LMFDB - Embedded newform 231.2.j.e.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:	$\Z[a_1, a_2, a_3]$
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.e.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.690983 + 2.12663i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.190983 + 0.587785i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.690983 + 2.12663i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.190983 + 0.587785i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.38197 q^{10} +(-0.309017 - 3.30220i) q^{11} -3.00000 q^{12} +(1.00000 + 3.07768i) q^{13} +(-1.80902 - 1.31433i) q^{14} +(-0.500000 + 0.363271i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.50000 - 4.61653i) q^{17} +(-1.80902 + 1.31433i) q^{18} +(-2.30902 - 1.67760i) q^{19} +(-0.572949 - 1.76336i) q^{20} -1.00000 q^{21} +(6.80902 - 2.93893i) q^{22} +4.38197 q^{23} +(-0.690983 - 2.12663i) q^{24} +(3.73607 + 2.71441i) q^{25} +(-5.85410 + 4.25325i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.927051 - 2.85317i) q^{28} +(4.85410 - 3.52671i) q^{29} +(-1.11803 - 0.812299i) q^{30} +(-0.954915 - 2.93893i) q^{31} -6.70820 q^{32} +(1.69098 - 2.85317i) q^{33} +10.8541 q^{34} +(-0.190983 - 0.587785i) q^{35} +(-2.42705 - 1.76336i) q^{36} +(-3.73607 + 2.71441i) q^{37} +(1.97214 - 6.06961i) q^{38} +(-1.00000 + 3.07768i) q^{39} +(1.11803 - 0.812299i) q^{40} +(-5.97214 - 4.33901i) q^{41} +(-0.690983 - 2.12663i) q^{42} +9.70820 q^{43} +(6.57295 + 7.46969i) q^{44} -0.618034 q^{45} +(3.02786 + 9.31881i) q^{46} +(-3.61803 - 2.62866i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.19098 + 9.82084i) q^{50} +(3.92705 - 2.85317i) q^{51} +(-7.85410 - 5.70634i) q^{52} +(2.09017 + 6.43288i) q^{53} -2.23607 q^{54} +(2.00000 + 0.449028i) q^{55} +2.23607 q^{56} +(-0.881966 - 2.71441i) q^{57} +(10.8541 + 7.88597i) q^{58} +(-2.61803 + 1.90211i) q^{59} +(0.572949 - 1.76336i) q^{60} +(5.59017 - 4.06150i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(-4.01722 - 12.3637i) q^{64} -2.00000 q^{65} +(7.23607 + 1.62460i) q^{66} +(4.50000 + 13.8496i) q^{68} +(3.54508 + 2.57565i) q^{69} +(1.11803 - 0.812299i) q^{70} +(-1.52786 + 4.70228i) q^{71} +(0.690983 - 2.12663i) q^{72} +(-11.0902 + 8.05748i) q^{73} +(-8.35410 - 6.06961i) q^{74} +(1.42705 + 4.39201i) q^{75} +8.56231 q^{76} +(2.19098 + 2.48990i) q^{77} -7.23607 q^{78} +(-3.09017 - 9.51057i) q^{79} +(-0.500000 - 0.363271i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(5.10081 - 15.6987i) q^{82} +(5.09017 - 15.6659i) q^{83} +(2.42705 - 1.76336i) q^{84} +(2.42705 + 1.76336i) q^{85} +(6.70820 + 20.6457i) q^{86} +6.00000 q^{87} +(-3.78115 + 6.37988i) q^{88} +5.61803 q^{89} +(-0.427051 - 1.31433i) q^{90} +(-2.61803 - 1.90211i) q^{91} +(-10.6353 + 7.72696i) q^{92} +(0.954915 - 2.93893i) q^{93} +(3.09017 - 9.51057i) q^{94} +(1.42705 - 1.03681i) q^{95} +(-5.42705 - 3.94298i) q^{96} +(-1.85410 - 5.70634i) q^{97} +2.23607 q^{98} +(3.04508 - 1.31433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 + q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 - q^7 - 5 * q^8 - q^9	$ 4 q + 5 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} - q^{9} - 10 q^{10} + q^{11} - 12 q^{12} + 4 q^{13} - 5 q^{14} - 2 q^{15} + q^{16} + 6 q^{17} - 5 q^{18} - 7 q^{19} - 9 q^{20} - 4 q^{21} + 25 q^{22} + 22 q^{23} - 5 q^{24} + 6 q^{25} - 10 q^{26} + q^{27} - 3 q^{28} + 6 q^{29} - 15 q^{31} + 9 q^{33} + 30 q^{34} - 3 q^{35} - 3 q^{36} - 6 q^{37} - 10 q^{38} - 4 q^{39} - 6 q^{41} - 5 q^{42} + 12 q^{43} + 33 q^{44} + 2 q^{45} + 30 q^{46} - 10 q^{47} - q^{48} - q^{49} - 15 q^{50} + 9 q^{51} - 18 q^{52} - 14 q^{53} + 8 q^{55} - 8 q^{57} + 30 q^{58} - 6 q^{59} + 9 q^{60} - q^{63} + 13 q^{64} - 8 q^{65} + 20 q^{66} + 18 q^{68} + 3 q^{69} - 24 q^{71} + 5 q^{72} - 22 q^{73} - 20 q^{74} - q^{75} - 6 q^{76} + 11 q^{77} - 20 q^{78} + 10 q^{79} - 2 q^{80} - q^{81} + 45 q^{82} - 2 q^{83} + 3 q^{84} + 3 q^{85} + 24 q^{87} + 5 q^{88} + 18 q^{89} + 5 q^{90} - 6 q^{91} - 9 q^{92} + 15 q^{93} - 10 q^{94} - q^{95} - 15 q^{96} + 6 q^{97} + q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 + q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 - q^7 - 5 * q^8 - q^9 - 10 * q^10 + q^11 - 12 * q^12 + 4 * q^13 - 5 * q^14 - 2 * q^15 + q^16 + 6 * q^17 - 5 * q^18 - 7 * q^19 - 9 * q^20 - 4 * q^21 + 25 * q^22 + 22 * q^23 - 5 * q^24 + 6 * q^25 - 10 * q^26 + q^27 - 3 * q^28 + 6 * q^29 - 15 * q^31 + 9 * q^33 + 30 * q^34 - 3 * q^35 - 3 * q^36 - 6 * q^37 - 10 * q^38 - 4 * q^39 - 6 * q^41 - 5 * q^42 + 12 * q^43 + 33 * q^44 + 2 * q^45 + 30 * q^46 - 10 * q^47 - q^48 - q^49 - 15 * q^50 + 9 * q^51 - 18 * q^52 - 14 * q^53 + 8 * q^55 - 8 * q^57 + 30 * q^58 - 6 * q^59 + 9 * q^60 - q^63 + 13 * q^64 - 8 * q^65 + 20 * q^66 + 18 * q^68 + 3 * q^69 - 24 * q^71 + 5 * q^72 - 22 * q^73 - 20 * q^74 - q^75 - 6 * q^76 + 11 * q^77 - 20 * q^78 + 10 * q^79 - 2 * q^80 - q^81 + 45 * q^82 - 2 * q^83 + 3 * q^84 + 3 * q^85 + 24 * q^87 + 5 * q^88 + 18 * q^89 + 5 * q^90 - 6 * q^91 - 9 * q^92 + 15 * q^93 - 10 * q^94 - q^95 - 15 * q^96 + 6 * q^97 + q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.690983	+	2.12663i	0.488599	+	1.50375i	0.826700	+	0.562643i	$0.190215\pi$
$2$	0.690983	+	2.12663i	0.488599	+	1.50375i	−0.338101	+	0.941110i	$0.609785\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−2.42705	+	1.76336i	−1.21353	+	0.881678i
$5$	−0.190983	+	0.587785i	−0.0854102	+	0.262866i	−0.984636	−	0.174619i	$-0.944131\pi$
$5$	−0.190983	+	0.587785i	−0.0854102	+	0.262866i	0.899226	+	0.437485i	$0.144131\pi$
$6$	−0.690983	+	2.12663i	−0.282093	+	0.868192i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−1.38197			−0.437016
$11$	−0.309017	−	3.30220i	−0.0931721	−	0.995650i
$11$	−0.309017	−	3.30220i	−0.0931721	−	0.995650i
$12$	−3.00000			−0.866025
$13$	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	$0.751865\pi$
$14$	−1.80902	−	1.31433i	−0.483480	−	0.351269i
$15$	−0.500000	+	0.363271i	−0.129099	+	0.0937962i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	1.50000	−	4.61653i	0.363803	−	1.11967i	−0.586924	−	0.809642i	$-0.699661\pi$
$17$	1.50000	−	4.61653i	0.363803	−	1.11967i	0.950727	−	0.310029i	$-0.100339\pi$
$18$	−1.80902	+	1.31433i	−0.426389	+	0.309790i
$19$	−2.30902	−	1.67760i	−0.529725	−	0.384868i	0.290530	−	0.956866i	$-0.406168\pi$
$19$	−2.30902	−	1.67760i	−0.529725	−	0.384868i	−0.820255	+	0.571998i	$0.806168\pi$
$20$	−0.572949	−	1.76336i	−0.128115	−	0.394298i
$21$	−1.00000			−0.218218
$22$	6.80902	−	2.93893i	1.45169	−	0.626581i
$23$	4.38197			0.913703			0.456852	−	0.889543i	$-0.348977\pi$
$23$	4.38197			0.913703			0.456852	+	0.889543i	$0.348977\pi$
$24$	−0.690983	−	2.12663i	−0.141046	−	0.434096i
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$	−5.85410	+	4.25325i	−1.14808	+	0.834132i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	0.927051	−	2.85317i	0.175196	−	0.539198i
$29$	4.85410	−	3.52671i	0.901384	−	0.654894i	−0.0374370	−	0.999299i	$-0.511919\pi$
$29$	4.85410	−	3.52671i	0.901384	−	0.654894i	0.938821	+	0.344405i	$0.111919\pi$
$30$	−1.11803	−	0.812299i	−0.204124	−	0.148305i
$31$	−0.954915	−	2.93893i	−0.171508	−	0.527847i	0.827949	−	0.560803i	$-0.189508\pi$
$31$	−0.954915	−	2.93893i	−0.171508	−	0.527847i	−0.999457	+	0.0329567i	$0.989508\pi$
$32$	−6.70820			−1.18585
$33$	1.69098	−	2.85317i	0.294362	−	0.496673i
$34$	10.8541			1.86146
$35$	−0.190983	−	0.587785i	−0.0322820	−	0.0993538i
$36$	−2.42705	−	1.76336i	−0.404508	−	0.293893i
$37$	−3.73607	+	2.71441i	−0.614206	+	0.446247i	−0.850893	−	0.525339i	$-0.823938\pi$
$37$	−3.73607	+	2.71441i	−0.614206	+	0.446247i	0.236687	+	0.971586i	$0.423938\pi$
$38$	1.97214	−	6.06961i	0.319923	−	0.984621i
$39$	−1.00000	+	3.07768i	−0.160128	+	0.492824i
$40$	1.11803	−	0.812299i	0.176777	−	0.128436i
$41$	−5.97214	−	4.33901i	−0.932691	−	0.677640i	0.0139593	−	0.999903i	$-0.495556\pi$
$41$	−5.97214	−	4.33901i	−0.932691	−	0.677640i	−0.946650	+	0.322263i	$0.895556\pi$
$42$	−0.690983	−	2.12663i	−0.106621	−	0.328146i
$43$	9.70820			1.48049			0.740244	−	0.672339i	$-0.234710\pi$
$43$	9.70820			1.48049			0.740244	+	0.672339i	$0.234710\pi$
$44$	6.57295	+	7.46969i	0.990909	+	1.12610i
$45$	−0.618034			−0.0921311
$46$	3.02786	+	9.31881i	0.446434	+	1.37398i
$47$	−3.61803	−	2.62866i	−0.527744	−	0.383429i	0.291769	−	0.956489i	$-0.405756\pi$
$47$	−3.61803	−	2.62866i	−0.527744	−	0.383429i	−0.819513	+	0.573060i	$0.805756\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−3.19098	+	9.82084i	−0.451273	+	1.38888i
$51$	3.92705	−	2.85317i	0.549897	−	0.399524i
$52$	−7.85410	−	5.70634i	−1.08917	−	0.791327i
$53$	2.09017	+	6.43288i	0.287107	+	0.883624i	0.985759	+	0.168163i	$0.0537835\pi$
$53$	2.09017	+	6.43288i	0.287107	+	0.883624i	−0.698652	+	0.715461i	$0.746217\pi$
$54$	−2.23607			−0.304290
$55$	2.00000	+	0.449028i	0.269680	+	0.0605469i
$56$	2.23607			0.298807
$57$	−0.881966	−	2.71441i	−0.116819	−	0.359533i
$58$	10.8541	+	7.88597i	1.42521	+	1.03548i
$59$	−2.61803	+	1.90211i	−0.340839	+	0.247634i	−0.745016	−	0.667047i	$-0.767558\pi$
$59$	−2.61803	+	1.90211i	−0.340839	+	0.247634i	0.404177	+	0.914681i	$0.367558\pi$
$60$	0.572949	−	1.76336i	0.0739674	−	0.227648i
$61$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$61$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$62$	5.59017	−	4.06150i	0.709952	−	0.515811i
$63$	−0.809017	−	0.587785i	−0.101927	−	0.0740540i
$64$	−4.01722	−	12.3637i	−0.502153	−	1.54547i
$65$	−2.00000			−0.248069
$66$	7.23607	+	1.62460i	0.890698	+	0.199974i
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$	4.50000	+	13.8496i	0.545705	+	1.67951i
$69$	3.54508	+	2.57565i	0.426778	+	0.310072i
$70$	1.11803	−	0.812299i	0.133631	−	0.0970883i
$71$	−1.52786	+	4.70228i	−0.181324	+	0.558058i	−0.999866	−	0.0163891i	$-0.994783\pi$
$71$	−1.52786	+	4.70228i	−0.181324	+	0.558058i	0.818542	+	0.574447i	$0.194783\pi$
$72$	0.690983	−	2.12663i	0.0814331	−	0.250625i
$73$	−11.0902	+	8.05748i	−1.29801	+	0.943057i	−0.999934	−	0.0114866i	$-0.996344\pi$
$73$	−11.0902	+	8.05748i	−1.29801	+	0.943057i	−0.298072	+	0.954543i	$0.596344\pi$
$74$	−8.35410	−	6.06961i	−0.971145	−	0.705578i
$75$	1.42705	+	4.39201i	0.164782	+	0.507146i
$76$	8.56231			0.982164
$77$	2.19098	+	2.48990i	0.249686	+	0.283750i
$78$	−7.23607			−0.819323
$79$	−3.09017	−	9.51057i	−0.347671	−	1.07002i	−0.960138	−	0.279526i	$-0.909823\pi$
$79$	−3.09017	−	9.51057i	−0.347671	−	1.07002i	0.612467	−	0.790496i	$-0.290177\pi$
$80$	−0.500000	−	0.363271i	−0.0559017	−	0.0406150i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	5.10081	−	15.6987i	0.563291	−	1.73363i
$83$	5.09017	−	15.6659i	0.558719	−	1.71956i	−0.127196	−	0.991878i	$-0.540598\pi$
$83$	5.09017	−	15.6659i	0.558719	−	1.71956i	0.685915	−	0.727682i	$-0.259402\pi$
$84$	2.42705	−	1.76336i	0.264813	−	0.192398i
$85$	2.42705	+	1.76336i	0.263251	+	0.191263i
$86$	6.70820	+	20.6457i	0.723364	+	2.22629i
$87$	6.00000			0.643268
$88$	−3.78115	+	6.37988i	−0.403072	+	0.680098i
$89$	5.61803			0.595510			0.297755	−	0.954642i	$-0.403762\pi$
$89$	5.61803			0.595510			0.297755	+	0.954642i	$0.403762\pi$
$90$	−0.427051	−	1.31433i	−0.0450151	−	0.138542i
$91$	−2.61803	−	1.90211i	−0.274445	−	0.199396i
$92$	−10.6353	+	7.72696i	−1.10880	+	0.805592i
$93$	0.954915	−	2.93893i	0.0990201	−	0.304752i
$94$	3.09017	−	9.51057i	0.318727	−	0.980940i
$95$	1.42705	−	1.03681i	0.146412	−	0.106375i
$96$	−5.42705	−	3.94298i	−0.553896	−	0.402429i
$97$	−1.85410	−	5.70634i	−0.188256	−	0.579391i	0.811734	−	0.584028i	$-0.198524\pi$
$97$	−1.85410	−	5.70634i	−0.188256	−	0.579391i	−0.999989	+	0.00463676i	$0.998524\pi$
$98$	2.23607			0.225877
$99$	3.04508	−	1.31433i	0.306043	−	0.132095i
$100$	−13.8541			−1.38541
$101$	−2.10081	−	6.46564i	−0.209039	−	0.643355i	−0.999523	−	0.0308731i	$-0.990171\pi$
$101$	−2.10081	−	6.46564i	−0.209039	−	0.643355i	0.790485	−	0.612482i	$-0.209829\pi$
$102$	8.78115	+	6.37988i	0.869464	+	0.631702i
$103$	−1.07295	+	0.779543i	−0.105721	+	0.0768107i	−0.639390	−	0.768883i	$-0.720813\pi$
$103$	−1.07295	+	0.779543i	−0.105721	+	0.0768107i	0.533669	+	0.845694i	$0.320813\pi$
$104$	2.23607	−	6.88191i	0.219265	−	0.674827i
$105$	0.190983	−	0.587785i	0.0186380	−	0.0573620i
$106$	−12.2361	+	8.89002i	−1.18847	+	0.863475i
$107$	−12.7812	−	9.28605i	−1.23560	−	0.897716i	−0.238304	−	0.971191i	$-0.576591\pi$
$107$	−12.7812	−	9.28605i	−1.23560	−	0.897716i	−0.997297	+	0.0734743i	$0.976591\pi$
$108$	−0.927051	−	2.85317i	−0.0892055	−	0.274546i
$109$	−17.5623			−1.68216			−0.841082	−	0.540908i	$-0.818081\pi$
$109$	−17.5623			−1.68216			−0.841082	+	0.540908i	$0.818081\pi$
$110$	0.427051	+	4.56352i	0.0407177	+	0.435115i
$111$	−4.61803			−0.438324
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	4.23607	+	3.07768i	0.398496	+	0.289524i	0.768928	−	0.639335i	$-0.220790\pi$
$113$	4.23607	+	3.07768i	0.398496	+	0.289524i	−0.370432	+	0.928859i	$0.620790\pi$
$114$	5.16312	−	3.75123i	0.483570	−	0.351334i
$115$	−0.836881	+	2.57565i	−0.0780396	+	0.240181i
$116$	−5.56231	+	17.1190i	−0.516447	+	1.58946i
$117$	−2.61803	+	1.90211i	−0.242037	+	0.175850i
$118$	−5.85410	−	4.25325i	−0.538914	−	0.391544i
$119$	1.50000	+	4.61653i	0.137505	+	0.423196i
$120$	1.38197			0.126156
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$		0			0
$123$	−2.28115	−	7.02067i	−0.205685	−	0.633032i
$124$	7.50000	+	5.44907i	0.673520	+	0.489341i
$125$	−4.80902	+	3.49396i	−0.430132	+	0.312509i
$126$	0.690983	−	2.12663i	0.0615577	−	0.189455i
$127$	0.0901699	−	0.277515i	0.00800129	−	0.0246254i	−0.946976	−	0.321304i	$-0.895879\pi$
$127$	0.0901699	−	0.277515i	0.00800129	−	0.0246254i	0.954977	+	0.296678i	$0.0958789\pi$
$128$	12.6631	−	9.20029i	1.11927	−	0.813199i
$129$	7.85410	+	5.70634i	0.691515	+	0.502415i
$130$	−1.38197	−	4.25325i	−0.121206	−	0.373035i
$131$	−16.6525			−1.45493			−0.727467	−	0.686143i	$-0.759302\pi$
$131$	−16.6525			−1.45493			−0.727467	+	0.686143i	$0.759302\pi$
$132$	0.927051	+	9.90659i	0.0806894	+	0.862258i
$133$	2.85410			0.247482
$134$		0			0
$135$	−0.500000	−	0.363271i	−0.0430331	−	0.0312654i
$136$	−8.78115	+	6.37988i	−0.752978	+	0.547070i
$137$	2.52786	−	7.77997i	0.215970	−	0.664687i	−0.783113	−	0.621879i	$-0.786370\pi$
$137$	2.52786	−	7.77997i	0.215970	−	0.664687i	0.999083	−	0.0428083i	$-0.0136305\pi$
$138$	−3.02786	+	9.31881i	−0.257749	+	0.793270i
$139$	−10.6353	+	7.72696i	−0.902071	+	0.655393i	−0.938997	−	0.343925i	$-0.888243\pi$
$139$	−10.6353	+	7.72696i	−0.902071	+	0.655393i	0.0369264	+	0.999318i	$0.488243\pi$
$140$	1.50000	+	1.08981i	0.126773	+	0.0921061i
$141$	−1.38197	−	4.25325i	−0.116383	−	0.358189i
$142$	−11.0557			−0.927776
$143$	9.85410	−	4.25325i	0.824041	−	0.355675i
$144$	−1.00000			−0.0833333
$145$	1.14590	+	3.52671i	0.0951617	+	0.292877i
$146$	−24.7984	−	18.0171i	−2.05233	−	1.49110i
$147$	0.809017	−	0.587785i	0.0667266	−	0.0484797i
$148$	4.28115	−	13.1760i	0.351909	−	1.08306i
$149$	−1.52786	+	4.70228i	−0.125167	+	0.385226i	−0.993932	−	0.110000i	$-0.964915\pi$
$149$	−1.52786	+	4.70228i	−0.125167	+	0.385226i	0.868764	+	0.495226i	$0.164915\pi$
$150$	−8.35410	+	6.06961i	−0.682110	+	0.495582i
$151$	12.5623	+	9.12705i	1.02231	+	0.742749i	0.966754	−	0.255707i	$-0.0823083\pi$
$151$	12.5623	+	9.12705i	1.02231	+	0.742749i	0.0555516	+	0.998456i	$0.482308\pi$
$152$	1.97214	+	6.06961i	0.159961	+	0.492310i
$153$	4.85410			0.392431
$154$	−3.78115	+	6.37988i	−0.304694	+	0.514105i
$155$	1.90983			0.153401
$156$	−3.00000	−	9.23305i	−0.240192	−	0.739236i
$157$	18.7082	+	13.5923i	1.49308	+	1.08478i	0.973039	+	0.230641i	$0.0740824\pi$
$157$	18.7082	+	13.5923i	1.49308	+	1.08478i	0.520038	+	0.854143i	$0.325918\pi$
$158$	18.0902	−	13.1433i	1.43918	−	1.04562i
$159$	−2.09017	+	6.43288i	−0.165761	+	0.510161i
$160$	1.28115	−	3.94298i	0.101284	−	0.311720i
$161$	−3.54508	+	2.57565i	−0.279392	+	0.202990i
$162$	−1.80902	−	1.31433i	−0.142130	−	0.103263i
$163$	−3.09017	−	9.51057i	−0.242041	−	0.744925i	−0.996109	−	0.0881289i	$-0.971911\pi$
$163$	−3.09017	−	9.51057i	−0.242041	−	0.744925i	0.754068	−	0.656796i	$-0.228089\pi$
$164$	22.1459			1.72930
$165$	1.35410	+	1.53884i	0.105417	+	0.119799i
$166$	36.8328			2.85878
$167$	−6.56231	−	20.1967i	−0.507806	−	1.56287i	−0.796001	−	0.605296i	$-0.793055\pi$
$167$	−6.56231	−	20.1967i	−0.507806	−	1.56287i	0.288194	−	0.957572i	$-0.406945\pi$
$168$	1.80902	+	1.31433i	0.139569	+	0.101403i
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$	−2.07295	+	6.37988i	−0.158988	+	0.489315i
$171$	0.881966	−	2.71441i	0.0674456	−	0.207576i
$172$	−23.5623	+	17.1190i	−1.79661	+	1.30531i
$173$	11.0172	+	8.00448i	0.837624	+	0.608569i	0.921706	−	0.387890i	$-0.126796\pi$
$173$	11.0172	+	8.00448i	0.837624	+	0.608569i	−0.0840821	+	0.996459i	$0.526796\pi$
$174$	4.14590	+	12.7598i	0.314300	+	0.967315i
$175$	−4.61803			−0.349091
$176$	3.23607	+	0.726543i	0.243928	+	0.0547652i
$177$	−3.23607			−0.243238
$178$	3.88197	+	11.9475i	0.290966	+	0.895500i
$179$	11.9721	+	8.69827i	0.894839	+	0.650139i	0.937135	−	0.348966i	$-0.113467\pi$
$179$	11.9721	+	8.69827i	0.894839	+	0.650139i	−0.0422959	+	0.999105i	$0.513467\pi$
$180$	1.50000	−	1.08981i	0.111803	−	0.0812299i
$181$	−6.14590	+	18.9151i	−0.456821	+	1.40595i	0.412163	+	0.911110i	$0.364773\pi$
$181$	−6.14590	+	18.9151i	−0.456821	+	1.40595i	−0.868984	+	0.494840i	$0.835227\pi$
$182$	2.23607	−	6.88191i	0.165748	−	0.510121i
$183$		0			0
$184$	−7.92705	−	5.75934i	−0.584390	−	0.424584i
$185$	−0.881966	−	2.71441i	−0.0648434	−	0.199568i
$186$	6.90983			0.506653
$187$	−15.7082	−	3.52671i	−1.14870	−	0.257899i
$188$	13.4164			0.978492
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	3.19098	+	2.31838i	0.231498	+	0.168193i
$191$	−3.97214	+	2.88593i	−0.287414	+	0.208818i	−0.722145	−	0.691742i	$-0.756843\pi$
$191$	−3.97214	+	2.88593i	−0.287414	+	0.208818i	0.434731	+	0.900560i	$0.356843\pi$
$192$	4.01722	−	12.3637i	0.289918	−	0.892276i
$193$	−6.75329	+	20.7845i	−0.486112	+	1.49610i	0.344251	+	0.938878i	$0.388133\pi$
$193$	−6.75329	+	20.7845i	−0.486112	+	1.49610i	−0.830363	+	0.557222i	$0.811867\pi$
$194$	10.8541	−	7.88597i	0.779279	−	0.566179i
$195$	−1.61803	−	1.17557i	−0.115870	−	0.0841844i
$196$	0.927051	+	2.85317i	0.0662179	+	0.203798i
$197$	22.4721			1.60107			0.800537	−	0.599284i	$-0.204548\pi$
$197$	22.4721			1.60107			0.800537	+	0.599284i	$0.204548\pi$
$198$	4.89919	+	5.56758i	0.348170	+	0.395671i
$199$	13.1459			0.931888			0.465944	−	0.884814i	$-0.345715\pi$
$199$	13.1459			0.931888			0.465944	+	0.884814i	$0.345715\pi$
$200$	−3.19098	−	9.82084i	−0.225637	−	0.694438i
$201$		0			0
$202$	12.2984	−	8.93529i	0.865311	−	0.628685i
$203$	−1.85410	+	5.70634i	−0.130132	+	0.400506i
$204$	−4.50000	+	13.8496i	−0.315063	+	0.969664i
$205$	3.69098	−	2.68166i	0.257789	−	0.187295i
$206$	−2.39919	−	1.74311i	−0.167159	−	0.121448i
$207$	1.35410	+	4.16750i	0.0941166	+	0.289661i
$208$	−3.23607			−0.224381
$209$	−4.82624	+	8.14324i	−0.333838	+	0.563279i
$210$	1.38197			0.0953647
$211$	−5.67376	−	17.4620i	−0.390598	−	1.20214i	−0.932337	−	0.361590i	$-0.882234\pi$
$211$	−5.67376	−	17.4620i	−0.390598	−	1.20214i	0.541739	−	0.840547i	$-0.317766\pi$
$212$	−16.4164	−	11.9272i	−1.12748	−	0.819165i
$213$	−4.00000	+	2.90617i	−0.274075	+	0.199127i
$214$	10.9164	−	33.5972i	0.746230	−	2.29666i
$215$	−1.85410	+	5.70634i	−0.126449	+	0.389169i
$216$	1.80902	−	1.31433i	0.123088	−	0.0894287i
$217$	2.50000	+	1.81636i	0.169711	+	0.123302i
$218$	−12.1353	−	37.3485i	−0.821903	−	2.52956i
$219$	−13.7082			−0.926315
$220$	−5.64590	+	2.43690i	−0.380646	+	0.164296i
$221$	15.7082			1.05665
$222$	−3.19098	−	9.82084i	−0.214165	−	0.659131i
$223$	−15.8713	−	11.5312i	−1.06282	−	0.772186i	−0.0882139	−	0.996102i	$-0.528116\pi$
$223$	−15.8713	−	11.5312i	−1.06282	−	0.772186i	−0.974608	+	0.223916i	$0.928116\pi$
$224$	5.42705	−	3.94298i	0.362610	−	0.263452i
$225$	−1.42705	+	4.39201i	−0.0951367	+	0.292801i
$226$	−3.61803	+	11.1352i	−0.240668	+	0.740700i
$227$	−10.0902	+	7.33094i	−0.669708	+	0.486571i	−0.869927	−	0.493180i	$-0.835835\pi$
$227$	−10.0902	+	7.33094i	−0.669708	+	0.486571i	0.200219	+	0.979751i	$0.435835\pi$
$228$	6.92705	+	5.03280i	0.458755	+	0.333305i
$229$	5.00000	+	15.3884i	0.330409	+	1.01690i	0.968939	+	0.247298i	$0.0795428\pi$
$229$	5.00000	+	15.3884i	0.330409	+	1.01690i	−0.638530	+	0.769597i	$0.720457\pi$
$230$	−6.05573			−0.399303
$231$	0.309017	+	3.30220i	0.0203318	+	0.217269i
$232$	−13.4164			−0.880830
$233$	−4.85410	−	14.9394i	−0.318003	−	0.978712i	−0.974501	−	0.224384i	$-0.927963\pi$
$233$	−4.85410	−	14.9394i	−0.318003	−	0.978712i	0.656498	−	0.754328i	$-0.272037\pi$
$234$	−5.85410	−	4.25325i	−0.382695	−	0.278044i
$235$	2.23607	−	1.62460i	0.145865	−	0.105977i
$236$	3.00000	−	9.23305i	0.195283	−	0.601020i
$237$	3.09017	−	9.51057i	0.200728	−	0.617778i
$238$	−8.78115	+	6.37988i	−0.569198	+	0.413546i
$239$	15.3992	+	11.1882i	0.996091	+	0.723702i	0.961246	−	0.275691i	$-0.0889065\pi$
$239$	15.3992	+	11.1882i	0.996091	+	0.723702i	0.0348442	+	0.999393i	$0.488907\pi$
$240$	−0.190983	−	0.587785i	−0.0123279	−	0.0379414i
$241$	12.0000			0.772988			0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000			0.772988			0.386494	+	0.922292i	$0.373686\pi$
$242$	−11.8090	−	21.5765i	−0.759112	−	1.38699i
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	0.500000	+	0.363271i	0.0319438	+	0.0232085i
$246$	13.3541	−	9.70232i	0.851426	−	0.618598i
$247$	2.85410	−	8.78402i	0.181602	−	0.558914i
$248$	−2.13525	+	6.57164i	−0.135589	+	0.417299i
$249$	13.3262	−	9.68208i	0.844516	−	0.613577i
$250$	−10.7533	−	7.81272i	−0.680098	−	0.494120i
$251$	8.56231	+	26.3521i	0.540448	+	1.66333i	0.731574	+	0.681762i	$0.238786\pi$
$251$	8.56231	+	26.3521i	0.540448	+	1.66333i	−0.191126	+	0.981566i	$0.561214\pi$
$252$	3.00000			0.188982
$253$	−1.35410	−	14.4701i	−0.0851317	−	0.909728i
$254$	0.652476			0.0409400
$255$	0.927051	+	2.85317i	0.0580542	+	0.178672i
$256$	7.28115	+	5.29007i	0.455072	+	0.330629i
$257$	−19.7812	+	14.3718i	−1.23391	+	0.896491i	−0.997177	−	0.0750824i	$-0.976078\pi$
$257$	−19.7812	+	14.3718i	−1.23391	+	0.896491i	−0.236737	+	0.971574i	$0.576078\pi$
$258$	−6.70820	+	20.6457i	−0.417635	+	1.28535i
$259$	1.42705	−	4.39201i	0.0886726	−	0.272906i
$260$	4.85410	−	3.52671i	0.301039	−	0.218717i
$261$	4.85410	+	3.52671i	0.300461	+	0.218298i
$262$	−11.5066	−	35.4136i	−0.710879	−	2.18786i
$263$	10.8541			0.669293			0.334646	−	0.942344i	$-0.391383\pi$
$263$	10.8541			0.669293			0.334646	+	0.942344i	$0.391383\pi$
$264$	−6.80902	+	2.93893i	−0.419066	+	0.180878i
$265$	−4.18034			−0.256796
$266$	1.97214	+	6.06961i	0.120919	+	0.372152i
$267$	4.54508	+	3.30220i	0.278155	+	0.202091i
$268$		0			0
$269$	−4.14590	+	12.7598i	−0.252780	+	0.777976i	0.741479	+	0.670976i	$0.234125\pi$
$269$	−4.14590	+	12.7598i	−0.252780	+	0.777976i	−0.994259	+	0.107000i	$0.965875\pi$
$270$	0.427051	−	1.31433i	0.0259895	−	0.0799874i
$271$	18.2082	−	13.2290i	1.10607	−	0.803607i	0.124029	−	0.992279i	$-0.460418\pi$
$271$	18.2082	−	13.2290i	1.10607	−	0.803607i	0.982040	+	0.188672i	$0.0604183\pi$
$272$	3.92705	+	2.85317i	0.238112	+	0.172999i
$273$	−1.00000	−	3.07768i	−0.0605228	−	0.186270i
$274$	18.2918			1.10505
$275$	7.80902	−	13.1760i	0.470901	−	0.794545i
$276$	−13.1459			−0.791290
$277$	−0.0278640	−	0.0857567i	−0.00167419	−	0.00515262i	0.950216	−	0.311592i	$-0.100862\pi$
$277$	−0.0278640	−	0.0857567i	−0.00167419	−	0.00515262i	−0.951890	+	0.306440i	$0.900862\pi$
$278$	−23.7812	−	17.2780i	−1.42630	−	1.03627i
$279$	2.50000	−	1.81636i	0.149671	−	0.108742i
$280$	−0.427051	+	1.31433i	−0.0255212	+	0.0785461i
$281$	−8.32624	+	25.6255i	−0.496702	+	1.52869i	0.317586	+	0.948229i	$0.397128\pi$
$281$	−8.32624	+	25.6255i	−0.496702	+	1.52869i	−0.814288	+	0.580461i	$0.802872\pi$
$282$	8.09017	−	5.87785i	0.481763	−	0.350021i
$283$	13.9721	+	10.1514i	0.830557	+	0.603435i	0.919717	−	0.392582i	$-0.128418\pi$
$283$	13.9721	+	10.1514i	0.830557	+	0.603435i	−0.0891597	+	0.996017i	$0.528418\pi$
$284$	−4.58359	−	14.1068i	−0.271986	−	0.837087i
$285$	1.76393			0.104486
$286$	15.8541	+	18.0171i	0.937473	+	1.06537i
$287$	7.38197			0.435744
$288$	−2.07295	−	6.37988i	−0.122150	−	0.375938i
$289$	−5.30902	−	3.85723i	−0.312295	−	0.226896i
$290$	−6.70820	+	4.87380i	−0.393919	+	0.286199i
$291$	1.85410	−	5.70634i	0.108689	−	0.334512i
$292$	12.7082	−	39.1118i	0.743691	−	2.28885i
$293$	14.7361	−	10.7064i	0.860890	−	0.625473i	−0.0672367	−	0.997737i	$-0.521418\pi$
$293$	14.7361	−	10.7064i	0.860890	−	0.625473i	0.928127	+	0.372264i	$0.121418\pi$
$294$	1.80902	+	1.31433i	0.105504	+	0.0766532i
$295$	−0.618034	−	1.90211i	−0.0359833	−	0.110745i
$296$	10.3262			0.600200
$297$	3.23607	+	0.726543i	0.187776	+	0.0421583i
$298$	−11.0557			−0.640441
$299$	4.38197	+	13.4863i	0.253416	+	0.779933i
$300$	−11.2082	−	8.14324i	−0.647106	−	0.470150i
$301$	−7.85410	+	5.70634i	−0.452703	+	0.328908i
$302$	−10.7295	+	33.0220i	−0.617413	+	1.90020i
$303$	2.10081	−	6.46564i	0.120689	−	0.371441i
$304$	2.30902	−	1.67760i	0.132431	−	0.0962169i
$305$		0			0
$306$	3.35410	+	10.3229i	0.191741	+	0.590119i
$307$	−17.5623			−1.00233			−0.501167	−	0.865351i	$-0.667096\pi$
$307$	−17.5623			−1.00233			−0.501167	+	0.865351i	$0.667096\pi$
$308$	−9.70820	−	2.17963i	−0.553176	−	0.124196i
$309$	−1.32624			−0.0754470
$310$	1.31966	+	4.06150i	0.0749517	+	0.230677i
$311$	−16.7082	−	12.1392i	−0.947435	−	0.688352i	0.00276357	−	0.999996i	$-0.499120\pi$
$311$	−16.7082	−	12.1392i	−0.947435	−	0.688352i	−0.950199	+	0.311644i	$0.899120\pi$
$312$	5.85410	−	4.25325i	0.331423	−	0.240793i
$313$	−2.41641	+	7.43694i	−0.136583	+	0.420361i	−0.995833	−	0.0911961i	$-0.970931\pi$
$313$	−2.41641	+	7.43694i	−0.136583	+	0.420361i	0.859250	+	0.511557i	$0.170931\pi$
$314$	−15.9787	+	49.1774i	−0.901731	+	2.77524i
$315$	0.500000	−	0.363271i	0.0281718	−	0.0204680i
$316$	24.2705	+	17.6336i	1.36532	+	0.991965i
$317$	2.09017	+	6.43288i	0.117396	+	0.361307i	0.992439	−	0.122738i	$-0.0391674\pi$
$317$	2.09017	+	6.43288i	0.117396	+	0.361307i	−0.875044	+	0.484044i	$0.839167\pi$
$318$	−15.1246			−0.848146
$319$	−13.1459	−	14.9394i	−0.736029	−	0.836445i
$320$	8.03444			0.449139
$321$	−4.88197	−	15.0251i	−0.272485	−	0.838622i
$322$	−7.92705	−	5.75934i	−0.441757	−	0.320955i
$323$	−11.2082	+	8.14324i	−0.623641	+	0.453102i
$324$	0.927051	−	2.85317i	0.0515028	−	0.158509i
$325$	−4.61803	+	14.2128i	−0.256162	+	0.788387i
$326$	18.0902	−	13.1433i	1.00192	−	0.727939i
$327$	−14.2082	−	10.3229i	−0.785715	−	0.570856i
$328$	5.10081	+	15.6987i	0.281645	+	0.866815i
$329$	4.47214			0.246557
$330$	−2.33688	+	3.94298i	−0.128641	+	0.217054i
$331$	17.4164			0.957292			0.478646	−	0.878008i	$-0.341128\pi$
$331$	17.4164			0.957292			0.478646	+	0.878008i	$0.341128\pi$
$332$	15.2705	+	46.9978i	0.838078	+	2.57934i
$333$	−3.73607	−	2.71441i	−0.204735	−	0.148749i
$334$	38.4164	−	27.9112i	2.10205	−	1.52723i
$335$		0			0
$336$	0.309017	−	0.951057i	0.0168583	−	0.0518844i
$337$	−21.9164	+	15.9232i	−1.19386	+	0.867392i	−0.993667	−	0.112364i	$-0.964158\pi$
$337$	−21.9164	+	15.9232i	−1.19386	+	0.867392i	−0.200196	+	0.979756i	$0.564158\pi$
$338$	4.57295	+	3.32244i	0.248736	+	0.180717i
$339$	1.61803	+	4.97980i	0.0878795	+	0.270465i
$340$	−9.00000			−0.488094
$341$	−9.40983	+	4.06150i	−0.509571	+	0.219942i
$342$	6.38197			0.345097
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−17.5623	−	12.7598i	−0.946896	−	0.687960i
$345$	−2.19098	+	1.59184i	−0.117959	+	0.0857019i
$346$	−9.40983	+	28.9605i	−0.505876	+	1.55692i
$347$	−4.48278	+	13.7966i	−0.240648	+	0.740639i	0.755674	+	0.654948i	$0.227310\pi$
$347$	−4.48278	+	13.7966i	−0.240648	+	0.740639i	−0.996322	+	0.0856906i	$0.972690\pi$
$348$	−14.5623	+	10.5801i	−0.780622	+	0.567155i
$349$	17.5623	+	12.7598i	0.940089	+	0.683014i	0.948442	−	0.316951i	$-0.102659\pi$
$349$	17.5623	+	12.7598i	0.940089	+	0.683014i	−0.00835333	+	0.999965i	$0.502659\pi$
$350$	−3.19098	−	9.82084i	−0.170565	−	0.524946i
$351$	−3.23607			−0.172729
$352$	2.07295	+	22.1518i	0.110489	+	1.18070i
$353$	−18.0000			−0.958043			−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000			−0.958043			−0.479022	+	0.877803i	$0.659008\pi$
$354$	−2.23607	−	6.88191i	−0.118846	−	0.365769i
$355$	−2.47214	−	1.79611i	−0.131207	−	0.0953277i
$356$	−13.6353	+	9.90659i	−0.722667	+	0.525048i
$357$	−1.50000	+	4.61653i	−0.0793884	+	0.244332i
$358$	−10.2254	+	31.4706i	−0.540430	+	1.66327i
$359$	−5.20820	+	3.78398i	−0.274878	+	0.199711i	−0.716680	−	0.697402i	$-0.754339\pi$
$359$	−5.20820	+	3.78398i	−0.274878	+	0.199711i	0.441802	+	0.897113i	$0.354339\pi$
$360$	1.11803	+	0.812299i	0.0589256	+	0.0428119i
$361$	−3.35410	−	10.3229i	−0.176532	−	0.543309i
$362$	−44.4721			−2.33740
$363$	−9.94427	−	4.70228i	−0.521939	−	0.246806i
$364$	9.70820			0.508848
$365$	−2.61803	−	8.05748i	−0.137034	−	0.421748i
$366$		0			0
$367$	−2.20820	+	1.60435i	−0.115267	+	0.0837466i	−0.643926	−	0.765088i	$-0.722695\pi$
$367$	−2.20820	+	1.60435i	−0.115267	+	0.0837466i	0.528658	+	0.848835i	$0.322695\pi$
$368$	−1.35410	+	4.16750i	−0.0705874	+	0.217246i
$369$	2.28115	−	7.02067i	0.118752	−	0.365481i
$370$	5.16312	−	3.75123i	0.268418	−	0.195017i
$371$	−5.47214	−	3.97574i	−0.284099	−	0.206410i
$372$	2.86475	+	8.81678i	0.148530	+	0.457129i
$373$	16.3262			0.845341			0.422670	−	0.906284i	$-0.361093\pi$
$373$	16.3262			0.845341			0.422670	+	0.906284i	$0.361093\pi$
$374$	−3.35410	−	35.8424i	−0.173436	−	1.85337i
$375$	−5.94427			−0.306961
$376$	3.09017	+	9.51057i	0.159363	+	0.490470i
$377$	15.7082	+	11.4127i	0.809014	+	0.587783i
$378$	1.80902	−	1.31433i	0.0930458	−	0.0676017i
$379$	6.65248	−	20.4742i	0.341715	−	1.05169i	−0.621604	−	0.783331i	$-0.713519\pi$
$379$	6.65248	−	20.4742i	0.341715	−	1.05169i	0.963319	−	0.268358i	$-0.0864812\pi$
$380$	−1.63525	+	5.03280i	−0.0838868	+	0.258177i
$381$	0.236068	−	0.171513i	0.0120941	−	0.00878690i
$382$	−8.88197	−	6.45313i	−0.454441	−	0.330171i
$383$	−6.43769	−	19.8132i	−0.328951	−	1.01241i	−0.969626	−	0.244594i	$-0.921345\pi$
$383$	−6.43769	−	19.8132i	−0.328951	−	1.01241i	0.640675	−	0.767812i	$-0.278655\pi$
$384$	15.6525			0.798762
$385$	−1.88197	+	0.812299i	−0.0959139	+	0.0413986i
$386$	−48.8673			−2.48728
$387$	3.00000	+	9.23305i	0.152499	+	0.469342i
$388$	14.5623	+	10.5801i	0.739289	+	0.537125i
$389$	−12.3262	+	8.95554i	−0.624965	+	0.454064i	−0.854652	−	0.519201i	$-0.826230\pi$
$389$	−12.3262	+	8.95554i	−0.624965	+	0.454064i	0.229687	+	0.973264i	$0.426230\pi$
$390$	1.38197	−	4.25325i	0.0699786	−	0.215372i
$391$	6.57295	−	20.2295i	0.332408	−	1.02305i
$392$	−1.80902	+	1.31433i	−0.0913692	+	0.0663836i
$393$	−13.4721	−	9.78808i	−0.679579	−	0.493743i
$394$	15.5279	+	47.7899i	0.782282	+	2.40762i
$395$	6.18034			0.310967
$396$	−5.07295	+	8.55951i	−0.254925	+	0.430131i
$397$	30.5410			1.53281			0.766405	−	0.642358i	$-0.222044\pi$
$397$	30.5410			1.53281			0.766405	+	0.642358i	$0.222044\pi$
$398$	9.08359	+	27.9564i	0.455319	+	1.40133i
$399$	2.30902	+	1.67760i	0.115595	+	0.0839850i
$400$	−3.73607	+	2.71441i	−0.186803	+	0.135721i
$401$	2.29180	−	7.05342i	0.114447	−	0.352231i	−0.877384	−	0.479788i	$-0.840714\pi$
$401$	2.29180	−	7.05342i	0.114447	−	0.352231i	0.991831	+	0.127557i	$0.0407136\pi$
$402$		0			0
$403$	8.09017	−	5.87785i	0.403000	−	0.292797i
$404$	16.5000	+	11.9880i	0.820906	+	0.596423i
$405$	−0.190983	−	0.587785i	−0.00949002	−	0.0292073i
$406$	−13.4164			−0.665845
$407$	10.1180	+	11.4984i	0.501532	+	0.569956i
$408$	−10.8541			−0.537358
$409$	−6.85410	−	21.0948i	−0.338914	−	1.04307i	−0.964762	−	0.263124i	$-0.915247\pi$
$409$	−6.85410	−	21.0948i	−0.338914	−	1.04307i	0.625849	−	0.779945i	$-0.284753\pi$
$410$	8.25329	+	5.99637i	0.407601	+	0.296139i
$411$	6.61803	−	4.80828i	0.326444	−	0.237175i
$412$	1.22949	−	3.78398i	0.0605726	−	0.186423i
$413$	1.00000	−	3.07768i	0.0492068	−	0.151443i
$414$	−7.92705	+	5.75934i	−0.389593	+	0.283056i
$415$	8.23607	+	5.98385i	0.404293	+	0.293736i
$416$	−6.70820	−	20.6457i	−0.328897	−	1.01224i
$417$	−13.1459			−0.643757
$418$	−20.6525	−	4.63677i	−1.01015	−	0.226792i
$419$	−3.23607			−0.158092			−0.0790461	−	0.996871i	$-0.525187\pi$
$419$	−3.23607			−0.158092			−0.0790461	+	0.996871i	$0.525187\pi$
$420$	0.572949	+	1.76336i	0.0279570	+	0.0860430i
$421$	−7.92705	−	5.75934i	−0.386341	−	0.280693i	0.377614	−	0.925963i	$-0.376745\pi$
$421$	−7.92705	−	5.75934i	−0.386341	−	0.280693i	−0.763954	+	0.645270i	$0.776745\pi$
$422$	33.2148	−	24.1320i	1.61687	−	1.17473i
$423$	1.38197	−	4.25325i	0.0671935	−	0.206800i
$424$	4.67376	−	14.3844i	0.226978	−	0.698566i
$425$	18.1353	−	13.1760i	0.879689	−	0.639132i
$426$	−8.94427	−	6.49839i	−0.433351	−	0.314848i
$427$		0			0
$428$	47.3951			2.29093
$429$	10.4721	+	2.35114i	0.505599	+	0.113514i
$430$	−13.4164			−0.646997
$431$	4.66312	+	14.3516i	0.224615	+	0.691292i	0.998331	+	0.0577598i	$0.0183958\pi$
$431$	4.66312	+	14.3516i	0.224615	+	0.691292i	−0.773716	+	0.633533i	$0.781604\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	25.2705	−	18.3601i	1.21442	−	0.882330i	0.218798	−	0.975770i	$-0.429786\pi$
$433$	25.2705	−	18.3601i	1.21442	−	0.882330i	0.995625	+	0.0934400i	$0.0297863\pi$
$434$	−2.13525	+	6.57164i	−0.102496	+	0.315449i
$435$	−1.14590	+	3.52671i	−0.0549416	+	0.169093i
$436$	42.6246	−	30.9686i	2.04135	−	1.48313i
$437$	−10.1180	−	7.35118i	−0.484011	−	0.351655i
$438$	−9.47214	−	29.1522i	−0.452596	−	1.39295i
$439$	1.85410			0.0884915			0.0442457	−	0.999021i	$-0.485912\pi$
$439$	1.85410			0.0884915			0.0442457	+	0.999021i	$0.485912\pi$
$440$	−3.02786	−	3.44095i	−0.144348	−	0.164041i
$441$	1.00000			0.0476190
$442$	10.8541	+	33.4055i	0.516277	+	1.58894i
$443$	−16.4894	−	11.9802i	−0.783433	−	0.569197i	0.122574	−	0.992459i	$-0.460885\pi$
$443$	−16.4894	−	11.9802i	−0.783433	−	0.569197i	−0.906007	+	0.423262i	$0.860885\pi$
$444$	11.2082	−	8.14324i	0.531918	−	0.386461i
$445$	−1.07295	+	3.30220i	−0.0508627	+	0.156539i
$446$	13.5557	−	41.7202i	0.641882	−	1.97551i
$447$	−4.00000	+	2.90617i	−0.189194	+	0.137457i
$448$	10.5172	+	7.64121i	0.496892	+	0.361013i
$449$	−12.9443	−	39.8384i	−0.610878	−	1.88009i	−0.449747	−	0.893156i	$-0.648486\pi$
$449$	−12.9443	−	39.8384i	−0.610878	−	1.88009i	−0.161131	−	0.986933i	$-0.551514\pi$
$450$	−10.3262			−0.486784
$451$	−12.4828	+	21.0620i	−0.587791	+	0.991771i
$452$	−15.7082			−0.738852
$453$	4.79837	+	14.7679i	0.225447	+	0.693855i
$454$	−22.5623	−	16.3925i	−1.05890	−	0.769337i
$455$	1.61803	−	1.17557i	0.0758546	−	0.0551116i
$456$	−1.97214	+	6.06961i	−0.0923537	+	0.284236i
$457$	6.61803	−	20.3682i	0.309579	−	0.952785i	−0.668350	−	0.743847i	$-0.732999\pi$
$457$	6.61803	−	20.3682i	0.309579	−	0.952785i	0.977929	−	0.208938i	$-0.0670007\pi$
$458$	−29.2705	+	21.2663i	−1.36772	+	0.993708i
$459$	3.92705	+	2.85317i	0.183299	+	0.133175i
$460$	−2.51064	−	7.72696i	−0.117059	−	0.360272i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$	−6.80902	+	2.93893i	−0.316784	+	0.136731i
$463$	−23.4164			−1.08825			−0.544126	−	0.839003i	$-0.683139\pi$
$463$	−23.4164			−1.08825			−0.544126	+	0.839003i	$0.683139\pi$
$464$	1.85410	+	5.70634i	0.0860745	+	0.264910i
$465$	1.54508	+	1.12257i	0.0716516	+	0.0520579i
$466$	28.4164	−	20.6457i	1.31636	−	0.956395i
$467$	8.09017	−	24.8990i	0.374368	−	1.15219i	−0.569535	−	0.821967i	$-0.692877\pi$
$467$	8.09017	−	24.8990i	0.374368	−	1.15219i	0.943904	−	0.330221i	$-0.107123\pi$
$468$	3.00000	−	9.23305i	0.138675	−	0.426798i
$469$		0			0
$470$	5.00000	+	3.63271i	0.230633	+	0.167565i
$471$	7.14590	+	21.9928i	0.329266	+	1.01338i
$472$	7.23607			0.333067
$473$	−3.00000	−	32.0584i	−0.137940	−	1.47405i
$474$	22.3607			1.02706
$475$	−4.07295	−	12.5352i	−0.186880	−	0.575157i
$476$	−11.7812	−	8.55951i	−0.539988	−	0.392324i
$477$	−5.47214	+	3.97574i	−0.250552	+	0.182037i
$478$	−13.1525	+	40.4792i	−0.601580	+	1.85147i
$479$	−0.291796	+	0.898056i	−0.0133325	+	0.0410332i	−0.957501	−	0.288428i	$-0.906867\pi$
$479$	−0.291796	+	0.898056i	−0.0133325	+	0.0410332i	0.944169	+	0.329462i	$0.106867\pi$
$480$	3.35410	−	2.43690i	0.153093	−	0.111229i
$481$	−12.0902	−	8.78402i	−0.551264	−	0.400517i
$482$	8.29180	+	25.5195i	0.377681	+	1.16238i
$483$	−4.38197			−0.199386
$484$	22.6353	−	24.0134i	1.02888	−	1.09152i
$485$	3.70820			0.168381
$486$	−0.690983	−	2.12663i	−0.0313436	−	0.0964658i
$487$	−22.4164	−	16.2865i	−1.01578	−	0.738011i	−0.0503700	−	0.998731i	$-0.516040\pi$
$487$	−22.4164	−	16.2865i	−1.01578	−	0.738011i	−0.965414	+	0.260720i	$0.916040\pi$
$488$		0			0
$489$	3.09017	−	9.51057i	0.139742	−	0.430083i
$490$	−0.427051	+	1.31433i	−0.0192922	+	0.0593753i
$491$	−1.21885	+	0.885544i	−0.0550058	+	0.0399641i	−0.614948	−	0.788567i	$-0.710823\pi$
$491$	−1.21885	+	0.885544i	−0.0550058	+	0.0399641i	0.559943	+	0.828531i	$0.310823\pi$
$492$	17.9164	+	13.0170i	0.807734	+	0.586853i
$493$	−9.00000	−	27.6992i	−0.405340	−	1.24751i
$494$	20.6525			0.929199
$495$	0.190983	+	2.04087i	0.00858405	+	0.0917303i
$496$	3.09017			0.138753
$497$	−1.52786	−	4.70228i	−0.0685341	−	0.210926i
$498$	29.7984	+	21.6498i	1.33530	+	0.970150i
$499$	−17.0902	+	12.4167i	−0.765061	+	0.555849i	−0.900458	−	0.434942i	$-0.856769\pi$
$499$	−17.0902	+	12.4167i	−0.765061	+	0.555849i	0.135397	+	0.990791i	$0.456769\pi$
$500$	5.51064	−	16.9600i	0.246443	−	0.758475i
$501$	6.56231	−	20.1967i	0.293182	−	0.902322i
$502$	−50.1246	+	36.4177i	−2.23717	+	1.62540i
$503$	11.7082	+	8.50651i	0.522043	+	0.379286i	0.817373	−	0.576109i	$-0.195430\pi$
$503$	11.7082	+	8.50651i	0.522043	+	0.379286i	−0.295330	+	0.955395i	$0.595430\pi$
$504$	0.690983	+	2.12663i	0.0307788	+	0.0947275i
$505$	4.20163			0.186970
$506$	29.8369	−	12.8783i	1.32641	−	0.572509i
$507$	2.52786			0.112266
$508$	0.270510	+	0.832544i	0.0120019	+	0.0369382i
$509$	21.9164	+	15.9232i	0.971428	+	0.705784i	0.955777	−	0.294094i	$-0.0950179\pi$
$509$	21.9164	+	15.9232i	0.971428	+	0.705784i	0.0156512	+	0.999878i	$0.495018\pi$
$510$	−5.42705	+	3.94298i	−0.240314	+	0.174598i
$511$	4.23607	−	13.0373i	0.187393	−	0.576735i
$512$	3.45492	−	10.6331i	0.152687	−	0.469923i
$513$	2.30902	−	1.67760i	0.101946	−	0.0740678i
$514$	−44.2320	−	32.1364i	−1.95099	−	1.41748i
$515$	−0.253289	−	0.779543i	−0.0111612	−	0.0343508i
$516$	−29.1246			−1.28214
$517$	−7.56231	+	12.7598i	−0.332590	+	0.561174i
$518$	10.3262			0.453709
$519$	4.20820	+	12.9515i	0.184720	+	0.568509i
$520$	3.61803	+	2.62866i	0.158661	+	0.115274i
$521$	9.97214	−	7.24518i	0.436887	−	0.317417i	−0.347510	−	0.937676i	$-0.612973\pi$
$521$	9.97214	−	7.24518i	0.436887	−	0.317417i	0.784397	+	0.620259i	$0.212973\pi$
$522$	−4.14590	+	12.7598i	−0.181461	+	0.558480i
$523$	4.06231	−	12.5025i	0.177632	−	0.546696i	−0.822112	−	0.569326i	$-0.807204\pi$
$523$	4.06231	−	12.5025i	0.177632	−	0.546696i	0.999744	+	0.0226305i	$0.00720412\pi$
$524$	40.4164	−	29.3642i	1.76560	−	1.28278i
$525$	−3.73607	−	2.71441i	−0.163055	−	0.118467i
$526$	7.50000	+	23.0826i	0.327016	+	1.00645i
$527$	−15.0000			−0.653410
$528$	2.19098	+	2.48990i	0.0953503	+	0.108359i
$529$	−3.79837			−0.165147
$530$	−2.88854	−	8.89002i	−0.125470	−	0.386158i
$531$	−2.61803	−	1.90211i	−0.113613	−	0.0825447i
$532$	−6.92705	+	5.03280i	−0.300326	+	0.218199i
$533$	7.38197	−	22.7194i	0.319748	−	0.984085i
$534$	−3.88197	+	11.9475i	−0.167989	+	0.517017i
$535$	7.89919	−	5.73910i	0.341512	−	0.248123i
$536$		0			0
$537$	4.57295	+	14.0741i	0.197337	+	0.607342i
$538$	−30.0000			−1.29339
$539$	−3.23607	−	0.726543i	−0.139387	−	0.0312944i
$540$	1.85410			0.0797878
$541$	−5.04508	−	15.5272i	−0.216905	−	0.667565i	−0.999013	−	0.0444221i	$-0.985855\pi$
$541$	−5.04508	−	15.5272i	−0.216905	−	0.667565i	0.782108	−	0.623143i	$-0.214145\pi$
$542$	40.7148	+	29.5810i	1.74885	+	1.27061i
$543$	−16.0902	+	11.6902i	−0.690495	+	0.501674i
$544$	−10.0623	+	30.9686i	−0.431418	+	1.32777i
$545$	3.35410	−	10.3229i	0.143674	−	0.442183i
$546$	5.85410	−	4.25325i	0.250532	−	0.182022i
$547$	29.5066	+	21.4378i	1.26161	+	0.916613i	0.998836	−	0.0482438i	$-0.0153624\pi$
$547$	29.5066	+	21.4378i	1.26161	+	0.916613i	0.262775	+	0.964857i	$0.415362\pi$
$548$	7.58359	+	23.3399i	0.323955	+	0.997031i
$549$		0			0
$550$	33.4164	+	7.50245i	1.42488	+	0.319906i
$551$	−17.1246			−0.729533
$552$	−3.02786	−	9.31881i	−0.128874	−	0.396635i
$553$	8.09017	+	5.87785i	0.344029	+	0.249952i
$554$	0.163119	−	0.118513i	0.00693026	−	0.00503513i
$555$	0.881966	−	2.71441i	0.0374374	−	0.115220i
$556$	12.1869	−	37.5075i	0.516840	−	1.59067i
$557$	−18.0902	+	13.1433i	−0.766505	+	0.556899i	−0.900899	−	0.434029i	$-0.857091\pi$
$557$	−18.0902	+	13.1433i	−0.766505	+	0.556899i	0.134394	+	0.990928i	$0.457091\pi$
$558$	5.59017	+	4.06150i	0.236651	+	0.171937i
$559$	9.70820	+	29.8788i	0.410613	+	1.26374i
$560$	0.618034			0.0261167
$561$	−10.6353	−	12.0862i	−0.449021	−	0.510281i
$562$	−60.2492			−2.54146
$563$	−2.94427	−	9.06154i	−0.124086	−	0.381898i	0.869647	−	0.493674i	$-0.164346\pi$
$563$	−2.94427	−	9.06154i	−0.124086	−	0.381898i	−0.993733	+	0.111775i	$0.964346\pi$
$564$	10.8541	+	7.88597i	0.457040	+	0.332059i
$565$	−2.61803	+	1.90211i	−0.110142	+	0.0800225i
$566$	−11.9336	+	36.7279i	−0.501608	+	1.54379i
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$	8.94427	−	6.49839i	0.375293	−	0.272667i
$569$	−9.38197	−	6.81640i	−0.393312	−	0.285758i	0.373499	−	0.927631i	$-0.378158\pi$
$569$	−9.38197	−	6.81640i	−0.393312	−	0.285758i	−0.766812	+	0.641872i	$0.778158\pi$
$570$	1.21885	+	3.75123i	0.0510519	+	0.157122i
$571$	15.3475			0.642274			0.321137	−	0.947033i	$-0.395935\pi$
$571$	15.3475			0.642274			0.321137	+	0.947033i	$0.395935\pi$
$572$	−16.4164	+	27.6992i	−0.686404	+	1.15816i
$573$	−4.90983			−0.205111
$574$	5.10081	+	15.6987i	0.212904	+	0.655251i
$575$	16.3713	+	11.8945i	0.682731	+	0.496033i
$576$	10.5172	−	7.64121i	0.438218	−	0.318384i
$577$	−11.0344	+	33.9605i	−0.459370	+	1.41379i	0.406558	+	0.913625i	$0.366729\pi$
$577$	−11.0344	+	33.9605i	−0.459370	+	1.41379i	−0.865927	+	0.500170i	$0.833271\pi$
$578$	4.53444	−	13.9556i	0.188608	−	0.580475i
$579$	−17.6803	+	12.8455i	−0.734770	+	0.533842i
$580$	−9.00000	−	6.53888i	−0.373705	−	0.271512i
$581$	5.09017	+	15.6659i	0.211176	+	0.649932i
$582$	13.4164			0.556128
$583$	20.5967	−	8.89002i	0.853030	−	0.368187i
$584$	30.6525			1.26841
$585$	−0.618034	−	1.90211i	−0.0255526	−	0.0786427i
$586$	32.9508	+	23.9402i	1.36119	+	0.988960i
$587$	1.14590	−	0.832544i	0.0472963	−	0.0343628i	−0.563886	−	0.825853i	$-0.690694\pi$
$587$	1.14590	−	0.832544i	0.0472963	−	0.0343628i	0.611182	+	0.791490i	$0.290694\pi$
$588$	−0.927051	+	2.85317i	−0.0382309	+	0.117663i
$589$	−2.72542	+	8.38800i	−0.112299	+	0.345621i
$590$	3.61803	−	2.62866i	0.148952	−	0.108220i
$591$	18.1803	+	13.2088i	0.747839	+	0.543337i
$592$	−1.42705	−	4.39201i	−0.0586514	−	0.180511i
$593$	22.5066			0.924234			0.462117	−	0.886819i	$-0.347090\pi$
$593$	22.5066			0.924234			0.462117	+	0.886819i	$0.347090\pi$
$594$	0.690983	+	7.38394i	0.0283514	+	0.302967i
$595$	−3.00000			−0.122988
$596$	−4.58359	−	14.1068i	−0.187751	−	0.577839i
$597$	10.6353	+	7.72696i	0.435272	+	0.316244i
$598$	−25.6525	+	18.6376i	−1.04901	+	0.762149i
$599$	−7.29837	+	22.4621i	−0.298203	+	0.917776i	0.683923	+	0.729554i	$0.260272\pi$
$599$	−7.29837	+	22.4621i	−0.298203	+	0.917776i	−0.982127	+	0.188222i	$0.939728\pi$
$600$	3.19098	−	9.82084i	0.130271	−	0.400934i
$601$	−2.85410	+	2.07363i	−0.116421	+	0.0845850i	−0.644472	−	0.764628i	$-0.722923\pi$
$601$	−2.85410	+	2.07363i	−0.116421	+	0.0845850i	0.528051	+	0.849213i	$0.322923\pi$
$602$	−17.5623	−	12.7598i	−0.715786	−	0.520049i
$603$		0			0
$604$	−46.5836			−1.89546
$605$	0.864745	−	6.74315i	0.0351569	−	0.274148i
$606$	15.2016			0.617524
$607$	−3.70163	−	11.3924i	−0.150244	−	0.462405i	0.847404	−	0.530949i	$-0.178164\pi$
$607$	−3.70163	−	11.3924i	−0.150244	−	0.462405i	−0.997648	+	0.0685445i	$0.978164\pi$
$608$	15.4894	+	11.2537i	0.628176	+	0.456397i
$609$	−4.85410	+	3.52671i	−0.196698	+	0.142910i
$610$		0			0
$611$	4.47214	−	13.7638i	0.180923	−	0.556825i
$612$	−11.7812	+	8.55951i	−0.476225	+	0.345998i
$613$	17.7812	+	12.9188i	0.718174	+	0.521784i	0.885800	−	0.464067i	$-0.153610\pi$
$613$	17.7812	+	12.9188i	0.718174	+	0.521784i	−0.167626	+	0.985851i	$0.553610\pi$
$614$	−12.1353	−	37.3485i	−0.489739	−	1.50726i
$615$	4.56231			0.183970
$616$	−0.690983	−	7.38394i	−0.0278405	−	0.297507i
$617$	−14.0689			−0.566392			−0.283196	−	0.959062i	$-0.591395\pi$
$617$	−14.0689			−0.566392			−0.283196	+	0.959062i	$0.591395\pi$
$618$	−0.916408	−	2.82041i	−0.0368633	−	0.113454i
$619$	29.6803	+	21.5640i	1.19295	+	0.866732i	0.993573	−	0.113191i	$-0.0361071\pi$
$619$	29.6803	+	21.5640i	1.19295	+	0.866732i	0.199380	+	0.979922i	$0.436107\pi$
$620$	−4.63525	+	3.36771i	−0.186156	+	0.135250i
$621$	−1.35410	+	4.16750i	−0.0543382	+	0.167236i
$622$	14.2705	−	43.9201i	0.572195	−	1.76104i
$623$	−4.54508	+	3.30220i	−0.182095	+	0.132300i
$624$	−2.61803	−	1.90211i	−0.104805	−	0.0761455i
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$	−17.4853			−0.698853
$627$	−8.69098	+	3.75123i	−0.347084	+	0.149810i
$628$	−69.3738			−2.76832
$629$	6.92705	+	21.3193i	0.276200	+	0.850055i
$630$	1.11803	+	0.812299i	0.0445435	+	0.0323628i
$631$	36.6525	−	26.6296i	1.45911	−	1.06011i	0.475519	−	0.879705i	$-0.342260\pi$
$631$	36.6525	−	26.6296i	1.45911	−	1.06011i	0.983593	−	0.180401i	$-0.0577397\pi$
$632$	−6.90983	+	21.2663i	−0.274858	+	0.845927i
$633$	5.67376	−	17.4620i	0.225512	−	0.694054i
$634$	−12.2361	+	8.89002i	−0.485956	+	0.353068i
$635$	0.145898	+	0.106001i	0.00578979	+	0.00420653i
$636$	−6.27051	−	19.2986i	−0.248642	−	0.765241i
$637$	3.23607			0.128218
$638$	22.6869	−	38.2793i	0.898184	−	1.51549i
$639$	−4.94427			−0.195592
$640$	2.98936	+	9.20029i	0.118165	+	0.363674i
$641$	−10.3262	−	7.50245i	−0.407862	−	0.296329i	0.364874	−	0.931057i	$-0.381112\pi$
$641$	−10.3262	−	7.50245i	−0.407862	−	0.296329i	−0.772736	+	0.634728i	$0.781112\pi$
$642$	28.5795	−	20.7642i	1.12794	−	0.819499i
$643$	3.17376	−	9.76784i	0.125161	−	0.385206i	−0.868769	−	0.495217i	$-0.835089\pi$
$643$	3.17376	−	9.76784i	0.125161	−	0.385206i	0.993930	+	0.110011i	$0.0350886\pi$
$644$	4.06231	−	12.5025i	0.160077	−	0.492667i
$645$	−4.85410	+	3.52671i	−0.191130	+	0.138864i
$646$	−25.0623	−	18.2088i	−0.986063	−	0.716417i
$647$	11.2705	+	34.6871i	0.443089	+	1.36369i	0.884565	+	0.466416i	$0.154455\pi$
$647$	11.2705	+	34.6871i	0.443089	+	1.36369i	−0.441476	+	0.897273i	$0.645545\pi$
$648$	2.23607			0.0878410
$649$	7.09017	+	8.05748i	0.278314	+	0.316284i
$650$	−33.4164			−1.31070
$651$	0.954915	+	2.93893i	0.0374261	+	0.115186i
$652$	24.2705	+	17.6336i	0.950507	+	0.690583i
$653$	−13.2361	+	9.61657i	−0.517967	+	0.376325i	−0.815838	−	0.578281i	$-0.803724\pi$
$653$	−13.2361	+	9.61657i	−0.517967	+	0.376325i	0.297870	+	0.954606i	$0.403724\pi$
$654$	12.1353	−	37.3485i	0.474526	−	1.46044i
$655$	3.18034	−	9.78808i	0.124266	−	0.382452i
$656$	5.97214	−	4.33901i	0.233173	−	0.169410i
$657$	−11.0902	−	8.05748i	−0.432669	−	0.314352i
$658$	3.09017	+	9.51057i	0.120467	+	0.370760i
$659$	−25.8541			−1.00713			−0.503566	−	0.863957i	$-0.667979\pi$
$659$	−25.8541			−1.00713			−0.503566	+	0.863957i	$0.667979\pi$
$660$	−6.00000	−	1.34708i	−0.233550	−	0.0524352i
$661$	−32.5410			−1.26570			−0.632849	−	0.774275i	$-0.718115\pi$
$661$	−32.5410			−1.26570			−0.632849	+	0.774275i	$0.718115\pi$
$662$	12.0344	+	37.0382i	0.467732	+	1.43953i
$663$	12.7082	+	9.23305i	0.493546	+	0.358582i
$664$	−29.7984	+	21.6498i	−1.15640	+	0.840175i
$665$	−0.545085	+	1.67760i	−0.0211375	+	0.0650545i
$666$	3.19098	−	9.82084i	0.123648	−	0.380550i
$667$	21.2705	−	15.4539i	0.823597	−	0.598379i
$668$	51.5410	+	37.4467i	1.99418	+	1.44886i
$669$	−6.06231	−	18.6579i	−0.234382	−	0.721355i
$670$		0			0
$671$		0			0
$672$	6.70820			0.258775
$673$	−13.8541	−	42.6385i	−0.534036	−	1.64359i	−0.745722	−	0.666257i	$-0.767895\pi$
$673$	−13.8541	−	42.6385i	−0.534036	−	1.64359i	0.211686	−	0.977338i	$-0.432105\pi$
$674$	−49.0066	−	35.6054i	−1.88766	−	1.37147i
$675$	−3.73607	+	2.71441i	−0.143801	+	0.104478i
$676$	−2.34346	+	7.21242i	−0.0901330	+	0.277401i
$677$	10.6180	−	32.6789i	0.408084	−	1.25595i	−0.510208	−	0.860051i	$-0.670432\pi$
$677$	10.6180	−	32.6789i	0.408084	−	1.25595i	0.918292	−	0.395903i	$-0.129568\pi$
$678$	−9.47214	+	6.88191i	−0.363775	+	0.264298i
$679$	4.85410	+	3.52671i	0.186283	+	0.135343i
$680$	−2.07295	−	6.37988i	−0.0794940	−	0.244657i
$681$	−12.4721			−0.477933
$682$	−15.1393	−	17.2048i	−0.579715	−	0.658805i
$683$	26.7984			1.02541			0.512706	−	0.858564i	$-0.328643\pi$
$683$	26.7984			1.02541			0.512706	+	0.858564i	$0.328643\pi$
$684$	2.64590	+	8.14324i	0.101168	+	0.311364i
$685$	4.09017	+	2.97168i	0.156277	+	0.113542i
$686$	−1.80902	+	1.31433i	−0.0690686	+	0.0501813i
$687$	−5.00000	+	15.3884i	−0.190762	+	0.587105i
$688$	−3.00000	+	9.23305i	−0.114374	+	0.352007i
$689$	−17.7082	+	12.8658i	−0.674629	+	0.490147i
$690$	−4.89919	−	3.55947i	−0.186509	−	0.135507i
$691$	15.0623	+	46.3570i	0.572997	+	1.76350i	0.642900	+	0.765950i	$0.277731\pi$
$691$	15.0623	+	46.3570i	0.572997	+	1.76350i	−0.0699030	+	0.997554i	$0.522269\pi$
$692$	−40.8541			−1.55304
$693$	−1.69098	+	2.85317i	−0.0642351	+	0.108383i
$694$	−32.4377			−1.23132
$695$	−2.51064	−	7.72696i	−0.0952341	−	0.293100i
$696$	−10.8541	−	7.88597i	−0.411424	−	0.298917i
$697$	−28.9894	+	21.0620i	−1.09805	+	0.797780i
$698$	−15.0000	+	46.1653i	−0.567758	+	1.74738i
$699$	4.85410	−	14.9394i	0.183599	−	0.565060i
$700$	11.2082	−	8.14324i	0.423630	−	0.307785i
$701$	−32.0344	−	23.2744i	−1.20992	−	0.879061i	−0.214700	−	0.976680i	$-0.568877\pi$
$701$	−32.0344	−	23.2744i	−1.20992	−	0.879061i	−0.995224	+	0.0976186i	$0.968877\pi$
$702$	−2.23607	−	6.88191i	−0.0843949	−	0.259741i
$703$	13.1803			0.497106
$704$	−39.5861	+	17.0863i	−1.49196	+	0.643963i
$705$	2.76393			0.104096
$706$	−12.4377	−	38.2793i	−0.468099	−	1.44066i
$707$	5.50000	+	3.99598i	0.206849	+	0.150284i
$708$	7.85410	−	5.70634i	0.295175	−	0.214457i
$709$	−2.48278	+	7.64121i	−0.0932427	+	0.286972i	−0.986792	−	0.161994i	$-0.948207\pi$
$709$	−2.48278	+	7.64121i	−0.0932427	+	0.286972i	0.893549	+	0.448966i	$0.148207\pi$
$710$	2.11146	−	6.49839i	0.0792415	−	0.243880i
$711$	8.09017	−	5.87785i	0.303405	−	0.220437i
$712$	−10.1631	−	7.38394i	−0.380879	−	0.276725i
$713$	−4.18441	−	12.8783i	−0.156707	−	0.482295i
$714$	−10.8541			−0.406205
$715$	0.618034	+	6.60440i	0.0231132	+	0.246990i
$716$	−44.3951			−1.65912
$717$	5.88197	+	18.1028i	0.219666	+	0.676063i
$718$	−11.6459	−	8.46124i	−0.434621	−	0.315771i
$719$	−31.5623	+	22.9314i	−1.17708	+	0.855195i	−0.991839	−	0.127499i	$-0.959305\pi$
$719$	−31.5623	+	22.9314i	−1.17708	+	0.855195i	−0.185237	+	0.982694i	$0.559305\pi$
$720$	0.190983	−	0.587785i	0.00711752	−	0.0219055i
$721$	0.409830	−	1.26133i	0.0152629	−	0.0469743i
$722$	19.6353	−	14.2658i	0.730749	−	0.530920i
$723$	9.70820	+	7.05342i	0.361052	+	0.262320i
$724$	−18.4377	−	56.7454i	−0.685232	−	2.10893i
$725$	27.7082			1.02906
$726$	3.12868	−	24.3970i	0.116116	−	0.905456i
$727$	−18.8541			−0.699260			−0.349630	−	0.936888i	$-0.613693\pi$
$727$	−18.8541			−0.699260			−0.349630	+	0.936888i	$0.613693\pi$
$728$	2.23607	+	6.88191i	0.0828742	+	0.255061i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	15.3262	−	11.1352i	0.567250	−	0.412131i
$731$	14.5623	−	44.8182i	0.538606	−	1.65766i
$732$		0			0
$733$	14.6180	−	10.6206i	0.539929	−	0.392282i	−0.284129	−	0.958786i	$-0.591705\pi$
$733$	14.6180	−	10.6206i	0.539929	−	0.392282i	0.824059	+	0.566504i	$0.191705\pi$
$734$	−4.93769	−	3.58744i	−0.182254	−	0.132415i
$735$	0.190983	+	0.587785i	0.00704451	+	0.0216808i
$736$	−29.3951			−1.08352
$737$		0			0
$738$	16.5066			0.607616
$739$	12.7082	+	39.1118i	0.467479	+	1.43875i	0.855838	+	0.517244i	$0.173042\pi$
$739$	12.7082	+	39.1118i	0.467479	+	1.43875i	−0.388359	+	0.921508i	$0.626958\pi$
$740$	6.92705	+	5.03280i	0.254643	+	0.185009i
$741$	7.47214	−	5.42882i	0.274496	−	0.199433i
$742$	4.67376	−	14.3844i	0.171579	−	0.528066i
$743$	−5.04508	+	15.5272i	−0.185086	+	0.569637i	−0.999950	−	0.0100159i	$-0.996812\pi$
$743$	−5.04508	+	15.5272i	−0.185086	+	0.569637i	0.814864	+	0.579653i	$0.196812\pi$
$744$	−5.59017	+	4.06150i	−0.204946	+	0.148902i
$745$	−2.47214	−	1.79611i	−0.0905721	−	0.0658044i
$746$	11.2812	+	34.7198i	0.413032	+	1.27118i
$747$	16.4721			0.602684
$748$	44.3435	−	19.1396i	1.62136	−	0.699815i
$749$	15.7984			0.577260
$750$	−4.10739	−	12.6412i	−0.149981	−	0.461593i
$751$	−19.4164	−	14.1068i	−0.708515	−	0.514766i	0.174179	−	0.984714i	$-0.444273\pi$
$751$	−19.4164	−	14.1068i	−0.708515	−	0.514766i	−0.882694	+	0.469948i	$0.844273\pi$
$752$	3.61803	−	2.62866i	0.131936	−	0.0958572i
$753$	−8.56231	+	26.3521i	−0.312028	+	0.960323i
$754$	−13.4164	+	41.2915i	−0.488597	+	1.50375i
$755$	−7.76393	+	5.64083i	−0.282558	+	0.205291i
$756$	2.42705	+	1.76336i	0.0882710	+	0.0641326i
$757$	3.26393	+	10.0453i	0.118630	+	0.365104i	0.992687	−	0.120719i	$-0.0385199\pi$
$757$	3.26393	+	10.0453i	0.118630	+	0.365104i	−0.874057	+	0.485823i	$0.838520\pi$
$758$	48.1378			1.74844
$759$	7.40983	−	12.5025i	0.268960	−	0.453812i
$760$	−3.94427			−0.143074
$761$	0.437694	+	1.34708i	0.0158664	+	0.0488318i	0.958676	−	0.284499i	$-0.0918273\pi$
$761$	0.437694	+	1.34708i	0.0158664	+	0.0488318i	−0.942810	+	0.333331i	$0.891827\pi$
$762$	0.527864	+	0.383516i	0.0191225	+	0.0138933i
$763$	14.2082	−	10.3229i	0.514372	−	0.373713i
$764$	4.55166	−	14.0086i	0.164673	−	0.506813i
$765$	−0.927051	+	2.85317i	−0.0335176	+	0.103157i
$766$	37.6869	−	27.3811i	1.36168	−	0.989321i
$767$	−8.47214	−	6.15537i	−0.305911	−	0.222257i
$768$	2.78115	+	8.55951i	0.100356	+	0.308865i
$769$	1.05573			0.0380705			0.0190353	−	0.999819i	$-0.493941\pi$
$769$	1.05573			0.0380705			0.0190353	+	0.999819i	$0.493941\pi$
$770$	−3.02786	−	3.44095i	−0.109117	−	0.124003i
$771$	−24.4508			−0.880576
$772$	−20.2599	−	62.3535i	−0.729169	−	2.24415i
$773$	−6.85410	−	4.97980i	−0.246525	−	0.179111i	0.457660	−	0.889127i	$-0.348688\pi$
$773$	−6.85410	−	4.97980i	−0.246525	−	0.179111i	−0.704185	+	0.710016i	$0.748688\pi$
$774$	−17.5623	+	12.7598i	−0.631264	+	0.458640i
$775$	4.40983	−	13.5721i	0.158406	−	0.487523i
$776$	−4.14590	+	12.7598i	−0.148829	+	0.458049i
$777$	3.73607	−	2.71441i	0.134031	−	0.0973790i
$778$	−27.5623	−	20.0252i	−0.988157	−	0.717938i
$779$	6.51064	+	20.0377i	0.233268	+	0.717925i
$780$	6.00000			0.214834
$781$	16.0000	+	3.59222i	0.572525	+	0.128540i
$782$	47.5623			1.70082
$783$	1.85410	+	5.70634i	0.0662602	+	0.203928i
$784$	0.809017	+	0.587785i	0.0288935	+	0.0209923i
$785$	−11.5623	+	8.40051i	−0.412676	+	0.299827i
$786$	11.5066	−	35.4136i	0.410426	−	1.26316i
$787$	−7.98936	+	24.5887i	−0.284790	+	0.876493i	0.701672	+	0.712500i	$0.252437\pi$
$787$	−7.98936	+	24.5887i	−0.284790	+	0.876493i	−0.986462	+	0.163993i	$0.947563\pi$
$788$	−54.5410	+	39.6264i	−1.94294	+	1.41163i
$789$	8.78115	+	6.37988i	0.312617	+	0.227130i
$790$	4.27051	+	13.1433i	0.151938	+	0.467617i
$791$	−5.23607			−0.186173
$792$	−7.23607	−	1.62460i	−0.257122	−	0.0577276i
$793$		0			0
$794$	21.1033	+	64.9494i	0.748929	+	2.30497i
$795$	−3.38197	−	2.45714i	−0.119946	−	0.0871459i
$796$	−31.9058	+	23.1809i	−1.13087	+	0.821625i
$797$	12.8435	−	39.5281i	0.454939	−	1.40016i	−0.416269	−	0.909242i	$-0.636662\pi$
$797$	12.8435	−	39.5281i	0.454939	−	1.40016i	0.871207	−	0.490915i	$-0.163338\pi$
$798$	−1.97214	+	6.06961i	−0.0698129	+	0.214862i
$799$	−17.5623	+	12.7598i	−0.621310	+	0.451408i
$800$	−25.0623	−	18.2088i	−0.886086	−	0.643779i
$801$	1.73607	+	5.34307i	0.0613409	+	0.188788i
$802$	16.5836			0.585587
$803$	30.0344	+	34.1320i	1.05989	+	1.20449i
$804$		0			0
$805$	−0.836881	−	2.57565i	−0.0294962	−	0.0907799i
$806$	18.0902	+	13.1433i	0.637199	+	0.462952i
$807$	−10.8541	+	7.88597i	−0.382082	+	0.277599i
$808$	−4.69756	+	14.4576i	−0.165260	+	0.508617i
$809$	2.23607	−	6.88191i	0.0786160	−	0.241955i	−0.904023	−	0.427484i	$-0.859400\pi$
$809$	2.23607	−	6.88191i	0.0786160	−	0.241955i	0.982639	+	0.185529i	$0.0593999\pi$
$810$	1.11803	−	0.812299i	0.0392837	−	0.0285413i
$811$	−6.94427	−	5.04531i	−0.243846	−	0.177165i	0.459149	−	0.888359i	$-0.348154\pi$
$811$	−6.94427	−	5.04531i	−0.243846	−	0.177165i	−0.702995	+	0.711195i	$0.748154\pi$
$812$	−5.56231	−	17.1190i	−0.195199	−	0.600760i
$813$	22.5066			0.789340
$814$	−17.4615	+	29.4625i	−0.612025	+	1.03266i
$815$	6.18034			0.216488
$816$	1.50000	+	4.61653i	0.0525105	+	0.161611i
$817$	−22.4164	−	16.2865i	−0.784251	−	0.569792i
$818$	40.1246	−	29.1522i	1.40292	−	1.01928i
$819$	1.00000	−	3.07768i	0.0349428	−	0.107543i
$820$	−4.22949	+	13.0170i	−0.147700	+	0.454574i
$821$	8.85410	−	6.43288i	0.309010	−	0.224509i	−0.422461	−	0.906381i	$-0.638834\pi$
$821$	8.85410	−	6.43288i	0.309010	−	0.224509i	0.731472	+	0.681872i	$0.238834\pi$
$822$	14.7984	+	10.7516i	0.516153	+	0.375007i
$823$	1.49342	+	4.59628i	0.0520574	+	0.160216i	0.973705	−	0.227811i	$-0.0731567\pi$
$823$	1.49342	+	4.59628i	0.0520574	+	0.160216i	−0.921648	+	0.388027i	$0.873157\pi$
$824$	2.96556			0.103310
$825$	14.0623	−	6.06961i	0.489587	−	0.211317i
$826$	7.23607			0.251775
$827$	9.22949	+	28.4054i	0.320941	+	0.987754i	0.973240	+	0.229792i	$0.0738047\pi$
$827$	9.22949	+	28.4054i	0.320941	+	0.987754i	−0.652299	+	0.757962i	$0.726195\pi$
$828$	−10.6353	−	7.72696i	−0.369601	−	0.268531i
$829$	24.4721	−	17.7800i	0.849952	−	0.617527i	−0.0751805	−	0.997170i	$-0.523953\pi$
$829$	24.4721	−	17.7800i	0.849952	−	0.617527i	0.925133	+	0.379643i	$0.123953\pi$
$830$	−7.03444	+	21.6498i	−0.244169	+	0.751475i
$831$	0.0278640	−	0.0857567i	0.000966593	−	0.00297487i
$832$	34.0344	−	24.7275i	1.17993	−	0.857271i
$833$	−3.92705	−	2.85317i	−0.136064	−	0.0988565i
$834$	−9.08359	−	27.9564i	−0.314539	−	0.968052i
$835$	13.1246			0.454196
$836$	−2.64590	−	28.2744i	−0.0915103	−	0.977891i
$837$	3.09017			0.106812
$838$	−2.23607	−	6.88191i	−0.0772437	−	0.237732i
$839$	32.5623	+	23.6579i	1.12418	+	0.816761i	0.984837	−	0.173483i	$-0.0555023\pi$
$839$	32.5623	+	23.6579i	1.12418	+	0.816761i	0.139339	+	0.990245i	$0.455502\pi$
$840$	−1.11803	+	0.812299i	−0.0385758	+	0.0280270i
$841$	2.16312	−	6.65740i	0.0745903	−	0.229565i
$842$	6.77051	−	20.8375i	0.233327	−	0.718107i
$843$	−21.7984	+	15.8374i	−0.750776	+	0.545471i
$844$	44.5623	+	32.3764i	1.53390	+	1.11444i
$845$	0.482779	+	1.48584i	0.0166081	+	0.0511145i
$846$	10.0000			0.343807
$847$	7.54508	−	8.00448i	0.259252	−	0.275037i
$848$	−6.76393			−0.232274
$849$	5.33688	+	16.4252i	0.183161	+	0.563712i
$850$	40.5517	+	29.4625i	1.39091	+	1.01056i
$851$	−16.3713	+	11.8945i	−0.561202	+	0.407737i
$852$	4.58359	−	14.1068i	0.157031	−	0.483293i
$853$	−12.8885	+	39.6669i	−0.441295	+	1.35817i	0.445201	+	0.895431i	$0.353132\pi$
$853$	−12.8885	+	39.6669i	−0.441295	+	1.35817i	−0.886496	+	0.462736i	$0.846868\pi$
$854$		0			0
$855$	1.42705	+	1.03681i	0.0488041	+	0.0354583i
$856$	10.9164	+	33.5972i	0.373115	+	1.14833i
$857$	−34.3607			−1.17374			−0.586869	−	0.809682i	$-0.699640\pi$
$857$	−34.3607			−1.17374			−0.586869	+	0.809682i	$0.699640\pi$
$858$	2.23607	+	23.8949i	0.0763381	+	0.815759i
$859$	12.0000			0.409435			0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000			0.409435			0.204717	+	0.978821i	$0.434372\pi$
$860$	−5.56231	−	17.1190i	−0.189673	−	0.583754i
$861$	5.97214	+	4.33901i	0.203530	+	0.147873i
$862$	−27.2984	+	19.8334i	−0.929786	+	0.675529i
$863$	−3.80902	+	11.7229i	−0.129660	+	0.399054i	−0.994721	−	0.102613i	$-0.967280\pi$
$863$	−3.80902	+	11.7229i	−0.129660	+	0.399054i	0.865061	+	0.501667i	$0.167280\pi$
$864$	2.07295	−	6.37988i	0.0705232	−	0.217048i
$865$	−6.80902	+	4.94704i	−0.231514	+	0.168204i
$866$	56.5066	+	41.0544i	1.92017	+	1.39509i
$867$	−2.02786	−	6.24112i	−0.0688699	−	0.211960i
$868$	−9.27051			−0.314662
$869$	−30.4508	+	13.1433i	−1.03297	+	0.445855i
$870$	−8.29180			−0.281118
$871$		0			0
$872$	31.7705	+	23.0826i	1.07589	+	0.781676i
$873$	4.85410	−	3.52671i	0.164286	−	0.119361i
$874$	8.64183	−	26.5968i	0.292314	−	0.899651i
$875$	1.83688	−	5.65334i	0.0620979	−	0.191118i
$876$	33.2705	−	24.1724i	1.12411	−	0.816711i
$877$	−10.0902	−	7.33094i	−0.340721	−	0.247548i	0.404245	−	0.914651i	$-0.367534\pi$
$877$	−10.0902	−	7.33094i	−0.340721	−	0.247548i	−0.744966	+	0.667103i	$0.767534\pi$
$878$	1.28115	+	3.94298i	0.0432368	+	0.133069i
$879$	18.2148			0.614369
$880$	−1.04508	+	1.76336i	−0.0352298	+	0.0594427i
$881$	11.3262			0.381591			0.190795	−	0.981630i	$-0.438893\pi$
$881$	11.3262			0.381591			0.190795	+	0.981630i	$0.438893\pi$
$882$	0.690983	+	2.12663i	0.0232666	+	0.0716073i
$883$	−15.8541	−	11.5187i	−0.533533	−	0.387634i	0.288145	−	0.957587i	$-0.406962\pi$
$883$	−15.8541	−	11.5187i	−0.533533	−	0.387634i	−0.821678	+	0.569952i	$0.806962\pi$
$884$	−38.1246	+	27.6992i	−1.28227	+	0.931623i
$885$	0.618034	−	1.90211i	0.0207750	−	0.0639388i
$886$	14.0836	−	43.3448i	0.473148	−	1.45620i
$887$	−22.3262	+	16.2210i	−0.749642	+	0.544647i	−0.895716	−	0.444627i	$-0.853336\pi$
$887$	−22.3262	+	16.2210i	−0.749642	+	0.544647i	0.146074	+	0.989274i	$0.453336\pi$
$888$	8.35410	+	6.06961i	0.280345	+	0.203683i
$889$	0.0901699	+	0.277515i	0.00302420	+	0.00930754i
$890$	−7.76393			−0.260248
$891$	2.19098	+	2.48990i	0.0734007	+	0.0834147i
$892$	58.8541			1.97058
$893$	3.94427	+	12.1392i	0.131990	+	0.406224i
$894$	−8.94427	−	6.49839i	−0.299141	−	0.217339i
$895$	−7.39919	+	5.37582i	−0.247328	+	0.179694i
$896$	−4.83688	+	14.8864i	−0.161589	+	0.497319i
$897$	−4.38197	+	13.4863i	−0.146310	+	0.450295i
$898$	75.7771	−	55.0553i	2.52871	−	1.83722i
$899$	−15.0000	−	10.8981i	−0.500278	−	0.363473i
$900$	−4.28115	−	13.1760i	−0.142705	−	0.439201i
$901$	32.8328			1.09382
$902$	−53.4164	−	11.9927i	−1.77857	−	0.399314i
$903$	−9.70820			−0.323069
$904$	−3.61803	−	11.1352i	−0.120334	−	0.370350i
$905$	−9.94427	−	7.22494i	−0.330559	−	0.240165i
$906$	−28.0902	+	20.4087i	−0.933233	+	0.678034i
$907$	5.03444	−	15.4944i	0.167166	−	0.514484i	−0.832023	−	0.554740i	$-0.812818\pi$
$907$	5.03444	−	15.4944i	0.167166	−	0.514484i	0.999189	+	0.0402567i	$0.0128176\pi$
$908$	11.5623	−	35.5851i	0.383709	−	1.18093i
$909$	5.50000	−	3.99598i	0.182423	−	0.132538i
$910$	3.61803	+	2.62866i	0.119937	+	0.0871391i
$911$	−0.291796	−	0.898056i	−0.00966764	−	0.0297539i	0.946106	−	0.323856i	$-0.104979\pi$
$911$	−0.291796	−	0.898056i	−0.00966764	−	0.0297539i	−0.955774	+	0.294102i	$0.904979\pi$
$912$	2.85410			0.0945088
$913$	−53.3050	−	11.9677i	−1.76414	−	0.396073i
$914$	47.8885			1.58401
$915$		0			0
$916$	−39.2705	−	28.5317i	−1.29753	−	0.942714i
$917$	13.4721	−	9.78808i	0.444889	−	0.323231i
$918$	−3.35410	+	10.3229i	−0.110702	+	0.340705i
$919$	−9.41641	+	28.9807i	−0.310619	+	0.955986i	0.666902	+	0.745146i	$0.267620\pi$
$919$	−9.41641	+	28.9807i	−0.310619	+	0.955986i	−0.977521	+	0.210840i	$0.932380\pi$
$920$	4.89919	−	3.55947i	0.161521	−	0.117352i
$921$	−14.2082	−	10.3229i	−0.468176	−	0.340150i
$922$	−4.14590	−	12.7598i	−0.136538	−	0.420220i
$923$	−16.0000			−0.526646
$924$	−6.57295	−	7.46969i	−0.216234	−	0.245735i
$925$	−21.3262			−0.701202
$926$	−16.1803	−	49.7980i	−0.531719	−	1.63646i
$927$	−1.07295	−	0.779543i	−0.0352403	−	0.0256036i
$928$	−32.5623	+	23.6579i	−1.06891	+	0.776609i
$929$	7.33282	−	22.5681i	0.240582	−	0.740435i	−0.755750	−	0.654860i	$-0.772727\pi$
$929$	7.33282	−	22.5681i	0.240582	−	0.740435i	0.996332	−	0.0855745i	$-0.0272726\pi$
$930$	−1.31966	+	4.06150i	−0.0432734	+	0.133182i
$931$	−2.30902	+	1.67760i	−0.0756750	+	0.0549811i
$932$	38.1246	+	27.6992i	1.24881	+	0.907316i
$933$	−6.38197	−	19.6417i	−0.208936	−	0.643039i
$934$	58.5410			1.91552
$935$	5.07295	−	8.55951i	0.165903	−	0.279926i
$936$	7.23607			0.236518
$937$	10.5279	+	32.4014i	0.343930	+	1.05851i	0.962154	+	0.272506i	$0.0878526\pi$
$937$	10.5279	+	32.4014i	0.343930	+	1.05851i	−0.618224	+	0.786002i	$0.712147\pi$
$938$		0			0
$939$	−6.32624	+	4.59628i	−0.206449	+	0.149994i
$940$	−2.56231	+	7.88597i	−0.0835732	+	0.257212i
$941$	−0.152476	+	0.469272i	−0.00497057	+	0.0152978i	−0.953511	−	0.301358i	$-0.902560\pi$
$941$	−0.152476	+	0.469272i	−0.00497057	+	0.0152978i	0.948540	+	0.316656i	$0.102560\pi$
$942$	−41.8328	+	30.3933i	−1.36299	+	0.990268i
$943$	−26.1697	−	19.0134i	−0.852203	−	0.619161i
$944$	−1.00000	−	3.07768i	−0.0325472	−	0.100170i
$945$	0.618034			0.0201046
$946$	66.1033	−	28.5317i	2.14920	−	0.927645i
$947$	13.8541			0.450198			0.225099	−	0.974336i	$-0.427729\pi$
$947$	13.8541			0.450198			0.225099	+	0.974336i	$0.427729\pi$
$948$	9.27051	+	28.5317i	0.301092	+	0.926666i
$949$	−35.8885	−	26.0746i	−1.16499	−	0.846416i
$950$	23.8435	−	17.3233i	0.773584	−	0.562042i
$951$	−2.09017	+	6.43288i	−0.0677784	+	0.208600i
$952$	3.35410	−	10.3229i	0.108707	−	0.334566i
$953$	−9.61803	+	6.98791i	−0.311559	+	0.226361i	−0.732565	−	0.680697i	$-0.761677\pi$
$953$	−9.61803	+	6.98791i	−0.311559	+	0.226361i	0.421006	+	0.907058i	$0.361677\pi$
$954$	−12.2361	−	8.89002i	−0.396157	−	0.287825i
$955$	−0.937694	−	2.88593i	−0.0303431	−	0.0933864i
$956$	−57.1033			−1.84685
$957$	−1.85410	−	19.8132i	−0.0599346	−	0.640469i
$958$	−2.11146			−0.0682181
$959$	2.52786	+	7.77997i	0.0816290	+	0.251228i
$960$	6.50000	+	4.72253i	0.209787	+	0.152419i
$961$	17.3541	−	12.6085i	0.559810	−	0.406726i
$962$	10.3262	−	31.7809i	0.332931	−	1.02466i
$963$	4.88197	−	15.0251i	0.157319	−	0.484179i
$964$	−29.1246	+	21.1603i	−0.938041	+	0.681526i
$965$	−10.9271	−	7.93897i	−0.351754	−	0.255564i
$966$	−3.02786	−	9.31881i	−0.0974199	−	0.299828i
$967$	−3.63932			−0.117033			−0.0585163	−	0.998286i	$-0.518637\pi$
$967$	−3.63932			−0.117033			−0.0585163	+	0.998286i	$0.518637\pi$
$968$	22.2361	+	10.5146i	0.714694	+	0.337953i
$969$	−13.8541			−0.445058
$970$	2.56231	+	7.88597i	0.0822707	+	0.253203i
$971$	−44.1246	−	32.0584i	−1.41603	−	1.02880i	−0.992412	−	0.122961i	$-0.960761\pi$
$971$	−44.1246	−	32.0584i	−1.41603	−	1.02880i	−0.423615	−	0.905842i	$-0.639239\pi$
$972$	2.42705	−	1.76336i	0.0778477	−	0.0565597i
$973$	4.06231	−	12.5025i	0.130232	−	0.400811i
$974$	19.1459	−	58.9250i	0.613474	−	1.88808i
$975$	−12.0902	+	8.78402i	−0.387195	+	0.281314i
$976$		0			0
$977$	−4.21478	−	12.9718i	−0.134843	−	0.415004i	0.860723	−	0.509074i	$-0.170012\pi$
$977$	−4.21478	−	12.9718i	−0.134843	−	0.415004i	−0.995566	+	0.0940706i	$0.970012\pi$
$978$	22.3607			0.715016
$979$	−1.73607	−	18.5519i	−0.0554850	−	0.592920i
$980$	−1.85410			−0.0592271
$981$	−5.42705	−	16.7027i	−0.173272	−	0.533278i
$982$	−2.72542	−	1.98014i	−0.0869718	−	0.0631887i
$983$	8.85410	−	6.43288i	0.282402	−	0.205177i	−0.437562	−	0.899188i	$-0.644158\pi$
$983$	8.85410	−	6.43288i	0.282402	−	0.205177i	0.719964	+	0.694011i	$0.244158\pi$
$984$	−5.10081	+	15.6987i	−0.162608	+	0.500456i
$985$	−4.29180	+	13.2088i	−0.136748	+	0.420867i
$986$	52.6869	−	38.2793i	1.67789	−	1.21906i
$987$	3.61803	+	2.62866i	0.115163	+	0.0836710i
$988$	8.56231	+	26.3521i	0.272403	+	0.838371i
$989$	42.5410			1.35273
$990$	−4.20820	+	1.81636i	−0.133746	+	0.0577276i
$991$	−33.2361			−1.05578			−0.527889	−	0.849313i	$-0.677016\pi$
$991$	−33.2361			−1.05578			−0.527889	+	0.849313i	$0.677016\pi$
$992$	6.40576	+	19.7149i	0.203383	+	0.625949i
$993$	14.0902	+	10.2371i	0.447138	+	0.324865i
$994$	8.94427	−	6.49839i	0.283695	−	0.206117i
$995$	−2.51064	+	7.72696i	−0.0795927	+	0.244961i
$996$	−15.2705	+	46.9978i	−0.483865	+	1.48918i
$997$	35.9443	−	26.1150i	1.13837	−	0.827072i	0.151476	−	0.988461i	$-0.451597\pi$
$997$	35.9443	−	26.1150i	1.13837	−	0.827072i	0.986891	+	0.161389i	$0.0515975\pi$
$998$	−38.2148	−	27.7647i	−1.20967	−	0.878875i
$999$	−1.42705	−	4.39201i	−0.0451499	−	0.138957i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.690983 + 2.12663i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.190983 + 0.587785i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.690983 + 2.12663i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.190983 + 0.587785i) q^{5} +(-0.690983 + 2.12663i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.38197 q^{10} +(-0.309017 - 3.30220i) q^{11} -3.00000 q^{12} +(1.00000 + 3.07768i) q^{13} +(-1.80902 - 1.31433i) q^{14} +(-0.500000 + 0.363271i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.50000 - 4.61653i) q^{17} +(-1.80902 + 1.31433i) q^{18} +(-2.30902 - 1.67760i) q^{19} +(-0.572949 - 1.76336i) q^{20} -1.00000 q^{21} +(6.80902 - 2.93893i) q^{22} +4.38197 q^{23} +(-0.690983 - 2.12663i) q^{24} +(3.73607 + 2.71441i) q^{25} +(-5.85410 + 4.25325i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.927051 - 2.85317i) q^{28} +(4.85410 - 3.52671i) q^{29} +(-1.11803 - 0.812299i) q^{30} +(-0.954915 - 2.93893i) q^{31} -6.70820 q^{32} +(1.69098 - 2.85317i) q^{33} +10.8541 q^{34} +(-0.190983 - 0.587785i) q^{35} +(-2.42705 - 1.76336i) q^{36} +(-3.73607 + 2.71441i) q^{37} +(1.97214 - 6.06961i) q^{38} +(-1.00000 + 3.07768i) q^{39} +(1.11803 - 0.812299i) q^{40} +(-5.97214 - 4.33901i) q^{41} +(-0.690983 - 2.12663i) q^{42} +9.70820 q^{43} +(6.57295 + 7.46969i) q^{44} -0.618034 q^{45} +(3.02786 + 9.31881i) q^{46} +(-3.61803 - 2.62866i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-3.19098 + 9.82084i) q^{50} +(3.92705 - 2.85317i) q^{51} +(-7.85410 - 5.70634i) q^{52} +(2.09017 + 6.43288i) q^{53} -2.23607 q^{54} +(2.00000 + 0.449028i) q^{55} +2.23607 q^{56} +(-0.881966 - 2.71441i) q^{57} +(10.8541 + 7.88597i) q^{58} +(-2.61803 + 1.90211i) q^{59} +(0.572949 - 1.76336i) q^{60} +(5.59017 - 4.06150i) q^{62} +(-0.809017 - 0.587785i) q^{63} +(-4.01722 - 12.3637i) q^{64} -2.00000 q^{65} +(7.23607 + 1.62460i) q^{66} +(4.50000 + 13.8496i) q^{68} +(3.54508 + 2.57565i) q^{69} +(1.11803 - 0.812299i) q^{70} +(-1.52786 + 4.70228i) q^{71} +(0.690983 - 2.12663i) q^{72} +(-11.0902 + 8.05748i) q^{73} +(-8.35410 - 6.06961i) q^{74} +(1.42705 + 4.39201i) q^{75} +8.56231 q^{76} +(2.19098 + 2.48990i) q^{77} -7.23607 q^{78} +(-3.09017 - 9.51057i) q^{79} +(-0.500000 - 0.363271i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(5.10081 - 15.6987i) q^{82} +(5.09017 - 15.6659i) q^{83} +(2.42705 - 1.76336i) q^{84} +(2.42705 + 1.76336i) q^{85} +(6.70820 + 20.6457i) q^{86} +6.00000 q^{87} +(-3.78115 + 6.37988i) q^{88} +5.61803 q^{89} +(-0.427051 - 1.31433i) q^{90} +(-2.61803 - 1.90211i) q^{91} +(-10.6353 + 7.72696i) q^{92} +(0.954915 - 2.93893i) q^{93} +(3.09017 - 9.51057i) q^{94} +(1.42705 - 1.03681i) q^{95} +(-5.42705 - 3.94298i) q^{96} +(-1.85410 - 5.70634i) q^{97} +2.23607 q^{98} +(3.04508 - 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 + q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 - q^7 - 5 * q^8 - q^9	\( 4 q + 5 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} - q^{9} - 10 q^{10} + q^{11} - 12 q^{12} + 4 q^{13} - 5 q^{14} - 2 q^{15} + q^{16} + 6 q^{17} - 5 q^{18} - 7 q^{19} - 9 q^{20} - 4 q^{21} + 25 q^{22} + 22 q^{23} - 5 q^{24} + 6 q^{25} - 10 q^{26} + q^{27} - 3 q^{28} + 6 q^{29} - 15 q^{31} + 9 q^{33} + 30 q^{34} - 3 q^{35} - 3 q^{36} - 6 q^{37} - 10 q^{38} - 4 q^{39} - 6 q^{41} - 5 q^{42} + 12 q^{43} + 33 q^{44} + 2 q^{45} + 30 q^{46} - 10 q^{47} - q^{48} - q^{49} - 15 q^{50} + 9 q^{51} - 18 q^{52} - 14 q^{53} + 8 q^{55} - 8 q^{57} + 30 q^{58} - 6 q^{59} + 9 q^{60} - q^{63} + 13 q^{64} - 8 q^{65} + 20 q^{66} + 18 q^{68} + 3 q^{69} - 24 q^{71} + 5 q^{72} - 22 q^{73} - 20 q^{74} - q^{75} - 6 q^{76} + 11 q^{77} - 20 q^{78} + 10 q^{79} - 2 q^{80} - q^{81} + 45 q^{82} - 2 q^{83} + 3 q^{84} + 3 q^{85} + 24 q^{87} + 5 q^{88} + 18 q^{89} + 5 q^{90} - 6 q^{91} - 9 q^{92} + 15 q^{93} - 10 q^{94} - q^{95} - 15 q^{96} + 6 q^{97} + q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 + q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 - q^7 - 5 * q^8 - q^9 - 10 * q^10 + q^11 - 12 * q^12 + 4 * q^13 - 5 * q^14 - 2 * q^15 + q^16 + 6 * q^17 - 5 * q^18 - 7 * q^19 - 9 * q^20 - 4 * q^21 + 25 * q^22 + 22 * q^23 - 5 * q^24 + 6 * q^25 - 10 * q^26 + q^27 - 3 * q^28 + 6 * q^29 - 15 * q^31 + 9 * q^33 + 30 * q^34 - 3 * q^35 - 3 * q^36 - 6 * q^37 - 10 * q^38 - 4 * q^39 - 6 * q^41 - 5 * q^42 + 12 * q^43 + 33 * q^44 + 2 * q^45 + 30 * q^46 - 10 * q^47 - q^48 - q^49 - 15 * q^50 + 9 * q^51 - 18 * q^52 - 14 * q^53 + 8 * q^55 - 8 * q^57 + 30 * q^58 - 6 * q^59 + 9 * q^60 - q^63 + 13 * q^64 - 8 * q^65 + 20 * q^66 + 18 * q^68 + 3 * q^69 - 24 * q^71 + 5 * q^72 - 22 * q^73 - 20 * q^74 - q^75 - 6 * q^76 + 11 * q^77 - 20 * q^78 + 10 * q^79 - 2 * q^80 - q^81 + 45 * q^82 - 2 * q^83 + 3 * q^84 + 3 * q^85 + 24 * q^87 + 5 * q^88 + 18 * q^89 + 5 * q^90 - 6 * q^91 - 9 * q^92 + 15 * q^93 - 10 * q^94 - q^95 - 15 * q^96 + 6 * q^97 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more