LMFDB - Embedded newform 390.2.bn.b.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			163.4
Root			$-0.709944 - 0.925217i$ of defining polynomial
Character	$\chi$	$=$	390.163
Dual form			390.2.bn.b.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.61532 - 1.54620i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.65408 - 0.954985i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.61532 - 1.54620i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.65408 - 0.954985i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.531389 - 2.17201i) q^{10} +(0.562653 + 2.09985i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(-2.75032 + 2.33147i) q^{13} -1.90997i q^{14} +(1.16009 - 1.91159i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.160023 + 0.597215i) q^{17} -1.00000i q^{18} +(-3.46041 - 0.927215i) q^{19} +(-2.14671 - 0.625808i) q^{20} +(1.35055 - 1.35055i) q^{21} +(2.09985 + 0.562653i) q^{22} +(-0.175094 - 0.653459i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(0.218523 - 4.99522i) q^{25} +(0.643951 + 3.54758i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.65408 - 0.954985i) q^{28} +(2.93087 + 1.69214i) q^{29} +(-1.07544 - 1.96047i) q^{30} +(0.691834 + 0.691834i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.08696 + 1.88267i) q^{33} +(0.437192 + 0.437192i) q^{34} +(1.19528 - 4.10015i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-2.47309 - 1.42784i) q^{37} +(-2.53320 + 2.53320i) q^{38} +(-2.05318 + 2.96386i) q^{39} +(-1.61532 + 1.54620i) q^{40} +(7.83418 - 2.09916i) q^{41} +(-0.494337 - 1.84489i) q^{42} +(-3.36512 - 0.901681i) q^{43} +(1.53720 - 1.53720i) q^{44} +(0.625808 - 2.14671i) q^{45} +(-0.653459 - 0.175094i) q^{46} +10.8506i q^{47} +(-0.258819 + 0.965926i) q^{48} +(-1.67601 + 2.90293i) q^{49} +(-4.21673 - 2.68686i) q^{50} +0.618283i q^{51} +(3.39427 + 1.21611i) q^{52} +(-1.54550 - 1.54550i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(4.15565 + 2.52196i) q^{55} +(-1.65408 + 0.954985i) q^{56} -3.58249 q^{57} +(2.93087 - 1.69214i) q^{58} +(-3.75207 + 14.0029i) q^{59} +(-2.23553 - 0.0488750i) q^{60} +(-2.85745 - 4.94925i) q^{61} +(0.945063 - 0.253229i) q^{62} +(0.954985 - 1.65408i) q^{63} +1.00000 q^{64} +(-0.837729 + 8.01862i) q^{65} +2.17392 q^{66} +(2.92806 - 5.07155i) q^{67} +(0.597215 - 0.160023i) q^{68} +(-0.338255 - 0.585876i) q^{69} +(-2.95320 - 3.08522i) q^{70} +(-1.78054 + 6.64505i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.15267 q^{73} +(-2.47309 + 1.42784i) q^{74} +(-1.08178 - 4.88157i) q^{75} +(0.927215 + 3.46041i) q^{76} +(2.93600 + 2.93600i) q^{77} +(1.54019 + 3.26003i) q^{78} +5.11418i q^{79} +(0.531389 + 2.17201i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.09916 - 7.83418i) q^{82} -3.84261i q^{83} +(-1.84489 - 0.494337i) q^{84} +(0.664926 + 1.21212i) q^{85} +(-2.46344 + 2.46344i) q^{86} +(3.26896 + 0.875916i) q^{87} +(-0.562653 - 2.09985i) q^{88} +(-0.804636 + 0.215602i) q^{89} +(-1.54620 - 1.61532i) q^{90} +(-2.32274 + 6.48296i) q^{91} +(-0.478365 + 0.478365i) q^{92} +(0.847320 + 0.489200i) q^{93} +(9.39693 + 5.42532i) q^{94} +(-7.02334 + 3.85275i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-9.16293 - 15.8707i) q^{97} +(1.67601 + 2.90293i) q^{98} +(1.53720 + 1.53720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	$ 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.61532	−	1.54620i	0.722393	−	0.691482i
$5$	1.61532	−	1.54620i	0.722393	−	0.691482i
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	1.65408	−	0.954985i	0.625185	−	0.360951i	−0.153700	−	0.988118i	$-0.549119\pi$
$7$	1.65408	−	0.954985i	0.625185	−	0.360951i	0.778885	+	0.627167i	$0.215786\pi$
$8$	−1.00000			−0.353553
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−0.531389	−	2.17201i	−0.168040	−	0.686850i
$11$	0.562653	+	2.09985i	0.169646	+	0.633128i	0.997402	+	0.0720394i	$0.0229507\pi$
$11$	0.562653	+	2.09985i	0.169646	+	0.633128i	−0.827756	+	0.561089i	$0.810383\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−2.75032	+	2.33147i	−0.762801	+	0.646633i
$13$	−2.75032	+	2.33147i	−0.762801	+	0.646633i
$14$		−	1.90997i		−	0.510461i
$15$	1.16009	−	1.91159i	0.299535	−	0.493571i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.160023	+	0.597215i	−0.0388114	+	0.144846i	−0.982613	−	0.185668i	$-0.940555\pi$
$17$	−0.160023	+	0.597215i	−0.0388114	+	0.144846i	0.943801	+	0.330514i	$0.107222\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−3.46041	−	0.927215i	−0.793874	−	0.212718i	−0.160981	−	0.986957i	$-0.551466\pi$
$19$	−3.46041	−	0.927215i	−0.793874	−	0.212718i	−0.632892	+	0.774240i	$0.718132\pi$
$20$	−2.14671	−	0.625808i	−0.480019	−	0.139935i
$21$	1.35055	−	1.35055i	0.294715	−	0.294715i
$22$	2.09985	+	0.562653i	0.447689	+	0.119958i
$23$	−0.175094	−	0.653459i	−0.0365096	−	0.136256i	0.945265	−	0.326302i	$-0.105803\pi$
$23$	−0.175094	−	0.653459i	−0.0365096	−	0.136256i	−0.981775	+	0.190047i	$0.939136\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	0.218523	−	4.99522i	0.0437047	−	0.999044i
$26$	0.643951	+	3.54758i	0.126289	+	0.695738i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.65408	−	0.954985i	−0.312592	−	0.180475i
$29$	2.93087	+	1.69214i	0.544249	+	0.314222i	0.746799	−	0.665050i	$-0.231590\pi$
$29$	2.93087	+	1.69214i	0.544249	+	0.314222i	−0.202550	+	0.979272i	$0.564923\pi$
$30$	−1.07544	−	1.96047i	−0.196348	−	0.357931i
$31$	0.691834	+	0.691834i	0.124257	+	0.124257i	0.766501	−	0.642244i	$-0.221996\pi$
$31$	0.691834	+	0.691834i	0.124257	+	0.124257i	−0.642244	+	0.766501i	$0.721996\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.08696	+	1.88267i	0.189216	+	0.327731i
$34$	0.437192	+	0.437192i	0.0749778	+	0.0749778i
$35$	1.19528	−	4.10015i	0.202038	−	0.693052i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−2.47309	−	1.42784i	−0.406573	−	0.234735i	0.282743	−	0.959196i	$-0.408756\pi$
$37$	−2.47309	−	1.42784i	−0.406573	−	0.234735i	−0.689316	+	0.724460i	$0.742089\pi$
$38$	−2.53320	+	2.53320i	−0.410939	+	0.410939i
$39$	−2.05318	+	2.96386i	−0.328771	+	0.474598i
$40$	−1.61532	+	1.54620i	−0.255405	+	0.244476i
$41$	7.83418	−	2.09916i	1.22349	−	0.327834i	0.411450	−	0.911432i	$-0.365022\pi$
$41$	7.83418	−	2.09916i	1.22349	−	0.327834i	0.812043	+	0.583598i	$0.198356\pi$
$42$	−0.494337	−	1.84489i	−0.0762778	−	0.284673i
$43$	−3.36512	−	0.901681i	−0.513176	−	0.137505i	−0.00706771	−	0.999975i	$-0.502250\pi$
$43$	−3.36512	−	0.901681i	−0.513176	−	0.137505i	−0.506108	+	0.862470i	$0.668916\pi$
$44$	1.53720	−	1.53720i	0.231741	−	0.231741i
$45$	0.625808	−	2.14671i	0.0932900	−	0.320013i
$46$	−0.653459	−	0.175094i	−0.0963473	−	0.0258162i
$47$			10.8506i			1.58273i	0.611344	+	0.791365i	$0.290629\pi$
$47$			10.8506i			1.58273i	−0.611344	+	0.791365i	$0.709371\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	−1.67601	+	2.90293i	−0.239429	+	0.414704i
$50$	−4.21673	−	2.68686i	−0.596335	−	0.379979i
$51$			0.618283i			0.0865769i
$52$	3.39427	+	1.21611i	0.470701	+	0.168644i
$53$	−1.54550	−	1.54550i	−0.212290	−	0.212290i	0.592949	−	0.805240i	$-0.297963\pi$
$53$	−1.54550	−	1.54550i	−0.212290	−	0.212290i	−0.805240	+	0.592949i	$0.797963\pi$
$54$	−0.258819	−	0.965926i	−0.0352208	−	0.131446i
$55$	4.15565	+	2.52196i	0.560348	+	0.340060i
$56$	−1.65408	+	0.954985i	−0.221036	+	0.127615i
$57$	−3.58249			−0.474512
$58$	2.93087	−	1.69214i	0.384842	−	0.222189i
$59$	−3.75207	+	14.0029i	−0.488478	+	1.82302i	0.0753830	+	0.997155i	$0.475982\pi$
$59$	−3.75207	+	14.0029i	−0.488478	+	1.82302i	−0.563861	+	0.825870i	$0.690685\pi$
$60$	−2.23553	−	0.0488750i	−0.288606	−	0.00630973i
$61$	−2.85745	−	4.94925i	−0.365859	−	0.633687i	0.623055	−	0.782178i	$-0.285891\pi$
$61$	−2.85745	−	4.94925i	−0.365859	−	0.633687i	−0.988914	+	0.148492i	$0.952558\pi$
$62$	0.945063	−	0.253229i	0.120023	−	0.0321601i
$63$	0.954985	−	1.65408i	0.120317	−	0.208395i
$64$	1.00000			0.125000
$65$	−0.837729	+	8.01862i	−0.103907	+	0.994587i
$66$	2.17392			0.267591
$67$	2.92806	−	5.07155i	0.357719	−	0.619588i	−0.629860	−	0.776709i	$-0.716888\pi$
$67$	2.92806	−	5.07155i	0.357719	−	0.619588i	0.987579	+	0.157120i	$0.0502211\pi$
$68$	0.597215	−	0.160023i	0.0724230	−	0.0194057i
$69$	−0.338255	−	0.585876i	−0.0407212	−	0.0705311i
$70$	−2.95320	−	3.08522i	−0.352975	−	0.368754i
$71$	−1.78054	+	6.64505i	−0.211311	+	0.788622i	0.776122	+	0.630583i	$0.217184\pi$
$71$	−1.78054	+	6.64505i	−0.211311	+	0.788622i	−0.987433	+	0.158039i	$0.949483\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	2.15267			0.251951			0.125976	−	0.992033i	$-0.459794\pi$
$73$	2.15267			0.251951			0.125976	+	0.992033i	$0.459794\pi$
$74$	−2.47309	+	1.42784i	−0.287491	+	0.165983i
$75$	−1.08178	−	4.88157i	−0.124913	−	0.563675i
$76$	0.927215	+	3.46041i	0.106359	+	0.396937i
$77$	2.93600	+	2.93600i	0.334588	+	0.334588i
$78$	1.54019	+	3.26003i	0.174392	+	0.369126i
$79$			5.11418i			0.575390i	0.957722	+	0.287695i	$0.0928890\pi$
$79$			5.11418i			0.575390i	−0.957722	+	0.287695i	$0.907111\pi$
$80$	0.531389	+	2.17201i	0.0594111	+	0.242838i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	2.09916	−	7.83418i	0.231814	−	0.865140i
$83$		−	3.84261i		−	0.421781i	−0.977510	−	0.210891i	$-0.932364\pi$
$83$		−	3.84261i		−	0.421781i	0.977510	−	0.210891i	$-0.0676364\pi$
$84$	−1.84489	−	0.494337i	−0.201294	−	0.0539366i
$85$	0.664926	+	1.21212i	0.0721214	+	0.131473i
$86$	−2.46344	+	2.46344i	−0.265639	+	0.265639i
$87$	3.26896	+	0.875916i	0.350470	+	0.0939080i
$88$	−0.562653	−	2.09985i	−0.0599790	−	0.223845i
$89$	−0.804636	+	0.215602i	−0.0852912	+	0.0228537i	−0.301212	−	0.953557i	$-0.597391\pi$
$89$	−0.804636	+	0.215602i	−0.0852912	+	0.0228537i	0.215921	+	0.976411i	$0.430725\pi$
$90$	−1.54620	−	1.61532i	−0.162984	−	0.170270i
$91$	−2.32274	+	6.48296i	−0.243489	+	0.679599i
$92$	−0.478365	+	0.478365i	−0.0498730	+	0.0498730i
$93$	0.847320	+	0.489200i	0.0878630	+	0.0507277i
$94$	9.39693	+	5.42532i	0.969220	+	0.559579i
$95$	−7.02334	+	3.85275i	−0.720580	+	0.395284i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−9.16293	−	15.8707i	−0.930354	−	1.61142i	−0.782715	−	0.622380i	$-0.786166\pi$
$97$	−9.16293	−	15.8707i	−0.930354	−	1.61142i	−0.147639	−	0.989041i	$-0.547167\pi$
$98$	1.67601	+	2.90293i	0.169302	+	0.293240i
$99$	1.53720	+	1.53720i	0.154494	+	0.154494i
$100$	−4.43525	+	2.30836i	−0.443525	+	0.230836i
$101$	14.6508	+	8.45864i	1.45781	+	0.841666i	0.998903	−	0.0468187i	$-0.0149083\pi$
$101$	14.6508	+	8.45864i	1.45781	+	0.841666i	0.458906	+	0.888485i	$0.348242\pi$
$102$	0.535449	+	0.309141i	0.0530173	+	0.0306096i
$103$	3.60087	−	3.60087i	0.354804	−	0.354804i	−0.507090	−	0.861893i	$-0.669279\pi$
$103$	3.60087	−	3.60087i	0.354804	−	0.354804i	0.861893	+	0.507090i	$0.169279\pi$
$104$	2.75032	−	2.33147i	0.269691	−	0.228619i
$105$	0.0933498	−	4.26980i	0.00911001	−	0.416690i
$106$	−2.11119	+	0.565691i	−0.205057	+	0.0549448i
$107$	2.46933	+	9.21566i	0.238719	+	0.890911i	0.976437	+	0.215802i	$0.0692367\pi$
$107$	2.46933	+	9.21566i	0.238719	+	0.890911i	−0.737718	+	0.675109i	$0.764097\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	−9.88219	+	9.88219i	−0.946542	+	0.946542i	−0.998642	−	0.0520997i	$-0.983409\pi$
$109$	−9.88219	+	9.88219i	−0.946542	+	0.946542i	0.0520997	+	0.998642i	$0.483409\pi$
$110$	4.26190	−	2.33792i	0.406357	−	0.222912i
$111$	−2.75837	−	0.739104i	−0.261813	−	0.0701526i
$112$			1.90997i			0.180475i
$113$	3.48791	−	13.0170i	0.328115	−	1.22454i	−0.583029	−	0.812451i	$-0.698133\pi$
$113$	3.48791	−	13.0170i	0.328115	−	1.22454i	0.911144	−	0.412089i	$-0.135201\pi$
$114$	−1.79124	+	3.10252i	−0.167765	+	0.290578i
$115$	−1.29321	−	0.784816i	−0.120593	−	0.0731845i
$116$		−	3.38428i		−	0.314222i
$117$	−1.21611	+	3.39427i	−0.112430	+	0.313800i
$118$	10.2508	+	10.2508i	0.943667	+	0.943667i
$119$	0.305640	+	1.14066i	0.0280180	+	0.104564i
$120$	−1.16009	+	1.91159i	−0.105902	+	0.174504i
$121$	5.43349	−	3.13703i	0.493954	−	0.285184i
$122$	−5.71490			−0.517403
$123$	7.02393	−	4.05527i	0.633327	−	0.365651i
$124$	0.253229	−	0.945063i	0.0227406	−	0.0848691i
$125$	−7.37063	−	8.40677i	−0.659250	−	0.751924i
$126$	−0.954985	−	1.65408i	−0.0850769	−	0.147357i
$127$	13.2534	−	3.55123i	1.17605	−	0.315121i	0.382690	−	0.923877i	$-0.374998\pi$
$127$	13.2534	−	3.55123i	1.17605	−	0.315121i	0.793357	+	0.608756i	$0.208331\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.48383			−0.306734
$130$	6.52546	+	4.73480i	0.572321	+	0.415270i
$131$	16.6377			1.45364			0.726820	−	0.686828i	$-0.240997\pi$
$131$	16.6377			1.45364			0.726820	+	0.686828i	$0.240997\pi$
$132$	1.08696	−	1.88267i	0.0946079	−	0.163866i
$133$	−6.60929	+	1.77095i	−0.573098	+	0.153561i
$134$	−2.92806	−	5.07155i	−0.252946	−	0.438115i
$135$	0.0488750	−	2.23553i	0.00420649	−	0.192404i
$136$	0.160023	−	0.597215i	0.0137219	−	0.0512108i
$137$	−7.14214	+	4.12352i	−0.610195	+	0.352296i	−0.773042	−	0.634355i	$-0.781266\pi$
$137$	−7.14214	+	4.12352i	−0.610195	+	0.352296i	0.162847	+	0.986651i	$0.447932\pi$
$138$	−0.676511			−0.0575884
$139$	−12.7043	+	7.33484i	−1.07757	+	0.622133i	−0.930239	−	0.366954i	$-0.880401\pi$
$139$	−12.7043	+	7.33484i	−1.07757	+	0.622133i	−0.147328	+	0.989088i	$0.547067\pi$
$140$	−4.14847	+	1.01494i	−0.350610	+	0.0857779i
$141$	2.80835	+	10.4809i	0.236506	+	0.882653i
$142$	4.86451	+	4.86451i	0.408221	+	0.408221i
$143$	−6.44321	−	4.46345i	−0.538808	−	0.373252i
$144$			1.00000i			0.0833333i
$145$	7.35069	−	1.79837i	0.610441	−	0.149346i
$146$	1.07634	−	1.86427i	0.0890782	−	0.154288i
$147$	−0.867565	+	3.23780i	−0.0715555	+	0.267049i
$148$			2.85568i			0.234735i
$149$	−12.3571	−	3.31108i	−1.01233	−	0.271254i	−0.285730	−	0.958310i	$-0.592236\pi$
$149$	−12.3571	−	3.31108i	−1.01233	−	0.271254i	−0.726605	+	0.687056i	$0.758903\pi$
$150$	−4.76846	−	1.50394i	−0.389343	−	0.122796i
$151$	−14.5027	+	14.5027i	−1.18021	+	1.18021i	−0.200521	+	0.979690i	$0.564263\pi$
$151$	−14.5027	+	14.5027i	−1.18021	+	1.18021i	−0.979690	+	0.200521i	$0.935737\pi$
$152$	3.46041	+	0.927215i	0.280677	+	0.0752071i
$153$	0.160023	+	0.597215i	0.0129371	+	0.0482820i
$154$	4.01065	−	1.07465i	0.323187	−	0.0865978i
$155$	2.18725	+	0.0478193i	0.175684	+	0.00384094i
$156$	3.59337	+	0.296172i	0.287700	+	0.0237128i
$157$	6.10791	−	6.10791i	0.487464	−	0.487464i	−0.420041	−	0.907505i	$-0.637984\pi$
$157$	6.10791	−	6.10791i	0.487464	−	0.487464i	0.907505	+	0.420041i	$0.137984\pi$
$158$	4.42901	+	2.55709i	0.352353	+	0.203431i
$159$	−1.89284	−	1.09283i	−0.150112	−	0.0866672i
$160$	2.14671	+	0.625808i	0.169712	+	0.0494745i
$161$	−0.913664	−	0.913664i	−0.0720068	−	0.0720068i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−5.25134	−	9.09558i	−0.411316	−	0.712421i	0.583718	−	0.811957i	$-0.301598\pi$
$163$	−5.25134	−	9.09558i	−0.411316	−	0.712421i	−0.995034	+	0.0995359i	$0.968264\pi$
$164$	−5.73502	−	5.73502i	−0.447830	−	0.447830i
$165$	4.66678	+	1.36046i	0.363309	+	0.105912i
$166$	−3.32780	−	1.92131i	−0.258287	−	0.149122i
$167$	−6.02056	−	3.47597i	−0.465885	−	0.268979i	0.248630	−	0.968598i	$-0.420020\pi$
$167$	−6.02056	−	3.47597i	−0.465885	−	0.268979i	−0.714516	+	0.699620i	$0.753353\pi$
$168$	−1.35055	+	1.35055i	−0.104197	+	0.104197i
$169$	2.12851	−	12.8246i	0.163732	−	0.986505i
$170$	1.38219	+	0.0302186i	0.106009	+	0.00231766i
$171$	−3.46041	+	0.927215i	−0.264625	+	0.0709059i
$172$	0.901681	+	3.36512i	0.0687526	+	0.256588i
$173$	−12.7288	−	3.41066i	−0.967750	−	0.259308i	−0.259872	−	0.965643i	$-0.583680\pi$
$173$	−12.7288	−	3.41066i	−0.967750	−	0.259308i	−0.707877	+	0.706335i	$0.750347\pi$
$174$	2.39305	−	2.39305i	0.181416	−	0.181416i
$175$	−4.40891	−	8.47120i	−0.333282	−	0.640363i
$176$	−2.09985	−	0.562653i	−0.158282	−	0.0424115i
$177$			14.4969i			1.08965i
$178$	−0.215602	+	0.804636i	−0.0161600	+	0.0603100i
$179$	8.17918	−	14.1668i	0.611341	−	1.05887i	−0.379674	−	0.925120i	$-0.623964\pi$
$179$	8.17918	−	14.1668i	0.611341	−	1.05887i	0.991015	−	0.133753i	$-0.0427028\pi$
$180$	−2.17201	+	0.531389i	−0.161892	+	0.0396074i
$181$		−	10.7578i		−	0.799622i	−0.916598	−	0.399811i	$-0.869076\pi$
$181$		−	10.7578i		−	0.799622i	0.916598	−	0.399811i	$-0.130924\pi$
$182$	4.45304	+	5.25303i	0.330081	+	0.389380i
$183$	−4.04105	−	4.04105i	−0.298723	−	0.298723i
$184$	0.175094	+	0.653459i	0.0129081	+	0.0481737i
$185$	−6.20256	+	1.51748i	−0.456021	+	0.111567i
$186$	0.847320	−	0.489200i	0.0621285	−	0.0358699i
$187$	−1.34410			−0.0982903
$188$	9.39693	−	5.42532i	0.685342	−	0.395682i
$189$	0.494337	−	1.84489i	0.0359577	−	0.134196i
$190$	−0.175094	+	8.00877i	−0.0127026	+	0.581017i
$191$	−12.2705	−	21.2531i	−0.887859	−	1.53782i	−0.842401	−	0.538851i	$-0.818859\pi$
$191$	−12.2705	−	21.2531i	−0.887859	−	1.53782i	−0.0454580	−	0.998966i	$-0.514475\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	9.45984	−	16.3849i	0.680934	−	1.17941i	−0.293762	−	0.955879i	$-0.594907\pi$
$193$	9.45984	−	16.3849i	0.680934	−	1.17941i	0.974696	−	0.223534i	$-0.0717595\pi$
$194$	−18.3259			−1.31572
$195$	1.26619	+	7.96221i	0.0906735	+	0.570186i
$196$	3.35201			0.239429
$197$	10.7874	−	18.6844i	0.768573	−	1.33121i	−0.169763	−	0.985485i	$-0.554300\pi$
$197$	10.7874	−	18.6844i	0.768573	−	1.33121i	0.938337	−	0.345723i	$-0.112366\pi$
$198$	2.09985	−	0.562653i	0.149230	−	0.0399860i
$199$	11.5656	+	20.0322i	0.819863	+	1.42004i	0.905783	+	0.423742i	$0.139284\pi$
$199$	11.5656	+	20.0322i	0.819863	+	1.42004i	−0.0859199	+	0.996302i	$0.527383\pi$
$200$	−0.218523	+	4.99522i	−0.0154519	+	0.353216i
$201$	1.51568	−	5.65658i	0.106907	−	0.398984i
$202$	14.6508	−	8.45864i	1.03083	−	0.595148i
$203$	6.46387			0.453675
$204$	0.535449	−	0.309141i	0.0374889	−	0.0216442i
$205$	9.40899	−	15.5040i	0.657152	−	1.08285i
$206$	−1.31801	−	4.91887i	−0.0918300	−	0.342714i
$207$	−0.478365	−	0.478365i	−0.0332487	−	0.0332487i
$208$	−0.643951	−	3.54758i	−0.0446500	−	0.245980i
$209$		−	7.78805i		−	0.538711i
$210$	−3.65108	−	2.21575i	−0.251949	−	0.152901i
$211$	−12.8509	+	22.2584i	−0.884692	+	1.53233i	−0.0386248	+	0.999254i	$0.512298\pi$
$211$	−12.8509	+	22.2584i	−0.884692	+	1.53233i	−0.846067	+	0.533077i	$0.821036\pi$
$212$	−0.565691	+	2.11119i	−0.0388518	+	0.144997i
$213$			6.87946i			0.471373i
$214$	9.21566	+	2.46933i	0.629969	+	0.168800i
$215$	−6.82993	+	3.74665i	−0.465797	+	0.255519i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	1.80504	+	0.483659i	0.122534	+	0.0328329i
$218$	3.61713	+	13.4993i	0.244983	+	0.914290i
$219$	2.07932	−	0.557152i	0.140507	−	0.0376489i
$220$	0.106250	−	4.85988i	0.00716341	−	0.327653i
$221$	−0.952273	−	2.01562i	−0.0640568	−	0.135585i
$222$	−2.01927	+	2.01927i	−0.135524	+	0.135524i
$223$	−23.8621	−	13.7768i	−1.59793	−	0.922563i	−0.991886	−	0.127129i	$-0.959424\pi$
$223$	−23.8621	−	13.7768i	−1.59793	−	0.922563i	−0.606040	−	0.795434i	$-0.707243\pi$
$224$	1.65408	+	0.954985i	0.110518	+	0.0638076i
$225$	−2.30836	−	4.43525i	−0.153891	−	0.295683i
$226$	−9.52913	−	9.52913i	−0.633869	−	0.633869i
$227$	−3.42247	−	5.92789i	−0.227157	−	0.393448i	0.729807	−	0.683653i	$-0.239610\pi$
$227$	−3.42247	−	5.92789i	−0.227157	−	0.393448i	−0.956964	+	0.290205i	$0.906276\pi$
$228$	1.79124	+	3.10252i	0.118628	+	0.205470i
$229$	−13.6008	−	13.6008i	−0.898766	−	0.898766i	0.0965608	−	0.995327i	$-0.469216\pi$
$229$	−13.6008	−	13.6008i	−0.898766	−	0.898766i	−0.995327	+	0.0965608i	$0.969216\pi$
$230$	−1.32628	+	0.727547i	−0.0874521	+	0.0479730i
$231$	3.59585	+	2.07606i	0.236590	+	0.136595i
$232$	−2.93087	−	1.69214i	−0.192421	−	0.111094i
$233$	6.74979	−	6.74979i	0.442194	−	0.442194i	−0.450555	−	0.892749i	$-0.648774\pi$
$233$	6.74979	−	6.74979i	0.442194	−	0.442194i	0.892749	+	0.450555i	$0.148774\pi$
$234$	2.33147	+	2.75032i	0.152413	+	0.179794i
$235$	16.7773	+	17.5273i	1.09443	+	1.14335i
$236$	14.0029	−	3.75207i	0.911512	−	0.244239i
$237$	1.32365	+	4.93992i	0.0859802	+	0.320882i
$238$	1.14066	+	0.305640i	0.0739383	+	0.0198117i
$239$	−3.90302	+	3.90302i	−0.252465	+	0.252465i	−0.821981	−	0.569515i	$-0.807131\pi$
$239$	−3.90302	+	3.90302i	−0.252465	+	0.252465i	0.569515	+	0.821981i	$0.307131\pi$
$240$	1.07544	+	1.96047i	0.0694193	+	0.126548i
$241$	−10.7613	−	2.88348i	−0.693196	−	0.185741i	−0.105015	−	0.994471i	$-0.533489\pi$
$241$	−10.7613	−	2.88348i	−0.693196	−	0.185741i	−0.588181	+	0.808729i	$0.700156\pi$
$242$		−	6.27406i		−	0.403312i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−2.85745	+	4.94925i	−0.182930	+	0.316843i
$245$	1.78122	+	7.28060i	0.113798	+	0.465141i
$246$		−	8.11054i		−	0.517109i
$247$	11.6790	−	5.51771i	0.743118	−	0.351083i
$248$	−0.691834	−	0.691834i	−0.0439315	−	0.0439315i
$249$	−0.994541	−	3.71168i	−0.0630265	−	0.235218i
$250$	−10.9658	+	2.17977i	−0.693538	+	0.137861i
$251$	11.9048	−	6.87325i	0.751426	−	0.433836i	−0.0747830	−	0.997200i	$-0.523826\pi$
$251$	11.9048	−	6.87325i	0.751426	−	0.433836i	0.826209	+	0.563364i	$0.190493\pi$
$252$	−1.90997			−0.120317
$253$	1.27365	−	0.735341i	0.0800736	−	0.0462305i
$254$	3.55123	−	13.2534i	0.222824	−	0.831591i
$255$	0.955990	+	0.998725i	0.0598664	+	0.0625426i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.126617	−	0.0339269i	0.00789815	−	0.00211630i	−0.254868	−	0.966976i	$-0.582032\pi$
$257$	0.126617	−	0.0339269i	0.00789815	−	0.00211630i	0.262766	+	0.964860i	$0.415365\pi$
$258$	−1.74191	+	3.01708i	−0.108447	+	0.187835i
$259$	−5.45426			−0.338911
$260$	7.36319	−	3.28381i	0.456646	−	0.203653i
$261$	3.38428			0.209482
$262$	8.31884	−	14.4086i	0.513939	−	0.890169i
$263$	−16.2917	+	4.36534i	−1.00459	+	0.269178i	−0.723366	−	0.690465i	$-0.757406\pi$
$263$	−16.2917	+	4.36534i	−1.00459	+	0.269178i	−0.281221	+	0.959643i	$0.590739\pi$
$264$	−1.08696	−	1.88267i	−0.0668979	−	0.115871i
$265$	−4.88612	−	0.106824i	−0.300152	−	0.00656216i
$266$	−1.77095	+	6.60929i	−0.108584	+	0.405242i
$267$	−0.721417	+	0.416510i	−0.0441500	+	0.0254900i
$268$	−5.85612			−0.357719
$269$	4.74801	−	2.74127i	0.289491	−	0.167138i	−0.348221	−	0.937412i	$-0.613214\pi$
$269$	4.74801	−	2.74127i	0.289491	−	0.167138i	0.637712	+	0.770275i	$0.279881\pi$
$270$	−1.91159	−	1.16009i	−0.116336	−	0.0706011i
$271$	1.56093	+	5.82549i	0.0948200	+	0.353873i	0.996992	−	0.0775032i	$-0.0246948\pi$
$271$	1.56093	+	5.82549i	0.0948200	+	0.353873i	−0.902172	+	0.431376i	$0.858028\pi$
$272$	−0.437192	−	0.437192i	−0.0265087	−	0.0265087i
$273$	−0.565680	+	6.86322i	−0.0342365	+	0.415381i
$274$			8.24704i			0.498222i
$275$	10.6122	−	2.35171i	0.639938	−	0.141813i
$276$	−0.338255	+	0.585876i	−0.0203606	+	0.0352656i
$277$	−3.03101	+	11.3119i	−0.182116	+	0.679666i	0.813114	+	0.582105i	$0.197771\pi$
$277$	−3.03101	+	11.3119i	−0.182116	+	0.679666i	−0.995230	+	0.0975609i	$0.968896\pi$
$278$			14.6697i			0.879830i
$279$	0.945063	+	0.253229i	0.0565794	+	0.0151604i
$280$	−1.19528	+	4.10015i	−0.0714314	+	0.245031i
$281$	15.6369	−	15.6369i	0.932818	−	0.932818i	−0.0650632	−	0.997881i	$-0.520725\pi$
$281$	15.6369	−	15.6369i	0.932818	−	0.932818i	0.997881	+	0.0650632i	$0.0207249\pi$
$282$	10.4809	+	2.80835i	0.624130	+	0.167235i
$283$	2.48163	+	9.26157i	0.147518	+	0.550543i	0.999630	+	0.0271852i	$0.00865438\pi$
$283$	2.48163	+	9.26157i	0.147518	+	0.550543i	−0.852113	+	0.523358i	$0.824679\pi$
$284$	6.64505	−	1.78054i	0.394311	−	0.105655i
$285$	−5.78686	+	5.53924i	−0.342784	+	0.328116i
$286$	−7.08706	+	3.34826i	−0.419067	+	0.197987i
$287$	10.9537	−	10.9537i	0.646577	−	0.646577i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	14.3914	+	8.30886i	0.846551	+	0.488757i
$290$	2.11791	−	7.26507i	0.124368	−	0.426619i
$291$	−12.9583	−	12.9583i	−0.759631	−	0.759631i
$292$	−1.07634	−	1.86427i	−0.0629878	−	0.109098i
$293$	5.68430	+	9.84550i	0.332080	+	0.575180i	0.982920	−	0.184035i	$-0.0589161\pi$
$293$	5.68430	+	9.84550i	0.332080	+	0.575180i	−0.650839	+	0.759216i	$0.725583\pi$
$294$	2.37023	+	2.37023i	0.138235	+	0.138235i
$295$	15.5905	+	28.4207i	0.907716	+	1.65471i
$296$	2.47309	+	1.42784i	0.143745	+	0.0829915i
$297$	1.88267	+	1.08696i	0.109244	+	0.0630719i
$298$	−9.04604	+	9.04604i	−0.524023	+	0.524023i
$299$	2.00508	+	1.38900i	0.115957	+	0.0803277i
$300$	−3.68668	+	3.37764i	−0.212850	+	0.195008i
$301$	−6.42728	+	1.72218i	−0.370462	+	0.0992651i
$302$	5.30834	+	19.8110i	0.305461	+	1.14000i
$303$	16.3408	+	4.37852i	0.938757	+	0.251539i
$304$	2.53320	−	2.53320i	0.145289	−	0.145289i
$305$	−12.2682	−	3.57643i	−0.702477	−	0.204786i
$306$	0.597215	+	0.160023i	0.0341405	+	0.00914793i
$307$			17.1833i			0.980702i	0.871525	+	0.490351i	$0.163131\pi$
$307$			17.1833i			0.980702i	−0.871525	+	0.490351i	$0.836869\pi$
$308$	1.07465	−	4.01065i	0.0612339	−	0.228528i
$309$	2.54620	−	4.41014i	0.144848	−	0.250884i
$310$	1.13504	−	1.87030i	0.0644658	−	0.106226i
$311$		−	16.2305i		−	0.920347i	−0.887829	−	0.460174i	$-0.847787\pi$
$311$		−	16.2305i		−	0.920347i	0.887829	−	0.460174i	$-0.152213\pi$
$312$	2.05318	−	2.96386i	0.116238	−	0.167796i
$313$	−14.8660	−	14.8660i	−0.840275	−	0.840275i	0.148620	−	0.988894i	$-0.452517\pi$
$313$	−14.8660	−	14.8660i	−0.840275	−	0.840275i	−0.988894	+	0.148620i	$0.952517\pi$
$314$	−2.23565	−	8.34356i	−0.126165	−	0.470854i
$315$	−1.01494	−	4.14847i	−0.0571853	−	0.233740i
$316$	4.42901	−	2.55709i	0.249151	−	0.143848i
$317$	−32.9862			−1.85269			−0.926345	−	0.376676i	$-0.877067\pi$
$317$	−32.9862			−1.85269			−0.926345	+	0.376676i	$0.877067\pi$
$318$	−1.89284	+	1.09283i	−0.106145	+	0.0612830i
$319$	−1.90417	+	7.10647i	−0.106613	+	0.397886i
$320$	1.61532	−	1.54620i	0.0902992	−	0.0864353i
$321$	4.77038	+	8.26253i	0.266256	+	0.461170i
$322$	−1.24809	+	0.334424i	−0.0695532	+	0.0186367i
$323$	1.10749	−	1.91824i	0.0616226	−	0.106734i
$324$	−1.00000			−0.0555556
$325$	11.0452	+	14.2479i	0.612677	+	0.790333i
$326$	−10.5027			−0.581689
$327$	−6.98776	+	12.1032i	−0.386424	+	0.669306i
$328$	−7.83418	+	2.09916i	−0.432570	+	0.115907i
$329$	10.3622	+	17.9479i	0.571287	+	0.989498i
$330$	3.51158	−	3.36132i	0.193306	−	0.185035i
$331$	−0.460244	+	1.71765i	−0.0252973	+	0.0944107i	−0.977420	−	0.211304i	$-0.932229\pi$
$331$	−0.460244	+	1.71765i	−0.0252973	+	0.0944107i	0.952123	+	0.305715i	$0.0988955\pi$
$332$	−3.32780	+	1.92131i	−0.182637	+	0.105445i
$333$	−2.85568			−0.156490
$334$	−6.02056	+	3.47597i	−0.329431	+	0.190197i
$335$	−3.11188	−	12.7195i	−0.170020	−	0.694943i
$336$	0.494337	+	1.84489i	0.0269683	+	0.100647i
$337$	8.61910	+	8.61910i	0.469512	+	0.469512i	0.901757	−	0.432244i	$-0.142278\pi$
$337$	8.61910	+	8.61910i	0.469512	+	0.469512i	−0.432244	+	0.901757i	$0.642278\pi$
$338$	−10.0421	−	8.25563i	−0.546221	−	0.449047i
$339$		−	13.4762i		−	0.731928i
$340$	0.717266	−	1.18190i	0.0388992	−	0.0640978i
$341$	−1.06348	+	1.84201i	−0.0575909	+	0.0997504i
$342$	−0.927215	+	3.46041i	−0.0501381	+	0.187118i
$343$			19.7720i			1.06759i
$344$	3.36512	+	0.901681i	0.181435	+	0.0486154i
$345$	−1.45227	−	0.423366i	−0.0781877	−	0.0227933i
$346$	−9.31810	+	9.31810i	−0.500944	+	0.500944i
$347$	−17.1107	−	4.58480i	−0.918550	−	0.246125i	−0.231585	−	0.972815i	$-0.574391\pi$
$347$	−17.1107	−	4.58480i	−0.918550	−	0.246125i	−0.686966	+	0.726690i	$0.741058\pi$
$348$	−0.875916	−	3.26896i	−0.0469540	−	0.175235i
$349$	16.2696	−	4.35943i	0.870892	−	0.233355i	0.204419	−	0.978884i	$-0.434470\pi$
$349$	16.2696	−	4.35943i	0.870892	−	0.233355i	0.666473	+	0.745529i	$0.267803\pi$
$350$	−9.54073	−	0.417373i	−0.509973	−	0.0223095i
$351$	−0.296172	+	3.59337i	−0.0158085	+	0.191800i
$352$	−1.53720	+	1.53720i	−0.0819328	+	0.0819328i
$353$	30.1361	+	17.3991i	1.60398	+	0.926061i	0.990679	+	0.136215i	$0.0434938\pi$
$353$	30.1361	+	17.3991i	1.60398	+	0.926061i	0.613305	+	0.789846i	$0.289840\pi$
$354$	12.5547	+	7.24844i	0.667273	+	0.385250i
$355$	7.39844	+	13.4869i	0.392669	+	0.715813i
$356$	0.589034	+	0.589034i	0.0312188	+	0.0312188i
$357$	0.590451	+	1.02269i	0.0312500	+	0.0541266i
$358$	−8.17918	−	14.1668i	−0.432283	−	0.748736i
$359$	11.3845	+	11.3845i	0.600849	+	0.600849i	0.940538	−	0.339689i	$-0.110322\pi$
$359$	11.3845	+	11.3845i	0.600849	+	0.600849i	−0.339689	+	0.940538i	$0.610322\pi$
$360$	−0.625808	+	2.14671i	−0.0329830	+	0.113142i
$361$	−5.33974	−	3.08290i	−0.281039	−	0.162258i
$362$	−9.31654	−	5.37891i	−0.489666	−	0.282709i
$363$	4.43643	−	4.43643i	0.232852	−	0.232852i
$364$	6.77577	−	1.22993i	0.355147	−	0.0644657i
$365$	3.47725	−	3.32846i	0.182008	−	0.174220i
$366$	−5.52017	+	1.47913i	−0.288544	+	0.0773151i
$367$	−3.43690	−	12.8267i	−0.179405	−	0.669547i	−0.995759	−	0.0919962i	$-0.970675\pi$
$367$	−3.43690	−	12.8267i	−0.179405	−	0.669547i	0.816355	−	0.577551i	$-0.195991\pi$
$368$	0.653459	+	0.175094i	0.0340639	+	0.00912740i
$369$	5.73502	−	5.73502i	0.298553	−	0.298553i
$370$	−1.78711	+	6.13031i	−0.0929073	+	0.318700i
$371$	−4.03231	−	1.08045i	−0.209347	−	0.0560944i
$372$		−	0.978401i		−	0.0507277i
$373$	−1.54383	+	5.76165i	−0.0799364	+	0.298327i	−0.994307	−	0.106551i	$-0.966019\pi$
$373$	−1.54383	+	5.76165i	−0.0799364	+	0.298327i	0.914371	+	0.404878i	$0.132686\pi$
$374$	−0.672050	+	1.16402i	−0.0347509	+	0.0601903i
$375$	−9.29532	−	6.21265i	−0.480008	−	0.320820i
$376$		−	10.8506i		−	0.559579i
$377$	−12.0060	+	2.17931i	−0.618341	+	0.112240i
$378$	−1.35055	−	1.35055i	−0.0694650	−	0.0694650i
$379$	2.67271	+	9.97467i	0.137288	+	0.512365i	0.999978	+	0.00663207i	$0.00211107\pi$
$379$	2.67271	+	9.97467i	0.137288	+	0.512365i	−0.862690	+	0.505733i	$0.831222\pi$
$380$	6.84825	+	4.15602i	0.351308	+	0.213199i
$381$	11.8827	−	6.86045i	0.608767	−	0.351472i
$382$	−24.5409			−1.25562
$383$	−3.83556	+	2.21446i	−0.195988	+	0.113154i	−0.594783	−	0.803886i	$-0.702762\pi$
$383$	−3.83556	+	2.21446i	−0.195988	+	0.113154i	0.398795	+	0.917040i	$0.369429\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	9.28223	+	0.202935i	0.473066	+	0.0103425i
$386$	−9.45984	−	16.3849i	−0.481493	−	0.833971i
$387$	−3.36512	+	0.901681i	−0.171059	+	0.0458350i
$388$	−9.16293	+	15.8707i	−0.465177	+	0.805711i
$389$	−1.11411			−0.0564874			−0.0282437	−	0.999601i	$-0.508991\pi$
$389$	−1.11411			−0.0564874			−0.0282437	+	0.999601i	$0.508991\pi$
$390$	7.52857	+	2.88455i	0.381224	+	0.146065i
$391$	0.418275			0.0211531
$392$	1.67601	−	2.90293i	0.0846511	−	0.146620i
$393$	16.0708	−	4.30615i	0.810663	−	0.217216i
$394$	−10.7874	−	18.6844i	−0.543463	−	0.941306i
$395$	7.90755	+	8.26105i	0.397872	+	0.415658i
$396$	0.562653	−	2.09985i	0.0282744	−	0.105521i
$397$	−33.3374	+	19.2474i	−1.67316	+	0.965998i	−0.707304	+	0.706910i	$0.750089\pi$
$397$	−33.3374	+	19.2474i	−1.67316	+	0.965998i	−0.965854	+	0.259088i	$0.916578\pi$
$398$	23.1312			1.15946
$399$	−5.92573	+	3.42122i	−0.296657	+	0.171275i
$400$	4.21673	+	2.68686i	0.210836	+	0.134343i
$401$	2.65088	+	9.89323i	0.132379	+	0.494044i	0.999995	−	0.00319033i	$-0.00101551\pi$
$401$	2.65088	+	9.89323i	0.132379	+	0.494044i	−0.867616	+	0.497235i	$0.834349\pi$
$402$	−4.14090	−	4.14090i	−0.206529	−	0.206529i
$403$	−3.51575	−	0.289775i	−0.175132	−	0.0144347i
$404$		−	16.9173i		−	0.841666i
$405$	−0.531389	−	2.17201i	−0.0264049	−	0.107928i
$406$	3.23194	−	5.59788i	0.160398	−	0.277818i
$407$	1.60676	−	5.99649i	0.0796439	−	0.297235i
$408$		−	0.618283i		−	0.0306096i
$409$	17.0104	+	4.55794i	0.841113	+	0.225375i	0.653556	−	0.756878i	$-0.273276\pi$
$409$	17.0104	+	4.55794i	0.841113	+	0.225375i	0.187557	+	0.982254i	$0.439943\pi$
$410$	−8.72240	−	15.9004i	−0.430768	−	0.785267i
$411$	−5.83154	+	5.83154i	−0.287649	+	0.287649i
$412$	−4.91887	−	1.31801i	−0.242336	−	0.0649336i
$413$	7.16634	+	26.7452i	0.352633	+	1.31604i
$414$	−0.653459	+	0.175094i	−0.0321158	+	0.00860540i
$415$	−5.94145	−	6.20705i	−0.291654	−	0.304692i
$416$	−3.39427	−	1.21611i	−0.166418	−	0.0596248i
$417$	−10.3730	+	10.3730i	−0.507970	+	0.507970i
$418$	−6.74465	−	3.89402i	−0.329891	−	0.190463i
$419$	5.44338	+	3.14274i	0.265926	+	0.153533i	0.627035	−	0.778991i	$-0.284268\pi$
$419$	5.44338	+	3.14274i	0.265926	+	0.153533i	−0.361109	+	0.932524i	$0.617602\pi$
$420$	−3.74443	+	2.05406i	−0.182710	+	0.100228i
$421$	−18.1111	−	18.1111i	−0.882681	−	0.882681i	0.111125	−	0.993806i	$-0.464554\pi$
$421$	−18.1111	−	18.1111i	−0.882681	−	0.882681i	−0.993806	+	0.111125i	$0.964554\pi$
$422$	12.8509	+	22.2584i	0.625571	+	1.08352i
$423$	5.42532	+	9.39693i	0.263788	+	0.456895i
$424$	1.54550	+	1.54550i	0.0750560	+	0.0750560i
$425$	2.94825	+	0.929858i	0.143011	+	0.0451047i
$426$	5.95779	+	3.43973i	0.288656	+	0.166655i
$427$	−9.45292	−	5.45765i	−0.457459	−	0.264114i
$428$	6.74633	−	6.74633i	0.326096	−	0.326096i
$429$	−7.37888	−	2.64373i	−0.356256	−	0.127641i
$430$	−0.170272	+	7.78822i	−0.00821125	+	0.375581i
$431$	−11.5686	+	3.09979i	−0.557239	+	0.149312i	−0.526437	−	0.850214i	$-0.676473\pi$
$431$	−11.5686	+	3.09979i	−0.557239	+	0.149312i	−0.0308013	+	0.999526i	$0.509806\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	34.2325	+	9.17258i	1.64511	+	0.440806i	0.958238	−	0.285972i	$-0.0923163\pi$
$433$	34.2325	+	9.17258i	1.64511	+	0.440806i	0.686873	+	0.726778i	$0.258983\pi$
$434$	1.32138	−	1.32138i	0.0634284	−	0.0634284i
$435$	6.63477	−	3.63959i	0.318113	−	0.174505i
$436$	13.4993	+	3.61713i	0.646500	+	0.173229i
$437$			2.42359i			0.115936i
$438$	0.557152	−	2.07932i	0.0266218	−	0.0993538i
$439$	15.1777	−	26.2886i	0.724394	−	1.25469i	−0.234829	−	0.972037i	$-0.575453\pi$
$439$	15.1777	−	26.2886i	0.724394	−	1.25469i	0.959223	−	0.282650i	$-0.0912136\pi$
$440$	−4.15565	−	2.52196i	−0.198113	−	0.120229i
$441$			3.35201i			0.159620i
$442$	−2.22172	−	0.183118i	−0.105676	−	0.00871005i
$443$	−19.2254	−	19.2254i	−0.913426	−	0.913426i	0.0831145	−	0.996540i	$-0.473513\pi$
$443$	−19.2254	−	19.2254i	−0.913426	−	0.913426i	−0.996540	+	0.0831145i	$0.973513\pi$
$444$	0.739104	+	2.75837i	0.0350763	+	0.130907i
$445$	−0.966382	+	1.59239i	−0.0458109	+	0.0754868i
$446$	−23.8621	+	13.7768i	−1.12990	+	0.652351i
$447$	−12.7930			−0.605090
$448$	1.65408	−	0.954985i	0.0781481	−	0.0451188i
$449$	3.49720	−	13.0517i	0.165043	−	0.615948i	−0.832992	−	0.553285i	$-0.813374\pi$
$449$	3.49720	−	13.0517i	0.165043	−	0.615948i	0.998035	−	0.0626632i	$-0.0199594\pi$
$450$	−4.99522	−	0.218523i	−0.235477	−	0.0103013i
$451$	8.81584	+	15.2695i	0.415122	+	0.719012i
$452$	−13.0170	+	3.48791i	−0.612270	+	0.164057i
$453$	−10.2549	+	17.7621i	−0.481819	+	0.834535i
$454$	−6.84494			−0.321249
$455$	6.27199	+	14.0635i	0.294035	+	0.659306i
$456$	3.58249			0.167765
$457$	−0.114554	+	0.198413i	−0.00535859	+	0.00928136i	−0.868692	−	0.495352i	$-0.835039\pi$
$457$	−0.114554	+	0.198413i	−0.00535859	+	0.00928136i	0.863334	+	0.504633i	$0.168372\pi$
$458$	−18.5790	+	4.97824i	−0.868142	+	0.232618i
$459$	0.309141	+	0.535449i	0.0144295	+	0.0249926i
$460$	−0.0330645	+	1.51236i	−0.00154164	+	0.0705143i
$461$	−9.53478	+	35.5843i	−0.444079	+	1.65733i	0.274278	+	0.961651i	$0.411561\pi$
$461$	−9.53478	+	35.5843i	−0.444079	+	1.65733i	−0.718357	+	0.695675i	$0.755105\pi$
$462$	3.59585	−	2.07606i	0.167294	−	0.0965873i
$463$	0.0626597			0.00291205			0.00145602	−	0.999999i	$-0.499537\pi$
$463$	0.0626597			0.00291205			0.00145602	+	0.999999i	$0.499537\pi$
$464$	−2.93087	+	1.69214i	−0.136062	+	0.0785556i
$465$	2.12510	−	0.519911i	0.0985490	−	0.0241103i
$466$	−2.47060	−	9.22039i	−0.114448	−	0.427126i
$467$	12.4618	+	12.4618i	0.576663	+	0.576663i	0.933982	−	0.357319i	$-0.116309\pi$
$467$	12.4618	+	12.4618i	0.576663	+	0.576663i	−0.357319	+	0.933982i	$0.616309\pi$
$468$	3.54758	−	0.643951i	0.163987	−	0.0297667i
$469$		−	11.1850i		−	0.516476i
$470$	23.5677	−	5.76591i	1.08710	−	0.265962i
$471$	4.31894	−	7.48063i	0.199006	−	0.344689i
$472$	3.75207	−	14.0029i	0.172703	−	0.644536i
$473$		−	7.57358i		−	0.348233i
$474$	4.93992	+	1.32365i	0.226898	+	0.0607972i
$475$	−5.38783	+	17.0829i	−0.247211	+	0.783818i
$476$	0.835024	−	0.835024i	0.0382733	−	0.0382733i
$477$	−2.11119	−	0.565691i	−0.0966647	−	0.0259012i
$478$	1.42860	+	5.33162i	0.0653428	+	0.243863i
$479$	−4.71886	+	1.26441i	−0.215610	+	0.0577726i	−0.365007	−	0.931005i	$-0.618933\pi$
$479$	−4.71886	+	1.26441i	−0.215610	+	0.0577726i	0.149397	+	0.988777i	$0.452267\pi$
$480$	2.23553	+	0.0488750i	0.102038	+	0.00223083i
$481$	10.1307	−	1.83892i	0.461922	−	0.0838474i
$482$	−7.87782	+	7.87782i	−0.358825	+	0.358825i
$483$	−1.11901	−	0.646058i	−0.0509165	−	0.0293967i
$484$	−5.43349	−	3.13703i	−0.246977	−	0.142592i
$485$	−39.3403	−	11.4685i	−1.78635	−	0.520757i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−9.74340	−	16.8761i	−0.441516	−	0.764728i	0.556287	−	0.830991i	$-0.312226\pi$
$487$	−9.74340	−	16.8761i	−0.441516	−	0.764728i	−0.997802	+	0.0662630i	$0.978892\pi$
$488$	2.85745	+	4.94925i	0.129351	+	0.224042i
$489$	−7.42651	−	7.42651i	−0.335838	−	0.335838i
$490$	7.19580	+	2.09772i	0.325073	+	0.0947652i
$491$	23.5658	+	13.6057i	1.06351	+	0.614017i	0.926401	−	0.376540i	$-0.122886\pi$
$491$	23.5658	+	13.6057i	1.06351	+	0.614017i	0.137107	+	0.990556i	$0.456219\pi$
$492$	−7.02393	−	4.05527i	−0.316663	−	0.182826i
$493$	−1.47958	+	1.47958i	−0.0666369	+	0.0666369i
$494$	1.06103	−	12.8732i	0.0477381	−	0.579192i
$495$	4.85988	+	0.106250i	0.218435	+	0.00477560i
$496$	−0.945063	+	0.253229i	−0.0424346	+	0.0113703i
$497$	3.40077	+	12.6918i	0.152545	+	0.569307i
$498$	−3.71168	−	0.994541i	−0.166324	−	0.0445664i
$499$	11.1781	−	11.1781i	0.500399	−	0.500399i	−0.411163	−	0.911562i	$-0.634877\pi$
$499$	11.1781	−	11.1781i	0.500399	−	0.500399i	0.911562	+	0.411163i	$0.134877\pi$
$500$	−3.59516	+	10.5865i	−0.160780	+	0.473444i
$501$	−6.71506	−	1.79930i	−0.300007	−	0.0803866i
$502$		−	13.7465i		−	0.613537i
$503$	−1.08946	+	4.06591i	−0.0485764	+	0.181290i	−0.985951	−	0.167032i	$-0.946582\pi$
$503$	−1.08946	+	4.06591i	−0.0485764	+	0.181290i	0.937375	+	0.348322i	$0.113248\pi$
$504$	−0.954985	+	1.65408i	−0.0425384	+	0.0736787i
$505$	36.7445	−	8.98966i	1.63511	−	0.400035i
$506$		−	1.47068i		−	0.0653798i
$507$	−1.26326	−	12.9385i	−0.0561032	−	0.574618i
$508$	−9.70214	−	9.70214i	−0.430463	−	0.430463i
$509$	9.73121	+	36.3174i	0.431328	+	1.60974i	0.749703	+	0.661774i	$0.230196\pi$
$509$	9.73121	+	36.3174i	0.431328	+	1.60974i	−0.318375	+	0.947965i	$0.603137\pi$
$510$	1.34292	−	0.328549i	0.0594653	−	0.0145484i
$511$	3.56070	−	2.05577i	0.157516	−	0.0909419i
$512$	−1.00000			−0.0441942
$513$	−3.10252	+	1.79124i	−0.136980	+	0.0790853i
$514$	0.0339269	−	0.126617i	0.00149645	−	0.00558484i
$515$	0.248891	−	11.3842i	0.0109674	−	0.501648i
$516$	1.74191	+	3.01708i	0.0766835	+	0.132820i
$517$	−22.7847	+	6.10515i	−1.00207	+	0.268504i
$518$	−2.72713	+	4.72353i	−0.119823	+	0.207540i
$519$	−13.1778			−0.578440
$520$	0.837729	−	8.01862i	0.0367368	−	0.351640i
$521$	0.544187			0.0238413			0.0119206	−	0.999929i	$-0.496205\pi$
$521$	0.544187			0.0238413			0.0119206	+	0.999929i	$0.496205\pi$
$522$	1.69214	−	2.93087i	0.0740629	−	0.128281i
$523$	1.31067	−	0.351192i	0.0573114	−	0.0153565i	−0.230049	−	0.973179i	$-0.573889\pi$
$523$	1.31067	−	0.351192i	0.0573114	−	0.0153565i	0.287361	+	0.957822i	$0.407222\pi$
$524$	−8.31884	−	14.4086i	−0.363410	−	0.629445i
$525$	−6.45119	−	7.04144i	−0.281553	−	0.307314i
$526$	−4.36534	+	16.2917i	−0.190338	+	0.710351i
$527$	−0.523883	+	0.302464i	−0.0228207	+	0.0131755i
$528$	−2.17392			−0.0946079
$529$	19.5222	−	11.2712i	0.848793	−	0.490051i
$530$	−2.53557	+	4.17810i	−0.110138	+	0.181485i
$531$	3.75207	+	14.0029i	0.162826	+	0.607675i
$532$	4.83834	+	4.83834i	0.209768	+	0.209768i
$533$	−16.6524	+	24.0385i	−0.721294	+	1.04122i
$534$			0.833020i			0.0360483i
$535$	18.2380	+	11.0682i	0.788498	+	0.478519i
$536$	−2.92806	+	5.07155i	−0.126473	+	0.219058i
$537$	4.23386	−	15.8010i	0.182704	−	0.681862i
$538$		−	5.48253i		−	0.236369i
$539$	−7.03872	−	1.88602i	−0.303179	−	0.0812366i
$540$	−1.96047	+	1.07544i	−0.0843650	+	0.0462796i
$541$	15.2374	−	15.2374i	0.655107	−	0.655107i	−0.299111	−	0.954218i	$-0.596690\pi$
$541$	15.2374	−	15.2374i	0.655107	−	0.655107i	0.954218	+	0.299111i	$0.0966901\pi$
$542$	5.82549	+	1.56093i	0.250226	+	0.0670479i
$543$	−2.78433	−	10.3912i	−0.119487	−	0.445931i
$544$	−0.597215	+	0.160023i	−0.0256054	+	0.00686095i
$545$	−0.683054	+	31.2428i	−0.0292588	+	1.33829i
$546$	5.66089	+	3.92151i	0.242264	+	0.167825i
$547$	24.5518	−	24.5518i	1.04976	−	1.04976i	0.0510651	−	0.998695i	$-0.483738\pi$
$547$	24.5518	−	24.5518i	1.04976	−	1.04976i	0.998695	−	0.0510651i	$-0.0162616\pi$
$548$	7.14214	+	4.12352i	0.305097	+	0.176148i
$549$	−4.94925	−	2.85745i	−0.211229	−	0.121953i
$550$	3.26944	−	10.3663i	0.139409	−	0.442019i
$551$	−8.57305	−	8.57305i	−0.365224	−	0.365224i
$552$	0.338255	+	0.585876i	0.0143971	+	0.0249365i
$553$	4.88397	+	8.45928i	0.207687	+	0.359725i
$554$	8.28088	+	8.28088i	0.351821	+	0.351821i
$555$	−5.59846	+	3.07111i	−0.237641	+	0.130361i
$556$	12.7043	+	7.33484i	0.538783	+	0.311067i
$557$	−5.98283	−	3.45419i	−0.253501	−	0.146359i	0.367866	−	0.929879i	$-0.380089\pi$
$557$	−5.98283	−	3.45419i	−0.253501	−	0.146359i	−0.621366	+	0.783520i	$0.713422\pi$
$558$	0.691834	−	0.691834i	0.0292877	−	0.0292877i
$559$	11.3574	−	5.36576i	0.480367	−	0.226947i
$560$	2.95320	+	3.08522i	0.124795	+	0.130374i
$561$	−1.29830	+	0.347879i	−0.0548143	+	0.0146874i
$562$	−5.72349	−	21.3604i	−0.241431	−	0.901033i
$563$	−11.1418	−	2.98545i	−0.469573	−	0.125822i	0.0162704	−	0.999868i	$-0.494821\pi$
$563$	−11.1418	−	2.98545i	−0.469573	−	0.125822i	−0.485843	+	0.874046i	$0.661487\pi$
$564$	7.67257	−	7.67257i	0.323073	−	0.323073i
$565$	−14.4929	−	26.4197i	−0.609720	−	1.11149i
$566$	9.26157	+	2.48163i	0.389293	+	0.104311i
$567$		−	1.90997i		−	0.0802112i
$568$	1.78054	−	6.64505i	0.0747096	−	0.278820i
$569$	13.9253	−	24.1194i	0.583780	−	1.01114i	−0.411247	−	0.911524i	$-0.634907\pi$
$569$	13.9253	−	24.1194i	0.583780	−	1.01114i	0.995026	−	0.0996118i	$-0.0317601\pi$
$570$	1.90369	+	7.78119i	0.0797369	+	0.325918i
$571$		−	36.5717i		−	1.53048i	−0.643745	−	0.765240i	$-0.722620\pi$
$571$		−	36.5717i		−	1.53048i	0.643745	−	0.765240i	$-0.277380\pi$
$572$	−0.643856	+	7.81170i	−0.0269210	+	0.326624i
$573$	−17.3530	−	17.3530i	−0.724934	−	0.724934i
$574$	−4.00934	−	14.9631i	−0.167347	−	0.624546i
$575$	−3.30244	+	0.731837i	−0.137721	+	0.0305197i
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	9.67542			0.402793			0.201397	−	0.979510i	$-0.435452\pi$
$577$	9.67542			0.402793			0.201397	+	0.979510i	$0.435452\pi$
$578$	14.3914	−	8.30886i	0.598602	−	0.345603i
$579$	4.89678	−	18.2750i	0.203503	−	0.759484i
$580$	−5.23278	−	5.46670i	−0.217279	−	0.226992i
$581$	−3.66964	−	6.35600i	−0.152242	−	0.263691i
$582$	−17.7014	+	4.74308i	−0.733747	+	0.196607i
$583$	2.37573	−	4.11489i	0.0983928	−	0.170421i
$584$	−2.15267			−0.0890782
$585$	3.28381	+	7.36319i	0.135769	+	0.304430i
$586$	11.3686			0.469633
$587$	23.0934	−	39.9990i	0.953168	−	1.65093i	0.214661	−	0.976689i	$-0.431135\pi$
$587$	23.0934	−	39.9990i	0.953168	−	1.65093i	0.738506	−	0.674246i	$-0.235531\pi$
$588$	3.23780	−	0.867565i	0.133524	−	0.0357778i
$589$	−1.75255	−	3.03551i	−0.0722127	−	0.125076i
$590$	32.4083	+	0.708535i	1.33423	+	0.0291699i
$591$	5.58399	−	20.8397i	0.229695	−	0.857232i
$592$	2.47309	−	1.42784i	0.101643	−	0.0586838i
$593$	26.6102			1.09275			0.546374	−	0.837541i	$-0.316008\pi$
$593$	26.6102			1.09275			0.546374	+	0.837541i	$0.316008\pi$
$594$	1.88267	−	1.08696i	0.0772470	−	0.0445986i
$595$	2.25740	+	1.36996i	0.0925445	+	0.0561628i
$596$	3.31108	+	12.3571i	0.135627	+	0.506167i
$597$	16.3562	+	16.3562i	0.669415	+	0.669415i
$598$	2.20545	−	1.04196i	0.0901875	−	0.0426087i
$599$		−	12.1568i		−	0.496711i	−0.968669	−	0.248356i	$-0.920110\pi$
$599$		−	12.1568i		−	0.496711i	0.968669	−	0.248356i	$-0.0798902\pi$
$600$	1.08178	+	4.88157i	0.0441635	+	0.199289i
$601$	3.24280	−	5.61669i	0.132276	−	0.229109i	−0.792277	−	0.610161i	$-0.791105\pi$
$601$	3.24280	−	5.61669i	0.132276	−	0.229109i	0.924554	+	0.381052i	$0.124438\pi$
$602$	−1.72218	+	6.42728i	−0.0701910	+	0.261956i
$603$		−	5.85612i		−	0.238480i
$604$	19.8110	+	5.30834i	0.806098	+	0.215993i
$605$	3.92636	−	13.4686i	0.159629	−	0.547576i
$606$	11.9623	−	11.9623i	0.485936	−	0.485936i
$607$	19.9692	+	5.35073i	0.810524	+	0.217179i	0.640200	−	0.768209i	$-0.278852\pi$
$607$	19.9692	+	5.35073i	0.810524	+	0.217179i	0.170325	+	0.985388i	$0.445518\pi$
$608$	−0.927215	−	3.46041i	−0.0376035	−	0.140338i
$609$	6.24362	−	1.67297i	0.253004	−	0.0677923i
$610$	−9.23140	+	8.83639i	−0.373768	+	0.357775i
$611$	−25.2979	−	29.8427i	−1.02344	−	1.20731i
$612$	0.437192	−	0.437192i	0.0176724	−	0.0176724i
$613$	−32.1225	−	18.5460i	−1.29742	−	0.749064i	−0.317460	−	0.948272i	$-0.602830\pi$
$613$	−32.1225	−	18.5460i	−1.29742	−	0.749064i	−0.979957	+	0.199208i	$0.936163\pi$
$614$	14.8812	+	8.59165i	0.600555	+	0.346731i
$615$	5.07564	−	17.4110i	0.204670	−	0.702078i
$616$	−2.93600	−	2.93600i	−0.118295	−	0.118295i
$617$	−2.52432	−	4.37225i	−0.101625	−	0.176020i	0.810729	−	0.585422i	$-0.199071\pi$
$617$	−2.52432	−	4.37225i	−0.101625	−	0.176020i	−0.912354	+	0.409401i	$0.865738\pi$
$618$	−2.54620	−	4.41014i	−0.102423	−	0.177402i
$619$	−18.2344	−	18.2344i	−0.732901	−	0.732901i	0.238292	−	0.971193i	$-0.423412\pi$
$619$	−18.2344	−	18.2344i	−0.732901	−	0.732901i	−0.971193	+	0.238292i	$0.923412\pi$
$620$	−1.05221	−	1.91812i	−0.0422578	−	0.0770336i
$621$	−0.585876	−	0.338255i	−0.0235104	−	0.0135737i
$622$	−14.0560	−	8.11525i	−0.563595	−	0.325392i
$623$	−1.12504	+	1.12504i	−0.0450737	+	0.0450737i
$624$	−1.54019	−	3.26003i	−0.0616570	−	0.130506i
$625$	−24.9045	−	2.18315i	−0.996180	−	0.0873258i
$626$	−20.3073	+	5.44132i	−0.811643	+	0.217479i
$627$	−2.01570	−	7.52268i	−0.0804991	−	0.300427i
$628$	−8.34356	−	2.23565i	−0.332944	−	0.0892121i
$629$	1.24848	−	1.24848i	0.0497801	−	0.0497801i
$630$	−4.10015	−	1.19528i	−0.163354	−	0.0476209i
$631$	14.7435	+	3.95051i	0.586930	+	0.157267i	0.540050	−	0.841633i	$-0.318405\pi$
$631$	14.7435	+	3.95051i	0.586930	+	0.157267i	0.0468803	+	0.998901i	$0.485072\pi$
$632$		−	5.11418i		−	0.203431i
$633$	−6.65211	+	24.8260i	−0.264398	+	0.986745i
$634$	−16.4931	+	28.5669i	−0.655025	+	1.13454i
$635$	15.9175	−	26.2288i	0.631668	−	1.04086i
$636$			2.18566i			0.0866672i
$637$	−2.15853	−	11.8915i	−0.0855242	−	0.471160i
$638$	5.20230	+	5.20230i	0.205961	+	0.205961i
$639$	1.78054	+	6.64505i	0.0704369	+	0.262874i
$640$	−0.531389	−	2.17201i	−0.0210050	−	0.0858562i
$641$	−41.2213	+	23.7991i	−1.62814	+	0.940008i	−0.643495	+	0.765450i	$0.722516\pi$
$641$	−41.2213	+	23.7991i	−1.62814	+	0.940008i	−0.984647	+	0.174558i	$0.944150\pi$
$642$	9.54075			0.376543
$643$	19.2959	−	11.1405i	0.760957	−	0.439339i	−0.0686821	−	0.997639i	$-0.521879\pi$
$643$	19.2959	−	11.1405i	0.760957	−	0.439339i	0.829639	+	0.558300i	$0.188546\pi$
$644$	−0.334424	+	1.24809i	−0.0131782	+	0.0491816i
$645$	−5.62750	+	5.38670i	−0.221583	+	0.212101i
$646$	−1.10749	−	1.91824i	−0.0435738	−	0.0754720i
$647$	18.1518	−	4.86376i	0.713620	−	0.191214i	0.116297	−	0.993214i	$-0.462898\pi$
$647$	18.1518	−	4.86376i	0.713620	−	0.191214i	0.597323	+	0.802001i	$0.296231\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−31.5151			−1.23708
$650$	17.8617	−	2.44145i	0.700592	−	0.0957616i
$651$	1.86872			0.0732408
$652$	−5.25134	+	9.09558i	−0.205658	+	0.356210i
$653$	−1.52020	+	0.407336i	−0.0594899	+	0.0159403i	−0.288441	−	0.957498i	$-0.593137\pi$
$653$	−1.52020	+	0.407336i	−0.0594899	+	0.0159403i	0.228951	+	0.973438i	$0.426470\pi$
$654$	6.98776	+	12.1032i	0.273243	+	0.473271i
$655$	26.8752	−	25.7252i	1.05010	−	1.00517i
$656$	−2.09916	+	7.83418i	−0.0819585	+	0.305873i
$657$	1.86427	−	1.07634i	0.0727320	−	0.0419918i
$658$	20.7244			0.807922
$659$	3.05103	−	1.76151i	0.118851	−	0.0686187i	−0.439396	−	0.898294i	$-0.644807\pi$
$659$	3.05103	−	1.76151i	0.118851	−	0.0686187i	0.558247	+	0.829675i	$0.311474\pi$
$660$	−1.15520	−	4.72178i	−0.0449661	−	0.183795i
$661$	12.5243	+	46.7413i	0.487139	+	1.81803i	0.570231	+	0.821484i	$0.306854\pi$
$661$	12.5243	+	46.7413i	0.487139	+	1.81803i	−0.0830924	+	0.996542i	$0.526480\pi$
$662$	1.25741	+	1.25741i	0.0488706	+	0.0488706i
$663$	−1.44151	−	1.70048i	−0.0559835	−	0.0660410i
$664$			3.84261i			0.149122i
$665$	−7.93787	+	13.0800i	−0.307818	+	0.507219i
$666$	−1.42784	+	2.47309i	−0.0553276	+	0.0958303i
$667$	0.592567	−	2.21149i	0.0229443	−	0.0856292i
$668$			6.95195i			0.268979i
$669$	−26.6147	−	7.13140i	−1.02899	−	0.275716i
$670$	−12.5714	−	3.66481i	−0.485675	−	0.141584i
$671$	8.78492	−	8.78492i	0.339138	−	0.339138i
$672$	1.84489	+	0.494337i	0.0711682	+	0.0190695i
$673$	5.80778	+	21.6749i	0.223873	+	0.835507i	0.982853	+	0.184392i	$0.0590317\pi$
$673$	5.80778	+	21.6749i	0.223873	+	0.835507i	−0.758979	+	0.651115i	$0.774302\pi$
$674$	11.7739	−	3.15481i	0.453514	−	0.121519i
$675$	−3.37764	−	3.68668i	−0.130005	−	0.141900i
$676$	−12.1707	+	4.56894i	−0.468102	+	0.175728i
$677$	−31.0923	+	31.0923i	−1.19497	+	1.19497i	−0.219322	+	0.975653i	$0.570384\pi$
$677$	−31.0923	+	31.0923i	−1.19497	+	1.19497i	−0.975653	+	0.219322i	$0.929616\pi$
$678$	−11.6708	−	6.73812i	−0.448213	−	0.258776i
$679$	−30.3125	−	17.5009i	−1.16329	−	0.671624i
$680$	−0.664926	−	1.21212i	−0.0254987	−	0.0464828i
$681$	−4.84010	−	4.84010i	−0.185473	−	0.185473i
$682$	1.06348	+	1.84201i	0.0407229	+	0.0705342i
$683$	−6.12989	−	10.6173i	−0.234554	−	0.406259i	0.724589	−	0.689181i	$-0.242030\pi$
$683$	−6.12989	−	10.6173i	−0.234554	−	0.406259i	−0.959143	+	0.282922i	$0.908696\pi$
$684$	2.53320	+	2.53320i	0.0968593	+	0.0968593i
$685$	−5.16107	+	17.7040i	−0.197194	+	0.676435i
$686$	17.1231	+	9.88602i	0.653763	+	0.377450i
$687$	−16.6575	−	9.61722i	−0.635524	−	0.366920i
$688$	2.46344	−	2.46344i	0.0939177	−	0.0939177i
$689$	7.85389	+	0.647333i	0.299209	+	0.0246614i
$690$	−1.09278	+	1.04602i	−0.0416015	+	0.0398214i
$691$	−41.9840	+	11.2496i	−1.59715	+	0.427954i	−0.944179	−	0.329432i	$-0.893143\pi$
$691$	−41.9840	+	11.2496i	−1.59715	+	0.427954i	−0.652967	+	0.757386i	$0.726476\pi$
$692$	3.41066	+	12.7288i	0.129654	+	0.483875i
$693$	4.01065	+	1.07465i	0.152352	+	0.0408226i
$694$	−12.5259	+	12.5259i	−0.475477	+	0.475477i
$695$	−9.18041	+	31.4916i	−0.348233	+	1.19454i
$696$	−3.26896	−	0.875916i	−0.123910	−	0.0332015i
$697$			5.01461i			0.189942i
$698$	4.35943	−	16.2696i	0.165007	−	0.615814i
$699$	4.77283	−	8.26678i	0.180525	−	0.312678i
$700$	−5.13182	+	8.05383i	−0.193965	+	0.304406i
$701$		−	2.09730i		−	0.0792141i	−0.999215	−	0.0396070i	$-0.987389\pi$
$701$		−	2.09730i		−	0.0792141i	0.999215	−	0.0396070i	$-0.0126106\pi$
$702$	2.96386	+	2.05318i	0.111864	+	0.0774921i
$703$	7.23400	+	7.23400i	0.272836	+	0.272836i
$704$	0.562653	+	2.09985i	0.0212058	+	0.0791410i
$705$	20.7420	+	12.5878i	0.781189	+	0.474083i
$706$	30.1361	−	17.3991i	1.13419	−	0.654824i
$707$	32.3115			1.21520
$708$	12.5547	−	7.24844i	0.471833	−	0.272413i
$709$	1.74277	−	6.50411i	0.0654511	−	0.244267i	−0.925448	−	0.378875i	$-0.876311\pi$
$709$	1.74277	−	6.50411i	0.0654511	−	0.244267i	0.990899	+	0.134608i	$0.0429776\pi$
$710$	15.3793	+	0.336233i	0.577173	+	0.0126186i
$711$	2.55709	+	4.42901i	0.0958984	+	0.166101i
$712$	0.804636	−	0.215602i	0.0301550	−	0.00808001i
$713$	0.330949	−	0.573221i	0.0123942	−	0.0214673i
$714$	1.18090			0.0441941
$715$	−17.3092	+	2.75259i	−0.647329	+	0.102941i
$716$	−16.3584			−0.611341
$717$	−2.75985	+	4.78020i	−0.103069	+	0.178520i
$718$	15.5515	−	4.16700i	0.580375	−	0.155511i
$719$	9.33097	+	16.1617i	0.347987	+	0.602730i	0.985892	−	0.167385i	$-0.0535321\pi$
$719$	9.33097	+	16.1617i	0.347987	+	0.602730i	−0.637905	+	0.770115i	$0.720199\pi$
$720$	1.54620	+	1.61532i	0.0576235	+	0.0601995i
$721$	2.51736	−	9.39490i	0.0937513	−	0.349885i
$722$	−5.33974	+	3.08290i	−0.198725	+	0.114734i
$723$	−11.1409			−0.414335
$724$	−9.31654	+	5.37891i	−0.346246	+	0.199905i
$725$	9.09308	−	14.2706i	0.337708	−	0.529996i
$726$	−1.62385	−	6.06027i	−0.0602666	−	0.224918i
$727$	25.5354	+	25.5354i	0.947057	+	0.947057i	0.998667	−	0.0516107i	$-0.0164355\pi$
$727$	25.5354	+	25.5354i	0.947057	+	0.947057i	−0.0516107	+	0.998667i	$0.516435\pi$
$728$	2.32274	−	6.48296i	0.0860864	−	0.240274i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.14391	−	4.67562i	−0.0423379	−	0.173053i
$731$	1.07700	−	1.86541i	0.0398341	−	0.0689947i
$732$	−1.47913	+	5.52017i	−0.0546700	+	0.204031i
$733$		−	3.90642i		−	0.144287i	−0.997394	−	0.0721435i	$-0.977016\pi$
$733$		−	3.90642i		−	0.144287i	0.997394	−	0.0721435i	$-0.0229839\pi$
$734$	−12.8267	−	3.43690i	−0.473441	−	0.126858i
$735$	3.60489	+	6.57151i	0.132968	+	0.242394i
$736$	0.478365	−	0.478365i	0.0176328	−	0.0176328i
$737$	12.2970	+	3.29496i	0.452965	+	0.121371i
$738$	−2.09916	−	7.83418i	−0.0772712	−	0.288380i
$739$	−4.49797	+	1.20523i	−0.165461	+	0.0443350i	−0.340598	−	0.940209i	$-0.610630\pi$
$739$	−4.49797	+	1.20523i	−0.165461	+	0.0443350i	0.175138	+	0.984544i	$0.443963\pi$
$740$	4.41545	+	4.61284i	0.162315	+	0.169571i
$741$	9.85298	−	8.35245i	0.361958	−	0.306835i
$742$	−2.95185	+	2.95185i	−0.108366	+	0.108366i
$743$	12.3938	+	7.15557i	0.454685	+	0.262512i	0.709807	−	0.704396i	$-0.248782\pi$
$743$	12.3938	+	7.15557i	0.454685	+	0.262512i	−0.255122	+	0.966909i	$0.582116\pi$
$744$	−0.847320	−	0.489200i	−0.0310643	−	0.0179350i
$745$	−25.0803	+	13.7581i	−0.918871	+	0.504059i
$746$	4.21782	+	4.21782i	0.154425	+	0.154425i
$747$	−1.92131	−	3.32780i	−0.0702969	−	0.121758i
$748$	0.672050	+	1.16402i	0.0245726	+	0.0425609i
$749$	12.8853	+	12.8853i	0.470818	+	0.470818i
$750$	−10.0280	+	4.94365i	−0.366170	+	0.180517i
$751$	−24.7594	−	14.2948i	−0.903482	−	0.521626i	−0.0251540	−	0.999684i	$-0.508008\pi$
$751$	−24.7594	−	14.2948i	−0.903482	−	0.521626i	−0.878328	+	0.478058i	$0.841341\pi$
$752$	−9.39693	−	5.42532i	−0.342671	−	0.197841i
$753$	9.72025	−	9.72025i	0.354226	−	0.354226i
$754$	−4.11566	+	11.4872i	−0.149884	+	0.418338i
$755$	−1.00242	+	45.8505i	−0.0364818	+	1.66867i
$756$	−1.84489	+	0.494337i	−0.0670980	+	0.0179789i
$757$	−1.66016	−	6.19580i	−0.0603395	−	0.225190i	0.929171	−	0.369650i	$-0.120522\pi$
$757$	−1.66016	−	6.19580i	−0.0603395	−	0.225190i	−0.989511	+	0.144460i	$0.953856\pi$
$758$	9.97467	+	2.67271i	0.362296	+	0.0970771i
$759$	1.03993	−	1.03993i	0.0377471	−	0.0377471i
$760$	7.02334	−	3.85275i	0.254763	−	0.139754i
$761$	9.47294	+	2.53827i	0.343394	+	0.0920121i	0.426394	−	0.904537i	$-0.359784\pi$
$761$	9.47294	+	2.53827i	0.343394	+	0.0920121i	−0.0830005	+	0.996550i	$0.526450\pi$
$762$		−	13.7209i		−	0.497056i
$763$	−6.90862	+	25.7833i	−0.250109	+	0.933419i
$764$	−12.2705	+	21.2531i	−0.443930	+	0.768909i
$765$	1.18190	+	0.717266i	0.0427318	+	0.0259328i
$766$			4.42893i			0.160024i
$767$	−22.3280	−	47.2603i	−0.806216	−	1.70647i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	4.48417	+	16.7351i	0.161703	+	0.603485i	0.998438	+	0.0558759i	$0.0177951\pi$
$769$	4.48417	+	16.7351i	0.161703	+	0.603485i	−0.836735	+	0.547609i	$0.815538\pi$
$770$	4.81686	−	7.93718i	0.173588	−	0.286036i
$771$	0.113522	−	0.0655418i	0.00408838	−	0.00236043i
$772$	−18.9197			−0.680934
$773$	−38.6416	+	22.3097i	−1.38984	+	0.802426i	−0.993297	−	0.115589i	$-0.963124\pi$
$773$	−38.6416	+	22.3097i	−1.38984	+	0.802426i	−0.396545	+	0.918015i	$0.629791\pi$
$774$	−0.901681	+	3.36512i	−0.0324103	+	0.120957i
$775$	3.60705	−	3.30468i	0.129569	−	0.118708i
$776$	9.16293	+	15.8707i	0.328930	+	0.569723i
$777$	−5.26841	+	1.41167i	−0.189003	+	0.0506433i
$778$	−0.557053	+	0.964844i	−0.0199713	+	0.0345913i
$779$	−29.0559			−1.04103
$780$	6.26238	−	5.07765i	0.224229	−	0.181809i
$781$	−14.9554			−0.535147
$782$	0.209138	−	0.362237i	0.00747874	−	0.0129536i
$783$	3.26896	−	0.875916i	0.116823	−	0.0313027i
$784$	−1.67601	−	2.90293i	−0.0598574	−	0.103676i
$785$	0.422177	−	19.3103i	0.0150681	−	0.689214i
$786$	4.30615	−	16.0708i	0.153595	−	0.573225i
$787$	−8.75584	+	5.05518i	−0.312112	+	0.180198i	−0.647871	−	0.761750i	$-0.724340\pi$
$787$	−8.75584	+	5.05518i	−0.312112	+	0.180198i	0.335759	+	0.941948i	$0.391007\pi$
$788$	−21.5749			−0.768573
$789$	−14.6067	+	8.43319i	−0.520013	+	0.300229i
$790$	11.1081	−	2.71762i	0.395207	−	0.0966886i
$791$	−6.66180	−	24.8622i	−0.236866	−	0.883997i
$792$	−1.53720	−	1.53720i	−0.0546219	−	0.0546219i
$793$	19.3979	+	6.94996i	0.688840	+	0.246800i
$794$			38.4947i			1.36613i
$795$	−4.74728	+	1.16144i	−0.168369	+	0.0411919i
$796$	11.5656	−	20.0322i	0.409931	−	0.710022i
$797$	−2.75765	+	10.2917i	−0.0976811	+	0.364551i	−0.997412	−	0.0718937i	$-0.977096\pi$
$797$	−2.75765	+	10.2917i	−0.0976811	+	0.364551i	0.899731	+	0.436444i	$0.143762\pi$
$798$			6.84244i			0.242220i
$799$	−6.48017	−	1.73636i	−0.229252	−	0.0614279i
$800$	4.43525	−	2.30836i	0.156810	−	0.0816130i
$801$	−0.589034	+	0.589034i	−0.0208125	+	0.0208125i
$802$	9.89323	+	2.65088i	0.349342	+	0.0936059i
$803$	1.21121	+	4.52028i	0.0427425	+	0.159517i
$804$	−5.65658	+	1.51568i	−0.199492	+	0.0534537i
$805$	−2.88857	−	0.0631521i	−0.101809	−	0.00222582i
$806$	−2.00883	+	2.89984i	−0.0707580	+	0.102143i
$807$	3.87674	−	3.87674i	0.136468	−	0.136468i
$808$	−14.6508	−	8.45864i	−0.515413	−	0.297574i
$809$	−1.08288	−	0.625203i	−0.0380722	−	0.0219810i	0.480843	−	0.876807i	$-0.340331\pi$
$809$	−1.08288	−	0.625203i	−0.0380722	−	0.0219810i	−0.518915	+	0.854826i	$0.673664\pi$
$810$	−2.14671	−	0.625808i	−0.0754277	−	0.0219887i
$811$	18.6976	+	18.6976i	0.656562	+	0.656562i	0.954565	−	0.298003i	$-0.0963206\pi$
$811$	18.6976	+	18.6976i	0.656562	+	0.656562i	−0.298003	+	0.954565i	$0.596321\pi$
$812$	−3.23194	−	5.59788i	−0.113419	−	0.196447i
$813$	3.01549	+	5.22299i	0.105758	+	0.183178i
$814$	−4.38974	−	4.38974i	−0.153860	−	0.153860i
$815$	−22.5462	−	6.57266i	−0.789759	−	0.230230i
$816$	−0.535449	−	0.309141i	−0.0187445	−	0.0108221i
$817$	10.8087	+	6.24038i	0.378147	+	0.218323i
$818$	12.4525	−	12.4525i	0.435392	−	0.435392i
$819$	1.22993	+	6.77577i	0.0429772	+	0.236765i
$820$	−18.1314	−	0.396402i	−0.633175	−	0.0138430i
$821$	−8.96564	+	2.40234i	−0.312903	+	0.0838421i	−0.411853	−	0.911250i	$-0.635118\pi$
$821$	−8.96564	+	2.40234i	−0.312903	+	0.0838421i	0.0989499	+	0.995092i	$0.468452\pi$
$822$	2.13449	+	7.96603i	0.0744489	+	0.277847i
$823$	4.74623	+	1.27175i	0.165443	+	0.0443304i	0.340590	−	0.940212i	$-0.389373\pi$
$823$	4.74623	+	1.27175i	0.165443	+	0.0443304i	−0.175147	+	0.984542i	$0.556040\pi$
$824$	−3.60087	+	3.60087i	−0.125442	+	0.125442i
$825$	9.64190	−	5.01821i	0.335688	−	0.174712i
$826$	26.7452	+	7.16634i	0.930583	+	0.249349i
$827$			32.9053i			1.14423i	0.820174	+	0.572114i	$0.193877\pi$
$827$			32.9053i			1.14423i	−0.820174	+	0.572114i	$0.806123\pi$
$828$	−0.175094	+	0.653459i	−0.00608493	+	0.0227093i
$829$	−1.27999	+	2.21701i	−0.0444559	+	0.0769998i	−0.887397	−	0.461006i	$-0.847489\pi$
$829$	−1.27999	+	2.21701i	−0.0444559	+	0.0769998i	0.842941	+	0.538006i	$0.180822\pi$
$830$	−8.34619	+	2.04192i	−0.289700	+	0.0708761i
$831$			11.7109i			0.406248i
$832$	−2.75032	+	2.33147i	−0.0953502	+	0.0808291i
$833$	−1.46547	−	1.46547i	−0.0507756	−	0.0507756i
$834$	3.79680	+	14.1698i	0.131472	+	0.490661i
$835$	−15.0997	+	3.69419i	−0.522546	+	0.127843i
$836$	−6.74465	+	3.89402i	−0.233269	+	0.134678i
$837$	0.978401			0.0338185
$838$	5.44338	−	3.14274i	0.188038	−	0.108564i
$839$	−3.70671	+	13.8336i	−0.127970	+	0.477590i	−0.999928	−	0.0119902i	$-0.996183\pi$
$839$	−3.70671	+	13.8336i	−0.127970	+	0.477590i	0.871958	+	0.489580i	$0.162850\pi$
$840$	−0.0933498	+	4.26980i	−0.00322087	+	0.147322i
$841$	−8.77333	−	15.1959i	−0.302529	−	0.523995i
$842$	−24.7402	+	6.62912i	−0.852604	+	0.228455i
$843$	11.0569	−	19.1512i	0.380821	−	0.659602i
$844$	25.7018			0.884692
$845$	−16.3911	−	24.0069i	−0.563872	−	0.825862i
$846$	10.8506			0.373053
$847$	5.99163	−	10.3778i	0.205875	−	0.356586i
$848$	2.11119	−	0.565691i	0.0724985	−	0.0194259i
$849$	4.79414	+	8.30370i	0.164535	+	0.284982i
$850$	2.27941	−	2.08833i	0.0781830	−	0.0716293i
$851$	−0.500012	+	1.86607i	−0.0171402	+	0.0639680i
$852$	5.95779	−	3.43973i	0.204110	−	0.117843i
$853$	5.12578			0.175503			0.0877516	−	0.996142i	$-0.472032\pi$
$853$	5.12578			0.175503			0.0877516	+	0.996142i	$0.472032\pi$
$854$	−9.45292	+	5.45765i	−0.323472	+	0.186757i
$855$	−4.15602	+	6.84825i	−0.142133	+	0.234205i
$856$	−2.46933	−	9.21566i	−0.0843999	−	0.314985i
$857$	25.5465	+	25.5465i	0.872652	+	0.872652i	0.992761	−	0.120109i	$-0.0383244\pi$
$857$	25.5465	+	25.5465i	0.872652	+	0.872652i	−0.120109	+	0.992761i	$0.538324\pi$
$858$	−5.97898	+	5.06843i	−0.204119	+	0.173033i
$859$			39.8525i			1.35975i	0.733328	+	0.679875i	$0.237966\pi$
$859$			39.8525i			1.35975i	−0.733328	+	0.679875i	$0.762034\pi$
$860$	6.65966	+	4.04157i	0.227092	+	0.137816i
$861$	7.74544	−	13.4155i	0.263964	−	0.457199i
$862$	−3.09979	+	11.5686i	−0.105579	+	0.394027i
$863$			46.1552i			1.57114i	0.618773	+	0.785570i	$0.287630\pi$
$863$			46.1552i			1.57114i	−0.618773	+	0.785570i	$0.712370\pi$
$864$	0.965926	+	0.258819i	0.0328615	+	0.00880520i
$865$	−25.8346	+	14.1719i	−0.878403	+	0.481859i
$866$	25.0600	−	25.0600i	0.851572	−	0.851572i
$867$	16.0515	+	4.30098i	0.545137	+	0.146069i
$868$	−0.483659	−	1.80504i	−0.0164165	−	0.0612671i
$869$	−10.7390	+	2.87751i	−0.364296	+	0.0976128i
$870$	0.165407	−	7.56567i	0.00560781	−	0.256500i
$871$	3.77106	+	20.7751i	0.127777	+	0.703936i
$872$	9.88219	−	9.88219i	0.334653	−	0.334653i
$873$	−15.8707	−	9.16293i	−0.537140	−	0.310118i
$874$	2.09889	+	1.21180i	0.0709960	+	0.0409896i
$875$	−20.2200	−	6.86665i	−0.683560	−	0.232135i
$876$	−1.52217	−	1.52217i	−0.0514293	−	0.0514293i
$877$	24.4763	+	42.3941i	0.826505	+	1.43155i	0.900764	+	0.434310i	$0.143008\pi$
$877$	24.4763	+	42.3941i	0.826505	+	1.43155i	−0.0742588	+	0.997239i	$0.523659\pi$
$878$	−15.1777	−	26.2886i	−0.512224	−	0.887198i
$879$	8.03881	+	8.03881i	0.271142	+	0.271142i
$880$	−4.26190	+	2.33792i	−0.143669	+	0.0788114i
$881$	10.4747	+	6.04758i	0.352902	+	0.203748i	0.665963	−	0.745985i	$-0.268021\pi$
$881$	10.4747	+	6.04758i	0.352902	+	0.203748i	−0.313060	+	0.949733i	$0.601354\pi$
$882$	2.90293	+	1.67601i	0.0977467	+	0.0564341i
$883$	−0.0376098	+	0.0376098i	−0.00126567	+	0.00126567i	−0.707739	−	0.706474i	$-0.750285\pi$
$883$	−0.0376098	+	0.0376098i	−0.00126567	+	0.00126567i	0.706474	+	0.707739i	$0.250285\pi$
$884$	−1.26944	+	1.83250i	−0.0426960	+	0.0616338i
$885$	22.4151	+	23.4171i	0.753475	+	0.787158i
$886$	−26.2624	+	7.03698i	−0.882301	+	0.236412i
$887$	−5.24258	−	19.5656i	−0.176029	−	0.656947i	−0.996374	−	0.0850794i	$-0.972886\pi$
$887$	−5.24258	−	19.5656i	−0.176029	−	0.656947i	0.820346	−	0.571868i	$-0.193781\pi$
$888$	2.75837	+	0.739104i	0.0925650	+	0.0248027i
$889$	18.5308	−	18.5308i	0.621503	−	0.621503i
$890$	0.895863	+	1.63311i	0.0300294	+	0.0547419i
$891$	2.09985	+	0.562653i	0.0703476	+	0.0188496i
$892$			27.5536i			0.922563i
$893$	10.0609	−	37.5477i	0.336675	−	1.25649i
$894$	−6.39651	+	11.0791i	−0.213931	+	0.370540i
$895$	−8.69265	−	35.5305i	−0.290563	−	1.18765i
$896$		−	1.90997i		−	0.0638076i
$897$	2.29626	+	0.822713i	0.0766699	+	0.0274696i
$898$	−9.55452	−	9.55452i	−0.318838	−	0.318838i
$899$	0.856997	+	3.19836i	0.0285824	+	0.106671i
$900$	−2.68686	+	4.21673i	−0.0895619	+	0.140558i
$901$	1.17031	−	0.675679i	0.0389887	−	0.0225101i
$902$	17.6317			0.587071
$903$	−5.76254	+	3.32701i	−0.191765	+	0.110716i
$904$	−3.48791	+	13.0170i	−0.116006	+	0.432940i
$905$	−16.6337	−	17.3773i	−0.552924	−	0.577642i
$906$	10.2549	+	17.7621i	0.340697	+	0.590105i
$907$	−50.0170	+	13.4020i	−1.66079	+	0.445006i	−0.962604	−	0.270914i	$-0.912674\pi$
$907$	−50.0170	+	13.4020i	−1.66079	+	0.445006i	−0.698182	+	0.715920i	$0.746007\pi$
$908$	−3.42247	+	5.92789i	−0.113579	+	0.196724i
$909$	16.9173			0.561111
$910$	15.3153	+	1.60004i	0.507698	+	0.0530407i
$911$	−0.617609			−0.0204623			−0.0102311	−	0.999948i	$-0.503257\pi$
$911$	−0.617609			−0.0204623			−0.0102311	+	0.999948i	$0.503257\pi$
$912$	1.79124	−	3.10252i	0.0593140	−	0.102735i
$913$	8.06890	−	2.16206i	0.267042	−	0.0715536i
$914$	0.114554	+	0.198413i	0.00378910	+	0.00656291i
$915$	−12.7759	−	0.279316i	−0.422357	−	0.00923389i
$916$	−4.97824	+	18.5790i	−0.164486	+	0.613869i
$917$	27.5201	−	15.8887i	0.908794	−	0.524692i
$918$	0.618283			0.0204064
$919$	13.3803	−	7.72510i	0.441374	−	0.254828i	−0.262806	−	0.964849i	$-0.584648\pi$
$919$	13.3803	−	7.72510i	0.441374	−	0.254828i	0.704180	+	0.710021i	$0.251315\pi$
$920$	1.29321	+	0.784816i	0.0426360	+	0.0258746i
$921$	4.44736	+	16.5978i	0.146546	+	0.546916i
$922$	26.0495	+	26.0495i	0.857895	+	0.857895i
$923$	−10.5957	−	22.4273i	−0.348761	−	0.738202i
$924$		−	4.15213i		−	0.136595i
$925$	−7.67280	+	12.0416i	−0.252280	+	0.395926i
$926$	0.0313299	−	0.0542649i	0.00102956	−	0.00178326i
$927$	1.31801	−	4.91887i	0.0432891	−	0.161557i
$928$			3.38428i			0.111094i
$929$	12.5676	+	3.36748i	0.412330	+	0.110483i	0.459020	−	0.888426i	$-0.348201\pi$
$929$	12.5676	+	3.36748i	0.412330	+	0.110483i	−0.0466902	+	0.998909i	$0.514867\pi$
$930$	0.612291	−	2.10034i	0.0200778	−	0.0688729i
$931$	8.49132	−	8.49132i	0.278292	−	0.278292i
$932$	−9.22039	−	2.47060i	−0.302024	−	0.0809271i
$933$	−4.20076	−	15.6775i	−0.137527	−	0.513257i
$934$	17.0231	−	4.56133i	0.557014	−	0.149251i
$935$	−2.17115	+	2.07825i	−0.0710043	+	0.0679660i
$936$	1.21611	−	3.39427i	0.0397499	−	0.110945i
$937$	−10.5551	+	10.5551i	−0.344821	+	0.344821i	−0.858176	−	0.513355i	$-0.828402\pi$
$937$	−10.5551	+	10.5551i	−0.344821	+	0.344821i	0.513355	+	0.858176i	$0.328402\pi$
$938$	−9.68651	−	5.59251i	−0.316276	−	0.182602i
$939$	−18.2070	−	10.5118i	−0.594164	−	0.343041i
$940$	6.79042	−	23.2932i	0.221479	−	0.759740i
$941$	29.8629	+	29.8629i	0.973501	+	0.973501i	0.999658	−	0.0261567i	$-0.00832690\pi$
$941$	29.8629	+	29.8629i	0.973501	+	0.973501i	−0.0261567	+	0.999658i	$0.508327\pi$
$942$	−4.31894	−	7.48063i	−0.140719	−	0.243732i
$943$	−2.74343	−	4.75177i	−0.0893385	−	0.154739i
$944$	−10.2508	−	10.2508i	−0.333637	−	0.333637i
$945$	−2.05406	−	3.74443i	−0.0668185	−	0.121806i
$946$	−6.55891	−	3.78679i	−0.213249	−	0.123119i
$947$	16.1195	+	9.30662i	0.523815	+	0.302424i	0.738494	−	0.674260i	$-0.235537\pi$
$947$	16.1195	+	9.30662i	0.523815	+	0.302424i	−0.214679	+	0.976685i	$0.568871\pi$
$948$	3.61627	−	3.61627i	0.117451	−	0.117451i
$949$	−5.92053	+	5.01888i	−0.192189	+	0.162920i
$950$	12.1003	+	13.2075i	0.392587	+	0.428507i
$951$	−31.8622	+	8.53746i	−1.03320	+	0.276846i
$952$	−0.305640	−	1.14066i	−0.00990585	−	0.0369691i
$953$	39.4440	+	10.5690i	1.27772	+	0.342363i	0.832982	−	0.553300i	$-0.186632\pi$
$953$	39.4440	+	10.5690i	1.27772	+	0.342363i	0.444733	+	0.895663i	$0.353298\pi$
$954$	−1.54550	+	1.54550i	−0.0500373	+	0.0500373i
$955$	−52.6822	−	15.3579i	−1.70476	−	0.496970i
$956$	5.33162	+	1.42860i	0.172437	+	0.0462044i
$957$			7.35716i			0.237823i
$958$	−1.26441	+	4.71886i	−0.0408514	+	0.152459i
$959$	−7.87580	+	13.6413i	−0.254323	+	0.440500i
$960$	1.16009	−	1.91159i	0.0374419	−	0.0616964i
$961$		−	30.0427i		−	0.969120i
$962$	3.47282	−	9.69294i	0.111968	−	0.312513i
$963$	6.74633	+	6.74633i	0.217397	+	0.217397i
$964$	2.88348	+	10.7613i	0.0928707	+	0.346598i
$965$	−10.0537	−	41.0937i	−0.323641	−	1.32285i
$966$	−1.11901	+	0.646058i	−0.0360034	+	0.0207866i
$967$	57.3191			1.84326			0.921629	−	0.388073i	$-0.126859\pi$
$967$	57.3191			1.84326			0.921629	+	0.388073i	$0.126859\pi$
$968$	−5.43349	+	3.13703i	−0.174639	+	0.100828i
$969$	0.573281	−	2.13952i	0.0184164	−	0.0687311i
$970$	−29.6021	+	28.3355i	−0.950467	+	0.909797i
$971$	−22.9605	−	39.7687i	−0.736836	−	1.27624i	−0.953913	−	0.300083i	$-0.902986\pi$
$971$	−22.9605	−	39.7687i	−0.736836	−	1.27624i	0.217077	−	0.976155i	$-0.430348\pi$
$972$	−0.965926	+	0.258819i	−0.0309821	+	0.00830162i
$973$	−14.0093	+	24.2649i	−0.449119	+	0.777897i
$974$	−19.4868			−0.624397
$975$	14.3565	+	10.9037i	0.459775	+	0.349199i
$976$	5.71490			0.182930
$977$	29.2570	−	50.6747i	0.936015	−	1.62123i	0.163201	−	0.986593i	$-0.447818\pi$
$977$	29.2570	−	50.6747i	0.936015	−	1.62123i	0.772814	−	0.634633i	$-0.218849\pi$
$978$	−10.1448	+	2.71829i	−0.324395	+	0.0869214i
$979$	−0.905461	−	1.56831i	−0.0289387	−	0.0501232i
$980$	5.41458	−	5.18289i	0.172962	−	0.165561i
$981$	−3.61713	+	13.4993i	−0.115486	+	0.431000i
$982$	23.5658	−	13.6057i	0.752014	−	0.434175i
$983$	−17.6084			−0.561621			−0.280811	−	0.959763i	$-0.590603\pi$
$983$	−17.6084			−0.561621			−0.280811	+	0.959763i	$0.590603\pi$
$984$	−7.02393	+	4.05527i	−0.223915	+	0.129277i
$985$	−11.4647	−	46.8608i	−0.365294	−	1.49311i
$986$	0.541564	+	2.02114i	0.0172469	+	0.0643663i
$987$	14.6544	+	14.6544i	0.466454	+	0.466454i
$988$	−10.6180	−	7.35547i	−0.337803	−	0.234009i
$989$			2.35685i			0.0749434i
$990$	2.52196	−	4.15565i	0.0801530	−	0.132075i
$991$	−5.36717	+	9.29621i	−0.170494	+	0.295304i	−0.938593	−	0.345027i	$-0.887870\pi$
$991$	−5.36717	+	9.29621i	−0.170494	+	0.295304i	0.768099	+	0.640331i	$0.221203\pi$
$992$	−0.253229	+	0.945063i	−0.00804002	+	0.0300058i
$993$			1.77824i			0.0564309i
$994$	12.6918	+	3.40077i	0.402561	+	0.107866i
$995$	49.6559	+	14.4757i	1.57420	+	0.458910i
$996$	−2.71714	+	2.71714i	−0.0860957	+	0.0860957i
$997$	12.3326	+	3.30451i	0.390577	+	0.104655i	0.448763	−	0.893651i	$-0.351865\pi$
$997$	12.3326	+	3.30451i	0.390577	+	0.104655i	−0.0581856	+	0.998306i	$0.518532\pi$
$998$	−4.09145	−	15.2695i	−0.129513	−	0.483348i
$999$	−2.75837	+	0.739104i	−0.0872711	+	0.0233842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.b.163.4	yes	16
5.2	odd	4		390.2.bd.b.7.1	✓	16
13.2	odd	12		390.2.bd.b.223.1	yes	16
65.2	even	12	inner	390.2.bn.b.67.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.b.7.1	✓	16	5.2	odd	4
390.2.bd.b.223.1	yes	16	13.2	odd	12
390.2.bn.b.67.4	yes	16	65.2	even	12	inner
390.2.bn.b.163.4	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.61532 - 1.54620i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.65408 - 0.954985i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.61532 - 1.54620i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.65408 - 0.954985i) q^{7} -1.00000 q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.531389 - 2.17201i) q^{10} +(0.562653 + 2.09985i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(-2.75032 + 2.33147i) q^{13} -1.90997i q^{14} +(1.16009 - 1.91159i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.160023 + 0.597215i) q^{17} -1.00000i q^{18} +(-3.46041 - 0.927215i) q^{19} +(-2.14671 - 0.625808i) q^{20} +(1.35055 - 1.35055i) q^{21} +(2.09985 + 0.562653i) q^{22} +(-0.175094 - 0.653459i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(0.218523 - 4.99522i) q^{25} +(0.643951 + 3.54758i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.65408 - 0.954985i) q^{28} +(2.93087 + 1.69214i) q^{29} +(-1.07544 - 1.96047i) q^{30} +(0.691834 + 0.691834i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.08696 + 1.88267i) q^{33} +(0.437192 + 0.437192i) q^{34} +(1.19528 - 4.10015i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-2.47309 - 1.42784i) q^{37} +(-2.53320 + 2.53320i) q^{38} +(-2.05318 + 2.96386i) q^{39} +(-1.61532 + 1.54620i) q^{40} +(7.83418 - 2.09916i) q^{41} +(-0.494337 - 1.84489i) q^{42} +(-3.36512 - 0.901681i) q^{43} +(1.53720 - 1.53720i) q^{44} +(0.625808 - 2.14671i) q^{45} +(-0.653459 - 0.175094i) q^{46} +10.8506i q^{47} +(-0.258819 + 0.965926i) q^{48} +(-1.67601 + 2.90293i) q^{49} +(-4.21673 - 2.68686i) q^{50} +0.618283i q^{51} +(3.39427 + 1.21611i) q^{52} +(-1.54550 - 1.54550i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(4.15565 + 2.52196i) q^{55} +(-1.65408 + 0.954985i) q^{56} -3.58249 q^{57} +(2.93087 - 1.69214i) q^{58} +(-3.75207 + 14.0029i) q^{59} +(-2.23553 - 0.0488750i) q^{60} +(-2.85745 - 4.94925i) q^{61} +(0.945063 - 0.253229i) q^{62} +(0.954985 - 1.65408i) q^{63} +1.00000 q^{64} +(-0.837729 + 8.01862i) q^{65} +2.17392 q^{66} +(2.92806 - 5.07155i) q^{67} +(0.597215 - 0.160023i) q^{68} +(-0.338255 - 0.585876i) q^{69} +(-2.95320 - 3.08522i) q^{70} +(-1.78054 + 6.64505i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.15267 q^{73} +(-2.47309 + 1.42784i) q^{74} +(-1.08178 - 4.88157i) q^{75} +(0.927215 + 3.46041i) q^{76} +(2.93600 + 2.93600i) q^{77} +(1.54019 + 3.26003i) q^{78} +5.11418i q^{79} +(0.531389 + 2.17201i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.09916 - 7.83418i) q^{82} -3.84261i q^{83} +(-1.84489 - 0.494337i) q^{84} +(0.664926 + 1.21212i) q^{85} +(-2.46344 + 2.46344i) q^{86} +(3.26896 + 0.875916i) q^{87} +(-0.562653 - 2.09985i) q^{88} +(-0.804636 + 0.215602i) q^{89} +(-1.54620 - 1.61532i) q^{90} +(-2.32274 + 6.48296i) q^{91} +(-0.478365 + 0.478365i) q^{92} +(0.847320 + 0.489200i) q^{93} +(9.39693 + 5.42532i) q^{94} +(-7.02334 + 3.85275i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-9.16293 - 15.8707i) q^{97} +(1.67601 + 2.90293i) q^{98} +(1.53720 + 1.53720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8	\( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 24 * q^7 - 16 * q^8 + 12 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^19 + 4 * q^23 + 4 * q^25 + 4 * q^26 - 24 * q^28 - 48 * q^29 - 4 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 20 * q^34 - 12 * q^35 + 12 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 + 20 * q^43 - 12 * q^44 + 8 * q^45 - 4 * q^46 - 4 * q^49 - 16 * q^50 - 4 * q^52 + 32 * q^53 + 16 * q^55 - 24 * q^56 - 8 * q^57 - 48 * q^58 + 4 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 16 * q^64 - 8 * q^65 + 32 * q^66 - 28 * q^67 - 16 * q^68 + 4 * q^69 - 36 * q^71 + 32 * q^73 + 12 * q^74 - 24 * q^75 + 8 * q^76 + 4 * q^77 + 20 * q^78 + 8 * q^81 - 24 * q^82 + 52 * q^85 + 16 * q^86 + 36 * q^87 - 12 * q^88 - 24 * q^89 + 4 * q^90 - 8 * q^92 + 36 * q^94 - 40 * q^95 - 4 * q^97 + 4 * q^98 - 12 * q^99

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