LMFDB - Embedded newform 300.2.j.d.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(7,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("300.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$-0.0912546 - 1.41127i$ of defining polynomial
Character	$\chi$	$=$	300.43
Dual form			300.2.j.d.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0912546 - 1.41127i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.06244 + 0.933389i) q^{6} +(1.86678 + 1.86678i) q^{7} +(0.544488 + 2.77552i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.0912546 - 1.41127i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.06244 + 0.933389i) q^{6} +(1.86678 + 1.86678i) q^{7} +(0.544488 + 2.77552i) q^{8} -1.00000i q^{9} +0.728515i q^{11} +(1.22031 - 1.58457i) q^{12} +(3.12489 + 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(3.86732 - 1.02170i) q^{16} +(-1.12489 + 1.12489i) q^{17} +(-1.41127 + 0.0912546i) q^{18} +3.73356 q^{19} -2.64002 q^{21} +(1.02813 - 0.0664803i) q^{22} +(5.83347 - 5.83347i) q^{23} +(-2.34760 - 1.57758i) q^{24} +(4.12489 - 4.69521i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.18329 - 3.22164i) q^{28} +2.64002i q^{29} +6.01008i q^{31} +(-1.79480 - 5.36458i) q^{32} +(-0.515138 - 0.515138i) q^{33} +(1.69016 + 1.48486i) q^{34} +(0.257569 + 1.98335i) q^{36} +(-3.12489 + 3.12489i) q^{37} +(-0.340704 - 5.26904i) q^{38} -4.41926 q^{39} -4.24977 q^{41} +(0.240914 + 3.72578i) q^{42} +(-5.10495 + 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(-8.76491 - 7.70025i) q^{46} +(-2.09991 - 2.09991i) q^{47} +(-2.01216 + 3.45705i) q^{48} -0.0302761i q^{49} -1.59083i q^{51} +(-7.00260 - 5.39285i) q^{52} +(-0.484862 - 0.484862i) q^{53} +(0.933389 - 1.06244i) q^{54} +(-4.16485 + 6.19773i) q^{56} +(-2.64002 + 2.64002i) q^{57} +(3.72578 - 0.240914i) q^{58} +4.92834 q^{59} +2.31032 q^{61} +(8.48183 - 0.548448i) q^{62} +(1.86678 - 1.86678i) q^{63} +(-7.40707 + 3.02248i) q^{64} +(-0.679988 + 0.774006i) q^{66} +(5.10495 + 5.10495i) q^{67} +(1.94130 - 2.52077i) q^{68} +8.24977i q^{69} -13.1240i q^{71} +(2.77552 - 0.544488i) q^{72} +(-3.96972 - 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(-7.40493 + 0.961649i) q^{76} +(-1.35998 + 1.35998i) q^{77} +(0.403277 + 6.23675i) q^{78} -7.11388 q^{79} -1.00000 q^{81} +(0.387811 + 5.99756i) q^{82} +(-3.55694 + 3.55694i) q^{83} +(5.23608 - 0.679988i) q^{84} +(7.67030 + 6.73860i) q^{86} +(-1.86678 - 1.86678i) q^{87} +(-2.02201 + 0.396668i) q^{88} +1.03028i q^{89} +11.6669i q^{91} +(-10.0673 + 13.0723i) q^{92} +(-4.24977 - 4.24977i) q^{93} +(-2.77191 + 3.15516i) q^{94} +(5.06244 + 2.52422i) q^{96} +(12.5298 - 12.5298i) q^{97} +(-0.0427276 + 0.00276283i) q^{98} +0.728515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q - 4 * q^6 + 12 * q^8	$ 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48} + 8 q^{52} - 4 q^{53} - 64 q^{56} + 20 q^{58} - 32 q^{61} + 56 q^{62} - 24 q^{66} + 16 q^{68} + 12 q^{72} - 44 q^{73} + 8 q^{76} - 48 q^{77} + 24 q^{78} - 12 q^{81} - 16 q^{82} + 64 q^{86} - 60 q^{88} - 56 q^{92} + 16 q^{93} + 44 q^{96} + 20 q^{97} - 24 q^{98}+O(q^{100}) $ 12 * q - 4 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 + 12 * q^16 + 20 * q^17 - 12 * q^22 + 16 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^38 + 16 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 - 64 * q^56 + 20 * q^58 - 32 * q^61 + 56 * q^62 - 24 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 + 8 * q^76 - 48 * q^77 + 24 * q^78 - 12 * q^81 - 16 * q^82 + 64 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 44 * q^96 + 20 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0912546	−	1.41127i	−0.0645267	−	0.997916i
$2$	−0.0912546	−	1.41127i	−0.0645267	−	0.997916i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.98335	+	0.257569i	−0.991673	+	0.128785i
$5$		0			0
$5$		0			0
$6$	1.06244	+	0.933389i	0.433740	+	0.381055i
$7$	1.86678	+	1.86678i	0.705576	+	0.705576i	0.965602	−	0.260026i	$-0.0837311\pi$
$7$	1.86678	+	1.86678i	0.705576	+	0.705576i	−0.260026	+	0.965602i	$0.583731\pi$
$8$	0.544488	+	2.77552i	0.192506	+	0.981296i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			0.728515i			0.219656i	0.993951	+	0.109828i	$0.0350299\pi$
$11$			0.728515i			0.219656i	−0.993951	+	0.109828i	$0.964970\pi$
$12$	1.22031	−	1.58457i	0.352273	−	0.457425i
$13$	3.12489	+	3.12489i	0.866687	+	0.866687i	0.992104	−	0.125417i	$-0.0400268\pi$
$13$	3.12489	+	3.12489i	0.866687	+	0.866687i	−0.125417	+	0.992104i	$0.540027\pi$
$14$	2.46417	−	2.80487i	0.658577	−	0.749634i
$15$		0			0
$16$	3.86732	−	1.02170i	0.966829	−	0.255424i
$17$	−1.12489	+	1.12489i	−0.272825	+	0.272825i	−0.830236	−	0.557412i	$-0.811795\pi$
$17$	−1.12489	+	1.12489i	−0.272825	+	0.272825i	0.557412	+	0.830236i	$0.311795\pi$
$18$	−1.41127	+	0.0912546i	−0.332639	+	0.0215089i
$19$	3.73356			0.856537			0.428268	−	0.903652i	$-0.359124\pi$
$19$	3.73356			0.856537			0.428268	+	0.903652i	$0.359124\pi$
$20$		0			0
$21$	−2.64002			−0.576100
$22$	1.02813	−	0.0664803i	0.219198	−	0.0141737i
$23$	5.83347	−	5.83347i	1.21636	−	1.21636i	0.247466	−	0.968897i	$-0.420402\pi$
$23$	5.83347	−	5.83347i	1.21636	−	1.21636i	0.968897	−	0.247466i	$-0.0795978\pi$
$24$	−2.34760	−	1.57758i	−0.479202	−	0.322022i
$25$		0			0
$26$	4.12489	−	4.69521i	0.808957	−	0.920806i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−4.18329	−	3.22164i	−0.790568	−	0.608833i
$29$			2.64002i			0.490240i	0.969493	+	0.245120i	$0.0788274\pi$
$29$			2.64002i			0.490240i	−0.969493	+	0.245120i	$0.921173\pi$
$30$		0			0
$31$			6.01008i			1.07944i	0.841844	+	0.539721i	$0.181470\pi$
$31$			6.01008i			1.07944i	−0.841844	+	0.539721i	$0.818530\pi$
$32$	−1.79480	−	5.36458i	−0.317278	−	0.948333i
$33$	−0.515138	−	0.515138i	−0.0896740	−	0.0896740i
$34$	1.69016	+	1.48486i	0.289861	+	0.254652i
$35$		0			0
$36$	0.257569	+	1.98335i	0.0429282	+	0.330558i
$37$	−3.12489	+	3.12489i	−0.513728	+	0.513728i	−0.915667	−	0.401939i	$-0.868337\pi$
$37$	−3.12489	+	3.12489i	−0.513728	+	0.513728i	0.401939	+	0.915667i	$0.368337\pi$
$38$	−0.340704	−	5.26904i	−0.0552695	−	0.854752i
$39$	−4.41926			−0.707647
$40$		0			0
$41$	−4.24977			−0.663703			−0.331851	−	0.943332i	$-0.607673\pi$
$41$	−4.24977			−0.663703			−0.331851	+	0.943332i	$0.607673\pi$
$42$	0.240914	+	3.72578i	0.0371739	+	0.574900i
$43$	−5.10495	+	5.10495i	−0.778498	+	0.778498i	−0.979575	−	0.201077i	$-0.935556\pi$
$43$	−5.10495	+	5.10495i	−0.778498	+	0.778498i	0.201077	+	0.979575i	$0.435556\pi$
$44$	−0.187643	−	1.44490i	−0.0282882	−	0.217826i
$45$		0			0
$46$	−8.76491	−	7.70025i	−1.29232	−	1.13534i
$47$	−2.09991	−	2.09991i	−0.306304	−	0.306304i	0.537170	−	0.843474i	$-0.319493\pi$
$47$	−2.09991	−	2.09991i	−0.306304	−	0.306304i	−0.843474	+	0.537170i	$0.819493\pi$
$48$	−2.01216	+	3.45705i	−0.290430	+	0.498983i
$49$		−	0.0302761i		−	0.00432516i
$50$		0			0
$51$		−	1.59083i		−	0.222761i
$52$	−7.00260	−	5.39285i	−0.971086	−	0.747854i
$53$	−0.484862	−	0.484862i	−0.0666009	−	0.0666009i	0.673022	−	0.739623i	$-0.264996\pi$
$53$	−0.484862	−	0.484862i	−0.0666009	−	0.0666009i	−0.739623	+	0.673022i	$0.764996\pi$
$54$	0.933389	−	1.06244i	0.127018	−	0.144580i
$55$		0			0
$56$	−4.16485	+	6.19773i	−0.556552	+	0.828206i
$57$	−2.64002	+	2.64002i	−0.349680	+	0.349680i
$58$	3.72578	−	0.240914i	0.489218	−	0.0316336i
$59$	4.92834			0.641615			0.320808	−	0.947144i	$-0.396046\pi$
$59$	4.92834			0.641615			0.320808	+	0.947144i	$0.396046\pi$
$60$		0			0
$61$	2.31032			0.295807			0.147903	−	0.989002i	$-0.452748\pi$
$61$	2.31032			0.295807			0.147903	+	0.989002i	$0.452748\pi$
$62$	8.48183	−	0.548448i	1.07719	−	0.0696529i
$63$	1.86678	−	1.86678i	0.235192	−	0.235192i
$64$	−7.40707	+	3.02248i	−0.925883	+	0.377810i
$65$		0			0
$66$	−0.679988	+	0.774006i	−0.0837008	+	0.0952735i
$67$	5.10495	+	5.10495i	0.623669	+	0.623669i	0.946468	−	0.322798i	$-0.104624\pi$
$67$	5.10495	+	5.10495i	0.623669	+	0.623669i	−0.322798	+	0.946468i	$0.604624\pi$
$68$	1.94130	−	2.52077i	0.235417	−	0.305688i
$69$			8.24977i			0.993156i
$70$		0			0
$71$		−	13.1240i		−	1.55753i	−0.627317	−	0.778764i	$-0.715847\pi$
$71$		−	13.1240i		−	1.55753i	0.627317	−	0.778764i	$-0.284153\pi$
$72$	2.77552	−	0.544488i	0.327099	−	0.0641685i
$73$	−3.96972	−	3.96972i	−0.464621	−	0.464621i	0.435546	−	0.900167i	$-0.356555\pi$
$73$	−3.96972	−	3.96972i	−0.464621	−	0.464621i	−0.900167	+	0.435546i	$0.856555\pi$
$74$	4.69521	+	4.12489i	0.545807	+	0.479508i
$75$		0			0
$76$	−7.40493	+	0.961649i	−0.849404	+	0.110309i
$77$	−1.35998	+	1.35998i	−0.154984	+	0.154984i
$78$	0.403277	+	6.23675i	0.0456622	+	0.706172i
$79$	−7.11388			−0.800375			−0.400187	−	0.916433i	$-0.631055\pi$
$79$	−7.11388			−0.800375			−0.400187	+	0.916433i	$0.631055\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	0.387811	+	5.99756i	0.0428266	+	0.662320i
$83$	−3.55694	+	3.55694i	−0.390425	+	0.390425i	−0.874839	−	0.484414i	$-0.839033\pi$
$83$	−3.55694	+	3.55694i	−0.390425	+	0.390425i	0.484414	+	0.874839i	$0.339033\pi$
$84$	5.23608	−	0.679988i	0.571303	−	0.0741928i
$85$		0			0
$86$	7.67030	+	6.73860i	0.827110	+	0.726642i
$87$	−1.86678	−	1.86678i	−0.200140	−	0.200140i
$88$	−2.02201	+	0.396668i	−0.215547	+	0.0422849i
$89$			1.03028i			0.109209i	0.998508	+	0.0546045i	$0.0173898\pi$
$89$			1.03028i			0.109209i	−0.998508	+	0.0546045i	$0.982610\pi$
$90$		0			0
$91$			11.6669i			1.22303i
$92$	−10.0673	+	13.0723i	−1.04958	+	1.36288i
$93$	−4.24977	−	4.24977i	−0.440681	−	0.440681i
$94$	−2.77191	+	3.15516i	−0.285901	+	0.325430i
$95$		0			0
$96$	5.06244	+	2.52422i	0.516683	+	0.257627i
$97$	12.5298	−	12.5298i	1.27221	−	1.27221i	0.327284	−	0.944926i	$-0.393867\pi$
$97$	12.5298	−	12.5298i	1.27221	−	1.27221i	0.944926	−	0.327284i	$-0.106133\pi$
$98$	−0.0427276	+	0.00276283i	−0.00431614	+	0.000279088i
$99$	0.728515			0.0732185
$100$		0			0
$101$	−5.67030			−0.564216			−0.282108	−	0.959383i	$-0.591034\pi$
$101$	−5.67030			−0.564216			−0.282108	+	0.959383i	$0.591034\pi$
$102$	−2.24508	+	0.145170i	−0.222296	+	0.0143740i
$103$	0.0565188	−	0.0565188i	0.00556896	−	0.00556896i	−0.704317	−	0.709886i	$-0.748747\pi$
$103$	0.0565188	−	0.0565188i	0.00556896	−	0.00556896i	0.709886	+	0.704317i	$0.248747\pi$
$104$	−6.97173	+	10.3747i	−0.683635	+	1.01732i
$105$		0			0
$106$	−0.640023	+	0.728515i	−0.0621646	+	0.0707597i
$107$	−3.91017	−	3.91017i	−0.378011	−	0.378011i	0.492373	−	0.870384i	$-0.336129\pi$
$107$	−3.91017	−	3.91017i	−0.378011	−	0.378011i	−0.870384	+	0.492373i	$0.836129\pi$
$108$	−1.58457	−	1.22031i	−0.152475	−	0.117424i
$109$		−	15.7796i		−	1.51141i	−0.654912	−	0.755705i	$-0.727294\pi$
$109$		−	15.7796i		−	1.51141i	0.654912	−	0.755705i	$-0.272706\pi$
$110$		0			0
$111$		−	4.41926i		−	0.419457i
$112$	9.12670	+	5.31214i	0.862392	+	0.501950i
$113$	1.84484	+	1.84484i	0.173548	+	0.173548i	0.788536	−	0.614988i	$-0.210839\pi$
$113$	1.84484	+	1.84484i	0.173548	+	0.173548i	−0.614988	+	0.788536i	$0.710839\pi$
$114$	3.96669	+	3.48486i	0.371515	+	0.326387i
$115$		0			0
$116$	−0.679988	−	5.23608i	−0.0631353	−	0.486158i
$117$	3.12489	−	3.12489i	0.288896	−	0.288896i
$118$	−0.449733	−	6.95520i	−0.0414013	−	0.640278i
$119$	−4.19982			−0.384997
$120$		0			0
$121$	10.4693			0.951751
$122$	−0.210828	−	3.26048i	−0.0190874	−	0.295190i
$123$	3.00504	−	3.00504i	0.270955	−	0.270955i
$124$	−1.54801	−	11.9201i	−0.139016	−	1.07045i
$125$		0			0
$126$	−2.80487	−	2.46417i	−0.249878	−	0.219526i
$127$	−11.2572	−	11.2572i	−0.998914	−	0.998914i	0.00108535	−	0.999999i	$-0.499655\pi$
$127$	−11.2572	−	11.2572i	−0.998914	−	0.998914i	−0.999999	+	0.00108535i	$0.999655\pi$
$128$	4.94145	+	10.1775i	0.436767	+	0.899575i
$129$		−	7.21949i		−	0.635641i
$130$		0			0
$131$			4.57511i			0.399729i	0.979824	+	0.199865i	$0.0640502\pi$
$131$			4.57511i			0.399729i	−0.979824	+	0.199865i	$0.935950\pi$
$132$	1.15438	+	0.889013i	0.100476	+	0.0773786i
$133$	6.96972	+	6.96972i	0.604352	+	0.604352i
$134$	6.73860	−	7.67030i	0.582126	−	0.662613i
$135$		0			0
$136$	−3.73463	−	2.50966i	−0.320242	−	0.215202i
$137$	4.09461	−	4.09461i	0.349826	−	0.349826i	−0.510219	−	0.860045i	$-0.670436\pi$
$137$	4.09461	−	4.09461i	0.349826	−	0.349826i	0.860045	+	0.510219i	$0.170436\pi$
$138$	11.6426	−	0.752829i	0.991086	−	0.0640851i
$139$	13.5902			1.15271			0.576354	−	0.817200i	$-0.304475\pi$
$139$	13.5902			1.15271			0.576354	+	0.817200i	$0.304475\pi$
$140$		0			0
$141$	2.96972			0.250096
$142$	−18.5214	+	1.19762i	−1.55428	+	0.100502i
$143$	−2.27653	+	2.27653i	−0.190373	+	0.190373i
$144$	−1.02170	−	3.86732i	−0.0851414	−	0.322276i
$145$		0			0
$146$	−5.24008	+	5.96459i	−0.433672	+	0.493633i
$147$	0.0214084	+	0.0214084i	0.00176574	+	0.00176574i
$148$	5.39285	−	7.00260i	0.443290	−	0.575610i
$149$		−	5.67030i		−	0.464529i	−0.972653	−	0.232265i	$-0.925386\pi$
$149$		−	5.67030i		−	0.464529i	0.972653	−	0.232265i	$-0.0746135\pi$
$150$		0			0
$151$		−	19.2471i		−	1.56631i	−0.621829	−	0.783153i	$-0.713610\pi$
$151$		−	19.2471i		−	1.56631i	0.621829	−	0.783153i	$-0.286390\pi$
$152$	2.03288	+	10.3626i	0.164888	+	0.840516i
$153$	1.12489	+	1.12489i	0.0909416	+	0.0909416i
$154$	2.04339	+	1.79518i	0.164661	+	0.144660i
$155$		0			0
$156$	8.76491	−	1.13826i	0.701754	−	0.0911340i
$157$	2.09461	−	2.09461i	0.167168	−	0.167168i	−0.618565	−	0.785733i	$-0.712286\pi$
$157$	2.09461	−	2.09461i	0.167168	−	0.167168i	0.785733	+	0.618565i	$0.212286\pi$
$158$	0.649175	+	10.0396i	0.0516456	+	0.798707i
$159$	0.685698			0.0543794
$160$		0			0
$161$	21.7796			1.71647
$162$	0.0912546	+	1.41127i	0.00716964	+	0.110880i
$163$	−4.28546	+	4.28546i	−0.335663	+	0.335663i	−0.854732	−	0.519069i	$-0.826279\pi$
$163$	−4.28546	+	4.28546i	−0.335663	+	0.335663i	0.519069	+	0.854732i	$0.326279\pi$
$164$	8.42876	−	1.09461i	0.658176	−	0.0854746i
$165$		0			0
$166$	5.34438	+	4.69521i	0.414804	+	0.364419i
$167$	4.37644	+	4.37644i	0.338659	+	0.338659i	0.855862	−	0.517203i	$-0.173027\pi$
$167$	4.37644	+	4.37644i	0.338659	+	0.338659i	−0.517203	+	0.855862i	$0.673027\pi$
$168$	−1.43746	−	7.32745i	−0.110902	−	0.565325i
$169$			6.52982i			0.502294i
$170$		0			0
$171$		−	3.73356i		−	0.285512i
$172$	8.81001	−	11.4398i	0.671757	−	0.872274i
$173$	−16.4049	−	16.4049i	−1.24724	−	1.24724i	−0.956932	−	0.290312i	$-0.906241\pi$
$173$	−16.4049	−	16.4049i	−1.24724	−	1.24724i	−0.290312	−	0.956932i	$-0.593759\pi$
$174$	−2.46417	+	2.80487i	−0.186808	+	0.212637i
$175$		0			0
$176$	0.744321	+	2.81740i	0.0561053	+	0.212369i
$177$	−3.48486	+	3.48486i	−0.261938	+	0.261938i
$178$	1.45399	−	0.0940174i	0.108981	−	0.00704690i
$179$	−24.4156			−1.82491			−0.912455	−	0.409178i	$-0.865815\pi$
$179$	−24.4156			−1.82491			−0.912455	+	0.409178i	$0.865815\pi$
$180$		0			0
$181$	11.2800			0.838439			0.419220	−	0.907885i	$-0.362304\pi$
$181$	11.2800			0.838439			0.419220	+	0.907885i	$0.362304\pi$
$182$	16.4652	−	1.06466i	1.22048	−	0.0789180i
$183$	−1.63365	+	1.63365i	−0.120763	+	0.120763i
$184$	19.3672	+	13.0147i	1.42777	+	0.959455i
$185$		0			0
$186$	−5.60975	+	6.38537i	−0.411327	+	0.468198i
$187$	−0.819496	−	0.819496i	−0.0599275	−	0.0599275i
$188$	4.70572	+	3.62398i	0.343200	+	0.264306i
$189$			2.64002i			0.192033i
$190$		0			0
$191$			3.26729i			0.236413i	0.992989	+	0.118206i	$0.0377144\pi$
$191$			3.26729i			0.236413i	−0.992989	+	0.118206i	$0.962286\pi$
$192$	3.10037	−	7.37480i	0.223750	−	0.532230i
$193$	−0.939448	−	0.939448i	−0.0676229	−	0.0676229i	0.672486	−	0.740109i	$-0.265226\pi$
$193$	−0.939448	−	0.939448i	−0.0676229	−	0.0676229i	−0.740109	+	0.672486i	$0.765226\pi$
$194$	−18.8263	−	16.5395i	−1.35165	−	1.18747i
$195$		0			0
$196$	0.00779818	+	0.0600479i	0.000557013	+	0.00428914i
$197$	1.45459	−	1.45459i	0.103635	−	0.103635i	−0.653388	−	0.757023i	$-0.726653\pi$
$197$	1.45459	−	1.45459i	0.103635	−	0.103635i	0.757023	+	0.653388i	$0.226653\pi$
$198$	−0.0664803	−	1.02813i	−0.00472455	−	0.0730659i
$199$	5.19059			0.367951			0.183975	−	0.982931i	$-0.441103\pi$
$199$	5.19059			0.367951			0.183975	+	0.982931i	$0.441103\pi$
$200$		0			0
$201$	−7.21949			−0.509224
$202$	0.517441	+	8.00230i	0.0364070	+	0.563040i
$203$	−4.92834	+	4.92834i	−0.345902	+	0.345902i
$204$	0.409748	+	3.15516i	0.0286881	+	0.220905i
$205$		0			0
$206$	−0.0849206	−	0.0746054i	−0.00591670	−	0.00519801i
$207$	−5.83347	−	5.83347i	−0.405454	−	0.405454i
$208$	15.2776	+	8.89224i	1.05931	+	0.616566i
$209$			2.71995i			0.188143i
$210$		0			0
$211$			11.7800i			0.810967i	0.914102	+	0.405483i	$0.132897\pi$
$211$			11.7800i			0.810967i	−0.914102	+	0.405483i	$0.867103\pi$
$212$	1.08653	+	0.836763i	0.0746235	+	0.0574691i
$213$	9.28005	+	9.28005i	0.635858	+	0.635858i
$214$	−5.16147	+	5.87511i	−0.352831	+	0.401615i
$215$		0			0
$216$	−1.57758	+	2.34760i	−0.107341	+	0.159734i
$217$	−11.2195	+	11.2195i	−0.761629	+	0.761629i
$218$	−22.2692	+	1.43996i	−1.50826	+	0.0975264i
$219$	5.61404			0.379361
$220$		0			0
$221$	−7.03028			−0.472908
$222$	−6.23675	+	0.403277i	−0.418583	+	0.0270662i
$223$	3.32381	−	3.32381i	0.222579	−	0.222579i	−0.587005	−	0.809583i	$-0.699693\pi$
$223$	3.32381	−	3.32381i	0.222579	−	0.222579i	0.809583	+	0.587005i	$0.199693\pi$
$224$	6.66399	−	13.3650i	0.445257	−	0.892984i
$225$		0			0
$226$	2.43521	−	2.77191i	0.161988	−	0.184385i
$227$	8.83851	+	8.83851i	0.586633	+	0.586633i	0.936718	−	0.350085i	$-0.113847\pi$
$227$	8.83851	+	8.83851i	0.586633	+	0.586633i	−0.350085	+	0.936718i	$0.613847\pi$
$228$	4.55609	−	5.91607i	0.301734	−	0.391801i
$229$			7.09083i			0.468575i	0.972167	+	0.234288i	$0.0752757\pi$
$229$			7.09083i			0.468575i	−0.972167	+	0.234288i	$0.924724\pi$
$230$		0			0
$231$		−	1.92330i		−	0.126544i
$232$	−7.32745	+	1.43746i	−0.481071	+	0.0943739i
$233$	15.3747	+	15.3747i	1.00723	+	1.00723i	0.999974	+	0.00725353i	$0.00230889\pi$
$233$	15.3747	+	15.3747i	1.00723	+	1.00723i	0.00725353	+	0.999974i	$0.497691\pi$
$234$	−4.69521	−	4.12489i	−0.306935	−	0.269652i
$235$		0			0
$236$	−9.77460	+	1.26939i	−0.636272	+	0.0826301i
$237$	5.03028	−	5.03028i	0.326752	−	0.326752i
$238$	0.383253	+	5.92707i	0.0248426	+	0.384195i
$239$	0.706459			0.0456970			0.0228485	−	0.999739i	$-0.492726\pi$
$239$	0.706459			0.0456970			0.0228485	+	0.999739i	$0.492726\pi$
$240$		0			0
$241$	−24.9991			−1.61033			−0.805166	−	0.593049i	$-0.797924\pi$
$241$	−24.9991			−1.61033			−0.805166	+	0.593049i	$0.797924\pi$
$242$	−0.955368	−	14.7749i	−0.0614134	−	0.949768i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−4.58217	+	0.595068i	−0.293343	+	0.0380953i
$245$		0			0
$246$	−4.51514	−	3.96669i	−0.287875	−	0.252907i
$247$	11.6669	+	11.6669i	0.742349	+	0.742349i
$248$	−16.6811	+	3.27242i	−1.05925	+	0.207799i
$249$		−	5.03028i		−	0.318781i
$250$		0			0
$251$			28.6154i			1.80619i	0.429440	+	0.903095i	$0.358711\pi$
$251$			28.6154i			1.80619i	−0.429440	+	0.903095i	$0.641289\pi$
$252$	−3.22164	+	4.18329i	−0.202944	+	0.263523i
$253$	4.24977	+	4.24977i	0.267181	+	0.267181i
$254$	−14.8596	+	16.9142i	−0.932376	+	1.06129i
$255$		0			0
$256$	13.9123	−	7.90245i	0.869517	−	0.493903i
$257$	3.90539	−	3.90539i	0.243612	−	0.243612i	−0.574731	−	0.818342i	$-0.694893\pi$
$257$	3.90539	−	3.90539i	0.243612	−	0.243612i	0.818342	+	0.574731i	$0.194893\pi$
$258$	−10.1886	+	0.658812i	−0.634316	+	0.0410158i
$259$	−11.6669			−0.724948
$260$		0			0
$261$	2.64002			0.163413
$262$	6.45670	−	0.417500i	0.398896	−	0.0257932i
$263$	−0.176615	+	0.176615i	−0.0108905	+	0.0108905i	−0.712531	−	0.701641i	$-0.752451\pi$
$263$	−0.176615	+	0.176615i	−0.0108905	+	0.0108905i	0.701641	+	0.712531i	$0.252451\pi$
$264$	1.14929	−	1.71026i	0.0707340	−	0.105259i
$265$		0			0
$266$	9.20012	−	10.4722i	0.564095	−	0.642089i
$267$	−0.728515	−	0.728515i	−0.0445844	−	0.0445844i
$268$	−11.4398	−	8.81001i	−0.698795	−	0.538157i
$269$			5.38934i			0.328594i	0.986411	+	0.164297i	$0.0525355\pi$
$269$			5.38934i			0.328594i	−0.986411	+	0.164297i	$0.947465\pi$
$270$		0			0
$271$		−	15.4005i		−	0.935513i	−0.883857	−	0.467757i	$-0.845062\pi$
$271$		−	15.4005i		−	0.935513i	0.883857	−	0.467757i	$-0.154938\pi$
$272$	−3.20100	+	5.49958i	−0.194089	+	0.333461i
$273$	−8.24977	−	8.24977i	−0.499299	−	0.499299i
$274$	−6.15224	−	5.40493i	−0.371670	−	0.326524i
$275$		0			0
$276$	−2.12489	−	16.3621i	−0.127903	−	0.984885i
$277$	−8.59415	+	8.59415i	−0.516372	+	0.516372i	−0.916472	−	0.400099i	$-0.868976\pi$
$277$	−8.59415	+	8.59415i	−0.516372	+	0.516372i	0.400099	+	0.916472i	$0.368976\pi$
$278$	−1.24017	−	19.1794i	−0.0743805	−	1.15031i
$279$	6.01008			0.359814
$280$		0			0
$281$	−20.7493			−1.23780			−0.618900	−	0.785470i	$-0.712421\pi$
$281$	−20.7493			−1.23780			−0.618900	+	0.785470i	$0.712421\pi$
$282$	−0.271001	−	4.19107i	−0.0161379	−	0.249575i
$283$	18.5822	−	18.5822i	1.10459	−	1.10459i	0.110745	−	0.993849i	$-0.464676\pi$
$283$	18.5822	−	18.5822i	1.10459	−	1.10459i	0.993849	−	0.110745i	$-0.0353238\pi$
$284$	3.38033	+	26.0294i	0.200586	+	1.54456i
$285$		0			0
$286$	3.42053	+	3.00504i	0.202260	+	0.177692i
$287$	−7.93338	−	7.93338i	−0.468293	−	0.468293i
$288$	−5.36458	+	1.79480i	−0.316111	+	0.105759i
$289$			14.4693i			0.851133i
$290$		0			0
$291$			17.7198i			1.03876i
$292$	8.89581	+	6.85085i	0.520588	+	0.400916i
$293$	−6.23509	−	6.23509i	−0.364258	−	0.364258i	0.501120	−	0.865378i	$-0.332922\pi$
$293$	−6.23509	−	6.23509i	−0.364258	−	0.364258i	−0.865378	+	0.501120i	$0.832922\pi$
$294$	0.0282594	−	0.0321666i	0.00164812	−	0.00187600i
$295$		0			0
$296$	−10.3747	−	6.97173i	−0.603015	−	0.405224i
$297$	−0.515138	+	0.515138i	−0.0298913	+	0.0298913i
$298$	−8.00230	+	0.517441i	−0.463561	+	0.0299745i
$299$	36.4578			2.10841
$300$		0			0
$301$	−19.0596			−1.09858
$302$	−27.1628	+	1.75639i	−1.56304	+	0.101069i
$303$	4.00951	−	4.00951i	0.230340	−	0.230340i
$304$	14.4388	−	3.81456i	0.828125	−	0.218780i
$305$		0			0
$306$	1.48486	−	1.69016i	0.0848839	−	0.0966202i
$307$	0.905130	+	0.905130i	0.0516585	+	0.0516585i	0.732464	−	0.680806i	$-0.238370\pi$
$307$	0.905130	+	0.905130i	0.0516585	+	0.0516585i	−0.680806	+	0.732464i	$0.738370\pi$
$308$	2.34702	−	3.04759i	0.133734	−	0.173653i
$309$			0.0799296i			0.00454704i
$310$		0			0
$311$		−	24.4377i		−	1.38573i	−0.721066	−	0.692867i	$-0.756347\pi$
$311$		−	24.4377i		−	1.38573i	0.721066	−	0.692867i	$-0.243653\pi$
$312$	−2.40623	−	12.2657i	−0.136226	−	0.694411i
$313$	−18.5904	−	18.5904i	−1.05079	−	1.05079i	−0.998639	−	0.0521506i	$-0.983392\pi$
$313$	−18.5904	−	18.5904i	−1.05079	−	1.05079i	−0.0521506	−	0.998639i	$-0.516608\pi$
$314$	−3.14719	−	2.76491i	−0.177606	−	0.156033i
$315$		0			0
$316$	14.1093	−	1.83232i	0.793710	−	0.103076i
$317$	−19.3141	+	19.3141i	−1.08479	+	1.08479i	−0.0887327	+	0.996055i	$0.528282\pi$
$317$	−19.3141	+	19.3141i	−1.08479	+	1.08479i	−0.996055	+	0.0887327i	$0.971718\pi$
$318$	−0.0625731	−	0.967703i	−0.00350893	−	0.0542661i
$319$	−1.92330			−0.107684
$320$		0			0
$321$	5.52982			0.308644
$322$	−1.98749	−	30.7368i	−0.110758	−	1.71289i
$323$	−4.19982	+	4.19982i	−0.233684	+	0.233684i
$324$	1.98335	−	0.257569i	0.110186	−	0.0143094i
$325$		0			0
$326$	6.43899	+	5.65685i	0.356623	+	0.313304i
$327$	11.1579	+	11.1579i	0.617031	+	0.617031i
$328$	−2.31395	−	11.7953i	−0.127766	−	0.651289i
$329$		−	7.84014i		−	0.432241i
$330$		0			0
$331$		−	11.0294i		−	0.606231i	−0.952954	−	0.303115i	$-0.901973\pi$
$331$		−	11.0294i		−	0.606231i	0.952954	−	0.303115i	$-0.0980268\pi$
$332$	6.13849	−	7.97080i	0.336893	−	0.437455i
$333$	3.12489	+	3.12489i	0.171243	+	0.171243i
$334$	5.77695	−	6.57569i	0.316101	−	0.359806i
$335$		0			0
$336$	−10.2098	+	2.69730i	−0.556991	+	0.147150i
$337$	−13.6206	+	13.6206i	−0.741964	+	0.741964i	−0.972956	−	0.230992i	$-0.925803\pi$
$337$	−13.6206	+	13.6206i	−0.741964	+	0.741964i	0.230992	+	0.972956i	$0.425803\pi$
$338$	9.21531	−	0.595876i	0.501247	−	0.0324114i
$339$	−2.60900			−0.141701
$340$		0			0
$341$	−4.37844			−0.237106
$342$	−5.26904	+	0.340704i	−0.284917	+	0.0184232i
$343$	13.1240	−	13.1240i	0.708628	−	0.708628i
$344$	−16.9485	−	11.3893i	−0.913802	−	0.614072i
$345$		0			0
$346$	−21.6547	+	24.6488i	−1.16416	+	1.32513i
$347$	17.7627	+	17.7627i	0.953549	+	0.953549i	0.998968	−	0.0454187i	$-0.0144622\pi$
$347$	17.7627	+	17.7627i	0.953549	+	0.953549i	−0.0454187	+	0.998968i	$0.514462\pi$
$348$	4.18329	+	3.22164i	0.224248	+	0.172698i
$349$			14.6888i			0.786271i	0.919480	+	0.393136i	$0.128610\pi$
$349$			14.6888i			0.786271i	−0.919480	+	0.393136i	$0.871390\pi$
$350$		0			0
$351$			4.41926i			0.235882i
$352$	3.90818	−	1.30754i	0.208307	−	0.0696919i
$353$	18.4049	+	18.4049i	0.979596	+	0.979596i	0.999796	−	0.0202002i	$-0.00643038\pi$
$353$	18.4049	+	18.4049i	0.979596	+	0.979596i	−0.0202002	+	0.999796i	$0.506430\pi$
$354$	5.23608	+	4.60006i	0.278294	+	0.244490i
$355$		0			0
$356$	−0.265367	−	2.04339i	−0.0140644	−	0.108300i
$357$	2.96972	−	2.96972i	0.157174	−	0.157174i
$358$	2.22804	+	34.4569i	0.117755	+	1.82111i
$359$	−9.63060			−0.508284			−0.254142	−	0.967167i	$-0.581793\pi$
$359$	−9.63060			−0.508284			−0.254142	+	0.967167i	$0.581793\pi$
$360$		0			0
$361$	−5.06055			−0.266345
$362$	−1.02936	−	15.9192i	−0.0541017	−	0.836692i
$363$	−7.40289	+	7.40289i	−0.388551	+	0.388551i
$364$	−3.00504	−	23.1396i	−0.157507	−	1.21284i
$365$		0			0
$366$	2.45459	+	2.15643i	0.128303	+	0.112718i
$367$	−15.4570	−	15.4570i	−0.806850	−	0.806850i	0.177306	−	0.984156i	$-0.443262\pi$
$367$	−15.4570	−	15.4570i	−0.806850	−	0.806850i	−0.984156	+	0.177306i	$0.943262\pi$
$368$	16.5998	−	28.5199i	0.865326	−	1.48670i
$369$			4.24977i			0.221234i
$370$		0			0
$371$		−	1.81026i		−	0.0939840i
$372$	9.52337	+	7.33415i	0.493764	+	0.380258i
$373$	−3.37466	−	3.37466i	−0.174733	−	0.174733i	0.614322	−	0.789055i	$-0.289430\pi$
$373$	−3.37466	−	3.37466i	−0.174733	−	0.174733i	−0.789055	+	0.614322i	$0.789430\pi$
$374$	−1.08174	+	1.23131i	−0.0559357	+	0.0636695i
$375$		0			0
$376$	4.68498	−	6.97173i	0.241609	−	0.359540i
$377$	−8.24977	+	8.24977i	−0.424885	+	0.424885i
$378$	3.72578	−	0.240914i	0.191633	−	0.0123913i
$379$	−5.89705			−0.302911			−0.151455	−	0.988464i	$-0.548396\pi$
$379$	−5.89705			−0.302911			−0.151455	+	0.988464i	$0.548396\pi$
$380$		0			0
$381$	15.9201			0.815610
$382$	4.61102	−	0.298155i	0.235920	−	0.0152549i
$383$	0.642881	−	0.642881i	0.0328497	−	0.0328497i	−0.690491	−	0.723341i	$-0.742606\pi$
$383$	0.642881	−	0.642881i	0.0328497	−	0.0328497i	0.723341	+	0.690491i	$0.242606\pi$
$384$	−10.6907	−	3.70247i	−0.545559	−	0.188941i
$385$		0			0
$386$	−1.24008	+	1.41154i	−0.0631185	+	0.0718455i
$387$	5.10495	+	5.10495i	0.259499	+	0.259499i
$388$	−21.6237	+	28.0782i	−1.09778	+	1.42546i
$389$		−	18.8292i		−	0.954680i	−0.878719	−	0.477340i	$-0.841601\pi$
$389$		−	18.8292i		−	0.954680i	0.878719	−	0.477340i	$-0.158399\pi$
$390$		0			0
$391$			13.1240i			0.663708i
$392$	0.0840320	−	0.0164850i	0.00424426	−	0.000832616i
$393$	−3.23509	−	3.23509i	−0.163189	−	0.163189i
$394$	−2.18555	−	1.92007i	−0.110106	−	0.0967317i
$395$		0			0
$396$	−1.44490	+	0.187643i	−0.0726088	+	0.00942941i
$397$	24.3444	−	24.3444i	1.22181	−	1.22181i	0.254821	−	0.966988i	$-0.417983\pi$
$397$	24.3444	−	24.3444i	1.22181	−	1.22181i	0.966988	−	0.254821i	$-0.0820166\pi$
$398$	−0.473665	−	7.32530i	−0.0237427	−	0.367184i
$399$	−9.85668			−0.493451
$400$		0			0
$401$	15.9394			0.795978			0.397989	−	0.917390i	$-0.369708\pi$
$401$	15.9394			0.795978			0.397989	+	0.917390i	$0.369708\pi$
$402$	0.658812	+	10.1886i	0.0328586	+	0.508163i
$403$	−18.7808	+	18.7808i	−0.935539	+	0.935539i
$404$	11.2462	−	1.46049i	0.559517	−	0.0726623i
$405$		0			0
$406$	7.40493	+	6.50547i	0.367501	+	0.322861i
$407$	−2.27653	−	2.27653i	−0.112843	−	0.112843i
$408$	4.41538	−	0.866187i	0.218594	−	0.0428826i
$409$		−	23.4087i		−	1.15749i	−0.815510	−	0.578743i	$-0.803543\pi$
$409$		−	23.4087i		−	1.15749i	0.815510	−	0.578743i	$-0.196457\pi$
$410$		0			0
$411$			5.79065i			0.285632i
$412$	−0.0975387	+	0.126654i	−0.00480539	+	0.00623978i
$413$	9.20012	+	9.20012i	0.452708	+	0.452708i
$414$	−7.70025	+	8.76491i	−0.378447	+	0.430772i
$415$		0			0
$416$	11.1552	−	22.3722i	0.546927	−	1.09689i
$417$	−9.60975	+	9.60975i	−0.470591	+	0.470591i
$418$	3.83858	−	0.248208i	0.187751	−	0.0121403i
$419$	28.0361			1.36966			0.684828	−	0.728705i	$-0.259878\pi$
$419$	28.0361			1.36966			0.684828	+	0.728705i	$0.259878\pi$
$420$		0			0
$421$	17.4087			0.848449			0.424224	−	0.905557i	$-0.360547\pi$
$421$	17.4087			0.848449			0.424224	+	0.905557i	$0.360547\pi$
$422$	16.6247	−	1.07498i	0.809277	−	0.0523290i
$423$	−2.09991	+	2.09991i	−0.102101	+	0.102101i
$424$	1.08174	−	1.60975i	0.0525342	−	0.0781762i
$425$		0			0
$426$	12.2498	−	13.9435i	0.593503	−	0.675563i
$427$	4.31286	+	4.31286i	0.208714	+	0.208714i
$428$	8.76236	+	6.74808i	0.423545	+	0.326181i
$429$		−	3.21949i		−	0.155439i
$430$		0			0
$431$			31.1542i			1.50065i	0.661071	+	0.750323i	$0.270102\pi$
$431$			31.1542i			1.50065i	−0.661071	+	0.750323i	$0.729898\pi$
$432$	3.45705	+	2.01216i	0.166328	+	0.0968100i
$433$	12.1589	+	12.1589i	0.584321	+	0.584321i	0.936088	−	0.351766i	$-0.114419\pi$
$433$	12.1589	+	12.1589i	0.584321	+	0.584321i	−0.351766	+	0.936088i	$0.614419\pi$
$434$	16.8575	+	14.8099i	0.809187	+	0.710896i
$435$		0			0
$436$	4.06433	+	31.2964i	0.194646	+	1.49882i
$437$	21.7796	−	21.7796i	1.04186	−	1.04186i
$438$	−0.512307	−	7.92290i	−0.0244790	−	0.378571i
$439$	−14.2967			−0.682344			−0.341172	−	0.940001i	$-0.610824\pi$
$439$	−14.2967			−0.682344			−0.341172	+	0.940001i	$0.610824\pi$
$440$		0			0
$441$	−0.0302761			−0.00144172
$442$	0.641545	+	9.92159i	0.0305152	+	0.471922i
$443$	7.02825	−	7.02825i	0.333922	−	0.333922i	−0.520152	−	0.854074i	$-0.674125\pi$
$443$	7.02825	−	7.02825i	0.333922	−	0.333922i	0.854074	+	0.520152i	$0.174125\pi$
$444$	1.13826	+	8.76491i	0.0540196	+	0.415964i
$445$		0			0
$446$	−4.99409	−	4.38747i	−0.236477	−	0.207753i
$447$	4.00951	+	4.00951i	0.189643	+	0.189643i
$448$	−19.4696	−	8.18505i	−0.919854	−	0.386707i
$449$			38.4608i			1.81508i	0.419969	+	0.907538i	$0.362041\pi$
$449$			38.4608i			1.81508i	−0.419969	+	0.907538i	$0.637959\pi$
$450$		0			0
$451$		−	3.09602i		−	0.145786i
$452$	−4.13412	−	3.18378i	−0.194453	−	0.149752i
$453$	13.6097	+	13.6097i	0.639442	+	0.639442i
$454$	11.6669	−	13.2800i	0.547557	−	0.623263i
$455$		0			0
$456$	−8.76491	−	5.88999i	−0.410454	−	0.275824i
$457$	−4.93945	+	4.93945i	−0.231058	+	0.231058i	−0.813134	−	0.582076i	$-0.802240\pi$
$457$	−4.93945	+	4.93945i	−0.231058	+	0.231058i	0.582076	+	0.813134i	$0.302240\pi$
$458$	10.0070	−	0.647071i	0.467599	−	0.0302356i
$459$	−1.59083			−0.0742535
$460$		0			0
$461$	27.1689			1.26538			0.632691	−	0.774404i	$-0.281950\pi$
$461$	27.1689			1.26538			0.632691	+	0.774404i	$0.281950\pi$
$462$	−2.71428	+	0.175510i	−0.126280	+	0.00816545i
$463$	4.96280	−	4.96280i	0.230641	−	0.230641i	−0.582319	−	0.812960i	$-0.697855\pi$
$463$	4.96280	−	4.96280i	0.230641	−	0.230641i	0.812960	+	0.582319i	$0.197855\pi$
$464$	2.69730	+	10.2098i	0.125219	+	0.473978i
$465$		0			0
$466$	20.2947	−	23.1007i	0.940135	−	1.07012i
$467$	−21.2340	−	21.2340i	−0.982591	−	0.982591i	0.0172604	−	0.999851i	$-0.494506\pi$
$467$	−21.2340	−	21.2340i	−0.982591	−	0.982591i	−0.999851	+	0.0172604i	$0.994506\pi$
$468$	−5.39285	+	7.00260i	−0.249285	+	0.323695i
$469$			19.0596i			0.880092i
$470$		0			0
$471$			2.96222i			0.136492i
$472$	2.68342	+	13.6787i	0.123514	+	0.629614i
$473$	−3.71904	−	3.71904i	−0.171001	−	0.171001i
$474$	−7.55809	−	6.64002i	−0.347155	−	0.304986i
$475$		0			0
$476$	8.32970	−	1.08174i	0.381791	−	0.0495817i
$477$	−0.484862	+	0.484862i	−0.0222003	+	0.0222003i
$478$	−0.0644676	−	0.997001i	−0.00294868	−	0.0456018i
$479$	−18.7808			−0.858118			−0.429059	−	0.903277i	$-0.641155\pi$
$479$	−18.7808			−0.858118			−0.429059	+	0.903277i	$0.641155\pi$
$480$		0			0
$481$	−19.5298			−0.890483
$482$	2.28128	+	35.2804i	0.103909	+	1.60698i
$483$	−15.4005	+	15.4005i	−0.700747	+	0.700747i
$484$	−20.7642	+	2.69656i	−0.943826	+	0.122571i
$485$		0			0
$486$	−1.06244	−	0.933389i	−0.0481934	−	0.0423394i
$487$	2.97058	+	2.97058i	0.134610	+	0.134610i	0.771201	−	0.636591i	$-0.219656\pi$
$487$	2.97058	+	2.97058i	0.134610	+	0.134610i	−0.636591	+	0.771201i	$0.719656\pi$
$488$	1.25794	+	6.41236i	0.0569444	+	0.290274i
$489$		−	6.06055i		−	0.274068i
$490$		0			0
$491$		−	29.5480i		−	1.33348i	−0.745290	−	0.666741i	$-0.767689\pi$
$491$		−	29.5480i		−	1.33348i	0.745290	−	0.666741i	$-0.232311\pi$
$492$	−5.18603	+	6.73404i	−0.233804	+	0.303594i
$493$	−2.96972	−	2.96972i	−0.133750	−	0.133750i
$494$	15.4005	−	17.5298i	0.692901	−	0.788704i
$495$		0			0
$496$	6.14048	+	23.2429i	0.275716	+	1.04364i
$497$	24.4995	−	24.4995i	1.09895	−	1.09895i
$498$	−7.09906	+	0.459036i	−0.318116	+	0.0205699i
$499$	−15.0473			−0.673608			−0.336804	−	0.941575i	$-0.609346\pi$
$499$	−15.0473			−0.673608			−0.336804	+	0.941575i	$0.609346\pi$
$500$		0			0
$501$	−6.18922			−0.276514
$502$	40.3840	−	2.61129i	1.80243	−	0.116548i
$503$	13.4136	−	13.4136i	0.598084	−	0.598084i	−0.341719	−	0.939802i	$-0.611009\pi$
$503$	13.4136	−	13.4136i	0.598084	−	0.598084i	0.939802	+	0.341719i	$0.111009\pi$
$504$	6.19773	+	4.16485i	0.276069	+	0.185517i
$505$		0			0
$506$	5.60975	−	6.38537i	0.249384	−	0.283864i
$507$	−4.61728	−	4.61728i	−0.205061	−	0.205061i
$508$	25.2264	+	19.4274i	1.11924	+	0.861951i
$509$		−	41.4187i		−	1.83585i	−0.396752	−	0.917926i	$-0.629863\pi$
$509$		−	41.4187i		−	1.83585i	0.396752	−	0.917926i	$-0.370137\pi$
$510$		0			0
$511$		−	14.8212i		−	0.655651i
$512$	−12.4220	−	18.9128i	−0.548981	−	0.835835i
$513$	2.64002	+	2.64002i	0.116560	+	0.116560i
$514$	−5.86793	−	5.15516i	−0.258823	−	0.227384i
$515$		0			0
$516$	1.85952	+	14.3188i	0.0818607	+	0.630348i
$517$	1.52982	−	1.52982i	0.0672813	−	0.0672813i
$518$	1.06466	+	16.4652i	0.0467785	+	0.723437i
$519$	23.2001			1.01837
$520$		0			0
$521$	30.8392			1.35109			0.675545	−	0.737318i	$-0.263908\pi$
$521$	30.8392			1.35109			0.675545	+	0.737318i	$0.263908\pi$
$522$	−0.240914	−	3.72578i	−0.0105445	−	0.163073i
$523$	−17.1251	+	17.1251i	−0.748829	+	0.748829i	−0.974259	−	0.225430i	$-0.927621\pi$
$523$	−17.1251	+	17.1251i	−0.748829	+	0.748829i	0.225430	+	0.974259i	$0.427621\pi$
$524$	−1.17841	−	9.07402i	−0.0514789	−	0.396400i
$525$		0			0
$526$	0.265367	+	0.233133i	0.0115706	+	0.0101651i
$527$	−6.76066	−	6.76066i	−0.294499	−	0.294499i
$528$	−2.51852	−	1.46589i	−0.109604	−	0.0637945i
$529$		−	45.0587i		−	1.95907i
$530$		0			0
$531$		−	4.92834i		−	0.213872i
$532$	−15.6186	−	12.0282i	−0.677150	−	0.521488i
$533$	−13.2800	−	13.2800i	−0.575223	−	0.575223i
$534$	−0.961649	+	1.09461i	−0.0416146	+	0.0473684i
$535$		0			0
$536$	−11.3893	+	16.9485i	−0.491944	+	0.732064i
$537$	17.2645	−	17.2645i	0.745016	−	0.745016i
$538$	7.60579	−	0.491802i	0.327909	−	0.0212031i
$539$	0.0220566			0.000950045
$540$		0			0
$541$	−22.3397			−0.960458			−0.480229	−	0.877143i	$-0.659446\pi$
$541$	−22.3397			−0.960458			−0.480229	+	0.877143i	$0.659446\pi$
$542$	−21.7342	+	1.40537i	−0.933564	+	0.0603656i
$543$	−7.97620	+	7.97620i	−0.342291	+	0.342291i
$544$	8.05348	+	4.01560i	0.345290	+	0.172167i
$545$		0			0
$546$	−10.8898	+	12.3955i	−0.466040	+	0.530476i
$547$	−25.3428	−	25.3428i	−1.08358	−	1.08358i	−0.996173	−	0.0874075i	$-0.972142\pi$
$547$	−25.3428	−	25.3428i	−1.08358	−	1.08358i	−0.0874075	−	0.996173i	$-0.527858\pi$
$548$	−7.06638	+	9.17567i	−0.301861	+	0.391965i
$549$		−	2.31032i		−	0.0986022i
$550$		0			0
$551$			9.85668i			0.419909i
$552$	−22.8974	+	4.49190i	−0.974580	+	0.191188i
$553$	−13.2800	−	13.2800i	−0.564725	−	0.564725i
$554$	12.9129	+	11.3444i	0.548616	+	0.481977i
$555$		0			0
$556$	−26.9541	+	3.50042i	−1.14311	+	0.148451i
$557$	−21.1055	+	21.1055i	−0.894269	+	0.894269i	−0.994922	−	0.100653i	$-0.967907\pi$
$557$	−21.1055	+	21.1055i	−0.894269	+	0.894269i	0.100653	+	0.994922i	$0.467907\pi$
$558$	−0.548448	−	8.48183i	−0.0232176	−	0.359064i
$559$	−31.9048			−1.34943
$560$		0			0
$561$	1.15894			0.0489306
$562$	1.89347	+	29.2828i	0.0798712	+	1.23522i
$563$	10.2955	−	10.2955i	0.433905	−	0.433905i	−0.456049	−	0.889955i	$-0.650736\pi$
$563$	10.2955	−	10.2955i	0.433905	−	0.433905i	0.889955	+	0.456049i	$0.150736\pi$
$564$	−5.88999	+	0.764909i	−0.248013	+	0.0322085i
$565$		0			0
$566$	−27.9201	−	24.5287i	−1.17357	−	1.03102i
$567$	−1.86678	−	1.86678i	−0.0783973	−	0.0783973i
$568$	36.4259	−	7.14584i	1.52840	−	0.299833i
$569$			28.3179i			1.18715i	0.804780	+	0.593574i	$0.202283\pi$
$569$			28.3179i			1.18715i	−0.804780	+	0.593574i	$0.797717\pi$
$570$		0			0
$571$		−	27.2387i		−	1.13990i	−0.821678	−	0.569952i	$-0.806962\pi$
$571$		−	27.2387i		−	1.13990i	0.821678	−	0.569952i	$-0.193038\pi$
$572$	3.92878	−	5.10150i	0.164270	−	0.213304i
$573$	−2.31032	−	2.31032i	−0.0965151	−	0.0965151i
$574$	−10.4722	+	11.9201i	−0.437099	+	0.497534i
$575$		0			0
$576$	3.02248	+	7.40707i	0.125937	+	0.308628i
$577$	−4.81078	+	4.81078i	−0.200275	+	0.200275i	−0.800118	−	0.599843i	$-0.795230\pi$
$577$	−4.81078	+	4.81078i	−0.200275	+	0.200275i	0.599843	+	0.800118i	$0.295230\pi$
$578$	20.4200	−	1.32039i	0.849359	−	0.0549208i
$579$	1.32858			0.0552139
$580$		0			0
$581$	−13.2800			−0.550949
$582$	25.0074	−	1.61702i	1.03659	−	0.0670275i
$583$	0.353229	−	0.353229i	0.0146293	−	0.0146293i
$584$	8.85660	−	13.1795i	0.366489	−	0.545373i
$585$		0			0
$586$	−8.23039	+	9.36835i	−0.339994	+	0.387003i
$587$	4.84271	+	4.84271i	0.199880	+	0.199880i	0.799948	−	0.600069i	$-0.204860\pi$
$587$	4.84271	+	4.84271i	0.199880	+	0.199880i	−0.600069	+	0.799948i	$0.704860\pi$
$588$	−0.0479745	−	0.0369462i	−0.00197843	−	0.00152363i
$589$			22.4390i			0.924582i
$590$		0			0
$591$			2.05710i			0.0846176i
$592$	−8.89224	+	15.2776i	−0.365469	+	0.627906i
$593$	−18.8439	−	18.8439i	−0.773827	−	0.773827i	0.204946	−	0.978773i	$-0.434298\pi$
$593$	−18.8439	−	18.8439i	−0.773827	−	0.773827i	−0.978773	+	0.204946i	$0.934298\pi$
$594$	0.774006	+	0.679988i	0.0317578	+	0.0279003i
$595$		0			0
$596$	1.46049	+	11.2462i	0.0598241	+	0.460661i
$597$	−3.67030	+	3.67030i	−0.150215	+	0.150215i
$598$	−3.32695	−	51.4517i	−0.136049	−	2.10402i
$599$	30.2765			1.23706			0.618532	−	0.785760i	$-0.287728\pi$
$599$	30.2765			1.23706			0.618532	+	0.785760i	$0.287728\pi$
$600$		0			0
$601$	30.1505			1.22986			0.614932	−	0.788581i	$-0.289184\pi$
$601$	30.1505			1.22986			0.614932	+	0.788581i	$0.289184\pi$
$602$	1.73928	+	26.8982i	0.0708877	+	1.09629i
$603$	5.10495	−	5.10495i	0.207890	−	0.207890i
$604$	4.95745	+	38.1736i	0.201716	+	1.55326i
$605$		0			0
$606$	−6.02437	−	5.29260i	−0.244723	−	0.214997i
$607$	19.5438	+	19.5438i	0.793258	+	0.793258i	0.982022	−	0.188764i	$-0.0604482\pi$
$607$	19.5438	+	19.5438i	0.793258	+	0.793258i	−0.188764	+	0.982022i	$0.560448\pi$
$608$	−6.70097	−	20.0290i	−0.271760	−	0.812282i
$609$		−	6.96972i		−	0.282427i
$610$		0			0
$611$		−	13.1240i		−	0.530939i
$612$	−2.52077	−	1.94130i	−0.101896	−	0.0784724i
$613$	−23.4040	−	23.4040i	−0.945279	−	0.945279i	0.0532993	−	0.998579i	$-0.483026\pi$
$613$	−23.4040	−	23.4040i	−0.945279	−	0.945279i	−0.998579	+	0.0532993i	$0.983026\pi$
$614$	1.19478	−	1.35998i	0.0482175	−	0.0548842i
$615$		0			0
$616$	−4.51514	−	3.03416i	−0.181920	−	0.122250i
$617$	17.9348	−	17.9348i	0.722026	−	0.722026i	−0.246992	−	0.969018i	$-0.579442\pi$
$617$	17.9348	−	17.9348i	0.722026	−	0.722026i	0.969018	+	0.246992i	$0.0794421\pi$
$618$	0.112802	−	0.00729394i	0.00453756	−	0.000293405i
$619$	38.9056			1.56375			0.781875	−	0.623435i	$-0.214264\pi$
$619$	38.9056			1.56375			0.781875	+	0.623435i	$0.214264\pi$
$620$		0			0
$621$	8.24977			0.331052
$622$	−34.4881	+	2.23005i	−1.38285	+	0.0894169i
$623$	−1.92330	+	1.92330i	−0.0770553	+	0.0770553i
$624$	−17.0907	+	4.51514i	−0.684174	+	0.180750i
$625$		0			0
$626$	−24.5395	+	27.9324i	−0.980796	+	1.11640i
$627$	−1.92330	−	1.92330i	−0.0768091	−	0.0768091i
$628$	−3.61483	+	4.69384i	−0.144247	+	0.187305i
$629$		−	7.03028i		−	0.280315i
$630$		0			0
$631$		−	12.7707i		−	0.508395i	−0.967152	−	0.254198i	$-0.918189\pi$
$631$		−	12.7707i		−	0.508395i	0.967152	−	0.254198i	$-0.0818113\pi$
$632$	−3.87342	−	19.7448i	−0.154077	−	0.785404i
$633$	−8.32970	−	8.32970i	−0.331076	−	0.331076i
$634$	29.0198	+	25.4948i	1.15253	+	1.01253i
$635$		0			0
$636$	−1.35998	+	0.176615i	−0.0539266	+	0.00700323i
$637$	0.0946093	−	0.0946093i	0.00374856	−	0.00374856i
$638$	0.175510	+	2.71428i	0.00694849	+	0.107460i
$639$	−13.1240			−0.519176
$640$		0			0
$641$	−16.4683			−0.650461			−0.325230	−	0.945635i	$-0.605442\pi$
$641$	−16.4683			−0.650461			−0.325230	+	0.945635i	$0.605442\pi$
$642$	−0.504621	−	7.80405i	−0.0199158	−	0.308001i
$643$	5.74249	−	5.74249i	0.226462	−	0.226462i	−0.584751	−	0.811213i	$-0.698808\pi$
$643$	5.74249	−	5.74249i	0.226462	−	0.226462i	0.811213	+	0.584751i	$0.198808\pi$
$644$	−43.1964	+	5.60975i	−1.70218	+	0.221055i
$645$		0			0
$646$	6.31032	+	5.54382i	0.248276	+	0.218119i
$647$	−4.61663	−	4.61663i	−0.181498	−	0.181498i	0.610510	−	0.792009i	$-0.290964\pi$
$647$	−4.61663	−	4.61663i	−0.181498	−	0.181498i	−0.792009	+	0.610510i	$0.790964\pi$
$648$	−0.544488	−	2.77552i	−0.0213895	−	0.109033i
$649$			3.59037i			0.140934i
$650$		0			0
$651$		−	15.8668i		−	0.621867i
$652$	7.39574	−	9.60334i	0.289640	−	0.376096i
$653$	−14.4655	−	14.4655i	−0.566078	−	0.566078i	0.364949	−	0.931027i	$-0.381086\pi$
$653$	−14.4655	−	14.4655i	−0.566078	−	0.566078i	−0.931027	+	0.364949i	$0.881086\pi$
$654$	14.7285	−	16.7649i	0.575930	−	0.655560i
$655$		0			0
$656$	−16.4352	+	4.34198i	−0.641687	+	0.169526i
$657$	−3.96972	+	3.96972i	−0.154874	+	0.154874i
$658$	−11.0645	+	0.715449i	−0.431340	+	0.0278911i
$659$	−35.5474			−1.38473			−0.692364	−	0.721548i	$-0.743431\pi$
$659$	−35.5474			−1.38473			−0.692364	+	0.721548i	$0.743431\pi$
$660$		0			0
$661$	15.1883			0.590756			0.295378	−	0.955380i	$-0.404554\pi$
$661$	15.1883			0.590756			0.295378	+	0.955380i	$0.404554\pi$
$662$	−15.5654	+	1.00648i	−0.604967	+	0.0391181i
$663$	4.97116	−	4.97116i	0.193064	−	0.193064i
$664$	−11.8091	−	7.93567i	−0.458282	−	0.307964i
$665$		0			0
$666$	4.12489	−	4.69521i	0.159836	−	0.181936i
$667$	15.4005	+	15.4005i	0.596310	+	0.596310i
$668$	−9.80722	−	7.55275i	−0.379453	−	0.292225i
$669$			4.70058i			0.181735i
$670$		0			0
$671$			1.68311i			0.0649756i
$672$	4.73830	+	14.1626i	0.182784	+	0.546335i
$673$	20.3700	+	20.3700i	0.785204	+	0.785204i	0.980704	−	0.195500i	$-0.0626328\pi$
$673$	20.3700	+	20.3700i	0.785204	+	0.785204i	−0.195500	+	0.980704i	$0.562633\pi$
$674$	20.4653	+	17.9794i	0.788294	+	0.692541i
$675$		0			0
$676$	−1.68188	−	12.9509i	−0.0646876	−	0.498111i
$677$	−9.06433	+	9.06433i	−0.348371	+	0.348371i	−0.859502	−	0.511132i	$-0.829226\pi$
$677$	−9.06433	+	9.06433i	−0.348371	+	0.348371i	0.511132	+	0.859502i	$0.329226\pi$
$678$	0.238083	+	3.68199i	0.00914351	+	0.141406i
$679$	46.7808			1.79528
$680$		0			0
$681$	−12.4995			−0.478983
$682$	0.399552	+	6.17914i	0.0152997	+	0.236612i
$683$	−24.8545	+	24.8545i	−0.951030	+	0.951030i	−0.998856	−	0.0478253i	$-0.984771\pi$
$683$	−24.8545	+	24.8545i	−0.951030	+	0.951030i	0.0478253	+	0.998856i	$0.484771\pi$
$684$	0.961649	+	7.40493i	0.0367696	+	0.283135i
$685$		0			0
$686$	−19.7190	−	17.3238i	−0.752876	−	0.661425i
$687$	−5.01397	−	5.01397i	−0.191295	−	0.191295i
$688$	−14.5268	+	24.9582i	−0.553827	+	0.951522i
$689$		−	3.03028i		−	0.115444i
$690$		0			0
$691$			40.8979i			1.55583i	0.628371	+	0.777914i	$0.283722\pi$
$691$			40.8979i			1.55583i	−0.628371	+	0.777914i	$0.716278\pi$
$692$	36.7620	+	28.3112i	1.39748	+	1.07623i
$693$	1.35998	+	1.35998i	0.0516612	+	0.0516612i
$694$	23.4469	−	26.6888i	0.890033	−	1.01309i
$695$		0			0
$696$	4.16485	−	6.19773i	0.157868	−	0.234924i
$697$	4.78051	−	4.78051i	0.181075	−	0.181075i
$698$	20.7298	−	1.34042i	0.784633	−	0.0507355i
$699$	−21.7430			−0.822398
$700$		0			0
$701$	−43.1396			−1.62936			−0.814679	−	0.579912i	$-0.803087\pi$
$701$	−43.1396			−1.62936			−0.814679	+	0.579912i	$0.803087\pi$
$702$	6.23675	−	0.403277i	0.235391	−	0.0152207i
$703$	−11.6669	+	11.6669i	−0.440027	+	0.440027i
$704$	−2.20192	−	5.39616i	−0.0829880	−	0.203375i
$705$		0			0
$706$	24.2947	−	27.6538i	0.914344	−	1.04076i
$707$	−10.5852	−	10.5852i	−0.398097	−	0.398097i
$708$	6.01409	−	7.80928i	0.226023	−	0.293491i
$709$			18.4702i			0.693662i	0.937928	+	0.346831i	$0.112742\pi$
$709$			18.4702i			0.693662i	−0.937928	+	0.346831i	$0.887258\pi$
$710$		0			0
$711$			7.11388i			0.266792i
$712$	−2.85956	+	0.560973i	−0.107166	+	0.0210233i
$713$	35.0596	+	35.0596i	1.31299	+	1.31299i
$714$	−4.46207	−	3.92007i	−0.166989	−	0.146705i
$715$		0			0
$716$	48.4246	−	6.28871i	1.80971	−	0.235020i
$717$	−0.499542	+	0.499542i	−0.0186557	+	0.0186557i
$718$	0.878837	+	13.5913i	0.0327979	+	0.507225i
$719$	−33.3725			−1.24458			−0.622292	−	0.782785i	$-0.713799\pi$
$719$	−33.3725			−1.24458			−0.622292	+	0.782785i	$0.713799\pi$
$720$		0			0
$721$	0.211016			0.00785865
$722$	0.461799	+	7.14179i	0.0171864	+	0.265790i
$723$	17.6770	−	17.6770i	0.657415	−	0.657415i
$724$	−22.3722	+	2.90539i	−0.831457	+	0.107978i
$725$		0			0
$726$	11.1230	+	9.77190i	0.412813	+	0.362669i
$727$	−23.2774	−	23.2774i	−0.863309	−	0.863309i	0.128412	−	0.991721i	$-0.459012\pi$
$727$	−23.2774	−	23.2774i	−0.863309	−	0.863309i	−0.991721	+	0.128412i	$0.959012\pi$
$728$	−32.3819	+	6.35251i	−1.20015	+	0.235440i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	11.4850i		−	0.424787i
$732$	2.81931	−	3.66086i	0.104205	−	0.135309i
$733$	16.2157	+	16.2157i	0.598941	+	0.598941i	0.940031	−	0.341090i	$-0.110796\pi$
$733$	16.2157	+	16.2157i	0.598941	+	0.598941i	−0.341090	+	0.940031i	$0.610796\pi$
$734$	−20.4034	+	23.2245i	−0.753105	+	0.857231i
$735$		0			0
$736$	−41.7640	−	20.8242i	−1.53944	−	0.767591i
$737$	−3.71904	+	3.71904i	−0.136992	+	0.136992i
$738$	5.99756	−	0.387811i	0.220773	−	0.0142755i
$739$	−14.3408			−0.527535			−0.263768	−	0.964586i	$-0.584965\pi$
$739$	−14.3408			−0.527535			−0.263768	+	0.964586i	$0.584965\pi$
$740$		0			0
$741$	−16.4995			−0.606126
$742$	−2.55476	+	0.165194i	−0.0937881	+	0.00606448i
$743$	−11.6034	+	11.6034i	−0.425686	+	0.425686i	−0.887156	−	0.461470i	$-0.847322\pi$
$743$	−11.6034	+	11.6034i	−0.425686	+	0.425686i	0.461470	+	0.887156i	$0.347322\pi$
$744$	9.48139	−	14.1093i	0.347605	−	0.517272i
$745$		0			0
$746$	−4.45459	+	5.07049i	−0.163094	+	0.185644i
$747$	3.55694	+	3.55694i	0.130142	+	0.130142i
$748$	1.83642	+	1.41427i	0.0671462	+	0.0517107i
$749$		−	14.5988i		−	0.533430i
$750$		0			0
$751$			35.1721i			1.28345i	0.766936	+	0.641724i	$0.221780\pi$
$751$			35.1721i			1.28345i	−0.766936	+	0.641724i	$0.778220\pi$
$752$	−10.2665	−	5.97555i	−0.374381	−	0.217906i
$753$	−20.2342	−	20.2342i	−0.737374	−	0.737374i
$754$	12.3955	+	10.8898i	0.451416	+	0.396583i
$755$		0			0
$756$	−0.679988	−	5.23608i	−0.0247309	−	0.190434i
$757$	15.7455	−	15.7455i	0.572281	−	0.572281i	−0.360484	−	0.932765i	$-0.617389\pi$
$757$	15.7455	−	15.7455i	0.572281	−	0.572281i	0.932765	+	0.360484i	$0.117389\pi$
$758$	0.538132	+	8.32230i	0.0195459	+	0.302280i
$759$	−6.01008			−0.218152
$760$		0			0
$761$	−24.4002			−0.884508			−0.442254	−	0.896890i	$-0.645821\pi$
$761$	−24.4002			−0.884508			−0.442254	+	0.896890i	$0.645821\pi$
$762$	−1.45278	−	22.4675i	−0.0526286	−	0.813910i
$763$	29.4570	−	29.4570i	1.06641	−	1.06641i
$764$	−0.841553	−	6.48016i	−0.0304463	−	0.234444i
$765$		0			0
$766$	−0.965943	−	0.848611i	−0.0349009	−	0.0306616i
$767$	15.4005	+	15.4005i	0.556080	+	0.556080i
$768$	−4.24959	+	15.4253i	−0.153344	+	0.556614i
$769$			15.9688i			0.575850i	0.957653	+	0.287925i	$0.0929654\pi$
$769$			15.9688i			0.575850i	−0.957653	+	0.287925i	$0.907035\pi$
$770$		0			0
$771$			5.52306i			0.198908i
$772$	2.10522	+	1.62128i	0.0757686	+	0.0583510i
$773$	2.84392	+	2.84392i	0.102289	+	0.102289i	0.756399	−	0.654110i	$-0.226957\pi$
$773$	2.84392	+	2.84392i	0.102289	+	0.102289i	−0.654110	+	0.756399i	$0.726957\pi$
$774$	6.73860	−	7.67030i	0.242214	−	0.275703i
$775$		0			0
$776$	41.5991	+	27.9545i	1.49332	+	1.00351i
$777$	8.24977	−	8.24977i	0.295959	−	0.295959i
$778$	−26.5731	+	1.71825i	−0.952691	+	0.0616024i
$779$	−15.8668			−0.568486
$780$		0			0
$781$	9.56101			0.342120
$782$	18.5214	−	1.19762i	0.662324	−	0.0428269i
$783$	−1.86678	+	1.86678i	−0.0667132	+	0.0667132i
$784$	−0.0309330	−	0.117087i	−0.00110475	−	0.00418169i
$785$		0			0
$786$	−4.27036	+	4.86079i	−0.152319	+	0.173379i
$787$	−7.49452	−	7.49452i	−0.267151	−	0.267151i	0.560800	−	0.827951i	$-0.310494\pi$
$787$	−7.49452	−	7.49452i	−0.267151	−	0.267151i	−0.827951	+	0.560800i	$0.810494\pi$
$788$	−2.51029	+	3.25960i	−0.0894254	+	0.116119i
$789$		−	0.249771i		−	0.00889208i
$790$		0			0
$791$			6.88781i			0.244902i
$792$	0.396668	+	2.02201i	0.0140950	+	0.0718490i
$793$	7.21949	+	7.21949i	0.256372	+	0.256372i
$794$	−36.5779	−	32.1349i	−1.29810	−	1.14042i
$795$		0			0
$796$	−10.2947	+	1.33693i	−0.364887	+	0.0473864i
$797$	−26.1552	+	26.1552i	−0.926463	+	0.926463i	−0.997475	−	0.0710121i	$-0.977377\pi$
$797$	−26.1552	+	26.1552i	−0.926463	+	0.926463i	0.0710121	+	0.997475i	$0.477377\pi$
$798$	0.899467	+	13.9104i	0.0318408	+	0.492423i
$799$	4.72432			0.167134
$800$		0			0
$801$	1.03028			0.0364030
$802$	−1.45455	−	22.4948i	−0.0513619	−	0.794319i
$803$	2.89200	−	2.89200i	0.102057	−	0.102057i
$804$	14.3188	−	1.85952i	0.504983	−	0.0655802i
$805$		0			0
$806$	28.2186	+	24.7909i	0.993957	+	0.873222i
$807$	−3.81084	−	3.81084i	−0.134148	−	0.134148i
$808$	−3.08741	−	15.7381i	−0.108615	−	0.553663i
$809$			23.7115i			0.833651i	0.908987	+	0.416826i	$0.136857\pi$
$809$			23.7115i			0.833651i	−0.908987	+	0.416826i	$0.863143\pi$
$810$		0			0
$811$		−	26.0077i		−	0.913255i	−0.889658	−	0.456628i	$-0.849057\pi$
$811$		−	26.0077i		−	0.913255i	0.889658	−	0.456628i	$-0.150943\pi$
$812$	8.50521	−	11.0440i	0.298474	−	0.387568i
$813$	10.8898	+	10.8898i	0.381922	+	0.381922i
$814$	−3.00504	+	3.42053i	−0.105327	+	0.119889i
$815$		0			0
$816$	−1.62534	−	6.15224i	−0.0568984	−	0.215371i
$817$	−19.0596	+	19.0596i	−0.666812	+	0.666812i
$818$	−33.0359	+	2.13615i	−1.15507	+	0.0746888i
$819$	11.6669			0.407676
$820$		0			0
$821$	33.0790			1.15447			0.577233	−	0.816580i	$-0.304133\pi$
$821$	33.0790			1.15447			0.577233	+	0.816580i	$0.304133\pi$
$822$	8.17215	−	0.528424i	0.285037	−	0.0184309i
$823$	−17.9737	+	17.9737i	−0.626525	+	0.626525i	−0.947192	−	0.320667i	$-0.896093\pi$
$823$	−17.9737	+	17.9737i	−0.626525	+	0.626525i	0.320667	+	0.947192i	$0.396093\pi$
$824$	0.187643	+	0.126095i	0.00653685	+	0.00439274i
$825$		0			0
$826$	12.1443	−	13.8234i	0.422553	−	0.480977i
$827$	18.8665	+	18.8665i	0.656051	+	0.656051i	0.954443	−	0.298392i	$-0.0964504\pi$
$827$	18.8665	+	18.8665i	0.656051	+	0.656051i	−0.298392	+	0.954443i	$0.596450\pi$
$828$	13.0723	+	10.0673i	0.454294	+	0.349862i
$829$		−	3.28005i		−	0.113921i	−0.998376	−	0.0569604i	$-0.981859\pi$
$829$		−	3.28005i		−	0.113921i	0.998376	−	0.0569604i	$-0.0181409\pi$
$830$		0			0
$831$		−	12.1540i		−	0.421616i
$832$	−32.5911	−	13.7013i	−1.12989	−	0.475008i
$833$	0.0340571	+	0.0340571i	0.00118001	+	0.00118001i
$834$	14.4388	+	12.6850i	0.499976	+	0.439245i
$835$		0			0
$836$	−0.700576	−	5.39461i	−0.0242299	−	0.186576i
$837$	−4.24977	+	4.24977i	−0.146894	+	0.146894i
$838$	−2.55843	−	39.5665i	−0.0883794	−	1.36680i
$839$	54.8854			1.89486			0.947428	−	0.319969i	$-0.103673\pi$
$839$	54.8854			1.89486			0.947428	+	0.319969i	$0.103673\pi$
$840$		0			0
$841$	22.0303			0.759665
$842$	−1.58862	−	24.5683i	−0.0547476	−	0.846681i
$843$	14.6720	−	14.6720i	0.505330	−	0.505330i
$844$	−3.03416	−	23.3638i	−0.104440	−	0.804214i
$845$		0			0
$846$	3.15516	+	2.77191i	0.108477	+	0.0953002i
$847$	19.5438	+	19.5438i	0.671533	+	0.671533i
$848$	−2.37050	−	1.37973i	−0.0814032	−	0.0473802i
$849$			26.2791i			0.901897i
$850$		0			0
$851$			36.4578i			1.24976i
$852$	−20.7958	−	16.0153i	−0.712452	−	0.548675i
$853$	17.9348	+	17.9348i	0.614074	+	0.614074i	0.944005	−	0.329931i	$-0.107025\pi$
$853$	17.9348	+	17.9348i	0.614074	+	0.614074i	−0.329931	+	0.944005i	$0.607025\pi$
$854$	5.69303	−	6.48016i	0.194811	−	0.221747i
$855$		0			0
$856$	8.72373	−	12.9818i	0.298171	−	0.443709i
$857$	9.00378	−	9.00378i	0.307563	−	0.307563i	−0.536400	−	0.843964i	$-0.680216\pi$
$857$	9.00378	−	9.00378i	0.307563	−	0.307563i	0.843964	+	0.536400i	$0.180216\pi$
$858$	−4.54356	+	0.293794i	−0.155115	+	0.0100299i
$859$	−24.6779			−0.841998			−0.420999	−	0.907061i	$-0.638320\pi$
$859$	−24.6779			−0.841998			−0.420999	+	0.907061i	$0.638320\pi$
$860$		0			0
$861$	11.2195			0.382359
$862$	43.9669	−	2.84297i	1.49752	−	0.0968318i
$863$	−40.4811	+	40.4811i	−1.37799	+	1.37799i	−0.529982	+	0.848009i	$0.677802\pi$
$863$	−40.4811	+	40.4811i	−1.37799	+	1.37799i	−0.848009	+	0.529982i	$0.822198\pi$
$864$	2.52422	−	5.06244i	0.0858756	−	0.172228i
$865$		0			0
$866$	16.0499	−	18.2691i	0.545399	−	0.620808i
$867$	−10.2313	−	10.2313i	−0.347474	−	0.347474i
$868$	19.3623	−	25.1419i	0.657201	−	0.853373i
$869$		−	5.18257i		−	0.175807i
$870$		0			0
$871$			31.9048i			1.08105i
$872$	43.7966	−	8.59179i	1.48314	−	0.290955i
$873$	−12.5298	−	12.5298i	−0.424070	−	0.424070i
$874$	−32.7243	−	28.7493i	−1.10692	−	0.972460i
$875$		0			0
$876$	−11.1346	+	1.44600i	−0.376202	+	0.0488559i
$877$	1.59507	−	1.59507i	0.0538616	−	0.0538616i	−0.679663	−	0.733525i	$-0.737874\pi$
$877$	1.59507	−	1.59507i	0.0538616	−	0.0538616i	0.733525	+	0.679663i	$0.237874\pi$
$878$	1.30464	+	20.1764i	0.0440294	+	0.680922i
$879$	8.81775			0.297415
$880$		0			0
$881$	33.2876			1.12149			0.560744	−	0.827989i	$-0.310515\pi$
$881$	33.2876			1.12149			0.560744	+	0.827989i	$0.310515\pi$
$882$	0.00276283	+	0.0427276i	9.30294e−5	+	0.00143871i
$883$	29.4296	−	29.4296i	0.990385	−	0.990385i	−0.00956956	−	0.999954i	$-0.503046\pi$
$883$	29.4296	−	29.4296i	0.990385	−	0.990385i	0.999954	+	0.00956956i	$0.00304613\pi$
$884$	13.9435	−	1.81078i	0.468969	−	0.0609032i
$885$		0			0
$886$	−10.5601	−	9.27737i	−0.354773	−	0.311679i
$887$	30.9776	+	30.9776i	1.04013	+	1.04013i	0.999161	+	0.0409656i	$0.0130434\pi$
$887$	30.9776	+	30.9776i	1.04013	+	1.04013i	0.0409656	+	0.999161i	$0.486957\pi$
$888$	12.2657	−	2.40623i	0.411612	−	0.0807478i
$889$		−	42.0294i		−	1.40962i
$890$		0			0
$891$		−	0.728515i		−	0.0244062i
$892$	−5.73615	+	7.44837i	−0.192061	+	0.249390i
$893$	−7.84014	−	7.84014i	−0.262360	−	0.262360i
$894$	5.29260	−	6.02437i	0.177011	−	0.201485i
$895$		0			0
$896$	−9.77460	+	28.2238i	−0.326546	+	0.942890i
$897$	−25.7796	+	25.7796i	−0.860755	+	0.860755i
$898$	54.2784	−	3.50972i	1.81129	−	0.117121i
$899$	−15.8668			−0.529186
$900$		0			0
$901$	1.09083			0.0363408
$902$	−4.36931	+	0.282526i	−0.145482	+	0.00940709i
$903$	13.4772	−	13.4772i	0.448493	−	0.448493i
$904$	−4.11590	+	6.12489i	−0.136893	+	0.203711i
$905$		0			0
$906$	17.9650	−	20.4489i	0.596848	−	0.679370i
$907$	28.6790	+	28.6790i	0.952271	+	0.952271i	0.998912	−	0.0466405i	$-0.0148515\pi$
$907$	28.6790	+	28.6790i	0.952271	+	0.952271i	−0.0466405	+	0.998912i	$0.514852\pi$
$908$	−19.8063	−	15.2533i	−0.657297	−	0.506198i
$909$			5.67030i			0.188072i
$910$		0			0
$911$		−	31.8607i		−	1.05559i	−0.849371	−	0.527796i	$-0.823019\pi$
$911$		−	31.8607i		−	1.05559i	0.849371	−	0.527796i	$-0.176981\pi$
$912$	−7.51250	+	12.9071i	−0.248764	+	0.427397i
$913$	−2.59129	−	2.59129i	−0.0857591	−	0.0857591i
$914$	7.42162	+	6.52013i	0.245485	+	0.215667i
$915$		0			0
$916$	−1.82638	−	14.0636i	−0.0603452	−	0.464673i
$917$	−8.54072	+	8.54072i	−0.282039	+	0.282039i
$918$	0.145170	+	2.24508i	0.00479134	+	0.0740988i
$919$	55.4206			1.82816			0.914079	−	0.405536i	$-0.132915\pi$
$919$	55.4206			1.82816			0.914079	+	0.405536i	$0.132915\pi$
$920$		0			0
$921$	−1.28005			−0.0421790
$922$	−2.47929	−	38.3426i	−0.0816510	−	1.26275i
$923$	41.0109	−	41.0109i	1.34989	−	1.34989i
$924$	0.495382	+	3.81456i	0.0162969	+	0.125490i
$925$		0			0
$926$	−7.45671	−	6.55096i	−0.245043	−	0.215278i
$927$	−0.0565188	−	0.0565188i	−0.00185632	−	0.00185632i
$928$	14.1626	−	4.73830i	0.464911	−	0.155542i
$929$		−	46.9603i		−	1.54072i	−0.637610	−	0.770359i	$-0.720077\pi$
$929$		−	46.9603i		−	1.54072i	0.637610	−	0.770359i	$-0.279923\pi$
$930$		0			0
$931$		−	0.113038i		−	0.00370466i
$932$	−34.4533	−	26.5332i	−1.12855	−	0.869124i
$933$	17.2800	+	17.2800i	0.565723	+	0.565723i
$934$	−28.0291	+	31.9045i	−0.917140	+	1.04395i
$935$		0			0
$936$	10.3747	+	6.97173i	0.339106	+	0.227878i
$937$	−10.4693	+	10.4693i	−0.342016	+	0.342016i	−0.857125	−	0.515109i	$-0.827752\pi$
$937$	−10.4693	+	10.4693i	−0.342016	+	0.342016i	0.515109	+	0.857125i	$0.327752\pi$
$938$	26.8982	−	1.73928i	0.878258	−	0.0567895i
$939$	26.2908			0.857966
$940$		0			0
$941$	−41.1084			−1.34009			−0.670047	−	0.742318i	$-0.733726\pi$
$941$	−41.1084			−1.34009			−0.670047	+	0.742318i	$0.733726\pi$
$942$	4.18049	−	0.270317i	0.136208	−	0.00880739i
$943$	−24.7909	+	24.7909i	−0.807303	+	0.807303i
$944$	19.0594	−	5.03527i	0.620332	−	0.163884i
$945$		0			0
$946$	−4.90917	+	5.58793i	−0.159611	+	0.181679i
$947$	−25.8091	−	25.8091i	−0.838682	−	0.838682i	0.150003	−	0.988685i	$-0.452072\pi$
$947$	−25.8091	−	25.8091i	−0.838682	−	0.838682i	−0.988685	+	0.150003i	$0.952072\pi$
$948$	−8.68113	+	11.2724i	−0.281950	+	0.366111i
$949$		−	24.8099i		−	0.805362i
$950$		0			0
$951$		−	27.3143i		−	0.885726i
$952$	−2.28675	−	11.6567i	−0.0741141	−	0.377796i
$953$	7.78429	+	7.78429i	0.252158	+	0.252158i	0.821855	−	0.569697i	$-0.192939\pi$
$953$	7.78429	+	7.78429i	0.252158	+	0.252158i	−0.569697	+	0.821855i	$0.692939\pi$
$954$	0.728515	+	0.640023i	0.0235866	+	0.0207215i
$955$		0			0
$956$	−1.40115	+	0.181962i	−0.0453165	+	0.00588507i
$957$	1.35998	−	1.35998i	0.0439618	−	0.0439618i
$958$	1.71384	+	26.5047i	0.0553715	+	0.856329i
$959$	15.2875			0.493658
$960$		0			0
$961$	−5.12110			−0.165197
$962$	1.78219	+	27.5618i	0.0574600	+	0.888627i
$963$	−3.91017	+	3.91017i	−0.126004	+	0.126004i
$964$	49.5818	−	6.43899i	1.59692	−	0.207386i
$965$		0			0
$966$	23.1396	+	20.3288i	0.744503	+	0.654070i
$967$	11.7235	+	11.7235i	0.377001	+	0.377001i	0.870019	−	0.493018i	$-0.164106\pi$
$967$	11.7235	+	11.7235i	0.377001	+	0.377001i	−0.493018	+	0.870019i	$0.664106\pi$
$968$	5.70039	+	29.0577i	0.183217	+	0.933950i
$969$		−	5.93945i		−	0.190803i
$970$		0			0
$971$		−	12.9748i		−	0.416380i	−0.978088	−	0.208190i	$-0.933243\pi$
$971$		−	12.9748i		−	0.416380i	0.978088	−	0.208190i	$-0.0667572\pi$
$972$	−1.22031	+	1.58457i	−0.0391414	+	0.0508250i
$973$	25.3700	+	25.3700i	0.813324	+	0.813324i
$974$	3.92120	−	4.46336i	0.125643	−	0.143015i
$975$		0			0
$976$	8.93475	−	2.36045i	0.285994	−	0.0755561i
$977$	13.9054	−	13.9054i	0.444873	−	0.444873i	−0.448773	−	0.893646i	$-0.648139\pi$
$977$	13.9054	−	13.9054i	0.444873	−	0.444873i	0.893646	+	0.448773i	$0.148139\pi$
$978$	−8.55305	+	0.553053i	−0.273496	+	0.0176847i
$979$	−0.750572			−0.0239884
$980$		0			0
$981$	−15.7796			−0.503803
$982$	−41.7001	+	2.69639i	−1.33070	+	0.0860452i
$983$	13.9381	−	13.9381i	0.444557	−	0.444557i	−0.448983	−	0.893540i	$-0.648214\pi$
$983$	13.9381	−	13.9381i	0.444557	−	0.444557i	0.893540	+	0.448983i	$0.148214\pi$
$984$	9.97677	+	6.70436i	0.318048	+	0.213727i
$985$		0			0
$986$	−3.92007	+	4.46207i	−0.124840	+	0.142101i
$987$	5.54382	+	5.54382i	0.176462	+	0.176462i
$988$	−26.1446	−	20.1345i	−0.831771	−	0.640565i
$989$			59.5592i			1.89387i
$990$		0			0
$991$			52.9621i			1.68240i	0.540726	+	0.841199i	$0.318150\pi$
$991$			52.9621i			1.68240i	−0.540726	+	0.841199i	$0.681850\pi$
$992$	32.2416	−	10.7869i	1.02367	−	0.342484i
$993$	7.79897	+	7.79897i	0.247493	+	0.247493i
$994$	−36.8111	−	32.3397i	−1.16758	−	1.02575i
$995$		0			0
$996$	1.29564	+	9.97677i	0.0410540	+	0.316126i
$997$	−1.53452	+	1.53452i	−0.0485986	+	0.0485986i	−0.730988	−	0.682390i	$-0.760941\pi$
$997$	−1.53452	+	1.53452i	−0.0485986	+	0.0485986i	0.682390	+	0.730988i	$0.260941\pi$
$998$	1.37313	+	21.2357i	0.0434657	+	0.672204i
$999$	−4.41926			−0.139819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.j.d.43.4		12
3.2	odd	2		900.2.k.n.343.3		12
4.3	odd	2	inner	300.2.j.d.43.6		12
5.2	odd	4	inner	300.2.j.d.7.6		12
5.3	odd	4		60.2.j.a.7.1	✓	12
5.4	even	2		60.2.j.a.43.3	yes	12
12.11	even	2		900.2.k.n.343.1		12
15.2	even	4		900.2.k.n.307.1		12
15.8	even	4		180.2.k.e.127.6		12
15.14	odd	2		180.2.k.e.163.4		12
20.3	even	4		60.2.j.a.7.3	yes	12
20.7	even	4	inner	300.2.j.d.7.4		12
20.19	odd	2		60.2.j.a.43.1	yes	12
40.3	even	4		960.2.w.g.127.1		12
40.13	odd	4		960.2.w.g.127.4		12
40.19	odd	2		960.2.w.g.703.4		12
40.29	even	2		960.2.w.g.703.1		12
60.23	odd	4		180.2.k.e.127.4		12
60.47	odd	4		900.2.k.n.307.3		12
60.59	even	2		180.2.k.e.163.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.1	✓	12	5.3	odd	4
60.2.j.a.7.3	yes	12	20.3	even	4
60.2.j.a.43.1	yes	12	20.19	odd	2
60.2.j.a.43.3	yes	12	5.4	even	2
180.2.k.e.127.4		12	60.23	odd	4
180.2.k.e.127.6		12	15.8	even	4
180.2.k.e.163.4		12	15.14	odd	2
180.2.k.e.163.6		12	60.59	even	2
300.2.j.d.7.4		12	20.7	even	4	inner
300.2.j.d.7.6		12	5.2	odd	4	inner
300.2.j.d.43.4		12	1.1	even	1	trivial
300.2.j.d.43.6		12	4.3	odd	2	inner
900.2.k.n.307.1		12	15.2	even	4
900.2.k.n.307.3		12	60.47	odd	4
900.2.k.n.343.1		12	12.11	even	2
900.2.k.n.343.3		12	3.2	odd	2
960.2.w.g.127.1		12	40.3	even	4
960.2.w.g.127.4		12	40.13	odd	4
960.2.w.g.703.1		12	40.29	even	2
960.2.w.g.703.4		12	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0912546 - 1.41127i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.06244 + 0.933389i) q^{6} +(1.86678 + 1.86678i) q^{7} +(0.544488 + 2.77552i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.0912546 - 1.41127i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.06244 + 0.933389i) q^{6} +(1.86678 + 1.86678i) q^{7} +(0.544488 + 2.77552i) q^{8} -1.00000i q^{9} +0.728515i q^{11} +(1.22031 - 1.58457i) q^{12} +(3.12489 + 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(3.86732 - 1.02170i) q^{16} +(-1.12489 + 1.12489i) q^{17} +(-1.41127 + 0.0912546i) q^{18} +3.73356 q^{19} -2.64002 q^{21} +(1.02813 - 0.0664803i) q^{22} +(5.83347 - 5.83347i) q^{23} +(-2.34760 - 1.57758i) q^{24} +(4.12489 - 4.69521i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.18329 - 3.22164i) q^{28} +2.64002i q^{29} +6.01008i q^{31} +(-1.79480 - 5.36458i) q^{32} +(-0.515138 - 0.515138i) q^{33} +(1.69016 + 1.48486i) q^{34} +(0.257569 + 1.98335i) q^{36} +(-3.12489 + 3.12489i) q^{37} +(-0.340704 - 5.26904i) q^{38} -4.41926 q^{39} -4.24977 q^{41} +(0.240914 + 3.72578i) q^{42} +(-5.10495 + 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(-8.76491 - 7.70025i) q^{46} +(-2.09991 - 2.09991i) q^{47} +(-2.01216 + 3.45705i) q^{48} -0.0302761i q^{49} -1.59083i q^{51} +(-7.00260 - 5.39285i) q^{52} +(-0.484862 - 0.484862i) q^{53} +(0.933389 - 1.06244i) q^{54} +(-4.16485 + 6.19773i) q^{56} +(-2.64002 + 2.64002i) q^{57} +(3.72578 - 0.240914i) q^{58} +4.92834 q^{59} +2.31032 q^{61} +(8.48183 - 0.548448i) q^{62} +(1.86678 - 1.86678i) q^{63} +(-7.40707 + 3.02248i) q^{64} +(-0.679988 + 0.774006i) q^{66} +(5.10495 + 5.10495i) q^{67} +(1.94130 - 2.52077i) q^{68} +8.24977i q^{69} -13.1240i q^{71} +(2.77552 - 0.544488i) q^{72} +(-3.96972 - 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(-7.40493 + 0.961649i) q^{76} +(-1.35998 + 1.35998i) q^{77} +(0.403277 + 6.23675i) q^{78} -7.11388 q^{79} -1.00000 q^{81} +(0.387811 + 5.99756i) q^{82} +(-3.55694 + 3.55694i) q^{83} +(5.23608 - 0.679988i) q^{84} +(7.67030 + 6.73860i) q^{86} +(-1.86678 - 1.86678i) q^{87} +(-2.02201 + 0.396668i) q^{88} +1.03028i q^{89} +11.6669i q^{91} +(-10.0673 + 13.0723i) q^{92} +(-4.24977 - 4.24977i) q^{93} +(-2.77191 + 3.15516i) q^{94} +(5.06244 + 2.52422i) q^{96} +(12.5298 - 12.5298i) q^{97} +(-0.0427276 + 0.00276283i) q^{98} +0.728515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q - 4 * q^6 + 12 * q^8	\( 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48} + 8 q^{52} - 4 q^{53} - 64 q^{56} + 20 q^{58} - 32 q^{61} + 56 q^{62} - 24 q^{66} + 16 q^{68} + 12 q^{72} - 44 q^{73} + 8 q^{76} - 48 q^{77} + 24 q^{78} - 12 q^{81} - 16 q^{82} + 64 q^{86} - 60 q^{88} - 56 q^{92} + 16 q^{93} + 44 q^{96} + 20 q^{97} - 24 q^{98}+O(q^{100}) \) 12 * q - 4 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 + 12 * q^16 + 20 * q^17 - 12 * q^22 + 16 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^38 + 16 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 - 64 * q^56 + 20 * q^58 - 32 * q^61 + 56 * q^62 - 24 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 + 8 * q^76 - 48 * q^77 + 24 * q^78 - 12 * q^81 - 16 * q^82 + 64 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 44 * q^96 + 20 * q^97 - 24 * q^98

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