LMFDB - Embedded newform 78.2.i.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(43,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("78.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.i (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:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.49
Dual form			78.2.i.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{5} +(0.866025 + 0.500000i) q^{6} +(-4.09808 - 2.36603i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{5} +(0.866025 + 0.500000i) q^{6} +(-4.09808 - 2.36603i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.866025 + 1.50000i) q^{10} +(4.09808 - 2.36603i) q^{11} +1.00000 q^{12} +(-3.59808 - 0.232051i) q^{13} -4.73205 q^{14} +(-1.50000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 + 4.50000i) q^{17} +1.00000i q^{18} +(1.09808 + 0.633975i) q^{19} +(1.50000 + 0.866025i) q^{20} -4.73205i q^{21} +(2.36603 - 4.09808i) q^{22} +(1.09808 + 1.90192i) q^{23} +(0.866025 - 0.500000i) q^{24} +2.00000 q^{25} +(-3.23205 + 1.59808i) q^{26} -1.00000 q^{27} +(-4.09808 + 2.36603i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-0.866025 + 1.50000i) q^{30} -2.53590i q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.09808 + 2.36603i) q^{33} +5.19615i q^{34} +(4.09808 - 7.09808i) q^{35} +(0.500000 + 0.866025i) q^{36} +(2.59808 - 1.50000i) q^{37} +1.26795 q^{38} +(-1.59808 - 3.23205i) q^{39} +1.73205 q^{40} +(0.401924 - 0.232051i) q^{41} +(-2.36603 - 4.09808i) q^{42} +(3.09808 - 5.36603i) q^{43} -4.73205i q^{44} +(-1.50000 - 0.866025i) q^{45} +(1.90192 + 1.09808i) q^{46} -1.26795i q^{47} +(0.500000 - 0.866025i) q^{48} +(7.69615 + 13.3301i) q^{49} +(1.73205 - 1.00000i) q^{50} -5.19615 q^{51} +(-2.00000 + 3.00000i) q^{52} +3.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(4.09808 + 7.09808i) q^{55} +(-2.36603 + 4.09808i) q^{56} +1.26795i q^{57} +(2.59808 + 1.50000i) q^{58} +(-12.0000 - 6.92820i) q^{59} +1.73205i q^{60} +(-2.40192 + 4.16025i) q^{61} +(-1.26795 - 2.19615i) q^{62} +(4.09808 - 2.36603i) q^{63} -1.00000 q^{64} +(0.401924 - 6.23205i) q^{65} +4.73205 q^{66} +(-9.29423 + 5.36603i) q^{67} +(2.59808 + 4.50000i) q^{68} +(-1.09808 + 1.90192i) q^{69} -8.19615i q^{70} +(7.09808 + 4.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} -12.1244i q^{73} +(1.50000 - 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{75} +(1.09808 - 0.633975i) q^{76} -22.3923 q^{77} +(-3.00000 - 2.00000i) q^{78} -12.3923 q^{79} +(1.50000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.232051 - 0.401924i) q^{82} +11.6603i q^{83} +(-4.09808 - 2.36603i) q^{84} +(-7.79423 - 4.50000i) q^{85} -6.19615i q^{86} +(-1.50000 + 2.59808i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(2.19615 - 1.26795i) q^{89} -1.73205 q^{90} +(14.1962 + 9.46410i) q^{91} +2.19615 q^{92} +(2.19615 - 1.26795i) q^{93} +(-0.633975 - 1.09808i) q^{94} +(-1.09808 + 1.90192i) q^{95} -1.00000i q^{96} +(5.19615 + 3.00000i) q^{97} +(13.3301 + 7.69615i) q^{98} +4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{12} - 4 q^{13} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{19} + 6 q^{20} + 6 q^{22} - 6 q^{23} + 8 q^{25} - 6 q^{26} - 4 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{33} + 6 q^{35} + 2 q^{36} + 12 q^{38} + 4 q^{39} + 12 q^{41} - 6 q^{42} + 2 q^{43} - 6 q^{45} + 18 q^{46} + 2 q^{48} + 10 q^{49} - 8 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 48 q^{59} - 20 q^{61} - 12 q^{62} + 6 q^{63} - 4 q^{64} + 12 q^{65} + 12 q^{66} - 6 q^{67} + 6 q^{69} + 18 q^{71} + 6 q^{74} + 4 q^{75} - 6 q^{76} - 48 q^{77} - 12 q^{78} - 8 q^{79} + 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{84} - 6 q^{87} - 6 q^{88} - 12 q^{89} + 36 q^{91} - 12 q^{92} - 12 q^{93} - 6 q^{94} + 6 q^{95} + 36 q^{98}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^12 - 4 * q^13 - 12 * q^14 - 6 * q^15 - 2 * q^16 - 6 * q^19 + 6 * q^20 + 6 * q^22 - 6 * q^23 + 8 * q^25 - 6 * q^26 - 4 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^33 + 6 * q^35 + 2 * q^36 + 12 * q^38 + 4 * q^39 + 12 * q^41 - 6 * q^42 + 2 * q^43 - 6 * q^45 + 18 * q^46 + 2 * q^48 + 10 * q^49 - 8 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 48 * q^59 - 20 * q^61 - 12 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^65 + 12 * q^66 - 6 * q^67 + 6 * q^69 + 18 * q^71 + 6 * q^74 + 4 * q^75 - 6 * q^76 - 48 * q^77 - 12 * q^78 - 8 * q^79 + 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^84 - 6 * q^87 - 6 * q^88 - 12 * q^89 + 36 * q^91 - 12 * q^92 - 12 * q^93 - 6 * q^94 + 6 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.73205i			0.774597i	0.921954	+	0.387298i	$0.126592\pi$
$5$			1.73205i			0.774597i	−0.921954	+	0.387298i	$0.873408\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−4.09808	−	2.36603i	−1.54893	−	0.894274i	−0.998224	−	0.0595724i	$-0.981026\pi$
$7$	−4.09808	−	2.36603i	−1.54893	−	0.894274i	−0.550703	−	0.834701i	$-0.685640\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.866025	+	1.50000i	0.273861	+	0.474342i
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.267421	−	0.963580i	$-0.413828\pi$
$11$	4.09808	−	2.36603i	1.23562	−	0.713384i	0.968195	+	0.250196i	$0.0804951\pi$
$12$	1.00000			0.288675
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$14$	−4.73205			−1.26469
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.59808	+	4.50000i	−0.630126	+	1.09141i	0.357400	+	0.933952i	$0.383663\pi$
$17$	−2.59808	+	4.50000i	−0.630126	+	1.09141i	−0.987526	+	0.157459i	$0.949670\pi$
$18$			1.00000i			0.235702i
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	0.620641	−	0.784095i	$-0.286872\pi$
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	−0.368725	+	0.929538i	$0.620206\pi$
$20$	1.50000	+	0.866025i	0.335410	+	0.193649i
$21$		−	4.73205i		−	1.03262i
$22$	2.36603	−	4.09808i	0.504438	−	0.873713i
$23$	1.09808	+	1.90192i	0.228965	+	0.396579i	0.957502	−	0.288428i	$-0.0931326\pi$
$23$	1.09808	+	1.90192i	0.228965	+	0.396579i	−0.728537	+	0.685007i	$0.759799\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	2.00000			0.400000
$26$	−3.23205	+	1.59808i	−0.633857	+	0.313409i
$27$	−1.00000			−0.192450
$28$	−4.09808	+	2.36603i	−0.774464	+	0.447137i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	−0.866025	+	1.50000i	−0.158114	+	0.273861i
$31$		−	2.53590i		−	0.455461i	−0.973724	−	0.227730i	$-0.926870\pi$
$31$		−	2.53590i		−	0.455461i	0.973724	−	0.227730i	$-0.0731305\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	4.09808	+	2.36603i	0.713384	+	0.411872i
$34$			5.19615i			0.891133i
$35$	4.09808	−	7.09808i	0.692701	−	1.19979i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$	1.26795			0.205689
$39$	−1.59808	−	3.23205i	−0.255897	−	0.517542i
$40$	1.73205			0.273861
$41$	0.401924	−	0.232051i	0.0627700	−	0.0362402i	−0.468287	−	0.883577i	$-0.655129\pi$
$41$	0.401924	−	0.232051i	0.0627700	−	0.0362402i	0.531057	+	0.847336i	$0.321795\pi$
$42$	−2.36603	−	4.09808i	−0.365086	−	0.632347i
$43$	3.09808	−	5.36603i	0.472452	−	0.818311i	−0.527051	−	0.849834i	$-0.676702\pi$
$43$	3.09808	−	5.36603i	0.472452	−	0.818311i	0.999503	+	0.0315225i	$0.0100356\pi$
$44$		−	4.73205i		−	0.713384i
$45$	−1.50000	−	0.866025i	−0.223607	−	0.129099i
$46$	1.90192	+	1.09808i	0.280423	+	0.161903i
$47$		−	1.26795i		−	0.184949i	−0.995715	−	0.0924747i	$-0.970522\pi$
$47$		−	1.26795i		−	0.184949i	0.995715	−	0.0924747i	$-0.0294777\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	7.69615	+	13.3301i	1.09945	+	1.90430i
$50$	1.73205	−	1.00000i	0.244949	−	0.141421i
$51$	−5.19615			−0.727607
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	4.09808	+	7.09808i	0.552584	+	0.957104i
$56$	−2.36603	+	4.09808i	−0.316173	+	0.547628i
$57$			1.26795i			0.167944i
$58$	2.59808	+	1.50000i	0.341144	+	0.196960i
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.997027	−	0.0770484i	$-0.975450\pi$
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.565240	−	0.824927i	$-0.691216\pi$
$60$			1.73205i			0.223607i
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	−0.977822	−	0.209435i	$-0.932837\pi$
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	0.670288	+	0.742101i	$0.266171\pi$
$62$	−1.26795	−	2.19615i	−0.161030	−	0.278912i
$63$	4.09808	−	2.36603i	0.516309	−	0.298091i
$64$	−1.00000			−0.125000
$65$	0.401924	−	6.23205i	0.0498525	−	0.772991i
$66$	4.73205			0.582475
$67$	−9.29423	+	5.36603i	−1.13547	+	0.655564i	−0.945305	−	0.326188i	$-0.894236\pi$
$67$	−9.29423	+	5.36603i	−1.13547	+	0.655564i	−0.190166	+	0.981752i	$0.560903\pi$
$68$	2.59808	+	4.50000i	0.315063	+	0.545705i
$69$	−1.09808	+	1.90192i	−0.132193	+	0.228965i
$70$		−	8.19615i		−	0.979628i
$71$	7.09808	+	4.09808i	0.842387	+	0.486352i	0.858075	−	0.513525i	$-0.171661\pi$
$71$	7.09808	+	4.09808i	0.842387	+	0.486352i	−0.0156881	+	0.999877i	$0.504994\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	12.1244i		−	1.41905i	−0.704681	−	0.709524i	$-0.748910\pi$
$73$		−	12.1244i		−	1.41905i	0.704681	−	0.709524i	$-0.251090\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$	1.09808	−	0.633975i	0.125958	−	0.0727219i
$77$	−22.3923			−2.55184
$78$	−3.00000	−	2.00000i	−0.339683	−	0.226455i
$79$	−12.3923			−1.39424			−0.697122	−	0.716953i	$-0.745536\pi$
$79$	−12.3923			−1.39424			−0.697122	+	0.716953i	$0.745536\pi$
$80$	1.50000	−	0.866025i	0.167705	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.232051	−	0.401924i	0.0256257	−	0.0443851i
$83$			11.6603i			1.27988i	0.768425	+	0.639940i	$0.221041\pi$
$83$			11.6603i			1.27988i	−0.768425	+	0.639940i	$0.778959\pi$
$84$	−4.09808	−	2.36603i	−0.447137	−	0.258155i
$85$	−7.79423	−	4.50000i	−0.845403	−	0.488094i
$86$		−	6.19615i		−	0.668148i
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	−2.36603	−	4.09808i	−0.252219	−	0.436856i
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	−0.379068	−	0.925369i	$-0.623755\pi$
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	0.611859	+	0.790967i	$0.290422\pi$
$90$	−1.73205			−0.182574
$91$	14.1962	+	9.46410i	1.48816	+	0.992107i
$92$	2.19615			0.228965
$93$	2.19615	−	1.26795i	0.227730	−	0.131480i
$94$	−0.633975	−	1.09808i	−0.0653895	−	0.113258i
$95$	−1.09808	+	1.90192i	−0.112660	+	0.195133i
$96$		−	1.00000i		−	0.102062i
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	0.740034	−	0.672569i	$-0.234809\pi$
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	−0.212445	+	0.977173i	$0.568143\pi$
$98$	13.3301	+	7.69615i	1.34655	+	0.777429i
$99$			4.73205i			0.475589i
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−0.696152	−	1.20577i	−0.0692698	−	0.119979i	0.829310	−	0.558788i	$-0.188734\pi$
$101$	−0.696152	−	1.20577i	−0.0692698	−	0.119979i	−0.898580	+	0.438810i	$0.855400\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$	4.19615			0.413459			0.206730	−	0.978398i	$-0.433718\pi$
$103$	4.19615			0.413459			0.206730	+	0.978398i	$0.433718\pi$
$104$	−0.232051	+	3.59808i	−0.0227545	+	0.352820i
$105$	8.19615			0.799863
$106$	2.59808	−	1.50000i	0.252347	−	0.145693i
$107$	−4.09808	−	7.09808i	−0.396176	−	0.686197i	0.597075	−	0.802186i	$-0.296330\pi$
$107$	−4.09808	−	7.09808i	−0.396176	−	0.686197i	−0.993251	+	0.115989i	$0.962996\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$		−	16.3923i		−	1.57010i	−0.619434	−	0.785049i	$-0.712638\pi$
$109$		−	16.3923i		−	1.57010i	0.619434	−	0.785049i	$-0.287362\pi$
$110$	7.09808	+	4.09808i	0.676775	+	0.390736i
$111$	2.59808	+	1.50000i	0.246598	+	0.142374i
$112$			4.73205i			0.447137i
$113$	−5.59808	+	9.69615i	−0.526623	+	0.912137i	0.472896	+	0.881118i	$0.343209\pi$
$113$	−5.59808	+	9.69615i	−0.526623	+	0.912137i	−0.999519	+	0.0310191i	$0.990125\pi$
$114$	0.633975	+	1.09808i	0.0593772	+	0.102844i
$115$	−3.29423	+	1.90192i	−0.307188	+	0.177355i
$116$	3.00000			0.278543
$117$	2.00000	−	3.00000i	0.184900	−	0.277350i
$118$	−13.8564			−1.27559
$119$	21.2942	−	12.2942i	1.95204	−	1.12701i
$120$	0.866025	+	1.50000i	0.0790569	+	0.136931i
$121$	5.69615	−	9.86603i	0.517832	−	0.896911i
$122$			4.80385i			0.434920i
$123$	0.401924	+	0.232051i	0.0362402	+	0.0209233i
$124$	−2.19615	−	1.26795i	−0.197220	−	0.113865i
$125$			12.1244i			1.08444i
$126$	2.36603	−	4.09808i	0.210782	−	0.365086i
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	6.19615			0.545541
$130$	−2.76795	−	5.59808i	−0.242765	−	0.490984i
$131$	16.3923			1.43220			0.716101	−	0.697997i	$-0.245925\pi$
$131$	16.3923			1.43220			0.716101	+	0.697997i	$0.245925\pi$
$132$	4.09808	−	2.36603i	0.356692	−	0.205936i
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$	−5.36603	+	9.29423i	−0.463554	+	0.802899i
$135$		−	1.73205i		−	0.149071i
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	0.794524	−	0.607233i	$-0.207721\pi$
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	−0.128618	+	0.991694i	$0.541054\pi$
$138$			2.19615i			0.186949i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	−4.09808	−	7.09808i	−0.346351	−	0.599897i
$141$	1.09808	−	0.633975i	0.0924747	−	0.0533903i
$142$	8.19615			0.687806
$143$	−15.2942	+	7.56218i	−1.27897	+	0.632381i
$144$	1.00000			0.0833333
$145$	−4.50000	+	2.59808i	−0.373705	+	0.215758i
$146$	−6.06218	−	10.5000i	−0.501709	−	0.868986i
$147$	−7.69615	+	13.3301i	−0.634768	+	1.09945i
$148$		−	3.00000i		−	0.246598i
$149$	−15.6962	−	9.06218i	−1.28588	−	0.742403i	−0.307962	−	0.951399i	$-0.599647\pi$
$149$	−15.6962	−	9.06218i	−1.28588	−	0.742403i	−0.977916	+	0.208996i	$0.932980\pi$
$150$	1.73205	+	1.00000i	0.141421	+	0.0816497i
$151$			7.26795i			0.591457i	0.955272	+	0.295729i	$0.0955624\pi$
$151$			7.26795i			0.591457i	−0.955272	+	0.295729i	$0.904438\pi$
$152$	0.633975	−	1.09808i	0.0514221	−	0.0890657i
$153$	−2.59808	−	4.50000i	−0.210042	−	0.363803i
$154$	−19.3923	+	11.1962i	−1.56268	+	0.902212i
$155$	4.39230			0.352798
$156$	−3.59808	−	0.232051i	−0.288077	−	0.0185789i
$157$	−3.19615			−0.255081			−0.127540	−	0.991833i	$-0.540708\pi$
$157$	−3.19615			−0.255081			−0.127540	+	0.991833i	$0.540708\pi$
$158$	−10.7321	+	6.19615i	−0.853796	+	0.492939i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$	0.866025	−	1.50000i	0.0684653	−	0.118585i
$161$		−	10.3923i		−	0.819028i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−8.19615	−	4.73205i	−0.641972	−	0.370643i	0.143402	−	0.989665i	$-0.454196\pi$
$163$	−8.19615	−	4.73205i	−0.641972	−	0.370643i	−0.785374	+	0.619022i	$0.787529\pi$
$164$		−	0.464102i		−	0.0362402i
$165$	−4.09808	+	7.09808i	−0.319035	+	0.552584i
$166$	5.83013	+	10.0981i	0.452506	+	0.783763i
$167$	−2.19615	+	1.26795i	−0.169943	+	0.0981169i	−0.582559	−	0.812788i	$-0.697949\pi$
$167$	−2.19615	+	1.26795i	−0.169943	+	0.0981169i	0.412616	+	0.910905i	$0.364615\pi$
$168$	−4.73205			−0.365086
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$	−9.00000			−0.690268
$171$	−1.09808	+	0.633975i	−0.0839720	+	0.0484812i
$172$	−3.09808	−	5.36603i	−0.236226	−	0.409156i
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	−0.365755	−	0.930711i	$-0.619189\pi$
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	0.988897	−	0.148602i	$-0.0474774\pi$
$174$			3.00000i			0.227429i
$175$	−8.19615	−	4.73205i	−0.619571	−	0.357709i
$176$	−4.09808	−	2.36603i	−0.308904	−	0.178346i
$177$		−	13.8564i		−	1.04151i
$178$	1.26795	−	2.19615i	0.0950368	−	0.164609i
$179$	−4.09808	−	7.09808i	−0.306305	−	0.530535i	0.671246	−	0.741234i	$-0.265759\pi$
$179$	−4.09808	−	7.09808i	−0.306305	−	0.530535i	−0.977551	+	0.210699i	$0.932426\pi$
$180$	−1.50000	+	0.866025i	−0.111803	+	0.0645497i
$181$	11.5885			0.861363			0.430682	−	0.902504i	$-0.358273\pi$
$181$	11.5885			0.861363			0.430682	+	0.902504i	$0.358273\pi$
$182$	17.0263	+	1.09808i	1.26207	+	0.0813948i
$183$	−4.80385			−0.355111
$184$	1.90192	−	1.09808i	0.140212	−	0.0809513i
$185$	2.59808	+	4.50000i	0.191014	+	0.330847i
$186$	1.26795	−	2.19615i	0.0929705	−	0.161030i
$187$			24.5885i			1.79809i
$188$	−1.09808	−	0.633975i	−0.0800854	−	0.0462373i
$189$	4.09808	+	2.36603i	0.298091	+	0.172103i
$190$			2.19615i			0.159326i
$191$	−10.3923	+	18.0000i	−0.751961	+	1.30243i	0.194910	+	0.980821i	$0.437558\pi$
$191$	−10.3923	+	18.0000i	−0.751961	+	1.30243i	−0.946871	+	0.321613i	$0.895775\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−11.0885	+	6.40192i	−0.798165	+	0.460821i	−0.842829	−	0.538181i	$-0.819111\pi$
$193$	−11.0885	+	6.40192i	−0.798165	+	0.460821i	0.0446644	+	0.999002i	$0.485778\pi$
$194$	6.00000			0.430775
$195$	5.59808	−	2.76795i	0.400887	−	0.198217i
$196$	15.3923			1.09945
$197$	−6.00000	+	3.46410i	−0.427482	+	0.246807i	−0.698273	−	0.715831i	$-0.746048\pi$
$197$	−6.00000	+	3.46410i	−0.427482	+	0.246807i	0.270791	+	0.962638i	$0.412715\pi$
$198$	2.36603	+	4.09808i	0.168146	+	0.291238i
$199$	4.29423	−	7.43782i	0.304410	−	0.527253i	−0.672720	−	0.739897i	$-0.734874\pi$
$199$	4.29423	−	7.43782i	0.304410	−	0.527253i	0.977130	+	0.212644i	$0.0682074\pi$
$200$		−	2.00000i		−	0.141421i
$201$	−9.29423	−	5.36603i	−0.655564	−	0.378490i
$202$	−1.20577	−	0.696152i	−0.0848378	−	0.0489811i
$203$		−	14.1962i		−	0.996375i
$204$	−2.59808	+	4.50000i	−0.181902	+	0.315063i
$205$	0.401924	+	0.696152i	0.0280716	+	0.0486214i
$206$	3.63397	−	2.09808i	0.253191	−	0.146180i
$207$	−2.19615			−0.152643
$208$	1.59808	+	3.23205i	0.110807	+	0.224102i
$209$	6.00000			0.415029
$210$	7.09808	−	4.09808i	0.489814	−	0.282794i
$211$	1.80385	+	3.12436i	0.124182	+	0.215090i	0.921413	−	0.388585i	$-0.127036\pi$
$211$	1.80385	+	3.12436i	0.124182	+	0.215090i	−0.797231	+	0.603674i	$0.793703\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$			8.19615i			0.561591i
$214$	−7.09808	−	4.09808i	−0.485215	−	0.280139i
$215$	9.29423	+	5.36603i	0.633861	+	0.365960i
$216$			1.00000i			0.0680414i
$217$	−6.00000	+	10.3923i	−0.407307	+	0.705476i
$218$	−8.19615	−	14.1962i	−0.555113	−	0.961485i
$219$	10.5000	−	6.06218i	0.709524	−	0.409644i
$220$	8.19615			0.552584
$221$	10.3923	−	15.5885i	0.699062	−	1.04859i
$222$	3.00000			0.201347
$223$	16.3923	−	9.46410i	1.09771	−	0.633763i	0.162091	−	0.986776i	$-0.448176\pi$
$223$	16.3923	−	9.46410i	1.09771	−	0.633763i	0.935619	+	0.353013i	$0.114843\pi$
$224$	2.36603	+	4.09808i	0.158087	+	0.273814i
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$			11.1962i			0.744757i
$227$	−8.49038	−	4.90192i	−0.563526	−	0.325352i	0.191033	−	0.981584i	$-0.438816\pi$
$227$	−8.49038	−	4.90192i	−0.563526	−	0.325352i	−0.754560	+	0.656231i	$0.772149\pi$
$228$	1.09808	+	0.633975i	0.0727219	+	0.0419860i
$229$			19.8564i			1.31215i	0.754696	+	0.656074i	$0.227784\pi$
$229$			19.8564i			1.31215i	−0.754696	+	0.656074i	$0.772216\pi$
$230$	−1.90192	+	3.29423i	−0.125409	+	0.217215i
$231$	−11.1962	−	19.3923i	−0.736653	−	1.27592i
$232$	2.59808	−	1.50000i	0.170572	−	0.0984798i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	0.232051	−	3.59808i	0.0151696	−	0.235214i
$235$	2.19615			0.143261
$236$	−12.0000	+	6.92820i	−0.781133	+	0.450988i
$237$	−6.19615	−	10.7321i	−0.402483	−	0.697122i
$238$	12.2942	−	21.2942i	0.796916	−	1.38030i
$239$			24.5885i			1.59050i	0.606285	+	0.795248i	$0.292659\pi$
$239$			24.5885i			1.59050i	−0.606285	+	0.795248i	$0.707341\pi$
$240$	1.50000	+	0.866025i	0.0968246	+	0.0559017i
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	0.477411	−	0.878680i	$-0.341575\pi$
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	−0.522254	+	0.852790i	$0.674909\pi$
$242$		−	11.3923i		−	0.732325i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.40192	+	4.16025i	0.153767	+	0.266333i
$245$	−23.0885	+	13.3301i	−1.47507	+	0.851631i
$246$	0.464102			0.0295900
$247$	−3.80385	−	2.53590i	−0.242033	−	0.161355i
$248$	−2.53590			−0.161030
$249$	−10.0981	+	5.83013i	−0.639940	+	0.369469i
$250$	6.06218	+	10.5000i	0.383406	+	0.664078i
$251$	−2.19615	+	3.80385i	−0.138620	+	0.240097i	−0.926974	−	0.375124i	$-0.877600\pi$
$251$	−2.19615	+	3.80385i	−0.138620	+	0.240097i	0.788355	+	0.615221i	$0.210933\pi$
$252$		−	4.73205i		−	0.298091i
$253$	9.00000	+	5.19615i	0.565825	+	0.326679i
$254$	−3.46410	−	2.00000i	−0.217357	−	0.125491i
$255$		−	9.00000i		−	0.563602i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.40192	+	11.0885i	0.399341	+	0.691679i	0.993645	−	0.112562i	$-0.0359056\pi$
$257$	6.40192	+	11.0885i	0.399341	+	0.691679i	−0.594304	+	0.804241i	$0.702572\pi$
$258$	5.36603	−	3.09808i	0.334074	−	0.192878i
$259$	−14.1962			−0.882106
$260$	−5.19615	−	3.46410i	−0.322252	−	0.214834i
$261$	−3.00000			−0.185695
$262$	14.1962	−	8.19615i	0.877041	−	0.506360i
$263$	1.09808	+	1.90192i	0.0677103	+	0.117278i	0.897893	−	0.440214i	$-0.145097\pi$
$263$	1.09808	+	1.90192i	0.0677103	+	0.117278i	−0.830183	+	0.557491i	$0.811764\pi$
$264$	2.36603	−	4.09808i	0.145619	−	0.252219i
$265$			5.19615i			0.319197i
$266$	−5.19615	−	3.00000i	−0.318597	−	0.183942i
$267$	2.19615	+	1.26795i	0.134402	+	0.0775972i
$268$			10.7321i			0.655564i
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	−0.000940662	−	1.00000i	$-0.500299\pi$
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	0.866495	−	0.499185i	$-0.166367\pi$
$270$	−0.866025	−	1.50000i	−0.0527046	−	0.0912871i
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$	5.19615			0.315063
$273$	−1.09808	+	17.0263i	−0.0664586	+	1.03048i
$274$	9.00000			0.543710
$275$	8.19615	−	4.73205i	0.494247	−	0.285353i
$276$	1.09808	+	1.90192i	0.0660964	+	0.114482i
$277$	7.59808	−	13.1603i	0.456524	−	0.790723i	−0.542250	−	0.840217i	$-0.682428\pi$
$277$	7.59808	−	13.1603i	0.456524	−	0.790723i	0.998774	+	0.0494940i	$0.0157609\pi$
$278$		−	4.00000i		−	0.239904i
$279$	2.19615	+	1.26795i	0.131480	+	0.0759101i
$280$	−7.09808	−	4.09808i	−0.424191	−	0.244907i
$281$			24.4641i			1.45941i	0.683764	+	0.729703i	$0.260342\pi$
$281$			24.4641i			1.45941i	−0.683764	+	0.729703i	$0.739658\pi$
$282$	0.633975	−	1.09808i	0.0377526	−	0.0653895i
$283$	−15.0981	−	26.1506i	−0.897487	−	1.55449i	−0.830696	−	0.556727i	$-0.812057\pi$
$283$	−15.0981	−	26.1506i	−0.897487	−	1.55449i	−0.0667919	−	0.997767i	$-0.521276\pi$
$284$	7.09808	−	4.09808i	0.421193	−	0.243176i
$285$	−2.19615			−0.130089
$286$	−9.46410	+	14.1962i	−0.559624	+	0.839436i
$287$	−2.19615			−0.129635
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−5.00000	−	8.66025i	−0.294118	−	0.509427i
$290$	−2.59808	+	4.50000i	−0.152564	+	0.264249i
$291$			6.00000i			0.351726i
$292$	−10.5000	−	6.06218i	−0.614466	−	0.354762i
$293$	12.6962	+	7.33013i	0.741717	+	0.428231i	0.822693	−	0.568485i	$-0.192470\pi$
$293$	12.6962	+	7.33013i	0.741717	+	0.428231i	−0.0809762	+	0.996716i	$0.525804\pi$
$294$			15.3923i			0.897697i
$295$	12.0000	−	20.7846i	0.698667	−	1.21013i
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$	−4.09808	+	2.36603i	−0.237795	+	0.137291i
$298$	−18.1244			−1.04992
$299$	−3.50962	−	7.09808i	−0.202967	−	0.410492i
$300$	2.00000			0.115470
$301$	−25.3923	+	14.6603i	−1.46359	+	0.845003i
$302$	3.63397	+	6.29423i	0.209112	+	0.362192i
$303$	0.696152	−	1.20577i	0.0399929	−	0.0692698i
$304$		−	1.26795i		−	0.0727219i
$305$	−7.20577	−	4.16025i	−0.412601	−	0.238215i
$306$	−4.50000	−	2.59808i	−0.257248	−	0.148522i
$307$			10.7321i			0.612510i	0.951949	+	0.306255i	$0.0990761\pi$
$307$			10.7321i			0.612510i	−0.951949	+	0.306255i	$0.900924\pi$
$308$	−11.1962	+	19.3923i	−0.637960	+	1.10498i
$309$	2.09808	+	3.63397i	0.119355	+	0.206730i
$310$	3.80385	−	2.19615i	0.216044	−	0.124733i
$311$	−2.19615			−0.124532			−0.0622662	−	0.998060i	$-0.519833\pi$
$311$	−2.19615			−0.124532			−0.0622662	+	0.998060i	$0.519833\pi$
$312$	−3.23205	+	1.59808i	−0.182979	+	0.0904732i
$313$	−24.3923			−1.37873			−0.689367	−	0.724412i	$-0.742111\pi$
$313$	−24.3923			−1.37873			−0.689367	+	0.724412i	$0.742111\pi$
$314$	−2.76795	+	1.59808i	−0.156204	+	0.0901847i
$315$	4.09808	+	7.09808i	0.230900	+	0.399931i
$316$	−6.19615	+	10.7321i	−0.348561	+	0.603725i
$317$		−	6.12436i		−	0.343978i	−0.985099	−	0.171989i	$-0.944981\pi$
$317$		−	6.12436i		−	0.343978i	0.985099	−	0.171989i	$-0.0550194\pi$
$318$	2.59808	+	1.50000i	0.145693	+	0.0841158i
$319$	12.2942	+	7.09808i	0.688345	+	0.397416i
$320$		−	1.73205i		−	0.0968246i
$321$	4.09808	−	7.09808i	0.228732	−	0.396176i
$322$	−5.19615	−	9.00000i	−0.289570	−	0.501550i
$323$	−5.70577	+	3.29423i	−0.317478	+	0.183296i
$324$	−1.00000			−0.0555556
$325$	−7.19615	−	0.464102i	−0.399171	−	0.0257437i
$326$	−9.46410			−0.524168
$327$	14.1962	−	8.19615i	0.785049	−	0.453248i
$328$	−0.232051	−	0.401924i	−0.0128129	−	0.0221925i
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$			8.19615i			0.451183i
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	0.757634	−	0.652680i	$-0.226355\pi$
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	−0.186421	+	0.982470i	$0.559689\pi$
$332$	10.0981	+	5.83013i	0.554204	+	0.319970i
$333$			3.00000i			0.164399i
$334$	−1.26795	+	2.19615i	−0.0693791	+	0.120168i
$335$	−9.29423	−	16.0981i	−0.507798	−	0.879532i
$336$	−4.09808	+	2.36603i	−0.223568	+	0.129077i
$337$	31.0000			1.68868			0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000			1.68868			0.844339	+	0.535810i	$0.179994\pi$
$338$	12.0000	−	5.00000i	0.652714	−	0.271964i
$339$	−11.1962			−0.608092
$340$	−7.79423	+	4.50000i	−0.422701	+	0.244047i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	−0.633975	+	1.09808i	−0.0342814	+	0.0593772i
$343$		−	39.7128i		−	2.14429i
$344$	−5.36603	−	3.09808i	−0.289317	−	0.167037i
$345$	−3.29423	−	1.90192i	−0.177355	−	0.102396i
$346$		−	16.3923i		−	0.881256i
$347$	6.29423	−	10.9019i	0.337892	−	0.585246i	−0.646144	−	0.763215i	$-0.723620\pi$
$347$	6.29423	−	10.9019i	0.337892	−	0.585246i	0.984036	+	0.177969i	$0.0569528\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	2.19615	−	1.26795i	0.117557	−	0.0678718i	−0.440068	−	0.897964i	$-0.645046\pi$
$349$	2.19615	−	1.26795i	0.117557	−	0.0678718i	0.557626	+	0.830093i	$0.311712\pi$
$350$	−9.46410			−0.505878
$351$	3.59808	+	0.232051i	0.192051	+	0.0123860i
$352$	−4.73205			−0.252219
$353$	−5.00962	+	2.89230i	−0.266635	+	0.153942i	−0.627358	−	0.778731i	$-0.715864\pi$
$353$	−5.00962	+	2.89230i	−0.266635	+	0.153942i	0.360722	+	0.932673i	$0.382530\pi$
$354$	−6.92820	−	12.0000i	−0.368230	−	0.637793i
$355$	−7.09808	+	12.2942i	−0.376727	+	0.652510i
$356$		−	2.53590i		−	0.134402i
$357$	21.2942	+	12.2942i	1.12701	+	0.650680i
$358$	−7.09808	−	4.09808i	−0.375145	−	0.216590i
$359$			22.0526i			1.16389i	0.813228	+	0.581945i	$0.197708\pi$
$359$			22.0526i			1.16389i	−0.813228	+	0.581945i	$0.802292\pi$
$360$	−0.866025	+	1.50000i	−0.0456435	+	0.0790569i
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$	10.0359	−	5.79423i	0.527475	−	0.304538i
$363$	11.3923			0.597941
$364$	15.2942	−	7.56218i	0.801635	−	0.396366i
$365$	21.0000			1.09919
$366$	−4.16025	+	2.40192i	−0.217460	+	0.125551i
$367$	12.0981	+	20.9545i	0.631514	+	1.09382i	0.987242	+	0.159225i	$0.0508997\pi$
$367$	12.0981	+	20.9545i	0.631514	+	1.09382i	−0.355728	+	0.934590i	$0.615767\pi$
$368$	1.09808	−	1.90192i	0.0572412	−	0.0991446i
$369$			0.464102i			0.0241602i
$370$	4.50000	+	2.59808i	0.233944	+	0.135068i
$371$	−12.2942	−	7.09808i	−0.638285	−	0.368514i
$372$		−	2.53590i		−	0.131480i
$373$	−11.9904	+	20.7679i	−0.620838	+	1.07532i	0.368492	+	0.929631i	$0.379874\pi$
$373$	−11.9904	+	20.7679i	−0.620838	+	1.07532i	−0.989330	+	0.145693i	$0.953459\pi$
$374$	12.2942	+	21.2942i	0.635719	+	1.10110i
$375$	−10.5000	+	6.06218i	−0.542218	+	0.313050i
$376$	−1.26795			−0.0653895
$377$	−4.79423	−	9.69615i	−0.246915	−	0.499377i
$378$	4.73205			0.243390
$379$	15.8038	−	9.12436i	0.811789	−	0.468687i	−0.0357877	−	0.999359i	$-0.511394\pi$
$379$	15.8038	−	9.12436i	0.811789	−	0.468687i	0.847577	+	0.530673i	$0.178061\pi$
$380$	1.09808	+	1.90192i	0.0563301	+	0.0975666i
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$			20.7846i			1.06343i
$383$	9.80385	+	5.66025i	0.500953	+	0.289225i	0.729107	−	0.684400i	$-0.239936\pi$
$383$	9.80385	+	5.66025i	0.500953	+	0.289225i	−0.228154	+	0.973625i	$0.573269\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		−	38.7846i		−	1.97665i
$386$	−6.40192	+	11.0885i	−0.325849	+	0.564388i
$387$	3.09808	+	5.36603i	0.157484	+	0.272770i
$388$	5.19615	−	3.00000i	0.263795	−	0.152302i
$389$	13.3923			0.679017			0.339508	−	0.940603i	$-0.389739\pi$
$389$	13.3923			0.679017			0.339508	+	0.940603i	$0.389739\pi$
$390$	3.46410	−	5.19615i	0.175412	−	0.263117i
$391$	−11.4115			−0.577107
$392$	13.3301	−	7.69615i	0.673273	−	0.388714i
$393$	8.19615	+	14.1962i	0.413441	+	0.716101i
$394$	−3.46410	+	6.00000i	−0.174519	+	0.302276i
$395$		−	21.4641i		−	1.07998i
$396$	4.09808	+	2.36603i	0.205936	+	0.118897i
$397$	14.1962	+	8.19615i	0.712484	+	0.411353i	0.811980	−	0.583685i	$-0.198390\pi$
$397$	14.1962	+	8.19615i	0.712484	+	0.411353i	−0.0994958	+	0.995038i	$0.531723\pi$
$398$		−	8.58846i		−	0.430500i
$399$	3.00000	−	5.19615i	0.150188	−	0.260133i
$400$	−1.00000	−	1.73205i	−0.0500000	−	0.0866025i
$401$	18.1865	−	10.5000i	0.908192	−	0.524345i	0.0283431	−	0.999598i	$-0.490977\pi$
$401$	18.1865	−	10.5000i	0.908192	−	0.524345i	0.879849	+	0.475253i	$0.157644\pi$
$402$	−10.7321			−0.535266
$403$	−0.588457	+	9.12436i	−0.0293131	+	0.454517i
$404$	−1.39230			−0.0692698
$405$	1.50000	−	0.866025i	0.0745356	−	0.0430331i
$406$	−7.09808	−	12.2942i	−0.352272	−	0.610152i
$407$	7.09808	−	12.2942i	0.351839	−	0.609402i
$408$			5.19615i			0.257248i
$409$	−2.89230	−	1.66987i	−0.143015	−	0.0825699i	0.426785	−	0.904353i	$-0.359646\pi$
$409$	−2.89230	−	1.66987i	−0.143015	−	0.0825699i	−0.569800	+	0.821783i	$0.692979\pi$
$410$	0.696152	+	0.401924i	0.0343805	+	0.0198496i
$411$			9.00000i			0.443937i
$412$	2.09808	−	3.63397i	0.103365	−	0.179033i
$413$	32.7846	+	56.7846i	1.61323	+	2.79419i
$414$	−1.90192	+	1.09808i	−0.0934745	+	0.0539675i
$415$	−20.1962			−0.991390
$416$	3.00000	+	2.00000i	0.147087	+	0.0980581i
$417$	4.00000			0.195881
$418$	5.19615	−	3.00000i	0.254152	−	0.146735i
$419$	−8.19615	−	14.1962i	−0.400408	−	0.693527i	0.593367	−	0.804932i	$-0.297798\pi$
$419$	−8.19615	−	14.1962i	−0.400408	−	0.693527i	−0.993775	+	0.111405i	$0.964465\pi$
$420$	4.09808	−	7.09808i	0.199966	−	0.346351i
$421$		−	0.464102i		−	0.0226189i	−0.999936	−	0.0113095i	$-0.996400\pi$
$421$		−	0.464102i		−	0.0226189i	0.999936	−	0.0113095i	$-0.00359999\pi$
$422$	3.12436	+	1.80385i	0.152091	+	0.0878099i
$423$	1.09808	+	0.633975i	0.0533903	+	0.0308249i
$424$		−	3.00000i		−	0.145693i
$425$	−5.19615	+	9.00000i	−0.252050	+	0.436564i
$426$	4.09808	+	7.09808i	0.198552	+	0.343903i
$427$	19.6865	−	11.3660i	0.952698	−	0.550041i
$428$	−8.19615			−0.396176
$429$	−14.1962	−	9.46410i	−0.685397	−	0.456931i
$430$	10.7321			0.517545
$431$	−24.0788	+	13.9019i	−1.15984	+	0.669632i	−0.951265	−	0.308375i	$-0.900215\pi$
$431$	−24.0788	+	13.9019i	−1.15984	+	0.669632i	−0.208572	+	0.978007i	$0.566882\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−16.8923	+	29.2583i	−0.811792	+	1.40607i	0.0998161	+	0.995006i	$0.468175\pi$
$433$	−16.8923	+	29.2583i	−0.811792	+	1.40607i	−0.911608	+	0.411060i	$0.865159\pi$
$434$			12.0000i			0.576018i
$435$	−4.50000	−	2.59808i	−0.215758	−	0.124568i
$436$	−14.1962	−	8.19615i	−0.679872	−	0.392525i
$437$			2.78461i			0.133206i
$438$	6.06218	−	10.5000i	0.289662	−	0.501709i
$439$	8.29423	+	14.3660i	0.395862	+	0.685653i	0.993211	−	0.116329i	$-0.0371125\pi$
$439$	8.29423	+	14.3660i	0.395862	+	0.685653i	−0.597349	+	0.801982i	$0.703779\pi$
$440$	7.09808	−	4.09808i	0.338388	−	0.195368i
$441$	−15.3923			−0.732967
$442$	1.20577	−	18.6962i	0.0573527	−	0.889285i
$443$	−4.39230			−0.208685			−0.104342	−	0.994541i	$-0.533274\pi$
$443$	−4.39230			−0.208685			−0.104342	+	0.994541i	$0.533274\pi$
$444$	2.59808	−	1.50000i	0.123299	−	0.0711868i
$445$	2.19615	+	3.80385i	0.104108	+	0.180320i
$446$	9.46410	−	16.3923i	0.448138	−	0.776198i
$447$		−	18.1244i		−	0.857253i
$448$	4.09808	+	2.36603i	0.193616	+	0.111784i
$449$	−28.9808	−	16.7321i	−1.36769	−	0.789634i	−0.377054	−	0.926191i	$-0.623063\pi$
$449$	−28.9808	−	16.7321i	−1.36769	−	0.789634i	−0.990632	+	0.136557i	$0.956396\pi$
$450$			2.00000i			0.0942809i
$451$	1.09808	−	1.90192i	0.0517064	−	0.0895581i
$452$	5.59808	+	9.69615i	0.263311	+	0.456069i
$453$	−6.29423	+	3.63397i	−0.295729	+	0.170739i
$454$	−9.80385			−0.460117
$455$	−16.3923	+	24.5885i	−0.768483	+	1.15272i
$456$	1.26795			0.0593772
$457$	−17.3038	+	9.99038i	−0.809440	+	0.467330i	−0.846761	−	0.531973i	$-0.821451\pi$
$457$	−17.3038	+	9.99038i	−0.809440	+	0.467330i	0.0373215	+	0.999303i	$0.488117\pi$
$458$	9.92820	+	17.1962i	0.463914	+	0.803523i
$459$	2.59808	−	4.50000i	0.121268	−	0.210042i
$460$			3.80385i			0.177355i
$461$	−17.3038	−	9.99038i	−0.805921	−	0.465298i	0.0396167	−	0.999215i	$-0.487386\pi$
$461$	−17.3038	−	9.99038i	−0.805921	−	0.465298i	−0.845537	+	0.533917i	$0.820720\pi$
$462$	−19.3923	−	11.1962i	−0.902212	−	0.520892i
$463$		−	26.1962i		−	1.21744i	−0.793386	−	0.608719i	$-0.791684\pi$
$463$		−	26.1962i		−	1.21744i	0.793386	−	0.608719i	$-0.208316\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	2.19615	+	3.80385i	0.101844	+	0.176399i
$466$	15.5885	−	9.00000i	0.722121	−	0.416917i
$467$	−36.5885			−1.69311			−0.846556	−	0.532300i	$-0.821328\pi$
$467$	−36.5885			−1.69311			−0.846556	+	0.532300i	$0.821328\pi$
$468$	−1.59808	−	3.23205i	−0.0738711	−	0.149402i
$469$	50.7846			2.34502
$470$	1.90192	−	1.09808i	0.0877292	−	0.0506505i
$471$	−1.59808	−	2.76795i	−0.0736355	−	0.127540i
$472$	−6.92820	+	12.0000i	−0.318896	+	0.552345i
$473$		−	29.3205i		−	1.34816i
$474$	−10.7321	−	6.19615i	−0.492939	−	0.284599i
$475$	2.19615	+	1.26795i	0.100766	+	0.0581775i
$476$		−	24.5885i		−	1.12701i
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$	12.2942	+	21.2942i	0.562325	+	0.973975i
$479$	−30.5885	+	17.6603i	−1.39762	+	0.806918i	−0.994143	−	0.108071i	$-0.965533\pi$
$479$	−30.5885	+	17.6603i	−1.39762	+	0.806918i	−0.403479	+	0.914989i	$0.632199\pi$
$480$	1.73205			0.0790569
$481$	−9.69615	+	4.79423i	−0.442106	+	0.218598i
$482$	−0.803848			−0.0366143
$483$	9.00000	−	5.19615i	0.409514	−	0.236433i
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	−5.19615	+	9.00000i	−0.235945	+	0.408669i
$486$		−	1.00000i		−	0.0453609i
$487$	7.90192	+	4.56218i	0.358070	+	0.206732i	0.668234	−	0.743951i	$-0.267051\pi$
$487$	7.90192	+	4.56218i	0.358070	+	0.206732i	−0.310164	+	0.950683i	$0.600384\pi$
$488$	4.16025	+	2.40192i	0.188326	+	0.108730i
$489$		−	9.46410i		−	0.427981i
$490$	−13.3301	+	23.0885i	−0.602194	+	1.04303i
$491$	0.294229	+	0.509619i	0.0132784	+	0.0229988i	0.872588	−	0.488457i	$-0.162440\pi$
$491$	0.294229	+	0.509619i	0.0132784	+	0.0229988i	−0.859310	+	0.511455i	$0.829107\pi$
$492$	0.401924	−	0.232051i	0.0181201	−	0.0104617i
$493$	−15.5885			−0.702069
$494$	−4.56218	−	0.294229i	−0.205262	−	0.0132380i
$495$	−8.19615			−0.368390
$496$	−2.19615	+	1.26795i	−0.0986102	+	0.0569326i
$497$	−19.3923	−	33.5885i	−0.869864	−	1.50665i
$498$	−5.83013	+	10.0981i	−0.261254	+	0.452506i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	10.5000	+	6.06218i	0.469574	+	0.271109i
$501$	−2.19615	−	1.26795i	−0.0981169	−	0.0566478i
$502$			4.39230i			0.196038i
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	−0.580957	−	0.813934i	$-0.697322\pi$
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	0.995366	+	0.0961565i	$0.0306549\pi$
$504$	−2.36603	−	4.09808i	−0.105391	−	0.182543i
$505$	2.08846	−	1.20577i	0.0929351	−	0.0536561i
$506$	10.3923			0.461994
$507$	5.00000	+	12.0000i	0.222058	+	0.532939i
$508$	−4.00000			−0.177471
$509$	−8.08846	+	4.66987i	−0.358515	+	0.206988i	−0.668429	−	0.743776i	$-0.733033\pi$
$509$	−8.08846	+	4.66987i	−0.358515	+	0.206988i	0.309914	+	0.950764i	$0.399700\pi$
$510$	−4.50000	−	7.79423i	−0.199263	−	0.345134i
$511$	−28.6865	+	49.6865i	−1.26902	+	2.19800i
$512$			1.00000i			0.0441942i
$513$	−1.09808	−	0.633975i	−0.0484812	−	0.0279907i
$514$	11.0885	+	6.40192i	0.489091	+	0.282377i
$515$			7.26795i			0.320264i
$516$	3.09808	−	5.36603i	0.136385	−	0.236226i
$517$	−3.00000	−	5.19615i	−0.131940	−	0.228527i
$518$	−12.2942	+	7.09808i	−0.540177	+	0.311872i
$519$	16.3923			0.719542
$520$	−6.23205	−	0.401924i	−0.273294	−	0.0176255i
$521$	−18.8038			−0.823812			−0.411906	−	0.911226i	$-0.635137\pi$
$521$	−18.8038			−0.823812			−0.411906	+	0.911226i	$0.635137\pi$
$522$	−2.59808	+	1.50000i	−0.113715	+	0.0656532i
$523$	−0.705771	−	1.22243i	−0.0308612	−	0.0534532i	0.850182	−	0.526488i	$-0.176492\pi$
$523$	−0.705771	−	1.22243i	−0.0308612	−	0.0534532i	−0.881044	+	0.473035i	$0.843158\pi$
$524$	8.19615	−	14.1962i	0.358051	−	0.620162i
$525$		−	9.46410i		−	0.413047i
$526$	1.90192	+	1.09808i	0.0829278	+	0.0478784i
$527$	11.4115	+	6.58846i	0.497095	+	0.286998i
$528$		−	4.73205i		−	0.205936i
$529$	9.08846	−	15.7417i	0.395150	−	0.684420i
$530$	2.59808	+	4.50000i	0.112853	+	0.195468i
$531$	12.0000	−	6.92820i	0.520756	−	0.300658i
$532$	−6.00000			−0.260133
$533$	−1.50000	+	0.741670i	−0.0649722	+	0.0321253i
$534$	2.53590			0.109739
$535$	12.2942	−	7.09808i	0.531526	−	0.306877i
$536$	5.36603	+	9.29423i	0.231777	+	0.401450i
$537$	4.09808	−	7.09808i	0.176845	−	0.306305i
$538$		−	28.3923i		−	1.22408i
$539$	63.0788	+	36.4186i	2.71700	+	1.56866i
$540$	−1.50000	−	0.866025i	−0.0645497	−	0.0372678i
$541$			16.8564i			0.724714i	0.932039	+	0.362357i	$0.118028\pi$
$541$			16.8564i			0.724714i	−0.932039	+	0.362357i	$0.881972\pi$
$542$		0			0
$543$	5.79423	+	10.0359i	0.248654	+	0.430682i
$544$	4.50000	−	2.59808i	0.192936	−	0.111392i
$545$	28.3923			1.21619
$546$	7.56218	+	15.2942i	0.323631	+	0.654533i
$547$	−6.19615			−0.264928			−0.132464	−	0.991188i	$-0.542289\pi$
$547$	−6.19615			−0.264928			−0.132464	+	0.991188i	$0.542289\pi$
$548$	7.79423	−	4.50000i	0.332953	−	0.192230i
$549$	−2.40192	−	4.16025i	−0.102512	−	0.177555i
$550$	4.73205	−	8.19615i	0.201775	−	0.349485i
$551$			3.80385i			0.162049i
$552$	1.90192	+	1.09808i	0.0809513	+	0.0467372i
$553$	50.7846	+	29.3205i	2.15958	+	1.24683i
$554$		−	15.1962i		−	0.645623i
$555$	−2.59808	+	4.50000i	−0.110282	+	0.191014i
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	19.2846	−	11.1340i	0.817115	−	0.471762i	−0.0323055	−	0.999478i	$-0.510285\pi$
$557$	19.2846	−	11.1340i	0.817115	−	0.471762i	0.849421	+	0.527716i	$0.176952\pi$
$558$	2.53590			0.107353
$559$	−12.3923	+	18.5885i	−0.524139	+	0.786208i
$560$	−8.19615			−0.346351
$561$	−21.2942	+	12.2942i	−0.899043	+	0.519063i
$562$	12.2321	+	21.1865i	0.515978	+	0.893700i
$563$	4.39230	−	7.60770i	0.185114	−	0.320626i	−0.758501	−	0.651672i	$-0.774068\pi$
$563$	4.39230	−	7.60770i	0.185114	−	0.320626i	0.943615	+	0.331046i	$0.107401\pi$
$564$		−	1.26795i		−	0.0533903i
$565$	−16.7942	−	9.69615i	−0.706539	−	0.407920i
$566$	−26.1506	−	15.0981i	−1.09919	−	0.634619i
$567$			4.73205i			0.198727i
$568$	4.09808	−	7.09808i	0.171951	−	0.297829i
$569$	−16.3923	−	28.3923i	−0.687201	−	1.19027i	−0.972740	−	0.231900i	$-0.925506\pi$
$569$	−16.3923	−	28.3923i	−0.687201	−	1.19027i	0.285538	−	0.958367i	$-0.407828\pi$
$570$	−1.90192	+	1.09808i	−0.0796628	+	0.0459934i
$571$	13.8038			0.577673			0.288837	−	0.957378i	$-0.406732\pi$
$571$	13.8038			0.577673			0.288837	+	0.957378i	$0.406732\pi$
$572$	−1.09808	+	17.0263i	−0.0459129	+	0.711905i
$573$	−20.7846			−0.868290
$574$	−1.90192	+	1.09808i	−0.0793848	+	0.0458328i
$575$	2.19615	+	3.80385i	0.0915859	+	0.158631i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			16.2679i			0.677244i	0.940923	+	0.338622i	$0.109961\pi$
$577$			16.2679i			0.677244i	−0.940923	+	0.338622i	$0.890039\pi$
$578$	−8.66025	−	5.00000i	−0.360219	−	0.207973i
$579$	−11.0885	−	6.40192i	−0.460821	−	0.266055i
$580$			5.19615i			0.215758i
$581$	27.5885	−	47.7846i	1.14456	−	1.98244i
$582$	3.00000	+	5.19615i	0.124354	+	0.215387i
$583$	12.2942	−	7.09808i	0.509175	−	0.293972i
$584$	−12.1244			−0.501709
$585$	5.19615	+	3.46410i	0.214834	+	0.143223i
$586$	14.6603			0.605610
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$	7.69615	+	13.3301i	0.317384	+	0.549725i
$589$	1.60770	−	2.78461i	0.0662439	−	0.114738i
$590$		−	24.0000i		−	0.988064i
$591$	−6.00000	−	3.46410i	−0.246807	−	0.142494i
$592$	−2.59808	−	1.50000i	−0.106780	−	0.0616496i
$593$		−	46.8564i		−	1.92416i	−0.272764	−	0.962081i	$-0.587938\pi$
$593$		−	46.8564i		−	1.92416i	0.272764	−	0.962081i	$-0.412062\pi$
$594$	−2.36603	+	4.09808i	−0.0970792	+	0.168146i
$595$	21.2942	+	36.8827i	0.872978	+	1.51204i
$596$	−15.6962	+	9.06218i	−0.642939	+	0.371201i
$597$	8.58846			0.351502
$598$	−6.58846	−	4.39230i	−0.269422	−	0.179615i
$599$	−4.39230			−0.179465			−0.0897324	−	0.995966i	$-0.528601\pi$
$599$	−4.39230			−0.179465			−0.0897324	+	0.995966i	$0.528601\pi$
$600$	1.73205	−	1.00000i	0.0707107	−	0.0408248i
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	0.553697	−	0.832718i	$-0.313216\pi$
$601$	−10.8923	−	18.8660i	−0.444306	−	0.769561i	−0.998004	+	0.0631568i	$0.979883\pi$
$602$	−14.6603	+	25.3923i	−0.597507	+	1.03491i
$603$		−	10.7321i		−	0.437043i
$604$	6.29423	+	3.63397i	0.256109	+	0.147864i
$605$	17.0885	+	9.86603i	0.694745	+	0.401111i
$606$		−	1.39230i		−	0.0565585i
$607$	24.3923	−	42.2487i	0.990053	−	1.71482i	0.373182	−	0.927758i	$-0.378267\pi$
$607$	24.3923	−	42.2487i	0.990053	−	1.71482i	0.616871	−	0.787064i	$-0.288400\pi$
$608$	−0.633975	−	1.09808i	−0.0257111	−	0.0445329i
$609$	12.2942	−	7.09808i	0.498187	−	0.287629i
$610$	−8.32051			−0.336888
$611$	−0.294229	+	4.56218i	−0.0119032	+	0.184566i
$612$	−5.19615			−0.210042
$613$	35.3827	−	20.4282i	1.42909	−	0.825087i	0.432044	−	0.901853i	$-0.357793\pi$
$613$	35.3827	−	20.4282i	1.42909	−	0.825087i	0.997049	+	0.0767652i	$0.0244592\pi$
$614$	5.36603	+	9.29423i	0.216555	+	0.375085i
$615$	−0.401924	+	0.696152i	−0.0162071	+	0.0280716i
$616$			22.3923i			0.902212i
$617$	9.18653	+	5.30385i	0.369836	+	0.213525i	0.673387	−	0.739290i	$-0.264839\pi$
$617$	9.18653	+	5.30385i	0.369836	+	0.213525i	−0.303551	+	0.952815i	$0.598172\pi$
$618$	3.63397	+	2.09808i	0.146180	+	0.0843970i
$619$		−	7.60770i		−	0.305779i	−0.988243	−	0.152890i	$-0.951142\pi$
$619$		−	7.60770i		−	0.305779i	0.988243	−	0.152890i	$-0.0488579\pi$
$620$	2.19615	−	3.80385i	0.0881996	−	0.152766i
$621$	−1.09808	−	1.90192i	−0.0440643	−	0.0763216i
$622$	−1.90192	+	1.09808i	−0.0762602	+	0.0440288i
$623$	−12.0000			−0.480770
$624$	−2.00000	+	3.00000i	−0.0800641	+	0.120096i
$625$	−11.0000			−0.440000
$626$	−21.1244	+	12.1962i	−0.844299	+	0.487456i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	−1.59808	+	2.76795i	−0.0637702	+	0.110453i
$629$			15.5885i			0.621552i
$630$	7.09808	+	4.09808i	0.282794	+	0.163271i
$631$	−22.3923	−	12.9282i	−0.891424	−	0.514664i	−0.0170157	−	0.999855i	$-0.505417\pi$
$631$	−22.3923	−	12.9282i	−0.891424	−	0.514664i	−0.874408	+	0.485192i	$0.838750\pi$
$632$			12.3923i			0.492939i
$633$	−1.80385	+	3.12436i	−0.0716965	+	0.124182i
$634$	−3.06218	−	5.30385i	−0.121615	−	0.210643i
$635$	6.00000	−	3.46410i	0.238103	−	0.137469i
$636$	3.00000			0.118958
$637$	−24.5981	−	49.7487i	−0.974611	−	1.97112i
$638$	14.1962			0.562031
$639$	−7.09808	+	4.09808i	−0.280796	+	0.162117i
$640$	−0.866025	−	1.50000i	−0.0342327	−	0.0592927i
$641$	−15.4019	+	26.6769i	−0.608339	+	1.05367i	0.383175	+	0.923676i	$0.374831\pi$
$641$	−15.4019	+	26.6769i	−0.608339	+	1.05367i	−0.991514	+	0.129999i	$0.958503\pi$
$642$		−	8.19615i		−	0.323476i
$643$	−24.0000	−	13.8564i	−0.946468	−	0.546443i	−0.0544858	−	0.998515i	$-0.517352\pi$
$643$	−24.0000	−	13.8564i	−0.946468	−	0.546443i	−0.891982	+	0.452071i	$0.850685\pi$
$644$	−9.00000	−	5.19615i	−0.354650	−	0.204757i
$645$			10.7321i			0.422574i
$646$	−3.29423	+	5.70577i	−0.129610	+	0.224491i
$647$	6.58846	+	11.4115i	0.259019	+	0.448634i	0.965979	−	0.258619i	$-0.0832674\pi$
$647$	6.58846	+	11.4115i	0.259019	+	0.448634i	−0.706960	+	0.707253i	$0.749934\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−65.5692			−2.57382
$650$	−6.46410	+	3.19615i	−0.253543	+	0.125363i
$651$	−12.0000			−0.470317
$652$	−8.19615	+	4.73205i	−0.320986	+	0.185321i
$653$	24.5885	+	42.5885i	0.962221	+	1.66662i	0.716904	+	0.697172i	$0.245559\pi$
$653$	24.5885	+	42.5885i	0.962221	+	1.66662i	0.245317	+	0.969443i	$0.421108\pi$
$654$	8.19615	−	14.1962i	0.320495	−	0.555113i
$655$			28.3923i			1.10938i
$656$	−0.401924	−	0.232051i	−0.0156925	−	0.00906006i
$657$	10.5000	+	6.06218i	0.409644	+	0.236508i
$658$			6.00000i			0.233904i
$659$	−12.5885	+	21.8038i	−0.490377	+	0.849357i	−0.999939	−	0.0110766i	$-0.996474\pi$
$659$	−12.5885	+	21.8038i	−0.490377	+	0.849357i	0.509562	+	0.860434i	$0.329807\pi$
$660$	4.09808	+	7.09808i	0.159517	+	0.276292i
$661$	7.79423	−	4.50000i	0.303160	−	0.175030i	−0.340701	−	0.940172i	$-0.610665\pi$
$661$	7.79423	−	4.50000i	0.303160	−	0.175030i	0.643862	+	0.765142i	$0.277331\pi$
$662$	12.0000			0.466393
$663$	18.6962	+	1.20577i	0.726098	+	0.0468283i
$664$	11.6603			0.452506
$665$	9.00000	−	5.19615i	0.349005	−	0.201498i
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	−3.29423	+	5.70577i	−0.127553	+	0.220928i
$668$			2.53590i			0.0981169i
$669$	16.3923	+	9.46410i	0.633763	+	0.365903i
$670$	−16.0981	−	9.29423i	−0.621923	−	0.359067i
$671$			22.7321i			0.877561i
$672$	−2.36603	+	4.09808i	−0.0912714	+	0.158087i
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	26.8468	−	15.5000i	1.03410	−	0.597038i
$675$	−2.00000			−0.0769800
$676$	7.89230	−	10.3301i	0.303550	−	0.397313i
$677$	4.39230			0.168810			0.0844050	−	0.996432i	$-0.473101\pi$
$677$	4.39230			0.168810			0.0844050	+	0.996432i	$0.473101\pi$
$678$	−9.69615	+	5.59808i	−0.372378	+	0.214993i
$679$	−14.1962	−	24.5885i	−0.544798	−	0.943618i
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$		−	9.80385i		−	0.375684i
$682$	−10.3923	−	6.00000i	−0.397942	−	0.229752i
$683$	−24.0000	−	13.8564i	−0.918334	−	0.530201i	−0.0352311	−	0.999379i	$-0.511217\pi$
$683$	−24.0000	−	13.8564i	−0.918334	−	0.530201i	−0.883103	+	0.469179i	$0.844550\pi$
$684$			1.26795i			0.0484812i
$685$	−7.79423	+	13.5000i	−0.297802	+	0.515808i
$686$	−19.8564	−	34.3923i	−0.758121	−	1.31310i
$687$	−17.1962	+	9.92820i	−0.656074	+	0.378785i
$688$	−6.19615			−0.236226
$689$	−10.7942	−	0.696152i	−0.411227	−	0.0265213i
$690$	−3.80385			−0.144810
$691$	16.9019	−	9.75833i	0.642979	−	0.371224i	−0.142782	−	0.989754i	$-0.545605\pi$
$691$	16.9019	−	9.75833i	0.642979	−	0.371224i	0.785761	+	0.618530i	$0.212271\pi$
$692$	−8.19615	−	14.1962i	−0.311571	−	0.539657i
$693$	11.1962	−	19.3923i	0.425307	−	0.736653i
$694$		−	12.5885i		−	0.477851i
$695$	6.00000	+	3.46410i	0.227593	+	0.131401i
$696$	2.59808	+	1.50000i	0.0984798	+	0.0568574i
$697$			2.41154i			0.0913437i
$698$	1.26795	−	2.19615i	0.0479926	−	0.0831256i
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$	−8.19615	+	4.73205i	−0.309785	+	0.178855i
$701$	−4.39230			−0.165895			−0.0829475	−	0.996554i	$-0.526433\pi$
$701$	−4.39230			−0.165895			−0.0829475	+	0.996554i	$0.526433\pi$
$702$	3.23205	−	1.59808i	0.121986	−	0.0603155i
$703$	3.80385			0.143465
$704$	−4.09808	+	2.36603i	−0.154452	+	0.0891729i
$705$	1.09808	+	1.90192i	0.0413559	+	0.0716306i
$706$	−2.89230	+	5.00962i	−0.108853	+	0.188539i
$707$			6.58846i			0.247784i
$708$	−12.0000	−	6.92820i	−0.450988	−	0.260378i
$709$	−2.81347	−	1.62436i	−0.105662	−	0.0610040i	0.446238	−	0.894914i	$-0.352764\pi$
$709$	−2.81347	−	1.62436i	−0.105662	−	0.0610040i	−0.551900	+	0.833910i	$0.686097\pi$
$710$			14.1962i			0.532772i
$711$	6.19615	−	10.7321i	0.232374	−	0.402483i
$712$	−1.26795	−	2.19615i	−0.0475184	−	0.0823043i
$713$	4.82309	−	2.78461i	0.180626	−	0.104284i
$714$	24.5885			0.920200
$715$	−13.0981	−	26.4904i	−0.489840	−	0.990684i
$716$	−8.19615			−0.306305
$717$	−21.2942	+	12.2942i	−0.795248	+	0.459136i
$718$	11.0263	+	19.0981i	0.411497	+	0.712734i
$719$	26.1962	−	45.3731i	0.976952	−	1.69213i	0.303613	−	0.952795i	$-0.401807\pi$
$719$	26.1962	−	45.3731i	0.976952	−	1.69213i	0.673338	−	0.739335i	$-0.264860\pi$
$720$			1.73205i			0.0645497i
$721$	−17.1962	−	9.92820i	−0.640418	−	0.369746i
$722$	−15.0622	−	8.69615i	−0.560556	−	0.323637i
$723$		−	0.803848i		−	0.0298954i
$724$	5.79423	−	10.0359i	0.215341	−	0.372981i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	9.86603	−	5.69615i	0.366163	−	0.211404i
$727$	24.1962			0.897386			0.448693	−	0.893686i	$-0.351890\pi$
$727$	24.1962			0.897386			0.448693	+	0.893686i	$0.351890\pi$
$728$	9.46410	−	14.1962i	0.350763	−	0.526144i
$729$	1.00000			0.0370370
$730$	18.1865	−	10.5000i	0.673114	−	0.388622i
$731$	16.0981	+	27.8827i	0.595409	+	1.03128i
$732$	−2.40192	+	4.16025i	−0.0887777	+	0.153767i
$733$			14.3205i			0.528940i	0.964394	+	0.264470i	$0.0851970\pi$
$733$			14.3205i			0.528940i	−0.964394	+	0.264470i	$0.914803\pi$
$734$	20.9545	+	12.0981i	0.773444	+	0.446548i
$735$	−23.0885	−	13.3301i	−0.851631	−	0.491689i
$736$		−	2.19615i		−	0.0809513i
$737$	−25.3923	+	43.9808i	−0.935338	+	1.62005i
$738$	0.232051	+	0.401924i	0.00854191	+	0.0147950i
$739$	−16.3923	+	9.46410i	−0.603001	+	0.348143i	−0.770221	−	0.637777i	$-0.779854\pi$
$739$	−16.3923	+	9.46410i	−0.603001	+	0.348143i	0.167220	+	0.985920i	$0.446521\pi$
$740$	5.19615			0.191014
$741$	0.294229	−	4.56218i	0.0108088	−	0.167596i
$742$	−14.1962			−0.521157
$743$	−3.80385	+	2.19615i	−0.139550	+	0.0805690i	−0.568149	−	0.822925i	$-0.692340\pi$
$743$	−3.80385	+	2.19615i	−0.139550	+	0.0805690i	0.428600	+	0.903494i	$0.359007\pi$
$744$	−1.26795	−	2.19615i	−0.0464853	−	0.0805149i
$745$	15.6962	−	27.1865i	0.575063	−	0.996038i
$746$			23.9808i			0.877998i
$747$	−10.0981	−	5.83013i	−0.369469	−	0.213313i
$748$	21.2942	+	12.2942i	0.778594	+	0.449522i
$749$			38.7846i			1.41716i
$750$	−6.06218	+	10.5000i	−0.221359	+	0.383406i
$751$	−12.4904	−	21.6340i	−0.455780	−	0.789435i	0.542952	−	0.839764i	$-0.317306\pi$
$751$	−12.4904	−	21.6340i	−0.455780	−	0.789435i	−0.998733	+	0.0503286i	$0.983973\pi$
$752$	−1.09808	+	0.633975i	−0.0400427	+	0.0231187i
$753$	−4.39230			−0.160064
$754$	−9.00000	−	6.00000i	−0.327761	−	0.218507i
$755$	−12.5885			−0.458141
$756$	4.09808	−	2.36603i	0.149046	−	0.0860515i
$757$	−9.39230	−	16.2679i	−0.341369	−	0.591269i	0.643318	−	0.765599i	$-0.277557\pi$
$757$	−9.39230	−	16.2679i	−0.341369	−	0.591269i	−0.984687	+	0.174330i	$0.944224\pi$
$758$	9.12436	−	15.8038i	0.331412	−	0.574022i
$759$			10.3923i			0.377217i
$760$	1.90192	+	1.09808i	0.0689900	+	0.0398314i
$761$	3.80385	+	2.19615i	0.137889	+	0.0796105i	0.567358	−	0.823471i	$-0.307966\pi$
$761$	3.80385	+	2.19615i	0.137889	+	0.0796105i	−0.429468	+	0.903082i	$0.641299\pi$
$762$		−	4.00000i		−	0.144905i
$763$	−38.7846	+	67.1769i	−1.40410	+	2.43197i
$764$	10.3923	+	18.0000i	0.375980	+	0.651217i
$765$	7.79423	−	4.50000i	0.281801	−	0.162698i
$766$	11.3205			0.409027
$767$	41.5692	+	27.7128i	1.50098	+	1.00065i
$768$	−1.00000			−0.0360844
$769$	−29.1962	+	16.8564i	−1.05284	+	0.607858i	−0.923443	−	0.383735i	$-0.874638\pi$
$769$	−29.1962	+	16.8564i	−1.05284	+	0.607858i	−0.129397	+	0.991593i	$0.541304\pi$
$770$	−19.3923	−	33.5885i	−0.698850	−	1.21044i
$771$	−6.40192	+	11.0885i	−0.230560	+	0.399341i
$772$			12.8038i			0.460821i
$773$	−43.9808	−	25.3923i	−1.58188	−	0.913298i	−0.994585	−	0.103923i	$-0.966860\pi$
$773$	−43.9808	−	25.3923i	−1.58188	−	0.913298i	−0.587293	−	0.809375i	$-0.699806\pi$
$774$	5.36603	+	3.09808i	0.192878	+	0.111358i
$775$		−	5.07180i		−	0.182184i
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	−7.09808	−	12.2942i	−0.254642	−	0.441053i
$778$	11.5981	−	6.69615i	0.415811	−	0.240069i
$779$	0.588457			0.0210837
$780$	0.401924	−	6.23205i	0.0143912	−	0.223143i
$781$	38.7846			1.38782
$782$	−9.88269	+	5.70577i	−0.353404	+	0.204038i
$783$	−1.50000	−	2.59808i	−0.0536056	−	0.0928477i
$784$	7.69615	−	13.3301i	0.274863	−	0.476076i
$785$		−	5.53590i		−	0.197585i
$786$	14.1962	+	8.19615i	0.506360	+	0.292347i
$787$	12.5885	+	7.26795i	0.448730	+	0.259074i	0.707294	−	0.706920i	$-0.249916\pi$
$787$	12.5885	+	7.26795i	0.448730	+	0.259074i	−0.258564	+	0.965994i	$0.583249\pi$
$788$			6.92820i			0.246807i
$789$	−1.09808	+	1.90192i	−0.0390925	+	0.0677103i
$790$	−10.7321	−	18.5885i	−0.381829	−	0.661348i
$791$	45.8827	−	26.4904i	1.63140	−	0.941890i
$792$	4.73205			0.168146
$793$	9.60770	−	14.4115i	0.341179	−	0.511769i
$794$	16.3923			0.581741
$795$	−4.50000	+	2.59808i	−0.159599	+	0.0921443i
$796$	−4.29423	−	7.43782i	−0.152205	−	0.263627i
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	−0.807989	−	0.589197i	$-0.799444\pi$
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	0.914255	+	0.405140i	$0.132777\pi$
$798$		−	6.00000i		−	0.212398i
$799$	5.70577	+	3.29423i	0.201856	+	0.116541i
$800$	−1.73205	−	1.00000i	−0.0612372	−	0.0353553i
$801$			2.53590i			0.0896016i
$802$	10.5000	−	18.1865i	0.370768	−	0.642189i
$803$	−28.6865	−	49.6865i	−1.01233	−	1.75340i
$804$	−9.29423	+	5.36603i	−0.327782	+	0.189245i
$805$	18.0000			0.634417
$806$	4.05256	+	8.19615i	0.142745	+	0.288697i
$807$	28.3923			0.999456
$808$	−1.20577	+	0.696152i	−0.0424189	+	0.0244906i
$809$	23.5981	+	40.8731i	0.829664	+	1.43702i	0.898302	+	0.439379i	$0.144801\pi$
$809$	23.5981	+	40.8731i	0.829664	+	1.43702i	−0.0686377	+	0.997642i	$0.521865\pi$
$810$	0.866025	−	1.50000i	0.0304290	−	0.0527046i
$811$		−	4.39230i		−	0.154235i	−0.997022	−	0.0771173i	$-0.975428\pi$
$811$		−	4.39230i		−	0.154235i	0.997022	−	0.0771173i	$-0.0245716\pi$
$812$	−12.2942	−	7.09808i	−0.431443	−	0.249094i
$813$		0			0
$814$		−	14.1962i		−	0.497575i
$815$	8.19615	−	14.1962i	0.287099	−	0.497270i
$816$	2.59808	+	4.50000i	0.0909509	+	0.157532i
$817$	6.80385	−	3.92820i	0.238036	−	0.137430i
$818$	−3.33975			−0.116771
$819$	−15.2942	+	7.56218i	−0.534424	+	0.264244i
$820$	0.803848			0.0280716
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.261669	−	0.965158i	$-0.415727\pi$
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.966685	+	0.255967i	$0.0823939\pi$
$822$	4.50000	+	7.79423i	0.156956	+	0.271855i
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$		−	4.19615i		−	0.146180i
$825$	8.19615	+	4.73205i	0.285353	+	0.164749i
$826$	56.7846	+	32.7846i	1.97579	+	1.14072i
$827$		−	32.1051i		−	1.11640i	−0.829705	−	0.558202i	$-0.811491\pi$
$827$		−	32.1051i		−	1.11640i	0.829705	−	0.558202i	$-0.188509\pi$
$828$	−1.09808	+	1.90192i	−0.0381608	+	0.0660964i
$829$	−5.99038	−	10.3756i	−0.208055	−	0.360361i	0.743047	−	0.669239i	$-0.233380\pi$
$829$	−5.99038	−	10.3756i	−0.208055	−	0.360361i	−0.951102	+	0.308878i	$0.900046\pi$
$830$	−17.4904	+	10.0981i	−0.607100	+	0.350509i
$831$	15.1962			0.527149
$832$	3.59808	+	0.232051i	0.124741	+	0.00804491i
$833$	−79.9808			−2.77117
$834$	3.46410	−	2.00000i	0.119952	−	0.0692543i
$835$	−2.19615	−	3.80385i	−0.0760010	−	0.131638i
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$			2.53590i			0.0876535i
$838$	−14.1962	−	8.19615i	−0.490398	−	0.283131i
$839$	10.3923	+	6.00000i	0.358782	+	0.207143i	0.668546	−	0.743670i	$-0.266917\pi$
$839$	10.3923	+	6.00000i	0.358782	+	0.207143i	−0.309764	+	0.950813i	$0.600250\pi$
$840$		−	8.19615i		−	0.282794i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−0.232051	−	0.401924i	−0.00799700	−	0.0138512i
$843$	−21.1865	+	12.2321i	−0.729703	+	0.421294i
$844$	3.60770			0.124182
$845$	−2.89230	+	22.3301i	−0.0994983	+	0.768180i
$846$	1.26795			0.0435930
$847$	−46.6865	+	26.9545i	−1.60417	+	0.926167i
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$	15.0981	−	26.1506i	0.518165	−	0.897487i
$850$			10.3923i			0.356453i
$851$	5.70577	+	3.29423i	0.195591	+	0.112925i
$852$	7.09808	+	4.09808i	0.243176	+	0.140398i
$853$			9.00000i			0.308154i	0.988059	+	0.154077i	$0.0492404\pi$
$853$			9.00000i			0.308154i	−0.988059	+	0.154077i	$0.950760\pi$
$854$	11.3660	−	19.6865i	0.388937	−	0.673659i
$855$	−1.09808	−	1.90192i	−0.0375534	−	0.0650444i
$856$	−7.09808	+	4.09808i	−0.242607	+	0.140069i
$857$	54.3731			1.85735			0.928674	−	0.370896i	$-0.120949\pi$
$857$	54.3731			1.85735			0.928674	+	0.370896i	$0.120949\pi$
$858$	−17.0263	−	1.09808i	−0.581268	−	0.0374877i
$859$	10.5885			0.361273			0.180637	−	0.983550i	$-0.442184\pi$
$859$	10.5885			0.361273			0.180637	+	0.983550i	$0.442184\pi$
$860$	9.29423	−	5.36603i	0.316931	−	0.182980i
$861$	−1.09808	−	1.90192i	−0.0374223	−	0.0648174i
$862$	−13.9019	+	24.0788i	−0.473501	+	0.820128i
$863$		−	4.48334i		−	0.152615i	−0.997084	−	0.0763073i	$-0.975687\pi$
$863$		−	4.48334i		−	0.152615i	0.997084	−	0.0763073i	$-0.0243130\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	24.5885	+	14.1962i	0.836033	+	0.482684i
$866$			33.7846i			1.14805i
$867$	5.00000	−	8.66025i	0.169809	−	0.294118i
$868$	6.00000	+	10.3923i	0.203653	+	0.352738i
$869$	−50.7846	+	29.3205i	−1.72275	+	0.994630i
$870$	−5.19615			−0.176166
$871$	34.6865	−	17.1506i	1.17531	−	0.581127i
$872$	−16.3923			−0.555113
$873$	−5.19615	+	3.00000i	−0.175863	+	0.101535i
$874$	1.39230	+	2.41154i	0.0470954	+	0.0815716i
$875$	28.6865	−	49.6865i	0.969782	−	1.67971i
$876$		−	12.1244i		−	0.409644i
$877$	37.5788	+	21.6962i	1.26895	+	0.732627i	0.974789	−	0.223130i	$-0.0716273\pi$
$877$	37.5788	+	21.6962i	1.26895	+	0.732627i	0.294158	+	0.955757i	$0.404961\pi$
$878$	14.3660	+	8.29423i	0.484830	+	0.279917i
$879$			14.6603i			0.494478i
$880$	4.09808	−	7.09808i	0.138146	−	0.239276i
$881$	18.9904	+	32.8923i	0.639802	+	1.10817i	0.985476	+	0.169815i	$0.0543171\pi$
$881$	18.9904	+	32.8923i	0.639802	+	1.10817i	−0.345674	+	0.938355i	$0.612350\pi$
$882$	−13.3301	+	7.69615i	−0.448849	+	0.259143i
$883$	24.7846			0.834069			0.417034	−	0.908891i	$-0.363070\pi$
$883$	24.7846			0.834069			0.417034	+	0.908891i	$0.363070\pi$
$884$	−8.30385	−	16.7942i	−0.279289	−	0.564851i
$885$	24.0000			0.806751
$886$	−3.80385	+	2.19615i	−0.127793	+	0.0737812i
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$	1.50000	−	2.59808i	0.0503367	−	0.0871857i
$889$			18.9282i			0.634832i
$890$	3.80385	+	2.19615i	0.127505	+	0.0736152i
$891$	−4.09808	−	2.36603i	−0.137291	−	0.0792648i
$892$		−	18.9282i		−	0.633763i
$893$	0.803848	−	1.39230i	0.0268997	−	0.0465917i
$894$	−9.06218	−	15.6962i	−0.303085	−	0.524958i
$895$	12.2942	−	7.09808i	0.410951	−	0.237263i
$896$	4.73205			0.158087
$897$	4.39230	−	6.58846i	0.146655	−	0.219982i
$898$	−33.4641			−1.11671
$899$	6.58846	−	3.80385i	0.219737	−	0.126865i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	−7.79423	+	13.5000i	−0.259663	+	0.449750i
$902$		−	2.19615i		−	0.0731239i
$903$	−25.3923	−	14.6603i	−0.845003	−	0.487863i
$904$	9.69615	+	5.59808i	0.322489	+	0.186189i
$905$			20.0718i			0.667209i
$906$	−3.63397	+	6.29423i	−0.120731	+	0.209112i
$907$	−20.5885	−	35.6603i	−0.683629	−	1.18408i	−0.973866	−	0.227125i	$-0.927068\pi$
$907$	−20.5885	−	35.6603i	−0.683629	−	1.18408i	0.290237	−	0.956955i	$-0.406266\pi$
$908$	−8.49038	+	4.90192i	−0.281763	+	0.162676i
$909$	1.39230			0.0461798
$910$	−1.90192	+	29.4904i	−0.0630482	+	0.977597i
$911$	37.1769			1.23173			0.615863	−	0.787853i	$-0.288807\pi$
$911$	37.1769			1.23173			0.615863	+	0.787853i	$0.288807\pi$
$912$	1.09808	−	0.633975i	0.0363609	−	0.0209930i
$913$	27.5885	+	47.7846i	0.913045	+	1.58144i
$914$	−9.99038	+	17.3038i	−0.330452	+	0.572360i
$915$		−	8.32051i		−	0.275068i
$916$	17.1962	+	9.92820i	0.568177	+	0.328037i
$917$	−67.1769	−	38.7846i	−2.21838	−	1.28078i
$918$		−	5.19615i		−	0.171499i
$919$	−16.1962	+	28.0526i	−0.534262	+	0.925369i	0.464937	+	0.885344i	$0.346077\pi$
$919$	−16.1962	+	28.0526i	−0.534262	+	0.925369i	−0.999199	+	0.0400247i	$0.987256\pi$
$920$	1.90192	+	3.29423i	0.0627046	+	0.108608i
$921$	−9.29423	+	5.36603i	−0.306255	+	0.176817i
$922$	−19.9808			−0.658031
$923$	−24.5885	−	16.3923i	−0.809339	−	0.539559i
$924$	−22.3923			−0.736653
$925$	5.19615	−	3.00000i	0.170848	−	0.0986394i
$926$	−13.0981	−	22.6865i	−0.430429	−	0.745526i
$927$	−2.09808	+	3.63397i	−0.0689099	+	0.119355i
$928$		−	3.00000i		−	0.0984798i
$929$	−29.9711	−	17.3038i	−0.983321	−	0.567721i	−0.0800501	−	0.996791i	$-0.525508\pi$
$929$	−29.9711	−	17.3038i	−0.983321	−	0.567721i	−0.903271	+	0.429070i	$0.858841\pi$
$930$	3.80385	+	2.19615i	0.124733	+	0.0720147i
$931$			19.5167i			0.639633i
$932$	9.00000	−	15.5885i	0.294805	−	0.510617i
$933$	−1.09808	−	1.90192i	−0.0359494	−	0.0622662i
$934$	−31.6865	+	18.2942i	−1.03682	+	0.598605i
$935$	−42.5885			−1.39279
$936$	−3.00000	−	2.00000i	−0.0980581	−	0.0653720i
$937$	5.39230			0.176159			0.0880795	−	0.996113i	$-0.471927\pi$
$937$	5.39230			0.176159			0.0880795	+	0.996113i	$0.471927\pi$
$938$	43.9808	−	25.3923i	1.43602	−	0.829088i
$939$	−12.1962	−	21.1244i	−0.398006	−	0.689367i
$940$	1.09808	−	1.90192i	0.0358153	−	0.0620339i
$941$		−	2.78461i		−	0.0907757i	−0.998969	−	0.0453878i	$-0.985548\pi$
$941$		−	2.78461i		−	0.0907757i	0.998969	−	0.0453878i	$-0.0144524\pi$
$942$	−2.76795	−	1.59808i	−0.0901847	−	0.0520681i
$943$	0.882686	+	0.509619i	0.0287442	+	0.0165955i
$944$			13.8564i			0.450988i
$945$	−4.09808	+	7.09808i	−0.133310	+	0.230900i
$946$	−14.6603	−	25.3923i	−0.476646	−	0.825575i
$947$	−37.1769	+	21.4641i	−1.20809	+	0.697490i	−0.962341	−	0.271845i	$-0.912366\pi$
$947$	−37.1769	+	21.4641i	−1.20809	+	0.697490i	−0.245746	+	0.969334i	$0.579033\pi$
$948$	−12.3923			−0.402483
$949$	−2.81347	+	43.6244i	−0.0913290	+	1.41611i
$950$	2.53590			0.0822754
$951$	5.30385	−	3.06218i	0.171989	−	0.0992979i
$952$	−12.2942	−	21.2942i	−0.398458	−	0.690150i
$953$	−12.0000	+	20.7846i	−0.388718	+	0.673280i	−0.992277	−	0.124039i	$-0.960415\pi$
$953$	−12.0000	+	20.7846i	−0.388718	+	0.673280i	0.603559	+	0.797318i	$0.293749\pi$
$954$			3.00000i			0.0971286i
$955$	−31.1769	−	18.0000i	−1.00886	−	0.582466i
$956$	21.2942	+	12.2942i	0.688705	+	0.397624i
$957$			14.1962i			0.458896i
$958$	−17.6603	+	30.5885i	−0.570577	+	0.988268i
$959$	−21.2942	−	36.8827i	−0.687627	−	1.19100i
$960$	1.50000	−	0.866025i	0.0484123	−	0.0279508i
$961$	24.5692			0.792555
$962$	−6.00000	+	9.00000i	−0.193448	+	0.290172i
$963$	8.19615			0.264117
$964$	−0.696152	+	0.401924i	−0.0224216	+	0.0129451i
$965$	−11.0885	−	19.2058i	−0.356950	−	0.618256i
$966$	5.19615	−	9.00000i	0.167183	−	0.289570i
$967$			14.8756i			0.478368i	0.970974	+	0.239184i	$0.0768800\pi$
$967$			14.8756i			0.478368i	−0.970974	+	0.239184i	$0.923120\pi$
$968$	−9.86603	−	5.69615i	−0.317106	−	0.183081i
$969$	−5.70577	−	3.29423i	−0.183296	−	0.105826i
$970$			10.3923i			0.333677i
$971$	6.58846	−	11.4115i	0.211434	−	0.366214i	−0.740730	−	0.671803i	$-0.765520\pi$
$971$	6.58846	−	11.4115i	0.211434	−	0.366214i	0.952163	+	0.305589i	$0.0988534\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−16.3923	+	9.46410i	−0.525513	+	0.303405i
$974$	9.12436			0.292363
$975$	−3.19615	−	6.46410i	−0.102359	−	0.207017i
$976$	4.80385			0.153767
$977$	14.5981	−	8.42820i	0.467034	−	0.269642i	−0.247963	−	0.968769i	$-0.579761\pi$
$977$	14.5981	−	8.42820i	0.467034	−	0.269642i	0.714997	+	0.699127i	$0.246428\pi$
$978$	−4.73205	−	8.19615i	−0.151314	−	0.262084i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$			26.6603i			0.851631i
$981$	14.1962	+	8.19615i	0.453248	+	0.261683i
$982$	0.509619	+	0.294229i	0.0162626	+	0.00938921i
$983$		−	20.7846i		−	0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$983$		−	20.7846i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$984$	0.232051	−	0.401924i	0.00739751	−	0.0128129i
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$	−13.5000	+	7.79423i	−0.429928	+	0.248219i
$987$	−6.00000			−0.190982
$988$	−4.09808	+	2.02628i	−0.130377	+	0.0644645i
$989$	13.6077			0.432700
$990$	−7.09808	+	4.09808i	−0.225592	+	0.130245i
$991$	−14.6865	−	25.4378i	−0.466533	−	0.808059i	0.532736	−	0.846281i	$-0.321164\pi$
$991$	−14.6865	−	25.4378i	−0.466533	−	0.808059i	−0.999269	+	0.0382223i	$0.987830\pi$
$992$	−1.26795	+	2.19615i	−0.0402574	+	0.0697279i
$993$			12.0000i			0.380808i
$994$	−33.5885	−	19.3923i	−1.06536	−	0.615087i
$995$	12.8827	+	7.43782i	0.408409	+	0.235795i
$996$			11.6603i			0.369469i
$997$	−6.59808	+	11.4282i	−0.208963	+	0.361935i	−0.951388	−	0.307994i	$-0.900342\pi$
$997$	−6.59808	+	11.4282i	−0.208963	+	0.361935i	0.742425	+	0.669929i	$0.233676\pi$
$998$		0			0
$999$	−2.59808	+	1.50000i	−0.0821995	+	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.i.b.49.2	yes	4
3.2	odd	2		234.2.l.a.127.1		4
4.3	odd	2		624.2.bv.d.49.2		4
5.2	odd	4		1950.2.y.h.49.2		4
5.3	odd	4		1950.2.y.a.49.1		4
5.4	even	2		1950.2.bc.c.751.1		4
12.11	even	2		1872.2.by.k.1297.2		4
13.2	odd	12		1014.2.a.j.1.2		2
13.3	even	3		1014.2.b.d.337.4		4
13.4	even	6	inner	78.2.i.b.43.2	✓	4
13.5	odd	4		1014.2.e.h.991.2		4
13.6	odd	12		1014.2.e.h.529.2		4
13.7	odd	12		1014.2.e.j.529.1		4
13.8	odd	4		1014.2.e.j.991.1		4
13.9	even	3		1014.2.i.f.823.1		4
13.10	even	6		1014.2.b.d.337.1		4
13.11	odd	12		1014.2.a.h.1.1		2
13.12	even	2		1014.2.i.f.361.1		4
39.2	even	12		3042.2.a.s.1.1		2
39.11	even	12		3042.2.a.v.1.2		2
39.17	odd	6		234.2.l.a.199.1		4
39.23	odd	6		3042.2.b.l.1351.4		4
39.29	odd	6		3042.2.b.l.1351.1		4
52.11	even	12		8112.2.a.bq.1.1		2
52.15	even	12		8112.2.a.bx.1.2		2
52.43	odd	6		624.2.bv.d.433.2		4
65.4	even	6		1950.2.bc.c.901.1		4
65.17	odd	12		1950.2.y.a.199.1		4
65.43	odd	12		1950.2.y.h.199.2		4
156.95	even	6		1872.2.by.k.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.2	✓	4	13.4	even	6	inner
78.2.i.b.49.2	yes	4	1.1	even	1	trivial
234.2.l.a.127.1		4	3.2	odd	2
234.2.l.a.199.1		4	39.17	odd	6
624.2.bv.d.49.2		4	4.3	odd	2
624.2.bv.d.433.2		4	52.43	odd	6
1014.2.a.h.1.1		2	13.11	odd	12
1014.2.a.j.1.2		2	13.2	odd	12
1014.2.b.d.337.1		4	13.10	even	6
1014.2.b.d.337.4		4	13.3	even	3
1014.2.e.h.529.2		4	13.6	odd	12
1014.2.e.h.991.2		4	13.5	odd	4
1014.2.e.j.529.1		4	13.7	odd	12
1014.2.e.j.991.1		4	13.8	odd	4
1014.2.i.f.361.1		4	13.12	even	2
1014.2.i.f.823.1		4	13.9	even	3
1872.2.by.k.433.2		4	156.95	even	6
1872.2.by.k.1297.2		4	12.11	even	2
1950.2.y.a.49.1		4	5.3	odd	4
1950.2.y.a.199.1		4	65.17	odd	12
1950.2.y.h.49.2		4	5.2	odd	4
1950.2.y.h.199.2		4	65.43	odd	12
1950.2.bc.c.751.1		4	5.4	even	2
1950.2.bc.c.901.1		4	65.4	even	6
3042.2.a.s.1.1		2	39.2	even	12
3042.2.a.v.1.2		2	39.11	even	12
3042.2.b.l.1351.1		4	39.29	odd	6
3042.2.b.l.1351.4		4	39.23	odd	6
8112.2.a.bq.1.1		2	52.11	even	12
8112.2.a.bx.1.2		2	52.15	even	12

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{5} +(0.866025 + 0.500000i) q^{6} +(-4.09808 - 2.36603i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{5} +(0.866025 + 0.500000i) q^{6} +(-4.09808 - 2.36603i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.866025 + 1.50000i) q^{10} +(4.09808 - 2.36603i) q^{11} +1.00000 q^{12} +(-3.59808 - 0.232051i) q^{13} -4.73205 q^{14} +(-1.50000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 + 4.50000i) q^{17} +1.00000i q^{18} +(1.09808 + 0.633975i) q^{19} +(1.50000 + 0.866025i) q^{20} -4.73205i q^{21} +(2.36603 - 4.09808i) q^{22} +(1.09808 + 1.90192i) q^{23} +(0.866025 - 0.500000i) q^{24} +2.00000 q^{25} +(-3.23205 + 1.59808i) q^{26} -1.00000 q^{27} +(-4.09808 + 2.36603i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-0.866025 + 1.50000i) q^{30} -2.53590i q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.09808 + 2.36603i) q^{33} +5.19615i q^{34} +(4.09808 - 7.09808i) q^{35} +(0.500000 + 0.866025i) q^{36} +(2.59808 - 1.50000i) q^{37} +1.26795 q^{38} +(-1.59808 - 3.23205i) q^{39} +1.73205 q^{40} +(0.401924 - 0.232051i) q^{41} +(-2.36603 - 4.09808i) q^{42} +(3.09808 - 5.36603i) q^{43} -4.73205i q^{44} +(-1.50000 - 0.866025i) q^{45} +(1.90192 + 1.09808i) q^{46} -1.26795i q^{47} +(0.500000 - 0.866025i) q^{48} +(7.69615 + 13.3301i) q^{49} +(1.73205 - 1.00000i) q^{50} -5.19615 q^{51} +(-2.00000 + 3.00000i) q^{52} +3.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(4.09808 + 7.09808i) q^{55} +(-2.36603 + 4.09808i) q^{56} +1.26795i q^{57} +(2.59808 + 1.50000i) q^{58} +(-12.0000 - 6.92820i) q^{59} +1.73205i q^{60} +(-2.40192 + 4.16025i) q^{61} +(-1.26795 - 2.19615i) q^{62} +(4.09808 - 2.36603i) q^{63} -1.00000 q^{64} +(0.401924 - 6.23205i) q^{65} +4.73205 q^{66} +(-9.29423 + 5.36603i) q^{67} +(2.59808 + 4.50000i) q^{68} +(-1.09808 + 1.90192i) q^{69} -8.19615i q^{70} +(7.09808 + 4.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} -12.1244i q^{73} +(1.50000 - 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{75} +(1.09808 - 0.633975i) q^{76} -22.3923 q^{77} +(-3.00000 - 2.00000i) q^{78} -12.3923 q^{79} +(1.50000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.232051 - 0.401924i) q^{82} +11.6603i q^{83} +(-4.09808 - 2.36603i) q^{84} +(-7.79423 - 4.50000i) q^{85} -6.19615i q^{86} +(-1.50000 + 2.59808i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(2.19615 - 1.26795i) q^{89} -1.73205 q^{90} +(14.1962 + 9.46410i) q^{91} +2.19615 q^{92} +(2.19615 - 1.26795i) q^{93} +(-0.633975 - 1.09808i) q^{94} +(-1.09808 + 1.90192i) q^{95} -1.00000i q^{96} +(5.19615 + 3.00000i) q^{97} +(13.3301 + 7.69615i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{12} - 4 q^{13} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{19} + 6 q^{20} + 6 q^{22} - 6 q^{23} + 8 q^{25} - 6 q^{26} - 4 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{33} + 6 q^{35} + 2 q^{36} + 12 q^{38} + 4 q^{39} + 12 q^{41} - 6 q^{42} + 2 q^{43} - 6 q^{45} + 18 q^{46} + 2 q^{48} + 10 q^{49} - 8 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 48 q^{59} - 20 q^{61} - 12 q^{62} + 6 q^{63} - 4 q^{64} + 12 q^{65} + 12 q^{66} - 6 q^{67} + 6 q^{69} + 18 q^{71} + 6 q^{74} + 4 q^{75} - 6 q^{76} - 48 q^{77} - 12 q^{78} - 8 q^{79} + 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{84} - 6 q^{87} - 6 q^{88} - 12 q^{89} + 36 q^{91} - 12 q^{92} - 12 q^{93} - 6 q^{94} + 6 q^{95} + 36 q^{98}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^12 - 4 * q^13 - 12 * q^14 - 6 * q^15 - 2 * q^16 - 6 * q^19 + 6 * q^20 + 6 * q^22 - 6 * q^23 + 8 * q^25 - 6 * q^26 - 4 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^33 + 6 * q^35 + 2 * q^36 + 12 * q^38 + 4 * q^39 + 12 * q^41 - 6 * q^42 + 2 * q^43 - 6 * q^45 + 18 * q^46 + 2 * q^48 + 10 * q^49 - 8 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 48 * q^59 - 20 * q^61 - 12 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^65 + 12 * q^66 - 6 * q^67 + 6 * q^69 + 18 * q^71 + 6 * q^74 + 4 * q^75 - 6 * q^76 - 48 * q^77 - 12 * q^78 - 8 * q^79 + 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^84 - 6 * q^87 - 6 * q^88 - 12 * q^89 + 36 * q^91 - 12 * q^92 - 12 * q^93 - 6 * q^94 + 6 * q^95 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more