LMFDB - Embedded newform 855.2.bs.c.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.2
Root			$-0.128481 - 0.222535i$ of defining polynomial
Character	$\chi$	$=$	855.271
Dual form			855.2.bs.c.631.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18116 - 0.429906i) q^{2} +(-0.321776 + 0.270002i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-1.86196 - 3.22501i) q^{7} +(-1.52095 + 2.63437i) q^{8} +O(q^{10})$	\(q+(1.18116 - 0.429906i) q^{2} +(-0.321776 + 0.270002i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-1.86196 - 3.22501i) q^{7} +(-1.52095 + 2.63437i) q^{8} +(-1.18116 - 0.429906i) q^{10} +(-1.67794 + 2.90627i) q^{11} +(0.840684 + 4.76776i) q^{13} +(-3.58572 - 3.00877i) q^{14} +(-0.518073 + 2.93814i) q^{16} +(-2.51392 + 0.914991i) q^{17} +(0.961823 + 4.25146i) q^{19} +0.420048 q^{20} +(-0.732484 + 4.15412i) q^{22} +(-1.43789 + 1.20653i) q^{23} +(0.173648 + 0.984808i) q^{25} +(3.04267 + 5.27006i) q^{26} +(1.46989 + 0.534997i) q^{28} +(-4.93461 - 1.79605i) q^{29} +(1.55945 + 2.70105i) q^{31} +(-0.405246 - 2.29826i) q^{32} +(-2.57597 + 2.16150i) q^{34} +(-0.646652 + 3.66734i) q^{35} +0.992927 q^{37} +(2.96379 + 4.60815i) q^{38} +(2.85846 - 1.04039i) q^{40} +(-0.0723041 + 0.410057i) q^{41} +(-5.52990 - 4.64013i) q^{43} +(-0.244780 - 1.38822i) q^{44} +(-1.17968 + 2.04326i) q^{46} +(2.10572 + 0.766421i) q^{47} +(-3.43378 + 5.94749i) q^{49} +(0.628481 + 1.08856i) q^{50} +(-1.55782 - 1.30716i) q^{52} +(-0.199365 + 0.167287i) q^{53} +(3.15349 - 1.14778i) q^{55} +11.3278 q^{56} -6.60069 q^{58} +(-4.87590 + 1.77468i) q^{59} +(0.589041 - 0.494264i) q^{61} +(3.00316 + 2.51995i) q^{62} +(-4.45016 - 7.70790i) q^{64} +(2.42065 - 4.19270i) q^{65} +(-10.1275 - 3.68611i) q^{67} +(0.561868 - 0.973185i) q^{68} +(0.812816 + 4.60971i) q^{70} +(-1.53320 - 1.28651i) q^{71} +(0.792291 - 4.49331i) q^{73} +(1.17280 - 0.426865i) q^{74} +(-1.45739 - 1.10832i) q^{76} +12.4970 q^{77} +(-2.09282 + 11.8690i) q^{79} +(2.28546 - 1.91773i) q^{80} +(0.0908835 + 0.515426i) q^{82} +(-6.78553 - 11.7529i) q^{83} +(2.51392 + 0.914991i) q^{85} +(-8.52650 - 3.10339i) q^{86} +(-5.10413 - 8.84062i) q^{88} +(1.33178 + 7.55289i) q^{89} +(13.8107 - 11.5886i) q^{91} +(0.136912 - 0.776465i) q^{92} +2.81668 q^{94} +(1.99599 - 3.87505i) q^{95} +(6.79298 - 2.47244i) q^{97} +(-1.49898 + 8.50112i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.18116	−	0.429906i	0.835204	−	0.303989i	0.111211	−	0.993797i	$-0.464527\pi$
$2$	1.18116	−	0.429906i	0.835204	−	0.303989i	0.723993	+	0.689807i	$0.242305\pi$
$3$		0			0
$3$		0			0
$4$	−0.321776	+	0.270002i	−0.160888	+	0.135001i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$6$		0			0
$7$	−1.86196	−	3.22501i	−0.703754	−	1.21894i	−0.967139	−	0.254247i	$-0.918172\pi$
$7$	−1.86196	−	3.22501i	−0.703754	−	1.21894i	0.263385	−	0.964691i	$-0.415161\pi$
$8$	−1.52095	+	2.63437i	−0.537738	+	0.931390i
$9$		0			0
$10$	−1.18116	−	0.429906i	−0.373515	−	0.135948i
$11$	−1.67794	+	2.90627i	−0.505917	+	0.876275i	0.494059	+	0.869428i	$0.335513\pi$
$11$	−1.67794	+	2.90627i	−0.505917	+	0.876275i	−0.999977	+	0.00684646i	$0.997821\pi$
$12$		0			0
$13$	0.840684	+	4.76776i	0.233164	+	1.32234i	0.846446	+	0.532474i	$0.178738\pi$
$13$	0.840684	+	4.76776i	0.233164	+	1.32234i	−0.613282	+	0.789864i	$0.710151\pi$
$14$	−3.58572	−	3.00877i	−0.958323	−	0.804129i
$15$		0			0
$16$	−0.518073	+	2.93814i	−0.129518	+	0.734534i
$17$	−2.51392	+	0.914991i	−0.609715	+	0.221918i	−0.628378	−	0.777908i	$-0.716281\pi$
$17$	−2.51392	+	0.914991i	−0.609715	+	0.221918i	0.0186637	+	0.999826i	$0.494059\pi$
$18$		0			0
$19$	0.961823	+	4.25146i	0.220657	+	0.975351i
$19$	0.961823	+	4.25146i	0.220657	+	0.975351i
$20$	0.420048			0.0939257
$21$		0			0
$22$	−0.732484	+	4.15412i	−0.156166	+	0.885662i
$23$	−1.43789	+	1.20653i	−0.299820	+	0.251579i	−0.780270	−	0.625443i	$-0.784918\pi$
$23$	−1.43789	+	1.20653i	−0.299820	+	0.251579i	0.480449	+	0.877023i	$0.340474\pi$
$24$		0			0
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	3.04267	+	5.27006i	0.596716	+	1.03354i
$27$		0			0
$28$	1.46989	+	0.534997i	0.277783	+	0.101105i
$29$	−4.93461	−	1.79605i	−0.916335	−	0.333519i	−0.159555	−	0.987189i	$-0.551006\pi$
$29$	−4.93461	−	1.79605i	−0.916335	−	0.333519i	−0.756779	+	0.653670i	$0.773228\pi$
$30$		0			0
$31$	1.55945	+	2.70105i	0.280086	+	0.485124i	0.971406	−	0.237426i	$-0.0763036\pi$
$31$	1.55945	+	2.70105i	0.280086	+	0.485124i	−0.691319	+	0.722549i	$0.742970\pi$
$32$	−0.405246	−	2.29826i	−0.0716380	−	0.406279i
$33$		0			0
$34$	−2.57597	+	2.16150i	−0.441776	+	0.370694i
$35$	−0.646652	+	3.66734i	−0.109304	+	0.619894i
$36$		0			0
$37$	0.992927			0.163236			0.0816181	−	0.996664i	$-0.473991\pi$
$37$	0.992927			0.163236			0.0816181	+	0.996664i	$0.473991\pi$
$38$	2.96379	+	4.60815i	0.480790	+	0.747540i
$39$		0			0
$40$	2.85846	−	1.04039i	0.451962	−	0.164501i
$41$	−0.0723041	+	0.410057i	−0.0112920	+	0.0640401i	−0.989933	−	0.141536i	$-0.954796\pi$
$41$	−0.0723041	+	0.410057i	−0.0112920	+	0.0640401i	0.978641	+	0.205576i	$0.0659069\pi$
$42$		0			0
$43$	−5.52990	−	4.64013i	−0.843301	−	0.707614i	0.115003	−	0.993365i	$-0.463312\pi$
$43$	−5.52990	−	4.64013i	−0.843301	−	0.707614i	−0.958304	+	0.285751i	$0.907757\pi$
$44$	−0.244780	−	1.38822i	−0.0369020	−	0.209281i
$45$		0			0
$46$	−1.17968	+	2.04326i	−0.173934	+	0.301262i
$47$	2.10572	+	0.766421i	0.307151	+	0.111794i	0.490997	−	0.871161i	$-0.336633\pi$
$47$	2.10572	+	0.766421i	0.307151	+	0.111794i	−0.183846	+	0.982955i	$0.558855\pi$
$48$		0			0
$49$	−3.43378	+	5.94749i	−0.490540	+	0.849641i
$50$	0.628481	+	1.08856i	0.0888806	+	0.153946i
$51$		0			0
$52$	−1.55782	−	1.30716i	−0.216030	−	0.181271i
$53$	−0.199365	+	0.167287i	−0.0273848	+	0.0229786i	−0.656377	−	0.754433i	$-0.727912\pi$
$53$	−0.199365	+	0.167287i	−0.0273848	+	0.0229786i	0.628993	+	0.777411i	$0.283468\pi$
$54$		0			0
$55$	3.15349	−	1.14778i	0.425217	−	0.154766i
$56$	11.3278			1.51374
$57$		0			0
$58$	−6.60069			−0.866713
$59$	−4.87590	+	1.77468i	−0.634789	+	0.231044i	−0.639314	−	0.768946i	$-0.720782\pi$
$59$	−4.87590	+	1.77468i	−0.634789	+	0.231044i	0.00452556	+	0.999990i	$0.498559\pi$
$60$		0			0
$61$	0.589041	−	0.494264i	0.0754189	−	0.0632840i	−0.604299	−	0.796758i	$-0.706547\pi$
$61$	0.589041	−	0.494264i	0.0754189	−	0.0632840i	0.679718	+	0.733474i	$0.262102\pi$
$62$	3.00316	+	2.51995i	0.381402	+	0.320034i
$63$		0			0
$64$	−4.45016	−	7.70790i	−0.556270	−	0.963488i
$65$	2.42065	−	4.19270i	0.300245	−	0.520040i
$66$		0			0
$67$	−10.1275	−	3.68611i	−1.23727	−	0.450330i	−0.361190	−	0.932492i	$-0.617629\pi$
$67$	−10.1275	−	3.68611i	−1.23727	−	0.450330i	−0.876082	+	0.482162i	$0.839852\pi$
$68$	0.561868	−	0.973185i	0.0681366	−	0.118016i
$69$		0			0
$70$	0.812816	+	4.60971i	0.0971501	+	0.550966i
$71$	−1.53320	−	1.28651i	−0.181958	−	0.152681i	0.547259	−	0.836963i	$-0.315671\pi$
$71$	−1.53320	−	1.28651i	−0.181958	−	0.152681i	−0.729217	+	0.684282i	$0.760116\pi$
$72$		0			0
$73$	0.792291	−	4.49331i	0.0927307	−	0.525902i	−0.902688	−	0.430295i	$-0.858410\pi$
$73$	0.792291	−	4.49331i	0.0927307	−	0.525902i	0.995419	−	0.0956071i	$-0.0304792\pi$
$74$	1.17280	−	0.426865i	0.136336	−	0.0496221i
$75$		0			0
$76$	−1.45739	−	1.10832i	−0.167174	−	0.127133i
$77$	12.4970			1.42417
$78$		0			0
$79$	−2.09282	+	11.8690i	−0.235460	+	1.33536i	0.606181	+	0.795326i	$0.292701\pi$
$79$	−2.09282	+	11.8690i	−0.235460	+	1.33536i	−0.841642	+	0.540036i	$0.818411\pi$
$80$	2.28546	−	1.91773i	0.255523	−	0.214409i
$81$		0			0
$82$	0.0908835	+	0.515426i	0.0100364	+	0.0569192i
$83$	−6.78553	−	11.7529i	−0.744809	−	1.29005i	−0.950284	−	0.311384i	$-0.899207\pi$
$83$	−6.78553	−	11.7529i	−0.744809	−	1.29005i	0.205475	−	0.978662i	$-0.434126\pi$
$84$		0			0
$85$	2.51392	+	0.914991i	0.272673	+	0.0992447i
$86$	−8.52650	−	3.10339i	−0.919436	−	0.334647i
$87$		0			0
$88$	−5.10413	−	8.84062i	−0.544102	−	0.942413i
$89$	1.33178	+	7.55289i	0.141168	+	0.800605i	0.970364	+	0.241647i	$0.0776876\pi$
$89$	1.33178	+	7.55289i	0.141168	+	0.800605i	−0.829196	+	0.558958i	$0.811201\pi$
$90$		0			0
$91$	13.8107	−	11.5886i	1.44776	−	1.21481i
$92$	0.136912	−	0.776465i	0.0142740	−	0.0809521i
$93$		0			0
$94$	2.81668			0.290518
$95$	1.99599	−	3.87505i	0.204784	−	0.397572i
$96$		0			0
$97$	6.79298	−	2.47244i	0.689723	−	0.251039i	0.0267064	−	0.999643i	$-0.491498\pi$
$97$	6.79298	−	2.47244i	0.689723	−	0.251039i	0.663017	+	0.748605i	$0.269276\pi$
$98$	−1.49898	+	8.50112i	−0.151420	+	0.858743i
$99$		0			0
$100$	−0.321776	−	0.270002i	−0.0321776	−	0.0270002i
$101$	−0.779999	−	4.42360i	−0.0776128	−	0.440164i	−0.998708	−	0.0508257i	$-0.983815\pi$
$101$	−0.779999	−	4.42360i	−0.0776128	−	0.440164i	0.921095	−	0.389339i	$-0.127296\pi$
$102$		0			0
$103$	−5.37227	+	9.30504i	−0.529345	+	0.916853i	0.470069	+	0.882630i	$0.344229\pi$
$103$	−5.37227	+	9.30504i	−0.529345	+	0.916853i	−0.999414	+	0.0342231i	$0.989104\pi$
$104$	−13.8387	−	5.03686i	−1.35699	−	0.493905i
$105$		0			0
$106$	−0.163563	+	0.283300i	−0.0158867	+	0.0275165i
$107$	0.689315	+	1.19393i	0.0666386	+	0.115421i	0.897420	−	0.441178i	$-0.145439\pi$
$107$	0.689315	+	1.19393i	0.0666386	+	0.115421i	−0.830781	+	0.556599i	$0.812106\pi$
$108$		0			0
$109$	7.27648	+	6.10570i	0.696961	+	0.584820i	0.920907	−	0.389782i	$-0.127450\pi$
$109$	7.27648	+	6.10570i	0.696961	+	0.584820i	−0.223946	+	0.974601i	$0.571894\pi$
$110$	3.23133	−	2.71141i	0.308096	−	0.258523i
$111$		0			0
$112$	10.4401	−	3.79990i	0.986501	−	0.359057i
$113$	17.0436			1.60333			0.801666	−	0.597772i	$-0.203947\pi$
$113$	17.0436			1.60333			0.801666	+	0.597772i	$0.203947\pi$
$114$		0			0
$115$	1.87703			0.175034
$116$	2.07278	−	0.754429i	0.192453	−	0.0700470i
$117$		0			0
$118$	−4.99626	+	4.19236i	−0.459943	+	0.385938i
$119$	7.63167	+	6.40373i	0.699594	+	0.587029i
$120$		0			0
$121$	−0.130955	−	0.226821i	−0.0119050	−	0.0206201i
$122$	0.483263	−	0.837035i	0.0437525	−	0.0757816i
$123$		0			0
$124$	−1.23108	−	0.448078i	−0.110555	−	0.0402386i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$		0			0
$127$	3.44862	+	19.5581i	0.306016	+	1.73550i	0.618685	+	0.785640i	$0.287666\pi$
$127$	3.44862	+	19.5581i	0.306016	+	1.73550i	−0.312669	+	0.949862i	$0.601223\pi$
$128$	−4.99455	−	4.19092i	−0.441460	−	0.370429i
$129$		0			0
$130$	1.05671	−	5.99289i	0.0926794	−	0.525611i
$131$	5.09611	−	1.85483i	0.445249	−	0.162057i	−0.109659	−	0.993969i	$-0.534976\pi$
$131$	5.09611	−	1.85483i	0.445249	−	0.162057i	0.554908	+	0.831912i	$0.312754\pi$
$132$		0			0
$133$	11.9201	−	11.0179i	1.03360	−	0.955375i
$134$	−13.5469			−1.17027
$135$		0			0
$136$	1.41313	−	8.01425i	0.121175	−	0.687216i
$137$	14.2189	−	11.9311i	1.21480	−	1.01934i	0.215723	−	0.976455i	$-0.430789\pi$
$137$	14.2189	−	11.9311i	1.21480	−	1.01934i	0.999080	−	0.0428860i	$-0.0136552\pi$
$138$		0			0
$139$	−1.82551	−	10.3530i	−0.154838	−	0.878128i	−0.958934	−	0.283629i	$-0.908461\pi$
$139$	−1.82551	−	10.3530i	−0.154838	−	0.878128i	0.804096	−	0.594499i	$-0.202650\pi$
$140$	−0.782113	−	1.35466i	−0.0661006	−	0.114490i
$141$		0			0
$142$	−2.36404	−	0.860438i	−0.198385	−	0.0722064i
$143$	−15.2670	−	5.55674i	−1.27669	−	0.464678i
$144$		0			0
$145$	2.62565	+	4.54776i	0.218049	+	0.377671i
$146$	−0.995879	−	5.64791i	−0.0824196	−	0.467425i
$147$		0			0
$148$	−0.319500	+	0.268092i	−0.0262627	+	0.0220370i
$149$	−2.62919	+	14.9109i	−0.215392	+	1.22155i	0.664834	+	0.746992i	$0.268502\pi$
$149$	−2.62919	+	14.9109i	−0.215392	+	1.22155i	−0.880225	+	0.474556i	$0.842609\pi$
$150$		0			0
$151$	11.3432			0.923095			0.461548	−	0.887115i	$-0.347294\pi$
$151$	11.3432			0.923095			0.461548	+	0.887115i	$0.347294\pi$
$152$	−12.6628	−	3.93248i	−1.02709	−	0.318966i
$153$		0			0
$154$	14.7609	−	5.37254i	1.18947	−	0.432932i
$155$	0.541593	−	3.07153i	0.0435018	−	0.246711i
$156$		0			0
$157$	−3.22909	−	2.70953i	−0.257710	−	0.216244i	0.504774	−	0.863252i	$-0.331576\pi$
$157$	−3.22909	−	2.70953i	−0.257710	−	0.216244i	−0.762484	+	0.647007i	$0.776020\pi$
$158$	2.63059	+	14.9188i	0.209279	+	1.18688i
$159$		0			0
$160$	−1.16686	+	2.02106i	−0.0922483	+	0.159779i
$161$	6.56836	+	2.39069i	0.517659	+	0.188413i
$162$		0			0
$163$	6.95280	−	12.0426i	0.544585	−	0.943249i	−0.454048	−	0.890977i	$-0.650020\pi$
$163$	6.95280	−	12.0426i	0.544585	−	0.943249i	0.998633	−	0.0522718i	$-0.0166462\pi$
$164$	−0.0874505	−	0.151469i	−0.00682873	−	0.0118277i
$165$		0			0
$166$	−13.0674	−	10.9649i	−1.01423	−	0.851038i
$167$	−13.4994	+	11.3273i	−1.04462	+	0.876537i	−0.992517	−	0.122105i	$-0.961035\pi$
$167$	−13.4994	+	11.3273i	−1.04462	+	0.876537i	−0.0520984	+	0.998642i	$0.516591\pi$
$168$		0			0
$169$	−9.80875	+	3.57009i	−0.754519	+	0.274623i
$170$	3.36269			0.257907
$171$		0			0
$172$	3.03223			0.231206
$173$	−12.5150	+	4.55510i	−0.951499	+	0.346317i	−0.770697	−	0.637202i	$-0.780092\pi$
$173$	−12.5150	+	4.55510i	−0.951499	+	0.346317i	−0.180803	+	0.983519i	$0.557869\pi$
$174$		0			0
$175$	2.85269	−	2.39369i	0.215643	−	0.180946i
$176$	−7.66974	−	6.43567i	−0.578128	−	0.485107i
$177$		0			0
$178$	4.82007	+	8.34861i	0.361280	+	0.625755i
$179$	7.31322	−	12.6669i	0.546616	−	0.946767i	−0.451887	−	0.892075i	$-0.649249\pi$
$179$	7.31322	−	12.6669i	0.546616	−	0.946767i	0.998503	−	0.0546916i	$-0.0174176\pi$
$180$		0			0
$181$	8.25497	+	3.00456i	0.613587	+	0.223328i	0.630072	−	0.776537i	$-0.283025\pi$
$181$	8.25497	+	3.00456i	0.613587	+	0.223328i	−0.0164849	+	0.999864i	$0.505248\pi$
$182$	11.3306	−	19.6253i	0.839883	−	1.45472i
$183$		0			0
$184$	−0.991488	−	5.62301i	−0.0730934	−	0.414533i
$185$	−0.760626	−	0.638241i	−0.0559223	−	0.0469244i
$186$		0			0
$187$	1.55898	−	8.84144i	0.114004	−	0.646550i
$188$	−0.884506	+	0.321934i	−0.0645092	+	0.0234794i
$189$		0			0
$190$	0.691664	−	5.43513i	0.0501786	−	0.394306i
$191$	9.70737			0.702401			0.351200	−	0.936300i	$-0.385774\pi$
$191$	9.70737			0.702401			0.351200	+	0.936300i	$0.385774\pi$
$192$		0			0
$193$	−3.51718	+	19.9469i	−0.253172	+	1.43581i	0.547549	+	0.836774i	$0.315561\pi$
$193$	−3.51718	+	19.9469i	−0.253172	+	1.43581i	−0.800721	+	0.599038i	$0.795550\pi$
$194$	6.96066	−	5.84069i	0.499747	−	0.419337i
$195$		0			0
$196$	−0.500925	−	2.84089i	−0.0357803	−	0.202920i
$197$	−4.63091	−	8.02097i	−0.329939	−	0.571470i	0.652561	−	0.757736i	$-0.273695\pi$
$197$	−4.63091	−	8.02097i	−0.329939	−	0.571470i	−0.982499	+	0.186266i	$0.940361\pi$
$198$		0			0
$199$	−17.0574	−	6.20837i	−1.20916	−	0.440100i	−0.342750	−	0.939427i	$-0.611358\pi$
$199$	−17.0574	−	6.20837i	−1.20916	−	0.440100i	−0.866414	+	0.499327i	$0.833581\pi$
$200$	−2.85846	−	1.04039i	−0.202123	−	0.0735669i
$201$		0			0
$202$	−2.82303	−	4.88964i	−0.198628	−	0.344034i
$203$	3.39577	+	19.2583i	0.238336	+	1.35167i
$204$		0			0
$205$	0.318968	−	0.267646i	0.0222777	−	0.0186932i
$206$	−2.34520	+	13.3003i	−0.163398	+	0.926675i
$207$		0			0
$208$	−14.4439			−1.00150
$209$	−13.9698	−	4.33836i	−0.966310	−	0.300091i
$210$		0			0
$211$	−16.3337	+	5.94498i	−1.12446	+	0.409269i	−0.836277	−	0.548307i	$-0.815273\pi$
$211$	−16.3337	+	5.94498i	−1.12446	+	0.409269i	−0.288181	+	0.957576i	$0.593050\pi$
$212$	0.0189829	−	0.107658i	0.00130375	−	0.00739396i
$213$		0			0
$214$	1.32747	+	1.11388i	0.0907438	+	0.0761431i
$215$	1.25353	+	7.10910i	0.0854897	+	0.484836i
$216$		0			0
$217$	5.80728	−	10.0585i	0.394224	−	0.682816i
$218$	11.2195	+	4.08358i	0.759884	+	0.276575i
$219$		0			0
$220$	−0.704815	+	1.22078i	−0.0475186	+	0.0823047i
$221$	−6.47587	−	11.2165i	−0.435614	−	0.754505i
$222$		0			0
$223$	−6.68504	−	5.60941i	−0.447663	−	0.375634i	0.390905	−	0.920431i	$-0.372162\pi$
$223$	−6.68504	−	5.60941i	−0.447663	−	0.375634i	−0.838568	+	0.544797i	$0.816607\pi$
$224$	−6.65737	+	5.58619i	−0.444814	+	0.373243i
$225$		0			0
$226$	20.1312	−	7.32717i	1.33911	−	0.487396i
$227$	20.1154			1.33510			0.667552	−	0.744563i	$-0.267342\pi$
$227$	20.1154			1.33510			0.667552	+	0.744563i	$0.267342\pi$
$228$		0			0
$229$	−20.8410			−1.37721			−0.688607	−	0.725135i	$-0.741778\pi$
$229$	−20.8410			−1.37721			−0.688607	+	0.725135i	$0.741778\pi$
$230$	2.21707	−	0.806946i	0.146189	−	0.0532085i
$231$		0			0
$232$	12.2368	−	10.2679i	0.803384	−	0.674119i
$233$	−0.416767	−	0.349709i	−0.0273033	−	0.0229102i	0.629034	−	0.777378i	$-0.283451\pi$
$233$	−0.416767	−	0.349709i	−0.0273033	−	0.0229102i	−0.656337	+	0.754468i	$0.727895\pi$
$234$		0			0
$235$	−1.12043	−	1.94064i	−0.0730889	−	0.126594i
$236$	1.08978	−	1.88755i	0.0709386	−	0.122869i
$237$		0			0
$238$	11.7672	+	4.28291i	0.762754	+	0.277620i
$239$	−11.1117	+	19.2461i	−0.718758	+	1.24493i	0.242733	+	0.970093i	$0.421956\pi$
$239$	−11.1117	+	19.2461i	−0.718758	+	1.24493i	−0.961492	+	0.274833i	$0.911377\pi$
$240$		0			0
$241$	3.77399	+	21.4034i	0.243104	+	1.37871i	0.824854	+	0.565345i	$0.191257\pi$
$241$	3.77399	+	21.4034i	0.243104	+	1.37871i	−0.581750	+	0.813368i	$0.697632\pi$
$242$	−0.252190	−	0.211613i	−0.0162114	−	0.0136030i
$243$		0			0
$244$	−0.0560868	+	0.318084i	−0.00359059	+	0.0203633i
$245$	6.45340	−	2.34885i	0.412293	−	0.150062i
$246$		0			0
$247$	−19.4613	+	8.15987i	−1.23829	+	0.519200i
$248$	−9.48743			−0.602452
$249$		0			0
$250$	0.218269	−	1.23787i	0.0138045	−	0.0782895i
$251$	−13.6539	+	11.4570i	−0.861828	+	0.723160i	−0.962361	−	0.271774i	$-0.912390\pi$
$251$	−13.6539	+	11.4570i	−0.861828	+	0.723160i	0.100533	+	0.994934i	$0.467945\pi$
$252$		0			0
$253$	−1.09382	−	6.20338i	−0.0687681	−	0.390003i
$254$	12.4815	+	21.6186i	0.783160	+	1.35647i
$255$		0			0
$256$	9.02608	+	3.28522i	0.564130	+	0.205326i
$257$	14.7756	+	5.37788i	0.921678	+	0.335463i	0.758906	−	0.651201i	$-0.225734\pi$
$257$	14.7756	+	5.37788i	0.921678	+	0.335463i	0.162772	+	0.986664i	$0.447957\pi$
$258$		0			0
$259$	−1.84879	−	3.20220i	−0.114878	−	0.198975i
$260$	0.353128	+	2.00269i	0.0219001	+	0.124201i
$261$		0			0
$262$	5.22190	−	4.38170i	0.322610	−	0.270702i
$263$	5.28766	−	29.9878i	0.326051	−	1.84913i	−0.176133	−	0.984366i	$-0.556359\pi$
$263$	5.28766	−	29.9878i	0.326051	−	1.84913i	0.502184	−	0.864761i	$-0.332530\pi$
$264$		0			0
$265$	0.260252			0.0159871
$266$	9.34285	−	18.1384i	0.572847	−	1.11214i
$267$		0			0
$268$	4.25404	−	1.54835i	0.259857	−	0.0945802i
$269$	−0.453555	+	2.57224i	−0.0276537	+	0.156832i	−0.995508	−	0.0946808i	$-0.969817\pi$
$269$	−0.453555	+	2.57224i	−0.0276537	+	0.156832i	0.967854	+	0.251513i	$0.0809281\pi$
$270$		0			0
$271$	−7.36033	−	6.17605i	−0.447108	−	0.375168i	0.391253	−	0.920283i	$-0.372042\pi$
$271$	−7.36033	−	6.17605i	−0.447108	−	0.375168i	−0.838361	+	0.545115i	$0.816486\pi$
$272$	−1.38598	−	7.86027i	−0.0840372	−	0.476599i
$273$		0			0
$274$	11.6655	−	20.2053i	0.704740	−	1.22064i
$275$	−3.15349	−	1.14778i	−0.190163	−	0.0692136i
$276$		0			0
$277$	−10.0336	+	17.3787i	−0.602860	+	1.04418i	0.389526	+	0.921015i	$0.372639\pi$
$277$	−10.0336	+	17.3787i	−0.602860	+	1.04418i	−0.992386	+	0.123168i	$0.960695\pi$
$278$	−6.60702	−	11.4437i	−0.396263	−	0.686348i
$279$		0			0
$280$	−8.67761	−	7.28138i	−0.518586	−	0.435146i
$281$	−20.3428	+	17.0696i	−1.21355	+	1.01829i	−0.214410	+	0.976744i	$0.568783\pi$
$281$	−20.3428	+	17.0696i	−1.21355	+	1.01829i	−0.999137	+	0.0415429i	$0.986773\pi$
$282$		0			0
$283$	15.7669	−	5.73869i	0.937247	−	0.341130i	0.172169	−	0.985067i	$-0.444923\pi$
$283$	15.7669	−	5.73869i	0.937247	−	0.341130i	0.765078	+	0.643938i	$0.222700\pi$
$284$	0.840709			0.0498869
$285$		0			0
$286$	−20.4216			−1.20756
$287$	1.45706	−	0.530328i	0.0860078	−	0.0313043i
$288$		0			0
$289$	−7.54018	+	6.32696i	−0.443540	+	0.372174i
$290$	5.05642	+	4.24284i	0.296923	+	0.249148i
$291$		0			0
$292$	0.958262	+	1.65976i	0.0560780	+	0.0971300i
$293$	6.68939	−	11.5864i	0.390799	−	0.676883i	−0.601757	−	0.798680i	$-0.705532\pi$
$293$	6.68939	−	11.5864i	0.390799	−	0.676883i	0.992555	+	0.121797i	$0.0388656\pi$
$294$		0			0
$295$	4.87590	+	1.77468i	0.283886	+	0.103326i
$296$	−1.51020	+	2.61574i	−0.0877783	+	0.152037i
$297$		0			0
$298$	3.30479	+	18.7424i	0.191441	+	1.08572i
$299$	−6.96126	−	5.84119i	−0.402580	−	0.337805i
$300$		0			0
$301$	−4.66803	+	26.4737i	−0.269061	+	1.52592i
$302$	13.3981	−	4.87650i	0.770973	−	0.280611i
$303$		0			0
$304$	−12.9897	+	0.623401i	−0.745008	+	0.0357545i
$305$	−0.768938			−0.0440293
$306$		0			0
$307$	4.85734	−	27.5473i	0.277223	−	1.57221i	−0.454588	−	0.890702i	$-0.650213\pi$
$307$	4.85734	−	27.5473i	0.277223	−	1.57221i	0.731811	−	0.681508i	$-0.238675\pi$
$308$	−4.02124	+	3.37422i	−0.229131	+	0.192264i
$309$		0			0
$310$	−0.680761	−	3.86079i	−0.0386646	−	0.219278i
$311$	12.4175	+	21.5078i	0.704132	+	1.21959i	0.967004	+	0.254762i	$0.0819972\pi$
$311$	12.4175	+	21.5078i	0.704132	+	1.21959i	−0.262871	+	0.964831i	$0.584669\pi$
$312$		0			0
$313$	20.9294	+	7.61769i	1.18300	+	0.430577i	0.857261	−	0.514882i	$-0.172164\pi$
$313$	20.9294	+	7.61769i	1.18300	+	0.430577i	0.325741	+	0.945459i	$0.394386\pi$
$314$	−4.97891	−	1.81218i	−0.280976	−	0.102267i
$315$		0			0
$316$	−2.53122	−	4.38421i	−0.142393	−	0.246631i
$317$	2.44421	+	13.8618i	0.137281	+	0.778557i	0.973244	+	0.229772i	$0.0737982\pi$
$317$	2.44421	+	13.8618i	0.137281	+	0.778557i	−0.835964	+	0.548785i	$0.815091\pi$
$318$		0			0
$319$	13.4998	−	11.3277i	0.755844	−	0.634228i
$320$	−1.54552	+	8.76510i	−0.0863974	+	0.489984i
$321$		0			0
$322$	8.78604			0.489627
$323$	−6.30799	−	9.80776i	−0.350986	−	0.545718i
$324$		0			0
$325$	−4.54934	+	1.65582i	−0.252352	+	0.0918486i
$326$	3.03516	−	17.2133i	0.168102	−	0.953354i
$327$		0			0
$328$	−0.970270	−	0.814153i	−0.0535742	−	0.0449541i
$329$	−1.44906	−	8.21802i	−0.0798892	−	0.453074i
$330$		0			0
$331$	2.64274	−	4.57737i	0.145258	−	0.251595i	−0.784211	−	0.620494i	$-0.786932\pi$
$331$	2.64274	−	4.57737i	0.145258	−	0.251595i	0.929469	+	0.368899i	$0.120265\pi$
$332$	5.35672	+	1.94969i	0.293988	+	0.107003i
$333$		0			0
$334$	−11.0752	+	19.1829i	−0.606009	+	1.04964i
$335$	5.38873	+	9.33356i	0.294418	+	0.509947i
$336$		0			0
$337$	18.2993	+	15.3550i	0.996828	+	0.836438i	0.986542	−	0.163509i	$-0.0522813\pi$
$337$	18.2993	+	15.3550i	0.996828	+	0.836438i	0.0102861	+	0.999947i	$0.496726\pi$
$338$	−10.0509	+	8.43368i	−0.546695	+	0.458732i
$339$		0			0
$340$	−1.05597	+	0.384341i	−0.0572679	+	0.0208438i
$341$	−10.4667			−0.566802
$342$		0			0
$343$	−0.493173			−0.0266288
$344$	20.6345	−	7.51036i	1.11254	−	0.404931i
$345$		0			0
$346$	−12.8239	+	10.7606i	−0.689419	+	0.578492i
$347$	6.71594	+	5.63534i	0.360531	+	0.302521i	0.805002	−	0.593272i	$-0.202164\pi$
$347$	6.71594	+	5.63534i	0.360531	+	0.302521i	−0.444472	+	0.895793i	$0.646609\pi$
$348$		0			0
$349$	−1.02005	−	1.76679i	−0.0546023	−	0.0945739i	0.837432	−	0.546541i	$-0.184056\pi$
$349$	−1.02005	−	1.76679i	−0.0546023	−	0.0945739i	−0.892035	+	0.451967i	$0.850722\pi$
$350$	2.34041	−	4.05371i	0.125100	−	0.216680i
$351$		0			0
$352$	7.35936	+	2.67859i	0.392255	+	0.142769i
$353$	4.53225	−	7.85009i	0.241227	−	0.417818i	−0.719837	−	0.694143i	$-0.755783\pi$
$353$	4.53225	−	7.85009i	0.241227	−	0.417818i	0.961064	+	0.276325i	$0.0891167\pi$
$354$		0			0
$355$	0.347549	+	1.97105i	0.0184460	+	0.104612i
$356$	−2.46783	−	2.07076i	−0.130795	−	0.109750i
$357$		0			0
$358$	3.19250	−	18.1056i	0.168729	−	0.956909i
$359$	−22.1964	+	8.07884i	−1.17148	+	0.426385i	−0.853186	−	0.521606i	$-0.825333\pi$
$359$	−22.1964	+	8.07884i	−1.17148	+	0.426385i	−0.318297	+	0.947991i	$0.603111\pi$
$360$		0			0
$361$	−17.1498	+	8.17830i	−0.902621	+	0.430437i
$362$	11.0421			0.580360
$363$		0			0
$364$	−1.31502	+	7.45785i	−0.0689258	+	0.390898i
$365$	−3.49517	+	2.93280i	−0.182946	+	0.153510i
$366$		0			0
$367$	1.80960	+	10.2628i	0.0944606	+	0.535713i	0.994911	+	0.100755i	$0.0321257\pi$
$367$	1.80960	+	10.2628i	0.0944606	+	0.535713i	−0.900451	+	0.434958i	$0.856763\pi$
$368$	−2.80002	−	4.84978i	−0.145961	−	0.252812i
$369$		0			0
$370$	−1.17280	−	0.426865i	−0.0609711	−	0.0221917i
$371$	0.910709	+	0.331471i	0.0472817	+	0.0172091i
$372$		0			0
$373$	−4.60227	−	7.97137i	−0.238297	−	0.412742i	0.721929	−	0.691967i	$-0.243256\pi$
$373$	−4.60227	−	7.97137i	−0.238297	−	0.412742i	−0.960226	+	0.279225i	$0.909922\pi$
$374$	−1.95958	−	11.1133i	−0.101328	−	0.574657i
$375$		0			0
$376$	−5.22174	+	4.38156i	−0.269291	+	0.225962i
$377$	4.41469	−	25.0370i	0.227368	−	1.28947i
$378$		0			0
$379$	12.6143			0.647954			0.323977	−	0.946065i	$-0.394980\pi$
$379$	12.6143			0.647954			0.323977	+	0.946065i	$0.394980\pi$
$380$	0.404012	+	1.78582i	0.0207254	+	0.0916106i
$381$		0			0
$382$	11.4659	−	4.17326i	0.586648	−	0.213522i
$383$	−0.0919877	+	0.521688i	−0.00470035	+	0.0266570i	−0.987068	−	0.160304i	$-0.948753\pi$
$383$	−0.0919877	+	0.521688i	−0.00470035	+	0.0266570i	0.982367	+	0.186961i	$0.0598637\pi$
$384$		0			0
$385$	−9.57327	−	8.03292i	−0.487899	−	0.409396i
$386$	4.42096	+	25.0725i	0.225021	+	1.27616i
$387$		0			0
$388$	−1.51825	+	2.62969i	−0.0770776	+	0.133502i
$389$	28.5541	+	10.3928i	1.44775	+	0.526938i	0.941962	−	0.335720i	$-0.108980\pi$
$389$	28.5541	+	10.3928i	1.44775	+	0.526938i	0.505788	+	0.862658i	$0.331202\pi$
$390$		0			0
$391$	2.51077	−	4.34878i	0.126975	−	0.219927i
$392$	−10.4452	−	18.0917i	−0.527565	−	0.913769i
$393$		0			0
$394$	−8.91809	−	7.48317i	−0.449287	−	0.376997i
$395$	9.23241	−	7.74692i	0.464533	−	0.389790i
$396$		0			0
$397$	11.3945	−	4.14727i	0.571875	−	0.208146i	−0.0398640	−	0.999205i	$-0.512692\pi$
$397$	11.3945	−	4.14727i	0.571875	−	0.208146i	0.611739	+	0.791060i	$0.290470\pi$
$398$	−22.8164			−1.14368
$399$		0			0
$400$	−2.98346			−0.149173
$401$	−10.8916	+	3.96422i	−0.543900	+	0.197963i	−0.599334	−	0.800499i	$-0.704568\pi$
$401$	−10.8916	+	3.96422i	−0.543900	+	0.197963i	0.0554341	+	0.998462i	$0.482346\pi$
$402$		0			0
$403$	−11.5670	+	9.70583i	−0.576191	+	0.483482i
$404$	1.44536	+	1.21280i	0.0719096	+	0.0603393i
$405$		0			0
$406$	12.2902	+	21.2873i	0.609953	+	1.05647i
$407$	−1.66607	+	2.88572i	−0.0825840	+	0.143040i
$408$		0			0
$409$	−4.54489	−	1.65420i	−0.224730	−	0.0817952i	0.227201	−	0.973848i	$-0.427043\pi$
$409$	−4.54489	−	1.65420i	−0.224730	−	0.0817952i	−0.451931	+	0.892053i	$0.649265\pi$
$410$	0.261688	−	0.453258i	0.0129239	−	0.0223848i
$411$		0			0
$412$	−0.783713	−	4.44466i	−0.0386108	−	0.218973i
$413$	14.8021	+	12.4204i	0.728364	+	0.611170i
$414$		0			0
$415$	−2.35659	+	13.3649i	−0.115680	+	0.656056i
$416$	10.6169	−	3.86423i	0.520535	−	0.189459i
$417$		0			0
$418$	−18.3656	+	0.881404i	−0.898291	+	0.0431109i
$419$	−12.4329			−0.607385			−0.303693	−	0.952770i	$-0.598220\pi$
$419$	−12.4329			−0.607385			−0.303693	+	0.952770i	$0.598220\pi$
$420$		0			0
$421$	4.79547	−	27.1965i	0.233717	−	1.32547i	−0.611582	−	0.791181i	$-0.709467\pi$
$421$	4.79547	−	27.1965i	0.233717	−	1.32547i	0.845299	−	0.534294i	$-0.179422\pi$
$422$	−16.7369	+	14.0439i	−0.814738	+	0.683647i
$423$		0			0
$424$	−0.137471	−	0.779635i	−0.00667617	−	0.0378624i
$425$	−1.33763	−	2.31684i	−0.0648845	−	0.112383i
$426$		0			0
$427$	−2.69077	−	0.979362i	−0.130216	−	0.0473946i
$428$	−0.544168	−	0.198061i	−0.0263034	−	0.00957364i
$429$		0			0
$430$	4.53686	+	7.85806i	0.218787	+	0.378949i
$431$	−1.23145	−	6.98391i	−0.0593170	−	0.336403i	0.940679	−	0.339298i	$-0.110190\pi$
$431$	−1.23145	−	6.98391i	−0.0593170	−	0.336403i	−0.999996	+	0.00289506i	$0.999078\pi$
$432$		0			0
$433$	−5.04353	+	4.23203i	−0.242377	+	0.203378i	−0.755881	−	0.654709i	$-0.772791\pi$
$433$	−5.04353	+	4.23203i	−0.242377	+	0.203378i	0.513505	+	0.858087i	$0.328347\pi$
$434$	2.53510	−	14.3773i	0.121689	−	0.690131i
$435$		0			0
$436$	−3.98995			−0.191084
$437$	−6.51251	−	4.95265i	−0.311536	−	0.236917i
$438$		0			0
$439$	−4.16119	+	1.51455i	−0.198603	+	0.0722855i	−0.439407	−	0.898288i	$-0.644811\pi$
$439$	−4.16119	+	1.51455i	−0.198603	+	0.0722855i	0.240804	+	0.970574i	$0.422589\pi$
$440$	−1.77265	+	10.0532i	−0.0845076	+	0.479267i
$441$		0			0
$442$	−12.4711	−	10.4645i	−0.593188	−	0.497744i
$443$	0.481376	+	2.73002i	0.0228709	+	0.129707i	0.994105	−	0.108418i	$-0.0345784\pi$
$443$	0.481376	+	2.73002i	0.0228709	+	0.129707i	−0.971235	+	0.238125i	$0.923467\pi$
$444$		0			0
$445$	3.83470	−	6.64190i	0.181782	−	0.314856i
$446$	−10.3076	−	3.75166i	−0.488079	−	0.177646i
$447$		0			0
$448$	−16.5720	+	28.7036i	−0.782955	+	1.35612i
$449$	13.1785	+	22.8258i	0.621930	+	1.07721i	0.989126	+	0.147071i	$0.0469845\pi$
$449$	13.1785	+	22.8258i	0.621930	+	1.07721i	−0.367196	+	0.930144i	$0.619682\pi$
$450$		0			0
$451$	−1.07042	−	0.898186i	−0.0504039	−	0.0422939i
$452$	−5.48423	+	4.60182i	−0.257957	+	0.216451i
$453$		0			0
$454$	23.7594	−	8.64772i	1.11508	−	0.405857i
$455$	−18.0286			−0.845195
$456$		0			0
$457$	33.5784			1.57073			0.785366	−	0.619032i	$-0.212475\pi$
$457$	33.5784			1.57073			0.785366	+	0.619032i	$0.212475\pi$
$458$	−24.6165	+	8.95969i	−1.15026	+	0.418659i
$459$		0			0
$460$	−0.603983	+	0.506802i	−0.0281608	+	0.0236297i
$461$	−23.3279	−	19.5745i	−1.08649	−	0.911674i	−0.0900469	−	0.995938i	$-0.528702\pi$
$461$	−23.3279	−	19.5745i	−1.08649	−	0.911674i	−0.996443	+	0.0842639i	$0.973146\pi$
$462$		0			0
$463$	14.2881	+	24.7477i	0.664025	+	1.15013i	0.979549	+	0.201208i	$0.0644866\pi$
$463$	14.2881	+	24.7477i	0.664025	+	1.15013i	−0.315523	+	0.948918i	$0.602180\pi$
$464$	7.83354	−	13.5681i	0.363663	−	0.629883i
$465$		0			0
$466$	−0.642610	−	0.233891i	−0.0297683	−	0.0108348i
$467$	−5.60863	+	9.71443i	−0.259536	+	0.449530i	−0.966118	−	0.258101i	$-0.916903\pi$
$467$	−5.60863	+	9.71443i	−0.259536	+	0.449530i	0.706581	+	0.707632i	$0.250236\pi$
$468$		0			0
$469$	6.96927	+	39.5247i	0.321811	+	1.82508i
$470$	−2.15770	−	1.81053i	−0.0995273	−	0.0835133i
$471$		0			0
$472$	2.74085	−	15.5441i	0.126158	−	0.715477i
$473$	22.7643	−	8.28554i	1.04670	−	0.380969i
$474$		0			0
$475$	−4.01985	+	1.68547i	−0.184443	+	0.0773346i
$476$	−4.18470			−0.191806
$477$		0			0
$478$	−4.85070	+	27.5097i	−0.221866	+	1.25826i
$479$	13.3219	−	11.1784i	0.608695	−	0.510755i	−0.285532	−	0.958369i	$-0.592170\pi$
$479$	13.3219	−	11.1784i	0.608695	−	0.510755i	0.894227	+	0.447614i	$0.147726\pi$
$480$		0			0
$481$	0.834738	+	4.73403i	0.0380608	+	0.215853i
$482$	13.6591	+	23.6583i	0.622156	+	1.07761i
$483$		0			0
$484$	0.103380	+	0.0376273i	0.00469910	+	0.00171033i
$485$	−6.79298	−	2.47244i	−0.308454	−	0.112268i
$486$		0			0
$487$	−7.67364	−	13.2911i	−0.347726	−	0.602278i	0.638119	−	0.769937i	$-0.279713\pi$
$487$	−7.67364	−	13.2911i	−0.347726	−	0.602278i	−0.985845	+	0.167659i	$0.946379\pi$
$488$	0.406170	+	2.30350i	0.0183864	+	0.104275i
$489$		0			0
$490$	6.61270	−	5.54871i	0.298731	−	0.250665i
$491$	−1.45066	+	8.22710i	−0.0654673	+	0.371284i	0.934419	+	0.356177i	$0.115920\pi$
$491$	−1.45066	+	8.22710i	−0.0654673	+	0.371284i	−0.999886	+	0.0151068i	$0.995191\pi$
$492$		0			0
$493$	14.0486			0.632717
$494$	−19.4789	+	18.0046i	−0.876398	+	0.810067i
$495$		0			0
$496$	−8.74398	+	3.18255i	−0.392616	+	0.142901i
$497$	−1.29425	+	7.34003i	−0.0580548	+	0.329245i
$498$		0			0
$499$	0.207470	+	0.174088i	0.00928764	+	0.00779325i	0.647420	−	0.762134i	$-0.275848\pi$
$499$	0.207470	+	0.174088i	0.00928764	+	0.00779325i	−0.638132	+	0.769927i	$0.720293\pi$
$500$	0.0729407	+	0.413667i	0.00326201	+	0.0184997i
$501$		0			0
$502$	−11.2020	+	19.4024i	−0.499970	+	0.865973i
$503$	39.0907	+	14.2279i	1.74297	+	0.634389i	0.999412	−	0.0342827i	$-0.0109147\pi$
$503$	39.0907	+	14.2279i	1.74297	+	0.634389i	0.743558	+	0.668672i	$0.233137\pi$
$504$		0			0
$505$	−2.24592	+	3.89005i	−0.0999421	+	0.173105i
$506$	−3.95885	−	6.85693i	−0.175992	−	0.304828i
$507$		0			0
$508$	−6.39041	−	5.36219i	−0.283529	−	0.237909i
$509$	−1.24694	+	1.04631i	−0.0552696	+	0.0463767i	−0.670004	−	0.742357i	$-0.733708\pi$
$509$	−1.24694	+	1.04631i	−0.0552696	+	0.0463767i	0.614734	+	0.788734i	$0.289263\pi$
$510$		0			0
$511$	−15.9662	+	5.81121i	−0.706301	+	0.257073i
$512$	25.1134			1.10987
$513$		0			0
$514$	19.7643			0.871766
$515$	10.0966	−	3.67485i	0.444908	−	0.161933i
$516$		0			0
$517$	−5.76070	+	4.83380i	−0.253355	+	0.212590i
$518$	−3.56035	−	2.98749i	−0.156433	−	0.131263i
$519$		0			0
$520$	7.36340	+	12.7538i	0.322907	+	0.559291i
$521$	−4.57062	+	7.91655i	−0.200243	+	0.346830i	−0.948607	−	0.316458i	$-0.897506\pi$
$521$	−4.57062	+	7.91655i	−0.200243	+	0.346830i	0.748364	+	0.663288i	$0.230840\pi$
$522$		0			0
$523$	−35.0501	−	12.7572i	−1.53263	−	0.557833i	−0.568368	−	0.822774i	$-0.692425\pi$
$523$	−35.0501	−	12.7572i	−1.53263	−	0.557833i	−0.964264	+	0.264942i	$0.914647\pi$
$524$	−1.13900	+	1.97280i	−0.0497573	+	0.0861822i
$525$		0			0
$526$	−6.64638	−	37.6935i	−0.289796	−	1.64351i
$527$	−6.39178	−	5.36334i	−0.278430	−	0.233631i
$528$		0			0
$529$	−3.38210	+	19.1809i	−0.147048	+	0.833951i
$530$	0.307398	−	0.111884i	0.0133525	−	0.00485992i
$531$		0			0
$532$	−0.860742	+	6.76376i	−0.0373179	+	0.293246i
$533$	−2.01584			−0.0873156
$534$		0			0
$535$	0.239397	−	1.35769i	0.0103500	−	0.0586979i
$536$	25.1140	−	21.0732i	1.08476	−	0.910223i
$537$		0			0
$538$	0.570101	+	3.23320i	0.0245788	+	0.139393i
$539$	−11.5234	−	19.9590i	−0.496346	−	0.859696i
$540$		0			0
$541$	34.0583	+	12.3962i	1.46428	+	0.532955i	0.946541	−	0.322582i	$-0.104551\pi$
$541$	34.0583	+	12.3962i	1.46428	+	0.532955i	0.517741	+	0.855538i	$0.326773\pi$
$542$	−11.3488	−	4.13063i	−0.487474	−	0.177426i
$543$		0			0
$544$	3.12165	+	5.40685i	0.133839	+	0.231817i
$545$	−1.64945	−	9.35447i	−0.0706545	−	0.400701i
$546$		0			0
$547$	−11.5698	+	9.70823i	−0.494690	+	0.415094i	−0.855704	−	0.517466i	$-0.826875\pi$
$547$	−11.5698	+	9.70823i	−0.494690	+	0.415094i	0.361014	+	0.932561i	$0.382431\pi$
$548$	−1.35388	+	7.67826i	−0.0578351	+	0.327999i
$549$		0			0
$550$	−4.21821			−0.179865
$551$	2.88962	−	22.7068i	0.123102	−	0.967342i
$552$		0			0
$553$	42.1742	−	15.3502i	1.79343	−	0.652755i
$554$	−4.38004	+	24.8404i	−0.186090	+	1.05537i
$555$		0			0
$556$	3.38273	+	2.83845i	0.143460	+	0.120377i
$557$	1.62582	+	9.22051i	0.0688884	+	0.390685i	0.999684	+	0.0251450i	$0.00800473\pi$
$557$	1.62582	+	9.22051i	0.0688884	+	0.390685i	−0.930795	+	0.365541i	$0.880884\pi$
$558$		0			0
$559$	17.4741	−	30.2661i	0.739077	−	1.28012i
$560$	−10.4401	−	3.79990i	−0.441177	−	0.160575i
$561$		0			0
$562$	−16.6897	+	28.9073i	−0.704011	+	1.21938i
$563$	−7.22271	−	12.5101i	−0.304401	−	0.527238i	0.672727	−	0.739891i	$-0.265123\pi$
$563$	−7.22271	−	12.5101i	−0.304401	−	0.527238i	−0.977128	+	0.212653i	$0.931790\pi$
$564$		0			0
$565$	−13.0562	−	10.9554i	−0.549278	−	0.460899i
$566$	16.1561	−	13.5566i	0.679092	−	0.569826i
$567$		0			0
$568$	5.72108	−	2.08230i	0.240051	−	0.0873715i
$569$	37.8642			1.58735			0.793675	−	0.608342i	$-0.208165\pi$
$569$	37.8642			1.58735			0.793675	+	0.608342i	$0.208165\pi$
$570$		0			0
$571$	−18.5203			−0.775048			−0.387524	−	0.921860i	$-0.626670\pi$
$571$	−18.5203			−0.775048			−0.387524	+	0.921860i	$0.626670\pi$
$572$	6.41289	−	2.33410i	0.268136	−	0.0975937i
$573$		0			0
$574$	1.49303	−	1.25280i	0.0623179	−	0.0522909i
$575$	−1.43789	−	1.20653i	−0.0599641	−	0.0503158i
$576$		0			0
$577$	4.54048	+	7.86434i	0.189022	+	0.327397i	0.944925	−	0.327288i	$-0.106135\pi$
$577$	4.54048	+	7.86434i	0.189022	+	0.327397i	−0.755902	+	0.654685i	$0.772801\pi$
$578$	−6.18614	+	10.7147i	−0.257309	+	0.445673i
$579$		0			0
$580$	−2.07278	−	0.754429i	−0.0860674	−	0.0313260i
$581$	−25.2688	+	43.7668i	−1.04832	+	1.81575i
$582$		0			0
$583$	−0.151660	−	0.860105i	−0.00628110	−	0.0356219i
$584$	10.6320	+	8.92130i	0.439955	+	0.369166i
$585$		0			0
$586$	2.92017	−	16.5611i	0.120631	−	0.684134i
$587$	−21.6480	+	7.87923i	−0.893509	+	0.325211i	−0.747649	−	0.664094i	$-0.768817\pi$
$587$	−21.6480	+	7.87923i	−0.893509	+	0.325211i	−0.145860	+	0.989305i	$0.546595\pi$
$588$		0			0
$589$	−9.98350	+	9.22789i	−0.411363	+	0.380229i
$590$	6.52216			0.268513
$591$		0			0
$592$	−0.514408	+	2.91735i	−0.0211421	+	0.119903i
$593$	−30.8280	+	25.8678i	−1.26596	+	1.06226i	−0.270935	+	0.962598i	$0.587333\pi$
$593$	−30.8280	+	25.8678i	−1.26596	+	1.06226i	−0.995021	+	0.0996654i	$0.968223\pi$
$594$		0			0
$595$	−1.72996	−	9.81108i	−0.0709214	−	0.402215i
$596$	−3.17996	−	5.50785i	−0.130256	−	0.225610i
$597$		0			0
$598$	−10.7335	−	3.90668i	−0.438926	−	0.159756i
$599$	−35.4913	−	12.9178i	−1.45014	−	0.527807i	−0.507507	−	0.861647i	$-0.669433\pi$
$599$	−35.4913	−	12.9178i	−1.45014	−	0.527807i	−0.942629	+	0.333841i	$0.891655\pi$
$600$		0			0
$601$	−21.9195	−	37.9656i	−0.894113	−	1.54865i	−0.834898	−	0.550404i	$-0.814474\pi$
$601$	−21.9195	−	37.9656i	−0.894113	−	1.54865i	−0.0592147	−	0.998245i	$-0.518860\pi$
$602$	5.86753	+	33.2764i	0.239143	+	1.35625i
$603$		0			0
$604$	−3.64996	+	3.06268i	−0.148515	+	0.124619i
$605$	−0.0454802	+	0.257931i	−0.00184903	+	0.0104864i
$606$		0			0
$607$	−7.80810			−0.316921			−0.158461	−	0.987365i	$-0.550653\pi$
$607$	−7.80810			−0.316921			−0.158461	+	0.987365i	$0.550653\pi$
$608$	9.38120	−	3.93341i	0.380458	−	0.159521i
$609$		0			0
$610$	−0.908236	+	0.330571i	−0.0367734	+	0.0133844i
$611$	−1.88386	+	10.6839i	−0.0762128	+	0.432224i
$612$		0			0
$613$	−29.7958	−	25.0017i	−1.20344	−	1.00981i	−0.999525	−	0.0308202i	$-0.990188\pi$
$613$	−29.7958	−	25.0017i	−1.20344	−	1.00981i	−0.203918	−	0.978988i	$-0.565367\pi$
$614$	−6.10549	−	34.6259i	−0.246397	−	1.39739i
$615$		0			0
$616$	−19.0074	+	32.9217i	−0.765829	+	1.32645i
$617$	11.7100	+	4.26208i	0.471426	+	0.171585i	0.566798	−	0.823857i	$-0.308182\pi$
$617$	11.7100	+	4.26208i	0.471426	+	0.171585i	−0.0953722	+	0.995442i	$0.530404\pi$
$618$		0			0
$619$	1.37870	−	2.38799i	0.0554148	−	0.0959813i	−0.836987	−	0.547222i	$-0.815685\pi$
$619$	1.37870	−	2.38799i	0.0554148	−	0.0959813i	0.892402	+	0.451241i	$0.149019\pi$
$620$	0.655046	+	1.13457i	0.0263073	+	0.0455656i
$621$		0			0
$622$	23.9133	+	20.0657i	0.958838	+	0.804561i
$623$	21.8784	−	18.3582i	0.876540	−	0.735505i
$624$		0			0
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	27.9958			1.11894
$627$		0			0
$628$	1.77062			0.0706555
$629$	−2.49614	+	0.908519i	−0.0995275	+	0.0362250i
$630$		0			0
$631$	−30.5821	+	25.6614i	−1.21745	+	1.02156i	−0.218498	+	0.975837i	$0.570116\pi$
$631$	−30.5821	+	25.6614i	−1.21745	+	1.02156i	−0.998954	+	0.0457265i	$0.985440\pi$
$632$	−28.0841	−	23.5654i	−1.11713	−	0.937381i
$633$		0			0
$634$	8.84628	+	15.3222i	0.351331	+	0.608522i
$635$	9.92991	−	17.1991i	0.394057	−	0.682526i
$636$		0			0
$637$	−31.2429	−	11.3715i	−1.23789	−	0.450555i
$638$	11.0755	−	19.1834i	0.438485	−	0.759479i
$639$		0			0
$640$	1.13217	+	6.42087i	0.0447530	+	0.253807i
$641$	3.83994	+	3.22209i	0.151668	+	0.127265i	0.715464	−	0.698649i	$-0.246215\pi$
$641$	3.83994	+	3.22209i	0.151668	+	0.127265i	−0.563796	+	0.825914i	$0.690660\pi$
$642$		0			0
$643$	8.67812	−	49.2161i	0.342232	−	1.94089i	0.00354380	−	0.999994i	$-0.498872\pi$
$643$	8.67812	−	49.2161i	0.342232	−	1.94089i	0.338688	−	0.940899i	$-0.390017\pi$
$644$	−2.75903	+	1.00420i	−0.108721	+	0.0395712i
$645$		0			0
$646$	−11.6671	−	8.87266i	−0.459038	−	0.349090i
$647$	−32.7681			−1.28825			−0.644123	−	0.764922i	$-0.722777\pi$
$647$	−32.7681			−1.28825			−0.644123	+	0.764922i	$0.722777\pi$
$648$		0			0
$649$	3.02375	−	17.1485i	0.118693	−	0.673139i
$650$	−4.66164	+	3.91158i	−0.182844	+	0.153425i
$651$		0			0
$652$	1.01428	+	5.75229i	0.0397224	+	0.225277i
$653$	7.89978	+	13.6828i	0.309142	+	0.535450i	0.978175	−	0.207783i	$-0.0666248\pi$
$653$	7.89978	+	13.6828i	0.309142	+	0.535450i	−0.669033	+	0.743233i	$0.733291\pi$
$654$		0			0
$655$	−5.09611	−	1.85483i	−0.199122	−	0.0724743i
$656$	−1.16734	−	0.424879i	−0.0455772	−	0.0165887i
$657$		0			0
$658$	−5.24454	−	9.08381i	−0.204453	−	0.354124i
$659$	2.35267	+	13.3426i	0.0916468	+	0.519755i	0.995723	+	0.0923845i	$0.0294489\pi$
$659$	2.35267	+	13.3426i	0.0916468	+	0.519755i	−0.904077	+	0.427370i	$0.859440\pi$
$660$		0			0
$661$	2.80202	−	2.35117i	0.108986	−	0.0914501i	−0.586666	−	0.809829i	$-0.699560\pi$
$661$	2.80202	−	2.35117i	0.108986	−	0.0914501i	0.695652	+	0.718379i	$0.255115\pi$
$662$	1.15366	−	6.54272i	0.0448382	−	0.254290i
$663$		0			0
$664$	41.2819			1.60205
$665$	−16.2135	+	0.778121i	−0.628733	+	0.0301743i
$666$		0			0
$667$	9.26242	−	3.37124i	0.358642	−	0.130535i
$668$	1.28538	−	7.28973i	0.0497327	−	0.282048i
$669$		0			0
$670$	10.3775	+	8.70775i	0.400918	+	0.336410i
$671$	0.448092	+	2.54126i	0.0172984	+	0.0981042i
$672$		0			0
$673$	13.4651	−	23.3223i	0.519043	−	0.899009i	−0.480712	−	0.876878i	$-0.659622\pi$
$673$	13.4651	−	23.3223i	0.519043	−	0.899009i	0.999755	−	0.0221303i	$-0.00704488\pi$
$674$	28.2156	+	10.2696i	1.08682	+	0.395571i
$675$		0			0
$676$	2.19229	−	3.79715i	0.0843187	−	0.146044i
$677$	10.3467	+	17.9209i	0.397654	+	0.688757i	0.993436	−	0.114389i	$-0.0364910\pi$
$677$	10.3467	+	17.9209i	0.397654	+	0.688757i	−0.595782	+	0.803146i	$0.703158\pi$
$678$		0			0
$679$	−20.6219	−	17.3038i	−0.791396	−	0.664060i
$680$	−6.23398	+	5.23093i	−0.239062	+	0.200597i
$681$		0			0
$682$	−12.3628	+	4.49969i	−0.473396	+	0.172302i
$683$	−26.9573			−1.03149			−0.515745	−	0.856742i	$-0.672485\pi$
$683$	−26.9573			−1.03149			−0.515745	+	0.856742i	$0.672485\pi$
$684$		0			0
$685$	−18.5615			−0.709197
$686$	−0.582515	+	0.212018i	−0.0222405	+	0.00809489i
$687$		0			0
$688$	16.4982	−	13.8437i	0.628989	−	0.527785i
$689$	−0.965185	−	0.809886i	−0.0367706	−	0.0308542i
$690$		0			0
$691$	−4.35021	−	7.53479i	−0.165490	−	0.286637i	0.771339	−	0.636424i	$-0.219587\pi$
$691$	−4.35021	−	7.53479i	−0.165490	−	0.286637i	−0.936829	+	0.349787i	$0.886254\pi$
$692$	2.79715	−	4.84480i	0.106332	−	0.184172i
$693$		0			0
$694$	10.3553	+	3.76900i	0.393080	+	0.143069i
$695$	−5.25635	+	9.10426i	−0.199385	+	0.345344i
$696$		0			0
$697$	−0.193432	−	1.09701i	−0.00732676	−	0.0415521i
$698$	−1.96440	−	1.64832i	−0.0743535	−	0.0623900i
$699$		0			0
$700$	−0.271625	+	1.54046i	−0.0102665	+	0.0582240i
$701$	−0.378762	+	0.137858i	−0.0143056	+	0.00520683i	−0.349163	−	0.937062i	$-0.613534\pi$
$701$	−0.378762	+	0.137858i	−0.0143056	+	0.00520683i	0.334857	+	0.942269i	$0.391312\pi$
$702$		0			0
$703$	0.955019	+	4.22139i	0.0360192	+	0.159213i
$704$	29.8684			1.12571
$705$		0			0
$706$	1.97850	−	11.2206i	0.0744618	−	0.422294i
$707$	−12.8138	+	10.7521i	−0.481913	+	0.404373i
$708$		0			0
$709$	6.95535	+	39.4457i	0.261214	+	1.48142i	0.779604	+	0.626272i	$0.215420\pi$
$709$	6.95535	+	39.4457i	0.261214	+	1.48142i	−0.518391	+	0.855144i	$0.673469\pi$
$710$	1.25788	+	2.17871i	0.0472073	+	0.0817654i
$711$		0			0
$712$	−21.9227	−	7.97920i	−0.821587	−	0.299033i
$713$	−5.50123	−	2.00228i	−0.206023	−	0.0749861i
$714$		0			0
$715$	8.12342	+	14.0702i	0.303799	+	0.526194i
$716$	1.06686	+	6.05048i	0.0398705	+	0.226117i
$717$		0			0
$718$	−22.7443	+	19.0848i	−0.848811	+	0.712237i
$719$	−3.13880	+	17.8010i	−0.117058	+	0.663867i	0.868653	+	0.495421i	$0.164986\pi$
$719$	−3.13880	+	17.8010i	−0.117058	+	0.663867i	−0.985711	+	0.168446i	$0.946125\pi$
$720$		0			0
$721$	40.0118			1.49012
$722$	−16.7407	+	17.0327i	−0.623024	+	0.633890i
$723$		0			0
$724$	−3.46749	+	1.26206i	−0.128868	+	0.0469042i
$725$	0.911880	−	5.17153i	0.0338664	−	0.192066i
$726$		0			0
$727$	20.1940	+	16.9448i	0.748953	+	0.628446i	0.935226	−	0.354052i	$-0.115196\pi$
$727$	20.1940	+	16.9448i	0.748953	+	0.628446i	−0.186273	+	0.982498i	$0.559641\pi$
$728$	9.52311	+	54.0083i	0.352950	+	2.00168i
$729$		0			0
$730$	−2.86752	+	4.96669i	−0.106132	+	0.183825i
$731$	18.1474	+	6.60511i	0.671205	+	0.244299i
$732$		0			0
$733$	1.65460	−	2.86584i	0.0611139	−	0.105852i	−0.833850	−	0.551992i	$-0.813868\pi$
$733$	1.65460	−	2.86584i	0.0611139	−	0.105852i	0.894964	+	0.446139i	$0.147201\pi$
$734$	6.54946	+	11.3440i	0.241745	+	0.418714i
$735$		0			0
$736$	3.35562	+	2.81570i	0.123690	+	0.103788i
$737$	27.7062	−	23.2482i	1.02057	−	0.856360i
$738$		0			0
$739$	−16.6272	+	6.05179i	−0.611640	+	0.222619i	−0.629221	−	0.777227i	$-0.716626\pi$
$739$	−16.6272	+	6.05179i	−0.611640	+	0.222619i	0.0175807	+	0.999845i	$0.494404\pi$
$740$	0.417077			0.0153321
$741$		0			0
$742$	1.21819			0.0447212
$743$	35.0065	−	12.7413i	1.28427	−	0.467434i	0.392425	−	0.919784i	$-0.371636\pi$
$743$	35.0065	−	12.7413i	1.28427	−	0.467434i	0.891841	+	0.452350i	$0.149414\pi$
$744$		0			0
$745$	11.5986	−	9.73239i	0.424940	−	0.356567i
$746$	−8.86295	−	7.43689i	−0.324496	−	0.272284i
$747$		0			0
$748$	1.88556	+	3.26589i	0.0689430	+	0.119413i
$749$	2.56695	−	4.44609i	0.0937944	−	0.162457i
$750$		0			0
$751$	12.7466	+	4.63939i	0.465131	+	0.169294i	0.563945	−	0.825812i	$-0.309283\pi$
$751$	12.7466	+	4.63939i	0.465131	+	0.169294i	−0.0988146	+	0.995106i	$0.531505\pi$
$752$	−3.34277	+	5.78984i	−0.121898	+	0.211134i
$753$		0			0
$754$	−5.54909	−	31.4705i	−0.202086	−	1.14609i
$755$	−8.68938	−	7.29126i	−0.316239	−	0.265356i
$756$		0			0
$757$	2.17703	−	12.3465i	0.0791255	−	0.448743i	−0.919345	−	0.393453i	$-0.871281\pi$
$757$	2.17703	−	12.3465i	0.0791255	−	0.448743i	0.998470	−	0.0552901i	$-0.0176084\pi$
$758$	14.8995	−	5.42297i	0.541174	−	0.196971i
$759$		0			0
$760$	7.17252	+	11.1519i	0.260175	+	0.404523i
$761$	27.2282			0.987022			0.493511	−	0.869740i	$-0.335713\pi$
$761$	27.2282			0.987022			0.493511	+	0.869740i	$0.335713\pi$
$762$		0			0
$763$	6.14240	−	34.8353i	0.222370	−	1.26112i
$764$	−3.12360	+	2.62101i	−0.113008	+	0.0948248i
$765$		0			0
$766$	0.115625	+	0.655742i	0.00417770	+	0.0236929i
$767$	−12.5604	−	21.7552i	−0.453528	−	0.785534i
$768$		0			0
$769$	0.864690	+	0.314721i	0.0311815	+	0.0113491i	0.357564	−	0.933889i	$-0.383607\pi$
$769$	0.864690	+	0.314721i	0.0311815	+	0.0113491i	−0.326382	+	0.945238i	$0.605830\pi$
$770$	−14.7609	−	5.37254i	−0.531947	−	0.193613i
$771$		0			0
$772$	−4.25397	−	7.36809i	−0.153104	−	0.265183i
$773$	0.317753	+	1.80207i	0.0114288	+	0.0648158i	0.989989	−	0.141146i	$-0.0450788\pi$
$773$	0.317753	+	1.80207i	0.0114288	+	0.0648158i	−0.978560	+	0.205962i	$0.933968\pi$
$774$		0			0
$775$	−2.38922	+	2.00480i	−0.0858234	+	0.0720144i
$776$	−3.81848	+	21.6557i	−0.137076	+	0.777394i
$777$		0			0
$778$	38.1948			1.36935
$779$	−1.81288	+	0.0870041i	−0.0649533	+	0.00311725i
$780$		0			0
$781$	6.31158	−	2.29723i	0.225846	−	0.0822013i
$782$	1.09605	−	6.21598i	0.0391945	−	0.222283i
$783$		0			0
$784$	−15.6956	−	13.1702i	−0.560556	−	0.470363i
$785$	0.731976	+	4.15124i	0.0261253	+	0.148164i
$786$		0			0
$787$	1.45244	−	2.51571i	0.0517740	−	0.0896752i	−0.838977	−	0.544167i	$-0.816846\pi$
$787$	1.45244	−	2.51571i	0.0517740	−	0.0896752i	0.890751	+	0.454492i	$0.150179\pi$
$788$	3.65579	+	1.33060i	0.130232	+	0.0474006i
$789$		0			0
$790$	7.57449	−	13.1194i	0.269488	−	0.466767i
$791$	−31.7346	−	54.9659i	−1.12835	−	1.95436i
$792$		0			0
$793$	2.85173	+	2.39288i	0.101268	+	0.0849737i
$794$	11.6758	−	9.79716i	0.414358	−	0.347688i
$795$		0			0
$796$	7.16491	−	2.60782i	0.253954	−	0.0924316i
$797$	−19.9042			−0.705044			−0.352522	−	0.935804i	$-0.614676\pi$
$797$	−19.9042			−0.705044			−0.352522	+	0.935804i	$0.614676\pi$
$798$		0			0
$799$	−5.99488			−0.212084
$800$	2.19298	−	0.798178i	0.0775335	−	0.0282199i
$801$		0			0
$802$	−11.1604	+	9.36472i	−0.394089	+	0.330680i
$803$	11.7294	+	9.84211i	0.413920	+	0.347320i
$804$		0			0
$805$	−3.49495	−	6.05343i	−0.123181	−	0.213356i
$806$	−9.48980	+	16.4368i	−0.334264	+	0.578962i
$807$		0			0
$808$	12.8397	+	4.67328i	0.451700	+	0.164405i
$809$	22.2093	−	38.4677i	0.780838	−	1.35245i	−0.150616	−	0.988592i	$-0.548126\pi$
$809$	22.2093	−	38.4677i	0.780838	−	1.35245i	0.931454	−	0.363859i	$-0.118541\pi$
$810$		0			0
$811$	5.91262	+	33.5322i	0.207620	+	1.17747i	0.893263	+	0.449535i	$0.148410\pi$
$811$	5.91262	+	33.5322i	0.207620	+	1.17747i	−0.685642	+	0.727939i	$0.740479\pi$
$812$	−6.29247	−	5.28001i	−0.220822	−	0.185292i
$813$		0			0
$814$	−0.727303	+	4.12474i	−0.0254920	+	0.144572i
$815$	−13.0670	+	4.75599i	−0.457717	+	0.166595i
$816$		0			0
$817$	14.4086	−	27.9731i	0.504092	−	0.978655i
$818$	−6.07938			−0.212561
$819$		0			0
$820$	−0.0303712	+	0.172244i	−0.00106061	+	0.00601501i
$821$	20.5350	−	17.2309i	0.716675	−	0.601362i	−0.209788	−	0.977747i	$-0.567277\pi$
$821$	20.5350	−	17.2309i	0.716675	−	0.601362i	0.926463	+	0.376385i	$0.122833\pi$
$822$		0			0
$823$	1.91719	+	10.8729i	0.0668290	+	0.379006i	0.999818	+	0.0191001i	$0.00608012\pi$
$823$	1.91719	+	10.8729i	0.0668290	+	0.379006i	−0.932989	+	0.359906i	$0.882809\pi$
$824$	−16.3419	−	28.3051i	−0.569298	−	0.986054i
$825$		0			0
$826$	22.8232	+	8.30698i	0.794122	+	0.289037i
$827$	11.1811	+	4.06958i	0.388804	+	0.141513i	0.529023	−	0.848607i	$-0.322558\pi$
$827$	11.1811	+	4.06958i	0.388804	+	0.141513i	−0.140219	+	0.990121i	$0.544781\pi$
$828$		0			0
$829$	−5.60968	−	9.71626i	−0.194832	−	0.337460i	0.752013	−	0.659148i	$-0.229083\pi$
$829$	−5.60968	−	9.71626i	−0.194832	−	0.337460i	−0.946846	+	0.321689i	$0.895750\pi$
$830$	2.96214	+	16.7991i	0.102817	+	0.583107i
$831$		0			0
$832$	33.0082	−	27.6972i	1.14435	−	0.960227i
$833$	3.19035	−	18.0934i	0.110539	−	0.626898i
$834$		0			0
$835$	17.6222			0.609842
$836$	5.66651	−	2.37589i	0.195980	−	0.0821718i
$837$		0			0
$838$	−14.6852	+	5.34496i	−0.507291	+	0.184639i
$839$	6.22171	−	35.2851i	0.214797	−	1.21818i	−0.666460	−	0.745540i	$-0.732191\pi$
$839$	6.22171	−	35.2851i	0.214797	−	1.21818i	0.881258	−	0.472636i	$-0.156697\pi$
$840$		0			0
$841$	−1.09068	−	0.915188i	−0.0376096	−	0.0315582i
$842$	−6.02772	−	34.1849i	−0.207729	−	1.17809i
$843$		0			0
$844$	3.65063	−	6.32308i	0.125660	−	0.217649i
$845$	9.80875	+	3.57009i	0.337431	+	0.122815i
$846$		0			0
$847$	−0.487666	+	0.844662i	−0.0167564	+	0.0290229i
$848$	−0.388226	−	0.672427i	−0.0133317	−	0.0230912i
$849$		0			0
$850$	−2.57597	−	2.16150i	−0.0883551	−	0.0741387i
$851$	−1.42772	+	1.19800i	−0.0489415	+	0.0410668i
$852$		0			0
$853$	−12.2754	+	4.46788i	−0.420302	+	0.152977i	−0.543509	−	0.839404i	$-0.682904\pi$
$853$	−12.2754	+	4.46788i	−0.420302	+	0.152977i	0.123207	+	0.992381i	$0.460682\pi$
$854$	−3.59926			−0.123164
$855$		0			0
$856$	−4.19366			−0.143337
$857$	−22.7314	+	8.27355i	−0.776489	+	0.282619i	−0.699708	−	0.714429i	$-0.746687\pi$
$857$	−22.7314	+	8.27355i	−0.776489	+	0.282619i	−0.0767813	+	0.997048i	$0.524464\pi$
$858$		0			0
$859$	41.4832	−	34.8086i	1.41539	−	1.18765i	0.461633	−	0.887071i	$-0.347264\pi$
$859$	41.4832	−	34.8086i	1.41539	−	1.18765i	0.953756	−	0.300581i	$-0.0971807\pi$
$860$	−2.32282	−	1.94908i	−0.0792077	−	0.0664631i
$861$		0			0
$862$	−4.45696	−	7.71969i	−0.151805	−	0.262934i
$863$	24.8426	−	43.0287i	0.845653	−	1.46471i	−0.0394004	−	0.999224i	$-0.512545\pi$
$863$	24.8426	−	43.0287i	0.845653	−	1.46471i	0.885053	−	0.465490i	$-0.154122\pi$
$864$		0			0
$865$	12.5150	+	4.55510i	0.425523	+	0.154878i
$866$	−4.13783	+	7.16693i	−0.140609	+	0.243542i
$867$		0			0
$868$	0.847174	+	4.80456i	0.0287549	+	0.163077i
$869$	−30.9828	−	25.9977i	−1.05102	−	0.881911i
$870$		0			0
$871$	9.06045	−	51.3843i	0.307001	−	1.74109i
$872$	−27.1518	+	9.88246i	−0.919478	+	0.334662i
$873$		0			0
$874$	−9.82147	−	3.05009i	−0.332216	−	0.103171i
$875$	−3.72392			−0.125891
$876$		0			0
$877$	−1.43631	+	8.14572i	−0.0485007	+	0.275061i	−0.999408	−	0.0344159i	$-0.989043\pi$
$877$	−1.43631	+	8.14572i	−0.0485007	+	0.275061i	0.950907	+	0.309477i	$0.100154\pi$
$878$	−4.26391	+	3.57784i	−0.143900	+	0.120746i
$879$		0			0
$880$	1.73859	+	9.86003i	0.0586078	+	0.332381i
$881$	−12.2596	−	21.2343i	−0.413037	−	0.715402i	0.582183	−	0.813058i	$-0.302199\pi$
$881$	−12.2596	−	21.2343i	−0.413037	−	0.715402i	−0.995220	+	0.0976562i	$0.968865\pi$
$882$		0			0
$883$	−46.2172	−	16.8217i	−1.55533	−	0.566095i	−0.585671	−	0.810549i	$-0.699169\pi$
$883$	−46.2172	−	16.8217i	−1.55533	−	0.566095i	−0.969661	+	0.244454i	$0.921391\pi$
$884$	5.11226	+	1.86071i	0.171944	+	0.0625825i
$885$		0			0
$886$	1.74223	+	3.01764i	0.0585315	+	0.101380i
$887$	−3.75889	−	21.3177i	−0.126211	−	0.715779i	−0.980581	−	0.196114i	$-0.937168\pi$
$887$	−3.75889	−	21.3177i	−0.126211	−	0.715779i	0.854370	−	0.519665i	$-0.173943\pi$
$888$		0			0
$889$	56.6539	−	47.5382i	1.90011	−	1.59438i
$890$	1.67399	−	9.49369i	0.0561124	−	0.318229i
$891$		0			0
$892$	3.66564			0.122735
$893$	−1.23307	+	9.68955i	−0.0412632	+	0.324249i
$894$		0			0
$895$	−13.7444	+	5.00254i	−0.459423	+	0.167216i
$896$	−4.21612	+	23.9108i	−0.140851	+	0.798803i
$897$		0			0
$898$	25.3788	+	21.2953i	0.846900	+	0.710634i
$899$	−2.84407	−	16.1295i	−0.0948550	−	0.537950i
$900$		0			0
$901$	0.348120	−	0.602962i	0.0115976	−	0.0200876i
$902$	−1.65047	−	0.600720i	−0.0549545	−	0.0200018i
$903$		0			0
$904$	−25.9226	+	44.8993i	−0.862173	+	1.49333i
$905$	−4.39238	−	7.60782i	−0.146008	−	0.252893i
$906$		0			0
$907$	10.3365	+	8.67336i	0.343218	+	0.287994i	0.798060	−	0.602578i	$-0.205860\pi$
$907$	10.3365	+	8.67336i	0.343218	+	0.287994i	−0.454842	+	0.890572i	$0.650304\pi$
$908$	−6.47264	+	5.43119i	−0.214802	+	0.180240i
$909$		0			0
$910$	−21.2946	+	7.75062i	−0.705911	+	0.256930i
$911$	−16.2069			−0.536958			−0.268479	−	0.963286i	$-0.586521\pi$
$911$	−16.2069			−0.536958			−0.268479	+	0.963286i	$0.586521\pi$
$912$		0			0
$913$	45.5428			1.50725
$914$	39.6614	−	14.4356i	1.31188	−	0.477486i
$915$		0			0
$916$	6.70614	−	5.62712i	0.221577	−	0.185925i
$917$	−15.4706	−	12.9814i	−0.510884	−	0.428683i
$918$		0			0
$919$	−9.86867	−	17.0930i	−0.325537	−	0.563847i	0.656084	−	0.754688i	$-0.272212\pi$
$919$	−9.86867	−	17.0930i	−0.325537	−	0.563847i	−0.981621	+	0.190841i	$0.938879\pi$
$920$	−2.85487	+	4.94479i	−0.0941224	+	0.163025i
$921$		0			0
$922$	−35.9691	−	13.0917i	−1.18458	−	0.431152i
$923$	4.84483	−	8.39150i	0.159470	−	0.276210i
$924$		0			0
$925$	0.172420	+	0.977842i	0.00566913	+	0.0321512i
$926$	27.5157	+	23.0884i	0.904223	+	0.758733i
$927$		0			0
$928$	−2.12807	+	12.0689i	−0.0698573	+	0.396181i
$929$	6.09658	−	2.21897i	0.200022	−	0.0728022i	−0.240066	−	0.970756i	$-0.577169\pi$
$929$	6.09658	−	2.21897i	0.200022	−	0.0728022i	0.440089	+	0.897954i	$0.354947\pi$
$930$		0			0
$931$	−28.5882	−	8.87816i	−0.936940	−	0.290970i
$932$	0.228528			0.00748568
$933$		0			0
$934$	−2.44838	+	13.8855i	−0.0801135	+	0.454346i
$935$	−6.87742	+	5.77084i	−0.224916	+	0.188727i
$936$		0			0
$937$	−1.28522	−	7.28885i	−0.0419863	−	0.238116i	0.956591	−	0.291433i	$-0.0941319\pi$
$937$	−1.28522	−	7.28885i	−0.0419863	−	0.238116i	−0.998578	+	0.0533164i	$0.983021\pi$
$938$	25.2237	+	43.6887i	0.823583	+	1.42649i
$939$		0			0
$940$	0.884506	+	0.321934i	0.0288494	+	0.0105003i
$941$	49.8981	+	18.1614i	1.62663	+	0.592046i	0.984629	−	0.174657i	$-0.0558817\pi$
$941$	49.8981	+	18.1614i	1.62663	+	0.592046i	0.642002	+	0.766703i	$0.278104\pi$
$942$		0			0
$943$	−0.390781	−	0.676853i	−0.0127256	−	0.0220414i
$944$	−2.68819	−	15.2455i	−0.0874932	−	0.496198i
$945$		0			0
$946$	23.3262	−	19.5730i	0.758402	−	0.636375i
$947$	−2.65283	+	15.0450i	−0.0862055	+	0.488896i	0.910884	+	0.412661i	$0.135401\pi$
$947$	−2.65283	+	15.0450i	−0.0862055	+	0.488896i	−0.997090	+	0.0762341i	$0.975710\pi$
$948$		0			0
$949$	22.0891			0.717041
$950$	−4.02348	+	3.71896i	−0.130539	+	0.120659i
$951$		0			0
$952$	−28.4772	+	10.3649i	−0.922951	+	0.335927i
$953$	2.93675	−	16.6552i	0.0951308	−	0.539514i	−0.899576	−	0.436763i	$-0.856125\pi$
$953$	2.93675	−	16.6552i	0.0951308	−	0.539514i	0.994707	−	0.102750i	$-0.0327642\pi$
$954$		0			0
$955$	−7.43628	−	6.23978i	−0.240632	−	0.201914i
$956$	−1.62099	−	9.19312i	−0.0524267	−	0.297327i
$957$		0			0
$958$	10.9296	−	18.9307i	0.353120	−	0.611622i
$959$	−64.9528	−	23.6409i	−2.09744	−	0.763404i
$960$		0			0
$961$	10.6362	−	18.4224i	0.343103	−	0.594272i
$962$	3.02115	+	5.23278i	0.0974057	+	0.168712i
$963$		0			0
$964$	−6.99333	−	5.86810i	−0.225240	−	0.188999i
$965$	15.5160	−	13.0194i	0.499476	−	0.419110i
$966$		0			0
$967$	−13.6496	+	4.96803i	−0.438940	+	0.159761i	−0.552031	−	0.833823i	$-0.686147\pi$
$967$	−13.6496	+	4.96803i	−0.438940	+	0.159761i	0.113091	+	0.993585i	$0.463925\pi$
$968$	0.796706			0.0256071
$969$		0			0
$970$	−9.08650			−0.291750
$971$	28.7590	−	10.4674i	0.922920	−	0.335915i	0.163520	−	0.986540i	$-0.447715\pi$
$971$	28.7590	−	10.4674i	0.922920	−	0.335915i	0.759400	+	0.650625i	$0.225493\pi$
$972$		0			0
$973$	−29.9894	+	25.1641i	−0.961417	+	0.806724i
$974$	−14.7777	−	12.4000i	−0.473508	−	0.397321i
$975$		0			0
$976$	1.14705	+	1.98675i	0.0367161	+	0.0635942i
$977$	−22.0007	+	38.1064i	−0.703865	+	1.21913i	0.263234	+	0.964732i	$0.415211\pi$
$977$	−22.0007	+	38.1064i	−0.703865	+	1.21913i	−0.967099	+	0.254399i	$0.918122\pi$
$978$		0			0
$979$	−24.1854	−	8.80277i	−0.772970	−	0.281338i
$980$	−1.44236	+	2.49823i	−0.0460743	+	0.0798031i
$981$		0			0
$982$	1.82342	+	10.3411i	0.0581878	+	0.329999i
$983$	−27.0888	−	22.7302i	−0.864000	−	0.724982i	0.0988259	−	0.995105i	$-0.468491\pi$
$983$	−27.0888	−	22.7302i	−0.864000	−	0.724982i	−0.962826	+	0.270123i	$0.912936\pi$
$984$		0			0
$985$	−1.60830	+	9.12111i	−0.0512446	+	0.290623i
$986$	16.5936	−	6.03957i	0.528448	−	0.192339i
$987$		0			0
$988$	4.05900	−	7.88025i	0.129134	−	0.250704i
$989$	13.5498			0.430860
$990$		0			0
$991$	5.58302	−	31.6629i	0.177350	−	1.00580i	−0.758045	−	0.652202i	$-0.773845\pi$
$991$	5.58302	−	31.6629i	0.177350	−	1.00580i	0.935396	−	0.353602i	$-0.115043\pi$
$992$	5.57577	−	4.67863i	0.177031	−	0.148547i
$993$		0			0
$994$	1.62682	+	9.22613i	0.0515995	+	0.292635i
$995$	9.07603	+	15.7201i	0.287729	+	0.498362i
$996$		0			0
$997$	7.81213	+	2.84338i	0.247413	+	0.0900509i	0.462750	−	0.886489i	$-0.346863\pi$
$997$	7.81213	+	2.84338i	0.247413	+	0.0900509i	−0.215337	+	0.976540i	$0.569085\pi$
$998$	0.319896	+	0.116433i	0.0101261	+	0.00368561i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.c.271.2		18
3.2	odd	2		95.2.k.a.81.2	yes	18
15.2	even	4		475.2.u.b.24.2		36
15.8	even	4		475.2.u.b.24.5		36
15.14	odd	2		475.2.l.c.176.2		18
19.4	even	9	inner	855.2.bs.c.631.2		18
57.2	even	18		1805.2.a.s.1.4		9
57.17	odd	18		1805.2.a.v.1.6		9
57.23	odd	18		95.2.k.a.61.2	✓	18
285.23	even	36		475.2.u.b.99.2		36
285.59	even	18		9025.2.a.cf.1.6		9
285.74	odd	18		9025.2.a.cc.1.4		9
285.137	even	36		475.2.u.b.99.5		36
285.194	odd	18		475.2.l.c.251.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.2	✓	18	57.23	odd	18
95.2.k.a.81.2	yes	18	3.2	odd	2
475.2.l.c.176.2		18	15.14	odd	2
475.2.l.c.251.2		18	285.194	odd	18
475.2.u.b.24.2		36	15.2	even	4
475.2.u.b.24.5		36	15.8	even	4
475.2.u.b.99.2		36	285.23	even	36
475.2.u.b.99.5		36	285.137	even	36
855.2.bs.c.271.2		18	1.1	even	1	trivial
855.2.bs.c.631.2		18	19.4	even	9	inner
1805.2.a.s.1.4		9	57.2	even	18
1805.2.a.v.1.6		9	57.17	odd	18
9025.2.a.cc.1.4		9	285.74	odd	18
9025.2.a.cf.1.6		9	285.59	even	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18116 - 0.429906i) q^{2} +(-0.321776 + 0.270002i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-1.86196 - 3.22501i) q^{7} +(-1.52095 + 2.63437i) q^{8} +O(q^{10})\)	\(q+(1.18116 - 0.429906i) q^{2} +(-0.321776 + 0.270002i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-1.86196 - 3.22501i) q^{7} +(-1.52095 + 2.63437i) q^{8} +(-1.18116 - 0.429906i) q^{10} +(-1.67794 + 2.90627i) q^{11} +(0.840684 + 4.76776i) q^{13} +(-3.58572 - 3.00877i) q^{14} +(-0.518073 + 2.93814i) q^{16} +(-2.51392 + 0.914991i) q^{17} +(0.961823 + 4.25146i) q^{19} +0.420048 q^{20} +(-0.732484 + 4.15412i) q^{22} +(-1.43789 + 1.20653i) q^{23} +(0.173648 + 0.984808i) q^{25} +(3.04267 + 5.27006i) q^{26} +(1.46989 + 0.534997i) q^{28} +(-4.93461 - 1.79605i) q^{29} +(1.55945 + 2.70105i) q^{31} +(-0.405246 - 2.29826i) q^{32} +(-2.57597 + 2.16150i) q^{34} +(-0.646652 + 3.66734i) q^{35} +0.992927 q^{37} +(2.96379 + 4.60815i) q^{38} +(2.85846 - 1.04039i) q^{40} +(-0.0723041 + 0.410057i) q^{41} +(-5.52990 - 4.64013i) q^{43} +(-0.244780 - 1.38822i) q^{44} +(-1.17968 + 2.04326i) q^{46} +(2.10572 + 0.766421i) q^{47} +(-3.43378 + 5.94749i) q^{49} +(0.628481 + 1.08856i) q^{50} +(-1.55782 - 1.30716i) q^{52} +(-0.199365 + 0.167287i) q^{53} +(3.15349 - 1.14778i) q^{55} +11.3278 q^{56} -6.60069 q^{58} +(-4.87590 + 1.77468i) q^{59} +(0.589041 - 0.494264i) q^{61} +(3.00316 + 2.51995i) q^{62} +(-4.45016 - 7.70790i) q^{64} +(2.42065 - 4.19270i) q^{65} +(-10.1275 - 3.68611i) q^{67} +(0.561868 - 0.973185i) q^{68} +(0.812816 + 4.60971i) q^{70} +(-1.53320 - 1.28651i) q^{71} +(0.792291 - 4.49331i) q^{73} +(1.17280 - 0.426865i) q^{74} +(-1.45739 - 1.10832i) q^{76} +12.4970 q^{77} +(-2.09282 + 11.8690i) q^{79} +(2.28546 - 1.91773i) q^{80} +(0.0908835 + 0.515426i) q^{82} +(-6.78553 - 11.7529i) q^{83} +(2.51392 + 0.914991i) q^{85} +(-8.52650 - 3.10339i) q^{86} +(-5.10413 - 8.84062i) q^{88} +(1.33178 + 7.55289i) q^{89} +(13.8107 - 11.5886i) q^{91} +(0.136912 - 0.776465i) q^{92} +2.81668 q^{94} +(1.99599 - 3.87505i) q^{95} +(6.79298 - 2.47244i) q^{97} +(-1.49898 + 8.50112i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

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