LMFDB - Embedded newform 231.2.j.c.148.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	231.148
Dual form			231.2.j.c.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.19098 - 3.66547i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.19098 - 3.66547i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 + 0.951057i) q^{9} -3.85410 q^{10} +(-2.54508 + 2.12663i) q^{11} +1.00000 q^{12} +(1.00000 + 3.07768i) q^{13} +(0.809017 + 0.587785i) q^{14} +(3.11803 - 2.26538i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.354102 - 1.08981i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-0.309017 - 0.224514i) q^{19} +(-1.19098 - 3.66547i) q^{20} -1.00000 q^{21} +(2.80902 + 1.76336i) q^{22} +8.09017 q^{23} +(-0.927051 - 2.85317i) q^{24} +(-7.97214 - 5.79210i) q^{25} +(2.61803 - 1.90211i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(1.61803 - 1.17557i) q^{29} +(-3.11803 - 2.26538i) q^{30} +(2.57295 + 7.91872i) q^{31} -5.00000 q^{32} +(-3.30902 + 0.224514i) q^{33} -1.14590 q^{34} +(1.19098 + 3.66547i) q^{35} +(0.809017 + 0.587785i) q^{36} +(0.736068 - 0.534785i) q^{37} +(-0.118034 + 0.363271i) q^{38} +(-1.00000 + 3.07768i) q^{39} +(-9.35410 + 6.79615i) q^{40} +(3.35410 + 2.43690i) q^{41} +(0.309017 + 0.951057i) q^{42} +3.23607 q^{43} +(-0.809017 + 3.21644i) q^{44} +3.85410 q^{45} +(-2.50000 - 7.69421i) q^{46} +(-1.61803 - 1.17557i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.04508 + 9.37181i) q^{50} +(0.927051 - 0.673542i) q^{51} +(2.61803 + 1.90211i) q^{52} +(-3.14590 - 9.68208i) q^{53} +1.00000 q^{54} +(4.76393 + 11.8617i) q^{55} +3.00000 q^{56} +(-0.118034 - 0.363271i) q^{57} +(-1.61803 - 1.17557i) q^{58} +(-9.09017 + 6.60440i) q^{59} +(1.19098 - 3.66547i) q^{60} +(-2.76393 + 8.50651i) q^{61} +(6.73607 - 4.89404i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(2.16312 + 6.65740i) q^{64} +12.4721 q^{65} +(1.23607 + 3.07768i) q^{66} +8.00000 q^{67} +(-0.354102 - 1.08981i) q^{68} +(6.54508 + 4.75528i) q^{69} +(3.11803 - 2.26538i) q^{70} +(-2.76393 + 8.50651i) q^{71} +(0.927051 - 2.85317i) q^{72} +(0.618034 - 0.449028i) q^{73} +(-0.736068 - 0.534785i) q^{74} +(-3.04508 - 9.37181i) q^{75} -0.381966 q^{76} +(0.809017 - 3.21644i) q^{77} +3.23607 q^{78} +(-4.32624 - 13.3148i) q^{79} +(3.11803 + 2.26538i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.28115 - 3.94298i) q^{82} +(-4.61803 + 14.2128i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(-3.57295 - 2.59590i) q^{85} +(-1.00000 - 3.07768i) q^{86} +2.00000 q^{87} +(9.92705 - 0.673542i) q^{88} -10.0902 q^{89} +(-1.19098 - 3.66547i) q^{90} +(-2.61803 - 1.90211i) q^{91} +(6.54508 - 4.75528i) q^{92} +(-2.57295 + 7.91872i) q^{93} +(-0.618034 + 1.90211i) q^{94} +(-1.19098 + 0.865300i) q^{95} +(-4.04508 - 2.93893i) q^{96} +(-3.85410 - 11.8617i) q^{97} -1.00000 q^{98} +(-2.80902 - 1.76336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + q^{4} + 7 q^{5} - q^{6} - q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 + q^4 + 7 * q^5 - q^6 - q^7 - 3 * q^8 - q^9	\( 4 q + q^{2} + q^{3} + q^{4} + 7 q^{5} - q^{6} - q^{7} - 3 q^{8} - q^{9} - 2 q^{10} + q^{11} + 4 q^{12} + 4 q^{13} + q^{14} + 8 q^{15} + q^{16} - 12 q^{17} + q^{18} + q^{19} - 7 q^{20} - 4 q^{21} + 9 q^{22} + 10 q^{23} + 3 q^{24} - 14 q^{25} + 6 q^{26} + q^{27} + q^{28} + 2 q^{29} - 8 q^{30} + 17 q^{31} - 20 q^{32} - 11 q^{33} - 18 q^{34} + 7 q^{35} + q^{36} - 6 q^{37} + 4 q^{38} - 4 q^{39} - 24 q^{40} - q^{42} + 4 q^{43} - q^{44} + 2 q^{45} - 10 q^{46} - 2 q^{47} - q^{48} - q^{49} - q^{50} - 3 q^{51} + 6 q^{52} - 26 q^{53} + 4 q^{54} + 28 q^{55} + 12 q^{56} + 4 q^{57} - 2 q^{58} - 14 q^{59} + 7 q^{60} - 20 q^{61} + 18 q^{62} - q^{63} - 7 q^{64} + 32 q^{65} - 4 q^{66} + 32 q^{67} + 12 q^{68} + 15 q^{69} + 8 q^{70} - 20 q^{71} - 3 q^{72} - 2 q^{73} + 6 q^{74} - q^{75} - 6 q^{76} + q^{77} + 4 q^{78} + 14 q^{79} + 8 q^{80} - q^{81} - 15 q^{82} - 14 q^{83} - q^{84} - 21 q^{85} - 4 q^{86} + 8 q^{87} + 33 q^{88} - 18 q^{89} - 7 q^{90} - 6 q^{91} + 15 q^{92} - 17 q^{93} + 2 q^{94} - 7 q^{95} - 5 q^{96} - 2 q^{97} - 4 q^{98} - 9 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + q^4 + 7 * q^5 - q^6 - q^7 - 3 * q^8 - q^9 - 2 * q^10 + q^11 + 4 * q^12 + 4 * q^13 + q^14 + 8 * q^15 + q^16 - 12 * q^17 + q^18 + q^19 - 7 * q^20 - 4 * q^21 + 9 * q^22 + 10 * q^23 + 3 * q^24 - 14 * q^25 + 6 * q^26 + q^27 + q^28 + 2 * q^29 - 8 * q^30 + 17 * q^31 - 20 * q^32 - 11 * q^33 - 18 * q^34 + 7 * q^35 + q^36 - 6 * q^37 + 4 * q^38 - 4 * q^39 - 24 * q^40 - q^42 + 4 * q^43 - q^44 + 2 * q^45 - 10 * q^46 - 2 * q^47 - q^48 - q^49 - q^50 - 3 * q^51 + 6 * q^52 - 26 * q^53 + 4 * q^54 + 28 * q^55 + 12 * q^56 + 4 * q^57 - 2 * q^58 - 14 * q^59 + 7 * q^60 - 20 * q^61 + 18 * q^62 - q^63 - 7 * q^64 + 32 * q^65 - 4 * q^66 + 32 * q^67 + 12 * q^68 + 15 * q^69 + 8 * q^70 - 20 * q^71 - 3 * q^72 - 2 * q^73 + 6 * q^74 - q^75 - 6 * q^76 + q^77 + 4 * q^78 + 14 * q^79 + 8 * q^80 - q^81 - 15 * q^82 - 14 * q^83 - q^84 - 21 * q^85 - 4 * q^86 + 8 * q^87 + 33 * q^88 - 18 * q^89 - 7 * q^90 - 6 * q^91 + 15 * q^92 - 17 * q^93 + 2 * q^94 - 7 * q^95 - 5 * q^96 - 2 * q^97 - 4 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i	−0.998886	−	0.0471903i	$-0.984973\pi$
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i	0.780378	−	0.625308i	$-0.215027\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	1.19098	−	3.66547i	0.532624	−	1.63925i	−0.216104	−	0.976370i	$-0.569335\pi$
$5$	1.19098	−	3.66547i	0.532624	−	1.63925i	0.748728	−	0.662877i	$-0.230665\pi$
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−2.42705	−	1.76336i	−0.858092	−	0.623440i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−3.85410			−1.21877
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$12$	1.00000			0.288675
$13$	1.00000	+	3.07768i	0.277350	+	0.853596i	0.988588	+	0.150644i	$0.0481349\pi$
$13$	1.00000	+	3.07768i	0.277350	+	0.853596i	−0.711238	+	0.702951i	$0.751865\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$	3.11803	−	2.26538i	0.805073	−	0.584920i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.354102	−	1.08981i	0.0858823	−	0.264319i	−0.898888	−	0.438178i	$-0.855624\pi$
$17$	0.354102	−	1.08981i	0.0858823	−	0.264319i	0.984770	+	0.173860i	$0.0556239\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	−0.309017	−	0.224514i	−0.0708934	−	0.0515070i	0.551774	−	0.833994i	$-0.313951\pi$
$19$	−0.309017	−	0.224514i	−0.0708934	−	0.0515070i	−0.622667	+	0.782487i	$0.713951\pi$
$20$	−1.19098	−	3.66547i	−0.266312	−	0.819624i
$21$	−1.00000			−0.218218
$22$	2.80902	+	1.76336i	0.598884	+	0.375949i
$23$	8.09017			1.68692			0.843459	−	0.537194i	$-0.180516\pi$
$23$	8.09017			1.68692			0.843459	+	0.537194i	$0.180516\pi$
$24$	−0.927051	−	2.85317i	−0.189233	−	0.582401i
$25$	−7.97214	−	5.79210i	−1.59443	−	1.15842i
$26$	2.61803	−	1.90211i	0.513439	−	0.373035i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.309017	+	0.951057i	−0.0583987	+	0.179733i
$29$	1.61803	−	1.17557i	0.300461	−	0.218298i	−0.427331	−	0.904095i	$-0.640546\pi$
$29$	1.61803	−	1.17557i	0.300461	−	0.218298i	0.727793	+	0.685797i	$0.240546\pi$
$30$	−3.11803	−	2.26538i	−0.569273	−	0.413601i
$31$	2.57295	+	7.91872i	0.462115	+	1.42224i	0.862575	+	0.505930i	$0.168851\pi$
$31$	2.57295	+	7.91872i	0.462115	+	1.42224i	−0.400459	+	0.916315i	$0.631149\pi$
$32$	−5.00000			−0.883883
$33$	−3.30902	+	0.224514i	−0.576026	+	0.0390829i
$34$	−1.14590			−0.196520
$35$	1.19098	+	3.66547i	0.201313	+	0.619577i
$36$	0.809017	+	0.587785i	0.134836	+	0.0979642i
$37$	0.736068	−	0.534785i	0.121009	−	0.0879181i	−0.525635	−	0.850710i	$-0.676172\pi$
$37$	0.736068	−	0.534785i	0.121009	−	0.0879181i	0.646644	+	0.762792i	$0.276172\pi$
$38$	−0.118034	+	0.363271i	−0.0191476	+	0.0589304i
$39$	−1.00000	+	3.07768i	−0.160128	+	0.492824i
$40$	−9.35410	+	6.79615i	−1.47901	+	1.07457i
$41$	3.35410	+	2.43690i	0.523823	+	0.380579i	0.818042	−	0.575158i	$-0.195060\pi$
$41$	3.35410	+	2.43690i	0.523823	+	0.380579i	−0.294219	+	0.955738i	$0.595060\pi$
$42$	0.309017	+	0.951057i	0.0476824	+	0.146751i
$43$	3.23607			0.493496			0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607			0.493496			0.246748	+	0.969080i	$0.420638\pi$
$44$	−0.809017	+	3.21644i	−0.121964	+	0.484897i
$45$	3.85410			0.574536
$46$	−2.50000	−	7.69421i	−0.368605	−	1.13445i
$47$	−1.61803	−	1.17557i	−0.236015	−	0.171475i	0.463491	−	0.886101i	$-0.346597\pi$
$47$	−1.61803	−	1.17557i	−0.236015	−	0.171475i	−0.699506	+	0.714627i	$0.746597\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−3.04508	+	9.37181i	−0.430640	+	1.32537i
$51$	0.927051	−	0.673542i	0.129813	−	0.0943147i
$52$	2.61803	+	1.90211i	0.363056	+	0.263776i
$53$	−3.14590	−	9.68208i	−0.432122	−	1.32994i	−0.896007	−	0.444040i	$-0.853545\pi$
$53$	−3.14590	−	9.68208i	−0.432122	−	1.32994i	0.463885	−	0.885896i	$-0.346455\pi$
$54$	1.00000			0.136083
$55$	4.76393	+	11.8617i	0.642368	+	1.59943i
$56$	3.00000			0.400892
$57$	−0.118034	−	0.363271i	−0.0156340	−	0.0481165i
$58$	−1.61803	−	1.17557i	−0.212458	−	0.154360i
$59$	−9.09017	+	6.60440i	−1.18344	+	0.859819i	−0.992555	−	0.121794i	$-0.961135\pi$
$59$	−9.09017	+	6.60440i	−1.18344	+	0.859819i	−0.190884	+	0.981613i	$0.561135\pi$
$60$	1.19098	−	3.66547i	0.153755	−	0.473210i
$61$	−2.76393	+	8.50651i	−0.353885	+	1.08915i	0.602768	+	0.797917i	$0.294065\pi$
$61$	−2.76393	+	8.50651i	−0.353885	+	1.08915i	−0.956653	+	0.291230i	$0.905935\pi$
$62$	6.73607	−	4.89404i	0.855481	−	0.621544i
$63$	−0.809017	−	0.587785i	−0.101927	−	0.0740540i
$64$	2.16312	+	6.65740i	0.270390	+	0.832174i
$65$	12.4721			1.54698
$66$	1.23607	+	3.07768i	0.152149	+	0.378837i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	−0.354102	−	1.08981i	−0.0429412	−	0.132159i
$69$	6.54508	+	4.75528i	0.787936	+	0.572469i
$70$	3.11803	−	2.26538i	0.372676	−	0.270765i
$71$	−2.76393	+	8.50651i	−0.328018	+	1.00954i	0.642041	+	0.766670i	$0.278088\pi$
$71$	−2.76393	+	8.50651i	−0.328018	+	1.00954i	−0.970060	+	0.242867i	$0.921912\pi$
$72$	0.927051	−	2.85317i	0.109254	−	0.336249i
$73$	0.618034	−	0.449028i	0.0723354	−	0.0525547i	−0.551030	−	0.834486i	$-0.685765\pi$
$73$	0.618034	−	0.449028i	0.0723354	−	0.0525547i	0.623365	+	0.781931i	$0.285765\pi$
$74$	−0.736068	−	0.534785i	−0.0855662	−	0.0621675i
$75$	−3.04508	−	9.37181i	−0.351616	−	1.08216i
$76$	−0.381966			−0.0438145
$77$	0.809017	−	3.21644i	0.0921960	−	0.366547i
$78$	3.23607			0.366413
$79$	−4.32624	−	13.3148i	−0.486740	−	1.49803i	−0.829445	−	0.558588i	$-0.811343\pi$
$79$	−4.32624	−	13.3148i	−0.486740	−	1.49803i	0.342705	−	0.939443i	$-0.388657\pi$
$80$	3.11803	+	2.26538i	0.348607	+	0.253278i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	1.28115	−	3.94298i	0.141480	−	0.435430i
$83$	−4.61803	+	14.2128i	−0.506895	+	1.56006i	0.290666	+	0.956825i	$0.406123\pi$
$83$	−4.61803	+	14.2128i	−0.506895	+	1.56006i	−0.797561	+	0.603238i	$0.793877\pi$
$84$	−0.809017	+	0.587785i	−0.0882710	+	0.0641326i
$85$	−3.57295	−	2.59590i	−0.387541	−	0.281565i
$86$	−1.00000	−	3.07768i	−0.107833	−	0.331875i
$87$	2.00000			0.214423
$88$	9.92705	−	0.673542i	1.05823	−	0.0717998i
$89$	−10.0902			−1.06956			−0.534778	−	0.844993i	$-0.679605\pi$
$89$	−10.0902			−1.06956			−0.534778	+	0.844993i	$0.679605\pi$
$90$	−1.19098	−	3.66547i	−0.125541	−	0.386374i
$91$	−2.61803	−	1.90211i	−0.274445	−	0.199396i
$92$	6.54508	−	4.75528i	0.682372	−	0.495772i
$93$	−2.57295	+	7.91872i	−0.266802	+	0.821133i
$94$	−0.618034	+	1.90211i	−0.0637453	+	0.196188i
$95$	−1.19098	+	0.865300i	−0.122192	+	0.0887779i
$96$	−4.04508	−	2.93893i	−0.412850	−	0.299953i
$97$	−3.85410	−	11.8617i	−0.391325	−	1.20437i	−0.931787	−	0.363006i	$-0.881751\pi$
$97$	−3.85410	−	11.8617i	−0.391325	−	1.20437i	0.540462	−	0.841368i	$-0.318249\pi$
$98$	−1.00000			−0.101015
$99$	−2.80902	−	1.76336i	−0.282317	−	0.177224i
$100$	−9.85410			−0.985410
$101$	2.80902	+	8.64527i	0.279508	+	0.860236i	0.987991	+	0.154509i	$0.0493795\pi$
$101$	2.80902	+	8.64527i	0.279508	+	0.860236i	−0.708484	+	0.705727i	$0.750620\pi$
$102$	−0.927051	−	0.673542i	−0.0917917	−	0.0666906i
$103$	−4.30902	+	3.13068i	−0.424580	+	0.308475i	−0.779478	−	0.626430i	$-0.784516\pi$
$103$	−4.30902	+	3.13068i	−0.424580	+	0.308475i	0.354898	+	0.934905i	$0.384516\pi$
$104$	3.00000	−	9.23305i	0.294174	−	0.905375i
$105$	−1.19098	+	3.66547i	−0.116228	+	0.357713i
$106$	−8.23607	+	5.98385i	−0.799958	+	0.581203i
$107$	−13.0172	−	9.45756i	−1.25842	−	0.914297i	−0.259743	−	0.965678i	$-0.583638\pi$
$107$	−13.0172	−	9.45756i	−1.25842	−	0.914297i	−0.998679	+	0.0513805i	$0.983638\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−9.56231			−0.915903			−0.457951	−	0.888977i	$-0.651417\pi$
$109$	−9.56231			−0.915903			−0.457951	+	0.888977i	$0.651417\pi$
$110$	9.80902	−	8.19624i	0.935253	−	0.781481i
$111$	0.909830			0.0863572
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	−4.23607	−	3.07768i	−0.398496	−	0.289524i	0.370432	−	0.928859i	$-0.379210\pi$
$113$	−4.23607	−	3.07768i	−0.398496	−	0.289524i	−0.768928	+	0.639335i	$0.779210\pi$
$114$	−0.309017	+	0.224514i	−0.0289421	+	0.0210277i
$115$	9.63525	−	29.6543i	0.898492	−	2.76527i
$116$	0.618034	−	1.90211i	0.0573830	−	0.176607i
$117$	−2.61803	+	1.90211i	−0.242037	+	0.175850i
$118$	9.09017	+	6.60440i	0.836818	+	0.607984i
$119$	0.354102	+	1.08981i	0.0324605	+	0.0999031i
$120$	−11.5623			−1.05549
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$	8.94427			0.809776
$123$	1.28115	+	3.94298i	0.115518	+	0.355527i
$124$	6.73607	+	4.89404i	0.604917	+	0.439498i
$125$	−15.1353	+	10.9964i	−1.35374	+	0.983548i
$126$	−0.309017	+	0.951057i	−0.0275294	+	0.0847268i
$127$	0.381966	−	1.17557i	0.0338940	−	0.104315i	−0.932678	−	0.360709i	$-0.882535\pi$
$127$	0.381966	−	1.17557i	0.0338940	−	0.104315i	0.966572	+	0.256394i	$0.0825346\pi$
$128$	−2.42705	+	1.76336i	−0.214523	+	0.155860i
$129$	2.61803	+	1.90211i	0.230505	+	0.167472i
$130$	−3.85410	−	11.8617i	−0.338027	−	1.04034i
$131$	15.7082			1.37243			0.686216	−	0.727398i	$-0.259270\pi$
$131$	15.7082			1.37243			0.686216	+	0.727398i	$0.259270\pi$
$132$	−2.54508	+	2.12663i	−0.221521	+	0.185099i
$133$	0.381966			0.0331207
$134$	−2.47214	−	7.60845i	−0.213560	−	0.657270i
$135$	3.11803	+	2.26538i	0.268358	+	0.194973i
$136$	−2.78115	+	2.02063i	−0.238482	+	0.173267i
$137$	3.47214	−	10.6861i	0.296645	−	0.912978i	−0.686019	−	0.727583i	$-0.740644\pi$
$137$	3.47214	−	10.6861i	0.296645	−	0.912978i	0.982664	−	0.185395i	$-0.0593565\pi$
$138$	2.50000	−	7.69421i	0.212814	−	0.654975i
$139$	16.0172	−	11.6372i	1.35856	−	0.987054i	0.360028	−	0.932941i	$-0.382767\pi$
$139$	16.0172	−	11.6372i	1.35856	−	0.987054i	0.998535	−	0.0541123i	$-0.0172329\pi$
$140$	3.11803	+	2.26538i	0.263522	+	0.191460i
$141$	−0.618034	−	1.90211i	−0.0520479	−	0.160187i
$142$	8.94427			0.750587
$143$	−9.09017	−	5.70634i	−0.760158	−	0.477188i
$144$	−1.00000			−0.0833333
$145$	−2.38197	−	7.33094i	−0.197812	−	0.608801i
$146$	−0.618034	−	0.449028i	−0.0511489	−	0.0371618i
$147$	0.809017	−	0.587785i	0.0667266	−	0.0484797i
$148$	0.281153	−	0.865300i	0.0231106	−	0.0711272i
$149$	−6.18034	+	19.0211i	−0.506313	+	1.55827i	0.292239	+	0.956345i	$0.405600\pi$
$149$	−6.18034	+	19.0211i	−0.506313	+	1.55827i	−0.798552	+	0.601926i	$0.794400\pi$
$150$	−7.97214	+	5.79210i	−0.650922	+	0.472923i
$151$	1.61803	+	1.17557i	0.131674	+	0.0956666i	0.651673	−	0.758500i	$-0.274068\pi$
$151$	1.61803	+	1.17557i	0.131674	+	0.0956666i	−0.519999	+	0.854167i	$0.674068\pi$
$152$	0.354102	+	1.08981i	0.0287215	+	0.0883956i
$153$	1.14590			0.0926404
$154$	−3.30902	+	0.224514i	−0.266648	+	0.0180919i
$155$	32.0902			2.57754
$156$	1.00000	+	3.07768i	0.0800641	+	0.246412i
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$	−11.3262	+	8.22899i	−0.901067	+	0.654664i
$159$	3.14590	−	9.68208i	0.249486	−	0.767839i
$160$	−5.95492	+	18.3273i	−0.470777	+	1.44890i
$161$	−6.54508	+	4.75528i	−0.515825	+	0.374769i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	6.61803	+	20.3682i	0.518364	+	1.59536i	0.777076	+	0.629407i	$0.216702\pi$
$163$	6.61803	+	20.3682i	0.518364	+	1.59536i	−0.258711	+	0.965955i	$0.583298\pi$
$164$	4.14590			0.323740
$165$	−3.11803	+	12.3965i	−0.242739	+	0.965066i
$166$	14.9443			1.15990
$167$	−4.38197	−	13.4863i	−0.339087	−	1.04360i	−0.964674	−	0.263447i	$-0.915141\pi$
$167$	−4.38197	−	13.4863i	−0.339087	−	1.04360i	0.625587	−	0.780154i	$-0.284859\pi$
$168$	2.42705	+	1.76336i	0.187251	+	0.136046i
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$	−1.36475	+	4.20025i	−0.104671	+	0.322145i
$171$	0.118034	−	0.363271i	0.00902628	−	0.0277800i
$172$	2.61803	−	1.90211i	0.199623	−	0.145035i
$173$	−10.6353	−	7.72696i	−0.808583	−	0.587470i	0.104836	−	0.994490i	$-0.466568\pi$
$173$	−10.6353	−	7.72696i	−0.808583	−	0.587470i	−0.913420	+	0.407019i	$0.866568\pi$
$174$	−0.618034	−	1.90211i	−0.0468530	−	0.144199i
$175$	9.85410			0.744900
$176$	−1.23607	−	3.07768i	−0.0931721	−	0.231989i
$177$	−11.2361			−0.844555
$178$	3.11803	+	9.59632i	0.233707	+	0.719275i
$179$	−8.59017	−	6.24112i	−0.642059	−	0.466483i	0.218498	−	0.975837i	$-0.429884\pi$
$179$	−8.59017	−	6.24112i	−0.642059	−	0.466483i	−0.860557	+	0.509354i	$0.829884\pi$
$180$	3.11803	−	2.26538i	0.232405	−	0.168852i
$181$	−0.326238	+	1.00406i	−0.0242491	+	0.0746310i	−0.962449	−	0.271464i	$-0.912492\pi$
$181$	−0.326238	+	1.00406i	−0.0242491	+	0.0746310i	0.938200	+	0.346095i	$0.112492\pi$
$182$	−1.00000	+	3.07768i	−0.0741249	+	0.228133i
$183$	−7.23607	+	5.25731i	−0.534906	+	0.388632i
$184$	−19.6353	−	14.2658i	−1.44753	−	1.05169i
$185$	−1.08359	−	3.33495i	−0.0796673	−	0.245191i
$186$	8.32624			0.610509
$187$	1.41641	+	3.52671i	0.103578	+	0.257899i
$188$	−2.00000			−0.145865
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	1.19098	+	0.865300i	0.0864030	+	0.0627754i
$191$	−12.3541	+	8.97578i	−0.893911	+	0.649465i	−0.936895	−	0.349611i	$-0.886314\pi$
$191$	−12.3541	+	8.97578i	−0.893911	+	0.649465i	0.0429835	+	0.999076i	$0.486314\pi$
$192$	−2.16312	+	6.65740i	−0.156110	+	0.480456i
$193$	6.37132	−	19.6089i	0.458618	−	1.41148i	−0.408217	−	0.912885i	$-0.633849\pi$
$193$	6.37132	−	19.6089i	0.458618	−	1.41148i	0.866835	−	0.498596i	$-0.166151\pi$
$194$	−10.0902	+	7.33094i	−0.724432	+	0.526331i
$195$	10.0902	+	7.33094i	0.722572	+	0.524979i
$196$	−0.309017	−	0.951057i	−0.0220726	−	0.0679326i
$197$	4.00000			0.284988			0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000			0.284988			0.142494	+	0.989796i	$0.454488\pi$
$198$	−0.809017	+	3.21644i	−0.0574943	+	0.228582i
$199$	−0.381966			−0.0270769			−0.0135384	−	0.999908i	$-0.504310\pi$
$199$	−0.381966			−0.0270769			−0.0135384	+	0.999908i	$0.504310\pi$
$200$	9.13525	+	28.1154i	0.645960	+	1.98806i
$201$	6.47214	+	4.70228i	0.456509	+	0.331673i
$202$	7.35410	−	5.34307i	0.517433	−	0.375937i
$203$	−0.618034	+	1.90211i	−0.0433775	+	0.133502i
$204$	0.354102	−	1.08981i	0.0247921	−	0.0763022i
$205$	12.9271	−	9.39205i	0.902864	−	0.655969i
$206$	4.30902	+	3.13068i	0.300223	+	0.218125i
$207$	2.50000	+	7.69421i	0.173762	+	0.534784i
$208$	−3.23607			−0.224381
$209$	1.26393	−	0.0857567i	0.0874280	−	0.00593192i
$210$	3.85410			0.265958
$211$	−0.618034	−	1.90211i	−0.0425472	−	0.130947i	0.927527	−	0.373757i	$-0.121931\pi$
$211$	−0.618034	−	1.90211i	−0.0425472	−	0.130947i	−0.970074	+	0.242810i	$0.921931\pi$
$212$	−8.23607	−	5.98385i	−0.565655	−	0.410973i
$213$	−7.23607	+	5.25731i	−0.495807	+	0.360225i
$214$	−4.97214	+	15.3027i	−0.339888	+	1.04607i
$215$	3.85410	−	11.8617i	0.262848	−	0.808962i
$216$	2.42705	−	1.76336i	0.165140	−	0.119981i
$217$	−6.73607	−	4.89404i	−0.457274	−	0.332229i
$218$	2.95492	+	9.09429i	0.200132	+	0.615943i
$219$	0.763932			0.0516217
$220$	10.8262	+	6.79615i	0.729905	+	0.458197i
$221$	3.70820			0.249441
$222$	−0.281153	−	0.865300i	−0.0188698	−	0.0580751i
$223$	3.07295	+	2.23263i	0.205780	+	0.149508i	0.685902	−	0.727694i	$-0.259408\pi$
$223$	3.07295	+	2.23263i	0.205780	+	0.149508i	−0.480122	+	0.877202i	$0.659408\pi$
$224$	4.04508	−	2.93893i	0.270274	−	0.196365i
$225$	3.04508	−	9.37181i	0.203006	−	0.624787i
$226$	−1.61803	+	4.97980i	−0.107630	+	0.331251i
$227$	4.38197	−	3.18368i	0.290841	−	0.211309i	−0.432791	−	0.901494i	$-0.642471\pi$
$227$	4.38197	−	3.18368i	0.290841	−	0.211309i	0.723632	+	0.690186i	$0.242471\pi$
$228$	−0.309017	−	0.224514i	−0.0204652	−	0.0148688i
$229$	5.18034	+	15.9434i	0.342326	+	1.05357i	0.963000	+	0.269503i	$0.0868595\pi$
$229$	5.18034	+	15.9434i	0.342326	+	1.05357i	−0.620673	+	0.784070i	$0.713141\pi$
$230$	−31.1803			−2.05597
$231$	2.54508	−	2.12663i	0.167454	−	0.139922i
$232$	−6.00000			−0.393919
$233$	2.38197	+	7.33094i	0.156048	+	0.480266i	0.998266	−	0.0588718i	$-0.0187503\pi$
$233$	2.38197	+	7.33094i	0.156048	+	0.480266i	−0.842218	+	0.539137i	$0.818750\pi$
$234$	2.61803	+	1.90211i	0.171146	+	0.124345i
$235$	−6.23607	+	4.53077i	−0.406796	+	0.295555i
$236$	−3.47214	+	10.6861i	−0.226017	+	0.695608i
$237$	4.32624	−	13.3148i	0.281019	−	0.864889i
$238$	0.927051	−	0.673542i	0.0600918	−	0.0436592i
$239$	−15.0172	−	10.9106i	−0.971383	−	0.705751i	−0.0156169	−	0.999878i	$-0.504971\pi$
$239$	−15.0172	−	10.9106i	−0.971383	−	0.705751i	−0.955766	+	0.294127i	$0.904971\pi$
$240$	1.19098	+	3.66547i	0.0768776	+	0.236605i
$241$	−12.9443			−0.833814			−0.416907	−	0.908949i	$-0.636886\pi$
$241$	−12.9443			−0.833814			−0.416907	+	0.908949i	$0.636886\pi$
$242$	−10.8992	+	1.48584i	−0.700626	+	0.0955135i
$243$	−1.00000			−0.0641500
$244$	2.76393	+	8.50651i	0.176943	+	0.544573i
$245$	−3.11803	−	2.26538i	−0.199204	−	0.144730i
$246$	3.35410	−	2.43690i	0.213850	−	0.155371i
$247$	0.381966	−	1.17557i	0.0243039	−	0.0747998i
$248$	7.71885	−	23.7562i	0.490147	−	1.50852i
$249$	−12.0902	+	8.78402i	−0.766183	+	0.556665i
$250$	15.1353	+	10.9964i	0.957238	+	0.695474i
$251$	0.562306	+	1.73060i	0.0354924	+	0.109234i	0.967233	−	0.253890i	$-0.0817100\pi$
$251$	0.562306	+	1.73060i	0.0354924	+	0.109234i	−0.931741	+	0.363124i	$0.881710\pi$
$252$	−1.00000			−0.0629941
$253$	−20.5902	+	17.2048i	−1.29449	+	1.08165i
$254$	−1.23607			−0.0775578
$255$	−1.36475	−	4.20025i	−0.0854637	−	0.263030i
$256$	13.7533	+	9.99235i	0.859581	+	0.624522i
$257$	−0.309017	+	0.224514i	−0.0192760	+	0.0140048i	−0.597382	−	0.801957i	$-0.703792\pi$
$257$	−0.309017	+	0.224514i	−0.0192760	+	0.0140048i	0.578106	+	0.815962i	$0.303792\pi$
$258$	1.00000	−	3.07768i	0.0622573	−	0.191608i
$259$	−0.281153	+	0.865300i	−0.0174700	+	0.0537671i
$260$	10.0902	−	7.33094i	0.625766	−	0.454645i
$261$	1.61803	+	1.17557i	0.100154	+	0.0727660i
$262$	−4.85410	−	14.9394i	−0.299887	−	0.922959i
$263$	22.5623			1.39125			0.695626	−	0.718404i	$-0.255127\pi$
$263$	22.5623			1.39125			0.695626	+	0.718404i	$0.255127\pi$
$264$	8.42705	+	5.29007i	0.518649	+	0.325581i
$265$	−39.2361			−2.41025
$266$	−0.118034	−	0.363271i	−0.00723713	−	0.0222736i
$267$	−8.16312	−	5.93085i	−0.499575	−	0.362962i
$268$	6.47214	−	4.70228i	0.395349	−	0.287238i
$269$	−2.43769	+	7.50245i	−0.148629	+	0.457433i	−0.997460	−	0.0712319i	$-0.977307\pi$
$269$	−2.43769	+	7.50245i	−0.148629	+	0.457433i	0.848831	+	0.528664i	$0.177307\pi$
$270$	1.19098	−	3.66547i	0.0724809	−	0.223073i
$271$	−10.4443	+	7.58821i	−0.634444	+	0.460951i	−0.857937	−	0.513755i	$-0.828254\pi$
$271$	−10.4443	+	7.58821i	−0.634444	+	0.460951i	0.223493	+	0.974706i	$0.428254\pi$
$272$	0.927051	+	0.673542i	0.0562107	+	0.0408395i
$273$	−1.00000	−	3.07768i	−0.0605228	−	0.186270i
$274$	−11.2361			−0.678796
$275$	32.6074	−	2.21238i	1.96630	−	0.133412i
$276$	8.09017			0.486971
$277$	−9.44427	−	29.0665i	−0.567451	−	1.74644i	−0.660554	−	0.750779i	$-0.729678\pi$
$277$	−9.44427	−	29.0665i	−0.567451	−	1.74644i	0.0931022	−	0.995657i	$-0.470322\pi$
$278$	−16.0172	−	11.6372i	−0.960649	−	0.697952i
$279$	−6.73607	+	4.89404i	−0.403278	+	0.292999i
$280$	3.57295	−	10.9964i	0.213525	−	0.657161i
$281$	5.85410	−	18.0171i	0.349226	−	1.07481i	−0.610056	−	0.792359i	$-0.708853\pi$
$281$	5.85410	−	18.0171i	0.349226	−	1.07481i	0.959282	−	0.282450i	$-0.0911471\pi$
$282$	−1.61803	+	1.17557i	−0.0963525	+	0.0700042i
$283$	−27.1525	−	19.7274i	−1.61405	−	1.17267i	−0.848261	−	0.529579i	$-0.822350\pi$
$283$	−27.1525	−	19.7274i	−1.61405	−	1.17267i	−0.765787	−	0.643095i	$-0.777650\pi$
$284$	2.76393	+	8.50651i	0.164009	+	0.504768i
$285$	−1.47214			−0.0872018
$286$	−2.61803	+	10.4086i	−0.154808	+	0.615475i
$287$	−4.14590			−0.244725
$288$	−1.54508	−	4.75528i	−0.0910450	−	0.280208i
$289$	12.6910	+	9.22054i	0.746528	+	0.542385i
$290$	−6.23607	+	4.53077i	−0.366195	+	0.266056i
$291$	3.85410	−	11.8617i	0.225931	−	0.695346i
$292$	0.236068	−	0.726543i	0.0138148	−	0.0425177i
$293$	3.88197	−	2.82041i	0.226787	−	0.164770i	−0.468590	−	0.883416i	$-0.655238\pi$
$293$	3.88197	−	2.82041i	0.226787	−	0.164770i	0.695376	+	0.718646i	$0.255238\pi$
$294$	−0.809017	−	0.587785i	−0.0471828	−	0.0342803i
$295$	13.3820	+	41.1855i	0.779128	+	2.39791i
$296$	−2.72949			−0.158648
$297$	−1.23607	−	3.07768i	−0.0717239	−	0.178585i
$298$	20.0000			1.15857
$299$	8.09017	+	24.8990i	0.467867	+	1.43995i
$300$	−7.97214	−	5.79210i	−0.460271	−	0.334407i
$301$	−2.61803	+	1.90211i	−0.150901	+	0.109636i
$302$	0.618034	−	1.90211i	0.0355639	−	0.109454i
$303$	−2.80902	+	8.64527i	−0.161374	+	0.496658i
$304$	0.309017	−	0.224514i	0.0177233	−	0.0128768i
$305$	27.8885	+	20.2622i	1.59689	+	1.16021i
$306$	−0.354102	−	1.08981i	−0.0202427	−	0.0623005i
$307$	9.27051			0.529096			0.264548	−	0.964373i	$-0.414777\pi$
$307$	9.27051			0.529096			0.264548	+	0.964373i	$0.414777\pi$
$308$	−1.23607	−	3.07768i	−0.0704315	−	0.175367i
$309$	−5.32624			−0.302999
$310$	−9.91641	−	30.5196i	−0.563214	−	1.73339i
$311$	4.23607	+	3.07768i	0.240205	+	0.174519i	0.701375	−	0.712793i	$-0.252570\pi$
$311$	4.23607	+	3.07768i	0.240205	+	0.174519i	−0.461169	+	0.887312i	$0.652570\pi$
$312$	7.85410	−	5.70634i	0.444651	−	0.323058i
$313$	−9.94427	+	30.6053i	−0.562083	+	1.72992i	0.114378	+	0.993437i	$0.463512\pi$
$313$	−9.94427	+	30.6053i	−0.562083	+	1.72992i	−0.676462	+	0.736478i	$0.736488\pi$
$314$	1.14590	−	3.52671i	0.0646668	−	0.199024i
$315$	−3.11803	+	2.26538i	−0.175681	+	0.127640i
$316$	−11.3262	−	8.22899i	−0.637151	−	0.462917i
$317$	6.67376	+	20.5397i	0.374836	+	1.15363i	0.943589	+	0.331118i	$0.107426\pi$
$317$	6.67376	+	20.5397i	0.374836	+	1.15363i	−0.568754	+	0.822508i	$0.692574\pi$
$318$	−10.1803			−0.570885
$319$	−1.61803	+	6.43288i	−0.0905925	+	0.360172i
$320$	26.9787			1.50816
$321$	−4.97214	−	15.3027i	−0.277518	−	0.854111i
$322$	6.54508	+	4.75528i	0.364743	+	0.265002i
$323$	−0.354102	+	0.257270i	−0.0197028	+	0.0143149i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	9.85410	−	30.3278i	0.546607	−	1.68228i
$326$	17.3262	−	12.5882i	0.959612	−	0.697199i
$327$	−7.73607	−	5.62058i	−0.427806	−	0.310819i
$328$	−3.84346	−	11.8290i	−0.212220	−	0.653145i
$329$	2.00000			0.110264
$330$	12.7533	−	0.865300i	0.702045	−	0.0476332i
$331$	−14.3607			−0.789334			−0.394667	−	0.918824i	$-0.629140\pi$
$331$	−14.3607			−0.789334			−0.394667	+	0.918824i	$0.629140\pi$
$332$	4.61803	+	14.2128i	0.253448	+	0.780031i
$333$	0.736068	+	0.534785i	0.0403363	+	0.0293060i
$334$	−11.4721	+	8.33499i	−0.627727	+	0.456071i
$335$	9.52786	−	29.3238i	0.520563	−	1.60213i
$336$	0.309017	−	0.951057i	0.0168583	−	0.0518844i
$337$	27.3885	−	19.8989i	1.49195	−	1.08396i	0.518495	−	0.855080i	$-0.326492\pi$
$337$	27.3885	−	19.8989i	1.49195	−	1.08396i	0.973454	−	0.228884i	$-0.0735076\pi$
$338$	−2.04508	−	1.48584i	−0.111238	−	0.0808191i
$339$	−1.61803	−	4.97980i	−0.0878795	−	0.270465i
$340$	−4.41641			−0.239513
$341$	−23.3885	−	14.6821i	−1.26656	−	0.795081i
$342$	−0.381966			−0.0206544
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−7.85410	−	5.70634i	−0.423465	−	0.307665i
$345$	25.2254	−	18.3273i	1.35809	−	0.986711i
$346$	−4.06231	+	12.5025i	−0.218391	+	0.672138i
$347$	−4.51722	+	13.9026i	−0.242497	+	0.746329i	0.753541	+	0.657401i	$0.228344\pi$
$347$	−4.51722	+	13.9026i	−0.242497	+	0.746329i	−0.996038	+	0.0889284i	$0.971656\pi$
$348$	1.61803	−	1.17557i	0.0867357	−	0.0630172i
$349$	−22.0344	−	16.0090i	−1.17948	−	0.856940i	−0.187364	−	0.982291i	$-0.559994\pi$
$349$	−22.0344	−	16.0090i	−1.17948	−	0.856940i	−0.992113	+	0.125351i	$0.959994\pi$
$350$	−3.04508	−	9.37181i	−0.162767	−	0.500944i
$351$	−3.23607			−0.172729
$352$	12.7254	−	10.6331i	0.678267	−	0.566748i
$353$	3.52786			0.187769			0.0938846	−	0.995583i	$-0.470072\pi$
$353$	3.52786			0.187769			0.0938846	+	0.995583i	$0.470072\pi$
$354$	3.47214	+	10.6861i	0.184542	+	0.567962i
$355$	27.8885	+	20.2622i	1.48017	+	1.07541i
$356$	−8.16312	+	5.93085i	−0.432644	+	0.314335i
$357$	−0.354102	+	1.08981i	−0.0187411	+	0.0576791i
$358$	−3.28115	+	10.0984i	−0.173414	+	0.533714i
$359$	17.8262	−	12.9515i	0.940833	−	0.683555i	−0.00778815	−	0.999970i	$-0.502479\pi$
$359$	17.8262	−	12.9515i	0.940833	−	0.683555i	0.948621	+	0.316415i	$0.102479\pi$
$360$	−9.35410	−	6.79615i	−0.493004	−	0.358189i
$361$	−5.82624	−	17.9313i	−0.306644	−	0.943754i
$362$	1.05573			0.0554878
$363$	7.94427	−	7.60845i	0.416966	−	0.399340i
$364$	−3.23607			−0.169616
$365$	−0.909830	−	2.80017i	−0.0476227	−	0.146568i
$366$	7.23607	+	5.25731i	0.378235	+	0.274804i
$367$	13.9721	−	10.1514i	0.729340	−	0.529896i	−0.160015	−	0.987115i	$-0.551154\pi$
$367$	13.9721	−	10.1514i	0.729340	−	0.529896i	0.889354	+	0.457218i	$0.151154\pi$
$368$	−2.50000	+	7.69421i	−0.130322	+	0.401088i
$369$	−1.28115	+	3.94298i	−0.0666942	+	0.205264i
$370$	−2.83688	+	2.06111i	−0.147482	+	0.107152i
$371$	8.23607	+	5.98385i	0.427595	+	0.310666i
$372$	2.57295	+	7.91872i	0.133401	+	0.410567i
$373$	−7.67376			−0.397332			−0.198666	−	0.980067i	$-0.563661\pi$
$373$	−7.67376			−0.397332			−0.198666	+	0.980067i	$0.563661\pi$
$374$	2.91641	−	2.43690i	0.150804	−	0.126009i
$375$	−18.7082			−0.966087
$376$	1.85410	+	5.70634i	0.0956180	+	0.294282i
$377$	5.23607	+	3.80423i	0.269671	+	0.195928i
$378$	−0.809017	+	0.587785i	−0.0416113	+	0.0302324i
$379$	−2.00000	+	6.15537i	−0.102733	+	0.316180i	−0.989192	−	0.146628i	$-0.953158\pi$
$379$	−2.00000	+	6.15537i	−0.102733	+	0.316180i	0.886459	+	0.462808i	$0.153158\pi$
$380$	−0.454915	+	1.40008i	−0.0233366	+	0.0718228i
$381$	1.00000	−	0.726543i	0.0512316	−	0.0372219i
$382$	12.3541	+	8.97578i	0.632091	+	0.459241i
$383$	−9.56231	−	29.4298i	−0.488611	−	1.50379i	−0.826682	−	0.562669i	$-0.809774\pi$
$383$	−9.56231	−	29.4298i	−0.488611	−	1.50379i	0.338071	−	0.941121i	$-0.390226\pi$
$384$	−3.00000			−0.153093
$385$	−10.8262	−	6.79615i	−0.551756	−	0.346364i
$386$	−20.6180			−1.04943
$387$	1.00000	+	3.07768i	0.0508329	+	0.156447i
$388$	−10.0902	−	7.33094i	−0.512251	−	0.372172i
$389$	0.145898	−	0.106001i	0.00739732	−	0.00537447i	−0.584080	−	0.811696i	$-0.698545\pi$
$389$	0.145898	−	0.106001i	0.00739732	−	0.00537447i	0.591478	+	0.806321i	$0.298545\pi$
$390$	3.85410	−	11.8617i	0.195160	−	0.600641i
$391$	2.86475	−	8.81678i	0.144876	−	0.445884i
$392$	−2.42705	+	1.76336i	−0.122585	+	0.0890629i
$393$	12.7082	+	9.23305i	0.641044	+	0.465746i
$394$	−1.23607	−	3.80423i	−0.0622722	−	0.191654i
$395$	−53.9574			−2.71489
$396$	−3.30902	+	0.224514i	−0.166284	+	0.0112823i
$397$	−16.6525			−0.835764			−0.417882	−	0.908501i	$-0.637227\pi$
$397$	−16.6525			−0.835764			−0.417882	+	0.908501i	$0.637227\pi$
$398$	0.118034	+	0.363271i	0.00591651	+	0.0182091i
$399$	0.309017	+	0.224514i	0.0154702	+	0.0112398i
$400$	7.97214	−	5.79210i	0.398607	−	0.289605i
$401$	2.94427	−	9.06154i	0.147030	−	0.452512i	−0.850237	−	0.526401i	$-0.823541\pi$
$401$	2.94427	−	9.06154i	0.147030	−	0.452512i	0.997266	+	0.0738893i	$0.0235411\pi$
$402$	2.47214	−	7.60845i	0.123299	−	0.379475i
$403$	−21.7984	+	15.8374i	−1.08585	+	0.788919i
$404$	7.35410	+	5.34307i	0.365880	+	0.265828i
$405$	1.19098	+	3.66547i	0.0591804	+	0.182139i
$406$	2.00000			0.0992583
$407$	−0.736068	+	2.92641i	−0.0364855	+	0.145057i
$408$	−3.43769			−0.170191
$409$	10.2705	+	31.6094i	0.507844	+	1.56298i	0.795936	+	0.605381i	$0.206979\pi$
$409$	10.2705	+	31.6094i	0.507844	+	1.56298i	−0.288092	+	0.957603i	$0.593021\pi$
$410$	−12.9271	−	9.39205i	−0.638422	−	0.463840i
$411$	9.09017	−	6.60440i	0.448385	−	0.325771i
$412$	−1.64590	+	5.06555i	−0.0810876	+	0.249562i
$413$	3.47214	−	10.6861i	0.170853	−	0.525830i
$414$	6.54508	−	4.75528i	0.321673	−	0.233709i
$415$	46.5967	+	33.8545i	2.28734	+	1.66185i
$416$	−5.00000	−	15.3884i	−0.245145	−	0.754479i
$417$	19.7984			0.969531
$418$	−0.472136	−	1.17557i	−0.0230929	−	0.0574990i
$419$	19.2361			0.939743			0.469872	−	0.882735i	$-0.344300\pi$
$419$	19.2361			0.939743			0.469872	+	0.882735i	$0.344300\pi$
$420$	1.19098	+	3.66547i	0.0581140	+	0.178857i
$421$	−9.16312	−	6.65740i	−0.446583	−	0.324462i	0.341662	−	0.939823i	$-0.389010\pi$
$421$	−9.16312	−	6.65740i	−0.446583	−	0.324462i	−0.788245	+	0.615361i	$0.789010\pi$
$422$	−1.61803	+	1.17557i	−0.0787647	+	0.0572259i
$423$	0.618034	−	1.90211i	0.0300498	−	0.0924839i
$424$	−9.43769	+	29.0462i	−0.458335	+	1.41061i
$425$	−9.13525	+	6.63715i	−0.443125	+	0.321949i
$426$	7.23607	+	5.25731i	0.350589	+	0.254718i
$427$	−2.76393	−	8.50651i	−0.133756	−	0.411659i
$428$	−16.0902			−0.777748
$429$	−4.00000	−	9.95959i	−0.193122	−	0.480854i
$430$	−12.4721			−0.601460
$431$	2.80902	+	8.64527i	0.135306	+	0.416428i	0.995637	−	0.0933066i	$-0.0297437\pi$
$431$	2.80902	+	8.64527i	0.135306	+	0.416428i	−0.860332	+	0.509734i	$0.829744\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	10.3262	−	7.50245i	0.496247	−	0.360545i	−0.311334	−	0.950300i	$-0.600776\pi$
$433$	10.3262	−	7.50245i	0.496247	−	0.360545i	0.807582	+	0.589756i	$0.200776\pi$
$434$	−2.57295	+	7.91872i	−0.123506	+	0.380111i
$435$	2.38197	−	7.33094i	0.114207	−	0.351492i
$436$	−7.73607	+	5.62058i	−0.370490	+	0.269177i
$437$	−2.50000	−	1.81636i	−0.119591	−	0.0868881i
$438$	−0.236068	−	0.726543i	−0.0112798	−	0.0347155i
$439$	2.79837			0.133559			0.0667795	−	0.997768i	$-0.478728\pi$
$439$	2.79837			0.133559			0.0667795	+	0.997768i	$0.478728\pi$
$440$	9.35410	−	37.1895i	0.445939	−	1.77294i
$441$	1.00000			0.0476190
$442$	−1.14590	−	3.52671i	−0.0545048	−	0.167749i
$443$	−13.0172	−	9.45756i	−0.618467	−	0.449342i	0.233919	−	0.972256i	$-0.424845\pi$
$443$	−13.0172	−	9.45756i	−0.618467	−	0.449342i	−0.852386	+	0.522914i	$0.824845\pi$
$444$	0.736068	−	0.534785i	0.0349322	−	0.0253798i
$445$	−12.0172	+	36.9852i	−0.569671	+	1.75327i
$446$	1.17376	−	3.61247i	0.0555792	−	0.171055i
$447$	−16.1803	+	11.7557i	−0.765304	+	0.556026i
$448$	−5.66312	−	4.11450i	−0.267557	−	0.194392i
$449$	1.88854	+	5.81234i	0.0891259	+	0.274301i	0.985678	−	0.168636i	$-0.0539363\pi$
$449$	1.88854	+	5.81234i	0.0891259	+	0.274301i	−0.896552	+	0.442938i	$0.853936\pi$
$450$	−9.85410			−0.464527
$451$	−13.7188	+	0.930812i	−0.645995	+	0.0438302i
$452$	−5.23607			−0.246284
$453$	0.618034	+	1.90211i	0.0290378	+	0.0893691i
$454$	−4.38197	−	3.18368i	−0.205656	−	0.149418i
$455$	−10.0902	+	7.33094i	−0.473034	+	0.343680i
$456$	−0.354102	+	1.08981i	−0.0165823	+	0.0510352i
$457$	1.09017	−	3.35520i	0.0509960	−	0.156950i	−0.922315	−	0.386438i	$-0.873705\pi$
$457$	1.09017	−	3.35520i	0.0509960	−	0.156950i	0.973311	+	0.229488i	$0.0737053\pi$
$458$	13.5623	−	9.85359i	0.633725	−	0.460428i
$459$	0.927051	+	0.673542i	0.0432710	+	0.0314382i
$460$	−9.63525	−	29.6543i	−0.449246	−	1.38264i
$461$	38.3607			1.78663			0.893317	−	0.449426i	$-0.148372\pi$
$461$	38.3607			1.78663			0.893317	+	0.449426i	$0.148372\pi$
$462$	−2.80902	−	1.76336i	−0.130687	−	0.0820387i
$463$	−15.4164			−0.716461			−0.358231	−	0.933633i	$-0.616620\pi$
$463$	−15.4164			−0.716461			−0.358231	+	0.933633i	$0.616620\pi$
$464$	0.618034	+	1.90211i	0.0286915	+	0.0883034i
$465$	25.9615	+	18.8621i	1.20394	+	0.874710i
$466$	6.23607	−	4.53077i	0.288880	−	0.209884i
$467$	4.56231	−	14.0413i	0.211118	−	0.649755i	−0.788288	−	0.615306i	$-0.789032\pi$
$467$	4.56231	−	14.0413i	0.211118	−	0.649755i	0.999406	−	0.0344491i	$-0.0109677\pi$
$468$	−1.00000	+	3.07768i	−0.0462250	+	0.142266i
$469$	−6.47214	+	4.70228i	−0.298855	+	0.217131i
$470$	6.23607	+	4.53077i	0.287648	+	0.208989i
$471$	1.14590	+	3.52671i	0.0528002	+	0.162502i
$472$	33.7082			1.55155
$473$	−8.23607	+	6.88191i	−0.378695	+	0.316431i
$474$	−14.0000			−0.643041
$475$	1.16312	+	3.57971i	0.0533676	+	0.164248i
$476$	0.927051	+	0.673542i	0.0424913	+	0.0308717i
$477$	8.23607	−	5.98385i	0.377104	−	0.273982i
$478$	−5.73607	+	17.6538i	−0.262362	+	0.807466i
$479$	−8.94427	+	27.5276i	−0.408674	+	1.25777i	0.509114	+	0.860699i	$0.329973\pi$
$479$	−8.94427	+	27.5276i	−0.408674	+	1.25777i	−0.917788	+	0.397071i	$0.870027\pi$
$480$	−15.5902	+	11.3269i	−0.711591	+	0.517001i
$481$	2.38197	+	1.73060i	0.108608	+	0.0789085i
$482$	4.00000	+	12.3107i	0.182195	+	0.560739i
$483$	−8.09017			−0.368115
$484$	−4.78115	−	9.90659i	−0.217325	−	0.450300i
$485$	−48.0689			−2.18270
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	28.1246	+	20.4337i	1.27445	+	0.925941i	0.999370	−	0.0354815i	$-0.0112965\pi$
$487$	28.1246	+	20.4337i	1.27445	+	0.925941i	0.275077	+	0.961422i	$0.411296\pi$
$488$	21.7082	−	15.7719i	0.982684	−	0.713962i
$489$	−6.61803	+	20.3682i	−0.299278	+	0.921082i
$490$	−1.19098	+	3.66547i	−0.0538031	+	0.165589i
$491$	−12.3992	+	9.00854i	−0.559567	+	0.406550i	−0.831301	−	0.555823i	$-0.812403\pi$
$491$	−12.3992	+	9.00854i	−0.559567	+	0.406550i	0.271733	+	0.962373i	$0.412403\pi$
$492$	3.35410	+	2.43690i	0.151215	+	0.109864i
$493$	−0.708204	−	2.17963i	−0.0318959	−	0.0981655i
$494$	−1.23607			−0.0556133
$495$	−9.80902	+	8.19624i	−0.440883	+	0.368393i
$496$	−8.32624			−0.373859
$497$	−2.76393	−	8.50651i	−0.123979	−	0.381569i
$498$	12.0902	+	8.78402i	0.541773	+	0.393621i
$499$	−3.09017	+	2.24514i	−0.138335	+	0.100506i	−0.654801	−	0.755802i	$-0.727247\pi$
$499$	−3.09017	+	2.24514i	−0.138335	+	0.100506i	0.516466	+	0.856308i	$0.327247\pi$
$500$	−5.78115	+	17.7926i	−0.258541	+	0.795707i
$501$	4.38197	−	13.4863i	0.195772	−	0.602524i
$502$	1.47214	−	1.06957i	0.0657046	−	0.0477372i
$503$	22.1803	+	16.1150i	0.988972	+	0.718531i	0.959696	−	0.281041i	$-0.0906796\pi$
$503$	22.1803	+	16.1150i	0.988972	+	0.718531i	0.0292766	+	0.999571i	$0.490680\pi$
$504$	0.927051	+	2.85317i	0.0412941	+	0.127090i
$505$	35.0344			1.55901
$506$	22.7254	+	14.2658i	1.01027	+	0.634194i
$507$	2.52786			0.112266
$508$	−0.381966	−	1.17557i	−0.0169470	−	0.0521575i
$509$	13.8262	+	10.0453i	0.612837	+	0.445252i	0.850412	−	0.526117i	$-0.176353\pi$
$509$	13.8262	+	10.0453i	0.612837	+	0.445252i	−0.237575	+	0.971369i	$0.576353\pi$
$510$	−3.57295	+	2.59590i	−0.158213	+	0.114948i
$511$	−0.236068	+	0.726543i	−0.0104430	+	0.0321403i
$512$	3.39919	−	10.4616i	0.150224	−	0.462343i
$513$	0.309017	−	0.224514i	0.0136434	−	0.00991253i
$514$	0.309017	+	0.224514i	0.0136302	+	0.00990289i
$515$	6.34346	+	19.5232i	0.279526	+	0.860293i
$516$	3.23607			0.142460
$517$	6.61803	−	0.449028i	0.291061	−	0.0197482i
$518$	0.909830			0.0399756
$519$	−4.06231	−	12.5025i	−0.178315	−	0.548798i
$520$	−30.2705	−	21.9928i	−1.32745	−	0.964449i
$521$	7.59017	−	5.51458i	0.332531	−	0.241598i	−0.408973	−	0.912547i	$-0.634113\pi$
$521$	7.59017	−	5.51458i	0.332531	−	0.241598i	0.741504	+	0.670948i	$0.234113\pi$
$522$	0.618034	−	1.90211i	0.0270506	−	0.0832532i
$523$	4.35410	−	13.4005i	0.190392	−	0.585965i	−0.809608	−	0.586971i	$-0.800320\pi$
$523$	4.35410	−	13.4005i	0.190392	−	0.585965i	0.999999	+	0.00100602i	$0.000320226\pi$
$524$	12.7082	−	9.23305i	0.555160	−	0.403348i
$525$	7.97214	+	5.79210i	0.347933	+	0.252788i
$526$	−6.97214	−	21.4580i	−0.304000	−	0.935614i
$527$	9.54102			0.415613
$528$	0.809017	−	3.21644i	0.0352079	−	0.139978i
$529$	42.4508			1.84569
$530$	12.1246	+	37.3157i	0.526659	+	1.62089i
$531$	−9.09017	−	6.60440i	−0.394480	−	0.286606i
$532$	0.309017	−	0.224514i	0.0133976	−	0.00973392i
$533$	−4.14590	+	12.7598i	−0.179579	+	0.552687i
$534$	−3.11803	+	9.59632i	−0.134931	+	0.415273i
$535$	−50.1697	+	36.4504i	−2.16903	+	1.57589i
$536$	−19.4164	−	14.1068i	−0.838661	−	0.609323i
$537$	−3.28115	−	10.0984i	−0.141592	−	0.435776i
$538$	7.88854			0.340099
$539$	1.23607	+	3.07768i	0.0532412	+	0.132565i
$540$	3.85410			0.165854
$541$	3.13525	+	9.64932i	0.134795	+	0.414857i	0.995558	−	0.0941492i	$-0.0300131\pi$
$541$	3.13525	+	9.64932i	0.134795	+	0.414857i	−0.860763	+	0.509006i	$0.830013\pi$
$542$	10.4443	+	7.58821i	0.448620	+	0.325941i
$543$	−0.854102	+	0.620541i	−0.0366530	+	0.0266300i
$544$	−1.77051	+	5.44907i	−0.0759100	+	0.233627i
$545$	−11.3885	+	35.0503i	−0.487832	+	1.50139i
$546$	−2.61803	+	1.90211i	−0.112042	+	0.0814029i
$547$	22.2705	+	16.1805i	0.952218	+	0.691827i	0.951330	−	0.308173i	$-0.0997174\pi$
$547$	22.2705	+	16.1805i	0.952218	+	0.691827i	0.000887764		1.00000i	$0.499717\pi$
$548$	−3.47214	−	10.6861i	−0.148322	−	0.456489i
$549$	−8.94427			−0.381732
$550$	−12.1803	−	30.3278i	−0.519371	−	1.29318i
$551$	−0.763932			−0.0325446
$552$	−7.50000	−	23.0826i	−0.319221	−	0.982462i
$553$	11.3262	+	8.22899i	0.481641	+	0.349932i
$554$	−24.7254	+	17.9641i	−1.05048	+	0.763220i
$555$	1.08359	−	3.33495i	0.0459959	−	0.141561i
$556$	6.11803	−	18.8294i	0.259462	−	0.798543i
$557$	−4.38197	+	3.18368i	−0.185670	+	0.134897i	−0.676737	−	0.736224i	$-0.736607\pi$
$557$	−4.38197	+	3.18368i	−0.185670	+	0.134897i	0.491068	+	0.871121i	$0.336607\pi$
$558$	6.73607	+	4.89404i	0.285160	+	0.207181i
$559$	3.23607	+	9.95959i	0.136871	+	0.421246i
$560$	−3.85410			−0.162866
$561$	−0.927051	+	3.68571i	−0.0391401	+	0.155611i
$562$	−18.9443			−0.799116
$563$	−1.34752	−	4.14725i	−0.0567914	−	0.174786i	0.918637	−	0.395103i	$-0.129291\pi$
$563$	−1.34752	−	4.14725i	−0.0567914	−	0.174786i	−0.975428	+	0.220317i	$0.929291\pi$
$564$	−1.61803	−	1.17557i	−0.0681315	−	0.0495004i
$565$	−16.3262	+	11.8617i	−0.686850	+	0.499026i
$566$	−10.3713	+	31.9196i	−0.435939	+	1.34168i
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$	21.7082	−	15.7719i	0.910856	−	0.661776i
$569$	−3.38197	−	2.45714i	−0.141779	−	0.103009i	0.514635	−	0.857410i	$-0.327928\pi$
$569$	−3.38197	−	2.45714i	−0.141779	−	0.103009i	−0.656414	+	0.754401i	$0.727928\pi$
$570$	0.454915	+	1.40008i	0.0190543	+	0.0586431i
$571$	−38.5410			−1.61289			−0.806446	−	0.591308i	$-0.798612\pi$
$571$	−38.5410			−1.61289			−0.806446	+	0.591308i	$0.798612\pi$
$572$	−10.7082	+	0.726543i	−0.447732	+	0.0303783i
$573$	−15.2705			−0.637935
$574$	1.28115	+	3.94298i	0.0534743	+	0.164577i
$575$	−64.4959	−	46.8590i	−2.68967	−	1.95416i
$576$	−5.66312	+	4.11450i	−0.235963	+	0.171437i
$577$	5.14590	−	15.8374i	0.214227	−	0.659321i	−0.784981	−	0.619520i	$-0.787327\pi$
$577$	5.14590	−	15.8374i	0.214227	−	0.659321i	0.999208	−	0.0398017i	$-0.0126726\pi$
$578$	4.84752	−	14.9191i	0.201630	−	0.620555i
$579$	16.6803	−	12.1190i	0.693211	−	0.503647i
$580$	−6.23607	−	4.53077i	−0.258939	−	0.188130i
$581$	−4.61803	−	14.2128i	−0.191588	−	0.589648i
$582$	−12.4721			−0.516987
$583$	28.5967	+	17.9516i	1.18436	+	0.743478i
$584$	−2.29180			−0.0948352
$585$	3.85410	+	11.8617i	0.159348	+	0.490421i
$586$	−3.88197	−	2.82041i	−0.160363	−	0.116510i
$587$	25.7984	−	18.7436i	1.06481	−	0.773632i	0.0898401	−	0.995956i	$-0.471364\pi$
$587$	25.7984	−	18.7436i	1.06481	−	0.773632i	0.974973	+	0.222324i	$0.0713644\pi$
$588$	0.309017	−	0.951057i	0.0127436	−	0.0392209i
$589$	0.982779	−	3.02468i	0.0404947	−	0.124630i
$590$	35.0344	−	25.4540i	1.44235	−	1.04793i
$591$	3.23607	+	2.35114i	0.133114	+	0.0967130i
$592$	0.281153	+	0.865300i	0.0115553	+	0.0355636i
$593$	23.5623			0.967588			0.483794	−	0.875182i	$-0.339258\pi$
$593$	23.5623			0.967588			0.483794	+	0.875182i	$0.339258\pi$
$594$	−2.54508	+	2.12663i	−0.104426	+	0.0872566i
$595$	4.41641			0.181055
$596$	6.18034	+	19.0211i	0.253157	+	0.779136i
$597$	−0.309017	−	0.224514i	−0.0126472	−	0.00918875i
$598$	21.1803	−	15.3884i	0.866129	−	0.629279i
$599$	5.73607	−	17.6538i	0.234369	−	0.721315i	−0.762835	−	0.646593i	$-0.776193\pi$
$599$	5.73607	−	17.6538i	0.234369	−	0.721315i	0.997204	−	0.0747217i	$-0.0238068\pi$
$600$	−9.13525	+	28.1154i	−0.372945	+	1.14781i
$601$	−4.85410	+	3.52671i	−0.198003	+	0.143858i	−0.682369	−	0.731008i	$-0.739050\pi$
$601$	−4.85410	+	3.52671i	−0.198003	+	0.143858i	0.484366	+	0.874865i	$0.339050\pi$
$602$	2.61803	+	1.90211i	0.106703	+	0.0775243i
$603$	2.47214	+	7.60845i	0.100673	+	0.309840i
$604$	2.00000			0.0813788
$605$	−37.3500	−	20.0579i	−1.51849	−	0.815471i
$606$	9.09017			0.369263
$607$	1.64590	+	5.06555i	0.0668049	+	0.205604i	0.978887	−	0.204404i	$-0.0655257\pi$
$607$	1.64590	+	5.06555i	0.0668049	+	0.205604i	−0.912082	+	0.410009i	$0.865526\pi$
$608$	1.54508	+	1.12257i	0.0626615	+	0.0455262i
$609$	−1.61803	+	1.17557i	−0.0655660	+	0.0476365i
$610$	10.6525	−	32.7849i	0.431306	−	1.32742i
$611$	2.00000	−	6.15537i	0.0809113	−	0.249019i
$612$	0.927051	−	0.673542i	0.0374738	−	0.0272263i
$613$	−0.690983	−	0.502029i	−0.0279085	−	0.0202767i	0.573744	−	0.819035i	$-0.305491\pi$
$613$	−0.690983	−	0.502029i	−0.0279085	−	0.0202767i	−0.601652	+	0.798758i	$0.705491\pi$
$614$	−2.86475	−	8.81678i	−0.115612	−	0.355816i
$615$	15.9787			0.644324
$616$	−7.63525	+	6.37988i	−0.307633	+	0.257053i
$617$	13.3475			0.537351			0.268676	−	0.963231i	$-0.413414\pi$
$617$	13.3475			0.537351			0.268676	+	0.963231i	$0.413414\pi$
$618$	1.64590	+	5.06555i	0.0662077	+	0.203766i
$619$	−21.4443	−	15.5802i	−0.861918	−	0.626220i	0.0664880	−	0.997787i	$-0.478821\pi$
$619$	−21.4443	−	15.5802i	−0.861918	−	0.626220i	−0.928406	+	0.371567i	$0.878821\pi$
$620$	25.9615	−	18.8621i	1.04264	−	0.757521i
$621$	−2.50000	+	7.69421i	−0.100322	+	0.308758i
$622$	1.61803	−	4.97980i	0.0648773	−	0.199672i
$623$	8.16312	−	5.93085i	0.327048	−	0.237615i
$624$	−2.61803	−	1.90211i	−0.104805	−	0.0761455i
$625$	7.05573	+	21.7153i	0.282229	+	0.868612i
$626$	32.1803			1.28619
$627$	1.07295	+	0.673542i	0.0428495	+	0.0268987i
$628$	3.70820			0.147973
$629$	−0.322173	−	0.991545i	−0.0128459	−	0.0395355i
$630$	3.11803	+	2.26538i	0.124225	+	0.0902551i
$631$	4.76393	−	3.46120i	0.189649	−	0.137788i	−0.488909	−	0.872335i	$-0.662605\pi$
$631$	4.76393	−	3.46120i	0.189649	−	0.137788i	0.678558	+	0.734547i	$0.262605\pi$
$632$	−12.9787	+	39.9444i	−0.516266	+	1.58890i
$633$	0.618034	−	1.90211i	0.0245646	−	0.0756022i
$634$	17.4721	−	12.6942i	0.693907	−	0.504153i
$635$	−3.85410	−	2.80017i	−0.152945	−	0.111121i
$636$	−3.14590	−	9.68208i	−0.124743	−	0.383919i
$637$	3.23607			0.128218
$638$	6.61803	−	0.449028i	0.262010	−	0.0177772i
$639$	−8.94427			−0.353830
$640$	3.57295	+	10.9964i	0.141233	+	0.434671i
$641$	18.3262	+	13.3148i	0.723843	+	0.525903i	0.887610	−	0.460596i	$-0.152364\pi$
$641$	18.3262	+	13.3148i	0.723843	+	0.525903i	−0.163767	+	0.986499i	$0.552364\pi$
$642$	−13.0172	+	9.45756i	−0.513749	+	0.373260i
$643$	−5.22949	+	16.0947i	−0.206231	+	0.634714i	0.793430	+	0.608662i	$0.208293\pi$
$643$	−5.22949	+	16.0947i	−0.206231	+	0.634714i	−0.999661	+	0.0260516i	$0.991707\pi$
$644$	−2.50000	+	7.69421i	−0.0985138	+	0.303194i
$645$	10.0902	−	7.33094i	0.397300	−	0.288655i
$646$	0.354102	+	0.257270i	0.0139320	+	0.0101222i
$647$	4.43769	+	13.6578i	0.174464	+	0.536944i	0.999609	−	0.0279770i	$-0.00890653\pi$
$647$	4.43769	+	13.6578i	0.174464	+	0.536944i	−0.825145	+	0.564921i	$0.808907\pi$
$648$	3.00000			0.117851
$649$	9.09017	−	36.1401i	0.356820	−	1.41862i
$650$	−31.8885			−1.25077
$651$	−2.57295	−	7.91872i	−0.100842	−	0.310359i
$652$	17.3262	+	12.5882i	0.678548	+	0.492994i
$653$	−8.00000	+	5.81234i	−0.313064	+	0.227454i	−0.733210	−	0.680002i	$-0.761979\pi$
$653$	−8.00000	+	5.81234i	−0.313064	+	0.227454i	0.420146	+	0.907457i	$0.361979\pi$
$654$	−2.95492	+	9.09429i	−0.115546	+	0.355615i
$655$	18.7082	−	57.5779i	0.730990	−	2.24976i
$656$	−3.35410	+	2.43690i	−0.130956	+	0.0951449i
$657$	0.618034	+	0.449028i	0.0241118	+	0.0175182i
$658$	−0.618034	−	1.90211i	−0.0240935	−	0.0741521i
$659$	−5.96556			−0.232385			−0.116193	−	0.993227i	$-0.537069\pi$
$659$	−5.96556			−0.232385			−0.116193	+	0.993227i	$0.537069\pi$
$660$	4.76393	+	11.8617i	0.185436	+	0.461716i
$661$	21.7082			0.844351			0.422176	−	0.906514i	$-0.361267\pi$
$661$	21.7082			0.844351			0.422176	+	0.906514i	$0.361267\pi$
$662$	4.43769	+	13.6578i	0.172476	+	0.530826i
$663$	3.00000	+	2.17963i	0.116510	+	0.0846497i
$664$	36.2705	−	26.3521i	1.40757	−	1.02266i
$665$	0.454915	−	1.40008i	0.0176408	−	0.0542929i
$666$	0.281153	−	0.865300i	0.0108945	−	0.0335297i
$667$	13.0902	−	9.51057i	0.506853	−	0.368251i
$668$	−11.4721	−	8.33499i	−0.443870	−	0.322491i
$669$	1.17376	+	3.61247i	0.0453803	+	0.139666i
$670$	−30.8328			−1.19118
$671$	−11.0557	−	27.5276i	−0.426802	−	1.06269i
$672$	5.00000			0.192879
$673$	0.0344419	+	0.106001i	0.00132764	+	0.00408604i	0.951718	−	0.306973i	$-0.0993162\pi$
$673$	0.0344419	+	0.106001i	0.00132764	+	0.00408604i	−0.950391	+	0.311059i	$0.899316\pi$
$674$	−27.3885	−	19.8989i	−1.05497	−	0.766479i
$675$	7.97214	−	5.79210i	0.306848	−	0.222938i
$676$	0.781153	−	2.40414i	0.0300443	−	0.0924670i
$677$	−3.67376	+	11.3067i	−0.141194	+	0.434551i	−0.996502	−	0.0835693i	$-0.973368\pi$
$677$	−3.67376	+	11.3067i	−0.141194	+	0.434551i	0.855308	+	0.518120i	$0.173368\pi$
$678$	−4.23607	+	3.07768i	−0.162685	+	0.118198i
$679$	10.0902	+	7.33094i	0.387225	+	0.281336i
$680$	4.09424	+	12.6008i	0.157007	+	0.483217i
$681$	5.41641			0.207557
$682$	−6.73607	+	26.7809i	−0.257937	+	1.02549i
$683$	−23.9230			−0.915388			−0.457694	−	0.889110i	$-0.651324\pi$
$683$	−23.9230			−0.915388			−0.457694	+	0.889110i	$0.651324\pi$
$684$	−0.118034	−	0.363271i	−0.00451314	−	0.0138900i
$685$	−35.0344	−	25.4540i	−1.33860	−	0.972548i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	−5.18034	+	15.9434i	−0.197642	+	0.608280i
$688$	−1.00000	+	3.07768i	−0.0381246	+	0.117336i
$689$	26.6525	−	19.3642i	1.01538	−	0.737716i
$690$	−25.2254	−	18.3273i	−0.960316	−	0.697710i
$691$	−7.70163	−	23.7032i	−0.292984	−	0.901711i	−0.983891	−	0.178768i	$-0.942789\pi$
$691$	−7.70163	−	23.7032i	−0.292984	−	0.901711i	0.690908	−	0.722943i	$-0.257211\pi$
$692$	−13.1459			−0.499732
$693$	3.30902	−	0.224514i	0.125699	−	0.00852858i
$694$	14.6180			0.554893
$695$	−23.5795	−	72.5703i	−0.894422	−	2.75275i
$696$	−4.85410	−	3.52671i	−0.183994	−	0.133680i
$697$	3.84346	−	2.79244i	0.145581	−	0.105771i
$698$	−8.41641	+	25.9030i	−0.318566	+	0.980445i
$699$	−2.38197	+	7.33094i	−0.0900942	+	0.277282i
$700$	7.97214	−	5.79210i	0.301318	−	0.218921i
$701$	27.5623	+	20.0252i	1.04101	+	0.756341i	0.970483	−	0.241169i	$-0.0775307\pi$
$701$	27.5623	+	20.0252i	1.04101	+	0.756341i	0.0705307	+	0.997510i	$0.477531\pi$
$702$	1.00000	+	3.07768i	0.0377426	+	0.116160i
$703$	−0.347524			−0.0131071
$704$	−19.6631	−	12.3435i	−0.741082	−	0.465213i
$705$	−7.70820			−0.290308
$706$	−1.09017	−	3.35520i	−0.0410291	−	0.126275i
$707$	−7.35410	−	5.34307i	−0.276579	−	0.200947i
$708$	−9.09017	+	6.60440i	−0.341630	+	0.248208i
$709$	12.5729	−	38.6956i	0.472187	−	1.45324i	−0.377527	−	0.925999i	$-0.623226\pi$
$709$	12.5729	−	38.6956i	0.472187	−	1.45324i	0.849714	−	0.527244i	$-0.176774\pi$
$710$	10.6525	−	32.7849i	0.399780	−	1.23040i
$711$	11.3262	−	8.22899i	0.424767	−	0.308611i
$712$	24.4894	+	17.7926i	0.917777	+	0.666804i
$713$	20.8156	+	64.0638i	0.779550	+	2.39921i
$714$	1.14590			0.0428842
$715$	−31.7426	+	26.5236i	−1.18711	+	0.991926i
$716$	−10.6180			−0.396815
$717$	−5.73607	−	17.6538i	−0.214217	−	0.659293i
$718$	−17.8262	−	12.9515i	−0.665269	−	0.483346i
$719$	−36.5066	+	26.5236i	−1.36147	+	0.989163i	−0.363115	+	0.931744i	$0.618287\pi$
$719$	−36.5066	+	26.5236i	−1.36147	+	0.989163i	−0.998350	+	0.0574185i	$0.981713\pi$
$720$	−1.19098	+	3.66547i	−0.0443853	+	0.136604i
$721$	1.64590	−	5.06555i	0.0612964	−	0.188651i
$722$	−15.2533	+	11.0822i	−0.567669	+	0.412435i
$723$	−10.4721	−	7.60845i	−0.389463	−	0.282961i
$724$	0.326238	+	1.00406i	0.0121245	+	0.0373155i
$725$	−19.7082			−0.731944
$726$	−9.69098	−	5.20431i	−0.359666	−	0.193150i
$727$	−16.7426			−0.620950			−0.310475	−	0.950581i	$-0.600488\pi$
$727$	−16.7426			−0.620950			−0.310475	+	0.950581i	$0.600488\pi$
$728$	3.00000	+	9.23305i	0.111187	+	0.342200i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−2.38197	+	1.73060i	−0.0881605	+	0.0640524i
$731$	1.14590	−	3.52671i	0.0423826	−	0.130440i
$732$	−2.76393	+	8.50651i	−0.102158	+	0.314410i
$733$	7.38197	−	5.36331i	0.272659	−	0.198098i	−0.443050	−	0.896497i	$-0.646104\pi$
$733$	7.38197	−	5.36331i	0.272659	−	0.198098i	0.715709	+	0.698398i	$0.246104\pi$
$734$	−13.9721	−	10.1514i	−0.515721	−	0.374693i
$735$	−1.19098	−	3.66547i	−0.0439301	−	0.135203i
$736$	−40.4508			−1.49104
$737$	−20.3607	+	17.0130i	−0.749995	+	0.626683i
$738$	4.14590			0.152613
$739$	−8.34752	−	25.6910i	−0.307069	−	0.945060i	−0.978897	−	0.204353i	$-0.934491\pi$
$739$	−8.34752	−	25.6910i	−0.307069	−	0.945060i	0.671829	−	0.740707i	$-0.265509\pi$
$740$	−2.83688	−	2.06111i	−0.104286	−	0.0757681i
$741$	1.00000	−	0.726543i	0.0367359	−	0.0266902i
$742$	3.14590	−	9.68208i	0.115490	−	0.355440i
$743$	0.517221	−	1.59184i	0.0189750	−	0.0583990i	−0.941121	−	0.338071i	$-0.890226\pi$
$743$	0.517221	−	1.59184i	0.0189750	−	0.0583990i	0.960096	+	0.279672i	$0.0902257\pi$
$744$	20.2082	−	14.6821i	0.740869	−	0.538273i
$745$	62.3607	+	45.3077i	2.28472	+	1.65995i
$746$	2.37132	+	7.29818i	0.0868203	+	0.267205i
$747$	−14.9443			−0.546782
$748$	3.21885	+	2.02063i	0.117693	+	0.0738814i
$749$	16.0902			0.587922
$750$	5.78115	+	17.7926i	0.211098	+	0.649692i
$751$	1.23607	+	0.898056i	0.0451048	+	0.0327705i	0.610109	−	0.792317i	$-0.291126\pi$
$751$	1.23607	+	0.898056i	0.0451048	+	0.0327705i	−0.565004	+	0.825088i	$0.691126\pi$
$752$	1.61803	−	1.17557i	0.0590036	−	0.0428686i
$753$	−0.562306	+	1.73060i	−0.0204916	+	0.0630666i
$754$	2.00000	−	6.15537i	0.0728357	−	0.224165i
$755$	6.23607	−	4.53077i	0.226954	−	0.164892i
$756$	−0.809017	−	0.587785i	−0.0294237	−	0.0213775i
$757$	−4.73607	−	14.5761i	−0.172135	−	0.529778i	0.827356	−	0.561678i	$-0.189844\pi$
$757$	−4.73607	−	14.5761i	−0.172135	−	0.529778i	−0.999491	+	0.0319002i	$0.989844\pi$
$758$	6.47214			0.235079
$759$	−26.7705	+	1.81636i	−0.971708	+	0.0659296i
$760$	4.41641			0.160200
$761$	−7.96556	−	24.5155i	−0.288751	−	0.888685i	−0.985249	−	0.171126i	$-0.945259\pi$
$761$	−7.96556	−	24.5155i	−0.288751	−	0.888685i	0.696498	−	0.717559i	$-0.254741\pi$
$762$	−1.00000	−	0.726543i	−0.0362262	−	0.0263199i
$763$	7.73607	−	5.62058i	0.280064	−	0.203479i
$764$	−4.71885	+	14.5231i	−0.170722	+	0.525428i
$765$	1.36475	−	4.20025i	0.0493425	−	0.151860i
$766$	−25.0344	+	18.1886i	−0.904531	+	0.657180i
$767$	−29.4164	−	21.3723i	−1.06216	−	0.771708i
$768$	5.25329	+	16.1680i	0.189562	+	0.583411i
$769$	41.4164			1.49351			0.746757	−	0.665097i	$-0.231610\pi$
$769$	41.4164			1.49351			0.746757	+	0.665097i	$0.231610\pi$
$770$	−3.11803	+	12.3965i	−0.112366	+	0.446739i
$771$	−0.381966			−0.0137562
$772$	−6.37132	−	19.6089i	−0.229309	−	0.705740i
$773$	17.0344	+	12.3762i	0.612686	+	0.445143i	0.850359	−	0.526203i	$-0.176385\pi$
$773$	17.0344	+	12.3762i	0.612686	+	0.445143i	−0.237673	+	0.971345i	$0.576385\pi$
$774$	2.61803	−	1.90211i	0.0941033	−	0.0683700i
$775$	25.3541	−	78.0319i	0.910746	−	2.80299i
$776$	−11.5623	+	35.5851i	−0.415063	+	1.27743i
$777$	−0.736068	+	0.534785i	−0.0264063	+	0.0191853i
$778$	−0.145898	−	0.106001i	−0.00523070	−	0.00380032i
$779$	−0.489357	−	1.50609i	−0.0175330	−	0.0539611i
$780$	12.4721			0.446574
$781$	−11.0557	−	27.5276i	−0.395605	−	0.985016i
$782$	−9.27051			−0.331513
$783$	0.618034	+	1.90211i	0.0220867	+	0.0679760i
$784$	0.809017	+	0.587785i	0.0288935	+	0.0209923i
$785$	11.5623	−	8.40051i	0.412676	−	0.299827i
$786$	4.85410	−	14.9394i	0.173140	−	0.532870i
$787$	−6.57295	+	20.2295i	−0.234300	+	0.721102i	0.762913	+	0.646501i	$0.223768\pi$
$787$	−6.57295	+	20.2295i	−0.234300	+	0.721102i	−0.997213	+	0.0746012i	$0.976232\pi$
$788$	3.23607	−	2.35114i	0.115280	−	0.0837559i
$789$	18.2533	+	13.2618i	0.649834	+	0.472132i
$790$	16.6738	+	51.3166i	0.593226	+	1.82576i
$791$	5.23607			0.186173
$792$	3.70820	+	9.23305i	0.131765	+	0.328082i
$793$	−28.9443			−1.02784
$794$	5.14590	+	15.8374i	0.182621	+	0.562050i
$795$	−31.7426	−	23.0624i	−1.12580	−	0.817938i
$796$	−0.309017	+	0.224514i	−0.0109528	+	0.00795769i
$797$	−7.19098	+	22.1316i	−0.254718	+	0.783940i	0.739167	+	0.673522i	$0.235219\pi$
$797$	−7.19098	+	22.1316i	−0.254718	+	0.783940i	−0.993885	+	0.110419i	$0.964781\pi$
$798$	0.118034	−	0.363271i	0.00417836	−	0.0128597i
$799$	−1.85410	+	1.34708i	−0.0655934	+	0.0476564i
$800$	39.8607	+	28.9605i	1.40929	+	1.02391i
$801$	−3.11803	−	9.59632i	−0.110170	−	0.339069i
$802$	−9.52786			−0.336441
$803$	−0.618034	+	2.45714i	−0.0218099	+	0.0867107i
$804$	8.00000			0.282138
$805$	9.63525	+	29.6543i	0.339598	+	1.04518i
$806$	21.7984	+	15.8374i	0.767815	+	0.557850i
$807$	−6.38197	+	4.63677i	−0.224656	+	0.163222i
$808$	8.42705	−	25.9358i	0.296463	−	0.912418i
$809$	0.819660	−	2.52265i	0.0288177	−	0.0886918i	−0.935613	−	0.353027i	$-0.885152\pi$
$809$	0.819660	−	2.52265i	0.0288177	−	0.0886918i	0.964431	+	0.264335i	$0.0851524\pi$
$810$	3.11803	−	2.26538i	0.109557	−	0.0795975i
$811$	−22.9443	−	16.6700i	−0.805682	−	0.585362i	0.106893	−	0.994271i	$-0.465910\pi$
$811$	−22.9443	−	16.6700i	−0.805682	−	0.585362i	−0.912576	+	0.408908i	$0.865910\pi$
$812$	0.618034	+	1.90211i	0.0216887	+	0.0667511i
$813$	−12.9098			−0.452768
$814$	3.01064	−	0.204270i	0.105523	−	0.00715964i
$815$	82.5410			2.89129
$816$	0.354102	+	1.08981i	0.0123960	+	0.0381511i
$817$	−1.00000	−	0.726543i	−0.0349856	−	0.0254185i
$818$	26.8885	−	19.5357i	0.940136	−	0.683049i
$819$	1.00000	−	3.07768i	0.0349428	−	0.107543i
$820$	4.93769	−	15.1967i	0.172432	−	0.530690i
$821$	11.6180	−	8.44100i	0.405472	−	0.294593i	−0.366294	−	0.930499i	$-0.619374\pi$
$821$	11.6180	−	8.44100i	0.405472	−	0.294593i	0.771766	+	0.635906i	$0.219374\pi$
$822$	−9.09017	−	6.60440i	−0.317056	−	0.230355i
$823$	4.79837	+	14.7679i	0.167261	+	0.514776i	0.999196	−	0.0400973i	$-0.0127668\pi$
$823$	4.79837	+	14.7679i	0.167261	+	0.514776i	−0.831935	+	0.554873i	$0.812767\pi$
$824$	15.9787			0.556645
$825$	27.6803	+	17.3763i	0.963706	+	0.604965i
$826$	−11.2361			−0.390953
$827$	3.50000	+	10.7719i	0.121707	+	0.374575i	0.993287	−	0.115678i	$-0.0369041\pi$
$827$	3.50000	+	10.7719i	0.121707	+	0.374575i	−0.871580	+	0.490254i	$0.836904\pi$
$828$	6.54508	+	4.75528i	0.227457	+	0.165257i
$829$	−8.94427	+	6.49839i	−0.310647	+	0.225699i	−0.732174	−	0.681117i	$-0.761494\pi$
$829$	−8.94427	+	6.49839i	−0.310647	+	0.225699i	0.421527	+	0.906816i	$0.361494\pi$
$830$	17.7984	−	54.7778i	0.617791	−	1.90136i
$831$	9.44427	−	29.0665i	0.327618	−	1.00831i
$832$	−18.3262	+	13.3148i	−0.635348	+	0.461607i
$833$	−0.927051	−	0.673542i	−0.0321204	−	0.0233368i
$834$	−6.11803	−	18.8294i	−0.211850	−	0.652008i
$835$	−54.6525			−1.89133
$836$	0.972136	−	0.812299i	0.0336220	−	0.0280940i
$837$	−8.32624			−0.287797
$838$	−5.94427	−	18.2946i	−0.205341	−	0.631976i
$839$	−5.32624	−	3.86974i	−0.183882	−	0.133598i	0.492036	−	0.870575i	$-0.336253\pi$
$839$	−5.32624	−	3.86974i	−0.183882	−	0.133598i	−0.675918	+	0.736977i	$0.736253\pi$
$840$	9.35410	−	6.79615i	0.322747	−	0.234490i
$841$	−7.72542	+	23.7764i	−0.266394	+	0.819876i
$842$	−3.50000	+	10.7719i	−0.120618	+	0.371224i
$843$	15.3262	−	11.1352i	0.527864	−	0.383515i
$844$	−1.61803	−	1.17557i	−0.0556950	−	0.0404648i
$845$	−3.01064	−	9.26581i	−0.103569	−	0.318753i
$846$	−2.00000			−0.0687614
$847$	4.78115	+	9.90659i	0.164282	+	0.340395i
$848$	10.1803			0.349594
$849$	−10.3713	−	31.9196i	−0.355943	−	1.09548i
$850$	9.13525	+	6.63715i	0.313337	+	0.227652i
$851$	5.95492	−	4.32650i	0.204132	−	0.148310i
$852$	−2.76393	+	8.50651i	−0.0946908	+	0.291428i
$853$	−0.708204	+	2.17963i	−0.0242484	+	0.0746290i	−0.962448	−	0.271465i	$-0.912492\pi$
$853$	−0.708204	+	2.17963i	−0.0242484	+	0.0746290i	0.938200	+	0.346094i	$0.112492\pi$
$854$	−7.23607	+	5.25731i	−0.247613	+	0.179901i
$855$	−1.19098	−	0.865300i	−0.0407308	−	0.0295926i
$856$	14.9164	+	45.9080i	0.509832	+	1.56910i
$857$	−1.05573			−0.0360630			−0.0180315	−	0.999837i	$-0.505740\pi$
$857$	−1.05573			−0.0360630			−0.0180315	+	0.999837i	$0.505740\pi$
$858$	−8.23607	+	6.88191i	−0.281175	+	0.234945i
$859$	29.8885			1.01978			0.509892	−	0.860238i	$-0.329685\pi$
$859$	29.8885			1.01978			0.509892	+	0.860238i	$0.329685\pi$
$860$	−3.85410	−	11.8617i	−0.131424	−	0.404481i
$861$	−3.35410	−	2.43690i	−0.114307	−	0.0830493i
$862$	7.35410	−	5.34307i	0.250482	−	0.181986i
$863$	−7.01064	+	21.5765i	−0.238645	+	0.734474i	0.757972	+	0.652287i	$0.226190\pi$
$863$	−7.01064	+	21.5765i	−0.238645	+	0.734474i	−0.996617	+	0.0821868i	$0.973810\pi$
$864$	1.54508	−	4.75528i	0.0525649	−	0.161778i
$865$	−40.9894	+	29.7805i	−1.39368	+	1.01257i
$866$	−10.3262	−	7.50245i	−0.350900	−	0.254944i
$867$	4.84752	+	14.9191i	0.164631	+	0.506681i
$868$	−8.32624			−0.282611
$869$	39.3262	+	24.6870i	1.33405	+	0.837448i
$870$	−7.70820			−0.261333
$871$	8.00000	+	24.6215i	0.271070	+	0.834267i
$872$	23.2082	+	16.8617i	0.785929	+	0.571011i
$873$	10.0902	−	7.33094i	0.341501	−	0.248115i
$874$	−0.954915	+	2.93893i	−0.0323005	+	0.0994107i
$875$	5.78115	−	17.7926i	0.195439	−	0.601498i
$876$	0.618034	−	0.449028i	0.0208814	−	0.0151712i
$877$	1.32624	+	0.963568i	0.0447839	+	0.0325374i	0.609952	−	0.792438i	$-0.291189\pi$
$877$	1.32624	+	0.963568i	0.0447839	+	0.0325374i	−0.565168	+	0.824976i	$0.691189\pi$
$878$	−0.864745	−	2.66141i	−0.0291837	−	0.0898183i
$879$	4.79837			0.161845
$880$	−12.7533	+	0.865300i	−0.429913	+	0.0291693i
$881$	22.4508			0.756388			0.378194	−	0.925726i	$-0.376545\pi$
$881$	22.4508			0.756388			0.378194	+	0.925726i	$0.376545\pi$
$882$	−0.309017	−	0.951057i	−0.0104051	−	0.0320237i
$883$	4.61803	+	3.35520i	0.155409	+	0.112911i	0.662772	−	0.748821i	$-0.269380\pi$
$883$	4.61803	+	3.35520i	0.155409	+	0.112911i	−0.507363	+	0.861732i	$0.669380\pi$
$884$	3.00000	−	2.17963i	0.100901	−	0.0733088i
$885$	−13.3820	+	41.1855i	−0.449830	+	1.38443i
$886$	−4.97214	+	15.3027i	−0.167042	+	0.514103i
$887$	−16.6180	+	12.0737i	−0.557979	+	0.405395i	−0.830719	−	0.556692i	$-0.812070\pi$
$887$	−16.6180	+	12.0737i	−0.557979	+	0.405395i	0.272740	+	0.962088i	$0.412070\pi$
$888$	−2.20820	−	1.60435i	−0.0741025	−	0.0538386i
$889$	0.381966	+	1.17557i	0.0128107	+	0.0394274i
$890$	38.8885			1.30355
$891$	0.809017	−	3.21644i	0.0271031	−	0.107755i
$892$	3.79837			0.127179
$893$	0.236068	+	0.726543i	0.00789971	+	0.0243128i
$894$	16.1803	+	11.7557i	0.541152	+	0.393170i
$895$	−33.1074	+	24.0539i	−1.10666	+	0.804034i
$896$	0.927051	−	2.85317i	0.0309706	−	0.0953177i
$897$	−8.09017	+	24.8990i	−0.270123	+	0.831353i
$898$	4.94427	−	3.59222i	0.164992	−	0.119874i
$899$	13.4721	+	9.78808i	0.449321	+	0.326451i
$900$	−3.04508	−	9.37181i	−0.101503	−	0.312394i
$901$	−11.6656			−0.388639
$902$	5.12461	+	12.7598i	0.170631	+	0.424854i
$903$	−3.23607			−0.107690
$904$	4.85410	+	14.9394i	0.161445	+	0.496877i
$905$	3.29180	+	2.39163i	0.109423	+	0.0795005i
$906$	1.61803	−	1.17557i	0.0537556	−	0.0390557i
$907$	−13.2148	+	40.6709i	−0.438790	+	1.35046i	0.450363	+	0.892845i	$0.351294\pi$
$907$	−13.2148	+	40.6709i	−0.438790	+	1.35046i	−0.889153	+	0.457610i	$0.848706\pi$
$908$	1.67376	−	5.15131i	0.0555457	−	0.170952i
$909$	−7.35410	+	5.34307i	−0.243920	+	0.177218i
$910$	10.0902	+	7.33094i	0.334486	+	0.243018i
$911$	−8.94427	−	27.5276i	−0.296337	−	0.912031i	−0.982769	−	0.184837i	$-0.940824\pi$
$911$	−8.94427	−	27.5276i	−0.296337	−	0.912031i	0.686432	−	0.727194i	$-0.259176\pi$
$912$	0.381966			0.0126482
$913$	−18.4721	−	45.9937i	−0.611338	−	1.52217i
$914$	−3.52786			−0.116691
$915$	10.6525	+	32.7849i	0.352160	+	1.08384i
$916$	13.5623	+	9.85359i	0.448111	+	0.325572i
$917$	−12.7082	+	9.23305i	−0.419662	+	0.304902i
$918$	0.354102	−	1.08981i	0.0116871	−	0.0359692i
$919$	−6.00000	+	18.4661i	−0.197922	+	0.609140i	0.802008	+	0.597313i	$0.203765\pi$
$919$	−6.00000	+	18.4661i	−0.197922	+	0.609140i	−0.999930	+	0.0118276i	$0.996235\pi$
$920$	−75.6763	+	54.9820i	−2.49497	+	1.81270i
$921$	7.50000	+	5.44907i	0.247133	+	0.179553i
$922$	−11.8541	−	36.4832i	−0.390394	−	1.20151i
$923$	−28.9443			−0.952712
$924$	0.809017	−	3.21644i	0.0266147	−	0.105813i
$925$	−8.96556			−0.294786
$926$	4.76393	+	14.6619i	0.156553	+	0.481819i
$927$	−4.30902	−	3.13068i	−0.141527	−	0.102825i
$928$	−8.09017	+	5.87785i	−0.265573	+	0.192950i
$929$	−1.29837	+	3.99598i	−0.0425983	+	0.131104i	−0.970094	−	0.242730i	$-0.921957\pi$
$929$	−1.29837	+	3.99598i	−0.0425983	+	0.131104i	0.927496	+	0.373834i	$0.121957\pi$
$930$	9.91641	−	30.5196i	0.325172	−	1.00078i
$931$	−0.309017	+	0.224514i	−0.0101276	+	0.00735815i
$932$	6.23607	+	4.53077i	0.204269	+	0.148410i
$933$	1.61803	+	4.97980i	0.0529721	+	0.163031i
$934$	−14.7639			−0.483091
$935$	14.6140	−	0.991545i	0.477928	−	0.0324270i
$936$	9.70820			0.317323
$937$	−0.527864	−	1.62460i	−0.0172446	−	0.0530733i	0.942064	−	0.335433i	$-0.108883\pi$
$937$	−0.527864	−	1.62460i	−0.0172446	−	0.0530733i	−0.959309	+	0.282360i	$0.908883\pi$
$938$	6.47214	+	4.70228i	0.211323	+	0.153535i
$939$	−26.0344	+	18.9151i	−0.849602	+	0.617272i
$940$	−2.38197	+	7.33094i	−0.0776912	+	0.239109i
$941$	−1.59017	+	4.89404i	−0.0518381	+	0.159541i	−0.973624	−	0.228158i	$-0.926730\pi$
$941$	−1.59017	+	4.89404i	−0.0518381	+	0.159541i	0.921786	+	0.387699i	$0.126730\pi$
$942$	3.00000	−	2.17963i	0.0977453	−	0.0710161i
$943$	27.1353	+	19.7149i	0.883645	+	0.642006i
$944$	−3.47214	−	10.6861i	−0.113008	−	0.347804i
$945$	−3.85410			−0.125374
$946$	9.09017	+	5.70634i	0.295547	+	0.185529i
$947$	−43.5623			−1.41558			−0.707792	−	0.706421i	$-0.750309\pi$
$947$	−43.5623			−1.41558			−0.707792	+	0.706421i	$0.750309\pi$
$948$	−4.32624	−	13.3148i	−0.140510	−	0.432444i
$949$	2.00000	+	1.45309i	0.0649227	+	0.0471691i
$950$	3.04508	−	2.21238i	0.0987956	−	0.0717792i
$951$	−6.67376	+	20.5397i	−0.216412	+	0.666046i
$952$	1.06231	−	3.26944i	0.0344295	−	0.105963i
$953$	39.5066	−	28.7032i	1.27974	−	0.929788i	0.280198	−	0.959942i	$-0.409600\pi$
$953$	39.5066	−	28.7032i	1.27974	−	0.929788i	0.999545	+	0.0301540i	$0.00959977\pi$
$954$	−8.23607	−	5.98385i	−0.266653	−	0.193734i
$955$	18.1869	+	55.9736i	0.588515	+	1.81126i
$956$	−18.5623			−0.600348
$957$	−5.09017	+	4.25325i	−0.164542	+	0.137488i
$958$	28.9443			0.935147
$959$	3.47214	+	10.6861i	0.112121	+	0.345073i
$960$	21.8262	+	15.8577i	0.704439	+	0.511805i
$961$	−31.0066	+	22.5276i	−1.00021	+	0.726697i
$962$	0.909830	−	2.80017i	0.0293341	−	0.0902811i
$963$	4.97214	−	15.3027i	0.160225	−	0.493121i
$964$	−10.4721	+	7.60845i	−0.337285	+	0.245052i
$965$	−64.2877	−	46.7078i	−2.06950	−	1.50358i
$966$	2.50000	+	7.69421i	0.0804362	+	0.247557i
$967$	−13.3050			−0.427858			−0.213929	−	0.976849i	$-0.568626\pi$
$967$	−13.3050			−0.427858			−0.213929	+	0.976849i	$0.568626\pi$
$968$	−23.8328	+	22.8254i	−0.766016	+	0.733635i
$969$	−0.437694			−0.0140608
$970$	14.8541	+	45.7162i	0.476936	+	1.46786i
$971$	13.0000	+	9.44505i	0.417190	+	0.303106i	0.776506	−	0.630110i	$-0.216990\pi$
$971$	13.0000	+	9.44505i	0.417190	+	0.303106i	−0.359316	+	0.933216i	$0.616990\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	−6.11803	+	18.8294i	−0.196135	+	0.603642i
$974$	10.7426	−	33.0625i	0.344217	−	1.05939i
$975$	25.7984	−	18.7436i	0.826209	−	0.600276i
$976$	−7.23607	−	5.25731i	−0.231621	−	0.168282i
$977$	−16.5066	−	50.8020i	−0.528092	−	1.62530i	−0.758119	−	0.652116i	$-0.773881\pi$
$977$	−16.5066	−	50.8020i	−0.528092	−	1.62530i	0.230027	−	0.973184i	$-0.426119\pi$
$978$	21.4164			0.684821
$979$	25.6803	−	21.4580i	0.820747	−	0.685802i
$980$	−3.85410			−0.123115
$981$	−2.95492	−	9.09429i	−0.0943432	−	0.290358i
$982$	12.3992	+	9.00854i	0.395674	+	0.287474i
$983$	−31.9787	+	23.2339i	−1.01996	+	0.741046i	−0.966275	−	0.257512i	$-0.917097\pi$
$983$	−31.9787	+	23.2339i	−1.01996	+	0.741046i	−0.0536874	+	0.998558i	$0.517097\pi$
$984$	3.84346	−	11.8290i	0.122525	−	0.377093i
$985$	4.76393	−	14.6619i	0.151791	−	0.467166i
$986$	−1.85410	+	1.34708i	−0.0590466	+	0.0428999i
$987$	1.61803	+	1.17557i	0.0515026	+	0.0374188i
$988$	−0.381966	−	1.17557i	−0.0121520	−	0.0373999i
$989$	26.1803			0.832486
$990$	10.8262	+	6.79615i	0.344080	+	0.215996i
$991$	−12.6525			−0.401919			−0.200960	−	0.979600i	$-0.564406\pi$
$991$	−12.6525			−0.401919			−0.200960	+	0.979600i	$0.564406\pi$
$992$	−12.8647	−	39.5936i	−0.408456	−	1.25710i
$993$	−11.6180	−	8.44100i	−0.368687	−	0.267867i
$994$	−7.23607	+	5.25731i	−0.229514	+	0.166752i
$995$	−0.454915	+	1.40008i	−0.0144218	+	0.0443857i
$996$	−4.61803	+	14.2128i	−0.146328	+	0.450351i
$997$	−11.7639	+	8.54700i	−0.372567	+	0.270686i	−0.758275	−	0.651935i	$-0.773957\pi$
$997$	−11.7639	+	8.54700i	−0.372567	+	0.270686i	0.385707	+	0.922621i	$0.373957\pi$
$998$	3.09017	+	2.24514i	0.0978176	+	0.0710687i
$999$	0.281153	+	0.865300i	0.00889529	+	0.0273769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.c.148.1	yes	4
3.2	odd	2		693.2.m.c.379.1		4
11.3	even	5		2541.2.a.n.1.2		2
11.8	odd	10		2541.2.a.bd.1.2		2
11.9	even	5	inner	231.2.j.c.64.1	✓	4
33.8	even	10		7623.2.a.w.1.1		2
33.14	odd	10		7623.2.a.bu.1.1		2
33.20	odd	10		693.2.m.c.64.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.c.64.1	✓	4	11.9	even	5	inner
231.2.j.c.148.1	yes	4	1.1	even	1	trivial
693.2.m.c.64.1		4	33.20	odd	10
693.2.m.c.379.1		4	3.2	odd	2
2541.2.a.n.1.2		2	11.3	even	5
2541.2.a.bd.1.2		2	11.8	odd	10
7623.2.a.w.1.1		2	33.8	even	10
7623.2.a.bu.1.1		2	33.14	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.19098 - 3.66547i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(1.19098 - 3.66547i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 + 0.951057i) q^{9} -3.85410 q^{10} +(-2.54508 + 2.12663i) q^{11} +1.00000 q^{12} +(1.00000 + 3.07768i) q^{13} +(0.809017 + 0.587785i) q^{14} +(3.11803 - 2.26538i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.354102 - 1.08981i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-0.309017 - 0.224514i) q^{19} +(-1.19098 - 3.66547i) q^{20} -1.00000 q^{21} +(2.80902 + 1.76336i) q^{22} +8.09017 q^{23} +(-0.927051 - 2.85317i) q^{24} +(-7.97214 - 5.79210i) q^{25} +(2.61803 - 1.90211i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(1.61803 - 1.17557i) q^{29} +(-3.11803 - 2.26538i) q^{30} +(2.57295 + 7.91872i) q^{31} -5.00000 q^{32} +(-3.30902 + 0.224514i) q^{33} -1.14590 q^{34} +(1.19098 + 3.66547i) q^{35} +(0.809017 + 0.587785i) q^{36} +(0.736068 - 0.534785i) q^{37} +(-0.118034 + 0.363271i) q^{38} +(-1.00000 + 3.07768i) q^{39} +(-9.35410 + 6.79615i) q^{40} +(3.35410 + 2.43690i) q^{41} +(0.309017 + 0.951057i) q^{42} +3.23607 q^{43} +(-0.809017 + 3.21644i) q^{44} +3.85410 q^{45} +(-2.50000 - 7.69421i) q^{46} +(-1.61803 - 1.17557i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.04508 + 9.37181i) q^{50} +(0.927051 - 0.673542i) q^{51} +(2.61803 + 1.90211i) q^{52} +(-3.14590 - 9.68208i) q^{53} +1.00000 q^{54} +(4.76393 + 11.8617i) q^{55} +3.00000 q^{56} +(-0.118034 - 0.363271i) q^{57} +(-1.61803 - 1.17557i) q^{58} +(-9.09017 + 6.60440i) q^{59} +(1.19098 - 3.66547i) q^{60} +(-2.76393 + 8.50651i) q^{61} +(6.73607 - 4.89404i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(2.16312 + 6.65740i) q^{64} +12.4721 q^{65} +(1.23607 + 3.07768i) q^{66} +8.00000 q^{67} +(-0.354102 - 1.08981i) q^{68} +(6.54508 + 4.75528i) q^{69} +(3.11803 - 2.26538i) q^{70} +(-2.76393 + 8.50651i) q^{71} +(0.927051 - 2.85317i) q^{72} +(0.618034 - 0.449028i) q^{73} +(-0.736068 - 0.534785i) q^{74} +(-3.04508 - 9.37181i) q^{75} -0.381966 q^{76} +(0.809017 - 3.21644i) q^{77} +3.23607 q^{78} +(-4.32624 - 13.3148i) q^{79} +(3.11803 + 2.26538i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.28115 - 3.94298i) q^{82} +(-4.61803 + 14.2128i) q^{83} +(-0.809017 + 0.587785i) q^{84} +(-3.57295 - 2.59590i) q^{85} +(-1.00000 - 3.07768i) q^{86} +2.00000 q^{87} +(9.92705 - 0.673542i) q^{88} -10.0902 q^{89} +(-1.19098 - 3.66547i) q^{90} +(-2.61803 - 1.90211i) q^{91} +(6.54508 - 4.75528i) q^{92} +(-2.57295 + 7.91872i) q^{93} +(-0.618034 + 1.90211i) q^{94} +(-1.19098 + 0.865300i) q^{95} +(-4.04508 - 2.93893i) q^{96} +(-3.85410 - 11.8617i) q^{97} -1.00000 q^{98} +(-2.80902 - 1.76336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + q^{4} + 7 q^{5} - q^{6} - q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 + q^4 + 7 * q^5 - q^6 - q^7 - 3 * q^8 - q^9	\( 4 q + q^{2} + q^{3} + q^{4} + 7 q^{5} - q^{6} - q^{7} - 3 q^{8} - q^{9} - 2 q^{10} + q^{11} + 4 q^{12} + 4 q^{13} + q^{14} + 8 q^{15} + q^{16} - 12 q^{17} + q^{18} + q^{19} - 7 q^{20} - 4 q^{21} + 9 q^{22} + 10 q^{23} + 3 q^{24} - 14 q^{25} + 6 q^{26} + q^{27} + q^{28} + 2 q^{29} - 8 q^{30} + 17 q^{31} - 20 q^{32} - 11 q^{33} - 18 q^{34} + 7 q^{35} + q^{36} - 6 q^{37} + 4 q^{38} - 4 q^{39} - 24 q^{40} - q^{42} + 4 q^{43} - q^{44} + 2 q^{45} - 10 q^{46} - 2 q^{47} - q^{48} - q^{49} - q^{50} - 3 q^{51} + 6 q^{52} - 26 q^{53} + 4 q^{54} + 28 q^{55} + 12 q^{56} + 4 q^{57} - 2 q^{58} - 14 q^{59} + 7 q^{60} - 20 q^{61} + 18 q^{62} - q^{63} - 7 q^{64} + 32 q^{65} - 4 q^{66} + 32 q^{67} + 12 q^{68} + 15 q^{69} + 8 q^{70} - 20 q^{71} - 3 q^{72} - 2 q^{73} + 6 q^{74} - q^{75} - 6 q^{76} + q^{77} + 4 q^{78} + 14 q^{79} + 8 q^{80} - q^{81} - 15 q^{82} - 14 q^{83} - q^{84} - 21 q^{85} - 4 q^{86} + 8 q^{87} + 33 q^{88} - 18 q^{89} - 7 q^{90} - 6 q^{91} + 15 q^{92} - 17 q^{93} + 2 q^{94} - 7 q^{95} - 5 q^{96} - 2 q^{97} - 4 q^{98} - 9 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + q^4 + 7 * q^5 - q^6 - q^7 - 3 * q^8 - q^9 - 2 * q^10 + q^11 + 4 * q^12 + 4 * q^13 + q^14 + 8 * q^15 + q^16 - 12 * q^17 + q^18 + q^19 - 7 * q^20 - 4 * q^21 + 9 * q^22 + 10 * q^23 + 3 * q^24 - 14 * q^25 + 6 * q^26 + q^27 + q^28 + 2 * q^29 - 8 * q^30 + 17 * q^31 - 20 * q^32 - 11 * q^33 - 18 * q^34 + 7 * q^35 + q^36 - 6 * q^37 + 4 * q^38 - 4 * q^39 - 24 * q^40 - q^42 + 4 * q^43 - q^44 + 2 * q^45 - 10 * q^46 - 2 * q^47 - q^48 - q^49 - q^50 - 3 * q^51 + 6 * q^52 - 26 * q^53 + 4 * q^54 + 28 * q^55 + 12 * q^56 + 4 * q^57 - 2 * q^58 - 14 * q^59 + 7 * q^60 - 20 * q^61 + 18 * q^62 - q^63 - 7 * q^64 + 32 * q^65 - 4 * q^66 + 32 * q^67 + 12 * q^68 + 15 * q^69 + 8 * q^70 - 20 * q^71 - 3 * q^72 - 2 * q^73 + 6 * q^74 - q^75 - 6 * q^76 + q^77 + 4 * q^78 + 14 * q^79 + 8 * q^80 - q^81 - 15 * q^82 - 14 * q^83 - q^84 - 21 * q^85 - 4 * q^86 + 8 * q^87 + 33 * q^88 - 18 * q^89 - 7 * q^90 - 6 * q^91 + 15 * q^92 - 17 * q^93 + 2 * q^94 - 7 * q^95 - 5 * q^96 - 2 * q^97 - 4 * q^98 - 9 * q^99

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