LMFDB - Embedded newform 143.2.h.b.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, 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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	16.0.273503893564697265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 9 x^{13} + 19 x^{12} - 16 x^{11} + 49 x^{10} - 32 x^{9} + 98 x^{8} + \cdots + 1 $ x^16 - 3x^15 + 7x^14 - 9x^13 + 19x^12 - 16x^11 + 49x^10 - 32x^9 + 98x^8 - 110x^7 + 145x^6 - 40x^5 + 52x^4 + 24x^3 + 19x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			53.4
Root			$-1.21883 + 0.885535i$ of defining polynomial
Character	$\chi$	$=$	143.53
Dual form			143.2.h.b.27.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.760439 - 2.34039i) q^{2} +(0.674152 - 0.489800i) q^{3} +(-3.28113 - 2.38388i) q^{4} +(-0.304593 - 0.937441i) q^{5} +(-0.633672 - 1.95024i) q^{6} +(3.14398 + 2.28423i) q^{7} +(-4.09261 + 2.97346i) q^{8} +(-0.712474 + 2.19277i) q^{9} +O(q^{10})$	\(q+(0.760439 - 2.34039i) q^{2} +(0.674152 - 0.489800i) q^{3} +(-3.28113 - 2.38388i) q^{4} +(-0.304593 - 0.937441i) q^{5} +(-0.633672 - 1.95024i) q^{6} +(3.14398 + 2.28423i) q^{7} +(-4.09261 + 2.97346i) q^{8} +(-0.712474 + 2.19277i) q^{9} -2.42560 q^{10} +(-3.26531 - 0.581158i) q^{11} -3.37961 q^{12} +(-0.309017 + 0.951057i) q^{13} +(7.73680 - 5.62112i) q^{14} +(-0.664500 - 0.482788i) q^{15} +(1.34031 + 4.12504i) q^{16} +(0.674544 + 2.07603i) q^{17} +(4.59015 + 3.33494i) q^{18} +(4.27306 - 3.10456i) q^{19} +(-1.23534 + 3.80198i) q^{20} +3.23833 q^{21} +(-3.84321 + 7.20017i) q^{22} -2.41996 q^{23} +(-1.30264 + 4.00912i) q^{24} +(3.25907 - 2.36785i) q^{25} +(1.99086 + 1.44644i) q^{26} +(1.36621 + 4.20477i) q^{27} +(-4.87046 - 14.9897i) q^{28} +(-5.51123 - 4.00414i) q^{29} +(-1.63522 + 1.18806i) q^{30} +(-1.01708 + 3.13025i) q^{31} +0.555943 q^{32} +(-2.48597 + 1.20756i) q^{33} +5.37168 q^{34} +(1.18370 - 3.64305i) q^{35} +(7.56503 - 5.49632i) q^{36} +(7.73413 + 5.61917i) q^{37} +(-4.01649 - 12.3615i) q^{38} +(0.257503 + 0.792513i) q^{39} +(4.03402 + 2.93089i) q^{40} +(-2.77633 + 2.01712i) q^{41} +(2.46256 - 7.57897i) q^{42} -7.11470 q^{43} +(9.32851 + 9.69097i) q^{44} +2.27261 q^{45} +(-1.84024 + 5.66366i) q^{46} +(-1.55981 + 1.13327i) q^{47} +(2.92401 + 2.12442i) q^{48} +(2.50375 + 7.70575i) q^{49} +(-3.06338 - 9.42810i) q^{50} +(1.47158 + 1.06917i) q^{51} +(3.28113 - 2.38388i) q^{52} +(1.42694 - 4.39166i) q^{53} +10.8797 q^{54} +(0.449790 + 3.23805i) q^{55} -19.6591 q^{56} +(1.36008 - 4.18589i) q^{57} +(-13.5622 + 9.85352i) q^{58} +(-0.0353035 - 0.0256495i) q^{59} +(1.02940 + 3.16818i) q^{60} +(-3.28165 - 10.0999i) q^{61} +(6.55259 + 4.76073i) q^{62} +(-7.24880 + 5.26656i) q^{63} +(-2.25785 + 6.94895i) q^{64} +0.985684 q^{65} +(0.935738 + 6.73641i) q^{66} -2.77390 q^{67} +(2.73575 - 8.41977i) q^{68} +(-1.63142 + 1.18530i) q^{69} +(-7.62604 - 5.54064i) q^{70} +(3.25083 + 10.0050i) q^{71} +(-3.60423 - 11.0927i) q^{72} +(-12.9700 - 9.42325i) q^{73} +(19.0324 - 13.8278i) q^{74} +(1.03733 - 3.19258i) q^{75} -21.4214 q^{76} +(-8.93856 - 9.28588i) q^{77} +2.05061 q^{78} +(-2.87172 + 8.83826i) q^{79} +(3.45873 - 2.51292i) q^{80} +(-2.61532 - 1.90014i) q^{81} +(2.60962 + 8.03160i) q^{82} +(3.79417 + 11.6773i) q^{83} +(-10.6254 - 7.71981i) q^{84} +(1.74070 - 1.26469i) q^{85} +(-5.41030 + 16.6512i) q^{86} -5.67663 q^{87} +(15.0917 - 7.33080i) q^{88} +2.97373 q^{89} +(1.72818 - 5.31879i) q^{90} +(-3.14398 + 2.28423i) q^{91} +(7.94022 + 5.76891i) q^{92} +(0.847530 + 2.60843i) q^{93} +(1.46615 + 4.51236i) q^{94} +(-4.21189 - 3.06011i) q^{95} +(0.374790 - 0.272301i) q^{96} +(-1.73159 + 5.32930i) q^{97} +19.9384 q^{98} +(3.60080 - 6.74602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 + 5 * q^5 - 4 * q^6 + 9 * q^7 - 4 * q^8 - 7 * q^9	\( 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9} - 12 q^{10} + 6 q^{11} - 14 q^{12} + 4 q^{13} - q^{14} - 10 q^{15} + 10 q^{16} - 6 q^{17} + 20 q^{18} + 2 q^{19} - 21 q^{20} - 8 q^{21} + 2 q^{22} - 46 q^{23} + 3 q^{24} + 23 q^{25} + 3 q^{26} + 17 q^{27} - 9 q^{28} - 25 q^{29} + 22 q^{30} + 3 q^{31} + 24 q^{32} - 10 q^{33} + 4 q^{34} + 26 q^{35} - 2 q^{36} - 7 q^{37} + 5 q^{38} + 25 q^{40} - 3 q^{41} - 12 q^{42} - 16 q^{43} + 32 q^{44} - 46 q^{45} - 11 q^{46} + 13 q^{47} - 24 q^{48} + 19 q^{49} - 19 q^{50} - 23 q^{51} + 8 q^{52} - 14 q^{53} + 6 q^{54} - 5 q^{55} - 68 q^{56} + 23 q^{57} + 20 q^{58} + 16 q^{59} + 34 q^{60} - 13 q^{61} + 28 q^{62} + 18 q^{63} - 40 q^{64} + 10 q^{65} + 41 q^{66} - 62 q^{67} + 13 q^{68} + 4 q^{69} - 2 q^{70} + 54 q^{71} + 21 q^{72} - 42 q^{73} + 42 q^{74} + 51 q^{75} - 4 q^{76} + 14 q^{77} - 6 q^{78} - 15 q^{79} - 19 q^{80} + q^{81} - 7 q^{82} - 43 q^{83} - 35 q^{84} - 3 q^{85} - 32 q^{86} + 4 q^{87} + 41 q^{88} - 30 q^{89} + 26 q^{90} - 9 q^{91} + 3 q^{92} + 49 q^{93} + 4 q^{94} + 23 q^{95} + 23 q^{96} - 12 q^{97} + 24 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 + 5 * q^5 - 4 * q^6 + 9 * q^7 - 4 * q^8 - 7 * q^9 - 12 * q^10 + 6 * q^11 - 14 * q^12 + 4 * q^13 - q^14 - 10 * q^15 + 10 * q^16 - 6 * q^17 + 20 * q^18 + 2 * q^19 - 21 * q^20 - 8 * q^21 + 2 * q^22 - 46 * q^23 + 3 * q^24 + 23 * q^25 + 3 * q^26 + 17 * q^27 - 9 * q^28 - 25 * q^29 + 22 * q^30 + 3 * q^31 + 24 * q^32 - 10 * q^33 + 4 * q^34 + 26 * q^35 - 2 * q^36 - 7 * q^37 + 5 * q^38 + 25 * q^40 - 3 * q^41 - 12 * q^42 - 16 * q^43 + 32 * q^44 - 46 * q^45 - 11 * q^46 + 13 * q^47 - 24 * q^48 + 19 * q^49 - 19 * q^50 - 23 * q^51 + 8 * q^52 - 14 * q^53 + 6 * q^54 - 5 * q^55 - 68 * q^56 + 23 * q^57 + 20 * q^58 + 16 * q^59 + 34 * q^60 - 13 * q^61 + 28 * q^62 + 18 * q^63 - 40 * q^64 + 10 * q^65 + 41 * q^66 - 62 * q^67 + 13 * q^68 + 4 * q^69 - 2 * q^70 + 54 * q^71 + 21 * q^72 - 42 * q^73 + 42 * q^74 + 51 * q^75 - 4 * q^76 + 14 * q^77 - 6 * q^78 - 15 * q^79 - 19 * q^80 + q^81 - 7 * q^82 - 43 * q^83 - 35 * q^84 - 3 * q^85 - 32 * q^86 + 4 * q^87 + 41 * q^88 - 30 * q^89 + 26 * q^90 - 9 * q^91 + 3 * q^92 + 49 * q^93 + 4 * q^94 + 23 * q^95 + 23 * q^96 - 12 * q^97 + 24 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.760439	−	2.34039i	0.537712	−	1.65491i	−0.200003	−	0.979795i	$-0.564095\pi$
$2$	0.760439	−	2.34039i	0.537712	−	1.65491i	0.737715	−	0.675112i	$-0.235905\pi$
$3$	0.674152	−	0.489800i	0.389222	−	0.282786i	−0.375915	−	0.926654i	$-0.622671\pi$
$3$	0.674152	−	0.489800i	0.389222	−	0.282786i	0.765136	+	0.643868i	$0.222671\pi$
$4$	−3.28113	−	2.38388i	−1.64057	−	1.19194i
$5$	−0.304593	−	0.937441i	−0.136218	−	0.419236i	0.859559	−	0.511036i	$-0.170738\pi$
$5$	−0.304593	−	0.937441i	−0.136218	−	0.419236i	−0.995778	+	0.0917996i	$0.970738\pi$
$6$	−0.633672	−	1.95024i	−0.258696	−	0.796183i
$7$	3.14398	+	2.28423i	1.18831	+	0.863359i	0.993085	−	0.117399i	$-0.0374557\pi$
$7$	3.14398	+	2.28423i	1.18831	+	0.863359i	0.195227	+	0.980758i	$0.437456\pi$
$8$	−4.09261	+	2.97346i	−1.44696	+	1.05128i
$9$	−0.712474	+	2.19277i	−0.237491	+	0.730924i
$10$	−2.42560			−0.767043
$11$	−3.26531	−	0.581158i	−0.984528	−	0.175226i
$11$	−3.26531	−	0.581158i	−0.984528	−	0.175226i
$12$	−3.37961			−0.975608
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	7.73680	−	5.62112i	2.06775	−	1.50231i
$15$	−0.664500	−	0.482788i	−0.171573	−	0.124655i
$16$	1.34031	+	4.12504i	0.335077	+	1.03126i
$17$	0.674544	+	2.07603i	0.163601	+	0.503512i	0.998930	−	0.0462378i	$-0.0147232\pi$
$17$	0.674544	+	2.07603i	0.163601	+	0.503512i	−0.835330	+	0.549749i	$0.814723\pi$
$18$	4.59015	+	3.33494i	1.08191	+	0.786053i
$19$	4.27306	−	3.10456i	0.980308	−	0.712235i	0.0225302	−	0.999746i	$-0.492828\pi$
$19$	4.27306	−	3.10456i	0.980308	−	0.712235i	0.957777	+	0.287511i	$0.0928278\pi$
$20$	−1.23534	+	3.80198i	−0.276230	+	0.850149i
$21$	3.23833			0.706662
$22$	−3.84321	+	7.20017i	−0.819375	+	1.53508i
$23$	−2.41996			−0.504597			−0.252299	−	0.967649i	$-0.581186\pi$
$23$	−2.41996			−0.504597			−0.252299	+	0.967649i	$0.581186\pi$
$24$	−1.30264	+	4.00912i	−0.265901	+	0.818358i
$25$	3.25907	−	2.36785i	0.651813	−	0.473570i
$26$	1.99086	+	1.44644i	0.390439	+	0.283671i
$27$	1.36621	+	4.20477i	0.262928	+	0.809208i
$28$	−4.87046	−	14.9897i	−0.920431	−	2.83280i
$29$	−5.51123	−	4.00414i	−1.02341	−	0.743550i	−0.0564299	−	0.998407i	$-0.517972\pi$
$29$	−5.51123	−	4.00414i	−1.02341	−	0.743550i	−0.966979	+	0.254857i	$0.917972\pi$
$30$	−1.63522	+	1.18806i	−0.298550	+	0.216909i
$31$	−1.01708	+	3.13025i	−0.182673	+	0.562210i	−0.999901	−	0.0141056i	$-0.995510\pi$
$31$	−1.01708	+	3.13025i	−0.182673	+	0.562210i	0.817228	+	0.576315i	$0.195510\pi$
$32$	0.555943			0.0982778
$33$	−2.48597	+	1.20756i	−0.432751	+	0.210209i
$34$	5.37168			0.921235
$35$	1.18370	−	3.64305i	0.200082	−	0.615788i
$36$	7.56503	−	5.49632i	1.26084	−	0.916053i
$37$	7.73413	+	5.61917i	1.27148	+	0.923786i	0.999261	−	0.0384485i	$-0.0122415\pi$
$37$	7.73413	+	5.61917i	1.27148	+	0.923786i	0.272222	+	0.962235i	$0.412242\pi$
$38$	−4.01649	−	12.3615i	−0.651560	−	2.00530i
$39$	0.257503	+	0.792513i	0.0412335	+	0.126904i
$40$	4.03402	+	2.93089i	0.637834	+	0.463414i
$41$	−2.77633	+	2.01712i	−0.433590	+	0.315021i	−0.783083	−	0.621918i	$-0.786354\pi$
$41$	−2.77633	+	2.01712i	−0.433590	+	0.315021i	0.349493	+	0.936939i	$0.386354\pi$
$42$	2.46256	−	7.57897i	0.379981	−	1.16946i
$43$	−7.11470			−1.08498			−0.542491	−	0.840062i	$-0.682519\pi$
$43$	−7.11470			−1.08498			−0.542491	+	0.840062i	$0.682519\pi$
$44$	9.32851	+	9.69097i	1.40633	+	1.46097i
$45$	2.27261			0.338780
$46$	−1.84024	+	5.66366i	−0.271328	+	0.835061i
$47$	−1.55981	+	1.13327i	−0.227522	+	0.165305i	−0.695706	−	0.718326i	$-0.744908\pi$
$47$	−1.55981	+	1.13327i	−0.227522	+	0.165305i	0.468184	+	0.883631i	$0.344908\pi$
$48$	2.92401	+	2.12442i	0.422045	+	0.306634i
$49$	2.50375	+	7.70575i	0.357679	+	1.10082i
$50$	−3.06338	−	9.42810i	−0.433227	−	1.33333i
$51$	1.47158	+	1.06917i	0.206063	+	0.149714i
$52$	3.28113	−	2.38388i	0.455011	−	0.330585i
$53$	1.42694	−	4.39166i	0.196005	−	0.603241i	−0.803958	−	0.594685i	$-0.797277\pi$
$53$	1.42694	−	4.39166i	0.196005	−	0.603241i	0.999963	−	0.00855577i	$-0.00272342\pi$
$54$	10.8797			1.48054
$55$	0.449790	+	3.23805i	0.0606496	+	0.436619i
$56$	−19.6591			−2.62706
$57$	1.36008	−	4.18589i	0.180147	−	0.554435i
$58$	−13.5622	+	9.85352i	−1.78081	+	1.29383i
$59$	−0.0353035	−	0.0256495i	−0.00459613	−	0.00333928i	0.585485	−	0.810683i	$-0.300904\pi$
$59$	−0.0353035	−	0.0256495i	−0.00459613	−	0.00333928i	−0.590081	+	0.807344i	$0.700904\pi$
$60$	1.02940	+	3.16818i	0.132896	+	0.409010i
$61$	−3.28165	−	10.0999i	−0.420172	−	1.29316i	−0.907542	−	0.419960i	$-0.862044\pi$
$61$	−3.28165	−	10.0999i	−0.420172	−	1.29316i	0.487371	−	0.873195i	$-0.337956\pi$
$62$	6.55259	+	4.76073i	0.832179	+	0.604614i
$63$	−7.24880	+	5.26656i	−0.913263	+	0.663525i
$64$	−2.25785	+	6.94895i	−0.282232	+	0.868619i
$65$	0.985684			0.122259
$66$	0.935738	+	6.73641i	0.115181	+	0.829195i
$67$	−2.77390			−0.338885			−0.169443	−	0.985540i	$-0.554197\pi$
$67$	−2.77390			−0.338885			−0.169443	+	0.985540i	$0.554197\pi$
$68$	2.73575	−	8.41977i	0.331758	−	1.02105i
$69$	−1.63142	+	1.18530i	−0.196400	+	0.142693i
$70$	−7.62604	−	5.54064i	−0.911486	−	0.662234i
$71$	3.25083	+	10.0050i	0.385802	+	1.18738i	0.935897	+	0.352275i	$0.114592\pi$
$71$	3.25083	+	10.0050i	0.385802	+	1.18738i	−0.550094	+	0.835103i	$0.685408\pi$
$72$	−3.60423	−	11.0927i	−0.424762	−	1.30728i
$73$	−12.9700	−	9.42325i	−1.51802	−	1.10291i	−0.962457	−	0.271434i	$-0.912502\pi$
$73$	−12.9700	−	9.42325i	−1.51802	−	1.10291i	−0.555565	−	0.831473i	$-0.687498\pi$
$74$	19.0324	−	13.8278i	2.21247	−	1.60745i
$75$	1.03733	−	3.19258i	0.119781	−	0.368647i
$76$	−21.4214			−2.45720
$77$	−8.93856	−	9.28588i	−1.01864	−	1.05822i
$78$	2.05061			0.232185
$79$	−2.87172	+	8.83826i	−0.323094	+	0.994382i	0.649199	+	0.760618i	$0.275104\pi$
$79$	−2.87172	+	8.83826i	−0.323094	+	0.994382i	−0.972294	+	0.233763i	$0.924896\pi$
$80$	3.45873	−	2.51292i	0.386698	−	0.280953i
$81$	−2.61532	−	1.90014i	−0.290591	−	0.211127i
$82$	2.60962	+	8.03160i	0.288185	+	0.886941i
$83$	3.79417	+	11.6773i	0.416464	+	1.28175i	0.910935	+	0.412551i	$0.135362\pi$
$83$	3.79417	+	11.6773i	0.416464	+	1.28175i	−0.494470	+	0.869194i	$0.664638\pi$
$84$	−10.6254	−	7.71981i	−1.15933	−	0.842300i
$85$	1.74070	−	1.26469i	0.188805	−	0.137175i
$86$	−5.41030	+	16.6512i	−0.583407	+	1.79554i
$87$	−5.67663			−0.608598
$88$	15.0917	−	7.33080i	1.60878	−	0.781466i
$89$	2.97373			0.315215			0.157607	−	0.987502i	$-0.449622\pi$
$89$	2.97373			0.315215			0.157607	+	0.987502i	$0.449622\pi$
$90$	1.72818	−	5.31879i	0.182166	−	0.560650i
$91$	−3.14398	+	2.28423i	−0.329578	+	0.239453i
$92$	7.94022	+	5.76891i	0.827825	+	0.601450i
$93$	0.847530	+	2.60843i	0.0878848	+	0.270481i
$94$	1.46615	+	4.51236i	0.151222	+	0.465414i
$95$	−4.21189	−	3.06011i	−0.432130	−	0.313961i
$96$	0.374790	−	0.272301i	0.0382519	−	0.0277916i
$97$	−1.73159	+	5.32930i	−0.175817	+	0.541109i	−0.999670	−	0.0256950i	$-0.991820\pi$
$97$	−1.73159	+	5.32930i	−0.175817	+	0.541109i	0.823853	+	0.566803i	$0.191820\pi$
$98$	19.9384			2.01409
$99$	3.60080	−	6.74602i	0.361894	−	0.678000i
$100$	−16.3381			−1.63381
$101$	4.18957	−	12.8942i	0.416878	−	1.28302i	−0.493683	−	0.869642i	$-0.664350\pi$
$101$	4.18957	−	12.8942i	0.416878	−	1.28302i	0.910560	−	0.413376i	$-0.135650\pi$
$102$	3.62133	−	2.63105i	0.358565	−	0.260512i
$103$	−1.56299	−	1.13558i	−0.154006	−	0.111892i	0.508114	−	0.861290i	$-0.330343\pi$
$103$	−1.56299	−	1.13558i	−0.154006	−	0.111892i	−0.662120	+	0.749398i	$0.730343\pi$
$104$	−1.56324	−	4.81115i	−0.153288	−	0.471772i
$105$	−0.986374	−	3.03575i	−0.0962602	−	0.296258i
$106$	−9.19311	−	6.67919i	−0.892914	−	0.648740i
$107$	11.7209	−	8.51570i	1.13310	−	0.823244i	0.146955	−	0.989143i	$-0.453053\pi$
$107$	11.7209	−	8.51570i	1.13310	−	0.823244i	0.986143	+	0.165900i	$0.0530528\pi$
$108$	5.54095	−	17.0533i	0.533178	−	1.64095i
$109$	11.8121			1.13139			0.565697	−	0.824613i	$-0.308607\pi$
$109$	11.8121			1.13139			0.565697	+	0.824613i	$0.308607\pi$
$110$	7.92035	+	1.40966i	0.755176	+	0.134406i
$111$	7.96624			0.756122
$112$	−5.20866	+	16.0306i	−0.492172	+	1.51475i
$113$	13.7666	−	10.0020i	1.29505	−	0.940908i	0.295155	−	0.955449i	$-0.404629\pi$
$113$	13.7666	−	10.0020i	1.29505	−	0.940908i	0.999894	+	0.0145410i	$0.00462870\pi$
$114$	−8.76237	−	6.36623i	−0.820671	−	0.596252i
$115$	0.737104	+	2.26857i	0.0687353	+	0.211545i
$116$	8.53766	+	26.2762i	0.792702	+	2.43969i
$117$	−1.86528	−	1.35521i	−0.172445	−	0.125289i
$118$	−0.0868761	+	0.0631192i	−0.00799760	+	0.00581059i
$119$	−2.62139	+	8.06781i	−0.240302	+	0.739575i
$120$	4.15509			0.379306
$121$	10.3245	+	3.79532i	0.938592	+	0.345029i
$122$	−26.1331			−2.36598
$123$	−0.883681	+	2.71969i	−0.0796788	+	0.245226i
$124$	10.7993	−	7.84617i	0.969808	−	0.704607i
$125$	−7.19958	−	5.23080i	−0.643950	−	0.467857i
$126$	6.81355	+	20.9699i	0.606999	+	1.86815i
$127$	−0.917423	−	2.82354i	−0.0814082	−	0.250549i	0.902066	−	0.431599i	$-0.142050\pi$
$127$	−0.917423	−	2.82354i	−0.0814082	−	0.250549i	−0.983474	+	0.181050i	$0.942050\pi$
$128$	15.4459	+	11.2221i	1.36523	+	0.991900i
$129$	−4.79638	+	3.48478i	−0.422298	+	0.306817i
$130$	0.749553	−	2.30689i	0.0657401	−	0.202327i
$131$	−15.8031			−1.38073			−0.690363	−	0.723463i	$-0.742549\pi$
$131$	−15.8031			−1.38073			−0.690363	+	0.723463i	$0.742549\pi$
$132$	11.0355	+	1.96408i	0.960514	+	0.170952i
$133$	20.5259			1.77983
$134$	−2.10938	+	6.49200i	−0.182223	+	0.560824i
$135$	3.52558	−	2.56149i	0.303434	−	0.220458i
$136$	−8.93363	−	6.49066i	−0.766053	−	0.556570i
$137$	−3.21702	−	9.90096i	−0.274848	−	0.845896i	−0.989259	−	0.146170i	$-0.953305\pi$
$137$	−3.21702	−	9.90096i	−0.274848	−	0.845896i	0.714411	−	0.699726i	$-0.246695\pi$
$138$	1.53346	+	4.71951i	0.130537	+	0.401752i
$139$	−14.0910	−	10.2377i	−1.19518	−	0.868351i	−0.201380	−	0.979513i	$-0.564543\pi$
$139$	−14.0910	−	10.2377i	−1.19518	−	0.868351i	−0.993802	+	0.111162i	$0.964543\pi$
$140$	−12.5685	+	9.13154i	−1.06223	+	0.771756i
$141$	−0.496475	+	1.52799i	−0.0418107	+	0.128680i
$142$	25.8877			2.17245
$143$	1.56175	−	2.92591i	0.130600	−	0.244677i
$144$	−10.0002			−0.833350
$145$	−2.07496	+	6.38608i	−0.172316	+	0.530335i
$146$	−31.9170	+	23.1890i	−2.64147	+	1.91914i
$147$	5.46218	+	3.96851i	0.450513	+	0.327317i
$148$	−11.9813	−	36.8745i	−0.984853	−	3.03106i
$149$	2.30339	+	7.08909i	0.188701	+	0.580761i	0.999992	−	0.00388046i	$-0.00123519\pi$
$149$	2.30339	+	7.08909i	0.188701	+	0.580761i	−0.811292	+	0.584641i	$0.801235\pi$
$150$	−6.68306	−	4.85553i	−0.545670	−	0.396452i
$151$	2.12189	−	1.54164i	0.172677	−	0.125457i	−0.498090	−	0.867125i	$-0.665965\pi$
$151$	2.12189	−	1.54164i	0.172677	−	0.125457i	0.670767	+	0.741668i	$0.265965\pi$
$152$	−8.25670	+	25.4115i	−0.669707	+	2.06115i
$153$	−5.03286			−0.406882
$154$	−28.5298	+	13.8584i	−2.29900	+	1.11674i
$155$	3.24422			0.260582
$156$	1.04436	−	3.21420i	0.0836154	−	0.257342i
$157$	11.4483	−	8.31765i	0.913671	−	0.663821i	−0.0282699	−	0.999600i	$-0.509000\pi$
$157$	11.4483	−	8.31765i	0.913671	−	0.663821i	0.941941	+	0.335780i	$0.109000\pi$
$158$	18.5012	+	13.4419i	1.47188	+	1.06938i
$159$	−1.18906	−	3.65956i	−0.0942988	−	0.290222i
$160$	−0.169336	−	0.521164i	−0.0133872	−	0.0412016i
$161$	−7.60831	−	5.52776i	−0.599618	−	0.435648i
$162$	−6.43586	+	4.67593i	−0.505649	+	0.367376i
$163$	−5.50742	+	16.9501i	−0.431374	+	1.32763i	0.465382	+	0.885110i	$0.345917\pi$
$163$	−5.50742	+	16.9501i	−0.431374	+	1.32763i	−0.896757	+	0.442524i	$0.854083\pi$
$164$	13.9181			1.08682
$165$	1.88922	+	1.96263i	0.147076	+	0.152791i
$166$	30.2146			2.34511
$167$	6.15119	−	18.9314i	0.475993	−	1.46496i	−0.368620	−	0.929580i	$-0.620170\pi$
$167$	6.15119	−	18.9314i	0.475993	−	1.46496i	0.844613	−	0.535377i	$-0.179830\pi$
$168$	−13.2532	+	9.62904i	−1.02251	+	0.742897i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−1.63618	−	5.03563i	−0.125489	−	0.386215i
$171$	3.76314	+	11.5818i	0.287775	+	0.885680i
$172$	23.3443	+	16.9606i	1.77998	+	1.29323i
$173$	−1.67141	+	1.21435i	−0.127075	+	0.0923253i	−0.649507	−	0.760355i	$-0.725025\pi$
$173$	−1.67141	+	1.21435i	−0.127075	+	0.0923253i	0.522432	+	0.852681i	$0.325025\pi$
$174$	−4.31673	+	13.2855i	−0.327251	+	1.00717i
$175$	15.6552			1.18342
$176$	−1.97922	−	14.2485i	−0.149189	−	1.07402i
$177$	−0.0363631			−0.00273322
$178$	2.26134	−	6.95970i	0.169495	−	0.521651i
$179$	−4.79652	+	3.48487i	−0.358509	+	0.260472i	−0.752430	−	0.658673i	$-0.771118\pi$
$179$	−4.79652	+	3.48487i	−0.358509	+	0.260472i	0.393921	+	0.919144i	$0.371118\pi$
$180$	−7.45673	−	5.41763i	−0.555792	−	0.403806i
$181$	−6.50777	−	20.0289i	−0.483719	−	1.48873i	−0.833828	−	0.552025i	$-0.813855\pi$
$181$	−6.50777	−	20.0289i	−0.483719	−	1.48873i	0.350108	−	0.936709i	$-0.386145\pi$
$182$	2.95520	+	9.09516i	0.219054	+	0.674178i
$183$	−7.15924	−	5.20149i	−0.529226	−	0.384505i
$184$	9.90396	−	7.19565i	0.730130	−	0.530470i
$185$	2.91188	−	8.96185i	0.214086	−	0.658888i
$186$	6.74924			0.494878
$187$	−0.996093	−	7.17091i	−0.0728415	−	0.524389i
$188$	7.81954			0.570299
$189$	−5.30933	+	16.3404i	−0.386197	+	1.18859i
$190$	−10.3648	+	7.53043i	−0.751938	+	0.546315i
$191$	7.83497	+	5.69244i	0.566919	+	0.411890i	0.833985	−	0.551788i	$-0.186054\pi$
$191$	7.83497	+	5.69244i	0.566919	+	0.411890i	−0.267066	+	0.963678i	$0.586054\pi$
$192$	1.88146	+	5.79054i	0.135783	+	0.417897i
$193$	0.534724	+	1.64571i	0.0384903	+	0.118461i	0.968455	−	0.249187i	$-0.0801633\pi$
$193$	0.534724	+	1.64571i	0.0384903	+	0.118461i	−0.929965	+	0.367648i	$0.880163\pi$
$194$	11.1559	+	8.10522i	0.800946	+	0.581921i
$195$	0.664500	−	0.482788i	0.0475858	−	0.0345731i
$196$	10.1545	−	31.2523i	0.725319	−	2.23230i
$197$	24.7399			1.76265			0.881323	−	0.472514i	$-0.156653\pi$
$197$	24.7399			1.76265			0.881323	+	0.472514i	$0.156653\pi$
$198$	−13.0501	−	13.5572i	−0.927433	−	0.963469i
$199$	−2.12759			−0.150821			−0.0754103	−	0.997153i	$-0.524027\pi$
$199$	−2.12759			−0.150821			−0.0754103	+	0.997153i	$0.524027\pi$
$200$	−6.29739	+	19.3814i	−0.445293	+	1.37047i
$201$	−1.87003	+	1.35865i	−0.131901	+	0.0958320i
$202$	−26.9915	−	19.6105i	−1.89912	−	1.37979i
$203$	−8.18078	−	25.1778i	−0.574178	−	1.76714i
$204$	−2.27969	−	7.01617i	−0.159610	−	0.491230i
$205$	2.73658	+	1.98824i	0.191131	+	0.138865i
$206$	−3.84626	+	2.79447i	−0.267981	+	0.194700i
$207$	1.72416	−	5.30642i	0.119838	−	0.368822i
$208$	−4.33732			−0.300739
$209$	−15.7571	+	7.65403i	−1.08994	+	0.529441i
$210$	−7.85491			−0.542041
$211$	−1.09851	+	3.38088i	−0.0756248	+	0.232749i	−0.981722	−	0.190320i	$-0.939047\pi$
$211$	−1.09851	+	3.38088i	−0.0756248	+	0.232749i	0.906097	+	0.423069i	$0.139047\pi$
$212$	−15.1512	+	11.0080i	−1.04059	+	0.756031i
$213$	7.09201	+	5.15265i	0.485936	+	0.353053i
$214$	−11.0171	−	33.9071i	−0.753112	−	2.31784i
$215$	2.16709	+	6.66961i	0.147794	+	0.454863i
$216$	−18.0941	−	13.1461i	−1.23115	−	0.894479i
$217$	−10.3479	+	7.51819i	−0.702461	+	0.510368i
$218$	8.98238	−	27.6449i	0.608364	−	1.87235i
$219$	−13.3592			−0.902734
$220$	6.24332	−	11.6967i	0.420924	−	0.788593i
$221$	−2.18287			−0.146836
$222$	6.05785	−	18.6441i	0.406576	−	1.25131i
$223$	15.1198	−	10.9852i	1.01250	−	0.735623i	0.0477664	−	0.998859i	$-0.484790\pi$
$223$	15.1198	−	10.9852i	1.01250	−	0.735623i	0.964732	+	0.263236i	$0.0847897\pi$
$224$	1.74787	+	1.26990i	0.116785	+	0.0848490i
$225$	2.87015	+	8.83342i	0.191343	+	0.588895i
$226$	−12.9399	−	39.8251i	−0.860753	−	2.64912i
$227$	−9.46579	−	6.87730i	−0.628266	−	0.456462i	0.227533	−	0.973770i	$-0.426934\pi$
$227$	−9.46579	−	6.87730i	−0.628266	−	0.456462i	−0.855799	+	0.517308i	$0.826934\pi$
$228$	−14.4413	+	10.4922i	−0.956396	+	0.694863i
$229$	1.67811	−	5.16470i	0.110893	−	0.341293i	−0.880176	−	0.474648i	$-0.842575\pi$
$229$	1.67811	−	5.16470i	0.110893	−	0.341293i	0.991068	+	0.133356i	$0.0425752\pi$
$230$	5.86987			0.387048
$231$	−10.5742	−	1.88198i	−0.695729	−	0.123825i
$232$	34.4614			2.26250
$233$	−4.05910	+	12.4926i	−0.265920	+	0.818418i	0.725560	+	0.688159i	$0.241581\pi$
$233$	−4.05910	+	12.4926i	−0.265920	+	0.818418i	−0.991480	+	0.130259i	$0.958419\pi$
$234$	−4.59015	+	3.33494i	−0.300067	+	0.218012i
$235$	1.53748	+	1.11705i	0.100294	+	0.0728681i
$236$	0.0546902	+	0.168319i	0.00356003	+	0.0109566i
$237$	2.39300	+	7.36489i	0.155442	+	0.478401i
$238$	16.8884	+	12.2702i	1.09471	+	0.795357i
$239$	7.16849	−	5.20821i	0.463691	−	0.336891i	−0.331286	−	0.943530i	$-0.607483\pi$
$239$	7.16849	−	5.20821i	0.463691	−	0.336891i	0.794977	+	0.606639i	$0.207483\pi$
$240$	1.10088	−	3.38817i	0.0710618	−	0.218706i
$241$	−19.9825			−1.28719			−0.643593	−	0.765368i	$-0.722557\pi$
$241$	−19.9825			−1.28719			−0.643593	+	0.765368i	$0.722557\pi$
$242$	16.7337	−	21.2773i	1.07568	−	1.36776i
$243$	−15.9573			−1.02366
$244$	−13.3094	+	40.9621i	−0.852046	+	2.62233i
$245$	6.46106	−	4.69424i	0.412782	−	0.299904i
$246$	5.69316	+	4.13632i	0.362982	+	0.263722i
$247$	1.63216	+	5.02329i	0.103852	+	0.319624i
$248$	−5.14515	−	15.8351i	−0.326717	−	1.00553i
$249$	8.27736	+	6.01386i	0.524557	+	0.381113i
$250$	−17.7170	+	12.8721i	−1.12052	+	0.814105i
$251$	−9.12759	+	28.0918i	−0.576128	+	1.77314i	0.0561768	+	0.998421i	$0.482109\pi$
$251$	−9.12759	+	28.0918i	−0.576128	+	1.77314i	−0.632305	+	0.774720i	$0.717891\pi$
$252$	36.3392			2.28915
$253$	7.90193	+	1.40638i	0.496790	+	0.0884184i
$254$	−7.30583			−0.458409
$255$	0.554048	−	1.70518i	0.0346958	−	0.106783i
$256$	26.1874	−	19.0263i	1.63671	−	1.18914i
$257$	6.94330	+	5.04460i	0.433111	+	0.314674i	0.782892	−	0.622158i	$-0.213744\pi$
$257$	6.94330	+	5.04460i	0.433111	+	0.314674i	−0.349781	+	0.936832i	$0.613744\pi$
$258$	4.50838	+	13.8754i	0.280680	+	0.863843i
$259$	11.4804	+	35.3331i	0.713358	+	2.19549i
$260$	−3.23416	−	2.34975i	−0.200574	−	0.145726i
$261$	12.7068	−	9.23201i	0.786529	−	0.571447i
$262$	−12.0173	+	36.9855i	−0.742433	+	2.28497i
$263$	−16.7442			−1.03249			−0.516245	−	0.856441i	$-0.672671\pi$
$263$	−16.7442			−1.03249			−0.516245	+	0.856441i	$0.672671\pi$
$264$	6.58346	−	12.3340i	0.405184	−	0.759104i
$265$	−4.55156			−0.279600
$266$	15.6087	−	48.0388i	0.957033	−	2.94545i
$267$	2.00475	−	1.45653i	0.122688	−	0.0891384i
$268$	9.10152	+	6.61264i	0.555964	+	0.403931i
$269$	2.26615	+	6.97449i	0.138170	+	0.425242i	0.996070	−	0.0885745i	$-0.0282311\pi$
$269$	2.26615	+	6.97449i	0.138170	+	0.425242i	−0.857900	+	0.513817i	$0.828231\pi$
$270$	−3.31389	−	10.1991i	−0.201677	−	0.620697i
$271$	17.7254	+	12.8783i	1.07674	+	0.782299i	0.977112	−	0.212726i	$-0.0682341\pi$
$271$	17.7254	+	12.8783i	1.07674	+	0.782299i	0.0996300	+	0.995025i	$0.468234\pi$
$272$	−7.65962	+	5.56504i	−0.464433	+	0.337430i
$273$	−1.00070	+	3.07984i	−0.0605651	+	0.186400i
$274$	−25.6185			−1.54767
$275$	−12.0180	+	5.83774i	−0.724710	+	0.352029i
$276$	8.17852			0.492289
$277$	−2.97124	+	9.14454i	−0.178525	+	0.549442i	−0.999777	−	0.0211232i	$-0.993276\pi$
$277$	−2.97124	+	9.14454i	−0.178525	+	0.549442i	0.821252	+	0.570565i	$0.193276\pi$
$278$	−34.6756	+	25.1933i	−2.07970	+	1.51099i
$279$	−6.13928	−	4.46045i	−0.367549	−	0.267040i
$280$	5.98803	+	18.4293i	0.357854	+	1.10136i
$281$	0.510273	+	1.57046i	0.0304404	+	0.0936858i	0.965122	−	0.261799i	$-0.0843158\pi$
$281$	0.510273	+	1.57046i	0.0304404	+	0.0936858i	−0.934682	+	0.355485i	$0.884316\pi$
$282$	3.19856	+	2.32389i	0.190472	+	0.138386i
$283$	−11.8431	+	8.60450i	−0.703998	+	0.511484i	−0.881232	−	0.472684i	$-0.843285\pi$
$283$	−11.8431	+	8.60450i	−0.703998	+	0.511484i	0.177234	+	0.984169i	$0.443285\pi$
$284$	13.1844	−	40.5774i	0.782350	−	2.40783i
$285$	−4.33829			−0.256978
$286$	−5.66015	−	5.88008i	−0.334692	−	0.347697i
$287$	−13.3363			−0.787216
$288$	−0.396095	+	1.21906i	−0.0233401	+	0.0718336i
$289$	9.89839	−	7.19160i	0.582258	−	0.423035i
$290$	13.3680	+	9.71245i	0.784999	+	0.570335i
$291$	1.44293	+	4.44089i	0.0845862	+	0.260330i
$292$	20.0923	+	61.8378i	1.17581	+	3.61879i
$293$	0.328275	+	0.238506i	0.0191780	+	0.0139337i	0.597333	−	0.801993i	$-0.296227\pi$
$293$	0.328275	+	0.238506i	0.0191780	+	0.0139337i	−0.578155	+	0.815927i	$0.696227\pi$
$294$	13.4415	−	9.76584i	0.783926	−	0.569555i
$295$	−0.0132917	+	0.0409076i	−0.000773873	+	0.00238173i
$296$	−48.3611			−2.81093
$297$	−2.01747	−	14.5239i	−0.117066	−	0.842760i
$298$	18.3428			1.06257
$299$	0.747810	−	2.30152i	0.0432469	−	0.133100i
$300$	−11.0144	+	8.00240i	−0.635914	+	0.462019i
$301$	−22.3684	−	16.2516i	−1.28930	−	0.936728i
$302$	−1.99448	−	6.13838i	−0.114769	−	0.353224i
$303$	−3.49116	−	10.7447i	−0.200562	−	0.617266i
$304$	18.5337	+	13.4655i	1.06298	+	0.772299i
$305$	−8.46846	+	6.15270i	−0.484903	+	0.352302i
$306$	−3.82718	+	11.7789i	−0.218786	+	0.673353i
$307$	9.00182			0.513761			0.256880	−	0.966443i	$-0.417305\pi$
$307$	9.00182			0.513761			0.256880	+	0.966443i	$0.417305\pi$
$308$	7.19217	+	51.7767i	0.409812	+	2.95025i
$309$	−1.60990			−0.0915839
$310$	2.46703	−	7.59275i	0.140118	−	0.431239i
$311$	−5.15507	+	3.74538i	−0.292317	+	0.212381i	−0.724272	−	0.689514i	$-0.757824\pi$
$311$	−5.15507	+	3.74538i	−0.292317	+	0.212381i	0.431955	+	0.901895i	$0.357824\pi$
$312$	−3.41036	−	2.47777i	−0.193074	−	0.140276i
$313$	5.68011	+	17.4816i	0.321059	+	0.988118i	0.973188	+	0.230010i	$0.0738759\pi$
$313$	5.68011	+	17.4816i	0.321059	+	0.988118i	−0.652129	+	0.758108i	$0.726124\pi$
$314$	−10.7608	−	33.1185i	−0.607270	−	1.86898i
$315$	7.14503	+	5.19116i	0.402577	+	0.292489i
$316$	30.4919	−	22.1536i	1.71530	−	1.24624i
$317$	−1.91129	+	5.88234i	−0.107349	+	0.330385i	−0.990274	−	0.139127i	$-0.955570\pi$
$317$	−1.91129	+	5.88234i	−0.107349	+	0.330385i	0.882926	+	0.469512i	$0.155570\pi$
$318$	−9.46902			−0.530996
$319$	15.6688	+	16.2777i	0.877286	+	0.911374i
$320$	7.20196			0.402602
$321$	3.73064	−	11.4817i	0.208224	−	0.640848i
$322$	−18.7228	+	13.6029i	−1.04338	+	0.758060i
$323$	9.32753	+	6.77685i	0.518998	+	0.377074i
$324$	4.05150	+	12.4692i	0.225083	+	0.692735i
$325$	1.24485	+	3.83126i	0.0690520	+	0.212520i
$326$	35.4818	+	25.7790i	1.96516	+	1.42777i
$327$	7.96314	−	5.78556i	0.440363	−	0.319942i
$328$	5.36461	−	16.5106i	0.296211	−	0.911644i
$329$	−7.49267			−0.413084
$330$	6.02997	−	2.92906i	0.331939	−	0.161240i
$331$	7.43488			0.408658			0.204329	−	0.978902i	$-0.434499\pi$
$331$	7.43488			0.408658			0.204329	+	0.978902i	$0.434499\pi$
$332$	15.3880	−	47.3595i	0.844528	−	2.59919i
$333$	−17.8319	+	12.9556i	−0.977183	+	0.709965i
$334$	−39.6293	−	28.7924i	−2.16842	−	1.57545i
$335$	0.844909	+	2.60036i	0.0461623	+	0.142073i
$336$	4.34036	+	13.3583i	0.236786	+	0.728753i
$337$	−29.1483	−	21.1775i	−1.58781	−	1.15361i	−0.906983	−	0.421167i	$-0.861621\pi$
$337$	−29.1483	−	21.1775i	−1.58781	−	1.15361i	−0.680827	−	0.732444i	$-0.738379\pi$
$338$	−1.99086	+	1.44644i	−0.108288	+	0.0786761i
$339$	4.38178	−	13.4857i	0.237985	−	0.732444i
$340$	−8.72633			−0.473251
$341$	5.14025	−	9.63016i	0.278360	−	0.521502i
$342$	29.9675			1.62046
$343$	−1.32375	+	4.07410i	−0.0714760	+	0.219981i
$344$	29.1177	−	21.1552i	1.56992	−	1.14061i
$345$	1.60807	+	1.16833i	0.0865753	+	0.0629007i
$346$	1.57105	+	4.83519i	0.0844601	+	0.259942i
$347$	−6.99220	−	21.5198i	−0.375361	−	1.15524i	−0.943235	−	0.332126i	$-0.892234\pi$
$347$	−6.99220	−	21.5198i	−0.375361	−	1.15524i	0.567874	−	0.823115i	$-0.307766\pi$
$348$	18.6258	+	13.5324i	0.998446	+	0.725414i
$349$	3.17606	−	2.30754i	0.170011	−	0.123520i	−0.499526	−	0.866299i	$-0.666493\pi$
$349$	3.17606	−	2.30754i	0.170011	−	0.123520i	0.669537	+	0.742779i	$0.266493\pi$
$350$	11.9048	−	36.6392i	0.636338	−	1.95845i
$351$	−4.42115			−0.235984
$352$	−1.81533	−	0.323091i	−0.0967573	−	0.0172208i
$353$	−15.8328			−0.842694			−0.421347	−	0.906900i	$-0.638443\pi$
$353$	−15.8328			−0.842694			−0.421347	+	0.906900i	$0.638443\pi$
$354$	−0.0276519	+	0.0851038i	−0.00146968	+	0.00452322i
$355$	8.38893	−	6.09492i	0.445238	−	0.323485i
$356$	−9.75721	−	7.08902i	−0.517131	−	0.375718i
$357$	2.18440	+	6.72288i	0.115611	+	0.355813i
$358$	4.50851	+	13.8758i	0.238282	+	0.733357i
$359$	1.94108	+	1.41028i	0.102446	+	0.0744317i	0.637829	−	0.770178i	$-0.279833\pi$
$359$	1.94108	+	1.41028i	0.102446	+	0.0744317i	−0.535383	+	0.844610i	$0.679833\pi$
$360$	−9.30090	+	6.75750i	−0.490200	+	0.356151i
$361$	2.74943	−	8.46189i	0.144707	−	0.445362i
$362$	−51.8242			−2.72382
$363$	8.81923	−	2.49832i	0.462890	−	0.131128i
$364$	15.7611			0.826109
$365$	−4.88317	+	15.0288i	−0.255597	+	0.786646i
$366$	−17.6177	+	12.8000i	−0.920892	+	0.669067i
$367$	14.7798	+	10.7381i	0.771498	+	0.560526i	0.902415	−	0.430867i	$-0.141792\pi$
$367$	14.7798	+	10.7381i	0.771498	+	0.560526i	−0.130917	+	0.991393i	$0.541792\pi$
$368$	−3.24349	−	9.98244i	−0.169079	−	0.520371i
$369$	−2.44502	−	7.52500i	−0.127283	−	0.391736i
$370$	−18.7599	−	13.6299i	−0.975282	−	0.708584i
$371$	14.5178	−	10.5478i	0.753729	−	0.547616i
$372$	3.43733	−	10.5790i	0.178217	−	0.548496i
$373$	9.31655			0.482393			0.241196	−	0.970476i	$-0.422460\pi$
$373$	9.31655			0.482393			0.241196	+	0.970476i	$0.422460\pi$
$374$	−17.5402	−	3.12179i	−0.906982	−	0.161424i
$375$	−7.41566			−0.382943
$376$	3.01398	−	9.27607i	0.155434	−	0.478377i
$377$	5.51123	−	4.00414i	0.283843	−	0.206224i
$378$	34.2056	+	24.8518i	1.75935	+	1.27824i
$379$	6.08659	+	18.7326i	0.312647	+	0.962229i	0.976712	+	0.214554i	$0.0688299\pi$
$379$	6.08659	+	18.7326i	0.312647	+	0.962229i	−0.664065	+	0.747675i	$0.731170\pi$
$380$	6.52481	+	20.0813i	0.334715	+	1.03015i
$381$	−2.00145	−	1.45414i	−0.102537	−	0.0744978i
$382$	19.2806	−	14.0081i	0.986479	−	0.716719i
$383$	1.51665	−	4.66776i	0.0774971	−	0.238511i	−0.904801	−	0.425834i	$-0.859981\pi$
$383$	1.51665	−	4.66776i	0.0774971	−	0.238511i	0.982299	+	0.187322i	$0.0599809\pi$
$384$	15.9094			0.811874
$385$	−5.98234	+	11.2078i	−0.304888	+	0.571202i
$386$	4.25823			0.216738
$387$	5.06904	−	15.6009i	0.257674	−	0.793038i
$388$	18.3860	−	13.3582i	0.933409	−	0.678161i
$389$	13.7454	+	9.98663i	0.696921	+	0.506342i	0.878928	−	0.476955i	$-0.158259\pi$
$389$	13.7454	+	9.98663i	0.696921	+	0.506342i	−0.182007	+	0.983297i	$0.558259\pi$
$390$	−0.624600	−	1.92232i	−0.0316279	−	0.0973405i
$391$	−1.63237	−	5.02392i	−0.0825525	−	0.254071i
$392$	−33.1596	−	24.0919i	−1.67481	−	1.21682i
$393$	−10.6537	+	7.74037i	−0.537408	+	0.390450i
$394$	18.8132	−	57.9011i	0.947796	−	2.91702i
$395$	9.16005			0.460892
$396$	−27.8964	+	13.5507i	−1.40185	+	0.680949i
$397$	16.8443			0.845391			0.422695	−	0.906272i	$-0.361084\pi$
$397$	16.8443			0.845391			0.422695	+	0.906272i	$0.361084\pi$
$398$	−1.61790	+	4.97938i	−0.0810980	+	0.249594i
$399$	13.8376	−	10.0536i	0.692746	−	0.503310i
$400$	14.1356	+	10.2701i	0.706781	+	0.513507i
$401$	10.8507	+	33.3950i	0.541858	+	1.66767i	0.728346	+	0.685210i	$0.240290\pi$
$401$	10.8507	+	33.3950i	0.541858	+	1.66767i	−0.186488	+	0.982457i	$0.559710\pi$
$402$	1.75774	+	5.40977i	0.0876681	+	0.269815i
$403$	−2.66275	−	1.93460i	−0.132641	−	0.0963693i
$404$	−44.4847	+	32.3201i	−2.21320	+	1.60798i
$405$	−0.984661	+	3.03048i	−0.0489282	+	0.150586i
$406$	−65.1470			−3.23319
$407$	−21.9887	−	22.8431i	−1.08994	−	1.13229i
$408$	−9.20175			−0.455554
$409$	−4.73216	+	14.5641i	−0.233990	+	0.720149i	0.763263	+	0.646088i	$0.223596\pi$
$409$	−4.73216	+	14.5641i	−0.233990	+	0.720149i	−0.997254	+	0.0740610i	$0.976404\pi$
$410$	6.73427	−	4.89274i	0.332582	−	0.241635i
$411$	−7.01825	−	5.09905i	−0.346185	−	0.251518i
$412$	2.42129	+	7.45197i	0.119288	+	0.367132i
$413$	−0.0524040	−	0.161283i	−0.00257863	−	0.00793622i
$414$	−11.1080	−	8.07043i	−0.545928	−	0.396640i
$415$	9.79106	−	7.11362i	0.480624	−	0.349194i
$416$	−0.171796	+	0.528734i	−0.00842299	+	0.0259233i
$417$	−14.5139			−0.710748
$418$	5.93111	+	42.6983i	0.290100	+	2.08844i
$419$	14.5369			0.710173			0.355086	−	0.934833i	$-0.384451\pi$
$419$	14.5369			0.710173			0.355086	+	0.934833i	$0.384451\pi$
$420$	−4.00044	+	12.3121i	−0.195201	+	0.600768i
$421$	4.88420	−	3.54858i	0.238041	−	0.172947i	−0.462369	−	0.886688i	$-0.653000\pi$
$421$	4.88420	−	3.54858i	0.238041	−	0.172947i	0.700410	+	0.713741i	$0.253000\pi$
$422$	7.07723	+	5.14191i	0.344514	+	0.250304i
$423$	−1.37368	−	4.22774i	−0.0667904	−	0.205560i
$424$	7.21851	+	22.2163i	0.350562	+	1.07892i
$425$	7.11412	+	5.16871i	0.345085	+	0.250719i
$426$	17.4523	−	12.6798i	0.845564	−	0.614339i
$427$	12.7530	−	39.2498i	0.617162	−	1.89943i
$428$	−58.7581			−2.84018
$429$	−0.380252	−	2.73745i	−0.0183588	−	0.132165i
$430$	17.2574			0.832227
$431$	1.52385	−	4.68994i	0.0734015	−	0.225907i	−0.907624	−	0.419783i	$-0.862106\pi$
$431$	1.52385	−	4.68994i	0.0734015	−	0.225907i	0.981026	+	0.193877i	$0.0621061\pi$
$432$	−15.5137	+	11.2714i	−0.746403	+	0.542293i
$433$	4.47522	+	3.25144i	0.215065	+	0.156254i	0.690103	−	0.723712i	$-0.257565\pi$
$433$	4.47522	+	3.25144i	0.215065	+	0.156254i	−0.475037	+	0.879966i	$0.657565\pi$
$434$	9.72656	+	29.9353i	0.466890	+	1.43694i
$435$	1.72906	+	5.32150i	0.0829021	+	0.255147i
$436$	−38.7570	−	28.1586i	−1.85613	−	1.34855i
$437$	−10.3406	+	7.51292i	−0.494660	+	0.359392i
$438$	−10.1589	+	31.2659i	−0.485411	+	1.49394i
$439$	16.1221			0.769468			0.384734	−	0.923028i	$-0.374293\pi$
$439$	16.1221			0.769468			0.384734	+	0.923028i	$0.374293\pi$
$440$	−11.4690	−	11.9147i	−0.546764	−	0.568009i
$441$	−18.6808			−0.889562
$442$	−1.65994	+	5.10877i	−0.0789553	+	0.242999i
$443$	−1.79332	+	1.30292i	−0.0852031	+	0.0619037i	−0.629571	−	0.776943i	$-0.716769\pi$
$443$	−1.79332	+	1.30292i	−0.0852031	+	0.0619037i	0.544368	+	0.838846i	$0.316769\pi$
$444$	−26.1383	−	18.9906i	−1.24047	−	0.901253i
$445$	−0.905777	−	2.78770i	−0.0429380	−	0.132149i
$446$	−14.2119	−	43.7399i	−0.672955	−	2.07114i
$447$	5.02507	+	3.65092i	0.237677	+	0.172683i
$448$	−22.9717	+	16.6899i	−1.08531	+	0.788523i
$449$	0.0647060	−	0.199145i	0.00305366	−	0.00939821i	−0.949518	−	0.313712i	$-0.898427\pi$
$449$	0.0647060	−	0.199145i	0.00305366	−	0.00939821i	0.952572	+	0.304314i	$0.0984272\pi$
$450$	22.8562			1.07745
$451$	10.2378	−	4.97304i	0.482081	−	0.234171i
$452$	−69.0135			−3.24612
$453$	0.675378	−	2.07860i	0.0317320	−	0.0976612i
$454$	−23.2937	+	16.9239i	−1.09323	+	0.794277i
$455$	3.09897	+	2.25153i	0.145282	+	0.105553i
$456$	6.88029	+	21.1753i	0.322199	+	0.991626i
$457$	−10.4030	−	32.0170i	−0.486630	−	1.49769i	−0.829607	−	0.558348i	$-0.811435\pi$
$457$	−10.4030	−	32.0170i	−0.486630	−	1.49769i	0.342977	−	0.939344i	$-0.388565\pi$
$458$	−10.8113	−	7.85488i	−0.505179	−	0.367034i
$459$	−7.80766	+	5.67260i	−0.364431	+	0.264774i
$460$	2.98947	−	9.20065i	0.139385	−	0.428983i
$461$	21.4300			0.998093			0.499046	−	0.866575i	$-0.333684\pi$
$461$	21.4300			0.998093			0.499046	+	0.866575i	$0.333684\pi$
$462$	−12.4456	+	23.3166i	−0.579021	+	1.08478i
$463$	−14.4598			−0.672005			−0.336002	−	0.941861i	$-0.609075\pi$
$463$	−14.4598			−0.672005			−0.336002	+	0.941861i	$0.609075\pi$
$464$	9.13050	−	28.1008i	0.423873	−	1.30455i
$465$	2.18710	−	1.58902i	0.101424	−	0.0736890i
$466$	26.1509	+	18.9997i	1.21142	+	0.880146i
$467$	−3.64605	−	11.2214i	−0.168719	−	0.519264i	0.830572	−	0.556911i	$-0.188014\pi$
$467$	−3.64605	−	11.2214i	−0.168719	−	0.519264i	−0.999291	+	0.0376470i	$0.988014\pi$
$468$	2.88959	+	8.89323i	0.133571	+	0.411090i
$469$	−8.72106	−	6.33622i	−0.402701	−	0.292580i
$470$	3.78349	−	2.74887i	0.174519	−	0.126796i
$471$	3.64388	−	11.2147i	0.167901	−	0.516747i
$472$	0.220751			0.0101609
$473$	23.2317	+	4.13476i	1.06819	+	0.190117i
$474$	19.0565			0.875293
$475$	6.57506	−	20.2359i	0.301684	−	0.928489i
$476$	27.8338	−	20.2225i	1.27576	−	0.926896i
$477$	8.61325	+	6.25789i	0.394374	+	0.286529i
$478$	−6.73806	−	20.7376i	−0.308192	−	0.948516i
$479$	9.08538	+	27.9619i	0.415122	+	1.27761i	0.912142	+	0.409874i	$0.134427\pi$
$479$	9.08538	+	27.9619i	0.415122	+	1.27761i	−0.497020	+	0.867739i	$0.665573\pi$
$480$	−0.369424	−	0.268403i	−0.0168618	−	0.0122508i
$481$	−7.73413	+	5.61917i	−0.352646	+	0.256212i
$482$	−15.1955	+	46.7669i	−0.692135	+	2.13017i
$483$	−7.83665			−0.356580
$484$	−24.8285	−	37.0654i	−1.12857	−	1.68479i
$485$	5.52334			0.250802
$486$	−12.1345	+	37.3463i	−0.550434	+	1.69406i
$487$	−0.0681851	+	0.0495394i	−0.00308976	+	0.00224484i	−0.589329	−	0.807893i	$-0.700608\pi$
$487$	−0.0681851	+	0.0495394i	−0.00308976	+	0.00224484i	0.586239	+	0.810138i	$0.300608\pi$
$488$	43.4620	+	31.5770i	1.96743	+	1.42942i
$489$	4.58932	+	14.1245i	0.207536	+	0.638731i
$490$	−6.07311	−	18.6911i	−0.274355	−	0.844378i
$491$	24.2208	+	17.5975i	1.09307	+	0.794162i	0.979915	−	0.199415i	$-0.0639042\pi$
$491$	24.2208	+	17.5975i	1.09307	+	0.794162i	0.113156	+	0.993577i	$0.463904\pi$
$492$	9.38290	−	6.81707i	0.423014	−	0.307337i
$493$	4.59516	−	14.1424i	0.206956	−	0.636944i
$494$	12.9976			0.584791
$495$	−7.42077	−	1.32074i	−0.333539	−	0.0593630i
$496$	−14.2756			−0.640994
$497$	−12.6333	+	38.8812i	−0.566679	+	1.74406i
$498$	20.3692	−	14.7991i	0.912766	−	0.663164i
$499$	26.1415	+	18.9929i	1.17026	+	0.850241i	0.991040	−	0.133569i	$-0.0426437\pi$
$499$	26.1415	+	18.9929i	1.17026	+	0.850241i	0.179217	+	0.983810i	$0.442644\pi$
$500$	11.1532	+	34.3259i	0.498785	+	1.53510i
$501$	−5.12577	−	15.7755i	−0.229002	−	0.704797i
$502$	58.8049	+	42.7243i	2.62459	+	1.90688i
$503$	5.54962	−	4.03204i	0.247446	−	0.179780i	−0.457148	−	0.889390i	$-0.651129\pi$
$503$	5.54962	−	4.03204i	0.247446	−	0.179780i	0.704594	+	0.709611i	$0.251129\pi$
$504$	14.0066	−	43.1080i	0.623905	−	1.92018i
$505$	−13.3636			−0.594674
$506$	9.30042	−	17.4241i	0.413454	−	0.774598i
$507$	−0.833297			−0.0370080
$508$	−3.72080	+	11.4514i	−0.165084	+	0.508075i
$509$	−2.33893	+	1.69933i	−0.103671	+	0.0753215i	−0.638413	−	0.769694i	$-0.720409\pi$
$509$	−2.33893	+	1.69933i	−0.103671	+	0.0753215i	0.534742	+	0.845015i	$0.320409\pi$
$510$	−3.56948	−	2.59338i	−0.158059	−	0.114837i
$511$	−19.2524	−	59.2529i	−0.851678	−	2.62120i
$512$	−12.8154	−	39.4418i	−0.566366	−	1.74310i
$513$	18.8919	+	13.7257i	0.834096	+	0.606006i
$514$	17.0863	−	12.4139i	0.753645	−	0.547555i
$515$	−0.588462	+	1.81110i	−0.0259307	+	0.0798066i
$516$	24.0449			1.05852
$517$	5.75189	−	2.79398i	0.252968	−	0.122879i
$518$	91.4234			4.01692
$519$	−0.531995	+	1.63731i	−0.0233520	+	0.0718700i
$520$	−4.03402	+	2.93089i	−0.176903	+	0.128528i
$521$	−18.2402	−	13.2523i	−0.799117	−	0.580593i	0.111538	−	0.993760i	$-0.464422\pi$
$521$	−18.2402	−	13.2523i	−0.799117	−	0.580593i	−0.910655	+	0.413168i	$0.864422\pi$
$522$	−11.9438	−	36.7592i	−0.522765	−	1.60891i
$523$	−7.53860	−	23.2014i	−0.329640	−	1.01453i	−0.969302	−	0.245871i	$-0.920926\pi$
$523$	−7.53860	−	23.2014i	−0.329640	−	1.01453i	0.639663	−	0.768656i	$-0.279074\pi$
$524$	51.8522	+	37.6728i	2.26517	+	1.64574i
$525$	10.5539	−	7.66789i	0.460612	−	0.334654i
$526$	−12.7329	+	39.1879i	−0.555182	+	1.70867i
$527$	−7.18456			−0.312965
$528$	−8.31319	−	8.63621i	−0.361785	−	0.375843i
$529$	−17.1438			−0.745382
$530$	−3.46119	+	10.6524i	−0.150344	+	0.462712i
$531$	0.0813964	−	0.0591379i	0.00353230	−	0.00256637i
$532$	−67.3484	−	48.9314i	−2.91992	−	2.12145i
$533$	−1.06046	−	3.26377i	−0.0459338	−	0.141370i
$534$	−1.88437	−	5.79949i	−0.0815447	−	0.250969i
$535$	−11.5531	−	8.39378i	−0.499482	−	0.362895i
$536$	11.3525	−	8.24806i	0.490352	−	0.356262i
$537$	−1.52669	+	4.69867i	−0.0658815	+	0.202762i
$538$	18.0463			0.778032
$539$	−3.69727	−	26.6168i	−0.159253	−	1.14646i
$540$	−17.6742			−0.760576
$541$	4.69482	−	14.4492i	0.201846	−	0.621218i	−0.797982	−	0.602681i	$-0.794099\pi$
$541$	4.69482	−	14.4492i	0.201846	−	0.621218i	0.999828	−	0.0185372i	$-0.00590091\pi$
$542$	43.6193	−	31.6913i	1.87361	−	1.36126i
$543$	−14.1974	−	10.3150i	−0.609267	−	0.442659i
$544$	0.375008	+	1.15416i	0.0160783	+	0.0494840i
$545$	−3.59788	−	11.0731i	−0.154116	−	0.474321i
$546$	6.44706	+	4.68406i	0.275909	+	0.200459i
$547$	3.68407	−	2.67664i	0.157520	−	0.114445i	−0.506233	−	0.862396i	$-0.668963\pi$
$547$	3.68407	−	2.67664i	0.157520	−	0.114445i	0.663753	+	0.747952i	$0.268963\pi$
$548$	−13.0473	+	40.1554i	−0.557352	+	1.71535i
$549$	24.4848			1.04499
$550$	4.52366	+	32.5660i	0.192889	+	1.38862i
$551$	−35.9809			−1.53284
$552$	3.15234	−	9.70192i	0.134173	−	0.412941i
$553$	−29.2173	+	21.2276i	−1.24244	+	0.902689i
$554$	19.1424	+	13.9077i	0.813281	+	0.590883i
$555$	−2.42646	−	7.46788i	−0.102998	−	0.316994i
$556$	21.8289	+	67.1825i	0.925753	+	2.84917i
$557$	−9.56758	−	6.95125i	−0.405391	−	0.294534i	0.366342	−	0.930480i	$-0.380610\pi$
$557$	−9.56758	−	6.95125i	−0.405391	−	0.294534i	−0.771733	+	0.635946i	$0.780610\pi$
$558$	−15.1077	+	10.9764i	−0.639562	+	0.464669i
$559$	2.19856	−	6.76648i	0.0929893	−	0.286192i
$560$	16.6143			0.702081
$561$	−4.18383	−	4.34639i	−0.176641	−	0.183505i
$562$	4.06352			0.171409
$563$	1.84982	−	5.69315i	0.0779605	−	0.239938i	−0.904479	−	0.426517i	$-0.859740\pi$
$563$	1.84982	−	5.69315i	0.0779605	−	0.239938i	0.982440	+	0.186580i	$0.0597403\pi$
$564$	5.27156	−	3.83001i	0.221973	−	0.161273i
$565$	−13.5695	−	9.85880i	−0.570872	−	0.414763i
$566$	11.1320	+	34.2606i	0.467911	+	1.44008i
$567$	−3.88214	−	11.9480i	−0.163034	−	0.501769i
$568$	−43.0539	−	31.2805i	−1.80650	−	1.31250i
$569$	−13.8956	+	10.0957i	−0.582533	+	0.423235i	−0.839637	−	0.543149i	$-0.817232\pi$
$569$	−13.8956	+	10.0957i	−0.582533	+	0.423235i	0.257103	+	0.966384i	$0.417232\pi$
$570$	−3.29901	+	10.1533i	−0.138180	+	0.425275i
$571$	−17.1160			−0.716282			−0.358141	−	0.933668i	$-0.616589\pi$
$571$	−17.1160			−0.716282			−0.358141	+	0.933668i	$0.616589\pi$
$572$	−12.0993	+	5.87726i	−0.505898	+	0.245741i
$573$	8.07011			0.337134
$574$	−10.1414	+	31.2121i	−0.423295	+	1.30277i
$575$	−7.88682	+	5.73011i	−0.328903	+	0.238962i
$576$	−13.6288	−	9.90190i	−0.567867	−	0.412579i
$577$	4.94909	+	15.2317i	0.206033	+	0.634106i	0.999669	+	0.0257128i	$0.00818554\pi$
$577$	4.94909	+	15.2317i	0.206033	+	0.634106i	−0.793636	+	0.608393i	$0.791814\pi$
$578$	−9.30404	−	28.6349i	−0.386997	−	1.19105i
$579$	1.16655	+	0.847551i	0.0484803	+	0.0352230i
$580$	22.0319	−	16.0071i	0.914825	−	0.664659i
$581$	−14.7448	+	45.3798i	−0.611717	+	1.88267i
$582$	11.4907			0.476304
$583$	−7.21164	+	13.5109i	−0.298676	+	0.559563i
$584$	81.1007			3.35597
$585$	−0.702274	+	2.16138i	−0.0290355	+	0.0893620i
$586$	0.807830	−	0.586923i	0.0333712	−	0.0242456i
$587$	15.0943	+	10.9666i	0.623007	+	0.452641i	0.853971	−	0.520321i	$-0.174188\pi$
$587$	15.0943	+	10.9666i	0.623007	+	0.452641i	−0.230964	+	0.972962i	$0.574188\pi$
$588$	−8.46169	−	26.0424i	−0.348954	−	1.07397i
$589$	5.37201	+	16.5333i	0.221350	+	0.681244i
$590$	0.0856324	+	0.0622156i	0.00352543	+	0.00256137i
$591$	16.6785	−	12.1176i	0.686060	−	0.498452i
$592$	−12.8132	+	39.4350i	−0.526619	+	1.62077i
$593$	−0.889024			−0.0365078			−0.0182539	−	0.999833i	$-0.505811\pi$
$593$	−0.889024			−0.0365078			−0.0182539	+	0.999833i	$0.505811\pi$
$594$	−35.5257	−	6.32284i	−1.45764	−	0.259429i
$595$	8.36155			0.342790
$596$	9.34185	−	28.7513i	0.382657	−	1.17770i
$597$	−1.43431	+	1.04209i	−0.0587026	+	0.0426499i
$598$	−4.81780	−	3.50034i	−0.197014	−	0.143139i
$599$	−1.73416	−	5.33720i	−0.0708559	−	0.218072i	0.909358	−	0.416016i	$-0.136574\pi$
$599$	−1.73416	−	5.33720i	−0.0708559	−	0.218072i	−0.980213	+	0.197943i	$0.936574\pi$
$600$	5.24760	+	16.1504i	0.214232	+	0.659339i
$601$	22.3377	+	16.2293i	0.911176	+	0.662008i	0.941312	−	0.337538i	$-0.109594\pi$
$601$	22.3377	+	16.2293i	0.911176	+	0.662008i	−0.0301363	+	0.999546i	$0.509594\pi$
$602$	−55.0450	+	39.9925i	−2.24347	+	1.62997i
$603$	1.97633	−	6.08252i	0.0804824	−	0.247699i
$604$	−10.6373			−0.432825
$605$	0.413116	−	10.8346i	0.0167956	−	0.440491i
$606$	−27.8016			−1.12936
$607$	−13.2444	+	40.7622i	−0.537575	+	1.65449i	0.200444	+	0.979705i	$0.435762\pi$
$607$	−13.2444	+	40.7622i	−0.537575	+	1.65449i	−0.738019	+	0.674780i	$0.764238\pi$
$608$	2.37558	−	1.72596i	0.0963425	−	0.0699969i
$609$	−17.8472	−	12.9667i	−0.723204	−	0.525439i
$610$	7.95997	+	24.4983i	0.322290	+	0.991906i
$611$	−0.595796	−	1.83367i	−0.0241033	−	0.0741824i
$612$	16.5135	+	11.9977i	0.667518	+	0.484980i
$613$	−14.6680	+	10.6569i	−0.592436	+	0.430430i	−0.843186	−	0.537622i	$-0.819323\pi$
$613$	−14.6680	+	10.6569i	−0.592436	+	0.430430i	0.250750	+	0.968052i	$0.419323\pi$
$614$	6.84534	−	21.0678i	0.276255	−	0.850227i
$615$	2.81871			0.113661
$616$	64.1932	+	11.4251i	2.58642	+	0.460329i
$617$	17.6030			0.708671			0.354336	−	0.935118i	$-0.384707\pi$
$617$	17.6030			0.708671			0.354336	+	0.935118i	$0.384707\pi$
$618$	−1.22423	+	3.76779i	−0.0492457	+	0.151563i
$619$	−10.7576	+	7.81582i	−0.432383	+	0.314144i	−0.782601	−	0.622524i	$-0.786107\pi$
$619$	−10.7576	+	7.81582i	−0.432383	+	0.314144i	0.350218	+	0.936668i	$0.386107\pi$
$620$	−10.6447	−	7.73384i	−0.427502	−	0.310598i
$621$	−3.30618	−	10.1754i	−0.132672	−	0.408324i
$622$	4.84553	+	14.9130i	0.194288	+	0.597957i
$623$	9.34934	+	6.79269i	0.374573	+	0.272143i
$624$	−2.92401	+	2.12442i	−0.117054	+	0.0850449i
$625$	3.51364	−	10.8139i	0.140546	−	0.432555i
$626$	45.2331			1.80788
$627$	−6.87374	+	12.8778i	−0.274511	+	0.514290i
$628$	−57.3916			−2.29017
$629$	−6.44857	+	19.8467i	−0.257121	+	0.791339i
$630$	17.5827	−	12.7746i	0.700512	−	0.508952i
$631$	31.6649	+	23.0059i	1.26056	+	0.915850i	0.998785	−	0.0492796i	$-0.0156925\pi$
$631$	31.6649	+	23.0059i	1.26056	+	0.915850i	0.261774	+	0.965129i	$0.415693\pi$
$632$	−14.5273	−	44.7105i	−0.577866	−	1.77849i
$633$	0.915389	+	2.81728i	0.0363834	+	0.111977i
$634$	12.3136	+	8.94632i	0.489034	+	0.355304i
$635$	−2.36746	+	1.72006i	−0.0939498	+	0.0682585i
$636$	−4.82249	+	14.8421i	−0.191224	+	0.588527i
$637$	−8.10231			−0.321025
$638$	50.0113	−	24.2930i	1.97997	−	0.961770i
$639$	−24.2548			−0.959507
$640$	5.81533	−	17.8977i	0.229871	−	0.707470i
$641$	−3.37901	+	2.45499i	−0.133463	+	0.0969664i	−0.652514	−	0.757777i	$-0.726286\pi$
$641$	−3.37901	+	2.45499i	−0.133463	+	0.0969664i	0.519051	+	0.854743i	$0.326286\pi$
$642$	−24.0348	−	17.4623i	−0.948580	−	0.689184i
$643$	−13.5563	−	41.7221i	−0.534610	−	1.64536i	−0.744490	−	0.667633i	$-0.767308\pi$
$643$	−13.5563	−	41.7221i	−0.534610	−	1.64536i	0.209881	−	0.977727i	$-0.432692\pi$
$644$	11.7863	+	36.2746i	0.464447	+	1.42942i
$645$	4.72772	+	3.43489i	0.186154	+	0.135249i
$646$	22.9535	−	16.6767i	0.903094	−	0.656136i
$647$	−1.04476	+	3.21545i	−0.0410739	+	0.126413i	−0.969491	−	0.245128i	$-0.921170\pi$
$647$	−1.04476	+	3.21545i	−0.0410739	+	0.126413i	0.928417	+	0.371540i	$0.121170\pi$
$648$	16.3535			0.642425
$649$	0.100371	+	0.104271i	0.00393989	+	0.00409298i
$650$	9.91329			0.388831
$651$	−3.29364	+	10.1368i	−0.129088	+	0.397292i
$652$	58.4776	−	42.4865i	2.29016	−	1.66390i
$653$	15.3886	+	11.1805i	0.602204	+	0.437527i	0.846660	−	0.532134i	$-0.178610\pi$
$653$	15.3886	+	11.1805i	0.602204	+	0.437527i	−0.244457	+	0.969660i	$0.578610\pi$
$654$	−7.48499	−	23.0364i	−0.292686	−	0.900796i
$655$	4.81352	+	14.8145i	0.188080	+	0.578850i
$656$	−12.0418	−	8.74891i	−0.470155	−	0.341587i
$657$	29.9038	−	21.7264i	1.16666	−	0.847627i
$658$	−5.69772	+	17.5358i	−0.222120	+	0.683616i
$659$	2.06130			0.0802970			0.0401485	−	0.999194i	$-0.487217\pi$
$659$	2.06130			0.0802970			0.0401485	+	0.999194i	$0.487217\pi$
$660$	−1.52011	−	10.9433i	−0.0591703	−	0.425969i
$661$	−42.9729			−1.67145			−0.835725	−	0.549148i	$-0.814952\pi$
$661$	−42.9729			−1.67145			−0.835725	+	0.549148i	$0.814952\pi$
$662$	5.65378	−	17.4005i	0.219740	−	0.676291i
$663$	−1.47158	+	1.06917i	−0.0571516	+	0.0415231i
$664$	−50.2499	−	36.5087i	−1.95007	−	1.41681i
$665$	−6.25206	−	19.2419i	−0.242444	−	0.746167i
$666$	16.7612	+	51.5857i	0.649483	+	1.99890i
$667$	13.3370	+	9.68987i	0.516409	+	0.375193i
$668$	−65.3131	+	47.4528i	−2.52704	+	1.83600i
$669$	4.81251	−	14.8114i	0.186062	−	0.572641i
$670$	6.72837			0.259940
$671$	4.84598	+	34.8864i	0.187077	+	1.34677i
$672$	1.80033			0.0694492
$673$	2.95858	−	9.10558i	0.114045	−	0.350994i	−0.877702	−	0.479207i	$-0.840924\pi$
$673$	2.95858	−	9.10558i	0.114045	−	0.350994i	0.991747	+	0.128213i	$0.0409242\pi$
$674$	−71.7292	+	52.1143i	−2.76290	+	2.00737i
$675$	14.4088	+	10.4686i	0.554596	+	0.402938i
$676$	1.25328	+	3.85720i	0.0482031	+	0.148354i
$677$	0.859249	+	2.64450i	0.0330236	+	0.101636i	0.966210	−	0.257757i	$-0.0829835\pi$
$677$	0.859249	+	2.64450i	0.0330236	+	0.101636i	−0.933186	+	0.359394i	$0.882984\pi$
$678$	−28.2298	−	20.5101i	−1.08416	−	0.787687i
$679$	−17.6175	+	12.7998i	−0.676096	+	0.491212i
$680$	−3.36349	+	10.3518i	−0.128984	+	0.396972i
$681$	−9.74988			−0.373616
$682$	−18.6295	−	19.3534i	−0.713360	−	0.741078i
$683$	−48.0798			−1.83972			−0.919861	−	0.392244i	$-0.871699\pi$
$683$	−48.0798			−1.83972			−0.919861	+	0.392244i	$0.871699\pi$
$684$	15.2622	−	46.9722i	0.583565	−	1.79603i
$685$	−8.30168	+	6.03153i	−0.317191	+	0.230453i
$686$	8.52835	+	6.19621i	0.325614	+	0.236572i
$687$	−1.39837	−	4.30373i	−0.0533510	−	0.164197i
$688$	−9.53588	−	29.3484i	−0.363552	−	1.11890i
$689$	3.73577	+	2.71420i	0.142322	+	0.103403i
$690$	3.95718	−	2.87506i	0.150647	−	0.109452i
$691$	7.82362	−	24.0786i	0.297625	−	0.915995i	−0.684703	−	0.728823i	$-0.740068\pi$
$691$	7.82362	−	24.0786i	0.297625	−	0.915995i	0.982327	−	0.187172i	$-0.0599321\pi$
$692$	8.37898			0.318521
$693$	26.7303	−	12.9843i	1.01540	−	0.493232i
$694$	−55.6818			−2.11365
$695$	−5.30522	+	16.3278i	−0.201239	+	0.619349i
$696$	23.2322	−	16.8792i	0.880615	−	0.639804i
$697$	−6.06036	−	4.40311i	−0.229553	−	0.166780i
$698$	−2.98535	−	9.18797i	−0.112997	−	0.347770i
$699$	3.38243	+	10.4101i	0.127935	+	0.393745i
$700$	−51.3666	−	37.3200i	−1.94148	−	1.41057i
$701$	9.77098	−	7.09903i	0.369045	−	0.268127i	−0.387770	−	0.921756i	$-0.626755\pi$
$701$	9.77098	−	7.09903i	0.369045	−	0.268127i	0.756815	+	0.653629i	$0.226755\pi$
$702$	−3.36202	+	10.3472i	−0.126891	+	0.390531i
$703$	50.4935			1.90440
$704$	11.4110	−	21.3783i	0.430069	−	0.805726i
$705$	1.58363			0.0596428
$706$	−12.0399	+	37.0549i	−0.453127	+	1.39458i
$707$	42.6252	−	30.9690i	1.60309	−	1.16471i
$708$	0.119312	+	0.0866853i	0.00448402	+	0.00325783i
$709$	−3.59971	−	11.0788i	−0.135190	−	0.416071i	0.860430	−	0.509569i	$-0.170195\pi$
$709$	−3.59971	−	11.0788i	−0.135190	−	0.416071i	−0.995619	+	0.0934977i	$0.970195\pi$
$710$	−7.88522	−	24.2682i	−0.295927	−	0.910770i
$711$	−17.3342	−	12.5941i	−0.650085	−	0.472314i
$712$	−12.1703	+	8.84226i	−0.456102	+	0.331378i
$713$	2.46130	−	7.57509i	0.0921762	−	0.283689i
$714$	17.3953			0.651002
$715$	−3.21856	−	0.572838i	−0.120367	−	0.0214229i
$716$	24.0455			0.898624
$717$	2.28167	−	7.02225i	0.0852104	−	0.262251i
$718$	4.77668	−	3.47046i	0.178264	−	0.129517i
$719$	−24.7235	−	17.9627i	−0.922031	−	0.669895i	0.0219979	−	0.999758i	$-0.492997\pi$
$719$	−24.7235	−	17.9627i	−0.922031	−	0.669895i	−0.944029	+	0.329863i	$0.892997\pi$
$720$	3.04599	+	9.37460i	0.113517	+	0.349371i
$721$	−2.32008	−	7.14046i	−0.0864042	−	0.265925i
$722$	−17.7134	−	12.8695i	−0.659223	−	0.478953i
$723$	−13.4712	+	9.78743i	−0.501001	+	0.363998i
$724$	−26.3936	+	81.2312i	−0.980911	+	3.01893i
$725$	−27.4427			−1.01919
$726$	0.859443	−	22.5403i	0.0318969	−	0.836549i
$727$	4.42686			0.164183			0.0820915	−	0.996625i	$-0.473840\pi$
$727$	4.42686			0.164183			0.0820915	+	0.996625i	$0.473840\pi$
$728$	6.07501	−	18.6969i	0.225155	−	0.692955i
$729$	−2.91167	+	2.11545i	−0.107839	+	0.0783500i
$730$	31.4600	+	22.8571i	1.16439	+	0.845978i
$731$	−4.79917	−	14.7703i	−0.177504	−	0.546301i
$732$	11.0907	+	34.1336i	0.409923	+	1.26161i
$733$	−38.1779	−	27.7379i	−1.41013	−	1.02452i	−0.993303	−	0.115539i	$-0.963140\pi$
$733$	−38.1779	−	27.7379i	−1.41013	−	1.02452i	−0.416832	−	0.908984i	$-0.636860\pi$
$734$	36.3706	−	26.4248i	1.34246	−	0.975356i
$735$	2.05650	−	6.32925i	0.0758551	−	0.233458i
$736$	−1.34536			−0.0495907
$737$	9.05763	+	1.61207i	0.333642	+	0.0593814i
$738$	−19.4707			−0.716728
$739$	−1.21861	+	3.75048i	−0.0448271	+	0.137964i	−0.970965	−	0.239221i	$-0.923108\pi$
$739$	−1.21861	+	3.75048i	−0.0448271	+	0.137964i	0.926138	+	0.377185i	$0.123108\pi$
$740$	−30.9183	+	22.4634i	−1.13658	+	0.825772i
$741$	3.56073	+	2.58702i	0.130807	+	0.0950366i
$742$	−13.6461	−	41.9984i	−0.500965	−	1.54181i
$743$	−3.93610	−	12.1141i	−0.144401	−	0.444422i	0.852532	−	0.522675i	$-0.175066\pi$
$743$	−3.93610	−	12.1141i	−0.144401	−	0.444422i	−0.996934	+	0.0782528i	$0.975066\pi$
$744$	−11.2247	−	8.15519i	−0.411516	−	0.298984i
$745$	5.94401	−	4.31858i	0.217772	−	0.158220i
$746$	7.08467	−	21.8044i	0.259388	−	0.798315i
$747$	−28.3088			−1.03576
$748$	−13.8263	+	25.9033i	−0.505539	+	0.947117i
$749$	56.3019			2.05723
$750$	−5.63916	+	17.3555i	−0.205913	+	0.633735i
$751$	−41.0691	+	29.8384i	−1.49863	+	1.08882i	−0.527708	+	0.849426i	$0.676949\pi$
$751$	−41.0691	+	29.8384i	−1.49863	+	1.08882i	−0.970923	+	0.239394i	$0.923051\pi$
$752$	−6.76542	−	4.91536i	−0.246709	−	0.179245i
$753$	7.60599	+	23.4088i	0.277178	+	0.853066i
$754$	−5.18030	−	15.9433i	−0.188656	−	0.580622i
$755$	−2.09151	−	1.51957i	−0.0761179	−	0.0553029i
$756$	56.3743	−	40.9583i	2.05031	−	1.48964i
$757$	−1.63711	+	5.03852i	−0.0595019	+	0.183128i	−0.976389	−	0.216017i	$-0.930693\pi$
$757$	−1.63711	+	5.03852i	−0.0595019	+	0.183128i	0.916888	+	0.399146i	$0.130693\pi$
$758$	48.4701			1.76051
$759$	6.01594	−	2.92225i	0.218365	−	0.106071i
$760$	26.3367			0.955333
$761$	12.4854	−	38.4262i	0.452597	−	1.39295i	−0.421337	−	0.906904i	$-0.638439\pi$
$761$	12.4854	−	38.4262i	0.452597	−	1.39295i	0.873934	−	0.486045i	$-0.161561\pi$
$762$	−4.92524	+	3.57840i	−0.178423	+	0.129632i
$763$	37.1369	+	26.9816i	1.34445	+	0.976798i
$764$	−12.1375	−	37.3553i	−0.439118	−	1.35147i
$765$	1.53297	+	4.71801i	0.0554248	+	0.170580i
$766$	−9.77107	−	7.09910i	−0.353043	−	0.256501i
$767$	0.0353035	−	0.0256495i	0.00127474	−	0.000926151i
$768$	8.33522	−	25.6532i	0.300771	−	0.925679i
$769$	3.32366			0.119854			0.0599270	−	0.998203i	$-0.480913\pi$
$769$	3.32366			0.119854			0.0599270	+	0.998203i	$0.480913\pi$
$770$	21.6814	+	22.5239i	0.781344	+	0.811703i
$771$	7.15168			0.257562
$772$	2.16868	−	6.67451i	0.0780525	−	0.240221i
$773$	22.6458	−	16.4531i	0.814511	−	0.591777i	−0.100624	−	0.994925i	$-0.532084\pi$
$773$	22.6458	−	16.4531i	0.814511	−	0.591777i	0.915135	+	0.403147i	$0.132084\pi$
$774$	−32.6575	−	23.7271i	−1.17385	−	0.852852i
$775$	4.09723	+	12.6100i	0.147177	+	0.452964i
$776$	−8.75970	−	26.9596i	−0.314455	−	0.967792i
$777$	25.0457	+	18.1968i	0.898509	+	0.652805i
$778$	33.8252	−	24.5754i	1.21269	−	0.881072i
$779$	−5.60115	+	17.2386i	−0.200682	+	0.617636i
$780$	−3.33122			−0.119277
$781$	−4.80047	−	34.5587i	−0.171774	−	1.23661i
$782$	−12.9993			−0.464853
$783$	9.30698	−	28.6439i	0.332604	−	1.02365i
$784$	−28.4307	+	20.6561i	−1.01538	+	0.737719i
$785$	−11.2844	−	8.19857i	−0.402756	−	0.292619i
$786$	10.0140	+	30.8199i	0.357188	+	1.09931i
$787$	−7.52940	−	23.1731i	−0.268394	−	0.826033i	−0.990892	−	0.134659i	$-0.957006\pi$
$787$	−7.52940	−	23.1731i	−0.268394	−	0.826033i	0.722498	−	0.691373i	$-0.242994\pi$
$788$	−81.1750	−	58.9771i	−2.89174	−	2.10097i
$789$	−11.2881	+	8.20129i	−0.401867	+	0.291974i
$790$	6.96566	−	21.4381i	0.247827	−	0.762734i
$791$	66.1286			2.35126
$792$	5.32233	+	38.3156i	0.189121	+	1.36149i
$793$	10.6196			0.377114
$794$	12.8091	−	39.4222i	0.454577	−	1.39904i
$795$	−3.06844	+	2.22935i	−0.108826	+	0.0790670i
$796$	6.98089	+	5.07191i	0.247431	+	0.179769i
$797$	16.0014	+	49.2473i	0.566800	+	1.74443i	0.662543	+	0.749024i	$0.269477\pi$
$797$	16.0014	+	49.2473i	0.566800	+	1.74443i	−0.0957428	+	0.995406i	$0.530523\pi$
$798$	−13.0067	−	40.0306i	−0.460433	−	1.41707i
$799$	−3.40487	−	2.47378i	−0.120456	−	0.0875161i
$800$	1.81186	−	1.31639i	0.0640588	−	0.0465414i
$801$	−2.11871	+	6.52071i	−0.0748608	+	0.230398i
$802$	86.4087			3.05120
$803$	36.8746	+	38.3074i	1.30128	+	1.35184i
$804$	9.37468			0.330619
$805$	−2.86451	+	8.81605i	−0.100961	+	0.310725i
$806$	−6.55259	+	4.76073i	−0.230805	+	0.167690i
$807$	4.94383	+	3.59191i	0.174031	+	0.126441i
$808$	21.1940	+	65.2283i	0.745601	+	2.29472i
$809$	6.98070	+	21.4844i	0.245428	+	0.755350i	0.995566	+	0.0940685i	$0.0299873\pi$
$809$	6.98070	+	21.4844i	0.245428	+	0.755350i	−0.750137	+	0.661282i	$0.770013\pi$
$810$	6.34373	+	4.60899i	0.222896	+	0.161943i
$811$	−10.3037	+	7.48610i	−0.361813	+	0.262873i	−0.753808	−	0.657095i	$-0.771785\pi$
$811$	−10.3037	+	7.48610i	−0.361813	+	0.262873i	0.391995	+	0.919967i	$0.371785\pi$
$812$	−33.1788	+	102.114i	−1.16435	+	3.58349i
$813$	18.2574			0.640314
$814$	−70.1829	+	34.0914i	−2.45991	+	1.19490i
$815$	17.5672			0.615353
$816$	−2.43799	+	7.50336i	−0.0853467	+	0.262670i
$817$	−30.4015	+	22.0880i	−1.06362	+	0.772762i
$818$	30.4872	+	22.1502i	1.06596	+	0.774465i
$819$	−2.76880	−	8.52148i	−0.0967496	−	0.297765i
$820$	−4.23935	−	13.0474i	−0.148045	−	0.455634i
$821$	28.8037	+	20.9271i	1.00526	+	0.730362i	0.963209	−	0.268754i	$-0.0866117\pi$
$821$	28.8037	+	20.9271i	1.00526	+	0.730362i	0.0420481	+	0.999116i	$0.486612\pi$
$822$	−17.2707	+	12.5479i	−0.602386	+	0.437659i
$823$	6.96994	−	21.4513i	0.242957	−	0.747745i	−0.753009	−	0.658011i	$-0.771398\pi$
$823$	6.96994	−	21.4513i	0.242957	−	0.747745i	0.995966	−	0.0897343i	$-0.0286018\pi$
$824$	9.77330			0.340469
$825$	−5.24261	+	9.82191i	−0.182524	+	0.341955i
$826$	−0.417316			−0.0145203
$827$	−8.30864	+	25.5713i	−0.288920	+	0.889203i	0.696277	+	0.717773i	$0.254839\pi$
$827$	−8.30864	+	25.5713i	−0.288920	+	0.889203i	−0.985196	+	0.171430i	$0.945161\pi$
$828$	−18.3071	+	13.3009i	−0.636215	+	0.462238i
$829$	−26.1559	−	19.0033i	−0.908430	−	0.660013i	0.0321871	−	0.999482i	$-0.489753\pi$
$829$	−26.1559	−	19.0033i	−0.908430	−	0.660013i	−0.940617	+	0.339469i	$0.889753\pi$
$830$	−9.20315	−	28.3244i	−0.319446	−	0.983154i
$831$	2.47593	+	7.62012i	0.0858889	+	0.264339i
$832$	−5.91113	−	4.29469i	−0.204932	−	0.148892i
$833$	−14.3085	+	10.3957i	−0.495760	+	0.360191i
$834$	−11.0369	+	33.9682i	−0.382178	+	1.17622i
$835$	−19.6207			−0.679002
$836$	69.9475	+	12.4492i	2.41919	+	0.430565i
$837$	−14.5515			−0.502974
$838$	11.0544	−	34.0220i	0.381868	−	1.17527i
$839$	−32.0494	+	23.2852i	−1.10647	+	0.803895i	−0.982104	−	0.188341i	$-0.939689\pi$
$839$	−32.0494	+	23.2852i	−1.10647	+	0.803895i	−0.124363	+	0.992237i	$0.539689\pi$
$840$	13.0635	+	9.49119i	0.450734	+	0.327477i
$841$	5.37898	+	16.5548i	0.185482	+	0.570855i
$842$	−4.59093	−	14.1294i	−0.158214	−	0.486932i
$843$	1.11321	+	0.808796i	0.0383411	+	0.0278564i
$844$	11.6640	−	8.47438i	0.401491	−	0.291700i
$845$	−0.304593	+	0.937441i	−0.0104783	+	0.0322489i
$846$	−10.9392			−0.376096
$847$	23.7906	+	35.5160i	0.817455	+	1.22034i
$848$	20.0283			0.687775
$849$	−3.76955	+	11.6015i	−0.129371	+	0.398162i
$850$	17.5067	−	12.7193i	0.600473	−	0.436269i
$851$	−18.7163	−	13.5982i	−0.641586	−	0.466140i
$852$	−10.9865	−	33.8130i	−0.376392	−	1.15842i
$853$	2.80194	+	8.62349i	0.0959367	+	0.295263i	0.987497	−	0.157640i	$-0.0503885\pi$
$853$	2.80194	+	8.62349i	0.0959367	+	0.295263i	−0.891560	+	0.452903i	$0.850389\pi$
$854$	−82.1620	−	59.6942i	−2.81153	−	2.04269i
$855$	9.71099	−	7.05545i	0.332109	−	0.241291i
$856$	−22.6478	+	69.7029i	−0.774087	+	2.38239i
$857$	−31.9836			−1.09254			−0.546269	−	0.837610i	$-0.683952\pi$
$857$	−31.9836			−1.09254			−0.546269	+	0.837610i	$0.683952\pi$
$858$	−6.69587	−	1.19173i	−0.228593	−	0.0406848i
$859$	−30.4821			−1.04004			−0.520018	−	0.854155i	$-0.674075\pi$
$859$	−30.4821			−1.04004			−0.520018	+	0.854155i	$0.674075\pi$
$860$	8.78906	−	27.0499i	0.299704	−	0.922396i
$861$	−8.99068	+	6.53211i	−0.306401	+	0.222614i
$862$	−9.81751	−	7.13284i	−0.334386	−	0.242945i
$863$	−3.47022	−	10.6802i	−0.118127	−	0.363559i	0.874459	−	0.485099i	$-0.161217\pi$
$863$	−3.47022	−	10.6802i	−0.118127	−	0.363559i	−0.992586	+	0.121540i	$0.961217\pi$
$864$	0.759536	+	2.33761i	0.0258400	+	0.0795272i
$865$	1.64748	+	1.19696i	0.0560160	+	0.0406980i
$866$	11.0128	−	8.00125i	0.374229	−	0.271893i
$867$	3.15057	−	9.69646i	0.106999	−	0.329309i
$868$	51.8753			1.76076
$869$	14.5135	−	27.1907i	0.492337	−	0.922382i
$870$	13.7692			0.466821
$871$	0.857181	−	2.63813i	0.0290445	−	0.0893897i
$872$	−48.3423	+	35.1227i	−1.63708	+	1.18941i
$873$	−10.4522	−	7.59398i	−0.353754	−	0.257017i
$874$	9.71974	+	29.9143i	0.328775	+	1.01187i
$875$	−10.6869	−	32.8910i	−0.361285	−	1.11192i
$876$	43.8334	+	31.8469i	1.48099	+	1.07601i
$877$	14.1491	−	10.2799i	0.477780	−	0.347127i	−0.322686	−	0.946506i	$-0.604586\pi$
$877$	14.1491	−	10.2799i	0.477780	−	0.347127i	0.800465	+	0.599379i	$0.204586\pi$
$878$	12.2599	−	37.7321i	0.413752	−	1.27340i
$879$	0.338127			0.0114047
$880$	−12.7542	+	6.19538i	−0.429945	+	0.208846i
$881$	35.5824			1.19880			0.599400	−	0.800450i	$-0.295406\pi$
$881$	35.5824			1.19880			0.599400	+	0.800450i	$0.295406\pi$
$882$	−14.2056	+	43.7204i	−0.478328	+	1.47214i
$883$	24.5673	−	17.8492i	0.826754	−	0.600672i	−0.0918849	−	0.995770i	$-0.529289\pi$
$883$	24.5673	−	17.8492i	0.826754	−	0.600672i	0.918639	+	0.395097i	$0.129289\pi$
$884$	7.16228	+	5.20370i	0.240894	+	0.175020i
$885$	0.0110759	+	0.0340882i	0.000372313	+	0.00114586i
$886$	1.68564	+	5.18786i	0.0566301	+	0.174289i
$887$	−7.87990	−	5.72508i	−0.264581	−	0.192229i	0.447583	−	0.894242i	$-0.352285\pi$
$887$	−7.87990	−	5.72508i	−0.264581	−	0.192229i	−0.712164	+	0.702013i	$0.752285\pi$
$888$	−32.6027	+	23.6873i	−1.09408	+	0.794893i
$889$	3.56526	−	10.9727i	0.119575	−	0.368014i
$890$	−7.21309			−0.241783
$891$	7.43555	+	7.72446i	0.249100	+	0.258779i
$892$	−75.7975			−2.53789
$893$	−3.14687	+	9.68507i	−0.105306	+	0.324099i
$894$	12.3659	−	8.98432i	0.413576	−	0.300481i
$895$	4.72785	+	3.43498i	0.158035	+	0.114819i
$896$	22.9276	+	70.5638i	0.765957	+	2.35737i
$897$	−0.623148	−	1.91785i	−0.0208063	−	0.0640352i
$898$	−0.416871	−	0.302875i	−0.0139112	−	0.0101071i
$899$	18.1393	−	13.1790i	0.604980	−	0.439544i
$900$	11.6405	−	35.8257i	0.388016	−	1.19419i
$901$	10.0798			0.335806
$902$	−3.85361	−	27.7423i	−0.128311	−	0.923716i
$903$	−23.0398			−0.766715
$904$	−26.6007	+	81.8685i	−0.884726	+	2.72291i
$905$	−16.7937	+	12.2013i	−0.558240	+	0.405585i
$906$	−4.35116	−	3.16130i	−0.144558	−	0.105027i
$907$	−0.959545	−	2.95318i	−0.0318612	−	0.0980586i	0.933861	−	0.357635i	$-0.116417\pi$
$907$	−0.959545	−	2.95318i	−0.0318612	−	0.0980586i	−0.965722	+	0.259577i	$0.916417\pi$
$908$	14.6638	+	45.1307i	0.486637	+	1.49771i
$909$	25.2890	+	18.3735i	0.838783	+	0.609412i
$910$	7.62604	−	5.54064i	0.252801	−	0.183671i
$911$	4.02609	−	12.3910i	0.133390	−	0.410533i	−0.861946	−	0.507000i	$-0.830754\pi$
$911$	4.02609	−	12.3910i	0.133390	−	0.410533i	0.995336	+	0.0964671i	$0.0307543\pi$
$912$	19.0899			0.632129
$913$	−5.60282	−	40.3349i	−0.185426	−	1.33489i
$914$	−82.8431			−2.74021
$915$	−2.69544	+	8.29570i	−0.0891084	+	0.274247i
$916$	−17.8181	+	12.9456i	−0.588728	+	0.427736i
$917$	−49.6847	−	36.0980i	−1.64073	−	1.19206i
$918$	7.33885	+	22.5867i	0.242218	+	0.745471i
$919$	10.6032	+	32.6332i	0.349766	+	1.07647i	0.958983	+	0.283465i	$0.0914840\pi$
$919$	10.6032	+	32.6332i	0.349766	+	1.07647i	−0.609217	+	0.793004i	$0.708516\pi$
$920$	−9.76217	−	7.09263i	−0.321849	−	0.233837i
$921$	6.06859	−	4.40909i	0.199967	−	0.145284i
$922$	16.2962	−	50.1545i	0.536686	−	1.65175i
$923$	−10.5199			−0.346267
$924$	30.2088	+	31.3826i	0.993797	+	1.03241i
$925$	38.5114			1.26625
$926$	−10.9958	+	33.8417i	−0.361345	+	1.11211i
$927$	3.60365	−	2.61821i	0.118359	−	0.0859932i
$928$	−3.06393	−	2.22607i	−0.100578	−	0.0730745i
$929$	11.0844	+	34.1141i	0.363666	+	1.11925i	0.950812	+	0.309767i	$0.100251\pi$
$929$	11.0844	+	34.1141i	0.363666	+	1.11925i	−0.587147	+	0.809481i	$0.699749\pi$
$930$	−2.05577	−	6.32701i	−0.0674114	−	0.207471i
$931$	34.6217	+	25.1541i	1.13468	+	0.824393i
$932$	43.0994	−	31.3135i	1.41177	−	1.02571i
$933$	−1.64081	+	5.04990i	−0.0537178	+	0.165326i
$934$	−29.0351			−0.950057
$935$	−6.41890	+	3.11799i	−0.209920	+	0.101969i
$936$	11.6635			0.381234
$937$	−6.80549	+	20.9451i	−0.222326	+	0.684248i	0.776226	+	0.630454i	$0.217131\pi$
$937$	−6.80549	+	20.9451i	−0.222326	+	0.684248i	−0.998552	+	0.0537936i	$0.982869\pi$
$938$	−21.4611	+	15.5924i	−0.700729	+	0.509110i
$939$	12.3917	+	9.00312i	0.404389	+	0.293806i
$940$	−2.38178	−	7.33036i	−0.0776850	−	0.239090i
$941$	−0.562388	−	1.73085i	−0.0183333	−	0.0564241i	0.941471	−	0.337093i	$-0.109444\pi$
$941$	−0.562388	−	1.73085i	−0.0183333	−	0.0564241i	−0.959805	+	0.280669i	$0.909444\pi$
$942$	−23.4759	−	17.0562i	−0.764885	−	0.555722i
$943$	6.71861	−	4.88136i	0.218788	−	0.158959i
$944$	0.0584877	−	0.180007i	0.00190361	−	0.00585872i
$945$	16.9354			0.550908
$946$	27.3433	−	51.2270i	0.889006	−	1.66553i
$947$	25.5160			0.829160			0.414580	−	0.910013i	$-0.363929\pi$
$947$	25.5160			0.829160			0.414580	+	0.910013i	$0.363929\pi$
$948$	9.70529	−	29.8698i	0.315213	−	0.970127i
$949$	12.9700	−	9.42325i	0.421024	−	0.305892i
$950$	−42.3601	−	30.7764i	−1.37434	−	0.998519i
$951$	1.59267	+	4.90174i	0.0516459	+	0.158950i
$952$	−13.2609	−	40.8130i	−0.429790	−	1.32276i
$953$	−16.2364	−	11.7965i	−0.525949	−	0.382125i	0.292891	−	0.956146i	$-0.405383\pi$
$953$	−16.2364	−	11.7965i	−0.525949	−	0.382125i	−0.818840	+	0.574021i	$0.805383\pi$
$954$	21.1958	−	15.3996i	0.686239	−	0.498582i
$955$	2.94985	−	9.07870i	0.0954548	−	0.293780i
$956$	−35.9365			−1.16227
$957$	18.5360	+	3.29902i	0.599182	+	0.106642i
$958$	72.3507			2.33755
$959$	12.5019	−	38.4768i	0.403707	−	1.24248i
$960$	4.85521	−	3.52752i	0.156701	−	0.113850i
$961$	16.3155	+	11.8539i	0.526307	+	0.382384i
$962$	7.26973	+	22.3739i	0.234385	+	0.721364i
$963$	10.3222	+	31.7684i	0.332627	+	1.02372i
$964$	65.5653	+	47.6359i	2.11171	+	1.53425i
$965$	1.37988	−	1.00254i	0.0444200	−	0.0322730i
$966$	−5.95930	+	18.3408i	−0.191737	+	0.590106i
$967$	−40.9837			−1.31795			−0.658973	−	0.752167i	$-0.729009\pi$
$967$	−40.9837			−1.31795			−0.658973	+	0.752167i	$0.729009\pi$
$968$	−53.5394	+	15.1667i	−1.72082	+	0.487476i
$969$	9.60747			0.308636
$970$	4.20016	−	12.9268i	0.134859	−	0.415054i
$971$	−16.9312	+	12.3012i	−0.543347	+	0.394765i	−0.825326	−	0.564656i	$-0.809009\pi$
$971$	−16.9312	+	12.3012i	−0.543347	+	0.394765i	0.281980	+	0.959420i	$0.409009\pi$
$972$	52.3579	+	38.0403i	1.67938	+	1.22014i
$973$	−20.9164	−	64.3742i	−0.670551	−	2.06374i
$974$	0.0640909	+	0.197252i	0.00205361	+	0.00632035i
$975$	2.71577	+	1.97312i	0.0869743	+	0.0631905i
$976$	37.2639	−	27.0738i	1.19279	−	0.866612i
$977$	−4.87505	+	15.0039i	−0.155967	+	0.480016i	−0.998258	−	0.0590071i	$-0.981207\pi$
$977$	−4.87505	+	15.0039i	−0.155967	+	0.480016i	0.842291	+	0.539023i	$0.181207\pi$
$978$	36.5467			1.16863
$979$	−9.71015	−	1.72821i	−0.310338	−	0.0552337i
$980$	−32.3901			−1.03466
$981$	−8.41581	+	25.9012i	−0.268696	+	0.826962i
$982$	59.6034	−	43.3044i	1.90202	−	1.38190i
$983$	−36.2112	−	26.3090i	−1.15496	−	0.839127i	−0.165826	−	0.986155i	$-0.553029\pi$
$983$	−36.2112	−	26.3090i	−1.15496	−	0.839127i	−0.989132	+	0.147028i	$0.953029\pi$
$984$	−4.47032	−	13.7582i	−0.142508	−	0.438596i
$985$	−7.53561	−	23.1922i	−0.240104	−	0.738965i
$986$	−29.6045	−	21.5089i	−0.942800	−	0.684984i
$987$	−5.05120	+	3.66991i	−0.160781	+	0.116815i
$988$	6.61957	−	20.3730i	0.210597	−	0.648150i
$989$	17.2173			0.547478
$990$	−8.73411	+	16.3632i	−0.277588	+	0.520056i
$991$	13.7020			0.435258			0.217629	−	0.976032i	$-0.430168\pi$
$991$	13.7020			0.435258			0.217629	+	0.976032i	$0.430168\pi$
$992$	−0.565439	+	1.74024i	−0.0179527	+	0.0552527i
$993$	5.01224	−	3.64160i	0.159058	−	0.115563i
$994$	81.3904	+	59.1336i	2.58155	+	1.87560i
$995$	0.648048	+	1.99449i	0.0205445	+	0.0632294i
$996$	−12.8228	−	39.4645i	−0.406306	−	1.25048i
$997$	8.97416	+	6.52011i	0.284214	+	0.206494i	0.720754	−	0.693191i	$-0.243796\pi$
$997$	8.97416	+	6.52011i	0.284214	+	0.206494i	−0.436539	+	0.899685i	$0.643796\pi$
$998$	64.3300	−	46.7385i	2.03633	−	1.47948i
$999$	−13.0609	+	40.1972i	−0.413227	+	1.27178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.b.53.4	yes	16
11.4	even	5		1573.2.a.o.1.8		8
11.5	even	5	inner	143.2.h.b.27.4	✓	16
11.7	odd	10		1573.2.a.n.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.b.27.4	✓	16	11.5	even	5	inner
143.2.h.b.53.4	yes	16	1.1	even	1	trivial
1573.2.a.n.1.1		8	11.7	odd	10
1573.2.a.o.1.8		8	11.4	even	5

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.760439 - 2.34039i) q^{2} +(0.674152 - 0.489800i) q^{3} +(-3.28113 - 2.38388i) q^{4} +(-0.304593 - 0.937441i) q^{5} +(-0.633672 - 1.95024i) q^{6} +(3.14398 + 2.28423i) q^{7} +(-4.09261 + 2.97346i) q^{8} +(-0.712474 + 2.19277i) q^{9} +O(q^{10})\)	\(q+(0.760439 - 2.34039i) q^{2} +(0.674152 - 0.489800i) q^{3} +(-3.28113 - 2.38388i) q^{4} +(-0.304593 - 0.937441i) q^{5} +(-0.633672 - 1.95024i) q^{6} +(3.14398 + 2.28423i) q^{7} +(-4.09261 + 2.97346i) q^{8} +(-0.712474 + 2.19277i) q^{9} -2.42560 q^{10} +(-3.26531 - 0.581158i) q^{11} -3.37961 q^{12} +(-0.309017 + 0.951057i) q^{13} +(7.73680 - 5.62112i) q^{14} +(-0.664500 - 0.482788i) q^{15} +(1.34031 + 4.12504i) q^{16} +(0.674544 + 2.07603i) q^{17} +(4.59015 + 3.33494i) q^{18} +(4.27306 - 3.10456i) q^{19} +(-1.23534 + 3.80198i) q^{20} +3.23833 q^{21} +(-3.84321 + 7.20017i) q^{22} -2.41996 q^{23} +(-1.30264 + 4.00912i) q^{24} +(3.25907 - 2.36785i) q^{25} +(1.99086 + 1.44644i) q^{26} +(1.36621 + 4.20477i) q^{27} +(-4.87046 - 14.9897i) q^{28} +(-5.51123 - 4.00414i) q^{29} +(-1.63522 + 1.18806i) q^{30} +(-1.01708 + 3.13025i) q^{31} +0.555943 q^{32} +(-2.48597 + 1.20756i) q^{33} +5.37168 q^{34} +(1.18370 - 3.64305i) q^{35} +(7.56503 - 5.49632i) q^{36} +(7.73413 + 5.61917i) q^{37} +(-4.01649 - 12.3615i) q^{38} +(0.257503 + 0.792513i) q^{39} +(4.03402 + 2.93089i) q^{40} +(-2.77633 + 2.01712i) q^{41} +(2.46256 - 7.57897i) q^{42} -7.11470 q^{43} +(9.32851 + 9.69097i) q^{44} +2.27261 q^{45} +(-1.84024 + 5.66366i) q^{46} +(-1.55981 + 1.13327i) q^{47} +(2.92401 + 2.12442i) q^{48} +(2.50375 + 7.70575i) q^{49} +(-3.06338 - 9.42810i) q^{50} +(1.47158 + 1.06917i) q^{51} +(3.28113 - 2.38388i) q^{52} +(1.42694 - 4.39166i) q^{53} +10.8797 q^{54} +(0.449790 + 3.23805i) q^{55} -19.6591 q^{56} +(1.36008 - 4.18589i) q^{57} +(-13.5622 + 9.85352i) q^{58} +(-0.0353035 - 0.0256495i) q^{59} +(1.02940 + 3.16818i) q^{60} +(-3.28165 - 10.0999i) q^{61} +(6.55259 + 4.76073i) q^{62} +(-7.24880 + 5.26656i) q^{63} +(-2.25785 + 6.94895i) q^{64} +0.985684 q^{65} +(0.935738 + 6.73641i) q^{66} -2.77390 q^{67} +(2.73575 - 8.41977i) q^{68} +(-1.63142 + 1.18530i) q^{69} +(-7.62604 - 5.54064i) q^{70} +(3.25083 + 10.0050i) q^{71} +(-3.60423 - 11.0927i) q^{72} +(-12.9700 - 9.42325i) q^{73} +(19.0324 - 13.8278i) q^{74} +(1.03733 - 3.19258i) q^{75} -21.4214 q^{76} +(-8.93856 - 9.28588i) q^{77} +2.05061 q^{78} +(-2.87172 + 8.83826i) q^{79} +(3.45873 - 2.51292i) q^{80} +(-2.61532 - 1.90014i) q^{81} +(2.60962 + 8.03160i) q^{82} +(3.79417 + 11.6773i) q^{83} +(-10.6254 - 7.71981i) q^{84} +(1.74070 - 1.26469i) q^{85} +(-5.41030 + 16.6512i) q^{86} -5.67663 q^{87} +(15.0917 - 7.33080i) q^{88} +2.97373 q^{89} +(1.72818 - 5.31879i) q^{90} +(-3.14398 + 2.28423i) q^{91} +(7.94022 + 5.76891i) q^{92} +(0.847530 + 2.60843i) q^{93} +(1.46615 + 4.51236i) q^{94} +(-4.21189 - 3.06011i) q^{95} +(0.374790 - 0.272301i) q^{96} +(-1.73159 + 5.32930i) q^{97} +19.9384 q^{98} +(3.60080 - 6.74602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 + 5 * q^5 - 4 * q^6 + 9 * q^7 - 4 * q^8 - 7 * q^9	\( 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9} - 12 q^{10} + 6 q^{11} - 14 q^{12} + 4 q^{13} - q^{14} - 10 q^{15} + 10 q^{16} - 6 q^{17} + 20 q^{18} + 2 q^{19} - 21 q^{20} - 8 q^{21} + 2 q^{22} - 46 q^{23} + 3 q^{24} + 23 q^{25} + 3 q^{26} + 17 q^{27} - 9 q^{28} - 25 q^{29} + 22 q^{30} + 3 q^{31} + 24 q^{32} - 10 q^{33} + 4 q^{34} + 26 q^{35} - 2 q^{36} - 7 q^{37} + 5 q^{38} + 25 q^{40} - 3 q^{41} - 12 q^{42} - 16 q^{43} + 32 q^{44} - 46 q^{45} - 11 q^{46} + 13 q^{47} - 24 q^{48} + 19 q^{49} - 19 q^{50} - 23 q^{51} + 8 q^{52} - 14 q^{53} + 6 q^{54} - 5 q^{55} - 68 q^{56} + 23 q^{57} + 20 q^{58} + 16 q^{59} + 34 q^{60} - 13 q^{61} + 28 q^{62} + 18 q^{63} - 40 q^{64} + 10 q^{65} + 41 q^{66} - 62 q^{67} + 13 q^{68} + 4 q^{69} - 2 q^{70} + 54 q^{71} + 21 q^{72} - 42 q^{73} + 42 q^{74} + 51 q^{75} - 4 q^{76} + 14 q^{77} - 6 q^{78} - 15 q^{79} - 19 q^{80} + q^{81} - 7 q^{82} - 43 q^{83} - 35 q^{84} - 3 q^{85} - 32 q^{86} + 4 q^{87} + 41 q^{88} - 30 q^{89} + 26 q^{90} - 9 q^{91} + 3 q^{92} + 49 q^{93} + 4 q^{94} + 23 q^{95} + 23 q^{96} - 12 q^{97} + 24 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 + 5 * q^5 - 4 * q^6 + 9 * q^7 - 4 * q^8 - 7 * q^9 - 12 * q^10 + 6 * q^11 - 14 * q^12 + 4 * q^13 - q^14 - 10 * q^15 + 10 * q^16 - 6 * q^17 + 20 * q^18 + 2 * q^19 - 21 * q^20 - 8 * q^21 + 2 * q^22 - 46 * q^23 + 3 * q^24 + 23 * q^25 + 3 * q^26 + 17 * q^27 - 9 * q^28 - 25 * q^29 + 22 * q^30 + 3 * q^31 + 24 * q^32 - 10 * q^33 + 4 * q^34 + 26 * q^35 - 2 * q^36 - 7 * q^37 + 5 * q^38 + 25 * q^40 - 3 * q^41 - 12 * q^42 - 16 * q^43 + 32 * q^44 - 46 * q^45 - 11 * q^46 + 13 * q^47 - 24 * q^48 + 19 * q^49 - 19 * q^50 - 23 * q^51 + 8 * q^52 - 14 * q^53 + 6 * q^54 - 5 * q^55 - 68 * q^56 + 23 * q^57 + 20 * q^58 + 16 * q^59 + 34 * q^60 - 13 * q^61 + 28 * q^62 + 18 * q^63 - 40 * q^64 + 10 * q^65 + 41 * q^66 - 62 * q^67 + 13 * q^68 + 4 * q^69 - 2 * q^70 + 54 * q^71 + 21 * q^72 - 42 * q^73 + 42 * q^74 + 51 * q^75 - 4 * q^76 + 14 * q^77 - 6 * q^78 - 15 * q^79 - 19 * q^80 + q^81 - 7 * q^82 - 43 * q^83 - 35 * q^84 - 3 * q^85 - 32 * q^86 + 4 * q^87 + 41 * q^88 - 30 * q^89 + 26 * q^90 - 9 * q^91 + 3 * q^92 + 49 * q^93 + 4 * q^94 + 23 * q^95 + 23 * q^96 - 12 * q^97 + 24 * q^98 - 7 * q^99

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