LMFDB - Embedded newform 99.2.f.b.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	99.82
Dual form			99.2.f.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 + 0.587785i) q^{2} +(1.30902 - 0.951057i) q^{4} +(0.809017 - 2.48990i) q^{5} +(-2.42705 + 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +O(q^{10})$	\(q+(0.190983 + 0.587785i) q^{2} +(1.30902 - 0.951057i) q^{4} +(0.809017 - 2.48990i) q^{5} +(-2.42705 + 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +1.61803 q^{10} +(-1.69098 + 2.85317i) q^{11} +(0.545085 + 1.67760i) q^{13} +(-1.50000 - 1.08981i) q^{14} +(0.572949 - 1.76336i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(-1.30902 - 4.02874i) q^{20} +(-2.00000 - 0.449028i) q^{22} -3.47214 q^{23} +(-1.50000 - 1.08981i) q^{25} +(-0.881966 + 0.640786i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(3.61803 - 2.62866i) q^{29} +(0.881966 + 2.71441i) q^{31} +5.61803 q^{32} -1.00000 q^{34} +(2.42705 + 7.46969i) q^{35} +(-0.190983 + 0.138757i) q^{37} +(1.11803 - 3.44095i) q^{38} +(4.73607 - 3.44095i) q^{40} +(-9.66312 - 7.02067i) q^{41} +6.23607 q^{43} +(0.500000 + 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(1.30902 + 0.951057i) q^{47} +(0.618034 - 1.90211i) q^{49} +(0.354102 - 1.08981i) q^{50} +(2.30902 + 1.67760i) q^{52} +(2.97214 + 9.14729i) q^{53} +(5.73607 + 6.51864i) q^{55} -6.70820 q^{56} +(2.23607 + 1.62460i) q^{58} +(8.35410 - 6.06961i) q^{59} +(2.42705 - 7.46969i) q^{61} +(-1.42705 + 1.03681i) q^{62} +(-0.0729490 - 0.224514i) q^{64} +4.61803 q^{65} -9.56231 q^{67} +(0.809017 + 2.48990i) q^{68} +(-3.92705 + 2.85317i) q^{70} +(1.71885 - 5.29007i) q^{71} +(2.61803 - 1.90211i) q^{73} +(-0.118034 - 0.0857567i) q^{74} -9.47214 q^{76} +(-0.927051 - 9.90659i) q^{77} +(2.92705 + 9.00854i) q^{79} +(-3.92705 - 2.85317i) q^{80} +(2.28115 - 7.02067i) q^{82} +(-0.218847 + 0.673542i) q^{83} +(3.42705 + 2.48990i) q^{85} +(1.19098 + 3.66547i) q^{86} +(-6.80902 + 2.93893i) q^{88} -0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-4.54508 + 3.30220i) q^{92} +(-0.309017 + 0.951057i) q^{94} +(-12.3992 + 9.00854i) q^{95} +(-4.33688 - 13.3475i) q^{97} +1.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 3 q^{4} + q^{5} - 3 q^{7} + 5 q^{8}+O(q^{10}) $ 4 * q + 3 * q^2 + 3 * q^4 + q^5 - 3 * q^7 + 5 * q^8	$ 4 q + 3 q^{2} + 3 q^{4} + q^{5} - 3 q^{7} + 5 q^{8} + 2 q^{10} - 9 q^{11} - 9 q^{13} - 6 q^{14} + 9 q^{16} - 2 q^{17} - 10 q^{19} - 3 q^{20} - 8 q^{22} + 4 q^{23} - 6 q^{25} - 8 q^{26} - 6 q^{28} + 10 q^{29} + 8 q^{31} + 18 q^{32} - 4 q^{34} + 3 q^{35} - 3 q^{37} + 10 q^{40} - 23 q^{41} + 16 q^{43} + 2 q^{44} + 13 q^{46} + 3 q^{47} - 2 q^{49} - 12 q^{50} + 7 q^{52} - 6 q^{53} + 14 q^{55} + 20 q^{59} + 3 q^{61} + q^{62} - 7 q^{64} + 14 q^{65} + 2 q^{67} + q^{68} - 9 q^{70} + 27 q^{71} + 6 q^{73} + 4 q^{74} - 20 q^{76} + 3 q^{77} + 5 q^{79} - 9 q^{80} - 11 q^{82} - 21 q^{83} + 7 q^{85} + 7 q^{86} - 25 q^{88} - 20 q^{89} + 3 q^{91} - 7 q^{92} + q^{94} - 25 q^{95} - 33 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 + 3 * q^4 + q^5 - 3 * q^7 + 5 * q^8 + 2 * q^10 - 9 * q^11 - 9 * q^13 - 6 * q^14 + 9 * q^16 - 2 * q^17 - 10 * q^19 - 3 * q^20 - 8 * q^22 + 4 * q^23 - 6 * q^25 - 8 * q^26 - 6 * q^28 + 10 * q^29 + 8 * q^31 + 18 * q^32 - 4 * q^34 + 3 * q^35 - 3 * q^37 + 10 * q^40 - 23 * q^41 + 16 * q^43 + 2 * q^44 + 13 * q^46 + 3 * q^47 - 2 * q^49 - 12 * q^50 + 7 * q^52 - 6 * q^53 + 14 * q^55 + 20 * q^59 + 3 * q^61 + q^62 - 7 * q^64 + 14 * q^65 + 2 * q^67 + q^68 - 9 * q^70 + 27 * q^71 + 6 * q^73 + 4 * q^74 - 20 * q^76 + 3 * q^77 + 5 * q^79 - 9 * q^80 - 11 * q^82 - 21 * q^83 + 7 * q^85 + 7 * q^86 - 25 * q^88 - 20 * q^89 + 3 * q^91 - 7 * q^92 + q^94 - 25 * q^95 - 33 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.190983	+	0.587785i	0.135045	+	0.415627i	0.995597	−	0.0937362i	$-0.0298810\pi$
$2$	0.190983	+	0.587785i	0.135045	+	0.415627i	−0.860552	+	0.509363i	$0.829881\pi$
$3$		0			0
$3$		0			0
$4$	1.30902	−	0.951057i	0.654508	−	0.475528i
$5$	0.809017	−	2.48990i	0.361803	−	1.11352i	−0.590155	−	0.807290i	$-0.700933\pi$
$5$	0.809017	−	2.48990i	0.361803	−	1.11352i	0.951959	−	0.306227i	$-0.0990665\pi$
$6$		0			0
$7$	−2.42705	+	1.76336i	−0.917339	+	0.666486i	−0.942860	−	0.333188i	$-0.891875\pi$
$7$	−2.42705	+	1.76336i	−0.917339	+	0.666486i	0.0255212	+	0.999674i	$0.491875\pi$
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$		0			0
$10$	1.61803			0.511667
$11$	−1.69098	+	2.85317i	−0.509851	+	0.860263i
$11$	−1.69098	+	2.85317i	−0.509851	+	0.860263i
$12$		0			0
$13$	0.545085	+	1.67760i	0.151179	+	0.465282i	0.997754	−	0.0669881i	$-0.0213390\pi$
$13$	0.545085	+	1.67760i	0.151179	+	0.465282i	−0.846574	+	0.532270i	$0.821339\pi$
$14$	−1.50000	−	1.08981i	−0.400892	−	0.291265i
$15$		0			0
$16$	0.572949	−	1.76336i	0.143237	−	0.440839i
$17$	−0.500000	+	1.53884i	−0.121268	+	0.373224i	−0.993203	−	0.116398i	$-0.962865\pi$
$17$	−0.500000	+	1.53884i	−0.121268	+	0.373224i	0.871935	+	0.489622i	$0.162865\pi$
$18$		0			0
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.107719	−	0.994181i	$-0.534355\pi$
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.978810	+	0.204772i	$0.934355\pi$
$20$	−1.30902	−	4.02874i	−0.292705	−	0.900854i
$21$		0			0
$22$	−2.00000	−	0.449028i	−0.426401	−	0.0957331i
$23$	−3.47214			−0.723990			−0.361995	−	0.932180i	$-0.617904\pi$
$23$	−3.47214			−0.723990			−0.361995	+	0.932180i	$0.617904\pi$
$24$		0			0
$25$	−1.50000	−	1.08981i	−0.300000	−	0.217963i
$26$	−0.881966	+	0.640786i	−0.172968	+	0.125668i
$27$		0			0
$28$	−1.50000	+	4.61653i	−0.283473	+	0.872441i
$29$	3.61803	−	2.62866i	0.671852	−	0.488129i	−0.198793	−	0.980042i	$-0.563702\pi$
$29$	3.61803	−	2.62866i	0.671852	−	0.488129i	0.870645	+	0.491912i	$0.163702\pi$
$30$		0			0
$31$	0.881966	+	2.71441i	0.158406	+	0.487523i	0.998490	−	0.0549331i	$-0.0174946\pi$
$31$	0.881966	+	2.71441i	0.158406	+	0.487523i	−0.840084	+	0.542456i	$0.817495\pi$
$32$	5.61803			0.993137
$33$		0			0
$34$	−1.00000			−0.171499
$35$	2.42705	+	7.46969i	0.410246	+	1.26261i
$36$		0			0
$37$	−0.190983	+	0.138757i	−0.0313974	+	0.0228116i	−0.603373	−	0.797459i	$-0.706177\pi$
$37$	−0.190983	+	0.138757i	−0.0313974	+	0.0228116i	0.571976	+	0.820270i	$0.306177\pi$
$38$	1.11803	−	3.44095i	0.181369	−	0.558197i
$39$		0			0
$40$	4.73607	−	3.44095i	0.748838	−	0.544063i
$41$	−9.66312	−	7.02067i	−1.50913	−	1.09644i	−0.966563	−	0.256428i	$-0.917454\pi$
$41$	−9.66312	−	7.02067i	−1.50913	−	1.09644i	−0.542562	−	0.840015i	$-0.682546\pi$
$42$		0			0
$43$	6.23607			0.950991			0.475496	−	0.879718i	$-0.342269\pi$
$43$	6.23607			0.950991			0.475496	+	0.879718i	$0.342269\pi$
$44$	0.500000	+	5.34307i	0.0753778	+	0.805498i
$45$		0			0
$46$	−0.663119	−	2.04087i	−0.0977716	−	0.300910i
$47$	1.30902	+	0.951057i	0.190940	+	0.138726i	0.679148	−	0.734001i	$-0.262349\pi$
$47$	1.30902	+	0.951057i	0.190940	+	0.138726i	−0.488208	+	0.872727i	$0.662349\pi$
$48$		0			0
$49$	0.618034	−	1.90211i	0.0882906	−	0.271730i
$50$	0.354102	−	1.08981i	0.0500776	−	0.154123i
$51$		0			0
$52$	2.30902	+	1.67760i	0.320203	+	0.232641i
$53$	2.97214	+	9.14729i	0.408254	+	1.25648i	0.918147	+	0.396240i	$0.129685\pi$
$53$	2.97214	+	9.14729i	0.408254	+	1.25648i	−0.509893	+	0.860238i	$0.670315\pi$
$54$		0			0
$55$	5.73607	+	6.51864i	0.773451	+	0.878973i
$56$	−6.70820			−0.896421
$57$		0			0
$58$	2.23607	+	1.62460i	0.293610	+	0.213320i
$59$	8.35410	−	6.06961i	1.08761	−	0.790196i	0.108617	−	0.994084i	$-0.465358\pi$
$59$	8.35410	−	6.06961i	1.08761	−	0.790196i	0.978994	+	0.203888i	$0.0653577\pi$
$60$		0			0
$61$	2.42705	−	7.46969i	0.310752	−	0.956396i	−0.666716	−	0.745312i	$-0.732301\pi$
$61$	2.42705	−	7.46969i	0.310752	−	0.956396i	0.977468	−	0.211084i	$-0.0676995\pi$
$62$	−1.42705	+	1.03681i	−0.181236	+	0.131675i
$63$		0			0
$64$	−0.0729490	−	0.224514i	−0.00911863	−	0.0280642i
$65$	4.61803			0.572797
$66$		0			0
$67$	−9.56231			−1.16822			−0.584111	−	0.811674i	$-0.698557\pi$
$67$	−9.56231			−1.16822			−0.584111	+	0.811674i	$0.698557\pi$
$68$	0.809017	+	2.48990i	0.0981077	+	0.301945i
$69$		0			0
$70$	−3.92705	+	2.85317i	−0.469372	+	0.341019i
$71$	1.71885	−	5.29007i	0.203990	−	0.627815i	−0.795764	−	0.605607i	$-0.792930\pi$
$71$	1.71885	−	5.29007i	0.203990	−	0.627815i	0.999753	−	0.0222083i	$-0.00706970\pi$
$72$		0			0
$73$	2.61803	−	1.90211i	0.306418	−	0.222625i	−0.423940	−	0.905690i	$-0.639353\pi$
$73$	2.61803	−	1.90211i	0.306418	−	0.222625i	0.730358	+	0.683065i	$0.239353\pi$
$74$	−0.118034	−	0.0857567i	−0.0137212	−	0.00996902i
$75$		0			0
$76$	−9.47214			−1.08653
$77$	−0.927051	−	9.90659i	−0.105647	−	1.12896i
$78$		0			0
$79$	2.92705	+	9.00854i	0.329319	+	1.01354i	0.969453	+	0.245276i	$0.0788787\pi$
$79$	2.92705	+	9.00854i	0.329319	+	1.01354i	−0.640134	+	0.768263i	$0.721121\pi$
$80$	−3.92705	−	2.85317i	−0.439058	−	0.318994i
$81$		0			0
$82$	2.28115	−	7.02067i	0.251911	−	0.775303i
$83$	−0.218847	+	0.673542i	−0.0240216	+	0.0739308i	−0.962349	−	0.271818i	$-0.912375\pi$
$83$	−0.218847	+	0.673542i	−0.0240216	+	0.0739308i	0.938327	+	0.345749i	$0.112375\pi$
$84$		0			0
$85$	3.42705	+	2.48990i	0.371716	+	0.270067i
$86$	1.19098	+	3.66547i	0.128427	+	0.395258i
$87$		0			0
$88$	−6.80902	+	2.93893i	−0.725844	+	0.313291i
$89$	−0.527864			−0.0559535			−0.0279767	−	0.999609i	$-0.508906\pi$
$89$	−0.527864			−0.0559535			−0.0279767	+	0.999609i	$0.508906\pi$
$90$		0			0
$91$	−4.28115	−	3.11044i	−0.448787	−	0.326063i
$92$	−4.54508	+	3.30220i	−0.473858	+	0.344278i
$93$		0			0
$94$	−0.309017	+	0.951057i	−0.0318727	+	0.0980940i
$95$	−12.3992	+	9.00854i	−1.27213	+	0.924256i
$96$		0			0
$97$	−4.33688	−	13.3475i	−0.440344	−	1.35524i	−0.887510	−	0.460788i	$-0.847567\pi$
$97$	−4.33688	−	13.3475i	−0.440344	−	1.35524i	0.447167	−	0.894451i	$-0.352433\pi$
$98$	1.23607			0.124862
$99$		0			0
$100$	−3.00000			−0.300000
$101$	0.927051	+	2.85317i	0.0922450	+	0.283901i	0.986526	−	0.163605i	$-0.0523123\pi$
$101$	0.927051	+	2.85317i	0.0922450	+	0.283901i	−0.894281	+	0.447506i	$0.852312\pi$
$102$		0			0
$103$	4.85410	−	3.52671i	0.478289	−	0.347497i	−0.322374	−	0.946612i	$-0.604481\pi$
$103$	4.85410	−	3.52671i	0.478289	−	0.347497i	0.800663	+	0.599115i	$0.204481\pi$
$104$	−1.21885	+	3.75123i	−0.119518	+	0.367838i
$105$		0			0
$106$	−4.80902	+	3.49396i	−0.467093	+	0.339363i
$107$	−3.42705	−	2.48990i	−0.331306	−	0.240708i	0.409679	−	0.912230i	$-0.365641\pi$
$107$	−3.42705	−	2.48990i	−0.331306	−	0.240708i	−0.740984	+	0.671522i	$0.765641\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	−2.73607	+	4.61653i	−0.260874	+	0.440168i
$111$		0			0
$112$	1.71885	+	5.29007i	0.162416	+	0.499864i
$113$	0.572949	+	0.416272i	0.0538985	+	0.0391596i	0.614408	−	0.788988i	$-0.289395\pi$
$113$	0.572949	+	0.416272i	0.0538985	+	0.0391596i	−0.560510	+	0.828148i	$0.689395\pi$
$114$		0			0
$115$	−2.80902	+	8.64527i	−0.261942	+	0.806175i
$116$	2.23607	−	6.88191i	0.207614	−	0.638969i
$117$		0			0
$118$	5.16312	+	3.75123i	0.475304	+	0.345328i
$119$	−1.50000	−	4.61653i	−0.137505	−	0.423196i
$120$		0			0
$121$	−5.28115	−	9.64932i	−0.480105	−	0.877211i
$122$	4.85410			0.439470
$123$		0			0
$124$	3.73607	+	2.71441i	0.335509	+	0.243761i
$125$	6.66312	−	4.84104i	0.595967	−	0.432996i
$126$		0			0
$127$	−1.14590	+	3.52671i	−0.101682	+	0.312945i	−0.988937	−	0.148333i	$-0.952609\pi$
$127$	−1.14590	+	3.52671i	−0.101682	+	0.312945i	0.887255	+	0.461279i	$0.152609\pi$
$128$	9.20820	−	6.69015i	0.813898	−	0.591331i
$129$		0			0
$130$	0.881966	+	2.71441i	0.0773535	+	0.238070i
$131$	7.14590			0.624340			0.312170	−	0.950026i	$-0.398944\pi$
$131$	7.14590			0.624340			0.312170	+	0.950026i	$0.398944\pi$
$132$		0			0
$133$	17.5623			1.52285
$134$	−1.82624	−	5.62058i	−0.157763	−	0.485544i
$135$		0			0
$136$	−2.92705	+	2.12663i	−0.250993	+	0.182357i
$137$	−2.30902	+	7.10642i	−0.197273	+	0.607143i	0.802670	+	0.596424i	$0.203412\pi$
$137$	−2.30902	+	7.10642i	−0.197273	+	0.607143i	−0.999943	+	0.0107192i	$0.996588\pi$
$138$		0			0
$139$	0.690983	−	0.502029i	0.0586084	−	0.0425815i	−0.558095	−	0.829777i	$-0.688468\pi$
$139$	0.690983	−	0.502029i	0.0586084	−	0.0425815i	0.616704	+	0.787195i	$0.288468\pi$
$140$	10.2812	+	7.46969i	0.868916	+	0.631304i
$141$		0			0
$142$	3.43769			0.288485
$143$	−5.70820	−	1.28157i	−0.477344	−	0.107170i
$144$		0			0
$145$	−3.61803	−	11.1352i	−0.300461	−	0.924725i
$146$	1.61803	+	1.17557i	0.133909	+	0.0972909i
$147$		0			0
$148$	−0.118034	+	0.363271i	−0.00970233	+	0.0298607i
$149$	−4.63525	+	14.2658i	−0.379735	+	1.16870i	0.560493	+	0.828159i	$0.310612\pi$
$149$	−4.63525	+	14.2658i	−0.379735	+	1.16870i	−0.940228	+	0.340545i	$0.889388\pi$
$150$		0			0
$151$	−1.61803	−	1.17557i	−0.131674	−	0.0956666i	0.519999	−	0.854167i	$-0.325932\pi$
$151$	−1.61803	−	1.17557i	−0.131674	−	0.0956666i	−0.651673	+	0.758500i	$0.725932\pi$
$152$	−4.04508	−	12.4495i	−0.328100	−	1.00979i
$153$		0			0
$154$	5.64590	−	2.43690i	0.454959	−	0.196371i
$155$	7.47214			0.600176
$156$		0			0
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$	−4.73607	+	3.44095i	−0.376781	+	0.273748i
$159$		0			0
$160$	4.54508	−	13.9883i	0.359321	−	1.10587i
$161$	8.42705	−	6.12261i	0.664145	−	0.482529i
$162$		0			0
$163$	5.64590	+	17.3763i	0.442221	+	1.36102i	0.885503	+	0.464634i	$0.153814\pi$
$163$	5.64590	+	17.3763i	0.442221	+	1.36102i	−0.443282	+	0.896382i	$0.646186\pi$
$164$	−19.3262			−1.50913
$165$		0			0
$166$	−0.437694			−0.0339717
$167$	−3.10081	−	9.54332i	−0.239948	−	0.738484i	−0.996426	−	0.0844656i	$-0.973082\pi$
$167$	−3.10081	−	9.54332i	−0.239948	−	0.738484i	0.756478	−	0.654019i	$-0.226918\pi$
$168$		0			0
$169$	8.00000	−	5.81234i	0.615385	−	0.447103i
$170$	−0.809017	+	2.48990i	−0.0620488	+	0.190966i
$171$		0			0
$172$	8.16312	−	5.93085i	0.622432	−	0.452223i
$173$	12.4443	+	9.04129i	0.946120	+	0.687397i	0.949886	−	0.312596i	$-0.101199\pi$
$173$	12.4443	+	9.04129i	0.946120	+	0.687397i	−0.00376565	+	0.999993i	$0.501199\pi$
$174$		0			0
$175$	5.56231			0.420471
$176$	4.06231	+	4.61653i	0.306208	+	0.347984i
$177$		0			0
$178$	−0.100813	−	0.310271i	−0.00755626	−	0.0232558i
$179$	−1.80902	−	1.31433i	−0.135212	−	0.0982375i	0.518123	−	0.855306i	$-0.326631\pi$
$179$	−1.80902	−	1.31433i	−0.135212	−	0.0982375i	−0.653335	+	0.757069i	$0.726631\pi$
$180$		0			0
$181$	−5.39919	+	16.6170i	−0.401318	+	1.23513i	0.522612	+	0.852571i	$0.324958\pi$
$181$	−5.39919	+	16.6170i	−0.401318	+	1.23513i	−0.923930	+	0.382560i	$0.875042\pi$
$182$	1.01064	−	3.11044i	0.0749139	−	0.230561i
$183$		0			0
$184$	−6.28115	−	4.56352i	−0.463053	−	0.336428i
$185$	0.190983	+	0.587785i	0.0140413	+	0.0432148i
$186$		0			0
$187$	−3.54508	−	4.02874i	−0.259242	−	0.294611i
$188$	2.61803			0.190940
$189$		0			0
$190$	−7.66312	−	5.56758i	−0.555941	−	0.403915i
$191$	−6.04508	+	4.39201i	−0.437407	+	0.317795i	−0.784604	−	0.619998i	$-0.787134\pi$
$191$	−6.04508	+	4.39201i	−0.437407	+	0.317795i	0.347197	+	0.937792i	$0.387134\pi$
$192$		0			0
$193$	−5.73607	+	17.6538i	−0.412891	+	1.27075i	0.501232	+	0.865313i	$0.332880\pi$
$193$	−5.73607	+	17.6538i	−0.412891	+	1.27075i	−0.914124	+	0.405436i	$0.867120\pi$
$194$	7.01722	−	5.09831i	0.503807	−	0.366037i
$195$		0			0
$196$	−1.00000	−	3.07768i	−0.0714286	−	0.219835i
$197$	−24.3820			−1.73714			−0.868572	−	0.495564i	$-0.834961\pi$
$197$	−24.3820			−1.73714			−0.868572	+	0.495564i	$0.834961\pi$
$198$		0			0
$199$	−16.7082			−1.18441			−0.592207	−	0.805786i	$-0.701743\pi$
$199$	−16.7082			−1.18441			−0.592207	+	0.805786i	$0.701743\pi$
$200$	−1.28115	−	3.94298i	−0.0905912	−	0.278811i
$201$		0			0
$202$	−1.50000	+	1.08981i	−0.105540	+	0.0766790i
$203$	−4.14590	+	12.7598i	−0.290985	+	0.895560i
$204$		0			0
$205$	−25.2984	+	18.3803i	−1.76692	+	1.28374i
$206$	3.00000	+	2.17963i	0.209020	+	0.151862i
$207$		0			0
$208$	3.27051			0.226769
$209$	17.8262	−	7.69421i	1.23307	−	0.532220i
$210$		0			0
$211$	−6.88197	−	21.1805i	−0.473774	−	1.45813i	−0.847604	−	0.530629i	$-0.821956\pi$
$211$	−6.88197	−	21.1805i	−0.473774	−	1.45813i	0.373830	−	0.927497i	$-0.378044\pi$
$212$	12.5902	+	9.14729i	0.864696	+	0.628239i
$213$		0			0
$214$	0.809017	−	2.48990i	0.0553033	−	0.170206i
$215$	5.04508	−	15.5272i	0.344072	−	1.05894i
$216$		0			0
$217$	−6.92705	−	5.03280i	−0.470239	−	0.341649i
$218$		0			0
$219$		0			0
$220$	13.7082	+	3.07768i	0.924207	+	0.207497i
$221$	−2.85410			−0.191988
$222$		0			0
$223$	−0.572949	−	0.416272i	−0.0383675	−	0.0278756i	0.568436	−	0.822727i	$-0.307549\pi$
$223$	−0.572949	−	0.416272i	−0.0383675	−	0.0278756i	−0.606804	+	0.794852i	$0.707549\pi$
$224$	−13.6353	+	9.90659i	−0.911044	+	0.661912i
$225$		0			0
$226$	−0.135255	+	0.416272i	−0.00899702	+	0.0276900i
$227$	−20.1353	+	14.6291i	−1.33642	+	0.970969i	−0.336856	+	0.941556i	$0.609364\pi$
$227$	−20.1353	+	14.6291i	−1.33642	+	0.970969i	−0.999567	+	0.0294127i	$0.990636\pi$
$228$		0			0
$229$	3.09017	+	9.51057i	0.204204	+	0.628476i	0.999745	+	0.0225760i	$0.00718678\pi$
$229$	3.09017	+	9.51057i	0.204204	+	0.628476i	−0.795541	+	0.605900i	$0.792813\pi$
$230$	−5.61803			−0.370442
$231$		0			0
$232$	10.0000			0.656532
$233$	−7.51722	−	23.1356i	−0.492470	−	1.51567i	−0.820863	−	0.571124i	$-0.806507\pi$
$233$	−7.51722	−	23.1356i	−0.492470	−	1.51567i	0.328394	−	0.944541i	$-0.393493\pi$
$234$		0			0
$235$	3.42705	−	2.48990i	0.223556	−	0.162423i
$236$	5.16312	−	15.8904i	0.336090	−	1.03438i
$237$		0			0
$238$	2.42705	−	1.76336i	0.157322	−	0.114301i
$239$	2.07295	+	1.50609i	0.134088	+	0.0974206i	0.652807	−	0.757524i	$-0.273591\pi$
$239$	2.07295	+	1.50609i	0.134088	+	0.0974206i	−0.518719	+	0.854945i	$0.673591\pi$
$240$		0			0
$241$	−23.1246			−1.48959			−0.744794	−	0.667295i	$-0.767452\pi$
$241$	−23.1246			−1.48959			−0.744794	+	0.667295i	$0.767452\pi$
$242$	4.66312	−	4.94704i	0.299757	−	0.318008i
$243$		0			0
$244$	−3.92705	−	12.0862i	−0.251404	−	0.773741i
$245$	−4.23607	−	3.07768i	−0.270632	−	0.196626i
$246$		0			0
$247$	3.19098	−	9.82084i	0.203037	−	0.624885i
$248$	−1.97214	+	6.06961i	−0.125231	+	0.385421i
$249$		0			0
$250$	4.11803	+	2.99193i	0.260447	+	0.189226i
$251$	2.40983	+	7.41669i	0.152107	+	0.468138i	0.997856	−	0.0654431i	$-0.0208461\pi$
$251$	2.40983	+	7.41669i	0.152107	+	0.468138i	−0.845749	+	0.533581i	$0.820846\pi$
$252$		0			0
$253$	5.87132	−	9.90659i	0.369127	−	0.622822i
$254$	−2.29180			−0.143800
$255$		0			0
$256$	5.30902	+	3.85723i	0.331814	+	0.241077i
$257$	−9.44427	+	6.86167i	−0.589117	+	0.428019i	−0.842000	−	0.539478i	$-0.818622\pi$
$257$	−9.44427	+	6.86167i	−0.589117	+	0.428019i	0.252882	+	0.967497i	$0.418622\pi$
$258$		0			0
$259$	0.218847	−	0.673542i	0.0135985	−	0.0418519i
$260$	6.04508	−	4.39201i	0.374900	−	0.272381i
$261$		0			0
$262$	1.36475	+	4.20025i	0.0843142	+	0.259493i
$263$	16.3262			1.00672			0.503359	−	0.864077i	$-0.332097\pi$
$263$	16.3262			1.00672			0.503359	+	0.864077i	$0.332097\pi$
$264$		0			0
$265$	25.1803			1.54682
$266$	3.35410	+	10.3229i	0.205653	+	0.632935i
$267$		0			0
$268$	−12.5172	+	9.09429i	−0.764611	+	0.555522i
$269$	−4.79837	+	14.7679i	−0.292562	+	0.900413i	0.691467	+	0.722408i	$0.256965\pi$
$269$	−4.79837	+	14.7679i	−0.292562	+	0.900413i	−0.984029	+	0.178006i	$0.943035\pi$
$270$		0			0
$271$	22.0623	−	16.0292i	1.34019	−	0.973705i	0.340753	−	0.940153i	$-0.389318\pi$
$271$	22.0623	−	16.0292i	1.34019	−	0.973705i	0.999437	−	0.0335518i	$-0.0106819\pi$
$272$	2.42705	+	1.76336i	0.147162	+	0.106919i
$273$		0			0
$274$	−4.61803			−0.278986
$275$	5.64590	−	2.43690i	0.340460	−	0.146950i
$276$		0			0
$277$	9.44427	+	29.0665i	0.567451	+	1.74644i	0.660554	+	0.750779i	$0.270322\pi$
$277$	9.44427	+	29.0665i	0.567451	+	1.74644i	−0.0931022	+	0.995657i	$0.529678\pi$
$278$	0.427051	+	0.310271i	0.0256128	+	0.0186088i
$279$		0			0
$280$	−5.42705	+	16.7027i	−0.324328	+	0.998180i
$281$	0.236068	−	0.726543i	0.0140826	−	0.0433419i	−0.943768	−	0.330608i	$-0.892746\pi$
$281$	0.236068	−	0.726543i	0.0140826	−	0.0433419i	0.957851	+	0.287266i	$0.0927463\pi$
$282$		0			0
$283$	−0.145898	−	0.106001i	−0.00867274	−	0.00630111i	0.583440	−	0.812156i	$-0.301706\pi$
$283$	−0.145898	−	0.106001i	−0.00867274	−	0.00630111i	−0.592113	+	0.805855i	$0.701706\pi$
$284$	−2.78115	−	8.55951i	−0.165031	−	0.507913i
$285$		0			0
$286$	−0.336881	−	3.59996i	−0.0199202	−	0.212870i
$287$	35.8328			2.11514
$288$		0			0
$289$	11.6353	+	8.45351i	0.684427	+	0.497265i
$290$	5.85410	−	4.25325i	0.343765	−	0.249760i
$291$		0			0
$292$	1.61803	−	4.97980i	0.0946883	−	0.291421i
$293$	0.0450850	−	0.0327561i	0.00263389	−	0.00191363i	−0.586468	−	0.809973i	$-0.699482\pi$
$293$	0.0450850	−	0.0327561i	0.00263389	−	0.00191363i	0.589101	+	0.808059i	$0.299482\pi$
$294$		0			0
$295$	−8.35410	−	25.7113i	−0.486395	−	1.49697i
$296$	−0.527864			−0.0306815
$297$		0			0
$298$	−9.27051			−0.537026
$299$	−1.89261	−	5.82485i	−0.109452	−	0.336860i
$300$		0			0
$301$	−15.1353	+	10.9964i	−0.872382	+	0.633822i
$302$	0.381966	−	1.17557i	0.0219797	−	0.0676465i
$303$		0			0
$304$	−8.78115	+	6.37988i	−0.503634	+	0.365911i
$305$	−16.6353	−	12.0862i	−0.952532	−	0.692055i
$306$		0			0
$307$	0.562306			0.0320925			0.0160462	−	0.999871i	$-0.494892\pi$
$307$	0.562306			0.0320925			0.0160462	+	0.999871i	$0.494892\pi$
$308$	−10.6353	−	12.0862i	−0.606000	−	0.688676i
$309$		0			0
$310$	1.42705	+	4.39201i	0.0810510	+	0.249449i
$311$	2.04508	+	1.48584i	0.115966	+	0.0842543i	0.644257	−	0.764809i	$-0.277167\pi$
$311$	2.04508	+	1.48584i	0.115966	+	0.0842543i	−0.528291	+	0.849064i	$0.677167\pi$
$312$		0			0
$313$	7.98278	−	24.5685i	0.451213	−	1.38869i	−0.424310	−	0.905517i	$-0.639483\pi$
$313$	7.98278	−	24.5685i	0.451213	−	1.38869i	0.875524	−	0.483175i	$-0.160517\pi$
$314$	−0.708204	+	2.17963i	−0.0399663	+	0.123004i
$315$		0			0
$316$	12.3992	+	9.00854i	0.697509	+	0.506770i
$317$	5.98278	+	18.4131i	0.336026	+	1.03418i	0.966214	+	0.257740i	$0.0829778\pi$
$317$	5.98278	+	18.4131i	0.336026	+	1.03418i	−0.630188	+	0.776443i	$0.717022\pi$
$318$		0			0
$319$	1.38197	+	14.7679i	0.0773752	+	0.826842i
$320$	−0.618034			−0.0345492
$321$		0			0
$322$	5.20820	+	3.78398i	0.290242	+	0.210873i
$323$	7.66312	−	5.56758i	0.426387	−	0.309789i
$324$		0			0
$325$	1.01064	−	3.11044i	0.0560604	−	0.172536i
$326$	−9.13525	+	6.63715i	−0.505955	+	0.367598i
$327$		0			0
$328$	−8.25329	−	25.4010i	−0.455712	−	1.40254i
$329$	−4.85410			−0.267615
$330$		0			0
$331$	26.5967			1.46189			0.730945	−	0.682437i	$-0.239080\pi$
$331$	26.5967			1.46189			0.730945	+	0.682437i	$0.239080\pi$
$332$	0.354102	+	1.08981i	0.0194339	+	0.0598113i
$333$		0			0
$334$	5.01722	−	3.64522i	0.274530	−	0.199458i
$335$	−7.73607	+	23.8092i	−0.422667	+	1.30083i
$336$		0			0
$337$	0.236068	−	0.171513i	0.0128594	−	0.00934293i	−0.581337	−	0.813663i	$-0.697470\pi$
$337$	0.236068	−	0.171513i	0.0128594	−	0.00934293i	0.594196	+	0.804320i	$0.297470\pi$
$338$	4.94427	+	3.59222i	0.268933	+	0.195391i
$339$		0			0
$340$	6.85410			0.371716
$341$	−9.23607	−	2.07363i	−0.500161	−	0.112293i
$342$		0			0
$343$	−4.63525	−	14.2658i	−0.250280	−	0.770283i
$344$	11.2812	+	8.19624i	0.608239	+	0.441912i
$345$		0			0
$346$	−2.93769	+	9.04129i	−0.157931	+	0.486063i
$347$	6.47214	−	19.9192i	0.347442	−	1.06932i	−0.612821	−	0.790222i	$-0.709965\pi$
$347$	6.47214	−	19.9192i	0.347442	−	1.06932i	0.960263	−	0.279096i	$-0.0900348\pi$
$348$		0			0
$349$	8.19098	+	5.95110i	0.438453	+	0.318555i	0.785020	−	0.619470i	$-0.212653\pi$
$349$	8.19098	+	5.95110i	0.438453	+	0.318555i	−0.346567	+	0.938025i	$0.612653\pi$
$350$	1.06231	+	3.26944i	0.0567826	+	0.174759i
$351$		0			0
$352$	−9.50000	+	16.0292i	−0.506352	+	0.854359i
$353$	10.4721			0.557376			0.278688	−	0.960382i	$-0.410101\pi$
$353$	10.4721			0.557376			0.278688	+	0.960382i	$0.410101\pi$
$354$		0			0
$355$	−11.7812	−	8.55951i	−0.625279	−	0.454292i
$356$	−0.690983	+	0.502029i	−0.0366220	+	0.0266075i
$357$		0			0
$358$	0.427051	−	1.31433i	0.0225703	−	0.0694644i
$359$	−10.3262	+	7.50245i	−0.544998	+	0.395964i	−0.825938	−	0.563761i	$-0.809354\pi$
$359$	−10.3262	+	7.50245i	−0.544998	+	0.395964i	0.280940	+	0.959725i	$0.409354\pi$
$360$		0			0
$361$	4.71885	+	14.5231i	0.248360	+	0.764375i
$362$	−10.7984			−0.567550
$363$		0			0
$364$	−8.56231			−0.448787
$365$	−2.61803	−	8.05748i	−0.137034	−	0.421748i
$366$		0			0
$367$	−4.50000	+	3.26944i	−0.234898	+	0.170663i	−0.699007	−	0.715115i	$-0.746375\pi$
$367$	−4.50000	+	3.26944i	−0.234898	+	0.170663i	0.464109	+	0.885778i	$0.346375\pi$
$368$	−1.98936	+	6.12261i	−0.103702	+	0.319163i
$369$		0			0
$370$	−0.309017	+	0.224514i	−0.0160650	+	0.0116719i
$371$	−23.3435	−	16.9600i	−1.21193	−	0.880520i
$372$		0			0
$373$	−4.41641			−0.228673			−0.114336	−	0.993442i	$-0.536474\pi$
$373$	−4.41641			−0.228673			−0.114336	+	0.993442i	$0.536474\pi$
$374$	1.69098	−	2.85317i	0.0874386	−	0.147534i
$375$		0			0
$376$	1.11803	+	3.44095i	0.0576582	+	0.177454i
$377$	6.38197	+	4.63677i	0.328688	+	0.238806i
$378$		0			0
$379$	0.489357	−	1.50609i	0.0251366	−	0.0773624i	−0.937701	−	0.347443i	$-0.887050\pi$
$379$	0.489357	−	1.50609i	0.0251366	−	0.0773624i	0.962838	+	0.270080i	$0.0870502\pi$
$380$	−7.66312	+	23.5847i	−0.393110	+	1.20987i
$381$		0			0
$382$	−3.73607	−	2.71441i	−0.191154	−	0.138881i
$383$	−8.30902	−	25.5725i	−0.424571	−	1.30669i	−0.903405	−	0.428789i	$-0.858940\pi$
$383$	−8.30902	−	25.5725i	−0.424571	−	1.30669i	0.478834	−	0.877906i	$-0.341060\pi$
$384$		0			0
$385$	−25.4164	−	5.70634i	−1.29534	−	0.290822i
$386$	−11.4721			−0.583916
$387$		0			0
$388$	−18.3713	−	13.3475i	−0.932663	−	0.677619i
$389$	19.6353	−	14.2658i	0.995547	−	0.723307i	0.0344181	−	0.999408i	$-0.489042\pi$
$389$	19.6353	−	14.2658i	0.995547	−	0.723307i	0.961129	+	0.276100i	$0.0890422\pi$
$390$		0			0
$391$	1.73607	−	5.34307i	0.0877967	−	0.270211i
$392$	3.61803	−	2.62866i	0.182738	−	0.132767i
$393$		0			0
$394$	−4.65654	−	14.3314i	−0.234593	−	0.722003i
$395$	24.7984			1.24774
$396$		0			0
$397$	−38.7082			−1.94271			−0.971355	−	0.237635i	$-0.923628\pi$
$397$	−38.7082			−1.94271			−0.971355	+	0.237635i	$0.923628\pi$
$398$	−3.19098	−	9.82084i	−0.159950	−	0.492274i
$399$		0			0
$400$	−2.78115	+	2.02063i	−0.139058	+	0.101031i
$401$	8.06231	−	24.8132i	0.402612	−	1.23911i	−0.520260	−	0.854008i	$-0.674165\pi$
$401$	8.06231	−	24.8132i	0.402612	−	1.23911i	0.922873	−	0.385106i	$-0.125835\pi$
$402$		0			0
$403$	−4.07295	+	2.95917i	−0.202888	+	0.147407i
$404$	3.92705	+	2.85317i	0.195378	+	0.141950i
$405$		0			0
$406$	−8.29180			−0.411515
$407$	−0.0729490	−	0.779543i	−0.00361595	−	0.0386405i
$408$		0			0
$409$	−3.41641	−	10.5146i	−0.168930	−	0.519915i	0.830374	−	0.557207i	$-0.188127\pi$
$409$	−3.41641	−	10.5146i	−0.168930	−	0.519915i	−0.999304	+	0.0372920i	$0.988127\pi$
$410$	−15.6353	−	11.3597i	−0.772170	−	0.561014i
$411$		0			0
$412$	3.00000	−	9.23305i	0.147799	−	0.454880i
$413$	−9.57295	+	29.4625i	−0.471054	+	1.44976i
$414$		0			0
$415$	1.50000	+	1.08981i	0.0736321	+	0.0534969i
$416$	3.06231	+	9.42481i	0.150142	+	0.462089i
$417$		0			0
$418$	7.92705	+	9.00854i	0.387725	+	0.440622i
$419$	−16.5066			−0.806399			−0.403200	−	0.915112i	$-0.632102\pi$
$419$	−16.5066			−0.806399			−0.403200	+	0.915112i	$0.632102\pi$
$420$		0			0
$421$	30.1525	+	21.9071i	1.46954	+	1.06768i	0.980746	+	0.195286i	$0.0625636\pi$
$421$	30.1525	+	21.9071i	1.46954	+	1.06768i	0.488795	+	0.872398i	$0.337436\pi$
$422$	11.1353	−	8.09024i	0.542056	−	0.393827i
$423$		0			0
$424$	−6.64590	+	20.4540i	−0.322753	+	0.993333i
$425$	2.42705	−	1.76336i	0.117729	−	0.0855353i
$426$		0			0
$427$	7.28115	+	22.4091i	0.352360	+	1.08445i
$428$	−6.85410			−0.331306
$429$		0			0
$430$	10.0902			0.486591
$431$	12.2082	+	37.5730i	0.588048	+	1.80983i	0.586667	+	0.809828i	$0.300440\pi$
$431$	12.2082	+	37.5730i	0.588048	+	1.80983i	0.00138127	+	0.999999i	$0.499560\pi$
$432$		0			0
$433$	4.85410	−	3.52671i	0.233273	−	0.169483i	−0.465008	−	0.885307i	$-0.653949\pi$
$433$	4.85410	−	3.52671i	0.233273	−	0.169483i	0.698281	+	0.715824i	$0.253949\pi$
$434$	1.63525	−	5.03280i	0.0784947	−	0.241582i
$435$		0			0
$436$		0			0
$437$	16.4443	+	11.9475i	0.786636	+	0.571525i
$438$		0			0
$439$	3.29180			0.157109			0.0785544	−	0.996910i	$-0.474970\pi$
$439$	3.29180			0.157109			0.0785544	+	0.996910i	$0.474970\pi$
$440$	1.80902	+	19.3314i	0.0862415	+	0.921588i
$441$		0			0
$442$	−0.545085	−	1.67760i	−0.0259270	−	0.0797952i
$443$	−33.2705	−	24.1724i	−1.58073	−	1.14847i	−0.915853	−	0.401514i	$-0.868484\pi$
$443$	−33.2705	−	24.1724i	−1.58073	−	1.14847i	−0.664877	−	0.746953i	$-0.731516\pi$
$444$		0			0
$445$	−0.427051	+	1.31433i	−0.0202442	+	0.0623051i
$446$	0.135255	−	0.416272i	0.00640451	−	0.0197110i
$447$		0			0
$448$	0.572949	+	0.416272i	0.0270693	+	0.0196670i
$449$	7.56231	+	23.2744i	0.356887	+	1.09839i	0.954907	+	0.296905i	$0.0959544\pi$
$449$	7.56231	+	23.2744i	0.356887	+	1.09839i	−0.598020	+	0.801481i	$0.704046\pi$
$450$		0			0
$451$	36.3713	−	15.6987i	1.71266	−	0.739222i
$452$	1.14590			0.0538985
$453$		0			0
$454$	−12.4443	−	9.04129i	−0.584039	−	0.424329i
$455$	−11.2082	+	8.14324i	−0.525449	+	0.381761i
$456$		0			0
$457$	2.53444	−	7.80021i	0.118556	−	0.364878i	−0.874116	−	0.485717i	$-0.838558\pi$
$457$	2.53444	−	7.80021i	0.118556	−	0.364878i	0.992672	+	0.120839i	$0.0385584\pi$
$458$	−5.00000	+	3.63271i	−0.233635	+	0.169746i
$459$		0			0
$460$	4.54508	+	13.9883i	0.211916	+	0.652209i
$461$	21.0902			0.982267			0.491134	−	0.871084i	$-0.336583\pi$
$461$	21.0902			0.982267			0.491134	+	0.871084i	$0.336583\pi$
$462$		0			0
$463$	−15.7984			−0.734213			−0.367106	−	0.930179i	$-0.619651\pi$
$463$	−15.7984			−0.734213			−0.367106	+	0.930179i	$0.619651\pi$
$464$	−2.56231	−	7.88597i	−0.118952	−	0.366097i
$465$		0			0
$466$	12.1631	−	8.83702i	0.563446	−	0.409367i
$467$	3.01722	−	9.28605i	0.139620	−	0.429707i	−0.856660	−	0.515882i	$-0.827464\pi$
$467$	3.01722	−	9.28605i	0.139620	−	0.429707i	0.996280	+	0.0861747i	$0.0274643\pi$
$468$		0			0
$469$	23.2082	−	16.8617i	1.07166	−	0.778603i
$470$	2.11803	+	1.53884i	0.0976976	+	0.0709815i
$471$		0			0
$472$	23.0902			1.06281
$473$	−10.5451	+	17.7926i	−0.484864	+	0.818103i
$474$		0			0
$475$	3.35410	+	10.3229i	0.153897	+	0.473646i
$476$	−6.35410	−	4.61653i	−0.291240	−	0.211598i
$477$		0			0
$478$	−0.489357	+	1.50609i	−0.0223827	+	0.0688868i
$479$	8.68034	−	26.7153i	0.396615	−	1.22066i	−0.531082	−	0.847320i	$-0.678214\pi$
$479$	8.68034	−	26.7153i	0.396615	−	1.22066i	0.927697	−	0.373335i	$-0.121786\pi$
$480$		0			0
$481$	−0.336881	−	0.244758i	−0.0153605	−	0.0111600i
$482$	−4.41641	−	13.5923i	−0.201162	−	0.619113i
$483$		0			0
$484$	−16.0902	−	7.60845i	−0.731371	−	0.345839i
$485$	−36.7426			−1.66840
$486$		0			0
$487$	−13.6074	−	9.88635i	−0.616610	−	0.447993i	0.235126	−	0.971965i	$-0.424450\pi$
$487$	−13.6074	−	9.88635i	−0.616610	−	0.447993i	−0.851736	+	0.523972i	$0.824450\pi$
$488$	14.2082	−	10.3229i	0.643175	−	0.467294i
$489$		0			0
$490$	1.00000	−	3.07768i	0.0451754	−	0.139036i
$491$	20.3992	−	14.8209i	0.920602	−	0.668857i	−0.0230715	−	0.999734i	$-0.507345\pi$
$491$	20.3992	−	14.8209i	0.920602	−	0.668857i	0.943674	+	0.330877i	$0.107345\pi$
$492$		0			0
$493$	2.23607	+	6.88191i	0.100707	+	0.309946i
$494$	6.38197			0.287138
$495$		0			0
$496$	5.29180			0.237609
$497$	5.15654	+	15.8702i	0.231302	+	0.711876i
$498$		0			0
$499$	14.2082	−	10.3229i	0.636047	−	0.462115i	−0.222443	−	0.974946i	$-0.571403\pi$
$499$	14.2082	−	10.3229i	0.636047	−	0.462115i	0.858490	+	0.512831i	$0.171403\pi$
$500$	4.11803	−	12.6740i	0.184164	−	0.566799i
$501$		0			0
$502$	−3.89919	+	2.83293i	−0.174029	+	0.126440i
$503$	22.7082	+	16.4985i	1.01251	+	0.735631i	0.964734	−	0.263227i	$-0.0847870\pi$
$503$	22.7082	+	16.4985i	1.01251	+	0.735631i	0.0477750	+	0.998858i	$0.484787\pi$
$504$		0			0
$505$	7.85410			0.349503
$506$	6.94427	+	1.55909i	0.308711	+	0.0693098i
$507$		0			0
$508$	1.85410	+	5.70634i	0.0822625	+	0.253178i
$509$	19.1074	+	13.8823i	0.846920	+	0.615324i	0.924295	−	0.381679i	$-0.124654\pi$
$509$	19.1074	+	13.8823i	0.846920	+	0.615324i	−0.0773749	+	0.997002i	$0.524654\pi$
$510$		0			0
$511$	−3.00000	+	9.23305i	−0.132712	+	0.408446i
$512$	5.78115	−	17.7926i	0.255493	−	0.786327i
$513$		0			0
$514$	−5.83688	−	4.24074i	−0.257454	−	0.187051i
$515$	−4.85410	−	14.9394i	−0.213897	−	0.658308i
$516$		0			0
$517$	−4.92705	+	2.12663i	−0.216691	+	0.0935289i
$518$	0.437694			0.0192312
$519$		0			0
$520$	8.35410	+	6.06961i	0.366352	+	0.266170i
$521$	−12.0000	+	8.71851i	−0.525730	+	0.381965i	−0.818758	−	0.574139i	$-0.805337\pi$
$521$	−12.0000	+	8.71851i	−0.525730	+	0.381965i	0.293028	+	0.956104i	$0.405337\pi$
$522$		0			0
$523$	−3.70163	+	11.3924i	−0.161861	+	0.498156i	−0.998791	−	0.0491529i	$-0.984348\pi$
$523$	−3.70163	+	11.3924i	−0.161861	+	0.498156i	0.836930	+	0.547309i	$0.184348\pi$
$524$	9.35410	−	6.79615i	0.408636	−	0.296891i
$525$		0			0
$526$	3.11803	+	9.59632i	0.135953	+	0.418420i
$527$	−4.61803			−0.201165
$528$		0			0
$529$	−10.9443			−0.475838
$530$	4.80902	+	14.8006i	0.208890	+	0.642898i
$531$		0			0
$532$	22.9894	−	16.7027i	0.996715	−	0.724156i
$533$	6.51064	−	20.0377i	0.282007	−	0.867929i
$534$		0			0
$535$	−8.97214	+	6.51864i	−0.387899	+	0.281825i
$536$	−17.2984	−	12.5680i	−0.747176	−	0.542855i
$537$		0			0
$538$	−9.59675			−0.413745
$539$	4.38197	+	4.97980i	0.188745	+	0.214495i
$540$		0			0
$541$	6.04508	+	18.6049i	0.259899	+	0.799885i	0.992825	+	0.119577i	$0.0381540\pi$
$541$	6.04508	+	18.6049i	0.259899	+	0.799885i	−0.732926	+	0.680308i	$0.761846\pi$
$542$	13.6353	+	9.90659i	0.585684	+	0.425525i
$543$		0			0
$544$	−2.80902	+	8.64527i	−0.120436	+	0.370663i
$545$		0			0
$546$		0			0
$547$	−17.4894	−	12.7068i	−0.747791	−	0.543302i	0.147350	−	0.989084i	$-0.452925\pi$
$547$	−17.4894	−	12.7068i	−0.747791	−	0.543302i	−0.895141	+	0.445782i	$0.852925\pi$
$548$	3.73607	+	11.4984i	0.159597	+	0.491189i
$549$		0			0
$550$	2.51064	+	2.85317i	0.107054	+	0.121660i
$551$	−26.1803			−1.11532
$552$		0			0
$553$	−22.9894	−	16.7027i	−0.977607	−	0.710273i
$554$	−15.2812	+	11.1024i	−0.649234	+	0.471696i
$555$		0			0
$556$	0.427051	−	1.31433i	0.0181110	−	0.0557399i
$557$	12.0623	−	8.76378i	0.511096	−	0.371333i	−0.302143	−	0.953263i	$-0.597702\pi$
$557$	12.0623	−	8.76378i	0.511096	−	0.371333i	0.813239	+	0.581929i	$0.197702\pi$
$558$		0			0
$559$	3.39919	+	10.4616i	0.143770	+	0.442479i
$560$	14.5623			0.615370
$561$		0			0
$562$	0.472136			0.0199159
$563$	2.74671	+	8.45351i	0.115760	+	0.356273i	0.992105	−	0.125412i	$-0.0400251\pi$
$563$	2.74671	+	8.45351i	0.115760	+	0.356273i	−0.876345	+	0.481684i	$0.840025\pi$
$564$		0			0
$565$	1.50000	−	1.08981i	0.0631055	−	0.0458488i
$566$	0.0344419	−	0.106001i	0.00144770	−	0.00445556i
$567$		0			0
$568$	10.0623	−	7.31069i	0.422205	−	0.306750i
$569$	−19.4721	−	14.1473i	−0.816314	−	0.593087i	0.0993400	−	0.995054i	$-0.468327\pi$
$569$	−19.4721	−	14.1473i	−0.816314	−	0.593087i	−0.915654	+	0.401966i	$0.868327\pi$
$570$		0			0
$571$	34.6869			1.45160			0.725801	−	0.687905i	$-0.241469\pi$
$571$	34.6869			1.45160			0.725801	+	0.687905i	$0.241469\pi$
$572$	−8.69098	+	3.75123i	−0.363388	+	0.156847i
$573$		0			0
$574$	6.84346	+	21.0620i	0.285640	+	0.879111i
$575$	5.20820	+	3.78398i	0.217197	+	0.157803i
$576$		0			0
$577$	3.32624	−	10.2371i	0.138473	−	0.426176i	−0.857641	−	0.514249i	$-0.828071\pi$
$577$	3.32624	−	10.2371i	0.138473	−	0.426176i	0.996114	+	0.0880726i	$0.0280707\pi$
$578$	−2.74671	+	8.45351i	−0.114248	+	0.351620i
$579$		0			0
$580$	−15.3262	−	11.1352i	−0.636387	−	0.462363i
$581$	−0.656541	−	2.02063i	−0.0272379	−	0.0838297i
$582$		0			0
$583$	−31.1246	−	6.98791i	−1.28905	−	0.289410i
$584$	7.23607			0.299431
$585$		0			0
$586$	0.0278640	+	0.0202444i	0.00115105	+	0.000836289i
$587$	−30.9894	+	22.5151i	−1.27907	+	0.929297i	−0.999524	−	0.0308361i	$-0.990183\pi$
$587$	−30.9894	+	22.5151i	−1.27907	+	0.929297i	−0.279543	+	0.960133i	$0.590183\pi$
$588$		0			0
$589$	5.16312	−	15.8904i	0.212743	−	0.654754i
$590$	13.5172	−	9.82084i	0.556495	−	0.404317i
$591$		0			0
$592$	0.135255	+	0.416272i	0.00555894	+	0.0171087i
$593$	−22.2148			−0.912252			−0.456126	−	0.889915i	$-0.650763\pi$
$593$	−22.2148			−0.912252			−0.456126	+	0.889915i	$0.650763\pi$
$594$		0			0
$595$	−12.7082			−0.520986
$596$	7.50000	+	23.0826i	0.307212	+	0.945501i
$597$		0			0
$598$	3.06231	−	2.22490i	0.125227	−	0.0909827i
$599$	2.56231	−	7.88597i	0.104693	−	0.322212i	−0.884965	−	0.465657i	$-0.845818\pi$
$599$	2.56231	−	7.88597i	0.104693	−	0.322212i	0.989658	+	0.143445i	$0.0458181\pi$
$600$		0			0
$601$	−27.3713	+	19.8864i	−1.11650	+	0.811184i	−0.983675	−	0.179955i	$-0.942405\pi$
$601$	−27.3713	+	19.8864i	−1.11650	+	0.811184i	−0.132825	+	0.991140i	$0.542405\pi$
$602$	−9.35410	−	6.79615i	−0.381245	−	0.276991i
$603$		0			0
$604$	−3.23607			−0.131674
$605$	−28.2984	+	5.34307i	−1.15049	+	0.217227i
$606$		0			0
$607$	4.11803	+	12.6740i	0.167146	+	0.514422i	0.999188	−	0.0402904i	$-0.0128283\pi$
$607$	4.11803	+	12.6740i	0.167146	+	0.514422i	−0.832042	+	0.554712i	$0.812828\pi$
$608$	−26.6074	−	19.3314i	−1.07907	−	0.783992i
$609$		0			0
$610$	3.92705	−	12.0862i	0.159002	−	0.489357i
$611$	−0.881966	+	2.71441i	−0.0356805	+	0.109813i
$612$		0			0
$613$	−28.0344	−	20.3682i	−1.13230	−	0.822664i	−0.146272	−	0.989244i	$-0.546728\pi$
$613$	−28.0344	−	20.3682i	−1.13230	−	0.822664i	−0.986028	+	0.166580i	$0.946728\pi$
$614$	0.107391	+	0.330515i	0.00433394	+	0.0133385i
$615$		0			0
$616$	11.3435	−	19.1396i	0.457041	−	0.771158i
$617$	−19.5836			−0.788406			−0.394203	−	0.919023i	$-0.628979\pi$
$617$	−19.5836			−0.788406			−0.394203	+	0.919023i	$0.628979\pi$
$618$		0			0
$619$	7.13525	+	5.18407i	0.286790	+	0.208365i	0.721874	−	0.692025i	$-0.243281\pi$
$619$	7.13525	+	5.18407i	0.286790	+	0.208365i	−0.435084	+	0.900390i	$0.643281\pi$
$620$	9.78115	−	7.10642i	0.392821	−	0.285401i
$621$		0			0
$622$	−0.482779	+	1.48584i	−0.0193577	+	0.0595768i
$623$	1.28115	−	0.930812i	0.0513283	−	0.0372922i
$624$		0			0
$625$	−9.52786	−	29.3238i	−0.381115	−	1.17295i
$626$	15.9656			0.638112
$627$		0			0
$628$	6.00000			0.239426
$629$	−0.118034	−	0.363271i	−0.00470632	−	0.0144846i
$630$		0			0
$631$	−37.4336	+	27.1971i	−1.49021	+	1.08270i	−0.516125	+	0.856513i	$0.672626\pi$
$631$	−37.4336	+	27.1971i	−1.49021	+	1.08270i	−0.974084	+	0.226187i	$0.927374\pi$
$632$	−6.54508	+	20.1437i	−0.260350	+	0.801273i
$633$		0			0
$634$	−9.68034	+	7.03318i	−0.384455	+	0.279323i
$635$	7.85410	+	5.70634i	0.311681	+	0.226449i
$636$		0			0
$637$	3.52786			0.139779
$638$	−8.41641	+	3.63271i	−0.333209	+	0.143820i
$639$		0			0
$640$	−9.20820	−	28.3399i	−0.363986	−	1.12023i
$641$	28.9164	+	21.0090i	1.14213	+	0.829806i	0.987415	−	0.158154i	$-0.0505541\pi$
$641$	28.9164	+	21.0090i	1.14213	+	0.829806i	0.154715	+	0.987959i	$0.450554\pi$
$642$		0			0
$643$	−11.9164	+	36.6749i	−0.469937	+	1.44632i	0.382728	+	0.923861i	$0.374985\pi$
$643$	−11.9164	+	36.6749i	−0.469937	+	1.44632i	−0.852666	+	0.522457i	$0.825015\pi$
$644$	5.20820	−	16.0292i	0.205232	−	0.631639i
$645$		0			0
$646$	4.73607	+	3.44095i	0.186338	+	0.135383i
$647$	−8.59017	−	26.4378i	−0.337714	−	1.03938i	−0.965369	−	0.260887i	$-0.915985\pi$
$647$	−8.59017	−	26.4378i	−0.337714	−	1.03938i	0.627655	−	0.778492i	$-0.284015\pi$
$648$		0			0
$649$	3.19098	+	34.0993i	0.125257	+	1.33851i
$650$	2.02129			0.0792814
$651$		0			0
$652$	23.9164	+	17.3763i	0.936639	+	0.680508i
$653$	41.2877	−	29.9973i	1.61571	−	1.17388i	0.776390	−	0.630252i	$-0.217049\pi$
$653$	41.2877	−	29.9973i	1.61571	−	1.17388i	0.839323	−	0.543632i	$-0.182951\pi$
$654$		0			0
$655$	5.78115	−	17.7926i	0.225888	−	0.695213i
$656$	−17.9164	+	13.0170i	−0.699518	+	0.508230i
$657$		0			0
$658$	−0.927051	−	2.85317i	−0.0361402	−	0.111228i
$659$	10.6525			0.414962			0.207481	−	0.978239i	$-0.433474\pi$
$659$	10.6525			0.414962			0.207481	+	0.978239i	$0.433474\pi$
$660$		0			0
$661$	−9.90983			−0.385448			−0.192724	−	0.981253i	$-0.561732\pi$
$661$	−9.90983			−0.385448			−0.192724	+	0.981253i	$0.561732\pi$
$662$	5.07953	+	15.6332i	0.197421	+	0.607601i
$663$		0			0
$664$	−1.28115	+	0.930812i	−0.0497184	+	0.0361225i
$665$	14.2082	−	43.7284i	0.550971	−	1.69571i
$666$		0			0
$667$	−12.5623	+	9.12705i	−0.486414	+	0.353401i
$668$	−13.1353	−	9.54332i	−0.508218	−	0.369242i
$669$		0			0
$670$	−15.4721			−0.597741
$671$	17.2082	+	19.5559i	0.664315	+	0.754948i
$672$		0			0
$673$	3.83688	+	11.8087i	0.147901	+	0.455192i	0.997373	−	0.0724420i	$-0.0230792\pi$
$673$	3.83688	+	11.8087i	0.147901	+	0.455192i	−0.849472	+	0.527634i	$0.823079\pi$
$674$	0.145898	+	0.106001i	0.00561978	+	0.00408301i
$675$		0			0
$676$	4.94427	−	15.2169i	0.190164	−	0.585266i
$677$	−4.18034	+	12.8658i	−0.160664	+	0.494471i	−0.998691	−	0.0511572i	$-0.983709\pi$
$677$	−4.18034	+	12.8658i	−0.160664	+	0.494471i	0.838027	+	0.545629i	$0.183709\pi$
$678$		0			0
$679$	34.0623	+	24.7477i	1.30719	+	0.949730i
$680$	2.92705	+	9.00854i	0.112247	+	0.345462i
$681$		0			0
$682$	−0.545085	−	5.82485i	−0.0208724	−	0.223045i
$683$	3.11146			0.119057			0.0595283	−	0.998227i	$-0.481040\pi$
$683$	3.11146			0.119057			0.0595283	+	0.998227i	$0.481040\pi$
$684$		0			0
$685$	15.8262	+	11.4984i	0.604689	+	0.439333i
$686$	7.50000	−	5.44907i	0.286351	−	0.208046i
$687$		0			0
$688$	3.57295	−	10.9964i	0.136217	−	0.419234i
$689$	−13.7254	+	9.97210i	−0.522897	+	0.379907i
$690$		0			0
$691$	−8.12461	−	25.0050i	−0.309075	−	0.951234i	−0.978125	−	0.208017i	$-0.933299\pi$
$691$	−8.12461	−	25.0050i	−0.309075	−	0.951234i	0.669050	−	0.743217i	$-0.266701\pi$
$692$	24.8885			0.946120
$693$		0			0
$694$	12.9443			0.491358
$695$	−0.690983	−	2.12663i	−0.0262105	−	0.0806676i
$696$		0			0
$697$	15.6353	−	11.3597i	0.592228	−	0.430278i
$698$	−1.93363	+	5.95110i	−0.0731889	+	0.225252i
$699$		0			0
$700$	7.28115	−	5.29007i	0.275202	−	0.199946i
$701$	−8.64590	−	6.28161i	−0.326551	−	0.237253i	0.412415	−	0.910996i	$-0.364685\pi$
$701$	−8.64590	−	6.28161i	−0.326551	−	0.237253i	−0.738966	+	0.673743i	$0.764685\pi$
$702$		0			0
$703$	1.38197			0.0521218
$704$	0.763932	+	0.171513i	0.0287918	+	0.00646416i
$705$		0			0
$706$	2.00000	+	6.15537i	0.0752710	+	0.231660i
$707$	−7.28115	−	5.29007i	−0.273836	−	0.198953i
$708$		0			0
$709$	15.0623	−	46.3570i	0.565677	−	1.74097i	−0.100255	−	0.994962i	$-0.531966\pi$
$709$	15.0623	−	46.3570i	0.565677	−	1.74097i	0.665932	−	0.746012i	$-0.268034\pi$
$710$	2.78115	−	8.55951i	0.104375	−	0.321233i
$711$		0			0
$712$	−0.954915	−	0.693786i	−0.0357870	−	0.0260007i
$713$	−3.06231	−	9.42481i	−0.114684	−	0.352962i
$714$		0			0
$715$	−7.80902	+	13.1760i	−0.292041	+	0.492756i
$716$	−3.61803			−0.135212
$717$		0			0
$718$	−6.38197	−	4.63677i	−0.238173	−	0.173043i
$719$	−1.28115	+	0.930812i	−0.0477789	+	0.0347134i	−0.611418	−	0.791307i	$-0.709401\pi$
$719$	−1.28115	+	0.930812i	−0.0477789	+	0.0347134i	0.563639	+	0.826021i	$0.309401\pi$
$720$		0			0
$721$	−5.56231	+	17.1190i	−0.207151	+	0.637546i
$722$	−7.63525	+	5.54734i	−0.284155	+	0.206451i
$723$		0			0
$724$	8.73607	+	26.8869i	0.324673	+	0.999242i
$725$	−8.29180			−0.307950
$726$		0			0
$727$	38.8541			1.44102			0.720509	−	0.693445i	$-0.243908\pi$
$727$	38.8541			1.44102			0.720509	+	0.693445i	$0.243908\pi$
$728$	−3.65654	−	11.2537i	−0.135520	−	0.417089i
$729$		0			0
$730$	4.23607	−	3.07768i	0.156784	−	0.113910i
$731$	−3.11803	+	9.59632i	−0.115325	+	0.354933i
$732$		0			0
$733$	30.5066	−	22.1643i	1.12679	−	0.818658i	0.141562	−	0.989929i	$-0.454787\pi$
$733$	30.5066	−	22.1643i	1.12679	−	0.818658i	0.985224	+	0.171271i	$0.0547875\pi$
$734$	−2.78115	−	2.02063i	−0.102654	−	0.0745827i
$735$		0			0
$736$	−19.5066			−0.719022
$737$	16.1697	−	27.2829i	0.595618	−	1.00498i
$738$		0			0
$739$	−7.72542	−	23.7764i	−0.284184	−	0.874629i	−0.986642	−	0.162904i	$-0.947914\pi$
$739$	−7.72542	−	23.7764i	−0.284184	−	0.874629i	0.702458	−	0.711726i	$-0.252086\pi$
$740$	0.809017	+	0.587785i	0.0297401	+	0.0216074i
$741$		0			0
$742$	5.51064	−	16.9600i	0.202302	−	0.622622i
$743$	−10.8713	+	33.4585i	−0.398830	+	1.22747i	0.527108	+	0.849798i	$0.323276\pi$
$743$	−10.8713	+	33.4585i	−0.398830	+	1.22747i	−0.925938	+	0.377675i	$0.876724\pi$
$744$		0			0
$745$	31.7705	+	23.0826i	1.16398	+	0.845682i
$746$	−0.843459	−	2.59590i	−0.0308812	−	0.0950426i
$747$		0			0
$748$	−8.47214	−	1.90211i	−0.309772	−	0.0695481i
$749$	12.7082			0.464348
$750$		0			0
$751$	−9.64590	−	7.00816i	−0.351984	−	0.255731i	0.397717	−	0.917508i	$-0.369803\pi$
$751$	−9.64590	−	7.00816i	−0.351984	−	0.255731i	−0.749701	+	0.661777i	$0.769803\pi$
$752$	2.42705	−	1.76336i	0.0885054	−	0.0643030i
$753$		0			0
$754$	−1.50658	+	4.63677i	−0.0548663	+	0.168861i
$755$	−4.23607	+	3.07768i	−0.154166	+	0.112008i
$756$		0			0
$757$	0.600813	+	1.84911i	0.0218369	+	0.0672071i	0.961381	−	0.275220i	$-0.0887509\pi$
$757$	0.600813	+	1.84911i	0.0218369	+	0.0672071i	−0.939544	+	0.342428i	$0.888751\pi$
$758$	0.978714			0.0355485
$759$		0			0
$760$	−34.2705			−1.24312
$761$	9.54508	+	29.3768i	0.346009	+	1.06491i	0.961041	+	0.276404i	$0.0891429\pi$
$761$	9.54508	+	29.3768i	0.346009	+	1.06491i	−0.615032	+	0.788502i	$0.710857\pi$
$762$		0			0
$763$		0			0
$764$	−3.73607	+	11.4984i	−0.135166	+	0.415999i
$765$		0			0
$766$	13.4443	−	9.76784i	0.485761	−	0.352926i
$767$	14.7361	+	10.7064i	0.532089	+	0.386585i
$768$		0			0
$769$	12.6869			0.457502			0.228751	−	0.973485i	$-0.426536\pi$
$769$	12.6869			0.457502			0.228751	+	0.973485i	$0.426536\pi$
$770$	−1.50000	−	16.0292i	−0.0540562	−	0.577652i
$771$		0			0
$772$	9.28115	+	28.5645i	0.334036	+	1.02806i
$773$	−25.2812	−	18.3678i	−0.909300	−	0.660645i	0.0315378	−	0.999503i	$-0.489960\pi$
$773$	−25.2812	−	18.3678i	−0.909300	−	0.660645i	−0.940838	+	0.338858i	$0.889960\pi$
$774$		0			0
$775$	1.63525	−	5.03280i	0.0587401	−	0.180783i
$776$	9.69756	−	29.8460i	0.348122	−	1.07141i
$777$		0			0
$778$	12.1353	+	8.81678i	0.435070	+	0.316097i
$779$	21.6074	+	66.5007i	0.774165	+	2.38264i
$780$		0			0
$781$	12.1869	+	13.8496i	0.436082	+	0.495577i
$782$	3.47214			0.124163
$783$		0			0
$784$	−3.00000	−	2.17963i	−0.107143	−	0.0778438i
$785$	7.85410	−	5.70634i	0.280325	−	0.203668i
$786$		0			0
$787$	−3.18034	+	9.78808i	−0.113367	+	0.348907i	−0.991603	−	0.129320i	$-0.958721\pi$
$787$	−3.18034	+	9.78808i	−0.113367	+	0.348907i	0.878236	+	0.478227i	$0.158721\pi$
$788$	−31.9164	+	23.1886i	−1.13697	+	0.826061i
$789$		0			0
$790$	4.73607	+	14.5761i	0.168502	+	0.518595i
$791$	−2.12461			−0.0755425
$792$		0			0
$793$	13.8541			0.491974
$794$	−7.39261	−	22.7521i	−0.262354	−	0.807442i
$795$		0			0
$796$	−21.8713	+	15.8904i	−0.775208	+	0.563222i
$797$	−3.32624	+	10.2371i	−0.117821	+	0.362617i	−0.992525	−	0.122041i	$-0.961056\pi$
$797$	−3.32624	+	10.2371i	−0.117821	+	0.362617i	0.874704	+	0.484658i	$0.161056\pi$
$798$		0			0
$799$	−2.11803	+	1.53884i	−0.0749307	+	0.0544403i
$800$	−8.42705	−	6.12261i	−0.297941	−	0.216467i
$801$		0			0
$802$	16.1246			0.569380
$803$	1.00000	+	10.6861i	0.0352892	+	0.377106i
$804$		0			0
$805$	−8.42705	−	25.9358i	−0.297015	−	0.914117i
$806$	−2.51722	−	1.82887i	−0.0886653	−	0.0644191i
$807$		0			0
$808$	−2.07295	+	6.37988i	−0.0729261	+	0.224443i
$809$	−2.98936	+	9.20029i	−0.105100	+	0.323465i	−0.989754	−	0.142783i	$-0.954395\pi$
$809$	−2.98936	+	9.20029i	−0.105100	+	0.323465i	0.884654	+	0.466249i	$0.154395\pi$
$810$		0			0
$811$	−2.63525	−	1.91462i	−0.0925363	−	0.0672316i	0.540555	−	0.841309i	$-0.318214\pi$
$811$	−2.63525	−	1.91462i	−0.0925363	−	0.0672316i	−0.633091	+	0.774077i	$0.718214\pi$
$812$	6.70820	+	20.6457i	0.235412	+	0.724523i
$813$		0			0
$814$	0.444272	−	0.191758i	0.0155717	−	0.00672111i
$815$	47.8328			1.67551
$816$		0			0
$817$	−29.5344	−	21.4580i	−1.03328	−	0.750721i
$818$	5.52786	−	4.01623i	0.193277	−	0.140424i
$819$		0			0
$820$	−15.6353	+	48.1204i	−0.546007	+	1.68044i
$821$	32.6976	−	23.7562i	1.14115	−	0.829096i	0.153873	−	0.988091i	$-0.450825\pi$
$821$	32.6976	−	23.7562i	1.14115	−	0.829096i	0.987279	+	0.158995i	$0.0508252\pi$
$822$		0			0
$823$	−10.9615	−	33.7360i	−0.382094	−	1.17596i	−0.938567	−	0.345098i	$-0.887846\pi$
$823$	−10.9615	−	33.7360i	−0.382094	−	1.17596i	0.556473	−	0.830866i	$-0.312154\pi$
$824$	13.4164			0.467383
$825$		0			0
$826$	−19.1459			−0.666171
$827$	−16.4164	−	50.5245i	−0.570854	−	1.75691i	−0.649880	−	0.760037i	$-0.725181\pi$
$827$	−16.4164	−	50.5245i	−0.570854	−	1.75691i	0.0790257	−	0.996873i	$-0.474819\pi$
$828$		0			0
$829$	−14.3090	+	10.3961i	−0.496973	+	0.361072i	−0.807859	−	0.589375i	$-0.799374\pi$
$829$	−14.3090	+	10.3961i	−0.496973	+	0.361072i	0.310887	+	0.950447i	$0.399374\pi$
$830$	−0.354102	+	1.08981i	−0.0122911	+	0.0378280i
$831$		0			0
$832$	0.336881	−	0.244758i	0.0116792	−	0.00848547i
$833$	2.61803	+	1.90211i	0.0907095	+	0.0659043i
$834$		0			0
$835$	−26.2705			−0.909128
$836$	16.0172	−	27.0256i	0.553967	−	0.934700i
$837$		0			0
$838$	−3.15248	−	9.70232i	−0.108900	−	0.335161i
$839$	−29.6976	−	21.5765i	−1.02527	−	0.744905i	−0.0579164	−	0.998321i	$-0.518446\pi$
$839$	−29.6976	−	21.5765i	−1.02527	−	0.744905i	−0.967357	+	0.253417i	$0.918446\pi$
$840$		0			0
$841$	−2.78115	+	8.55951i	−0.0959018	+	0.295155i
$842$	−7.11803	+	21.9071i	−0.245304	+	0.754967i
$843$		0			0
$844$	−29.1525	−	21.1805i	−1.00347	−	0.729063i
$845$	−8.00000	−	24.6215i	−0.275208	−	0.847004i
$846$		0			0
$847$	29.8328	+	14.1068i	1.02507	+	0.484717i
$848$	17.8328			0.612381
$849$		0			0
$850$	1.50000	+	1.08981i	0.0514496	+	0.0373803i
$851$	0.663119	−	0.481784i	0.0227314	−	0.0165153i
$852$		0			0
$853$	−3.07295	+	9.45756i	−0.105216	+	0.323821i	−0.989781	−	0.142596i	$-0.954455\pi$
$853$	−3.07295	+	9.45756i	−0.105216	+	0.323821i	0.884565	+	0.466416i	$0.154455\pi$
$854$	−11.7812	+	8.55951i	−0.403143	+	0.292900i
$855$		0			0
$856$	−2.92705	−	9.00854i	−0.100045	−	0.307905i
$857$	−47.7214			−1.63013			−0.815065	−	0.579369i	$-0.803299\pi$
$857$	−47.7214			−1.63013			−0.815065	+	0.579369i	$0.803299\pi$
$858$		0			0
$859$	7.11146			0.242640			0.121320	−	0.992613i	$-0.461287\pi$
$859$	7.11146			0.242640			0.121320	+	0.992613i	$0.461287\pi$
$860$	−8.16312	−	25.1235i	−0.278360	−	0.856704i
$861$		0			0
$862$	−19.7533	+	14.3516i	−0.672800	+	0.488818i
$863$	−3.67376	+	11.3067i	−0.125056	+	0.384884i	−0.993911	−	0.110183i	$-0.964856\pi$
$863$	−3.67376	+	11.3067i	−0.125056	+	0.384884i	0.868855	+	0.495067i	$0.164856\pi$
$864$		0			0
$865$	32.5795	−	23.6704i	1.10774	−	0.804818i
$866$	3.00000	+	2.17963i	0.101944	+	0.0740668i
$867$		0			0
$868$	−13.8541			−0.470239
$869$	−30.6525	−	6.88191i	−1.03981	−	0.233453i
$870$		0			0
$871$	−5.21227	−	16.0417i	−0.176611	−	0.543553i
$872$		0			0
$873$		0			0
$874$	−3.88197	+	11.9475i	−0.131309	+	0.404129i
$875$	−7.63525	+	23.4989i	−0.258119	+	0.794408i
$876$		0			0
$877$	−5.19098	−	3.77147i	−0.175287	−	0.127353i	0.496682	−	0.867932i	$-0.334551\pi$
$877$	−5.19098	−	3.77147i	−0.175287	−	0.127353i	−0.671969	+	0.740579i	$0.734551\pi$
$878$	0.628677	+	1.93487i	0.0212168	+	0.0652987i
$879$		0			0
$880$	14.7812	−	6.37988i	0.498273	−	0.215066i
$881$	−13.9098			−0.468634			−0.234317	−	0.972160i	$-0.575285\pi$
$881$	−13.9098			−0.468634			−0.234317	+	0.972160i	$0.575285\pi$
$882$		0			0
$883$	−8.56231	−	6.22088i	−0.288145	−	0.209349i	0.434318	−	0.900760i	$-0.356990\pi$
$883$	−8.56231	−	6.22088i	−0.288145	−	0.209349i	−0.722462	+	0.691411i	$0.756990\pi$
$884$	−3.73607	+	2.71441i	−0.125658	+	0.0912956i
$885$		0			0
$886$	7.85410	−	24.1724i	0.263864	−	0.812089i
$887$	2.42705	−	1.76336i	0.0814924	−	0.0592077i	−0.546293	−	0.837594i	$-0.683962\pi$
$887$	2.42705	−	1.76336i	0.0814924	−	0.0592077i	0.627785	+	0.778386i	$0.283962\pi$
$888$		0			0
$889$	−3.43769	−	10.5801i	−0.115297	−	0.354846i
$890$	−0.854102			−0.0286296
$891$		0			0
$892$	−1.14590			−0.0383675
$893$	−2.92705	−	9.00854i	−0.0979500	−	0.301459i
$894$		0			0
$895$	−4.73607	+	3.44095i	−0.158309	+	0.115018i
$896$	−10.5517	+	32.4747i	−0.352506	+	1.08490i
$897$		0			0
$898$	−12.2361	+	8.89002i	−0.408323	+	0.296664i
$899$	10.3262	+	7.50245i	0.344399	+	0.250221i
$900$		0			0
$901$	−15.5623			−0.518456
$902$	16.1738	+	18.3803i	0.538527	+	0.611999i
$903$		0			0
$904$	0.489357	+	1.50609i	0.0162758	+	0.0500917i
$905$	37.0066	+	26.8869i	1.23014	+	0.893749i
$906$		0			0
$907$	−13.2812	+	40.8752i	−0.440993	+	1.35724i	0.445825	+	0.895120i	$0.352910\pi$
$907$	−13.2812	+	40.8752i	−0.440993	+	1.35724i	−0.886818	+	0.462118i	$0.847090\pi$
$908$	−12.4443	+	38.2995i	−0.412978	+	1.27101i
$909$		0			0
$910$	−6.92705	−	5.03280i	−0.229630	−	0.166836i
$911$	−5.57953	−	17.1720i	−0.184858	−	0.568934i	0.815088	−	0.579337i	$-0.196689\pi$
$911$	−5.57953	−	17.1720i	−0.184858	−	0.568934i	−0.999946	+	0.0104029i	$0.996689\pi$
$912$		0			0
$913$	−1.55166	−	1.76336i	−0.0513525	−	0.0583586i
$914$	5.06888			0.167664
$915$		0			0
$916$	13.0902	+	9.51057i	0.432511	+	0.314238i
$917$	−17.3435	+	12.6008i	−0.572731	+	0.416114i
$918$		0			0
$919$	14.5106	−	44.6592i	0.478662	−	1.47317i	−0.362293	−	0.932064i	$-0.618006\pi$
$919$	14.5106	−	44.6592i	0.478662	−	1.47317i	0.840955	−	0.541106i	$-0.181994\pi$
$920$	−16.4443	+	11.9475i	−0.542152	+	0.393896i
$921$		0			0
$922$	4.02786	+	12.3965i	0.132651	+	0.408257i
$923$	9.81153			0.322950
$924$		0			0
$925$	0.437694			0.0143913
$926$	−3.01722	−	9.28605i	−0.0991520	−	0.305159i
$927$		0			0
$928$	20.3262	−	14.7679i	0.667241	−	0.484779i
$929$	10.1631	−	31.2789i	0.333441	−	1.02623i	−0.634044	−	0.773297i	$-0.718606\pi$
$929$	10.1631	−	31.2789i	0.333441	−	1.02623i	0.967485	−	0.252929i	$-0.0813939\pi$
$930$		0			0
$931$	−9.47214	+	6.88191i	−0.310437	+	0.225545i
$932$	−31.8435	−	23.1356i	−1.04307	−	0.757833i
$933$		0			0
$934$	6.03444			0.197453
$935$	−12.8992	+	5.56758i	−0.421849	+	0.182079i
$936$		0			0
$937$	−5.12868	−	15.7844i	−0.167547	−	0.515655i	0.831668	−	0.555273i	$-0.187386\pi$
$937$	−5.12868	−	15.7844i	−0.167547	−	0.515655i	−0.999215	+	0.0396173i	$0.987386\pi$
$938$	14.3435	+	10.4211i	0.468331	+	0.340262i
$939$		0			0
$940$	2.11803	−	6.51864i	0.0690827	−	0.212615i
$941$	13.7918	−	42.4468i	0.449600	−	1.38373i	−0.427760	−	0.903892i	$-0.640697\pi$
$941$	13.7918	−	42.4468i	0.449600	−	1.38373i	0.877360	−	0.479833i	$-0.159303\pi$
$942$		0			0
$943$	33.5517	+	24.3767i	1.09259	+	0.793815i
$944$	−5.91641	−	18.2088i	−0.192563	−	0.592647i
$945$		0			0
$946$	−12.4721	−	2.80017i	−0.405504	−	0.0910413i
$947$	−18.3262			−0.595523			−0.297761	−	0.954640i	$-0.596240\pi$
$947$	−18.3262			−0.595523			−0.297761	+	0.954640i	$0.596240\pi$
$948$		0			0
$949$	4.61803	+	3.35520i	0.149908	+	0.108914i
$950$	−5.42705	+	3.94298i	−0.176077	+	0.127927i
$951$		0			0
$952$	3.35410	−	10.3229i	0.108707	−	0.334566i
$953$	30.5967	−	22.2298i	0.991126	−	0.720095i	0.0309585	−	0.999521i	$-0.490144\pi$
$953$	30.5967	−	22.2298i	0.991126	−	0.720095i	0.960167	+	0.279426i	$0.0901440\pi$
$954$		0			0
$955$	6.04508	+	18.6049i	0.195614	+	0.602039i
$956$	4.14590			0.134088
$957$		0			0
$958$	17.3607			0.560898
$959$	−6.92705	−	21.3193i	−0.223686	−	0.688435i
$960$		0			0
$961$	18.4894	−	13.4333i	0.596431	−	0.433332i
$962$	0.0795268	−	0.244758i	0.00256405	−	0.00789133i
$963$		0			0
$964$	−30.2705	+	21.9928i	−0.974947	+	0.708341i
$965$	39.3156	+	28.5645i	1.26561	+	0.919522i
$966$		0			0
$967$	−34.6869			−1.11546			−0.557728	−	0.830024i	$-0.688327\pi$
$967$	−34.6869			−1.11546			−0.557728	+	0.830024i	$0.688327\pi$
$968$	3.12868	−	24.3970i	0.100559	−	0.784148i
$969$		0			0
$970$	−7.01722	−	21.5968i	−0.225309	−	0.693431i
$971$	30.5623	+	22.2048i	0.980791	+	0.712586i	0.957885	−	0.287151i	$-0.0927082\pi$
$971$	30.5623	+	22.2048i	0.980791	+	0.712586i	0.0229058	+	0.999738i	$0.492708\pi$
$972$		0			0
$973$	−0.791796	+	2.43690i	−0.0253838	+	0.0781234i
$974$	3.21227	−	9.88635i	0.102928	−	0.316779i
$975$		0			0
$976$	−11.7812	−	8.55951i	−0.377106	−	0.273983i
$977$	1.43363	+	4.41226i	0.0458658	+	0.141161i	0.971367	−	0.237585i	$-0.0763557\pi$
$977$	1.43363	+	4.41226i	0.0458658	+	0.141161i	−0.925501	+	0.378745i	$0.876356\pi$
$978$		0			0
$979$	0.892609	−	1.50609i	0.0285279	−	0.0481347i
$980$	−8.47214			−0.270632
$981$		0			0
$982$	12.6074	+	9.15981i	0.402318	+	0.292301i
$983$	−22.0902	+	16.0494i	−0.704567	+	0.511898i	−0.881416	−	0.472340i	$-0.843409\pi$
$983$	−22.0902	+	16.0494i	−0.704567	+	0.511898i	0.176849	+	0.984238i	$0.443409\pi$
$984$		0			0
$985$	−19.7254	+	60.7086i	−0.628504	+	1.93434i
$986$	−3.61803	+	2.62866i	−0.115222	+	0.0837134i
$987$		0			0
$988$	−5.16312	−	15.8904i	−0.164261	−	0.505542i
$989$	−21.6525			−0.688509
$990$		0			0
$991$	21.2705			0.675680			0.337840	−	0.941204i	$-0.390304\pi$
$991$	21.2705			0.675680			0.337840	+	0.941204i	$0.390304\pi$
$992$	4.95492	+	15.2497i	0.157319	+	0.484177i
$993$		0			0
$994$	−8.34346	+	6.06188i	−0.264638	+	0.192271i
$995$	−13.5172	+	41.6017i	−0.428525	+	1.31886i
$996$		0			0
$997$	10.5000	−	7.62870i	0.332538	−	0.241603i	−0.408969	−	0.912548i	$-0.634111\pi$
$997$	10.5000	−	7.62870i	0.332538	−	0.241603i	0.741507	+	0.670945i	$0.234111\pi$
$998$	8.78115	+	6.37988i	0.277963	+	0.201952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.f.b.82.1		4
3.2	odd	2		33.2.e.a.16.1	✓	4
9.2	odd	6		891.2.n.d.676.1		8
9.4	even	3		891.2.n.a.379.1		8
9.5	odd	6		891.2.n.d.379.1		8
9.7	even	3		891.2.n.a.676.1		8
11.3	even	5		1089.2.a.m.1.2		2
11.8	odd	10		1089.2.a.s.1.1		2
11.9	even	5	inner	99.2.f.b.64.1		4
12.11	even	2		528.2.y.f.49.1		4
15.2	even	4		825.2.bx.b.49.2		8
15.8	even	4		825.2.bx.b.49.1		8
15.14	odd	2		825.2.n.f.676.1		4
33.2	even	10		363.2.e.j.130.1		4
33.5	odd	10		363.2.e.h.202.1		4
33.8	even	10		363.2.a.e.1.2		2
33.14	odd	10		363.2.a.h.1.1		2
33.17	even	10		363.2.e.c.202.1		4
33.20	odd	10		33.2.e.a.31.1	yes	4
33.26	odd	10		363.2.e.h.124.1		4
33.29	even	10		363.2.e.c.124.1		4
33.32	even	2		363.2.e.j.148.1		4
99.20	odd	30		891.2.n.d.757.1		8
99.31	even	15		891.2.n.a.460.1		8
99.86	odd	30		891.2.n.d.460.1		8
99.97	even	15		891.2.n.a.757.1		8
132.47	even	10		5808.2.a.bl.1.1		2
132.107	odd	10		5808.2.a.bm.1.1		2
132.119	even	10		528.2.y.f.97.1		4
165.14	odd	10		9075.2.a.x.1.2		2
165.53	even	20		825.2.bx.b.724.2		8
165.74	even	10		9075.2.a.bv.1.1		2
165.119	odd	10		825.2.n.f.526.1		4
165.152	even	20		825.2.bx.b.724.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.16.1	✓	4	3.2	odd	2
33.2.e.a.31.1	yes	4	33.20	odd	10
99.2.f.b.64.1		4	11.9	even	5	inner
99.2.f.b.82.1		4	1.1	even	1	trivial
363.2.a.e.1.2		2	33.8	even	10
363.2.a.h.1.1		2	33.14	odd	10
363.2.e.c.124.1		4	33.29	even	10
363.2.e.c.202.1		4	33.17	even	10
363.2.e.h.124.1		4	33.26	odd	10
363.2.e.h.202.1		4	33.5	odd	10
363.2.e.j.130.1		4	33.2	even	10
363.2.e.j.148.1		4	33.32	even	2
528.2.y.f.49.1		4	12.11	even	2
528.2.y.f.97.1		4	132.119	even	10
825.2.n.f.526.1		4	165.119	odd	10
825.2.n.f.676.1		4	15.14	odd	2
825.2.bx.b.49.1		8	15.8	even	4
825.2.bx.b.49.2		8	15.2	even	4
825.2.bx.b.724.1		8	165.152	even	20
825.2.bx.b.724.2		8	165.53	even	20
891.2.n.a.379.1		8	9.4	even	3
891.2.n.a.460.1		8	99.31	even	15
891.2.n.a.676.1		8	9.7	even	3
891.2.n.a.757.1		8	99.97	even	15
891.2.n.d.379.1		8	9.5	odd	6
891.2.n.d.460.1		8	99.86	odd	30
891.2.n.d.676.1		8	9.2	odd	6
891.2.n.d.757.1		8	99.20	odd	30
1089.2.a.m.1.2		2	11.3	even	5
1089.2.a.s.1.1		2	11.8	odd	10
5808.2.a.bl.1.1		2	132.47	even	10
5808.2.a.bm.1.1		2	132.107	odd	10
9075.2.a.x.1.2		2	165.14	odd	10
9075.2.a.bv.1.1		2	165.74	even	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 + 0.587785i) q^{2} +(1.30902 - 0.951057i) q^{4} +(0.809017 - 2.48990i) q^{5} +(-2.42705 + 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +O(q^{10})\)	\(q+(0.190983 + 0.587785i) q^{2} +(1.30902 - 0.951057i) q^{4} +(0.809017 - 2.48990i) q^{5} +(-2.42705 + 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +1.61803 q^{10} +(-1.69098 + 2.85317i) q^{11} +(0.545085 + 1.67760i) q^{13} +(-1.50000 - 1.08981i) q^{14} +(0.572949 - 1.76336i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(-1.30902 - 4.02874i) q^{20} +(-2.00000 - 0.449028i) q^{22} -3.47214 q^{23} +(-1.50000 - 1.08981i) q^{25} +(-0.881966 + 0.640786i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(3.61803 - 2.62866i) q^{29} +(0.881966 + 2.71441i) q^{31} +5.61803 q^{32} -1.00000 q^{34} +(2.42705 + 7.46969i) q^{35} +(-0.190983 + 0.138757i) q^{37} +(1.11803 - 3.44095i) q^{38} +(4.73607 - 3.44095i) q^{40} +(-9.66312 - 7.02067i) q^{41} +6.23607 q^{43} +(0.500000 + 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(1.30902 + 0.951057i) q^{47} +(0.618034 - 1.90211i) q^{49} +(0.354102 - 1.08981i) q^{50} +(2.30902 + 1.67760i) q^{52} +(2.97214 + 9.14729i) q^{53} +(5.73607 + 6.51864i) q^{55} -6.70820 q^{56} +(2.23607 + 1.62460i) q^{58} +(8.35410 - 6.06961i) q^{59} +(2.42705 - 7.46969i) q^{61} +(-1.42705 + 1.03681i) q^{62} +(-0.0729490 - 0.224514i) q^{64} +4.61803 q^{65} -9.56231 q^{67} +(0.809017 + 2.48990i) q^{68} +(-3.92705 + 2.85317i) q^{70} +(1.71885 - 5.29007i) q^{71} +(2.61803 - 1.90211i) q^{73} +(-0.118034 - 0.0857567i) q^{74} -9.47214 q^{76} +(-0.927051 - 9.90659i) q^{77} +(2.92705 + 9.00854i) q^{79} +(-3.92705 - 2.85317i) q^{80} +(2.28115 - 7.02067i) q^{82} +(-0.218847 + 0.673542i) q^{83} +(3.42705 + 2.48990i) q^{85} +(1.19098 + 3.66547i) q^{86} +(-6.80902 + 2.93893i) q^{88} -0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-4.54508 + 3.30220i) q^{92} +(-0.309017 + 0.951057i) q^{94} +(-12.3992 + 9.00854i) q^{95} +(-4.33688 - 13.3475i) q^{97} +1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 3 q^{4} + q^{5} - 3 q^{7} + 5 q^{8}+O(q^{10}) \) 4 * q + 3 * q^2 + 3 * q^4 + q^5 - 3 * q^7 + 5 * q^8	\( 4 q + 3 q^{2} + 3 q^{4} + q^{5} - 3 q^{7} + 5 q^{8} + 2 q^{10} - 9 q^{11} - 9 q^{13} - 6 q^{14} + 9 q^{16} - 2 q^{17} - 10 q^{19} - 3 q^{20} - 8 q^{22} + 4 q^{23} - 6 q^{25} - 8 q^{26} - 6 q^{28} + 10 q^{29} + 8 q^{31} + 18 q^{32} - 4 q^{34} + 3 q^{35} - 3 q^{37} + 10 q^{40} - 23 q^{41} + 16 q^{43} + 2 q^{44} + 13 q^{46} + 3 q^{47} - 2 q^{49} - 12 q^{50} + 7 q^{52} - 6 q^{53} + 14 q^{55} + 20 q^{59} + 3 q^{61} + q^{62} - 7 q^{64} + 14 q^{65} + 2 q^{67} + q^{68} - 9 q^{70} + 27 q^{71} + 6 q^{73} + 4 q^{74} - 20 q^{76} + 3 q^{77} + 5 q^{79} - 9 q^{80} - 11 q^{82} - 21 q^{83} + 7 q^{85} + 7 q^{86} - 25 q^{88} - 20 q^{89} + 3 q^{91} - 7 q^{92} + q^{94} - 25 q^{95} - 33 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 + 3 * q^4 + q^5 - 3 * q^7 + 5 * q^8 + 2 * q^10 - 9 * q^11 - 9 * q^13 - 6 * q^14 + 9 * q^16 - 2 * q^17 - 10 * q^19 - 3 * q^20 - 8 * q^22 + 4 * q^23 - 6 * q^25 - 8 * q^26 - 6 * q^28 + 10 * q^29 + 8 * q^31 + 18 * q^32 - 4 * q^34 + 3 * q^35 - 3 * q^37 + 10 * q^40 - 23 * q^41 + 16 * q^43 + 2 * q^44 + 13 * q^46 + 3 * q^47 - 2 * q^49 - 12 * q^50 + 7 * q^52 - 6 * q^53 + 14 * q^55 + 20 * q^59 + 3 * q^61 + q^62 - 7 * q^64 + 14 * q^65 + 2 * q^67 + q^68 - 9 * q^70 + 27 * q^71 + 6 * q^73 + 4 * q^74 - 20 * q^76 + 3 * q^77 + 5 * q^79 - 9 * q^80 - 11 * q^82 - 21 * q^83 + 7 * q^85 + 7 * q^86 - 25 * q^88 - 20 * q^89 + 3 * q^91 - 7 * q^92 + q^94 - 25 * q^95 - 33 * q^97 - 4 * q^98

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