LMFDB - Embedded newform 143.2.e.c.133.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 9x^{10} - 2x^{9} + 59x^{8} - 13x^{7} + 175x^{6} - 50x^{5} + 380x^{4} - 64x^{3} + 280x^{2} + 48x + 144 $ x^12 + 9x^10 - 2x^9 + 59x^8 - 13x^7 + 175x^6 - 50x^5 + 380x^4 - 64x^3 + 280x^2 + 48x + 144
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.4
Root			$0.790735 + 1.36959i$ of defining polynomial
Character	$\chi$	$=$	143.133
Dual form			143.2.e.c.100.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.249477 + 0.432106i) q^{2} +(0.120298 + 0.208363i) q^{3} +(0.875523 - 1.51645i) q^{4} +0.581470 q^{5} +(-0.0600233 + 0.103963i) q^{6} +(-0.705086 + 1.22125i) q^{7} +1.87160 q^{8} +(1.47106 - 2.54794i) q^{9} +O(q^{10})$	\(q+(0.249477 + 0.432106i) q^{2} +(0.120298 + 0.208363i) q^{3} +(0.875523 - 1.51645i) q^{4} +0.581470 q^{5} +(-0.0600233 + 0.103963i) q^{6} +(-0.705086 + 1.22125i) q^{7} +1.87160 q^{8} +(1.47106 - 2.54794i) q^{9} +(0.145063 + 0.251257i) q^{10} +(0.500000 + 0.866025i) q^{11} +0.421296 q^{12} +(-2.39697 + 2.69342i) q^{13} -0.703610 q^{14} +(0.0699499 + 0.121157i) q^{15} +(-1.28413 - 2.22417i) q^{16} +(-0.225759 + 0.391026i) q^{17} +1.46798 q^{18} +(-1.59526 + 2.76307i) q^{19} +(0.509090 - 0.881770i) q^{20} -0.339283 q^{21} +(-0.249477 + 0.432106i) q^{22} +(2.01727 + 3.49401i) q^{23} +(0.225150 + 0.389971i) q^{24} -4.66189 q^{25} +(-1.76183 - 0.363799i) q^{26} +1.42965 q^{27} +(1.23464 + 2.13846i) q^{28} +(-5.10097 - 8.83513i) q^{29} +(-0.0349017 + 0.0604515i) q^{30} -7.10174 q^{31} +(2.51231 - 4.35146i) q^{32} +(-0.120298 + 0.208363i) q^{33} -0.225286 q^{34} +(-0.409986 + 0.710117i) q^{35} +(-2.57589 - 4.46157i) q^{36} +(-2.34056 - 4.05397i) q^{37} -1.59192 q^{38} +(-0.849562 - 0.175425i) q^{39} +1.08828 q^{40} +(4.43162 + 7.67579i) q^{41} +(-0.0846432 - 0.146606i) q^{42} +(-2.20752 + 3.82353i) q^{43} +1.75105 q^{44} +(0.855375 - 1.48155i) q^{45} +(-1.00652 + 1.74335i) q^{46} +3.77409 q^{47} +(0.308957 - 0.535129i) q^{48} +(2.50571 + 4.34001i) q^{49} +(-1.16303 - 2.01443i) q^{50} -0.108634 q^{51} +(1.98584 + 5.99304i) q^{52} -0.0779742 q^{53} +(0.356665 + 0.617762i) q^{54} +(0.290735 + 0.503568i) q^{55} +(-1.31964 + 2.28568i) q^{56} -0.767629 q^{57} +(2.54514 - 4.40832i) q^{58} +(3.85067 - 6.66956i) q^{59} +0.244971 q^{60} +(2.16383 - 3.74786i) q^{61} +(-1.77172 - 3.06871i) q^{62} +(2.07444 + 3.59304i) q^{63} -2.62945 q^{64} +(-1.39377 + 1.56615i) q^{65} -0.120047 q^{66} +(5.61585 + 9.72693i) q^{67} +(0.395314 + 0.684704i) q^{68} +(-0.485348 + 0.840648i) q^{69} -0.409128 q^{70} +(0.992545 - 1.71914i) q^{71} +(2.75322 - 4.76872i) q^{72} -2.84192 q^{73} +(1.16783 - 2.02274i) q^{74} +(-0.560818 - 0.971366i) q^{75} +(2.79338 + 4.83827i) q^{76} -1.41017 q^{77} +(-0.136144 - 0.410865i) q^{78} +14.6900 q^{79} +(-0.746681 - 1.29329i) q^{80} +(-4.24118 - 7.34595i) q^{81} +(-2.21117 + 3.82986i) q^{82} +4.03491 q^{83} +(-0.297050 + 0.514506i) q^{84} +(-0.131272 + 0.227370i) q^{85} -2.20289 q^{86} +(1.22728 - 2.12571i) q^{87} +(0.935798 + 1.62085i) q^{88} +(5.11869 + 8.86582i) q^{89} +0.853584 q^{90} +(-1.59926 - 4.82639i) q^{91} +7.06466 q^{92} +(-0.854328 - 1.47974i) q^{93} +(0.941546 + 1.63081i) q^{94} +(-0.927596 + 1.60664i) q^{95} +1.20891 q^{96} +(6.25778 - 10.8388i) q^{97} +(-1.25023 + 2.16546i) q^{98} +2.94211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - 34 q^{12} - 4 q^{13} + 24 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} + 12 q^{18} + 10 q^{19} + 15 q^{20} - 24 q^{21} - 3 q^{23} + 14 q^{24} - 12 q^{25} - 3 q^{26} + 20 q^{27} + 16 q^{28} - 3 q^{29} - 19 q^{30} - 10 q^{31} - q^{32} + q^{33} + 10 q^{34} + 13 q^{35} - 20 q^{36} + 25 q^{37} - 54 q^{38} - 12 q^{39} - 16 q^{40} + 24 q^{41} - 13 q^{42} + 8 q^{43} - 16 q^{44} + 27 q^{45} + 18 q^{46} - 20 q^{47} + 28 q^{48} + q^{49} - 26 q^{50} - 34 q^{51} - 39 q^{52} + 20 q^{53} + 47 q^{54} - 6 q^{55} - 15 q^{56} + 6 q^{58} - 4 q^{59} + 122 q^{60} + 21 q^{61} + 5 q^{62} + 6 q^{63} - 54 q^{64} - 32 q^{65} + 24 q^{66} + 21 q^{67} - 14 q^{68} - 5 q^{69} - 62 q^{70} - 3 q^{71} - 50 q^{72} - 26 q^{73} + 38 q^{74} + 23 q^{75} + 8 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} + 44 q^{80} - 34 q^{81} + 33 q^{82} - 16 q^{83} + 47 q^{84} - 13 q^{85} + 22 q^{86} + 51 q^{87} + 3 q^{88} - 9 q^{89} - 140 q^{90} - 19 q^{91} + 30 q^{92} - 21 q^{93} - 10 q^{94} - 27 q^{95} + 38 q^{96} + 15 q^{97} + 21 q^{98} - 14 q^{99}+O(q^{100}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - 34 * q^12 - 4 * q^13 + 24 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^17 + 12 * q^18 + 10 * q^19 + 15 * q^20 - 24 * q^21 - 3 * q^23 + 14 * q^24 - 12 * q^25 - 3 * q^26 + 20 * q^27 + 16 * q^28 - 3 * q^29 - 19 * q^30 - 10 * q^31 - q^32 + q^33 + 10 * q^34 + 13 * q^35 - 20 * q^36 + 25 * q^37 - 54 * q^38 - 12 * q^39 - 16 * q^40 + 24 * q^41 - 13 * q^42 + 8 * q^43 - 16 * q^44 + 27 * q^45 + 18 * q^46 - 20 * q^47 + 28 * q^48 + q^49 - 26 * q^50 - 34 * q^51 - 39 * q^52 + 20 * q^53 + 47 * q^54 - 6 * q^55 - 15 * q^56 + 6 * q^58 - 4 * q^59 + 122 * q^60 + 21 * q^61 + 5 * q^62 + 6 * q^63 - 54 * q^64 - 32 * q^65 + 24 * q^66 + 21 * q^67 - 14 * q^68 - 5 * q^69 - 62 * q^70 - 3 * q^71 - 50 * q^72 - 26 * q^73 + 38 * q^74 + 23 * q^75 + 8 * q^76 + 6 * q^77 + 36 * q^78 - 8 * q^79 + 44 * q^80 - 34 * q^81 + 33 * q^82 - 16 * q^83 + 47 * q^84 - 13 * q^85 + 22 * q^86 + 51 * q^87 + 3 * q^88 - 9 * q^89 - 140 * q^90 - 19 * q^91 + 30 * q^92 - 21 * q^93 - 10 * q^94 - 27 * q^95 + 38 * q^96 + 15 * q^97 + 21 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.249477	+	0.432106i	0.176407	+	0.305545i	0.940647	−	0.339386i	$-0.110219\pi$
$2$	0.249477	+	0.432106i	0.176407	+	0.305545i	−0.764241	+	0.644931i	$0.776886\pi$
$3$	0.120298	+	0.208363i	0.0694543	+	0.120298i	0.898661	−	0.438643i	$-0.144541\pi$
$3$	0.120298	+	0.208363i	0.0694543	+	0.120298i	−0.829207	+	0.558942i	$0.811208\pi$
$4$	0.875523	−	1.51645i	0.437761	−	0.758225i
$5$	0.581470			0.260041			0.130021	−	0.991511i	$-0.458496\pi$
$5$	0.581470			0.260041			0.130021	+	0.991511i	$0.458496\pi$
$6$	−0.0600233	+	0.103963i	−0.0245044	+	0.0424429i
$7$	−0.705086	+	1.22125i	−0.266498	+	0.461587i	−0.967955	−	0.251124i	$-0.919200\pi$
$7$	−0.705086	+	1.22125i	−0.266498	+	0.461587i	0.701457	+	0.712711i	$0.252533\pi$
$8$	1.87160			0.661709
$9$	1.47106	−	2.54794i	0.490352	−	0.849315i
$10$	0.145063	+	0.251257i	0.0458730	+	0.0794543i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.421296			0.121618
$13$	−2.39697	+	2.69342i	−0.664800	+	0.747022i
$13$	−2.39697	+	2.69342i	−0.664800	+	0.747022i
$14$	−0.703610			−0.188048
$15$	0.0699499	+	0.121157i	0.0180610	+	0.0312825i
$16$	−1.28413	−	2.22417i	−0.321032	−	0.556043i
$17$	−0.225759	+	0.391026i	−0.0547545	+	0.0948376i	−0.892103	−	0.451831i	$-0.850771\pi$
$17$	−0.225759	+	0.391026i	−0.0547545	+	0.0948376i	0.837349	+	0.546669i	$0.184104\pi$
$18$	1.46798			0.346005
$19$	−1.59526	+	2.76307i	−0.365978	+	0.633892i	−0.988933	−	0.148366i	$-0.952599\pi$
$19$	−1.59526	+	2.76307i	−0.365978	+	0.633892i	0.622955	+	0.782258i	$0.285932\pi$
$20$	0.509090	−	0.881770i	0.113836	−	0.197170i
$21$	−0.339283			−0.0740376
$22$	−0.249477	+	0.432106i	−0.0531886	+	0.0921253i
$23$	2.01727	+	3.49401i	0.420629	+	0.728552i	0.996001	−	0.0893405i	$-0.0284759\pi$
$23$	2.01727	+	3.49401i	0.420629	+	0.728552i	−0.575372	+	0.817892i	$0.695143\pi$
$24$	0.225150	+	0.389971i	0.0459586	+	0.0796026i
$25$	−4.66189			−0.932379
$26$	−1.76183	−	0.363799i	−0.345524	−	0.0713468i
$27$	1.42965			0.275137
$28$	1.23464	+	2.13846i	0.233325	+	0.404130i
$29$	−5.10097	−	8.83513i	−0.947226	−	1.64064i	−0.751232	−	0.660038i	$-0.770540\pi$
$29$	−5.10097	−	8.83513i	−0.947226	−	1.64064i	−0.195994	−	0.980605i	$-0.562793\pi$
$30$	−0.0349017	+	0.0604515i	−0.00637215	+	0.0110369i
$31$	−7.10174			−1.27551			−0.637755	−	0.770239i	$-0.720137\pi$
$31$	−7.10174			−1.27551			−0.637755	+	0.770239i	$0.720137\pi$
$32$	2.51231	−	4.35146i	0.444119	−	0.769236i
$33$	−0.120298	+	0.208363i	−0.0209413	+	0.0362713i
$34$	−0.225286			−0.0386362
$35$	−0.409986	+	0.710117i	−0.0693004	+	0.120032i
$36$	−2.57589	−	4.46157i	−0.429315	−	0.743595i
$37$	−2.34056	−	4.05397i	−0.384786	−	0.666468i	0.606954	−	0.794737i	$-0.292391\pi$
$37$	−2.34056	−	4.05397i	−0.384786	−	0.666468i	−0.991739	+	0.128269i	$0.959058\pi$
$38$	−1.59192			−0.258244
$39$	−0.849562	−	0.175425i	−0.136039	−	0.0280905i
$40$	1.08828			0.172072
$41$	4.43162	+	7.67579i	0.692103	+	1.19876i	0.971148	+	0.238479i	$0.0766488\pi$
$41$	4.43162	+	7.67579i	0.692103	+	1.19876i	−0.279045	+	0.960278i	$0.590018\pi$
$42$	−0.0846432	−	0.146606i	−0.0130607	−	0.0226218i
$43$	−2.20752	+	3.82353i	−0.336643	+	0.583083i	−0.983799	−	0.179275i	$-0.942625\pi$
$43$	−2.20752	+	3.82353i	−0.336643	+	0.583083i	0.647156	+	0.762358i	$0.275958\pi$
$44$	1.75105			0.263980
$45$	0.855375	−	1.48155i	0.127512	−	0.220857i
$46$	−1.00652	+	1.74335i	−0.148404	+	0.257043i
$47$	3.77409			0.550507			0.275253	−	0.961372i	$-0.411238\pi$
$47$	3.77409			0.550507			0.275253	+	0.961372i	$0.411238\pi$
$48$	0.308957	−	0.535129i	0.0445941	−	0.0772392i
$49$	2.50571	+	4.34001i	0.357958	+	0.620002i
$50$	−1.16303	−	2.01443i	−0.164478	−	0.284884i
$51$	−0.108634			−0.0152118
$52$	1.98584	+	5.99304i	0.275387	+	0.831085i
$53$	−0.0779742			−0.0107106			−0.00535529	−	0.999986i	$-0.501705\pi$
$53$	−0.0779742			−0.0107106			−0.00535529	+	0.999986i	$0.501705\pi$
$54$	0.356665	+	0.617762i	0.0485360	+	0.0840668i
$55$	0.290735	+	0.503568i	0.0392027	+	0.0679010i
$56$	−1.31964	+	2.28568i	−0.176344	+	0.305437i
$57$	−0.767629			−0.101675
$58$	2.54514	−	4.40832i	0.334194	−	0.578841i
$59$	3.85067	−	6.66956i	0.501315	−	0.868303i	−0.498684	−	0.866784i	$-0.666183\pi$
$59$	3.85067	−	6.66956i	0.501315	−	0.868303i	0.999999	−	0.00151883i	$-0.000483459\pi$
$60$	0.244971			0.0316256
$61$	2.16383	−	3.74786i	0.277050	−	0.479864i	−0.693600	−	0.720360i	$-0.743977\pi$
$61$	2.16383	−	3.74786i	0.277050	−	0.479864i	0.970650	+	0.240496i	$0.0773100\pi$
$62$	−1.77172	−	3.06871i	−0.225008	−	0.389726i
$63$	2.07444	+	3.59304i	0.261355	+	0.452681i
$64$	−2.62945			−0.328681
$65$	−1.39377	+	1.56615i	−0.172875	+	0.194256i
$66$	−0.120047			−0.0147767
$67$	5.61585	+	9.72693i	0.686085	+	1.18833i	0.973095	+	0.230406i	$0.0740055\pi$
$67$	5.61585	+	9.72693i	0.686085	+	1.18833i	−0.287010	+	0.957928i	$0.592661\pi$
$68$	0.395314	+	0.684704i	0.0479388	+	0.0830325i
$69$	−0.485348	+	0.840648i	−0.0584291	+	0.101202i
$70$	−0.409128			−0.0489002
$71$	0.992545	−	1.71914i	0.117793	−	0.204024i	−0.801100	−	0.598531i	$-0.795751\pi$
$71$	0.992545	−	1.71914i	0.117793	−	0.204024i	0.918893	+	0.394507i	$0.129085\pi$
$72$	2.75322	−	4.76872i	0.324471	−	0.561999i
$73$	−2.84192			−0.332622			−0.166311	−	0.986073i	$-0.553185\pi$
$73$	−2.84192			−0.332622			−0.166311	+	0.986073i	$0.553185\pi$
$74$	1.16783	−	2.02274i	0.135757	−	0.235139i
$75$	−0.560818	−	0.971366i	−0.0647577	−	0.112164i
$76$	2.79338	+	4.83827i	0.320422	+	0.554987i
$77$	−1.41017			−0.160704
$78$	−0.136144	−	0.410865i	−0.0154152	−	0.0465213i
$79$	14.6900			1.65276			0.826379	−	0.563114i	$-0.190397\pi$
$79$	14.6900			1.65276			0.826379	+	0.563114i	$0.190397\pi$
$80$	−0.746681	−	1.29329i	−0.0834814	−	0.144594i
$81$	−4.24118	−	7.34595i	−0.471243	−	0.816216i
$82$	−2.21117	+	3.82986i	−0.244183	+	0.422937i
$83$	4.03491			0.442889			0.221444	−	0.975173i	$-0.428923\pi$
$83$	4.03491			0.442889			0.221444	+	0.975173i	$0.428923\pi$
$84$	−0.297050	+	0.514506i	−0.0324108	+	0.0561372i
$85$	−0.131272	+	0.227370i	−0.0142384	+	0.0246617i
$86$	−2.20289			−0.237544
$87$	1.22728	−	2.12571i	0.131578	−	0.227900i
$88$	0.935798	+	1.62085i	0.0997564	+	0.172783i
$89$	5.11869	+	8.86582i	0.542580	+	0.939775i	0.998755	+	0.0498855i	$0.0158856\pi$
$89$	5.11869	+	8.86582i	0.542580	+	0.939775i	−0.456175	+	0.889890i	$0.650781\pi$
$90$	0.853584			0.0899757
$91$	−1.59926	−	4.82639i	−0.167648	−	0.505943i
$92$	7.06466			0.736541
$93$	−0.854328	−	1.47974i	−0.0885897	−	0.153442i
$94$	0.941546	+	1.63081i	0.0971130	+	0.168205i
$95$	−0.927596	+	1.60664i	−0.0951694	+	0.164838i
$96$	1.20891			0.123384
$97$	6.25778	−	10.8388i	0.635381	−	1.10051i	−0.351053	−	0.936356i	$-0.614176\pi$
$97$	6.25778	−	10.8388i	0.635381	−	1.10051i	0.986434	−	0.164157i	$-0.0524903\pi$
$98$	−1.25023	+	2.16546i	−0.126292	+	0.218745i
$99$	2.94211			0.295694
$100$	−4.08159	+	7.06953i	−0.408159	+	0.706953i
$101$	−4.50203	−	7.79774i	−0.447969	−	0.775904i	0.550285	−	0.834977i	$-0.314519\pi$
$101$	−4.50203	−	7.79774i	−0.447969	−	0.775904i	−0.998254	+	0.0590724i	$0.981186\pi$
$102$	−0.0271016	−	0.0469413i	−0.00268345	−	0.00464788i
$103$	−14.3214			−1.41113			−0.705564	−	0.708646i	$-0.749306\pi$
$103$	−14.3214			−1.41113			−0.705564	+	0.708646i	$0.749306\pi$
$104$	−4.48616	+	5.04100i	−0.439904	+	0.494311i
$105$	−0.197283			−0.0192528
$106$	−0.0194527	−	0.0336931i	−0.00188942	−	0.00327257i
$107$	3.13830	+	5.43569i	0.303391	+	0.525488i	0.976902	−	0.213689i	$-0.0685479\pi$
$107$	3.13830	+	5.43569i	0.303391	+	0.525488i	−0.673511	+	0.739177i	$0.735215\pi$
$108$	1.25169	−	2.16800i	0.120444	−	0.208616i
$109$	−6.86332			−0.657387			−0.328693	−	0.944437i	$-0.606608\pi$
$109$	−6.86332			−0.657387			−0.328693	+	0.944437i	$0.606608\pi$
$110$	−0.145063	+	0.251257i	−0.0138312	+	0.0239564i
$111$	0.563131	−	0.975371i	0.0534500	−	0.0925782i
$112$	3.62168			0.342217
$113$	7.55305	−	13.0823i	0.710531	−	1.23068i	−0.254127	−	0.967171i	$-0.581788\pi$
$113$	7.55305	−	13.0823i	0.710531	−	1.23068i	0.964658	−	0.263505i	$-0.0848786\pi$
$114$	−0.191506	−	0.331697i	−0.0179361	−	0.0310663i
$115$	1.17298	+	2.03166i	0.109381	+	0.189453i
$116$	−17.8641			−1.65864
$117$	3.33662	+	10.0695i	0.308471	+	0.930928i
$118$	3.84261			0.353741
$119$	−0.318359	−	0.551414i	−0.0291839	−	0.0505480i
$120$	0.130918	+	0.226757i	0.0119511	+	0.0206999i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.15930			0.195494
$123$	−1.06623	+	1.84677i	−0.0961390	+	0.166518i
$124$	−6.21774	+	10.7694i	−0.558369	+	0.967124i
$125$	−5.61810			−0.502498
$126$	−1.03505	+	1.79276i	−0.0922096	+	0.159712i
$127$	1.12328	+	1.94558i	0.0996748	+	0.172642i	0.911550	−	0.411189i	$-0.134886\pi$
$127$	1.12328	+	1.94558i	0.0996748	+	0.172642i	−0.811875	+	0.583831i	$0.801553\pi$
$128$	−5.68062	−	9.83912i	−0.502100	−	0.869663i
$129$	−1.06224			−0.0935253
$130$	−1.02445	−	0.211538i	−0.0898505	−	0.0185531i
$131$	−6.82807			−0.596572			−0.298286	−	0.954477i	$-0.596415\pi$
$131$	−6.82807			−0.596572			−0.298286	+	0.954477i	$0.596415\pi$
$132$	0.210648	+	0.364853i	0.0183346	+	0.0317564i
$133$	−2.24959	−	3.89641i	−0.195065	−	0.337862i
$134$	−2.80204	+	4.85328i	−0.242060	+	0.419260i
$135$	0.831300			0.0715469
$136$	−0.422529	+	0.731842i	−0.0362316	+	0.0627549i
$137$	9.41969	−	16.3154i	0.804779	−	1.39392i	−0.111662	−	0.993746i	$-0.535617\pi$
$137$	9.41969	−	16.3154i	0.804779	−	1.39392i	0.916440	−	0.400171i	$-0.131049\pi$
$138$	−0.484332			−0.0412291
$139$	7.03908	−	12.1920i	0.597047	−	1.03412i	−0.396208	−	0.918161i	$-0.629674\pi$
$139$	7.03908	−	12.1920i	0.597047	−	1.03412i	0.993255	−	0.115955i	$-0.0369927\pi$
$140$	0.717905	+	1.24345i	0.0606741	+	0.105091i
$141$	0.454016	+	0.786380i	0.0382351	+	0.0662251i
$142$	0.990467			0.0831181
$143$	−3.53106	−	0.729124i	−0.295282	−	0.0609724i
$144$	−7.55609			−0.629674
$145$	−2.96606	−	5.13736i	−0.246318	−	0.426635i
$146$	−0.708992	−	1.22801i	−0.0586766	−	0.101631i
$147$	−0.602865	+	1.04419i	−0.0497235	+	0.0861236i
$148$	−8.19685			−0.673777
$149$	−0.936362	+	1.62183i	−0.0767098	+	0.132865i	−0.901829	−	0.432094i	$-0.857775\pi$
$149$	−0.936362	+	1.62183i	−0.0767098	+	0.132865i	0.825119	+	0.564959i	$0.191108\pi$
$150$	0.279822	−	0.484666i	0.0228474	−	0.0395728i
$151$	−14.7657			−1.20162			−0.600809	−	0.799393i	$-0.705155\pi$
$151$	−14.7657			−1.20162			−0.600809	+	0.799393i	$0.705155\pi$
$152$	−2.98568	+	5.17136i	−0.242171	+	0.419452i
$153$	0.664208	+	1.15044i	0.0536980	+	0.0930077i
$154$	−0.351805	−	0.609344i	−0.0283493	−	0.0491024i
$155$	−4.12945			−0.331685
$156$	−1.00983	+	1.13473i	−0.0808514	+	0.0908510i
$157$	−6.92557			−0.552721			−0.276360	−	0.961054i	$-0.589128\pi$
$157$	−6.92557			−0.552721			−0.276360	+	0.961054i	$0.589128\pi$
$158$	3.66482	+	6.34765i	0.291557	+	0.504992i
$159$	−0.00938017	−	0.0162469i	−0.000743896	−	0.00128847i
$160$	1.46084	−	2.53024i	0.115489	−	0.200033i
$161$	−5.68939			−0.448387
$162$	2.11615	−	3.66528i	0.166261	−	0.287972i
$163$	−6.19848	+	10.7361i	−0.485502	+	0.840914i	−0.999861	−	0.0166606i	$-0.994697\pi$
$163$	−6.19848	+	10.7361i	−0.485502	+	0.840914i	0.514359	+	0.857575i	$0.328030\pi$
$164$	15.5199			1.21190
$165$	−0.0699499	+	0.121157i	−0.00544559	+	0.00943204i
$166$	1.00662	+	1.74351i	0.0781285	+	0.135322i
$167$	10.1850	+	17.6410i	0.788142	+	1.36510i	0.927104	+	0.374805i	$0.122290\pi$
$167$	10.1850	+	17.6410i	0.788142	+	1.36510i	−0.138961	+	0.990298i	$0.544376\pi$
$168$	−0.635001			−0.0489914
$169$	−1.50907	−	12.9121i	−0.116083	−	0.993240i
$170$	−0.130997			−0.0100470
$171$	4.69344	+	8.12927i	0.358916	+	0.621661i
$172$	3.86546	+	6.69518i	0.294739	+	0.510502i
$173$	0.542693	−	0.939972i	0.0412602	−	0.0714648i	−0.844658	−	0.535307i	$-0.820196\pi$
$173$	0.542693	−	0.939972i	0.0412602	−	0.0714648i	0.885918	+	0.463842i	$0.153529\pi$
$174$	1.22471			0.0928448
$175$	3.28704	−	5.69332i	0.248477	−	0.430374i
$176$	1.28413	−	2.22417i	0.0967947	−	0.167653i
$177$	1.85292			0.139274
$178$	−2.55398	+	4.42363i	−0.191429	+	0.331565i
$179$	3.48748	+	6.04049i	0.260666	+	0.451488i	0.966419	−	0.256971i	$-0.0827244\pi$
$179$	3.48748	+	6.04049i	0.260666	+	0.451488i	−0.705753	+	0.708458i	$0.749391\pi$
$180$	−1.49780	−	2.59427i	−0.111639	−	0.193365i
$181$	7.09724			0.527534			0.263767	−	0.964586i	$-0.415035\pi$
$181$	7.09724			0.527534			0.263767	+	0.964586i	$0.415035\pi$
$182$	1.68653	−	1.89512i	0.125014	−	0.140476i
$183$	1.04122			0.0769692
$184$	3.77551	+	6.53938i	0.278334	+	0.482089i
$185$	−1.36096	−	2.35726i	−0.100060	−	0.173309i
$186$	0.426270	−	0.738321i	0.0312556	−	0.0541363i
$187$	−0.451517			−0.0330182
$188$	3.30430	−	5.72321i	0.240991	−	0.417408i
$189$	−1.00803	+	1.74596i	−0.0733233	+	0.127000i
$190$	−0.925654			−0.0671540
$191$	−5.91490	+	10.2449i	−0.427987	+	0.741296i	−0.996694	−	0.0812443i	$-0.974111\pi$
$191$	−5.91490	+	10.2449i	−0.427987	+	0.741296i	0.568707	+	0.822540i	$0.307444\pi$
$192$	−0.316319	−	0.547880i	−0.0228283	−	0.0395398i
$193$	−0.337990	−	0.585415i	−0.0243290	−	0.0421391i	0.853605	−	0.520922i	$-0.174412\pi$
$193$	−0.337990	−	0.585415i	−0.0243290	−	0.0421391i	−0.877934	+	0.478782i	$0.841078\pi$
$194$	6.24468			0.448342
$195$	−0.493994	−	0.102004i	−0.0353757	−	0.00730468i
$196$	8.77521			0.626801
$197$	−5.25534	−	9.10252i	−0.374427	−	0.648527i	0.615814	−	0.787892i	$-0.288827\pi$
$197$	−5.25534	−	9.10252i	−0.374427	−	0.648527i	−0.990241	+	0.139364i	$0.955494\pi$
$198$	0.733988	+	1.27131i	0.0521623	+	0.0903477i
$199$	10.1274	−	17.5412i	0.717913	−	1.24346i	−0.243912	−	0.969797i	$-0.578431\pi$
$199$	10.1274	−	17.5412i	0.717913	−	1.24346i	0.961825	−	0.273665i	$-0.0882358\pi$
$200$	−8.72518			−0.616963
$201$	−1.35115	+	2.34027i	−0.0953031	+	0.165070i
$202$	2.24630	−	3.89071i	0.158049	−	0.273749i
$203$	14.3865			1.00973
$204$	−0.0951113	+	0.164738i	−0.00665912	+	0.0115339i
$205$	2.57685	+	4.46324i	0.179975	+	0.311726i
$206$	−3.57285	−	6.18836i	−0.248932	−	0.431163i
$207$	11.8701			0.825026
$208$	9.06865	+	1.87257i	0.628798	+	0.129840i
$209$	−3.19052			−0.220693
$210$	−0.0492175	−	0.0852471i	−0.00339633	−	0.00588261i
$211$	−5.93969	−	10.2879i	−0.408905	−	0.708245i	0.585862	−	0.810411i	$-0.300756\pi$
$211$	−5.93969	−	10.2879i	−0.408905	−	0.708245i	−0.994767	+	0.102166i	$0.967423\pi$
$212$	−0.0682682	+	0.118244i	−0.00468868	+	0.00812103i
$213$	0.477606			0.0327250
$214$	−1.56586	+	2.71216i	−0.107040	+	0.185399i
$215$	−1.28360	+	2.22327i	−0.0875411	+	0.151626i
$216$	2.67573			0.182061
$217$	5.00734	−	8.67297i	0.339920	−	0.588760i
$218$	−1.71224	−	2.96568i	−0.115967	−	0.200861i
$219$	−0.341878	−	0.592151i	−0.0231020	−	0.0400138i
$220$	1.01818			0.0686457
$221$	−0.512061	−	1.54534i	−0.0344450	−	0.103951i
$222$	0.561952			0.0377157
$223$	4.92416	+	8.52890i	0.329746	+	0.571138i	0.982461	−	0.186466i	$-0.0597034\pi$
$223$	4.92416	+	8.52890i	0.329746	+	0.571138i	−0.652715	+	0.757604i	$0.726370\pi$
$224$	3.54280	+	6.13631i	0.236713	+	0.409999i
$225$	−6.85791	+	11.8782i	−0.457194	+	0.791883i
$226$	7.53723			0.501369
$227$	−0.0339827	+	0.0588598i	−0.00225551	+	0.00390666i	−0.867151	−	0.498045i	$-0.834051\pi$
$227$	−0.0339827	+	0.0588598i	−0.00225551	+	0.00390666i	0.864895	+	0.501952i	$0.167385\pi$
$228$	−0.672077	+	1.16407i	−0.0445094	+	0.0770925i
$229$	13.1872			0.871434			0.435717	−	0.900084i	$-0.356495\pi$
$229$	13.1872			0.871434			0.435717	+	0.900084i	$0.356495\pi$
$230$	−0.585262	+	1.01370i	−0.0385911	+	0.0668417i
$231$	−0.169642	−	0.293828i	−0.0111616	−	0.0193324i
$232$	−9.54695	−	16.5358i	−0.626788	−	1.08563i
$233$	18.2397			1.19493			0.597463	−	0.801897i	$-0.296176\pi$
$233$	18.2397			1.19493			0.597463	+	0.801897i	$0.296176\pi$
$234$	−3.51870	+	3.95388i	−0.230024	+	0.258474i
$235$	2.19452			0.143155
$236$	−6.74270	−	11.6787i	−0.438913	−	0.760219i
$237$	1.76719	+	3.06086i	0.114791	+	0.198824i
$238$	0.158846	−	0.275130i	0.0102965	−	0.0178340i
$239$	10.9341			0.707266			0.353633	−	0.935384i	$-0.384946\pi$
$239$	10.9341			0.707266			0.353633	+	0.935384i	$0.384946\pi$
$240$	0.179649	−	0.311161i	0.0115963	−	0.0200854i
$241$	−2.59706	+	4.49824i	−0.167291	+	0.289757i	−0.937467	−	0.348075i	$-0.886835\pi$
$241$	−2.59706	+	4.49824i	−0.167291	+	0.289757i	0.770175	+	0.637832i	$0.220169\pi$
$242$	−0.498953			−0.0320739
$243$	3.16490	−	5.48176i	0.203028	−	0.351655i
$244$	−3.78896	−	6.56267i	−0.242563	−	0.420132i
$245$	1.45699	+	2.52359i	0.0930839	+	0.161226i
$246$	−1.06400			−0.0678382
$247$	−3.61834	−	10.9197i	−0.230229	−	0.694805i
$248$	−13.2916			−0.844017
$249$	0.485393	+	0.840725i	0.0307605	+	0.0532788i
$250$	−1.40158	−	2.42761i	−0.0886440	−	0.153536i
$251$	−5.65717	+	9.79851i	−0.357077	+	0.618476i	−0.987471	−	0.157799i	$-0.949560\pi$
$251$	−5.65717	+	9.79851i	−0.357077	+	0.618476i	0.630394	+	0.776276i	$0.282893\pi$
$252$	7.26489			0.457645
$253$	−2.01727	+	3.49401i	−0.126825	+	0.219667i
$254$	−0.560463	+	0.970751i	−0.0351666	+	0.0609103i
$255$	−0.0631672			−0.00395568
$256$	0.204910	−	0.354915i	0.0128069	−	0.0221822i
$257$	13.8248	+	23.9453i	0.862370	+	1.49367i	0.869635	+	0.493694i	$0.164354\pi$
$257$	13.8248	+	23.9453i	0.862370	+	1.49367i	−0.00726578	+	0.999974i	$0.502313\pi$
$258$	−0.265005	−	0.459002i	−0.0164985	−	0.0285762i
$259$	6.60118			0.410178
$260$	1.15471	+	3.48477i	0.0716119	+	0.216116i
$261$	−30.0152			−1.85790
$262$	−1.70344	−	2.95045i	−0.105239	−	0.182280i
$263$	−2.57679	−	4.46313i	−0.158892	−	0.275209i	0.775578	−	0.631252i	$-0.217459\pi$
$263$	−2.57679	−	4.46313i	−0.158892	−	0.275209i	−0.934469	+	0.356044i	$0.884125\pi$
$264$	−0.225150	+	0.389971i	−0.0138570	+	0.0240011i
$265$	−0.0453396			−0.00278519
$266$	1.12244	−	1.94413i	0.0688213	−	0.119202i
$267$	−1.23154	+	2.13309i	−0.0753690	+	0.130543i
$268$	19.6672			1.20137
$269$	−11.3345	+	19.6319i	−0.691076	+	1.19698i	0.280409	+	0.959881i	$0.409530\pi$
$269$	−11.3345	+	19.6319i	−0.691076	+	1.19698i	−0.971486	+	0.237099i	$0.923804\pi$
$270$	0.207390	+	0.359210i	0.0126214	+	0.0218608i
$271$	3.37505	+	5.84576i	0.205020	+	0.355105i	0.950139	−	0.311827i	$-0.100941\pi$
$271$	3.37505	+	5.84576i	0.205020	+	0.355105i	−0.745119	+	0.666931i	$0.767607\pi$
$272$	1.15961			0.0703117
$273$	0.813251	−	0.913833i	0.0492202	−	0.0553077i
$274$	9.39997			0.567873
$275$	−2.33095	−	4.03732i	−0.140561	−	0.243459i
$276$	0.849867	+	1.47201i	0.0511560	+	0.0886048i
$277$	2.32229	−	4.02232i	0.139533	−	0.241678i	−0.787787	−	0.615948i	$-0.788773\pi$
$277$	2.32229	−	4.02232i	0.139533	−	0.241678i	0.927320	+	0.374270i	$0.122107\pi$
$278$	7.02434			0.421292
$279$	−10.4471	+	18.0948i	−0.625449	+	1.08331i
$280$	−0.767329	+	1.32905i	−0.0458567	+	0.0794261i
$281$	−21.0948			−1.25841			−0.629206	−	0.777238i	$-0.716620\pi$
$281$	−21.0948			−1.25841			−0.629206	+	0.777238i	$0.716620\pi$
$282$	−0.226533	+	0.392367i	−0.0134898	+	0.0233651i
$283$	−13.6656	−	23.6695i	−0.812336	−	1.40701i	−0.911225	−	0.411908i	$-0.864862\pi$
$283$	−13.6656	−	23.6695i	−0.812336	−	1.40701i	0.0988898	−	0.995098i	$-0.468471\pi$
$284$	−1.73799	−	3.01029i	−0.103131	−	0.178628i
$285$	−0.446353			−0.0264397
$286$	−0.565858	−	1.70769i	−0.0334599	−	0.100978i
$287$	−12.4987			−0.737775
$288$	−7.39151	−	12.8025i	−0.435549	−	0.754393i
$289$	8.39807	+	14.5459i	0.494004	+	0.855640i
$290$	1.47992	−	2.56330i	0.0869041	−	0.150522i
$291$	3.01120			0.176520
$292$	−2.48817	+	4.30963i	−0.145609	+	0.252202i
$293$	−15.0061	+	25.9914i	−0.876667	+	1.51843i	−0.0216900	+	0.999765i	$0.506905\pi$
$293$	−15.0061	+	25.9914i	−0.876667	+	1.51843i	−0.854977	+	0.518666i	$0.826429\pi$
$294$	−0.601603			−0.0350862
$295$	2.23905	−	3.87815i	0.130363	−	0.225794i
$296$	−4.38058	−	7.58739i	−0.254616	−	0.441008i
$297$	0.714827	+	1.23812i	0.0414785	+	0.0718428i
$298$	−0.934401			−0.0541284
$299$	−14.2462	−	2.94168i	−0.823878	−	0.170122i
$300$	−1.96404			−0.113394
$301$	−3.11298	−	5.39184i	−0.179429	−	0.310780i
$302$	−3.68370	−	6.38036i	−0.211973	−	0.367149i
$303$	1.08317	−	1.87611i	0.0622267	−	0.107780i
$304$	8.19407			0.469962
$305$	1.25820	−	2.17927i	0.0720444	−	0.124784i
$306$	−0.331409	+	0.574016i	−0.0189454	+	0.0328143i
$307$	−28.9631			−1.65301			−0.826506	−	0.562927i	$-0.809675\pi$
$307$	−28.9631			−1.65301			−0.826506	+	0.562927i	$0.809675\pi$
$308$	−1.23464	+	2.13846i	−0.0703501	+	0.121850i
$309$	−1.72284	−	2.98405i	−0.0980089	−	0.169756i
$310$	−1.03020	−	1.78436i	−0.0585115	−	0.101345i
$311$	10.3363			0.586117			0.293059	−	0.956094i	$-0.405327\pi$
$311$	10.3363			0.586117			0.293059	+	0.956094i	$0.405327\pi$
$312$	−1.59004	−	0.328325i	−0.0900181	−	0.0185877i
$313$	23.0075			1.30046			0.650230	−	0.759737i	$-0.274672\pi$
$313$	23.0075			1.30046			0.650230	+	0.759737i	$0.274672\pi$
$314$	−1.72777	−	2.99258i	−0.0975036	−	0.168881i
$315$	1.20623	+	2.08925i	0.0679632	+	0.117716i
$316$	12.8615	−	22.2767i	0.723514	−	1.25316i
$317$	−19.3410			−1.08630			−0.543149	−	0.839636i	$-0.682768\pi$
$317$	−19.3410			−1.08630			−0.543149	+	0.839636i	$0.682768\pi$
$318$	0.00468027	−	0.00810646i	0.000262456	−	0.000454588i
$319$	5.10097	−	8.83513i	0.285599	−	0.494673i
$320$	−1.52895			−0.0854707
$321$	−0.755065	+	1.30781i	−0.0421436	+	0.0729949i
$322$	−1.41937	−	2.45842i	−0.0790984	−	0.137002i
$323$	−0.720288	−	1.24758i	−0.0400779	−	0.0694170i
$324$	−14.8530			−0.825168
$325$	11.1744	−	12.5565i	0.619845	−	0.696507i
$326$	−6.18550			−0.342583
$327$	−0.825647	−	1.43006i	−0.0456584	−	0.0790826i
$328$	8.29420	+	14.3660i	0.457971	+	0.793228i
$329$	−2.66106	+	4.60908i	−0.146709	+	0.254107i
$330$	−0.0698034			−0.00384255
$331$	−7.92385	+	13.7245i	−0.435534	+	0.754367i	−0.997339	−	0.0729024i	$-0.976774\pi$
$331$	−7.92385	+	13.7245i	−0.435534	+	0.754367i	0.561805	+	0.827270i	$0.310107\pi$
$332$	3.53265	−	6.11874i	0.193880	−	0.335809i
$333$	−13.7724			−0.754722
$334$	−5.08186	+	8.80204i	−0.278067	+	0.481626i
$335$	3.26545	+	5.65592i	0.178410	+	0.309016i
$336$	0.435682	+	0.754624i	0.0237684	+	0.0411681i
$337$	5.84238			0.318254			0.159127	−	0.987258i	$-0.449132\pi$
$337$	5.84238			0.318254			0.159127	+	0.987258i	$0.449132\pi$
$338$	5.20292	−	3.87335i	0.283002	−	0.210682i
$339$	3.63448			0.197398
$340$	0.229863	+	0.398135i	0.0124661	+	0.0215919i
$341$	−3.55087	−	6.15029i	−0.192290	−	0.333057i
$342$	−2.34181	+	4.05613i	−0.126630	+	0.219330i
$343$	−16.9382			−0.914575
$344$	−4.13158	+	7.15610i	−0.222760	+	0.385831i
$345$	−0.282215	+	0.488811i	−0.0151940	+	0.0263167i
$346$	0.541557			0.0291143
$347$	4.10596	−	7.11173i	0.220420	−	0.381778i	−0.734516	−	0.678591i	$-0.762591\pi$
$347$	4.10596	−	7.11173i	0.220420	−	0.381778i	0.954935	+	0.296814i	$0.0959240\pi$
$348$	−2.14902	−	3.72221i	−0.115199	−	0.199531i
$349$	−6.17514	−	10.6957i	−0.330548	−	0.572525i	0.652072	−	0.758157i	$-0.273900\pi$
$349$	−6.17514	−	10.6957i	−0.330548	−	0.572525i	−0.982619	+	0.185632i	$0.940567\pi$
$350$	3.28015			0.175332
$351$	−3.42684	+	3.85066i	−0.182911	+	0.205533i
$352$	5.02463			0.267814
$353$	−8.19404	−	14.1925i	−0.436125	−	0.755390i	0.561262	−	0.827638i	$-0.310316\pi$
$353$	−8.19404	−	14.1925i	−0.436125	−	0.755390i	−0.997387	+	0.0722480i	$0.976983\pi$
$354$	0.462260	+	0.800657i	0.0245688	+	0.0425545i
$355$	0.577135	−	0.999627i	0.0306311	−	0.0530547i
$356$	17.9261			0.950082
$357$	0.0765961	−	0.132668i	0.00405390	−	0.00702155i
$358$	−1.74009	+	3.01392i	−0.0919665	+	0.159291i
$359$	−0.450004			−0.0237503			−0.0118751	−	0.999929i	$-0.503780\pi$
$359$	−0.450004			−0.0237503			−0.0118751	+	0.999929i	$0.503780\pi$
$360$	1.60092	−	2.77287i	0.0843757	−	0.146143i
$361$	4.41028	+	7.63884i	0.232120	+	0.402044i
$362$	1.77060	+	3.06676i	0.0930604	+	0.161185i
$363$	−0.240597			−0.0126281
$364$	−8.71916	−	1.80041i	−0.457008	−	0.0943671i
$365$	−1.65249			−0.0864953
$366$	0.259760	+	0.449918i	0.0135779	+	0.0235176i
$367$	9.79506	+	16.9655i	0.511298	+	0.885594i	0.999914	+	0.0130952i	$0.00416844\pi$
$367$	9.79506	+	16.9655i	0.511298	+	0.885594i	−0.488616	+	0.872499i	$0.662498\pi$
$368$	5.18085	−	8.97350i	0.270071	−	0.467776i
$369$	26.0767			1.35750
$370$	0.679057	−	1.17616i	0.0353025	−	0.0611458i
$371$	0.0549785	−	0.0952256i	0.00285434	−	0.00494387i
$372$	−2.99194			−0.155125
$373$	−6.03947	+	10.4607i	−0.312712	+	0.541633i	−0.978948	−	0.204108i	$-0.934571\pi$
$373$	−6.03947	+	10.4607i	−0.312712	+	0.541633i	0.666237	+	0.745740i	$0.267904\pi$
$374$	−0.112643	−	0.195103i	−0.00582463	−	0.0100886i
$375$	−0.675848	−	1.17060i	−0.0349007	−	0.0604497i
$376$	7.06356			0.364275
$377$	36.0236	+	7.43848i	1.85531	+	0.383101i
$378$	−1.00592			−0.0517389
$379$	−16.1124	−	27.9074i	−0.827636	−	1.43351i	−0.899888	−	0.436122i	$-0.856352\pi$
$379$	−16.1124	−	27.9074i	−0.827636	−	1.43351i	0.0722515	−	0.997386i	$-0.476982\pi$
$380$	1.62426	+	2.81331i	0.0833230	+	0.144320i
$381$	−0.270257	+	0.468099i	−0.0138457	+	0.0239814i
$382$	−5.90252			−0.301999
$383$	−16.8296	+	29.1496i	−0.859950	+	1.48948i	0.0120258	+	0.999928i	$0.496172\pi$
$383$	−16.8296	+	29.1496i	−0.859950	+	1.48948i	−0.871976	+	0.489549i	$0.837161\pi$
$384$	1.36674	−	2.36726i	0.0697461	−	0.120804i
$385$	−0.819973			−0.0417897
$386$	0.168641	−	0.292095i	0.00858360	−	0.0148672i
$387$	6.49476	+	11.2493i	0.330147	+	0.571832i
$388$	−10.9577	−	18.9792i	−0.556291	−	0.963524i
$389$	9.54985			0.484197			0.242098	−	0.970252i	$-0.422164\pi$
$389$	9.54985			0.484197			0.242098	+	0.970252i	$0.422164\pi$
$390$	−0.0791634	−	0.238906i	−0.00400859	−	0.0120975i
$391$	−1.82166			−0.0921255
$392$	4.68967	+	8.12275i	0.236864	+	0.410261i
$393$	−0.821406	−	1.42272i	−0.0414345	−	0.0717666i
$394$	2.62217	−	4.54173i	0.132103	−	0.228809i
$395$	8.54181			0.429785
$396$	2.57589	−	4.46157i	0.129443	−	0.224202i
$397$	9.77934	−	16.9383i	0.490811	−	0.850110i	−0.509133	−	0.860688i	$-0.670034\pi$
$397$	9.77934	−	16.9383i	0.490811	−	0.850110i	0.999944	+	0.0105782i	$0.00336722\pi$
$398$	10.1062			0.506578
$399$	0.541245	−	0.937464i	0.0270961	−	0.0469319i
$400$	5.98646	+	10.3689i	0.299323	+	0.518443i
$401$	12.6887	+	21.9774i	0.633642	+	1.09750i	0.986801	+	0.161937i	$0.0517740\pi$
$401$	12.6887	+	21.9774i	0.633642	+	1.09750i	−0.353159	+	0.935563i	$0.614893\pi$
$402$	−1.34833			−0.0672484
$403$	17.0227	−	19.1280i	0.847959	−	0.952834i
$404$	−15.7665			−0.784414
$405$	−2.46612	−	4.27145i	−0.122543	−	0.212250i
$406$	3.58909	+	6.21649i	0.178124	+	0.308519i
$407$	2.34056	−	4.05397i	0.116017	−	0.200948i
$408$	−0.203318			−0.0100658
$409$	7.61600	−	13.1913i	0.376587	−	0.652267i	−0.613976	−	0.789324i	$-0.710431\pi$
$409$	7.61600	−	13.1913i	0.376587	−	0.652267i	0.990563	+	0.137057i	$0.0437643\pi$
$410$	−1.28573	+	2.22695i	−0.0634976	+	0.109981i
$411$	4.53270			0.223581
$412$	−12.5387	+	21.7177i	−0.617738	+	1.06995i
$413$	5.43011	+	9.40523i	0.267198	+	0.462801i
$414$	2.96130	+	5.12913i	0.145540	+	0.252083i
$415$	2.34618			0.115169
$416$	5.69838	+	17.1970i	0.279386	+	0.843154i
$417$	3.38716			0.165870
$418$	−0.795961	−	1.37864i	−0.0389317	−	0.0674317i
$419$	3.98090	+	6.89512i	0.194480	+	0.336848i	0.946730	−	0.322029i	$-0.104365\pi$
$419$	3.98090	+	6.89512i	0.194480	+	0.336848i	−0.752250	+	0.658878i	$0.771032\pi$
$420$	−0.172726	+	0.299170i	−0.00842815	+	0.0145980i
$421$	−6.44783			−0.314248			−0.157124	−	0.987579i	$-0.550222\pi$
$421$	−6.44783			−0.314248			−0.157124	+	0.987579i	$0.550222\pi$
$422$	2.96363	−	5.13316i	0.144267	−	0.249878i
$423$	5.55189	−	9.61616i	0.269942	−	0.467554i
$424$	−0.145936			−0.00708729
$425$	1.05246	−	1.82292i	0.0510520	−	0.0884246i
$426$	0.119152	+	0.206377i	0.00577291	+	0.00999898i
$427$	3.05137	+	5.28513i	0.147666	+	0.255765i
$428$	10.9906			0.531251
$429$	−0.272858	−	0.823454i	−0.0131737	−	0.0397567i
$430$	−1.28092			−0.0617713
$431$	−20.4332	−	35.3913i	−0.984232	−	1.70474i	−0.645300	−	0.763929i	$-0.723268\pi$
$431$	−20.4332	−	35.3913i	−0.984232	−	1.70474i	−0.338932	−	0.940811i	$-0.610066\pi$
$432$	−1.83586	−	3.17980i	−0.0883277	−	0.152988i
$433$	−6.49069	+	11.2422i	−0.311923	+	0.540266i	−0.978779	−	0.204921i	$-0.934306\pi$
$433$	−6.49069	+	11.2422i	−0.311923	+	0.540266i	0.666856	+	0.745187i	$0.267640\pi$
$434$	4.99686			0.239857
$435$	0.713624	−	1.23603i	0.0342157	−	0.0592633i
$436$	−6.00900	+	10.4079i	−0.287779	+	0.498447i
$437$	−12.8723			−0.615764
$438$	0.170581	−	0.295455i	0.00815069	−	0.0141174i
$439$	−10.5236	−	18.2275i	−0.502266	−	0.869950i	−0.999997	−	0.00261814i	$-0.999167\pi$
$439$	−10.5236	−	18.2275i	−0.502266	−	0.869950i	0.497731	−	0.867332i	$-0.334167\pi$
$440$	0.544138	+	0.942475i	0.0259408	+	0.0449307i
$441$	14.7441			0.702102
$442$	0.540004	−	0.606791i	0.0256854	−	0.0288621i
$443$	18.8136			0.893862			0.446931	−	0.894569i	$-0.352517\pi$
$443$	18.8136			0.893862			0.446931	+	0.894569i	$0.352517\pi$
$444$	−0.986068	−	1.70792i	−0.0467967	−	0.0810543i
$445$	2.97636	+	5.15521i	0.141093	+	0.244380i
$446$	−2.45693	+	4.25552i	−0.116339	+	0.201505i
$447$	−0.450571			−0.0213113
$448$	1.85399	−	3.21120i	0.0875928	−	0.151715i
$449$	8.03401	−	13.9153i	0.379149	−	0.656705i	−0.611790	−	0.791020i	$-0.709550\pi$
$449$	8.03401	−	13.9153i	0.379149	−	0.656705i	0.990939	+	0.134316i	$0.0428836\pi$
$450$	−6.84355			−0.322608
$451$	−4.43162	+	7.67579i	−0.208677	+	0.361439i
$452$	−13.2257	−	22.9076i	−0.622086	−	1.07748i
$453$	−1.77629	−	3.07663i	−0.0834575	−	0.144553i
$454$	−0.0339116			−0.00159155
$455$	−0.929923	−	2.80640i	−0.0435955	−	0.131566i
$456$	−1.43669			−0.0672793
$457$	17.7061	+	30.6678i	0.828256	+	1.43458i	0.899405	+	0.437116i	$0.144000\pi$
$457$	17.7061	+	30.6678i	0.828256	+	1.43458i	−0.0711493	+	0.997466i	$0.522667\pi$
$458$	3.28989	+	5.69826i	0.153727	+	0.266262i
$459$	−0.322757	+	0.559031i	−0.0150650	+	0.0260933i
$460$	4.10788			0.191531
$461$	−7.92993	+	13.7350i	−0.369334	+	0.639705i	−0.989462	−	0.144796i	$-0.953747\pi$
$461$	−7.92993	+	13.7350i	−0.369334	+	0.639705i	0.620128	+	0.784501i	$0.287081\pi$
$462$	0.0846432	−	0.146606i	0.00393796	−	0.00682074i
$463$	−16.8149			−0.781453			−0.390727	−	0.920507i	$-0.627776\pi$
$463$	−16.8149			−0.781453			−0.390727	+	0.920507i	$0.627776\pi$
$464$	−13.1006	+	22.6909i	−0.608179	+	1.05340i
$465$	−0.496766	−	0.860424i	−0.0230370	−	0.0399012i
$466$	4.55039	+	7.88151i	0.210793	+	0.365104i
$467$	24.5686			1.13690			0.568449	−	0.822718i	$-0.307544\pi$
$467$	24.5686			1.13690			0.568449	+	0.822718i	$0.307544\pi$
$468$	18.1912	+	3.75628i	0.840889	+	0.173634i
$469$	−15.8386			−0.731360
$470$	0.547481	+	0.948264i	0.0252534	+	0.0437402i
$471$	−0.833135	−	1.44303i	−0.0383888	−	0.0664914i
$472$	7.20690	−	12.4827i	0.331725	−	0.574564i
$473$	−4.41503			−0.203003
$474$	−0.881744	+	1.52723i	−0.0404998	+	0.0701478i
$475$	7.43694	−	12.8812i	0.341230	−	0.591028i
$476$	−1.11492			−0.0511024
$477$	−0.114704	+	0.198674i	−0.00525196	+	0.00909666i
$478$	2.72779	+	4.72468i	0.124766	+	0.216102i
$479$	−16.7091	−	28.9410i	−0.763458	−	1.32235i	−0.941058	−	0.338245i	$-0.890167\pi$
$479$	−16.7091	−	28.9410i	−0.763458	−	1.32235i	0.177600	−	0.984103i	$-0.443167\pi$
$480$	0.702945			0.0320849
$481$	16.5293	+	3.41312i	0.753671	+	0.155625i
$482$	−2.59162			−0.118045
$483$	−0.684425	−	1.18546i	−0.0311424	−	0.0539402i
$484$	0.875523	+	1.51645i	0.0397965	+	0.0689296i
$485$	3.63871	−	6.30243i	0.165225	−	0.286179i
$486$	3.15827			0.143262
$487$	−6.07654	+	10.5249i	−0.275354	+	0.476928i	−0.970224	−	0.242208i	$-0.922129\pi$
$487$	−6.07654	+	10.5249i	−0.275354	+	0.476928i	0.694870	+	0.719135i	$0.255462\pi$
$488$	4.04981	−	7.01448i	0.183326	−	0.317531i
$489$	−2.98267			−0.134881
$490$	−0.726971	+	1.25915i	−0.0328412	+	0.0568826i
$491$	−1.52488	−	2.64117i	−0.0688169	−	0.119194i	0.829564	−	0.558412i	$-0.188589\pi$
$491$	−1.52488	−	2.64117i	−0.0688169	−	0.119194i	−0.898381	+	0.439217i	$0.855256\pi$
$492$	1.86702	+	3.23378i	0.0841719	+	0.145790i
$493$	4.60635			0.207460
$494$	3.81579	−	4.28772i	0.171680	−	0.192914i
$495$	1.71075			0.0768925
$496$	9.11953	+	15.7955i	0.409479	+	0.709239i
$497$	1.39966	+	2.42428i	0.0627833	+	0.108744i
$498$	−0.242188	+	0.419483i	−0.0108527	+	0.0187975i
$499$	−17.6401			−0.789678			−0.394839	−	0.918750i	$-0.629200\pi$
$499$	−17.6401			−0.789678			−0.394839	+	0.918750i	$0.629200\pi$
$500$	−4.91877	+	8.51957i	−0.219974	+	0.381007i
$501$	−2.45049	+	4.24437i	−0.109480	+	0.189625i
$502$	−5.64533			−0.251963
$503$	17.9182	−	31.0351i	0.798931	−	1.38379i	−0.121382	−	0.992606i	$-0.538733\pi$
$503$	17.9182	−	31.0351i	0.798931	−	1.38379i	0.920313	−	0.391183i	$-0.127934\pi$
$504$	3.88252	+	6.72472i	0.172941	+	0.299543i
$505$	−2.61779	−	4.53415i	−0.116490	−	0.201767i
$506$	−2.01304			−0.0894907
$507$	2.50887	−	1.86774i	0.111423	−	0.0829493i
$508$	3.93382			0.174535
$509$	9.71898	+	16.8338i	0.430786	+	0.746143i	0.996941	−	0.0781553i	$-0.0249030\pi$
$509$	9.71898	+	16.8338i	0.430786	+	0.746143i	−0.566155	+	0.824299i	$0.691570\pi$
$510$	−0.0157587	−	0.0272949i	−0.000697809	−	0.00120864i
$511$	2.00380	−	3.47068i	0.0886428	−	0.153534i
$512$	−22.5180			−0.995164
$513$	−2.28067	+	3.95024i	−0.100694	+	0.174407i
$514$	−6.89795	+	11.9476i	−0.304255	+	0.526986i
$515$	−8.32746			−0.366952
$516$	−0.930018	+	1.61084i	−0.0409417	+	0.0709132i
$517$	1.88704	+	3.26845i	0.0829920	+	0.143746i
$518$	1.64684	+	2.85241i	0.0723580	+	0.125328i
$519$	0.261140			0.0114628
$520$	−2.60857	+	2.93119i	−0.114393	+	0.128541i
$521$	15.3874			0.674132			0.337066	−	0.941481i	$-0.390565\pi$
$521$	15.3874			0.674132			0.337066	+	0.941481i	$0.390565\pi$
$522$	−7.48810	−	12.9698i	−0.327745	−	0.567671i
$523$	5.23209	+	9.06225i	0.228784	+	0.396265i	0.957448	−	0.288606i	$-0.0931919\pi$
$523$	5.23209	+	9.06225i	0.228784	+	0.396265i	−0.728664	+	0.684871i	$0.759859\pi$
$524$	−5.97814	+	10.3544i	−0.261156	+	0.452336i
$525$	1.58170			0.0690311
$526$	1.28570	−	2.22689i	0.0560591	−	0.0970972i
$527$	1.60328	−	2.77696i	0.0698400	−	0.120966i
$528$	0.617913			0.0268912
$529$	3.36126	−	5.82187i	0.146142	−	0.253125i
$530$	−0.0113112	−	0.0195915i	−0.000491326	−	0.000851002i
$531$	−11.3291	−	19.6226i	−0.491642	−	0.851548i
$532$	−7.87828			−0.341567
$533$	−31.2966	−	6.46240i	−1.35561	−	0.279918i
$534$	−1.22896			−0.0531823
$535$	1.82483	+	3.16069i	0.0788941	+	0.136649i
$536$	10.5106	+	18.2049i	0.453989	+	0.786331i
$537$	−0.839076	+	1.45332i	−0.0362088	+	0.0627155i
$538$	−11.3108			−0.487642
$539$	−2.50571	+	4.34001i	−0.107928	+	0.186938i
$540$	0.727822	−	1.26063i	0.0313205	−	0.0542487i
$541$	6.85555			0.294743			0.147372	−	0.989081i	$-0.452919\pi$
$541$	6.85555			0.294743			0.147372	+	0.989081i	$0.452919\pi$
$542$	−1.68399	+	2.91676i	−0.0723337	+	0.125286i
$543$	0.853787	+	1.47880i	0.0366395	+	0.0634615i
$544$	1.13435	+	1.96476i	0.0486350	+	0.0842383i
$545$	−3.99081			−0.170948
$546$	0.597760	+	0.123431i	0.0255818	+	0.00528235i
$547$	−36.9564			−1.58014			−0.790070	−	0.613016i	$-0.789956\pi$
$547$	−36.9564			−1.58014			−0.790070	+	0.613016i	$0.789956\pi$
$548$	−16.4943	−	28.5690i	−0.704602	−	1.22041i
$549$	−6.36623	−	11.0266i	−0.271704	−	0.470605i
$550$	1.16303	−	2.01443i	0.0495919	−	0.0858957i
$551$	32.5495			1.38666
$552$	−0.908376	+	1.57335i	−0.0386630	+	0.0669664i
$553$	−10.3577	+	17.9401i	−0.440456	+	0.762892i
$554$	2.31742			0.0984579
$555$	0.327444	−	0.567149i	0.0138992	−	0.0240741i
$556$	−12.3257	−	21.3488i	−0.522728	−	0.905392i
$557$	−9.01161	−	15.6086i	−0.381834	−	0.661356i	0.609490	−	0.792793i	$-0.291374\pi$
$557$	−9.01161	−	15.6086i	−0.381834	−	0.661356i	−0.991324	+	0.131437i	$0.958041\pi$
$558$	−10.4252			−0.441334
$559$	−5.00704	−	15.1107i	−0.211775	−	0.639113i
$560$	2.10590			0.0889904
$561$	−0.0543168	−	0.0940795i	−0.00229326	−	0.00397204i
$562$	−5.26267	−	9.11521i	−0.221992	−	0.384502i
$563$	−14.4670	+	25.0576i	−0.609712	+	1.05605i	0.381575	+	0.924338i	$0.375382\pi$
$563$	−14.4670	+	25.0576i	−0.609712	+	1.05605i	−0.991288	+	0.131715i	$0.957952\pi$
$564$	1.59001			0.0669514
$565$	4.39187	−	7.60694i	0.184767	−	0.320026i
$566$	6.81849	−	11.8100i	0.286603	−	0.496410i
$567$	11.9616			0.502340
$568$	1.85764	−	3.21753i	0.0779450	−	0.135005i
$569$	−7.54410	−	13.0668i	−0.316265	−	0.547788i	0.663440	−	0.748229i	$-0.269096\pi$
$569$	−7.54410	−	13.0668i	−0.316265	−	0.547788i	−0.979706	+	0.200442i	$0.935762\pi$
$570$	−0.111355	−	0.192872i	−0.00466414	−	0.00807852i
$571$	17.5630			0.734988			0.367494	−	0.930026i	$-0.380216\pi$
$571$	17.5630			0.734988			0.367494	+	0.930026i	$0.380216\pi$
$572$	−4.19720	+	4.71631i	−0.175494	+	0.197199i
$573$	−2.84621			−0.118902
$574$	−3.11813	−	5.40076i	−0.130148	−	0.225424i
$575$	−9.40429	−	16.2887i	−0.392186	−	0.679286i
$576$	−3.86807	+	6.69970i	−0.161170	+	0.279154i
$577$	−38.7780			−1.61435			−0.807174	−	0.590314i	$-0.799004\pi$
$577$	−38.7780			−1.61435			−0.807174	+	0.590314i	$0.799004\pi$
$578$	−4.19024	+	7.25771i	−0.174291	+	0.301881i
$579$	0.0813192	−	0.140849i	0.00337951	−	0.00585349i
$580$	−10.3874			−0.431314
$581$	−2.84496	+	4.92761i	−0.118029	+	0.204432i
$582$	0.751225	+	1.30116i	0.0311393	+	0.0539348i
$583$	−0.0389871	−	0.0675276i	−0.00161468	−	0.00279671i
$584$	−5.31893			−0.220099
$585$	1.94014	+	5.85513i	0.0802151	+	0.242080i
$586$	−14.9747			−0.618599
$587$	−22.1103	−	38.2962i	−0.912591	−	1.58065i	−0.810391	−	0.585889i	$-0.800745\pi$
$587$	−22.1103	−	38.2962i	−0.912591	−	1.58065i	−0.102200	−	0.994764i	$-0.532588\pi$
$588$	1.05564	+	1.82843i	0.0435340	+	0.0754032i
$589$	11.3291	−	19.6226i	0.466809	−	0.808536i
$590$	2.23436			0.0919872
$591$	1.26442	−	2.19004i	0.0520112	−	0.0900860i
$592$	−6.01115	+	10.4116i	−0.247057	+	0.427915i
$593$	10.0591			0.413077			0.206538	−	0.978439i	$-0.433780\pi$
$593$	10.0591			0.413077			0.206538	+	0.978439i	$0.433780\pi$
$594$	−0.356665	+	0.617762i	−0.0146341	+	0.0253471i
$595$	−0.185116	−	0.320630i	−0.00758902	−	0.0131446i
$596$	1.63961	+	2.83989i	0.0671611	+	0.116327i
$597$	4.87324			0.199449
$598$	−2.28297	−	6.88974i	−0.0933577	−	0.281743i
$599$	42.4291			1.73360			0.866802	−	0.498652i	$-0.166172\pi$
$599$	42.4291			1.73360			0.866802	+	0.498652i	$0.166172\pi$
$600$	−1.04963	−	1.81800i	−0.0428508	−	0.0742197i
$601$	17.3339	+	30.0232i	0.707064	+	1.22467i	0.965942	+	0.258760i	$0.0833140\pi$
$601$	17.3339	+	30.0232i	0.707064	+	1.22467i	−0.258878	+	0.965910i	$0.583353\pi$
$602$	1.55323	−	2.69027i	0.0633050	−	0.109647i
$603$	33.0449			1.34569
$604$	−12.9277	+	22.3915i	−0.526022	+	0.911097i
$605$	−0.290735	+	0.503568i	−0.0118201	+	0.0204729i
$606$	1.08091			0.0439088
$607$	−23.5526	+	40.7943i	−0.955971	+	1.65579i	−0.223840	+	0.974626i	$0.571859\pi$
$607$	−23.5526	+	40.7943i	−0.955971	+	1.65579i	−0.732130	+	0.681164i	$0.761474\pi$
$608$	8.01560	+	13.8834i	0.325075	+	0.563047i
$609$	1.73067	+	2.99761i	0.0701304	+	0.121469i
$610$	1.25557			0.0508364
$611$	−9.04637	+	10.1652i	−0.365977	+	0.411241i
$612$	2.32612			0.0940277
$613$	23.3780	+	40.4919i	0.944229	+	1.63545i	0.757287	+	0.653083i	$0.226525\pi$
$613$	23.3780	+	40.4919i	0.944229	+	1.63545i	0.186943	+	0.982371i	$0.440142\pi$
$614$	−7.22562	−	12.5151i	−0.291602	−	0.505070i
$615$	−0.619983	+	1.07384i	−0.0250001	+	0.0433015i
$616$	−2.63927			−0.106339
$617$	0.737929	−	1.27813i	0.0297079	−	0.0514556i	−0.850789	−	0.525507i	$-0.823876\pi$
$617$	0.737929	−	1.27813i	0.0297079	−	0.0514556i	0.880497	+	0.474052i	$0.157209\pi$
$618$	0.859616	−	1.48890i	0.0345788	−	0.0598923i
$619$	−26.4523			−1.06321			−0.531603	−	0.846994i	$-0.678410\pi$
$619$	−26.4523			−1.06321			−0.531603	+	0.846994i	$0.678410\pi$
$620$	−3.61543	+	6.26210i	−0.145199	+	0.251492i
$621$	2.88399	+	4.99522i	0.115731	+	0.200451i
$622$	2.57866	+	4.46637i	0.103395	+	0.179085i
$623$	−14.4365			−0.578385
$624$	0.700769	+	2.11484i	0.0280532	+	0.0846613i
$625$	20.0427			0.801708
$626$	5.73983	+	9.94168i	0.229410	+	0.397349i
$627$	−0.383815	−	0.664787i	−0.0153281	−	0.0265490i
$628$	−6.06350	+	10.5023i	−0.241960	+	0.419087i
$629$	2.11361			0.0842750
$630$	−0.601851	+	1.04244i	−0.0239783	+	0.0415316i
$631$	−1.77481	+	3.07406i	−0.0706540	+	0.122376i	−0.899188	−	0.437562i	$-0.855842\pi$
$631$	−1.77481	+	3.07406i	−0.0706540	+	0.122376i	0.828534	+	0.559939i	$0.189175\pi$
$632$	27.4938			1.09364
$633$	1.42907	−	2.47522i	0.0568005	−	0.0983813i
$634$	−4.82512	−	8.35735i	−0.191630	−	0.331913i
$635$	0.653152	+	1.13129i	0.0259196	+	0.0448940i
$636$	−0.0328502			−0.00130260
$637$	−17.6956	−	3.65394i	−0.701125	−	0.144774i
$638$	5.09029			0.201526
$639$	−2.92018	−	5.05790i	−0.115520	−	0.200087i
$640$	−3.30311	−	5.72115i	−0.130567	−	0.226148i
$641$	14.6768	−	25.4210i	0.579700	−	1.00407i	−0.415813	−	0.909450i	$-0.636503\pi$
$641$	14.6768	−	25.4210i	0.579700	−	1.00407i	0.995513	−	0.0946199i	$-0.0301636\pi$
$642$	−0.753484			−0.0297376
$643$	−2.66263	+	4.61182i	−0.105004	+	0.181872i	−0.913740	−	0.406300i	$-0.866819\pi$
$643$	−2.66263	+	4.61182i	−0.105004	+	0.181872i	0.808736	+	0.588172i	$0.200152\pi$
$644$	−4.98119	+	8.62768i	−0.196287	+	0.339978i
$645$	−0.617662			−0.0243204
$646$	0.359390	−	0.622482i	0.0141400	−	0.0244912i
$647$	−9.20786	−	15.9485i	−0.361998	−	0.626999i	0.626291	−	0.779589i	$-0.284572\pi$
$647$	−9.20786	−	15.9485i	−0.361998	−	0.626999i	−0.988290	+	0.152590i	$0.951239\pi$
$648$	−7.93778	−	13.7486i	−0.311826	−	0.540098i
$649$	7.70134			0.302304
$650$	8.21348	+	1.69599i	0.322159	+	0.0665222i
$651$	2.40950			0.0944358
$652$	10.8538	+	18.7994i	0.425068	+	0.736240i
$653$	−12.0175	−	20.8150i	−0.470283	−	0.814553i	0.529140	−	0.848535i	$-0.322515\pi$
$653$	−12.0175	−	20.8150i	−0.470283	−	0.814553i	−0.999422	+	0.0339812i	$0.989181\pi$
$654$	0.411959	−	0.713534i	0.0161089	−	0.0279014i
$655$	−3.97032			−0.155133
$656$	11.3815	−	19.7134i	0.444374	−	0.769678i
$657$	−4.18063	+	7.24105i	−0.163102	+	0.282500i
$658$	−2.65548			−0.103522
$659$	11.7284	−	20.3142i	0.456873	−	0.791327i	−0.541921	−	0.840430i	$-0.682303\pi$
$659$	11.7284	−	20.3142i	0.456873	−	0.791327i	0.998794	+	0.0491024i	$0.0156361\pi$
$660$	0.122485	+	0.212151i	0.00476774	+	0.00825797i
$661$	19.6658	+	34.0621i	0.764911	+	1.32486i	0.940294	+	0.340364i	$0.110550\pi$
$661$	19.6658	+	34.0621i	0.764911	+	1.32486i	−0.175383	+	0.984500i	$0.556116\pi$
$662$	−7.90726			−0.307324
$663$	0.260392	−	0.292597i	0.0101128	−	0.0113635i
$664$	7.55172			0.293064
$665$	−1.30807	−	2.26565i	−0.0507248	−	0.0878580i
$666$	−3.43589	−	5.95113i	−0.133138	−	0.230602i
$667$	20.5800	−	35.6457i	0.796862	−	1.38021i
$668$	35.6690			1.38007
$669$	−1.18474	+	2.05203i	−0.0458046	+	0.0793359i
$670$	−1.62930	+	2.82204i	−0.0629455	+	0.109025i
$671$	4.32766			0.167067
$672$	−0.852386	+	1.47638i	−0.0328815	+	0.0569524i
$673$	14.8100	+	25.6516i	0.570882	+	0.988797i	0.996476	+	0.0838825i	$0.0267320\pi$
$673$	14.8100	+	25.6516i	0.570882	+	0.988797i	−0.425593	+	0.904914i	$0.639935\pi$
$674$	1.45754	+	2.52453i	0.0561422	+	0.0972411i
$675$	−6.66489			−0.256532
$676$	−20.9018	−	9.01641i	−0.803916	−	0.346785i
$677$	−39.7317			−1.52701			−0.763507	−	0.645800i	$-0.776524\pi$
$677$	−39.7317			−1.52701			−0.763507	+	0.645800i	$0.776524\pi$
$678$	0.906717	+	1.57048i	0.0348223	+	0.0603139i
$679$	8.82455	+	15.2846i	0.338655	+	0.586568i
$680$	−0.245688	+	0.425544i	−0.00942170	+	0.0163189i
$681$	−0.0163523			−0.000626620
$682$	1.77172	−	3.06871i	0.0678426	−	0.117507i
$683$	−14.1383	+	24.4882i	−0.540986	+	0.937016i	0.457861	+	0.889024i	$0.348616\pi$
$683$	−14.1383	+	24.4882i	−0.540986	+	0.937016i	−0.998848	+	0.0479921i	$0.984718\pi$
$684$	16.4369			0.628479
$685$	5.47727	−	9.48690i	0.209276	−	0.362476i
$686$	−4.22568	−	7.31909i	−0.161337	−	0.279444i
$687$	1.58640	+	2.74772i	0.0605249	+	0.104832i
$688$	11.3389			0.432292
$689$	0.186902	−	0.210018i	0.00712039	−	0.00800104i
$690$	−0.281624			−0.0107213
$691$	13.5606	+	23.4876i	0.515869	+	0.893512i	0.999830	+	0.0184221i	$0.00586427\pi$
$691$	13.5606	+	23.4876i	0.515869	+	0.893512i	−0.483961	+	0.875089i	$0.660802\pi$
$692$	−0.950281	−	1.64593i	−0.0361242	−	0.0625690i
$693$	−2.07444	+	3.59304i	−0.0788016	+	0.136488i
$694$	4.09736			0.155534
$695$	4.09301	−	7.08930i	0.155257	−	0.268913i
$696$	2.29697	−	3.97846i	0.0870663	−	0.150803i
$697$	−4.00191			−0.151583
$698$	3.08111	−	5.33663i	0.116622	−	0.201994i
$699$	2.19421	+	3.80049i	0.0829927	+	0.143748i
$700$	−5.75575	−	9.96926i	−0.217547	−	0.376802i
$701$	26.8389			1.01369			0.506845	−	0.862037i	$-0.330812\pi$
$701$	26.8389			1.01369			0.506845	+	0.862037i	$0.330812\pi$
$702$	−2.51881	−	0.520106i	−0.0950664	−	0.0196301i
$703$	14.9352			0.563292
$704$	−1.31473	−	2.27717i	−0.0495506	−	0.0858241i
$705$	0.263997	+	0.457256i	0.00994270	+	0.0172213i
$706$	4.08844	−	7.08139i	0.153871	−	0.266512i
$707$	12.6973			0.477530
$708$	1.62227	−	2.80986i	0.0609687	−	0.105601i
$709$	12.5044	−	21.6583i	0.469614	−	0.813396i	−0.529782	−	0.848134i	$-0.677726\pi$
$709$	12.5044	−	21.6583i	0.469614	−	0.813396i	0.999396	+	0.0347378i	$0.0110596\pi$
$710$	0.575926			0.0216141
$711$	21.6099	−	37.4294i	0.810433	−	1.40371i
$712$	9.58011	+	16.5932i	0.359030	+	0.621858i
$713$	−14.3261	−	24.8136i	−0.536517	−	0.929275i
$714$	0.0764357			0.00286054
$715$	−2.05320	−	0.423964i	−0.0767855	−	0.0158553i
$716$	12.2135			0.456439
$717$	1.31535	+	2.27825i	0.0491227	+	0.0850829i
$718$	−0.112265	−	0.194449i	−0.00418971	−	0.00725679i
$719$	−14.1242	+	24.4638i	−0.526743	+	0.912346i	0.472771	+	0.881185i	$0.343254\pi$
$719$	−14.1242	+	24.4638i	−0.526743	+	0.912346i	−0.999514	+	0.0311608i	$0.990080\pi$
$720$	−4.39364			−0.163741
$721$	10.0978	−	17.4899i	0.376062	−	0.651359i
$722$	−2.20053	+	3.81142i	−0.0818951	+	0.141846i
$723$	−1.24969			−0.0464764
$724$	6.21380	−	10.7626i	0.230934	−	0.399989i
$725$	23.7802	+	41.1885i	0.883173	+	1.52970i
$726$	−0.0600233	−	0.103963i	−0.00222767	−	0.00385844i
$727$	−10.0496			−0.372718			−0.186359	−	0.982482i	$-0.559669\pi$
$727$	−10.0496			−0.372718			−0.186359	+	0.982482i	$0.559669\pi$
$728$	−2.99317	−	9.03304i	−0.110934	−	0.334787i
$729$	−23.9242			−0.886081
$730$	−0.412258	−	0.714051i	−0.0152583	−	0.0264282i
$731$	−0.996732	−	1.72639i	−0.0368655	−	0.0638529i
$732$	0.911612	−	1.57896i	0.0336942	−	0.0583600i
$733$	−17.7381			−0.655171			−0.327586	−	0.944822i	$-0.606235\pi$
$733$	−17.7381			−0.655171			−0.327586	+	0.944822i	$0.606235\pi$
$734$	−4.88727	+	8.46501i	−0.180393	+	0.312449i
$735$	−0.350548	+	0.607167i	−0.0129302	+	0.0223957i
$736$	20.2720			0.747238
$737$	−5.61585	+	9.72693i	−0.206862	+	0.358296i
$738$	6.50551	+	11.2679i	0.239471	+	0.414776i
$739$	25.1017	+	43.4775i	0.923382	+	1.59934i	0.794143	+	0.607731i	$0.207920\pi$
$739$	25.1017	+	43.4775i	0.923382	+	1.59934i	0.129239	+	0.991613i	$0.458746\pi$
$740$	−4.76622			−0.175210
$741$	1.83998	−	2.06755i	0.0675935	−	0.0759534i
$742$	0.0548634			0.00201410
$743$	−1.86589	−	3.23182i	−0.0684529	−	0.118564i	0.829768	−	0.558109i	$-0.188473\pi$
$743$	−1.86589	−	3.23182i	−0.0684529	−	0.118564i	−0.898220	+	0.439545i	$0.855140\pi$
$744$	−1.59896	−	2.76948i	−0.0586206	−	0.101534i
$745$	−0.544466	+	0.943043i	−0.0199477	+	0.0345504i
$746$	−6.02682			−0.220658
$747$	5.93558	−	10.2807i	0.217171	−	0.376152i
$748$	−0.395314	+	0.684704i	−0.0144541	+	0.0250352i
$749$	−8.85109			−0.323412
$750$	0.337217	−	0.584076i	0.0123134	−	0.0213275i
$751$	−15.1103	−	26.1718i	−0.551384	−	0.955024i	−0.998175	−	0.0603862i	$-0.980767\pi$
$751$	−15.1103	−	26.1718i	−0.551384	−	0.955024i	0.446792	−	0.894638i	$-0.352567\pi$
$752$	−4.84640	−	8.39422i	−0.176730	−	0.306106i
$753$	−2.72219			−0.0992023
$754$	5.77284	+	17.4218i	0.210235	+	0.634463i
$755$	−8.58583			−0.312470
$756$	1.76511	+	3.05725i	0.0641963	+	0.111191i
$757$	−14.8882	−	25.7871i	−0.541120	−	0.937247i	−0.998840	−	0.0481507i	$-0.984667\pi$
$757$	−14.8882	−	25.7871i	−0.541120	−	0.937247i	0.457720	−	0.889096i	$-0.348666\pi$
$758$	8.03931	−	13.9245i	0.292001	−	0.505760i
$759$	−0.970696			−0.0352340
$760$	−1.73609	+	3.00699i	−0.0629744	+	0.109075i
$761$	23.7071	−	41.0619i	0.859381	−	1.48849i	−0.0131399	−	0.999914i	$-0.504183\pi$
$761$	23.7071	−	41.0619i	0.859381	−	1.48849i	0.872521	−	0.488577i	$-0.162484\pi$
$762$	−0.269691			−0.00976989
$763$	4.83923	−	8.38180i	0.175192	−	0.303442i
$764$	10.3573	+	17.9393i	0.374713	+	0.649022i
$765$	0.386217	+	0.668947i	0.0139637	+	0.0241858i
$766$	−16.7943			−0.606803
$767$	8.73401	+	26.3582i	0.315367	+	0.951740i
$768$	0.0986016			0.00355798
$769$	2.64945	+	4.58898i	0.0955415	+	0.165483i	0.909834	−	0.414971i	$-0.136208\pi$
$769$	2.64945	+	4.58898i	0.0955415	+	0.165483i	−0.814293	+	0.580454i	$0.802875\pi$
$770$	−0.204564	−	0.354315i	−0.00737198	−	0.0127686i
$771$	−3.32621	+	5.76117i	−0.119791	+	0.207483i
$772$	−1.18367			−0.0426013
$773$	13.4786	−	23.3457i	0.484793	−	0.839686i	−0.515054	−	0.857158i	$-0.672228\pi$
$773$	13.4786	−	23.3457i	0.484793	−	0.839686i	0.999847	+	0.0174714i	$0.00556160\pi$
$774$	−3.24058	+	5.61285i	−0.116480	+	0.201750i
$775$	33.1076			1.18926
$776$	11.7120	−	20.2858i	0.420437	−	0.728219i
$777$	0.794112	+	1.37544i	0.0284886	+	0.0493437i
$778$	2.38246	+	4.12655i	0.0854155	+	0.147944i
$779$	−28.2784			−1.01318
$780$	−0.587188	+	0.659811i	−0.0210247	+	0.0236250i
$781$	1.98509			0.0710321
$782$	−0.454462	−	0.787152i	−0.0162515	−	0.0281485i
$783$	−7.29262	−	12.6312i	−0.260617	−	0.451402i
$784$	6.43529	−	11.1462i	0.229832	−	0.398080i
$785$	−4.02701			−0.143730
$786$	0.409843	−	0.709869i	0.0146186	−	0.0253202i
$787$	−15.8797	+	27.5044i	−0.566050	+	0.980427i	0.430901	+	0.902399i	$0.358196\pi$
$787$	−15.8797	+	27.5044i	−0.566050	+	0.980427i	−0.996951	+	0.0780282i	$0.975138\pi$
$788$	−18.4047			−0.655640
$789$	0.619968	−	1.07382i	0.0220714	−	0.0382288i
$790$	2.13098	+	3.69097i	0.0758169	+	0.131319i
$791$	10.6511	+	18.4483i	0.378710	+	0.655944i
$792$	5.50645			0.195663
$793$	4.90795	+	14.8116i	0.174286	+	0.525976i
$794$	9.75886			0.346329
$795$	−0.00545429	−	0.00944710i	−0.000193444	−	0.000335054i
$796$	−17.7336	−	30.7154i	−0.628549	−	1.08868i
$797$	−19.5893	+	33.9296i	−0.693887	+	1.20185i	0.276667	+	0.960966i	$0.410770\pi$
$797$	−19.5893	+	33.9296i	−0.693887	+	1.20185i	−0.970554	+	0.240882i	$0.922563\pi$
$798$	0.540112			0.0191198
$799$	−0.852033	+	1.47576i	−0.0301428	+	0.0522088i
$800$	−11.7121	+	20.2860i	−0.414087	+	0.717219i
$801$	30.1195			1.06422
$802$	−6.33105	+	10.9657i	−0.223557	+	0.387212i
$803$	−1.42096	−	2.46117i	−0.0501446	−	0.0868530i
$804$	2.36593	+	4.09792i	0.0834401	+	0.144522i
$805$	−3.30821			−0.116599
$806$	12.5121	+	2.58360i	0.440719	+	0.0910036i
$807$	−5.45409			−0.191993
$808$	−8.42598	−	14.5942i	−0.296425	−	0.513423i
$809$	−3.14630	−	5.44955i	−0.110618	−	0.191596i	0.805402	−	0.592729i	$-0.201950\pi$
$809$	−3.14630	−	5.44955i	−0.110618	−	0.191596i	−0.916020	+	0.401134i	$0.868616\pi$
$810$	1.23048	−	2.13125i	0.0432346	−	0.0748846i
$811$	1.88117			0.0660569			0.0330284	−	0.999454i	$-0.489485\pi$
$811$	1.88117			0.0660569			0.0330284	+	0.999454i	$0.489485\pi$
$812$	12.5957	−	21.8164i	0.442022	−	0.765605i
$813$	−0.812027	+	1.40647i	−0.0284790	+	0.0493271i
$814$	2.33566			0.0818648
$815$	−3.60423	+	6.24270i	−0.126251	+	0.218672i
$816$	0.139499	+	0.241620i	0.00488345	+	0.00845839i
$817$	−7.04313	−	12.1991i	−0.246408	−	0.426791i
$818$	7.60005			0.265730
$819$	−14.6500	−	3.02505i	−0.511911	−	0.105704i
$820$	9.02438			0.315145
$821$	18.5964	+	32.2099i	0.649019	+	1.12413i	0.983358	+	0.181681i	$0.0581538\pi$
$821$	18.5964	+	32.2099i	0.649019	+	1.12413i	−0.334339	+	0.942453i	$0.608513\pi$
$822$	1.13080	+	1.95861i	0.0394412	+	0.0683142i
$823$	−16.3150	+	28.2585i	−0.568706	+	0.985028i	0.427988	+	0.903784i	$0.359223\pi$
$823$	−16.3150	+	28.2585i	−0.568706	+	0.985028i	−0.996694	+	0.0812439i	$0.974111\pi$
$824$	−26.8039			−0.933756
$825$	0.560818	−	0.971366i	0.0195252	−	0.0338186i
$826$	−2.70937	+	4.69277i	−0.0942711	+	0.163282i
$827$	24.7521			0.860713			0.430357	−	0.902659i	$-0.358388\pi$
$827$	24.7521			0.860713			0.430357	+	0.902659i	$0.358388\pi$
$828$	10.3925	−	18.0004i	0.361165	−	0.625556i
$829$	−13.4168	−	23.2386i	−0.465986	−	0.807112i	0.533259	−	0.845952i	$-0.320967\pi$
$829$	−13.4168	−	23.2386i	−0.465986	−	0.807112i	−0.999245	+	0.0388402i	$0.987634\pi$
$830$	0.585316	+	1.01380i	0.0203166	+	0.0351894i
$831$	1.11747			0.0387646
$832$	6.30271	−	7.08223i	0.218507	−	0.245532i
$833$	−2.26274			−0.0783993
$834$	0.845017	+	1.46361i	0.0292605	+	0.0506807i
$835$	5.92230	+	10.2577i	0.204950	+	0.354983i
$836$	−2.79338	+	4.83827i	−0.0966109	+	0.167335i
$837$	−10.1530			−0.350940
$838$	−1.98628	+	3.44034i	−0.0686149	+	0.118845i
$839$	0.117315	−	0.203195i	0.00405015	−	0.00701507i	−0.863993	−	0.503503i	$-0.832044\pi$
$839$	0.117315	−	0.203195i	0.00405015	−	0.00701507i	0.868043	+	0.496488i	$0.165377\pi$
$840$	−0.369234			−0.0127398
$841$	−37.5397	+	65.0207i	−1.29447	+	2.24209i
$842$	−1.60858	−	2.78615i	−0.0554354	−	0.0960170i
$843$	−2.53768	−	4.39538i	−0.0874022	−	0.151385i
$844$	−20.8013			−0.716012
$845$	−0.877481	−	7.50801i	−0.0301863	−	0.258283i
$846$	5.54027			0.190478
$847$	−0.705086	−	1.22125i	−0.0242271	−	0.0419625i
$848$	0.100129	+	0.173428i	0.00343843	+	0.00595554i
$849$	3.28790	−	5.69481i	0.112840	−	0.195445i
$850$	1.05026			0.0360236
$851$	9.44307	−	16.3559i	0.323704	−	0.560672i
$852$	0.418155	−	0.724266i	0.0143258	−	0.0248129i
$853$	−34.3397			−1.17577			−0.587884	−	0.808945i	$-0.700039\pi$
$853$	−34.3397			−1.17577			−0.587884	+	0.808945i	$0.700039\pi$
$854$	−1.52249	+	2.63703i	−0.0520986	+	0.0902374i
$855$	2.72909	+	4.72693i	0.0933330	+	0.161658i
$856$	5.87363	+	10.1734i	0.200756	+	0.347720i
$857$	−52.5142			−1.79385			−0.896925	−	0.442182i	$-0.854205\pi$
$857$	−52.5142			−1.79385			−0.896925	+	0.442182i	$0.854205\pi$
$858$	0.287748	−	0.323336i	0.00982355	−	0.0110385i
$859$	−4.82353			−0.164577			−0.0822883	−	0.996609i	$-0.526223\pi$
$859$	−4.82353			−0.164577			−0.0822883	+	0.996609i	$0.526223\pi$
$860$	2.24765	+	3.89304i	0.0766442	+	0.132752i
$861$	−1.50357	−	2.60427i	−0.0512416	−	0.0887531i
$862$	10.1952	−	17.6586i	0.347250	−	0.601455i
$863$	−22.2969			−0.758997			−0.379498	−	0.925192i	$-0.623903\pi$
$863$	−22.2969			−0.758997			−0.379498	+	0.925192i	$0.623903\pi$
$864$	3.59174	−	6.22108i	0.122193	−	0.211645i
$865$	0.315560	−	0.546565i	0.0107294	−	0.0185838i
$866$	−6.47710			−0.220101
$867$	−2.02055	+	3.49969i	−0.0686214	+	0.118856i
$868$	−8.76808	−	15.1868i	−0.297608	−	0.515472i
$869$	7.34502	+	12.7219i	0.249163	+	0.431562i
$870$	0.712130			0.0241435
$871$	−39.6598	−	8.18930i	−1.34382	−	0.277484i
$872$	−12.8454			−0.434999
$873$	−18.4111	−	31.8889i	−0.623121	−	1.07928i
$874$	−3.21133	−	5.56219i	−0.108625	−	0.188144i
$875$	3.96125	−	6.86108i	0.133915	−	0.231947i
$876$	−1.19729			−0.0404527
$877$	8.76638	−	15.1838i	0.296019	−	0.512721i	−0.679202	−	0.733951i	$-0.737674\pi$
$877$	8.76638	−	15.1838i	0.296019	−	0.512721i	0.975222	+	0.221231i	$0.0710073\pi$
$878$	5.25080	−	9.09465i	0.177206	−	0.306930i
$879$	−7.22085			−0.243553
$880$	0.746681	−	1.29329i	0.0251706	−	0.0435968i
$881$	−0.471751	−	0.817097i	−0.0158937	−	0.0275287i	0.857969	−	0.513701i	$-0.171726\pi$
$881$	−0.471751	−	0.817097i	−0.0158937	−	0.0275287i	−0.873863	+	0.486172i	$0.838393\pi$
$882$	3.67832	+	6.37103i	0.123855	+	0.214524i
$883$	−43.2575			−1.45573			−0.727866	−	0.685719i	$-0.759488\pi$
$883$	−43.2575			−1.45573			−0.727866	+	0.685719i	$0.759488\pi$
$884$	−2.79175	−	0.576466i	−0.0938968	−	0.0193886i
$885$	1.07742			0.0362170
$886$	4.69356	+	8.12948i	0.157683	+	0.273115i
$887$	−18.0242	−	31.2189i	−0.605195	−	1.04823i	−0.992021	−	0.126076i	$-0.959762\pi$
$887$	−18.0242	−	31.2189i	−0.605195	−	1.04823i	0.386826	−	0.922153i	$-0.373572\pi$
$888$	1.05395	−	1.82550i	0.0353684	−	0.0612598i
$889$	−3.16803			−0.106252
$890$	−1.48506	+	2.57221i	−0.0497795	+	0.0862206i
$891$	4.24118	−	7.34595i	0.142085	−	0.246098i
$892$	17.2449			0.577401
$893$	−6.02065	+	10.4281i	−0.201473	+	0.348962i
$894$	−0.112407	−	0.194695i	−0.00375945	−	0.00651156i
$895$	2.02786	+	3.51236i	0.0677840	+	0.117405i
$896$	16.0213			0.535234
$897$	−1.10086	−	3.32226i	−0.0367565	−	0.110927i
$898$	8.01719			0.267537
$899$	36.2258	+	62.7448i	1.20820	+	2.09266i
$900$	12.0085	+	20.7994i	0.400284	+	0.693312i
$901$	0.0176034	−	0.0304899i	0.000586453	−	0.00101577i
$902$	−4.42234			−0.147248
$903$	0.748973	−	1.29726i	0.0249243	−	0.0431701i
$904$	14.1363	−	24.4847i	0.470165	−	0.814349i
$905$	4.12683			0.137181
$906$	0.886287	−	1.53509i	0.0294449	−	0.0510001i
$907$	−18.0172	−	31.2067i	−0.598250	−	1.03620i	−0.993079	−	0.117446i	$-0.962529\pi$
$907$	−18.0172	−	31.2067i	−0.598250	−	1.03620i	0.394829	−	0.918755i	$-0.370804\pi$
$908$	0.0595053	+	0.103066i	0.00197475	+	0.00342037i
$909$	−26.4910			−0.878650
$910$	0.980667	−	1.10196i	0.0325088	−	0.0365295i
$911$	−26.9133			−0.891677			−0.445839	−	0.895113i	$-0.647094\pi$
$911$	−26.9133			−0.891677			−0.445839	+	0.895113i	$0.647094\pi$
$912$	0.985733	+	1.70734i	0.0326409	+	0.0565357i
$913$	2.01745	+	3.49433i	0.0667680	+	0.115646i
$914$	−8.83451	+	15.3018i	−0.292220	+	0.506139i
$915$	0.605438			0.0200152
$916$	11.5457	−	19.9977i	0.381480	−	0.660743i
$917$	4.81438	−	8.33875i	0.158985	−	0.275370i
$918$	−0.322081			−0.0106303
$919$	23.0200	−	39.8717i	0.759359	−	1.31525i	−0.183820	−	0.982960i	$-0.558846\pi$
$919$	23.0200	−	39.8717i	0.759359	−	1.31525i	0.943178	−	0.332288i	$-0.107820\pi$
$920$	2.19535	+	3.80245i	0.0723784	+	0.125363i
$921$	−3.48422	−	6.03484i	−0.114809	−	0.198855i
$922$	−7.91333			−0.260612
$923$	2.25127	+	6.79407i	0.0741014	+	0.223629i
$924$	−0.594100			−0.0195445
$925$	10.9114	+	18.8992i	0.358766	+	0.621401i
$926$	−4.19492	−	7.26581i	−0.137853	−	0.238769i
$927$	−21.0676	+	36.4901i	−0.691950	+	1.19849i
$928$	−51.2609			−1.68272
$929$	4.22620	−	7.31999i	0.138657	−	0.240161i	−0.788331	−	0.615251i	$-0.789055\pi$
$929$	4.22620	−	7.31999i	0.138657	−	0.240161i	0.926989	+	0.375090i	$0.122388\pi$
$930$	0.247863	−	0.429311i	0.00812775	−	0.0140777i
$931$	−15.9890			−0.524019
$932$	15.9693	−	27.6597i	0.523092	−	0.906023i
$933$	1.24344	+	2.15370i	0.0407084	+	0.0705090i
$934$	6.12929	+	10.6162i	0.200556	+	0.347374i
$935$	−0.262544			−0.00858610
$936$	6.24480	+	18.8461i	0.204118	+	0.616004i
$937$	30.6941			1.00273			0.501366	−	0.865236i	$-0.332831\pi$
$937$	30.6941			1.00273			0.501366	+	0.865236i	$0.332831\pi$
$938$	−3.95137	−	6.84397i	−0.129017	−	0.223463i
$939$	2.76776	+	4.79391i	0.0903226	+	0.156443i
$940$	1.92135	−	3.32788i	0.0626675	−	0.108543i
$941$	−8.73917			−0.284889			−0.142444	−	0.989803i	$-0.545496\pi$
$941$	−8.73917			−0.284889			−0.142444	+	0.989803i	$0.545496\pi$
$942$	0.415695	−	0.720006i	0.0135441	−	0.0234590i
$943$	−17.8795	+	30.9682i	−0.582237	+	1.00846i
$944$	−19.7790			−0.643752
$945$	−0.586139	+	1.01522i	−0.0190671	+	0.0330252i
$946$	−1.10145	−	1.90776i	−0.0358111	−	0.0620267i
$947$	−0.641432	−	1.11099i	−0.0208437	−	0.0361024i	0.855415	−	0.517943i	$-0.173302\pi$
$947$	−0.641432	−	1.11099i	−0.0208437	−	0.0361024i	−0.876259	+	0.481840i	$0.839969\pi$
$948$	6.18885			0.201005
$949$	6.81200	−	7.65450i	0.221127	−	0.248476i
$950$	7.42137			0.240781
$951$	−2.32669	−	4.02994i	−0.0754481	−	0.130680i
$952$	−0.595839	−	1.03202i	−0.0193113	−	0.0334481i
$953$	−14.1522	+	24.5124i	−0.458435	+	0.794033i	−0.998878	−	0.0473473i	$-0.984923\pi$
$953$	−14.1522	+	24.5124i	−0.458435	+	0.794033i	0.540443	+	0.841381i	$0.318257\pi$
$954$	−0.114464			−0.00370592
$955$	−3.43934	+	5.95711i	−0.111294	+	0.192768i
$956$	9.57302	−	16.5810i	0.309614	−	0.536267i
$957$	2.45455			0.0793444
$958$	8.33705	−	14.4402i	0.269358	−	0.466542i
$959$	13.2834	+	23.0075i	0.428943	+	0.742951i
$960$	−0.183930	−	0.318576i	−0.00593631	−	0.0102820i
$961$	19.4347			0.626927
$962$	2.64885	+	7.99391i	0.0854022	+	0.257734i
$963$	18.4665			0.595073
$964$	4.54757	+	7.87662i	0.146467	+	0.253689i
$965$	−0.196531	−	0.340401i	−0.00632655	−	0.0109579i
$966$	0.341496	−	0.591488i	0.0109875	−	0.0190308i
$967$	53.1966			1.71069			0.855343	−	0.518062i	$-0.173346\pi$
$967$	53.1966			1.71069			0.855343	+	0.518062i	$0.173346\pi$
$968$	−0.935798	+	1.62085i	−0.0300777	+	0.0520961i
$969$	0.173299	−	0.300163i	0.00556717	−	0.00964262i
$970$	3.63109			0.116587
$971$	23.6409	−	40.9472i	0.758671	−	1.31406i	−0.184857	−	0.982765i	$-0.559182\pi$
$971$	23.6409	−	40.9472i	0.758671	−	1.31406i	0.943528	−	0.331291i	$-0.107484\pi$
$972$	−5.54188	−	9.59881i	−0.177756	−	0.307882i
$973$	9.92632	+	17.1929i	0.318223	+	0.551179i
$974$	−6.06382			−0.194297
$975$	3.96056	+	0.817812i	0.126840	+	0.0261909i
$976$	−11.1145			−0.355767
$977$	−2.72765	−	4.72442i	−0.0872651	−	0.151148i	0.819089	−	0.573666i	$-0.194479\pi$
$977$	−2.72765	−	4.72442i	−0.0872651	−	0.151148i	−0.906354	+	0.422519i	$0.861146\pi$
$978$	−0.744105	−	1.28883i	−0.0237939	−	0.0412122i
$979$	−5.11869	+	8.86582i	−0.163594	+	0.283353i
$980$	5.10252			0.162994
$981$	−10.0963	+	17.4874i	−0.322351	+	0.558329i
$982$	0.760844	−	1.31782i	0.0242795	−	0.0420533i
$983$	40.9873			1.30729			0.653645	−	0.756801i	$-0.273239\pi$
$983$	40.9873			1.30729			0.653645	+	0.756801i	$0.273239\pi$
$984$	−1.99556	+	3.45641i	−0.0636161	+	0.110186i
$985$	−3.05582	−	5.29284i	−0.0973666	−	0.168644i
$986$	1.14918	+	1.99043i	0.0365972	+	0.0633883i
$987$	−1.28048			−0.0407582
$988$	−19.7271	−	4.07343i	−0.627604	−	0.129593i
$989$	−17.8126			−0.566408
$990$	0.426792	+	0.739226i	0.0135643	+	0.0234941i
$991$	24.0971	+	41.7374i	0.765469	+	1.32583i	0.939998	+	0.341180i	$0.110827\pi$
$991$	24.0971	+	41.7374i	0.765469	+	1.32583i	−0.174529	+	0.984652i	$0.555840\pi$
$992$	−17.8418	+	30.9029i	−0.566478	+	0.981169i
$993$	−3.81291			−0.120999
$994$	−0.698364	+	1.20960i	−0.0221508	+	0.0383663i
$995$	5.88878	−	10.1997i	0.186687	−	0.323351i
$996$	1.69989			0.0538631
$997$	−1.27486	+	2.20812i	−0.0403752	+	0.0699319i	−0.885507	−	0.464626i	$-0.846189\pi$
$997$	−1.27486	+	2.20812i	−0.0403752	+	0.0699319i	0.845132	+	0.534558i	$0.179522\pi$
$998$	−4.40078	−	7.62238i	−0.139304	−	0.241282i
$999$	−3.34619	−	5.79577i	−0.105869	−	0.183370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.e.c.133.4	yes	12
13.3	even	3		1859.2.a.k.1.3		6
13.9	even	3	inner	143.2.e.c.100.4	✓	12
13.10	even	6		1859.2.a.l.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.4	✓	12	13.9	even	3	inner
143.2.e.c.133.4	yes	12	1.1	even	1	trivial
1859.2.a.k.1.3		6	13.3	even	3
1859.2.a.l.1.4		6	13.10	even	6

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.249477 + 0.432106i) q^{2} +(0.120298 + 0.208363i) q^{3} +(0.875523 - 1.51645i) q^{4} +0.581470 q^{5} +(-0.0600233 + 0.103963i) q^{6} +(-0.705086 + 1.22125i) q^{7} +1.87160 q^{8} +(1.47106 - 2.54794i) q^{9} +O(q^{10})\)	\(q+(0.249477 + 0.432106i) q^{2} +(0.120298 + 0.208363i) q^{3} +(0.875523 - 1.51645i) q^{4} +0.581470 q^{5} +(-0.0600233 + 0.103963i) q^{6} +(-0.705086 + 1.22125i) q^{7} +1.87160 q^{8} +(1.47106 - 2.54794i) q^{9} +(0.145063 + 0.251257i) q^{10} +(0.500000 + 0.866025i) q^{11} +0.421296 q^{12} +(-2.39697 + 2.69342i) q^{13} -0.703610 q^{14} +(0.0699499 + 0.121157i) q^{15} +(-1.28413 - 2.22417i) q^{16} +(-0.225759 + 0.391026i) q^{17} +1.46798 q^{18} +(-1.59526 + 2.76307i) q^{19} +(0.509090 - 0.881770i) q^{20} -0.339283 q^{21} +(-0.249477 + 0.432106i) q^{22} +(2.01727 + 3.49401i) q^{23} +(0.225150 + 0.389971i) q^{24} -4.66189 q^{25} +(-1.76183 - 0.363799i) q^{26} +1.42965 q^{27} +(1.23464 + 2.13846i) q^{28} +(-5.10097 - 8.83513i) q^{29} +(-0.0349017 + 0.0604515i) q^{30} -7.10174 q^{31} +(2.51231 - 4.35146i) q^{32} +(-0.120298 + 0.208363i) q^{33} -0.225286 q^{34} +(-0.409986 + 0.710117i) q^{35} +(-2.57589 - 4.46157i) q^{36} +(-2.34056 - 4.05397i) q^{37} -1.59192 q^{38} +(-0.849562 - 0.175425i) q^{39} +1.08828 q^{40} +(4.43162 + 7.67579i) q^{41} +(-0.0846432 - 0.146606i) q^{42} +(-2.20752 + 3.82353i) q^{43} +1.75105 q^{44} +(0.855375 - 1.48155i) q^{45} +(-1.00652 + 1.74335i) q^{46} +3.77409 q^{47} +(0.308957 - 0.535129i) q^{48} +(2.50571 + 4.34001i) q^{49} +(-1.16303 - 2.01443i) q^{50} -0.108634 q^{51} +(1.98584 + 5.99304i) q^{52} -0.0779742 q^{53} +(0.356665 + 0.617762i) q^{54} +(0.290735 + 0.503568i) q^{55} +(-1.31964 + 2.28568i) q^{56} -0.767629 q^{57} +(2.54514 - 4.40832i) q^{58} +(3.85067 - 6.66956i) q^{59} +0.244971 q^{60} +(2.16383 - 3.74786i) q^{61} +(-1.77172 - 3.06871i) q^{62} +(2.07444 + 3.59304i) q^{63} -2.62945 q^{64} +(-1.39377 + 1.56615i) q^{65} -0.120047 q^{66} +(5.61585 + 9.72693i) q^{67} +(0.395314 + 0.684704i) q^{68} +(-0.485348 + 0.840648i) q^{69} -0.409128 q^{70} +(0.992545 - 1.71914i) q^{71} +(2.75322 - 4.76872i) q^{72} -2.84192 q^{73} +(1.16783 - 2.02274i) q^{74} +(-0.560818 - 0.971366i) q^{75} +(2.79338 + 4.83827i) q^{76} -1.41017 q^{77} +(-0.136144 - 0.410865i) q^{78} +14.6900 q^{79} +(-0.746681 - 1.29329i) q^{80} +(-4.24118 - 7.34595i) q^{81} +(-2.21117 + 3.82986i) q^{82} +4.03491 q^{83} +(-0.297050 + 0.514506i) q^{84} +(-0.131272 + 0.227370i) q^{85} -2.20289 q^{86} +(1.22728 - 2.12571i) q^{87} +(0.935798 + 1.62085i) q^{88} +(5.11869 + 8.86582i) q^{89} +0.853584 q^{90} +(-1.59926 - 4.82639i) q^{91} +7.06466 q^{92} +(-0.854328 - 1.47974i) q^{93} +(0.941546 + 1.63081i) q^{94} +(-0.927596 + 1.60664i) q^{95} +1.20891 q^{96} +(6.25778 - 10.8388i) q^{97} +(-1.25023 + 2.16546i) q^{98} +2.94211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9	\( 12 q - q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - 34 q^{12} - 4 q^{13} + 24 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{17} + 12 q^{18} + 10 q^{19} + 15 q^{20} - 24 q^{21} - 3 q^{23} + 14 q^{24} - 12 q^{25} - 3 q^{26} + 20 q^{27} + 16 q^{28} - 3 q^{29} - 19 q^{30} - 10 q^{31} - q^{32} + q^{33} + 10 q^{34} + 13 q^{35} - 20 q^{36} + 25 q^{37} - 54 q^{38} - 12 q^{39} - 16 q^{40} + 24 q^{41} - 13 q^{42} + 8 q^{43} - 16 q^{44} + 27 q^{45} + 18 q^{46} - 20 q^{47} + 28 q^{48} + q^{49} - 26 q^{50} - 34 q^{51} - 39 q^{52} + 20 q^{53} + 47 q^{54} - 6 q^{55} - 15 q^{56} + 6 q^{58} - 4 q^{59} + 122 q^{60} + 21 q^{61} + 5 q^{62} + 6 q^{63} - 54 q^{64} - 32 q^{65} + 24 q^{66} + 21 q^{67} - 14 q^{68} - 5 q^{69} - 62 q^{70} - 3 q^{71} - 50 q^{72} - 26 q^{73} + 38 q^{74} + 23 q^{75} + 8 q^{76} + 6 q^{77} + 36 q^{78} - 8 q^{79} + 44 q^{80} - 34 q^{81} + 33 q^{82} - 16 q^{83} + 47 q^{84} - 13 q^{85} + 22 q^{86} + 51 q^{87} + 3 q^{88} - 9 q^{89} - 140 q^{90} - 19 q^{91} + 30 q^{92} - 21 q^{93} - 10 q^{94} - 27 q^{95} + 38 q^{96} + 15 q^{97} + 21 q^{98} - 14 q^{99}+O(q^{100}) \) 12 * q - q^3 - 8 * q^4 - 12 * q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - 34 * q^12 - 4 * q^13 + 24 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^17 + 12 * q^18 + 10 * q^19 + 15 * q^20 - 24 * q^21 - 3 * q^23 + 14 * q^24 - 12 * q^25 - 3 * q^26 + 20 * q^27 + 16 * q^28 - 3 * q^29 - 19 * q^30 - 10 * q^31 - q^32 + q^33 + 10 * q^34 + 13 * q^35 - 20 * q^36 + 25 * q^37 - 54 * q^38 - 12 * q^39 - 16 * q^40 + 24 * q^41 - 13 * q^42 + 8 * q^43 - 16 * q^44 + 27 * q^45 + 18 * q^46 - 20 * q^47 + 28 * q^48 + q^49 - 26 * q^50 - 34 * q^51 - 39 * q^52 + 20 * q^53 + 47 * q^54 - 6 * q^55 - 15 * q^56 + 6 * q^58 - 4 * q^59 + 122 * q^60 + 21 * q^61 + 5 * q^62 + 6 * q^63 - 54 * q^64 - 32 * q^65 + 24 * q^66 + 21 * q^67 - 14 * q^68 - 5 * q^69 - 62 * q^70 - 3 * q^71 - 50 * q^72 - 26 * q^73 + 38 * q^74 + 23 * q^75 + 8 * q^76 + 6 * q^77 + 36 * q^78 - 8 * q^79 + 44 * q^80 - 34 * q^81 + 33 * q^82 - 16 * q^83 + 47 * q^84 - 13 * q^85 + 22 * q^86 + 51 * q^87 + 3 * q^88 - 9 * q^89 - 140 * q^90 - 19 * q^91 + 30 * q^92 - 21 * q^93 - 10 * q^94 - 27 * q^95 + 38 * q^96 + 15 * q^97 + 21 * q^98 - 14 * q^99

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