LMFDB - Embedded newform 961.2.g.c.547.1

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)

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);

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")

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 = [8,-6,1,6,6,-2,3] 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:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
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			547.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	961.547
Dual form			961.2.g.c.448.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.190983 - 0.587785i) q^{2} +(0.669131 + 0.743145i) q^{3} +(1.30902 - 0.951057i) q^{4} +(1.30902 + 2.26728i) q^{5} +(0.309017 - 0.535233i) q^{6} +(-0.313585 - 2.98357i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.209057 - 1.98904i) q^{9} +(1.08268 - 1.20243i) q^{10} +(0.697887 + 0.310719i) q^{11} +(1.58268 + 0.336408i) q^{12} +(4.74803 - 1.00922i) q^{13} +(-1.69381 + 0.754131i) q^{14} +(-0.809017 + 2.48990i) q^{15} +(0.572949 - 1.76336i) q^{16} +(-0.215659 + 0.0960175i) q^{17} +(-1.20906 + 0.256993i) q^{18} +(-4.89074 - 1.03956i) q^{19} +(3.86984 + 1.72296i) q^{20} +(2.00739 - 2.22943i) q^{21} +(0.0493516 - 0.469550i) q^{22} +(-4.42705 - 3.21644i) q^{23} +(-0.233733 - 2.22382i) q^{24} +(-0.927051 + 1.60570i) q^{25} +(-1.50000 - 2.59808i) q^{26} +(4.04508 - 2.93893i) q^{27} +(-3.24803 - 3.60730i) q^{28} +(2.66312 + 8.19624i) q^{29} +1.61803 q^{30} -5.61803 q^{32} +(0.236068 + 0.726543i) q^{33} +(0.0976248 + 0.108423i) q^{34} +(6.35410 - 4.61653i) q^{35} +(-1.61803 - 2.80252i) q^{36} +(0.118034 - 0.204441i) q^{37} +(0.323011 + 3.07324i) q^{38} +(3.92705 + 2.85317i) q^{39} +(0.611920 - 5.82203i) q^{40} +(4.33070 - 4.80973i) q^{41} +(-1.69381 - 0.754131i) q^{42} +(-4.51712 - 0.960143i) q^{43} +(1.20906 - 0.256993i) q^{44} +(4.78339 - 2.12970i) q^{45} +(-1.04508 + 3.21644i) q^{46} +(-1.04508 + 3.21644i) q^{47} +(1.69381 - 0.754131i) q^{48} +(-1.95630 + 0.415823i) q^{49} +(1.12086 + 0.238246i) q^{50} +(-0.215659 - 0.0960175i) q^{51} +(5.25542 - 5.83674i) q^{52} +(-1.32837 + 12.6386i) q^{53} +(-2.50000 - 1.81636i) q^{54} +(0.209057 + 1.98904i) q^{55} +(-3.35410 + 5.80948i) q^{56} +(-2.50000 - 4.33013i) q^{57} +(4.30902 - 3.13068i) q^{58} +(6.33810 + 7.03917i) q^{59} +(1.30902 + 4.02874i) q^{60} +6.94427 q^{61} -6.00000 q^{63} +(-0.0729490 - 0.224514i) q^{64} +(8.50345 + 9.44404i) q^{65} +(0.381966 - 0.277515i) q^{66} +(2.11803 + 3.66854i) q^{67} +(-0.190983 + 0.330792i) q^{68} +(-0.571994 - 5.44216i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-0.00942533 + 0.0896760i) q^{71} +(-2.99244 + 3.32344i) q^{72} +(7.82206 + 3.48260i) q^{73} +(-0.142710 - 0.0303339i) q^{74} +(-1.81359 + 0.385489i) q^{75} +(-7.39074 + 3.29057i) q^{76} +(0.708204 - 2.17963i) q^{77} +(0.927051 - 2.85317i) q^{78} +(4.74803 - 1.00922i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.65418 - 1.62695i) q^{82} +(2.73686 - 3.03959i) q^{83} +(0.507392 - 4.82751i) q^{84} +(-0.500000 - 0.363271i) q^{85} +(0.298335 + 2.83847i) q^{86} +(-4.30902 + 7.46344i) q^{87} +(-0.854102 - 1.47935i) q^{88} +(-5.16312 + 3.75123i) q^{89} +(-2.16535 - 2.40487i) q^{90} +(-4.50000 - 13.8496i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(-4.04508 - 12.4495i) q^{95} +(-3.75920 - 4.17501i) q^{96} +(4.28115 - 3.11044i) q^{97} +(0.618034 + 1.07047i) q^{98} +(0.763932 - 1.32317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} - 10 q^{8} - 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 6 q^{14} - 2 q^{15} + 18 q^{16} - 3 q^{17} - 6 q^{18} + 5 q^{19} + 7 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) $ 8 * q - 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 - 10 * q^8 - 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 6 * q^14 - 2 * q^15 + 18 * q^16 - 3 * q^17 - 6 * q^18 + 5 * q^19 + 7 * q^20 + 3 * q^21 - 6 * q^22 - 22 * q^23 + 5 * q^24 + 6 * q^25 - 12 * q^26 + 10 * q^27 + 6 * q^28 - 10 * q^29 + 4 * q^30 - 36 * q^32 - 16 * q^33 + 11 * q^34 + 24 * q^35 - 4 * q^36 - 8 * q^37 - 10 * q^38 + 18 * q^39 - 10 * q^40 - 8 * q^41 - 6 * q^42 + q^43 + 6 * q^44 + 8 * q^45 + 14 * q^46 + 14 * q^47 + 6 * q^48 + 2 * q^49 - 12 * q^50 - 3 * q^51 - 3 * q^52 + 21 * q^53 - 20 * q^54 - 2 * q^55 - 20 * q^57 + 30 * q^58 - 5 * q^59 + 6 * q^60 - 16 * q^61 - 48 * q^63 - 14 * q^64 - 9 * q^65 + 12 * q^66 + 8 * q^67 - 6 * q^68 + 11 * q^69 - 18 * q^70 + 7 * q^71 + 10 * q^72 + 21 * q^73 + 11 * q^74 - 9 * q^75 - 15 * q^76 - 48 * q^77 - 6 * q^78 + 6 * q^80 + q^81 - 4 * q^82 - 14 * q^83 - 9 * q^84 - 4 * q^85 - 7 * q^86 - 30 * q^87 + 20 * q^88 - 10 * q^89 + 4 * q^90 - 36 * q^91 - 44 * q^92 - 28 * q^94 - 10 * q^95 - 2 * q^96 - 6 * q^97 - 4 * q^98 + 24 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.190983	−	0.587785i	−0.135045	−	0.415627i	0.860552	−	0.509363i	$-0.170119\pi$
$2$	−0.190983	−	0.587785i	−0.135045	−	0.415627i	−0.995597	+	0.0937362i	$0.970119\pi$
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i	0.904668	−	0.426116i	$-0.140119\pi$
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i	−0.518346	+	0.855171i	$0.673452\pi$
$4$	1.30902	−	0.951057i	0.654508	−	0.475528i
$5$	1.30902	+	2.26728i	0.585410	+	1.01396i	0.994824	+	0.101611i	$0.0323999\pi$
$5$	1.30902	+	2.26728i	0.585410	+	1.01396i	−0.409414	+	0.912349i	$0.634267\pi$
$6$	0.309017	−	0.535233i	0.126156	−	0.218508i
$7$	−0.313585	−	2.98357i	−0.118524	−	1.12768i	−0.878504	−	0.477735i	$-0.841458\pi$
$7$	−0.313585	−	2.98357i	−0.118524	−	1.12768i	0.759980	−	0.649947i	$-0.225209\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	0.209057	−	1.98904i	0.0696856	−	0.663015i
$10$	1.08268	−	1.20243i	0.342372	−	0.380243i
$11$	0.697887	+	0.310719i	0.210421	+	0.0936853i	0.509241	−	0.860624i	$-0.329926\pi$
$11$	0.697887	+	0.310719i	0.210421	+	0.0936853i	−0.298820	+	0.954310i	$0.596593\pi$
$12$	1.58268	+	0.336408i	0.456879	+	0.0971127i
$13$	4.74803	−	1.00922i	1.31687	−	0.279909i	0.504680	−	0.863307i	$-0.331611\pi$
$13$	4.74803	−	1.00922i	1.31687	−	0.279909i	0.812186	+	0.583398i	$0.198277\pi$
$14$	−1.69381	+	0.754131i	−0.452689	+	0.201550i
$15$	−0.809017	+	2.48990i	−0.208887	+	0.642889i
$16$	0.572949	−	1.76336i	0.143237	−	0.440839i
$17$	−0.215659	+	0.0960175i	−0.0523049	+	0.0232877i	−0.432722	−	0.901527i	$-0.642447\pi$
$17$	−0.215659	+	0.0960175i	−0.0523049	+	0.0232877i	0.380417	+	0.924815i	$0.375780\pi$
$18$	−1.20906	+	0.256993i	−0.284977	+	0.0605738i
$19$	−4.89074	−	1.03956i	−1.12201	−	0.238491i	−0.390689	−	0.920523i	$-0.627763\pi$
$19$	−4.89074	−	1.03956i	−1.12201	−	0.238491i	−0.731323	+	0.682031i	$0.761097\pi$
$20$	3.86984	+	1.72296i	0.865323	+	0.385266i
$21$	2.00739	−	2.22943i	0.438049	−	0.486502i
$22$	0.0493516	−	0.469550i	0.0105218	−	0.100108i
$23$	−4.42705	−	3.21644i	−0.923104	−	0.670674i	0.0211907	−	0.999775i	$-0.493254\pi$
$23$	−4.42705	−	3.21644i	−0.923104	−	0.670674i	−0.944295	+	0.329101i	$0.893254\pi$
$24$	−0.233733	−	2.22382i	−0.0477105	−	0.453935i
$25$	−0.927051	+	1.60570i	−0.185410	+	0.321140i
$26$	−1.50000	−	2.59808i	−0.294174	−	0.509525i
$27$	4.04508	−	2.93893i	0.778477	−	0.565597i
$28$	−3.24803	−	3.60730i	−0.613820	−	0.681716i
$29$	2.66312	+	8.19624i	0.494529	+	1.52200i	0.817690	+	0.575659i	$0.195254\pi$
$29$	2.66312	+	8.19624i	0.494529	+	1.52200i	−0.323161	+	0.946344i	$0.604746\pi$
$30$	1.61803			0.295411
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	0.236068	+	0.726543i	0.0410942	+	0.126475i
$34$	0.0976248	+	0.108423i	0.0167425	+	0.0185945i
$35$	6.35410	−	4.61653i	1.07404	−	0.780335i
$36$	−1.61803	−	2.80252i	−0.269672	−	0.467086i
$37$	0.118034	−	0.204441i	0.0194047	−	0.0336099i	−0.856160	−	0.516711i	$-0.827156\pi$
$37$	0.118034	−	0.204441i	0.0194047	−	0.0336099i	0.875565	+	0.483101i	$0.160490\pi$
$38$	0.323011	+	3.07324i	0.0523993	+	0.498546i
$39$	3.92705	+	2.85317i	0.628831	+	0.456873i
$40$	0.611920	−	5.82203i	0.0967531	−	0.920544i
$41$	4.33070	−	4.80973i	0.676342	−	0.751154i	−0.303082	−	0.952964i	$-0.598016\pi$
$41$	4.33070	−	4.80973i	0.676342	−	0.751154i	0.979425	+	0.201810i	$0.0646824\pi$
$42$	−1.69381	−	0.754131i	−0.261360	−	0.116365i
$43$	−4.51712	−	0.960143i	−0.688854	−	0.146420i	−0.149831	−	0.988712i	$-0.547873\pi$
$43$	−4.51712	−	0.960143i	−0.688854	−	0.146420i	−0.539023	+	0.842291i	$0.681206\pi$
$44$	1.20906	−	0.256993i	0.182272	−	0.0387431i
$45$	4.78339	−	2.12970i	0.713065	−	0.317477i
$46$	−1.04508	+	3.21644i	−0.154089	+	0.474238i
$47$	−1.04508	+	3.21644i	−0.152441	+	0.469166i	−0.997893	−	0.0648863i	$-0.979332\pi$
$47$	−1.04508	+	3.21644i	−0.152441	+	0.469166i	0.845451	+	0.534052i	$0.179332\pi$
$48$	1.69381	−	0.754131i	0.244480	−	0.108849i
$49$	−1.95630	+	0.415823i	−0.279471	+	0.0594033i
$50$	1.12086	+	0.238246i	0.158513	+	0.0336930i
$51$	−0.215659	−	0.0960175i	−0.0301983	−	0.0134451i
$52$	5.25542	−	5.83674i	0.728796	−	0.809410i
$53$	−1.32837	+	12.6386i	−0.182466	+	1.73604i	0.394166	+	0.919039i	$0.371033\pi$
$53$	−1.32837	+	12.6386i	−0.182466	+	1.73604i	−0.576632	+	0.817004i	$0.695633\pi$
$54$	−2.50000	−	1.81636i	−0.340207	−	0.247175i
$55$	0.209057	+	1.98904i	0.0281892	+	0.268203i
$56$	−3.35410	+	5.80948i	−0.448211	+	0.776324i
$57$	−2.50000	−	4.33013i	−0.331133	−	0.573539i
$58$	4.30902	−	3.13068i	0.565802	−	0.411079i
$59$	6.33810	+	7.03917i	0.825150	+	0.916422i	0.997645	−	0.0685886i	$-0.0218496\pi$
$59$	6.33810	+	7.03917i	0.825150	+	0.916422i	−0.172495	+	0.985010i	$0.555183\pi$
$60$	1.30902	+	4.02874i	0.168993	+	0.520108i
$61$	6.94427			0.889123			0.444561	−	0.895748i	$-0.353360\pi$
$61$	6.94427			0.889123			0.444561	+	0.895748i	$0.353360\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	−0.0729490	−	0.224514i	−0.00911863	−	0.0280642i
$65$	8.50345	+	9.44404i	1.05472	+	1.17139i
$66$	0.381966	−	0.277515i	0.0470168	−	0.0341597i
$67$	2.11803	+	3.66854i	0.258759	+	0.448184i	0.965910	−	0.258879i	$-0.0833531\pi$
$67$	2.11803	+	3.66854i	0.258759	+	0.448184i	−0.707151	+	0.707063i	$0.750020\pi$
$68$	−0.190983	+	0.330792i	−0.0231601	+	0.0401145i
$69$	−0.571994	−	5.44216i	−0.0688600	−	0.655159i
$70$	−3.92705	−	2.85317i	−0.469372	−	0.341019i
$71$	−0.00942533	+	0.0896760i	−0.00111858	+	0.0106426i	−0.995067	−	0.0992057i	$-0.968370\pi$
$71$	−0.00942533	+	0.0896760i	−0.00111858	+	0.0106426i	0.993948	+	0.109848i	$0.0350365\pi$
$72$	−2.99244	+	3.32344i	−0.352663	+	0.391672i
$73$	7.82206	+	3.48260i	0.915502	+	0.407608i	0.809744	−	0.586784i	$-0.199606\pi$
$73$	7.82206	+	3.48260i	0.915502	+	0.407608i	0.105759	+	0.994392i	$0.466273\pi$
$74$	−0.142710	−	0.0303339i	−0.0165897	−	0.00352625i
$75$	−1.81359	+	0.385489i	−0.209415	+	0.0445125i
$76$	−7.39074	+	3.29057i	−0.847776	+	0.377454i
$77$	0.708204	−	2.17963i	0.0807073	−	0.248392i
$78$	0.927051	−	2.85317i	0.104968	−	0.323058i
$79$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$79$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$80$	4.74803	−	1.00922i	0.530846	−	0.112835i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−3.65418	−	1.62695i	−0.403537	−	0.179666i
$83$	2.73686	−	3.03959i	0.300409	−	0.333638i	−0.573975	−	0.818873i	$-0.694599\pi$
$83$	2.73686	−	3.03959i	0.300409	−	0.333638i	0.874384	+	0.485235i	$0.161266\pi$
$84$	0.507392	−	4.82751i	0.0553610	−	0.526725i
$85$	−0.500000	−	0.363271i	−0.0542326	−	0.0394023i
$86$	0.298335	+	2.83847i	0.0321703	+	0.306080i
$87$	−4.30902	+	7.46344i	−0.461975	+	0.800164i
$88$	−0.854102	−	1.47935i	−0.0910476	−	0.157699i
$89$	−5.16312	+	3.75123i	−0.547290	+	0.397629i	−0.826785	−	0.562518i	$-0.809833\pi$
$89$	−5.16312	+	3.75123i	−0.547290	+	0.397629i	0.279496	+	0.960147i	$0.409833\pi$
$90$	−2.16535	−	2.40487i	−0.228248	−	0.253495i
$91$	−4.50000	−	13.8496i	−0.471728	−	1.45183i
$92$	−8.85410			−0.923104
$93$		0			0
$94$	2.09017			0.215585
$95$	−4.04508	−	12.4495i	−0.415017	−	1.27729i
$96$	−3.75920	−	4.17501i	−0.383672	−	0.426110i
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	−0.348834	−	0.937184i	$-0.613422\pi$
$97$	4.28115	−	3.11044i	0.434685	−	0.315817i	0.783520	+	0.621367i	$0.213422\pi$
$98$	0.618034	+	1.07047i	0.0624309	+	0.108133i
$99$	0.763932	−	1.32317i	0.0767781	−	0.132983i
$100$	0.313585	+	2.98357i	0.0313585	+	0.298357i
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	0.379288	−	0.925279i	$-0.376169\pi$
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	−0.762786	+	0.646651i	$0.776169\pi$
$102$	−0.0152505	+	0.145099i	−0.00151002	+	0.0143669i
$103$	−0.0976248	+	0.108423i	−0.00961926	+	0.0106833i	−0.747935	−	0.663772i	$-0.768955\pi$
$103$	−0.0976248	+	0.108423i	−0.00961926	+	0.0106833i	0.738316	+	0.674455i	$0.235621\pi$
$104$	−9.91572	−	4.41476i	−0.972316	−	0.432903i
$105$	7.68247	+	1.63296i	0.749732	+	0.159361i
$106$	7.68247	−	1.63296i	0.746188	−	0.158607i
$107$	0.995920	−	0.443412i	0.0962792	−	0.0428663i	−0.358032	−	0.933709i	$-0.616552\pi$
$107$	0.995920	−	0.443412i	0.0962792	−	0.0428663i	0.454311	+	0.890843i	$0.349885\pi$
$108$	2.50000	−	7.69421i	0.240563	−	0.740376i
$109$	−2.60081	+	8.00448i	−0.249113	+	0.766690i	0.745820	+	0.666147i	$0.232058\pi$
$109$	−2.60081	+	8.00448i	−0.249113	+	0.766690i	−0.994933	+	0.100543i	$0.967942\pi$
$110$	1.12920	−	0.502754i	0.107665	−	0.0479357i
$111$	0.230909	−	0.0490813i	0.0219169	−	0.00465859i
$112$	−5.44076	−	1.15647i	−0.514103	−	0.109276i
$113$	−1.69381	−	0.754131i	−0.159340	−	0.0709427i	0.325517	−	0.945536i	$-0.394462\pi$
$113$	−1.69381	−	0.754131i	−0.159340	−	0.0709427i	−0.484857	+	0.874593i	$0.661128\pi$
$114$	−2.06773	+	2.29644i	−0.193660	+	0.215082i
$115$	1.49750	−	14.2478i	0.139643	−	1.32861i
$116$	11.2812	+	8.19624i	1.04743	+	0.761002i
$117$	−1.01478	−	9.65502i	−0.0938168	−	0.892607i
$118$	2.92705	−	5.06980i	0.269457	−	0.466713i
$119$	0.354102	+	0.613323i	0.0324605	+	0.0562232i
$120$	4.73607	−	3.44095i	0.432342	−	0.314115i
$121$	−6.96994	−	7.74090i	−0.633631	−	0.703718i
$122$	−1.32624	−	4.08174i	−0.120072	−	0.369543i
$123$	6.47214			0.583573
$124$		0			0
$125$	8.23607			0.736656
$126$	1.14590	+	3.52671i	0.102085	+	0.314184i
$127$	−6.84927	−	7.60688i	−0.607774	−	0.675002i	0.358199	−	0.933645i	$-0.383391\pi$
$127$	−6.84927	−	7.60688i	−0.607774	−	0.675002i	−0.965973	+	0.258644i	$0.916724\pi$
$128$	−9.20820	+	6.69015i	−0.813898	+	0.591331i
$129$	−2.30902	−	3.99933i	−0.203298	−	0.352122i
$130$	3.92705	−	6.80185i	0.344425	−	0.596562i
$131$	−0.00942533	−	0.0896760i	−0.000823495	−	0.00783503i	0.994102	−	0.108445i	$-0.0345872\pi$
$131$	−0.00942533	−	0.0896760i	−0.000823495	−	0.00783503i	−0.994926	+	0.100610i	$0.967921\pi$
$132$	1.00000	+	0.726543i	0.0870388	+	0.0632374i
$133$	−1.56793	+	14.9178i	−0.135957	+	1.29354i
$134$	1.75181	−	1.94558i	0.151333	−	0.168072i
$135$	11.9585	+	5.32425i	1.02922	+	0.458239i
$136$	0.516329	+	0.109749i	0.0442748	+	0.00941091i
$137$	−6.33070	+	1.34563i	−0.540869	+	0.114965i	−0.470242	−	0.882538i	$-0.655833\pi$
$137$	−6.33070	+	1.34563i	−0.540869	+	0.114965i	−0.0706268	+	0.997503i	$0.522500\pi$
$138$	−3.08958	+	1.37557i	−0.263002	+	0.117096i
$139$	−1.80902	+	5.56758i	−0.153439	+	0.472236i	−0.997999	−	0.0632239i	$-0.979862\pi$
$139$	−1.80902	+	5.56758i	−0.153439	+	0.472236i	0.844561	+	0.535460i	$0.179862\pi$
$140$	3.92705	−	12.0862i	0.331896	−	1.02147i
$141$	−3.08958	+	1.37557i	−0.260190	+	0.115844i
$142$	0.0545103	−	0.0115865i	0.00457440	−	0.000972319i
$143$	3.62717	+	0.770979i	0.303319	+	0.0644725i
$144$	−3.38761	−	1.50826i	−0.282301	−	0.125689i
$145$	−15.0971	+	16.7671i	−1.25375	+	1.39243i
$146$	0.553143	−	5.26281i	0.0457785	−	0.435553i
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$	−0.0399263	−	0.379874i	−0.00328192	−	0.0312254i
$149$	8.51722	−	14.7523i	0.697758	−	1.20855i	−0.271484	−	0.962443i	$-0.587514\pi$
$149$	8.51722	−	14.7523i	0.697758	−	1.20855i	0.969242	−	0.246109i	$-0.0791522\pi$
$150$	0.572949	+	0.992377i	0.0467811	+	0.0810272i
$151$	−15.7812	+	11.4657i	−1.28425	+	0.933064i	−0.999673	−	0.0255888i	$-0.991854\pi$
$151$	−15.7812	+	11.4657i	−1.28425	+	0.933064i	−0.284579	+	0.958652i	$0.591854\pi$
$152$	7.48111	+	8.30861i	0.606798	+	0.673917i
$153$	0.145898	+	0.449028i	0.0117952	+	0.0363018i
$154$	−1.41641			−0.114137
$155$		0			0
$156$	7.85410			0.628831
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	0.996503	+	0.0835524i	$0.0266266\pi$
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	−0.757077	+	0.653325i	$0.773373\pi$
$158$		0			0
$159$	−10.2812	+	7.46969i	−0.815348	+	0.592385i
$160$	−7.35410	−	12.7377i	−0.581393	−	1.00700i
$161$	−8.20820	+	14.2170i	−0.646897	+	1.12046i
$162$	0.0646021	+	0.614648i	0.00507562	+	0.0482913i
$163$	10.2812	+	7.46969i	0.805282	+	0.585072i	0.912459	−	0.409168i	$-0.134181\pi$
$163$	10.2812	+	7.46969i	0.805282	+	0.585072i	−0.107177	+	0.994240i	$0.534181\pi$
$164$	1.09464	−	10.4148i	0.0854767	−	0.813257i
$165$	−1.33826	+	1.48629i	−0.104183	+	0.115707i
$166$	−2.30932	−	1.02817i	−0.179238	−	0.0798019i
$167$	−9.03424	−	1.92029i	−0.699090	−	0.148596i	−0.155362	−	0.987858i	$-0.549654\pi$
$167$	−9.03424	−	1.92029i	−0.699090	−	0.148596i	−0.543728	+	0.839261i	$0.682988\pi$
$168$	−6.56161	+	1.39471i	−0.506239	+	0.107605i
$169$	9.64915	−	4.29608i	0.742242	−	0.330467i
$170$	−0.118034	+	0.363271i	−0.00905279	+	0.0278616i
$171$	−3.09017	+	9.51057i	−0.236311	+	0.727291i
$172$	−6.82614	+	3.03919i	−0.520488	+	0.231736i
$173$	−0.889948	+	0.189164i	−0.0676615	+	0.0143819i	−0.241618	−	0.970371i	$-0.577678\pi$
$173$	−0.889948	+	0.189164i	−0.0676615	+	0.0143819i	0.173957	+	0.984753i	$0.444345\pi$
$174$	5.20985	+	1.10739i	0.394957	+	0.0839508i
$175$	5.08142	+	2.26239i	0.384119	+	0.171021i
$176$	0.947762	−	1.05260i	0.0714402	−	0.0793424i
$177$	−0.990108	+	9.42025i	−0.0744211	+	0.708069i
$178$	3.19098	+	2.31838i	0.239174	+	0.173770i
$179$	2.06949	+	19.6899i	0.154681	+	1.47169i	0.746372	+	0.665529i	$0.231794\pi$
$179$	2.06949	+	19.6899i	0.154681	+	1.47169i	−0.591691	+	0.806165i	$0.701539\pi$
$180$	4.23607	−	7.33708i	0.315738	−	0.546874i
$181$	8.50000	+	14.7224i	0.631800	+	1.09431i	0.987184	+	0.159589i	$0.0510169\pi$
$181$	8.50000	+	14.7224i	0.631800	+	1.09431i	−0.355383	+	0.934721i	$0.615650\pi$
$182$	−7.28115	+	5.29007i	−0.539715	+	0.392126i
$183$	4.64662	+	5.16060i	0.343488	+	0.381483i
$184$	3.78115	+	11.6372i	0.278750	+	0.857905i
$185$	0.618034			0.0454388
$186$		0			0
$187$	−0.180340			−0.0131878
$188$	1.69098	+	5.20431i	0.123328	+	0.379563i
$189$	−10.0370	−	11.1472i	−0.730081	−	0.810837i
$190$	−6.54508	+	4.75528i	−0.474830	+	0.344984i
$191$	8.04508	+	13.9345i	0.582122	+	1.00826i	0.995228	+	0.0975816i	$0.0311107\pi$
$191$	8.04508	+	13.9345i	0.582122	+	1.00826i	−0.413106	+	0.910683i	$0.635556\pi$
$192$	0.118034	−	0.204441i	0.00851837	−	0.0147542i
$193$	0.248983	+	2.36892i	0.0179222	+	0.170518i	0.999822	−	0.0188844i	$-0.00601146\pi$
$193$	0.248983	+	2.36892i	0.0179222	+	0.170518i	−0.981899	+	0.189403i	$0.939345\pi$
$194$	−2.64590	−	1.92236i	−0.189964	−	0.138017i
$195$	−1.32837	+	12.6386i	−0.0951265	+	0.905068i
$196$	−2.16535	+	2.40487i	−0.154668	+	0.171776i
$197$	−14.9971	−	6.67715i	−1.06850	−	0.475728i	−0.204318	−	0.978905i	$-0.565498\pi$
$197$	−14.9971	−	6.67715i	−1.06850	−	0.475728i	−0.864183	+	0.503177i	$0.832164\pi$
$198$	−0.923637	−	0.196325i	−0.0656400	−	0.0139522i
$199$	−26.1246	+	5.55295i	−1.85192	+	0.393638i	−0.992965	−	0.118410i	$-0.962220\pi$
$199$	−26.1246	+	5.55295i	−1.85192	+	0.393638i	−0.858957	+	0.512048i	$0.828887\pi$
$200$	3.78747	−	1.68629i	0.267814	−	0.119239i
$201$	−1.30902	+	4.02874i	−0.0923309	+	0.284165i
$202$	−0.909830	+	2.80017i	−0.0640154	+	0.197019i
$203$	23.6189	−	10.5158i	1.65772	−	0.738065i
$204$	−0.373619	+	0.0794152i	−0.0261586	+	0.00556018i
$205$	16.5740	+	3.52291i	1.15758	+	0.246051i
$206$	0.0823743	+	0.0366754i	0.00573929	+	0.00255530i
$207$	−7.32315	+	8.13318i	−0.508994	+	0.565295i
$208$	0.940756	−	8.95070i	0.0652297	−	0.620619i
$209$	−3.09017	−	2.24514i	−0.213752	−	0.155300i
$210$	−0.507392	−	4.82751i	−0.0350134	−	0.333130i
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	10.2812	+	17.8075i	0.706112	+	1.22302i
$213$	−0.0729490	+	0.0530006i	−0.00499838	+	0.00363154i
$214$	−0.450835	−	0.500703i	−0.0308184	−	0.0342273i
$215$	−3.73607	−	11.4984i	−0.254798	−	0.784187i
$216$	−11.1803			−0.760726
$217$		0			0
$218$	5.20163			0.352299
$219$	2.64590	+	8.14324i	0.178793	+	0.550269i
$220$	2.16535	+	2.40487i	0.145988	+	0.162136i
$221$	−0.927051	+	0.673542i	−0.0623602	+	0.0453073i
$222$	−0.0729490	−	0.126351i	−0.00489602	−	0.00848015i
$223$	0.354102	−	0.613323i	0.0237124	−	0.0410711i	−0.853926	−	0.520395i	$-0.825785\pi$
$223$	0.354102	−	0.613323i	0.0237124	−	0.0410711i	0.877638	+	0.479324i	$0.159118\pi$
$224$	1.76173	+	16.7618i	0.117711	+	1.11994i
$225$	3.00000	+	2.17963i	0.200000	+	0.145309i
$226$	−0.119779	+	1.13962i	−0.00796758	+	0.0758064i
$227$	−13.8795	+	15.4148i	−0.921217	+	1.02312i	0.0784394	+	0.996919i	$0.475006\pi$
$227$	−13.8795	+	15.4148i	−0.921217	+	1.02312i	−0.999657	+	0.0261967i	$0.991660\pi$
$228$	−7.39074	−	3.29057i	−0.489464	−	0.217923i
$229$	−7.07794	−	1.50446i	−0.467724	−	0.0994177i	−0.0319799	−	0.999489i	$-0.510181\pi$
$229$	−7.07794	−	1.50446i	−0.467724	−	0.0994177i	−0.435744	+	0.900071i	$0.643515\pi$
$230$	−8.66062	+	1.84087i	−0.571064	+	0.121383i
$231$	2.09366	−	0.932157i	0.137753	−	0.0613315i
$232$	5.95492	−	18.3273i	0.390959	−	1.20325i
$233$	5.80902	−	17.8783i	0.380561	−	1.17125i	−0.559088	−	0.829108i	$-0.688849\pi$
$233$	5.80902	−	17.8783i	0.380561	−	1.17125i	0.939649	−	0.342139i	$-0.111151\pi$
$234$	−5.48127	+	2.44042i	−0.358322	+	0.159535i
$235$	−8.66062	+	1.84087i	−0.564956	+	0.120085i
$236$	14.9913	+	3.18650i	0.975852	+	0.207424i
$237$		0			0
$238$	0.292875	−	0.325270i	0.0189842	−	0.0210841i
$239$	−1.40240	+	13.3429i	−0.0907135	+	0.863081i	0.850660	+	0.525716i	$0.176202\pi$
$239$	−1.40240	+	13.3429i	−0.0907135	+	0.863081i	−0.941374	+	0.337365i	$0.890464\pi$
$240$	3.92705	+	2.85317i	0.253490	+	0.184171i
$241$	−0.891405	−	8.48115i	−0.0574204	−	0.546319i	−0.984983	−	0.172651i	$-0.944767\pi$
$241$	−0.891405	−	8.48115i	−0.0574204	−	0.546319i	0.927563	−	0.373668i	$-0.121900\pi$
$242$	−3.21885	+	5.57521i	−0.206915	+	0.358388i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	9.09017	−	6.60440i	0.581938	−	0.422803i
$245$	−3.50361	−	3.89116i	−0.223838	−	0.248597i
$246$	−1.23607	−	3.80423i	−0.0788088	−	0.242549i
$247$	−24.2705			−1.54430
$248$		0			0
$249$	4.09017			0.259204
$250$	−1.57295	−	4.84104i	−0.0994820	−	0.306174i
$251$	−0.631841	−	0.701731i	−0.0398815	−	0.0442929i	0.722874	−	0.690980i	$-0.242821\pi$
$251$	−0.631841	−	0.701731i	−0.0398815	−	0.0442929i	−0.762755	+	0.646687i	$0.776154\pi$
$252$	−7.85410	+	5.70634i	−0.494762	+	0.359466i
$253$	−2.09017	−	3.62028i	−0.131408	−	0.227605i
$254$	−3.16312	+	5.47868i	−0.198472	+	0.343763i
$255$	−0.0646021	−	0.614648i	−0.00404554	−	0.0384908i
$256$	5.30902	+	3.85723i	0.331814	+	0.241077i
$257$	−0.148055	+	1.40865i	−0.00923541	+	0.0878691i	−0.998169	−	0.0604919i	$-0.980733\pi$
$257$	−0.148055	+	1.40865i	−0.00923541	+	0.0878691i	0.988933	+	0.148361i	$0.0473997\pi$
$258$	−1.90977	+	2.12101i	−0.118897	+	0.132048i
$259$	−0.646976	−	0.288052i	−0.0402012	−	0.0178987i
$260$	20.1130	+	4.27514i	1.24735	+	0.265133i
$261$	16.8594	−	3.58358i	1.04357	−	0.221818i
$262$	−0.0509101	+	0.0226667i	−0.00314524	+	0.00140035i
$263$	3.33688	−	10.2699i	0.205761	−	0.633267i	−0.793920	−	0.608022i	$-0.791963\pi$
$263$	3.33688	−	10.2699i	0.205761	−	0.633267i	0.999681	−	0.0252452i	$-0.00803665\pi$
$264$	0.527864	−	1.62460i	0.0324878	−	0.0999871i
$265$	−30.3941	+	13.5323i	−1.86710	+	0.831285i
$266$	9.06793	−	1.92745i	0.555990	−	0.118179i
$267$	−6.24250	−	1.32689i	−0.382035	−	0.0812041i
$268$	6.26153	+	2.78781i	0.382484	+	0.170293i
$269$	0.924716	−	1.02700i	0.0563809	−	0.0626173i	−0.714295	−	0.699845i	$-0.753252\pi$
$269$	0.924716	−	1.02700i	0.0563809	−	0.0626173i	0.770675	+	0.637228i	$0.219919\pi$
$270$	0.845653	−	8.04585i	0.0514648	−	0.489655i
$271$	7.73607	+	5.62058i	0.469933	+	0.341426i	0.797415	−	0.603431i	$-0.206200\pi$
$271$	7.73607	+	5.62058i	0.469933	+	0.341426i	−0.327482	+	0.944857i	$0.606200\pi$
$272$	0.0457515	+	0.435296i	0.00277409	+	0.0263937i
$273$	7.28115	−	12.6113i	0.440675	−	0.763272i
$274$	2.00000	+	3.46410i	0.120824	+	0.209274i
$275$	−1.14590	+	0.832544i	−0.0691003	+	0.0502043i
$276$	−5.92455	−	6.57988i	−0.356616	−	0.396062i
$277$	−4.11803	−	12.6740i	−0.247429	−	0.761507i	−0.995228	−	0.0975818i	$-0.968889\pi$
$277$	−4.11803	−	12.6740i	−0.247429	−	0.761507i	0.747799	−	0.663925i	$-0.231111\pi$
$278$	3.61803			0.216995
$279$		0			0
$280$	−17.5623			−1.04955
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	0.958355	+	0.285579i	$0.0921859\pi$
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	−0.607466	+	0.794345i	$0.707814\pi$
$282$	1.39860	+	1.55330i	0.0832852	+	0.0924976i
$283$	−5.30902	+	3.85723i	−0.315588	+	0.229288i	−0.734291	−	0.678835i	$-0.762485\pi$
$283$	−5.30902	+	3.85723i	−0.315588	+	0.229288i	0.418702	+	0.908124i	$0.362485\pi$
$284$	0.0729490	+	0.126351i	0.00432873	+	0.00749758i
$285$	6.54508	−	11.3364i	0.387697	−	0.671512i
$286$	−0.239558	−	2.27924i	−0.0141654	−	0.134774i
$287$	−15.7082	−	11.4127i	−0.927226	−	0.673669i
$288$	−1.17449	+	11.1745i	−0.0692074	+	0.658465i
$289$	−11.3379	+	12.5920i	−0.666937	+	0.740709i
$290$	12.7387	+	5.67165i	0.748044	+	0.333051i
$291$	5.17616	+	1.10023i	0.303432	+	0.0644964i
$292$	13.5514	−	2.88043i	0.793033	−	0.168564i
$293$	−7.52402	+	3.34991i	−0.439558	+	0.195704i	−0.614570	−	0.788862i	$-0.710670\pi$
$293$	−7.52402	+	3.34991i	−0.439558	+	0.195704i	0.175012	+	0.984566i	$0.444004\pi$
$294$	−0.381966	+	1.17557i	−0.0222767	+	0.0685607i
$295$	−7.66312	+	23.5847i	−0.446164	+	1.37315i
$296$	−0.482228	+	0.214702i	−0.0280289	+	0.0124793i
$297$	3.73619	−	0.794152i	0.216796	−	0.0460814i
$298$	−10.2978	−	2.18887i	−0.596536	−	0.126798i
$299$	−24.2659	−	10.8039i	−1.40333	−	0.624804i
$300$	−2.00739	+	2.22943i	−0.115897	+	0.128716i
$301$	−1.44815	+	13.7782i	−0.0834699	+	0.794163i
$302$	9.75329	+	7.08618i	0.561239	+	0.407764i
$303$	−0.497966	−	4.73783i	−0.0286074	−	0.272181i
$304$	−4.63525	+	8.02850i	−0.265850	+	0.460466i
$305$	9.09017	+	15.7446i	0.520502	+	0.901535i
$306$	0.236068	−	0.171513i	0.0134951	−	0.00980477i
$307$	4.07512	+	4.52588i	0.232579	+	0.258306i	0.848126	−	0.529795i	$-0.177731\pi$
$307$	4.07512	+	4.52588i	0.232579	+	0.258306i	−0.615546	+	0.788101i	$0.711065\pi$
$308$	−1.14590	−	3.52671i	−0.0652936	−	0.200953i
$309$	−0.145898			−0.00829985
$310$		0			0
$311$	16.4721			0.934049			0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721			0.934049			0.467025	+	0.884244i	$0.345326\pi$
$312$	−3.35410	−	10.3229i	−0.189889	−	0.584417i
$313$	−0.827091	−	0.918578i	−0.0467499	−	0.0519211i	0.719316	−	0.694683i	$-0.244455\pi$
$313$	−0.827091	−	0.918578i	−0.0467499	−	0.0519211i	−0.766066	+	0.642762i	$0.777789\pi$
$314$	4.85410	−	3.52671i	0.273933	−	0.199024i
$315$	−7.85410	−	13.6037i	−0.442529	−	0.766482i
$316$		0			0
$317$	−2.70609	−	25.7467i	−0.151989	−	1.44608i	−0.758847	−	0.651269i	$-0.774237\pi$
$317$	−2.70609	−	25.7467i	−0.151989	−	1.44608i	0.606857	−	0.794811i	$-0.292430\pi$
$318$	6.35410	+	4.61653i	0.356320	+	0.258882i
$319$	−0.688173	+	6.54753i	−0.0385303	+	0.366591i
$320$	0.413545	−	0.459289i	0.0231179	−	0.0256750i
$321$	0.995920	+	0.443412i	0.0555868	+	0.0247488i
$322$	9.92419	+	2.10945i	0.553053	+	0.117555i
$323$	1.15455	−	0.245406i	0.0642407	−	0.0136548i
$324$	−1.47815	+	0.658114i	−0.0821193	+	0.0365619i
$325$	−2.78115	+	8.55951i	−0.154271	+	0.474796i
$326$	2.42705	−	7.46969i	0.134422	−	0.413708i
$327$	−7.68877	+	3.42326i	−0.425190	+	0.189307i
$328$	−14.1559	+	3.00893i	−0.781628	+	0.166140i
$329$	9.92419	+	2.10945i	0.547138	+	0.116298i
$330$	1.12920	+	0.502754i	0.0621607	+	0.0276757i
$331$	−7.54144	+	8.37562i	−0.414515	+	0.460366i	−0.913855	−	0.406040i	$-0.866909\pi$
$331$	−7.54144	+	8.37562i	−0.414515	+	0.460366i	0.499340	+	0.866406i	$0.333576\pi$
$332$	0.691773	−	6.58178i	0.0379660	−	0.361222i
$333$	−0.381966	−	0.277515i	−0.0209316	−	0.0152077i
$334$	0.596670	+	5.67693i	0.0326483	+	0.310628i
$335$	−5.54508	+	9.60437i	−0.302960	+	0.524743i
$336$	−2.78115	−	4.81710i	−0.151724	−	0.262794i
$337$	15.3541	−	11.1554i	0.836391	−	0.607674i	−0.0849690	−	0.996384i	$-0.527079\pi$
$337$	15.3541	−	11.1554i	0.836391	−	0.607674i	0.921360	+	0.388710i	$0.127079\pi$
$338$	−4.36799	−	4.85115i	−0.237588	−	0.263868i
$339$	−0.572949	−	1.76336i	−0.0311183	−	0.0957723i
$340$	−1.00000			−0.0542326
$341$		0			0
$342$	6.18034			0.334195
$343$	−4.63525	−	14.2658i	−0.250280	−	0.770283i
$344$	6.90960	+	7.67389i	0.372541	+	0.413748i
$345$	11.5902	−	8.42075i	0.623994	−	0.453358i
$346$	0.281153	+	0.486971i	0.0151149	+	0.0261797i
$347$	4.06231	−	7.03612i	0.218076	−	0.377719i	−0.736144	−	0.676825i	$-0.763355\pi$
$347$	4.06231	−	7.03612i	0.218076	−	0.377719i	0.954220	+	0.299107i	$0.0966886\pi$
$348$	1.45757	+	13.8679i	0.0781341	+	0.743397i
$349$	13.5172	+	9.82084i	0.723560	+	0.525697i	0.887520	−	0.460770i	$-0.152427\pi$
$349$	13.5172	+	9.82084i	0.723560	+	0.525697i	−0.163959	+	0.986467i	$0.552427\pi$
$350$	0.359337	−	3.41886i	0.0192074	−	0.182746i
$351$	16.2401	−	18.0365i	0.866835	−	0.962717i
$352$	−3.92075	−	1.74563i	−0.208977	−	0.0930424i
$353$	−31.6743	−	6.73259i	−1.68586	−	0.358340i	−0.737450	−	0.675401i	$-0.763970\pi$
$353$	−31.6743	−	6.73259i	−1.68586	−	0.358340i	−0.948405	+	0.317062i	$0.897304\pi$
$354$	5.72618	−	1.21714i	0.304343	−	0.0646901i
$355$	−0.215659	+	0.0960175i	−0.0114460	+	0.00509608i
$356$	−3.19098	+	9.82084i	−0.169122	+	0.520503i
$357$	−0.218847	+	0.673542i	−0.0115826	+	0.0356476i
$358$	11.1782	−	4.97686i	0.590786	−	0.263035i
$359$	24.7728	−	5.26562i	1.30746	−	0.277909i	0.499072	−	0.866561i	$-0.333674\pi$
$359$	24.7728	−	5.26562i	1.30746	−	0.277909i	0.808387	+	0.588652i	$0.200341\pi$
$360$	−11.4524	−	2.43427i	−0.603592	−	0.128297i
$361$	5.48127	+	2.44042i	0.288488	+	0.128443i
$362$	7.03027	−	7.80791i	0.369503	−	0.410375i
$363$	1.08881	−	10.3593i	0.0571478	−	0.543725i
$364$	−19.0623	−	13.8496i	−0.999136	−	0.725915i
$365$	2.34315	+	22.2936i	0.122646	+	1.16690i
$366$	2.14590	−	3.71680i	0.112168	−	0.194280i
$367$	−18.1353	−	31.4112i	−0.946653	−	1.63965i	−0.752408	−	0.658697i	$-0.771108\pi$
$367$	−18.1353	−	31.4112i	−0.946653	−	1.63965i	−0.194245	−	0.980953i	$-0.562226\pi$
$368$	−8.20820	+	5.96361i	−0.427882	+	0.310875i
$369$	−8.66141	−	9.61947i	−0.450895	−	0.500770i
$370$	−0.118034	−	0.363271i	−0.00613629	−	0.0188856i
$371$	38.1246			1.97933
$372$		0			0
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$	0.0344419	+	0.106001i	0.00178095	+	0.00548119i
$375$	5.51101	+	6.12059i	0.284587	+	0.316066i
$376$	6.11803	−	4.44501i	0.315514	−	0.229234i
$377$	20.9164	+	36.2283i	1.07725	+	1.86585i
$378$	−4.63525	+	8.02850i	−0.238412	+	0.412941i
$379$	1.92504	+	18.3155i	0.0988826	+	0.940805i	0.925681	+	0.378306i	$0.123493\pi$
$379$	1.92504	+	18.3155i	0.0988826	+	0.940805i	−0.826798	+	0.562499i	$0.809840\pi$
$380$	−17.1353	−	12.4495i	−0.879020	−	0.638645i
$381$	1.06996	−	10.1800i	0.0548157	−	0.521537i
$382$	6.65402	−	7.39003i	0.340449	−	0.378107i
$383$	15.3970	+	6.85518i	0.786749	+	0.350283i	0.760472	−	0.649371i	$-0.224968\pi$
$383$	15.3970	+	6.85518i	0.786749	+	0.350283i	0.0262778	+	0.999655i	$0.491635\pi$
$384$	−11.1332	−	2.36644i	−0.568141	−	0.120762i
$385$	5.86889	−	1.24747i	0.299106	−	0.0635770i
$386$	1.34486	−	0.598772i	0.0684517	−	0.0304767i
$387$	−2.85410	+	8.78402i	−0.145082	+	0.446517i
$388$	2.64590	−	8.14324i	0.134325	−	0.413410i
$389$	26.5557	−	11.8234i	1.34643	−	0.599469i	0.398271	−	0.917268i	$-0.369610\pi$
$389$	26.5557	−	11.8234i	1.34643	−	0.599469i	0.948158	+	0.317798i	$0.102944\pi$
$390$	7.68247	−	1.63296i	0.389017	−	0.0826881i
$391$	1.26357	+	0.268580i	0.0639013	+	0.0135826i
$392$	4.08550	+	1.81898i	0.206349	+	0.0918724i
$393$	0.0603355	−	0.0670093i	0.00304352	−	0.00338017i
$394$	−1.06054	+	10.0903i	−0.0534290	+	0.508343i
$395$		0			0
$396$	−0.258409	−	2.45859i	−0.0129855	−	0.123549i
$397$	−8.14590	+	14.1091i	−0.408831	+	0.708116i	−0.994759	−	0.102247i	$-0.967397\pi$
$397$	−8.14590	+	14.1091i	−0.408831	+	0.708116i	0.585928	+	0.810363i	$0.300730\pi$
$398$	8.25329	+	14.2951i	0.413700	+	0.716549i
$399$	−12.1353	+	8.81678i	−0.607523	+	0.441391i
$400$	2.30027	+	2.55470i	0.115013	+	0.127735i
$401$	9.21885	+	28.3727i	0.460367	+	1.41686i	0.864717	+	0.502260i	$0.167498\pi$
$401$	9.21885	+	28.3727i	0.460367	+	1.41686i	−0.404349	+	0.914605i	$0.632502\pi$
$402$	2.61803			0.130576
$403$		0			0
$404$	−7.70820			−0.383497
$405$	−0.809017	−	2.48990i	−0.0402004	−	0.123724i
$406$	−10.6918	−	11.8745i	−0.530627	−	0.589321i
$407$	0.145898	−	0.106001i	0.00723190	−	0.00525428i
$408$	0.263932	+	0.457144i	0.0130666	+	0.0226320i
$409$	−3.09017	+	5.35233i	−0.152799	+	0.264656i	−0.932255	−	0.361801i	$-0.882162\pi$
$409$	−3.09017	+	5.35233i	−0.152799	+	0.264656i	0.779456	+	0.626457i	$0.215495\pi$
$410$	−1.09464	−	10.4148i	−0.0540602	−	0.514349i
$411$	−5.23607	−	3.80423i	−0.258276	−	0.187649i
$412$	−0.0246758	+	0.234775i	−0.00121569	+	0.0115665i
$413$	19.0143	−	21.1175i	0.935632	−	1.03912i
$414$	6.17916	+	2.75114i	0.303689	+	0.135211i
$415$	10.4742	+	2.22636i	0.514158	+	0.109288i
$416$	−26.6746	+	5.66986i	−1.30783	+	0.277988i
$417$	−5.34799	+	2.38108i	−0.261892	+	0.116602i
$418$	−0.729490	+	2.24514i	−0.0356805	+	0.109813i
$419$	1.38197	−	4.25325i	0.0675135	−	0.207785i	−0.911608	−	0.411060i	$-0.865159\pi$
$419$	1.38197	−	4.25325i	0.0675135	−	0.207785i	0.979122	+	0.203275i	$0.0651586\pi$
$420$	11.6095	−	5.16889i	0.566487	−	0.252216i
$421$	−14.4413	+	3.06959i	−0.703826	+	0.149603i	−0.545903	−	0.837849i	$-0.683813\pi$
$421$	−14.4413	+	3.06959i	−0.703826	+	0.149603i	−0.157923	+	0.987451i	$0.550480\pi$
$422$	−4.83623	−	1.02797i	−0.235424	−	0.0500409i
$423$	6.17916	+	2.75114i	0.300441	+	0.133765i
$424$	19.0143	−	21.1175i	0.923415	−	1.02556i
$425$	0.0457515	−	0.435296i	0.00221927	−	0.0211150i
$426$	0.0450850	+	0.0327561i	0.00218437	+	0.00158704i
$427$	−2.17762	−	20.7187i	−0.105383	−	1.00265i
$428$	0.881966	−	1.52761i	0.0426314	−	0.0738398i
$429$	1.85410	+	3.21140i	0.0895169	+	0.155048i
$430$	−6.04508	+	4.39201i	−0.291520	+	0.211802i
$431$	19.5627	+	21.7266i	0.942304	+	1.04654i	0.998841	+	0.0481345i	$0.0153276\pi$
$431$	19.5627	+	21.7266i	0.942304	+	1.04654i	−0.0565365	+	0.998401i	$0.518006\pi$
$432$	−2.86475	−	8.81678i	−0.137830	−	0.424197i
$433$	−0.583592			−0.0280456			−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592			−0.0280456			−0.0140228	+	0.999902i	$0.504464\pi$
$434$		0			0
$435$	−22.5623			−1.08178
$436$	4.20820	+	12.9515i	0.201536	+	0.620265i
$437$	18.3079	+	20.3329i	0.875784	+	0.972657i
$438$	4.28115	−	3.11044i	0.204561	−	0.148623i
$439$	−20.9164	−	36.2283i	−0.998286	−	1.72908i	−0.549831	−	0.835276i	$-0.685308\pi$
$439$	−20.9164	−	36.2283i	−0.998286	−	1.72908i	−0.448455	−	0.893805i	$-0.648026\pi$
$440$	2.23607	−	3.87298i	0.106600	−	0.184637i
$441$	0.418114	+	3.97809i	0.0199102	+	0.189433i
$442$	0.572949	+	0.416272i	0.0272524	+	0.0198000i
$443$	4.29869	−	40.8993i	0.204237	−	1.94319i	−0.110205	−	0.993909i	$-0.535151\pi$
$443$	4.29869	−	40.8993i	0.204237	−	1.94319i	0.314442	−	0.949277i	$-0.398183\pi$
$444$	0.255585	−	0.283856i	0.0121295	−	0.0134712i
$445$	−15.2637	−	6.79584i	−0.723569	−	0.322154i
$446$	−0.428129	−	0.0910017i	−0.0202725	−	0.00430906i
$447$	16.6622	−	3.54166i	0.788095	−	0.167515i
$448$	−0.646976	+	0.288052i	−0.0305668	+	0.0136092i
$449$	−7.43769	+	22.8909i	−0.351006	+	1.08029i	0.607283	+	0.794486i	$0.292260\pi$
$449$	−7.43769	+	22.8909i	−0.351006	+	1.08029i	−0.958289	+	0.285801i	$0.907740\pi$
$450$	0.708204	−	2.17963i	0.0333851	−	0.102749i
$451$	4.51682	−	2.01102i	0.212689	−	0.0946951i
$452$	−2.93444	+	0.623735i	−0.138025	+	0.0293380i
$453$	−19.0803	−	4.05565i	−0.896471	−	0.190551i
$454$	11.7113	+	5.21423i	0.549641	+	0.244716i
$455$	25.5103	−	28.3321i	1.19594	−	1.32823i
$456$	−1.16866	+	11.1191i	−0.0547277	+	0.520699i
$457$	−12.7361	−	9.25330i	−0.595768	−	0.432851i	0.248606	−	0.968605i	$-0.420028\pi$
$457$	−12.7361	−	9.25330i	−0.595768	−	0.432851i	−0.844374	+	0.535754i	$0.820028\pi$
$458$	0.467465	+	4.44764i	0.0218432	+	0.207824i
$459$	−0.590170	+	1.02220i	−0.0275468	+	0.0477124i
$460$	−11.5902	−	20.0748i	−0.540394	−	0.935991i
$461$	8.69098	−	6.31437i	0.404779	−	0.294089i	−0.366705	−	0.930337i	$-0.619514\pi$
$461$	8.69098	−	6.31437i	0.404779	−	0.294089i	0.771485	+	0.636248i	$0.219514\pi$
$462$	−0.947762	−	1.05260i	−0.0440939	−	0.0489712i
$463$	9.61803	+	29.6013i	0.446988	+	1.37569i	0.880289	+	0.474438i	$0.157349\pi$
$463$	9.61803	+	29.6013i	0.446988	+	1.37569i	−0.433301	+	0.901249i	$0.642651\pi$
$464$	15.9787			0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	−10.1287	−	31.1729i	−0.468699	−	1.44251i	−0.854270	−	0.519830i	$-0.825995\pi$
$467$	−10.1287	−	31.1729i	−0.468699	−	1.44251i	0.385571	−	0.922678i	$-0.374005\pi$
$468$	−10.5108	−	11.6735i	−0.485864	−	0.539606i
$469$	10.2812	−	7.46969i	0.474740	−	0.344918i
$470$	2.73607	+	4.73901i	0.126205	+	0.218594i
$471$	−4.85410	+	8.40755i	−0.223665	+	0.387400i
$472$	−2.21395	−	21.0643i	−0.101905	−	0.969564i
$473$	−2.85410	−	2.07363i	−0.131232	−	0.0953454i
$474$		0			0
$475$	6.20318	−	6.88933i	0.284622	−	0.316104i
$476$	1.04683	+	0.466079i	0.0479814	+	0.0213627i
$477$	24.8610	+	5.28437i	1.13831	+	0.241955i
$478$	8.11060	−	1.72396i	0.370970	−	0.0788522i
$479$	−8.17100	+	3.63796i	−0.373342	+	0.166223i	−0.584826	−	0.811159i	$-0.698837\pi$
$479$	−8.17100	+	3.63796i	−0.373342	+	0.166223i	0.211483	+	0.977382i	$0.432171\pi$
$480$	4.54508	−	13.9883i	0.207454	−	0.638477i
$481$	0.354102	−	1.08981i	0.0161457	−	0.0496912i
$482$	−4.81485	+	2.14371i	−0.219310	+	0.0976433i
$483$	−16.0577	+	3.41316i	−0.730649	+	0.155304i
$484$	−16.4858	−	3.50416i	−0.749355	−	0.159280i
$485$	12.6564	+	5.63497i	0.574695	+	0.255871i
$486$	−6.61673	+	7.34862i	−0.300141	+	0.333340i
$487$	2.39610	−	22.7974i	0.108578	−	1.03305i	−0.795579	−	0.605849i	$-0.792833\pi$
$487$	2.39610	−	22.7974i	0.108578	−	1.03305i	0.904157	−	0.427200i	$-0.140500\pi$
$488$	−12.5623	−	9.12705i	−0.568669	−	0.413162i
$489$	1.32837	+	12.6386i	0.0600709	+	0.571537i
$490$	−1.61803	+	2.80252i	−0.0730953	+	0.126605i
$491$	−13.7984	−	23.8995i	−0.622712	−	1.07857i	−0.988979	−	0.148059i	$-0.952698\pi$
$491$	−13.7984	−	23.8995i	−0.622712	−	1.07857i	0.366267	−	0.930510i	$-0.380636\pi$
$492$	8.47214	−	6.15537i	0.381953	−	0.277505i
$493$	−1.36131	−	1.51188i	−0.0613102	−	0.0680919i
$494$	4.63525	+	14.2658i	0.208550	+	0.641851i
$495$	4.00000			0.179787
$496$		0			0
$497$	0.270510			0.0121340
$498$	−0.781153	−	2.40414i	−0.0350043	−	0.107732i
$499$	−2.77415	−	3.08100i	−0.124188	−	0.137925i	0.677844	−	0.735206i	$-0.262914\pi$
$499$	−2.77415	−	3.08100i	−0.124188	−	0.137925i	−0.802032	+	0.597281i	$0.796248\pi$
$500$	10.7812	−	7.83297i	0.482148	−	0.350301i
$501$	−4.61803	−	7.99867i	−0.206319	−	0.357354i
$502$	−0.291796	+	0.505406i	−0.0130235	+	0.0225574i
$503$	−1.37412	−	13.0739i	−0.0612690	−	0.582936i	−0.981487	−	0.191529i	$-0.938655\pi$
$503$	−1.37412	−	13.0739i	−0.0612690	−	0.582936i	0.920218	−	0.391406i	$-0.128011\pi$
$504$	10.8541	+	7.88597i	0.483480	+	0.351269i
$505$	1.30369	−	12.4038i	0.0580136	−	0.551962i
$506$	−1.72876	+	1.91998i	−0.0768528	+	0.0853537i
$507$	9.64915	+	4.29608i	0.428534	+	0.190795i
$508$	−16.2004	−	3.44350i	−0.718776	−	0.152780i
$509$	−1.86810	+	0.397076i	−0.0828019	+	0.0176001i	−0.249126	−	0.968471i	$-0.580143\pi$
$509$	−1.86810	+	0.397076i	−0.0828019	+	0.0176001i	0.166324	+	0.986071i	$0.446810\pi$
$510$	−0.348943	+	0.155360i	−0.0154515	+	0.00687944i
$511$	7.93769	−	24.4297i	0.351143	−	1.08071i
$512$	−5.78115	+	17.7926i	−0.255493	+	0.786327i
$513$	−22.8386	+	10.1684i	−1.00835	+	0.448947i
$514$	0.856259	−	0.182003i	0.0377680	−	0.00802783i
$515$	−0.373619	−	0.0794152i	−0.0164636	−	0.00349945i
$516$	−6.82614	−	3.03919i	−0.300504	−	0.133793i
$517$	−1.72876	+	1.91998i	−0.0760308	+	0.0844408i
$518$	−0.0457515	+	0.435296i	−0.00201021	+	0.0191258i
$519$	−0.736068	−	0.534785i	−0.0323098	−	0.0234744i
$520$	−2.97032	−	28.2607i	−0.130257	−	1.23932i
$521$	−15.5344	+	26.9064i	−0.680576	+	1.17879i	0.294229	+	0.955735i	$0.404937\pi$
$521$	−15.5344	+	26.9064i	−0.680576	+	1.17879i	−0.974805	+	0.223058i	$0.928396\pi$
$522$	−5.32624	−	9.22531i	−0.233123	−	0.403781i
$523$	27.6074	−	20.0579i	1.20719	−	0.877073i	0.212215	−	0.977223i	$-0.431932\pi$
$523$	27.6074	−	20.0579i	1.20719	−	0.877073i	0.994972	+	0.100150i	$0.0319324\pi$
$524$	−0.0976248	−	0.108423i	−0.00426476	−	0.00473650i
$525$	1.71885	+	5.29007i	0.0750166	+	0.230877i
$526$	−6.67376			−0.290990
$527$		0			0
$528$	1.41641			0.0616412
$529$	2.14590	+	6.60440i	0.0932999	+	0.287148i
$530$	13.7589	+	15.2808i	0.597647	+	0.663754i
$531$	15.3262	−	11.1352i	0.665102	−	0.483225i
$532$	12.1353	+	21.0189i	0.526130	+	0.911284i
$533$	15.7082	−	27.2074i	0.680398	−	1.17848i
$534$	0.412289	+	3.92266i	0.0178415	+	0.169750i
$535$	2.30902	+	1.67760i	0.0998275	+	0.0725289i
$536$	0.990108	−	9.42025i	0.0427661	−	0.406893i
$537$	−13.2477	+	14.7131i	−0.571680	+	0.634915i
$538$	−0.780261	−	0.347395i	−0.0336394	−	0.0149772i
$539$	−1.49448	−	0.317661i	−0.0643717	−	0.0136826i
$540$	20.7175	−	4.40364i	0.891539	−	0.189503i
$541$	20.0980	−	8.94821i	0.864081	−	0.384713i	0.0736639	−	0.997283i	$-0.476531\pi$
$541$	20.0980	−	8.94821i	0.864081	−	0.384713i	0.790417	+	0.612570i	$0.209864\pi$
$542$	1.82624	−	5.62058i	0.0784436	−	0.241425i
$543$	−5.25329	+	16.1680i	−0.225440	+	0.693834i
$544$	1.21158	−	0.539430i	0.0519460	−	0.0231279i
$545$	−21.5529	+	4.58122i	−0.923226	+	0.196238i
$546$	−8.80333	−	1.87121i	−0.376748	−	0.0800802i
$547$	−21.6585	−	9.64300i	−0.926052	−	0.412305i	−0.112404	−	0.993663i	$-0.535855\pi$
$547$	−21.6585	−	9.64300i	−0.926052	−	0.412305i	−0.813648	+	0.581358i	$0.802522\pi$
$548$	−7.00723	+	7.78231i	−0.299334	+	0.332444i
$549$	1.45175	−	13.8125i	0.0619591	−	0.589501i
$550$	0.708204	+	0.514540i	0.0301979	+	0.0219401i
$551$	−4.50415	−	42.8541i	−0.191883	−	1.82565i
$552$	−6.11803	+	10.5967i	−0.260401	+	0.451027i
$553$		0			0
$554$	−6.66312	+	4.84104i	−0.283089	+	0.205676i
$555$	0.413545	+	0.459289i	0.0175540	+	0.0194957i
$556$	2.92705	+	9.00854i	0.124135	+	0.382047i
$557$	−35.8885			−1.52065			−0.760323	−	0.649545i	$-0.774959\pi$
$557$	−35.8885			−1.52065			−0.760323	+	0.649545i	$0.774959\pi$
$558$		0			0
$559$	−22.4164			−0.948113
$560$	−4.50000	−	13.8496i	−0.190160	−	0.585251i
$561$	−0.120671	−	0.134019i	−0.00509473	−	0.00565827i
$562$	9.51722	−	6.91467i	0.401460	−	0.291678i
$563$	4.28115	+	7.41517i	0.180429	+	0.312512i	0.942027	−	0.335538i	$-0.108918\pi$
$563$	4.28115	+	7.41517i	0.180429	+	0.312512i	−0.761598	+	0.648050i	$0.775585\pi$
$564$	−2.73607	+	4.73901i	−0.115209	+	0.199548i
$565$	−0.507392	−	4.82751i	−0.0213461	−	0.203095i
$566$	3.28115	+	2.38390i	0.137917	+	0.100203i
$567$	−0.313585	+	2.98357i	−0.0131693	+	0.125298i
$568$	0.134914	−	0.149837i	0.00566087	−	0.00628704i
$569$	−14.1854	−	6.31575i	−0.594683	−	0.264770i	0.0872476	−	0.996187i	$-0.472193\pi$
$569$	−14.1854	−	6.31575i	−0.594683	−	0.264770i	−0.681931	+	0.731417i	$0.738860\pi$
$570$	−7.91338	−	1.68204i	−0.331455	−	0.0704529i
$571$	6.84703	−	1.45538i	0.286539	−	0.0609058i	−0.0623997	−	0.998051i	$-0.519875\pi$
$571$	6.84703	−	1.45538i	0.286539	−	0.0609058i	0.348939	+	0.937145i	$0.386542\pi$
$572$	5.48127	−	2.44042i	0.229184	−	0.102039i
$573$	−4.97214	+	15.3027i	−0.207714	+	0.639278i
$574$	−3.70820	+	11.4127i	−0.154777	+	0.476356i
$575$	9.26874	−	4.12671i	0.386533	−	0.172096i
$576$	−0.461819	+	0.0981626i	−0.0192424	+	0.00409011i
$577$	−38.1269	−	8.10413i	−1.58725	−	0.337379i	−0.672086	−	0.740473i	$-0.734602\pi$
$577$	−38.1269	−	8.10413i	−1.58725	−	0.337379i	−0.915159	+	0.403093i	$0.867935\pi$
$578$	9.56677	+	4.25940i	0.397925	+	0.177168i
$579$	−1.59385	+	1.77015i	−0.0662380	+	0.0735647i
$580$	−3.81598	+	36.3066i	−0.158450	+	1.50755i
$581$	−9.92705	−	7.21242i	−0.411843	−	0.299222i
$582$	−0.341861	−	3.25259i	−0.0141706	−	0.134824i
$583$	−4.85410	+	8.40755i	−0.201036	+	0.348205i
$584$	−9.57295	−	16.5808i	−0.396131	−	0.686120i
$585$	20.5623	−	14.9394i	0.850147	−	0.617668i
$586$	3.40599	+	3.78273i	0.140700	+	0.156263i
$587$	−11.1287	−	34.2505i	−0.459330	−	1.41367i	−0.865976	−	0.500086i	$-0.833302\pi$
$587$	−11.1287	−	34.2505i	−0.459330	−	1.41367i	0.406646	−	0.913586i	$-0.366698\pi$
$588$	−3.23607			−0.133453
$589$		0			0
$590$	15.3262			0.630971
$591$	−5.07295	−	15.6129i	−0.208673	−	0.642230i
$592$	−0.292875	−	0.325270i	−0.0120371	−	0.0133685i
$593$	−4.94427	+	3.59222i	−0.203037	+	0.147515i	−0.684658	−	0.728865i	$-0.740048\pi$
$593$	−4.94427	+	3.59222i	−0.203037	+	0.147515i	0.481621	+	0.876380i	$0.340048\pi$
$594$	−1.18034	−	2.04441i	−0.0484299	−	0.0838831i
$595$	−0.927051	+	1.60570i	−0.0380054	+	0.0658273i
$596$	−2.88105	−	27.4113i	−0.118012	−	1.12281i
$597$	−21.6074	−	15.6987i	−0.884332	−	0.642505i
$598$	−1.71598	+	16.3265i	−0.0701717	+	0.667639i
$599$	19.9390	−	22.1445i	0.814686	−	0.904800i	−0.182232	−	0.983256i	$-0.558332\pi$
$599$	19.9390	−	22.1445i	0.814686	−	0.904800i	0.996918	+	0.0784555i	$0.0249989\pi$
$600$	3.78747	+	1.68629i	0.154623	+	0.0688424i
$601$	21.5192	+	4.57406i	0.877788	+	0.186580i	0.624701	−	0.780864i	$-0.285221\pi$
$601$	21.5192	+	4.57406i	0.877788	+	0.186580i	0.253087	+	0.967443i	$0.418554\pi$
$602$	8.37520	−	1.78020i	0.341348	−	0.0725557i
$603$	7.73968	−	3.44593i	0.315184	−	0.140329i
$604$	−9.75329	+	30.0175i	−0.396856	+	1.22140i
$605$	8.42705	−	25.9358i	0.342608	−	1.05444i
$606$	−2.68973	+	1.19754i	−0.109263	+	0.0486469i
$607$	24.8610	−	5.28437i	1.00908	−	0.214486i	0.326420	−	0.945225i	$-0.394158\pi$
$607$	24.8610	−	5.28437i	1.00908	−	0.214486i	0.682657	+	0.730739i	$0.260824\pi$
$608$	27.4763	+	5.84027i	1.11431	+	0.236854i
$609$	23.6189	+	10.5158i	0.957086	+	0.426122i
$610$	7.51840	−	8.35003i	0.304411	−	0.338083i
$611$	−1.71598	+	16.3265i	−0.0694212	+	0.660499i
$612$	0.618034	+	0.449028i	0.0249825	+	0.0181509i
$613$	2.61904	+	24.9185i	0.105782	+	1.00645i	0.910702	+	0.413064i	$0.135541\pi$
$613$	2.61904	+	24.9185i	0.105782	+	1.00645i	−0.804920	+	0.593383i	$0.797792\pi$
$614$	1.88197	−	3.25966i	0.0759500	−	0.131549i
$615$	8.47214	+	14.6742i	0.341629	+	0.591720i
$616$	−4.14590	+	3.01217i	−0.167043	+	0.121364i
$617$	−9.52579	−	10.5795i	−0.383494	−	0.425913i	0.520232	−	0.854025i	$-0.325846\pi$
$617$	−9.52579	−	10.5795i	−0.383494	−	0.425913i	−0.903726	+	0.428112i	$0.859179\pi$
$618$	0.0278640	+	0.0857567i	0.00112086	+	0.00344964i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$	−3.14590	−	9.68208i	−0.126139	−	0.388216i
$623$	12.8111	+	14.2282i	0.513266	+	0.570040i
$624$	7.28115	−	5.29007i	0.291479	−	0.211772i
$625$	15.4164	+	26.7020i	0.616656	+	1.06808i
$626$	−0.381966	+	0.661585i	−0.0152664	+	0.0264422i
$627$	−0.399263	−	3.79874i	−0.0159450	−	0.151707i
$628$	12.7082	+	9.23305i	0.507113	+	0.368439i
$629$	−0.00582517	+	0.0554228i	−0.000232265	+	0.00220985i
$630$	−6.49606	+	7.21460i	−0.258809	+	0.287437i
$631$	7.97479	+	3.55060i	0.317471	+	0.141347i	0.559285	−	0.828975i	$-0.311076\pi$
$631$	7.97479	+	3.55060i	0.317471	+	0.141347i	−0.241814	+	0.970323i	$0.577742\pi$
$632$		0			0
$633$	7.82518	−	1.66329i	0.311023	−	0.0661100i
$634$	−14.6167	+	6.50779i	−0.580504	+	0.258457i
$635$	8.28115	−	25.4868i	0.328628	−	1.01141i
$636$	−6.35410	+	19.5559i	−0.251957	+	0.775442i
$637$	−8.86889	+	3.94868i	−0.351398	+	0.156452i
$638$	3.97997	−	0.845968i	0.157568	−	0.0334922i
$639$	0.176399	+	0.0374948i	0.00697824	+	0.00148327i
$640$	−27.2222	−	12.1201i	−1.07605	−	0.479089i
$641$	27.4947	−	30.5359i	1.08597	−	1.20610i	0.108711	−	0.994073i	$-0.465328\pi$
$641$	27.4947	−	30.5359i	1.08597	−	1.20610i	0.977264	−	0.212024i	$-0.0680055\pi$
$642$	0.0704273	−	0.670071i	0.00277954	−	0.0264456i
$643$	6.59017	+	4.78804i	0.259891	+	0.188822i	0.710099	−	0.704102i	$-0.248650\pi$
$643$	6.59017	+	4.78804i	0.259891	+	0.188822i	−0.450208	+	0.892924i	$0.648650\pi$
$644$	2.77652	+	26.4168i	0.109410	+	1.04097i
$645$	6.04508	−	10.4704i	0.238025	−	0.412271i
$646$	−0.364745	−	0.631757i	−0.0143507	−	0.0248561i
$647$	−24.1803	+	17.5680i	−0.950627	+	0.690671i	−0.950955	−	0.309329i	$-0.899896\pi$
$647$	−24.1803	+	17.5680i	−0.950627	+	0.690671i	0.000327889		1.00000i	$0.499896\pi$
$648$	1.49622	+	1.66172i	0.0587771	+	0.0652786i
$649$	2.23607	+	6.88191i	0.0877733	+	0.270139i
$650$	5.56231			0.218172
$651$		0			0
$652$	20.5623			0.805282
$653$	12.2533	+	37.7117i	0.479508	+	1.47577i	0.839780	+	0.542927i	$0.182684\pi$
$653$	12.2533	+	37.7117i	0.479508	+	1.47577i	−0.360272	+	0.932847i	$0.617316\pi$
$654$	3.48057	+	3.86556i	0.136101	+	0.151155i
$655$	0.190983	−	0.138757i	0.00746232	−	0.00542170i
$656$	−6.00000	−	10.3923i	−0.234261	−	0.405751i
$657$	8.56231	−	14.8303i	0.334047	−	0.578587i
$658$	−0.655447	−	6.23616i	−0.0255520	−	0.243111i
$659$	−18.3541	−	13.3350i	−0.714974	−	0.519459i	0.169800	−	0.985478i	$-0.445688\pi$
$659$	−18.3541	−	13.3350i	−0.714974	−	0.519459i	−0.884775	+	0.466019i	$0.845688\pi$
$660$	−0.338261	+	3.21834i	−0.0131668	+	0.125274i
$661$	−11.1196	+	12.3496i	−0.432504	+	0.480344i	−0.919517	−	0.393051i	$-0.871420\pi$
$661$	−11.1196	+	12.3496i	−0.432504	+	0.480344i	0.487013	+	0.873395i	$0.338086\pi$
$662$	6.36335	+	2.83315i	0.247319	+	0.110113i
$663$	−1.12086	−	0.238246i	−0.0435305	−	0.00925269i
$664$	−8.94604	+	1.90154i	−0.347174	+	0.0737940i
$665$	−35.8754	+	15.9728i	−1.39119	+	0.619397i
$666$	−0.0901699	+	0.277515i	−0.00349401	+	0.0107535i
$667$	14.5729	−	44.8509i	0.564267	−	1.73663i
$668$	−13.6523	+	6.07838i	−0.528222	+	0.235180i
$669$	0.692728	−	0.147244i	0.0267824	−	0.00569278i
$670$	6.70432	+	1.42505i	0.259011	+	0.0550544i
$671$	4.84631	+	2.15772i	0.187090	+	0.0832978i
$672$	−11.2776	+	12.5250i	−0.435043	+	0.483164i
$673$	−0.461640	+	4.39221i	−0.0177949	+	0.169307i	−0.999810	−	0.0194954i	$-0.993794\pi$
$673$	−0.461640	+	4.39221i	−0.0177949	+	0.169307i	0.982015	+	0.188803i	$0.0604607\pi$
$674$	−9.48936	−	6.89442i	−0.365516	−	0.265563i
$675$	0.969032	+	9.21973i	0.0372981	+	0.354867i
$676$	8.54508	−	14.8005i	0.328657	−	0.569251i
$677$	14.3262	+	24.8138i	0.550602	+	0.953671i	0.998231	+	0.0594514i	$0.0189351\pi$
$677$	14.3262	+	24.8138i	0.550602	+	0.953671i	−0.447629	+	0.894219i	$0.647732\pi$
$678$	−0.927051	+	0.673542i	−0.0356032	+	0.0258672i
$679$	−10.6227	−	11.7977i	−0.407662	−	0.452755i
$680$	0.427051	+	1.31433i	0.0163767	+	0.0504022i
$681$	−20.7426			−0.794860
$682$		0			0
$683$	10.0557			0.384772			0.192386	−	0.981319i	$-0.438377\pi$
$683$	10.0557			0.384772			0.192386	+	0.981319i	$0.438377\pi$
$684$	5.00000	+	15.3884i	0.191180	+	0.588391i
$685$	−11.3379	−	12.5920i	−0.433200	−	0.481117i
$686$	−7.50000	+	5.44907i	−0.286351	+	0.208046i
$687$	−3.61803	−	6.26662i	−0.138037	−	0.239086i
$688$	−4.28115	+	7.41517i	−0.163217	+	0.282701i
$689$	6.44804	+	61.3490i	0.245651	+	2.33721i
$690$	−7.16312	−	5.20431i	−0.272695	−	0.198125i
$691$	−0.400638	+	3.81182i	−0.0152410	+	0.145008i	−0.999496	−	0.0317461i	$-0.989893\pi$
$691$	−0.400638	+	3.81182i	−0.0152410	+	0.145008i	0.984255	+	0.176755i	$0.0565599\pi$
$692$	−0.985051	+	1.09401i	−0.0374460	+	0.0415880i
$693$	−4.18732	−	1.86431i	−0.159063	−	0.0708195i
$694$	−4.91156	−	1.04398i	−0.186440	−	0.0396291i
$695$	−14.9913	+	3.18650i	−0.568653	+	0.120871i
$696$	17.6045	−	7.83802i	0.667296	−	0.297099i
$697$	−0.472136	+	1.45309i	−0.0178834	+	0.0550395i
$698$	3.19098	−	9.82084i	0.120780	−	0.371724i
$699$	17.1732	−	7.64599i	0.649549	−	0.289198i
$700$	8.80333	−	1.87121i	0.332735	−	0.0707249i
$701$	29.3781	+	6.24451i	1.10960	+	0.235852i	0.726031	−	0.687662i	$-0.241363\pi$
$701$	29.3781	+	6.24451i	1.10960	+	0.235852i	0.383565	+	0.923514i	$0.374696\pi$
$702$	−13.7032	−	6.10105i	−0.517193	−	0.230269i
$703$	−0.789802	+	0.877163i	−0.0297879	+	0.0330828i
$704$	0.0188507	−	0.179352i	0.000710461	−	0.00675958i
$705$	−7.16312	−	5.20431i	−0.269779	−	0.196006i
$706$	2.09194	+	19.9035i	0.0787314	+	0.749079i
$707$	−7.14590	+	12.3771i	−0.268749	+	0.465487i
$708$	7.66312	+	13.2729i	0.287998	+	0.498827i
$709$	3.35410	−	2.43690i	0.125966	−	0.0915196i	−0.523018	−	0.852321i	$-0.675194\pi$
$709$	3.35410	−	2.43690i	0.125966	−	0.0915196i	0.648984	+	0.760802i	$0.275194\pi$
$710$	0.0976248	+	0.108423i	0.00366379	+	0.00406906i
$711$		0			0
$712$	14.2705			0.534810
$713$		0			0
$714$	0.437694			0.0163803
$715$	3.00000	+	9.23305i	0.112194	+	0.345297i
$716$	21.4352	+	23.8062i	0.801072	+	0.889681i
$717$	−10.8541	+	7.88597i	−0.405354	+	0.294507i
$718$	−7.82624	−	13.5554i	−0.292073	−	0.505885i
$719$	−20.6910	+	35.8378i	−0.771643	+	1.33653i	0.165018	+	0.986290i	$0.447232\pi$
$719$	−20.6910	+	35.8378i	−0.771643	+	1.33653i	−0.936662	+	0.350235i	$0.886102\pi$
$720$	−1.01478	−	9.65502i	−0.0378188	−	0.359821i
$721$	0.354102	+	0.257270i	0.0131874	+	0.00958124i
$722$	0.387613	−	3.68789i	0.0144255	−	0.137249i
$723$	5.70625	−	6.33744i	0.212218	−	0.235692i
$724$	25.1285	+	11.1879i	0.933894	+	0.415796i
$725$	−15.6295	−	3.32216i	−0.580467	−	0.123382i
$726$	−6.29702	+	1.33847i	−0.233704	+	0.0496754i
$727$	−21.7724	+	9.69368i	−0.807492	+	0.359519i	−0.768604	−	0.639725i	$-0.779048\pi$
$727$	−21.7724	+	9.69368i	−0.807492	+	0.359519i	−0.0388882	+	0.999244i	$0.512382\pi$
$728$	−10.0623	+	30.9686i	−0.372934	+	1.14777i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	12.6564	−	5.63497i	0.468433	−	0.208560i
$731$	1.06635	−	0.226659i	0.0394403	−	0.00838329i
$732$	10.9905	+	2.33611i	0.406222	+	0.0863451i
$733$	25.5284	+	11.3660i	0.942912	+	0.419811i	0.819844	−	0.572587i	$-0.194060\pi$
$733$	25.5284	+	11.3660i	0.942912	+	0.419811i	0.123068	+	0.992398i	$0.460727\pi$
$734$	−14.9995	+	16.6586i	−0.553642	+	0.614882i
$735$	0.547318	−	5.20738i	0.0201881	−	0.192077i
$736$	24.8713	+	18.0701i	0.916769	+	0.666072i
$737$	0.338261	+	3.21834i	0.0124600	+	0.118549i
$738$	−4.00000	+	6.92820i	−0.147242	+	0.255031i
$739$	10.8541	+	18.7999i	0.399275	+	0.691564i	0.993637	−	0.112634i	$-0.0359287\pi$
$739$	10.8541	+	18.7999i	0.399275	+	0.691564i	−0.594362	+	0.804198i	$0.702595\pi$
$740$	0.809017	−	0.587785i	0.0297401	−	0.0216074i
$741$	−16.2401	−	18.0365i	−0.596596	−	0.662588i
$742$	−7.28115	−	22.4091i	−0.267300	−	0.822663i
$743$	3.43769			0.126117			0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$		0			0
$745$	44.5967			1.63390
$746$	0.0663712	+	0.204270i	0.00243002	+	0.00747884i
$747$	−5.47372	−	6.07918i	−0.200273	−	0.222425i
$748$	−0.236068	+	0.171513i	−0.00863150	+	0.00627115i
$749$	−1.63525	−	2.83234i	−0.0597509	−	0.103492i
$750$	2.54508	−	4.40822i	0.0929334	−	0.160965i
$751$	4.16366	+	39.6146i	0.151934	+	1.44556i	0.759096	+	0.650979i	$0.225641\pi$
$751$	4.16366	+	39.6146i	0.151934	+	1.44556i	−0.607161	+	0.794578i	$0.707692\pi$
$752$	5.07295	+	3.68571i	0.184991	+	0.134404i
$753$	0.0987033	−	0.939099i	0.00359695	−	0.0342227i
$754$	17.2998	−	19.2133i	0.630020	−	0.699709i
$755$	−46.6537	−	20.7716i	−1.69790	−	0.755955i
$756$	−23.7401	−	5.04612i	−0.863421	−	0.183526i
$757$	42.1822	−	8.96611i	1.53314	−	0.325879i	0.637426	−	0.770511i	$-0.279999\pi$
$757$	42.1822	−	8.96611i	1.53314	−	0.325879i	0.895713	+	0.444632i	$0.146666\pi$
$758$	10.3979	−	4.62946i	0.377670	−	0.168150i
$759$	1.29180	−	3.97574i	0.0468892	−	0.144310i
$760$	−9.04508	+	27.8379i	−0.328100	+	1.00979i
$761$	−3.20342	+	1.42625i	−0.116124	+	0.0517017i	−0.463976	−	0.885848i	$-0.653578\pi$
$761$	−3.20342	+	1.42625i	−0.116124	+	0.0517017i	0.347852	+	0.937549i	$0.386911\pi$
$762$	−6.18799	+	1.31530i	−0.224167	+	0.0476482i
$763$	24.6975	+	5.24961i	0.894108	+	0.190049i
$764$	23.7836	+	10.5892i	0.860462	+	0.383102i
$765$	−0.827091	+	0.918578i	−0.0299035	+	0.0332112i
$766$	1.08881	−	10.3593i	0.0393403	−	0.374298i
$767$	37.1976	+	27.0256i	1.34313	+	0.975838i
$768$	0.685948	+	6.52636i	0.0247520	+	0.235500i
$769$	26.8713	−	46.5425i	0.969005	−	1.67837i	0.270557	−	0.962704i	$-0.412792\pi$
$769$	26.8713	−	46.5425i	0.969005	−	1.67837i	0.698447	−	0.715662i	$-0.253875\pi$
$770$	−1.85410	−	3.21140i	−0.0668172	−	0.115731i
$771$	−1.14590	+	0.832544i	−0.0412685	+	0.0299833i
$772$	2.57890	+	2.86416i	0.0928166	+	0.103083i
$773$	5.89919	+	18.1558i	0.212179	+	0.653020i	0.999342	+	0.0362746i	$0.0115491\pi$
$773$	5.89919	+	18.1558i	0.212179	+	0.653020i	−0.787163	+	0.616745i	$0.788451\pi$
$774$	5.70820			0.205177
$775$		0			0
$776$	−11.8328			−0.424773
$777$	−0.218847	−	0.673542i	−0.00785109	−	0.0241632i
$778$	−12.0213	−	13.3510i	−0.430985	−	0.478657i
$779$	−26.1803	+	19.0211i	−0.938008	+	0.681503i
$780$	10.2812	+	17.8075i	0.368124	+	0.637610i
$781$	−0.0344419	+	0.0596550i	−0.00123243	+	0.00213463i
$782$	−0.0834528	−	0.794000i	−0.00298427	−	0.0283934i
$783$	34.8607	+	25.3278i	1.24582	+	0.905141i
$784$	−0.387613	+	3.68789i	−0.0138433	+	0.131710i
$785$	−17.0069	+	18.8881i	−0.607002	+	0.674144i
$786$	−0.0509101	−	0.0226667i	−0.00181590	−	0.000808493i
$787$	30.6080	+	6.50593i	1.09106	+	0.231911i	0.718102	−	0.695938i	$-0.245011\pi$
$787$	30.6080	+	6.50593i	1.09106	+	0.231911i	0.372955	+	0.927849i	$0.378344\pi$
$788$	−25.9819	+	5.52261i	−0.925565	+	0.196735i
$789$	9.86481	−	4.39209i	0.351196	−	0.156363i
$790$		0			0
$791$	−1.71885	+	5.29007i	−0.0611152	+	0.188093i
$792$	−3.12104	+	1.38958i	−0.110901	+	0.0493765i
$793$	32.9716	−	7.00833i	1.17086	−	0.248873i
$794$	9.84885	+	2.09344i	0.349523	+	0.0742934i
$795$	−30.3941	−	13.5323i	−1.07797	−	0.479942i
$796$	−28.9163	+	32.1148i	−1.02491	+	1.13828i
$797$	0.946581	−	9.00612i	0.0335296	−	0.319013i	−0.964883	−	0.262682i	$-0.915393\pi$
$797$	0.946581	−	9.00612i	0.0335296	−	0.319013i	0.998412	−	0.0563313i	$-0.0179403\pi$
$798$	7.50000	+	5.44907i	0.265497	+	0.192895i
$799$	−0.0834528	−	0.794000i	−0.00295235	−	0.0280897i
$800$	5.20820	−	9.02087i	0.184138	−	0.318936i
$801$	6.38197	+	11.0539i	0.225496	+	0.390570i
$802$	14.9164	−	10.8374i	0.526717	−	0.382682i
$803$	4.37680	+	4.86092i	0.154454	+	0.171538i
$804$	2.11803	+	6.51864i	0.0746973	+	0.229895i
$805$	−42.9787			−1.51480
$806$		0			0
$807$	1.38197			0.0486475
$808$	3.29180	+	10.1311i	0.115805	+	0.356411i
$809$	−36.6673	−	40.7231i	−1.28915	−	1.43175i	−0.844046	−	0.536272i	$-0.819832\pi$
$809$	−36.6673	−	40.7231i	−1.28915	−	1.43175i	−0.445107	−	0.895477i	$-0.646834\pi$
$810$	−1.30902	+	0.951057i	−0.0459942	+	0.0334167i
$811$	−21.3885	−	37.0460i	−0.751053	−	1.30086i	−0.947313	−	0.320311i	$-0.896213\pi$
$811$	−21.3885	−	37.0460i	−0.751053	−	1.30086i	0.196259	−	0.980552i	$-0.437121\pi$
$812$	20.9164	−	36.2283i	0.734022	−	1.27136i
$813$	0.999533	+	9.50992i	0.0350552	+	0.333528i
$814$	−0.0901699	−	0.0655123i	−0.00316045	−	0.00229620i
$815$	−3.47772	+	33.0883i	−0.121819	+	1.15903i
$816$	−0.292875	+	0.325270i	−0.0102527	+	0.0113867i
$817$	21.0939	+	9.39162i	0.737983	+	0.328571i
$818$	3.73619	+	0.794152i	0.130633	+	0.0277669i
$819$	−28.4882	+	6.05535i	−0.995457	+	0.211591i
$820$	25.0461	−	11.1513i	0.874649	−	0.389419i
$821$	10.0344	−	30.8828i	0.350204	−	1.07782i	−0.608534	−	0.793528i	$-0.708242\pi$
$821$	10.0344	−	30.8828i	0.350204	−	1.07782i	0.958738	−	0.284290i	$-0.0917580\pi$
$822$	−1.23607	+	3.80423i	−0.0431128	+	0.132688i
$823$	5.59511	−	2.49110i	0.195033	−	0.0868344i	−0.306896	−	0.951743i	$-0.599290\pi$
$823$	5.59511	−	2.49110i	0.195033	−	0.0868344i	0.501929	+	0.864909i	$0.332624\pi$
$824$	0.319109	−	0.0678287i	0.0111167	−	0.00236292i
$825$	−1.38546	−	0.294488i	−0.0482354	−	0.0102527i
$826$	−16.0440	−	7.14323i	−0.558241	−	0.248545i
$827$	−1.78910	+	1.98699i	−0.0622130	+	0.0690945i	−0.773448	−	0.633860i	$-0.781470\pi$
$827$	−1.78910	+	1.98699i	−0.0622130	+	0.0690945i	0.711235	+	0.702954i	$0.248136\pi$
$828$	−1.85101	+	17.6112i	−0.0643271	+	0.612031i
$829$	−17.5623	−	12.7598i	−0.609964	−	0.443165i	0.239438	−	0.970912i	$-0.423037\pi$
$829$	−17.5623	−	12.7598i	−0.609964	−	0.443165i	−0.849402	+	0.527747i	$0.823037\pi$
$830$	−0.691773	−	6.58178i	−0.0240118	−	0.228457i
$831$	6.66312	−	11.5409i	0.231141	−	0.400348i
$832$	−0.572949	−	0.992377i	−0.0198634	−	0.0344045i
$833$	0.381966	−	0.277515i	0.0132343	−	0.00961531i
$834$	2.42094	+	2.68872i	0.0838302	+	0.0931029i
$835$	−7.47214	−	22.9969i	−0.258584	−	0.795839i
$836$	−6.18034			−0.213752
$837$		0			0
$838$	−2.76393			−0.0954784
$839$	3.45492	+	10.6331i	0.119277	+	0.367097i	0.992815	−	0.119659i	$-0.0381802\pi$
$839$	3.45492	+	10.6331i	0.119277	+	0.367097i	−0.873538	+	0.486756i	$0.838180\pi$
$840$	−11.7515	−	13.0513i	−0.405464	−	0.450314i
$841$	−36.6246	+	26.6093i	−1.26292	+	0.917563i
$842$	4.56231	+	7.90215i	0.157227	+	0.272326i
$843$	−9.51722	+	16.4843i	−0.327791	+	0.567750i
$844$	−1.35304	−	12.8734i	−0.0465737	−	0.443119i
$845$	22.3713	+	16.2537i	0.769597	+	0.559145i
$846$	0.436965	−	4.15744i	0.0150231	−	0.142936i
$847$	−20.9098	+	23.2227i	−0.718470	+	0.797941i
$848$	21.5252	+	9.58365i	0.739180	+	0.329104i
$849$	−6.41890	−	1.36438i	−0.220296	−	0.0468254i
$850$	−0.264599	+	0.0562422i	−0.00907566	+	0.00192909i
$851$	−1.18011	+	0.525421i	−0.0404538	+	0.0180112i
$852$	−0.0450850	+	0.138757i	−0.00154459	+	0.00475375i
$853$	1.23607	−	3.80423i	0.0423222	−	0.130254i	−0.927663	−	0.373419i	$-0.878185\pi$
$853$	1.23607	−	3.80423i	0.0423222	−	0.130254i	0.969985	+	0.243164i	$0.0781855\pi$
$854$	−11.7623	+	5.23689i	−0.402496	+	0.179203i
$855$	−25.6082	+	5.44320i	−0.875783	+	0.186153i
$856$	−2.38442	−	0.506825i	−0.0814980	−	0.0173229i
$857$	−7.47311	−	3.32724i	−0.255277	−	0.113656i	0.275109	−	0.961413i	$-0.411286\pi$
$857$	−7.47311	−	3.32724i	−0.255277	−	0.113656i	−0.530385	+	0.847757i	$0.677953\pi$
$858$	1.53351	−	1.70314i	0.0523532	−	0.0581441i
$859$	4.52522	−	43.0546i	0.154399	−	1.46901i	−0.593308	−	0.804976i	$-0.702178\pi$
$859$	4.52522	−	43.0546i	0.154399	−	1.46901i	0.747706	−	0.664030i	$-0.231155\pi$
$860$	−15.8262	−	11.4984i	−0.539670	−	0.392093i
$861$	−2.02957	−	19.3100i	−0.0691675	−	0.658084i
$862$	9.03444	−	15.6481i	0.307714	−	0.532977i
$863$	1.24671	+	2.15937i	0.0424385	+	0.0735057i	0.886464	−	0.462797i	$-0.153154\pi$
$863$	1.24671	+	2.15937i	0.0424385	+	0.0735057i	−0.844026	+	0.536302i	$0.819821\pi$
$864$	−22.7254	+	16.5110i	−0.773135	+	0.561715i
$865$	−1.59385	−	1.77015i	−0.0541924	−	0.0601868i
$866$	0.111456	+	0.343027i	0.00378744	+	0.0116565i
$867$	−16.9443			−0.575458
$868$		0			0
$869$		0			0
$870$	4.30902	+	13.2618i	0.146089	+	0.449617i
$871$	13.7589	+	15.2808i	0.466201	+	0.517769i
$872$	15.2254	−	11.0619i	0.515598	−	0.374604i
$873$	−5.29180	−	9.16566i	−0.179100	−	0.310211i
$874$	8.45492	−	14.6443i	0.285992	−	0.495352i
$875$	−2.58271	−	24.5728i	−0.0873116	−	0.830714i
$876$	11.2082	+	8.14324i	0.378690	+	0.275134i
$877$	−1.70296	+	16.2025i	−0.0575048	+	0.547121i	0.927406	+	0.374057i	$0.122034\pi$
$877$	−1.70296	+	16.2025i	−0.0575048	+	0.547121i	−0.984911	+	0.173064i	$0.944633\pi$
$878$	−17.2998	+	19.2133i	−0.583839	+	0.648419i
$879$	−7.52402	−	3.34991i	−0.253779	−	0.112990i
$880$	3.62717	+	0.770979i	0.122272	+	0.0259897i
$881$	−15.0250	+	3.19366i	−0.506206	+	0.107597i	−0.453933	−	0.891036i	$-0.649980\pi$
$881$	−15.0250	+	3.19366i	−0.506206	+	0.107597i	−0.0522720	+	0.998633i	$0.516646\pi$
$882$	2.25841	−	1.00551i	0.0760446	−	0.0338572i
$883$	0.309017	−	0.951057i	0.0103992	−	0.0320056i	−0.945722	−	0.324976i	$-0.894644\pi$
$883$	0.309017	−	0.951057i	0.0103992	−	0.0320056i	0.956121	+	0.292970i	$0.0946438\pi$
$884$	−0.572949	+	1.76336i	−0.0192704	+	0.0593081i
$885$	−22.6544	+	10.0864i	−0.761521	+	0.339051i
$886$	−24.8610	+	5.28437i	−0.835222	+	0.177532i
$887$	−38.2488	−	8.13004i	−1.28427	−	0.272980i	−0.485298	−	0.874349i	$-0.661289\pi$
$887$	−38.2488	−	8.13004i	−1.28427	−	0.272980i	−0.798972	+	0.601369i	$0.794622\pi$
$888$	−0.482228	−	0.214702i	−0.0161825	−	0.00720492i
$889$	−20.5478	+	22.8206i	−0.689151	+	0.765380i
$890$	−1.07939	+	10.2697i	−0.0361811	+	0.344240i
$891$	−0.618034	−	0.449028i	−0.0207049	−	0.0150430i
$892$	−0.119779	−	1.13962i	−0.00401050	−	0.0381573i
$893$	8.45492	−	14.6443i	0.282933	−	0.490054i
$894$	−5.26393	−	9.11740i	−0.176052	−	0.304931i
$895$	−41.9336	+	30.4666i	−1.40169	+	1.01838i
$896$	22.8481	+	25.3753i	0.763300	+	0.847731i
$897$	−8.20820	−	25.2623i	−0.274064	−	0.843482i
$898$	14.8754			0.496398
$899$		0			0
$900$	6.00000			0.200000
$901$	−0.927051	−	2.85317i	−0.0308845	−	0.0950529i
$902$	−2.04468	−	2.27085i	−0.0680804	−	0.0756110i
$903$	−11.2082	+	8.14324i	−0.372986	+	0.270990i
$904$	2.07295	+	3.59045i	0.0689453	+	0.119417i
$905$	−22.2533	+	38.5438i	−0.739724	+	1.28124i
$906$	1.26017	+	11.9897i	0.0418662	+	0.398331i
$907$	−42.8156	−	31.1074i	−1.42167	−	1.03290i	−0.991493	−	0.130157i	$-0.958452\pi$
$907$	−42.8156	−	31.1074i	−1.42167	−	1.03290i	−0.430175	−	0.902745i	$-0.641548\pi$
$908$	−3.50822	+	33.3784i	−0.116424	+	1.10770i
$909$	−6.37539	+	7.08058i	−0.211458	+	0.234848i
$910$	−21.5252	−	9.58365i	−0.713555	−	0.317695i
$911$	8.00158	+	1.70079i	0.265104	+	0.0563496i	0.338546	−	0.940950i	$-0.390065\pi$
$911$	8.00158	+	1.70079i	0.265104	+	0.0563496i	−0.0734417	+	0.997300i	$0.523398\pi$
$912$	−9.06793	+	1.92745i	−0.300269	+	0.0638242i
$913$	2.85447	−	1.27089i	0.0944693	−	0.0420605i
$914$	−3.00658	+	9.25330i	−0.0994488	+	0.306072i
$915$	−5.61803	+	17.2905i	−0.185726	+	0.571607i
$916$	−10.6960	+	4.76216i	−0.353405	+	0.157346i
$917$	−0.264599	+	0.0562422i	−0.00873781	+	0.00185728i
$918$	0.713549	+	0.151670i	0.0235506	+	0.00500584i
$919$	9.02162	+	4.01668i	0.297596	+	0.132498i	0.550103	−	0.835097i	$-0.314588\pi$
$919$	9.02162	+	4.01668i	0.297596	+	0.132498i	−0.252507	+	0.967595i	$0.581255\pi$
$920$	−21.4352	+	23.8062i	−0.706698	+	0.784868i
$921$	−0.636596	+	6.05681i	−0.0209766	+	0.199579i
$922$	−5.37132	−	3.90249i	−0.176895	−	0.128522i
$923$	0.0457515	+	0.435296i	0.00150593	+	0.0143280i
$924$	1.85410	−	3.21140i	0.0609955	−	0.105647i
$925$	0.218847	+	0.379054i	0.00719565	+	0.0124632i
$926$	15.5623	−	11.3067i	0.511409	−	0.371560i
$927$	0.195250	+	0.216847i	0.00641284	+	0.00712218i
$928$	−14.9615	−	46.0467i	−0.491135	−	1.51156i
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	−9.39919	−	28.9277i	−0.307881	−	0.947559i
$933$	11.0220	+	12.2412i	0.360844	+	0.400758i
$934$	−16.3885	+	11.9070i	−0.536250	+	0.389608i
$935$	−0.236068	−	0.408882i	−0.00772025	−	0.0133719i
$936$	−10.8541	+	18.7999i	−0.354777	+	0.614493i
$937$	−4.23187	−	40.2635i	−0.138249	−	1.31535i	−0.815138	−	0.579267i	$-0.803339\pi$
$937$	−4.23187	−	40.2635i	−0.138249	−	1.31535i	0.676889	−	0.736085i	$-0.263328\pi$
$938$	−6.35410	−	4.61653i	−0.207469	−	0.150735i
$939$	0.129204	−	1.22930i	0.00421642	−	0.0401166i
$940$	−9.58612	+	10.6465i	−0.312665	+	0.347250i
$941$	−26.1124	−	11.6260i	−0.851240	−	0.378997i	−0.0657242	−	0.997838i	$-0.520936\pi$
$941$	−26.1124	−	11.6260i	−0.851240	−	0.378997i	−0.785516	+	0.618841i	$0.787602\pi$
$942$	5.86889	+	1.24747i	0.191219	+	0.0406448i
$943$	−34.6425	+	7.36349i	−1.12811	+	0.239788i
$944$	16.0440	−	7.14323i	0.522187	−	0.232492i
$945$	12.1353	−	37.3485i	0.394760	−	1.21495i
$946$	−0.673762	+	2.07363i	−0.0219059	+	0.0674194i
$947$	−20.1609	+	8.97622i	−0.655142	+	0.291688i	−0.707261	−	0.706953i	$-0.750069\pi$
$947$	−20.1609	+	8.97622i	−0.655142	+	0.291688i	0.0521186	+	0.998641i	$0.483403\pi$
$948$		0			0
$949$	40.6541	+	8.64129i	1.31969	+	0.280508i
$950$	−5.23415	−	2.33039i	−0.169818	−	0.0756080i
$951$	17.3228	−	19.2389i	0.561731	−	0.623865i
$952$	0.165530	−	1.57492i	0.00536487	−	0.0510434i
$953$	34.1525	+	24.8132i	1.10631	+	0.803779i	0.982078	−	0.188474i	$-0.0603542\pi$
$953$	34.1525	+	24.8132i	1.10631	+	0.803779i	0.124229	+	0.992254i	$0.460354\pi$
$954$	−1.64195	−	15.6222i	−0.0531602	−	0.505786i
$955$	−21.0623	+	36.4810i	−0.681560	+	1.18050i
$956$	10.8541	+	18.7999i	0.351047	+	0.608031i
$957$	−5.32624	+	3.86974i	−0.172173	+	0.125091i
$958$	3.69886	+	4.10800i	0.119505	+	0.132724i
$959$	6.00000	+	18.4661i	0.193750	+	0.596302i
$960$	0.618034			0.0199470
$961$		0			0
$962$	−0.708204			−0.0228334
$963$	−0.673762	−	2.07363i	−0.0217117	−	0.0668217i
$964$	−9.23291	−	10.2542i	−0.297372	−	0.330265i
$965$	−5.04508	+	3.66547i	−0.162407	+	0.117996i
$966$	5.07295	+	8.78661i	0.163219	+	0.282704i
$967$	21.8262	−	37.8042i	0.701884	−	1.21570i	−0.265920	−	0.963995i	$-0.585676\pi$
$967$	21.8262	−	37.8042i	0.701884	−	1.21570i	0.967804	−	0.251704i	$-0.0809911\pi$
$968$	2.43466	+	23.1642i	0.0782528	+	0.744526i
$969$	0.954915	+	0.693786i	0.0306763	+	0.0222876i
$970$	0.895005	−	8.51540i	0.0287369	−	0.273413i
$971$	−13.7589	+	15.2808i	−0.441543	+	0.490383i	−0.922302	−	0.386469i	$-0.873694\pi$
$971$	−13.7589	+	15.2808i	−0.441543	+	0.490383i	0.480759	+	0.876853i	$0.340361\pi$
$972$	−23.6504	−	10.5298i	−0.758586	−	0.337744i
$973$	17.1785	+	3.65141i	0.550718	+	0.117059i
$974$	−13.8576	+	2.94552i	−0.444026	+	0.0943807i
$975$	−8.22191	+	3.66063i	−0.263312	+	0.117234i
$976$	3.97871	−	12.2452i	0.127356	−	0.391960i
$977$	−1.87539	+	5.77185i	−0.0599990	+	0.184658i	−0.976564	−	0.215228i	$-0.930950\pi$
$977$	−1.87539	+	5.77185i	−0.0599990	+	0.184658i	0.916565	+	0.399886i	$0.130950\pi$
$978$	7.17508	−	3.19455i	0.229434	−	0.102150i
$979$	−4.76885	+	1.01365i	−0.152413	+	0.0323964i
$980$	−8.28700	−	1.76146i	−0.264718	−	0.0562677i
$981$	15.3775	+	6.84652i	0.490967	+	0.218593i
$982$	−11.4125	+	12.6749i	−0.364188	+	0.404472i
$983$	2.19870	−	20.9192i	0.0701276	−	0.667219i	−0.901835	−	0.432082i	$-0.857779\pi$
$983$	2.19870	−	20.9192i	0.0701276	−	0.667219i	0.971962	−	0.235138i	$-0.0755541\pi$
$984$	−11.7082	−	8.50651i	−0.373244	−	0.271178i
$985$	−4.49250	−	42.7433i	−0.143143	−	1.36191i
$986$	−0.628677	+	1.08890i	−0.0200212	+	0.0346777i
$987$	5.07295	+	8.78661i	0.161474	+	0.279681i
$988$	−31.7705	+	23.0826i	−1.01075	+	0.734356i
$989$	16.9093	+	18.7796i	0.537684	+	0.597158i
$990$	−0.763932	−	2.35114i	−0.0242794	−	0.0747242i
$991$	17.2705			0.548616			0.274308	−	0.961642i	$-0.411551\pi$
$991$	17.2705			0.548616			0.274308	+	0.961642i	$0.411551\pi$
$992$		0			0
$993$	−11.2705			−0.357659
$994$	−0.0516628	−	0.159002i	−0.00163864	−	0.00504323i
$995$	−46.7876	−	51.9629i	−1.48327	−	1.64733i
$996$	5.35410	−	3.88998i	0.169651	−	0.123259i
$997$	13.6246	+	23.5985i	0.431496	+	0.747373i	0.997002	−	0.0773712i	$-0.0246526\pi$
$997$	13.6246	+	23.5985i	0.431496	+	0.747373i	−0.565507	+	0.824744i	$0.691319\pi$
$998$	−1.28115	+	2.21902i	−0.0405542	+	0.0702419i
$999$	−0.123379	−	1.17387i	−0.00390354	−	0.0371397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.c.547.1		8
31.2	even	5		961.2.g.g.235.1		8
31.3	odd	30		961.2.c.f.521.1		4
31.4	even	5		961.2.g.g.816.1		8
31.5	even	3		961.2.d.b.531.1		4
31.6	odd	6		961.2.g.b.844.1		8
31.7	even	15		961.2.g.g.732.1		8
31.8	even	5	inner	961.2.g.c.846.1		8
31.9	even	15		961.2.d.b.628.1		4
31.10	even	15		961.2.d.e.388.1		4
31.11	odd	30		961.2.d.f.374.1		4
31.12	odd	30		961.2.g.f.338.1		8
31.13	odd	30		961.2.a.d.1.1		2
31.14	even	15	inner	961.2.g.c.448.1		8
31.15	odd	10		961.2.c.f.439.1		4
31.16	even	5		961.2.c.d.439.1		4
31.17	odd	30		961.2.g.b.448.1		8
31.18	even	15		961.2.a.e.1.1		2
31.19	even	15		961.2.g.g.338.1		8
31.20	even	15		961.2.d.e.374.1		4
31.21	odd	30		961.2.d.f.388.1		4
31.22	odd	30		31.2.d.a.8.1	yes	4
31.23	odd	10		961.2.g.b.846.1		8
31.24	odd	30		961.2.g.f.732.1		8
31.25	even	3	inner	961.2.g.c.844.1		8
31.26	odd	6		31.2.d.a.4.1	✓	4
31.27	odd	10		961.2.g.f.816.1		8
31.28	even	15		961.2.c.d.521.1		4
31.29	odd	10		961.2.g.f.235.1		8
31.30	odd	2		961.2.g.b.547.1		8
93.26	even	6		279.2.i.a.190.1		4
93.44	even	30		8649.2.a.g.1.2		2
93.53	even	30		279.2.i.a.163.1		4
93.80	odd	30		8649.2.a.f.1.2		2
124.115	even	30		496.2.n.b.225.1		4
124.119	even	6		496.2.n.b.97.1		4
155.22	even	60		775.2.bf.a.349.1		8
155.53	even	60		775.2.bf.a.349.2		8
155.57	even	12		775.2.bf.a.624.2		8
155.84	odd	30		775.2.k.c.101.1		4
155.88	even	12		775.2.bf.a.624.1		8
155.119	odd	6		775.2.k.c.376.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	31.26	odd	6
31.2.d.a.8.1	yes	4	31.22	odd	30
279.2.i.a.163.1		4	93.53	even	30
279.2.i.a.190.1		4	93.26	even	6
496.2.n.b.97.1		4	124.119	even	6
496.2.n.b.225.1		4	124.115	even	30
775.2.k.c.101.1		4	155.84	odd	30
775.2.k.c.376.1		4	155.119	odd	6
775.2.bf.a.349.1		8	155.22	even	60
775.2.bf.a.349.2		8	155.53	even	60
775.2.bf.a.624.1		8	155.88	even	12
775.2.bf.a.624.2		8	155.57	even	12
961.2.a.d.1.1		2	31.13	odd	30
961.2.a.e.1.1		2	31.18	even	15
961.2.c.d.439.1		4	31.16	even	5
961.2.c.d.521.1		4	31.28	even	15
961.2.c.f.439.1		4	31.15	odd	10
961.2.c.f.521.1		4	31.3	odd	30
961.2.d.b.531.1		4	31.5	even	3
961.2.d.b.628.1		4	31.9	even	15
961.2.d.e.374.1		4	31.20	even	15
961.2.d.e.388.1		4	31.10	even	15
961.2.d.f.374.1		4	31.11	odd	30
961.2.d.f.388.1		4	31.21	odd	30
961.2.g.b.448.1		8	31.17	odd	30
961.2.g.b.547.1		8	31.30	odd	2
961.2.g.b.844.1		8	31.6	odd	6
961.2.g.b.846.1		8	31.23	odd	10
961.2.g.c.448.1		8	31.14	even	15	inner
961.2.g.c.547.1		8	1.1	even	1	trivial
961.2.g.c.844.1		8	31.25	even	3	inner
961.2.g.c.846.1		8	31.8	even	5	inner
961.2.g.f.235.1		8	31.29	odd	10
961.2.g.f.338.1		8	31.12	odd	30
961.2.g.f.732.1		8	31.24	odd	30
961.2.g.f.816.1		8	31.27	odd	10
961.2.g.g.235.1		8	31.2	even	5
961.2.g.g.338.1		8	31.19	even	15
961.2.g.g.732.1		8	31.7	even	15
961.2.g.g.816.1		8	31.4	even	5
8649.2.a.f.1.2		2	93.80	odd	30
8649.2.a.g.1.2		2	93.44	even	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+(-0.190983 - 0.587785i) q^{2} +(0.669131 + 0.743145i) q^{3} +(1.30902 - 0.951057i) q^{4} +(1.30902 + 2.26728i) q^{5} +(0.309017 - 0.535233i) q^{6} +(-0.313585 - 2.98357i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.209057 - 1.98904i) q^{9} +(1.08268 - 1.20243i) q^{10} +(0.697887 + 0.310719i) q^{11} +(1.58268 + 0.336408i) q^{12} +(4.74803 - 1.00922i) q^{13} +(-1.69381 + 0.754131i) q^{14} +(-0.809017 + 2.48990i) q^{15} +(0.572949 - 1.76336i) q^{16} +(-0.215659 + 0.0960175i) q^{17} +(-1.20906 + 0.256993i) q^{18} +(-4.89074 - 1.03956i) q^{19} +(3.86984 + 1.72296i) q^{20} +(2.00739 - 2.22943i) q^{21} +(0.0493516 - 0.469550i) q^{22} +(-4.42705 - 3.21644i) q^{23} +(-0.233733 - 2.22382i) q^{24} +(-0.927051 + 1.60570i) q^{25} +(-1.50000 - 2.59808i) q^{26} +(4.04508 - 2.93893i) q^{27} +(-3.24803 - 3.60730i) q^{28} +(2.66312 + 8.19624i) q^{29} +1.61803 q^{30} -5.61803 q^{32} +(0.236068 + 0.726543i) q^{33} +(0.0976248 + 0.108423i) q^{34} +(6.35410 - 4.61653i) q^{35} +(-1.61803 - 2.80252i) q^{36} +(0.118034 - 0.204441i) q^{37} +(0.323011 + 3.07324i) q^{38} +(3.92705 + 2.85317i) q^{39} +(0.611920 - 5.82203i) q^{40} +(4.33070 - 4.80973i) q^{41} +(-1.69381 - 0.754131i) q^{42} +(-4.51712 - 0.960143i) q^{43} +(1.20906 - 0.256993i) q^{44} +(4.78339 - 2.12970i) q^{45} +(-1.04508 + 3.21644i) q^{46} +(-1.04508 + 3.21644i) q^{47} +(1.69381 - 0.754131i) q^{48} +(-1.95630 + 0.415823i) q^{49} +(1.12086 + 0.238246i) q^{50} +(-0.215659 - 0.0960175i) q^{51} +(5.25542 - 5.83674i) q^{52} +(-1.32837 + 12.6386i) q^{53} +(-2.50000 - 1.81636i) q^{54} +(0.209057 + 1.98904i) q^{55} +(-3.35410 + 5.80948i) q^{56} +(-2.50000 - 4.33013i) q^{57} +(4.30902 - 3.13068i) q^{58} +(6.33810 + 7.03917i) q^{59} +(1.30902 + 4.02874i) q^{60} +6.94427 q^{61} -6.00000 q^{63} +(-0.0729490 - 0.224514i) q^{64} +(8.50345 + 9.44404i) q^{65} +(0.381966 - 0.277515i) q^{66} +(2.11803 + 3.66854i) q^{67} +(-0.190983 + 0.330792i) q^{68} +(-0.571994 - 5.44216i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-0.00942533 + 0.0896760i) q^{71} +(-2.99244 + 3.32344i) q^{72} +(7.82206 + 3.48260i) q^{73} +(-0.142710 - 0.0303339i) q^{74} +(-1.81359 + 0.385489i) q^{75} +(-7.39074 + 3.29057i) q^{76} +(0.708204 - 2.17963i) q^{77} +(0.927051 - 2.85317i) q^{78} +(4.74803 - 1.00922i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-3.65418 - 1.62695i) q^{82} +(2.73686 - 3.03959i) q^{83} +(0.507392 - 4.82751i) q^{84} +(-0.500000 - 0.363271i) q^{85} +(0.298335 + 2.83847i) q^{86} +(-4.30902 + 7.46344i) q^{87} +(-0.854102 - 1.47935i) q^{88} +(-5.16312 + 3.75123i) q^{89} +(-2.16535 - 2.40487i) q^{90} +(-4.50000 - 13.8496i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(-4.04508 - 12.4495i) q^{95} +(-3.75920 - 4.17501i) q^{96} +(4.28115 - 3.11044i) q^{97} +(0.618034 + 1.07047i) q^{98} +(0.763932 - 1.32317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} - 10 q^{8} - 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} - 6 q^{14} - 2 q^{15} + 18 q^{16} - 3 q^{17} - 6 q^{18} + 5 q^{19} + 7 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 + q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 - 10 * q^8 - 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 - 6 * q^14 - 2 * q^15 + 18 * q^16 - 3 * q^17 - 6 * q^18 + 5 * q^19 + 7 * q^20 + 3 * q^21 - 6 * q^22 - 22 * q^23 + 5 * q^24 + 6 * q^25 - 12 * q^26 + 10 * q^27 + 6 * q^28 - 10 * q^29 + 4 * q^30 - 36 * q^32 - 16 * q^33 + 11 * q^34 + 24 * q^35 - 4 * q^36 - 8 * q^37 - 10 * q^38 + 18 * q^39 - 10 * q^40 - 8 * q^41 - 6 * q^42 + q^43 + 6 * q^44 + 8 * q^45 + 14 * q^46 + 14 * q^47 + 6 * q^48 + 2 * q^49 - 12 * q^50 - 3 * q^51 - 3 * q^52 + 21 * q^53 - 20 * q^54 - 2 * q^55 - 20 * q^57 + 30 * q^58 - 5 * q^59 + 6 * q^60 - 16 * q^61 - 48 * q^63 - 14 * q^64 - 9 * q^65 + 12 * q^66 + 8 * q^67 - 6 * q^68 + 11 * q^69 - 18 * q^70 + 7 * q^71 + 10 * q^72 + 21 * q^73 + 11 * q^74 - 9 * q^75 - 15 * q^76 - 48 * q^77 - 6 * q^78 + 6 * q^80 + q^81 - 4 * q^82 - 14 * q^83 - 9 * q^84 - 4 * q^85 - 7 * q^86 - 30 * q^87 + 20 * q^88 - 10 * q^89 + 4 * q^90 - 36 * q^91 - 44 * q^92 - 28 * q^94 - 10 * q^95 - 2 * q^96 - 6 * q^97 - 4 * q^98 + 24 * q^99

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