LMFDB - Embedded newform 300.2.j.d.7.6

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			7.6
Root			$1.41127 - 0.0912546i$ of defining polynomial
Character	$\chi$	$=$	300.7
Dual form			300.2.j.d.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41127 - 0.0912546i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.98335 - 0.257569i) q^{4} +(1.06244 + 0.933389i) q^{6} +(-1.86678 + 1.86678i) q^{7} +(2.77552 - 0.544488i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.41127 - 0.0912546i) 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} +(2.77552 - 0.544488i) q^{8} +1.00000i q^{9} +0.728515i q^{11} +(1.58457 + 1.22031i) 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} +(0.0912546 + 1.41127i) q^{18} -3.73356 q^{19} -2.64002 q^{21} +(0.0664803 + 1.02813i) 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} +(-3.22164 + 4.18329i) q^{28} -2.64002i q^{29} +6.01008i q^{31} +(5.36458 - 1.79480i) 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} +(-5.26904 + 0.340704i) q^{38} +4.41926 q^{39} -4.24977 q^{41} +(-3.72578 + 0.240914i) 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} +(3.45705 + 2.01216i) q^{48} +0.0302761i q^{49} -1.59083i q^{51} +(5.39285 - 7.00260i) 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} +(-0.240914 - 3.72578i) q^{58} -4.92834 q^{59} +2.31032 q^{61} +(0.548448 + 8.48183i) 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} +(-2.52077 - 1.94130i) q^{68} -8.24977i q^{69} -13.1240i q^{71} +(0.544488 + 2.77552i) 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} +(6.23675 - 0.403277i) q^{78} +7.11388 q^{79} -1.00000 q^{81} +(-5.99756 + 0.387811i) 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} +(0.396668 + 2.02201i) q^{88} -1.03028i q^{89} +11.6669i q^{91} +(-13.0723 - 10.0673i) 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} +(0.00276283 + 0.0427276i) 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.41127	−	0.0912546i	0.997916	−	0.0645267i
$2$	1.41127	−	0.0912546i	0.997916	−	0.0645267i
$3$	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	$-0.916269\pi$
$7$	−1.86678	+	1.86678i	−0.705576	+	0.705576i	0.260026	+	0.965602i	$0.416269\pi$
$8$	2.77552	−	0.544488i	0.981296	−	0.192506i
$9$			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	$0.964970\pi$
$12$	1.58457	+	1.22031i	0.457425	+	0.352273i
$13$	3.12489	−	3.12489i	0.866687	−	0.866687i	−0.125417	−	0.992104i	$-0.540027\pi$
$13$	3.12489	−	3.12489i	0.866687	−	0.866687i	0.992104	+	0.125417i	$0.0400268\pi$
$14$	−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	0.557412	−	0.830236i	$-0.311795\pi$
$17$	−1.12489	−	1.12489i	−0.272825	−	0.272825i	−0.830236	+	0.557412i	$0.811795\pi$
$18$	0.0912546	+	1.41127i	0.0215089	+	0.332639i
$19$	−3.73356			−0.856537			−0.428268	−	0.903652i	$-0.640876\pi$
$19$	−3.73356			−0.856537			−0.428268	+	0.903652i	$0.640876\pi$
$20$		0			0
$21$	−2.64002			−0.576100
$22$	0.0664803	+	1.02813i	0.0141737	+	0.219198i
$23$	−5.83347	−	5.83347i	−1.21636	−	1.21636i	−0.968897	−	0.247466i	$-0.920402\pi$
$23$	−5.83347	−	5.83347i	−1.21636	−	1.21636i	−0.247466	−	0.968897i	$-0.579598\pi$
$24$	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
$28$	−3.22164	+	4.18329i	−0.608833	+	0.790568i
$29$		−	2.64002i		−	0.490240i	−0.969493	−	0.245120i	$-0.921173\pi$
$29$		−	2.64002i		−	0.490240i	0.969493	−	0.245120i	$-0.0788274\pi$
$30$		0			0
$31$			6.01008i			1.07944i	0.841844	+	0.539721i	$0.181470\pi$
$31$			6.01008i			1.07944i	−0.841844	+	0.539721i	$0.818530\pi$
$32$	5.36458	−	1.79480i	0.948333	−	0.317278i
$33$	−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	0.401939	−	0.915667i	$-0.368337\pi$
$37$	−3.12489	−	3.12489i	−0.513728	−	0.513728i	−0.915667	+	0.401939i	$0.868337\pi$
$38$	−5.26904	+	0.340704i	−0.854752	+	0.0552695i
$39$	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	$0.607673\pi$
$42$	−3.72578	+	0.240914i	−0.574900	+	0.0371739i
$43$	5.10495	+	5.10495i	0.778498	+	0.778498i	0.979575	−	0.201077i	$-0.0644442\pi$
$43$	5.10495	+	5.10495i	0.778498	+	0.778498i	−0.201077	+	0.979575i	$0.564444\pi$
$44$	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	$-0.680507\pi$
$47$	2.09991	−	2.09991i	0.306304	−	0.306304i	0.843474	+	0.537170i	$0.180507\pi$
$48$	3.45705	+	2.01216i	0.498983	+	0.290430i
$49$			0.0302761i			0.00432516i
$50$		0			0
$51$		−	1.59083i		−	0.222761i
$52$	5.39285	−	7.00260i	0.747854	−	0.971086i
$53$	−0.484862	+	0.484862i	−0.0666009	+	0.0666009i	−0.739623	−	0.673022i	$-0.764996\pi$
$53$	−0.484862	+	0.484862i	−0.0666009	+	0.0666009i	0.673022	+	0.739623i	$0.264996\pi$
$54$	−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
$58$	−0.240914	−	3.72578i	−0.0316336	−	0.489218i
$59$	−4.92834			−0.641615			−0.320808	−	0.947144i	$-0.603954\pi$
$59$	−4.92834			−0.641615			−0.320808	+	0.947144i	$0.603954\pi$
$60$		0			0
$61$	2.31032			0.295807			0.147903	−	0.989002i	$-0.452748\pi$
$61$	2.31032			0.295807			0.147903	+	0.989002i	$0.452748\pi$
$62$	0.548448	+	8.48183i	0.0696529	+	1.07719i
$63$	−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	$-0.895376\pi$
$67$	−5.10495	+	5.10495i	−0.623669	+	0.623669i	0.322798	+	0.946468i	$0.395376\pi$
$68$	−2.52077	−	1.94130i	−0.305688	−	0.235417i
$69$		−	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	$-0.284153\pi$
$72$	0.544488	+	2.77552i	0.0641685	+	0.327099i
$73$	−3.96972	+	3.96972i	−0.464621	+	0.464621i	−0.900167	−	0.435546i	$-0.856555\pi$
$73$	−3.96972	+	3.96972i	−0.464621	+	0.464621i	0.435546	+	0.900167i	$0.356555\pi$
$74$	−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
$78$	6.23675	−	0.403277i	0.706172	−	0.0456622i
$79$	7.11388			0.800375			0.400187	−	0.916433i	$-0.368945\pi$
$79$	7.11388			0.800375			0.400187	+	0.916433i	$0.368945\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−5.99756	+	0.387811i	−0.662320	+	0.0428266i
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	0.874839	−	0.484414i	$-0.160967\pi$
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	−0.484414	+	0.874839i	$0.660967\pi$
$84$	−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
$88$	0.396668	+	2.02201i	0.0422849	+	0.215547i
$89$		−	1.03028i		−	0.109209i	−0.998508	−	0.0546045i	$-0.982610\pi$
$89$		−	1.03028i		−	0.109209i	0.998508	−	0.0546045i	$-0.0173898\pi$
$90$		0			0
$91$			11.6669i			1.22303i
$92$	−13.0723	−	10.0673i	−1.36288	−	1.04958i
$93$	−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	0.944926	+	0.327284i	$0.106133\pi$
$97$	12.5298	+	12.5298i	1.27221	+	1.27221i	0.327284	+	0.944926i	$0.393867\pi$
$98$	0.00276283	+	0.0427276i	0.000279088	+	0.00431614i
$99$	−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	$0.591034\pi$
$102$	−0.145170	−	2.24508i	−0.0143740	−	0.222296i
$103$	−0.0565188	−	0.0565188i	−0.00556896	−	0.00556896i	0.704317	−	0.709886i	$-0.251253\pi$
$103$	−0.0565188	−	0.0565188i	−0.00556896	−	0.00556896i	−0.709886	+	0.704317i	$0.751253\pi$
$104$	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	$-0.663871\pi$
$107$	3.91017	−	3.91017i	0.378011	−	0.378011i	0.870384	+	0.492373i	$0.163871\pi$
$108$	−1.22031	+	1.58457i	−0.117424	+	0.152475i
$109$			15.7796i			1.51141i	0.654912	+	0.755705i	$0.272706\pi$
$109$			15.7796i			1.51141i	−0.654912	+	0.755705i	$0.727294\pi$
$110$		0			0
$111$		−	4.41926i		−	0.419457i
$112$	−5.31214	+	9.12670i	−0.501950	+	0.862392i
$113$	1.84484	−	1.84484i	0.173548	−	0.173548i	−0.614988	−	0.788536i	$-0.710839\pi$
$113$	1.84484	−	1.84484i	0.173548	−	0.173548i	0.788536	+	0.614988i	$0.210839\pi$
$114$	−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
$118$	−6.95520	+	0.449733i	−0.640278	+	0.0414013i
$119$	4.19982			0.384997
$120$		0			0
$121$	10.4693			0.951751
$122$	3.26048	−	0.210828i	0.295190	−	0.0190874i
$123$	−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	$-0.500345\pi$
$127$	11.2572	−	11.2572i	0.998914	−	0.998914i	0.999999	+	0.00108535i	$0.000345478\pi$
$128$	10.1775	−	4.94145i	0.899575	−	0.436767i
$129$			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	$0.935950\pi$
$132$	−0.889013	+	1.15438i	−0.0773786	+	0.100476i
$133$	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	0.860045	−	0.510219i	$-0.170436\pi$
$137$	4.09461	+	4.09461i	0.349826	+	0.349826i	−0.510219	+	0.860045i	$0.670436\pi$
$138$	−0.752829	−	11.6426i	−0.0640851	−	0.991086i
$139$	−13.5902			−1.15271			−0.576354	−	0.817200i	$-0.695525\pi$
$139$	−13.5902			−1.15271			−0.576354	+	0.817200i	$0.695525\pi$
$140$		0			0
$141$	2.96972			0.250096
$142$	−1.19762	−	18.5214i	−0.100502	−	1.55428i
$143$	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
$148$	−7.00260	−	5.39285i	−0.575610	−	0.443290i
$149$			5.67030i			0.464529i	0.972653	+	0.232265i	$0.0746135\pi$
$149$			5.67030i			0.464529i	−0.972653	+	0.232265i	$0.925386\pi$
$150$		0			0
$151$		−	19.2471i		−	1.56631i	−0.621829	−	0.783153i	$-0.713610\pi$
$151$		−	19.2471i		−	1.56631i	0.621829	−	0.783153i	$-0.286390\pi$
$152$	−10.3626	+	2.03288i	−0.840516	+	0.164888i
$153$	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	0.785733	−	0.618565i	$-0.212286\pi$
$157$	2.09461	+	2.09461i	0.167168	+	0.167168i	−0.618565	+	0.785733i	$0.712286\pi$
$158$	10.0396	−	0.649175i	0.798707	−	0.0516456i
$159$	−0.685698			−0.0543794
$160$		0			0
$161$	21.7796			1.71647
$162$	−1.41127	+	0.0912546i	−0.110880	+	0.00716964i
$163$	4.28546	+	4.28546i	0.335663	+	0.335663i	0.854732	−	0.519069i	$-0.173721\pi$
$163$	4.28546	+	4.28546i	0.335663	+	0.335663i	−0.519069	+	0.854732i	$0.673721\pi$
$164$	−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	$-0.826973\pi$
$167$	−4.37644	+	4.37644i	−0.338659	+	0.338659i	0.517203	+	0.855862i	$0.326973\pi$
$168$	−7.32745	+	1.43746i	−0.565325	+	0.110902i
$169$		−	6.52982i		−	0.502294i
$170$		0			0
$171$		−	3.73356i		−	0.285512i
$172$	11.4398	+	8.81001i	0.872274	+	0.671757i
$173$	−16.4049	+	16.4049i	−1.24724	+	1.24724i	−0.290312	+	0.956932i	$0.593759\pi$
$173$	−16.4049	+	16.4049i	−1.24724	+	1.24724i	−0.956932	+	0.290312i	$0.906241\pi$
$174$	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
$178$	−0.0940174	−	1.45399i	−0.00704690	−	0.108981i
$179$	24.4156			1.82491			0.912455	−	0.409178i	$-0.134185\pi$
$179$	24.4156			1.82491			0.912455	+	0.409178i	$0.134185\pi$
$180$		0			0
$181$	11.2800			0.838439			0.419220	−	0.907885i	$-0.362304\pi$
$181$	11.2800			0.838439			0.419220	+	0.907885i	$0.362304\pi$
$182$	1.06466	+	16.4652i	0.0789180	+	1.22048i
$183$	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
$188$	3.62398	−	4.70572i	0.264306	−	0.343200i
$189$		−	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	$0.962286\pi$
$192$	7.37480	+	3.10037i	0.532230	+	0.223750i
$193$	−0.939448	+	0.939448i	−0.0676229	+	0.0676229i	−0.740109	−	0.672486i	$-0.765226\pi$
$193$	−0.939448	+	0.939448i	−0.0676229	+	0.0676229i	0.672486	+	0.740109i	$0.265226\pi$
$194$	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	0.757023	−	0.653388i	$-0.226653\pi$
$197$	1.45459	+	1.45459i	0.103635	+	0.103635i	−0.653388	+	0.757023i	$0.726653\pi$
$198$	−1.02813	+	0.0664803i	−0.0730659	+	0.00472455i
$199$	−5.19059			−0.367951			−0.183975	−	0.982931i	$-0.558897\pi$
$199$	−5.19059			−0.367951			−0.183975	+	0.982931i	$0.558897\pi$
$200$		0			0
$201$	−7.21949			−0.509224
$202$	−8.00230	+	0.517441i	−0.563040	+	0.0364070i
$203$	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
$208$	8.89224	−	15.2776i	0.616566	−	1.05931i
$209$		−	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	$0.867103\pi$
$212$	−0.836763	+	1.08653i	−0.0574691	+	0.0746235i
$213$	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
$218$	1.43996	+	22.2692i	0.0975264	+	1.50826i
$219$	−5.61404			−0.379361
$220$		0			0
$221$	−7.03028			−0.472908
$222$	−0.403277	−	6.23675i	−0.0270662	−	0.418583i
$223$	−3.32381	−	3.32381i	−0.222579	−	0.222579i	0.587005	−	0.809583i	$-0.300307\pi$
$223$	−3.32381	−	3.32381i	−0.222579	−	0.222579i	−0.809583	+	0.587005i	$0.800307\pi$
$224$	−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	$-0.886153\pi$
$227$	−8.83851	+	8.83851i	−0.586633	+	0.586633i	0.350085	+	0.936718i	$0.386153\pi$
$228$	−5.91607	−	4.55609i	−0.391801	−	0.301734i
$229$		−	7.09083i		−	0.468575i	−0.972167	−	0.234288i	$-0.924724\pi$
$229$		−	7.09083i		−	0.468575i	0.972167	−	0.234288i	$-0.0752757\pi$
$230$		0			0
$231$		−	1.92330i		−	0.126544i
$232$	−1.43746	−	7.32745i	−0.0943739	−	0.481071i
$233$	15.3747	−	15.3747i	1.00723	−	1.00723i	0.00725353	−	0.999974i	$-0.497691\pi$
$233$	15.3747	−	15.3747i	1.00723	−	1.00723i	0.999974	−	0.00725353i	$-0.00230889\pi$
$234$	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
$238$	5.92707	−	0.383253i	0.384195	−	0.0248426i
$239$	−0.706459			−0.0456970			−0.0228485	−	0.999739i	$-0.507274\pi$
$239$	−0.706459			−0.0456970			−0.0228485	+	0.999739i	$0.507274\pi$
$240$		0			0
$241$	−24.9991			−1.61033			−0.805166	−	0.593049i	$-0.797924\pi$
$241$	−24.9991			−1.61033			−0.805166	+	0.593049i	$0.797924\pi$
$242$	14.7749	−	0.955368i	0.949768	−	0.0614134i
$243$	−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
$248$	3.27242	+	16.6811i	0.207799	+	1.05925i
$249$			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	$0.641289\pi$
$252$	−4.18329	−	3.22164i	−0.263523	−	0.202944i
$253$	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	0.818342	−	0.574731i	$-0.194893\pi$
$257$	3.90539	+	3.90539i	0.243612	+	0.243612i	−0.574731	+	0.818342i	$0.694893\pi$
$258$	0.658812	+	10.1886i	0.0410158	+	0.634316i
$259$	11.6669			0.724948
$260$		0			0
$261$	2.64002			0.163413
$262$	0.417500	+	6.45670i	0.0257932	+	0.398896i
$263$	0.176615	+	0.176615i	0.0108905	+	0.0108905i	0.712531	−	0.701641i	$-0.247549\pi$
$263$	0.176615	+	0.176615i	0.0108905	+	0.0108905i	−0.701641	+	0.712531i	$0.747549\pi$
$264$	−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
$268$	−8.81001	+	11.4398i	−0.538157	+	0.698795i
$269$		−	5.38934i		−	0.328594i	−0.986411	−	0.164297i	$-0.947465\pi$
$269$		−	5.38934i		−	0.328594i	0.986411	−	0.164297i	$-0.0525355\pi$
$270$		0			0
$271$		−	15.4005i		−	0.935513i	−0.883857	−	0.467757i	$-0.845062\pi$
$271$		−	15.4005i		−	0.935513i	0.883857	−	0.467757i	$-0.154938\pi$
$272$	−5.49958	−	3.20100i	−0.333461	−	0.194089i
$273$	−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	0.400099	−	0.916472i	$-0.368976\pi$
$277$	−8.59415	−	8.59415i	−0.516372	−	0.516372i	−0.916472	+	0.400099i	$0.868976\pi$
$278$	−19.1794	+	1.24017i	−1.15031	+	0.0743805i
$279$	−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	$0.712421\pi$
$282$	4.19107	−	0.271001i	0.249575	−	0.0161379i
$283$	−18.5822	−	18.5822i	−1.10459	−	1.10459i	−0.993849	−	0.110745i	$-0.964676\pi$
$283$	−18.5822	−	18.5822i	−1.10459	−	1.10459i	−0.110745	−	0.993849i	$-0.535324\pi$
$284$	−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
$288$	1.79480	+	5.36458i	0.105759	+	0.316111i
$289$		−	14.4693i		−	0.851133i
$290$		0			0
$291$			17.7198i			1.03876i
$292$	−6.85085	+	8.89581i	−0.400916	+	0.520588i
$293$	−6.23509	+	6.23509i	−0.364258	+	0.364258i	−0.865378	−	0.501120i	$-0.832922\pi$
$293$	−6.23509	+	6.23509i	−0.364258	+	0.364258i	0.501120	+	0.865378i	$0.332922\pi$
$294$	−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
$298$	0.517441	+	8.00230i	0.0299745	+	0.463561i
$299$	−36.4578			−2.10841
$300$		0			0
$301$	−19.0596			−1.09858
$302$	−1.75639	−	27.1628i	−0.101069	−	1.56304i
$303$	−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	$-0.761630\pi$
$307$	−0.905130	+	0.905130i	−0.0516585	+	0.0516585i	0.680806	+	0.732464i	$0.261630\pi$
$308$	−3.04759	−	2.34702i	−0.173653	−	0.133734i
$309$		−	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	$-0.243653\pi$
$312$	12.2657	−	2.40623i	0.694411	−	0.136226i
$313$	−18.5904	+	18.5904i	−1.05079	+	1.05079i	−0.0521506	+	0.998639i	$0.516608\pi$
$313$	−18.5904	+	18.5904i	−1.05079	+	1.05079i	−0.998639	+	0.0521506i	$0.983392\pi$
$314$	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	−0.996055	−	0.0887327i	$-0.971718\pi$
$317$	−19.3141	−	19.3141i	−1.08479	−	1.08479i	−0.0887327	−	0.996055i	$-0.528282\pi$
$318$	−0.967703	+	0.0625731i	−0.0542661	+	0.00350893i
$319$	1.92330			0.107684
$320$		0			0
$321$	5.52982			0.308644
$322$	30.7368	−	1.98749i	1.71289	−	0.110758i
$323$	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
$328$	−11.7953	+	2.31395i	−0.651289	+	0.127766i
$329$			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	$-0.0980268\pi$
$332$	7.97080	+	6.13849i	0.437455	+	0.336893i
$333$	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	0.230992	−	0.972956i	$-0.425803\pi$
$337$	−13.6206	−	13.6206i	−0.741964	−	0.741964i	−0.972956	+	0.230992i	$0.925803\pi$
$338$	−0.595876	−	9.21531i	−0.0324114	−	0.501247i
$339$	2.60900			0.141701
$340$		0			0
$341$	−4.37844			−0.237106
$342$	−0.340704	−	5.26904i	−0.0184232	−	0.284917i
$343$	−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	$-0.985538\pi$
$347$	−17.7627	+	17.7627i	−0.953549	+	0.953549i	0.0454187	+	0.998968i	$0.485538\pi$
$348$	3.22164	−	4.18329i	0.172698	−	0.224248i
$349$		−	14.6888i		−	0.786271i	−0.919480	−	0.393136i	$-0.871390\pi$
$349$		−	14.6888i		−	0.786271i	0.919480	−	0.393136i	$-0.128610\pi$
$350$		0			0
$351$			4.41926i			0.235882i
$352$	1.30754	+	3.90818i	0.0696919	+	0.208307i
$353$	18.4049	−	18.4049i	0.979596	−	0.979596i	−0.0202002	−	0.999796i	$-0.506430\pi$
$353$	18.4049	−	18.4049i	0.979596	−	0.979596i	0.999796	+	0.0202002i	$0.00643038\pi$
$354$	−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
$358$	34.4569	−	2.22804i	1.82111	−	0.117755i
$359$	9.63060			0.508284			0.254142	−	0.967167i	$-0.418207\pi$
$359$	9.63060			0.508284			0.254142	+	0.967167i	$0.418207\pi$
$360$		0			0
$361$	−5.06055			−0.266345
$362$	15.9192	−	1.02936i	0.836692	−	0.0541017i
$363$	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	$-0.556738\pi$
$367$	15.4570	−	15.4570i	0.806850	−	0.806850i	0.984156	+	0.177306i	$0.0567383\pi$
$368$	−28.5199	−	16.5998i	−1.48670	−	0.865326i
$369$		−	4.24977i		−	0.221234i
$370$		0			0
$371$		−	1.81026i		−	0.0939840i
$372$	−7.33415	+	9.52337i	−0.380258	+	0.493764i
$373$	−3.37466	+	3.37466i	−0.174733	+	0.174733i	−0.789055	−	0.614322i	$-0.789430\pi$
$373$	−3.37466	+	3.37466i	−0.174733	+	0.174733i	0.614322	+	0.789055i	$0.289430\pi$
$374$	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
$378$	−0.240914	−	3.72578i	−0.0123913	−	0.191633i
$379$	5.89705			0.302911			0.151455	−	0.988464i	$-0.451604\pi$
$379$	5.89705			0.302911			0.151455	+	0.988464i	$0.451604\pi$
$380$		0			0
$381$	15.9201			0.815610
$382$	0.298155	+	4.61102i	0.0152549	+	0.235920i
$383$	−0.642881	−	0.642881i	−0.0328497	−	0.0328497i	0.690491	−	0.723341i	$-0.257394\pi$
$383$	−0.642881	−	0.642881i	−0.0328497	−	0.0328497i	−0.723341	+	0.690491i	$0.757394\pi$
$384$	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
$388$	28.0782	+	21.6237i	1.42546	+	1.09778i
$389$			18.8292i			0.954680i	0.878719	+	0.477340i	$0.158399\pi$
$389$			18.8292i			0.954680i	−0.878719	+	0.477340i	$0.841601\pi$
$390$		0			0
$391$			13.1240i			0.663708i
$392$	0.0164850	+	0.0840320i	0.000832616	+	0.00424426i
$393$	−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	0.966988	+	0.254821i	$0.0820166\pi$
$397$	24.3444	+	24.3444i	1.22181	+	1.22181i	0.254821	+	0.966988i	$0.417983\pi$
$398$	−7.32530	+	0.473665i	−0.367184	+	0.0237427i
$399$	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	$0.369708\pi$
$402$	−10.1886	+	0.658812i	−0.508163	+	0.0328586i
$403$	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
$408$	−0.866187	−	4.41538i	−0.0428826	−	0.218594i
$409$			23.4087i			1.15749i	0.815510	+	0.578743i	$0.196457\pi$
$409$			23.4087i			1.15749i	−0.815510	+	0.578743i	$0.803543\pi$
$410$		0			0
$411$			5.79065i			0.285632i
$412$	−0.126654	−	0.0975387i	−0.00623978	−	0.00480539i
$413$	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
$418$	−0.248208	−	3.83858i	−0.0121403	−	0.187751i
$419$	−28.0361			−1.36966			−0.684828	−	0.728705i	$-0.740122\pi$
$419$	−28.0361			−1.36966			−0.684828	+	0.728705i	$0.740122\pi$
$420$		0			0
$421$	17.4087			0.848449			0.424224	−	0.905557i	$-0.360547\pi$
$421$	17.4087			0.848449			0.424224	+	0.905557i	$0.360547\pi$
$422$	1.07498	+	16.6247i	0.0523290	+	0.809277i
$423$	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
$428$	6.74808	−	8.76236i	0.326181	−	0.423545i
$429$			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	$0.729898\pi$
$432$	−2.01216	+	3.45705i	−0.0968100	+	0.166328i
$433$	12.1589	−	12.1589i	0.584321	−	0.584321i	−0.351766	−	0.936088i	$-0.614419\pi$
$433$	12.1589	−	12.1589i	0.584321	−	0.584321i	0.936088	+	0.351766i	$0.114419\pi$
$434$	−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
$438$	−7.92290	+	0.512307i	−0.378571	+	0.0244790i
$439$	14.2967			0.682344			0.341172	−	0.940001i	$-0.389176\pi$
$439$	14.2967			0.682344			0.341172	+	0.940001i	$0.389176\pi$
$440$		0			0
$441$	−0.0302761			−0.00144172
$442$	−9.92159	+	0.641545i	−0.471922	+	0.0305152i
$443$	−7.02825	−	7.02825i	−0.333922	−	0.333922i	0.520152	−	0.854074i	$-0.325875\pi$
$443$	−7.02825	−	7.02825i	−0.333922	−	0.333922i	−0.854074	+	0.520152i	$0.825875\pi$
$444$	−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
$448$	−8.18505	+	19.4696i	−0.386707	+	0.919854i
$449$		−	38.4608i		−	1.81508i	−0.419969	−	0.907538i	$-0.637959\pi$
$449$		−	38.4608i		−	1.81508i	0.419969	−	0.907538i	$-0.362041\pi$
$450$		0			0
$451$		−	3.09602i		−	0.145786i
$452$	3.18378	−	4.13412i	0.149752	−	0.194453i
$453$	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	0.582076	−	0.813134i	$-0.302240\pi$
$457$	−4.93945	−	4.93945i	−0.231058	−	0.231058i	−0.813134	+	0.582076i	$0.802240\pi$
$458$	−0.647071	−	10.0070i	−0.0302356	−	0.467599i
$459$	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	$0.281950\pi$
$462$	−0.175510	−	2.71428i	−0.00816545	−	0.126280i
$463$	−4.96280	−	4.96280i	−0.230641	−	0.230641i	0.582319	−	0.812960i	$-0.302145\pi$
$463$	−4.96280	−	4.96280i	−0.230641	−	0.230641i	−0.812960	+	0.582319i	$0.802145\pi$
$464$	−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	$-0.505494\pi$
$467$	21.2340	−	21.2340i	0.982591	−	0.982591i	0.999851	+	0.0172604i	$0.00549442\pi$
$468$	7.00260	+	5.39285i	0.323695	+	0.249285i
$469$		−	19.0596i		−	0.880092i
$470$		0			0
$471$			2.96222i			0.136492i
$472$	−13.6787	+	2.68342i	−0.629614	+	0.123514i
$473$	−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
$478$	−0.997001	+	0.0644676i	−0.0456018	+	0.00294868i
$479$	18.7808			0.858118			0.429059	−	0.903277i	$-0.358845\pi$
$479$	18.7808			0.858118			0.429059	+	0.903277i	$0.358845\pi$
$480$		0			0
$481$	−19.5298			−0.890483
$482$	−35.2804	+	2.28128i	−1.60698	+	0.103909i
$483$	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	$-0.780344\pi$
$487$	−2.97058	+	2.97058i	−0.134610	+	0.134610i	0.636591	+	0.771201i	$0.280344\pi$
$488$	6.41236	−	1.25794i	0.290274	−	0.0569444i
$489$			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	$-0.232311\pi$
$492$	−6.73404	−	5.18603i	−0.303594	−	0.233804i
$493$	−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
$498$	0.459036	+	7.09906i	0.0205699	+	0.318116i
$499$	15.0473			0.673608			0.336804	−	0.941575i	$-0.390654\pi$
$499$	15.0473			0.673608			0.336804	+	0.941575i	$0.390654\pi$
$500$		0			0
$501$	−6.18922			−0.276514
$502$	2.61129	+	40.3840i	0.116548	+	1.80243i
$503$	−13.4136	−	13.4136i	−0.598084	−	0.598084i	0.341719	−	0.939802i	$-0.388991\pi$
$503$	−13.4136	−	13.4136i	−0.598084	−	0.598084i	−0.939802	+	0.341719i	$0.888991\pi$
$504$	−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
$508$	19.4274	−	25.2264i	0.861951	−	1.11924i
$509$			41.4187i			1.83585i	0.396752	+	0.917926i	$0.370137\pi$
$509$			41.4187i			1.83585i	−0.396752	+	0.917926i	$0.629863\pi$
$510$		0			0
$511$		−	14.8212i		−	0.655651i
$512$	18.9128	−	12.4220i	0.835835	−	0.548981i
$513$	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
$518$	16.4652	−	1.06466i	0.723437	−	0.0467785i
$519$	−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	$0.263908\pi$
$522$	3.72578	−	0.240914i	0.163073	−	0.0105445i
$523$	17.1251	+	17.1251i	0.748829	+	0.748829i	0.974259	−	0.225430i	$-0.0723787\pi$
$523$	17.1251	+	17.1251i	0.748829	+	0.748829i	−0.225430	+	0.974259i	$0.572379\pi$
$524$	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
$528$	−1.46589	+	2.51852i	−0.0637945	+	0.109604i
$529$			45.0587i			1.95907i
$530$		0			0
$531$		−	4.92834i		−	0.213872i
$532$	12.0282	−	15.6186i	0.521488	−	0.677150i
$533$	−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
$538$	−0.491802	−	7.60579i	−0.0212031	−	0.327909i
$539$	−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	$0.659446\pi$
$542$	−1.40537	−	21.7342i	−0.0603656	−	0.933564i
$543$	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	0.0874075	−	0.996173i	$-0.472142\pi$
$547$	25.3428	−	25.3428i	1.08358	−	1.08358i	0.996173	−	0.0874075i	$-0.0278582\pi$
$548$	9.17567	+	7.06638i	0.391965	+	0.301861i
$549$			2.31032i			0.0986022i
$550$		0			0
$551$			9.85668i			0.419909i
$552$	−4.49190	−	22.8974i	−0.191188	−	0.974580i
$553$	−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	0.100653	−	0.994922i	$-0.467907\pi$
$557$	−21.1055	−	21.1055i	−0.894269	−	0.894269i	−0.994922	+	0.100653i	$0.967907\pi$
$558$	−8.48183	+	0.548448i	−0.359064	+	0.0232176i
$559$	31.9048			1.34943
$560$		0			0
$561$	1.15894			0.0489306
$562$	−29.2828	+	1.89347i	−1.23522	+	0.0798712i
$563$	−10.2955	−	10.2955i	−0.433905	−	0.433905i	0.456049	−	0.889955i	$-0.349264\pi$
$563$	−10.2955	−	10.2955i	−0.433905	−	0.433905i	−0.889955	+	0.456049i	$0.849264\pi$
$564$	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
$568$	−7.14584	−	36.4259i	−0.299833	−	1.52840i
$569$		−	28.3179i		−	1.18715i	−0.804780	−	0.593574i	$-0.797717\pi$
$569$		−	28.3179i		−	1.18715i	0.804780	−	0.593574i	$-0.202283\pi$
$570$		0			0
$571$		−	27.2387i		−	1.13990i	−0.821678	−	0.569952i	$-0.806962\pi$
$571$		−	27.2387i		−	1.13990i	0.821678	−	0.569952i	$-0.193038\pi$
$572$	5.10150	+	3.92878i	0.213304	+	0.164270i
$573$	−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	0.599843	−	0.800118i	$-0.295230\pi$
$577$	−4.81078	−	4.81078i	−0.200275	−	0.200275i	−0.800118	+	0.599843i	$0.795230\pi$
$578$	−1.32039	−	20.4200i	−0.0549208	−	0.849359i
$579$	−1.32858			−0.0552139
$580$		0			0
$581$	−13.2800			−0.550949
$582$	1.61702	+	25.0074i	0.0670275	+	1.03659i
$583$	−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	$-0.795140\pi$
$587$	−4.84271	+	4.84271i	−0.199880	+	0.199880i	0.600069	+	0.799948i	$0.295140\pi$
$588$	−0.0369462	+	0.0479745i	−0.00152363	+	0.00197843i
$589$		−	22.4390i		−	0.924582i
$590$		0			0
$591$			2.05710i			0.0846176i
$592$	−15.2776	−	8.89224i	−0.627906	−	0.365469i
$593$	−18.8439	+	18.8439i	−0.773827	+	0.773827i	−0.978773	−	0.204946i	$-0.934298\pi$
$593$	−18.8439	+	18.8439i	−0.773827	+	0.773827i	0.204946	+	0.978773i	$0.434298\pi$
$594$	−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
$598$	−51.4517	+	3.32695i	−2.10402	+	0.136049i
$599$	−30.2765			−1.23706			−0.618532	−	0.785760i	$-0.712272\pi$
$599$	−30.2765			−1.23706			−0.618532	+	0.785760i	$0.712272\pi$
$600$		0			0
$601$	30.1505			1.22986			0.614932	−	0.788581i	$-0.289184\pi$
$601$	30.1505			1.22986			0.614932	+	0.788581i	$0.289184\pi$
$602$	−26.8982	+	1.73928i	−1.09629	+	0.0708877i
$603$	−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	$-0.939552\pi$
$607$	−19.5438	+	19.5438i	−0.793258	+	0.793258i	0.188764	+	0.982022i	$0.439552\pi$
$608$	−20.0290	+	6.70097i	−0.812282	+	0.271760i
$609$			6.96972i			0.282427i
$610$		0			0
$611$		−	13.1240i		−	0.530939i
$612$	1.94130	−	2.52077i	0.0784724	−	0.101896i
$613$	−23.4040	+	23.4040i	−0.945279	+	0.945279i	−0.998579	−	0.0532993i	$-0.983026\pi$
$613$	−23.4040	+	23.4040i	−0.945279	+	0.945279i	0.0532993	+	0.998579i	$0.483026\pi$
$614$	−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	0.969018	−	0.246992i	$-0.0794421\pi$
$617$	17.9348	+	17.9348i	0.722026	+	0.722026i	−0.246992	+	0.969018i	$0.579442\pi$
$618$	−0.00729394	−	0.112802i	−0.000293405	−	0.00453756i
$619$	−38.9056			−1.56375			−0.781875	−	0.623435i	$-0.785736\pi$
$619$	−38.9056			−1.56375			−0.781875	+	0.623435i	$0.785736\pi$
$620$		0			0
$621$	8.24977			0.331052
$622$	−2.23005	−	34.4881i	−0.0894169	−	1.38285i
$623$	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
$628$	4.69384	+	3.61483i	0.187305	+	0.144247i
$629$			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	$-0.0818113\pi$
$632$	19.7448	−	3.87342i	0.785404	−	0.154077i
$633$	−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
$638$	2.71428	−	0.175510i	0.107460	−	0.00694849i
$639$	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	$0.605442\pi$
$642$	7.80405	−	0.504621i	0.308001	−	0.0199158i
$643$	−5.74249	−	5.74249i	−0.226462	−	0.226462i	0.584751	−	0.811213i	$-0.301192\pi$
$643$	−5.74249	−	5.74249i	−0.226462	−	0.226462i	−0.811213	+	0.584751i	$0.801192\pi$
$644$	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	$-0.709036\pi$
$647$	4.61663	−	4.61663i	0.181498	−	0.181498i	0.792009	+	0.610510i	$0.209036\pi$
$648$	−2.77552	+	0.544488i	−0.109033	+	0.0213895i
$649$		−	3.59037i		−	0.140934i
$650$		0			0
$651$		−	15.8668i		−	0.621867i
$652$	9.60334	+	7.39574i	0.376096	+	0.289640i
$653$	−14.4655	+	14.4655i	−0.566078	+	0.566078i	−0.931027	−	0.364949i	$-0.881086\pi$
$653$	−14.4655	+	14.4655i	−0.566078	+	0.566078i	0.364949	+	0.931027i	$0.381086\pi$
$654$	−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
$658$	0.715449	+	11.0645i	0.0278911	+	0.431340i
$659$	35.5474			1.38473			0.692364	−	0.721548i	$-0.256569\pi$
$659$	35.5474			1.38473			0.692364	+	0.721548i	$0.256569\pi$
$660$		0			0
$661$	15.1883			0.590756			0.295378	−	0.955380i	$-0.404554\pi$
$661$	15.1883			0.590756			0.295378	+	0.955380i	$0.404554\pi$
$662$	−1.00648	−	15.5654i	−0.0391181	−	0.604967i
$663$	−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
$668$	−7.55275	+	9.80722i	−0.292225	+	0.379453i
$669$		−	4.70058i		−	0.181735i
$670$		0			0
$671$			1.68311i			0.0649756i
$672$	−14.1626	+	4.73830i	−0.546335	+	0.182784i
$673$	20.3700	−	20.3700i	0.785204	−	0.785204i	−0.195500	−	0.980704i	$-0.562633\pi$
$673$	20.3700	−	20.3700i	0.785204	−	0.785204i	0.980704	+	0.195500i	$0.0626328\pi$
$674$	−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	0.511132	−	0.859502i	$-0.329226\pi$
$677$	−9.06433	−	9.06433i	−0.348371	−	0.348371i	−0.859502	+	0.511132i	$0.829226\pi$
$678$	3.68199	−	0.238083i	0.141406	−	0.00914351i
$679$	−46.7808			−1.79528
$680$		0			0
$681$	−12.4995			−0.478983
$682$	−6.17914	+	0.399552i	−0.236612	+	0.0152997i
$683$	24.8545	+	24.8545i	0.951030	+	0.951030i	0.998856	−	0.0478253i	$-0.0152291\pi$
$683$	24.8545	+	24.8545i	0.951030	+	0.951030i	−0.0478253	+	0.998856i	$0.515229\pi$
$684$	−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
$688$	24.9582	+	14.5268i	0.951522	+	0.553827i
$689$			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	$0.716278\pi$
$692$	−28.3112	+	36.7620i	−1.07623	+	1.39748i
$693$	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
$698$	−1.34042	−	20.7298i	−0.0507355	−	0.784633i
$699$	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	$0.803087\pi$
$702$	0.403277	+	6.23675i	0.0152207	+	0.235391i
$703$	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
$708$	−7.80928	−	6.01409i	−0.293491	−	0.226023i
$709$		−	18.4702i		−	0.693662i	−0.937928	−	0.346831i	$-0.887258\pi$
$709$		−	18.4702i		−	0.693662i	0.937928	−	0.346831i	$-0.112742\pi$
$710$		0			0
$711$			7.11388i			0.266792i
$712$	−0.560973	−	2.85956i	−0.0210233	−	0.107166i
$713$	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
$718$	13.5913	−	0.878837i	0.507225	−	0.0327979i
$719$	33.3725			1.24458			0.622292	−	0.782785i	$-0.286201\pi$
$719$	33.3725			1.24458			0.622292	+	0.782785i	$0.286201\pi$
$720$		0			0
$721$	0.211016			0.00785865
$722$	−7.14179	+	0.461799i	−0.265790	+	0.0171864i
$723$	−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	$-0.540988\pi$
$727$	23.2774	−	23.2774i	0.863309	−	0.863309i	0.991721	+	0.128412i	$0.0409879\pi$
$728$	6.35251	+	32.3819i	0.235440	+	1.20015i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	11.4850i		−	0.424787i
$732$	3.66086	+	2.81931i	0.135309	+	0.104205i
$733$	16.2157	−	16.2157i	0.598941	−	0.598941i	−0.341090	−	0.940031i	$-0.610796\pi$
$733$	16.2157	−	16.2157i	0.598941	−	0.598941i	0.940031	+	0.341090i	$0.110796\pi$
$734$	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
$738$	−0.387811	−	5.99756i	−0.0142755	−	0.220773i
$739$	14.3408			0.527535			0.263768	−	0.964586i	$-0.415035\pi$
$739$	14.3408			0.527535			0.263768	+	0.964586i	$0.415035\pi$
$740$		0			0
$741$	−16.4995			−0.606126
$742$	−0.165194	−	2.55476i	−0.00606448	−	0.0937881i
$743$	11.6034	+	11.6034i	0.425686	+	0.425686i	0.887156	−	0.461470i	$-0.152678\pi$
$743$	11.6034	+	11.6034i	0.425686	+	0.425686i	−0.461470	+	0.887156i	$0.652678\pi$
$744$	−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
$748$	1.41427	−	1.83642i	0.0517107	−	0.0671462i
$749$			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	$0.778220\pi$
$752$	5.97555	−	10.2665i	0.217906	−	0.374381i
$753$	−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	0.932765	−	0.360484i	$-0.117389\pi$
$757$	15.7455	+	15.7455i	0.572281	+	0.572281i	−0.360484	+	0.932765i	$0.617389\pi$
$758$	8.32230	−	0.538132i	0.302280	−	0.0195459i
$759$	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	$0.645821\pi$
$762$	22.4675	−	1.45278i	0.813910	−	0.0526286i
$763$	−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
$768$	15.4253	+	4.24959i	0.556614	+	0.153344i
$769$		−	15.9688i		−	0.575850i	−0.957653	−	0.287925i	$-0.907035\pi$
$769$		−	15.9688i		−	0.575850i	0.957653	−	0.287925i	$-0.0929654\pi$
$770$		0			0
$771$			5.52306i			0.198908i
$772$	−1.62128	+	2.10522i	−0.0583510	+	0.0757686i
$773$	2.84392	−	2.84392i	0.102289	−	0.102289i	−0.654110	−	0.756399i	$-0.726957\pi$
$773$	2.84392	−	2.84392i	0.102289	−	0.102289i	0.756399	+	0.654110i	$0.226957\pi$
$774$	−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
$778$	1.71825	+	26.5731i	0.0616024	+	0.952691i
$779$	15.8668			0.568486
$780$		0			0
$781$	9.56101			0.342120
$782$	1.19762	+	18.5214i	0.0428269	+	0.662324i
$783$	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	$-0.689506\pi$
$787$	7.49452	−	7.49452i	0.267151	−	0.267151i	0.827951	+	0.560800i	$0.189506\pi$
$788$	3.25960	+	2.51029i	0.116119	+	0.0894254i
$789$			0.249771i			0.00889208i
$790$		0			0
$791$			6.88781i			0.244902i
$792$	−2.02201	+	0.396668i	−0.0718490	+	0.0140950i
$793$	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	0.0710121	−	0.997475i	$-0.477377\pi$
$797$	−26.1552	−	26.1552i	−0.926463	−	0.926463i	−0.997475	+	0.0710121i	$0.977377\pi$
$798$	13.9104	−	0.899467i	0.492423	−	0.0318408i
$799$	−4.72432			−0.167134
$800$		0			0
$801$	1.03028			0.0364030
$802$	22.4948	−	1.45455i	0.794319	−	0.0513619i
$803$	−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
$808$	−15.7381	+	3.08741i	−0.553663	+	0.108615i
$809$		−	23.7115i		−	0.833651i	−0.908987	−	0.416826i	$-0.863143\pi$
$809$		−	23.7115i		−	0.833651i	0.908987	−	0.416826i	$-0.136857\pi$
$810$		0			0
$811$		−	26.0077i		−	0.913255i	−0.889658	−	0.456628i	$-0.849057\pi$
$811$		−	26.0077i		−	0.913255i	0.889658	−	0.456628i	$-0.150943\pi$
$812$	11.0440	+	8.50521i	0.387568	+	0.298474i
$813$	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
$818$	2.13615	+	33.0359i	0.0746888	+	1.15507i
$819$	−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	$0.304133\pi$
$822$	0.528424	+	8.17215i	0.0184309	+	0.285037i
$823$	17.9737	+	17.9737i	0.626525	+	0.626525i	0.947192	−	0.320667i	$-0.103907\pi$
$823$	17.9737	+	17.9737i	0.626525	+	0.626525i	−0.320667	+	0.947192i	$0.603907\pi$
$824$	−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	$-0.903550\pi$
$827$	−18.8665	+	18.8665i	−0.656051	+	0.656051i	0.298392	+	0.954443i	$0.403550\pi$
$828$	10.0673	−	13.0723i	0.349862	−	0.454294i
$829$			3.28005i			0.113921i	0.998376	+	0.0569604i	$0.0181409\pi$
$829$			3.28005i			0.113921i	−0.998376	+	0.0569604i	$0.981859\pi$
$830$		0			0
$831$		−	12.1540i		−	0.421616i
$832$	13.7013	−	32.5911i	0.475008	−	1.12989i
$833$	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
$838$	−39.5665	+	2.55843i	−1.36680	+	0.0883794i
$839$	−54.8854			−1.89486			−0.947428	−	0.319969i	$-0.896327\pi$
$839$	−54.8854			−1.89486			−0.947428	+	0.319969i	$0.896327\pi$
$840$		0			0
$841$	22.0303			0.759665
$842$	24.5683	−	1.58862i	0.846681	−	0.0547476i
$843$	−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
$848$	−1.37973	+	2.37050i	−0.0473802	+	0.0814032i
$849$		−	26.2791i		−	0.901897i
$850$		0			0
$851$			36.4578i			1.24976i
$852$	16.0153	−	20.7958i	0.548675	−	0.712452i
$853$	17.9348	−	17.9348i	0.614074	−	0.614074i	−0.329931	−	0.944005i	$-0.607025\pi$
$853$	17.9348	−	17.9348i	0.614074	−	0.614074i	0.944005	+	0.329931i	$0.107025\pi$
$854$	−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	0.843964	−	0.536400i	$-0.180216\pi$
$857$	9.00378	+	9.00378i	0.307563	+	0.307563i	−0.536400	+	0.843964i	$0.680216\pi$
$858$	0.293794	+	4.54356i	0.0100299	+	0.155115i
$859$	24.6779			0.841998			0.420999	−	0.907061i	$-0.361680\pi$
$859$	24.6779			0.841998			0.420999	+	0.907061i	$0.361680\pi$
$860$		0			0
$861$	11.2195			0.382359
$862$	2.84297	+	43.9669i	0.0968318	+	1.49752i
$863$	40.4811	+	40.4811i	1.37799	+	1.37799i	0.848009	+	0.529982i	$0.177802\pi$
$863$	40.4811	+	40.4811i	1.37799	+	1.37799i	0.529982	+	0.848009i	$0.322198\pi$
$864$	−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
$868$	−25.1419	−	19.3623i	−0.853373	−	0.657201i
$869$			5.18257i			0.175807i
$870$		0			0
$871$			31.9048i			1.08105i
$872$	8.59179	+	43.7966i	0.290955	+	1.48314i
$873$	−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	0.733525	−	0.679663i	$-0.237874\pi$
$877$	1.59507	+	1.59507i	0.0538616	+	0.0538616i	−0.679663	+	0.733525i	$0.737874\pi$
$878$	20.1764	−	1.30464i	0.680922	−	0.0440294i
$879$	−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	$0.310515\pi$
$882$	−0.0427276	+	0.00276283i	−0.00143871	+	9.30294e-5i
$883$	−29.4296	−	29.4296i	−0.990385	−	0.990385i	0.00956956	−	0.999954i	$-0.496954\pi$
$883$	−29.4296	−	29.4296i	−0.990385	−	0.990385i	−0.999954	+	0.00956956i	$0.996954\pi$
$884$	−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	−0.0409656	+	0.999161i	$0.513043\pi$
$887$	−30.9776	+	30.9776i	−1.04013	+	1.04013i	−0.999161	+	0.0409656i	$0.986957\pi$
$888$	−2.40623	−	12.2657i	−0.0807478	−	0.411612i
$889$			42.0294i			1.40962i
$890$		0			0
$891$		−	0.728515i		−	0.0244062i
$892$	−7.44837	−	5.73615i	−0.249390	−	0.192061i
$893$	−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
$898$	−3.50972	−	54.2784i	−0.117121	−	1.81129i
$899$	15.8668			0.529186
$900$		0			0
$901$	1.09083			0.0363408
$902$	−0.282526	−	4.36931i	−0.00940709	−	0.145482i
$903$	−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	$-0.985148\pi$
$907$	−28.6790	+	28.6790i	−0.952271	+	0.952271i	0.0466405	+	0.998912i	$0.485148\pi$
$908$	−15.2533	+	19.8063i	−0.506198	+	0.657297i
$909$		−	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	$-0.176981\pi$
$912$	−12.9071	−	7.51250i	−0.427397	−	0.248764i
$913$	−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
$918$	2.24508	−	0.145170i	0.0740988	−	0.00479134i
$919$	−55.4206			−1.82816			−0.914079	−	0.405536i	$-0.867085\pi$
$919$	−55.4206			−1.82816			−0.914079	+	0.405536i	$0.867085\pi$
$920$		0			0
$921$	−1.28005			−0.0421790
$922$	38.3426	−	2.47929i	1.26275	−	0.0816510i
$923$	−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
$928$	−4.73830	−	14.1626i	−0.155542	−	0.464911i
$929$			46.9603i			1.54072i	0.637610	+	0.770359i	$0.279923\pi$
$929$			46.9603i			1.54072i	−0.637610	+	0.770359i	$0.720077\pi$
$930$		0			0
$931$		−	0.113038i		−	0.00370466i
$932$	26.5332	−	34.4533i	0.869124	−	1.12855i
$933$	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	0.515109	−	0.857125i	$-0.327752\pi$
$937$	−10.4693	−	10.4693i	−0.342016	−	0.342016i	−0.857125	+	0.515109i	$0.827752\pi$
$938$	−1.73928	−	26.8982i	−0.0567895	−	0.878258i
$939$	−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	$0.733726\pi$
$942$	0.270317	+	4.18049i	0.00880739	+	0.136208i
$943$	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	$-0.547928\pi$
$947$	25.8091	−	25.8091i	0.838682	−	0.838682i	0.988685	+	0.150003i	$0.0479284\pi$
$948$	11.2724	+	8.68113i	0.366111	+	0.281950i
$949$			24.8099i			0.805362i
$950$		0			0
$951$		−	27.3143i		−	0.885726i
$952$	11.6567	−	2.28675i	0.377796	−	0.0741141i
$953$	7.78429	−	7.78429i	0.252158	−	0.252158i	−0.569697	−	0.821855i	$-0.692939\pi$
$953$	7.78429	−	7.78429i	0.252158	−	0.252158i	0.821855	+	0.569697i	$0.192939\pi$
$954$	−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
$958$	26.5047	−	1.71384i	0.856329	−	0.0553715i
$959$	−15.2875			−0.493658
$960$		0			0
$961$	−5.12110			−0.165197
$962$	−27.5618	+	1.78219i	−0.888627	+	0.0574600i
$963$	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	$-0.835894\pi$
$967$	−11.7235	+	11.7235i	−0.377001	+	0.377001i	0.493018	+	0.870019i	$0.335894\pi$
$968$	29.0577	−	5.70039i	0.933950	−	0.183217i
$969$			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	$-0.0667572\pi$
$972$	−1.58457	−	1.22031i	−0.0508250	−	0.0391414i
$973$	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	0.893646	−	0.448773i	$-0.148139\pi$
$977$	13.9054	+	13.9054i	0.444873	+	0.444873i	−0.448773	+	0.893646i	$0.648139\pi$
$978$	0.553053	+	8.55305i	0.0176847	+	0.273496i
$979$	0.750572			0.0239884
$980$		0			0
$981$	−15.7796			−0.503803
$982$	−2.69639	−	41.7001i	−0.0860452	−	1.33070i
$983$	−13.9381	−	13.9381i	−0.444557	−	0.444557i	0.448983	−	0.893540i	$-0.351786\pi$
$983$	−13.9381	−	13.9381i	−0.444557	−	0.444557i	−0.893540	+	0.448983i	$0.851786\pi$
$984$	−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
$988$	−20.1345	+	26.1446i	−0.640565	+	0.831771i
$989$		−	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	$0.681850\pi$
$992$	10.7869	+	32.2416i	0.342484	+	1.02367i
$993$	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	0.682390	−	0.730988i	$-0.260941\pi$
$997$	−1.53452	−	1.53452i	−0.0485986	−	0.0485986i	−0.730988	+	0.682390i	$0.760941\pi$
$998$	21.2357	−	1.37313i	0.672204	−	0.0434657i
$999$	4.41926			0.139819

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.1	✓	12	5.4	even	2
60.2.j.a.7.3	yes	12	20.19	odd	2
60.2.j.a.43.1	yes	12	20.7	even	4
60.2.j.a.43.3	yes	12	5.2	odd	4
180.2.k.e.127.4		12	60.59	even	2
180.2.k.e.127.6		12	15.14	odd	2
180.2.k.e.163.4		12	15.2	even	4
180.2.k.e.163.6		12	60.47	odd	4
300.2.j.d.7.4		12	4.3	odd	2	inner
300.2.j.d.7.6		12	1.1	even	1	trivial
300.2.j.d.43.4		12	5.3	odd	4	inner
300.2.j.d.43.6		12	20.3	even	4	inner
900.2.k.n.307.1		12	3.2	odd	2
900.2.k.n.307.3		12	12.11	even	2
900.2.k.n.343.1		12	60.23	odd	4
900.2.k.n.343.3		12	15.8	even	4
960.2.w.g.127.1		12	40.19	odd	2
960.2.w.g.127.4		12	40.29	even	2
960.2.w.g.703.1		12	40.37	odd	4
960.2.w.g.703.4		12	40.27	even	4

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)

\(f(q)\)	\(=\)	\(q+(1.41127 - 0.0912546i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.98335 - 0.257569i) q^{4} +(1.06244 + 0.933389i) q^{6} +(-1.86678 + 1.86678i) q^{7} +(2.77552 - 0.544488i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.41127 - 0.0912546i) 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} +(2.77552 - 0.544488i) q^{8} +1.00000i q^{9} +0.728515i q^{11} +(1.58457 + 1.22031i) 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} +(0.0912546 + 1.41127i) q^{18} -3.73356 q^{19} -2.64002 q^{21} +(0.0664803 + 1.02813i) 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} +(-3.22164 + 4.18329i) q^{28} -2.64002i q^{29} +6.01008i q^{31} +(5.36458 - 1.79480i) 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} +(-5.26904 + 0.340704i) q^{38} +4.41926 q^{39} -4.24977 q^{41} +(-3.72578 + 0.240914i) 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} +(3.45705 + 2.01216i) q^{48} +0.0302761i q^{49} -1.59083i q^{51} +(5.39285 - 7.00260i) 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} +(-0.240914 - 3.72578i) q^{58} -4.92834 q^{59} +2.31032 q^{61} +(0.548448 + 8.48183i) 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} +(-2.52077 - 1.94130i) q^{68} -8.24977i q^{69} -13.1240i q^{71} +(0.544488 + 2.77552i) 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} +(6.23675 - 0.403277i) q^{78} +7.11388 q^{79} -1.00000 q^{81} +(-5.99756 + 0.387811i) 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} +(0.396668 + 2.02201i) q^{88} -1.03028i q^{89} +11.6669i q^{91} +(-13.0723 - 10.0673i) 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} +(0.00276283 + 0.0427276i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more