.485759	+	0.841360i
$367$	9.00193	−	15.5918i	0.469897	−	0.813886i	−0.529510	−	0.848303i	$-0.677624\pi$
$367$	9.00193	−	15.5918i	0.469897	−	0.813886i	0.999408	+	0.0344178i	$0.0109577\pi$
$368$	3.05847	−	5.29743i	0.159434	−	0.276147i
$369$	0.442841	+	0.767024i	0.0230534	+	0.0399297i
$370$	30.9907			1.61113
$371$	5.35968	+	5.64465i	0.278261	+	0.293055i
$372$	−34.5759			−1.79268
$373$	−13.8817	−	24.0437i	−0.718765	−	1.24494i	−0.961489	−	0.274842i	$-0.911374\pi$
$373$	−13.8817	−	24.0437i	−0.718765	−	1.24494i	0.242724	−	0.970095i	$-0.421959\pi$
$374$	5.20036	−	9.00728i	0.268904	−	0.465755i
$375$	5.02003	−	8.69494i	0.259233	−	0.449005i
$376$	16.7191	+	28.9584i	0.862223	+	1.49341i
$377$	8.84817			0.455704
$378$	6.47435	−	1.55634i	0.333005	−	0.0800494i
$379$	8.91763			0.458068			0.229034	−	0.973418i	$-0.426443\pi$
$379$	8.91763			0.458068			0.229034	+	0.973418i	$0.426443\pi$
$380$	18.9708	+	32.8584i	0.973182	+	1.68560i
$381$	−2.44636	+	4.23722i	−0.125331	+	0.217079i
$382$	−25.6679	+	44.4581i	−1.31328	+	2.27467i
$383$	0.906931	+	1.57085i	0.0463420	+	0.0802667i	0.888266	−	0.459329i	$-0.151910\pi$
$383$	0.906931	+	1.57085i	0.0463420	+	0.0802667i	−0.841924	+	0.539596i	$0.818577\pi$
$384$	−14.9891			−0.764912
$385$	−2.26639	+	7.65937i	−0.115506	+	0.390358i
$386$	62.9687			3.20502
$387$	−4.97266	−	8.61290i	−0.252775	−	0.437818i
$388$	−36.1845	+	62.6735i	−1.83699	+	3.18176i
$389$	3.96318	−	6.86443i	0.200941	−	0.348040i	−0.747891	−	0.663822i	$-0.768933\pi$
$389$	3.96318	−	6.86443i	0.200941	−	0.348040i	0.948832	+	0.315781i	$0.102267\pi$
$390$	−6.29417	−	10.9018i	−0.318718	−	0.552036i
$391$	3.31028			0.167408
$392$	−34.5015	−	22.3771i	−1.74259	−	1.13022i
$393$	−1.52601			−0.0769768
$394$	30.8471	+	53.4287i	1.55405	+	2.69170i
$395$	18.4066	−	31.8811i	0.926136	−	1.60411i
$396$	−2.70540	+	4.68590i	−0.135952	+	0.235475i
$397$	−8.92440	−	15.4575i	−0.447903	−	0.775791i	0.550346	−	0.834936i	$-0.314496\pi$
$397$	−8.92440	−	15.4575i	−0.447903	−	0.775791i	−0.998249	+	0.0591458i	$0.981162\pi$
$398$	34.7687			1.74280
$399$	2.71741	−	9.18358i	0.136040	−	0.459754i
$400$	5.18943			0.259471
$401$	15.4801	+	26.8123i	0.773040	+	1.33894i	0.935890	+	0.352293i	$0.114598\pi$
$401$	15.4801	+	26.8123i	0.773040	+	1.33894i	−0.162850	+	0.986651i	$0.552069\pi$
$402$	−10.4242	+	18.0553i	−0.519914	+	0.900517i
$403$	8.24971	−	14.2889i	0.410947	−	0.711781i
$404$	19.6299	+	34.0000i	0.976625	+	1.69156i
$405$	2.41834			0.120168
$406$	27.6978	−	6.65813i	1.37462	−	0.330438i
$407$	6.35653			0.315081
$408$	9.72344	+	16.8415i	0.481382	+	0.833779i
$409$	0.813092	−	1.40832i	0.0402048	−	0.0696368i	−0.845223	−	0.534414i	$-0.820532\pi$
$409$	0.813092	−	1.40832i	0.0402048	−	0.0696368i	0.885428	+	0.464777i	$0.153866\pi$
$410$	2.69533	−	4.66845i	0.133113	−	0.230558i
$411$	−7.04942	−	12.2100i	−0.347722	−	0.602273i
$412$	33.4062			1.64581
$413$	−3.68807	−	3.88416i	−0.181478	−	0.191127i
$414$	−2.51679			−0.123693
$415$	−19.0548	−	33.0040i	−0.935365	−	1.62010i
$416$	−3.77005	+	6.52992i	−0.184842	+	0.320156i
$417$	−1.38278	+	2.39505i	−0.0677151	+	0.117286i
$418$	5.68666	+	9.84959i	0.278144	+	0.481759i
$419$	7.77197			0.379685			0.189843	−	0.981815i	$-0.439202\pi$
$419$	7.77197			0.379685			0.189843	+	0.981815i	$0.439202\pi$
$420$	−19.0951	−	20.1103i	−0.931743	−	0.981283i
$421$	24.1012			1.17462			0.587311	−	0.809362i	$-0.300187\pi$
$421$	24.1012			1.17462			0.587311	+	0.809362i	$0.300187\pi$
$422$	14.1170	+	24.4513i	0.687203	+	1.19027i
$423$	2.84595	−	4.92934i	0.138375	−	0.239673i
$424$	8.64173	−	14.9679i	0.419679	−	0.726906i
$425$	1.40417	+	2.43209i	0.0681123	+	0.117974i
$426$	−20.8297			−1.00920
$427$	−18.9975	+	4.56671i	−0.919352	+	0.220999i
$428$	64.2275			3.10455
$429$	−1.29100	−	2.23608i	−0.0623303	−	0.107959i
$430$	−30.2658	+	52.4219i	−1.45955	+	2.52801i
$431$	1.80922	−	3.13366i	0.0871469	−	0.150943i	−0.819157	−	0.573569i	$-0.805558\pi$
$431$	1.80922	−	3.13366i	0.0871469	−	0.150943i	0.906304	+	0.422626i	$0.138892\pi$
$432$	−3.05847	−	5.29743i	−0.147151	−	0.254873i
$433$	19.6817			0.945840			0.472920	−	0.881105i	$-0.343200\pi$
$433$	19.6817			0.945840			0.472920	+	0.881105i	$0.343200\pi$
$434$	15.0722	−	50.9369i	0.723487	−	2.44505i
$435$	10.3458			0.496045
$436$	8.77523	+	15.1992i	0.420257	+	0.727907i
$437$	−1.80992	+	3.13487i	−0.0865801	+	0.149961i
$438$	15.0847	−	26.1275i	0.720776	−	1.24842i
$439$	−16.4305	−	28.4584i	−0.784183	−	1.35824i	−0.929486	−	0.368857i	$-0.879749\pi$
$439$	−16.4305	−	28.4584i	−0.784183	−	1.35824i	0.145304	−	0.989387i	$-0.453584\pi$
$440$	17.7360			0.845530
$441$	−0.362301	+	6.99062i	−0.0172524	+	0.332887i
$442$	−17.2312			−0.819605
$443$	8.90420	+	15.4225i	0.423051	+	0.732746i	0.996236	−	0.0866797i	$-0.0276257\pi$
$443$	8.90420	+	15.4225i	0.423051	+	0.732746i	−0.573185	+	0.819426i	$0.694292\pi$
$444$	−11.0344	+	19.1121i	−0.523668	+	0.907019i
$445$	19.6689	−	34.0675i	0.932395	−	1.61495i
$446$	−26.8143	−	46.4437i	−1.26969	−	2.19917i
$447$	−7.03150			−0.332578
$448$	2.29610	−	7.75977i	0.108481	−	0.366615i
$449$	22.1041			1.04316			0.521578	−	0.853204i	$-0.325344\pi$
$449$	22.1041			1.04316			0.521578	+	0.853204i	$0.325344\pi$
$450$	−1.06758	−	1.84911i	−0.0503263	−	0.0871677i
$451$	0.552841	−	0.957549i	0.0260323	−	0.0450892i
$452$	−8.61534	+	14.9222i	−0.405231	+	0.701881i
$453$	−11.5176	−	19.9490i	−0.541143	−	0.937287i
$454$	−10.9757			−0.515115
$455$	12.8669	−	3.09301i	0.603208	−	0.145002i
$456$	−21.2654			−0.995846
$457$	9.94948	+	17.2330i	0.465417	+	0.806126i	0.999220	−	0.0394830i	$-0.0125711\pi$
$457$	9.94948	+	17.2330i	0.465417	+	0.806126i	−0.533803	+	0.845609i	$0.679238\pi$
$458$	−12.8686	+	22.2890i	−0.601308	+	1.04150i
$459$	1.65514	−	2.86679i	0.0772553	−	0.133810i
$460$	5.24079	+	9.07732i	0.244353	+	0.423232i
$461$	3.00723			0.140061			0.0700303	−	0.997545i	$-0.477690\pi$
$461$	3.00723			0.140061			0.0700303	+	0.997545i	$0.477690\pi$
$462$	−5.72390	−	6.02824i	−0.266300	−	0.280459i
$463$	−17.9023			−0.831992			−0.415996	−	0.909366i	$-0.636567\pi$
$463$	−17.9023			−0.831992			−0.415996	+	0.909366i	$0.636567\pi$
$464$	−13.0844	−	22.6628i	−0.607426	−	1.05209i
$465$	9.64608	−	16.7075i	0.447326	−	0.774792i
$466$	−5.49452	+	9.51678i	−0.254529	+	0.440857i
$467$	3.96911	+	6.87471i	0.183669	+	0.318124i	0.943127	−	0.332432i	$-0.107869\pi$
$467$	3.96911	+	6.87471i	0.183669	+	0.318124i	−0.759458	+	0.650556i	$0.774536\pi$
$468$	8.96427			0.414373
$469$	−15.0911	−	15.8935i	−0.696844	−	0.733895i
$470$	−34.6435			−1.59798
$471$	9.12339	+	15.8022i	0.420384	+	0.728126i
$472$	−5.94649	+	10.2996i	−0.273709	+	0.474079i
$473$	−6.20785	+	10.7523i	−0.285437	+	0.494392i
$474$	19.1559	+	33.1789i	0.879858	+	1.52396i
$475$	−3.07096			−0.140905
$476$	−36.9083	+	8.87222i	−1.69169	+	0.406658i
$477$	−2.94202			−0.134706
$478$	16.9955	+	29.4371i	0.777357	+	1.34642i
$479$	−12.8732	+	22.2971i	−0.588193	+	1.01878i	0.406276	+	0.913750i	$0.366827\pi$
$479$	−12.8732	+	22.2971i	−0.588193	+	1.01878i	−0.994469	+	0.105029i	$0.966506\pi$
$480$	−4.40818	+	7.63520i	−0.201205	+	0.348497i
$481$	−5.26554	−	9.12018i	−0.240088	−	0.415844i
$482$	−13.0969			−0.596550
$483$	0.750699	−	2.53702i	0.0341580	−	0.115438i
$484$	−40.9215			−1.86007
$485$	−20.1897	−	34.9697i	−0.916769	−	1.58789i
$486$	−1.25839	+	2.17960i	−0.0570818	+	0.0988687i
$487$	14.1676	−	24.5390i	0.641994	−	1.11197i	−0.342993	−	0.939338i	$-0.611441\pi$
$487$	14.1676	−	24.5390i	0.641994	−	1.11197i	0.984987	−	0.172628i	$-0.0552259\pi$
$488$	21.6921	+	37.5718i	0.981954	+	1.70079i
$489$	5.05395			0.228547
$490$	37.9502	−	19.3643i	1.71442	−	0.874790i
$491$	−10.5092			−0.474272			−0.237136	−	0.971476i	$-0.576209\pi$
$491$	−10.5092			−0.474272			−0.237136	+	0.971476i	$0.576209\pi$
$492$	1.91937	+	3.32444i	0.0865317	+	0.149877i
$493$	7.08081	−	12.2643i	0.318904	−	0.552357i
$494$	9.42129	−	16.3181i	0.423884	−	0.734188i
$495$	−1.50952	−	2.61457i	−0.0678480	−	0.117516i
$496$	−48.7975			−2.19107
$497$	6.21302	−	20.9971i	0.278692	−	0.941850i
$498$	39.6610			1.77725
$499$	4.11374	+	7.12521i	0.184156	+	0.318968i	0.943292	−	0.331964i	$-0.107711\pi$
$499$	4.11374	+	7.12521i	0.184156	+	0.318968i	−0.759136	+	0.650933i	$0.774378\pi$
$500$	21.7578	−	37.6857i	0.973040	−	1.68536i
$501$	−9.65961	+	16.7309i	−0.431559	+	0.747483i
$502$	22.0153	+	38.1316i	0.982590	+	1.70190i
$503$	−1.55855			−0.0694922			−0.0347461	−	0.999396i	$-0.511062\pi$
$503$	−1.55855			−0.0694922			−0.0347461	+	0.999396i	$0.511062\pi$
$504$	15.1125	−	3.63282i	0.673164	−	0.161819i
$505$	−21.9056			−0.974788
$506$	1.57097	+	2.72100i	0.0698382	+	0.120963i
$507$	4.36115	−	7.55373i	0.193685	−	0.335473i
$508$	−10.6030	+	18.3650i	−0.470433	+	0.814814i
$509$	0.173736	+	0.300920i	0.00770071	+	0.0133380i	0.869850	−	0.493316i	$-0.164215\pi$
$509$	0.173736	+	0.300920i	0.00770071	+	0.0133380i	−0.862149	+	0.506654i	$0.830882\pi$
$510$	−20.1478			−0.892161
$511$	21.8381	+	22.9992i	0.966061	+	1.01743i
$512$	−49.5703			−2.19072
$513$	1.80992	+	3.13487i	0.0799098	+	0.138408i
$514$	−23.5989	+	40.8745i	−1.04090	+	1.80290i
$515$	−9.31977	+	16.1423i	−0.410678	+	0.711316i
$516$	−21.5525	−	37.3301i	−0.948798	−	1.64337i
$517$	−7.10576			−0.312511
$518$	−23.3457	−	24.5870i	−1.02575	−	1.08029i
$519$	9.44702			0.414678
$520$	−14.6919	−	25.4471i	−0.644283	−	1.11593i
$521$	0.969238	−	1.67877i	0.0424631	−	0.0735482i	−0.844013	−	0.536323i	$-0.819813\pi$
$521$	0.969238	−	1.67877i	0.0424631	−	0.0735482i	0.886476	+	0.462775i	$0.153146\pi$
$522$	−5.38350	+	9.32449i	−0.235629	+	0.408122i
$523$	20.2180	+	35.0186i	0.884070	+	1.53125i	0.846776	+	0.531950i	$0.178541\pi$
$523$	20.2180	+	35.0186i	0.884070	+	1.53125i	0.0372943	+	0.999304i	$0.488126\pi$
$524$	−6.61403			−0.288935
$525$	2.18241	−	0.524618i	0.0952480	−	0.0228962i
$526$	1.82440			0.0795476
$527$	−13.2038	−	22.8696i	−0.575165	−	0.996215i
$528$	−3.81818	+	6.61329i	−0.166165	+	0.287806i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	8.95320	+	15.5074i	0.388902	+	0.673599i
$531$	2.02444			0.0878533
$532$	11.7778	−	39.8036i	0.510633	−	1.72570i
$533$	−1.83182			−0.0793450
$534$	20.4696	+	35.4543i	0.885804	+	1.53426i
$535$	−17.9184	+	31.0356i	−0.774679	+	1.34178i
$536$	−24.3323	+	42.1449i	−1.05100	+	1.82038i
$537$	8.13253	+	14.0859i	0.350944	+	0.607854i
$538$	29.3927			1.26721
$539$	7.78400	−	3.97183i	0.335281	−	0.171079i
$540$	10.4816			0.451056
$541$	−11.7277	−	20.3130i	−0.504214	−	0.873323i	−0.999988	−	0.00487221i	$-0.998449\pi$
$541$	−11.7277	−	20.3130i	−0.504214	−	0.873323i	0.495775	−	0.868451i	$-0.334884\pi$
$542$	16.8137	−	29.1222i	0.722211	−	1.25091i
$543$	0.193134	−	0.334518i	0.00828816	−	0.0143555i
$544$	6.03402	+	10.4512i	0.258706	+	0.448093i
$545$	−9.79256			−0.419467
$546$	−3.90766	+	13.2061i	−0.167233	+	0.565169i
$547$	28.6726			1.22595			0.612976	−	0.790102i	$-0.289972\pi$
$547$	28.6726			1.22595			0.612976	+	0.790102i	$0.289972\pi$
$548$	−30.5537	−	52.9205i	−1.30519	−	2.26065i
$549$	3.69246	−	6.39553i	0.157590	−	0.272954i
$550$	−1.33277	+	2.30842i	−0.0568293	+	0.0984313i
$551$	7.74296	+	13.4112i	0.329861	+	0.571337i
$552$	−5.87470			−0.250044
$553$	−39.1594	+	9.41334i	−1.66523	+	0.400296i
$554$	−51.5801			−2.19143
$555$	−6.15680	−	10.6639i	−0.261342	−	0.452657i
$556$	−5.99326	+	10.3806i	−0.254171	+	0.440237i
$557$	−15.0660	+	26.0950i	−0.638365	+	1.10568i	0.347426	+	0.937707i	$0.387056\pi$
$557$	−15.0660	+	26.0950i	−0.638365	+	1.10568i	−0.985791	+	0.167974i	$0.946278\pi$
$558$	10.0387	+	17.3876i	0.424974	+	0.736077i
$559$	20.5695			0.869998
$560$	−26.9492	−	28.3820i	−1.13881	−	1.19936i
$561$	−4.13254			−0.174476
$562$	9.30256	+	16.1125i	0.392405	+	0.679665i
$563$	−11.8656	+	20.5518i	−0.500074	+	0.866154i	0.499926	+	0.866068i	$0.333361\pi$
$563$	−11.8656	+	20.5518i	−0.500074	+	0.866154i	−1.00000		8.59958e-5i	$0.999973\pi$
$564$	12.3350	−	21.3648i	0.519395	−	0.899619i
$565$	−4.80707	−	8.32608i	−0.202235	−	0.350281i
$566$	−13.6844			−0.575197
$567$	−1.82177	−	1.91863i	−0.0765072	−	0.0805750i
$568$	−48.6208			−2.04009
$569$	6.42535	+	11.1290i	0.269365	+	0.466553i	0.968698	−	0.248242i	$-0.0798529\pi$
$569$	6.42535	+	11.1290i	0.269365	+	0.466553i	−0.699333	+	0.714796i	$0.746520\pi$
$570$	11.0160	−	19.0802i	0.461408	−	0.799182i
$571$	−19.5128	+	33.7971i	−0.816584	+	1.41437i	0.0916005	+	0.995796i	$0.470802\pi$
$571$	−19.5128	+	33.7971i	−0.816584	+	1.41437i	−0.908185	+	0.418570i	$0.862532\pi$
$572$	−5.59548	−	9.69165i	−0.233959	−	0.405228i
$573$	20.3974			0.852112
$574$	−5.73422	+	1.37842i	−0.239342	+	0.0575342i
$575$	−0.848370			−0.0353795
$576$	1.52931	+	2.64884i	0.0637213	+	0.110369i
$577$	9.08285	−	15.7320i	0.378124	−	0.654930i	−0.612665	−	0.790342i	$-0.709903\pi$
$577$	9.08285	−	15.7320i	0.378124	−	0.654930i	0.990789	+	0.135413i	$0.0432360\pi$
$578$	7.60328	−	13.1693i	0.316255	−	0.547769i
$579$	−12.5098	−	21.6675i	−0.519888	−	0.900472i
$580$	44.8410			1.86192
$581$	−11.8300	+	39.9798i	−0.490790	+	1.65864i
$582$	42.0232			1.74192
$583$	1.83640	+	3.18074i	0.0760559	+	0.131733i
$584$	35.2109	−	60.9871i	1.45704	−	2.52366i
$585$	−2.50088	+	4.33165i	−0.103399	+	0.179092i
$586$	−27.6968	−	47.9722i	−1.14414	−	1.98171i
$587$	−7.81464			−0.322545			−0.161272	−	0.986910i	$-0.551560\pi$
$587$	−7.81464			−0.322545			−0.161272	+	0.986910i	$0.551560\pi$
$588$	−1.57029	+	30.2988i	−0.0647575	+	1.24950i
$589$	28.8770			1.18986
$590$	−6.16082	−	10.6709i	−0.253637	−	0.439312i
$591$	12.2565	−	21.2290i	0.504167	−	0.873243i
$592$	−15.5730	+	26.9732i	−0.640046	+	1.10859i
$593$	13.2055	+	22.8727i	0.542287	+	0.939268i	0.998772	+	0.0495372i	$0.0157746\pi$
$593$	13.2055	+	22.8727i	0.542287	+	0.939268i	−0.456486	+	0.889731i	$0.650892\pi$
$594$	3.14194			0.128916
$595$	6.00963	−	20.3098i	0.246371	−	0.832620i
$596$	−30.4760			−1.24834
$597$	−6.90736	−	11.9639i	−0.282699	−	0.489650i
$598$	2.60268	−	4.50798i	0.106432	−	0.184345i
$599$	−17.6973	+	30.6526i	−0.723091	+	1.25243i	0.236663	+	0.971592i	$0.423946\pi$
$599$	−17.6973	+	30.6526i	−0.723091	+	1.25243i	−0.959755	+	0.280839i	$0.909387\pi$
$600$	−2.49196	−	4.31620i	−0.101734	−	0.176208i
$601$	−25.3306			−1.03326			−0.516629	−	0.856210i	$-0.672813\pi$
$601$	−25.3306			−1.03326			−0.516629	+	0.856210i	$0.672813\pi$
$602$	64.3895	−	15.4783i	2.62432	−	0.630848i
$603$	8.28378			0.337341
$604$	−49.9196	−	86.4632i	−2.03120	−	3.51814i
$605$	11.4164	−	19.7738i	0.464142	−	0.803918i
$606$	11.3987	−	19.7431i	0.463040	−	0.802009i
$607$	−14.9968	−	25.9753i	−0.608703	−	1.05431i	−0.991454	−	0.130454i	$-0.958357\pi$
$607$	−14.9968	−	25.9753i	−0.608703	−	1.05431i	0.382751	−	0.923851i	$-0.374977\pi$
$608$	−13.1966			−0.535192
$609$	−7.79367	−	8.20805i	−0.315816	−	0.332607i
$610$	−44.9479			−1.81989
$611$	5.88617	+	10.1952i	0.238129	+	0.412452i
$612$	7.17372	−	12.4252i	0.289980	−	0.502261i
$613$	1.25506	−	2.17383i	0.0506916	−	0.0878004i	−0.839566	−	0.543257i	$-0.817191\pi$
$613$	1.25506	−	2.17383i	0.0506916	−	0.0878004i	0.890258	+	0.455457i	$0.150524\pi$
$614$	0.162445	+	0.281363i	0.00655574	+	0.0113549i
$615$	−2.14188			−0.0863690
$616$	−13.3608	−	14.0712i	−0.538321	−	0.566943i
$617$	10.5953			0.426550			0.213275	−	0.976992i	$-0.431587\pi$
$617$	10.5953			0.426550			0.213275	+	0.976992i	$0.431587\pi$
$618$	−9.69916	−	16.7994i	−0.390157	−	0.675772i
$619$	−0.0982746	+	0.170217i	−0.00394999	+	0.00684158i	−0.867994	−	0.496575i	$-0.834591\pi$
$619$	−0.0982746	+	0.170217i	−0.00394999	+	0.00684158i	0.864044	+	0.503417i	$0.167924\pi$
$620$	41.8081	−	72.4138i	1.67905	−	2.90821i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−19.9701			−0.800728
$623$	−41.8449	+	10.0589i	−1.67648	+	0.403001i
$624$	12.6514			0.506462
$625$	14.2611	+	24.7009i	0.570442	+	0.988035i
$626$	12.1843	−	21.1038i	0.486983	−	0.843479i
$627$	2.25949	−	3.91356i	0.0902355	−	0.156292i
$628$	39.5427	+	68.4899i	1.57792	+	2.73305i
$629$	−16.8551			−0.672058
$630$	−4.56909	+	15.4414i	−0.182037	+	0.615200i
$631$	18.3191			0.729270			0.364635	−	0.931150i	$-0.381194\pi$
$631$	18.3191			0.729270			0.364635	+	0.931150i	$0.381194\pi$
$632$	44.7138	+	77.4465i	1.77862	+	3.08066i
$633$	5.60912	−	9.71529i	0.222943	−	0.386148i
$634$	22.4062	−	38.8086i	0.889863	−	1.54129i
$635$	−5.91612	−	10.2470i	−0.234774	−	0.406641i
$636$	−12.7513			−0.505622
$637$	−12.1467	−	7.87815i	−0.481269	−	0.312144i
$638$	13.4415			0.532153
$639$	4.13816	+	7.16750i	0.163703	+	0.283542i
$640$	18.1244	−	31.3924i	0.716431	−	1.24089i
$641$	−10.7688	+	18.6520i	−0.425340	+	0.736711i	−0.996452	−	0.0841614i	$-0.973179\pi$
$641$	−10.7688	+	18.6520i	−0.425340	+	0.736711i	0.571112	+	0.820872i	$0.306512\pi$
$642$	−18.6478	−	32.2989i	−0.735970	−	1.27474i
$643$	−14.0708			−0.554897			−0.277449	−	0.960740i	$-0.589489\pi$
$643$	−14.0708			−0.554897			−0.277449	+	0.960740i	$0.589489\pi$
$644$	3.25368	−	10.9960i	0.128213	−	0.433301i
$645$	24.0512			0.947014
$646$	−15.0789	−	26.1174i	−0.593271	−	1.02758i
$647$	−15.6943	+	27.1833i	−0.617006	+	1.06869i	0.373023	+	0.927822i	$0.378321\pi$
$647$	−15.6943	+	27.1833i	−0.617006	+	1.06869i	−0.990029	+	0.140864i	$0.955012\pi$
$648$	−2.93735	+	5.08764i	−0.115390	+	0.199861i
$649$	−1.26365	−	2.18871i	−0.0496027	−	0.0859144i
$650$	4.41608			0.173213
$651$	−20.5217	+	4.93312i	−0.804310	+	0.193344i
$652$	21.9049			0.857861
$653$	−1.22959	−	2.12971i	−0.0481175	−	0.0833419i	0.840964	−	0.541092i	$-0.181989\pi$
$653$	−1.22959	−	2.12971i	−0.0481175	−	0.0833419i	−0.889081	+	0.457750i	$0.848656\pi$
$654$	5.09560	−	8.82583i	0.199254	−	0.345117i
$655$	1.84520	−	3.19598i	0.0720980	−	0.124877i
$656$	2.70883	+	4.69184i	0.105762	+	0.183185i
$657$	−11.9873			−0.467669
$658$	26.0974	+	27.4850i	1.01738	+	1.07148i
$659$	27.0472			1.05361			0.526805	−	0.849986i	$-0.323390\pi$
$659$	27.0472			1.05361			0.526805	+	0.849986i	$0.323390\pi$
$660$	−6.54259	−	11.3321i	−0.254670	−	0.441101i
$661$	22.4288	−	38.8478i	0.872378	−	1.51100i	0.0128488	−	0.999917i	$-0.495910\pi$
$661$	22.4288	−	38.8478i	0.872378	−	1.51100i	0.859530	−	0.511086i	$-0.170757\pi$
$662$	−29.9720	+	51.9130i	−1.16489	+	2.01765i
$663$	3.42326	+	5.92926i	0.132948	+	0.230273i
$664$	92.5771			3.59269
$665$	15.9478	+	16.7957i	0.618428	+	0.651309i
$666$	12.8149			0.496565
$667$	2.13904	+	3.70492i	0.0828239	+	0.143455i
$668$	−41.8667	+	72.5153i	−1.61987	+	2.80570i
$669$	−10.6542	+	18.4536i	−0.411915	+	0.713457i
$670$	−25.2094	−	43.6639i	−0.973923	−	1.68688i
$671$	−9.21930			−0.355907
$672$	9.37826	−	2.25440i	0.361774	−	0.0869652i
$673$	−40.8475			−1.57456			−0.787279	−	0.616598i	$-0.788511\pi$
$673$	−40.8475			−1.57456			−0.787279	+	0.616598i	$0.788511\pi$
$674$	5.77975	+	10.0108i	0.222627	+	0.385602i
$675$	−0.424185	+	0.734710i	−0.0163269	+	0.0282790i
$676$	18.9021	−	32.7394i	0.727005	−	1.25921i
$677$	−21.2579	−	36.8198i	−0.817009	−	1.41510i	−0.907876	−	0.419238i	$-0.862297\pi$
$677$	−21.2579	−	36.8198i	−0.817009	−	1.41510i	0.0908674	−	0.995863i	$-0.471036\pi$
$678$	10.0055			0.384259
$679$	−12.5346	+	42.3610i	−0.481032	+	1.62567i
$680$	−47.0292			−1.80349
$681$	2.18050	+	3.77674i	0.0835570	+	0.144725i
$682$	12.5323	−	21.7066i	0.479888	−	0.831190i
$683$	3.12178	−	5.40709i	0.119452	−	0.206896i	−0.800099	−	0.599868i	$-0.795220\pi$
$683$	3.12178	−	5.40709i	0.119452	−	0.206896i	0.919551	+	0.392972i	$0.128553\pi$
$684$	7.84456	+	13.5872i	0.299944	+	0.519519i
$685$	34.0958			1.30273
$686$	−43.9515	−	15.5210i	−1.67807	−	0.592596i
$687$	10.2262			0.390153
$688$	−30.4175	−	52.6846i	−1.15966	−	2.00858i
$689$	3.04243	−	5.26964i	0.115907	−	0.200757i
$690$	3.04322	−	5.27101i	0.115853	−	0.200664i
$691$	5.44381	+	9.42895i	0.207092	+	0.358694i	0.950797	−	0.309814i	$-0.100267\pi$
$691$	5.44381	+	9.42895i	0.207092	+	0.358694i	−0.743705	+	0.668508i	$0.766933\pi$
$692$	40.9454			1.55651
$693$	−0.937170	+	3.16720i	−0.0356001	+	0.120312i
$694$	−79.2995			−3.01017
$695$	−3.34403	−	5.79204i	−0.126846	−	0.219705i
$696$	−12.5662	+	21.7653i	−0.476321	+	0.825011i
$697$	−1.46593	+	2.53906i	−0.0555260	+	0.0961738i
$698$	39.6241	+	68.6309i	1.49979	+	2.59772i
$699$	4.36630			0.165149
$700$	9.45900	−	2.27380i	0.357517	−	0.0859417i
$701$	5.23763			0.197822			0.0989112	−	0.995096i	$-0.468464\pi$
$701$	5.23763			0.197822			0.0989112	+	0.995096i	$0.468464\pi$
$702$	−2.60268	−	4.50798i	−0.0982319	−	0.170143i
$703$	9.21566	−	15.9620i	0.347575	−	0.602018i
$704$	1.90919	−	3.30681i	0.0719551	−	0.124630i
$705$	6.88249	+	11.9208i	0.259209	+	0.448964i
$706$	87.8707			3.30706
$707$	16.5018	+	17.3792i	0.620616	+	0.653613i
$708$	8.77435			0.329760
$709$	10.4973	+	18.1818i	0.394234	+	0.682833i	0.993003	−	0.118088i	$-0.0376766\pi$
$709$	10.4973	+	18.1818i	0.394234	+	0.682833i	−0.598769	+	0.800922i	$0.704343\pi$
$710$	25.1867	−	43.6246i	0.945238	−	1.63720i
$711$	7.61124	−	13.1831i	0.285444	−	0.494403i
$712$	47.7802	+	82.7577i	1.79064	+	3.10148i
$713$	7.97744			0.298757
$714$	15.1776	+	15.9846i	0.568009	+	0.598210i
$715$	6.24417			0.233519
$716$	35.2481	+	61.0514i	1.31728	+	2.28160i
$717$	6.75287	−	11.6963i	0.252190	−	0.436807i
$718$	−20.2866	+	35.1374i	−0.757088	+	1.31131i
$719$	11.2422	+	19.4721i	0.419265	+	0.726188i	0.995866	−	0.0908381i	$-0.0289546\pi$
$719$	11.2422	+	19.4721i	0.419265	+	0.726188i	−0.576601	+	0.817026i	$0.695621\pi$
$720$	14.7928			0.551297
$721$	19.8275	−	4.76624i	0.738415	−	0.177504i
$722$	−14.8410			−0.552323
$723$	2.60192	+	4.50666i	0.0967664	+	0.167604i
$724$	0.837082	−	1.44987i	0.0311099	−	0.0538839i
$725$	−1.81469	+	3.14314i	−0.0673961	+	0.116733i
$726$	11.8811	+	20.5787i	0.440950	+	0.763747i
$727$	−20.7141			−0.768242			−0.384121	−	0.923283i	$-0.625496\pi$
$727$	−20.7141			−0.768242			−0.384121	+	0.923283i	$0.625496\pi$
$728$	−9.12130	+	30.8258i	−0.338058	+	1.14248i
$729$	1.00000			0.0370370
$730$	36.4800	+	63.1852i	1.35019	+	2.33859i
$731$	16.4609	−	28.5111i	0.608828	−	1.05452i
$732$	16.0039	−	27.7195i	0.591520	−	1.02454i
$733$	−6.14330	−	10.6405i	−0.226908	−	0.393016i	0.729982	−	0.683466i	$-0.239528\pi$
$733$	−6.14330	−	10.6405i	−0.226908	−	0.393016i	−0.956890	+	0.290450i	$0.906195\pi$
$734$	−45.3119			−1.67249
$735$	−14.2027	−	9.21163i	−0.523874	−	0.339776i
$736$	−3.64563			−0.134380
$737$	−5.17072	−	8.95594i	−0.190466	−	0.329896i
$738$	1.11454	−	1.93043i	0.0410266	−	0.0710602i
$739$	−5.47782	+	9.48786i	−0.201505	+	0.349016i	−0.949013	−	0.315236i	$-0.897916\pi$
$739$	−5.47782	+	9.48786i	−0.201505	+	0.349016i	0.747509	+	0.664252i	$0.231250\pi$
$740$	−26.6848	−	46.2195i	−0.980954	−	1.69906i
$741$	−7.48676			−0.275033
$742$	5.55849	−	18.7851i	0.204059	−	0.689624i
$743$	−38.8827			−1.42647			−0.713235	−	0.700925i	$-0.752771\pi$
$743$	−38.8827			−1.42647			−0.713235	+	0.700925i	$0.752771\pi$
$744$	23.4325	+	40.5863i	0.859078	+	1.48797i
$745$	8.50228	−	14.7264i	0.311499	−	0.539533i
$746$	−34.9372	+	60.5129i	−1.27914	+	2.21554i
$747$	−7.87930	−	13.6474i	−0.288289	−	0.499331i
$748$	−17.9113			−0.654901
$749$	38.1208	−	9.16367i	1.39290	−	0.334833i
$750$	−25.2687			−0.922681
$751$	0.210377	+	0.364383i	0.00767675	+	0.0132965i	0.869838	−	0.493337i	$-0.164223\pi$
$751$	0.210377	+	0.364383i	0.00767675	+	0.0132965i	−0.862162	+	0.506634i	$0.830890\pi$
$752$	17.4085	−	30.1525i	0.634824	−	1.09955i
$753$	8.74738	−	15.1509i	0.318772	−	0.552130i
$754$	−11.1345	−	19.2855i	−0.405494	−	0.702335i
$755$	55.7068			2.02738
$756$	−7.89593	−	8.31575i	−0.287172	−	0.302441i
$757$	31.5476			1.14662			0.573309	−	0.819339i	$-0.305660\pi$
$757$	31.5476			1.14662			0.573309	+	0.819339i	$0.305660\pi$
$758$	−11.2219	−	19.4369i	−0.407597	−	0.705979i
$759$	0.624198	−	1.08114i	0.0226570	−	0.0392430i
$760$	25.7135	−	44.5372i	0.932728	−	1.61553i
$761$	5.46626	+	9.46784i	0.198152	+	0.343209i	0.947929	−	0.318481i	$-0.103173\pi$
$761$	5.46626	+	9.46784i	0.198152	+	0.343209i	−0.749777	+	0.661690i	$0.769839\pi$
$762$	12.3139			0.446086
$763$	7.37688	+	7.76910i	0.267061	+	0.281260i
$764$	88.4064			3.19843
$765$	4.00269	+	6.93286i	0.144718	+	0.250658i
$766$	2.28255	−	3.95349i	0.0824719	−	0.142846i
$767$	−2.09354	+	3.62611i	−0.0755932	+	0.130931i
$768$	15.8036	+	27.3727i	0.570264	+	0.987726i
$769$	0.569674			0.0205430			0.0102715	−	0.999947i	$-0.496730\pi$
$769$	0.569674			0.0205430			0.0102715	+	0.999947i	$0.496730\pi$
$770$	19.5464	−	4.69866i	0.704403	−	0.169328i
$771$	18.7532			0.675381
$772$	−54.2199	−	93.9116i	−1.95142	−	3.37995i
$773$	−17.2897	+	29.9466i	−0.621867	+	1.07711i	0.367271	+	0.930114i	$0.380292\pi$
$773$	−17.2897	+	29.9466i	−0.621867	+	1.07711i	−0.989138	+	0.146991i	$0.953041\pi$
$774$	−12.5151	+	21.6768i	−0.449847	+	0.779157i
$775$	3.38391	+	5.86110i	0.121554	+	0.210537i
$776$	98.0909			3.52126
$777$	−3.82237	+	12.9179i	−0.137127	+	0.463426i
$778$	−19.9489			−0.715204
$779$	−1.60301	−	2.77650i	−0.0574339	−	0.0994784i
$780$	−10.8393	+	18.7743i	−0.388110	+	0.672226i
$781$	5.16606	−	8.94787i	0.184856	−	0.320180i
$782$	−4.16563	−	7.21508i	−0.148963	−	0.258011i
$783$	4.27807			0.152886
$784$	−2.21617	+	42.7612i	−0.0791490	+	1.52719i
$785$	−44.1269			−1.57496
$786$	1.92032	+	3.32608i	0.0684954	+	0.118637i
$787$	5.74231	−	9.94597i	0.204691	−	0.354535i	−0.745343	−	0.666681i	$-0.767714\pi$
$787$	5.74231	−	9.94597i	0.204691	−	0.354535i	0.950034	+	0.312146i	$0.101048\pi$
$788$	53.1224	−	92.0107i	1.89241	−	3.27775i
$789$	−0.362446	−	0.627776i	−0.0129034	−	0.0223494i
$790$	−92.6508			−3.29637
$791$	−2.98441	+	10.0859i	−0.106113	+	0.358614i
$792$	7.33395			0.260601
$793$	7.63696	+	13.2276i	0.271197	+	0.469726i
$794$	−22.4608	+	38.9033i	−0.797104	+	1.38062i
$795$	3.55740	−	6.16159i	0.126168	−	0.218529i
$796$	−29.9379	−	51.8540i	−1.06112	−	1.83792i
$797$	−16.1795			−0.573109			−0.286555	−	0.958064i	$-0.592510\pi$
$797$	−16.1795			−0.573109			−0.286555	+	0.958064i	$0.592510\pi$
$798$	−23.4361	+	5.63369i	−0.829629	+	0.199431i
$799$	18.8418			0.666575
$800$	−1.54642	−	2.67848i	−0.0546742	−	0.0946985i
$801$	8.13322	−	14.0871i	0.287373	−	0.497745i
$802$	38.9601	−	67.4809i	1.37573	−	2.38283i
$803$	7.48245	+	12.9600i	0.264050	+	0.457348i
$804$	35.9036			1.26622
$805$	4.40566	+	4.63991i	0.155279	+	0.163535i
$806$	−41.5255			−1.46267
$807$	−5.83934	−	10.1140i	−0.205555	−	0.356031i
$808$	26.6069	−	46.0845i	0.936027	−	1.62125i
$809$	17.1102	−	29.6358i	0.601564	−	1.04194i	−0.391021	−	0.920382i	$-0.627878\pi$
$809$	17.1102	−	29.6358i	0.601564	−	1.04194i	0.992584	−	0.121557i	$-0.0387887\pi$
$810$	−3.04322	−	5.27101i	−0.106928	−	0.185205i
$811$	16.6256			0.583804			0.291902	−	0.956448i	$-0.405712\pi$
$811$	16.6256			0.583804			0.291902	+	0.956448i	$0.405712\pi$
$812$	−33.7794	−	35.5754i	−1.18542	−	1.24845i
$813$	−13.3613			−0.468600
$814$	−7.99901	−	13.8547i	−0.280365	−	0.485606i
$815$	−6.11108	+	10.5847i	−0.214062	+	0.370766i
$816$	10.1244	−	17.5360i	0.354424	−	0.613881i
$817$	18.0002	+	31.1773i	0.629748	+	1.09076i
$818$	−4.09276			−0.143100
$819$	5.32054	−	1.27898i	0.185915	−	0.0446911i
$820$	−9.28336			−0.324189
$821$	3.81334	+	6.60490i	0.133086	+	0.230513i	0.924865	−	0.380296i	$-0.124178\pi$
$821$	3.81334	+	6.60490i	0.133086	+	0.230513i	−0.791778	+	0.610808i	$0.790845\pi$
$822$	−17.7419	+	30.7298i	−0.618819	+	1.07183i
$823$	15.5725	−	26.9723i	0.542823	−	0.940196i	−0.455918	−	0.890022i	$-0.650689\pi$
$823$	15.5725	−	26.9723i	0.542823	−	0.940196i	0.998740	−	0.0501744i	$-0.0159777\pi$
$824$	−22.6398	−	39.2134i	−0.788696	−	1.36606i
$825$	1.05910			0.0368732
$826$	−3.82487	+	12.9263i	−0.133084	+	0.449764i
$827$	−29.5643			−1.02805			−0.514026	−	0.857774i	$-0.671847\pi$
$827$	−29.5643			−1.02805			−0.514026	+	0.857774i	$0.671847\pi$
$828$	2.16710	+	3.75353i	0.0753121	+	0.130444i
$829$	8.57292	−	14.8487i	0.297750	−	0.515718i	−0.677871	−	0.735181i	$-0.737097\pi$
$829$	8.57292	−	14.8487i	0.297750	−	0.515718i	0.975621	+	0.219463i	$0.0704305\pi$
$830$	−47.9569	+	83.0639i	−1.66461	+	2.88319i
$831$	10.2472	+	17.7487i	0.355472	+	0.615696i
$832$	−6.32603			−0.219315
$833$	−20.6403	+	10.5318i	−0.715143	+	0.364905i
$834$	6.96032			0.241016
$835$	−23.3602	−	40.4611i	−0.808414	−	1.40021i
$836$	9.79312	−	16.9622i	0.338702	−	0.586649i
$837$	3.98872	−	6.90866i	0.137870	−	0.238798i
$838$	−9.78018	−	16.9398i	−0.337851	−	0.585175i
$839$	9.06553			0.312977			0.156488	−	0.987680i	$-0.449983\pi$
$839$	9.06553			0.312977			0.156488	+	0.987680i	$0.449983\pi$
$840$	−10.6652	+	36.0434i	−0.367984	+	1.24362i
$841$	−10.6981			−0.368899
$842$	−30.3288	−	52.5310i	−1.04520	−	1.81034i
$843$	3.69621	−	6.40202i	0.127304	−	0.220497i
$844$	24.3111	−	42.1081i	0.836823	−	1.44942i
$845$	10.5467	+	18.2675i	0.362819	+	0.628421i
$846$	−14.3253			−0.492514
$847$	−24.2880	+	5.83847i	−0.834545	+	0.200612i
$848$	−17.9961			−0.617990
$849$	2.71862	+	4.70879i	0.0933029	+	0.161605i
$850$	3.53400	−	6.12106i	0.121215	−	0.209951i
$851$	2.54588	−	4.40959i	0.0872716	−	0.151159i
$852$	17.9356	+	31.0654i	0.614464	+	1.06428i
$853$	−22.1968			−0.760003			−0.380002	−	0.924986i	$-0.624077\pi$
$853$	−22.1968			−0.760003			−0.380002	+	0.924986i	$0.624077\pi$
$854$	33.8599	+	35.6602i	1.15866	+	1.22027i
$855$	−8.75399			−0.299380
$856$	−43.5278	−	75.3924i	−1.48775	−	2.57686i
$857$	−8.35335	+	14.4684i	−0.285345	+	0.494232i	−0.972693	−	0.232096i	$-0.925441\pi$
$857$	−8.35335	+	14.4684i	−0.285345	+	0.494232i	0.687348	+	0.726328i	$0.258775\pi$
$858$	−3.24918	+	5.62774i	−0.110925	+	0.192128i
$859$	14.2871	+	24.7460i	0.487471	+	0.844324i	0.999896	−	0.0144076i	$-0.00458625\pi$
$859$	14.2871	+	24.7460i	0.487471	+	0.844324i	−0.512425	+	0.858732i	$0.671253\pi$
$860$	104.243			3.55465
$861$	1.61351	+	1.69930i	0.0549883	+	0.0579120i
$862$	−9.10682			−0.310180
$863$	2.21982	+	3.84485i	0.0755637	+	0.130880i	0.901331	−	0.433130i	$-0.142591\pi$
$863$	2.21982	+	3.84485i	0.0755637	+	0.130880i	−0.825768	+	0.564011i	$0.809258\pi$
$864$	−1.82281	+	3.15721i	−0.0620134	+	0.107410i
$865$	−11.4231	+	19.7853i	−0.388396	+	0.672721i
$866$	−24.7673	−	42.8982i	−0.841626	−	1.45774i
$867$	−6.04206			−0.205199
$868$	−88.9454	+	21.3812i	−3.01900	+	0.725724i
$869$	−19.0037			−0.644656
$870$	−13.0191	−	22.5498i	−0.441390	−	0.764510i
$871$	−8.56650	+	14.8376i	−0.290265	+	0.502753i
$872$	11.8942	−	20.6013i	0.402788	−	0.697649i
$873$	−8.34859	−	14.4602i	−0.282557	−	0.489403i
$874$	9.11035			0.308162
$875$	7.53706	−	25.4718i	0.254799	−	0.861103i
$876$	−51.9555			−1.75541
$877$	−4.94656	−	8.56770i	−0.167034	−	0.289311i	0.770342	−	0.637631i	$-0.220086\pi$
$877$	−4.94656	−	8.56770i	−0.167034	−	0.289311i	−0.937376	+	0.348320i	$0.886752\pi$
$878$	−41.3519	+	71.6236i	−1.39556	+	2.41718i
$879$	−11.0048	+	19.0609i	−0.371183	+	0.642908i
$880$	−9.23366	−	15.9932i	−0.311267	−	0.539130i
$881$	19.1692			0.645825			0.322913	−	0.946429i	$-0.395338\pi$
$881$	19.1692			0.645825			0.322913	+	0.946429i	$0.395338\pi$
$882$	15.6927	−	8.00727i	0.528400	−	0.269619i
$883$	−21.3067			−0.717026			−0.358513	−	0.933525i	$-0.616716\pi$
$883$	−21.3067			−0.717026			−0.358513	+	0.933525i	$0.616716\pi$
$884$	14.8371	+	25.6986i	0.499026	+	0.864339i
$885$	−2.44789	+	4.23988i	−0.0822850	+	0.142522i
$886$	22.4100	−	38.8152i	0.752877	−	1.30402i
$887$	−3.05664	−	5.29426i	−0.102632	−	0.177764i	0.810136	−	0.586242i	$-0.199393\pi$
$887$	−3.05664	−	5.29426i	−0.102632	−	0.177764i	−0.912768	+	0.408478i	$0.866060\pi$
$888$	29.9125			1.00380
$889$	−3.67296	+	12.4129i	−0.123187	+	0.416315i
$890$	−99.0047			−3.31865
$891$	−0.624198	−	1.08114i	−0.0209114	−	0.0362196i
$892$	−46.1775	+	79.9817i	−1.54614	+	2.67799i
$893$	−10.3019	+	17.8434i	−0.344740	+	0.597106i
$894$	8.84839	+	15.3259i	0.295934	+	0.512573i
$895$	−39.3344			−1.31481
$896$	−38.5591	+	9.26905i	−1.28817	+	0.309657i
$897$	−2.06826			−0.0690572
$898$	−27.8156	−	48.1780i	−0.928218	−	1.60772i
$899$	17.0640	−	29.5558i	0.569117	−	0.985740i
$900$	−1.83851	+	3.18439i	−0.0612835	+	0.106146i
$901$	−4.86944	−	8.43413i	−0.162225	−	0.280981i
$902$	−2.78277			−0.0926560
$903$	−18.1181	−	19.0814i	−0.602933	−	0.634990i
$904$	23.3549			0.776773
$905$	0.467063	+	0.808977i	0.0155257	+	0.0268913i
$906$	−28.9873	+	50.2074i	−0.963037	+	1.66803i
$907$	−14.1099	+	24.4391i	−0.468512	+	0.811486i	−0.999352	−	0.0359854i	$-0.988543\pi$
$907$	−14.1099	+	24.4391i	−0.468512	+	0.811486i	0.530840	+	0.847472i	$0.321876\pi$
$908$	9.45074	+	16.3692i	0.313634	+	0.543230i
$909$	−9.05813			−0.300439
$910$	−22.9331	−	24.1524i	−0.760224	−	0.800645i
$911$	37.5458			1.24395			0.621974	−	0.783038i	$-0.286331\pi$
$911$	37.5458			1.24395			0.621974	+	0.783038i	$0.286331\pi$
$912$	11.0712	+	19.1758i	0.366603	+	0.634975i
$913$	−9.83649	+	17.0373i	−0.325540	+	0.563853i
$914$	25.0407	−	43.3718i	0.828272	−	1.43461i
$915$	8.92962	+	15.4666i	0.295204	+	0.511309i
$916$	44.3224			1.46445
$917$	−3.92561	+	0.943658i	−0.129635	+	0.0311623i
$918$	−8.33126			−0.274973
$919$	3.66411	+	6.34643i	0.120868	+	0.209349i	0.920110	−	0.391660i	$-0.128099\pi$
$919$	3.66411	+	6.34643i	0.120868	+	0.209349i	−0.799242	+	0.601009i	$0.794766\pi$
$920$	7.10351	−	12.3036i	0.234196	−	0.405639i
$921$	0.0645446	−	0.111795i	0.00212682	−	0.00368375i
$922$	−3.78427	−	6.55455i	−0.124628	−	0.215863i
$923$	−17.1176			−0.563432
$924$	−4.06189	+	13.7273i	−0.133626	+	0.451595i
$925$	4.31969			0.142031
$926$	22.5282	+	39.0199i	0.740322	+	1.28227i
$927$	−3.85379	+	6.67496i	−0.126575	+	0.219234i
$928$	−7.79813	+	13.5068i	−0.255986	+	0.443381i
$929$	−18.4368	−	31.9335i	−0.604893	−	1.04771i	−0.992068	−	0.125700i	$-0.959882\pi$
$929$	−18.4368	−	31.9335i	−0.604893	−	1.04771i	0.387175	−	0.922006i	$-0.373451\pi$
$930$	−48.5542			−1.59216
$931$	1.31147	−	25.3049i	0.0429817	−	0.829334i
$932$	18.9244			0.619891
$933$	3.96738	+	6.87171i	0.129886	+	0.224970i
$934$	9.98941	−	17.3022i	0.326863	−	0.566144i
$935$	4.99694	−	8.65496i	0.163417	−	0.283047i
$936$	−6.07520	−	10.5226i	−0.198574	−	0.343941i
$937$	−4.03995			−0.131980			−0.0659898	−	0.997820i	$-0.521020\pi$
$937$	−4.03995			−0.131980			−0.0659898	+	0.997820i	$0.521020\pi$
$938$	−15.6509	+	52.8929i	−0.511021	+	1.72702i
$939$	−9.68244			−0.315974
$940$	29.8301	+	51.6673i	0.972952	+	1.68520i
$941$	13.0324	−	22.5729i	0.424846	−	0.735854i	−0.571560	−	0.820560i	$-0.693662\pi$
$941$	13.0324	−	22.5729i	0.424846	−	0.735854i	0.996406	+	0.0847057i	$0.0269950\pi$
$942$	22.9616	−	39.7707i	0.748130	−	1.29580i
$943$	−0.442841	−	0.767024i	−0.0144209	−	0.0249777i
$944$	12.3834			0.403045
$945$	6.22111	−	1.49546i	0.202373	−	0.0486474i
$946$	31.2477			1.01595
$947$	−18.5219	−	32.0809i	−0.601882	−	1.04249i	−0.992536	−	0.121952i	$-0.961085\pi$
$947$	−18.5219	−	32.0809i	−0.601882	−	1.04249i	0.390654	−	0.920537i	$-0.372249\pi$
$948$	32.9887	−	57.1381i	1.07142	−	1.85576i
$949$	12.3964	−	21.4712i	0.402405	−	0.696986i
$950$	3.86447	+	6.69346i	0.125380	+	0.217165i
$951$	−17.8054			−0.577380
$952$	35.4278	+	37.3114i	1.14822	+	1.20927i
$953$	−23.2816			−0.754166			−0.377083	−	0.926179i	$-0.623073\pi$
$953$	−23.2816			−0.754166			−0.377083	+	0.926179i	$0.623073\pi$
$954$	3.70221	+	6.41242i	0.119863	+	0.207610i
$955$	−24.6639	+	42.7191i	−0.798104	+	1.38236i
$956$	29.2683	−	50.6942i	0.946605	−	1.63957i
$957$	−2.67037	−	4.62521i	−0.0863207	−	0.149512i
$958$	64.7983			2.09354
$959$	−25.6849	−	27.0505i	−0.829408	−	0.873506i
$960$	−7.39679			−0.238730
$961$	−16.3198	−	28.2666i	−0.526444	−	0.911827i
$962$	−13.2522	+	22.9535i	−0.427269	+	0.740051i
$963$	−7.40937	+	12.8334i	−0.238764	+	0.413551i
$964$	11.2773	+	19.5328i	0.363216	+	0.629109i
$965$	60.5057			1.94775
$966$	−6.47435	+	1.55634i	−0.208309	+	0.0500744i
$967$	30.3867			0.977170			0.488585	−	0.872516i	$-0.337513\pi$
$967$	30.3867			0.977170			0.488585	+	0.872516i	$0.337513\pi$
$968$	27.7330	+	48.0350i	0.891373	+	1.54390i
$969$	−5.99133	+	10.3773i	−0.192469	+	0.333367i
$970$	−50.8132	+	88.0111i	−1.63151	+	2.82587i
$971$	−2.94972	−	5.10907i	−0.0946611	−	0.163958i	0.814806	−	0.579734i	$-0.196843\pi$
$971$	−2.94972	−	5.10907i	−0.0946611	−	0.163958i	−0.909467	+	0.415776i	$0.863510\pi$
$972$	4.33421			0.139020
$973$	−2.07610	+	7.01628i	−0.0665568	+	0.224931i
$974$	−71.3135			−2.28503
$975$	−0.877325	−	1.51957i	−0.0280969	−	0.0486652i
$976$	22.5865	−	39.1210i	0.722978	−	1.25223i
$977$	−19.3055	+	33.4381i	−0.617638	+	1.06978i	0.372278	+	0.928121i	$0.378577\pi$
$977$	−19.3055	+	33.4381i	−0.617638	+	1.06978i	−0.989916	+	0.141659i	$0.954756\pi$
$978$	−6.35985	−	11.0156i	−0.203366	−	0.352240i
$979$	−20.3070			−0.649013
$980$	−61.5573	−	39.9251i	−1.96638	−	1.27536i
$981$	−4.04929			−0.129284
$982$	13.2247	+	22.9058i	0.422016	+	0.730953i
$983$	−20.7955	+	36.0189i	−0.663274	+	1.14882i	0.316476	+	0.948600i	$0.397500\pi$
$983$	−20.7955	+	36.0189i	−0.663274	+	1.14882i	−0.979750	+	0.200224i	$0.935833\pi$
$984$	2.60156	−	4.50603i	0.0829347	−	0.143647i
$985$	29.6405	+	51.3389i	0.944425	+	1.63579i
$986$	−35.6417			−1.13506
$987$	4.27291	−	14.4405i	0.136008	−	0.459645i
$988$	−32.4492			−1.03235
$989$	4.97266	+	8.61290i	0.158121	+	0.273874i
$990$	−3.79915	+	6.58031i	−0.120745	+	0.209136i
$991$	−24.8343	+	43.0143i	−0.788888	+	1.36639i	0.137761	+	0.990465i	$0.456009\pi$
$991$	−24.8343	+	43.0143i	−0.788888	+	1.36639i	−0.926649	+	0.375928i	$0.877324\pi$
$992$	14.5414	+	25.1864i	0.461689	+	0.799669i
$993$	23.8177			0.755831
$994$	−53.5838	+	12.8807i	−1.69957	+	0.408553i
$995$	33.4087			1.05913
$996$	−34.1505	−	59.1505i	−1.08210	−	1.87425i
$997$	17.5620	−	30.4183i	0.556194	−	0.963356i	−0.441616	−	0.897204i	$-0.645595\pi$
$997$	17.5620	−	30.4183i	0.556194	−	0.963356i	0.997810	−	0.0661516i	$-0.0210721\pi$
$998$	10.3534	−	17.9326i	0.327731	−	0.567647i
$999$	−2.54588	−	4.40959i	−0.0805480	−	0.139513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.g.277.2	✓	16
7.2	even	3	inner	483.2.i.g.415.2	yes	16
7.3	odd	6		3381.2.a.be.1.7		8
7.4	even	3		3381.2.a.bf.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.2	✓	16	1.1	even	1	trivial
483.2.i.g.415.2	yes	16	7.2	even	3	inner
3381.2.a.be.1.7		8	7.3	odd	6
3381.2.a.bf.1.7		8	7.4	even	3

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25839 - 2.17960i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.16710 + 3.75353i) q^{4} +(-1.20917 - 2.09434i) q^{5} +2.51679 q^{6} +(-0.750699 + 2.53702i) q^{7} +5.87470 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.25839 - 2.17960i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.16710 + 3.75353i) q^{4} +(-1.20917 - 2.09434i) q^{5} +2.51679 q^{6} +(-0.750699 + 2.53702i) q^{7} +5.87470 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.04322 + 5.27101i) q^{10} +(-0.624198 + 1.08114i) q^{11} +(-2.16710 - 3.75353i) q^{12} +2.06826 q^{13} +(6.47435 - 1.55634i) q^{14} +2.41834 q^{15} +(-3.05847 - 5.29743i) q^{16} +(1.65514 - 2.86679i) q^{17} +(-1.25839 + 2.17960i) q^{18} +(1.80992 + 3.13487i) q^{19} +10.4816 q^{20} +(-1.82177 - 1.91863i) q^{21} +3.14194 q^{22} +(0.500000 + 0.866025i) q^{23} +(-2.93735 + 5.08764i) q^{24} +(-0.424185 + 0.734710i) q^{25} +(-2.60268 - 4.50798i) q^{26} +1.00000 q^{27} +(-7.89593 - 8.31575i) q^{28} +4.27807 q^{29} +(-3.04322 - 5.27101i) q^{30} +(3.98872 - 6.90866i) q^{31} +(-1.82281 + 3.15721i) q^{32} +(-0.624198 - 1.08114i) q^{33} -8.33126 q^{34} +(6.22111 - 1.49546i) q^{35} +4.33421 q^{36} +(-2.54588 - 4.40959i) q^{37} +(4.55517 - 7.88979i) q^{38} +(-1.03413 + 1.79117i) q^{39} +(-7.10351 - 12.3036i) q^{40} -0.885683 q^{41} +(-1.88935 + 6.38512i) q^{42} +9.94532 q^{43} +(-2.70540 - 4.68590i) q^{44} +(-1.20917 + 2.09434i) q^{45} +(1.25839 - 2.17960i) q^{46} +(2.84595 + 4.92934i) q^{47} +6.11694 q^{48} +(-5.87290 - 3.80907i) q^{49} +2.13516 q^{50} +(1.65514 + 2.86679i) q^{51} +(-4.48213 + 7.76328i) q^{52} +(1.47101 - 2.54786i) q^{53} +(-1.25839 - 2.17960i) q^{54} +3.01905 q^{55} +(-4.41013 + 14.9042i) q^{56} -3.61984 q^{57} +(-5.38350 - 9.32449i) q^{58} +(-1.01222 + 1.75322i) q^{59} +(-5.24079 + 9.07732i) q^{60} +(3.69246 + 6.39553i) q^{61} -20.0775 q^{62} +(2.57247 - 0.618384i) q^{63} -3.05862 q^{64} +(-2.50088 - 4.33165i) q^{65} +(-1.57097 + 2.72100i) q^{66} +(-4.14189 + 7.17396i) q^{67} +(7.17372 + 12.4252i) q^{68} -1.00000 q^{69} +(-11.0881 - 11.6776i) q^{70} -8.27631 q^{71} +(-2.93735 - 5.08764i) q^{72} +(5.99365 - 10.3813i) q^{73} +(-6.40743 + 11.0980i) q^{74} +(-0.424185 - 0.734710i) q^{75} -15.6891 q^{76} +(-2.27429 - 2.39521i) q^{77} +5.20537 q^{78} +(7.61124 + 13.1831i) q^{79} +(-7.39642 + 12.8110i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.11454 + 1.93043i) q^{82} +15.7586 q^{83} +(11.1496 - 2.68020i) q^{84} -8.00538 q^{85} +(-12.5151 - 21.6768i) q^{86} +(-2.13904 + 3.70492i) q^{87} +(-3.66698 + 6.35139i) q^{88} +(8.13322 + 14.0871i) q^{89} +6.08644 q^{90} +(-1.55264 + 5.24721i) q^{91} -4.33421 q^{92} +(3.98872 + 6.90866i) q^{93} +(7.16266 - 12.4061i) q^{94} +(4.37700 - 7.58118i) q^{95} +(-1.82281 - 3.15721i) q^{96} +16.6972 q^{97} +(-0.911833 + 17.5939i) q^{98} +1.24840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Introduction

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