LMFDB - Embedded newform 930.2.s.b.439.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.2
Root			$-0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	930.439
Dual form			930.2.s.b.769.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-1.86603 - 1.23205i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.29129 + 1.32288i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-1.86603 - 1.23205i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.29129 + 1.32288i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.23205 + 1.86603i) q^{10} +(0.322876 + 0.559237i) q^{11} +(0.866025 + 0.500000i) q^{12} +(4.58258 - 2.64575i) q^{13} +(1.32288 - 2.29129i) q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +(5.19615 + 3.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.64575 + 4.58258i) q^{19} +(1.86603 + 1.23205i) q^{20} +(-1.32288 - 2.29129i) q^{21} +(0.559237 - 0.322876i) q^{22} -9.29150i q^{23} +(0.500000 - 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(-2.64575 - 4.58258i) q^{26} -1.00000i q^{27} +(-2.29129 - 1.32288i) q^{28} -2.64575 q^{29} +(2.00000 - 1.00000i) q^{30} +(1.14575 - 5.44860i) q^{31} -1.00000i q^{32} -0.645751i q^{33} +(3.00000 - 5.19615i) q^{34} +(-2.64575 - 5.29150i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.46410 - 2.00000i) q^{37} +(4.58258 + 2.64575i) q^{38} -5.29150 q^{39} +(1.23205 - 1.86603i) q^{40} +(-1.64575 - 2.85052i) q^{41} +(-2.29129 + 1.32288i) q^{42} +(9.77873 + 5.64575i) q^{43} +(-0.322876 - 0.559237i) q^{44} +(0.133975 - 2.23205i) q^{45} -9.29150 q^{46} -9.29150i q^{47} +(-0.866025 - 0.500000i) q^{48} +(4.59808 - 1.96410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(-4.58258 + 2.64575i) q^{52} +(1.98450 - 1.14575i) q^{53} -1.00000 q^{54} +(0.0865143 - 1.44135i) q^{55} +(-1.32288 + 2.29129i) q^{56} +(4.58258 - 2.64575i) q^{57} +2.64575i q^{58} +(-0.322876 + 0.559237i) q^{59} +(-1.00000 - 2.00000i) q^{60} +10.0000 q^{61} +(-5.44860 - 1.14575i) q^{62} +2.64575i q^{63} -1.00000 q^{64} +(-11.8109 - 0.708927i) q^{65} -0.645751 q^{66} +(-9.77873 + 5.64575i) q^{67} +(-5.19615 - 3.00000i) q^{68} +(-4.64575 + 8.04668i) q^{69} +(-5.29150 + 2.64575i) q^{70} +(-3.29150 - 5.70105i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.70105 - 3.29150i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(0.598076 - 4.96410i) q^{75} +(2.64575 - 4.58258i) q^{76} +1.70850i q^{77} +5.29150i q^{78} +(7.29150 - 12.6293i) q^{79} +(-1.86603 - 1.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.85052 + 1.64575i) q^{82} +(-8.29913 + 4.79150i) q^{83} +(1.32288 + 2.29129i) q^{84} +(-6.00000 - 12.0000i) q^{85} +(5.64575 - 9.77873i) q^{86} +(2.29129 + 1.32288i) q^{87} +(-0.559237 + 0.322876i) q^{88} +3.29150 q^{89} +(-2.23205 - 0.133975i) q^{90} +14.0000 q^{91} +9.29150i q^{92} +(-3.71655 + 4.14575i) q^{93} -9.29150 q^{94} +(10.5830 - 5.29150i) q^{95} +(-0.500000 + 0.866025i) q^{96} +11.2288i q^{97} +(-0.322876 + 0.559237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9	$ 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{15} + 8 q^{16} + 8 q^{20} + 4 q^{24} - 12 q^{25} + 16 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{36} - 4 q^{40} + 8 q^{41} + 8 q^{44} + 8 q^{45} - 32 q^{46} + 16 q^{50} - 24 q^{51} - 8 q^{54} - 16 q^{55} + 8 q^{59} - 8 q^{60} + 80 q^{61} - 8 q^{64} + 16 q^{66} - 16 q^{69} + 16 q^{71} - 16 q^{74} - 16 q^{75} + 16 q^{79} - 8 q^{80} - 4 q^{81} - 48 q^{85} + 24 q^{86} - 16 q^{89} - 4 q^{90} + 112 q^{91} - 32 q^{94} - 4 q^{96} + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^15 + 8 * q^16 + 8 * q^20 + 4 * q^24 - 12 * q^25 + 16 * q^30 - 12 * q^31 + 24 * q^34 - 4 * q^36 - 4 * q^40 + 8 * q^41 + 8 * q^44 + 8 * q^45 - 32 * q^46 + 16 * q^50 - 24 * q^51 - 8 * q^54 - 16 * q^55 + 8 * q^59 - 8 * q^60 + 80 * q^61 - 8 * q^64 + 16 * q^66 - 16 * q^69 + 16 * q^71 - 16 * q^74 - 16 * q^75 + 16 * q^79 - 8 * q^80 - 4 * q^81 - 48 * q^85 + 24 * q^86 - 16 * q^89 - 4 * q^90 + 112 * q^91 - 32 * q^94 - 4 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.00000			−0.500000
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	2.29129	+	1.32288i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$7$	2.29129	+	1.32288i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.23205	+	1.86603i	−0.389609	+	0.590089i
$11$	0.322876	+	0.559237i	0.0973507	+	0.168616i	0.910587	−	0.413317i	$-0.135630\pi$
$11$	0.322876	+	0.559237i	0.0973507	+	0.168616i	−0.813237	+	0.581933i	$0.802296\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	4.58258	−	2.64575i	1.27098	−	0.733799i	0.295806	−	0.955248i	$-0.404412\pi$
$13$	4.58258	−	2.64575i	1.27098	−	0.733799i	0.975172	+	0.221449i	$0.0710785\pi$
$14$	1.32288	−	2.29129i	0.353553	−	0.612372i
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$	1.00000			0.250000
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.973123	−	0.230285i	$-0.0739659\pi$
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.287129	+	0.957892i	$0.407299\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−2.64575	+	4.58258i	−0.606977	+	1.05131i	0.384759	+	0.923017i	$0.374285\pi$
$19$	−2.64575	+	4.58258i	−0.606977	+	1.05131i	−0.991736	+	0.128298i	$0.959049\pi$
$20$	1.86603	+	1.23205i	0.417256	+	0.275495i
$21$	−1.32288	−	2.29129i	−0.288675	−	0.500000i
$22$	0.559237	−	0.322876i	0.119230	−	0.0688373i
$23$		−	9.29150i		−	1.93741i	−0.248211	−	0.968706i	$-0.579842\pi$
$23$		−	9.29150i		−	1.93741i	0.248211	−	0.968706i	$-0.420158\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	−2.64575	−	4.58258i	−0.518875	−	0.898717i
$27$		−	1.00000i		−	0.192450i
$28$	−2.29129	−	1.32288i	−0.433013	−	0.250000i
$29$	−2.64575			−0.491304			−0.245652	−	0.969358i	$-0.579002\pi$
$29$	−2.64575			−0.491304			−0.245652	+	0.969358i	$0.579002\pi$
$30$	2.00000	−	1.00000i	0.365148	−	0.182574i
$31$	1.14575	−	5.44860i	0.205783	−	0.978598i
$31$	1.14575	−	5.44860i	0.205783	−	0.978598i
$32$		−	1.00000i		−	0.176777i
$33$		−	0.645751i		−	0.112411i
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$	−2.64575	−	5.29150i	−0.447214	−	0.894427i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	0.187453	−	0.982274i	$-0.439977\pi$
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	−0.756948	+	0.653476i	$0.773310\pi$
$38$	4.58258	+	2.64575i	0.743392	+	0.429198i
$39$	−5.29150			−0.847319
$40$	1.23205	−	1.86603i	0.194804	−	0.295045i
$41$	−1.64575	−	2.85052i	−0.257023	−	0.445177i	0.708420	−	0.705791i	$-0.249408\pi$
$41$	−1.64575	−	2.85052i	−0.257023	−	0.445177i	−0.965443	+	0.260614i	$0.916075\pi$
$42$	−2.29129	+	1.32288i	−0.353553	+	0.204124i
$43$	9.77873	+	5.64575i	1.49124	+	0.860969i	0.999950	−	0.0100257i	$-0.00319135\pi$
$43$	9.77873	+	5.64575i	1.49124	+	0.860969i	0.491292	+	0.870995i	$0.336525\pi$
$44$	−0.322876	−	0.559237i	−0.0486753	−	0.0843082i
$45$	0.133975	−	2.23205i	0.0199718	−	0.332734i
$46$	−9.29150			−1.36996
$47$		−	9.29150i		−	1.35530i	−0.735382	−	0.677652i	$-0.762997\pi$
$47$		−	9.29150i		−	1.35530i	0.735382	−	0.677652i	$-0.237003\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$		0			0
$50$	4.59808	−	1.96410i	0.650266	−	0.277766i
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	−4.58258	+	2.64575i	−0.635489	+	0.366900i
$53$	1.98450	−	1.14575i	0.272592	−	0.157381i	−0.357473	−	0.933923i	$-0.616362\pi$
$53$	1.98450	−	1.14575i	0.272592	−	0.157381i	0.630065	+	0.776542i	$0.283028\pi$
$54$	−1.00000			−0.136083
$55$	0.0865143	−	1.44135i	0.0116656	−	0.194352i
$56$	−1.32288	+	2.29129i	−0.176777	+	0.306186i
$57$	4.58258	−	2.64575i	0.606977	−	0.350438i
$58$			2.64575i			0.347404i
$59$	−0.322876	+	0.559237i	−0.0420348	+	0.0728065i	−0.886277	−	0.463155i	$-0.846717\pi$
$59$	−0.322876	+	0.559237i	−0.0420348	+	0.0728065i	0.844243	+	0.535961i	$0.180051\pi$
$60$	−1.00000	−	2.00000i	−0.129099	−	0.258199i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	−5.44860	−	1.14575i	−0.691973	−	0.145511i
$63$			2.64575i			0.333333i
$64$	−1.00000			−0.125000
$65$	−11.8109	−	0.708927i	−1.46496	−	0.0879316i
$66$	−0.645751			−0.0794865
$67$	−9.77873	+	5.64575i	−1.19466	+	0.689738i	−0.959360	−	0.282184i	$-0.908941\pi$
$67$	−9.77873	+	5.64575i	−1.19466	+	0.689738i	−0.235302	+	0.971922i	$0.575608\pi$
$68$	−5.19615	−	3.00000i	−0.630126	−	0.363803i
$69$	−4.64575	+	8.04668i	−0.559283	+	0.968706i
$70$	−5.29150	+	2.64575i	−0.632456	+	0.316228i
$71$	−3.29150	−	5.70105i	−0.390629	−	0.676590i	0.601903	−	0.798569i	$-0.294409\pi$
$71$	−3.29150	−	5.70105i	−0.390629	−	0.676590i	−0.992533	+	0.121979i	$0.961076\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	5.70105	−	3.29150i	0.667257	−	0.385241i	−0.127779	−	0.991803i	$-0.540785\pi$
$73$	5.70105	−	3.29150i	0.667257	−	0.385241i	0.795037	+	0.606561i	$0.207452\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$	0.598076	−	4.96410i	0.0690599	−	0.573205i
$76$	2.64575	−	4.58258i	0.303488	−	0.525657i
$77$			1.70850i			0.194701i
$78$			5.29150i			0.599145i
$79$	7.29150	−	12.6293i	0.820358	−	1.42090i	−0.0850576	−	0.996376i	$-0.527107\pi$
$79$	7.29150	−	12.6293i	0.820358	−	1.42090i	0.905416	−	0.424526i	$-0.139559\pi$
$80$	−1.86603	−	1.23205i	−0.208628	−	0.137747i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.85052	+	1.64575i	−0.314788	+	0.181743i
$83$	−8.29913	+	4.79150i	−0.910947	+	0.525936i	−0.880736	−	0.473608i	$-0.842951\pi$
$83$	−8.29913	+	4.79150i	−0.910947	+	0.525936i	−0.0302116	+	0.999544i	$0.509618\pi$
$84$	1.32288	+	2.29129i	0.144338	+	0.250000i
$85$	−6.00000	−	12.0000i	−0.650791	−	1.30158i
$86$	5.64575	−	9.77873i	0.608797	−	1.05447i
$87$	2.29129	+	1.32288i	0.245652	+	0.141827i
$88$	−0.559237	+	0.322876i	−0.0596149	+	0.0344187i
$89$	3.29150			0.348899			0.174449	−	0.984666i	$-0.444185\pi$
$89$	3.29150			0.348899			0.174449	+	0.984666i	$0.444185\pi$
$90$	−2.23205	−	0.133975i	−0.235279	−	0.0141222i
$91$	14.0000			1.46760
$92$			9.29150i			0.968706i
$93$	−3.71655	+	4.14575i	−0.385388	+	0.429894i
$94$	−9.29150			−0.958345
$95$	10.5830	−	5.29150i	1.08579	−	0.542897i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			11.2288i			1.14011i	0.821607	+	0.570054i	$0.193078\pi$
$97$			11.2288i			1.14011i	−0.821607	+	0.570054i	$0.806922\pi$
$98$		0			0
$99$	−0.322876	+	0.559237i	−0.0324502	+	0.0562054i
$100$	−1.96410	−	4.59808i	−0.196410	−	0.459808i
$101$	6.64575			0.661277			0.330638	−	0.943757i	$-0.392736\pi$
$101$	6.64575			0.661277			0.330638	+	0.943757i	$0.392736\pi$
$102$	−5.19615	+	3.00000i	−0.514496	+	0.297044i
$103$	5.75539	−	3.32288i	0.567095	−	0.327413i	−0.188893	−	0.981998i	$-0.560490\pi$
$103$	5.75539	−	3.32288i	0.567095	−	0.327413i	0.755988	+	0.654585i	$0.227157\pi$
$104$	2.64575	+	4.58258i	0.259437	+	0.449359i
$105$	−0.354463	+	5.90545i	−0.0345921	+	0.576313i
$106$	−1.14575	−	1.98450i	−0.111285	−	0.192752i
$107$	4.33013	+	2.50000i	0.418609	+	0.241684i	0.694482	−	0.719510i	$-0.255634\pi$
$107$	4.33013	+	2.50000i	0.418609	+	0.241684i	−0.275873	+	0.961194i	$0.588967\pi$
$108$			1.00000i			0.0962250i
$109$	−6.70850			−0.642558			−0.321279	−	0.946985i	$-0.604113\pi$
$109$	−6.70850			−0.642558			−0.321279	+	0.946985i	$0.604113\pi$
$110$	−1.44135	−	0.0865143i	−0.137427	−	0.00824881i
$111$	2.00000	+	3.46410i	0.189832	+	0.328798i
$112$	2.29129	+	1.32288i	0.216506	+	0.125000i
$113$	11.5108	−	6.64575i	1.08284	−	0.625180i	0.151181	−	0.988506i	$-0.451692\pi$
$113$	11.5108	−	6.64575i	1.08284	−	0.625180i	0.931662	+	0.363326i	$0.118359\pi$
$114$	−2.64575	−	4.58258i	−0.247797	−	0.429198i
$115$	−11.4476	+	17.3382i	−1.06749	+	1.61679i
$116$	2.64575			0.245652
$117$	4.58258	+	2.64575i	0.423659	+	0.244600i
$118$	0.559237	+	0.322876i	0.0514819	+	0.0297231i
$119$	7.93725	+	13.7477i	0.727607	+	1.26025i
$120$	−2.00000	+	1.00000i	−0.182574	+	0.0912871i
$121$	5.29150	−	9.16515i	0.481046	−	0.833196i
$122$		−	10.0000i		−	0.905357i
$123$			3.29150i			0.296785i
$124$	−1.14575	+	5.44860i	−0.102892	+	0.489299i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	2.64575			0.235702
$127$	11.4564	+	6.61438i	1.01659	+	0.586931i	0.913116	−	0.407700i	$-0.133669\pi$
$127$	11.4564	+	6.61438i	1.01659	+	0.586931i	0.103479	+	0.994632i	$0.467003\pi$
$128$			1.00000i			0.0883883i
$129$	−5.64575	−	9.77873i	−0.497081	−	0.860969i
$130$	−0.708927	+	11.8109i	−0.0621770	+	1.03588i
$131$	−1.35425	+	2.34563i	−0.118321	+	0.204938i	−0.919103	−	0.394018i	$-0.871085\pi$
$131$	−1.35425	+	2.34563i	−0.118321	+	0.204938i	0.800781	+	0.598957i	$0.204418\pi$
$132$			0.645751i			0.0562054i
$133$	−12.1244	+	7.00000i	−1.05131	+	0.606977i
$134$	5.64575	+	9.77873i	0.487719	+	0.844753i
$135$	−1.23205	+	1.86603i	−0.106038	+	0.160602i
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	9.16515	−	5.29150i	0.783032	−	0.452084i	−0.0544719	−	0.998515i	$-0.517348\pi$
$137$	9.16515	−	5.29150i	0.783032	−	0.452084i	0.837504	+	0.546432i	$0.184014\pi$
$138$	8.04668	+	4.64575i	0.684979	+	0.395473i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	2.64575	+	5.29150i	0.223607	+	0.447214i
$141$	−4.64575	+	8.04668i	−0.391243	+	0.677652i
$142$	−5.70105	+	3.29150i	−0.478421	+	0.276217i
$143$	2.95920	+	1.70850i	0.247461	+	0.142872i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	4.93704	+	3.25970i	0.409999	+	0.270703i
$146$	−3.29150	−	5.70105i	−0.272407	−	0.471822i
$147$		0			0
$148$	3.46410	+	2.00000i	0.284747	+	0.164399i
$149$	−9.32288	+	16.1477i	−0.763760	+	1.32287i	0.177140	+	0.984186i	$0.443315\pi$
$149$	−9.32288	+	16.1477i	−0.763760	+	1.32287i	−0.940900	+	0.338685i	$0.890018\pi$
$150$	−4.96410	−	0.598076i	−0.405317	−	0.0488327i
$151$	−11.7085			−0.952824			−0.476412	−	0.879222i	$-0.658063\pi$
$151$	−11.7085			−0.952824			−0.476412	+	0.879222i	$0.658063\pi$
$152$	−4.58258	−	2.64575i	−0.371696	−	0.214599i
$153$			6.00000i			0.485071i
$154$	1.70850			0.137675
$155$	−8.85095	+	8.75560i	−0.710926	+	0.703267i
$156$	5.29150			0.423659
$157$		−	1.29150i		−	0.103073i	−0.998671	−	0.0515366i	$-0.983588\pi$
$157$		−	1.29150i		−	0.103073i	0.998671	−	0.0515366i	$-0.0164119\pi$
$158$	−12.6293	−	7.29150i	−1.00473	−	0.580081i
$159$	−2.29150			−0.181728
$160$	−1.23205	+	1.86603i	−0.0974022	+	0.147522i
$161$	12.2915	−	21.2895i	0.968706	−	1.67785i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$			10.0000i			0.783260i	0.920123	+	0.391630i	$0.128089\pi$
$163$			10.0000i			0.783260i	−0.920123	+	0.391630i	$0.871911\pi$
$164$	1.64575	+	2.85052i	0.128512	+	0.222589i
$165$	−0.795598	+	1.20499i	−0.0619373	+	0.0938082i
$166$	4.79150	+	8.29913i	0.371893	+	0.644137i
$167$	−18.9439	−	10.9373i	−1.46592	−	0.846350i	−0.466647	−	0.884444i	$-0.654538\pi$
$167$	−18.9439	−	10.9373i	−1.46592	−	0.846350i	−0.999274	+	0.0380934i	$0.987872\pi$
$168$	2.29129	−	1.32288i	0.176777	−	0.102062i
$169$	7.50000	−	12.9904i	0.576923	−	0.999260i
$170$	−12.0000	+	6.00000i	−0.920358	+	0.460179i
$171$	−5.29150			−0.404651
$172$	−9.77873	−	5.64575i	−0.745621	−	0.430485i
$173$	5.44860	−	3.14575i	0.414249	−	0.239167i	−0.278364	−	0.960476i	$-0.589792\pi$
$173$	5.44860	−	3.14575i	0.414249	−	0.239167i	0.692614	+	0.721308i	$0.256459\pi$
$174$	1.32288	−	2.29129i	0.100287	−	0.173702i
$175$	−1.58236	+	13.1338i	−0.119615	+	0.992820i
$176$	0.322876	+	0.559237i	0.0243377	+	0.0421541i
$177$	0.559237	−	0.322876i	0.0420348	−	0.0242688i
$178$		−	3.29150i		−	0.246709i
$179$	−1.61438	+	2.79619i	−0.120664	+	0.208997i	−0.920030	−	0.391848i	$-0.871836\pi$
$179$	−1.61438	+	2.79619i	−0.120664	+	0.208997i	0.799366	+	0.600845i	$0.205169\pi$
$180$	−0.133975	+	2.23205i	−0.00998588	+	0.166367i
$181$	0.354249	+	0.613577i	0.0263311	+	0.0456068i	0.878891	−	0.477023i	$-0.158284\pi$
$181$	0.354249	+	0.613577i	0.0263311	+	0.0456068i	−0.852560	+	0.522630i	$0.824951\pi$
$182$		−	14.0000i		−	1.03775i
$183$	−8.66025	−	5.00000i	−0.640184	−	0.369611i
$184$	9.29150			0.684979
$185$	4.00000	+	8.00000i	0.294086	+	0.588172i
$186$	4.14575	+	3.71655i	0.303981	+	0.272511i
$187$			3.87451i			0.283332i
$188$			9.29150i			0.677652i
$189$	1.32288	−	2.29129i	0.0962250	−	0.166667i
$190$	−5.29150	−	10.5830i	−0.383886	−	0.767772i
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	17.8797	+	10.3229i	1.28701	+	0.743057i	0.978120	−	0.208040i	$-0.0667085\pi$
$193$	17.8797	+	10.3229i	1.28701	+	0.743057i	0.308892	+	0.951097i	$0.400042\pi$
$194$	11.2288			0.806178
$195$	9.87408	+	6.51940i	0.707097	+	0.466864i
$196$		0			0
$197$	20.0624	−	11.5830i	1.42938	−	0.825255i	0.432312	−	0.901724i	$-0.357698\pi$
$197$	20.0624	−	11.5830i	1.42938	−	0.825255i	0.997072	+	0.0764693i	$0.0243647\pi$
$198$	0.559237	+	0.322876i	0.0397432	+	0.0229458i
$199$	8.14575	+	14.1089i	0.577437	+	1.00015i	0.995772	+	0.0918575i	$0.0292804\pi$
$199$	8.14575	+	14.1089i	0.577437	+	1.00015i	−0.418335	+	0.908293i	$0.637386\pi$
$200$	−4.59808	+	1.96410i	−0.325133	+	0.138883i
$201$	11.2915			0.796441
$202$		−	6.64575i		−	0.467593i
$203$	−6.06218	−	3.50000i	−0.425481	−	0.245652i
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$	−0.440978	+	7.34680i	−0.0307992	+	0.513123i
$206$	−3.32288	−	5.75539i	−0.231516	−	0.400997i
$207$	8.04668	−	4.64575i	0.559283	−	0.322902i
$208$	4.58258	−	2.64575i	0.317744	−	0.183450i
$209$	−3.41699			−0.236358
$210$	5.90545	+	0.354463i	0.407515	+	0.0244603i
$211$	8.29150	−	14.3613i	0.570811	−	0.988673i	−0.425672	−	0.904877i	$-0.639962\pi$
$211$	8.29150	−	14.3613i	0.570811	−	0.988673i	0.996483	−	0.0837956i	$-0.0267043\pi$
$212$	−1.98450	+	1.14575i	−0.136296	+	0.0786905i
$213$			6.58301i			0.451060i
$214$	2.50000	−	4.33013i	0.170896	−	0.296001i
$215$	−11.2915	−	22.5830i	−0.770074	−	1.54015i
$216$	1.00000			0.0680414
$217$	9.83307	−	10.9686i	0.667512	−	0.744599i
$218$			6.70850i			0.454357i
$219$	−6.58301			−0.444838
$220$	−0.0865143	+	1.44135i	−0.00583279	+	0.0971758i
$221$	31.7490			2.13567
$222$	3.46410	−	2.00000i	0.232495	−	0.134231i
$223$	−23.0759	−	13.3229i	−1.54528	−	0.892166i	−0.998492	−	0.0548921i	$-0.982519\pi$
$223$	−23.0759	−	13.3229i	−1.54528	−	0.892166i	−0.546784	−	0.837274i	$-0.684148\pi$
$224$	1.32288	−	2.29129i	0.0883883	−	0.153093i
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$	−6.64575	−	11.5108i	−0.442069	−	0.765686i
$227$	−12.9904	+	7.50000i	−0.862202	+	0.497792i	−0.864749	−	0.502204i	$-0.832523\pi$
$227$	−12.9904	+	7.50000i	−0.862202	+	0.497792i	0.00254715	+	0.999997i	$0.499189\pi$
$228$	−4.58258	+	2.64575i	−0.303488	+	0.175219i
$229$	−8.58301	+	14.8662i	−0.567181	+	0.982386i	0.429662	+	0.902990i	$0.358633\pi$
$229$	−8.58301	+	14.8662i	−0.567181	+	0.982386i	−0.996843	+	0.0793965i	$0.974701\pi$
$230$	17.3382	+	11.4476i	1.14325	+	0.754833i
$231$	0.854249	−	1.47960i	0.0562054	−	0.0973507i
$232$		−	2.64575i		−	0.173702i
$233$		−	7.29150i		−	0.477682i	−0.971059	−	0.238841i	$-0.923232\pi$
$233$		−	7.29150i		−	0.477682i	0.971059	−	0.238841i	$-0.0767675\pi$
$234$	2.64575	−	4.58258i	0.172958	−	0.299572i
$235$	−11.4476	+	17.3382i	−0.746759	+	1.13102i
$236$	0.322876	−	0.559237i	0.0210174	−	0.0364032i
$237$	−12.6293	+	7.29150i	−0.820358	+	0.473634i
$238$	13.7477	−	7.93725i	0.891133	−	0.514496i
$239$	12.2915	+	21.2895i	0.795071	+	1.37710i	0.922794	+	0.385294i	$0.125900\pi$
$239$	12.2915	+	21.2895i	0.795071	+	1.37710i	−0.127723	+	0.991810i	$0.540767\pi$
$240$	1.00000	+	2.00000i	0.0645497	+	0.129099i
$241$	−10.5000	+	18.1865i	−0.676364	+	1.17150i	0.299704	+	0.954032i	$0.403112\pi$
$241$	−10.5000	+	18.1865i	−0.676364	+	1.17150i	−0.976068	+	0.217465i	$0.930221\pi$
$242$	−9.16515	−	5.29150i	−0.589158	−	0.340151i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	3.29150			0.209859
$247$			28.0000i			1.78160i
$248$	5.44860	+	1.14575i	0.345987	+	0.0727553i
$249$	9.58301			0.607298
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$	−5.35425	+	9.27383i	−0.337957	+	0.585359i	−0.984048	−	0.177901i	$-0.943069\pi$
$251$	−5.35425	+	9.27383i	−0.337957	+	0.585359i	0.646091	+	0.763260i	$0.276403\pi$
$252$		−	2.64575i		−	0.166667i
$253$	5.19615	−	3.00000i	0.326679	−	0.188608i
$254$	6.61438	−	11.4564i	0.415023	−	0.718841i
$255$	−0.803848	+	13.3923i	−0.0503389	+	0.838659i
$256$	1.00000			0.0625000
$257$	−4.58258	+	2.64575i	−0.285853	+	0.165037i	−0.636070	−	0.771631i	$-0.719441\pi$
$257$	−4.58258	+	2.64575i	−0.285853	+	0.165037i	0.350217	+	0.936669i	$0.386108\pi$
$258$	−9.77873	+	5.64575i	−0.608797	+	0.351489i
$259$	−5.29150	−	9.16515i	−0.328798	−	0.569495i
$260$	11.8109	+	0.708927i	0.732481	+	0.0439658i
$261$	−1.32288	−	2.29129i	−0.0818839	−	0.141827i
$262$	2.34563	+	1.35425i	0.144913	+	0.0836658i
$263$			23.1660i			1.42848i	0.699902	+	0.714239i	$0.253227\pi$
$263$			23.1660i			1.42848i	−0.699902	+	0.714239i	$0.746773\pi$
$264$	0.645751			0.0397432
$265$	−5.11475	−	0.307003i	−0.314197	−	0.0188591i
$266$	7.00000	+	12.1244i	0.429198	+	0.743392i
$267$	−2.85052	−	1.64575i	−0.174449	−	0.100718i
$268$	9.77873	−	5.64575i	0.597331	−	0.344869i
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	0.961817	−	0.273692i	$-0.0882449\pi$
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	−0.717933	+	0.696112i	$0.754912\pi$
$270$	1.86603	+	1.23205i	0.113563	+	0.0749802i
$271$	−22.2915			−1.35411			−0.677056	−	0.735931i	$-0.736745\pi$
$271$	−22.2915			−1.35411			−0.677056	+	0.735931i	$0.736745\pi$
$272$	5.19615	+	3.00000i	0.315063	+	0.181902i
$273$	−12.1244	−	7.00000i	−0.733799	−	0.423659i
$274$	−5.29150	−	9.16515i	−0.319671	−	0.553687i
$275$	−1.93725	+	2.58301i	−0.116821	+	0.155761i
$276$	4.64575	−	8.04668i	0.279641	−	0.484353i
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$			4.00000i			0.239904i
$279$	5.29150	−	1.73205i	0.316794	−	0.103695i
$280$	5.29150	−	2.64575i	0.316228	−	0.158114i
$281$	18.5830			1.10857			0.554285	−	0.832327i	$-0.312992\pi$
$281$	18.5830			1.10857			0.554285	+	0.832327i	$0.312992\pi$
$282$	8.04668	+	4.64575i	0.479173	+	0.276650i
$283$		−	18.7085i		−	1.11210i	−0.831147	−	0.556052i	$-0.812315\pi$
$283$		−	18.7085i		−	1.11210i	0.831147	−	0.556052i	$-0.187685\pi$
$284$	3.29150	+	5.70105i	0.195315	+	0.338295i
$285$	−11.8109	−	0.708927i	−0.699617	−	0.0419932i
$286$	1.70850	−	2.95920i	0.101026	−	0.174981i
$287$		−	8.70850i		−	0.514046i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$	3.25970	−	4.93704i	0.191416	−	0.289913i
$291$	5.61438	−	9.72439i	0.329121	−	0.570054i
$292$	−5.70105	+	3.29150i	−0.333629	+	0.192621i
$293$	11.8719	+	6.85425i	0.693564	+	0.400429i	0.804946	−	0.593348i	$-0.202194\pi$
$293$	11.8719	+	6.85425i	0.693564	+	0.400429i	−0.111382	+	0.993778i	$0.535528\pi$
$294$		0			0
$295$	1.29150	−	0.645751i	0.0751942	−	0.0375971i
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	0.559237	−	0.322876i	0.0324502	−	0.0187351i
$298$	16.1477	+	9.32288i	0.935411	+	0.540060i
$299$	−24.5830	−	42.5790i	−1.42167	−	2.46241i
$300$	−0.598076	+	4.96410i	−0.0345299	+	0.286603i
$301$	14.9373	+	25.8721i	0.860969	+	1.49124i
$302$			11.7085i			0.673748i
$303$	−5.75539	−	3.32288i	−0.330638	−	0.190894i
$304$	−2.64575	+	4.58258i	−0.151744	+	0.262829i
$305$	−18.6603	−	12.3205i	−1.06848	−	0.705470i
$306$	6.00000			0.342997
$307$	12.0157	+	6.93725i	0.685771	+	0.395930i	0.802026	−	0.597289i	$-0.203756\pi$
$307$	12.0157	+	6.93725i	0.685771	+	0.395930i	−0.116255	+	0.993219i	$0.537089\pi$
$308$		−	1.70850i		−	0.0973507i
$309$	−6.64575			−0.378064
$310$	8.75560	+	8.85095i	0.497285	+	0.502700i
$311$	−11.8745			−0.673342			−0.336671	−	0.941622i	$-0.609301\pi$
$311$	−11.8745			−0.673342			−0.336671	+	0.941622i	$0.609301\pi$
$312$		−	5.29150i		−	0.299572i
$313$	12.0700	+	6.96863i	0.682238	+	0.393890i	0.800698	−	0.599069i	$-0.204462\pi$
$313$	12.0700	+	6.96863i	0.682238	+	0.393890i	−0.118460	+	0.992959i	$0.537796\pi$
$314$	−1.29150			−0.0728837
$315$	3.25970	−	4.93704i	0.183663	−	0.278171i
$316$	−7.29150	+	12.6293i	−0.410179	+	0.710451i
$317$	14.1089	+	8.14575i	0.792432	+	0.457511i	0.840818	−	0.541318i	$-0.182074\pi$
$317$	14.1089	+	8.14575i	0.792432	+	0.457511i	−0.0483859	+	0.998829i	$0.515408\pi$
$318$			2.29150i			0.128501i
$319$	−0.854249	−	1.47960i	−0.0478287	−	0.0828418i
$320$	1.86603	+	1.23205i	0.104314	+	0.0688737i
$321$	−2.50000	−	4.33013i	−0.139536	−	0.241684i
$322$	−21.2895	−	12.2915i	−1.18642	−	0.684979i
$323$	−27.4955	+	15.8745i	−1.52989	+	0.883281i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	21.1660	+	15.8745i	1.17408	+	0.880559i
$326$	10.0000			0.553849
$327$	5.80973	+	3.35425i	0.321279	+	0.185490i
$328$	2.85052	−	1.64575i	0.157394	−	0.0908714i
$329$	12.2915	−	21.2895i	0.677652	−	1.17373i
$330$	1.20499	+	0.795598i	0.0663324	+	0.0437963i
$331$	−9.58301	−	16.5983i	−0.526730	−	0.912322i	−0.999515	−	0.0311448i	$-0.990085\pi$
$331$	−9.58301	−	16.5983i	−0.526730	−	0.912322i	0.472785	−	0.881178i	$-0.343249\pi$
$332$	8.29913	−	4.79150i	0.455474	−	0.262968i
$333$		−	4.00000i		−	0.219199i
$334$	−10.9373	+	18.9439i	−0.598460	+	1.03656i
$335$	25.2032	+	1.51277i	1.37700	+	0.0826517i
$336$	−1.32288	−	2.29129i	−0.0721688	−	0.125000i
$337$		−	35.1033i		−	1.91220i	−0.293046	−	0.956098i	$-0.594669\pi$
$337$		−	35.1033i		−	1.91220i	0.293046	−	0.956098i	$-0.405331\pi$
$338$	−12.9904	−	7.50000i	−0.706584	−	0.407946i
$339$	−13.2915			−0.721895
$340$	6.00000	+	12.0000i	0.325396	+	0.650791i
$341$	3.41699	−	1.11847i	0.185041	−	0.0605688i
$342$			5.29150i			0.286132i
$343$		−	18.5203i		−	1.00000i
$344$	−5.64575	+	9.77873i	−0.304399	+	0.527234i
$345$	18.5830	−	9.29150i	1.00048	−	0.500238i
$346$	−3.14575	−	5.44860i	−0.169117	−	0.292919i
$347$	3.10297	+	1.79150i	0.166576	+	0.0961729i	0.580970	−	0.813925i	$-0.302673\pi$
$347$	3.10297	+	1.79150i	0.166576	+	0.0961729i	−0.414394	+	0.910098i	$0.636006\pi$
$348$	−2.29129	−	1.32288i	−0.122826	−	0.0709136i
$349$	5.29150			0.283248			0.141624	−	0.989921i	$-0.454768\pi$
$349$	5.29150			0.283248			0.141624	+	0.989921i	$0.454768\pi$
$350$	13.1338	+	1.58236i	0.702030	+	0.0845807i
$351$	−2.64575	−	4.58258i	−0.141220	−	0.244600i
$352$	0.559237	−	0.322876i	0.0298074	−	0.0172093i
$353$	−19.6661	−	11.3542i	−1.04672	−	0.604326i	−0.124993	−	0.992158i	$-0.539891\pi$
$353$	−19.6661	−	11.3542i	−1.04672	−	0.604326i	−0.921730	+	0.387832i	$0.873224\pi$
$354$	−0.322876	−	0.559237i	−0.0171606	−	0.0297231i
$355$	−0.881955	+	14.6936i	−0.0468093	+	0.779855i
$356$	−3.29150			−0.174449
$357$		−	15.8745i		−	0.840168i
$358$	2.79619	+	1.61438i	0.147783	+	0.0853225i
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	0.999590	−	0.0286287i	$-0.00911406\pi$
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	−0.524588	+	0.851356i	$0.675781\pi$
$360$	2.23205	+	0.133975i	0.117639	+	0.00706108i
$361$	−4.50000	−	7.79423i	−0.236842	−	0.410223i
$362$	0.613577	−	0.354249i	0.0322489	−	0.0186189i
$363$	−9.16515	+	5.29150i	−0.481046	+	0.277732i
$364$	−14.0000			−0.733799
$365$	−14.6936	−	0.881955i	−0.769098	−	0.0461637i
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	−29.8411	+	17.2288i	−1.55769	+	0.899334i	−0.560214	+	0.828348i	$0.689281\pi$
$367$	−29.8411	+	17.2288i	−1.55769	+	0.899334i	−0.997477	+	0.0709862i	$0.977385\pi$
$368$		−	9.29150i		−	0.484353i
$369$	1.64575	−	2.85052i	0.0856744	−	0.148392i
$370$	8.00000	−	4.00000i	0.415900	−	0.207950i
$371$	6.06275			0.314762
$372$	3.71655	−	4.14575i	0.192694	−	0.214947i
$373$		−	15.1660i		−	0.785266i	−0.919695	−	0.392633i	$-0.871564\pi$
$373$		−	15.1660i		−	0.785266i	0.919695	−	0.392633i	$-0.128436\pi$
$374$	3.87451			0.200346
$375$	−7.23205	+	8.52628i	−0.373461	+	0.440295i
$376$	9.29150			0.479173
$377$	−12.1244	+	7.00000i	−0.624436	+	0.360518i
$378$	−2.29129	−	1.32288i	−0.117851	−	0.0680414i
$379$	−2.35425	+	4.07768i	−0.120930	+	0.209456i	−0.920135	−	0.391602i	$-0.871921\pi$
$379$	−2.35425	+	4.07768i	−0.120930	+	0.209456i	0.799205	+	0.601059i	$0.205254\pi$
$380$	−10.5830	+	5.29150i	−0.542897	+	0.271448i
$381$	−6.61438	−	11.4564i	−0.338865	−	0.586931i
$382$	−6.92820	+	4.00000i	−0.354478	+	0.204658i
$383$	−14.2526	+	8.22876i	−0.728275	+	0.420470i	−0.817791	−	0.575516i	$-0.804801\pi$
$383$	−14.2526	+	8.22876i	−0.728275	+	0.420470i	0.0895157	+	0.995985i	$0.471468\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	2.10496	−	3.18810i	0.107278	−	0.162481i
$386$	10.3229	−	17.8797i	0.525421	−	0.910055i
$387$			11.2915i			0.573979i
$388$		−	11.2288i		−	0.570054i
$389$	−8.00000	+	13.8564i	−0.405616	+	0.702548i	−0.994393	−	0.105748i	$-0.966276\pi$
$389$	−8.00000	+	13.8564i	−0.405616	+	0.702548i	0.588777	+	0.808296i	$0.299610\pi$
$390$	6.51940	−	9.87408i	0.330123	−	0.499993i
$391$	27.8745	−	48.2801i	1.40967	−	2.44163i
$392$		0			0
$393$	2.34563	−	1.35425i	0.118321	−	0.0683128i
$394$	−11.5830	−	20.0624i	−0.583543	−	1.01073i
$395$	−29.1660	+	14.5830i	−1.46750	+	0.733751i
$396$	0.322876	−	0.559237i	0.0162251	−	0.0281027i
$397$	−32.1867	−	18.5830i	−1.61540	−	0.932654i	−0.988088	−	0.153890i	$-0.950820\pi$
$397$	−32.1867	−	18.5830i	−1.61540	−	0.932654i	−0.627317	−	0.778764i	$-0.715847\pi$
$398$	14.1089	−	8.14575i	0.707213	−	0.408310i
$399$	14.0000			0.700877
$400$	1.96410	+	4.59808i	0.0982051	+	0.229904i
$401$	−22.0000			−1.09863			−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000			−1.09863			−0.549314	+	0.835616i	$0.685111\pi$
$402$		−	11.2915i		−	0.563169i
$403$	−9.16515	−	28.0000i	−0.456549	−	1.39478i
$404$	−6.64575			−0.330638
$405$	2.00000	−	1.00000i	0.0993808	−	0.0496904i
$406$	−3.50000	+	6.06218i	−0.173702	+	0.300861i
$407$		−	2.58301i		−	0.128035i
$408$	5.19615	−	3.00000i	0.257248	−	0.148522i
$409$	5.20850	−	9.02138i	0.257544	−	0.446079i	−0.708040	−	0.706173i	$-0.750420\pi$
$409$	5.20850	−	9.02138i	0.257544	−	0.446079i	0.965583	+	0.260094i	$0.0837536\pi$
$410$	7.34680	+	0.440978i	0.362833	+	0.0217783i
$411$	−10.5830			−0.522021
$412$	−5.75539	+	3.32288i	−0.283548	+	0.163706i
$413$	−1.47960	+	0.854249i	−0.0728065	+	0.0420348i
$414$	−4.64575	−	8.04668i	−0.228326	−	0.395473i
$415$	21.3898	+	1.28388i	1.04998	+	0.0630232i
$416$	−2.64575	−	4.58258i	−0.129719	−	0.224679i
$417$	3.46410	+	2.00000i	0.169638	+	0.0979404i
$418$			3.41699i			0.167131i
$419$	13.9373			0.680879			0.340440	−	0.940266i	$-0.389424\pi$
$419$	13.9373			0.680879			0.340440	+	0.940266i	$0.389424\pi$
$420$	0.354463	−	5.90545i	0.0172960	−	0.288157i
$421$	−15.9373	−	27.6041i	−0.776734	−	1.34534i	−0.933815	−	0.357757i	$-0.883542\pi$
$421$	−15.9373	−	27.6041i	−0.776734	−	1.34534i	0.157080	−	0.987586i	$-0.449792\pi$
$422$	−14.3613	−	8.29150i	−0.699097	−	0.403624i
$423$	8.04668	−	4.64575i	0.391243	−	0.225884i
$424$	1.14575	+	1.98450i	0.0556426	+	0.0963758i
$425$	−3.58846	+	29.7846i	−0.174066	+	1.44477i
$426$	6.58301			0.318948
$427$	22.9129	+	13.2288i	1.10883	+	0.640184i
$428$	−4.33013	−	2.50000i	−0.209305	−	0.120842i
$429$	−1.70850	−	2.95920i	−0.0824870	−	0.142872i
$430$	−22.5830	+	11.2915i	−1.08905	+	0.544525i
$431$	−19.5203	+	33.8101i	−0.940258	+	1.62857i	−0.175279	+	0.984519i	$0.556083\pi$
$431$	−19.5203	+	33.8101i	−0.940258	+	1.62857i	−0.764979	+	0.644055i	$0.777251\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	9.16601i		−	0.440490i	−0.975445	−	0.220245i	$-0.929314\pi$
$433$		−	9.16601i		−	0.440490i	0.975445	−	0.220245i	$-0.0706857\pi$
$434$	−10.9686	−	9.83307i	−0.526511	−	0.472002i
$435$	−2.64575	−	5.29150i	−0.126854	−	0.253708i
$436$	6.70850			0.321279
$437$	42.5790	+	24.5830i	2.03683	+	1.17596i
$438$			6.58301i			0.314548i
$439$	−2.43725	−	4.22145i	−0.116324	−	0.201479i	0.801984	−	0.597345i	$-0.203778\pi$
$439$	−2.43725	−	4.22145i	−0.116324	−	0.201479i	−0.918308	+	0.395866i	$0.870444\pi$
$440$	1.44135	+	0.0865143i	0.0687137	+	0.00412441i
$441$		0			0
$442$		−	31.7490i		−	1.51015i
$443$	−6.92820	+	4.00000i	−0.329169	+	0.190046i	−0.655472	−	0.755219i	$-0.727530\pi$
$443$	−6.92820	+	4.00000i	−0.329169	+	0.190046i	0.326303	+	0.945265i	$0.394197\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$	−6.14203	−	4.05530i	−0.291160	−	0.192240i
$446$	−13.3229	+	23.0759i	−0.630856	+	1.09268i
$447$	16.1477	−	9.32288i	0.763760	−	0.440957i
$448$	−2.29129	−	1.32288i	−0.108253	−	0.0625000i
$449$	−13.1660			−0.621342			−0.310671	−	0.950517i	$-0.600554\pi$
$449$	−13.1660			−0.621342			−0.310671	+	0.950517i	$0.600554\pi$
$450$	4.00000	+	3.00000i	0.188562	+	0.141421i
$451$	1.06275	−	1.84073i	0.0500428	−	0.0866766i
$452$	−11.5108	+	6.64575i	−0.541421	+	0.312590i
$453$	10.1399	+	5.85425i	0.476412	+	0.275057i
$454$	7.50000	+	12.9904i	0.351992	+	0.609669i
$455$	−26.1244	−	17.2487i	−1.22473	−	0.808632i
$456$	2.64575	+	4.58258i	0.123899	+	0.214599i
$457$			17.1660i			0.802992i	0.915861	+	0.401496i	$0.131510\pi$
$457$			17.1660i			0.802992i	−0.915861	+	0.401496i	$0.868490\pi$
$458$	14.8662	+	8.58301i	0.694652	+	0.401057i
$459$	3.00000	−	5.19615i	0.140028	−	0.242536i
$460$	11.4476	−	17.3382i	0.533747	−	0.808397i
$461$	−17.2288			−0.802423			−0.401212	−	0.915985i	$-0.631411\pi$
$461$	−17.2288			−0.802423			−0.401212	+	0.915985i	$0.631411\pi$
$462$	−1.47960	−	0.854249i	−0.0688373	−	0.0397432i
$463$			13.3542i			0.620625i	0.950635	+	0.310312i	$0.100434\pi$
$463$			13.3542i			0.620625i	−0.950635	+	0.310312i	$0.899566\pi$
$464$	−2.64575			−0.122826
$465$	12.0430	−	3.15710i	0.558479	−	0.146407i
$466$	−7.29150			−0.337772
$467$			26.7490i			1.23780i	0.785471	+	0.618898i	$0.212421\pi$
$467$			26.7490i			1.23780i	−0.785471	+	0.618898i	$0.787579\pi$
$468$	−4.58258	−	2.64575i	−0.211830	−	0.122300i
$469$	−29.8745			−1.37948
$470$	17.3382	+	11.4476i	0.799751	+	0.528039i
$471$	−0.645751	+	1.11847i	−0.0297546	+	0.0515366i
$472$	−0.559237	−	0.322876i	−0.0257410	−	0.0148616i
$473$			7.29150i			0.335264i
$474$	7.29150	+	12.6293i	0.334910	+	0.580081i
$475$	−26.2676	−	3.16472i	−1.20524	−	0.145207i
$476$	−7.93725	−	13.7477i	−0.363803	−	0.630126i
$477$	1.98450	+	1.14575i	0.0908640	+	0.0524603i
$478$	21.2895	−	12.2915i	0.973759	−	0.562200i
$479$	5.70850	−	9.88741i	0.260828	−	0.451767i	−0.705634	−	0.708576i	$-0.749338\pi$
$479$	5.70850	−	9.88741i	0.260828	−	0.451767i	0.966462	+	0.256809i	$0.0826712\pi$
$480$	2.00000	−	1.00000i	0.0912871	−	0.0456435i
$481$	−21.1660			−0.965087
$482$	18.1865	+	10.5000i	0.828374	+	0.478262i
$483$	−21.2895	+	12.2915i	−0.968706	+	0.559283i
$484$	−5.29150	+	9.16515i	−0.240523	+	0.416598i
$485$	13.8344	−	20.9531i	0.628188	−	0.951433i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	14.9205	−	8.61438i	0.676114	−	0.390355i	−0.122275	−	0.992496i	$-0.539019\pi$
$487$	14.9205	−	8.61438i	0.676114	−	0.390355i	0.798389	+	0.602142i	$0.205686\pi$
$488$			10.0000i			0.452679i
$489$	5.00000	−	8.66025i	0.226108	−	0.391630i
$490$		0			0
$491$	−14.9059	−	25.8177i	−0.672693	−	1.16514i	−0.977137	−	0.212608i	$-0.931804\pi$
$491$	−14.9059	−	25.8177i	−0.672693	−	1.16514i	0.304445	−	0.952530i	$-0.401529\pi$
$492$		−	3.29150i		−	0.148392i
$493$	−13.7477	−	7.93725i	−0.619166	−	0.357476i
$494$	28.0000			1.25978
$495$	1.29150	−	0.645751i	0.0580487	−	0.0290244i
$496$	1.14575	−	5.44860i	0.0514458	−	0.244649i
$497$		−	17.4170i		−	0.781259i
$498$		−	9.58301i		−	0.429425i
$499$	8.22876	−	14.2526i	0.368370	−	0.638035i	−0.620941	−	0.783857i	$-0.713249\pi$
$499$	8.22876	−	14.2526i	0.368370	−	0.638035i	0.989311	+	0.145822i	$0.0465827\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$	10.9373	+	18.9439i	0.488640	+	0.846350i
$502$	9.27383	+	5.35425i	0.413911	+	0.238972i
$503$	6.92820	+	4.00000i	0.308913	+	0.178351i	0.646440	−	0.762965i	$-0.276257\pi$
$503$	6.92820	+	4.00000i	0.308913	+	0.178351i	−0.337527	+	0.941316i	$0.609590\pi$
$504$	−2.64575			−0.117851
$505$	−12.4011	−	8.18790i	−0.551844	−	0.364357i
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$	−12.9904	+	7.50000i	−0.576923	+	0.333087i
$508$	−11.4564	−	6.61438i	−0.508297	−	0.293466i
$509$	1.32288	+	2.29129i	0.0586354	+	0.101560i	0.893853	−	0.448360i	$-0.147992\pi$
$509$	1.32288	+	2.29129i	0.0586354	+	0.101560i	−0.835218	+	0.549920i	$0.814658\pi$
$510$	13.3923	+	0.803848i	0.593021	+	0.0355950i
$511$	17.4170			0.770482
$512$		−	1.00000i		−	0.0441942i
$513$	4.58258	+	2.64575i	0.202326	+	0.116813i
$514$	2.64575	+	4.58258i	0.116699	+	0.202129i
$515$	−14.8337	−	0.890362i	−0.653649	−	0.0392340i
$516$	5.64575	+	9.77873i	0.248540	+	0.430485i
$517$	5.19615	−	3.00000i	0.228527	−	0.131940i
$518$	−9.16515	+	5.29150i	−0.402694	+	0.232495i
$519$	−6.29150			−0.276166
$520$	0.708927	−	11.8109i	0.0310885	−	0.517942i
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$	−2.29129	+	1.32288i	−0.100287	+	0.0579007i
$523$			29.8745i			1.30632i	0.757219	+	0.653161i	$0.226557\pi$
$523$			29.8745i			1.30632i	−0.757219	+	0.653161i	$0.773443\pi$
$524$	1.35425	−	2.34563i	0.0591606	−	0.102469i
$525$	7.93725	−	10.5830i	0.346410	−	0.461880i
$526$	23.1660			1.01009
$527$	22.2993	−	24.8745i	0.971373	−	1.08355i
$528$		−	0.645751i		−	0.0281027i
$529$	−63.3320			−2.75357
$530$	−0.307003	+	5.11475i	−0.0133354	+	0.222171i
$531$	−0.645751			−0.0280232
$532$	12.1244	−	7.00000i	0.525657	−	0.303488i
$533$	−15.0836	−	8.70850i	−0.653342	−	0.377207i
$534$	−1.64575	+	2.85052i	−0.0712186	+	0.123354i
$535$	−5.00000	−	10.0000i	−0.216169	−	0.432338i
$536$	−5.64575	−	9.77873i	−0.243859	−	0.422377i
$537$	2.79619	−	1.61438i	0.120664	−	0.0696656i
$538$	6.92820	−	4.00000i	0.298696	−	0.172452i
$539$		0			0
$540$	1.23205	−	1.86603i	0.0530190	−	0.0803009i
$541$	13.9373	−	24.1400i	0.599209	−	1.03786i	−0.393729	−	0.919227i	$-0.628815\pi$
$541$	13.9373	−	24.1400i	0.599209	−	1.03786i	0.992938	−	0.118634i	$-0.0378516\pi$
$542$			22.2915i			0.957502i
$543$		−	0.708497i		−	0.0304045i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	12.5182	+	8.26521i	0.536222	+	0.354043i
$546$	−7.00000	+	12.1244i	−0.299572	+	0.518875i
$547$	20.1710	−	11.6458i	0.862451	−	0.497936i	−0.00238124	−	0.999997i	$-0.500758\pi$
$547$	20.1710	−	11.6458i	0.862451	−	0.497936i	0.864832	+	0.502061i	$0.167425\pi$
$548$	−9.16515	+	5.29150i	−0.391516	+	0.226042i
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$	2.58301	+	1.93725i	0.110140	+	0.0826048i
$551$	7.00000	−	12.1244i	0.298210	−	0.516515i
$552$	−8.04668	−	4.64575i	−0.342489	−	0.197736i
$553$	33.4139	−	19.2915i	1.42090	−	0.820358i
$554$	2.00000			0.0849719
$555$	0.535898	−	8.92820i	0.0227476	−	0.378981i
$556$	4.00000			0.169638
$557$		−	4.29150i		−	0.181837i	−0.995858	−	0.0909184i	$-0.971020\pi$
$557$		−	4.29150i		−	0.181837i	0.995858	−	0.0909184i	$-0.0289802\pi$
$558$	−1.73205	−	5.29150i	−0.0733236	−	0.224007i
$559$	59.7490			2.52711
$560$	−2.64575	−	5.29150i	−0.111803	−	0.223607i
$561$	1.93725	−	3.35542i	0.0817909	−	0.141666i
$562$		−	18.5830i		−	0.783877i
$563$	−25.6196	+	14.7915i	−1.07974	+	0.623388i	−0.930826	−	0.365463i	$-0.880911\pi$
$563$	−25.6196	+	14.7915i	−1.07974	+	0.623388i	−0.148913	+	0.988850i	$0.547577\pi$
$564$	4.64575	−	8.04668i	0.195621	−	0.338826i
$565$	−29.6673	−	1.78072i	−1.24811	−	0.0749156i
$566$	−18.7085			−0.786377
$567$	−2.29129	+	1.32288i	−0.0962250	+	0.0555556i
$568$	5.70105	−	3.29150i	0.239211	−	0.138108i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	−0.708927	+	11.8109i	−0.0296937	+	0.494704i
$571$	20.0000	+	34.6410i	0.836974	+	1.44968i	0.892413	+	0.451219i	$0.149011\pi$
$571$	20.0000	+	34.6410i	0.836974	+	1.44968i	−0.0554391	+	0.998462i	$0.517656\pi$
$572$	−2.95920	−	1.70850i	−0.123731	−	0.0714359i
$573$			8.00000i			0.334205i
$574$	−8.70850			−0.363486
$575$	42.7230	−	18.2495i	1.78167	−	0.761055i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	30.9596	+	17.8745i	1.28886	+	0.744125i	0.978452	−	0.206477i	$-0.0661998\pi$
$577$	30.9596	+	17.8745i	1.28886	+	0.744125i	0.310412	+	0.950602i	$0.399533\pi$
$578$	16.4545	−	9.50000i	0.684416	−	0.395148i
$579$	−10.3229	−	17.8797i	−0.429004	−	0.743057i
$580$	−4.93704	−	3.25970i	−0.204999	−	0.135352i
$581$	−25.3542			−1.05187
$582$	−9.72439	−	5.61438i	−0.403089	−	0.232723i
$583$	1.28149	+	0.739870i	0.0530740	+	0.0306423i
$584$	3.29150	+	5.70105i	0.136203	+	0.235911i
$585$	−5.29150	−	10.5830i	−0.218777	−	0.437553i
$586$	6.85425	−	11.8719i	0.283146	−	0.490424i
$587$		−	3.00000i		−	0.123823i	−0.998082	−	0.0619116i	$-0.980280\pi$
$587$		−	3.00000i		−	0.123823i	0.998082	−	0.0619116i	$-0.0197197\pi$
$588$		0			0
$589$	21.9373	+	19.6661i	0.903909	+	0.810329i
$590$	−0.645751	−	1.29150i	−0.0265852	−	0.0531703i
$591$	−23.1660			−0.952922
$592$	−3.46410	−	2.00000i	−0.142374	−	0.0821995i
$593$			24.4575i			1.00435i	0.864766	+	0.502175i	$0.167467\pi$
$593$			24.4575i			1.00435i	−0.864766	+	0.502175i	$0.832533\pi$
$594$	−0.322876	−	0.559237i	−0.0132477	−	0.0229458i
$595$	2.12678	−	35.4327i	0.0871895	−	1.45260i
$596$	9.32288	−	16.1477i	0.381880	−	0.661435i
$597$		−	16.2915i		−	0.666767i
$598$	−42.5790	+	24.5830i	−1.74119	+	1.00527i
$599$	−1.64575	−	2.85052i	−0.0672436	−	0.116469i	0.830443	−	0.557103i	$-0.188087\pi$
$599$	−1.64575	−	2.85052i	−0.0672436	−	0.116469i	−0.897687	+	0.440634i	$0.854754\pi$
$600$	4.96410	+	0.598076i	0.202659	+	0.0244164i
$601$	3.58301	−	6.20595i	0.146154	−	0.253146i	−0.783649	−	0.621204i	$-0.786644\pi$
$601$	3.58301	−	6.20595i	0.146154	−	0.253146i	0.929803	+	0.368058i	$0.119977\pi$
$602$	25.8721	−	14.9373i	1.05447	−	0.608797i
$603$	−9.77873	−	5.64575i	−0.398221	−	0.229913i
$604$	11.7085			0.476412
$605$	−21.1660	+	10.5830i	−0.860521	+	0.430260i
$606$	−3.32288	+	5.75539i	−0.134983	+	0.233797i
$607$	−32.2954	+	18.6458i	−1.31083	+	0.756808i	−0.982233	−	0.187663i	$-0.939909\pi$
$607$	−32.2954	+	18.6458i	−1.31083	+	0.756808i	−0.328596	+	0.944471i	$0.606575\pi$
$608$	4.58258	+	2.64575i	0.185848	+	0.107299i
$609$	3.50000	+	6.06218i	0.141827	+	0.245652i
$610$	−12.3205	+	18.6603i	−0.498843	+	0.755532i
$611$	−24.5830	−	42.5790i	−0.994522	−	1.72256i
$612$		−	6.00000i		−	0.242536i
$613$	14.4700	+	8.35425i	0.584437	+	0.337425i	0.762895	−	0.646523i	$-0.223777\pi$
$613$	14.4700	+	8.35425i	0.584437	+	0.337425i	−0.178458	+	0.983948i	$0.557111\pi$
$614$	6.93725	−	12.0157i	0.279965	−	0.484913i
$615$	4.05530	−	6.14203i	0.163525	−	0.247670i
$616$	−1.70850			−0.0688373
$617$	21.2895	+	12.2915i	0.857083	+	0.494837i	0.863034	−	0.505145i	$-0.168561\pi$
$617$	21.2895	+	12.2915i	0.857083	+	0.494837i	−0.00595119	+	0.999982i	$0.501894\pi$
$618$			6.64575i			0.267331i
$619$	14.5830			0.586140			0.293070	−	0.956091i	$-0.405323\pi$
$619$	14.5830			0.586140			0.293070	+	0.956091i	$0.405323\pi$
$620$	8.85095	−	8.75560i	0.355463	−	0.351634i
$621$	−9.29150			−0.372855
$622$			11.8745i			0.476124i
$623$	7.54178	+	4.35425i	0.302155	+	0.174449i
$624$	−5.29150			−0.211830
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	6.96863	−	12.0700i	0.278522	−	0.482415i
$627$	2.95920	+	1.70850i	0.118179	+	0.0682308i
$628$			1.29150i			0.0515366i
$629$	−12.0000	−	20.7846i	−0.478471	−	0.828737i
$630$	−4.93704	−	3.25970i	−0.196696	−	0.129870i
$631$	13.4373	+	23.2740i	0.534929	+	0.926524i	0.999167	+	0.0408132i	$0.0129948\pi$
$631$	13.4373	+	23.2740i	0.534929	+	0.926524i	−0.464238	+	0.885710i	$0.653672\pi$
$632$	12.6293	+	7.29150i	0.502365	+	0.290040i
$633$	−14.3613	+	8.29150i	−0.570811	+	0.329558i
$634$	8.14575	−	14.1089i	0.323509	−	0.560334i
$635$	−13.2288	−	26.4575i	−0.524967	−	1.04993i
$636$	2.29150			0.0908640
$637$		0			0
$638$	−1.47960	+	0.854249i	−0.0585780	+	0.0338200i
$639$	3.29150	−	5.70105i	0.130210	−	0.225530i
$640$	1.23205	−	1.86603i	0.0487011	−	0.0737611i
$641$	24.5203	+	42.4703i	0.968492	+	1.67748i	0.699925	+	0.714216i	$0.253217\pi$
$641$	24.5203	+	42.4703i	0.968492	+	1.67748i	0.268567	+	0.963261i	$0.413450\pi$
$642$	−4.33013	+	2.50000i	−0.170896	+	0.0986671i
$643$		−	23.8745i		−	0.941519i	−0.882262	−	0.470759i	$-0.843980\pi$
$643$		−	23.8745i		−	0.941519i	0.882262	−	0.470759i	$-0.156020\pi$
$644$	−12.2915	+	21.2895i	−0.484353	+	0.838924i
$645$	−1.51277	+	25.2032i	−0.0595654	+	0.992375i
$646$	15.8745	+	27.4955i	0.624574	+	1.08179i
$647$		−	2.00000i		−	0.0786281i	−0.999227	−	0.0393141i	$-0.987483\pi$
$647$		−	2.00000i		−	0.0786281i	0.999227	−	0.0393141i	$-0.0125173\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−0.416995			−0.0163685
$650$	15.8745	−	21.1660i	0.622649	−	0.830199i
$651$	−14.0000	+	4.58258i	−0.548703	+	0.179605i
$652$		−	10.0000i		−	0.391630i
$653$			0.874508i			0.0342221i	0.999854	+	0.0171111i	$0.00544689\pi$
$653$			0.874508i			0.0342221i	−0.999854	+	0.0171111i	$0.994553\pi$
$654$	3.35425	−	5.80973i	0.131162	−	0.227178i
$655$	5.41699	−	2.70850i	0.211659	−	0.105830i
$656$	−1.64575	−	2.85052i	−0.0642558	−	0.111294i
$657$	5.70105	+	3.29150i	0.222419	+	0.128414i
$658$	−21.2895	−	12.2915i	−0.829951	−	0.479173i
$659$	−34.0627			−1.32690			−0.663448	−	0.748222i	$-0.730908\pi$
$659$	−34.0627			−1.32690			−0.663448	+	0.748222i	$0.730908\pi$
$660$	0.795598	−	1.20499i	0.0309686	−	0.0469041i
$661$	3.22876	+	5.59237i	0.125584	+	0.217518i	0.921961	−	0.387282i	$-0.126586\pi$
$661$	3.22876	+	5.59237i	0.125584	+	0.217518i	−0.796377	+	0.604800i	$0.793253\pi$
$662$	−16.5983	+	9.58301i	−0.645109	+	0.372454i
$663$	−27.4955	−	15.8745i	−1.06783	−	0.616515i
$664$	−4.79150	−	8.29913i	−0.185946	−	0.322069i
$665$	31.2487	+	1.87564i	1.21177	+	0.0727344i
$666$	−4.00000			−0.154997
$667$			24.5830i			0.951858i
$668$	18.9439	+	10.9373i	0.732961	+	0.423175i
$669$	13.3229	+	23.0759i	0.515092	+	0.892166i
$670$	1.51277	−	25.2032i	0.0584436	−	0.973685i
$671$	3.22876	+	5.59237i	0.124645	+	0.215891i
$672$	−2.29129	+	1.32288i	−0.0883883	+	0.0510310i
$673$	−6.47765	+	3.73987i	−0.249695	+	0.144161i	−0.619625	−	0.784898i	$-0.712715\pi$
$673$	−6.47765	+	3.73987i	−0.249695	+	0.144161i	0.369930	+	0.929060i	$0.379382\pi$
$674$	−35.1033			−1.35213
$675$	4.59808	−	1.96410i	0.176980	−	0.0755983i
$676$	−7.50000	+	12.9904i	−0.288462	+	0.499630i
$677$	−26.2332	+	15.1458i	−1.00822	+	0.582099i	−0.910671	−	0.413132i	$-0.864435\pi$
$677$	−26.2332	+	15.1458i	−1.00822	+	0.582099i	−0.0975530	+	0.995230i	$0.531102\pi$
$678$			13.2915i			0.510457i
$679$	−14.8542	+	25.7283i	−0.570054	+	0.987362i
$680$	12.0000	−	6.00000i	0.460179	−	0.230089i
$681$	15.0000			0.574801
$682$	−1.11847	−	3.41699i	−0.0428286	−	0.130843i
$683$		−	22.1660i		−	0.848159i	−0.905625	−	0.424079i	$-0.860598\pi$
$683$		−	22.1660i		−	0.848159i	0.905625	−	0.424079i	$-0.139402\pi$
$684$	5.29150			0.202326
$685$	−23.6218	−	1.41785i	−0.902543	−	0.0541734i
$686$	−18.5203			−0.707107
$687$	14.8662	−	8.58301i	0.567181	−	0.327462i
$688$	9.77873	+	5.64575i	0.372811	+	0.215242i
$689$	6.06275	−	10.5010i	0.230972	−	0.400056i
$690$	−9.29150	−	18.5830i	−0.353721	−	0.707443i
$691$	0.583005	+	1.00979i	0.0221786	+	0.0384144i	0.876902	−	0.480670i	$-0.159606\pi$
$691$	0.583005	+	1.00979i	0.0221786	+	0.0384144i	−0.854723	+	0.519084i	$0.826273\pi$
$692$	−5.44860	+	3.14575i	−0.207125	+	0.119584i
$693$	−1.47960	+	0.854249i	−0.0562054	+	0.0324502i
$694$	1.79150	−	3.10297i	0.0680045	−	0.117787i
$695$	7.46410	+	4.92820i	0.283130	+	0.186937i
$696$	−1.32288	+	2.29129i	−0.0501435	+	0.0868510i
$697$		−	19.7490i		−	0.748047i
$698$		−	5.29150i		−	0.200286i
$699$	−3.64575	+	6.31463i	−0.137895	+	0.238841i
$700$	1.58236	−	13.1338i	0.0598076	−	0.496410i
$701$	11.3856	−	19.7205i	0.430029	−	0.744832i	−0.566846	−	0.823824i	$-0.691837\pi$
$701$	11.3856	−	19.7205i	0.430029	−	0.744832i	0.996875	+	0.0789915i	$0.0251700\pi$
$702$	−4.58258	+	2.64575i	−0.172958	+	0.0998574i
$703$	18.3303	−	10.5830i	0.691340	−	0.399146i
$704$	−0.322876	−	0.559237i	−0.0121688	−	0.0210770i
$705$	18.5830	−	9.29150i	0.699876	−	0.349938i
$706$	−11.3542	+	19.6661i	−0.427323	+	0.740145i
$707$	15.2273	+	8.79150i	0.572683	+	0.330638i
$708$	−0.559237	+	0.322876i	−0.0210174	+	0.0121344i
$709$	−12.7085			−0.477278			−0.238639	−	0.971108i	$-0.576701\pi$
$709$	−12.7085			−0.477278			−0.238639	+	0.971108i	$0.576701\pi$
$710$	14.6936	+	0.881955i	0.551441	+	0.0330992i
$711$	14.5830			0.546905
$712$			3.29150i			0.123354i
$713$	−50.6257	−	10.6458i	−1.89595	−	0.398687i
$714$	−15.8745			−0.594089
$715$	−3.41699	−	6.83399i	−0.127788	−	0.255577i
$716$	1.61438	−	2.79619i	0.0603321	−	0.104498i
$717$		−	24.5830i		−	0.918069i
$718$	15.5885	−	9.00000i	0.581756	−	0.335877i
$719$	3.29150	−	5.70105i	0.122752	−	0.212613i	−0.798100	−	0.602525i	$-0.794161\pi$
$719$	3.29150	−	5.70105i	0.122752	−	0.212613i	0.920852	+	0.389912i	$0.127495\pi$
$720$	0.133975	−	2.23205i	0.00499294	−	0.0831836i
$721$	17.5830			0.654825
$722$	−7.79423	+	4.50000i	−0.290071	+	0.167473i
$723$	18.1865	−	10.5000i	0.676364	−	0.390499i
$724$	−0.354249	−	0.613577i	−0.0131655	−	0.0228034i
$725$	−5.19652	−	12.1654i	−0.192994	−	0.451810i
$726$	5.29150	+	9.16515i	0.196386	+	0.340151i
$727$	−1.06413	−	0.614378i	−0.0394666	−	0.0227860i	0.480137	−	0.877194i	$-0.340587\pi$
$727$	−1.06413	−	0.614378i	−0.0394666	−	0.0227860i	−0.519603	+	0.854408i	$0.673920\pi$
$728$			14.0000i			0.518875i
$729$	−1.00000			−0.0370370
$730$	−0.881955	+	14.6936i	−0.0326426	+	0.543835i
$731$	33.8745	+	58.6724i	1.25289	+	2.17008i
$732$	8.66025	+	5.00000i	0.320092	+	0.184805i
$733$	37.9964	−	21.9373i	1.40343	−	0.810271i	0.408688	−	0.912674i	$-0.365987\pi$
$733$	37.9964	−	21.9373i	1.40343	−	0.810271i	0.994743	+	0.102403i	$0.0326533\pi$
$734$	17.2288	+	29.8411i	0.635925	+	1.10145i
$735$		0			0
$736$	−9.29150			−0.342489
$737$	−6.31463	−	3.64575i	−0.232602	−	0.134293i
$738$	−2.85052	−	1.64575i	−0.104929	−	0.0605809i
$739$	−14.3542	−	24.8623i	−0.528030	−	0.914574i	−0.999466	−	0.0326740i	$-0.989598\pi$
$739$	−14.3542	−	24.8623i	−0.528030	−	0.914574i	0.471436	−	0.881900i	$-0.343736\pi$
$740$	−4.00000	−	8.00000i	−0.147043	−	0.294086i
$741$	14.0000	−	24.2487i	0.514303	−	0.890799i
$742$		−	6.06275i		−	0.222570i
$743$			2.58301i			0.0947613i	0.998877	+	0.0473806i	$0.0150874\pi$
$743$			2.58301i			0.0947613i	−0.998877	+	0.0473806i	$0.984913\pi$
$744$	−4.14575	−	3.71655i	−0.151991	−	0.136255i
$745$	37.2915	−	18.6458i	1.36625	−	0.683127i
$746$	−15.1660			−0.555267
$747$	−8.29913	−	4.79150i	−0.303649	−	0.175312i
$748$		−	3.87451i		−	0.141666i
$749$	6.61438	+	11.4564i	0.241684	+	0.418609i
$750$	8.52628	+	7.23205i	0.311336	+	0.264077i
$751$	−17.8542	+	30.9245i	−0.651511	+	1.12845i	0.331246	+	0.943545i	$0.392531\pi$
$751$	−17.8542	+	30.9245i	−0.651511	+	1.12845i	−0.982756	+	0.184905i	$0.940802\pi$
$752$		−	9.29150i		−	0.338826i
$753$	9.27383	−	5.35425i	0.337957	−	0.195120i
$754$	7.00000	+	12.1244i	0.254925	+	0.441543i
$755$	21.8484	+	14.4255i	0.795143	+	0.524996i
$756$	−1.32288	+	2.29129i	−0.0481125	+	0.0833333i
$757$	−5.30483	+	3.06275i	−0.192807	+	0.111317i	−0.593296	−	0.804984i	$-0.702174\pi$
$757$	−5.30483	+	3.06275i	−0.192807	+	0.111317i	0.400489	+	0.916302i	$0.368840\pi$
$758$	4.07768	+	2.35425i	0.148108	+	0.0855102i
$759$	−6.00000			−0.217786
$760$	5.29150	+	10.5830i	0.191943	+	0.383886i
$761$	−12.0000	+	20.7846i	−0.435000	+	0.753442i	−0.997296	−	0.0734946i	$-0.976585\pi$
$761$	−12.0000	+	20.7846i	−0.435000	+	0.753442i	0.562296	+	0.826936i	$0.309918\pi$
$762$	−11.4564	+	6.61438i	−0.415023	+	0.239614i
$763$	−15.3711	−	8.87451i	−0.556471	−	0.321279i
$764$	4.00000	+	6.92820i	0.144715	+	0.250654i
$765$	7.39230	−	11.1962i	0.267269	−	0.404798i
$766$	8.22876	+	14.2526i	0.297317	+	0.514968i
$767$			3.41699i			0.123381i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	3.20850	−	5.55728i	0.115701	−	0.200401i	−0.802359	−	0.596842i	$-0.796422\pi$
$769$	3.20850	−	5.55728i	0.115701	−	0.200401i	0.918060	+	0.396442i	$0.129755\pi$
$770$	−3.18810	−	2.10496i	−0.114891	−	0.0758573i
$771$	5.29150			0.190569
$772$	−17.8797	−	10.3229i	−0.643506	−	0.371528i
$773$		−	4.83399i		−	0.173867i	−0.996214	−	0.0869333i	$-0.972293\pi$
$773$		−	4.83399i		−	0.173867i	0.996214	−	0.0869333i	$-0.0277067\pi$
$774$	11.2915			0.405865
$775$	27.3035	−	5.43335i	0.980769	−	0.195172i
$776$	−11.2288			−0.403089
$777$			10.5830i			0.379663i
$778$	13.8564	+	8.00000i	0.496776	+	0.286814i
$779$	17.4170			0.624029
$780$	−9.87408	−	6.51940i	−0.353549	−	0.233432i
$781$	2.12549	−	3.68146i	0.0760561	−	0.131733i
$782$	−48.2801	−	27.8745i	−1.72649	−	0.996790i
$783$			2.64575i			0.0945514i
$784$		0			0
$785$	−1.59120	+	2.40998i	−0.0567923	+	0.0860158i
$786$	−1.35425	−	2.34563i	−0.0483045	−	0.0836658i
$787$	21.9031	+	12.6458i	0.780761	+	0.450772i	0.836700	−	0.547662i	$-0.184482\pi$
$787$	21.9031	+	12.6458i	0.780761	+	0.450772i	−0.0559392	+	0.998434i	$0.517815\pi$
$788$	−20.0624	+	11.5830i	−0.714692	+	0.412627i
$789$	11.5830	−	20.0624i	0.412366	−	0.714239i
$790$	14.5830	+	29.1660i	0.518840	+	1.03768i
$791$	35.1660			1.25036
$792$	−0.559237	−	0.322876i	−0.0198716	−	0.0114729i
$793$	45.8258	−	26.4575i	1.62732	−	0.939534i
$794$	−18.5830	+	32.1867i	−0.659486	+	1.14226i
$795$	4.27600	+	2.82325i	0.151654	+	0.100130i
$796$	−8.14575	−	14.1089i	−0.288719	−	0.500075i
$797$	−45.7907	+	26.4373i	−1.62199	+	0.936456i	−0.635601	+	0.772018i	$0.719248\pi$
$797$	−45.7907	+	26.4373i	−1.62199	+	0.936456i	−0.986387	+	0.164438i	$0.947419\pi$
$798$		−	14.0000i		−	0.495595i
$799$	27.8745	−	48.2801i	0.986129	−	1.70803i
$800$	4.59808	−	1.96410i	0.162567	−	0.0694415i
$801$	1.64575	+	2.85052i	0.0581498	+	0.100718i
$802$			22.0000i			0.776847i
$803$	3.68146	+	2.12549i	0.129916	+	0.0750070i
$804$	−11.2915			−0.398221
$805$	−49.1660	+	24.5830i	−1.73287	+	0.866437i
$806$	−28.0000	+	9.16515i	−0.986258	+	0.322829i
$807$		−	8.00000i		−	0.281613i
$808$			6.64575i			0.233797i
$809$	−22.2915	+	38.6100i	−0.783727	+	1.35746i	0.146029	+	0.989280i	$0.453351\pi$
$809$	−22.2915	+	38.6100i	−0.783727	+	1.35746i	−0.929756	+	0.368176i	$0.879983\pi$
$810$	−1.00000	−	2.00000i	−0.0351364	−	0.0702728i
$811$	2.64575	+	4.58258i	0.0929049	+	0.160916i	0.908732	−	0.417379i	$-0.137051\pi$
$811$	2.64575	+	4.58258i	0.0929049	+	0.160916i	−0.815827	+	0.578295i	$0.803718\pi$
$812$	6.06218	+	3.50000i	0.212741	+	0.122826i
$813$	19.3050	+	11.1458i	0.677056	+	0.390899i
$814$	−2.58301			−0.0905343
$815$	12.3205	−	18.6603i	0.431569	−	0.653640i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	−51.7442	+	29.8745i	−1.81030	+	1.04518i
$818$	−9.02138	−	5.20850i	−0.315425	−	0.182111i
$819$	7.00000	+	12.1244i	0.244600	+	0.423659i
$820$	0.440978	−	7.34680i	0.0153996	−	0.256561i
$821$	49.1033			1.71372			0.856858	−	0.515553i	$-0.172413\pi$
$821$	49.1033			1.71372			0.856858	+	0.515553i	$0.172413\pi$
$822$			10.5830i			0.369125i
$823$	−15.0292	−	8.67712i	−0.523886	−	0.302466i	0.214637	−	0.976694i	$-0.431143\pi$
$823$	−15.0292	−	8.67712i	−0.523886	−	0.302466i	−0.738523	+	0.674228i	$0.764476\pi$
$824$	3.32288	+	5.75539i	0.115758	+	0.200498i
$825$	2.96921	−	1.26832i	0.103375	−	0.0441573i
$826$	0.854249	+	1.47960i	0.0297231	+	0.0514819i
$827$	−11.6195	+	6.70850i	−0.404048	+	0.233277i	−0.688229	−	0.725493i	$-0.741612\pi$
$827$	−11.6195	+	6.70850i	−0.404048	+	0.233277i	0.284181	+	0.958771i	$0.408278\pi$
$828$	−8.04668	+	4.64575i	−0.279641	+	0.161451i
$829$	17.7490			0.616449			0.308224	−	0.951314i	$-0.400265\pi$
$829$	17.7490			0.616449			0.308224	+	0.951314i	$0.400265\pi$
$830$	1.28388	−	21.3898i	0.0445641	−	0.742449i
$831$	1.00000	−	1.73205i	0.0346896	−	0.0600842i
$832$	−4.58258	+	2.64575i	−0.158872	+	0.0917249i
$833$		0			0
$834$	2.00000	−	3.46410i	0.0692543	−	0.119952i
$835$	21.8745	+	43.7490i	0.756999	+	1.51400i
$836$	3.41699			0.118179
$837$	−5.44860	−	1.14575i	−0.188331	−	0.0396030i
$838$		−	13.9373i		−	0.481454i
$839$	−42.0000			−1.45000			−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000			−1.45000			−0.725001	+	0.688748i	$0.758161\pi$
$840$	−5.90545	−	0.354463i	−0.203757	−	0.0122302i
$841$	−22.0000			−0.758621
$842$	−27.6041	+	15.9373i	−0.951301	+	0.549234i
$843$	−16.0934	−	9.29150i	−0.554285	−	0.320016i
$844$	−8.29150	+	14.3613i	−0.285405	+	0.494336i
$845$	−30.0000	+	15.0000i	−1.03203	+	0.516016i
$846$	−4.64575	−	8.04668i	−0.159724	−	0.276650i
$847$	24.2487	−	14.0000i	0.833196	−	0.481046i
$848$	1.98450	−	1.14575i	0.0681480	−	0.0393453i
$849$	−9.35425	+	16.2020i	−0.321037	+	0.556052i
$850$	29.7846	+	3.58846i	1.02160	+	0.123083i
$851$	−18.5830	+	32.1867i	−0.637017	+	1.10335i
$852$		−	6.58301i		−	0.225530i
$853$			40.4575i			1.38524i	0.721303	+	0.692619i	$0.243543\pi$
$853$			40.4575i			1.38524i	−0.721303	+	0.692619i	$0.756457\pi$
$854$	13.2288	−	22.9129i	0.452679	−	0.784063i
$855$	9.87408	+	6.51940i	0.337686	+	0.222959i
$856$	−2.50000	+	4.33013i	−0.0854482	+	0.148001i
$857$	19.1612	−	11.0627i	0.654535	−	0.377896i	−0.135656	−	0.990756i	$-0.543314\pi$
$857$	19.1612	−	11.0627i	0.654535	−	0.377896i	0.790192	+	0.612860i	$0.209981\pi$
$858$	−2.95920	+	1.70850i	−0.101026	+	0.0583271i
$859$	4.35425	+	7.54178i	0.148565	+	0.257322i	0.930697	−	0.365790i	$-0.119201\pi$
$859$	4.35425	+	7.54178i	0.148565	+	0.257322i	−0.782132	+	0.623112i	$0.785868\pi$
$860$	11.2915	+	22.5830i	0.385037	+	0.770074i
$861$	−4.35425	+	7.54178i	−0.148392	+	0.257023i
$862$	33.8101	+	19.5203i	1.15158	+	0.664863i
$863$	24.0314	−	13.8745i	0.818037	−	0.472294i	−0.0317022	−	0.999497i	$-0.510093\pi$
$863$	24.0314	−	13.8745i	0.818037	−	0.472294i	0.849739	+	0.527204i	$0.176759\pi$
$864$	−1.00000			−0.0340207
$865$	−14.0430	−	0.842902i	−0.477475	−	0.0286595i
$866$	−9.16601			−0.311474
$867$		−	19.0000i		−	0.645274i
$868$	−9.83307	+	10.9686i	−0.333756	+	0.372299i
$869$	9.41699			0.319450
$870$	−5.29150	+	2.64575i	−0.179399	+	0.0896994i
$871$	−29.8745	+	51.7442i	−1.01226	+	1.75328i
$872$		−	6.70850i		−	0.227178i
$873$	−9.72439	+	5.61438i	−0.329121	+	0.190018i
$874$	24.5830	−	42.5790i	0.831533	−	1.44026i
$875$	19.1342	−	22.5584i	0.646854	−	0.762614i
$876$	6.58301			0.222419
$877$	13.7477	−	7.93725i	0.464228	−	0.268022i	−0.249593	−	0.968351i	$-0.580297\pi$
$877$	13.7477	−	7.93725i	0.464228	−	0.268022i	0.713820	+	0.700329i	$0.246963\pi$
$878$	−4.22145	+	2.43725i	−0.142467	+	0.0822533i
$879$	−6.85425	−	11.8719i	−0.231188	−	0.400429i
$880$	0.0865143	−	1.44135i	0.00291640	−	0.0485879i
$881$	12.0000	+	20.7846i	0.404290	+	0.700251i	0.994239	−	0.107190i	$-0.0341852\pi$
$881$	12.0000	+	20.7846i	0.404290	+	0.700251i	−0.589948	+	0.807441i	$0.700852\pi$
$882$		0			0
$883$			8.00000i			0.269221i	0.990899	+	0.134611i	$0.0429784\pi$
$883$			8.00000i			0.269221i	−0.990899	+	0.134611i	$0.957022\pi$
$884$	−31.7490			−1.06783
$885$	−1.44135	−	0.0865143i	−0.0484504	−	0.00290815i
$886$	4.00000	+	6.92820i	0.134383	+	0.232758i
$887$	29.7324	+	17.1660i	0.998316	+	0.576378i	0.907750	−	0.419512i	$-0.137799\pi$
$887$	29.7324	+	17.1660i	0.998316	+	0.576378i	0.0905667	+	0.995890i	$0.471132\pi$
$888$	−3.46410	+	2.00000i	−0.116248	+	0.0671156i
$889$	17.5000	+	30.3109i	0.586931	+	1.01659i
$890$	−4.05530	+	6.14203i	−0.135934	+	0.205881i
$891$	−0.645751			−0.0216335
$892$	23.0759	+	13.3229i	0.772638	+	0.446083i
$893$	42.5790	+	24.5830i	1.42485	+	0.822639i
$894$	−9.32288	−	16.1477i	−0.311804	−	0.540060i
$895$	6.45751	−	3.22876i	0.215851	−	0.107925i
$896$	−1.32288	+	2.29129i	−0.0441942	+	0.0765466i
$897$			49.1660i			1.64161i
$898$			13.1660i			0.439355i
$899$	−3.03137	+	14.4156i	−0.101102	+	0.480789i
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$	13.7490			0.458046
$902$	−1.84073	−	1.06275i	−0.0612896	−	0.0353856i
$903$		−	29.8745i		−	0.994161i
$904$	6.64575	+	11.5108i	0.221034	+	0.382843i
$905$	0.0949207	−	1.58140i	0.00315527	−	0.0525676i
$906$	5.85425	−	10.1399i	0.194494	−	0.336874i
$907$		−	15.4170i		−	0.511913i	−0.966688	−	0.255956i	$-0.917610\pi$
$907$		−	15.4170i		−	0.511913i	0.966688	−	0.255956i	$-0.0823904\pi$
$908$	12.9904	−	7.50000i	0.431101	−	0.248896i
$909$	3.32288	+	5.75539i	0.110213	+	0.190894i
$910$	−17.2487	+	26.1244i	−0.571789	+	0.866014i
$911$	−19.6458	+	34.0274i	−0.650893	+	1.12738i	0.332014	+	0.943275i	$0.392272\pi$
$911$	−19.6458	+	34.0274i	−0.650893	+	1.12738i	−0.982907	+	0.184105i	$0.941061\pi$
$912$	4.58258	−	2.64575i	0.151744	−	0.0876096i
$913$	−5.35917	−	3.09412i	−0.177363	−	0.102400i
$914$	17.1660			0.567801
$915$	10.0000	+	20.0000i	0.330590	+	0.661180i
$916$	8.58301	−	14.8662i	0.283590	−	0.491193i
$917$	−6.20595	+	3.58301i	−0.204938	+	0.118321i
$918$	−5.19615	−	3.00000i	−0.171499	−	0.0990148i
$919$	8.72876	+	15.1186i	0.287935	+	0.498718i	0.973317	−	0.229466i	$-0.0736979\pi$
$919$	8.72876	+	15.1186i	0.287935	+	0.498718i	−0.685382	+	0.728184i	$0.740365\pi$
$920$	−17.3382	−	11.4476i	−0.571623	−	0.377416i
$921$	−6.93725	−	12.0157i	−0.228590	−	0.395930i
$922$			17.2288i			0.567399i
$923$	−30.1671	−	17.4170i	−0.992963	−	0.573287i
$924$	−0.854249	+	1.47960i	−0.0281027	+	0.0486753i
$925$	2.39230	−	19.8564i	0.0786585	−	0.652875i
$926$	13.3542			0.438848
$927$	5.75539	+	3.32288i	0.189032	+	0.109138i
$928$			2.64575i			0.0868510i
$929$	17.2915			0.567316			0.283658	−	0.958926i	$-0.408452\pi$
$929$	17.2915			0.567316			0.283658	+	0.958926i	$0.408452\pi$
$930$	−3.15710	−	12.0430i	−0.103525	−	0.394904i
$931$		0			0
$932$			7.29150i			0.238841i
$933$	10.2836	+	5.93725i	0.336671	+	0.194377i
$934$	26.7490			0.875255
$935$	4.77359	−	7.22993i	0.156113	−	0.236444i
$936$	−2.64575	+	4.58258i	−0.0864791	+	0.149786i
$937$	−5.70105	−	3.29150i	−0.186245	−	0.107529i	0.403978	−	0.914769i	$-0.367627\pi$
$937$	−5.70105	−	3.29150i	−0.186245	−	0.107529i	−0.590224	+	0.807240i	$0.700960\pi$
$938$			29.8745i			0.975437i
$939$	−6.96863	−	12.0700i	−0.227413	−	0.393890i
$940$	11.4476	−	17.3382i	0.373380	−	0.565509i
$941$	16.5516	+	28.6683i	0.539568	+	0.934559i	0.998927	+	0.0463083i	$0.0147457\pi$
$941$	16.5516	+	28.6683i	0.539568	+	0.934559i	−0.459359	+	0.888250i	$0.651921\pi$
$942$	1.11847	+	0.645751i	0.0364419	+	0.0210397i
$943$	−26.4857	+	15.2915i	−0.862492	+	0.497960i
$944$	−0.322876	+	0.559237i	−0.0105087	+	0.0182016i
$945$	−5.29150	+	2.64575i	−0.172133	+	0.0860663i
$946$	7.29150			0.237067
$947$	−3.46410	−	2.00000i	−0.112568	−	0.0649913i	0.442659	−	0.896690i	$-0.354035\pi$
$947$	−3.46410	−	2.00000i	−0.112568	−	0.0649913i	−0.555227	+	0.831699i	$0.687369\pi$
$948$	12.6293	−	7.29150i	0.410179	−	0.236817i
$949$	17.4170	−	30.1671i	0.565380	−	0.979266i
$950$	−3.16472	+	26.2676i	−0.102677	+	0.852232i
$951$	−8.14575	−	14.1089i	−0.264144	−	0.457511i
$952$	−13.7477	+	7.93725i	−0.445566	+	0.257248i
$953$			7.41699i			0.240260i	0.992758	+	0.120130i	$0.0383311\pi$
$953$			7.41699i			0.240260i	−0.992758	+	0.120130i	$0.961669\pi$
$954$	1.14575	−	1.98450i	0.0370951	−	0.0642505i
$955$	−1.07180	+	17.8564i	−0.0346825	+	0.577820i
$956$	−12.2915	−	21.2895i	−0.397536	−	0.688552i
$957$			1.70850i			0.0552279i
$958$	−9.88741	−	5.70850i	−0.319448	−	0.184433i
$959$	28.0000			0.904167
$960$	−1.00000	−	2.00000i	−0.0322749	−	0.0645497i
$961$	−28.3745	−	12.4855i	−0.915307	−	0.402758i
$962$			21.1660i			0.682420i
$963$			5.00000i			0.161123i
$964$	10.5000	−	18.1865i	0.338182	−	0.585749i
$965$	−20.6458	−	41.2915i	−0.664610	−	1.32922i
$966$	12.2915	+	21.2895i	0.395473	+	0.684979i
$967$	22.9129	+	13.2288i	0.736828	+	0.425408i	0.820915	−	0.571050i	$-0.193464\pi$
$967$	22.9129	+	13.2288i	0.736828	+	0.425408i	−0.0840866	+	0.996458i	$0.526797\pi$
$968$	9.16515	+	5.29150i	0.294579	+	0.170075i
$969$	31.7490			1.01993
$970$	−20.9531	−	13.8344i	−0.672765	−	0.444196i
$971$	3.55163	+	6.15161i	0.113977	+	0.197414i	0.917370	−	0.398034i	$-0.130308\pi$
$971$	3.55163	+	6.15161i	0.113977	+	0.197414i	−0.803393	+	0.595449i	$0.796974\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−9.16515	−	5.29150i	−0.293821	−	0.169638i
$974$	−8.61438	−	14.9205i	−0.276022	−	0.478085i
$975$	−10.3930	−	24.3307i	−0.332844	−	0.779207i
$976$	10.0000			0.320092
$977$		−	9.41699i		−	0.301276i	−0.988589	−	0.150638i	$-0.951867\pi$
$977$		−	9.41699i		−	0.301276i	0.988589	−	0.150638i	$-0.0481328\pi$
$978$	−8.66025	−	5.00000i	−0.276924	−	0.159882i
$979$	1.06275	+	1.84073i	0.0339655	+	0.0588300i
$980$		0			0
$981$	−3.35425	−	5.80973i	−0.107093	−	0.185490i
$982$	−25.8177	+	14.9059i	−0.823877	+	0.475666i
$983$	−16.7069	+	9.64575i	−0.532868	+	0.307652i	−0.742184	−	0.670197i	$-0.766210\pi$
$983$	−16.7069	+	9.64575i	−0.532868	+	0.307652i	0.209315	+	0.977848i	$0.432876\pi$
$984$	−3.29150			−0.104929
$985$	−51.7077	−	3.10366i	−1.64754	−	0.0988907i
$986$	−7.93725	+	13.7477i	−0.252774	+	0.437817i
$987$	−21.2895	+	12.2915i	−0.677652	+	0.391243i
$988$		−	28.0000i		−	0.890799i
$989$	52.4575	−	90.8591i	1.66805	−	2.88915i
$990$	−0.645751	−	1.29150i	−0.0205233	−	0.0410466i
$991$	18.5830			0.590309			0.295154	−	0.955450i	$-0.404629\pi$
$991$	18.5830			0.590309			0.295154	+	0.955450i	$0.404629\pi$
$992$	−5.44860	−	1.14575i	−0.172993	−	0.0363776i
$993$			19.1660i			0.608215i
$994$	−17.4170			−0.552434
$995$	2.18265	−	36.3635i	0.0691946	−	1.15280i
$996$	−9.58301			−0.303649
$997$	−29.3362	+	16.9373i	−0.929086	+	0.536408i	−0.886522	−	0.462686i	$-0.846886\pi$
$997$	−29.3362	+	16.9373i	−0.929086	+	0.536408i	−0.0425638	+	0.999094i	$0.513553\pi$
$998$	−14.2526	−	8.22876i	−0.451159	−	0.260477i
$999$	−2.00000	+	3.46410i	−0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.b.439.2	✓	8
5.4	even	2	inner	930.2.s.b.439.3	yes	8
31.25	even	3	inner	930.2.s.b.769.1	yes	8
155.149	even	6	inner	930.2.s.b.769.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.b.439.2	✓	8	1.1	even	1	trivial
930.2.s.b.439.3	yes	8	5.4	even	2	inner
930.2.s.b.769.1	yes	8	31.25	even	3	inner
930.2.s.b.769.4	yes	8	155.149	even	6	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-1.86603 - 1.23205i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.29129 + 1.32288i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(-1.86603 - 1.23205i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.29129 + 1.32288i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.23205 + 1.86603i) q^{10} +(0.322876 + 0.559237i) q^{11} +(0.866025 + 0.500000i) q^{12} +(4.58258 - 2.64575i) q^{13} +(1.32288 - 2.29129i) q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +(5.19615 + 3.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.64575 + 4.58258i) q^{19} +(1.86603 + 1.23205i) q^{20} +(-1.32288 - 2.29129i) q^{21} +(0.559237 - 0.322876i) q^{22} -9.29150i q^{23} +(0.500000 - 0.866025i) q^{24} +(1.96410 + 4.59808i) q^{25} +(-2.64575 - 4.58258i) q^{26} -1.00000i q^{27} +(-2.29129 - 1.32288i) q^{28} -2.64575 q^{29} +(2.00000 - 1.00000i) q^{30} +(1.14575 - 5.44860i) q^{31} -1.00000i q^{32} -0.645751i q^{33} +(3.00000 - 5.19615i) q^{34} +(-2.64575 - 5.29150i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.46410 - 2.00000i) q^{37} +(4.58258 + 2.64575i) q^{38} -5.29150 q^{39} +(1.23205 - 1.86603i) q^{40} +(-1.64575 - 2.85052i) q^{41} +(-2.29129 + 1.32288i) q^{42} +(9.77873 + 5.64575i) q^{43} +(-0.322876 - 0.559237i) q^{44} +(0.133975 - 2.23205i) q^{45} -9.29150 q^{46} -9.29150i q^{47} +(-0.866025 - 0.500000i) q^{48} +(4.59808 - 1.96410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(-4.58258 + 2.64575i) q^{52} +(1.98450 - 1.14575i) q^{53} -1.00000 q^{54} +(0.0865143 - 1.44135i) q^{55} +(-1.32288 + 2.29129i) q^{56} +(4.58258 - 2.64575i) q^{57} +2.64575i q^{58} +(-0.322876 + 0.559237i) q^{59} +(-1.00000 - 2.00000i) q^{60} +10.0000 q^{61} +(-5.44860 - 1.14575i) q^{62} +2.64575i q^{63} -1.00000 q^{64} +(-11.8109 - 0.708927i) q^{65} -0.645751 q^{66} +(-9.77873 + 5.64575i) q^{67} +(-5.19615 - 3.00000i) q^{68} +(-4.64575 + 8.04668i) q^{69} +(-5.29150 + 2.64575i) q^{70} +(-3.29150 - 5.70105i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.70105 - 3.29150i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(0.598076 - 4.96410i) q^{75} +(2.64575 - 4.58258i) q^{76} +1.70850i q^{77} +5.29150i q^{78} +(7.29150 - 12.6293i) q^{79} +(-1.86603 - 1.23205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.85052 + 1.64575i) q^{82} +(-8.29913 + 4.79150i) q^{83} +(1.32288 + 2.29129i) q^{84} +(-6.00000 - 12.0000i) q^{85} +(5.64575 - 9.77873i) q^{86} +(2.29129 + 1.32288i) q^{87} +(-0.559237 + 0.322876i) q^{88} +3.29150 q^{89} +(-2.23205 - 0.133975i) q^{90} +14.0000 q^{91} +9.29150i q^{92} +(-3.71655 + 4.14575i) q^{93} -9.29150 q^{94} +(10.5830 - 5.29150i) q^{95} +(-0.500000 + 0.866025i) q^{96} +11.2288i q^{97} +(-0.322876 + 0.559237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9	\( 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{15} + 8 q^{16} + 8 q^{20} + 4 q^{24} - 12 q^{25} + 16 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{36} - 4 q^{40} + 8 q^{41} + 8 q^{44} + 8 q^{45} - 32 q^{46} + 16 q^{50} - 24 q^{51} - 8 q^{54} - 16 q^{55} + 8 q^{59} - 8 q^{60} + 80 q^{61} - 8 q^{64} + 16 q^{66} - 16 q^{69} + 16 q^{71} - 16 q^{74} - 16 q^{75} + 16 q^{79} - 8 q^{80} - 4 q^{81} - 48 q^{85} + 24 q^{86} - 16 q^{89} - 4 q^{90} + 112 q^{91} - 32 q^{94} - 4 q^{96} + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^15 + 8 * q^16 + 8 * q^20 + 4 * q^24 - 12 * q^25 + 16 * q^30 - 12 * q^31 + 24 * q^34 - 4 * q^36 - 4 * q^40 + 8 * q^41 + 8 * q^44 + 8 * q^45 - 32 * q^46 + 16 * q^50 - 24 * q^51 - 8 * q^54 - 16 * q^55 + 8 * q^59 - 8 * q^60 + 80 * q^61 - 8 * q^64 + 16 * q^66 - 16 * q^69 + 16 * q^71 - 16 * q^74 - 16 * q^75 + 16 * q^79 - 8 * q^80 - 4 * q^81 - 48 * q^85 + 24 * q^86 - 16 * q^89 - 4 * q^90 + 112 * q^91 - 32 * q^94 - 4 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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