LMFDB - Embedded newform 261.2.k.b.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(82,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			82.2
Root			$0.0185039 - 0.0810709i$ of defining polynomial
Character	$\chi$	$=$	261.82
Dual form			261.2.k.b.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0518468 + 0.0650138i) q^{2} +(0.443503 - 1.94311i) q^{4} +(-1.20357 - 1.50923i) q^{5} +(-0.0765305 - 0.335302i) q^{7} +(0.299165 - 0.144070i) q^{8} +O(q^{10})$	\(q+(0.0518468 + 0.0650138i) q^{2} +(0.443503 - 1.94311i) q^{4} +(-1.20357 - 1.50923i) q^{5} +(-0.0765305 - 0.335302i) q^{7} +(0.299165 - 0.144070i) q^{8} +(0.0357195 - 0.156498i) q^{10} +(-2.18408 - 1.05180i) q^{11} +(-3.27160 - 1.57552i) q^{13} +(0.0178314 - 0.0223599i) q^{14} +(-3.56654 - 1.71755i) q^{16} +6.15354 q^{17} +(0.300553 - 1.31681i) q^{19} +(-3.46640 + 1.66933i) q^{20} +(-0.0448561 - 0.196528i) q^{22} +(2.16114 - 2.70998i) q^{23} +(0.283411 - 1.24171i) q^{25} +(-0.0671914 - 0.294385i) q^{26} -0.685471 q^{28} +(4.26305 + 3.29035i) q^{29} +(6.85222 + 8.59242i) q^{31} +(-0.221024 - 0.968370i) q^{32} +(0.319041 + 0.400065i) q^{34} +(-0.413938 + 0.519062i) q^{35} +(2.78149 - 1.33950i) q^{37} +(0.101193 - 0.0487322i) q^{38} +(-0.577502 - 0.278110i) q^{40} -5.28313 q^{41} +(-0.00526324 + 0.00659989i) q^{43} +(-3.01241 + 3.77744i) q^{44} +0.288234 q^{46} +(-5.22270 - 2.51512i) q^{47} +(6.20021 - 2.98586i) q^{49} +(0.0954221 - 0.0459528i) q^{50} +(-4.51238 + 5.65834i) q^{52} +(2.58271 + 3.23861i) q^{53} +(1.04129 + 4.56219i) q^{55} +(-0.0712023 - 0.0892849i) q^{56} +(0.00710697 + 0.447751i) q^{58} -5.76819 q^{59} +(1.38805 + 6.08144i) q^{61} +(-0.203360 + 0.890979i) q^{62} +(-4.88474 + 6.12527i) q^{64} +(1.55978 + 6.83384i) q^{65} +(-9.92346 + 4.77889i) q^{67} +(2.72912 - 11.9570i) q^{68} -0.0552076 q^{70} +(11.5818 + 5.57748i) q^{71} +(0.286311 - 0.359022i) q^{73} +(0.231297 + 0.111387i) q^{74} +(-2.42541 - 1.16802i) q^{76} +(-0.185521 + 0.812820i) q^{77} +(11.2434 - 5.41452i) q^{79} +(1.70040 + 7.44993i) q^{80} +(-0.273913 - 0.343476i) q^{82} +(0.640518 - 2.80629i) q^{83} +(-7.40623 - 9.28712i) q^{85} -0.000701966 q^{86} -0.804933 q^{88} +(7.62150 + 9.55706i) q^{89} +(-0.277897 + 1.21755i) q^{91} +(-4.30733 - 5.40122i) q^{92} +(-0.107263 - 0.469948i) q^{94} +(-2.34911 + 1.13127i) q^{95} +(0.606191 - 2.65590i) q^{97} +(0.515584 + 0.248292i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8}+O(q^{10}) $ 18 * q + 2 * q^2 - 6 * q^4 + 7 * q^5 - 4 * q^7 + 3 * q^8	$ 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} - 11 q^{13} + 2 q^{14} + 18 q^{16} + 32 q^{17} + 2 q^{19} - 51 q^{20} + 20 q^{22} + 6 q^{23} + 4 q^{25} + 3 q^{26} - 48 q^{28} + 10 q^{29} + 8 q^{31} - 55 q^{32} + 6 q^{34} - 31 q^{35} + 20 q^{37} + 20 q^{38} - 59 q^{40} + 68 q^{41} - 3 q^{43} + 10 q^{44} - 12 q^{46} - 19 q^{47} + 17 q^{49} - 23 q^{50} - 4 q^{52} + q^{53} + 3 q^{55} - 7 q^{56} - 30 q^{58} - 20 q^{59} + 24 q^{61} - 79 q^{62} - 23 q^{64} - 6 q^{65} - 14 q^{67} + 8 q^{68} + 28 q^{70} + 28 q^{71} + 43 q^{73} + 47 q^{74} + 19 q^{76} - 26 q^{77} + 9 q^{79} + 74 q^{80} - 17 q^{82} - 8 q^{83} - 21 q^{85} + 140 q^{86} - 58 q^{88} + 6 q^{89} - 15 q^{91} - 11 q^{92} + 6 q^{94} + 16 q^{95} - 81 q^{97} + 11 q^{98}+O(q^{100}) $ 18 * q + 2 * q^2 - 6 * q^4 + 7 * q^5 - 4 * q^7 + 3 * q^8 + 6 * q^10 + 6 * q^11 - 11 * q^13 + 2 * q^14 + 18 * q^16 + 32 * q^17 + 2 * q^19 - 51 * q^20 + 20 * q^22 + 6 * q^23 + 4 * q^25 + 3 * q^26 - 48 * q^28 + 10 * q^29 + 8 * q^31 - 55 * q^32 + 6 * q^34 - 31 * q^35 + 20 * q^37 + 20 * q^38 - 59 * q^40 + 68 * q^41 - 3 * q^43 + 10 * q^44 - 12 * q^46 - 19 * q^47 + 17 * q^49 - 23 * q^50 - 4 * q^52 + q^53 + 3 * q^55 - 7 * q^56 - 30 * q^58 - 20 * q^59 + 24 * q^61 - 79 * q^62 - 23 * q^64 - 6 * q^65 - 14 * q^67 + 8 * q^68 + 28 * q^70 + 28 * q^71 + 43 * q^73 + 47 * q^74 + 19 * q^76 - 26 * q^77 + 9 * q^79 + 74 * q^80 - 17 * q^82 - 8 * q^83 - 21 * q^85 + 140 * q^86 - 58 * q^88 + 6 * q^89 - 15 * q^91 - 11 * q^92 + 6 * q^94 + 16 * q^95 - 81 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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 $

$2$	0.0518468	+	0.0650138i	0.0366612	+	0.0459717i	0.799824	−	0.600234i	$-0.204926\pi$
$2$	0.0518468	+	0.0650138i	0.0366612	+	0.0459717i	−0.763163	+	0.646206i	$0.776355\pi$
$3$		0			0
$3$		0			0
$4$	0.443503	−	1.94311i	0.221752	−	0.971557i
$5$	−1.20357	−	1.50923i	−0.538253	−	0.674948i	0.436119	−	0.899889i	$-0.356353\pi$
$5$	−1.20357	−	1.50923i	−0.538253	−	0.674948i	−0.974372	+	0.224941i	$0.927781\pi$
$6$		0			0
$7$	−0.0765305	−	0.335302i	−0.0289258	−	0.126732i	0.958404	−	0.285417i	$-0.0921319\pi$
$7$	−0.0765305	−	0.335302i	−0.0289258	−	0.126732i	−0.987329	+	0.158684i	$0.949275\pi$
$8$	0.299165	−	0.144070i	0.105771	−	0.0509365i
$9$		0			0
$10$	0.0357195	−	0.156498i	0.0112955	−	0.0494889i
$11$	−2.18408	−	1.05180i	−0.658525	−	0.317129i	0.0746095	−	0.997213i	$-0.476229\pi$
$11$	−2.18408	−	1.05180i	−0.658525	−	0.317129i	−0.733134	+	0.680084i	$0.761943\pi$
$12$		0			0
$13$	−3.27160	−	1.57552i	−0.907378	−	0.436970i	−0.0788298	−	0.996888i	$-0.525118\pi$
$13$	−3.27160	−	1.57552i	−0.907378	−	0.436970i	−0.828548	+	0.559918i	$0.810833\pi$
$14$	0.0178314	−	0.0223599i	0.00476564	−	0.00597593i
$15$		0			0
$16$	−3.56654	−	1.71755i	−0.891634	−	0.429389i
$17$	6.15354			1.49245			0.746227	−	0.665692i	$-0.231863\pi$
$17$	6.15354			1.49245			0.746227	+	0.665692i	$0.231863\pi$
$18$		0			0
$19$	0.300553	−	1.31681i	0.0689516	−	0.302097i	−0.928680	−	0.370882i	$-0.879055\pi$
$19$	0.300553	−	1.31681i	0.0689516	−	0.302097i	0.997631	+	0.0687856i	$0.0219125\pi$
$20$	−3.46640	+	1.66933i	−0.775110	+	0.373273i
$21$		0			0
$22$	−0.0448561	−	0.196528i	−0.00956336	−	0.0418998i
$23$	2.16114	−	2.70998i	0.450628	−	0.565070i	−0.503681	−	0.863889i	$-0.668021\pi$
$23$	2.16114	−	2.70998i	0.450628	−	0.565070i	0.954310	+	0.298820i	$0.0965929\pi$
$24$		0			0
$25$	0.283411	−	1.24171i	0.0566823	−	0.248341i
$26$	−0.0671914	−	0.294385i	−0.0131773	−	0.0577336i
$27$		0			0
$28$	−0.685471			−0.129542
$29$	4.26305	+	3.29035i	0.791628	+	0.611003i
$29$	4.26305	+	3.29035i	0.791628	+	0.611003i
$30$		0			0
$31$	6.85222	+	8.59242i	1.23070	+	1.54324i	0.741285	+	0.671190i	$0.234217\pi$
$31$	6.85222	+	8.59242i	1.23070	+	1.54324i	0.489411	+	0.872053i	$0.337212\pi$
$32$	−0.221024	−	0.968370i	−0.0390719	−	0.171185i
$33$		0			0
$34$	0.319041	+	0.400065i	0.0547152	+	0.0686106i
$35$	−0.413938	+	0.519062i	−0.0699683	+	0.0877375i
$36$		0			0
$37$	2.78149	−	1.33950i	0.457275	−	0.220212i	−0.191043	−	0.981582i	$-0.561187\pi$
$37$	2.78149	−	1.33950i	0.457275	−	0.220212i	0.648318	+	0.761370i	$0.275473\pi$
$38$	0.101193	−	0.0487322i	0.0164158	−	0.00790541i
$39$		0			0
$40$	−0.577502	−	0.278110i	−0.0913111	−	0.0439731i
$41$	−5.28313			−0.825086			−0.412543	−	0.910938i	$-0.635359\pi$
$41$	−5.28313			−0.825086			−0.412543	+	0.910938i	$0.635359\pi$
$42$		0			0
$43$	−0.00526324	+	0.00659989i	−0.000802636	+	0.00100647i	−0.782233	−	0.622986i	$-0.785919\pi$
$43$	−0.00526324	+	0.00659989i	−0.000802636	+	0.00100647i	0.781430	+	0.623993i	$0.214491\pi$
$44$	−3.01241	+	3.77744i	−0.454138	+	0.569470i
$45$		0			0
$46$	0.288234			0.0424978
$47$	−5.22270	−	2.51512i	−0.761809	−	0.366868i	0.0122968	−	0.999924i	$-0.496086\pi$
$47$	−5.22270	−	2.51512i	−0.761809	−	0.366868i	−0.774105	+	0.633057i	$0.781800\pi$
$48$		0			0
$49$	6.20021	−	2.98586i	0.885745	−	0.426552i
$50$	0.0954221	−	0.0459528i	0.0134947	−	0.00649871i
$51$		0			0
$52$	−4.51238	+	5.65834i	−0.625754	+	0.784671i
$53$	2.58271	+	3.23861i	0.354762	+	0.444857i	0.926905	−	0.375297i	$-0.122459\pi$
$53$	2.58271	+	3.23861i	0.354762	+	0.444857i	−0.572143	+	0.820154i	$0.693888\pi$
$54$		0			0
$55$	1.04129	+	4.56219i	0.140408	+	0.615166i
$56$	−0.0712023	−	0.0892849i	−0.00951481	−	0.0119312i
$57$		0			0
$58$	0.00710697	+	0.447751i	0.000933191	+	0.0587926i
$59$	−5.76819			−0.750955			−0.375477	−	0.926832i	$-0.622521\pi$
$59$	−5.76819			−0.750955			−0.375477	+	0.926832i	$0.622521\pi$
$60$		0			0
$61$	1.38805	+	6.08144i	0.177722	+	0.778649i	0.982679	+	0.185316i	$0.0593310\pi$
$61$	1.38805	+	6.08144i	0.177722	+	0.778649i	−0.804957	+	0.593333i	$0.797812\pi$
$62$	−0.203360	+	0.890979i	−0.0258268	+	0.113154i
$63$		0			0
$64$	−4.88474	+	6.12527i	−0.610593	+	0.765659i
$65$	1.55978	+	6.83384i	0.193467	+	0.847634i
$66$		0			0
$67$	−9.92346	+	4.77889i	−1.21234	+	0.583834i	−0.927170	−	0.374642i	$-0.877766\pi$
$67$	−9.92346	+	4.77889i	−1.21234	+	0.583834i	−0.285174	+	0.958476i	$0.592051\pi$
$68$	2.72912	−	11.9570i	0.330954	−	1.45000i
$69$		0			0
$70$	−0.0552076			−0.00659856
$71$	11.5818	+	5.57748i	1.37450	+	0.661925i	0.967820	−	0.251645i	$-0.0809714\pi$
$71$	11.5818	+	5.57748i	1.37450	+	0.661925i	0.406682	+	0.913570i	$0.366686\pi$
$72$		0			0
$73$	0.286311	−	0.359022i	0.0335102	−	0.0420204i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	0.286311	−	0.359022i	0.0335102	−	0.0420204i	0.798304	+	0.602254i	$0.205731\pi$
$74$	0.231297	+	0.111387i	0.0268878	+	0.0129485i
$75$		0			0
$76$	−2.42541	−	1.16802i	−0.278214	−	0.133981i
$77$	−0.185521	+	0.812820i	−0.0211421	+	0.0926295i
$78$		0			0
$79$	11.2434	−	5.41452i	1.26498	−	0.609181i	0.323491	−	0.946231i	$-0.395143\pi$
$79$	11.2434	−	5.41452i	1.26498	−	0.609181i	0.941487	+	0.337050i	$0.109429\pi$
$80$	1.70040	+	7.44993i	0.190110	+	0.832927i
$81$		0			0
$82$	−0.273913	−	0.343476i	−0.0302487	−	0.0379306i
$83$	0.640518	−	2.80629i	0.0703060	−	0.308031i	−0.927533	−	0.373742i	$-0.878075\pi$
$83$	0.640518	−	2.80629i	0.0703060	−	0.308031i	0.997839	+	0.0657114i	$0.0209317\pi$
$84$		0			0
$85$	−7.40623	−	9.28712i	−0.803318	−	1.00733i
$86$	−0.000701966	0		−7.56950e−5	0
$87$		0			0
$88$	−0.804933			−0.0858061
$89$	7.62150	+	9.55706i	0.807878	+	1.01305i	0.999501	+	0.0315781i	$0.0100533\pi$
$89$	7.62150	+	9.55706i	0.807878	+	1.01305i	−0.191624	+	0.981468i	$0.561375\pi$
$90$		0			0
$91$	−0.277897	+	1.21755i	−0.0291316	+	0.127634i
$92$	−4.30733	−	5.40122i	−0.449070	−	0.563116i
$93$		0			0
$94$	−0.107263	−	0.469948i	−0.0110633	−	0.0484715i
$95$	−2.34911	+	1.13127i	−0.241013	+	0.116066i
$96$		0			0
$97$	0.606191	−	2.65590i	0.0615494	−	0.269666i	−0.934784	−	0.355215i	$-0.884408\pi$
$97$	0.606191	−	2.65590i	0.0615494	−	0.269666i	0.996334	+	0.0855498i	$0.0272647\pi$
$98$	0.515584	+	0.248292i	0.0520818	+	0.0250813i
$99$		0			0
$100$	−2.28708	−	1.10140i	−0.228708	−	0.110140i
$101$	11.3909	−	14.2838i	1.13344	−	1.42129i	0.240765	−	0.970583i	$-0.422602\pi$
$101$	11.3909	−	14.2838i	1.13344	−	1.42129i	0.892673	−	0.450704i	$-0.148827\pi$
$102$		0			0
$103$	14.4782	+	6.97235i	1.42658	+	0.687006i	0.978359	−	0.206916i	$-0.0663425\pi$
$103$	14.4782	+	6.97235i	1.42658	+	0.687006i	0.448224	+	0.893921i	$0.352057\pi$
$104$	−1.20573			−0.118232
$105$		0			0
$106$	−0.0766494	+	0.335823i	−0.00744485	+	0.0326180i
$107$	−14.5741	+	7.01851i	−1.40893	+	0.678505i	−0.974951	−	0.222419i	$-0.928605\pi$
$107$	−14.5741	+	7.01851i	−1.40893	+	0.678505i	−0.433978	+	0.900923i	$0.642890\pi$
$108$		0			0
$109$	−2.04709	−	8.96888i	−0.196075	−	0.859063i	−0.973245	−	0.229771i	$-0.926202\pi$
$109$	−2.04709	−	8.96888i	−0.196075	−	0.859063i	0.777169	−	0.629292i	$-0.216655\pi$
$110$	−0.242618	+	0.304233i	−0.0231327	+	0.0290075i
$111$		0			0
$112$	−0.302950	+	1.32731i	−0.0286261	+	0.125419i
$113$	−4.50744	−	19.7484i	−0.424024	−	1.85777i	−0.508078	−	0.861311i	$-0.669644\pi$
$113$	−4.50744	−	19.7484i	−0.424024	−	1.85777i	0.0840533	−	0.996461i	$-0.473213\pi$
$114$		0			0
$115$	−6.69107			−0.623945
$116$	8.28421	−	6.82431i	0.769169	−	0.633621i
$117$		0			0
$118$	−0.299062	−	0.375012i	−0.0275309	−	0.0345227i
$119$	−0.470934	−	2.06329i	−0.0431704	−	0.189142i
$120$		0			0
$121$	−3.19446	−	4.00573i	−0.290406	−	0.364157i
$122$	−0.323412	+	0.405546i	−0.0292803	+	0.0367164i
$123$		0			0
$124$	19.7350	−	9.50389i	1.77226	−	0.853475i
$125$	−10.9112	+	5.25455i	−0.975926	+	0.469981i
$126$		0			0
$127$	−8.61739	−	4.14992i	−0.764670	−	0.368246i	0.0105441	−	0.999944i	$-0.496644\pi$
$127$	−8.61739	−	4.14992i	−0.764670	−	0.368246i	−0.775214	+	0.631699i	$0.782358\pi$
$128$	−2.63803			−0.233171
$129$		0			0
$130$	−0.363425	+	0.455720i	−0.0318745	+	0.0399693i
$131$	−10.4762	+	13.1367i	−0.915307	+	1.14776i	0.0733108	+	0.997309i	$0.476644\pi$
$131$	−10.4762	+	13.1367i	−0.915307	+	1.14776i	−0.988618	+	0.150449i	$0.951928\pi$
$132$		0			0
$133$	−0.464530			−0.0402799
$134$	−0.825193	−	0.397392i	−0.0712859	−	0.0343295i
$135$		0			0
$136$	1.84093	−	0.886543i	0.157858	−	0.0760204i
$137$	−5.18170	+	2.49538i	−0.442703	+	0.213194i	−0.641937	−	0.766757i	$-0.721869\pi$
$137$	−5.18170	+	2.49538i	−0.442703	+	0.213194i	0.199234	+	0.979952i	$0.436155\pi$
$138$		0			0
$139$	0.976909	−	1.22501i	0.0828603	−	0.103904i	−0.738673	−	0.674064i	$-0.764547\pi$
$139$	0.976909	−	1.22501i	0.0828603	−	0.103904i	0.821534	+	0.570160i	$0.193119\pi$
$140$	0.825014	+	1.03453i	0.0697264	+	0.0874341i
$141$		0			0
$142$	0.237864	+	1.04215i	0.0199611	+	0.0874552i
$143$	5.48830	+	6.88211i	0.458955	+	0.575511i
$144$		0			0
$145$	−0.164981	−	10.3941i	−0.0137009	−	0.863183i
$146$	0.0381857			0.00316027
$147$		0			0
$148$	−1.36919	−	5.99883i	−0.112547	−	0.493101i
$149$	2.81077	−	12.3148i	0.230267	−	1.00887i	−0.719151	−	0.694854i	$-0.755469\pi$
$149$	2.81077	−	12.3148i	0.230267	−	1.00887i	0.949418	−	0.314014i	$-0.101674\pi$
$150$		0			0
$151$	−6.40179	+	8.02760i	−0.520971	+	0.653277i	−0.970815	−	0.239831i	$-0.922908\pi$
$151$	−6.40179	+	8.02760i	−0.520971	+	0.653277i	0.449844	+	0.893107i	$0.351480\pi$
$152$	−0.0997981	−	0.437244i	−0.00809469	−	0.0354652i
$153$		0			0
$154$	−0.0624632	+	0.0300807i	−0.00503343	+	0.00242397i
$155$	4.72080	−	20.6832i	0.379184	−	1.66131i
$156$		0			0
$157$	−3.78665			−0.302207			−0.151104	−	0.988518i	$-0.548283\pi$
$157$	−3.78665			−0.302207			−0.151104	+	0.988518i	$0.548283\pi$
$158$	0.934952	+	0.450249i	0.0743808	+	0.0358199i
$159$		0			0
$160$	−1.19548	+	1.49908i	−0.0945106	+	0.118513i
$161$	−1.07405	−	0.517237i	−0.0846473	−	0.0407640i
$162$		0			0
$163$	5.47952	+	2.63880i	0.429189	+	0.206687i	0.635991	−	0.771696i	$-0.280591\pi$
$163$	5.47952	+	2.63880i	0.429189	+	0.206687i	−0.206802	+	0.978383i	$0.566306\pi$
$164$	−2.34308	+	10.2657i	−0.182964	+	0.801618i
$165$		0			0
$166$	0.215657	−	0.103855i	0.0167382	−	0.00806069i
$167$	−1.70796	−	7.48305i	−0.132166	−	0.579056i	−0.997028	−	0.0770460i	$-0.975451\pi$
$167$	−1.70796	−	7.48305i	−0.132166	−	0.579056i	0.864862	−	0.502010i	$-0.167406\pi$
$168$		0			0
$169$	0.115724	+	0.145113i	0.00890183	+	0.0111625i
$170$	0.219802	−	0.963014i	0.0168580	−	0.0738598i
$171$		0			0
$172$	0.0104901	+	0.0131541i	0.000799861	+	0.00100299i
$173$	14.9932			1.13991			0.569956	−	0.821675i	$-0.306960\pi$
$173$	14.9932			1.13991			0.569956	+	0.821675i	$0.306960\pi$
$174$		0			0
$175$	−0.438036			−0.0331124
$176$	5.98308	+	7.50255i	0.450992	+	0.565526i
$177$		0			0
$178$	−0.226191	+	0.991006i	−0.0169537	+	0.0742790i
$179$	10.0259	+	12.5720i	0.749369	+	0.939679i	0.999594	−	0.0285091i	$-0.00907596\pi$
$179$	10.0259	+	12.5720i	0.749369	+	0.939679i	−0.250225	+	0.968188i	$0.580505\pi$
$180$		0			0
$181$	1.26245	+	5.53117i	0.0938375	+	0.411129i	0.999929	−	0.0119539i	$-0.00380512\pi$
$181$	1.26245	+	5.53117i	0.0938375	+	0.411129i	−0.906091	+	0.423083i	$0.860948\pi$
$182$	−0.0935655	+	0.0450588i	−0.00693554	+	0.00333998i
$183$		0			0
$184$	0.256109	−	1.12209i	0.0188806	−	0.0827213i
$185$	−5.36933	−	2.58573i	−0.394761	−	0.190107i
$186$		0			0
$187$	−13.4398	−	6.47228i	−0.982817	−	0.473300i
$188$	−7.20344	+	9.03283i	−0.525365	+	0.658787i
$189$		0			0
$190$	−0.195342	−	0.0940716i	−0.0141716	−	0.00682467i
$191$	−0.636893			−0.0460839			−0.0230420	−	0.999734i	$-0.507335\pi$
$191$	−0.636893			−0.0460839			−0.0230420	+	0.999734i	$0.507335\pi$
$192$		0			0
$193$	2.52413	−	11.0589i	0.181691	−	0.796039i	−0.799135	−	0.601152i	$-0.794709\pi$
$193$	2.52413	−	11.0589i	0.181691	−	0.796039i	0.980826	−	0.194887i	$-0.0624341\pi$
$194$	0.204099	−	0.0982890i	0.0146535	−	0.00705674i
$195$		0			0
$196$	−3.05206	−	13.3720i	−0.218004	−	0.955140i
$197$	10.5545	−	13.2349i	0.751976	−	0.942949i	−0.247688	−	0.968840i	$-0.579671\pi$
$197$	10.5545	−	13.2349i	0.751976	−	0.942949i	0.999665	+	0.0258911i	$0.00824231\pi$
$198$		0			0
$199$	−1.93102	+	8.46037i	−0.136887	+	0.599740i	0.859222	+	0.511603i	$0.170948\pi$
$199$	−1.93102	+	8.46037i	−0.136887	+	0.599740i	−0.996108	+	0.0881362i	$0.971909\pi$
$200$	−0.0941063	−	0.412306i	−0.00665432	−	0.0291545i
$201$		0			0
$202$	1.51922			0.106892
$203$	0.777008	−	1.68122i	0.0545353	−	0.117999i
$204$		0			0
$205$	6.35862	+	7.97346i	0.444105	+	0.556891i
$206$	0.297351	+	1.30278i	0.0207174	+	0.0907689i
$207$		0			0
$208$	8.96224	+	11.2383i	0.621419	+	0.779235i
$209$	−2.04145	+	2.55989i	−0.141210	+	0.177072i
$210$		0			0
$211$	−11.4887	+	5.53267i	−0.790916	+	0.380885i	−0.785313	−	0.619099i	$-0.787498\pi$
$211$	−11.4887	+	5.53267i	−0.790916	+	0.380885i	−0.00560320	+	0.999984i	$0.501784\pi$
$212$	7.43843	−	3.58216i	0.510873	−	0.246024i
$213$		0			0
$214$	−1.21192	−	0.583629i	−0.0828451	−	0.0398961i
$215$	0.0162954			0.00111134
$216$		0			0
$217$	2.35665	−	2.95515i	0.159980	−	0.200608i
$218$	0.476966	−	0.598096i	0.0323042	−	0.0405082i
$219$		0			0
$220$	9.32667			0.628804
$221$	−20.1319	−	9.69502i	−1.35422	−	0.652158i
$222$		0			0
$223$	−17.2436	+	8.30407i	−1.15472	+	0.556082i	−0.910447	−	0.413626i	$-0.864262\pi$
$223$	−17.2436	+	8.30407i	−1.15472	+	0.556082i	−0.244268	+	0.969708i	$0.578548\pi$
$224$	−0.307781	+	0.148220i	−0.0205645	+	0.00990334i
$225$		0			0
$226$	1.05022	−	1.31694i	0.0698597	−	0.0876013i
$227$	15.4320	+	19.3511i	1.02426	+	1.28438i	0.958060	+	0.286569i	$0.0925148\pi$
$227$	15.4320	+	19.3511i	1.02426	+	1.28438i	0.0661958	+	0.997807i	$0.478914\pi$
$228$		0			0
$229$	4.32439	+	18.9464i	0.285764	+	1.25201i	0.890277	+	0.455419i	$0.150510\pi$
$229$	4.32439	+	18.9464i	0.285764	+	1.25201i	−0.604514	+	0.796595i	$0.706632\pi$
$230$	−0.346910	−	0.435012i	−0.0228746	−	0.0286838i
$231$		0			0
$232$	1.74940	+	0.370180i	0.114854	+	0.0243035i
$233$	−18.2842			−1.19784			−0.598918	−	0.800810i	$-0.704402\pi$
$233$	−18.2842			−1.19784			−0.598918	+	0.800810i	$0.704402\pi$
$234$		0			0
$235$	2.48999	+	10.9094i	0.162429	+	0.711649i
$236$	−2.55821	+	11.2083i	−0.166525	+	0.729596i
$237$		0			0
$238$	0.109726	−	0.137592i	0.00711250	−	0.00891879i
$239$	1.82330	+	7.98840i	0.117939	+	0.516727i	0.999040	+	0.0437983i	$0.0139459\pi$
$239$	1.82330	+	7.98840i	0.117939	+	0.516727i	−0.881101	+	0.472928i	$0.843197\pi$
$240$		0			0
$241$	6.43502	−	3.09894i	0.414516	−	0.199620i	−0.214989	−	0.976616i	$-0.568972\pi$
$241$	6.43502	−	3.09894i	0.414516	−	0.199620i	0.629506	+	0.776996i	$0.283257\pi$
$242$	0.0948052	−	0.415369i	0.00609431	−	0.0267009i
$243$		0			0
$244$	12.4325			0.795912
$245$	−11.9688	−	5.76385i	−0.764656	−	0.368239i
$246$		0			0
$247$	−3.05795	+	3.83454i	−0.194572	+	0.243986i
$248$	3.28786	+	1.58335i	0.208779	+	0.100543i
$249$		0			0
$250$	−0.907328	−	0.436946i	−0.0573845	−	0.0276349i
$251$	0.516642	−	2.26356i	0.0326102	−	0.142874i	−0.956002	−	0.293360i	$-0.905227\pi$
$251$	0.516642	−	2.26356i	0.0326102	−	0.142874i	0.988612	+	0.150486i	$0.0480837\pi$
$252$		0			0
$253$	−7.57044	+	3.64573i	−0.475950	+	0.229205i
$254$	−0.176982	−	0.775409i	−0.0111048	−	0.0486535i
$255$		0			0
$256$	9.63271	+	12.0790i	0.602045	+	0.754940i
$257$	−5.06951	+	22.2110i	−0.316228	+	1.38548i	0.527884	+	0.849316i	$0.322985\pi$
$257$	−5.06951	+	22.2110i	−0.316228	+	1.38548i	−0.844112	+	0.536167i	$0.819872\pi$
$258$		0			0
$259$	−0.662005	−	0.830127i	−0.0411350	−	0.0515816i
$260$	13.9707			0.866426
$261$		0			0
$262$	−1.39722			−0.0863207
$263$	0.595714	+	0.747002i	0.0367333	+	0.0460621i	0.799859	−	0.600188i	$-0.204908\pi$
$263$	0.595714	+	0.747002i	0.0367333	+	0.0460621i	−0.763126	+	0.646250i	$0.776336\pi$
$264$		0			0
$265$	1.77934	−	7.79580i	0.109304	−	0.478892i
$266$	−0.0240844	−	0.0302009i	−0.00147671	−	0.00185173i
$267$		0			0
$268$	4.88484	+	21.4019i	0.298389	+	1.30733i
$269$	13.6464	−	6.57178i	0.832038	−	0.400688i	0.0311589	−	0.999514i	$-0.490080\pi$
$269$	13.6464	−	6.57178i	0.832038	−	0.400688i	0.800879	+	0.598826i	$0.204366\pi$
$270$		0			0
$271$	1.83597	−	8.04392i	0.111527	−	0.488633i	−0.888055	−	0.459737i	$-0.847944\pi$
$271$	1.83597	−	8.04392i	0.111527	−	0.488633i	0.999582	−	0.0288962i	$-0.00919922\pi$
$272$	−21.9468	−	10.5690i	−1.33072	−	0.640842i
$273$		0			0
$274$	−0.430889	−	0.207505i	−0.0260309	−	0.0125358i
$275$	−1.92502	+	2.41389i	−0.116083	+	0.145563i
$276$		0			0
$277$	−15.0761	−	7.26026i	−0.905834	−	0.436227i	−0.0778412	−	0.996966i	$-0.524803\pi$
$277$	−15.0761	−	7.26026i	−0.905834	−	0.436227i	−0.827992	+	0.560739i	$0.810517\pi$
$278$	0.130292			0.00781439
$279$		0			0
$280$	−0.0490544	+	0.214921i	−0.00293156	+	0.0128440i
$281$	−19.9509	+	9.60786i	−1.19017	+	0.573157i	−0.920859	−	0.389896i	$-0.872511\pi$
$281$	−19.9509	+	9.60786i	−1.19017	+	0.573157i	−0.269313	+	0.963053i	$0.586797\pi$
$282$		0			0
$283$	3.92964	+	17.2169i	0.233593	+	1.02344i	0.946633	+	0.322314i	$0.104461\pi$
$283$	3.92964	+	17.2169i	0.233593	+	1.02344i	−0.713040	+	0.701123i	$0.752682\pi$
$284$	15.9742	−	20.0310i	0.947896	−	1.18862i
$285$		0			0
$286$	−0.162882	+	0.713631i	−0.00963139	+	0.0421979i
$287$	0.404320	+	1.77144i	0.0238663	+	0.104565i
$288$		0			0
$289$	20.8661			1.22742
$290$	0.667206	−	0.549627i	0.0391797	−	0.0322752i
$291$		0			0
$292$	−0.570642	−	0.715562i	−0.0333943	−	0.0418751i
$293$	5.15017	+	22.5644i	0.300876	+	1.31823i	0.868808	+	0.495150i	$0.164887\pi$
$293$	5.15017	+	22.5644i	0.300876	+	1.31823i	−0.567931	+	0.823076i	$0.692256\pi$
$294$		0			0
$295$	6.94243	+	8.70553i	0.404204	+	0.506856i
$296$	0.639144	−	0.801461i	0.0371495	−	0.0465840i
$297$		0			0
$298$	0.946362	−	0.455744i	0.0548213	−	0.0264005i
$299$	−11.3400	+	5.46105i	−0.655809	+	0.315821i
$300$		0			0
$301$	0.00261575	+	0.00125968i	0.000150770	+	7.26068e-5i
$302$	−0.853817			−0.0491317
$303$		0			0
$304$	−3.33362	+	4.18023i	−0.191196	+	0.239753i
$305$	7.50768	−	9.41434i	0.429889	−	0.539063i
$306$		0			0
$307$	−22.9984			−1.31259			−0.656293	−	0.754506i	$-0.727876\pi$
$307$	−22.9984			−1.31259			−0.656293	+	0.754506i	$0.727876\pi$
$308$	1.49712	+	0.720977i	0.0853065	+	0.0410815i
$309$		0			0
$310$	1.58945	−	0.765439i	0.0902747	−	0.0434740i
$311$	3.67659	−	1.77055i	0.208480	−	0.100399i	−0.326730	−	0.945118i	$-0.605947\pi$
$311$	3.67659	−	1.77055i	0.208480	−	0.100399i	0.535210	+	0.844719i	$0.320232\pi$
$312$		0			0
$313$	17.9270	−	22.4797i	1.01329	−	1.27063i	0.0509742	−	0.998700i	$-0.483767\pi$
$313$	17.9270	−	22.4797i	1.01329	−	1.27063i	0.962318	−	0.271928i	$-0.0876612\pi$
$314$	−0.196325	−	0.246184i	−0.0110793	−	0.0138930i
$315$		0			0
$316$	−5.53457	−	24.2485i	−0.311344	−	1.36409i
$317$	−7.18877	−	9.01443i	−0.403762	−	0.506301i	0.537832	−	0.843052i	$-0.319243\pi$
$317$	−7.18877	−	9.01443i	−0.403762	−	0.506301i	−0.941594	+	0.336751i	$0.890672\pi$
$318$		0			0
$319$	−5.85005	−	11.6703i	−0.327540	−	0.653409i
$320$	15.1236			0.845434
$321$		0			0
$322$	−0.0220587	−	0.0966455i	−0.00122928	−	0.00538584i
$323$	1.84947	−	8.10304i	0.102907	−	0.450865i
$324$		0			0
$325$	−2.88354	+	3.61584i	−0.159950	+	0.200571i
$326$	0.112537	+	0.493058i	0.00623286	+	0.0273080i
$327$		0			0
$328$	−1.58053	+	0.761142i	−0.0872700	+	0.0420270i
$329$	−0.443628	+	1.94366i	−0.0244580	+	0.107158i
$330$		0			0
$331$	12.3038			0.676277			0.338139	−	0.941096i	$-0.390203\pi$
$331$	12.3038			0.676277			0.338139	+	0.941096i	$0.390203\pi$
$332$	−5.16888	−	2.48920i	−0.283679	−	0.136613i
$333$		0			0
$334$	0.397950	−	0.499013i	0.0217748	−	0.0273048i
$335$	19.1560	+	9.22506i	1.04661	+	0.504019i
$336$		0			0
$337$	−27.5590	−	13.2717i	−1.50123	−	0.722956i	−0.510640	−	0.859794i	$-0.670592\pi$
$337$	−27.5590	−	13.2717i	−1.50123	−	0.722956i	−0.990593	+	0.136838i	$0.956306\pi$
$338$	−0.00343445	+	0.0150473i	−0.000186809	+	0.000818465i
$339$		0			0
$340$	−21.3306	+	10.2723i	−1.15681	+	0.557093i
$341$	−5.92832	−	25.9737i	−0.321037	−	1.40655i
$342$		0			0
$343$	−2.97671	−	3.73267i	−0.160727	−	0.201545i
$344$	−0.000623729		0.00273273i	−3.36292e−5		0.000147339i
$345$		0			0
$346$	0.777349	+	0.974765i	0.0417906	+	0.0524037i
$347$	2.30431			0.123702			0.0618508	−	0.998085i	$-0.480300\pi$
$347$	2.30431			0.123702			0.0618508	+	0.998085i	$0.480300\pi$
$348$		0			0
$349$	9.12305			0.488345			0.244173	−	0.969732i	$-0.421484\pi$
$349$	9.12305			0.488345			0.244173	+	0.969732i	$0.421484\pi$
$350$	−0.0227108	−	0.0284784i	−0.00121394	−	0.00152223i
$351$		0			0
$352$	−0.535795	+	2.34747i	−0.0285579	+	0.125121i
$353$	9.08165	+	11.3880i	0.483368	+	0.606124i	0.962388	−	0.271680i	$-0.0875793\pi$
$353$	9.08165	+	11.3880i	0.483368	+	0.606124i	−0.479020	+	0.877804i	$0.659008\pi$
$354$		0			0
$355$	−5.52177	−	24.1924i	−0.293065	−	1.28400i
$356$	21.9506	−	10.5709i	1.16338	−	0.560255i
$357$		0			0
$358$	−0.297547	+	1.30364i	−0.0157259	+	0.0688995i
$359$	3.37960	+	1.62753i	0.178368	+	0.0858976i	0.520937	−	0.853595i	$-0.325583\pi$
$359$	3.37960	+	1.62753i	0.178368	+	0.0858976i	−0.342569	+	0.939493i	$0.611297\pi$
$360$		0			0
$361$	15.4748	+	7.45225i	0.814461	+	0.392224i
$362$	−0.294148	+	0.368851i	−0.0154601	+	0.0193864i
$363$		0			0
$364$	2.24259	+	1.07997i	0.117543	+	0.0566060i
$365$	−0.886443			−0.0463986
$366$		0			0
$367$	−3.10389	+	13.5990i	−0.162022	+	0.709864i	0.827013	+	0.562182i	$0.190038\pi$
$367$	−3.10389	+	13.5990i	−0.162022	+	0.709864i	−0.989035	+	0.147681i	$0.952819\pi$
$368$	−12.3623	+	5.95338i	−0.644430	+	0.310341i
$369$		0			0
$370$	−0.110274	−	0.483143i	−0.00573288	−	0.0251174i
$371$	0.888257	−	1.11384i	0.0461160	−	0.0578276i
$372$		0			0
$373$	1.70453	−	7.46802i	0.0882571	−	0.386679i	−0.911436	−	0.411441i	$-0.865026\pi$
$373$	1.70453	−	7.46802i	0.0882571	−	0.386679i	0.999693	+	0.0247617i	$0.00788271\pi$
$374$	−0.276024	−	1.20934i	−0.0142729	−	0.0625335i
$375$		0			0
$376$	−1.92480			−0.0992641
$377$	−8.76297	−	17.4812i	−0.451316	−	0.900329i
$378$		0			0
$379$	−7.83725	−	9.82760i	−0.402573	−	0.504810i	0.538681	−	0.842510i	$-0.318923\pi$
$379$	−7.83725	−	9.82760i	−0.402573	−	0.504810i	−0.941254	+	0.337700i	$0.890351\pi$
$380$	1.15635	+	5.06630i	0.0593195	+	0.259896i
$381$		0			0
$382$	−0.0330208	−	0.0414068i	−0.00168949	−	0.00211856i
$383$	−14.6837	+	18.4128i	−0.750305	+	0.940852i	−0.999620	−	0.0275703i	$-0.991223\pi$
$383$	−14.6837	+	18.4128i	−0.750305	+	0.940852i	0.249315	+	0.968422i	$0.419794\pi$
$384$		0			0
$385$	1.45002	−	0.698293i	0.0738999	−	0.0355883i
$386$	0.849851	−	0.409267i	0.0432563	−	0.0208311i
$387$		0			0
$388$	−4.89187	−	2.35580i	−0.248347	−	0.119598i
$389$	21.2485			1.07734			0.538671	−	0.842516i	$-0.318927\pi$
$389$	21.2485			1.07734			0.538671	+	0.842516i	$0.318927\pi$
$390$		0			0
$391$	13.2986	−	16.6760i	0.672542	−	0.843340i
$392$	1.42471	−	1.78653i	0.0719588	−	0.0902335i
$393$		0			0
$394$	1.40767			0.0709173
$395$	−21.7040	−	10.4521i	−1.09204	−	0.525901i
$396$		0			0
$397$	−13.2705	+	6.39072i	−0.666026	+	0.320741i	−0.736171	−	0.676796i	$-0.763368\pi$
$397$	−13.2705	+	6.39072i	−0.666026	+	0.320741i	0.0701450	+	0.997537i	$0.477654\pi$
$398$	−0.650158	+	0.313100i	−0.0325895	+	0.0156943i
$399$		0			0
$400$	−3.14350	+	3.94182i	−0.157175	+	0.197091i
$401$	7.87447	+	9.87428i	0.393233	+	0.493098i	0.938556	−	0.345128i	$-0.112164\pi$
$401$	7.87447	+	9.87428i	0.393233	+	0.493098i	−0.545323	+	0.838226i	$0.683593\pi$
$402$		0			0
$403$	−8.88021	−	38.9067i	−0.442355	−	1.93808i
$404$	−22.7031	−	28.4688i	−1.12952	−	1.41637i
$405$		0			0
$406$	0.149588	−	0.0366496i	0.00742393	−	0.00181889i
$407$	−7.48388			−0.370962
$408$		0			0
$409$	7.51172	+	32.9110i	0.371430	+	1.62734i	0.722766	+	0.691093i	$0.242871\pi$
$409$	7.51172	+	32.9110i	0.371430	+	1.62734i	−0.351335	+	0.936250i	$0.614272\pi$
$410$	−0.188711	+	0.826797i	−0.00931977	+	0.0408326i
$411$		0			0
$412$	19.9692	−	25.0406i	0.983812	−	1.23366i
$413$	0.441443	+	1.93409i	0.0217220	+	0.0951702i
$414$		0			0
$415$	−5.00625	+	2.41088i	−0.245747	+	0.118346i
$416$	−0.802583	+	3.51634i	−0.0393499	+	0.172403i
$417$		0			0
$418$	−0.272271			−0.0133172
$419$	−22.2013	−	10.6916i	−1.08461	−	0.522319i	−0.195819	−	0.980640i	$-0.562737\pi$
$419$	−22.2013	−	10.6916i	−1.08461	−	0.522319i	−0.888787	+	0.458321i	$0.848451\pi$
$420$		0			0
$421$	7.64133	−	9.58193i	0.372416	−	0.466995i	−0.559942	−	0.828532i	$-0.689177\pi$
$421$	7.64133	−	9.58193i	0.372416	−	0.466995i	0.932358	+	0.361537i	$0.117748\pi$
$422$	−0.955354	−	0.460074i	−0.0465059	−	0.0223961i
$423$		0			0
$424$	1.23924	+	0.596788i	0.0601830	+	0.0289826i
$425$	1.74398	−	7.64090i	0.0845957	−	0.370638i
$426$		0			0
$427$	1.93289	−	0.930832i	0.0935392	−	0.0450461i
$428$	7.17411	+	31.4318i	0.346774	+	1.51931i
$429$		0			0
$430$	0.000844866		0.00105943i	4.07431e−5		5.10902e-5i
$431$	−1.86817	+	8.18500i	−0.0899867	+	0.394257i	−0.999784	−	0.0207960i	$-0.993380\pi$
$431$	−1.86817	+	8.18500i	−0.0899867	+	0.394257i	0.909797	+	0.415053i	$0.136237\pi$
$432$		0			0
$433$	5.76203	+	7.22535i	0.276905	+	0.347228i	0.900764	−	0.434309i	$-0.143007\pi$
$433$	5.76203	+	7.22535i	0.276905	+	0.347228i	−0.623859	+	0.781537i	$0.714436\pi$
$434$	0.314310			0.0150874
$435$		0			0
$436$	−18.3354			−0.878108
$437$	−2.91899	−	3.66030i	−0.139634	−	0.175096i
$438$		0			0
$439$	−3.87697	+	16.9861i	−0.185038	+	0.810704i	0.794146	+	0.607727i	$0.207919\pi$
$439$	−3.87697	+	16.9861i	−0.185038	+	0.810704i	−0.979184	+	0.202976i	$0.934939\pi$
$440$	0.968794	+	1.21483i	0.0461854	+	0.0579147i
$441$		0			0
$442$	−0.413465	−	1.81151i	−0.0196665	−	0.0861647i
$443$	26.1256	−	12.5814i	1.24127	−	0.597762i	0.306109	−	0.951997i	$-0.400973\pi$
$443$	26.1256	−	12.5814i	1.24127	−	0.597762i	0.935156	+	0.354235i	$0.115259\pi$
$444$		0			0
$445$	5.25079	−	23.0052i	0.248911	−	1.09055i
$446$	−1.43390	−	0.690532i	−0.0678973	−	0.0326976i
$447$		0			0
$448$	2.42765	+	1.16909i	0.114696	+	0.0552345i
$449$	8.67883	−	10.8829i	0.409579	−	0.513596i	−0.533665	−	0.845696i	$-0.679186\pi$
$449$	8.67883	−	10.8829i	0.409579	−	0.513596i	0.943244	+	0.332100i	$0.107757\pi$
$450$		0			0
$451$	11.5388	+	5.55678i	0.543339	+	0.261658i
$452$	−40.3724			−1.89896
$453$		0			0
$454$	−0.457989	+	2.00658i	−0.0214945	+	0.0941736i
$455$	2.17203	−	1.04599i	0.101826	−	0.0490370i
$456$		0			0
$457$	0.222385	+	0.974330i	0.0104027	+	0.0455773i	0.979863	−	0.199672i	$-0.0639875\pi$
$457$	0.222385	+	0.974330i	0.0104027	+	0.0455773i	−0.969460	+	0.245249i	$0.921130\pi$
$458$	−1.00757	+	1.26346i	−0.0470807	+	0.0590374i
$459$		0			0
$460$	−2.96751	+	13.0015i	−0.138361	+	0.606198i
$461$	3.45431	+	15.1343i	0.160883	+	0.704876i	0.989437	+	0.144966i	$0.0463072\pi$
$461$	3.45431	+	15.1343i	0.160883	+	0.704876i	−0.828553	+	0.559910i	$0.810836\pi$
$462$		0			0
$463$	35.8295			1.66514			0.832568	−	0.553923i	$-0.186870\pi$
$463$	35.8295			1.66514			0.832568	+	0.553923i	$0.186870\pi$
$464$	−9.55296	−	19.0572i	−0.443485	−	0.884708i
$465$		0			0
$466$	−0.947976	−	1.18872i	−0.0439141	−	0.0550666i
$467$	−0.929323	−	4.07163i	−0.0430039	−	0.188413i	0.948864	−	0.315686i	$-0.102235\pi$
$467$	−0.929323	−	4.07163i	−0.0430039	−	0.188413i	−0.991868	+	0.127273i	$0.959377\pi$
$468$		0			0
$469$	2.36182	+	2.96163i	0.109059	+	0.136755i
$470$	−0.580162	+	0.727500i	−0.0267609	+	0.0335571i
$471$		0			0
$472$	−1.72564	+	0.831026i	−0.0794291	+	0.0382510i
$473$	0.0184371	−	0.00887883i	0.000847738	−	0.000408249i
$474$		0			0
$475$	−1.54991	−	0.746397i	−0.0711148	−	0.0342471i
$476$	−4.21808			−0.193335
$477$		0			0
$478$	−0.424824	+	0.532713i	−0.0194310	+	0.0243657i
$479$	11.5627	−	14.4992i	0.528315	−	0.662486i	−0.444037	−	0.896009i	$-0.646454\pi$
$479$	11.5627	−	14.4992i	0.528315	−	0.662486i	0.972351	+	0.233523i	$0.0750254\pi$
$480$		0			0
$481$	−11.2103			−0.511147
$482$	0.535109	+	0.257695i	0.0243736	+	0.0117377i
$483$		0			0
$484$	−9.20035	+	4.43065i	−0.418198	+	0.201393i
$485$	−4.73796	+	2.28168i	−0.215140	+	0.103606i
$486$		0			0
$487$	12.1972	−	15.2948i	0.552708	−	0.693074i	−0.424483	−	0.905436i	$-0.639544\pi$
$487$	12.1972	−	15.2948i	0.552708	−	0.693074i	0.977191	+	0.212362i	$0.0681157\pi$
$488$	1.29141	+	1.61938i	0.0584595	+	0.0733058i
$489$		0			0
$490$	−0.245812	−	1.07697i	−0.0111046	−	0.0486526i
$491$	−1.49134	−	1.87008i	−0.0673030	−	0.0843953i	0.747040	−	0.664779i	$-0.231474\pi$
$491$	−1.49134	−	1.87008i	−0.0673030	−	0.0843953i	−0.814343	+	0.580383i	$0.802903\pi$
$492$		0			0
$493$	26.2329	+	20.2473i	1.18147	+	0.911894i
$494$	−0.407843			−0.0183497
$495$		0			0
$496$	−9.68078	−	42.4142i	−0.434680	−	1.90446i
$497$	0.983782	−	4.31023i	0.0441287	−	0.193340i
$498$		0			0
$499$	−10.8423	+	13.5958i	−0.485367	+	0.608631i	−0.962859	−	0.270005i	$-0.912974\pi$
$499$	−10.8423	+	13.5958i	−0.485367	+	0.608631i	0.477492	+	0.878636i	$0.341546\pi$
$500$	5.37104	+	23.5321i	0.240200	+	1.05239i
$501$		0			0
$502$	0.173949	−	0.0837693i	0.00776371	−	0.00373881i
$503$	4.48348	−	19.6434i	0.199909	−	0.875857i	−0.771081	−	0.636737i	$-0.780284\pi$
$503$	4.48348	−	19.6434i	0.199909	−	0.875857i	0.970990	−	0.239120i	$-0.0768590\pi$
$504$		0			0
$505$	−35.2673			−1.56937
$506$	−0.629526	−	0.303164i	−0.0279858	−	0.0134773i
$507$		0			0
$508$	−11.8856	+	14.9041i	−0.527338	+	0.661261i
$509$	26.0740	+	12.5566i	1.15571	+	0.556560i	0.910743	−	0.412973i	$-0.135509\pi$
$509$	26.0740	+	12.5566i	1.15571	+	0.556560i	0.244964	+	0.969532i	$0.421224\pi$
$510$		0			0
$511$	−0.142292	−	0.0685244i	−0.00629465	−	0.00303134i
$512$	−1.45991	+	6.39630i	−0.0645197	+	0.282679i
$513$		0			0
$514$	−1.70686	+	0.821980i	−0.0752863	+	0.0362560i
$515$	−6.90270	−	30.2427i	−0.304169	−	1.33265i
$516$		0			0
$517$	8.76139	+	10.9864i	0.385325	+	0.483183i
$518$	0.0196469	−	0.0860789i	0.000863237	−	0.00378209i
$519$		0			0
$520$	1.45119	+	1.81973i	0.0636387	+	0.0798004i
$521$	3.28970			0.144125			0.0720623	−	0.997400i	$-0.477042\pi$
$521$	3.28970			0.144125			0.0720623	+	0.997400i	$0.477042\pi$
$522$		0			0
$523$	−0.291341			−0.0127395			−0.00636974	−	0.999980i	$-0.502028\pi$
$523$	−0.291341			−0.0127395			−0.00636974	+	0.999980i	$0.502028\pi$
$524$	20.8799	+	26.1826i	0.912142	+	1.14379i
$525$		0			0
$526$	−0.0176796	+	0.0774593i	−0.000770867	+	0.00337739i
$527$	42.1655	+	52.8738i	1.83676	+	2.30322i
$528$		0			0
$529$	2.44450	+	10.7101i	0.106283	+	0.465655i
$530$	0.599088	−	0.288505i	0.0260227	−	0.0125319i
$531$		0			0
$532$	−0.206021	+	0.902635i	−0.00893212	+	0.0391342i
$533$	17.2843	+	8.32367i	0.748665	+	0.360538i
$534$		0			0
$535$	28.1335	+	13.5484i	1.21632	+	0.585747i
$536$	−2.28026	+	2.85935i	−0.0984921	+	0.123505i
$537$		0			0
$538$	1.13478	+	0.546482i	0.0489239	+	0.0235605i
$539$	−16.6823			−0.718556
$540$		0			0
$541$	−6.15415	+	26.9631i	−0.264588	+	1.15923i	0.651625	+	0.758542i	$0.274088\pi$
$541$	−6.15415	+	26.9631i	−0.264588	+	1.15923i	−0.916212	+	0.400693i	$0.868769\pi$
$542$	0.618155	−	0.297688i	0.0265520	−	0.0127868i
$543$		0			0
$544$	−1.36008	−	5.95891i	−0.0583130	−	0.255486i
$545$	−11.0723	+	13.8842i	−0.474285	+	0.594734i
$546$		0			0
$547$	−1.12752	+	4.93998i	−0.0482091	+	0.211218i	−0.993296	−	0.115602i	$-0.963120\pi$
$547$	−1.12752	+	4.93998i	−0.0482091	+	0.211218i	0.945086	+	0.326821i	$0.105977\pi$
$548$	2.55070	+	11.1754i	0.108961	+	0.477387i
$549$		0			0
$550$	−0.256742			−0.0109475
$551$	5.61404	−	4.62469i	0.239166	−	0.197019i
$552$		0			0
$553$	−2.67596	−	3.35555i	−0.113793	−	0.142692i
$554$	−0.309629	−	1.35657i	−0.0131549	−	0.0576353i
$555$		0			0
$556$	−1.94706	−	2.44154i	−0.0825739	−	0.103544i
$557$	−10.0780	+	12.6374i	−0.427019	+	0.535465i	−0.948070	−	0.318060i	$-0.896969\pi$
$557$	−10.0780	+	12.6374i	−0.427019	+	0.535465i	0.521051	+	0.853525i	$0.325540\pi$
$558$		0			0
$559$	0.0276175	−	0.0132999i	0.00116809	−	0.000562524i
$560$	2.36784	−	1.14029i	0.100060	−	0.0481862i
$561$		0			0
$562$	−1.65904	−	0.798949i	−0.0699822	−	0.0337016i
$563$	−7.45712			−0.314280			−0.157140	−	0.987576i	$-0.550227\pi$
$563$	−7.45712			−0.314280			−0.157140	+	0.987576i	$0.550227\pi$
$564$		0			0
$565$	−24.3799	+	30.5714i	−1.02567	+	1.28615i
$566$	−0.915595	+	1.14812i	−0.0384853	+	0.0482591i
$567$		0			0
$568$	4.26841			0.179098
$569$	15.8967	+	7.65544i	0.666424	+	0.320933i	0.736332	−	0.676621i	$-0.236556\pi$
$569$	15.8967	+	7.65544i	0.666424	+	0.320933i	−0.0699080	+	0.997553i	$0.522271\pi$
$570$		0			0
$571$	−26.3470	+	12.6880i	−1.10259	+	0.530978i	−0.894471	−	0.447126i	$-0.852448\pi$
$571$	−26.3470	+	12.6880i	−1.10259	+	0.530978i	−0.208116	+	0.978104i	$0.566733\pi$
$572$	15.8068	−	7.61216i	0.660916	−	0.318280i
$573$		0			0
$574$	−0.0942056	+	0.118130i	−0.00393206	+	0.00493065i
$575$	−2.75251	−	3.45154i	−0.114788	−	0.143939i
$576$		0			0
$577$	3.80051	+	16.6511i	0.158217	+	0.693196i	0.990347	+	0.138614i	$0.0442647\pi$
$577$	3.80051	+	16.6511i	0.158217	+	0.693196i	−0.832129	+	0.554582i	$0.812878\pi$
$578$	1.08184	+	1.35658i	0.0449986	+	0.0564265i
$579$		0			0
$580$	−20.2701	−	4.28924i	−0.841670	−	0.178101i
$581$	−0.989975			−0.0410711
$582$		0			0
$583$	−2.23447	−	9.78986i	−0.0925424	−	0.405455i
$584$	0.0339297	−	0.148656i	0.00140402	−	0.00615142i
$585$		0			0
$586$	−1.19998	+	1.50472i	−0.0495706	+	0.0621596i
$587$	−7.58007	−	33.2104i	−0.312863	−	1.37074i	−0.849794	−	0.527115i	$-0.823274\pi$
$587$	−7.58007	−	33.2104i	−0.312863	−	1.37074i	0.536931	−	0.843626i	$-0.319584\pi$
$588$		0			0
$589$	13.3740	−	6.44059i	0.551067	−	0.265380i
$590$	−0.206037	+	0.902708i	−0.00848242	+	0.0371639i
$591$		0			0
$592$	−12.2210			−0.502278
$593$	−38.6075	−	18.5924i	−1.58542	−	0.763499i	−0.586501	−	0.809948i	$-0.699495\pi$
$593$	−38.6075	−	18.5924i	−1.58542	−	0.763499i	−0.998921	+	0.0464494i	$0.985209\pi$
$594$		0			0
$595$	−2.54719	+	3.19407i	−0.104424	+	0.130944i
$596$	−22.6825	−	10.9233i	−0.929110	−	0.447436i
$597$		0			0
$598$	−0.942986	−	0.454118i	−0.0385616	−	0.0185703i
$599$	1.26691	−	5.55071i	0.0517646	−	0.226796i	−0.942428	−	0.334408i	$-0.891464\pi$
$599$	1.26691	−	5.55071i	0.0517646	−	0.226796i	0.994193	+	0.107613i	$0.0343207\pi$
$600$		0			0
$601$	8.07342	−	3.88796i	0.329322	−	0.158593i	−0.261915	−	0.965091i	$-0.584354\pi$
$601$	8.07342	−	3.88796i	0.329322	−	0.158593i	0.591237	+	0.806498i	$0.298640\pi$
$602$	5.37218e−5	0	0.000235371i	2.18954e−6	0	9.59299e-6i
$603$		0			0
$604$	12.7593	+	15.9997i	0.519169	+	0.651018i
$605$	−2.20081	+	9.64236i	−0.0894755	+	0.392018i
$606$		0			0
$607$	17.6557	+	22.1395i	0.716621	+	0.898614i	0.998141	−	0.0609410i	$-0.0194101\pi$
$607$	17.6557	+	22.1395i	0.716621	+	0.898614i	−0.281520	+	0.959555i	$0.590839\pi$
$608$	−1.34159			−0.0544086
$609$		0			0
$610$	1.00131			0.0405419
$611$	13.1239	+	16.4569i	0.530938	+	0.665775i
$612$		0			0
$613$	7.12340	−	31.2097i	0.287712	−	1.26055i	−0.599945	−	0.800041i	$-0.704811\pi$
$613$	7.12340	−	31.2097i	0.287712	−	1.26055i	0.887657	−	0.460506i	$-0.152332\pi$
$614$	−1.19239	−	1.49521i	−0.0481210	−	0.0603418i
$615$		0			0
$616$	0.0616019	+	0.269896i	0.00248201	+	0.0108744i
$617$	−5.49638	+	2.64692i	−0.221276	+	0.106561i	−0.541238	−	0.840870i	$-0.682044\pi$
$617$	−5.49638	+	2.64692i	−0.221276	+	0.106561i	0.319962	+	0.947430i	$0.396330\pi$
$618$		0			0
$619$	−0.158208	+	0.693153i	−0.00635890	+	0.0278602i	−0.978008	−	0.208568i	$-0.933120\pi$
$619$	−0.158208	+	0.693153i	−0.00635890	+	0.0278602i	0.971649	+	0.236428i	$0.0759768\pi$
$620$	−38.0961	−	18.3461i	−1.52998	−	0.736797i
$621$		0			0
$622$	0.305730	+	0.147232i	0.0122587	+	0.00590346i
$623$	2.62122	−	3.28691i	0.105017	−	0.131687i
$624$		0			0
$625$	15.3252	+	7.38021i	0.613006	+	0.295208i
$626$	2.39095			0.0955615
$627$		0			0
$628$	−1.67939	+	7.35788i	−0.0670149	+	0.293612i
$629$	17.1160	−	8.24265i	0.682461	−	0.328656i
$630$		0			0
$631$	6.02722	+	26.4070i	0.239940	+	1.05125i	0.941070	+	0.338212i	$0.109822\pi$
$631$	6.02722	+	26.4070i	0.239940	+	1.05125i	−0.701130	+	0.713033i	$0.747321\pi$
$632$	2.58355	−	3.23967i	0.102768	−	0.128867i
$633$		0			0
$634$	0.213348	−	0.934739i	0.00847313	−	0.0371232i
$635$	4.10846	+	18.0003i	0.163039	+	0.714322i
$636$		0			0
$637$	−24.9889			−0.990095
$638$	0.455421	−	0.985399i	0.0180303	−	0.0390123i
$639$		0			0
$640$	3.17506	+	3.98140i	0.125505	+	0.157379i
$641$	6.11273	+	26.7816i	0.241438	+	1.05781i	0.939709	+	0.341976i	$0.111096\pi$
$641$	6.11273	+	26.7816i	0.241438	+	1.05781i	−0.698270	+	0.715834i	$0.746047\pi$
$642$		0			0
$643$	−16.5799	−	20.7905i	−0.653848	−	0.819899i	0.338810	−	0.940855i	$-0.389976\pi$
$643$	−16.5799	−	20.7905i	−0.653848	−	0.819899i	−0.992658	+	0.120956i	$0.961404\pi$
$644$	−1.48140	+	1.85761i	−0.0583752	+	0.0732002i
$645$		0			0
$646$	0.622699	−	0.299876i	0.0244997	−	0.0117985i
$647$	−21.9390	+	10.5653i	−0.862510	+	0.415363i	−0.812206	−	0.583371i	$-0.801733\pi$
$647$	−21.9390	+	10.5653i	−0.862510	+	0.415363i	−0.0503045	+	0.998734i	$0.516019\pi$
$648$		0			0
$649$	12.5982	+	6.06697i	0.494522	+	0.238149i
$650$	−0.384582			−0.0150846
$651$		0			0
$652$	7.55767	−	9.47702i	0.295981	−	0.371149i
$653$	−12.9368	+	16.2223i	−0.506257	+	0.634826i	−0.967628	−	0.252381i	$-0.918786\pi$
$653$	−12.9368	+	16.2223i	−0.506257	+	0.634826i	0.461371	+	0.887207i	$0.347358\pi$
$654$		0			0
$655$	32.4351			1.26734
$656$	18.8425	+	9.07406i	0.735675	+	0.354283i
$657$		0			0
$658$	−0.149366	+	0.0719307i	−0.00582288	+	0.00280415i
$659$	−12.0386	+	5.79749i	−0.468958	+	0.225838i	−0.653411	−	0.757003i	$-0.726663\pi$
$659$	−12.0386	+	5.79749i	−0.468958	+	0.225838i	0.184454	+	0.982841i	$0.440948\pi$
$660$		0			0
$661$	21.5768	−	27.0564i	0.839240	−	1.05237i	−0.158643	−	0.987336i	$-0.550712\pi$
$661$	21.5768	−	27.0564i	0.839240	−	1.05237i	0.997883	−	0.0650374i	$-0.0207167\pi$
$662$	0.637912	+	0.799916i	0.0247932	+	0.0310896i
$663$		0			0
$664$	−0.212683	−	0.931825i	−0.00825370	−	0.0361618i
$665$	0.559095	+	0.701083i	0.0216808	+	0.0271868i
$666$		0			0
$667$	18.1298	−	4.44187i	0.701989	−	0.171990i
$668$	−15.2979			−0.591894
$669$		0			0
$670$	0.393423	+	1.72370i	0.0151992	+	0.0665922i
$671$	3.36483	−	14.7423i	0.129898	−	0.569120i
$672$		0			0
$673$	23.0254	−	28.8729i	0.887562	−	1.11297i	−0.105387	−	0.994431i	$-0.533608\pi$
$673$	23.0254	−	28.8729i	0.887562	−	1.11297i	0.992950	−	0.118537i	$-0.0378204\pi$
$674$	−0.566001	−	2.47981i	−0.0218015	−	0.0955187i
$675$		0			0
$676$	0.333295	−	0.160506i	0.0128190	−	0.00617332i
$677$	−0.875640	+	3.83643i	−0.0336536	+	0.147446i	−0.988963	−	0.148161i	$-0.952665\pi$
$677$	−0.875640	+	3.83643i	−0.0336536	+	0.147446i	0.955310	+	0.295607i	$0.0955218\pi$
$678$		0			0
$679$	−0.936920			−0.0359557
$680$	−3.55368	−	1.71136i	−0.136277	−	0.0656278i
$681$		0			0
$682$	1.38128	−	1.73207i	0.0528921	−	0.0663245i
$683$	3.50044	+	1.68572i	0.133941	+	0.0645024i	0.499654	−	0.866225i	$-0.333461\pi$
$683$	3.50044	+	1.68572i	0.133941	+	0.0645024i	−0.365713	+	0.930728i	$0.619175\pi$
$684$		0			0
$685$	10.0026	+	4.81702i	0.382182	+	0.184049i
$686$	0.0883426	−	0.387054i	0.00337294	−	0.0147778i
$687$		0			0
$688$	0.0301072	−	0.0144989i	0.00114783	−	0.000552764i
$689$	−3.34708	−	14.6645i	−0.127514	−	0.558674i
$690$		0			0
$691$	4.78202	+	5.99646i	0.181917	+	0.228116i	0.864425	−	0.502761i	$-0.167683\pi$
$691$	4.78202	+	5.99646i	0.181917	+	0.228116i	−0.682509	+	0.730877i	$0.739111\pi$
$692$	6.64953	−	29.1335i	0.252777	−	1.10749i
$693$		0			0
$694$	0.119471	+	0.149812i	0.00453505	+	0.00568678i
$695$	−3.02459			−0.114729
$696$		0			0
$697$	−32.5100			−1.23140
$698$	0.473001	+	0.593124i	0.0179033	+	0.0224501i
$699$		0			0
$700$	−0.194270	+	0.851154i	−0.00734273	+	0.0321706i
$701$	−24.5309	−	30.7608i	−0.926520	−	1.16182i	−0.986523	−	0.163621i	$-0.947683\pi$
$701$	−24.5309	−	30.7608i	−0.926520	−	1.16182i	0.0600034	−	0.998198i	$-0.480889\pi$
$702$		0			0
$703$	−0.927874	−	4.06528i	−0.0349954	−	0.153325i
$704$	17.1112	−	8.24033i	0.644903	−	0.310569i
$705$		0			0
$706$	−0.269525	+	1.18087i	−0.0101437	+	0.0444425i
$707$	−5.66113	−	2.72625i	−0.212909	−	0.102531i
$708$		0			0
$709$	−33.8628	−	16.3075i	−1.27175	−	0.612440i	−0.328490	−	0.944508i	$-0.606540\pi$
$709$	−33.8628	−	16.3075i	−1.27175	−	0.612440i	−0.943256	+	0.332067i	$0.892254\pi$
$710$	1.28656	−	1.61329i	0.0482836	−	0.0605457i
$711$		0			0
$712$	3.65698	+	1.76111i	0.137051	+	0.0660003i
$713$	38.0939			1.42663
$714$		0			0
$715$	3.78113	−	16.5662i	0.141406	−	0.619542i
$716$	28.8754	−	13.9057i	1.07913	−	0.519679i
$717$		0			0
$718$	0.0694094	+	0.304102i	0.00259034	+	0.0113490i
$719$	−2.88863	+	3.62223i	−0.107728	+	0.135086i	−0.832772	−	0.553616i	$-0.813248\pi$
$719$	−2.88863	+	3.62223i	−0.107728	+	0.135086i	0.725045	+	0.688702i	$0.241819\pi$
$720$		0			0
$721$	1.22982	−	5.38818i	0.0458007	−	0.200666i
$722$	0.317817	+	1.39245i	0.0118279	+	0.0518216i
$723$		0			0
$724$	11.3076			0.420244
$725$	5.29385	−	4.36093i	0.196609	−	0.161961i
$726$		0			0
$727$	3.43787	+	4.31095i	0.127503	+	0.159884i	0.841485	−	0.540280i	$-0.181682\pi$
$727$	3.43787	+	4.31095i	0.127503	+	0.159884i	−0.713982	+	0.700164i	$0.753110\pi$
$728$	0.0922753	+	0.404285i	0.00341995	+	0.0149838i
$729$		0			0
$730$	−0.0459592	−	0.0576311i	−0.00170103	−	0.00213302i
$731$	−0.0323876	+	0.0406127i	−0.00119790	+	0.00150212i
$732$		0			0
$733$	−39.1400	+	18.8488i	−1.44567	+	0.696197i	−0.981837	−	0.189727i	$-0.939240\pi$
$733$	−39.1400	+	18.8488i	−1.44567	+	0.696197i	−0.463831	+	0.885924i	$0.653525\pi$
$734$	−1.04505	+	0.503271i	−0.0385736	+	0.0185761i
$735$		0			0
$736$	−3.10193	−	1.49381i	−0.114339	−	0.0550625i
$737$	26.7000			0.983509
$738$		0			0
$739$	27.6111	−	34.6233i	1.01569	−	1.27364i	0.0542802	−	0.998526i	$-0.482714\pi$
$739$	27.6111	−	34.6233i	1.01569	−	1.27364i	0.961412	−	0.275112i	$-0.0887150\pi$
$740$	−7.40569	+	9.28645i	−0.272239	+	0.341377i
$741$		0			0
$742$	0.118468			0.00434910
$743$	−31.8973	−	15.3609i	−1.17020	−	0.563538i	−0.255157	−	0.966900i	$-0.582127\pi$
$743$	−31.8973	−	15.3609i	−1.17020	−	0.563538i	−0.915041	+	0.403362i	$0.867842\pi$
$744$		0			0
$745$	−21.9688	+	10.5796i	−0.804876	+	0.387608i
$746$	0.573899	−	0.276375i	0.0210119	−	0.0101188i
$747$		0			0
$748$	−18.5370	+	23.2446i	−0.677779	+	0.849908i
$749$	3.46868	+	4.34959i	0.126743	+	0.158930i
$750$		0			0
$751$	0.791159	+	3.46629i	0.0288698	+	0.126487i	0.987309	−	0.158809i	$-0.0507654\pi$
$751$	0.791159	+	3.46629i	0.0288698	+	0.126487i	−0.958440	+	0.285296i	$0.907908\pi$
$752$	14.3071	+	17.9405i	0.521726	+	0.654224i
$753$		0			0
$754$	0.682189	−	1.47606i	0.0248439	−	0.0537549i
$755$	19.8205			0.721342
$756$		0			0
$757$	−4.80769	−	21.0639i	−0.174739	−	0.765580i	−0.984005	−	0.178139i	$-0.942992\pi$
$757$	−4.80769	−	21.0639i	−0.174739	−	0.765580i	0.809267	−	0.587441i	$-0.199865\pi$
$758$	0.232594	−	1.01906i	0.00844818	−	0.0370139i
$759$		0			0
$760$	−0.539788	+	0.676873i	−0.0195802	+	0.0245528i
$761$	3.67857	+	16.1169i	0.133348	+	0.584236i	0.996809	+	0.0798205i	$0.0254347\pi$
$761$	3.67857	+	16.1169i	0.133348	+	0.584236i	−0.863461	+	0.504415i	$0.831708\pi$
$762$		0			0
$763$	−2.85062	+	1.37278i	−0.103199	+	0.0496981i
$764$	−0.282464	+	1.23755i	−0.0102192	+	0.0447732i
$765$		0			0
$766$	−1.95839			−0.0707597
$767$	18.8712	+	9.08789i	0.681400	+	0.328145i
$768$		0			0
$769$	−0.126258	+	0.158322i	−0.00455298	+	0.00570925i	−0.784103	−	0.620631i	$-0.786877\pi$
$769$	−0.126258	+	0.158322i	−0.00455298	+	0.00570925i	0.779550	+	0.626340i	$0.215448\pi$
$770$	0.120578	+	0.0580671i	0.00434532	+	0.00209259i
$771$		0			0
$772$	−20.3693	−	9.80933i	−0.733107	−	0.353046i
$773$	−3.23009	+	14.1519i	−0.116178	+	0.509010i	0.883033	+	0.469310i	$0.155497\pi$
$773$	−3.23009	+	14.1519i	−0.116178	+	0.509010i	−0.999212	+	0.0397000i	$0.987360\pi$
$774$		0			0
$775$	12.6113	−	6.07326i	0.453010	−	0.218158i
$776$	−0.201285	−	0.881886i	−0.00722570	−	0.0316579i
$777$		0			0
$778$	1.10167	+	1.38145i	0.0394967	+	0.0495272i
$779$	−1.58786	+	6.95687i	−0.0568910	+	0.249256i
$780$		0			0
$781$	−19.4291	−	24.3633i	−0.695228	−	0.871788i
$782$	1.77366			0.0634260
$783$		0			0
$784$	−27.2417			−0.972917
$785$	4.55750	+	5.71492i	0.162664	+	0.203974i
$786$		0			0
$787$	7.58479	−	33.2311i	0.270369	−	1.18456i	−0.639211	−	0.769032i	$-0.720739\pi$
$787$	7.58479	−	33.2311i	0.270369	−	1.18456i	0.909579	−	0.415530i	$-0.136404\pi$
$788$	−21.0360	−	26.3783i	−0.749377	−	0.939688i
$789$		0			0
$790$	−0.445751	−	1.95296i	−0.0158591	−	0.0694834i
$791$	−6.27672	+	3.02271i	−0.223174	+	0.107475i
$792$		0			0
$793$	5.04029	−	22.0829i	0.178986	−	0.784188i
$794$	−1.10352	−	0.531426i	−0.0391624	−	0.0188596i
$795$		0			0
$796$	15.5830	+	7.50440i	0.552326	+	0.265986i
$797$	−8.95279	+	11.2264i	−0.317124	+	0.397661i	−0.914688	−	0.404160i	$-0.867564\pi$
$797$	−8.95279	+	11.2264i	−0.317124	+	0.397661i	0.597564	+	0.801821i	$0.296135\pi$
$798$		0			0
$799$	−32.1381	−	15.4769i	−1.13696	−	0.547533i
$800$	−1.26507			−0.0447271
$801$		0			0
$802$	−0.233698	+	1.02390i	−0.00825218	+	0.0361551i
$803$	−1.00294	+	0.482992i	−0.0353931	+	0.0170444i
$804$		0			0
$805$	0.512070	+	2.24353i	0.0180481	+	0.0790739i
$806$	2.06907	−	2.59453i	0.0728797	−	0.0913883i
$807$		0			0
$808$	1.34990	−	5.91430i	0.0474893	−	0.208064i
$809$	−6.31920	−	27.6862i	−0.222171	−	0.973396i	−0.955840	−	0.293888i	$-0.905051\pi$
$809$	−6.31920	−	27.6862i	−0.222171	−	0.973396i	0.733669	−	0.679508i	$-0.237807\pi$
$810$		0			0
$811$	−41.4768			−1.45645			−0.728224	−	0.685339i	$-0.759654\pi$
$811$	−41.4768			−1.45645			−0.728224	+	0.685339i	$0.759654\pi$
$812$	−2.92220	−	2.25544i	−0.102549	−	0.0791505i
$813$		0			0
$814$	−0.388015	−	0.486555i	−0.0135999	−	0.0170538i
$815$	−2.61244	−	11.4458i	−0.0915098	−	0.400930i
$816$		0			0
$817$	0.00710892	+	0.00891430i	0.000248709	+	0.000311872i
$818$	−1.75021	+	2.19469i	−0.0611947	+	0.0767357i
$819$		0			0
$820$	18.3134	−	8.81927i	0.639532	−	0.307982i
$821$	−40.7646	+	19.6312i	−1.42269	+	0.685133i	−0.977623	−	0.210363i	$-0.932535\pi$
$821$	−40.7646	+	19.6312i	−1.42269	+	0.685133i	−0.445070	+	0.895496i	$0.646821\pi$
$822$		0			0
$823$	1.62926	+	0.784611i	0.0567925	+	0.0273498i	0.462064	−	0.886846i	$-0.347109\pi$
$823$	1.62926	+	0.784611i	0.0567925	+	0.0273498i	−0.405272	+	0.914196i	$0.632823\pi$
$824$	5.33589			0.185885
$825$		0			0
$826$	−0.102855	+	0.128976i	−0.00357878	+	0.00448765i
$827$	14.2992	−	17.9306i	0.497231	−	0.623508i	−0.468371	−	0.883532i	$-0.655159\pi$
$827$	14.2992	−	17.9306i	0.497231	−	0.623508i	0.965602	+	0.260024i	$0.0837304\pi$
$828$		0			0
$829$	−9.99341			−0.347085			−0.173543	−	0.984826i	$-0.555521\pi$
$829$	−9.99341			−0.347085			−0.173543	+	0.984826i	$0.555521\pi$
$830$	−0.416299	−	0.200479i	−0.0144499	−	0.00695873i
$831$		0			0
$832$	25.6314	−	12.3434i	0.888609	−	0.427931i
$833$	38.1533	−	18.3736i	1.32193	−	0.636609i
$834$		0			0
$835$	−9.23801	+	11.5841i	−0.319694	+	0.400884i
$836$	4.06878	+	5.10209i	0.140722	+	0.176459i
$837$		0			0
$838$	−0.455966	−	1.99772i	−0.0157511	−	0.0690100i
$839$	−15.0625	−	18.8878i	−0.520016	−	0.652080i	0.450596	−	0.892728i	$-0.351211\pi$
$839$	−15.0625	−	18.8878i	−0.520016	−	0.652080i	−0.970612	+	0.240648i	$0.922640\pi$
$840$		0			0
$841$	7.34716	+	28.0539i	0.253350	+	0.967375i
$842$	1.01914			0.0351218
$843$		0			0
$844$	5.65534	+	24.7777i	0.194665	+	0.852882i
$845$	0.0797272	−	0.349308i	0.00274270	−	0.0120165i
$846$		0			0
$847$	−1.09866	+	1.37767i	−0.0377502	+	0.0473373i
$848$	−3.64883	−	15.9866i	−0.125301	−	0.548981i
$849$		0			0
$850$	0.587184	−	0.282773i	0.0201402	−	0.00969903i
$851$	2.38118	−	10.4326i	0.0816257	−	0.357626i
$852$		0			0
$853$	12.9629			0.443842			0.221921	−	0.975065i	$-0.428767\pi$
$853$	12.9629			0.443842			0.221921	+	0.975065i	$0.428767\pi$
$854$	0.160731	+	0.0774040i	0.00550011	+	0.00264871i
$855$		0			0
$856$	−3.34890	+	4.19938i	−0.114463	+	0.143532i
$857$	−19.3854	−	9.33554i	−0.662194	−	0.318896i	0.0724268	−	0.997374i	$-0.476926\pi$
$857$	−19.3854	−	9.33554i	−0.662194	−	0.318896i	−0.734621	+	0.678478i	$0.762640\pi$
$858$		0			0
$859$	4.15015	+	1.99861i	0.141601	+	0.0681915i	0.503343	−	0.864087i	$-0.332103\pi$
$859$	4.15015	+	1.99861i	0.141601	+	0.0681915i	−0.361741	+	0.932278i	$0.617818\pi$
$860$	0.00722708	−	0.0316639i	0.000246441	−	0.00107973i
$861$		0			0
$862$	−0.628997	+	0.302909i	−0.0214237	+	0.0103171i
$863$	−4.27980	−	18.7510i	−0.145686	−	0.638292i	−0.994054	−	0.108886i	$-0.965272\pi$
$863$	−4.27980	−	18.7510i	−0.145686	−	0.638292i	0.848368	−	0.529407i	$-0.177585\pi$
$864$		0			0
$865$	−18.0454	−	22.6282i	−0.613561	−	0.769382i
$866$	−0.171005	+	0.749223i	−0.00581099	+	0.0254596i
$867$		0			0
$868$	−4.69700	−	5.88986i	−0.159427	−	0.199915i
$869$	−30.2514			−1.02621
$870$		0			0
$871$	39.9948			1.35517
$872$	−1.90457	−	2.38825i	−0.0644967	−	0.0808763i
$873$		0			0
$874$	0.0866297	−	0.379549i	0.00293029	−	0.0128384i
$875$	2.59690	+	3.25641i	0.0877912	+	0.110087i
$876$		0			0
$877$	6.20282	+	27.1763i	0.209454	+	0.917679i	0.964931	+	0.262504i	$0.0845482\pi$
$877$	6.20282	+	27.1763i	0.209454	+	0.917679i	−0.755477	+	0.655176i	$0.772595\pi$
$878$	−1.30534	+	0.628619i	−0.0440532	+	0.0212149i
$879$		0			0
$880$	4.12201	−	18.0597i	0.138953	−	0.608792i
$881$	25.0177	+	12.0479i	0.842869	+	0.405904i	0.804926	−	0.593375i	$-0.202205\pi$
$881$	25.0177	+	12.0479i	0.842869	+	0.405904i	0.0379434	+	0.999280i	$0.487919\pi$
$882$		0			0
$883$	0.288502	+	0.138935i	0.00970888	+	0.00467555i	0.438732	−	0.898618i	$-0.355428\pi$
$883$	0.288502	+	0.138935i	0.00970888	+	0.00467555i	−0.429023	+	0.903294i	$0.641142\pi$
$884$	−27.7671	+	34.8188i	−0.933909	+	1.17108i
$885$		0			0
$886$	2.17250	+	1.04622i	0.0729864	+	0.0351484i
$887$	24.7909			0.832397			0.416198	−	0.909274i	$-0.363362\pi$
$887$	24.7909			0.832397			0.416198	+	0.909274i	$0.363362\pi$
$888$		0			0
$889$	−0.731982	+	3.20702i	−0.0245499	+	0.107560i
$890$	1.76789	−	0.851373i	0.0592599	−	0.0285381i
$891$		0			0
$892$	8.48817	+	37.1891i	0.284205	+	1.24518i
$893$	−4.88163	+	6.12137i	−0.163357	+	0.204844i
$894$		0			0
$895$	6.90726	−	30.2627i	0.230884	−	1.01157i
$896$	0.201890	+	0.884537i	0.00674467	+	0.0295503i
$897$		0			0
$898$	1.15751			0.0386266
$899$	0.939278	+	59.1761i	0.0313267	+	1.97363i
$900$		0			0
$901$	15.8928	+	19.9289i	0.529466	+	0.663929i
$902$	0.236981	+	1.03828i	0.00789060	+	0.0345710i
$903$		0			0
$904$	−4.19363	−	5.25864i	−0.139478	−	0.174900i
$905$	6.82836	−	8.56249i	0.226982	−	0.284627i
$906$		0			0
$907$	39.6611	−	19.0998i	1.31693	−	0.634198i	0.362316	−	0.932055i	$-0.381986\pi$
$907$	39.6611	−	19.0998i	1.31693	−	0.634198i	0.954611	+	0.297857i	$0.0962718\pi$
$908$	44.4455	−	21.4038i	1.47497	−	0.710310i
$909$		0			0
$910$	0.180617	+	0.0869805i	0.00598739	+	0.00288338i
$911$	−58.6374			−1.94275			−0.971373	−	0.237561i	$-0.923652\pi$
$911$	−58.6374			−1.94275			−0.971373	+	0.237561i	$0.923652\pi$
$912$		0			0
$913$	−4.35059	+	5.45547i	−0.143984	+	0.180550i
$914$	−0.0518150	+	0.0649740i	−0.00171389	+	0.00214915i
$915$		0			0
$916$	38.7329			1.27977
$917$	5.20651	+	2.50732i	0.171934	+	0.0827990i
$918$		0			0
$919$	32.7665	−	15.7795i	1.08087	−	0.520519i	0.193274	−	0.981145i	$-0.438089\pi$
$919$	32.7665	−	15.7795i	1.08087	−	0.520519i	0.887594	+	0.460626i	$0.152375\pi$
$920$	−2.00173	+	0.963984i	−0.0659952	+	0.0317816i
$921$		0			0
$922$	−0.804846	+	1.00924i	−0.0265062	+	0.0332377i
$923$	−29.1034	−	36.4945i	−0.957951	−	1.20123i
$924$		0			0
$925$	−0.874954	−	3.83343i	−0.0287683	−	0.126042i
$926$	1.85764	+	2.32941i	0.0610459	+	0.0765492i
$927$		0			0
$928$	2.24404	−	4.85546i	0.0736643	−	0.159388i
$929$	−0.895129			−0.0293682			−0.0146841	−	0.999892i	$-0.504674\pi$
$929$	−0.895129			−0.0293682			−0.0146841	+	0.999892i	$0.504674\pi$
$930$		0			0
$931$	−2.06832	−	9.06191i	−0.0677865	−	0.296992i
$932$	−8.10909	+	35.5282i	−0.265622	+	1.16377i
$933$		0			0
$934$	0.216530	−	0.271520i	0.00708507	−	0.00888440i
$935$	6.40763	+	28.0736i	0.209552	+	0.918106i
$936$		0			0
$937$	−20.9176	+	10.0734i	−0.683349	+	0.329083i	−0.743148	−	0.669127i	$-0.766668\pi$
$937$	−20.9176	+	10.0734i	−0.683349	+	0.329083i	0.0597994	+	0.998210i	$0.480954\pi$
$938$	−0.0700939	+	0.307102i	−0.00228865	+	0.0100272i
$939$		0			0
$940$	22.3025			0.727427
$941$	23.7548	+	11.4397i	0.774383	+	0.372923i	0.778966	−	0.627066i	$-0.215744\pi$
$941$	23.7548	+	11.4397i	0.774383	+	0.372923i	−0.00458264	+	0.999989i	$0.501459\pi$
$942$		0			0
$943$	−11.4176	+	14.3172i	−0.371807	+	0.466231i
$944$	20.5725	+	9.90719i	0.669577	+	0.322451i
$945$		0			0
$946$	0.00153315		0.000738326i	4.98470e−5		2.40051e-5i
$947$	11.3405	−	49.6860i	0.368517	−	1.61458i	−0.362338	−	0.932047i	$-0.618021\pi$
$947$	11.3405	−	49.6860i	0.368517	−	1.61458i	0.730855	−	0.682533i	$-0.239122\pi$
$948$		0			0
$949$	−1.50234	+	0.723489i	−0.0487680	+	0.0234854i
$950$	−0.0318317	−	0.139464i	−0.00103276	−	0.00452481i
$951$		0			0
$952$	−0.438146	−	0.549418i	−0.0142004	−	0.0178067i
$953$	−5.59449	+	24.5111i	−0.181223	+	0.793991i	0.799826	+	0.600232i	$0.204925\pi$
$953$	−5.59449	+	24.5111i	−0.181223	+	0.793991i	−0.981049	+	0.193759i	$0.937932\pi$
$954$		0			0
$955$	0.766545	+	0.961218i	0.0248048	+	0.0311043i
$956$	16.3310			0.528183
$957$		0			0
$958$	1.54214			0.0498243
$959$	1.23326	+	1.54646i	0.0398241	+	0.0499379i
$960$		0			0
$961$	−19.9785	+	87.5316i	−0.644468	+	2.82360i
$962$	−0.581219	−	0.728826i	−0.0187393	−	0.0234983i
$963$		0			0
$964$	−3.16765	−	13.8784i	−0.102023	−	0.446992i
$965$	−19.7284	+	9.50071i	−0.635081	+	0.305839i
$966$		0			0
$967$	−11.1729	+	48.9516i	−0.359296	+	1.57418i	0.395657	+	0.918398i	$0.370517\pi$
$967$	−11.1729	+	48.9516i	−0.359296	+	1.57418i	−0.754953	+	0.655779i	$0.772340\pi$
$968$	−1.53278	−	0.738147i	−0.0492654	−	0.0237250i
$969$		0			0
$970$	−0.393989	−	0.189735i	−0.0126502	−	0.00609202i
$971$	20.2855	−	25.4372i	0.650991	−	0.816317i	−0.341338	−	0.939941i	$-0.610880\pi$
$971$	20.2855	−	25.4372i	0.650991	−	0.816317i	0.992329	+	0.123623i	$0.0394514\pi$
$972$		0			0
$973$	−0.485510	−	0.233809i	−0.0155647	−	0.00749558i
$974$	1.62676			0.0521247
$975$		0			0
$976$	5.49468	−	24.0738i	0.175880	−	0.770582i
$977$	−29.4287	+	14.1721i	−0.941509	+	0.453407i	−0.840701	−	0.541499i	$-0.817857\pi$
$977$	−29.4287	+	14.1721i	−0.941509	+	0.453407i	−0.100807	+	0.994906i	$0.532143\pi$
$978$		0			0
$979$	−6.59387	−	28.8897i	−0.210741	−	0.923317i
$980$	−16.5080	+	20.7004i	−0.527329	+	0.661249i
$981$		0			0
$982$	0.0442598	−	0.193915i	0.00141239	−	0.00618807i
$983$	0.398538	+	1.74611i	0.0127114	+	0.0556922i	0.980886	−	0.194584i	$-0.0623357\pi$
$983$	0.398538	+	1.74611i	0.0127114	+	0.0556922i	−0.968174	+	0.250276i	$0.919479\pi$
$984$		0			0
$985$	−32.6776			−1.04120
$986$	0.0437331	+	2.75526i	0.00139274	+	0.0877453i
$987$		0			0
$988$	6.09474	+	7.64257i	0.193900	+	0.243142i
$989$	0.00651100	+	0.0285265i	0.000207038	+	0.000907091i
$990$		0			0
$991$	17.8799	+	22.4207i	0.567975	+	0.712218i	0.980010	−	0.198950i	$-0.0637533\pi$
$991$	17.8799	+	22.4207i	0.567975	+	0.712218i	−0.412035	+	0.911168i	$0.635182\pi$
$992$	6.80613	−	8.53462i	0.216095	−	0.270974i
$993$		0			0
$994$	0.331231	−	0.159512i	0.0105060	−	0.00505942i
$995$	15.0928	−	7.26829i	0.478473	−	0.230420i
$996$		0			0
$997$	31.2342	+	15.0416i	0.989198	+	0.476373i	0.857259	−	0.514885i	$-0.172165\pi$
$997$	31.2342	+	15.0416i	0.989198	+	0.476373i	0.131939	+	0.991258i	$0.457880\pi$
$998$	−1.44605			−0.0457739
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.b.82.2		18
3.2	odd	2		87.2.g.b.82.2	yes	18
29.9	even	14		7569.2.a.bk.1.5		9
29.20	even	7		7569.2.a.bl.1.5		9
29.23	even	7	inner	261.2.k.b.226.2		18
87.20	odd	14		2523.2.a.p.1.5		9
87.23	odd	14		87.2.g.b.52.2	✓	18
87.38	odd	14		2523.2.a.q.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.b.52.2	✓	18	87.23	odd	14
87.2.g.b.82.2	yes	18	3.2	odd	2
261.2.k.b.82.2		18	1.1	even	1	trivial
261.2.k.b.226.2		18	29.23	even	7	inner
2523.2.a.p.1.5		9	87.20	odd	14
2523.2.a.q.1.5		9	87.38	odd	14
7569.2.a.bk.1.5		9	29.9	even	14
7569.2.a.bl.1.5		9	29.20	even	7

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0518468 + 0.0650138i) q^{2} +(0.443503 - 1.94311i) q^{4} +(-1.20357 - 1.50923i) q^{5} +(-0.0765305 - 0.335302i) q^{7} +(0.299165 - 0.144070i) q^{8} +O(q^{10})\)	\(q+(0.0518468 + 0.0650138i) q^{2} +(0.443503 - 1.94311i) q^{4} +(-1.20357 - 1.50923i) q^{5} +(-0.0765305 - 0.335302i) q^{7} +(0.299165 - 0.144070i) q^{8} +(0.0357195 - 0.156498i) q^{10} +(-2.18408 - 1.05180i) q^{11} +(-3.27160 - 1.57552i) q^{13} +(0.0178314 - 0.0223599i) q^{14} +(-3.56654 - 1.71755i) q^{16} +6.15354 q^{17} +(0.300553 - 1.31681i) q^{19} +(-3.46640 + 1.66933i) q^{20} +(-0.0448561 - 0.196528i) q^{22} +(2.16114 - 2.70998i) q^{23} +(0.283411 - 1.24171i) q^{25} +(-0.0671914 - 0.294385i) q^{26} -0.685471 q^{28} +(4.26305 + 3.29035i) q^{29} +(6.85222 + 8.59242i) q^{31} +(-0.221024 - 0.968370i) q^{32} +(0.319041 + 0.400065i) q^{34} +(-0.413938 + 0.519062i) q^{35} +(2.78149 - 1.33950i) q^{37} +(0.101193 - 0.0487322i) q^{38} +(-0.577502 - 0.278110i) q^{40} -5.28313 q^{41} +(-0.00526324 + 0.00659989i) q^{43} +(-3.01241 + 3.77744i) q^{44} +0.288234 q^{46} +(-5.22270 - 2.51512i) q^{47} +(6.20021 - 2.98586i) q^{49} +(0.0954221 - 0.0459528i) q^{50} +(-4.51238 + 5.65834i) q^{52} +(2.58271 + 3.23861i) q^{53} +(1.04129 + 4.56219i) q^{55} +(-0.0712023 - 0.0892849i) q^{56} +(0.00710697 + 0.447751i) q^{58} -5.76819 q^{59} +(1.38805 + 6.08144i) q^{61} +(-0.203360 + 0.890979i) q^{62} +(-4.88474 + 6.12527i) q^{64} +(1.55978 + 6.83384i) q^{65} +(-9.92346 + 4.77889i) q^{67} +(2.72912 - 11.9570i) q^{68} -0.0552076 q^{70} +(11.5818 + 5.57748i) q^{71} +(0.286311 - 0.359022i) q^{73} +(0.231297 + 0.111387i) q^{74} +(-2.42541 - 1.16802i) q^{76} +(-0.185521 + 0.812820i) q^{77} +(11.2434 - 5.41452i) q^{79} +(1.70040 + 7.44993i) q^{80} +(-0.273913 - 0.343476i) q^{82} +(0.640518 - 2.80629i) q^{83} +(-7.40623 - 9.28712i) q^{85} -0.000701966 q^{86} -0.804933 q^{88} +(7.62150 + 9.55706i) q^{89} +(-0.277897 + 1.21755i) q^{91} +(-4.30733 - 5.40122i) q^{92} +(-0.107263 - 0.469948i) q^{94} +(-2.34911 + 1.13127i) q^{95} +(0.606191 - 2.65590i) q^{97} +(0.515584 + 0.248292i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8}+O(q^{10}) \) 18 * q + 2 * q^2 - 6 * q^4 + 7 * q^5 - 4 * q^7 + 3 * q^8	\( 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} - 11 q^{13} + 2 q^{14} + 18 q^{16} + 32 q^{17} + 2 q^{19} - 51 q^{20} + 20 q^{22} + 6 q^{23} + 4 q^{25} + 3 q^{26} - 48 q^{28} + 10 q^{29} + 8 q^{31} - 55 q^{32} + 6 q^{34} - 31 q^{35} + 20 q^{37} + 20 q^{38} - 59 q^{40} + 68 q^{41} - 3 q^{43} + 10 q^{44} - 12 q^{46} - 19 q^{47} + 17 q^{49} - 23 q^{50} - 4 q^{52} + q^{53} + 3 q^{55} - 7 q^{56} - 30 q^{58} - 20 q^{59} + 24 q^{61} - 79 q^{62} - 23 q^{64} - 6 q^{65} - 14 q^{67} + 8 q^{68} + 28 q^{70} + 28 q^{71} + 43 q^{73} + 47 q^{74} + 19 q^{76} - 26 q^{77} + 9 q^{79} + 74 q^{80} - 17 q^{82} - 8 q^{83} - 21 q^{85} + 140 q^{86} - 58 q^{88} + 6 q^{89} - 15 q^{91} - 11 q^{92} + 6 q^{94} + 16 q^{95} - 81 q^{97} + 11 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 - 6 * q^4 + 7 * q^5 - 4 * q^7 + 3 * q^8 + 6 * q^10 + 6 * q^11 - 11 * q^13 + 2 * q^14 + 18 * q^16 + 32 * q^17 + 2 * q^19 - 51 * q^20 + 20 * q^22 + 6 * q^23 + 4 * q^25 + 3 * q^26 - 48 * q^28 + 10 * q^29 + 8 * q^31 - 55 * q^32 + 6 * q^34 - 31 * q^35 + 20 * q^37 + 20 * q^38 - 59 * q^40 + 68 * q^41 - 3 * q^43 + 10 * q^44 - 12 * q^46 - 19 * q^47 + 17 * q^49 - 23 * q^50 - 4 * q^52 + q^53 + 3 * q^55 - 7 * q^56 - 30 * q^58 - 20 * q^59 + 24 * q^61 - 79 * q^62 - 23 * q^64 - 6 * q^65 - 14 * q^67 + 8 * q^68 + 28 * q^70 + 28 * q^71 + 43 * q^73 + 47 * q^74 + 19 * q^76 - 26 * q^77 + 9 * q^79 + 74 * q^80 - 17 * q^82 - 8 * q^83 - 21 * q^85 + 140 * q^86 - 58 * q^88 + 6 * q^89 - 15 * q^91 - 11 * q^92 + 6 * q^94 + 16 * q^95 - 81 * q^97 + 11 * q^98

Introduction

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