LMFDB - Embedded newform 143.2.h.a.14.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$1$
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			14.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	143.14
Dual form			143.2.h.a.92.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80902 + 1.31433i) q^{2} +(-1.00000 - 3.07768i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.00000 - 0.726543i) q^{5} +(5.85410 + 4.25325i) q^{6} +(-0.881966 + 2.71441i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-6.04508 + 4.39201i) q^{9} +O(q^{10})$	\(q+(-1.80902 + 1.31433i) q^{2} +(-1.00000 - 3.07768i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.00000 - 0.726543i) q^{5} +(5.85410 + 4.25325i) q^{6} +(-0.881966 + 2.71441i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-6.04508 + 4.39201i) q^{9} +2.76393 q^{10} +(-1.69098 + 2.85317i) q^{11} -9.70820 q^{12} +(0.809017 - 0.587785i) q^{13} +(-1.97214 - 6.06961i) q^{14} +(-1.23607 + 3.80423i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.92705 - 1.40008i) q^{17} +(5.16312 - 15.8904i) q^{18} +(0.190983 + 0.587785i) q^{19} +(-3.00000 + 2.17963i) q^{20} +9.23607 q^{21} +(-0.690983 - 7.38394i) q^{22} -8.00000 q^{23} +(5.85410 - 4.25325i) q^{24} +(-1.07295 - 3.30220i) q^{25} +(-0.690983 + 2.12663i) q^{26} +(11.7082 + 8.50651i) q^{27} +(6.92705 + 5.03280i) q^{28} +(-1.04508 + 3.21644i) q^{29} +(-2.76393 - 8.50651i) q^{30} +(-2.73607 + 1.98787i) q^{31} -6.70820 q^{32} +(10.4721 + 2.35114i) q^{33} +5.32624 q^{34} +(2.85410 - 2.07363i) q^{35} +(6.92705 + 21.3193i) q^{36} +(1.23607 - 3.80423i) q^{37} +(-1.11803 - 0.812299i) q^{38} +(-2.61803 - 1.90211i) q^{39} +(0.854102 - 2.62866i) q^{40} +(-16.7082 + 12.1392i) q^{42} -4.00000 q^{43} +(6.57295 + 7.46969i) q^{44} +9.23607 q^{45} +(14.4721 - 10.5146i) q^{46} +(-2.88197 - 8.86978i) q^{47} +(1.00000 - 3.07768i) q^{48} +(-0.927051 - 0.673542i) q^{49} +(6.28115 + 4.56352i) q^{50} +(-2.38197 + 7.33094i) q^{51} +(-0.927051 - 2.85317i) q^{52} +(8.97214 - 6.51864i) q^{53} -32.3607 q^{54} +(3.76393 - 1.62460i) q^{55} -6.38197 q^{56} +(1.61803 - 1.17557i) q^{57} +(-2.33688 - 7.19218i) q^{58} +(-2.28115 + 7.02067i) q^{59} +(9.70820 + 7.05342i) q^{60} +(-6.73607 - 4.89404i) q^{61} +(2.33688 - 7.19218i) q^{62} +(-6.59017 - 20.2825i) q^{63} +(10.5172 - 7.64121i) q^{64} -1.23607 q^{65} +(-22.0344 + 9.51057i) q^{66} -10.4721 q^{67} +(-5.78115 + 4.20025i) q^{68} +(8.00000 + 24.6215i) q^{69} +(-2.43769 + 7.50245i) q^{70} +(-6.92705 - 5.03280i) q^{71} +(-13.5172 - 9.82084i) q^{72} +(-2.38197 + 7.33094i) q^{73} +(2.76393 + 8.50651i) q^{74} +(-9.09017 + 6.60440i) q^{75} +1.85410 q^{76} +(-6.25329 - 7.10642i) q^{77} +7.23607 q^{78} +(1.61803 - 1.17557i) q^{79} +(-0.381966 - 1.17557i) q^{80} +(7.54508 - 23.2214i) q^{81} +(2.50000 + 1.81636i) q^{83} +(8.56231 - 26.3521i) q^{84} +(0.909830 + 2.80017i) q^{85} +(7.23607 - 5.25731i) q^{86} +10.9443 q^{87} +(-7.23607 - 1.62460i) q^{88} +11.4164 q^{89} +(-16.7082 + 12.1392i) q^{90} +(0.881966 + 2.71441i) q^{91} +(-7.41641 + 22.8254i) q^{92} +(8.85410 + 6.43288i) q^{93} +(16.8713 + 12.2577i) q^{94} +(0.236068 - 0.726543i) q^{95} +(6.70820 + 20.6457i) q^{96} +(-3.00000 + 2.17963i) q^{97} +2.56231 q^{98} +(-2.30902 - 24.6745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 4 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} + 5 q^{8} - 13 q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 - 4 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 + 5 * q^8 - 13 * q^9	\( 4 q - 5 q^{2} - 4 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} + 5 q^{8} - 13 q^{9} + 20 q^{10} - 9 q^{11} - 12 q^{12} + q^{13} + 10 q^{14} + 4 q^{15} + q^{16} - q^{17} + 5 q^{18} + 3 q^{19} - 12 q^{20} + 28 q^{21} - 5 q^{22} - 32 q^{23} + 10 q^{24} - 11 q^{25} - 5 q^{26} + 20 q^{27} + 21 q^{28} + 7 q^{29} - 20 q^{30} - 2 q^{31} + 24 q^{33} - 10 q^{34} - 2 q^{35} + 21 q^{36} - 4 q^{37} - 6 q^{39} - 10 q^{40} - 40 q^{42} - 16 q^{43} + 33 q^{44} + 28 q^{45} + 40 q^{46} - 16 q^{47} + 4 q^{48} + 3 q^{49} + 5 q^{50} - 14 q^{51} + 3 q^{52} + 18 q^{53} - 40 q^{54} + 24 q^{55} - 30 q^{56} + 2 q^{57} - 25 q^{58} + 11 q^{59} + 12 q^{60} - 18 q^{61} + 25 q^{62} - 4 q^{63} + 13 q^{64} + 4 q^{65} - 30 q^{66} - 24 q^{67} - 3 q^{68} + 32 q^{69} - 50 q^{70} - 21 q^{71} - 25 q^{72} - 14 q^{73} + 20 q^{74} - 14 q^{75} - 6 q^{76} + 13 q^{77} + 20 q^{78} + 2 q^{79} - 6 q^{80} + 19 q^{81} + 10 q^{83} - 6 q^{84} + 26 q^{85} + 20 q^{86} + 8 q^{87} - 20 q^{88} - 8 q^{89} - 40 q^{90} + 8 q^{91} + 24 q^{92} + 22 q^{93} + 25 q^{94} - 8 q^{95} - 12 q^{97} - 30 q^{98} - 7 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 4 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 + 5 * q^8 - 13 * q^9 + 20 * q^10 - 9 * q^11 - 12 * q^12 + q^13 + 10 * q^14 + 4 * q^15 + q^16 - q^17 + 5 * q^18 + 3 * q^19 - 12 * q^20 + 28 * q^21 - 5 * q^22 - 32 * q^23 + 10 * q^24 - 11 * q^25 - 5 * q^26 + 20 * q^27 + 21 * q^28 + 7 * q^29 - 20 * q^30 - 2 * q^31 + 24 * q^33 - 10 * q^34 - 2 * q^35 + 21 * q^36 - 4 * q^37 - 6 * q^39 - 10 * q^40 - 40 * q^42 - 16 * q^43 + 33 * q^44 + 28 * q^45 + 40 * q^46 - 16 * q^47 + 4 * q^48 + 3 * q^49 + 5 * q^50 - 14 * q^51 + 3 * q^52 + 18 * q^53 - 40 * q^54 + 24 * q^55 - 30 * q^56 + 2 * q^57 - 25 * q^58 + 11 * q^59 + 12 * q^60 - 18 * q^61 + 25 * q^62 - 4 * q^63 + 13 * q^64 + 4 * q^65 - 30 * q^66 - 24 * q^67 - 3 * q^68 + 32 * q^69 - 50 * q^70 - 21 * q^71 - 25 * q^72 - 14 * q^73 + 20 * q^74 - 14 * q^75 - 6 * q^76 + 13 * q^77 + 20 * q^78 + 2 * q^79 - 6 * q^80 + 19 * q^81 + 10 * q^83 - 6 * q^84 + 26 * q^85 + 20 * q^86 + 8 * q^87 - 20 * q^88 - 8 * q^89 - 40 * q^90 + 8 * q^91 + 24 * q^92 + 22 * q^93 + 25 * q^94 - 8 * q^95 - 12 * q^97 - 30 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.80902	+	1.31433i	−1.27917	+	0.929370i	−0.999528	−	0.0307347i	$-0.990215\pi$
$2$	−1.80902	+	1.31433i	−1.27917	+	0.929370i	−0.279641	+	0.960105i	$0.590215\pi$
$3$	−1.00000	−	3.07768i	−0.577350	−	1.77690i	−0.628033	−	0.778187i	$-0.716140\pi$
$3$	−1.00000	−	3.07768i	−0.577350	−	1.77690i	0.0506828	−	0.998715i	$-0.483860\pi$
$4$	0.927051	−	2.85317i	0.463525	−	1.42658i
$5$	−1.00000	−	0.726543i	−0.447214	−	0.324920i	0.341281	−	0.939961i	$-0.389139\pi$
$5$	−1.00000	−	0.726543i	−0.447214	−	0.324920i	−0.788495	+	0.615042i	$0.789139\pi$
$6$	5.85410	+	4.25325i	2.38993	+	1.73638i
$7$	−0.881966	+	2.71441i	−0.333352	+	1.02595i	0.634176	+	0.773188i	$0.281339\pi$
$7$	−0.881966	+	2.71441i	−0.333352	+	1.02595i	−0.967528	+	0.252763i	$0.918661\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	−6.04508	+	4.39201i	−2.01503	+	1.46400i
$10$	2.76393			0.874032
$11$	−1.69098	+	2.85317i	−0.509851	+	0.860263i
$11$	−1.69098	+	2.85317i	−0.509851	+	0.860263i
$12$	−9.70820			−2.80252
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	−1.97214	−	6.06961i	−0.527076	−	1.62217i
$15$	−1.23607	+	3.80423i	−0.319151	+	0.982247i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−1.92705	−	1.40008i	−0.467379	−	0.339570i	0.329040	−	0.944316i	$-0.393275\pi$
$17$	−1.92705	−	1.40008i	−0.467379	−	0.339570i	−0.796419	+	0.604746i	$0.793275\pi$
$18$	5.16312	−	15.8904i	1.21696	−	3.74541i
$19$	0.190983	+	0.587785i	0.0438145	+	0.134847i	0.970571	−	0.240816i	$-0.0774150\pi$
$19$	0.190983	+	0.587785i	0.0438145	+	0.134847i	−0.926756	+	0.375663i	$0.877415\pi$
$20$	−3.00000	+	2.17963i	−0.670820	+	0.487380i
$21$	9.23607			2.01548
$22$	−0.690983	−	7.38394i	−0.147318	−	1.57426i
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$	5.85410	−	4.25325i	1.19496	−	0.868192i
$25$	−1.07295	−	3.30220i	−0.214590	−	0.660440i
$26$	−0.690983	+	2.12663i	−0.135513	+	0.417066i
$27$	11.7082	+	8.50651i	2.25324	+	1.63708i
$28$	6.92705	+	5.03280i	1.30909	+	0.951109i
$29$	−1.04508	+	3.21644i	−0.194067	+	0.597278i	0.805919	+	0.592026i	$0.201672\pi$
$29$	−1.04508	+	3.21644i	−0.194067	+	0.597278i	−0.999986	+	0.00525198i	$0.998328\pi$
$30$	−2.76393	−	8.50651i	−0.504623	−	1.55307i
$31$	−2.73607	+	1.98787i	−0.491412	+	0.357032i	−0.805727	−	0.592287i	$-0.798225\pi$
$31$	−2.73607	+	1.98787i	−0.491412	+	0.357032i	0.314315	+	0.949319i	$0.398225\pi$
$32$	−6.70820			−1.18585
$33$	10.4721	+	2.35114i	1.82296	+	0.409281i
$34$	5.32624			0.913442
$35$	2.85410	−	2.07363i	0.482431	−	0.350507i
$36$	6.92705	+	21.3193i	1.15451	+	3.55321i
$37$	1.23607	−	3.80423i	0.203208	−	0.625411i	−0.796574	−	0.604541i	$-0.793356\pi$
$37$	1.23607	−	3.80423i	0.203208	−	0.625411i	0.999782	−	0.0208697i	$-0.00664352\pi$
$38$	−1.11803	−	0.812299i	−0.181369	−	0.131772i
$39$	−2.61803	−	1.90211i	−0.419221	−	0.304582i
$40$	0.854102	−	2.62866i	0.135045	−	0.415627i
$41$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$41$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$42$	−16.7082	+	12.1392i	−2.57813	+	1.87312i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	6.57295	+	7.46969i	0.990909	+	1.12610i
$45$	9.23607			1.37683
$46$	14.4721	−	10.5146i	2.13380	−	1.55030i
$47$	−2.88197	−	8.86978i	−0.420378	−	1.29379i	−0.907351	−	0.420373i	$-0.861899\pi$
$47$	−2.88197	−	8.86978i	−0.420378	−	1.29379i	0.486973	−	0.873417i	$-0.338101\pi$
$48$	1.00000	−	3.07768i	0.144338	−	0.444225i
$49$	−0.927051	−	0.673542i	−0.132436	−	0.0962203i
$50$	6.28115	+	4.56352i	0.888289	+	0.645380i
$51$	−2.38197	+	7.33094i	−0.333542	+	1.02654i
$52$	−0.927051	−	2.85317i	−0.128559	−	0.395663i
$53$	8.97214	−	6.51864i	1.23242	−	0.895404i	0.235349	−	0.971911i	$-0.424377\pi$
$53$	8.97214	−	6.51864i	1.23242	−	0.895404i	0.997069	+	0.0765072i	$0.0243768\pi$
$54$	−32.3607			−4.40373
$55$	3.76393	−	1.62460i	0.507528	−	0.219061i
$56$	−6.38197			−0.852826
$57$	1.61803	−	1.17557i	0.214314	−	0.155708i
$58$	−2.33688	−	7.19218i	−0.306848	−	0.944380i
$59$	−2.28115	+	7.02067i	−0.296981	+	0.914013i	0.685568	+	0.728009i	$0.259554\pi$
$59$	−2.28115	+	7.02067i	−0.296981	+	0.914013i	−0.982549	+	0.186004i	$0.940446\pi$
$60$	9.70820	+	7.05342i	1.25332	+	0.910593i
$61$	−6.73607	−	4.89404i	−0.862465	−	0.626618i	0.0660894	−	0.997814i	$-0.478948\pi$
$61$	−6.73607	−	4.89404i	−0.862465	−	0.626618i	−0.928554	+	0.371196i	$0.878948\pi$
$62$	2.33688	−	7.19218i	0.296784	−	0.913408i
$63$	−6.59017	−	20.2825i	−0.830283	−	2.55535i
$64$	10.5172	−	7.64121i	1.31465	−	0.955151i
$65$	−1.23607			−0.153315
$66$	−22.0344	+	9.51057i	−2.71225	+	1.17067i
$67$	−10.4721			−1.27938			−0.639688	−	0.768635i	$-0.720936\pi$
$67$	−10.4721			−1.27938			−0.639688	+	0.768635i	$0.720936\pi$
$68$	−5.78115	+	4.20025i	−0.701068	+	0.509356i
$69$	8.00000	+	24.6215i	0.963087	+	2.96408i
$70$	−2.43769	+	7.50245i	−0.291360	+	0.896714i
$71$	−6.92705	−	5.03280i	−0.822090	−	0.597283i	0.0952206	−	0.995456i	$-0.469644\pi$
$71$	−6.92705	−	5.03280i	−0.822090	−	0.597283i	−0.917310	+	0.398173i	$0.869644\pi$
$72$	−13.5172	−	9.82084i	−1.59302	−	1.15740i
$73$	−2.38197	+	7.33094i	−0.278788	+	0.858021i	0.709404	+	0.704802i	$0.248964\pi$
$73$	−2.38197	+	7.33094i	−0.278788	+	0.858021i	−0.988192	+	0.153219i	$0.951036\pi$
$74$	2.76393	+	8.50651i	0.321301	+	0.988861i
$75$	−9.09017	+	6.60440i	−1.04964	+	0.762610i
$76$	1.85410			0.212680
$77$	−6.25329	−	7.10642i	−0.712628	−	0.809852i
$78$	7.23607			0.819323
$79$	1.61803	−	1.17557i	0.182043	−	0.132262i	−0.493032	−	0.870011i	$-0.664111\pi$
$79$	1.61803	−	1.17557i	0.182043	−	0.132262i	0.675075	+	0.737749i	$0.264111\pi$
$80$	−0.381966	−	1.17557i	−0.0427051	−	0.131433i
$81$	7.54508	−	23.2214i	0.838343	−	2.58015i
$82$		0			0
$83$	2.50000	+	1.81636i	0.274411	+	0.199371i	0.716476	−	0.697612i	$-0.245754\pi$
$83$	2.50000	+	1.81636i	0.274411	+	0.199371i	−0.442065	+	0.896983i	$0.645754\pi$
$84$	8.56231	−	26.3521i	0.934224	−	2.87525i
$85$	0.909830	+	2.80017i	0.0986849	+	0.303721i
$86$	7.23607	−	5.25731i	0.780285	−	0.566910i
$87$	10.9443			1.17335
$88$	−7.23607	−	1.62460i	−0.771367	−	0.173183i
$89$	11.4164			1.21014			0.605068	−	0.796173i	$-0.293146\pi$
$89$	11.4164			1.21014			0.605068	+	0.796173i	$0.293146\pi$
$90$	−16.7082	+	12.1392i	−1.76120	+	1.27959i
$91$	0.881966	+	2.71441i	0.0924552	+	0.284548i
$92$	−7.41641	+	22.8254i	−0.773214	+	2.37971i
$93$	8.85410	+	6.43288i	0.918128	+	0.667059i
$94$	16.8713	+	12.2577i	1.74014	+	1.26429i
$95$	0.236068	−	0.726543i	0.0242201	−	0.0745417i
$96$	6.70820	+	20.6457i	0.684653	+	2.10715i
$97$	−3.00000	+	2.17963i	−0.304604	+	0.221308i	−0.729578	−	0.683898i	$-0.760283\pi$
$97$	−3.00000	+	2.17963i	−0.304604	+	0.221308i	0.424974	+	0.905206i	$0.360283\pi$
$98$	2.56231			0.258832
$99$	−2.30902	−	24.6745i	−0.232065	−	2.47988i
$100$	−10.4164			−1.04164
$101$	4.54508	−	3.30220i	0.452253	−	0.328581i	−0.338232	−	0.941063i	$-0.609829\pi$
$101$	4.54508	−	3.30220i	0.452253	−	0.328581i	0.790485	+	0.612482i	$0.209829\pi$
$102$	−5.32624	−	16.3925i	−0.527376	−	1.62310i
$103$	−0.618034	+	1.90211i	−0.0608967	+	0.187421i	−0.976877	−	0.213803i	$-0.931415\pi$
$103$	−0.618034	+	1.90211i	−0.0608967	+	0.187421i	0.915980	+	0.401224i	$0.131415\pi$
$104$	1.80902	+	1.31433i	0.177389	+	0.128880i
$105$	−9.23607	−	6.71040i	−0.901348	−	0.654868i
$106$	−7.66312	+	23.5847i	−0.744308	+	2.29074i
$107$	6.09017	+	18.7436i	0.588759	+	1.81201i	0.583620	+	0.812027i	$0.301636\pi$
$107$	6.09017	+	18.7436i	0.588759	+	1.81201i	0.00513899	+	0.999987i	$0.498364\pi$
$108$	35.1246	−	25.5195i	3.37987	−	2.45562i
$109$	−12.1803			−1.16666			−0.583332	−	0.812233i	$-0.698252\pi$
$109$	−12.1803			−1.16666			−0.583332	+	0.812233i	$0.698252\pi$
$110$	−4.67376	+	7.88597i	−0.445626	+	0.751897i
$111$	−12.9443			−1.22862
$112$	−2.30902	+	1.67760i	−0.218182	+	0.158518i
$113$	−1.50000	−	4.61653i	−0.141108	−	0.434286i	0.855382	−	0.517998i	$-0.173323\pi$
$113$	−1.50000	−	4.61653i	−0.141108	−	0.434286i	−0.996490	+	0.0837117i	$0.973323\pi$
$114$	−1.38197	+	4.25325i	−0.129433	+	0.398354i
$115$	8.00000	+	5.81234i	0.746004	+	0.542004i
$116$	8.20820	+	5.96361i	0.762113	+	0.553707i
$117$	−2.30902	+	7.10642i	−0.213469	+	0.656989i
$118$	−5.10081	−	15.6987i	−0.469568	−	1.44518i
$119$	5.50000	−	3.99598i	0.504184	−	0.366311i
$120$	−8.94427			−0.816497
$121$	−5.28115	−	9.64932i	−0.480105	−	0.877211i
$122$	18.6180			1.68560
$123$		0			0
$124$	3.13525	+	9.64932i	0.281554	+	0.866535i
$125$	−3.23607	+	9.95959i	−0.289443	+	0.890813i
$126$	38.5795	+	28.0297i	3.43694	+	2.49708i
$127$	−7.47214	−	5.42882i	−0.663045	−	0.481730i	0.204645	−	0.978836i	$-0.434396\pi$
$127$	−7.47214	−	5.42882i	−0.663045	−	0.481730i	−0.867690	+	0.497106i	$0.834396\pi$
$128$	−4.83688	+	14.8864i	−0.427524	+	1.31578i
$129$	4.00000	+	12.3107i	0.352180	+	1.08390i
$130$	2.23607	−	1.62460i	0.196116	−	0.142487i
$131$	15.8885			1.38819			0.694094	−	0.719884i	$-0.255805\pi$
$131$	15.8885			1.38819			0.694094	+	0.719884i	$0.255805\pi$
$132$	16.4164	−	27.6992i	1.42886	−	2.41090i
$133$	−1.76393			−0.152952
$134$	18.9443	−	13.7638i	1.63654	−	1.18901i
$135$	−5.52786	−	17.0130i	−0.475763	−	1.46425i
$136$	1.64590	−	5.06555i	0.141135	−	0.434368i
$137$	0.236068	+	0.171513i	0.0201686	+	0.0146534i	0.597824	−	0.801627i	$-0.296032\pi$
$137$	0.236068	+	0.171513i	0.0201686	+	0.0146534i	−0.577655	+	0.816281i	$0.696032\pi$
$138$	−46.8328	−	34.0260i	−3.98667	−	2.89649i
$139$	1.29180	−	3.97574i	0.109569	−	0.337218i	−0.881207	−	0.472731i	$-0.843268\pi$
$139$	1.29180	−	3.97574i	0.109569	−	0.337218i	0.990776	+	0.135513i	$0.0432683\pi$
$140$	−3.27051	−	10.0656i	−0.276409	−	0.850698i
$141$	−24.4164	+	17.7396i	−2.05623	+	1.49394i
$142$	19.1459			1.60669
$143$	0.309017	+	3.30220i	0.0258413	+	0.276144i
$144$	−7.47214			−0.622678
$145$	3.38197	−	2.45714i	0.280857	−	0.204055i
$146$	−5.32624	−	16.3925i	−0.440803	−	1.35665i
$147$	−1.14590	+	3.52671i	−0.0945121	+	0.290878i
$148$	−9.70820	−	7.05342i	−0.798009	−	0.579788i
$149$	−4.61803	−	3.35520i	−0.378324	−	0.274869i	0.382330	−	0.924026i	$-0.375122\pi$
$149$	−4.61803	−	3.35520i	−0.378324	−	0.274869i	−0.760654	+	0.649157i	$0.775122\pi$
$150$	7.76393	−	23.8949i	0.633922	−	1.95101i
$151$	0.281153	+	0.865300i	0.0228799	+	0.0704171i	0.961845	−	0.273597i	$-0.0882133\pi$
$151$	0.281153	+	0.865300i	0.0228799	+	0.0704171i	−0.938965	+	0.344014i	$0.888213\pi$
$152$	−1.11803	+	0.812299i	−0.0906845	+	0.0658862i
$153$	17.7984			1.43891
$154$	20.6525	+	4.63677i	1.66422	+	0.373642i
$155$	4.18034			0.335773
$156$	−7.85410	+	5.70634i	−0.628831	+	0.456873i
$157$	3.02786	+	9.31881i	0.241650	+	0.743722i	0.996169	+	0.0874442i	$0.0278700\pi$
$157$	3.02786	+	9.31881i	0.241650	+	0.743722i	−0.754520	+	0.656278i	$0.772130\pi$
$158$	−1.38197	+	4.25325i	−0.109943	+	0.338371i
$159$	−29.0344	−	21.0948i	−2.30258	−	1.67292i
$160$	6.70820	+	4.87380i	0.530330	+	0.385307i
$161$	7.05573	−	21.7153i	0.556069	−	1.71141i
$162$	16.8713	+	51.9246i	1.32554	+	4.07958i
$163$	6.16312	−	4.47777i	0.482733	−	0.350726i	−0.319650	−	0.947536i	$-0.603565\pi$
$163$	6.16312	−	4.47777i	0.482733	−	0.350726i	0.802383	+	0.596810i	$0.203565\pi$
$164$		0			0
$165$	−8.76393	−	9.95959i	−0.682271	−	0.775353i
$166$	−6.90983			−0.536307
$167$	−7.97214	+	5.79210i	−0.616902	+	0.448206i	−0.851838	−	0.523805i	$-0.824512\pi$
$167$	−7.97214	+	5.79210i	−0.616902	+	0.448206i	0.234936	+	0.972011i	$0.424512\pi$
$168$	6.38197	+	19.6417i	0.492379	+	1.51539i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−5.32624	−	3.86974i	−0.408504	−	0.296795i
$171$	−3.73607	−	2.71441i	−0.285704	−	0.207576i
$172$	−3.70820	+	11.4127i	−0.282748	+	0.870209i
$173$	−1.09017	−	3.35520i	−0.0828841	−	0.255091i	0.901023	−	0.433771i	$-0.142817\pi$
$173$	−1.09017	−	3.35520i	−0.0828841	−	0.255091i	−0.983907	+	0.178680i	$0.942817\pi$
$174$	−19.7984	+	14.3844i	−1.50091	+	1.09048i
$175$	9.90983			0.749113
$176$	−3.04508	+	1.31433i	−0.229532	+	0.0990712i
$177$	23.8885			1.79557
$178$	−20.6525	+	15.0049i	−1.54797	+	1.12466i
$179$	−2.56231	−	7.88597i	−0.191516	−	0.589425i	−1.00000		0.000906466i	$-0.999711\pi$
$179$	−2.56231	−	7.88597i	−0.191516	−	0.589425i	0.808484	−	0.588518i	$-0.200289\pi$
$180$	8.56231	−	26.3521i	0.638197	−	1.96417i
$181$	−4.54508	−	3.30220i	−0.337834	−	0.245450i	0.405914	−	0.913911i	$-0.366953\pi$
$181$	−4.54508	−	3.30220i	−0.337834	−	0.245450i	−0.743747	+	0.668461i	$0.766953\pi$
$182$	−5.16312	−	3.75123i	−0.382716	−	0.278059i
$183$	−8.32624	+	25.6255i	−0.615493	+	1.89429i
$184$	−5.52786	−	17.0130i	−0.407520	−	1.25422i
$185$	−4.00000	+	2.90617i	−0.294086	+	0.213666i
$186$	−24.4721			−1.79438
$187$	7.25329	−	3.13068i	0.530413	−	0.228938i
$188$	−27.9787			−2.04056
$189$	−33.4164	+	24.2784i	−2.43069	+	1.76600i
$190$	0.527864	+	1.62460i	0.0382953	+	0.117861i
$191$	−2.76393	+	8.50651i	−0.199991	+	0.615509i	0.799891	+	0.600145i	$0.204891\pi$
$191$	−2.76393	+	8.50651i	−0.199991	+	0.615509i	−0.999882	+	0.0153638i	$0.995109\pi$
$192$	−34.0344	−	24.7275i	−2.45622	−	1.78455i
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	0.915357	−	0.402644i	$-0.131909\pi$
$193$	11.3262	+	8.22899i	0.815280	+	0.592336i	−0.100076	+	0.994980i	$0.531909\pi$
$194$	2.56231	−	7.88597i	0.183963	−	0.566179i
$195$	1.23607	+	3.80423i	0.0885167	+	0.272426i
$196$	−2.78115	+	2.02063i	−0.198654	+	0.144330i
$197$	17.8885			1.27451			0.637253	−	0.770655i	$-0.280071\pi$
$197$	17.8885			1.27451			0.637253	+	0.770655i	$0.280071\pi$
$198$	36.6074	+	41.6017i	2.60157	+	2.95651i
$199$	4.94427			0.350490			0.175245	−	0.984525i	$-0.443928\pi$
$199$	4.94427			0.350490			0.175245	+	0.984525i	$0.443928\pi$
$200$	6.28115	−	4.56352i	0.444145	−	0.322690i
$201$	10.4721	+	32.2299i	0.738648	+	2.27332i
$202$	−3.88197	+	11.9475i	−0.273134	+	0.840621i
$203$	−7.80902	−	5.67358i	−0.548086	−	0.398207i
$204$	18.7082	+	13.5923i	1.30984	+	0.951652i
$205$		0			0
$206$	−1.38197	−	4.25325i	−0.0962861	−	0.296338i
$207$	48.3607	−	35.1361i	3.36130	−	2.44213i
$208$	1.00000			0.0693375
$209$	−2.00000	−	0.449028i	−0.138343	−	0.0310599i
$210$	25.5279			1.76159
$211$	14.9443	−	10.8576i	1.02881	−	0.747471i	0.0607367	−	0.998154i	$-0.480655\pi$
$211$	14.9443	−	10.8576i	1.02881	−	0.747471i	0.968069	+	0.250682i	$0.0806550\pi$
$212$	−10.2812	−	31.6421i	−0.706112	−	2.17319i
$213$	−8.56231	+	26.3521i	−0.586680	+	1.80561i
$214$	−35.6525	−	25.9030i	−2.43715	−	1.77070i
$215$	4.00000	+	2.90617i	0.272798	+	0.198199i
$216$	−10.0000	+	30.7768i	−0.680414	+	2.09410i
$217$	−2.98278	−	9.18005i	−0.202484	−	0.623182i
$218$	22.0344	−	16.0090i	1.49236	−	1.08426i
$219$	24.9443			1.68558
$220$	−1.14590	−	12.2452i	−0.0772564	−	0.825573i
$221$	−2.38197			−0.160228
$222$	23.4164	−	17.0130i	1.57161	−	1.14184i
$223$	2.76393	+	8.50651i	0.185087	+	0.569638i	0.999950	−	0.0100153i	$-0.00318802\pi$
$223$	2.76393	+	8.50651i	0.185087	+	0.569638i	−0.814863	+	0.579653i	$0.803188\pi$
$224$	5.91641	−	18.2088i	0.395307	−	1.21663i
$225$	20.9894	+	15.2497i	1.39929	+	1.01664i
$226$	8.78115	+	6.37988i	0.584114	+	0.424383i
$227$	3.35410	−	10.3229i	0.222620	−	0.685153i	−0.775905	−	0.630850i	$-0.782706\pi$
$227$	3.35410	−	10.3229i	0.222620	−	0.685153i	0.998525	−	0.0543027i	$-0.0172936\pi$
$228$	−1.85410	−	5.70634i	−0.122791	−	0.377912i
$229$	3.47214	−	2.52265i	0.229445	−	0.166702i	−0.467123	−	0.884192i	$-0.654709\pi$
$229$	3.47214	−	2.52265i	0.229445	−	0.166702i	0.696568	+	0.717491i	$0.254709\pi$
$230$	−22.1115			−1.45799
$231$	−15.6180	+	26.3521i	−1.02759	+	1.73384i
$232$	−7.56231			−0.496490
$233$	−19.6803	+	14.2986i	−1.28930	+	0.936733i	−0.999791	−	0.0204420i	$-0.993493\pi$
$233$	−19.6803	+	14.2986i	−1.28930	+	0.936733i	−0.289511	+	0.957175i	$0.593493\pi$
$234$	−5.16312	−	15.8904i	−0.337524	−	1.03879i
$235$	−3.56231	+	10.9637i	−0.232379	+	0.715190i
$236$	17.9164	+	13.0170i	1.16626	+	0.847337i
$237$	−5.23607	−	3.80423i	−0.340119	−	0.247111i
$238$	−4.69756	+	14.4576i	−0.304498	+	0.937147i
$239$	−1.64590	−	5.06555i	−0.106464	−	0.327663i	0.883607	−	0.468229i	$-0.155108\pi$
$239$	−1.64590	−	5.06555i	−0.106464	−	0.327663i	−0.990071	+	0.140566i	$0.955108\pi$
$240$	−3.23607	+	2.35114i	−0.208887	+	0.151765i
$241$	−17.2361			−1.11027			−0.555136	−	0.831759i	$-0.687334\pi$
$241$	−17.2361			−1.11027			−0.555136	+	0.831759i	$0.687334\pi$
$242$	22.2361	+	10.5146i	1.42939	+	0.675906i
$243$	−35.5967			−2.28353
$244$	−20.2082	+	14.6821i	−1.29370	+	0.939926i
$245$	0.437694	+	1.34708i	0.0279633	+	0.0860620i
$246$		0			0
$247$	0.500000	+	0.363271i	0.0318142	+	0.0231144i
$248$	−6.11803	−	4.44501i	−0.388496	−	0.282259i
$249$	3.09017	−	9.51057i	0.195832	−	0.602708i
$250$	−7.23607	−	22.2703i	−0.457649	−	1.40850i
$251$	−5.70820	+	4.14725i	−0.360299	+	0.261772i	−0.753177	−	0.657818i	$-0.771479\pi$
$251$	−5.70820	+	4.14725i	−0.360299	+	0.261772i	0.392878	+	0.919591i	$0.371479\pi$
$252$	−63.9787			−4.03028
$253$	13.5279	−	22.8254i	0.850490	−	1.43502i
$254$	20.6525			1.29585
$255$	7.70820	−	5.60034i	0.482706	−	0.350707i
$256$	−2.78115	−	8.55951i	−0.173822	−	0.534969i
$257$	6.02786	−	18.5519i	0.376008	−	1.15723i	−0.566788	−	0.823863i	$-0.691814\pi$
$257$	6.02786	−	18.5519i	0.376008	−	1.15723i	0.942796	−	0.333370i	$-0.108186\pi$
$258$	−23.4164	−	17.0130i	−1.45784	−	1.05918i
$259$	9.23607	+	6.71040i	0.573901	+	0.416964i
$260$	−1.14590	+	3.52671i	−0.0710656	+	0.218717i
$261$	−7.80902	−	24.0337i	−0.483366	−	1.48765i
$262$	−28.7426	+	20.8828i	−1.77573	+	1.29014i
$263$	−28.6525			−1.76679			−0.883394	−	0.468632i	$-0.844747\pi$
$263$	−28.6525			−1.76679			−0.883394	+	0.468632i	$0.844747\pi$
$264$	2.23607	+	23.8949i	0.137620	+	1.47063i
$265$	−13.7082			−0.842088
$266$	3.19098	−	2.31838i	0.195652	−	0.142149i
$267$	−11.4164	−	35.1361i	−0.698673	−	2.15029i
$268$	−9.70820	+	29.8788i	−0.593023	+	1.82514i
$269$	7.50000	+	5.44907i	0.457283	+	0.332236i	0.792465	−	0.609918i	$-0.208798\pi$
$269$	7.50000	+	5.44907i	0.457283	+	0.332236i	−0.335181	+	0.942154i	$0.608798\pi$
$270$	32.3607	+	23.5114i	1.96941	+	1.43086i
$271$	6.88197	−	21.1805i	0.418050	−	1.28662i	−0.491445	−	0.870909i	$-0.663531\pi$
$271$	6.88197	−	21.1805i	0.418050	−	1.28662i	0.909495	−	0.415716i	$-0.136469\pi$
$272$	−0.736068	−	2.26538i	−0.0446307	−	0.137359i
$273$	7.47214	−	5.42882i	0.452234	−	0.328567i
$274$	−0.652476			−0.0394175
$275$	11.2361	+	2.52265i	0.677560	+	0.152122i
$276$	77.6656			4.67492
$277$	−23.6353	+	17.1720i	−1.42010	+	1.03177i	−0.428351	+	0.903613i	$0.640905\pi$
$277$	−23.6353	+	17.1720i	−1.42010	+	1.03177i	−0.991754	+	0.128154i	$0.959095\pi$
$278$	2.88854	+	8.89002i	0.173243	+	0.533188i
$279$	7.80902	−	24.0337i	0.467514	−	1.43886i
$280$	6.38197	+	4.63677i	0.381395	+	0.277100i
$281$	11.6180	+	8.44100i	0.693074	+	0.503548i	0.877669	−	0.479267i	$-0.159097\pi$
$281$	11.6180	+	8.44100i	0.693074	+	0.503548i	−0.184595	+	0.982815i	$0.559097\pi$
$282$	20.8541	−	64.1823i	1.24184	−	3.82200i
$283$	8.61803	+	26.5236i	0.512289	+	1.57666i	0.788161	+	0.615469i	$0.211033\pi$
$283$	8.61803	+	26.5236i	0.512289	+	1.57666i	−0.275872	+	0.961194i	$0.588967\pi$
$284$	−20.7812	+	15.0984i	−1.23313	+	0.895925i
$285$	−2.47214			−0.146437
$286$	−4.89919	−	5.56758i	−0.289695	−	0.329218i
$287$		0			0
$288$	40.5517	−	29.4625i	2.38953	−	1.73609i
$289$	−3.50000	−	10.7719i	−0.205882	−	0.633641i
$290$	−2.88854	+	8.89002i	−0.169621	+	0.522040i
$291$	9.70820	+	7.05342i	0.569105	+	0.413479i
$292$	18.7082	+	13.5923i	1.09481	+	0.795430i
$293$	−1.85410	+	5.70634i	−0.108318	+	0.333368i	−0.990495	−	0.137550i	$-0.956077\pi$
$293$	−1.85410	+	5.70634i	−0.108318	+	0.333368i	0.882177	+	0.470918i	$0.156077\pi$
$294$	−2.56231	−	7.88597i	−0.149437	−	0.459919i
$295$	7.38197	−	5.36331i	0.429795	−	0.312264i
$296$	8.94427			0.519875
$297$	−44.0689	+	19.0211i	−2.55714	+	1.10372i
$298$	12.7639			0.739395
$299$	−6.47214	+	4.70228i	−0.374293	+	0.271940i
$300$	10.4164	+	32.0584i	0.601392	+	1.85089i
$301$	3.52786	−	10.8576i	0.203343	−	0.625824i
$302$	−1.64590	−	1.19581i	−0.0947108	−	0.0688114i
$303$	−14.7082	−	10.6861i	−0.844964	−	0.613902i
$304$	−0.190983	+	0.587785i	−0.0109536	+	0.0337118i
$305$	3.18034	+	9.78808i	0.182106	+	0.560464i
$306$	−32.1976	+	23.3929i	−1.84061	+	1.33728i
$307$	−19.7984			−1.12995			−0.564976	−	0.825107i	$-0.691115\pi$
$307$	−19.7984			−1.12995			−0.564976	+	0.825107i	$0.691115\pi$
$308$	−26.0729	+	11.2537i	−1.48564	+	0.641238i
$309$	6.47214			0.368187
$310$	−7.56231	+	5.49434i	−0.429510	+	0.312057i
$311$	−0.819660	−	2.52265i	−0.0464787	−	0.143047i	0.925124	−	0.379665i	$-0.123961\pi$
$311$	−0.819660	−	2.52265i	−0.0464787	−	0.143047i	−0.971603	+	0.236619i	$0.923961\pi$
$312$	2.23607	−	6.88191i	0.126592	−	0.389611i
$313$	−4.07295	−	2.95917i	−0.230217	−	0.167262i	0.466697	−	0.884417i	$-0.345444\pi$
$313$	−4.07295	−	2.95917i	−0.230217	−	0.167262i	−0.696914	+	0.717155i	$0.745444\pi$
$314$	−17.7254	−	12.8783i	−1.00030	−	0.726763i
$315$	−8.14590	+	25.0705i	−0.458969	+	1.41256i
$316$	−1.85410	−	5.70634i	−0.104301	−	0.321007i
$317$	14.3262	−	10.4086i	0.804642	−	0.584606i	−0.107630	−	0.994191i	$-0.534326\pi$
$317$	14.3262	−	10.4086i	0.804642	−	0.584606i	0.912272	+	0.409585i	$0.134326\pi$
$318$	80.2492			4.50015
$319$	−7.40983	−	8.42075i	−0.414871	−	0.471472i
$320$	−16.0689			−0.898278
$321$	51.5967	−	37.4872i	2.87985	−	2.09233i
$322$	15.7771	+	48.5569i	0.879223	+	2.70597i
$323$	0.454915	−	1.40008i	0.0253121	−	0.0779028i
$324$	−59.2599	−	43.0548i	−3.29221	−	2.39193i
$325$	−2.80902	−	2.04087i	−0.155816	−	0.113207i
$326$	−5.26393	+	16.2007i	−0.291542	+	0.897275i
$327$	12.1803	+	37.4872i	0.673574	+	2.07305i
$328$		0			0
$329$	26.6180			1.46750
$330$	28.9443	+	6.49839i	1.59333	+	0.357725i
$331$	−25.2705			−1.38899			−0.694496	−	0.719496i	$-0.744373\pi$
$331$	−25.2705			−1.38899			−0.694496	+	0.719496i	$0.744373\pi$
$332$	7.50000	−	5.44907i	0.411616	−	0.299057i
$333$	9.23607	+	28.4257i	0.506133	+	1.55772i
$334$	6.80902	−	20.9560i	0.372573	−	1.14666i
$335$	10.4721	+	7.60845i	0.572154	+	0.415694i
$336$	7.47214	+	5.42882i	0.407638	+	0.296167i
$337$	1.60739	−	4.94704i	0.0875602	−	0.269482i	−0.897683	−	0.440641i	$-0.854751\pi$
$337$	1.60739	−	4.94704i	0.0875602	−	0.269482i	0.985243	+	0.171159i	$0.0547511\pi$
$338$	0.690983	+	2.12663i	0.0375845	+	0.115673i
$339$	−12.7082	+	9.23305i	−0.690215	+	0.501470i
$340$	8.83282			0.479027
$341$	−1.04508	−	11.1679i	−0.0565945	−	0.604777i
$342$	10.3262			0.558379
$343$	−13.5172	+	9.82084i	−0.729861	+	0.530275i
$344$	−2.76393	−	8.50651i	−0.149021	−	0.458640i
$345$	9.88854	−	30.4338i	0.532381	−	1.63850i
$346$	6.38197	+	4.63677i	0.343097	+	0.249274i
$347$	8.00000	+	5.81234i	0.429463	+	0.312023i	0.781434	−	0.623988i	$-0.214489\pi$
$347$	8.00000	+	5.81234i	0.429463	+	0.312023i	−0.351971	+	0.936011i	$0.614489\pi$
$348$	10.1459	−	31.2259i	0.543877	−	1.67388i
$349$	−3.14590	−	9.68208i	−0.168396	−	0.518270i	0.830874	−	0.556460i	$-0.187841\pi$
$349$	−3.14590	−	9.68208i	−0.168396	−	0.518270i	−0.999270	+	0.0381902i	$0.987841\pi$
$350$	−17.9271	+	13.0248i	−0.958241	+	0.696203i
$351$	14.4721			0.772465
$352$	11.3435	−	19.1396i	0.604608	−	1.02015i
$353$	−14.4721			−0.770274			−0.385137	−	0.922859i	$-0.625846\pi$
$353$	−14.4721			−0.770274			−0.385137	+	0.922859i	$0.625846\pi$
$354$	−43.2148	+	31.3974i	−2.29684	+	1.66875i
$355$	3.27051	+	10.0656i	0.173581	+	0.534226i
$356$	10.5836	−	32.5729i	0.560929	−	1.72636i
$357$	−17.7984	−	12.9313i	−0.941990	−	0.684396i
$358$	15.0000	+	10.8981i	0.792775	+	0.575984i
$359$	−3.62868	+	11.1679i	−0.191514	+	0.589420i	0.808485	+	0.588516i	$0.200288\pi$
$359$	−3.62868	+	11.1679i	−0.191514	+	0.589420i	−1.00000		0.000903944i	$0.999712\pi$
$360$	6.38197	+	19.6417i	0.336359	+	1.03521i
$361$	15.0623	−	10.9434i	0.792753	−	0.575969i
$362$	12.5623			0.660260
$363$	−24.4164	+	25.9030i	−1.28153	+	1.35956i
$364$	8.56231			0.448787
$365$	7.70820	−	5.60034i	0.403466	−	0.293135i
$366$	−18.6180	−	57.3004i	−0.973180	−	2.99514i
$367$	−1.14590	+	3.52671i	−0.0598154	+	0.184093i	−0.976499	−	0.215520i	$-0.930855\pi$
$367$	−1.14590	+	3.52671i	−0.0598154	+	0.184093i	0.916684	+	0.399613i	$0.130855\pi$
$368$	−6.47214	−	4.70228i	−0.337383	−	0.245123i
$369$		0			0
$370$	3.41641	−	10.5146i	0.177611	−	0.546629i
$371$	9.78115	+	30.1033i	0.507812	+	1.56289i
$372$	26.5623	−	19.2986i	1.37719	−	1.00059i
$373$	−3.14590			−0.162888			−0.0814442	−	0.996678i	$-0.525953\pi$
$373$	−3.14590			−0.162888			−0.0814442	+	0.996678i	$0.525953\pi$
$374$	−9.00658	+	15.1967i	−0.465719	+	0.785801i
$375$	33.8885			1.75000
$376$	16.8713	−	12.2577i	0.870072	−	0.632144i
$377$	1.04508	+	3.21644i	0.0538246	+	0.165655i
$378$	28.5410	−	87.8402i	1.46799	−	4.51801i
$379$	22.9443	+	16.6700i	1.17857	+	0.856280i	0.992009	−	0.126164i	$-0.0402666\pi$
$379$	22.9443	+	16.6700i	1.17857	+	0.856280i	0.186559	+	0.982444i	$0.440267\pi$
$380$	−1.85410	−	1.34708i	−0.0951134	−	0.0691039i
$381$	−9.23607	+	28.4257i	−0.473178	+	1.45629i
$382$	−6.18034	−	19.0211i	−0.316214	−	0.973206i
$383$	−25.8713	+	18.7966i	−1.32196	+	0.960462i	−0.322057	+	0.946720i	$0.604374\pi$
$383$	−25.8713	+	18.7966i	−1.32196	+	0.960462i	−0.999906	+	0.0137420i	$0.995626\pi$
$384$	50.6525			2.58485
$385$	1.09017	+	11.6497i	0.0555602	+	0.593724i
$386$	−31.3050			−1.59338
$387$	24.1803	−	17.5680i	1.22916	−	0.893034i
$388$	3.43769	+	10.5801i	0.174522	+	0.537125i
$389$	−2.48278	+	7.64121i	−0.125882	+	0.387425i	−0.994061	−	0.108827i	$-0.965291\pi$
$389$	−2.48278	+	7.64121i	−0.125882	+	0.387425i	0.868179	+	0.496251i	$0.165291\pi$
$390$	−7.23607	−	5.25731i	−0.366413	−	0.266214i
$391$	15.4164	+	11.2007i	0.779641	+	0.566443i
$392$	0.791796	−	2.43690i	0.0399917	−	0.123082i
$393$	−15.8885	−	48.8999i	−0.801471	−	2.46667i
$394$	−32.3607	+	23.5114i	−1.63031	+	1.18449i
$395$	−2.47214			−0.124387
$396$	−72.5410	−	16.2865i	−3.64532	−	0.818426i
$397$	−4.18034			−0.209805			−0.104903	−	0.994482i	$-0.533453\pi$
$397$	−4.18034			−0.209805			−0.104903	+	0.994482i	$0.533453\pi$
$398$	−8.94427	+	6.49839i	−0.448336	+	0.325735i
$399$	1.76393	+	5.42882i	0.0883071	+	0.271781i
$400$	1.07295	−	3.30220i	0.0536475	−	0.165110i
$401$	0.0901699	+	0.0655123i	0.00450287	+	0.00327153i	0.590034	−	0.807378i	$-0.299114\pi$
$401$	0.0901699	+	0.0655123i	0.00450287	+	0.00327153i	−0.585532	+	0.810650i	$0.699114\pi$
$402$	−61.3050	−	44.5407i	−3.05761	−	2.22149i
$403$	−1.04508	+	3.21644i	−0.0520594	+	0.160222i
$404$	−5.20820	−	16.0292i	−0.259118	−	0.797483i
$405$	−24.4164	+	17.7396i	−1.21326	+	0.881486i
$406$	21.5836			1.07118
$407$	8.76393	+	9.95959i	0.434412	+	0.493679i
$408$	−17.2361			−0.853313
$409$	−25.5623	+	18.5721i	−1.26397	+	0.918331i	−0.998946	−	0.0459091i	$-0.985382\pi$
$409$	−25.5623	+	18.5721i	−1.26397	+	0.918331i	−0.265029	+	0.964240i	$0.585382\pi$
$410$		0			0
$411$	0.291796	−	0.898056i	0.0143932	−	0.0442978i
$412$	4.85410	+	3.52671i	0.239144	+	0.173749i
$413$	−17.0451	−	12.3840i	−0.838734	−	0.609376i
$414$	−41.3050	+	127.124i	−2.03003	+	6.24778i
$415$	−1.18034	−	3.63271i	−0.0579406	−	0.178323i
$416$	−5.42705	+	3.94298i	−0.266083	+	0.193321i
$417$	−13.5279			−0.662462
$418$	4.20820	−	1.81636i	0.205830	−	0.0888409i
$419$	5.81966			0.284309			0.142155	−	0.989844i	$-0.454597\pi$
$419$	5.81966			0.284309			0.142155	+	0.989844i	$0.454597\pi$
$420$	−27.7082	+	20.1312i	−1.35202	+	0.982301i
$421$	0.763932	+	2.35114i	0.0372318	+	0.114588i	0.967945	−	0.251162i	$-0.0808127\pi$
$421$	0.763932	+	2.35114i	0.0372318	+	0.114588i	−0.930713	+	0.365750i	$0.880813\pi$
$422$	−12.7639	+	39.2833i	−0.621338	+	1.91228i
$423$	56.3779	+	40.9609i	2.74119	+	1.99159i
$424$	20.0623	+	14.5761i	0.974312	+	0.707879i
$425$	−2.55573	+	7.86572i	−0.123971	+	0.381544i
$426$	−19.1459	−	58.9250i	−0.927622	−	2.85493i
$427$	19.2254	−	13.9681i	0.930384	−	0.675963i
$428$	59.1246			2.85790
$429$	9.85410	−	4.25325i	0.475761	−	0.205349i
$430$	−11.0557			−0.533155
$431$	−14.6353	+	10.6331i	−0.704955	+	0.512180i	−0.881542	−	0.472105i	$-0.843494\pi$
$431$	−14.6353	+	10.6331i	−0.704955	+	0.512180i	0.176587	+	0.984285i	$0.443494\pi$
$432$	4.47214	+	13.7638i	0.215166	+	0.662212i
$433$	6.68034	−	20.5600i	0.321037	−	0.988049i	−0.652161	−	0.758080i	$-0.726138\pi$
$433$	6.68034	−	20.5600i	0.321037	−	0.988049i	0.973198	−	0.229969i	$-0.0738625\pi$
$434$	17.4615	+	12.6865i	0.838178	+	0.608972i
$435$	−10.9443	−	7.95148i	−0.524738	−	0.381244i
$436$	−11.2918	+	34.7526i	−0.540779	+	1.66435i
$437$	−1.52786	−	4.70228i	−0.0730876	−	0.224941i
$438$	−45.1246	+	32.7849i	−2.15614	+	1.56653i
$439$	1.52786			0.0729210			0.0364605	−	0.999335i	$-0.488392\pi$
$439$	1.52786			0.0729210			0.0364605	+	0.999335i	$0.488392\pi$
$440$	6.05573	+	6.88191i	0.288696	+	0.328082i
$441$	8.56231			0.407729
$442$	4.30902	−	3.13068i	0.204959	−	0.148911i
$443$	−7.79837	−	24.0009i	−0.370512	−	1.14032i	−0.946457	−	0.322830i	$-0.895366\pi$
$443$	−7.79837	−	24.0009i	−0.370512	−	1.14032i	0.575945	−	0.817488i	$-0.304634\pi$
$444$	−12.0000	+	36.9322i	−0.569495	+	1.75272i
$445$	−11.4164	−	8.29451i	−0.541190	−	0.393197i
$446$	−16.1803	−	11.7557i	−0.766161	−	0.556649i
$447$	−5.70820	+	17.5680i	−0.269989	+	0.830940i
$448$	11.4656	+	35.2874i	0.541697	+	1.66717i
$449$	7.38197	−	5.36331i	0.348377	−	0.253110i	−0.399811	−	0.916598i	$-0.630924\pi$
$449$	7.38197	−	5.36331i	0.348377	−	0.253110i	0.748188	+	0.663487i	$0.230924\pi$
$450$	−58.0132			−2.73477
$451$		0			0
$452$	−14.5623			−0.684953
$453$	2.38197	−	1.73060i	0.111915	−	0.0813107i
$454$	7.50000	+	23.0826i	0.351992	+	1.08332i
$455$	1.09017	−	3.35520i	0.0511080	−	0.157294i
$456$	3.61803	+	2.62866i	0.169430	+	0.123098i
$457$	−12.1803	−	8.84953i	−0.569772	−	0.413964i	0.265250	−	0.964180i	$-0.414545\pi$
$457$	−12.1803	−	8.84953i	−0.569772	−	0.413964i	−0.835022	+	0.550216i	$0.814545\pi$
$458$	−2.96556	+	9.12705i	−0.138571	+	0.426479i
$459$	−10.6525	−	32.7849i	−0.497215	−	1.53027i
$460$	24.0000	−	17.4370i	1.11901	−	0.813005i
$461$	10.6525			0.496135			0.248068	−	0.968743i	$-0.420204\pi$
$461$	10.6525			0.496135			0.248068	+	0.968743i	$0.420204\pi$
$462$	−6.38197	−	68.1986i	−0.296916	−	3.17288i
$463$	1.85410			0.0861674			0.0430837	−	0.999071i	$-0.486282\pi$
$463$	1.85410			0.0861674			0.0430837	+	0.999071i	$0.486282\pi$
$464$	−2.73607	+	1.98787i	−0.127019	+	0.0922845i
$465$	−4.18034	−	12.8658i	−0.193859	−	0.596635i
$466$	16.8090	−	51.7328i	0.778663	−	2.39648i
$467$	10.9443	+	7.95148i	0.506441	+	0.367951i	0.811472	−	0.584392i	$-0.198667\pi$
$467$	10.9443	+	7.95148i	0.506441	+	0.367951i	−0.305031	+	0.952342i	$0.598667\pi$
$468$	18.1353	+	13.1760i	0.838302	+	0.609062i
$469$	9.23607	−	28.4257i	0.426482	−	1.31258i
$470$	−7.96556	−	24.5155i	−0.367424	−	1.13081i
$471$	25.6525	−	18.6376i	1.18200	−	0.858776i
$472$	−16.5066			−0.759777
$473$	6.76393	−	11.4127i	0.311006	−	0.524756i
$474$	14.4721			0.664727
$475$	1.73607	−	1.26133i	0.0796563	−	0.0578737i
$476$	−6.30244	−	19.3969i	−0.288872	−	0.889056i
$477$	−25.6074	+	78.8114i	−1.17248	+	3.60853i
$478$	9.63525	+	7.00042i	0.440706	+	0.320192i
$479$	−31.6246	−	22.9766i	−1.44497	−	1.04983i	−0.986975	−	0.160871i	$-0.948570\pi$
$479$	−31.6246	−	22.9766i	−1.44497	−	1.04983i	−0.457990	−	0.888957i	$-0.651430\pi$
$480$	8.29180	−	25.5195i	0.378467	−	1.16480i
$481$	−1.23607	−	3.80423i	−0.0563598	−	0.173458i
$482$	31.1803	−	22.6538i	1.42023	−	1.03185i
$483$	−73.8885			−3.36205
$484$	−32.4271	+	6.12261i	−1.47396	+	0.278300i
$485$	4.58359			0.208130
$486$	64.3951	−	46.7858i	2.92102	−	2.12225i
$487$	−1.64590	−	5.06555i	−0.0745828	−	0.229542i	0.906815	−	0.421530i	$-0.138507\pi$
$487$	−1.64590	−	5.06555i	−0.0745828	−	0.229542i	−0.981397	+	0.191988i	$0.938507\pi$
$488$	5.75329	−	17.7068i	0.260439	−	0.801549i
$489$	−19.9443	−	14.4904i	−0.901911	−	0.655277i
$490$	−2.56231	−	1.86162i	−0.115753	−	0.0840996i
$491$	2.32624	−	7.15942i	0.104982	−	0.323100i	−0.884744	−	0.466076i	$-0.845667\pi$
$491$	2.32624	−	7.15942i	0.104982	−	0.323100i	0.989726	+	0.142976i	$0.0456672\pi$
$492$		0			0
$493$	6.51722	−	4.73504i	0.293521	−	0.213255i
$494$	−1.38197			−0.0621776
$495$	−15.6180	+	26.3521i	−0.701978	+	1.18444i
$496$	−3.38197			−0.151855
$497$	19.7705	−	14.3641i	0.886829	−	0.644319i
$498$	6.90983	+	21.2663i	0.309637	+	0.952964i
$499$	3.59017	−	11.0494i	0.160718	−	0.494639i	−0.837977	−	0.545705i	$-0.816262\pi$
$499$	3.59017	−	11.0494i	0.160718	−	0.494639i	0.998695	+	0.0510658i	$0.0162618\pi$
$500$	25.4164	+	18.4661i	1.13666	+	0.825829i
$501$	25.7984	+	18.7436i	1.15259	+	0.837403i
$502$	4.87539	−	15.0049i	0.217599	−	0.669702i
$503$	−0.326238	−	1.00406i	−0.0145462	−	0.0447687i	0.943520	−	0.331316i	$-0.107493\pi$
$503$	−0.326238	−	1.00406i	−0.0145462	−	0.0447687i	−0.958066	+	0.286547i	$0.907493\pi$
$504$	38.5795	−	28.0297i	1.71847	−	1.24854i
$505$	−6.94427			−0.309016
$506$	5.52786	+	59.0715i	0.245744	+	2.62605i
$507$	−3.23607			−0.143719
$508$	−22.4164	+	16.2865i	−0.994567	+	0.722595i
$509$	−12.9098	−	39.7324i	−0.572218	−	1.76111i	−0.645462	−	0.763792i	$-0.723335\pi$
$509$	−12.9098	−	39.7324i	−0.572218	−	1.76111i	0.0732439	−	0.997314i	$-0.476665\pi$
$510$	−6.58359	+	20.2622i	−0.291526	+	0.897226i
$511$	−17.7984	−	12.9313i	−0.787354	−	0.572046i
$512$	−9.04508	−	6.57164i	−0.399740	−	0.290428i
$513$	−2.76393	+	8.50651i	−0.122031	+	0.375572i
$514$	13.4787	+	41.4832i	0.594521	+	1.82975i
$515$	2.00000	−	1.45309i	0.0881305	−	0.0640306i
$516$	38.8328			1.70952
$517$	30.1803	+	6.77591i	1.32733	+	0.298004i
$518$	−25.5279			−1.12163
$519$	−9.23607	+	6.71040i	−0.405418	+	0.294554i
$520$	−0.854102	−	2.62866i	−0.0374548	−	0.115274i
$521$	−12.6631	+	38.9731i	−0.554781	+	1.70744i	0.141739	+	0.989904i	$0.454731\pi$
$521$	−12.6631	+	38.9731i	−0.554781	+	1.70744i	−0.696520	+	0.717537i	$0.745269\pi$
$522$	45.7148	+	33.2137i	2.00088	+	1.45373i
$523$	−14.8541	−	10.7921i	−0.649525	−	0.471907i	0.213585	−	0.976925i	$-0.431486\pi$
$523$	−14.8541	−	10.7921i	−0.649525	−	0.471907i	−0.863109	+	0.505017i	$0.831486\pi$
$524$	14.7295	−	45.3327i	0.643461	−	1.98037i
$525$	−9.90983	−	30.4993i	−0.432500	−	1.33110i
$526$	51.8328	−	37.6587i	2.26002	−	1.64200i
$527$	8.05573			0.350913
$528$	7.09017	+	8.05748i	0.308560	+	0.350657i
$529$	41.0000			1.78261
$530$	24.7984	−	18.0171i	1.07717	−	0.782612i
$531$	−17.0451	−	52.4594i	−0.739694	−	2.27654i
$532$	−1.63525	+	5.03280i	−0.0708973	+	0.218199i
$533$		0			0
$534$	66.8328	+	48.5569i	2.89214	+	2.10126i
$535$	7.52786	−	23.1684i	0.325458	−	1.00166i
$536$	−7.23607	−	22.2703i	−0.312551	−	0.961932i
$537$	−21.7082	+	15.7719i	−0.936778	+	0.680609i
$538$	−20.7295			−0.893712
$539$	3.48936	−	1.50609i	0.150297	−	0.0648717i
$540$	−53.6656			−2.30940
$541$	−11.1803	+	8.12299i	−0.480680	+	0.349235i	−0.801589	−	0.597875i	$-0.796012\pi$
$541$	−11.1803	+	8.12299i	−0.480680	+	0.349235i	0.320909	+	0.947110i	$0.396012\pi$
$542$	15.3885	+	47.3611i	0.660995	+	2.03433i
$543$	−5.61803	+	17.2905i	−0.241093	+	0.742008i
$544$	12.9271	+	9.39205i	0.554243	+	0.402681i
$545$	12.1803	+	8.84953i	0.521748	+	0.379072i
$546$	−6.38197	+	19.6417i	−0.273123	+	0.840586i
$547$	−0.0901699	−	0.277515i	−0.00385539	−	0.0118657i	0.949110	−	0.314944i	$-0.101986\pi$
$547$	−0.0901699	−	0.277515i	−0.00385539	−	0.0118657i	−0.952966	+	0.303078i	$0.901986\pi$
$548$	0.708204	−	0.514540i	0.0302530	−	0.0219801i
$549$	62.2148			2.65526
$550$	−23.6418	+	10.2044i	−1.00809	+	0.435115i
$551$	−2.09017			−0.0890442
$552$	−46.8328	+	34.0260i	−1.99334	+	1.44824i
$553$	1.76393	+	5.42882i	0.0750100	+	0.230857i
$554$	20.1869	−	62.1289i	0.857660	−	2.63961i
$555$	12.9443	+	9.40456i	0.549454	+	0.399202i
$556$	−10.1459	−	7.37143i	−0.430282	−	0.312618i
$557$	−3.20163	+	9.85359i	−0.135657	+	0.417510i	−0.995692	−	0.0927259i	$-0.970442\pi$
$557$	−3.20163	+	9.85359i	−0.135657	+	0.417510i	0.860034	+	0.510236i	$0.170442\pi$
$558$	17.4615	+	53.7409i	0.739204	+	2.27504i
$559$	−3.23607	+	2.35114i	−0.136871	+	0.0994427i
$560$	3.52786			0.149079
$561$	−16.8885	−	19.1926i	−0.713035	−	0.810314i
$562$	−32.1115			−1.35454
$563$	37.2705	−	27.0786i	1.57076	−	1.14123i	0.644345	−	0.764735i	$-0.277130\pi$
$563$	37.2705	−	27.0786i	1.57076	−	1.14123i	0.926420	−	0.376492i	$-0.122870\pi$
$564$	27.9787	+	86.1096i	1.17812	+	3.62587i
$565$	−1.85410	+	5.70634i	−0.0780027	+	0.240067i
$566$	−50.4508	−	36.6547i	−2.12061	−	1.54071i
$567$	56.3779	+	40.9609i	2.36765	+	1.72020i
$568$	5.91641	−	18.2088i	0.248247	−	0.764026i
$569$	−0.555728	−	1.71036i	−0.0232973	−	0.0717018i	0.938732	−	0.344648i	$-0.112002\pi$
$569$	−0.555728	−	1.71036i	−0.0232973	−	0.0717018i	−0.962029	+	0.272946i	$0.912002\pi$
$570$	4.47214	−	3.24920i	0.187317	−	0.136094i
$571$	−39.5967			−1.65707			−0.828536	−	0.559936i	$-0.810826\pi$
$571$	−39.5967			−1.65707			−0.828536	+	0.559936i	$0.810826\pi$
$572$	9.70820	+	2.17963i	0.405920	+	0.0911348i
$573$	28.9443			1.20916
$574$		0			0
$575$	8.58359	+	26.4176i	0.357961	+	1.10169i
$576$	−30.0172	+	92.3835i	−1.25072	+	3.84931i
$577$	23.0344	+	16.7355i	0.958936	+	0.696708i	0.952903	−	0.303274i	$-0.0980797\pi$
$577$	23.0344	+	16.7355i	0.958936	+	0.696708i	0.00603289	+	0.999982i	$0.498080\pi$
$578$	20.4894	+	14.8864i	0.852245	+	0.619192i
$579$	14.0000	−	43.0876i	0.581820	−	1.79066i
$580$	−3.87539	−	11.9272i	−0.160917	−	0.495251i
$581$	−7.13525	+	5.18407i	−0.296020	+	0.215071i
$582$	−26.8328			−1.11226
$583$	3.42705	+	36.6219i	0.141934	+	1.51673i
$584$	−17.2361			−0.713234
$585$	7.47214	−	5.42882i	0.308935	−	0.224454i
$586$	−4.14590	−	12.7598i	−0.171265	−	0.527101i
$587$	−8.18034	+	25.1765i	−0.337639	+	1.03915i	0.627769	+	0.778400i	$0.283968\pi$
$587$	−8.18034	+	25.1765i	−0.337639	+	1.03915i	−0.965408	+	0.260745i	$0.916032\pi$
$588$	9.00000	+	6.53888i	0.371154	+	0.269659i
$589$	−1.69098	−	1.22857i	−0.0696757	−	0.0506224i
$590$	−6.30495	+	19.4046i	−0.259571	+	0.798877i
$591$	−17.8885	−	55.0553i	−0.735836	−	2.26467i
$592$	3.23607	−	2.35114i	0.133002	−	0.0966313i
$593$	−32.8328			−1.34828			−0.674141	−	0.738603i	$-0.735486\pi$
$593$	−32.8328			−1.34828			−0.674141	+	0.738603i	$0.735486\pi$
$594$	54.7214	−	92.3305i	2.24524	−	3.78837i
$595$	−8.40325			−0.344500
$596$	−13.8541	+	10.0656i	−0.567486	+	0.412303i
$597$	−4.94427	−	15.2169i	−0.202356	−	0.622786i
$598$	5.52786	−	17.0130i	0.226051	−	0.695714i
$599$	7.09017	+	5.15131i	0.289696	+	0.210477i	0.723136	−	0.690706i	$-0.242700\pi$
$599$	7.09017	+	5.15131i	0.289696	+	0.210477i	−0.433439	+	0.901183i	$0.642700\pi$
$600$	−20.3262	−	14.7679i	−0.829815	−	0.602896i
$601$	−13.3820	+	41.1855i	−0.545862	+	1.67999i	0.173070	+	0.984909i	$0.444631\pi$
$601$	−13.3820	+	41.1855i	−0.545862	+	1.67999i	−0.718932	+	0.695080i	$0.755369\pi$
$602$	7.88854	+	24.2784i	0.321513	+	0.989515i
$603$	63.3050	−	45.9937i	2.57798	−	1.87301i
$604$	2.72949			0.111061
$605$	−1.72949	+	13.4863i	−0.0703138	+	0.548296i
$606$	40.6525			1.65139
$607$	21.9443	−	15.9434i	0.890691	−	0.647125i	−0.0453674	−	0.998970i	$-0.514446\pi$
$607$	21.9443	−	15.9434i	0.890691	−	0.647125i	0.936058	+	0.351846i	$0.114446\pi$
$608$	−1.28115	−	3.94298i	−0.0519576	−	0.159909i
$609$	−9.65248	+	29.7073i	−0.391138	+	1.20380i
$610$	−18.6180	−	13.5268i	−0.753822	−	0.547684i
$611$	−7.54508	−	5.48183i	−0.305241	−	0.221771i
$612$	16.5000	−	50.7818i	0.666973	−	2.05273i
$613$	−8.70820	−	26.8011i	−0.351721	−	1.08249i	−0.957886	−	0.287147i	$-0.907293\pi$
$613$	−8.70820	−	26.8011i	−0.351721	−	1.08249i	0.606165	−	0.795339i	$-0.292707\pi$
$614$	35.8156	−	26.0216i	1.44540	−	1.05014i
$615$		0			0
$616$	10.7918	−	18.2088i	0.434814	−	0.733655i
$617$	−11.4164			−0.459607			−0.229804	−	0.973237i	$-0.573808\pi$
$617$	−11.4164			−0.459607			−0.229804	+	0.973237i	$0.573808\pi$
$618$	−11.7082	+	8.50651i	−0.470973	+	0.342182i
$619$	−11.0066	−	33.8748i	−0.442392	−	1.36154i	−0.885319	−	0.464984i	$-0.846060\pi$
$619$	−11.0066	−	33.8748i	−0.442392	−	1.36154i	0.442927	−	0.896558i	$-0.353940\pi$
$620$	3.87539	−	11.9272i	0.155639	−	0.479009i
$621$	−93.6656	−	68.0521i	−3.75867	−	2.73084i
$622$	4.79837	+	3.48622i	0.192397	+	0.139785i
$623$	−10.0689	+	30.9888i	−0.403401	+	1.24154i
$624$	−1.00000	−	3.07768i	−0.0400320	−	0.123206i
$625$	−3.57295	+	2.59590i	−0.142918	+	0.103836i
$626$	11.2574			0.449934
$627$	0.618034	+	6.60440i	0.0246819	+	0.263754i
$628$	29.3951			1.17299
$629$	−7.70820	+	5.60034i	−0.307346	+	0.223300i
$630$	−18.2148	−	56.0593i	−0.725694	−	2.23346i
$631$	11.8820	−	36.5689i	0.473014	−	1.45579i	−0.375604	−	0.926780i	$-0.622565\pi$
$631$	11.8820	−	36.5689i	0.473014	−	1.45579i	0.848618	−	0.529006i	$-0.177435\pi$
$632$	3.61803	+	2.62866i	0.143918	+	0.104562i
$633$	−48.3607	−	35.1361i	−1.92216	−	1.39653i
$634$	−12.2361	+	37.6587i	−0.485956	+	1.49562i
$635$	3.52786	+	10.8576i	0.139999	+	0.430873i
$636$	−87.1033	+	63.2843i	−3.45387	+	2.50938i
$637$	−1.14590			−0.0454021
$638$	24.4721	+	5.49434i	0.968861	+	0.217523i
$639$	63.9787			2.53096
$640$	15.6525	−	11.3722i	0.618718	−	0.449525i
$641$	10.8435	+	33.3727i	0.428291	+	1.31814i	0.899808	+	0.436287i	$0.143707\pi$
$641$	10.8435	+	33.3727i	0.428291	+	1.31814i	−0.471517	+	0.881857i	$0.656293\pi$
$642$	−44.0689	+	135.630i	−1.73926	+	5.35289i
$643$	31.9164	+	23.1886i	1.25866	+	0.914470i	0.998691	−	0.0511467i	$-0.0162876\pi$
$643$	31.9164	+	23.1886i	1.25866	+	0.914470i	0.259969	+	0.965617i	$0.416288\pi$
$644$	−55.4164	−	40.2624i	−2.18371	−	1.58656i
$645$	4.94427	−	15.2169i	0.194681	−	0.599165i
$646$	1.01722	+	3.13068i	0.0400220	+	0.123175i
$647$	−8.09017	+	5.87785i	−0.318057	+	0.231082i	−0.735346	−	0.677692i	$-0.762980\pi$
$647$	−8.09017	+	5.87785i	−0.318057	+	0.231082i	0.417289	+	0.908774i	$0.362980\pi$
$648$	54.5967			2.14476
$649$	−16.1738	−	18.3803i	−0.634876	−	0.721492i
$650$	7.76393			0.304526
$651$	−25.2705	+	18.3601i	−0.990429	+	0.719589i
$652$	−7.06231	−	21.7355i	−0.276581	−	0.851230i
$653$	−8.38854	+	25.8173i	−0.328269	+	1.01031i	0.641674	+	0.766977i	$0.278240\pi$
$653$	−8.38854	+	25.8173i	−0.328269	+	1.01031i	−0.969943	+	0.243331i	$0.921760\pi$
$654$	−71.3050	−	51.8061i	−2.78824	−	2.02578i
$655$	−15.8885	−	11.5437i	−0.620817	−	0.451050i
$656$		0			0
$657$	−17.7984	−	54.7778i	−0.694381	−	2.13708i
$658$	−48.1525	+	34.9848i	−1.87718	+	1.36385i
$659$	−10.5836			−0.412278			−0.206139	−	0.978523i	$-0.566090\pi$
$659$	−10.5836			−0.412278			−0.206139	+	0.978523i	$0.566090\pi$
$660$	−36.5410	+	15.7719i	−1.42236	+	0.613922i
$661$	−19.1246			−0.743861			−0.371931	−	0.928261i	$-0.621304\pi$
$661$	−19.1246			−0.743861			−0.371931	+	0.928261i	$0.621304\pi$
$662$	45.7148	−	33.2137i	1.77676	−	1.29089i
$663$	2.38197	+	7.33094i	0.0925079	+	0.284710i
$664$	−2.13525	+	6.57164i	−0.0828640	+	0.255029i
$665$	1.76393	+	1.28157i	0.0684023	+	0.0496972i
$666$	−54.0689	−	39.2833i	−2.09513	−	1.52220i
$667$	8.36068	−	25.7315i	0.323727	−	0.996329i
$668$	9.13525	+	28.1154i	0.353454	+	1.08782i
$669$	23.4164	−	17.0130i	0.905331	−	0.657761i
$670$	−28.9443			−1.11821
$671$	25.3541	−	10.9434i	0.978784	−	0.422465i
$672$	−61.9574			−2.39006
$673$	−39.1525	+	28.4459i	−1.50922	+	1.09651i	−0.542694	+	0.839930i	$0.682596\pi$
$673$	−39.1525	+	28.4459i	−1.50922	+	1.09651i	−0.966523	+	0.256580i	$0.917404\pi$
$674$	3.59424	+	11.0619i	0.138445	+	0.426089i
$675$	15.5279	−	47.7899i	0.597668	−	1.83943i
$676$	−2.42705	−	1.76336i	−0.0933481	−	0.0678214i
$677$	12.9721	+	9.42481i	0.498560	+	0.362225i	0.808467	−	0.588542i	$-0.200298\pi$
$677$	12.9721	+	9.42481i	0.498560	+	0.362225i	−0.309907	+	0.950767i	$0.600298\pi$
$678$	10.8541	−	33.4055i	0.416849	−	1.28293i
$679$	−3.27051	−	10.0656i	−0.125511	−	0.386282i
$680$	−5.32624	+	3.86974i	−0.204252	+	0.148398i
$681$	−35.1246			−1.34598
$682$	16.5689	+	18.8294i	0.634455	+	0.721014i
$683$	16.9787			0.649672			0.324836	−	0.945770i	$-0.394691\pi$
$683$	16.9787			0.649672			0.324836	+	0.945770i	$0.394691\pi$
$684$	−11.2082	+	8.14324i	−0.428556	+	0.311364i
$685$	−0.111456	−	0.343027i	−0.00425852	−	0.0131064i
$686$	11.5451	−	35.5321i	0.440793	−	1.35662i
$687$	−11.2361	−	8.16348i	−0.428683	−	0.311456i
$688$	−3.23607	−	2.35114i	−0.123374	−	0.0896364i
$689$	3.42705	−	10.5474i	0.130560	−	0.401823i
$690$	22.1115	+	68.0521i	0.841769	+	2.59070i
$691$	16.4443	−	11.9475i	0.625570	−	0.454503i	−0.229293	−	0.973357i	$-0.573641\pi$
$691$	16.4443	−	11.9475i	0.625570	−	0.454503i	0.854863	+	0.518855i	$0.173641\pi$
$692$	−10.5836			−0.402328
$693$	69.0132	+	15.4944i	2.62159	+	0.588584i
$694$	−22.1115			−0.839339
$695$	−4.18034	+	3.03719i	−0.158569	+	0.115207i
$696$	7.56231	+	23.2744i	0.286648	+	0.882213i
$697$		0			0
$698$	18.4164	+	13.3803i	0.697071	+	0.506452i
$699$	63.6869	+	46.2713i	2.40886	+	1.75014i
$700$	9.18692	−	28.2744i	0.347233	−	1.06867i
$701$	5.26393	+	16.2007i	0.198816	+	0.611893i	0.999911	+	0.0133552i	$0.00425122\pi$
$701$	5.26393	+	16.2007i	0.198816	+	0.611893i	−0.801095	+	0.598537i	$0.795749\pi$
$702$	−26.1803	+	19.0211i	−0.988113	+	0.717906i
$703$	2.47214			0.0932384
$704$	4.01722	+	42.9286i	0.151405	+	1.61793i
$705$	37.3050			1.40499
$706$	26.1803	−	19.0211i	0.985310	−	0.715870i
$707$	4.95492	+	15.2497i	0.186349	+	0.573523i
$708$	22.1459	−	68.1581i	0.832294	−	2.56154i
$709$	−4.47214	−	3.24920i	−0.167955	−	0.122026i	0.500633	−	0.865660i	$-0.333101\pi$
$709$	−4.47214	−	3.24920i	−0.167955	−	0.122026i	−0.668587	+	0.743634i	$0.733101\pi$
$710$	−19.1459	−	13.9103i	−0.718533	−	0.522045i
$711$	−4.61803	+	14.2128i	−0.173190	+	0.533023i
$712$	7.88854	+	24.2784i	0.295636	+	0.909873i
$713$	21.8885	−	15.9030i	0.819732	−	0.595570i
$714$	49.1935			1.84102
$715$	2.09017	−	3.52671i	0.0781679	−	0.131892i
$716$	−24.8754			−0.929637
$717$	−13.9443	+	10.1311i	−0.520758	+	0.378353i
$718$	−8.11397	−	24.9722i	−0.302811	−	0.931955i
$719$	−0.145898	+	0.449028i	−0.00544108	+	0.0167459i	−0.953740	−	0.300632i	$-0.902802\pi$
$719$	−0.145898	+	0.449028i	−0.00544108	+	0.0167459i	0.948299	+	0.317378i	$0.102802\pi$
$720$	7.47214	+	5.42882i	0.278470	+	0.202320i
$721$	−4.61803	−	3.35520i	−0.171985	−	0.124954i
$722$	−12.8647	+	39.5936i	−0.478776	+	1.47352i
$723$	17.2361	+	53.0472i	0.641016	+	1.97285i
$724$	−13.6353	+	9.90659i	−0.506750	+	0.368176i
$725$	11.7426			0.436111
$726$	10.1246	−	78.9502i	0.375760	−	2.93012i
$727$	31.8885			1.18268			0.591340	−	0.806422i	$-0.298599\pi$
$727$	31.8885			1.18268			0.591340	+	0.806422i	$0.298599\pi$
$728$	−5.16312	+	3.75123i	−0.191358	+	0.139030i
$729$	12.9615	+	39.8914i	0.480055	+	1.47746i
$730$	−6.58359	+	20.2622i	−0.243670	+	0.749938i
$731$	7.70820	+	5.60034i	0.285098	+	0.207136i
$732$	65.3951	+	47.5123i	2.41707	+	1.75611i
$733$	−3.03444	+	9.33905i	−0.112080	+	0.344946i	−0.991327	−	0.131420i	$-0.958046\pi$
$733$	−3.03444	+	9.33905i	−0.112080	+	0.344946i	0.879247	+	0.476366i	$0.158046\pi$
$734$	−2.56231	−	7.88597i	−0.0945764	−	0.291076i
$735$	3.70820	−	2.69417i	0.136779	−	0.0993759i
$736$	53.6656			1.97814
$737$	17.7082	−	29.8788i	0.652290	−	1.10060i
$738$		0			0
$739$	−26.6353	+	19.3516i	−0.979794	+	0.711862i	−0.957662	−	0.287893i	$-0.907045\pi$
$739$	−26.6353	+	19.3516i	−0.979794	+	0.711862i	−0.0221312	+	0.999755i	$0.507045\pi$
$740$	4.58359	+	14.1068i	0.168496	+	0.518578i
$741$	0.618034	−	1.90211i	0.0227040	−	0.0698759i
$742$	−57.2599	−	41.6017i	−2.10208	−	1.52725i
$743$	−14.9721	−	10.8779i	−0.549274	−	0.399071i	0.278243	−	0.960511i	$-0.410248\pi$
$743$	−14.9721	−	10.8779i	−0.549274	−	0.399071i	−0.827518	+	0.561439i	$0.810248\pi$
$744$	−7.56231	+	23.2744i	−0.277248	+	0.853280i
$745$	2.18034	+	6.71040i	0.0798815	+	0.245850i
$746$	5.69098	−	4.13474i	0.208362	−	0.151384i
$747$	−23.0902			−0.844825
$748$	−2.20820	−	23.5972i	−0.0807399	−	0.862798i
$749$	−56.2492			−2.05530
$750$	−61.3050	+	44.5407i	−2.23854	+	1.62639i
$751$	12.0557	+	37.1037i	0.439920	+	1.35393i	0.887960	+	0.459920i	$0.152122\pi$
$751$	12.0557	+	37.1037i	0.439920	+	1.35393i	−0.448040	+	0.894013i	$0.647878\pi$
$752$	2.88197	−	8.86978i	0.105094	−	0.323448i
$753$	18.4721	+	13.4208i	0.673162	+	0.489081i
$754$	−6.11803	−	4.44501i	−0.222806	−	0.161878i
$755$	0.347524	−	1.06957i	0.0126477	−	0.0389256i
$756$	38.2918	+	117.850i	1.39266	+	4.28616i
$757$	−31.6697	+	23.0094i	−1.15105	+	0.836290i	−0.988621	−	0.150429i	$-0.951934\pi$
$757$	−31.6697	+	23.0094i	−1.15105	+	0.836290i	−0.162434	+	0.986719i	$0.551934\pi$
$758$	−63.4164			−2.30339
$759$	−83.7771	−	18.8091i	−3.04092	−	0.682728i
$760$	1.70820			0.0619631
$761$	26.6525	−	19.3642i	0.966151	−	0.701950i	0.0115803	−	0.999933i	$-0.496314\pi$
$761$	26.6525	−	19.3642i	0.966151	−	0.701950i	0.954571	+	0.297983i	$0.0963138\pi$
$762$	−20.6525	−	63.5618i	−0.748160	−	2.30260i
$763$	10.7426	−	33.0625i	0.388910	−	1.19694i
$764$	21.7082	+	15.7719i	0.785375	+	0.570609i
$765$	−17.7984	−	12.9313i	−0.643502	−	0.467531i
$766$	22.0967	−	68.0068i	0.798388	−	2.45719i
$767$	2.28115	+	7.02067i	0.0823677	+	0.253502i
$768$	−23.5623	+	17.1190i	−0.850231	+	0.617729i
$769$	11.3050			0.407667			0.203833	−	0.979006i	$-0.434660\pi$
$769$	11.3050			0.407667			0.203833	+	0.979006i	$0.434660\pi$
$770$	−17.2837	−	19.6417i	−0.622860	−	0.707837i
$771$	−63.1246			−2.27338
$772$	33.9787	−	24.6870i	1.22292	−	0.888504i
$773$	8.94427	+	27.5276i	0.321703	+	0.990100i	0.972907	+	0.231197i	$0.0742643\pi$
$773$	8.94427	+	27.5276i	0.321703	+	0.990100i	−0.651204	+	0.758903i	$0.725736\pi$
$774$	−20.6525	+	63.5618i	−0.742338	+	2.28468i
$775$	9.50000	+	6.90215i	0.341250	+	0.247933i
$776$	−6.70820	−	4.87380i	−0.240810	−	0.174959i
$777$	11.4164	−	35.1361i	0.409561	−	1.26050i
$778$	−5.55166	−	17.0863i	−0.199037	−	0.612572i
$779$		0			0
$780$	12.0000			0.429669
$781$	26.0729	−	11.2537i	0.932963	−	0.402688i
$782$	−42.6099			−1.52373
$783$	−39.5967	+	28.7687i	−1.41507	+	1.02811i
$784$	−0.354102	−	1.08981i	−0.0126465	−	0.0389219i
$785$	3.74265	−	11.5187i	0.133581	−	0.411119i
$786$	93.0132	+	67.5780i	3.31767	+	2.41043i
$787$	4.76393	+	3.46120i	0.169816	+	0.123378i	0.669447	−	0.742860i	$-0.266531\pi$
$787$	4.76393	+	3.46120i	0.169816	+	0.123378i	−0.499631	+	0.866238i	$0.666531\pi$
$788$	16.5836	−	51.0390i	0.590766	−	1.81819i
$789$	28.6525	+	88.1833i	1.02006	+	3.13941i
$790$	4.47214	−	3.24920i	0.159111	−	0.115601i
$791$	13.8541			0.492595
$792$	50.8779	−	21.9601i	1.80787	−	0.780317i
$793$	−8.32624			−0.295673
$794$	7.56231	−	5.49434i	0.268376	−	0.194987i
$795$	13.7082	+	42.1895i	0.486180	+	1.49631i
$796$	4.58359	−	14.1068i	0.162461	−	0.500004i
$797$	8.97214	+	6.51864i	0.317809	+	0.230902i	0.735240	−	0.677807i	$-0.237069\pi$
$797$	8.97214	+	6.51864i	0.317809	+	0.230902i	−0.417431	+	0.908709i	$0.637069\pi$
$798$	−10.3262	−	7.50245i	−0.365545	−	0.265584i
$799$	−6.86475	+	21.1275i	−0.242857	+	0.747438i
$800$	7.19756	+	22.1518i	0.254472	+	0.783185i
$801$	−69.0132	+	50.1410i	−2.43846	+	1.77164i
$802$	−0.249224			−0.00880039
$803$	−16.8885	−	19.1926i	−0.595984	−	0.677294i
$804$	101.666			3.58547
$805$	−22.8328	+	16.5890i	−0.804751	+	0.584686i
$806$	−2.33688	−	7.19218i	−0.0823131	−	0.253334i
$807$	9.27051	−	28.5317i	0.326337	−	1.00436i
$808$	10.1631	+	7.38394i	0.357537	+	0.259766i
$809$	13.7984	+	10.0251i	0.485125	+	0.352464i	0.803306	−	0.595566i	$-0.203072\pi$
$809$	13.7984	+	10.0251i	0.485125	+	0.352464i	−0.318181	+	0.948030i	$0.603072\pi$
$810$	20.8541	−	64.1823i	0.732738	−	2.25514i
$811$	12.9443	+	39.8384i	0.454535	+	1.39891i	0.871680	+	0.490075i	$0.163031\pi$
$811$	12.9443	+	39.8384i	0.454535	+	1.39891i	−0.417146	+	0.908840i	$0.636969\pi$
$812$	−23.4271	+	17.0207i	−0.822128	+	0.597311i
$813$	−72.0689			−2.52757
$814$	−28.9443	−	6.49839i	−1.01450	−	0.227769i
$815$	−9.41641			−0.329842
$816$	−6.23607	+	4.53077i	−0.218306	+	0.158609i
$817$	−0.763932	−	2.35114i	−0.0267266	−	0.0822560i
$818$	21.8328	−	67.1945i	0.763367	−	2.34940i
$819$	−17.2533	−	12.5352i	−0.602879	−	0.438017i
$820$		0			0
$821$	12.8885	−	39.6669i	0.449813	−	1.38438i	−0.427305	−	0.904108i	$-0.640537\pi$
$821$	12.8885	−	39.6669i	0.449813	−	1.38438i	0.877118	−	0.480275i	$-0.159463\pi$
$822$	0.652476	+	2.00811i	0.0227577	+	0.0700410i
$823$	29.4164	−	21.3723i	1.02539	−	0.744991i	0.0580104	−	0.998316i	$-0.481524\pi$
$823$	29.4164	−	21.3723i	1.02539	−	0.744991i	0.967381	+	0.253325i	$0.0815243\pi$
$824$	−4.47214			−0.155794
$825$	−3.47214	−	37.1037i	−0.120884	−	1.29179i
$826$	47.1115			1.63922
$827$	8.94427	−	6.49839i	0.311023	−	0.225971i	−0.421312	−	0.906916i	$-0.638430\pi$
$827$	8.94427	−	6.49839i	0.311023	−	0.225971i	0.732335	+	0.680944i	$0.238430\pi$
$828$	−55.4164	−	170.554i	−1.92585	−	5.92717i
$829$	−7.80902	+	24.0337i	−0.271218	+	0.834724i	0.718977	+	0.695034i	$0.244611\pi$
$829$	−7.80902	+	24.0337i	−0.271218	+	0.834724i	−0.990195	+	0.139690i	$0.955389\pi$
$830$	6.90983	+	5.02029i	0.239844	+	0.174257i
$831$	76.4853	+	55.5698i	2.65325	+	1.92770i
$832$	4.01722	−	12.3637i	0.139272	−	0.428635i
$833$	0.843459	+	2.59590i	0.0292241	+	0.0899426i
$834$	24.4721	−	17.7800i	0.847401	−	0.615673i
$835$	12.1803			0.421518
$836$	−3.13525	+	5.29007i	−0.108435	+	0.182961i
$837$	−48.9443			−1.69176
$838$	−10.5279	+	7.64894i	−0.363679	+	0.264228i
$839$	−11.0451	−	33.9933i	−0.381319	−	1.17358i	−0.939116	−	0.343601i	$-0.888353\pi$
$839$	−11.0451	−	33.9933i	−0.381319	−	1.17358i	0.557797	−	0.829977i	$-0.311647\pi$
$840$	7.88854	−	24.2784i	0.272181	−	0.837686i
$841$	14.2082	+	10.3229i	0.489938	+	0.355961i
$842$	−4.47214	−	3.24920i	−0.154120	−	0.111975i
$843$	14.3607	−	44.1976i	0.494608	−	1.52225i
$844$	−17.1246	−	52.7041i	−0.589453	−	1.81415i
$845$	−1.00000	+	0.726543i	−0.0344010	+	0.0249938i
$846$	−155.825			−5.35736
$847$	30.8500	−	5.82485i	1.06002	−	0.200144i
$848$	11.0902			0.380838
$849$	73.0132	−	53.0472i	2.50581	−	1.82057i
$850$	−5.71478	−	17.5883i	−0.196015	−	0.603273i
$851$	−9.88854	+	30.4338i	−0.338975	+	1.04326i
$852$	67.2492	+	48.8594i	2.30392	+	1.67390i
$853$	36.5066	+	26.5236i	1.24996	+	0.908150i	0.998220	−	0.0596443i	$-0.0189967\pi$
$853$	36.5066	+	26.5236i	1.24996	+	0.908150i	0.251742	+	0.967794i	$0.418997\pi$
$854$	−16.4205	+	50.5370i	−0.561897	+	1.72934i
$855$	1.76393	+	5.42882i	0.0603252	+	0.185662i
$856$	−35.6525	+	25.9030i	−1.21858	+	0.885348i
$857$	−34.1591			−1.16685			−0.583426	−	0.812167i	$-0.698288\pi$
$857$	−34.1591			−1.16685			−0.583426	+	0.812167i	$0.698288\pi$
$858$	−12.2361	+	20.6457i	−0.417732	+	0.704834i
$859$	43.1246			1.47139			0.735696	−	0.677311i	$-0.236855\pi$
$859$	43.1246			1.47139			0.735696	+	0.677311i	$0.236855\pi$
$860$	12.0000	−	8.71851i	0.409197	−	0.297299i
$861$		0			0
$862$	12.5000	−	38.4710i	0.425752	−	1.31033i
$863$	−38.8328	−	28.2137i	−1.32188	−	0.960405i	−0.999907	−	0.0136580i	$-0.995652\pi$
$863$	−38.8328	−	28.2137i	−1.32188	−	0.960405i	−0.321978	−	0.946747i	$-0.604348\pi$
$864$	−78.5410	−	57.0634i	−2.67202	−	1.94134i
$865$	−1.34752	+	4.14725i	−0.0458172	+	0.141011i
$866$	14.9377	+	45.9735i	0.507604	+	1.56224i
$867$	−29.6525	+	21.5438i	−1.00705	+	0.731665i
$868$	−28.9574			−0.982879
$869$	0.618034	+	6.60440i	0.0209654	+	0.224039i
$870$	30.2492			1.02554
$871$	−8.47214	+	6.15537i	−0.287067	+	0.208567i
$872$	−8.41641	−	25.9030i	−0.285016	−	0.877188i
$873$	8.56231	−	26.3521i	0.289790	−	0.891882i
$874$	8.94427	+	6.49839i	0.302545	+	0.219811i
$875$	−24.1803	−	17.5680i	−0.817445	−	0.593908i
$876$	23.1246	−	71.1702i	0.781308	−	2.40462i
$877$	1.94427	+	5.98385i	0.0656534	+	0.202060i	0.978502	−	0.206238i	$-0.0661222\pi$
$877$	1.94427	+	5.98385i	0.0656534	+	0.202060i	−0.912848	+	0.408299i	$0.866122\pi$
$878$	−2.76393	+	2.00811i	−0.0932782	+	0.0677706i
$879$	19.4164			0.654899
$880$	4.00000	+	0.898056i	0.134840	+	0.0302735i
$881$	33.8541			1.14057			0.570287	−	0.821446i	$-0.306832\pi$
$881$	33.8541			1.14057			0.570287	+	0.821446i	$0.306832\pi$
$882$	−15.4894	+	11.2537i	−0.521554	+	0.378931i
$883$	−3.38197	−	10.4086i	−0.113812	−	0.350278i	0.877885	−	0.478871i	$-0.158954\pi$
$883$	−3.38197	−	10.4086i	−0.113812	−	0.350278i	−0.991697	+	0.128593i	$0.958954\pi$
$884$	−2.20820	+	6.79615i	−0.0742699	+	0.228579i
$885$	−23.8885	−	17.3560i	−0.803005	−	0.583417i
$886$	45.6525	+	33.1685i	1.53372	+	1.11432i
$887$	−15.0344	+	46.2713i	−0.504807	+	1.55364i	0.296287	+	0.955099i	$0.404251\pi$
$887$	−15.0344	+	46.2713i	−0.504807	+	1.55364i	−0.801095	+	0.598538i	$0.795749\pi$
$888$	−8.94427	−	27.5276i	−0.300150	−	0.923767i
$889$	21.3262	−	15.4944i	0.715259	−	0.519666i
$890$	31.5542			1.05770
$891$	53.4959	+	60.7944i	1.79218	+	2.03669i
$892$	26.8328			0.898429
$893$	4.66312	−	3.38795i	0.156045	−	0.113374i
$894$	−12.7639	−	39.2833i	−0.426890	−	1.31383i
$895$	−3.16718	+	9.74759i	−0.105867	+	0.325826i
$896$	−36.1418	−	26.2586i	−1.20741	−	0.877238i
$897$	20.9443	+	15.2169i	0.699309	+	0.508078i
$898$	−6.30495	+	19.4046i	−0.210399	+	0.647541i
$899$	−3.53444	−	10.8779i	−0.117880	−	0.362798i
$900$	62.9681	−	45.7490i	2.09894	−	1.52497i
$901$	−26.4164			−0.880058
$902$		0			0
$903$	−36.9443			−1.22943
$904$	8.78115	−	6.37988i	0.292057	−	0.212192i
$905$	2.14590	+	6.60440i	0.0713321	+	0.219538i
$906$	−2.03444	+	6.26137i	−0.0675898	+	0.208020i
$907$	−2.14590	−	1.55909i	−0.0712534	−	0.0517686i	0.551588	−	0.834116i	$-0.314022\pi$
$907$	−2.14590	−	1.55909i	−0.0712534	−	0.0517686i	−0.622842	+	0.782348i	$0.714022\pi$
$908$	−26.3435	−	19.1396i	−0.874238	−	0.635171i
$909$	−12.9721	+	39.9241i	−0.430259	+	1.32420i
$910$	2.43769	+	7.50245i	0.0808088	+	0.248704i
$911$	−27.4721	+	19.9597i	−0.910192	+	0.661294i	−0.941064	−	0.338230i	$-0.890172\pi$
$911$	−27.4721	+	19.9597i	−0.910192	+	0.661294i	0.0308711	+	0.999523i	$0.490172\pi$
$912$	2.00000			0.0662266
$913$	−9.40983	+	4.06150i	−0.311420	+	0.134416i
$914$	33.6656			1.11356
$915$	26.9443	−	19.5762i	0.890750	−	0.647168i
$916$	−3.97871	−	12.2452i	−0.131460	−	0.404594i
$917$	−14.0132	+	43.1281i	−0.462755	+	1.42421i
$918$	62.3607	+	45.3077i	2.05821	+	1.49538i
$919$	−31.5066	−	22.8909i	−1.03931	−	0.755100i	−0.0691561	−	0.997606i	$-0.522031\pi$
$919$	−31.5066	−	22.8909i	−1.03931	−	0.755100i	−0.970150	+	0.242506i	$0.922031\pi$
$920$	−6.83282	+	21.0292i	−0.225271	+	0.693314i
$921$	19.7984	+	60.9331i	0.652379	+	2.00781i
$922$	−19.2705	+	14.0008i	−0.634640	+	0.461093i
$923$	−8.56231			−0.281832
$924$	60.7082	+	68.9906i	1.99715	+	2.26962i
$925$	−13.8885			−0.456653
$926$	−3.35410	+	2.43690i	−0.110223	+	0.0800814i
$927$	−4.61803	−	14.2128i	−0.151676	−	0.466811i
$928$	7.01064	−	21.5765i	0.230136	−	0.708285i
$929$	−40.7426	−	29.6013i	−1.33672	−	0.971186i	−0.999558	−	0.0297405i	$-0.990532\pi$
$929$	−40.7426	−	29.6013i	−1.33672	−	0.971186i	−0.337165	−	0.941446i	$-0.609468\pi$
$930$	24.4721	+	17.7800i	0.802473	+	0.583031i
$931$	0.218847	−	0.673542i	0.00717242	−	0.0220744i
$932$	22.5517	+	69.4069i	0.738704	+	2.27350i
$933$	−6.94427	+	5.04531i	−0.227345	+	0.165176i
$934$	−30.2492			−0.989785
$935$	−9.52786	−	2.13914i	−0.311594	−	0.0699573i
$936$	−16.7082			−0.546125
$937$	−3.44427	+	2.50241i	−0.112519	+	0.0817502i	−0.642622	−	0.766183i	$-0.722153\pi$
$937$	−3.44427	+	2.50241i	−0.112519	+	0.0817502i	0.530103	+	0.847934i	$0.322153\pi$
$938$	20.6525	+	63.5618i	0.674327	+	2.07537i
$939$	−5.03444	+	15.4944i	−0.164293	+	0.505641i
$940$	27.9787	+	20.3277i	0.912565	+	0.663017i
$941$	−12.3820	−	8.99602i	−0.403641	−	0.293262i	0.367382	−	0.930070i	$-0.380254\pi$
$941$	−12.3820	−	8.99602i	−0.403641	−	0.293262i	−0.771022	+	0.636808i	$0.780254\pi$
$942$	−21.9098	+	67.4315i	−0.713861	+	2.19704i
$943$		0			0
$944$	−5.97214	+	4.33901i	−0.194376	+	0.141223i
$945$	51.0557			1.66084
$946$	2.76393	+	29.5358i	0.0898632	+	0.960290i
$947$	−2.49342			−0.0810253			−0.0405127	−	0.999179i	$-0.512899\pi$
$947$	−2.49342			−0.0810253			−0.0405127	+	0.999179i	$0.512899\pi$
$948$	−15.7082	+	11.4127i	−0.510179	+	0.370667i
$949$	2.38197	+	7.33094i	0.0773219	+	0.237972i
$950$	−1.48278	+	4.56352i	−0.0481077	+	0.148060i
$951$	−46.3607	−	33.6830i	−1.50335	−	1.09225i
$952$	12.2984	+	8.93529i	0.398593	+	0.289594i
$953$	4.14590	−	12.7598i	0.134299	−	0.413329i	−0.861181	−	0.508298i	$-0.830275\pi$
$953$	4.14590	−	12.7598i	0.134299	−	0.413329i	0.995480	+	0.0949684i	$0.0302750\pi$
$954$	−57.2599	−	176.228i	−1.85386	−	5.70558i
$955$	8.94427	−	6.49839i	0.289430	−	0.210283i
$956$	−15.9787			−0.516789
$957$	−18.5066	+	31.2259i	−0.598233	+	1.00939i
$958$	87.4083			2.82403
$959$	−0.673762	+	0.489517i	−0.0217569	+	0.0158073i
$960$	16.0689	+	49.4549i	0.518621	+	1.59615i
$961$	−6.04508	+	18.6049i	−0.195003	+	0.600157i
$962$	7.23607	+	5.25731i	0.233300	+	0.169503i
$963$	−119.138	−	86.5587i	−3.83916	−	2.78931i
$964$	−15.9787	+	49.1774i	−0.514640	+	1.58390i
$965$	−5.34752	−	16.4580i	−0.172143	−	0.529801i
$966$	133.666	−	97.1138i	4.30062	−	3.12458i
$967$	22.4721			0.722655			0.361328	−	0.932439i	$-0.382324\pi$
$967$	22.4721			0.722655			0.361328	+	0.932439i	$0.382324\pi$
$968$	16.8713	−	17.8986i	0.542265	−	0.575282i
$969$	−4.76393			−0.153040
$970$	−8.29180	+	6.02434i	−0.266234	+	0.193430i
$971$	1.52786	+	4.70228i	0.0490315	+	0.150903i	0.972575	−	0.232591i	$-0.0747204\pi$
$971$	1.52786	+	4.70228i	0.0490315	+	0.150903i	−0.923543	+	0.383495i	$0.874720\pi$
$972$	−33.0000	+	101.564i	−1.05848	+	3.25765i
$973$	9.65248	+	7.01293i	0.309444	+	0.224824i
$974$	9.63525	+	7.00042i	0.308733	+	0.224308i
$975$	−3.47214	+	10.6861i	−0.111197	+	0.342230i
$976$	−2.57295	−	7.91872i	−0.0823581	−	0.253472i
$977$	−16.5623	+	12.0332i	−0.529875	+	0.384977i	−0.820311	−	0.571918i	$-0.806200\pi$
$977$	−16.5623	+	12.0332i	−0.529875	+	0.384977i	0.290436	+	0.956894i	$0.406200\pi$
$978$	55.1246			1.76269
$979$	−19.3050	+	32.5729i	−0.616989	+	1.04104i
$980$	4.24922			0.135736
$981$	73.6312	−	53.4962i	2.35086	−	1.70800i
$982$	5.20163	+	16.0090i	0.165991	+	0.510866i
$983$	7.51722	−	23.1356i	0.239762	−	0.737912i	−0.756692	−	0.653772i	$-0.773186\pi$
$983$	7.51722	−	23.1356i	0.239762	−	0.737912i	0.996454	−	0.0841402i	$-0.0268143\pi$
$984$		0			0
$985$	−17.8885	−	12.9968i	−0.569976	−	0.414112i
$986$	−5.56637	+	17.1315i	−0.177269	+	0.545579i
$987$	−26.6180	−	81.9219i	−0.847261	−	2.60760i
$988$	1.50000	−	1.08981i	0.0477214	−	0.0346716i
$989$	32.0000			1.01754
$990$	−6.38197	−	68.1986i	−0.202832	−	2.16749i
$991$	−38.6525			−1.22784			−0.613918	−	0.789370i	$-0.710408\pi$
$991$	−38.6525			−1.22784			−0.613918	+	0.789370i	$0.710408\pi$
$992$	18.3541	−	13.3350i	0.582743	−	0.423388i
$993$	25.2705	+	77.7746i	0.801935	+	2.46810i
$994$	−16.8860	+	51.9699i	−0.535592	+	1.64838i
$995$	−4.94427	−	3.59222i	−0.156744	−	0.113881i
$996$	−24.2705	−	17.6336i	−0.769041	−	0.558741i
$997$	10.0279	−	30.8626i	0.317586	−	0.977428i	−0.657091	−	0.753811i	$-0.728213\pi$
$997$	10.0279	−	30.8626i	0.317586	−	0.977428i	0.974677	−	0.223617i	$-0.0717865\pi$
$998$	8.02786	+	24.7072i	0.254118	+	0.782094i
$999$	46.8328	−	34.0260i	1.48172	−	1.07654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.a.14.1	✓	4
11.2	odd	10		1573.2.a.e.1.1		2
11.4	even	5	inner	143.2.h.a.92.1	yes	4
11.9	even	5		1573.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.a.14.1	✓	4	1.1	even	1	trivial
143.2.h.a.92.1	yes	4	11.4	even	5	inner
1573.2.a.d.1.2		2	11.9	even	5
1573.2.a.e.1.1		2	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.80902 + 1.31433i) q^{2} +(-1.00000 - 3.07768i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.00000 - 0.726543i) q^{5} +(5.85410 + 4.25325i) q^{6} +(-0.881966 + 2.71441i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-6.04508 + 4.39201i) q^{9} +O(q^{10})\)	\(q+(-1.80902 + 1.31433i) q^{2} +(-1.00000 - 3.07768i) q^{3} +(0.927051 - 2.85317i) q^{4} +(-1.00000 - 0.726543i) q^{5} +(5.85410 + 4.25325i) q^{6} +(-0.881966 + 2.71441i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-6.04508 + 4.39201i) q^{9} +2.76393 q^{10} +(-1.69098 + 2.85317i) q^{11} -9.70820 q^{12} +(0.809017 - 0.587785i) q^{13} +(-1.97214 - 6.06961i) q^{14} +(-1.23607 + 3.80423i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.92705 - 1.40008i) q^{17} +(5.16312 - 15.8904i) q^{18} +(0.190983 + 0.587785i) q^{19} +(-3.00000 + 2.17963i) q^{20} +9.23607 q^{21} +(-0.690983 - 7.38394i) q^{22} -8.00000 q^{23} +(5.85410 - 4.25325i) q^{24} +(-1.07295 - 3.30220i) q^{25} +(-0.690983 + 2.12663i) q^{26} +(11.7082 + 8.50651i) q^{27} +(6.92705 + 5.03280i) q^{28} +(-1.04508 + 3.21644i) q^{29} +(-2.76393 - 8.50651i) q^{30} +(-2.73607 + 1.98787i) q^{31} -6.70820 q^{32} +(10.4721 + 2.35114i) q^{33} +5.32624 q^{34} +(2.85410 - 2.07363i) q^{35} +(6.92705 + 21.3193i) q^{36} +(1.23607 - 3.80423i) q^{37} +(-1.11803 - 0.812299i) q^{38} +(-2.61803 - 1.90211i) q^{39} +(0.854102 - 2.62866i) q^{40} +(-16.7082 + 12.1392i) q^{42} -4.00000 q^{43} +(6.57295 + 7.46969i) q^{44} +9.23607 q^{45} +(14.4721 - 10.5146i) q^{46} +(-2.88197 - 8.86978i) q^{47} +(1.00000 - 3.07768i) q^{48} +(-0.927051 - 0.673542i) q^{49} +(6.28115 + 4.56352i) q^{50} +(-2.38197 + 7.33094i) q^{51} +(-0.927051 - 2.85317i) q^{52} +(8.97214 - 6.51864i) q^{53} -32.3607 q^{54} +(3.76393 - 1.62460i) q^{55} -6.38197 q^{56} +(1.61803 - 1.17557i) q^{57} +(-2.33688 - 7.19218i) q^{58} +(-2.28115 + 7.02067i) q^{59} +(9.70820 + 7.05342i) q^{60} +(-6.73607 - 4.89404i) q^{61} +(2.33688 - 7.19218i) q^{62} +(-6.59017 - 20.2825i) q^{63} +(10.5172 - 7.64121i) q^{64} -1.23607 q^{65} +(-22.0344 + 9.51057i) q^{66} -10.4721 q^{67} +(-5.78115 + 4.20025i) q^{68} +(8.00000 + 24.6215i) q^{69} +(-2.43769 + 7.50245i) q^{70} +(-6.92705 - 5.03280i) q^{71} +(-13.5172 - 9.82084i) q^{72} +(-2.38197 + 7.33094i) q^{73} +(2.76393 + 8.50651i) q^{74} +(-9.09017 + 6.60440i) q^{75} +1.85410 q^{76} +(-6.25329 - 7.10642i) q^{77} +7.23607 q^{78} +(1.61803 - 1.17557i) q^{79} +(-0.381966 - 1.17557i) q^{80} +(7.54508 - 23.2214i) q^{81} +(2.50000 + 1.81636i) q^{83} +(8.56231 - 26.3521i) q^{84} +(0.909830 + 2.80017i) q^{85} +(7.23607 - 5.25731i) q^{86} +10.9443 q^{87} +(-7.23607 - 1.62460i) q^{88} +11.4164 q^{89} +(-16.7082 + 12.1392i) q^{90} +(0.881966 + 2.71441i) q^{91} +(-7.41641 + 22.8254i) q^{92} +(8.85410 + 6.43288i) q^{93} +(16.8713 + 12.2577i) q^{94} +(0.236068 - 0.726543i) q^{95} +(6.70820 + 20.6457i) q^{96} +(-3.00000 + 2.17963i) q^{97} +2.56231 q^{98} +(-2.30902 - 24.6745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 4 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} + 5 q^{8} - 13 q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 - 4 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 + 5 * q^8 - 13 * q^9	\( 4 q - 5 q^{2} - 4 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} + 5 q^{8} - 13 q^{9} + 20 q^{10} - 9 q^{11} - 12 q^{12} + q^{13} + 10 q^{14} + 4 q^{15} + q^{16} - q^{17} + 5 q^{18} + 3 q^{19} - 12 q^{20} + 28 q^{21} - 5 q^{22} - 32 q^{23} + 10 q^{24} - 11 q^{25} - 5 q^{26} + 20 q^{27} + 21 q^{28} + 7 q^{29} - 20 q^{30} - 2 q^{31} + 24 q^{33} - 10 q^{34} - 2 q^{35} + 21 q^{36} - 4 q^{37} - 6 q^{39} - 10 q^{40} - 40 q^{42} - 16 q^{43} + 33 q^{44} + 28 q^{45} + 40 q^{46} - 16 q^{47} + 4 q^{48} + 3 q^{49} + 5 q^{50} - 14 q^{51} + 3 q^{52} + 18 q^{53} - 40 q^{54} + 24 q^{55} - 30 q^{56} + 2 q^{57} - 25 q^{58} + 11 q^{59} + 12 q^{60} - 18 q^{61} + 25 q^{62} - 4 q^{63} + 13 q^{64} + 4 q^{65} - 30 q^{66} - 24 q^{67} - 3 q^{68} + 32 q^{69} - 50 q^{70} - 21 q^{71} - 25 q^{72} - 14 q^{73} + 20 q^{74} - 14 q^{75} - 6 q^{76} + 13 q^{77} + 20 q^{78} + 2 q^{79} - 6 q^{80} + 19 q^{81} + 10 q^{83} - 6 q^{84} + 26 q^{85} + 20 q^{86} + 8 q^{87} - 20 q^{88} - 8 q^{89} - 40 q^{90} + 8 q^{91} + 24 q^{92} + 22 q^{93} + 25 q^{94} - 8 q^{95} - 12 q^{97} - 30 q^{98} - 7 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 4 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 + 5 * q^8 - 13 * q^9 + 20 * q^10 - 9 * q^11 - 12 * q^12 + q^13 + 10 * q^14 + 4 * q^15 + q^16 - q^17 + 5 * q^18 + 3 * q^19 - 12 * q^20 + 28 * q^21 - 5 * q^22 - 32 * q^23 + 10 * q^24 - 11 * q^25 - 5 * q^26 + 20 * q^27 + 21 * q^28 + 7 * q^29 - 20 * q^30 - 2 * q^31 + 24 * q^33 - 10 * q^34 - 2 * q^35 + 21 * q^36 - 4 * q^37 - 6 * q^39 - 10 * q^40 - 40 * q^42 - 16 * q^43 + 33 * q^44 + 28 * q^45 + 40 * q^46 - 16 * q^47 + 4 * q^48 + 3 * q^49 + 5 * q^50 - 14 * q^51 + 3 * q^52 + 18 * q^53 - 40 * q^54 + 24 * q^55 - 30 * q^56 + 2 * q^57 - 25 * q^58 + 11 * q^59 + 12 * q^60 - 18 * q^61 + 25 * q^62 - 4 * q^63 + 13 * q^64 + 4 * q^65 - 30 * q^66 - 24 * q^67 - 3 * q^68 + 32 * q^69 - 50 * q^70 - 21 * q^71 - 25 * q^72 - 14 * q^73 + 20 * q^74 - 14 * q^75 - 6 * q^76 + 13 * q^77 + 20 * q^78 + 2 * q^79 - 6 * q^80 + 19 * q^81 + 10 * q^83 - 6 * q^84 + 26 * q^85 + 20 * q^86 + 8 * q^87 - 20 * q^88 - 8 * q^89 - 40 * q^90 + 8 * q^91 + 24 * q^92 + 22 * q^93 + 25 * q^94 - 8 * q^95 - 12 * q^97 - 30 * q^98 - 7 * q^99

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