LMFDB - Embedded newform 495.2.bj.c.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(28,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 18]))

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

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

chi := DirichletCharacter("495.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.5
Character	$\chi$	$=$	495.73
Dual form			495.2.bj.c.217.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.178502 - 1.12702i) q^{2} +(0.663811 - 0.215685i) q^{4} +(-1.98355 + 1.03225i) q^{5} +(0.694338 - 1.36271i) q^{7} +(-1.39764 - 2.74302i) q^{8} +O(q^{10})$	\(q+(-0.178502 - 1.12702i) q^{2} +(0.663811 - 0.215685i) q^{4} +(-1.98355 + 1.03225i) q^{5} +(0.694338 - 1.36271i) q^{7} +(-1.39764 - 2.74302i) q^{8} +(1.51742 + 2.05123i) q^{10} +(-1.00122 - 3.16189i) q^{11} +(-5.09369 + 0.806762i) q^{13} +(-1.65974 - 0.539283i) q^{14} +(-1.71260 + 1.24428i) q^{16} +(4.76995 + 0.755485i) q^{17} +(1.65150 - 5.08279i) q^{19} +(-1.09406 + 1.11304i) q^{20} +(-3.38478 + 1.69280i) q^{22} +(-4.97973 - 4.97973i) q^{23} +(2.86894 - 4.09502i) q^{25} +(1.81847 + 5.59667i) q^{26} +(0.166992 - 1.05434i) q^{28} +(0.562510 + 1.73123i) q^{29} +(-2.07975 - 1.51103i) q^{31} +(-2.64572 - 2.64572i) q^{32} -5.51066i q^{34} +(0.0294027 + 3.41974i) q^{35} +(-8.27261 - 4.21510i) q^{37} +(-6.02318 - 0.953978i) q^{38} +(5.60375 + 3.99821i) q^{40} +(10.1057 + 3.28353i) q^{41} +(-0.373613 + 0.373613i) q^{43} +(-1.34660 - 1.88295i) q^{44} +(-4.72334 + 6.50112i) q^{46} +(-0.702519 - 1.37877i) q^{47} +(2.73961 + 3.77075i) q^{49} +(-5.12726 - 2.50237i) q^{50} +(-3.20725 + 1.63417i) q^{52} +(1.75355 + 11.0715i) q^{53} +(5.24982 + 5.23826i) q^{55} -4.70838 q^{56} +(1.85071 - 0.942986i) q^{58} +(1.41843 - 0.460877i) q^{59} +(2.06914 + 2.84793i) q^{61} +(-1.33171 + 2.61364i) q^{62} +(-4.99806 + 6.87923i) q^{64} +(9.27082 - 6.85820i) q^{65} +(0.161671 - 0.161671i) q^{67} +(3.32929 - 0.527308i) q^{68} +(3.84885 - 0.643567i) q^{70} +(1.37579 - 0.999573i) q^{71} +(2.78166 + 1.41733i) q^{73} +(-3.27381 + 10.0758i) q^{74} -3.73022i q^{76} +(-5.00394 - 0.831042i) q^{77} +(-1.71158 - 1.24354i) q^{79} +(2.11263 - 4.23591i) q^{80} +(1.89671 - 11.9753i) q^{82} +(1.10640 - 6.98551i) q^{83} +(-10.2413 + 3.42521i) q^{85} +(0.487759 + 0.354378i) q^{86} +(-7.27378 + 7.16554i) q^{88} -11.0867i q^{89} +(-2.43736 + 7.50142i) q^{91} +(-4.37965 - 2.23155i) q^{92} +(-1.42850 + 1.03786i) q^{94} +(1.97086 + 11.7867i) q^{95} +(18.0446 - 2.85798i) q^{97} +(3.76067 - 3.76067i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{5} - 20 q^{7}+O(q^{10}) $ 96 * q + 8 * q^5 - 20 * q^7	$ 96 q + 8 q^{5} - 20 q^{7} - 8 q^{11} + 8 q^{16} + 20 q^{17} + 60 q^{20} - 32 q^{22} - 32 q^{23} - 32 q^{25} - 60 q^{28} + 16 q^{31} + 8 q^{37} - 56 q^{38} + 120 q^{41} - 200 q^{46} - 60 q^{47} - 80 q^{50} + 40 q^{52} - 36 q^{53} + 80 q^{55} + 80 q^{56} + 44 q^{58} + 40 q^{61} - 80 q^{62} - 48 q^{67} - 80 q^{68} - 92 q^{70} - 32 q^{71} - 60 q^{73} + 24 q^{77} + 80 q^{80} + 32 q^{82} + 200 q^{83} - 80 q^{85} + 80 q^{86} - 144 q^{88} + 56 q^{91} - 20 q^{92} - 60 q^{95} + 32 q^{97}+O(q^{100}) $ 96 * q + 8 * q^5 - 20 * q^7 - 8 * q^11 + 8 * q^16 + 20 * q^17 + 60 * q^20 - 32 * q^22 - 32 * q^23 - 32 * q^25 - 60 * q^28 + 16 * q^31 + 8 * q^37 - 56 * q^38 + 120 * q^41 - 200 * q^46 - 60 * q^47 - 80 * q^50 + 40 * q^52 - 36 * q^53 + 80 * q^55 + 80 * q^56 + 44 * q^58 + 40 * q^61 - 80 * q^62 - 48 * q^67 - 80 * q^68 - 92 * q^70 - 32 * q^71 - 60 * q^73 + 24 * q^77 + 80 * q^80 + 32 * q^82 + 200 * q^83 - 80 * q^85 + 80 * q^86 - 144 * q^88 + 56 * q^91 - 20 * q^92 - 60 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.178502	−	1.12702i	−0.126220	−	0.796920i	−0.966856	−	0.255321i	$-0.917819\pi$
$2$	−0.178502	−	1.12702i	−0.126220	−	0.796920i	0.840637	−	0.541600i	$-0.182181\pi$
$3$		0			0
$3$		0			0
$4$	0.663811	−	0.215685i	0.331906	−	0.107843i
$5$	−1.98355	+	1.03225i	−0.887070	+	0.461634i
$5$	−1.98355	+	1.03225i	−0.887070	+	0.461634i
$6$		0			0
$7$	0.694338	−	1.36271i	0.262435	−	0.515058i	−0.721761	−	0.692143i	$-0.756667\pi$
$7$	0.694338	−	1.36271i	0.262435	−	0.515058i	0.984196	+	0.177085i	$0.0566668\pi$
$8$	−1.39764	−	2.74302i	−0.494139	−	0.969803i
$9$		0			0
$10$	1.51742	+	2.05123i	0.479852	+	0.648657i
$11$	−1.00122	−	3.16189i	−0.301880	−	0.953346i
$11$	−1.00122	−	3.16189i	−0.301880	−	0.953346i
$12$		0			0
$13$	−5.09369	+	0.806762i	−1.41274	+	0.223756i	−0.815708	−	0.578464i	$-0.803652\pi$
$13$	−5.09369	+	0.806762i	−1.41274	+	0.223756i	−0.597029	+	0.802220i	$0.703652\pi$
$14$	−1.65974	−	0.539283i	−0.443585	−	0.144129i
$15$		0			0
$16$	−1.71260	+	1.24428i	−0.428150	+	0.311069i
$17$	4.76995	+	0.755485i	1.15688	+	0.183232i	0.705241	−	0.708968i	$-0.250839\pi$
$17$	4.76995	+	0.755485i	1.15688	+	0.183232i	0.451641	+	0.892200i	$0.350839\pi$
$18$		0			0
$19$	1.65150	−	5.08279i	0.378880	−	1.16607i	−0.561944	−	0.827176i	$-0.689946\pi$
$19$	1.65150	−	5.08279i	0.378880	−	1.16607i	0.940823	−	0.338897i	$-0.110054\pi$
$20$	−1.09406	+	1.11304i	−0.244640	+	0.248883i
$21$		0			0
$22$	−3.38478	+	1.69280i	−0.721638	+	0.360905i
$23$	−4.97973	−	4.97973i	−1.03834	−	1.03834i	−0.999235	−	0.0391100i	$-0.987548\pi$
$23$	−4.97973	−	4.97973i	−1.03834	−	1.03834i	−0.0391100	−	0.999235i	$-0.512452\pi$
$24$		0			0
$25$	2.86894	−	4.09502i	0.573788	−	0.819004i
$26$	1.81847	+	5.59667i	0.356631	+	1.09760i
$27$		0			0
$28$	0.166992	−	1.05434i	0.0315585	−	0.199252i
$29$	0.562510	+	1.73123i	0.104456	+	0.321481i	0.989602	−	0.143831i	$-0.0459421\pi$
$29$	0.562510	+	1.73123i	0.104456	+	0.321481i	−0.885147	+	0.465312i	$0.845942\pi$
$30$		0			0
$31$	−2.07975	−	1.51103i	−0.373535	−	0.271389i	0.385140	−	0.922858i	$-0.374153\pi$
$31$	−2.07975	−	1.51103i	−0.373535	−	0.271389i	−0.758675	+	0.651469i	$0.774153\pi$
$32$	−2.64572	−	2.64572i	−0.467702	−	0.467702i
$33$		0			0
$34$		−	5.51066i		−	0.945071i
$35$	0.0294027	+	3.41974i	0.00496997	+	0.578041i
$36$		0			0
$37$	−8.27261	−	4.21510i	−1.36001	−	0.692959i	−0.386645	−	0.922229i	$-0.626366\pi$
$37$	−8.27261	−	4.21510i	−1.36001	−	0.692959i	−0.973363	+	0.229270i	$0.926366\pi$
$38$	−6.02318	−	0.953978i	−0.977089	−	0.154756i
$39$		0			0
$40$	5.60375	+	3.99821i	0.886031	+	0.632172i
$41$	10.1057	+	3.28353i	1.57824	+	0.512801i	0.961602	−	0.274448i	$-0.0884951\pi$
$41$	10.1057	+	3.28353i	1.57824	+	0.512801i	0.616636	+	0.787248i	$0.288495\pi$
$42$		0			0
$43$	−0.373613	+	0.373613i	−0.0569755	+	0.0569755i	−0.735020	−	0.678045i	$-0.762827\pi$
$43$	−0.373613	+	0.373613i	−0.0569755	+	0.0569755i	0.678045	+	0.735020i	$0.262827\pi$
$44$	−1.34660	−	1.88295i	−0.203007	−	0.283865i
$45$		0			0
$46$	−4.72334	+	6.50112i	−0.696419	+	0.958538i
$47$	−0.702519	−	1.37877i	−0.102473	−	0.201115i	0.834077	−	0.551647i	$-0.186001\pi$
$47$	−0.702519	−	1.37877i	−0.102473	−	0.201115i	−0.936550	+	0.350533i	$0.886001\pi$
$48$		0			0
$49$	2.73961	+	3.77075i	0.391373	+	0.538679i
$50$	−5.12726	−	2.50237i	−0.725105	−	0.353889i
$51$		0			0
$52$	−3.20725	+	1.63417i	−0.444765	+	0.226619i
$53$	1.75355	+	11.0715i	0.240869	+	1.52079i	0.750776	+	0.660557i	$0.229680\pi$
$53$	1.75355	+	11.0715i	0.240869	+	1.52079i	−0.509907	+	0.860230i	$0.670320\pi$
$54$		0			0
$55$	5.24982	+	5.23826i	0.707886	+	0.706327i
$56$	−4.70838			−0.629184
$57$		0			0
$58$	1.85071	−	0.942986i	0.243011	−	0.123820i
$59$	1.41843	−	0.460877i	0.184664	−	0.0600011i	−0.215225	−	0.976564i	$-0.569049\pi$
$59$	1.41843	−	0.460877i	0.184664	−	0.0600011i	0.399889	+	0.916563i	$0.369049\pi$
$60$		0			0
$61$	2.06914	+	2.84793i	0.264926	+	0.364640i	0.920669	−	0.390345i	$-0.127644\pi$
$61$	2.06914	+	2.84793i	0.264926	+	0.364640i	−0.655742	+	0.754985i	$0.727644\pi$
$62$	−1.33171	+	2.61364i	−0.169128	+	0.331932i
$63$		0			0
$64$	−4.99806	+	6.87923i	−0.624757	+	0.859904i
$65$	9.27082	−	6.85820i	1.14990	−	0.850655i
$66$		0			0
$67$	0.161671	−	0.161671i	0.0197513	−	0.0197513i	−0.697162	−	0.716913i	$-0.745554\pi$
$67$	0.161671	−	0.161671i	0.0197513	−	0.0197513i	0.716913	+	0.697162i	$0.245554\pi$
$68$	3.32929	−	0.527308i	0.403736	−	0.0639455i
$69$		0			0
$70$	3.84885	−	0.643567i	0.460026	−	0.0769210i
$71$	1.37579	−	0.999573i	0.163277	−	0.118627i	−0.503147	−	0.864201i	$-0.667824\pi$
$71$	1.37579	−	0.999573i	0.163277	−	0.118627i	0.666423	+	0.745574i	$0.267824\pi$
$72$		0			0
$73$	2.78166	+	1.41733i	0.325569	+	0.165886i	0.609134	−	0.793067i	$-0.291517\pi$
$73$	2.78166	+	1.41733i	0.325569	+	0.165886i	−0.283565	+	0.958953i	$0.591517\pi$
$74$	−3.27381	+	10.0758i	−0.380573	+	1.17128i
$75$		0			0
$76$		−	3.73022i		−	0.427886i
$77$	−5.00394	−	0.831042i	−0.570252	−	0.0947060i
$78$		0			0
$79$	−1.71158	−	1.24354i	−0.192568	−	0.139909i	0.487323	−	0.873222i	$-0.337973\pi$
$79$	−1.71158	−	1.24354i	−0.192568	−	0.139909i	−0.679892	+	0.733312i	$0.737973\pi$
$80$	2.11263	−	4.23591i	0.236199	−	0.473589i
$81$		0			0
$82$	1.89671	−	11.9753i	0.209456	−	1.32246i
$83$	1.10640	−	6.98551i	0.121443	−	0.766759i	−0.849525	−	0.527548i	$-0.823111\pi$
$83$	1.10640	−	6.98551i	0.121443	−	0.766759i	0.970968	−	0.239211i	$-0.0768887\pi$
$84$		0			0
$85$	−10.2413	+	3.42521i	−1.11082	+	0.371517i
$86$	0.487759	+	0.354378i	0.0525964	+	0.0382135i
$87$		0			0
$88$	−7.27378	+	7.16554i	−0.775387	+	0.763849i
$89$		−	11.0867i		−	1.17518i	−0.809158	−	0.587591i	$-0.800076\pi$
$89$		−	11.0867i		−	1.17518i	0.809158	−	0.587591i	$-0.199924\pi$
$90$		0			0
$91$	−2.43736	+	7.50142i	−0.255505	+	0.786362i
$92$	−4.37965	−	2.23155i	−0.456610	−	0.232655i
$93$		0			0
$94$	−1.42850	+	1.03786i	−0.147338	+	0.107047i
$95$	1.97086	+	11.7867i	0.202206	+	1.20929i
$96$		0			0
$97$	18.0446	−	2.85798i	1.83215	−	0.290184i	0.857594	−	0.514327i	$-0.171958\pi$
$97$	18.0446	−	2.85798i	1.83215	−	0.290184i	0.974556	+	0.224143i	$0.0719583\pi$
$98$	3.76067	−	3.76067i	0.379885	−	0.379885i
$99$		0			0
$100$	1.02120	−	3.33711i	0.102120	−	0.333711i
$101$	1.50802	−	2.07561i	0.150053	−	0.206531i	−0.727373	−	0.686243i	$-0.759259\pi$
$101$	1.50802	−	2.07561i	0.150053	−	0.206531i	0.877426	+	0.479712i	$0.159259\pi$
$102$		0			0
$103$	1.94230	−	3.81197i	0.191380	−	0.375605i	−0.775300	−	0.631594i	$-0.782401\pi$
$103$	1.94230	−	3.81197i	0.191380	−	0.375605i	0.966680	+	0.255989i	$0.0824011\pi$
$104$	9.33210	+	12.8445i	0.915087	+	1.25951i
$105$		0			0
$106$	12.1647	−	3.95256i	1.18154	−	0.383907i
$107$	8.99672	−	4.58406i	0.869746	−	0.443157i	0.0386276	−	0.999254i	$-0.487701\pi$
$107$	8.99672	−	4.58406i	0.869746	−	0.443157i	0.831118	+	0.556096i	$0.187701\pi$
$108$		0			0
$109$	15.9895			1.53152			0.765758	−	0.643129i	$-0.222364\pi$
$109$	15.9895			1.53152			0.765758	+	0.643129i	$0.222364\pi$
$110$	4.96650	−	6.85167i	0.473537	−	0.653281i
$111$		0			0
$112$	0.506471	+	3.19773i	0.0478570	+	0.302157i
$113$	−6.36008	+	3.24062i	−0.598306	+	0.304852i	−0.726790	−	0.686859i	$-0.758989\pi$
$113$	−6.36008	+	3.24062i	−0.598306	+	0.304852i	0.128484	+	0.991712i	$0.458989\pi$
$114$		0			0
$115$	15.0178	+	4.73723i	1.40042	+	0.441749i
$116$	0.746802	+	1.02788i	0.0693388	+	0.0954367i
$117$		0			0
$118$	−0.772609	−	1.51633i	−0.0711244	−	0.139589i
$119$	4.34147	−	5.97551i	0.397981	−	0.547775i
$120$		0			0
$121$	−8.99511	+	6.33151i	−0.817737	+	0.575591i
$122$	2.84031	−	2.84031i	0.257150	−	0.257150i
$123$		0			0
$124$	−1.70647	−	0.554466i	−0.153246	−	0.0497925i
$125$	−1.46361	+	11.0841i	−0.130910	+	0.991394i
$126$		0			0
$127$	0.950634	+	0.150566i	0.0843551	+	0.0133605i	0.198469	−	0.980107i	$-0.436403\pi$
$127$	0.950634	+	0.150566i	0.0843551	+	0.0133605i	−0.114114	+	0.993468i	$0.536403\pi$
$128$	1.97756	+	1.00762i	0.174793	+	0.0890617i
$129$		0			0
$130$	−9.38415	−	9.22416i	−0.823045	−	0.809012i
$131$			6.91325i			0.604013i	0.953306	+	0.302007i	$0.0976565\pi$
$131$			6.91325i			0.604013i	−0.953306	+	0.302007i	$0.902344\pi$
$132$		0			0
$133$	−5.77970	−	5.77970i	−0.501163	−	0.501163i
$134$	−0.211065	−	0.153348i	−0.0182332	−	0.0132472i
$135$		0			0
$136$	−4.59434	−	14.1399i	−0.393962	−	1.21249i
$137$	−0.110994	+	0.700789i	−0.00948286	+	0.0598724i	−0.991976	−	0.126426i	$-0.959649\pi$
$137$	−0.110994	+	0.700789i	−0.00948286	+	0.0598724i	0.982493	+	0.186299i	$0.0596493\pi$
$138$		0			0
$139$	3.23794	+	9.96534i	0.274638	+	0.845249i	0.989315	+	0.145794i	$0.0465738\pi$
$139$	3.23794	+	9.96534i	0.274638	+	0.845249i	−0.714677	+	0.699455i	$0.753426\pi$
$140$	0.757106	+	2.26372i	0.0639871	+	0.191319i
$141$		0			0
$142$	−1.37212	−	1.37212i	−0.115145	−	0.115145i
$143$	7.65081	+	15.2980i	0.639793	+	1.27928i
$144$		0			0
$145$	−2.90282	−	2.85333i	−0.241066	−	0.236956i
$146$	1.10082	−	3.38797i	0.0911045	−	0.280391i
$147$		0			0
$148$	−6.40059	−	1.01375i	−0.526125	−	0.0833300i
$149$	3.78796	−	2.75211i	0.310322	−	0.225462i	−0.421713	−	0.906729i	$-0.638571\pi$
$149$	3.78796	−	2.75211i	0.310322	−	0.225462i	0.732035	+	0.681267i	$0.238571\pi$
$150$		0			0
$151$	17.1709	+	5.57917i	1.39735	+	0.454027i	0.908333	−	0.418247i	$-0.137355\pi$
$151$	17.1709	+	5.57917i	1.39735	+	0.454027i	0.489017	+	0.872274i	$0.337355\pi$
$152$	−16.2504	+	2.57381i	−1.31808	+	0.208763i
$153$		0			0
$154$	−0.0433847	+	5.78786i	−0.00349604	+	0.466399i
$155$	5.68505	+	0.850385i	0.456634	+	0.0683046i
$156$		0			0
$157$	−7.23471	−	14.1989i	−0.577393	−	1.13320i	−0.976344	−	0.216225i	$-0.930625\pi$
$157$	−7.23471	−	14.1989i	−0.577393	−	1.13320i	0.398951	−	0.916972i	$-0.369375\pi$
$158$	−1.09597	+	2.15096i	−0.0871905	+	0.171121i
$159$		0			0
$160$	7.97895	+	2.51688i	0.630791	+	0.198977i
$161$	−10.2436	+	3.32833i	−0.807306	+	0.262309i
$162$		0			0
$163$	0.725442	+	4.58026i	0.0568210	+	0.358754i	0.999674	+	0.0255440i	$0.00813178\pi$
$163$	0.725442	+	4.58026i	0.0568210	+	0.358754i	−0.942853	+	0.333210i	$0.891868\pi$
$164$	7.41646			0.579128
$165$		0			0
$166$	−8.07027			−0.626374
$167$	−1.00552	−	6.34862i	−0.0778097	−	0.491271i	−0.995561	−	0.0941162i	$-0.969997\pi$
$167$	−1.00552	−	6.34862i	−0.0778097	−	0.491271i	0.917751	−	0.397155i	$-0.130003\pi$
$168$		0			0
$169$	12.9311	−	4.20158i	0.994702	−	0.323198i
$170$	5.68836	+	10.9307i	0.436277	+	0.838344i
$171$		0			0
$172$	−0.167426	+	0.328592i	−0.0127661	+	0.0250549i
$173$	0.868748	+	1.70501i	0.0660497	+	0.129630i	0.921671	−	0.387973i	$-0.126825\pi$
$173$	0.868748	+	1.70501i	0.0660497	+	0.129630i	−0.855621	+	0.517603i	$0.826825\pi$
$174$		0			0
$175$	−3.58833	−	6.75287i	−0.271252	−	0.510469i
$176$	5.64896	+	4.16926i	0.425806	+	0.314270i
$177$		0			0
$178$	−12.4948	+	1.97899i	−0.936527	+	0.148331i
$179$	7.59792	+	2.46871i	0.567895	+	0.184520i	0.578871	−	0.815419i	$-0.303494\pi$
$179$	7.59792	+	2.46871i	0.567895	+	0.184520i	−0.0109754	+	0.999940i	$0.503494\pi$
$180$		0			0
$181$	−8.76400	+	6.36742i	−0.651423	+	0.473287i	−0.863756	−	0.503911i	$-0.831894\pi$
$181$	−8.76400	+	6.36742i	−0.651423	+	0.473287i	0.212332	+	0.977197i	$0.431894\pi$
$182$	8.88929	+	1.40793i	0.658918	+	0.104362i
$183$		0			0
$184$	−6.69963	+	20.6193i	−0.493903	+	1.52008i
$185$	20.7601	−	0.178495i	1.52632	−	0.0131232i
$186$		0			0
$187$	−2.38701	−	15.8385i	−0.174555	−	1.15822i
$188$	−0.763721	−	0.763721i	−0.0557001	−	0.0557001i
$189$		0			0
$190$	12.9320	−	4.32514i	0.938188	−	0.313779i
$191$	−4.71158	−	14.5007i	−0.340918	−	1.04924i	−0.963733	−	0.266868i	$-0.914011\pi$
$191$	−4.71158	−	14.5007i	−0.340918	−	1.04924i	0.622815	−	0.782369i	$-0.285989\pi$
$192$		0			0
$193$	−1.87221	+	11.8207i	−0.134765	+	0.850872i	0.823983	+	0.566615i	$0.191747\pi$
$193$	−1.87221	+	11.8207i	−0.134765	+	0.850872i	−0.958748	+	0.284258i	$0.908253\pi$
$194$	−6.44198	−	19.8264i	−0.462507	−	1.42345i
$195$		0			0
$196$	2.63188	+	1.91217i	0.187991	+	0.136584i
$197$	−11.1163	−	11.1163i	−0.792004	−	0.792004i	0.189816	−	0.981820i	$-0.439211\pi$
$197$	−11.1163	−	11.1163i	−0.792004	−	0.792004i	−0.981820	+	0.189816i	$0.939211\pi$
$198$		0			0
$199$		−	21.5416i		−	1.52704i	−0.645783	−	0.763521i	$-0.723469\pi$
$199$		−	21.5416i		−	1.52704i	0.645783	−	0.763521i	$-0.276531\pi$
$200$	−15.2424	−	2.14619i	−1.07780	−	0.151759i
$201$		0			0
$202$	−2.60843	−	1.32906i	−0.183528	−	0.0935124i
$203$	2.74974	+	0.435517i	0.192994	+	0.0305673i
$204$		0			0
$205$	−23.4345	+	3.91848i	−1.63673	+	0.273678i
$206$	−4.64285	−	1.50855i	−0.323483	−	0.105106i
$207$		0			0
$208$	7.71962	−	7.71962i	0.535260	−	0.535260i
$209$	−17.7248	−	0.132861i	−1.22605	−	0.00919022i
$210$		0			0
$211$	−4.13145	+	5.68646i	−0.284421	+	0.391472i	−0.927192	−	0.374587i	$-0.877785\pi$
$211$	−4.13145	+	5.68646i	−0.284421	+	0.391472i	0.642771	+	0.766058i	$0.277785\pi$
$212$	3.55199	+	6.97117i	0.243952	+	0.478782i
$213$		0			0
$214$	−6.77223	−	9.32118i	−0.462940	−	0.637183i
$215$	0.355420	−	1.12674i	0.0242394	−	0.0768431i
$216$		0			0
$217$	−3.50315	+	1.78495i	−0.237810	+	0.121170i
$218$	−2.85415	−	18.0204i	−0.193308	−	1.22050i
$219$		0			0
$220$	4.61471	+	2.34491i	0.311123	+	0.158094i
$221$	−24.9062			−1.67537
$222$		0			0
$223$	15.1020	−	7.69484i	1.01130	−	0.515285i	0.131850	−	0.991270i	$-0.457908\pi$
$223$	15.1020	−	7.69484i	1.01130	−	0.515285i	0.879454	+	0.475985i	$0.157908\pi$
$224$	−5.44239	+	1.76834i	−0.363635	+	0.118152i
$225$		0			0
$226$	4.78752	+	6.58946i	0.318461	+	0.438324i
$227$	−6.23734	+	12.2415i	−0.413987	+	0.812495i	0.586011	+	0.810303i	$0.300698\pi$
$227$	−6.23734	+	12.2415i	−0.413987	+	0.812495i	−0.999998	+	0.00219156i	$0.999302\pi$
$228$		0			0
$229$	−12.1652	+	16.7439i	−0.803897	+	1.10647i	0.188339	+	0.982104i	$0.439690\pi$
$229$	−12.1652	+	16.7439i	−0.803897	+	1.10647i	−0.992236	+	0.124365i	$0.960310\pi$
$230$	2.65823	−	17.7709i	0.175278	−	1.17178i
$231$		0			0
$232$	3.96261	−	3.96261i	0.260158	−	0.260158i
$233$	−16.4801	+	2.61019i	−1.07965	+	0.170999i	−0.670825	−	0.741615i	$-0.734060\pi$
$233$	−16.4801	+	2.61019i	−1.07965	+	0.170999i	−0.408821	+	0.912615i	$0.634060\pi$
$234$		0			0
$235$	2.81671	+	2.00969i	0.183742	+	0.131098i
$236$	0.842168	−	0.611871i	0.0548205	−	0.0398294i
$237$		0			0
$238$	−7.50946	−	3.82626i	−0.486766	−	0.248020i
$239$	−0.433057	+	1.33281i	−0.0280121	+	0.0862124i	−0.964085	−	0.265593i	$-0.914432\pi$
$239$	−0.433057	+	1.33281i	−0.0280121	+	0.0862124i	0.936073	+	0.351806i	$0.114432\pi$
$240$		0			0
$241$		−	1.19156i		−	0.0767551i	−0.999263	−	0.0383775i	$-0.987781\pi$
$241$		−	1.19156i		−	0.0767551i	0.999263	−	0.0383775i	$-0.0122190\pi$
$242$	8.74135	+	9.00745i	0.561915	+	0.579021i
$243$		0			0
$244$	1.98777	+	1.44420i	0.127254	+	0.0924556i
$245$	−9.32649	−	4.65152i	−0.595848	−	0.297175i
$246$		0			0
$247$	−4.31163	+	27.2226i	−0.274342	+	1.73213i
$248$	−1.23804	+	7.81667i	−0.0786155	+	0.496359i
$249$		0			0
$250$	12.7532	−	0.329020i	0.806586	−	0.0208091i
$251$	−22.6893	−	16.4847i	−1.43213	−	1.04051i	−0.989614	−	0.143749i	$-0.954084\pi$
$251$	−22.6893	−	16.4847i	−1.43213	−	1.04051i	−0.442521	−	0.896758i	$-0.645916\pi$
$252$		0			0
$253$	−10.7595	+	20.7312i	−0.676447	+	1.30336i
$254$		−	1.09826i		−	0.0689107i
$255$		0			0
$256$	−4.47266	+	13.7654i	−0.279541	+	0.860340i
$257$	7.36549	+	3.75290i	0.459446	+	0.234100i	0.668365	−	0.743833i	$-0.266994\pi$
$257$	7.36549	+	3.75290i	0.459446	+	0.234100i	−0.208919	+	0.977933i	$0.566994\pi$
$258$		0			0
$259$	−11.4880	+	8.34650i	−0.713827	+	0.518626i
$260$	4.67486	−	6.55213i	0.289923	−	0.406346i
$261$		0			0
$262$	7.79134	−	1.23403i	0.481351	−	0.0762385i
$263$	−11.5967	+	11.5967i	−0.715083	+	0.715083i	−0.967594	−	0.252511i	$-0.918744\pi$
$263$	−11.5967	+	11.5967i	−0.715083	+	0.715083i	0.252511	+	0.967594i	$0.418744\pi$
$264$		0			0
$265$	−14.9068	−	20.1508i	−0.915715	−	1.23785i
$266$	−5.48212	+	7.54550i	−0.336131	+	0.462644i
$267$		0			0
$268$	0.0724491	−	0.142189i	0.00442554	−	0.00868560i
$269$	−7.41230	−	10.2022i	−0.451936	−	0.622036i	0.520876	−	0.853632i	$-0.325605\pi$
$269$	−7.41230	−	10.2022i	−0.451936	−	0.622036i	−0.972812	+	0.231596i	$0.925605\pi$
$270$		0			0
$271$	5.44539	−	1.76932i	0.330784	−	0.107478i	−0.138916	−	0.990304i	$-0.544362\pi$
$271$	5.44539	−	1.76932i	0.330784	−	0.107478i	0.469700	+	0.882826i	$0.344362\pi$
$272$	−9.10904	+	4.64129i	−0.552317	+	0.281419i
$273$		0			0
$274$	0.809613			0.0489105
$275$	−15.8205	−	4.97125i	−0.954009	−	0.299778i
$276$		0			0
$277$	−2.75443	−	17.3908i	−0.165498	−	1.04491i	−0.920942	−	0.389699i	$-0.872579\pi$
$277$	−2.75443	−	17.3908i	−0.165498	−	1.04491i	0.755444	−	0.655213i	$-0.227421\pi$
$278$	10.6531	−	5.42804i	0.638932	−	0.325552i
$279$		0			0
$280$	9.33931	−	4.86021i	0.558130	−	0.290453i
$281$	7.90740	+	10.8836i	0.471716	+	0.649261i	0.976887	−	0.213758i	$-0.0685704\pi$
$281$	7.90740	+	10.8836i	0.471716	+	0.649261i	−0.505171	+	0.863020i	$0.668570\pi$
$282$		0			0
$283$	5.64529	+	11.0795i	0.335578	+	0.658608i	0.995709	−	0.0925422i	$-0.0294993\pi$
$283$	5.64529	+	11.0795i	0.335578	+	0.658608i	−0.660131	+	0.751150i	$0.729499\pi$
$284$	0.697674	−	0.960266i	0.0413994	−	0.0569813i
$285$		0			0
$286$	15.8754	−	11.3533i	0.938730	−	0.671334i
$287$	11.4912	−	11.4912i	0.678307	−	0.678307i
$288$		0			0
$289$	6.01367	+	1.95396i	0.353746	+	0.114939i
$290$	−2.69759	+	3.78085i	−0.158408	+	0.222019i
$291$		0			0
$292$	2.15220	+	0.340874i	0.125948	+	0.0199482i
$293$	15.1593	+	7.72404i	0.885615	+	0.451243i	0.836764	−	0.547563i	$-0.184444\pi$
$293$	15.1593	+	7.72404i	0.885615	+	0.451243i	0.0488501	+	0.998806i	$0.484444\pi$
$294$		0			0
$295$	−2.33780	+	2.37834i	−0.136112	+	0.138473i
$296$			28.5831i			1.66136i
$297$		0			0
$298$	−3.77783	−	3.77783i	−0.218844	−	0.218844i
$299$	29.3827	+	21.3478i	1.69924	+	1.23457i
$300$		0			0
$301$	0.249715	+	0.768543i	0.0143933	+	0.0442981i
$302$	3.22278	−	20.3478i	0.185450	−	1.17088i
$303$		0			0
$304$	3.49604	+	10.7597i	0.200512	+	0.617112i
$305$	−7.04400	−	3.51314i	−0.403338	−	0.201162i
$306$		0			0
$307$	−3.41893	−	3.41893i	−0.195128	−	0.195128i	0.602779	−	0.797908i	$-0.294060\pi$
$307$	−3.41893	−	3.41893i	−0.195128	−	0.195128i	−0.797908	+	0.602779i	$0.794060\pi$
$308$	−3.50092	+	0.527622i	−0.199483	+	0.0300641i
$309$		0			0
$310$	−0.0563934	−	6.55893i	−0.00320293	−	0.372522i
$311$	4.08382	−	12.5687i	0.231572	−	0.712706i	−0.765985	−	0.642858i	$-0.777748\pi$
$311$	4.08382	−	12.5687i	0.231572	−	0.712706i	0.997558	−	0.0698483i	$-0.0222515\pi$
$312$		0			0
$313$	−2.66537	−	0.422154i	−0.150656	−	0.0238615i	0.0806510	−	0.996742i	$-0.474300\pi$
$313$	−2.66537	−	0.422154i	−0.150656	−	0.0238615i	−0.231307	+	0.972881i	$0.574300\pi$
$314$	−14.7110	+	10.6882i	−0.830190	+	0.603168i
$315$		0			0
$316$	−1.40438	−	0.456311i	−0.0790027	−	0.0256695i
$317$	4.11199	−	0.651276i	0.230953	−	0.0365793i	−0.0398853	−	0.999204i	$-0.512699\pi$
$317$	4.11199	−	0.651276i	0.230953	−	0.0365793i	0.270838	+	0.962625i	$0.412699\pi$
$318$		0			0
$319$	4.91076	−	3.51194i	0.274950	−	0.196631i
$320$	2.81283	−	18.8045i	0.157242	−	1.05120i
$321$		0			0
$322$	5.57958	+	10.9505i	0.310938	+	0.610250i
$323$	11.7175	−	22.9970i	0.651981	−	1.27959i
$324$		0			0
$325$	−11.3098	+	23.1733i	−0.627354	+	1.28543i
$326$	5.03254	−	1.63517i	0.278726	−	0.0905637i
$327$		0			0
$328$	−5.11727	−	32.3092i	−0.282554	−	1.78397i
$329$	−2.36666			−0.130478
$330$		0			0
$331$	−34.3521			−1.88816			−0.944082	−	0.329710i	$-0.893049\pi$
$331$	−34.3521			−1.88816			−0.944082	+	0.329710i	$0.893049\pi$
$332$	−0.772234	−	4.87569i	−0.0423818	−	0.267588i
$333$		0			0
$334$	−6.97551	+	2.26648i	−0.381683	+	0.124016i
$335$	−0.153799	+	0.487568i	−0.00840292	+	0.0266387i
$336$		0			0
$337$	5.05306	−	9.91719i	0.275258	−	0.540224i	−0.711448	−	0.702738i	$-0.751960\pi$
$337$	5.05306	−	9.91719i	0.275258	−	0.540224i	0.986706	+	0.162514i	$0.0519604\pi$
$338$	−7.04347	−	13.8236i	−0.383114	−	0.751904i
$339$		0			0
$340$	−6.05950	+	4.48259i	−0.328623	+	0.243102i
$341$	−2.69542	+	8.08883i	−0.145965	+	0.438035i
$342$		0			0
$343$	17.6147	−	2.78990i	0.951106	−	0.150640i
$344$	1.54700	+	0.502652i	0.0834089	+	0.0271012i
$345$		0			0
$346$	1.76651	−	1.28344i	0.0949679	−	0.0689982i
$347$	8.37634	+	1.32668i	0.449665	+	0.0712200i	0.377160	−	0.926148i	$-0.376901\pi$
$347$	8.37634	+	1.32668i	0.449665	+	0.0712200i	0.0725052	+	0.997368i	$0.476901\pi$
$348$		0			0
$349$	10.7385	−	33.0498i	0.574820	−	1.76911i	−0.0619732	−	0.998078i	$-0.519739\pi$
$349$	10.7385	−	33.0498i	0.574820	−	1.76911i	0.636793	−	0.771035i	$-0.280261\pi$
$350$	−6.97007	+	5.24951i	−0.372566	+	0.280598i
$351$		0			0
$352$	−5.71653	+	11.0144i	−0.304692	+	0.587071i
$353$	−1.39846	−	1.39846i	−0.0744324	−	0.0744324i	0.668911	−	0.743343i	$-0.266761\pi$
$353$	−1.39846	−	1.39846i	−0.0744324	−	0.0744324i	−0.743343	+	0.668911i	$0.766761\pi$
$354$		0			0
$355$	−1.69715	+	3.40286i	−0.0900754	+	0.180605i
$356$	−2.39123	−	7.35945i	−0.126735	−	0.390050i
$357$		0			0
$358$	1.42604	−	9.00364i	0.0753684	−	0.475857i
$359$	−1.56703	−	4.82281i	−0.0827045	−	0.254538i	0.901150	−	0.433507i	$-0.142724\pi$
$359$	−1.56703	−	4.82281i	−0.0827045	−	0.254538i	−0.983855	+	0.178969i	$0.942724\pi$
$360$		0			0
$361$	−7.73601	−	5.62054i	−0.407158	−	0.295818i
$362$	8.74057	+	8.74057i	0.459394	+	0.459394i
$363$		0			0
$364$			5.50523i			0.288552i
$365$	−6.98060	+	0.0600188i	−0.365381	+	0.00314153i
$366$		0			0
$367$	29.2526	+	14.9050i	1.52697	+	0.778033i	0.997525	−	0.0703089i	$-0.0223985\pi$
$367$	29.2526	+	14.9050i	1.52697	+	0.778033i	0.529450	+	0.848341i	$0.322398\pi$
$368$	14.7244	+	2.33212i	0.767564	+	0.121570i
$369$		0			0
$370$	−3.90689	−	23.3651i	−0.203109	−	1.21470i
$371$	16.3048	+	5.29777i	0.846505	+	0.275046i
$372$		0			0
$373$	21.3362	−	21.3362i	1.10475	−	1.10475i	0.110918	−	0.993830i	$-0.464621\pi$
$373$	21.3362	−	21.3362i	1.10475	−	1.10475i	0.993830	−	0.110918i	$-0.0353792\pi$
$374$	−17.4241	+	5.51739i	−0.900979	+	0.285297i
$375$		0			0
$376$	−2.80013	+	3.85405i	−0.144406	+	0.198757i
$377$	−4.26195	−	8.36454i	−0.219501	−	0.430796i
$378$		0			0
$379$	−17.2174	−	23.6978i	−0.884400	−	1.21727i	−0.975183	−	0.221401i	$-0.928937\pi$
$379$	−17.2174	−	23.6978i	−0.884400	−	1.21727i	0.0907827	−	0.995871i	$-0.471063\pi$
$380$	3.85050	+	7.39908i	0.197527	+	0.379565i
$381$		0			0
$382$	−15.5015	+	7.89843i	−0.793128	+	0.404119i
$383$	3.46880	+	21.9012i	0.177248	+	1.11910i	0.902524	+	0.430639i	$0.141712\pi$
$383$	3.46880	+	21.9012i	0.177248	+	1.11910i	−0.725276	+	0.688458i	$0.758288\pi$
$384$		0			0
$385$	10.7834	−	3.51688i	0.549573	−	0.179237i
$386$	13.6563			0.695088
$387$		0			0
$388$	11.3618	−	5.78911i	0.576807	−	0.293898i
$389$	3.18340	−	1.03435i	0.161405	−	0.0524437i	−0.227200	−	0.973848i	$-0.572957\pi$
$389$	3.18340	−	1.03435i	0.161405	−	0.0524437i	0.388605	+	0.921404i	$0.372957\pi$
$390$		0			0
$391$	−19.9909	−	27.5151i	−1.01098	−	1.39150i
$392$	6.51425	−	12.7849i	0.329019	−	0.645737i
$393$		0			0
$394$	−10.5440	+	14.5125i	−0.531197	+	0.731131i
$395$	4.67865	+	0.699846i	0.235408	+	0.0352131i
$396$		0			0
$397$	−13.1144	+	13.1144i	−0.658193	+	0.658193i	−0.954952	−	0.296759i	$-0.904094\pi$
$397$	−13.1144	+	13.1144i	−0.658193	+	0.658193i	0.296759	+	0.954952i	$0.404094\pi$
$398$	−24.2777	+	3.84521i	−1.21693	+	0.192743i
$399$		0			0
$400$	0.181996	+	10.5829i	0.00909978	+	0.529144i
$401$	−11.5293	+	8.37654i	−0.575747	+	0.418305i	−0.837188	−	0.546915i	$-0.815802\pi$
$401$	−11.5293	+	8.37654i	−0.575747	+	0.418305i	0.261441	+	0.965219i	$0.415802\pi$
$402$		0			0
$403$	11.8127	+	6.01886i	0.588431	+	0.299821i
$404$	0.553361	−	1.70307i	0.0275307	−	0.0847309i
$405$		0			0
$406$		−	3.17675i		−	0.157659i
$407$	−5.04499	+	30.3773i	−0.250071	+	1.50575i
$408$		0			0
$409$	−23.5669	−	17.1224i	−1.16531	−	0.846646i	−0.174869	−	0.984592i	$-0.555950\pi$
$409$	−23.5669	−	17.1224i	−1.16531	−	0.846646i	−0.990440	+	0.137946i	$0.955950\pi$
$410$	8.59928	+	25.7116i	0.424688	+	1.26980i
$411$		0			0
$412$	0.467132	−	2.94935i	0.0230139	−	0.145304i
$413$	0.356828	−	2.25293i	0.0175584	−	0.110859i
$414$		0			0
$415$	5.01617	+	14.9982i	0.246234	+	0.736231i
$416$	15.6110	+	11.3420i	0.765390	+	0.556088i
$417$		0			0
$418$	3.01416	+	19.9998i	0.147428	+	0.978222i
$419$			24.0358i			1.17423i	0.809505	+	0.587113i	$0.199735\pi$
$419$			24.0358i			1.17423i	−0.809505	+	0.587113i	$0.800265\pi$
$420$		0			0
$421$	5.17693	−	15.9330i	0.252308	−	0.776525i	−0.742040	−	0.670356i	$-0.766142\pi$
$421$	5.17693	−	15.9330i	0.252308	−	0.776525i	0.994348	−	0.106169i	$-0.0338584\pi$
$422$	7.14620	+	3.64117i	0.347871	+	0.177249i
$423$		0			0
$424$	27.9185	−	20.2840i	1.35584	−	0.985076i
$425$	16.7784	−	17.3656i	0.813872	−	0.842355i
$426$		0			0
$427$	5.31759	−	0.842224i	0.257336	−	0.0407581i
$428$	4.98341	−	4.98341i	0.240882	−	0.240882i
$429$		0			0
$430$	−1.33330	−	0.199439i	−0.0642974	−	0.00961778i
$431$	16.3046	−	22.4413i	0.785363	−	1.08096i	−0.209307	−	0.977850i	$-0.567121\pi$
$431$	16.3046	−	22.4413i	0.785363	−	1.08096i	0.994670	−	0.103110i	$-0.0328793\pi$
$432$		0			0
$433$	−12.9918	+	25.4978i	−0.624344	+	1.22534i	0.334764	+	0.942302i	$0.391344\pi$
$433$	−12.9918	+	25.4978i	−0.624344	+	1.22534i	−0.959108	+	0.283042i	$0.908656\pi$
$434$	2.63698	+	3.62949i	0.126579	+	0.174221i
$435$		0			0
$436$	10.6140	−	3.44870i	0.508319	−	0.165163i
$437$	−33.5349	+	17.0869i	−1.60419	+	0.817377i
$438$		0			0
$439$	25.4805			1.21612			0.608059	−	0.793892i	$-0.291949\pi$
$439$	25.4805			1.21612			0.608059	+	0.793892i	$0.291949\pi$
$440$	7.03130	−	21.7215i	0.335204	−	1.03553i
$441$		0			0
$442$	4.44579	+	28.0696i	0.211465	+	1.33514i
$443$	15.9292	−	8.11633i	0.756819	−	0.385619i	−0.0326037	−	0.999468i	$-0.510380\pi$
$443$	15.9292	−	8.11633i	0.756819	−	0.385619i	0.789423	+	0.613850i	$0.210380\pi$
$444$		0			0
$445$	11.4441	+	21.9909i	0.542505	+	1.04247i
$446$	−11.3679	−	15.6466i	−0.538288	−	0.740889i
$447$		0			0
$448$	5.90409	+	11.5874i	0.278942	+	0.547455i
$449$	2.89649	−	3.98668i	0.136694	−	0.188143i	−0.735182	−	0.677870i	$-0.762903\pi$
$449$	2.89649	−	3.98668i	0.136694	−	0.188143i	0.871876	+	0.489726i	$0.162903\pi$
$450$		0			0
$451$	0.264156	−	35.2405i	0.0124386	−	1.65941i
$452$	−3.52294	+	3.52294i	−0.165705	+	0.165705i
$453$		0			0
$454$	14.9097	+	4.84446i	0.699747	+	0.227362i
$455$	−2.90868	−	17.3954i	−0.136361	−	0.815508i
$456$		0			0
$457$	−3.53972	−	0.560637i	−0.165581	−	0.0262255i	0.0730934	−	0.997325i	$-0.476713\pi$
$457$	−3.53972	−	0.560637i	−0.165581	−	0.0262255i	−0.238674	+	0.971100i	$0.576713\pi$
$458$	21.0422	+	10.7215i	0.983236	+	0.500984i
$459$		0			0
$460$	10.9908	−	0.0944980i	0.512447	−	0.00440599i
$461$		−	6.46205i		−	0.300968i	−0.988612	−	0.150484i	$-0.951917\pi$
$461$		−	6.46205i		−	0.300968i	0.988612	−	0.150484i	$-0.0480832\pi$
$462$		0			0
$463$	8.69314	+	8.69314i	0.404005	+	0.404005i	0.879642	−	0.475637i	$-0.157782\pi$
$463$	8.69314	+	8.69314i	0.404005	+	0.404005i	−0.475637	+	0.879642i	$0.657782\pi$
$464$	−3.11748	−	2.26498i	−0.144725	−	0.105149i
$465$		0			0
$466$	5.88345	+	18.1074i	0.272546	+	0.838809i
$467$	4.87697	−	30.7920i	0.225679	−	1.42488i	−0.571232	−	0.820788i	$-0.693534\pi$
$467$	4.87697	−	30.7920i	0.225679	−	1.42488i	0.796912	−	0.604096i	$-0.206466\pi$
$468$		0			0
$469$	−0.108057	−	0.332566i	−0.00498963	−	0.0153565i
$470$	1.76216	−	3.53321i	0.0812826	−	0.162975i
$471$		0			0
$472$	−3.24665	−	3.24665i	−0.149439	−	0.149439i
$473$	1.55539	+	0.807255i	0.0715171	+	0.0371176i
$474$		0			0
$475$	−16.0761	−	21.3451i	−0.737622	−	0.979382i
$476$	1.59308	−	4.90300i	0.0730188	−	0.224729i
$477$		0			0
$478$	1.57940	+	0.250152i	0.0722401	+	0.0114417i
$479$	−28.8664	+	20.9727i	−1.31894	+	0.958265i	−0.318994	+	0.947757i	$0.603345\pi$
$479$	−28.8664	+	20.9727i	−1.31894	+	0.958265i	−0.999945	+	0.0105085i	$0.996655\pi$
$480$		0			0
$481$	45.5387	+	14.7964i	2.07639	+	0.674659i
$482$	−1.34291	+	0.212695i	−0.0611677	+	0.00968801i
$483$		0			0
$484$	−4.60544	+	6.14304i	−0.209338	+	0.279229i
$485$	−32.8422	+	24.2954i	−1.49129	+	1.10320i
$486$		0			0
$487$	6.70725	+	13.1637i	0.303934	+	0.596505i	0.991573	−	0.129548i	$-0.0413527\pi$
$487$	6.70725	+	13.1637i	0.303934	+	0.596505i	−0.687639	+	0.726053i	$0.741353\pi$
$488$	4.92000	−	9.65605i	0.222718	−	0.437109i
$489$		0			0
$490$	−3.57754	+	11.3414i	−0.161617	+	0.512353i
$491$	30.7738	−	9.99901i	1.38880	−	0.451249i	0.483249	−	0.875483i	$-0.339457\pi$
$491$	30.7738	−	9.99901i	1.38880	−	0.451249i	0.905553	+	0.424234i	$0.139457\pi$
$492$		0			0
$493$	1.37523	+	8.68284i	0.0619371	+	0.391055i
$494$	31.4499			1.41500
$495$		0			0
$496$	5.44192			0.244350
$497$	−0.406867	−	2.56886i	−0.0182505	−	0.115229i
$498$		0			0
$499$	−22.6752	+	7.36761i	−1.01508	+	0.329819i	−0.768875	−	0.639399i	$-0.779183\pi$
$499$	−22.6752	+	7.36761i	−1.01508	+	0.329819i	−0.246204	+	0.969218i	$0.579183\pi$
$500$	1.41912	+	7.67345i	0.0634650	+	0.343167i
$501$		0			0
$502$	−14.5285	+	28.5137i	−0.648438	+	1.27263i
$503$	6.56640	+	12.8873i	0.292781	+	0.574615i	0.989804	−	0.142433i	$-0.0454926\pi$
$503$	6.56640	+	12.8873i	0.292781	+	0.574615i	−0.697023	+	0.717048i	$0.745493\pi$
$504$		0			0
$505$	−0.848691	+	5.67372i	−0.0377662	+	0.252477i
$506$	25.2849	+	8.42563i	1.12405	+	0.374565i
$507$		0			0
$508$	0.663516	−	0.105091i	0.0294388	−	0.00466264i
$509$	27.4102	+	8.90613i	1.21494	+	0.394757i	0.845236	−	0.534394i	$-0.179460\pi$
$509$	27.4102	+	8.90613i	1.21494	+	0.394757i	0.369702	+	0.929151i	$0.379460\pi$
$510$		0			0
$511$	3.86283	−	2.80651i	0.170881	−	0.124153i
$512$	20.6965	+	3.27801i	0.914666	+	0.144869i
$513$		0			0
$514$	2.91483	−	8.97092i	0.128568	−	0.395690i
$515$	0.0822493	+	9.56616i	0.00362434	+	0.421535i
$516$		0			0
$517$	−3.65615	+	3.60175i	−0.160797	+	0.158405i
$518$	11.4573	+	11.4573i	0.503403	+	0.503403i
$519$		0			0
$520$	−31.7694	−	15.8447i	−1.39318	−	0.694838i
$521$	−6.78813	−	20.8917i	−0.297394	−	0.915283i	−0.982407	−	0.186753i	$-0.940204\pi$
$521$	−6.78813	−	20.8917i	−0.297394	−	0.915283i	0.685013	−	0.728531i	$-0.259796\pi$
$522$		0			0
$523$	−1.34203	+	8.47327i	−0.0586831	+	0.370510i	0.940818	+	0.338913i	$0.110059\pi$
$523$	−1.34203	+	8.47327i	−0.0586831	+	0.370510i	−0.999501	+	0.0315970i	$0.989941\pi$
$524$	1.49109	+	4.58909i	0.0651384	+	0.200475i
$525$		0			0
$526$	15.1397	+	10.9996i	0.660122	+	0.479607i
$527$	−8.77875	−	8.77875i	−0.382408	−	0.382408i
$528$		0			0
$529$			26.5954i			1.15632i
$530$	−20.0493	+	20.3971i	−0.870888	+	0.885993i
$531$		0			0
$532$	−5.08323	−	2.59003i	−0.220386	−	0.112292i
$533$	−54.1241	−	8.57242i	−2.34438	−	0.371313i
$534$		0			0
$535$	−13.1136	+	18.3795i	−0.566949	+	0.794616i
$536$	−0.669425	−	0.217509i	−0.0289148	−	0.00939498i
$537$		0			0
$538$	−10.1749	+	10.1749i	−0.438670	+	0.438670i
$539$	9.17975	−	12.4377i	0.395400	−	0.535730i
$540$		0			0
$541$	−11.0577	+	15.2196i	−0.475406	+	0.654340i	−0.977614	−	0.210407i	$-0.932521\pi$
$541$	−11.0577	+	15.2196i	−0.475406	+	0.654340i	0.502208	+	0.864747i	$0.332521\pi$
$542$	−2.96606	−	5.82122i	−0.127403	−	0.250043i
$543$		0			0
$544$	−10.6211	−	14.6187i	−0.455378	−	0.626774i
$545$	−31.7160	+	16.5051i	−1.35856	+	0.707000i
$546$		0			0
$547$	−14.5409	+	7.40894i	−0.621723	+	0.316783i	−0.736325	−	0.676628i	$-0.763441\pi$
$547$	−14.5409	+	7.40894i	−0.621723	+	0.316783i	0.114602	+	0.993411i	$0.463441\pi$
$548$	0.0774708	+	0.489131i	0.00330939	+	0.0208947i
$549$		0			0
$550$	−2.77870	+	18.7173i	−0.118484	+	0.798107i
$551$	9.72846			0.414447
$552$		0			0
$553$	−2.88301	+	1.46897i	−0.122598	+	0.0624667i
$554$	−19.1080	+	6.20858i	−0.811823	+	0.263777i
$555$		0			0
$556$	4.29876	+	5.91673i	0.182308	+	0.250925i
$557$	−17.7910	+	34.9168i	−0.753828	+	1.47947i	0.119758	+	0.992803i	$0.461788\pi$
$557$	−17.7910	+	34.9168i	−0.753828	+	1.47947i	−0.873587	+	0.486668i	$0.838212\pi$
$558$		0			0
$559$	1.60166	−	2.20449i	0.0677428	−	0.0932400i
$560$	−4.30546	−	5.82006i	−0.181939	−	0.245942i
$561$		0			0
$562$	10.8545	−	10.8545i	0.457870	−	0.457870i
$563$	24.9534	−	3.95223i	1.05166	−	0.166567i	0.393408	−	0.919364i	$-0.371296\pi$
$563$	24.9534	−	3.95223i	1.05166	−	0.166567i	0.658253	+	0.752797i	$0.271296\pi$
$564$		0			0
$565$	9.27042	−	12.9931i	0.390009	−	0.546624i
$566$	11.4791	−	8.34004i	0.482502	−	0.350558i
$567$		0			0
$568$	−4.66471	−	2.37679i	−0.195727	−	0.0997277i
$569$	6.03151	−	18.5631i	0.252854	−	0.778205i	−0.741391	−	0.671074i	$-0.765833\pi$
$569$	6.03151	−	18.5631i	0.252854	−	0.778205i	0.994245	−	0.107131i	$-0.0341666\pi$
$570$		0			0
$571$		−	36.8794i		−	1.54335i	−0.636015	−	0.771677i	$-0.719418\pi$
$571$		−	36.8794i		−	1.54335i	0.636015	−	0.771677i	$-0.280582\pi$
$572$	8.37824	+	8.50479i	0.350312	+	0.355603i
$573$		0			0
$574$	−15.0020	−	10.8996i	−0.626172	−	0.454941i
$575$	−34.6786	+	6.10556i	−1.44620	+	0.254619i
$576$		0			0
$577$	1.59230	−	10.0534i	0.0662884	−	0.418528i	−0.932121	−	0.362147i	$-0.882044\pi$
$577$	1.59230	−	10.0534i	0.0662884	−	0.418528i	0.998409	−	0.0563813i	$-0.0179562\pi$
$578$	1.12869	−	7.12629i	0.0469475	−	0.296415i
$579$		0			0
$580$	−2.54235	−	1.26798i	−0.105565	−	0.0526499i
$581$	−8.75104	−	6.35800i	−0.363054	−	0.263774i
$582$		0			0
$583$	33.2512	−	16.6296i	1.37712	−	0.688726i
$584$		−	9.61106i		−	0.397708i
$585$		0			0
$586$	5.99916	−	18.4635i	0.247823	−	0.762720i
$587$	27.6148	+	14.0705i	1.13979	+	0.580750i	0.918877	−	0.394544i	$-0.129097\pi$
$587$	27.6148	+	14.0705i	1.13979	+	0.580750i	0.220910	+	0.975294i	$0.429097\pi$
$588$		0			0
$589$	−11.1150	+	8.07549i	−0.457984	+	0.332745i
$590$	3.09773	+	2.21019i	0.127532	+	0.0909922i
$591$		0			0
$592$	19.4124	−	3.07462i	0.797845	−	0.126366i
$593$	14.3239	−	14.3239i	0.588212	−	0.588212i	−0.348935	−	0.937147i	$-0.613457\pi$
$593$	14.3239	−	14.3239i	0.588212	−	0.588212i	0.937147	+	0.348935i	$0.113457\pi$
$594$		0			0
$595$	−2.44331	+	16.3342i	−0.100166	+	0.669636i
$596$	1.92090	−	2.64389i	0.0786832	−	0.108298i
$597$		0			0
$598$	18.8144	−	36.9253i	0.769378	−	1.50999i
$599$	5.02516	+	6.91653i	0.205322	+	0.282602i	0.899243	−	0.437450i	$-0.144118\pi$
$599$	5.02516	+	6.91653i	0.205322	+	0.282602i	−0.693921	+	0.720052i	$0.744118\pi$
$600$		0			0
$601$	−19.5570	+	6.35445i	−0.797746	+	0.259204i	−0.679399	−	0.733769i	$-0.737760\pi$
$601$	−19.5570	+	6.35445i	−0.797746	+	0.259204i	−0.118347	+	0.992972i	$0.537760\pi$
$602$	0.821585	−	0.418618i	0.0334853	−	0.0170616i
$603$		0			0
$604$	12.6016			0.512752
$605$	11.3066	−	21.8440i	0.459678	−	0.888086i
$606$		0			0
$607$	3.71230	+	23.4385i	0.150678	+	0.951341i	0.940940	+	0.338572i	$0.109944\pi$
$607$	3.71230	+	23.4385i	0.150678	+	0.951341i	−0.790263	+	0.612768i	$0.790056\pi$
$608$	−17.8171	+	9.07824i	−0.722577	+	0.368171i
$609$		0			0
$610$	−2.70200	+	8.56580i	−0.109401	+	0.346819i
$611$	4.69076	+	6.45628i	0.189768	+	0.261193i
$612$		0			0
$613$	−7.16345	−	14.0591i	−0.289329	−	0.567840i	0.699896	−	0.714245i	$-0.253230\pi$
$613$	−7.16345	−	14.0591i	−0.289329	−	0.567840i	−0.989225	+	0.146405i	$0.953230\pi$
$614$	−3.24290	+	4.46347i	−0.130873	+	0.180131i
$615$		0			0
$616$	4.71413	+	14.8874i	0.189938	+	0.599830i
$617$	3.71959	−	3.71959i	0.149745	−	0.149745i	−0.628259	−	0.778004i	$-0.716232\pi$
$617$	3.71959	−	3.71959i	0.149745	−	0.149745i	0.778004	+	0.628259i	$0.216232\pi$
$618$		0			0
$619$	3.25418	+	1.05735i	0.130796	+	0.0424983i	0.373684	−	0.927556i	$-0.378095\pi$
$619$	3.25418	+	1.05735i	0.130796	+	0.0424983i	−0.242887	+	0.970055i	$0.578095\pi$
$620$	3.95721	−	0.661686i	0.158926	−	0.0265740i
$621$		0			0
$622$	−14.8941	−	2.35900i	−0.597199	−	0.0945871i
$623$	−15.1079	−	7.69788i	−0.605287	−	0.308409i
$624$		0			0
$625$	−8.53839	−	23.4967i	−0.341536	−	0.939869i
$626$			3.07927i			0.123072i
$627$		0			0
$628$	−7.86499	−	7.86499i	−0.313847	−	0.313847i
$629$	−36.2754	−	26.3556i	−1.44640	−	1.05087i
$630$		0			0
$631$	−7.93923	−	24.4344i	−0.316056	−	0.972720i	−0.975318	−	0.220806i	$-0.929131\pi$
$631$	−7.93923	−	24.4344i	−0.316056	−	0.972720i	0.659262	−	0.751913i	$-0.270869\pi$
$632$	−1.01887	+	6.43292i	−0.0405287	+	0.255888i
$633$		0			0
$634$	−1.46800	−	4.51803i	−0.0583016	−	0.179434i
$635$	−2.04105	+	0.682633i	−0.0809966	+	0.0270895i
$636$		0			0
$637$	−16.9968	−	16.9968i	−0.673439	−	0.673439i
$638$	−4.83459	−	4.90762i	−0.191403	−	0.194294i
$639$		0			0
$640$	−4.96270	+	0.0426690i	−0.196168	+	0.00168664i
$641$	−13.0377	+	40.1258i	−0.514956	+	1.58487i	0.268405	+	0.963306i	$0.413503\pi$
$641$	−13.0377	+	40.1258i	−0.514956	+	1.58487i	−0.783362	+	0.621566i	$0.786497\pi$
$642$		0			0
$643$	−30.6900	−	4.86082i	−1.21030	−	0.191692i	−0.481514	−	0.876438i	$-0.659913\pi$
$643$	−30.6900	−	4.86082i	−1.21030	−	0.191692i	−0.728782	+	0.684746i	$0.759913\pi$
$644$	−6.08192	+	4.41877i	−0.239661	+	0.174124i
$645$		0			0
$646$	−28.0095	−	9.10085i	−1.10202	−	0.358068i
$647$	14.2373	−	2.25497i	0.559727	−	0.0886521i	0.129840	−	0.991535i	$-0.458553\pi$
$647$	14.2373	−	2.25497i	0.559727	−	0.0886521i	0.429887	+	0.902883i	$0.358553\pi$
$648$		0			0
$649$	−2.87741	−	4.02349i	−0.112948	−	0.157936i
$650$	28.1355	+	8.60983i	1.10357	+	0.337705i
$651$		0			0
$652$	1.46945	+	2.88396i	0.0575482	+	0.112945i
$653$	7.46123	−	14.6435i	0.291980	−	0.573044i	−0.697691	−	0.716399i	$-0.745789\pi$
$653$	7.46123	−	14.6435i	0.291980	−	0.573044i	0.989671	+	0.143355i	$0.0457891\pi$
$654$		0			0
$655$	−7.13617	−	13.7128i	−0.278833	−	0.535802i
$656$	−21.3925	+	6.95086i	−0.835239	+	0.271385i
$657$		0			0
$658$	0.422453	+	2.66726i	0.0164689	+	0.103981i
$659$	−27.5121			−1.07172			−0.535860	−	0.844307i	$-0.680012\pi$
$659$	−27.5121			−1.07172			−0.535860	+	0.844307i	$0.680012\pi$
$660$		0			0
$661$	47.5374			1.84899			0.924496	−	0.381193i	$-0.124487\pi$
$661$	47.5374			1.84899			0.924496	+	0.381193i	$0.124487\pi$
$662$	6.13192	+	38.7154i	0.238324	+	1.50472i
$663$		0			0
$664$	−20.7077	+	6.72834i	−0.803615	+	0.261110i
$665$	17.4304	+	5.49825i	0.675921	+	0.213213i
$666$		0			0
$667$	5.81990	−	11.4222i	0.225347	−	0.442269i
$668$	−2.03678	−	3.99741i	−0.0788055	−	0.154665i
$669$		0			0
$670$	0.576950	+	0.0863018i	0.0222895	+	0.00333413i
$671$	6.93317	−	9.39380i	0.267652	−	0.362644i
$672$		0			0
$673$	36.5676	−	5.79174i	1.40958	−	0.223255i	0.595194	−	0.803582i	$-0.297075\pi$
$673$	36.5676	−	5.79174i	1.40958	−	0.223255i	0.814384	+	0.580327i	$0.197075\pi$
$674$	−12.0788	−	3.92464i	−0.465259	−	0.151172i
$675$		0			0
$676$	7.67761	−	5.57811i	0.295293	−	0.214543i
$677$	2.16419	+	0.342773i	0.0831764	+	0.0131739i	0.197884	−	0.980225i	$-0.436593\pi$
$677$	2.16419	+	0.342773i	0.0831764	+	0.0131739i	−0.114708	+	0.993399i	$0.536593\pi$
$678$		0			0
$679$	8.63443	−	26.5740i	0.331359	−	1.01982i
$680$	23.7090	+	23.3048i	0.909199	+	0.893697i
$681$		0			0
$682$	9.59737	+	1.59391i	0.367502	+	0.0610339i
$683$	8.84087	+	8.84087i	0.338286	+	0.338286i	0.855722	−	0.517436i	$-0.173113\pi$
$683$	8.84087	+	8.84087i	0.338286	+	0.338286i	−0.517436	+	0.855722i	$0.673113\pi$
$684$		0			0
$685$	−0.503224	−	1.50462i	−0.0192272	−	0.0574887i
$686$	−6.28852	−	19.3541i	−0.240097	−	0.738942i
$687$		0			0
$688$	0.174972	−	1.10473i	0.00667074	−	0.0421174i
$689$	−17.8641	−	54.9801i	−0.680569	−	2.09458i
$690$		0			0
$691$	10.3561	+	7.52417i	0.393966	+	0.286233i	0.767079	−	0.641553i	$-0.221710\pi$
$691$	10.3561	+	7.52417i	0.393966	+	0.286233i	−0.373113	+	0.927786i	$0.621710\pi$
$692$	0.944432	+	0.944432i	0.0359019	+	0.0359019i
$693$		0			0
$694$		−	9.67708i		−	0.367337i
$695$	−16.7093	−	16.4244i	−0.633819	−	0.623013i
$696$		0			0
$697$	45.7228	+	23.2969i	1.73187	+	0.882434i
$698$	−39.1644	−	6.20304i	−1.48240	−	0.234788i
$699$		0			0
$700$	−3.83847	−	3.70868i	−0.145081	−	0.140175i
$701$	15.0984	+	4.90578i	0.570260	+	0.185289i	0.579932	−	0.814665i	$-0.303079\pi$
$701$	15.0984	+	4.90578i	0.570260	+	0.185289i	−0.00967259	+	0.999953i	$0.503079\pi$
$702$		0			0
$703$	−35.0867	+	35.0867i	−1.32332	+	1.32332i
$704$	26.7555	+	8.91567i	1.00839	+	0.336022i
$705$		0			0
$706$	−1.32646	+	1.82571i	−0.0499219	+	0.0687116i
$707$	−1.78139	−	3.49617i	−0.0669960	−	0.131487i
$708$		0			0
$709$	9.51797	+	13.1004i	0.357455	+	0.491995i	0.949437	−	0.313956i	$-0.101655\pi$
$709$	9.51797	+	13.1004i	0.357455	+	0.491995i	−0.591982	+	0.805951i	$0.701655\pi$
$710$	4.13802	+	1.30530i	0.155297	+	0.0489870i
$711$		0			0
$712$	−30.4109	+	15.4951i	−1.13970	+	0.580704i
$713$	2.83209	+	17.8811i	0.106063	+	0.669653i
$714$		0			0
$715$	−30.9670	−	22.4468i	−1.15810	−	0.839461i
$716$	5.57605			0.208387
$717$		0			0
$718$	−5.15567	+	2.62694i	−0.192408	+	0.0980366i
$719$	−11.5085	+	3.73935i	−0.429196	+	0.139454i	−0.515646	−	0.856802i	$-0.672448\pi$
$719$	−11.5085	+	3.73935i	−0.429196	+	0.139454i	0.0864496	+	0.996256i	$0.472448\pi$
$720$		0			0
$721$	−3.84602	−	5.29359i	−0.143233	−	0.197144i
$722$	−4.95354	+	9.72188i	−0.184352	+	0.361811i
$723$		0			0
$724$	−4.44429	+	6.11703i	−0.165171	+	0.227338i
$725$	8.70323	+	2.66330i	0.323230	+	0.0989124i
$726$		0			0
$727$	−7.08408	+	7.08408i	−0.262734	+	0.262734i	−0.826164	−	0.563430i	$-0.809481\pi$
$727$	−7.08408	+	7.08408i	−0.262734	+	0.262734i	0.563430	+	0.826164i	$0.309481\pi$
$728$	23.9831	−	3.79854i	0.888871	−	0.140783i
$729$		0			0
$730$	1.31369	+	7.85653i	0.0486219	+	0.290783i
$731$	−2.06438	+	1.49986i	−0.0763537	+	0.0554742i
$732$		0			0
$733$	−4.50478	−	2.29530i	−0.166388	−	0.0847788i	0.368813	−	0.929504i	$-0.379764\pi$
$733$	−4.50478	−	2.29530i	−0.166388	−	0.0847788i	−0.535201	+	0.844725i	$0.679764\pi$
$734$	11.5765	−	35.6287i	0.427296	−	1.31508i
$735$		0			0
$736$			26.3499i			0.971271i
$737$	−0.673056	−	0.349318i	−0.0247923	−	0.0128673i
$738$		0			0
$739$	−15.2930	−	11.1110i	−0.562562	−	0.408725i	0.269834	−	0.962907i	$-0.413031\pi$
$739$	−15.2930	−	11.1110i	−0.562562	−	0.408725i	−0.832396	+	0.554182i	$0.813031\pi$
$740$	13.7423	−	4.59615i	0.505178	−	0.168958i
$741$		0			0
$742$	3.06022	−	19.3215i	0.112344	−	0.709314i
$743$	6.00526	−	37.9157i	0.220312	−	1.39099i	−0.591138	−	0.806570i	$-0.701321\pi$
$743$	6.00526	−	37.9157i	0.220312	−	1.39099i	0.811450	−	0.584422i	$-0.198679\pi$
$744$		0			0
$745$	−4.67275	+	9.36906i	−0.171196	+	0.343256i
$746$	−27.8548	−	20.2377i	−1.01984	−	0.740955i
$747$		0			0
$748$	−5.00065	−	9.99891i	−0.182842	−	0.365596i
$749$		−	15.4428i		−	0.564269i
$750$		0			0
$751$	−15.8889	+	48.9010i	−0.579794	+	1.78442i	0.0394461	+	0.999222i	$0.487441\pi$
$751$	−15.8889	+	48.9010i	−0.579794	+	1.78442i	−0.619240	+	0.785202i	$0.712559\pi$
$752$	2.91871	+	1.48716i	0.106434	+	0.0542310i
$753$		0			0
$754$	−8.66621	+	6.29637i	−0.315605	+	0.229300i
$755$	−39.8185	+	6.65805i	−1.44914	+	0.242311i
$756$		0			0
$757$	−11.4556	+	1.81438i	−0.416360	+	0.0659449i	−0.361100	−	0.932527i	$-0.617599\pi$
$757$	−11.4556	+	1.81438i	−0.416360	+	0.0659449i	−0.0552598	+	0.998472i	$0.517599\pi$
$758$	−23.6344	+	23.6344i	−0.858440	+	0.858440i
$759$		0			0
$760$	29.5766	−	21.8797i	1.07286	−	0.793659i
$761$	−14.5038	+	19.9627i	−0.525761	+	0.723648i	−0.986477	−	0.163900i	$-0.947593\pi$
$761$	−14.5038	+	19.9627i	−0.525761	+	0.723648i	0.460716	+	0.887548i	$0.347593\pi$
$762$		0			0
$763$	11.1021	−	21.7891i	0.401924	−	0.788819i
$764$	−6.25520	−	8.60954i	−0.226305	−	0.311482i
$765$		0			0
$766$	24.0638	−	7.81879i	0.869459	−	0.282504i
$767$	−6.85325	+	3.49191i	−0.247457	+	0.126085i
$768$		0			0
$769$	1.44960			0.0522737			0.0261369	−	0.999658i	$-0.491679\pi$
$769$	1.44960			0.0522737			0.0261369	+	0.999658i	$0.491679\pi$
$770$	−5.88844	−	11.5253i	−0.212205	−	0.415343i
$771$		0			0
$772$	1.30675	+	8.25052i	0.0470311	+	0.296943i
$773$	16.6690	−	8.49326i	0.599541	−	0.305481i	−0.127754	−	0.991806i	$-0.540777\pi$
$773$	16.6690	−	8.49326i	0.599541	−	0.305481i	0.727296	+	0.686324i	$0.240777\pi$
$774$		0			0
$775$	−12.1544	+	4.18158i	−0.436598	+	0.150207i
$776$	−33.0593	−	45.5022i	−1.18676	−	1.63343i
$777$		0			0
$778$	−1.73397	−	3.40311i	−0.0621660	−	0.122008i
$779$	33.3790	−	45.9422i	1.19593	−	1.64605i
$780$		0			0
$781$	−4.53801	−	3.34932i	−0.162383	−	0.119848i
$782$	−27.4416	+	27.4416i	−0.981309	+	0.981309i
$783$		0			0
$784$	−9.38371	−	3.04895i	−0.335133	−	0.108891i
$785$	29.0072	+	20.6963i	1.03531	+	0.738682i
$786$		0			0
$787$	47.3293	+	7.49622i	1.68711	+	0.267211i	0.924925	−	0.380151i	$-0.124128\pi$
$787$	47.3293	+	7.49622i	1.68711	+	0.267211i	0.762182	+	0.647362i	$0.224128\pi$
$788$	−9.77675	−	4.98150i	−0.348282	−	0.177459i
$789$		0			0
$790$	−0.0464103	−	5.39784i	−0.00165120	−	0.192046i
$791$			10.9171i			0.388166i
$792$		0			0
$793$	−12.8372	−	12.8372i	−0.455861	−	0.455861i
$794$	17.1211	+	12.4392i	0.607604	+	0.441450i
$795$		0			0
$796$	−4.64620	−	14.2995i	−0.164680	−	0.506834i
$797$	1.01261	−	6.39340i	0.0358686	−	0.226466i	−0.963242	−	0.268636i	$-0.913427\pi$
$797$	1.01261	−	6.39340i	0.0358686	−	0.226466i	0.999110	+	0.0421702i	$0.0134272\pi$
$798$		0			0
$799$	−2.30934	−	7.10741i	−0.0816985	−	0.251442i
$800$	−18.4247	+	3.24387i	−0.651411	+	0.114688i
$801$		0			0
$802$	11.4985	+	11.4985i	0.406026	+	0.406026i
$803$	1.69638	−	10.2144i	0.0598639	−	0.360458i
$804$		0			0
$805$	16.8830	−	17.1758i	0.595046	−	0.605367i
$806$	4.67476	−	14.3874i	0.164662	−	0.506776i
$807$		0			0
$808$	−7.80109	−	1.23557i	−0.274442	−	0.0434673i
$809$	−6.35210	+	4.61507i	−0.223328	+	0.162257i	−0.693823	−	0.720145i	$-0.744075\pi$
$809$	−6.35210	+	4.61507i	−0.223328	+	0.162257i	0.470496	+	0.882402i	$0.344075\pi$
$810$		0			0
$811$	10.7006	+	3.47684i	0.375749	+	0.122088i	0.490802	−	0.871271i	$-0.336704\pi$
$811$	10.7006	+	3.47684i	0.375749	+	0.122088i	−0.115053	+	0.993359i	$0.536704\pi$
$812$	1.91925	−	0.303979i	0.0673523	−	0.0106676i
$813$		0			0
$814$	35.1363	+	0.263375i	1.23153	+	0.00923129i
$815$	−6.16691	−	8.33634i	−0.216017	−	0.292009i
$816$		0			0
$817$	1.28198	+	2.51602i	0.0448507	+	0.0880245i
$818$	−15.0904	+	29.6166i	−0.527625	+	1.03552i
$819$		0			0
$820$	−14.7109	+	7.65560i	−0.513727	+	0.267345i
$821$	0.129033	−	0.0419254i	0.00450329	−	0.00146321i	−0.306764	−	0.951785i	$-0.599246\pi$
$821$	0.129033	−	0.0419254i	0.00450329	−	0.00146321i	0.311268	+	0.950322i	$0.399246\pi$
$822$		0			0
$823$	1.96582	+	12.4117i	0.0685243	+	0.432646i	0.997970	+	0.0636865i	$0.0202858\pi$
$823$	1.96582	+	12.4117i	0.0685243	+	0.432646i	−0.929446	+	0.368959i	$0.879714\pi$
$824$	−13.1709			−0.458831
$825$		0			0
$826$	−2.60278			−0.0905622
$827$	−6.55948	−	41.4149i	−0.228096	−	1.44014i	−0.790086	−	0.612995i	$-0.789964\pi$
$827$	−6.55948	−	41.4149i	−0.228096	−	1.44014i	0.561991	−	0.827143i	$-0.310036\pi$
$828$		0			0
$829$	−0.734919	+	0.238790i	−0.0255248	+	0.00829351i	−0.321752	−	0.946824i	$-0.604272\pi$
$829$	−0.734919	+	0.238790i	−0.0255248	+	0.00829351i	0.296227	+	0.955118i	$0.404272\pi$
$830$	16.0078	−	8.33050i	0.555638	−	0.289156i
$831$		0			0
$832$	19.9087	−	39.0730i	0.690209	−	1.35461i
$833$	10.2190	+	20.0560i	0.354069	+	0.694900i
$834$		0			0
$835$	8.54784	+	11.5549i	0.295810	+	0.399873i
$836$	−11.7945	+	3.73478i	−0.407923	+	0.129170i
$837$		0			0
$838$	27.0887	−	4.29043i	0.935764	−	0.148210i
$839$	30.3509	+	9.86162i	1.04783	+	0.340461i	0.781817	−	0.623508i	$-0.214293\pi$
$839$	30.3509	+	9.86162i	1.04783	+	0.340461i	0.266014	+	0.963969i	$0.414293\pi$
$840$		0			0
$841$	20.7808	−	15.0981i	0.716578	−	0.520624i
$842$	−18.8808	−	2.99042i	−0.650675	−	0.103057i
$843$		0			0
$844$	−1.51602	+	4.66583i	−0.0521835	+	0.160604i
$845$	−21.3125	+	21.6821i	−0.733171	+	0.745888i
$846$		0			0
$847$	2.38239	+	16.6540i	0.0818599	+	0.572237i
$848$	−16.7791	−	16.7791i	−0.576198	−	0.576198i
$849$		0			0
$850$	−22.5663	−	15.8097i	−0.774017	−	0.542270i
$851$	20.2053	+	62.1854i	0.692627	+	2.13169i
$852$		0			0
$853$	−3.38848	+	21.3940i	−0.116019	+	0.732517i	0.859260	+	0.511540i	$0.170925\pi$
$853$	−3.38848	+	21.3940i	−0.116019	+	0.732517i	−0.975279	+	0.220977i	$0.929075\pi$
$854$	−1.89840	−	5.84267i	−0.0649619	−	0.199932i
$855$		0			0
$856$	−25.1483	−	18.2713i	−0.859551	−	0.624500i
$857$	−20.0724	−	20.0724i	−0.685660	−	0.685660i	0.275610	−	0.961270i	$-0.411120\pi$
$857$	−20.0724	−	20.0724i	−0.685660	−	0.685660i	−0.961270	+	0.275610i	$0.911120\pi$
$858$		0			0
$859$			42.2029i			1.43994i	0.694003	+	0.719972i	$0.255846\pi$
$859$			42.2029i			1.43994i	−0.694003	+	0.719972i	$0.744154\pi$
$860$	−0.00708989	−	0.824603i	−0.000241763	−	0.0281187i
$861$		0			0
$862$	−28.2021	−	14.3697i	−0.960568	−	0.489434i
$863$	−4.31065	−	0.682739i	−0.146736	−	0.0232407i	0.0826342	−	0.996580i	$-0.473667\pi$
$863$	−4.31065	−	0.682739i	−0.146736	−	0.0232407i	−0.229370	+	0.973339i	$0.573667\pi$
$864$		0			0
$865$	−3.48320	−	2.48522i	−0.118432	−	0.0845000i
$866$	31.0554	+	10.0905i	1.05531	+	0.342890i
$867$		0			0
$868$	−1.94045	+	1.94045i	−0.0658630	+	0.0658630i
$869$	−2.21826	+	6.65690i	−0.0752493	+	0.225820i
$870$		0			0
$871$	−0.693074	+	0.953935i	−0.0234839	+	0.0323229i
$872$	−22.3475	−	43.8595i	−0.756782	−	1.48527i
$873$		0			0
$874$	25.2433	+	34.7444i	0.853866	+	1.17525i
$875$	14.0883	+	9.69062i	0.476270	+	0.327603i
$876$		0			0
$877$	40.6149	−	20.6943i	1.37147	−	0.698797i	0.395858	−	0.918312i	$-0.370447\pi$
$877$	40.6149	−	20.6943i	1.37147	−	0.698797i	0.975609	+	0.219514i	$0.0704473\pi$
$878$	−4.54831	−	28.7169i	−0.153498	−	0.969149i
$879$		0			0
$880$	−15.5087	−	2.43882i	−0.522798	−	0.0822125i
$881$	4.08780			0.137721			0.0688607	−	0.997626i	$-0.478064\pi$
$881$	4.08780			0.137721			0.0688607	+	0.997626i	$0.478064\pi$
$882$		0			0
$883$	0.352882	−	0.179803i	0.0118754	−	0.00605084i	−0.448043	−	0.894012i	$-0.647879\pi$
$883$	0.352882	−	0.179803i	0.0118754	−	0.00605084i	0.459918	+	0.887961i	$0.347879\pi$
$884$	−16.5330	+	5.37189i	−0.556064	+	0.180676i
$885$		0			0
$886$	−11.9906	−	16.5037i	−0.402833	−	0.554452i
$887$	−10.7322	+	21.0632i	−0.360353	+	0.707233i	−0.998008	−	0.0630894i	$-0.979905\pi$
$887$	−10.7322	+	21.0632i	−0.360353	+	0.707233i	0.637655	+	0.770322i	$0.279905\pi$
$888$		0			0
$889$	0.865239	−	1.19090i	0.0290192	−	0.0399415i
$890$	22.7413	−	16.8232i	0.762291	−	0.563913i
$891$		0			0
$892$	8.36520	−	8.36520i	0.280088	−	0.280088i
$893$	−8.16822	+	1.29372i	−0.273339	+	0.0432927i
$894$		0			0
$895$	−17.6192	+	2.94610i	−0.588944	+	0.0984774i
$896$	2.74619	−	1.99523i	0.0917438	−	0.0666558i
$897$		0			0
$898$	−5.01008	−	2.55277i	−0.167189	−	0.0851869i
$899$	1.44606	−	4.45050i	0.0482286	−	0.148432i
$900$		0			0
$901$			54.1352i			1.80351i
$902$	−39.7638	+	5.99279i	−1.32399	+	0.199538i
$903$		0			0
$904$	17.7782	+	12.9166i	0.591293	+	0.429600i
$905$	10.8111	−	21.6767i	0.359373	−	0.720558i
$906$		0			0
$907$	−3.25040	+	20.5222i	−0.107928	+	0.681429i	0.873097	+	0.487547i	$0.162108\pi$
$907$	−3.25040	+	20.5222i	−0.107928	+	0.681429i	−0.981025	+	0.193883i	$0.937892\pi$
$908$	−1.50011	+	9.47133i	−0.0497829	+	0.314317i
$909$		0			0
$910$	−19.0857	+	6.38324i	−0.632684	+	0.211602i
$911$	−31.2914	−	22.7346i	−1.03673	−	0.753229i	−0.0670864	−	0.997747i	$-0.521370\pi$
$911$	−31.2914	−	22.7346i	−1.03673	−	0.753229i	−0.969645	+	0.244518i	$0.921370\pi$
$912$		0			0
$913$	−23.1952	+	3.49574i	−0.767648	+	0.115692i
$914$			4.08940i			0.135265i
$915$		0			0
$916$	−4.46396	+	13.7387i	−0.147493	+	0.453938i
$917$	9.42079	+	4.80013i	0.311102	+	0.158514i
$918$		0			0
$919$	12.4240	−	9.02653i	0.409828	−	0.297758i	−0.363704	−	0.931515i	$-0.618488\pi$
$919$	12.4240	−	9.02653i	0.409828	−	0.297758i	0.773532	+	0.633757i	$0.218488\pi$
$920$	−7.99517	−	47.8151i	−0.263593	−	1.57642i
$921$		0			0
$922$	−7.28284	+	1.15349i	−0.239847	+	0.0379881i
$923$	−6.20146	+	6.20146i	−0.204123	+	0.204123i
$924$		0			0
$925$	−40.9945	+	21.7836i	−1.34789	+	0.716241i
$926$	8.24557	−	11.3490i	0.270966	−	0.372953i
$927$		0			0
$928$	3.09210	−	6.06859i	0.101503	−	0.199211i
$929$	30.4150	+	41.8626i	0.997882	+	1.37347i	0.926616	+	0.376010i	$0.122704\pi$
$929$	30.4150	+	41.8626i	0.997882	+	1.37347i	0.0712667	+	0.997457i	$0.477296\pi$
$930$		0			0
$931$	23.6904	−	7.69748i	0.776422	−	0.252275i
$932$	−10.3767	+	5.28719i	−0.339900	+	0.173188i
$933$		0			0
$934$	−35.5736			−1.16400
$935$	21.0839	+	28.9524i	0.689518	+	0.946844i
$936$		0			0
$937$	−2.22128	−	14.0246i	−0.0725659	−	0.458163i	−0.997038	−	0.0769129i	$-0.975494\pi$
$937$	−2.22128	−	14.0246i	−0.0725659	−	0.458163i	0.924472	−	0.381250i	$-0.124506\pi$
$938$	−0.355519	+	0.181146i	−0.0116081	+	0.00591463i
$939$		0			0
$940$	2.30323	+	0.726531i	0.0751230	+	0.0236968i
$941$	1.00940	+	1.38932i	0.0329054	+	0.0452904i	0.825153	−	0.564910i	$-0.191089\pi$
$941$	1.00940	+	1.38932i	0.0329054	+	0.0452904i	−0.792247	+	0.610200i	$0.791089\pi$
$942$		0			0
$943$	−33.9723	−	66.6745i	−1.10629	−	2.17122i
$944$	−1.85575	+	2.55422i	−0.0603995	+	0.0831328i
$945$		0			0
$946$	0.632149	−	1.89705i	0.0205529	−	0.0616785i
$947$	−36.4494	+	36.4494i	−1.18444	+	1.18444i	−0.205864	+	0.978581i	$0.566001\pi$
$947$	−36.4494	+	36.4494i	−1.18444	+	1.18444i	−0.978581	+	0.205864i	$0.933999\pi$
$948$		0			0
$949$	−15.3124	−	4.97530i	−0.497061	−	0.161505i
$950$	−21.1867	+	21.9282i	−0.687387	+	0.711443i
$951$		0			0
$952$	−22.4587	−	3.55711i	−0.727892	−	0.115287i
$953$	28.7053	+	14.6261i	0.929856	+	0.473785i	0.852213	−	0.523196i	$-0.175260\pi$
$953$	28.7053	+	14.6261i	0.929856	+	0.473785i	0.0776436	+	0.996981i	$0.475260\pi$
$954$		0			0
$955$	24.3140	+	23.8994i	0.786782	+	0.773368i
$956$			0.978139i			0.0316353i
$957$		0			0
$958$	28.7892	+	28.7892i	0.930137	+	0.930137i
$959$	0.877908	+	0.637837i	0.0283491	+	0.0205968i
$960$		0			0
$961$	−7.53736	−	23.1976i	−0.243141	−	0.748310i
$962$	8.54706	−	53.9640i	0.275568	−	1.73987i
$963$		0			0
$964$	−0.257002	−	0.790971i	−0.00827748	−	0.0254755i
$965$	−8.48823	−	25.3795i	−0.273246	−	0.816996i
$966$		0			0
$967$	−42.0426	−	42.0426i	−1.35200	−	1.35200i	−0.883424	−	0.468574i	$-0.844768\pi$
$967$	−42.0426	−	42.0426i	−1.35200	−	1.35200i	−0.468574	−	0.883424i	$-0.655232\pi$
$968$	29.9393	+	15.8246i	0.962286	+	0.508622i
$969$		0			0
$970$	33.2437	+	32.6769i	1.06739	+	1.04919i
$971$	−11.6094	+	35.7301i	−0.372564	+	1.14664i	0.572543	+	0.819875i	$0.305957\pi$
$971$	−11.6094	+	35.7301i	−0.372564	+	1.14664i	−0.945107	+	0.326760i	$0.894043\pi$
$972$		0			0
$973$	15.8281	+	2.50693i	0.507427	+	0.0803685i
$974$	13.6385	−	9.90892i	0.437004	−	0.317502i
$975$		0			0
$976$	−7.08722	−	2.30278i	−0.226856	−	0.0737101i
$977$	56.0810	−	8.88236i	1.79419	−	0.284172i	0.831648	−	0.555303i	$-0.187398\pi$
$977$	56.0810	−	8.88236i	1.79419	−	0.284172i	0.962542	+	0.271132i	$0.0873979\pi$
$978$		0			0
$979$	−35.0548	+	11.1002i	−1.12036	+	0.354764i
$980$	−7.19430	−	1.07614i	−0.229813	−	0.0343761i
$981$		0			0
$982$	−16.7622	−	32.8977i	−0.534904	−	1.04981i
$983$	−11.8357	+	23.2288i	−0.377500	+	0.740885i	−0.999099	−	0.0424509i	$-0.986483\pi$
$983$	−11.8357	+	23.2288i	−0.377500	+	0.740885i	0.621599	+	0.783336i	$0.286483\pi$
$984$		0			0
$985$	33.5245	+	10.5750i	1.06818	+	0.336947i
$986$	9.54022	−	3.09980i	0.303822	−	0.0987179i
$987$		0			0
$988$	3.00940	+	19.0006i	0.0957418	+	0.604490i
$989$	3.72099			0.118320
$990$		0			0
$991$	20.4321			0.649046			0.324523	−	0.945878i	$-0.394796\pi$
$991$	20.4321			0.649046			0.324523	+	0.945878i	$0.394796\pi$
$992$	1.50468	+	9.50021i	0.0477738	+	0.301632i
$993$		0			0
$994$	−2.82251	+	0.917091i	−0.0895247	+	0.0290883i
$995$	22.2362	+	42.7288i	0.704935	+	1.35459i
$996$		0			0
$997$	−9.76731	+	19.1694i	−0.309334	+	0.607102i	−0.992372	−	0.123281i	$-0.960658\pi$
$997$	−9.76731	+	19.1694i	−0.309334	+	0.607102i	0.683038	+	0.730383i	$0.260658\pi$
$998$	12.3510	+	24.2401i	0.390963	+	0.767308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.c.73.5		96
3.2	odd	2		165.2.w.a.73.8	yes	96
5.2	odd	4	inner	495.2.bj.c.172.8		96
11.8	odd	10	inner	495.2.bj.c.118.8		96
15.2	even	4		165.2.w.a.7.5	✓	96
15.8	even	4		825.2.cw.b.7.8		96
15.14	odd	2		825.2.cw.b.568.5		96
33.8	even	10		165.2.w.a.118.5	yes	96
55.52	even	20	inner	495.2.bj.c.217.5		96
165.8	odd	20		825.2.cw.b.382.5		96
165.74	even	10		825.2.cw.b.118.8		96
165.107	odd	20		165.2.w.a.52.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.w.a.7.5	✓	96	15.2	even	4
165.2.w.a.52.8	yes	96	165.107	odd	20
165.2.w.a.73.8	yes	96	3.2	odd	2
165.2.w.a.118.5	yes	96	33.8	even	10
495.2.bj.c.73.5		96	1.1	even	1	trivial
495.2.bj.c.118.8		96	11.8	odd	10	inner
495.2.bj.c.172.8		96	5.2	odd	4	inner
495.2.bj.c.217.5		96	55.52	even	20	inner
825.2.cw.b.7.8		96	15.8	even	4
825.2.cw.b.118.8		96	165.74	even	10
825.2.cw.b.382.5		96	165.8	odd	20
825.2.cw.b.568.5		96	15.14	odd	2

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.178502 - 1.12702i) q^{2} +(0.663811 - 0.215685i) q^{4} +(-1.98355 + 1.03225i) q^{5} +(0.694338 - 1.36271i) q^{7} +(-1.39764 - 2.74302i) q^{8} +O(q^{10})\)	\(q+(-0.178502 - 1.12702i) q^{2} +(0.663811 - 0.215685i) q^{4} +(-1.98355 + 1.03225i) q^{5} +(0.694338 - 1.36271i) q^{7} +(-1.39764 - 2.74302i) q^{8} +(1.51742 + 2.05123i) q^{10} +(-1.00122 - 3.16189i) q^{11} +(-5.09369 + 0.806762i) q^{13} +(-1.65974 - 0.539283i) q^{14} +(-1.71260 + 1.24428i) q^{16} +(4.76995 + 0.755485i) q^{17} +(1.65150 - 5.08279i) q^{19} +(-1.09406 + 1.11304i) q^{20} +(-3.38478 + 1.69280i) q^{22} +(-4.97973 - 4.97973i) q^{23} +(2.86894 - 4.09502i) q^{25} +(1.81847 + 5.59667i) q^{26} +(0.166992 - 1.05434i) q^{28} +(0.562510 + 1.73123i) q^{29} +(-2.07975 - 1.51103i) q^{31} +(-2.64572 - 2.64572i) q^{32} -5.51066i q^{34} +(0.0294027 + 3.41974i) q^{35} +(-8.27261 - 4.21510i) q^{37} +(-6.02318 - 0.953978i) q^{38} +(5.60375 + 3.99821i) q^{40} +(10.1057 + 3.28353i) q^{41} +(-0.373613 + 0.373613i) q^{43} +(-1.34660 - 1.88295i) q^{44} +(-4.72334 + 6.50112i) q^{46} +(-0.702519 - 1.37877i) q^{47} +(2.73961 + 3.77075i) q^{49} +(-5.12726 - 2.50237i) q^{50} +(-3.20725 + 1.63417i) q^{52} +(1.75355 + 11.0715i) q^{53} +(5.24982 + 5.23826i) q^{55} -4.70838 q^{56} +(1.85071 - 0.942986i) q^{58} +(1.41843 - 0.460877i) q^{59} +(2.06914 + 2.84793i) q^{61} +(-1.33171 + 2.61364i) q^{62} +(-4.99806 + 6.87923i) q^{64} +(9.27082 - 6.85820i) q^{65} +(0.161671 - 0.161671i) q^{67} +(3.32929 - 0.527308i) q^{68} +(3.84885 - 0.643567i) q^{70} +(1.37579 - 0.999573i) q^{71} +(2.78166 + 1.41733i) q^{73} +(-3.27381 + 10.0758i) q^{74} -3.73022i q^{76} +(-5.00394 - 0.831042i) q^{77} +(-1.71158 - 1.24354i) q^{79} +(2.11263 - 4.23591i) q^{80} +(1.89671 - 11.9753i) q^{82} +(1.10640 - 6.98551i) q^{83} +(-10.2413 + 3.42521i) q^{85} +(0.487759 + 0.354378i) q^{86} +(-7.27378 + 7.16554i) q^{88} -11.0867i q^{89} +(-2.43736 + 7.50142i) q^{91} +(-4.37965 - 2.23155i) q^{92} +(-1.42850 + 1.03786i) q^{94} +(1.97086 + 11.7867i) q^{95} +(18.0446 - 2.85798i) q^{97} +(3.76067 - 3.76067i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{5} - 20 q^{7}+O(q^{10}) \) 96 * q + 8 * q^5 - 20 * q^7	\( 96 q + 8 q^{5} - 20 q^{7} - 8 q^{11} + 8 q^{16} + 20 q^{17} + 60 q^{20} - 32 q^{22} - 32 q^{23} - 32 q^{25} - 60 q^{28} + 16 q^{31} + 8 q^{37} - 56 q^{38} + 120 q^{41} - 200 q^{46} - 60 q^{47} - 80 q^{50} + 40 q^{52} - 36 q^{53} + 80 q^{55} + 80 q^{56} + 44 q^{58} + 40 q^{61} - 80 q^{62} - 48 q^{67} - 80 q^{68} - 92 q^{70} - 32 q^{71} - 60 q^{73} + 24 q^{77} + 80 q^{80} + 32 q^{82} + 200 q^{83} - 80 q^{85} + 80 q^{86} - 144 q^{88} + 56 q^{91} - 20 q^{92} - 60 q^{95} + 32 q^{97}+O(q^{100}) \) 96 * q + 8 * q^5 - 20 * q^7 - 8 * q^11 + 8 * q^16 + 20 * q^17 + 60 * q^20 - 32 * q^22 - 32 * q^23 - 32 * q^25 - 60 * q^28 + 16 * q^31 + 8 * q^37 - 56 * q^38 + 120 * q^41 - 200 * q^46 - 60 * q^47 - 80 * q^50 + 40 * q^52 - 36 * q^53 + 80 * q^55 + 80 * q^56 + 44 * q^58 + 40 * q^61 - 80 * q^62 - 48 * q^67 - 80 * q^68 - 92 * q^70 - 32 * q^71 - 60 * q^73 + 24 * q^77 + 80 * q^80 + 32 * q^82 + 200 * q^83 - 80 * q^85 + 80 * q^86 - 144 * q^88 + 56 * q^91 - 20 * q^92 - 60 * q^95 + 32 * q^97

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