LMFDB - Embedded newform 231.2.j.g.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.4
Root			$-0.557915 - 1.71709i$ of defining polynomial
Character	$\chi$	$=$	231.64
Dual form			231.2.j.g.148.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.557915 - 1.71709i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.01908 - 0.740407i) q^{4} +(0.858186 + 2.64122i) q^{5} +(0.557915 + 1.71709i) q^{6} +(0.809017 + 0.587785i) q^{7} +(1.08138 - 0.785667i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.557915 - 1.71709i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.01908 - 0.740407i) q^{4} +(0.858186 + 2.64122i) q^{5} +(0.557915 + 1.71709i) q^{6} +(0.809017 + 0.587785i) q^{7} +(1.08138 - 0.785667i) q^{8} +(0.309017 - 0.951057i) q^{9} +5.01400 q^{10} +(3.22976 - 0.754083i) q^{11} +1.25966 q^{12} +(0.714790 - 2.19990i) q^{13} +(1.46064 - 1.06122i) q^{14} +(-2.24676 - 1.63237i) q^{15} +(-1.52425 - 4.69116i) q^{16} +(0.822488 + 2.53136i) q^{17} +(-1.46064 - 1.06122i) q^{18} +(-6.53904 + 4.75089i) q^{19} +(1.08102 - 3.32703i) q^{20} -1.00000 q^{21} +(0.507107 - 5.96649i) q^{22} -2.43007 q^{23} +(-0.413049 + 1.27124i) q^{24} +(-2.19449 + 1.59439i) q^{25} +(-3.37862 - 2.45471i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.389255 - 1.19800i) q^{28} +(6.11424 + 4.44226i) q^{29} +(-4.05641 + 2.94716i) q^{30} +(2.85707 - 8.79315i) q^{31} -6.23222 q^{32} +(-2.16969 + 2.50847i) q^{33} +4.80544 q^{34} +(-0.858186 + 2.64122i) q^{35} +(-1.01908 + 0.740407i) q^{36} +(-9.05906 - 6.58179i) q^{37} +(4.50946 + 13.8787i) q^{38} +(0.714790 + 2.19990i) q^{39} +(3.00314 + 2.18191i) q^{40} +(0.242620 - 0.176274i) q^{41} +(-0.557915 + 1.71709i) q^{42} -7.29328 q^{43} +(-3.84972 - 1.62287i) q^{44} +2.77715 q^{45} +(-1.35577 + 4.17264i) q^{46} +(-0.370412 + 0.269120i) q^{47} +(3.99054 + 2.89930i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.51337 + 4.65767i) q^{50} +(-2.15330 - 1.56446i) q^{51} +(-2.35725 + 1.71264i) q^{52} +(-1.60485 + 4.93922i) q^{53} +1.80545 q^{54} +(4.76344 + 7.88338i) q^{55} +1.33666 q^{56} +(2.49769 - 7.68710i) q^{57} +(11.0390 - 8.02028i) q^{58} +(-9.93687 - 7.21956i) q^{59} +(1.08102 + 3.32703i) q^{60} +(-0.561755 - 1.72890i) q^{61} +(-13.5046 - 9.81167i) q^{62} +(0.809017 - 0.587785i) q^{63} +(-0.428550 + 1.31894i) q^{64} +6.42384 q^{65} +(3.09676 + 5.12507i) q^{66} -1.42267 q^{67} +(1.03605 - 3.18864i) q^{68} +(1.96597 - 1.42836i) q^{69} +(4.05641 + 2.94716i) q^{70} +(0.172462 + 0.530784i) q^{71} +(-0.413049 - 1.27124i) q^{72} +(7.81740 + 5.67967i) q^{73} +(-16.3557 + 11.8831i) q^{74} +(0.838222 - 2.57978i) q^{75} +10.1814 q^{76} +(3.05617 + 1.28834i) q^{77} +4.17621 q^{78} +(-3.18905 + 9.81489i) q^{79} +(11.0823 - 8.05177i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.167316 - 0.514945i) q^{82} +(-2.62997 - 8.09421i) q^{83} +(1.01908 + 0.740407i) q^{84} +(-5.98003 + 4.34475i) q^{85} +(-4.06903 + 12.5232i) q^{86} -7.55762 q^{87} +(2.90013 - 3.35296i) q^{88} -1.56616 q^{89} +(1.54941 - 4.76860i) q^{90} +(1.87134 - 1.35961i) q^{91} +(2.47644 + 1.79924i) q^{92} +(2.85707 + 8.79315i) q^{93} +(0.255444 + 0.786176i) q^{94} +(-18.1599 - 13.1939i) q^{95} +(5.04197 - 3.66321i) q^{96} +(-0.164972 + 0.507733i) q^{97} +1.80545 q^{98} +(0.280876 - 3.30471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.557915	−	1.71709i	0.394506	−	1.21416i	−0.534840	−	0.844953i	$-0.679628\pi$
$2$	0.557915	−	1.71709i	0.394506	−	1.21416i	0.929346	−	0.369210i	$-0.120372\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−1.01908	−	0.740407i	−0.509541	−	0.370204i
$5$	0.858186	+	2.64122i	0.383792	+	1.18119i	0.937353	+	0.348382i	$0.113269\pi$
$5$	0.858186	+	2.64122i	0.383792	+	1.18119i	−0.553560	+	0.832809i	$0.686731\pi$
$6$	0.557915	+	1.71709i	0.227768	+	0.700998i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	1.08138	−	0.785667i	0.382325	−	0.277775i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	5.01400			1.58557
$11$	3.22976	−	0.754083i	0.973810	−	0.227365i
$11$	3.22976	−	0.754083i	0.973810	−	0.227365i
$12$	1.25966			0.363631
$13$	0.714790	−	2.19990i	0.198247	−	0.610142i	−0.801676	−	0.597758i	$-0.796058\pi$
$13$	0.714790	−	2.19990i	0.198247	−	0.610142i	0.999923	−	0.0123833i	$-0.00394183\pi$
$14$	1.46064	−	1.06122i	0.390373	−	0.283622i
$15$	−2.24676	−	1.63237i	−0.580111	−	0.421475i
$16$	−1.52425	−	4.69116i	−0.381063	−	1.17279i
$17$	0.822488	+	2.53136i	0.199483	+	0.613944i	0.999895	+	0.0144945i	$0.00461390\pi$
$17$	0.822488	+	2.53136i	0.199483	+	0.613944i	−0.800412	+	0.599450i	$0.795386\pi$
$18$	−1.46064	−	1.06122i	−0.344276	−	0.250131i
$19$	−6.53904	+	4.75089i	−1.50016	+	1.08993i	−0.529841	+	0.848097i	$0.677748\pi$
$19$	−6.53904	+	4.75089i	−1.50016	+	1.08993i	−0.970318	+	0.241832i	$0.922252\pi$
$20$	1.08102	−	3.32703i	0.241723	−	0.743947i
$21$	−1.00000			−0.218218
$22$	0.507107	−	5.96649i	0.108116	−	1.27206i
$23$	−2.43007			−0.506704			−0.253352	−	0.967374i	$-0.581533\pi$
$23$	−2.43007			−0.506704			−0.253352	+	0.967374i	$0.581533\pi$
$24$	−0.413049	+	1.27124i	−0.0843133	+	0.259490i
$25$	−2.19449	+	1.59439i	−0.438899	+	0.318879i
$26$	−3.37862	−	2.45471i	−0.662602	−	0.481409i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.389255	−	1.19800i	−0.0735623	−	0.226401i
$29$	6.11424	+	4.44226i	1.13539	+	0.824907i	0.986470	−	0.163943i	$-0.0524213\pi$
$29$	6.11424	+	4.44226i	1.13539	+	0.824907i	0.148917	+	0.988850i	$0.452421\pi$
$30$	−4.05641	+	2.94716i	−0.740597	+	0.538075i
$31$	2.85707	−	8.79315i	0.513145	−	1.57930i	−0.273488	−	0.961875i	$-0.588177\pi$
$31$	2.85707	−	8.79315i	0.513145	−	1.57930i	0.786633	−	0.617421i	$-0.211823\pi$
$32$	−6.23222			−1.10171
$33$	−2.16969	+	2.50847i	−0.377695	+	0.436669i
$34$	4.80544			0.824126
$35$	−0.858186	+	2.64122i	−0.145060	+	0.446448i
$36$	−1.01908	+	0.740407i	−0.169847	+	0.123401i
$37$	−9.05906	−	6.58179i	−1.48930	−	1.08204i	−0.974408	−	0.224785i	$-0.927832\pi$
$37$	−9.05906	−	6.58179i	−1.48930	−	1.08204i	−0.514892	−	0.857255i	$-0.672168\pi$
$38$	4.50946	+	13.8787i	0.731531	+	2.25142i
$39$	0.714790	+	2.19990i	0.114458	+	0.352266i
$40$	3.00314	+	2.18191i	0.474839	+	0.344990i
$41$	0.242620	−	0.176274i	0.0378908	−	0.0275293i	−0.568679	−	0.822560i	$-0.692545\pi$
$41$	0.242620	−	0.176274i	0.0378908	−	0.0275293i	0.606569	+	0.795030i	$0.292545\pi$
$42$	−0.557915	+	1.71709i	−0.0860882	+	0.264952i
$43$	−7.29328			−1.11221			−0.556107	−	0.831110i	$-0.687706\pi$
$43$	−7.29328			−1.11221			−0.556107	+	0.831110i	$0.687706\pi$
$44$	−3.84972	−	1.62287i	−0.580368	−	0.244656i
$45$	2.77715			0.413993
$46$	−1.35577	+	4.17264i	−0.199898	+	0.615222i
$47$	−0.370412	+	0.269120i	−0.0540302	+	0.0392552i	−0.614473	−	0.788938i	$-0.710631\pi$
$47$	−0.370412	+	0.269120i	−0.0540302	+	0.0392552i	0.560442	+	0.828193i	$0.310631\pi$
$48$	3.99054	+	2.89930i	0.575985	+	0.418477i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	1.51337	+	4.65767i	0.214023	+	0.658694i
$51$	−2.15330	−	1.56446i	−0.301522	−	0.219069i
$52$	−2.35725	+	1.71264i	−0.326892	+	0.237501i
$53$	−1.60485	+	4.93922i	−0.220443	+	0.678454i	0.778279	+	0.627918i	$0.216093\pi$
$53$	−1.60485	+	4.93922i	−0.220443	+	0.678454i	−0.998722	+	0.0505357i	$0.983907\pi$
$54$	1.80545			0.245691
$55$	4.76344	+	7.88338i	0.642302	+	1.06299i
$56$	1.33666			0.178618
$57$	2.49769	−	7.68710i	0.330827	−	1.01818i
$58$	11.0390	−	8.02028i	1.44949	−	1.05311i
$59$	−9.93687	−	7.21956i	−1.29367	−	0.939906i	−0.293797	−	0.955868i	$-0.594919\pi$
$59$	−9.93687	−	7.21956i	−1.29367	−	0.939906i	−0.999873	+	0.0159615i	$0.994919\pi$
$60$	1.08102	+	3.32703i	0.139559	+	0.429518i
$61$	−0.561755	−	1.72890i	−0.0719253	−	0.221363i	0.908631	−	0.417599i	$-0.137128\pi$
$61$	−0.561755	−	1.72890i	−0.0719253	−	0.221363i	−0.980557	+	0.196236i	$0.937128\pi$
$62$	−13.5046	−	9.81167i	−1.71509	−	1.24608i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	−0.428550	+	1.31894i	−0.0535687	+	0.164868i
$65$	6.42384			0.796780
$66$	3.09676	+	5.12507i	0.381185	+	0.630852i
$67$	−1.42267			−0.173807			−0.0869036	−	0.996217i	$-0.527697\pi$
$67$	−1.42267			−0.173807			−0.0869036	+	0.996217i	$0.527697\pi$
$68$	1.03605	−	3.18864i	0.125640	−	0.386679i
$69$	1.96597	−	1.42836i	0.236675	−	0.171954i
$70$	4.05641	+	2.94716i	0.484834	+	0.352253i
$71$	0.172462	+	0.530784i	0.0204675	+	0.0629924i	0.960769	−	0.277351i	$-0.0894566\pi$
$71$	0.172462	+	0.530784i	0.0204675	+	0.0629924i	−0.940301	+	0.340344i	$0.889457\pi$
$72$	−0.413049	−	1.27124i	−0.0486783	−	0.149816i
$73$	7.81740	+	5.67967i	0.914957	+	0.664755i	0.942264	−	0.334872i	$-0.108693\pi$
$73$	7.81740	+	5.67967i	0.914957	+	0.664755i	−0.0273067	+	0.999627i	$0.508693\pi$
$74$	−16.3557	+	11.8831i	−1.90131	+	1.38138i
$75$	0.838222	−	2.57978i	0.0967896	−	0.297888i
$76$	10.1814			1.16789
$77$	3.05617	+	1.28834i	0.348283	+	0.146820i
$78$	4.17621			0.472862
$79$	−3.18905	+	9.81489i	−0.358796	+	1.10426i	0.594979	+	0.803741i	$0.297160\pi$
$79$	−3.18905	+	9.81489i	−0.358796	+	1.10426i	−0.953775	+	0.300520i	$0.902840\pi$
$80$	11.0823	−	8.05177i	1.23904	−	0.900216i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.167316	−	0.514945i	−0.0184769	−	0.0568661i
$83$	−2.62997	−	8.09421i	−0.288676	−	0.888455i	−0.985273	−	0.170991i	$-0.945303\pi$
$83$	−2.62997	−	8.09421i	−0.288676	−	0.888455i	0.696596	−	0.717464i	$-0.254697\pi$
$84$	1.01908	+	0.740407i	0.111191	+	0.0807850i
$85$	−5.98003	+	4.34475i	−0.648626	+	0.471254i
$86$	−4.06903	+	12.5232i	−0.438775	+	1.35041i
$87$	−7.55762			−0.810262
$88$	2.90013	−	3.35296i	0.309155	−	0.357427i
$89$	−1.56616			−0.166012			−0.0830062	−	0.996549i	$-0.526452\pi$
$89$	−1.56616			−0.166012			−0.0830062	+	0.996549i	$0.526452\pi$
$90$	1.54941	−	4.76860i	0.163322	−	0.502655i
$91$	1.87134	−	1.35961i	0.196170	−	0.142526i
$92$	2.47644	+	1.79924i	0.258187	+	0.187584i
$93$	2.85707	+	8.79315i	0.296264	+	0.911807i
$94$	0.255444	+	0.786176i	0.0263470	+	0.0810878i
$95$	−18.1599	−	13.1939i	−1.86316	−	1.35367i
$96$	5.04197	−	3.66321i	0.514594	−	0.373875i
$97$	−0.164972	+	0.507733i	−0.0167504	+	0.0515525i	−0.959082	−	0.283127i	$-0.908628\pi$
$97$	−0.164972	+	0.507733i	−0.0167504	+	0.0515525i	0.942332	+	0.334680i	$0.108628\pi$
$98$	1.80545			0.182378
$99$	0.280876	−	3.30471i	0.0282291	−	0.332136i
$100$	3.41687			0.341687
$101$	−1.64323	+	5.05735i	−0.163508	+	0.503225i	−0.998923	−	0.0463938i	$-0.985227\pi$
$101$	−1.64323	+	5.05735i	−0.163508	+	0.503225i	0.835415	+	0.549619i	$0.185227\pi$
$102$	−3.88768	+	2.82457i	−0.384938	+	0.279674i
$103$	−15.0158	−	10.9096i	−1.47955	−	1.07496i	−0.977700	−	0.210004i	$-0.932652\pi$
$103$	−15.0158	−	10.9096i	−1.47955	−	1.07496i	−0.501852	−	0.864953i	$-0.667348\pi$
$104$	−0.955428	−	2.94051i	−0.0936874	−	0.288340i
$105$	−0.858186	−	2.64122i	−0.0837503	−	0.257757i
$106$	7.58570	+	5.51133i	0.736788	+	0.535308i
$107$	7.62681	−	5.54120i	0.737311	−	0.535688i	−0.154557	−	0.987984i	$-0.549395\pi$
$107$	7.62681	−	5.54120i	0.737311	−	0.535688i	0.891868	+	0.452296i	$0.149395\pi$
$108$	0.389255	−	1.19800i	0.0374561	−	0.115278i
$109$	1.11200			0.106511			0.0532553	−	0.998581i	$-0.483040\pi$
$109$	1.11200			0.106511			0.0532553	+	0.998581i	$0.483040\pi$
$110$	16.1940	−	3.78098i	1.54404	−	0.360502i
$111$	11.1976			1.06283
$112$	1.52425	−	4.69116i	0.144028	−	0.443273i
$113$	7.30116	−	5.30460i	0.686835	−	0.499015i	−0.188783	−	0.982019i	$-0.560454\pi$
$113$	7.30116	−	5.30460i	0.686835	−	0.499015i	0.875618	+	0.483004i	$0.160454\pi$
$114$	−11.8059	−	8.57750i	−1.10573	−	0.803357i
$115$	−2.08545	−	6.41835i	−0.194469	−	0.598515i
$116$	−2.94184	−	9.05406i	−0.273143	−	0.840648i
$117$	−1.87134	−	1.35961i	−0.173006	−	0.125696i
$118$	−17.9405	+	13.0346i	−1.65156	+	1.19993i
$119$	−0.822488	+	2.53136i	−0.0753973	+	0.232049i
$120$	−3.71209			−0.338866
$121$	9.86272	−	4.87102i	0.896611	−	0.442820i
$122$	−3.28209			−0.297146
$123$	−0.0926725	+	0.285217i	−0.00835600	+	0.0257171i
$124$	−9.42210	+	6.84556i	−0.846130	+	0.614749i
$125$	5.13936	+	3.73396i	0.459678	+	0.333976i
$126$	−0.557915	−	1.71709i	−0.0497030	−	0.152970i
$127$	−2.57579	−	7.92746i	−0.228564	−	0.703448i	−0.997910	−	0.0646158i	$-0.979418\pi$
$127$	−2.57579	−	7.92746i	−0.228564	−	0.703448i	0.769346	−	0.638832i	$-0.220582\pi$
$128$	−8.05830	−	5.85470i	−0.712260	−	0.517487i
$129$	5.90039	−	4.28688i	0.519500	−	0.377439i
$130$	3.58396	−	11.0303i	0.314334	−	0.967421i
$131$	7.97862			0.697095			0.348548	−	0.937291i	$-0.386675\pi$
$131$	7.97862			0.697095			0.348548	+	0.937291i	$0.386675\pi$
$132$	4.06839	−	0.949885i	0.354108	−	0.0826769i
$133$	−8.08270			−0.700859
$134$	−0.793731	+	2.44285i	−0.0685680	+	0.211030i
$135$	−2.24676	+	1.63237i	−0.193370	+	0.140492i
$136$	2.87822	+	2.09115i	0.246806	+	0.179315i
$137$	−3.19265	−	9.82597i	−0.272766	−	0.839489i	−0.989802	−	0.142452i	$-0.954501\pi$
$137$	−3.19265	−	9.82597i	−0.272766	−	0.839489i	0.717035	−	0.697037i	$-0.245499\pi$
$138$	−1.35577	−	4.17264i	−0.115411	−	0.355198i
$139$	4.48166	+	3.25612i	0.380130	+	0.276181i	0.761399	−	0.648284i	$-0.224513\pi$
$139$	4.48166	+	3.25612i	0.380130	+	0.276181i	−0.381269	+	0.924464i	$0.624513\pi$
$140$	2.83014	−	2.05622i	0.239191	−	0.173782i
$141$	0.141485	−	0.435446i	0.0119152	−	0.0366711i
$142$	1.00762			0.0845576
$143$	0.649696	−	7.64416i	0.0543303	−	0.639236i
$144$	−4.93258			−0.411048
$145$	−6.48584	+	19.9614i	−0.538620	+	1.65770i
$146$	14.1139	−	10.2544i	1.16808	−	0.848658i
$147$	−0.809017	−	0.587785i	−0.0667266	−	0.0484797i
$148$	4.35873	+	13.4148i	0.358285	+	1.10269i
$149$	6.79477	+	20.9122i	0.556649	+	1.71319i	0.691547	+	0.722331i	$0.256929\pi$
$149$	6.79477	+	20.9122i	0.556649	+	1.71319i	−0.134898	+	0.990859i	$0.543071\pi$
$150$	−3.96205	−	2.87860i	−0.323500	−	0.235037i
$151$	11.4604	−	8.32647i	0.932634	−	0.677598i	−0.0140021	−	0.999902i	$-0.504457\pi$
$151$	11.4604	−	8.32647i	0.932634	−	0.677598i	0.946636	+	0.322304i	$0.104457\pi$
$152$	−3.33855	+	10.2750i	−0.270792	+	0.833413i
$153$	2.66163			0.215180
$154$	3.91728	−	4.52893i	0.315663	−	0.364951i
$155$	25.6766			2.06239
$156$	0.900389	−	2.77111i	0.0720888	−	0.221867i
$157$	1.11561	−	0.810540i	0.0890356	−	0.0646881i	−0.542377	−	0.840135i	$-0.682476\pi$
$157$	1.11561	−	0.810540i	0.0890356	−	0.0646881i	0.631412	+	0.775447i	$0.282476\pi$
$158$	15.0738	+	10.9518i	1.19921	+	0.871274i
$159$	−1.60485	−	4.93922i	−0.127273	−	0.391706i
$160$	−5.34840	−	16.4607i	−0.422828	−	1.30133i
$161$	−1.96597	−	1.42836i	−0.154940	−	0.112570i
$162$	−1.46064	+	1.06122i	−0.114759	+	0.0833772i
$163$	−5.26590	+	16.2068i	−0.412457	+	1.26941i	0.502049	+	0.864839i	$0.332580\pi$
$163$	−5.26590	+	16.2068i	−0.412457	+	1.26941i	−0.914506	+	0.404573i	$0.867420\pi$
$164$	−0.377764			−0.0294984
$165$	−8.48743	−	3.57791i	−0.660746	−	0.278540i
$166$	−15.3658			−1.19261
$167$	−2.45988	+	7.57073i	−0.190351	+	0.585840i	−0.999999	−	0.00107492i	$-0.999658\pi$
$167$	−2.45988	+	7.57073i	−0.190351	+	0.585840i	0.809648	+	0.586915i	$0.199658\pi$
$168$	−1.08138	+	0.785667i	−0.0834301	+	0.0606155i
$169$	6.18860	+	4.49628i	0.476046	+	0.345868i
$170$	4.12396	+	12.6922i	0.316293	+	0.973450i
$171$	2.49769	+	7.68710i	0.191003	+	0.587847i
$172$	7.43246	+	5.40000i	0.566720	+	0.411746i
$173$	8.27626	−	6.01306i	0.629233	−	0.457164i	−0.226902	−	0.973918i	$-0.572860\pi$
$173$	8.27626	−	6.01306i	0.629233	−	0.457164i	0.856134	+	0.516753i	$0.172860\pi$
$174$	−4.21651	+	12.9771i	−0.319653	+	0.983791i
$175$	−2.71254			−0.205049
$176$	−8.46049	−	14.0019i	−0.637733	−	1.05543i
$177$	12.2826			0.923220
$178$	−0.873784	+	2.68923i	−0.0654928	+	0.201566i
$179$	−1.42152	+	1.03279i	−0.106249	+	0.0771945i	−0.639641	−	0.768674i	$-0.720917\pi$
$179$	−1.42152	+	1.03279i	−0.106249	+	0.0771945i	0.533392	+	0.845868i	$0.320917\pi$
$180$	−2.83014	−	2.05622i	−0.210946	−	0.153262i
$181$	3.86799	+	11.9044i	0.287505	+	0.884850i	0.985637	+	0.168880i	$0.0540151\pi$
$181$	3.86799	+	11.9044i	0.287505	+	0.884850i	−0.698131	+	0.715970i	$0.745985\pi$
$182$	−1.29052	−	3.97181i	−0.0956596	−	0.294410i
$183$	1.47069	+	1.06852i	0.108717	+	0.0789873i
$184$	−2.62782	+	1.90922i	−0.193725	+	0.140750i
$185$	9.60963	−	29.5754i	0.706514	−	2.17443i
$186$	16.6926			1.22396
$187$	4.56529	+	7.55546i	0.333847	+	0.552510i
$188$	0.576739			0.0420630
$189$	−0.309017	+	0.951057i	−0.0224777	+	0.0691792i
$190$	−32.7868	+	23.8210i	−2.37860	+	1.72816i
$191$	15.8631	+	11.5252i	1.14781	+	0.833936i	0.988189	−	0.153241i	$-0.0489712\pi$
$191$	15.8631	+	11.5252i	1.14781	+	0.833936i	0.159626	+	0.987178i	$0.448971\pi$
$192$	−0.428550	−	1.31894i	−0.0309279	−	0.0951864i
$193$	−0.189283	−	0.582553i	−0.0136249	−	0.0419331i	0.944013	−	0.329908i	$-0.107018\pi$
$193$	−0.189283	−	0.582553i	−0.0136249	−	0.0419331i	−0.957638	+	0.287975i	$0.907018\pi$
$194$	0.779781	+	0.566544i	0.0559850	+	0.0406755i
$195$	−5.19700	+	3.77584i	−0.372165	+	0.270394i
$196$	0.389255	−	1.19800i	0.0278039	−	0.0855717i
$197$	−13.5754			−0.967204			−0.483602	−	0.875288i	$-0.660672\pi$
$197$	−13.5754			−0.967204			−0.483602	+	0.875288i	$0.660672\pi$
$198$	−5.51777	−	2.32604i	−0.392131	−	0.165304i
$199$	4.17314			0.295826			0.147913	−	0.989000i	$-0.452744\pi$
$199$	4.17314			0.295826			0.147913	+	0.989000i	$0.452744\pi$
$200$	−1.12041	+	3.44828i	−0.0792253	+	0.243830i
$201$	1.15097	−	0.836227i	0.0811830	−	0.0589829i
$202$	7.76712	+	5.64314i	0.546493	+	0.397050i
$203$	2.33543	+	7.18773i	0.163915	+	0.504479i
$204$	1.03605	+	3.18864i	0.0725381	+	0.223249i
$205$	0.673790	+	0.489537i	0.0470596	+	0.0341908i
$206$	−27.1103	+	19.6968i	−1.88887	+	1.37234i
$207$	−0.750932	+	2.31113i	−0.0521934	+	0.160635i
$208$	−11.4096			−0.791113
$209$	−17.5370	+	20.2752i	−1.21306	+	1.40247i
$210$	−5.01400			−0.345999
$211$	3.29506	−	10.1411i	0.226841	−	0.698145i	−0.771258	−	0.636522i	$-0.780372\pi$
$211$	3.29506	−	10.1411i	0.226841	−	0.698145i	0.998099	−	0.0616230i	$-0.0196276\pi$
$212$	5.29251	−	3.84523i	0.363491	−	0.264092i
$213$	−0.451511	−	0.328042i	−0.0309371	−	0.0224771i
$214$	−5.25961	−	16.1874i	−0.359539	−	1.10655i
$215$	−6.25899	−	19.2632i	−0.426859	−	1.31374i
$216$	1.08138	+	0.785667i	0.0735784	+	0.0534578i
$217$	7.47990	−	5.43447i	0.507769	−	0.368916i
$218$	0.620403	−	1.90940i	0.0420190	−	0.129321i
$219$	−9.66283			−0.652954
$220$	0.982573	−	11.5607i	0.0662451	−	0.779422i
$221$	6.15663			0.414140
$222$	6.24732	−	19.2273i	0.419293	−	1.29045i
$223$	−2.94742	+	2.14143i	−0.197374	+	0.143400i	−0.682083	−	0.731275i	$-0.738926\pi$
$223$	−2.94742	+	2.14143i	−0.197374	+	0.143400i	0.484709	+	0.874676i	$0.338926\pi$
$224$	−5.04197	−	3.66321i	−0.336881	−	0.244758i
$225$	0.838222	+	2.57978i	0.0558815	+	0.171986i
$226$	−5.03503	−	15.4962i	−0.334926	−	1.03079i
$227$	−16.9311	−	12.3011i	−1.12375	−	0.816455i	−0.138980	−	0.990295i	$-0.544382\pi$
$227$	−16.9311	−	12.3011i	−1.12375	−	0.816455i	−0.984774	+	0.173840i	$0.944382\pi$
$228$	−8.23694	+	5.98449i	−0.545505	+	0.396332i
$229$	−5.10030	+	15.6971i	−0.337037	+	1.03729i	0.628672	+	0.777670i	$0.283599\pi$
$229$	−5.10030	+	15.6971i	−0.337037	+	1.03729i	−0.965710	+	0.259624i	$0.916401\pi$
$230$	−12.1844			−0.803414
$231$	−3.22976	+	0.754083i	−0.212503	+	0.0496150i
$232$	10.1019			0.663225
$233$	2.25175	−	6.93019i	0.147517	−	0.454012i	−0.849809	−	0.527091i	$-0.823283\pi$
$233$	2.25175	−	6.93019i	0.147517	−	0.454012i	0.997326	+	0.0730795i	$0.0232827\pi$
$234$	−3.37862	+	2.45471i	−0.220867	+	0.160470i
$235$	−1.02869	−	0.747386i	−0.0671043	−	0.0487541i
$236$	4.78108	+	14.7147i	0.311222	+	0.957842i
$237$	−3.18905	−	9.81489i	−0.207151	−	0.637545i
$238$	3.88768	+	2.82457i	0.252001	+	0.183089i
$239$	9.67797	−	7.03146i	0.626016	−	0.454827i	−0.229002	−	0.973426i	$-0.573546\pi$
$239$	9.67797	−	7.03146i	0.626016	−	0.454827i	0.855018	+	0.518599i	$0.173546\pi$
$240$	−4.23307	+	13.0280i	−0.273243	+	0.840957i
$241$	−4.39102			−0.282850			−0.141425	−	0.989949i	$-0.545168\pi$
$241$	−4.39102			−0.282850			−0.141425	+	0.989949i	$0.545168\pi$
$242$	−2.86140	−	19.6528i	−0.183937	−	1.26333i
$243$	1.00000			0.0641500
$244$	−0.707618	+	2.17782i	−0.0453006	+	0.139421i
$245$	−2.24676	+	1.63237i	−0.143540	+	0.104288i
$246$	0.438038	+	0.318253i	0.0279283	+	0.0202911i
$247$	5.77743	+	17.7811i	0.367609	+	1.13138i
$248$	−3.81892	−	11.7534i	−0.242501	−	0.746343i
$249$	6.88534	+	5.00250i	0.436341	+	0.317020i
$250$	9.27887	−	6.74149i	0.586847	−	0.426369i
$251$	−4.18412	+	12.8774i	−0.264099	+	0.812814i	0.727800	+	0.685789i	$0.240543\pi$
$251$	−4.18412	+	12.8774i	−0.264099	+	0.812814i	−0.991900	+	0.127025i	$0.959457\pi$
$252$	−1.25966			−0.0793509
$253$	−7.84854	+	1.83247i	−0.493433	+	0.115207i
$254$	−15.0492			−0.944271
$255$	2.28417	−	7.02995i	0.143040	−	0.440233i
$256$	−16.7928	+	12.2007i	−1.04955	+	0.762543i
$257$	−0.0983107	−	0.0714269i	−0.00613245	−	0.00445549i	0.584715	−	0.811239i	$-0.301206\pi$
$257$	−0.0983107	−	0.0714269i	−0.00613245	−	0.00445549i	−0.590847	+	0.806783i	$0.701206\pi$
$258$	−4.06903	−	12.5232i	−0.253327	−	0.779660i
$259$	−3.46025	−	10.6496i	−0.215010	−	0.661732i
$260$	−6.54643	−	4.75626i	−0.405992	−	0.294971i
$261$	6.11424	−	4.44226i	0.378462	−	0.274969i
$262$	4.45139	−	13.7000i	0.275008	−	0.846387i
$263$	5.88836			0.363092			0.181546	−	0.983382i	$-0.441890\pi$
$263$	5.88836			0.363092			0.181546	+	0.983382i	$0.441890\pi$
$264$	−0.375434	+	4.41726i	−0.0231064	+	0.271864i
$265$	−14.4228			−0.885988
$266$	−4.50946	+	13.8787i	−0.276493	+	0.850957i
$267$	1.26705	−	0.920565i	0.0775421	−	0.0563376i
$268$	1.44982	+	1.05336i	0.0885620	+	0.0643441i
$269$	−0.683407	−	2.10331i	−0.0416680	−	0.128241i	0.928059	−	0.372434i	$-0.121477\pi$
$269$	−0.683407	−	2.10331i	−0.0416680	−	0.128241i	−0.969727	+	0.244193i	$0.921477\pi$
$270$	1.54941	+	4.76860i	0.0942942	+	0.290208i
$271$	6.14391	+	4.46381i	0.373216	+	0.271157i	0.758543	−	0.651623i	$-0.225911\pi$
$271$	6.14391	+	4.46381i	0.373216	+	0.271157i	−0.385327	+	0.922780i	$0.625911\pi$
$272$	10.6213	−	7.71685i	0.644013	−	0.467903i
$273$	−0.714790	+	2.19990i	−0.0432611	+	0.133144i
$274$	−18.6533			−1.12688
$275$	−5.88539	+	6.80434i	−0.354902	+	0.410317i
$276$	−3.06105			−0.184254
$277$	−7.46239	+	22.9669i	−0.448372	+	1.37995i	0.430372	+	0.902652i	$0.358382\pi$
$277$	−7.46239	+	22.9669i	−0.448372	+	1.37995i	−0.878743	+	0.477294i	$0.841618\pi$
$278$	8.09143	−	5.87877i	0.485292	−	0.352585i
$279$	−7.47990	−	5.43447i	−0.447810	−	0.325353i
$280$	1.14710	+	3.53041i	0.0685523	+	0.210982i
$281$	8.43515	+	25.9607i	0.503199	+	1.54869i	0.803778	+	0.594929i	$0.202820\pi$
$281$	8.43515	+	25.9607i	0.503199	+	1.54869i	−0.300580	+	0.953757i	$0.597180\pi$
$282$	−0.668761	−	0.485883i	−0.0398241	−	0.0289339i
$283$	−20.7177	+	15.0523i	−1.23154	+	0.894768i	−0.997005	−	0.0773395i	$-0.975357\pi$
$283$	−20.7177	+	15.0523i	−1.23154	+	0.894768i	−0.234537	+	0.972107i	$0.575357\pi$
$284$	0.217243	−	0.668605i	0.0128910	−	0.0396744i
$285$	22.4468			1.32964
$286$	−12.7632	−	5.38038i	−0.754704	−	0.318148i
$287$	0.299894			0.0177022
$288$	−1.92586	+	5.92719i	−0.113483	+	0.349263i
$289$	8.02201	−	5.82833i	0.471883	−	0.342843i
$290$	30.6568	+	22.2735i	1.80023	+	1.30795i
$291$	−0.164972	−	0.507733i	−0.00967086	−	0.0297638i
$292$	−3.76131	−	11.5761i	−0.220114	−	0.677441i
$293$	9.46496	+	6.87670i	0.552949	+	0.401741i	0.828872	−	0.559439i	$-0.188983\pi$
$293$	9.46496	+	6.87670i	0.552949	+	0.401741i	−0.275923	+	0.961180i	$0.588983\pi$
$294$	−1.46064	+	1.06122i	−0.0851863	+	0.0618915i
$295$	10.5408	−	32.4412i	0.613708	−	1.88880i
$296$	−14.9674			−0.869960
$297$	1.71523	+	2.83866i	0.0995275	+	0.164716i
$298$	39.6989			2.29969
$299$	−1.73699	+	5.34590i	−0.100453	+	0.309161i
$300$	−2.76431	+	2.00839i	−0.159597	+	0.115954i
$301$	−5.90039	−	4.28688i	−0.340093	−	0.247092i
$302$	−7.90334	−	24.3240i	−0.454786	−	1.39969i
$303$	−1.64323	−	5.05735i	−0.0944012	−	0.290537i
$304$	32.2543	+	23.4341i	1.84991	+	1.34404i
$305$	4.08433	−	2.96744i	0.233868	−	0.169915i
$306$	1.48496	−	4.57024i	0.0848896	−	0.261263i
$307$	28.0637			1.60168			0.800839	−	0.598880i	$-0.204387\pi$
$307$	28.0637			1.60168			0.800839	+	0.598880i	$0.204387\pi$
$308$	−2.16060	−	3.57574i	−0.123111	−	0.203746i
$309$	18.5606			1.05587
$310$	14.3253	−	44.0889i	0.813625	−	2.50408i
$311$	−23.2299	+	16.8775i	−1.31724	+	0.957034i	−0.317283	+	0.948331i	$0.602770\pi$
$311$	−23.2299	+	16.8775i	−1.31724	+	0.957034i	−0.999962	+	0.00870323i	$0.997230\pi$
$312$	2.50134	+	1.81733i	0.141611	+	0.102886i
$313$	−9.10001	−	28.0070i	−0.514363	−	1.58305i	−0.784438	−	0.620207i	$-0.787048\pi$
$313$	−9.10001	−	28.0070i	−0.514363	−	1.58305i	0.270075	−	0.962839i	$-0.412952\pi$
$314$	−0.769350	−	2.36782i	−0.0434169	−	0.133624i
$315$	2.24676	+	1.63237i	0.126591	+	0.0919734i
$316$	10.5169	−	7.64099i	0.591623	−	0.429839i
$317$	−0.0103992	+	0.0320055i	−0.000584078	+	0.00179761i	−0.951348	−	0.308118i	$-0.900301\pi$
$317$	−0.0103992	+	0.0320055i	−0.000584078	+	0.00179761i	0.950764	+	0.309916i	$0.100301\pi$
$318$	−9.37644			−0.525805
$319$	23.0974	+	9.73679i	1.29321	+	0.545155i
$320$	−3.85139			−0.215299
$321$	−2.91318	+	8.96585i	−0.162598	+	0.500425i
$322$	−3.54946	+	2.57883i	−0.197804	+	0.143713i
$323$	−17.4045	−	12.6451i	−0.968411	−	0.703592i
$324$	0.389255	+	1.19800i	0.0216253	+	0.0665558i
$325$	1.93890	+	5.96732i	0.107551	+	0.331007i
$326$	24.8905	+	18.0840i	1.37856	+	1.00158i
$327$	−0.899629	+	0.653619i	−0.0497496	+	0.0361452i
$328$	0.123871	−	0.381236i	0.00683964	−	0.0210503i
$329$	−0.457855			−0.0252423
$330$	−10.8789	+	12.5775i	−0.598861	+	0.692368i
$331$	16.4575			0.904588			0.452294	−	0.891869i	$-0.350606\pi$
$331$	16.4575			0.904588			0.452294	+	0.891869i	$0.350606\pi$
$332$	−3.31285	+	10.1959i	−0.181816	+	0.559574i
$333$	−9.05906	+	6.58179i	−0.496434	+	0.360680i
$334$	11.6272	+	8.44765i	0.636211	+	0.462235i
$335$	−1.22092	−	3.75760i	−0.0667059	−	0.205300i
$336$	1.52425	+	4.69116i	0.0831547	+	0.255924i
$337$	−10.6970	−	7.77185i	−0.582704	−	0.423359i	0.256994	−	0.966413i	$-0.417268\pi$
$337$	−10.6970	−	7.77185i	−0.582704	−	0.423359i	−0.839698	+	0.543054i	$0.817268\pi$
$338$	11.1732	−	8.11781i	0.607743	−	0.441551i
$339$	−2.78880	+	8.58303i	−0.151467	+	0.466166i
$340$	9.31103			0.504962
$341$	2.59688	−	30.5542i	0.140629	−	1.65461i
$342$	14.5929			0.789095
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−7.88679	+	5.73009i	−0.425227	+	0.308946i
$345$	5.45978	+	3.96676i	0.293945	+	0.213563i
$346$	−5.70749	−	17.5658i	−0.306836	−	0.944345i
$347$	5.31337	+	16.3529i	0.285237	+	0.877868i	0.986328	+	0.164796i	$0.0526967\pi$
$347$	5.31337	+	16.3529i	0.285237	+	0.877868i	−0.701091	+	0.713072i	$0.747303\pi$
$348$	7.70184	+	5.59572i	0.412862	+	0.299962i
$349$	20.4635	−	14.8676i	1.09539	−	0.795846i	0.115087	−	0.993355i	$-0.463285\pi$
$349$	20.4635	−	14.8676i	1.09539	−	0.795846i	0.980301	+	0.197510i	$0.0632854\pi$
$350$	−1.51337	+	4.65767i	−0.0808930	+	0.248963i
$351$	2.31311			0.123465
$352$	−20.1286	+	4.69961i	−1.07286	+	0.250490i
$353$	6.60477			0.351536			0.175768	−	0.984432i	$-0.443759\pi$
$353$	6.60477			0.351536			0.175768	+	0.984432i	$0.443759\pi$
$354$	6.85267	−	21.0904i	0.364216	−	1.12094i
$355$	−1.25391	+	0.911022i	−0.0665508	+	0.0483520i
$356$	1.59605	+	1.15959i	0.0845902	+	0.0614584i
$357$	−0.822488	−	2.53136i	−0.0435307	−	0.133974i
$358$	0.980308	+	3.01708i	0.0518109	+	0.159458i
$359$	−29.4693	−	21.4107i	−1.55533	−	1.13001i	−0.939712	−	0.341967i	$-0.888907\pi$
$359$	−29.4693	−	21.4107i	−1.55533	−	1.13001i	−0.615617	−	0.788046i	$-0.711093\pi$
$360$	3.00314	−	2.18191i	0.158280	−	0.114997i
$361$	14.3168	−	44.0625i	0.753514	−	2.31908i
$362$	22.5990			1.18777
$363$	−5.11599	+	9.73789i	−0.268520	+	0.511107i
$364$	−2.91372			−0.152720
$365$	−8.29250	+	25.5217i	−0.434049	+	1.33587i
$366$	2.65526	−	1.92916i	0.138793	−	0.100839i
$367$	−7.92852	−	5.76041i	−0.413865	−	0.300691i	0.361299	−	0.932450i	$-0.382333\pi$
$367$	−7.92852	−	5.76041i	−0.413865	−	0.300691i	−0.775165	+	0.631759i	$0.782333\pi$
$368$	3.70403	+	11.3998i	0.193086	+	0.594258i
$369$	−0.0926725	−	0.285217i	−0.00482434	−	0.0148478i
$370$	−45.4222	−	33.0011i	−2.36139	−	1.71565i
$371$	−4.20155	+	3.05261i	−0.218134	+	0.158483i
$372$	3.59892	−	11.0763i	0.186595	−	0.574282i
$373$	11.7043			0.606027			0.303013	−	0.952986i	$-0.402007\pi$
$373$	11.7043			0.606027			0.303013	+	0.952986i	$0.402007\pi$
$374$	15.5204	−	3.62370i	0.802542	−	0.187377i
$375$	−6.35260			−0.328047
$376$	−0.189117	+	0.582041i	−0.00975294	+	0.0300165i
$377$	14.1429	−	10.2754i	0.728397	−	0.529212i
$378$	1.46064	+	1.06122i	0.0751273	+	0.0545832i
$379$	6.82381	+	21.0015i	0.350516	+	1.07878i	0.958564	+	0.284877i	$0.0919526\pi$
$379$	6.82381	+	21.0015i	0.350516	+	1.07878i	−0.608048	+	0.793900i	$0.708047\pi$
$380$	8.73755	+	26.8914i	0.448227	+	1.37950i
$381$	6.74350	+	4.89944i	0.345480	+	0.251006i
$382$	28.6401	−	20.8082i	1.46535	−	1.06464i
$383$	−6.73549	+	20.7297i	−0.344167	+	1.05924i	0.617861	+	0.786287i	$0.287999\pi$
$383$	−6.73549	+	20.7297i	−0.344167	+	1.05924i	−0.962028	+	0.272950i	$0.912001\pi$
$384$	9.96061			0.508300
$385$	−0.780033	+	9.17767i	−0.0397542	+	0.467737i
$386$	−1.10590			−0.0562887
$387$	−2.25375	+	6.93632i	−0.114564	+	0.352593i
$388$	0.544050	−	0.395275i	0.0276199	−	0.0200671i
$389$	15.0513	+	10.9354i	0.763130	+	0.554446i	0.899869	−	0.436161i	$-0.143662\pi$
$389$	15.0513	+	10.9354i	0.763130	+	0.554446i	−0.136739	+	0.990607i	$0.543662\pi$
$390$	3.58396	+	11.0303i	0.181481	+	0.558541i
$391$	−1.99870	−	6.15137i	−0.101079	−	0.311088i
$392$	1.08138	+	0.785667i	0.0546178	+	0.0396822i
$393$	−6.45484	+	4.68971i	−0.325603	+	0.236565i
$394$	−7.57390	+	23.3101i	−0.381567	+	1.17434i
$395$	−28.6601			−1.44205
$396$	−2.73307	+	3.15981i	−0.137342	+	0.158786i
$397$	−17.4492			−0.875750			−0.437875	−	0.899036i	$-0.644269\pi$
$397$	−17.4492			−0.875750			−0.437875	+	0.899036i	$0.644269\pi$
$398$	2.32826	−	7.16564i	0.116705	−	0.359181i
$399$	6.53904	−	4.75089i	0.327361	−	0.237842i
$400$	10.8245	+	7.86447i	0.541226	+	0.393224i
$401$	−11.5759	−	35.6268i	−0.578071	−	1.77912i	−0.625475	−	0.780244i	$-0.715095\pi$
$401$	−11.5759	−	35.6268i	−0.578071	−	1.77912i	0.0474042	−	0.998876i	$-0.484905\pi$
$402$	−0.793731	−	2.44285i	−0.0395877	−	0.121838i
$403$	−17.3018	−	12.5705i	−0.861865	−	0.626182i
$404$	5.41909	−	3.93720i	0.269610	−	0.195883i
$405$	0.858186	−	2.64122i	0.0426436	−	0.131243i
$406$	13.6449			0.677186
$407$	−34.2218	−	14.4263i	−1.69631	−	0.715087i
$408$	−3.55768			−0.176131
$409$	0.598752	−	1.84277i	0.0296064	−	0.0911191i	−0.935161	−	0.354222i	$-0.884746\pi$
$409$	0.598752	−	1.84277i	0.0296064	−	0.0911191i	0.964768	+	0.263103i	$0.0847458\pi$
$410$	1.21650	−	0.883836i	0.0600785	−	0.0436496i
$411$	8.35847	+	6.07278i	0.412293	+	0.299548i
$412$	7.22480	+	22.2356i	0.355940	+	1.09547i
$413$	−3.79555	−	11.6815i	−0.186767	−	0.574808i
$414$	3.54946	+	2.57883i	0.174446	+	0.126743i
$415$	19.1216	−	13.8927i	0.938643	−	0.681964i
$416$	−4.45473	+	13.7102i	−0.218411	+	0.672200i
$417$	−5.53964			−0.271277
$418$	25.0302	+	41.4244i	1.22427	+	2.02613i
$419$	−17.2226			−0.841378			−0.420689	−	0.907205i	$-0.638212\pi$
$419$	−17.2226			−0.841378			−0.420689	+	0.907205i	$0.638212\pi$
$420$	−1.08102	+	3.32703i	−0.0527483	+	0.162343i
$421$	−5.85585	+	4.25453i	−0.285397	+	0.207353i	−0.721268	−	0.692656i	$-0.756440\pi$
$421$	−5.85585	+	4.25453i	−0.285397	+	0.207353i	0.435871	+	0.900009i	$0.356440\pi$
$422$	−15.5749	−	11.3158i	−0.758172	−	0.550844i
$423$	0.141485	+	0.435446i	0.00687923	+	0.0211721i
$424$	2.14513	+	6.60204i	0.104177	+	0.320623i
$425$	−5.84092	−	4.24368i	−0.283326	−	0.205849i
$426$	−0.815182	+	0.592265i	−0.0394957	+	0.0286953i
$427$	0.561755	−	1.72890i	0.0271852	−	0.0836675i
$428$	−11.8751			−0.574004
$429$	3.96751	+	6.56613i	0.191553	+	0.317016i
$430$	−36.5685			−1.76349
$431$	−10.0294	+	30.8672i	−0.483098	+	1.48682i	0.351620	+	0.936143i	$0.385631\pi$
$431$	−10.0294	+	30.8672i	−0.483098	+	1.48682i	−0.834717	+	0.550678i	$0.814369\pi$
$432$	3.99054	−	2.89930i	0.191995	−	0.139492i
$433$	−18.4249	−	13.3865i	−0.885445	−	0.643313i	0.0492414	−	0.998787i	$-0.484320\pi$
$433$	−18.4249	−	13.3865i	−0.885445	−	0.643313i	−0.934686	+	0.355473i	$0.884320\pi$
$434$	−5.15830	−	15.8756i	−0.247606	−	0.762054i
$435$	−6.48584	−	19.9614i	−0.310972	−	0.957074i
$436$	−1.13322	−	0.823335i	−0.0542715	−	0.0394306i
$437$	15.8903	−	11.5450i	0.760137	−	0.552272i
$438$	−5.39104	+	16.5919i	−0.257594	+	0.792793i
$439$	30.4359			1.45263			0.726314	−	0.687363i	$-0.241232\pi$
$439$	30.4359			1.45263			0.726314	+	0.687363i	$0.241232\pi$
$440$	11.3448	+	4.78243i	0.540841	+	0.227994i
$441$	1.00000			0.0476190
$442$	3.43488	−	10.5715i	0.163381	−	0.502834i
$443$	16.1643	−	11.7440i	0.767988	−	0.557976i	−0.133362	−	0.991067i	$-0.542577\pi$
$443$	16.1643	−	11.7440i	0.767988	−	0.557976i	0.901350	+	0.433091i	$0.142577\pi$
$444$	−11.4113	−	8.29079i	−0.541556	−	0.393464i
$445$	−1.34405	−	4.13657i	−0.0637143	−	0.196092i
$446$	2.03260	+	6.25571i	0.0962465	+	0.296216i
$447$	−17.7889	−	12.9244i	−0.841388	−	0.611304i
$448$	−1.12196	+	0.815151i	−0.0530076	+	0.0385122i
$449$	3.65472	−	11.2481i	0.172477	−	0.530830i	−0.827032	−	0.562155i	$-0.809973\pi$
$449$	3.65472	−	11.2481i	0.172477	−	0.530830i	0.999509	+	0.0313247i	$0.00997259\pi$
$450$	4.89737			0.230864
$451$	0.650679	−	0.752277i	0.0306393	−	0.0354233i
$452$	−11.3681			−0.534708
$453$	−4.37748	+	13.4725i	−0.205672	+	0.632994i
$454$	−30.5682	+	22.2091i	−1.43464	+	1.04233i
$455$	5.19700	+	3.77584i	0.243639	+	0.177014i
$456$	−3.33855	−	10.2750i	−0.156342	−	0.481171i
$457$	−0.606598	−	1.86692i	−0.0283754	−	0.0873306i	0.935866	−	0.352356i	$-0.114620\pi$
$457$	−0.606598	−	1.86692i	−0.0283754	−	0.0873306i	−0.964241	+	0.265026i	$0.914620\pi$
$458$	24.1078	+	17.5153i	1.12648	+	0.818437i
$459$	−2.15330	+	1.56446i	−0.100507	+	0.0730230i
$460$	−2.62695	+	8.08492i	−0.122482	+	0.376961i
$461$	−15.5498			−0.724226			−0.362113	−	0.932134i	$-0.617945\pi$
$461$	−15.5498			−0.724226			−0.362113	+	0.932134i	$0.617945\pi$
$462$	−0.507107	+	5.96649i	−0.0235928	+	0.277586i
$463$	−3.73913			−0.173772			−0.0868860	−	0.996218i	$-0.527692\pi$
$463$	−3.73913			−0.173772			−0.0868860	+	0.996218i	$0.527692\pi$
$464$	11.5197	−	35.4540i	0.534789	−	1.64591i
$465$	−20.7728	+	15.0923i	−0.963315	+	0.699889i
$466$	−10.6434	−	7.73291i	−0.493048	−	0.358220i
$467$	3.15102	+	9.69785i	0.145812	+	0.448763i	0.997115	−	0.0759121i	$-0.0241868\pi$
$467$	3.15102	+	9.69785i	0.145812	+	0.448763i	−0.851303	+	0.524675i	$0.824187\pi$
$468$	0.900389	+	2.77111i	0.0416205	+	0.128095i
$469$	−1.15097	−	0.836227i	−0.0531467	−	0.0386134i
$470$	−1.85725	+	1.34937i	−0.0856685	+	0.0622418i
$471$	−0.426126	+	1.31148i	−0.0196349	+	0.0604299i
$472$	−16.4177			−0.755684
$473$	−23.5556	+	5.49974i	−1.08309	+	0.252878i
$474$	−18.6322			−0.855807
$475$	6.77510	−	20.8516i	0.310863	−	0.956737i
$476$	2.71242	−	1.97069i	0.124323	−	0.0903263i
$477$	4.20155	+	3.05261i	0.192376	+	0.139769i
$478$	−6.67413	−	20.5409i	−0.305268	−	0.939518i
$479$	6.99712	+	21.5349i	0.319706	+	0.983955i	0.973774	+	0.227519i	$0.0730613\pi$
$479$	6.99712	+	21.5349i	0.319706	+	0.983955i	−0.654067	+	0.756436i	$0.726939\pi$
$480$	14.0023	+	10.1733i	0.639115	+	0.464344i
$481$	−20.9546	+	15.2244i	−0.955447	+	0.694173i
$482$	−2.44982	+	7.53976i	−0.111586	+	0.343427i
$483$	2.43007			0.110572
$484$	−13.6575	−	2.33846i	−0.620794	−	0.106293i
$485$	−1.48261			−0.0673220
$486$	0.557915	−	1.71709i	0.0253075	−	0.0778886i
$487$	18.6947	−	13.5825i	0.847137	−	0.615481i	−0.0772181	−	0.997014i	$-0.524604\pi$
$487$	18.6947	−	13.5825i	0.847137	−	0.615481i	0.924355	+	0.381533i	$0.124604\pi$
$488$	−1.96581	−	1.42824i	−0.0889880	−	0.0646536i
$489$	−5.26590	−	16.2068i	−0.238132	−	0.732896i
$490$	1.54941	+	4.76860i	0.0699953	+	0.215423i
$491$	26.5190	+	19.2672i	1.19678	+	0.869515i	0.993965	−	0.109701i	$-0.0349894\pi$
$491$	26.5190	+	19.2672i	1.19678	+	0.869515i	0.202820	+	0.979216i	$0.434989\pi$
$492$	0.305617	−	0.222044i	0.0137783	−	0.0100105i
$493$	−6.21605	+	19.1310i	−0.279957	+	0.861619i
$494$	33.7550			1.51871
$495$	8.96952	−	2.09420i	0.403150	−	0.0941272i
$496$	−45.6050			−2.04772
$497$	−0.172462	+	0.530784i	−0.00773598	+	0.0238089i
$498$	12.4312	−	9.03176i	0.557053	−	0.404723i
$499$	−14.3810	−	10.4484i	−0.643781	−	0.467734i	0.217366	−	0.976090i	$-0.430253\pi$
$499$	−14.3810	−	10.4484i	−0.643781	−	0.467734i	−0.861147	+	0.508356i	$0.830253\pi$
$500$	−2.47278	−	7.61044i	−0.110586	−	0.340349i
$501$	−2.45988	−	7.57073i	−0.109899	−	0.338235i
$502$	19.7772	+	14.3690i	0.882700	+	0.641319i
$503$	12.1364	−	8.81760i	0.541134	−	0.393157i	−0.283372	−	0.959010i	$-0.591453\pi$
$503$	12.1364	−	8.81760i	0.541134	−	0.393157i	0.824506	+	0.565853i	$0.191453\pi$
$504$	0.413049	−	1.27124i	0.0183987	−	0.0566253i
$505$	−14.7678			−0.657158
$506$	−1.23231	+	14.4990i	−0.0547827	+	0.644559i
$507$	−7.64953			−0.339727
$508$	−3.24460	+	9.98587i	−0.143956	+	0.443051i
$509$	19.7324	−	14.3364i	0.874623	−	0.635451i	−0.0572004	−	0.998363i	$-0.518217\pi$
$509$	19.7324	−	14.3364i	0.874623	−	0.635451i	0.931823	+	0.362912i	$0.118217\pi$
$510$	−10.7967	−	7.84423i	−0.478084	−	0.347348i
$511$	2.98598	+	9.18990i	0.132092	+	0.406537i
$512$	5.42467	+	16.6954i	0.239739	+	0.737840i
$513$	−6.53904	−	4.75089i	−0.288706	−	0.209757i
$514$	−0.177495	+	0.128958i	−0.00782898	+	0.00568809i
$515$	15.9284	−	49.0226i	0.701890	−	2.16019i
$516$	−9.18702			−0.404436
$517$	−0.993404	+	1.14852i	−0.0436898	+	0.0505116i
$518$	−20.2168			−0.888273
$519$	−3.16125	+	9.72933i	−0.138764	+	0.427070i
$520$	6.94660	−	5.04700i	0.304628	−	0.221326i
$521$	−6.53026	−	4.74452i	−0.286096	−	0.207861i	0.435476	−	0.900200i	$-0.356580\pi$
$521$	−6.53026	−	4.74452i	−0.286096	−	0.207861i	−0.721572	+	0.692339i	$0.756580\pi$
$522$	−4.21651	−	12.9771i	−0.184552	−	0.567992i
$523$	−0.114411	−	0.352121i	−0.00500285	−	0.0153972i	0.948524	−	0.316705i	$-0.102577\pi$
$523$	−0.114411	−	0.352121i	−0.00500285	−	0.0153972i	−0.953527	+	0.301308i	$0.902577\pi$
$524$	−8.13087	−	5.90742i	−0.355199	−	0.258067i
$525$	2.19449	−	1.59439i	0.0957756	−	0.0695850i
$526$	3.28521	−	10.1108i	0.143242	−	0.440853i
$527$	24.6085			1.07196
$528$	15.0748	+	6.35484i	0.656047	+	0.276559i
$529$	−17.0948			−0.743251
$530$	−8.04673	+	24.7653i	−0.349527	+	1.07573i
$531$	−9.93687	+	7.21956i	−0.431223	+	0.313302i
$532$	8.23694	+	5.98449i	0.357117	+	0.259460i
$533$	−0.214362	−	0.659737i	−0.00928503	−	0.0285764i
$534$	−0.873784	−	2.68923i	−0.0378123	−	0.116374i
$535$	21.1808	+	15.3887i	0.915724	+	0.665313i
$536$	−1.53845	+	1.11775i	−0.0664508	+	0.0482793i
$537$	0.542971	−	1.67109i	0.0234309	−	0.0721130i
$538$	−3.99285			−0.172144
$539$	1.71523	+	2.83866i	0.0738800	+	0.122270i
$540$	3.49825			0.150541
$541$	−0.917614	+	2.82413i	−0.0394513	+	0.121419i	−0.968843	−	0.247677i	$-0.920333\pi$
$541$	−0.917614	+	2.82413i	−0.0394513	+	0.121419i	0.929391	+	0.369096i	$0.120333\pi$
$542$	11.0925	−	8.05920i	0.476465	−	0.346172i
$543$	−10.1265	−	7.35735i	−0.434571	−	0.315734i
$544$	−5.12593	−	15.7760i	−0.219772	−	0.676389i
$545$	0.954305	+	2.93705i	0.0408779	+	0.125809i
$546$	3.37862	+	2.45471i	0.144592	+	0.105052i
$547$	−13.4823	+	9.79546i	−0.576461	+	0.418824i	−0.837447	−	0.546519i	$-0.815953\pi$
$547$	−13.4823	+	9.79546i	−0.576461	+	0.418824i	0.260985	+	0.965343i	$0.415953\pi$
$548$	−4.02164	+	12.3773i	−0.171796	+	0.528734i
$549$	−1.81788			−0.0775851
$550$	8.40010	+	13.9020i	0.358181	+	0.592782i
$551$	−61.0860			−2.60235
$552$	1.00374	−	3.08919i	0.0427219	−	0.131485i
$553$	−8.34904	+	6.06593i	−0.355037	+	0.257950i
$554$	35.2727	+	25.6271i	1.49860	+	1.08879i
$555$	9.60963	+	29.5754i	0.407906	+	1.25541i
$556$	−2.15633	−	6.63651i	−0.0914489	−	0.281451i
$557$	24.3971	+	17.7255i	1.03374	+	0.751055i	0.969053	−	0.246851i	$-0.0793958\pi$
$557$	24.3971	+	17.7255i	1.03374	+	0.751055i	0.0646849	+	0.997906i	$0.479396\pi$
$558$	−13.5046	+	9.81167i	−0.571695	+	0.415361i
$559$	−5.21316	+	16.0445i	−0.220493	+	0.678609i
$560$	13.6985			0.578867
$561$	−8.13438	−	3.42908i	−0.343434	−	0.144776i
$562$	49.2829			2.07887
$563$	−1.30514	+	4.01682i	−0.0550053	+	0.169289i	−0.974785	−	0.223146i	$-0.928367\pi$
$563$	−1.30514	+	4.01682i	−0.0550053	+	0.169289i	0.919780	+	0.392435i	$0.128367\pi$
$564$	−0.466592	+	0.338999i	−0.0196471	+	0.0142744i
$565$	20.2764	+	14.7317i	0.853034	+	0.619766i
$566$	14.2874	+	43.9721i	0.600544	+	1.84828i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	0.603515	+	0.438480i	0.0253229	+	0.0183982i
$569$	−20.4047	+	14.8249i	−0.855410	+	0.621492i	−0.926632	−	0.375969i	$-0.877310\pi$
$569$	−20.4047	+	14.8249i	−0.855410	+	0.621492i	0.0712223	+	0.997460i	$0.477310\pi$
$570$	12.5234	−	38.5432i	0.524549	−	1.61440i
$571$	−42.9041			−1.79548			−0.897740	−	0.440525i	$-0.854792\pi$
$571$	−42.9041			−1.79548			−0.897740	+	0.440525i	$0.854792\pi$
$572$	−6.32188	+	7.30899i	−0.264331	+	0.305604i
$573$	−19.6079			−0.819131
$574$	0.167316	−	0.514945i	0.00698362	−	0.0214934i
$575$	5.33277	−	3.87448i	0.222392	−	0.161577i
$576$	1.12196	+	0.815151i	0.0467483	+	0.0339646i
$577$	−8.91078	−	27.4246i	−0.370961	−	1.14170i	−0.946164	−	0.323689i	$-0.895077\pi$
$577$	−8.91078	−	27.4246i	−0.370961	−	1.14170i	0.575203	−	0.818011i	$-0.304923\pi$
$578$	−5.53215	−	17.0262i	−0.230107	−	0.708196i
$579$	0.495549	+	0.360038i	0.0205943	+	0.0149627i
$580$	21.3891	−	15.5401i	0.888136	−	0.645269i
$581$	2.62997	−	8.09421i	0.109109	−	0.335804i
$582$	−0.963862			−0.0399534
$583$	−1.45870	+	17.1627i	−0.0604132	+	0.710806i
$584$	12.9159			0.534463
$585$	1.98508	−	6.10944i	0.0820728	−	0.252594i
$586$	17.0885	−	12.4155i	0.705921	−	0.512881i
$587$	30.5613	+	22.2041i	1.26140	+	0.916461i	0.998826	−	0.0484511i	$-0.0154285\pi$
$587$	30.5613	+	22.2041i	1.26140	+	0.916461i	0.262574	+	0.964912i	$0.415429\pi$
$588$	0.389255	+	1.19800i	0.0160526	+	0.0494048i
$589$	23.0928	+	71.0724i	0.951523	+	2.92849i
$590$	−49.8235	−	36.1989i	−2.05120	−	1.49028i
$591$	10.9827	−	7.97939i	0.451768	−	0.328228i
$592$	−17.0680	+	52.5298i	−0.701489	+	2.15896i
$593$	−10.8394			−0.445119			−0.222559	−	0.974919i	$-0.571441\pi$
$593$	−10.8394			−0.445119			−0.222559	+	0.974919i	$0.571441\pi$
$594$	5.83118	−	1.36146i	0.239256	−	0.0558614i
$595$	−7.39173			−0.303031
$596$	8.55907	−	26.3421i	0.350593	−	1.07902i
$597$	−3.37614	+	2.45291i	−0.138176	+	0.100391i
$598$	8.21028	+	5.96512i	0.335743	+	0.243932i
$599$	13.4183	+	41.2973i	0.548257	+	1.68736i	0.713119	+	0.701043i	$0.247282\pi$
$599$	13.4183	+	41.2973i	0.548257	+	1.68736i	−0.164862	+	0.986317i	$0.552718\pi$
$600$	−1.12041	−	3.44828i	−0.0457407	−	0.140776i
$601$	−0.385408	−	0.280015i	−0.0157211	−	0.0114221i	0.579897	−	0.814690i	$-0.303093\pi$
$601$	−0.385408	−	0.280015i	−0.0157211	−	0.0114221i	−0.595618	+	0.803268i	$0.703093\pi$
$602$	−10.6529	+	7.73976i	−0.434178	+	0.315449i
$603$	−0.439630	+	1.35304i	−0.0179031	+	0.0551002i
$604$	−17.8441			−0.726065
$605$	21.3295	+	21.8694i	0.867167	+	0.889118i
$606$	−9.60069			−0.390001
$607$	−1.51616	+	4.66625i	−0.0615389	+	0.189397i	−0.977100	−	0.212783i	$-0.931747\pi$
$607$	−1.51616	+	4.66625i	−0.0615389	+	0.189397i	0.915561	+	0.402180i	$0.131747\pi$
$608$	40.7527	−	29.6086i	1.65274	−	1.20079i
$609$	−6.11424	−	4.44226i	−0.247762	−	0.180009i
$610$	−2.81664	−	8.66873i	−0.114042	−	0.350987i
$611$	0.327270	+	1.00723i	0.0132399	+	0.0407483i
$612$	−2.71242	−	1.97069i	−0.109643	−	0.0796603i
$613$	4.97234	−	3.61262i	0.200831	−	0.145912i	−0.482825	−	0.875717i	$-0.660389\pi$
$613$	4.97234	−	3.61262i	0.200831	−	0.145912i	0.683655	+	0.729805i	$0.260389\pi$
$614$	15.6571	−	48.1877i	0.631871	−	1.94470i
$615$	−0.832851			−0.0335838
$616$	4.31708	−	1.00795i	0.173940	−	0.0406114i
$617$	−11.2456			−0.452730			−0.226365	−	0.974043i	$-0.572684\pi$
$617$	−11.2456			−0.452730			−0.226365	+	0.974043i	$0.572684\pi$
$618$	10.3552	−	31.8701i	0.416548	−	1.28200i
$619$	27.0033	−	19.6191i	1.08535	−	0.788556i	0.106746	−	0.994286i	$-0.465957\pi$
$619$	27.0033	−	19.6191i	1.08535	−	0.788556i	0.978609	+	0.205730i	$0.0659569\pi$
$620$	−26.1666	−	19.0111i	−1.05087	−	0.763505i
$621$	−0.750932	−	2.31113i	−0.0301339	−	0.0927425i
$622$	16.0198	+	49.3039i	0.642336	+	1.97691i
$623$	−1.26705	−	0.920565i	−0.0507632	−	0.0368816i
$624$	9.23056	−	6.70639i	0.369518	−	0.268470i
$625$	−9.64282	+	29.6776i	−0.385713	+	1.18710i
$626$	−53.1674			−2.12500
$627$	2.27023	−	26.7110i	0.0906644	−	1.06673i
$628$	−1.73703			−0.0693151
$629$	9.20990	−	28.3452i	0.367223	−	1.13020i
$630$	4.05641	−	2.94716i	0.161611	−	0.117418i
$631$	−29.9441	−	21.7557i	−1.19206	−	0.866079i	−0.198576	−	0.980085i	$-0.563632\pi$
$631$	−29.9441	−	21.7557i	−1.19206	−	0.866079i	−0.993480	+	0.114006i	$0.963632\pi$
$632$	4.26266	+	13.1191i	0.169560	+	0.521851i
$633$	3.29506	+	10.1411i	0.130967	+	0.403074i
$634$	0.0491543	+	0.0357127i	0.00195217	+	0.00141833i
$635$	18.7277	−	13.6065i	0.743185	−	0.539956i
$636$	−2.02156	+	6.22172i	−0.0801600	+	0.246707i
$637$	2.31311			0.0916487
$638$	29.6053	−	34.2279i	1.17208	−	1.35510i
$639$	0.558099			0.0220781
$640$	8.54805	−	26.3082i	0.337891	−	1.03992i
$641$	14.5767	−	10.5906i	0.575747	−	0.418305i	−0.261441	−	0.965219i	$-0.584198\pi$
$641$	14.5767	−	10.5906i	0.575747	−	0.418305i	0.837188	+	0.546915i	$0.184198\pi$
$642$	13.7698	+	10.0044i	0.543452	+	0.394841i
$643$	2.13099	+	6.55851i	0.0840380	+	0.258643i	0.984242	−	0.176826i	$-0.0565829\pi$
$643$	2.13099	+	6.55851i	0.0840380	+	0.258643i	−0.900204	+	0.435468i	$0.856583\pi$
$644$	0.945916	+	2.91123i	0.0372743	+	0.114719i
$645$	16.3862	+	11.9053i	0.645208	+	0.468771i
$646$	−31.4230	+	22.8301i	−1.23632	+	0.898239i
$647$	11.6338	−	35.8051i	0.457371	−	1.40764i	−0.410958	−	0.911654i	$-0.634806\pi$
$647$	11.6338	−	35.8051i	0.457371	−	1.40764i	0.868329	−	0.495988i	$-0.165194\pi$
$648$	−1.33666			−0.0525088
$649$	−37.5379	−	15.8242i	−1.47349	−	0.621155i
$650$	11.3281			0.444326
$651$	−2.85707	+	8.79315i	−0.111977	+	0.344631i
$652$	17.3660	−	12.6171i	0.680105	−	0.494125i
$653$	5.64304	+	4.09991i	0.220829	+	0.160442i	0.692700	−	0.721226i	$-0.256421\pi$
$653$	5.64304	+	4.09991i	0.220829	+	0.160442i	−0.471871	+	0.881668i	$0.656421\pi$
$654$	0.620403	+	1.90940i	0.0242597	+	0.0746636i
$655$	6.84713	+	21.0733i	0.267540	+	0.823402i
$656$	−1.19674	−	0.869483i	−0.0467249	−	0.0339476i
$657$	7.81740	−	5.67967i	0.304986	−	0.221585i
$658$	−0.255444	+	0.786176i	−0.00995824	+	0.0306483i
$659$	−0.567182			−0.0220943			−0.0110471	−	0.999939i	$-0.503516\pi$
$659$	−0.567182			−0.0220943			−0.0110471	+	0.999939i	$0.503516\pi$
$660$	6.00029	+	9.93034i	0.233561	+	0.386538i
$661$	0.107429			0.00417852			0.00208926	−	0.999998i	$-0.499335\pi$
$661$	0.107429			0.00417852			0.00208926	+	0.999998i	$0.499335\pi$
$662$	9.18191	−	28.2590i	0.356865	−	1.09832i
$663$	−4.98082	+	3.61878i	−0.193439	+	0.140542i
$664$	−9.20334	−	6.68661i	−0.357159	−	0.259491i
$665$	−6.93646	−	21.3482i	−0.268984	−	0.827848i
$666$	6.24732	+	19.2273i	0.242079	+	0.745042i
$667$	−14.8580	−	10.7950i	−0.575305	−	0.417984i
$668$	8.11224	−	5.89389i	0.313872	−	0.228041i
$669$	1.12581	−	3.46490i	0.0435265	−	0.133961i
$670$	−7.13329			−0.275583
$671$	−3.11807	−	5.16034i	−0.120372	−	0.199213i
$672$	6.23222			0.240413
$673$	6.23363	−	19.1851i	0.240289	−	0.739533i	−0.756087	−	0.654471i	$-0.772891\pi$
$673$	6.23363	−	19.1851i	0.240289	−	0.739533i	0.996376	−	0.0850616i	$-0.0271087\pi$
$674$	−19.3130	+	14.0317i	−0.743908	+	0.540481i
$675$	−2.19449	−	1.59439i	−0.0844661	−	0.0613682i
$676$	−2.97762	−	9.16416i	−0.114524	−	0.352468i
$677$	3.11090	+	9.57438i	0.119562	+	0.367973i	0.992871	−	0.119193i	$-0.0380307\pi$
$677$	3.11090	+	9.57438i	0.119562	+	0.367973i	−0.873309	+	0.487166i	$0.838031\pi$
$678$	13.1819	+	9.57721i	0.506248	+	0.367810i
$679$	−0.431904	+	0.313796i	−0.0165749	+	0.0120424i
$680$	−3.05315	+	9.39662i	−0.117083	+	0.360344i
$681$	20.9279			0.801961
$682$	−51.0154	−	21.5058i	−1.95348	−	0.823498i
$683$	−32.4580			−1.24197			−0.620985	−	0.783822i	$-0.713267\pi$
$683$	−32.4580			−1.24197			−0.620985	+	0.783822i	$0.713267\pi$
$684$	3.14623	−	9.68310i	0.120299	−	0.370243i
$685$	23.2127	−	16.8650i	0.886911	−	0.644379i
$686$	1.46064	+	1.06122i	0.0557675	+	0.0405175i
$687$	−5.10030	−	15.6971i	−0.194589	−	0.598882i
$688$	11.1168	+	34.2140i	0.423824	+	1.30439i
$689$	9.71865	+	7.06101i	0.370251	+	0.269003i
$690$	9.85736	−	7.16179i	0.375263	−	0.272645i
$691$	14.5569	−	44.8015i	0.553770	−	1.70433i	−0.145401	−	0.989373i	$-0.546447\pi$
$691$	14.5569	−	44.8015i	0.553770	−	1.70433i	0.699171	−	0.714955i	$-0.253553\pi$
$692$	−12.8863			−0.489864
$693$	2.16969	−	2.50847i	0.0824198	−	0.0952890i
$694$	31.0437			1.17840
$695$	−4.75404	+	14.6314i	−0.180331	+	0.555002i
$696$	−8.17264	+	5.93777i	−0.309783	+	0.225071i
$697$	0.645763	+	0.469174i	0.0244600	+	0.0177712i
$698$	−14.1121	−	43.4325i	−0.534150	−	1.64395i
$699$	2.25175	+	6.93019i	0.0851692	+	0.262124i
$700$	2.76431	+	2.00839i	0.104481	+	0.0759099i
$701$	−16.5443	+	12.0201i	−0.624868	+	0.453993i	−0.854618	−	0.519256i	$-0.826209\pi$
$701$	−16.5443	+	12.0201i	−0.624868	+	0.453993i	0.229751	+	0.973250i	$0.426209\pi$
$702$	1.29052	−	3.97181i	0.0487075	−	0.149906i
$703$	90.5070			3.41353
$704$	−0.389523	+	4.58303i	−0.0146807	+	0.172729i
$705$	1.27153			0.0478886
$706$	3.68490	−	11.3410i	0.138683	−	0.426823i
$707$	−4.30204	+	3.12561i	−0.161795	+	0.117551i
$708$	−12.5170	−	9.09416i	−0.470419	−	0.341779i
$709$	−3.07362	−	9.45961i	−0.115432	−	0.355263i	0.876605	−	0.481211i	$-0.159803\pi$
$709$	−3.07362	−	9.45961i	−0.115432	−	0.355263i	−0.992037	+	0.125948i	$0.959803\pi$
$710$	0.864725	+	2.66135i	0.0324526	+	0.0998787i
$711$	8.34904	+	6.06593i	0.313114	+	0.227490i
$712$	−1.69361	+	1.23048i	−0.0634706	+	0.0461141i
$713$	−6.94287	+	21.3680i	−0.260012	+	0.800236i
$714$	−4.80544			−0.179839
$715$	20.7475	−	4.84411i	0.775912	−	0.181159i
$716$	2.21333			0.0827160
$717$	−3.69666	+	11.3771i	−0.138054	+	0.424887i
$718$	−53.2053	+	38.6559i	−1.98561	+	1.44263i
$719$	−5.53121	−	4.01866i	−0.206280	−	0.149871i	0.479849	−	0.877351i	$-0.340691\pi$
$719$	−5.53121	−	4.01866i	−0.206280	−	0.149871i	−0.686129	+	0.727480i	$0.740691\pi$
$720$	−4.23307	−	13.0280i	−0.157757	−	0.485527i
$721$	−5.73553	−	17.6522i	−0.213602	−	0.657401i
$722$	−67.6715	−	49.1662i	−2.51847	−	1.82978i
$723$	3.55241	−	2.58098i	0.132116	−	0.0959876i
$724$	4.87233	−	14.9955i	0.181079	−	0.557303i
$725$	−20.5004			−0.761365
$726$	13.8665	+	14.2175i	0.514635	+	0.527662i
$727$	49.3919			1.83184			0.915922	−	0.401357i	$-0.131461\pi$
$727$	49.3919			1.83184			0.915922	+	0.401357i	$0.131461\pi$
$728$	0.955428	−	2.94051i	0.0354105	−	0.108982i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	39.1965	+	28.4779i	1.45073	+	1.05401i
$731$	−5.99863	−	18.4619i	−0.221867	−	0.682838i
$732$	−0.707618	−	2.17782i	−0.0261543	−	0.0804946i
$733$	−32.1408	−	23.3516i	−1.18715	−	0.862512i	−0.194186	−	0.980965i	$-0.562207\pi$
$733$	−32.1408	−	23.3516i	−1.18715	−	0.862512i	−0.992960	+	0.118453i	$0.962207\pi$
$734$	−14.3146	+	10.4001i	−0.528360	+	0.383876i
$735$	0.858186	−	2.64122i	0.0316547	−	0.0974230i
$736$	15.1447			0.558242
$737$	−4.59490	+	1.07281i	−0.169255	+	0.0395176i
$738$	−0.541445			−0.0199309
$739$	9.63869	−	29.6648i	0.354565	−	1.09124i	−0.601696	−	0.798725i	$-0.705508\pi$
$739$	9.63869	−	29.6648i	0.354565	−	1.09124i	0.956261	−	0.292514i	$-0.0944918\pi$
$740$	−31.6909	+	23.0248i	−1.16498	+	0.846407i
$741$	−15.1255	−	10.9893i	−0.555650	−	0.403703i
$742$	2.89748	+	8.91752i	0.106370	+	0.327373i
$743$	9.54988	+	29.3915i	0.350351	+	1.07827i	0.958656	+	0.284567i	$0.0918497\pi$
$743$	9.54988	+	29.3915i	0.350351	+	1.07827i	−0.608305	+	0.793703i	$0.708150\pi$
$744$	9.99805	+	7.26401i	0.366546	+	0.266312i
$745$	−49.4025	+	35.8930i	−1.80997	+	1.31502i
$746$	6.53002	−	20.0973i	0.239081	−	0.735816i
$747$	−8.51075			−0.311392
$748$	0.941701	−	11.0798i	0.0344320	−	0.405118i
$749$	9.42725			0.344464
$750$	−3.54421	+	10.9080i	−0.129416	+	0.398303i
$751$	13.9132	−	10.1085i	0.507698	−	0.368864i	−0.304252	−	0.952592i	$-0.598406\pi$
$751$	13.9132	−	10.1085i	0.507698	−	0.368864i	0.811950	+	0.583727i	$0.198406\pi$
$752$	1.82709	+	1.32746i	0.0666270	+	0.0484073i
$753$	−4.18412	−	12.8774i	−0.152478	−	0.469278i
$754$	−9.75325	−	30.0174i	−0.355193	−	1.09317i
$755$	31.8272	+	23.1238i	1.15831	+	0.841562i
$756$	1.01908	−	0.740407i	0.0370637	−	0.0269283i
$757$	1.75367	−	5.39725i	0.0637383	−	0.196166i	−0.914116	−	0.405452i	$-0.867114\pi$
$757$	1.75367	−	5.39725i	0.0637383	−	0.196166i	0.977854	+	0.209286i	$0.0671140\pi$
$758$	39.8686			1.44809
$759$	5.27250	−	6.09576i	0.191380	−	0.221262i
$760$	−30.0037			−1.08835
$761$	2.69915	−	8.30713i	0.0978441	−	0.301133i	−0.890140	−	0.455686i	$-0.849394\pi$
$761$	2.69915	−	8.30713i	0.0978441	−	0.301133i	0.987984	+	0.154553i	$0.0493938\pi$
$762$	12.1751	−	8.84570i	0.441056	−	0.320446i
$763$	0.899629	+	0.653619i	0.0325688	+	0.0236626i
$764$	−7.63247	−	23.4903i	−0.276133	−	0.849850i
$765$	2.28417	+	7.02995i	0.0825843	+	0.254168i
$766$	31.8368	+	23.1308i	1.15031	+	0.835751i
$767$	−22.9851	+	16.6996i	−0.829942	+	0.602988i
$768$	6.41428	−	19.7411i	0.231455	−	0.712346i
$769$	7.76277			0.279933			0.139966	−	0.990156i	$-0.455301\pi$
$769$	7.76277			0.279933			0.139966	+	0.990156i	$0.455301\pi$
$770$	15.3237	+	6.45974i	0.552226	+	0.232793i
$771$	0.121519			0.00437639
$772$	−0.238431	+	0.733816i	−0.00858133	+	0.0264106i
$773$	−26.6837	+	19.3869i	−0.959747	+	0.697297i	−0.953092	−	0.302681i	$-0.902118\pi$
$773$	−26.6837	+	19.3869i	−0.959747	+	0.697297i	−0.00665502	+	0.999978i	$0.502118\pi$
$774$	10.6529	+	7.73976i	0.382909	+	0.278200i
$775$	7.74992	+	23.8518i	0.278385	+	0.856782i
$776$	0.220511	+	0.678664i	0.00791590	+	0.0243626i
$777$	9.05906	+	6.58179i	0.324992	+	0.236121i
$778$	27.1743	−	19.7433i	0.974248	−	0.707832i
$779$	−0.749044	+	2.30532i	−0.0268373	+	0.0825966i
$780$	8.09183			0.289734
$781$	0.957266	+	1.58425i	0.0342537	+	0.0566891i
$782$	−11.6775			−0.417588
$783$	−2.33543	+	7.18773i	−0.0834616	+	0.256868i
$784$	3.99054	−	2.89930i	0.142519	−	0.103546i
$785$	3.09822	+	2.25099i	0.110580	+	0.0803412i
$786$	4.45139	+	13.7000i	0.158776	+	0.488662i
$787$	5.07003	+	15.6039i	0.180727	+	0.556220i	0.999849	−	0.0173995i	$-0.00553872\pi$
$787$	5.07003	+	15.6039i	0.180727	+	0.556220i	−0.819122	+	0.573620i	$0.805539\pi$
$788$	13.8344	+	10.0513i	0.492830	+	0.358062i
$789$	−4.76378	+	3.46109i	−0.169595	+	0.123218i
$790$	−15.9899	+	49.2119i	−0.568896	+	1.75088i
$791$	9.02473			0.320882
$792$	−2.29267	−	3.79431i	−0.0814664	−	0.134825i
$793$	−4.20495			−0.149322
$794$	−9.73517	+	29.9618i	−0.345488	+	1.06330i
$795$	11.6683	−	8.47754i	0.413833	−	0.300667i
$796$	−4.25278	−	3.08982i	−0.150736	−	0.109516i
$797$	−1.81230	−	5.57769i	−0.0641951	−	0.197572i	0.913815	−	0.406132i	$-0.133123\pi$
$797$	−1.81230	−	5.57769i	−0.0641951	−	0.197572i	−0.978010	+	0.208559i	$0.933123\pi$
$798$	−4.50946	−	13.8787i	−0.159633	−	0.491300i
$799$	−0.985899	−	0.716297i	−0.0348786	−	0.0253408i
$800$	13.6766	−	9.93661i	0.483540	−	0.351312i
$801$	−0.483970	+	1.48951i	−0.0171002	+	0.0526291i
$802$	−67.6327			−2.38819
$803$	29.5313	+	12.4490i	1.04214	+	0.439316i
$804$	−1.79208			−0.0632018
$805$	2.08545	−	6.41835i	0.0735024	−	0.226217i
$806$	−31.2376	+	22.6955i	−1.10030	+	0.799413i
$807$	1.78918	+	1.29992i	0.0629822	+	0.0457592i
$808$	2.19644	+	6.75994i	0.0772704	+	0.237814i
$809$	−5.54294	−	17.0594i	−0.194880	−	0.599778i	−0.999978	−	0.00663634i	$-0.997888\pi$
$809$	−5.54294	−	17.0594i	−0.194880	−	0.599778i	0.805098	−	0.593141i	$-0.202112\pi$
$810$	−4.05641	−	2.94716i	−0.142528	−	0.103553i
$811$	22.0254	−	16.0024i	0.773417	−	0.561920i	−0.129579	−	0.991569i	$-0.541363\pi$
$811$	22.0254	−	16.0024i	0.773417	−	0.561920i	0.902996	+	0.429649i	$0.141363\pi$
$812$	2.94184	−	9.05406i	0.103238	−	0.317735i
$813$	−7.59429			−0.266344
$814$	−43.8642	+	50.7132i	−1.53744	+	1.77750i
$815$	−47.3248			−1.65772
$816$	−4.05699	+	12.4861i	−0.142023	+	0.437102i
$817$	47.6911	−	34.6496i	1.66850	−	1.21224i
$818$	−2.83014	−	2.05622i	−0.0989536	−	0.0718940i
$819$	−0.714790	−	2.19990i	−0.0249768	−	0.0768706i
$820$	−0.324191	−	0.997758i	−0.0113213	−	0.0348432i
$821$	−3.28980	−	2.39018i	−0.114815	−	0.0834179i	0.528896	−	0.848687i	$-0.322606\pi$
$821$	−3.28980	−	2.39018i	−0.114815	−	0.0834179i	−0.643711	+	0.765269i	$0.722606\pi$
$822$	15.0908	−	10.9641i	0.526352	−	0.382417i
$823$	−10.0477	+	30.9236i	−0.350240	+	1.07793i	0.608478	+	0.793571i	$0.291780\pi$
$823$	−10.0477	+	30.9236i	−0.350240	+	1.07793i	−0.958718	+	0.284358i	$0.908220\pi$
$824$	−24.8091			−0.864266
$825$	0.761888	−	8.96417i	0.0265255	−	0.312092i
$826$	−22.1757			−0.771592
$827$	5.75272	−	17.7051i	0.200042	−	0.615665i	−0.799839	−	0.600215i	$-0.795082\pi$
$827$	5.75272	−	17.7051i	0.200042	−	0.615665i	0.999881	−	0.0154505i	$-0.00491826\pi$
$828$	2.47644	−	1.79924i	0.0860623	−	0.0625279i
$829$	−39.5855	−	28.7606i	−1.37486	−	0.998896i	−0.997340	−	0.0728964i	$-0.976776\pi$
$829$	−39.5855	−	28.7606i	−1.37486	−	0.998896i	−0.377523	−	0.926000i	$-0.623224\pi$
$830$	−13.1867	−	40.5844i	−0.457716	−	1.40870i
$831$	−7.46239	−	22.9669i	−0.258867	−	0.796712i
$832$	2.59521	+	1.88553i	0.0899728	+	0.0653691i
$833$	−2.15330	+	1.56446i	−0.0746075	+	0.0542055i
$834$	−3.09065	+	9.51205i	−0.107020	+	0.329375i
$835$	−22.1070			−0.765045
$836$	32.8836	−	7.67763i	1.13730	−	0.265537i
$837$	9.24567			0.319577
$838$	−9.60873	+	29.5726i	−0.331928	+	1.02157i
$839$	2.35247	−	1.70917i	0.0812162	−	0.0590070i	−0.546436	−	0.837501i	$-0.684016\pi$
$839$	2.35247	−	1.70917i	0.0812162	−	0.0590070i	0.627652	+	0.778494i	$0.284016\pi$
$840$	−3.00314	−	2.18191i	−0.103618	−	0.0752831i
$841$	8.68883	+	26.7415i	0.299615	+	0.922120i
$842$	4.03832	+	12.4287i	0.139170	+	0.428320i
$843$	−22.0835	−	16.0446i	−0.760596	−	0.552605i
$844$	−10.8665	+	7.89498i	−0.374041	+	0.271757i
$845$	−6.56471	+	20.2041i	−0.225833	+	0.695042i
$846$	0.826634			0.0284203
$847$	10.8422	+	1.85643i	0.372543	+	0.0637875i
$848$	25.6169			0.879687
$849$	7.91347	−	24.3552i	0.271590	−	0.835867i
$850$	−10.5455	+	7.66176i	−0.361708	+	0.262796i
$851$	22.0141	+	15.9942i	0.754635	+	0.548274i
$852$	0.217243	+	0.668605i	0.00744262	+	0.0229060i
$853$	8.19855	+	25.2325i	0.280713	+	0.863946i	0.987651	+	0.156670i	$0.0500760\pi$
$853$	8.19855	+	25.2325i	0.280713	+	0.863946i	−0.706938	+	0.707276i	$0.749924\pi$
$854$	−2.65526	−	1.92916i	−0.0908613	−	0.0660146i
$855$	−18.1599	+	13.1939i	−0.621055	+	0.451223i
$856$	3.89392	−	11.9843i	0.133091	−	0.409613i
$857$	32.5818			1.11297			0.556487	−	0.830856i	$-0.312149\pi$
$857$	32.5818			1.11297			0.556487	+	0.830856i	$0.312149\pi$
$858$	13.4882	−	3.14921i	0.460478	−	0.107512i
$859$	30.4695			1.03961			0.519803	−	0.854286i	$-0.326005\pi$
$859$	30.4695			1.03961			0.519803	+	0.854286i	$0.326005\pi$
$860$	−7.88417	+	24.2650i	−0.268848	+	0.827429i
$861$	−0.242620	+	0.176274i	−0.00826846	+	0.00600739i
$862$	47.4061	+	34.4426i	1.61466	+	1.17312i
$863$	6.50720	+	20.0271i	0.221508	+	0.681730i	0.998627	+	0.0523775i	$0.0166799\pi$
$863$	6.50720	+	20.0271i	0.221508	+	0.681730i	−0.777120	+	0.629353i	$0.783320\pi$
$864$	−1.92586	−	5.92719i	−0.0655192	−	0.201647i
$865$	22.9844	+	16.6991i	0.781493	+	0.567788i
$866$	−33.2653	+	24.1687i	−1.13040	+	0.821284i
$867$	−3.06413	+	9.43043i	−0.104063	+	0.320274i
$868$	−11.6464			−0.395303
$869$	−2.89863	+	34.1046i	−0.0983294	+	1.15692i
$870$	−37.8939			−1.28473
$871$	−1.01691	+	3.12974i	−0.0344568	+	0.106047i
$872$	1.20249	−	0.873663i	0.0407216	−	0.0295860i
$873$	0.431904	+	0.313796i	0.0146177	+	0.0106204i
$874$	−10.9583	−	33.7262i	−0.370670	−	1.14080i
$875$	1.96306	+	6.04168i	0.0663636	+	0.204246i
$876$	9.84723	+	7.15443i	0.332707	+	0.241726i
$877$	−7.94695	+	5.77379i	−0.268349	+	0.194967i	−0.713820	−	0.700329i	$-0.753036\pi$
$877$	−7.94695	+	5.77379i	−0.268349	+	0.194967i	0.445470	+	0.895297i	$0.353036\pi$
$878$	16.9807	−	52.2611i	0.573070	−	1.76373i
$879$	−11.6993			−0.394609
$880$	29.7215	−	34.3623i	1.00191	−	1.15835i
$881$	16.4077			0.552789			0.276394	−	0.961044i	$-0.410860\pi$
$881$	16.4077			0.552789			0.276394	+	0.961044i	$0.410860\pi$
$882$	0.557915	−	1.71709i	0.0187860	−	0.0578173i
$883$	−22.4283	+	16.2951i	−0.754772	+	0.548374i	−0.897302	−	0.441417i	$-0.854476\pi$
$883$	−22.4283	+	16.2951i	−0.754772	+	0.548374i	0.142531	+	0.989790i	$0.454476\pi$
$884$	−6.27412	−	4.55841i	−0.211021	−	0.153316i
$885$	10.5408	+	32.4412i	0.354325	+	1.09050i
$886$	−11.1472	−	34.3076i	−0.374498	−	1.15259i
$887$	26.8181	+	19.4845i	0.900465	+	0.654226i	0.938585	−	0.345047i	$-0.112137\pi$
$887$	26.8181	+	19.4845i	0.900465	+	0.654226i	−0.0381206	+	0.999273i	$0.512137\pi$
$888$	12.1088	−	8.79759i	0.406346	−	0.295228i
$889$	2.57579	−	7.92746i	0.0863891	−	0.265878i
$890$	−7.85272			−0.263224
$891$	−3.05617	−	1.28834i	−0.102386	−	0.0431610i
$892$	4.58919			0.153657
$893$	1.14358	−	3.51957i	0.0382684	−	0.117778i
$894$	−32.1171	+	23.3344i	−1.07416	+	0.780420i
$895$	−3.94776	−	2.86822i	−0.131959	−	0.0958739i
$896$	−3.07800	−	9.47310i	−0.102829	−	0.316474i
$897$	−1.73699	−	5.34590i	−0.0579964	−	0.178494i
$898$	−17.2749	−	12.5510i	−0.576471	−	0.418831i
$899$	56.5303	−	41.0716i	1.88539	−	1.36982i
$900$	1.05587	−	3.24964i	0.0351957	−	0.108321i
$901$	−13.8229			−0.460508
$902$	−0.928701	−	1.53698i	−0.0309224	−	0.0511758i
$903$	7.29328			0.242705
$904$	3.72766	−	11.4726i	0.123980	−	0.381571i
$905$	−28.1228	+	20.4324i	−0.934835	+	0.679197i
$906$	20.6912	+	15.0330i	0.687419	+	0.499439i
$907$	0.833843	+	2.56631i	0.0276873	+	0.0852128i	0.963945	−	0.266100i	$-0.0857353\pi$
$907$	0.833843	+	2.56631i	0.0276873	+	0.0852128i	−0.936258	+	0.351313i	$0.885735\pi$
$908$	8.14631	+	25.0718i	0.270345	+	0.832036i
$909$	4.30204	+	3.12561i	0.142690	+	0.103670i
$910$	9.38293	−	6.81710i	0.311041	−	0.225985i
$911$	9.35605	−	28.7950i	0.309980	−	0.954019i	−0.667792	−	0.744348i	$-0.732761\pi$
$911$	9.35605	−	28.7950i	0.309980	−	0.954019i	0.977772	−	0.209672i	$-0.0672395\pi$
$912$	−39.8685			−1.32018
$913$	−14.5979	−	24.1591i	−0.483119	−	0.799551i
$914$	−3.54408			−0.117228
$915$	−1.56008	+	4.80142i	−0.0515745	+	0.158730i
$916$	16.8199	−	12.2204i	0.555745	−	0.403772i
$917$	6.45484	+	4.68971i	0.213157	+	0.154868i
$918$	1.48496	+	4.57024i	0.0490110	+	0.150840i
$919$	11.8327	+	36.4172i	0.390324	+	1.20129i	0.932544	+	0.361057i	$0.117584\pi$
$919$	11.8327	+	36.4172i	0.390324	+	1.20129i	−0.542220	+	0.840236i	$0.682416\pi$
$920$	−7.29784	−	5.30219i	−0.240603	−	0.174808i
$921$	−22.7040	+	16.4954i	−0.748121	+	0.543542i
$922$	−8.67546	+	26.7003i	−0.285711	+	0.879329i
$923$	1.29094			0.0424919
$924$	3.84972	+	1.62287i	0.126647	+	0.0533883i
$925$	30.3740			0.998692
$926$	−2.08612	+	6.42040i	−0.0685540	+	0.210988i
$927$	−15.0158	+	10.9096i	−0.493184	+	0.358319i
$928$	−38.1053	−	27.6851i	−1.25087	−	0.908809i
$929$	−0.608874	−	1.87392i	−0.0199765	−	0.0614814i	0.940571	−	0.339596i	$-0.110290\pi$
$929$	−0.608874	−	1.87392i	−0.0199765	−	0.0614814i	−0.960548	+	0.278115i	$0.910290\pi$
$930$	14.3253	+	44.0889i	0.469747	+	1.44573i
$931$	−6.53904	−	4.75089i	−0.214308	−	0.155704i
$932$	−7.42588	+	5.39522i	−0.243243	+	0.176726i
$933$	8.87302	−	27.3083i	0.290490	−	0.894035i
$934$	18.4101			0.602395
$935$	−16.0378	+	18.5419i	−0.524491	+	0.606386i
$936$	−3.09183			−0.101060
$937$	11.4956	−	35.3800i	0.375547	−	1.15581i	−0.567563	−	0.823330i	$-0.692114\pi$
$937$	11.4956	−	35.3800i	0.375547	−	1.15581i	0.943109	−	0.332483i	$-0.107886\pi$
$938$	−2.07802	+	1.50977i	−0.0678496	+	0.0492956i
$939$	23.8241	+	17.3093i	0.777471	+	0.564866i
$940$	0.494949	+	1.52330i	0.0161435	+	0.0496845i
$941$	−9.32725	−	28.7063i	−0.304060	−	0.935799i	−0.980026	−	0.198867i	$-0.936274\pi$
$941$	−9.32725	−	28.7063i	−0.304060	−	0.935799i	0.675967	−	0.736932i	$-0.263726\pi$
$942$	2.01418	+	1.46339i	0.0656257	+	0.0476799i
$943$	−0.589582	+	0.428357i	−0.0191994	+	0.0139492i
$944$	−18.7218	+	57.6199i	−0.609344	+	1.87537i
$945$	−2.77715			−0.0903406
$946$	−3.69848	+	43.5153i	−0.120248	+	1.41480i
$947$	54.8775			1.78328			0.891639	−	0.452746i	$-0.149556\pi$
$947$	54.8775			1.78328			0.891639	+	0.452746i	$0.149556\pi$
$948$	−4.01711	+	12.3634i	−0.130470	+	0.401544i
$949$	18.0825	−	13.1377i	0.586982	−	0.426468i
$950$	−32.0241	−	23.2669i	−1.03900	−	0.754877i
$951$	−0.0103992	−	0.0320055i	−0.000337218	−	0.00103785i
$952$	1.09938	+	3.38355i	0.0356312	+	0.109662i
$953$	20.6300	+	14.9886i	0.668271	+	0.485527i	0.869446	−	0.494028i	$-0.164476\pi$
$953$	20.6300	+	14.9886i	0.668271	+	0.485527i	−0.201175	+	0.979555i	$0.564476\pi$
$954$	7.58570	−	5.51133i	0.245596	−	0.178436i
$955$	−16.8272	+	51.7888i	−0.544516	+	1.67585i
$956$	−15.0688			−0.487360
$957$	−24.4093	+	5.69907i	−0.789041	+	0.184225i
$958$	40.8811			1.32081
$959$	3.19265	−	9.82597i	0.103096	−	0.317297i
$960$	3.11584	−	2.26379i	0.100563	−	0.0730636i
$961$	−44.0771	−	32.0239i	−1.42184	−	1.03303i
$962$	14.4507	+	44.4748i	0.465910	+	1.43392i
$963$	−2.91318	−	8.96585i	−0.0938760	−	0.288920i
$964$	4.47481	+	3.25114i	0.144124	+	0.104712i
$965$	1.37621	−	0.999877i	0.0443019	−	0.0321872i
$966$	1.35577	−	4.17264i	0.0436213	−	0.134252i
$967$	−52.7171			−1.69527			−0.847633	−	0.530583i	$-0.821973\pi$
$967$	−52.7171			−1.69527			−0.847633	+	0.530583i	$0.821973\pi$
$968$	6.83832	−	13.0162i	0.219792	−	0.418357i
$969$	21.5131			0.691101
$970$	−0.827173	+	2.54578i	−0.0265589	+	0.0817399i
$971$	−26.7415	+	19.4288i	−0.858176	+	0.623501i	−0.927388	−	0.374101i	$-0.877951\pi$
$971$	−26.7415	+	19.4288i	−0.858176	+	0.623501i	0.0692124	+	0.997602i	$0.477951\pi$
$972$	−1.01908	−	0.740407i	−0.0326871	−	0.0237486i
$973$	1.71184	+	5.26851i	0.0548792	+	0.168901i
$974$	−12.8923	−	39.6783i	−0.413094	−	1.27137i
$975$	−5.07611	−	3.68801i	−0.162565	−	0.118111i
$976$	−7.25431	+	5.27056i	−0.232205	+	0.168707i
$977$	−9.77802	+	30.0937i	−0.312827	+	0.962781i	0.663813	+	0.747898i	$0.268937\pi$
$977$	−9.77802	+	30.0937i	−0.312827	+	0.962781i	−0.976640	+	0.214883i	$0.931063\pi$
$978$	−30.7664			−0.983800
$979$	−5.05832	+	1.18101i	−0.161665	+	0.0377453i
$980$	3.49825			0.111747
$981$	0.343628	−	1.05758i	0.0109712	−	0.0337658i
$982$	47.8787	−	34.7859i	1.52787	−	1.11006i
$983$	−11.3325	−	8.23355i	−0.361451	−	0.262609i	0.392206	−	0.919877i	$-0.371712\pi$
$983$	−11.3325	−	8.23355i	−0.361451	−	0.262609i	−0.753657	+	0.657268i	$0.771712\pi$
$984$	0.123871	+	0.381236i	0.00394887	+	0.0121534i
$985$	−11.6502	−	35.8555i	−0.371205	−	1.14245i
$986$	29.3816	+	21.3470i	0.935701	+	0.679827i
$987$	0.370412	−	0.269120i	0.0117903	−	0.00856619i
$988$	7.27758	−	22.3981i	0.231531	−	0.712578i
$989$	17.7232			0.563564
$990$	1.40831	−	16.5698i	0.0447591	−	0.526624i
$991$	21.2818			0.676038			0.338019	−	0.941139i	$-0.390243\pi$
$991$	21.2818			0.676038			0.338019	+	0.941139i	$0.390243\pi$
$992$	−17.8059	+	54.8009i	−0.565337	+	1.73993i
$993$	−13.3144	+	9.67350i	−0.422521	+	0.306979i
$994$	0.815182	+	0.592265i	0.0258560	+	0.0187855i
$995$	3.58133	+	11.0222i	0.113536	+	0.349427i
$996$	−3.31285	−	10.1959i	−0.104972	−	0.323070i
$997$	17.7250	+	12.8780i	0.561358	+	0.407850i	0.831956	−	0.554842i	$-0.187221\pi$
$997$	17.7250	+	12.8780i	0.561358	+	0.407850i	−0.270598	+	0.962692i	$0.587221\pi$
$998$	−25.9641	+	18.8641i	−0.821881	+	0.597131i
$999$	3.46025	−	10.6496i	0.109478	−	0.336937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.64.4	✓	20
3.2	odd	2		693.2.m.j.64.2		20
11.4	even	5		2541.2.a.bq.1.8		10
11.5	even	5	inner	231.2.j.g.148.4	yes	20
11.7	odd	10		2541.2.a.br.1.3		10
33.5	odd	10		693.2.m.j.379.2		20
33.26	odd	10		7623.2.a.cx.1.3		10
33.29	even	10		7623.2.a.cy.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.4	✓	20	1.1	even	1	trivial
231.2.j.g.148.4	yes	20	11.5	even	5	inner
693.2.m.j.64.2		20	3.2	odd	2
693.2.m.j.379.2		20	33.5	odd	10
2541.2.a.bq.1.8		10	11.4	even	5
2541.2.a.br.1.3		10	11.7	odd	10
7623.2.a.cx.1.3		10	33.26	odd	10
7623.2.a.cy.1.8		10	33.29	even	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.557915 - 1.71709i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.01908 - 0.740407i) q^{4} +(0.858186 + 2.64122i) q^{5} +(0.557915 + 1.71709i) q^{6} +(0.809017 + 0.587785i) q^{7} +(1.08138 - 0.785667i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.557915 - 1.71709i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.01908 - 0.740407i) q^{4} +(0.858186 + 2.64122i) q^{5} +(0.557915 + 1.71709i) q^{6} +(0.809017 + 0.587785i) q^{7} +(1.08138 - 0.785667i) q^{8} +(0.309017 - 0.951057i) q^{9} +5.01400 q^{10} +(3.22976 - 0.754083i) q^{11} +1.25966 q^{12} +(0.714790 - 2.19990i) q^{13} +(1.46064 - 1.06122i) q^{14} +(-2.24676 - 1.63237i) q^{15} +(-1.52425 - 4.69116i) q^{16} +(0.822488 + 2.53136i) q^{17} +(-1.46064 - 1.06122i) q^{18} +(-6.53904 + 4.75089i) q^{19} +(1.08102 - 3.32703i) q^{20} -1.00000 q^{21} +(0.507107 - 5.96649i) q^{22} -2.43007 q^{23} +(-0.413049 + 1.27124i) q^{24} +(-2.19449 + 1.59439i) q^{25} +(-3.37862 - 2.45471i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.389255 - 1.19800i) q^{28} +(6.11424 + 4.44226i) q^{29} +(-4.05641 + 2.94716i) q^{30} +(2.85707 - 8.79315i) q^{31} -6.23222 q^{32} +(-2.16969 + 2.50847i) q^{33} +4.80544 q^{34} +(-0.858186 + 2.64122i) q^{35} +(-1.01908 + 0.740407i) q^{36} +(-9.05906 - 6.58179i) q^{37} +(4.50946 + 13.8787i) q^{38} +(0.714790 + 2.19990i) q^{39} +(3.00314 + 2.18191i) q^{40} +(0.242620 - 0.176274i) q^{41} +(-0.557915 + 1.71709i) q^{42} -7.29328 q^{43} +(-3.84972 - 1.62287i) q^{44} +2.77715 q^{45} +(-1.35577 + 4.17264i) q^{46} +(-0.370412 + 0.269120i) q^{47} +(3.99054 + 2.89930i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.51337 + 4.65767i) q^{50} +(-2.15330 - 1.56446i) q^{51} +(-2.35725 + 1.71264i) q^{52} +(-1.60485 + 4.93922i) q^{53} +1.80545 q^{54} +(4.76344 + 7.88338i) q^{55} +1.33666 q^{56} +(2.49769 - 7.68710i) q^{57} +(11.0390 - 8.02028i) q^{58} +(-9.93687 - 7.21956i) q^{59} +(1.08102 + 3.32703i) q^{60} +(-0.561755 - 1.72890i) q^{61} +(-13.5046 - 9.81167i) q^{62} +(0.809017 - 0.587785i) q^{63} +(-0.428550 + 1.31894i) q^{64} +6.42384 q^{65} +(3.09676 + 5.12507i) q^{66} -1.42267 q^{67} +(1.03605 - 3.18864i) q^{68} +(1.96597 - 1.42836i) q^{69} +(4.05641 + 2.94716i) q^{70} +(0.172462 + 0.530784i) q^{71} +(-0.413049 - 1.27124i) q^{72} +(7.81740 + 5.67967i) q^{73} +(-16.3557 + 11.8831i) q^{74} +(0.838222 - 2.57978i) q^{75} +10.1814 q^{76} +(3.05617 + 1.28834i) q^{77} +4.17621 q^{78} +(-3.18905 + 9.81489i) q^{79} +(11.0823 - 8.05177i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.167316 - 0.514945i) q^{82} +(-2.62997 - 8.09421i) q^{83} +(1.01908 + 0.740407i) q^{84} +(-5.98003 + 4.34475i) q^{85} +(-4.06903 + 12.5232i) q^{86} -7.55762 q^{87} +(2.90013 - 3.35296i) q^{88} -1.56616 q^{89} +(1.54941 - 4.76860i) q^{90} +(1.87134 - 1.35961i) q^{91} +(2.47644 + 1.79924i) q^{92} +(2.85707 + 8.79315i) q^{93} +(0.255444 + 0.786176i) q^{94} +(-18.1599 - 13.1939i) q^{95} +(5.04197 - 3.66321i) q^{96} +(-0.164972 + 0.507733i) q^{97} +1.80545 q^{98} +(0.280876 - 3.30471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

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