LMFDB - Embedded newform 370.2.n.d.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(269,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("370.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.n (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:	$2.95446487479$
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			269.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.269
Dual form			370.2.n.d.359.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +3.00000 q^{6} +(1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +3.00000 q^{6} +(1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(-1.00000 - 2.00000i) q^{10} +(-2.59808 - 1.50000i) q^{12} +(-0.866025 + 0.500000i) q^{13} -2.00000 q^{14} +(-6.69615 - 0.401924i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.19615 + 3.00000i) q^{17} +(-5.19615 + 3.00000i) q^{18} +(-0.133975 + 2.23205i) q^{20} +(-3.00000 + 5.19615i) q^{21} +4.00000i q^{23} +(1.50000 + 2.59808i) q^{24} +(1.96410 + 4.59808i) q^{25} +1.00000 q^{26} +9.00000i q^{27} +(1.73205 + 1.00000i) q^{28} +6.00000 q^{29} +(5.59808 + 3.69615i) q^{30} -7.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.00000 - 5.19615i) q^{34} +(4.46410 + 0.267949i) q^{35} +6.00000 q^{36} +(-2.59808 + 5.50000i) q^{37} +(1.50000 - 2.59808i) q^{39} +(1.23205 - 1.86603i) q^{40} +(0.500000 + 0.866025i) q^{41} +(5.19615 - 3.00000i) q^{42} +11.0000i q^{43} +(12.0000 - 6.00000i) q^{45} +(2.00000 - 3.46410i) q^{46} -10.0000i q^{47} -3.00000i q^{48} +(-1.50000 + 2.59808i) q^{49} +(0.598076 - 4.96410i) q^{50} -18.0000 q^{51} +(-0.866025 - 0.500000i) q^{52} +(-4.33013 - 2.50000i) q^{53} +(4.50000 - 7.79423i) q^{54} +(-1.00000 - 1.73205i) q^{56} +(-5.19615 - 3.00000i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-3.00000 - 6.00000i) q^{60} +(3.00000 + 5.19615i) q^{61} +(6.06218 + 3.50000i) q^{62} -12.0000i q^{63} -1.00000 q^{64} +(-2.23205 - 0.133975i) q^{65} +(3.46410 - 2.00000i) q^{67} +6.00000i q^{68} +(-6.00000 - 10.3923i) q^{69} +(-3.73205 - 2.46410i) q^{70} +(6.00000 + 10.3923i) q^{71} +(-5.19615 - 3.00000i) q^{72} -16.0000i q^{73} +(5.00000 - 3.46410i) q^{74} +(-12.0000 - 9.00000i) q^{75} +(-2.59808 + 1.50000i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(-2.00000 + 1.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} -1.00000i q^{82} +(10.3923 + 6.00000i) q^{83} -6.00000 q^{84} +(6.00000 + 12.0000i) q^{85} +(5.50000 - 9.52628i) q^{86} +(-15.5885 + 9.00000i) q^{87} +(9.00000 - 15.5885i) q^{89} +(-13.3923 - 0.803848i) q^{90} +(-1.00000 + 1.73205i) q^{91} +(-3.46410 + 2.00000i) q^{92} +(18.1865 - 10.5000i) q^{93} +(-5.00000 + 8.66025i) q^{94} +(-1.50000 + 2.59808i) q^{96} -2.00000i q^{97} +(2.59808 - 1.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} + 12 q^{6} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5 + 12 * q^6 + 12 * q^9	$ 4 q + 2 q^{4} + 4 q^{5} + 12 q^{6} + 12 q^{9} - 4 q^{10} - 8 q^{14} - 6 q^{15} - 2 q^{16} - 4 q^{20} - 12 q^{21} + 6 q^{24} - 6 q^{25} + 4 q^{26} + 24 q^{29} + 12 q^{30} - 28 q^{31} - 12 q^{34} + 4 q^{35} + 24 q^{36} + 6 q^{39} - 2 q^{40} + 2 q^{41} + 48 q^{45} + 8 q^{46} - 6 q^{49} - 8 q^{50} - 72 q^{51} + 18 q^{54} - 4 q^{56} - 12 q^{59} - 12 q^{60} + 12 q^{61} - 4 q^{64} - 2 q^{65} - 24 q^{69} - 8 q^{70} + 24 q^{71} + 20 q^{74} - 48 q^{75} - 16 q^{79} - 8 q^{80} - 18 q^{81} - 24 q^{84} + 24 q^{85} + 22 q^{86} + 36 q^{89} - 12 q^{90} - 4 q^{91} - 20 q^{94} - 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 + 12 * q^6 + 12 * q^9 - 4 * q^10 - 8 * q^14 - 6 * q^15 - 2 * q^16 - 4 * q^20 - 12 * q^21 + 6 * q^24 - 6 * q^25 + 4 * q^26 + 24 * q^29 + 12 * q^30 - 28 * q^31 - 12 * q^34 + 4 * q^35 + 24 * q^36 + 6 * q^39 - 2 * q^40 + 2 * q^41 + 48 * q^45 + 8 * q^46 - 6 * q^49 - 8 * q^50 - 72 * q^51 + 18 * q^54 - 4 * q^56 - 12 * q^59 - 12 * q^60 + 12 * q^61 - 4 * q^64 - 2 * q^65 - 24 * q^69 - 8 * q^70 + 24 * q^71 + 20 * q^74 - 48 * q^75 - 16 * q^79 - 8 * q^80 - 18 * q^81 - 24 * q^84 + 24 * q^85 + 22 * q^86 + 36 * q^89 - 12 * q^90 - 4 * q^91 - 20 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	−2.59808	+	1.50000i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−2.59808	+	1.50000i	−1.50000	+	0.866025i	−1.00000			$\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$6$	3.00000			1.22474
$7$	1.73205	−	1.00000i	0.654654	−	0.377964i	−0.135583	−	0.990766i	$-0.543291\pi$
$7$	1.73205	−	1.00000i	0.654654	−	0.377964i	0.790237	+	0.612801i	$0.209957\pi$
$8$		−	1.00000i		−	0.353553i
$9$	3.00000	−	5.19615i	1.00000	−	1.73205i
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−2.59808	−	1.50000i	−0.750000	−	0.433013i
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i	−0.615265	−	0.788320i	$-0.710951\pi$
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i	0.375073	+	0.926995i	$0.377618\pi$
$14$	−2.00000			−0.534522
$15$	−6.69615	−	0.401924i	−1.72894	−	0.103776i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	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	$0.407299\pi$
$18$	−5.19615	+	3.00000i	−1.22474	+	0.707107i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−0.133975	+	2.23205i	−0.0299576	+	0.499102i
$21$	−3.00000	+	5.19615i	−0.654654	+	1.13389i
$22$		0			0
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	1.00000			0.196116
$27$			9.00000i			1.73205i
$28$	1.73205	+	1.00000i	0.327327	+	0.188982i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	5.59808	+	3.69615i	1.02206	+	0.674822i
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$	4.46410	+	0.267949i	0.754571	+	0.0452917i
$36$	6.00000			1.00000
$37$	−2.59808	+	5.50000i	−0.427121	+	0.904194i
$37$	−2.59808	+	5.50000i	−0.427121	+	0.904194i
$38$		0			0
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$	1.23205	−	1.86603i	0.194804	−	0.295045i
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	0.902424	−	0.430848i	$-0.141786\pi$
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	−0.824338	+	0.566099i	$0.808452\pi$
$42$	5.19615	−	3.00000i	0.801784	−	0.462910i
$43$			11.0000i			1.67748i	0.544529	+	0.838742i	$0.316708\pi$
$43$			11.0000i			1.67748i	−0.544529	+	0.838742i	$0.683292\pi$
$44$		0			0
$45$	12.0000	−	6.00000i	1.78885	−	0.894427i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$		−	10.0000i		−	1.45865i	−0.684167	−	0.729325i	$-0.739834\pi$
$47$		−	10.0000i		−	1.45865i	0.684167	−	0.729325i	$-0.260166\pi$
$48$		−	3.00000i		−	0.433013i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$	0.598076	−	4.96410i	0.0845807	−	0.702030i
$51$	−18.0000			−2.52050
$52$	−0.866025	−	0.500000i	−0.120096	−	0.0693375i
$53$	−4.33013	−	2.50000i	−0.594789	−	0.343401i	0.172200	−	0.985062i	$-0.444912\pi$
$53$	−4.33013	−	2.50000i	−0.594789	−	0.343401i	−0.766989	+	0.641661i	$0.778246\pi$
$54$	4.50000	−	7.79423i	0.612372	−	1.06066i
$55$		0			0
$56$	−1.00000	−	1.73205i	−0.133631	−	0.231455i
$57$		0			0
$58$	−5.19615	−	3.00000i	−0.682288	−	0.393919i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$	−3.00000	−	6.00000i	−0.387298	−	0.774597i
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	6.06218	+	3.50000i	0.769897	+	0.444500i
$63$		−	12.0000i		−	1.51186i
$64$	−1.00000			−0.125000
$65$	−2.23205	−	0.133975i	−0.276852	−	0.0166175i
$66$		0			0
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	0.696449	+	0.717607i	$0.254762\pi$
$68$			6.00000i			0.727607i
$69$	−6.00000	−	10.3923i	−0.722315	−	1.25109i
$70$	−3.73205	−	2.46410i	−0.446065	−	0.294516i
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$	−5.19615	−	3.00000i	−0.612372	−	0.353553i
$73$		−	16.0000i		−	1.87266i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$		−	16.0000i		−	1.87266i	0.351123	−	0.936329i	$-0.385800\pi$
$74$	5.00000	−	3.46410i	0.581238	−	0.402694i
$75$	−12.0000	−	9.00000i	−1.38564	−	1.03923i
$76$		0			0
$77$		0			0
$78$	−2.59808	+	1.50000i	−0.294174	+	0.169842i
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−2.00000	+	1.00000i	−0.223607	+	0.111803i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		−	1.00000i		−	0.110432i
$83$	10.3923	+	6.00000i	1.14070	+	0.658586i	0.946605	−	0.322396i	$-0.104488\pi$
$83$	10.3923	+	6.00000i	1.14070	+	0.658586i	0.194099	+	0.980982i	$0.437822\pi$
$84$	−6.00000			−0.654654
$85$	6.00000	+	12.0000i	0.650791	+	1.30158i
$86$	5.50000	−	9.52628i	0.593080	−	1.02725i
$87$	−15.5885	+	9.00000i	−1.67126	+	0.964901i
$88$		0			0
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.217354	−	0.976093i	$-0.430258\pi$
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.736644	−	0.676280i	$-0.236409\pi$
$90$	−13.3923	−	0.803848i	−1.41167	−	0.0847330i
$91$	−1.00000	+	1.73205i	−0.104828	+	0.181568i
$92$	−3.46410	+	2.00000i	−0.361158	+	0.208514i
$93$	18.1865	−	10.5000i	1.88586	−	1.08880i
$94$	−5.00000	+	8.66025i	−0.515711	+	0.893237i
$95$		0			0
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$	2.59808	−	1.50000i	0.262445	−	0.151523i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	14.0000			1.39305			0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000			1.39305			0.696526	+	0.717532i	$0.254728\pi$
$102$	15.5885	+	9.00000i	1.54349	+	0.891133i
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	0.500000	+	0.866025i	0.0490290	+	0.0849208i
$105$	−12.0000	+	6.00000i	−1.17108	+	0.585540i
$106$	2.50000	+	4.33013i	0.242821	+	0.420579i
$107$	−9.52628	+	5.50000i	−0.920940	+	0.531705i	−0.883935	−	0.467610i	$-0.845115\pi$
$107$	−9.52628	+	5.50000i	−0.920940	+	0.531705i	−0.0370053	+	0.999315i	$0.511782\pi$
$108$	−7.79423	+	4.50000i	−0.750000	+	0.433013i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$		0			0
$111$	−1.50000	−	18.1865i	−0.142374	−	1.72619i
$112$			2.00000i			0.188982i
$113$	3.46410	+	2.00000i	0.325875	+	0.188144i	0.654008	−	0.756487i	$-0.273086\pi$
$113$	3.46410	+	2.00000i	0.325875	+	0.188144i	−0.328133	+	0.944632i	$0.606419\pi$
$114$		0			0
$115$	−4.92820	+	7.46410i	−0.459557	+	0.696031i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$			6.00000i			0.554700i
$118$	5.19615	−	3.00000i	0.478345	−	0.276172i
$119$	12.0000			1.10004
$120$	−0.401924	+	6.69615i	−0.0366905	+	0.611272i
$121$	−11.0000			−1.00000
$122$		−	6.00000i		−	0.543214i
$123$	−2.59808	−	1.50000i	−0.234261	−	0.135250i
$124$	−3.50000	−	6.06218i	−0.314309	−	0.544400i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	−6.00000	+	10.3923i	−0.534522	+	0.925820i
$127$	8.66025	+	5.00000i	0.768473	+	0.443678i	0.832330	−	0.554281i	$-0.187007\pi$
$127$	8.66025	+	5.00000i	0.768473	+	0.443678i	−0.0638564	+	0.997959i	$0.520340\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−16.5000	−	28.5788i	−1.45274	−	2.51623i
$130$	1.86603	+	1.23205i	0.163661	+	0.108058i
$131$	5.00000	−	8.66025i	0.436852	−	0.756650i	−0.560593	−	0.828092i	$-0.689427\pi$
$131$	5.00000	−	8.66025i	0.436852	−	0.756650i	0.997445	+	0.0714417i	$0.0227600\pi$
$132$		0			0
$133$		0			0
$134$	−4.00000			−0.345547
$135$	−11.0885	+	16.7942i	−0.954342	+	1.44542i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$		−	12.0000i		−	1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$		−	12.0000i		−	1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$			12.0000i			1.02151i
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$	2.00000	+	4.00000i	0.169031	+	0.338062i
$141$	15.0000	+	25.9808i	1.26323	+	2.18797i
$142$		−	12.0000i		−	1.00702i
$143$		0			0
$144$	3.00000	+	5.19615i	0.250000	+	0.433013i
$145$	11.1962	+	7.39230i	0.929790	+	0.613898i
$146$	−8.00000	+	13.8564i	−0.662085	+	1.14676i
$147$		−	9.00000i		−	0.742307i
$148$	−6.06218	+	0.500000i	−0.498308	+	0.0410997i
$149$	−2.00000			−0.163846			−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000			−0.163846			−0.0819232	+	0.996639i	$0.526106\pi$
$150$	5.89230	+	13.7942i	0.481105	+	1.12629i
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	0.687741	−	0.725956i	$-0.258602\pi$
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	−0.972567	+	0.232623i	$0.925269\pi$
$152$		0			0
$153$	31.1769	−	18.0000i	2.52050	−	1.45521i
$154$		0			0
$155$	−13.0622	−	8.62436i	−1.04918	−	0.692725i
$156$	3.00000			0.240192
$157$	−14.7224	−	8.50000i	−1.17498	−	0.678374i	−0.220131	−	0.975470i	$-0.570648\pi$
$157$	−14.7224	−	8.50000i	−1.17498	−	0.678374i	−0.954847	+	0.297097i	$0.903982\pi$
$158$			8.00000i			0.636446i
$159$	15.0000			1.18958
$160$	2.23205	+	0.133975i	0.176459	+	0.0105916i
$161$	4.00000	+	6.92820i	0.315244	+	0.546019i
$162$			9.00000i			0.707107i
$163$	−2.59808	−	1.50000i	−0.203497	−	0.117489i	0.394789	−	0.918772i	$-0.370818\pi$
$163$	−2.59808	−	1.50000i	−0.203497	−	0.117489i	−0.598286	+	0.801283i	$0.704151\pi$
$164$	−0.500000	+	0.866025i	−0.0390434	+	0.0676252i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	6.92820	−	4.00000i	0.536120	−	0.309529i	−0.207385	−	0.978259i	$-0.566495\pi$
$167$	6.92820	−	4.00000i	0.536120	−	0.309529i	0.743505	+	0.668730i	$0.233162\pi$
$168$	5.19615	+	3.00000i	0.400892	+	0.231455i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	0.803848	−	13.3923i	0.0616523	−	1.02714i
$171$		0			0
$172$	−9.52628	+	5.50000i	−0.726372	+	0.419371i
$173$	8.66025	+	5.00000i	0.658427	+	0.380143i	0.791677	−	0.610939i	$-0.209208\pi$
$173$	8.66025	+	5.00000i	0.658427	+	0.380143i	−0.133250	+	0.991082i	$0.542541\pi$
$174$	18.0000			1.36458
$175$	8.00000	+	6.00000i	0.604743	+	0.453557i
$176$		0			0
$177$		−	18.0000i		−	1.35296i
$178$	−15.5885	+	9.00000i	−1.16840	+	0.674579i
$179$	8.00000			0.597948			0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000			0.597948			0.298974	+	0.954261i	$0.403356\pi$
$180$	11.1962	+	7.39230i	0.834512	+	0.550990i
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	0.993598	+	0.112972i	$0.0360369\pi$
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	−0.398963	+	0.916967i	$0.630630\pi$
$182$	1.73205	−	1.00000i	0.128388	−	0.0741249i
$183$	−15.5885	−	9.00000i	−1.15233	−	0.665299i
$184$	4.00000			0.294884
$185$	−11.6244	+	7.06218i	−0.854640	+	0.519222i
$186$	−21.0000			−1.53979
$187$		0			0
$188$	8.66025	−	5.00000i	0.631614	−	0.364662i
$189$	9.00000	+	15.5885i	0.654654	+	1.13389i
$190$		0			0
$191$	13.0000			0.940647			0.470323	−	0.882494i	$-0.344137\pi$
$191$	13.0000			0.940647			0.470323	+	0.882494i	$0.344137\pi$
$192$	2.59808	−	1.50000i	0.187500	−	0.108253i
$193$		−	2.00000i		−	0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$		−	2.00000i		−	0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$	6.00000	−	3.00000i	0.429669	−	0.214834i
$196$	−3.00000			−0.214286
$197$	−11.2583	−	6.50000i	−0.802123	−	0.463106i	0.0420901	−	0.999114i	$-0.486598\pi$
$197$	−11.2583	−	6.50000i	−0.802123	−	0.463106i	−0.844213	+	0.536008i	$0.819932\pi$
$198$		0			0
$199$	−1.00000			−0.0708881			−0.0354441	−	0.999372i	$-0.511285\pi$
$199$	−1.00000			−0.0708881			−0.0354441	+	0.999372i	$0.511285\pi$
$200$	4.59808	−	1.96410i	0.325133	−	0.138883i
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$	−12.1244	−	7.00000i	−0.853067	−	0.492518i
$203$	10.3923	−	6.00000i	0.729397	−	0.421117i
$204$	−9.00000	−	15.5885i	−0.630126	−	1.09141i
$205$	−0.133975	+	2.23205i	−0.00935719	+	0.155893i
$206$	−3.00000	+	5.19615i	−0.209020	+	0.362033i
$207$	20.7846	+	12.0000i	1.44463	+	0.834058i
$208$		−	1.00000i		−	0.0693375i
$209$		0			0
$210$	13.3923	+	0.803848i	0.924157	+	0.0554708i
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$		−	5.00000i		−	0.343401i
$213$	−31.1769	−	18.0000i	−2.13621	−	1.23334i
$214$	11.0000			0.751945
$215$	−13.5526	+	20.5263i	−0.924277	+	1.39988i
$216$	9.00000			0.612372
$217$	−12.1244	+	7.00000i	−0.823055	+	0.475191i
$218$	12.1244	−	7.00000i	0.821165	−	0.474100i
$219$	24.0000	+	41.5692i	1.62177	+	2.80899i
$220$		0			0
$221$	−6.00000			−0.403604
$222$	−7.79423	+	16.5000i	−0.523114	+	1.10741i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	1.00000	−	1.73205i	0.0668153	−	0.115728i
$225$	29.7846	+	3.58846i	1.98564	+	0.239230i
$226$	−2.00000	−	3.46410i	−0.133038	−	0.230429i
$227$	−9.52628	+	5.50000i	−0.632281	+	0.365048i	−0.781635	−	0.623736i	$-0.785614\pi$
$227$	−9.52628	+	5.50000i	−0.632281	+	0.365048i	0.149354	+	0.988784i	$0.452281\pi$
$228$		0			0
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	−0.999442	−	0.0334101i	$-0.989363\pi$
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$230$	8.00000	−	4.00000i	0.527504	−	0.263752i
$231$		0			0
$232$		−	6.00000i		−	0.393919i
$233$			30.0000i			1.96537i	0.185296	+	0.982683i	$0.440675\pi$
$233$			30.0000i			1.96537i	−0.185296	+	0.982683i	$0.559325\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	12.3205	−	18.6603i	0.803701	−	1.21726i
$236$	−6.00000			−0.390567
$237$	20.7846	+	12.0000i	1.35011	+	0.779484i
$238$	−10.3923	−	6.00000i	−0.673633	−	0.388922i
$239$	8.00000	−	13.8564i	0.517477	−	0.896296i	−0.482317	−	0.875997i	$-0.660205\pi$
$239$	8.00000	−	13.8564i	0.517477	−	0.896296i	0.999794	−	0.0202996i	$-0.00646202\pi$
$240$	3.69615	−	5.59808i	0.238586	−	0.361354i
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	−0.965387	−	0.260822i	$-0.916006\pi$
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	0.256814	−	0.966461i	$-0.417327\pi$
$242$	9.52628	+	5.50000i	0.612372	+	0.353553i
$243$		0			0
$244$	−3.00000	+	5.19615i	−0.192055	+	0.332650i
$245$	−6.00000	+	3.00000i	−0.383326	+	0.191663i
$246$	1.50000	+	2.59808i	0.0956365	+	0.165647i
$247$		0			0
$248$			7.00000i			0.444500i
$249$	−36.0000			−2.28141
$250$	7.23205	−	8.52628i	0.457395	−	0.539249i
$251$	8.00000			0.504956			0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000			0.504956			0.252478	+	0.967603i	$0.418755\pi$
$252$	10.3923	−	6.00000i	0.654654	−	0.377964i
$253$		0			0
$254$	−5.00000	−	8.66025i	−0.313728	−	0.543393i
$255$	−33.5885	−	22.1769i	−2.10339	−	1.38877i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−20.7846	−	12.0000i	−1.29651	−	0.748539i	−0.316709	−	0.948523i	$-0.602578\pi$
$257$	−20.7846	−	12.0000i	−1.29651	−	0.748539i	−0.979799	+	0.199983i	$0.935911\pi$
$258$			33.0000i			2.05449i
$259$	1.00000	+	12.1244i	0.0621370	+	0.753371i
$260$	−1.00000	−	2.00000i	−0.0620174	−	0.124035i
$261$	18.0000	−	31.1769i	1.11417	−	1.92980i
$262$	−8.66025	+	5.00000i	−0.535032	+	0.308901i
$263$	3.46410	−	2.00000i	0.213606	−	0.123325i	−0.389380	−	0.921077i	$-0.627311\pi$
$263$	3.46410	−	2.00000i	0.213606	−	0.123325i	0.602986	+	0.797752i	$0.293977\pi$
$264$		0			0
$265$	−5.00000	−	10.0000i	−0.307148	−	0.614295i
$266$		0			0
$267$			54.0000i			3.30475i
$268$	3.46410	+	2.00000i	0.211604	+	0.122169i
$269$	−14.0000			−0.853595			−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000			−0.853595			−0.426798	+	0.904347i	$0.640358\pi$
$270$	18.0000	−	9.00000i	1.09545	−	0.547723i
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	0.850439	+	0.526073i	$0.176336\pi$
$272$	−5.19615	+	3.00000i	−0.315063	+	0.181902i
$273$		−	6.00000i		−	0.363137i
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$	6.00000	−	10.3923i	0.361158	−	0.625543i
$277$	23.3827	−	13.5000i	1.40493	−	0.811136i	0.410036	−	0.912069i	$-0.365516\pi$
$277$	23.3827	−	13.5000i	1.40493	−	0.811136i	0.994893	+	0.100933i	$0.0321827\pi$
$278$	−13.8564	+	8.00000i	−0.831052	+	0.479808i
$279$	−21.0000	+	36.3731i	−1.25724	+	2.17760i
$280$	0.267949	−	4.46410i	0.0160130	−	0.266781i
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	−0.550804	−	0.834634i	$-0.685679\pi$
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	0.998217	+	0.0596933i	$0.0190123\pi$
$282$		−	30.0000i		−	1.78647i
$283$	0.866025	−	0.500000i	0.0514799	−	0.0297219i	−0.474039	−	0.880504i	$-0.657204\pi$
$283$	0.866025	−	0.500000i	0.0514799	−	0.0297219i	0.525519	+	0.850782i	$0.323871\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$		0			0
$287$	1.73205	+	1.00000i	0.102240	+	0.0590281i
$288$		−	6.00000i		−	0.353553i
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$	−6.00000	−	12.0000i	−0.352332	−	0.704664i
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	13.8564	−	8.00000i	0.810885	−	0.468165i
$293$	−7.79423	+	4.50000i	−0.455344	+	0.262893i	−0.710084	−	0.704117i	$-0.751343\pi$
$293$	−7.79423	+	4.50000i	−0.455344	+	0.262893i	0.254741	+	0.967009i	$0.418010\pi$
$294$	−4.50000	+	7.79423i	−0.262445	+	0.454569i
$295$	−12.0000	+	6.00000i	−0.698667	+	0.349334i
$296$	5.50000	+	2.59808i	0.319681	+	0.151010i
$297$		0			0
$298$	1.73205	+	1.00000i	0.100335	+	0.0579284i
$299$	−2.00000	−	3.46410i	−0.115663	−	0.200334i
$300$	1.79423	−	14.8923i	0.103590	−	0.859808i
$301$	11.0000	+	19.0526i	0.634029	+	1.09817i
$302$			7.00000i			0.402805i
$303$	−36.3731	+	21.0000i	−2.08958	+	1.20642i
$304$		0			0
$305$	−0.803848	+	13.3923i	−0.0460282	+	0.766841i
$306$	−36.0000			−2.05798
$307$		−	25.0000i		−	1.42683i	−0.700744	−	0.713413i	$-0.747149\pi$
$307$		−	25.0000i		−	1.42683i	0.700744	−	0.713413i	$-0.252851\pi$
$308$		0			0
$309$	9.00000	+	15.5885i	0.511992	+	0.886796i
$310$	7.00000	+	14.0000i	0.397573	+	0.795147i
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	−0.905416	−	0.424526i	$-0.860441\pi$
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	0.820358	+	0.571850i	$0.193774\pi$
$312$	−2.59808	−	1.50000i	−0.147087	−	0.0849208i
$313$	1.73205	+	1.00000i	0.0979013	+	0.0565233i	0.548151	−	0.836379i	$-0.315332\pi$
$313$	1.73205	+	1.00000i	0.0979013	+	0.0565233i	−0.450250	+	0.892903i	$0.648665\pi$
$314$	8.50000	+	14.7224i	0.479683	+	0.830835i
$315$	14.7846	−	22.3923i	0.833018	−	1.26166i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	−23.3827	−	13.5000i	−1.31330	−	0.758236i	−0.330661	−	0.943750i	$-0.607272\pi$
$317$	−23.3827	−	13.5000i	−1.31330	−	0.758236i	−0.982642	+	0.185514i	$0.940605\pi$
$318$	−12.9904	−	7.50000i	−0.728464	−	0.420579i
$319$		0			0
$320$	−1.86603	−	1.23205i	−0.104314	−	0.0688737i
$321$	16.5000	−	28.5788i	0.920940	−	1.59512i
$322$		−	8.00000i		−	0.445823i
$323$		0			0
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−4.00000	−	3.00000i	−0.221880	−	0.166410i
$326$	1.50000	+	2.59808i	0.0830773	+	0.143894i
$327$		−	42.0000i		−	2.32261i
$328$	0.866025	−	0.500000i	0.0478183	−	0.0276079i
$329$	−10.0000	−	17.3205i	−0.551318	−	0.954911i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$			12.0000i			0.658586i
$333$	20.7846	+	30.0000i	1.13899	+	1.64399i
$334$	−8.00000			−0.437741
$335$	8.92820	+	0.535898i	0.487800	+	0.0292793i
$336$	−3.00000	−	5.19615i	−0.163663	−	0.283473i
$337$	13.8564	−	8.00000i	0.754807	−	0.435788i	−0.0726214	−	0.997360i	$-0.523136\pi$
$337$	13.8564	−	8.00000i	0.754807	−	0.435788i	0.827428	+	0.561572i	$0.189803\pi$
$338$	10.3923	−	6.00000i	0.565267	−	0.326357i
$339$	−12.0000			−0.651751
$340$	−7.39230	+	11.1962i	−0.400904	+	0.607197i
$341$		0			0
$342$		0			0
$343$			20.0000i			1.07990i
$344$	11.0000			0.593080
$345$	1.60770	−	26.7846i	0.0865554	−	1.44203i
$346$	−5.00000	−	8.66025i	−0.268802	−	0.465578i
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$	−15.5885	−	9.00000i	−0.835629	−	0.482451i
$349$	6.00000	−	10.3923i	0.321173	−	0.556287i	−0.659558	−	0.751654i	$-0.729256\pi$
$349$	6.00000	−	10.3923i	0.321173	−	0.556287i	0.980730	+	0.195367i	$0.0625897\pi$
$350$	−3.92820	−	9.19615i	−0.209971	−	0.491555i
$351$	−4.50000	−	7.79423i	−0.240192	−	0.416025i
$352$		0			0
$353$	−15.5885	−	9.00000i	−0.829690	−	0.479022i	0.0240566	−	0.999711i	$-0.492342\pi$
$353$	−15.5885	−	9.00000i	−0.829690	−	0.479022i	−0.853746	+	0.520689i	$0.825675\pi$
$354$	−9.00000	+	15.5885i	−0.478345	+	0.828517i
$355$	−1.60770	+	26.7846i	−0.0853276	+	1.42158i
$356$	18.0000			0.953998
$357$	−31.1769	+	18.0000i	−1.65006	+	0.952661i
$358$	−6.92820	−	4.00000i	−0.366167	−	0.211407i
$359$	−25.0000			−1.31945			−0.659725	−	0.751507i	$-0.729327\pi$
$359$	−25.0000			−1.31945			−0.659725	+	0.751507i	$0.729327\pi$
$360$	−6.00000	−	12.0000i	−0.316228	−	0.632456i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$		−	16.0000i		−	0.840941i
$363$	28.5788	−	16.5000i	1.50000	−	0.866025i
$364$	−2.00000			−0.104828
$365$	19.7128	−	29.8564i	1.03182	−	1.56276i
$366$	9.00000	+	15.5885i	0.470438	+	0.814822i
$367$	12.1244	−	7.00000i	0.632886	−	0.365397i	−0.148983	−	0.988840i	$-0.547600\pi$
$367$	12.1244	−	7.00000i	0.632886	−	0.365397i	0.781869	+	0.623443i	$0.214267\pi$
$368$	−3.46410	−	2.00000i	−0.180579	−	0.104257i
$369$	6.00000			0.312348
$370$	13.5981	−	0.303848i	0.706930	−	0.0157963i
$371$	−10.0000			−0.519174
$372$	18.1865	+	10.5000i	0.942928	+	0.544400i
$373$	9.52628	−	5.50000i	0.493252	−	0.284779i	−0.232671	−	0.972556i	$-0.574746\pi$
$373$	9.52628	−	5.50000i	0.493252	−	0.284779i	0.725923	+	0.687776i	$0.241413\pi$
$374$		0			0
$375$	−11.3038	−	31.5788i	−0.583728	−	1.63072i
$376$	−10.0000			−0.515711
$377$	−5.19615	+	3.00000i	−0.267615	+	0.154508i
$378$		−	18.0000i		−	0.925820i
$379$	18.0000	−	31.1769i	0.924598	−	1.60145i	0.132391	−	0.991198i	$-0.457734\pi$
$379$	18.0000	−	31.1769i	0.924598	−	1.60145i	0.792207	−	0.610253i	$-0.208932\pi$
$380$		0			0
$381$	−30.0000			−1.53695
$382$	−11.2583	−	6.50000i	−0.576026	−	0.332569i
$383$	22.5167	−	13.0000i	1.15055	−	0.664269i	0.201527	−	0.979483i	$-0.435410\pi$
$383$	22.5167	−	13.0000i	1.15055	−	0.664269i	0.949021	+	0.315214i	$0.102076\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	−1.00000	+	1.73205i	−0.0508987	+	0.0881591i
$387$	57.1577	+	33.0000i	2.90549	+	1.67748i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$	−6.69615	−	0.401924i	−0.339073	−	0.0203522i
$391$	−12.0000	+	20.7846i	−0.606866	+	1.05112i
$392$	2.59808	+	1.50000i	0.131223	+	0.0757614i
$393$			30.0000i			1.51330i
$394$	6.50000	+	11.2583i	0.327465	+	0.567186i
$395$	1.07180	−	17.8564i	0.0539279	−	0.898453i
$396$		0			0
$397$		−	17.0000i		−	0.853206i	−0.904439	−	0.426603i	$-0.859710\pi$
$397$		−	17.0000i		−	0.853206i	0.904439	−	0.426603i	$-0.140290\pi$
$398$	0.866025	+	0.500000i	0.0434099	+	0.0250627i
$399$		0			0
$400$	−4.96410	−	0.598076i	−0.248205	−	0.0299038i
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$	10.3923	−	6.00000i	0.518321	−	0.299253i
$403$	6.06218	−	3.50000i	0.301979	−	0.174347i
$404$	7.00000	+	12.1244i	0.348263	+	0.603209i
$405$	1.20577	−	20.0885i	0.0599153	−	0.998203i
$406$	−12.0000			−0.595550
$407$		0			0
$408$			18.0000i			0.891133i
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	1.23205	−	1.86603i	0.0608467	−	0.0921564i
$411$	18.0000	+	31.1769i	0.887875	+	1.53784i
$412$	5.19615	−	3.00000i	0.255996	−	0.147799i
$413$			12.0000i			0.590481i
$414$	−12.0000	−	20.7846i	−0.589768	−	1.02151i
$415$	12.0000	+	24.0000i	0.589057	+	1.17811i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$			48.0000i			2.35057i
$418$		0			0
$419$	−5.00000	+	8.66025i	−0.244266	+	0.423081i	−0.961925	−	0.273314i	$-0.911880\pi$
$419$	−5.00000	+	8.66025i	−0.244266	+	0.423081i	0.717659	+	0.696395i	$0.245214\pi$
$420$	−11.1962	−	7.39230i	−0.546316	−	0.360708i
$421$	−36.0000			−1.75453			−0.877266	−	0.480004i	$-0.840635\pi$
$421$	−36.0000			−1.75453			−0.877266	+	0.480004i	$0.840635\pi$
$422$	8.66025	+	5.00000i	0.421575	+	0.243396i
$423$	−51.9615	−	30.0000i	−2.52646	−	1.45865i
$424$	−2.50000	+	4.33013i	−0.121411	+	0.210290i
$425$	−3.58846	+	29.7846i	−0.174066	+	1.44477i
$426$	18.0000	+	31.1769i	0.872103	+	1.51053i
$427$	10.3923	+	6.00000i	0.502919	+	0.290360i
$428$	−9.52628	−	5.50000i	−0.460470	−	0.265853i
$429$		0			0
$430$	22.0000	−	11.0000i	1.06093	−	0.530467i
$431$	−20.5000	−	35.5070i	−0.987450	−	1.71031i	−0.630497	−	0.776192i	$-0.717149\pi$
$431$	−20.5000	−	35.5070i	−0.987450	−	1.71031i	−0.356953	−	0.934122i	$-0.616185\pi$
$432$	−7.79423	−	4.50000i	−0.375000	−	0.216506i
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$	14.0000			0.672022
$435$	−40.1769	−	2.41154i	−1.92634	−	0.115625i
$436$	−14.0000			−0.670478
$437$		0			0
$438$		−	48.0000i		−	2.29353i
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	0.937380	−	0.348309i	$-0.113244\pi$
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	−0.770334	+	0.637641i	$0.779911\pi$
$440$		0			0
$441$	9.00000	+	15.5885i	0.428571	+	0.742307i
$442$	5.19615	+	3.00000i	0.247156	+	0.142695i
$443$			7.00000i			0.332580i	0.986077	+	0.166290i	$0.0531788\pi$
$443$			7.00000i			0.332580i	−0.986077	+	0.166290i	$0.946821\pi$
$444$	15.0000	−	10.3923i	0.711868	−	0.493197i
$445$	36.0000	−	18.0000i	1.70656	−	0.853282i
$446$	4.00000	−	6.92820i	0.189405	−	0.328060i
$447$	5.19615	−	3.00000i	0.245770	−	0.141895i
$448$	−1.73205	+	1.00000i	−0.0818317	+	0.0472456i
$449$	4.50000	+	7.79423i	0.212368	+	0.367832i	0.952455	−	0.304679i	$-0.0985491\pi$
$449$	4.50000	+	7.79423i	0.212368	+	0.367832i	−0.740087	+	0.672511i	$0.765216\pi$
$450$	−24.0000	−	18.0000i	−1.13137	−	0.848528i
$451$		0			0
$452$			4.00000i			0.188144i
$453$	18.1865	+	10.5000i	0.854478	+	0.493333i
$454$	11.0000			0.516256
$455$	−4.00000	+	2.00000i	−0.187523	+	0.0937614i
$456$		0			0
$457$	−6.92820	+	4.00000i	−0.324088	+	0.187112i	−0.653213	−	0.757174i	$-0.726579\pi$
$457$	−6.92820	+	4.00000i	−0.324088	+	0.187112i	0.329125	+	0.944286i	$0.393246\pi$
$458$			16.0000i			0.747631i
$459$	−27.0000	+	46.7654i	−1.26025	+	2.18282i
$460$	−8.92820	−	0.535898i	−0.416280	−	0.0249864i
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$		0			0
$463$	12.1244	−	7.00000i	0.563467	−	0.325318i	−0.191069	−	0.981577i	$-0.561195\pi$
$463$	12.1244	−	7.00000i	0.563467	−	0.325318i	0.754536	+	0.656259i	$0.227862\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	46.8731	+	2.81347i	2.17369	+	0.130471i
$466$	15.0000	−	25.9808i	0.694862	−	1.20354i
$467$			15.0000i			0.694117i	0.937843	+	0.347059i	$0.112820\pi$
$467$			15.0000i			0.694117i	−0.937843	+	0.347059i	$0.887180\pi$
$468$	−5.19615	+	3.00000i	−0.240192	+	0.138675i
$469$	4.00000	−	6.92820i	0.184703	−	0.319915i
$470$	−20.0000	+	10.0000i	−0.922531	+	0.461266i
$471$	51.0000			2.34996
$472$	5.19615	+	3.00000i	0.239172	+	0.138086i
$473$		0			0
$474$	−12.0000	−	20.7846i	−0.551178	−	0.954669i
$475$		0			0
$476$	6.00000	+	10.3923i	0.275010	+	0.476331i
$477$	−25.9808	+	15.0000i	−1.18958	+	0.686803i
$478$	−13.8564	+	8.00000i	−0.633777	+	0.365911i
$479$	1.50000	−	2.59808i	0.0685367	−	0.118709i	−0.829721	−	0.558179i	$-0.811500\pi$
$479$	1.50000	−	2.59808i	0.0685367	−	0.118709i	0.898257	+	0.439470i	$0.144834\pi$
$480$	−6.00000	+	3.00000i	−0.273861	+	0.136931i
$481$	−0.500000	−	6.06218i	−0.0227980	−	0.276412i
$482$			22.0000i			1.00207i
$483$	−20.7846	−	12.0000i	−0.945732	−	0.546019i
$484$	−5.50000	−	9.52628i	−0.250000	−	0.433013i
$485$	2.46410	−	3.73205i	0.111889	−	0.169464i
$486$		0			0
$487$			42.0000i			1.90320i	0.307337	+	0.951601i	$0.400562\pi$
$487$			42.0000i			1.90320i	−0.307337	+	0.951601i	$0.599438\pi$
$488$	5.19615	−	3.00000i	0.235219	−	0.135804i
$489$	9.00000			0.406994
$490$	6.69615	+	0.401924i	0.302501	+	0.0181571i
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$		−	3.00000i		−	0.135250i
$493$	31.1769	+	18.0000i	1.40414	+	0.810679i
$494$		0			0
$495$		0			0
$496$	3.50000	−	6.06218i	0.157155	−	0.272200i
$497$	20.7846	+	12.0000i	0.932317	+	0.538274i
$498$	31.1769	+	18.0000i	1.39707	+	0.806599i
$499$	18.0000	+	31.1769i	0.805791	+	1.39567i	0.915756	+	0.401735i	$0.131593\pi$
$499$	18.0000	+	31.1769i	0.805791	+	1.39567i	−0.109965	+	0.993935i	$0.535074\pi$
$500$	−10.5263	+	3.76795i	−0.470750	+	0.168508i
$501$	−12.0000	+	20.7846i	−0.536120	+	0.928588i
$502$	−6.92820	−	4.00000i	−0.309221	−	0.178529i
$503$	−3.46410	−	2.00000i	−0.154457	−	0.0891756i	0.420780	−	0.907163i	$-0.361757\pi$
$503$	−3.46410	−	2.00000i	−0.154457	−	0.0891756i	−0.575236	+	0.817987i	$0.695090\pi$
$504$	−12.0000			−0.534522
$505$	26.1244	+	17.2487i	1.16252	+	0.767558i
$506$		0			0
$507$		−	36.0000i		−	1.59882i
$508$			10.0000i			0.443678i
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$	18.0000	+	36.0000i	0.797053	+	1.59411i
$511$	−16.0000	−	27.7128i	−0.707798	−	1.22594i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	12.0000	+	20.7846i	0.529297	+	0.916770i
$515$	7.39230	−	11.1962i	0.325744	−	0.493361i
$516$	16.5000	−	28.5788i	0.726372	−	1.25811i
$517$		0			0
$518$	5.19615	−	11.0000i	0.228306	−	0.483312i
$519$	−30.0000			−1.31685
$520$	−0.133975	+	2.23205i	−0.00587517	+	0.0978819i
$521$	3.50000	+	6.06218i	0.153338	+	0.265589i	0.932453	−	0.361293i	$-0.117664\pi$
$521$	3.50000	+	6.06218i	0.153338	+	0.265589i	−0.779115	+	0.626881i	$0.784331\pi$
$522$	−31.1769	+	18.0000i	−1.36458	+	0.787839i
$523$	16.4545	−	9.50000i	0.719504	−	0.415406i	−0.0950659	−	0.995471i	$-0.530306\pi$
$523$	16.4545	−	9.50000i	0.719504	−	0.415406i	0.814570	+	0.580065i	$0.196973\pi$
$524$	10.0000			0.436852
$525$	−29.7846	−	3.58846i	−1.29991	−	0.156613i
$526$	−4.00000			−0.174408
$527$	−36.3731	−	21.0000i	−1.58444	−	0.914774i
$528$		0			0
$529$	7.00000			0.304348
$530$	−0.669873	+	11.1603i	−0.0290974	+	0.484770i
$531$	18.0000	+	31.1769i	0.781133	+	1.35296i
$532$		0			0
$533$	−0.866025	−	0.500000i	−0.0375117	−	0.0216574i
$534$	27.0000	−	46.7654i	1.16840	−	2.02374i
$535$	−24.5526	−	1.47372i	−1.06150	−	0.0637145i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−20.7846	+	12.0000i	−0.896922	+	0.517838i
$538$	12.1244	+	7.00000i	0.522718	+	0.301791i
$539$		0			0
$540$	−20.0885	−	1.20577i	−0.864470	−	0.0518881i
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	0.866025	−	0.500000i	0.0371990	−	0.0214768i
$543$	−41.5692	−	24.0000i	−1.78391	−	1.02994i
$544$	6.00000			0.257248
$545$	−28.0000	+	14.0000i	−1.19939	+	0.599694i
$546$	−3.00000	+	5.19615i	−0.128388	+	0.222375i
$547$			19.0000i			0.812381i	0.913788	+	0.406191i	$0.133143\pi$
$547$			19.0000i			0.812381i	−0.913788	+	0.406191i	$0.866857\pi$
$548$	10.3923	−	6.00000i	0.443937	−	0.256307i
$549$	36.0000			1.53644
$550$		0			0
$551$		0			0
$552$	−10.3923	+	6.00000i	−0.442326	+	0.255377i
$553$	−13.8564	−	8.00000i	−0.589234	−	0.340195i
$554$	−27.0000			−1.14712
$555$	19.6077	−	35.7846i	0.832300	−	1.51897i
$556$	16.0000			0.678551
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	0.554031	−	0.832496i	$-0.313089\pi$
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	−0.443947	+	0.896053i	$0.646422\pi$
$558$	36.3731	−	21.0000i	1.53979	−	0.889001i
$559$	−5.50000	−	9.52628i	−0.232625	−	0.402919i
$560$	−2.46410	+	3.73205i	−0.104127	+	0.157708i
$561$		0			0
$562$	−12.9904	+	7.50000i	−0.547966	+	0.316368i
$563$		−	4.00000i		−	0.168580i	−0.996441	−	0.0842900i	$-0.973138\pi$
$563$		−	4.00000i		−	0.168580i	0.996441	−	0.0842900i	$-0.0268622\pi$
$564$	−15.0000	+	25.9808i	−0.631614	+	1.09399i
$565$	4.00000	+	8.00000i	0.168281	+	0.336563i
$566$	−1.00000			−0.0420331
$567$	−15.5885	−	9.00000i	−0.654654	−	0.377964i
$568$	10.3923	−	6.00000i	0.436051	−	0.251754i
$569$	19.0000			0.796521			0.398261	−	0.917272i	$-0.369614\pi$
$569$	19.0000			0.796521			0.398261	+	0.917272i	$0.369614\pi$
$570$		0			0
$571$	−11.0000	+	19.0526i	−0.460336	+	0.797325i	−0.998978	−	0.0452101i	$-0.985604\pi$
$571$	−11.0000	+	19.0526i	−0.460336	+	0.797325i	0.538642	+	0.842535i	$0.318938\pi$
$572$		0			0
$573$	−33.7750	+	19.5000i	−1.41097	+	0.814624i
$574$	−1.00000	−	1.73205i	−0.0417392	−	0.0722944i
$575$	−18.3923	+	7.85641i	−0.767012	+	0.327635i
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	−1.73205	−	1.00000i	−0.0721062	−	0.0416305i	0.463513	−	0.886090i	$-0.346589\pi$
$577$	−1.73205	−	1.00000i	−0.0721062	−	0.0416305i	−0.535620	+	0.844459i	$0.679922\pi$
$578$		−	19.0000i		−	0.790296i
$579$	3.00000	+	5.19615i	0.124676	+	0.215945i
$580$	−0.803848	+	13.3923i	−0.0333780	+	0.556085i
$581$	24.0000			0.995688
$582$		−	6.00000i		−	0.248708i
$583$		0			0
$584$	−16.0000			−0.662085
$585$	−7.39230	+	11.1962i	−0.305634	+	0.462904i
$586$	9.00000			0.371787
$587$	23.3827	−	13.5000i	0.965107	−	0.557205i	0.0673658	−	0.997728i	$-0.478541\pi$
$587$	23.3827	−	13.5000i	0.965107	−	0.557205i	0.897741	+	0.440524i	$0.145207\pi$
$588$	7.79423	−	4.50000i	0.321429	−	0.185577i
$589$		0			0
$590$	13.3923	+	0.803848i	0.551352	+	0.0330939i
$591$	39.0000			1.60425
$592$	−3.46410	−	5.00000i	−0.142374	−	0.205499i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$		0			0
$595$	22.3923	+	14.7846i	0.917995	+	0.606110i
$596$	−1.00000	−	1.73205i	−0.0409616	−	0.0709476i
$597$	2.59808	−	1.50000i	0.106332	−	0.0613909i
$598$			4.00000i			0.163572i
$599$	12.5000	+	21.6506i	0.510736	+	0.884621i	0.999923	+	0.0124417i	$0.00396043\pi$
$599$	12.5000	+	21.6506i	0.510736	+	0.884621i	−0.489186	+	0.872179i	$0.662706\pi$
$600$	−9.00000	+	12.0000i	−0.367423	+	0.489898i
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$		−	22.0000i		−	0.896653i
$603$		−	24.0000i		−	0.977356i
$604$	3.50000	−	6.06218i	0.142413	−	0.246667i
$605$	−20.5263	−	13.5526i	−0.834512	−	0.550990i
$606$	42.0000			1.70613
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$	−18.0000	+	31.1769i	−0.729397	+	1.26335i
$610$	7.39230	−	11.1962i	0.299306	−	0.453319i
$611$	5.00000	+	8.66025i	0.202278	+	0.350356i
$612$	31.1769	+	18.0000i	1.26025	+	0.727607i
$613$	−25.9808	−	15.0000i	−1.04935	−	0.605844i	−0.126885	−	0.991917i	$-0.540498\pi$
$613$	−25.9808	−	15.0000i	−1.04935	−	0.605844i	−0.922468	+	0.386073i	$0.873831\pi$
$614$	−12.5000	+	21.6506i	−0.504459	+	0.873749i
$615$	−3.00000	−	6.00000i	−0.120972	−	0.241943i
$616$		0			0
$617$	20.7846	+	12.0000i	0.836757	+	0.483102i	0.856161	−	0.516710i	$-0.172843\pi$
$617$	20.7846	+	12.0000i	0.836757	+	0.483102i	−0.0194037	+	0.999812i	$0.506177\pi$
$618$		−	18.0000i		−	0.724066i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$	0.937822	−	15.6244i	0.0376638	−	0.627489i
$621$	−36.0000			−1.44463
$622$	2.59808	−	1.50000i	0.104173	−	0.0601445i
$623$		−	36.0000i		−	1.44231i
$624$	1.50000	+	2.59808i	0.0600481	+	0.104006i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	−1.00000	−	1.73205i	−0.0399680	−	0.0692267i
$627$		0			0
$628$		−	17.0000i		−	0.678374i
$629$	−30.0000	+	20.7846i	−1.19618	+	0.828737i
$630$	−24.0000	+	12.0000i	−0.956183	+	0.478091i
$631$	2.50000	−	4.33013i	0.0995234	−	0.172380i	−0.811964	−	0.583707i	$-0.801602\pi$
$631$	2.50000	−	4.33013i	0.0995234	−	0.172380i	0.911487	+	0.411328i	$0.134935\pi$
$632$	−6.92820	+	4.00000i	−0.275589	+	0.159111i
$633$	25.9808	−	15.0000i	1.03264	−	0.596196i
$634$	13.5000	+	23.3827i	0.536153	+	0.928645i
$635$	10.0000	+	20.0000i	0.396838	+	0.793676i
$636$	7.50000	+	12.9904i	0.297394	+	0.515102i
$637$		−	3.00000i		−	0.118864i
$638$		0			0
$639$	72.0000			2.84828
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	−0.708631	−	0.705580i	$-0.750687\pi$
$641$	6.50000	−	11.2583i	0.256735	−	0.444677i	0.965365	+	0.260902i	$0.0840201\pi$
$642$	−28.5788	+	16.5000i	−1.12792	+	0.651203i
$643$			13.0000i			0.512670i	0.966588	+	0.256335i	$0.0825150\pi$
$643$			13.0000i			0.512670i	−0.966588	+	0.256335i	$0.917485\pi$
$644$	−4.00000	+	6.92820i	−0.157622	+	0.273009i
$645$	4.42116	−	73.6577i	0.174083	−	2.90027i
$646$		0			0
$647$	19.0526	−	11.0000i	0.749033	−	0.432455i	−0.0763112	−	0.997084i	$-0.524314\pi$
$647$	19.0526	−	11.0000i	0.749033	−	0.432455i	0.825345	+	0.564629i	$0.190981\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$		0			0
$650$	1.96410	+	4.59808i	0.0770384	+	0.180351i
$651$	21.0000	−	36.3731i	0.823055	−	1.42557i
$652$		−	3.00000i		−	0.117489i
$653$	40.7032	−	23.5000i	1.59284	−	0.919626i	0.600022	−	0.799983i	$-0.295158\pi$
$653$	40.7032	−	23.5000i	1.59284	−	0.919626i	0.992817	−	0.119643i	$-0.0381749\pi$
$654$	−21.0000	+	36.3731i	−0.821165	+	1.42230i
$655$	20.0000	−	10.0000i	0.781465	−	0.390732i
$656$	−1.00000			−0.0390434
$657$	−83.1384	−	48.0000i	−3.24354	−	1.87266i
$658$			20.0000i			0.779681i
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	0.531855	−	0.846836i	$-0.321495\pi$
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	−0.999309	+	0.0371821i	$0.988162\pi$
$660$		0			0
$661$	−4.00000	−	6.92820i	−0.155582	−	0.269476i	0.777689	−	0.628649i	$-0.216392\pi$
$661$	−4.00000	−	6.92820i	−0.155582	−	0.269476i	−0.933271	+	0.359174i	$0.883059\pi$
$662$	−24.2487	+	14.0000i	−0.942453	+	0.544125i
$663$	15.5885	−	9.00000i	0.605406	−	0.349531i
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$		0			0
$666$	−3.00000	−	36.3731i	−0.116248	−	1.40943i
$667$			24.0000i			0.929284i
$668$	6.92820	+	4.00000i	0.268060	+	0.154765i
$669$	−12.0000	−	20.7846i	−0.463947	−	0.803579i
$670$	−7.46410	−	4.92820i	−0.288363	−	0.190393i
$671$		0			0
$672$			6.00000i			0.231455i
$673$	−20.7846	+	12.0000i	−0.801188	+	0.462566i	−0.843886	−	0.536522i	$-0.819738\pi$
$673$	−20.7846	+	12.0000i	−0.801188	+	0.462566i	0.0426985	+	0.999088i	$0.486405\pi$
$674$	−16.0000			−0.616297
$675$	−41.3827	+	17.6769i	−1.59282	+	0.680385i
$676$	−12.0000			−0.461538
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$	10.3923	+	6.00000i	0.399114	+	0.230429i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	12.0000	−	6.00000i	0.460179	−	0.230089i
$681$	16.5000	−	28.5788i	0.632281	−	1.09514i
$682$		0			0
$683$	40.7032	+	23.5000i	1.55746	+	0.899203i	0.997499	+	0.0706868i	$0.0225191\pi$
$683$	40.7032	+	23.5000i	1.55746	+	0.899203i	0.559966	+	0.828516i	$0.310814\pi$
$684$		0			0
$685$	14.7846	−	22.3923i	0.564891	−	0.855566i
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	41.5692	+	24.0000i	1.58596	+	0.915657i
$688$	−9.52628	−	5.50000i	−0.363186	−	0.209686i
$689$	5.00000			0.190485
$690$	−14.7846	+	22.3923i	−0.562840	+	0.852460i
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	0.466691	+	0.884420i	$0.345446\pi$
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	−0.999276	+	0.0380440i	$0.987887\pi$
$692$			10.0000i			0.380143i
$693$		0			0
$694$	−6.00000	+	10.3923i	−0.227757	+	0.394486i
$695$	32.0000	−	16.0000i	1.21383	−	0.606915i
$696$	9.00000	+	15.5885i	0.341144	+	0.590879i
$697$			6.00000i			0.227266i
$698$	−10.3923	+	6.00000i	−0.393355	+	0.227103i
$699$	−45.0000	−	77.9423i	−1.70206	−	2.94805i
$700$	−1.19615	+	9.92820i	−0.0452103	+	0.375251i
$701$	−16.0000	+	27.7128i	−0.604312	+	1.04670i	0.387848	+	0.921723i	$0.373218\pi$
$701$	−16.0000	+	27.7128i	−0.604312	+	1.04670i	−0.992160	+	0.124975i	$0.960115\pi$
$702$			9.00000i			0.339683i
$703$		0			0
$704$		0			0
$705$	−4.01924	+	66.9615i	−0.151373	+	2.52192i
$706$	9.00000	+	15.5885i	0.338719	+	0.586679i
$707$	24.2487	−	14.0000i	0.911967	−	0.526524i
$708$	15.5885	−	9.00000i	0.585850	−	0.338241i
$709$	10.0000			0.375558			0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000			0.375558			0.187779	+	0.982211i	$0.439871\pi$
$710$	14.7846	−	22.3923i	0.554857	−	0.840368i
$711$	−48.0000			−1.80014
$712$	−15.5885	−	9.00000i	−0.584202	−	0.337289i
$713$		−	28.0000i		−	1.04861i
$714$	36.0000			1.34727
$715$		0			0
$716$	4.00000	+	6.92820i	0.149487	+	0.258919i
$717$			48.0000i			1.79259i
$718$	21.6506	+	12.5000i	0.807995	+	0.466496i
$719$	11.5000	−	19.9186i	0.428878	−	0.742838i	−0.567896	−	0.823100i	$-0.692242\pi$
$719$	11.5000	−	19.9186i	0.428878	−	0.742838i	0.996774	+	0.0802624i	$0.0255758\pi$
$720$	−0.803848	+	13.3923i	−0.0299576	+	0.499102i
$721$	−6.00000	−	10.3923i	−0.223452	−	0.387030i
$722$	−16.4545	+	9.50000i	−0.612372	+	0.353553i
$723$	57.1577	+	33.0000i	2.12572	+	1.22728i
$724$	−8.00000	+	13.8564i	−0.297318	+	0.514969i
$725$	11.7846	+	27.5885i	0.437669	+	1.02461i
$726$	−33.0000			−1.22474
$727$	27.7128	−	16.0000i	1.02781	−	0.593407i	0.111454	−	0.993770i	$-0.464449\pi$
$727$	27.7128	−	16.0000i	1.02781	−	0.593407i	0.916357	+	0.400362i	$0.131116\pi$
$728$	1.73205	+	1.00000i	0.0641941	+	0.0370625i
$729$	27.0000			1.00000
$730$	−32.0000	+	16.0000i	−1.18437	+	0.592187i
$731$	−33.0000	+	57.1577i	−1.22055	+	2.11405i
$732$		−	18.0000i		−	0.665299i
$733$	−12.1244	+	7.00000i	−0.447823	+	0.258551i	−0.706910	−	0.707303i	$-0.749912\pi$
$733$	−12.1244	+	7.00000i	−0.447823	+	0.258551i	0.259087	+	0.965854i	$0.416578\pi$
$734$	−14.0000			−0.516749
$735$	11.0885	−	16.7942i	0.409004	−	0.619464i
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$		0			0
$738$	−5.19615	−	3.00000i	−0.191273	−	0.110432i
$739$	18.0000			0.662141			0.331070	−	0.943606i	$-0.392590\pi$
$739$	18.0000			0.662141			0.331070	+	0.943606i	$0.392590\pi$
$740$	−11.9282	−	6.53590i	−0.438489	−	0.240264i
$741$		0			0
$742$	8.66025	+	5.00000i	0.317928	+	0.183556i
$743$	−29.4449	+	17.0000i	−1.08023	+	0.623670i	−0.930958	−	0.365127i	$-0.881026\pi$
$743$	−29.4449	+	17.0000i	−1.08023	+	0.623670i	−0.149270	+	0.988797i	$0.547692\pi$
$744$	−10.5000	−	18.1865i	−0.384949	−	0.666751i
$745$	−3.73205	−	2.46410i	−0.136732	−	0.0902777i
$746$	−11.0000			−0.402739
$747$	62.3538	−	36.0000i	2.28141	−	1.31717i
$748$		0			0
$749$	−11.0000	+	19.0526i	−0.401931	+	0.696165i
$750$	−6.00000	+	33.0000i	−0.219089	+	1.20499i
$751$	−53.0000			−1.93400			−0.966999	−	0.254781i	$-0.917997\pi$
$751$	−53.0000			−1.93400			−0.966999	+	0.254781i	$0.917997\pi$
$752$	8.66025	+	5.00000i	0.315807	+	0.182331i
$753$	−20.7846	+	12.0000i	−0.757433	+	0.437304i
$754$	6.00000			0.218507
$755$	0.937822	−	15.6244i	0.0341308	−	0.568629i
$756$	−9.00000	+	15.5885i	−0.327327	+	0.566947i
$757$	4.33013	+	2.50000i	0.157381	+	0.0908640i	0.576622	−	0.817011i	$-0.304370\pi$
$757$	4.33013	+	2.50000i	0.157381	+	0.0908640i	−0.419241	+	0.907875i	$0.637704\pi$
$758$	−31.1769	+	18.0000i	−1.13240	+	0.653789i
$759$		0			0
$760$		0			0
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	0.373914	+	0.927463i	$0.378015\pi$
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	−0.990164	+	0.139912i	$0.955318\pi$
$762$	25.9808	+	15.0000i	0.941184	+	0.543393i
$763$			28.0000i			1.01367i
$764$	6.50000	+	11.2583i	0.235162	+	0.407312i
$765$	80.3538	+	4.82309i	2.90520	+	0.174379i
$766$	−26.0000			−0.939418
$767$		−	6.00000i		−	0.216647i
$768$	2.59808	+	1.50000i	0.0937500	+	0.0541266i
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	72.0000			2.59302
$772$	1.73205	−	1.00000i	0.0623379	−	0.0359908i
$773$	−23.3827	+	13.5000i	−0.841017	+	0.485561i	−0.857610	−	0.514301i	$-0.828051\pi$
$773$	−23.3827	+	13.5000i	−0.841017	+	0.485561i	0.0165929	+	0.999862i	$0.494718\pi$
$774$	−33.0000	−	57.1577i	−1.18616	−	2.05449i
$775$	−13.7487	−	32.1865i	−0.493868	−	1.15617i
$776$	−2.00000			−0.0717958
$777$	−20.7846	−	30.0000i	−0.745644	−	1.07624i
$778$			10.0000i			0.358517i
$779$		0			0
$780$	5.59808	+	3.69615i	0.200443	+	0.132343i
$781$		0			0
$782$	20.7846	−	12.0000i	0.743256	−	0.429119i
$783$			54.0000i			1.92980i
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$	−17.0000	−	34.0000i	−0.606756	−	1.21351i
$786$	15.0000	−	25.9808i	0.535032	−	0.926703i
$787$			11.0000i			0.392108i	0.980593	+	0.196054i	$0.0628127\pi$
$787$			11.0000i			0.392108i	−0.980593	+	0.196054i	$0.937187\pi$
$788$		−	13.0000i		−	0.463106i
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$	−9.85641	+	14.9282i	−0.350675	+	0.531122i
$791$	8.00000			0.284447
$792$		0			0
$793$	−5.19615	−	3.00000i	−0.184521	−	0.106533i
$794$	−8.50000	+	14.7224i	−0.301654	+	0.522480i
$795$	27.9904	+	18.4808i	0.992717	+	0.655445i
$796$	−0.500000	−	0.866025i	−0.0177220	−	0.0306955i
$797$	−33.7750	−	19.5000i	−1.19637	−	0.690725i	−0.236627	−	0.971601i	$-0.576042\pi$
$797$	−33.7750	−	19.5000i	−1.19637	−	0.690725i	−0.959744	+	0.280875i	$0.909375\pi$
$798$		0			0
$799$	30.0000	−	51.9615i	1.06132	−	1.83827i
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$	−54.0000	−	93.5307i	−1.90800	−	3.30475i
$802$	−8.66025	−	5.00000i	−0.305804	−	0.176556i
$803$		0			0
$804$	−12.0000			−0.423207
$805$	−1.07180	+	17.8564i	−0.0377759	+	0.629356i
$806$	−7.00000			−0.246564
$807$	36.3731	−	21.0000i	1.28039	−	0.739235i
$808$		−	14.0000i		−	0.492518i
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	0.891189	−	0.453632i	$-0.149872\pi$
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	−0.838452	+	0.544976i	$0.816539\pi$
$810$	−11.0885	+	16.7942i	−0.389609	+	0.590089i
$811$	−21.0000	−	36.3731i	−0.737410	−	1.27723i	−0.953658	−	0.300893i	$-0.902715\pi$
$811$	−21.0000	−	36.3731i	−0.737410	−	1.27723i	0.216248	−	0.976338i	$-0.430618\pi$
$812$	10.3923	+	6.00000i	0.364698	+	0.210559i
$813$		−	3.00000i		−	0.105215i
$814$		0			0
$815$	−3.00000	−	6.00000i	−0.105085	−	0.210171i
$816$	9.00000	−	15.5885i	0.315063	−	0.545705i
$817$		0			0
$818$	26.8468	−	15.5000i	0.938676	−	0.541945i
$819$	6.00000	+	10.3923i	0.209657	+	0.363137i
$820$	−2.00000	+	1.00000i	−0.0698430	+	0.0349215i
$821$	−14.0000	−	24.2487i	−0.488603	−	0.846286i	0.511311	−	0.859396i	$-0.329160\pi$
$821$	−14.0000	−	24.2487i	−0.488603	−	0.846286i	−0.999914	+	0.0131101i	$0.995827\pi$
$822$		−	36.0000i		−	1.25564i
$823$	−13.8564	−	8.00000i	−0.483004	−	0.278862i	0.238664	−	0.971102i	$-0.423291\pi$
$823$	−13.8564	−	8.00000i	−0.483004	−	0.278862i	−0.721668	+	0.692240i	$0.756624\pi$
$824$	−6.00000			−0.209020
$825$		0			0
$826$	6.00000	−	10.3923i	0.208767	−	0.361595i
$827$	−10.3923	+	6.00000i	−0.361376	+	0.208640i	−0.669684	−	0.742646i	$-0.733571\pi$
$827$	−10.3923	+	6.00000i	−0.361376	+	0.208640i	0.308308	+	0.951286i	$0.400237\pi$
$828$			24.0000i			0.834058i
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	−0.513635	−	0.858009i	$-0.671701\pi$
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	0.999875	+	0.0158163i	$0.00503471\pi$
$830$	1.60770	−	26.7846i	0.0558039	−	0.929707i
$831$	−40.5000	+	70.1481i	−1.40493	+	2.43341i
$832$	0.866025	−	0.500000i	0.0300240	−	0.0173344i
$833$	−15.5885	+	9.00000i	−0.540108	+	0.311832i
$834$	24.0000	−	41.5692i	0.831052	−	1.43942i
$835$	17.8564	+	1.07180i	0.617946	+	0.0370911i
$836$		0			0
$837$		−	63.0000i		−	2.17760i
$838$	8.66025	−	5.00000i	0.299164	−	0.172722i
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	−0.777832	−	0.628473i	$-0.783680\pi$
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	0.933189	+	0.359386i	$0.117014\pi$
$840$	6.00000	+	12.0000i	0.207020	+	0.414039i
$841$	7.00000			0.241379
$842$	31.1769	+	18.0000i	1.07443	+	0.620321i
$843$			45.0000i			1.54988i
$844$	−5.00000	−	8.66025i	−0.172107	−	0.298098i
$845$	−24.0000	+	12.0000i	−0.825625	+	0.412813i
$846$	30.0000	+	51.9615i	1.03142	+	1.78647i
$847$	−19.0526	+	11.0000i	−0.654654	+	0.377964i
$848$	4.33013	−	2.50000i	0.148697	−	0.0858504i
$849$	−1.50000	+	2.59808i	−0.0514799	+	0.0891657i
$850$	18.0000	−	24.0000i	0.617395	−	0.823193i
$851$	−22.0000	−	10.3923i	−0.754150	−	0.356244i
$852$		−	36.0000i		−	1.23334i
$853$	−28.5788	−	16.5000i	−0.978521	−	0.564949i	−0.0766976	−	0.997054i	$-0.524438\pi$
$853$	−28.5788	−	16.5000i	−0.978521	−	0.564949i	−0.901823	+	0.432105i	$0.857771\pi$
$854$	−6.00000	−	10.3923i	−0.205316	−	0.355617i
$855$		0			0
$856$	5.50000	+	9.52628i	0.187986	+	0.325602i
$857$		−	10.0000i		−	0.341593i	−0.985306	−	0.170797i	$-0.945366\pi$
$857$		−	10.0000i		−	0.341593i	0.985306	−	0.170797i	$-0.0546341\pi$
$858$		0			0
$859$	−22.0000			−0.750630			−0.375315	−	0.926897i	$-0.622466\pi$
$859$	−22.0000			−0.750630			−0.375315	+	0.926897i	$0.622466\pi$
$860$	−24.5526	−	1.47372i	−0.837235	−	0.0502535i
$861$	−6.00000			−0.204479
$862$			41.0000i			1.39647i
$863$	−15.5885	−	9.00000i	−0.530637	−	0.306364i	0.210639	−	0.977564i	$-0.432446\pi$
$863$	−15.5885	−	9.00000i	−0.530637	−	0.306364i	−0.741276	+	0.671200i	$0.765779\pi$
$864$	4.50000	+	7.79423i	0.153093	+	0.265165i
$865$	10.0000	+	20.0000i	0.340010	+	0.680020i
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$	−49.3634	−	28.5000i	−1.67647	−	0.967911i
$868$	−12.1244	−	7.00000i	−0.411527	−	0.237595i
$869$		0			0
$870$	33.5885	+	22.1769i	1.13876	+	0.751868i
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$	12.1244	+	7.00000i	0.410582	+	0.237050i
$873$	−10.3923	−	6.00000i	−0.351726	−	0.203069i
$874$		0			0
$875$	7.53590	+	21.0526i	0.254760	+	0.711706i
$876$	−24.0000	+	41.5692i	−0.810885	+	1.40449i
$877$			25.0000i			0.844190i	0.906552	+	0.422095i	$0.138705\pi$
$877$			25.0000i			0.844190i	−0.906552	+	0.422095i	$0.861295\pi$
$878$		−	7.00000i		−	0.236239i
$879$	13.5000	−	23.3827i	0.455344	−	0.788678i
$880$		0			0
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	0.976863	−	0.213866i	$-0.0686057\pi$
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	−0.673645	+	0.739055i	$0.735272\pi$
$882$		−	18.0000i		−	0.606092i
$883$	−6.06218	+	3.50000i	−0.204009	+	0.117784i	−0.598524	−	0.801105i	$-0.704246\pi$
$883$	−6.06218	+	3.50000i	−0.204009	+	0.117784i	0.394515	+	0.918889i	$0.370912\pi$
$884$	−3.00000	−	5.19615i	−0.100901	−	0.174766i
$885$	22.1769	−	33.5885i	0.745469	−	1.12906i
$886$	3.50000	−	6.06218i	0.117585	−	0.203663i
$887$		−	28.0000i		−	0.940148i	−0.882627	−	0.470074i	$-0.844227\pi$
$887$		−	28.0000i		−	0.940148i	0.882627	−	0.470074i	$-0.155773\pi$
$888$	−18.1865	+	1.50000i	−0.610300	+	0.0503367i
$889$	20.0000			0.670778
$890$	−40.1769	−	2.41154i	−1.34673	−	0.0808351i
$891$		0			0
$892$	−6.92820	+	4.00000i	−0.231973	+	0.133930i
$893$		0			0
$894$	−6.00000			−0.200670
$895$	14.9282	+	9.85641i	0.498995	+	0.329463i
$896$	2.00000			0.0668153
$897$	10.3923	+	6.00000i	0.346989	+	0.200334i
$898$		−	9.00000i		−	0.300334i
$899$	−42.0000			−1.40078
$900$	11.7846	+	27.5885i	0.392820	+	0.919615i
$901$	−15.0000	−	25.9808i	−0.499722	−	0.865545i
$902$		0			0
$903$	−57.1577	−	33.0000i	−1.90209	−	1.09817i
$904$	2.00000	−	3.46410i	0.0665190	−	0.115214i
$905$	−2.14359	+	35.7128i	−0.0712555	+	1.18713i
$906$	−10.5000	−	18.1865i	−0.348839	−	0.604207i
$907$	27.7128	−	16.0000i	0.920189	−	0.531271i	0.0364935	−	0.999334i	$-0.488381\pi$
$907$	27.7128	−	16.0000i	0.920189	−	0.531271i	0.883695	+	0.468063i	$0.155048\pi$
$908$	−9.52628	−	5.50000i	−0.316141	−	0.182524i
$909$	42.0000	−	72.7461i	1.39305	−	2.41284i
$910$	4.46410	+	0.267949i	0.147984	+	0.00888243i
$911$	57.0000			1.88849			0.944247	−	0.329238i	$-0.106792\pi$
$911$	57.0000			1.88849			0.944247	+	0.329238i	$0.106792\pi$
$912$		0			0
$913$		0			0
$914$	8.00000			0.264616
$915$	−18.0000	−	36.0000i	−0.595062	−	1.19012i
$916$	8.00000	−	13.8564i	0.264327	−	0.457829i
$917$		−	20.0000i		−	0.660458i
$918$	46.7654	−	27.0000i	1.54349	−	0.891133i
$919$	−8.00000			−0.263896			−0.131948	−	0.991257i	$-0.542123\pi$
$919$	−8.00000			−0.263896			−0.131948	+	0.991257i	$0.542123\pi$
$920$	7.46410	+	4.92820i	0.246084	+	0.162478i
$921$	37.5000	+	64.9519i	1.23567	+	2.14024i
$922$	25.9808	−	15.0000i	0.855631	−	0.493999i
$923$	−10.3923	−	6.00000i	−0.342067	−	0.197492i
$924$		0			0
$925$	−30.3923	−	1.14359i	−0.999293	−	0.0376011i
$926$	−14.0000			−0.460069
$927$	−31.1769	−	18.0000i	−1.02398	−	0.591198i
$928$	5.19615	−	3.00000i	0.170572	−	0.0984798i
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$	−39.1865	−	25.8731i	−1.28498	−	0.848411i
$931$		0			0
$932$	−25.9808	+	15.0000i	−0.851028	+	0.491341i
$933$		−	9.00000i		−	0.294647i
$934$	7.50000	−	12.9904i	0.245407	−	0.425058i
$935$		0			0
$936$	6.00000			0.196116
$937$	−27.7128	−	16.0000i	−0.905338	−	0.522697i	−0.0264099	−	0.999651i	$-0.508407\pi$
$937$	−27.7128	−	16.0000i	−0.905338	−	0.522697i	−0.878928	+	0.476954i	$0.841741\pi$
$938$	−6.92820	+	4.00000i	−0.226214	+	0.130605i
$939$	−6.00000			−0.195803
$940$	22.3205	+	1.33975i	0.728015	+	0.0436977i
$941$	−10.0000	+	17.3205i	−0.325991	+	0.564632i	−0.981712	−	0.190370i	$-0.939031\pi$
$941$	−10.0000	+	17.3205i	−0.325991	+	0.564632i	0.655722	+	0.755003i	$0.272364\pi$
$942$	−44.1673	−	25.5000i	−1.43905	−	0.830835i
$943$	−3.46410	+	2.00000i	−0.112807	+	0.0651290i
$944$	−3.00000	−	5.19615i	−0.0976417	−	0.169120i
$945$	−2.41154	+	40.1769i	−0.0784475	+	1.30696i
$946$		0			0
$947$	−45.8993	−	26.5000i	−1.49153	−	0.861134i	−0.491575	−	0.870835i	$-0.663579\pi$
$947$	−45.8993	−	26.5000i	−1.49153	−	0.861134i	−0.999953	+	0.00970072i	$0.996912\pi$
$948$			24.0000i			0.779484i
$949$	8.00000	+	13.8564i	0.259691	+	0.449798i
$950$		0			0
$951$	81.0000			2.62660
$952$		−	12.0000i		−	0.388922i
$953$	10.3923	+	6.00000i	0.336640	+	0.194359i	0.658785	−	0.752331i	$-0.271071\pi$
$953$	10.3923	+	6.00000i	0.336640	+	0.194359i	−0.322145	+	0.946690i	$0.604404\pi$
$954$	30.0000			0.971286
$955$	24.2583	+	16.0167i	0.784981	+	0.518287i
$956$	16.0000			0.517477
$957$		0			0
$958$	−2.59808	+	1.50000i	−0.0839400	+	0.0484628i
$959$	−12.0000	−	20.7846i	−0.387500	−	0.671170i
$960$	6.69615	+	0.401924i	0.216117	+	0.0129720i
$961$	18.0000			0.580645
$962$	−2.59808	+	5.50000i	−0.0837653	+	0.177327i
$963$			66.0000i			2.12682i
$964$	11.0000	−	19.0526i	0.354286	−	0.613642i
$965$	2.46410	−	3.73205i	0.0793222	−	0.120139i
$966$	12.0000	+	20.7846i	0.386094	+	0.668734i
$967$	−32.9090	+	19.0000i	−1.05828	+	0.610999i	−0.924956	−	0.380074i	$-0.875899\pi$
$967$	−32.9090	+	19.0000i	−1.05828	+	0.610999i	−0.133325	+	0.991072i	$0.542565\pi$
$968$			11.0000i			0.353553i
$969$		0			0
$970$	−4.00000	+	2.00000i	−0.128432	+	0.0642161i
$971$	17.0000	−	29.4449i	0.545556	−	0.944931i	−0.453016	−	0.891503i	$-0.649652\pi$
$971$	17.0000	−	29.4449i	0.545556	−	0.944931i	0.998572	−	0.0534281i	$-0.0170148\pi$
$972$		0			0
$973$		−	32.0000i		−	1.02587i
$974$	21.0000	−	36.3731i	0.672883	−	1.16547i
$975$	14.8923	+	1.79423i	0.476935	+	0.0574613i
$976$	−6.00000			−0.192055
$977$	10.3923	+	6.00000i	0.332479	+	0.191957i	0.656941	−	0.753942i	$-0.271850\pi$
$977$	10.3923	+	6.00000i	0.332479	+	0.191957i	−0.324462	+	0.945899i	$0.605183\pi$
$978$	−7.79423	−	4.50000i	−0.249232	−	0.143894i
$979$		0			0
$980$	−5.59808	−	3.69615i	−0.178824	−	0.118069i
$981$	42.0000	+	72.7461i	1.34096	+	2.32261i
$982$	25.9808	+	15.0000i	0.829079	+	0.478669i
$983$	1.73205	+	1.00000i	0.0552438	+	0.0318950i	0.527368	−	0.849637i	$-0.323179\pi$
$983$	1.73205	+	1.00000i	0.0552438	+	0.0318950i	−0.472124	+	0.881532i	$0.656512\pi$
$984$	−1.50000	+	2.59808i	−0.0478183	+	0.0828236i
$985$	−13.0000	−	26.0000i	−0.414214	−	0.828429i
$986$	−18.0000	−	31.1769i	−0.573237	−	0.992875i
$987$	51.9615	+	30.0000i	1.65395	+	0.954911i
$988$		0			0
$989$	−44.0000			−1.39912
$990$		0			0
$991$	−51.0000			−1.62007			−0.810034	−	0.586383i	$-0.800552\pi$
$991$	−51.0000			−1.62007			−0.810034	+	0.586383i	$0.800552\pi$
$992$	−6.06218	+	3.50000i	−0.192474	+	0.111125i
$993$			84.0000i			2.66566i
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$	−1.86603	−	1.23205i	−0.0591570	−	0.0390586i
$996$	−18.0000	−	31.1769i	−0.570352	−	0.987878i
$997$	16.4545	+	9.50000i	0.521119	+	0.300868i	0.737392	−	0.675465i	$-0.236057\pi$
$997$	16.4545	+	9.50000i	0.521119	+	0.300868i	−0.216274	+	0.976333i	$0.569390\pi$
$998$		−	36.0000i		−	1.13956i
$999$	−49.5000	−	23.3827i	−1.56611	−	0.739795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.n.d.269.1	✓	4
5.4	even	2	inner	370.2.n.d.269.2	yes	4
37.26	even	3	inner	370.2.n.d.359.2	yes	4
185.174	even	6	inner	370.2.n.d.359.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.d.269.1	✓	4	1.1	even	1	trivial
370.2.n.d.269.2	yes	4	5.4	even	2	inner
370.2.n.d.359.1	yes	4	185.174	even	6	inner
370.2.n.d.359.2	yes	4	37.26	even	3	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +3.00000 q^{6} +(1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +3.00000 q^{6} +(1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(-1.00000 - 2.00000i) q^{10} +(-2.59808 - 1.50000i) q^{12} +(-0.866025 + 0.500000i) q^{13} -2.00000 q^{14} +(-6.69615 - 0.401924i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.19615 + 3.00000i) q^{17} +(-5.19615 + 3.00000i) q^{18} +(-0.133975 + 2.23205i) q^{20} +(-3.00000 + 5.19615i) q^{21} +4.00000i q^{23} +(1.50000 + 2.59808i) q^{24} +(1.96410 + 4.59808i) q^{25} +1.00000 q^{26} +9.00000i q^{27} +(1.73205 + 1.00000i) q^{28} +6.00000 q^{29} +(5.59808 + 3.69615i) q^{30} -7.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.00000 - 5.19615i) q^{34} +(4.46410 + 0.267949i) q^{35} +6.00000 q^{36} +(-2.59808 + 5.50000i) q^{37} +(1.50000 - 2.59808i) q^{39} +(1.23205 - 1.86603i) q^{40} +(0.500000 + 0.866025i) q^{41} +(5.19615 - 3.00000i) q^{42} +11.0000i q^{43} +(12.0000 - 6.00000i) q^{45} +(2.00000 - 3.46410i) q^{46} -10.0000i q^{47} -3.00000i q^{48} +(-1.50000 + 2.59808i) q^{49} +(0.598076 - 4.96410i) q^{50} -18.0000 q^{51} +(-0.866025 - 0.500000i) q^{52} +(-4.33013 - 2.50000i) q^{53} +(4.50000 - 7.79423i) q^{54} +(-1.00000 - 1.73205i) q^{56} +(-5.19615 - 3.00000i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-3.00000 - 6.00000i) q^{60} +(3.00000 + 5.19615i) q^{61} +(6.06218 + 3.50000i) q^{62} -12.0000i q^{63} -1.00000 q^{64} +(-2.23205 - 0.133975i) q^{65} +(3.46410 - 2.00000i) q^{67} +6.00000i q^{68} +(-6.00000 - 10.3923i) q^{69} +(-3.73205 - 2.46410i) q^{70} +(6.00000 + 10.3923i) q^{71} +(-5.19615 - 3.00000i) q^{72} -16.0000i q^{73} +(5.00000 - 3.46410i) q^{74} +(-12.0000 - 9.00000i) q^{75} +(-2.59808 + 1.50000i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(-2.00000 + 1.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} -1.00000i q^{82} +(10.3923 + 6.00000i) q^{83} -6.00000 q^{84} +(6.00000 + 12.0000i) q^{85} +(5.50000 - 9.52628i) q^{86} +(-15.5885 + 9.00000i) q^{87} +(9.00000 - 15.5885i) q^{89} +(-13.3923 - 0.803848i) q^{90} +(-1.00000 + 1.73205i) q^{91} +(-3.46410 + 2.00000i) q^{92} +(18.1865 - 10.5000i) q^{93} +(-5.00000 + 8.66025i) q^{94} +(-1.50000 + 2.59808i) q^{96} -2.00000i q^{97} +(2.59808 - 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5 + 12 * q^6 + 12 * q^9	\( 4 q + 2 q^{4} + 4 q^{5} + 12 q^{6} + 12 q^{9} - 4 q^{10} - 8 q^{14} - 6 q^{15} - 2 q^{16} - 4 q^{20} - 12 q^{21} + 6 q^{24} - 6 q^{25} + 4 q^{26} + 24 q^{29} + 12 q^{30} - 28 q^{31} - 12 q^{34} + 4 q^{35} + 24 q^{36} + 6 q^{39} - 2 q^{40} + 2 q^{41} + 48 q^{45} + 8 q^{46} - 6 q^{49} - 8 q^{50} - 72 q^{51} + 18 q^{54} - 4 q^{56} - 12 q^{59} - 12 q^{60} + 12 q^{61} - 4 q^{64} - 2 q^{65} - 24 q^{69} - 8 q^{70} + 24 q^{71} + 20 q^{74} - 48 q^{75} - 16 q^{79} - 8 q^{80} - 18 q^{81} - 24 q^{84} + 24 q^{85} + 22 q^{86} + 36 q^{89} - 12 q^{90} - 4 q^{91} - 20 q^{94} - 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 + 12 * q^6 + 12 * q^9 - 4 * q^10 - 8 * q^14 - 6 * q^15 - 2 * q^16 - 4 * q^20 - 12 * q^21 + 6 * q^24 - 6 * q^25 + 4 * q^26 + 24 * q^29 + 12 * q^30 - 28 * q^31 - 12 * q^34 + 4 * q^35 + 24 * q^36 + 6 * q^39 - 2 * q^40 + 2 * q^41 + 48 * q^45 + 8 * q^46 - 6 * q^49 - 8 * q^50 - 72 * q^51 + 18 * q^54 - 4 * q^56 - 12 * q^59 - 12 * q^60 + 12 * q^61 - 4 * q^64 - 2 * q^65 - 24 * q^69 - 8 * q^70 + 24 * q^71 + 20 * q^74 - 48 * q^75 - 16 * q^79 - 8 * q^80 - 18 * q^81 - 24 * q^84 + 24 * q^85 + 22 * q^86 + 36 * q^89 - 12 * q^90 - 4 * q^91 - 20 * q^94 - 6 * q^96

Introduction

L-functions

Modular forms

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Database

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