LMFDB - Embedded newform 546.2.bk.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(25,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bk (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.2
Root			$0.578737 + 2.15988i$ of defining polynomial
Character	$\chi$	$=$	546.25
Dual form			546.2.bk.a.415.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.87259 - 1.08114i) q^{5} -1.00000i q^{6} +(-2.59808 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.87259 - 1.08114i) q^{5} -1.00000i q^{6} +(-2.59808 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.08114 + 1.87259i) q^{10} +(-3.60464 - 2.08114i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.418861 - 3.58114i) q^{13} +(2.00000 - 1.73205i) q^{14} +2.16228i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.58114 + 4.47066i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-5.47723 + 3.16228i) q^{19} -2.16228i q^{20} +(0.866025 - 2.50000i) q^{21} +4.16228 q^{22} +(-0.581139 - 1.00656i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-0.162278 + 0.281073i) q^{25} +(2.15331 + 2.89193i) q^{26} +1.00000 q^{27} +(-0.866025 + 2.50000i) q^{28} +4.16228 q^{29} +(-1.08114 - 1.87259i) q^{30} +(-7.79423 - 4.50000i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.60464 - 2.08114i) q^{33} -5.16228i q^{34} +(-4.32456 + 3.74517i) q^{35} -1.00000 q^{36} +(-5.47723 + 3.16228i) q^{37} +(3.16228 - 5.47723i) q^{38} +(3.31079 + 1.42783i) q^{39} +(1.08114 + 1.87259i) q^{40} +(0.500000 + 2.59808i) q^{42} -9.16228 q^{43} +(-3.60464 + 2.08114i) q^{44} +(-1.87259 - 1.08114i) q^{45} +(1.00656 + 0.581139i) q^{46} +(11.6799 - 6.74342i) q^{47} +1.00000 q^{48} +(6.50000 - 2.59808i) q^{49} -0.324555i q^{50} +(-2.58114 - 4.47066i) q^{51} +(-3.31079 - 1.42783i) q^{52} +(3.08114 - 5.33669i) q^{53} +(-0.866025 + 0.500000i) q^{54} -9.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} -6.32456i q^{57} +(-3.60464 + 2.08114i) q^{58} +(-1.59151 - 0.918861i) q^{59} +(1.87259 + 1.08114i) q^{60} +(-7.74342 - 13.4120i) q^{61} +9.00000 q^{62} +(1.73205 + 2.00000i) q^{63} -1.00000 q^{64} +(-4.65606 - 6.25315i) q^{65} +(-2.08114 + 3.60464i) q^{66} +(2.45754 + 1.41886i) q^{67} +(2.58114 + 4.47066i) q^{68} +1.16228 q^{69} +(1.87259 - 5.40569i) q^{70} -3.67544i q^{71} +(0.866025 - 0.500000i) q^{72} +(5.47723 + 3.16228i) q^{73} +(3.16228 - 5.47723i) q^{74} +(-0.162278 - 0.281073i) q^{75} +6.32456i q^{76} +(10.4057 + 3.60464i) q^{77} +(-3.58114 + 0.418861i) q^{78} +(-4.50000 - 7.79423i) q^{79} +(-1.87259 - 1.08114i) q^{80} +(-0.500000 + 0.866025i) q^{81} +16.8114i q^{83} +(-1.73205 - 2.00000i) q^{84} +11.1623i q^{85} +(7.93477 - 4.58114i) q^{86} +(-2.08114 + 3.60464i) q^{87} +(2.08114 - 3.60464i) q^{88} +(2.73861 - 1.58114i) q^{89} +2.16228 q^{90} +(2.87880 + 9.09464i) q^{91} -1.16228 q^{92} +(7.79423 - 4.50000i) q^{93} +(-6.74342 + 11.6799i) q^{94} +(-6.83772 + 11.8433i) q^{95} +(-0.866025 + 0.500000i) q^{96} +11.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} +4.16228i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} + 4 q^{10} + 4 q^{12} - 16 q^{13} + 16 q^{14} - 4 q^{16} - 8 q^{17} + 8 q^{22} + 8 q^{23} + 24 q^{25} + 8 q^{26} + 8 q^{27} + 8 q^{29} + 4 q^{30} + 16 q^{35} - 8 q^{36} + 8 q^{39} - 4 q^{40} + 4 q^{42} - 48 q^{43} + 8 q^{48} + 52 q^{49} - 8 q^{51} - 8 q^{52} + 12 q^{53} - 72 q^{55} - 4 q^{56} - 24 q^{61} + 72 q^{62} - 8 q^{64} - 12 q^{65} - 4 q^{66} + 8 q^{68} - 16 q^{69} + 24 q^{75} + 20 q^{77} - 16 q^{78} - 36 q^{79} - 4 q^{81} - 4 q^{87} + 4 q^{88} - 8 q^{90} + 8 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 + 4 * q^10 + 4 * q^12 - 16 * q^13 + 16 * q^14 - 4 * q^16 - 8 * q^17 + 8 * q^22 + 8 * q^23 + 24 * q^25 + 8 * q^26 + 8 * q^27 + 8 * q^29 + 4 * q^30 + 16 * q^35 - 8 * q^36 + 8 * q^39 - 4 * q^40 + 4 * q^42 - 48 * q^43 + 8 * q^48 + 52 * q^49 - 8 * q^51 - 8 * q^52 + 12 * q^53 - 72 * q^55 - 4 * q^56 - 24 * q^61 + 72 * q^62 - 8 * q^64 - 12 * q^65 - 4 * q^66 + 8 * q^68 - 16 * q^69 + 24 * q^75 + 20 * q^77 - 16 * q^78 - 36 * q^79 - 4 * q^81 - 4 * q^87 + 4 * q^88 - 8 * q^90 + 8 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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
$3$	−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
$5$	1.87259	−	1.08114i	0.837447	−	0.483500i	−0.0189489	−	0.999820i	$-0.506032\pi$
$5$	1.87259	−	1.08114i	0.837447	−	0.483500i	0.856395	+	0.516320i	$0.172699\pi$
$6$		−	1.00000i		−	0.408248i
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.08114	+	1.87259i	−0.341886	+	0.592164i
$11$	−3.60464	−	2.08114i	−1.08684	−	0.627487i	−0.154106	−	0.988054i	$-0.549250\pi$
$11$	−3.60464	−	2.08114i	−1.08684	−	0.627487i	−0.932733	+	0.360567i	$0.882583\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.418861	−	3.58114i	−0.116171	−	0.993229i
$13$	−0.418861	−	3.58114i	−0.116171	−	0.993229i
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$			2.16228i			0.558298i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.58114	+	4.47066i	−0.626018	+	1.08430i	0.362325	+	0.932052i	$0.381983\pi$
$17$	−2.58114	+	4.47066i	−0.626018	+	1.08430i	−0.988343	+	0.152243i	$0.951350\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−5.47723	+	3.16228i	−1.25656	+	0.725476i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−5.47723	+	3.16228i	−1.25656	+	0.725476i	−0.284157	+	0.958778i	$0.591714\pi$
$20$		−	2.16228i		−	0.483500i
$21$	0.866025	−	2.50000i	0.188982	−	0.545545i
$22$	4.16228			0.887401
$23$	−0.581139	−	1.00656i	−0.121176	−	0.209883i	0.799056	−	0.601257i	$-0.205333\pi$
$23$	−0.581139	−	1.00656i	−0.121176	−	0.209883i	−0.920232	+	0.391374i	$0.872000\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−0.162278	+	0.281073i	−0.0324555	+	0.0562146i
$26$	2.15331	+	2.89193i	0.422300	+	0.567153i
$27$	1.00000			0.192450
$28$	−0.866025	+	2.50000i	−0.163663	+	0.472456i
$29$	4.16228			0.772916			0.386458	−	0.922307i	$-0.373698\pi$
$29$	4.16228			0.772916			0.386458	+	0.922307i	$0.373698\pi$
$30$	−1.08114	−	1.87259i	−0.197388	−	0.341886i
$31$	−7.79423	−	4.50000i	−1.39988	−	0.808224i	−0.405505	−	0.914093i	$-0.632904\pi$
$31$	−7.79423	−	4.50000i	−1.39988	−	0.808224i	−0.994380	+	0.105869i	$0.966238\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.60464	−	2.08114i	0.627487	−	0.362280i
$34$		−	5.16228i		−	0.885323i
$35$	−4.32456	+	3.74517i	−0.730983	+	0.633050i
$36$	−1.00000			−0.166667
$37$	−5.47723	+	3.16228i	−0.900450	+	0.519875i	−0.877346	−	0.479858i	$-0.840688\pi$
$37$	−5.47723	+	3.16228i	−0.900450	+	0.519875i	−0.0231041	+	0.999733i	$0.507355\pi$
$38$	3.16228	−	5.47723i	0.512989	−	0.888523i
$39$	3.31079	+	1.42783i	0.530150	+	0.228635i
$40$	1.08114	+	1.87259i	0.170943	+	0.296082i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	0.500000	+	2.59808i	0.0771517	+	0.400892i
$43$	−9.16228			−1.39723			−0.698617	−	0.715496i	$-0.746201\pi$
$43$	−9.16228			−1.39723			−0.698617	+	0.715496i	$0.746201\pi$
$44$	−3.60464	+	2.08114i	−0.543420	+	0.313743i
$45$	−1.87259	−	1.08114i	−0.279149	−	0.161167i
$46$	1.00656	+	0.581139i	0.148409	+	0.0856842i
$47$	11.6799	−	6.74342i	1.70369	−	0.983628i	0.761743	−	0.647880i	$-0.224344\pi$
$47$	11.6799	−	6.74342i	1.70369	−	0.983628i	0.941952	−	0.335749i	$-0.108989\pi$
$48$	1.00000			0.144338
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$		−	0.324555i		−	0.0458991i
$51$	−2.58114	−	4.47066i	−0.361432	−	0.626018i
$52$	−3.31079	−	1.42783i	−0.459124	−	0.198004i
$53$	3.08114	−	5.33669i	0.423227	−	0.733051i	−0.573026	−	0.819537i	$-0.694231\pi$
$53$	3.08114	−	5.33669i	0.423227	−	0.733051i	0.996253	+	0.0864865i	$0.0275640\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−9.00000			−1.21356
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$		−	6.32456i		−	0.837708i
$58$	−3.60464	+	2.08114i	−0.473312	+	0.273267i
$59$	−1.59151	−	0.918861i	−0.207198	−	0.119626i	0.392811	−	0.919619i	$-0.371503\pi$
$59$	−1.59151	−	0.918861i	−0.207198	−	0.119626i	−0.600008	+	0.799994i	$0.704836\pi$
$60$	1.87259	+	1.08114i	0.241750	+	0.139574i
$61$	−7.74342	−	13.4120i	−0.991443	−	1.71723i	−0.608773	−	0.793344i	$-0.708338\pi$
$61$	−7.74342	−	13.4120i	−0.991443	−	1.71723i	−0.382669	−	0.923885i	$-0.624995\pi$
$62$	9.00000			1.14300
$63$	1.73205	+	2.00000i	0.218218	+	0.251976i
$64$	−1.00000			−0.125000
$65$	−4.65606	−	6.25315i	−0.577513	−	0.775608i
$66$	−2.08114	+	3.60464i	−0.256170	+	0.443700i
$67$	2.45754	+	1.41886i	0.300236	+	0.173341i	0.642549	−	0.766245i	$-0.277877\pi$
$67$	2.45754	+	1.41886i	0.300236	+	0.173341i	−0.342313	+	0.939586i	$0.611210\pi$
$68$	2.58114	+	4.47066i	0.313009	+	0.542148i
$69$	1.16228			0.139922
$70$	1.87259	−	5.40569i	0.223817	−	0.646104i
$71$		−	3.67544i		−	0.436195i	−0.975927	−	0.218098i	$-0.930015\pi$
$71$		−	3.67544i		−	0.436195i	0.975927	−	0.218098i	$-0.0699851\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	5.47723	+	3.16228i	0.641061	+	0.370117i	0.785023	−	0.619467i	$-0.212651\pi$
$73$	5.47723	+	3.16228i	0.641061	+	0.370117i	−0.143962	+	0.989583i	$0.545984\pi$
$74$	3.16228	−	5.47723i	0.367607	−	0.636715i
$75$	−0.162278	−	0.281073i	−0.0187382	−	0.0324555i
$76$			6.32456i			0.725476i
$77$	10.4057	+	3.60464i	1.18584	+	0.410787i
$78$	−3.58114	+	0.418861i	−0.405484	+	0.0474267i
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	−0.999974	−	0.00727784i	$-0.997683\pi$
$79$	−4.50000	−	7.79423i	−0.506290	−	0.876919i	0.493684	−	0.869641i	$-0.335650\pi$
$80$	−1.87259	−	1.08114i	−0.209362	−	0.120875i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			16.8114i			1.84529i	0.385651	+	0.922645i	$0.373977\pi$
$83$			16.8114i			1.84529i	−0.385651	+	0.922645i	$0.626023\pi$
$84$	−1.73205	−	2.00000i	−0.188982	−	0.218218i
$85$			11.1623i			1.21072i
$86$	7.93477	−	4.58114i	0.855628	−	0.493997i
$87$	−2.08114	+	3.60464i	−0.223122	+	0.386458i
$88$	2.08114	−	3.60464i	0.221850	−	0.384256i
$89$	2.73861	−	1.58114i	0.290292	−	0.167600i	−0.347781	−	0.937576i	$-0.613065\pi$
$89$	2.73861	−	1.58114i	0.290292	−	0.167600i	0.638074	+	0.769975i	$0.279732\pi$
$90$	2.16228			0.227924
$91$	2.87880	+	9.09464i	0.301781	+	0.953377i
$92$	−1.16228			−0.121176
$93$	7.79423	−	4.50000i	0.808224	−	0.466628i
$94$	−6.74342	+	11.6799i	−0.695530	+	1.20469i
$95$	−6.83772	+	11.8433i	−0.701536	+	1.21510i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$			11.0000i			1.11688i	0.829545	+	0.558440i	$0.188600\pi$
$97$			11.0000i			1.11688i	−0.829545	+	0.558440i	$0.811400\pi$
$98$	−4.33013	+	5.50000i	−0.437409	+	0.555584i
$99$			4.16228i			0.418325i
$100$	0.162278	+	0.281073i	0.0162278	+	0.0281073i
$101$	−8.16228	+	14.1375i	−0.812177	+	1.40673i	0.0991604	+	0.995071i	$0.468384\pi$
$101$	−8.16228	+	14.1375i	−0.812177	+	1.40673i	−0.911337	+	0.411660i	$0.864949\pi$
$102$	4.47066	+	2.58114i	0.442662	+	0.255571i
$103$	6.16228	+	10.6734i	0.607187	+	1.05168i	0.991702	+	0.128560i	$0.0410356\pi$
$103$	6.16228	+	10.6734i	0.607187	+	1.05168i	−0.384514	+	0.923119i	$0.625631\pi$
$104$	3.58114	−	0.418861i	0.351160	−	0.0410727i
$105$	−1.08114	−	5.61776i	−0.105508	−	0.548237i
$106$			6.16228i			0.598533i
$107$	−6.24342	−	10.8139i	−0.603574	−	1.04542i	−0.992275	−	0.124057i	$-0.960410\pi$
$107$	−6.24342	−	10.8139i	−0.603574	−	1.04542i	0.388701	−	0.921364i	$-0.372924\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−3.01969	−	1.74342i	−0.289233	−	0.166989i	0.348363	−	0.937360i	$-0.386738\pi$
$109$	−3.01969	−	1.74342i	−0.289233	−	0.166989i	−0.637596	+	0.770371i	$0.720071\pi$
$110$	7.79423	−	4.50000i	0.743151	−	0.429058i
$111$		−	6.32456i		−	0.600300i
$112$	1.73205	+	2.00000i	0.163663	+	0.188982i
$113$	−1.67544			−0.157613			−0.0788063	−	0.996890i	$-0.525111\pi$
$113$	−1.67544			−0.157613			−0.0788063	+	0.996890i	$0.525111\pi$
$114$	3.16228	+	5.47723i	0.296174	+	0.512989i
$115$	−2.17647	−	1.25658i	−0.202957	−	0.117177i
$116$	2.08114	−	3.60464i	0.193229	−	0.334682i
$117$	−2.89193	+	2.15331i	−0.267359	+	0.199074i
$118$	1.83772			0.169176
$119$	4.47066	−	12.9057i	0.409825	−	1.18306i
$120$	−2.16228			−0.197388
$121$	3.16228	+	5.47723i	0.287480	+	0.497930i
$122$	13.4120	+	7.74342i	1.21426	+	0.701056i
$123$		0			0
$124$	−7.79423	+	4.50000i	−0.699942	+	0.404112i
$125$			11.5132i			1.02977i
$126$	−2.50000	−	0.866025i	−0.222718	−	0.0771517i
$127$	15.9737			1.41743			0.708717	−	0.705493i	$-0.249274\pi$
$127$	15.9737			1.41743			0.708717	+	0.705493i	$0.249274\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	4.58114	−	7.93477i	0.403347	−	0.698617i
$130$	7.15884	+	3.08735i	0.627872	+	0.270779i
$131$	2.08114	+	3.60464i	0.181830	+	0.314939i	0.942504	−	0.334196i	$-0.108465\pi$
$131$	2.08114	+	3.60464i	0.181830	+	0.314939i	−0.760674	+	0.649134i	$0.775131\pi$
$132$		−	4.16228i		−	0.362280i
$133$	12.6491	−	10.9545i	1.09682	−	0.949871i
$134$	−2.83772			−0.245142
$135$	1.87259	−	1.08114i	0.161167	−	0.0930496i
$136$	−4.47066	−	2.58114i	−0.383356	−	0.221331i
$137$	−0.725489	−	0.418861i	−0.0619827	−	0.0357857i	0.468688	−	0.883364i	$-0.344727\pi$
$137$	−0.725489	−	0.418861i	−0.0619827	−	0.0357857i	−0.530671	+	0.847578i	$0.678060\pi$
$138$	−1.00656	+	0.581139i	−0.0856842	+	0.0494698i
$139$	11.4868			0.974300			0.487150	−	0.873318i	$-0.338036\pi$
$139$	11.4868			0.974300			0.487150	+	0.873318i	$0.338036\pi$
$140$	1.08114	+	5.61776i	0.0913729	+	0.474788i
$141$			13.4868i			1.13580i
$142$	1.83772	+	3.18303i	0.154218	+	0.267114i
$143$	−5.94300	+	13.7804i	−0.496979	+	1.15238i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	7.79423	−	4.50000i	0.647275	−	0.373705i
$146$	−6.32456			−0.523424
$147$	−1.00000	+	6.92820i	−0.0824786	+	0.571429i
$148$			6.32456i			0.519875i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$	0.281073	+	0.162278i	0.0229495	+	0.0132499i
$151$	−2.59808	−	1.50000i	−0.211428	−	0.122068i	0.390547	−	0.920583i	$-0.372286\pi$
$151$	−2.59808	−	1.50000i	−0.211428	−	0.122068i	−0.601975	+	0.798515i	$0.705619\pi$
$152$	−3.16228	−	5.47723i	−0.256495	−	0.444262i
$153$	5.16228			0.417345
$154$	−10.8139	+	2.08114i	−0.871410	+	0.167703i
$155$	−19.4605			−1.56310
$156$	2.89193	−	2.15331i	0.231539	−	0.172403i
$157$	4.41886	−	7.65369i	0.352664	−	0.610831i	−0.634052	−	0.773291i	$-0.718609\pi$
$157$	4.41886	−	7.65369i	0.352664	−	0.610831i	0.986715	+	0.162460i	$0.0519427\pi$
$158$	7.79423	+	4.50000i	0.620076	+	0.358001i
$159$	3.08114	+	5.33669i	0.244350	+	0.423227i
$160$	2.16228			0.170943
$161$	2.01312	+	2.32456i	0.158656	+	0.183201i
$162$		−	1.00000i		−	0.0785674i
$163$	10.9545	−	6.32456i	0.858019	−	0.495377i	−0.00532951	−	0.999986i	$-0.501696\pi$
$163$	10.9545	−	6.32456i	0.858019	−	0.495377i	0.863348	+	0.504608i	$0.168363\pi$
$164$		0			0
$165$	4.50000	−	7.79423i	0.350325	−	0.606780i
$166$	−8.40569	−	14.5591i	−0.652408	−	1.13000i
$167$			4.83772i			0.374354i	0.982326	+	0.187177i	$0.0599338\pi$
$167$			4.83772i			0.374354i	−0.982326	+	0.187177i	$0.940066\pi$
$168$	2.50000	+	0.866025i	0.192879	+	0.0668153i
$169$	−12.6491	+	3.00000i	−0.973009	+	0.230769i
$170$	−5.58114	−	9.66682i	−0.428054	−	0.741411i
$171$	5.47723	+	3.16228i	0.418854	+	0.241825i
$172$	−4.58114	+	7.93477i	−0.349309	+	0.605020i
$173$	−1.16228	−	2.01312i	−0.0883663	−	0.153055i	0.818454	−	0.574572i	$-0.194831\pi$
$173$	−1.16228	−	2.01312i	−0.0883663	−	0.153055i	−0.906821	+	0.421517i	$0.861498\pi$
$174$		−	4.16228i		−	0.315541i
$175$	0.281073	−	0.811388i	0.0212471	−	0.0613352i
$176$			4.16228i			0.313743i
$177$	1.59151	−	0.918861i	0.119626	−	0.0690658i
$178$	−1.58114	+	2.73861i	−0.118511	+	0.205268i
$179$	4.00000	−	6.92820i	0.298974	−	0.517838i	−0.676927	−	0.736050i	$-0.736689\pi$
$179$	4.00000	−	6.92820i	0.298974	−	0.517838i	0.975901	+	0.218212i	$0.0700223\pi$
$180$	−1.87259	+	1.08114i	−0.139574	+	0.0805833i
$181$	−2.32456			−0.172783			−0.0863914	−	0.996261i	$-0.527534\pi$
$181$	−2.32456			−0.172783			−0.0863914	+	0.996261i	$0.527534\pi$
$182$	−7.04044	−	6.43679i	−0.521872	−	0.477127i
$183$	15.4868			1.14482
$184$	1.00656	−	0.581139i	0.0742047	−	0.0428421i
$185$	−6.83772	+	11.8433i	−0.502719	+	0.870735i
$186$	−4.50000	+	7.79423i	−0.329956	+	0.571501i
$187$	18.6081	−	10.7434i	1.36076	−	0.785636i
$188$		−	13.4868i		−	0.983628i
$189$	−2.59808	+	0.500000i	−0.188982	+	0.0363696i
$190$		−	13.6754i		−	0.992121i
$191$	−2.25658	−	3.90852i	−0.163281	−	0.282810i	0.772763	−	0.634695i	$-0.218874\pi$
$191$	−2.25658	−	3.90852i	−0.163281	−	0.282810i	−0.936043	+	0.351885i	$0.885541\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−13.2715	−	7.66228i	−0.955300	−	0.551543i	−0.0605768	−	0.998164i	$-0.519294\pi$
$193$	−13.2715	−	7.66228i	−0.955300	−	0.551543i	−0.894723	+	0.446621i	$0.852627\pi$
$194$	−5.50000	−	9.52628i	−0.394877	−	0.683947i
$195$	7.74342	−	0.905694i	0.554518	−	0.0648581i
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$		−	26.3246i		−	1.87555i	−0.347248	−	0.937773i	$-0.612884\pi$
$197$		−	26.3246i		−	1.87555i	0.347248	−	0.937773i	$-0.387116\pi$
$198$	−2.08114	−	3.60464i	−0.147900	−	0.256170i
$199$	−9.32456	+	16.1506i	−0.661000	+	1.14489i	0.319353	+	0.947636i	$0.396534\pi$
$199$	−9.32456	+	16.1506i	−0.661000	+	1.14489i	−0.980353	+	0.197250i	$0.936799\pi$
$200$	−0.281073	−	0.162278i	−0.0198749	−	0.0114748i
$201$	−2.45754	+	1.41886i	−0.173341	+	0.100079i
$202$		−	16.3246i		−	1.14859i
$203$	−10.8139	+	2.08114i	−0.758988	+	0.146067i
$204$	−5.16228			−0.361432
$205$		0			0
$206$	−10.6734	−	6.16228i	−0.743649	−	0.429346i
$207$	−0.581139	+	1.00656i	−0.0403919	+	0.0699609i
$208$	−2.89193	+	2.15331i	−0.200519	+	0.149305i
$209$	26.3246			1.82091
$210$	3.74517	+	4.32456i	0.258442	+	0.298423i
$211$	−19.4868			−1.34153			−0.670764	−	0.741670i	$-0.734034\pi$
$211$	−19.4868			−1.34153			−0.670764	+	0.741670i	$0.734034\pi$
$212$	−3.08114	−	5.33669i	−0.211613	−	0.366525i
$213$	3.18303	+	1.83772i	0.218098	+	0.125919i
$214$	10.8139	+	6.24342i	0.739224	+	0.426791i
$215$	−17.1572	+	9.90569i	−1.17011	+	0.675563i
$216$			1.00000i			0.0680414i
$217$	22.5000	+	7.79423i	1.52740	+	0.529107i
$218$	3.48683			0.236158
$219$	−5.47723	+	3.16228i	−0.370117	+	0.213687i
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$	17.0912	+	7.37083i	1.14968	+	0.495816i
$222$	3.16228	+	5.47723i	0.212238	+	0.367607i
$223$			11.9737i			0.801816i	0.916118	+	0.400908i	$0.131305\pi$
$223$			11.9737i			0.801816i	−0.916118	+	0.400908i	$0.868695\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$	0.324555			0.0216370
$226$	1.45098	−	0.837722i	0.0965176	−	0.0557245i
$227$	7.34981	+	4.24342i	0.487824	+	0.281645i	0.723671	−	0.690145i	$-0.242453\pi$
$227$	7.34981	+	4.24342i	0.487824	+	0.281645i	−0.235847	+	0.971790i	$0.575786\pi$
$228$	−5.47723	−	3.16228i	−0.362738	−	0.209427i
$229$	−19.1703	+	11.0680i	−1.26681	+	0.731392i	−0.974383	−	0.224896i	$-0.927796\pi$
$229$	−19.1703	+	11.0680i	−1.26681	+	0.731392i	−0.292426	+	0.956288i	$0.594462\pi$
$230$	2.51317			0.165713
$231$	−8.32456	+	7.20928i	−0.547716	+	0.474336i
$232$			4.16228i			0.273267i
$233$	2.90569	+	5.03281i	0.190358	+	0.329710i	0.945369	−	0.326002i	$-0.105702\pi$
$233$	2.90569	+	5.03281i	0.190358	+	0.329710i	−0.755011	+	0.655713i	$0.772368\pi$
$234$	1.42783	−	3.31079i	0.0933398	−	0.216433i
$235$	14.5811	−	25.2553i	0.951169	−	1.64747i
$236$	−1.59151	+	0.918861i	−0.103599	+	0.0598128i
$237$	9.00000			0.584613
$238$	2.58114	+	13.4120i	0.167310	+	0.869370i
$239$		−	9.16228i		−	0.592658i	−0.955086	−	0.296329i	$-0.904237\pi$
$239$		−	9.16228i		−	0.592658i	0.955086	−	0.296329i	$-0.0957626\pi$
$240$	1.87259	−	1.08114i	0.120875	−	0.0697872i
$241$	−10.3695	−	5.98683i	−0.667958	−	0.385646i	0.127344	−	0.991859i	$-0.459355\pi$
$241$	−10.3695	−	5.98683i	−0.667958	−	0.385646i	−0.795303	+	0.606213i	$0.792688\pi$
$242$	−5.47723	−	3.16228i	−0.352089	−	0.203279i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−15.4868			−0.991443
$245$	9.36294	−	11.8925i	0.598176	−	0.759786i
$246$		0			0
$247$	13.6188	+	18.2901i	0.866540	+	1.16377i
$248$	4.50000	−	7.79423i	0.285750	−	0.494934i
$249$	−14.5591	−	8.40569i	−0.922645	−	0.532689i
$250$	−5.75658	−	9.97070i	−0.364078	−	0.630602i
$251$	2.48683			0.156968			0.0784838	−	0.996915i	$-0.474992\pi$
$251$	2.48683			0.156968			0.0784838	+	0.996915i	$0.474992\pi$
$252$	2.59808	−	0.500000i	0.163663	−	0.0314970i
$253$			4.83772i			0.304145i
$254$	−13.8336	+	7.98683i	−0.867997	+	0.501138i
$255$	−9.66682	−	5.58114i	−0.605360	−	0.349504i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.48683	−	11.2355i	−0.404638	−	0.700853i	0.589642	−	0.807665i	$-0.299269\pi$
$257$	−6.48683	−	11.2355i	−0.404638	−	0.700853i	−0.994279	+	0.106812i	$0.965936\pi$
$258$			9.16228i			0.570418i
$259$	12.6491	−	10.9545i	0.785977	−	0.680676i
$260$	−7.74342	+	0.905694i	−0.480226	+	0.0561688i
$261$	−2.08114	−	3.60464i	−0.128819	−	0.223122i
$262$	−3.60464	−	2.08114i	−0.222695	−	0.128573i
$263$	−12.4868	+	21.6278i	−0.769971	+	1.33363i	0.167607	+	0.985854i	$0.446396\pi$
$263$	−12.4868	+	21.6278i	−0.769971	+	1.33363i	−0.937578	+	0.347775i	$0.886937\pi$
$264$	2.08114	+	3.60464i	0.128085	+	0.221850i
$265$		−	13.3246i		−	0.818521i
$266$	−5.47723	+	15.8114i	−0.335830	+	0.969458i
$267$			3.16228i			0.193528i
$268$	2.45754	−	1.41886i	0.150118	−	0.0866707i
$269$	10.9189	−	18.9120i	0.665735	−	1.15309i	−0.313351	−	0.949637i	$-0.601452\pi$
$269$	10.9189	−	18.9120i	0.665735	−	1.15309i	0.979086	−	0.203449i	$-0.0652151\pi$
$270$	−1.08114	+	1.87259i	−0.0657960	+	0.113962i
$271$	12.9904	−	7.50000i	0.789109	−	0.455593i	−0.0505395	−	0.998722i	$-0.516094\pi$
$271$	12.9904	−	7.50000i	0.789109	−	0.455593i	0.839649	+	0.543130i	$0.182761\pi$
$272$	5.16228			0.313009
$273$	−9.31559	−	2.05420i	−0.563805	−	0.124326i
$274$	0.837722			0.0506087
$275$	1.16990	−	0.675445i	0.0705479	−	0.0407308i
$276$	0.581139	−	1.00656i	0.0349804	−	0.0605879i
$277$	7.90569	−	13.6931i	0.475007	−	0.822736i	−0.524583	−	0.851359i	$-0.675779\pi$
$277$	7.90569	−	13.6931i	0.475007	−	0.822736i	0.999590	+	0.0286227i	$0.00911214\pi$
$278$	−9.94789	+	5.74342i	−0.596635	+	0.344467i
$279$			9.00000i			0.538816i
$280$	−3.74517	−	4.32456i	−0.223817	−	0.258442i
$281$			4.83772i			0.288594i	0.989534	+	0.144297i	$0.0460921\pi$
$281$			4.83772i			0.288594i	−0.989534	+	0.144297i	$0.953908\pi$
$282$	−6.74342	−	11.6799i	−0.401565	−	0.695530i
$283$	−10.4868	+	18.1637i	−0.623378	+	1.07972i	0.365475	+	0.930821i	$0.380907\pi$
$283$	−10.4868	+	18.1637i	−0.623378	+	1.07972i	−0.988852	+	0.148900i	$0.952427\pi$
$284$	−3.18303	−	1.83772i	−0.188878	−	0.109049i
$285$	−6.83772	−	11.8433i	−0.405032	−	0.701536i
$286$	−1.74342	−	14.9057i	−0.103090	−	0.881392i
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−4.82456	−	8.35637i	−0.283797	−	0.491551i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$	−9.52628	−	5.50000i	−0.558440	−	0.322416i
$292$	5.47723	−	3.16228i	0.320530	−	0.185058i
$293$			18.4868i			1.08001i	0.841661	+	0.540006i	$0.181578\pi$
$293$			18.4868i			1.08001i	−0.841661	+	0.540006i	$0.818422\pi$
$294$	−2.59808	−	6.50000i	−0.151523	−	0.379088i
$295$	−3.97367			−0.231356
$296$	−3.16228	−	5.47723i	−0.183804	−	0.318357i
$297$	−3.60464	−	2.08114i	−0.209162	−	0.120760i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−3.36122	+	2.50275i	−0.194384	+	0.144738i
$300$	−0.324555			−0.0187382
$301$	23.8043	−	4.58114i	1.37206	−	0.264052i
$302$	3.00000			0.172631
$303$	−8.16228	−	14.1375i	−0.468911	−	0.812177i
$304$	5.47723	+	3.16228i	0.314140	+	0.181369i
$305$	−29.0004	−	16.7434i	−1.66056	−	0.958725i
$306$	−4.47066	+	2.58114i	−0.255571	+	0.147554i
$307$			15.1623i			0.865357i	0.901548	+	0.432678i	$0.142431\pi$
$307$			15.1623i			0.865357i	−0.901548	+	0.432678i	$0.857569\pi$
$308$	8.32456	−	7.20928i	0.474336	−	0.410787i
$309$	−12.3246			−0.701119
$310$	16.8533	−	9.73025i	0.957202	−	0.552641i
$311$	16.0680	−	27.8305i	0.911131	−	1.57813i	0.0986621	−	0.995121i	$-0.468544\pi$
$311$	16.0680	−	27.8305i	0.911131	−	1.57813i	0.812469	−	0.583004i	$-0.198123\pi$
$312$	−1.42783	+	3.31079i	−0.0808347	+	0.187436i
$313$	−7.50000	−	12.9904i	−0.423925	−	0.734260i	0.572394	−	0.819979i	$-0.306015\pi$
$313$	−7.50000	−	12.9904i	−0.423925	−	0.734260i	−0.996319	+	0.0857188i	$0.972681\pi$
$314$			8.83772i			0.498742i
$315$	5.40569	+	1.87259i	0.304576	+	0.105508i
$316$	−9.00000			−0.506290
$317$	−11.0950	+	6.40569i	−0.623157	+	0.359780i	−0.778097	−	0.628144i	$-0.783815\pi$
$317$	−11.0950	+	6.40569i	−0.623157	+	0.359780i	0.154940	+	0.987924i	$0.450481\pi$
$318$	−5.33669	−	3.08114i	−0.299267	−	0.172782i
$319$	−15.0035	−	8.66228i	−0.840035	−	0.484994i
$320$	−1.87259	+	1.08114i	−0.104681	+	0.0604375i
$321$	12.4868			0.696947
$322$	−2.90569	−	1.00656i	−0.161928	−	0.0560935i
$323$		−	32.6491i		−	1.81665i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	1.07453	+	0.463408i	0.0596044	+	0.0257053i
$326$	−6.32456	+	10.9545i	−0.350285	+	0.606711i
$327$	3.01969	−	1.74342i	0.166989	−	0.0964112i
$328$		0			0
$329$	−26.9737	+	23.3599i	−1.48711	+	1.28787i
$330$			9.00000i			0.495434i
$331$	−6.92820	+	4.00000i	−0.380808	+	0.219860i	−0.678170	−	0.734905i	$-0.737227\pi$
$331$	−6.92820	+	4.00000i	−0.380808	+	0.219860i	0.297361	+	0.954765i	$0.403893\pi$
$332$	14.5591	+	8.40569i	0.799034	+	0.461322i
$333$	5.47723	+	3.16228i	0.300150	+	0.173292i
$334$	−2.41886	−	4.18959i	−0.132354	−	0.229244i
$335$	6.13594			0.335242
$336$	−2.59808	+	0.500000i	−0.141737	+	0.0272772i
$337$	−4.67544			−0.254688			−0.127344	−	0.991859i	$-0.540645\pi$
$337$	−4.67544			−0.254688			−0.127344	+	0.991859i	$0.540645\pi$
$338$	9.45445	−	8.92263i	0.514254	−	0.485327i
$339$	0.837722	−	1.45098i	0.0454988	−	0.0788063i
$340$	9.66682	+	5.58114i	0.524257	+	0.302680i
$341$	18.7302	+	32.4417i	1.01430	+	1.75682i
$342$	−6.32456			−0.341993
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		−	9.16228i		−	0.493997i
$345$	2.17647	−	1.25658i	0.117177	−	0.0676522i
$346$	2.01312	+	1.16228i	0.108226	+	0.0624844i
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	−0.614664	−	0.788789i	$-0.710708\pi$
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	0.990443	+	0.137920i	$0.0440416\pi$
$348$	2.08114	+	3.60464i	0.111561	+	0.193229i
$349$		−	20.9737i		−	1.12269i	−0.827580	−	0.561347i	$-0.810283\pi$
$349$		−	20.9737i		−	1.12269i	0.827580	−	0.561347i	$-0.189717\pi$
$350$	0.162278	+	0.843219i	0.00867411	+	0.0450720i
$351$	−0.418861	−	3.58114i	−0.0223572	−	0.191147i
$352$	−2.08114	−	3.60464i	−0.110925	−	0.192128i
$353$	−7.37262	−	4.25658i	−0.392405	−	0.226555i	0.290797	−	0.956785i	$-0.406080\pi$
$353$	−7.37262	−	4.25658i	−0.392405	−	0.226555i	−0.683202	+	0.730230i	$0.739413\pi$
$354$	−0.918861	+	1.59151i	−0.0488369	+	0.0845880i
$355$	−3.97367	−	6.88259i	−0.210900	−	0.365290i
$356$		−	3.16228i		−	0.167600i
$357$	8.94133	+	10.3246i	0.473225	+	0.546433i
$358$			8.00000i			0.422813i
$359$	−27.9939	+	16.1623i	−1.47746	+	0.853012i	−0.999676	−	0.0254644i	$-0.991894\pi$
$359$	−27.9939	+	16.1623i	−1.47746	+	0.853012i	−0.477785	+	0.878477i	$0.658560\pi$
$360$	1.08114	−	1.87259i	0.0569810	−	0.0986940i
$361$	10.5000	−	18.1865i	0.552632	−	0.957186i
$362$	2.01312	−	1.16228i	0.105807	−	0.0610880i
$363$	−6.32456			−0.331953
$364$	9.31559	+	2.05420i	0.488270	+	0.107670i
$365$	13.6754			0.715805
$366$	−13.4120	+	7.74342i	−0.701056	+	0.404755i
$367$	−4.33772	+	7.51316i	−0.226427	+	0.392184i	−0.956747	−	0.290922i	$-0.906038\pi$
$367$	−4.33772	+	7.51316i	−0.226427	+	0.392184i	0.730319	+	0.683106i	$0.239371\pi$
$368$	−0.581139	+	1.00656i	−0.0302940	+	0.0524707i
$369$		0			0
$370$		−	13.6754i		−	0.710953i
$371$	−5.33669	+	15.4057i	−0.277067	+	0.799824i
$372$		−	9.00000i		−	0.466628i
$373$	−0.743416	−	1.28764i	−0.0384926	−	0.0666712i	0.846137	−	0.532965i	$-0.178922\pi$
$373$	−0.743416	−	1.28764i	−0.0384926	−	0.0666712i	−0.884630	+	0.466294i	$0.845589\pi$
$374$	−10.7434	+	18.6081i	−0.555529	+	0.962204i
$375$	−9.97070	−	5.75658i	−0.514884	−	0.297269i
$376$	6.74342	+	11.6799i	0.347765	+	0.602347i
$377$	−1.74342	−	14.9057i	−0.0897905	−	0.767682i
$378$	2.00000	−	1.73205i	0.102869	−	0.0890871i
$379$		−	22.9737i		−	1.18008i	−0.807375	−	0.590039i	$-0.799112\pi$
$379$		−	22.9737i		−	1.18008i	0.807375	−	0.590039i	$-0.200888\pi$
$380$	6.83772	+	11.8433i	0.350768	+	0.607548i
$381$	−7.98683	+	13.8336i	−0.409178	+	0.708717i
$382$	3.90852	+	2.25658i	0.199977	+	0.115457i
$383$	9.22240	−	5.32456i	0.471243	−	0.272072i	−0.245517	−	0.969392i	$-0.578958\pi$
$383$	9.22240	−	5.32456i	0.471243	−	0.272072i	0.716760	+	0.697320i	$0.245624\pi$
$384$			1.00000i			0.0510310i
$385$	23.3827	−	4.50000i	1.19169	−	0.229341i
$386$	15.3246			0.779999
$387$	4.58114	+	7.93477i	0.232872	+	0.403347i
$388$	9.52628	+	5.50000i	0.483624	+	0.279220i
$389$	3.83772	−	6.64713i	0.194580	−	0.337023i	−0.752183	−	0.658955i	$-0.770999\pi$
$389$	3.83772	−	6.64713i	0.194580	−	0.337023i	0.946763	+	0.321932i	$0.104332\pi$
$390$	−6.25315	+	4.65606i	−0.316640	+	0.235769i
$391$	6.00000			0.303433
$392$	2.59808	+	6.50000i	0.131223	+	0.328300i
$393$	−4.16228			−0.209959
$394$	13.1623	+	22.7977i	0.663106	+	1.14853i
$395$	−16.8533	−	9.73025i	−0.847981	−	0.489582i
$396$	3.60464	+	2.08114i	0.181140	+	0.104581i
$397$	18.6081	−	10.7434i	0.933916	−	0.539197i	0.0458680	−	0.998948i	$-0.485395\pi$
$397$	18.6081	−	10.7434i	0.933916	−	0.539197i	0.888048	+	0.459751i	$0.152061\pi$
$398$		−	18.6491i		−	0.934795i
$399$	3.16228	+	16.4317i	0.158312	+	0.822613i
$400$	0.324555			0.0162278
$401$	−13.4120	+	7.74342i	−0.669763	+	0.386688i	−0.795987	−	0.605314i	$-0.793048\pi$
$401$	−13.4120	+	7.74342i	−0.669763	+	0.386688i	0.126224	+	0.992002i	$0.459714\pi$
$402$	1.41886	−	2.45754i	0.0707664	−	0.122571i
$403$	−12.8504	+	29.7971i	−0.640125	+	1.48430i
$404$	8.16228	+	14.1375i	0.406088	+	0.703366i
$405$			2.16228i			0.107444i
$406$	8.32456	−	7.20928i	0.413141	−	0.357790i
$407$	26.3246			1.30486
$408$	4.47066	−	2.58114i	0.221331	−	0.127785i
$409$	24.7881	+	14.3114i	1.22569	+	0.707653i	0.966125	−	0.258073i	$-0.0830875\pi$
$409$	24.7881	+	14.3114i	1.22569	+	0.707653i	0.259565	+	0.965726i	$0.416421\pi$
$410$		0			0
$411$	0.725489	−	0.418861i	0.0357857	−	0.0206609i
$412$	12.3246			0.607187
$413$	4.59431	+	1.59151i	0.226071	+	0.0783133i
$414$		−	1.16228i		−	0.0571228i
$415$	18.1754	+	31.4808i	0.892197	+	1.54533i
$416$	1.42783	−	3.31079i	0.0700049	−	0.162325i
$417$	−5.74342	+	9.94789i	−0.281256	+	0.487150i
$418$	−22.7977	+	13.1623i	−1.11507	+	0.643788i
$419$	−5.35089			−0.261408			−0.130704	−	0.991421i	$-0.541724\pi$
$419$	−5.35089			−0.261408			−0.130704	+	0.991421i	$0.541724\pi$
$420$	−5.40569	−	1.87259i	−0.263771	−	0.0913729i
$421$		−	20.5132i		−	0.999751i	−0.866097	−	0.499875i	$-0.833379\pi$
$421$		−	20.5132i		−	0.999751i	0.866097	−	0.499875i	$-0.166621\pi$
$422$	16.8761	−	9.74342i	0.821515	−	0.474302i
$423$	−11.6799	−	6.74342i	−0.567898	−	0.327876i
$424$	5.33669	+	3.08114i	0.259173	+	0.149633i
$425$	−0.837722	−	1.45098i	−0.0406355	−	0.0703828i
$426$	−3.67544			−0.178076
$427$	26.8240	+	30.9737i	1.29810	+	1.49892i
$428$	−12.4868			−0.603574
$429$	−8.96269	−	12.0370i	−0.432723	−	0.581152i
$430$	9.90569	−	17.1572i	0.477695	−	0.827392i
$431$	13.4120	+	7.74342i	0.646033	+	0.372987i	0.786935	−	0.617036i	$-0.211667\pi$
$431$	13.4120	+	7.74342i	0.646033	+	0.372987i	−0.140902	+	0.990024i	$0.545000\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−20.0000			−0.961139			−0.480569	−	0.876957i	$-0.659570\pi$
$433$	−20.0000			−0.961139			−0.480569	+	0.876957i	$0.659570\pi$
$434$	−23.3827	+	4.50000i	−1.12240	+	0.216007i
$435$			9.00000i			0.431517i
$436$	−3.01969	+	1.74342i	−0.144617	+	0.0834945i
$437$	6.36606	+	3.67544i	0.304530	+	0.175820i
$438$	3.16228	−	5.47723i	0.151099	−	0.261712i
$439$	1.98683	+	3.44130i	0.0948264	+	0.164244i	0.909536	−	0.415625i	$-0.136437\pi$
$439$	1.98683	+	3.44130i	0.0948264	+	0.164244i	−0.814710	+	0.579869i	$0.803104\pi$
$440$		−	9.00000i		−	0.429058i
$441$	−5.50000	−	4.33013i	−0.261905	−	0.206197i
$442$	−18.4868	+	2.16228i	−0.879329	+	0.102849i
$443$	−16.5680	−	28.6966i	−0.787168	−	1.36342i	−0.927695	−	0.373338i	$-0.878213\pi$
$443$	−16.5680	−	28.6966i	−0.787168	−	1.36342i	0.140527	−	0.990077i	$-0.455120\pi$
$444$	−5.47723	−	3.16228i	−0.259938	−	0.150075i
$445$	3.41886	−	5.92164i	0.162070	−	0.280713i
$446$	−5.98683	−	10.3695i	−0.283485	−	0.491010i
$447$		−	6.00000i		−	0.283790i
$448$	2.59808	−	0.500000i	0.122748	−	0.0236228i
$449$			25.6754i			1.21170i	0.795579	+	0.605850i	$0.207167\pi$
$449$			25.6754i			1.21170i	−0.795579	+	0.605850i	$0.792833\pi$
$450$	−0.281073	+	0.162278i	−0.0132499	+	0.00764984i
$451$		0			0
$452$	−0.837722	+	1.45098i	−0.0394031	+	0.0682482i
$453$	2.59808	−	1.50000i	0.122068	−	0.0704761i
$454$	−8.48683			−0.398307
$455$	15.2234	+	13.9181i	0.713683	+	0.652492i
$456$	6.32456			0.296174
$457$	6.06218	−	3.50000i	0.283577	−	0.163723i	−0.351465	−	0.936201i	$-0.614316\pi$
$457$	6.06218	−	3.50000i	0.283577	−	0.163723i	0.635042	+	0.772478i	$0.280983\pi$
$458$	11.0680	−	19.1703i	0.517172	−	0.895769i
$459$	−2.58114	+	4.47066i	−0.120477	+	0.208673i
$460$	−2.17647	+	1.25658i	−0.101478	+	0.0585885i
$461$		−	14.6491i		−	0.682277i	−0.940013	−	0.341139i	$-0.889187\pi$
$461$		−	14.6491i		−	0.682277i	0.940013	−	0.341139i	$-0.110813\pi$
$462$	3.60464	−	10.4057i	0.167703	−	0.484117i
$463$		−	24.3246i		−	1.13046i	−0.824934	−	0.565229i	$-0.808788\pi$
$463$		−	24.3246i		−	1.13046i	0.824934	−	0.565229i	$-0.191212\pi$
$464$	−2.08114	−	3.60464i	−0.0966144	−	0.167341i
$465$	9.73025	−	16.8533i	0.451230	−	0.781552i
$466$	−5.03281	−	2.90569i	−0.233140	−	0.134604i
$467$	−8.32456	−	14.4186i	−0.385214	−	0.667211i	0.606584	−	0.795019i	$-0.292539\pi$
$467$	−8.32456	−	14.4186i	−0.385214	−	0.667211i	−0.991799	+	0.127808i	$0.959206\pi$
$468$	0.418861	+	3.58114i	0.0193619	+	0.165538i
$469$	−7.09431	−	2.45754i	−0.327585	−	0.113479i
$470$			29.1623i			1.34516i
$471$	4.41886	+	7.65369i	0.203610	+	0.352664i
$472$	0.918861	−	1.59151i	0.0422940	−	0.0732554i
$473$	33.0267	+	19.0680i	1.51857	+	0.876746i
$474$	−7.79423	+	4.50000i	−0.358001	+	0.206692i
$475$		−	2.05267i		−	0.0941829i
$476$	−8.94133	−	10.3246i	−0.409825	−	0.473225i
$477$	−6.16228			−0.282151
$478$	4.58114	+	7.93477i	0.209536	+	0.362928i
$479$	24.5298	+	14.1623i	1.12079	+	0.647091i	0.941604	−	0.336723i	$-0.109319\pi$
$479$	24.5298	+	14.1623i	1.12079	+	0.647091i	0.179191	+	0.983814i	$0.442652\pi$
$480$	−1.08114	+	1.87259i	−0.0493470	+	0.0854715i
$481$	13.6188	+	18.2901i	0.620962	+	0.833959i
$482$	11.9737			0.545386
$483$	−3.01969	+	0.581139i	−0.137400	+	0.0264427i
$484$	6.32456			0.287480
$485$	11.8925	+	20.5985i	0.540012	+	0.935328i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	16.4545	+	9.50000i	0.745624	+	0.430486i	0.824110	−	0.566429i	$-0.191675\pi$
$487$	16.4545	+	9.50000i	0.745624	+	0.430486i	−0.0784867	+	0.996915i	$0.525009\pi$
$488$	13.4120	−	7.74342i	0.607132	−	0.350528i
$489$			12.6491i			0.572013i
$490$	−2.16228	+	14.9807i	−0.0976817	+	0.676759i
$491$	−24.1623			−1.09043			−0.545214	−	0.838297i	$-0.683552\pi$
$491$	−24.1623			−1.09043			−0.545214	+	0.838297i	$0.683552\pi$
$492$		0			0
$493$	−10.7434	+	18.6081i	−0.483859	+	0.838069i
$494$	−20.9393	−	9.03036i	−0.942102	−	0.406295i
$495$	4.50000	+	7.79423i	0.202260	+	0.350325i
$496$			9.00000i			0.404112i
$497$	1.83772	+	9.54909i	0.0824331	+	0.428335i
$498$	16.8114			0.753336
$499$	6.48379	−	3.74342i	0.290254	−	0.167578i	−0.347802	−	0.937568i	$-0.613072\pi$
$499$	6.48379	−	3.74342i	0.290254	−	0.167578i	0.638056	+	0.769990i	$0.279739\pi$
$500$	9.97070	+	5.75658i	0.445903	+	0.257442i
$501$	−4.18959	−	2.41886i	−0.187177	−	0.108067i
$502$	−2.15366	+	1.24342i	−0.0961226	+	0.0554964i
$503$	−3.48683			−0.155470			−0.0777351	−	0.996974i	$-0.524769\pi$
$503$	−3.48683			−0.155470			−0.0777351	+	0.996974i	$0.524769\pi$
$504$	−2.00000	+	1.73205i	−0.0890871	+	0.0771517i
$505$			35.2982i			1.57075i
$506$	−2.41886	−	4.18959i	−0.107531	−	0.186250i
$507$	3.72648	−	12.4545i	0.165499	−	0.553122i
$508$	7.98683	−	13.8336i	0.354358	−	0.613767i
$509$	−15.4479	+	8.91886i	−0.684717	+	0.395322i	−0.801630	−	0.597821i	$-0.796034\pi$
$509$	−15.4479	+	8.91886i	−0.684717	+	0.395322i	0.116913	+	0.993142i	$0.462700\pi$
$510$	11.1623			0.494274
$511$	−15.8114	−	5.47723i	−0.699455	−	0.242298i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.47723	+	3.16228i	−0.241825	+	0.139618i
$514$	11.2355	+	6.48683i	0.495578	+	0.286122i
$515$	23.0788	+	13.3246i	1.01697	+	0.587150i
$516$	−4.58114	−	7.93477i	−0.201673	−	0.349309i
$517$	−56.1359			−2.46886
$518$	−5.47723	+	15.8114i	−0.240655	+	0.694713i
$519$	2.32456			0.102037
$520$	6.25315	−	4.65606i	0.274219	−	0.204182i
$521$	1.25658	−	2.17647i	0.0550519	−	0.0953527i	−0.837186	−	0.546918i	$-0.815801\pi$
$521$	1.25658	−	2.17647i	0.0550519	−	0.0953527i	0.892238	+	0.451565i	$0.149134\pi$
$522$	3.60464	+	2.08114i	0.157771	+	0.0910890i
$523$	−5.67544	−	9.83016i	−0.248170	−	0.429843i	0.714848	−	0.699280i	$-0.246496\pi$
$523$	−5.67544	−	9.83016i	−0.248170	−	0.429843i	−0.963018	+	0.269437i	$0.913162\pi$
$524$	4.16228			0.181830
$525$	0.562146	+	0.649111i	0.0245341	+	0.0283295i
$526$		−	24.9737i		−	1.08890i
$527$	40.2360	−	23.2302i	1.75271	−	1.01193i
$528$	−3.60464	−	2.08114i	−0.156872	−	0.0905699i
$529$	10.8246	−	18.7487i	0.470633	−	0.815160i
$530$	6.66228	+	11.5394i	0.289391	+	0.501240i
$531$			1.83772i			0.0797504i
$532$	−3.16228	−	16.4317i	−0.137102	−	0.712404i
$533$		0			0
$534$	−1.58114	−	2.73861i	−0.0684226	−	0.118511i
$535$	−23.3827	−	13.5000i	−1.01092	−	0.583656i
$536$	−1.41886	+	2.45754i	−0.0612855	+	0.106150i
$537$	4.00000	+	6.92820i	0.172613	+	0.298974i
$538$			21.8377i			0.941491i
$539$	−28.8371	−	4.16228i	−1.24210	−	0.179282i
$540$		−	2.16228i		−	0.0930496i
$541$	9.05906	−	5.23025i	0.389479	−	0.224866i	−0.292455	−	0.956279i	$-0.594472\pi$
$541$	9.05906	−	5.23025i	0.389479	−	0.224866i	0.681935	+	0.731413i	$0.261139\pi$
$542$	−7.50000	+	12.9904i	−0.322153	+	0.557985i
$543$	1.16228	−	2.01312i	0.0498781	−	0.0863914i
$544$	−4.47066	+	2.58114i	−0.191678	+	0.110665i
$545$	−7.53950			−0.322957
$546$	9.09464	−	2.87880i	0.389215	−	0.123201i
$547$	−16.6491			−0.711865			−0.355932	−	0.934512i	$-0.615837\pi$
$547$	−16.6491			−0.711865			−0.355932	+	0.934512i	$0.615837\pi$
$548$	−0.725489	+	0.418861i	−0.0309913	+	0.0178929i
$549$	−7.74342	+	13.4120i	−0.330481	+	0.572410i
$550$	−0.675445	+	1.16990i	−0.0288011	+	0.0498849i
$551$	−22.7977	+	13.1623i	−0.971216	+	0.560732i
$552$			1.16228i			0.0494698i
$553$	15.5885	+	18.0000i	0.662889	+	0.765438i
$554$			15.8114i			0.671762i
$555$	−6.83772	−	11.8433i	−0.290245	−	0.502719i
$556$	5.74342	−	9.94789i	0.243575	−	0.421884i
$557$	−6.78767	−	3.91886i	−0.287603	−	0.166047i	0.349258	−	0.937027i	$-0.386434\pi$
$557$	−6.78767	−	3.91886i	−0.287603	−	0.166047i	−0.636860	+	0.770979i	$0.719767\pi$
$558$	−4.50000	−	7.79423i	−0.190500	−	0.329956i
$559$	3.83772	+	32.8114i	0.162318	+	1.38777i
$560$	5.40569	+	1.87259i	0.228432	+	0.0791313i
$561$			21.4868i			0.907175i
$562$	−2.41886	−	4.18959i	−0.102034	−	0.176727i
$563$	5.40569	−	9.36294i	0.227823	−	0.394601i	−0.729340	−	0.684152i	$-0.760173\pi$
$563$	5.40569	−	9.36294i	0.227823	−	0.394601i	0.957163	+	0.289551i	$0.0935060\pi$
$564$	11.6799	+	6.74342i	0.491814	+	0.283949i
$565$	−3.13742	+	1.81139i	−0.131992	+	0.0762057i
$566$		−	20.9737i		−	0.881589i
$567$	0.866025	−	2.50000i	0.0363696	−	0.104990i
$568$	3.67544			0.154218
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$	11.8433	+	6.83772i	0.496061	+	0.286401i
$571$	2.90569	−	5.03281i	0.121600	−	0.210617i	−0.798799	−	0.601598i	$-0.794531\pi$
$571$	2.90569	−	5.03281i	0.121600	−	0.210617i	0.920399	+	0.390981i	$0.127864\pi$
$572$	8.96269	+	12.0370i	0.374749	+	0.503292i
$573$	4.51317			0.188540
$574$		0			0
$575$	0.377223			0.0157313
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	20.7618	+	11.9868i	0.864325	+	0.499018i	0.865458	−	0.500981i	$-0.167027\pi$
$577$	20.7618	+	11.9868i	0.864325	+	0.499018i	−0.00113310	+	0.999999i	$0.500361\pi$
$578$	8.35637	+	4.82456i	0.347579	+	0.200675i
$579$	13.2715	−	7.66228i	0.551543	−	0.318433i
$580$		−	9.00000i		−	0.373705i
$581$	−8.40569	−	43.6773i	−0.348727	−	1.81204i
$582$	11.0000			0.455965
$583$	−22.2128	+	12.8246i	−0.919959	+	0.531139i
$584$	−3.16228	+	5.47723i	−0.130856	+	0.226649i
$585$	−3.08735	+	7.15884i	−0.127646	+	0.295982i
$586$	−9.24342	−	16.0101i	−0.381842	−	0.661370i
$587$			7.83772i			0.323497i	0.986832	+	0.161749i	$0.0517134\pi$
$587$			7.83772i			0.323497i	−0.986832	+	0.161749i	$0.948287\pi$
$588$	5.50000	+	4.33013i	0.226816	+	0.178571i
$589$	56.9210			2.34539
$590$	3.44130	−	1.98683i	0.141676	−	0.0817966i
$591$	22.7977	+	13.1623i	0.937773	+	0.541424i
$592$	5.47723	+	3.16228i	0.225113	+	0.129969i
$593$	−20.7846	+	12.0000i	−0.853522	+	0.492781i	−0.861838	−	0.507184i	$-0.830686\pi$
$593$	−20.7846	+	12.0000i	−0.853522	+	0.492781i	0.00831589	+	0.999965i	$0.497353\pi$
$594$	4.16228			0.170780
$595$	−5.58114	−	29.0004i	−0.228804	−	1.18890i
$596$			6.00000i			0.245770i
$597$	−9.32456	−	16.1506i	−0.381629	−	0.661000i
$598$	1.65953	−	3.84805i	0.0678632	−	0.157359i
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	−0.920783	−	0.390075i	$-0.872449\pi$
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	0.798206	+	0.602384i	$0.205782\pi$
$600$	0.281073	−	0.162278i	0.0114748	−	0.00662496i
$601$	−46.9473			−1.91502			−0.957511	−	0.288397i	$-0.906878\pi$
$601$	−46.9473			−1.91502			−0.957511	+	0.288397i	$0.906878\pi$
$602$	−18.3246	+	15.8695i	−0.746853	+	0.646794i
$603$		−	2.83772i		−	0.115561i
$604$	−2.59808	+	1.50000i	−0.105714	+	0.0610341i
$605$	11.8433	+	6.83772i	0.481498	+	0.277993i
$606$	14.1375	+	8.16228i	0.574296	+	0.331570i
$607$	11.1754	+	19.3564i	0.453597	+	0.785654i	0.998606	−	0.0527766i	$-0.0168071\pi$
$607$	11.1754	+	19.3564i	0.453597	+	0.785654i	−0.545009	+	0.838430i	$0.683474\pi$
$608$	−6.32456			−0.256495
$609$	3.60464	−	10.4057i	0.146067	−	0.421660i
$610$	33.4868			1.35584
$611$	−29.0414	−	39.0029i	−1.17489	−	1.57789i
$612$	2.58114	−	4.47066i	0.104336	−	0.180716i
$613$	−28.2750	−	16.3246i	−1.14201	−	0.659343i	−0.195086	−	0.980786i	$-0.562499\pi$
$613$	−28.2750	−	16.3246i	−1.14201	−	0.659343i	−0.946929	+	0.321444i	$0.895832\pi$
$614$	−7.58114	−	13.1309i	−0.305950	−	0.529921i
$615$		0			0
$616$	−3.60464	+	10.4057i	−0.145235	+	0.419257i
$617$		−	4.83772i		−	0.194759i	−0.995247	−	0.0973797i	$-0.968954\pi$
$617$		−	4.83772i		−	0.194759i	0.995247	−	0.0973797i	$-0.0310461\pi$
$618$	10.6734	−	6.16228i	0.429346	−	0.247883i
$619$	−8.49691	−	4.90569i	−0.341520	−	0.197176i	0.319424	−	0.947612i	$-0.396511\pi$
$619$	−8.49691	−	4.90569i	−0.341520	−	0.197176i	−0.660944	+	0.750435i	$0.729844\pi$
$620$	−9.73025	+	16.8533i	−0.390776	+	0.676844i
$621$	−0.581139	−	1.00656i	−0.0233203	−	0.0403919i
$622$			32.1359i			1.28853i
$623$	−6.32456	+	5.47723i	−0.253388	+	0.219440i
$624$	−0.418861	−	3.58114i	−0.0167679	−	0.143360i
$625$	11.6359	+	20.1540i	0.465438	+	0.806162i
$626$	12.9904	+	7.50000i	0.519200	+	0.299760i
$627$	−13.1623	+	22.7977i	−0.525651	+	0.910454i
$628$	−4.41886	−	7.65369i	−0.176332	−	0.305416i
$629$		−	32.6491i		−	1.30181i
$630$	−5.61776	+	1.08114i	−0.223817	+	0.0430736i
$631$		−	28.2982i		−	1.12653i	−0.826275	−	0.563267i	$-0.809544\pi$
$631$		−	28.2982i		−	1.12653i	0.826275	−	0.563267i	$-0.190456\pi$
$632$	7.79423	−	4.50000i	0.310038	−	0.179000i
$633$	9.74342	−	16.8761i	0.387266	−	0.670764i
$634$	6.40569	−	11.0950i	0.254403	−	0.440638i
$635$	29.9121	−	17.2698i	1.18702	−	0.685329i
$636$	6.16228			0.244350
$637$	−12.0267	−	22.1892i	−0.476514	−	0.879167i
$638$	17.3246			0.685886
$639$	−3.18303	+	1.83772i	−0.125919	+	0.0726992i
$640$	1.08114	−	1.87259i	0.0427358	−	0.0740205i
$641$	−14.4189	+	24.9742i	−0.569511	+	0.986422i	0.427104	+	0.904203i	$0.359534\pi$
$641$	−14.4189	+	24.9742i	−0.569511	+	0.986422i	−0.996614	+	0.0822189i	$0.973799\pi$
$642$	−10.8139	+	6.24342i	−0.426791	+	0.246408i
$643$		−	14.8377i		−	0.585143i	−0.956244	−	0.292571i	$-0.905489\pi$
$643$		−	14.8377i		−	0.585143i	0.956244	−	0.292571i	$-0.0945109\pi$
$644$	3.01969	−	0.581139i	0.118992	−	0.0229001i
$645$		−	19.8114i		−	0.780073i
$646$	16.3246	+	28.2750i	0.642281	+	1.11246i
$647$	−10.2302	+	17.7193i	−0.402193	+	0.696618i	−0.993990	−	0.109469i	$-0.965085\pi$
$647$	−10.2302	+	17.7193i	−0.402193	+	0.696618i	0.591798	+	0.806087i	$0.298418\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	3.82456	+	6.62432i	0.150127	+	0.260027i
$650$	−1.16228	+	0.135944i	−0.0455883	+	0.00533215i
$651$	−18.0000	+	15.5885i	−0.705476	+	0.610960i
$652$		−	12.6491i		−	0.495377i
$653$	15.5680	+	26.9645i	0.609222	+	1.05520i	0.991369	+	0.131102i	$0.0418514\pi$
$653$	15.5680	+	26.9645i	0.609222	+	1.05520i	−0.382147	+	0.924101i	$0.624815\pi$
$654$	−1.74342	+	3.01969i	−0.0681730	+	0.118079i
$655$	7.79423	+	4.50000i	0.304546	+	0.175830i
$656$		0			0
$657$		−	6.32456i		−	0.246744i
$658$	11.6799	−	33.7171i	0.455331	−	1.31443i
$659$	48.2719			1.88041			0.940203	−	0.340615i	$-0.110635\pi$
$659$	48.2719			1.88041			0.940203	+	0.340615i	$0.110635\pi$
$660$	−4.50000	−	7.79423i	−0.175162	−	0.303390i
$661$	−16.1506	−	9.32456i	−0.628186	−	0.362683i	0.151863	−	0.988401i	$-0.451473\pi$
$661$	−16.1506	−	9.32456i	−0.628186	−	0.362683i	−0.780049	+	0.625718i	$0.784806\pi$
$662$	4.00000	−	6.92820i	0.155464	−	0.269272i
$663$	−14.9289	+	11.1160i	−0.579792	+	0.431710i
$664$	−16.8114			−0.652408
$665$	11.8433	−	34.1886i	0.459263	−	1.32578i
$666$	−6.32456			−0.245072
$667$	−2.41886	−	4.18959i	−0.0936587	−	0.162222i
$668$	4.18959	+	2.41886i	0.162100	+	0.0935885i
$669$	−10.3695	−	5.98683i	−0.400908	−	0.231464i
$670$	−5.31388	+	3.06797i	−0.205293	+	0.118526i
$671$			64.4605i			2.48847i
$672$	2.00000	−	1.73205i	0.0771517	−	0.0668153i
$673$	−3.32456			−0.128152			−0.0640761	−	0.997945i	$-0.520410\pi$
$673$	−3.32456			−0.128152			−0.0640761	+	0.997945i	$0.520410\pi$
$674$	4.04905	−	2.33772i	0.155964	−	0.0900457i
$675$	−0.162278	+	0.281073i	−0.00624607	+	0.0108185i
$676$	−3.72648	+	12.4545i	−0.143326	+	0.479017i
$677$	1.75658	+	3.04249i	0.0675110	+	0.116932i	0.897805	−	0.440393i	$-0.145161\pi$
$677$	1.75658	+	3.04249i	0.0675110	+	0.116932i	−0.830294	+	0.557325i	$0.811828\pi$
$678$			1.67544i			0.0643451i
$679$	−5.50000	−	28.5788i	−0.211071	−	1.09676i
$680$	−11.1623			−0.428054
$681$	−7.34981	+	4.24342i	−0.281645	+	0.162608i
$682$	−32.4417	−	18.7302i	−1.24226	−	0.717218i
$683$	−33.3306	−	19.2434i	−1.27536	−	0.736329i	−0.299368	−	0.954138i	$-0.596776\pi$
$683$	−33.3306	−	19.2434i	−1.27536	−	0.736329i	−0.975991	+	0.217809i	$0.930109\pi$
$684$	5.47723	−	3.16228i	0.209427	−	0.120913i
$685$	−1.81139			−0.0692096
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		−	22.1359i		−	0.844539i
$688$	4.58114	+	7.93477i	0.174654	+	0.302510i
$689$	−20.4020	−	8.79865i	−0.777254	−	0.335202i
$690$	−1.25658	+	2.17647i	−0.0478373	+	0.0828567i
$691$	−6.92820	+	4.00000i	−0.263561	+	0.152167i	−0.625958	−	0.779857i	$-0.715292\pi$
$691$	−6.92820	+	4.00000i	−0.263561	+	0.152167i	0.362397	+	0.932024i	$0.381959\pi$
$692$	−2.32456			−0.0883663
$693$	−2.08114	−	10.8139i	−0.0790559	−	0.410787i
$694$			14.0000i			0.531433i
$695$	21.5101	−	12.4189i	0.815925	−	0.471074i
$696$	−3.60464	−	2.08114i	−0.136633	−	0.0788854i
$697$		0			0
$698$	10.4868	+	18.1637i	0.396932	+	0.687507i
$699$	−5.81139			−0.219807
$700$	−0.562146	−	0.649111i	−0.0212471	−	0.0245341i
$701$	9.18861			0.347049			0.173525	−	0.984830i	$-0.444484\pi$
$701$	9.18861			0.347049			0.173525	+	0.984830i	$0.444484\pi$
$702$	2.15331	+	2.89193i	0.0812716	+	0.109149i
$703$	20.0000	−	34.6410i	0.754314	−	1.30651i
$704$	3.60464	+	2.08114i	0.135855	+	0.0784359i
$705$	14.5811	+	25.2553i	0.549157	+	0.951169i
$706$	8.51317			0.320397
$707$	14.1375	−	40.8114i	0.531695	−	1.53487i
$708$		−	1.83772i		−	0.0690658i
$709$	0.281073	−	0.162278i	0.0105559	−	0.00609447i	−0.494713	−	0.869057i	$-0.664727\pi$
$709$	0.281073	−	0.162278i	0.0105559	−	0.00609447i	0.505269	+	0.862962i	$0.331393\pi$
$710$	6.88259	+	3.97367i	0.258299	+	0.149129i
$711$	−4.50000	+	7.79423i	−0.168763	+	0.292306i
$712$	1.58114	+	2.73861i	0.0592557	+	0.102634i
$713$			10.4605i			0.391749i
$714$	−12.9057	−	4.47066i	−0.482983	−	0.167310i
$715$	3.76975	+	32.2302i	0.140981	+	1.20534i
$716$	−4.00000	−	6.92820i	−0.149487	−	0.258919i
$717$	7.93477	+	4.58114i	0.296329	+	0.171086i
$718$	16.1623	−	27.9939i	0.603171	−	1.04472i
$719$	−18.8114	−	32.5823i	−0.701546	−	1.21511i	−0.967923	−	0.251245i	$-0.919160\pi$
$719$	−18.8114	−	32.5823i	−0.701546	−	1.21511i	0.266377	−	0.963869i	$-0.414173\pi$
$720$			2.16228i			0.0805833i
$721$	−21.3468	−	24.6491i	−0.794995	−	0.917981i
$722$			21.0000i			0.781539i
$723$	10.3695	−	5.98683i	0.385646	−	0.222653i
$724$	−1.16228	+	2.01312i	−0.0431957	+	0.0748172i
$725$	−0.675445	+	1.16990i	−0.0250854	+	0.0434492i
$726$	5.47723	−	3.16228i	0.203279	−	0.117363i
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$	−9.09464	+	2.87880i	−0.337070	+	0.106696i
$729$	1.00000			0.0370370
$730$	−11.8433	+	6.83772i	−0.438340	+	0.253075i
$731$	23.6491	−	40.9615i	0.874694	−	1.51501i
$732$	7.74342	−	13.4120i	0.286205	−	0.495721i
$733$	−33.4711	+	19.3246i	−1.23628	+	0.713769i	−0.968333	−	0.249664i	$-0.919680\pi$
$733$	−33.4711	+	19.3246i	−1.23628	+	0.713769i	−0.267951	+	0.963433i	$0.586347\pi$
$734$		−	8.67544i		−	0.320217i
$735$	5.61776	+	14.0548i	0.207214	+	0.518419i
$736$		−	1.16228i		−	0.0428421i
$737$	−5.90569	−	10.2290i	−0.217539	−	0.376789i
$738$		0			0
$739$	−30.5692	−	17.6491i	−1.12450	−	0.649233i	−0.181958	−	0.983306i	$-0.558243\pi$
$739$	−30.5692	−	17.6491i	−1.12450	−	0.649233i	−0.942547	+	0.334073i	$0.891577\pi$
$740$	6.83772	+	11.8433i	0.251360	+	0.435368i
$741$	−22.6491	+	2.64911i	−0.832036	+	0.0973175i
$742$	−3.08114	−	16.0101i	−0.113112	−	0.587748i
$743$		−	20.8377i		−	0.764462i	−0.924067	−	0.382231i	$-0.875156\pi$
$743$		−	20.8377i		−	0.764462i	0.924067	−	0.382231i	$-0.124844\pi$
$744$	4.50000	+	7.79423i	0.164978	+	0.285750i
$745$	−6.48683	+	11.2355i	−0.237659	+	0.411638i
$746$	1.28764	+	0.743416i	0.0471437	+	0.0272184i
$747$	14.5591	−	8.40569i	0.532689	−	0.307548i
$748$		−	21.4868i		−	0.785636i
$749$	21.6278	+	24.9737i	0.790264	+	0.912518i
$750$	11.5132			0.420401
$751$	26.4737	+	45.8537i	0.966038	+	1.67323i	0.706801	+	0.707413i	$0.250138\pi$
$751$	26.4737	+	45.8537i	0.966038	+	1.67323i	0.259237	+	0.965814i	$0.416529\pi$
$752$	−11.6799	−	6.74342i	−0.425924	−	0.245907i
$753$	−1.24342	+	2.15366i	−0.0453126	+	0.0784838i
$754$	8.96269	+	12.0370i	0.326402	+	0.438362i
$755$	−6.48683			−0.236080
$756$	−0.866025	+	2.50000i	−0.0314970	+	0.0909241i
$757$	−36.9737			−1.34383			−0.671915	−	0.740628i	$-0.734528\pi$
$757$	−36.9737			−1.34383			−0.671915	+	0.740628i	$0.734528\pi$
$758$	11.4868	+	19.8958i	0.417221	+	0.722647i
$759$	−4.18959	−	2.41886i	−0.152072	−	0.0877991i
$760$	−11.8433	−	6.83772i	−0.429601	−	0.248030i
$761$	25.3730	−	14.6491i	0.919771	−	0.531030i	0.0362088	−	0.999344i	$-0.488472\pi$
$761$	25.3730	−	14.6491i	0.919771	−	0.531030i	0.883562	+	0.468314i	$0.155139\pi$
$762$		−	15.9737i		−	0.578665i
$763$	8.71708	+	3.01969i	0.315580	+	0.109320i
$764$	−4.51317			−0.163281
$765$	9.66682	−	5.58114i	0.349504	−	0.201787i
$766$	−5.32456	+	9.22240i	−0.192384	+	0.333219i
$767$	−2.62395	+	6.08431i	−0.0947452	+	0.219692i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$			8.67544i			0.312845i	0.987690	+	0.156422i	$0.0499961\pi$
$769$			8.67544i			0.312845i	−0.987690	+	0.156422i	$0.950004\pi$
$770$	−18.0000	+	15.5885i	−0.648675	+	0.561769i
$771$	12.9737			0.467235
$772$	−13.2715	+	7.66228i	−0.477650	+	0.275771i
$773$	−6.64713	−	3.83772i	−0.239081	−	0.138033i	0.375673	−	0.926752i	$-0.377411\pi$
$773$	−6.64713	−	3.83772i	−0.239081	−	0.138033i	−0.614754	+	0.788719i	$0.710745\pi$
$774$	−7.93477	−	4.58114i	−0.285209	−	0.164666i
$775$	2.52966	−	1.46050i	0.0908680	−	0.0524627i
$776$	−11.0000			−0.394877
$777$	3.16228	+	16.4317i	0.113446	+	0.589483i
$778$			7.67544i			0.275178i
$779$		0			0
$780$	3.08735	−	7.15884i	0.110545	−	0.256328i
$781$	−7.64911	+	13.2486i	−0.273707	+	0.474074i
$782$	−5.19615	+	3.00000i	−0.185814	+	0.107280i
$783$	4.16228			0.148748
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$		−	19.1096i		−	0.682051i
$786$	3.60464	−	2.08114i	0.128573	−	0.0742318i
$787$	9.38574	+	5.41886i	0.334566	+	0.193162i	0.657866	−	0.753135i	$-0.271459\pi$
$787$	9.38574	+	5.41886i	0.334566	+	0.193162i	−0.323301	+	0.946296i	$0.604793\pi$
$788$	−22.7977	−	13.1623i	−0.812136	−	0.468887i
$789$	−12.4868	−	21.6278i	−0.444543	−	0.769971i
$790$	19.4605			0.692373
$791$	4.35293	−	0.837722i	0.154772	−	0.0297860i
$792$	−4.16228			−0.147900
$793$	−44.7868	+	33.3480i	−1.59043	+	1.18422i
$794$	−10.7434	+	18.6081i	−0.381270	+	0.660378i
$795$	11.5394	+	6.66228i	0.409260	+	0.236287i
$796$	9.32456	+	16.1506i	0.330500	+	0.572443i
$797$	23.5132			0.832879			0.416440	−	0.909163i	$-0.363278\pi$
$797$	23.5132			0.832879			0.416440	+	0.909163i	$0.363278\pi$
$798$	−10.9545	−	12.6491i	−0.387783	−	0.447774i
$799$			69.6228i			2.46308i
$800$	−0.281073	+	0.162278i	−0.00993744	+	0.00573738i
$801$	−2.73861	−	1.58114i	−0.0967641	−	0.0558668i
$802$	7.74342	−	13.4120i	0.273430	−	0.473594i
$803$	−13.1623	−	22.7977i	−0.464487	−	0.804515i
$804$			2.83772i			0.100079i
$805$	6.28292	+	2.17647i	0.221444	+	0.0767104i
$806$	−3.76975	−	32.2302i	−0.132784	−	1.13526i
$807$	10.9189	+	18.9120i	0.384362	+	0.665735i
$808$	−14.1375	−	8.16228i	−0.497355	−	0.287148i
$809$	6.83772	−	11.8433i	0.240402	−	0.416388i	−0.720427	−	0.693531i	$-0.756054\pi$
$809$	6.83772	−	11.8433i	0.240402	−	0.416388i	0.960829	+	0.277143i	$0.0893876\pi$
$810$	−1.08114	−	1.87259i	−0.0379873	−	0.0657960i
$811$		−	28.5132i		−	1.00123i	−0.865669	−	0.500616i	$-0.833107\pi$
$811$		−	28.5132i		−	1.00123i	0.865669	−	0.500616i	$-0.166893\pi$
$812$	−3.60464	+	10.4057i	−0.126498	+	0.365168i
$813$			15.0000i			0.526073i
$814$	−22.7977	+	13.1623i	−0.799060	+	0.461338i
$815$	13.6754	−	23.6866i	0.479030	−	0.829704i
$816$	−2.58114	+	4.47066i	−0.0903579	+	0.156505i
$817$	50.1839	−	28.9737i	1.75571	−	1.01366i
$818$	−28.6228			−1.00077
$819$	6.43679	−	7.04044i	0.224920	−	0.246013i
$820$		0			0
$821$	−37.9646	+	21.9189i	−1.32497	+	0.764974i	−0.984517	−	0.175287i	$-0.943915\pi$
$821$	−37.9646	+	21.9189i	−1.32497	+	0.764974i	−0.340456	+	0.940261i	$0.610581\pi$
$822$	−0.418861	+	0.725489i	−0.0146095	+	0.0253043i
$823$	−21.6491	+	37.4974i	−0.754641	+	1.30708i	0.190912	+	0.981607i	$0.438855\pi$
$823$	−21.6491	+	37.4974i	−0.754641	+	1.30708i	−0.945553	+	0.325469i	$0.894478\pi$
$824$	−10.6734	+	6.16228i	−0.371825	+	0.214673i
$825$			1.35089i			0.0470319i
$826$	−4.77454	+	0.918861i	−0.166128	+	0.0319713i
$827$		−	18.8114i		−	0.654136i	−0.945001	−	0.327068i	$-0.893939\pi$
$827$		−	18.8114i		−	0.654136i	0.945001	−	0.327068i	$-0.106061\pi$
$828$	0.581139	+	1.00656i	0.0201960	+	0.0349804i
$829$	−5.25658	+	9.10467i	−0.182569	+	0.316218i	−0.942755	−	0.333487i	$-0.891775\pi$
$829$	−5.25658	+	9.10467i	−0.182569	+	0.316218i	0.760186	+	0.649706i	$0.225108\pi$
$830$	−31.4808	−	18.1754i	−1.09271	−	0.630879i
$831$	7.90569	+	13.6931i	0.274245	+	0.475007i
$832$	0.418861	+	3.58114i	0.0145214	+	0.124154i
$833$	−5.16228	+	35.7653i	−0.178862	+	1.23919i
$834$		−	11.4868i		−	0.397756i
$835$	5.23025	+	9.05906i	0.181000	+	0.313502i
$836$	13.1623	−	22.7977i	0.455227	−	0.788476i
$837$	−7.79423	−	4.50000i	−0.269408	−	0.155543i
$838$	4.63401	−	2.67544i	0.160079	−	0.0924217i
$839$		−	32.6491i		−	1.12717i	−0.826057	−	0.563586i	$-0.809421\pi$
$839$		−	32.6491i		−	1.12717i	0.826057	−	0.563586i	$-0.190579\pi$
$840$	5.61776	−	1.08114i	0.193831	−	0.0373028i
$841$	−11.6754			−0.402602
$842$	10.2566	+	17.7649i	0.353465	+	0.612220i
$843$	−4.18959	−	2.41886i	−0.144297	−	0.0833100i
$844$	−9.74342	+	16.8761i	−0.335382	+	0.580899i
$845$	−20.4431	+	19.2932i	−0.703266	+	0.663706i
$846$	13.4868			0.463687
$847$	−10.9545	−	12.6491i	−0.376399	−	0.434629i
$848$	−6.16228			−0.211613
$849$	−10.4868	−	18.1637i	−0.359907	−	0.623378i
$850$	1.45098	+	0.837722i	0.0497681	+	0.0287336i
$851$	6.36606	+	3.67544i	0.218226	+	0.125993i
$852$	3.18303	−	1.83772i	0.109049	−	0.0629593i
$853$			0.324555i			0.0111126i	0.999985	+	0.00555628i	$0.00176863\pi$
$853$			0.324555i			0.0111126i	−0.999985	+	0.00555628i	$0.998231\pi$
$854$	−38.7171	−	13.4120i	−1.32487	−	0.458949i
$855$	13.6754			0.467690
$856$	10.8139	−	6.24342i	0.369612	−	0.213396i
$857$	12.4868	−	21.6278i	0.426542	−	0.738793i	−0.570021	−	0.821630i	$-0.693065\pi$
$857$	12.4868	−	21.6278i	0.426542	−	0.738793i	0.996563	+	0.0828376i	$0.0263983\pi$
$858$	13.7804	+	5.94300i	0.470456	+	0.202891i
$859$	−26.0680	−	45.1511i	−0.889428	−	1.54053i	−0.840553	−	0.541729i	$-0.817770\pi$
$859$	−26.0680	−	45.1511i	−0.889428	−	1.54053i	−0.0488746	−	0.998805i	$-0.515563\pi$
$860$			19.8114i			0.675563i
$861$		0			0
$862$	−15.4868			−0.527484
$863$	17.1572	−	9.90569i	0.584037	−	0.337194i	−0.178699	−	0.983904i	$-0.557189\pi$
$863$	17.1572	−	9.90569i	0.584037	−	0.337194i	0.762736	+	0.646710i	$0.223856\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−4.35293	−	2.51317i	−0.148004	−	0.0854502i
$866$	17.3205	−	10.0000i	0.588575	−	0.339814i
$867$	9.64911			0.327701
$868$	18.0000	−	15.5885i	0.610960	−	0.529107i
$869$			37.4605i			1.27076i
$870$	−4.50000	−	7.79423i	−0.152564	−	0.264249i
$871$	4.05177	−	9.39510i	0.137289	−	0.318341i
$872$	1.74342	−	3.01969i	0.0590395	−	0.102259i
$873$	9.52628	−	5.50000i	0.322416	−	0.186147i
$874$	−7.35089			−0.248648
$875$	−5.75658	−	29.9121i	−0.194608	−	1.01121i
$876$			6.32456i			0.213687i
$877$	−28.4383	+	16.4189i	−0.960293	+	0.554426i	−0.896263	−	0.443522i	$-0.853729\pi$
$877$	−28.4383	+	16.4189i	−0.960293	+	0.554426i	−0.0640299	+	0.997948i	$0.520395\pi$
$878$	−3.44130	−	1.98683i	−0.116138	−	0.0670524i
$879$	−16.0101	−	9.24342i	−0.540006	−	0.311773i
$880$	4.50000	+	7.79423i	0.151695	+	0.262743i
$881$	42.6491			1.43689			0.718443	−	0.695586i	$-0.244855\pi$
$881$	42.6491			1.43689			0.718443	+	0.695586i	$0.244855\pi$
$882$	6.92820	+	1.00000i	0.233285	+	0.0336718i
$883$	44.4605			1.49621			0.748107	−	0.663578i	$-0.230963\pi$
$883$	44.4605			1.49621			0.748107	+	0.663578i	$0.230963\pi$
$884$	14.9289	−	11.1160i	0.502114	−	0.373872i
$885$	1.98683	−	3.44130i	0.0667867	−	0.115678i
$886$	28.6966	+	16.5680i	0.964080	+	0.556612i
$887$	15.1623	+	26.2618i	0.509099	+	0.881786i	0.999944	+	0.0105392i	$0.00335480\pi$
$887$	15.1623	+	26.2618i	0.509099	+	0.881786i	−0.490845	+	0.871247i	$0.663312\pi$
$888$	6.32456			0.212238
$889$	−41.5008	+	7.98683i	−1.39189	+	0.267870i
$890$			6.83772i			0.229201i
$891$	3.60464	−	2.08114i	0.120760	−	0.0697208i
$892$	10.3695	+	5.98683i	0.347197	+	0.200454i
$893$	−42.6491	+	73.8704i	−1.42720	+	2.47198i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$		−	17.2982i		−	0.578216i
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$	−0.486833	−	4.16228i	−0.0162549	−	0.138974i
$898$	−12.8377	−	22.2356i	−0.428400	−	0.742011i
$899$	−32.4417	−	18.7302i	−1.08199	−	0.624689i
$900$	0.162278	−	0.281073i	0.00540926	−	0.00936911i
$901$	15.9057	+	27.5495i	0.529896	+	0.917806i
$902$		0			0
$903$	−7.93477	+	22.9057i	−0.264052	+	0.762254i
$904$		−	1.67544i		−	0.0557245i
$905$	−4.35293	+	2.51317i	−0.144696	+	0.0835405i
$906$	−1.50000	+	2.59808i	−0.0498342	+	0.0863153i
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	−0.595082	−	0.803665i	$-0.702880\pi$
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	0.993535	+	0.113523i	$0.0362137\pi$
$908$	7.34981	−	4.24342i	0.243912	−	0.140823i
$909$	16.3246			0.541451
$910$	−20.1429	−	4.44176i	−0.667730	−	0.147243i
$911$	−23.6754			−0.784402			−0.392201	−	0.919879i	$-0.628286\pi$
$911$	−23.6754			−0.784402			−0.392201	+	0.919879i	$0.628286\pi$
$912$	−5.47723	+	3.16228i	−0.181369	+	0.104713i
$913$	34.9868	−	60.5990i	1.15790	−	2.00553i
$914$	−3.50000	+	6.06218i	−0.115770	+	0.200519i
$915$	29.0004	−	16.7434i	0.958725	−	0.553520i
$916$			22.1359i			0.731392i
$917$	−7.20928	−	8.32456i	−0.238071	−	0.274901i
$918$		−	5.16228i		−	0.170381i
$919$	16.4868	+	28.5560i	0.543850	+	0.941977i	0.998678	+	0.0513972i	$0.0163675\pi$
$919$	16.4868	+	28.5560i	0.543850	+	0.941977i	−0.454828	+	0.890579i	$0.650299\pi$
$920$	1.25658	−	2.17647i	0.0414283	−	0.0717560i
$921$	−13.1309	−	7.58114i	−0.432678	−	0.249807i
$922$	7.32456	+	12.6865i	0.241221	+	0.417808i
$923$	−13.1623	+	1.53950i	−0.433242	+	0.0506733i
$924$	2.08114	+	10.8139i	0.0684644	+	0.355752i
$925$		−	2.05267i		−	0.0674913i
$926$	12.1623	+	21.0657i	0.399677	+	0.692261i
$927$	6.16228	−	10.6734i	0.202396	−	0.350560i
$928$	3.60464	+	2.08114i	0.118328	+	0.0683167i
$929$	−14.2552	+	8.23025i	−0.467698	+	0.270026i	−0.715276	−	0.698842i	$-0.753699\pi$
$929$	−14.2552	+	8.23025i	−0.467698	+	0.270026i	0.247577	+	0.968868i	$0.420366\pi$
$930$			19.4605i			0.638135i
$931$	−27.3861	+	34.7851i	−0.897544	+	1.14003i
$932$	5.81139			0.190358
$933$	16.0680	+	27.8305i	0.526042	+	0.911131i
$934$	14.4186	+	8.32456i	0.471789	+	0.272388i
$935$	23.2302	−	40.2360i	0.759710	−	1.31586i
$936$	−2.15331	−	2.89193i	−0.0703833	−	0.0945256i
$937$	3.64911			0.119211			0.0596056	−	0.998222i	$-0.481016\pi$
$937$	3.64911			0.119211			0.0596056	+	0.998222i	$0.481016\pi$
$938$	7.37262	−	1.41886i	0.240725	−	0.0463275i
$939$	15.0000			0.489506
$940$	−14.5811	−	25.2553i	−0.475584	−	0.823736i
$941$	40.5399	+	23.4057i	1.32156	+	0.763004i	0.983978	−	0.178292i	$-0.0570571\pi$
$941$	40.5399	+	23.4057i	1.32156	+	0.763004i	0.337584	+	0.941296i	$0.390390\pi$
$942$	−7.65369	−	4.41886i	−0.249371	−	0.143974i
$943$		0			0
$944$			1.83772i			0.0598128i
$945$	−4.32456	+	3.74517i	−0.140678	+	0.121831i
$946$	−38.1359			−1.23991
$947$	40.1182	−	23.1623i	1.30367	−	0.752673i	0.322637	−	0.946523i	$-0.395431\pi$
$947$	40.1182	−	23.1623i	1.30367	−	0.752673i	0.981031	+	0.193850i	$0.0620975\pi$
$948$	4.50000	−	7.79423i	0.146153	−	0.253145i
$949$	9.03036	−	20.9393i	0.293138	−	0.679717i
$950$	1.02633	+	1.77766i	0.0332987	+	0.0576750i
$951$		−	12.8114i		−	0.415438i
$952$	12.9057	+	4.47066i	0.418276	+	0.144895i
$953$	−50.7851			−1.64509			−0.822545	−	0.568701i	$-0.807446\pi$
$953$	−50.7851			−1.64509			−0.822545	+	0.568701i	$0.807446\pi$
$954$	5.33669	−	3.08114i	0.172782	−	0.0997556i
$955$	−8.45130	−	4.87936i	−0.273478	−	0.157892i
$956$	−7.93477	−	4.58114i	−0.256629	−	0.148165i
$957$	15.0035	−	8.66228i	0.484994	−	0.280012i
$958$	−28.3246			−0.915125
$959$	2.09431	+	0.725489i	0.0676287	+	0.0234273i
$960$		−	2.16228i		−	0.0697872i
$961$	25.0000	+	43.3013i	0.806452	+	1.39682i
$962$	−20.9393	−	9.03036i	−0.675109	−	0.291150i
$963$	−6.24342	+	10.8139i	−0.201191	+	0.348474i
$964$	−10.3695	+	5.98683i	−0.333979	+	0.192823i
$965$	−33.1359			−1.06668
$966$	2.32456	−	2.01312i	0.0747913	−	0.0647712i
$967$		−	6.02633i		−	0.193794i	−0.995294	−	0.0968969i	$-0.969108\pi$
$967$		−	6.02633i		−	0.193794i	0.995294	−	0.0968969i	$-0.0308917\pi$
$968$	−5.47723	+	3.16228i	−0.176045	+	0.101639i
$969$	28.2750	+	16.3246i	0.908323	+	0.524420i
$970$	−20.5985	−	11.8925i	−0.661377	−	0.381846i
$971$	8.73025	+	15.1212i	0.280167	+	0.485264i	0.971426	−	0.237344i	$-0.0762768\pi$
$971$	8.73025	+	15.1212i	0.280167	+	0.485264i	−0.691259	+	0.722607i	$0.742943\pi$
$972$	−1.00000			−0.0320750
$973$	−29.8437	+	5.74342i	−0.956744	+	0.184125i
$974$	−19.0000			−0.608799
$975$	−0.938590	+	0.698869i	−0.0300589	+	0.0223817i
$976$	−7.74342	+	13.4120i	−0.247861	+	0.429307i
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	0.728184	−	0.685381i	$-0.240364\pi$
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	−0.229465	+	0.973317i	$0.573698\pi$
$978$	−6.32456	−	10.9545i	−0.202237	−	0.350285i
$979$	−13.1623			−0.420668
$980$	−5.61776	−	14.0548i	−0.179453	−	0.448964i
$981$			3.48683i			0.111326i
$982$	20.9251	−	12.0811i	0.667748	−	0.385525i
$983$	−43.7001	−	25.2302i	−1.39382	−	0.804720i	−0.400081	−	0.916480i	$-0.631018\pi$
$983$	−43.7001	−	25.2302i	−1.39382	−	0.804720i	−0.993735	+	0.111760i	$0.964351\pi$
$984$		0			0
$985$	−28.4605	−	49.2950i	−0.906827	−	1.57067i
$986$		−	21.4868i		−	0.684280i
$987$	−6.74342	−	35.0398i	−0.214645	−	1.11533i
$988$	22.6491	−	2.64911i	0.720564	−	0.0842794i
$989$	5.32456	+	9.22240i	0.169311	+	0.293255i
$990$	−7.79423	−	4.50000i	−0.247717	−	0.143019i
$991$	19.8246	−	34.3371i	0.629748	−	1.09076i	−0.357854	−	0.933777i	$-0.616492\pi$
$991$	19.8246	−	34.3371i	0.629748	−	1.09076i	0.987602	−	0.156978i	$-0.0501751\pi$
$992$	−4.50000	−	7.79423i	−0.142875	−	0.247467i
$993$		−	8.00000i		−	0.253872i
$994$	−6.36606	−	7.35089i	−0.201919	−	0.233156i
$995$			40.3246i			1.27837i
$996$	−14.5591	+	8.40569i	−0.461322	+	0.266345i
$997$	−19.4189	+	33.6345i	−0.615002	+	1.06521i	0.375383	+	0.926870i	$0.377511\pi$
$997$	−19.4189	+	33.6345i	−0.615002	+	1.06521i	−0.990384	+	0.138344i	$0.955822\pi$
$998$	−3.74342	+	6.48379i	−0.118496	+	0.205241i
$999$	−5.47723	+	3.16228i	−0.173292	+	0.100050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.a.25.2	✓	8
3.2	odd	2		1638.2.dm.b.1117.3		8
7.2	even	3	inner	546.2.bk.a.415.3	yes	8
7.3	odd	6		3822.2.c.f.883.1		4
7.4	even	3		3822.2.c.g.883.2		4
13.12	even	2	inner	546.2.bk.a.25.3	yes	8
21.2	odd	6		1638.2.dm.b.415.2		8
39.38	odd	2		1638.2.dm.b.1117.2		8
91.25	even	6		3822.2.c.g.883.3		4
91.38	odd	6		3822.2.c.f.883.4		4
91.51	even	6	inner	546.2.bk.a.415.2	yes	8
273.233	odd	6		1638.2.dm.b.415.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.a.25.2	✓	8	1.1	even	1	trivial
546.2.bk.a.25.3	yes	8	13.12	even	2	inner
546.2.bk.a.415.2	yes	8	91.51	even	6	inner
546.2.bk.a.415.3	yes	8	7.2	even	3	inner
1638.2.dm.b.415.2		8	21.2	odd	6
1638.2.dm.b.415.3		8	273.233	odd	6
1638.2.dm.b.1117.2		8	39.38	odd	2
1638.2.dm.b.1117.3		8	3.2	odd	2
3822.2.c.f.883.1		4	7.3	odd	6
3822.2.c.f.883.4		4	91.38	odd	6
3822.2.c.g.883.2		4	7.4	even	3
3822.2.c.g.883.3		4	91.25	even	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.87259 - 1.08114i) q^{5} -1.00000i q^{6} +(-2.59808 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.87259 - 1.08114i) q^{5} -1.00000i q^{6} +(-2.59808 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.08114 + 1.87259i) q^{10} +(-3.60464 - 2.08114i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.418861 - 3.58114i) q^{13} +(2.00000 - 1.73205i) q^{14} +2.16228i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.58114 + 4.47066i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-5.47723 + 3.16228i) q^{19} -2.16228i q^{20} +(0.866025 - 2.50000i) q^{21} +4.16228 q^{22} +(-0.581139 - 1.00656i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-0.162278 + 0.281073i) q^{25} +(2.15331 + 2.89193i) q^{26} +1.00000 q^{27} +(-0.866025 + 2.50000i) q^{28} +4.16228 q^{29} +(-1.08114 - 1.87259i) q^{30} +(-7.79423 - 4.50000i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.60464 - 2.08114i) q^{33} -5.16228i q^{34} +(-4.32456 + 3.74517i) q^{35} -1.00000 q^{36} +(-5.47723 + 3.16228i) q^{37} +(3.16228 - 5.47723i) q^{38} +(3.31079 + 1.42783i) q^{39} +(1.08114 + 1.87259i) q^{40} +(0.500000 + 2.59808i) q^{42} -9.16228 q^{43} +(-3.60464 + 2.08114i) q^{44} +(-1.87259 - 1.08114i) q^{45} +(1.00656 + 0.581139i) q^{46} +(11.6799 - 6.74342i) q^{47} +1.00000 q^{48} +(6.50000 - 2.59808i) q^{49} -0.324555i q^{50} +(-2.58114 - 4.47066i) q^{51} +(-3.31079 - 1.42783i) q^{52} +(3.08114 - 5.33669i) q^{53} +(-0.866025 + 0.500000i) q^{54} -9.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} -6.32456i q^{57} +(-3.60464 + 2.08114i) q^{58} +(-1.59151 - 0.918861i) q^{59} +(1.87259 + 1.08114i) q^{60} +(-7.74342 - 13.4120i) q^{61} +9.00000 q^{62} +(1.73205 + 2.00000i) q^{63} -1.00000 q^{64} +(-4.65606 - 6.25315i) q^{65} +(-2.08114 + 3.60464i) q^{66} +(2.45754 + 1.41886i) q^{67} +(2.58114 + 4.47066i) q^{68} +1.16228 q^{69} +(1.87259 - 5.40569i) q^{70} -3.67544i q^{71} +(0.866025 - 0.500000i) q^{72} +(5.47723 + 3.16228i) q^{73} +(3.16228 - 5.47723i) q^{74} +(-0.162278 - 0.281073i) q^{75} +6.32456i q^{76} +(10.4057 + 3.60464i) q^{77} +(-3.58114 + 0.418861i) q^{78} +(-4.50000 - 7.79423i) q^{79} +(-1.87259 - 1.08114i) q^{80} +(-0.500000 + 0.866025i) q^{81} +16.8114i q^{83} +(-1.73205 - 2.00000i) q^{84} +11.1623i q^{85} +(7.93477 - 4.58114i) q^{86} +(-2.08114 + 3.60464i) q^{87} +(2.08114 - 3.60464i) q^{88} +(2.73861 - 1.58114i) q^{89} +2.16228 q^{90} +(2.87880 + 9.09464i) q^{91} -1.16228 q^{92} +(7.79423 - 4.50000i) q^{93} +(-6.74342 + 11.6799i) q^{94} +(-6.83772 + 11.8433i) q^{95} +(-0.866025 + 0.500000i) q^{96} +11.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} +4.16228i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} + 4 q^{10} + 4 q^{12} - 16 q^{13} + 16 q^{14} - 4 q^{16} - 8 q^{17} + 8 q^{22} + 8 q^{23} + 24 q^{25} + 8 q^{26} + 8 q^{27} + 8 q^{29} + 4 q^{30} + 16 q^{35} - 8 q^{36} + 8 q^{39} - 4 q^{40} + 4 q^{42} - 48 q^{43} + 8 q^{48} + 52 q^{49} - 8 q^{51} - 8 q^{52} + 12 q^{53} - 72 q^{55} - 4 q^{56} - 24 q^{61} + 72 q^{62} - 8 q^{64} - 12 q^{65} - 4 q^{66} + 8 q^{68} - 16 q^{69} + 24 q^{75} + 20 q^{77} - 16 q^{78} - 36 q^{79} - 4 q^{81} - 4 q^{87} + 4 q^{88} - 8 q^{90} + 8 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 + 4 * q^10 + 4 * q^12 - 16 * q^13 + 16 * q^14 - 4 * q^16 - 8 * q^17 + 8 * q^22 + 8 * q^23 + 24 * q^25 + 8 * q^26 + 8 * q^27 + 8 * q^29 + 4 * q^30 + 16 * q^35 - 8 * q^36 + 8 * q^39 - 4 * q^40 + 4 * q^42 - 48 * q^43 + 8 * q^48 + 52 * q^49 - 8 * q^51 - 8 * q^52 + 12 * q^53 - 72 * q^55 - 4 * q^56 - 24 * q^61 + 72 * q^62 - 8 * q^64 - 12 * q^65 - 4 * q^66 + 8 * q^68 - 16 * q^69 + 24 * q^75 + 20 * q^77 - 16 * q^78 - 36 * q^79 - 4 * q^81 - 4 * q^87 + 4 * q^88 - 8 * q^90 + 8 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95

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