LMFDB - Embedded newform 273.2.cg.a.115.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.2
Character	$\chi$	$=$	273.115
Dual form			273.2.cg.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53002 + 0.409967i) q^{2} +1.00000i q^{3} +(0.440828 - 0.254512i) q^{4} +(-3.63307 - 0.973479i) q^{5} +(-0.409967 - 1.53002i) q^{6} +(-1.31124 + 2.29797i) q^{7} +(1.66997 - 1.66997i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.53002 + 0.409967i) q^{2} +1.00000i q^{3} +(0.440828 - 0.254512i) q^{4} +(-3.63307 - 0.973479i) q^{5} +(-0.409967 - 1.53002i) q^{6} +(-1.31124 + 2.29797i) q^{7} +(1.66997 - 1.66997i) q^{8} -1.00000 q^{9} +5.95776 q^{10} +(2.38426 - 2.38426i) q^{11} +(0.254512 + 0.440828i) q^{12} +(3.03769 - 1.94228i) q^{13} +(1.06413 - 4.05349i) q^{14} +(0.973479 - 3.63307i) q^{15} +(-2.37947 + 4.12137i) q^{16} +(-1.66896 - 2.89072i) q^{17} +(1.53002 - 0.409967i) q^{18} +(0.537206 - 0.537206i) q^{19} +(-1.84932 + 0.495525i) q^{20} +(-2.29797 - 1.31124i) q^{21} +(-2.67049 + 4.62542i) q^{22} +(3.08517 + 1.78122i) q^{23} +(1.66997 + 1.66997i) q^{24} +(7.92144 + 4.57345i) q^{25} +(-3.85145 + 4.21707i) q^{26} -1.00000i q^{27} +(0.00683031 + 1.34673i) q^{28} +(-1.42199 - 2.46295i) q^{29} +5.95776i q^{30} +(-2.38635 - 8.90596i) q^{31} +(0.728508 - 2.71883i) q^{32} +(2.38426 + 2.38426i) q^{33} +(3.73864 + 3.73864i) q^{34} +(7.00085 - 7.07223i) q^{35} +(-0.440828 + 0.254512i) q^{36} +(-2.93212 - 10.9428i) q^{37} +(-0.601698 + 1.04217i) q^{38} +(1.94228 + 3.03769i) q^{39} +(-7.69280 + 4.44144i) q^{40} +(-6.84386 - 1.83381i) q^{41} +(4.05349 + 1.06413i) q^{42} +(10.9295 + 6.31017i) q^{43} +(0.444225 - 1.65787i) q^{44} +(3.63307 + 0.973479i) q^{45} +(-5.45060 - 1.46048i) q^{46} +(0.356118 - 1.32905i) q^{47} +(-4.12137 - 2.37947i) q^{48} +(-3.56131 - 6.02636i) q^{49} +(-13.9949 - 3.74992i) q^{50} +(2.89072 - 1.66896i) q^{51} +(0.844767 - 1.62934i) q^{52} +(-3.59290 + 6.22308i) q^{53} +(0.409967 + 1.53002i) q^{54} +(-10.9832 + 6.34116i) q^{55} +(1.64781 + 6.02726i) q^{56} +(0.537206 + 0.537206i) q^{57} +(3.18539 + 3.18539i) q^{58} +(0.816620 - 3.04767i) q^{59} +(-0.495525 - 1.84932i) q^{60} -1.04213i q^{61} +(7.30230 + 12.6480i) q^{62} +(1.31124 - 2.29797i) q^{63} -5.05937i q^{64} +(-12.9269 + 4.09930i) q^{65} +(-4.62542 - 2.67049i) q^{66} +(-2.09191 - 2.09191i) q^{67} +(-1.47145 - 0.849541i) q^{68} +(-1.78122 + 3.08517i) q^{69} +(-7.81204 + 13.6907i) q^{70} +(-7.00412 + 1.87675i) q^{71} +(-1.66997 + 1.66997i) q^{72} +(2.08933 - 0.559835i) q^{73} +(8.97239 + 15.5406i) q^{74} +(-4.57345 + 7.92144i) q^{75} +(0.100090 - 0.373541i) q^{76} +(2.35262 + 8.60528i) q^{77} +(-4.21707 - 3.85145i) q^{78} +(-5.54357 - 9.60175i) q^{79} +(12.6569 - 12.6569i) q^{80} +1.00000 q^{81} +11.2230 q^{82} +(1.51210 - 1.51210i) q^{83} +(-1.34673 + 0.00683031i) q^{84} +(3.24940 + 12.1269i) q^{85} +(-19.3093 - 5.17392i) q^{86} +(2.46295 - 1.42199i) q^{87} -7.96327i q^{88} +(-3.05671 + 0.819042i) q^{89} -5.95776 q^{90} +(0.480151 + 9.52730i) q^{91} +1.81337 q^{92} +(8.90596 - 2.38635i) q^{93} +2.17947i q^{94} +(-2.47467 + 1.42875i) q^{95} +(2.71883 + 0.728508i) q^{96} +(3.23001 + 12.0545i) q^{97} +(7.91947 + 7.76042i) q^{98} +(-2.38426 + 2.38426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.53002	+	0.409967i	−1.08189	+	0.289890i	−0.755368	−	0.655301i	$-0.772542\pi$
$2$	−1.53002	+	0.409967i	−1.08189	+	0.289890i	−0.326517	+	0.945191i	$0.605875\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.440828	−	0.254512i	0.220414	−	0.127256i
$5$	−3.63307	−	0.973479i	−1.62476	−	0.435353i	−0.672365	−	0.740219i	$-0.734722\pi$
$5$	−3.63307	−	0.973479i	−1.62476	−	0.435353i	−0.952395	+	0.304866i	$0.901388\pi$
$6$	−0.409967	−	1.53002i	−0.167368	−	0.624627i
$7$	−1.31124	+	2.29797i	−0.495601	+	0.868550i
$7$	−1.31124	+	2.29797i	−0.495601	+	0.868550i
$8$	1.66997	−	1.66997i	0.590423	−	0.590423i
$9$	−1.00000			−0.333333
$10$	5.95776			1.88401
$11$	2.38426	−	2.38426i	0.718881	−	0.718881i	−0.249495	−	0.968376i	$-0.580265\pi$
$11$	2.38426	−	2.38426i	0.718881	−	0.718881i	0.968376	+	0.249495i	$0.0802646\pi$
$12$	0.254512	+	0.440828i	0.0734713	+	0.127256i
$13$	3.03769	−	1.94228i	0.842504	−	0.538690i
$13$	3.03769	−	1.94228i	0.842504	−	0.538690i
$14$	1.06413	−	4.05349i	0.284400	−	1.08334i
$15$	0.973479	−	3.63307i	0.251351	−	0.938056i
$16$	−2.37947	+	4.12137i	−0.594868	+	1.03034i
$17$	−1.66896	−	2.89072i	−0.404782	−	0.701103i	0.589514	−	0.807758i	$-0.299319\pi$
$17$	−1.66896	−	2.89072i	−0.404782	−	0.701103i	−0.994296	+	0.106655i	$0.965986\pi$
$18$	1.53002	−	0.409967i	0.360628	−	0.0966301i
$19$	0.537206	−	0.537206i	0.123244	−	0.123244i	−0.642795	−	0.766038i	$-0.722225\pi$
$19$	0.537206	−	0.537206i	0.123244	−	0.123244i	0.766038	+	0.642795i	$0.222225\pi$
$20$	−1.84932	+	0.495525i	−0.413521	+	0.110803i
$21$	−2.29797	−	1.31124i	−0.501458	−	0.286136i
$22$	−2.67049	+	4.62542i	−0.569350	+	0.986143i
$23$	3.08517	+	1.78122i	0.643302	+	0.371411i	0.785886	−	0.618372i	$-0.212207\pi$
$23$	3.08517	+	1.78122i	0.643302	+	0.371411i	−0.142583	+	0.989783i	$0.545541\pi$
$24$	1.66997	+	1.66997i	0.340881	+	0.340881i
$25$	7.92144	+	4.57345i	1.58429	+	0.914690i
$26$	−3.85145	+	4.21707i	−0.755331	+	0.827035i
$27$		−	1.00000i		−	0.192450i
$28$	0.00683031	+	1.34673i	0.00129081	+	0.254509i
$29$	−1.42199	−	2.46295i	−0.264056	−	0.457358i	0.703260	−	0.710933i	$-0.251727\pi$
$29$	−1.42199	−	2.46295i	−0.264056	−	0.457358i	−0.967316	+	0.253574i	$0.918394\pi$
$30$			5.95776i			1.08773i
$31$	−2.38635	−	8.90596i	−0.428600	−	1.59956i	−0.755933	−	0.654649i	$-0.772816\pi$
$31$	−2.38635	−	8.90596i	−0.428600	−	1.59956i	0.327332	−	0.944909i	$-0.393850\pi$
$32$	0.728508	−	2.71883i	0.128783	−	0.480625i
$33$	2.38426	+	2.38426i	0.415046	+	0.415046i
$34$	3.73864	+	3.73864i	0.641171	+	0.641171i
$35$	7.00085	−	7.07223i	1.18336	−	1.19542i
$36$	−0.440828	+	0.254512i	−0.0734713	+	0.0424187i
$37$	−2.93212	−	10.9428i	−0.482038	−	1.79899i	−0.593045	−	0.805169i	$-0.702074\pi$
$37$	−2.93212	−	10.9428i	−0.482038	−	1.79899i	0.111007	−	0.993820i	$-0.464592\pi$
$38$	−0.601698	+	1.04217i	−0.0976083	+	0.169063i
$39$	1.94228	+	3.03769i	0.311013	+	0.486420i
$40$	−7.69280	+	4.44144i	−1.21634	+	0.702253i
$41$	−6.84386	−	1.83381i	−1.06883	−	0.286393i	−0.318819	−	0.947816i	$-0.603286\pi$
$41$	−6.84386	−	1.83381i	−1.06883	−	0.286393i	−0.750013	+	0.661423i	$0.769953\pi$
$42$	4.05349	+	1.06413i	0.625468	+	0.164198i
$43$	10.9295	+	6.31017i	1.66674	+	0.962291i	0.969379	+	0.245568i	$0.0789746\pi$
$43$	10.9295	+	6.31017i	1.66674	+	0.962291i	0.697358	+	0.716723i	$0.254359\pi$
$44$	0.444225	−	1.65787i	0.0669695	−	0.249933i
$45$	3.63307	+	0.973479i	0.541587	+	0.145118i
$46$	−5.45060	−	1.46048i	−0.803648	−	0.215337i
$47$	0.356118	−	1.32905i	0.0519452	−	0.193862i	−0.935077	−	0.354444i	$-0.884670\pi$
$47$	0.356118	−	1.32905i	0.0519452	−	0.193862i	0.987023	+	0.160582i	$0.0513370\pi$
$48$	−4.12137	−	2.37947i	−0.594868	−	0.343447i
$49$	−3.56131	−	6.02636i	−0.508759	−	0.860909i
$50$	−13.9949	−	3.74992i	−1.97918	−	0.530319i
$51$	2.89072	−	1.66896i	0.404782	−	0.233701i
$52$	0.844767	−	1.62934i	0.117148	−	0.225949i
$53$	−3.59290	+	6.22308i	−0.493523	+	0.854806i	−0.999972	−	0.00746338i	$-0.997624\pi$
$53$	−3.59290	+	6.22308i	−0.493523	+	0.854806i	0.506450	+	0.862270i	$0.330958\pi$
$54$	0.409967	+	1.53002i	0.0557894	+	0.208209i
$55$	−10.9832	+	6.34116i	−1.48098	+	0.855042i
$56$	1.64781	+	6.02726i	0.220197	+	0.805426i
$57$	0.537206	+	0.537206i	0.0711547	+	0.0711547i
$58$	3.18539	+	3.18539i	0.418262	+	0.418262i
$59$	0.816620	−	3.04767i	0.106315	−	0.396772i	−0.892176	−	0.451688i	$-0.850822\pi$
$59$	0.816620	−	3.04767i	0.106315	−	0.396772i	0.998491	+	0.0549152i	$0.0174888\pi$
$60$	−0.495525	−	1.84932i	−0.0639720	−	0.238747i
$61$		−	1.04213i		−	0.133432i	−0.997772	−	0.0667158i	$-0.978748\pi$
$61$		−	1.04213i		−	0.133432i	0.997772	−	0.0667158i	$-0.0212521\pi$
$62$	7.30230	+	12.6480i	0.927393	+	1.60629i
$63$	1.31124	−	2.29797i	0.165200	−	0.289517i
$64$		−	5.05937i		−	0.632421i
$65$	−12.9269	+	4.09930i	−1.60339	+	0.508456i
$66$	−4.62542	−	2.67049i	−0.569350	−	0.328714i
$67$	−2.09191	−	2.09191i	−0.255567	−	0.255567i	0.567681	−	0.823248i	$-0.307841\pi$
$67$	−2.09191	−	2.09191i	−0.255567	−	0.255567i	−0.823248	+	0.567681i	$0.807841\pi$
$68$	−1.47145	−	0.849541i	−0.178439	−	0.103022i
$69$	−1.78122	+	3.08517i	−0.214434	+	0.371411i
$70$	−7.81204	+	13.6907i	−0.933717	+	1.63636i
$71$	−7.00412	+	1.87675i	−0.831236	+	0.222729i	−0.649253	−	0.760573i	$-0.724918\pi$
$71$	−7.00412	+	1.87675i	−0.831236	+	0.222729i	−0.181983	+	0.983302i	$0.558252\pi$
$72$	−1.66997	+	1.66997i	−0.196808	+	0.196808i
$73$	2.08933	−	0.559835i	0.244538	−	0.0655238i	−0.134468	−	0.990918i	$-0.542933\pi$
$73$	2.08933	−	0.559835i	0.244538	−	0.0655238i	0.379006	+	0.925394i	$0.376266\pi$
$74$	8.97239	+	15.5406i	1.04302	+	1.80656i
$75$	−4.57345	+	7.92144i	−0.528096	+	0.914690i
$76$	0.100090	−	0.373541i	0.0114811	−	0.0428481i
$77$	2.35262	+	8.60528i	0.268106	+	0.980663i
$78$	−4.21707	−	3.85145i	−0.477489	−	0.436091i
$79$	−5.54357	−	9.60175i	−0.623700	−	1.08028i	−0.988791	−	0.149309i	$-0.952295\pi$
$79$	−5.54357	−	9.60175i	−0.623700	−	1.08028i	0.365090	−	0.930972i	$-0.381038\pi$
$80$	12.6569	−	12.6569i	1.41508	−	1.41508i
$81$	1.00000			0.111111
$82$	11.2230			1.23938
$83$	1.51210	−	1.51210i	0.165975	−	0.165975i	−0.619233	−	0.785208i	$-0.712556\pi$
$83$	1.51210	−	1.51210i	0.165975	−	0.165975i	0.785208	+	0.619233i	$0.212556\pi$
$84$	−1.34673	+	0.00683031i	−0.146941	+	0.000745248i
$85$	3.24940	+	12.1269i	0.352447	+	1.31535i
$86$	−19.3093	−	5.17392i	−2.08218	−	0.557918i
$87$	2.46295	−	1.42199i	0.264056	−	0.152453i
$88$		−	7.96327i		−	0.848887i
$89$	−3.05671	+	0.819042i	−0.324010	+	0.0868183i	−0.417158	−	0.908834i	$-0.636974\pi$
$89$	−3.05671	+	0.819042i	−0.324010	+	0.0868183i	0.0931477	+	0.995652i	$0.470307\pi$
$90$	−5.95776			−0.628003
$91$	0.480151	+	9.52730i	0.0503335	+	0.998732i
$92$	1.81337			0.189057
$93$	8.90596	−	2.38635i	0.923505	−	0.247453i
$94$			2.17947i			0.224795i
$95$	−2.47467	+	1.42875i	−0.253896	+	0.146587i
$96$	2.71883	+	0.728508i	0.277489	+	0.0743530i
$97$	3.23001	+	12.0545i	0.327957	+	1.22395i	0.911305	+	0.411731i	$0.135076\pi$
$97$	3.23001	+	12.0545i	0.327957	+	1.22395i	−0.583348	+	0.812222i	$0.698258\pi$
$98$	7.91947	+	7.76042i	0.799988	+	0.783921i
$99$	−2.38426	+	2.38426i	−0.239627	+	0.239627i
$100$	4.65599			0.465599
$101$	−4.39234			−0.437054			−0.218527	−	0.975831i	$-0.570125\pi$
$101$	−4.39234			−0.437054			−0.218527	+	0.975831i	$0.570125\pi$
$102$	−3.73864	+	3.73864i	−0.370180	+	0.370180i
$103$	−6.67838	−	11.5673i	−0.658040	−	1.13976i	−0.981122	−	0.193389i	$-0.938052\pi$
$103$	−6.67838	−	11.5673i	−0.658040	−	1.13976i	0.323082	−	0.946371i	$-0.395281\pi$
$104$	1.82931	−	8.31638i	0.179378	−	0.815488i
$105$	7.07223	+	7.00085i	0.690179	+	0.683213i
$106$	2.94594	−	10.9944i	0.286135	−	1.06787i
$107$	−0.0887791	+	0.153770i	−0.00858260	+	0.0148655i	−0.870285	−	0.492549i	$-0.836065\pi$
$107$	−0.0887791	+	0.153770i	−0.00858260	+	0.0148655i	0.861702	+	0.507414i	$0.169399\pi$
$108$	−0.254512	−	0.440828i	−0.0244904	−	0.0424187i
$109$	5.01713	−	1.34434i	0.480554	−	0.128764i	−0.0104068	−	0.999946i	$-0.503313\pi$
$109$	5.01713	−	1.34434i	0.480554	−	0.128764i	0.490960	+	0.871182i	$0.336646\pi$
$110$	14.2048	−	14.2048i	1.35438	−	1.35438i
$111$	10.9428	−	2.93212i	1.03865	−	0.278305i
$112$	−6.35071	−	10.8720i	−0.600086	−	1.02731i
$113$	10.0079	−	17.3342i	0.941462	−	1.63066i	0.178778	−	0.983889i	$-0.442785\pi$
$113$	10.0079	−	17.3342i	0.941462	−	1.63066i	0.762684	−	0.646771i	$-0.223881\pi$
$114$	−1.04217	−	0.601698i	−0.0976083	−	0.0563542i
$115$	−9.47467	−	9.47467i	−0.883517	−	0.883517i
$116$	−1.25370	−	0.723825i	−0.116403	−	0.0672055i
$117$	−3.03769	+	1.94228i	−0.280835	+	0.179563i
$118$			4.99777i			0.460082i
$119$	8.83119	−	0.0447897i	0.809554	−	0.00410586i
$120$	−4.44144	−	7.69280i	−0.405446	−	0.702253i
$121$		−	0.369378i		−	0.0335798i
$122$	0.427240	+	1.59448i	0.0386805	+	0.144358i
$123$	1.83381	−	6.84386i	0.165349	−	0.617090i
$124$	−3.31864	−	3.31864i	−0.298023	−	0.298023i
$125$	−11.0291	−	11.0291i	−0.986469	−	0.986469i
$126$	−1.06413	+	4.05349i	−0.0947999	+	0.361114i
$127$	6.74547	−	3.89450i	0.598564	−	0.345581i	−0.169913	−	0.985459i	$-0.554349\pi$
$127$	6.74547	−	3.89450i	0.598564	−	0.345581i	0.768476	+	0.639878i	$0.221015\pi$
$128$	3.53119	+	13.1786i	0.312116	+	1.16483i
$129$	−6.31017	+	10.9295i	−0.555579	+	0.962291i
$130$	18.0978	−	11.5716i	1.58729	−	1.01490i
$131$	8.40782	−	4.85426i	0.734595	−	0.424118i	−0.0855060	−	0.996338i	$-0.527251\pi$
$131$	8.40782	−	4.85426i	0.734595	−	0.424118i	0.820101	+	0.572219i	$0.193917\pi$
$132$	1.65787	+	0.444225i	0.144299	+	0.0386648i
$133$	0.530077	+	1.93889i	0.0459635	+	0.168123i
$134$	4.05826	+	2.34304i	0.350580	+	0.202408i
$135$	−0.973479	+	3.63307i	−0.0837838	+	0.312685i
$136$	−7.61452	−	2.04031i	−0.652940	−	0.174955i
$137$	8.77818	+	2.35211i	0.749970	+	0.200954i	0.613505	−	0.789691i	$-0.289759\pi$
$137$	8.77818	+	2.35211i	0.749970	+	0.200954i	0.136465	+	0.990645i	$0.456426\pi$
$138$	1.46048	−	5.45060i	0.124325	−	0.463986i
$139$	−8.85473	−	5.11228i	−0.751048	−	0.433618i	0.0750244	−	0.997182i	$-0.476097\pi$
$139$	−8.85473	−	5.11228i	−0.751048	−	0.433618i	−0.826073	+	0.563564i	$0.809430\pi$
$140$	1.28620	−	4.89944i	0.108704	−	0.414078i
$141$	1.32905	+	0.356118i	0.111926	+	0.0299906i
$142$	9.94701	−	5.74291i	0.834735	−	0.481934i
$143$	2.61175	−	11.8735i	0.218406	−	0.992914i
$144$	2.37947	−	4.12137i	0.198289	−	0.343447i
$145$	2.76855	+	10.3324i	0.229915	+	0.858056i
$146$	−2.96720	+	1.71311i	−0.245567	+	0.141778i
$147$	6.02636	−	3.56131i	0.497046	−	0.293732i
$148$	−4.07764	−	4.07764i	−0.335180	−	0.335180i
$149$	10.6236	+	10.6236i	0.870318	+	0.870318i	0.992507	−	0.122189i	$-0.0389913\pi$
$149$	10.6236	+	10.6236i	0.870318	+	0.870318i	−0.122189	+	0.992507i	$0.538991\pi$
$150$	3.74992	−	13.9949i	0.306180	−	1.14268i
$151$	0.0718719	+	0.268230i	0.00584885	+	0.0218282i	0.968789	−	0.247888i	$-0.0797366\pi$
$151$	0.0718719	+	0.268230i	0.00584885	+	0.0218282i	−0.962940	+	0.269717i	$0.913070\pi$
$152$		−	1.79423i		−	0.145532i
$153$	1.66896	+	2.89072i	0.134927	+	0.233701i
$154$	−7.12742	−	12.2017i	−0.574344	−	0.983243i
$155$			34.6791i			2.78549i
$156$	1.62934	+	0.844767i	0.130452	+	0.0676355i
$157$	0.272321	+	0.157225i	0.0217336	+	0.0125479i	0.510827	−	0.859683i	$-0.329339\pi$
$157$	0.272321	+	0.157225i	0.0217336	+	0.0125479i	−0.489094	+	0.872231i	$0.662672\pi$
$158$	12.4182	+	12.4182i	0.987935	+	0.987935i
$159$	−6.22308	−	3.59290i	−0.493523	−	0.284935i
$160$	−5.29344	+	9.16852i	−0.418484	+	0.724835i
$161$	−8.13859	+	4.75401i	−0.641410	+	0.374669i
$162$	−1.53002	+	0.409967i	−0.120209	+	0.0322100i
$163$	0.667599	−	0.667599i	0.0522904	−	0.0522904i	−0.680478	−	0.732768i	$-0.738228\pi$
$163$	0.667599	−	0.667599i	0.0522904	−	0.0522904i	0.732768	+	0.680478i	$0.238228\pi$
$164$	−3.48369	+	0.933452i	−0.272031	+	0.0728904i
$165$	−6.34116	−	10.9832i	−0.493659	−	0.855042i
$166$	−1.69363	+	2.93346i	−0.131451	+	0.227680i
$167$	−0.626601	+	2.33851i	−0.0484878	+	0.180959i	−0.985923	−	0.167202i	$-0.946527\pi$
$167$	−0.626601	+	2.33851i	−0.0484878	+	0.180959i	0.937435	+	0.348161i	$0.113194\pi$
$168$	−6.02726	+	1.64781i	−0.465013	+	0.127131i
$169$	5.45513	−	11.8001i	0.419626	−	0.907697i
$170$	−9.94326	−	17.2222i	−0.762614	−	1.32089i
$171$	−0.537206	+	0.537206i	−0.0410812	+	0.0410812i
$172$	6.42406			0.489830
$173$	17.2215			1.30933			0.654664	−	0.755920i	$-0.272810\pi$
$173$	17.2215			1.30933			0.654664	+	0.755920i	$0.272810\pi$
$174$	−3.18539	+	3.18539i	−0.241484	+	0.241484i
$175$	−20.8965	+	12.2063i	−1.57963	+	0.922713i
$176$	4.15313	+	15.4997i	0.313054	+	1.16833i
$177$	3.04767	+	0.816620i	0.229077	+	0.0613809i
$178$	4.34103	−	2.50630i	0.325374	−	0.187855i
$179$		−	3.44245i		−	0.257301i	−0.991690	−	0.128651i	$-0.958935\pi$
$179$		−	3.44245i		−	0.257301i	0.991690	−	0.128651i	$-0.0410646\pi$
$180$	1.84932	−	0.495525i	0.137840	−	0.0369342i
$181$	−25.9767			−1.93084			−0.965418	−	0.260708i	$-0.916044\pi$
$181$	−25.9767			−1.93084			−0.965418	+	0.260708i	$0.916044\pi$
$182$	−4.64052	−	14.3801i	−0.343978	−	1.06592i
$183$	1.04213			0.0770368
$184$	8.12672	−	2.17755i	0.599110	−	0.160531i
$185$			42.6105i			3.13278i
$186$	−12.6480	+	7.30230i	−0.927393	+	0.535431i
$187$	−10.8715	−	2.91300i	−0.795000	−	0.213020i
$188$	−0.181273	−	0.676520i	−0.0132207	−	0.0493403i
$189$	2.29797	+	1.31124i	0.167153	+	0.0953785i
$190$	3.20055	−	3.20055i	0.232192	−	0.232192i
$191$	2.98307			0.215848			0.107924	−	0.994159i	$-0.465580\pi$
$191$	2.98307			0.215848			0.107924	+	0.994159i	$0.465580\pi$
$192$	5.05937			0.365129
$193$	1.84850	−	1.84850i	0.133058	−	0.133058i	−0.637441	−	0.770499i	$-0.720007\pi$
$193$	1.84850	−	1.84850i	0.133058	−	0.133058i	0.770499	+	0.637441i	$0.220007\pi$
$194$	−9.88393	−	17.1195i	−0.709624	−	1.22911i
$195$	−4.09930	−	12.9269i	−0.293557	−	0.925716i
$196$	−3.10371	−	1.75019i	−0.221693	−	0.125014i
$197$	0.213689	−	0.797498i	0.0152247	−	0.0568194i	−0.957896	−	0.287117i	$-0.907303\pi$
$197$	0.213689	−	0.797498i	0.0152247	−	0.0568194i	0.973120	+	0.230297i	$0.0739699\pi$
$198$	2.67049	−	4.62542i	0.189783	−	0.328714i
$199$	−4.10087	−	7.10291i	−0.290703	−	0.503512i	0.683273	−	0.730163i	$-0.260556\pi$
$199$	−4.10087	−	7.10291i	−0.290703	−	0.503512i	−0.973976	+	0.226651i	$0.927222\pi$
$200$	20.8661	−	5.59104i	1.47545	−	0.395347i
$201$	2.09191	−	2.09191i	0.147552	−	0.147552i
$202$	6.72036	−	1.80071i	0.472843	−	0.126698i
$203$	7.52434	−	0.0381616i	0.528105	−	0.00267842i
$204$	0.849541	−	1.47145i	0.0594798	−	0.103022i
$205$	23.0791	+	13.3247i	1.61191	+	0.930638i
$206$	14.9602	+	14.9602i	1.04233	+	1.04233i
$207$	−3.08517	−	1.78122i	−0.214434	−	0.123804i
$208$	0.776728	+	17.1410i	0.0538564	+	1.18852i
$209$		−	2.56168i		−	0.177195i
$210$	−13.6907	−	7.81204i	−0.944751	−	0.539082i
$211$	5.37441	+	9.30875i	0.369989	+	0.640841i	0.989563	−	0.144098i	$-0.0460280\pi$
$211$	5.37441	+	9.30875i	0.369989	+	0.640841i	−0.619574	+	0.784938i	$0.712695\pi$
$212$			3.65775i			0.251215i
$213$	−1.87675	−	7.00412i	−0.128593	−	0.479914i
$214$	0.0727929	−	0.271667i	0.00497602	−	0.0185708i
$215$	−33.5650	−	33.5650i	−2.28911	−	2.28911i
$216$	−1.66997	−	1.66997i	−0.113627	−	0.113627i
$217$	23.5947	+	6.19409i	1.60171	+	0.420482i
$218$	−7.12516	+	4.11371i	−0.482576	+	0.278616i
$219$	0.559835	+	2.08933i	0.0378302	+	0.141184i
$220$	−3.22781	+	5.59072i	−0.217619	+	0.376927i
$221$	−10.6844	−	5.53954i	−0.718708	−	0.372630i
$222$	−15.5406	+	8.97239i	−1.04302	+	0.602187i
$223$	−5.74055	−	1.53818i	−0.384416	−	0.103004i	0.0614354	−	0.998111i	$-0.480432\pi$
$223$	−5.74055	−	1.53818i	−0.384416	−	0.103004i	−0.445851	+	0.895107i	$0.647099\pi$
$224$	5.29253	+	5.23912i	0.353622	+	0.350053i
$225$	−7.92144	−	4.57345i	−0.528096	−	0.304897i
$226$	−8.20580	+	30.6245i	−0.545842	+	2.03711i
$227$	−19.6924	−	5.27657i	−1.30703	−	0.350218i	−0.462928	−	0.886396i	$-0.653201\pi$
$227$	−19.6924	−	5.27657i	−1.30703	−	0.350218i	−0.844105	+	0.536178i	$0.819868\pi$
$228$	0.373541	+	0.100090i	0.0247384	+	0.00662863i
$229$	−2.22135	+	8.29019i	−0.146791	+	0.547831i	0.852878	+	0.522110i	$0.174855\pi$
$229$	−2.22135	+	8.29019i	−0.146791	+	0.547831i	−0.999669	+	0.0257212i	$0.991812\pi$
$230$	18.3807	+	10.6121i	1.21199	+	0.699741i
$231$	−8.60528	+	2.35262i	−0.566186	+	0.154791i
$232$	−6.48772	−	1.73838i	−0.425939	−	0.114130i
$233$	−4.35471	+	2.51419i	−0.285286	+	0.164710i	−0.635814	−	0.771842i	$-0.719336\pi$
$233$	−4.35471	+	2.51419i	−0.285286	+	0.164710i	0.350528	+	0.936552i	$0.386002\pi$
$234$	3.85145	−	4.21707i	0.251777	−	0.275678i
$235$	−2.58761	+	4.48187i	−0.168797	+	0.292365i
$236$	−0.415679	−	1.55134i	−0.0270584	−	0.100983i
$237$	9.60175	−	5.54357i	0.623700	−	0.360094i
$238$	−13.4935	+	3.68902i	−0.874654	+	0.239124i
$239$	−11.6568	−	11.6568i	−0.754018	−	0.754018i	0.221208	−	0.975227i	$-0.429000\pi$
$239$	−11.6568	−	11.6568i	−0.754018	−	0.754018i	−0.975227	+	0.221208i	$0.929000\pi$
$240$	12.6569	+	12.6569i	0.816997	+	0.816997i
$241$	−1.46113	+	5.45299i	−0.0941193	+	0.351258i	−0.996884	−	0.0788757i	$-0.974867\pi$
$241$	−1.46113	+	5.45299i	−0.0941193	+	0.351258i	0.902765	+	0.430134i	$0.141534\pi$
$242$	0.151433	+	0.565154i	0.00973446	+	0.0363295i
$243$			1.00000i			0.0641500i
$244$	−0.265236	−	0.459402i	−0.0169800	−	0.0294102i
$245$	7.07196	+	25.3611i	0.451811	+	1.62026i
$246$			11.2230i			0.715554i
$247$	0.588464	−	2.67527i	0.0374431	−	0.170223i
$248$	−18.8578	−	10.8875i	−1.19747	−	0.691360i
$249$	1.51210	+	1.51210i	0.0958257	+	0.0958257i
$250$	21.3962	+	12.3531i	1.35321	+	0.781279i
$251$	5.54226	−	9.59948i	0.349825	−	0.605914i	−0.636394	−	0.771365i	$-0.719575\pi$
$251$	5.54226	−	9.59948i	0.349825	−	0.605914i	0.986218	+	0.165451i	$0.0529079\pi$
$252$	−0.00683031	−	1.34673i	−0.000430269	−	0.0848363i
$253$	11.6027	−	3.10894i	0.729458	−	0.195458i
$254$	−8.72407	+	8.72407i	−0.547397	+	0.547397i
$255$	−12.1269	+	3.24940i	−0.759417	+	0.203485i
$256$	−5.74619	−	9.95269i	−0.359137	−	0.622043i
$257$	−1.20160	+	2.08124i	−0.0749540	+	0.129824i	−0.901066	−	0.433681i	$-0.857214\pi$
$257$	−1.20160	+	2.08124i	−0.0749540	+	0.129824i	0.826112	+	0.563506i	$0.190548\pi$
$258$	5.17392	−	19.3093i	0.322114	−	1.20215i
$259$	28.9910	+	7.61073i	1.80141	+	0.472908i
$260$	−4.65523	+	5.09715i	−0.288705	+	0.316112i
$261$	1.42199	+	2.46295i	0.0880187	+	0.152453i
$262$	−10.8740	+	10.8740i	−0.671799	+	0.671799i
$263$	−26.1246			−1.61091			−0.805456	−	0.592655i	$-0.798080\pi$
$263$	−26.1246			−1.61091			−0.805456	+	0.592655i	$0.798080\pi$
$264$	7.96327			0.490105
$265$	19.1113	−	19.1113i	1.17400	−	1.17400i
$266$	−1.60591	−	2.74922i	−0.0984645	−	0.168565i
$267$	−0.819042	−	3.05671i	−0.0501246	−	0.187067i
$268$	−1.45459	−	0.389755i	−0.0888530	−	0.0238081i
$269$	−22.8806	+	13.2101i	−1.39505	+	0.805435i	−0.993869	−	0.110562i	$-0.964735\pi$
$269$	−22.8806	+	13.2101i	−1.39505	+	0.805435i	−0.401185	+	0.915997i	$0.631402\pi$
$270$		−	5.95776i		−	0.362578i
$271$	−7.31591	+	1.96029i	−0.444410	+	0.119079i	−0.474082	−	0.880480i	$-0.657220\pi$
$271$	−7.31591	+	1.96029i	−0.444410	+	0.119079i	0.0296728	+	0.999560i	$0.490553\pi$
$272$	15.8850			0.963168
$273$	−9.52730	+	0.480151i	−0.576618	+	0.0290600i
$274$	−14.3950			−0.869637
$275$	29.7911	−	7.98249i	1.79647	−	0.481362i
$276$			1.81337i			0.109152i
$277$	−19.5228	+	11.2715i	−1.17301	+	0.677238i	−0.954387	−	0.298571i	$-0.903490\pi$
$277$	−19.5228	+	11.2715i	−1.17301	+	0.677238i	−0.218624	+	0.975809i	$0.570157\pi$
$278$	15.6437	+	4.19173i	0.938250	+	0.251403i
$279$	2.38635	+	8.90596i	0.142867	+	0.533186i
$280$	−0.119194	−	23.5016i	−0.00712322	−	1.40449i
$281$	−7.73479	+	7.73479i	−0.461419	+	0.461419i	−0.899120	−	0.437701i	$-0.855793\pi$
$281$	−7.73479	+	7.73479i	−0.461419	+	0.461419i	0.437701	+	0.899120i	$0.355793\pi$
$282$	−2.17947			−0.129785
$283$	17.7305			1.05397			0.526984	−	0.849875i	$-0.323323\pi$
$283$	17.7305			1.05397			0.526984	+	0.849875i	$0.323323\pi$
$284$	−2.60996	+	2.60996i	−0.154872	+	0.154872i
$285$	−1.42875	−	2.47467i	−0.0846319	−	0.146587i
$286$	0.871725	+	19.2374i	0.0515462	+	1.13753i
$287$	13.1880	−	13.3224i	0.778461	−	0.786397i
$288$	−0.728508	+	2.71883i	−0.0429277	+	0.160208i
$289$	2.92914	−	5.07343i	0.172303	−	0.298437i
$290$	−8.47185	−	14.6737i	−0.497484	−	0.861667i
$291$	−12.0545	+	3.23001i	−0.706650	+	0.189346i
$292$	0.778552	−	0.778552i	0.0455613	−	0.0455613i
$293$	12.4507	−	3.33616i	0.727379	−	0.194901i	0.123917	−	0.992293i	$-0.460454\pi$
$293$	12.4507	−	3.33616i	0.727379	−	0.194901i	0.603462	+	0.797392i	$0.293788\pi$
$294$	−7.76042	+	7.91947i	−0.452597	+	0.461873i
$295$	−5.93368	+	10.2774i	−0.345472	+	0.598376i
$296$	−23.1707	−	13.3776i	−1.34677	−	0.777558i
$297$	−2.38426	−	2.38426i	−0.138349	−	0.138349i
$298$	−20.6096	−	11.8990i	−1.19388	−	0.689288i
$299$	12.8314	−	0.581443i	0.742060	−	0.0336257i
$300$			4.65599i			0.268814i
$301$	−28.8318	+	16.8416i	−1.66184	+	0.970732i
$302$	−0.219930	−	0.380931i	−0.0126556	−	0.0219201i
$303$		−	4.39234i		−	0.252333i
$304$	0.935756	+	3.49229i	0.0536693	+	0.200297i
$305$	−1.01450	+	3.78615i	−0.0580899	+	0.216794i
$306$	−3.73864	−	3.73864i	−0.213724	−	0.213724i
$307$	5.82305	+	5.82305i	0.332339	+	0.332339i	0.853474	−	0.521135i	$-0.174491\pi$
$307$	5.82305	+	5.82305i	0.332339	+	0.332339i	−0.521135	+	0.853474i	$0.674491\pi$
$308$	3.22725	+	3.19468i	0.183890	+	0.182034i
$309$	11.5673	−	6.67838i	0.658040	−	0.379920i
$310$	−14.2173	−	53.0596i	−0.807487	−	3.01358i
$311$	13.5284	−	23.4318i	0.767124	−	1.32870i	−0.171992	−	0.985098i	$-0.555020\pi$
$311$	13.5284	−	23.4318i	0.767124	−	1.32870i	0.939116	−	0.343600i	$-0.111646\pi$
$312$	8.31638	+	1.82931i	0.470822	+	0.103564i
$313$	11.8883	−	6.86374i	0.671969	−	0.387962i	−0.124853	−	0.992175i	$-0.539846\pi$
$313$	11.8883	−	6.86374i	0.671969	−	0.387962i	0.796822	+	0.604214i	$0.206513\pi$
$314$	−0.481113	−	0.128914i	−0.0271508	−	0.00727502i
$315$	−7.00085	+	7.07223i	−0.394453	+	0.398475i
$316$	−4.88752	−	2.82181i	−0.274945	−	0.158739i
$317$	−0.599689	+	2.23807i	−0.0336819	+	0.125702i	−0.980720	−	0.195419i	$-0.937393\pi$
$317$	−0.599689	+	2.23807i	−0.0336819	+	0.125702i	0.947038	+	0.321122i	$0.104060\pi$
$318$	10.9944	+	2.94594i	0.616535	+	0.165200i
$319$	−9.26269	−	2.48193i	−0.518611	−	0.138961i
$320$	−4.92519	+	18.3811i	−0.275327	+	1.02753i
$321$	−0.153770	−	0.0887791i	−0.00858260	−	0.00495516i
$322$	10.5032	−	10.6103i	0.585320	−	0.591287i
$323$	−2.44949	−	0.656339i	−0.136293	−	0.0365197i
$324$	0.440828	−	0.254512i	0.0244904	−	0.0141396i
$325$	32.9458	−	1.49291i	1.82750	−	0.0828115i
$326$	−0.747745	+	1.29513i	−0.0414138	+	0.0717307i
$327$	1.34434	+	5.01713i	0.0743419	+	0.277448i
$328$	−14.4914	+	8.36663i	−0.800155	+	0.461970i
$329$	2.58716	+	2.56105i	0.142635	+	0.141195i
$330$	14.2048	+	14.2048i	0.781951	+	0.781951i
$331$	18.2666	+	18.2666i	1.00402	+	1.00402i	0.999992	+	0.00403235i	$0.00128354\pi$
$331$	18.2666	+	18.2666i	1.00402	+	1.00402i	0.00403235	+	0.999992i	$0.498716\pi$
$332$	0.281729	−	1.05143i	0.0154619	−	0.0577045i
$333$	2.93212	+	10.9428i	0.160679	+	0.599663i
$334$		−	3.83484i		−	0.209833i
$335$	5.56362	+	9.63647i	0.303973	+	0.526497i
$336$	10.8720	−	6.35071i	0.593118	−	0.346460i
$337$		−	32.4074i		−	1.76534i	−0.469990	−	0.882672i	$-0.655743\pi$
$337$		−	32.4074i		−	1.76534i	0.469990	−	0.882672i	$-0.344257\pi$
$338$	−3.50881	+	20.2907i	−0.190854	+	1.10367i
$339$	17.3342	+	10.0079i	0.941462	+	0.543554i
$340$	4.51887	+	4.51887i	0.245070	+	0.245070i
$341$	−26.9238	−	15.5445i	−1.45800	−	0.841779i
$342$	0.601698	−	1.04217i	0.0325361	−	0.0563542i
$343$	18.5181	−	0.281778i	0.999884	−	0.0152146i
$344$	28.7897	−	7.71418i	1.55224	−	0.415921i
$345$	9.47467	−	9.47467i	0.510099	−	0.510099i
$346$	−26.3492	+	7.06025i	−1.41654	+	0.379562i
$347$	15.5107	+	26.8654i	0.832660	+	1.44221i	0.895921	+	0.444213i	$0.146517\pi$
$347$	15.5107	+	26.8654i	0.832660	+	1.44221i	−0.0632613	+	0.997997i	$0.520150\pi$
$348$	0.723825	−	1.25370i	0.0388011	−	0.0672055i
$349$	−0.142223	+	0.530784i	−0.00761303	+	0.0284122i	−0.969628	−	0.244585i	$-0.921348\pi$
$349$	−0.142223	+	0.530784i	−0.00761303	+	0.0284122i	0.962015	+	0.272997i	$0.0880150\pi$
$350$	26.9679	−	27.2428i	1.44149	−	1.45619i
$351$	−1.94228	−	3.03769i	−0.103671	−	0.162140i
$352$	−4.74544	−	8.21934i	−0.252933	−	0.438092i
$353$	−8.74784	+	8.74784i	−0.465601	+	0.465601i	−0.900486	−	0.434885i	$-0.856789\pi$
$353$	−8.74784	+	8.74784i	−0.465601	+	0.465601i	0.434885	+	0.900486i	$0.356789\pi$
$354$	−4.99777			−0.265628
$355$	27.2735			1.44752
$356$	−1.13903	+	1.13903i	−0.0603682	+	0.0603682i
$357$	0.0447897	+	8.83119i	0.00237052	+	0.467396i
$358$	1.41129	+	5.26701i	0.0745891	+	0.278370i
$359$	−7.03362	−	1.88465i	−0.371220	−	0.0994682i	0.0683856	−	0.997659i	$-0.478215\pi$
$359$	−7.03362	−	1.88465i	−0.371220	−	0.0994682i	−0.439606	+	0.898191i	$0.644882\pi$
$360$	7.69280	−	4.44144i	0.405446	−	0.234084i
$361$			18.4228i			0.969622i
$362$	39.7448	−	10.6496i	2.08894	−	0.559730i
$363$	0.369378			0.0193873
$364$	2.63648	+	4.07770i	0.138189	+	0.213729i
$365$	−8.13569			−0.425842
$366$	−1.59448	+	0.427240i	−0.0833450	+	0.0223322i
$367$			4.31177i			0.225073i	0.993648	+	0.112536i	$0.0358975\pi$
$367$			4.31177i			0.225073i	−0.993648	+	0.112536i	$0.964103\pi$
$368$	−14.6821	+	8.47674i	−0.765360	+	0.441881i
$369$	6.84386	+	1.83381i	0.356277	+	0.0954642i
$370$	−17.4689	−	65.1947i	−0.908163	−	3.38931i
$371$	−9.58930	−	16.4163i	−0.497852	−	0.852292i
$372$	3.31864	−	3.31864i	0.172064	−	0.172064i
$373$	−17.1750			−0.889289			−0.444645	−	0.895707i	$-0.646670\pi$
$373$	−17.1750			−0.889289			−0.444645	+	0.895707i	$0.646670\pi$
$374$	17.8278			0.921851
$375$	11.0291	−	11.0291i	0.569538	−	0.569538i
$376$	−1.62477	−	2.81418i	−0.0837909	−	0.145130i
$377$	−9.10328	−	4.71980i	−0.468843	−	0.243082i
$378$	−4.05349	−	1.06413i	−0.208489	−	0.0547327i
$379$	0.602843	−	2.24984i	0.0309659	−	0.115566i	−0.948713	−	0.316139i	$-0.897613\pi$
$379$	0.602843	−	2.24984i	0.0309659	−	0.115566i	0.979679	+	0.200572i	$0.0642801\pi$
$380$	−0.727269	+	1.25967i	−0.0373081	+	0.0646196i
$381$	3.89450	+	6.74547i	0.199521	+	0.345581i
$382$	−4.56415	+	1.22296i	−0.233522	+	0.0625721i
$383$	−19.4875	+	19.4875i	−0.995766	+	0.995766i	−0.999991	−	0.00422533i	$-0.998655\pi$
$383$	−19.4875	+	19.4875i	−0.995766	+	0.995766i	0.00422533	+	0.999991i	$0.498655\pi$
$384$	−13.1786	+	3.53119i	−0.672516	+	0.180200i
$385$	−0.170177	−	33.5538i	−0.00867302	−	1.71006i
$386$	−2.07041	+	3.58606i	−0.105381	+	0.182526i
$387$	−10.9295	−	6.31017i	−0.555579	−	0.320764i
$388$	4.49191	+	4.49191i	0.228042	+	0.228042i
$389$	10.7596	+	6.21203i	0.545531	+	0.314962i	0.747318	−	0.664467i	$-0.231341\pi$
$389$	10.7596	+	6.21203i	0.545531	+	0.314962i	−0.201787	+	0.979430i	$0.564675\pi$
$390$	11.5716	+	18.0978i	0.585951	+	0.916419i
$391$		−	11.8912i		−	0.601362i
$392$	−16.0111	−	4.11656i	−0.808683	−	0.207918i
$393$	4.85426	+	8.40782i	0.244865	+	0.424118i
$394$			1.30779i			0.0658855i
$395$	10.7931	+	40.2804i	0.543060	+	2.02673i
$396$	−0.444225	+	1.65787i	−0.0223232	+	0.0833111i
$397$	22.8495	+	22.8495i	1.14679	+	1.14679i	0.987181	+	0.159604i	$0.0510217\pi$
$397$	22.8495	+	22.8495i	1.14679	+	1.14679i	0.159604	+	0.987181i	$0.448978\pi$
$398$	9.18635	+	9.18635i	0.460470	+	0.460470i
$399$	−1.93889	+	0.530077i	−0.0970658	+	0.0265371i
$400$	−37.6977	+	21.7648i	−1.88488	+	1.08824i
$401$	−3.64535	−	13.6046i	−0.182040	−	0.679383i	−0.995245	−	0.0974054i	$-0.968946\pi$
$401$	−3.64535	−	13.6046i	−0.182040	−	0.679383i	0.813205	−	0.581978i	$-0.197721\pi$
$402$	−2.34304	+	4.05826i	−0.116860	+	0.202408i
$403$	−24.5468	−	22.4186i	−1.22276	−	1.11675i
$404$	−1.93627	+	1.11790i	−0.0963329	+	0.0556178i
$405$	−3.63307	−	0.973479i	−0.180529	−	0.0483726i
$406$	−11.4967	+	3.14312i	−0.570573	+	0.155990i
$407$	−33.0815	−	19.0996i	−1.63979	−	0.946731i
$408$	2.04031	−	7.61452i	0.101010	−	0.376975i
$409$	−28.4643	−	7.62699i	−1.40747	−	0.377130i	−0.526448	−	0.850207i	$-0.676477\pi$
$409$	−28.4643	−	7.62699i	−1.40747	−	0.377130i	−0.881021	+	0.473077i	$0.843143\pi$
$410$	−40.7741	−	10.9254i	−2.01369	−	0.539566i
$411$	−2.35211	+	8.77818i	−0.116021	+	0.432996i
$412$	−5.88804	−	3.39946i	−0.290083	−	0.167479i
$413$	5.93266	+	5.87278i	0.291927	+	0.288981i
$414$	5.45060	+	1.46048i	0.267883	+	0.0717789i
$415$	−6.96559	+	4.02159i	−0.341927	+	0.197412i
$416$	−3.06773	−	9.67392i	−0.150408	−	0.474303i
$417$	5.11228	−	8.85473i	0.250349	−	0.433618i
$418$	1.05020	+	3.91941i	0.0513671	+	0.191705i
$419$	10.6429	−	6.14470i	0.519941	−	0.300188i	−0.216970	−	0.976178i	$-0.569617\pi$
$419$	10.6429	−	6.14470i	0.519941	−	0.300188i	0.736911	+	0.675990i	$0.236284\pi$
$420$	4.89944	+	1.28620i	0.239068	+	0.0627603i
$421$	6.08177	+	6.08177i	0.296407	+	0.296407i	0.839605	−	0.543197i	$-0.182787\pi$
$421$	6.08177	+	6.08177i	0.296407	+	0.296407i	−0.543197	+	0.839605i	$0.682787\pi$
$422$	−12.0392	−	12.0392i	−0.586060	−	0.586060i
$423$	−0.356118	+	1.32905i	−0.0173151	+	0.0646207i
$424$	4.39232	+	16.3924i	0.213310	+	0.796084i
$425$		−	30.5316i		−	1.48100i
$426$	5.74291	+	9.94701i	0.278245	+	0.481934i
$427$	2.39479	+	1.36649i	0.115892	+	0.0661289i
$428$			0.0903814i			0.00436875i
$429$	11.8735	+	2.61175i	0.573259	+	0.126097i
$430$	65.1155	+	37.5945i	3.14015	+	1.81297i
$431$	−24.1214	−	24.1214i	−1.16189	−	1.16189i	−0.984062	−	0.177826i	$-0.943093\pi$
$431$	−24.1214	−	24.1214i	−1.16189	−	1.16189i	−0.177826	−	0.984062i	$-0.556907\pi$
$432$	4.12137	+	2.37947i	0.198289	+	0.114482i
$433$	−14.7993	+	25.6331i	−0.711209	+	1.23185i	0.253194	+	0.967415i	$0.418519\pi$
$433$	−14.7993	+	25.6331i	−0.711209	+	1.23185i	−0.964403	+	0.264435i	$0.914815\pi$
$434$	−38.6396	+	0.195971i	−1.85476	+	0.00940690i
$435$	−10.3324	+	2.76855i	−0.495399	+	0.132742i
$436$	1.86954	−	1.86954i	0.0895348	−	0.0895348i
$437$	2.61426	−	0.700488i	0.125057	−	0.0335089i
$438$	−1.71311	−	2.96720i	−0.0818558	−	0.141778i
$439$	9.21425	−	15.9596i	0.439772	−	0.761708i	−0.557899	−	0.829909i	$-0.688392\pi$
$439$	9.21425	−	15.9596i	0.439772	−	0.761708i	0.997672	+	0.0682006i	$0.0217258\pi$
$440$	−7.75208	+	28.9311i	−0.369566	+	1.37924i
$441$	3.56131	+	6.02636i	0.169586	+	0.286970i
$442$	18.6183	+	4.09536i	0.885582	+	0.194796i
$443$	−2.87530	−	4.98017i	−0.136610	−	0.236615i	0.789601	−	0.613620i	$-0.210287\pi$
$443$	−2.87530	−	4.98017i	−0.136610	−	0.236615i	−0.926211	+	0.377005i	$0.876954\pi$
$444$	4.07764	−	4.07764i	0.193516	−	0.193516i
$445$	11.9026			0.564236
$446$	9.41374			0.445753
$447$	−10.6236	+	10.6236i	−0.502478	+	0.502478i
$448$	11.6263	+	6.63404i	0.549290	+	0.313429i
$449$	5.09748	+	19.0241i	0.240565	+	0.897801i	0.975561	+	0.219729i	$0.0705174\pi$
$449$	5.09748	+	19.0241i	0.240565	+	0.897801i	−0.734996	+	0.678072i	$0.762816\pi$
$450$	13.9949	+	3.74992i	0.659726	+	0.176773i
$451$	−20.6898	+	11.9453i	−0.974245	+	0.562480i
$452$		−	10.1885i		−	0.479227i
$453$	−0.268230	+	0.0718719i	−0.0126025	+	0.00337684i
$454$	32.2930			1.51558
$455$	7.53021	−	35.0808i	0.353022	−	1.64461i
$456$	1.79423			0.0840227
$457$	−3.00408	+	0.804940i	−0.140525	+	0.0376535i	−0.328396	−	0.944540i	$-0.606508\pi$
$457$	−3.00408	+	0.804940i	−0.140525	+	0.0376535i	0.187871	+	0.982194i	$0.439841\pi$
$458$		−	13.5948i		−	0.635243i
$459$	−2.89072	+	1.66896i	−0.134927	+	0.0779004i
$460$	−6.58812	−	1.76528i	−0.307173	−	0.0823066i
$461$	−8.13643	−	30.3656i	−0.378951	−	1.41427i	−0.847485	−	0.530820i	$-0.821884\pi$
$461$	−8.13643	−	30.3656i	−0.378951	−	1.41427i	0.468533	−	0.883446i	$-0.344783\pi$
$462$	12.2017	−	7.12742i	0.567676	−	0.331598i
$463$	10.2951	−	10.2951i	0.478455	−	0.478455i	−0.426182	−	0.904637i	$-0.640142\pi$
$463$	10.2951	−	10.2951i	0.478455	−	0.478455i	0.904637	+	0.426182i	$0.140142\pi$
$464$	13.5343			0.628314
$465$	−34.6791			−1.60820
$466$	5.63204	−	5.63204i	0.260899	−	0.260899i
$467$	6.26532	+	10.8518i	0.289924	+	0.502164i	0.973791	−	0.227443i	$-0.0730365\pi$
$467$	6.26532	+	10.8518i	0.289924	+	0.502164i	−0.683867	+	0.729607i	$0.739703\pi$
$468$	−0.844767	+	1.62934i	−0.0390493	+	0.0753162i
$469$	7.55012	−	2.06414i	0.348632	−	0.0953133i
$470$	2.12167	−	7.91817i	0.0978652	−	0.365238i
$471$	−0.157225	+	0.272321i	−0.00724453	+	0.0125479i
$472$	−3.72578	−	6.45323i	−0.171493	−	0.297034i
$473$	41.1039	−	11.0138i	1.88996	−	0.506413i
$474$	−12.4182	+	12.4182i	−0.570385	+	0.570385i
$475$	6.71233	−	1.79856i	0.307983	−	0.0825238i
$476$	3.88164	−	2.26739i	0.177915	−	0.103926i
$477$	3.59290	−	6.22308i	0.164508	−	0.284935i
$478$	22.6141	+	13.0562i	1.03434	+	0.597179i
$479$	14.8262	+	14.8262i	0.677424	+	0.677424i	0.959417	−	0.281992i	$-0.0909953\pi$
$479$	14.8262	+	14.8262i	0.677424	+	0.677424i	−0.281992	+	0.959417i	$0.590995\pi$
$480$	−9.16852	−	5.29344i	−0.418484	−	0.241612i
$481$	−30.1609	−	27.5459i	−1.37522	−	1.25599i
$482$		−	8.94218i		−	0.407305i
$483$	−4.75401	−	8.13859i	−0.216315	−	0.370318i
$484$	−0.0940112	−	0.162832i	−0.00427324	−	0.00740146i
$485$		−	46.9394i		−	2.13141i
$486$	−0.409967	−	1.53002i	−0.0185965	−	0.0694030i
$487$	2.79170	−	10.4187i	0.126504	−	0.472119i	−0.873385	−	0.487030i	$-0.838080\pi$
$487$	2.79170	−	10.4187i	0.126504	−	0.472119i	0.999889	+	0.0149118i	$0.00474676\pi$
$488$	−1.74033	−	1.74033i	−0.0787811	−	0.0787811i
$489$	0.667599	+	0.667599i	0.0301899	+	0.0301899i
$490$	−21.2174	−	35.9036i	−0.958506	−	1.62196i
$491$	30.7318	−	17.7430i	1.38691	−	0.800730i	0.393940	−	0.919136i	$-0.371112\pi$
$491$	30.7318	−	17.7430i	1.38691	−	0.800730i	0.992965	+	0.118406i	$0.0377785\pi$
$492$	−0.933452	−	3.48369i	−0.0420833	−	0.157057i
$493$	−4.74647	+	8.22113i	−0.213770	+	0.370261i
$494$	0.196412	+	4.33446i	0.00883698	+	0.195016i
$495$	10.9832	−	6.34116i	0.493659	−	0.285014i
$496$	42.3830	+	11.3565i	1.90305	+	0.509921i
$497$	4.87136	−	18.5561i	0.218510	−	0.832355i
$498$	−2.93346	−	1.69363i	−0.131451	−	0.0758935i
$499$	1.32898	−	4.95983i	0.0594935	−	0.222033i	−0.929778	−	0.368120i	$-0.880001\pi$
$499$	1.32898	−	4.95983i	0.0594935	−	0.222033i	0.989272	+	0.146088i	$0.0466681\pi$
$500$	−7.66895	−	2.05489i	−0.342966	−	0.0918974i
$501$	−2.33851	−	0.626601i	−0.104477	−	0.0279945i
$502$	−4.54429	+	16.9595i	−0.202821	+	0.756940i
$503$	31.3005	+	18.0713i	1.39562	+	0.805761i	0.993930	−	0.110015i	$-0.0350897\pi$
$503$	31.3005	+	18.0713i	1.39562	+	0.805761i	0.401690	+	0.915776i	$0.368423\pi$
$504$	−1.64781	−	6.02726i	−0.0733991	−	0.268475i
$505$	15.9577	+	4.27585i	0.710108	+	0.190273i
$506$	−16.4778	+	9.51348i	−0.732529	+	0.422926i
$507$	11.8001	+	5.45513i	0.524059	+	0.242271i
$508$	1.98239	−	3.43361i	0.0879546	−	0.152342i
$509$	7.45841	+	27.8352i	0.330588	+	1.23377i	0.908574	+	0.417725i	$0.137172\pi$
$509$	7.45841	+	27.8352i	0.330588	+	1.23377i	−0.577985	+	0.816047i	$0.696161\pi$
$510$	17.2222	−	9.94326i	0.762614	−	0.440295i
$511$	−1.45313	+	5.53530i	−0.0642827	+	0.244867i
$512$	−6.42274	−	6.42274i	−0.283848	−	0.283848i
$513$	−0.537206	−	0.537206i	−0.0237182	−	0.0237182i
$514$	0.985235	−	3.67695i	0.0434569	−	0.162183i
$515$	13.0025	+	48.5261i	0.572960	+	2.13832i
$516$			6.42406i			0.282803i
$517$	−2.31972	−	4.01788i	−0.102021	−	0.176706i
$518$	−47.4768	+	0.240791i	−2.08601	+	0.0105797i
$519$			17.2215i			0.755941i
$520$	−14.7418	+	28.4332i	−0.646472	+	1.24688i
$521$	15.6852	+	9.05586i	0.687182	+	0.396745i	0.802555	−	0.596578i	$-0.203473\pi$
$521$	15.6852	+	9.05586i	0.687182	+	0.396745i	−0.115374	+	0.993322i	$0.536807\pi$
$522$	−3.18539	−	3.18539i	−0.139421	−	0.139421i
$523$	1.47572	+	0.852009i	0.0645288	+	0.0372557i	0.531917	−	0.846796i	$-0.321472\pi$
$523$	1.47572	+	0.852009i	0.0645288	+	0.0372557i	−0.467388	+	0.884052i	$0.654805\pi$
$524$	2.47094	−	4.27979i	0.107943	−	0.186963i
$525$	−12.2063	−	20.8965i	−0.532728	−	0.911999i
$526$	39.9711	−	10.7102i	1.74282	−	0.466988i
$527$	−21.7620	+	21.7620i	−0.947966	+	0.947966i
$528$	−15.4997	+	4.15313i	−0.674537	+	0.180742i
$529$	−5.15449	−	8.92783i	−0.224108	−	0.388167i
$530$	−21.4056	+	37.0756i	−0.929801	+	1.61046i
$531$	−0.816620	+	3.04767i	−0.0354383	+	0.132257i
$532$	0.727144	+	0.719805i	0.0315257	+	0.0312075i
$533$	−24.3513	+	7.72212i	−1.05477	+	0.334482i
$534$	2.50630	+	4.34103i	0.108458	+	0.187855i
$535$	0.472233	−	0.472233i	0.0204164	−	0.0204164i
$536$	−6.98683			−0.301785
$537$	3.44245			0.148553
$538$	29.5920	−	29.5920i	1.27580	−	1.27580i
$539$	−22.8595	−	5.87733i	−0.984628	−	0.253154i
$540$	0.495525	+	1.84932i	0.0213240	+	0.0795822i
$541$	7.67860	+	2.05747i	0.330129	+	0.0884577i	0.420076	−	0.907489i	$-0.362003\pi$
$541$	7.67860	+	2.05747i	0.330129	+	0.0884577i	−0.0899476	+	0.995946i	$0.528670\pi$
$542$	10.3898	−	5.99856i	0.446280	−	0.257660i
$543$		−	25.9767i		−	1.11477i
$544$	−9.07523	+	2.43170i	−0.389097	+	0.104258i
$545$	−19.5363			−0.836842
$546$	14.3801	−	4.64052i	0.615411	−	0.198596i
$547$	−45.6503			−1.95187			−0.975933	−	0.218072i	$-0.930023\pi$
$547$	−45.6503			−1.95187			−0.975933	+	0.218072i	$0.930023\pi$
$548$	4.46831	−	1.19728i	0.190877	−	0.0511452i
$549$			1.04213i			0.0444772i
$550$	−42.3083	+	24.4267i	−1.80403	+	1.04156i
$551$	−2.08701	−	0.559213i	−0.0889097	−	0.0238233i
$552$	2.17755	+	8.12672i	0.0926826	+	0.345896i
$553$	29.3334	−	0.148772i	1.24738	−	0.00632643i
$554$	25.2493	−	25.2493i	1.07274	−	1.07274i
$555$	−42.6105			−1.80871
$556$	−5.20455			−0.220722
$557$	−8.86445	+	8.86445i	−0.375599	+	0.375599i	−0.869511	−	0.493913i	$-0.835566\pi$
$557$	−8.86445	+	8.86445i	−0.375599	+	0.375599i	0.493913	+	0.869511i	$0.335566\pi$
$558$	−7.30230	−	12.6480i	−0.309131	−	0.535431i
$559$	45.4566	−	2.05982i	1.92261	−	0.0871211i
$560$	12.4889	+	45.6812i	0.527752	+	1.93038i
$561$	2.91300	−	10.8715i	0.122987	−	0.458994i
$562$	8.66336	−	15.0054i	0.365442	−	0.632963i
$563$	−7.35106	−	12.7324i	−0.309810	−	0.536607i	0.668510	−	0.743703i	$-0.266932\pi$
$563$	−7.35106	−	12.7324i	−0.309810	−	0.536607i	−0.978321	+	0.207096i	$0.933599\pi$
$564$	0.676520	−	0.181273i	0.0284866	−	0.00763297i
$565$	−53.2338	+	53.2338i	−2.23956	+	2.23956i
$566$	−27.1279	+	7.26891i	−1.14027	+	0.305535i
$567$	−1.31124	+	2.29797i	−0.0550668	+	0.0965056i
$568$	−8.56254	+	14.8308i	−0.359276	+	0.622285i
$569$	−18.3098	−	10.5712i	−0.767588	−	0.443167i	0.0644254	−	0.997923i	$-0.479479\pi$
$569$	−18.3098	−	10.5712i	−0.767588	−	0.443167i	−0.832014	+	0.554755i	$0.812812\pi$
$570$	3.20055	+	3.20055i	0.134056	+	0.134056i
$571$	2.38493	+	1.37694i	0.0998064	+	0.0576232i	0.549072	−	0.835775i	$-0.314981\pi$
$571$	2.38493	+	1.37694i	0.0998064	+	0.0576232i	−0.449266	+	0.893398i	$0.648314\pi$
$572$	−1.87062	−	5.89891i	−0.0782147	−	0.246646i
$573$			2.98307i			0.124620i
$574$	−14.7161	+	25.7901i	−0.614236	+	1.07646i
$575$	16.2927	+	28.2197i	0.679451	+	1.17684i
$576$			5.05937i			0.210807i
$577$	−1.61848	−	6.04026i	−0.0673783	−	0.251459i	0.924019	−	0.382347i	$-0.124884\pi$
$577$	−1.61848	−	6.04026i	−0.0673783	−	0.251459i	−0.991397	+	0.130888i	$0.958217\pi$
$578$	−2.40170	+	8.96328i	−0.0998977	+	0.372823i
$579$	1.84850	+	1.84850i	0.0768211	+	0.0768211i
$580$	3.85016	+	3.85016i	0.159869	+	0.159869i
$581$	1.49204	+	5.45749i	0.0619002	+	0.226415i
$582$	17.1195	−	9.88393i	0.709624	−	0.409702i
$583$	6.27104	+	23.4038i	0.259720	+	0.969288i
$584$	2.55421	−	4.42403i	0.105694	−	0.183067i
$585$	12.9269	−	4.09930i	0.534463	−	0.169485i
$586$	−17.6821	+	10.2088i	−0.730441	+	0.421720i
$587$	15.8338	+	4.24265i	0.653530	+	0.175113i	0.570324	−	0.821420i	$-0.306817\pi$
$587$	15.8338	+	4.24265i	0.653530	+	0.175113i	0.0832057	+	0.996532i	$0.473484\pi$
$588$	1.75019	−	3.10371i	0.0721768	−	0.127995i
$589$	−6.06630	−	3.50238i	−0.249958	−	0.144313i
$590$	4.86523	−	18.1573i	0.200298	−	0.747523i
$591$	0.797498	+	0.213689i	0.0328047	+	0.00878999i
$592$	52.0763	+	13.9538i	2.14032	+	0.573497i
$593$	3.98614	−	14.8765i	0.163691	−	0.610904i	−0.834512	−	0.550989i	$-0.814250\pi$
$593$	3.98614	−	14.8765i	0.163691	−	0.610904i	0.998203	−	0.0599148i	$-0.0190829\pi$
$594$	4.62542	+	2.67049i	0.189783	+	0.109571i
$595$	−32.1280	−	8.43426i	−1.31712	−	0.345771i
$596$	7.38701	+	1.97934i	0.302584	+	0.0810770i
$597$	7.10291	−	4.10087i	0.290703	−	0.167837i
$598$	−19.3939	+	6.15007i	−0.793076	+	0.251495i
$599$	13.0357	−	22.5784i	0.532623	−	0.922530i	−0.466651	−	0.884441i	$-0.654540\pi$
$599$	13.0357	−	22.5784i	0.532623	−	0.922530i	0.999274	−	0.0380886i	$-0.0121269\pi$
$600$	5.59104	+	20.8661i	0.228253	+	0.851853i
$601$	36.7529	−	21.2193i	1.49918	−	0.865554i	0.499183	−	0.866496i	$-0.333633\pi$
$601$	36.7529	−	21.2193i	1.49918	−	0.865554i	1.00000		0.000942846i	$0.000300117\pi$
$602$	37.2086	−	37.5880i	1.51651	−	1.53197i
$603$	2.09191	+	2.09191i	0.0851890	+	0.0851890i
$604$	0.0999508	+	0.0999508i	0.00406694	+	0.00406694i
$605$	−0.359582	+	1.34198i	−0.0146191	+	0.0545591i
$606$	1.80071	+	6.72036i	0.0731490	+	0.272996i
$607$			6.78525i			0.275405i	0.990474	+	0.137702i	$0.0439718\pi$
$607$			6.78525i			0.275405i	−0.990474	+	0.137702i	$0.956028\pi$
$608$	−1.06921	−	1.85193i	−0.0433623	−	0.0751057i
$609$	0.0381616	+	7.52434i	0.00154639	+	0.304902i
$610$		−	6.20879i		−	0.251386i
$611$	−1.49961	−	4.72893i	−0.0606676	−	0.191312i
$612$	1.47145	+	0.849541i	0.0594798	+	0.0343407i
$613$	−24.0356	−	24.0356i	−0.970790	−	0.970790i	0.0287955	−	0.999585i	$-0.490833\pi$
$613$	−24.0356	−	24.0356i	−0.970790	−	0.970790i	−0.999585	+	0.0287955i	$0.990833\pi$
$614$	−11.2966	−	6.52211i	−0.455895	−	0.263211i
$615$	−13.3247	+	23.0791i	−0.537304	+	0.930638i
$616$	18.2993	+	10.4417i	0.737301	+	0.420710i
$617$	−7.13892	+	1.91287i	−0.287402	+	0.0770091i	−0.399640	−	0.916672i	$-0.630865\pi$
$617$	−7.13892	+	1.91287i	−0.287402	+	0.0770091i	0.112238	+	0.993681i	$0.464198\pi$
$618$	−14.9602	+	14.9602i	−0.601789	+	0.601789i
$619$	0.685897	−	0.183786i	0.0275685	−	0.00738697i	−0.245008	−	0.969521i	$-0.578791\pi$
$619$	0.685897	−	0.183786i	0.0275685	−	0.00738697i	0.272577	+	0.962134i	$0.412124\pi$
$620$	8.82625	+	15.2875i	0.354471	+	0.613961i
$621$	1.78122	−	3.08517i	0.0714780	−	0.123804i
$622$	−11.0924	+	41.3973i	−0.444764	+	1.65988i
$623$	2.12594	−	8.09817i	0.0851739	−	0.324446i
$624$	−17.1410	+	0.776728i	−0.686190	+	0.0310940i
$625$	6.46561	+	11.1988i	0.258624	+	0.447951i
$626$	−15.3755	+	15.3755i	−0.614527	+	0.614527i
$627$	2.56168			0.102304
$628$	0.160062			0.00638718
$629$	−26.7391	+	26.7391i	−1.06616	+	1.06616i
$630$	7.81204	−	13.6907i	0.311239	−	0.545452i
$631$	7.80744	+	29.1378i	0.310809	+	1.15996i	0.927828	+	0.373008i	$0.121674\pi$
$631$	7.80744	+	29.1378i	0.310809	+	1.15996i	−0.617019	+	0.786948i	$0.711660\pi$
$632$	−25.2922	−	6.77702i	−1.00607	−	0.269575i
$633$	−9.30875	+	5.37441i	−0.369989	+	0.213614i
$634$		−	3.67013i		−	0.145760i
$635$	−28.2980	+	7.58243i	−1.12297	+	0.300900i
$636$	−3.65775			−0.145039
$637$	−22.5230	−	11.3892i	−0.892395	−	0.451256i
$638$	15.1896			0.601361
$639$	7.00412	−	1.87675i	0.277079	−	0.0742430i
$640$		−	51.3163i		−	2.02845i
$641$	−12.5033	+	7.21880i	−0.493852	+	0.285126i	−0.726171	−	0.687514i	$-0.758702\pi$
$641$	−12.5033	+	7.21880i	−0.493852	+	0.285126i	0.232319	+	0.972640i	$0.425369\pi$
$642$	0.271667	+	0.0727929i	0.0107218	+	0.00287291i
$643$	4.71705	+	17.6043i	0.186022	+	0.694244i	0.994409	+	0.105593i	$0.0336741\pi$
$643$	4.71705	+	17.6043i	0.186022	+	0.694244i	−0.808387	+	0.588651i	$0.799659\pi$
$644$	−2.37776	+	4.16707i	−0.0936970	+	0.164206i
$645$	33.5650	−	33.5650i	1.32162	−	1.32162i
$646$	4.01684			0.158040
$647$	37.7666			1.48476			0.742379	−	0.669980i	$-0.233697\pi$
$647$	37.7666			1.48476			0.742379	+	0.669980i	$0.233697\pi$
$648$	1.66997	−	1.66997i	0.0656025	−	0.0656025i
$649$	−5.31939	−	9.21346i	−0.208804	−	0.361660i
$650$	−49.7956	+	15.7909i	−1.95314	+	0.619368i
$651$	−6.19409	+	23.5947i	−0.242766	+	0.924749i
$652$	0.124384	−	0.464209i	0.00487127	−	0.0181798i
$653$	13.2771	−	22.9966i	0.519573	−	0.899927i	−0.480168	−	0.877176i	$-0.659424\pi$
$653$	13.2771	−	22.9966i	0.519573	−	0.899927i	0.999741	−	0.0227503i	$-0.00724227\pi$
$654$	−4.11371	−	7.12516i	−0.160859	−	0.278616i
$655$	−35.2718	+	9.45104i	−1.37818	+	0.369283i
$656$	23.8426	−	23.8426i	0.930896	−	0.930896i
$657$	−2.08933	+	0.559835i	−0.0815127	+	0.0218413i
$658$	−5.00835	−	2.85780i	−0.195246	−	0.111409i
$659$	2.28186	−	3.95230i	0.0888888	−	0.153960i	−0.818153	−	0.575001i	$-0.805002\pi$
$659$	2.28186	−	3.95230i	0.0888888	−	0.153960i	0.907042	+	0.421041i	$0.138335\pi$
$660$	−5.59072	−	3.22781i	−0.217619	−	0.125642i
$661$	29.7654	+	29.7654i	1.15774	+	1.15774i	0.984961	+	0.172778i	$0.0552743\pi$
$661$	29.7654	+	29.7654i	1.15774	+	1.15774i	0.172778	+	0.984961i	$0.444726\pi$
$662$	−35.4369	−	20.4595i	−1.37730	−	0.795182i
$663$	5.53954	−	10.6844i	0.215138	−	0.414946i
$664$		−	5.05033i		−	0.195991i
$665$	−0.0383432	−	7.56014i	−0.00148689	−	0.293170i
$666$	−8.97239	−	15.5406i	−0.347673	−	0.602187i
$667$		−	10.1315i		−	0.392293i
$668$	0.318955	+	1.19036i	0.0123407	+	0.0460563i
$669$	1.53818	−	5.74055i	0.0594693	−	0.221942i
$670$	−12.4631	−	12.4631i	−0.481490	−	0.481490i
$671$	−2.48472	−	2.48472i	−0.0959215	−	0.0959215i
$672$	−5.23912	+	5.29253i	−0.202103	+	0.204164i
$673$	−22.4576	+	12.9659i	−0.865675	+	0.499798i	−0.865909	−	0.500202i	$-0.833259\pi$
$673$	−22.4576	+	12.9659i	−0.865675	+	0.499798i	0.000233516		1.00000i	$0.499926\pi$
$674$	13.2860	+	49.5839i	0.511756	+	1.90990i
$675$	4.57345	−	7.92144i	0.176032	−	0.304897i
$676$	−0.598485	−	6.59020i	−0.0230187	−	0.253469i
$677$	15.4910	−	8.94374i	0.595368	−	0.343736i	−0.171849	−	0.985123i	$-0.554974\pi$
$677$	15.4910	−	8.94374i	0.595368	−	0.343736i	0.767217	+	0.641387i	$0.221641\pi$
$678$	−30.6245	−	8.20580i	−1.17613	−	0.315142i
$679$	−31.9363	−	8.38393i	−1.22560	−	0.321746i
$680$	25.6779	+	14.8252i	0.984704	+	0.568519i
$681$	5.27657	−	19.6924i	0.202199	−	0.754616i
$682$	47.5666	+	12.7454i	1.82142	+	0.488047i
$683$	30.8734	+	8.27250i	1.18134	+	0.316538i	0.795457	−	0.606010i	$-0.207231\pi$
$683$	30.8734	+	8.27250i	1.18134	+	0.316538i	0.385881	+	0.922549i	$0.373898\pi$
$684$	−0.100090	+	0.373541i	−0.00382704	+	0.0142827i
$685$	−29.6021	−	17.0908i	−1.13104	−	0.653004i
$686$	−28.2175	+	8.02294i	−1.07735	+	0.306317i
$687$	−8.29019	−	2.22135i	−0.316290	−	0.0847497i
$688$	−52.0130	+	30.0297i	−1.98298	+	1.14487i
$689$	1.17283	+	25.8822i	0.0446811	+	0.986033i
$690$	−10.6121	+	18.3807i	−0.403996	+	0.699741i
$691$	−3.88609	−	14.5031i	−0.147834	−	0.551723i	−0.999613	−	0.0278221i	$-0.991143\pi$
$691$	−3.88609	−	14.5031i	−0.147834	−	0.551723i	0.851779	−	0.523901i	$-0.175524\pi$
$692$	7.59173	−	4.38309i	0.288594	−	0.166620i
$693$	−2.35262	−	8.60528i	−0.0893686	−	0.326888i
$694$	−34.7456	−	34.7456i	−1.31893	−	1.31893i
$695$	27.1932	+	27.1932i	1.03150	+	1.03150i
$696$	1.73838	−	6.48772i	0.0658931	−	0.245916i
$697$	6.12110	+	22.8443i	0.231853	+	0.865288i
$698$		−	0.870416i		−	0.0329457i
$699$	−2.51419	−	4.35471i	−0.0950955	−	0.164710i
$700$	−6.10511	+	10.6993i	−0.230752	+	0.404396i
$701$			17.3022i			0.653495i	0.945112	+	0.326747i	$0.105953\pi$
$701$			17.3022i			0.653495i	−0.945112	+	0.326747i	$0.894047\pi$
$702$	4.21707	+	3.85145i	0.159163	+	0.145364i
$703$	−7.45371	−	4.30340i	−0.281122	−	0.162306i
$704$	−12.0628	−	12.0628i	−0.454636	−	0.454636i
$705$	−4.48187	−	2.58761i	−0.168797	−	0.0974550i
$706$	9.79802	−	16.9707i	0.368753	−	0.638700i
$707$	5.75940	−	10.0935i	0.216605	−	0.379604i
$708$	1.55134	−	0.415679i	0.0583028	−	0.0156222i
$709$	9.82865	−	9.82865i	0.369123	−	0.369123i	−0.498034	−	0.867157i	$-0.665945\pi$
$709$	9.82865	−	9.82865i	0.369123	−	0.369123i	0.867157	+	0.498034i	$0.165945\pi$
$710$	−41.7289	+	11.1812i	−1.56606	+	0.419623i
$711$	5.54357	+	9.60175i	0.207900	+	0.360094i
$712$	−3.73683	+	6.47237i	−0.140043	+	0.242562i
$713$	8.50123	−	31.7270i	0.318374	−	1.18819i
$714$	−3.68902	−	13.4935i	−0.138058	−	0.504982i
$715$	−21.0473	+	40.5949i	−0.787126	+	1.51816i
$716$	−0.876146	−	1.51753i	−0.0327431	−	0.0567128i
$717$	11.6568	−	11.6568i	0.435333	−	0.435333i
$718$	11.5342			0.430453
$719$	49.1299			1.83224			0.916118	−	0.400909i	$-0.131306\pi$
$719$	49.1299			1.83224			0.916118	+	0.400909i	$0.131306\pi$
$720$	−12.6569	+	12.6569i	−0.471693	+	0.471693i
$721$	35.3382	−	0.179227i	1.31606	−	0.00667476i
$722$	−7.55274	−	28.1872i	−0.281084	−	1.04902i
$723$	−5.45299	−	1.46113i	−0.202799	−	0.0543398i
$724$	−11.4513	+	6.61139i	−0.425583	+	0.245711i
$725$		−	26.0135i		−	0.966117i
$726$	−0.565154	+	0.151433i	−0.0209748	+	0.00562019i
$727$	−19.4676			−0.722014			−0.361007	−	0.932563i	$-0.617567\pi$
$727$	−19.4676			−0.722014			−0.361007	+	0.932563i	$0.617567\pi$
$728$	16.7121	+	15.1084i	0.619392	+	0.559956i
$729$	−1.00000			−0.0370370
$730$	12.4477	−	3.33536i	0.460712	−	0.123447i
$731$		−	42.1257i		−	1.55807i
$732$	0.459402	−	0.265236i	0.0169800	−	0.00980340i
$733$	6.78026	+	1.81677i	0.250435	+	0.0671038i	0.381852	−	0.924223i	$-0.375286\pi$
$733$	6.78026	+	1.81677i	0.250435	+	0.0671038i	−0.131418	+	0.991327i	$0.541953\pi$
$734$	−1.76768	−	6.59709i	−0.0652464	−	0.243503i
$735$	−25.3611	+	7.07196i	−0.935458	+	0.260853i
$736$	7.09041	−	7.09041i	0.261356	−	0.261356i
$737$	−9.97529			−0.367444
$738$	−11.2230			−0.413125
$739$	28.2471	−	28.2471i	1.03909	−	1.03909i	0.0398827	−	0.999204i	$-0.487302\pi$
$739$	28.2471	−	28.2471i	1.03909	−	1.03909i	0.999204	−	0.0398827i	$-0.0126984\pi$
$740$	10.8449	+	18.7839i	0.398666	+	0.690509i
$741$	2.67527	+	0.588464i	0.0982785	+	0.0216178i
$742$	21.4019	+	21.1859i	0.785690	+	0.777760i
$743$	−9.49010	+	35.4175i	−0.348158	+	1.29934i	0.540721	+	0.841202i	$0.318151\pi$
$743$	−9.49010	+	35.4175i	−0.348158	+	1.29934i	−0.888879	+	0.458141i	$0.848515\pi$
$744$	10.8875	−	18.8578i	0.399157	−	0.691360i
$745$	−28.2544	−	48.9381i	−1.03516	−	1.79295i
$746$	26.2781	−	7.04119i	0.962109	−	0.257796i
$747$	−1.51210	+	1.51210i	−0.0553250	+	0.0553250i
$748$	−5.53384	+	1.48279i	−0.202337	+	0.0542161i
$749$	−0.236948	−	0.405640i	−0.00865788	−	0.0148218i
$750$	−12.3531	+	21.3962i	−0.451072	+	0.781279i
$751$	16.8445	+	9.72520i	0.614666	+	0.354877i	0.774789	−	0.632220i	$-0.217856\pi$
$751$	16.8445	+	9.72520i	0.614666	+	0.354877i	−0.160124	+	0.987097i	$0.551189\pi$
$752$	4.63013	+	4.63013i	0.168844	+	0.168844i
$753$	9.59948	+	5.54226i	0.349825	+	0.201971i
$754$	15.8631	+	3.48932i	0.577701	+	0.127074i
$755$		−	1.04446i		−	0.0380119i
$756$	1.34673	−	0.00683031i	0.0489803	−	0.000248416i
$757$	3.02968	+	5.24756i	0.110116	+	0.190726i	0.915817	−	0.401597i	$-0.131545\pi$
$757$	3.02968	+	5.24756i	0.110116	+	0.190726i	−0.805701	+	0.592322i	$0.798211\pi$
$758$			3.68944i			0.134006i
$759$	3.10894	+	11.6027i	0.112848	+	0.421153i
$760$	−1.74665	+	6.51859i	−0.0633577	+	0.236454i
$761$	21.3246	+	21.3246i	0.773016	+	0.773016i	0.978633	−	0.205616i	$-0.0659199\pi$
$761$	21.3246	+	21.3246i	0.773016	+	0.773016i	−0.205616	+	0.978633i	$0.565920\pi$
$762$	−8.72407	−	8.72407i	−0.316040	−	0.316040i
$763$	−3.48941	+	13.2919i	−0.126325	+	0.481200i
$764$	1.31502	−	0.759229i	0.0475759	−	0.0274679i
$765$	−3.24940	−	12.1269i	−0.117482	−	0.438449i
$766$	21.8270	−	37.8055i	0.788641	−	1.36597i
$767$	−3.43877	−	10.8440i	−0.124167	−	0.391553i
$768$	9.95269	−	5.74619i	0.359137	−	0.207348i
$769$	−22.1109	−	5.92460i	−0.797339	−	0.213646i	−0.162924	−	0.986639i	$-0.552092\pi$
$769$	−22.1109	−	5.92460i	−0.797339	−	0.213646i	−0.634415	+	0.772992i	$0.718759\pi$
$770$	14.0163	+	51.2682i	0.505114	+	1.84758i
$771$	−2.08124	−	1.20160i	−0.0749540	−	0.0432747i
$772$	0.344405	−	1.28534i	0.0123954	−	0.0462603i
$773$	14.5083	+	3.88749i	0.521827	+	0.139823i	0.510112	−	0.860108i	$-0.329604\pi$
$773$	14.5083	+	3.88749i	0.521827	+	0.139823i	0.0117156	+	0.999931i	$0.496271\pi$
$774$	19.3093	+	5.17392i	0.694059	+	0.185973i
$775$	21.8277	−	81.4619i	0.784073	−	2.92620i
$776$	25.5247	+	14.7367i	0.916283	+	0.529016i
$777$	−7.61073	+	28.9910i	−0.273033	+	1.04004i
$778$	−19.0090	−	5.09345i	−0.681506	−	0.182609i
$779$	−4.66170	+	2.69143i	−0.167023	+	0.0964306i
$780$	−5.09715	−	4.65523i	−0.182507	−	0.166684i
$781$	−12.2250	+	21.1743i	−0.437444	+	0.757675i
$782$	4.87498	+	18.1937i	0.174329	+	0.650605i
$783$	−2.46295	+	1.42199i	−0.0880187	+	0.0508176i
$784$	33.3109	−	0.337898i	1.18967	−	0.0120678i
$785$	−0.836308	−	0.836308i	−0.0298491	−	0.0298491i
$786$	−10.8740	−	10.8740i	−0.387864	−	0.387864i
$787$	2.26888	−	8.46757i	0.0808768	−	0.301836i	−0.913625	−	0.406559i	$-0.866729\pi$
$787$	2.26888	−	8.46757i	0.0808768	−	0.301836i	0.994501	+	0.104722i	$0.0333954\pi$
$788$	−0.108773	−	0.405946i	−0.00387487	−	0.0144612i
$789$		−	26.1246i		−	0.930061i
$790$	−33.0273	−	57.2049i	−1.17506	−	2.03526i
$791$	26.7106	+	45.7270i	0.949721	+	1.62586i
$792$			7.96327i			0.282962i
$793$	−2.02411	−	3.16568i	−0.0718783	−	0.112417i
$794$	−44.3277	−	25.5926i	−1.57313	−	0.908248i
$795$	19.1113	+	19.1113i	0.677808	+	0.677808i
$796$	−3.61555	−	2.08744i	−0.128150	−	0.0739874i
$797$	−21.7995	+	37.7578i	−0.772177	+	1.33745i	0.164190	+	0.986429i	$0.447499\pi$
$797$	−21.7995	+	37.7578i	−0.772177	+	1.33745i	−0.936367	+	0.351021i	$0.885834\pi$
$798$	2.74922	−	1.60591i	0.0973212	−	0.0568485i
$799$	−4.43627	+	1.18869i	−0.156944	+	0.0420530i
$800$	18.2052	−	18.2052i	0.643653	−	0.643653i
$801$	3.05671	−	0.819042i	0.108003	−	0.0289394i
$802$	11.1549	+	19.3209i	0.393893	+	0.682243i
$803$	3.64672	−	6.31630i	0.128690	−	0.222898i
$804$	0.389755	−	1.45459i	0.0137456	−	0.0512993i
$805$	34.1960	−	9.34894i	1.20525	−	0.329507i
$806$	46.7479	+	24.2375i	1.64663	+	0.853729i
$807$	−13.2101	−	22.8806i	−0.465018	−	0.805435i
$808$	−7.33507	+	7.33507i	−0.258047	+	0.258047i
$809$	12.6023			0.443072			0.221536	−	0.975152i	$-0.428893\pi$
$809$	12.6023			0.443072			0.221536	+	0.975152i	$0.428893\pi$
$810$	5.95776			0.209334
$811$	13.6469	−	13.6469i	0.479208	−	0.479208i	−0.425670	−	0.904878i	$-0.639962\pi$
$811$	13.6469	−	13.6469i	0.479208	−	0.479208i	0.904878	+	0.425670i	$0.139962\pi$
$812$	3.30723	−	1.93186i	0.116061	−	0.0677950i
$813$	−1.96029	−	7.31591i	−0.0687504	−	0.256580i
$814$	58.4454	+	15.6604i	2.04851	+	0.548896i
$815$	−3.07533	+	1.77554i	−0.107724	+	0.0621946i
$816$			15.8850i			0.556085i
$817$	9.26127	−	2.48155i	0.324011	−	0.0868185i
$818$	46.6777			1.63205
$819$	−0.480151	−	9.52730i	−0.0167778	−	0.332911i
$820$	13.5652			0.473718
$821$	26.7083	−	7.15646i	0.932125	−	0.249762i	0.239364	−	0.970930i	$-0.423061\pi$
$821$	26.7083	−	7.15646i	0.932125	−	0.249762i	0.692761	+	0.721168i	$0.256394\pi$
$822$		−	14.3950i		−	0.502085i
$823$	12.1313	−	7.00400i	0.422870	−	0.244144i	−0.273434	−	0.961891i	$-0.588160\pi$
$823$	12.1313	−	7.00400i	0.422870	−	0.244144i	0.696305	+	0.717746i	$0.254826\pi$
$824$	−30.4697	−	8.16433i	−1.06146	−	0.284418i
$825$	7.98249	+	29.7911i	0.277915	+	1.03719i
$826$	−11.4847	−	6.55326i	−0.399604	−	0.228017i
$827$	25.9908	−	25.9908i	0.903790	−	0.903790i	−0.0919718	−	0.995762i	$-0.529317\pi$
$827$	25.9908	−	25.9908i	0.903790	−	0.903790i	0.995762	+	0.0919718i	$0.0293170\pi$
$828$	−1.81337			−0.0630190
$829$	−3.18287			−0.110546			−0.0552728	−	0.998471i	$-0.517603\pi$
$829$	−3.18287			−0.110546			−0.0552728	+	0.998471i	$0.517603\pi$
$830$	9.00875	−	9.00875i	0.312698	−	0.312698i
$831$	−11.2715	−	19.5228i	−0.391004	−	0.677238i
$832$	−9.82669	−	15.3688i	−0.340679	−	0.532817i
$833$	−11.4769	+	20.3525i	−0.397650	+	0.705173i
$834$	−4.19173	+	15.6437i	−0.145148	+	0.541699i
$835$	4.55297	−	7.88598i	0.157562	−	0.272906i
$836$	−0.651978	−	1.12926i	−0.0225491	−	0.0390562i
$837$	−8.90596	+	2.38635i	−0.307835	+	0.0824842i
$838$	−13.7647	+	13.7647i	−0.475495	+	0.475495i
$839$	−15.7489	+	4.21991i	−0.543713	+	0.145687i	−0.520213	−	0.854036i	$-0.674148\pi$
$839$	−15.7489	+	4.21991i	−0.543713	+	0.145687i	−0.0234997	+	0.999724i	$0.507481\pi$
$840$	23.5016	−	0.119194i	0.810881	−	0.00411259i
$841$	10.4559	−	18.1102i	0.360549	−	0.624489i
$842$	−11.7985	−	6.81189i	−0.406605	−	0.234753i
$843$	−7.73479	−	7.73479i	−0.266400	−	0.266400i
$844$	4.73838	+	2.73570i	0.163102	+	0.0941668i
$845$	−31.3060	+	37.5601i	−1.07696	+	1.29211i
$846$		−	2.17947i		−	0.0749316i
$847$	0.848818	+	0.484342i	0.0291657	+	0.0166422i
$848$	−17.0984	−	29.6153i	−0.587161	−	1.01699i
$849$			17.7305i			0.608508i
$850$	12.5169	+	46.7139i	0.429328	+	1.60227i
$851$	10.4455	−	38.9832i	0.358068	−	1.33633i
$852$	−2.60996	−	2.60996i	−0.0894156	−	0.0894156i
$853$	−1.18686	−	1.18686i	−0.0406374	−	0.0406374i	0.686496	−	0.727133i	$-0.259148\pi$
$853$	−1.18686	−	1.18686i	−0.0406374	−	0.0406374i	−0.727133	+	0.686496i	$0.759148\pi$
$854$	−4.22428	−	1.10896i	−0.144552	−	0.0379479i
$855$	2.47467	−	1.42875i	0.0846319	−	0.0488623i
$856$	0.108532	+	0.405049i	0.00370956	+	0.0138443i
$857$	13.8735	−	24.0297i	0.473911	−	0.820838i	−0.525643	−	0.850705i	$-0.676175\pi$
$857$	13.8735	−	24.0297i	0.473911	−	0.820838i	0.999554	+	0.0298676i	$0.00950857\pi$
$858$	−19.2374	+	0.871725i	−0.656755	+	0.0297602i
$859$	33.2801	−	19.2142i	1.13550	−	0.655582i	0.190188	−	0.981748i	$-0.439090\pi$
$859$	33.2801	−	19.2142i	1.13550	−	0.655582i	0.945313	+	0.326166i	$0.105757\pi$
$860$	−23.3391	−	6.25369i	−0.795856	−	0.213249i
$861$	13.3224	+	13.1880i	0.454027	+	0.449444i
$862$	46.7952	+	27.0172i	1.59385	+	0.920210i
$863$	9.55027	−	35.6421i	0.325095	−	1.21327i	−0.589122	−	0.808044i	$-0.700526\pi$
$863$	9.55027	−	35.6421i	0.325095	−	1.21327i	0.914216	−	0.405226i	$-0.132807\pi$
$864$	−2.71883	−	0.728508i	−0.0924964	−	0.0247843i
$865$	−62.5671	−	16.7648i	−2.12735	−	0.570020i
$866$	12.1344	−	45.2864i	0.412345	−	1.53889i
$867$	5.07343	+	2.92914i	0.172303	+	0.0994790i
$868$	11.9777	−	3.27460i	0.406549	−	0.111147i
$869$	−36.1104	−	9.67574i	−1.22496	−	0.328227i
$870$	14.6737	−	8.47185i	0.497484	−	0.287222i
$871$	−10.4176	−	2.29150i	−0.352987	−	0.0776447i
$872$	6.13344	−	10.6234i	0.207705	−	0.359755i
$873$	−3.23001	−	12.0545i	−0.109319	−	0.407985i
$874$	−3.71268	+	2.14352i	−0.125583	+	0.0725055i
$875$	39.8062	−	10.8827i	1.34569	−	0.367903i
$876$	0.778552	+	0.778552i	0.0263048	+	0.0263048i
$877$	−33.3596	−	33.3596i	−1.12647	−	1.12647i	−0.990746	−	0.135727i	$-0.956663\pi$
$877$	−33.3596	−	33.3596i	−1.12647	−	1.12647i	−0.135727	−	0.990746i	$-0.543337\pi$
$878$	−7.55508	+	28.1959i	−0.254971	+	0.951566i
$879$	3.33616	+	12.4507i	0.112526	+	0.419953i
$880$		−	60.3545i		−	2.03455i
$881$	−6.77602	−	11.7364i	−0.228290	−	0.395410i	0.729011	−	0.684501i	$-0.239980\pi$
$881$	−6.77602	−	11.7364i	−0.228290	−	0.395410i	−0.957301	+	0.289092i	$0.906647\pi$
$882$	−7.91947	−	7.76042i	−0.266663	−	0.261307i
$883$			35.2962i			1.18781i	0.804534	+	0.593907i	$0.202415\pi$
$883$			35.2962i			1.18781i	−0.804534	+	0.593907i	$0.797585\pi$
$884$	−6.11985	+	0.277315i	−0.205833	+	0.00932711i
$885$	−10.2774	−	5.93368i	−0.345472	−	0.199459i
$886$	6.44097	+	6.44097i	0.216389	+	0.216389i
$887$	10.8483	+	6.26326i	0.364250	+	0.210300i	0.670943	−	0.741509i	$-0.265889\pi$
$887$	10.8483	+	6.26326i	0.364250	+	0.210300i	−0.306694	+	0.951808i	$0.599223\pi$
$888$	13.3776	−	23.1707i	0.448923	−	0.777558i
$889$	0.104516	+	20.6075i	0.00350536	+	0.691153i
$890$	−18.2111	+	4.87966i	−0.610438	+	0.163566i
$891$	2.38426	−	2.38426i	0.0798757	−	0.0798757i
$892$	−2.92208	+	0.782969i	−0.0978384	+	0.0262157i
$893$	−0.522666	−	0.905284i	−0.0174903	−	0.0302942i
$894$	11.8990	−	20.6096i	0.397960	−	0.689288i
$895$	−3.35116	+	12.5067i	−0.112017	+	0.418053i
$896$	−34.9142	−	9.16569i	−1.16640	−	0.306204i
$897$	0.581443	+	12.8314i	0.0194138	+	0.428429i
$898$	−15.5985	−	27.0173i	−0.520528	−	0.901580i
$899$	−18.5416	+	18.5416i	−0.618397	+	0.618397i
$900$	−4.65599			−0.155200
$901$	23.9856			0.799077
$902$	26.7586	−	26.7586i	0.890963	−	0.890963i
$903$	−16.8416	−	28.8318i	−0.560452	−	0.959461i
$904$	−12.2346	−	45.6603i	−0.406918	−	1.51864i
$905$	94.3754	+	25.2878i	3.13714	+	0.840595i
$906$	0.380931	−	0.219930i	0.0126556	−	0.00730670i
$907$		−	37.7929i		−	1.25489i	−0.778659	−	0.627447i	$-0.784100\pi$
$907$		−	37.7929i		−	1.25489i	0.778659	−	0.627447i	$-0.215900\pi$
$908$	−10.0239	+	2.68590i	−0.332656	+	0.0891349i
$909$	4.39234			0.145685
$910$	2.86062	+	56.7614i	0.0948287	+	1.88162i
$911$	−15.1976			−0.503520			−0.251760	−	0.967790i	$-0.581009\pi$
$911$	−15.1976			−0.503520			−0.251760	+	0.967790i	$0.581009\pi$
$912$	−3.49229	+	0.935756i	−0.115641	+	0.0309860i
$913$		−	7.21049i		−	0.238633i
$914$	4.26629	−	2.46314i	0.141116	−	0.0814736i
$915$	−3.78615	−	1.01450i	−0.125166	−	0.0335382i
$916$	1.13072	+	4.21991i	0.0373601	+	0.139430i
$917$	0.130273	+	25.6860i	0.00430200	+	0.848226i
$918$	3.73864	−	3.73864i	0.123393	−	0.123393i
$919$	−18.9861			−0.626294			−0.313147	−	0.949705i	$-0.601383\pi$
$919$	−18.9861			−0.626294			−0.313147	+	0.949705i	$0.601383\pi$
$920$	−31.6448			−1.04330
$921$	−5.82305	+	5.82305i	−0.191876	+	0.191876i
$922$	24.8978	+	43.1242i	0.819964	+	1.42022i
$923$	−17.6312	+	19.3049i	−0.580337	+	0.635429i
$924$	−3.19468	+	3.22725i	−0.105097	+	0.106169i
$925$	26.8198	−	100.093i	0.881830	−	3.29103i
$926$	−11.5311	+	19.9724i	−0.378934	+	0.656333i
$927$	6.67838	+	11.5673i	0.219347	+	0.379920i
$928$	−7.73226	+	2.07185i	−0.253824	+	0.0680119i
$929$	19.0139	−	19.0139i	0.623827	−	0.623827i	−0.322681	−	0.946508i	$-0.604584\pi$
$929$	19.0139	−	19.0139i	0.623827	−	0.623827i	0.946508	+	0.322681i	$0.104584\pi$
$930$	53.0596	−	14.2173i	1.73989	−	0.466203i
$931$	−5.15056	−	1.32424i	−0.168803	−	0.0434003i
$932$	−1.27978	+	2.21665i	−0.0419207	+	0.0726089i
$933$	23.4318	+	13.5284i	0.767124	+	0.442899i
$934$	−14.0349	−	14.0349i	−0.459237	−	0.459237i
$935$	36.6611	+	21.1663i	1.19895	+	0.692212i
$936$	−1.82931	+	8.31638i	−0.0597928	+	0.271829i
$937$			55.8288i			1.82385i	0.410358	+	0.911924i	$0.365404\pi$
$937$			55.8288i			1.82385i	−0.410358	+	0.911924i	$0.634596\pi$
$938$	−10.7056	+	6.25347i	−0.349549	+	0.204183i
$939$	6.86374	+	11.8883i	0.223990	+	0.387962i
$940$			2.63431i			0.0859218i
$941$	−12.8732	−	48.0434i	−0.419654	−	1.56617i	−0.775328	−	0.631559i	$-0.782416\pi$
$941$	−12.8732	−	48.0434i	−0.419654	−	1.56617i	0.355675	−	0.934610i	$-0.384251\pi$
$942$	0.128914	−	0.481113i	0.00420024	−	0.0156755i
$943$	−17.8481	−	17.8481i	−0.581213	−	0.581213i
$944$	10.6174	+	10.6174i	0.345568	+	0.345568i
$945$	−7.07223	−	7.00085i	−0.230060	−	0.227738i
$946$	−58.3744	+	33.7025i	−1.89791	+	1.09576i
$947$	8.29083	+	30.9418i	0.269416	+	1.00547i	0.959492	+	0.281736i	$0.0909103\pi$
$947$	8.29083	+	30.9418i	0.269416	+	1.00547i	−0.690076	+	0.723737i	$0.742423\pi$
$948$	2.82181	−	4.88752i	0.0916482	−	0.158739i
$949$	5.25940	−	5.75867i	0.170727	−	0.186934i
$950$	−9.53263	+	5.50367i	−0.309279	+	0.178563i
$951$	−2.23807	−	0.599689i	−0.0725743	−	0.0194462i
$952$	14.6730	−	14.8226i	0.475555	−	0.480403i
$953$	−25.2887	−	14.6005i	−0.819182	−	0.472955i	0.0309522	−	0.999521i	$-0.490146\pi$
$953$	−25.2887	−	14.6005i	−0.819182	−	0.472955i	−0.850134	+	0.526566i	$0.823479\pi$
$954$	−2.94594	+	10.9944i	−0.0953783	+	0.355957i
$955$	−10.8377	−	2.90396i	−0.350701	−	0.0939700i
$956$	−8.10547	−	2.17185i	−0.262150	−	0.0702428i
$957$	2.48193	−	9.26269i	0.0802294	−	0.299420i
$958$	−28.7625	−	16.6060i	−0.929274	−	0.536517i
$959$	−16.9153	+	17.0878i	−0.546225	+	0.551794i
$960$	−18.3811	−	4.92519i	−0.593247	−	0.158960i
$961$	−46.7748	+	27.0054i	−1.50886	+	0.871143i
$962$	57.4395	+	29.7808i	1.85192	+	0.960171i
$963$	0.0887791	−	0.153770i	0.00286087	−	0.00495516i
$964$	0.743748	+	2.77571i	0.0239545	+	0.0893995i
$965$	−8.51522	+	4.91627i	−0.274115	+	0.158260i
$966$	10.6103	+	10.5032i	0.341380	+	0.337934i
$967$	−28.2620	−	28.2620i	−0.908844	−	0.908844i	0.0873352	−	0.996179i	$-0.472165\pi$
$967$	−28.2620	−	28.2620i	−0.908844	−	0.908844i	−0.996179	+	0.0873352i	$0.972165\pi$
$968$	−0.616849	−	0.616849i	−0.0198263	−	0.0198263i
$969$	0.656339	−	2.44949i	0.0210846	−	0.0786890i
$970$	19.2436	+	71.8181i	0.617875	+	2.30594i
$971$			14.0049i			0.449439i	0.974424	+	0.224719i	$0.0721465\pi$
$971$			14.0049i			0.449439i	−0.974424	+	0.224719i	$0.927853\pi$
$972$	0.254512	+	0.440828i	0.00816348	+	0.0141396i
$973$	23.3585	−	13.6445i	0.748839	−	0.437421i
$974$			17.0854i			0.547450i
$975$	1.49291	+	32.9458i	0.0478113	+	1.05511i
$976$	4.29502	+	2.47973i	0.137480	+	0.0793742i
$977$	14.8724	+	14.8724i	0.475811	+	0.475811i	0.903789	−	0.427978i	$-0.140774\pi$
$977$	14.8724	+	14.8724i	0.475811	+	0.475811i	−0.427978	+	0.903789i	$0.640774\pi$
$978$	−1.29513	−	0.747745i	−0.0414138	−	0.0239102i
$979$	−5.33517	+	9.24079i	−0.170513	+	0.295337i
$980$	9.57223	+	9.37998i	0.305774	+	0.299633i
$981$	−5.01713	+	1.34434i	−0.160185	+	0.0429213i
$982$	−39.7461	+	39.7461i	−1.26835	+	1.26835i
$983$	7.34307	−	1.96757i	0.234208	−	0.0627558i	−0.139806	−	0.990179i	$-0.544648\pi$
$983$	7.34307	−	1.96757i	0.234208	−	0.0627558i	0.374014	+	0.927423i	$0.377981\pi$
$984$	−8.36663	−	14.4914i	−0.266718	−	0.461970i
$985$	−1.55270	+	2.68935i	−0.0494730	+	0.0856897i
$986$	3.89179	−	14.5244i	0.123940	−	0.462550i
$987$	−2.56105	+	2.58716i	−0.0815192	+	0.0823503i
$988$	−0.421477	−	1.32910i	−0.0134090	−	0.0422845i
$989$	22.4796	+	38.9359i	0.714811	+	1.23809i
$990$	−14.2048	+	14.2048i	−0.451459	+	0.451459i
$991$	24.6261			0.782275			0.391138	−	0.920332i	$-0.372082\pi$
$991$	24.6261			0.782275			0.391138	+	0.920332i	$0.372082\pi$
$992$	−25.9522			−0.823985
$993$	−18.2666	+	18.2666i	−0.579674	+	0.579674i
$994$	0.154122	+	30.3882i	0.00488845	+	0.963856i
$995$	7.98422	+	29.7975i	0.253117	+	0.944645i
$996$	1.05143	+	0.281729i	0.0333157	+	0.00892692i
$997$	−14.2687	+	8.23802i	−0.451893	+	0.260901i	−0.708629	−	0.705581i	$-0.750686\pi$
$997$	−14.2687	+	8.23802i	−0.451893	+	0.260901i	0.256736	+	0.966482i	$0.417353\pi$
$998$			8.13347i			0.257461i
$999$	−10.9428	+	2.93212i	−0.346216	+	0.0927682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.115.2	yes	36
3.2	odd	2		819.2.gh.c.388.8		36
7.5	odd	6		273.2.bt.a.271.8	yes	36
13.6	odd	12		273.2.bt.a.136.8	✓	36
21.5	even	6		819.2.et.c.271.2		36
39.32	even	12		819.2.et.c.136.2		36
91.19	even	12	inner	273.2.cg.a.19.2	yes	36
273.110	odd	12		819.2.gh.c.19.8		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.8	✓	36	13.6	odd	12
273.2.bt.a.271.8	yes	36	7.5	odd	6
273.2.cg.a.19.2	yes	36	91.19	even	12	inner
273.2.cg.a.115.2	yes	36	1.1	even	1	trivial
819.2.et.c.136.2		36	39.32	even	12
819.2.et.c.271.2		36	21.5	even	6
819.2.gh.c.19.8		36	273.110	odd	12
819.2.gh.c.388.8		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53002 + 0.409967i) q^{2} +1.00000i q^{3} +(0.440828 - 0.254512i) q^{4} +(-3.63307 - 0.973479i) q^{5} +(-0.409967 - 1.53002i) q^{6} +(-1.31124 + 2.29797i) q^{7} +(1.66997 - 1.66997i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.53002 + 0.409967i) q^{2} +1.00000i q^{3} +(0.440828 - 0.254512i) q^{4} +(-3.63307 - 0.973479i) q^{5} +(-0.409967 - 1.53002i) q^{6} +(-1.31124 + 2.29797i) q^{7} +(1.66997 - 1.66997i) q^{8} -1.00000 q^{9} +5.95776 q^{10} +(2.38426 - 2.38426i) q^{11} +(0.254512 + 0.440828i) q^{12} +(3.03769 - 1.94228i) q^{13} +(1.06413 - 4.05349i) q^{14} +(0.973479 - 3.63307i) q^{15} +(-2.37947 + 4.12137i) q^{16} +(-1.66896 - 2.89072i) q^{17} +(1.53002 - 0.409967i) q^{18} +(0.537206 - 0.537206i) q^{19} +(-1.84932 + 0.495525i) q^{20} +(-2.29797 - 1.31124i) q^{21} +(-2.67049 + 4.62542i) q^{22} +(3.08517 + 1.78122i) q^{23} +(1.66997 + 1.66997i) q^{24} +(7.92144 + 4.57345i) q^{25} +(-3.85145 + 4.21707i) q^{26} -1.00000i q^{27} +(0.00683031 + 1.34673i) q^{28} +(-1.42199 - 2.46295i) q^{29} +5.95776i q^{30} +(-2.38635 - 8.90596i) q^{31} +(0.728508 - 2.71883i) q^{32} +(2.38426 + 2.38426i) q^{33} +(3.73864 + 3.73864i) q^{34} +(7.00085 - 7.07223i) q^{35} +(-0.440828 + 0.254512i) q^{36} +(-2.93212 - 10.9428i) q^{37} +(-0.601698 + 1.04217i) q^{38} +(1.94228 + 3.03769i) q^{39} +(-7.69280 + 4.44144i) q^{40} +(-6.84386 - 1.83381i) q^{41} +(4.05349 + 1.06413i) q^{42} +(10.9295 + 6.31017i) q^{43} +(0.444225 - 1.65787i) q^{44} +(3.63307 + 0.973479i) q^{45} +(-5.45060 - 1.46048i) q^{46} +(0.356118 - 1.32905i) q^{47} +(-4.12137 - 2.37947i) q^{48} +(-3.56131 - 6.02636i) q^{49} +(-13.9949 - 3.74992i) q^{50} +(2.89072 - 1.66896i) q^{51} +(0.844767 - 1.62934i) q^{52} +(-3.59290 + 6.22308i) q^{53} +(0.409967 + 1.53002i) q^{54} +(-10.9832 + 6.34116i) q^{55} +(1.64781 + 6.02726i) q^{56} +(0.537206 + 0.537206i) q^{57} +(3.18539 + 3.18539i) q^{58} +(0.816620 - 3.04767i) q^{59} +(-0.495525 - 1.84932i) q^{60} -1.04213i q^{61} +(7.30230 + 12.6480i) q^{62} +(1.31124 - 2.29797i) q^{63} -5.05937i q^{64} +(-12.9269 + 4.09930i) q^{65} +(-4.62542 - 2.67049i) q^{66} +(-2.09191 - 2.09191i) q^{67} +(-1.47145 - 0.849541i) q^{68} +(-1.78122 + 3.08517i) q^{69} +(-7.81204 + 13.6907i) q^{70} +(-7.00412 + 1.87675i) q^{71} +(-1.66997 + 1.66997i) q^{72} +(2.08933 - 0.559835i) q^{73} +(8.97239 + 15.5406i) q^{74} +(-4.57345 + 7.92144i) q^{75} +(0.100090 - 0.373541i) q^{76} +(2.35262 + 8.60528i) q^{77} +(-4.21707 - 3.85145i) q^{78} +(-5.54357 - 9.60175i) q^{79} +(12.6569 - 12.6569i) q^{80} +1.00000 q^{81} +11.2230 q^{82} +(1.51210 - 1.51210i) q^{83} +(-1.34673 + 0.00683031i) q^{84} +(3.24940 + 12.1269i) q^{85} +(-19.3093 - 5.17392i) q^{86} +(2.46295 - 1.42199i) q^{87} -7.96327i q^{88} +(-3.05671 + 0.819042i) q^{89} -5.95776 q^{90} +(0.480151 + 9.52730i) q^{91} +1.81337 q^{92} +(8.90596 - 2.38635i) q^{93} +2.17947i q^{94} +(-2.47467 + 1.42875i) q^{95} +(2.71883 + 0.728508i) q^{96} +(3.23001 + 12.0545i) q^{97} +(7.91947 + 7.76042i) q^{98} +(-2.38426 + 2.38426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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