LMFDB - Embedded newform 522.2.k.h.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [522,2,Mod(181,522)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(522, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("522.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 522 = 2 \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	522.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:	$4.16819098551$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 $ x^12 - 3x^11 + 13x^10 - 9x^9 - 5x^8 + 35x^7 + 197x^6 - 140x^5 - 80x^4 + 576x^3 + 3328x^2 + 3072*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			199.1
Root			$2.06920 + 0.996473i$ of defining polynomial
Character	$\chi$	$=$	522.199
Dual form			522.2.k.h.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.974928i) q^{2} +(-0.900969 - 0.433884i) q^{4} +(-0.110081 + 0.482295i) q^{5} +(-2.82760 + 1.36170i) q^{7} +(-0.623490 + 0.781831i) q^{8} +O(q^{10})$	\(q+(0.222521 - 0.974928i) q^{2} +(-0.900969 - 0.433884i) q^{4} +(-0.110081 + 0.482295i) q^{5} +(-2.82760 + 1.36170i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.445708 + 0.214642i) q^{10} +(-0.870839 - 1.09200i) q^{11} +(-3.56353 - 4.46852i) q^{13} +(0.698359 + 3.05971i) q^{14} +(0.623490 + 0.781831i) q^{16} -5.31800 q^{17} +(-4.47471 - 2.15491i) q^{19} +(0.308439 - 0.386771i) q^{20} +(-1.25840 + 0.606013i) q^{22} +(-0.181045 - 0.793210i) q^{23} +(4.28435 + 2.06324i) q^{25} +(-5.14944 + 2.47984i) q^{26} +3.13840 q^{28} +(-5.38501 + 0.0414712i) q^{29} +(-1.41596 + 6.20373i) q^{31} +(0.900969 - 0.433884i) q^{32} +(-1.18337 + 5.18466i) q^{34} +(-0.345477 - 1.51363i) q^{35} +(5.56630 - 6.97992i) q^{37} +(-3.09660 + 3.88301i) q^{38} +(-0.308439 - 0.386771i) q^{40} +4.01226 q^{41} +(0.310799 + 1.36170i) q^{43} +(0.310799 + 1.36170i) q^{44} -0.813609 q^{46} +(6.42079 + 8.05142i) q^{47} +(1.77665 - 2.22785i) q^{49} +(2.96486 - 3.71782i) q^{50} +(1.27181 + 5.57215i) q^{52} +(0.944288 - 4.13720i) q^{53} +(0.622528 - 0.299794i) q^{55} +(0.698359 - 3.05971i) q^{56} +(-1.15784 + 5.25922i) q^{58} -11.1598 q^{59} +(-4.38454 + 2.11149i) q^{61} +(5.73311 + 2.76092i) q^{62} +(-0.222521 - 0.974928i) q^{64} +(2.54742 - 1.22677i) q^{65} +(4.45072 - 5.58102i) q^{67} +(4.79135 + 2.30739i) q^{68} -1.55256 q^{70} +(-3.76423 - 4.72019i) q^{71} +(-2.73238 - 11.9713i) q^{73} +(-5.56630 - 6.97992i) q^{74} +(3.09660 + 3.88301i) q^{76} +(3.94935 + 1.90191i) q^{77} +(-5.86220 + 7.35096i) q^{79} +(-0.445708 + 0.214642i) q^{80} +(0.892813 - 3.91167i) q^{82} +(11.4508 + 5.51441i) q^{83} +(0.585409 - 2.56484i) q^{85} +1.39672 q^{86} +1.39672 q^{88} +(0.398796 - 1.74724i) q^{89} +(16.1610 + 7.78272i) q^{91} +(-0.181045 + 0.793210i) q^{92} +(9.27831 - 4.46820i) q^{94} +(1.53188 - 1.92092i) q^{95} +(-3.42035 - 1.64715i) q^{97} +(-1.77665 - 2.22785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{4} + q^{7} + 2 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^4 + q^7 + 2 * q^8	$ 12 q + 2 q^{2} - 2 q^{4} + q^{7} + 2 q^{8} - 7 q^{10} + 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{19} - 7 q^{20} - 2 q^{22} - 35 q^{23} - 6 q^{25} - 8 q^{26} - 6 q^{28} + 14 q^{29} - 8 q^{31} + 2 q^{32} - 5 q^{34} + 18 q^{35} + 31 q^{37} - q^{38} + 7 q^{40} + 30 q^{41} - 5 q^{43} - 5 q^{44} - 28 q^{46} + 33 q^{47} + 37 q^{49} - q^{50} - 6 q^{52} - 13 q^{53} + 36 q^{55} - q^{56} - 38 q^{59} - 5 q^{61} + 8 q^{62} - 2 q^{64} + 20 q^{65} - 7 q^{67} + 19 q^{68} - 18 q^{70} - 3 q^{71} - 22 q^{73} - 31 q^{74} + q^{76} - 10 q^{77} - 60 q^{79} + 7 q^{80} + 26 q^{82} + 39 q^{83} + 38 q^{85} - 2 q^{86} - 2 q^{88} - 39 q^{89} + 61 q^{91} - 35 q^{92} + 16 q^{94} - 55 q^{95} - 19 q^{97} - 37 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^4 + q^7 + 2 * q^8 - 7 * q^10 + 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 6 * q^19 - 7 * q^20 - 2 * q^22 - 35 * q^23 - 6 * q^25 - 8 * q^26 - 6 * q^28 + 14 * q^29 - 8 * q^31 + 2 * q^32 - 5 * q^34 + 18 * q^35 + 31 * q^37 - q^38 + 7 * q^40 + 30 * q^41 - 5 * q^43 - 5 * q^44 - 28 * q^46 + 33 * q^47 + 37 * q^49 - q^50 - 6 * q^52 - 13 * q^53 + 36 * q^55 - q^56 - 38 * q^59 - 5 * q^61 + 8 * q^62 - 2 * q^64 + 20 * q^65 - 7 * q^67 + 19 * q^68 - 18 * q^70 - 3 * q^71 - 22 * q^73 - 31 * q^74 + q^76 - 10 * q^77 - 60 * q^79 + 7 * q^80 + 26 * q^82 + 39 * q^83 + 38 * q^85 - 2 * q^86 - 2 * q^88 - 39 * q^89 + 61 * q^91 - 35 * q^92 + 16 * q^94 - 55 * q^95 - 19 * q^97 - 37 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/522\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

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 $

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$		0			0
$3$		0			0
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.110081	+	0.482295i	−0.0492296	+	0.215689i	−0.993560	−	0.113311i	$-0.963854\pi$
$5$	−0.110081	+	0.482295i	−0.0492296	+	0.215689i	0.944330	+	0.329000i	$0.106712\pi$
$6$		0			0
$7$	−2.82760	+	1.36170i	−1.06873	+	0.514674i	−0.883697	−	0.468059i	$-0.844954\pi$
$7$	−2.82760	+	1.36170i	−1.06873	+	0.514674i	−0.185033	+	0.982732i	$0.559239\pi$
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$		0			0
$10$	0.445708	+	0.214642i	0.140945	+	0.0678756i
$11$	−0.870839	−	1.09200i	−0.262568	−	0.329250i	0.633019	−	0.774136i	$-0.281815\pi$
$11$	−0.870839	−	1.09200i	−0.262568	−	0.329250i	−0.895587	+	0.444887i	$0.853244\pi$
$12$		0			0
$13$	−3.56353	−	4.46852i	−0.988344	−	1.23934i	−0.970897	−	0.239497i	$-0.923018\pi$
$13$	−3.56353	−	4.46852i	−0.988344	−	1.23934i	−0.0174472	−	0.999848i	$-0.505554\pi$
$14$	0.698359	+	3.05971i	0.186644	+	0.817742i
$15$		0			0
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−5.31800			−1.28980			−0.644902	−	0.764265i	$-0.723102\pi$
$17$	−5.31800			−1.28980			−0.644902	+	0.764265i	$0.723102\pi$
$18$		0			0
$19$	−4.47471	−	2.15491i	−1.02657	−	0.494370i	−0.156697	−	0.987647i	$-0.550085\pi$
$19$	−4.47471	−	2.15491i	−1.02657	−	0.494370i	−0.869872	+	0.493277i	$0.835799\pi$
$20$	0.308439	−	0.386771i	0.0689691	−	0.0864845i
$21$		0			0
$22$	−1.25840	+	0.606013i	−0.268292	+	0.129202i
$23$	−0.181045	−	0.793210i	−0.0377505	−	0.165396i	0.952539	−	0.304417i	$-0.0984616\pi$
$23$	−0.181045	−	0.793210i	−0.0377505	−	0.165396i	−0.990289	+	0.139021i	$0.955604\pi$
$24$		0			0
$25$	4.28435	+	2.06324i	0.856871	+	0.412647i
$26$	−5.14944	+	2.47984i	−1.00989	+	0.486337i
$27$		0			0
$28$	3.13840			0.593101
$29$	−5.38501	+	0.0414712i	−0.999970	+	0.00770101i
$29$	−5.38501	+	0.0414712i	−0.999970	+	0.00770101i
$30$		0			0
$31$	−1.41596	+	6.20373i	−0.254314	+	1.11422i	0.672912	+	0.739722i	$0.265043\pi$
$31$	−1.41596	+	6.20373i	−0.254314	+	1.11422i	−0.927226	+	0.374501i	$0.877814\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$		0			0
$34$	−1.18337	+	5.18466i	−0.202946	+	0.889162i
$35$	−0.345477	−	1.51363i	−0.0583962	−	0.255851i
$36$		0			0
$37$	5.56630	−	6.97992i	0.915095	−	1.14749i	−0.0735606	−	0.997291i	$-0.523436\pi$
$37$	5.56630	−	6.97992i	0.915095	−	1.14749i	0.988655	−	0.150202i	$-0.0479923\pi$
$38$	−3.09660	+	3.88301i	−0.502335	+	0.629908i
$39$		0			0
$40$	−0.308439	−	0.386771i	−0.0487685	−	0.0611538i
$41$	4.01226			0.626610			0.313305	−	0.949652i	$-0.398564\pi$
$41$	4.01226			0.626610			0.313305	+	0.949652i	$0.398564\pi$
$42$		0			0
$43$	0.310799	+	1.36170i	0.0473964	+	0.207657i	0.993082	−	0.117427i	$-0.0374646\pi$
$43$	0.310799	+	1.36170i	0.0473964	+	0.207657i	−0.945685	+	0.325084i	$0.894607\pi$
$44$	0.310799	+	1.36170i	0.0468547	+	0.205284i
$45$		0			0
$46$	−0.813609			−0.119960
$47$	6.42079	+	8.05142i	0.936569	+	1.17442i	0.984467	+	0.175568i	$0.0561761\pi$
$47$	6.42079	+	8.05142i	0.936569	+	1.17442i	−0.0478986	+	0.998852i	$0.515252\pi$
$48$		0			0
$49$	1.77665	−	2.22785i	0.253807	−	0.318264i
$50$	2.96486	−	3.71782i	0.419295	−	0.525780i
$51$		0			0
$52$	1.27181	+	5.57215i	0.176368	+	0.772719i
$53$	0.944288	−	4.13720i	0.129708	−	0.568288i	−0.867748	−	0.497004i	$-0.834433\pi$
$53$	0.944288	−	4.13720i	0.129708	−	0.568288i	0.997456	−	0.0712835i	$-0.0227095\pi$
$54$		0			0
$55$	0.622528	−	0.299794i	0.0839416	−	0.0404241i
$56$	0.698359	−	3.05971i	0.0933221	−	0.408871i
$57$		0			0
$58$	−1.15784	+	5.25922i	−0.152032	+	0.690569i
$59$	−11.1598			−1.45288			−0.726438	−	0.687232i	$-0.758826\pi$
$59$	−11.1598			−1.45288			−0.726438	+	0.687232i	$0.758826\pi$
$60$		0			0
$61$	−4.38454	+	2.11149i	−0.561383	+	0.270348i	−0.692982	−	0.720955i	$-0.743703\pi$
$61$	−4.38454	+	2.11149i	−0.561383	+	0.270348i	0.131598	+	0.991303i	$0.457989\pi$
$62$	5.73311	+	2.76092i	0.728106	+	0.350637i
$63$		0			0
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	2.54742	−	1.22677i	0.315969	−	0.152163i
$66$		0			0
$67$	4.45072	−	5.58102i	0.543742	−	0.681830i	−0.431718	−	0.902009i	$-0.642092\pi$
$67$	4.45072	−	5.58102i	0.543742	−	0.681830i	0.975460	+	0.220178i	$0.0706639\pi$
$68$	4.79135	+	2.30739i	0.581036	+	0.279812i
$69$		0			0
$70$	−1.55256			−0.185566
$71$	−3.76423	−	4.72019i	−0.446732	−	0.560184i	0.506572	−	0.862198i	$-0.330913\pi$
$71$	−3.76423	−	4.72019i	−0.446732	−	0.560184i	−0.953304	+	0.302014i	$0.902341\pi$
$72$		0			0
$73$	−2.73238	−	11.9713i	−0.319801	−	1.40114i	−0.837903	−	0.545819i	$-0.816219\pi$
$73$	−2.73238	−	11.9713i	−0.319801	−	1.40114i	0.518103	−	0.855319i	$-0.326639\pi$
$74$	−5.56630	−	6.97992i	−0.647070	−	0.811400i
$75$		0			0
$76$	3.09660	+	3.88301i	0.355204	+	0.445412i
$77$	3.94935	+	1.90191i	0.450070	+	0.216743i
$78$		0			0
$79$	−5.86220	+	7.35096i	−0.659549	+	0.827048i	−0.993294	−	0.115615i	$-0.963116\pi$
$79$	−5.86220	+	7.35096i	−0.659549	+	0.827048i	0.333745	+	0.942663i	$0.391687\pi$
$80$	−0.445708	+	0.214642i	−0.0498316	+	0.0239977i
$81$		0			0
$82$	0.892813	−	3.91167i	0.0985947	−	0.431971i
$83$	11.4508	+	5.51441i	1.25689	+	0.605285i	0.939350	−	0.342960i	$-0.111430\pi$
$83$	11.4508	+	5.51441i	1.25689	+	0.605285i	0.317538	+	0.948246i	$0.397144\pi$
$84$		0			0
$85$	0.585409	−	2.56484i	0.0634965	−	0.278196i
$86$	1.39672			0.150612
$87$		0			0
$88$	1.39672			0.148891
$89$	0.398796	−	1.74724i	0.0422722	−	0.185207i	−0.949384	−	0.314118i	$-0.898291\pi$
$89$	0.398796	−	1.74724i	0.0422722	−	0.185207i	0.991656	+	0.128911i	$0.0411483\pi$
$90$		0			0
$91$	16.1610	+	7.78272i	1.69413	+	0.815851i
$92$	−0.181045	+	0.793210i	−0.0188753	+	0.0826979i
$93$		0			0
$94$	9.27831	−	4.46820i	0.956985	−	0.460860i
$95$	1.53188	−	1.92092i	0.157168	−	0.197082i
$96$		0			0
$97$	−3.42035	−	1.64715i	−0.347283	−	0.167243i	0.252108	−	0.967699i	$-0.418876\pi$
$97$	−3.42035	−	1.64715i	−0.347283	−	0.167243i	−0.599391	+	0.800456i	$0.704591\pi$
$98$	−1.77665	−	2.22785i	−0.179469	−	0.225047i
$99$		0			0
$100$	−2.96486	−	3.71782i	−0.296486	−	0.371782i
$101$	−0.271881	−	1.19119i	−0.0270532	−	0.118528i	0.959598	−	0.281373i	$-0.0907899\pi$
$101$	−0.271881	−	1.19119i	−0.0270532	−	0.118528i	−0.986652	+	0.162846i	$0.947933\pi$
$102$		0			0
$103$	1.12736	+	1.41366i	0.111082	+	0.139292i	0.834264	−	0.551365i	$-0.185893\pi$
$103$	1.12736	+	1.41366i	0.111082	+	0.139292i	−0.723182	+	0.690657i	$0.757321\pi$
$104$	5.71545			0.560446
$105$		0			0
$106$	−3.82334	−	1.84123i	−0.371356	−	0.178836i
$107$	−2.58788	+	3.24509i	−0.250179	+	0.313715i	−0.891025	−	0.453955i	$-0.850013\pi$
$107$	−2.58788	+	3.24509i	−0.250179	+	0.313715i	0.640845	+	0.767670i	$0.278584\pi$
$108$		0			0
$109$	−13.0682	+	6.29330i	−1.25170	+	0.602789i	−0.937968	−	0.346721i	$-0.887295\pi$
$109$	−13.0682	+	6.29330i	−1.25170	+	0.602789i	−0.313736	+	0.949510i	$0.601581\pi$
$110$	−0.153752	−	0.673630i	−0.0146596	−	0.0642281i
$111$		0			0
$112$	−2.82760	−	1.36170i	−0.267183	−	0.128668i
$113$	15.0312	−	7.23864i	1.41402	−	0.680954i	0.438065	−	0.898943i	$-0.355664\pi$
$113$	15.0312	−	7.23864i	1.41402	−	0.680954i	0.975951	+	0.217989i	$0.0699497\pi$
$114$		0			0
$115$	0.402491			0.0375325
$116$	4.86972	+	2.29910i	0.452142	+	0.213466i
$117$		0			0
$118$	−2.48328	+	10.8800i	−0.228604	+	1.00158i
$119$	15.0371	−	7.24151i	1.37845	−	0.663828i
$120$		0			0
$121$	2.01363	−	8.82230i	0.183057	−	0.802027i
$122$	1.08289	+	4.74446i	0.0980405	+	0.429544i
$123$		0			0
$124$	3.96744	−	4.97501i	0.356286	−	0.446769i
$125$	−3.00891	+	3.77305i	−0.269125	+	0.337472i
$126$		0			0
$127$	−7.91387	−	9.92368i	−0.702243	−	0.880584i	0.294946	−	0.955514i	$-0.404698\pi$
$127$	−7.91387	−	9.92368i	−0.702243	−	0.880584i	−0.997189	+	0.0749295i	$0.976127\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−0.629161	−	2.75653i	−0.0551811	−	0.241764i
$131$	−3.29243	−	14.4251i	−0.287661	−	1.26033i	−0.887725	−	0.460374i	$-0.847715\pi$
$131$	−3.29243	−	14.4251i	−0.287661	−	1.26033i	0.600064	−	0.799952i	$-0.295142\pi$
$132$		0			0
$133$	15.5870			1.35157
$134$	−4.45072	−	5.58102i	−0.384483	−	0.482127i
$135$		0			0
$136$	3.31572	−	4.15778i	0.284320	−	0.356526i
$137$	0.941003	−	1.17998i	0.0803953	−	0.100813i	−0.740007	−	0.672599i	$-0.765178\pi$
$137$	0.941003	−	1.17998i	0.0803953	−	0.100813i	0.820403	+	0.571786i	$0.193749\pi$
$138$		0			0
$139$	−1.94848	−	8.53684i	−0.165268	−	0.724086i	−0.987846	−	0.155434i	$-0.950322\pi$
$139$	−1.94848	−	8.53684i	−0.165268	−	0.724086i	0.822578	−	0.568652i	$-0.192535\pi$
$140$	−0.345477	+	1.51363i	−0.0291981	+	0.127925i
$141$		0			0
$142$	−5.43947	+	2.61951i	−0.456470	+	0.219824i
$143$	−1.77636	+	7.78272i	−0.148546	+	0.650824i
$144$		0			0
$145$	0.572784	−	2.60173i	0.0475671	−	0.216062i
$146$	−12.2792			−1.01623
$147$		0			0
$148$	−8.04354	+	3.87357i	−0.661175	+	0.318405i
$149$	−4.27124	−	2.05692i	−0.349914	−	0.168510i	0.250668	−	0.968073i	$-0.419350\pi$
$149$	−4.27124	−	2.05692i	−0.349914	−	0.168510i	−0.600581	+	0.799564i	$0.705064\pi$
$150$		0			0
$151$	1.44508	+	6.33133i	0.117599	+	0.515236i	0.999075	+	0.0430064i	$0.0136936\pi$
$151$	1.44508	+	6.33133i	0.117599	+	0.515236i	−0.881475	+	0.472230i	$0.843449\pi$
$152$	4.47471	−	2.15491i	0.362947	−	0.174786i
$153$		0			0
$154$	2.73304	−	3.42712i	0.220234	−	0.276165i
$155$	−2.83616	−	1.36582i	−0.227806	−	0.109706i
$156$		0			0
$157$	6.56139			0.523656			0.261828	−	0.965115i	$-0.415675\pi$
$157$	6.56139			0.523656			0.261828	+	0.965115i	$0.415675\pi$
$158$	5.86220	+	7.35096i	0.466371	+	0.584811i
$159$		0			0
$160$	0.110081	+	0.482295i	0.00870264	+	0.0381288i
$161$	1.59204	+	1.99635i	0.125470	+	0.157334i
$162$		0			0
$163$	3.52776	+	4.42367i	0.276315	+	0.346488i	0.900553	−	0.434746i	$-0.143162\pi$
$163$	3.52776	+	4.42367i	0.276315	+	0.346488i	−0.624238	+	0.781234i	$0.714590\pi$
$164$	−3.61493	−	1.74086i	−0.282278	−	0.135938i
$165$		0			0
$166$	7.92419	−	9.93663i	0.615037	−	0.771232i
$167$	−10.8919	+	5.24527i	−0.842842	+	0.405891i	−0.804915	−	0.593389i	$-0.797789\pi$
$167$	−10.8919	+	5.24527i	−0.842842	+	0.405891i	−0.0379260	+	0.999281i	$0.512075\pi$
$168$		0			0
$169$	−4.37618	+	19.1733i	−0.336630	+	1.47487i
$170$	−2.37027	−	1.14146i	−0.181792	−	0.0875462i
$171$		0			0
$172$	0.310799	−	1.36170i	0.0236982	−	0.103829i
$173$	−11.6405			−0.885008			−0.442504	−	0.896767i	$-0.645910\pi$
$173$	−11.6405			−0.885008			−0.442504	+	0.896767i	$0.645910\pi$
$174$		0			0
$175$	−14.9239			−1.12814
$176$	0.310799	−	1.36170i	0.0234273	−	0.102642i
$177$		0			0
$178$	−1.61469	−	0.777594i	−0.121026	−	0.0582831i
$179$	−4.08440	+	17.8949i	−0.305282	+	1.33753i	0.556752	+	0.830678i	$0.312047\pi$
$179$	−4.08440	+	17.8949i	−0.305282	+	1.33753i	−0.862034	+	0.506850i	$0.830810\pi$
$180$		0			0
$181$	8.91422	−	4.29286i	0.662589	−	0.319086i	−0.0721917	−	0.997391i	$-0.522999\pi$
$181$	8.91422	−	4.29286i	0.662589	−	0.319086i	0.734781	+	0.678305i	$0.237285\pi$
$182$	11.1838	−	14.0240i	0.828995	−	1.03953i
$183$		0			0
$184$	0.733037	+	0.353012i	0.0540402	+	0.0260244i
$185$	2.75364	+	3.45296i	0.202452	+	0.253866i
$186$		0			0
$187$	4.63112	+	5.80724i	0.338661	+	0.424667i
$188$	−2.29155	−	10.0400i	−0.167129	−	0.732239i
$189$		0			0
$190$	−1.53188	−	1.92092i	−0.111134	−	0.139358i
$191$	−0.424259			−0.0306983			−0.0153492	−	0.999882i	$-0.504886\pi$
$191$	−0.424259			−0.0306983			−0.0153492	+	0.999882i	$0.504886\pi$
$192$		0			0
$193$	9.30230	+	4.47975i	0.669594	+	0.322460i	0.737612	−	0.675225i	$-0.235953\pi$
$193$	9.30230	+	4.47975i	0.669594	+	0.322460i	−0.0680181	+	0.997684i	$0.521668\pi$
$194$	−2.36695	+	2.96806i	−0.169937	+	0.213095i
$195$		0			0
$196$	−2.56733	+	1.23636i	−0.183381	+	0.0883116i
$197$	−5.97308	−	26.1698i	−0.425564	−	1.86452i	−0.498050	−	0.867148i	$-0.665950\pi$
$197$	−5.97308	−	26.1698i	−0.425564	−	1.86452i	0.0724862	−	0.997369i	$-0.476907\pi$
$198$		0			0
$199$	6.12924	+	2.95169i	0.434490	+	0.209239i	0.638327	−	0.769765i	$-0.279627\pi$
$199$	6.12924	+	2.95169i	0.434490	+	0.209239i	−0.203837	+	0.979005i	$0.565341\pi$
$200$	−4.28435	+	2.06324i	−0.302950	+	0.145893i
$201$		0			0
$202$	−1.22182			−0.0859671
$203$	15.1701	−	7.45002i	1.06474	−	0.522889i
$204$		0			0
$205$	−0.441673	+	1.93510i	−0.0308478	+	0.135153i
$206$	1.62908	−	0.784523i	0.113503	−	0.0546603i
$207$		0			0
$208$	1.27181	−	5.57215i	0.0881840	−	0.386359i
$209$	1.54360	+	6.76296i	0.106773	+	0.467803i
$210$		0			0
$211$	3.64156	−	4.56638i	0.250696	−	0.314362i	−0.640521	−	0.767941i	$-0.721281\pi$
$211$	3.64156	−	4.56638i	0.250696	−	0.314362i	0.891216	+	0.453579i	$0.149853\pi$
$212$	−2.64584	+	3.31777i	−0.181717	+	0.227866i
$213$		0			0
$214$	2.58788	+	3.24509i	0.176904	+	0.221830i
$215$	−0.690954			−0.0471226
$216$		0			0
$217$	−4.44385	−	19.4698i	−0.301668	−	1.32169i
$218$	3.22757	+	14.1409i	0.218599	+	0.957744i
$219$		0			0
$220$	−0.690954			−0.0465841
$221$	18.9508	+	23.7636i	1.27477	+	1.59851i
$222$		0			0
$223$	−13.6769	+	17.1503i	−0.915874	+	1.14847i	0.0726432	+	0.997358i	$0.476857\pi$
$223$	−13.6769	+	17.1503i	−0.915874	+	1.14847i	−0.988517	+	0.151111i	$0.951715\pi$
$224$	−1.95676	+	2.45370i	−0.130741	+	0.163944i
$225$		0			0
$226$	−3.71240	−	16.2651i	−0.246945	−	1.08194i
$227$	−0.479626	+	2.10138i	−0.0318339	+	0.139474i	−0.988348	−	0.152214i	$-0.951360\pi$
$227$	−0.479626	+	2.10138i	−0.0318339	+	0.139474i	0.956514	+	0.291688i	$0.0942168\pi$
$228$		0			0
$229$	−8.37172	+	4.03161i	−0.553219	+	0.266416i	−0.689539	−	0.724249i	$-0.742187\pi$
$229$	−8.37172	+	4.03161i	−0.553219	+	0.266416i	0.136320	+	0.990665i	$0.456472\pi$
$230$	0.0895627	−	0.392400i	0.00590559	−	0.0258741i
$231$		0			0
$232$	3.32507	−	4.23602i	0.218302	−	0.278109i
$233$	11.7848			0.772045			0.386022	−	0.922489i	$-0.373849\pi$
$233$	11.7848			0.772045			0.386022	+	0.922489i	$0.373849\pi$
$234$		0			0
$235$	−4.58996	+	2.21041i	−0.299416	+	0.144191i
$236$	10.0546	+	4.84204i	0.654498	+	0.315190i
$237$		0			0
$238$	−3.71387	−	16.2715i	−0.240734	−	1.05473i
$239$	−12.9462	+	6.23455i	−0.837419	+	0.403280i	−0.802892	−	0.596124i	$-0.796707\pi$
$239$	−12.9462	+	6.23455i	−0.837419	+	0.403280i	−0.0345265	+	0.999404i	$0.510992\pi$
$240$		0			0
$241$	−5.73880	+	7.19623i	−0.369669	+	0.463550i	−0.931521	−	0.363688i	$-0.881517\pi$
$241$	−5.73880	+	7.19623i	−0.369669	+	0.463550i	0.561852	+	0.827238i	$0.310089\pi$
$242$	−8.15303	−	3.92629i	−0.524097	−	0.252392i
$243$		0			0
$244$	4.86648			0.311544
$245$	0.878905	+	1.10211i	0.0561512	+	0.0704114i
$246$		0			0
$247$	6.31651	+	27.6744i	0.401910	+	1.76088i
$248$	−3.96744	−	4.97501i	−0.251933	−	0.315913i
$249$		0			0
$250$	3.00891	+	3.77305i	0.190300	+	0.238629i
$251$	5.33012	+	2.56685i	0.336434	+	0.162018i	0.594471	−	0.804117i	$-0.297361\pi$
$251$	5.33012	+	2.56685i	0.336434	+	0.162018i	−0.258037	+	0.966135i	$0.583076\pi$
$252$		0			0
$253$	−0.708523	+	0.888459i	−0.0445444	+	0.0558569i
$254$	−11.4359	+	5.50723i	−0.717551	+	0.345554i
$255$		0			0
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−24.0750	−	11.5939i	−1.50176	−	0.723209i	−0.511094	−	0.859525i	$-0.670759\pi$
$257$	−24.0750	−	11.5939i	−1.50176	−	0.723209i	−0.990665	+	0.136316i	$0.956474\pi$
$258$		0			0
$259$	−6.23471	+	27.3160i	−0.387406	+	1.69734i
$260$	−2.82742			−0.175349
$261$		0			0
$262$	−14.7961			−0.914104
$263$	−5.19684	+	22.7688i	−0.320451	+	1.40399i	0.516302	+	0.856407i	$0.327308\pi$
$263$	−5.19684	+	22.7688i	−0.320451	+	1.40399i	−0.836753	+	0.547581i	$0.815549\pi$
$264$		0			0
$265$	1.89140	+	0.910851i	0.116188	+	0.0559531i
$266$	3.46844	−	15.1962i	0.212664	−	0.931740i
$267$		0			0
$268$	−6.43147	+	3.09723i	−0.392865	+	0.189194i
$269$	−9.73222	+	12.2038i	−0.593384	+	0.744080i	−0.984331	−	0.176333i	$-0.943576\pi$
$269$	−9.73222	+	12.2038i	−0.593384	+	0.744080i	0.390946	+	0.920413i	$0.372148\pi$
$270$		0			0
$271$	−0.197924	−	0.0953153i	−0.0120230	−	0.00578999i	0.427863	−	0.903844i	$-0.359267\pi$
$271$	−0.197924	−	0.0953153i	−0.0120230	−	0.00578999i	−0.439886	+	0.898054i	$0.644981\pi$
$272$	−3.31572	−	4.15778i	−0.201045	−	0.252102i
$273$		0			0
$274$	−0.941003	−	1.17998i	−0.0568481	−	0.0712853i
$275$	−1.47793	−	6.47525i	−0.0891227	−	0.390472i
$276$		0			0
$277$	2.33928	+	2.93336i	0.140554	+	0.176249i	0.847126	−	0.531392i	$-0.178331\pi$
$277$	2.33928	+	2.93336i	0.140554	+	0.176249i	−0.706572	+	0.707641i	$0.749759\pi$
$278$	−8.75639			−0.525173
$279$		0			0
$280$	1.39881	+	0.673630i	0.0835947	+	0.0402571i
$281$	15.2450	−	19.1167i	0.909442	−	1.14040i	−0.0801905	−	0.996780i	$-0.525553\pi$
$281$	15.2450	−	19.1167i	0.909442	−	1.14040i	0.989632	−	0.143624i	$-0.0458757\pi$
$282$		0			0
$283$	−6.84512	+	3.29644i	−0.406900	+	0.195953i	−0.626127	−	0.779721i	$-0.715361\pi$
$283$	−6.84512	+	3.29644i	−0.406900	+	0.195953i	0.219227	+	0.975674i	$0.429647\pi$
$284$	1.34344	+	5.88599i	0.0797184	+	0.349269i
$285$		0			0
$286$	7.19232	+	3.46364i	0.425291	+	0.204809i
$287$	−11.3451	+	5.46349i	−0.669678	+	0.322500i
$288$		0			0
$289$	11.2811			0.663593
$290$	−2.40904	−	1.13736i	−0.141464	−	0.0667882i
$291$		0			0
$292$	−2.73238	+	11.9713i	−0.159900	+	0.700569i
$293$	−23.1750	+	11.1605i	−1.35390	+	0.652003i	−0.963267	−	0.268545i	$-0.913457\pi$
$293$	−23.1750	+	11.1605i	−1.35390	+	0.652003i	−0.390631	+	0.920547i	$0.627743\pi$
$294$		0			0
$295$	1.22847	−	5.38230i	0.0715245	−	0.313369i
$296$	1.98659	+	8.70382i	0.115468	+	0.505899i
$297$		0			0
$298$	−2.95579	+	3.70644i	−0.171224	+	0.214709i
$299$	−2.89932	+	3.63563i	−0.167672	+	0.210254i
$300$		0			0
$301$	−2.73304	−	3.42712i	−0.157530	−	0.197536i
$302$	6.49415			0.373696
$303$		0			0
$304$	−1.10516	−	4.84204i	−0.0633855	−	0.277710i
$305$	−0.535705	−	2.34708i	−0.0306744	−	0.134393i
$306$		0			0
$307$	1.81399			0.103530			0.0517649	−	0.998659i	$-0.483515\pi$
$307$	1.81399			0.103530			0.0517649	+	0.998659i	$0.483515\pi$
$308$	−2.73304	−	3.42712i	−0.155729	−	0.195278i
$309$		0			0
$310$	−1.96268	+	2.46113i	−0.111473	+	0.139783i
$311$	−12.1020	+	15.1754i	−0.686239	+	0.860517i	−0.995912	−	0.0903265i	$-0.971209\pi$
$311$	−12.1020	+	15.1754i	−0.686239	+	0.860517i	0.309673	+	0.950843i	$0.399780\pi$
$312$		0			0
$313$	−7.54006	−	33.0352i	−0.426189	−	1.86726i	−0.493847	−	0.869549i	$-0.664410\pi$
$313$	−7.54006	−	33.0352i	−0.426189	−	1.86726i	0.0676576	−	0.997709i	$-0.478447\pi$
$314$	1.46005	−	6.39688i	0.0823952	−	0.360997i
$315$		0			0
$316$	8.47112	−	4.07948i	0.476538	−	0.229489i
$317$	1.22333	−	5.35977i	0.0687092	−	0.301035i	−0.928884	−	0.370370i	$-0.879231\pi$
$317$	1.22333	−	5.35977i	0.0687092	−	0.301035i	0.997593	+	0.0693356i	$0.0220879\pi$
$318$		0			0
$319$	4.73476	+	5.84430i	0.265096	+	0.327218i
$320$	0.494698			0.0276545
$321$		0			0
$322$	2.30056	−	1.10789i	0.128205	−	0.0617403i
$323$	23.7965	+	11.4598i	1.32407	+	0.637640i
$324$		0			0
$325$	−6.04779	−	26.4971i	−0.335471	−	1.46980i
$326$	5.09776	−	2.45495i	0.282339	−	0.135967i
$327$		0			0
$328$	−2.50161	+	3.13691i	−0.138128	+	0.173207i
$329$	−29.1190	−	14.0230i	−1.60538	−	0.773112i
$330$		0			0
$331$	−13.6463			−0.750067			−0.375034	−	0.927011i	$-0.622369\pi$
$331$	−13.6463			−0.750067			−0.375034	+	0.927011i	$0.622369\pi$
$332$	−7.92419	−	9.93663i	−0.434897	−	0.545343i
$333$		0			0
$334$	2.69008	+	11.7860i	0.147195	+	0.644902i
$335$	2.20176	+	2.76092i	0.120295	+	0.150845i
$336$		0			0
$337$	14.0705	+	17.6438i	0.766469	+	0.961122i	0.999937	−	0.0112429i	$-0.00357882\pi$
$337$	14.0705	+	17.6438i	0.766469	+	0.961122i	−0.233468	+	0.972365i	$0.575007\pi$
$338$	17.7188	+	8.53293i	0.963776	+	0.464130i
$339$		0			0
$340$	−1.64028	+	2.05684i	−0.0889566	+	0.111548i
$341$	8.00754	−	3.85623i	0.433632	−	0.208826i
$342$		0			0
$343$	2.89852	−	12.6993i	0.156505	−	0.685695i
$344$	−1.25840	−	0.606013i	−0.0678483	−	0.0326740i
$345$		0			0
$346$	−2.59025	+	11.3486i	−0.139253	+	0.610105i
$347$	2.97305			0.159602			0.0798008	−	0.996811i	$-0.474572\pi$
$347$	2.97305			0.159602			0.0798008	+	0.996811i	$0.474572\pi$
$348$		0			0
$349$	−5.73913			−0.307208			−0.153604	−	0.988132i	$-0.549088\pi$
$349$	−5.73913			−0.307208			−0.153604	+	0.988132i	$0.549088\pi$
$350$	−3.32089	+	14.5498i	−0.177509	+	0.777717i
$351$		0			0
$352$	−1.25840	−	0.606013i	−0.0670729	−	0.0323006i
$353$	−1.44019	+	6.30988i	−0.0766536	+	0.335841i	−0.998685	−	0.0512748i	$-0.983672\pi$
$353$	−1.44019	+	6.30988i	−0.0766536	+	0.335841i	0.922031	+	0.387116i	$0.126529\pi$
$354$		0			0
$355$	2.69090	−	1.29587i	0.142818	−	0.0687775i
$356$	−1.11740	+	1.40118i	−0.0592221	+	0.0742622i
$357$		0			0
$358$	16.5374	+	7.96398i	0.874028	+	0.420910i
$359$	−6.69717	−	8.39798i	−0.353463	−	0.443229i	0.573034	−	0.819532i	$-0.305766\pi$
$359$	−6.69717	−	8.39798i	−0.353463	−	0.443229i	−0.926496	+	0.376303i	$0.877195\pi$
$360$		0			0
$361$	3.53313	+	4.43041i	0.185954	+	0.233179i
$362$	−2.20163	−	9.64598i	−0.115715	−	0.506981i
$363$		0			0
$364$	−11.1838	−	14.0240i	−0.586188	−	0.735056i
$365$	6.07449			0.317954
$366$		0			0
$367$	−17.0637	−	8.21747i	−0.890720	−	0.428948i	−0.0681919	−	0.997672i	$-0.521723\pi$
$367$	−17.0637	−	8.21747i	−0.890720	−	0.428948i	−0.822529	+	0.568724i	$0.807437\pi$
$368$	0.507277	−	0.636105i	0.0264436	−	0.0331593i
$369$		0			0
$370$	3.97913	−	1.91625i	0.206865	−	0.0996209i
$371$	2.96355	+	12.9842i	0.153860	+	0.674104i
$372$		0			0
$373$	−2.19298	−	1.05608i	−0.113548	−	0.0546819i	0.376247	−	0.926519i	$-0.377214\pi$
$373$	−2.19298	−	1.05608i	−0.113548	−	0.0546819i	−0.489796	+	0.871837i	$0.662929\pi$
$374$	6.69216	−	3.22277i	0.346043	−	0.166646i
$375$		0			0
$376$	−10.2982			−0.531087
$377$	19.3749	+	23.9152i	0.997859	+	1.23170i
$378$		0			0
$379$	3.81433	−	16.7117i	0.195929	−	0.858422i	−0.777400	−	0.629007i	$-0.783462\pi$
$379$	3.81433	−	16.7117i	0.195929	−	0.858422i	0.973329	−	0.229415i	$-0.0736812\pi$
$380$	−2.21363	+	1.06603i	−0.113557	+	0.0546862i
$381$		0			0
$382$	−0.0944066	+	0.413622i	−0.00483026	+	0.0211628i
$383$	−5.29096	−	23.1812i	−0.270355	−	1.18450i	−0.909595	−	0.415497i	$-0.863608\pi$
$383$	−5.29096	−	23.1812i	−0.270355	−	1.18450i	0.639239	−	0.769008i	$-0.279249\pi$
$384$		0			0
$385$	−1.35203	+	1.69539i	−0.0689057	+	0.0864051i
$386$	6.43739	−	8.07223i	0.327655	−	0.410866i
$387$		0			0
$388$	2.36695	+	2.96806i	0.120164	+	0.150681i
$389$	11.5272			0.584453			0.292227	−	0.956349i	$-0.405604\pi$
$389$	11.5272			0.584453			0.292227	+	0.956349i	$0.405604\pi$
$390$		0			0
$391$	0.962797	+	4.21829i	0.0486907	+	0.213328i
$392$	0.634079	+	2.77808i	0.0320258	+	0.140314i
$393$		0			0
$394$	−26.8428			−1.35232
$395$	−2.90002	−	3.63651i	−0.145916	−	0.182973i
$396$		0			0
$397$	18.0708	−	22.6601i	0.906948	−	1.13728i	−0.0830990	−	0.996541i	$-0.526482\pi$
$397$	18.0708	−	22.6601i	0.906948	−	1.13728i	0.990047	−	0.140736i	$-0.0449468\pi$
$398$	4.24156	−	5.31875i	0.212610	−	0.266605i
$399$		0			0
$400$	1.05815	+	4.63605i	0.0529074	+	0.231802i
$401$	2.29856	−	10.0707i	0.114785	−	0.502905i	−0.884550	−	0.466445i	$-0.845535\pi$
$401$	2.29856	−	10.0707i	0.114785	−	0.502905i	0.999335	−	0.0364602i	$-0.0116082\pi$
$402$		0			0
$403$	32.7673	−	15.7799i	1.63226	−	0.786054i
$404$	−0.271881	+	1.19119i	−0.0135266	+	0.0592638i
$405$		0			0
$406$	−3.88755	−	16.4476i	−0.192936	−	0.816280i
$407$	−12.4694			−0.618086
$408$		0			0
$409$	−8.97519	+	4.32222i	−0.443794	+	0.213720i	−0.642416	−	0.766356i	$-0.722068\pi$
$409$	−8.97519	+	4.32222i	−0.443794	+	0.213720i	0.198622	+	0.980076i	$0.436354\pi$
$410$	1.78830	+	0.861198i	0.0883177	+	0.0425316i
$411$		0			0
$412$	−0.402349	−	1.76281i	−0.0198223	−	0.0868473i
$413$	31.5553	−	15.1962i	1.55273	−	0.747757i
$414$		0			0
$415$	−3.92009	+	4.91563i	−0.192429	+	0.241299i
$416$	−5.14944	−	2.47984i	−0.252472	−	0.121584i
$417$		0			0
$418$	6.93688			0.339294
$419$	−17.6773	−	22.1667i	−0.863595	−	1.08291i	−0.995788	−	0.0916894i	$-0.970773\pi$
$419$	−17.6773	−	22.1667i	−0.863595	−	1.08291i	0.132193	−	0.991224i	$-0.457798\pi$
$420$		0			0
$421$	2.11840	+	9.28130i	0.103244	+	0.452343i	0.999953	+	0.00972116i	$0.00309439\pi$
$421$	2.11840	+	9.28130i	0.103244	+	0.452343i	−0.896708	+	0.442622i	$0.854048\pi$
$422$	−3.64156	−	4.56638i	−0.177268	−	0.222288i
$423$		0			0
$424$	2.64584	+	3.31777i	0.128493	+	0.161125i
$425$	−22.7842	−	10.9723i	−1.10519	−	0.532234i
$426$		0			0
$427$	9.52251	−	11.9409i	0.460827	−	0.577859i
$428$	3.73959	−	1.80089i	0.180760	−	0.0870493i
$429$		0			0
$430$	−0.153752	+	0.673630i	−0.00741456	+	0.0324853i
$431$	−17.0958	−	8.23291i	−0.823477	−	0.396566i	−0.0258122	−	0.999667i	$-0.508217\pi$
$431$	−17.0958	−	8.23291i	−0.823477	−	0.396566i	−0.797665	+	0.603101i	$0.793931\pi$
$432$		0			0
$433$	−6.30063	+	27.6049i	−0.302789	+	1.32661i	0.563108	+	0.826383i	$0.309605\pi$
$433$	−6.30063	+	27.6049i	−0.302789	+	1.32661i	−0.865897	+	0.500222i	$0.833252\pi$
$434$	−19.9705			−0.958613
$435$		0			0
$436$	14.5046			0.694644
$437$	−0.899171	+	3.93953i	−0.0430132	+	0.188453i
$438$		0			0
$439$	17.9255	+	8.63248i	0.855539	+	0.412006i	0.809631	−	0.586940i	$-0.199667\pi$
$439$	17.9255	+	8.63248i	0.855539	+	0.412006i	0.0459084	+	0.998946i	$0.485382\pi$
$440$	−0.153752	+	0.673630i	−0.00732982	+	0.0321140i
$441$		0			0
$442$	27.3847	−	13.1878i	1.30256	−	0.627279i
$443$	22.1713	−	27.8019i	1.05339	−	1.32091i	0.108292	−	0.994119i	$-0.465462\pi$
$443$	22.1713	−	27.8019i	1.05339	−	1.32091i	0.945097	−	0.326790i	$-0.105967\pi$
$444$		0			0
$445$	0.798784	+	0.384674i	0.0378660	+	0.0182353i
$446$	13.6769	+	17.1503i	0.647620	+	0.812090i
$447$		0			0
$448$	1.95676	+	2.45370i	0.0924481	+	0.115926i
$449$	2.41460	+	10.5790i	0.113952	+	0.499256i	0.999404	+	0.0345250i	$0.0109918\pi$
$449$	2.41460	+	10.5790i	0.113952	+	0.499256i	−0.885452	+	0.464731i	$0.846151\pi$
$450$		0			0
$451$	−3.49404	−	4.38138i	−0.164528	−	0.206311i
$452$	−16.6834			−0.784720
$453$		0			0
$454$	1.94197	+	0.935202i	0.0911411	+	0.0438912i
$455$	−5.53258	+	6.93764i	−0.259371	+	0.325242i
$456$		0			0
$457$	−29.1336	+	14.0300i	−1.36281	+	0.656296i	−0.965262	−	0.261285i	$-0.915854\pi$
$457$	−29.1336	+	14.0300i	−1.36281	+	0.656296i	−0.397550	+	0.917580i	$0.630140\pi$
$458$	2.06764	+	9.05894i	0.0966146	+	0.423296i
$459$		0			0
$460$	−0.362632	−	0.174634i	−0.0169078	−	0.00814237i
$461$	22.8888	−	11.0227i	1.06604	−	0.513377i	0.183211	−	0.983074i	$-0.441351\pi$
$461$	22.8888	−	11.0227i	1.06604	−	0.513377i	0.882828	+	0.469696i	$0.155637\pi$
$462$		0			0
$463$	3.22072			0.149680			0.0748398	−	0.997196i	$-0.476155\pi$
$463$	3.22072			0.149680			0.0748398	+	0.997196i	$0.476155\pi$
$464$	−3.38992	−	4.18431i	−0.157373	−	0.194252i
$465$		0			0
$466$	2.62235	−	11.4893i	0.121478	−	0.532231i
$467$	20.5930	−	9.91706i	0.952929	−	0.458907i	0.108217	−	0.994127i	$-0.465486\pi$
$467$	20.5930	−	9.91706i	0.952929	−	0.458907i	0.844712	+	0.535221i	$0.179772\pi$
$468$		0			0
$469$	−4.98516	+	21.8414i	−0.230193	+	1.00854i
$470$	1.13363	+	4.96675i	0.0522903	+	0.229099i
$471$		0			0
$472$	6.95799	−	8.72505i	0.320268	−	0.401603i
$473$	1.21632	−	1.52521i	0.0559263	−	0.0701293i
$474$		0			0
$475$	−14.7252	−	18.4648i	−0.675637	−	0.847222i
$476$	−16.6900			−0.764984
$477$		0			0
$478$	3.19744	+	14.0089i	0.146248	+	0.640753i
$479$	0.477409	+	2.09166i	0.0218134	+	0.0955706i	0.984663	−	0.174468i	$-0.0558206\pi$
$479$	0.477409	+	2.09166i	0.0218134	+	0.0955706i	−0.962849	+	0.270039i	$0.912963\pi$
$480$		0			0
$481$	−51.0256			−2.32657
$482$	5.73880	+	7.19623i	0.261395	+	0.327779i
$483$		0			0
$484$	−5.64207	+	7.07493i	−0.256458	+	0.321588i
$485$	1.17093	−	1.46830i	0.0531691	−	0.0666719i
$486$		0			0
$487$	−4.84560	−	21.2300i	−0.219575	−	0.962021i	−0.957793	−	0.287459i	$-0.907190\pi$
$487$	−4.84560	−	21.2300i	−0.219575	−	0.962021i	0.738218	−	0.674562i	$-0.235668\pi$
$488$	1.08289	−	4.74446i	0.0490203	−	0.214772i
$489$		0			0
$490$	1.27005	−	0.611626i	0.0573752	−	0.0276304i
$491$	−8.64786	+	37.8888i	−0.390273	+	1.70990i	0.273423	+	0.961894i	$0.411844\pi$
$491$	−8.64786	+	37.8888i	−0.390273	+	1.70990i	−0.663696	+	0.748002i	$0.731013\pi$
$492$		0			0
$493$	28.6374	−	0.220544i	1.28977	−	0.00993279i
$494$	28.3861			1.27715
$495$		0			0
$496$	−5.73311	+	2.76092i	−0.257424	+	0.123969i
$497$	17.0712	+	8.22106i	0.765748	+	0.368765i
$498$		0			0
$499$	−8.74490	−	38.3139i	−0.391476	−	1.71517i	−0.659457	−	0.751742i	$-0.729214\pi$
$499$	−8.74490	−	38.3139i	−0.391476	−	1.71517i	0.267981	−	0.963424i	$-0.413643\pi$
$500$	4.34800	−	2.09389i	0.194449	−	0.0936415i
$501$		0			0
$502$	3.68856	−	4.62530i	0.164628	−	0.206437i
$503$	25.2735	+	12.1711i	1.12689	+	0.542680i	0.902014	−	0.431707i	$-0.142089\pi$
$503$	25.2735	+	12.1711i	1.12689	+	0.542680i	0.224874	+	0.974388i	$0.427803\pi$
$504$		0			0
$505$	0.604433			0.0268969
$506$	0.708523	+	0.888459i	0.0314977	+	0.0394968i
$507$		0			0
$508$	2.82443	+	12.3746i	0.125314	+	0.549035i
$509$	−1.06278	−	1.33268i	−0.0471069	−	0.0590701i	0.757720	−	0.652580i	$-0.226313\pi$
$509$	−1.06278	−	1.33268i	−0.0471069	−	0.0590701i	−0.804827	+	0.593510i	$0.797742\pi$
$510$		0			0
$511$	24.0274	+	30.1294i	1.06291	+	1.33285i
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$		0			0
$514$	−16.6604	+	20.8915i	−0.734860	+	0.921486i
$515$	−0.805903	+	0.388102i	−0.0355123	+	0.0171018i
$516$		0			0
$517$	3.20065	−	14.0230i	0.140765	−	0.616730i
$518$	25.2438	+	12.1568i	1.10915	+	0.534138i
$519$		0			0
$520$	−0.629161	+	2.75653i	−0.0275905	+	0.120882i
$521$	21.0834			0.923678			0.461839	−	0.886964i	$-0.347190\pi$
$521$	21.0834			0.923678			0.461839	+	0.886964i	$0.347190\pi$
$522$		0			0
$523$	−8.93606			−0.390747			−0.195373	−	0.980729i	$-0.562592\pi$
$523$	−8.93606			−0.390747			−0.195373	+	0.980729i	$0.562592\pi$
$524$	−3.29243	+	14.4251i	−0.143831	+	0.630163i
$525$		0			0
$526$	21.0416	+	10.1331i	0.917457	+	0.441824i
$527$	7.53008	−	32.9914i	0.328015	−	1.43713i
$528$		0			0
$529$	20.1259	−	9.69211i	0.875038	−	0.421396i
$530$	1.30889	−	1.64130i	0.0568546	−	0.0712934i
$531$		0			0
$532$	−14.0434	−	6.76296i	−0.608860	−	0.293211i
$533$	−14.2978	−	17.9289i	−0.619307	−	0.776586i
$534$		0			0
$535$	−1.28022	−	1.60534i	−0.0553486	−	0.0694050i
$536$	1.58844	+	6.95942i	0.0686103	+	0.300601i
$537$		0			0
$538$	9.73222	+	12.2038i	0.419586	+	0.526144i
$539$	−3.97998			−0.171430
$540$		0			0
$541$	10.7827	+	5.19269i	0.463586	+	0.223251i	0.651072	−	0.759016i	$-0.274320\pi$
$541$	10.7827	+	5.19269i	0.463586	+	0.223251i	−0.187486	+	0.982267i	$0.560034\pi$
$542$	−0.136968	+	0.171752i	−0.00588327	+	0.00737739i
$543$		0			0
$544$	−4.79135	+	2.30739i	−0.205427	+	0.0989286i
$545$	−1.59668	−	6.99549i	−0.0683940	−	0.299654i
$546$		0			0
$547$	21.7331	+	10.4661i	0.929239	+	0.447498i	0.836361	−	0.548180i	$-0.184679\pi$
$547$	21.7331	+	10.4661i	0.929239	+	0.447498i	0.0928783	+	0.995677i	$0.470393\pi$
$548$	−1.35979	+	0.654840i	−0.0580873	+	0.0279734i
$549$		0			0
$550$	−6.64177			−0.283206
$551$	24.1857	+	11.4186i	1.03035	+	0.486450i
$552$		0			0
$553$	6.56613	−	28.7681i	0.279220	−	1.22334i
$554$	3.38036	−	1.62789i	0.143618	−	0.0691626i
$555$		0			0
$556$	−1.94848	+	8.53684i	−0.0826339	+	0.362043i
$557$	−4.05033	−	17.7456i	−0.171618	−	0.751907i	−0.985333	−	0.170643i	$-0.945416\pi$
$557$	−4.05033	−	17.7456i	−0.171618	−	0.751907i	0.813715	−	0.581264i	$-0.197442\pi$
$558$		0			0
$559$	4.97724	−	6.24126i	0.210515	−	0.263977i
$560$	0.968004	−	1.21384i	0.0409057	−	0.0512941i
$561$		0			0
$562$	−15.2450	−	19.1167i	−0.643072	−	0.806387i
$563$	31.5149			1.32820			0.664098	−	0.747646i	$-0.268816\pi$
$563$	31.5149			1.32820			0.664098	+	0.747646i	$0.268816\pi$
$564$		0			0
$565$	1.83652	+	8.04631i	0.0772629	+	0.338511i
$566$	1.69060	+	7.40702i	0.0710614	+	0.311340i
$567$		0			0
$568$	6.03736			0.253322
$569$	17.7477	+	22.2549i	0.744023	+	0.932975i	0.999427	−	0.0338594i	$-0.0107798\pi$
$569$	17.7477	+	22.2549i	0.744023	+	0.932975i	−0.255404	+	0.966834i	$0.582208\pi$
$570$		0			0
$571$	−2.65790	+	3.33290i	−0.111230	+	0.139478i	−0.834330	−	0.551266i	$-0.814145\pi$
$571$	−2.65790	+	3.33290i	−0.111230	+	0.139478i	0.723100	+	0.690743i	$0.242717\pi$
$572$	4.97724	−	6.24126i	0.208109	−	0.260960i
$573$		0			0
$574$	2.80200	+	12.2764i	0.116953	+	0.512405i
$575$	0.860919	−	3.77193i	0.0359028	−	0.157300i
$576$		0			0
$577$	−20.3474	+	9.79878i	−0.847072	+	0.407929i	−0.806490	−	0.591248i	$-0.798636\pi$
$577$	−20.3474	+	9.79878i	−0.847072	+	0.407929i	−0.0405823	+	0.999176i	$0.512921\pi$
$578$	2.51028	−	10.9982i	0.104414	−	0.457467i
$579$		0			0
$580$	−1.64491	+	2.09555i	−0.0683011	+	0.0870131i
$581$	−39.8872			−1.65480
$582$		0			0
$583$	−5.34013	+	2.57167i	−0.221166	+	0.106508i
$584$	11.0632	+	5.32774i	0.457797	+	0.220463i
$585$		0			0
$586$	5.72375	+	25.0774i	0.236446	+	1.03594i
$587$	−30.1868	+	14.5372i	−1.24594	+	0.600015i	−0.936422	−	0.350877i	$-0.885884\pi$
$587$	−30.1868	+	14.5372i	−1.24594	+	0.600015i	−0.309523	+	0.950892i	$0.600169\pi$
$588$		0			0
$589$	19.7045	−	24.7087i	0.811910	−	1.01810i
$590$	−4.97399	−	2.39535i	−0.204776	−	0.0986149i
$591$		0			0
$592$	8.92766			0.366925
$593$	−8.32767	−	10.4426i	−0.341977	−	0.428825i	0.580868	−	0.813998i	$-0.302713\pi$
$593$	−8.32767	−	10.4426i	−0.341977	−	0.428825i	−0.922844	+	0.385173i	$0.874142\pi$
$594$		0			0
$595$	1.83724	+	8.04949i	0.0753197	+	0.329997i
$596$	2.95579	+	3.70644i	0.121074	+	0.151822i
$597$		0			0
$598$	2.89932	+	3.63563i	0.118562	+	0.148672i
$599$	0.824990	+	0.397294i	0.0337082	+	0.0162330i	0.450662	−	0.892695i	$-0.351188\pi$
$599$	0.824990	+	0.397294i	0.0337082	+	0.0162330i	−0.416954	+	0.908928i	$0.636902\pi$
$600$		0			0
$601$	3.60037	−	4.51472i	0.146862	−	0.184159i	−0.702959	−	0.711230i	$-0.748138\pi$
$601$	3.60037	−	4.51472i	0.146862	−	0.184159i	0.849821	+	0.527071i	$0.176710\pi$
$602$	−3.94935	+	1.90191i	−0.160964	+	0.0775160i
$603$		0			0
$604$	1.44508	−	6.33133i	0.0587996	−	0.257618i
$605$	4.03329	+	1.94233i	0.163977	+	0.0789669i
$606$		0			0
$607$	3.33385	−	14.6065i	0.135317	−	0.592861i	−0.861111	−	0.508416i	$-0.830231\pi$
$607$	3.33385	−	14.6065i	0.135317	−	0.592861i	0.996428	−	0.0844449i	$-0.0269117\pi$
$608$	−4.96656			−0.201421
$609$		0			0
$610$	−2.40744			−0.0974743
$611$	13.0973	−	57.3829i	0.529859	−	2.32146i
$612$		0			0
$613$	21.5458	+	10.3759i	0.870228	+	0.419080i	0.815046	−	0.579396i	$-0.196712\pi$
$613$	21.5458	+	10.3759i	0.870228	+	0.419080i	0.0551825	+	0.998476i	$0.482426\pi$
$614$	0.403651	−	1.76851i	0.0162900	−	0.0713712i
$615$		0			0
$616$	−3.94935	+	1.90191i	−0.159124	+	0.0766300i
$617$	9.16964	−	11.4984i	0.369156	−	0.462907i	−0.562208	−	0.826996i	$-0.690048\pi$
$617$	9.16964	−	11.4984i	0.369156	−	0.462907i	0.931364	+	0.364089i	$0.118620\pi$
$618$		0			0
$619$	−20.6449	−	9.94208i	−0.829790	−	0.399606i	−0.0297537	−	0.999557i	$-0.509472\pi$
$619$	−20.6449	−	9.94208i	−0.829790	−	0.399606i	−0.800036	+	0.599951i	$0.795187\pi$
$620$	1.96268	+	2.46113i	0.0788233	+	0.0988413i
$621$		0			0
$622$	12.1020	+	15.1754i	0.485244	+	0.608477i
$623$	1.25158	+	5.48352i	0.0501434	+	0.219693i
$624$		0			0
$625$	13.3358	+	16.7226i	0.533433	+	0.668904i
$626$	−33.8847			−1.35431
$627$		0			0
$628$	−5.91161	−	2.84688i	−0.235899	−	0.113603i
$629$	−29.6016	+	37.1192i	−1.18029	+	1.48004i
$630$		0			0
$631$	−11.8128	+	5.68872i	−0.470258	+	0.226465i	−0.653977	−	0.756514i	$-0.726901\pi$
$631$	−11.8128	+	5.68872i	−0.470258	+	0.226465i	0.183719	+	0.982979i	$0.441186\pi$
$632$	−2.09219	−	9.16650i	−0.0832230	−	0.364624i
$633$		0			0
$634$	−4.95317	−	2.38532i	−0.196716	−	0.0947333i
$635$	5.65731	−	2.72442i	0.224503	−	0.108115i
$636$		0			0
$637$	−16.2863			−0.645287
$638$	6.75135	−	3.31557i	0.267289	−	0.131265i
$639$		0			0
$640$	0.110081	−	0.482295i	0.00435132	−	0.0190644i
$641$	−38.8282	+	18.6987i	−1.53362	+	0.738553i	−0.994604	−	0.103742i	$-0.966918\pi$
$641$	−38.8282	+	18.6987i	−1.53362	+	0.738553i	−0.539017	+	0.842295i	$0.681204\pi$
$642$		0			0
$643$	1.92324	−	8.42626i	0.0758451	−	0.332299i	−0.922743	−	0.385415i	$-0.874058\pi$
$643$	1.92324	−	8.42626i	0.0758451	−	0.332299i	0.998588	+	0.0531161i	$0.0169153\pi$
$644$	−0.568191	−	2.48941i	−0.0223899	−	0.0980964i
$645$		0			0
$646$	16.4677	−	20.6498i	0.647913	−	0.812457i
$647$	2.98700	−	3.74558i	0.117431	−	0.147254i	−0.719641	−	0.694346i	$-0.755694\pi$
$647$	2.98700	−	3.74558i	0.117431	−	0.147254i	0.837073	+	0.547092i	$0.184265\pi$
$648$		0			0
$649$	9.71835	+	12.1864i	0.381479	+	0.478359i
$650$	−27.1785			−1.06603
$651$		0			0
$652$	−1.25904	−	5.51622i	−0.0493079	−	0.216032i
$653$	1.22812	+	5.38073i	0.0480599	+	0.210564i	0.993257	−	0.115938i	$-0.0369872\pi$
$653$	1.22812	+	5.38073i	0.0480599	+	0.210564i	−0.945197	+	0.326502i	$0.894130\pi$
$654$		0			0
$655$	7.31958			0.286000
$656$	2.50161	+	3.13691i	0.0976713	+	0.122476i
$657$		0			0
$658$	−20.1510	+	25.2685i	−0.785567	+	0.985070i
$659$	1.14932	−	1.44120i	0.0447712	−	0.0561413i	−0.758942	−	0.651158i	$-0.774283\pi$
$659$	1.14932	−	1.44120i	0.0447712	−	0.0561413i	0.803713	+	0.595017i	$0.202855\pi$
$660$		0			0
$661$	5.80735	+	25.4436i	0.225880	+	0.989643i	0.952961	+	0.303092i	$0.0980190\pi$
$661$	5.80735	+	25.4436i	0.225880	+	0.989643i	−0.727082	+	0.686551i	$0.759124\pi$
$662$	−3.03658	+	13.3041i	−0.118020	+	0.517080i
$663$		0			0
$664$	−11.4508	+	5.51441i	−0.444377	+	0.214001i
$665$	−1.71583	+	7.51754i	−0.0665371	+	0.291518i
$666$		0			0
$667$	1.00782	+	4.26393i	0.0390231	+	0.165100i
$668$	12.0891			0.467742
$669$		0			0
$670$	3.18164	−	1.53220i	0.122917	−	0.0591939i
$671$	6.12397	+	2.94915i	0.236413	+	0.113851i
$672$		0			0
$673$	−4.88021	−	21.3816i	−0.188118	−	0.824200i	−0.977608	−	0.210436i	$-0.932512\pi$
$673$	−4.88021	−	21.3816i	−0.188118	−	0.824200i	0.789489	−	0.613764i	$-0.210345\pi$
$674$	20.3325	−	9.79160i	0.783177	−	0.377158i
$675$		0			0
$676$	12.2618	−	15.3758i	0.471608	−	0.591377i
$677$	9.15884	+	4.41066i	0.352003	+	0.169516i	0.601526	−	0.798853i	$-0.294560\pi$
$677$	9.15884	+	4.41066i	0.352003	+	0.169516i	−0.249523	+	0.968369i	$0.580274\pi$
$678$		0			0
$679$	11.9143			0.457228
$680$	1.64028	+	2.05684i	0.0629018	+	0.0788764i
$681$		0			0
$682$	−1.97770	−	8.66486i	−0.0757300	−	0.331795i
$683$	−12.7734	−	16.0173i	−0.488760	−	0.612886i	0.474893	−	0.880044i	$-0.342487\pi$
$683$	−12.7734	−	16.0173i	−0.488760	−	0.612886i	−0.963653	+	0.267158i	$0.913915\pi$
$684$		0			0
$685$	0.465513	+	0.583735i	0.0177863	+	0.0223033i
$686$	−11.7359	−	5.65170i	−0.448078	−	0.215783i
$687$		0			0
$688$	−0.870839	+	1.09200i	−0.0332004	+	0.0416320i
$689$	−21.8521	+	10.5234i	−0.832500	+	0.400911i
$690$		0			0
$691$	6.86393	−	30.0728i	0.261116	−	1.14402i	−0.658927	−	0.752207i	$-0.728989\pi$
$691$	6.86393	−	30.0728i	0.261116	−	1.14402i	0.920043	−	0.391817i	$-0.128154\pi$
$692$	10.4877	+	5.05061i	0.398682	+	0.191995i
$693$		0			0
$694$	0.661565	−	2.89851i	0.0251127	−	0.110026i
$695$	4.33177			0.164313
$696$		0			0
$697$	−21.3372			−0.808204
$698$	−1.27708	+	5.59523i	−0.0483380	+	0.211783i
$699$		0			0
$700$	13.4460	+	6.47525i	0.508211	+	0.244741i
$701$	−4.60087	+	20.1577i	−0.173773	+	0.761347i	0.810650	+	0.585530i	$0.199114\pi$
$701$	−4.60087	+	20.1577i	−0.173773	+	0.761347i	−0.984423	+	0.175817i	$0.943743\pi$
$702$		0			0
$703$	−39.9487	+	19.2383i	−1.50669	+	0.725586i
$704$	−0.870839	+	1.09200i	−0.0328210	+	0.0411562i
$705$		0			0
$706$	5.83121	+	2.80816i	0.219460	+	0.105687i
$707$	2.39081	+	2.99798i	0.0899156	+	0.112751i
$708$		0			0
$709$	−28.0695	−	35.1981i	−1.05417	−	1.32189i	−0.944712	−	0.327901i	$-0.893659\pi$
$709$	−28.0695	−	35.1981i	−1.05417	−	1.32189i	−0.109461	−	0.993991i	$-0.534913\pi$
$710$	−0.664596	−	2.91179i	−0.0249419	−	0.109277i
$711$		0			0
$712$	1.11740	+	1.40118i	0.0418763	+	0.0525113i
$713$	5.17722			0.193888
$714$		0			0
$715$	−3.55803	−	1.71346i	−0.133063	−	0.0640796i
$716$	11.4442	−	14.3506i	0.427691	−	0.536307i
$717$		0			0
$718$	−9.67769	+	4.66053i	−0.361168	+	0.173929i
$719$	−2.24249	−	9.82501i	−0.0836309	−	0.366411i	0.915744	−	0.401762i	$-0.131602\pi$
$719$	−2.24249	−	9.82501i	−0.0836309	−	0.366411i	−0.999375	+	0.0353512i	$0.988745\pi$
$720$		0			0
$721$	−5.11269	−	2.46214i	−0.190407	−	0.0916950i
$722$	5.10552	−	2.45869i	0.190008	−	0.0915029i
$723$		0			0
$724$	−9.89404			−0.367709
$725$	−23.1568	−	10.9329i	−0.860023	−	0.406036i
$726$		0			0
$727$	−4.98758	+	21.8520i	−0.184979	+	0.810447i	0.794234	+	0.607612i	$0.207872\pi$
$727$	−4.98758	+	21.8520i	−0.184979	+	0.810447i	−0.979213	+	0.202835i	$0.934985\pi$
$728$	−16.1610	+	7.78272i	−0.598966	+	0.288447i
$729$		0			0
$730$	1.35170	−	5.92219i	0.0500287	−	0.219190i
$731$	−1.65283	−	7.24151i	−0.0611320	−	0.267837i
$732$		0			0
$733$	2.46035	−	3.08518i	0.0908749	−	0.113954i	−0.734315	−	0.678809i	$-0.762497\pi$
$733$	2.46035	−	3.08518i	0.0908749	−	0.113954i	0.825190	+	0.564855i	$0.191068\pi$
$734$	−11.8085	+	14.8074i	−0.435859	+	0.546550i
$735$		0			0
$736$	−0.507277	−	0.636105i	−0.0186985	−	0.0234472i
$737$	−9.97032			−0.367261
$738$		0			0
$739$	−1.38003	−	6.04632i	−0.0507653	−	0.222417i	0.943182	−	0.332277i	$-0.107817\pi$
$739$	−1.38003	−	6.04632i	−0.0507653	−	0.222417i	−0.993947	+	0.109860i	$0.964960\pi$
$740$	−0.982763	−	4.30577i	−0.0361271	−	0.158283i
$741$		0			0
$742$	13.3181			0.488922
$743$	−30.3589	−	38.0689i	−1.11376	−	1.39661i	−0.908490	−	0.417907i	$-0.862764\pi$
$743$	−30.3589	−	38.0689i	−1.11376	−	1.39661i	−0.205271	−	0.978705i	$-0.565808\pi$
$744$		0			0
$745$	1.46222	−	1.83357i	0.0535718	−	0.0671769i
$746$	−1.51759	+	1.90300i	−0.0555629	+	0.0696737i
$747$		0			0
$748$	−1.65283	−	7.24151i	−0.0604333	−	0.264776i
$749$	2.89863	−	12.6997i	0.105914	−	0.464038i
$750$		0			0
$751$	−23.7677	+	11.4459i	−0.867296	+	0.417668i	−0.813968	−	0.580909i	$-0.802697\pi$
$751$	−23.7677	+	11.4459i	−0.867296	+	0.417668i	−0.0533277	+	0.998577i	$0.516983\pi$
$752$	−2.29155	+	10.0400i	−0.0835644	+	0.366119i
$753$		0			0
$754$	27.6269	−	13.5675i	1.00611	−	0.494100i
$755$	−3.21264			−0.116920
$756$		0			0
$757$	−34.4086	+	16.5703i	−1.25060	+	0.602259i	−0.937673	−	0.347518i	$-0.887025\pi$
$757$	−34.4086	+	16.5703i	−1.25060	+	0.602259i	−0.312930	+	0.949776i	$0.601310\pi$
$758$	−15.4439	−	7.43740i	−0.560949	−	0.270139i
$759$		0			0
$760$	0.546722	+	2.39535i	0.0198317	+	0.0868884i
$761$	5.62055	−	2.70672i	0.203745	−	0.0981183i	−0.329229	−	0.944250i	$-0.606789\pi$
$761$	5.62055	−	2.70672i	0.203745	−	0.0981183i	0.532974	+	0.846132i	$0.321074\pi$
$762$		0			0
$763$	28.3820	−	35.5898i	1.02750	−	1.28844i
$764$	0.382244	+	0.184079i	0.0138291	+	0.00665975i
$765$		0			0
$766$	−23.7774			−0.859111
$767$	39.7681	+	49.8676i	1.43594	+	1.80061i
$768$		0			0
$769$	6.26532	+	27.4502i	0.225933	+	0.989879i	0.952919	+	0.303226i	$0.0980637\pi$
$769$	6.26532	+	27.4502i	0.225933	+	0.989879i	−0.726985	+	0.686653i	$0.759079\pi$
$770$	1.35203	+	1.69539i	0.0487237	+	0.0610976i
$771$		0			0
$772$	−6.43739	−	8.07223i	−0.231687	−	0.290526i
$773$	31.5991	+	15.2173i	1.13654	+	0.547329i	0.904964	−	0.425488i	$-0.139897\pi$
$773$	31.5991	+	15.2173i	1.13654	+	0.547329i	0.231576	+	0.972817i	$0.425612\pi$
$774$		0			0
$775$	−18.8663	+	23.6575i	−0.677696	+	0.849804i
$776$	3.42035	−	1.64715i	0.122783	−	0.0591293i
$777$		0			0
$778$	2.56505	−	11.2382i	0.0919614	−	0.402909i
$779$	−17.9537	−	8.64606i	−0.643259	−	0.309777i
$780$		0			0
$781$	−1.87640	+	8.22106i	−0.0671430	+	0.294173i
$782$	4.32677			0.154725
$783$		0			0
$784$	2.84952			0.101769
$785$	−0.722283	+	3.16453i	−0.0257794	+	0.112947i
$786$		0			0
$787$	24.5984	+	11.8459i	0.876837	+	0.422262i	0.817468	−	0.575974i	$-0.195377\pi$
$787$	24.5984	+	11.8459i	0.876837	+	0.422262i	0.0593688	+	0.998236i	$0.481091\pi$
$788$	−5.97308	+	26.1698i	−0.212782	+	0.932259i
$789$		0			0
$790$	−4.19065	+	2.01811i	−0.149097	+	0.0718011i
$791$	−32.6453	+	40.9359i	−1.16073	+	1.45551i
$792$		0			0
$793$	25.0597	+	12.0681i	0.889894	+	0.428551i
$794$	−18.0708	−	22.6601i	−0.641309	−	0.804176i
$795$		0			0
$796$	−4.24156	−	5.31875i	−0.150338	−	0.188518i
$797$	9.11491	+	39.9350i	0.322867	+	1.41457i	0.832426	+	0.554136i	$0.186951\pi$
$797$	9.11491	+	39.9350i	0.322867	+	1.41457i	−0.509560	+	0.860435i	$0.670192\pi$
$798$		0			0
$799$	−34.1457	−	42.8174i	−1.20799	−	1.51477i
$800$	4.75527			0.168124
$801$		0			0
$802$	−9.30669	−	4.48187i	−0.328631	−	0.158260i
$803$	−10.6932	+	13.4088i	−0.377355	+	0.473188i
$804$		0			0
$805$	−1.13808	+	0.548071i	−0.0401121	+	0.0193170i
$806$	−8.09286	−	35.4572i	−0.285059	−	1.24892i
$807$		0			0
$808$	1.10082	+	0.530129i	0.0387268	+	0.0186499i
$809$	−38.8637	+	18.7158i	−1.36638	+	0.658012i	−0.966049	−	0.258360i	$-0.916818\pi$
$809$	−38.8637	+	18.7158i	−1.36638	+	0.658012i	−0.400327	+	0.916372i	$0.631104\pi$
$810$		0			0
$811$	38.0001			1.33436			0.667182	−	0.744894i	$-0.267500\pi$
$811$	38.0001			1.33436			0.667182	+	0.744894i	$0.267500\pi$
$812$	−16.9003	+	0.130153i	−0.593083	+	0.00456748i
$813$		0			0
$814$	−2.77471	+	12.1568i	−0.0972534	+	0.426095i
$815$	−2.52185	+	1.21446i	−0.0883366	+	0.0425407i
$816$		0			0
$817$	1.54360	−	6.76296i	0.0540037	−	0.236606i
$818$	2.21669	+	9.71194i	0.0775047	+	0.339570i
$819$		0			0
$820$	1.23754	−	1.55183i	0.0432168	−	0.0541921i
$821$	7.61753	−	9.55208i	0.265854	−	0.333370i	−0.630930	−	0.775840i	$-0.717326\pi$
$821$	7.61753	−	9.55208i	0.265854	−	0.333370i	0.896783	+	0.442470i	$0.145898\pi$
$822$		0			0
$823$	22.8365	+	28.6361i	0.796030	+	0.998190i	0.999816	+	0.0191747i	$0.00610387\pi$
$823$	22.8365	+	28.6361i	0.796030	+	0.998190i	−0.203786	+	0.979015i	$0.565325\pi$
$824$	−1.80814			−0.0629896
$825$		0			0
$826$	−7.79351	−	34.1456i	−0.271171	−	1.18808i
$827$	−5.74425	−	25.1672i	−0.199747	−	0.875149i	−0.971087	−	0.238726i	$-0.923270\pi$
$827$	−5.74425	−	25.1672i	−0.199747	−	0.875149i	0.771340	−	0.636423i	$-0.219587\pi$
$828$		0			0
$829$	−15.7732			−0.547825			−0.273913	−	0.961755i	$-0.588318\pi$
$829$	−15.7732			−0.547825			−0.273913	+	0.961755i	$0.588318\pi$
$830$	3.92009	+	4.91563i	0.136068	+	0.170624i
$831$		0			0
$832$	−3.56353	+	4.46852i	−0.123543	+	0.154918i
$833$	−9.44821	+	11.8477i	−0.327361	+	0.410498i
$834$		0			0
$835$	−1.33078	−	5.83052i	−0.0460535	−	0.201773i
$836$	1.54360	−	6.76296i	0.0533865	−	0.233902i
$837$		0			0
$838$	−25.5445	+	12.3016i	−0.882420	+	0.424951i
$839$	0.479893	−	2.10255i	0.0165677	−	0.0725880i	−0.965968	−	0.258661i	$-0.916719\pi$
$839$	0.479893	−	2.10255i	0.0165677	−	0.0725880i	0.982536	+	0.186073i	$0.0595760\pi$
$840$		0			0
$841$	28.9966	−	0.446646i	0.999881	−	0.0154016i
$842$	9.51999			0.328080
$843$		0			0
$844$	−5.26221	+	2.53415i	−0.181133	+	0.0872289i
$845$	−8.76546	−	4.22123i	−0.301541	−	0.145215i
$846$		0			0
$847$	6.31957	+	27.6879i	0.217143	+	0.951366i
$848$	3.82334	−	1.84123i	0.131294	−	0.0632279i
$849$		0			0
$850$	−15.7671	+	19.7714i	−0.540808	+	0.678152i
$851$	−6.54430	−	3.15157i	−0.224336	−	0.108034i
$852$		0			0
$853$	−21.6578			−0.741548			−0.370774	−	0.928723i	$-0.620908\pi$
$853$	−21.6578			−0.741548			−0.370774	+	0.928723i	$0.620908\pi$
$854$	−9.52251	−	11.9409i	−0.325854	−	0.408608i
$855$		0			0
$856$	−0.923602	−	4.04656i	−0.0315681	−	0.138309i
$857$	7.86892	+	9.86732i	0.268797	+	0.337061i	0.897850	−	0.440302i	$-0.145128\pi$
$857$	7.86892	+	9.86732i	0.268797	+	0.337061i	−0.629053	+	0.777363i	$0.716557\pi$
$858$		0			0
$859$	−12.1127	−	15.1888i	−0.413280	−	0.518236i	0.531004	−	0.847369i	$-0.321815\pi$
$859$	−12.1127	−	15.1888i	−0.413280	−	0.518236i	−0.944284	+	0.329133i	$0.893244\pi$
$860$	0.622528	+	0.299794i	0.0212280	+	0.0102229i
$861$		0			0
$862$	−11.8307	+	14.8352i	−0.402954	+	0.505289i
$863$	−41.3801	+	19.9276i	−1.40860	+	0.678344i	−0.974885	−	0.222708i	$-0.928510\pi$
$863$	−41.3801	+	19.9276i	−1.40860	+	0.678344i	−0.433711	+	0.901052i	$0.642796\pi$
$864$		0			0
$865$	1.28139	−	5.61414i	0.0435686	−	0.190886i
$866$	25.5107	+	12.2853i	0.866890	+	0.417472i
$867$		0			0
$868$	−4.44385	+	19.4698i	−0.150834	+	0.660847i
$869$	13.1323			0.445482
$870$		0			0
$871$	−40.7992			−1.38243
$872$	3.22757	−	14.1409i	0.109299	−	0.478872i
$873$		0			0
$874$	3.64067	+	1.75325i	0.123147	+	0.0593047i
$875$	3.37022	−	14.7659i	0.113934	−	0.499179i
$876$		0			0
$877$	−7.29358	+	3.51240i	−0.246287	+	0.118605i	−0.552955	−	0.833211i	$-0.686500\pi$
$877$	−7.29358	+	3.51240i	−0.246287	+	0.118605i	0.306669	+	0.951816i	$0.400786\pi$
$878$	12.4049	−	15.5552i	0.418644	−	0.524962i
$879$		0			0
$880$	0.622528	+	0.299794i	0.0209854	+	0.0101060i
$881$	−1.87163	−	2.34695i	−0.0630569	−	0.0790709i	0.749303	−	0.662228i	$-0.230389\pi$
$881$	−1.87163	−	2.34695i	−0.0630569	−	0.0790709i	−0.812360	+	0.583157i	$0.801817\pi$
$882$		0			0
$883$	−24.0764	−	30.1908i	−0.810235	−	1.01600i	−0.999420	−	0.0340614i	$-0.989156\pi$
$883$	−24.0764	−	30.1908i	−0.810235	−	1.01600i	0.189184	−	0.981942i	$-0.439416\pi$
$884$	−6.76347	−	29.6327i	−0.227480	−	0.996655i
$885$		0			0
$886$	−22.1713	−	27.8019i	−0.744859	−	0.934023i
$887$	29.4281			0.988100			0.494050	−	0.869433i	$-0.335516\pi$
$887$	29.4281			0.988100			0.494050	+	0.869433i	$0.335516\pi$
$888$		0			0
$889$	35.8903	+	17.2839i	1.20372	+	0.579682i
$890$	0.552776	−	0.693159i	0.0185291	−	0.0232347i
$891$		0			0
$892$	19.7637	−	9.51770i	0.661738	−	0.318676i
$893$	−11.3811	−	49.8640i	−0.380855	−	1.66864i
$894$		0			0
$895$	−8.18101	−	3.93977i	−0.273461	−	0.131692i
$896$	2.82760	−	1.36170i	0.0944634	−	0.0454912i
$897$		0			0
$898$	10.8511			0.362106
$899$	7.36769	−	33.4659i	0.245726	−	1.11615i
$900$		0			0
$901$	−5.02172	+	22.0016i	−0.167298	+	0.732979i
$902$	−5.04903	+	2.43148i	−0.168114	+	0.0809596i
$903$		0			0
$904$	−3.71240	+	16.2651i	−0.123473	+	0.540969i
$905$	1.08914	+	4.77185i	0.0362043	+	0.158622i
$906$		0			0
$907$	2.90939	−	3.64825i	0.0966046	−	0.121138i	−0.731179	−	0.682185i	$-0.761030\pi$
$907$	2.90939	−	3.64825i	0.0966046	−	0.121138i	0.827784	+	0.561047i	$0.189601\pi$
$908$	1.34388	−	1.68518i	0.0445983	−	0.0559245i
$909$		0			0
$910$	5.53258	+	6.93764i	0.183403	+	0.229981i
$911$	37.9571			1.25758			0.628788	−	0.777577i	$-0.283551\pi$
$911$	37.9571			1.25758			0.628788	+	0.777577i	$0.283551\pi$
$912$		0			0
$913$	−3.95007	−	17.3064i	−0.130728	−	0.572758i
$914$	7.19540	+	31.5251i	0.238003	+	1.04276i
$915$		0			0
$916$	9.29190			0.307013
$917$	28.9523	+	36.3050i	0.956089	+	1.19890i
$918$		0			0
$919$	15.8113	−	19.8268i	0.521568	−	0.654026i	−0.449373	−	0.893344i	$-0.648353\pi$
$919$	15.8113	−	19.8268i	0.521568	−	0.654026i	0.970941	+	0.239318i	$0.0769240\pi$
$920$	−0.250949	+	0.314680i	−0.00827355	+	0.0103747i
$921$		0			0
$922$	−5.65307	−	24.7677i	−0.186174	−	0.815682i
$923$	−7.67836	+	33.6411i	−0.252736	+	1.10731i
$924$		0			0
$925$	38.2492	−	18.4199i	1.25763	−	0.605641i
$926$	0.716678	−	3.13997i	0.0235515	−	0.103186i
$927$		0			0
$928$	−4.83373	+	2.37383i	−0.158675	+	0.0779248i
$929$	−36.8642			−1.20947			−0.604737	−	0.796425i	$-0.706722\pi$
$929$	−36.8642			−1.20947			−0.604737	+	0.796425i	$0.706722\pi$
$930$		0			0
$931$	−12.7508	+	6.14046i	−0.417891	+	0.201246i
$932$	−10.6177	−	5.11321i	−0.347794	−	0.167489i
$933$		0			0
$934$	−5.08605	−	22.2834i	−0.166421	−	0.729136i
$935$	−3.31060	+	1.59430i	−0.108268	+	0.0521392i
$936$		0			0
$937$	−1.45551	+	1.82515i	−0.0475493	+	0.0596249i	−0.805038	−	0.593224i	$-0.797855\pi$
$937$	−1.45551	+	1.82515i	−0.0475493	+	0.0596249i	0.757488	+	0.652849i	$0.226426\pi$
$938$	20.1845	+	9.72034i	0.659047	+	0.317380i
$939$		0			0
$940$	5.09448			0.166164
$941$	−5.47972	−	6.87136i	−0.178634	−	0.224000i	0.684451	−	0.729059i	$-0.260042\pi$
$941$	−5.47972	−	6.87136i	−0.178634	−	0.224000i	−0.863085	+	0.505059i	$0.831471\pi$
$942$		0			0
$943$	−0.726401	−	3.18257i	−0.0236549	−	0.103639i
$944$	−6.95799	−	8.72505i	−0.226463	−	0.283976i
$945$		0			0
$946$	−1.21632	−	1.52521i	−0.0395458	−	0.0495889i
$947$	−11.4402	−	5.50930i	−0.371756	−	0.179028i	0.238672	−	0.971100i	$-0.423288\pi$
$947$	−11.4402	−	5.50930i	−0.371756	−	0.179028i	−0.610428	+	0.792072i	$0.709002\pi$
$948$		0			0
$949$	−43.7572	+	54.8698i	−1.42042	+	1.78115i
$950$	−21.2785	+	10.2472i	−0.690365	+	0.332462i
$951$		0			0
$952$	−3.71387	+	16.2715i	−0.120367	+	0.527363i
$953$	49.0633	+	23.6277i	1.58932	+	0.765375i	0.999122	−	0.0418854i	$-0.0133364\pi$
$953$	49.0633	+	23.6277i	1.58932	+	0.765375i	0.590195	+	0.807261i	$0.299051\pi$
$954$		0			0
$955$	0.0467028	−	0.204618i	0.00151127	−	0.00662129i
$956$	14.3692			0.464732
$957$		0			0
$958$	2.14546			0.0693165
$959$	−1.05400	+	4.61787i	−0.0340354	+	0.149119i
$960$		0			0
$961$	−8.55134	−	4.11811i	−0.275850	−	0.132842i
$962$	−11.3543	+	49.7463i	−0.366076	+	1.60388i
$963$		0			0
$964$	8.29280	−	3.99360i	0.267093	−	0.128625i
$965$	−3.18457	+	3.99332i	−0.102515	+	0.128549i
$966$		0			0
$967$	−44.6567	−	21.5055i	−1.43606	−	0.691572i	−0.455949	−	0.890006i	$-0.650700\pi$
$967$	−44.6567	−	21.5055i	−1.43606	−	0.691572i	−0.980114	+	0.198434i	$0.936414\pi$
$968$	5.64207	+	7.07493i	0.181343	+	0.227397i
$969$		0			0
$970$	−1.17093	−	1.46830i	−0.0375962	−	0.0471442i
$971$	−6.13766	−	26.8909i	−0.196967	−	0.862969i	−0.972729	−	0.231944i	$-0.925492\pi$
$971$	−6.13766	−	26.8909i	−0.196967	−	0.862969i	0.775762	−	0.631025i	$-0.217366\pi$
$972$		0			0
$973$	17.1341	+	21.4855i	0.549295	+	0.688794i
$974$	−21.7759			−0.697746
$975$		0			0
$976$	−4.38454	−	2.11149i	−0.140346	−	0.0675870i
$977$	27.7654	−	34.8167i	0.888294	−	1.11389i	−0.104556	−	0.994519i	$-0.533342\pi$
$977$	27.7654	−	34.8167i	0.888294	−	1.11389i	0.992850	−	0.119367i	$-0.0380864\pi$
$978$		0			0
$979$	−2.25527	+	1.08608i	−0.0720786	+	0.0347112i
$980$	−0.313678	−	1.37431i	−0.0100201	−	0.0439008i
$981$		0			0
$982$	35.0145	+	16.8621i	1.11736	+	0.538091i
$983$	−1.07817	+	0.519217i	−0.0343882	+	0.0165605i	−0.450999	−	0.892525i	$-0.648932\pi$
$983$	−1.07817	+	0.519217i	−0.0343882	+	0.0165605i	0.416611	+	0.909085i	$0.363218\pi$
$984$		0			0
$985$	13.2791			0.423106
$986$	6.15741	−	27.9685i	0.196092	−	0.890699i
$987$		0			0
$988$	6.31651	−	27.6744i	0.200955	−	0.880441i
$989$	1.02384	−	0.493058i	0.0325564	−	0.0156783i
$990$		0			0
$991$	−7.79435	+	34.1493i	−0.247596	+	1.08479i	0.686321	+	0.727298i	$0.259224\pi$
$991$	−7.79435	+	34.1493i	−0.247596	+	1.08479i	−0.933917	+	0.357490i	$0.883633\pi$
$992$	1.41596	+	6.20373i	0.0449568	+	0.196969i
$993$		0			0
$994$	11.8136	−	14.8138i	0.374706	−	0.469866i
$995$	−2.09829	+	2.63118i	−0.0665204	+	0.0834139i
$996$		0			0
$997$	19.4359	+	24.3719i	0.615543	+	0.771866i	0.987710	−	0.156300i	$-0.0499566\pi$
$997$	19.4359	+	24.3719i	0.615543	+	0.771866i	−0.372167	+	0.928166i	$0.621385\pi$
$998$	−39.2992			−1.24400
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	522.2.k.h.199.1		12
3.2	odd	2		58.2.d.b.25.2	yes	12
12.11	even	2		464.2.u.h.257.1		12
29.7	even	7	inner	522.2.k.h.181.1		12
87.14	even	28		1682.2.b.i.1681.5		12
87.23	odd	14		1682.2.a.t.1.2		6
87.35	odd	14		1682.2.a.q.1.5		6
87.44	even	28		1682.2.b.i.1681.8		12
87.65	odd	14		58.2.d.b.7.2	✓	12
348.239	even	14		464.2.u.h.65.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.7.2	✓	12	87.65	odd	14
58.2.d.b.25.2	yes	12	3.2	odd	2
464.2.u.h.65.1		12	348.239	even	14
464.2.u.h.257.1		12	12.11	even	2
522.2.k.h.181.1		12	29.7	even	7	inner
522.2.k.h.199.1		12	1.1	even	1	trivial
1682.2.a.q.1.5		6	87.35	odd	14
1682.2.a.t.1.2		6	87.23	odd	14
1682.2.b.i.1681.5		12	87.14	even	28
1682.2.b.i.1681.8		12	87.44	even	28

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:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(-0.900969 - 0.433884i) q^{4} +(-0.110081 + 0.482295i) q^{5} +(-2.82760 + 1.36170i) q^{7} +(-0.623490 + 0.781831i) q^{8} +O(q^{10})\)	\(q+(0.222521 - 0.974928i) q^{2} +(-0.900969 - 0.433884i) q^{4} +(-0.110081 + 0.482295i) q^{5} +(-2.82760 + 1.36170i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.445708 + 0.214642i) q^{10} +(-0.870839 - 1.09200i) q^{11} +(-3.56353 - 4.46852i) q^{13} +(0.698359 + 3.05971i) q^{14} +(0.623490 + 0.781831i) q^{16} -5.31800 q^{17} +(-4.47471 - 2.15491i) q^{19} +(0.308439 - 0.386771i) q^{20} +(-1.25840 + 0.606013i) q^{22} +(-0.181045 - 0.793210i) q^{23} +(4.28435 + 2.06324i) q^{25} +(-5.14944 + 2.47984i) q^{26} +3.13840 q^{28} +(-5.38501 + 0.0414712i) q^{29} +(-1.41596 + 6.20373i) q^{31} +(0.900969 - 0.433884i) q^{32} +(-1.18337 + 5.18466i) q^{34} +(-0.345477 - 1.51363i) q^{35} +(5.56630 - 6.97992i) q^{37} +(-3.09660 + 3.88301i) q^{38} +(-0.308439 - 0.386771i) q^{40} +4.01226 q^{41} +(0.310799 + 1.36170i) q^{43} +(0.310799 + 1.36170i) q^{44} -0.813609 q^{46} +(6.42079 + 8.05142i) q^{47} +(1.77665 - 2.22785i) q^{49} +(2.96486 - 3.71782i) q^{50} +(1.27181 + 5.57215i) q^{52} +(0.944288 - 4.13720i) q^{53} +(0.622528 - 0.299794i) q^{55} +(0.698359 - 3.05971i) q^{56} +(-1.15784 + 5.25922i) q^{58} -11.1598 q^{59} +(-4.38454 + 2.11149i) q^{61} +(5.73311 + 2.76092i) q^{62} +(-0.222521 - 0.974928i) q^{64} +(2.54742 - 1.22677i) q^{65} +(4.45072 - 5.58102i) q^{67} +(4.79135 + 2.30739i) q^{68} -1.55256 q^{70} +(-3.76423 - 4.72019i) q^{71} +(-2.73238 - 11.9713i) q^{73} +(-5.56630 - 6.97992i) q^{74} +(3.09660 + 3.88301i) q^{76} +(3.94935 + 1.90191i) q^{77} +(-5.86220 + 7.35096i) q^{79} +(-0.445708 + 0.214642i) q^{80} +(0.892813 - 3.91167i) q^{82} +(11.4508 + 5.51441i) q^{83} +(0.585409 - 2.56484i) q^{85} +1.39672 q^{86} +1.39672 q^{88} +(0.398796 - 1.74724i) q^{89} +(16.1610 + 7.78272i) q^{91} +(-0.181045 + 0.793210i) q^{92} +(9.27831 - 4.46820i) q^{94} +(1.53188 - 1.92092i) q^{95} +(-3.42035 - 1.64715i) q^{97} +(-1.77665 - 2.22785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{4} + q^{7} + 2 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^4 + q^7 + 2 * q^8	\( 12 q + 2 q^{2} - 2 q^{4} + q^{7} + 2 q^{8} - 7 q^{10} + 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{19} - 7 q^{20} - 2 q^{22} - 35 q^{23} - 6 q^{25} - 8 q^{26} - 6 q^{28} + 14 q^{29} - 8 q^{31} + 2 q^{32} - 5 q^{34} + 18 q^{35} + 31 q^{37} - q^{38} + 7 q^{40} + 30 q^{41} - 5 q^{43} - 5 q^{44} - 28 q^{46} + 33 q^{47} + 37 q^{49} - q^{50} - 6 q^{52} - 13 q^{53} + 36 q^{55} - q^{56} - 38 q^{59} - 5 q^{61} + 8 q^{62} - 2 q^{64} + 20 q^{65} - 7 q^{67} + 19 q^{68} - 18 q^{70} - 3 q^{71} - 22 q^{73} - 31 q^{74} + q^{76} - 10 q^{77} - 60 q^{79} + 7 q^{80} + 26 q^{82} + 39 q^{83} + 38 q^{85} - 2 q^{86} - 2 q^{88} - 39 q^{89} + 61 q^{91} - 35 q^{92} + 16 q^{94} - 55 q^{95} - 19 q^{97} - 37 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^4 + q^7 + 2 * q^8 - 7 * q^10 + 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 6 * q^19 - 7 * q^20 - 2 * q^22 - 35 * q^23 - 6 * q^25 - 8 * q^26 - 6 * q^28 + 14 * q^29 - 8 * q^31 + 2 * q^32 - 5 * q^34 + 18 * q^35 + 31 * q^37 - q^38 + 7 * q^40 + 30 * q^41 - 5 * q^43 - 5 * q^44 - 28 * q^46 + 33 * q^47 + 37 * q^49 - q^50 - 6 * q^52 - 13 * q^53 + 36 * q^55 - q^56 - 38 * q^59 - 5 * q^61 + 8 * q^62 - 2 * q^64 + 20 * q^65 - 7 * q^67 + 19 * q^68 - 18 * q^70 - 3 * q^71 - 22 * q^73 - 31 * q^74 + q^76 - 10 * q^77 - 60 * q^79 + 7 * q^80 + 26 * q^82 + 39 * q^83 + 38 * q^85 - 2 * q^86 - 2 * q^88 - 39 * q^89 + 61 * q^91 - 35 * q^92 + 16 * q^94 - 55 * q^95 - 19 * q^97 - 37 * q^98

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