LMFDB - Embedded newform 693.2.m.i.190.2

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			190.2
Root			$0.183009 - 0.132964i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.i.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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	−0.521199	−	0.853435i	$-0.674515\pi$
$2$	0.183009	−	0.132964i	0.129407	−	0.0940195i	0.650606	+	0.759416i	$0.274515\pi$
$3$		0			0
$3$		0			0
$4$	−0.602221	+	1.85345i	−0.301111	+	0.926723i
$5$	−2.01892	−	1.46683i	−0.902889	−	0.655987i	0.0363174	−	0.999340i	$-0.488437\pi$
$5$	−2.01892	−	1.46683i	−0.902889	−	0.655987i	−0.939206	+	0.343353i	$0.888437\pi$
$6$		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	−0.988771	−	0.149439i	$-0.952253\pi$
$13$	−4.15429	+	3.01827i	−1.15219	+	0.837117i	−0.163422	+	0.986556i	$0.552253\pi$
$14$	−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	0.437753	−	0.899095i	$-0.355774\pi$
$17$	−1.16298	−	0.844956i	−0.282065	−	0.204932i	−0.719817	+	0.694163i	$0.755774\pi$
$18$		0			0
$19$	−1.87526	−	5.77147i	−0.430215	−	1.32406i	−0.897912	−	0.440176i	$-0.854916\pi$
$19$	−1.87526	−	5.77147i	−0.430215	−	1.32406i	0.467697	−	0.883889i	$-0.345084\pi$
$20$	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	0.570143	+	0.821545i	$0.306888\pi$
$29$	−2.01408	+	6.19869i	−0.374004	+	1.15107i	−0.944148	+	0.329522i	$0.893112\pi$
$30$		0			0
$31$	−6.22049	+	4.51945i	−1.11723	+	0.811718i	−0.983787	−	0.179338i	$-0.942604\pi$
$31$	−6.22049	+	4.51945i	−1.11723	+	0.811718i	−0.133446	+	0.991056i	$0.542604\pi$
$32$	−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	0.797398	+	0.603454i	$0.206209\pi$
$37$	−1.23122	+	3.78932i	−0.202412	+	0.622960i	−0.999810	+	0.0195059i	$0.993791\pi$
$38$	−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	−0.971120	−	0.238594i	$-0.923314\pi$
$41$	−2.08556	−	6.41868i	−0.325709	−	1.00243i	0.645410	−	0.763836i	$-0.276686\pi$
$42$		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	−0.979917	−	0.199405i	$-0.936099\pi$
$47$	−2.08655	−	6.42174i	−0.304355	−	0.936707i	0.675563	−	0.737303i	$-0.263901\pi$
$48$		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	−0.158605	−	0.987342i	$-0.550700\pi$
$53$	5.32469	−	3.86861i	0.731402	−	0.531394i	0.890007	+	0.455948i	$0.150700\pi$
$54$		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	−0.992095	−	0.125488i	$-0.959950\pi$
$59$	−0.888810	+	2.73548i	−0.115713	+	0.356129i	0.876382	+	0.481617i	$0.159950\pi$
$60$		0			0
$61$	0.691986	+	0.502757i	0.0885997	+	0.0643715i	0.631203	−	0.775617i	$-0.282561\pi$
$61$	0.691986	+	0.502757i	0.0885997	+	0.0643715i	−0.542604	+	0.839989i	$0.682561\pi$
$62$	−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	0.783267	−	0.621686i	$-0.213552\pi$
$71$	3.65738	+	2.65724i	0.434051	+	0.315357i	−0.349216	+	0.937042i	$0.613552\pi$
$72$		0			0
$73$	−4.58827	+	14.1212i	−0.537016	+	1.65277i	0.202236	+	0.979337i	$0.435179\pi$
$73$	−4.58827	+	14.1212i	−0.537016	+	1.65277i	−0.739252	+	0.673429i	$0.764821\pi$
$74$	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	−0.693796	−	0.720171i	$-0.744063\pi$
$79$	−1.98444	+	1.44178i	−0.223267	+	0.162213i	0.470529	+	0.882385i	$0.344063\pi$
$80$	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	0.683099	−	0.730326i	$-0.260632\pi$
$83$	1.81851	+	1.32122i	0.199607	+	0.145023i	−0.483492	+	0.875349i	$0.660632\pi$
$84$		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	0.0317117	−	0.999497i	$-0.489904\pi$
$97$	9.77095	−	7.09901i	0.992089	−	0.720795i	0.960378	+	0.278702i	$0.0899042\pi$
$98$	−0.226211			−0.0228508
$99$		0			0
$100$	−2.39246			−0.239246
$101$	−2.98801	+	2.17091i	−0.297318	+	0.216014i	−0.726436	−	0.687234i	$-0.758825\pi$
$101$	−2.98801	+	2.17091i	−0.297318	+	0.216014i	0.429118	+	0.903249i	$0.358825\pi$
$102$		0			0
$103$	−0.355853	+	1.09520i	−0.0350632	+	0.107913i	−0.967056	−	0.254563i	$-0.918069\pi$
$103$	−0.355853	+	1.09520i	−0.0350632	+	0.107913i	0.931993	+	0.362476i	$0.118069\pi$
$104$	−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	0.932108	−	0.362179i	$-0.117967\pi$
$107$	−0.360665	−	1.11001i	−0.0348668	−	0.107309i	−0.966975	+	0.254870i	$0.917967\pi$
$108$		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	0.891622	−	0.452780i	$-0.149568\pi$
$113$	−1.01893	−	3.13595i	−0.0958529	−	0.295005i	−0.987475	+	0.157775i	$0.949568\pi$
$114$		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	0.598118	−	0.801408i	$-0.295916\pi$
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	−0.577356	+	0.816492i	$0.695916\pi$
$128$	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	0.861426	−	0.507883i	$-0.169572\pi$
$137$	7.54479	+	5.48161i	0.644595	+	0.468326i	−0.216831	+	0.976209i	$0.569572\pi$
$138$		0			0
$139$	1.49147	−	4.59026i	0.126505	−	0.389341i	−0.867668	−	0.497145i	$-0.834382\pi$
$139$	1.49147	−	4.59026i	0.126505	−	0.389341i	0.994172	+	0.107804i	$0.0343818\pi$
$140$	−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	0.617917	−	0.786243i	$-0.287977\pi$
$149$	0.745845	+	0.541888i	0.0611020	+	0.0443932i	−0.556815	+	0.830637i	$0.687977\pi$
$150$		0			0
$151$	5.59210	+	17.2107i	0.455079	+	1.40059i	0.871043	+	0.491207i	$0.163444\pi$
$151$	5.59210	+	17.2107i	0.455079	+	1.40059i	−0.415964	+	0.909381i	$0.636556\pi$
$152$	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	−0.980530	−	0.196369i	$-0.937085\pi$
$157$	−3.79267	−	11.6726i	−0.302688	−	0.931577i	0.677842	−	0.735207i	$-0.262915\pi$
$158$	−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	−0.814043	−	0.580804i	$-0.802738\pi$
$163$	−6.55233	+	4.76055i	−0.513218	+	0.372875i	0.300825	+	0.953679i	$0.402738\pi$
$164$	13.1526			1.02705
$165$		0			0
$166$	0.508478			0.0394655
$167$	−10.5590	+	7.67154i	−0.817077	+	0.593641i	−0.915874	−	0.401466i	$-0.868501\pi$
$167$	−10.5590	+	7.67154i	−0.817077	+	0.593641i	0.0987965	+	0.995108i	$0.468501\pi$
$168$		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	0.857275	−	0.514859i	$-0.172156\pi$
$173$	−1.82697	−	5.62283i	−0.138902	−	0.427496i	−0.996176	+	0.0873636i	$0.972156\pi$
$174$		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	0.888429	−	0.459015i	$-0.151798\pi$
$179$	−1.33961	−	4.12290i	−0.100127	−	0.308160i	−0.988556	+	0.150854i	$0.951798\pi$
$180$		0			0
$181$	−8.76223	−	6.36613i	−0.651291	−	0.473191i	0.212420	−	0.977179i	$-0.431866\pi$
$181$	−8.76223	−	6.36613i	−0.651291	−	0.473191i	−0.863711	+	0.503988i	$0.831866\pi$
$182$	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	0.732055	+	0.681245i	$0.238561\pi$
$191$	−3.60178	+	11.0851i	−0.260616	+	0.802093i	−0.992671	+	0.120848i	$0.961439\pi$
$192$		0			0
$193$	−18.1587	−	13.1931i	−1.30709	−	0.949659i	−0.307096	−	0.951679i	$-0.599357\pi$
$193$	−18.1587	−	13.1931i	−1.30709	−	0.949659i	−0.999998	+	0.00201912i	$0.999357\pi$
$194$	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	−0.356796	−	0.934182i	$-0.616131\pi$
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	0.778204	+	0.628011i	$0.216131\pi$
$212$	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	0.951447	+	0.307811i	$0.0995966\pi$
$223$	5.41533	+	16.6667i	0.362637	+	1.11608i	−0.588810	+	0.808271i	$0.700403\pi$
$224$	−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	−0.234394	−	0.972142i	$-0.575311\pi$
$227$	7.93471	−	24.4205i	0.526645	−	1.62085i	0.761039	−	0.648706i	$-0.224689\pi$
$228$		0			0
$229$	16.0484	−	11.6598i	1.06051	−	0.770503i	0.0863246	−	0.996267i	$-0.472488\pi$
$229$	16.0484	−	11.6598i	1.06051	−	0.770503i	0.974182	+	0.225764i	$0.0724878\pi$
$230$	3.99842			0.263648
$231$		0			0
$232$	−5.82205			−0.382236
$233$	−16.3539	+	11.8818i	−1.07138	+	0.778405i	−0.976160	−	0.217051i	$-0.930356\pi$
$233$	−16.3539	+	11.8818i	−1.07138	+	0.778405i	−0.0952219	+	0.995456i	$0.530356\pi$
$234$		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	−0.963267	−	0.268544i	$-0.913458\pi$
$239$	−5.28431	−	16.2634i	−0.341814	−	1.05199i	0.621454	−	0.783451i	$-0.286542\pi$
$240$		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	−0.241097	−	0.970501i	$-0.577507\pi$
$251$	9.62305	−	6.99156i	0.607402	−	0.441303i	0.848498	+	0.529198i	$0.177507\pi$
$252$		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	0.442509	+	0.896764i	$0.354089\pi$
$257$	−7.09531	+	21.8371i	−0.442593	+	1.36216i	−0.885102	+	0.465397i	$0.845911\pi$
$258$		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	0.750754	−	0.660582i	$-0.229690\pi$
$269$	5.81421	+	4.22427i	0.354499	+	0.257558i	−0.396255	+	0.918140i	$0.629690\pi$
$270$		0			0
$271$	0.368071	−	1.13281i	0.0223587	−	0.0688130i	−0.939255	−	0.343221i	$-0.888482\pi$
$271$	0.368071	−	1.13281i	0.0223587	−	0.0688130i	0.961613	+	0.274408i	$0.0884819\pi$
$272$	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	−0.810021	−	0.586401i	$-0.800544\pi$
$277$	−8.36543	+	6.07784i	−0.502630	+	0.365182i	0.307391	+	0.951583i	$0.400544\pi$
$278$	−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	0.223321	−	0.974745i	$-0.428310\pi$
$281$	−10.6396	−	7.73015i	−0.634707	−	0.461142i	−0.858028	+	0.513603i	$0.828310\pi$
$282$		0			0
$283$	0.0927146	+	0.285346i	0.00551131	+	0.0169621i	0.953774	−	0.300524i	$-0.0971614\pi$
$283$	0.0927146	+	0.285346i	0.00551131	+	0.0169621i	−0.948263	+	0.317486i	$0.897161\pi$
$284$	−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	0.692942	+	0.720993i	$0.256314\pi$
$293$	−4.98880	+	15.3539i	−0.291449	+	0.896987i	−0.984391	+	0.175994i	$0.943686\pi$
$294$		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	0.688916	+	0.724841i	$0.258087\pi$
$311$	9.83377	+	30.2652i	0.557622	+	1.71618i	−0.131294	+	0.991343i	$0.541913\pi$
$312$		0			0
$313$	−0.0276872	−	0.0201159i	−0.00156497	−	0.00113702i	0.587002	−	0.809585i	$-0.300308\pi$
$313$	−0.0276872	−	0.0201159i	−0.00156497	−	0.00113702i	−0.588567	+	0.808448i	$0.700308\pi$
$314$	−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	0.0516132	−	0.998667i	$-0.483564\pi$
$317$	18.1134	−	13.1602i	1.01735	−	0.739149i	0.965738	+	0.259518i	$0.0835637\pi$
$318$		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	−0.867809	−	0.496897i	$-0.834473\pi$
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	0.994141	+	0.108087i	$0.0344726\pi$
$338$	−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	−0.207727	−	0.978187i	$-0.566607\pi$
$347$	−22.3950	−	16.2710i	−1.20223	−	0.873471i	−0.994502	+	0.104716i	$0.966607\pi$
$348$		0			0
$349$	−3.41788	−	10.5192i	−0.182955	−	0.563078i	0.816952	−	0.576706i	$-0.195662\pi$
$349$	−3.41788	−	10.5192i	−0.182955	−	0.563078i	−0.999907	+	0.0136278i	$0.995662\pi$
$350$	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	−0.975986	−	0.217831i	$-0.930102\pi$
$359$	−1.10574	+	3.40313i	−0.0583590	+	0.179610i	0.917628	+	0.397441i	$0.130102\pi$
$360$		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	−0.930849	−	0.365404i	$-0.880931\pi$
$367$	0.708875	−	2.18169i	0.0370030	−	0.113883i	0.967852	+	0.251521i	$0.0809307\pi$
$368$	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	0.802461	−	0.596705i	$-0.203524\pi$
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	−0.319526	+	0.947578i	$0.603524\pi$
$380$	−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	−0.296617	−	0.954996i	$-0.595859\pi$
$383$	10.1762	−	7.39343i	0.519979	−	0.377787i	0.816596	+	0.577210i	$0.195859\pi$
$384$		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	−0.947564	−	0.319565i	$-0.896463\pi$
$389$	0.135440	−	0.416842i	0.00686709	−	0.0211347i	0.954431	+	0.298431i	$0.0964631\pi$
$390$		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	0.974446	+	0.224621i	$0.0721143\pi$
$401$	29.8211	+	21.6663i	1.48919	+	1.08196i	0.514747	+	0.857342i	$0.327886\pi$
$402$		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	−0.863615	−	0.504152i	$-0.831805\pi$
$409$	−13.1659	+	9.56556i	−0.651010	+	0.472986i	0.212605	+	0.977138i	$0.431805\pi$
$410$	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	0.972036	+	0.234831i	$0.0754536\pi$
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	−0.648364	+	0.761331i	$0.724546\pi$
$422$	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	−0.977713	−	0.209947i	$-0.932671\pi$
$431$	−22.4249	+	16.2927i	−1.08017	+	0.784791i	−0.102459	+	0.994737i	$0.532671\pi$
$432$		0			0
$433$	2.87019	−	8.83352i	0.137932	−	0.424512i	−0.858102	−	0.513479i	$-0.828356\pi$
$433$	2.87019	−	8.83352i	0.137932	−	0.424512i	0.996035	+	0.0889667i	$0.0283565\pi$
$434$	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	0.931516	−	0.363701i	$-0.118487\pi$
$443$	−0.755067	−	2.32386i	−0.0358743	−	0.110410i	−0.967390	+	0.253291i	$0.918487\pi$
$444$		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	−0.493005	−	0.870027i	$-0.664101\pi$
$449$	3.85849	−	2.80335i	0.182093	−	0.132298i	0.675098	+	0.737728i	$0.264101\pi$
$450$		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	−0.184712	−	0.982793i	$-0.559135\pi$
$457$	−25.1503	−	18.2728i	−1.17648	−	0.854764i	−0.991770	+	0.128028i	$0.959135\pi$
$458$	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	0.526571	−	0.850131i	$-0.323478\pi$
$467$	−2.57665	−	1.87204i	−0.119233	−	0.0866279i	−0.645804	+	0.763503i	$0.723478\pi$
$468$		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	0.645943	−	0.763386i	$-0.276464\pi$
$479$	2.61599	+	1.90062i	0.119527	+	0.0868418i	−0.526416	+	0.850227i	$0.676464\pi$
$480$		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	0.996077	−	0.0884878i	$-0.0282034\pi$
$487$	3.05029	+	9.38784i	0.138222	+	0.425404i	−0.857855	+	0.513891i	$0.828203\pi$
$488$	−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	−0.976190	−	0.216918i	$-0.930400\pi$
$491$	−1.30591	+	4.01917i	−0.0589348	+	0.181383i	0.917255	+	0.398300i	$0.130400\pi$
$492$		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	0.705104	+	0.709104i	$0.250900\pi$
$499$	−6.30249	+	19.3971i	−0.282138	+	0.868332i	−0.987242	+	0.159228i	$0.949100\pi$
$500$	−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	0.969076	+	0.246762i	$0.0793665\pi$
$503$	7.40382	+	22.7866i	0.330120	+	1.01600i	−0.638956	+	0.769243i	$0.720634\pi$
$504$		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	0.922571	−	0.385828i	$-0.126084\pi$
$509$	−1.14133	−	3.51264i	−0.0505884	−	0.155695i	−0.973159	+	0.230132i	$0.926084\pi$
$510$		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	−0.949431	−	0.313977i	$-0.898339\pi$
$521$	0.0736294	−	0.226608i	0.00322576	−	0.00992787i	0.952656	+	0.304049i	$0.0983386\pi$
$522$		0			0
$523$	17.7914	+	12.9262i	0.777966	+	0.565225i	0.904368	−	0.426754i	$-0.140343\pi$
$523$	17.7914	+	12.9262i	0.777966	+	0.565225i	−0.126402	+	0.991979i	$0.540343\pi$
$524$	−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	−0.961195	−	0.275871i	$-0.911034\pi$
$541$	−23.1629	+	16.8288i	−0.995851	+	0.723528i	−0.0346561	+	0.999399i	$0.511034\pi$
$542$	−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	0.984425	−	0.175805i	$-0.0562529\pi$
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	−0.899752	+	0.436401i	$0.856253\pi$
$548$	−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	−0.688415	−	0.725317i	$-0.741693\pi$
$557$	6.95884	−	21.4171i	0.294855	−	0.907471i	0.983270	−	0.182154i	$-0.0583070\pi$
$558$		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	−0.965660	−	0.259810i	$-0.916340\pi$
$563$	−24.1303	+	17.5317i	−1.01697	+	0.738873i	−0.0513116	+	0.998683i	$0.516340\pi$
$564$		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	−0.940555	−	0.339640i	$-0.889695\pi$
$569$	−9.04690	−	27.8435i	−0.379266	−	1.16726i	0.561290	−	0.827619i	$-0.310305\pi$
$570$		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	0.430172	−	0.902747i	$-0.358453\pi$
$577$	−7.09721	−	5.15642i	−0.295461	−	0.214665i	−0.725633	+	0.688082i	$0.758453\pi$
$578$	−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	−0.992351	−	0.123450i	$-0.960604\pi$
$587$	−2.83372	+	8.72130i	−0.116960	+	0.359966i	0.875391	+	0.483416i	$0.160604\pi$
$588$		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	0.205532	−	0.978650i	$-0.434108\pi$
$599$	−16.1949	−	11.7663i	−0.661708	−	0.480759i	−0.867239	+	0.497892i	$0.834108\pi$
$600$		0			0
$601$	−3.48280	+	10.7189i	−0.142066	+	0.437235i	−0.996622	−	0.0821246i	$-0.973829\pi$
$601$	−3.48280	+	10.7189i	−0.142066	+	0.437235i	0.854556	+	0.519360i	$0.173829\pi$
$602$	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	−0.343129	−	0.939288i	$-0.611487\pi$
$607$	10.9428	−	7.95040i	0.444154	−	0.322697i	0.787283	+	0.616591i	$0.211487\pi$
$608$	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	−0.936931	−	0.349514i	$-0.886347\pi$
$613$	−9.51673	−	29.2895i	−0.384377	−	1.18299i	0.552554	−	0.833477i	$-0.313653\pi$
$614$	−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	−0.922131	−	0.386878i	$-0.873553\pi$
$619$	−10.0393	−	30.8977i	−0.403513	−	1.24188i	0.518618	−	0.855006i	$-0.326447\pi$
$620$	−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	−0.999967	−	0.00818299i	$-0.997395\pi$
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	0.813800	+	0.581145i	$0.197395\pi$
$632$	−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	0.999823	+	0.0188056i	$0.00598637\pi$
$641$	5.11431	+	15.7402i	0.202003	+	0.621701i	−0.797820	+	0.602895i	$0.794014\pi$
$642$		0			0
$643$	−1.61403	−	1.17266i	−0.0636513	−	0.0462454i	0.555505	−	0.831513i	$-0.312525\pi$
$643$	−1.61403	−	1.17266i	−0.0636513	−	0.0462454i	−0.619156	+	0.785268i	$0.712525\pi$
$644$	−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	0.286866	−	0.957971i	$-0.407387\pi$
$647$	32.7261	−	23.7769i	1.28660	−	0.934767i	0.999731	+	0.0232039i	$0.00738670\pi$
$648$		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	−0.304611	−	0.952477i	$-0.598527\pi$
$653$	12.8198	−	39.4552i	0.501676	−	1.54400i	0.806288	−	0.591524i	$-0.201473\pi$
$654$		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	−0.125078	−	0.992147i	$-0.539918\pi$
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	0.904936	+	0.425547i	$0.139918\pi$
$674$	−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	0.422805	−	0.906221i	$-0.361046\pi$
$677$	−8.02456	−	5.83018i	−0.308409	−	0.224072i	−0.731213	+	0.682149i	$0.761046\pi$
$678$		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	−0.481338	−	0.876535i	$-0.659849\pi$
$691$	5.35084	−	3.88762i	0.203556	−	0.147892i	0.684893	+	0.728643i	$0.259849\pi$
$692$	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	0.828973	−	0.559288i	$-0.188925\pi$
$701$	−4.51215	−	13.8870i	−0.170421	−	0.524503i	−0.999395	+	0.0347848i	$0.988925\pi$
$702$		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	0.648958	−	0.760824i	$-0.275205\pi$
$709$	3.35261	+	2.43582i	0.125910	+	0.0914790i	−0.523048	+	0.852303i	$0.675205\pi$
$710$	−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	0.803790	+	0.594914i	$0.202814\pi$
$719$	−5.26017	+	16.1891i	−0.196171	+	0.603753i	−0.999961	+	0.00883941i	$0.997186\pi$
$720$		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	0.156981	+	0.987602i	$0.449824\pi$
$733$	−14.9047	+	45.8719i	−0.550517	+	1.69432i	−0.707498	+	0.706715i	$0.750176\pi$
$734$	−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	−0.459649	−	0.888101i	$-0.652025\pi$
$739$	6.60439	−	4.79837i	0.242946	−	0.176511i	0.702595	+	0.711590i	$0.252025\pi$
$740$	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	0.838932	−	0.544236i	$-0.183180\pi$
$743$	15.8254	+	11.4978i	0.580577	+	0.421814i	−0.258355	+	0.966050i	$0.583180\pi$
$744$		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	0.957153	−	0.289583i	$-0.0935165\pi$
$751$	0.344955	+	1.06166i	0.0125876	+	0.0387406i	−0.944565	+	0.328323i	$0.893516\pi$
$752$	−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	−0.123939	−	0.992290i	$-0.539553\pi$
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	0.905424	+	0.424508i	$0.139553\pi$
$758$	2.62885			0.0954840
$759$		0			0
$760$	−13.5277			−0.490701
$761$	5.09683	−	3.70306i	0.184760	−	0.134236i	−0.491561	−	0.870843i	$-0.663573\pi$
$761$	5.09683	−	3.70306i	0.184760	−	0.134236i	0.676321	+	0.736607i	$0.263573\pi$
$762$		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	−0.793515	−	0.608550i	$-0.791751\pi$
$773$	−14.1585	−	43.5753i	−0.509245	−	1.56729i	0.284270	−	0.958744i	$-0.408249\pi$
$774$		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	0.825399	−	0.564549i	$-0.190950\pi$
$787$	15.2483	+	11.0785i	0.543543	+	0.394907i	−0.281856	+	0.959457i	$0.590950\pi$
$788$	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	0.105948	−	0.994372i	$-0.466212\pi$
$797$	−22.7830	−	16.5528i	−0.807016	−	0.586331i	−0.912964	+	0.408040i	$0.866212\pi$
$798$		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	0.490792	−	0.871277i	$-0.336707\pi$
$809$	−5.29544	−	3.84736i	−0.186178	−	0.135266i	−0.676970	+	0.736011i	$0.736707\pi$
$810$		0			0
$811$	5.81096	+	17.8843i	0.204050	+	0.628002i	0.999751	+	0.0223122i	$0.00710279\pi$
$811$	5.81096	+	17.8843i	0.204050	+	0.628002i	−0.795701	+	0.605690i	$0.792897\pi$
$812$	−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	−0.868922	−	0.494948i	$-0.835187\pi$
$821$	3.58089	−	11.0208i	0.124974	−	0.384630i	0.993896	+	0.110318i	$0.0351870\pi$
$822$		0			0
$823$	−9.98844	+	7.25702i	−0.348175	+	0.252964i	−0.748103	−	0.663583i	$-0.769035\pi$
$823$	−9.98844	+	7.25702i	−0.348175	+	0.252964i	0.399928	+	0.916547i	$0.369035\pi$
$824$	−1.02866			−0.0358349
$825$		0			0
$826$	0.650640			0.0226387
$827$	−3.63717	+	2.64256i	−0.126477	+	0.0918907i	−0.649225	−	0.760596i	$-0.724907\pi$
$827$	−3.63717	+	2.64256i	−0.126477	+	0.0918907i	0.522748	+	0.852487i	$0.324907\pi$
$828$		0			0
$829$	−6.13796	+	18.8907i	−0.213180	+	0.656101i	0.786098	+	0.618102i	$0.212098\pi$
$829$	−6.13796	+	18.8907i	−0.213180	+	0.656101i	−0.999278	+	0.0379987i	$0.987902\pi$
$830$	−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	0.855373	+	0.518012i	$0.173328\pi$
$839$	13.5513	+	41.7065i	0.467842	+	1.43987i	−0.387532	+	0.921856i	$0.626672\pi$
$840$		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	−0.105794	−	0.994388i	$-0.533738\pi$
$853$	−31.6655	−	23.0063i	−1.08421	−	0.787721i	−0.978411	+	0.206667i	$0.933738\pi$
$854$	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	0.748694	−	0.662916i	$-0.230681\pi$
$863$	10.2696	+	7.46132i	0.349582	+	0.253986i	−0.399111	+	0.916902i	$0.630681\pi$
$864$		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	−0.983698	−	0.179831i	$-0.942445\pi$
$877$	−8.69388	−	26.7570i	−0.293571	−	0.903520i	0.690126	−	0.723689i	$-0.257555\pi$
$878$	−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	0.938477	−	0.345342i	$-0.112237\pi$
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	−0.962231	+	0.272235i	$0.912237\pi$
$884$	−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	0.450835	+	0.892607i	$0.351126\pi$
$887$	−13.0614	+	40.1989i	−0.438560	+	1.34975i	−0.889395	+	0.457140i	$0.848874\pi$
$888$		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	−0.0874240	−	0.996171i	$-0.527864\pi$
$907$	−31.9793	−	23.2343i	−1.06185	−	0.771483i	−0.974431	+	0.224689i	$0.927864\pi$
$908$	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	−0.949450	−	0.313919i	$-0.898358\pi$
$911$	−28.5013	+	20.7074i	−0.944291	+	0.686067i	0.00515893	+	0.999987i	$0.498358\pi$
$912$		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	0.973547	−	0.228488i	$-0.0733780\pi$
$919$	32.0455	+	23.2824i	1.05708	+	0.768017i	0.0835379	+	0.996505i	$0.473378\pi$
$920$	−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	0.621969	−	0.783042i	$-0.286333\pi$
$929$	2.11685	+	1.53798i	0.0694516	+	0.0504595i	−0.552518	+	0.833501i	$0.686333\pi$
$930$		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	−0.431689	+	0.902022i	$0.642082\pi$
$937$	−43.5575	+	31.6464i	−1.42296	+	1.03384i	−0.991274	+	0.131820i	$0.957918\pi$
$938$	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	0.905549	−	0.424241i	$-0.139459\pi$
$941$	23.9854	+	17.4264i	0.781902	+	0.568085i	−0.123647	+	0.992326i	$0.539459\pi$
$942$		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	−0.606555	−	0.795041i	$-0.707449\pi$
$953$	10.8502	−	33.3934i	0.351472	−	1.08172i	0.958027	−	0.286678i	$-0.0925509\pi$
$954$		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	−0.946583	−	0.322460i	$-0.895490\pi$
$971$	−11.5394	−	35.5148i	−0.370318	−	1.13972i	0.576265	−	0.817263i	$-0.304510\pi$
$972$		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	0.0669524	−	0.997756i	$-0.478672\pi$
$977$	32.3999	−	23.5399i	1.03656	−	0.753108i	0.969612	+	0.244648i	$0.0786724\pi$
$978$		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	−0.274098	−	0.961702i	$-0.588379\pi$
$983$	16.0817	−	49.4944i	0.512926	−	1.57862i	0.787024	−	0.616923i	$-0.211621\pi$
$984$		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	−0.715950	−	0.698152i	$-0.754006\pi$
$997$	8.63992	−	26.5909i	0.273629	−	0.842143i	0.989579	−	0.143992i	$-0.0459939\pi$
$998$	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.190.2		16
3.2	odd	2		77.2.f.b.36.3	yes	16
11.2	odd	10		7623.2.a.cw.1.4		8
11.4	even	5	inner	693.2.m.i.631.2		16
11.9	even	5		7623.2.a.ct.1.5		8
21.2	odd	6		539.2.q.g.410.2		32
21.5	even	6		539.2.q.f.410.2		32
21.11	odd	6		539.2.q.g.520.3		32
21.17	even	6		539.2.q.f.520.3		32
21.20	even	2		539.2.f.e.344.3		16
33.2	even	10		847.2.a.o.1.5		8
33.5	odd	10		847.2.f.w.372.2		16
33.8	even	10		847.2.f.v.148.3		16
33.14	odd	10		847.2.f.w.148.2		16
33.17	even	10		847.2.f.v.372.3		16
33.20	odd	10		847.2.a.p.1.4		8
33.26	odd	10		77.2.f.b.15.3	✓	16
33.29	even	10		847.2.f.x.323.2		16
33.32	even	2		847.2.f.x.729.2		16
231.20	even	10		5929.2.a.bt.1.4		8
231.26	even	30		539.2.q.f.312.3		32
231.59	even	30		539.2.q.f.422.2		32
231.125	even	10		539.2.f.e.246.3		16
231.158	odd	30		539.2.q.g.422.2		32
231.167	odd	10		5929.2.a.bs.1.5		8
231.191	odd	30		539.2.q.g.312.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.3	✓	16	33.26	odd	10
77.2.f.b.36.3	yes	16	3.2	odd	2
539.2.f.e.246.3		16	231.125	even	10
539.2.f.e.344.3		16	21.20	even	2
539.2.q.f.312.3		32	231.26	even	30
539.2.q.f.410.2		32	21.5	even	6
539.2.q.f.422.2		32	231.59	even	30
539.2.q.f.520.3		32	21.17	even	6
539.2.q.g.312.3		32	231.191	odd	30
539.2.q.g.410.2		32	21.2	odd	6
539.2.q.g.422.2		32	231.158	odd	30
539.2.q.g.520.3		32	21.11	odd	6
693.2.m.i.190.2		16	1.1	even	1	trivial
693.2.m.i.631.2		16	11.4	even	5	inner
847.2.a.o.1.5		8	33.2	even	10
847.2.a.p.1.4		8	33.20	odd	10
847.2.f.v.148.3		16	33.8	even	10
847.2.f.v.372.3		16	33.17	even	10
847.2.f.w.148.2		16	33.14	odd	10
847.2.f.w.372.2		16	33.5	odd	10
847.2.f.x.323.2		16	33.29	even	10
847.2.f.x.729.2		16	33.32	even	2
5929.2.a.bs.1.5		8	231.167	odd	10
5929.2.a.bt.1.4		8	231.20	even	10
7623.2.a.ct.1.5		8	11.9	even	5
7623.2.a.cw.1.4		8	11.2	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)

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