LMFDB - Embedded newform 693.2.m.i.631.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.2
Root			$0.183009 + 0.132964i$ of defining polynomial
Character	$\chi$	$=$	693.631
Dual form			693.2.m.i.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.183009 + 0.132964i) q^{2} +(-0.602221 - 1.85345i) q^{4} +(-2.01892 + 1.46683i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.276036 - 0.849550i) q^{8} +O(q^{10})$	\(q+(0.183009 + 0.132964i) q^{2} +(-0.602221 - 1.85345i) q^{4} +(-2.01892 + 1.46683i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.276036 - 0.849550i) q^{8} -0.564516 q^{10} +(2.66598 - 1.97296i) q^{11} +(-4.15429 - 3.01827i) q^{13} +(-0.0699031 + 0.215140i) q^{14} +(-2.98979 + 2.17221i) q^{16} +(-1.16298 + 0.844956i) q^{17} +(-1.87526 + 5.77147i) q^{19} +(3.93453 + 2.85860i) q^{20} +(0.750229 - 0.00659095i) q^{22} -7.08292 q^{23} +(0.379361 - 1.16755i) q^{25} +(-0.358952 - 1.10474i) q^{26} +(1.57664 - 1.14549i) q^{28} +(-2.01408 - 6.19869i) q^{29} +(-6.22049 - 4.51945i) q^{31} -2.62252 q^{32} -0.325184 q^{34} +(-2.01892 - 1.46683i) q^{35} +(-1.23122 - 3.78932i) q^{37} +(-1.11058 + 0.806887i) q^{38} +(0.688853 + 2.12007i) q^{40} +(-2.08556 + 6.41868i) q^{41} -0.802299 q^{43} +(-5.26228 - 3.75309i) q^{44} +(-1.29624 - 0.941771i) q^{46} +(-2.08655 + 6.42174i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(0.224669 - 0.163231i) q^{50} +(-3.09240 + 9.51742i) q^{52} +(5.32469 + 3.86861i) q^{53} +(-2.48840 + 7.89379i) q^{55} +0.893270 q^{56} +(0.455607 - 1.40221i) q^{58} +(-0.888810 - 2.73548i) q^{59} +(0.691986 - 0.502757i) q^{61} +(-0.537482 - 1.65420i) q^{62} +(5.49964 + 3.99573i) q^{64} +12.8145 q^{65} -1.64668 q^{67} +(2.26645 + 1.64667i) q^{68} +(-0.174445 - 0.536886i) q^{70} +(3.65738 - 2.65724i) q^{71} +(-4.58827 - 14.1212i) q^{73} +(0.278517 - 0.857187i) q^{74} +11.8264 q^{76} +(2.70023 + 1.92582i) q^{77} +(-1.98444 - 1.44178i) q^{79} +(2.84989 - 8.77105i) q^{80} +(-1.23513 + 0.897372i) q^{82} +(1.81851 - 1.32122i) q^{83} +(1.10856 - 3.41180i) q^{85} +(-0.146828 - 0.106677i) q^{86} +(-0.940224 - 2.80949i) q^{88} -1.73566 q^{89} +(1.58680 - 4.88366i) q^{91} +(4.26549 + 13.1278i) q^{92} +(-1.23572 + 0.897800i) q^{94} +(-4.67976 - 14.4028i) q^{95} +(9.77095 + 7.09901i) q^{97} -0.226211 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.183009	+	0.132964i	0.129407	+	0.0940195i	0.650606	−	0.759416i	$-0.274515\pi$
$2$	0.183009	+	0.132964i	0.129407	+	0.0940195i	−0.521199	+	0.853435i	$0.674515\pi$
$3$		0			0
$3$		0			0
$4$	−0.602221	−	1.85345i	−0.301111	−	0.926723i
$5$	−2.01892	+	1.46683i	−0.902889	+	0.655987i	−0.939206	−	0.343353i	$-0.888437\pi$
$5$	−2.01892	+	1.46683i	−0.902889	+	0.655987i	0.0363174	+	0.999340i	$0.488437\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.276036	−	0.849550i	0.0975933	−	0.300361i
$9$		0			0
$10$	−0.564516			−0.178516
$11$	2.66598	−	1.97296i	0.803822	−	0.594870i
$11$	2.66598	−	1.97296i	0.803822	−	0.594870i
$12$		0			0
$13$	−4.15429	−	3.01827i	−1.15219	−	0.837117i	−0.163422	−	0.986556i	$-0.552253\pi$
$13$	−4.15429	−	3.01827i	−1.15219	−	0.837117i	−0.988771	+	0.149439i	$0.952253\pi$
$14$	−0.0699031	+	0.215140i	−0.0186824	+	0.0574985i
$15$		0			0
$16$	−2.98979	+	2.17221i	−0.747449	+	0.543053i
$17$	−1.16298	+	0.844956i	−0.282065	+	0.204932i	−0.719817	−	0.694163i	$-0.755774\pi$
$17$	−1.16298	+	0.844956i	−0.282065	+	0.204932i	0.437753	+	0.899095i	$0.355774\pi$
$18$		0			0
$19$	−1.87526	+	5.77147i	−0.430215	+	1.32406i	0.467697	+	0.883889i	$0.345084\pi$
$19$	−1.87526	+	5.77147i	−0.430215	+	1.32406i	−0.897912	+	0.440176i	$0.854916\pi$
$20$	3.93453	+	2.85860i	0.879788	+	0.639203i
$21$		0			0
$22$	0.750229	−	0.00659095i	0.159949	−	0.00140520i
$23$	−7.08292			−1.47689			−0.738446	−	0.674313i	$-0.764440\pi$
$23$	−7.08292			−1.47689			−0.738446	+	0.674313i	$0.764440\pi$
$24$		0			0
$25$	0.379361	−	1.16755i	0.0758722	−	0.233511i
$26$	−0.358952	−	1.10474i	−0.0703962	−	0.216657i
$27$		0			0
$28$	1.57664	−	1.14549i	0.297956	−	0.216478i
$29$	−2.01408	−	6.19869i	−0.374004	−	1.15107i	−0.944148	−	0.329522i	$-0.893112\pi$
$29$	−2.01408	−	6.19869i	−0.374004	−	1.15107i	0.570143	−	0.821545i	$-0.306888\pi$
$30$		0			0
$31$	−6.22049	−	4.51945i	−1.11723	−	0.811718i	−0.133446	−	0.991056i	$-0.542604\pi$
$31$	−6.22049	−	4.51945i	−1.11723	−	0.811718i	−0.983787	+	0.179338i	$0.942604\pi$
$32$	−2.62252			−0.463601
$33$		0			0
$34$	−0.325184			−0.0557687
$35$	−2.01892	−	1.46683i	−0.341260	−	0.247940i
$36$		0			0
$37$	−1.23122	−	3.78932i	−0.202412	−	0.622960i	−0.999810	−	0.0195059i	$-0.993791\pi$
$37$	−1.23122	−	3.78932i	−0.202412	−	0.622960i	0.797398	−	0.603454i	$-0.206209\pi$
$38$	−1.11058	+	0.806887i	−0.180161	+	0.130894i
$39$		0			0
$40$	0.688853	+	2.12007i	0.108917	+	0.335213i
$41$	−2.08556	+	6.41868i	−0.325709	+	1.00243i	0.645410	+	0.763836i	$0.276686\pi$
$41$	−2.08556	+	6.41868i	−0.325709	+	1.00243i	−0.971120	+	0.238594i	$0.923314\pi$
$42$		0			0
$43$	−0.802299			−0.122349			−0.0611747	−	0.998127i	$-0.519485\pi$
$43$	−0.802299			−0.122349			−0.0611747	+	0.998127i	$0.519485\pi$
$44$	−5.26228	−	3.75309i	−0.793319	−	0.565799i
$45$		0			0
$46$	−1.29624	−	0.941771i	−0.191120	−	0.138857i
$47$	−2.08655	+	6.42174i	−0.304355	+	0.936707i	0.675563	+	0.737303i	$0.263901\pi$
$47$	−2.08655	+	6.42174i	−0.304355	+	0.936707i	−0.979917	+	0.199405i	$0.936099\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	0.224669	−	0.163231i	0.0317729	−	0.0230844i
$51$		0			0
$52$	−3.09240	+	9.51742i	−0.428838	+	1.31983i
$53$	5.32469	+	3.86861i	0.731402	+	0.531394i	0.890007	−	0.455948i	$-0.150700\pi$
$53$	5.32469	+	3.86861i	0.731402	+	0.531394i	−0.158605	+	0.987342i	$0.550700\pi$
$54$		0			0
$55$	−2.48840	+	7.89379i	−0.335535	+	1.06440i
$56$	0.893270			0.119368
$57$		0			0
$58$	0.455607	−	1.40221i	0.0598241	−	0.184120i
$59$	−0.888810	−	2.73548i	−0.115713	−	0.356129i	0.876382	−	0.481617i	$-0.159950\pi$
$59$	−0.888810	−	2.73548i	−0.115713	−	0.356129i	−0.992095	+	0.125488i	$0.959950\pi$
$60$		0			0
$61$	0.691986	−	0.502757i	0.0885997	−	0.0643715i	−0.542604	−	0.839989i	$-0.682561\pi$
$61$	0.691986	−	0.502757i	0.0885997	−	0.0643715i	0.631203	+	0.775617i	$0.282561\pi$
$62$	−0.537482	−	1.65420i	−0.0682603	−	0.210084i
$63$		0			0
$64$	5.49964	+	3.99573i	0.687455	+	0.499466i
$65$	12.8145			1.58944
$66$		0			0
$67$	−1.64668			−0.201174			−0.100587	−	0.994928i	$-0.532072\pi$
$67$	−1.64668			−0.201174			−0.100587	+	0.994928i	$0.532072\pi$
$68$	2.26645	+	1.64667i	0.274848	+	0.199689i
$69$		0			0
$70$	−0.174445	−	0.536886i	−0.0208502	−	0.0641702i
$71$	3.65738	−	2.65724i	0.434051	−	0.315357i	−0.349216	−	0.937042i	$-0.613552\pi$
$71$	3.65738	−	2.65724i	0.434051	−	0.315357i	0.783267	+	0.621686i	$0.213552\pi$
$72$		0			0
$73$	−4.58827	−	14.1212i	−0.537016	−	1.65277i	−0.739252	−	0.673429i	$-0.764821\pi$
$73$	−4.58827	−	14.1212i	−0.537016	−	1.65277i	0.202236	−	0.979337i	$-0.435179\pi$
$74$	0.278517	−	0.857187i	0.0323769	−	0.0996459i
$75$		0			0
$76$	11.8264			1.35658
$77$	2.70023	+	1.92582i	0.307720	+	0.219467i
$78$		0			0
$79$	−1.98444	−	1.44178i	−0.223267	−	0.162213i	0.470529	−	0.882385i	$-0.344063\pi$
$79$	−1.98444	−	1.44178i	−0.223267	−	0.162213i	−0.693796	+	0.720171i	$0.744063\pi$
$80$	2.84989	−	8.77105i	0.318627	−	0.980633i
$81$		0			0
$82$	−1.23513	+	0.897372i	−0.136397	+	0.0990982i
$83$	1.81851	−	1.32122i	0.199607	−	0.145023i	−0.483492	−	0.875349i	$-0.660632\pi$
$83$	1.81851	−	1.32122i	0.199607	−	0.145023i	0.683099	+	0.730326i	$0.260632\pi$
$84$		0			0
$85$	1.10856	−	3.41180i	0.120240	−	0.370061i
$86$	−0.146828	−	0.106677i	−0.0158328	−	0.0115032i
$87$		0			0
$88$	−0.940224	−	2.80949i	−0.100228	−	0.299492i
$89$	−1.73566			−0.183980			−0.0919898	−	0.995760i	$-0.529323\pi$
$89$	−1.73566			−0.183980			−0.0919898	+	0.995760i	$0.529323\pi$
$90$		0			0
$91$	1.58680	−	4.88366i	0.166342	−	0.511947i
$92$	4.26549	+	13.1278i	0.444708	+	1.36867i
$93$		0			0
$94$	−1.23572	+	0.897800i	−0.127454	+	0.0926010i
$95$	−4.67976	−	14.4028i	−0.480134	−	1.47770i
$96$		0			0
$97$	9.77095	+	7.09901i	0.992089	+	0.720795i	0.960378	−	0.278702i	$-0.0899042\pi$
$97$	9.77095	+	7.09901i	0.992089	+	0.720795i	0.0317117	+	0.999497i	$0.489904\pi$
$98$	−0.226211			−0.0228508
$99$		0			0
$100$	−2.39246			−0.239246
$101$	−2.98801	−	2.17091i	−0.297318	−	0.216014i	0.429118	−	0.903249i	$-0.358825\pi$
$101$	−2.98801	−	2.17091i	−0.297318	−	0.216014i	−0.726436	+	0.687234i	$0.758825\pi$
$102$		0			0
$103$	−0.355853	−	1.09520i	−0.0350632	−	0.107913i	0.931993	−	0.362476i	$-0.118069\pi$
$103$	−0.355853	−	1.09520i	−0.0350632	−	0.107913i	−0.967056	+	0.254563i	$0.918069\pi$
$104$	−3.71090	+	2.69613i	−0.363884	+	0.264377i
$105$		0			0
$106$	0.460080	+	1.41598i	0.0446869	+	0.137532i
$107$	−0.360665	+	1.11001i	−0.0348668	+	0.107309i	−0.966975	−	0.254870i	$-0.917967\pi$
$107$	−0.360665	+	1.11001i	−0.0348668	+	0.107309i	0.932108	+	0.362179i	$0.117967\pi$
$108$		0			0
$109$	9.30234			0.891003			0.445501	−	0.895281i	$-0.353025\pi$
$109$	9.30234			0.891003			0.445501	+	0.895281i	$0.353025\pi$
$110$	−1.50499	+	1.11377i	−0.143495	+	0.106194i
$111$		0			0
$112$	−2.98979	−	2.17221i	−0.282509	−	0.205255i
$113$	−1.01893	+	3.13595i	−0.0958529	+	0.295005i	−0.987475	−	0.157775i	$-0.949568\pi$
$113$	−1.01893	+	3.13595i	−0.0958529	+	0.295005i	0.891622	+	0.452780i	$0.149568\pi$
$114$		0			0
$115$	14.2999	−	10.3895i	1.33347	−	0.968822i
$116$	−10.2760	+	7.46596i	−0.954104	+	0.693197i
$117$		0			0
$118$	0.201059	−	0.618796i	0.0185090	−	0.0569648i
$119$	−1.16298	−	0.844956i	−0.106610	−	0.0774570i
$120$		0			0
$121$	3.21486	−	10.5197i	0.292260	−	0.956339i
$122$	0.193488			0.0175176
$123$		0			0
$124$	−4.63045	+	14.2511i	−0.415827	+	1.27978i
$125$	−2.90909	−	8.95326i	−0.260197	−	0.800804i
$126$		0			0
$127$	0.233972	−	0.169990i	0.0207616	−	0.0150842i	−0.577356	−	0.816492i	$-0.695916\pi$
$127$	0.233972	−	0.169990i	0.0207616	−	0.0150842i	0.598118	+	0.801408i	$0.295916\pi$
$128$	2.09601	+	6.45084i	0.185262	+	0.570179i
$129$		0			0
$130$	2.34516	+	1.70386i	0.205684	+	0.149438i
$131$	16.5059			1.44212			0.721062	−	0.692871i	$-0.243654\pi$
$131$	16.5059			1.44212			0.721062	+	0.692871i	$0.243654\pi$
$132$		0			0
$133$	−6.06848			−0.526204
$134$	−0.301357	−	0.218949i	−0.0260333	−	0.0189143i
$135$		0			0
$136$	0.396808	+	1.22125i	0.0340260	+	0.104721i
$137$	7.54479	−	5.48161i	0.644595	−	0.468326i	−0.216831	−	0.976209i	$-0.569572\pi$
$137$	7.54479	−	5.48161i	0.644595	−	0.468326i	0.861426	+	0.507883i	$0.169572\pi$
$138$		0			0
$139$	1.49147	+	4.59026i	0.126505	+	0.389341i	0.994172	−	0.107804i	$-0.0343818\pi$
$139$	1.49147	+	4.59026i	0.126505	+	0.389341i	−0.867668	+	0.497145i	$0.834382\pi$
$140$	−1.50286	+	4.62532i	−0.127015	+	0.390911i
$141$		0			0
$142$	1.02265			0.0858189
$143$	−17.0302	+	0.149614i	−1.42413	+	0.0125114i
$144$		0			0
$145$	13.1587	+	9.56035i	1.09277	+	0.793944i
$146$	1.03792	−	3.19438i	0.0858987	−	0.264369i
$147$		0			0
$148$	−6.28183	+	4.56401i	−0.516363	+	0.375160i
$149$	0.745845	−	0.541888i	0.0611020	−	0.0443932i	−0.556815	−	0.830637i	$-0.687977\pi$
$149$	0.745845	−	0.541888i	0.0611020	−	0.0443932i	0.617917	+	0.786243i	$0.287977\pi$
$150$		0			0
$151$	5.59210	−	17.2107i	0.455079	−	1.40059i	−0.415964	−	0.909381i	$-0.636556\pi$
$151$	5.59210	−	17.2107i	0.455079	−	1.40059i	0.871043	−	0.491207i	$-0.163444\pi$
$152$	4.38551	+	3.18626i	0.355712	+	0.258440i
$153$		0			0
$154$	0.238102	+	0.711474i	0.0191868	+	0.0573322i
$155$	19.1880			1.54121
$156$		0			0
$157$	−3.79267	+	11.6726i	−0.302688	+	0.931577i	0.677842	+	0.735207i	$0.262915\pi$
$157$	−3.79267	+	11.6726i	−0.302688	+	0.931577i	−0.980530	+	0.196369i	$0.937085\pi$
$158$	−0.171466	−	0.527718i	−0.0136411	−	0.0419830i
$159$		0			0
$160$	5.29467	−	3.84680i	0.418580	−	0.304116i
$161$	−2.18874	−	6.73626i	−0.172497	−	0.530892i
$162$		0			0
$163$	−6.55233	−	4.76055i	−0.513218	−	0.372875i	0.300825	−	0.953679i	$-0.402738\pi$
$163$	−6.55233	−	4.76055i	−0.513218	−	0.372875i	−0.814043	+	0.580804i	$0.802738\pi$
$164$	13.1526			1.02705
$165$		0			0
$166$	0.508478			0.0394655
$167$	−10.5590	−	7.67154i	−0.817077	−	0.593641i	0.0987965	−	0.995108i	$-0.468501\pi$
$167$	−10.5590	−	7.67154i	−0.817077	−	0.593641i	−0.915874	+	0.401466i	$0.868501\pi$
$168$		0			0
$169$	4.13096	+	12.7138i	0.317766	+	0.977985i
$170$	0.656522	−	0.476991i	0.0503529	−	0.0365835i
$171$		0			0
$172$	0.483161	+	1.48702i	0.0368407	+	0.113384i
$173$	−1.82697	+	5.62283i	−0.138902	+	0.427496i	−0.996176	−	0.0873636i	$-0.972156\pi$
$173$	−1.82697	+	5.62283i	−0.138902	+	0.427496i	0.857275	+	0.514859i	$0.172156\pi$
$174$		0			0
$175$	1.22764			0.0928007
$176$	−3.68503	+	11.6898i	−0.277770	+	0.881153i
$177$		0			0
$178$	−0.317641	−	0.230780i	−0.0238082	−	0.0172977i
$179$	−1.33961	+	4.12290i	−0.100127	+	0.308160i	−0.988556	−	0.150854i	$-0.951798\pi$
$179$	−1.33961	+	4.12290i	−0.100127	+	0.308160i	0.888429	+	0.459015i	$0.151798\pi$
$180$		0			0
$181$	−8.76223	+	6.36613i	−0.651291	+	0.473191i	−0.863711	−	0.503988i	$-0.831866\pi$
$181$	−8.76223	+	6.36613i	−0.651291	+	0.473191i	0.212420	+	0.977179i	$0.431866\pi$
$182$	0.939748	−	0.682767i	0.0696587	−	0.0506100i
$183$		0			0
$184$	−1.95514	+	6.01730i	−0.144135	+	0.443601i
$185$	8.04404	+	5.84433i	0.591409	+	0.429684i
$186$		0			0
$187$	−1.43342	+	4.54715i	−0.104822	+	0.332520i
$188$	13.1589			0.959713
$189$		0			0
$190$	1.05862	−	3.25808i	0.0768000	−	0.236366i
$191$	−3.60178	−	11.0851i	−0.260616	−	0.802093i	−0.992671	−	0.120848i	$-0.961439\pi$
$191$	−3.60178	−	11.0851i	−0.260616	−	0.802093i	0.732055	−	0.681245i	$-0.238561\pi$
$192$		0			0
$193$	−18.1587	+	13.1931i	−1.30709	+	0.949659i	−0.999998	−	0.00201912i	$-0.999357\pi$
$193$	−18.1587	+	13.1931i	−1.30709	+	0.949659i	−0.307096	+	0.951679i	$0.599357\pi$
$194$	0.844259	+	2.59836i	0.0606143	+	0.186552i
$195$		0			0
$196$	1.57664	+	1.14549i	0.112617	+	0.0818209i
$197$	−24.1022			−1.71721			−0.858604	−	0.512639i	$-0.828668\pi$
$197$	−24.1022			−1.71721			−0.858604	+	0.512639i	$0.828668\pi$
$198$		0			0
$199$	18.7205			1.32706			0.663531	−	0.748148i	$-0.269057\pi$
$199$	18.7205			1.32706			0.663531	+	0.748148i	$0.269057\pi$
$200$	−0.887178	−	0.644573i	−0.0627330	−	0.0455782i
$201$		0			0
$202$	−0.258179	−	0.794593i	−0.0181654	−	0.0559074i
$203$	5.27292	−	3.83100i	0.370086	−	0.268883i
$204$		0			0
$205$	−5.20455	−	16.0180i	−0.363502	−	1.11874i
$206$	0.0804979	−	0.247747i	0.00560855	−	0.0172614i
$207$		0			0
$208$	18.9768			1.31580
$209$	6.38746	+	19.0864i	0.441830	+	1.32023i
$210$		0			0
$211$	6.12131	+	4.44739i	0.421408	+	0.306171i	0.778204	−	0.628011i	$-0.216131\pi$
$211$	6.12131	+	4.44739i	0.421408	+	0.306171i	−0.356796	+	0.934182i	$0.616131\pi$
$212$	3.96362	−	12.1988i	0.272223	−	0.837815i
$213$		0			0
$214$	−0.213596	+	0.155187i	−0.0146011	+	0.0106083i
$215$	1.61978	−	1.17684i	0.110468	−	0.0802596i
$216$		0			0
$217$	2.37602	−	7.31263i	0.161295	−	0.496414i
$218$	1.70241	+	1.23687i	0.115302	+	0.0837717i
$219$		0			0
$220$	16.1293	−	0.141700i	1.08744	−	0.00955340i
$221$	7.38167			0.496545
$222$		0			0
$223$	5.41533	−	16.6667i	0.362637	−	1.11608i	−0.588810	−	0.808271i	$-0.700403\pi$
$223$	5.41533	−	16.6667i	0.362637	−	1.11608i	0.951447	−	0.307811i	$-0.0995966\pi$
$224$	−0.810404	−	2.49417i	−0.0541474	−	0.166649i
$225$		0			0
$226$	−0.603440	+	0.438425i	−0.0401403	+	0.0291636i
$227$	7.93471	+	24.4205i	0.526645	+	1.62085i	0.761039	+	0.648706i	$0.224689\pi$
$227$	7.93471	+	24.4205i	0.526645	+	1.62085i	−0.234394	+	0.972142i	$0.575311\pi$
$228$		0			0
$229$	16.0484	+	11.6598i	1.06051	+	0.770503i	0.974182	−	0.225764i	$-0.0724878\pi$
$229$	16.0484	+	11.6598i	1.06051	+	0.770503i	0.0863246	+	0.996267i	$0.472488\pi$
$230$	3.99842			0.263648
$231$		0			0
$232$	−5.82205			−0.382236
$233$	−16.3539	−	11.8818i	−1.07138	−	0.778405i	−0.0952219	−	0.995456i	$-0.530356\pi$
$233$	−16.3539	−	11.8818i	−1.07138	−	0.778405i	−0.976160	+	0.217051i	$0.930356\pi$
$234$		0			0
$235$	−5.20704	−	16.0256i	−0.339670	−	1.04540i
$236$	−4.53480	+	3.29472i	−0.295190	+	0.214468i
$237$		0			0
$238$	−0.100488	−	0.309269i	−0.00651364	−	0.0200469i
$239$	−5.28431	+	16.2634i	−0.341814	+	1.05199i	0.621454	+	0.783451i	$0.286542\pi$
$239$	−5.28431	+	16.2634i	−0.341814	+	1.05199i	−0.963267	+	0.268544i	$0.913458\pi$
$240$		0			0
$241$	−24.1529			−1.55582			−0.777912	−	0.628373i	$-0.783721\pi$
$241$	−24.1529			−1.55582			−0.777912	+	0.628373i	$0.783721\pi$
$242$	1.98709	−	1.49774i	0.127735	−	0.0962786i
$243$		0			0
$244$	−1.34856	−	0.979787i	−0.0863328	−	0.0627245i
$245$	0.771159	−	2.37338i	0.0492676	−	0.151630i
$246$		0			0
$247$	25.2102	−	18.3163i	1.60409	−	1.16544i
$248$	−5.55658	+	4.03709i	−0.352843	+	0.256356i
$249$		0			0
$250$	0.658069	−	2.02533i	0.0416200	−	0.128093i
$251$	9.62305	+	6.99156i	0.607402	+	0.441303i	0.848498	−	0.529198i	$-0.177507\pi$
$251$	9.62305	+	6.99156i	0.607402	+	0.441303i	−0.241097	+	0.970501i	$0.577507\pi$
$252$		0			0
$253$	−18.8829	+	13.9743i	−1.18716	+	0.878558i
$254$	0.0654215			0.00410491
$255$		0			0
$256$	3.72721	−	11.4712i	0.232951	−	0.716949i
$257$	−7.09531	−	21.8371i	−0.442593	−	1.36216i	−0.885102	−	0.465397i	$-0.845911\pi$
$257$	−7.09531	−	21.8371i	−0.442593	−	1.36216i	0.442509	−	0.896764i	$-0.354089\pi$
$258$		0			0
$259$	3.22339	−	2.34193i	0.200291	−	0.145520i
$260$	−7.71715	−	23.7509i	−0.478597	−	1.47297i
$261$		0			0
$262$	3.02072	+	2.19468i	0.186621	+	0.135588i
$263$	−1.93774			−0.119486			−0.0597432	−	0.998214i	$-0.519028\pi$
$263$	−1.93774			−0.119486			−0.0597432	+	0.998214i	$0.519028\pi$
$264$		0			0
$265$	−16.4247			−1.00896
$266$	−1.11058	−	0.806887i	−0.0680943	−	0.0494734i
$267$		0			0
$268$	0.991666	+	3.05203i	0.0605756	+	0.186433i
$269$	5.81421	−	4.22427i	0.354499	−	0.257558i	−0.396255	−	0.918140i	$-0.629690\pi$
$269$	5.81421	−	4.22427i	0.354499	−	0.257558i	0.750754	+	0.660582i	$0.229690\pi$
$270$		0			0
$271$	0.368071	+	1.13281i	0.0223587	+	0.0688130i	0.961613	−	0.274408i	$-0.0884819\pi$
$271$	0.368071	+	1.13281i	0.0223587	+	0.0688130i	−0.939255	+	0.343221i	$0.888482\pi$
$272$	1.64165	−	5.05249i	0.0995398	−	0.306352i
$273$		0			0
$274$	2.10962			0.127447
$275$	−1.29217	−	3.86113i	−0.0779207	−	0.232835i
$276$		0			0
$277$	−8.36543	−	6.07784i	−0.502630	−	0.365182i	0.307391	−	0.951583i	$-0.400544\pi$
$277$	−8.36543	−	6.07784i	−0.502630	−	0.365182i	−0.810021	+	0.586401i	$0.800544\pi$
$278$	−0.337387	+	1.03837i	−0.0202351	+	0.0622773i
$279$		0			0
$280$	−1.80344	+	1.31028i	−0.107776	+	0.0783040i
$281$	−10.6396	+	7.73015i	−0.634707	+	0.461142i	−0.858028	−	0.513603i	$-0.828310\pi$
$281$	−10.6396	+	7.73015i	−0.634707	+	0.461142i	0.223321	+	0.974745i	$0.428310\pi$
$282$		0			0
$283$	0.0927146	−	0.285346i	0.00551131	−	0.0169621i	−0.948263	−	0.317486i	$-0.897161\pi$
$283$	0.0927146	−	0.285346i	0.00551131	−	0.0169621i	0.953774	+	0.300524i	$0.0971614\pi$
$284$	−7.12761	−	5.17851i	−0.422946	−	0.307288i
$285$		0			0
$286$	−3.13656	−	2.23701i	−0.185469	−	0.132277i
$287$	−6.74900			−0.398381
$288$		0			0
$289$	−4.61471	+	14.2026i	−0.271454	+	0.835448i
$290$	1.13698	+	3.49926i	0.0667656	+	0.205483i
$291$		0			0
$292$	−23.4098	+	17.0082i	−1.36995	+	0.995330i
$293$	−4.98880	−	15.3539i	−0.291449	−	0.896987i	−0.984391	−	0.175994i	$-0.943686\pi$
$293$	−4.98880	−	15.3539i	−0.291449	−	0.896987i	0.692942	−	0.720993i	$-0.256314\pi$
$294$		0			0
$295$	5.80692	+	4.21898i	0.338092	+	0.245638i
$296$	−3.55908			−0.206867
$297$		0			0
$298$	0.208548			0.0120808
$299$	29.4245	+	21.3782i	1.70166	+	1.23633i
$300$		0			0
$301$	−0.247924	−	0.763031i	−0.0142901	−	0.0439804i
$302$	3.31180	−	2.40617i	0.190573	−	0.138459i
$303$		0			0
$304$	−6.93020	−	21.3290i	−0.397474	−	1.22330i
$305$	−0.659605	+	2.03005i	−0.0377688	+	0.116241i
$306$		0			0
$307$	−28.6376			−1.63443			−0.817217	−	0.576330i	$-0.804484\pi$
$307$	−28.6376			−1.63443			−0.817217	+	0.576330i	$0.804484\pi$
$308$	1.94326	−	6.16449i	0.110728	−	0.351255i
$309$		0			0
$310$	3.51157	+	2.55130i	0.199444	+	0.144904i
$311$	9.83377	−	30.2652i	0.557622	−	1.71618i	−0.131294	−	0.991343i	$-0.541913\pi$
$311$	9.83377	−	30.2652i	0.557622	−	1.71618i	0.688916	−	0.724841i	$-0.258087\pi$
$312$		0			0
$313$	−0.0276872	+	0.0201159i	−0.00156497	+	0.00113702i	−0.588567	−	0.808448i	$-0.700308\pi$
$313$	−0.0276872	+	0.0201159i	−0.00156497	+	0.00113702i	0.587002	+	0.809585i	$0.300308\pi$
$314$	−2.24613	+	1.63191i	−0.126756	+	0.0920938i
$315$		0			0
$316$	−1.47719	+	4.54633i	−0.0830985	+	0.255751i
$317$	18.1134	+	13.1602i	1.01735	+	0.739149i	0.965738	−	0.259518i	$-0.0835637\pi$
$317$	18.1134	+	13.1602i	1.01735	+	0.739149i	0.0516132	+	0.998667i	$0.483564\pi$
$318$		0			0
$319$	−17.5992	−	12.5519i	−0.985368	−	0.702770i
$320$	−16.9644			−0.948339
$321$		0			0
$322$	0.495119	−	1.52382i	0.0275919	−	0.0849191i
$323$	−2.69574	−	8.29662i	−0.149995	−	0.461636i
$324$		0			0
$325$	−5.09997	+	3.70534i	−0.282895	+	0.205535i
$326$	−0.566155	−	1.74244i	−0.0313564	−	0.0965051i
$327$		0			0
$328$	4.87730	+	3.54357i	0.269304	+	0.195661i
$329$	−6.75222			−0.372262
$330$		0			0
$331$	10.7577			0.591297			0.295648	−	0.955297i	$-0.404464\pi$
$331$	10.7577			0.591297			0.295648	+	0.955297i	$0.404464\pi$
$332$	−3.54396	−	2.57484i	−0.194500	−	0.141313i
$333$		0			0
$334$	−0.912348	−	2.80792i	−0.0499215	−	0.153642i
$335$	3.32452	−	2.41540i	0.181638	−	0.131968i
$336$		0			0
$337$	2.31915	+	7.13761i	0.126332	+	0.388810i	0.994141	−	0.108087i	$-0.0344726\pi$
$337$	2.31915	+	7.13761i	0.126332	+	0.388810i	−0.867809	+	0.496897i	$0.834473\pi$
$338$	−0.934471	+	2.87601i	−0.0508285	+	0.156434i
$339$		0			0
$340$	−6.99118			−0.379150
$341$	−25.5004	+	0.224027i	−1.38092	+	0.0121318i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−0.221463	+	0.681593i	−0.0119405	+	0.0367490i
$345$		0			0
$346$	−1.08198	+	0.786107i	−0.0581678	+	0.0422614i
$347$	−22.3950	+	16.2710i	−1.20223	+	0.873471i	−0.994502	−	0.104716i	$-0.966607\pi$
$347$	−22.3950	+	16.2710i	−1.20223	+	0.873471i	−0.207727	+	0.978187i	$0.566607\pi$
$348$		0			0
$349$	−3.41788	+	10.5192i	−0.182955	+	0.563078i	−0.999907	−	0.0136278i	$-0.995662\pi$
$349$	−3.41788	+	10.5192i	−0.182955	+	0.563078i	0.816952	+	0.576706i	$0.195662\pi$
$350$	0.224669	+	0.163231i	0.0120090	+	0.00872508i
$351$		0			0
$352$	−6.99159	+	5.17413i	−0.372653	+	0.275782i
$353$	−31.9202			−1.69894			−0.849469	−	0.527638i	$-0.823078\pi$
$353$	−31.9202			−1.69894			−0.849469	+	0.527638i	$0.823078\pi$
$354$		0			0
$355$	−3.48623	+	10.7295i	−0.185030	+	0.569464i
$356$	1.04525	+	3.21695i	0.0553982	+	0.170498i
$357$		0			0
$358$	−0.793358	+	0.576408i	−0.0419303	+	0.0304641i
$359$	−1.10574	−	3.40313i	−0.0583590	−	0.179610i	0.917628	−	0.397441i	$-0.130102\pi$
$359$	−1.10574	−	3.40313i	−0.0583590	−	0.179610i	−0.975986	+	0.217831i	$0.930102\pi$
$360$		0			0
$361$	−14.4219	−	10.4781i	−0.759046	−	0.551479i
$362$	−2.45003			−0.128771
$363$		0			0
$364$	−10.0072			−0.524520
$365$	29.9768	+	21.7794i	1.56906	+	1.13999i
$366$		0			0
$367$	0.708875	+	2.18169i	0.0370030	+	0.113883i	0.967852	−	0.251521i	$-0.0809307\pi$
$367$	0.708875	+	2.18169i	0.0370030	+	0.113883i	−0.930849	+	0.365404i	$0.880931\pi$
$368$	21.1765	−	15.3856i	1.10390	−	0.802031i
$369$		0			0
$370$	0.695045	+	2.13913i	0.0361337	+	0.111208i
$371$	−2.03385	+	6.25954i	−0.105592	+	0.324979i
$372$		0			0
$373$	7.96856			0.412596			0.206298	−	0.978489i	$-0.433858\pi$
$373$	7.96856			0.412596			0.206298	+	0.978489i	$0.433858\pi$
$374$	−0.866934	+	0.641576i	−0.0448281	+	0.0331751i
$375$		0			0
$376$	4.87963	+	3.54526i	0.251648	+	0.182833i
$377$	−10.3423	+	31.8302i	−0.532653	+	1.63934i
$378$		0			0
$379$	9.40174	−	6.83077i	0.482935	−	0.350873i	−0.319526	−	0.947578i	$-0.603524\pi$
$379$	9.40174	−	6.83077i	0.482935	−	0.350873i	0.802461	+	0.596705i	$0.203524\pi$
$380$	−23.8766	+	17.3474i	−1.22484	+	0.889902i
$381$		0			0
$382$	0.814764	−	2.50759i	0.0416869	−	0.128299i
$383$	10.1762	+	7.39343i	0.519979	+	0.377787i	0.816596	−	0.577210i	$-0.195859\pi$
$383$	10.1762	+	7.39343i	0.519979	+	0.377787i	−0.296617	+	0.954996i	$0.595859\pi$
$384$		0			0
$385$	−8.27640	+	0.0727103i	−0.421804	+	0.00370566i
$386$	−5.07741			−0.258433
$387$		0			0
$388$	7.27336	−	22.3851i	0.369249	−	1.13643i
$389$	0.135440	+	0.416842i	0.00686709	+	0.0211347i	0.954431	−	0.298431i	$-0.0964631\pi$
$389$	0.135440	+	0.416842i	0.00686709	+	0.0211347i	−0.947564	+	0.319565i	$0.896463\pi$
$390$		0			0
$391$	8.23731	−	5.98476i	0.416579	−	0.302662i
$392$	0.276036	+	0.849550i	0.0139419	+	0.0429088i
$393$		0			0
$394$	−4.41091	−	3.20471i	−0.222218	−	0.161451i
$395$	6.12128			0.307995
$396$		0			0
$397$	16.8147			0.843905			0.421952	−	0.906618i	$-0.361345\pi$
$397$	16.8147			0.843905			0.421952	+	0.906618i	$0.361345\pi$
$398$	3.42602	+	2.48915i	0.171731	+	0.124770i
$399$		0			0
$400$	1.40196	+	4.31480i	0.0700981	+	0.215740i
$401$	29.8211	−	21.6663i	1.48919	−	1.08196i	0.514747	−	0.857342i	$-0.327886\pi$
$401$	29.8211	−	21.6663i	1.48919	−	1.08196i	0.974446	−	0.224621i	$-0.0721143\pi$
$402$		0			0
$403$	12.2008	+	37.5502i	0.607766	+	1.87051i
$404$	−2.22423	+	6.84548i	−0.110660	+	0.340575i
$405$		0			0
$406$	1.47437			0.0731720
$407$	−10.7586	−	7.67308i	−0.533283	−	0.380340i
$408$		0			0
$409$	−13.1659	−	9.56556i	−0.651010	−	0.472986i	0.212605	−	0.977138i	$-0.431805\pi$
$409$	−13.1659	−	9.56556i	−0.651010	−	0.472986i	−0.863615	+	0.504152i	$0.831805\pi$
$410$	1.17733	−	3.62345i	0.0581441	−	0.178949i
$411$		0			0
$412$	−1.81559	+	1.31911i	−0.0894479	+	0.0649877i
$413$	2.32694	−	1.69062i	0.114501	−	0.0831898i
$414$		0			0
$415$	−1.73341	+	5.33489i	−0.0850898	+	0.261879i
$416$	10.8947	+	7.91548i	0.534158	+	0.388088i
$417$		0			0
$418$	−1.36884	+	4.34228i	−0.0669520	+	0.212388i
$419$	−5.56352			−0.271796			−0.135898	−	0.990723i	$-0.543392\pi$
$419$	−5.56352			−0.271796			−0.135898	+	0.990723i	$0.543392\pi$
$420$		0			0
$421$	6.64120	−	20.4395i	0.323672	−	0.996161i	−0.648364	−	0.761331i	$-0.724546\pi$
$421$	6.64120	−	20.4395i	0.323672	−	0.996161i	0.972036	−	0.234831i	$-0.0754536\pi$
$422$	0.528912	+	1.62782i	0.0257470	+	0.0792412i
$423$		0			0
$424$	4.75638	−	3.45571i	0.230990	−	0.167824i
$425$	0.545341	+	1.67839i	0.0264529	+	0.0814137i
$426$		0			0
$427$	0.691986	+	0.502757i	0.0334875	+	0.0243301i
$428$	2.27455			0.109944
$429$		0			0
$430$	0.452910			0.0218413
$431$	−22.4249	−	16.2927i	−1.08017	−	0.784791i	−0.102459	−	0.994737i	$-0.532671\pi$
$431$	−22.4249	−	16.2927i	−1.08017	−	0.784791i	−0.977713	+	0.209947i	$0.932671\pi$
$432$		0			0
$433$	2.87019	+	8.83352i	0.137932	+	0.424512i	0.996035	−	0.0889667i	$-0.0283565\pi$
$433$	2.87019	+	8.83352i	0.137932	+	0.424512i	−0.858102	+	0.513479i	$0.828356\pi$
$434$	1.40715	−	1.02235i	0.0675452	−	0.0490744i
$435$		0			0
$436$	−5.60207	−	17.2414i	−0.268290	−	0.825713i
$437$	13.2823	−	40.8788i	0.635380	−	1.95550i
$438$		0			0
$439$	−14.7118			−0.702156			−0.351078	−	0.936346i	$-0.614185\pi$
$439$	−14.7118			−0.702156			−0.351078	+	0.936346i	$0.614185\pi$
$440$	6.01928	+	4.29298i	0.286958	+	0.204660i
$441$		0			0
$442$	1.35091	+	0.981494i	0.0642563	+	0.0466849i
$443$	−0.755067	+	2.32386i	−0.0358743	+	0.110410i	−0.967390	−	0.253291i	$-0.918487\pi$
$443$	−0.755067	+	2.32386i	−0.0358743	+	0.110410i	0.931516	+	0.363701i	$0.118487\pi$
$444$		0			0
$445$	3.50416	−	2.54592i	0.166113	−	0.120688i
$446$	3.20712	−	2.33011i	0.151861	−	0.110334i
$447$		0			0
$448$	−2.10068	+	6.46522i	−0.0992477	+	0.305453i
$449$	3.85849	+	2.80335i	0.182093	+	0.132298i	0.675098	−	0.737728i	$-0.264101\pi$
$449$	3.85849	+	2.80335i	0.182093	+	0.132298i	−0.493005	+	0.870027i	$0.664101\pi$
$450$		0			0
$451$	7.10376	+	21.2268i	0.334503	+	0.999530i
$452$	6.42593			0.302250
$453$		0			0
$454$	−1.79492	+	5.52420i	−0.0842398	+	0.259264i
$455$	3.95989	+	12.1873i	0.185643	+	0.571349i
$456$		0			0
$457$	−25.1503	+	18.2728i	−1.17648	+	0.854764i	−0.991770	−	0.128028i	$-0.959135\pi$
$457$	−25.1503	+	18.2728i	−1.17648	+	0.854764i	−0.184712	+	0.982793i	$0.559135\pi$
$458$	1.38666	+	4.26770i	0.0647944	+	0.199417i
$459$		0			0
$460$	−27.8680	−	20.2473i	−1.29935	−	0.944034i
$461$	−29.7215			−1.38427			−0.692134	−	0.721769i	$-0.743329\pi$
$461$	−29.7215			−1.38427			−0.692134	+	0.721769i	$0.743329\pi$
$462$		0			0
$463$	−25.4553			−1.18301			−0.591505	−	0.806302i	$-0.701466\pi$
$463$	−25.4553			−1.18301			−0.591505	+	0.806302i	$0.701466\pi$
$464$	19.4865	+	14.1578i	0.904640	+	0.657259i
$465$		0			0
$466$	−1.41306	−	4.34896i	−0.0654589	−	0.201462i
$467$	−2.57665	+	1.87204i	−0.119233	+	0.0866279i	−0.645804	−	0.763503i	$-0.723478\pi$
$467$	−2.57665	+	1.87204i	−0.119233	+	0.0866279i	0.526571	+	0.850131i	$0.323478\pi$
$468$		0			0
$469$	−0.508852	−	1.56609i	−0.0234966	−	0.0723151i
$470$	1.17789	−	3.62517i	0.0543320	−	0.167217i
$471$		0			0
$472$	−2.56927			−0.118260
$473$	−2.13891	+	1.58290i	−0.0983472	+	0.0727820i
$474$		0			0
$475$	6.02709	+	4.37894i	0.276542	+	0.200920i
$476$	−0.865708	+	2.66437i	−0.0396796	+	0.122121i
$477$		0			0
$478$	−3.12952	+	2.27373i	−0.143141	+	0.103998i
$479$	2.61599	−	1.90062i	0.119527	−	0.0868418i	−0.526416	−	0.850227i	$-0.676464\pi$
$479$	2.61599	−	1.90062i	0.119527	−	0.0868418i	0.645943	+	0.763386i	$0.276464\pi$
$480$		0			0
$481$	−6.32232	+	19.4581i	−0.288273	+	0.887213i
$482$	−4.42019	−	3.21146i	−0.201334	−	0.146278i
$483$		0			0
$484$	−21.4338	+	0.376632i	−0.974264	+	0.0171196i
$485$	−30.1398			−1.36858
$486$		0			0
$487$	3.05029	−	9.38784i	0.138222	−	0.425404i	−0.857855	−	0.513891i	$-0.828203\pi$
$487$	3.05029	−	9.38784i	0.138222	−	0.425404i	0.996077	+	0.0884878i	$0.0282034\pi$
$488$	−0.236105	−	0.726655i	−0.0106880	−	0.0328941i
$489$		0			0
$490$	0.456703	−	0.331814i	0.0206317	−	0.0149898i
$491$	−1.30591	−	4.01917i	−0.0589348	−	0.181383i	0.917255	−	0.398300i	$-0.130400\pi$
$491$	−1.30591	−	4.01917i	−0.0589348	−	0.181383i	−0.976190	+	0.216918i	$0.930400\pi$
$492$		0			0
$493$	7.57995	+	5.50716i	0.341384	+	0.248030i
$494$	7.04910			0.317154
$495$		0			0
$496$	28.4152			1.27588
$497$	3.65738	+	2.65724i	0.164056	+	0.119194i
$498$		0			0
$499$	−6.30249	−	19.3971i	−0.282138	−	0.868332i	−0.987242	−	0.159228i	$-0.949100\pi$
$499$	−6.30249	−	19.3971i	−0.282138	−	0.868332i	0.705104	−	0.709104i	$-0.250900\pi$
$500$	−14.8425	+	10.7837i	−0.663776	+	0.482261i
$501$		0			0
$502$	0.831480	+	2.55903i	0.0371108	+	0.114215i
$503$	7.40382	−	22.7866i	0.330120	−	1.01600i	−0.638956	−	0.769243i	$-0.720634\pi$
$503$	7.40382	−	22.7866i	0.330120	−	1.01600i	0.969076	−	0.246762i	$-0.0793665\pi$
$504$		0			0
$505$	9.21692			0.410147
$506$	−5.31381	+	0.0466832i	−0.236228	+	0.00207532i
$507$		0			0
$508$	−0.455971	−	0.331282i	−0.0202304	−	0.0146983i
$509$	−1.14133	+	3.51264i	−0.0505884	+	0.155695i	−0.973159	−	0.230132i	$-0.926084\pi$
$509$	−1.14133	+	3.51264i	−0.0505884	+	0.155695i	0.922571	+	0.385828i	$0.126084\pi$
$510$		0			0
$511$	12.0122	−	8.72740i	0.531390	−	0.386078i
$512$	13.1822	−	9.57742i	0.582576	−	0.423266i
$513$		0			0
$514$	1.60504	−	4.93980i	0.0707952	−	0.217885i
$515$	2.32491	+	1.68915i	0.102448	+	0.0744328i
$516$		0			0
$517$	7.10714	+	21.2369i	0.312572	+	0.933997i
$518$	0.901299			0.0396008
$519$		0			0
$520$	3.53725	−	10.8865i	0.155119	−	0.477406i
$521$	0.0736294	+	0.226608i	0.00322576	+	0.00992787i	0.952656	−	0.304049i	$-0.0983386\pi$
$521$	0.0736294	+	0.226608i	0.00322576	+	0.00992787i	−0.949431	+	0.313977i	$0.898339\pi$
$522$		0			0
$523$	17.7914	−	12.9262i	0.777966	−	0.565225i	−0.126402	−	0.991979i	$-0.540343\pi$
$523$	17.7914	−	12.9262i	0.777966	−	0.565225i	0.904368	+	0.426754i	$0.140343\pi$
$524$	−9.94018	−	30.5927i	−0.434239	−	1.33645i
$525$		0			0
$526$	−0.354624	−	0.257649i	−0.0154623	−	0.0112340i
$527$	11.0531			0.481479
$528$		0			0
$529$	27.1678			1.18121
$530$	−3.00587	−	2.18389i	−0.130567	−	0.0948622i
$531$		0			0
$532$	3.65457	+	11.2476i	0.158446	+	0.487645i
$533$	28.0373	−	20.3703i	1.21443	−	0.882336i
$534$		0			0
$535$	−0.900048	−	2.77006i	−0.0389125	−	0.119760i
$536$	−0.454542	+	1.39894i	−0.0196332	+	0.0604249i
$537$		0			0
$538$	1.62573			0.0700900
$539$	−0.997144	+	3.16318i	−0.0429500	+	0.136248i
$540$		0			0
$541$	−23.1629	−	16.8288i	−0.995851	−	0.723528i	−0.0346561	−	0.999399i	$-0.511034\pi$
$541$	−23.1629	−	16.8288i	−0.995851	−	0.723528i	−0.961195	+	0.275871i	$0.911034\pi$
$542$	−0.0832618	+	0.256253i	−0.00357640	+	0.0110070i
$543$		0			0
$544$	3.04995	−	2.21592i	0.130765	−	0.0950066i
$545$	−18.7807	+	13.6450i	−0.804477	+	0.584486i
$546$		0			0
$547$	1.98033	−	6.09482i	0.0846727	−	0.260596i	−0.899752	−	0.436401i	$-0.856253\pi$
$547$	1.98033	−	6.09482i	0.0846727	−	0.260596i	0.984425	+	0.175805i	$0.0562529\pi$
$548$	−14.7035	−	10.6827i	−0.628103	−	0.456343i
$549$		0			0
$550$	0.276913	−	0.878433i	0.0118076	−	0.0374565i
$551$	39.5524			1.68499
$552$		0			0
$553$	0.757990	−	2.33285i	0.0322330	−	0.0992030i
$554$	−0.722815	−	2.22460i	−0.0307095	−	0.0945141i
$555$		0			0
$556$	7.60961	−	5.52871i	0.322719	−	0.234469i
$557$	6.95884	+	21.4171i	0.294855	+	0.907471i	0.983270	+	0.182154i	$0.0583070\pi$
$557$	6.95884	+	21.4171i	0.294855	+	0.907471i	−0.688415	+	0.725317i	$0.741693\pi$
$558$		0			0
$559$	3.33298	+	2.42155i	0.140970	+	0.102421i
$560$	9.22243			0.389719
$561$		0			0
$562$	−2.97498			−0.125492
$563$	−24.1303	−	17.5317i	−1.01697	−	0.738873i	−0.0513116	−	0.998683i	$-0.516340\pi$
$563$	−24.1303	−	17.5317i	−1.01697	−	0.738873i	−0.965660	+	0.259810i	$0.916340\pi$
$564$		0			0
$565$	−2.54277	−	7.82583i	−0.106975	−	0.329235i
$566$	0.0549082	−	0.0398932i	0.00230797	−	0.00167684i
$567$		0			0
$568$	−1.24789	−	3.84062i	−0.0523604	−	0.161149i
$569$	−9.04690	+	27.8435i	−0.379266	+	1.16726i	0.561290	+	0.827619i	$0.310305\pi$
$569$	−9.04690	+	27.8435i	−0.379266	+	1.16726i	−0.940555	+	0.339640i	$0.889695\pi$
$570$		0			0
$571$	37.9252			1.58712			0.793559	−	0.608493i	$-0.208226\pi$
$571$	37.9252			1.58712			0.793559	+	0.608493i	$0.208226\pi$
$572$	10.5332	+	31.4744i	0.440416	+	1.31601i
$573$		0			0
$574$	−1.23513	−	0.897372i	−0.0515532	−	0.0374556i
$575$	−2.68699	+	8.26969i	−0.112055	+	0.344870i
$576$		0			0
$577$	−7.09721	+	5.15642i	−0.295461	+	0.214665i	−0.725633	−	0.688082i	$-0.758453\pi$
$577$	−7.09721	+	5.15642i	−0.295461	+	0.214665i	0.430172	+	0.902747i	$0.358453\pi$
$578$	−2.73297	+	1.98562i	−0.113676	+	0.0825908i
$579$		0			0
$580$	9.79515	−	30.1464i	0.406721	−	1.25176i
$581$	1.81851	+	1.32122i	0.0754444	+	0.0548136i
$582$		0			0
$583$	21.8281	−	0.191765i	0.904027	−	0.00794211i
$584$	−13.2632			−0.548836
$585$		0			0
$586$	1.12852	−	3.47324i	0.0466189	−	0.143478i
$587$	−2.83372	−	8.72130i	−0.116960	−	0.359966i	0.875391	−	0.483416i	$-0.160604\pi$
$587$	−2.83372	−	8.72130i	−0.116960	−	0.359966i	−0.992351	+	0.123450i	$0.960604\pi$
$588$		0			0
$589$	37.7489	−	27.4262i	1.55542	−	1.13008i
$590$	0.501747	+	1.54422i	0.0206566	+	0.0635745i
$591$		0			0
$592$	11.9123	+	8.65480i	0.489593	+	0.355710i
$593$	−7.25596			−0.297967			−0.148983	−	0.988840i	$-0.547600\pi$
$593$	−7.25596			−0.297967			−0.148983	+	0.988840i	$0.547600\pi$
$594$		0			0
$595$	3.58738			0.147068
$596$	−1.45352	−	1.05605i	−0.0595386	−	0.0432573i
$597$		0			0
$598$	2.54243	+	7.82479i	0.103968	+	0.319979i
$599$	−16.1949	+	11.7663i	−0.661708	+	0.480759i	−0.867239	−	0.497892i	$-0.834108\pi$
$599$	−16.1949	+	11.7663i	−0.661708	+	0.480759i	0.205532	+	0.978650i	$0.434108\pi$
$600$		0			0
$601$	−3.48280	−	10.7189i	−0.142066	−	0.437235i	0.854556	−	0.519360i	$-0.173829\pi$
$601$	−3.48280	−	10.7189i	−0.142066	−	0.437235i	−0.996622	+	0.0821246i	$0.973829\pi$
$602$	0.0560832	−	0.172606i	0.00228578	−	0.00703491i
$603$		0			0
$604$	−35.2668			−1.43499
$605$	8.94012	+	25.9542i	0.363468	+	1.05519i
$606$		0			0
$607$	10.9428	+	7.95040i	0.444154	+	0.322697i	0.787283	−	0.616591i	$-0.211487\pi$
$607$	10.9428	+	7.95040i	0.444154	+	0.322697i	−0.343129	+	0.939288i	$0.611487\pi$
$608$	4.91792	−	15.1358i	0.199448	−	0.613838i
$609$		0			0
$610$	−0.390637	+	0.283814i	−0.0158164	+	0.0114913i
$611$	28.0507	−	20.3800i	1.13481	−	0.824487i
$612$		0			0
$613$	−9.51673	+	29.2895i	−0.384377	+	1.18299i	0.552554	+	0.833477i	$0.313653\pi$
$613$	−9.51673	+	29.2895i	−0.384377	+	1.18299i	−0.936931	+	0.349514i	$0.886347\pi$
$614$	−5.24093	−	3.80776i	−0.211507	−	0.153669i
$615$		0			0
$616$	2.38144	−	1.76239i	0.0959508	−	0.0710085i
$617$	−23.6896			−0.953707			−0.476853	−	0.878983i	$-0.658223\pi$
$617$	−23.6896			−0.953707			−0.476853	+	0.878983i	$0.658223\pi$
$618$		0			0
$619$	−10.0393	+	30.8977i	−0.403513	+	1.24188i	0.518618	+	0.855006i	$0.326447\pi$
$619$	−10.0393	+	30.8977i	−0.403513	+	1.24188i	−0.922131	+	0.386878i	$0.873553\pi$
$620$	−11.5554	−	35.5639i	−0.464076	−	1.42828i
$621$		0			0
$622$	5.82385	−	4.23127i	0.233515	−	0.169659i
$623$	−0.536349	−	1.65071i	−0.0214884	−	0.0661344i
$624$		0			0
$625$	23.9721	+	17.4167i	0.958882	+	0.696669i
$626$	−0.00774169			−0.000309420
$627$		0			0
$628$	23.9186			0.954456
$629$	4.63370	+	3.36658i	0.184758	+	0.134234i
$630$		0			0
$631$	−4.67646	−	14.3927i	−0.186167	−	0.572962i	0.813800	−	0.581145i	$-0.197395\pi$
$631$	−4.67646	−	14.3927i	−0.186167	−	0.572962i	−0.999967	+	0.00818299i	$0.997395\pi$
$632$	−1.77264	+	1.28790i	−0.0705119	+	0.0512299i
$633$		0			0
$634$	1.56509	+	4.81686i	0.0621577	+	0.191302i
$635$	−0.223023	+	0.686395i	−0.00885041	+	0.0272387i
$636$		0			0
$637$	5.13499			0.203456
$638$	−1.55187	−	4.63716i	−0.0614393	−	0.183587i
$639$		0			0
$640$	−13.6940	−	9.94925i	−0.541302	−	0.393279i
$641$	5.11431	−	15.7402i	0.202003	−	0.621701i	−0.797820	−	0.602895i	$-0.794014\pi$
$641$	5.11431	−	15.7402i	0.202003	−	0.621701i	0.999823	−	0.0188056i	$-0.00598637\pi$
$642$		0			0
$643$	−1.61403	+	1.17266i	−0.0636513	+	0.0462454i	−0.619156	−	0.785268i	$-0.712525\pi$
$643$	−1.61403	+	1.17266i	−0.0636513	+	0.0462454i	0.555505	+	0.831513i	$0.312525\pi$
$644$	−11.1672	+	8.11343i	−0.440049	+	0.319714i
$645$		0			0
$646$	0.609806	−	1.87679i	0.0239925	−	0.0738413i
$647$	32.7261	+	23.7769i	1.28660	+	0.934767i	0.999731	−	0.0232039i	$-0.00738670\pi$
$647$	32.7261	+	23.7769i	1.28660	+	0.934767i	0.286866	+	0.957971i	$0.407387\pi$
$648$		0			0
$649$	−7.76653	−	5.53913i	−0.304863	−	0.217430i
$650$	−1.42602			−0.0559329
$651$		0			0
$652$	−4.87747	+	15.0113i	−0.191016	+	0.587888i
$653$	12.8198	+	39.4552i	0.501676	+	1.54400i	0.806288	+	0.591524i	$0.201473\pi$
$653$	12.8198	+	39.4552i	0.501676	+	1.54400i	−0.304611	+	0.952477i	$0.598527\pi$
$654$		0			0
$655$	−33.3240	+	24.2113i	−1.30208	+	0.946015i
$656$	−7.70736	−	23.7208i	−0.300922	−	0.926142i
$657$		0			0
$658$	−1.23572	−	0.897800i	−0.0481732	−	0.0349999i
$659$	51.1359			1.99197			0.995985	−	0.0895158i	$-0.0285320\pi$
$659$	51.1359			1.99197			0.995985	+	0.0895158i	$0.0285320\pi$
$660$		0			0
$661$	−42.8840			−1.66800			−0.833998	−	0.551768i	$-0.813954\pi$
$661$	−42.8840			−1.66800			−0.833998	+	0.551768i	$0.813954\pi$
$662$	1.96875	+	1.43038i	0.0765178	+	0.0555934i
$663$		0			0
$664$	−0.620472	−	1.90962i	−0.0240790	−	0.0741075i
$665$	12.2518	−	8.90144i	0.475104	−	0.345183i
$666$		0			0
$667$	14.2655	+	43.9048i	0.552364	+	1.70000i
$668$	−7.85995	+	24.1904i	−0.304111	+	0.935956i
$669$		0			0
$670$	0.929577			0.0359127
$671$	0.852898	−	2.70560i	0.0329258	−	0.104448i
$672$		0			0
$673$	20.2313	+	14.6989i	0.779858	+	0.566600i	0.904936	−	0.425547i	$-0.139918\pi$
$673$	20.2313	+	14.6989i	0.779858	+	0.566600i	−0.125078	+	0.992147i	$0.539918\pi$
$674$	−0.524618	+	1.61461i	−0.0202075	+	0.0621923i
$675$		0			0
$676$	21.0766	−	15.3130i	0.810638	−	0.588963i
$677$	−8.02456	+	5.83018i	−0.308409	+	0.224072i	−0.731213	−	0.682149i	$-0.761046\pi$
$677$	−8.02456	+	5.83018i	−0.308409	+	0.224072i	0.422805	+	0.906221i	$0.361046\pi$
$678$		0			0
$679$	−3.73217	+	11.4864i	−0.143228	+	0.440809i
$680$	−2.59249	−	1.88356i	−0.0994175	−	0.0722310i
$681$		0			0
$682$	−4.69658	−	3.34963i	−0.179841	−	0.128264i
$683$	39.8980			1.52666			0.763328	−	0.646011i	$-0.223564\pi$
$683$	39.8980			1.52666			0.763328	+	0.646011i	$0.223564\pi$
$684$		0			0
$685$	−7.19174	+	22.1339i	−0.274782	+	0.845692i
$686$	−0.0699031	−	0.215140i	−0.00266891	−	0.00821407i
$687$		0			0
$688$	2.39871	−	1.74276i	0.0914499	−	0.0664422i
$689$	−10.4438	−	32.1427i	−0.397877	−	1.22454i
$690$		0			0
$691$	5.35084	+	3.88762i	0.203556	+	0.147892i	0.684893	−	0.728643i	$-0.259849\pi$
$691$	5.35084	+	3.88762i	0.203556	+	0.147892i	−0.481338	+	0.876535i	$0.659849\pi$
$692$	11.5218			0.437995
$693$		0			0
$694$	−6.26194			−0.237700
$695$	−9.74430	−	7.07965i	−0.369622	−	0.268546i
$696$		0			0
$697$	−2.99804	−	9.22701i	−0.113559	−	0.349498i
$698$	−2.02417	+	1.47065i	−0.0766159	+	0.0556647i
$699$		0			0
$700$	−0.739310	−	2.27536i	−0.0279433	−	0.0860006i
$701$	−4.51215	+	13.8870i	−0.170421	+	0.524503i	−0.999395	−	0.0347848i	$-0.988925\pi$
$701$	−4.51215	+	13.8870i	−0.170421	+	0.524503i	0.828973	+	0.559288i	$0.188925\pi$
$702$		0			0
$703$	24.1788			0.911920
$704$	22.5453	−	0.198066i	0.849709	−	0.00746491i
$705$		0			0
$706$	−5.84167	−	4.24422i	−0.219854	−	0.159733i
$707$	1.14132	−	3.51261i	0.0429237	−	0.132105i
$708$		0			0
$709$	3.35261	−	2.43582i	0.125910	−	0.0914790i	−0.523048	−	0.852303i	$-0.675205\pi$
$709$	3.35261	−	2.43582i	0.125910	−	0.0914790i	0.648958	+	0.760824i	$0.275205\pi$
$710$	−2.06465	+	1.50006i	−0.0774849	+	0.0562961i
$711$		0			0
$712$	−0.479104	+	1.47453i	−0.0179552	+	0.0552604i
$713$	44.0593	+	32.0109i	1.65003	+	1.19882i
$714$		0			0
$715$	34.1631	−	25.2824i	1.27763	−	0.945510i
$716$	8.44832			0.315729
$717$		0			0
$718$	0.250132	−	0.769827i	0.00933484	−	0.0287297i
$719$	−5.26017	−	16.1891i	−0.196171	−	0.603753i	−0.999961	−	0.00883941i	$-0.997186\pi$
$719$	−5.26017	−	16.1891i	−0.196171	−	0.603753i	0.803790	−	0.594914i	$-0.202814\pi$
$720$		0			0
$721$	0.931634	−	0.676872i	0.0346959	−	0.0252080i
$722$	−1.24612	−	3.83517i	−0.0463759	−	0.142730i
$723$		0			0
$724$	17.0761	+	12.4065i	0.634627	+	0.461084i
$725$	−8.00136			−0.297163
$726$		0			0
$727$	−21.6199			−0.801837			−0.400918	−	0.916114i	$-0.631309\pi$
$727$	−21.6199			−0.801837			−0.400918	+	0.916114i	$0.631309\pi$
$728$	−3.71090	−	2.69613i	−0.137535	−	0.0999252i
$729$		0			0
$730$	2.59015	+	7.97166i	0.0958657	+	0.295044i
$731$	0.933059	−	0.677907i	0.0345104	−	0.0250733i
$732$		0			0
$733$	−14.9047	−	45.8719i	−0.550517	−	1.69432i	−0.707498	−	0.706715i	$-0.750176\pi$
$733$	−14.9047	−	45.8719i	−0.550517	−	1.69432i	0.156981	−	0.987602i	$-0.449824\pi$
$734$	−0.160355	+	0.493523i	−0.00591883	+	0.0182163i
$735$		0			0
$736$	18.5751			0.684688
$737$	−4.39001	+	3.24883i	−0.161708	+	0.119672i
$738$		0			0
$739$	6.60439	+	4.79837i	0.242946	+	0.176511i	0.702595	−	0.711590i	$-0.252025\pi$
$739$	6.60439	+	4.79837i	0.242946	+	0.176511i	−0.459649	+	0.888101i	$0.652025\pi$
$740$	5.98787	−	18.4288i	0.220118	−	0.677455i
$741$		0			0
$742$	−1.20450	+	0.875124i	−0.0442187	+	0.0321268i
$743$	15.8254	−	11.4978i	0.580577	−	0.421814i	−0.258355	−	0.966050i	$-0.583180\pi$
$743$	15.8254	−	11.4978i	0.580577	−	0.421814i	0.838932	+	0.544236i	$0.183180\pi$
$744$		0			0
$745$	−0.710943	+	2.18806i	−0.0260469	+	0.0801642i
$746$	1.45832	+	1.05953i	0.0533927	+	0.0387921i
$747$		0			0
$748$	9.29113	−	0.0816249i	0.339717	−	0.00298450i
$749$	−1.16714			−0.0426462
$750$		0			0
$751$	0.344955	−	1.06166i	0.0125876	−	0.0387406i	−0.944565	−	0.328323i	$-0.893516\pi$
$751$	0.344955	−	1.06166i	0.0125876	−	0.0387406i	0.957153	+	0.289583i	$0.0935165\pi$
$752$	−7.71103	−	23.7321i	−0.281192	−	0.865421i
$753$		0			0
$754$	−6.12498	+	4.45006i	−0.223059	+	0.162062i
$755$	13.9552	+	42.9497i	0.507882	+	1.56310i
$756$		0			0
$757$	21.5015	+	15.6218i	0.781485	+	0.567782i	0.905424	−	0.424508i	$-0.139553\pi$
$757$	21.5015	+	15.6218i	0.781485	+	0.567782i	−0.123939	+	0.992290i	$0.539553\pi$
$758$	2.62885			0.0954840
$759$		0			0
$760$	−13.5277			−0.490701
$761$	5.09683	+	3.70306i	0.184760	+	0.134236i	0.676321	−	0.736607i	$-0.263573\pi$
$761$	5.09683	+	3.70306i	0.184760	+	0.134236i	−0.491561	+	0.870843i	$0.663573\pi$
$762$		0			0
$763$	2.87458	+	8.84705i	0.104067	+	0.320285i
$764$	−18.3766	+	13.3514i	−0.664844	+	0.483037i
$765$		0			0
$766$	0.879273	+	2.70613i	0.0317694	+	0.0977763i
$767$	−4.56403	+	14.0466i	−0.164797	+	0.507195i
$768$		0			0
$769$	13.1916			0.475700			0.237850	−	0.971302i	$-0.423557\pi$
$769$	13.1916			0.475700			0.237850	+	0.971302i	$0.423557\pi$
$770$	−1.52432	−	1.08715i	−0.0549327	−	0.0391783i
$771$		0			0
$772$	35.3883	+	25.7111i	1.27365	+	0.925362i
$773$	−14.1585	+	43.5753i	−0.509245	+	1.56729i	0.284270	+	0.958744i	$0.408249\pi$
$773$	−14.1585	+	43.5753i	−0.509245	+	1.56729i	−0.793515	+	0.608550i	$0.791751\pi$
$774$		0			0
$775$	−7.63652	+	5.54825i	−0.274312	+	0.199299i
$776$	8.72809	−	6.34133i	0.313320	−	0.227640i
$777$		0			0
$778$	−0.0306381	+	0.0942944i	−0.00109843	+	0.00338062i
$779$	−33.1342	−	24.0734i	−1.18716	−	0.862520i
$780$		0			0
$781$	4.50786	−	14.3000i	0.161304	−	0.511695i
$782$	2.30326			0.0823643
$783$		0			0
$784$	1.14200	−	3.51471i	0.0407857	−	0.125526i
$785$	−9.46469	−	29.1293i	−0.337809	−	1.03967i
$786$		0			0
$787$	15.2483	−	11.0785i	0.543543	−	0.394907i	−0.281856	−	0.959457i	$-0.590950\pi$
$787$	15.2483	−	11.0785i	0.543543	−	0.394907i	0.825399	+	0.564549i	$0.190950\pi$
$788$	14.5148	+	44.6721i	0.517070	+	1.59138i
$789$		0			0
$790$	1.12025	+	0.813909i	0.0398567	+	0.0289576i
$791$	−3.29733			−0.117240
$792$		0			0
$793$	−4.39217			−0.155970
$794$	3.07724	+	2.23574i	0.109207	+	0.0793435i
$795$		0			0
$796$	−11.2739	−	34.6975i	−0.399593	−	1.22982i
$797$	−22.7830	+	16.5528i	−0.807016	+	0.586331i	−0.912964	−	0.408040i	$-0.866212\pi$
$797$	−22.7830	+	16.5528i	−0.807016	+	0.586331i	0.105948	+	0.994372i	$0.466212\pi$
$798$		0			0
$799$	−2.99947	−	9.23141i	−0.106114	−	0.326584i
$800$	−0.994884	+	3.06194i	−0.0351744	+	0.108256i
$801$		0			0
$802$	8.33835			0.294437
$803$	−40.0928	−	28.5944i	−1.41485	−	1.00907i
$804$		0			0
$805$	14.2999	+	10.3895i	0.504004	+	0.366180i
$806$	−2.75996	+	8.49429i	−0.0972155	+	0.299199i
$807$		0			0
$808$	−2.66910	+	1.93921i	−0.0938985	+	0.0682213i
$809$	−5.29544	+	3.84736i	−0.186178	+	0.135266i	−0.676970	−	0.736011i	$-0.736707\pi$
$809$	−5.29544	+	3.84736i	−0.186178	+	0.135266i	0.490792	+	0.871277i	$0.336707\pi$
$810$		0			0
$811$	5.81096	−	17.8843i	0.204050	−	0.628002i	−0.795701	−	0.605690i	$-0.792897\pi$
$811$	5.81096	−	17.8843i	0.204050	−	0.628002i	0.999751	−	0.0223122i	$-0.00710279\pi$
$812$	−10.2760	−	7.46596i	−0.360617	−	0.262004i
$813$		0			0
$814$	−0.948675	−	2.83474i	−0.0332511	−	0.0993576i
$815$	20.2116			0.707980
$816$		0			0
$817$	1.50452	−	4.63044i	0.0526365	−	0.161999i
$818$	−1.13760	−	3.50116i	−0.0397751	−	0.122415i
$819$		0			0
$820$	−26.5542	+	19.2927i	−0.927311	+	0.673731i
$821$	3.58089	+	11.0208i	0.124974	+	0.384630i	0.993896	−	0.110318i	$-0.0351870\pi$
$821$	3.58089	+	11.0208i	0.124974	+	0.384630i	−0.868922	+	0.494948i	$0.835187\pi$
$822$		0			0
$823$	−9.98844	−	7.25702i	−0.348175	−	0.252964i	0.399928	−	0.916547i	$-0.369035\pi$
$823$	−9.98844	−	7.25702i	−0.348175	−	0.252964i	−0.748103	+	0.663583i	$0.769035\pi$
$824$	−1.02866			−0.0358349
$825$		0			0
$826$	0.650640			0.0226387
$827$	−3.63717	−	2.64256i	−0.126477	−	0.0918907i	0.522748	−	0.852487i	$-0.324907\pi$
$827$	−3.63717	−	2.64256i	−0.126477	−	0.0918907i	−0.649225	+	0.760596i	$0.724907\pi$
$828$		0			0
$829$	−6.13796	−	18.8907i	−0.213180	−	0.656101i	−0.999278	−	0.0379987i	$-0.987902\pi$
$829$	−6.13796	−	18.8907i	−0.213180	−	0.656101i	0.786098	−	0.618102i	$-0.212098\pi$
$830$	−1.02658	+	0.745851i	−0.0356330	+	0.0258889i
$831$		0			0
$832$	−10.7869	−	33.1988i	−0.373970	−	1.15096i
$833$	0.444220	−	1.36717i	0.0153913	−	0.0473695i
$834$		0			0
$835$	32.5706			1.12715
$836$	31.5290	−	23.3331i	1.09045	−	0.806991i
$837$		0			0
$838$	−1.01817	−	0.739747i	−0.0351722	−	0.0255541i
$839$	13.5513	−	41.7065i	0.467842	−	1.43987i	−0.387532	−	0.921856i	$-0.626672\pi$
$839$	13.5513	−	41.7065i	0.467842	−	1.43987i	0.855373	−	0.518012i	$-0.173328\pi$
$840$		0			0
$841$	−10.9057	+	7.92348i	−0.376060	+	0.273224i
$842$	3.93311	−	2.85757i	0.135544	−	0.0984785i
$843$		0			0
$844$	4.55662	−	14.0238i	0.156845	−	0.482720i
$845$	−26.9891	−	19.6087i	−0.928453	−	0.674561i
$846$		0			0
$847$	10.9983	−	0.193261i	0.377906	−	0.00664052i
$848$	−24.3232			−0.835261
$849$		0			0
$850$	−0.123362	+	0.379670i	−0.00423129	+	0.0130226i
$851$	8.72066	+	26.8394i	0.298940	+	0.920044i
$852$		0			0
$853$	−31.6655	+	23.0063i	−1.08421	+	0.787721i	−0.978411	−	0.206667i	$-0.933738\pi$
$853$	−31.6655	+	23.0063i	−1.08421	+	0.787721i	−0.105794	+	0.994388i	$0.533738\pi$
$854$	0.0597911	+	0.184018i	0.00204601	+	0.00629697i
$855$		0			0
$856$	0.843455	+	0.612806i	0.0288287	+	0.0209453i
$857$	−35.0524			−1.19737			−0.598684	−	0.800986i	$-0.704309\pi$
$857$	−35.0524			−1.19737			−0.598684	+	0.800986i	$0.704309\pi$
$858$		0			0
$859$	−32.5206			−1.10959			−0.554794	−	0.831988i	$-0.687203\pi$
$859$	−32.5206			−1.10959			−0.554794	+	0.831988i	$0.687203\pi$
$860$	−3.15667	−	2.29345i	−0.107642	−	0.0782061i
$861$		0			0
$862$	−1.93763	−	5.96341i	−0.0659959	−	0.203114i
$863$	10.2696	−	7.46132i	0.349582	−	0.253986i	−0.399111	−	0.916902i	$-0.630681\pi$
$863$	10.2696	−	7.46132i	0.349582	−	0.253986i	0.748694	+	0.662916i	$0.230681\pi$
$864$		0			0
$865$	−4.55924	−	14.0319i	−0.155019	−	0.477099i
$866$	−0.649269	+	1.99824i	−0.0220630	+	0.0679031i
$867$		0			0
$868$	−14.9844			−0.508605
$869$	−8.13505	+	0.0714685i	−0.275963	+	0.00242440i
$870$		0			0
$871$	6.84079	+	4.97012i	0.231791	+	0.168406i
$872$	2.56778	−	7.90281i	0.0869559	−	0.267623i
$873$		0			0
$874$	7.86619	−	5.71512i	0.266078	−	0.193317i
$875$	7.61610	−	5.53342i	0.257471	−	0.187064i
$876$		0			0
$877$	−8.69388	+	26.7570i	−0.293571	+	0.903520i	0.690126	+	0.723689i	$0.257555\pi$
$877$	−8.69388	+	26.7570i	−0.293571	+	0.903520i	−0.983698	+	0.179831i	$0.942445\pi$
$878$	−2.69239	−	1.95614i	−0.0908638	−	0.0660164i
$879$		0			0
$880$	−9.70720	−	29.0061i	−0.327230	−	0.977797i
$881$	36.7964			1.23970			0.619850	−	0.784720i	$-0.287193\pi$
$881$	36.7964			1.23970			0.619850	+	0.784720i	$0.287193\pi$
$882$		0			0
$883$	−0.705855	+	2.17240i	−0.0237539	+	0.0731070i	−0.962231	−	0.272235i	$-0.912237\pi$
$883$	−0.705855	+	2.17240i	−0.0237539	+	0.0731070i	0.938477	+	0.345342i	$0.112237\pi$
$884$	−4.44540	−	13.6815i	−0.149515	−	0.460159i
$885$		0			0
$886$	−0.447173	+	0.324890i	−0.0150231	+	0.0109149i
$887$	−13.0614	−	40.1989i	−0.438560	−	1.34975i	−0.889395	−	0.457140i	$-0.848874\pi$
$887$	−13.0614	−	40.1989i	−0.438560	−	1.34975i	0.450835	−	0.892607i	$-0.351126\pi$
$888$		0			0
$889$	0.233972	+	0.169990i	0.00784716	+	0.00570130i
$890$	0.979808			0.0328432
$891$		0			0
$892$	−34.1520			−1.14349
$893$	−33.1500	−	24.0849i	−1.10932	−	0.805971i
$894$		0			0
$895$	−3.34304	−	10.2888i	−0.111745	−	0.343917i
$896$	−5.48741	+	3.98684i	−0.183322	+	0.133191i
$897$		0			0
$898$	0.333393	+	1.02608i	0.0111255	+	0.0342406i
$899$	−15.4861	+	47.6614i	−0.516491	+	1.58960i
$900$		0			0
$901$	−9.46132			−0.315202
$902$	−1.52234	+	4.82923i	−0.0506884	+	0.160796i
$903$		0			0
$904$	2.38288	+	1.73127i	0.0792535	+	0.0575810i
$905$	8.35220	−	25.7054i	0.277636	−	0.854477i
$906$		0			0
$907$	−31.9793	+	23.2343i	−1.06185	+	0.771483i	−0.974431	−	0.224689i	$-0.927864\pi$
$907$	−31.9793	+	23.2343i	−1.06185	+	0.771483i	−0.0874240	+	0.996171i	$0.527864\pi$
$908$	40.4837	−	29.4131i	1.34350	−	0.976108i
$909$		0			0
$910$	−0.895772	+	2.75690i	−0.0296946	+	0.0913905i
$911$	−28.5013	−	20.7074i	−0.944291	−	0.686067i	0.00515893	−	0.999987i	$-0.498358\pi$
$911$	−28.5013	−	20.7074i	−0.944291	−	0.686067i	−0.949450	+	0.313919i	$0.898358\pi$
$912$		0			0
$913$	2.24138	−	7.11019i	0.0741788	−	0.235313i
$914$	−7.03234			−0.232609
$915$		0			0
$916$	11.9462	−	36.7666i	0.394713	−	1.21480i
$917$	5.10059	+	15.6980i	0.168436	+	0.518394i
$918$		0			0
$919$	32.0455	−	23.2824i	1.05708	−	0.768017i	0.0835379	−	0.996505i	$-0.473378\pi$
$919$	32.0455	−	23.2824i	1.05708	−	0.768017i	0.973547	+	0.228488i	$0.0733780\pi$
$920$	−4.87909	−	15.0163i	−0.160859	−	0.495073i
$921$		0			0
$922$	−5.43930	−	3.95188i	−0.179134	−	0.130148i
$923$	−23.2141			−0.764101
$924$		0			0
$925$	−4.89131			−0.160825
$926$	−4.65855	−	3.38463i	−0.153089	−	0.111226i
$927$		0			0
$928$	5.28196	+	16.2562i	0.173389	+	0.533636i
$929$	2.11685	−	1.53798i	0.0694516	−	0.0504595i	−0.552518	−	0.833501i	$-0.686333\pi$
$929$	2.11685	−	1.53798i	0.0694516	−	0.0504595i	0.621969	+	0.783042i	$0.286333\pi$
$930$		0			0
$931$	−1.87526	−	5.77147i	−0.0614593	−	0.189152i
$932$	−12.1736	+	37.4666i	−0.398761	+	1.22726i
$933$		0			0
$934$	−0.720463			−0.0235743
$935$	−3.77594	−	11.2829i	−0.123487	−	0.368991i
$936$		0			0
$937$	−43.5575	−	31.6464i	−1.42296	−	1.03384i	−0.991274	−	0.131820i	$-0.957918\pi$
$937$	−43.5575	−	31.6464i	−1.42296	−	1.03384i	−0.431689	−	0.902022i	$-0.642082\pi$
$938$	0.115108	−	0.354266i	0.00375841	−	0.0115672i
$939$		0			0
$940$	−26.5668	+	19.3019i	−0.866514	+	0.629559i
$941$	23.9854	−	17.4264i	0.781902	−	0.568085i	−0.123647	−	0.992326i	$-0.539459\pi$
$941$	23.9854	−	17.4264i	0.781902	−	0.568085i	0.905549	+	0.424241i	$0.139459\pi$
$942$		0			0
$943$	14.7718	−	45.4630i	0.481037	−	1.48048i
$944$	8.59940	+	6.24783i	0.279887	+	0.203349i
$945$		0			0
$946$	−0.601908	+	0.00528791i	−0.0195697	+	0.000171925i
$947$	15.7861			0.512980			0.256490	−	0.966547i	$-0.417434\pi$
$947$	15.7861			0.512980			0.256490	+	0.966547i	$0.417434\pi$
$948$		0			0
$949$	−23.5607	+	72.5123i	−0.764812	+	2.35385i
$950$	0.520771	+	1.60277i	0.0168961	+	0.0520007i
$951$		0			0
$952$	−1.03886	+	0.754773i	−0.0336695	+	0.0244623i
$953$	10.8502	+	33.3934i	0.351472	+	1.08172i	0.958027	+	0.286678i	$0.0925509\pi$
$953$	10.8502	+	33.3934i	0.351472	+	1.08172i	−0.606555	+	0.795041i	$0.707449\pi$
$954$		0			0
$955$	23.5318	+	17.0968i	0.761470	+	0.553240i
$956$	33.3257			1.07783
$957$		0			0
$958$	0.731463			0.0236325
$959$	7.54479	+	5.48161i	0.243634	+	0.177011i
$960$		0			0
$961$	8.68955	+	26.7437i	0.280308	+	0.862700i
$962$	−3.74426	+	2.72036i	−0.120720	+	0.0877080i
$963$		0			0
$964$	14.5454	+	44.7661i	0.468475	+	1.44182i
$965$	17.3090	−	53.2716i	0.557196	−	1.71487i
$966$		0			0
$967$	−49.2820			−1.58480			−0.792401	−	0.610001i	$-0.791169\pi$
$967$	−49.2820			−1.58480			−0.792401	+	0.610001i	$0.791169\pi$
$968$	−8.04962	−	5.63500i	−0.258725	−	0.181116i
$969$		0			0
$970$	−5.51585	−	4.00750i	−0.177103	−	0.128673i
$971$	−11.5394	+	35.5148i	−0.370318	+	1.13972i	0.576265	+	0.817263i	$0.304510\pi$
$971$	−11.5394	+	35.5148i	−0.370318	+	1.13972i	−0.946583	+	0.322460i	$0.895490\pi$
$972$		0			0
$973$	−3.90471	+	2.83694i	−0.125179	+	0.0909481i
$974$	1.80647	−	1.31248i	0.0578831	−	0.0420545i
$975$		0			0
$976$	−0.976800	+	3.00628i	−0.0312666	+	0.0962287i
$977$	32.3999	+	23.5399i	1.03656	+	0.753108i	0.969612	−	0.244648i	$-0.0786724\pi$
$977$	32.3999	+	23.5399i	1.03656	+	0.753108i	0.0669524	+	0.997756i	$0.478672\pi$
$978$		0			0
$979$	−4.62723	+	3.42439i	−0.147887	+	0.109444i
$980$	−4.86335			−0.155354
$981$		0			0
$982$	0.295411	−	0.909181i	0.00942694	−	0.0290131i
$983$	16.0817	+	49.4944i	0.512926	+	1.57862i	0.787024	+	0.616923i	$0.211621\pi$
$983$	16.0817	+	49.4944i	0.512926	+	1.57862i	−0.274098	+	0.961702i	$0.588379\pi$
$984$		0			0
$985$	48.6604	−	35.3538i	1.55045	−	1.12647i
$986$	0.654946	+	2.01572i	0.0208577	+	0.0641935i
$987$		0			0
$988$	−49.1304	−	35.6953i	−1.56305	−	1.13562i
$989$	5.68262			0.180697
$990$		0			0
$991$	45.4828			1.44481			0.722404	−	0.691471i	$-0.243037\pi$
$991$	45.4828			1.44481			0.722404	+	0.691471i	$0.243037\pi$
$992$	16.3134	+	11.8524i	0.517951	+	0.376313i
$993$		0			0
$994$	0.316016	+	0.972598i	0.0100234	+	0.0308489i
$995$	−37.7953	+	27.4599i	−1.19819	+	0.870536i
$996$		0			0
$997$	8.63992	+	26.5909i	0.273629	+	0.842143i	0.989579	+	0.143992i	$0.0459939\pi$
$997$	8.63992	+	26.5909i	0.273629	+	0.842143i	−0.715950	+	0.698152i	$0.754006\pi$
$998$	1.42569	−	4.38783i	0.0451296	−	0.138894i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.i.631.2		16
3.2	odd	2		77.2.f.b.15.3	✓	16
11.3	even	5	inner	693.2.m.i.190.2		16
11.5	even	5		7623.2.a.ct.1.5		8
11.6	odd	10		7623.2.a.cw.1.4		8
21.2	odd	6		539.2.q.g.312.3		32
21.5	even	6		539.2.q.f.312.3		32
21.11	odd	6		539.2.q.g.422.2		32
21.17	even	6		539.2.q.f.422.2		32
21.20	even	2		539.2.f.e.246.3		16
33.2	even	10		847.2.f.v.148.3		16
33.5	odd	10		847.2.a.p.1.4		8
33.8	even	10		847.2.f.x.729.2		16
33.14	odd	10		77.2.f.b.36.3	yes	16
33.17	even	10		847.2.a.o.1.5		8
33.20	odd	10		847.2.f.w.148.2		16
33.26	odd	10		847.2.f.w.372.2		16
33.29	even	10		847.2.f.v.372.3		16
33.32	even	2		847.2.f.x.323.2		16
231.47	even	30		539.2.q.f.410.2		32
231.80	even	30		539.2.q.f.520.3		32
231.83	odd	10		5929.2.a.bs.1.5		8
231.104	even	10		5929.2.a.bt.1.4		8
231.146	even	10		539.2.f.e.344.3		16
231.179	odd	30		539.2.q.g.520.3		32
231.212	odd	30		539.2.q.g.410.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.3	✓	16	3.2	odd	2
77.2.f.b.36.3	yes	16	33.14	odd	10
539.2.f.e.246.3		16	21.20	even	2
539.2.f.e.344.3		16	231.146	even	10
539.2.q.f.312.3		32	21.5	even	6
539.2.q.f.410.2		32	231.47	even	30
539.2.q.f.422.2		32	21.17	even	6
539.2.q.f.520.3		32	231.80	even	30
539.2.q.g.312.3		32	21.2	odd	6
539.2.q.g.410.2		32	231.212	odd	30
539.2.q.g.422.2		32	21.11	odd	6
539.2.q.g.520.3		32	231.179	odd	30
693.2.m.i.190.2		16	11.3	even	5	inner
693.2.m.i.631.2		16	1.1	even	1	trivial
847.2.a.o.1.5		8	33.17	even	10
847.2.a.p.1.4		8	33.5	odd	10
847.2.f.v.148.3		16	33.2	even	10
847.2.f.v.372.3		16	33.29	even	10
847.2.f.w.148.2		16	33.20	odd	10
847.2.f.w.372.2		16	33.26	odd	10
847.2.f.x.323.2		16	33.32	even	2
847.2.f.x.729.2		16	33.8	even	10
5929.2.a.bs.1.5		8	231.83	odd	10
5929.2.a.bt.1.4		8	231.104	even	10
7623.2.a.ct.1.5		8	11.5	even	5
7623.2.a.cw.1.4		8	11.6	odd	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.183009 + 0.132964i) q^{2} +(-0.602221 - 1.85345i) q^{4} +(-2.01892 + 1.46683i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.276036 - 0.849550i) q^{8} +O(q^{10})\)	\(q+(0.183009 + 0.132964i) q^{2} +(-0.602221 - 1.85345i) q^{4} +(-2.01892 + 1.46683i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.276036 - 0.849550i) q^{8} -0.564516 q^{10} +(2.66598 - 1.97296i) q^{11} +(-4.15429 - 3.01827i) q^{13} +(-0.0699031 + 0.215140i) q^{14} +(-2.98979 + 2.17221i) q^{16} +(-1.16298 + 0.844956i) q^{17} +(-1.87526 + 5.77147i) q^{19} +(3.93453 + 2.85860i) q^{20} +(0.750229 - 0.00659095i) q^{22} -7.08292 q^{23} +(0.379361 - 1.16755i) q^{25} +(-0.358952 - 1.10474i) q^{26} +(1.57664 - 1.14549i) q^{28} +(-2.01408 - 6.19869i) q^{29} +(-6.22049 - 4.51945i) q^{31} -2.62252 q^{32} -0.325184 q^{34} +(-2.01892 - 1.46683i) q^{35} +(-1.23122 - 3.78932i) q^{37} +(-1.11058 + 0.806887i) q^{38} +(0.688853 + 2.12007i) q^{40} +(-2.08556 + 6.41868i) q^{41} -0.802299 q^{43} +(-5.26228 - 3.75309i) q^{44} +(-1.29624 - 0.941771i) q^{46} +(-2.08655 + 6.42174i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(0.224669 - 0.163231i) q^{50} +(-3.09240 + 9.51742i) q^{52} +(5.32469 + 3.86861i) q^{53} +(-2.48840 + 7.89379i) q^{55} +0.893270 q^{56} +(0.455607 - 1.40221i) q^{58} +(-0.888810 - 2.73548i) q^{59} +(0.691986 - 0.502757i) q^{61} +(-0.537482 - 1.65420i) q^{62} +(5.49964 + 3.99573i) q^{64} +12.8145 q^{65} -1.64668 q^{67} +(2.26645 + 1.64667i) q^{68} +(-0.174445 - 0.536886i) q^{70} +(3.65738 - 2.65724i) q^{71} +(-4.58827 - 14.1212i) q^{73} +(0.278517 - 0.857187i) q^{74} +11.8264 q^{76} +(2.70023 + 1.92582i) q^{77} +(-1.98444 - 1.44178i) q^{79} +(2.84989 - 8.77105i) q^{80} +(-1.23513 + 0.897372i) q^{82} +(1.81851 - 1.32122i) q^{83} +(1.10856 - 3.41180i) q^{85} +(-0.146828 - 0.106677i) q^{86} +(-0.940224 - 2.80949i) q^{88} -1.73566 q^{89} +(1.58680 - 4.88366i) q^{91} +(4.26549 + 13.1278i) q^{92} +(-1.23572 + 0.897800i) q^{94} +(-4.67976 - 14.4028i) q^{95} +(9.77095 + 7.09901i) q^{97} -0.226211 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

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