LMFDB - Embedded newform 287.2.h.b.78.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			78.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	287.78
Dual form			287.2.h.b.92.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.224514i) q^{2} +0.381966 q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.500000 + 1.53884i) q^{5} +(-0.118034 + 0.0857567i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.454915 - 1.40008i) q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.224514i) q^{2} +0.381966 q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.500000 + 1.53884i) q^{5} +(-0.118034 + 0.0857567i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.454915 - 1.40008i) q^{8} -2.85410 q^{9} +(-0.190983 - 0.587785i) q^{10} +(1.19098 + 3.66547i) q^{11} +(-0.218847 + 0.673542i) q^{12} +(-1.80902 + 1.31433i) q^{13} +0.381966 q^{14} +(-0.190983 + 0.587785i) q^{15} +(-2.54508 - 1.84911i) q^{16} +(-0.454915 - 1.40008i) q^{17} +(0.881966 - 0.640786i) q^{18} +(-0.618034 - 0.449028i) q^{19} +(-2.42705 - 1.76336i) q^{20} +(-0.309017 - 0.224514i) q^{21} +(-1.19098 - 0.865300i) q^{22} +(0.190983 - 0.138757i) q^{23} +(-0.173762 - 0.534785i) q^{24} +(1.92705 + 1.40008i) q^{25} +(0.263932 - 0.812299i) q^{26} -2.23607 q^{27} +(1.50000 - 1.08981i) q^{28} +(-1.23607 + 3.80423i) q^{29} +(-0.0729490 - 0.224514i) q^{30} +(2.69098 + 8.28199i) q^{31} +4.14590 q^{32} +(0.454915 + 1.40008i) q^{33} +(0.454915 + 0.330515i) q^{34} +(1.30902 - 0.951057i) q^{35} +(1.63525 - 5.03280i) q^{36} +(-1.66312 + 5.11855i) q^{37} +0.291796 q^{38} +(-0.690983 + 0.502029i) q^{39} +2.38197 q^{40} +(6.39919 + 0.224514i) q^{41} +0.145898 q^{42} +(-3.61803 + 2.62866i) q^{43} -7.14590 q^{44} +(1.42705 - 4.39201i) q^{45} +(-0.0278640 + 0.0857567i) q^{46} +(9.35410 - 6.79615i) q^{47} +(-0.972136 - 0.706298i) q^{48} +(0.309017 + 0.951057i) q^{49} -0.909830 q^{50} +(-0.173762 - 0.534785i) q^{51} +(-1.28115 - 3.94298i) q^{52} +(3.47214 - 10.6861i) q^{53} +(0.690983 - 0.502029i) q^{54} -6.23607 q^{55} +(-0.454915 + 1.40008i) q^{56} +(-0.236068 - 0.171513i) q^{57} +(-0.472136 - 1.45309i) q^{58} +(4.35410 - 3.16344i) q^{59} +(-0.927051 - 0.673542i) q^{60} +(-2.04508 - 1.48584i) q^{61} +(-2.69098 - 1.95511i) q^{62} +(2.30902 + 1.67760i) q^{63} +(3.80902 - 2.76741i) q^{64} +(-1.11803 - 3.44095i) q^{65} +(-0.454915 - 0.330515i) q^{66} +(-1.21885 + 3.75123i) q^{67} +2.72949 q^{68} +(0.0729490 - 0.0530006i) q^{69} +(-0.190983 + 0.587785i) q^{70} +(2.71885 + 8.36775i) q^{71} +(1.29837 + 3.99598i) q^{72} +10.7082 q^{73} +(-0.635255 - 1.95511i) q^{74} +(0.736068 + 0.534785i) q^{75} +(1.14590 - 0.832544i) q^{76} +(1.19098 - 3.66547i) q^{77} +(0.100813 - 0.310271i) q^{78} -12.0902 q^{79} +(4.11803 - 2.99193i) q^{80} +7.70820 q^{81} +(-2.02786 + 1.36733i) q^{82} -6.85410 q^{83} +(0.572949 - 0.416272i) q^{84} +2.38197 q^{85} +(0.527864 - 1.62460i) q^{86} +(-0.472136 + 1.45309i) q^{87} +(4.59017 - 3.33495i) q^{88} +(4.11803 + 2.99193i) q^{89} +(0.545085 + 1.67760i) q^{90} +2.23607 q^{91} +(0.135255 + 0.416272i) q^{92} +(1.02786 + 3.16344i) q^{93} +(-1.36475 + 4.20025i) q^{94} +(1.00000 - 0.726543i) q^{95} +1.58359 q^{96} +(2.97214 - 9.14729i) q^{97} +(-0.309017 - 0.224514i) q^{98} +(-3.39919 - 10.4616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 6 q^{3} - 9 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 13 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + q^2 + 6 * q^3 - 9 * q^4 - 2 * q^5 + 4 * q^6 - q^7 - 13 * q^8 + 2 * q^9	\( 4 q + q^{2} + 6 q^{3} - 9 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 13 q^{8} + 2 q^{9} - 3 q^{10} + 7 q^{11} - 21 q^{12} - 5 q^{13} + 6 q^{14} - 3 q^{15} + q^{16} - 13 q^{17} + 8 q^{18} + 2 q^{19} - 3 q^{20} + q^{21} - 7 q^{22} + 3 q^{23} - 32 q^{24} + q^{25} + 10 q^{26} + 6 q^{28} + 4 q^{29} - 7 q^{30} + 13 q^{31} + 30 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} - 27 q^{36} + 9 q^{37} + 28 q^{38} - 5 q^{39} + 14 q^{40} + q^{41} + 14 q^{42} - 10 q^{43} - 42 q^{44} - q^{45} - 18 q^{46} + 24 q^{47} + 14 q^{48} - q^{49} - 26 q^{50} - 32 q^{51} + 15 q^{52} - 4 q^{53} + 5 q^{54} - 16 q^{55} - 13 q^{56} + 8 q^{57} + 16 q^{58} + 4 q^{59} + 3 q^{60} + 3 q^{61} - 13 q^{62} + 7 q^{63} + 13 q^{64} - 13 q^{66} - 25 q^{67} + 78 q^{68} + 7 q^{69} - 3 q^{70} + 31 q^{71} - 44 q^{72} + 16 q^{73} + 31 q^{74} - 6 q^{75} + 18 q^{76} + 7 q^{77} + 25 q^{78} - 26 q^{79} + 12 q^{80} + 4 q^{81} - 26 q^{82} - 14 q^{83} + 9 q^{84} + 14 q^{85} + 20 q^{86} + 16 q^{87} - 4 q^{88} + 12 q^{89} - 9 q^{90} - 33 q^{92} + 22 q^{93} - 39 q^{94} + 4 q^{95} + 60 q^{96} - 6 q^{97} + q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q + q^2 + 6 * q^3 - 9 * q^4 - 2 * q^5 + 4 * q^6 - q^7 - 13 * q^8 + 2 * q^9 - 3 * q^10 + 7 * q^11 - 21 * q^12 - 5 * q^13 + 6 * q^14 - 3 * q^15 + q^16 - 13 * q^17 + 8 * q^18 + 2 * q^19 - 3 * q^20 + q^21 - 7 * q^22 + 3 * q^23 - 32 * q^24 + q^25 + 10 * q^26 + 6 * q^28 + 4 * q^29 - 7 * q^30 + 13 * q^31 + 30 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 - 27 * q^36 + 9 * q^37 + 28 * q^38 - 5 * q^39 + 14 * q^40 + q^41 + 14 * q^42 - 10 * q^43 - 42 * q^44 - q^45 - 18 * q^46 + 24 * q^47 + 14 * q^48 - q^49 - 26 * q^50 - 32 * q^51 + 15 * q^52 - 4 * q^53 + 5 * q^54 - 16 * q^55 - 13 * q^56 + 8 * q^57 + 16 * q^58 + 4 * q^59 + 3 * q^60 + 3 * q^61 - 13 * q^62 + 7 * q^63 + 13 * q^64 - 13 * q^66 - 25 * q^67 + 78 * q^68 + 7 * q^69 - 3 * q^70 + 31 * q^71 - 44 * q^72 + 16 * q^73 + 31 * q^74 - 6 * q^75 + 18 * q^76 + 7 * q^77 + 25 * q^78 - 26 * q^79 + 12 * q^80 + 4 * q^81 - 26 * q^82 - 14 * q^83 + 9 * q^84 + 14 * q^85 + 20 * q^86 + 16 * q^87 - 4 * q^88 + 12 * q^89 - 9 * q^90 - 33 * q^92 + 22 * q^93 - 39 * q^94 + 4 * q^95 + 60 * q^96 - 6 * q^97 + q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.309017	+	0.224514i	−0.218508	+	0.158755i	−0.691655	−	0.722228i	$-0.743118\pi$
$2$	−0.309017	+	0.224514i	−0.218508	+	0.158755i	0.473147	+	0.880984i	$0.343118\pi$
$3$	0.381966			0.220528			0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966			0.220528			0.110264	+	0.993902i	$0.464830\pi$
$4$	−0.572949	+	1.76336i	−0.286475	+	0.881678i
$5$	−0.500000	+	1.53884i	−0.223607	+	0.688191i	0.774823	+	0.632178i	$0.217839\pi$
$5$	−0.500000	+	1.53884i	−0.223607	+	0.688191i	−0.998430	+	0.0560130i	$0.982161\pi$
$6$	−0.118034	+	0.0857567i	−0.0481872	+	0.0350100i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−0.454915	−	1.40008i	−0.160837	−	0.495005i
$9$	−2.85410			−0.951367
$10$	−0.190983	−	0.587785i	−0.0603941	−	0.185874i
$11$	1.19098	+	3.66547i	0.359095	+	1.10518i	0.953597	+	0.301086i	$0.0973492\pi$
$11$	1.19098	+	3.66547i	0.359095	+	1.10518i	−0.594502	+	0.804094i	$0.702651\pi$
$12$	−0.218847	+	0.673542i	−0.0631757	+	0.194435i
$13$	−1.80902	+	1.31433i	−0.501731	+	0.364529i	−0.809678	−	0.586875i	$-0.800358\pi$
$13$	−1.80902	+	1.31433i	−0.501731	+	0.364529i	0.307947	+	0.951404i	$0.400358\pi$
$14$	0.381966			0.102085
$15$	−0.190983	+	0.587785i	−0.0493116	+	0.151765i
$16$	−2.54508	−	1.84911i	−0.636271	−	0.462278i
$17$	−0.454915	−	1.40008i	−0.110333	−	0.339570i	0.880612	−	0.473838i	$-0.157132\pi$
$17$	−0.454915	−	1.40008i	−0.110333	−	0.339570i	−0.990945	+	0.134268i	$0.957132\pi$
$18$	0.881966	−	0.640786i	0.207881	−	0.151035i
$19$	−0.618034	−	0.449028i	−0.141787	−	0.103014i	0.514631	−	0.857412i	$-0.327929\pi$
$19$	−0.618034	−	0.449028i	−0.141787	−	0.103014i	−0.656418	+	0.754398i	$0.727929\pi$
$20$	−2.42705	−	1.76336i	−0.542705	−	0.394298i
$21$	−0.309017	−	0.224514i	−0.0674330	−	0.0489930i
$22$	−1.19098	−	0.865300i	−0.253918	−	0.184483i
$23$	0.190983	−	0.138757i	0.0398227	−	0.0289329i	−0.567696	−	0.823238i	$-0.692165\pi$
$23$	0.190983	−	0.138757i	0.0398227	−	0.0289329i	0.607519	+	0.794305i	$0.292165\pi$
$24$	−0.173762	−	0.534785i	−0.0354690	−	0.109162i
$25$	1.92705	+	1.40008i	0.385410	+	0.280017i
$26$	0.263932	−	0.812299i	0.0517613	−	0.159305i
$27$	−2.23607			−0.430331
$28$	1.50000	−	1.08981i	0.283473	−	0.205955i
$29$	−1.23607	+	3.80423i	−0.229532	+	0.706427i	0.768268	+	0.640129i	$0.221119\pi$
$29$	−1.23607	+	3.80423i	−0.229532	+	0.706427i	−0.997800	+	0.0662984i	$0.978881\pi$
$30$	−0.0729490	−	0.224514i	−0.0133186	−	0.0409905i
$31$	2.69098	+	8.28199i	0.483315	+	1.48749i	0.834407	+	0.551149i	$0.185810\pi$
$31$	2.69098	+	8.28199i	0.483315	+	1.48749i	−0.351092	+	0.936341i	$0.614190\pi$
$32$	4.14590			0.732898
$33$	0.454915	+	1.40008i	0.0791905	+	0.243723i
$34$	0.454915	+	0.330515i	0.0780173	+	0.0566829i
$35$	1.30902	−	0.951057i	0.221264	−	0.160758i
$36$	1.63525	−	5.03280i	0.272542	−	0.838800i
$37$	−1.66312	+	5.11855i	−0.273415	+	0.841485i	0.716219	+	0.697875i	$0.245871\pi$
$37$	−1.66312	+	5.11855i	−0.273415	+	0.841485i	−0.989634	+	0.143610i	$0.954129\pi$
$38$	0.291796			0.0473356
$39$	−0.690983	+	0.502029i	−0.110646	+	0.0803889i
$40$	2.38197			0.376622
$41$	6.39919	+	0.224514i	0.999385	+	0.0350632i
$41$	6.39919	+	0.224514i	0.999385	+	0.0350632i
$42$	0.145898			0.0225126
$43$	−3.61803	+	2.62866i	−0.551745	+	0.400866i	−0.828428	−	0.560095i	$-0.810765\pi$
$43$	−3.61803	+	2.62866i	−0.551745	+	0.400866i	0.276683	+	0.960961i	$0.410765\pi$
$44$	−7.14590			−1.07728
$45$	1.42705	−	4.39201i	0.212732	−	0.654722i
$46$	−0.0278640	+	0.0857567i	−0.00410833	+	0.0126441i
$47$	9.35410	−	6.79615i	1.36444	−	0.991321i	0.366287	−	0.930502i	$-0.380629\pi$
$47$	9.35410	−	6.79615i	1.36444	−	0.991321i	0.998149	−	0.0608189i	$-0.0193712\pi$
$48$	−0.972136	−	0.706298i	−0.140316	−	0.101945i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.909830			−0.128669
$51$	−0.173762	−	0.534785i	−0.0243316	−	0.0748848i
$52$	−1.28115	−	3.94298i	−0.177664	−	0.546793i
$53$	3.47214	−	10.6861i	0.476935	−	1.46785i	−0.366396	−	0.930459i	$-0.619409\pi$
$53$	3.47214	−	10.6861i	0.476935	−	1.46785i	0.843331	−	0.537395i	$-0.180591\pi$
$54$	0.690983	−	0.502029i	0.0940309	−	0.0683174i
$55$	−6.23607			−0.840871
$56$	−0.454915	+	1.40008i	−0.0607906	+	0.187094i
$57$	−0.236068	−	0.171513i	−0.0312680	−	0.0227175i
$58$	−0.472136	−	1.45309i	−0.0619945	−	0.190799i
$59$	4.35410	−	3.16344i	0.566856	−	0.411845i	−0.267106	−	0.963667i	$-0.586067\pi$
$59$	4.35410	−	3.16344i	0.566856	−	0.411845i	0.833962	+	0.551822i	$0.186067\pi$
$60$	−0.927051	−	0.673542i	−0.119682	−	0.0869539i
$61$	−2.04508	−	1.48584i	−0.261846	−	0.190242i	0.449114	−	0.893474i	$-0.351740\pi$
$61$	−2.04508	−	1.48584i	−0.261846	−	0.190242i	−0.710961	+	0.703232i	$0.751740\pi$
$62$	−2.69098	−	1.95511i	−0.341755	−	0.248300i
$63$	2.30902	+	1.67760i	0.290909	+	0.211358i
$64$	3.80902	−	2.76741i	0.476127	−	0.345927i
$65$	−1.11803	−	3.44095i	−0.138675	−	0.426798i
$66$	−0.454915	−	0.330515i	−0.0559962	−	0.0406836i
$67$	−1.21885	+	3.75123i	−0.148906	+	0.458285i	−0.997493	−	0.0707712i	$-0.977454\pi$
$67$	−1.21885	+	3.75123i	−0.148906	+	0.458285i	0.848587	+	0.529056i	$0.177454\pi$
$68$	2.72949			0.330999
$69$	0.0729490	−	0.0530006i	0.00878203	−	0.00638052i
$70$	−0.190983	+	0.587785i	−0.0228268	+	0.0702538i
$71$	2.71885	+	8.36775i	0.322668	+	0.993069i	0.972482	+	0.232977i	$0.0748465\pi$
$71$	2.71885	+	8.36775i	0.322668	+	0.993069i	−0.649815	+	0.760093i	$0.725153\pi$
$72$	1.29837	+	3.99598i	0.153015	+	0.470931i
$73$	10.7082			1.25330			0.626650	−	0.779301i	$-0.284425\pi$
$73$	10.7082			1.25330			0.626650	+	0.779301i	$0.284425\pi$
$74$	−0.635255	−	1.95511i	−0.0738469	−	0.227277i
$75$	0.736068	+	0.534785i	0.0849938	+	0.0617516i
$76$	1.14590	−	0.832544i	0.131444	−	0.0954993i
$77$	1.19098	−	3.66547i	0.135725	−	0.417719i
$78$	0.100813	−	0.310271i	0.0114148	−	0.0351312i
$79$	−12.0902			−1.36025			−0.680125	−	0.733096i	$-0.738075\pi$
$79$	−12.0902			−1.36025			−0.680125	+	0.733096i	$0.738075\pi$
$80$	4.11803	−	2.99193i	0.460410	−	0.334508i
$81$	7.70820			0.856467
$82$	−2.02786	+	1.36733i	−0.223940	+	0.150996i
$83$	−6.85410			−0.752335			−0.376168	−	0.926552i	$-0.622758\pi$
$83$	−6.85410			−0.752335			−0.376168	+	0.926552i	$0.622758\pi$
$84$	0.572949	−	0.416272i	0.0625139	−	0.0454190i
$85$	2.38197			0.258360
$86$	0.527864	−	1.62460i	0.0569210	−	0.175185i
$87$	−0.472136	+	1.45309i	−0.0506183	+	0.155787i
$88$	4.59017	−	3.33495i	0.489314	−	0.355507i
$89$	4.11803	+	2.99193i	0.436511	+	0.317144i	0.784247	−	0.620449i	$-0.213050\pi$
$89$	4.11803	+	2.99193i	0.436511	+	0.317144i	−0.347736	+	0.937592i	$0.613050\pi$
$90$	0.545085	+	1.67760i	0.0574570	+	0.176834i
$91$	2.23607			0.234404
$92$	0.135255	+	0.416272i	0.0141013	+	0.0433993i
$93$	1.02786	+	3.16344i	0.106585	+	0.328033i
$94$	−1.36475	+	4.20025i	−0.140763	+	0.433223i
$95$	1.00000	−	0.726543i	0.102598	−	0.0745417i
$96$	1.58359			0.161625
$97$	2.97214	−	9.14729i	0.301775	−	0.928767i	−0.679086	−	0.734058i	$-0.737624\pi$
$97$	2.97214	−	9.14729i	0.301775	−	0.928767i	0.980861	−	0.194709i	$-0.0623761\pi$
$98$	−0.309017	−	0.224514i	−0.0312154	−	0.0226793i
$99$	−3.39919	−	10.4616i	−0.341631	−	1.05143i
$100$	−3.57295	+	2.59590i	−0.357295	+	0.259590i
$101$	9.51722	+	6.91467i	0.946999	+	0.688035i	0.950095	−	0.311960i	$-0.100986\pi$
$101$	9.51722	+	6.91467i	0.946999	+	0.688035i	−0.00309628	+	0.999995i	$0.500986\pi$
$102$	0.173762	+	0.126246i	0.0172050	+	0.0125002i
$103$	3.92705	+	2.85317i	0.386944	+	0.281131i	0.764202	−	0.644977i	$-0.223133\pi$
$103$	3.92705	+	2.85317i	0.386944	+	0.281131i	−0.377258	+	0.926108i	$0.623133\pi$
$104$	2.66312	+	1.93487i	0.261140	+	0.189730i
$105$	0.500000	−	0.363271i	0.0487950	−	0.0354516i
$106$	1.32624	+	4.08174i	0.128816	+	0.396454i
$107$	−7.97214	−	5.79210i	−0.770695	−	0.559943i	0.131477	−	0.991319i	$-0.458028\pi$
$107$	−7.97214	−	5.79210i	−0.770695	−	0.559943i	−0.902172	+	0.431376i	$0.858028\pi$
$108$	1.28115	−	3.94298i	0.123279	−	0.379414i
$109$	−16.0902			−1.54116			−0.770579	−	0.637344i	$-0.780033\pi$
$109$	−16.0902			−1.54116			−0.770579	+	0.637344i	$0.780033\pi$
$110$	1.92705	−	1.40008i	0.183737	−	0.133493i
$111$	−0.635255	+	1.95511i	−0.0602957	+	0.185571i
$112$	0.972136	+	2.99193i	0.0918582	+	0.282711i
$113$	1.54508	+	4.75528i	0.145349	+	0.447339i	0.997056	−	0.0766799i	$-0.0244320\pi$
$113$	1.54508	+	4.75528i	0.145349	+	0.447339i	−0.851706	+	0.524019i	$0.824432\pi$
$114$	0.111456			0.0104388
$115$	0.118034	+	0.363271i	0.0110067	+	0.0338752i
$116$	−6.00000	−	4.35926i	−0.557086	−	0.404747i
$117$	5.16312	−	3.75123i	0.477331	−	0.346801i
$118$	−0.635255	+	1.95511i	−0.0584800	+	0.179983i
$119$	−0.454915	+	1.40008i	−0.0417020	+	0.128346i
$120$	0.909830			0.0830557
$121$	−3.11803	+	2.26538i	−0.283458	+	0.205944i
$122$	0.965558			0.0874175
$123$	2.44427	+	0.0857567i	0.220393	+	0.00773242i
$124$	−16.1459			−1.44994
$125$	−9.66312	+	7.02067i	−0.864296	+	0.627948i
$126$	−1.09017			−0.0971201
$127$	−4.76393	+	14.6619i	−0.422731	+	1.30103i	0.482420	+	0.875940i	$0.339758\pi$
$127$	−4.76393	+	14.6619i	−0.422731	+	1.30103i	−0.905151	+	0.425091i	$0.860242\pi$
$128$	−3.11803	+	9.59632i	−0.275598	+	0.848203i
$129$	−1.38197	+	1.00406i	−0.121675	+	0.0884023i
$130$	1.11803	+	0.812299i	0.0980581	+	0.0712434i
$131$	1.57295	+	4.84104i	0.137429	+	0.422964i	0.995960	−	0.0897985i	$-0.0286223\pi$
$131$	1.57295	+	4.84104i	0.137429	+	0.422964i	−0.858531	+	0.512762i	$0.828622\pi$
$132$	−2.72949			−0.237572
$133$	0.236068	+	0.726543i	0.0204697	+	0.0629992i
$134$	−0.465558	−	1.43284i	−0.0402181	−	0.123779i
$135$	1.11803	−	3.44095i	0.0962250	−	0.296150i
$136$	−1.75329	+	1.27384i	−0.150343	+	0.109231i
$137$	5.38197			0.459812			0.229906	−	0.973213i	$-0.426158\pi$
$137$	5.38197			0.459812			0.229906	+	0.973213i	$0.426158\pi$
$138$	−0.0106431	+	0.0327561i	−0.000906002	+	0.00278839i
$139$	−11.5902	−	8.42075i	−0.983065	−	0.714239i	−0.0246738	−	0.999696i	$-0.507855\pi$
$139$	−11.5902	−	8.42075i	−0.983065	−	0.714239i	−0.958392	+	0.285457i	$0.907855\pi$
$140$	0.927051	+	2.85317i	0.0783501	+	0.241137i
$141$	3.57295	−	2.59590i	0.300897	−	0.218614i
$142$	−2.71885	−	1.97536i	−0.228161	−	0.165768i
$143$	−6.97214	−	5.06555i	−0.583039	−	0.423603i
$144$	7.26393	+	5.27756i	0.605328	+	0.439796i
$145$	−5.23607	−	3.80423i	−0.434832	−	0.315924i
$146$	−3.30902	+	2.40414i	−0.273856	+	0.198968i
$147$	0.118034	+	0.363271i	0.00973528	+	0.0299621i
$148$	−8.07295	−	5.86534i	−0.663592	−	0.482128i
$149$	3.20820	−	9.87384i	0.262826	−	0.808896i	−0.729360	−	0.684130i	$-0.760182\pi$
$149$	3.20820	−	9.87384i	0.262826	−	0.808896i	0.992186	−	0.124766i	$-0.0398180\pi$
$150$	−0.347524			−0.0283752
$151$	−9.42705	+	6.84915i	−0.767163	+	0.557376i	−0.901099	−	0.433614i	$-0.857238\pi$
$151$	−9.42705	+	6.84915i	−0.767163	+	0.557376i	0.133936	+	0.990990i	$0.457238\pi$
$152$	−0.347524	+	1.06957i	−0.0281879	+	0.0867535i
$153$	1.29837	+	3.99598i	0.104967	+	0.323056i
$154$	0.454915	+	1.40008i	0.0366581	+	0.112822i
$155$	−14.0902			−1.13175
$156$	−0.489357	−	1.50609i	−0.0391799	−	0.120583i
$157$	16.5172	+	12.0005i	1.31822	+	0.957741i	0.999953	+	0.00973952i	$0.00310023\pi$
$157$	16.5172	+	12.0005i	1.31822	+	0.957741i	0.318265	+	0.948002i	$0.396900\pi$
$158$	3.73607	−	2.71441i	0.297226	−	0.215947i
$159$	1.32624	−	4.08174i	0.105178	−	0.323703i
$160$	−2.07295	+	6.37988i	−0.163881	+	0.504374i
$161$	−0.236068			−0.0186048
$162$	−2.38197	+	1.73060i	−0.187145	+	0.135969i
$163$	−14.7639			−1.15640			−0.578200	−	0.815895i	$-0.696245\pi$
$163$	−14.7639			−1.15640			−0.578200	+	0.815895i	$0.696245\pi$
$164$	−4.06231	+	11.1554i	−0.317213	+	0.871091i
$165$	−2.38197			−0.185436
$166$	2.11803	−	1.53884i	0.164391	−	0.119437i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	−0.173762	+	0.534785i	−0.0134060	+	0.0412595i
$169$	−2.47214	+	7.60845i	−0.190164	+	0.585266i
$170$	−0.736068	+	0.534785i	−0.0564538	+	0.0410161i
$171$	1.76393	+	1.28157i	0.134891	+	0.0980042i
$172$	−2.56231	−	7.88597i	−0.195374	−	0.601299i
$173$	−1.00000			−0.0760286			−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000			−0.0760286			−0.0380143	+	0.999277i	$0.512103\pi$
$174$	−0.180340	−	0.555029i	−0.0136715	−	0.0420766i
$175$	−0.736068	−	2.26538i	−0.0556415	−	0.171247i
$176$	3.74671	−	11.5312i	0.282419	−	0.869196i
$177$	1.66312	−	1.20833i	0.125008	−	0.0908234i
$178$	−1.94427			−0.145729
$179$	3.36475	−	10.3556i	0.251493	−	0.774015i	−0.743008	−	0.669283i	$-0.766601\pi$
$179$	3.36475	−	10.3556i	0.251493	−	0.774015i	0.994500	−	0.104732i	$-0.0333986\pi$
$180$	6.92705	+	5.03280i	0.516312	+	0.375123i
$181$	0.909830	+	2.80017i	0.0676271	+	0.208135i	0.979159	−	0.203094i	$-0.0650997\pi$
$181$	0.909830	+	2.80017i	0.0676271	+	0.208135i	−0.911532	+	0.411229i	$0.865100\pi$
$182$	−0.690983	+	0.502029i	−0.0512191	+	0.0372128i
$183$	−0.781153	−	0.567541i	−0.0577445	−	0.0419538i
$184$	−0.281153	−	0.204270i	−0.0207269	−	0.0150590i
$185$	−7.04508	−	5.11855i	−0.517965	−	0.376324i
$186$	−1.02786	−	0.746787i	−0.0753666	−	0.0547571i
$187$	4.59017	−	3.33495i	0.335666	−	0.243876i
$188$	6.62461	+	20.3885i	0.483149	+	1.48698i
$189$	1.80902	+	1.31433i	0.131587	+	0.0956033i
$190$	−0.145898	+	0.449028i	−0.0105846	+	0.0325759i
$191$	−2.29180			−0.165829			−0.0829143	−	0.996557i	$-0.526423\pi$
$191$	−2.29180			−0.165829			−0.0829143	+	0.996557i	$0.526423\pi$
$192$	1.45492	−	1.05706i	0.104999	−	0.0762866i
$193$	−2.40983	+	7.41669i	−0.173463	+	0.533865i	−0.999560	−	0.0296632i	$-0.990557\pi$
$193$	−2.40983	+	7.41669i	−0.173463	+	0.533865i	0.826097	+	0.563529i	$0.190557\pi$
$194$	1.13525	+	3.49396i	0.0815066	+	0.250851i
$195$	−0.427051	−	1.31433i	−0.0305818	−	0.0941210i
$196$	−1.85410			−0.132436
$197$	−1.32624	−	4.08174i	−0.0944905	−	0.290812i	0.892630	−	0.450790i	$-0.148858\pi$
$197$	−1.32624	−	4.08174i	−0.0944905	−	0.290812i	−0.987121	+	0.159978i	$0.948858\pi$
$198$	3.39919	+	2.46965i	0.241570	+	0.175511i
$199$	0.381966	−	0.277515i	0.0270769	−	0.0196725i	−0.574165	−	0.818740i	$-0.694673\pi$
$199$	0.381966	−	0.277515i	0.0270769	−	0.0196725i	0.601241	+	0.799067i	$0.294673\pi$
$200$	1.08359	−	3.33495i	0.0766215	−	0.235817i
$201$	−0.465558	+	1.43284i	−0.0328379	+	0.101065i
$202$	−4.49342			−0.316156
$203$	3.23607	−	2.35114i	0.227127	−	0.165018i
$204$	1.04257			0.0729947
$205$	−3.54508	+	9.73508i	−0.247599	+	0.679927i
$206$	−1.85410			−0.129181
$207$	−0.545085	+	0.396027i	−0.0378860	+	0.0275258i
$208$	7.03444			0.487751
$209$	0.909830	−	2.80017i	0.0629343	−	0.193692i
$210$	−0.0729490	+	0.224514i	−0.00503396	+	0.0154929i
$211$	−1.04508	+	0.759299i	−0.0719466	+	0.0522723i	−0.623177	−	0.782081i	$-0.714158\pi$
$211$	−1.04508	+	0.759299i	−0.0719466	+	0.0522723i	0.551231	+	0.834353i	$0.314158\pi$
$212$	16.8541	+	12.2452i	1.15754	+	0.841005i
$213$	1.03851	+	3.19620i	0.0711573	+	0.219000i
$214$	3.76393			0.257297
$215$	−2.23607	−	6.88191i	−0.152499	−	0.469342i
$216$	1.01722	+	3.13068i	0.0692131	+	0.213016i
$217$	2.69098	−	8.28199i	0.182676	−	0.562218i
$218$	4.97214	−	3.61247i	0.336756	−	0.244667i
$219$	4.09017			0.276388
$220$	3.57295	−	10.9964i	0.240888	−	0.741378i
$221$	2.66312	+	1.93487i	0.179141	+	0.130153i
$222$	−0.242646	−	0.746787i	−0.0162853	−	0.0501211i
$223$	13.1353	−	9.54332i	0.879602	−	0.639068i	−0.0535444	−	0.998565i	$-0.517052\pi$
$223$	13.1353	−	9.54332i	0.879602	−	0.639068i	0.933146	+	0.359497i	$0.117052\pi$
$224$	−3.35410	−	2.43690i	−0.224105	−	0.162822i
$225$	−5.50000	−	3.99598i	−0.366667	−	0.266399i
$226$	−1.54508	−	1.12257i	−0.102778	−	0.0746722i
$227$	−17.5172	−	12.7270i	−1.16266	−	0.844721i	−0.172547	−	0.985001i	$-0.555200\pi$
$227$	−17.5172	−	12.7270i	−1.16266	−	0.844721i	−0.990112	+	0.140280i	$0.955200\pi$
$228$	0.437694	−	0.318003i	0.0289870	−	0.0210603i
$229$	1.64590	+	5.06555i	0.108764	+	0.334741i	0.990595	−	0.136824i	$-0.0436893\pi$
$229$	1.64590	+	5.06555i	0.108764	+	0.334741i	−0.881831	+	0.471565i	$0.843689\pi$
$230$	−0.118034	−	0.0857567i	−0.00778293	−	0.00565463i
$231$	0.454915	−	1.40008i	0.0299312	−	0.0921188i
$232$	5.88854			0.386602
$233$	12.3541	−	8.97578i	0.809344	−	0.588023i	−0.104296	−	0.994546i	$-0.533259\pi$
$233$	12.3541	−	8.97578i	0.809344	−	0.588023i	0.913640	+	0.406523i	$0.133259\pi$
$234$	−0.753289	+	2.31838i	−0.0492440	+	0.151558i
$235$	5.78115	+	17.7926i	0.377121	+	1.16066i
$236$	3.08359	+	9.49032i	0.200725	+	0.617767i
$237$	−4.61803			−0.299974
$238$	−0.173762	−	0.534785i	−0.0112633	−	0.0346649i
$239$	−16.1803	−	11.7557i	−1.04662	−	0.760413i	−0.0750525	−	0.997180i	$-0.523912\pi$
$239$	−16.1803	−	11.7557i	−1.04662	−	0.760413i	−0.971567	+	0.236766i	$0.923912\pi$
$240$	1.57295	−	1.14281i	0.101533	−	0.0737683i
$241$	6.42705	−	19.7804i	0.414003	−	1.27417i	−0.499137	−	0.866523i	$-0.666350\pi$
$241$	6.42705	−	19.7804i	0.414003	−	1.27417i	0.913140	−	0.407646i	$-0.133650\pi$
$242$	0.454915	−	1.40008i	0.0292430	−	0.0900008i
$243$	9.65248			0.619207
$244$	3.79180	−	2.75490i	0.242745	−	0.176364i
$245$	−1.61803			−0.103372
$246$	−0.774575	+	0.522273i	−0.0493851	+	0.0332989i
$247$	1.70820			0.108690
$248$	10.3713	−	7.53521i	0.658580	−	0.478486i
$249$	−2.61803			−0.165911
$250$	1.40983	−	4.33901i	0.0891655	−	0.274423i
$251$	3.78115	−	11.6372i	0.238664	−	0.734533i	−0.757950	−	0.652313i	$-0.773799\pi$
$251$	3.78115	−	11.6372i	0.238664	−	0.734533i	0.996614	−	0.0822203i	$-0.0262011\pi$
$252$	−4.28115	+	3.11044i	−0.269687	+	0.195939i
$253$	0.736068	+	0.534785i	0.0462762	+	0.0336216i
$254$	−1.81966	−	5.60034i	−0.114176	−	0.351396i
$255$	0.909830			0.0569758
$256$	1.71885	+	5.29007i	0.107428	+	0.330629i
$257$	2.74671	+	8.45351i	0.171335	+	0.527315i	0.999447	−	0.0332473i	$-0.0105849\pi$
$257$	2.74671	+	8.45351i	0.171335	+	0.527315i	−0.828112	+	0.560563i	$0.810585\pi$
$258$	0.201626	−	0.620541i	0.0125527	−	0.0386332i
$259$	4.35410	−	3.16344i	0.270551	−	0.196567i
$260$	6.70820			0.416025
$261$	3.52786	−	10.8576i	0.218369	−	0.672072i
$262$	−1.57295	−	1.14281i	−0.0971771	−	0.0706033i
$263$	6.97214	+	21.4580i	0.429920	+	1.32316i	0.898203	+	0.439580i	$0.144873\pi$
$263$	6.97214	+	21.4580i	0.429920	+	1.32316i	−0.468283	+	0.883579i	$0.655127\pi$
$264$	1.75329	−	1.27384i	0.107907	−	0.0783994i
$265$	14.7082	+	10.6861i	0.903518	+	0.656444i
$266$	−0.236068	−	0.171513i	−0.0144743	−	0.0105162i
$267$	1.57295	+	1.14281i	0.0962629	+	0.0699391i
$268$	−5.91641	−	4.29852i	−0.361402	−	0.262574i
$269$	−21.4443	+	15.5802i	−1.30748	+	0.949940i	−0.999999	−	0.00161395i	$-0.999486\pi$
$269$	−21.4443	+	15.5802i	−1.30748	+	0.949940i	−0.307482	+	0.951554i	$0.599486\pi$
$270$	0.427051	+	1.31433i	0.0259895	+	0.0799874i
$271$	−21.1074	−	15.3354i	−1.28218	−	0.931560i	−0.282566	−	0.959248i	$-0.591186\pi$
$271$	−21.1074	−	15.3354i	−1.28218	−	0.931560i	−0.999617	+	0.0276876i	$0.991186\pi$
$272$	−1.43112	+	4.40452i	−0.0867742	+	0.267063i
$273$	0.854102			0.0516926
$274$	−1.66312	+	1.20833i	−0.100473	+	0.0729977i
$275$	−2.83688	+	8.73102i	−0.171070	+	0.526500i
$276$	0.0516628	+	0.159002i	0.00310973	+	0.00957078i
$277$	0.173762	+	0.534785i	0.0104404	+	0.0321321i	0.956141	−	0.292907i	$-0.0946226\pi$
$277$	0.173762	+	0.534785i	0.0104404	+	0.0321321i	−0.945701	+	0.325039i	$0.894623\pi$
$278$	5.47214			0.328197
$279$	−7.68034	−	23.6377i	−0.459810	−	1.41515i
$280$	−1.92705	−	1.40008i	−0.115163	−	0.0836711i
$281$	10.1631	−	7.38394i	0.606281	−	0.440489i	−0.241822	−	0.970321i	$-0.577745\pi$
$281$	10.1631	−	7.38394i	0.606281	−	0.440489i	0.848103	+	0.529832i	$0.177745\pi$
$282$	−0.521286	+	1.60435i	−0.0310421	+	0.0955379i
$283$	−2.29837	+	7.07367i	−0.136624	+	0.420486i	−0.995839	−	0.0911289i	$-0.970952\pi$
$283$	−2.29837	+	7.07367i	−0.136624	+	0.420486i	0.859215	+	0.511615i	$0.170952\pi$
$284$	−16.3131			−0.968003
$285$	0.381966	−	0.277515i	0.0226257	−	0.0164385i
$286$	3.29180			0.194648
$287$	−5.04508	−	3.94298i	−0.297802	−	0.232747i
$288$	−11.8328			−0.697255
$289$	12.0000	−	8.71851i	0.705882	−	0.512854i
$290$	2.47214			0.145169
$291$	1.13525	−	3.49396i	0.0665498	−	0.204819i
$292$	−6.13525	+	18.8824i	−0.359039	+	1.10501i
$293$	16.1353	−	11.7229i	0.942632	−	0.684862i	−0.00642104	−	0.999979i	$-0.502044\pi$
$293$	16.1353	−	11.7229i	0.942632	−	0.684862i	0.949053	+	0.315117i	$0.102044\pi$
$294$	−0.118034	−	0.0857567i	−0.00688388	−	0.00500143i
$295$	2.69098	+	8.28199i	0.156675	+	0.482196i
$296$	7.92299			0.460514
$297$	−2.66312	−	8.19624i	−0.154530	−	0.475594i
$298$	1.22542	+	3.77147i	0.0709870	+	0.218475i
$299$	−0.163119	+	0.502029i	−0.00943341	+	0.0290331i
$300$	−1.36475	+	0.991545i	−0.0787936	+	0.0572469i
$301$	4.47214			0.257770
$302$	1.37539	−	4.23301i	0.0791447	−	0.243582i
$303$	3.63525	+	2.64117i	0.208840	+	0.151731i
$304$	0.742646	+	2.28563i	0.0425937	+	0.131090i
$305$	3.30902	−	2.40414i	0.189474	−	0.137661i
$306$	−1.29837	−	0.943324i	−0.0742231	−	0.0539262i
$307$	−4.09017	−	2.97168i	−0.233438	−	0.169603i	0.464917	−	0.885354i	$-0.346084\pi$
$307$	−4.09017	−	2.97168i	−0.233438	−	0.169603i	−0.698355	+	0.715752i	$0.746084\pi$
$308$	5.78115	+	4.20025i	0.329412	+	0.239332i
$309$	1.50000	+	1.08981i	0.0853320	+	0.0619973i
$310$	4.35410	−	3.16344i	0.247296	−	0.179671i
$311$	−1.97214	−	6.06961i	−0.111830	−	0.344176i	0.879443	−	0.476004i	$-0.157915\pi$
$311$	−1.97214	−	6.06961i	−0.111830	−	0.344176i	−0.991273	+	0.131828i	$0.957915\pi$
$312$	1.01722	+	0.739054i	0.0575888	+	0.0418407i
$313$	7.68034	−	23.6377i	0.434118	−	1.33608i	−0.459869	−	0.887987i	$-0.652104\pi$
$313$	7.68034	−	23.6377i	0.434118	−	1.33608i	0.893987	−	0.448092i	$-0.147896\pi$
$314$	−7.79837			−0.440088
$315$	−3.73607	+	2.71441i	−0.210504	+	0.152940i
$316$	6.92705	−	21.3193i	0.389677	−	1.19930i
$317$	3.42705	+	10.5474i	0.192482	+	0.592400i	0.999997	+	0.00255191i	$0.000812300\pi$
$317$	3.42705	+	10.5474i	0.192482	+	0.592400i	−0.807514	+	0.589848i	$0.799188\pi$
$318$	0.506578	+	1.55909i	0.0284075	+	0.0874292i
$319$	−15.4164			−0.863153
$320$	2.35410	+	7.24518i	0.131598	+	0.405018i
$321$	−3.04508	−	2.21238i	−0.169960	−	0.123483i
$322$	0.0729490	−	0.0530006i	0.00406529	−	0.00295361i
$323$	−0.347524	+	1.06957i	−0.0193368	+	0.0595124i
$324$	−4.41641	+	13.5923i	−0.245356	+	0.755128i
$325$	−5.32624			−0.295447
$326$	4.56231	−	3.31471i	0.252683	−	0.183585i
$327$	−6.14590			−0.339869
$328$	−2.59675	−	9.06154i	−0.143381	−	0.500340i
$329$	−11.5623			−0.637451
$330$	0.736068	−	0.534785i	0.0405192	−	0.0294389i
$331$	19.2361			1.05731			0.528655	−	0.848837i	$-0.322697\pi$
$331$	19.2361			1.05731			0.528655	+	0.848837i	$0.322697\pi$
$332$	3.92705	−	12.0862i	0.215525	−	0.663318i
$333$	4.74671	−	14.6089i	0.260118	−	0.800561i
$334$	−3.70820	+	2.69417i	−0.202904	+	0.147418i
$335$	−5.16312	−	3.75123i	−0.282091	−	0.204951i
$336$	0.371323	+	1.14281i	0.0202573	+	0.0623456i
$337$	36.0000			1.96104			0.980522	−	0.196407i	$-0.0629273\pi$
$337$	36.0000			1.96104			0.980522	+	0.196407i	$0.0629273\pi$
$338$	−0.944272	−	2.90617i	−0.0513616	−	0.158075i
$339$	0.590170	+	1.81636i	0.0320536	+	0.0986509i
$340$	−1.36475	+	4.20025i	−0.0740137	+	0.227791i
$341$	−27.1525	+	19.7274i	−1.47039	+	1.06830i
$342$	−0.832816			−0.0450335
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	5.32624	+	3.86974i	0.287172	+	0.208642i
$345$	0.0450850	+	0.138757i	0.00242729	+	0.00747044i
$346$	0.309017	−	0.224514i	0.0166129	−	0.0120699i
$347$	14.9894	+	10.8904i	0.804671	+	0.584628i	0.912281	−	0.409566i	$-0.134320\pi$
$347$	14.9894	+	10.8904i	0.804671	+	0.584628i	−0.107610	+	0.994193i	$0.534320\pi$
$348$	−2.29180	−	1.66509i	−0.122853	−	0.0892580i
$349$	22.2984	+	16.2007i	1.19360	+	0.867204i	0.993641	−	0.112599i	$-0.0359175\pi$
$349$	22.2984	+	16.2007i	1.19360	+	0.867204i	0.199964	+	0.979803i	$0.435917\pi$
$350$	0.736068	+	0.534785i	0.0393445	+	0.0285854i
$351$	4.04508	−	2.93893i	0.215911	−	0.156868i
$352$	4.93769	+	15.1967i	0.263180	+	0.809985i
$353$	−2.80902	−	2.04087i	−0.149509	−	0.108625i	0.510516	−	0.859868i	$-0.329454\pi$
$353$	−2.80902	−	2.04087i	−0.149509	−	0.108625i	−0.660025	+	0.751244i	$0.729454\pi$
$354$	−0.242646	+	0.746787i	−0.0128965	+	0.0396913i
$355$	−14.2361			−0.755572
$356$	−7.63525	+	5.54734i	−0.404668	+	0.294008i
$357$	−0.173762	+	0.534785i	−0.00919646	+	0.0283038i
$358$	1.28522	+	3.95550i	0.0679259	+	0.209054i
$359$	1.85410	+	5.70634i	0.0978558	+	0.301169i	0.987987	−	0.154534i	$-0.0493877\pi$
$359$	1.85410	+	5.70634i	0.0978558	+	0.301169i	−0.890132	+	0.455703i	$0.849388\pi$
$360$	−6.79837			−0.358306
$361$	−5.69098	−	17.5150i	−0.299525	−	0.921844i
$362$	−0.909830	−	0.661030i	−0.0478196	−	0.0347430i
$363$	−1.19098	+	0.865300i	−0.0625104	+	0.0454165i
$364$	−1.28115	+	3.94298i	−0.0671507	+	0.206668i
$365$	−5.35410	+	16.4782i	−0.280247	+	0.862510i
$366$	0.368810			0.0192780
$367$	−25.6803	+	18.6579i	−1.34050	+	0.973932i	−0.341078	+	0.940035i	$0.610792\pi$
$367$	−25.6803	+	18.6579i	−1.34050	+	0.973932i	−0.999425	+	0.0338971i	$0.989208\pi$
$368$	−0.742646			−0.0387131
$369$	−18.2639	−	0.640786i	−0.950782	−	0.0333580i
$370$	3.32624			0.172923
$371$	−9.09017	+	6.60440i	−0.471938	+	0.342883i
$372$	−6.16718			−0.319754
$373$	6.95492	−	21.4050i	0.360112	−	1.10831i	−0.592874	−	0.805295i	$-0.702007\pi$
$373$	6.95492	−	21.4050i	0.360112	−	1.10831i	0.952986	−	0.303015i	$-0.0979932\pi$
$374$	−0.669697	+	2.06111i	−0.0346292	+	0.106578i
$375$	−3.69098	+	2.68166i	−0.190602	+	0.138480i
$376$	−13.7705	−	10.0049i	−0.710160	−	0.515961i
$377$	−2.76393	−	8.50651i	−0.142350	−	0.438107i
$378$	−0.854102			−0.0439303
$379$	8.25329	+	25.4010i	0.423943	+	1.30476i	0.904003	+	0.427527i	$0.140615\pi$
$379$	8.25329	+	25.4010i	0.423943	+	1.30476i	−0.480060	+	0.877236i	$0.659385\pi$
$380$	0.708204	+	2.17963i	0.0363301	+	0.111813i
$381$	−1.81966	+	5.60034i	−0.0932240	+	0.286914i
$382$	0.708204	−	0.514540i	0.0362349	−	0.0263262i
$383$	21.8885			1.11845			0.559226	−	0.829015i	$-0.311098\pi$
$383$	21.8885			1.11845			0.559226	+	0.829015i	$0.311098\pi$
$384$	−1.19098	+	3.66547i	−0.0607771	+	0.187053i
$385$	5.04508	+	3.66547i	0.257121	+	0.186810i
$386$	−0.920473	−	2.83293i	−0.0468509	−	0.144192i
$387$	10.3262	−	7.50245i	0.524912	−	0.381371i
$388$	14.4271	+	10.4819i	0.732423	+	0.532136i
$389$	−18.4443	−	13.4005i	−0.935162	−	0.679435i	0.0120895	−	0.999927i	$-0.496152\pi$
$389$	−18.4443	−	13.4005i	−0.935162	−	0.679435i	−0.947251	+	0.320492i	$0.896152\pi$
$390$	0.427051	+	0.310271i	0.0216246	+	0.0157112i
$391$	−0.281153	−	0.204270i	−0.0142185	−	0.0103304i
$392$	1.19098	−	0.865300i	0.0601537	−	0.0437042i
$393$	0.600813	+	1.84911i	0.0303070	+	0.0932754i
$394$	1.32624	+	0.963568i	0.0668149	+	0.0485439i
$395$	6.04508	−	18.6049i	0.304161	−	0.936112i
$396$	20.3951			1.02489
$397$	11.4271	−	8.30224i	0.573507	−	0.416677i	−0.262870	−	0.964831i	$-0.584669\pi$
$397$	11.4271	−	8.30224i	0.573507	−	0.416677i	0.836378	+	0.548154i	$0.184669\pi$
$398$	−0.0557281	+	0.171513i	−0.00279340	+	0.00859719i
$399$	0.0901699	+	0.277515i	0.00451414	+	0.0138931i
$400$	−2.31559	−	7.12667i	−0.115780	−	0.356333i
$401$	10.6180			0.530239			0.265120	−	0.964216i	$-0.414589\pi$
$401$	10.6180			0.530239			0.265120	+	0.964216i	$0.414589\pi$
$402$	−0.177827	−	0.547296i	−0.00886922	−	0.0272967i
$403$	−15.7533	−	11.4454i	−0.784727	−	0.570138i
$404$	−17.6459	+	12.8205i	−0.877916	+	0.637843i
$405$	−3.85410	+	11.8617i	−0.191512	+	0.589413i
$406$	−0.472136	+	1.45309i	−0.0234317	+	0.0721154i
$407$	−20.7426			−1.02817
$408$	−0.669697	+	0.486563i	−0.0331549	+	0.0240885i
$409$	−5.43769			−0.268877			−0.134438	−	0.990922i	$-0.542923\pi$
$409$	−5.43769			−0.268877			−0.134438	+	0.990922i	$0.542923\pi$
$410$	−1.09017	−	3.80423i	−0.0538397	−	0.187877i
$411$	2.05573			0.101402
$412$	−7.28115	+	5.29007i	−0.358717	+	0.260623i
$413$	−5.38197			−0.264829
$414$	0.0795268	−	0.244758i	0.00390853	−	0.0120292i
$415$	3.42705	−	10.5474i	0.168227	−	0.517750i
$416$	−7.50000	+	5.44907i	−0.367718	+	0.267163i
$417$	−4.42705	−	3.21644i	−0.216794	−	0.157510i
$418$	0.347524	+	1.06957i	0.0169980	+	0.0523143i
$419$	−8.94427			−0.436956			−0.218478	−	0.975842i	$-0.570109\pi$
$419$	−8.94427			−0.436956			−0.218478	+	0.975842i	$0.570109\pi$
$420$	0.354102	+	1.08981i	0.0172784	+	0.0531775i
$421$	10.4164	+	32.0584i	0.507665	+	1.56243i	0.796244	+	0.604975i	$0.206817\pi$
$421$	10.4164	+	32.0584i	0.507665	+	1.56243i	−0.288580	+	0.957456i	$0.593183\pi$
$422$	0.152476	−	0.469272i	0.00742241	−	0.0228438i
$423$	−26.6976	+	19.3969i	−1.29808	+	0.943110i
$424$	−16.5410			−0.803303
$425$	1.08359	−	3.33495i	0.0525619	−	0.161769i
$426$	−1.03851	−	0.754520i	−0.0503158	−	0.0365566i
$427$	0.781153	+	2.40414i	0.0378026	+	0.116345i
$428$	14.7812	−	10.7391i	0.714474	−	0.519096i
$429$	−2.66312	−	1.93487i	−0.128577	−	0.0934164i
$430$	2.23607	+	1.62460i	0.107833	+	0.0783451i
$431$	0.736068	+	0.534785i	0.0354551	+	0.0257597i	0.605372	−	0.795943i	$-0.293024\pi$
$431$	0.736068	+	0.534785i	0.0354551	+	0.0257597i	−0.569917	+	0.821703i	$0.693024\pi$
$432$	5.69098	+	4.13474i	0.273808	+	0.198933i
$433$	26.9164	−	19.5559i	1.29352	−	0.939797i	0.293650	−	0.955913i	$-0.405130\pi$
$433$	26.9164	−	19.5559i	1.29352	−	0.939797i	0.999870	+	0.0161157i	$0.00513002\pi$
$434$	1.02786	+	3.16344i	0.0493391	+	0.151850i
$435$	−2.00000	−	1.45309i	−0.0958927	−	0.0696701i
$436$	9.21885	−	28.3727i	0.441503	−	1.35881i
$437$	−0.180340			−0.00862683
$438$	−1.26393	+	0.918300i	−0.0603930	+	0.0438781i
$439$	−4.93769	+	15.1967i	−0.235663	+	0.725297i	0.761369	+	0.648318i	$0.224527\pi$
$439$	−4.93769	+	15.1967i	−0.235663	+	0.725297i	−0.997033	+	0.0769787i	$0.975473\pi$
$440$	2.83688	+	8.73102i	0.135243	+	0.416235i
$441$	−0.881966	−	2.71441i	−0.0419984	−	0.129258i
$442$	−1.25735			−0.0598062
$443$	5.73607	+	17.6538i	0.272529	+	0.838757i	0.989863	+	0.142028i	$0.0453623\pi$
$443$	5.73607	+	17.6538i	0.272529	+	0.838757i	−0.717334	+	0.696730i	$0.754638\pi$
$444$	−3.08359	−	2.24036i	−0.146341	−	0.106323i
$445$	−6.66312	+	4.84104i	−0.315862	+	0.229487i
$446$	−1.91641	+	5.89810i	−0.0907445	+	0.279283i
$447$	1.22542	−	3.77147i	0.0579606	−	0.178384i
$448$	−4.70820			−0.222442
$449$	−0.427051	+	0.310271i	−0.0201538	+	0.0146426i	−0.597817	−	0.801633i	$-0.703965\pi$
$449$	−0.427051	+	0.310271i	−0.0201538	+	0.0146426i	0.577663	+	0.816276i	$0.303965\pi$
$450$	2.59675			0.122412
$451$	6.79837	+	23.7234i	0.320123	+	1.11709i
$452$	−9.27051			−0.436048
$453$	−3.60081	+	2.61614i	−0.169181	+	0.122917i
$454$	8.27051			0.388154
$455$	−1.11803	+	3.44095i	−0.0524142	+	0.161314i
$456$	−0.132742	+	0.408539i	−0.00621623	+	0.0191316i
$457$	−23.9894	+	17.4293i	−1.12217	+	0.815308i	−0.984537	−	0.175175i	$-0.943951\pi$
$457$	−23.9894	+	17.4293i	−1.12217	+	0.815308i	−0.137637	+	0.990483i	$0.543951\pi$
$458$	−1.64590	−	1.19581i	−0.0769078	−	0.0558768i
$459$	1.01722	+	3.13068i	0.0474798	+	0.146128i
$460$	−0.708204			−0.0330202
$461$	−1.04508	−	3.21644i	−0.0486745	−	0.149805i	0.923765	−	0.382959i	$-0.125095\pi$
$461$	−1.04508	−	3.21644i	−0.0486745	−	0.149805i	−0.972440	+	0.233155i	$0.925095\pi$
$462$	0.173762	+	0.534785i	0.00808414	+	0.0248804i
$463$	5.78115	−	17.7926i	0.268673	−	0.826890i	−0.722151	−	0.691735i	$-0.756847\pi$
$463$	5.78115	−	17.7926i	0.268673	−	0.826890i	0.990824	−	0.135155i	$-0.0431534\pi$
$464$	10.1803	−	7.39645i	0.472610	−	0.343372i
$465$	−5.38197			−0.249583
$466$	−1.80244	+	5.54734i	−0.0834964	+	0.256975i
$467$	−24.6976	−	17.9438i	−1.14287	−	0.830341i	−0.155351	−	0.987859i	$-0.549651\pi$
$467$	−24.6976	−	17.9438i	−1.14287	−	0.830341i	−0.987516	+	0.157518i	$0.949651\pi$
$468$	3.65654	+	11.2537i	0.169024	+	0.520201i
$469$	3.19098	−	2.31838i	0.147346	−	0.107053i
$470$	−5.78115	−	4.20025i	−0.266665	−	0.193743i
$471$	6.30902	+	4.58377i	0.290704	+	0.211209i
$472$	−6.40983	−	4.65701i	−0.295036	−	0.214356i
$473$	−13.9443	−	10.1311i	−0.641158	−	0.465829i
$474$	1.42705	−	1.03681i	0.0655466	−	0.0476224i
$475$	−0.562306	−	1.73060i	−0.0258004	−	0.0794054i
$476$	−2.20820	−	1.60435i	−0.101213	−	0.0735354i
$477$	−9.90983	+	30.4993i	−0.453740	+	1.39647i
$478$	7.63932			0.349414
$479$	−33.0517	+	24.0134i	−1.51017	+	1.09720i	−0.544067	+	0.839042i	$0.683116\pi$
$479$	−33.0517	+	24.0134i	−1.51017	+	1.09720i	−0.966102	+	0.258160i	$0.916884\pi$
$480$	−0.791796	+	2.43690i	−0.0361404	+	0.111229i
$481$	−3.71885	−	11.4454i	−0.169565	−	0.521867i
$482$	2.45492	+	7.55545i	0.111818	+	0.344141i
$483$	−0.0901699			−0.00410287
$484$	−2.20820	−	6.79615i	−0.100373	−	0.308916i
$485$	12.5902	+	9.14729i	0.571690	+	0.415357i
$486$	−2.98278	+	2.16712i	−0.135302	+	0.0983024i
$487$	8.20820	−	25.2623i	0.371949	−	1.14474i	−0.573565	−	0.819160i	$-0.694440\pi$
$487$	8.20820	−	25.2623i	0.371949	−	1.14474i	0.945514	−	0.325582i	$-0.105560\pi$
$488$	−1.14996	+	3.53922i	−0.0520564	+	0.160213i
$489$	−5.63932			−0.255019
$490$	0.500000	−	0.363271i	0.0225877	−	0.0164109i
$491$	22.7984			1.02888			0.514438	−	0.857528i	$-0.328001\pi$
$491$	22.7984			1.02888			0.514438	+	0.857528i	$0.328001\pi$
$492$	−1.55166	+	4.26099i	−0.0699544	+	0.192100i
$493$	5.88854			0.265207
$494$	−0.527864	+	0.383516i	−0.0237497	+	0.0172552i
$495$	17.7984			0.799977
$496$	8.46556	−	26.0543i	0.380115	−	1.16987i
$497$	2.71885	−	8.36775i	0.121957	−	0.375345i
$498$	0.809017	−	0.587785i	0.0362529	−	0.0263393i
$499$	8.57295	+	6.22861i	0.383778	+	0.278831i	0.762901	−	0.646515i	$-0.223774\pi$
$499$	8.57295	+	6.22861i	0.383778	+	0.278831i	−0.379123	+	0.925346i	$0.623774\pi$
$500$	−6.84346	−	21.0620i	−0.306049	−	0.941921i
$501$	4.58359			0.204780
$502$	1.44427	+	4.44501i	0.0644610	+	0.198391i
$503$	12.4828	+	38.4180i	0.556580	+	1.71298i	0.691735	+	0.722151i	$0.256847\pi$
$503$	12.4828	+	38.4180i	0.556580	+	1.71298i	−0.135155	+	0.990824i	$0.543153\pi$
$504$	1.29837	−	3.99598i	0.0578342	−	0.177995i
$505$	−15.3992	+	11.1882i	−0.685255	+	0.497867i
$506$	−0.347524			−0.0154493
$507$	−0.944272	+	2.90617i	−0.0419366	+	0.129068i
$508$	−23.1246	−	16.8010i	−1.02599	−	0.745424i
$509$	−8.57295	−	26.3848i	−0.379989	−	1.16949i	−0.940050	−	0.341035i	$-0.889222\pi$
$509$	−8.57295	−	26.3848i	−0.379989	−	1.16949i	0.560061	−	0.828451i	$-0.310778\pi$
$510$	−0.281153	+	0.204270i	−0.0124497	+	0.00904521i
$511$	−8.66312	−	6.29412i	−0.383234	−	0.278436i
$512$	−18.0451	−	13.1105i	−0.797488	−	0.579409i
$513$	1.38197	+	1.00406i	0.0610153	+	0.0443302i
$514$	−2.74671	−	1.99560i	−0.121152	−	0.0880222i
$515$	−6.35410	+	4.61653i	−0.279995	+	0.203428i
$516$	−0.978714	−	3.01217i	−0.0430855	−	0.132603i
$517$	36.0517	+	26.1931i	1.58555	+	1.15197i
$518$	−0.635255	+	1.95511i	−0.0279115	+	0.0859028i
$519$	−0.381966			−0.0167664
$520$	−4.30902	+	3.13068i	−0.188963	+	0.137290i
$521$	−3.11803	+	9.59632i	−0.136604	+	0.420422i	−0.995836	−	0.0911629i	$-0.970942\pi$
$521$	−3.11803	+	9.59632i	−0.136604	+	0.420422i	0.859232	+	0.511585i	$0.170942\pi$
$522$	1.34752	+	4.14725i	0.0589795	+	0.181520i
$523$	2.64590	+	8.14324i	0.115697	+	0.356079i	0.992092	−	0.125515i	$-0.0400582\pi$
$523$	2.64590	+	8.14324i	0.115697	+	0.356079i	−0.876395	+	0.481593i	$0.840058\pi$
$524$	−9.43769			−0.412288
$525$	−0.281153	−	0.865300i	−0.0122705	−	0.0377648i
$526$	−6.97214	−	5.06555i	−0.304000	−	0.220869i
$527$	10.3713	−	7.53521i	0.451782	−	0.328239i
$528$	1.43112	−	4.40452i	0.0622813	−	0.191682i
$529$	−7.09017	+	21.8213i	−0.308268	+	0.948752i
$530$	−6.94427			−0.301640
$531$	−12.4271	+	9.02878i	−0.539288	+	0.391816i
$532$	−1.41641			−0.0614091
$533$	−11.8713	+	8.00448i	−0.514204	+	0.346712i
$534$	−0.742646			−0.0321374
$535$	12.8992	−	9.37181i	0.557680	−	0.405179i
$536$	5.80650			0.250803
$537$	1.28522	−	3.95550i	0.0554613	−	0.170692i
$538$	3.12868	−	9.62908i	0.134887	−	0.415139i
$539$	−3.11803	+	2.26538i	−0.134303	+	0.0975770i
$540$	5.42705	+	3.94298i	0.233543	+	0.169679i
$541$	−4.61803	−	14.2128i	−0.198545	−	0.611058i	−0.999917	−	0.0128919i	$-0.995896\pi$
$541$	−4.61803	−	14.2128i	−0.198545	−	0.611058i	0.801372	−	0.598166i	$-0.204104\pi$
$542$	9.96556			0.428057
$543$	0.347524	+	1.06957i	0.0149137	+	0.0458996i
$544$	−1.88603	−	5.80461i	−0.0808629	−	0.248870i
$545$	8.04508	−	24.7602i	0.344614	−	1.06061i
$546$	−0.263932	+	0.191758i	−0.0112952	+	0.00820648i
$547$	26.2361			1.12177			0.560887	−	0.827893i	$-0.310460\pi$
$547$	26.2361			1.12177			0.560887	+	0.827893i	$0.310460\pi$
$548$	−3.08359	+	9.49032i	−0.131725	+	0.405406i
$549$	5.83688	+	4.24074i	0.249112	+	0.180990i
$550$	−1.08359	−	3.33495i	−0.0462045	−	0.142203i
$551$	2.47214	−	1.79611i	0.105317	−	0.0765169i
$552$	−0.107391	−	0.0780240i	−0.00457086	−	0.00332092i
$553$	9.78115	+	7.10642i	0.415937	+	0.302196i
$554$	−0.173762	−	0.126246i	−0.00738244	−	0.00536366i
$555$	−2.69098	−	1.95511i	−0.114226	−	0.0829900i
$556$	21.4894	−	15.6129i	0.911352	−	0.662136i
$557$	4.25329	+	13.0903i	0.180218	+	0.554653i	0.999833	−	0.0182610i	$-0.00581297\pi$
$557$	4.25329	+	13.0903i	0.180218	+	0.554653i	−0.819616	+	0.572914i	$0.805813\pi$
$558$	7.68034	+	5.58009i	0.325135	+	0.236224i
$559$	3.09017	−	9.51057i	0.130700	−	0.402254i
$560$	−5.09017			−0.215099
$561$	1.75329	−	1.27384i	0.0740239	−	0.0537815i
$562$	−1.48278	+	4.56352i	−0.0625473	+	0.192501i
$563$	2.01722	+	6.20837i	0.0850157	+	0.261652i	0.984523	−	0.175254i	$-0.0560745\pi$
$563$	2.01722	+	6.20837i	0.0850157	+	0.261652i	−0.899508	+	0.436905i	$0.856075\pi$
$564$	2.53038	+	7.78770i	0.106548	+	0.327921i
$565$	−8.09017			−0.340356
$566$	−0.877901	−	2.70190i	−0.0369009	−	0.113569i
$567$	−6.23607	−	4.53077i	−0.261890	−	0.190274i
$568$	10.4787	−	7.61323i	0.439677	−	0.319444i
$569$	13.0623	−	40.2016i	0.547600	−	1.68534i	−0.167125	−	0.985936i	$-0.553448\pi$
$569$	13.0623	−	40.2016i	0.547600	−	1.68534i	0.714726	−	0.699405i	$-0.246552\pi$
$570$	−0.0557281	+	0.171513i	−0.00233419	+	0.00718391i
$571$	−6.88854			−0.288277			−0.144138	−	0.989558i	$-0.546041\pi$
$571$	−6.88854			−0.288277			−0.144138	+	0.989558i	$0.546041\pi$
$572$	12.9271	−	9.39205i	0.540507	−	0.392701i
$573$	−0.875388			−0.0365699
$574$	2.44427	+	0.0857567i	0.102022	+	0.00357942i
$575$	0.562306			0.0234498
$576$	−10.8713	+	7.89848i	−0.452972	+	0.329103i
$577$	19.3607			0.805996			0.402998	−	0.915201i	$-0.367968\pi$
$577$	19.3607			0.805996			0.402998	+	0.915201i	$0.367968\pi$
$578$	−1.75078	+	5.38834i	−0.0728227	+	0.224125i
$579$	−0.920473	+	2.83293i	−0.0382536	+	0.117732i
$580$	9.70820	−	7.05342i	0.403111	−	0.292877i
$581$	5.54508	+	4.02874i	0.230049	+	0.167140i
$582$	0.433629	+	1.33457i	0.0179745	+	0.0553198i
$583$	43.3050			1.79351
$584$	−4.87132	−	14.9924i	−0.201577	−	0.620390i
$585$	3.19098	+	9.82084i	0.131931	+	0.406042i
$586$	−2.35410	+	7.24518i	−0.0972471	+	0.299296i
$587$	−17.8992	+	13.0045i	−0.738779	+	0.536754i	−0.892328	−	0.451387i	$-0.850929\pi$
$587$	−17.8992	+	13.0045i	−0.738779	+	0.536754i	0.153550	+	0.988141i	$0.450929\pi$
$588$	−0.708204			−0.0292058
$589$	2.05573	−	6.32688i	0.0847048	−	0.260695i
$590$	−2.69098	−	1.95511i	−0.110786	−	0.0804908i
$591$	−0.506578	−	1.55909i	−0.0208378	−	0.0641322i
$592$	13.6976	−	9.95186i	0.562966	−	0.409019i
$593$	−2.73607	−	1.98787i	−0.112357	−	0.0816320i	0.530188	−	0.847880i	$-0.322121\pi$
$593$	−2.73607	−	1.98787i	−0.112357	−	0.0816320i	−0.642545	+	0.766248i	$0.722121\pi$
$594$	2.66312	+	1.93487i	0.109269	+	0.0793886i
$595$	−1.92705	−	1.40008i	−0.0790014	−	0.0573979i
$596$	15.5729	+	11.3144i	0.637893	+	0.463456i
$597$	0.145898	−	0.106001i	0.00597121	−	0.00433834i
$598$	−0.0623059	−	0.191758i	−0.00254788	−	0.00784156i
$599$	35.4615	+	25.7643i	1.44892	+	1.05270i	0.986083	+	0.166255i	$0.0531676\pi$
$599$	35.4615	+	25.7643i	1.44892	+	1.05270i	0.462835	+	0.886445i	$0.346832\pi$
$600$	0.413895	−	1.27384i	0.0168972	−	0.0520043i
$601$	−12.7639			−0.520652			−0.260326	−	0.965521i	$-0.583830\pi$
$601$	−12.7639			−0.520652			−0.260326	+	0.965521i	$0.583830\pi$
$602$	−1.38197	+	1.00406i	−0.0563247	+	0.0409223i
$603$	3.47871	−	10.7064i	0.141664	−	0.435998i
$604$	−6.67627	−	20.5475i	−0.271654	−	0.836064i
$605$	−1.92705	−	5.93085i	−0.0783458	−	0.241123i
$606$	−1.71633			−0.0697213
$607$	−4.67376	−	14.3844i	−0.189702	−	0.583843i	0.810295	−	0.586022i	$-0.199307\pi$
$607$	−4.67376	−	14.3844i	−0.189702	−	0.583843i	−0.999998	+	0.00217835i	$0.999307\pi$
$608$	−2.56231	−	1.86162i	−0.103915	−	0.0754988i
$609$	1.23607	−	0.898056i	0.0500880	−	0.0363911i
$610$	−0.482779	+	1.48584i	−0.0195472	+	0.0601600i
$611$	−7.98936	+	24.5887i	−0.323215	+	0.994753i
$612$	−7.79024			−0.314902
$613$	−11.2812	+	8.19624i	−0.455641	+	0.331043i	−0.791819	−	0.610756i	$-0.790866\pi$
$613$	−11.2812	+	8.19624i	−0.455641	+	0.331043i	0.336178	+	0.941799i	$0.390866\pi$
$614$	1.93112			0.0779335
$615$	−1.35410	+	3.71847i	−0.0546027	+	0.149943i
$616$	−5.67376			−0.228602
$617$	1.61803	−	1.17557i	0.0651396	−	0.0473267i	−0.554739	−	0.832024i	$-0.687182\pi$
$617$	1.61803	−	1.17557i	0.0651396	−	0.0473267i	0.619879	+	0.784698i	$0.287182\pi$
$618$	−0.708204			−0.0284881
$619$	12.8262	−	39.4751i	0.515530	−	1.58664i	−0.266785	−	0.963756i	$-0.585962\pi$
$619$	12.8262	−	39.4751i	0.515530	−	1.58664i	0.782316	−	0.622882i	$-0.214038\pi$
$620$	8.07295	−	24.8460i	0.324217	−	0.997839i
$621$	−0.427051	+	0.310271i	−0.0171370	+	0.0124507i
$622$	1.97214	+	1.43284i	0.0790754	+	0.0574517i
$623$	−1.57295	−	4.84104i	−0.0630189	−	0.193952i
$624$	2.68692			0.107563
$625$	−2.29180	−	7.05342i	−0.0916718	−	0.282137i
$626$	2.93363	+	9.02878i	0.117251	+	0.360863i
$627$	0.347524	−	1.06957i	0.0138788	−	0.0427145i
$628$	−30.6246	+	22.2501i	−1.22206	+	0.887875i
$629$	7.92299			0.315910
$630$	0.545085	−	1.67760i	0.0217167	−	0.0668371i
$631$	−2.89919	−	2.10638i	−0.115415	−	0.0838538i	0.528581	−	0.848883i	$-0.322724\pi$
$631$	−2.89919	−	2.10638i	−0.115415	−	0.0838538i	−0.643995	+	0.765029i	$0.722724\pi$
$632$	5.50000	+	16.9273i	0.218778	+	0.673330i
$633$	−0.399187	+	0.290026i	−0.0158663	+	0.0115275i
$634$	−3.42705	−	2.48990i	−0.136106	−	0.0988865i
$635$	−20.1803	−	14.6619i	−0.800832	−	0.581839i
$636$	6.43769	+	4.67726i	0.255271	+	0.185465i
$637$	−1.80902	−	1.31433i	−0.0716759	−	0.0520756i
$638$	4.76393	−	3.46120i	0.188606	−	0.137030i
$639$	−7.75987	−	23.8824i	−0.306976	−	0.944774i
$640$	−13.2082	−	9.59632i	−0.522100	−	0.379328i
$641$	0.656541	−	2.02063i	0.0259318	−	0.0798099i	−0.937253	−	0.348650i	$-0.886640\pi$
$641$	0.656541	−	2.02063i	0.0259318	−	0.0798099i	0.963185	+	0.268840i	$0.0866403\pi$
$642$	1.43769			0.0567413
$643$	1.66312	−	1.20833i	0.0655870	−	0.0476518i	−0.554509	−	0.832178i	$-0.687094\pi$
$643$	1.66312	−	1.20833i	0.0655870	−	0.0476518i	0.620096	+	0.784526i	$0.287094\pi$
$644$	0.135255	−	0.416272i	0.00532979	−	0.0164034i
$645$	−0.854102	−	2.62866i	−0.0336302	−	0.103503i
$646$	−0.132742	−	0.408539i	−0.00522268	−	0.0160738i
$647$	34.2148			1.34512			0.672561	−	0.740042i	$-0.265194\pi$
$647$	34.2148			1.34512			0.672561	+	0.740042i	$0.265194\pi$
$648$	−3.50658	−	10.7921i	−0.137751	−	0.423955i
$649$	16.7812	+	12.1922i	0.658718	+	0.478587i
$650$	1.64590	−	1.19581i	0.0645574	−	0.0469037i
$651$	1.02786	−	3.16344i	0.0402852	−	0.123985i
$652$	8.45898	−	26.0341i	0.331279	−	1.01957i
$653$	5.70820			0.223379			0.111690	−	0.993743i	$-0.464374\pi$
$653$	5.70820			0.223379			0.111690	+	0.993743i	$0.464374\pi$
$654$	1.89919	−	1.37984i	0.0742641	−	0.0539560i
$655$	−8.23607			−0.321810
$656$	−15.8713	−	12.4042i	−0.619671	−	0.484304i
$657$	−30.5623			−1.19235
$658$	3.57295	−	2.59590i	0.139288	−	0.101199i
$659$	17.5066			0.681959			0.340980	−	0.940071i	$-0.389241\pi$
$659$	17.5066			0.681959			0.340980	+	0.940071i	$0.389241\pi$
$660$	1.36475	−	4.20025i	0.0531226	−	0.163495i
$661$	−8.25329	+	25.4010i	−0.321016	+	0.987985i	0.652191	+	0.758054i	$0.273850\pi$
$661$	−8.25329	+	25.4010i	−0.321016	+	0.987985i	−0.973207	+	0.229930i	$0.926150\pi$
$662$	−5.94427	+	4.31877i	−0.231031	+	0.167854i
$663$	1.01722	+	0.739054i	0.0395056	+	0.0287025i
$664$	3.11803	+	9.59632i	0.121003	+	0.372410i
$665$	−1.23607			−0.0479327
$666$	1.81308	+	5.58009i	0.0702555	+	0.216224i
$667$	0.291796	+	0.898056i	0.0112984	+	0.0347729i
$668$	−6.87539	+	21.1603i	−0.266017	+	0.818715i
$669$	5.01722	−	3.64522i	0.193977	−	0.140933i
$670$	2.43769			0.0941763
$671$	3.01064	−	9.26581i	0.116225	−	0.357703i
$672$	−1.28115	−	0.930812i	−0.0494215	−	0.0359069i
$673$	−15.3713	−	47.3081i	−0.592521	−	1.82359i	−0.566698	−	0.823925i	$-0.691779\pi$
$673$	−15.3713	−	47.3081i	−0.592521	−	1.82359i	−0.0258227	−	0.999667i	$-0.508221\pi$
$674$	−11.1246	+	8.08250i	−0.428504	+	0.311326i
$675$	−4.30902	−	3.13068i	−0.165854	−	0.120500i
$676$	−12.0000	−	8.71851i	−0.461538	−	0.335327i
$677$	−11.0451	−	8.02472i	−0.424497	−	0.308415i	0.354948	−	0.934886i	$-0.384499\pi$
$677$	−11.0451	−	8.02472i	−0.424497	−	0.308415i	−0.779445	+	0.626471i	$0.784499\pi$
$678$	−0.590170	−	0.428784i	−0.0226653	−	0.0164673i
$679$	−7.78115	+	5.65334i	−0.298613	+	0.216955i
$680$	−1.08359	−	3.33495i	−0.0415539	−	0.127890i
$681$	−6.69098	−	4.86128i	−0.256399	−	0.186285i
$682$	3.96149	−	12.1922i	0.151693	−	0.466864i
$683$	28.1591			1.07748			0.538738	−	0.842473i	$-0.318901\pi$
$683$	28.1591			1.07748			0.538738	+	0.842473i	$0.318901\pi$
$684$	−3.27051	+	2.37616i	−0.125051	+	0.0908549i
$685$	−2.69098	+	8.28199i	−0.102817	+	0.316439i
$686$	0.118034	+	0.363271i	0.00450656	+	0.0138698i
$687$	0.628677	+	1.93487i	0.0239855	+	0.0738199i
$688$	14.0689			0.536371
$689$	7.76393	+	23.8949i	0.295782	+	0.910324i
$690$	−0.0450850	−	0.0327561i	−0.00171636	−	0.00124701i
$691$	16.6353	−	12.0862i	0.632835	−	0.459781i	−0.224546	−	0.974463i	$-0.572090\pi$
$691$	16.6353	−	12.0862i	0.632835	−	0.459781i	0.857381	+	0.514682i	$0.172090\pi$
$692$	0.572949	−	1.76336i	0.0217803	−	0.0670327i
$693$	−3.39919	+	10.4616i	−0.129124	+	0.397404i
$694$	−7.07701			−0.268640
$695$	18.7533	−	13.6251i	0.711353	−	0.516828i
$696$	2.24922			0.0852566
$697$	−2.59675	−	9.06154i	−0.0983588	−	0.343230i
$698$	−10.5279			−0.398486
$699$	4.71885	−	3.42844i	0.178483	−	0.129676i
$700$	4.41641			0.166925
$701$	−11.1631	+	34.3565i	−0.421625	+	1.29763i	0.484564	+	0.874756i	$0.338978\pi$
$701$	−11.1631	+	34.3565i	−0.421625	+	1.29763i	−0.906189	+	0.422873i	$0.861022\pi$
$702$	−0.590170	+	1.81636i	−0.0222745	+	0.0685540i
$703$	3.32624	−	2.41665i	0.125451	−	0.0911458i
$704$	14.6803	+	10.6659i	0.553286	+	0.401986i
$705$	2.20820	+	6.79615i	0.0831658	+	0.255958i
$706$	1.32624			0.0499136
$707$	−3.63525	−	11.1882i	−0.136718	−	0.420774i
$708$	1.17783	+	3.62498i	0.0442655	+	0.136235i
$709$	−7.72542	+	23.7764i	−0.290134	+	0.892942i	0.694678	+	0.719321i	$0.255547\pi$
$709$	−7.72542	+	23.7764i	−0.290134	+	0.892942i	−0.984813	+	0.173621i	$0.944453\pi$
$710$	4.39919	−	3.19620i	0.165099	−	0.119951i
$711$	34.5066			1.29410
$712$	2.31559	−	7.12667i	0.0867806	−	0.267083i
$713$	1.66312	+	1.20833i	0.0622843	+	0.0452522i
$714$	−0.0663712	−	0.204270i	−0.00248388	−	0.00764460i
$715$	11.2812	−	8.19624i	0.421891	−	0.306522i
$716$	16.3328	+	11.8665i	0.610386	+	0.443471i
$717$	−6.18034	−	4.49028i	−0.230809	−	0.167693i
$718$	−1.85410	−	1.34708i	−0.0691945	−	0.0502727i
$719$	40.1074	+	29.1397i	1.49575	+	1.08673i	0.972035	+	0.234837i	$0.0754556\pi$
$719$	40.1074	+	29.1397i	1.49575	+	1.08673i	0.523719	+	0.851891i	$0.324544\pi$
$720$	−11.7533	+	8.53926i	−0.438019	+	0.318240i
$721$	−1.50000	−	4.61653i	−0.0558629	−	0.171928i
$722$	5.69098	+	4.13474i	0.211796	+	0.153879i
$723$	2.45492	−	7.55545i	0.0912993	−	0.280990i
$724$	−5.45898			−0.202881
$725$	−7.70820	+	5.60034i	−0.286276	+	0.207991i
$726$	0.173762	−	0.534785i	0.00644892	−	0.0198477i
$727$	−4.98936	−	15.3557i	−0.185045	−	0.569510i	0.814904	−	0.579596i	$-0.196790\pi$
$727$	−4.98936	−	15.3557i	−0.185045	−	0.569510i	−0.999949	+	0.0100858i	$0.996790\pi$
$728$	−1.01722	−	3.13068i	−0.0377007	−	0.116031i
$729$	−19.4377			−0.719915
$730$	−2.04508	−	6.29412i	−0.0756920	−	0.232956i
$731$	5.32624	+	3.86974i	0.196998	+	0.143127i
$732$	1.44834	−	1.05228i	0.0535321	−	0.0388933i
$733$	−5.00658	+	15.4087i	−0.184922	+	0.569132i	−0.999947	−	0.0102941i	$-0.996723\pi$
$733$	−5.00658	+	15.4087i	−0.184922	+	0.569132i	0.815025	+	0.579426i	$0.196723\pi$
$734$	3.74671	−	11.5312i	0.138294	−	0.425624i
$735$	−0.618034			−0.0227965
$736$	0.791796	−	0.575274i	0.0291860	−	0.0212049i
$737$	−15.2016			−0.559959
$738$	5.78773	−	3.90249i	0.213049	−	0.143653i
$739$	3.74265			0.137675			0.0688377	−	0.997628i	$-0.478071\pi$
$739$	3.74265			0.137675			0.0688377	+	0.997628i	$0.478071\pi$
$740$	13.0623	−	9.49032i	0.480180	−	0.348871i
$741$	0.652476			0.0239693
$742$	1.32624	−	4.08174i	0.0486877	−	0.149845i
$743$	−5.50000	+	16.9273i	−0.201775	+	0.621001i	0.798055	+	0.602585i	$0.205862\pi$
$743$	−5.50000	+	16.9273i	−0.201775	+	0.621001i	−0.999830	+	0.0184163i	$0.994138\pi$
$744$	3.96149	−	2.87819i	0.145235	−	0.105520i
$745$	13.5902	+	9.87384i	0.497905	+	0.361749i
$746$	2.65654	+	8.17599i	0.0972629	+	0.299344i
$747$	19.5623			0.715747
$748$	3.25078	+	10.0049i	0.118860	+	0.365814i
$749$	3.04508	+	9.37181i	0.111265	+	0.342438i
$750$	0.538507	−	1.65735i	0.0196635	−	0.0605180i
$751$	−23.8435	+	17.3233i	−0.870060	+	0.632136i	−0.930603	−	0.366030i	$-0.880717\pi$
$751$	−23.8435	+	17.3233i	−0.870060	+	0.632136i	0.0605429	+	0.998166i	$0.480717\pi$
$752$	−36.3738			−1.32642
$753$	1.44427	−	4.44501i	0.0526322	−	0.161985i
$754$	2.76393	+	2.00811i	0.100656	+	0.0731312i
$755$	−5.82624	−	17.9313i	−0.212039	−	0.652587i
$756$	−3.35410	+	2.43690i	−0.121988	+	0.0886291i
$757$	14.7812	+	10.7391i	0.537230	+	0.390321i	0.823055	−	0.567961i	$-0.192268\pi$
$757$	14.7812	+	10.7391i	0.537230	+	0.390321i	−0.285825	+	0.958282i	$0.592268\pi$
$758$	−8.25329	−	5.99637i	−0.299773	−	0.217798i
$759$	0.281153	+	0.204270i	0.0102052	+	0.00741452i
$760$	−1.47214	−	1.06957i	−0.0534000	−	0.0387974i
$761$	40.5967	−	29.4953i	1.47163	−	1.06920i	0.491494	−	0.870881i	$-0.336451\pi$
$761$	40.5967	−	29.4953i	1.47163	−	1.06920i	0.980137	−	0.198321i	$-0.0635490\pi$
$762$	−0.695048	−	2.13914i	−0.0251789	−	0.0774928i
$763$	13.0172	+	9.45756i	0.471255	+	0.342387i
$764$	1.31308	−	4.04125i	0.0475057	−	0.146207i
$765$	−6.79837			−0.245796
$766$	−6.76393	+	4.91428i	−0.244391	+	0.177560i
$767$	−3.71885	+	11.4454i	−0.134280	+	0.413271i
$768$	0.656541	+	2.02063i	0.0236909	+	0.0729131i
$769$	−6.14590	−	18.9151i	−0.221627	−	0.682097i	−0.998617	−	0.0525838i	$-0.983254\pi$
$769$	−6.14590	−	18.9151i	−0.221627	−	0.682097i	0.776990	−	0.629513i	$-0.216746\pi$
$770$	−2.38197			−0.0858401
$771$	1.04915	+	3.22895i	0.0377842	+	0.116288i
$772$	−11.6976	−	8.49878i	−0.421004	−	0.305878i
$773$	−24.6803	+	17.9313i	−0.887690	+	0.644945i	−0.935275	−	0.353923i	$-0.884848\pi$
$773$	−24.6803	+	17.9313i	−0.887690	+	0.644945i	0.0475846	+	0.998867i	$0.484848\pi$
$774$	−1.50658	+	4.63677i	−0.0541528	+	0.166665i
$775$	−6.40983	+	19.7274i	−0.230248	+	0.708630i
$776$	−14.1591			−0.508280
$777$	1.66312	−	1.20833i	0.0596641	−	0.0433485i
$778$	8.70820			0.312204
$779$	−3.85410	−	3.01217i	−0.138088	−	0.107922i
$780$	2.56231			0.0917453
$781$	−27.4336	+	19.9317i	−0.981652	+	0.713212i
$782$	0.132742			0.00474686
$783$	2.76393	−	8.50651i	0.0987749	−	0.303998i
$784$	0.972136	−	2.99193i	0.0347191	−	0.106855i
$785$	−26.7254	+	19.4172i	−0.953871	+	0.693028i
$786$	−0.600813	−	0.436516i	−0.0214303	−	0.0155700i
$787$	−4.45492	−	13.7108i	−0.158801	−	0.488738i	0.839726	−	0.543011i	$-0.182716\pi$
$787$	−4.45492	−	13.7108i	−0.158801	−	0.488738i	−0.998526	+	0.0542731i	$0.982716\pi$
$788$	7.95743			0.283472
$789$	2.66312	+	8.19624i	0.0948095	+	0.291794i
$790$	2.30902	+	7.10642i	0.0821511	+	0.252835i
$791$	1.54508	−	4.75528i	0.0549369	−	0.169078i
$792$	−13.1008	+	9.51830i	−0.465517	+	0.338218i
$793$	5.65248			0.200725
$794$	−1.66718	+	5.13107i	−0.0591662	+	0.182095i
$795$	5.61803	+	4.08174i	0.199251	+	0.144764i
$796$	0.270510	+	0.832544i	0.00958797	+	0.0295087i
$797$	9.85410	−	7.15942i	0.349050	−	0.253600i	−0.399420	−	0.916768i	$-0.630789\pi$
$797$	9.85410	−	7.15942i	0.349050	−	0.253600i	0.748470	+	0.663168i	$0.230789\pi$
$798$	−0.0901699	−	0.0655123i	−0.00319198	−	0.00231911i
$799$	−13.7705	−	10.0049i	−0.487166	−	0.353947i
$800$	7.98936	+	5.80461i	0.282466	+	0.205224i
$801$	−11.7533	−	8.53926i	−0.415282	−	0.301720i
$802$	−3.28115	+	2.38390i	−0.115862	+	0.0841783i
$803$	12.7533	+	39.2506i	0.450054	+	1.38512i
$804$	−2.25987	−	1.64189i	−0.0796994	−	0.0579050i
$805$	0.118034	−	0.363271i	0.00416015	−	0.0128036i
$806$	7.43769			0.261982
$807$	−8.19098	+	5.95110i	−0.288336	+	0.209489i
$808$	5.35159	−	16.4705i	0.188268	−	0.579430i
$809$	8.57953	+	26.4051i	0.301640	+	0.928353i	0.980910	+	0.194464i	$0.0622967\pi$
$809$	8.57953	+	26.4051i	0.301640	+	0.928353i	−0.679270	+	0.733889i	$0.737703\pi$
$810$	−1.47214	−	4.53077i	−0.0517256	−	0.159195i
$811$	−19.9443			−0.700338			−0.350169	−	0.936687i	$-0.613876\pi$
$811$	−19.9443			−0.700338			−0.350169	+	0.936687i	$0.613876\pi$
$812$	2.29180	+	7.05342i	0.0804263	+	0.247527i
$813$	−8.06231	−	5.85761i	−0.282757	−	0.205435i
$814$	6.40983	−	4.65701i	0.224664	−	0.163228i
$815$	7.38197	−	22.7194i	0.258579	−	0.795824i
$816$	−0.546638	+	1.68238i	−0.0191361	+	0.0588950i
$817$	3.41641			0.119525
$818$	1.68034	−	1.22084i	0.0587517	−	0.0426856i
$819$	−6.38197			−0.223004
$820$	−15.1353	−	11.8290i	−0.528546	−	0.413085i
$821$	−44.3951			−1.54940			−0.774700	−	0.632329i	$-0.782099\pi$
$821$	−44.3951			−1.54940			−0.774700	+	0.632329i	$0.782099\pi$
$822$	−0.635255	+	0.461540i	−0.0221571	+	0.0160980i
$823$	−33.0344			−1.15151			−0.575754	−	0.817623i	$-0.695291\pi$
$823$	−33.0344			−1.15151			−0.575754	+	0.817623i	$0.695291\pi$
$824$	2.20820	−	6.79615i	0.0769264	−	0.236755i
$825$	−1.08359	+	3.33495i	−0.0377258	+	0.116108i
$826$	1.66312	−	1.20833i	0.0578673	−	0.0420431i
$827$	6.32624	+	4.59628i	0.219985	+	0.159828i	0.692320	−	0.721591i	$-0.256589\pi$
$827$	6.32624	+	4.59628i	0.219985	+	0.159828i	−0.472335	+	0.881419i	$0.656589\pi$
$828$	−0.386031	−	1.18808i	−0.0134155	−	0.0412887i
$829$	54.9787			1.90949			0.954745	−	0.297426i	$-0.0961282\pi$
$829$	54.9787			1.90949			0.954745	+	0.297426i	$0.0961282\pi$
$830$	1.30902	+	4.02874i	0.0454366	+	0.139840i
$831$	0.0663712	+	0.204270i	0.00230239	+	0.00708603i
$832$	−3.25329	+	10.0126i	−0.112787	+	0.347124i
$833$	1.19098	−	0.865300i	0.0412651	−	0.0299809i
$834$	2.09017			0.0723767
$835$	−6.00000	+	18.4661i	−0.207639	+	0.639046i
$836$	4.41641	+	3.20871i	0.152745	+	0.110975i
$837$	−6.01722	−	18.5191i	−0.207986	−	0.640114i
$838$	2.76393	−	2.00811i	0.0954784	−	0.0693692i
$839$	−19.8992	−	14.4576i	−0.686996	−	0.499132i	0.188675	−	0.982040i	$-0.439581\pi$
$839$	−19.8992	−	14.4576i	−0.686996	−	0.499132i	−0.875671	+	0.482908i	$0.839581\pi$
$840$	−0.736068	−	0.534785i	−0.0253968	−	0.0184518i
$841$	10.5172	+	7.64121i	0.362663	+	0.263490i
$842$	−10.4164	−	7.56796i	−0.358973	−	0.260809i
$843$	3.88197	−	2.82041i	0.133702	−	0.0971402i
$844$	−0.740133	−	2.27790i	−0.0254764	−	0.0784084i
$845$	−10.4721	−	7.60845i	−0.360252	−	0.261739i
$846$	3.89512	−	11.9880i	0.133917	−	0.412154i
$847$	3.85410			0.132429
$848$	−28.5967	+	20.7768i	−0.982016	+	0.713477i
$849$	−0.877901	+	2.70190i	−0.0301295	+	0.0927290i
$850$	0.413895	+	1.27384i	0.0141965	+	0.0436923i
$851$	0.392609	+	1.20833i	0.0134585	+	0.0414209i
$852$	−6.23104			−0.213472
$853$	14.9164	+	45.9080i	0.510728	+	1.57186i	0.790923	+	0.611916i	$0.209601\pi$
$853$	14.9164	+	45.9080i	0.510728	+	1.57186i	−0.280195	+	0.959943i	$0.590399\pi$
$854$	−0.781153	−	0.567541i	−0.0267305	−	0.0194208i
$855$	−2.85410	+	2.07363i	−0.0976082	+	0.0709165i
$856$	−4.48278	+	13.7966i	−0.153218	+	0.471557i
$857$	−2.68441	+	8.26175i	−0.0916975	+	0.282216i	−0.986379	−	0.164489i	$-0.947403\pi$
$857$	−2.68441	+	8.26175i	−0.0916975	+	0.282216i	0.894681	+	0.446705i	$0.147403\pi$
$858$	1.25735			0.0429254
$859$	−30.8435	+	22.4091i	−1.05237	+	0.764588i	−0.972661	−	0.232230i	$-0.925398\pi$
$859$	−30.8435	+	22.4091i	−1.05237	+	0.764588i	−0.0797044	+	0.996819i	$0.525398\pi$
$860$	13.4164			0.457496
$861$	−1.92705	−	1.50609i	−0.0656737	−	0.0513273i
$862$	−0.347524			−0.0118367
$863$	1.59017	−	1.15533i	0.0541300	−	0.0393278i	−0.560391	−	0.828228i	$-0.689349\pi$
$863$	1.59017	−	1.15533i	0.0541300	−	0.0393278i	0.614521	+	0.788900i	$0.289349\pi$
$864$	−9.27051			−0.315389
$865$	0.500000	−	1.53884i	0.0170005	−	0.0523222i
$866$	−3.92705	+	12.0862i	−0.133447	+	0.410706i
$867$	4.58359	−	3.33017i	0.155667	−	0.113099i
$868$	13.0623	+	9.49032i	0.443364	+	0.322122i
$869$	−14.3992	−	44.3161i	−0.488459	−	1.50332i
$870$	0.944272			0.0320138
$871$	−2.72542	−	8.38800i	−0.0923475	−	0.284216i
$872$	7.31966	+	22.5276i	0.247875	+	0.762881i
$873$	−8.48278	+	26.1073i	−0.287099	+	0.883599i
$874$	0.0557281	−	0.0404888i	0.00188503	−	0.00136956i
$875$	11.9443			0.403790
$876$	−2.34346	+	7.21242i	−0.0791781	+	0.243685i
$877$	−19.2984	−	14.0211i	−0.651660	−	0.473459i	0.212176	−	0.977231i	$-0.431945\pi$
$877$	−19.2984	−	14.0211i	−0.651660	−	0.473459i	−0.863836	+	0.503773i	$0.831945\pi$
$878$	−1.88603	−	5.80461i	−0.0636505	−	0.195896i
$879$	6.16312	−	4.47777i	0.207877	−	0.151031i
$880$	15.8713	+	11.5312i	0.535022	+	0.388716i
$881$	−21.8713	−	15.8904i	−0.736864	−	0.535363i	0.154864	−	0.987936i	$-0.450506\pi$
$881$	−21.8713	−	15.8904i	−0.736864	−	0.535363i	−0.891727	+	0.452573i	$0.850506\pi$
$882$	0.881966	+	0.640786i	0.0296973	+	0.0215764i
$883$	−28.9615	−	21.0418i	−0.974632	−	0.708111i	−0.0181293	−	0.999836i	$-0.505771\pi$
$883$	−28.9615	−	21.0418i	−0.974632	−	0.708111i	−0.956502	+	0.291724i	$0.905771\pi$
$884$	−4.93769	+	3.58744i	−0.166073	+	0.120659i
$885$	1.02786	+	3.16344i	0.0345513	+	0.106338i
$886$	−5.73607	−	4.16750i	−0.192707	−	0.140010i
$887$	4.98936	−	15.3557i	0.167526	−	0.515593i	−0.831687	−	0.555244i	$-0.812625\pi$
$887$	4.98936	−	15.3557i	0.167526	−	0.515593i	0.999214	+	0.0396516i	$0.0126248\pi$
$888$	3.02631			0.101556
$889$	12.4721	−	9.06154i	0.418302	−	0.303914i
$890$	0.972136	−	2.99193i	0.0325861	−	0.100290i
$891$	9.18034	+	28.2542i	0.307553	+	0.946551i
$892$	9.30244	+	28.6300i	0.311469	+	0.958602i
$893$	−8.83282			−0.295579
$894$	0.468071	+	1.44057i	0.0156546	+	0.0481800i
$895$	14.2533	+	10.3556i	0.476435	+	0.346150i
$896$	8.16312	−	5.93085i	0.272711	−	0.198136i
$897$	−0.0623059	+	0.191758i	−0.00208033	+	0.00640261i
$898$	0.0623059	−	0.191758i	0.00207917	−	0.00639904i
$899$	−34.8328			−1.16174
$900$	10.1976	−	7.40896i	0.339919	−	0.246965i
$901$	−16.5410			−0.551061
$902$	−7.42705	−	5.80461i	−0.247294	−	0.193272i
$903$	1.70820			0.0568455
$904$	5.95492	−	4.32650i	0.198058	−	0.143897i
$905$	−4.76393			−0.158358
$906$	0.525352	−	1.61687i	0.0174536	−	0.0537168i
$907$	6.35410	−	19.5559i	0.210984	−	0.649344i	−0.788430	−	0.615125i	$-0.789106\pi$
$907$	6.35410	−	19.5559i	0.210984	−	0.649344i	0.999414	−	0.0342188i	$-0.0108943\pi$
$908$	32.4787	−	23.5972i	1.07784	−	0.783099i
$909$	−27.1631	−	19.7352i	−0.900944	−	0.654574i
$910$	−0.427051	−	1.31433i	−0.0141566	−	0.0435695i
$911$	−42.3951			−1.40461			−0.702307	−	0.711875i	$-0.747846\pi$
$911$	−42.3951			−1.40461			−0.702307	+	0.711875i	$0.747846\pi$
$912$	0.283665	+	0.873032i	0.00939310	+	0.0289090i
$913$	−8.16312	−	25.1235i	−0.270160	−	0.831466i
$914$	3.50000	−	10.7719i	0.115770	−	0.356303i
$915$	1.26393	−	0.918300i	0.0417843	−	0.0303581i
$916$	−9.87539			−0.326292
$917$	1.57295	−	4.84104i	0.0519434	−	0.159865i
$918$	−1.01722	−	0.739054i	−0.0335733	−	0.0243924i
$919$	9.29180	+	28.5972i	0.306508	+	0.943335i	0.979110	+	0.203330i	$0.0651766\pi$
$919$	9.29180	+	28.5972i	0.306508	+	0.943335i	−0.672602	+	0.740004i	$0.734823\pi$
$920$	0.454915	−	0.330515i	0.0149981	−	0.0108968i
$921$	−1.56231	−	1.13508i	−0.0514797	−	0.0374022i
$922$	1.04508	+	0.759299i	0.0344180	+	0.0250062i
$923$	−15.9164	−	11.5639i	−0.523895	−	0.380632i
$924$	2.20820	+	1.60435i	0.0726446	+	0.0527794i
$925$	−10.3713	+	7.53521i	−0.341007	+	0.247756i
$926$	2.20820	+	6.79615i	0.0725661	+	0.223335i
$927$	−11.2082	−	8.14324i	−0.368126	−	0.267459i
$928$	−5.12461	+	15.7719i	−0.168224	+	0.517739i
$929$	−26.2148			−0.860079			−0.430040	−	0.902810i	$-0.641500\pi$
$929$	−26.2148			−0.860079			−0.430040	+	0.902810i	$0.641500\pi$
$930$	1.66312	−	1.20833i	0.0545358	−	0.0396226i
$931$	0.236068	−	0.726543i	0.00773682	−	0.0238115i
$932$	8.74922	+	26.9273i	0.286590	+	0.882034i
$933$	−0.753289	−	2.31838i	−0.0246616	−	0.0759005i
$934$	11.6606			0.381547
$935$	2.83688	+	8.73102i	0.0927759	+	0.285535i
$936$	−7.60081	−	5.52231i	−0.248440	−	0.180502i
$937$	6.09017	−	4.42477i	0.198957	−	0.144551i	−0.483846	−	0.875153i	$-0.660761\pi$
$937$	6.09017	−	4.42477i	0.198957	−	0.144551i	0.682803	+	0.730602i	$0.260761\pi$
$938$	−0.465558	+	1.43284i	−0.0152010	+	0.0467839i
$939$	2.93363	−	9.02878i	0.0957354	−	0.294643i
$940$	−34.6869			−1.13136
$941$	14.9894	−	10.8904i	0.488639	−	0.355017i	−0.316022	−	0.948752i	$-0.602347\pi$
$941$	14.9894	−	10.8904i	0.488639	−	0.355017i	0.804661	+	0.593735i	$0.202347\pi$
$942$	−2.97871			−0.0970517
$943$	1.25329	−	0.845055i	0.0408127	−	0.0275188i
$944$	−16.9311			−0.551061
$945$	−2.92705	+	2.12663i	−0.0952170	+	0.0691792i
$946$	6.58359			0.214051
$947$	−3.50000	+	10.7719i	−0.113735	+	0.350039i	−0.991681	−	0.128720i	$-0.958913\pi$
$947$	−3.50000	+	10.7719i	−0.113735	+	0.350039i	0.877946	+	0.478759i	$0.158913\pi$
$948$	2.64590	−	8.14324i	0.0859348	−	0.264480i
$949$	−19.3713	+	14.0741i	−0.628820	+	0.456864i
$950$	0.562306	+	0.408539i	0.0182436	+	0.0132548i
$951$	1.30902	+	4.02874i	0.0424478	+	0.130641i
$952$	2.16718			0.0702388
$953$	−4.23607	−	13.0373i	−0.137220	−	0.422319i	0.858709	−	0.512464i	$-0.171267\pi$
$953$	−4.23607	−	13.0373i	−0.137220	−	0.422319i	−0.995929	+	0.0901447i	$0.971267\pi$
$954$	−3.78522	−	11.6497i	−0.122551	−	0.377173i
$955$	1.14590	−	3.52671i	0.0370804	−	0.114122i
$956$	30.0000	−	21.7963i	0.970269	−	0.704942i
$957$	−5.88854			−0.190350
$958$	4.82217	−	14.8411i	0.155797	−	0.479495i
$959$	−4.35410	−	3.16344i	−0.140601	−	0.102153i
$960$	0.899187	+	2.76741i	0.0290211	+	0.0893179i
$961$	−36.2705	+	26.3521i	−1.17002	+	0.850067i
$962$	3.71885	+	2.70190i	0.119900	+	0.0871128i
$963$	22.7533	+	16.5312i	0.733214	+	0.532712i
$964$	31.1976	+	22.6664i	1.00481	+	0.730034i
$965$	−10.2082	−	7.41669i	−0.328614	−	0.238752i
$966$	0.0278640	−	0.0202444i	0.000896511	−	0.000651353i
$967$	4.52786	+	13.9353i	0.145606	+	0.448130i	0.997088	−	0.0762535i	$-0.0242958\pi$
$967$	4.52786	+	13.9353i	0.145606	+	0.448130i	−0.851482	+	0.524384i	$0.824296\pi$
$968$	4.59017	+	3.33495i	0.147534	+	0.107189i
$969$	−0.132742	+	0.408539i	−0.00426430	+	0.0131242i
$970$	−5.94427			−0.190859
$971$	41.6697	−	30.2748i	1.33724	−	0.971565i	0.337704	−	0.941252i	$-0.390350\pi$
$971$	41.6697	−	30.2748i	1.33724	−	0.971565i	0.999540	−	0.0303123i	$-0.00965019\pi$
$972$	−5.53038	+	17.0207i	−0.177387	+	0.545941i
$973$	4.42705	+	13.6251i	0.141925	+	0.436799i
$974$	3.13525	+	9.64932i	0.100460	+	0.309184i
$975$	−2.03444			−0.0651543
$976$	2.45743	+	7.56318i	0.0786603	+	0.242092i
$977$	−32.7705	−	23.8092i	−1.04842	−	0.761723i	−0.0765098	−	0.997069i	$-0.524378\pi$
$977$	−32.7705	−	23.8092i	−1.04842	−	0.761723i	−0.971912	+	0.235346i	$0.924378\pi$
$978$	1.74265	−	1.26611i	0.0557237	−	0.0404856i
$979$	−6.06231	+	18.6579i	−0.193752	+	0.596308i
$980$	0.927051	−	2.85317i	0.0296136	−	0.0911412i
$981$	45.9230			1.46621
$982$	−7.04508	+	5.11855i	−0.224818	+	0.163340i
$983$	−17.8754			−0.570136			−0.285068	−	0.958507i	$-0.592016\pi$
$983$	−17.8754			−0.570136			−0.285068	+	0.958507i	$0.592016\pi$
$984$	−0.991869	−	3.46120i	−0.0316196	−	0.110339i
$985$	6.94427			0.221263
$986$	−1.81966	+	1.32206i	−0.0579498	+	0.0421030i
$987$	−4.41641			−0.140576
$988$	−0.978714	+	3.01217i	−0.0311370	+	0.0958299i
$989$	−0.326238	+	1.00406i	−0.0103738	+	0.0319272i
$990$	−5.50000	+	3.99598i	−0.174801	+	0.127001i
$991$	42.0066	+	30.5196i	1.33438	+	0.969486i	0.999631	+	0.0271798i	$0.00865267\pi$
$991$	42.0066	+	30.5196i	1.33438	+	0.969486i	0.334752	+	0.942306i	$0.391347\pi$
$992$	11.1565	+	34.3363i	0.354221	+	1.09018i
$993$	7.34752			0.233167
$994$	1.03851	+	3.19620i	0.0329394	+	0.101377i
$995$	0.236068	+	0.726543i	0.00748386	+	0.0230329i
$996$	1.50000	−	4.61653i	0.0475293	−	0.146280i
$997$	37.4164	−	27.1846i	1.18499	−	0.860945i	0.192264	−	0.981343i	$-0.438417\pi$
$997$	37.4164	−	27.1846i	1.18499	−	0.860945i	0.992726	+	0.120398i	$0.0384171\pi$
$998$	−4.04760			−0.128124
$999$	3.71885	−	11.4454i	0.117659	−	0.362118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.b.78.1	✓	4
41.10	even	5	inner	287.2.h.b.92.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.b.78.1	✓	4	1.1	even	1	trivial
287.2.h.b.92.1	yes	4	41.10	even	5	inner

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.224514i) q^{2} +0.381966 q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.500000 + 1.53884i) q^{5} +(-0.118034 + 0.0857567i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.454915 - 1.40008i) q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.224514i) q^{2} +0.381966 q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.500000 + 1.53884i) q^{5} +(-0.118034 + 0.0857567i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.454915 - 1.40008i) q^{8} -2.85410 q^{9} +(-0.190983 - 0.587785i) q^{10} +(1.19098 + 3.66547i) q^{11} +(-0.218847 + 0.673542i) q^{12} +(-1.80902 + 1.31433i) q^{13} +0.381966 q^{14} +(-0.190983 + 0.587785i) q^{15} +(-2.54508 - 1.84911i) q^{16} +(-0.454915 - 1.40008i) q^{17} +(0.881966 - 0.640786i) q^{18} +(-0.618034 - 0.449028i) q^{19} +(-2.42705 - 1.76336i) q^{20} +(-0.309017 - 0.224514i) q^{21} +(-1.19098 - 0.865300i) q^{22} +(0.190983 - 0.138757i) q^{23} +(-0.173762 - 0.534785i) q^{24} +(1.92705 + 1.40008i) q^{25} +(0.263932 - 0.812299i) q^{26} -2.23607 q^{27} +(1.50000 - 1.08981i) q^{28} +(-1.23607 + 3.80423i) q^{29} +(-0.0729490 - 0.224514i) q^{30} +(2.69098 + 8.28199i) q^{31} +4.14590 q^{32} +(0.454915 + 1.40008i) q^{33} +(0.454915 + 0.330515i) q^{34} +(1.30902 - 0.951057i) q^{35} +(1.63525 - 5.03280i) q^{36} +(-1.66312 + 5.11855i) q^{37} +0.291796 q^{38} +(-0.690983 + 0.502029i) q^{39} +2.38197 q^{40} +(6.39919 + 0.224514i) q^{41} +0.145898 q^{42} +(-3.61803 + 2.62866i) q^{43} -7.14590 q^{44} +(1.42705 - 4.39201i) q^{45} +(-0.0278640 + 0.0857567i) q^{46} +(9.35410 - 6.79615i) q^{47} +(-0.972136 - 0.706298i) q^{48} +(0.309017 + 0.951057i) q^{49} -0.909830 q^{50} +(-0.173762 - 0.534785i) q^{51} +(-1.28115 - 3.94298i) q^{52} +(3.47214 - 10.6861i) q^{53} +(0.690983 - 0.502029i) q^{54} -6.23607 q^{55} +(-0.454915 + 1.40008i) q^{56} +(-0.236068 - 0.171513i) q^{57} +(-0.472136 - 1.45309i) q^{58} +(4.35410 - 3.16344i) q^{59} +(-0.927051 - 0.673542i) q^{60} +(-2.04508 - 1.48584i) q^{61} +(-2.69098 - 1.95511i) q^{62} +(2.30902 + 1.67760i) q^{63} +(3.80902 - 2.76741i) q^{64} +(-1.11803 - 3.44095i) q^{65} +(-0.454915 - 0.330515i) q^{66} +(-1.21885 + 3.75123i) q^{67} +2.72949 q^{68} +(0.0729490 - 0.0530006i) q^{69} +(-0.190983 + 0.587785i) q^{70} +(2.71885 + 8.36775i) q^{71} +(1.29837 + 3.99598i) q^{72} +10.7082 q^{73} +(-0.635255 - 1.95511i) q^{74} +(0.736068 + 0.534785i) q^{75} +(1.14590 - 0.832544i) q^{76} +(1.19098 - 3.66547i) q^{77} +(0.100813 - 0.310271i) q^{78} -12.0902 q^{79} +(4.11803 - 2.99193i) q^{80} +7.70820 q^{81} +(-2.02786 + 1.36733i) q^{82} -6.85410 q^{83} +(0.572949 - 0.416272i) q^{84} +2.38197 q^{85} +(0.527864 - 1.62460i) q^{86} +(-0.472136 + 1.45309i) q^{87} +(4.59017 - 3.33495i) q^{88} +(4.11803 + 2.99193i) q^{89} +(0.545085 + 1.67760i) q^{90} +2.23607 q^{91} +(0.135255 + 0.416272i) q^{92} +(1.02786 + 3.16344i) q^{93} +(-1.36475 + 4.20025i) q^{94} +(1.00000 - 0.726543i) q^{95} +1.58359 q^{96} +(2.97214 - 9.14729i) q^{97} +(-0.309017 - 0.224514i) q^{98} +(-3.39919 - 10.4616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 6 q^{3} - 9 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 13 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + q^2 + 6 * q^3 - 9 * q^4 - 2 * q^5 + 4 * q^6 - q^7 - 13 * q^8 + 2 * q^9	\( 4 q + q^{2} + 6 q^{3} - 9 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 13 q^{8} + 2 q^{9} - 3 q^{10} + 7 q^{11} - 21 q^{12} - 5 q^{13} + 6 q^{14} - 3 q^{15} + q^{16} - 13 q^{17} + 8 q^{18} + 2 q^{19} - 3 q^{20} + q^{21} - 7 q^{22} + 3 q^{23} - 32 q^{24} + q^{25} + 10 q^{26} + 6 q^{28} + 4 q^{29} - 7 q^{30} + 13 q^{31} + 30 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} - 27 q^{36} + 9 q^{37} + 28 q^{38} - 5 q^{39} + 14 q^{40} + q^{41} + 14 q^{42} - 10 q^{43} - 42 q^{44} - q^{45} - 18 q^{46} + 24 q^{47} + 14 q^{48} - q^{49} - 26 q^{50} - 32 q^{51} + 15 q^{52} - 4 q^{53} + 5 q^{54} - 16 q^{55} - 13 q^{56} + 8 q^{57} + 16 q^{58} + 4 q^{59} + 3 q^{60} + 3 q^{61} - 13 q^{62} + 7 q^{63} + 13 q^{64} - 13 q^{66} - 25 q^{67} + 78 q^{68} + 7 q^{69} - 3 q^{70} + 31 q^{71} - 44 q^{72} + 16 q^{73} + 31 q^{74} - 6 q^{75} + 18 q^{76} + 7 q^{77} + 25 q^{78} - 26 q^{79} + 12 q^{80} + 4 q^{81} - 26 q^{82} - 14 q^{83} + 9 q^{84} + 14 q^{85} + 20 q^{86} + 16 q^{87} - 4 q^{88} + 12 q^{89} - 9 q^{90} - 33 q^{92} + 22 q^{93} - 39 q^{94} + 4 q^{95} + 60 q^{96} - 6 q^{97} + q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q + q^2 + 6 * q^3 - 9 * q^4 - 2 * q^5 + 4 * q^6 - q^7 - 13 * q^8 + 2 * q^9 - 3 * q^10 + 7 * q^11 - 21 * q^12 - 5 * q^13 + 6 * q^14 - 3 * q^15 + q^16 - 13 * q^17 + 8 * q^18 + 2 * q^19 - 3 * q^20 + q^21 - 7 * q^22 + 3 * q^23 - 32 * q^24 + q^25 + 10 * q^26 + 6 * q^28 + 4 * q^29 - 7 * q^30 + 13 * q^31 + 30 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 - 27 * q^36 + 9 * q^37 + 28 * q^38 - 5 * q^39 + 14 * q^40 + q^41 + 14 * q^42 - 10 * q^43 - 42 * q^44 - q^45 - 18 * q^46 + 24 * q^47 + 14 * q^48 - q^49 - 26 * q^50 - 32 * q^51 + 15 * q^52 - 4 * q^53 + 5 * q^54 - 16 * q^55 - 13 * q^56 + 8 * q^57 + 16 * q^58 + 4 * q^59 + 3 * q^60 + 3 * q^61 - 13 * q^62 + 7 * q^63 + 13 * q^64 - 13 * q^66 - 25 * q^67 + 78 * q^68 + 7 * q^69 - 3 * q^70 + 31 * q^71 - 44 * q^72 + 16 * q^73 + 31 * q^74 - 6 * q^75 + 18 * q^76 + 7 * q^77 + 25 * q^78 - 26 * q^79 + 12 * q^80 + 4 * q^81 - 26 * q^82 - 14 * q^83 + 9 * q^84 + 14 * q^85 + 20 * q^86 + 16 * q^87 - 4 * q^88 + 12 * q^89 - 9 * q^90 - 33 * q^92 + 22 * q^93 - 39 * q^94 + 4 * q^95 + 60 * q^96 - 6 * q^97 + q^98 + 11 * q^99

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