LMFDB - Embedded newform 891.2.u.b.431.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, degree $8$, not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			431.3
Character	$\chi$	$=$	891.431
Dual form			891.2.u.b.215.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.530442 + 0.589116i) q^{2} +(0.143369 - 1.36406i) q^{4} +(2.46396 + 2.21856i) q^{5} +(-1.94006 - 4.35745i) q^{7} +(2.16231 - 1.57101i) q^{8} +O(q^{10})$	\(q+(0.530442 + 0.589116i) q^{2} +(0.143369 - 1.36406i) q^{4} +(2.46396 + 2.21856i) q^{5} +(-1.94006 - 4.35745i) q^{7} +(2.16231 - 1.57101i) q^{8} +2.62838i q^{10} +(-2.32073 - 2.36943i) q^{11} +(-0.685674 - 3.22584i) q^{13} +(1.53795 - 3.45430i) q^{14} +(-0.610720 - 0.129813i) q^{16} +(0.204370 + 0.628985i) q^{17} +(-2.30484 - 3.17234i) q^{19} +(3.37951 - 3.04292i) q^{20} +(0.164852 - 2.62403i) q^{22} +(-2.58864 + 1.49455i) q^{23} +(0.626454 + 5.96031i) q^{25} +(1.53668 - 2.11506i) q^{26} +(-6.22197 + 2.02164i) q^{28} +(-1.46482 + 0.652180i) q^{29} +(1.72784 - 0.367264i) q^{31} +(-2.92024 - 5.05800i) q^{32} +(-0.262139 + 0.454037i) q^{34} +(4.88704 - 15.0408i) q^{35} +(7.22526 + 5.24946i) q^{37} +(0.646291 - 3.04056i) q^{38} +(8.81323 + 0.926308i) q^{40} +(3.07730 + 1.37010i) q^{41} +(6.23639 + 3.60058i) q^{43} +(-3.56476 + 2.82592i) q^{44} +(-2.25359 - 0.732235i) q^{46} +(-7.26084 + 0.763145i) q^{47} +(-10.5396 + 11.7054i) q^{49} +(-3.17902 + 3.53065i) q^{50} +(-4.49855 + 0.472816i) q^{52} +(2.84114 + 0.923142i) q^{53} +(-0.461481 - 10.9869i) q^{55} +(-11.0406 - 6.37430i) q^{56} +(-1.16121 - 0.517005i) q^{58} +(13.7031 + 1.44025i) q^{59} +(-0.200666 + 0.944061i) q^{61} +(1.13288 + 0.823086i) q^{62} +(1.04485 - 3.21572i) q^{64} +(5.46726 - 9.46957i) q^{65} +(0.535376 + 0.927299i) q^{67} +(0.887274 - 0.188596i) q^{68} +(11.4530 - 5.09922i) q^{70} +(14.2493 - 4.62987i) q^{71} +(5.33171 - 7.33847i) q^{73} +(0.740044 + 7.04105i) q^{74} +(-4.65771 + 2.68913i) q^{76} +(-5.82230 + 14.7093i) q^{77} +(5.76410 - 5.19002i) q^{79} +(-1.21679 - 1.67477i) q^{80} +(0.825180 + 2.53964i) q^{82} +(5.17290 + 1.09953i) q^{83} +(-0.891883 + 2.00320i) q^{85} +(1.18689 + 5.58386i) q^{86} +(-8.74053 - 1.47754i) q^{88} +3.98865i q^{89} +(-12.7262 + 9.24613i) q^{91} +(1.66753 + 3.74533i) q^{92} +(-4.30104 - 3.87267i) q^{94} +(1.35900 - 12.9300i) q^{95} +(-2.46270 - 2.73510i) q^{97} -12.4865 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} - 15 q^{5}+O(q^{10}) $ 32 * q + 4 * q^4 - 15 * q^5	$ 32 q + 4 q^{4} - 15 q^{5} - 33 q^{11} + 12 q^{14} - 16 q^{16} + 36 q^{20} + 15 q^{22} - 18 q^{23} - 13 q^{25} - 10 q^{28} - 15 q^{29} + 8 q^{31} - 22 q^{34} + 18 q^{37} + 105 q^{38} - 15 q^{40} + 75 q^{41} + 40 q^{46} - 36 q^{47} + 12 q^{49} - 15 q^{50} + 40 q^{52} - 16 q^{55} - 60 q^{56} + 24 q^{58} + 39 q^{59} + 30 q^{61} + 48 q^{67} - 165 q^{68} + 41 q^{70} - 70 q^{73} + 15 q^{74} + 42 q^{77} + 60 q^{79} - 66 q^{82} + 60 q^{83} - 80 q^{85} - 6 q^{86} - 24 q^{88} - 60 q^{91} - 42 q^{92} - 100 q^{94} + 60 q^{95} - 24 q^{97}+O(q^{100}) $ 32 * q + 4 * q^4 - 15 * q^5 - 33 * q^11 + 12 * q^14 - 16 * q^16 + 36 * q^20 + 15 * q^22 - 18 * q^23 - 13 * q^25 - 10 * q^28 - 15 * q^29 + 8 * q^31 - 22 * q^34 + 18 * q^37 + 105 * q^38 - 15 * q^40 + 75 * q^41 + 40 * q^46 - 36 * q^47 + 12 * q^49 - 15 * q^50 + 40 * q^52 - 16 * q^55 - 60 * q^56 + 24 * q^58 + 39 * q^59 + 30 * q^61 + 48 * q^67 - 165 * q^68 + 41 * q^70 - 70 * q^73 + 15 * q^74 + 42 * q^77 + 60 * q^79 - 66 * q^82 + 60 * q^83 - 80 * q^85 - 6 * q^86 - 24 * q^88 - 60 * q^91 - 42 * q^92 - 100 * q^94 + 60 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.530442	+	0.589116i	0.375079	+	0.416568i	0.900899	−	0.434028i	$-0.142908\pi$
$2$	0.530442	+	0.589116i	0.375079	+	0.416568i	−0.525820	+	0.850596i	$0.676242\pi$
$3$		0			0
$3$		0			0
$4$	0.143369	−	1.36406i	0.0716843	−	0.682030i
$5$	2.46396	+	2.21856i	1.10192	+	0.992172i	0.999997	−	0.00262067i	$-0.000834187\pi$
$5$	2.46396	+	2.21856i	1.10192	+	0.992172i	0.101922	+	0.994792i	$0.467501\pi$
$6$		0			0
$7$	−1.94006	−	4.35745i	−0.733275	−	1.64696i	−0.762168	−	0.647380i	$-0.775865\pi$
$7$	−1.94006	−	4.35745i	−0.733275	−	1.64696i	0.0288929	−	0.999583i	$-0.490802\pi$
$8$	2.16231	−	1.57101i	0.764491	−	0.555435i
$9$		0			0
$10$			2.62838i			0.831166i
$11$	−2.32073	−	2.36943i	−0.699728	−	0.714409i
$11$	−2.32073	−	2.36943i	−0.699728	−	0.714409i
$12$		0			0
$13$	−0.685674	−	3.22584i	−0.190172	−	0.894688i	−0.964946	−	0.262449i	$-0.915470\pi$
$13$	−0.685674	−	3.22584i	−0.190172	−	0.894688i	0.774774	−	0.632238i	$-0.217864\pi$
$14$	1.53795	−	3.45430i	0.411035	−	0.923200i
$15$		0			0
$16$	−0.610720	−	0.129813i	−0.152680	−	0.0324531i
$17$	0.204370	+	0.628985i	0.0495669	+	0.152551i	0.972776	−	0.231746i	$-0.0744438\pi$
$17$	0.204370	+	0.628985i	0.0495669	+	0.152551i	−0.923209	+	0.384297i	$0.874444\pi$
$18$		0			0
$19$	−2.30484	−	3.17234i	−0.528767	−	0.727785i	0.458175	−	0.888862i	$-0.348503\pi$
$19$	−2.30484	−	3.17234i	−0.528767	−	0.727785i	−0.986942	+	0.161077i	$0.948503\pi$
$20$	3.37951	−	3.04292i	0.755681	−	0.680419i
$21$		0			0
$22$	0.164852	−	2.62403i	0.0351465	−	0.559444i
$23$	−2.58864	+	1.49455i	−0.539769	+	0.311636i	−0.744985	−	0.667081i	$-0.767543\pi$
$23$	−2.58864	+	1.49455i	−0.539769	+	0.311636i	0.205217	+	0.978717i	$0.434210\pi$
$24$		0			0
$25$	0.626454	+	5.96031i	0.125291	+	1.19206i
$26$	1.53668	−	2.11506i	0.301368	−	0.414798i
$27$		0			0
$28$	−6.22197	+	2.02164i	−1.17584	+	0.382054i
$29$	−1.46482	+	0.652180i	−0.272010	+	0.121107i	−0.538209	−	0.842811i	$-0.680899\pi$
$29$	−1.46482	+	0.652180i	−0.272010	+	0.121107i	0.266199	+	0.963918i	$0.414232\pi$
$30$		0			0
$31$	1.72784	−	0.367264i	0.310329	−	0.0659626i	−0.0501143	−	0.998743i	$-0.515959\pi$
$31$	1.72784	−	0.367264i	0.310329	−	0.0659626i	0.360444	+	0.932781i	$0.382625\pi$
$32$	−2.92024	−	5.05800i	−0.516230	−	0.894136i
$33$		0			0
$34$	−0.262139	+	0.454037i	−0.0449564	+	0.0778668i
$35$	4.88704	−	15.0408i	0.826060	−	2.54235i
$36$		0			0
$37$	7.22526	+	5.24946i	1.18783	+	0.863006i	0.993033	−	0.117839i	$-0.0375967\pi$
$37$	7.22526	+	5.24946i	1.18783	+	0.863006i	0.194793	+	0.980844i	$0.437597\pi$
$38$	0.646291	−	3.04056i	0.104842	−	0.493244i
$39$		0			0
$40$	8.81323	+	0.926308i	1.39349	+	0.146462i
$41$	3.07730	+	1.37010i	0.480593	+	0.213974i	0.632710	−	0.774389i	$-0.281942\pi$
$41$	3.07730	+	1.37010i	0.480593	+	0.213974i	−0.152117	+	0.988362i	$0.548609\pi$
$42$		0			0
$43$	6.23639	+	3.60058i	0.951041	+	0.549084i	0.893404	−	0.449254i	$-0.148310\pi$
$43$	6.23639	+	3.60058i	0.951041	+	0.549084i	0.0576370	+	0.998338i	$0.481643\pi$
$44$	−3.56476	+	2.82592i	−0.537408	+	0.426024i
$45$		0			0
$46$	−2.25359	−	0.732235i	−0.332273	−	0.107962i
$47$	−7.26084	+	0.763145i	−1.05910	+	0.111316i	−0.618030	−	0.786155i	$-0.712069\pi$
$47$	−7.26084	+	0.763145i	−1.05910	+	0.111316i	−0.441073	+	0.897471i	$0.645402\pi$
$48$		0			0
$49$	−10.5396	+	11.7054i	−1.50566	+	1.67221i
$50$	−3.17902	+	3.53065i	−0.449581	+	0.499310i
$51$		0			0
$52$	−4.49855	+	0.472816i	−0.623836	+	0.0655678i
$53$	2.84114	+	0.923142i	0.390261	+	0.126803i	0.497573	−	0.867422i	$-0.334225\pi$
$53$	2.84114	+	0.923142i	0.390261	+	0.126803i	−0.107313	+	0.994225i	$0.534225\pi$
$54$		0			0
$55$	−0.461481	−	10.9869i	−0.0622261	−	1.48147i
$56$	−11.0406	−	6.37430i	−1.47536	−	0.851801i
$57$		0			0
$58$	−1.16121	−	0.517005i	−0.152475	−	0.0678861i
$59$	13.7031	+	1.44025i	1.78399	+	0.187505i	0.938220	−	0.346040i	$-0.112474\pi$
$59$	13.7031	+	1.44025i	1.78399	+	0.187505i	0.845772	+	0.533545i	$0.179140\pi$
$60$		0			0
$61$	−0.200666	+	0.944061i	−0.0256927	+	0.120875i	−0.989125	−	0.147077i	$-0.953013\pi$
$61$	−0.200666	+	0.944061i	−0.0256927	+	0.120875i	0.963432	+	0.267952i	$0.0863468\pi$
$62$	1.13288	+	0.823086i	0.143876	+	0.104532i
$63$		0			0
$64$	1.04485	−	3.21572i	0.130606	−	0.401965i
$65$	5.46726	−	9.46957i	0.678130	−	1.17456i
$66$		0			0
$67$	0.535376	+	0.927299i	0.0654066	+	0.113288i	0.896874	−	0.442286i	$-0.145832\pi$
$67$	0.535376	+	0.927299i	0.0654066	+	0.113288i	−0.831468	+	0.555573i	$0.812499\pi$
$68$	0.887274	−	0.188596i	0.107598	−	0.0228706i
$69$		0			0
$70$	11.4530	−	5.09922i	1.36890	−	0.609473i
$71$	14.2493	−	4.62987i	1.69108	−	0.549464i	0.704069	−	0.710131i	$-0.251364\pi$
$71$	14.2493	−	4.62987i	1.69108	−	0.549464i	0.987009	+	0.160667i	$0.0513645\pi$
$72$		0			0
$73$	5.33171	−	7.33847i	0.624030	−	0.858903i	−0.373609	−	0.927586i	$-0.621880\pi$
$73$	5.33171	−	7.33847i	0.624030	−	0.858903i	0.997639	+	0.0686831i	$0.0218797\pi$
$74$	0.740044	+	7.04105i	0.0860283	+	0.818505i
$75$		0			0
$76$	−4.65771	+	2.68913i	−0.534276	+	0.308464i
$77$	−5.82230	+	14.7093i	−0.663513	+	1.67628i
$78$		0			0
$79$	5.76410	−	5.19002i	0.648512	−	0.583923i	−0.277819	−	0.960633i	$-0.589612\pi$
$79$	5.76410	−	5.19002i	0.648512	−	0.583923i	0.926331	+	0.376710i	$0.122945\pi$
$80$	−1.21679	−	1.67477i	−0.136042	−	0.187245i
$81$		0			0
$82$	0.825180	+	2.53964i	0.0911259	+	0.280457i
$83$	5.17290	+	1.09953i	0.567799	+	0.120689i	0.482861	−	0.875697i	$-0.339597\pi$
$83$	5.17290	+	1.09953i	0.567799	+	0.120689i	0.0849379	+	0.996386i	$0.472931\pi$
$84$		0			0
$85$	−0.891883	+	2.00320i	−0.0967383	+	0.217278i
$86$	1.18689	+	5.58386i	0.127985	+	0.602123i
$87$		0			0
$88$	−8.74053	−	1.47754i	−0.931744	−	0.157506i
$89$			3.98865i			0.422796i	0.977400	+	0.211398i	$0.0678016\pi$
$89$			3.98865i			0.422796i	−0.977400	+	0.211398i	$0.932198\pi$
$90$		0			0
$91$	−12.7262	+	9.24613i	−1.33407	+	0.969258i
$92$	1.66753	+	3.74533i	0.173852	+	0.390478i
$93$		0			0
$94$	−4.30104	−	3.87267i	−0.443618	−	0.399436i
$95$	1.35900	−	12.9300i	0.139430	−	1.32659i
$96$		0			0
$97$	−2.46270	−	2.73510i	−0.250049	−	0.277708i	0.605033	−	0.796201i	$-0.293160\pi$
$97$	−2.46270	−	2.73510i	−0.250049	−	0.277708i	−0.855082	+	0.518493i	$0.826493\pi$
$98$	−12.4865			−1.26133
$99$		0			0
$100$	8.22004			0.822004
$101$	4.29094	+	4.76558i	0.426965	+	0.474193i	0.917790	−	0.397065i	$-0.129971\pi$
$101$	4.29094	+	4.76558i	0.426965	+	0.474193i	−0.490825	+	0.871258i	$0.663305\pi$
$102$		0			0
$103$	0.598048	−	5.69005i	0.0589275	−	0.560657i	−0.924732	−	0.380619i	$-0.875711\pi$
$103$	0.598048	−	5.69005i	0.0589275	−	0.560657i	0.983660	−	0.180039i	$-0.0576223\pi$
$104$	−6.55046	−	5.89806i	−0.642326	−	0.578353i
$105$		0			0
$106$	0.963223	+	2.16343i	0.0935564	+	0.210131i
$107$	−8.47423	+	6.15689i	−0.819234	+	0.595209i	−0.916493	−	0.400051i	$-0.868993\pi$
$107$	−8.47423	+	6.15689i	−0.819234	+	0.595209i	0.0972587	+	0.995259i	$0.468993\pi$
$108$		0			0
$109$		−	0.517675i		−	0.0495842i	−0.999693	−	0.0247921i	$-0.992108\pi$
$109$		−	0.517675i		−	0.0495842i	0.999693	−	0.0247921i	$-0.00789239\pi$
$110$	6.22776	−	6.09977i	0.593793	−	0.581590i
$111$		0			0
$112$	0.619183	+	2.91303i	0.0585073	+	0.275255i
$113$	7.81600	−	17.5550i	0.735268	−	1.65144i	−0.0232030	−	0.999731i	$-0.507386\pi$
$113$	7.81600	−	17.5550i	0.735268	−	1.65144i	0.758471	−	0.651707i	$-0.225947\pi$
$114$		0			0
$115$	−9.69407	−	2.06054i	−0.903977	−	0.192146i
$116$	0.679604	+	2.09161i	0.0630997	+	0.194201i
$117$		0			0
$118$	6.42022	+	8.83668i	0.591030	+	0.813482i
$119$	2.34428	−	2.11080i	0.214900	−	0.193497i
$120$		0			0
$121$	−0.228379	+	10.9976i	−0.0207618	+	0.999784i
$122$	−0.662603	+	0.382554i	−0.0599892	+	0.0346348i
$123$		0			0
$124$	−0.253252	−	2.40953i	−0.0227427	−	0.216383i
$125$	−1.93549	+	2.66398i	−0.173116	+	0.238274i
$126$		0			0
$127$	10.9568	−	3.56007i	0.972255	−	0.315905i	0.220529	−	0.975380i	$-0.429222\pi$
$127$	10.9568	−	3.56007i	0.972255	−	0.315905i	0.751726	+	0.659476i	$0.229222\pi$
$128$	−8.22241	+	3.66085i	−0.726765	+	0.323577i
$129$		0			0
$130$	8.47874	−	1.80221i	0.743634	−	0.158064i
$131$	2.87408	+	4.97804i	0.251109	+	0.434934i	0.963831	−	0.266512i	$-0.0858714\pi$
$131$	2.87408	+	4.97804i	0.251109	+	0.434934i	−0.712722	+	0.701446i	$0.752538\pi$
$132$		0			0
$133$	−9.35179	+	16.1978i	−0.810903	+	1.40453i
$134$	−0.262300	+	0.807277i	−0.0226593	+	0.0697381i
$135$		0			0
$136$	1.43005	+	1.03899i	0.122626	+	0.0890928i
$137$	−3.92518	+	18.4665i	−0.335351	+	1.57770i	0.410674	+	0.911782i	$0.365293\pi$
$137$	−3.92518	+	18.4665i	−0.335351	+	1.57770i	−0.746025	+	0.665918i	$0.768040\pi$
$138$		0			0
$139$	0.195732	+	0.0205723i	0.0166018	+	0.00174492i	0.112826	−	0.993615i	$-0.464010\pi$
$139$	0.195732	+	0.0205723i	0.0166018	+	0.00174492i	−0.0962239	+	0.995360i	$0.530676\pi$
$140$	−19.8159	−	8.82259i	−1.67475	−	0.745645i
$141$		0			0
$142$	10.2859	+	5.93859i	0.863177	+	0.498356i
$143$	−6.05213	+	9.11098i	−0.506105	+	0.761898i
$144$		0			0
$145$	−5.05617	−	1.64285i	−0.419892	−	0.136431i
$146$	7.15137	−	0.751640i	0.591852	−	0.0622061i
$147$		0			0
$148$	8.19645	−	9.10308i	0.673744	−	0.748269i
$149$	−3.20146	+	3.55558i	−0.262273	+	0.291284i	−0.859870	−	0.510513i	$-0.829456\pi$
$149$	−3.20146	+	3.55558i	−0.262273	+	0.291284i	0.597597	+	0.801797i	$0.296122\pi$
$150$		0			0
$151$	−16.1527	+	1.69772i	−1.31449	+	0.138158i	−0.735693	−	0.677316i	$-0.763143\pi$
$151$	−16.1527	+	1.69772i	−1.31449	+	0.138158i	−0.578794	+	0.815474i	$0.696476\pi$
$152$	−9.96755	−	3.23865i	−0.808475	−	0.262690i
$153$		0			0
$154$	−11.7539	+	4.37244i	−0.947155	+	0.352341i
$155$	5.07214	+	2.92840i	0.407404	+	0.235215i
$156$		0			0
$157$	0.274867	+	0.122379i	0.0219368	+	0.00976687i	0.417676	−	0.908596i	$-0.362845\pi$
$157$	0.274867	+	0.122379i	0.0219368	+	0.00976687i	−0.395739	+	0.918363i	$0.629511\pi$
$158$	6.11504	+	0.642717i	0.486487	+	0.0511318i
$159$		0			0
$160$	4.02613	−	18.9415i	0.318293	−	1.49745i
$161$	11.5346	+	8.38035i	0.909051	+	0.660464i
$162$		0			0
$163$	−5.47886	+	16.8622i	−0.429138	+	1.32075i	0.469838	+	0.882753i	$0.344312\pi$
$163$	−5.47886	+	16.8622i	−0.429138	+	1.32075i	−0.898976	+	0.437998i	$0.855688\pi$
$164$	2.31009	−	4.00119i	0.180388	−	0.312440i
$165$		0			0
$166$	2.09617	+	3.63067i	0.162694	+	0.281795i
$167$	−14.0537	+	2.98720i	−1.08750	+	0.231156i	−0.716579	−	0.697506i	$-0.754293\pi$
$167$	−14.0537	+	2.98720i	−1.08750	+	0.231156i	−0.370926	+	0.928662i	$0.620960\pi$
$168$		0			0
$169$	1.94018	−	0.863824i	0.149245	−	0.0664480i
$170$	−1.65321	+	0.537161i	−0.126795	+	0.0411983i
$171$		0			0
$172$	5.80552	−	7.99061i	0.442667	−	0.609278i
$173$	1.17428	+	11.1726i	0.0892791	+	0.849434i	0.943911	+	0.330200i	$0.107116\pi$
$173$	1.17428	+	11.1726i	0.0892791	+	0.849434i	−0.854632	+	0.519234i	$0.826217\pi$
$174$		0			0
$175$	24.7564	−	14.2931i	1.87141	−	1.08046i
$176$	1.10974	+	1.74832i	0.0836496	+	0.131784i
$177$		0			0
$178$	−2.34977	+	2.11575i	−0.176123	+	0.158582i
$179$	−3.57441	−	4.91976i	−0.267164	−	0.367720i	0.654266	−	0.756265i	$-0.272978\pi$
$179$	−3.57441	−	4.91976i	−0.267164	−	0.367720i	−0.921430	+	0.388545i	$0.872978\pi$
$180$		0			0
$181$	2.95565	+	9.09656i	0.219692	+	0.676142i	0.998787	+	0.0492363i	$0.0156787\pi$
$181$	2.95565	+	9.09656i	0.219692	+	0.676142i	−0.779095	+	0.626905i	$0.784321\pi$
$182$	−12.1976	−	2.59267i	−0.904143	−	0.192181i
$183$		0			0
$184$	−3.24948	+	7.29845i	−0.239555	+	0.538049i
$185$	6.15652	+	28.9642i	0.452637	+	2.12949i
$186$		0			0
$187$	1.01605	−	1.94395i	0.0743007	−	0.142155i
$188$			10.0136i			0.730320i
$189$		0			0
$190$	8.33812	−	6.05800i	0.604911	−	0.439493i
$191$	−1.33335	−	2.99475i	−0.0964776	−	0.216692i	0.858859	−	0.512212i	$-0.171174\pi$
$191$	−1.33335	−	2.99475i	−0.0964776	−	0.216692i	−0.955337	+	0.295520i	$0.904507\pi$
$192$		0			0
$193$	−8.15534	−	7.34310i	−0.587034	−	0.528568i	0.321210	−	0.947008i	$-0.395910\pi$
$193$	−8.15534	−	7.34310i	−0.587034	−	0.528568i	−0.908244	+	0.418440i	$0.862577\pi$
$194$	0.304973	−	2.90163i	0.0218958	−	0.208325i
$195$		0			0
$196$	14.4559	+	16.0549i	1.03256	+	1.14678i
$197$	−0.0669719			−0.00477155			−0.00238578	−	0.999997i	$-0.500759\pi$
$197$	−0.0669719			−0.00477155			−0.00238578	+	0.999997i	$0.500759\pi$
$198$		0			0
$199$	−14.8726			−1.05429			−0.527145	−	0.849776i	$-0.676737\pi$
$199$	−14.8726			−1.05429			−0.527145	+	0.849776i	$0.676737\pi$
$200$	10.7183	+	11.9039i	0.757897	+	0.841730i
$201$		0			0
$202$	−0.531378	+	5.05572i	−0.0373876	+	0.355719i
$203$	5.68369	+	5.11762i	0.398917	+	0.359186i
$204$		0			0
$205$	4.54269	+	10.2031i	0.317275	+	0.712612i
$206$	3.66933	−	2.66592i	0.255654	−	0.185744i
$207$		0			0
$208$			2.05910i			0.142773i
$209$	−2.16771	+	12.8233i	−0.149944	+	0.887008i
$210$		0			0
$211$	−4.11768	−	19.3722i	−0.283473	−	1.33363i	−0.857367	−	0.514705i	$-0.827901\pi$
$211$	−4.11768	−	19.3722i	−0.283473	−	1.33363i	0.573895	−	0.818929i	$-0.305432\pi$
$212$	1.66655	−	3.74314i	0.114459	−	0.257080i
$213$		0			0
$214$	−8.12220	−	1.72643i	−0.555222	−	0.118016i
$215$	7.37813	+	22.7075i	0.503184	+	1.54864i
$216$		0			0
$217$	−4.95246	−	6.81647i	−0.336195	−	0.462732i
$218$	0.304970	−	0.274596i	0.0206552	−	0.0185980i
$219$		0			0
$220$	−15.0529	−	0.945685i	−1.01487	−	0.0637581i
$221$	1.88888	−	1.09054i	0.127059	−	0.0733578i
$222$		0			0
$223$	−0.538061	−	5.11931i	−0.0360313	−	0.342814i	−0.997655	−	0.0684430i	$-0.978197\pi$
$223$	−0.538061	−	5.11931i	−0.0360313	−	0.342814i	0.961624	−	0.274371i	$-0.0884698\pi$
$224$	−16.3745	+	22.5376i	−1.09407	+	1.50586i
$225$		0			0
$226$	14.4879	−	4.70740i	0.963719	−	0.313131i
$227$	16.4027	−	7.30293i	1.08868	−	0.484713i	0.217694	−	0.976017i	$-0.430146\pi$
$227$	16.4027	−	7.30293i	1.08868	−	0.484713i	0.870988	+	0.491304i	$0.163480\pi$
$228$		0			0
$229$	2.31623	−	0.492330i	0.153061	−	0.0325341i	−0.130744	−	0.991416i	$-0.541737\pi$
$229$	2.31623	−	0.492330i	0.153061	−	0.0325341i	0.283805	+	0.958882i	$0.408403\pi$
$230$	−3.92825	−	6.80392i	−0.259021	−	0.448638i
$231$		0			0
$232$	−2.14281	+	3.71146i	−0.140683	+	0.243669i
$233$	2.74226	−	8.43981i	0.179651	−	0.552910i	−0.820164	−	0.572129i	$-0.806118\pi$
$233$	2.74226	−	8.43981i	0.179651	−	0.552910i	0.999815	+	0.0192185i	$0.00611781\pi$
$234$		0			0
$235$	−19.5835	−	14.2283i	−1.27749	−	0.928151i
$236$	3.92919	−	18.4854i	0.255768	−	1.20330i
$237$		0			0
$238$	2.48701	+	0.261395i	0.161209	+	0.0169437i
$239$	1.07662	+	0.479341i	0.0696405	+	0.0310060i	0.441261	−	0.897379i	$-0.354531\pi$
$239$	1.07662	+	0.479341i	0.0696405	+	0.0310060i	−0.371621	+	0.928385i	$0.621198\pi$
$240$		0			0
$241$	−5.93043	−	3.42393i	−0.382012	−	0.220555i	0.296681	−	0.954977i	$-0.404120\pi$
$241$	−5.93043	−	3.42393i	−0.382012	−	0.220555i	−0.678694	+	0.734422i	$0.737454\pi$
$242$	−6.60002	+	5.69906i	−0.424265	+	0.366350i
$243$		0			0
$244$	1.25899	+	0.409070i	0.0805984	+	0.0261880i
$245$	−51.9386	+	5.45896i	−3.31823	+	0.348760i
$246$		0			0
$247$	−8.65311	+	9.61025i	−0.550584	+	0.611486i
$248$	3.15915	−	3.50859i	0.200606	−	0.222796i
$249$		0			0
$250$	−2.59606	+	0.272857i	−0.164189	+	0.0172570i
$251$	−22.3051	−	7.24736i	−1.40788	−	0.457449i	−0.496152	−	0.868235i	$-0.665254\pi$
$251$	−22.3051	−	7.24736i	−1.40788	−	0.457449i	−0.911732	+	0.410786i	$0.865254\pi$
$252$		0			0
$253$	9.54878	+	2.66514i	0.600326	+	0.167556i
$254$	7.90921	+	4.56639i	0.496268	+	0.286521i
$255$		0			0
$256$	−12.6959	−	5.65260i	−0.793497	−	0.353288i
$257$	−23.5220	−	2.47226i	−1.46726	−	0.154215i	−0.663058	−	0.748568i	$-0.730742\pi$
$257$	−23.5220	−	2.47226i	−1.46726	−	0.154215i	−0.804204	+	0.594353i	$0.797408\pi$
$258$		0			0
$259$	8.85681	−	41.6680i	0.550335	−	2.58912i
$260$	−12.1332	−	8.81531i	−0.752471	−	0.546702i
$261$		0			0
$262$	−1.40811	+	4.33373i	−0.0869935	+	0.267739i
$263$	4.46908	−	7.74068i	0.275575	−	0.477311i	−0.694705	−	0.719295i	$-0.744465\pi$
$263$	4.46908	−	7.74068i	0.275575	−	0.477311i	0.970280	+	0.241984i	$0.0777983\pi$
$264$		0			0
$265$	4.95242	+	8.57784i	0.304225	+	0.526932i
$266$	−14.5030	+	3.08270i	−0.889233	+	0.189012i
$267$		0			0
$268$	1.34165	−	0.597340i	0.0819542	−	0.0364884i
$269$	−5.63805	+	1.83191i	−0.343758	+	0.111694i	−0.475808	−	0.879549i	$-0.657844\pi$
$269$	−5.63805	+	1.83191i	−0.343758	+	0.111694i	0.132050	+	0.991243i	$0.457844\pi$
$270$		0			0
$271$	−15.8509	+	21.8169i	−0.962874	+	1.32528i	−0.0173080	+	0.999850i	$0.505510\pi$
$271$	−15.8509	+	21.8169i	−0.962874	+	1.32528i	−0.945566	+	0.325432i	$0.894490\pi$
$272$	−0.0431625	−	0.410663i	−0.00261711	−	0.0249001i
$273$		0			0
$274$	−12.9610	+	7.48303i	−0.783002	+	0.452066i
$275$	12.6687	−	15.3166i	0.763951	−	0.923628i
$276$		0			0
$277$	18.5815	−	16.7309i	1.11646	−	1.00526i	0.116529	−	0.993187i	$-0.462823\pi$
$277$	18.5815	−	16.7309i	1.11646	−	1.00526i	0.999927	−	0.0120739i	$-0.00384335\pi$
$278$	0.0917051	+	0.126221i	0.00550011	+	0.00757025i
$279$		0			0
$280$	−13.0619	−	40.2003i	−0.780596	−	2.40243i
$281$	19.7838	+	4.20519i	1.18021	+	0.250860i	0.755917	−	0.654667i	$-0.227191\pi$
$281$	19.7838	+	4.20519i	1.18021	+	0.250860i	0.424288	+	0.905527i	$0.360525\pi$
$282$		0			0
$283$	−9.89046	+	22.2143i	−0.587927	+	1.32051i	0.337409	+	0.941358i	$0.390449\pi$
$283$	−9.89046	+	22.2143i	−0.587927	+	1.32051i	−0.925336	+	0.379148i	$0.876217\pi$
$284$	−4.27253	−	20.1007i	−0.253528	−	1.19275i
$285$		0			0
$286$	−8.57773	+	1.26744i	−0.507212	+	0.0749453i
$287$		−	16.0673i		−	0.948420i
$288$		0			0
$289$	13.3994	−	9.73526i	0.788202	−	0.572662i
$290$	−1.71418	−	3.85010i	−0.100660	−	0.226086i
$291$		0			0
$292$	−9.24572	−	8.32488i	−0.541065	−	0.487177i
$293$	0.279160	−	2.65603i	0.0163087	−	0.155167i	−0.983337	−	0.181793i	$-0.941810\pi$
$293$	0.279160	−	2.65603i	0.0163087	−	0.155167i	0.999645	+	0.0266264i	$0.00847645\pi$
$294$		0			0
$295$	30.5687	+	33.9499i	1.77978	+	1.97664i
$296$	23.8702			1.38743
$297$		0			0
$298$	−3.79283			−0.219713
$299$	6.59615	+	7.32577i	0.381465	+	0.423660i
$300$		0			0
$301$	3.59038	−	34.1602i	0.206946	−	1.96896i
$302$	−9.56821	−	8.61526i	−0.550589	−	0.495752i
$303$		0			0
$304$	0.995803	+	2.23661i	0.0571132	+	0.128278i
$305$	−2.58889	+	1.88094i	−0.148240	+	0.107702i
$306$		0			0
$307$		−	4.02205i		−	0.229551i	−0.993391	−	0.114775i	$-0.963385\pi$
$307$		−	4.02205i		−	0.229551i	0.993391	−	0.114775i	$-0.0366148\pi$
$308$	19.2297	+	10.0508i	1.09571	+	0.572699i
$309$		0			0
$310$	0.965309	+	4.54142i	0.0548259	+	0.257935i
$311$	−6.42118	+	14.4222i	−0.364112	+	0.817808i	0.634867	+	0.772622i	$0.281055\pi$
$311$	−6.42118	+	14.4222i	−0.364112	+	0.817808i	−0.998979	+	0.0451868i	$0.985612\pi$
$312$		0			0
$313$	−16.0923	−	3.42052i	−0.909590	−	0.193339i	−0.270723	−	0.962657i	$-0.587263\pi$
$313$	−16.0923	−	3.42052i	−0.909590	−	0.193339i	−0.638866	+	0.769318i	$0.720596\pi$
$314$	0.0737057	+	0.226843i	0.00415946	+	0.0128015i
$315$		0			0
$316$	−6.25311	−	8.60667i	−0.351765	−	0.484163i
$317$	−1.38696	+	1.24883i	−0.0778996	+	0.0701411i	−0.707161	−	0.707053i	$-0.750024\pi$
$317$	−1.38696	+	1.24883i	−0.0778996	+	0.0701411i	0.629261	+	0.777194i	$0.283358\pi$
$318$		0			0
$319$	4.94476	+	1.95725i	0.276853	+	0.109585i
$320$	9.70875	−	5.60535i	0.542736	−	0.313349i
$321$		0			0
$322$	1.18142	+	11.2405i	0.0658381	+	0.626407i
$323$	1.52432	−	2.09804i	0.0848152	−	0.116738i
$324$		0			0
$325$	18.7975	−	6.10767i	1.04270	−	0.338793i
$326$	−12.8400	+	5.71674i	−0.711142	+	0.316621i
$327$		0			0
$328$	8.80650	−	1.87188i	0.486258	−	0.103357i
$329$	17.4119	+	30.1582i	0.959947	+	1.66268i
$330$		0			0
$331$	9.96555	−	17.2608i	0.547756	−	0.948742i	−0.450672	−	0.892690i	$-0.648815\pi$
$331$	9.96555	−	17.2608i	0.547756	−	0.948742i	0.998428	−	0.0560518i	$-0.0178512\pi$
$332$	2.24146	−	6.89851i	0.123016	−	0.378605i
$333$		0			0
$334$	−9.21445	−	6.69469i	−0.504192	−	0.366317i
$335$	−0.738123	+	3.47260i	−0.0403280	+	0.189728i
$336$		0			0
$337$	−20.5345	−	2.15827i	−1.11859	−	0.117568i	−0.472861	−	0.881137i	$-0.656779\pi$
$337$	−20.5345	−	2.15827i	−1.11859	−	0.117568i	−0.645726	+	0.763569i	$0.723445\pi$
$338$	1.53805	+	0.684782i	0.0836587	+	0.0372472i
$339$		0			0
$340$	2.60462	+	1.50378i	0.141255	+	0.0815539i
$341$	−4.88007	−	3.24167i	−0.264270	−	0.175546i
$342$		0			0
$343$	39.6989	+	12.8989i	2.14354	+	0.696477i
$344$	19.1415	−	2.01186i	1.03204	−	0.108472i
$345$		0			0
$346$	−5.95904	+	6.61818i	−0.320360	+	0.355796i
$347$	2.29997	−	2.55438i	0.123469	−	0.137126i	−0.678241	−	0.734840i	$-0.737257\pi$
$347$	2.29997	−	2.55438i	0.123469	−	0.137126i	0.801710	+	0.597714i	$0.203924\pi$
$348$		0			0
$349$	23.0294	−	2.42048i	1.23273	−	0.129566i	0.534334	−	0.845273i	$-0.320562\pi$
$349$	23.0294	−	2.42048i	1.23273	−	0.129566i	0.698400	+	0.715708i	$0.253896\pi$
$350$	21.5521	+	7.00272i	1.15201	+	0.374311i
$351$		0			0
$352$	−5.20747	+	18.6576i	−0.277559	+	0.994451i
$353$	0.415567	+	0.239928i	0.0221184	+	0.0127701i	0.511018	−	0.859570i	$-0.329268\pi$
$353$	0.415567	+	0.239928i	0.0221184	+	0.0127701i	−0.488900	+	0.872340i	$0.662602\pi$
$354$		0			0
$355$	45.3814	+	20.2051i	2.40859	+	1.07237i
$356$	5.44076	+	0.571847i	0.288360	+	0.0303078i
$357$		0			0
$358$	1.00229	−	4.71539i	0.0529725	−	0.249216i
$359$	26.8228	+	19.4879i	1.41565	+	1.02853i	0.992470	+	0.122490i	$0.0390880\pi$
$359$	26.8228	+	19.4879i	1.41565	+	1.02853i	0.423185	+	0.906043i	$0.360912\pi$
$360$		0			0
$361$	1.11986	−	3.44658i	0.0589400	−	0.181399i
$362$	−3.79112	+	6.56641i	−0.199257	+	0.345123i
$363$		0			0
$364$	10.7877	+	18.6849i	0.565431	+	0.979356i
$365$	29.4180	−	6.25299i	1.53981	−	0.327297i
$366$		0			0
$367$	−20.4242	+	9.09344i	−1.06613	+	0.474674i	−0.863379	−	0.504555i	$-0.831656\pi$
$367$	−20.4242	+	9.09344i	−1.06613	+	0.474674i	−0.202756	+	0.979229i	$0.564990\pi$
$368$	1.77495	−	0.576715i	0.0925254	−	0.0300633i
$369$		0			0
$370$	−13.7976	+	18.9907i	−0.717301	+	0.987280i
$371$	−1.48944	−	14.1711i	−0.0773279	−	0.735726i
$372$		0			0
$373$	11.6985	−	6.75413i	0.605725	−	0.349716i	−0.165565	−	0.986199i	$-0.552945\pi$
$373$	11.6985	−	6.75413i	0.605725	−	0.349716i	0.771291	+	0.636483i	$0.219612\pi$
$374$	1.68416	−	0.432582i	0.0870860	−	0.0223683i
$375$		0			0
$376$	−14.5013	+	13.0570i	−0.747846	+	0.673363i
$377$	3.10822	+	4.27810i	0.160081	+	0.220333i
$378$		0			0
$379$	2.40016	+	7.38694i	0.123288	+	0.379442i	0.993585	−	0.113085i	$-0.0360733\pi$
$379$	2.40016	+	7.38694i	0.123288	+	0.379442i	−0.870297	+	0.492527i	$0.836073\pi$
$380$	−17.4424	−	3.70750i	−0.894778	−	0.190191i
$381$		0			0
$382$	1.05699	−	2.37404i	0.0540803	−	0.121466i
$383$	−4.47221	−	21.0401i	−0.228519	−	1.07510i	−0.931458	−	0.363849i	$-0.881463\pi$
$383$	−4.47221	−	21.0401i	−0.228519	−	1.07510i	0.702939	−	0.711250i	$-0.251871\pi$
$384$		0			0
$385$	−46.9795	+	23.3261i	−2.39430	+	1.18881i
$386$		−	8.69953i		−	0.442794i
$387$		0			0
$388$	−4.08392	+	2.96714i	−0.207330	+	0.150634i
$389$	−5.10223	−	11.4598i	−0.258693	−	0.581035i	0.736774	−	0.676139i	$-0.236348\pi$
$389$	−5.10223	−	11.4598i	−0.258693	−	0.581035i	−0.995467	+	0.0951044i	$0.969681\pi$
$390$		0			0
$391$	−1.46909	−	1.32277i	−0.0742950	−	0.0668956i
$392$	−4.40057	+	41.8686i	−0.222262	+	2.11468i
$393$		0			0
$394$	−0.0355247	−	0.0394542i	−0.00178971	−	0.00198767i
$395$	25.7169			1.29396
$396$		0			0
$397$	−17.7862			−0.892665			−0.446333	−	0.894867i	$-0.647270\pi$
$397$	−17.7862			−0.892665			−0.446333	+	0.894867i	$0.647270\pi$
$398$	−7.88904	−	8.76167i	−0.395442	−	0.439183i
$399$		0			0
$400$	0.391135	−	3.72140i	0.0195568	−	0.186070i
$401$	7.48914	+	6.74325i	0.373990	+	0.336742i	0.834596	−	0.550863i	$-0.185701\pi$
$401$	7.48914	+	6.74325i	0.373990	+	0.336742i	−0.460606	+	0.887605i	$0.652368\pi$
$402$		0			0
$403$	−2.36947	−	5.32192i	−0.118032	−	0.265104i
$404$	7.11572	−	5.16987i	0.354020	−	0.257211i
$405$		0			0
$406$			6.06295i			0.300899i
$407$	−4.32970	−	29.3023i	−0.214615	−	1.45246i
$408$		0			0
$409$	2.50978	+	11.8076i	0.124101	+	0.583848i	0.995620	+	0.0934874i	$0.0298015\pi$
$409$	2.50978	+	11.8076i	0.124101	+	0.583848i	−0.871520	+	0.490360i	$0.836865\pi$
$410$	−3.60114	+	8.08830i	−0.177848	+	0.399453i
$411$		0			0
$412$	−7.67583	−	1.63155i	−0.378161	−	0.0803806i
$413$	−20.3090	−	62.5048i	−0.999342	−	3.07566i
$414$		0			0
$415$	10.3065	+	14.1856i	0.505924	+	0.696344i
$416$	−14.3140	+	12.8884i	−0.701800	+	0.631904i
$417$		0			0
$418$	−8.70426	+	5.52500i	−0.425739	+	0.270236i
$419$	14.9620	−	8.63832i	0.730942	−	0.422010i	−0.0878247	−	0.996136i	$-0.527992\pi$
$419$	14.9620	−	8.63832i	0.730942	−	0.422010i	0.818767	+	0.574126i	$0.194658\pi$
$420$		0			0
$421$	2.53689	+	24.1369i	0.123641	+	1.17636i	0.863766	+	0.503893i	$0.168100\pi$
$421$	2.53689	+	24.1369i	0.123641	+	1.17636i	−0.740125	+	0.672469i	$0.765234\pi$
$422$	9.22825	−	12.7016i	0.449224	−	0.618304i
$423$		0			0
$424$	7.59368	−	2.46734i	0.368782	−	0.119824i
$425$	−3.62092	+	1.61214i	−0.175640	+	0.0782001i
$426$		0			0
$427$	4.50301	−	0.957143i	0.217916	−	0.0463194i
$428$	7.18343	+	12.4421i	0.347224	+	0.601410i
$429$		0			0
$430$	−9.46370	+	16.3916i	−0.456380	+	0.790474i
$431$	−6.57416	+	20.2332i	−0.316666	+	0.974598i	0.658397	+	0.752671i	$0.271235\pi$
$431$	−6.57416	+	20.2332i	−0.316666	+	0.974598i	−0.975063	+	0.221927i	$0.928765\pi$
$432$		0			0
$433$	11.7221	+	8.51659i	0.563327	+	0.409281i	0.832675	−	0.553762i	$-0.186808\pi$
$433$	11.7221	+	8.51659i	0.563327	+	0.409281i	−0.269348	+	0.963043i	$0.586808\pi$
$434$	1.38870	−	6.53331i	0.0666597	−	0.313609i
$435$		0			0
$436$	−0.706140	−	0.0742183i	−0.0338180	−	0.00355441i
$437$	10.7076	+	4.76735i	0.512216	+	0.228053i
$438$		0			0
$439$	20.6688	+	11.9331i	0.986467	+	0.569537i	0.904216	−	0.427075i	$-0.140456\pi$
$439$	20.6688	+	11.9331i	0.986467	+	0.569537i	0.0822508	+	0.996612i	$0.473789\pi$
$440$	−18.2583	−	23.0320i	−0.870433	−	1.09801i
$441$		0			0
$442$	1.64439	+	0.534296i	0.0782159	+	0.0254139i
$443$	25.7704	−	2.70858i	1.22439	−	0.128688i	0.529816	−	0.848112i	$-0.322261\pi$
$443$	25.7704	−	2.70858i	1.22439	−	0.128688i	0.694571	+	0.719424i	$0.255594\pi$
$444$		0			0
$445$	−8.84907	+	9.82789i	−0.419486	+	0.465886i
$446$	2.73046	−	3.03248i	0.129291	−	0.143592i
$447$		0			0
$448$	−16.0394	+	1.68581i	−0.757791	+	0.0796471i
$449$	−10.5364	−	3.42348i	−0.497243	−	0.161564i	0.0496500	−	0.998767i	$-0.484189\pi$
$449$	−10.5364	−	3.42348i	−0.497243	−	0.161564i	−0.546893	+	0.837203i	$0.684189\pi$
$450$		0			0
$451$	−3.89523	−	10.4711i	−0.183419	−	0.493064i
$452$	−22.8256	−	13.1783i	−1.07362	−	0.619857i
$453$		0			0
$454$	13.0029	+	5.78928i	0.610258	+	0.271704i
$455$	−51.8700	−	5.45176i	−2.43170	−	0.255582i
$456$		0			0
$457$	8.20829	−	38.6169i	0.383967	−	1.80642i	−0.183490	−	0.983022i	$-0.558739\pi$
$457$	8.20829	−	38.6169i	0.383967	−	1.80642i	0.567457	−	0.823403i	$-0.307927\pi$
$458$	1.51867	+	1.10338i	0.0709626	+	0.0515573i
$459$		0			0
$460$	−4.20052	+	12.9279i	−0.195850	+	0.602766i
$461$	−8.22340	+	14.2433i	−0.383002	+	0.663379i	−0.991490	−	0.130184i	$-0.958443\pi$
$461$	−8.22340	+	14.2433i	−0.383002	+	0.663379i	0.608488	+	0.793563i	$0.291776\pi$
$462$		0			0
$463$	−4.13046	−	7.15417i	−0.191959	−	0.332482i	0.753941	−	0.656943i	$-0.228151\pi$
$463$	−4.13046	−	7.15417i	−0.191959	−	0.332482i	−0.945899	+	0.324460i	$0.894817\pi$
$464$	0.979257	−	0.208147i	0.0454608	−	0.00966300i
$465$		0			0
$466$	6.42663	−	2.86132i	0.297708	−	0.132548i
$467$	33.3479	−	10.8354i	1.54316	−	0.501402i	0.590912	−	0.806736i	$-0.298768\pi$
$467$	33.3479	−	10.8354i	1.54316	−	0.501402i	0.952245	+	0.305334i	$0.0987682\pi$
$468$		0			0
$469$	3.00200	−	4.13189i	0.138619	−	0.190793i
$470$	−2.00584	−	19.0842i	−0.0925223	−	0.880291i
$471$		0			0
$472$	31.8930	−	18.4134i	1.46799	−	0.847546i
$473$	−5.94169	−	23.1327i	−0.273199	−	1.06364i
$474$		0			0
$475$	17.4643	−	15.7249i	0.801316	−	0.721508i
$476$	−2.54316	−	3.50036i	−0.116566	−	0.160439i
$477$		0			0
$478$	0.288696	+	0.888514i	0.0132046	+	0.0406397i
$479$	25.1354	+	5.34269i	1.14846	+	0.244114i	0.742546	−	0.669795i	$-0.233618\pi$
$479$	25.1354	+	5.34269i	1.14846	+	0.244114i	0.405919	+	0.913909i	$0.366952\pi$
$480$		0			0
$481$	11.9798	−	26.9070i	0.546230	−	1.22685i
$482$	−1.12866	−	5.30991i	−0.0514088	−	0.241860i
$483$		0			0
$484$	14.9687	+	1.88824i	0.680395	+	0.0858290i
$485$		−	12.2029i		−	0.554103i
$486$		0			0
$487$	4.95416	−	3.59941i	0.224494	−	0.163105i	−0.469853	−	0.882745i	$-0.655693\pi$
$487$	4.95416	−	3.59941i	0.224494	−	0.163105i	0.694347	+	0.719640i	$0.255693\pi$
$488$	1.04923	+	2.35660i	0.0474962	+	0.106678i
$489$		0			0
$490$	−30.7664	−	27.7021i	−1.38988	−	1.25146i
$491$	2.42483	−	23.0707i	0.109431	−	1.04117i	−0.792673	−	0.609647i	$-0.791311\pi$
$491$	2.42483	−	23.0707i	0.109431	−	1.04117i	0.902104	−	0.431519i	$-0.142022\pi$
$492$		0			0
$493$	−0.709576	−	0.788064i	−0.0319577	−	0.0354926i
$494$	−10.2515			−0.461238
$495$		0			0
$496$	−1.10290			−0.0495218
$497$	−47.8189	−	53.1083i	−2.14497	−	2.38223i
$498$		0			0
$499$	−3.16311	+	30.0950i	−0.141600	+	1.34724i	0.660850	+	0.750518i	$0.270196\pi$
$499$	−3.16311	+	30.0950i	−0.141600	+	1.34724i	−0.802450	+	0.596719i	$0.796471\pi$
$500$	3.35634	+	3.02206i	0.150100	+	0.135151i
$501$		0			0
$502$	−7.56202	−	16.9846i	−0.337509	−	0.758059i
$503$	−19.3352	+	14.0478i	−0.862112	+	0.626361i	−0.928459	−	0.371436i	$-0.878866\pi$
$503$	−19.3352	+	14.0478i	−0.862112	+	0.626361i	0.0663467	+	0.997797i	$0.478866\pi$
$504$		0			0
$505$			21.2619i			0.946144i
$506$	3.49500	+	7.03903i	0.155372	+	0.312923i
$507$		0			0
$508$	−3.28529	−	15.4561i	−0.145761	−	0.685753i
$509$	−5.59252	+	12.5610i	−0.247884	+	0.556757i	−0.994040	−	0.109014i	$-0.965231\pi$
$509$	−5.59252	+	12.5610i	−0.247884	+	0.556757i	0.746156	+	0.665771i	$0.231897\pi$
$510$		0			0
$511$	−42.3209	−	8.99559i	−1.87217	−	0.397941i
$512$	2.15821	+	6.64230i	0.0953805	+	0.293551i
$513$		0			0
$514$	−11.0206	−	15.1686i	−0.486098	−	0.669057i
$515$	14.0973	−	12.6933i	0.621202	−	0.559333i
$516$		0			0
$517$	18.6587	+	15.4330i	0.820609	+	0.678742i
$518$	29.2453	−	16.8848i	1.28496	−	0.741874i
$519$		0			0
$520$	−3.05488	−	29.0652i	−0.133965	−	1.27459i
$521$	0.418797	−	0.576425i	0.0183478	−	0.0252536i	−0.799745	−	0.600340i	$-0.795032\pi$
$521$	0.418797	−	0.576425i	0.0183478	−	0.0252536i	0.818092	+	0.575087i	$0.195032\pi$
$522$		0			0
$523$	−8.13356	+	2.64275i	−0.355656	+	0.115560i	−0.481395	−	0.876504i	$-0.659870\pi$
$523$	−8.13356	+	2.64275i	−0.355656	+	0.115560i	0.125739	+	0.992063i	$0.459870\pi$
$524$	7.20241	−	3.20672i	0.314639	−	0.140086i
$525$		0			0
$526$	6.93074	−	1.47317i	0.302195	−	0.0642335i
$527$	0.584122	+	1.01173i	0.0254447	+	0.0440716i
$528$		0			0
$529$	−7.03263	+	12.1809i	−0.305767	+	0.529603i
$530$	−2.42637	+	7.46759i	−0.105395	+	0.324371i
$531$		0			0
$532$	20.7540	+	15.0787i	0.899800	+	0.653743i
$533$	2.30971	−	10.8663i	0.100045	−	0.470672i
$534$		0			0
$535$	−34.5396	−	3.63026i	−1.49328	−	0.156950i
$536$	2.61444	+	1.16402i	0.112927	+	0.0502782i
$537$		0			0
$538$	−4.06987	−	2.34974i	−0.175465	−	0.101305i
$539$	52.1949	−	2.19234i	2.24819	−	0.0944307i
$540$		0			0
$541$	−8.16353	−	2.65249i	−0.350977	−	0.114039i	0.128222	−	0.991745i	$-0.459073\pi$
$541$	−8.16353	−	2.65249i	−0.350977	−	0.114039i	−0.479200	+	0.877706i	$0.659073\pi$
$542$	−21.2607	+	2.23458i	−0.913223	+	0.0959836i
$543$		0			0
$544$	2.58460	−	2.87048i	0.110814	−	0.123071i
$545$	1.14849	−	1.27553i	0.0491961	−	0.0546378i
$546$		0			0
$547$	−26.4593	+	2.78098i	−1.13132	+	0.118906i	−0.651633	−	0.758534i	$-0.725916\pi$
$547$	−26.4593	+	2.78098i	−1.13132	+	0.118906i	−0.479685	+	0.877441i	$0.659249\pi$
$548$	24.6267	+	8.00170i	1.05200	+	0.341815i
$549$		0			0
$550$	15.7433	−	0.661264i	0.671296	−	0.0281964i
$551$	5.44512	+	3.14374i	0.231970	+	0.133928i
$552$		0			0
$553$	−33.7980	−	15.0478i	−1.43724	−	0.639899i
$554$	19.7128	+	2.07190i	0.837519	+	0.0880267i
$555$		0			0
$556$	0.0561237	−	0.264041i	0.00238017	−	0.0111978i
$557$	−25.4748	−	18.5085i	−1.07940	−	0.784231i	−0.101823	−	0.994803i	$-0.532467\pi$
$557$	−25.4748	−	18.5085i	−1.07940	−	0.784231i	−0.977578	+	0.210572i	$0.932467\pi$
$558$		0			0
$559$	7.33878	−	22.5865i	0.310397	−	0.955305i
$560$	−4.93709	+	8.55129i	−0.208630	+	0.361358i
$561$		0			0
$562$	8.01684	+	13.8856i	0.338170	+	0.585728i
$563$	−22.9668	+	4.88174i	−0.967934	+	0.205741i	−0.664646	−	0.747158i	$-0.731418\pi$
$563$	−22.9668	+	4.88174i	−0.967934	+	0.205741i	−0.303288	+	0.952899i	$0.598084\pi$
$564$		0			0
$565$	58.2053	−	25.9147i	2.44872	−	1.09024i
$566$	−18.3331	+	5.95680i	−0.770599	+	0.250383i
$567$		0			0
$568$	23.5377	−	32.3969i	0.987622	−	1.35934i
$569$	2.69812	+	25.6709i	0.113111	+	1.07618i	0.892937	+	0.450182i	$0.148641\pi$
$569$	2.69812	+	25.6709i	0.113111	+	1.07618i	−0.779826	+	0.625997i	$0.784692\pi$
$570$		0			0
$571$	−20.7455	+	11.9774i	−0.868171	+	0.501239i	−0.866740	−	0.498760i	$-0.833789\pi$
$571$	−20.7455	+	11.9774i	−0.868171	+	0.501239i	−0.00143110	+	0.999999i	$0.500456\pi$
$572$	11.5602	+	9.56170i	0.483358	+	0.399795i
$573$		0			0
$574$	9.46547	−	8.52275i	0.395081	−	0.355733i
$575$	−10.5297	−	14.4928i	−0.439117	−	0.604393i
$576$		0			0
$577$	−3.31423	−	10.2001i	−0.137973	−	0.424638i	0.858067	−	0.513537i	$-0.171665\pi$
$577$	−3.31423	−	10.2001i	−0.137973	−	0.424638i	−0.996041	+	0.0888993i	$0.971665\pi$
$578$	12.8428	+	2.72982i	0.534191	+	0.113546i
$579$		0			0
$580$	−2.96584	+	6.66139i	−0.123150	+	0.276599i
$581$	−5.24458	−	24.6738i	−0.217582	−	1.02364i
$582$		0			0
$583$	−4.40621	−	8.87425i	−0.182487	−	0.367534i
$584$		−	24.2442i		−	1.00323i
$585$		0			0
$586$	1.71279	−	1.24441i	0.0707546	−	0.0514062i
$587$	3.67144	+	8.24620i	0.151537	+	0.340357i	0.973323	−	0.229439i	$-0.0736890\pi$
$587$	3.67144	+	8.24620i	0.151537	+	0.340357i	−0.821786	+	0.569796i	$0.807022\pi$
$588$		0			0
$589$	−5.14749	−	4.63482i	−0.212099	−	0.190974i
$590$	−3.78553	+	36.0169i	−0.155848	+	1.48279i
$591$		0			0
$592$	−3.73116	−	4.14388i	−0.153350	−	0.170312i
$593$	37.7184			1.54891			0.774455	−	0.632629i	$-0.218024\pi$
$593$	37.7184			1.54891			0.774455	+	0.632629i	$0.218024\pi$
$594$		0			0
$595$	10.4592			0.428784
$596$	4.39103	+	4.87674i	0.179864	+	0.199759i
$597$		0			0
$598$	−0.816848	+	7.77179i	−0.0334034	+	0.317812i
$599$	−9.70203	−	8.73575i	−0.396414	−	0.356933i	0.446685	−	0.894691i	$-0.352605\pi$
$599$	−9.70203	−	8.73575i	−0.396414	−	0.356933i	−0.843099	+	0.537758i	$0.819271\pi$
$600$		0			0
$601$	10.4306	+	23.4274i	0.425472	+	0.955625i	0.991363	+	0.131145i	$0.0418654\pi$
$601$	10.4306	+	23.4274i	0.425472	+	0.955625i	−0.565892	+	0.824480i	$0.691468\pi$
$602$	22.0288	−	16.0048i	0.897825	−	0.652308i
$603$		0			0
$604$			22.2766i			0.906423i
$605$	−24.9617	+	26.5911i	−1.01484	+	1.08108i
$606$		0			0
$607$	−3.69174	−	17.3683i	−0.149843	−	0.704956i	−0.987353	−	0.158535i	$-0.949323\pi$
$607$	−3.69174	−	17.3683i	−0.149843	−	0.704956i	0.837510	−	0.546421i	$-0.184010\pi$
$608$	−9.31502	+	20.9219i	−0.377774	+	0.848494i
$609$		0			0
$610$	−2.48135	−	0.527427i	−0.100467	−	0.0213549i
$611$	7.44036	+	22.8991i	0.301005	+	0.926397i
$612$		0			0
$613$	−19.9197	−	27.4172i	−0.804550	−	1.10737i	−0.992141	−	0.125121i	$-0.960068\pi$
$613$	−19.9197	−	27.4172i	−0.804550	−	1.10737i	0.187591	−	0.982247i	$-0.439932\pi$
$614$	2.36945	−	2.13347i	0.0956234	−	0.0860997i
$615$		0			0
$616$	10.5189	+	40.9530i	0.423818	+	1.65004i
$617$	−41.9619	+	24.2267i	−1.68932	+	0.975331i	−0.734287	+	0.678839i	$0.762483\pi$
$617$	−41.9619	+	24.2267i	−1.68932	+	0.975331i	−0.955035	+	0.296492i	$0.904183\pi$
$618$		0			0
$619$	4.10645	+	39.0703i	0.165052	+	1.57037i	0.692903	+	0.721031i	$0.256331\pi$
$619$	4.10645	+	39.0703i	0.165052	+	1.57037i	−0.527851	+	0.849337i	$0.677002\pi$
$620$	4.72170	−	6.49886i	0.189628	−	0.261001i
$621$		0			0
$622$	−11.9024	+	3.86733i	−0.477243	+	0.155066i
$623$	17.3803	−	7.73823i	0.696329	−	0.310026i
$624$		0			0
$625$	18.6317	−	3.96029i	0.745268	−	0.158412i
$626$	−6.52094	−	11.2946i	−0.260629	−	0.451423i
$627$		0			0
$628$	0.206339	−	0.357390i	0.00823382	−	0.0142614i
$629$	−1.82521	+	5.61741i	−0.0727757	+	0.223981i
$630$		0			0
$631$	4.88193	+	3.54693i	0.194347	+	0.141201i	0.680703	−	0.732559i	$-0.261674\pi$
$631$	4.88193	+	3.54693i	0.194347	+	0.141201i	−0.486357	+	0.873760i	$0.661674\pi$
$632$	4.31019	−	20.2779i	0.171450	−	0.806610i
$633$		0			0
$634$	−1.47141	−	0.154651i	−0.0584370	−	0.00614198i
$635$	34.8953	+	15.5364i	1.38478	+	0.616542i
$636$		0			0
$637$	44.9867	+	25.9731i	1.78244	+	1.02909i
$638$	1.46986	+	3.95124i	0.0581923	+	0.156431i
$639$		0			0
$640$	−28.3816	−	9.22173i	−1.12188	−	0.364521i
$641$	18.3950	−	1.93339i	0.726558	−	0.0763644i	0.265974	−	0.963980i	$-0.414307\pi$
$641$	18.3950	−	1.93339i	0.726558	−	0.0763644i	0.460584	+	0.887616i	$0.347640\pi$
$642$		0			0
$643$	10.0968	−	11.2137i	0.398180	−	0.442223i	−0.510399	−	0.859938i	$-0.670502\pi$
$643$	10.0968	−	11.2137i	0.398180	−	0.442223i	0.908578	+	0.417715i	$0.137169\pi$
$644$	13.0850	−	14.5324i	0.515621	−	0.572655i
$645$		0			0
$646$	2.04455	−	0.214891i	0.0804417	−	0.00845477i
$647$	7.91036	+	2.57023i	0.310988	+	0.101046i	0.460353	−	0.887736i	$-0.347723\pi$
$647$	7.91036	+	2.57023i	0.310988	+	0.101046i	−0.149365	+	0.988782i	$0.547723\pi$
$648$		0			0
$649$	−28.3887	−	35.8110i	−1.11435	−	1.40570i
$650$	13.5691	+	7.83412i	0.532224	+	0.307280i
$651$		0			0
$652$	22.2156	+	9.89101i	0.870029	+	0.387362i
$653$	20.7914	+	2.18526i	0.813630	+	0.0855160i	0.502198	−	0.864753i	$-0.332525\pi$
$653$	20.7914	+	2.18526i	0.813630	+	0.0855160i	0.311432	+	0.950268i	$0.399191\pi$
$654$		0			0
$655$	−3.96249	+	18.6420i	−0.154827	+	0.728405i
$656$	−1.70151	−	1.23622i	−0.0664328	−	0.0482663i
$657$		0			0
$658$	−8.53070	+	26.2548i	−0.332561	+	1.02352i
$659$	−1.56299	+	2.70718i	−0.0608854	+	0.105457i	−0.894861	−	0.446344i	$-0.852726\pi$
$659$	−1.56299	+	2.70718i	−0.0608854	+	0.105457i	0.833976	+	0.551801i	$0.186059\pi$
$660$		0			0
$661$	−19.0623	−	33.0168i	−0.741436	−	1.28421i	−0.951841	−	0.306591i	$-0.900812\pi$
$661$	−19.0623	−	33.0168i	−0.741436	−	1.28421i	0.210405	−	0.977614i	$-0.432522\pi$
$662$	15.4548	−	3.28501i	0.600667	−	0.127676i
$663$		0			0
$664$	12.9128	−	5.74914i	0.501113	−	0.223110i
$665$	−58.9783	+	19.1632i	−2.28708	+	0.743117i
$666$		0			0
$667$	2.81718	−	3.87751i	0.109081	−	0.150138i
$668$	2.05986	+	19.5983i	0.0796986	+	0.758281i
$669$		0			0
$670$	−2.43729	+	1.40717i	−0.0941608	+	0.0543638i
$671$	2.70258	−	1.71545i	0.104332	−	0.0662242i
$672$		0			0
$673$	6.21540	−	5.59637i	0.239586	−	0.215724i	−0.540587	−	0.841288i	$-0.681798\pi$
$673$	6.21540	−	5.59637i	0.239586	−	0.215724i	0.780173	+	0.625564i	$0.215131\pi$
$674$	−9.62091	−	13.2420i	−0.370584	−	0.510065i
$675$		0			0
$676$	−0.900148	−	2.77037i	−0.0346211	−	0.106553i
$677$	−40.7330	−	8.65806i	−1.56550	−	0.332756i	−0.658066	−	0.752961i	$-0.728625\pi$
$677$	−40.7330	−	8.65806i	−1.56550	−	0.332756i	−0.907430	+	0.420204i	$0.861958\pi$
$678$		0			0
$679$	−7.14030	+	16.0374i	−0.274019	+	0.615458i
$680$	1.21852	+	5.73270i	0.0467282	+	0.219839i
$681$		0			0
$682$	−0.678873	−	4.59444i	−0.0259954	−	0.175930i
$683$			12.0252i			0.460132i	0.973175	+	0.230066i	$0.0738941\pi$
$683$			12.0252i			0.460132i	−0.973175	+	0.230066i	$0.926106\pi$
$684$		0			0
$685$	−50.6406	+	36.7926i	−1.93488	+	1.40577i
$686$	13.4590	+	30.2294i	0.513866	+	1.15416i
$687$		0			0
$688$	−3.34129	−	3.00851i	−0.127385	−	0.114698i
$689$	1.02982	−	9.79804i	0.0392329	−	0.373276i
$690$		0			0
$691$	18.6418	+	20.7038i	0.709167	+	0.787610i	0.984807	−	0.173651i	$-0.0555564\pi$
$691$	18.6418	+	20.7038i	0.709167	+	0.787610i	−0.275640	+	0.961261i	$0.588890\pi$
$692$	15.4084			0.585739
$693$		0			0
$694$	2.72483			0.103433
$695$	0.436636	+	0.484934i	0.0165626	+	0.0183946i
$696$		0			0
$697$	−0.232867	+	2.21558i	−0.00882046	+	0.0839211i
$698$	13.6417	+	12.2830i	0.516346	+	0.464920i
$699$		0			0
$700$	−15.9474	−	35.8184i	−0.602755	−	1.35381i
$701$	−35.6066	+	25.8697i	−1.34484	+	0.977085i	−0.345592	+	0.938385i	$0.612322\pi$
$701$	−35.6066	+	25.8697i	−1.34484	+	0.977085i	−0.999251	+	0.0387005i	$0.987678\pi$
$702$		0			0
$703$		−	35.0202i		−	1.32081i
$704$	−10.0442	+	4.98713i	−0.378556	+	0.187960i
$705$		0			0
$706$	0.0790891	+	0.372085i	0.00297656	+	0.0140036i
$707$	12.4411	−	27.9431i	0.467895	−	1.05091i
$708$		0			0
$709$	9.25521	+	1.96726i	0.347587	+	0.0738818i	0.378397	−	0.925643i	$-0.376475\pi$
$709$	9.25521	+	1.96726i	0.347587	+	0.0738818i	−0.0308103	+	0.999525i	$0.509809\pi$
$710$	12.1691	+	37.4525i	0.456696	+	1.40557i
$711$		0			0
$712$	6.26620	+	8.62468i	0.234836	+	0.323224i
$713$	−3.92386	+	3.53306i	−0.146950	+	0.132314i
$714$		0			0
$715$	−35.1255	+	9.02209i	−1.31362	+	0.337407i
$716$	−7.22331	+	4.17038i	−0.269948	+	0.155854i
$717$		0			0
$718$	2.74732	+	26.1390i	0.102529	+	0.975497i
$719$	−2.48450	+	3.41962i	−0.0926563	+	0.127530i	−0.852828	−	0.522191i	$-0.825115\pi$
$719$	−2.48450	+	3.41962i	−0.0926563	+	0.127530i	0.760172	+	0.649722i	$0.225115\pi$
$720$		0			0
$721$	−25.9544	+	8.43309i	−0.966592	+	0.314065i
$722$	2.62445	−	1.16848i	0.0976720	−	0.0434864i
$723$		0			0
$724$	12.8320	−	2.72753i	0.476898	−	0.101368i
$725$	−4.80484	−	8.32223i	−0.178447	−	0.309080i
$726$		0			0
$727$	−13.9942	+	24.2387i	−0.519018	+	0.898965i	0.480738	+	0.876864i	$0.340369\pi$
$727$	−13.9942	+	24.2387i	−0.519018	+	0.898965i	−0.999756	+	0.0221010i	$0.992964\pi$
$728$	−12.9922	+	39.9859i	−0.481524	+	1.48198i
$729$		0			0
$730$	19.2883	+	14.0138i	0.713892	+	0.518673i
$731$	−0.990184	+	4.65845i	−0.0366233	+	0.172299i
$732$		0			0
$733$	24.7407	+	2.60036i	0.913820	+	0.0960464i	0.549754	−	0.835327i	$-0.314722\pi$
$733$	24.7407	+	2.60036i	0.913820	+	0.0960464i	0.364066	+	0.931373i	$0.381388\pi$
$734$	−16.1909	−	7.20867i	−0.597619	−	0.266077i
$735$		0			0
$736$	15.1189	+	8.72888i	0.557289	+	0.321751i
$737$	0.954702	−	3.42055i	0.0351669	−	0.125998i
$738$		0			0
$739$	−5.13765	−	1.66932i	−0.188992	−	0.0614071i	0.212992	−	0.977054i	$-0.431679\pi$
$739$	−5.13765	−	1.66932i	−0.188992	−	0.0614071i	−0.401984	+	0.915647i	$0.631679\pi$
$740$	40.3915	−	4.24532i	1.48482	−	0.156061i
$741$		0			0
$742$	7.55834	−	8.39439i	0.277476	−	0.308168i
$743$	7.35233	−	8.16559i	0.269731	−	0.299566i	−0.593028	−	0.805182i	$-0.702068\pi$
$743$	7.35233	−	8.16559i	0.269731	−	0.299566i	0.862759	+	0.505615i	$0.168734\pi$
$744$		0			0
$745$	−15.7765	+	1.65818i	−0.578008	+	0.0607511i
$746$	10.1843	+	3.30909i	0.372875	+	0.121154i
$747$		0			0
$748$	−2.50599	−	1.66465i	−0.0916281	−	0.0608656i
$749$	43.2689	+	24.9813i	1.58101	+	0.912797i
$750$		0			0
$751$	−11.1997	−	4.98643i	−0.408683	−	0.181958i	0.192089	−	0.981377i	$-0.438474\pi$
$751$	−11.1997	−	4.98643i	−0.408683	−	0.181958i	−0.600773	+	0.799420i	$0.705140\pi$
$752$	4.53341	+	0.476480i	0.165316	+	0.0173755i
$753$		0			0
$754$	−0.871564	+	4.10038i	−0.0317405	+	0.149327i
$755$	−43.5661	−	31.6526i	−1.58553	−	1.15196i
$756$		0			0
$757$	10.2311	−	31.4882i	0.371857	−	1.14446i	−0.573718	−	0.819053i	$-0.694499\pi$
$757$	10.2311	−	31.4882i	0.371857	−	1.14446i	0.945575	−	0.325405i	$-0.105501\pi$
$758$	−3.07861	+	5.33232i	−0.111820	+	0.193678i
$759$		0			0
$760$	−17.3745	−	30.0936i	−0.630241	−	1.09161i
$761$	−10.2861	+	2.18638i	−0.372872	+	0.0792563i	−0.390536	−	0.920588i	$-0.627710\pi$
$761$	−10.2861	+	2.18638i	−0.372872	+	0.0792563i	0.0176644	+	0.999844i	$0.494377\pi$
$762$		0			0
$763$	−2.25574	+	1.00432i	−0.0816634	+	0.0363589i
$764$	−4.27618	+	1.38941i	−0.154707	+	0.0502672i
$765$		0			0
$766$	10.0228	−	13.7952i	0.362139	−	0.498441i
$767$	−4.74983	−	45.1916i	−0.171506	−	1.63177i
$768$		0			0
$769$	26.2654	−	15.1644i	0.947156	−	0.546841i	0.0549598	−	0.998489i	$-0.482497\pi$
$769$	26.2654	−	15.1644i	0.947156	−	0.546841i	0.892196	+	0.451648i	$0.149164\pi$
$770$	−38.6617	−	15.3032i	−1.39327	−	0.551489i
$771$		0			0
$772$	−11.1857	+	10.0716i	−0.402580	+	0.362485i
$773$	17.7240	+	24.3950i	0.637488	+	0.877427i	0.998478	−	0.0551427i	$-0.0175614\pi$
$773$	17.7240	+	24.3950i	0.637488	+	0.877427i	−0.360991	+	0.932569i	$0.617561\pi$
$774$		0			0
$775$	3.27142	+	10.0684i	0.117513	+	0.361668i
$776$	−9.62198	−	2.04522i	−0.345409	−	0.0734190i
$777$		0			0
$778$	4.04471	−	9.08456i	0.145010	−	0.325697i
$779$	−2.74625	−	12.9201i	−0.0983947	−	0.462911i
$780$		0			0
$781$	−44.0389	−	23.0179i	−1.57584	−	0.823646i
$782$		−	1.56712i		−	0.0560400i
$783$		0			0
$784$	7.95628	−	5.78057i	0.284153	−	0.206449i
$785$	0.405757	+	0.911346i	0.0144821	+	0.0325273i
$786$		0			0
$787$	−20.6406	−	18.5849i	−0.735758	−	0.662479i	0.213513	−	0.976940i	$-0.431510\pi$
$787$	−20.6406	−	18.5849i	−0.735758	−	0.662479i	−0.949270	+	0.314461i	$0.898176\pi$
$788$	−0.00960166	+	0.0913537i	−0.000342045	+	0.00325434i
$789$		0			0
$790$	13.6413	+	15.1502i	0.485337	+	0.539022i
$791$	−91.6587			−3.25901
$792$		0			0
$793$	3.18298			0.113031
$794$	−9.43456	−	10.4781i	−0.334820	−	0.371855i
$795$		0			0
$796$	−2.13226	+	20.2871i	−0.0755760	+	0.719057i
$797$	−4.54457	−	4.09195i	−0.160977	−	0.144944i	0.584706	−	0.811245i	$-0.301210\pi$
$797$	−4.54457	−	4.09195i	−0.160977	−	0.144944i	−0.745683	+	0.666301i	$0.767877\pi$
$798$		0			0
$799$	−1.96390	−	4.41100i	−0.0694779	−	0.156050i
$800$	28.3178	−	20.5741i	1.00119	−	0.727405i
$801$		0			0
$802$			7.98888i			0.282097i
$803$	−29.7615	+	4.39754i	−1.05026	+	0.155186i
$804$		0			0
$805$	9.82841	+	46.2390i	0.346406	+	1.62971i
$806$	1.87836	−	4.21886i	0.0661624	−	0.148603i
$807$		0			0
$808$	16.7651	+	3.56353i	0.589794	+	0.125365i
$809$	3.10568	+	9.55831i	0.109190	+	0.336052i	0.990691	−	0.136130i	$-0.0434664\pi$
$809$	3.10568	+	9.55831i	0.109190	+	0.336052i	−0.881501	+	0.472182i	$0.843466\pi$
$810$		0			0
$811$	14.7145	+	20.2527i	0.516695	+	0.711170i	0.985030	−	0.172381i	$-0.0551460\pi$
$811$	14.7145	+	20.2527i	0.516695	+	0.711170i	−0.468335	+	0.883551i	$0.655146\pi$
$812$	7.79560	−	7.01919i	0.273572	−	0.246325i
$813$		0			0
$814$	14.9658	−	18.0939i	0.524551	−	0.634190i
$815$	−50.9096	+	29.3927i	−1.78329	+	1.02958i
$816$		0			0
$817$	−2.95162	−	28.0828i	−0.103264	−	0.982491i
$818$	−5.62474	+	7.74179i	−0.196664	+	0.270685i
$819$		0			0
$820$	14.5689	−	4.73371i	0.508767	−	0.165308i
$821$	−2.42327	+	1.07891i	−0.0845728	+	0.0376543i	−0.448587	−	0.893739i	$-0.648073\pi$
$821$	−2.42327	+	1.07891i	−0.0845728	+	0.0376543i	0.364014	+	0.931393i	$0.381406\pi$
$822$		0			0
$823$	34.0730	−	7.24245i	1.18771	−	0.252456i	0.428648	−	0.903472i	$-0.358990\pi$
$823$	34.0730	−	7.24245i	1.18771	−	0.252456i	0.759064	+	0.651016i	$0.225657\pi$
$824$	−7.64595	−	13.2432i	−0.266359	−	0.461348i
$825$		0			0
$826$	26.0498	−	45.1195i	0.906388	−	1.56991i
$827$	−8.80337	+	27.0940i	−0.306123	+	0.942150i	0.673133	+	0.739522i	$0.264948\pi$
$827$	−8.80337	+	27.0940i	−0.306123	+	0.942150i	−0.979256	+	0.202628i	$0.935052\pi$
$828$		0			0
$829$	36.6638	+	26.6378i	1.27339	+	0.925170i	0.999332	−	0.0365440i	$-0.0116349\pi$
$829$	36.6638	+	26.6378i	1.27339	+	0.925170i	0.274055	+	0.961714i	$0.411635\pi$
$830$	−2.88999	+	13.5963i	−0.100313	+	0.471936i
$831$		0			0
$832$	−11.0898	−	1.16559i	−0.384471	−	0.0404095i
$833$	−9.51653	−	4.23703i	−0.329728	−	0.146804i
$834$		0			0
$835$	−41.2550	−	23.8186i	−1.42769	−	0.824276i
$836$	17.1810	+	4.79535i	0.594218	+	0.165851i
$837$		0			0
$838$	13.0254	+	4.23222i	0.449957	+	0.146200i
$839$	38.8002	−	4.07806i	1.33953	−	0.140790i	0.592495	−	0.805574i	$-0.298143\pi$
$839$	38.8002	−	4.07806i	1.33953	−	0.140790i	0.747036	+	0.664784i	$0.231476\pi$
$840$		0			0
$841$	−17.6844	+	19.6405i	−0.609808	+	0.677260i
$842$	−12.8738	+	14.2978i	−0.443659	+	0.492734i
$843$		0			0
$844$	−27.0151	+	2.83941i	−0.929899	+	0.0977364i
$845$	6.69699	+	2.17598i	0.230383	+	0.0748561i
$846$		0			0
$847$	48.3647	−	20.3409i	1.66183	−	0.698923i
$848$	−1.61531	−	0.932597i	−0.0554698	−	0.0320255i
$849$		0			0
$850$	−2.87042	−	1.27799i	−0.0984547	−	0.0438348i
$851$	−26.5492	−	2.79043i	−0.910094	−	0.0956547i
$852$		0			0
$853$	8.30491	−	39.0715i	0.284355	−	1.33778i	−0.571515	−	0.820592i	$-0.693644\pi$
$853$	8.30491	−	39.0715i	0.284355	−	1.33778i	0.855870	−	0.517192i	$-0.173023\pi$
$854$	2.95245	+	2.14508i	0.101031	+	0.0734032i
$855$		0			0
$856$	−8.65136	+	26.6262i	−0.295697	+	0.910063i
$857$	−19.3608	+	33.5340i	−0.661354	+	1.14550i	0.318906	+	0.947786i	$0.396684\pi$
$857$	−19.3608	+	33.5340i	−0.661354	+	1.14550i	−0.980260	+	0.197712i	$0.936649\pi$
$858$		0			0
$859$	13.8956	+	24.0679i	0.474112	+	0.821187i	0.999561	−	0.0296388i	$-0.00943572\pi$
$859$	13.8956	+	24.0679i	0.474112	+	0.821187i	−0.525448	+	0.850826i	$0.676102\pi$
$860$	32.0323	−	6.80867i	1.09229	−	0.232174i
$861$		0			0
$862$	−15.4069	+	6.85959i	−0.524761	+	0.233639i
$863$	−8.62080	+	2.80107i	−0.293455	+	0.0953494i	−0.452045	−	0.891995i	$-0.649305\pi$
$863$	−8.62080	+	2.80107i	−0.293455	+	0.0953494i	0.158590	+	0.987345i	$0.449305\pi$
$864$		0			0
$865$	−21.8936	+	30.1340i	−0.744406	+	1.02459i
$866$	1.20063	+	11.4232i	0.0407990	+	0.388177i
$867$		0			0
$868$	−10.0081	+	5.77818i	−0.339697	+	0.196124i
$869$	−25.6743	−	1.61296i	−0.870942	−	0.0547160i
$870$		0			0
$871$	2.62423	−	2.36286i	0.0889185	−	0.0800626i
$872$	−0.813271	−	1.11937i	−0.0275408	−	0.0379067i
$873$		0			0
$874$	2.87126	+	8.83683i	0.0971219	+	0.298910i
$875$	15.3631	+	3.26554i	0.519369	+	0.110395i
$876$		0			0
$877$	3.40773	−	7.65390i	0.115071	−	0.258454i	−0.846824	−	0.531874i	$-0.821488\pi$
$877$	3.40773	−	7.65390i	0.115071	−	0.258454i	0.961895	+	0.273420i	$0.0881548\pi$
$878$	3.93360	+	18.5061i	0.132753	+	0.624552i
$879$		0			0
$880$	−1.14440	+	6.76982i	−0.0385777	+	0.228210i
$881$			34.4290i			1.15994i	0.814636	+	0.579972i	$0.196937\pi$
$881$			34.4290i			1.15994i	−0.814636	+	0.579972i	$0.803063\pi$
$882$		0			0
$883$	−16.7870	+	12.1964i	−0.564926	+	0.410443i	−0.833259	−	0.552883i	$-0.813528\pi$
$883$	−16.7870	+	12.1964i	−0.564926	+	0.410443i	0.268332	+	0.963326i	$0.413528\pi$
$884$	−1.21676	−	2.73289i	−0.0409241	−	0.0919170i
$885$		0			0
$886$	15.2654	+	13.7450i	0.512850	+	0.461772i
$887$	−0.169964	+	1.61710i	−0.00570684	+	0.0542970i	−0.997005	−	0.0773410i	$-0.975357\pi$
$887$	−0.169964	+	1.61710i	−0.00570684	+	0.0542970i	0.991298	+	0.131638i	$0.0420236\pi$
$888$		0			0
$889$	−36.7696	−	40.8368i	−1.23321	−	1.36962i
$890$	−10.4837			−0.351414
$891$		0			0
$892$	−7.06019			−0.236393
$893$	19.1561	+	21.2750i	0.641033	+	0.711939i
$894$		0			0
$895$	2.10757	−	20.0522i	0.0704482	−	0.670270i
$896$	31.9040	+	28.7265i	1.06584	+	0.959684i
$897$		0			0
$898$	−3.57212	−	8.02310i	−0.119203	−	0.267734i
$899$	−2.29146	+	1.66484i	−0.0764243	+	0.0555255i
$900$		0			0
$901$			1.97570i			0.0658200i
$902$	4.10248	−	7.84904i	0.136598	−	0.261344i
$903$		0			0
$904$	−10.6785	−	50.2384i	−0.355161	−	1.67090i
$905$	−12.8987	+	28.9709i	−0.428766	+	0.963025i
$906$		0			0
$907$	50.1442	+	10.6585i	1.66501	+	0.353909i	0.941658	−	0.336571i	$-0.109267\pi$
$907$	50.1442	+	10.6585i	1.66501	+	0.353909i	0.723352	+	0.690480i	$0.242601\pi$
$908$	−7.61002	−	23.4212i	−0.252547	−	0.777261i
$909$		0			0
$910$	−24.3023	−	33.4493i	−0.805614	−	1.10883i
$911$	−35.5797	+	32.0361i	−1.17881	+	1.06140i	−0.181861	+	0.983324i	$0.558212\pi$
$911$	−35.5797	+	32.0361i	−1.17881	+	1.06140i	−0.996947	+	0.0780795i	$0.975121\pi$
$912$		0			0
$913$	−9.39966	−	14.8085i	−0.311083	−	0.490091i
$914$	27.1039	−	15.6484i	0.896516	−	0.517604i
$915$		0			0
$916$	−0.339493	−	3.23006i	−0.0112172	−	0.106724i
$917$	16.1157	−	22.1814i	0.532188	−	0.732493i
$918$		0			0
$919$	−6.95498	+	2.25981i	−0.229424	+	0.0745442i	−0.421473	−	0.906841i	$-0.638487\pi$
$919$	−6.95498	+	2.25981i	−0.229424	+	0.0745442i	0.192049	+	0.981385i	$0.438487\pi$
$920$	−24.1987	+	10.7739i	−0.797807	+	0.355207i
$921$		0			0
$922$	−12.7530	+	2.71074i	−0.419998	+	0.0892734i
$923$	−24.7056	−	42.7913i	−0.813194	−	1.40849i
$924$		0			0
$925$	−26.7621	+	46.3533i	−0.879933	+	1.52409i
$926$	2.02366	−	6.22819i	0.0665016	−	0.204671i
$927$		0			0
$928$	7.57635	+	5.50454i	0.248706	+	0.180695i
$929$	−9.05604	+	42.6053i	−0.297119	+	1.39783i	0.535756	+	0.844373i	$0.320027\pi$
$929$	−9.05604	+	42.6053i	−0.297119	+	1.39783i	−0.832875	+	0.553462i	$0.813307\pi$
$930$		0			0
$931$	61.4259	+	6.45612i	2.01315	+	0.211591i
$932$	−11.1193	−	4.95061i	−0.364223	−	0.162163i
$933$		0			0
$934$	24.0724	+	13.8982i	0.787674	+	0.454764i
$935$	6.81627	−	2.53565i	0.222916	−	0.0829246i
$936$		0			0
$937$	23.4312	+	7.61326i	0.765464	+	0.248714i	0.665622	−	0.746289i	$-0.268166\pi$
$937$	23.4312	+	7.61326i	0.765464	+	0.248714i	0.0998421	+	0.995003i	$0.468166\pi$
$938$	4.02655	−	0.423207i	0.131471	−	0.0138182i
$939$		0			0
$940$	−22.2159	+	24.6733i	−0.724603	+	0.804753i
$941$	−17.5822	+	19.5270i	−0.573163	+	0.636563i	−0.958118	−	0.286373i	$-0.907550\pi$
$941$	−17.5822	+	19.5270i	−0.573163	+	0.636563i	0.384955	+	0.922935i	$0.374217\pi$
$942$		0			0
$943$	−10.0137	+	1.05248i	−0.326091	+	0.0342735i
$944$	−8.18179	−	2.65843i	−0.266295	−	0.0865244i
$945$		0			0
$946$	10.4761	−	15.7709i	0.340608	−	0.512756i
$947$	−41.0112	−	23.6778i	−1.33268	−	0.769426i	−0.346974	−	0.937875i	$-0.612791\pi$
$947$	−41.0112	−	23.6778i	−1.33268	−	0.769426i	−0.985710	+	0.168449i	$0.946124\pi$
$948$		0			0
$949$	−27.3286	−	12.1675i	−0.887123	−	0.394973i
$950$	18.5276	+	1.94733i	0.601114	+	0.0631796i
$951$		0			0
$952$	1.75297	−	8.24709i	0.0568141	−	0.267290i
$953$	14.2453	+	10.3498i	0.461451	+	0.335264i	0.794100	−	0.607787i	$-0.207943\pi$
$953$	14.2453	+	10.3498i	0.461451	+	0.335264i	−0.332649	+	0.943051i	$0.607943\pi$
$954$		0			0
$955$	3.35872	−	10.3371i	0.108686	−	0.334500i
$956$	0.808202	−	1.39985i	0.0261391	−	0.0452743i
$957$		0			0
$958$	10.1854	+	17.6416i	0.329075	+	0.569975i
$959$	88.0820	−	18.7224i	2.84432	−	0.604578i
$960$		0			0
$961$	−25.4694	+	11.3397i	−0.821592	+	0.365796i
$962$	22.2059	−	7.21513i	0.715946	−	0.232625i
$963$		0			0
$964$	−5.52069	+	7.59858i	−0.177809	+	0.244734i
$965$	−3.80333	−	36.1863i	−0.122434	−	1.16488i
$966$		0			0
$967$	−49.6682	+	28.6759i	−1.59722	+	0.922156i	−0.605201	+	0.796073i	$0.706907\pi$
$967$	−49.6682	+	28.6759i	−1.59722	+	0.922156i	−0.992020	+	0.126082i	$0.959760\pi$
$968$	16.7835	+	24.1390i	0.539443	+	0.775858i
$969$		0			0
$970$	7.18889	−	6.47291i	0.230821	−	0.207833i
$971$	−2.43578	−	3.35256i	−0.0781678	−	0.107589i	0.768143	−	0.640279i	$-0.221181\pi$
$971$	−2.43578	−	3.35256i	−0.0781678	−	0.107589i	−0.846310	+	0.532690i	$0.821181\pi$
$972$		0			0
$973$	−0.290090	−	0.892805i	−0.00929986	−	0.0286220i
$974$	4.74836	+	1.00930i	0.152147	+	0.0323399i
$975$		0			0
$976$	0.245102	−	0.550508i	0.00784552	−	0.0176213i
$977$	5.13699	+	24.1676i	0.164347	+	0.773191i	0.980681	+	0.195612i	$0.0626692\pi$
$977$	5.13699	+	24.1676i	0.164347	+	0.773191i	−0.816335	+	0.577579i	$0.803997\pi$
$978$		0			0
$979$	9.45081	−	9.25659i	0.302049	−	0.295842i
$980$			71.6300i			2.28814i
$981$		0			0
$982$	14.8775	−	10.8092i	0.474762	−	0.344934i
$983$	7.49604	+	16.8364i	0.239087	+	0.536997i	0.992741	−	0.120274i	$-0.0383773\pi$
$983$	7.49604	+	16.8364i	0.239087	+	0.536997i	−0.753654	+	0.657271i	$0.771711\pi$
$984$		0			0
$985$	−0.165016	−	0.148581i	−0.00525786	−	0.00473420i
$986$	0.0878719	−	0.836045i	0.00279841	−	0.0266251i
$987$		0			0
$988$	11.8684	+	13.1812i	0.377583	+	0.419349i
$989$	−21.5250			−0.684456
$990$		0			0
$991$	12.7050			0.403588			0.201794	−	0.979428i	$-0.435323\pi$
$991$	12.7050			0.403588			0.201794	+	0.979428i	$0.435323\pi$
$992$	−6.90332	−	7.66692i	−0.219181	−	0.243425i
$993$		0			0
$994$	5.92176	−	56.3417i	0.187827	−	1.78705i
$995$	−36.6455	−	32.9958i	−1.16174	−	1.04604i
$996$		0			0
$997$	−9.97683	−	22.4083i	−0.315969	−	0.709679i	0.683831	−	0.729640i	$-0.260312\pi$
$997$	−9.97683	−	22.4083i	−0.315969	−	0.709679i	−0.999801	+	0.0199613i	$0.993646\pi$
$998$	−19.4073	+	14.1002i	−0.614327	+	0.446334i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.b.431.3		32
3.2	odd	2		891.2.u.d.431.2		32
9.2	odd	6		297.2.k.b.134.3	✓	32
9.4	even	3		891.2.u.d.134.2		32
9.5	odd	6	inner	891.2.u.b.134.3		32
9.7	even	3		297.2.k.b.134.6	yes	32
11.6	odd	10	inner	891.2.u.b.512.3		32
33.17	even	10		891.2.u.d.512.2		32
99.50	even	30	inner	891.2.u.b.215.3		32
99.61	odd	30		297.2.k.b.215.3	yes	32
99.83	even	30		297.2.k.b.215.6	yes	32
99.94	odd	30		891.2.u.d.215.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.b.134.3	✓	32	9.2	odd	6
297.2.k.b.134.6	yes	32	9.7	even	3
297.2.k.b.215.3	yes	32	99.61	odd	30
297.2.k.b.215.6	yes	32	99.83	even	30
891.2.u.b.134.3		32	9.5	odd	6	inner
891.2.u.b.215.3		32	99.50	even	30	inner
891.2.u.b.431.3		32	1.1	even	1	trivial
891.2.u.b.512.3		32	11.6	odd	10	inner
891.2.u.d.134.2		32	9.4	even	3
891.2.u.d.215.2		32	99.94	odd	30
891.2.u.d.431.2		32	3.2	odd	2
891.2.u.d.512.2		32	33.17	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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.530442 + 0.589116i) q^{2} +(0.143369 - 1.36406i) q^{4} +(2.46396 + 2.21856i) q^{5} +(-1.94006 - 4.35745i) q^{7} +(2.16231 - 1.57101i) q^{8} +O(q^{10})\)	\(q+(0.530442 + 0.589116i) q^{2} +(0.143369 - 1.36406i) q^{4} +(2.46396 + 2.21856i) q^{5} +(-1.94006 - 4.35745i) q^{7} +(2.16231 - 1.57101i) q^{8} +2.62838i q^{10} +(-2.32073 - 2.36943i) q^{11} +(-0.685674 - 3.22584i) q^{13} +(1.53795 - 3.45430i) q^{14} +(-0.610720 - 0.129813i) q^{16} +(0.204370 + 0.628985i) q^{17} +(-2.30484 - 3.17234i) q^{19} +(3.37951 - 3.04292i) q^{20} +(0.164852 - 2.62403i) q^{22} +(-2.58864 + 1.49455i) q^{23} +(0.626454 + 5.96031i) q^{25} +(1.53668 - 2.11506i) q^{26} +(-6.22197 + 2.02164i) q^{28} +(-1.46482 + 0.652180i) q^{29} +(1.72784 - 0.367264i) q^{31} +(-2.92024 - 5.05800i) q^{32} +(-0.262139 + 0.454037i) q^{34} +(4.88704 - 15.0408i) q^{35} +(7.22526 + 5.24946i) q^{37} +(0.646291 - 3.04056i) q^{38} +(8.81323 + 0.926308i) q^{40} +(3.07730 + 1.37010i) q^{41} +(6.23639 + 3.60058i) q^{43} +(-3.56476 + 2.82592i) q^{44} +(-2.25359 - 0.732235i) q^{46} +(-7.26084 + 0.763145i) q^{47} +(-10.5396 + 11.7054i) q^{49} +(-3.17902 + 3.53065i) q^{50} +(-4.49855 + 0.472816i) q^{52} +(2.84114 + 0.923142i) q^{53} +(-0.461481 - 10.9869i) q^{55} +(-11.0406 - 6.37430i) q^{56} +(-1.16121 - 0.517005i) q^{58} +(13.7031 + 1.44025i) q^{59} +(-0.200666 + 0.944061i) q^{61} +(1.13288 + 0.823086i) q^{62} +(1.04485 - 3.21572i) q^{64} +(5.46726 - 9.46957i) q^{65} +(0.535376 + 0.927299i) q^{67} +(0.887274 - 0.188596i) q^{68} +(11.4530 - 5.09922i) q^{70} +(14.2493 - 4.62987i) q^{71} +(5.33171 - 7.33847i) q^{73} +(0.740044 + 7.04105i) q^{74} +(-4.65771 + 2.68913i) q^{76} +(-5.82230 + 14.7093i) q^{77} +(5.76410 - 5.19002i) q^{79} +(-1.21679 - 1.67477i) q^{80} +(0.825180 + 2.53964i) q^{82} +(5.17290 + 1.09953i) q^{83} +(-0.891883 + 2.00320i) q^{85} +(1.18689 + 5.58386i) q^{86} +(-8.74053 - 1.47754i) q^{88} +3.98865i q^{89} +(-12.7262 + 9.24613i) q^{91} +(1.66753 + 3.74533i) q^{92} +(-4.30104 - 3.87267i) q^{94} +(1.35900 - 12.9300i) q^{95} +(-2.46270 - 2.73510i) q^{97} -12.4865 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} - 15 q^{5}+O(q^{10}) \) 32 * q + 4 * q^4 - 15 * q^5	\( 32 q + 4 q^{4} - 15 q^{5} - 33 q^{11} + 12 q^{14} - 16 q^{16} + 36 q^{20} + 15 q^{22} - 18 q^{23} - 13 q^{25} - 10 q^{28} - 15 q^{29} + 8 q^{31} - 22 q^{34} + 18 q^{37} + 105 q^{38} - 15 q^{40} + 75 q^{41} + 40 q^{46} - 36 q^{47} + 12 q^{49} - 15 q^{50} + 40 q^{52} - 16 q^{55} - 60 q^{56} + 24 q^{58} + 39 q^{59} + 30 q^{61} + 48 q^{67} - 165 q^{68} + 41 q^{70} - 70 q^{73} + 15 q^{74} + 42 q^{77} + 60 q^{79} - 66 q^{82} + 60 q^{83} - 80 q^{85} - 6 q^{86} - 24 q^{88} - 60 q^{91} - 42 q^{92} - 100 q^{94} + 60 q^{95} - 24 q^{97}+O(q^{100}) \) 32 * q + 4 * q^4 - 15 * q^5 - 33 * q^11 + 12 * q^14 - 16 * q^16 + 36 * q^20 + 15 * q^22 - 18 * q^23 - 13 * q^25 - 10 * q^28 - 15 * q^29 + 8 * q^31 - 22 * q^34 + 18 * q^37 + 105 * q^38 - 15 * q^40 + 75 * q^41 + 40 * q^46 - 36 * q^47 + 12 * q^49 - 15 * q^50 + 40 * q^52 - 16 * q^55 - 60 * q^56 + 24 * q^58 + 39 * q^59 + 30 * q^61 + 48 * q^67 - 165 * q^68 + 41 * q^70 - 70 * q^73 + 15 * q^74 + 42 * q^77 + 60 * q^79 - 66 * q^82 + 60 * q^83 - 80 * q^85 - 6 * q^86 - 24 * q^88 - 60 * q^91 - 42 * q^92 - 100 * q^94 + 60 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more