LMFDB - Embedded newform 961.2.g.o.844.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,-2,-4,-8,-24,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			844.1
Root			$1.29195 + 0.575212i$ of defining polynomial
Character	$\chi$	$=$	961.844
Dual form			961.2.g.o.846.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.746033 - 2.29605i) q^{2} +(2.36146 - 0.501943i) q^{3} +(-3.09726 + 2.25029i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.91421 - 5.04757i) q^{6} +(2.20549 + 0.981949i) q^{7} +(3.57117 + 2.59461i) q^{8} +(2.58390 - 1.15042i) q^{9} +(2.36146 + 0.501943i) q^{10} +(0.548005 + 5.21392i) q^{11} +(-6.18453 + 6.86862i) q^{12} +(1.22346 + 1.35879i) q^{13} +(0.609237 - 5.79650i) q^{14} +(-0.746033 + 2.29605i) q^{15} +(0.927051 - 2.85317i) q^{16} +(0.0179342 - 0.170633i) q^{17} +(-4.56911 - 5.07451i) q^{18} +(1.06110 - 1.17847i) q^{19} +(-0.400180 - 3.80745i) q^{20} +(5.70106 + 1.21180i) q^{21} +(11.5626 - 5.14801i) q^{22} +(3.23607 + 2.35114i) q^{23} +(9.73552 + 4.33453i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.20711 - 3.82282i) q^{26} +(-0.335106 + 0.243469i) q^{27} +(-9.04067 + 1.92165i) q^{28} +(-0.362036 - 1.11423i) q^{29} +5.82843 q^{30} +1.58579 q^{32} +(3.91118 + 12.0374i) q^{33} +(-0.405162 + 0.0861198i) q^{34} +(-1.95314 + 1.41904i) q^{35} +(-5.41421 + 9.37769i) q^{36} +(-0.500000 - 0.866025i) q^{37} +(-3.49744 - 1.55716i) q^{38} +(3.57117 + 2.59461i) q^{39} +(-4.03258 + 1.79542i) q^{40} +(-9.27801 - 1.97210i) q^{41} +(-1.47083 - 13.9940i) q^{42} +(5.95492 - 6.61361i) q^{43} +(-13.4302 - 14.9157i) q^{44} +(-0.295651 + 2.81293i) q^{45} +(2.98413 - 9.18421i) q^{46} +(-0.511996 + 1.57576i) q^{47} +(0.757062 - 7.20296i) q^{48} +(-0.783935 - 0.870648i) q^{49} +(6.46170 - 7.17644i) q^{50} +(-0.0432971 - 0.411944i) q^{51} +(-6.84703 - 1.45538i) q^{52} +(0.156740 - 0.0697850i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-4.78939 - 2.13237i) q^{55} +(5.32843 + 9.22911i) q^{56} +(1.91421 - 3.31552i) q^{57} +(-2.28825 + 1.66251i) q^{58} +(9.85099 - 2.09389i) q^{59} +(-2.85613 - 8.79027i) q^{60} +2.82843 q^{61} +6.82843 q^{63} +(-3.03715 - 9.34739i) q^{64} +(-1.78847 + 0.380151i) q^{65} +(24.7206 - 17.9606i) q^{66} +(2.62132 - 4.54026i) q^{67} +(0.328427 + 0.568852i) q^{68} +(8.82198 + 3.92780i) q^{69} +(4.71530 + 3.42586i) q^{70} +(-12.8546 + 5.72322i) q^{71} +(12.2124 + 2.59584i) q^{72} +(-0.400180 - 3.80745i) q^{73} +(-1.61542 + 1.79411i) q^{74} +(6.46170 + 7.17644i) q^{75} +(-0.634599 + 6.03781i) q^{76} +(-3.91118 + 12.0374i) q^{77} +(3.29315 - 10.1353i) q^{78} +(1.59329 - 15.1591i) q^{79} +(2.00739 + 2.22943i) q^{80} +(-6.34689 + 7.04894i) q^{81} +(2.39365 + 22.7740i) q^{82} +(-3.98211 - 0.846423i) q^{83} +(-20.3846 + 9.07580i) q^{84} +(0.138805 + 0.100848i) q^{85} +(-19.6278 - 8.73885i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(-11.5711 + 20.0417i) q^{88} +(10.1008 - 7.33866i) q^{89} +(6.67921 - 1.41971i) q^{90} +(1.36407 + 4.19817i) q^{91} -15.3137 q^{92} +4.00000 q^{94} +(0.490035 + 1.50817i) q^{95} +(3.74477 - 0.795975i) q^{96} +(-8.76038 + 6.36479i) q^{97} +(-1.41421 + 2.44949i) q^{98} +(7.41421 + 12.8418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots + 96 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	−0.746033	−	2.29605i	−0.527525	−	1.62356i	−0.759268	−	0.650778i	$-0.774443\pi$
$2$	−0.746033	−	2.29605i	−0.527525	−	1.62356i	0.231743	−	0.972777i	$-0.425557\pi$
$3$	2.36146	−	0.501943i	1.36339	−	0.289797i	0.532591	−	0.846373i	$-0.321218\pi$
$3$	2.36146	−	0.501943i	1.36339	−	0.289797i	0.830797	+	0.556576i	$0.187885\pi$
$4$	−3.09726	+	2.25029i	−1.54863	+	1.12515i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−2.91421	−	5.04757i	−1.18972	−	2.06066i
$7$	2.20549	+	0.981949i	0.833598	+	0.371142i	0.778736	−	0.627352i	$-0.215861\pi$
$7$	2.20549	+	0.981949i	0.833598	+	0.371142i	0.0548625	+	0.998494i	$0.482528\pi$
$8$	3.57117	+	2.59461i	1.26260	+	0.917333i
$9$	2.58390	−	1.15042i	0.861299	−	0.383475i
$10$	2.36146	+	0.501943i	0.746758	+	0.158728i
$11$	0.548005	+	5.21392i	0.165230	+	1.57206i	0.691904	+	0.721989i	$0.256772\pi$
$11$	0.548005	+	5.21392i	0.165230	+	1.57206i	−0.526674	+	0.850067i	$0.676561\pi$
$12$	−6.18453	+	6.86862i	−1.78532	+	1.98280i
$13$	1.22346	+	1.35879i	0.339326	+	0.376859i	0.888522	−	0.458834i	$-0.151733\pi$
$13$	1.22346	+	1.35879i	0.339326	+	0.376859i	−0.549196	+	0.835693i	$0.685066\pi$
$14$	0.609237	−	5.79650i	0.162825	−	1.54918i
$15$	−0.746033	+	2.29605i	−0.192625	+	0.592838i
$16$	0.927051	−	2.85317i	0.231763	−	0.713292i
$17$	0.0179342	−	0.170633i	0.00434969	−	0.0413846i	−0.992132	−	0.125198i	$-0.960043\pi$
$17$	0.0179342	−	0.170633i	0.00434969	−	0.0413846i	0.996481	+	0.0838135i	$0.0267100\pi$
$18$	−4.56911	−	5.07451i	−1.07695	−	1.19607i
$19$	1.06110	−	1.17847i	0.243433	−	0.270359i	−0.609030	−	0.793147i	$-0.708441\pi$
$19$	1.06110	−	1.17847i	0.243433	−	0.270359i	0.852463	+	0.522788i	$0.175108\pi$
$20$	−0.400180	−	3.80745i	−0.0894829	−	0.851373i
$21$	5.70106	+	1.21180i	1.24407	+	0.264436i
$22$	11.5626	−	5.14801i	2.46516	−	1.09756i
$23$	3.23607	+	2.35114i	0.674767	+	0.490247i	0.871617	−	0.490187i	$-0.163071\pi$
$23$	3.23607	+	2.35114i	0.674767	+	0.490247i	−0.196851	+	0.980433i	$0.563071\pi$
$24$	9.73552	+	4.33453i	1.98725	+	0.884783i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	2.20711	−	3.82282i	0.432849	−	0.749717i
$27$	−0.335106	+	0.243469i	−0.0644911	+	0.0468556i
$28$	−9.04067	+	1.92165i	−1.70853	+	0.363158i
$29$	−0.362036	−	1.11423i	−0.0672284	−	0.206908i	0.911799	−	0.410637i	$-0.134694\pi$
$29$	−0.362036	−	1.11423i	−0.0672284	−	0.206908i	−0.979027	+	0.203729i	$0.934694\pi$
$30$	5.82843			1.06412
$31$		0			0
$31$		0			0
$32$	1.58579			0.280330
$33$	3.91118	+	12.0374i	0.680850	+	2.09544i
$34$	−0.405162	+	0.0861198i	−0.0694847	+	0.0147694i
$35$	−1.95314	+	1.41904i	−0.330141	+	0.239861i
$36$	−5.41421	+	9.37769i	−0.902369	+	1.56295i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−3.49744	−	1.55716i	−0.567360	−	0.252605i
$39$	3.57117	+	2.59461i	0.571845	+	0.415470i
$40$	−4.03258	+	1.79542i	−0.637608	+	0.283881i
$41$	−9.27801	−	1.97210i	−1.44898	−	0.307990i	−0.584802	−	0.811176i	$-0.698828\pi$
$41$	−9.27801	−	1.97210i	−1.44898	−	0.307990i	−0.864179	+	0.503185i	$0.832161\pi$
$42$	−1.47083	−	13.9940i	−0.226954	−	2.15932i
$43$	5.95492	−	6.61361i	0.908117	−	1.00857i	−0.0918008	−	0.995777i	$-0.529262\pi$
$43$	5.95492	−	6.61361i	0.908117	−	1.00857i	0.999918	−	0.0127892i	$-0.00407105\pi$
$44$	−13.4302	−	14.9157i	−2.02467	−	2.24863i
$45$	−0.295651	+	2.81293i	−0.0440731	+	0.419327i
$46$	2.98413	−	9.18421i	0.439986	−	1.35414i
$47$	−0.511996	+	1.57576i	−0.0746823	+	0.229849i	−0.981428	−	0.191828i	$-0.938558\pi$
$47$	−0.511996	+	1.57576i	−0.0746823	+	0.229849i	0.906746	+	0.421677i	$0.138558\pi$
$48$	0.757062	−	7.20296i	0.109273	−	1.03966i
$49$	−0.783935	−	0.870648i	−0.111991	−	0.124378i
$50$	6.46170	−	7.17644i	0.913822	−	1.01490i
$51$	−0.0432971	−	0.411944i	−0.00606281	−	0.0576838i
$52$	−6.84703	−	1.45538i	−0.949513	−	0.201825i
$53$	0.156740	−	0.0697850i	0.0215298	−	0.00958570i	−0.395943	−	0.918275i	$-0.629582\pi$
$53$	0.156740	−	0.0697850i	0.0215298	−	0.00958570i	0.417473	+	0.908689i	$0.362916\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	−4.78939	−	2.13237i	−0.645801	−	0.287529i
$56$	5.32843	+	9.22911i	0.712041	+	1.23329i
$57$	1.91421	−	3.31552i	0.253544	−	0.439151i
$58$	−2.28825	+	1.66251i	−0.300461	+	0.218298i
$59$	9.85099	−	2.09389i	1.28249	−	0.272602i	0.484244	−	0.874933i	$-0.339095\pi$
$59$	9.85099	−	2.09389i	1.28249	−	0.272602i	0.798246	+	0.602332i	$0.205761\pi$
$60$	−2.85613	−	8.79027i	−0.368725	−	1.13482i
$61$	2.82843			0.362143			0.181071	−	0.983470i	$-0.442043\pi$
$61$	2.82843			0.362143			0.181071	+	0.983470i	$0.442043\pi$
$62$		0			0
$63$	6.82843			0.860301
$64$	−3.03715	−	9.34739i	−0.379644	−	1.16842i
$65$	−1.78847	+	0.380151i	−0.221833	+	0.0471520i
$66$	24.7206	−	17.9606i	3.04290	−	2.21079i
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	−0.660293	−	0.751008i	$-0.729568\pi$
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	0.980539	+	0.196327i	$0.0629013\pi$
$68$	0.328427	+	0.568852i	0.0398276	+	0.0689835i
$69$	8.82198	+	3.92780i	1.06204	+	0.472851i
$70$	4.71530	+	3.42586i	0.563586	+	0.409469i
$71$	−12.8546	+	5.72322i	−1.52556	+	0.679221i	−0.986607	−	0.163117i	$-0.947845\pi$
$71$	−12.8546	+	5.72322i	−1.52556	+	0.679221i	−0.538949	+	0.842338i	$0.681178\pi$
$72$	12.2124	+	2.59584i	1.43925	+	0.305922i
$73$	−0.400180	−	3.80745i	−0.0468375	−	0.445629i	−0.992659	−	0.120943i	$-0.961408\pi$
$73$	−0.400180	−	3.80745i	−0.0468375	−	0.445629i	0.945822	−	0.324686i	$-0.105259\pi$
$74$	−1.61542	+	1.79411i	−0.187789	+	0.208561i
$75$	6.46170	+	7.17644i	0.746132	+	0.828664i
$76$	−0.634599	+	6.03781i	−0.0727935	+	0.692584i
$77$	−3.91118	+	12.0374i	−0.445721	+	1.37179i
$78$	3.29315	−	10.1353i	0.372876	−	1.14759i
$79$	1.59329	−	15.1591i	0.179259	−	1.70554i	−0.422093	−	0.906552i	$-0.638704\pi$
$79$	1.59329	−	15.1591i	0.179259	−	1.70554i	0.601352	−	0.798984i	$-0.294629\pi$
$80$	2.00739	+	2.22943i	0.224433	+	0.249258i
$81$	−6.34689	+	7.04894i	−0.705210	+	0.783215i
$82$	2.39365	+	22.7740i	0.264334	+	2.51497i
$83$	−3.98211	−	0.846423i	−0.437093	−	0.0929069i	−0.0158907	−	0.999874i	$-0.505058\pi$
$83$	−3.98211	−	0.846423i	−0.437093	−	0.0929069i	−0.421202	+	0.906967i	$0.638392\pi$
$84$	−20.3846	+	9.07580i	−2.22414	+	0.990251i
$85$	0.138805	+	0.100848i	0.0150556	+	0.0109385i
$86$	−19.6278	−	8.73885i	−2.11652	−	0.942335i
$87$	−1.41421	−	2.44949i	−0.151620	−	0.262613i
$88$	−11.5711	+	20.0417i	−1.23348	+	2.13645i
$89$	10.1008	−	7.33866i	1.07068	−	0.777897i	0.0946482	−	0.995511i	$-0.469827\pi$
$89$	10.1008	−	7.33866i	1.07068	−	0.777897i	0.976035	+	0.217614i	$0.0698274\pi$
$90$	6.67921	−	1.41971i	0.704051	−	0.149651i
$91$	1.36407	+	4.19817i	0.142993	+	0.440087i
$92$	−15.3137			−1.59656
$93$		0			0
$94$	4.00000			0.412568
$95$	0.490035	+	1.50817i	0.0502765	+	0.154735i
$96$	3.74477	−	0.795975i	0.382199	−	0.0812388i
$97$	−8.76038	+	6.36479i	−0.889482	+	0.646246i	−0.935743	−	0.352683i	$-0.885269\pi$
$97$	−8.76038	+	6.36479i	−0.889482	+	0.646246i	0.0462609	+	0.998929i	$0.485269\pi$
$98$	−1.41421	+	2.44949i	−0.142857	+	0.247436i
$99$	7.41421	+	12.8418i	0.745157	+	1.29065i
$100$	−13.9898	−	6.22865i	−1.39898	−	0.622865i
$101$	−6.86474	−	4.98752i	−0.683067	−	0.496277i	0.191307	−	0.981530i	$-0.438727\pi$
$101$	−6.86474	−	4.98752i	−0.683067	−	0.496277i	−0.874374	+	0.485253i	$0.838727\pi$
$102$	−0.913545	+	0.406737i	−0.0904545	+	0.0402729i
$103$	11.8073	+	2.50972i	1.16341	+	0.247290i	0.748854	−	0.662736i	$-0.230605\pi$
$103$	11.8073	+	2.50972i	1.16341	+	0.247290i	0.414553	+	0.910025i	$0.363938\pi$
$104$	0.843656	+	8.02685i	0.0827273	+	0.787098i
$105$	−3.89998	+	4.33137i	−0.380599	+	0.422698i
$106$	−0.277163	−	0.307821i	−0.0269204	−	0.0298982i
$107$	−1.00199	+	9.53327i	−0.0968658	+	0.921616i	0.832890	+	0.553439i	$0.186685\pi$
$107$	−1.00199	+	9.53327i	−0.0968658	+	0.921616i	−0.929756	+	0.368177i	$0.879982\pi$
$108$	0.490035	−	1.50817i	0.0471536	−	0.145124i
$109$	−1.59810	+	4.91846i	−0.153071	+	0.471103i	−0.997960	−	0.0638377i	$-0.979666\pi$
$109$	−1.59810	+	4.91846i	−0.153071	+	0.471103i	0.844890	+	0.534941i	$0.179666\pi$
$110$	−1.32300	+	12.5875i	−0.126143	+	1.20017i
$111$	−1.61542	−	1.79411i	−0.153329	−	0.170289i
$112$	4.84627	−	5.38233i	0.457930	−	0.508582i
$113$	−0.558511	−	5.31388i	−0.0525403	−	0.499887i	−0.988872	−	0.148770i	$-0.952469\pi$
$113$	−0.558511	−	5.31388i	−0.0525403	−	0.499887i	0.936332	−	0.351117i	$-0.114198\pi$
$114$	−9.04067	−	1.92165i	−0.846736	−	0.179979i
$115$	−3.65418	+	1.62695i	−0.340754	+	0.151714i
$116$	3.62867	+	2.63638i	0.336913	+	0.244782i
$117$	4.72447	+	2.10347i	0.436777	+	0.194466i
$118$	−12.1569	−	21.0563i	−1.11913	−	1.93839i
$119$	0.207107	−	0.358719i	0.0189854	−	0.0328838i
$120$	−8.62158	+	6.26394i	−0.787039	+	0.571817i
$121$	−16.1250	+	3.42748i	−1.46591	+	0.311589i
$122$	−2.11010	−	6.49422i	−0.191039	−	0.587959i
$123$	−22.8995			−2.06478
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−5.09423	−	15.6784i	−0.453830	−	1.39675i
$127$	10.6613	−	2.26613i	0.946039	−	0.201087i	0.291035	−	0.956712i	$-0.406000\pi$
$127$	10.6613	−	2.26613i	0.946039	−	0.201087i	0.655004	+	0.755626i	$0.272667\pi$
$128$	−16.6304	+	12.0827i	−1.46994	+	1.06797i
$129$	10.7426	−	18.6068i	0.945837	−	1.63824i
$130$	2.20711	+	3.82282i	0.193576	+	0.335284i
$131$	−4.34606	−	1.93499i	−0.379717	−	0.169061i	0.207997	−	0.978129i	$-0.433306\pi$
$131$	−4.34606	−	1.93499i	−0.379717	−	0.169061i	−0.587715	+	0.809068i	$0.699972\pi$
$132$	−39.2016	−	28.4816i	−3.41206	−	2.47901i
$133$	3.49744	−	1.55716i	0.303267	−	0.135023i
$134$	−12.3803	−	2.63151i	−1.06949	−	0.227328i
$135$	−0.0432971	−	0.411944i	−0.00372642	−	0.0354545i
$136$	0.506772	−	0.562828i	0.0434554	−	0.0482621i
$137$	−5.00863	−	5.56265i	−0.427916	−	0.475249i	0.490172	−	0.871626i	$-0.336934\pi$
$137$	−5.00863	−	5.56265i	−0.427916	−	0.475249i	−0.918088	+	0.396377i	$0.870267\pi$
$138$	2.43695	−	23.1860i	0.207447	−	1.97372i
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$	2.85613	−	8.79027i	0.241387	−	0.742914i
$141$	−0.418114	+	3.97809i	−0.0352115	+	0.335015i
$142$	22.7307	+	25.2450i	1.90752	+	2.11852i
$143$	−6.41414	+	7.12363i	−0.536378	+	0.595708i
$144$	−0.886953	−	8.43880i	−0.0739128	−	0.703233i
$145$	1.14597	+	0.243584i	0.0951677	+	0.0202285i
$146$	−8.44357	+	3.75932i	−0.698795	+	0.311124i
$147$	−2.28825	−	1.66251i	−0.188731	−	0.137121i
$148$	3.49744	+	1.55716i	0.287488	+	0.127998i
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	11.6569	−	20.1903i	0.951778	−	1.64853i
$151$	14.0071	−	10.1767i	1.13988	−	0.828172i	0.152778	−	0.988261i	$-0.451178\pi$
$151$	14.0071	−	10.1767i	1.13988	−	0.828172i	0.987103	+	0.160089i	$0.0511781\pi$
$152$	6.84703	−	1.45538i	0.555368	−	0.118047i
$153$	−0.149960	−	0.461530i	−0.0121236	−	0.0373125i
$154$	30.5563			2.46230
$155$		0			0
$156$	−16.8995			−1.35304
$157$	4.58224	+	14.1027i	0.365702	+	1.12552i	0.949540	+	0.313646i	$0.101550\pi$
$157$	4.58224	+	14.1027i	0.365702	+	1.12552i	−0.583838	+	0.811870i	$0.698450\pi$
$158$	−35.9948	+	7.65094i	−2.86360	+	0.608676i
$159$	0.335106	−	0.243469i	0.0265756	−	0.0193083i
$160$	−0.792893	+	1.37333i	−0.0626837	+	0.108571i
$161$	4.82843	+	8.36308i	0.380533	+	0.659103i
$162$	20.9197	+	9.31406i	1.64361	+	0.731782i
$163$	10.4934	+	7.62391i	0.821907	+	0.597150i	0.917258	−	0.398293i	$-0.130397\pi$
$163$	10.4934	+	7.62391i	0.821907	+	0.597150i	−0.0953511	+	0.995444i	$0.530397\pi$
$164$	33.1742	−	14.7701i	2.59047	−	1.15335i
$165$	−12.3803	−	2.63151i	−0.963803	−	0.204863i
$166$	1.02735	+	9.77459i	0.0797379	+	0.758655i
$167$	−5.72532	+	6.35861i	−0.443038	+	0.492044i	−0.922759	−	0.385377i	$-0.874071\pi$
$167$	−5.72532	+	6.35861i	−0.443038	+	0.492044i	0.479721	+	0.877421i	$0.340738\pi$
$168$	17.2153	+	19.1196i	1.32819	+	1.47511i
$169$	1.00942	−	9.60395i	0.0776474	−	0.738766i
$170$	0.127999	−	0.393941i	0.00981708	−	0.0302139i
$171$	1.38603	−	4.26576i	0.105992	−	0.326211i
$172$	−3.56140	+	33.8844i	−0.271554	+	2.58366i
$173$	−9.57774	−	10.6372i	−0.728182	−	0.808728i	0.259410	−	0.965767i	$-0.416472\pi$
$173$	−9.57774	−	10.6372i	−0.728182	−	0.808728i	−0.987592	+	0.157039i	$0.949805\pi$
$174$	−4.56911	+	5.07451i	−0.346383	+	0.384698i
$175$	1.00942	+	9.60395i	0.0763047	+	0.725991i
$176$	15.3842	+	3.27002i	1.15963	+	0.246487i
$177$	22.2117	−	9.88928i	1.66953	−	0.743324i
$178$	−24.3855	−	17.7171i	−1.82777	−	1.32795i
$179$	−6.17315	−	2.74847i	−0.461403	−	0.205430i	0.162852	−	0.986651i	$-0.447931\pi$
$179$	−6.17315	−	2.74847i	−0.461403	−	0.205430i	−0.624255	+	0.781221i	$0.714597\pi$
$180$	−5.41421	−	9.37769i	−0.403552	−	0.698972i
$181$	5.15685	−	8.93193i	0.383306	−	0.663905i	−0.608227	−	0.793763i	$-0.708119\pi$
$181$	5.15685	−	8.93193i	0.383306	−	0.663905i	0.991533	+	0.129858i	$0.0414522\pi$
$182$	8.62158	−	6.26394i	0.639074	−	0.464314i
$183$	6.67921	−	1.41971i	0.493741	−	0.104948i
$184$	5.45627	+	16.7927i	0.402241	+	1.23797i
$185$	1.00000			0.0735215
$186$		0			0
$187$	0.899495			0.0657776
$188$	−1.96014	−	6.03269i	−0.142958	−	0.439979i
$189$	−0.978148	+	0.207912i	−0.0711498	+	0.0151234i
$190$	3.09726	−	2.25029i	0.224699	−	0.163253i
$191$	0.550253	−	0.953065i	0.0398149	−	0.0689614i	−0.845431	−	0.534084i	$-0.820657\pi$
$191$	0.550253	−	0.953065i	0.0398149	−	0.0689614i	0.885246	+	0.465123i	$0.153990\pi$
$192$	−11.8640	−	20.5490i	−0.856208	−	1.48300i
$193$	−19.3143	−	8.59928i	−1.39027	−	0.618990i	−0.431229	−	0.902243i	$-0.641920\pi$
$193$	−19.3143	−	8.59928i	−1.39027	−	0.618990i	−0.959045	+	0.283253i	$0.908586\pi$
$194$	21.1494	+	15.3660i	1.51844	+	1.10321i
$195$	−4.03258	+	1.79542i	−0.288779	+	0.128573i
$196$	4.38727	+	0.932542i	0.313376	+	0.0666102i
$197$	−0.364311	−	3.46619i	−0.0259561	−	0.246956i	−0.999805	−	0.0197582i	$-0.993710\pi$
$197$	−0.364311	−	3.46619i	−0.0259561	−	0.246956i	0.973849	−	0.227198i	$-0.0729563\pi$
$198$	23.9542	−	26.6038i	1.70235	−	1.89065i
$199$	10.4289	+	11.5825i	0.739287	+	0.821061i	0.989102	−	0.147232i	$-0.0470365\pi$
$199$	10.4289	+	11.5825i	0.739287	+	0.821061i	−0.249815	+	0.968294i	$0.580370\pi$
$200$	−1.84564	+	17.5601i	−0.130507	+	1.24169i
$201$	3.91118	−	12.0374i	0.275874	−	0.849052i
$202$	−6.33030	+	19.4827i	−0.445398	+	1.37080i
$203$	0.295651	−	2.81293i	0.0207506	−	0.197429i
$204$	1.06110	+	1.17847i	0.0742917	+	0.0825093i
$205$	6.34689	−	7.04894i	0.443286	−	0.492319i
$206$	−3.04618	−	28.9825i	−0.212238	−	2.01931i
$207$	11.0665	+	2.35225i	0.769173	+	0.163493i
$208$	5.01105	−	2.23106i	0.347454	−	0.154697i
$209$	6.72593	+	4.88668i	0.465242	+	0.338018i
$210$	12.8546	+	5.72322i	0.887049	+	0.394940i
$211$	−3.79289	−	6.56948i	−0.261114	−	0.452262i	0.705425	−	0.708785i	$-0.250756\pi$
$211$	−3.79289	−	6.56948i	−0.261114	−	0.452262i	−0.966538	+	0.256523i	$0.917423\pi$
$212$	−0.328427	+	0.568852i	−0.0225565	+	0.0390689i
$213$	−27.4828	+	19.9674i	−1.88309	+	1.36814i
$214$	22.6364	−	4.81152i	1.54739	−	0.328909i
$215$	2.75010	+	8.46392i	0.187555	+	0.577235i
$216$	−1.82843			−0.124409
$217$		0			0
$218$	12.4853			0.845610
$219$	−2.85613	−	8.79027i	−0.193000	−	0.593992i
$220$	19.6325	−	4.17301i	1.32362	−	0.281344i
$221$	0.253796	−	0.184393i	0.0170721	−	0.0124036i
$222$	−2.91421	+	5.04757i	−0.195589	+	0.338770i
$223$	−0.863961	−	1.49642i	−0.0578551	−	0.100208i	0.835647	−	0.549266i	$-0.185093\pi$
$223$	−0.863961	−	1.49642i	−0.0578551	−	0.100208i	−0.893502	+	0.449059i	$0.851759\pi$
$224$	3.49744	+	1.55716i	0.233683	+	0.104042i
$225$	9.15298	+	6.65003i	0.610199	+	0.443335i
$226$	−11.7843	+	5.24670i	−0.783878	+	0.349005i
$227$	15.2452	+	3.24047i	1.01186	+	0.215077i	0.683870	−	0.729604i	$-0.260296\pi$
$227$	15.2452	+	3.24047i	1.01186	+	0.215077i	0.327990	+	0.944681i	$0.393629\pi$
$228$	1.53206	+	14.5766i	0.101463	+	0.965356i
$229$	7.68515	−	8.53523i	0.507849	−	0.564024i	−0.433632	−	0.901090i	$-0.642768\pi$
$229$	7.68515	−	8.53523i	0.507849	−	0.564024i	0.941481	+	0.337067i	$0.109435\pi$
$230$	6.46170	+	7.17644i	0.426072	+	0.473201i
$231$	−3.19401	+	30.3890i	−0.210150	+	1.99945i
$232$	1.59810	−	4.91846i	0.104921	−	0.322913i
$233$	−4.58224	+	14.1027i	−0.300192	+	0.923897i	0.681235	+	0.732064i	$0.261443\pi$
$233$	−4.58224	+	14.1027i	−0.300192	+	0.923897i	−0.981428	+	0.191832i	$0.938557\pi$
$234$	1.30507	−	12.4169i	0.0853149	−	0.811717i
$235$	−1.10865	−	1.23128i	−0.0723205	−	0.0803200i
$236$	−25.7992	+	28.6530i	−1.67939	+	1.86515i
$237$	−3.84654	−	36.5974i	−0.249860	−	2.37726i
$238$	−0.978148	−	0.207912i	−0.0634039	−	0.0134769i
$239$	−11.6544	+	5.18889i	−0.753862	+	0.335641i	−0.747432	−	0.664338i	$-0.768713\pi$
$239$	−11.6544	+	5.18889i	−0.753862	+	0.335641i	−0.00643017	+	0.999979i	$0.502047\pi$
$240$	5.85942	+	4.25712i	0.378224	+	0.274796i
$241$	22.5252	+	10.0288i	1.45097	+	0.646015i	0.972672	−	0.232181i	$-0.0745863\pi$
$241$	22.5252	+	10.0288i	1.45097	+	0.646015i	0.478300	+	0.878196i	$0.341253\pi$
$242$	19.8995	+	34.4669i	1.27919	+	2.21562i
$243$	−10.8284	+	18.7554i	−0.694644	+	1.20316i
$244$	−8.76038	+	6.36479i	−0.560826	+	0.407464i
$245$	1.14597	−	0.243584i	0.0732134	−	0.0155620i
$246$	17.0838	+	52.5785i	1.08922	+	3.35228i
$247$	2.89949			0.184490
$248$		0			0
$249$	−9.82843			−0.622851
$250$	6.71430	+	20.6645i	0.424649	+	1.30694i
$251$	−3.50743	+	0.745527i	−0.221387	+	0.0470572i	−0.317270	−	0.948335i	$-0.602766\pi$
$251$	−3.50743	+	0.745527i	−0.221387	+	0.0470572i	0.0958826	+	0.995393i	$0.469433\pi$
$252$	−21.1494	+	15.3660i	−1.33229	+	0.967965i
$253$	−10.4853	+	18.1610i	−0.659204	+	1.14177i
$254$	−13.1569	−	22.7883i	−0.825534	−	1.42987i
$255$	0.378403	+	0.168476i	0.0236965	+	0.0105504i
$256$	24.2467	+	17.6163i	1.51542	+	1.10102i
$257$	−0.286587	+	0.127597i	−0.0178768	+	0.00795927i	−0.415656	−	0.909522i	$-0.636448\pi$
$257$	−0.286587	+	0.127597i	−0.0178768	+	0.00795927i	0.397779	+	0.917481i	$0.369781\pi$
$258$	−50.7366	−	10.7844i	−3.15872	−	0.671407i
$259$	−0.252354	−	2.40099i	−0.0156805	−	0.149190i
$260$	4.68391	−	5.20201i	0.290484	−	0.322615i
$261$	−2.21730	−	2.46257i	−0.137248	−	0.152429i
$262$	−1.20054	+	11.4224i	−0.0741695	+	0.705676i
$263$	−0.212076	+	0.652702i	−0.0130772	+	0.0402473i	−0.957382	−	0.288824i	$-0.906736\pi$
$263$	−0.212076	+	0.652702i	−0.0130772	+	0.0402473i	0.944305	+	0.329071i	$0.106736\pi$
$264$	−17.2648	+	53.1356i	−1.06257	+	3.27027i
$265$	−0.0179342	+	0.170633i	−0.00110169	+	0.0104819i
$266$	−6.18453	−	6.86862i	−0.379198	−	0.421142i
$267$	20.1690	−	22.4000i	1.23432	−	1.37086i
$268$	2.09800	+	19.9611i	0.128156	+	1.21932i
$269$	31.1329	+	6.61750i	1.89821	+	0.403476i	0.999392	−	0.0348541i	$-0.0110966\pi$
$269$	31.1329	+	6.61750i	1.89821	+	0.403476i	0.898814	+	0.438330i	$0.144430\pi$
$270$	−0.913545	+	0.406737i	−0.0555966	+	0.0247532i
$271$	18.8612	+	13.7035i	1.14574	+	0.832426i	0.987908	−	0.155041i	$-0.0495510\pi$
$271$	18.8612	+	13.7035i	1.14574	+	0.832426i	0.157827	+	0.987467i	$0.449551\pi$
$272$	−0.470219	−	0.209355i	−0.0285112	−	0.0126940i
$273$	5.32843	+	9.22911i	0.322491	+	0.558571i
$274$	−9.03553	+	15.6500i	−0.545857	+	0.945451i
$275$	−16.9655	+	12.3262i	−1.02306	+	0.743297i
$276$	−36.1627	+	7.68661i	−2.17674	+	0.462680i
$277$	−4.37016	−	13.4500i	−0.262577	−	0.808130i	−0.992242	−	0.124325i	$-0.960324\pi$
$277$	−4.37016	−	13.4500i	−0.262577	−	0.808130i	0.729664	−	0.683806i	$-0.239676\pi$
$278$		0			0
$279$		0			0
$280$	−10.6569			−0.636869
$281$	0.618034	+	1.90211i	0.0368688	+	0.113471i	0.967797	−	0.251731i	$-0.0809999\pi$
$281$	0.618034	+	1.90211i	0.0368688	+	0.113471i	−0.930928	+	0.365202i	$0.881000\pi$
$282$	9.44583	−	2.00777i	0.562491	−	0.119561i
$283$	1.89564	−	1.37727i	0.112684	−	0.0818700i	−0.530016	−	0.847988i	$-0.677814\pi$
$283$	1.89564	−	1.37727i	0.112684	−	0.0818700i	0.642700	+	0.766118i	$0.277814\pi$
$284$	26.9350	−	46.6528i	1.59830	−	2.76834i
$285$	1.91421	+	3.31552i	0.113388	+	0.196394i
$286$	21.1414	+	9.41275i	1.25012	+	0.556588i
$287$	−18.5261	−	13.4600i	−1.09356	−	0.794518i
$288$	4.09751	−	1.82433i	0.241448	−	0.107500i
$289$	16.5997	+	3.52838i	0.976454	+	0.207552i
$290$	−0.295651	−	2.81293i	−0.0173612	−	0.165181i
$291$	−17.4925	+	19.4274i	−1.02543	+	1.13885i
$292$	9.80735	+	10.8922i	0.573932	+	0.637416i
$293$	2.59220	−	24.6631i	0.151438	−	1.44084i	−0.609899	−	0.792479i	$-0.708790\pi$
$293$	2.59220	−	24.6631i	0.151438	−	1.44084i	0.761337	−	0.648357i	$-0.224543\pi$
$294$	−2.11010	+	6.49422i	−0.123064	+	0.378751i
$295$	−3.11213	+	9.57815i	−0.181195	+	0.557662i
$296$	0.461411	−	4.39003i	0.0268190	−	0.255165i
$297$	−1.45307	−	1.61379i	−0.0843154	−	0.0936418i
$298$	−1.61542	+	1.79411i	−0.0935790	+	0.103930i
$299$	0.764491	+	7.27364i	0.0442116	+	0.420646i
$300$	−36.1627	−	7.68661i	−2.08785	−	0.443787i
$301$	19.6278	−	8.73885i	1.13133	−	0.503699i
$302$	−33.8161	−	24.5688i	−1.94590	−	1.41378i
$303$	−18.7142	−	8.33211i	−1.07510	−	0.478667i
$304$	−2.37868	−	4.11999i	−0.136427	−	0.236298i
$305$	−1.41421	+	2.44949i	−0.0809776	+	0.140257i
$306$	−0.947822	+	0.688633i	−0.0541834	+	0.0393665i
$307$	2.69710	−	0.573287i	0.153932	−	0.0327192i	−0.130301	−	0.991474i	$-0.541594\pi$
$307$	2.69710	−	0.573287i	0.153932	−	0.0327192i	0.284233	+	0.958755i	$0.408261\pi$
$308$	−14.9737	−	46.0842i	−0.853205	−	2.62589i
$309$	29.1421			1.65784
$310$		0			0
$311$	−11.3137			−0.641542			−0.320771	−	0.947157i	$-0.603942\pi$
$311$	−11.3137			−0.641542			−0.320771	+	0.947157i	$0.603942\pi$
$312$	6.02128	+	18.5316i	0.340888	+	1.04915i
$313$	−3.74477	+	0.795975i	−0.211667	+	0.0449912i	−0.312524	−	0.949910i	$-0.601175\pi$
$313$	−3.74477	+	0.795975i	−0.211667	+	0.0449912i	0.100858	+	0.994901i	$0.467841\pi$
$314$	28.9620	−	21.0421i	1.63442	−	1.18748i
$315$	−3.41421	+	5.91359i	−0.192369	+	0.333193i
$316$	29.1777	+	50.5372i	1.64137	+	2.84294i
$317$	−1.98383	−	0.883258i	−0.111423	−	0.0496087i	0.350268	−	0.936649i	$-0.386090\pi$
$317$	−1.98383	−	0.883258i	−0.111423	−	0.0496087i	−0.461691	+	0.887041i	$0.652757\pi$
$318$	−0.809017	−	0.587785i	−0.0453674	−	0.0329614i
$319$	5.61112	−	2.49823i	0.314162	−	0.139874i
$320$	9.61365	+	2.04344i	0.537420	+	0.114232i
$321$	2.41901	+	23.0154i	0.135016	+	1.28459i
$322$	15.5999	−	17.3255i	0.869349	−	0.965510i
$323$	−0.182056	−	0.202193i	−0.0101298	−	0.0112503i
$324$	3.79582	−	36.1148i	0.210879	−	2.00638i
$325$	−2.26006	+	6.95575i	−0.125366	+	0.385836i
$326$	9.67647	−	29.7811i	0.535930	−	1.64942i
$327$	−1.30507	+	12.4169i	−0.0721704	+	0.686655i
$328$	−28.0165	−	31.1155i	−1.54695	−	1.71807i
$329$	−2.67652	+	2.97258i	−0.147561	+	0.163884i
$330$	3.19401	+	30.3890i	0.175824	+	1.67286i
$331$	−0.740809	−	0.157464i	−0.0407186	−	0.00865500i	0.187507	−	0.982263i	$-0.439959\pi$
$331$	−0.740809	−	0.157464i	−0.0407186	−	0.00865500i	−0.228226	+	0.973608i	$0.573292\pi$
$332$	14.2383	−	6.33931i	0.781430	−	0.347915i
$333$	−2.28825	−	1.66251i	−0.125395	−	0.0911049i
$334$	18.8710	+	8.40190i	1.03257	+	0.459731i
$335$	2.62132	+	4.54026i	0.143218	+	0.248061i
$336$	8.74264	−	15.1427i	0.476950	−	0.826102i
$337$	10.7710	−	7.82560i	0.586735	−	0.426288i	−0.254411	−	0.967096i	$-0.581882\pi$
$337$	10.7710	−	7.82560i	0.586735	−	0.426288i	0.841146	+	0.540808i	$0.181882\pi$
$338$	−22.8042	+	4.84719i	−1.24039	+	0.263653i
$339$	−3.98616	−	12.2681i	−0.216499	−	0.666314i
$340$	−0.656854			−0.0356229
$341$		0			0
$342$	−10.8284			−0.585534
$343$	−6.09626	−	18.7624i	−0.329167	−	1.01307i
$344$	38.4258	−	8.16766i	2.07178	−	0.440371i
$345$	−7.81256	+	5.67616i	−0.420614	+	0.305594i
$346$	−17.2782	+	29.9267i	−0.928880	+	1.60887i
$347$	−11.2782	−	19.5344i	−0.605444	−	1.04866i	−0.991981	−	0.126386i	$-0.959662\pi$
$347$	−11.2782	−	19.5344i	−0.605444	−	1.04866i	0.386537	−	0.922274i	$-0.373671\pi$
$348$	9.89226	+	4.40432i	0.530281	+	0.236096i
$349$	−28.4068	−	20.6387i	−1.52058	−	1.10477i	−0.961199	−	0.275854i	$-0.911039\pi$
$349$	−28.4068	−	20.6387i	−1.52058	−	1.10477i	−0.559380	−	0.828911i	$-0.688961\pi$
$350$	21.2981	−	9.48254i	1.13843	−	0.506863i
$351$	−0.740809	−	0.157464i	−0.0395415	−	0.00840480i
$352$	0.869019	+	8.26817i	0.0463189	+	0.440695i
$353$	2.00739	−	2.22943i	0.106843	−	0.118661i	−0.687351	−	0.726325i	$-0.741227\pi$
$353$	2.00739	−	2.22943i	0.106843	−	0.118661i	0.794194	+	0.607664i	$0.207893\pi$
$354$	−39.2770	−	43.6215i	−2.08755	−	2.31846i
$355$	1.47083	−	13.9940i	0.0780634	−	0.742724i
$356$	−14.7707	+	45.4595i	−0.782846	+	2.40935i
$357$	0.309017	−	0.951057i	0.0163549	−	0.0503352i
$358$	−1.70525	+	16.2243i	−0.0901251	+	0.857483i
$359$	17.9993	+	19.9902i	0.949965	+	1.05504i	0.998419	+	0.0562180i	$0.0179042\pi$
$359$	17.9993	+	19.9902i	0.949965	+	1.05504i	−0.0484531	+	0.998825i	$0.515429\pi$
$360$	−8.35428	+	9.27837i	−0.440309	+	0.489013i
$361$	1.72318	+	16.3950i	0.0906937	+	0.862893i
$362$	−24.3554	−	5.17690i	−1.28009	−	0.272092i
$363$	−36.3582	+	16.1877i	−1.90831	+	0.849634i
$364$	−13.6720	−	9.93327i	−0.716606	−	0.520645i
$365$	3.49744	+	1.55716i	0.183064	+	0.0815056i
$366$	−8.24264	−	14.2767i	−0.430850	−	0.746254i
$367$	−9.10660	+	15.7731i	−0.475361	+	0.823349i	−0.999602	−	0.0282210i	$-0.991016\pi$
$367$	−9.10660	+	15.7731i	−0.475361	+	0.823349i	0.524241	+	0.851570i	$0.324349\pi$
$368$	9.70820	−	7.05342i	0.506075	−	0.367685i
$369$	−26.2422	+	5.57794i	−1.36611	+	0.290376i
$370$	−0.746033	−	2.29605i	−0.0387844	−	0.119366i
$371$	0.414214			0.0215049
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−0.671053	−	2.06529i	−0.0346993	−	0.106794i
$375$	−21.2531	+	4.51749i	−1.09751	+	0.233282i
$376$	−5.91691	+	4.29889i	−0.305142	+	0.221698i
$377$	1.07107	−	1.85514i	0.0551628	−	0.0955448i
$378$	1.20711	+	2.09077i	0.0620869	+	0.107538i
$379$	−26.8443	−	11.9519i	−1.37890	−	0.613926i	−0.422601	−	0.906316i	$-0.638883\pi$
$379$	−26.8443	−	11.9519i	−1.37890	−	0.613926i	−0.956299	+	0.292390i	$0.905550\pi$
$380$	−4.91160	−	3.56848i	−0.251960	−	0.183059i
$381$	24.0388	−	10.7027i	1.23154	−	0.548318i
$382$	−2.59880	−	0.552391i	−0.132966	−	0.0282628i
$383$	−2.60271	−	24.7631i	−0.132992	−	1.26533i	−0.833833	−	0.552017i	$-0.813858\pi$
$383$	−2.60271	−	24.7631i	−0.132992	−	1.26533i	0.700841	−	0.713318i	$-0.252808\pi$
$384$	−33.2072	+	36.8804i	−1.69460	+	1.88204i
$385$	−8.46909	−	9.40588i	−0.431625	−	0.479368i
$386$	−5.33530	+	50.7620i	−0.271560	+	2.58372i
$387$	7.77844	−	23.9396i	0.395401	−	1.21692i
$388$	12.8106	−	39.4269i	0.650358	−	2.00160i
$389$	−1.79184	+	17.0482i	−0.0908499	+	0.864380i	0.850279	+	0.526332i	$0.176433\pi$
$389$	−1.79184	+	17.0482i	−0.0908499	+	0.864380i	−0.941129	+	0.338047i	$0.890234\pi$
$390$	7.13083	+	7.91959i	0.361083	+	0.401024i
$391$	0.459219	−	0.510014i	0.0232237	−	0.0257925i
$392$	−0.540577	−	5.14324i	−0.0273032	−	0.259773i
$393$	−11.2343	−	2.38792i	−0.566695	−	0.120455i
$394$	−7.68677	+	3.42237i	−0.387254	+	0.172416i
$395$	12.3316	+	8.95940i	0.620468	+	0.450796i
$396$	−51.8616	−	23.0903i	−2.60614	−	1.16033i
$397$	8.25736	+	14.3022i	0.414425	+	0.717805i	0.995368	−	0.0961392i	$-0.0306494\pi$
$397$	8.25736	+	14.3022i	0.414425	+	0.717805i	−0.580943	+	0.813944i	$0.697316\pi$
$398$	18.8137	−	32.5863i	0.943046	−	1.63340i
$399$	7.47745	−	5.43269i	0.374341	−	0.271975i
$400$	11.7378	−	2.49494i	0.586889	−	0.124747i
$401$	−6.54238	−	20.1354i	−0.326711	−	1.00551i	−0.970663	−	0.240446i	$-0.922706\pi$
$401$	−6.54238	−	20.1354i	−0.326711	−	1.00551i	0.643952	−	0.765066i	$-0.277294\pi$
$402$	−30.5563			−1.52401
$403$		0			0
$404$	32.4853			1.61620
$405$	−2.93111	−	9.02104i	−0.145648	−	0.448259i
$406$	−6.67921	+	1.41971i	−0.331484	+	0.0704590i
$407$	4.24139	−	3.08155i	0.210238	−	0.152747i
$408$	0.914214	−	1.58346i	0.0452603	−	0.0783932i
$409$	−4.67157	−	8.09140i	−0.230994	−	0.400094i	0.727107	−	0.686525i	$-0.240865\pi$
$409$	−4.67157	−	8.09140i	−0.230994	−	0.400094i	−0.958101	+	0.286431i	$0.907531\pi$
$410$	−20.9197	−	9.31406i	−1.03315	−	0.459989i
$411$	−14.6198	−	10.6219i	−0.721142	−	0.523940i
$412$	−42.2179	+	18.7966i	−2.07992	+	0.926042i
$413$	23.7824	+	5.05510i	1.17026	+	0.248745i
$414$	−2.85506	−	27.1641i	−0.140319	−	1.33504i
$415$	2.72408	−	3.02539i	0.133720	−	0.148511i
$416$	1.94014	+	2.15474i	0.0951232	+	0.105645i
$417$		0			0
$418$	6.20230	−	19.0887i	0.303364	−	0.933660i
$419$	8.65248	−	26.6296i	0.422701	−	1.30094i	−0.482477	−	0.875908i	$-0.660263\pi$
$419$	8.65248	−	26.6296i	0.422701	−	1.30094i	0.905178	−	0.425032i	$-0.139737\pi$
$420$	2.33242	−	22.1915i	0.113810	−	1.08283i
$421$	−1.91228	−	2.12381i	−0.0931990	−	0.103508i	0.694741	−	0.719260i	$-0.255519\pi$
$421$	−1.91228	−	2.12381i	−0.0931990	−	0.103508i	−0.787940	+	0.615752i	$0.788852\pi$
$422$	−12.2543	+	13.6097i	−0.596528	+	0.662512i
$423$	0.489851	+	4.66062i	0.0238174	+	0.226607i
$424$	0.740809	+	0.157464i	0.0359769	+	0.00764712i
$425$	0.626958	−	0.279140i	0.0304120	−	0.0135403i
$426$	66.3493	+	48.2056i	3.21463	+	2.33557i
$427$	6.23808	+	2.77737i	0.301882	+	0.134406i
$428$	−18.3492	−	31.7818i	−0.886944	−	1.53623i
$429$	−11.5711	+	20.0417i	−0.558656	+	0.967621i
$430$	17.3820	−	12.6287i	0.838232	−	0.609012i
$431$	24.6910	−	5.24824i	1.18932	−	0.252799i	0.429585	−	0.903026i	$-0.358660\pi$
$431$	24.6910	−	5.24824i	1.18932	−	0.252799i	0.759740	+	0.650227i	$0.225326\pi$
$432$	0.383997	+	1.18182i	0.0184751	+	0.0568604i
$433$	−35.1127			−1.68741			−0.843704	−	0.536808i	$-0.819630\pi$
$433$	−35.1127			−1.68741			−0.843704	+	0.536808i	$0.819630\pi$
$434$		0			0
$435$	2.82843			0.135613
$436$	−6.11822	−	18.8300i	−0.293010	−	0.901791i
$437$	6.20453	−	1.31881i	0.296803	−	0.0630874i
$438$	−18.0522	+	13.1157i	−0.862566	+	0.626691i
$439$	6.03553	−	10.4539i	0.288060	−	0.498935i	−0.685286	−	0.728274i	$-0.740323\pi$
$439$	6.03553	−	10.4539i	0.288060	−	0.498935i	0.973347	+	0.229339i	$0.0736563\pi$
$440$	−11.5711	−	20.0417i	−0.551629	−	0.955449i
$441$	−3.02722	−	1.34781i	−0.144153	−	0.0641813i
$442$	−0.612717	−	0.445165i	−0.0291440	−	0.0211743i
$443$	−12.0978	+	5.38627i	−0.574782	+	0.255909i	−0.673477	−	0.739208i	$-0.735200\pi$
$443$	−12.0978	+	5.38627i	−0.574782	+	0.255909i	0.0986951	+	0.995118i	$0.468533\pi$
$444$	9.04067	+	1.92165i	0.429051	+	0.0911976i
$445$	1.30507	+	12.4169i	0.0618661	+	0.588617i
$446$	−2.79133	+	3.10008i	−0.132173	+	0.146793i
$447$	−1.61542	−	1.79411i	−0.0764069	−	0.0848585i
$448$	2.48024	−	23.5979i	0.117180	−	1.11490i
$449$	1.42995	−	4.40094i	0.0674835	−	0.207693i	−0.911628	−	0.411016i	$-0.865174\pi$
$449$	1.42995	−	4.40094i	0.0674835	−	0.207693i	0.979112	+	0.203323i	$0.0651741\pi$
$450$	8.44040	−	25.9769i	0.397884	−	1.22456i
$451$	5.19798	−	49.4555i	0.244763	−	2.32877i
$452$	13.6876	+	15.2017i	0.643812	+	0.715026i
$453$	27.9690	−	31.0627i	1.31410	−	1.45945i
$454$	−3.93314	−	37.4213i	−0.184591	−	1.75627i
$455$	−4.31775	−	0.917767i	−0.202419	−	0.0430256i
$456$	15.4385	−	6.87364i	0.722972	−	0.321888i
$457$	−25.1707	−	18.2876i	−1.17744	−	0.855457i	−0.185556	−	0.982634i	$-0.559409\pi$
$457$	−25.1707	−	18.2876i	−1.17744	−	0.855457i	−0.991880	+	0.127177i	$0.959409\pi$
$458$	−25.3307	−	11.2780i	−1.18363	−	0.526985i
$459$	0.0355339	+	0.0615465i	0.00165858	+	0.00287275i
$460$	7.65685	−	13.2621i	0.357003	−	0.618347i
$461$	−21.1494	+	15.3660i	−0.985027	+	0.715664i	−0.958826	−	0.283993i	$-0.908341\pi$
$461$	−21.1494	+	15.3660i	−0.985027	+	0.715664i	−0.0262008	+	0.999657i	$0.508341\pi$
$462$	72.1575	−	15.3376i	3.35707	−	0.713568i
$463$	7.71633	+	23.7484i	0.358608	+	1.10368i	0.953888	+	0.300164i	$0.0970413\pi$
$463$	7.71633	+	23.7484i	0.358608	+	1.10368i	−0.595279	+	0.803519i	$0.702959\pi$
$464$	−3.51472			−0.163167
$465$		0			0
$466$	35.7990			1.65836
$467$	−2.47214	−	7.60845i	−0.114397	−	0.352077i	0.877424	−	0.479716i	$-0.159260\pi$
$467$	−2.47214	−	7.60845i	−0.114397	−	0.352077i	−0.991821	+	0.127639i	$0.959260\pi$
$468$	−19.3663	+	4.11644i	−0.895209	+	0.190283i
$469$	10.2396	−	7.43951i	0.472821	−	0.343525i
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	17.8995	+	31.0028i	0.824765	+	1.42854i
$472$	40.6124	+	18.0818i	1.86934	+	0.832283i
$473$	37.7462	+	27.4242i	1.73557	+	1.26097i
$474$	−81.1599	+	36.1347i	−3.72780	+	1.65972i
$475$	6.20453	+	1.31881i	0.284683	+	0.0605113i
$476$	0.165760	+	1.57710i	0.00759759	+	0.0722862i
$477$	0.324717	−	0.360634i	0.0148678	−	0.0165123i
$478$	20.6085	+	22.8881i	0.942613	+	1.04688i
$479$	−1.01684	+	9.67463i	−0.0464608	+	0.442045i	0.946420	+	0.322937i	$0.104670\pi$
$479$	−1.01684	+	9.67463i	−0.0464608	+	0.442045i	−0.992881	+	0.119108i	$0.961996\pi$
$480$	−1.18305	+	3.64105i	−0.0539986	+	0.166190i
$481$	0.565015	−	1.73894i	0.0257625	−	0.0792887i
$482$	6.22226	−	59.2008i	0.283416	−	2.69652i
$483$	15.5999	+	17.3255i	0.709821	+	0.788336i
$484$	42.2306	−	46.9019i	1.91957	−	2.13190i
$485$	−1.13188	−	10.7691i	−0.0513960	−	0.489000i
$486$	51.1417	+	10.8705i	2.31984	+	0.493096i
$487$	−15.8818	+	7.07103i	−0.719672	+	0.320419i	−0.733691	−	0.679483i	$-0.762204\pi$
$487$	−15.8818	+	7.07103i	−0.719672	+	0.320419i	0.0140190	+	0.999902i	$0.495537\pi$
$488$	10.1008	+	7.33866i	0.457242	+	0.332206i
$489$	28.6065	+	12.7364i	1.29363	+	0.575961i
$490$	−1.41421	−	2.44949i	−0.0638877	−	0.110657i
$491$	−2.20711	+	3.82282i	−0.0996053	+	0.172522i	−0.911521	−	0.411253i	$-0.865091\pi$
$491$	−2.20711	+	3.82282i	−0.0996053	+	0.172522i	0.811916	+	0.583774i	$0.198425\pi$
$492$	70.9257	−	51.5306i	3.19758	−	2.32318i
$493$	−0.196618	+	0.0417924i	−0.00885521	+	0.00188223i
$494$	−2.16312	−	6.65740i	−0.0973233	−	0.299530i
$495$	−14.8284			−0.666488
$496$		0			0
$497$	−33.9706			−1.52379
$498$	7.33233	+	22.5666i	0.328570	+	1.01123i
$499$	−39.3344	+	8.36080i	−1.76085	+	0.374281i	−0.971012	−	0.239032i	$-0.923170\pi$
$499$	−39.3344	+	8.36080i	−1.76085	+	0.374281i	−0.789840	+	0.613313i	$0.789837\pi$
$500$	27.8754	−	20.2526i	1.24662	−	0.905725i
$501$	−10.3284	+	17.8894i	−0.461440	+	0.799238i
$502$	4.32843	+	7.49706i	0.193187	+	0.334610i
$503$	21.3631	+	9.51145i	0.952532	+	0.424094i	0.823355	−	0.567527i	$-0.192100\pi$
$503$	21.3631	+	9.51145i	0.952532	+	0.424094i	0.129177	+	0.991622i	$0.458766\pi$
$504$	24.3855	+	17.7171i	1.08622	+	0.789182i
$505$	7.75169	−	3.45127i	0.344946	−	0.153580i
$506$	49.5211	+	10.5260i	2.20148	+	0.467939i
$507$	−2.43695	−	23.1860i	−0.108229	−	1.02973i
$508$	−27.9214	+	31.0099i	−1.23881	+	1.37584i
$509$	4.54941	+	5.05263i	0.201649	+	0.223954i	0.835485	−	0.549514i	$-0.185187\pi$
$509$	4.54941	+	5.05263i	0.201649	+	0.223954i	−0.633835	+	0.773468i	$0.718520\pi$
$510$	0.104528	−	0.994522i	0.00462860	−	0.0440382i
$511$	2.85613	−	8.79027i	0.126348	−	0.388859i
$512$	9.65451	−	29.7135i	0.426673	−	1.31316i
$513$	−0.0686600	+	0.653256i	−0.00303141	+	0.0288420i
$514$	0.506772	+	0.562828i	0.0223528	+	0.0248253i
$515$	−8.07712	+	8.97055i	−0.355920	+	0.395290i
$516$	8.59797	+	81.8042i	0.378505	+	3.60123i
$517$	−8.49648	−	1.80598i	−0.373675	−	0.0794270i
$518$	−5.32453	+	2.37063i	−0.233947	+	0.104160i
$519$	−27.9567	−	20.3117i	−1.22716	−	0.891585i
$520$	−7.37329	−	3.28280i	−0.323340	−	0.143960i
$521$	−15.2279	−	26.3755i	−0.667147	−	1.15553i	−0.978698	−	0.205304i	$-0.934182\pi$
$521$	−15.2279	−	26.3755i	−0.667147	−	1.15553i	0.311551	−	0.950229i	$-0.399152\pi$
$522$	−4.00000	+	6.92820i	−0.175075	+	0.303239i
$523$	6.47214	−	4.70228i	0.283007	−	0.205616i	−0.437221	−	0.899354i	$-0.644037\pi$
$523$	6.47214	−	4.70228i	0.283007	−	0.205616i	0.720228	+	0.693738i	$0.244037\pi$
$524$	17.8152	−	3.78674i	0.778261	−	0.165424i
$525$	7.20433	+	22.1727i	0.314423	+	0.967694i
$526$	1.65685			0.0722423
$527$		0			0
$528$	37.9706			1.65246
$529$	−2.16312	−	6.65740i	−0.0940487	−	0.289452i
$530$	0.405162	−	0.0861198i	0.0175991	−	0.00374081i
$531$	23.0451	−	16.7432i	1.00007	−	0.726594i
$532$	−7.32843	+	12.6932i	−0.317728	+	0.550320i
$533$	−8.67157	−	15.0196i	−0.375608	−	0.650571i
$534$	−66.4783	−	29.5980i	−2.87680	−	1.28083i
$535$	−7.75506	−	5.63438i	−0.335281	−	0.243596i
$536$	21.1414	−	9.41275i	0.913169	−	0.406569i
$537$	−15.9572	−	3.39181i	−0.688605	−	0.146367i
$538$	−8.03203	−	76.4197i	−0.346285	−	3.29469i
$539$	4.10989	−	4.56450i	0.177026	−	0.196607i
$540$	1.06110	+	1.17847i	0.0456624	+	0.0507132i
$541$	−2.64293	+	25.1458i	−0.113628	+	1.08110i	0.777979	+	0.628291i	$0.216245\pi$
$541$	−2.64293	+	25.1458i	−0.113628	+	1.08110i	−0.891607	+	0.452810i	$0.850422\pi$
$542$	17.3928	−	53.5295i	0.747085	−	2.29929i
$543$	7.69437	−	23.6808i	0.330197	−	1.01624i
$544$	0.0284399	−	0.270587i	0.00121935	−	0.0116013i
$545$	−3.46046	−	3.84323i	−0.148230	−	0.164626i
$546$	17.2153	−	19.1196i	0.736749	−	0.818242i
$547$	−0.598731	−	5.69654i	−0.0255999	−	0.243567i	−0.999837	−	0.0180415i	$-0.994257\pi$
$547$	−0.598731	−	5.69654i	−0.0255999	−	0.243567i	0.974237	−	0.225525i	$-0.0724098\pi$
$548$	28.0306	+	5.95810i	1.19741	+	0.254517i
$549$	7.30836	−	3.25389i	0.311913	−	0.138873i
$550$	40.9584	+	29.7580i	1.74647	+	1.26889i
$551$	−1.69724	−	0.755662i	−0.0723050	−	0.0321923i
$552$	21.3137	+	36.9164i	0.907172	+	1.57127i
$553$	18.3995	−	31.8689i	0.782426	−	1.35520i
$554$	−27.6216	+	20.0682i	−1.17353	+	0.852618i
$555$	2.36146	−	0.501943i	0.100238	−	0.0213063i
$556$		0			0
$557$	44.4853			1.88490			0.942451	−	0.334344i	$-0.108515\pi$
$557$	44.4853			1.88490			0.942451	+	0.334344i	$0.108515\pi$
$558$		0			0
$559$	16.2721			0.688236
$560$	2.23810	+	6.88816i	0.0945769	+	0.291078i
$561$	2.12412	−	0.451495i	0.0896804	−	0.0190622i
$562$	3.90628	−	2.83808i	0.164776	−	0.119717i
$563$	−2.37868	+	4.11999i	−0.100249	+	0.173637i	−0.911787	−	0.410663i	$-0.865297\pi$
$563$	−2.37868	+	4.11999i	−0.100249	+	0.173637i	0.811538	+	0.584300i	$0.198631\pi$
$564$	−7.65685	−	13.2621i	−0.322412	−	0.558433i
$565$	4.88121	+	2.17325i	0.205354	+	0.0914294i
$566$	−4.57649	−	3.32502i	−0.192364	−	0.139761i
$567$	−20.9197	+	9.31406i	−0.878546	+	0.391154i
$568$	−60.7554	−	12.9140i	−2.54924	−	0.541858i
$569$	−1.58278	−	15.0592i	−0.0663538	−	0.631314i	−0.976275	−	0.216533i	$-0.930525\pi$
$569$	−1.58278	−	15.0592i	−0.0663538	−	0.631314i	0.909921	−	0.414781i	$-0.136142\pi$
$570$	6.18453	−	6.86862i	0.259042	−	0.287695i
$571$	−27.3671	−	30.3942i	−1.14528	−	1.27196i	−0.957079	−	0.289829i	$-0.906402\pi$
$571$	−27.3671	−	30.3942i	−1.14528	−	1.27196i	−0.188199	−	0.982131i	$-0.560265\pi$
$572$	3.83604	−	36.4974i	0.160393	−	1.52603i
$573$	0.821013	−	2.52682i	0.0342983	−	0.105559i
$574$	−17.0838	+	52.5785i	−0.713063	+	2.19458i
$575$	−1.67246	+	15.9124i	−0.0697462	+	0.663591i
$576$	−18.6012	−	20.6587i	−0.775048	−	0.860778i
$577$	−22.7307	+	25.2450i	−0.946293	+	1.05097i	0.0523363	+	0.998630i	$0.483333\pi$
$577$	−22.7307	+	25.2450i	−0.946293	+	1.05097i	−0.998630	+	0.0523356i	$0.983333\pi$
$578$	−4.28259	−	40.7461i	−0.178132	−	1.69482i
$579$	−49.9262	−	10.6122i	−2.07486	−	0.441026i
$580$	−4.09751	+	1.82433i	−0.170140	+	0.0757511i
$581$	−7.95136	−	5.77700i	−0.329878	−	0.239671i
$582$	57.6563	+	25.6702i	2.38993	+	1.06407i
$583$	0.449747	+	0.778985i	0.0186266	+	0.0322623i
$584$	8.44975	−	14.6354i	0.349653	−	0.605617i
$585$	−4.18389	+	3.03977i	−0.172983	+	0.125679i
$586$	−58.5618	+	12.4477i	−2.41916	+	0.514209i
$587$	−6.28638	−	19.3475i	−0.259467	−	0.798556i	−0.992917	−	0.118813i	$-0.962091\pi$
$587$	−6.28638	−	19.3475i	−0.259467	−	0.798556i	0.733450	−	0.679743i	$-0.237909\pi$
$588$	10.8284			0.446557
$589$		0			0
$590$	24.3137			1.00098
$591$	−2.60013	−	8.00239i	−0.106955	−	0.329174i
$592$	−2.93444	+	0.623735i	−0.120605	+	0.0256354i
$593$	−17.2432	+	12.5279i	−0.708091	+	0.514459i	−0.882557	−	0.470205i	$-0.844180\pi$
$593$	−17.2432	+	12.5279i	−0.708091	+	0.514459i	0.174466	+	0.984663i	$0.444180\pi$
$594$	−2.62132	+	4.54026i	−0.107554	+	0.186289i
$595$	0.207107	+	0.358719i	0.00849055	+	0.0147061i
$596$	3.49744	+	1.55716i	0.143261	+	0.0637838i
$597$	30.4412	+	22.1168i	1.24588	+	0.905182i
$598$	16.1303	−	7.18169i	0.659619	−	0.293681i
$599$	−34.1369	−	7.25601i	−1.39479	−	0.296473i	−0.551612	−	0.834101i	$-0.685987\pi$
$599$	−34.1369	−	7.25601i	−1.39479	−	0.296473i	−0.843182	+	0.537628i	$0.819320\pi$
$600$	4.45578	+	42.3939i	0.181906	+	1.73072i
$601$	−15.7147	+	17.4530i	−0.641017	+	0.711921i	−0.972855	−	0.231415i	$-0.925664\pi$
$601$	−15.7147	+	17.4530i	−0.641017	+	0.711921i	0.331838	+	0.943336i	$0.392331\pi$
$602$	−34.7078	−	38.5470i	−1.41459	−	1.57106i
$603$	1.54999	−	14.7472i	0.0631206	−	0.600552i
$604$	−20.4830	+	63.0401i	−0.833440	+	2.56506i
$605$	5.09423	−	15.6784i	0.207110	−	0.637419i
$606$	−5.16954	+	49.1849i	−0.209998	+	1.99800i
$607$	−2.95369	−	3.28040i	−0.119886	−	0.133147i	0.680214	−	0.733014i	$-0.261887\pi$
$607$	−2.95369	−	3.28040i	−0.119886	−	0.133147i	−0.800100	+	0.599867i	$0.795220\pi$
$608$	1.68268	−	1.86880i	0.0682415	−	0.0757899i
$609$	−0.713765	−	6.79102i	−0.0289232	−	0.275186i
$610$	6.67921	+	1.41971i	0.270433	+	0.0574824i
$611$	−2.76753	+	1.23218i	−0.111962	+	0.0498488i
$612$	1.50304	+	1.09203i	0.0607569	+	0.0441425i
$613$	−9.42204	−	4.19496i	−0.380553	−	0.169433i	0.207540	−	0.978227i	$-0.433454\pi$
$613$	−9.42204	−	4.19496i	−0.380553	−	0.169433i	−0.588093	+	0.808794i	$0.700121\pi$
$614$	−3.32843	−	5.76500i	−0.134324	−	0.232657i
$615$	11.4497	−	19.8315i	0.461698	−	0.799685i
$616$	−45.1998	+	32.8396i	−1.82115	+	1.32315i
$617$	−22.7755	+	4.84107i	−0.916905	+	0.194894i	−0.642114	−	0.766610i	$-0.721942\pi$
$617$	−22.7755	+	4.84107i	−0.916905	+	0.194894i	−0.274792	+	0.961504i	$0.588609\pi$
$618$	−21.7410	−	66.9119i	−0.874551	−	2.69159i
$619$	−31.6569			−1.27240			−0.636198	−	0.771526i	$-0.719494\pi$
$619$	−31.6569			−1.27240			−0.636198	+	0.771526i	$0.719494\pi$
$620$		0			0
$621$	−1.65685			−0.0664873
$622$	8.44040	+	25.9769i	0.338429	+	1.04158i
$623$	29.4835	−	6.26690i	1.18123	−	0.251078i
$624$	10.7135	−	7.78383i	0.428884	−	0.311603i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	4.62132	+	8.00436i	0.184705	+	0.319919i
$627$	18.3358	+	8.16364i	0.732263	+	0.326024i
$628$	−45.9275	−	33.3683i	−1.83271	−	1.33154i
$629$	−0.156740	+	0.0697850i	−0.00624962	+	0.00278251i
$630$	16.1250	+	3.42748i	0.642437	+	0.136554i
$631$	3.34619	+	31.8368i	0.133210	+	1.26740i	0.833087	+	0.553141i	$0.186571\pi$
$631$	3.34619	+	31.8368i	0.133210	+	1.26740i	−0.699878	+	0.714263i	$0.746762\pi$
$632$	45.0220	−	50.0020i	1.79088	−	1.98897i
$633$	−12.2543	−	13.6097i	−0.487063	−	0.540939i
$634$	−0.548005	+	5.21392i	−0.0217641	+	0.207071i
$635$	−3.36813	+	10.3660i	−0.133660	+	0.411364i
$636$	−0.490035	+	1.50817i	−0.0194312	+	0.0598029i
$637$	0.223914	−	2.13040i	0.00887180	−	0.0844096i
$638$	−9.92215	−	11.0197i	−0.392822	−	0.436273i
$639$	−26.6307	+	29.5764i	−1.05350	+	1.17002i
$640$	−2.14872	−	20.4437i	−0.0849358	−	0.808110i
$641$	−19.5342	−	4.15211i	−0.771553	−	0.163999i	−0.194718	−	0.980859i	$-0.562379\pi$
$641$	−19.5342	−	4.15211i	−0.771553	−	0.163999i	−0.576835	+	0.816861i	$0.695712\pi$
$642$	51.0398	−	22.7244i	2.01438	−	0.896861i
$643$	−10.2634	−	7.45682i	−0.404750	−	0.294068i	0.366723	−	0.930330i	$-0.380480\pi$
$643$	−10.2634	−	7.45682i	−0.404750	−	0.294068i	−0.771473	+	0.636262i	$0.780480\pi$
$644$	−33.7743	−	15.0373i	−1.33089	−	0.592552i
$645$	10.7426	+	18.6068i	0.422991	+	0.732642i
$646$	−0.328427	+	0.568852i	−0.0129218	+	0.0223812i
$647$	18.3536	−	13.3347i	0.721554	−	0.524240i	−0.165326	−	0.986239i	$-0.552868\pi$
$647$	18.3536	−	13.3347i	0.721554	−	0.524240i	0.886880	+	0.461999i	$0.152868\pi$
$648$	−40.9551	+	8.70527i	−1.60887	+	0.341975i
$649$	16.3158	+	50.2148i	0.640451	+	1.97110i
$650$	17.6569			0.692559
$651$		0			0
$652$	−49.6569			−1.94471
$653$	6.84230	+	21.0584i	0.267760	+	0.824080i	0.991045	+	0.133530i	$0.0426313\pi$
$653$	6.84230	+	21.0584i	0.267760	+	0.824080i	−0.723285	+	0.690550i	$0.757369\pi$
$654$	29.4835	−	6.26690i	1.15289	−	0.245055i
$655$	3.84878	−	2.79631i	0.150384	−	0.109261i
$656$	−14.2279	+	24.6435i	−0.555507	+	0.962166i
$657$	−5.41421	−	9.37769i	−0.211229	−	0.365859i
$658$	8.82198	+	3.92780i	0.343916	+	0.153121i
$659$	−7.81256	−	5.67616i	−0.304334	−	0.221112i	0.425127	−	0.905134i	$-0.360229\pi$
$659$	−7.81256	−	5.67616i	−0.304334	−	0.221112i	−0.729462	+	0.684022i	$0.760229\pi$
$660$	44.2666	−	19.7088i	1.72308	−	0.767163i
$661$	−32.4179	−	6.89064i	−1.26091	−	0.268015i	−0.471492	−	0.881870i	$-0.656284\pi$
$661$	−32.4179	−	6.89064i	−1.26091	−	0.268015i	−0.789418	+	0.613856i	$0.789618\pi$
$662$	0.191123	+	1.81841i	0.00742819	+	0.0706745i
$663$	0.506772	−	0.562828i	0.0196814	−	0.0218584i
$664$	−12.0247	−	13.3547i	−0.466647	−	0.518264i
$665$	−0.400180	+	3.80745i	−0.0155183	+	0.147647i
$666$	−2.11010	+	6.49422i	−0.0817647	+	0.251646i
$667$	1.44814	−	4.45693i	0.0560723	−	0.172573i
$668$	3.42408	−	32.5779i	0.132481	−	1.26048i
$669$	−2.79133	−	3.10008i	−0.107919	−	0.119856i
$670$	8.46909	−	9.40588i	0.327189	−	0.363381i
$671$	1.54999	+	14.7472i	0.0598368	+	0.569309i
$672$	9.04067	+	1.92165i	0.348751	+	0.0741294i
$673$	18.8710	−	8.40190i	0.727423	−	0.323869i	−0.00939971	−	0.999956i	$-0.502992\pi$
$673$	18.8710	−	8.40190i	0.727423	−	0.323869i	0.736822	+	0.676086i	$0.236325\pi$
$674$	−26.0035	−	18.8927i	−1.00162	−	0.727719i
$675$	−1.51361	−	0.673903i	−0.0582589	−	0.0259386i
$676$	18.4853	+	32.0174i	0.710972	+	1.23144i
$677$	−20.2990	+	35.1589i	−0.780154	+	1.35127i	0.151698	+	0.988427i	$0.451526\pi$
$677$	−20.2990	+	35.1589i	−0.780154	+	1.35127i	−0.931852	+	0.362839i	$0.881808\pi$
$678$	−25.1945	+	18.3049i	−0.967590	+	0.702995i
$679$	−25.5709	+	5.43526i	−0.981320	+	0.208586i
$680$	0.234037	+	0.720292i	0.00897491	+	0.0276219i
$681$	37.6274			1.44189
$682$		0			0
$683$	−46.6274			−1.78415			−0.892074	−	0.451889i	$-0.850750\pi$
$683$	−46.6274			−1.78415			−0.892074	+	0.451889i	$0.850750\pi$
$684$	5.30631	+	16.3311i	0.202892	+	0.624437i
$685$	7.32171	−	1.55628i	0.279748	−	0.0594623i
$686$	−38.5314	+	27.9947i	−1.47114	+	1.06884i
$687$	13.8640	−	24.0131i	0.528943	−	0.916156i
$688$	−13.3492	−	23.1216i	−0.508935	−	0.881501i
$689$	0.286587	+	0.127597i	0.0109181	+	0.00486105i
$690$	18.8612	+	13.7035i	0.718033	+	0.521682i
$691$	12.8546	−	5.72322i	0.489011	−	0.217722i	−0.147393	−	0.989078i	$-0.547088\pi$
$691$	12.8546	−	5.72322i	0.489011	−	0.217722i	0.636403	+	0.771357i	$0.280421\pi$
$692$	53.6015	+	11.3934i	2.03762	+	0.433110i
$693$	3.74201	+	35.6029i	0.142147	+	1.35244i
$694$	−36.4381	+	40.4686i	−1.38317	+	1.53617i
$695$		0			0
$696$	1.30507	−	12.4169i	0.0494684	−	0.470661i
$697$	−0.502900	+	1.54777i	−0.0190487	+	0.0586258i
$698$	−26.1952	+	80.6206i	−0.991504	+	3.05154i
$699$	−3.74201	+	35.6029i	−0.141536	+	1.34662i
$700$	−24.7381	−	27.4745i	−0.935014	−	1.03844i
$701$	2.33211	−	2.59007i	0.0880825	−	0.0978255i	−0.697492	−	0.716592i	$-0.745701\pi$
$701$	2.33211	−	2.59007i	0.0880825	−	0.0978255i	0.785575	+	0.618767i	$0.212367\pi$
$702$	0.191123	+	1.81841i	0.00721346	+	0.0686315i
$703$	−1.55113	−	0.329704i	−0.0585021	−	0.0124350i
$704$	47.0722	−	20.9579i	1.77410	−	0.789880i
$705$	−3.23607	−	2.35114i	−0.121877	−	0.0885491i
$706$	−6.61648	−	2.94585i	−0.249015	−	0.110868i
$707$	−10.2426	−	17.7408i	−0.385214	−	0.667210i
$708$	−46.5416	+	80.6125i	−1.74914	+	3.02960i
$709$	4.29888	−	3.12332i	0.161448	−	0.117299i	−0.504128	−	0.863629i	$-0.668186\pi$
$709$	4.29888	−	3.12332i	0.161448	−	0.117299i	0.665576	+	0.746330i	$0.268186\pi$
$710$	−33.2282	+	7.06288i	−1.24703	+	0.265065i
$711$	−13.3226	−	41.0026i	−0.499635	−	1.53772i
$712$	55.1127			2.06544
$713$		0			0
$714$	−2.41421			−0.0903497
$715$	−2.96217	−	9.11662i	−0.110779	−	0.340942i
$716$	25.3047	−	5.37869i	0.945682	−	0.201011i
$717$	−24.9169	+	18.1032i	−0.930539	+	0.676076i
$718$	32.4706	−	56.2407i	1.21179	−	2.09888i
$719$	−3.03553	−	5.25770i	−0.113206	−	0.196079i	0.803855	−	0.594825i	$-0.202779\pi$
$719$	−3.03553	−	5.25770i	−0.113206	−	0.196079i	−0.917061	+	0.398746i	$0.869445\pi$
$720$	7.75169	+	3.45127i	0.288888	+	0.128621i
$721$	23.5765	+	17.1293i	0.878034	+	0.637929i
$722$	36.3582	−	16.1877i	1.35311	−	0.602444i
$723$	58.2261	+	12.3763i	2.16545	+	0.460281i
$724$	4.12734	+	39.2690i	0.153391	+	1.45942i
$725$	3.13574	−	3.48259i	0.116458	−	0.129340i
$726$	64.2923	+	71.4038i	2.38611	+	2.65004i
$727$	4.89618	−	46.5840i	0.181589	−	1.72771i	−0.401985	−	0.915646i	$-0.631680\pi$
$727$	4.89618	−	46.5840i	0.181589	−	1.72771i	0.583574	−	0.812060i	$-0.301654\pi$
$728$	−6.02128	+	18.5316i	−0.223164	+	0.686827i
$729$	−7.36339	+	22.6622i	−0.272718	+	0.839340i
$730$	0.966119	−	9.19201i	0.0357577	−	0.340211i
$731$	−1.02170	−	1.13472i	−0.0377891	−	0.0419690i
$732$	−17.4925	+	19.4274i	−0.646542	+	0.718057i
$733$	3.09691	+	29.4651i	0.114387	+	1.08832i	0.889638	+	0.456666i	$0.150957\pi$
$733$	3.09691	+	29.4651i	0.114387	+	1.08832i	−0.775251	+	0.631653i	$0.782377\pi$
$734$	43.0097	+	9.14199i	1.58752	+	0.337437i
$735$	2.58390	−	1.15042i	0.0953085	−	0.0424341i
$736$	5.13171	+	3.72841i	0.189157	+	0.137431i
$737$	25.1091	+	11.1793i	0.924904	+	0.411794i
$738$	32.3848	+	56.0921i	1.19210	+	2.06478i
$739$	3.93503	−	6.81567i	0.144752	−	0.250718i	−0.784528	−	0.620093i	$-0.787095\pi$
$739$	3.93503	−	6.81567i	0.144752	−	0.250718i	0.929281	+	0.369375i	$0.120428\pi$
$740$	−3.09726	+	2.25029i	−0.113858	+	0.0827224i
$741$	6.84703	−	1.45538i	0.251532	−	0.0534648i
$742$	−0.309017	−	0.951057i	−0.0113444	−	0.0349144i
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	−7.46033	−	22.9605i	−0.273142	−	0.840645i
$747$	−11.2631	+	2.39404i	−0.412095	+	0.0875935i
$748$	−2.78597	+	2.02413i	−0.101865	+	0.0740094i
$749$	−11.5711	+	20.0417i	−0.422798	+	0.732307i
$750$	26.2279	+	45.4281i	0.957708	+	1.65880i
$751$	−1.13521	−	0.505428i	−0.0414244	−	0.0184433i	0.385920	−	0.922532i	$-0.373884\pi$
$751$	−1.13521	−	0.505428i	−0.0414244	−	0.0184433i	−0.427344	+	0.904089i	$0.640551\pi$
$752$	4.02127	+	2.92162i	0.146641	+	0.106541i
$753$	−7.90843	+	3.52106i	−0.288199	+	0.128315i
$754$	−5.05856	−	1.07523i	−0.184222	−	0.0391576i
$755$	1.80978	+	17.2189i	0.0658645	+	0.626659i
$756$	2.56172	−	2.84508i	0.0931688	−	0.103474i
$757$	23.1900	+	25.7551i	0.842854	+	0.936084i	0.998662	−	0.0517036i	$-0.0164651\pi$
$757$	23.1900	+	25.7551i	0.842854	+	0.936084i	−0.155809	+	0.987787i	$0.549798\pi$
$758$	−7.41537	+	70.5525i	−0.269338	+	2.56258i
$759$	−15.6447	+	48.1495i	−0.567868	+	1.74772i
$760$	−2.16312	+	6.65740i	−0.0784646	+	0.241489i
$761$	2.13822	−	20.3438i	0.0775103	−	0.737462i	−0.884885	−	0.465809i	$-0.845763\pi$
$761$	2.13822	−	20.3438i	0.0775103	−	0.737462i	0.962395	−	0.271652i	$-0.0875701\pi$
$762$	−42.5078	−	47.2097i	−1.53990	−	1.71023i
$763$	−8.35428	+	9.27837i	−0.302445	+	0.335900i
$764$	0.440400	+	4.19012i	0.0159331	+	0.151593i
$765$	0.474677	+	0.100896i	0.0171620	+	0.00364789i
$766$	−54.9157	+	24.4500i	−1.98418	+	0.883416i
$767$	14.8974	+	10.8236i	0.537914	+	0.390818i
$768$	66.0999	+	29.4296i	2.38517	+	1.06195i
$769$	13.0563	+	22.6143i	0.470824	+	0.815491i	0.999443	−	0.0333680i	$-0.0106233\pi$
$769$	13.0563	+	22.6143i	0.470824	+	0.815491i	−0.528619	+	0.848859i	$0.677290\pi$
$770$	−15.2782	+	26.4626i	−0.550587	+	0.953645i
$771$	−0.612717	+	0.445165i	−0.0220664	+	0.0160322i
$772$	79.1724	−	16.8286i	2.84948	−	0.605675i
$773$	5.56231	+	17.1190i	0.200062	+	0.615728i	0.999880	+	0.0154855i	$0.00492938\pi$
$773$	5.56231	+	17.1190i	0.200062	+	0.615728i	−0.799818	+	0.600243i	$0.795071\pi$
$774$	−60.7696			−2.18432
$775$		0			0
$776$	−47.7990			−1.71588
$777$	−1.80108	−	5.54316i	−0.0646135	−	0.198860i
$778$	40.4804	−	8.60438i	1.45129	−	0.308482i
$779$	−12.1689	+	8.84125i	−0.435997	+	0.316771i
$780$	8.44975	−	14.6354i	0.302549	−	0.524031i
$781$	−36.8848	−	63.8863i	−1.31984	−	2.28603i
$782$	−1.51361	−	0.673903i	−0.0541266	−	0.0240987i
$783$	0.392601	+	0.285241i	0.0140304	+	0.0101937i
$784$	−3.21086	+	1.42956i	−0.114673	+	0.0510559i
$785$	−14.5044	−	3.08300i	−0.517684	−	0.110037i
$786$	2.89836	+	27.5760i	0.103381	+	0.983604i
$787$	26.4881	−	29.4180i	0.944197	−	1.04864i	−0.0545455	−	0.998511i	$-0.517371\pi$
$787$	26.4881	−	29.4180i	0.944197	−	1.04864i	0.998743	−	0.0501262i	$-0.0159623\pi$
$788$	8.92831	+	9.91589i	0.318058	+	0.353239i
$789$	−0.173188	+	1.64778i	−0.00616567	+	0.0586624i
$790$	11.3715	−	34.9979i	0.404580	−	1.24517i
$791$	3.98616	−	12.2681i	0.141732	−	0.436205i
$792$	−6.84200	+	65.0973i	−0.243120	+	2.31313i
$793$	3.46046	+	3.84323i	0.122884	+	0.136477i
$794$	26.6783	−	29.6292i	0.946777	−	1.05150i
$795$	0.0432971	+	0.411944i	0.00153559	+	0.0146102i
$796$	−58.3651	−	12.4059i	−2.06870	−	0.439715i
$797$	−20.5144	+	9.13361i	−0.726659	+	0.323529i	−0.736514	−	0.676422i	$-0.763529\pi$
$797$	−20.5144	+	9.13361i	−0.726659	+	0.323529i	0.00985554	+	0.999951i	$0.496863\pi$
$798$	−18.0522	−	13.1157i	−0.639040	−	0.464290i
$799$	0.259695	+	0.115624i	0.00918734	+	0.00409047i
$800$	3.17157	+	5.49333i	0.112132	+	0.194218i
$801$	17.6569	−	30.5826i	0.623874	−	1.08058i
$802$	−41.3510	+	30.0433i	−1.46016	+	1.06087i
$803$	19.6325	−	4.17301i	0.692815	−	0.147262i
$804$	14.9737	+	46.0842i	0.528081	+	1.62527i
$805$	−9.65685			−0.340359
$806$		0			0
$807$	76.8406			2.70492
$808$	−11.5745	−	35.6226i	−0.407189	−	1.25320i
$809$	44.9660	−	9.55782i	1.58092	−	0.336035i	0.667996	−	0.744165i	$-0.267152\pi$
$809$	44.9660	−	9.55782i	1.58092	−	0.336035i	0.912924	+	0.408130i	$0.133819\pi$
$810$	−18.5261	+	13.4600i	−0.650940	+	0.472936i
$811$	−5.86396	+	10.1567i	−0.205912	+	0.356649i	−0.950423	−	0.310961i	$-0.899349\pi$
$811$	−5.86396	+	10.1567i	−0.205912	+	0.356649i	0.744511	+	0.667610i	$0.232683\pi$
$812$	5.41421	+	9.37769i	0.190002	+	0.329093i
$813$	51.4182	+	22.8929i	1.80332	+	0.802888i
$814$	−10.2396	−	7.43951i	−0.358898	−	0.260755i
$815$	−11.8492	+	5.27560i	−0.415059	+	0.184796i
$816$	−1.21549	−	0.258360i	−0.0425505	−	0.00904439i
$817$	−1.47518	−	14.0354i	−0.0516100	−	0.491036i
$818$	−15.0931	+	16.7626i	−0.527719	+	0.586092i
$819$	8.35428	+	9.27837i	0.291922	+	0.324213i
$820$	−3.79582	+	36.1148i	−0.132556	+	1.26118i
$821$	−2.62210	+	8.06998i	−0.0915118	+	0.281644i	−0.986329	−	0.164789i	$-0.947306\pi$
$821$	−2.62210	+	8.06998i	−0.0915118	+	0.281644i	0.894817	+	0.446433i	$0.147306\pi$
$822$	−13.4816	+	41.4921i	−0.470225	+	1.44720i
$823$	0.649457	−	6.17917i	0.0226386	−	0.215392i	−0.977354	−	0.211610i	$-0.932129\pi$
$823$	0.649457	−	6.17917i	0.0226386	−	0.215392i	0.999993	−	0.00378233i	$-0.00120396\pi$
$824$	35.6541	+	39.5979i	1.24207	+	1.37946i
$825$	−33.8764	+	37.6235i	−1.17942	+	1.30988i
$826$	−6.13566	−	58.3769i	−0.213487	−	2.03119i
$827$	−16.7268	−	3.55539i	−0.581648	−	0.123633i	−0.0923148	−	0.995730i	$-0.529427\pi$
$827$	−16.7268	−	3.55539i	−0.581648	−	0.123633i	−0.489334	+	0.872097i	$0.662760\pi$
$828$	−39.5690	+	17.6173i	−1.37512	+	0.612243i
$829$	37.5598	+	27.2888i	1.30450	+	0.947778i	0.999989	−	0.00472973i	$-0.00150553\pi$
$829$	37.5598	+	27.2888i	1.30450	+	0.947778i	0.304515	+	0.952507i	$0.401506\pi$
$830$	−8.97871	−	3.99758i	−0.311656	−	0.138758i
$831$	−17.0711	−	29.5680i	−0.592189	−	1.02570i
$832$	8.98528	−	15.5630i	0.311509	−	0.539549i
$833$	−0.162621	+	0.118151i	−0.00563447	+	0.00409368i
$834$		0			0
$835$	−2.64406	−	8.13757i	−0.0915014	−	0.281612i
$836$	−31.8284			−1.10081
$837$		0			0
$838$	−67.5980			−2.33513
$839$	9.46439	+	29.1284i	0.326747	+	1.00562i	0.970646	+	0.240513i	$0.0773158\pi$
$839$	9.46439	+	29.1284i	0.326747	+	1.00562i	−0.643899	+	0.765111i	$0.722684\pi$
$840$	−25.1657	+	5.34914i	−0.868299	+	0.184563i
$841$	22.3510	−	16.2390i	0.770726	−	0.559965i
$842$	−3.44975	+	5.97514i	−0.118886	+	0.205917i
$843$	2.41421	+	4.18154i	0.0831499	+	0.144020i
$844$	26.5308	+	11.8123i	0.913230	+	0.406596i
$845$	7.81256	+	5.67616i	0.268760	+	0.195266i
$846$	10.3356	−	4.60170i	0.355345	−	0.158210i
$847$	−38.9293	−	8.27468i	−1.33763	−	0.284321i
$848$	−0.0538027	−	0.511899i	−0.00184759	−	0.0175787i
$849$	3.78517	−	4.20386i	0.129907	−	0.144276i
$850$	−1.10865	−	1.23128i	−0.0380264	−	0.0422326i
$851$	0.418114	−	3.97809i	0.0143328	−	0.136367i
$852$	40.1888	−	123.689i	1.37685	−	4.23750i
$853$	−10.0385	+	30.8953i	−0.343712	+	1.05784i	0.618558	+	0.785739i	$0.287717\pi$
$853$	−10.0385	+	30.8953i	−0.343712	+	1.05784i	−0.962270	+	0.272097i	$0.912283\pi$
$854$	1.72318	−	16.3950i	0.0589660	−	0.561024i
$855$	3.00124	+	3.33321i	0.102640	+	0.113994i
$856$	−28.3134	+	31.4452i	−0.967732	+	1.07478i
$857$	0.262860	+	2.50094i	0.00897912	+	0.0854306i	0.998094	−	0.0617167i	$-0.0196575\pi$
$857$	0.262860	+	2.50094i	0.00897912	+	0.0854306i	−0.989115	+	0.147147i	$0.952991\pi$
$858$	54.6492	+	11.6160i	1.86569	+	0.396565i
$859$	−11.5246	+	5.13107i	−0.393214	+	0.175070i	−0.593812	−	0.804603i	$-0.702378\pi$
$859$	−11.5246	+	5.13107i	−0.393214	+	0.175070i	0.200599	+	0.979673i	$0.435711\pi$
$860$	−27.5641	−	20.0265i	−0.939927	−	0.682897i
$861$	−50.5047	−	22.4861i	−1.72120	−	0.766326i
$862$	−30.4706	−	52.7766i	−1.03783	−	1.79758i
$863$	19.6924	−	34.1082i	0.670337	−	1.16106i	−0.307472	−	0.951557i	$-0.599483\pi$
$863$	19.6924	−	34.1082i	0.670337	−	1.16106i	0.977809	−	0.209500i	$-0.0671836\pi$
$864$	−0.531406	+	0.386089i	−0.0180788	+	0.0131350i
$865$	14.0009	−	2.97599i	0.476046	−	0.101187i
$866$	26.1952	+	80.6206i	0.890150	+	2.73960i
$867$	40.9706			1.39143
$868$		0			0
$869$	79.9117			2.71082
$870$	−2.11010	−	6.49422i	−0.0715391	−	0.220175i
$871$	9.37631	−	1.99300i	0.317704	−	0.0675301i
$872$	−18.4686	+	13.4182i	−0.625425	+	0.454398i
$873$	−15.3137	+	26.5241i	−0.518291	+	0.897705i
$874$	−7.65685	−	13.2621i	−0.258997	−	0.448596i
$875$	−19.8494	−	8.83754i	−0.671034	−	0.298763i
$876$	28.6269	+	20.7986i	0.967213	+	0.702721i
$877$	44.0069	−	19.5931i	1.48601	−	0.661613i	0.506357	−	0.862324i	$-0.330992\pi$
$877$	44.0069	−	19.5931i	1.48601	−	0.661613i	0.979651	+	0.200710i	$0.0643250\pi$
$878$	−28.5053	−	6.05899i	−0.962008	−	0.204481i
$879$	−6.25813	−	59.5421i	−0.211081	−	2.00830i
$880$	−10.5240	+	11.6881i	−0.354765	+	0.394007i
$881$	22.9604	+	25.5001i	0.773554	+	0.859119i	0.993195	−	0.116462i	$-0.0371553\pi$
$881$	22.9604	+	25.5001i	0.773554	+	0.859119i	−0.219641	+	0.975581i	$0.570489\pi$
$882$	−0.836228	+	7.95618i	−0.0281573	+	0.267898i
$883$	8.12229	−	24.9978i	0.273337	−	0.841244i	−0.716318	−	0.697774i	$-0.754174\pi$
$883$	8.12229	−	24.9978i	0.273337	−	0.841244i	0.989655	−	0.143470i	$-0.0458260\pi$
$884$	−0.371133	+	1.14223i	−0.0124825	+	0.0384173i
$885$	−2.54147	+	24.1805i	−0.0854307	+	0.812819i
$886$	21.3925	+	23.7588i	0.718694	+	0.798191i
$887$	35.6820	−	39.6289i	1.19808	−	1.33061i	0.267930	−	0.963438i	$-0.413661\pi$
$887$	35.6820	−	39.6289i	1.19808	−	1.33061i	0.930154	−	0.367169i	$-0.119673\pi$
$888$	−1.11394	−	10.5985i	−0.0373815	−	0.355662i
$889$	25.7387	+	5.47093i	0.863248	+	0.183489i
$890$	27.5362	−	12.2599i	0.923016	−	0.410953i
$891$	−40.2307	−	29.2293i	−1.34778	−	0.979220i
$892$	6.04331	+	2.69065i	0.202345	+	0.0900898i
$893$	1.31371	+	2.27541i	0.0439616	+	0.0761437i
$894$	−2.91421	+	5.04757i	−0.0974659	+	0.168816i
$895$	5.46682	−	3.97188i	0.182736	−	0.132765i
$896$	−48.5429	+	10.3181i	−1.62171	+	0.344704i
$897$	5.45627	+	16.7927i	0.182179	+	0.560691i
$898$	−11.1716			−0.372800
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−0.00909661	−	0.0279965i	−0.000303052	−	0.000932698i
$902$	−117.430	+	24.9606i	−3.91000	+	0.831097i
$903$	41.9638	−	30.4885i	1.39647	−	1.01459i
$904$	11.7929	−	20.4259i	0.392226	−	0.679355i
$905$	5.15685	+	8.93193i	0.171420	+	0.296908i
$906$	−92.1874	−	41.0445i	−3.06272	−	1.36361i
$907$	−44.7497	−	32.5126i	−1.48589	−	1.07956i	−0.975599	−	0.219561i	$-0.929537\pi$
$907$	−44.7497	−	32.5126i	−1.48589	−	1.07956i	−0.510292	−	0.860001i	$-0.670463\pi$
$908$	−54.5104	+	24.2696i	−1.80899	+	0.805415i
$909$	−23.4755	−	4.98988i	−0.778635	−	0.165504i
$910$	1.11394	+	10.5985i	0.0369269	+	0.351336i
$911$	32.8153	−	36.4450i	1.08722	−	1.20748i	0.110292	−	0.993899i	$-0.464821\pi$
$911$	32.8153	−	36.4450i	1.08722	−	1.20748i	0.976926	−	0.213579i	$-0.0685120\pi$
$912$	−7.68515	−	8.53523i	−0.254481	−	0.282630i
$913$	2.23097	−	21.2262i	0.0738342	−	0.702486i
$914$	−23.2111	+	71.4364i	−0.767755	+	2.36291i
$915$	−2.11010	+	6.49422i	−0.0697578	+	0.214692i
$916$	−4.59618	+	43.7297i	−0.151862	+	1.44487i
$917$	−7.68515	−	8.53523i	−0.253786	−	0.281858i
$918$	0.114805	−	0.127503i	0.00378912	−	0.00420824i
$919$	1.57843	+	15.0178i	0.0520677	+	0.495391i	0.989216	+	0.146461i	$0.0467883\pi$
$919$	1.57843	+	15.0178i	0.0520677	+	0.495391i	−0.937149	+	0.348930i	$0.886545\pi$
$920$	−17.2710	−	3.67107i	−0.569408	−	0.121031i
$921$	6.08134	−	2.70759i	0.200387	−	0.0892180i
$922$	51.0592	+	37.0967i	1.68155	+	1.22172i
$923$	−23.5036	−	10.4645i	−0.773631	−	0.344443i
$924$	−58.4914	−	101.310i	−1.92423	−	3.33286i
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	48.7710	−	35.4342i	1.60271	−	1.16444i
$927$	33.3960	−	7.09855i	1.09687	−	0.233147i
$928$	−0.574112	−	1.76693i	−0.0188461	−	0.0580025i
$929$	24.4853			0.803336			0.401668	−	0.915785i	$-0.368431\pi$
$929$	24.4853			0.803336			0.401668	+	0.915785i	$0.368431\pi$
$930$		0			0
$931$	−1.85786			−0.0608890
$932$	−17.5428	−	53.9911i	−0.574632	−	1.76854i
$933$	−26.7168	+	5.67884i	−0.874670	+	0.185917i
$934$	−15.6251	+	11.3523i	−0.511269	+	0.371459i
$935$	−0.449747	+	0.778985i	−0.0147083	+	0.0254755i
$936$	11.4142	+	19.7700i	0.373085	+	0.646203i
$937$	35.0013	+	15.5836i	1.14344	+	0.509094i	0.888961	−	0.457984i	$-0.151428\pi$
$937$	35.0013	+	15.5836i	1.14344	+	0.509094i	0.254483	+	0.967077i	$0.418095\pi$
$938$	−24.7206	−	17.9606i	−0.807156	−	0.586433i
$939$	−8.44357	+	3.75932i	−0.275546	+	0.122681i
$940$	6.20453	+	1.31881i	0.202370	+	0.0430150i
$941$	3.65850	+	34.8083i	0.119264	+	1.13472i	0.876441	+	0.481508i	$0.159911\pi$
$941$	3.65850	+	34.8083i	0.119264	+	1.13472i	−0.757178	+	0.653209i	$0.773422\pi$
$942$	57.8306	−	64.2273i	1.88422	−	2.09264i
$943$	−25.3876	−	28.1958i	−0.826733	−	0.918180i
$944$	3.15814	−	30.0477i	0.102789	−	0.977969i
$945$	0.309017	−	0.951057i	0.0100523	−	0.0309379i
$946$	34.8076	−	107.127i	1.13169	−	3.48299i
$947$	−4.06610	+	38.6864i	−0.132131	+	1.25714i	0.704632	+	0.709573i	$0.251112\pi$
$947$	−4.06610	+	38.6864i	−0.132131	+	1.25714i	−0.836763	+	0.547566i	$0.815555\pi$
$948$	94.2686	+	104.696i	3.06170	+	3.40037i
$949$	4.68391	−	5.20201i	0.152046	−	0.168865i
$950$	−1.60072	−	15.2298i	−0.0519342	−	0.494121i
$951$	−5.12808	−	1.09001i	−0.166289	−	0.0353459i
$952$	1.67035	−	0.743688i	0.0541364	−	0.0241031i
$953$	−16.5729	−	12.0409i	−0.536850	−	0.390045i	0.286064	−	0.958211i	$-0.407653\pi$
$953$	−16.5729	−	12.0409i	−0.536850	−	0.390045i	−0.822914	+	0.568166i	$0.807653\pi$
$954$	−1.07029	−	0.476522i	−0.0346518	−	0.0154280i
$955$	0.550253	+	0.953065i	0.0178058	+	0.0308405i
$956$	24.4203	−	42.2972i	0.789809	−	1.36799i
$957$	11.9964	−	8.71593i	0.387790	−	0.281746i
$958$	22.9721	−	4.88286i	0.742194	−	0.157758i
$959$	−5.58427	−	17.1866i	−0.180325	−	0.554984i
$960$	23.7279			0.765815
$961$		0			0
$962$	−4.41421			−0.142320
$963$	8.37828	+	25.7857i	0.269986	+	0.830933i
$964$	−92.3342	+	19.6262i	−2.97388	+	0.632118i
$965$	17.1043	−	12.4270i	0.550608	−	0.400040i
$966$	28.1421	−	48.7436i	0.905458	−	1.56830i
$967$	23.2782	+	40.3190i	0.748576	+	1.29657i	0.948505	+	0.316761i	$0.102595\pi$
$967$	23.2782	+	40.3190i	0.748576	+	1.29657i	−0.199930	+	0.979810i	$0.564071\pi$
$968$	−66.4783	−	29.5980i	−2.13669	−	0.951317i
$969$	−0.531406	−	0.386089i	−0.0170712	−	0.0124030i
$970$	−23.8820	+	10.6330i	−0.766806	+	0.341404i
$971$	−57.4158	−	12.2041i	−1.84256	−	0.391648i	−0.851422	−	0.524482i	$-0.824259\pi$
$971$	−57.4158	−	12.2041i	−1.84256	−	0.391648i	−0.991138	+	0.132833i	$0.957592\pi$
$972$	−8.66663	−	82.4575i	−0.277982	−	2.64483i
$973$		0			0
$974$	28.0838	+	31.1902i	0.899863	+	0.999399i
$975$	−1.84564	+	17.5601i	−0.0591079	+	0.562374i
$976$	2.62210	−	8.06998i	0.0839313	−	0.258314i
$977$	5.09423	−	15.6784i	0.162979	−	0.501598i	−0.835903	−	0.548878i	$-0.815055\pi$
$977$	5.09423	−	15.6784i	0.162979	−	0.501598i	0.998882	+	0.0472800i	$0.0150553\pi$
$978$	7.90214	−	75.1838i	0.252683	−	2.40411i
$979$	43.7985	+	48.6432i	1.39981	+	1.55464i
$980$	−3.00124	+	3.33321i	−0.0958711	+	0.106476i
$981$	1.52898	+	14.5473i	0.0488166	+	0.464459i
$982$	10.4240	+	2.21568i	0.332642	+	0.0707053i
$983$	44.6181	−	19.8653i	1.42310	−	0.633604i	0.456458	−	0.889745i	$-0.349118\pi$
$983$	44.6181	−	19.8653i	1.42310	−	0.633604i	0.966639	+	0.256141i	$0.0824512\pi$
$984$	−81.7781	−	59.4153i	−2.60699	−	1.89409i
$985$	3.18396	+	1.41759i	0.101449	+	0.0451682i
$986$	0.242641	+	0.420266i	0.00772725	+	0.0133840i
$987$	−4.82843	+	8.36308i	−0.153691	+	0.266200i
$988$	−8.98050	+	6.52471i	−0.285708	+	0.207579i
$989$	34.8201	−	7.40124i	1.10721	−	0.235346i
$990$	11.0625	+	34.0469i	0.351589	+	1.08208i
$991$	−19.9411			−0.633451			−0.316725	−	0.948517i	$-0.602583\pi$
$991$	−19.9411			−0.633451			−0.316725	+	0.948517i	$0.602583\pi$
$992$		0			0
$993$	−1.82843			−0.0580234
$994$	25.3432	+	77.9982i	0.803836	+	2.47395i
$995$	−15.2452	+	3.24047i	−0.483305	+	0.102730i
$996$	30.4412	−	22.1168i	0.964567	−	0.700799i
$997$	23.2990	−	40.3550i	0.737886	−	1.27806i	−0.215559	−	0.976491i	$-0.569157\pi$
$997$	23.2990	−	40.3550i	0.737886	−	1.27806i	0.953445	−	0.301566i	$-0.0975093\pi$
$998$	48.5416	+	84.0766i	1.53656	+	2.66140i
$999$	0.378403	+	0.168476i	0.0119721	+	0.00533034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.o.844.1		16
31.2	even	5	inner	961.2.g.o.338.2		16
31.3	odd	30		961.2.a.c.1.1		2
31.4	even	5	inner	961.2.g.o.732.2		16
31.5	even	3	inner	961.2.g.o.547.1		16
31.6	odd	6		961.2.d.i.531.1		8
31.7	even	15		961.2.d.l.374.2		8
31.8	even	5	inner	961.2.g.o.448.1		16
31.9	even	15	inner	961.2.g.o.846.1		16
31.10	even	15	inner	961.2.g.o.235.2		16
31.11	odd	30		961.2.g.r.816.2		16
31.12	odd	30		961.2.d.i.388.2		8
31.13	odd	30		961.2.c.a.439.1		4
31.14	even	15		961.2.d.l.628.1		8
31.15	odd	10		961.2.c.a.521.1		4
31.16	even	5		31.2.c.a.25.1	yes	4
31.17	odd	30		961.2.d.i.628.1		8
31.18	even	15		31.2.c.a.5.1	✓	4
31.19	even	15		961.2.d.l.388.2		8
31.20	even	15	inner	961.2.g.o.816.2		16
31.21	odd	30		961.2.g.r.235.2		16
31.22	odd	30		961.2.g.r.846.1		16
31.23	odd	10		961.2.g.r.448.1		16
31.24	odd	30		961.2.d.i.374.2		8
31.25	even	3		961.2.d.l.531.1		8
31.26	odd	6		961.2.g.r.547.1		16
31.27	odd	10		961.2.g.r.732.2		16
31.28	even	15		961.2.a.a.1.1		2
31.29	odd	10		961.2.g.r.338.2		16
31.30	odd	2		961.2.g.r.844.1		16
93.47	odd	10		279.2.h.c.118.2		4
93.59	odd	30		8649.2.a.l.1.2		2
93.65	even	30		8649.2.a.k.1.2		2
93.80	odd	30		279.2.h.c.253.2		4
124.47	odd	10		496.2.i.h.273.1		4
124.111	odd	30		496.2.i.h.129.1		4
155.18	odd	60		775.2.o.d.749.4		8
155.47	odd	20		775.2.o.d.149.1		8
155.49	even	30		775.2.e.e.501.2		4
155.78	odd	20		775.2.o.d.149.4		8
155.109	even	10		775.2.e.e.676.2		4
155.142	odd	60		775.2.o.d.749.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.1	✓	4	31.18	even	15
31.2.c.a.25.1	yes	4	31.16	even	5
279.2.h.c.118.2		4	93.47	odd	10
279.2.h.c.253.2		4	93.80	odd	30
496.2.i.h.129.1		4	124.111	odd	30
496.2.i.h.273.1		4	124.47	odd	10
775.2.e.e.501.2		4	155.49	even	30
775.2.e.e.676.2		4	155.109	even	10
775.2.o.d.149.1		8	155.47	odd	20
775.2.o.d.149.4		8	155.78	odd	20
775.2.o.d.749.1		8	155.142	odd	60
775.2.o.d.749.4		8	155.18	odd	60
961.2.a.a.1.1		2	31.28	even	15
961.2.a.c.1.1		2	31.3	odd	30
961.2.c.a.439.1		4	31.13	odd	30
961.2.c.a.521.1		4	31.15	odd	10
961.2.d.i.374.2		8	31.24	odd	30
961.2.d.i.388.2		8	31.12	odd	30
961.2.d.i.531.1		8	31.6	odd	6
961.2.d.i.628.1		8	31.17	odd	30
961.2.d.l.374.2		8	31.7	even	15
961.2.d.l.388.2		8	31.19	even	15
961.2.d.l.531.1		8	31.25	even	3
961.2.d.l.628.1		8	31.14	even	15
961.2.g.o.235.2		16	31.10	even	15	inner
961.2.g.o.338.2		16	31.2	even	5	inner
961.2.g.o.448.1		16	31.8	even	5	inner
961.2.g.o.547.1		16	31.5	even	3	inner
961.2.g.o.732.2		16	31.4	even	5	inner
961.2.g.o.816.2		16	31.20	even	15	inner
961.2.g.o.844.1		16	1.1	even	1	trivial
961.2.g.o.846.1		16	31.9	even	15	inner
961.2.g.r.235.2		16	31.21	odd	30
961.2.g.r.338.2		16	31.29	odd	10
961.2.g.r.448.1		16	31.23	odd	10
961.2.g.r.547.1		16	31.26	odd	6
961.2.g.r.732.2		16	31.27	odd	10
961.2.g.r.816.2		16	31.11	odd	30
961.2.g.r.844.1		16	31.30	odd	2
961.2.g.r.846.1		16	31.22	odd	30
8649.2.a.k.1.2		2	93.65	even	30
8649.2.a.l.1.2		2	93.59	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.746033 - 2.29605i) q^{2} +(2.36146 - 0.501943i) q^{3} +(-3.09726 + 2.25029i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.91421 - 5.04757i) q^{6} +(2.20549 + 0.981949i) q^{7} +(3.57117 + 2.59461i) q^{8} +(2.58390 - 1.15042i) q^{9} +(2.36146 + 0.501943i) q^{10} +(0.548005 + 5.21392i) q^{11} +(-6.18453 + 6.86862i) q^{12} +(1.22346 + 1.35879i) q^{13} +(0.609237 - 5.79650i) q^{14} +(-0.746033 + 2.29605i) q^{15} +(0.927051 - 2.85317i) q^{16} +(0.0179342 - 0.170633i) q^{17} +(-4.56911 - 5.07451i) q^{18} +(1.06110 - 1.17847i) q^{19} +(-0.400180 - 3.80745i) q^{20} +(5.70106 + 1.21180i) q^{21} +(11.5626 - 5.14801i) q^{22} +(3.23607 + 2.35114i) q^{23} +(9.73552 + 4.33453i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.20711 - 3.82282i) q^{26} +(-0.335106 + 0.243469i) q^{27} +(-9.04067 + 1.92165i) q^{28} +(-0.362036 - 1.11423i) q^{29} +5.82843 q^{30} +1.58579 q^{32} +(3.91118 + 12.0374i) q^{33} +(-0.405162 + 0.0861198i) q^{34} +(-1.95314 + 1.41904i) q^{35} +(-5.41421 + 9.37769i) q^{36} +(-0.500000 - 0.866025i) q^{37} +(-3.49744 - 1.55716i) q^{38} +(3.57117 + 2.59461i) q^{39} +(-4.03258 + 1.79542i) q^{40} +(-9.27801 - 1.97210i) q^{41} +(-1.47083 - 13.9940i) q^{42} +(5.95492 - 6.61361i) q^{43} +(-13.4302 - 14.9157i) q^{44} +(-0.295651 + 2.81293i) q^{45} +(2.98413 - 9.18421i) q^{46} +(-0.511996 + 1.57576i) q^{47} +(0.757062 - 7.20296i) q^{48} +(-0.783935 - 0.870648i) q^{49} +(6.46170 - 7.17644i) q^{50} +(-0.0432971 - 0.411944i) q^{51} +(-6.84703 - 1.45538i) q^{52} +(0.156740 - 0.0697850i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-4.78939 - 2.13237i) q^{55} +(5.32843 + 9.22911i) q^{56} +(1.91421 - 3.31552i) q^{57} +(-2.28825 + 1.66251i) q^{58} +(9.85099 - 2.09389i) q^{59} +(-2.85613 - 8.79027i) q^{60} +2.82843 q^{61} +6.82843 q^{63} +(-3.03715 - 9.34739i) q^{64} +(-1.78847 + 0.380151i) q^{65} +(24.7206 - 17.9606i) q^{66} +(2.62132 - 4.54026i) q^{67} +(0.328427 + 0.568852i) q^{68} +(8.82198 + 3.92780i) q^{69} +(4.71530 + 3.42586i) q^{70} +(-12.8546 + 5.72322i) q^{71} +(12.2124 + 2.59584i) q^{72} +(-0.400180 - 3.80745i) q^{73} +(-1.61542 + 1.79411i) q^{74} +(6.46170 + 7.17644i) q^{75} +(-0.634599 + 6.03781i) q^{76} +(-3.91118 + 12.0374i) q^{77} +(3.29315 - 10.1353i) q^{78} +(1.59329 - 15.1591i) q^{79} +(2.00739 + 2.22943i) q^{80} +(-6.34689 + 7.04894i) q^{81} +(2.39365 + 22.7740i) q^{82} +(-3.98211 - 0.846423i) q^{83} +(-20.3846 + 9.07580i) q^{84} +(0.138805 + 0.100848i) q^{85} +(-19.6278 - 8.73885i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(-11.5711 + 20.0417i) q^{88} +(10.1008 - 7.33866i) q^{89} +(6.67921 - 1.41971i) q^{90} +(1.36407 + 4.19817i) q^{91} -15.3137 q^{92} +4.00000 q^{94} +(0.490035 + 1.50817i) q^{95} +(3.74477 - 0.795975i) q^{96} +(-8.76038 + 6.36479i) q^{97} +(-1.41421 + 2.44949i) q^{98} +(7.41421 + 12.8418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots + 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

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