LMFDB - Embedded newform 143.2.h.c.92.4

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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			92.4
Character	$\chi$	$=$	143.92
Dual form			143.2.h.c.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.335814 - 0.243983i) q^{2} +(-0.228957 + 0.704657i) q^{3} +(-0.564791 - 1.73825i) q^{4} +(0.645264 - 0.468812i) q^{5} +(0.248811 - 0.180772i) q^{6} +(-1.50645 - 4.63638i) q^{7} +(-0.490978 + 1.51107i) q^{8} +(1.98293 + 1.44068i) q^{9} +O(q^{10})$	\(q+(-0.335814 - 0.243983i) q^{2} +(-0.228957 + 0.704657i) q^{3} +(-0.564791 - 1.73825i) q^{4} +(0.645264 - 0.468812i) q^{5} +(0.248811 - 0.180772i) q^{6} +(-1.50645 - 4.63638i) q^{7} +(-0.490978 + 1.51107i) q^{8} +(1.98293 + 1.44068i) q^{9} -0.331071 q^{10} +(2.69082 - 1.93893i) q^{11} +1.35418 q^{12} +(-0.809017 - 0.587785i) q^{13} +(-0.625312 + 1.92451i) q^{14} +(0.182614 + 0.562028i) q^{15} +(-2.42373 + 1.76094i) q^{16} +(2.44396 - 1.77564i) q^{17} +(-0.314394 - 0.967604i) q^{18} +(-0.336721 + 1.03632i) q^{19} +(-1.17935 - 0.856848i) q^{20} +3.61197 q^{21} +(-1.37668 - 0.00539411i) q^{22} -2.58574 q^{23} +(-0.952376 - 0.691942i) q^{24} +(-1.34850 + 4.15027i) q^{25} +(0.128270 + 0.394773i) q^{26} +(-3.26744 + 2.37394i) q^{27} +(-7.20835 + 5.23717i) q^{28} +(0.373092 + 1.14826i) q^{29} +(0.0758011 - 0.233292i) q^{30} +(4.99657 + 3.63022i) q^{31} +4.42124 q^{32} +(0.750201 + 2.34004i) q^{33} -1.25394 q^{34} +(-3.14565 - 2.28545i) q^{35} +(1.38432 - 4.26051i) q^{36} +(1.15466 + 3.55367i) q^{37} +(0.365920 - 0.265857i) q^{38} +(0.599417 - 0.435502i) q^{39} +(0.391599 + 1.20522i) q^{40} +(-1.50563 + 4.63385i) q^{41} +(-1.21295 - 0.881261i) q^{42} +4.58442 q^{43} +(-4.89010 - 3.58222i) q^{44} +1.95493 q^{45} +(0.868329 + 0.630878i) q^{46} +(3.88517 - 11.9573i) q^{47} +(-0.685930 - 2.11108i) q^{48} +(-13.5635 + 9.85449i) q^{49} +(1.46544 - 1.06471i) q^{50} +(0.691655 + 2.12869i) q^{51} +(-0.564791 + 1.73825i) q^{52} +(2.59992 + 1.88896i) q^{53} +1.67646 q^{54} +(0.827297 - 2.51262i) q^{55} +7.74556 q^{56} +(-0.653155 - 0.474545i) q^{57} +(0.154867 - 0.476631i) q^{58} +(2.45554 + 7.55738i) q^{59} +(0.873804 - 0.634856i) q^{60} +(2.95070 - 2.14381i) q^{61} +(-0.792207 - 2.43816i) q^{62} +(3.69237 - 11.3640i) q^{63} +(3.36274 + 2.44317i) q^{64} -0.797591 q^{65} +(0.319002 - 0.968855i) q^{66} -0.723989 q^{67} +(-4.46682 - 3.24533i) q^{68} +(0.592024 - 1.82206i) q^{69} +(0.498743 + 1.53497i) q^{70} +(1.12420 - 0.816777i) q^{71} +(-3.15056 + 2.28901i) q^{72} +(-2.84599 - 8.75906i) q^{73} +(0.479285 - 1.47509i) q^{74} +(-2.61576 - 1.90046i) q^{75} +1.99156 q^{76} +(-13.0432 - 9.55478i) q^{77} -0.307548 q^{78} +(-11.7088 - 8.50696i) q^{79} +(-0.738395 + 2.27255i) q^{80} +(1.34753 + 4.14727i) q^{81} +(1.63619 - 1.18876i) q^{82} +(10.2650 - 7.45793i) q^{83} +(-2.04001 - 6.27850i) q^{84} +(0.744557 - 2.29151i) q^{85} +(-1.53951 - 1.11852i) q^{86} -0.894551 q^{87} +(1.60874 + 5.01801i) q^{88} +14.4003 q^{89} +(-0.656492 - 0.476969i) q^{90} +(-1.50645 + 4.63638i) q^{91} +(1.46040 + 4.49466i) q^{92} +(-3.70206 + 2.68971i) q^{93} +(-4.22208 + 3.06752i) q^{94} +(0.268565 + 0.826559i) q^{95} +(-1.01227 + 3.11546i) q^{96} +(-4.99059 - 3.62588i) q^{97} +6.95916 q^{98} +(8.12911 + 0.0318514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.335814	−	0.243983i	−0.237457	−	0.172522i	0.462693	−	0.886519i	$-0.346883\pi$
$2$	−0.335814	−	0.243983i	−0.237457	−	0.172522i	−0.700149	+	0.713996i	$0.746883\pi$
$3$	−0.228957	+	0.704657i	−0.132188	+	0.406834i	−0.995142	−	0.0984491i	$-0.968612\pi$
$3$	−0.228957	+	0.704657i	−0.132188	+	0.406834i	0.862954	+	0.505283i	$0.168612\pi$
$4$	−0.564791	−	1.73825i	−0.282395	−	0.869123i
$5$	0.645264	−	0.468812i	0.288571	−	0.209659i	−0.434076	−	0.900876i	$-0.642925\pi$
$5$	0.645264	−	0.468812i	0.288571	−	0.209659i	0.722647	+	0.691217i	$0.242925\pi$
$6$	0.248811	−	0.180772i	0.101577	−	0.0737999i
$7$	−1.50645	−	4.63638i	−0.569386	−	1.75239i	−0.654547	−	0.756021i	$-0.727141\pi$
$7$	−1.50645	−	4.63638i	−0.569386	−	1.75239i	0.0851613	−	0.996367i	$-0.472859\pi$
$8$	−0.490978	+	1.51107i	−0.173587	+	0.534245i
$9$	1.98293	+	1.44068i	0.660977	+	0.480228i
$10$	−0.331071			−0.104694
$11$	2.69082	−	1.93893i	0.811314	−	0.584611i
$11$	2.69082	−	1.93893i	0.811314	−	0.584611i
$12$	1.35418			0.390918
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	−0.625312	+	1.92451i	−0.167122	+	0.514348i
$15$	0.182614	+	0.562028i	0.0471507	+	0.145115i
$16$	−2.42373	+	1.76094i	−0.605932	+	0.440235i
$17$	2.44396	−	1.77564i	0.592746	−	0.430655i	−0.250551	−	0.968104i	$-0.580612\pi$
$17$	2.44396	−	1.77564i	0.592746	−	0.430655i	0.843297	+	0.537448i	$0.180612\pi$
$18$	−0.314394	−	0.967604i	−0.0741033	−	0.228067i
$19$	−0.336721	+	1.03632i	−0.0772490	+	0.237748i	−0.982223	−	0.187720i	$-0.939890\pi$
$19$	−0.336721	+	1.03632i	−0.0772490	+	0.237748i	0.904974	+	0.425468i	$0.139890\pi$
$20$	−1.17935	−	0.856848i	−0.263711	−	0.191597i
$21$	3.61197			0.788197
$22$	−1.37668	−	0.00539411i	−0.293510	−	0.00115003i
$23$	−2.58574			−0.539165			−0.269582	−	0.962977i	$-0.586886\pi$
$23$	−2.58574			−0.539165			−0.269582	+	0.962977i	$0.586886\pi$
$24$	−0.952376	−	0.691942i	−0.194403	−	0.141242i
$25$	−1.34850	+	4.15027i	−0.269701	+	0.830053i
$26$	0.128270	+	0.394773i	0.0251557	+	0.0774214i
$27$	−3.26744	+	2.37394i	−0.628820	+	0.456864i
$28$	−7.20835	+	5.23717i	−1.36225	+	0.989733i
$29$	0.373092	+	1.14826i	0.0692815	+	0.213227i	0.979703	−	0.200456i	$-0.0642424\pi$
$29$	0.373092	+	1.14826i	0.0692815	+	0.213227i	−0.910421	+	0.413683i	$0.864242\pi$
$30$	0.0758011	−	0.233292i	0.0138393	−	0.0425930i
$31$	4.99657	+	3.63022i	0.897411	+	0.652008i	0.937800	−	0.347177i	$-0.112860\pi$
$31$	4.99657	+	3.63022i	0.897411	+	0.652008i	−0.0403884	+	0.999184i	$0.512860\pi$
$32$	4.42124			0.781572
$33$	0.750201	+	2.34004i	0.130593	+	0.407349i
$34$	−1.25394			−0.215049
$35$	−3.14565	−	2.28545i	−0.531712	−	0.386312i
$36$	1.38432	−	4.26051i	0.230721	−	0.710085i
$37$	1.15466	+	3.55367i	0.189824	+	0.584219i	0.999998	−	0.00197069i	$-0.000627289\pi$
$37$	1.15466	+	3.55367i	0.189824	+	0.584219i	−0.810174	+	0.586190i	$0.800627\pi$
$38$	0.365920	−	0.265857i	0.0593601	−	0.0431276i
$39$	0.599417	−	0.435502i	0.0959835	−	0.0697361i
$40$	0.391599	+	1.20522i	0.0619173	+	0.190562i
$41$	−1.50563	+	4.63385i	−0.235140	+	0.723686i	0.761963	+	0.647620i	$0.224236\pi$
$41$	−1.50563	+	4.63385i	−0.235140	+	0.723686i	−0.997103	+	0.0760652i	$0.975764\pi$
$42$	−1.21295	−	0.881261i	−0.187163	−	0.135982i
$43$	4.58442			0.699117			0.349559	−	0.936914i	$-0.386332\pi$
$43$	4.58442			0.699117			0.349559	+	0.936914i	$0.386332\pi$
$44$	−4.89010	−	3.58222i	−0.737210	−	0.540040i
$45$	1.95493			0.291423
$46$	0.868329	+	0.630878i	0.128028	+	0.0930179i
$47$	3.88517	−	11.9573i	0.566710	−	1.74416i	−0.0961040	−	0.995371i	$-0.530638\pi$
$47$	3.88517	−	11.9573i	0.566710	−	1.74416i	0.662814	−	0.748784i	$-0.269362\pi$
$48$	−0.685930	−	2.11108i	−0.0990055	−	0.304708i
$49$	−13.5635	+	9.85449i	−1.93765	+	1.40778i
$50$	1.46544	−	1.06471i	0.207245	−	0.150572i
$51$	0.691655	+	2.12869i	0.0968510	+	0.298077i
$52$	−0.564791	+	1.73825i	−0.0783224	+	0.241051i
$53$	2.59992	+	1.88896i	0.357127	+	0.259468i	0.751853	−	0.659331i	$-0.229160\pi$
$53$	2.59992	+	1.88896i	0.357127	+	0.259468i	−0.394726	+	0.918799i	$0.629160\pi$
$54$	1.67646			0.228137
$55$	0.827297	−	2.51262i	0.111553	−	0.338801i
$56$	7.74556			1.03504
$57$	−0.653155	−	0.474545i	−0.0865125	−	0.0628550i
$58$	0.154867	−	0.476631i	0.0203350	−	0.0625847i
$59$	2.45554	+	7.55738i	0.319684	+	0.983887i	0.973783	+	0.227478i	$0.0730480\pi$
$59$	2.45554	+	7.55738i	0.319684	+	0.983887i	−0.654099	+	0.756409i	$0.726952\pi$
$60$	0.873804	−	0.634856i	0.112808	−	0.0819596i
$61$	2.95070	−	2.14381i	0.377799	−	0.274487i	−0.382639	−	0.923898i	$-0.624985\pi$
$61$	2.95070	−	2.14381i	0.377799	−	0.274487i	0.760437	+	0.649411i	$0.224985\pi$
$62$	−0.792207	−	2.43816i	−0.100610	−	0.309647i
$63$	3.69237	−	11.3640i	0.465195	−	1.43172i
$64$	3.36274	+	2.44317i	0.420343	+	0.305397i
$65$	−0.797591			−0.0989290
$66$	0.319002	−	0.968855i	0.0392665	−	0.119258i
$67$	−0.723989			−0.0884494			−0.0442247	−	0.999022i	$-0.514082\pi$
$67$	−0.723989			−0.0884494			−0.0442247	+	0.999022i	$0.514082\pi$
$68$	−4.46682	−	3.24533i	−0.541681	−	0.393555i
$69$	0.592024	−	1.82206i	0.0712713	−	0.219350i
$70$	0.498743	+	1.53497i	0.0596112	+	0.183465i
$71$	1.12420	−	0.816777i	0.133418	−	0.0969336i	−0.519075	−	0.854729i	$-0.673723\pi$
$71$	1.12420	−	0.816777i	0.133418	−	0.0969336i	0.652492	+	0.757795i	$0.273723\pi$
$72$	−3.15056	+	2.28901i	−0.371297	+	0.269763i
$73$	−2.84599	−	8.75906i	−0.333098	−	1.02517i	−0.967651	−	0.252291i	$-0.918816\pi$
$73$	−2.84599	−	8.75906i	−0.333098	−	1.02517i	0.634553	−	0.772879i	$-0.281184\pi$
$74$	0.479285	−	1.47509i	0.0557158	−	0.171476i
$75$	−2.61576	−	1.90046i	−0.302042	−	0.219447i
$76$	1.99156			0.228447
$77$	−13.0432	−	9.55478i	−1.48642	−	1.08887i
$78$	−0.307548			−0.0348229
$79$	−11.7088	−	8.50696i	−1.31735	−	0.957107i	−0.999961	−	0.00881044i	$-0.997196\pi$
$79$	−11.7088	−	8.50696i	−1.31735	−	0.957107i	−0.317384	−	0.948297i	$-0.602804\pi$
$80$	−0.738395	+	2.27255i	−0.0825551	+	0.254078i
$81$	1.34753	+	4.14727i	0.149726	+	0.460808i
$82$	1.63619	−	1.18876i	0.180687	−	0.131277i
$83$	10.2650	−	7.45793i	1.12673	−	0.818614i	0.141511	−	0.989937i	$-0.454804\pi$
$83$	10.2650	−	7.45793i	1.12673	−	0.818614i	0.985215	+	0.171322i	$0.0548040\pi$
$84$	−2.04001	−	6.27850i	−0.222583	−	0.685040i
$85$	0.744557	−	2.29151i	0.0807586	−	0.248549i
$86$	−1.53951	−	1.11852i	−0.166010	−	0.120613i
$87$	−0.894551			−0.0959060
$88$	1.60874	+	5.01801i	0.171492	+	0.534921i
$89$	14.4003			1.52643			0.763216	−	0.646143i	$-0.223619\pi$
$89$	14.4003			1.52643			0.763216	+	0.646143i	$0.223619\pi$
$90$	−0.656492	−	0.476969i	−0.0692003	−	0.0502770i
$91$	−1.50645	+	4.63638i	−0.157919	+	0.486025i
$92$	1.46040	+	4.49466i	0.152258	+	0.468601i
$93$	−3.70206	+	2.68971i	−0.383886	+	0.278909i
$94$	−4.22208	+	3.06752i	−0.435475	+	0.316391i
$95$	0.268565	+	0.826559i	0.0275542	+	0.0848031i
$96$	−1.01227	+	3.11546i	−0.103315	+	0.317970i
$97$	−4.99059	−	3.62588i	−0.506718	−	0.368152i	0.304859	−	0.952397i	$-0.401391\pi$
$97$	−4.99059	−	3.62588i	−0.506718	−	0.368152i	−0.811577	+	0.584245i	$0.801391\pi$
$98$	6.95916			0.702982
$99$	8.12911	+	0.0318514i	0.817006	+	0.00320118i
$100$	7.97581			0.797581
$101$	11.1196	+	8.07883i	1.10644	+	0.803874i	0.982099	−	0.188366i	$-0.0603191\pi$
$101$	11.1196	+	8.07883i	1.10644	+	0.803874i	0.124339	+	0.992240i	$0.460319\pi$
$102$	0.287098	−	0.883598i	0.0284270	−	0.0874892i
$103$	0.874603	+	2.69175i	0.0861772	+	0.265226i	0.984854	−	0.173385i	$-0.0554705\pi$
$103$	0.874603	+	2.69175i	0.0861772	+	0.265226i	−0.898677	+	0.438611i	$0.855471\pi$
$104$	1.28540	−	0.933895i	0.126044	−	0.0915760i
$105$	2.33068	−	1.69334i	0.227451	−	0.165253i
$106$	−0.412218	−	1.26868i	−0.0400381	−	0.123225i
$107$	−3.32755	+	10.2412i	−0.321687	+	0.990050i	0.651227	+	0.758883i	$0.274254\pi$
$107$	−3.32755	+	10.2412i	−0.321687	+	0.990050i	−0.972914	+	0.231167i	$0.925746\pi$
$108$	5.97191	+	4.33885i	0.574647	+	0.417506i
$109$	−13.1062			−1.25534			−0.627672	−	0.778478i	$-0.715992\pi$
$109$	−13.1062			−1.25534			−0.627672	+	0.778478i	$0.715992\pi$
$110$	−0.890855	+	0.641926i	−0.0849397	+	0.0612052i
$111$	−2.76848			−0.262773
$112$	11.8156	+	8.58456i	1.11647	+	0.811165i
$113$	−6.13108	+	18.8695i	−0.576763	+	1.77510i	0.0533309	+	0.998577i	$0.483016\pi$
$113$	−6.13108	+	18.8695i	−0.576763	+	1.77510i	−0.630094	+	0.776519i	$0.716984\pi$
$114$	0.103558	+	0.318718i	0.00969907	+	0.0298507i
$115$	−1.66849	+	1.21223i	−0.155587	+	0.113041i
$116$	1.78524	−	1.29705i	0.165755	−	0.120428i
$117$	−0.757412	−	2.33108i	−0.0700228	−	0.215508i
$118$	1.01927	−	3.13699i	0.0938313	−	0.288783i
$119$	−11.9142	−	8.65620i	−1.09218	−	0.793513i
$120$	−0.938925			−0.0857117
$121$	3.48106	−	10.4347i	0.316460	−	0.948606i
$122$	−1.51394			−0.137066
$123$	−2.92055	−	2.12190i	−0.263337	−	0.191326i
$124$	3.48821	−	10.7356i	0.313250	−	0.964085i
$125$	2.30790	+	7.10298i	0.206425	+	0.635310i
$126$	−4.01257	+	2.91530i	−0.357468	+	0.259716i
$127$	−14.2222	+	10.3330i	−1.26201	+	0.916906i	−0.998855	−	0.0478468i	$-0.984764\pi$
$127$	−14.2222	+	10.3330i	−1.26201	+	0.916906i	−0.263158	+	0.964753i	$0.584764\pi$
$128$	−3.26564	−	10.0506i	−0.288644	−	0.888356i
$129$	−1.04963	+	3.23044i	−0.0924151	+	0.284425i
$130$	0.267842	+	0.194599i	0.0234913	+	0.0170674i
$131$	−15.5456			−1.35822			−0.679112	−	0.734035i	$-0.737635\pi$
$131$	−15.5456			−1.35822			−0.679112	+	0.734035i	$0.737635\pi$
$132$	3.64386	−	2.62567i	0.317157	−	0.228535i
$133$	5.31203			0.460611
$134$	0.243126	+	0.176641i	0.0210029	+	0.0152595i
$135$	−0.995435	+	3.06363i	−0.0856734	+	0.263676i
$136$	1.48319	+	4.56480i	0.127183	+	0.391428i
$137$	−6.80896	+	4.94700i	−0.581728	+	0.422650i	−0.839347	−	0.543596i	$-0.817062\pi$
$137$	−6.80896	+	4.94700i	−0.581728	+	0.422650i	0.257618	+	0.966247i	$0.417062\pi$
$138$	−0.643363	+	0.467430i	−0.0547667	+	0.0397903i
$139$	1.54301	+	4.74890i	0.130876	+	0.402796i	0.994926	−	0.100611i	$-0.0320797\pi$
$139$	1.54301	+	4.74890i	0.130876	+	0.402796i	−0.864049	+	0.503407i	$0.832080\pi$
$140$	−2.19604	+	6.75872i	−0.185599	+	0.571216i
$141$	7.53627	+	5.47542i	0.634669	+	0.461114i
$142$	−0.576801			−0.0484041
$143$	−3.31660	−	0.0129950i	−0.277348	−	0.00108670i
$144$	−7.34304			−0.611920
$145$	0.779062	+	0.566021i	0.0646975	+	0.0470055i
$146$	−1.18134	+	3.63579i	−0.0977684	+	0.300900i
$147$	−3.83857	−	11.8139i	−0.316600	−	0.974394i
$148$	5.52501	−	4.01415i	0.454153	−	0.329961i
$149$	9.64825	−	7.00987i	0.790416	−	0.574271i	−0.117671	−	0.993053i	$-0.537543\pi$
$149$	9.64825	−	7.00987i	0.790416	−	0.574271i	0.908087	+	0.418782i	$0.137543\pi$
$150$	0.414729	+	1.27641i	0.0338625	+	0.104218i
$151$	−3.51999	+	10.8334i	−0.286453	+	0.881611i	0.699507	+	0.714626i	$0.253403\pi$
$151$	−3.51999	+	10.8334i	−0.286453	+	0.881611i	−0.985959	+	0.166985i	$0.946597\pi$
$152$	−1.40063	−	1.01762i	−0.113606	−	0.0825398i
$153$	7.40433			0.598604
$154$	2.04890	+	6.39097i	0.165105	+	0.514999i
$155$	4.92601			0.395666
$156$	−1.09555	−	0.795967i	−0.0877146	−	0.0637284i
$157$	0.118559	−	0.364888i	0.00946207	−	0.0291213i	−0.946214	−	0.323541i	$-0.895126\pi$
$157$	0.118559	−	0.364888i	0.00946207	−	0.0291213i	0.955676	+	0.294420i	$0.0951265\pi$
$158$	1.85643	+	5.71352i	0.147690	+	0.454543i
$159$	−1.92634	+	1.39956i	−0.152768	+	0.110993i
$160$	2.85287	−	2.07273i	0.225539	−	0.163864i
$161$	3.89530	+	11.9885i	0.306993	+	0.944826i
$162$	0.559345	−	1.72149i	0.0439463	−	0.135253i
$163$	−12.2085	−	8.87003i	−0.956247	−	0.694754i	−0.00397092	−	0.999992i	$-0.501264\pi$
$163$	−12.2085	−	8.87003i	−0.956247	−	0.694754i	−0.952276	+	0.305238i	$0.901264\pi$
$164$	8.90514			0.695374
$165$	1.58112	+	1.15824i	0.123090	+	0.0901689i
$166$	−5.26673			−0.408778
$167$	−11.8717	−	8.62527i	−0.918657	−	0.667444i	0.0245322	−	0.999699i	$-0.492190\pi$
$167$	−11.8717	−	8.62527i	−0.918657	−	0.667444i	−0.943189	+	0.332256i	$0.892190\pi$
$168$	−1.77340	+	5.45796i	−0.136821	+	0.421091i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	−0.809124	+	0.587863i	−0.0620569	+	0.0450870i
$171$	−2.16070	+	1.56984i	−0.165233	+	0.120049i
$172$	−2.58924	−	7.96885i	−0.197427	−	0.607619i
$173$	0.774868	−	2.38480i	0.0589121	−	0.181313i	−0.917270	−	0.398266i	$-0.869612\pi$
$173$	0.774868	−	2.38480i	0.0589121	−	0.181313i	0.976182	+	0.216953i	$0.0696120\pi$
$174$	0.300403	+	0.218256i	0.0227735	+	0.0165459i
$175$	21.2737			1.60814
$176$	−3.10747	+	9.43783i	−0.234235	+	0.711403i
$177$	−5.88757			−0.442537
$178$	−4.83584	−	3.51344i	−0.362462	−	0.263344i
$179$	7.25938	−	22.3421i	0.542592	−	1.66993i	−0.184056	−	0.982916i	$-0.558923\pi$
$179$	7.25938	−	22.3421i	0.542592	−	1.66993i	0.726648	−	0.687010i	$-0.241077\pi$
$180$	−1.10412	−	3.39814i	−0.0822965	−	0.253283i
$181$	10.4657	−	7.60379i	0.777910	−	0.565185i	−0.126441	−	0.991974i	$-0.540355\pi$
$181$	10.4657	−	7.60379i	0.777910	−	0.565185i	0.904351	+	0.426789i	$0.140355\pi$
$182$	1.63709	−	1.18941i	0.121349	−	0.0881653i
$183$	0.835067	+	2.57007i	0.0617300	+	0.189985i
$184$	1.26954	−	3.90725i	0.0935919	−	0.288046i
$185$	2.41106	+	1.75174i	0.177265	+	0.128790i
$186$	1.89945			0.139274
$187$	3.13341	−	9.51660i	0.229137	−	0.695922i
$188$	−22.9791			−1.67592
$189$	15.9287	+	11.5729i	1.15864	+	0.841805i
$190$	0.111479	−	0.343096i	0.00808750	−	0.0248908i
$191$	−2.15217	−	6.62370i	−0.155726	−	0.479274i	0.842508	−	0.538684i	$-0.181078\pi$
$191$	−2.15217	−	6.62370i	−0.155726	−	0.479274i	−0.998234	+	0.0594097i	$0.981078\pi$
$192$	−2.49152	+	1.81020i	−0.179810	+	0.130640i
$193$	−8.05724	+	5.85392i	−0.579972	+	0.421375i	−0.838714	−	0.544572i	$-0.816692\pi$
$193$	−8.05724	+	5.85392i	−0.579972	+	0.421375i	0.258742	+	0.965947i	$0.416692\pi$
$194$	0.791259	+	2.43524i	0.0568090	+	0.174840i
$195$	0.182614	−	0.562028i	0.0130773	−	0.0402476i
$196$	24.7901	+	18.0111i	1.77072	+	1.28650i
$197$	−1.61161			−0.114822			−0.0574112	−	0.998351i	$-0.518285\pi$
$197$	−1.61161			−0.114822			−0.0574112	+	0.998351i	$0.518285\pi$
$198$	−2.72210	−	1.99406i	−0.193451	−	0.141712i
$199$	−7.54311			−0.534717			−0.267358	−	0.963597i	$-0.586151\pi$
$199$	−7.54311			−0.534717			−0.267358	+	0.963597i	$0.586151\pi$
$200$	−5.60928	−	4.07538i	−0.396636	−	0.288173i
$201$	0.165762	−	0.510164i	0.0116920	−	0.0359842i
$202$	−1.76301	−	5.42597i	−0.124045	−	0.381770i
$203$	4.76173	−	3.45960i	0.334208	−	0.242816i
$204$	3.30956	−	2.40453i	0.231715	−	0.168351i
$205$	1.20088	+	3.69592i	0.0838728	+	0.258134i
$206$	0.363038	−	1.11732i	0.0252941	−	0.0778472i
$207$	−5.12735	−	3.72524i	−0.356375	−	0.258922i
$208$	2.99589			0.207728
$209$	1.10330	+	3.44143i	0.0763169	+	0.238049i
$210$	−1.19582			−0.0825195
$211$	9.04565	+	6.57205i	0.622728	+	0.452439i	0.853873	−	0.520481i	$-0.174247\pi$
$211$	9.04565	+	6.57205i	0.622728	+	0.452439i	−0.231145	+	0.972919i	$0.574247\pi$
$212$	1.81506	−	5.58617i	0.124659	−	0.383660i
$213$	0.318155	+	0.979180i	0.0217996	+	0.0670923i
$214$	3.61611	−	2.62726i	0.247192	−	0.179596i
$215$	2.95816	−	2.14923i	0.201745	−	0.146576i
$216$	−1.98295	−	6.10290i	−0.134923	−	0.415250i
$217$	9.30401	−	28.6348i	0.631597	−	1.94386i
$218$	4.40124	+	3.19769i	0.298090	+	0.216575i
$219$	6.82374			0.461106
$220$	−4.83480	−	0.0189436i	−0.325962	−	0.00127718i
$221$	−3.02089			−0.203207
$222$	0.929695	+	0.675463i	0.0623971	+	0.0453341i
$223$	0.298397	−	0.918372i	0.0199821	−	0.0614987i	−0.940568	−	0.339605i	$-0.889707\pi$
$223$	0.298397	−	0.918372i	0.0199821	−	0.0614987i	0.960550	+	0.278106i	$0.0897067\pi$
$224$	−6.66039	−	20.4986i	−0.445016	−	1.36962i
$225$	−8.65321	+	6.28693i	−0.576881	+	0.419128i
$226$	6.66275	−	4.84077i	0.443200	−	0.322003i
$227$	7.47426	+	23.0034i	0.496084	+	1.52679i	0.815261	+	0.579094i	$0.196594\pi$
$227$	7.47426	+	23.0034i	0.496084	+	1.52679i	−0.319177	+	0.947695i	$0.603406\pi$
$228$	−0.455980	+	1.40336i	−0.0301980	+	0.0929400i
$229$	−22.7683	−	16.5421i	−1.50457	−	1.09313i	−0.968516	−	0.248951i	$-0.919914\pi$
$229$	−22.7683	−	16.5421i	−1.50457	−	1.09313i	−0.536054	−	0.844183i	$-0.680086\pi$
$230$	0.856066			0.0564473
$231$	9.71918	−	7.00338i	0.639475	−	0.460789i
$232$	−1.91829			−0.125942
$233$	−9.06676	−	6.58738i	−0.593983	−	0.431554i	0.249755	−	0.968309i	$-0.419650\pi$
$233$	−9.06676	−	6.58738i	−0.593983	−	0.431554i	−0.843738	+	0.536755i	$0.819650\pi$
$234$	−0.314394	+	0.967604i	−0.0205526	+	0.0632543i
$235$	−3.09878	−	9.53705i	−0.202142	−	0.622129i
$236$	11.7497	−	8.53667i	0.764842	−	0.555690i
$237$	8.67530	−	6.30297i	0.563521	−	0.409422i
$238$	1.88900	+	5.81375i	0.122446	+	0.376850i
$239$	−5.73771	+	17.6589i	−0.371142	+	1.14226i	0.574903	+	0.818221i	$0.305040\pi$
$239$	−5.73771	+	17.6589i	−0.371142	+	1.14226i	−0.946045	+	0.324035i	$0.894960\pi$
$240$	−1.43230	−	1.04063i	−0.0924548	−	0.0671724i
$241$	−1.98430			−0.127820			−0.0639100	−	0.997956i	$-0.520357\pi$
$241$	−1.98430			−0.127820			−0.0639100	+	0.997956i	$0.520357\pi$
$242$	−3.71487	+	2.65479i	−0.238801	+	0.170656i
$243$	−15.3473			−0.984528
$244$	−5.39300	−	3.91825i	−0.345252	−	0.250840i
$245$	−4.13217	+	12.7175i	−0.263995	+	0.812492i
$246$	0.463053	+	1.42513i	0.0295232	+	0.0908630i
$247$	0.881546	−	0.640481i	0.0560914	−	0.0407528i
$248$	−7.93875	+	5.76784i	−0.504111	+	0.366258i
$249$	2.90505	+	8.94082i	0.184100	+	0.566601i
$250$	0.957984	−	2.94837i	0.0605882	−	0.186471i
$251$	6.41529	+	4.66098i	0.404930	+	0.294199i	0.771546	−	0.636174i	$-0.219484\pi$
$251$	6.41529	+	4.66098i	0.404930	+	0.294199i	−0.366616	+	0.930372i	$0.619484\pi$
$252$	−21.8388			−1.37571
$253$	−6.95778	+	5.01359i	−0.437432	+	0.315202i
$254$	7.29709			0.457860
$255$	1.44426	+	1.04931i	0.0904429	+	0.0657106i
$256$	1.21337	−	3.73438i	0.0758359	−	0.233399i
$257$	−3.14299	−	9.67314i	−0.196055	−	0.603394i	−0.999963	−	0.00864039i	$-0.997250\pi$
$257$	−3.14299	−	9.67314i	−0.196055	−	0.603394i	0.803908	−	0.594754i	$-0.202750\pi$
$258$	1.14066	−	0.828735i	0.0710141	−	0.0515948i
$259$	14.7367	−	10.7069i	0.915696	−	0.665292i
$260$	0.450472	+	1.38641i	0.0279371	+	0.0859815i
$261$	−0.914463	+	2.81443i	−0.0566039	+	0.174209i
$262$	5.22043	+	3.79286i	0.322519	+	0.234324i
$263$	−1.92258			−0.118551			−0.0592756	−	0.998242i	$-0.518879\pi$
$263$	−1.92258			−0.118551			−0.0592756	+	0.998242i	$0.518879\pi$
$264$	−3.90431	−	0.0152978i	−0.240293	−	0.000941514i
$265$	2.56320			0.157456
$266$	−1.78385	−	1.29605i	−0.109375	−	0.0794657i
$267$	−3.29706	+	10.1473i	−0.201777	+	0.621004i
$268$	0.408902	+	1.25847i	0.0249777	+	0.0768734i
$269$	14.7663	−	10.7283i	0.900317	−	0.654119i	−0.0382305	−	0.999269i	$-0.512172\pi$
$269$	14.7663	−	10.7283i	0.900317	−	0.654119i	0.938547	+	0.345150i	$0.112172\pi$
$270$	1.08176	−	0.785943i	0.0658336	−	0.0478309i
$271$	0.916096	+	2.81945i	0.0556489	+	0.171270i	0.975018	−	0.222127i	$-0.0712999\pi$
$271$	0.916096	+	2.81945i	0.0556489	+	0.171270i	−0.919369	+	0.393397i	$0.871300\pi$
$272$	−2.79669	+	8.60732i	−0.169574	+	0.521896i
$273$	−2.92215	−	2.12306i	−0.176856	−	0.128494i
$274$	3.49353			0.211052
$275$	4.41851	+	13.7823i	0.266446	+	0.831104i
$276$	−3.50156			−0.210769
$277$	15.1972	+	11.0414i	0.913114	+	0.663416i	0.941801	−	0.336172i	$-0.109132\pi$
$277$	15.1972	+	11.0414i	0.913114	+	0.663416i	−0.0286865	+	0.999588i	$0.509132\pi$
$278$	0.640487	−	1.97122i	0.0384139	−	0.118226i
$279$	4.67786	+	14.3970i	0.280056	+	0.861924i
$280$	4.99793	−	3.63121i	0.298684	−	0.217006i
$281$	−3.37143	+	2.44949i	−0.201123	+	0.146124i	−0.683788	−	0.729681i	$-0.739669\pi$
$281$	−3.37143	+	2.44949i	−0.201123	+	0.146124i	0.482665	+	0.875805i	$0.339669\pi$
$282$	−1.19488	−	3.67745i	−0.0711538	−	0.218989i
$283$	3.74477	−	11.5252i	0.222604	−	0.685103i	−0.775922	−	0.630828i	$-0.782715\pi$
$283$	3.74477	−	11.5252i	0.222604	−	0.685103i	0.998526	−	0.0542751i	$-0.0172848\pi$
$284$	−2.05470	−	1.49282i	−0.121924	−	0.0885828i
$285$	−0.643930			−0.0381431
$286$	1.11059	+	0.813559i	0.0656706	+	0.0481067i
$287$	23.7525			1.40206
$288$	8.76701	+	6.36961i	0.516601	+	0.375333i
$289$	−2.43326	+	7.48881i	−0.143133	+	0.440518i
$290$	−0.123520	−	0.380156i	−0.00725336	−	0.0223235i
$291$	3.69763	−	2.68649i	0.216759	−	0.157485i
$292$	−13.6180	+	9.89407i	−0.796934	+	0.579007i
$293$	−2.95415	−	9.09195i	−0.172583	−	0.531157i	0.826931	−	0.562303i	$-0.190084\pi$
$293$	−2.95415	−	9.09195i	−0.172583	−	0.531157i	−0.999515	+	0.0311456i	$0.990084\pi$
$294$	−1.59335	+	4.90382i	−0.0929259	+	0.285997i
$295$	5.12746	+	3.72532i	0.298533	+	0.216897i
$296$	−5.93676			−0.345067
$297$	−4.18921	+	12.7232i	−0.243082	+	0.738275i
$298$	−4.95031			−0.286764
$299$	2.09191	+	1.51986i	0.120978	+	0.0878959i
$300$	−1.82612	+	5.62021i	−0.105431	+	0.324483i
$301$	−6.90621	−	21.2551i	−0.398067	−	1.22513i
$302$	3.82523	−	2.77920i	0.220118	−	0.159925i
$303$	−8.23870	+	5.98577i	−0.473301	+	0.343873i
$304$	−1.00878	−	3.10470i	−0.0578574	−	0.178067i
$305$	0.898939	−	2.76665i	0.0514731	−	0.158418i
$306$	−2.48648	−	1.80653i	−0.142143	−	0.103273i
$307$	−16.3755			−0.934598			−0.467299	−	0.884099i	$-0.654773\pi$
$307$	−16.3755			−0.934598			−0.467299	+	0.884099i	$0.654773\pi$
$308$	−9.24186	+	28.0688i	−0.526604	+	1.59937i
$309$	−2.09701			−0.119295
$310$	−1.65422	−	1.20186i	−0.0939535	−	0.0682612i
$311$	3.23200	−	9.94708i	0.183270	−	0.564047i	−0.816644	−	0.577141i	$-0.804168\pi$
$311$	3.23200	−	9.94708i	0.183270	−	0.564047i	0.999914	+	0.0130941i	$0.00416811\pi$
$312$	0.363775	+	1.11959i	0.0205947	+	0.0633840i
$313$	6.18807	−	4.49590i	0.349770	−	0.254123i	−0.399002	−	0.916950i	$-0.630643\pi$
$313$	6.18807	−	4.49590i	0.349770	−	0.254123i	0.748773	+	0.662827i	$0.230643\pi$
$314$	−0.128841	+	0.0936082i	−0.00727090	+	0.00528262i
$315$	−2.94500	−	9.06378i	−0.165932	−	0.510686i
$316$	−8.17416	+	25.1575i	−0.459832	+	1.41522i
$317$	7.53737	+	5.47622i	0.423341	+	0.307575i	0.778981	−	0.627048i	$-0.215737\pi$
$317$	7.53737	+	5.47622i	0.423341	+	0.307575i	−0.355640	+	0.934623i	$0.615737\pi$
$318$	0.988361			0.0554246
$319$	3.23033	+	2.36636i	0.180864	+	0.132491i
$320$	3.31525			0.185328
$321$	−6.45464	−	4.68957i	−0.360263	−	0.261746i
$322$	1.61690	−	4.97630i	0.0901061	−	0.277318i
$323$	1.01720	+	3.13061i	0.0565984	+	0.174192i
$324$	6.44791	−	4.68468i	0.358217	−	0.260260i
$325$	3.53043	−	2.56501i	0.195833	−	0.142281i
$326$	1.93566	+	5.95736i	0.107207	+	0.329948i
$327$	3.00075	−	9.23536i	0.165942	−	0.510717i
$328$	−6.26286	−	4.55023i	−0.345809	−	0.251245i
$329$	−61.2916			−3.37911
$330$	−0.248370	−	0.774720i	−0.0136723	−	0.0426469i
$331$	−1.48696			−0.0817306			−0.0408653	−	0.999165i	$-0.513011\pi$
$331$	−1.48696			−0.0817306			−0.0408653	+	0.999165i	$0.513011\pi$
$332$	−18.7613	−	13.6309i	−1.02966	−	0.748091i
$333$	−2.83011	+	8.71017i	−0.155089	+	0.477314i
$334$	1.88225	+	5.79298i	0.102992	+	0.316978i
$335$	−0.467165	+	0.339415i	−0.0255239	+	0.0185442i
$336$	−8.75444	+	6.36047i	−0.477594	+	0.346992i
$337$	3.64303	+	11.2121i	0.198448	+	0.610762i	0.999919	+	0.0127273i	$0.00405133\pi$
$337$	3.64303	+	11.2121i	0.198448	+	0.610762i	−0.801471	+	0.598034i	$0.795949\pi$
$338$	0.128270	−	0.394773i	0.00697695	−	0.0214728i
$339$	−11.8928	−	8.64061i	−0.645927	−	0.469294i
$340$	−4.40373			−0.238826
$341$	20.4837	+	0.0802588i	1.10925	+	0.00434626i
$342$	1.10861			0.0599468
$343$	38.5144	+	27.9824i	2.07958	+	1.51091i
$344$	−2.25085	+	6.92740i	−0.121358	+	0.373500i
$345$	−0.472193	−	1.45326i	−0.0254220	−	0.0782409i
$346$	−0.842063	+	0.611794i	−0.0452696	+	0.0328903i
$347$	−18.6328	+	13.5376i	−1.00026	+	0.726734i	−0.962145	−	0.272539i	$-0.912137\pi$
$347$	−18.6328	+	13.5376i	−1.00026	+	0.726734i	−0.0381190	+	0.999273i	$0.512137\pi$
$348$	0.505234	+	1.55495i	0.0270834	+	0.0833541i
$349$	5.02081	−	15.4525i	0.268758	−	0.827152i	−0.722046	−	0.691845i	$-0.756798\pi$
$349$	5.02081	−	15.4525i	0.268758	−	0.827152i	0.990804	−	0.135307i	$-0.0432019\pi$
$350$	−7.14401	−	5.19043i	−0.381863	−	0.277440i
$351$	4.03878			0.215574
$352$	11.8968	−	8.57249i	0.634100	−	0.456915i
$353$	13.6642			0.727271			0.363636	−	0.931541i	$-0.381535\pi$
$353$	13.6642			0.727271			0.363636	+	0.931541i	$0.381535\pi$
$354$	1.97713	+	1.43647i	0.105083	+	0.0763475i
$355$	0.342490	−	1.05407i	0.0181775	−	0.0559445i
$356$	−8.13318	−	25.0313i	−0.431058	−	1.32666i
$357$	8.82750	−	6.41355i	0.467201	−	0.339441i
$358$	−7.88890	+	5.73162i	−0.416941	+	0.302926i
$359$	6.48554	+	19.9604i	0.342293	+	1.05347i	0.963017	+	0.269441i	$0.0868390\pi$
$359$	6.48554	+	19.9604i	0.342293	+	1.05347i	−0.620723	+	0.784030i	$0.713161\pi$
$360$	−0.959825	+	2.95404i	−0.0505872	+	0.155691i
$361$	14.4107	+	10.4700i	0.758460	+	0.551054i
$362$	−5.36973			−0.282227
$363$	6.55584	+	4.84204i	0.344093	+	0.254141i
$364$	8.91001			0.467011
$365$	−5.94277	−	4.31768i	−0.311059	−	0.225997i
$366$	0.346628	−	1.06681i	0.0181185	−	0.0557630i
$367$	10.5215	+	32.3819i	0.549219	+	1.69032i	0.710741	+	0.703453i	$0.248360\pi$
$367$	10.5215	+	32.3819i	0.549219	+	1.69032i	−0.161522	+	0.986869i	$0.551640\pi$
$368$	6.26714	−	4.55334i	0.326697	−	0.237359i
$369$	−9.66147	+	7.01947i	−0.502956	+	0.365419i
$370$	−0.382274	−	1.17652i	−0.0198735	−	0.0611642i
$371$	4.84126	−	14.8999i	0.251346	−	0.773563i
$372$	6.76626	+	4.91598i	0.350814	+	0.254882i
$373$	25.7410			1.33282			0.666409	−	0.745587i	$-0.267831\pi$
$373$	25.7410			1.33282			0.666409	+	0.745587i	$0.267831\pi$
$374$	−3.37413	+	2.43131i	−0.174472	+	0.125720i
$375$	−5.53358			−0.285753
$376$	16.1609	+	11.7416i	0.833433	+	0.605525i
$377$	0.373092	−	1.14826i	0.0192152	−	0.0591384i
$378$	−2.52550	−	7.77269i	−0.129898	−	0.399784i
$379$	18.4317	−	13.3914i	0.946771	−	0.687870i	−0.00326967	−	0.999995i	$-0.501041\pi$
$379$	18.4317	−	13.3914i	0.946771	−	0.687870i	0.950041	+	0.312125i	$0.101041\pi$
$380$	1.28508	−	0.933665i	0.0659232	−	0.0478960i
$381$	−4.02496	−	12.3876i	−0.206205	−	0.634634i
$382$	−0.893342	+	2.74943i	−0.0457074	+	0.140673i
$383$	−20.8632	−	15.1580i	−1.06606	−	0.774537i	−0.0908595	−	0.995864i	$-0.528961\pi$
$383$	−20.8632	−	15.1580i	−1.06606	−	0.774537i	−0.975200	+	0.221326i	$0.928961\pi$
$384$	7.82991			0.399569
$385$	−12.8957	−	0.0505279i	−0.657228	−	0.00257514i
$386$	4.13399			0.210415
$387$	9.09059	+	6.60470i	0.462100	+	0.335736i
$388$	−3.48403	+	10.7227i	−0.176875	+	0.544365i
$389$	4.99030	+	15.3586i	0.253018	+	0.778710i	0.994214	+	0.107421i	$0.0342593\pi$
$389$	4.99030	+	15.3586i	0.253018	+	0.778710i	−0.741195	+	0.671289i	$0.765741\pi$
$390$	−0.198450	+	0.144182i	−0.0100489	+	0.00730095i
$391$	−6.31944	+	4.59134i	−0.319588	+	0.232194i
$392$	−8.23147	−	25.3339i	−0.415752	−	1.27955i
$393$	3.55927	−	10.9543i	0.179541	−	0.552571i
$394$	0.541202	+	0.393206i	0.0272653	+	0.0198094i
$395$	−11.5435			−0.580814
$396$	−4.53588	−	14.1484i	−0.227937	−	0.710983i
$397$	−22.6993			−1.13925			−0.569623	−	0.821906i	$-0.692911\pi$
$397$	−22.6993			−1.13925			−0.569623	+	0.821906i	$0.692911\pi$
$398$	2.53308	+	1.84039i	0.126972	+	0.0922506i
$399$	−1.21623	+	3.74316i	−0.0608874	+	0.187392i
$400$	−4.03997	−	12.4338i	−0.201999	−	0.621688i
$401$	−25.1122	+	18.2451i	−1.25405	+	0.911117i	−0.998449	−	0.0556662i	$-0.982272\pi$
$401$	−25.1122	+	18.2451i	−1.25405	+	0.911117i	−0.255596	+	0.966784i	$0.582272\pi$
$402$	−0.180137	+	0.130877i	−0.00898441	+	0.00652756i
$403$	−1.90852	−	5.87383i	−0.0950702	−	0.292596i
$404$	7.76278	−	23.8914i	0.386213	−	1.18864i
$405$	2.81380	+	2.04435i	0.139819	+	0.101584i
$406$	−2.44314			−0.121251
$407$	9.99730	+	7.32349i	0.495548	+	0.363012i
$408$	−3.55620			−0.176058
$409$	−14.9743	−	10.8794i	−0.740430	−	0.537954i	0.152416	−	0.988316i	$-0.451295\pi$
$409$	−14.9743	−	10.8794i	−0.740430	−	0.537954i	−0.892846	+	0.450363i	$0.851295\pi$
$410$	0.498471	−	1.53413i	0.0246177	−	0.0757655i
$411$	−1.92698	−	5.93063i	−0.0950508	−	0.292536i
$412$	4.18496	−	3.04055i	0.206178	−	0.149797i
$413$	31.3398	−	22.7697i	1.54213	−	1.12042i
$414$	0.812941	+	2.50198i	0.0399539	+	0.122965i
$415$	3.12725	−	9.62468i	0.153511	−	0.472457i
$416$	−3.57686	−	2.59874i	−0.175370	−	0.127414i
$417$	−3.69963			−0.181171
$418$	0.469148	−	1.42487i	0.0229468	−	0.0696926i
$419$	14.2243			0.694904			0.347452	−	0.937698i	$-0.387047\pi$
$419$	14.2243			0.694904			0.347452	+	0.937698i	$0.387047\pi$
$420$	−4.25978	−	3.09491i	−0.207856	−	0.151016i
$421$	8.47273	−	26.0764i	0.412936	−	1.27089i	−0.501149	−	0.865361i	$-0.667089\pi$
$421$	8.47273	−	26.0764i	0.412936	−	1.27089i	0.914084	−	0.405524i	$-0.132911\pi$
$422$	−1.43419	−	4.41398i	−0.0698152	−	0.214869i
$423$	24.9307	−	18.1132i	1.21217	−	0.880696i
$424$	−4.13086	+	3.00124i	−0.200612	+	0.145753i
$425$	4.07369	+	12.5375i	0.197603	+	0.608159i
$426$	0.132063	−	0.406447i	0.00639846	−	0.0196924i
$427$	−14.3846	−	10.4510i	−0.696121	−	0.505761i
$428$	19.6810			0.951319
$429$	0.768515	−	2.33409i	0.0371043	−	0.112691i
$430$	−1.51777			−0.0731934
$431$	−4.32479	−	3.14214i	−0.208318	−	0.151352i	0.478734	−	0.877960i	$-0.341096\pi$
$431$	−4.32479	−	3.14214i	−0.208318	−	0.151352i	−0.687052	+	0.726608i	$0.741096\pi$
$432$	3.73903	−	11.5076i	0.179894	−	0.553657i
$433$	−1.07747	−	3.31612i	−0.0517801	−	0.159363i	0.921823	−	0.387612i	$-0.126700\pi$
$433$	−1.07747	−	3.31612i	−0.0517801	−	0.159363i	−0.973603	+	0.228249i	$0.926700\pi$
$434$	−10.1108	+	7.34595i	−0.485336	+	0.352617i
$435$	−0.577222	+	0.419377i	−0.0276757	+	0.0201076i
$436$	7.40225	+	22.7818i	0.354503	+	1.09105i
$437$	0.870673	−	2.67966i	0.0416499	−	0.128185i
$438$	−2.29151	−	1.66488i	−0.109493	−	0.0795510i
$439$	−33.5680			−1.60211			−0.801056	−	0.598589i	$-0.795728\pi$
$439$	−33.5680			−1.60211			−0.801056	+	0.598589i	$0.795728\pi$
$440$	3.39057	+	2.48375i	0.161639	+	0.118408i
$441$	−41.0928			−1.95680
$442$	1.01446	+	0.737048i	0.0482529	+	0.0350578i
$443$	12.2961	−	37.8435i	0.584205	−	1.79800i	−0.0182341	−	0.999834i	$-0.505804\pi$
$443$	12.2961	−	37.8435i	0.584205	−	1.79800i	0.602439	−	0.798165i	$-0.294196\pi$
$444$	1.56361	+	4.81230i	0.0742058	+	0.228382i
$445$	9.29203	−	6.75105i	0.440484	−	0.320031i
$446$	−0.324273	+	0.235598i	−0.0153548	+	0.0111559i
$447$	2.73052	+	8.40366i	0.129149	+	0.397480i
$448$	6.26169	−	19.2715i	0.295837	−	0.910492i
$449$	10.8722	+	7.89911i	0.513091	+	0.372782i	0.813995	−	0.580872i	$-0.197288\pi$
$449$	10.8722	+	7.89911i	0.513091	+	0.372782i	−0.300904	+	0.953654i	$0.597288\pi$
$450$	4.43978			0.209293
$451$	4.93335	+	15.3882i	0.232302	+	0.724601i
$452$	36.2627			1.70565
$453$	−6.82791	−	4.96077i	−0.320803	−	0.233077i
$454$	3.10248	−	9.54847i	0.145607	−	0.448132i
$455$	1.20153	+	3.69794i	0.0563287	+	0.173362i
$456$	1.03776	−	0.753975i	0.0485974	−	0.0353081i
$457$	23.5906	−	17.1395i	1.10352	−	0.801754i	0.121889	−	0.992544i	$-0.461105\pi$
$457$	23.5906	−	17.1395i	1.10352	−	0.801754i	0.981631	+	0.190790i	$0.0611048\pi$
$458$	3.60991	+	11.1102i	0.168680	+	0.519144i
$459$	−3.77023	+	11.6036i	−0.175979	+	0.541609i
$460$	3.04950	+	2.21559i	0.142184	+	0.103302i
$461$	6.75536			0.314629			0.157314	−	0.987549i	$-0.449716\pi$
$461$	6.75536			0.314629			0.157314	+	0.987549i	$0.449716\pi$
$462$	−4.97255	−	0.0194834i	−0.231344	−	0.000906448i
$463$	−14.4033			−0.669378			−0.334689	−	0.942329i	$-0.608631\pi$
$463$	−14.4033			−0.669378			−0.334689	+	0.942329i	$0.608631\pi$
$464$	−2.92629	−	2.12608i	−0.135850	−	0.0987006i
$465$	−1.12784	+	3.47114i	−0.0523025	+	0.160970i
$466$	1.43753	+	4.42428i	0.0665925	+	0.204951i
$467$	−27.8923	+	20.2650i	−1.29070	+	0.937751i	−0.999819	−	0.0190072i	$-0.993949\pi$
$467$	−27.8923	+	20.2650i	−1.29070	+	0.937751i	−0.290884	+	0.956758i	$0.593949\pi$
$468$	−3.62420	+	2.63314i	−0.167529	+	0.121717i
$469$	1.09066	+	3.35669i	0.0503618	+	0.154998i
$470$	−1.28627	+	3.95873i	−0.0593311	+	0.182602i
$471$	0.229976	+	0.167087i	0.0105967	+	0.00769898i
$472$	−12.6254			−0.581130
$473$	12.3359	−	8.88889i	0.567203	−	0.408712i
$474$	−4.45111			−0.204446
$475$	−3.84693	−	2.79496i	−0.176509	−	0.128242i
$476$	−8.31756	+	25.5988i	−0.381235	+	1.17332i
$477$	2.43408	+	7.49134i	0.111449	+	0.343005i
$478$	6.23527	−	4.53019i	0.285195	−	0.207206i
$479$	−0.899912	+	0.653825i	−0.0411180	+	0.0298740i	−0.608154	−	0.793819i	$-0.708090\pi$
$479$	−0.899912	+	0.653825i	−0.0411180	+	0.0298740i	0.567036	+	0.823693i	$0.308090\pi$
$480$	0.807379	+	2.48486i	0.0368517	+	0.113418i
$481$	1.15466	−	3.55367i	0.0526478	−	0.162033i
$482$	0.666356	+	0.484136i	0.0303517	+	0.0220518i
$483$	−9.33963			−0.424968
$484$	−20.1041	−	0.157546i	−0.913822	−	0.00716116i
$485$	−4.92011			−0.223411
$486$	5.15383	+	3.74448i	0.233783	+	0.169853i
$487$	−3.78860	+	11.6601i	−0.171678	+	0.528370i	−0.999466	−	0.0326705i	$-0.989599\pi$
$487$	−3.78860	+	11.6601i	−0.171678	+	0.528370i	0.827788	+	0.561040i	$0.189599\pi$
$488$	1.79073	+	5.51130i	0.0810625	+	0.249485i
$489$	9.04555	−	6.57198i	0.409054	−	0.297195i
$490$	4.49050	−	3.26254i	0.202860	−	0.147387i
$491$	8.07538	+	24.8535i	0.364437	+	1.12162i	0.950333	+	0.311235i	$0.100743\pi$
$491$	8.07538	+	24.8535i	0.364437	+	1.12162i	−0.585896	+	0.810386i	$0.699257\pi$
$492$	−2.03889	+	6.27507i	−0.0919204	+	0.282902i
$493$	2.95071	+	2.14382i	0.132894	+	0.0965528i
$494$	−0.452302			−0.0203500
$495$	5.26036	−	3.79047i	0.236436	−	0.170369i
$496$	−18.5029			−0.830807
$497$	−5.48044	−	3.98177i	−0.245831	−	0.178607i
$498$	1.20585	−	3.71124i	0.0540356	−	0.166305i
$499$	−8.91572	−	27.4398i	−0.399123	−	1.22837i	−0.925704	−	0.378249i	$-0.876526\pi$
$499$	−8.91572	−	27.4398i	−0.399123	−	1.22837i	0.526581	−	0.850125i	$-0.323474\pi$
$500$	11.0433	−	8.02340i	0.493870	−	0.358817i
$501$	8.79596	−	6.39064i	0.392974	−	0.285513i
$502$	−1.01714	−	3.13045i	−0.0453974	−	0.139719i
$503$	8.65395	−	26.6341i	0.385861	−	1.18756i	−0.549993	−	0.835169i	$-0.685370\pi$
$503$	8.65395	−	26.6341i	0.385861	−	1.18756i	0.935854	−	0.352388i	$-0.114630\pi$
$504$	15.3589	+	11.1589i	0.684140	+	0.497057i
$505$	10.9625			0.487825
$506$	3.55975	+	0.0139478i	0.158250	+	0.000620054i
$507$	−0.740920			−0.0329054
$508$	25.9939	+	18.8856i	1.15329	+	0.837915i
$509$	0.309666	−	0.953053i	0.0137257	−	0.0422433i	−0.943959	−	0.330062i	$-0.892930\pi$
$509$	0.309666	−	0.953053i	0.0137257	−	0.0422433i	0.957685	+	0.287819i	$0.0929302\pi$
$510$	−0.228987	−	0.704750i	−0.0101397	−	0.0312068i
$511$	−36.3230	+	26.3902i	−1.60684	+	1.16743i
$512$	−18.4177	+	13.3812i	−0.813955	+	0.591373i
$513$	−1.35994	−	4.18547i	−0.0600429	−	0.184793i
$514$	−1.30462	+	4.01522i	−0.0575445	+	0.177104i
$515$	1.82628	+	1.32687i	0.0804754	+	0.0584688i
$516$	6.20813			0.273298
$517$	−12.7302	−	39.7081i	−0.559872	−	1.74636i
$518$	−7.56110			−0.332216
$519$	1.50305	+	1.09203i	0.0659767	+	0.0479349i
$520$	0.391599	−	1.20522i	0.0171728	−	0.0528523i
$521$	−6.78934	−	20.8954i	−0.297446	−	0.915446i	−0.982389	−	0.186849i	$-0.940173\pi$
$521$	−6.78934	−	20.8954i	−0.297446	−	0.915446i	0.684942	−	0.728597i	$-0.259827\pi$
$522$	0.993764	−	0.722012i	0.0434959	−	0.0316016i
$523$	1.13021	−	0.821148i	0.0494208	−	0.0359063i	−0.562801	−	0.826593i	$-0.690276\pi$
$523$	1.13021	−	0.821148i	0.0494208	−	0.0359063i	0.612221	+	0.790686i	$0.290276\pi$
$524$	8.78000	+	27.0221i	0.383556	+	1.18046i
$525$	−4.87076	+	14.9906i	−0.212577	+	0.654246i
$526$	0.645629	+	0.469077i	0.0281507	+	0.0204527i
$527$	18.6574			0.812728
$528$	−5.93896	−	4.35056i	−0.258460	−	0.189334i
$529$	−16.3139			−0.709301
$530$	−0.860760	−	0.625379i	−0.0373890	−	0.0271647i
$531$	−6.01862	+	18.5234i	−0.261186	+	0.803848i
$532$	−3.00018	−	9.23362i	−0.130074	−	0.400328i
$533$	3.94179	−	2.86388i	0.170738	−	0.124048i
$534$	3.58297	−	2.60318i	0.155050	−	0.112651i
$535$	2.65403	+	8.16825i	0.114744	+	0.353144i
$536$	0.355463	−	1.09400i	0.0153537	−	0.0472537i
$537$	14.0814	+	10.2307i	0.607658	+	0.441489i
$538$	−7.57627			−0.326636
$539$	−17.3899	+	52.8155i	−0.749035	+	2.27493i
$540$	5.88757			0.253360
$541$	−31.0530	−	22.5613i	−1.33507	−	0.969987i	−0.999610	−	0.0279329i	$-0.991108\pi$
$541$	−31.0530	−	22.5613i	−1.33507	−	0.969987i	−0.335462	−	0.942054i	$-0.608892\pi$
$542$	0.380262	−	1.17032i	0.0163336	−	0.0502698i
$543$	2.96186	+	9.11567i	0.127106	+	0.391191i
$544$	10.8053	−	7.85051i	0.463274	−	0.336588i
$545$	−8.45696	+	6.14434i	−0.362256	+	0.263195i
$546$	0.463306	+	1.42591i	0.0198277	+	0.0610233i
$547$	−5.45449	+	16.7872i	−0.233217	+	0.717768i	0.764136	+	0.645055i	$0.223166\pi$
$547$	−5.45449	+	16.7872i	−0.233217	+	0.717768i	−0.997353	+	0.0727131i	$0.976834\pi$
$548$	12.4447	+	9.04163i	0.531613	+	0.386239i
$549$	8.93960			0.381533
$550$	1.87885	−	5.70634i	0.0801145	−	0.243319i
$551$	−1.31559			−0.0560461
$552$	2.46260	+	1.78918i	0.104815	+	0.0761527i
$553$	−21.8027	+	67.1019i	−0.927147	+	2.85346i
$554$	−2.40952	−	7.41575i	−0.102371	−	0.315065i
$555$	−1.78640	+	1.29790i	−0.0758286	+	0.0550927i
$556$	7.38328	−	5.36427i	0.313121	−	0.227496i
$557$	0.213506	+	0.657105i	0.00904655	+	0.0278424i	0.955478	−	0.295063i	$-0.0953405\pi$
$557$	0.213506	+	0.657105i	0.00904655	+	0.0278424i	−0.946431	+	0.322905i	$0.895341\pi$
$558$	1.94173	−	5.97603i	0.0821999	−	0.252985i
$559$	−3.70887	−	2.69465i	−0.156869	−	0.113972i
$560$	11.6488			0.492250
$561$	5.98852	+	4.38687i	0.252835	+	0.185214i
$562$	1.72981			0.0729675
$563$	14.9432	+	10.8569i	0.629780	+	0.457562i	0.856324	−	0.516439i	$-0.172743\pi$
$563$	14.9432	+	10.8569i	0.629780	+	0.457562i	−0.226544	+	0.974001i	$0.572743\pi$
$564$	5.26122	−	16.1924i	0.221537	−	0.681822i
$565$	4.89009	+	15.0502i	0.205728	+	0.633165i
$566$	−4.06951	+	2.95667i	−0.171054	+	0.124278i
$567$	17.1984	−	12.4953i	0.722263	−	0.524755i
$568$	0.682255	+	2.09976i	0.0286268	+	0.0881042i
$569$	−4.20800	+	12.9509i	−0.176408	+	0.542930i	−0.999695	−	0.0246965i	$-0.992138\pi$
$569$	−4.20800	+	12.9509i	−0.176408	+	0.542930i	0.823286	+	0.567626i	$0.192138\pi$
$570$	0.216241	+	0.157108i	0.00905733	+	0.00658054i
$571$	19.9176			0.833525			0.416762	−	0.909015i	$-0.363165\pi$
$571$	19.9176			0.833525			0.416762	+	0.909015i	$0.363165\pi$
$572$	1.85060	+	5.77241i	0.0773773	+	0.241356i
$573$	5.16019			0.215570
$574$	−7.97642	−	5.79521i	−0.332929	−	0.241887i
$575$	3.48688	−	10.7315i	0.145413	−	0.447536i
$576$	3.14824	+	9.68929i	0.131177	+	0.403721i
$577$	−7.85258	+	5.70523i	−0.326907	+	0.237512i	−0.739117	−	0.673577i	$-0.764757\pi$
$577$	−7.85258	+	5.70523i	−0.326907	+	0.237512i	0.412210	+	0.911089i	$0.364757\pi$
$578$	2.64427	−	1.92117i	0.109987	−	0.0799102i
$579$	−2.28025	−	7.01788i	−0.0947639	−	0.291653i
$580$	0.543878	−	1.67388i	0.0225833	−	0.0695043i
$581$	−50.0415	−	36.3573i	−2.07607	−	1.50835i
$582$	−1.89717			−0.0786404
$583$	10.6585	+	0.0417620i	0.441430	+	0.00172960i
$584$	14.6329			0.605514
$585$	−1.58157	−	1.14908i	−0.0653898	−	0.0475084i
$586$	−1.22624	+	3.77397i	−0.0506554	+	0.155901i
$587$	9.01141	+	27.7343i	0.371941	+	1.14472i	0.945519	+	0.325566i	$0.105555\pi$
$587$	9.01141	+	27.7343i	0.371941	+	1.14472i	−0.573579	+	0.819151i	$0.694445\pi$
$588$	−18.3675	+	13.3448i	−0.757462	+	0.550328i
$589$	−5.44452	+	3.95568i	−0.224338	+	0.162991i
$590$	−0.812959	−	2.50203i	−0.0334690	−	0.103007i
$591$	0.368989	−	1.13563i	0.0151782	−	0.0467136i
$592$	−9.05637	−	6.57984i	−0.372215	−	0.270430i
$593$	−11.9616			−0.491203			−0.245601	−	0.969371i	$-0.578985\pi$
$593$	−11.9616			−0.491203			−0.245601	+	0.969371i	$0.578985\pi$
$594$	4.51105	−	3.25054i	0.185090	−	0.133371i
$595$	−11.7460			−0.481538
$596$	−17.6341	−	12.8119i	−0.722322	−	0.524797i
$597$	1.72705	−	5.31530i	0.0706833	−	0.217541i
$598$	−0.331672	−	1.02078i	−0.0135631	−	0.0417429i
$599$	−28.8253	+	20.9428i	−1.17777	+	0.855699i	−0.991918	−	0.126879i	$-0.959504\pi$
$599$	−28.8253	+	20.9428i	−1.17777	+	0.855699i	−0.185851	+	0.982578i	$0.559504\pi$
$600$	4.15602	−	3.01953i	0.169669	−	0.123272i
$601$	−6.46276	−	19.8903i	−0.263622	−	0.811344i	−0.992008	−	0.126177i	$-0.959729\pi$
$601$	−6.46276	−	19.8903i	−0.263622	−	0.811344i	0.728386	−	0.685167i	$-0.240271\pi$
$602$	−2.86669	+	8.82277i	−0.116838	+	0.359589i
$603$	−1.43562	−	1.04304i	−0.0584630	−	0.0424759i
$604$	20.8192			0.847121
$605$	−2.64569	−	8.36508i	−0.107563	−	0.340089i
$606$	4.22710			0.171714
$607$	8.69339	+	6.31612i	0.352854	+	0.256363i	0.750065	−	0.661364i	$-0.230022\pi$
$607$	8.69339	+	6.31612i	0.352854	+	0.256363i	−0.397212	+	0.917727i	$0.630022\pi$
$608$	−1.48872	+	4.58181i	−0.0603756	+	0.185817i
$609$	1.34760	+	4.14748i	0.0546075	+	0.168065i
$610$	−0.976893	+	0.709755i	−0.0395533	+	0.0287371i
$611$	−10.1715	+	7.39003i	−0.411495	+	0.298969i
$612$	−4.18189	−	12.8705i	−0.169043	−	0.520261i
$613$	−5.05134	+	15.5464i	−0.204022	+	0.627914i	0.795730	+	0.605651i	$0.207087\pi$
$613$	−5.05134	+	15.5464i	−0.204022	+	0.627914i	−0.999752	+	0.0222634i	$0.992913\pi$
$614$	5.49912	+	3.99534i	0.221926	+	0.161239i
$615$	−2.87930			−0.116105
$616$	20.8419	−	15.0181i	0.839745	−	0.605098i
$617$	23.7760			0.957184			0.478592	−	0.878037i	$-0.341147\pi$
$617$	23.7760			0.957184			0.478592	+	0.878037i	$0.341147\pi$
$618$	0.704205	+	0.511635i	0.0283273	+	0.0205810i
$619$	−5.92596	+	18.2382i	−0.238185	+	0.733057i	0.758498	+	0.651675i	$0.225933\pi$
$619$	−5.92596	+	18.2382i	−0.238185	+	0.733057i	−0.996683	+	0.0813818i	$0.974067\pi$
$620$	−2.78216	−	8.56261i	−0.111734	−	0.343883i
$621$	8.44877	−	6.13839i	0.339037	−	0.246325i
$622$	−3.51228	+	2.55182i	−0.140829	+	0.102319i
$623$	−21.6934	−	66.7655i	−0.869129	−	2.67490i
$624$	−0.685930	+	2.11108i	−0.0274592	+	0.0845107i
$625$	−12.8330	−	9.32370i	−0.513319	−	0.372948i
$626$	−3.17497			−0.126897
$627$	−2.67764	−	0.0104915i	−0.106934	−	0.000418989i
$628$	−0.701227			−0.0279820
$629$	9.13195	+	6.63475i	0.364115	+	0.264545i
$630$	−1.22244	+	3.76228i	−0.0487031	+	0.149893i
$631$	−5.48109	−	16.8691i	−0.218199	−	0.671546i	−0.998911	−	0.0466558i	$-0.985144\pi$
$631$	−5.48109	−	16.8691i	−0.218199	−	0.671546i	0.780712	−	0.624891i	$-0.214856\pi$
$632$	18.6034	−	13.5162i	0.740004	−	0.537644i
$633$	−6.70210	+	4.86936i	−0.266385	+	0.193540i
$634$	−1.19505	−	3.67798i	−0.0474615	−	0.146071i
$635$	−4.33282	+	13.3350i	−0.171943	+	0.529185i
$636$	3.52076	+	2.55799i	0.139607	+	0.101431i
$637$	16.7655			0.664272
$638$	−0.507437	−	1.58280i	−0.0200896	−	0.0626638i
$639$	3.40592			0.134736
$640$	−6.81904	−	4.95432i	−0.269546	−	0.195837i
$641$	11.4566	−	35.2598i	0.452509	−	1.39268i	−0.421527	−	0.906816i	$-0.638506\pi$
$641$	11.4566	−	35.2598i	0.452509	−	1.39268i	0.874035	−	0.485862i	$-0.161494\pi$
$642$	1.02338	+	3.14965i	0.0403897	+	0.124307i
$643$	−24.0598	+	17.4804i	−0.948824	+	0.689361i	−0.950528	−	0.310638i	$-0.899457\pi$
$643$	−24.0598	+	17.4804i	−0.948824	+	0.689361i	0.00170439	+	0.999999i	$0.499457\pi$
$644$	18.6389	−	13.5420i	0.734477	−	0.533629i
$645$	0.837178	+	2.57657i	0.0329639	+	0.101452i
$646$	0.422228	−	1.29948i	0.0166123	−	0.0511275i
$647$	29.6309	+	21.5281i	1.16491	+	0.846356i	0.990391	−	0.138298i	$-0.0441631\pi$
$647$	29.6309	+	21.5281i	1.16491	+	0.846356i	0.174519	+	0.984654i	$0.444163\pi$
$648$	−6.92844			−0.272175
$649$	21.2607	+	15.5744i	0.834555	+	0.611350i
$650$	−1.81139			−0.0710484
$651$	18.0475	+	13.1123i	0.707337	+	0.513910i
$652$	−8.52302	+	26.2312i	−0.333787	+	1.02729i
$653$	−4.84991	−	14.9265i	−0.189792	−	0.584119i	0.810206	−	0.586145i	$-0.199355\pi$
$653$	−4.84991	−	14.9265i	−0.189792	−	0.584119i	−0.999998	+	0.00202587i	$0.999355\pi$
$654$	−3.26097	+	2.36923i	−0.127514	+	0.0926443i
$655$	−10.0310	+	7.28796i	−0.391944	+	0.284764i
$656$	−4.51070	−	13.8825i	−0.176113	−	0.542021i
$657$	6.97563	−	21.4688i	0.272145	−	0.837577i
$658$	20.5826	+	14.9541i	0.802393	+	0.582972i
$659$	17.8382			0.694879			0.347439	−	0.937702i	$-0.387051\pi$
$659$	17.8382			0.694879			0.347439	+	0.937702i	$0.387051\pi$
$660$	1.12031	−	3.40254i	0.0436080	−	0.132444i
$661$	9.05533			0.352211			0.176106	−	0.984371i	$-0.443650\pi$
$661$	9.05533			0.352211			0.176106	+	0.984371i	$0.443650\pi$
$662$	0.499342	+	0.362793i	0.0194075	+	0.0141004i
$663$	0.691655	−	2.12869i	0.0268616	−	0.0826716i
$664$	6.22962	+	19.1728i	0.241756	+	0.744049i
$665$	3.42766	−	2.49034i	0.132919	−	0.0965714i
$666$	3.07553	−	2.23450i	0.119174	−	0.0865851i
$667$	−0.964721	−	2.96911i	−0.0373541	−	0.114964i
$668$	−8.28784	+	25.5074i	−0.320666	+	0.986909i
$669$	0.578817	+	0.420535i	0.0223784	+	0.0162588i
$670$	0.239692			0.00926012
$671$	3.78311	−	11.4898i	0.146045	−	0.443560i
$672$	15.9694			0.616033
$673$	−27.4453	−	19.9402i	−1.05794	−	0.768637i	−0.0842319	−	0.996446i	$-0.526844\pi$
$673$	−27.4453	−	19.9402i	−1.05794	−	0.768637i	−0.973706	+	0.227810i	$0.926844\pi$
$674$	1.51218	−	4.65402i	0.0582471	−	0.179266i
$675$	−5.44631	−	16.7620i	−0.209629	−	0.645171i
$676$	1.47864	−	1.07430i	0.0568708	−	0.0413191i
$677$	1.86991	−	1.35857i	0.0718665	−	0.0522141i	−0.551272	−	0.834326i	$-0.685857\pi$
$677$	1.86991	−	1.35857i	0.0718665	−	0.0522141i	0.623138	+	0.782112i	$0.285857\pi$
$678$	1.88560	+	5.80328i	0.0724161	+	0.222874i
$679$	−9.29287	+	28.6005i	−0.356628	+	1.09759i
$680$	3.09708	+	2.25016i	0.118768	+	0.0862898i
$681$	−17.9208			−0.686726
$682$	−6.85913	−	5.02463i	−0.262650	−	0.192403i
$683$	28.2334			1.08032			0.540160	−	0.841562i	$-0.318364\pi$
$683$	28.2334			1.08032			0.540160	+	0.841562i	$0.318364\pi$
$684$	3.94912	+	2.86920i	0.150998	+	0.109707i
$685$	−2.07437	+	6.38424i	−0.0792575	+	0.243929i
$686$	−6.10646	−	18.7938i	−0.233146	−	0.717549i
$687$	16.8695	−	12.2564i	0.643611	−	0.467611i
$688$	−11.1114	+	8.07289i	−0.423617	+	0.307776i
$689$	−0.993083	−	3.05639i	−0.0378334	−	0.116439i
$690$	−0.196002	+	0.603232i	−0.00746167	+	0.0229647i
$691$	−16.7000	−	12.1333i	−0.635300	−	0.461572i	0.222932	−	0.974834i	$-0.428437\pi$
$691$	−16.7000	−	12.1333i	−0.635300	−	0.461572i	−0.858232	+	0.513262i	$0.828437\pi$
$692$	−4.58301			−0.174220
$693$	−12.0984	−	37.7377i	−0.459582	−	1.43354i
$694$	9.56012			0.362897
$695$	3.22199	+	2.34091i	0.122217	+	0.0887959i
$696$	0.439205	−	1.35173i	0.0166480	−	0.0512373i
$697$	4.54835	+	13.9984i	0.172281	+	0.530226i
$698$	−5.45620	+	3.96416i	−0.206520	+	0.150046i
$699$	6.71774	−	4.88072i	0.254088	−	0.184606i
$700$	−12.0152	−	36.9789i	−0.454131	−	1.39767i
$701$	−13.1435	+	40.4515i	−0.496422	+	1.52783i	0.318306	+	0.947988i	$0.396886\pi$
$701$	−13.1435	+	40.4515i	−0.496422	+	1.52783i	−0.814728	+	0.579843i	$0.803114\pi$
$702$	−1.35628	−	0.985396i	−0.0511895	−	0.0371914i
$703$	−4.07153			−0.153561
$704$	13.7857	+	0.0540149i	0.519568	+	0.00203576i
$705$	7.42983			0.279824
$706$	−4.58863	−	3.33383i	−0.172695	−	0.125470i
$707$	20.7055	−	63.7249i	0.778710	−	2.39662i
$708$	3.32525	+	10.2341i	0.124970	+	0.384619i
$709$	8.35349	−	6.06917i	0.313722	−	0.227932i	−0.419770	−	0.907631i	$-0.637889\pi$
$709$	8.35349	−	6.06917i	0.313722	−	0.227932i	0.733492	+	0.679698i	$0.237889\pi$
$710$	−0.372190	+	0.270412i	−0.0139680	+	0.0101484i
$711$	−10.9620	−	33.7374i	−0.411105	−	1.26525i
$712$	−7.07025	+	21.7600i	−0.264969	+	0.815490i
$713$	−12.9199	−	9.38683i	−0.483853	−	0.351539i
$714$	−4.52920			−0.169501
$715$	−2.14618	+	1.54648i	−0.0802624	+	0.0578349i
$716$	−42.9361			−1.60460
$717$	−11.1297	−	8.08623i	−0.415648	−	0.301986i
$718$	2.69208	−	8.28536i	0.100467	−	0.309207i
$719$	−4.77354	−	14.6914i	−0.178023	−	0.547898i	0.821736	−	0.569869i	$-0.193006\pi$
$719$	−4.77354	−	14.6914i	−0.178023	−	0.547898i	−0.999759	+	0.0219706i	$0.993006\pi$
$720$	−4.73821	+	3.44251i	−0.176583	+	0.128295i
$721$	11.1625	−	8.11000i	0.415711	−	0.302032i
$722$	−2.28482	−	7.03196i	−0.0850323	−	0.261703i
$723$	0.454319	−	1.39825i	0.0168963	−	0.0520015i
$724$	−19.1282	−	13.8974i	−0.710894	−	0.516495i
$725$	−5.26870			−0.195675
$726$	−1.02017	−	3.22554i	−0.0378620	−	0.119711i
$727$	5.57910			0.206917			0.103459	−	0.994634i	$-0.467009\pi$
$727$	5.57910			0.206917			0.103459	+	0.994634i	$0.467009\pi$
$728$	−6.26629	−	4.55272i	−0.232244	−	0.168735i
$729$	−0.528725	+	1.62725i	−0.0195824	+	0.0602685i
$730$	0.942226	+	2.89987i	0.0348734	+	0.107329i
$731$	11.2041	−	8.14026i	0.414399	−	0.301079i
$732$	3.99578	−	2.90311i	0.147688	−	0.107302i
$733$	10.3552	+	31.8700i	0.382478	+	1.17715i	0.938293	+	0.345841i	$0.112406\pi$
$733$	10.3552	+	31.8700i	0.382478	+	1.17715i	−0.555815	+	0.831306i	$0.687594\pi$
$734$	4.36737	−	13.4414i	0.161203	−	0.496131i
$735$	−8.01539	−	5.82352i	−0.295652	−	0.214804i
$736$	−11.4322			−0.421396
$737$	−1.94813	+	1.40377i	−0.0717602	+	0.0517085i
$738$	4.95709			0.182473
$739$	8.10445	+	5.88823i	0.298127	+	0.216602i	0.726785	−	0.686865i	$-0.241014\pi$
$739$	8.10445	+	5.88823i	0.298127	+	0.216602i	−0.428658	+	0.903467i	$0.641014\pi$
$740$	1.68321	−	5.18038i	0.0618760	−	0.190435i
$741$	0.249483	+	0.767830i	0.00916499	+	0.0282069i
$742$	−5.26108	+	3.82240i	−0.193140	+	0.140325i
$743$	5.77462	−	4.19550i	0.211850	−	0.153918i	−0.476800	−	0.879012i	$-0.658203\pi$
$743$	5.77462	−	4.19550i	0.211850	−	0.153918i	0.688650	+	0.725094i	$0.258203\pi$
$744$	−2.24671	−	6.91468i	−0.0823686	−	0.253504i
$745$	2.93937	−	9.04644i	0.107690	−	0.331436i
$746$	−8.64419	−	6.28037i	−0.316486	−	0.229941i
$747$	31.0992			1.13786
$748$	−18.3119	−	0.0717495i	−0.669550	−	0.00262342i
$749$	52.4947			1.91812
$750$	1.85825	+	1.35010i	0.0678538	+	0.0492987i
$751$	−5.60281	+	17.2437i	−0.204450	+	0.629231i	0.795286	+	0.606234i	$0.207321\pi$
$751$	−5.60281	+	17.2437i	−0.204450	+	0.629231i	−0.999736	+	0.0229966i	$0.992679\pi$
$752$	11.6396	+	35.8229i	0.424451	+	1.30633i
$753$	−4.75322	+	3.45341i	−0.173217	+	0.125849i
$754$	−0.405446	+	0.294574i	−0.0147655	+	0.0107277i
$755$	2.80751	+	8.64063i	0.102176	+	0.314465i
$756$	11.1202	−	34.2243i	0.404436	−	1.24473i
$757$	21.5481	+	15.6556i	0.783179	+	0.569013i	0.905931	−	0.423425i	$-0.139172\pi$
$757$	21.5481	+	15.6556i	0.783179	+	0.569013i	−0.122753	+	0.992437i	$0.539172\pi$
$758$	−9.45690			−0.343490
$759$	−1.93983	−	6.05074i	−0.0704113	−	0.219628i
$760$	−1.38085			−0.0500887
$761$	−36.4412	−	26.4761i	−1.32099	−	0.959758i	−0.999919	−	0.0127044i	$-0.995956\pi$
$761$	−36.4412	−	26.4761i	−1.32099	−	0.959758i	−0.321075	−	0.947054i	$-0.604044\pi$
$762$	−1.67072	+	5.14194i	−0.0605237	+	0.186273i
$763$	19.7438	+	60.7653i	0.714775	+	2.19985i
$764$	−10.2981	+	7.48200i	−0.372572	+	0.270689i
$765$	4.77775	−	3.47124i	0.172740	−	0.125503i
$766$	3.30786	+	10.1805i	0.119518	+	0.367838i
$767$	2.45554	−	7.55738i	0.0886645	−	0.272881i
$768$	2.35365	+	1.71002i	0.0849299	+	0.0617052i
$769$	7.53433			0.271695			0.135847	−	0.990730i	$-0.456624\pi$
$769$	7.53433			0.271695			0.135847	+	0.990730i	$0.456624\pi$
$770$	4.31825	+	3.16331i	0.155619	+	0.113998i
$771$	7.53585			0.271397
$772$	14.7262	+	10.6992i	0.530008	+	0.385073i
$773$	−4.43947	+	13.6633i	−0.159677	+	0.491435i	−0.998605	−	0.0528080i	$-0.983183\pi$
$773$	−4.43947	+	13.6633i	−0.159677	+	0.491435i	0.838928	+	0.544243i	$0.183183\pi$
$774$	−1.44131	−	4.43590i	−0.0518069	−	0.159445i
$775$	−21.8043	+	15.8418i	−0.783234	+	0.569052i
$776$	7.92924	−	5.76093i	0.284643	−	0.206805i
$777$	4.17059	+	12.8357i	0.149619	+	0.460480i
$778$	2.07142	−	6.37518i	0.0742640	−	0.228561i
$779$	−4.29517	−	3.12062i	−0.153890	−	0.111808i
$780$	−1.08008			−0.0386731
$781$	1.44134	−	4.37755i	0.0515752	−	0.156641i
$782$	3.24237			0.115947
$783$	−3.94496	−	2.86618i	−0.140981	−	0.102429i
$784$	15.5212	−	47.7692i	0.554327	−	1.70604i
$785$	−0.0945619	−	0.291032i	−0.00337506	−	0.0103874i
$786$	−3.86792	+	2.81021i	−0.137964	+	0.100237i
$787$	−15.3984	+	11.1876i	−0.548893	+	0.398794i	−0.827377	−	0.561647i	$-0.810168\pi$
$787$	−15.3984	+	11.1876i	−0.548893	+	0.398794i	0.278484	+	0.960441i	$0.410168\pi$
$788$	0.910222	+	2.80138i	0.0324253	+	0.0997949i
$789$	0.440187	−	1.35476i	0.0156711	−	0.0482306i
$790$	3.87646	+	2.81641i	0.137918	+	0.100203i
$791$	96.7225			3.43906
$792$	−4.03934	+	12.2681i	−0.143532	+	0.435926i
$793$	−3.64727			−0.129518
$794$	7.62276	+	5.53826i	0.270521	+	0.196545i
$795$	−0.586863	+	1.80618i	−0.0208139	+	0.0640586i
$796$	4.26028	+	13.1118i	0.151002	+	0.464735i
$797$	34.7913	−	25.2774i	1.23237	−	0.895370i	0.235306	−	0.971921i	$-0.424391\pi$
$797$	34.7913	−	25.2774i	1.23237	−	0.895370i	0.997066	+	0.0765509i	$0.0243908\pi$
$798$	1.32169	−	0.960267i	0.0467874	−	0.0339931i
$799$	−11.7367	−	36.1218i	−0.415214	−	1.27790i
$800$	−5.96205	+	18.3493i	−0.210790	+	0.648746i
$801$	28.5549	+	20.7463i	1.00894	+	0.733036i
$802$	12.8846			0.454969
$803$	−24.6413	−	18.0509i	−0.869573	−	0.637002i
$804$	−0.980412			−0.0345765
$805$	8.13385	+	5.90959i	0.286681	+	0.208286i
$806$	−0.792207	+	2.43816i	−0.0279043	+	0.0858806i
$807$	4.17895	+	12.8615i	0.147106	+	0.452746i
$808$	−17.6672	+	12.8360i	−0.621529	+	0.451567i
$809$	−41.9351	+	30.4676i	−1.47436	+	1.07119i	−0.495040	+	0.868870i	$0.664846\pi$
$809$	−41.9351	+	30.4676i	−1.47436	+	1.07119i	−0.979320	+	0.202315i	$0.935154\pi$
$810$	−0.446129	−	1.37304i	−0.0156754	−	0.0482438i
$811$	0.933716	−	2.87368i	0.0327872	−	0.100909i	−0.933324	−	0.359036i	$-0.883105\pi$
$811$	0.933716	−	2.87368i	0.0327872	−	0.100909i	0.966111	+	0.258128i	$0.0831055\pi$
$812$	−8.70302	−	6.32311i	−0.305416	−	0.221898i
$813$	−2.19649			−0.0770344
$814$	−1.57043	−	4.89851i	−0.0550435	−	0.171693i
$815$	−12.0361			−0.421607
$816$	−5.42489	−	3.94141i	−0.189909	−	0.137977i
$817$	−1.54367	+	4.75092i	−0.0540061	+	0.166214i
$818$	2.37417	+	7.30694i	0.0830109	+	0.255481i
$819$	−9.66676	+	7.02331i	−0.337784	+	0.245414i
$820$	5.74617	−	4.17484i	0.200665	−	0.145792i
$821$	3.27014	+	10.0644i	0.114129	+	0.351252i	0.991764	−	0.128077i	$-0.0408803\pi$
$821$	3.27014	+	10.0644i	0.114129	+	0.351252i	−0.877636	+	0.479328i	$0.840880\pi$
$822$	−0.799868	+	2.46174i	−0.0278986	+	0.0858630i
$823$	25.5226	+	18.5433i	0.889663	+	0.646378i	0.935790	−	0.352557i	$-0.114688\pi$
$823$	25.5226	+	18.5433i	0.889663	+	0.646378i	−0.0461270	+	0.998936i	$0.514688\pi$
$824$	−4.49685			−0.156655
$825$	−10.7234	−	0.0420164i	−0.373342	−	0.00146282i
$826$	−16.0798			−0.559486
$827$	−16.3160	−	11.8543i	−0.567364	−	0.412214i	0.266783	−	0.963757i	$-0.414039\pi$
$827$	−16.3160	−	11.8543i	−0.567364	−	0.412214i	−0.834147	+	0.551543i	$0.814039\pi$
$828$	−3.57950	+	11.0166i	−0.124396	+	0.382853i
$829$	−2.13419	−	6.56836i	−0.0741234	−	0.228128i	0.907130	−	0.420851i	$-0.138268\pi$
$829$	−2.13419	−	6.56836i	−0.0741234	−	0.228128i	−0.981253	+	0.192722i	$0.938268\pi$
$830$	−3.39844	+	2.46911i	−0.117961	+	0.0857040i
$831$	−11.2599	+	8.18083i	−0.390603	+	0.283790i
$832$	−1.28445	−	3.95314i	−0.0445304	−	0.137050i
$833$	−15.6507	+	48.1679i	−0.542264	+	1.66892i
$834$	1.24239	+	0.902647i	0.0430204	+	0.0312561i
$835$	−11.7040			−0.405034
$836$	5.35892	−	3.86150i	0.185342	−	0.133553i
$837$	−24.9440			−0.862189
$838$	−4.77674	−	3.47050i	−0.165010	−	0.119886i
$839$	1.24286	−	3.82512i	0.0429081	−	0.132058i	−0.927308	−	0.374300i	$-0.877883\pi$
$839$	1.24286	−	3.82512i	0.0429081	−	0.132058i	0.970216	+	0.242243i	$0.0778830\pi$
$840$	1.41445	+	4.35322i	0.0488030	+	0.150200i
$841$	22.2822	−	16.1890i	0.768351	−	0.558240i
$842$	−9.20747	+	6.68962i	−0.317310	+	0.230539i
$843$	−0.954135	−	2.93653i	−0.0328622	−	0.101139i
$844$	6.31495	−	19.4354i	0.217369	−	0.668994i
$845$	0.645264	+	0.468812i	0.0221978	+	0.0161276i
$846$	−12.7914			−0.439778
$847$	−53.6232	−	0.420217i	−1.84251	−	0.0144388i
$848$	−9.62785			−0.330622
$849$	7.26394	+	5.27756i	0.249298	+	0.181125i
$850$	1.69094	−	5.20419i	0.0579989	−	0.178502i
$851$	−2.98564	−	9.18887i	−0.102347	−	0.314990i
$852$	1.52237	−	1.10606i	0.0521554	−	0.0378931i
$853$	2.72795	−	1.98197i	0.0934031	−	0.0678613i	−0.540104	−	0.841599i	$-0.681615\pi$
$853$	2.72795	−	1.98197i	0.0934031	−	0.0678613i	0.633507	+	0.773737i	$0.281615\pi$
$854$	2.28068	+	7.01922i	0.0780434	+	0.240193i
$855$	−0.658263	+	2.02593i	−0.0225121	+	0.0692852i
$856$	−13.8414	−	10.0564i	−0.473089	−	0.343719i
$857$	15.2615			0.521324			0.260662	−	0.965430i	$-0.416059\pi$
$857$	15.2615			0.521324			0.260662	+	0.965430i	$0.416059\pi$
$858$	−0.827557	+	0.596315i	−0.0282523	+	0.0203579i
$859$	36.4915			1.24507			0.622537	−	0.782591i	$-0.286102\pi$
$859$	36.4915			1.24507			0.622537	+	0.782591i	$0.286102\pi$
$860$	−5.40664	−	3.92815i	−0.184365	−	0.133949i
$861$	−5.43829	+	16.7373i	−0.185336	+	0.570407i
$862$	0.685695	+	2.11035i	0.0233549	+	0.0718789i
$863$	−43.4772	+	31.5880i	−1.47998	+	1.07527i	−0.502418	+	0.864625i	$0.667556\pi$
$863$	−43.4772	+	31.5880i	−1.47998	+	1.07527i	−0.977563	+	0.210645i	$0.932444\pi$
$864$	−14.4461	+	10.4957i	−0.491468	+	0.357072i
$865$	−0.618027	−	1.90209i	−0.0210136	−	0.0646731i
$866$	−0.447248	+	1.37649i	−0.0151981	+	0.0467749i
$867$	−4.71993	−	3.42923i	−0.160297	−	0.116463i
$868$	−55.0292			−1.86781
$869$	−48.0008	−	0.188076i	−1.62832	−	0.00638004i
$870$	0.296160			0.0100408
$871$	0.585720	+	0.425550i	0.0198464	+	0.0144192i
$872$	6.43485	−	19.8044i	0.217911	−	0.670662i
$873$	−4.67226	−	14.3797i	−0.158132	−	0.486680i
$874$	−0.946176	+	0.687437i	−0.0320049	+	0.0232529i
$875$	29.4554	−	21.4006i	0.995775	−	0.723473i
$876$	−3.85398	−	11.8613i	−0.130214	−	0.400758i
$877$	12.1568	−	37.4146i	0.410504	−	1.26340i	−0.505706	−	0.862706i	$-0.668768\pi$
$877$	12.1568	−	37.4146i	0.410504	−	1.26340i	0.916211	−	0.400697i	$-0.131232\pi$
$878$	11.2726	+	8.19003i	0.380432	+	0.276400i
$879$	7.08308			0.238906
$880$	2.41943	+	7.54672i	0.0815589	+	0.254400i
$881$	−16.7039			−0.562769			−0.281385	−	0.959595i	$-0.590794\pi$
$881$	−16.7039			−0.562769			−0.281385	+	0.959595i	$0.590794\pi$
$882$	13.7995	+	10.0260i	0.464655	+	0.337591i
$883$	8.45843	−	26.0324i	0.284649	−	0.876059i	−0.701855	−	0.712320i	$-0.747645\pi$
$883$	8.45843	−	26.0324i	0.284649	−	0.876059i	0.986504	−	0.163739i	$-0.0523555\pi$
$884$	1.70617	+	5.25106i	0.0573848	+	0.176612i
$885$	−3.79904	+	2.76016i	−0.127703	+	0.0927819i
$886$	−13.3624	+	9.70834i	−0.448918	+	0.326158i
$887$	4.13851	+	12.7370i	0.138957	+	0.427667i	0.996185	−	0.0872715i	$-0.0278148\pi$
$887$	4.13851	+	12.7370i	0.138957	+	0.427667i	−0.857227	+	0.514938i	$0.827815\pi$
$888$	1.35926	−	4.18338i	0.0456139	−	0.140385i
$889$	69.3328	+	50.3732i	2.32535	+	1.68946i
$890$	−4.76754			−0.159808
$891$	11.6673	+	8.54680i	0.390868	+	0.286329i
$892$	−1.76489			−0.0590928
$893$	11.0834	+	8.05255i	0.370891	+	0.269468i
$894$	1.13341	−	3.48827i	0.0379068	−	0.116665i
$895$	−5.79002	−	17.8198i	−0.193539	−	0.595652i
$896$	−41.6789	+	30.2815i	−1.39239	+	1.01163i
$897$	−1.54994	+	1.12610i	−0.0517509	+	0.0375992i
$898$	−1.72379	−	5.30527i	−0.0575235	−	0.177039i
$899$	−2.30426	+	7.09178i	−0.0768513	+	0.236524i
$900$	15.8155	+	11.4906i	0.527183	+	0.383021i
$901$	9.70820			0.323427
$902$	2.09777	−	6.37123i	0.0698482	−	0.212139i
$903$	16.5588			0.551042
$904$	−25.5030	−	18.5290i	−0.848218	−	0.616267i
$905$	3.18841	−	9.81291i	0.105986	−	0.326192i
$906$	1.08257	+	3.33179i	0.0359658	+	0.110691i
$907$	−27.4211	+	19.9226i	−0.910502	+	0.661518i	−0.941142	−	0.338012i	$-0.890246\pi$
$907$	−27.4211	+	19.9226i	−0.910502	+	0.661518i	0.0306398	+	0.999530i	$0.490246\pi$
$908$	35.7642	−	25.9842i	1.18688	−	0.862316i
$909$	10.4103	+	32.0395i	0.345287	+	1.06268i
$910$	0.498743	−	1.53497i	0.0165332	−	0.0508839i
$911$	−0.00392471	−	0.00285147i	−0.000130031	−	9.44734e-5i	0.587720	−	0.809064i	$-0.300026\pi$
$911$	−0.00392471	−	0.00285147i	−0.000130031	−	9.44734e-5i	−0.587850	+	0.808970i	$0.700026\pi$
$912$	2.41872			0.0800917
$913$	13.1608	−	39.9711i	0.435557	−	1.32285i
$914$	−12.1038			−0.400358
$915$	1.74372	+	1.26689i	0.0576456	+	0.0418820i
$916$	−15.8950	+	48.9197i	−0.525185	+	1.61635i
$917$	23.4187	+	72.0753i	0.773353	+	2.38014i
$918$	4.09718	−	2.97678i	0.135227	−	0.0982483i
$919$	−17.7182	+	12.8730i	−0.584469	+	0.424642i	−0.840333	−	0.542071i	$-0.817640\pi$
$919$	−17.7182	+	12.8730i	−0.584469	+	0.424642i	0.255863	+	0.966713i	$0.417640\pi$
$920$	−1.01258	−	3.11639i	−0.0333836	−	0.102744i
$921$	3.74928	−	11.5391i	0.123543	−	0.380226i
$922$	−2.26855	−	1.64820i	−0.0747106	−	0.0542804i
$923$	−1.38958			−0.0457387
$924$	−17.6629	−	12.9389i	−0.581067	−	0.425658i
$925$	−16.3057			−0.536129
$926$	4.83683	+	3.51416i	0.158948	+	0.115483i
$927$	−2.14369	+	6.59759i	−0.0704079	+	0.216693i
$928$	1.64953	+	5.07673i	0.0541485	+	0.166652i
$929$	30.1442	−	21.9010i	0.988998	−	0.718549i	0.0292964	−	0.999571i	$-0.490673\pi$
$929$	30.1442	−	21.9010i	0.988998	−	0.718549i	0.959701	+	0.281022i	$0.0906733\pi$
$930$	1.22565	−	0.890484i	0.0401905	−	0.0292001i
$931$	−5.64527	−	17.3744i	−0.185016	−	0.569422i
$932$	−6.32968	+	19.4808i	−0.207336	+	0.638113i
$933$	6.26929	+	4.55491i	0.205247	+	0.149121i
$934$	14.3110			0.468269
$935$	−2.43962	−	7.60970i	−0.0797841	−	0.248864i
$936$	3.89430			0.127289
$937$	−2.55307	−	1.85492i	−0.0834053	−	0.0605975i	0.545301	−	0.838240i	$-0.316415\pi$
$937$	−2.55307	−	1.85492i	−0.0834053	−	0.0605975i	−0.628706	+	0.777643i	$0.716415\pi$
$938$	0.452720	−	1.39333i	0.0147818	−	0.0454938i
$939$	1.75126	+	5.38983i	0.0571503	+	0.175891i
$940$	−14.8276	+	10.7729i	−0.483623	+	0.351372i
$941$	15.2062	−	11.0480i	0.495709	−	0.360154i	−0.311666	−	0.950192i	$-0.600887\pi$
$941$	15.2062	−	11.0480i	0.495709	−	0.360154i	0.807376	+	0.590038i	$0.200887\pi$
$942$	−0.0364627	−	0.112221i	−0.00118802	−	0.00365635i
$943$	3.89317	−	11.9819i	0.126779	−	0.390186i
$944$	−19.2597	−	13.9930i	−0.626849	−	0.455432i
$945$	15.7038			0.510843
$946$	−6.31130	−	0.0247288i	−0.205198	−	0.000804004i
$947$	2.39026			0.0776730			0.0388365	−	0.999246i	$-0.487635\pi$
$947$	2.39026			0.0776730			0.0388365	+	0.999246i	$0.487635\pi$
$948$	−15.8559	−	11.5200i	−0.514974	−	0.374151i
$949$	−2.84599	+	8.75906i	−0.0923848	+	0.284331i
$950$	0.609931	+	1.87718i	0.0197888	+	0.0609036i
$951$	−5.58459	+	4.05744i	−0.181093	+	0.131571i
$952$	18.9298	−	13.7533i	0.613518	−	0.445747i
$953$	1.23908	+	3.81348i	0.0401376	+	0.123531i	0.969118	−	0.246599i	$-0.0793131\pi$
$953$	1.23908	+	3.81348i	0.0401376	+	0.123531i	−0.928980	+	0.370130i	$0.879313\pi$
$954$	1.01036	−	3.10957i	0.0327117	−	0.100676i
$955$	−4.49399	−	3.26507i	−0.145422	−	0.105655i
$956$	33.9361			1.09757
$957$	−2.40708	+	1.73448i	−0.0778098	+	0.0560677i
$958$	0.461726			0.0149177
$959$	33.1935	+	24.1165i	1.07188	+	0.778763i
$960$	−0.759049	+	2.33611i	−0.0244982	+	0.0753977i
$961$	2.20771	+	6.79462i	0.0712163	+	0.219181i
$962$	−1.25479	+	0.911655i	−0.0404559	+	0.0293929i
$963$	−21.3526	+	15.5136i	−0.688077	+	0.499917i
$964$	1.12071	+	3.44920i	0.0360958	+	0.111091i
$965$	−2.45466	+	7.55466i	−0.0790182	+	0.243193i
$966$	3.13638	+	2.27871i	0.100911	+	0.0733164i
$967$	−22.2188			−0.714510			−0.357255	−	0.934007i	$-0.616287\pi$
$967$	−22.2188			−0.714510			−0.357255	+	0.934007i	$0.616287\pi$
$968$	14.0584	+	10.3833i	0.451855	+	0.333733i
$969$	−2.43890			−0.0783488
$970$	1.65224	+	1.20042i	0.0530503	+	0.0385433i
$971$	−3.14583	+	9.68188i	−0.100955	+	0.310706i	−0.988760	−	0.149513i	$-0.952229\pi$
$971$	−3.14583	+	9.68188i	−0.100955	+	0.310706i	0.887805	+	0.460220i	$0.152229\pi$
$972$	8.66800	+	26.6774i	0.278026	+	0.855677i
$973$	19.6932	−	14.3080i	0.631337	−	0.458693i
$974$	4.11714	−	2.99128i	0.131922	−	0.0958467i
$975$	0.999133	+	3.07502i	0.0319979	+	0.0984793i
$976$	−3.37658	+	10.3920i	−0.108082	+	0.332641i
$977$	−8.34087	−	6.05999i	−0.266848	−	0.193876i	0.446313	−	0.894877i	$-0.352737\pi$
$977$	−8.34087	−	6.05999i	−0.266848	−	0.193876i	−0.713161	+	0.701001i	$0.752737\pi$
$978$	−4.64108			−0.148405
$979$	38.7488	−	27.9213i	1.23842	−	0.892369i
$980$	24.4400			0.780706
$981$	−25.9887	−	18.8819i	−0.829754	−	0.602852i
$982$	3.35200	−	10.3164i	0.106967	−	0.329210i
$983$	−12.3243	−	37.9304i	−0.393085	−	1.20979i	−0.930443	−	0.366437i	$-0.880578\pi$
$983$	−12.3243	−	37.9304i	−0.393085	−	1.20979i	0.537358	−	0.843354i	$-0.319422\pi$
$984$	4.64028	−	3.37136i	0.147927	−	0.107475i
$985$	−1.03991	+	0.755542i	−0.0331344	+	0.0240736i
$986$	−0.467836	−	1.43985i	−0.0148989	−	0.0458542i
$987$	14.0331	−	43.1895i	0.446679	−	1.37474i
$988$	−1.61120	−	1.17061i	−0.0512592	−	0.0372420i
$989$	−11.8541			−0.376939
$990$	−2.69132	−	0.0105451i	−0.0855356	−	0.000335144i
$991$	−13.5868			−0.431600			−0.215800	−	0.976438i	$-0.569236\pi$
$991$	−13.5868			−0.431600			−0.215800	+	0.976438i	$0.569236\pi$
$992$	22.0910	+	16.0501i	0.701391	+	0.509591i
$993$	0.340449	−	1.04780i	0.0108038	−	0.0332508i
$994$	0.868924	+	2.67427i	0.0275606	+	0.0848228i
$995$	−4.86730	+	3.53630i	−0.154304	+	0.112108i
$996$	13.9006	−	10.0994i	0.440458	−	0.320011i
$997$	−10.5870	−	32.5834i	−0.335294	−	1.03193i	−0.966577	−	0.256376i	$-0.917472\pi$
$997$	−10.5870	−	32.5834i	−0.335294	−	1.03193i	0.631284	−	0.775552i	$-0.282528\pi$
$998$	−3.70082	+	11.3900i	−0.117147	+	0.360543i
$999$	−12.2090	−	8.87032i	−0.386274	−	0.280645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.92.4	yes	28
11.3	even	5	inner	143.2.h.c.14.4	✓	28
11.5	even	5		1573.2.a.s.1.8		14
11.6	odd	10		1573.2.a.r.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.4	✓	28	11.3	even	5	inner
143.2.h.c.92.4	yes	28	1.1	even	1	trivial
1573.2.a.r.1.7		14	11.6	odd	10
1573.2.a.s.1.8		14	11.5	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)

\(f(q)\)	\(=\)	\(q+(-0.335814 - 0.243983i) q^{2} +(-0.228957 + 0.704657i) q^{3} +(-0.564791 - 1.73825i) q^{4} +(0.645264 - 0.468812i) q^{5} +(0.248811 - 0.180772i) q^{6} +(-1.50645 - 4.63638i) q^{7} +(-0.490978 + 1.51107i) q^{8} +(1.98293 + 1.44068i) q^{9} +O(q^{10})\)	\(q+(-0.335814 - 0.243983i) q^{2} +(-0.228957 + 0.704657i) q^{3} +(-0.564791 - 1.73825i) q^{4} +(0.645264 - 0.468812i) q^{5} +(0.248811 - 0.180772i) q^{6} +(-1.50645 - 4.63638i) q^{7} +(-0.490978 + 1.51107i) q^{8} +(1.98293 + 1.44068i) q^{9} -0.331071 q^{10} +(2.69082 - 1.93893i) q^{11} +1.35418 q^{12} +(-0.809017 - 0.587785i) q^{13} +(-0.625312 + 1.92451i) q^{14} +(0.182614 + 0.562028i) q^{15} +(-2.42373 + 1.76094i) q^{16} +(2.44396 - 1.77564i) q^{17} +(-0.314394 - 0.967604i) q^{18} +(-0.336721 + 1.03632i) q^{19} +(-1.17935 - 0.856848i) q^{20} +3.61197 q^{21} +(-1.37668 - 0.00539411i) q^{22} -2.58574 q^{23} +(-0.952376 - 0.691942i) q^{24} +(-1.34850 + 4.15027i) q^{25} +(0.128270 + 0.394773i) q^{26} +(-3.26744 + 2.37394i) q^{27} +(-7.20835 + 5.23717i) q^{28} +(0.373092 + 1.14826i) q^{29} +(0.0758011 - 0.233292i) q^{30} +(4.99657 + 3.63022i) q^{31} +4.42124 q^{32} +(0.750201 + 2.34004i) q^{33} -1.25394 q^{34} +(-3.14565 - 2.28545i) q^{35} +(1.38432 - 4.26051i) q^{36} +(1.15466 + 3.55367i) q^{37} +(0.365920 - 0.265857i) q^{38} +(0.599417 - 0.435502i) q^{39} +(0.391599 + 1.20522i) q^{40} +(-1.50563 + 4.63385i) q^{41} +(-1.21295 - 0.881261i) q^{42} +4.58442 q^{43} +(-4.89010 - 3.58222i) q^{44} +1.95493 q^{45} +(0.868329 + 0.630878i) q^{46} +(3.88517 - 11.9573i) q^{47} +(-0.685930 - 2.11108i) q^{48} +(-13.5635 + 9.85449i) q^{49} +(1.46544 - 1.06471i) q^{50} +(0.691655 + 2.12869i) q^{51} +(-0.564791 + 1.73825i) q^{52} +(2.59992 + 1.88896i) q^{53} +1.67646 q^{54} +(0.827297 - 2.51262i) q^{55} +7.74556 q^{56} +(-0.653155 - 0.474545i) q^{57} +(0.154867 - 0.476631i) q^{58} +(2.45554 + 7.55738i) q^{59} +(0.873804 - 0.634856i) q^{60} +(2.95070 - 2.14381i) q^{61} +(-0.792207 - 2.43816i) q^{62} +(3.69237 - 11.3640i) q^{63} +(3.36274 + 2.44317i) q^{64} -0.797591 q^{65} +(0.319002 - 0.968855i) q^{66} -0.723989 q^{67} +(-4.46682 - 3.24533i) q^{68} +(0.592024 - 1.82206i) q^{69} +(0.498743 + 1.53497i) q^{70} +(1.12420 - 0.816777i) q^{71} +(-3.15056 + 2.28901i) q^{72} +(-2.84599 - 8.75906i) q^{73} +(0.479285 - 1.47509i) q^{74} +(-2.61576 - 1.90046i) q^{75} +1.99156 q^{76} +(-13.0432 - 9.55478i) q^{77} -0.307548 q^{78} +(-11.7088 - 8.50696i) q^{79} +(-0.738395 + 2.27255i) q^{80} +(1.34753 + 4.14727i) q^{81} +(1.63619 - 1.18876i) q^{82} +(10.2650 - 7.45793i) q^{83} +(-2.04001 - 6.27850i) q^{84} +(0.744557 - 2.29151i) q^{85} +(-1.53951 - 1.11852i) q^{86} -0.894551 q^{87} +(1.60874 + 5.01801i) q^{88} +14.4003 q^{89} +(-0.656492 - 0.476969i) q^{90} +(-1.50645 + 4.63638i) q^{91} +(1.46040 + 4.49466i) q^{92} +(-3.70206 + 2.68971i) q^{93} +(-4.22208 + 3.06752i) q^{94} +(0.268565 + 0.826559i) q^{95} +(-1.01227 + 3.11546i) q^{96} +(-4.99059 - 3.62588i) q^{97} +6.95916 q^{98} +(8.12911 + 0.0318514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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