LMFDB - Embedded newform 495.2.bj.b.28.3

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			28.3
Character	$\chi$	$=$	495.28
Dual form			495.2.bj.b.442.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.717635 + 1.40844i) q^{2} +(-0.293128 - 0.403456i) q^{4} +(-2.22726 + 0.198299i) q^{5} +(-1.38435 - 0.219259i) q^{7} +(-2.34393 + 0.371242i) q^{8} +O(q^{10})$	\(q+(-0.717635 + 1.40844i) q^{2} +(-0.293128 - 0.403456i) q^{4} +(-2.22726 + 0.198299i) q^{5} +(-1.38435 - 0.219259i) q^{7} +(-2.34393 + 0.371242i) q^{8} +(1.31907 - 3.27926i) q^{10} +(-2.66778 - 1.97053i) q^{11} +(3.52738 + 1.79729i) q^{13} +(1.30227 - 1.79242i) q^{14} +(1.46743 - 4.51628i) q^{16} +(5.73220 - 2.92070i) q^{17} +(-5.32069 - 3.86571i) q^{19} +(0.732877 + 0.840474i) q^{20} +(4.68985 - 2.34328i) q^{22} +(-1.11787 - 1.11787i) q^{23} +(4.92135 - 0.883328i) q^{25} +(-5.06274 + 3.67830i) q^{26} +(0.317330 + 0.622796i) q^{28} +(-5.95846 + 4.32907i) q^{29} +(-3.32844 - 10.2439i) q^{31} +(1.95169 + 1.95169i) q^{32} +10.1694i q^{34} +(3.12678 + 0.213832i) q^{35} +(0.0713104 - 0.450236i) q^{37} +(9.26293 - 4.71970i) q^{38} +(5.14692 - 1.29165i) q^{40} +(6.01541 - 8.27950i) q^{41} +(-6.93289 + 6.93289i) q^{43} +(-0.0130212 + 1.65395i) q^{44} +(2.37667 - 0.772228i) q^{46} +(-3.74738 + 0.593527i) q^{47} +(-4.78905 - 1.55606i) q^{49} +(-2.28763 + 7.56533i) q^{50} +(-0.308846 - 1.94998i) q^{52} +(-0.248980 + 0.488651i) q^{53} +(6.33258 + 3.85985i) q^{55} +3.32622 q^{56} +(-1.82123 - 11.4988i) q^{58} +(3.38411 + 4.65783i) q^{59} +(-5.32421 - 1.72994i) q^{61} +(16.8165 + 2.66347i) q^{62} +(4.88313 - 1.58662i) q^{64} +(-8.21278 - 3.30355i) q^{65} +(1.40496 - 1.40496i) q^{67} +(-2.85864 - 1.45655i) q^{68} +(-2.54506 + 4.25043i) q^{70} +(1.21832 - 3.74960i) q^{71} +(-2.11527 + 13.3553i) q^{73} +(0.582955 + 0.423542i) q^{74} +3.27981i q^{76} +(3.26108 + 3.31283i) q^{77} +(1.07007 + 3.29335i) q^{79} +(-2.37277 + 10.3499i) q^{80} +(7.34430 + 14.4140i) q^{82} +(-2.33282 - 4.57841i) q^{83} +(-12.1879 + 7.64184i) q^{85} +(-4.78926 - 14.7398i) q^{86} +(6.98462 + 3.62839i) q^{88} -7.54227i q^{89} +(-4.48905 - 3.26149i) q^{91} +(-0.123332 + 0.778690i) q^{92} +(1.85331 - 5.70389i) q^{94} +(12.6171 + 7.55484i) q^{95} +(-2.39124 - 1.21840i) q^{97} +(5.62840 - 5.62840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 20 q^{7}+O(q^{10}) $ 96 * q + 20 * q^7	$ 96 q + 20 q^{7} + 40 q^{16} + 8 q^{22} - 16 q^{25} - 60 q^{28} + 16 q^{31} - 40 q^{37} + 280 q^{46} + 40 q^{52} + 24 q^{55} - 68 q^{58} + 40 q^{61} + 16 q^{67} + 52 q^{70} - 60 q^{73} - 112 q^{82} + 80 q^{85} + 24 q^{88} - 56 q^{91} - 112 q^{97}+O(q^{100}) $ 96 * q + 20 * q^7 + 40 * q^16 + 8 * q^22 - 16 * q^25 - 60 * q^28 + 16 * q^31 - 40 * q^37 + 280 * q^46 + 40 * q^52 + 24 * q^55 - 68 * q^58 + 40 * q^61 + 16 * q^67 + 52 * q^70 - 60 * q^73 - 112 * q^82 + 80 * q^85 + 24 * q^88 - 56 * q^91 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.717635	+	1.40844i	−0.507445	+	0.995916i	0.485149	+	0.874432i	$0.338766\pi$
$2$	−0.717635	+	1.40844i	−0.507445	+	0.995916i	−0.992593	+	0.121485i	$0.961234\pi$
$3$		0			0
$3$		0			0
$4$	−0.293128	−	0.403456i	−0.146564	−	0.201728i
$5$	−2.22726	+	0.198299i	−0.996060	+	0.0886822i
$5$	−2.22726	+	0.198299i	−0.996060	+	0.0886822i
$6$		0			0
$7$	−1.38435	−	0.219259i	−0.523235	−	0.0828723i	−0.110771	−	0.993846i	$-0.535332\pi$
$7$	−1.38435	−	0.219259i	−0.523235	−	0.0828723i	−0.412464	+	0.910974i	$0.635332\pi$
$8$	−2.34393	+	0.371242i	−0.828704	+	0.131254i
$9$		0			0
$10$	1.31907	−	3.27926i	0.417125	−	1.03699i
$11$	−2.66778	−	1.97053i	−0.804365	−	0.594136i
$11$	−2.66778	−	1.97053i	−0.804365	−	0.594136i
$12$		0			0
$13$	3.52738	+	1.79729i	0.978319	+	0.498478i	0.868616	−	0.495486i	$-0.165010\pi$
$13$	3.52738	+	1.79729i	0.978319	+	0.498478i	0.109703	+	0.993964i	$0.465010\pi$
$14$	1.30227	−	1.79242i	0.348047	−	0.479045i
$15$		0			0
$16$	1.46743	−	4.51628i	0.366857	−	1.12907i
$17$	5.73220	−	2.92070i	1.39026	−	0.708374i	0.411126	−	0.911579i	$-0.365136\pi$
$17$	5.73220	−	2.92070i	1.39026	−	0.708374i	0.979136	+	0.203205i	$0.0651358\pi$
$18$		0			0
$19$	−5.32069	−	3.86571i	−1.22065	−	0.886854i	−0.224496	−	0.974475i	$-0.572074\pi$
$19$	−5.32069	−	3.86571i	−1.22065	−	0.886854i	−0.996154	+	0.0876204i	$0.972074\pi$
$20$	0.732877	+	0.840474i	0.163876	+	0.187936i
$21$		0			0
$22$	4.68985	−	2.34328i	0.999880	−	0.499589i
$23$	−1.11787	−	1.11787i	−0.233092	−	0.233092i	0.580890	−	0.813982i	$-0.302705\pi$
$23$	−1.11787	−	1.11787i	−0.233092	−	0.233092i	−0.813982	+	0.580890i	$0.802705\pi$
$24$		0			0
$25$	4.92135	−	0.883328i	0.984271	−	0.176666i
$26$	−5.06274	+	3.67830i	−0.992885	+	0.721373i
$27$		0			0
$28$	0.317330	+	0.622796i	0.0599698	+	0.117697i
$29$	−5.95846	+	4.32907i	−1.10646	+	0.803889i	−0.982102	−	0.188349i	$-0.939686\pi$
$29$	−5.95846	+	4.32907i	−1.10646	+	0.803889i	−0.124356	+	0.992238i	$0.539686\pi$
$30$		0			0
$31$	−3.32844	−	10.2439i	−0.597805	−	1.83986i	−0.540234	−	0.841515i	$-0.681664\pi$
$31$	−3.32844	−	10.2439i	−0.597805	−	1.83986i	−0.0575711	−	0.998341i	$-0.518336\pi$
$32$	1.95169	+	1.95169i	0.345013	+	0.345013i
$33$		0			0
$34$			10.1694i			1.74405i
$35$	3.12678	+	0.213832i	0.528523	+	0.0361442i
$36$		0			0
$37$	0.0713104	−	0.450236i	0.0117234	−	0.0740184i	−0.981133	−	0.193334i	$-0.938070\pi$
$37$	0.0713104	−	0.450236i	0.0117234	−	0.0740184i	0.992856	+	0.119315i	$0.0380700\pi$
$38$	9.26293	−	4.71970i	1.50265	−	0.765636i
$39$		0			0
$40$	5.14692	−	1.29165i	0.813799	−	0.204228i
$41$	6.01541	−	8.27950i	0.939449	−	1.29304i	−0.0166085	−	0.999862i	$-0.505287\pi$
$41$	6.01541	−	8.27950i	0.939449	−	1.29304i	0.956058	−	0.293179i	$-0.0947131\pi$
$42$		0			0
$43$	−6.93289	+	6.93289i	−1.05726	+	1.05726i	−0.0589971	+	0.998258i	$0.518790\pi$
$43$	−6.93289	+	6.93289i	−1.05726	+	1.05726i	−0.998258	+	0.0589971i	$0.981210\pi$
$44$	−0.0130212	+	1.65395i	−0.00196301	+	0.249342i
$45$		0			0
$46$	2.37667	−	0.772228i	0.350421	−	0.113859i
$47$	−3.74738	+	0.593527i	−0.546612	+	0.0865748i	−0.423632	−	0.905834i	$-0.639245\pi$
$47$	−3.74738	+	0.593527i	−0.546612	+	0.0865748i	−0.122980	+	0.992409i	$0.539245\pi$
$48$		0			0
$49$	−4.78905	−	1.55606i	−0.684149	−	0.222294i
$50$	−2.28763	+	7.56533i	−0.323519	+	1.06990i
$51$		0			0
$52$	−0.308846	−	1.94998i	−0.0428293	−	0.270413i
$53$	−0.248980	+	0.488651i	−0.0342001	+	0.0671214i	−0.907474	−	0.420108i	$-0.861992\pi$
$53$	−0.248980	+	0.488651i	−0.0342001	+	0.0671214i	0.873274	+	0.487229i	$0.161992\pi$
$54$		0			0
$55$	6.33258	+	3.85985i	0.853885	+	0.520462i
$56$	3.32622			0.444484
$57$		0			0
$58$	−1.82123	−	11.4988i	−0.239140	−	1.50987i
$59$	3.38411	+	4.65783i	0.440573	+	0.606397i	0.970339	−	0.241747i	$-0.0777203\pi$
$59$	3.38411	+	4.65783i	0.440573	+	0.606397i	−0.529766	+	0.848144i	$0.677720\pi$
$60$		0			0
$61$	−5.32421	−	1.72994i	−0.681695	−	0.221496i	−0.0523575	−	0.998628i	$-0.516674\pi$
$61$	−5.32421	−	1.72994i	−0.681695	−	0.221496i	−0.629337	+	0.777132i	$0.716674\pi$
$62$	16.8165	+	2.66347i	2.13570	+	0.338261i
$63$		0			0
$64$	4.88313	−	1.58662i	0.610391	−	0.198328i
$65$	−8.21278	−	3.30355i	−1.01867	−	0.409755i
$66$		0			0
$67$	1.40496	−	1.40496i	0.171644	−	0.171644i	−0.616057	−	0.787701i	$-0.711271\pi$
$67$	1.40496	−	1.40496i	0.171644	−	0.171644i	0.787701	+	0.616057i	$0.211271\pi$
$68$	−2.85864	−	1.45655i	−0.346661	−	0.176633i
$69$		0			0
$70$	−2.54506	+	4.25043i	−0.304193	+	0.508023i
$71$	1.21832	−	3.74960i	0.144588	−	0.444995i	−0.852370	−	0.522939i	$-0.824836\pi$
$71$	1.21832	−	3.74960i	0.144588	−	0.444995i	0.996958	+	0.0779439i	$0.0248355\pi$
$72$		0			0
$73$	−2.11527	+	13.3553i	−0.247573	+	1.56312i	0.480113	+	0.877207i	$0.340596\pi$
$73$	−2.11527	+	13.3553i	−0.247573	+	1.56312i	−0.727686	+	0.685910i	$0.759404\pi$
$74$	0.582955	+	0.423542i	0.0677672	+	0.0492357i
$75$		0			0
$76$			3.27981i			0.376221i
$77$	3.26108	+	3.31283i	0.371634	+	0.377532i
$78$		0			0
$79$	1.07007	+	3.29335i	0.120393	+	0.370531i	0.993034	−	0.117832i	$-0.0375944\pi$
$79$	1.07007	+	3.29335i	0.120393	+	0.370531i	−0.872641	+	0.488362i	$0.837594\pi$
$80$	−2.37277	+	10.3499i	−0.265283	+	1.15716i
$81$		0			0
$82$	7.34430	+	14.4140i	0.811042	+	1.59176i
$83$	−2.33282	−	4.57841i	−0.256060	−	0.502546i	0.726812	−	0.686837i	$-0.241001\pi$
$83$	−2.33282	−	4.57841i	−0.256060	−	0.502546i	−0.982872	+	0.184291i	$0.941001\pi$
$84$		0			0
$85$	−12.1879	+	7.64184i	−1.32196	+	0.828874i
$86$	−4.78926	−	14.7398i	−0.516439	−	1.58944i
$87$		0			0
$88$	6.98462	+	3.62839i	0.744563	+	0.386787i
$89$		−	7.54227i		−	0.799479i	−0.916629	−	0.399739i	$-0.869101\pi$
$89$		−	7.54227i		−	0.799479i	0.916629	−	0.399739i	$-0.130899\pi$
$90$		0			0
$91$	−4.48905	−	3.26149i	−0.470581	−	0.341897i
$92$	−0.123332	+	0.778690i	−0.0128583	+	0.0811841i
$93$		0			0
$94$	1.85331	−	5.70389i	0.191154	−	0.588312i
$95$	12.6171	+	7.55484i	1.29449	+	0.775110i
$96$		0			0
$97$	−2.39124	−	1.21840i	−0.242793	−	0.123709i	0.328360	−	0.944553i	$-0.393504\pi$
$97$	−2.39124	−	1.21840i	−0.242793	−	0.123709i	−0.571154	+	0.820843i	$0.693504\pi$
$98$	5.62840	−	5.62840i	0.568554	−	0.568554i
$99$		0			0
$100$	−1.79897	−	1.72662i	−0.179897	−	0.172662i
$101$	−12.4733	+	4.05282i	−1.24114	+	0.403270i	−0.854738	−	0.519060i	$-0.826282\pi$
$101$	−12.4733	+	4.05282i	−1.24114	+	0.403270i	−0.386401	+	0.922331i	$0.626282\pi$
$102$		0			0
$103$	−13.8385	−	2.19180i	−1.36354	−	0.215964i	−0.568583	−	0.822626i	$-0.692508\pi$
$103$	−13.8385	−	2.19180i	−1.36354	−	0.215964i	−0.794960	+	0.606661i	$0.792508\pi$
$104$	−8.93516	−	2.90321i	−0.876164	−	0.284683i
$105$		0			0
$106$	−0.509558	−	0.701347i	−0.0494927	−	0.0681208i
$107$	0.211825	+	1.33741i	0.0204779	+	0.129292i	0.995809	−	0.0914529i	$-0.0291511\pi$
$107$	0.211825	+	1.33741i	0.0204779	+	0.129292i	−0.975332	+	0.220745i	$0.929151\pi$
$108$		0			0
$109$	−4.58833			−0.439482			−0.219741	−	0.975558i	$-0.570521\pi$
$109$	−4.58833			−0.439482			−0.219741	+	0.975558i	$0.570521\pi$
$110$	−9.98085	+	6.14908i	−0.951636	+	0.586292i
$111$		0			0
$112$	−3.02167	+	5.93036i	−0.285521	+	0.560367i
$113$	−2.13331	−	13.4692i	−0.200685	−	1.26707i	−0.858076	−	0.513524i	$-0.828340\pi$
$113$	−2.13331	−	13.4692i	−0.200685	−	1.26707i	0.657391	−	0.753550i	$-0.271660\pi$
$114$		0			0
$115$	2.71146	+	2.26811i	0.252845	+	0.211502i
$116$	3.49318	+	1.13500i	0.324334	+	0.105382i
$117$		0			0
$118$	−8.98882	+	1.42369i	−0.827488	+	0.131061i
$119$	−8.57576	+	2.78643i	−0.786138	+	0.255432i
$120$		0			0
$121$	3.23405	+	10.5138i	0.294005	+	0.955804i
$122$	6.25735	−	6.25735i	0.566514	−	0.566514i
$123$		0			0
$124$	−3.15730	+	4.34565i	−0.283534	+	0.390251i
$125$	−10.7860	+	2.94330i	−0.964726	+	0.263257i
$126$		0			0
$127$	−9.24508	+	4.71060i	−0.820368	+	0.417998i	−0.813206	−	0.581976i	$-0.802280\pi$
$127$	−9.24508	+	4.71060i	−0.820368	+	0.417998i	−0.00716194	+	0.999974i	$0.502280\pi$
$128$	−2.13319	+	13.4684i	−0.188549	+	1.19045i
$129$		0			0
$130$	10.5466	−	9.19645i	0.925000	−	0.806582i
$131$			12.0194i			1.05014i	0.851059	+	0.525070i	$0.175961\pi$
$131$			12.0194i			1.05014i	−0.851059	+	0.525070i	$0.824039\pi$
$132$		0			0
$133$	6.51811	+	6.51811i	0.565191	+	0.565191i
$134$	0.970554	+	2.98706i	0.0838431	+	0.258042i
$135$		0			0
$136$	−12.3516	+	8.97395i	−1.05914	+	0.769510i
$137$	−2.95358	−	5.79672i	−0.252341	−	0.495247i	0.729735	−	0.683730i	$-0.239643\pi$
$137$	−2.95358	−	5.79672i	−0.252341	−	0.495247i	−0.982077	+	0.188482i	$0.939643\pi$
$138$		0			0
$139$	4.01448	−	2.91669i	0.340503	−	0.247390i	−0.404371	−	0.914595i	$-0.632509\pi$
$139$	4.01448	−	2.91669i	0.340503	−	0.247390i	0.744874	+	0.667205i	$0.232509\pi$
$140$	−0.830276	−	1.32420i	−0.0701712	−	0.111915i
$141$		0			0
$142$	4.40677	+	4.40677i	0.369808	+	0.369808i
$143$	−5.86865	−	11.7456i	−0.490761	−	0.982213i
$144$		0			0
$145$	12.4126	−	10.8235i	1.03081	−	0.898844i
$146$	−17.2921	−	12.5634i	−1.43110	−	1.03976i
$147$		0			0
$148$	−0.202554	+	0.103206i	−0.0166498	+	0.00848350i
$149$	−0.957138	+	2.94577i	−0.0784118	+	0.241327i	−0.982577	−	0.185856i	$-0.940494\pi$
$149$	−0.957138	+	2.94577i	−0.0784118	+	0.241327i	0.904165	+	0.427183i	$0.140494\pi$
$150$		0			0
$151$	−4.41152	+	6.07194i	−0.359005	+	0.494127i	−0.949871	−	0.312642i	$-0.898786\pi$
$151$	−4.41152	+	6.07194i	−0.359005	+	0.494127i	0.590867	+	0.806769i	$0.298786\pi$
$152$	13.9064	+	7.08569i	1.12796	+	0.574725i
$153$		0			0
$154$	−7.00619	+	2.21562i	−0.564575	+	0.178540i
$155$	9.44465	+	22.1557i	0.758613	+	1.77959i
$156$		0			0
$157$	10.2353	−	1.62111i	0.816862	−	0.129378i	0.265999	−	0.963973i	$-0.414298\pi$
$157$	10.2353	−	1.62111i	0.816862	−	0.129378i	0.550864	+	0.834595i	$0.314298\pi$
$158$	−5.40640	−	0.856290i	−0.430110	−	0.0681228i
$159$		0			0
$160$	−4.73393	−	3.95989i	−0.374250	−	0.313057i
$161$	1.30242	+	1.79263i	0.102645	+	0.141279i
$162$		0			0
$163$	6.86747	−	13.4782i	0.537902	−	1.05569i	−0.448873	−	0.893595i	$-0.648175\pi$
$163$	6.86747	−	13.4782i	0.537902	−	1.05569i	0.986775	−	0.162096i	$-0.0518255\pi$
$164$	−5.10370			−0.398532
$165$		0			0
$166$	8.12252			0.630430
$167$	−1.50543	+	2.95458i	−0.116494	+	0.228632i	−0.941890	−	0.335922i	$-0.890952\pi$
$167$	−1.50543	+	2.95458i	−0.116494	+	0.228632i	0.825396	+	0.564554i	$0.190952\pi$
$168$		0			0
$169$	1.57094	+	2.16221i	0.120842	+	0.166324i
$170$	−2.01659	−	22.6500i	−0.154666	−	1.73717i
$171$		0			0
$172$	4.82934	+	0.764892i	0.368234	+	0.0583225i
$173$	6.40011	−	1.01368i	0.486591	−	0.0770685i	0.0916816	−	0.995788i	$-0.470776\pi$
$173$	6.40011	−	1.01368i	0.486591	−	0.0770685i	0.394910	+	0.918720i	$0.370776\pi$
$174$		0			0
$175$	−7.00655	+	0.143781i	−0.529646	+	0.0108688i
$176$	−12.8142	+	9.15681i	−0.965908	+	0.690221i
$177$		0			0
$178$	10.6228	+	5.41260i	0.796214	+	0.405691i
$179$	−2.88906	+	3.97646i	−0.215939	+	0.297214i	−0.903221	−	0.429177i	$-0.858804\pi$
$179$	−2.88906	+	3.97646i	−0.215939	+	0.297214i	0.687282	+	0.726391i	$0.258804\pi$
$180$		0			0
$181$	1.42235	−	4.37755i	0.105723	−	0.325381i	−0.884177	−	0.467152i	$-0.845280\pi$
$181$	1.42235	−	4.37755i	0.105723	−	0.325381i	0.989899	+	0.141772i	$0.0452799\pi$
$182$	7.81511	−	3.98200i	0.579294	−	0.295165i
$183$		0			0
$184$	3.03521	+	2.20521i	0.223758	+	0.162570i
$185$	−0.0695451	+	1.01693i	−0.00511306	+	0.0747664i
$186$		0			0
$187$	−21.0475	−	3.50367i	−1.53915	−	0.256214i
$188$	1.33793	+	1.33793i	0.0975782	+	0.0975782i
$189$		0			0
$190$	−19.6950	+	12.3488i	−1.42883	+	0.895877i
$191$	1.39154	−	1.01101i	0.100688	−	0.0731545i	−0.536302	−	0.844026i	$-0.680179\pi$
$191$	1.39154	−	1.01101i	0.100688	−	0.0731545i	0.636990	+	0.770872i	$0.280179\pi$
$192$		0			0
$193$	−8.12375	−	15.9438i	−0.584760	−	1.14766i	−0.974006	−	0.226522i	$-0.927264\pi$
$193$	−8.12375	−	15.9438i	−0.584760	−	1.14766i	0.389246	−	0.921134i	$-0.372736\pi$
$194$	3.43207	−	2.49355i	0.246409	−	0.179026i
$195$		0			0
$196$	0.776004	+	2.38829i	0.0554288	+	0.170592i
$197$	3.46623	+	3.46623i	0.246959	+	0.246959i	0.819721	−	0.572762i	$-0.194128\pi$
$197$	3.46623	+	3.46623i	0.246959	+	0.246959i	−0.572762	+	0.819721i	$0.694128\pi$
$198$		0			0
$199$		−	9.15196i		−	0.648765i	−0.945926	−	0.324383i	$-0.894843\pi$
$199$		−	9.15196i		−	0.648765i	0.945926	−	0.324383i	$-0.105157\pi$
$200$	−11.2074	+	3.89747i	−0.792482	+	0.275593i
$201$		0			0
$202$	3.24313	−	20.4763i	0.228186	−	1.44071i
$203$	9.19778	−	4.68650i	0.645558	−	0.328928i
$204$		0			0
$205$	−11.7560	+	19.6334i	−0.821078	+	1.37126i
$206$	13.0180	−	17.9177i	0.907005	−	1.24839i
$207$		0			0
$208$	13.2932	−	13.2932i	0.921720	−	0.921720i
$209$	6.57693	+	20.7974i	0.454936	+	1.43859i
$210$		0			0
$211$	11.0942	−	3.60472i	0.763755	−	0.248159i	0.0988657	−	0.995101i	$-0.468479\pi$
$211$	11.0942	−	3.60472i	0.763755	−	0.248159i	0.664890	+	0.746942i	$0.268479\pi$
$212$	0.270133	−	0.0427848i	0.0185528	−	0.00293847i
$213$		0			0
$214$	−2.03567	−	0.661430i	−0.139156	−	0.0452144i
$215$	14.0665	−	16.8161i	0.959330	−	1.14685i
$216$		0			0
$217$	2.36166	+	14.9109i	0.160320	+	1.01222i
$218$	3.29274	−	6.46237i	0.223013	−	0.437687i
$219$		0			0
$220$	−0.298975	−	3.68635i	−0.0201569	−	0.248534i
$221$	25.4690			1.71323
$222$		0			0
$223$	0.742757	+	4.68958i	0.0497387	+	0.314038i	0.999997	+	0.00257386i	$0.000819287\pi$
$223$	0.742757	+	4.68958i	0.0497387	+	0.314038i	−0.950258	+	0.311464i	$0.899181\pi$
$224$	−2.27389	−	3.12974i	−0.151931	−	0.209115i
$225$		0			0
$226$	20.5014	+	6.66132i	1.36374	+	0.443105i
$227$	22.2688	+	3.52703i	1.47803	+	0.234097i	0.842800	−	0.538226i	$-0.180905\pi$
$227$	22.2688	+	3.52703i	1.47803	+	0.234097i	0.635230	+	0.772323i	$0.280905\pi$
$228$		0			0
$229$	20.1415	−	6.54438i	1.33099	−	0.432465i	0.444735	−	0.895662i	$-0.353298\pi$
$229$	20.1415	−	6.54438i	1.33099	−	0.432465i	0.886255	+	0.463198i	$0.153298\pi$
$230$	−5.14033	+	2.19124i	−0.338943	+	0.144486i
$231$		0			0
$232$	12.3591	−	12.3591i	0.811413	−	0.811413i
$233$	3.23360	+	1.64760i	0.211840	+	0.107938i	0.556691	−	0.830719i	$-0.312071\pi$
$233$	3.23360	+	1.64760i	0.211840	+	0.107938i	−0.344851	+	0.938657i	$0.612071\pi$
$234$		0			0
$235$	8.22869	−	2.06504i	0.536781	−	0.134708i
$236$	0.887252	−	2.73068i	0.0577552	−	0.177752i
$237$		0			0
$238$	2.22975	−	14.0781i	0.144533	−	0.912545i
$239$	−4.47663	−	3.25246i	−0.289569	−	0.210384i	0.433511	−	0.901148i	$-0.357274\pi$
$239$	−4.47663	−	3.25246i	−0.289569	−	0.210384i	−0.723080	+	0.690764i	$0.757274\pi$
$240$		0			0
$241$			12.3439i			0.795140i	0.917572	+	0.397570i	$0.130146\pi$
$241$			12.3439i			0.795140i	−0.917572	+	0.397570i	$0.869854\pi$
$242$	−17.1290	−	2.99014i	−1.10109	−	0.192214i
$243$		0			0
$244$	0.862720	+	2.65518i	0.0552300	+	0.169980i
$245$	10.9750	+	2.51607i	0.701167	+	0.160746i
$246$		0			0
$247$	−11.8203	−	23.1986i	−0.752107	−	1.47609i
$248$	11.6046	+	22.7753i	0.736892	+	1.44623i
$249$		0			0
$250$	3.59493	−	17.3036i	0.227363	−	1.09437i
$251$	−5.69434	−	17.5254i	−0.359423	−	1.10619i	−0.953400	−	0.301709i	$-0.902443\pi$
$251$	−5.69434	−	17.5254i	−0.359423	−	1.10619i	0.593977	−	0.804482i	$-0.297557\pi$
$252$		0			0
$253$	0.779433	+	5.18501i	0.0490025	+	0.325979i
$254$		−	16.4016i		−	1.02913i
$255$		0			0
$256$	−9.13095	−	6.63402i	−0.570684	−	0.414626i
$257$	−3.94278	+	24.8937i	−0.245944	+	1.55283i	0.487527	+	0.873108i	$0.337899\pi$
$257$	−3.94278	+	24.8937i	−0.245944	+	1.55283i	−0.733471	+	0.679721i	$0.762101\pi$
$258$		0			0
$259$	−0.197437	+	0.607649i	−0.0122681	+	0.0377575i
$260$	1.07456	+	4.28186i	0.0666414	+	0.265550i
$261$		0			0
$262$	−16.9286	−	8.62555i	−1.04585	−	0.532888i
$263$	10.1971	−	10.1971i	0.628780	−	0.628780i	−0.318981	−	0.947761i	$-0.603341\pi$
$263$	10.1971	−	10.1971i	0.628780	−	0.628780i	0.947761	+	0.318981i	$0.103341\pi$
$264$		0			0
$265$	0.457644	−	1.13773i	0.0281129	−	0.0698899i
$266$	−13.8580	+	4.50273i	−0.849687	+	0.276080i
$267$		0			0
$268$	−0.978676	−	0.155007i	−0.0597822	−	0.00946856i
$269$	19.5051	+	6.33760i	1.18925	+	0.386410i	0.835795	−	0.549042i	$-0.185007\pi$
$269$	19.5051	+	6.33760i	1.18925	+	0.386410i	0.353454	+	0.935452i	$0.385007\pi$
$270$		0			0
$271$	−4.70924	−	6.48172i	−0.286066	−	0.393736i	0.641665	−	0.766985i	$-0.278244\pi$
$271$	−4.70924	−	6.48172i	−0.286066	−	0.393736i	−0.927731	+	0.373249i	$0.878244\pi$
$272$	−4.77911	−	30.1741i	−0.289776	−	1.82957i
$273$		0			0
$274$	10.2839			0.621274
$275$	−14.8697	−	7.34114i	−0.896676	−	0.442687i
$276$		0			0
$277$	−2.29466	+	4.50352i	−0.137873	+	0.270590i	−0.949611	−	0.313431i	$-0.898522\pi$
$277$	−2.29466	+	4.50352i	−0.137873	+	0.270590i	0.811738	+	0.584021i	$0.198522\pi$
$278$	1.22705	+	7.74726i	0.0735933	+	0.464650i
$279$		0			0
$280$	−7.40834	+	0.659587i	−0.442733	+	0.0394178i
$281$	1.90584	+	0.619245i	0.113693	+	0.0369410i	0.365311	−	0.930886i	$-0.380963\pi$
$281$	1.90584	+	0.619245i	0.113693	+	0.0369410i	−0.251618	+	0.967827i	$0.580963\pi$
$282$		0			0
$283$	19.7406	−	3.12661i	1.17346	−	0.185857i	0.460888	−	0.887459i	$-0.347531\pi$
$283$	19.7406	−	3.12661i	1.17346	−	0.185857i	0.712570	+	0.701601i	$0.247531\pi$
$284$	−1.86992	+	0.607574i	−0.110959	+	0.0360529i
$285$		0			0
$286$	20.7544	+	0.163395i	1.22724	+	0.00966176i
$287$	−10.1428	+	10.1428i	−0.598710	+	0.598710i
$288$		0			0
$289$	14.3352	−	19.7308i	0.843249	−	1.16063i
$290$	6.33656	+	25.2497i	0.372096	+	1.48271i
$291$		0			0
$292$	6.00832	−	3.06139i	0.351610	−	0.179154i
$293$	−1.99657	+	12.6058i	−0.116641	+	0.736440i	0.858163	+	0.513377i	$0.171606\pi$
$293$	−1.99657	+	12.6058i	−0.116641	+	0.736440i	−0.974804	+	0.223063i	$0.928394\pi$
$294$		0			0
$295$	−8.46093	−	9.70311i	−0.492614	−	0.564937i
$296$			1.08180i			0.0628781i
$297$		0			0
$298$	−3.46206	−	3.46206i	−0.200552	−	0.200552i
$299$	−1.93401	−	5.95228i	−0.111847	−	0.344229i
$300$		0			0
$301$	11.1176	−	8.07744i	0.640810	−	0.465576i
$302$	−5.38609	−	10.5708i	−0.309935	−	0.608281i
$303$		0			0
$304$	−25.2664	+	18.3571i	−1.44912	+	1.05285i
$305$	12.2014	+	2.79723i	0.698651	+	0.160169i
$306$		0			0
$307$	−17.2702	−	17.2702i	−0.985663	−	0.985663i	0.0142355	−	0.999899i	$-0.495469\pi$
$307$	−17.2702	−	17.2702i	−0.985663	−	0.985663i	−0.999899	+	0.0142355i	$0.995469\pi$
$308$	0.380669	−	2.28679i	0.0216907	−	0.130302i
$309$		0			0
$310$	−37.9828	−	2.59754i	−2.15728	−	0.147530i
$311$	−1.75637	−	1.27607i	−0.0995944	−	0.0723595i	0.536874	−	0.843663i	$-0.319605\pi$
$311$	−1.75637	−	1.27607i	−0.0995944	−	0.0723595i	−0.636468	+	0.771303i	$0.719605\pi$
$312$		0			0
$313$	10.6777	−	5.44055i	0.603539	−	0.307518i	−0.125391	−	0.992107i	$-0.540018\pi$
$313$	10.6777	−	5.44055i	0.603539	−	0.307518i	0.728929	+	0.684589i	$0.240018\pi$
$314$	−5.06195	+	15.5791i	−0.285663	+	0.879179i
$315$		0			0
$316$	1.01505	−	1.39710i	0.0571012	−	0.0785931i
$317$	−17.8487	−	9.09439i	−1.00249	−	0.510792i	−0.125902	−	0.992043i	$-0.540183\pi$
$317$	−17.8487	−	9.09439i	−1.00249	−	0.510792i	−0.876583	+	0.481251i	$0.840183\pi$
$318$		0			0
$319$	24.4264	+	0.192303i	1.36761	+	0.0107669i
$320$	−10.5614	+	4.50214i	−0.590398	+	0.251677i
$321$		0			0
$322$	−3.45946	+	0.547925i	−0.192788	+	0.0305347i
$323$	−41.7898	−	6.61886i	−2.32525	−	0.368283i
$324$		0			0
$325$	18.9471	+	5.72927i	1.05099	+	0.317802i
$326$	14.0548	+	19.3448i	0.778425	+	1.07141i
$327$		0			0
$328$	−11.0260	+	21.6397i	−0.608809	+	1.19485i
$329$	5.31782			0.293181
$330$		0			0
$331$	−17.2147			−0.946208			−0.473104	−	0.881007i	$-0.656866\pi$
$331$	−17.2147			−0.946208			−0.473104	+	0.881007i	$0.656866\pi$
$332$	−1.16337	+	2.28325i	−0.0638485	+	0.125310i
$333$		0			0
$334$	−3.08099	−	4.24062i	−0.168584	−	0.232036i
$335$	−2.85061	+	3.40782i	−0.155746	+	0.186189i
$336$		0			0
$337$	14.4414	+	2.28729i	0.786673	+	0.124597i	0.536831	−	0.843690i	$-0.319621\pi$
$337$	14.4414	+	2.28729i	0.786673	+	0.124597i	0.249842	+	0.968287i	$0.419621\pi$
$338$	−4.17271	+	0.660892i	−0.226965	+	0.0359478i
$339$		0			0
$340$	6.65577	+	2.67725i	0.360960	+	0.145194i
$341$	−11.3063	+	33.8872i	−0.612271	+	1.83509i
$342$		0			0
$343$	15.0304	+	7.65838i	0.811566	+	0.413514i
$344$	13.6764	−	18.8240i	0.737383	−	1.01492i
$345$		0			0
$346$	−3.16524	+	9.74161i	−0.170164	+	0.523712i
$347$	7.54128	−	3.84247i	0.404837	−	0.206275i	−0.239701	−	0.970847i	$-0.577050\pi$
$347$	7.54128	−	3.84247i	0.404837	−	0.206275i	0.644538	+	0.764572i	$0.277050\pi$
$348$		0			0
$349$	13.6359	+	9.90704i	0.729911	+	0.530312i	0.889535	−	0.456866i	$-0.151028\pi$
$349$	13.6359	+	9.90704i	0.729911	+	0.530312i	−0.159624	+	0.987178i	$0.551028\pi$
$350$	4.82564	−	9.97148i	0.257942	−	0.532998i
$351$		0			0
$352$	−1.36081	−	9.05251i	−0.0725315	−	0.482501i
$353$	−19.3999	−	19.3999i	−1.03255	−	1.03255i	−0.999452	−	0.0330995i	$-0.989462\pi$
$353$	−19.3999	−	19.3999i	−1.03255	−	1.03255i	−0.0330995	−	0.999452i	$-0.510538\pi$
$354$		0			0
$355$	−1.96996	+	8.59291i	−0.104555	+	0.456064i
$356$	−3.04297	+	2.21085i	−0.161277	+	0.117175i
$357$		0			0
$358$	−3.52730	−	6.92271i	−0.186424	−	0.365877i
$359$	−10.2947	+	7.47952i	−0.543332	+	0.394754i	−0.825321	−	0.564664i	$-0.809006\pi$
$359$	−10.2947	+	7.47952i	−0.543332	+	0.394754i	0.281989	+	0.959418i	$0.409006\pi$
$360$		0			0
$361$	7.49473	+	23.0664i	0.394460	+	1.21402i
$362$	5.14478	+	5.14478i	0.270404	+	0.270404i
$363$		0			0
$364$			2.76717i			0.145039i
$365$	2.06290	−	30.1651i	0.107977	−	1.57891i
$366$		0			0
$367$	−5.61634	+	35.4602i	−0.293171	+	1.85101i	0.198337	+	0.980134i	$0.436446\pi$
$367$	−5.61634	+	35.4602i	−0.293171	+	1.85101i	−0.491508	+	0.870873i	$0.663554\pi$
$368$	−6.68900	+	3.40822i	−0.348688	+	0.177666i
$369$		0			0
$370$	−1.38238	−	0.827737i	−0.0718665	−	0.0430320i
$371$	0.451817	−	0.621873i	0.0234572	−	0.0322860i
$372$		0			0
$373$	−9.14793	+	9.14793i	−0.473662	+	0.473662i	−0.903097	−	0.429436i	$-0.858713\pi$
$373$	−9.14793	+	9.14793i	−0.473662	+	0.473662i	0.429436	+	0.903097i	$0.358713\pi$
$374$	20.0392	−	27.1298i	1.03620	−	1.40285i
$375$		0			0
$376$	8.56326	−	2.78237i	0.441616	−	0.143490i
$377$	−28.7983	+	4.56121i	−1.48319	+	0.234914i
$378$		0			0
$379$	−14.1551	−	4.59927i	−0.727099	−	0.236249i	−0.0780007	−	0.996953i	$-0.524854\pi$
$379$	−14.1551	−	4.59927i	−0.727099	−	0.236249i	−0.649098	+	0.760705i	$0.724854\pi$
$380$	−0.650385	−	7.30499i	−0.0333641	−	0.374738i
$381$		0			0
$382$	0.425332	+	2.68544i	0.0217619	+	0.137399i
$383$	−9.80958	+	19.2524i	−0.501246	+	0.983751i	0.492311	+	0.870419i	$0.336152\pi$
$383$	−9.80958	+	19.2524i	−0.501246	+	0.983751i	−0.993557	+	0.113331i	$0.963848\pi$
$384$		0			0
$385$	−7.92019	−	6.73186i	−0.403650	−	0.343088i
$386$	28.2857			1.43970
$387$		0			0
$388$	0.209369	+	1.32191i	0.0106291	+	0.0671096i
$389$	−12.6276	−	17.3803i	−0.640243	−	0.881218i	0.358386	−	0.933573i	$-0.383327\pi$
$389$	−12.6276	−	17.3803i	−0.640243	−	0.881218i	−0.998629	+	0.0523553i	$0.983327\pi$
$390$		0			0
$391$	−9.67281	−	3.14289i	−0.489175	−	0.158943i
$392$	11.8029	+	1.86939i	0.596134	+	0.0944184i
$393$		0			0
$394$	−7.36947	+	2.39449i	−0.371268	+	0.120632i
$395$	−3.03640	−	7.12294i	−0.152778	−	0.358394i
$396$		0			0
$397$	−5.36424	+	5.36424i	−0.269223	+	0.269223i	−0.828787	−	0.559564i	$-0.810969\pi$
$397$	−5.36424	+	5.36424i	−0.269223	+	0.269223i	0.559564	+	0.828787i	$0.310969\pi$
$398$	12.8900	+	6.56777i	0.646116	+	0.329213i
$399$		0			0
$400$	3.23238	−	23.5224i	0.161619	−	1.17612i
$401$	6.51732	−	20.0583i	0.325459	−	1.00166i	−0.645773	−	0.763529i	$-0.723465\pi$
$401$	6.51732	−	20.0583i	0.325459	−	1.00166i	0.971233	−	0.238132i	$-0.0765351\pi$
$402$		0			0
$403$	6.67055	−	42.1162i	0.332284	−	2.09796i
$404$	5.29141	+	3.84443i	0.263257	+	0.191268i
$405$		0			0
$406$			16.3177i			0.809834i
$407$	−1.07744	+	1.06061i	−0.0534069	+	0.0525725i
$408$		0			0
$409$	−7.80314	−	24.0156i	−0.385840	−	1.18749i	−0.935869	−	0.352349i	$-0.885383\pi$
$409$	−7.80314	−	24.0156i	−0.385840	−	1.18749i	0.550028	−	0.835146i	$-0.314617\pi$
$410$	−19.2159	−	30.6473i	−0.949007	−	1.51356i
$411$		0			0
$412$	3.17215	+	6.22569i	0.156280	+	0.306718i
$413$	−3.66352	−	7.19006i	−0.180270	−	0.353800i
$414$		0			0
$415$	6.10368	+	9.73470i	0.299618	+	0.477858i
$416$	3.37659	+	10.3921i	0.165551	+	0.509514i
$417$		0			0
$418$	−34.0117	−	5.66175i	−1.66357	−	0.276925i
$419$			1.94550i			0.0950438i	0.998870	+	0.0475219i	$0.0151324\pi$
$419$			1.94550i			0.0950438i	−0.998870	+	0.0475219i	$0.984868\pi$
$420$		0			0
$421$	12.9179	+	9.38540i	0.629580	+	0.457417i	0.856255	−	0.516554i	$-0.172785\pi$
$421$	12.9179	+	9.38540i	0.629580	+	0.457417i	−0.226675	+	0.973971i	$0.572785\pi$
$422$	−2.88455	+	18.2124i	−0.140418	+	0.886563i
$423$		0			0
$424$	0.402184	−	1.23780i	0.0195318	−	0.0601127i
$425$	25.6302	−	19.4372i	1.24325	−	0.942843i
$426$		0			0
$427$	6.99126	+	3.56222i	0.338331	+	0.172388i
$428$	0.477495	−	0.477495i	0.0230806	−	0.0230806i
$429$		0			0
$430$	13.5898	+	31.8797i	0.655359	+	1.53738i
$431$	−18.4509	+	5.99507i	−0.888749	+	0.288772i	−0.717585	−	0.696470i	$-0.754753\pi$
$431$	−18.4509	+	5.99507i	−0.888749	+	0.288772i	−0.171164	+	0.985243i	$0.554753\pi$
$432$		0			0
$433$	7.39845	+	1.17180i	0.355547	+	0.0563131i	0.331653	−	0.943401i	$-0.392394\pi$
$433$	7.39845	+	1.17180i	0.355547	+	0.0563131i	0.0238937	+	0.999715i	$0.492394\pi$
$434$	−22.6959	−	7.37435i	−1.08944	−	0.353980i
$435$		0			0
$436$	1.34497	+	1.85119i	0.0644122	+	0.0886559i
$437$	1.62648	+	10.2692i	0.0778051	+	0.491242i
$438$		0			0
$439$	23.6395			1.12825			0.564127	−	0.825688i	$-0.309213\pi$
$439$	23.6395			1.12825			0.564127	+	0.825688i	$0.309213\pi$
$440$	−16.2761	−	6.69630i	−0.775931	−	0.319234i
$441$		0			0
$442$	−18.2774	+	35.8715i	−0.869369	+	1.70623i
$443$	3.46877	+	21.9010i	0.164806	+	1.04055i	0.921953	+	0.387301i	$0.126593\pi$
$443$	3.46877	+	21.9010i	0.164806	+	1.04055i	−0.757147	+	0.653245i	$0.773407\pi$
$444$		0			0
$445$	1.49563	+	16.7986i	0.0708995	+	0.796329i
$446$	−7.13802	−	2.31928i	−0.337995	−	0.109821i
$447$		0			0
$448$	−7.10784	+	1.12577i	−0.335814	+	0.0531877i
$449$	−14.4350	+	4.69021i	−0.681229	+	0.221345i	−0.629133	−	0.777297i	$-0.716590\pi$
$449$	−14.4350	+	4.69021i	−0.681229	+	0.221345i	−0.0520956	+	0.998642i	$0.516590\pi$
$450$		0			0
$451$	−32.3627	+	10.2343i	−1.52390	+	0.481916i
$452$	−4.80889	+	4.80889i	−0.226191	+	0.226191i
$453$		0			0
$454$	−20.9485	+	28.8331i	−0.983160	+	1.35320i
$455$	10.6450	+	6.37400i	0.499047	+	0.298818i
$456$		0			0
$457$	1.86215	−	0.948815i	0.0871079	−	0.0443837i	−0.409894	−	0.912133i	$-0.634434\pi$
$457$	1.86215	−	0.948815i	0.0871079	−	0.0443837i	0.497002	+	0.867750i	$0.334434\pi$
$458$	−5.23692	+	33.0646i	−0.244705	+	1.54501i
$459$		0			0
$460$	0.120279	−	1.75880i	0.00560805	−	0.0820045i
$461$			27.1510i			1.26455i	0.774745	+	0.632274i	$0.217878\pi$
$461$			27.1510i			1.26455i	−0.774745	+	0.632274i	$0.782122\pi$
$462$		0			0
$463$	−9.07571	−	9.07571i	−0.421784	−	0.421784i	0.464034	−	0.885818i	$-0.346402\pi$
$463$	−9.07571	−	9.07571i	−0.421784	−	0.421784i	−0.885818	+	0.464034i	$0.846402\pi$
$464$	10.8077	+	33.2627i	0.501735	+	1.54418i
$465$		0			0
$466$	−4.64109	+	3.37195i	−0.214994	+	0.156202i
$467$	−11.6854	−	22.9339i	−0.540735	−	1.06125i	−0.986139	−	0.165923i	$-0.946940\pi$
$467$	−11.6854	−	22.9339i	−0.540735	−	1.06125i	0.445403	−	0.895330i	$-0.353060\pi$
$468$		0			0
$469$	−2.25301	+	1.63691i	−0.104035	+	0.0755855i
$470$	−2.99671	+	13.0716i	−0.138228	+	0.602946i
$471$		0			0
$472$	−9.66129	−	9.66129i	−0.444697	−	0.444697i
$473$	32.1568	−	4.83395i	1.47857	−	0.222265i
$474$		0			0
$475$	−29.5997	−	14.3246i	−1.35813	−	0.657258i
$476$	3.63800	+	2.64316i	0.166747	+	0.121149i
$477$		0			0
$478$	7.79347	−	3.97097i	0.356465	−	0.181628i
$479$	2.23116	−	6.86681i	0.101944	−	0.313753i	−0.887057	−	0.461660i	$-0.847254\pi$
$479$	2.23116	−	6.86681i	0.101944	−	0.313753i	0.989001	+	0.147908i	$0.0472539\pi$
$480$		0			0
$481$	1.06074	−	1.45999i	0.0483657	−	0.0665697i
$482$	−17.3856	−	8.85841i	−0.791893	−	0.403489i
$483$		0			0
$484$	3.29388	−	4.38670i	0.149722	−	0.199396i
$485$	5.56751	+	2.23950i	0.252808	+	0.101691i
$486$		0			0
$487$	40.4124	−	6.40070i	1.83126	−	0.290043i	0.856975	−	0.515358i	$-0.172341\pi$
$487$	40.4124	−	6.40070i	1.83126	−	0.290043i	0.974286	+	0.225314i	$0.0723409\pi$
$488$	13.1218	+	2.07829i	0.593996	+	0.0940796i
$489$		0			0
$490$	−11.4198	+	13.6520i	−0.515893	+	0.616734i
$491$	0.0967305	+	0.133138i	0.00436539	+	0.00600844i	0.811194	−	0.584777i	$-0.198818\pi$
$491$	0.0967305	+	0.133138i	0.00436539	+	0.00600844i	−0.806829	+	0.590785i	$0.798818\pi$
$492$		0			0
$493$	−21.5111	+	42.2180i	−0.968812	+	1.90140i
$494$	41.1565			1.85172
$495$		0			0
$496$	−51.1485			−2.29664
$497$	−2.50871	+	4.92362i	−0.112531	+	0.220855i
$498$		0			0
$499$	11.9487	+	16.4460i	0.534897	+	0.736223i	0.987867	−	0.155303i	$-0.0496355\pi$
$499$	11.9487	+	16.4460i	0.534897	+	0.736223i	−0.452970	+	0.891526i	$0.649635\pi$
$500$	4.34916	+	3.48890i	0.194500	+	0.156028i
$501$		0			0
$502$	28.7699	+	4.55670i	1.28406	+	0.203375i
$503$	2.74172	−	0.434246i	0.122247	−	0.0193621i	−0.0950110	−	0.995476i	$-0.530289\pi$
$503$	2.74172	−	0.434246i	0.122247	−	0.0193621i	0.217258	+	0.976114i	$0.430289\pi$
$504$		0			0
$505$	26.9776	−	11.5001i	1.20049	−	0.511748i
$506$	−7.86212	−	2.62317i	−0.349514	−	0.116614i
$507$		0			0
$508$	4.61051	+	2.34917i	0.204558	+	0.104228i
$509$	−10.1462	+	13.9650i	−0.449721	+	0.618989i	−0.972338	−	0.233580i	$-0.924956\pi$
$509$	−10.1462	+	13.9650i	−0.449721	+	0.618989i	0.522616	+	0.852568i	$0.324956\pi$
$510$		0			0
$511$	5.85654	−	18.0246i	0.259078	−	0.797361i
$512$	−8.40382	+	4.28196i	−0.371400	+	0.189238i
$513$		0			0
$514$	−32.2318	−	23.4178i	−1.42169	−	1.03291i
$515$	31.2564	+	2.13754i	1.37732	+	0.0941912i
$516$		0			0
$517$	11.1667	+	5.80092i	0.491112	+	0.255124i
$518$	−0.714148	−	0.714148i	−0.0313779	−	0.0313779i
$519$		0			0
$520$	20.4766	+	4.69436i	0.897958	+	0.205861i
$521$	31.3410	−	22.7706i	1.37307	−	0.997597i	0.375584	−	0.926788i	$-0.377442\pi$
$521$	31.3410	−	22.7706i	1.37307	−	0.997597i	0.997490	−	0.0708081i	$-0.0225578\pi$
$522$		0			0
$523$	7.01532	+	13.7683i	0.306759	+	0.602048i	0.991996	−	0.126272i	$-0.0403014\pi$
$523$	7.01532	+	13.7683i	0.306759	+	0.602048i	−0.685237	+	0.728320i	$0.740301\pi$
$524$	4.84931	−	3.52323i	0.211843	−	0.153913i
$525$		0			0
$526$	7.04419	+	21.6798i	0.307141	+	0.945284i
$527$	−48.9986	−	48.9986i	−2.13441	−	2.13441i
$528$		0			0
$529$		−	20.5007i		−	0.891336i
$530$	1.27399	+	1.46104i	0.0553388	+	0.0634633i
$531$		0			0
$532$	0.719130	−	4.54041i	0.0311783	−	0.196852i
$533$	36.0993	−	18.3935i	1.56363	−	0.796711i
$534$		0			0
$535$	−0.736996	−	2.93675i	−0.0318631	−	0.126967i
$536$	−2.77156	+	3.81472i	−0.119713	+	0.164771i
$537$		0			0
$538$	−22.9237	+	22.9237i	−0.988311	+	0.988311i
$539$	9.70985	+	13.5881i	0.418233	+	0.585283i
$540$		0			0
$541$	2.80223	−	0.910499i	0.120477	−	0.0391454i	−0.248158	−	0.968720i	$-0.579825\pi$
$541$	2.80223	−	0.910499i	0.120477	−	0.0391454i	0.368635	+	0.929574i	$0.379825\pi$
$542$	12.5086	−	1.98117i	0.537291	−	0.0850986i
$543$		0			0
$544$	16.8877	+	5.48716i	0.724056	+	0.235260i
$545$	10.2194	−	0.909862i	0.437750	−	0.0389742i
$546$		0			0
$547$	−2.74744	−	17.3466i	−0.117472	−	0.741689i	−0.974161	−	0.225856i	$-0.927482\pi$
$547$	−2.74744	−	17.3466i	−0.117472	−	0.741689i	0.856689	−	0.515834i	$-0.172518\pi$
$548$	−1.47295	+	2.89082i	−0.0629212	+	0.123490i
$549$		0			0
$550$	21.0106	−	15.6748i	0.895893	−	0.668375i
$551$	48.4380			2.06353
$552$		0			0
$553$	−0.759258	−	4.79377i	−0.0322870	−	0.203852i
$554$	−4.69620	−	6.46376i	−0.199522	−	0.274619i
$555$		0			0
$556$	−2.35351	−	0.764702i	−0.0998111	−	0.0324306i
$557$	−18.5868	−	2.94386i	−0.787549	−	0.124736i	−0.250310	−	0.968166i	$-0.580533\pi$
$557$	−18.5868	−	2.94386i	−0.787549	−	0.124736i	−0.537239	+	0.843430i	$0.680533\pi$
$558$		0			0
$559$	−36.9153	+	11.9945i	−1.56135	+	0.507314i
$560$	5.55405	−	13.8076i	0.234702	−	0.583479i
$561$		0			0
$562$	−2.23987	+	2.23987i	−0.0944830	+	0.0944830i
$563$	−13.2421	−	6.74718i	−0.558088	−	0.284360i	0.152108	−	0.988364i	$-0.451394\pi$
$563$	−13.2421	−	6.74718i	−0.558088	−	0.284360i	−0.710196	+	0.704004i	$0.751394\pi$
$564$		0			0
$565$	7.42235	+	29.5763i	0.312261	+	1.24428i
$566$	−9.76293	+	30.0472i	−0.410366	+	1.26298i
$567$		0			0
$568$	−1.46364	+	9.24108i	−0.0614131	+	0.387747i
$569$	−21.0954	−	15.3267i	−0.884367	−	0.642530i	0.0500362	−	0.998747i	$-0.484066\pi$
$569$	−21.0954	−	15.3267i	−0.884367	−	0.642530i	−0.934403	+	0.356217i	$0.884066\pi$
$570$		0			0
$571$		−	43.2972i		−	1.81193i	−0.423353	−	0.905965i	$-0.639147\pi$
$571$		−	43.2972i		−	1.81193i	0.423353	−	0.905965i	$-0.360853\pi$
$572$	−3.01855	+	5.81070i	−0.126212	+	0.242957i
$573$		0			0
$574$	−7.00667	−	21.5643i	−0.292453	−	0.900077i
$575$	−6.48888	−	4.51399i	−0.270605	−	0.188246i
$576$		0			0
$577$	16.1266	+	31.6503i	0.671360	+	1.31762i	0.935566	+	0.353152i	$0.114890\pi$
$577$	16.1266	+	31.6503i	0.671360	+	1.31762i	−0.264206	+	0.964466i	$0.585110\pi$
$578$	17.5021	+	34.3498i	0.727991	+	1.42876i
$579$		0			0
$580$	−8.00529	−	1.83525i	−0.332402	−	0.0762046i
$581$	2.22557	+	6.84961i	0.0923324	+	0.284170i
$582$		0			0
$583$	1.62712	−	0.812990i	0.0673886	−	0.0336706i
$584$		−	32.0891i		−	1.32786i
$585$		0			0
$586$	−16.3217	−	11.8584i	−0.674244	−	0.489867i
$587$	5.10611	−	32.2387i	0.210752	−	1.33063i	−0.624611	−	0.780936i	$-0.714743\pi$
$587$	5.10611	−	32.2387i	0.210752	−	1.33063i	0.835363	−	0.549699i	$-0.185257\pi$
$588$		0			0
$589$	−21.8903	+	67.3713i	−0.901973	+	2.77599i
$590$	19.7381	−	4.95340i	0.812605	−	0.203928i
$591$		0			0
$592$	−1.92875	−	0.982747i	−0.0792711	−	0.0403907i
$593$	−16.9460	+	16.9460i	−0.695890	+	0.695890i	−0.963521	−	0.267631i	$-0.913759\pi$
$593$	−16.9460	+	16.9460i	−0.695890	+	0.695890i	0.267631	+	0.963521i	$0.413759\pi$
$594$		0			0
$595$	18.5479	−	7.90667i	0.760389	−	0.324142i
$596$	1.46905	−	0.477324i	0.0601747	−	0.0195520i
$597$		0			0
$598$	9.77134	+	1.54763i	0.399580	+	0.0632872i
$599$	43.3500	+	14.0853i	1.77123	+	0.575508i	0.998262	−	0.0589357i	$-0.0187707\pi$
$599$	43.3500	+	14.0853i	1.77123	+	0.575508i	0.772969	+	0.634444i	$0.218771\pi$
$600$		0			0
$601$	−21.2237	−	29.2120i	−0.865734	−	1.19158i	−0.980172	−	0.198151i	$-0.936506\pi$
$601$	−21.2237	−	29.2120i	−0.865734	−	1.19158i	0.114437	−	0.993430i	$-0.463494\pi$
$602$	3.39816	+	21.4552i	0.138499	+	0.874447i
$603$		0			0
$604$	3.74290			0.152297
$605$	−9.28796	−	22.7757i	−0.377609	−	0.925965i
$606$		0			0
$607$	−14.1774	+	27.8246i	−0.575441	+	1.12937i	0.401500	+	0.915859i	$0.368489\pi$
$607$	−14.1774	+	27.8246i	−0.575441	+	1.12937i	−0.976941	+	0.213508i	$0.931511\pi$
$608$	−2.83967	−	17.9290i	−0.115164	−	0.727116i
$609$		0			0
$610$	−12.6959	+	15.1776i	−0.514042	+	0.614521i
$611$	−14.2852	−	4.64153i	−0.577916	−	0.187776i
$612$		0			0
$613$	33.1413	−	5.24907i	1.33857	−	0.212008i	0.554240	−	0.832357i	$-0.313009\pi$
$613$	33.1413	−	5.24907i	1.33857	−	0.212008i	0.784326	+	0.620349i	$0.213009\pi$
$614$	36.7177	−	11.9303i	1.48181	−	0.481469i
$615$		0			0
$616$	−8.87360	−	6.55440i	−0.357528	−	0.264084i
$617$	−31.5731	+	31.5731i	−1.27108	+	1.27108i	−0.325565	+	0.945520i	$0.605554\pi$
$617$	−31.5731	+	31.5731i	−1.27108	+	1.27108i	−0.945520	+	0.325565i	$0.894446\pi$
$618$		0			0
$619$	−2.31259	+	3.18300i	−0.0929507	+	0.127936i	−0.852959	−	0.521977i	$-0.825195\pi$
$619$	−2.31259	+	3.18300i	−0.0929507	+	0.127936i	0.760009	+	0.649913i	$0.225195\pi$
$620$	6.17038	−	10.3050i	0.247808	−	0.413858i
$621$		0			0
$622$	3.05770	−	1.55798i	0.122603	−	0.0624692i
$623$	−1.65371	+	10.4411i	−0.0662546	+	0.418315i
$624$		0			0
$625$	23.4395	−	8.69434i	0.937579	−	0.347773i
$626$			18.9432i			0.757122i
$627$		0			0
$628$	−3.65429	−	3.65429i	−0.145822	−	0.145822i
$629$	−0.906240	−	2.78912i	−0.0361341	−	0.111209i
$630$		0			0
$631$	10.2489	−	7.44623i	0.408000	−	0.296430i	−0.364791	−	0.931089i	$-0.618860\pi$
$631$	10.2489	−	7.44623i	0.408000	−	0.296430i	0.772792	+	0.634660i	$0.218860\pi$
$632$	−3.73081	−	7.32212i	−0.148404	−	0.291258i
$633$		0			0
$634$	25.6178	−	18.6124i	1.01741	−	0.739193i
$635$	19.6571	−	12.3250i	0.780067	−	0.489103i
$636$		0			0
$637$	−14.0961	−	14.0961i	−0.558508	−	0.558508i
$638$	−17.8001	+	34.2650i	−0.704712	+	1.35657i
$639$		0			0
$640$	2.08038	−	30.4207i	0.0822344	−	1.20248i
$641$	12.8506	+	9.33654i	0.507570	+	0.368771i	0.811901	−	0.583795i	$-0.198433\pi$
$641$	12.8506	+	9.33654i	0.507570	+	0.368771i	−0.304331	+	0.952566i	$0.598433\pi$
$642$		0			0
$643$	−17.6266	+	8.98121i	−0.695126	+	0.354184i	−0.765589	−	0.643330i	$-0.777552\pi$
$643$	−17.6266	+	8.98121i	−0.695126	+	0.354184i	0.0704632	+	0.997514i	$0.477552\pi$
$644$	0.341470	−	1.05094i	0.0134558	−	0.0414128i
$645$		0			0
$646$	39.3121	−	54.1085i	1.54671	−	2.12887i
$647$	17.8682	+	9.10429i	0.702471	+	0.357927i	0.768464	−	0.639893i	$-0.221021\pi$
$647$	17.8682	+	9.10429i	0.702471	+	0.357927i	−0.0659929	+	0.997820i	$0.521021\pi$
$648$		0			0
$649$	0.150327	−	19.0945i	0.00590085	−	0.749525i
$650$	−21.6664	+	22.5743i	−0.849826	+	0.885436i
$651$		0			0
$652$	−7.45090	+	1.18011i	−0.291800	+	0.0462165i
$653$	−6.58004	−	1.04218i	−0.257497	−	0.0407835i	0.0263513	−	0.999653i	$-0.491611\pi$
$653$	−6.58004	−	1.04218i	−0.257497	−	0.0407835i	−0.283848	+	0.958869i	$0.591611\pi$
$654$		0			0
$655$	−2.38344	−	26.7703i	−0.0931288	−	1.04600i
$656$	−28.5654	−	39.3168i	−1.11529	−	1.53506i
$657$		0			0
$658$	−3.81626	+	7.48983i	−0.148773	+	0.291984i
$659$	−8.18914			−0.319004			−0.159502	−	0.987198i	$-0.550989\pi$
$659$	−8.18914			−0.319004			−0.159502	+	0.987198i	$0.550989\pi$
$660$		0			0
$661$	25.9988			1.01124			0.505618	−	0.862757i	$-0.331264\pi$
$661$	25.9988			1.01124			0.505618	+	0.862757i	$0.331264\pi$
$662$	12.3539	−	24.2459i	0.480148	−	0.942344i
$663$		0			0
$664$	7.16766	+	9.86543i	0.278159	+	0.382853i
$665$	−15.8100	−	13.2250i	−0.613087	−	0.512842i
$666$		0			0
$667$	11.5001	+	1.82144i	0.445286	+	0.0705264i
$668$	1.63333	−	0.258694i	0.0631953	−	0.0100092i
$669$		0			0
$670$	−2.75401	−	6.46049i	−0.106397	−	0.249590i
$671$	10.7949	+	15.1066i	0.416732	+	0.583183i
$672$		0			0
$673$	−31.8970	−	16.2523i	−1.22954	−	0.626481i	−0.286154	−	0.958184i	$-0.592377\pi$
$673$	−31.8970	−	16.2523i	−1.22954	−	0.626481i	−0.943384	+	0.331703i	$0.892377\pi$
$674$	−13.5852	+	18.6984i	−0.523281	+	0.720234i
$675$		0			0
$676$	0.411872	−	1.26761i	0.0158412	−	0.0487543i
$677$	−9.63380	+	4.90867i	−0.370257	+	0.188655i	−0.629212	−	0.777234i	$-0.716622\pi$
$677$	−9.63380	+	4.90867i	−0.370257	+	0.188655i	0.258954	+	0.965890i	$0.416622\pi$
$678$		0			0
$679$	3.04316	+	2.21099i	0.116786	+	0.0848500i
$680$	25.7306	−	22.4366i	0.986724	−	0.860405i
$681$		0			0
$682$	−39.6142	−	40.2429i	−1.51691	−	1.54098i
$683$	−27.4104	−	27.4104i	−1.04883	−	1.04883i	−0.998745	−	0.0500857i	$-0.984051\pi$
$683$	−27.4104	−	27.4104i	−1.04883	−	1.04883i	−0.0500857	−	0.998745i	$-0.515949\pi$
$684$		0			0
$685$	7.72787	+	12.3251i	0.295267	+	0.470918i
$686$	−21.5727	+	15.6735i	−0.823650	+	0.598417i
$687$		0			0
$688$	21.1373	+	41.4844i	0.805854	+	1.58158i
$689$	−1.75650	+	1.27617i	−0.0669172	+	0.0486182i
$690$		0			0
$691$	9.94384	+	30.6040i	0.378281	+	1.16423i	0.941238	+	0.337744i	$0.109664\pi$
$691$	9.94384	+	30.6040i	0.378281	+	1.16423i	−0.562957	+	0.826487i	$0.690336\pi$
$692$	−2.28503	−	2.28503i	−0.0868637	−	0.0868637i
$693$		0			0
$694$			13.3789i			0.507857i
$695$	−8.36290	+	7.29228i	−0.317223	+	0.276612i
$696$		0			0
$697$	10.2996	−	65.0289i	0.390124	−	2.46315i
$698$	−23.7390	+	12.0956i	−0.898536	+	0.457827i
$699$		0			0
$700$	2.11183	+	2.78469i	0.0798196	+	0.105251i
$701$	13.3169	−	18.3291i	0.502971	−	0.692280i	−0.479744	−	0.877409i	$-0.659270\pi$
$701$	13.3169	−	18.3291i	0.502971	−	0.692280i	0.982714	+	0.185129i	$0.0592703\pi$
$702$		0			0
$703$	−2.11990	+	2.11990i	−0.0799537	+	0.0799537i
$704$	−16.1536	−	5.38958i	−0.608811	−	0.203127i
$705$		0			0
$706$	41.2456	−	13.4015i	1.55230	−	0.504372i
$707$	18.1560	−	2.87563i	0.682827	−	0.108149i
$708$		0			0
$709$	12.7234	+	4.13408i	0.477837	+	0.155259i	0.538026	−	0.842928i	$-0.319170\pi$
$709$	12.7234	+	4.13408i	0.477837	+	0.155259i	−0.0601890	+	0.998187i	$0.519170\pi$
$710$	−10.6889	−	8.94115i	−0.401146	−	0.335555i
$711$		0			0
$712$	2.80001	+	17.6785i	0.104935	+	0.662531i
$713$	−7.73056	+	15.1721i	−0.289512	+	0.568199i
$714$		0			0
$715$	15.4001	+	24.9966i	0.575932	+	0.934821i
$716$	2.45119			0.0916053
$717$		0			0
$718$	−3.14662	−	19.8670i	−0.117431	−	0.741430i
$719$	18.4419	+	25.3831i	0.687768	+	0.946631i	0.999994	−	0.00337661i	$-0.00107481\pi$
$719$	18.4419	+	25.3831i	0.687768	+	0.946631i	−0.312227	+	0.950008i	$0.601075\pi$
$720$		0			0
$721$	18.6767	+	6.06843i	0.695556	+	0.226000i
$722$	−37.8661	−	5.99740i	−1.40923	−	0.223200i
$723$		0			0
$724$	−2.18308	+	0.709326i	−0.0811336	+	0.0263619i
$725$	−25.4997	+	26.5682i	−0.947035	+	0.986717i
$726$		0			0
$727$	3.50392	−	3.50392i	0.129953	−	0.129953i	−0.639138	−	0.769092i	$-0.720709\pi$
$727$	3.50392	−	3.50392i	0.129953	−	0.129953i	0.769092	+	0.639138i	$0.220709\pi$
$728$	11.7328	+	5.97817i	0.434847	+	0.221566i
$729$		0			0
$730$	41.0053	+	24.5530i	1.51767	+	0.908748i
$731$	−19.4918	+	59.9895i	−0.720930	+	2.21879i
$732$		0			0
$733$	−1.32278	+	8.35169i	−0.0488579	+	0.308477i	−1.00000		0.000276861i	$-0.999912\pi$
$733$	−1.32278	+	8.35169i	−0.0488579	+	0.308477i	0.951142	+	0.308754i	$0.0999119\pi$
$734$	−45.9130	−	33.3578i	−1.69468	−	1.23126i
$735$		0			0
$736$		−	4.36346i		−	0.160839i
$737$	−6.51665	+	0.979610i	−0.240044	+	0.0360844i
$738$		0			0
$739$	−5.24050	−	16.1286i	−0.192775	−	0.593300i	−0.999995	−	0.00304986i	$-0.999029\pi$
$739$	−5.24050	−	16.1286i	−0.192775	−	0.593300i	0.807221	−	0.590250i	$-0.200971\pi$
$740$	0.430674	−	0.270033i	0.0158319	−	0.00992662i
$741$		0			0
$742$	0.551630	+	1.08264i	0.0202510	+	0.0397448i
$743$	−14.3122	−	28.0892i	−0.525063	−	1.03049i	−0.989452	−	0.144863i	$-0.953726\pi$
$743$	−14.3122	−	28.0892i	−0.525063	−	1.03049i	0.464389	−	0.885631i	$-0.346274\pi$
$744$		0			0
$745$	1.54765	−	6.75079i	0.0567015	−	0.247330i
$746$	−6.31942	−	19.4492i	−0.231370	−	0.712085i
$747$		0			0
$748$	4.75604	+	9.51878i	0.173898	+	0.348041i
$749$		−	1.89789i		−	0.0693473i
$750$		0			0
$751$	−32.3883	−	23.5315i	−1.18187	−	0.858677i	−0.189486	−	0.981883i	$-0.560682\pi$
$751$	−32.3883	−	23.5315i	−1.18187	−	0.858677i	−0.992381	+	0.123207i	$0.960682\pi$
$752$	−2.81848	+	17.7952i	−0.102779	+	0.648924i
$753$		0			0
$754$	14.2425	−	43.8340i	0.518682	−	1.59634i
$755$	8.62153	−	14.3986i	0.313770	−	0.524018i
$756$		0			0
$757$	−28.7805	−	14.6644i	−1.04605	−	0.532988i	−0.155480	−	0.987839i	$-0.549692\pi$
$757$	−28.7805	−	14.6644i	−1.04605	−	0.532988i	−0.890567	+	0.454852i	$0.849692\pi$
$758$	16.6360	−	16.6360i	0.604247	−	0.604247i
$759$		0			0
$760$	−32.3783	−	13.0240i	−1.17449	−	0.472431i
$761$	15.9174	−	5.17188i	0.577005	−	0.187480i	−0.00595324	−	0.999982i	$-0.501895\pi$
$761$	15.9174	−	5.17188i	0.577005	−	0.187480i	0.582959	+	0.812502i	$0.301895\pi$
$762$		0			0
$763$	6.35185	+	1.00603i	0.229952	+	0.0364209i
$764$	−0.815801	−	0.265070i	−0.0295146	−	0.00958988i
$765$		0			0
$766$	−20.0761	−	27.6324i	−0.725379	−	0.998398i
$767$	3.56557	+	22.5121i	0.128745	+	0.812866i
$768$		0			0
$769$	−35.6075			−1.28404			−0.642019	−	0.766689i	$-0.721903\pi$
$769$	−35.6075			−1.28404			−0.642019	+	0.766689i	$0.721903\pi$
$770$	15.1652	−	6.32408i	0.546517	−	0.227904i
$771$		0			0
$772$	−4.05131	+	7.95114i	−0.145810	+	0.286168i
$773$	−1.72132	−	10.8680i	−0.0619115	−	0.390894i	−0.999113	−	0.0421059i	$-0.986593\pi$
$773$	−1.72132	−	10.8680i	−0.0619115	−	0.390894i	0.937202	−	0.348788i	$-0.113407\pi$
$774$		0			0
$775$	−25.4291	−	47.4737i	−0.913442	−	1.70531i
$776$	6.05721	+	1.96811i	0.217441	+	0.0706510i
$777$		0			0
$778$	33.5411	−	5.31239i	1.20251	−	0.190458i
$779$	−64.0123	+	20.7989i	−2.29348	+	0.745196i
$780$		0			0
$781$	−10.6389	+	7.60235i	−0.380689	+	0.272034i
$782$	11.3681	−	11.3681i	0.406523	−	0.406523i
$783$		0			0
$784$	−14.0552	+	19.3453i	−0.501970	+	0.690903i
$785$	−22.4751	+	5.64027i	−0.802170	+	0.201310i
$786$		0			0
$787$	−18.7557	+	9.55650i	−0.668568	+	0.340653i	−0.755112	−	0.655595i	$-0.772418\pi$
$787$	−18.7557	+	9.55650i	−0.668568	+	0.340653i	0.0865440	+	0.996248i	$0.472418\pi$
$788$	0.382423	−	2.41452i	0.0136233	−	0.0860139i
$789$		0			0
$790$	12.2112	+	0.835092i	0.434457	+	0.0297112i
$791$			19.1138i			0.679608i
$792$		0			0
$793$	−15.6713	−	15.6713i	−0.556504	−	0.556504i
$794$	−3.70563	−	11.4048i	−0.131508	−	0.404740i
$795$		0			0
$796$	−3.69242	+	2.68270i	−0.130874	+	0.0950857i
$797$	13.5291	+	26.5523i	0.479224	+	0.940529i	0.996410	+	0.0846567i	$0.0269793\pi$
$797$	13.5291	+	26.5523i	0.479224	+	0.940529i	−0.517187	+	0.855873i	$0.673021\pi$
$798$		0			0
$799$	−19.7472	+	14.3472i	−0.698606	+	0.507567i
$800$	11.3289	+	7.88097i	0.400538	+	0.278634i
$801$		0			0
$802$	23.5738	+	23.5738i	0.832418	+	0.832418i
$803$	31.9600	−	31.4607i	1.12784	−	1.11022i
$804$		0			0
$805$	−3.25630	−	3.73437i	−0.114769	−	0.131619i
$806$	54.5311	+	39.6192i	1.92078	+	1.39553i
$807$		0			0
$808$	27.7319	−	14.1301i	0.975606	−	0.497096i
$809$	16.8364	−	51.8170i	0.591936	−	1.82179i	0.0225111	−	0.999747i	$-0.492834\pi$
$809$	16.8364	−	51.8170i	0.591936	−	1.82179i	0.569424	−	0.822044i	$-0.307166\pi$
$810$		0			0
$811$	7.28498	−	10.0269i	0.255810	−	0.352093i	−0.661725	−	0.749746i	$-0.730175\pi$
$811$	7.28498	−	10.0269i	0.255810	−	0.352093i	0.917536	+	0.397654i	$0.130175\pi$
$812$	−4.58693	−	2.33716i	−0.160970	−	0.0820181i
$813$		0			0
$814$	−0.720593	−	2.27864i	−0.0252568	−	0.0798664i
$815$	−12.6229	+	31.3812i	−0.442161	+	1.09923i
$816$		0			0
$817$	63.6883	−	10.0872i	2.22817	−	0.352908i
$818$	39.4243	+	6.24419i	1.37844	+	0.218323i
$819$		0			0
$820$	11.3673	−	1.01206i	0.396962	−	0.0353427i
$821$	−30.3673	−	41.7970i	−1.05983	−	1.45873i	−0.879968	−	0.475033i	$-0.842436\pi$
$821$	−30.3673	−	41.7970i	−1.05983	−	1.45873i	−0.179858	−	0.983693i	$-0.557564\pi$
$822$		0			0
$823$	−6.89758	+	13.5373i	−0.240435	+	0.471879i	−0.979418	−	0.201845i	$-0.935306\pi$
$823$	−6.89758	+	13.5373i	−0.240435	+	0.471879i	0.738983	+	0.673724i	$0.235306\pi$
$824$	33.2501			1.15832
$825$		0			0
$826$	12.7558			0.443832
$827$	−3.86367	+	7.58288i	−0.134353	+	0.263682i	−0.948375	−	0.317152i	$-0.897274\pi$
$827$	−3.86367	+	7.58288i	−0.134353	+	0.263682i	0.814022	+	0.580834i	$0.197274\pi$
$828$		0			0
$829$	−2.59036	−	3.56532i	−0.0899668	−	0.123829i	0.761661	−	0.647976i	$-0.224384\pi$
$829$	−2.59036	−	3.56532i	−0.0899668	−	0.123829i	−0.851628	+	0.524147i	$0.824384\pi$
$830$	−18.0909	+	1.61069i	−0.627946	+	0.0559079i
$831$		0			0
$832$	20.0763	+	3.17977i	0.696019	+	0.110239i
$833$	−31.9965	+	5.06775i	−1.10861	+	0.175587i
$834$		0			0
$835$	2.76709	−	6.87913i	0.0957593	−	0.238062i
$836$	6.46296	−	8.74981i	0.223526	−	0.302618i
$837$		0			0
$838$	−2.74012	−	1.39616i	−0.0946557	−	0.0482295i
$839$	8.77148	−	12.0729i	0.302825	−	0.416803i	−0.630302	−	0.776350i	$-0.717069\pi$
$839$	8.77148	−	12.0729i	0.302825	−	0.416803i	0.933127	+	0.359547i	$0.117069\pi$
$840$		0			0
$841$	7.80085	−	24.0085i	0.268995	−	0.827881i
$842$	−22.4891	+	11.4588i	−0.775026	+	0.394895i
$843$		0			0
$844$	−4.70636	−	3.41937i	−0.162000	−	0.117700i
$845$	−3.92765	−	4.50429i	−0.135115	−	0.154952i
$846$		0			0
$847$	−2.17180	−	15.2639i	−0.0746239	−	0.524475i
$848$	1.84153	+	1.84153i	0.0632383	+	0.0632383i
$849$		0			0
$850$	8.98295	+	50.0474i	0.308113	+	1.71661i
$851$	−0.583021	+	0.423590i	−0.0199857	+	0.0145205i
$852$		0			0
$853$	2.66129	+	5.22308i	0.0911209	+	0.178835i	0.932069	−	0.362281i	$-0.118002\pi$
$853$	2.66129	+	5.22308i	0.0911209	+	0.178835i	−0.840948	+	0.541116i	$0.818002\pi$
$854$	−10.0343	+	7.29038i	−0.343368	+	0.249472i
$855$		0			0
$856$	−0.993006	−	3.05616i	−0.0339402	−	0.104457i
$857$	−3.12077	−	3.12077i	−0.106603	−	0.106603i	0.651793	−	0.758397i	$-0.274017\pi$
$857$	−3.12077	−	3.12077i	−0.106603	−	0.106603i	−0.758397	+	0.651793i	$0.774017\pi$
$858$		0			0
$859$			17.4274i			0.594616i	0.954782	+	0.297308i	$0.0960888\pi$
$859$			17.4274i			0.594616i	−0.954782	+	0.297308i	$0.903911\pi$
$860$	−10.9079	−	0.745957i	−0.371955	−	0.0254369i
$861$		0			0
$862$	4.79735	−	30.2892i	0.163398	−	1.03166i
$863$	−27.0191	+	13.7669i	−0.919741	+	0.468632i	−0.848720	−	0.528843i	$-0.822626\pi$
$863$	−27.0191	+	13.7669i	−0.919741	+	0.468632i	−0.0710218	+	0.997475i	$0.522626\pi$
$864$		0			0
$865$	−14.0537	+	3.52686i	−0.477840	+	0.119917i
$866$	−6.95979	+	9.57933i	−0.236503	+	0.325519i
$867$		0			0
$868$	5.32363	−	5.32363i	0.180696	−	0.180696i
$869$	3.63491	−	10.8945i	0.123306	−	0.369571i
$870$		0			0
$871$	7.48097	−	2.43071i	0.253483	−	0.0823616i
$872$	10.7547	−	1.70338i	0.364201	−	0.0576837i
$873$		0			0
$874$	−15.6307	−	5.07874i	−0.528718	−	0.171791i
$875$	15.5769	−	1.70963i	0.526595	−	0.0577961i
$876$		0			0
$877$	4.37212	+	27.6045i	0.147636	+	0.932137i	0.944627	+	0.328146i	$0.106424\pi$
$877$	4.37212	+	27.6045i	0.147636	+	0.932137i	−0.796991	+	0.603991i	$0.793576\pi$
$878$	−16.9646	+	33.2948i	−0.572526	+	1.12365i
$879$		0			0
$880$	26.7248	−	22.9356i	0.900892	−	0.773160i
$881$	1.31606			0.0443393			0.0221696	−	0.999754i	$-0.492943\pi$
$881$	1.31606			0.0443393			0.0221696	+	0.999754i	$0.492943\pi$
$882$		0			0
$883$	−0.555003	−	3.50415i	−0.0186773	−	0.117924i	0.976588	−	0.215118i	$-0.0690135\pi$
$883$	−0.555003	−	3.50415i	−0.0186773	−	0.117924i	−0.995266	+	0.0971934i	$0.969013\pi$
$884$	−7.46567	−	10.2756i	−0.251098	−	0.345606i
$885$		0			0
$886$	−33.3355	−	10.8314i	−1.11993	−	0.363886i
$887$	20.2465	+	3.20673i	0.679811	+	0.107671i	0.486785	−	0.873522i	$-0.338170\pi$
$887$	20.2465	+	3.20673i	0.679811	+	0.107671i	0.193026	+	0.981194i	$0.438170\pi$
$888$		0			0
$889$	13.8313	−	4.49405i	0.463886	−	0.150726i
$890$	−24.7331	−	9.94875i	−0.829054	−	0.333483i
$891$		0			0
$892$	1.67432	−	1.67432i	0.0560603	−	0.0560603i
$893$	22.2331	+	11.3283i	0.744001	+	0.379088i
$894$		0			0
$895$	5.64616	−	9.42949i	0.188730	−	0.315193i
$896$	5.90617	−	18.1773i	0.197311	−	0.607262i
$897$		0			0
$898$	3.75318	−	23.6966i	0.125245	−	0.790767i
$899$	64.1789	+	46.6287i	2.14049	+	1.55515i
$900$		0			0
$901$			3.52824i			0.117543i
$902$	8.81022	−	52.9254i	0.293348	−	1.76222i
$903$		0			0
$904$	10.0006	+	30.7788i	0.332617	+	1.02369i
$905$	−2.29988	+	10.0320i	−0.0764506	+	0.333474i
$906$		0			0
$907$	18.0620	+	35.4488i	0.599740	+	1.17706i	0.968845	+	0.247669i	$0.0796645\pi$
$907$	18.0620	+	35.4488i	0.599740	+	1.17706i	−0.369104	+	0.929388i	$0.620336\pi$
$908$	−5.10460	−	10.0183i	−0.169402	−	0.332470i
$909$		0			0
$910$	−16.6166	+	10.4187i	−0.550836	+	0.345375i
$911$	−16.8451	−	51.8440i	−0.558105	−	1.71767i	−0.687600	−	0.726089i	$-0.741336\pi$
$911$	−16.8451	−	51.8440i	−0.558105	−	1.71767i	0.129496	−	0.991580i	$-0.458664\pi$
$912$		0			0
$913$	−2.79845	+	16.8110i	−0.0926151	+	0.556365i
$914$			3.30363i			0.109274i
$915$		0			0
$916$	−8.54442	−	6.20788i	−0.282316	−	0.205114i
$917$	2.63537	−	16.6391i	0.0870276	−	0.549470i
$918$		0			0
$919$	12.6863	−	39.0443i	0.418481	−	1.28795i	−0.490619	−	0.871374i	$-0.663229\pi$
$919$	12.6863	−	39.0443i	0.418481	−	1.28795i	0.909100	−	0.416578i	$-0.136771\pi$
$920$	−7.19748	−	4.30968i	−0.237294	−	0.142086i
$921$		0			0
$922$	−38.2405	−	19.4845i	−1.25938	−	0.641688i
$923$	11.0366	−	11.0366i	0.363273	−	0.363273i
$924$		0			0
$925$	−0.0467623	−	2.27876i	−0.00153753	−	0.0749253i
$926$	19.2956	−	6.26953i	0.634094	−	0.206029i
$927$		0			0
$928$	−20.0780	−	3.18005i	−0.659094	−	0.104390i
$929$	23.5756	+	7.66016i	0.773489	+	0.251322i	0.669058	−	0.743210i	$-0.266698\pi$
$929$	23.5756	+	7.66016i	0.773489	+	0.251322i	0.104431	+	0.994532i	$0.466698\pi$
$930$		0			0
$931$	19.4658	+	26.7923i	0.637965	+	0.878084i
$932$	−0.283124	−	1.78757i	−0.00927403	−	0.0585539i
$933$		0			0
$934$	40.6868			1.33131
$935$	47.5730	+	3.62987i	1.55581	+	0.118709i
$936$		0			0
$937$	−8.99811	+	17.6598i	−0.293955	+	0.576920i	−0.989998	−	0.141080i	$-0.954942\pi$
$937$	−8.99811	+	17.6598i	−0.293955	+	0.576920i	0.696043	+	0.718000i	$0.254942\pi$
$938$	−0.688645	−	4.34794i	−0.0224851	−	0.141965i
$939$		0			0
$940$	−3.24521	−	2.71459i	−0.105847	−	0.0885403i
$941$	−3.86566	−	1.25603i	−0.126017	−	0.0409454i	0.245330	−	0.969440i	$-0.421104\pi$
$941$	−3.86566	−	1.25603i	−0.126017	−	0.0409454i	−0.371347	+	0.928494i	$0.621104\pi$
$942$		0			0
$943$	−15.9798	+	2.53096i	−0.520375	+	0.0824193i
$944$	26.0020	−	8.44856i	0.846292	−	0.274977i
$945$		0			0
$946$	−16.2685	+	48.7599i	−0.528936	+	1.58532i
$947$	11.8088	−	11.8088i	0.383736	−	0.383736i	−0.488710	−	0.872446i	$-0.662532\pi$
$947$	11.8088	−	11.8088i	0.383736	−	0.383736i	0.872446	+	0.488710i	$0.162532\pi$
$948$		0			0
$949$	−31.4646	+	43.3074i	−1.02139	+	1.40582i
$950$	41.4171	−	31.4095i	1.34375	−	1.01906i
$951$		0			0
$952$	19.0665	−	9.71488i	0.617950	−	0.314861i
$953$	−1.54583	+	9.75997i	−0.0500742	+	0.316156i	0.949919	+	0.312496i	$0.101165\pi$
$953$	−1.54583	+	9.75997i	−0.0500742	+	0.316156i	−0.999993	+	0.00366029i	$0.998835\pi$
$954$		0			0
$955$	−2.89884	+	2.52773i	−0.0938043	+	0.0817955i
$956$			2.75951i			0.0892489i
$957$		0			0
$958$	8.07032	+	8.07032i	0.260740	+	0.260740i
$959$	2.81780	+	8.67229i	0.0909915	+	0.280043i
$960$		0			0
$961$	−68.7791	+	49.9710i	−2.21868	+	1.61197i
$962$	1.29508	+	2.54173i	0.0417549	+	0.0819487i
$963$		0			0
$964$	4.98022	−	3.61834i	0.160402	−	0.116539i
$965$	21.2553	+	33.8999i	0.684233	+	1.09128i
$966$		0			0
$967$	−2.97070	−	2.97070i	−0.0955312	−	0.0955312i	0.657726	−	0.753257i	$-0.271518\pi$
$967$	−2.97070	−	2.97070i	−0.0955312	−	0.0955312i	−0.753257	+	0.657726i	$0.771518\pi$
$968$	−11.4836	−	23.4431i	−0.369096	−	0.753490i
$969$		0			0
$970$	−7.14964	+	6.23435i	−0.229561	+	0.200173i
$971$	−1.35587	−	0.985094i	−0.0435118	−	0.0316132i	0.565817	−	0.824531i	$-0.308561\pi$
$971$	−1.35587	−	0.985094i	−0.0435118	−	0.0316132i	−0.609329	+	0.792918i	$0.708561\pi$
$972$		0			0
$973$	−6.19695	+	3.15750i	−0.198665	+	0.101225i
$974$	−19.9864	+	61.5118i	−0.640405	+	1.97096i
$975$		0			0
$976$	−15.6258	+	21.5070i	−0.500169	+	0.688424i
$977$	47.8761	+	24.3941i	1.53169	+	0.780435i	0.997874	−	0.0651653i	$-0.0207575\pi$
$977$	47.8761	+	24.3941i	1.53169	+	0.780435i	0.533816	+	0.845601i	$0.320757\pi$
$978$		0			0
$979$	−14.8622	+	20.1211i	−0.474999	+	0.643072i
$980$	−2.20196	−	5.16547i	−0.0703390	−	0.165005i
$981$		0			0
$982$	−0.256934	+	0.0406944i	−0.00819910	+	0.00129861i
$983$	19.5601	+	3.09802i	0.623870	+	0.0988114i	0.460363	−	0.887731i	$-0.347719\pi$
$983$	19.5601	+	3.09802i	0.623870	+	0.0988114i	0.163507	+	0.986542i	$0.447719\pi$
$984$		0			0
$985$	−8.40755	−	7.03284i	−0.267887	−	0.224085i
$986$	−44.0243	−	60.5942i	−1.40202	−	1.92971i
$987$		0			0
$988$	−5.89477	+	11.5691i	−0.187538	+	0.368064i
$989$	15.5001			0.492875
$990$		0			0
$991$	28.7534			0.913382			0.456691	−	0.889625i	$-0.349034\pi$
$991$	28.7534			0.913382			0.456691	+	0.889625i	$0.349034\pi$
$992$	13.4968	−	26.4889i	0.428523	−	0.841024i
$993$		0			0
$994$	−5.13428	−	7.06673i	−0.162850	−	0.224143i
$995$	1.81483	+	20.3838i	0.0575339	+	0.646209i
$996$		0			0
$997$	−47.3692	−	7.50254i	−1.50020	−	0.237608i	−0.648327	−	0.761362i	$-0.724531\pi$
$997$	−47.3692	−	7.50254i	−1.50020	−	0.237608i	−0.851870	+	0.523754i	$0.824531\pi$
$998$	−31.7379	+	5.02680i	−1.00465	+	0.159120i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.b.28.3	✓	96
3.2	odd	2	inner	495.2.bj.b.28.10	yes	96
5.2	odd	4	inner	495.2.bj.b.127.3	yes	96
11.2	odd	10	inner	495.2.bj.b.343.3	yes	96
15.2	even	4	inner	495.2.bj.b.127.10	yes	96
33.2	even	10	inner	495.2.bj.b.343.10	yes	96
55.2	even	20	inner	495.2.bj.b.442.3	yes	96
165.2	odd	20	inner	495.2.bj.b.442.10	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.bj.b.28.3	✓	96	1.1	even	1	trivial
495.2.bj.b.28.10	yes	96	3.2	odd	2	inner
495.2.bj.b.127.3	yes	96	5.2	odd	4	inner
495.2.bj.b.127.10	yes	96	15.2	even	4	inner
495.2.bj.b.343.3	yes	96	11.2	odd	10	inner
495.2.bj.b.343.10	yes	96	33.2	even	10	inner
495.2.bj.b.442.3	yes	96	55.2	even	20	inner
495.2.bj.b.442.10	yes	96	165.2	odd	20	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.717635 + 1.40844i) q^{2} +(-0.293128 - 0.403456i) q^{4} +(-2.22726 + 0.198299i) q^{5} +(-1.38435 - 0.219259i) q^{7} +(-2.34393 + 0.371242i) q^{8} +O(q^{10})\)	\(q+(-0.717635 + 1.40844i) q^{2} +(-0.293128 - 0.403456i) q^{4} +(-2.22726 + 0.198299i) q^{5} +(-1.38435 - 0.219259i) q^{7} +(-2.34393 + 0.371242i) q^{8} +(1.31907 - 3.27926i) q^{10} +(-2.66778 - 1.97053i) q^{11} +(3.52738 + 1.79729i) q^{13} +(1.30227 - 1.79242i) q^{14} +(1.46743 - 4.51628i) q^{16} +(5.73220 - 2.92070i) q^{17} +(-5.32069 - 3.86571i) q^{19} +(0.732877 + 0.840474i) q^{20} +(4.68985 - 2.34328i) q^{22} +(-1.11787 - 1.11787i) q^{23} +(4.92135 - 0.883328i) q^{25} +(-5.06274 + 3.67830i) q^{26} +(0.317330 + 0.622796i) q^{28} +(-5.95846 + 4.32907i) q^{29} +(-3.32844 - 10.2439i) q^{31} +(1.95169 + 1.95169i) q^{32} +10.1694i q^{34} +(3.12678 + 0.213832i) q^{35} +(0.0713104 - 0.450236i) q^{37} +(9.26293 - 4.71970i) q^{38} +(5.14692 - 1.29165i) q^{40} +(6.01541 - 8.27950i) q^{41} +(-6.93289 + 6.93289i) q^{43} +(-0.0130212 + 1.65395i) q^{44} +(2.37667 - 0.772228i) q^{46} +(-3.74738 + 0.593527i) q^{47} +(-4.78905 - 1.55606i) q^{49} +(-2.28763 + 7.56533i) q^{50} +(-0.308846 - 1.94998i) q^{52} +(-0.248980 + 0.488651i) q^{53} +(6.33258 + 3.85985i) q^{55} +3.32622 q^{56} +(-1.82123 - 11.4988i) q^{58} +(3.38411 + 4.65783i) q^{59} +(-5.32421 - 1.72994i) q^{61} +(16.8165 + 2.66347i) q^{62} +(4.88313 - 1.58662i) q^{64} +(-8.21278 - 3.30355i) q^{65} +(1.40496 - 1.40496i) q^{67} +(-2.85864 - 1.45655i) q^{68} +(-2.54506 + 4.25043i) q^{70} +(1.21832 - 3.74960i) q^{71} +(-2.11527 + 13.3553i) q^{73} +(0.582955 + 0.423542i) q^{74} +3.27981i q^{76} +(3.26108 + 3.31283i) q^{77} +(1.07007 + 3.29335i) q^{79} +(-2.37277 + 10.3499i) q^{80} +(7.34430 + 14.4140i) q^{82} +(-2.33282 - 4.57841i) q^{83} +(-12.1879 + 7.64184i) q^{85} +(-4.78926 - 14.7398i) q^{86} +(6.98462 + 3.62839i) q^{88} -7.54227i q^{89} +(-4.48905 - 3.26149i) q^{91} +(-0.123332 + 0.778690i) q^{92} +(1.85331 - 5.70389i) q^{94} +(12.6171 + 7.55484i) q^{95} +(-2.39124 - 1.21840i) q^{97} +(5.62840 - 5.62840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 20 q^{7}+O(q^{10}) \) 96 * q + 20 * q^7	\( 96 q + 20 q^{7} + 40 q^{16} + 8 q^{22} - 16 q^{25} - 60 q^{28} + 16 q^{31} - 40 q^{37} + 280 q^{46} + 40 q^{52} + 24 q^{55} - 68 q^{58} + 40 q^{61} + 16 q^{67} + 52 q^{70} - 60 q^{73} - 112 q^{82} + 80 q^{85} + 24 q^{88} - 56 q^{91} - 112 q^{97}+O(q^{100}) \) 96 * q + 20 * q^7 + 40 * q^16 + 8 * q^22 - 16 * q^25 - 60 * q^28 + 16 * q^31 - 40 * q^37 + 280 * q^46 + 40 * q^52 + 24 * q^55 - 68 * q^58 + 40 * q^61 + 16 * q^67 + 52 * q^70 - 60 * q^73 - 112 * q^82 + 80 * q^85 + 24 * q^88 - 56 * q^91 - 112 * q^97

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