LMFDB - Embedded newform 225.2.m.a.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.2
Root			$-0.357358 - 1.86824i$ of defining polynomial
Character	$\chi$	$=$	225.64
Dual form			225.2.m.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35736 + 1.86824i) q^{2} +(-1.02988 + 3.16963i) q^{4} +(-2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.92705 + 0.951057i) q^{8} +O(q^{10})$	\(q+(1.35736 + 1.86824i) q^{2} +(-1.02988 + 3.16963i) q^{4} +(-2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.92705 + 0.951057i) q^{8} +(-3.76594 - 3.53290i) q^{10} +(1.61803 - 1.17557i) q^{11} +(0.838893 - 1.15464i) q^{13} +(-5.67164 + 4.12069i) q^{14} +(-0.357358 - 0.259635i) q^{16} +(1.76920 - 0.574848i) q^{17} +(-0.279141 - 0.859107i) q^{19} +(0.930307 - 7.39396i) q^{20} +(4.39250 + 1.42721i) q^{22} +(1.95693 + 2.69348i) q^{23} +(4.64703 - 1.84529i) q^{25} +3.29582 q^{26} +(-9.62243 - 3.12652i) q^{28} +(1.22466 - 3.76910i) q^{29} +(-1.99006 - 6.12477i) q^{31} +5.13532i q^{32} +(3.47539 + 2.52502i) q^{34} +(-1.27534 - 6.66742i) q^{35} +(2.24547 - 3.09062i) q^{37} +(1.22613 - 1.68762i) q^{38} +(6.02900 - 3.31841i) q^{40} +(-1.48391 - 1.07813i) q^{41} +3.59445i q^{43} +(2.05975 + 6.33927i) q^{44} +(-2.37582 + 7.31203i) q^{46} +(4.56502 + 1.48326i) q^{47} -2.21619 q^{49} +(9.75513 + 6.17707i) q^{50} +(2.79582 + 3.84812i) q^{52} +(-9.03953 - 2.93712i) q^{53} +(-3.05975 + 3.26158i) q^{55} +(-2.88723 - 8.88599i) q^{56} +(8.70390 - 2.82807i) q^{58} +(-8.61248 - 6.25734i) q^{59} +(-11.5481 + 8.39016i) q^{61} +(8.74134 - 12.0314i) q^{62} +(-10.3087 + 7.48973i) q^{64} +(-1.35736 + 2.88829i) q^{65} +(10.1670 - 3.30345i) q^{67} +6.19974i q^{68} +(10.7253 - 11.4327i) q^{70} +(-3.85030 + 11.8500i) q^{71} +(0.157310 + 0.216518i) q^{73} +8.82193 q^{74} +3.01054 q^{76} +(3.56882 + 4.91206i) q^{77} +(2.64882 - 8.15223i) q^{79} +(0.893919 + 0.420099i) q^{80} -4.23572i q^{82} +(12.0006 - 3.89923i) q^{83} +(-3.64411 + 2.00575i) q^{85} +(-6.71531 + 4.87896i) q^{86} +(-3.61803 + 4.97980i) q^{88} +(3.85736 - 2.80253i) q^{89} +(3.50527 + 2.54673i) q^{91} +(-10.5527 + 3.42879i) q^{92} +(3.42527 + 10.5419i) q^{94} +(0.973973 + 1.76955i) q^{95} +(-9.47067 - 3.07721i) q^{97} +(-3.00816 - 4.14037i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - q^{4} - 10 q^{8}+O(q^{10}) $ 8 * q + 5 * q^2 - q^4 - 10 * q^8	$ 8 q + 5 q^{2} - q^{4} - 10 q^{8} - 5 q^{10} + 4 q^{11} - 5 q^{13} - 13 q^{14} + 3 q^{16} + 10 q^{17} - 5 q^{19} + 15 q^{20} - 5 q^{23} - 10 q^{25} - 6 q^{26} - 15 q^{28} + 5 q^{29} - 9 q^{31} + 13 q^{34} - 15 q^{35} + 30 q^{37} - 15 q^{38} + 10 q^{40} + 4 q^{41} + 2 q^{44} - 19 q^{46} + 14 q^{49} + 15 q^{50} - 10 q^{52} + 10 q^{53} - 10 q^{55} - 10 q^{56} + 20 q^{58} - 9 q^{61} + 30 q^{62} + 4 q^{64} - 5 q^{65} + 20 q^{67} + 30 q^{70} - 6 q^{71} + 15 q^{73} + 12 q^{74} - 20 q^{76} - 10 q^{77} + 15 q^{79} - 20 q^{80} + 45 q^{83} - 15 q^{85} + 9 q^{86} - 20 q^{88} + 25 q^{89} + 6 q^{91} - 30 q^{92} - 27 q^{94} - 15 q^{95} - 60 q^{97} + 10 q^{98}+O(q^{100}) $ 8 * q + 5 * q^2 - q^4 - 10 * q^8 - 5 * q^10 + 4 * q^11 - 5 * q^13 - 13 * q^14 + 3 * q^16 + 10 * q^17 - 5 * q^19 + 15 * q^20 - 5 * q^23 - 10 * q^25 - 6 * q^26 - 15 * q^28 + 5 * q^29 - 9 * q^31 + 13 * q^34 - 15 * q^35 + 30 * q^37 - 15 * q^38 + 10 * q^40 + 4 * q^41 + 2 * q^44 - 19 * q^46 + 14 * q^49 + 15 * q^50 - 10 * q^52 + 10 * q^53 - 10 * q^55 - 10 * q^56 + 20 * q^58 - 9 * q^61 + 30 * q^62 + 4 * q^64 - 5 * q^65 + 20 * q^67 + 30 * q^70 - 6 * q^71 + 15 * q^73 + 12 * q^74 - 20 * q^76 - 10 * q^77 + 15 * q^79 - 20 * q^80 + 45 * q^83 - 15 * q^85 + 9 * q^86 - 20 * q^88 + 25 * q^89 + 6 * q^91 - 30 * q^92 - 27 * q^94 - 15 * q^95 - 60 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.35736	+	1.86824i	0.959797	+	1.32105i	0.947036	+	0.321128i	$0.104062\pi$
$2$	1.35736	+	1.86824i	0.959797	+	1.32105i	0.0127610	+	0.999919i	$0.495938\pi$
$3$		0			0
$3$		0			0
$4$	−1.02988	+	3.16963i	−0.514938	+	1.58482i
$5$	−2.19625	+	0.420099i	−0.982193	+	0.187874i
$5$	−2.19625	+	0.420099i	−0.982193	+	0.187874i
$6$		0			0
$7$			3.03582i			1.14743i	0.819055	+	0.573716i	$0.194498\pi$
$7$			3.03582i			1.14743i	−0.819055	+	0.573716i	$0.805502\pi$
$8$	−2.92705	+	0.951057i	−1.03487	+	0.336249i
$9$		0			0
$10$	−3.76594	−	3.53290i	−1.19090	−	1.11720i
$11$	1.61803	−	1.17557i	0.487856	−	0.354448i	−0.316503	−	0.948591i	$-0.602509\pi$
$11$	1.61803	−	1.17557i	0.487856	−	0.354448i	0.804359	+	0.594144i	$0.202509\pi$
$12$		0			0
$13$	0.838893	−	1.15464i	0.232667	−	0.320239i	−0.676680	−	0.736277i	$-0.736582\pi$
$13$	0.838893	−	1.15464i	0.232667	−	0.320239i	0.909347	+	0.416039i	$0.136582\pi$
$14$	−5.67164	+	4.12069i	−1.51581	+	1.10130i
$15$		0			0
$16$	−0.357358	−	0.259635i	−0.0893394	−	0.0649089i
$17$	1.76920	−	0.574848i	0.429094	−	0.139421i	−0.0865044	−	0.996251i	$-0.527570\pi$
$17$	1.76920	−	0.574848i	0.429094	−	0.139421i	0.515598	+	0.856830i	$0.327570\pi$
$18$		0			0
$19$	−0.279141	−	0.859107i	−0.0640393	−	0.197093i	0.913918	−	0.405900i	$-0.133042\pi$
$19$	−0.279141	−	0.859107i	−0.0640393	−	0.197093i	−0.977957	+	0.208807i	$0.933042\pi$
$20$	0.930307	−	7.39396i	0.208023	−	1.65334i
$21$		0			0
$22$	4.39250	+	1.42721i	0.936484	+	0.304282i
$23$	1.95693	+	2.69348i	0.408048	+	0.561629i	0.962741	−	0.270426i	$-0.0871644\pi$
$23$	1.95693	+	2.69348i	0.408048	+	0.561629i	−0.554693	+	0.832055i	$0.687164\pi$
$24$		0			0
$25$	4.64703	−	1.84529i	0.929407	−	0.369057i
$26$	3.29582			0.646364
$27$		0			0
$28$	−9.62243	−	3.12652i	−1.81847	−	0.590856i
$29$	1.22466	−	3.76910i	0.227413	−	0.699905i	−0.770625	−	0.637289i	$-0.780056\pi$
$29$	1.22466	−	3.76910i	0.227413	−	0.699905i	0.998038	−	0.0626159i	$-0.0199443\pi$
$30$		0			0
$31$	−1.99006	−	6.12477i	−0.357425	−	1.10004i	−0.954590	−	0.297923i	$-0.903706\pi$
$31$	−1.99006	−	6.12477i	−0.357425	−	1.10004i	0.597165	−	0.802119i	$-0.296294\pi$
$32$			5.13532i			0.907805i
$33$		0			0
$34$	3.47539	+	2.52502i	0.596025	+	0.433037i
$35$	−1.27534	−	6.66742i	−0.215572	−	1.12700i
$36$		0			0
$37$	2.24547	−	3.09062i	0.369153	−	0.508095i	−0.583518	−	0.812100i	$-0.698324\pi$
$37$	2.24547	−	3.09062i	0.369153	−	0.508095i	0.952670	+	0.304005i	$0.0983241\pi$
$38$	1.22613	−	1.68762i	0.198904	−	0.273768i
$39$		0			0
$40$	6.02900	−	3.31841i	0.953269	−	0.524687i
$41$	−1.48391	−	1.07813i	−0.231749	−	0.168375i	0.465851	−	0.884863i	$-0.345748\pi$
$41$	−1.48391	−	1.07813i	−0.231749	−	0.168375i	−0.697599	+	0.716488i	$0.745748\pi$
$42$		0			0
$43$			3.59445i			0.548149i	0.961708	+	0.274074i	$0.0883715\pi$
$43$			3.59445i			0.548149i	−0.961708	+	0.274074i	$0.911629\pi$
$44$	2.05975	+	6.33927i	0.310519	+	0.955680i
$45$		0			0
$46$	−2.37582	+	7.31203i	−0.350296	+	1.07810i
$47$	4.56502	+	1.48326i	0.665877	+	0.216356i	0.622402	−	0.782698i	$-0.286157\pi$
$47$	4.56502	+	1.48326i	0.665877	+	0.216356i	0.0434750	+	0.999055i	$0.486157\pi$
$48$		0			0
$49$	−2.21619			−0.316598
$50$	9.75513	+	6.17707i	1.37958	+	0.873570i
$51$		0			0
$52$	2.79582	+	3.84812i	0.387711	+	0.533638i
$53$	−9.03953	−	2.93712i	−1.24168	−	0.403445i	−0.386745	−	0.922187i	$-0.626401\pi$
$53$	−9.03953	−	2.93712i	−1.24168	−	0.403445i	−0.854931	+	0.518742i	$0.826401\pi$
$54$		0			0
$55$	−3.05975	+	3.26158i	−0.412577	+	0.439792i
$56$	−2.88723	−	8.88599i	−0.385823	−	1.18744i
$57$		0			0
$58$	8.70390	−	2.82807i	1.14288	−	0.371343i
$59$	−8.61248	−	6.25734i	−1.12125	−	0.814636i	−0.136852	−	0.990592i	$-0.543698\pi$
$59$	−8.61248	−	6.25734i	−1.12125	−	0.814636i	−0.984398	+	0.175956i	$0.943698\pi$
$60$		0			0
$61$	−11.5481	+	8.39016i	−1.47858	+	1.07425i	−0.500566	+	0.865698i	$0.666875\pi$
$61$	−11.5481	+	8.39016i	−1.47858	+	1.07425i	−0.978012	+	0.208551i	$0.933125\pi$
$62$	8.74134	−	12.0314i	1.11015	−	1.52799i
$63$		0			0
$64$	−10.3087	+	7.48973i	−1.28859	+	0.936217i
$65$	−1.35736	+	2.88829i	−0.168359	+	0.358248i
$66$		0			0
$67$	10.1670	−	3.30345i	1.24209	−	0.403580i	0.387012	−	0.922075i	$-0.373507\pi$
$67$	10.1670	−	3.30345i	1.24209	−	0.403580i	0.855081	+	0.518494i	$0.173507\pi$
$68$			6.19974i			0.751828i
$69$		0			0
$70$	10.7253	−	11.4327i	1.28191	−	1.36647i
$71$	−3.85030	+	11.8500i	−0.456947	+	1.40634i	0.411887	+	0.911235i	$0.364870\pi$
$71$	−3.85030	+	11.8500i	−0.456947	+	1.40634i	−0.868834	+	0.495104i	$0.835130\pi$
$72$		0			0
$73$	0.157310	+	0.216518i	0.0184117	+	0.0253415i	0.818124	−	0.575042i	$-0.195014\pi$
$73$	0.157310	+	0.216518i	0.0184117	+	0.0253415i	−0.799712	+	0.600384i	$0.795014\pi$
$74$	8.82193			1.02553
$75$		0			0
$76$	3.01054			0.345332
$77$	3.56882	+	4.91206i	0.406704	+	0.559781i
$78$		0			0
$79$	2.64882	−	8.15223i	0.298015	−	0.917197i	−0.684176	−	0.729316i	$-0.739838\pi$
$79$	2.64882	−	8.15223i	0.298015	−	0.917197i	0.982192	−	0.187881i	$-0.0601618\pi$
$80$	0.893919	+	0.420099i	0.0999432	+	0.0469685i
$81$		0			0
$82$		−	4.23572i		−	0.467757i
$83$	12.0006	−	3.89923i	1.31724	−	0.427996i	0.435691	−	0.900096i	$-0.356504\pi$
$83$	12.0006	−	3.89923i	1.31724	−	0.427996i	0.881545	+	0.472100i	$0.156504\pi$
$84$		0			0
$85$	−3.64411	+	2.00575i	−0.395260	+	0.217554i
$86$	−6.71531	+	4.87896i	−0.724130	+	0.526112i
$87$		0			0
$88$	−3.61803	+	4.97980i	−0.385684	+	0.530848i
$89$	3.85736	−	2.80253i	0.408879	−	0.297068i	−0.364269	−	0.931294i	$-0.618681\pi$
$89$	3.85736	−	2.80253i	0.408879	−	0.297068i	0.773148	+	0.634226i	$0.218681\pi$
$90$		0			0
$91$	3.50527	+	2.54673i	0.367452	+	0.266969i
$92$	−10.5527	+	3.42879i	−1.10020	+	0.357476i
$93$		0			0
$94$	3.42527	+	10.5419i	0.353289	+	1.08731i
$95$	0.973973	+	1.76955i	0.0999276	+	0.181552i
$96$		0			0
$97$	−9.47067	−	3.07721i	−0.961600	−	0.312443i	−0.214180	−	0.976794i	$-0.568708\pi$
$97$	−9.47067	−	3.07721i	−0.961600	−	0.312443i	−0.747420	+	0.664351i	$0.768708\pi$
$98$	−3.00816	−	4.14037i	−0.303870	−	0.418241i
$99$		0			0
$100$	1.06301	+	16.6298i	0.106301	+	1.66298i
$101$	−9.34612			−0.929974			−0.464987	−	0.885318i	$-0.653941\pi$
$101$	−9.34612			−0.929974			−0.464987	+	0.885318i	$0.653941\pi$
$102$		0			0
$103$	−8.63947	−	2.80713i	−0.851272	−	0.276595i	−0.149294	−	0.988793i	$-0.547700\pi$
$103$	−8.63947	−	2.80713i	−0.851272	−	0.276595i	−0.701979	+	0.712198i	$0.747700\pi$
$104$	−1.35736	+	4.17752i	−0.133100	+	0.409639i
$105$		0			0
$106$	−6.78262	−	20.8748i	−0.658787	−	2.02754i
$107$		−	5.62871i		−	0.544148i	−0.962276	−	0.272074i	$-0.912290\pi$
$107$		−	5.62871i		−	0.544148i	0.962276	−	0.272074i	$-0.0877096\pi$
$108$		0			0
$109$	−8.18158	−	5.94427i	−0.783654	−	0.569358i	0.122420	−	0.992478i	$-0.460935\pi$
$109$	−8.18158	−	5.94427i	−0.783654	−	0.569358i	−0.906073	+	0.423121i	$0.860935\pi$
$110$	−10.2466	−	1.28923i	−0.976975	−	0.122923i
$111$		0			0
$112$	0.788206	−	1.08487i	0.0744784	−	0.102511i
$113$	6.29636	−	8.66620i	0.592312	−	0.815247i	−0.402666	−	0.915347i	$-0.631916\pi$
$113$	6.29636	−	8.66620i	0.592312	−	0.815247i	0.994977	+	0.100100i	$0.0319162\pi$
$114$		0			0
$115$	−5.42943	−	5.09345i	−0.506297	−	0.474967i
$116$	10.6854	+	7.76342i	0.992118	+	0.720816i
$117$		0			0
$118$		−	24.5836i		−	2.26311i
$119$	1.74513	+	5.37097i	0.159976	+	0.492356i
$120$		0			0
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$	−31.3497	−	10.1861i	−2.83827	−	0.922209i
$123$		0			0
$124$	21.4628			1.92742
$125$	−9.43085	+	6.00492i	−0.843521	+	0.537097i
$126$		0			0
$127$	6.67779	+	9.19118i	0.592558	+	0.815586i	0.995002	−	0.0998589i	$-0.0318392\pi$
$127$	6.67779	+	9.19118i	0.592558	+	0.815586i	−0.402444	+	0.915445i	$0.631839\pi$
$128$	−18.2173	−	5.91917i	−1.61020	−	0.523185i
$129$		0			0
$130$	−7.23845	+	1.38457i	−0.634854	+	0.121435i
$131$	−2.46834	−	7.59677i	−0.215660	−	0.663732i	−0.999106	−	0.0422730i	$-0.986540\pi$
$131$	−2.46834	−	7.59677i	−0.215660	−	0.663732i	0.783446	−	0.621459i	$-0.213460\pi$
$132$		0			0
$133$	2.60809	−	0.847421i	0.226150	−	0.0734807i
$134$	19.9719	+	14.5104i	1.72531	+	1.25351i
$135$		0			0
$136$	−4.63182	+	3.36522i	−0.397176	+	0.288565i
$137$	−5.48831	+	7.55401i	−0.468898	+	0.645382i	−0.976324	−	0.216313i	$-0.930597\pi$
$137$	−5.48831	+	7.55401i	−0.468898	+	0.645382i	0.507426	+	0.861695i	$0.330597\pi$
$138$		0			0
$139$	14.4936	−	10.5302i	1.22933	−	0.893160i	0.232489	−	0.972599i	$-0.425313\pi$
$139$	14.4936	−	10.5302i	1.22933	−	0.893160i	0.996840	+	0.0794393i	$0.0253130\pi$
$140$	22.4467	+	2.82424i	1.89709	+	0.238692i
$141$		0			0
$142$	−27.3649	+	8.89141i	−2.29642	+	0.746151i
$143$		−	2.85442i		−	0.238699i
$144$		0			0
$145$	−1.10626	+	8.79238i	−0.0918695	+	0.730167i
$146$	−0.190983	+	0.587785i	−0.0158059	+	0.0486455i
$147$		0			0
$148$	7.48358	+	10.3003i	0.615146	+	0.846676i
$149$	−6.31395			−0.517259			−0.258629	−	0.965977i	$-0.583271\pi$
$149$	−6.31395			−0.517259			−0.258629	+	0.965977i	$0.583271\pi$
$150$		0			0
$151$	4.71947			0.384065			0.192033	−	0.981389i	$-0.438492\pi$
$151$	4.71947			0.384065			0.192033	+	0.981389i	$0.438492\pi$
$152$	1.63412	+	2.24917i	0.132545	+	0.182432i
$153$		0			0
$154$	−4.33275	+	13.3348i	−0.349143	+	1.07455i
$155$	6.94368	+	12.6155i	0.557730	+	1.01330i
$156$		0			0
$157$			1.46908i			0.117245i	0.998280	+	0.0586225i	$0.0186708\pi$
$157$			1.46908i			0.117245i	−0.998280	+	0.0586225i	$0.981329\pi$
$158$	18.8257	−	6.11685i	1.49769	−	0.486630i
$159$		0			0
$160$	−2.15734	−	11.2784i	−0.170553	−	0.891639i
$161$	−8.17691	+	5.94087i	−0.644431	+	0.468206i
$162$		0			0
$163$	−2.62134	+	3.60797i	−0.205319	+	0.282598i	−0.899242	−	0.437452i	$-0.855881\pi$
$163$	−2.62134	+	3.60797i	−0.205319	+	0.282598i	0.693922	+	0.720050i	$0.255881\pi$
$164$	4.94552	−	3.59313i	0.386180	−	0.280576i
$165$		0			0
$166$	23.5738	+	17.1274i	1.82968	+	1.32934i
$167$	9.92300	−	3.22418i	0.767865	−	0.249494i	0.101214	−	0.994865i	$-0.467727\pi$
$167$	9.92300	−	3.22418i	0.767865	−	0.249494i	0.666651	+	0.745370i	$0.267727\pi$
$168$		0			0
$169$	3.38778	+	10.4265i	0.260598	+	0.802038i
$170$	−8.69359	−	4.08557i	−0.666768	−	0.313349i
$171$		0			0
$172$	−11.3931	−	3.70184i	−0.868715	−	0.282263i
$173$	4.51195	+	6.21017i	0.343037	+	0.472151i	0.945326	−	0.326128i	$-0.105744\pi$
$173$	4.51195	+	6.21017i	0.343037	+	0.472151i	−0.602288	+	0.798279i	$0.705744\pi$
$174$		0			0
$175$	5.60195	+	14.1075i	0.423468	+	1.06643i
$176$	−0.883436			−0.0665915
$177$		0			0
$178$	10.4716	+	3.40244i	0.784882	+	0.255023i
$179$	4.79494	−	14.7573i	0.358391	−	1.10301i	−0.595626	−	0.803262i	$-0.703096\pi$
$179$	4.79494	−	14.7573i	0.358391	−	1.10301i	0.954017	−	0.299752i	$-0.0969040\pi$
$180$		0			0
$181$	−0.491509	−	1.51271i	−0.0365336	−	0.112439i	0.931127	−	0.364696i	$-0.118827\pi$
$181$	−0.491509	−	1.51271i	−0.0365336	−	0.112439i	−0.967660	+	0.252257i	$0.918827\pi$
$182$			10.0055i			0.741658i
$183$		0			0
$184$	−8.28968	−	6.02280i	−0.611123	−	0.444007i
$185$	−3.63324	+	7.73110i	−0.267121	+	0.568402i
$186$		0			0
$187$	2.18685	−	3.00994i	0.159918	−	0.220109i
$188$	−9.40281	+	12.9419i	−0.685770	+	0.943882i
$189$		0			0
$190$	−1.98391	+	4.22153i	−0.143928	+	0.306262i
$191$	15.9121	+	11.5608i	1.15136	+	0.836511i	0.988661	−	0.150164i	$-0.0479803\pi$
$191$	15.9121	+	11.5608i	1.15136	+	0.836511i	0.162698	+	0.986676i	$0.447980\pi$
$192$		0			0
$193$		−	13.1100i		−	0.943680i	−0.881684	−	0.471840i	$-0.843590\pi$
$193$		−	13.1100i		−	0.943680i	0.881684	−	0.471840i	$-0.156410\pi$
$194$	−7.10611	−	21.8704i	−0.510189	−	1.57020i
$195$		0			0
$196$	2.28240	−	7.02449i	0.163028	−	0.501750i
$197$	3.26164	+	1.05977i	0.232382	+	0.0755055i	0.422893	−	0.906180i	$-0.361015\pi$
$197$	3.26164	+	1.05977i	0.232382	+	0.0755055i	−0.190511	+	0.981685i	$0.561015\pi$
$198$		0			0
$199$	−17.6959			−1.25443			−0.627215	−	0.778846i	$-0.715805\pi$
$199$	−17.6959			−1.25443			−0.627215	+	0.778846i	$0.715805\pi$
$200$	−11.8471	+	9.82084i	−0.837719	+	0.694438i
$201$		0			0
$202$	−12.6860	−	17.4608i	−0.892586	−	1.22854i
$203$	11.4423	+	3.71783i	0.803093	+	0.260941i
$204$		0			0
$205$	3.71197	+	1.74445i	0.259255	+	0.121837i
$206$	−6.48244	−	19.9509i	−0.451653	−	1.39005i
$207$		0			0
$208$	−0.599570	+	0.194812i	−0.0415727	+	0.0135078i
$209$	−1.46160	−	1.06192i	−0.101101	−	0.0734542i
$210$		0			0
$211$	2.62418	−	1.90658i	0.180656	−	0.131254i	−0.493782	−	0.869586i	$-0.664386\pi$
$211$	2.62418	−	1.90658i	0.180656	−	0.131254i	0.674438	+	0.738331i	$0.264386\pi$
$212$	18.6192	−	25.6271i	1.27877	−	1.76008i
$213$		0			0
$214$	10.5158	−	7.64018i	0.718845	−	0.522272i
$215$	−1.51003	−	7.89432i	−0.102983	−	0.538388i
$216$		0			0
$217$	18.5937	−	6.04145i	1.26222	−	0.410121i
$218$		−	23.3537i		−	1.58171i
$219$		0			0
$220$	−7.18685	−	13.0573i	−0.484537	−	0.880324i
$221$	0.820429	−	2.52502i	0.0551880	−	0.169851i
$222$		0			0
$223$	16.8781	+	23.2307i	1.13024	+	1.55564i	0.787609	+	0.616175i	$0.211319\pi$
$223$	16.8781	+	23.2307i	1.13024	+	1.55564i	0.342633	+	0.939469i	$0.388681\pi$
$224$	−15.5899			−1.04164
$225$		0			0
$226$	24.7370			1.64548
$227$	6.88921	+	9.48219i	0.457253	+	0.629355i	0.973936	−	0.226822i	$-0.0728335\pi$
$227$	6.88921	+	9.48219i	0.457253	+	0.629355i	−0.516683	+	0.856177i	$0.672833\pi$
$228$		0			0
$229$	5.06828	−	15.5985i	0.334921	−	1.03078i	−0.631840	−	0.775099i	$-0.717700\pi$
$229$	5.06828	−	15.5985i	0.334921	−	1.03078i	0.966761	−	0.255682i	$-0.0823000\pi$
$230$	2.14612	−	17.0571i	0.141511	−	1.12471i
$231$		0			0
$232$			12.1971i			0.800777i
$233$	−21.4126	+	6.95739i	−1.40279	+	0.455794i	−0.910092	−	0.414407i	$-0.863989\pi$
$233$	−21.4126	+	6.95739i	−1.40279	+	0.455794i	−0.492697	+	0.870201i	$0.663989\pi$
$234$		0			0
$235$	−10.6490	−	1.33986i	−0.694667	−	0.0874029i
$236$	28.7032	−	20.8541i	1.86842	−	1.35749i
$237$		0			0
$238$	−7.66550	+	10.5507i	−0.496880	+	0.683897i
$239$	5.36647	−	3.89897i	0.347128	−	0.252204i	−0.400535	−	0.916281i	$-0.631176\pi$
$239$	5.36647	−	3.89897i	0.347128	−	0.252204i	0.747663	+	0.664078i	$0.231176\pi$
$240$		0			0
$241$	−21.2173	−	15.4153i	−1.36673	−	0.992986i	−0.997985	−	0.0634545i	$-0.979788\pi$
$241$	−21.2173	−	15.4153i	−1.36673	−	0.992986i	−0.368743	−	0.929531i	$-0.620212\pi$
$242$	−15.3738	+	4.99524i	−0.988262	+	0.321106i
$243$		0			0
$244$	−14.7006	−	45.2439i	−0.941112	−	2.89645i
$245$	4.86730	−	0.931017i	0.310960	−	0.0594805i
$246$		0			0
$247$	−1.22613	−	0.398393i	−0.0780166	−	0.0253491i
$248$	11.6500	+	16.0349i	0.739776	+	1.01821i
$249$		0			0
$250$	−24.0197	−	9.46828i	−1.51914	−	0.598827i
$251$	10.9121			0.688766			0.344383	−	0.938829i	$-0.388088\pi$
$251$	10.9121			0.688766			0.344383	+	0.938829i	$0.388088\pi$
$252$		0			0
$253$	6.33275	+	2.05763i	0.398137	+	0.129362i
$254$	−8.10722	+	24.9514i	−0.508692	+	1.56559i
$255$		0			0
$256$	−5.79381	−	17.8315i	−0.362113	−	1.11447i
$257$		−	6.58051i		−	0.410481i	−0.978712	−	0.205240i	$-0.934202\pi$
$257$		−	6.58051i		−	0.410481i	0.978712	−	0.205240i	$-0.0657976\pi$
$258$		0			0
$259$	9.38256	+	6.81683i	0.583004	+	0.423577i
$260$	−7.75691	−	7.27691i	−0.481063	−	0.451295i
$261$		0			0
$262$	10.8422	−	14.9230i	0.669832	−	0.921945i
$263$	−15.9332	+	21.9302i	−0.982486	+	1.35228i	−0.0470069	+	0.998895i	$0.514968\pi$
$263$	−15.9332	+	21.9302i	−0.982486	+	1.35228i	−0.935479	+	0.353382i	$0.885032\pi$
$264$		0			0
$265$	21.0870	+	2.65316i	1.29536	+	0.162982i
$266$	5.12330	+	3.72230i	0.314130	+	0.228229i
$267$		0			0
$268$			35.6277i			2.17631i
$269$	0.311938	+	0.960046i	0.0190192	+	0.0585350i	0.960116	−	0.279603i	$-0.0902029\pi$
$269$	0.311938	+	0.960046i	0.0190192	+	0.0585350i	−0.941096	+	0.338138i	$0.890203\pi$
$270$		0			0
$271$	1.93198	−	5.94603i	0.117360	−	0.361196i	−0.875072	−	0.483992i	$-0.839186\pi$
$271$	1.93198	−	5.94603i	0.117360	−	0.361196i	0.992432	+	0.122796i	$0.0391862\pi$
$272$	−0.781488	−	0.253921i	−0.0473847	−	0.0153962i
$273$		0			0
$274$	−21.5623			−1.30263
$275$	5.34980	−	8.44865i	0.322605	−	0.509473i
$276$		0			0
$277$	14.5009	+	19.9587i	0.871272	+	1.19920i	0.978763	+	0.204997i	$0.0657184\pi$
$277$	14.5009	+	19.9587i	0.871272	+	1.19920i	−0.107491	+	0.994206i	$0.534282\pi$
$278$	39.3459	+	12.7843i	2.35981	+	0.766749i
$279$		0			0
$280$	10.0741	+	18.3029i	0.602042	+	1.09381i
$281$	−0.568255	−	1.74891i	−0.0338993	−	0.104331i	0.932675	−	0.360717i	$-0.117468\pi$
$281$	−0.568255	−	1.74891i	−0.0338993	−	0.104331i	−0.966574	+	0.256386i	$0.917468\pi$
$282$		0			0
$283$	−8.21823	+	2.67026i	−0.488523	+	0.158731i	−0.542913	−	0.839789i	$-0.682679\pi$
$283$	−8.21823	+	2.67026i	−0.488523	+	0.158731i	0.0543898	+	0.998520i	$0.482679\pi$
$284$	−33.5949	−	24.4081i	−1.99349	−	1.44835i
$285$		0			0
$286$	5.33275	−	3.87447i	0.315332	−	0.229102i
$287$	3.27300	−	4.50489i	0.193199	−	0.265915i
$288$		0			0
$289$	−10.9537	+	7.95831i	−0.644334	+	0.468136i
$290$	−17.9279	+	9.86764i	−1.05276	+	0.579448i
$291$		0			0
$292$	−0.848293	+	0.275627i	−0.0496426	+	0.0161299i
$293$			6.29156i			0.367557i	0.982968	+	0.183779i	$0.0588329\pi$
$293$			6.29156i			0.367557i	−0.982968	+	0.183779i	$0.941167\pi$
$294$		0			0
$295$	21.5439	+	10.1246i	1.25433	+	0.589476i
$296$	−3.63324	+	11.1820i	−0.211178	+	0.649939i
$297$		0			0
$298$	−8.57029	−	11.7960i	−0.496463	−	0.683323i
$299$	4.75164			0.274795
$300$		0			0
$301$	−10.9121			−0.628963
$302$	6.40601	+	8.81712i	0.368625	+	0.507368i
$303$		0			0
$304$	−0.123302	+	0.379483i	−0.00707183	+	0.0217649i
$305$	21.8377	−	23.2782i	1.25043	−	1.33291i
$306$		0			0
$307$		−	28.6661i		−	1.63606i	−0.575175	−	0.818030i	$-0.695066\pi$
$307$		−	28.6661i		−	1.63606i	0.575175	−	0.818030i	$-0.304934\pi$
$308$	−19.2449	+	6.25303i	−1.09658	+	0.356300i
$309$		0			0
$310$	−14.1438	+	30.0962i	−0.803313	+	1.70935i
$311$	−6.33985	+	4.60617i	−0.359500	+	0.261192i	−0.752844	−	0.658199i	$-0.771318\pi$
$311$	−6.33985	+	4.60617i	−0.359500	+	0.261192i	0.393343	+	0.919392i	$0.371318\pi$
$312$		0			0
$313$	−12.5840	+	17.3205i	−0.711292	+	0.979010i	0.288476	+	0.957487i	$0.406851\pi$
$313$	−12.5840	+	17.3205i	−0.711292	+	0.979010i	−0.999768	+	0.0215228i	$0.993149\pi$
$314$	−2.74459	+	1.99406i	−0.154886	+	0.112531i
$315$		0			0
$316$	23.1116	+	16.7916i	1.30013	+	0.944599i
$317$	3.82309	−	1.24220i	0.214726	−	0.0697688i	−0.199679	−	0.979861i	$-0.563990\pi$
$317$	3.82309	−	1.24220i	0.214726	−	0.0697688i	0.414405	+	0.910093i	$0.363990\pi$
$318$		0			0
$319$	−2.44931	−	7.53821i	−0.137135	−	0.422059i
$320$	19.4941	−	20.7800i	1.08976	−	1.16164i
$321$		0			0
$322$	−22.1980	−	7.21256i	−1.23705	−	0.401940i
$323$	−0.987712	−	1.35947i	−0.0549578	−	0.0756429i
$324$		0			0
$325$	1.76773	−	6.91364i	0.0980560	−	0.383499i
$326$	−10.2987			−0.570390
$327$		0			0
$328$	5.36885	+	1.74445i	0.296445	+	0.0963209i
$329$	−4.50292	+	13.8586i	−0.248254	+	0.764047i
$330$		0			0
$331$	3.59815	+	11.0740i	0.197772	+	0.608681i	0.999933	+	0.0115724i	$0.00368369\pi$
$331$	3.59815	+	11.0740i	0.197772	+	0.608681i	−0.802161	+	0.597108i	$0.796316\pi$
$332$			42.0532i			2.30797i
$333$		0			0
$334$	19.4926	+	14.1622i	1.06659	+	0.774922i
$335$	−20.9414	+	11.5263i	−1.14415	+	0.629751i
$336$		0			0
$337$	−12.6578	+	17.4220i	−0.689516	+	0.949037i	−0.999999	−	0.00154181i	$-0.999509\pi$
$337$	−12.6578	+	17.4220i	−0.689516	+	0.949037i	0.310483	+	0.950579i	$0.399509\pi$
$338$	−14.8808	+	20.4817i	−0.809409	+	1.11406i
$339$		0			0
$340$	−2.60450	−	13.6162i	−0.141249	−	0.738441i
$341$	−10.4201	−	7.57063i	−0.564279	−	0.409973i
$342$		0			0
$343$			14.5228i			0.784157i
$344$	−3.41853	−	10.5211i	−0.184315	−	0.567262i
$345$		0			0
$346$	−5.47777	+	16.8588i	−0.294487	+	0.906337i
$347$	−14.8339	−	4.81981i	−0.796323	−	0.258741i	−0.117529	−	0.993069i	$-0.537497\pi$
$347$	−14.8339	−	4.81981i	−0.796323	−	0.258741i	−0.678794	+	0.734328i	$0.737497\pi$
$348$		0			0
$349$	−5.56598			−0.297940			−0.148970	−	0.988842i	$-0.547596\pi$
$349$	−5.56598			−0.297940			−0.148970	+	0.988842i	$0.547596\pi$
$350$	−18.7525	+	29.6148i	−1.00236	+	1.58298i
$351$		0			0
$352$	6.03693	+	8.30912i	0.321769	+	0.442878i
$353$	7.62953	+	2.47898i	0.406079	+	0.131943i	0.504932	−	0.863159i	$-0.331517\pi$
$353$	7.62953	+	2.47898i	0.406079	+	0.131943i	−0.0988533	+	0.995102i	$0.531517\pi$
$354$		0			0
$355$	3.47805	−	27.6431i	0.184596	−	1.46714i
$356$	4.91040	+	15.1127i	0.260251	+	0.800970i
$357$		0			0
$358$	34.0787	−	11.0728i	1.80112	−	0.585218i
$359$	9.98547	+	7.25487i	0.527013	+	0.382897i	0.819239	−	0.573452i	$-0.194396\pi$
$359$	9.98547	+	7.25487i	0.527013	+	0.382897i	−0.292226	+	0.956349i	$0.594396\pi$
$360$		0			0
$361$	14.7112	−	10.6883i	0.774272	−	0.562542i
$362$	2.15895	−	2.97155i	0.113472	−	0.156181i
$363$		0			0
$364$	−11.6822	+	8.48760i	−0.612312	+	0.444871i
$365$	−0.436451	−	0.409443i	−0.0228449	−	0.0214312i
$366$		0			0
$367$	−25.5596	+	8.30481i	−1.33420	+	0.433508i	−0.887348	−	0.461100i	$-0.847455\pi$
$367$	−25.5596	+	8.30481i	−1.33420	+	0.433508i	−0.446852	+	0.894608i	$0.647455\pi$
$368$		−	1.47062i		−	0.0766615i
$369$		0			0
$370$	−19.3752	+	3.70608i	−1.00727	+	0.192670i
$371$	8.91657	−	27.4424i	0.462925	−	1.42474i
$372$		0			0
$373$	−16.2457	−	22.3604i	−0.841173	−	1.15778i	−0.985739	−	0.168280i	$-0.946179\pi$
$373$	−16.2457	−	22.3604i	−0.841173	−	1.15778i	0.144566	−	0.989495i	$-0.453821\pi$
$374$	8.59164			0.444263
$375$		0			0
$376$	−14.7727			−0.761845
$377$	−3.32459	−	4.57591i	−0.171225	−	0.235671i
$378$		0			0
$379$	1.07372	−	3.30456i	0.0551532	−	0.169744i	−0.919685	−	0.392656i	$-0.871556\pi$
$379$	1.07372	−	3.30456i	0.0551532	−	0.169744i	0.974839	+	0.222912i	$0.0715563\pi$
$380$	−6.61189	+	1.26472i	−0.339183	+	0.0648789i
$381$		0			0
$382$			45.4198i			2.32388i
$383$	−26.0322	+	8.45837i	−1.33018	+	0.432203i	−0.885980	−	0.463723i	$-0.846513\pi$
$383$	−26.0322	+	8.45837i	−1.33018	+	0.432203i	−0.444203	+	0.895926i	$0.646513\pi$
$384$		0			0
$385$	−9.90157	−	9.28885i	−0.504631	−	0.473404i
$386$	24.4927	−	17.7950i	1.24665	−	0.905741i
$387$		0			0
$388$	19.5072	−	26.8494i	0.990329	−	1.36307i
$389$	−8.80576	+	6.39776i	−0.446470	+	0.324379i	−0.788200	−	0.615419i	$-0.788987\pi$
$389$	−8.80576	+	6.39776i	−0.446470	+	0.324379i	0.341731	+	0.939798i	$0.388987\pi$
$390$		0			0
$391$	5.01054	+	3.64037i	0.253394	+	0.184101i
$392$	6.48689	−	2.10772i	0.327637	−	0.106456i
$393$		0			0
$394$	2.44730	+	7.53202i	0.123293	+	0.379458i
$395$	−2.39273	+	19.0171i	−0.120391	+	0.956854i
$396$		0			0
$397$	15.4273	+	5.01264i	0.774275	+	0.251577i	0.669394	−	0.742908i	$-0.266554\pi$
$397$	15.4273	+	5.01264i	0.774275	+	0.251577i	0.104881	+	0.994485i	$0.466554\pi$
$398$	−24.0197	−	33.0603i	−1.20400	−	1.65716i
$399$		0			0
$400$	−2.13975	−	0.547108i	−0.106988	−	0.0273554i
$401$	−3.78686			−0.189107			−0.0945534	−	0.995520i	$-0.530142\pi$
$401$	−3.78686			−0.189107			−0.0945534	+	0.995520i	$0.530142\pi$
$402$		0			0
$403$	−8.74134	−	2.84023i	−0.435437	−	0.141482i
$404$	9.62535	−	29.6238i	0.478879	−	1.47384i
$405$		0			0
$406$	8.58550	+	26.4234i	0.426091	+	1.31137i
$407$		−	7.64044i		−	0.378722i
$408$		0			0
$409$	1.50142	+	1.09084i	0.0742403	+	0.0539388i	0.624286	−	0.781196i	$-0.285390\pi$
$409$	1.50142	+	1.09084i	0.0742403	+	0.0539388i	−0.550046	+	0.835134i	$0.685390\pi$
$410$	1.77942	+	9.30269i	0.0878793	+	0.459427i
$411$		0			0
$412$	17.7952	−	24.4930i	0.876705	−	1.20668i
$413$	18.9961	−	26.1459i	0.934738	−	1.28656i
$414$		0			0
$415$	−24.7182	+	13.6051i	−1.21337	+	0.667849i
$416$	5.92943	+	4.30798i	0.290714	+	0.211216i
$417$		0			0
$418$		−	4.17202i		−	0.204060i
$419$	4.43353	+	13.6450i	0.216592	+	0.666602i	0.999037	+	0.0438818i	$0.0139725\pi$
$419$	4.43353	+	13.6450i	0.216592	+	0.666602i	−0.782445	+	0.622720i	$0.786028\pi$
$420$		0			0
$421$	4.77571	−	14.6981i	0.232754	−	0.716343i	−0.764658	−	0.644437i	$-0.777092\pi$
$421$	4.77571	−	14.6981i	0.232754	−	0.716343i	0.997411	−	0.0719060i	$-0.0229082\pi$
$422$	7.12390	+	2.31469i	0.346786	+	0.112678i
$423$		0			0
$424$	29.2525			1.42063
$425$	7.16077	−	5.93602i	0.347348	−	0.287939i
$426$		0			0
$427$	−25.4710	−	35.0578i	−1.23263	−	1.69657i
$428$	17.8410	+	5.79688i	0.862375	+	0.280203i
$429$		0			0
$430$	12.6989	−	13.5365i	0.612393	−	0.652788i
$431$	−3.86404	−	11.8923i	−0.186124	−	0.572832i	0.813842	−	0.581087i	$-0.197372\pi$
$431$	−3.86404	−	11.8923i	−0.186124	−	0.572832i	−0.999966	+	0.00825486i	$0.997372\pi$
$432$		0			0
$433$	−21.3941	+	6.95138i	−1.02814	+	0.334062i	−0.774053	−	0.633120i	$-0.781774\pi$
$433$	−21.3941	+	6.95138i	−1.02814	+	0.334062i	−0.254084	+	0.967182i	$0.581774\pi$
$434$	36.5252	+	26.5371i	1.75326	+	1.27382i
$435$		0			0
$436$	27.2672	−	19.8108i	1.30586	−	0.948763i
$437$	1.76773	−	2.43307i	0.0845620	−	0.116390i
$438$		0			0
$439$	9.85186	−	7.15780i	0.470204	−	0.341623i	−0.327317	−	0.944915i	$-0.606145\pi$
$439$	9.85186	−	7.15780i	0.470204	−	0.341623i	0.797521	+	0.603292i	$0.206145\pi$
$440$	5.85410	−	12.4568i	0.279083	−	0.593855i
$441$		0			0
$442$	5.83096	−	1.89460i	0.277351	−	0.0901167i
$443$		−	20.7101i		−	0.983968i	−0.870604	−	0.491984i	$-0.836272\pi$
$443$		−	20.7101i		−	0.983968i	0.870604	−	0.491984i	$-0.163728\pi$
$444$		0			0
$445$	−7.29438	+	7.77554i	−0.345787	+	0.368596i
$446$	−20.4910	+	63.0648i	−0.970277	+	2.98621i
$447$		0			0
$448$	−22.7375	−	31.2954i	−1.07424	−	1.47857i
$449$	−25.9539			−1.22484			−0.612420	−	0.790533i	$-0.709804\pi$
$449$	−25.9539			−1.22484			−0.612420	+	0.790533i	$0.709804\pi$
$450$		0			0
$451$	−3.66844			−0.172740
$452$	20.9842	+	28.8823i	0.987013	+	1.35851i
$453$		0			0
$454$	−8.36390	+	25.7414i	−0.392537	+	1.20811i
$455$	−8.76832	−	4.12069i	−0.411065	−	0.193181i
$456$		0			0
$457$		−	8.50150i		−	0.397684i	−0.980032	−	0.198842i	$-0.936282\pi$
$457$		−	8.50150i		−	0.397684i	0.980032	−	0.198842i	$-0.0637180\pi$
$458$	36.0213	−	11.7040i	1.68317	−	0.546894i
$459$		0			0
$460$	21.7360	−	11.9637i	1.01345	−	0.557809i
$461$	11.9614	−	8.69044i	0.557097	−	0.404754i	−0.273299	−	0.961929i	$-0.588115\pi$
$461$	11.9614	−	8.69044i	0.557097	−	0.404754i	0.830395	+	0.557175i	$0.188115\pi$
$462$		0			0
$463$	13.0442	−	17.9538i	0.606215	−	0.834384i	−0.390044	−	0.920796i	$-0.627540\pi$
$463$	13.0442	−	17.9538i	0.606215	−	0.834384i	0.996259	+	0.0864125i	$0.0275403\pi$
$464$	−1.41623	+	1.02895i	−0.0657470	+	0.0477680i
$465$		0			0
$466$	−42.0627	−	30.5603i	−1.94852	−	1.41568i
$467$	−27.1064	+	8.80741i	−1.25434	+	0.407558i	−0.859473	−	0.511182i	$-0.829208\pi$
$467$	−27.1064	+	8.80741i	−1.25434	+	0.407558i	−0.394863	+	0.918740i	$0.629208\pi$
$468$		0			0
$469$	10.0287	+	30.8651i	0.463081	+	1.42522i
$470$	−11.9514	−	21.7137i	−0.551276	−	1.00158i
$471$		0			0
$472$	31.1603	+	10.1246i	1.43427	+	0.466022i
$473$	4.22553	+	5.81595i	0.194290	+	0.267418i
$474$		0			0
$475$	−2.88248	−	3.47721i	−0.132257	−	0.159545i
$476$	−18.8213			−0.862671
$477$		0			0
$478$	14.5684	+	4.73358i	0.666345	+	0.216509i
$479$	7.74301	−	23.8305i	0.353787	−	1.08885i	−0.602922	−	0.797800i	$-0.705997\pi$
$479$	7.74301	−	23.8305i	0.353787	−	1.08885i	0.956709	−	0.291045i	$-0.0940030\pi$
$480$		0			0
$481$	−1.68484	−	5.18540i	−0.0768220	−	0.236434i
$482$		−	60.5632i		−	2.75858i
$483$		0			0
$484$	−18.8738	−	13.7126i	−0.857898	−	0.623299i
$485$	22.0927	+	2.77970i	1.00318	+	0.126220i
$486$		0			0
$487$	−0.860980	+	1.18504i	−0.0390147	+	0.0536992i	−0.828079	−	0.560612i	$-0.810566\pi$
$487$	−0.860980	+	1.18504i	−0.0390147	+	0.0536992i	0.789064	+	0.614311i	$0.210566\pi$
$488$	25.8222	−	35.5413i	1.16892	−	1.60888i
$489$		0			0
$490$	8.34603	+	7.82957i	0.377035	+	0.353704i
$491$	−16.2359	−	11.7961i	−0.732715	−	0.532348i	0.157706	−	0.987486i	$-0.449590\pi$
$491$	−16.2359	−	11.7961i	−0.732715	−	0.532348i	−0.890421	+	0.455138i	$0.849590\pi$
$492$		0			0
$493$		−	7.37229i		−	0.332031i
$494$	−0.919998	−	2.83146i	−0.0413927	−	0.127394i
$495$		0			0
$496$	−0.879045	+	2.70542i	−0.0394703	+	0.121477i
$497$	−35.9745	−	11.6888i	−1.61368	−	0.524315i
$498$		0			0
$499$	−0.624999			−0.0279788			−0.0139894	−	0.999902i	$-0.504453\pi$
$499$	−0.624999			−0.0279788			−0.0139894	+	0.999902i	$0.504453\pi$
$500$	−9.32080	−	36.0767i	−0.416839	−	1.61340i
$501$		0			0
$502$	14.8116	+	20.3865i	0.661075	+	0.909892i
$503$	−18.3603	−	5.96563i	−0.818647	−	0.265994i	−0.130391	−	0.991463i	$-0.541623\pi$
$503$	−18.3603	−	5.96563i	−0.818647	−	0.265994i	−0.688256	+	0.725468i	$0.741623\pi$
$504$		0			0
$505$	20.5264	−	3.92630i	0.913414	−	0.174718i
$506$	4.75164	+	14.6241i	0.211236	+	0.650119i
$507$		0			0
$508$	−36.0100	+	11.7003i	−1.59768	+	0.519119i
$509$	8.51099	+	6.18360i	0.377243	+	0.274083i	0.760208	−	0.649680i	$-0.225097\pi$
$509$	8.51099	+	6.18360i	0.377243	+	0.274083i	−0.382965	+	0.923763i	$0.625097\pi$
$510$		0			0
$511$	−0.657310	+	0.477563i	−0.0290777	+	0.0211262i
$512$	2.93146	−	4.03481i	0.129554	−	0.178315i
$513$		0			0
$514$	12.2940	−	8.93210i	0.542264	−	0.393978i
$515$	20.1537	+	2.53574i	0.888079	+	0.111738i
$516$		0			0
$517$	9.13004	−	2.96653i	0.401539	−	0.130468i
$518$			26.7818i			1.17672i
$519$		0			0
$520$	1.22613	−	9.74510i	0.0537692	−	0.427351i
$521$	3.09232	−	9.51719i	0.135477	−	0.416956i	−0.860187	−	0.509979i	$-0.829653\pi$
$521$	3.09232	−	9.51719i	0.135477	−	0.416956i	0.995664	+	0.0930234i	$0.0296531\pi$
$522$		0			0
$523$	13.3915	+	18.4319i	0.585571	+	0.805970i	0.994292	−	0.106690i	$-0.0340252\pi$
$523$	13.3915	+	18.4319i	0.585571	+	0.805970i	−0.408721	+	0.912659i	$0.634025\pi$
$524$	26.6210			1.16295
$525$		0			0
$526$	−62.5981			−2.72941
$527$	−7.04162	−	9.69196i	−0.306738	−	0.422188i
$528$		0			0
$529$	3.68213	−	11.3324i	0.160092	−	0.492714i
$530$	23.6658	+	42.9968i	1.02798	+	1.86766i
$531$		0			0
$532$			9.13943i			0.396245i
$533$	−2.48969	+	0.808950i	−0.107841	+	0.0350395i
$534$		0			0
$535$	2.36462	+	12.3621i	0.102231	+	0.534459i
$536$	−26.6175	+	19.3387i	−1.14970	+	0.835306i
$537$		0			0
$538$	−1.37019	+	1.88590i	−0.0590730	+	0.0813070i
$539$	−3.58586	+	2.60528i	−0.154454	+	0.112217i
$540$		0			0
$541$	−2.63658	−	1.91559i	−0.113356	−	0.0823576i	0.529663	−	0.848208i	$-0.322318\pi$
$541$	−2.63658	−	1.91559i	−0.113356	−	0.0823576i	−0.643019	+	0.765850i	$0.722318\pi$
$542$	13.7310	−	4.46148i	0.589798	−	0.191637i
$543$		0			0
$544$	2.95203	+	9.08540i	0.126567	+	0.389533i
$545$	20.4660	+	9.61803i	0.876667	+	0.411991i
$546$		0			0
$547$	−12.9232	−	4.19901i	−0.552557	−	0.179537i	0.0194122	−	0.999812i	$-0.493821\pi$
$547$	−12.9232	−	4.19901i	−0.552557	−	0.179537i	−0.571970	+	0.820275i	$0.693821\pi$
$548$	−18.2911	−	25.1756i	−0.781359	−	1.07545i
$549$		0			0
$550$	23.0457	−	1.47312i	0.982672	−	0.0628142i
$551$	−3.57992			−0.152510
$552$		0			0
$553$	24.7487	+	8.04133i	1.05242	+	0.341952i
$554$	−17.6049	+	54.1822i	−0.747959	+	2.30198i
$555$		0			0
$556$	18.4503	+	56.7841i	0.782466	+	2.40818i
$557$			27.6399i			1.17114i	0.810621	+	0.585571i	$0.199130\pi$
$557$			27.6399i			1.17114i	−0.810621	+	0.585571i	$0.800870\pi$
$558$		0			0
$559$	4.15029	+	3.01536i	0.175539	+	0.127536i
$560$	−1.27534	+	2.71378i	−0.0538931	+	0.114678i
$561$		0			0
$562$	2.49606	−	3.43554i	0.105290	−	0.144919i
$563$	−0.975284	+	1.34236i	−0.0411033	+	0.0565738i	−0.829074	−	0.559139i	$-0.811132\pi$
$563$	−0.975284	+	1.34236i	−0.0411033	+	0.0565738i	0.787971	+	0.615713i	$0.211132\pi$
$564$		0			0
$565$	−10.1877	+	21.6782i	−0.428601	+	0.912010i
$566$	−16.1438	−	11.7291i	−0.678574	−	0.493013i
$567$		0			0
$568$		−	38.3475i		−	1.60902i
$569$	5.52609	+	17.0076i	0.231666	+	0.712994i	0.997546	+	0.0700110i	$0.0223034\pi$
$569$	5.52609	+	17.0076i	0.231666	+	0.712994i	−0.765880	+	0.642983i	$0.777697\pi$
$570$		0			0
$571$	−11.3942	+	35.0677i	−0.476832	+	1.46754i	0.366640	+	0.930363i	$0.380508\pi$
$571$	−11.3942	+	35.0677i	−0.476832	+	1.46754i	−0.843472	+	0.537174i	$0.819492\pi$
$572$	9.04746	+	2.93970i	0.378293	+	0.122915i
$573$		0			0
$574$	12.8589			0.536718
$575$	14.0641	+	8.90560i	0.586515	+	0.371389i
$576$		0			0
$577$	13.4095	+	18.4567i	0.558247	+	0.768361i	0.991102	−	0.133103i	$-0.0424940\pi$
$577$	13.4095	+	18.4567i	0.558247	+	0.768361i	−0.432855	+	0.901463i	$0.642494\pi$
$578$	−29.7361	−	9.66184i	−1.23686	−	0.401880i
$579$		0			0
$580$	−26.7293	−	12.5615i	−1.10987	−	0.521587i
$581$	11.8373	+	36.4316i	0.491096	+	1.51144i
$582$		0			0
$583$	−18.0791	+	5.87425i	−0.748759	+	0.243286i
$584$	−0.666375	−	0.484149i	−0.0275748	−	0.0200342i
$585$		0			0
$586$	−11.7542	+	8.53990i	−0.485560	+	0.352780i
$587$	6.51588	−	8.96834i	0.268939	−	0.370163i	−0.653092	−	0.757278i	$-0.726529\pi$
$587$	6.51588	−	8.96834i	0.268939	−	0.370163i	0.922031	+	0.387116i	$0.126529\pi$
$588$		0			0
$589$	−4.70633	+	3.41935i	−0.193921	+	0.140892i
$590$	10.3276	+	53.9919i	0.425179	+	2.22281i
$591$		0			0
$592$	−1.60487	+	0.521454i	−0.0659597	+	0.0214316i
$593$			11.1321i			0.457139i	0.973528	+	0.228570i	$0.0734049\pi$
$593$			11.1321i			0.457139i	−0.973528	+	0.228570i	$0.926595\pi$
$594$		0			0
$595$	−6.08909	−	11.0629i	−0.249628	−	0.453533i
$596$	6.50259	−	20.0129i	0.266356	−	0.819760i
$597$		0			0
$598$	6.44968	+	8.87722i	0.263747	+	0.363017i
$599$	36.2736			1.48210			0.741049	−	0.671451i	$-0.234329\pi$
$599$	36.2736			1.48210			0.741049	+	0.671451i	$0.234329\pi$
$600$		0			0
$601$	−15.1051			−0.616150			−0.308075	−	0.951362i	$-0.599685\pi$
$601$	−15.1051			−0.616150			−0.308075	+	0.951362i	$0.599685\pi$
$602$	−14.8116	−	20.3865i	−0.603677	−	0.830890i
$603$		0			0
$604$	−4.86047	+	14.9590i	−0.197770	+	0.608673i
$605$	1.95399	−	15.5300i	0.0794408	−	0.631386i
$606$		0			0
$607$		−	33.5066i		−	1.35999i	−0.733216	−	0.679996i	$-0.761982\pi$
$607$		−	33.5066i		−	1.35999i	0.733216	−	0.679996i	$-0.238018\pi$
$608$	4.41179	−	1.43348i	0.178922	−	0.0581352i
$609$		0			0
$610$	73.1310	+	9.20132i	2.96099	+	0.372551i
$611$	5.54220	−	4.02664i	0.224213	−	0.162900i
$612$		0			0
$613$	16.4750	−	22.6758i	0.665418	−	0.915869i	−0.334228	−	0.942492i	$-0.608476\pi$
$613$	16.4750	−	22.6758i	0.665418	−	0.915869i	0.999646	+	0.0266235i	$0.00847552\pi$
$614$	53.5552	−	38.9102i	2.16131	−	1.57029i
$615$		0			0
$616$	−15.1178	−	10.9837i	−0.609112	−	0.442545i
$617$	29.0284	−	9.43191i	1.16864	−	0.379714i	0.340505	−	0.940243i	$-0.389402\pi$
$617$	29.0284	−	9.43191i	1.16864	−	0.379714i	0.828135	+	0.560528i	$0.189402\pi$
$618$		0			0
$619$	6.70477	+	20.6352i	0.269488	+	0.829398i	0.990625	+	0.136606i	$0.0436194\pi$
$619$	6.70477	+	20.6352i	0.269488	+	0.829398i	−0.721138	+	0.692792i	$0.756381\pi$
$620$	−47.1377	+	9.01650i	−1.89309	+	0.362111i
$621$		0			0
$622$	−17.2109	−	5.59216i	−0.690094	−	0.224225i
$623$	8.50798	+	11.7102i	0.340865	+	0.469161i
$624$		0			0
$625$	18.1898	−	17.1502i	0.727594	−	0.686008i
$626$	−49.4399			−1.97601
$627$		0			0
$628$	−4.65643	−	1.51297i	−0.185812	−	0.0603740i
$629$	2.19604	−	6.75873i	0.0875620	−	0.269488i
$630$		0			0
$631$	−5.01463	−	15.4335i	−0.199629	−	0.614396i	−0.999891	−	0.0147456i	$-0.995306\pi$
$631$	−5.01463	−	15.4335i	−0.199629	−	0.614396i	0.800262	−	0.599651i	$-0.204694\pi$
$632$			26.3812i			1.04939i
$633$		0			0
$634$	7.51003	+	5.45635i	0.298261	+	0.216699i
$635$	−18.5273	−	17.3808i	−0.735233	−	0.689737i
$636$		0			0
$637$	−1.85914	+	2.55889i	−0.0736619	+	0.101387i
$638$	10.7586	−	14.8080i	0.425937	−	0.586253i
$639$		0			0
$640$	42.4964	+	5.34689i	1.67982	+	0.211355i
$641$	−17.9419	−	13.0356i	−0.708663	−	0.514874i	0.174079	−	0.984732i	$-0.444305\pi$
$641$	−17.9419	−	13.0356i	−0.708663	−	0.514874i	−0.882742	+	0.469858i	$0.844305\pi$
$642$		0			0
$643$			13.2767i			0.523583i	0.965124	+	0.261792i	$0.0843133\pi$
$643$			13.2767i			0.523583i	−0.965124	+	0.261792i	$0.915687\pi$
$644$	−10.4092	−	32.0362i	−0.410179	−	1.26240i
$645$		0			0
$646$	1.19914	−	3.69057i	0.0471795	−	0.145204i
$647$	10.7329	+	3.48735i	0.421956	+	0.137102i	0.512295	−	0.858809i	$-0.328795\pi$
$647$	10.7329	+	3.48735i	0.421956	+	0.137102i	−0.0903397	+	0.995911i	$0.528795\pi$
$648$		0			0
$649$	−21.2912			−0.835754
$650$	15.3158	−	6.08173i	0.600735	−	0.238545i
$651$		0			0
$652$	−8.73627	−	12.0245i	−0.342139	−	0.470914i
$653$	−34.0606	−	11.0669i	−1.33289	−	0.433083i	−0.445989	−	0.895038i	$-0.647148\pi$
$653$	−34.0606	−	11.0669i	−1.33289	−	0.433083i	−0.886903	+	0.461955i	$0.847148\pi$
$654$		0			0
$655$	8.61248	+	15.6475i	0.336518	+	0.611397i
$656$	0.250368	+	0.770554i	0.00977523	+	0.0300851i
$657$		0			0
$658$	−32.0032	+	10.3985i	−1.24762	+	0.405375i
$659$	−32.1710	−	23.3736i	−1.25320	−	0.910506i	−0.254801	−	0.966994i	$-0.582010\pi$
$659$	−32.1710	−	23.3736i	−1.25320	−	0.910506i	−0.998403	+	0.0564876i	$0.982010\pi$
$660$		0			0
$661$	5.05420	−	3.67209i	0.196586	−	0.142828i	−0.485138	−	0.874438i	$-0.661231\pi$
$661$	5.05420	−	3.67209i	0.196586	−	0.142828i	0.681724	+	0.731610i	$0.261231\pi$
$662$	−15.8049	+	21.7536i	−0.614274	+	0.845476i
$663$		0			0
$664$	−31.4180	+	22.8265i	−1.21925	+	0.885839i
$665$	−5.37202	+	2.95681i	−0.208318	+	0.114660i
$666$		0			0
$667$	12.5486	−	4.07728i	0.485882	−	0.157873i
$668$			34.7728i			1.34540i
$669$		0			0
$670$	−49.9590	−	23.4783i	−1.93008	−	0.907047i
$671$	−8.82193	+	27.1511i	−0.340567	+	1.04816i
$672$		0			0
$673$	−24.3712	−	33.5441i	−0.939440	−	1.29303i	−0.956061	−	0.293166i	$-0.905291\pi$
$673$	−24.3712	−	33.5441i	−0.939440	−	1.29303i	0.0166215	−	0.999862i	$-0.494709\pi$
$674$	−49.7297			−1.91552
$675$		0			0
$676$	−36.5372			−1.40528
$677$	−0.845914	−	1.16430i	−0.0325111	−	0.0447477i	0.792452	−	0.609934i	$-0.208804\pi$
$677$	−0.845914	−	1.16430i	−0.0325111	−	0.0447477i	−0.824963	+	0.565187i	$0.808804\pi$
$678$		0			0
$679$	9.34183	−	28.7512i	0.358507	−	1.10337i
$680$	8.75892	−	9.33669i	0.335889	−	0.358046i
$681$		0			0
$682$		−	29.7433i		−	1.13893i
$683$	8.07088	−	2.62239i	0.308824	−	0.100343i	−0.150505	−	0.988609i	$-0.548090\pi$
$683$	8.07088	−	2.62239i	0.308824	−	0.100343i	0.459329	+	0.888266i	$0.348090\pi$
$684$		0			0
$685$	8.88027	−	18.8961i	0.339298	−	0.721984i
$686$	−27.1321	+	19.7126i	−1.03591	+	0.752631i
$687$		0			0
$688$	0.933247	−	1.28450i	0.0355797	−	0.0489713i
$689$	−10.9745	+	7.97345i	−0.418096	+	0.303764i
$690$		0			0
$691$	35.4186	+	25.7331i	1.34739	+	0.978933i	0.999137	+	0.0415304i	$0.0132233\pi$
$691$	35.4186	+	25.7331i	1.34739	+	0.978933i	0.348248	+	0.937402i	$0.386777\pi$
$692$	−24.3307	+	7.90553i	−0.924915	+	0.300523i
$693$		0			0
$694$	−11.1303	−	34.2554i	−0.422499	−	1.30032i
$695$	−27.4078	+	29.2157i	−1.03964	+	1.10821i
$696$		0			0
$697$	−3.24510	−	1.05440i	−0.122917	−	0.0399381i
$698$	−7.55503	−	10.3986i	−0.285962	−	0.393593i
$699$		0			0
$700$	−50.4850	+	3.22710i	−1.90816	+	0.121973i
$701$	−0.840795			−0.0317564			−0.0158782	−	0.999874i	$-0.505054\pi$
$701$	−0.840795			−0.0317564			−0.0158782	+	0.999874i	$0.505054\pi$
$702$		0			0
$703$	−3.28198	−	1.06638i	−0.123782	−	0.0402192i
$704$	−7.87517	+	24.2373i	−0.296807	+	0.913477i
$705$		0			0
$706$	5.72466	+	17.6187i	0.215450	+	0.663088i
$707$		−	28.3731i		−	1.06708i
$708$		0			0
$709$	−10.8256	−	7.86529i	−0.406566	−	0.295387i	0.365644	−	0.930755i	$-0.380849\pi$
$709$	−10.8256	−	7.86529i	−0.406566	−	0.295387i	−0.772210	+	0.635367i	$0.780849\pi$
$710$	56.3650	−	31.0238i	2.11534	−	1.16430i
$711$		0			0
$712$	−8.62531	+	11.8717i	−0.323247	+	0.444912i
$713$	12.6025	−	17.3459i	0.471969	−	0.649610i
$714$		0			0
$715$	1.19914	+	6.26902i	0.0448453	+	0.234448i
$716$	41.8371	+	30.3964i	1.56353	+	1.13597i
$717$		0			0
$718$			28.5027i			1.06371i
$719$	13.4159	+	41.2900i	0.500329	+	1.53986i	0.808483	+	0.588519i	$0.200289\pi$
$719$	13.4159	+	41.2900i	0.500329	+	1.53986i	−0.308154	+	0.951336i	$0.599711\pi$
$720$		0			0
$721$	8.52195	−	26.2279i	0.317374	−	0.976776i
$722$	39.9367	+	12.9762i	1.48629	+	0.482924i
$723$		0			0
$724$	5.30093			0.197007
$725$	−1.26405	−	19.7750i	−0.0469458	−	0.734425i
$726$		0			0
$727$	18.8373	+	25.9274i	0.698639	+	0.961593i	0.999967	+	0.00807318i	$0.00256980\pi$
$727$	18.8373	+	25.9274i	0.698639	+	0.961593i	−0.301329	+	0.953520i	$0.597430\pi$
$728$	−12.6822	−	4.12069i	−0.470033	−	0.152723i
$729$		0			0
$730$	0.172519	−	1.37116i	0.00638520	−	0.0507487i
$731$	2.06626	+	6.35930i	0.0764235	+	0.235207i
$732$		0			0
$733$	7.74091	−	2.51517i	0.285917	−	0.0929001i	−0.162547	−	0.986701i	$-0.551971\pi$
$733$	7.74091	−	2.51517i	0.285917	−	0.0929001i	0.448465	+	0.893801i	$0.351971\pi$
$734$	−50.2089	−	36.4789i	−1.85324	−	1.34646i
$735$		0			0
$736$	−13.8319	+	10.0494i	−0.509850	+	0.370427i
$737$	12.5671	−	17.2971i	0.462914	−	0.637146i
$738$		0			0
$739$	−5.76598	+	4.18923i	−0.212105	+	0.154103i	−0.688766	−	0.724984i	$-0.741847\pi$
$739$	−5.76598	+	4.18923i	−0.212105	+	0.154103i	0.476661	+	0.879087i	$0.341847\pi$
$740$	−20.7629	−	19.4781i	−0.763261	−	0.716030i
$741$		0			0
$742$	63.3720	−	20.5908i	2.32646	−	0.755912i
$743$			21.9040i			0.803578i	0.915732	+	0.401789i	$0.131612\pi$
$743$			21.9040i			0.803578i	−0.915732	+	0.401789i	$0.868388\pi$
$744$		0			0
$745$	13.8670	−	2.65248i	0.508048	−	0.0971795i
$746$	19.7233	−	60.7020i	0.722120	−	2.22246i
$747$		0			0
$748$	7.28823	+	10.0314i	0.266484	+	0.366784i
$749$	17.0877			0.624373
$750$		0			0
$751$	9.21909			0.336409			0.168205	−	0.985752i	$-0.446203\pi$
$751$	9.21909			0.336409			0.168205	+	0.985752i	$0.446203\pi$
$752$	−1.24624	−	1.71530i	−0.0454456	−	0.0625504i
$753$		0			0
$754$	4.03625	−	12.4223i	0.146991	−	0.452393i
$755$	−10.3651	+	1.98265i	−0.377226	+	0.0721559i
$756$		0			0
$757$			45.6524i			1.65926i	0.558311	+	0.829632i	$0.311450\pi$
$757$			45.6524i			1.65926i	−0.558311	+	0.829632i	$0.688550\pi$
$758$	7.63114	−	2.47951i	0.277176	−	0.0900598i
$759$		0			0
$760$	−4.53381	−	4.25325i	−0.164459	−	0.154282i
$761$	32.2844	−	23.4560i	1.17031	−	0.850280i	0.179264	−	0.983801i	$-0.442628\pi$
$761$	32.2844	−	23.4560i	1.17031	−	0.850280i	0.991046	+	0.133521i	$0.0426284\pi$
$762$		0			0
$763$	18.0457	−	24.8378i	0.653299	−	0.899188i
$764$	−53.0310	+	38.5293i	−1.91860	+	1.39394i
$765$		0			0
$766$	−51.1373	−	37.1534i	−1.84767	−	1.34241i
$767$	−14.4499	+	4.69506i	−0.521756	+	0.169529i
$768$		0			0
$769$	13.7024	+	42.1717i	0.494122	+	1.52075i	0.818320	+	0.574762i	$0.194906\pi$
$769$	13.7024	+	42.1717i	0.494122	+	1.52075i	−0.324198	+	0.945989i	$0.605094\pi$
$770$	3.91385	−	31.1068i	0.141046	−	1.12101i
$771$		0			0
$772$	41.5540	+	13.5017i	1.49556	+	0.485937i
$773$	22.6264	+	31.1426i	0.813816	+	1.12012i	0.990723	+	0.135894i	$0.0433907\pi$
$773$	22.6264	+	31.1426i	0.813816	+	1.12012i	−0.176907	+	0.984228i	$0.556609\pi$
$774$		0			0
$775$	−20.5498	−	24.7898i	−0.738171	−	0.890476i
$776$	30.6477			1.10019
$777$		0			0
$778$	−23.9051	−	7.76725i	−0.857041	−	0.278469i
$779$	−0.512006	+	1.57579i	−0.0183445	+	0.0564586i
$780$		0			0
$781$	7.70061	+	23.7000i	0.275549	+	0.848054i
$782$			14.3022i			0.511445i
$783$		0			0
$784$	0.791971	+	0.575400i	0.0282847	+	0.0205500i
$785$	−0.617158	−	3.22646i	−0.0220273	−	0.115157i
$786$		0			0
$787$	−31.1645	+	42.8942i	−1.11089	+	1.52901i	−0.290801	+	0.956784i	$0.593922\pi$
$787$	−31.1645	+	42.8942i	−1.11089	+	1.52901i	−0.820093	+	0.572231i	$0.806078\pi$
$788$	−6.71817	+	9.24676i	−0.239325	+	0.329402i
$789$		0			0
$790$	−38.7763	+	21.3428i	−1.37960	+	0.759343i
$791$	26.3090	+	19.1146i	0.935440	+	0.679637i
$792$		0			0
$793$			20.3723i			0.723440i
$794$	11.5756	+	35.6259i	0.410801	+	1.26432i
$795$		0			0
$796$	18.2246	−	56.0896i	0.645954	−	1.98804i
$797$	12.0564	+	3.91737i	0.427060	+	0.138760i	0.514658	−	0.857396i	$-0.327919\pi$
$797$	12.0564	+	3.91737i	0.427060	+	0.138760i	−0.0875977	+	0.996156i	$0.527919\pi$
$798$		0			0
$799$	8.92908			0.315888
$800$	9.47613	+	23.8640i	0.335032	+	0.843720i
$801$		0			0
$802$	−5.14012	−	7.07477i	−0.181504	−	0.249819i
$803$	0.509065	+	0.165405i	0.0179645	+	0.00583702i
$804$		0			0
$805$	15.4628	−	16.4828i	0.544992	−	0.580941i
$806$	−6.55888	−	20.1861i	−0.231027	−	0.711027i
$807$		0			0
$808$	27.3566	−	8.88869i	0.962401	−	0.312703i
$809$	33.8926	+	24.6244i	1.19160	+	0.865747i	0.993432	−	0.114421i	$-0.0365013\pi$
$809$	33.8926	+	24.6244i	1.19160	+	0.865747i	0.198167	+	0.980168i	$0.436501\pi$
$810$		0			0
$811$	27.9504	−	20.3072i	0.981472	−	0.713081i	0.0234348	−	0.999725i	$-0.492540\pi$
$811$	27.9504	−	20.3072i	0.981472	−	0.713081i	0.958037	+	0.286644i	$0.0925398\pi$
$812$	−23.5683	+	32.4390i	−0.827086	+	1.13839i
$813$		0			0
$814$	14.2742	−	10.3708i	0.500310	−	0.363496i
$815$	4.24142	−	9.02522i	0.148570	−	0.316140i
$816$		0			0
$817$	3.08802	−	1.00336i	0.108036	−	0.0351031i
$818$			4.28568i			0.149845i
$819$		0			0
$820$	−9.35212	+	9.96901i	−0.326590	+	0.348133i
$821$	6.53103	−	20.1004i	0.227935	−	0.701511i	−0.770046	−	0.637989i	$-0.779767\pi$
$821$	6.53103	−	20.1004i	0.227935	−	0.701511i	0.997980	−	0.0635220i	$-0.0202333\pi$
$822$		0			0
$823$	1.86747	+	2.57036i	0.0650960	+	0.0895970i	0.840324	−	0.542085i	$-0.182365\pi$
$823$	1.86747	+	2.57036i	0.0650960	+	0.0895970i	−0.775228	+	0.631682i	$0.782365\pi$
$824$	27.9579			0.973960
$825$		0			0
$826$	74.6315			2.59676
$827$	5.72786	+	7.88372i	0.199177	+	0.274144i	0.896909	−	0.442215i	$-0.145807\pi$
$827$	5.72786	+	7.88372i	0.199177	+	0.274144i	−0.697732	+	0.716359i	$0.745807\pi$
$828$		0			0
$829$	−7.24188	+	22.2882i	−0.251521	+	0.774101i	0.742974	+	0.669320i	$0.233414\pi$
$829$	−7.24188	+	22.2882i	−0.251521	+	0.774101i	−0.994495	+	0.104782i	$0.966586\pi$
$830$	−58.9692	−	27.7127i	−2.04685	−	0.961921i
$831$		0			0
$832$			18.1859i			0.630484i
$833$	−3.92087	+	1.27397i	−0.135850	+	0.0441404i
$834$		0			0
$835$	−20.4389	+	11.2497i	−0.707318	+	0.389314i
$836$	4.87115	−	3.53910i	0.168472	−	0.122402i
$837$		0			0
$838$	−19.4743	+	26.8041i	−0.672728	+	0.925931i
$839$	−34.5304	+	25.0878i	−1.19212	+	0.866126i	−0.993487	−	0.113948i	$-0.963650\pi$
$839$	−34.5304	+	25.0878i	−1.19212	+	0.866126i	−0.198634	+	0.980074i	$0.563650\pi$
$840$		0			0
$841$	10.7551	+	7.81406i	0.370866	+	0.269450i
$842$	33.9420	−	11.0284i	1.16972	−	0.380065i
$843$		0			0
$844$	3.34057	+	10.2812i	0.114987	+	0.353894i
$845$	−11.8206	−	21.4760i	−0.406640	−	0.738797i
$846$		0			0
$847$	−20.2106	−	6.56683i	−0.694446	−	0.225639i
$848$	2.46776	+	3.39659i	0.0847434	+	0.116639i
$849$		0			0
$850$	20.8096	+	5.32076i	0.713765	+	0.182501i
$851$	12.7187			0.435993
$852$		0			0
$853$	−16.1309	−	5.24124i	−0.552310	−	0.179456i	0.0195480	−	0.999809i	$-0.493777\pi$
$853$	−16.1309	−	5.24124i	−0.552310	−	0.179456i	−0.571858	+	0.820352i	$0.693777\pi$
$854$	30.9232	−	95.1719i	1.05817	−	3.25672i
$855$		0			0
$856$	5.35323	+	16.4755i	0.182969	+	0.563122i
$857$			39.3176i			1.34306i	0.740976	+	0.671531i	$0.234363\pi$
$857$			39.3176i			1.34306i	−0.740976	+	0.671531i	$0.765637\pi$
$858$		0			0
$859$	0.572020	+	0.415597i	0.0195171	+	0.0141800i	0.597501	−	0.801868i	$-0.296160\pi$
$859$	0.572020	+	0.415597i	0.0195171	+	0.0141800i	−0.577984	+	0.816048i	$0.696160\pi$
$860$	26.5772	+	3.34394i	0.906276	+	0.114028i
$861$		0			0
$862$	16.9728	−	23.3611i	0.578096	−	0.795681i
$863$	0.534537	−	0.735728i	0.0181959	−	0.0250445i	−0.799822	−	0.600237i	$-0.795073\pi$
$863$	0.534537	−	0.735728i	0.0181959	−	0.0250445i	0.818018	+	0.575193i	$0.195073\pi$
$864$		0			0
$865$	−12.5183	−	11.7436i	−0.425634	−	0.399295i
$866$	−42.0264	−	30.5339i	−1.42811	−	1.03759i
$867$		0			0
$868$			65.1571i			2.21158i
$869$	−5.29764	−	16.3045i	−0.179710	−	0.553091i
$870$		0			0
$871$	4.71472	−	14.5104i	0.159752	−	0.491666i
$872$	29.6012	+	9.61803i	1.00242	+	0.325708i
$873$		0			0
$874$	6.94501			0.234918
$875$	−18.2298	−	28.6303i	−0.616281	−	0.967882i
$876$		0			0
$877$	−19.7856	−	27.2326i	−0.668113	−	0.919578i	0.331603	−	0.943419i	$-0.392411\pi$
$877$	−19.7856	−	27.2326i	−0.668113	−	0.919578i	−0.999716	+	0.0238407i	$0.992411\pi$
$878$	26.7450	+	8.68997i	0.902600	+	0.293272i
$879$		0			0
$880$	1.94025	−	0.371131i	0.0654057	−	0.0125108i
$881$	6.15819	+	18.9529i	0.207475	+	0.638541i	0.999603	+	0.0281862i	$0.00897314\pi$
$881$	6.15819	+	18.9529i	0.207475	+	0.638541i	−0.792128	+	0.610355i	$0.791027\pi$
$882$		0			0
$883$	14.8442	−	4.82317i	0.499547	−	0.162313i	−0.0483963	−	0.998828i	$-0.515411\pi$
$883$	14.8442	−	4.82317i	0.499547	−	0.162313i	0.547943	+	0.836516i	$0.315411\pi$
$884$	7.15845	+	5.20091i	0.240765	+	0.174926i
$885$		0			0
$886$	38.6916	−	28.1111i	1.29987	−	0.944410i
$887$	−27.5652	+	37.9403i	−0.925550	+	1.27391i	0.0360196	+	0.999351i	$0.488532\pi$
$887$	−27.5652	+	37.9403i	−0.925550	+	1.27391i	−0.961570	+	0.274560i	$0.911468\pi$
$888$		0			0
$889$	−27.9028	+	20.2725i	−0.935828	+	0.679919i
$890$	−24.4277	−	3.07349i	−0.818818	−	0.103023i
$891$		0			0
$892$	−91.0152	+	29.5726i	−3.04742	+	0.990165i
$893$		−	4.33588i		−	0.145095i
$894$		0			0
$895$	−4.33136	+	34.4251i	−0.144782	+	1.15070i
$896$	17.9695	−	55.3045i	0.600319	−	1.84759i
$897$		0			0
$898$	−35.2287	−	48.4882i	−1.17560	−	1.61807i
$899$	−25.5220			−0.851208
$900$		0			0
$901$	−17.6811			−0.589044
$902$	−4.97938	−	6.85353i	−0.165795	−	0.228198i
$903$		0			0
$904$	−10.1877	+	31.3546i	−0.338839	+	1.04284i
$905$	1.71497	+	3.11581i	0.0570074	+	0.103573i
$906$		0			0
$907$			1.43447i			0.0476308i	0.999716	+	0.0238154i	$0.00758139\pi$
$907$			1.43447i			0.0476308i	−0.999716	+	0.0238154i	$0.992419\pi$
$908$	−37.1501	+	12.0708i	−1.23287	+	0.400583i
$909$		0			0
$910$	−4.20330	−	21.9746i	−0.139338	−	0.728451i
$911$	−2.27438	+	1.65244i	−0.0753537	+	0.0547476i	−0.624824	−	0.780765i	$-0.714829\pi$
$911$	−2.27438	+	1.65244i	−0.0753537	+	0.0547476i	0.549471	+	0.835513i	$0.314829\pi$
$912$		0			0
$913$	14.8335	−	20.4166i	0.490919	−	0.675692i
$914$	15.8829	−	11.5396i	0.525359	−	0.381695i
$915$		0			0
$916$	44.2220	+	32.1291i	1.46114	+	1.06158i
$917$	23.0624	−	7.49342i	0.761587	−	0.247455i
$918$		0			0
$919$	−0.306618	−	0.943673i	−0.0101144	−	0.0311289i	0.945872	−	0.324540i	$-0.105210\pi$
$919$	−0.306618	−	0.943673i	−0.0101144	−	0.0311289i	−0.955986	+	0.293411i	$0.905210\pi$
$920$	20.7364	+	9.74510i	0.683658	+	0.321286i
$921$		0			0
$922$	32.4717	+	10.5507i	1.06940	+	0.347469i
$923$	10.4525	+	14.3866i	0.344048	+	0.473541i
$924$		0			0
$925$	4.73169	−	18.5057i	0.155577	−	0.608465i
$926$	51.2477			1.68410
$927$		0			0
$928$	19.3556	+	6.28900i	0.635377	+	0.206447i
$929$	10.2973	−	31.6918i	0.337843	−	1.03977i	−0.627461	−	0.778648i	$-0.715906\pi$
$929$	10.2973	−	31.6918i	0.337843	−	1.03977i	0.965305	−	0.261127i	$-0.0840940\pi$
$930$		0			0
$931$	0.618628	+	1.90394i	0.0202747	+	0.0623992i
$932$		−	75.0355i		−	2.45787i
$933$		0			0
$934$	−53.2475	−	38.6866i	−1.74231	−	1.26586i
$935$	−3.53840	+	7.52928i	−0.115718	+	0.246234i
$936$		0			0
$937$	7.85724	−	10.8146i	0.256685	−	0.353296i	−0.661154	−	0.750251i	$-0.729933\pi$
$937$	7.85724	−	10.8146i	0.256685	−	0.353296i	0.917838	+	0.396954i	$0.129933\pi$
$938$	−44.0509	+	60.6309i	−1.43831	+	1.97967i
$939$		0			0
$940$	15.2141	−	32.3737i	0.496228	−	1.05591i
$941$	−1.73924	−	1.26363i	−0.0566976	−	0.0411932i	0.559075	−	0.829117i	$-0.311156\pi$
$941$	−1.73924	−	1.26363i	−0.0566976	−	0.0411932i	−0.615773	+	0.787924i	$0.711156\pi$
$942$		0			0
$943$		−	6.10671i		−	0.198862i
$944$	1.45311	+	4.47221i	0.0472947	+	0.145558i
$945$		0			0
$946$	−5.13004	+	15.7886i	−0.166792	+	0.513333i
$947$	−33.2093	−	10.7903i	−1.07916	−	0.350639i	−0.285109	−	0.958495i	$-0.592030\pi$
$947$	−33.2093	−	10.7903i	−1.07916	−	0.350639i	−0.794047	+	0.607856i	$0.792030\pi$
$948$		0			0
$949$	0.381966			0.0123991
$950$	2.58371	−	10.1050i	0.0838268	−	0.327849i
$951$		0			0
$952$	−10.2162	−	14.0614i	−0.331108	−	0.455732i
$953$	−7.87364	−	2.55830i	−0.255052	−	0.0828715i	0.178700	−	0.983904i	$-0.442811\pi$
$953$	−7.87364	−	2.55830i	−0.255052	−	0.0828715i	−0.433752	+	0.901032i	$0.642811\pi$
$954$		0			0
$955$	−39.8037	−	18.7058i	−1.28802	−	0.605305i
$956$	6.83151	+	21.0252i	0.220947	+	0.680004i
$957$		0			0
$958$	55.0313	−	17.8807i	1.77798	−	0.577701i
$959$	−22.9326	−	16.6615i	−0.740532	−	0.538028i
$960$		0			0
$961$	−8.47296	+	6.15597i	−0.273321	+	0.198580i
$962$	7.40066	−	10.1861i	0.238607	−	0.328414i
$963$		0			0
$964$	70.7120	−	51.3753i	2.27748	−	1.65469i
$965$	5.50751	+	28.7929i	0.177293	+	0.926876i
$966$		0			0
$967$	−28.0439	+	9.11201i	−0.901831	+	0.293023i	−0.722993	−	0.690856i	$-0.757234\pi$
$967$	−28.0439	+	9.11201i	−0.901831	+	0.293023i	−0.178838	+	0.983878i	$0.557234\pi$
$968$		−	21.5438i		−	0.692443i
$969$		0			0
$970$	24.7945	+	45.0475i	0.796104	+	1.44639i
$971$	−6.75716	+	20.7964i	−0.216848	+	0.667388i	0.782170	+	0.623065i	$0.214113\pi$
$971$	−6.75716	+	20.7964i	−0.216848	+	0.667388i	−0.999017	+	0.0443227i	$0.985887\pi$
$972$		0			0
$973$	31.9678	+	43.9998i	1.02484	+	1.41057i
$974$	−3.38260			−0.108385
$975$		0			0
$976$	6.30517			0.201823
$977$	8.13976	+	11.2034i	0.260414	+	0.358429i	0.919124	−	0.393967i	$-0.128898\pi$
$977$	8.13976	+	11.2034i	0.260414	+	0.358429i	−0.658710	+	0.752397i	$0.728898\pi$
$978$		0			0
$979$	2.94676	−	9.06919i	0.0941788	−	0.289853i
$980$	−2.06173	+	16.3864i	−0.0658596	+	0.523444i
$981$		0			0
$982$		−	46.3440i		−	1.47890i
$983$	−2.79171	+	0.907082i	−0.0890418	+	0.0289314i	−0.353199	−	0.935548i	$-0.614906\pi$
$983$	−2.79171	+	0.907082i	−0.0890418	+	0.0289314i	0.264157	+	0.964480i	$0.414906\pi$
$984$		0			0
$985$	−7.60858	−	0.957311i	−0.242430	−	0.0305025i
$986$	13.7732	−	10.0068i	0.438629	−	0.318682i
$987$		0			0
$988$	2.52552	−	3.47608i	0.0803474	−	0.110589i
$989$	−9.68158	+	7.03408i	−0.307856	+	0.223671i
$990$		0			0
$991$	−25.5760	−	18.5821i	−0.812450	−	0.590279i	0.102090	−	0.994775i	$-0.467447\pi$
$991$	−25.5760	−	18.5821i	−0.812450	−	0.590279i	−0.914540	+	0.404496i	$0.867447\pi$
$992$	31.4526	−	10.2196i	0.998623	−	0.324472i
$993$		0			0
$994$	−26.9927	−	83.0750i	−0.856156	−	2.63498i
$995$	38.8647	−	7.43404i	1.23209	−	0.235675i
$996$		0			0
$997$	−11.4968	−	3.73554i	−0.364108	−	0.118306i	0.121249	−	0.992622i	$-0.461310\pi$
$997$	−11.4968	−	3.73554i	−0.364108	−	0.118306i	−0.485356	+	0.874316i	$0.661310\pi$
$998$	−0.848347	−	1.16765i	−0.0268540	−	0.0369613i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.a.64.2		8
3.2	odd	2		25.2.e.a.14.1	yes	8
12.11	even	2		400.2.y.c.289.1		8
15.2	even	4		125.2.d.b.51.4		16
15.8	even	4		125.2.d.b.51.1		16
15.14	odd	2		125.2.e.b.74.2		8
25.3	odd	20		5625.2.a.x.1.1		8
25.9	even	10	inner	225.2.m.a.109.2		8
25.22	odd	20		5625.2.a.x.1.8		8
75.2	even	20		625.2.d.o.126.1		16
75.8	even	20		625.2.d.o.501.4		16
75.11	odd	10		625.2.e.i.499.1		8
75.14	odd	10		625.2.e.a.499.2		8
75.17	even	20		625.2.d.o.501.1		16
75.23	even	20		625.2.d.o.126.4		16
75.29	odd	10		625.2.b.c.624.1		8
75.38	even	20		125.2.d.b.76.1		16
75.41	odd	10		125.2.e.b.49.2		8
75.44	odd	10		625.2.e.i.124.1		8
75.47	even	20		625.2.a.f.1.1		8
75.53	even	20		625.2.a.f.1.8		8
75.56	odd	10		625.2.e.a.124.2		8
75.59	odd	10		25.2.e.a.9.1	✓	8
75.62	even	20		125.2.d.b.76.4		16
75.71	odd	10		625.2.b.c.624.8		8
300.47	odd	20		10000.2.a.bj.1.5		8
300.59	even	10		400.2.y.c.209.1		8
300.203	odd	20		10000.2.a.bj.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.1	✓	8	75.59	odd	10
25.2.e.a.14.1	yes	8	3.2	odd	2
125.2.d.b.51.1		16	15.8	even	4
125.2.d.b.51.4		16	15.2	even	4
125.2.d.b.76.1		16	75.38	even	20
125.2.d.b.76.4		16	75.62	even	20
125.2.e.b.49.2		8	75.41	odd	10
125.2.e.b.74.2		8	15.14	odd	2
225.2.m.a.64.2		8	1.1	even	1	trivial
225.2.m.a.109.2		8	25.9	even	10	inner
400.2.y.c.209.1		8	300.59	even	10
400.2.y.c.289.1		8	12.11	even	2
625.2.a.f.1.1		8	75.47	even	20
625.2.a.f.1.8		8	75.53	even	20
625.2.b.c.624.1		8	75.29	odd	10
625.2.b.c.624.8		8	75.71	odd	10
625.2.d.o.126.1		16	75.2	even	20
625.2.d.o.126.4		16	75.23	even	20
625.2.d.o.501.1		16	75.17	even	20
625.2.d.o.501.4		16	75.8	even	20
625.2.e.a.124.2		8	75.56	odd	10
625.2.e.a.499.2		8	75.14	odd	10
625.2.e.i.124.1		8	75.44	odd	10
625.2.e.i.499.1		8	75.11	odd	10
5625.2.a.x.1.1		8	25.3	odd	20
5625.2.a.x.1.8		8	25.22	odd	20
10000.2.a.bj.1.4		8	300.203	odd	20
10000.2.a.bj.1.5		8	300.47	odd	20

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35736 + 1.86824i) q^{2} +(-1.02988 + 3.16963i) q^{4} +(-2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.92705 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(1.35736 + 1.86824i) q^{2} +(-1.02988 + 3.16963i) q^{4} +(-2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.92705 + 0.951057i) q^{8} +(-3.76594 - 3.53290i) q^{10} +(1.61803 - 1.17557i) q^{11} +(0.838893 - 1.15464i) q^{13} +(-5.67164 + 4.12069i) q^{14} +(-0.357358 - 0.259635i) q^{16} +(1.76920 - 0.574848i) q^{17} +(-0.279141 - 0.859107i) q^{19} +(0.930307 - 7.39396i) q^{20} +(4.39250 + 1.42721i) q^{22} +(1.95693 + 2.69348i) q^{23} +(4.64703 - 1.84529i) q^{25} +3.29582 q^{26} +(-9.62243 - 3.12652i) q^{28} +(1.22466 - 3.76910i) q^{29} +(-1.99006 - 6.12477i) q^{31} +5.13532i q^{32} +(3.47539 + 2.52502i) q^{34} +(-1.27534 - 6.66742i) q^{35} +(2.24547 - 3.09062i) q^{37} +(1.22613 - 1.68762i) q^{38} +(6.02900 - 3.31841i) q^{40} +(-1.48391 - 1.07813i) q^{41} +3.59445i q^{43} +(2.05975 + 6.33927i) q^{44} +(-2.37582 + 7.31203i) q^{46} +(4.56502 + 1.48326i) q^{47} -2.21619 q^{49} +(9.75513 + 6.17707i) q^{50} +(2.79582 + 3.84812i) q^{52} +(-9.03953 - 2.93712i) q^{53} +(-3.05975 + 3.26158i) q^{55} +(-2.88723 - 8.88599i) q^{56} +(8.70390 - 2.82807i) q^{58} +(-8.61248 - 6.25734i) q^{59} +(-11.5481 + 8.39016i) q^{61} +(8.74134 - 12.0314i) q^{62} +(-10.3087 + 7.48973i) q^{64} +(-1.35736 + 2.88829i) q^{65} +(10.1670 - 3.30345i) q^{67} +6.19974i q^{68} +(10.7253 - 11.4327i) q^{70} +(-3.85030 + 11.8500i) q^{71} +(0.157310 + 0.216518i) q^{73} +8.82193 q^{74} +3.01054 q^{76} +(3.56882 + 4.91206i) q^{77} +(2.64882 - 8.15223i) q^{79} +(0.893919 + 0.420099i) q^{80} -4.23572i q^{82} +(12.0006 - 3.89923i) q^{83} +(-3.64411 + 2.00575i) q^{85} +(-6.71531 + 4.87896i) q^{86} +(-3.61803 + 4.97980i) q^{88} +(3.85736 - 2.80253i) q^{89} +(3.50527 + 2.54673i) q^{91} +(-10.5527 + 3.42879i) q^{92} +(3.42527 + 10.5419i) q^{94} +(0.973973 + 1.76955i) q^{95} +(-9.47067 - 3.07721i) q^{97} +(-3.00816 - 4.14037i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - q^{4} - 10 q^{8}+O(q^{10}) \) 8 * q + 5 * q^2 - q^4 - 10 * q^8	\( 8 q + 5 q^{2} - q^{4} - 10 q^{8} - 5 q^{10} + 4 q^{11} - 5 q^{13} - 13 q^{14} + 3 q^{16} + 10 q^{17} - 5 q^{19} + 15 q^{20} - 5 q^{23} - 10 q^{25} - 6 q^{26} - 15 q^{28} + 5 q^{29} - 9 q^{31} + 13 q^{34} - 15 q^{35} + 30 q^{37} - 15 q^{38} + 10 q^{40} + 4 q^{41} + 2 q^{44} - 19 q^{46} + 14 q^{49} + 15 q^{50} - 10 q^{52} + 10 q^{53} - 10 q^{55} - 10 q^{56} + 20 q^{58} - 9 q^{61} + 30 q^{62} + 4 q^{64} - 5 q^{65} + 20 q^{67} + 30 q^{70} - 6 q^{71} + 15 q^{73} + 12 q^{74} - 20 q^{76} - 10 q^{77} + 15 q^{79} - 20 q^{80} + 45 q^{83} - 15 q^{85} + 9 q^{86} - 20 q^{88} + 25 q^{89} + 6 q^{91} - 30 q^{92} - 27 q^{94} - 15 q^{95} - 60 q^{97} + 10 q^{98}+O(q^{100}) \) 8 * q + 5 * q^2 - q^4 - 10 * q^8 - 5 * q^10 + 4 * q^11 - 5 * q^13 - 13 * q^14 + 3 * q^16 + 10 * q^17 - 5 * q^19 + 15 * q^20 - 5 * q^23 - 10 * q^25 - 6 * q^26 - 15 * q^28 + 5 * q^29 - 9 * q^31 + 13 * q^34 - 15 * q^35 + 30 * q^37 - 15 * q^38 + 10 * q^40 + 4 * q^41 + 2 * q^44 - 19 * q^46 + 14 * q^49 + 15 * q^50 - 10 * q^52 + 10 * q^53 - 10 * q^55 - 10 * q^56 + 20 * q^58 - 9 * q^61 + 30 * q^62 + 4 * q^64 - 5 * q^65 + 20 * q^67 + 30 * q^70 - 6 * q^71 + 15 * q^73 + 12 * q^74 - 20 * q^76 - 10 * q^77 + 15 * q^79 - 20 * q^80 + 45 * q^83 - 15 * q^85 + 9 * q^86 - 20 * q^88 + 25 * q^89 + 6 * q^91 - 30 * q^92 - 27 * q^94 - 15 * q^95 - 60 * q^97 + 10 * q^98

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