LMFDB - Embedded newform 225.2.h.d.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.1
Root			$1.97423 + 1.43436i$ of defining polynomial
Character	$\chi$	$=$	225.46
Dual form			225.2.h.d.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.754089 + 2.32085i) q^{2} +(-3.19965 - 2.32468i) q^{4} +(-0.824264 - 2.07860i) q^{5} -3.44028 q^{7} +(3.85959 - 2.80415i) q^{8} +O(q^{10})$	\(q+(-0.754089 + 2.32085i) q^{2} +(-3.19965 - 2.32468i) q^{4} +(-0.824264 - 2.07860i) q^{5} -3.44028 q^{7} +(3.85959 - 2.80415i) q^{8} +(5.44569 - 0.345540i) q^{10} +(1.00942 - 3.10669i) q^{11} +(-0.998755 - 3.07385i) q^{13} +(2.59428 - 7.98437i) q^{14} +(1.15323 + 3.54927i) q^{16} +(-4.08826 + 2.97030i) q^{17} +(2.49274 - 1.81108i) q^{19} +(-2.19473 + 8.56695i) q^{20} +(6.44895 + 4.68544i) q^{22} +(-0.478250 + 1.47190i) q^{23} +(-3.64118 + 3.42664i) q^{25} +7.88709 q^{26} +(11.0077 + 7.99756i) q^{28} +(-2.52590 - 1.83517i) q^{29} +(-6.02080 + 4.37437i) q^{31} +0.434479 q^{32} +(-3.81069 - 11.7281i) q^{34} +(2.83570 + 7.15098i) q^{35} +(-1.77944 - 5.47655i) q^{37} +(2.32349 + 7.15098i) q^{38} +(-9.01004 - 5.71118i) q^{40} +(-1.67476 - 5.15437i) q^{41} +2.53106 q^{43} +(-10.4519 + 7.59371i) q^{44} +(-3.05541 - 2.21989i) q^{46} +(5.72106 + 4.15659i) q^{47} +4.83555 q^{49} +(-5.20693 - 11.0346i) q^{50} +(-3.95006 + 12.1570i) q^{52} +(-8.21277 - 5.96693i) q^{53} +(-7.28960 + 0.462540i) q^{55} +(-13.2781 + 9.64708i) q^{56} +(6.16391 - 4.47834i) q^{58} +(-0.534773 - 1.64586i) q^{59} +(2.42149 - 7.45259i) q^{61} +(-5.61202 - 17.2720i) q^{62} +(-2.63409 + 8.10689i) q^{64} +(-5.56608 + 4.60968i) q^{65} +(1.49595 - 1.08687i) q^{67} +19.9860 q^{68} +(-18.7347 + 1.18876i) q^{70} +(-0.577613 - 0.419660i) q^{71} +(-0.581036 + 1.78825i) q^{73} +14.0521 q^{74} -12.1861 q^{76} +(-3.47270 + 10.6879i) q^{77} +(10.7868 + 7.83708i) q^{79} +(6.42695 - 5.32263i) q^{80} +13.2254 q^{82} +(3.20166 - 2.32614i) q^{83} +(9.54388 + 6.04956i) q^{85} +(-1.90864 + 5.87419i) q^{86} +(-4.81567 - 14.8211i) q^{88} +(-2.63713 + 8.11624i) q^{89} +(3.43600 + 10.5749i) q^{91} +(4.95193 - 3.59779i) q^{92} +(-13.9610 + 10.1433i) q^{94} +(-5.81919 - 3.68860i) q^{95} +(8.61831 + 6.26157i) q^{97} +(-3.64643 + 11.2226i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.754089	+	2.32085i	−0.533221	+	1.64109i	0.214240	+	0.976781i	$0.431273\pi$
$2$	−0.754089	+	2.32085i	−0.533221	+	1.64109i	−0.747461	+	0.664306i	$0.768727\pi$
$3$		0			0
$3$		0			0
$4$	−3.19965	−	2.32468i	−1.59982	−	1.16234i
$5$	−0.824264	−	2.07860i	−0.368622	−	0.929579i
$5$	−0.824264	−	2.07860i	−0.368622	−	0.929579i
$6$		0			0
$7$	−3.44028			−1.30030			−0.650152	−	0.759804i	$-0.725295\pi$
$7$	−3.44028			−1.30030			−0.650152	+	0.759804i	$0.725295\pi$
$8$	3.85959	−	2.80415i	1.36457	−	0.991418i
$9$		0			0
$10$	5.44569	−	0.345540i	1.72208	−	0.109269i
$11$	1.00942	−	3.10669i	0.304353	−	0.936701i	−0.675565	−	0.737300i	$-0.736100\pi$
$11$	1.00942	−	3.10669i	0.304353	−	0.936701i	0.979918	−	0.199401i	$-0.0638996\pi$
$12$		0			0
$13$	−0.998755	−	3.07385i	−0.277005	−	0.852533i	−0.988682	−	0.150026i	$-0.952064\pi$
$13$	−0.998755	−	3.07385i	−0.277005	−	0.852533i	0.711677	−	0.702506i	$-0.247936\pi$
$14$	2.59428	−	7.98437i	0.693350	−	2.13391i
$15$		0			0
$16$	1.15323	+	3.54927i	0.288307	+	0.887317i
$17$	−4.08826	+	2.97030i	−0.991550	+	0.720403i	−0.960260	−	0.279107i	$-0.909961\pi$
$17$	−4.08826	+	2.97030i	−0.991550	+	0.720403i	−0.0312897	+	0.999510i	$0.509961\pi$
$18$		0			0
$19$	2.49274	−	1.81108i	0.571873	−	0.415490i	−0.263912	−	0.964547i	$-0.585013\pi$
$19$	2.49274	−	1.81108i	0.571873	−	0.415490i	0.835785	+	0.549056i	$0.185013\pi$
$20$	−2.19473	+	8.56695i	−0.490757	+	1.91563i
$21$		0			0
$22$	6.44895	+	4.68544i	1.37492	+	0.998938i
$23$	−0.478250	+	1.47190i	−0.0997219	+	0.306913i	−0.988455	−	0.151512i	$-0.951586\pi$
$23$	−0.478250	+	1.47190i	−0.0997219	+	0.306913i	0.888734	+	0.458424i	$0.151586\pi$
$24$		0			0
$25$	−3.64118	+	3.42664i	−0.728235	+	0.685327i
$26$	7.88709			1.54679
$27$		0			0
$28$	11.0077	+	7.99756i	2.08026	+	1.51140i
$29$	−2.52590	−	1.83517i	−0.469047	−	0.340783i	0.328022	−	0.944670i	$-0.393618\pi$
$29$	−2.52590	−	1.83517i	−0.469047	−	0.340783i	−0.797070	+	0.603887i	$0.793618\pi$
$30$		0			0
$31$	−6.02080	+	4.37437i	−1.08137	+	0.785659i	−0.977921	−	0.208976i	$-0.932987\pi$
$31$	−6.02080	+	4.37437i	−1.08137	+	0.785659i	−0.103446	+	0.994635i	$0.532987\pi$
$32$	0.434479			0.0768057
$33$		0			0
$34$	−3.81069	−	11.7281i	−0.653528	−	2.01135i
$35$	2.83570	+	7.15098i	0.479321	+	1.20874i
$36$		0			0
$37$	−1.77944	−	5.47655i	−0.292538	−	0.900339i	−0.984037	−	0.177962i	$-0.943050\pi$
$37$	−1.77944	−	5.47655i	−0.292538	−	0.900339i	0.691499	−	0.722377i	$-0.256950\pi$
$38$	2.32349	+	7.15098i	0.376921	+	1.16004i
$39$		0			0
$40$	−9.01004	−	5.71118i	−1.42461	−	0.903017i
$41$	−1.67476	−	5.15437i	−0.261553	−	0.804977i	−0.992468	−	0.122508i	$-0.960906\pi$
$41$	−1.67476	−	5.15437i	−0.261553	−	0.804977i	0.730915	−	0.682469i	$-0.239094\pi$
$42$		0			0
$43$	2.53106			0.385982			0.192991	−	0.981201i	$-0.438181\pi$
$43$	2.53106			0.385982			0.192991	+	0.981201i	$0.438181\pi$
$44$	−10.4519	+	7.59371i	−1.57568	+	1.14480i
$45$		0			0
$46$	−3.05541	−	2.21989i	−0.450496	−	0.327305i
$47$	5.72106	+	4.15659i	0.834502	+	0.606301i	0.920829	−	0.389966i	$-0.127513\pi$
$47$	5.72106	+	4.15659i	0.834502	+	0.606301i	−0.0863273	+	0.996267i	$0.527513\pi$
$48$		0			0
$49$	4.83555			0.690793
$50$	−5.20693	−	11.0346i	−0.736371	−	1.56053i
$51$		0			0
$52$	−3.95006	+	12.1570i	−0.547774	+	1.68588i
$53$	−8.21277	−	5.96693i	−1.12811	−	0.819621i	−0.142692	−	0.989767i	$-0.545576\pi$
$53$	−8.21277	−	5.96693i	−1.12811	−	0.819621i	−0.985419	+	0.170147i	$0.945576\pi$
$54$		0			0
$55$	−7.28960	+	0.462540i	−0.982929	+	0.0623689i
$56$	−13.2781	+	9.64708i	−1.77436	+	1.28915i
$57$		0			0
$58$	6.16391	−	4.47834i	0.809361	−	0.588035i
$59$	−0.534773	−	1.64586i	−0.0696215	−	0.214273i	0.910192	−	0.414187i	$-0.135934\pi$
$59$	−0.534773	−	1.64586i	−0.0696215	−	0.214273i	−0.979814	+	0.199913i	$0.935934\pi$
$60$		0			0
$61$	2.42149	−	7.45259i	0.310040	−	0.954206i	−0.667708	−	0.744424i	$-0.732724\pi$
$61$	2.42149	−	7.45259i	0.310040	−	0.954206i	0.977748	−	0.209783i	$-0.0672756\pi$
$62$	−5.61202	−	17.2720i	−0.712727	−	2.19355i
$63$		0			0
$64$	−2.63409	+	8.10689i	−0.329261	+	1.01336i
$65$	−5.56608	+	4.60968i	−0.690387	+	0.571760i
$66$		0			0
$67$	1.49595	−	1.08687i	0.182760	−	0.132783i	−0.492644	−	0.870231i	$-0.663969\pi$
$67$	1.49595	−	1.08687i	0.182760	−	0.132783i	0.675404	+	0.737448i	$0.263969\pi$
$68$	19.9860			2.42366
$69$		0			0
$70$	−18.7347	+	1.18876i	−2.23923	+	0.142084i
$71$	−0.577613	−	0.419660i	−0.0685500	−	0.0498045i	0.552982	−	0.833193i	$-0.313490\pi$
$71$	−0.577613	−	0.419660i	−0.0685500	−	0.0498045i	−0.621533	+	0.783388i	$0.713490\pi$
$72$		0			0
$73$	−0.581036	+	1.78825i	−0.0680052	+	0.209298i	−0.979284	−	0.202491i	$-0.935096\pi$
$73$	−0.581036	+	1.78825i	−0.0680052	+	0.209298i	0.911279	+	0.411790i	$0.135096\pi$
$74$	14.0521			1.63352
$75$		0			0
$76$	−12.1861			−1.39784
$77$	−3.47270	+	10.6879i	−0.395751	+	1.21800i
$78$		0			0
$79$	10.7868	+	7.83708i	1.21361	+	0.881740i	0.995554	−	0.0941957i	$-0.0300279\pi$
$79$	10.7868	+	7.83708i	1.21361	+	0.881740i	0.218058	+	0.975936i	$0.430028\pi$
$80$	6.42695	−	5.32263i	0.718555	−	0.595089i
$81$		0			0
$82$	13.2254			1.46050
$83$	3.20166	−	2.32614i	0.351428	−	0.255328i	−0.398040	−	0.917368i	$-0.630309\pi$
$83$	3.20166	−	2.32614i	0.351428	−	0.255328i	0.749468	+	0.662041i	$0.230309\pi$
$84$		0			0
$85$	9.54388	+	6.04956i	1.03518	+	0.656167i
$86$	−1.90864	+	5.87419i	−0.205814	+	0.633430i
$87$		0			0
$88$	−4.81567	−	14.8211i	−0.513352	−	1.57993i
$89$	−2.63713	+	8.11624i	−0.279535	+	0.860320i	0.708449	+	0.705762i	$0.249395\pi$
$89$	−2.63713	+	8.11624i	−0.279535	+	0.860320i	−0.987984	+	0.154558i	$0.950605\pi$
$90$		0			0
$91$	3.43600	+	10.5749i	0.360191	+	1.10855i
$92$	4.95193	−	3.59779i	0.516274	−	0.375095i
$93$		0			0
$94$	−13.9610	+	10.1433i	−1.43997	+	1.04620i
$95$	−5.81919	−	3.68860i	−0.597037	−	0.378443i
$96$		0			0
$97$	8.61831	+	6.26157i	0.875057	+	0.635766i	0.931939	−	0.362615i	$-0.118116\pi$
$97$	8.61831	+	6.26157i	0.875057	+	0.635766i	−0.0568823	+	0.998381i	$0.518116\pi$
$98$	−3.64643	+	11.2226i	−0.368345	+	1.13365i
$99$		0			0
$100$	19.6163	−	2.49946i	1.96163	−	0.249946i
$101$	−1.76173			−0.175299			−0.0876496	−	0.996151i	$-0.527936\pi$
$101$	−1.76173			−0.175299			−0.0876496	+	0.996151i	$0.527936\pi$
$102$		0			0
$103$	−12.8749	−	9.35416i	−1.26860	−	0.921693i	−0.269456	−	0.963013i	$-0.586844\pi$
$103$	−12.8749	−	9.35416i	−1.26860	−	0.921693i	−0.999146	+	0.0413198i	$0.986844\pi$
$104$	−12.4743	−	9.06313i	−1.22321	−	0.888713i
$105$		0			0
$106$	20.0415	−	14.5610i	1.94660	−	1.41429i
$107$	15.7807			1.52558			0.762788	−	0.646649i	$-0.223830\pi$
$107$	15.7807			1.52558			0.762788	+	0.646649i	$0.223830\pi$
$108$		0			0
$109$	−3.06539	−	9.43429i	−0.293611	−	0.903641i	−0.983685	−	0.179902i	$-0.942422\pi$
$109$	−3.06539	−	9.43429i	−0.293611	−	0.903641i	0.690074	−	0.723739i	$-0.257578\pi$
$110$	4.42352	−	17.2668i	0.421766	−	1.64633i
$111$		0			0
$112$	−3.96743	−	12.2105i	−0.374887	−	1.15378i
$113$	−1.70388	−	5.24399i	−0.160287	−	0.493313i	0.838371	−	0.545100i	$-0.183508\pi$
$113$	−1.70388	−	5.24399i	−0.160287	−	0.493313i	−0.998658	+	0.0517868i	$0.983508\pi$
$114$		0			0
$115$	3.45370	−	0.219145i	0.322059	−	0.0204353i
$116$	3.81580	+	11.7438i	0.354288	+	1.09039i
$117$		0			0
$118$	4.22306			0.388764
$119$	14.0648	−	10.2187i	1.28932	−	0.936743i
$120$		0			0
$121$	0.266626	+	0.193715i	0.0242387	+	0.0176105i
$122$	15.4703	+	11.2398i	1.40061	+	1.01761i
$123$		0			0
$124$	29.4334			2.64320
$125$	10.1239	+	4.74410i	0.905510	+	0.424326i
$126$		0			0
$127$	−0.306572	+	0.943532i	−0.0272039	+	0.0837250i	−0.963737	−	0.266855i	$-0.914016\pi$
$127$	−0.306572	+	0.943532i	−0.0272039	+	0.0837250i	0.936533	+	0.350580i	$0.114016\pi$
$128$	−16.1255	−	11.7159i	−1.42531	−	1.03555i
$129$		0			0
$130$	−6.50105	−	16.3941i	−0.570179	−	1.43786i
$131$	−10.2029	+	7.41286i	−0.891434	+	0.647665i	−0.936252	−	0.351330i	$-0.885729\pi$
$131$	−10.2029	+	7.41286i	−0.891434	+	0.647665i	0.0448175	+	0.998995i	$0.485729\pi$
$132$		0			0
$133$	−8.57573	+	6.23063i	−0.743610	+	0.540264i
$134$	1.39438	+	4.29147i	0.120456	+	0.370727i
$135$		0			0
$136$	−7.44984	+	22.9282i	−0.638818	+	1.96608i
$137$	−2.54650	−	7.83732i	−0.217562	−	0.669588i	−0.998962	−	0.0455566i	$-0.985494\pi$
$137$	−2.54650	−	7.83732i	−0.217562	−	0.669588i	0.781400	−	0.624031i	$-0.214506\pi$
$138$		0			0
$139$	2.49182	−	7.66904i	0.211354	−	0.650479i	−0.788039	−	0.615626i	$-0.788903\pi$
$139$	2.49182	−	7.66904i	0.211354	−	0.650479i	0.999392	−	0.0348539i	$-0.0110966\pi$
$140$	7.55049	−	29.4727i	0.638133	−	2.49090i
$141$		0			0
$142$	1.40954	−	1.02409i	0.118286	−	0.0859397i
$143$	−10.5577			−0.882875
$144$		0			0
$145$	−1.73259	+	6.76301i	−0.143883	+	0.561637i
$146$	−3.71209	−	2.69699i	−0.307215	−	0.223205i
$147$		0			0
$148$	−7.03765	+	21.6597i	−0.578491	+	1.78041i
$149$	19.1101			1.56556			0.782781	−	0.622298i	$-0.213801\pi$
$149$	19.1101			1.56556			0.782781	+	0.622298i	$0.213801\pi$
$150$		0			0
$151$	1.58550			0.129026			0.0645132	−	0.997917i	$-0.479451\pi$
$151$	1.58550			0.129026			0.0645132	+	0.997917i	$0.479451\pi$
$152$	4.54239	−	13.9800i	0.368437	−	1.13393i
$153$		0			0
$154$	−22.1862	−	16.1192i	−1.78782	−	1.29892i
$155$	14.0553	+	8.90921i	1.12895	+	0.715605i
$156$		0			0
$157$	−21.8510			−1.74390			−0.871948	−	0.489599i	$-0.837143\pi$
$157$	−21.8510			−1.74390			−0.871948	+	0.489599i	$0.837143\pi$
$158$	−26.3229	+	19.1247i	−2.09414	+	1.52148i
$159$		0			0
$160$	−0.358125	−	0.903108i	−0.0283123	−	0.0713970i
$161$	1.64531	−	5.06376i	0.129669	−	0.399080i
$162$		0			0
$163$	3.13153	+	9.63786i	0.245280	+	0.754896i	0.995590	+	0.0938092i	$0.0299044\pi$
$163$	3.13153	+	9.63786i	0.245280	+	0.754896i	−0.750310	+	0.661087i	$0.770096\pi$
$164$	−6.62363	+	20.3854i	−0.517219	+	1.59184i
$165$		0			0
$166$	2.98429	+	9.18469i	0.231626	+	0.712870i
$167$	−1.22250	+	0.888195i	−0.0945996	+	0.0687306i	−0.634080	−	0.773268i	$-0.718621\pi$
$167$	−1.22250	+	0.888195i	−0.0945996	+	0.0687306i	0.539480	+	0.841998i	$0.318621\pi$
$168$		0			0
$169$	2.06617	−	1.50116i	0.158936	−	0.115474i
$170$	−21.2370	+	17.5880i	−1.62881	+	1.34894i
$171$		0			0
$172$	−8.09848	−	5.88389i	−0.617504	−	0.448643i
$173$	4.28153	−	13.1772i	0.325518	−	1.00184i	−0.645688	−	0.763602i	$-0.723429\pi$
$173$	4.28153	−	13.1772i	0.325518	−	1.00184i	0.971206	−	0.238241i	$-0.0765709\pi$
$174$		0			0
$175$	12.5267	−	11.7886i	0.946928	−	0.891134i
$176$	12.1906			0.918897
$177$		0			0
$178$	−16.8479	−	12.2407i	−1.26281	−	0.917482i
$179$	11.6949	+	8.49685i	0.874119	+	0.635085i	0.931689	−	0.363257i	$-0.118335\pi$
$179$	11.6949	+	8.49685i	0.874119	+	0.635085i	−0.0575701	+	0.998341i	$0.518335\pi$
$180$		0			0
$181$	−13.9068	+	10.1039i	−1.03369	+	0.751017i	−0.969043	−	0.246891i	$-0.920591\pi$
$181$	−13.9068	+	10.1039i	−1.03369	+	0.751017i	−0.0646435	+	0.997908i	$0.520591\pi$
$182$	−27.1338			−2.01129
$183$		0			0
$184$	2.28159	+	7.02201i	0.168201	+	0.517670i
$185$	−9.91684	+	8.21287i	−0.729101	+	0.603822i
$186$		0			0
$187$	5.10099	+	15.6992i	0.373021	+	1.14804i
$188$	−8.64262	−	26.5993i	−0.630328	−	1.93995i
$189$		0			0
$190$	12.9489	−	10.7239i	0.939410	−	0.777995i
$191$	−3.25778	−	10.0264i	−0.235725	−	0.725486i	−0.997024	−	0.0770858i	$-0.975438\pi$
$191$	−3.25778	−	10.0264i	−0.235725	−	0.725486i	0.761300	−	0.648400i	$-0.224562\pi$
$192$		0			0
$193$	−0.682908			−0.0491568			−0.0245784	−	0.999698i	$-0.507824\pi$
$193$	−0.682908			−0.0491568			−0.0245784	+	0.999698i	$0.507824\pi$
$194$	−21.0311	+	15.2800i	−1.50995	+	1.09704i
$195$		0			0
$196$	−15.4721	−	11.2411i	−1.10515	−	0.802936i
$197$	−18.8478	−	13.6937i	−1.34285	−	0.975639i	−0.999334	−	0.0364929i	$-0.988381\pi$
$197$	−18.8478	−	13.6937i	−1.34285	−	0.975639i	−0.343518	−	0.939146i	$-0.611619\pi$
$198$		0			0
$199$	10.1946			0.722679			0.361339	−	0.932434i	$-0.382320\pi$
$199$	10.1946			0.722679			0.361339	+	0.932434i	$0.382320\pi$
$200$	−4.44462	+	23.4358i	−0.314282	+	1.65716i
$201$		0			0
$202$	1.32850	−	4.08872i	0.0934733	−	0.287681i
$203$	8.68980	+	6.31351i	0.609905	+	0.443122i
$204$		0			0
$205$	−9.33344	+	7.72971i	−0.651876	+	0.539867i
$206$	31.4184	−	22.8268i	2.18902	−	1.59042i
$207$		0			0
$208$	9.75813	−	7.08969i	0.676604	−	0.491582i
$209$	−3.11023	−	9.57230i	−0.215139	−	0.662130i
$210$		0			0
$211$	5.64172	−	17.3634i	0.388392	−	1.19535i	−0.545598	−	0.838047i	$-0.683697\pi$
$211$	5.64172	−	17.3634i	0.388392	−	1.19535i	0.933990	−	0.357300i	$-0.116303\pi$
$212$	12.4068	+	38.1841i	0.852101	+	2.62250i
$213$		0			0
$214$	−11.9000	+	36.6245i	−0.813470	+	2.50360i
$215$	−2.08626	−	5.26106i	−0.142282	−	0.358801i
$216$		0			0
$217$	20.7133	−	15.0491i	1.40611	−	1.02160i
$218$	24.2071			1.63951
$219$		0			0
$220$	24.3994	+	15.4660i	1.64501	+	1.04272i
$221$	13.2134	+	9.60011i	0.888831	+	0.645774i
$222$		0			0
$223$	5.32262	−	16.3813i	0.356429	−	1.09698i	−0.598748	−	0.800938i	$-0.704335\pi$
$223$	5.32262	−	16.3813i	0.356429	−	1.09698i	0.955176	−	0.296037i	$-0.0956653\pi$
$224$	−1.49473			−0.0998708
$225$		0			0
$226$	13.4554			0.895039
$227$	1.33767	−	4.11692i	0.0887842	−	0.273250i	−0.896800	−	0.442437i	$-0.854114\pi$
$227$	1.33767	−	4.11692i	0.0887842	−	0.273250i	0.985584	+	0.169187i	$0.0541142\pi$
$228$		0			0
$229$	−16.4349	−	11.9407i	−1.08605	−	0.789062i	−0.107322	−	0.994224i	$-0.534228\pi$
$229$	−16.4349	−	11.9407i	−1.08605	−	0.789062i	−0.978728	+	0.205163i	$0.934228\pi$
$230$	−2.09580	+	8.18077i	−0.138193	+	0.539424i
$231$		0			0
$232$	−14.8950			−0.977906
$233$	−0.275839	+	0.200409i	−0.0180708	+	0.0131292i	−0.596784	−	0.802402i	$-0.703555\pi$
$233$	−0.275839	+	0.200409i	−0.0180708	+	0.0131292i	0.578713	+	0.815531i	$0.303555\pi$
$234$		0			0
$235$	3.92424	−	15.3179i	0.255989	−	0.999232i
$236$	−2.11502	+	6.50936i	−0.137676	+	0.423723i
$237$		0			0
$238$	13.1099	+	40.3480i	0.849786	+	2.61537i
$239$	2.21407	−	6.81421i	0.143216	−	0.440774i	−0.853561	−	0.520993i	$-0.825562\pi$
$239$	2.21407	−	6.81421i	0.143216	−	0.440774i	0.996777	+	0.0802185i	$0.0255618\pi$
$240$		0			0
$241$	−3.88194	−	11.9474i	−0.250058	−	0.769599i	−0.994763	−	0.102206i	$-0.967410\pi$
$241$	−3.88194	−	11.9474i	−0.250058	−	0.769599i	0.744705	−	0.667393i	$-0.232590\pi$
$242$	−0.650643	+	0.472720i	−0.0418249	+	0.0303876i
$243$		0			0
$244$	−25.0728	+	18.2165i	−1.60512	+	1.16619i
$245$	−3.98577	−	10.0512i	−0.254642	−	0.642147i
$246$		0			0
$247$	−8.05662	−	5.85348i	−0.512631	−	0.372448i
$248$	−10.9714	+	33.7665i	−0.696684	+	2.14417i
$249$		0			0
$250$	−18.6447	+	19.9186i	−1.17919	+	1.25976i
$251$	−17.0160			−1.07404			−0.537022	−	0.843568i	$-0.680451\pi$
$251$	−17.0160			−1.07404			−0.537022	+	0.843568i	$0.680451\pi$
$252$		0			0
$253$	4.08998	+	2.97154i	0.257135	+	0.186819i
$254$	−1.95861	−	1.42301i	−0.122894	−	0.0892879i
$255$		0			0
$256$	25.5586	−	18.5694i	1.59741	−	1.16059i
$257$	−4.13200			−0.257747			−0.128874	−	0.991661i	$-0.541136\pi$
$257$	−4.13200			−0.257747			−0.128874	+	0.991661i	$0.541136\pi$
$258$		0			0
$259$	6.12177	+	18.8409i	0.380388	+	1.17072i
$260$	28.5255	−	1.81000i	1.76908	−	0.112252i
$261$		0			0
$262$	−9.51020	−	29.2694i	−0.587542	−	1.80827i
$263$	0.320676	+	0.986940i	0.0197737	+	0.0608573i	0.960456	−	0.278430i	$-0.0898141\pi$
$263$	0.320676	+	0.986940i	0.0197737	+	0.0608573i	−0.940683	+	0.339287i	$0.889814\pi$
$264$		0			0
$265$	−5.63338	+	21.9894i	−0.346056	+	1.35080i
$266$	−7.99348	−	24.6014i	−0.490112	−	1.50841i
$267$		0			0
$268$	−7.31315			−0.446722
$269$	−12.7741	+	9.28093i	−0.778851	+	0.565869i	−0.904634	−	0.426189i	$-0.859856\pi$
$269$	−12.7741	+	9.28093i	−0.778851	+	0.565869i	0.125783	+	0.992058i	$0.459856\pi$
$270$		0			0
$271$	11.0838	+	8.05286i	0.673294	+	0.489176i	0.871126	−	0.491059i	$-0.163390\pi$
$271$	11.0838	+	8.05286i	0.673294	+	0.489176i	−0.197832	+	0.980236i	$0.563390\pi$
$272$	−15.2571	−	11.0849i	−0.925096	−	0.672122i
$273$		0			0
$274$	20.1095			1.21486
$275$	6.96999	+	14.7709i	0.420306	+	0.890720i
$276$		0			0
$277$	2.15691	−	6.63827i	0.129596	−	0.398855i	−0.865114	−	0.501574i	$-0.832754\pi$
$277$	2.15691	−	6.63827i	0.129596	−	0.398855i	0.994710	+	0.102719i	$0.0327543\pi$
$278$	15.9196	+	11.5663i	0.954795	+	0.693699i
$279$		0			0
$280$	30.9971	+	19.6481i	1.85243	+	1.17420i
$281$	6.43834	−	4.67773i	0.384079	−	0.279050i	−0.378946	−	0.925419i	$-0.623713\pi$
$281$	6.43834	−	4.67773i	0.384079	−	0.279050i	0.763025	+	0.646369i	$0.223713\pi$
$282$		0			0
$283$	22.4868	−	16.3376i	1.33670	−	0.971169i	0.337141	−	0.941454i	$-0.390540\pi$
$283$	22.4868	−	16.3376i	1.33670	−	0.971169i	0.999558	−	0.0297149i	$-0.00945992\pi$
$284$	0.872582	+	2.68553i	0.0517782	+	0.159357i
$285$		0			0
$286$	7.96141	−	24.5027i	0.470768	−	1.44888i
$287$	5.76163	+	17.7325i	0.340099	+	1.04672i
$288$		0			0
$289$	2.63794	−	8.11876i	0.155173	−	0.477574i
$290$	−14.3894	−	9.12098i	−0.844973	−	0.535602i
$291$		0			0
$292$	6.01621	−	4.37103i	0.352072	−	0.255795i
$293$	14.2098			0.830146			0.415073	−	0.909788i	$-0.363756\pi$
$293$	14.2098			0.830146			0.415073	+	0.909788i	$0.363756\pi$
$294$		0			0
$295$	−2.98030	+	2.46821i	−0.173520	+	0.143705i
$296$	−22.2250	−	16.1474i	−1.29180	−	0.938548i
$297$		0			0
$298$	−14.4107	+	44.3517i	−0.834791	+	2.56922i
$299$	5.00206			0.289276
$300$		0			0
$301$	−8.70755			−0.501895
$302$	−1.19561	+	3.67971i	−0.0687997	+	0.211744i
$303$		0			0
$304$	9.30270	+	6.75881i	0.533547	+	0.387644i
$305$	−17.4869	+	1.10958i	−1.00130	+	0.0635345i
$306$		0			0
$307$	−23.2911			−1.32930			−0.664648	−	0.747157i	$-0.731418\pi$
$307$	−23.2911			−1.32930			−0.664648	+	0.747157i	$0.731418\pi$
$308$	35.9573	−	26.1245i	2.04886	−	1.48858i
$309$		0			0
$310$	−31.2759	+	25.9019i	−1.77635	+	1.47113i
$311$	2.33284	−	7.17976i	0.132283	−	0.407127i	−0.862874	−	0.505419i	$-0.831338\pi$
$311$	2.33284	−	7.17976i	0.132283	−	0.407127i	0.995158	+	0.0982923i	$0.0313380\pi$
$312$		0			0
$313$	−9.78241	−	30.1072i	−0.552934	−	1.70176i	−0.701337	−	0.712830i	$-0.747413\pi$
$313$	−9.78241	−	30.1072i	−0.552934	−	1.70176i	0.148402	−	0.988927i	$-0.452587\pi$
$314$	16.4776	−	50.7127i	0.929883	−	2.86188i
$315$		0			0
$316$	−16.2953	−	50.1518i	−0.916682	−	2.82126i
$317$	20.9019	−	15.1861i	1.17397	−	0.852938i	0.182490	−	0.983208i	$-0.441584\pi$
$317$	20.9019	−	15.1861i	1.17397	−	0.852938i	0.991479	+	0.130270i	$0.0415844\pi$
$318$		0			0
$319$	−8.25100	+	5.99471i	−0.461968	+	0.335639i
$320$	19.0222	−	1.20700i	1.06337	−	0.0674733i
$321$		0			0
$322$	10.5115	+	7.63705i	0.585783	+	0.425596i
$323$	−4.81152	+	14.8083i	−0.267720	+	0.823959i
$324$		0			0
$325$	14.1696	+	7.77006i	0.785988	+	0.431006i
$326$	−24.7295			−1.36964
$327$		0			0
$328$	−20.9175	−	15.1975i	−1.15498	−	0.839139i
$329$	−19.6821	−	14.2999i	−1.08511	−	0.788376i
$330$		0			0
$331$	−16.2679	+	11.8193i	−0.894166	+	0.649650i	−0.936961	−	0.349434i	$-0.886374\pi$
$331$	−16.2679	+	11.8193i	−0.894166	+	0.649650i	0.0427948	+	0.999084i	$0.486374\pi$
$332$	−15.6517			−0.859001
$333$		0			0
$334$	−1.13949	−	3.50700i	−0.0623504	−	0.191895i
$335$	−3.49224	−	2.21362i	−0.190801	−	0.120943i
$336$		0			0
$337$	1.04564	+	3.21816i	0.0569599	+	0.175304i	0.975489	−	0.220050i	$-0.0706219\pi$
$337$	1.04564	+	3.21816i	0.0569599	+	0.175304i	−0.918529	+	0.395354i	$0.870622\pi$
$338$	1.92589	+	5.92729i	0.104755	+	0.322402i
$339$		0			0
$340$	−16.4737	−	41.5429i	−0.893414	−	2.25298i
$341$	7.51225	+	23.1203i	0.406811	+	1.25204i
$342$		0			0
$343$	7.44633			0.402064
$344$	9.76882	−	7.09747i	0.526700	−	0.382670i
$345$		0			0
$346$	27.3536	+	19.8735i	1.47054	+	1.06841i
$347$	−23.6204	−	17.1612i	−1.26801	−	0.921262i	−0.268887	−	0.963172i	$-0.586656\pi$
$347$	−23.6204	−	17.1612i	−1.26801	−	0.921262i	−0.999121	+	0.0419100i	$0.986656\pi$
$348$		0			0
$349$	−20.3979			−1.09187			−0.545937	−	0.837826i	$-0.683826\pi$
$349$	−20.3979			−1.09187			−0.545937	+	0.837826i	$0.683826\pi$
$350$	17.9133	+	37.9622i	0.957506	+	2.02916i
$351$		0			0
$352$	0.438573	−	1.34979i	0.0233760	−	0.0719440i
$353$	−1.50757	−	1.09532i	−0.0802400	−	0.0582978i	0.546942	−	0.837170i	$-0.315792\pi$
$353$	−1.50757	−	1.09532i	−0.0802400	−	0.0582978i	−0.627182	+	0.778873i	$0.715792\pi$
$354$		0			0
$355$	−0.396201	+	1.54654i	−0.0210282	+	0.0820818i
$356$	27.3055	−	19.8386i	1.44719	−	1.05145i
$357$		0			0
$358$	−28.5389	+	20.7347i	−1.50833	+	1.09586i
$359$	−1.18599	−	3.65011i	−0.0625943	−	0.192645i	0.914869	−	0.403751i	$-0.132294\pi$
$359$	−1.18599	−	3.65011i	−0.0625943	−	0.192645i	−0.977463	+	0.211105i	$0.932294\pi$
$360$		0			0
$361$	−2.93759	+	9.04097i	−0.154610	+	0.475841i
$362$	−12.9626	−	39.8949i	−0.681301	−	2.09683i
$363$		0			0
$364$	13.5893	−	41.8236i	0.712274	−	2.19215i
$365$	4.19598	−	0.266244i	0.219628	−	0.0139358i
$366$		0			0
$367$	−20.7335	+	15.0638i	−1.08228	+	0.786324i	−0.978079	−	0.208232i	$-0.933229\pi$
$367$	−20.7335	+	15.0638i	−1.08228	+	0.786324i	−0.104203	+	0.994556i	$0.533229\pi$
$368$	−5.77570			−0.301079
$369$		0			0
$370$	−11.5826	−	29.2087i	−0.602153	−	1.51849i
$371$	28.2543	+	20.5279i	1.46689	+	1.06576i
$372$		0			0
$373$	6.62437	−	20.3877i	0.342997	−	1.05564i	−0.619651	−	0.784878i	$-0.712726\pi$
$373$	6.62437	−	20.3877i	0.342997	−	1.05564i	0.962648	−	0.270758i	$-0.0872742\pi$
$374$	−40.2821			−2.08294
$375$		0			0
$376$	33.7366			1.73983
$377$	−3.11829	+	9.59712i	−0.160600	+	0.494277i
$378$		0			0
$379$	20.9304	+	15.2068i	1.07512	+	0.781120i	0.976826	−	0.214037i	$-0.0686613\pi$
$379$	20.9304	+	15.2068i	1.07512	+	0.781120i	0.0982945	+	0.995157i	$0.468661\pi$
$380$	10.0445	+	25.3300i	0.515274	+	1.29940i
$381$		0			0
$382$	25.7264			1.31628
$383$	−11.7579	+	8.54263i	−0.600802	+	0.436508i	−0.846163	−	0.532924i	$-0.821093\pi$
$383$	−11.7579	+	8.54263i	−0.600802	+	0.436508i	0.245362	+	0.969432i	$0.421093\pi$
$384$		0			0
$385$	25.0783	−	1.59127i	1.27811	−	0.0810986i
$386$	0.514974	−	1.58493i	0.0262115	−	0.0806706i
$387$		0			0
$388$	−13.0194	−	40.0696i	−0.660960	−	2.03423i
$389$	−7.13973	+	21.9738i	−0.361999	+	1.11412i	0.589840	+	0.807520i	$0.299191\pi$
$389$	−7.13973	+	21.9738i	−0.361999	+	1.11412i	−0.951839	+	0.306598i	$0.900809\pi$
$390$		0			0
$391$	−2.41677	−	7.43806i	−0.122221	−	0.376159i
$392$	18.6632	−	13.5596i	0.942635	−	0.684864i
$393$		0			0
$394$	45.9940	−	33.4166i	2.31715	−	1.68350i
$395$	7.39898	−	28.8813i	0.372283	−	1.45318i
$396$		0			0
$397$	−11.2733	−	8.19052i	−0.565790	−	0.411070i	0.267784	−	0.963479i	$-0.413709\pi$
$397$	−11.2733	−	8.19052i	−0.565790	−	0.411070i	−0.833573	+	0.552409i	$0.813709\pi$
$398$	−7.68766	+	23.6602i	−0.385348	+	1.18598i
$399$		0			0
$400$	−16.3611	−	8.97182i	−0.818057	−	0.448591i
$401$	27.5822			1.37739			0.688694	−	0.725052i	$-0.258184\pi$
$401$	27.5822			1.37739			0.688694	+	0.725052i	$0.258184\pi$
$402$		0			0
$403$	19.4594	+	14.1381i	0.969344	+	0.704270i
$404$	5.63693	+	4.09547i	0.280448	+	0.203757i
$405$		0			0
$406$	−21.2056	+	15.4068i	−1.05242	+	0.764625i
$407$	−18.8101			−0.932383
$408$		0			0
$409$	4.08288	+	12.5658i	0.201886	+	0.621340i	0.999827	+	0.0186048i	$0.00592242\pi$
$409$	4.08288	+	12.5658i	0.201886	+	0.621340i	−0.797941	+	0.602735i	$0.794078\pi$
$410$	−10.9012	−	27.4904i	−0.538374	−	1.35765i
$411$		0			0
$412$	19.4497	+	59.8601i	0.958218	+	2.94909i
$413$	1.83977	+	5.66223i	0.0905292	+	0.278620i
$414$		0			0
$415$	−7.47415	−	4.73763i	−0.366891	−	0.232561i
$416$	−0.433937	−	1.33552i	−0.0212755	−	0.0654794i
$417$		0			0
$418$	24.5612			1.20133
$419$	−7.15797	+	5.20057i	−0.349690	+	0.254064i	−0.748739	−	0.662865i	$-0.769340\pi$
$419$	−7.15797	+	5.20057i	−0.349690	+	0.254064i	0.399049	+	0.916930i	$0.369340\pi$
$420$		0			0
$421$	30.3192	+	22.0282i	1.47767	+	1.07359i	0.978299	+	0.207197i	$0.0664341\pi$
$421$	30.3192	+	22.0282i	1.47767	+	1.07359i	0.499367	+	0.866390i	$0.333566\pi$
$422$	36.0435	+	26.1871i	1.75457	+	1.27477i
$423$		0			0
$424$	−48.4301			−2.35197
$425$	4.70796	−	24.8244i	0.228370	−	1.20416i
$426$		0			0
$427$	−8.33062	+	25.6390i	−0.403147	+	1.24076i
$428$	−50.4926	−	36.6850i	−2.44065	−	1.77324i
$429$		0			0
$430$	13.7833	−	0.874582i	0.664691	−	0.0421761i
$431$	−21.5397	+	15.6495i	−1.03753	+	0.753809i	−0.969802	−	0.243895i	$-0.921575\pi$
$431$	−21.5397	+	15.6495i	−1.03753	+	0.753809i	−0.0677274	+	0.997704i	$0.521575\pi$
$432$		0			0
$433$	−28.3133	+	20.5708i	−1.36065	+	0.988571i	−0.362248	+	0.932082i	$0.617990\pi$
$433$	−28.3133	+	20.5708i	−1.36065	+	0.988571i	−0.998403	+	0.0564887i	$0.982010\pi$
$434$	19.3069	+	59.4206i	0.926762	+	2.85228i
$435$		0			0
$436$	−12.1235	+	37.3124i	−0.580613	+	1.78694i
$437$	1.47358	+	4.53521i	0.0704909	+	0.216949i
$438$		0			0
$439$	6.19701	−	19.0724i	0.295767	−	0.910277i	−0.687196	−	0.726472i	$-0.741159\pi$
$439$	6.19701	−	19.0724i	0.295767	−	0.910277i	0.982963	−	0.183805i	$-0.0588415\pi$
$440$	−26.8378	+	22.2264i	−1.27944	+	1.05960i
$441$		0			0
$442$	−32.2445	+	23.4270i	−1.53371	+	1.11431i
$443$	−4.14871			−0.197111			−0.0985556	−	0.995132i	$-0.531422\pi$
$443$	−4.14871			−0.197111			−0.0985556	+	0.995132i	$0.531422\pi$
$444$		0			0
$445$	19.0441	−	1.20839i	0.902778	−	0.0572832i
$446$	34.0048	+	24.7060i	1.61018	+	1.16986i
$447$		0			0
$448$	9.06201	−	27.8900i	0.428140	−	1.31768i
$449$	8.34804			0.393969			0.196984	−	0.980407i	$-0.436885\pi$
$449$	8.34804			0.393969			0.196984	+	0.980407i	$0.436885\pi$
$450$		0			0
$451$	−17.7035			−0.833627
$452$	−6.73880	+	20.7399i	−0.316967	+	0.975523i
$453$		0			0
$454$	8.54602	+	6.20905i	0.401085	+	0.291405i
$455$	19.1489	−	15.8586i	0.897713	−	0.743463i
$456$		0			0
$457$	20.5774			0.962571			0.481285	−	0.876564i	$-0.340170\pi$
$457$	20.5774			0.962571			0.481285	+	0.876564i	$0.340170\pi$
$458$	40.1059	−	29.1386i	1.87402	−	1.36156i
$459$		0			0
$460$	−11.5601	−	7.32757i	−0.538991	−	0.341650i
$461$	−8.86541	+	27.2849i	−0.412903	+	1.27079i	0.501210	+	0.865326i	$0.332889\pi$
$461$	−8.86541	+	27.2849i	−0.412903	+	1.27079i	−0.914113	+	0.405460i	$0.867111\pi$
$462$		0			0
$463$	12.3853	+	38.1181i	0.575594	+	1.77150i	0.634146	+	0.773213i	$0.281352\pi$
$463$	12.3853	+	38.1181i	0.575594	+	1.77150i	−0.0585520	+	0.998284i	$0.518648\pi$
$464$	3.60058	−	11.0815i	0.167153	−	0.514444i
$465$		0			0
$466$	−0.257111	−	0.791307i	−0.0119105	−	0.0366566i
$467$	−6.58694	+	4.78569i	−0.304807	+	0.221456i	−0.729665	−	0.683805i	$-0.760324\pi$
$467$	−6.58694	+	4.78569i	−0.304807	+	0.221456i	0.424858	+	0.905260i	$0.360324\pi$
$468$		0			0
$469$	−5.14650	+	3.73915i	−0.237643	+	0.172658i
$470$	32.5914	+	20.6586i	1.50333	+	0.952912i
$471$		0			0
$472$	−6.67925	−	4.85276i	−0.307438	−	0.223366i
$473$	2.55491	−	7.86319i	0.117475	−	0.361550i
$474$		0			0
$475$	−2.87059	+	15.1362i	−0.131712	+	0.694495i
$476$	−68.7575			−3.15149
$477$		0			0
$478$	14.1451	+	10.2770i	0.646983	+	0.470061i
$479$	−22.7027	−	16.4945i	−1.03731	−	0.753652i	−0.0675535	−	0.997716i	$-0.521519\pi$
$479$	−22.7027	−	16.4945i	−1.03731	−	0.753652i	−0.969759	+	0.244064i	$0.921519\pi$
$480$		0			0
$481$	−15.0569	+	10.9395i	−0.686534	+	0.498796i
$482$	30.6554			1.39631
$483$		0			0
$484$	−0.402784	−	1.23964i	−0.0183084	−	0.0563473i
$485$	5.91155	−	23.0752i	0.268429	−	1.04779i
$486$		0			0
$487$	−4.70239	−	14.4725i	−0.213086	−	0.655810i	−0.999284	−	0.0378360i	$-0.987954\pi$
$487$	−4.70239	−	14.4725i	−0.213086	−	0.655810i	0.786198	−	0.617974i	$-0.212046\pi$
$488$	−11.5522	−	35.5541i	−0.522945	−	1.60946i
$489$		0			0
$490$	26.3329	−	1.67088i	1.18960	−	0.0754826i
$491$	−2.56246	−	7.88645i	−0.115642	−	0.355910i	0.876438	−	0.481514i	$-0.159913\pi$
$491$	−2.56246	−	7.88645i	−0.115642	−	0.355910i	−0.992080	+	0.125604i	$0.959913\pi$
$492$		0			0
$493$	15.7775			0.710585
$494$	19.6604	−	14.2842i	0.884565	−	0.642674i
$495$		0			0
$496$	−22.4691	−	16.3248i	−1.00889	−	0.733005i
$497$	1.98715	+	1.44375i	0.0891360	+	0.0647611i
$498$		0			0
$499$	−24.4006			−1.09232			−0.546160	−	0.837681i	$-0.683911\pi$
$499$	−24.4006			−1.09232			−0.546160	+	0.837681i	$0.683911\pi$
$500$	−21.3644	−	38.7143i	−0.955445	−	1.73136i
$501$		0			0
$502$	12.8316	−	39.4916i	0.572703	−	1.76260i
$503$	8.47295	+	6.15596i	0.377790	+	0.274481i	0.760434	−	0.649415i	$-0.224986\pi$
$503$	8.47295	+	6.15596i	0.377790	+	0.274481i	−0.382644	+	0.923896i	$0.624986\pi$
$504$		0			0
$505$	1.45214	+	3.66195i	0.0646192	+	0.162954i
$506$	−9.98070	+	7.25141i	−0.443696	+	0.322364i
$507$		0			0
$508$	3.17433	−	2.30629i	0.140838	−	0.102325i
$509$	3.41769	+	10.5186i	0.151486	+	0.466227i	0.997788	−	0.0664770i	$-0.0211759\pi$
$509$	3.41769	+	10.5186i	0.151486	+	0.466227i	−0.846302	+	0.532704i	$0.821176\pi$
$510$		0			0
$511$	1.99893	−	6.15207i	0.0884274	−	0.272152i
$512$	11.5045	+	35.4071i	0.508431	+	1.56479i
$513$		0			0
$514$	3.11590	−	9.58974i	0.137436	−	0.422985i
$515$	−8.83126	+	34.4721i	−0.389152	+	1.51902i
$516$		0			0
$517$	18.6882	−	13.5778i	0.821906	−	0.597150i
$518$	−48.3432			−2.12408
$519$		0			0
$520$	−8.55650	+	33.3996i	−0.375227	+	1.46467i
$521$	−33.5105	−	24.3468i	−1.46812	−	1.06665i	−0.981153	−	0.193231i	$-0.938103\pi$
$521$	−33.5105	−	24.3468i	−1.46812	−	1.06665i	−0.486967	−	0.873420i	$-0.661897\pi$
$522$		0			0
$523$	4.21576	−	12.9748i	0.184342	−	0.567347i	−0.815594	−	0.578624i	$-0.803590\pi$
$523$	4.21576	−	12.9748i	0.184342	−	0.567347i	0.999936	+	0.0112775i	$0.00358982\pi$
$524$	49.8783			2.17894
$525$		0			0
$526$	−2.53235			−0.110416
$527$	11.6214	−	35.7671i	0.506238	−	1.55804i
$528$		0			0
$529$	16.6696	+	12.1112i	0.724766	+	0.526573i
$530$	−46.7860	−	29.6562i	−2.03225	−	1.28818i
$531$		0			0
$532$	41.9235			1.81762
$533$	−14.1711	+	10.2959i	−0.613818	+	0.445965i
$534$		0			0
$535$	−13.0075	−	32.8018i	−0.562361	−	1.41814i
$536$	2.72600	−	8.38976i	0.117745	−	0.362382i
$537$		0			0
$538$	−11.9068	−	36.6454i	−0.513339	−	1.57990i
$539$	4.88112	−	15.0225i	0.210245	−	0.647066i
$540$		0			0
$541$	4.53011	+	13.9423i	0.194765	+	0.599424i	0.999979	+	0.00644072i	$0.00205016\pi$
$541$	4.53011	+	13.9423i	0.194765	+	0.599424i	−0.805214	+	0.592984i	$0.797950\pi$
$542$	−27.0476	+	19.6513i	−1.16180	+	0.844094i
$543$		0			0
$544$	−1.77626	+	1.29053i	−0.0761566	+	0.0553310i
$545$	−17.0834	+	14.1481i	−0.731775	+	0.606037i
$546$		0			0
$547$	−21.5298	−	15.6423i	−0.920549	−	0.668818i	0.0231115	−	0.999733i	$-0.492643\pi$
$547$	−21.5298	−	15.6423i	−0.920549	−	0.668818i	−0.943661	+	0.330915i	$0.892643\pi$
$548$	−10.0714	+	30.9965i	−0.430227	+	1.32410i
$549$		0			0
$550$	−39.5370	+	5.03770i	−1.68586	+	0.214808i
$551$	−9.62005			−0.409828
$552$		0			0
$553$	−37.1097	−	26.9618i	−1.57806	−	1.14653i
$554$	13.7799	+	10.0117i	0.585453	+	0.425356i
$555$		0			0
$556$	−25.8010	+	18.7455i	−1.09421	+	0.794988i
$557$	10.3141			0.437020			0.218510	−	0.975835i	$-0.429880\pi$
$557$	10.3141			0.437020			0.218510	+	0.975835i	$0.429880\pi$
$558$		0			0
$559$	−2.52790	−	7.78008i	−0.106919	−	0.329063i
$560$	−22.1105	+	18.3114i	−0.934341	+	0.773797i
$561$		0			0
$562$	6.00121	+	18.4698i	0.253146	+	0.779103i
$563$	10.6311	+	32.7193i	0.448049	+	1.37895i	0.879105	+	0.476628i	$0.158141\pi$
$563$	10.6311	+	32.7193i	0.448049	+	1.37895i	−0.431056	+	0.902325i	$0.641859\pi$
$564$		0			0
$565$	−9.49573	+	7.86412i	−0.399488	+	0.330846i
$566$	20.9600	+	64.5083i	0.881016	+	2.71149i
$567$		0			0
$568$	−3.40614			−0.142918
$569$	−9.87387	+	7.17378i	−0.413934	+	0.300741i	−0.775193	−	0.631725i	$-0.782347\pi$
$569$	−9.87387	+	7.17378i	−0.413934	+	0.300741i	0.361259	+	0.932466i	$0.382347\pi$
$570$		0			0
$571$	−34.0308	−	24.7248i	−1.42415	−	1.03470i	−0.991070	−	0.133345i	$-0.957428\pi$
$571$	−34.0308	−	24.7248i	−1.42415	−	1.03470i	−0.433076	−	0.901357i	$-0.642572\pi$
$572$	33.7808	+	24.5432i	1.41245	+	1.02620i
$573$		0			0
$574$	−45.4992			−1.89910
$575$	−3.30228	−	6.99824i	−0.137715	−	0.291847i
$576$		0			0
$577$	5.41863	−	16.6768i	0.225581	−	0.694266i	−0.772652	−	0.634830i	$-0.781070\pi$
$577$	5.41863	−	16.6768i	0.225581	−	0.694266i	0.998232	−	0.0594353i	$-0.0189300\pi$
$578$	16.8532	+	12.2445i	0.700999	+	0.509305i
$579$		0			0
$580$	21.2655	−	17.6115i	0.883001	−	0.731279i
$581$	−11.0146	+	8.00260i	−0.456964	+	0.332004i
$582$		0			0
$583$	−26.8275	+	19.4913i	−1.11108	+	0.807249i
$584$	2.77196	+	8.53120i	0.114704	+	0.353024i
$585$		0			0
$586$	−10.7155	+	32.9788i	−0.442651	+	1.36234i
$587$	6.77115	+	20.8395i	0.279475	+	0.860137i	0.988000	+	0.154451i	$0.0493610\pi$
$587$	6.77115	+	20.8395i	0.279475	+	0.860137i	−0.708525	+	0.705686i	$0.750639\pi$
$588$		0			0
$589$	−7.08595	+	21.8083i	−0.291971	+	0.898595i
$590$	−3.48092	−	8.77807i	−0.143307	−	0.361387i
$591$		0			0
$592$	17.3856	−	12.6314i	0.714545	−	0.519148i
$593$	38.0061			1.56072			0.780361	−	0.625330i	$-0.215035\pi$
$593$	38.0061			1.56072			0.780361	+	0.625330i	$0.215035\pi$
$594$		0			0
$595$	−32.8336	−	20.8122i	−1.34605	−	0.853218i
$596$	−61.1456	−	44.4249i	−2.50462	−	1.81971i
$597$		0			0
$598$	−3.77200	+	11.6090i	−0.154248	+	0.474728i
$599$	−16.3154			−0.666629			−0.333314	−	0.942816i	$-0.608167\pi$
$599$	−16.3154			−0.666629			−0.333314	+	0.942816i	$0.608167\pi$
$600$		0			0
$601$	2.31871			0.0945822			0.0472911	−	0.998881i	$-0.484941\pi$
$601$	2.31871			0.0945822			0.0472911	+	0.998881i	$0.484941\pi$
$602$	6.56626	−	20.2089i	0.267621	−	0.823653i
$603$		0			0
$604$	−5.07305	−	3.68579i	−0.206420	−	0.149973i
$605$	0.182887	−	0.713882i	0.00743539	−	0.0290234i
$606$		0			0
$607$	32.2134			1.30750			0.653752	−	0.756709i	$-0.273194\pi$
$607$	32.2134			1.30750			0.653752	+	0.756709i	$0.273194\pi$
$608$	1.08304	−	0.786876i	0.0439231	−	0.0319120i
$609$		0			0
$610$	10.6115	−	41.4212i	0.429648	−	1.67709i
$611$	7.06281	−	21.7371i	0.285731	−	0.879389i
$612$		0			0
$613$	8.01843	+	24.6782i	0.323861	+	0.996742i	0.971952	+	0.235179i	$0.0755677\pi$
$613$	8.01843	+	24.6782i	0.323861	+	0.996742i	−0.648091	+	0.761563i	$0.724432\pi$
$614$	17.5636	−	54.0552i	0.708809	−	2.18149i
$615$		0			0
$616$	16.5673	+	50.9888i	0.667514	+	2.05440i
$617$	1.54016	−	1.11899i	0.0620043	−	0.0450488i	−0.556351	−	0.830947i	$-0.687799\pi$
$617$	1.54016	−	1.11899i	0.0620043	−	0.0450488i	0.618356	+	0.785898i	$0.287799\pi$
$618$		0			0
$619$	16.0829	−	11.6849i	0.646425	−	0.469655i	−0.215627	−	0.976476i	$-0.569179\pi$
$619$	16.0829	−	11.6849i	0.646425	−	0.469655i	0.862052	+	0.506821i	$0.169179\pi$
$620$	−24.2609	−	61.1804i	−0.974343	−	2.45706i
$621$		0			0
$622$	14.9039	+	10.8283i	0.597594	+	0.434177i
$623$	9.07246	−	27.9222i	0.363480	−	1.11868i
$624$		0			0
$625$	1.51633	−	24.9540i	0.0606533	−	0.998159i
$626$	77.2509			3.08757
$627$		0			0
$628$	69.9154	+	50.7965i	2.78993	+	2.02700i
$629$	23.5418	+	17.1041i	0.938673	+	0.681986i
$630$		0			0
$631$	26.6152	−	19.3371i	1.05953	−	0.769796i	0.0855315	−	0.996335i	$-0.472741\pi$
$631$	26.6152	−	19.3371i	1.05953	−	0.769796i	0.974002	+	0.226539i	$0.0727412\pi$
$632$	63.6090			2.53023
$633$		0			0
$634$	19.4828	+	59.9618i	0.773760	+	2.38139i
$635$	2.21393	−	0.140478i	0.0878570	−	0.00557471i
$636$		0			0
$637$	−4.82953	−	14.8638i	−0.191353	−	0.588923i
$638$	−7.69080	−	23.6699i	−0.304482	−	0.937099i
$639$		0			0
$640$	−11.0610	+	43.1755i	−0.437223	+	1.70666i
$641$	12.5963	+	38.7673i	0.497523	+	1.53122i	0.812988	+	0.582280i	$0.197839\pi$
$641$	12.5963	+	38.7673i	0.497523	+	1.53122i	−0.315465	+	0.948937i	$0.602161\pi$
$642$		0			0
$643$	24.9947			0.985695			0.492847	−	0.870116i	$-0.335956\pi$
$643$	24.9947			0.985695			0.492847	+	0.870116i	$0.335956\pi$
$644$	−17.0360	+	12.3774i	−0.671314	+	0.487738i
$645$		0			0
$646$	−30.7396	−	22.3336i	−1.20943	−	0.878705i
$647$	−25.9073	−	18.8228i	−1.01852	−	0.739999i	−0.0525420	−	0.998619i	$-0.516732\pi$
$647$	−25.9073	−	18.8228i	−1.01852	−	0.739999i	−0.965979	+	0.258620i	$0.916732\pi$
$648$		0			0
$649$	−5.65299			−0.221899
$650$	−28.7183	+	27.0262i	−1.12642	+	1.06005i
$651$		0			0
$652$	12.3852	−	38.1176i	0.485040	−	1.49280i
$653$	−36.1446	−	26.2606i	−1.41445	−	1.02766i	−0.992657	−	0.120964i	$-0.961401\pi$
$653$	−36.1446	−	26.2606i	−1.41445	−	1.02766i	−0.421791	−	0.906693i	$-0.638599\pi$
$654$		0			0
$655$	23.8183	+	15.0977i	0.930658	+	0.589915i
$656$	16.3629	−	11.8883i	0.638862	−	0.464161i
$657$		0			0
$658$	48.0298	−	34.8957i	1.87240	−	1.36038i
$659$	7.42307	+	22.8458i	0.289162	+	0.889948i	0.985120	+	0.171866i	$0.0549796\pi$
$659$	7.42307	+	22.8458i	0.289162	+	0.889948i	−0.695959	+	0.718082i	$0.745020\pi$
$660$		0			0
$661$	11.7095	−	36.0382i	0.455447	−	1.40172i	−0.415163	−	0.909747i	$-0.636275\pi$
$661$	11.7095	−	36.0382i	0.455447	−	1.40172i	0.870610	−	0.491974i	$-0.163725\pi$
$662$	−15.1634	−	46.6682i	−0.589343	−	1.81381i
$663$		0			0
$664$	5.83423	−	17.9559i	0.226412	−	0.696824i
$665$	20.0197	+	12.6898i	0.776329	+	0.492091i
$666$		0			0
$667$	3.90920	−	2.84020i	0.151365	−	0.109973i
$668$	5.97633			0.231231
$669$		0			0
$670$	7.77093	−	6.43568i	0.300217	−	0.248632i
$671$	−20.7085	−	15.0456i	−0.799444	−	0.580830i
$672$		0			0
$673$	−5.69418	+	17.5249i	−0.219494	+	0.675534i	0.779310	+	0.626639i	$0.215570\pi$
$673$	−5.69418	+	17.5249i	−0.219494	+	0.675534i	−0.998804	+	0.0488951i	$0.984430\pi$
$674$	−8.25737			−0.318062
$675$		0			0
$676$	−10.1008			−0.388491
$677$	7.05064	−	21.6996i	0.270978	−	0.833985i	−0.719277	−	0.694723i	$-0.755527\pi$
$677$	7.05064	−	21.6996i	0.270978	−	0.833985i	0.990256	−	0.139262i	$-0.0444730\pi$
$678$		0			0
$679$	−29.6494	−	21.5416i	−1.13784	−	0.826690i
$680$	53.7993	−	3.41368i	2.06311	−	0.130909i
$681$		0			0
$682$	−59.3236			−2.27162
$683$	26.0555	−	18.9304i	0.996987	−	0.724353i	0.0355465	−	0.999368i	$-0.488683\pi$
$683$	26.0555	−	18.9304i	0.996987	−	0.724353i	0.961440	+	0.275015i	$0.0886828\pi$
$684$		0			0
$685$	−14.1917	+	11.7532i	−0.542237	+	0.449066i
$686$	−5.61519	+	17.2818i	−0.214389	+	0.659822i
$687$		0			0
$688$	2.91888	+	8.98339i	0.111281	+	0.342489i
$689$	−10.1389	+	31.2043i	−0.386261	+	1.18879i
$690$		0			0
$691$	7.59466	+	23.3740i	0.288915	+	0.889188i	0.985198	+	0.171421i	$0.0548358\pi$
$691$	7.59466	+	23.3740i	0.288915	+	0.889188i	−0.696283	+	0.717767i	$0.745164\pi$
$692$	−44.3321	+	32.2092i	−1.68525	+	1.22441i
$693$		0			0
$694$	57.6404	−	41.8782i	2.18800	−	1.58967i
$695$	−17.9948	+	1.14181i	−0.682582	+	0.0433113i
$696$		0			0
$697$	22.1568	+	16.0979i	0.839251	+	0.609751i
$698$	15.3818	−	47.3404i	0.582211	−	1.79186i
$699$		0			0
$700$	−67.4857	+	8.59884i	−2.55072	+	0.325006i
$701$	3.66355			0.138370			0.0691852	−	0.997604i	$-0.477960\pi$
$701$	3.66355			0.138370			0.0691852	+	0.997604i	$0.477960\pi$
$702$		0			0
$703$	−14.3541	−	10.4289i	−0.541377	−	0.393333i
$704$	22.5267	+	16.3666i	0.849005	+	0.616838i
$705$		0			0
$706$	3.67890	−	2.67288i	0.138457	−	0.100595i
$707$	6.06087			0.227942
$708$		0			0
$709$	−8.24980	−	25.3903i	−0.309828	−	0.953552i	−0.977831	−	0.209394i	$-0.932851\pi$
$709$	−8.24980	−	25.3903i	−0.309828	−	0.953552i	0.668003	−	0.744158i	$-0.267149\pi$
$710$	−3.29051	−	2.08575i	−0.123491	−	0.0782768i
$711$		0			0
$712$	12.5810	+	38.7202i	0.471492	+	1.45110i
$713$	−3.55919	−	10.9541i	−0.133293	−	0.410233i
$714$		0			0
$715$	8.70230	+	21.9452i	0.325447	+	0.820703i
$716$	−17.6671	−	54.3739i	−0.660252	−	2.03205i
$717$		0			0
$718$	9.36569			0.349524
$719$	14.4570	−	10.5036i	0.539156	−	0.391720i	−0.284616	−	0.958642i	$-0.591866\pi$
$719$	14.4570	−	10.5036i	0.539156	−	0.391720i	0.823771	+	0.566922i	$0.191866\pi$
$720$		0			0
$721$	44.2933	+	32.1810i	1.64957	+	1.19848i
$722$	−18.7675	−	13.6354i	−0.698455	−	0.507457i
$723$		0			0
$724$	67.9853			2.52665
$725$	15.4857	−	1.97315i	0.575125	−	0.0732808i
$726$		0			0
$727$	−10.5290	+	32.4050i	−0.390500	+	1.20184i	0.541910	+	0.840436i	$0.317701\pi$
$727$	−10.5290	+	32.4050i	−0.390500	+	1.20184i	−0.932411	+	0.361400i	$0.882299\pi$
$728$	42.9152	+	31.1797i	1.59054	+	1.15560i
$729$		0			0
$730$	−2.54623	+	9.93900i	−0.0942402	+	0.367859i
$731$	−10.3476	+	7.51799i	−0.382721	+	0.278063i
$732$		0			0
$733$	32.5068	−	23.6176i	1.20067	−	0.872335i	0.206316	−	0.978485i	$-0.433853\pi$
$733$	32.5068	−	23.6176i	1.20067	−	0.872335i	0.994350	+	0.106150i	$0.0338525\pi$
$734$	−19.3258	−	59.4788i	−0.713330	−	2.19540i
$735$		0			0
$736$	−0.207789	+	0.639509i	−0.00765921	+	0.0235726i
$737$	−1.86652	−	5.74457i	−0.0687542	−	0.211604i
$738$		0			0
$739$	4.78203	−	14.7176i	0.175910	−	0.541395i	−0.823764	−	0.566933i	$-0.808130\pi$
$739$	4.78203	−	14.7176i	0.175910	−	0.541395i	0.999674	+	0.0255381i	$0.00812990\pi$
$740$	50.8227	−	3.22481i	1.86828	−	0.118546i
$741$		0			0
$742$	−68.9484	+	50.0939i	−2.53118	+	1.83901i
$743$	17.1140			0.627853			0.313926	−	0.949447i	$-0.398355\pi$
$743$	17.1140			0.627853			0.313926	+	0.949447i	$0.398355\pi$
$744$		0			0
$745$	−15.7518	−	39.7223i	−0.577101	−	1.45531i
$746$	42.3214	+	30.7483i	1.54950	+	1.12577i
$747$		0			0
$748$	20.1743	−	62.0902i	0.737647	−	2.27024i
$749$	−54.2900			−1.98371
$750$		0			0
$751$	−11.1559			−0.407086			−0.203543	−	0.979066i	$-0.565246\pi$
$751$	−11.1559			−0.407086			−0.203543	+	0.979066i	$0.565246\pi$
$752$	−8.15518	+	25.0991i	−0.297389	+	0.915268i
$753$		0			0
$754$	−19.9220	−	14.4742i	−0.725516	−	0.527118i
$755$	−1.30687	−	3.29563i	−0.0475620	−	0.119940i
$756$		0			0
$757$	24.6773			0.896911			0.448456	−	0.893805i	$-0.351974\pi$
$757$	24.6773			0.896911			0.448456	+	0.893805i	$0.351974\pi$
$758$	−51.0760	+	37.1089i	−1.85516	+	1.34786i
$759$		0			0
$760$	−32.8031	+	2.08143i	−1.18989	+	0.0755012i
$761$	12.4372	−	38.2779i	0.450850	−	1.38757i	−0.425089	−	0.905151i	$-0.639757\pi$
$761$	12.4372	−	38.2779i	0.450850	−	1.38757i	0.875939	−	0.482422i	$-0.160243\pi$
$762$		0			0
$763$	10.5458	+	32.4566i	0.381784	+	1.17501i
$764$	−12.8845	+	39.6543i	−0.466143	+	1.43464i
$765$		0			0
$766$	−10.9596	−	33.7302i	−0.395987	−	1.21872i
$767$	−4.52503	+	3.28763i	−0.163389	+	0.118709i
$768$		0			0
$769$	−17.8801	+	12.9907i	−0.644773	+	0.468455i	−0.861487	−	0.507780i	$-0.830466\pi$
$769$	−17.8801	+	12.9907i	−0.644773	+	0.468455i	0.216714	+	0.976235i	$0.430466\pi$
$770$	−15.2182	+	59.4028i	−0.548424	+	2.14073i
$771$		0			0
$772$	2.18507	+	1.58754i	0.0786423	+	0.0571370i
$773$	−1.51429	+	4.66049i	−0.0544651	+	0.167626i	−0.974589	−	0.224002i	$-0.928088\pi$
$773$	−1.51429	+	4.66049i	−0.0544651	+	0.167626i	0.920124	+	0.391628i	$0.128088\pi$
$774$		0			0
$775$	6.93343	−	36.5589i	0.249056	−	1.31324i
$776$	50.8215			1.82439
$777$		0			0
$778$	−45.6139	−	33.1405i	−1.63534	−	1.18814i
$779$	−13.5097	−	9.81537i	−0.484035	−	0.351672i
$780$		0			0
$781$	−1.88681	+	1.37085i	−0.0675153	+	0.0490528i
$782$	19.0851			0.682481
$783$		0			0
$784$	5.57648	+	17.1627i	0.199160	+	0.612952i
$785$	18.0110	+	45.4194i	0.642839	+	1.62109i
$786$		0			0
$787$	−1.15411	−	3.55198i	−0.0411395	−	0.126614i	0.928377	−	0.371639i	$-0.121204\pi$
$787$	−1.15411	−	3.55198i	−0.0411395	−	0.126614i	−0.969517	+	0.245024i	$0.921204\pi$
$788$	28.4728	+	87.6303i	1.01430	+	3.12170i
$789$		0			0
$790$	61.4496	+	38.9510i	2.18628	+	1.38581i
$791$	5.86182	+	18.0408i	0.208422	+	0.641458i
$792$		0			0
$793$	−25.3266			−0.899375
$794$	27.5100	−	19.9872i	0.976294	−	0.709319i
$795$		0			0
$796$	−32.6193	−	23.6993i	−1.15616	−	0.839998i
$797$	2.70538	+	1.96557i	0.0958295	+	0.0696242i	0.634668	−	0.772785i	$-0.281137\pi$
$797$	2.70538	+	1.96557i	0.0958295	+	0.0696242i	−0.538839	+	0.842409i	$0.681137\pi$
$798$		0			0
$799$	−35.7355			−1.26423
$800$	−1.58201	+	1.48880i	−0.0559326	+	0.0526370i
$801$		0			0
$802$	−20.7994	+	64.0140i	−0.734453	+	2.26041i
$803$	4.96901	+	3.61019i	0.175352	+	0.127401i
$804$		0			0
$805$	−11.8817	+	0.753920i	−0.418775	+	0.0265722i
$806$	−47.4866	+	34.5010i	−1.67264	+	1.21525i
$807$		0			0
$808$	−6.79957	+	4.94017i	−0.239208	+	0.173795i
$809$	−10.5954	−	32.6094i	−0.372516	−	1.14649i	−0.945140	−	0.326667i	$-0.894074\pi$
$809$	−10.5954	−	32.6094i	−0.372516	−	1.14649i	0.572624	−	0.819818i	$-0.305926\pi$
$810$		0			0
$811$	−1.07152	+	3.29778i	−0.0376260	+	0.115801i	−0.968105	−	0.250543i	$-0.919391\pi$
$811$	−1.07152	+	3.29778i	−0.0376260	+	0.115801i	0.930479	+	0.366344i	$0.119391\pi$
$812$	−13.1274	−	40.4020i	−0.460682	−	1.41783i
$813$		0			0
$814$	14.1845	−	43.6554i	0.497167	−	1.53012i
$815$	17.4521	−	14.4534i	0.611320	−	0.506279i
$816$		0			0
$817$	6.30926	−	4.58394i	0.220733	−	0.160372i
$818$	−32.2422			−1.12732
$819$		0			0
$820$	47.8328	−	3.03510i	1.67040	−	0.105990i
$821$	−11.8771	−	8.62922i	−0.414514	−	0.301162i	0.360913	−	0.932600i	$-0.382465\pi$
$821$	−11.8771	−	8.62922i	−0.414514	−	0.301162i	−0.775427	+	0.631438i	$0.782465\pi$
$822$		0			0
$823$	−6.44912	+	19.8483i	−0.224802	+	0.691870i	0.773510	+	0.633785i	$0.218499\pi$
$823$	−6.44912	+	19.8483i	−0.224802	+	0.691870i	−0.998312	+	0.0580851i	$0.981501\pi$
$824$	−75.9223			−2.64488
$825$		0			0
$826$	−14.5285			−0.505512
$827$	−13.9946	+	43.0710i	−0.486641	+	1.49773i	0.342950	+	0.939354i	$0.388574\pi$
$827$	−13.9946	+	43.0710i	−0.486641	+	1.49773i	−0.829590	+	0.558372i	$0.811426\pi$
$828$		0			0
$829$	7.81291	+	5.67641i	0.271354	+	0.197150i	0.715137	−	0.698984i	$-0.246364\pi$
$829$	7.81291	+	5.67641i	0.271354	+	0.197150i	−0.443784	+	0.896134i	$0.646364\pi$
$830$	16.6315	−	13.7738i	0.577287	−	0.478094i
$831$		0			0
$832$	27.5502			0.955131
$833$	−19.7690	+	14.3630i	−0.684955	+	0.497649i
$834$		0			0
$835$	2.85386	+	1.80897i	0.0987620	+	0.0626022i
$836$	−12.3009	+	37.8583i	−0.425436	+	1.30936i
$837$		0			0
$838$	−6.67198	−	20.5342i	−0.230480	−	0.709344i
$839$	7.77848	−	23.9397i	0.268543	−	0.826490i	−0.722313	−	0.691566i	$-0.756921\pi$
$839$	7.77848	−	23.9397i	0.268543	−	0.826490i	0.990856	−	0.134924i	$-0.0430789\pi$
$840$		0			0
$841$	−5.94919	−	18.3097i	−0.205144	−	0.631370i
$842$	−73.9874	+	53.7550i	−2.54977	+	1.85252i
$843$		0			0
$844$	−58.4159	+	42.4416i	−2.01076	+	1.46090i
$845$	−4.82340	−	3.05740i	−0.165930	−	0.105178i
$846$		0			0
$847$	−0.917269	−	0.666435i	−0.0315177	−	0.0228990i
$848$	11.7070	−	36.0305i	0.402021	−	1.23729i
$849$		0			0
$850$	54.0633	+	29.6462i	1.85436	+	1.01686i
$851$	8.91196			0.305498
$852$		0			0
$853$	2.59571	+	1.88589i	0.0888753	+	0.0645717i	0.631336	−	0.775510i	$-0.282507\pi$
$853$	2.59571	+	1.88589i	0.0888753	+	0.0645717i	−0.542460	+	0.840081i	$0.682507\pi$
$854$	−53.2222	−	38.6682i	−1.82123	−	1.32320i
$855$		0			0
$856$	60.9069	−	44.2514i	2.08175	−	1.51248i
$857$	−19.4569			−0.664634			−0.332317	−	0.943168i	$-0.607830\pi$
$857$	−19.4569			−0.664634			−0.332317	+	0.943168i	$0.607830\pi$
$858$		0			0
$859$	5.20173	+	16.0093i	0.177481	+	0.546230i	0.999738	−	0.0228862i	$-0.00728553\pi$
$859$	5.20173	+	16.0093i	0.177481	+	0.546230i	−0.822257	+	0.569116i	$0.807286\pi$
$860$	−5.55498	+	21.6834i	−0.189423	+	0.739398i
$861$		0			0
$862$	−20.0772	−	61.7914i	−0.683833	−	2.10462i
$863$	−1.17803	−	3.62560i	−0.0401006	−	0.123417i	0.929002	−	0.370074i	$-0.120668\pi$
$863$	−1.17803	−	3.62560i	−0.0401006	−	0.123417i	−0.969103	+	0.246657i	$0.920668\pi$
$864$		0			0
$865$	−30.9192	+	1.96189i	−1.05129	+	0.0667063i
$866$	−26.3910	−	81.2231i	−0.896802	−	2.76007i
$867$		0			0
$868$	−101.259			−3.43697
$869$	35.2358	−	25.6003i	1.19529	−	0.868431i
$870$		0			0
$871$	−4.83497	−	3.51281i	−0.163827	−	0.119027i
$872$	−38.2863	−	27.8166i	−1.29654	−	0.941990i
$873$		0			0
$874$	−11.6367			−0.393619
$875$	−34.8291	−	16.3211i	−1.17744	−	0.551753i
$876$		0			0
$877$	−7.95569	+	24.4851i	−0.268644	+	0.826803i	0.722187	+	0.691698i	$0.243137\pi$
$877$	−7.95569	+	24.4851i	−0.268644	+	0.826803i	−0.990831	+	0.135105i	$0.956863\pi$
$878$	39.5911	+	28.7646i	1.33613	+	0.970759i
$879$		0			0
$880$	−10.0482	−	25.3393i	−0.338726	−	0.854188i
$881$	36.6110	−	26.5995i	1.23346	−	0.896159i	0.236313	−	0.971677i	$-0.424061\pi$
$881$	36.6110	−	26.5995i	1.23346	−	0.896159i	0.997144	+	0.0755181i	$0.0240611\pi$
$882$		0			0
$883$	−35.9186	+	26.0964i	−1.20876	+	0.878212i	−0.995117	−	0.0987003i	$-0.968531\pi$
$883$	−35.9186	+	26.0964i	−1.20876	+	0.878212i	−0.213639	+	0.976913i	$0.568531\pi$
$884$	−19.9611	−	61.4340i	−0.671365	−	2.06625i
$885$		0			0
$886$	3.12850	−	9.62853i	0.105104	−	0.323477i
$887$	12.0495	+	37.0844i	0.404581	+	1.24517i	0.921245	+	0.388984i	$0.127174\pi$
$887$	12.0495	+	37.0844i	0.404581	+	1.24517i	−0.516664	+	0.856189i	$0.672826\pi$
$888$		0			0
$889$	1.05470	−	3.24602i	0.0353734	−	0.108868i
$890$	−11.5565	+	45.1097i	−0.387374	+	1.51208i
$891$		0			0
$892$	−55.1119	+	40.0411i	−1.84528	+	1.34068i
$893$	21.7890			0.729142
$894$		0			0
$895$	8.02188	−	31.3127i	0.268142	−	1.04667i
$896$	55.4764	+	40.3059i	1.85334	+	1.34653i
$897$		0			0
$898$	−6.29517	+	19.3745i	−0.210072	+	0.646537i
$899$	23.2356			0.774952
$900$		0			0
$901$	51.2995			1.70903
$902$	13.3500	−	41.0872i	0.444508	−	1.36805i
$903$		0			0
$904$	−21.2812	−	15.4617i	−0.707803	−	0.514249i
$905$	32.4649	+	20.5785i	1.07917	+	0.684052i
$906$		0			0
$907$	11.0201			0.365915			0.182958	−	0.983121i	$-0.441433\pi$
$907$	11.0201			0.365915			0.182958	+	0.983121i	$0.441433\pi$
$908$	−13.8506	+	10.0630i	−0.459648	+	0.333954i
$909$		0			0
$910$	22.3654	+	56.4004i	0.741407	+	1.86966i
$911$	16.3540	−	50.3325i	0.541833	−	1.66759i	−0.186571	−	0.982441i	$-0.559737\pi$
$911$	16.3540	−	50.3325i	0.541833	−	1.66759i	0.728404	−	0.685148i	$-0.240263\pi$
$912$		0			0
$913$	−3.99477	−	12.2946i	−0.132207	−	0.406893i
$914$	−15.5172	+	47.7570i	−0.513263	+	1.57966i
$915$		0			0
$916$	24.8277	+	76.4119i	0.820331	+	2.52472i
$917$	35.1010	−	25.5023i	1.15914	−	0.842162i
$918$		0			0
$919$	38.5129	−	27.9812i	1.27042	−	0.923016i	0.271203	−	0.962522i	$-0.412579\pi$
$919$	38.5129	−	27.9812i	1.27042	−	0.923016i	0.999219	+	0.0395064i	$0.0125786\pi$
$920$	12.7153	−	10.5305i	0.419212	−	0.347181i
$921$		0			0
$922$	−56.6388	−	41.1505i	−1.86530	−	1.35522i
$923$	−0.713080	+	2.19463i	−0.0234713	+	0.0722372i
$924$		0			0
$925$	25.2454	+	13.8436i	0.830063	+	0.455175i
$926$	−97.8059			−3.21410
$927$		0			0
$928$	−1.09745	−	0.797343i	−0.0360255	−	0.0261741i
$929$	17.5465	+	12.7483i	0.575682	+	0.418258i	0.837165	−	0.546951i	$-0.184211\pi$
$929$	17.5465	+	12.7483i	0.575682	+	0.418258i	−0.261483	+	0.965208i	$0.584211\pi$
$930$		0			0
$931$	12.0538	−	8.75757i	0.395046	−	0.287018i
$932$	1.34848			0.0441708
$933$		0			0
$934$	−6.13972	−	18.8961i	−0.200898	−	0.618300i
$935$	28.4279	−	23.5433i	0.929692	−	0.769947i
$936$		0			0
$937$	0.680112	+	2.09317i	0.0222183	+	0.0683809i	0.961551	−	0.274627i	$-0.0885543\pi$
$937$	0.680112	+	2.09317i	0.0222183	+	0.0683809i	−0.939333	+	0.343008i	$0.888554\pi$
$938$	−4.79708	−	14.7639i	−0.156630	−	0.482058i
$939$		0			0
$940$	−48.1655	+	39.8894i	−1.57098	+	1.30105i
$941$	5.18833	+	15.9680i	0.169135	+	0.520543i	0.999317	−	0.0369489i	$-0.0117639\pi$
$941$	5.18833	+	15.9680i	0.169135	+	0.520543i	−0.830183	+	0.557492i	$0.811764\pi$
$942$		0			0
$943$	8.38767			0.273140
$944$	5.22489	−	3.79611i	0.170056	−	0.123553i
$945$		0			0
$946$	16.3226	+	11.8591i	0.530695	+	0.385572i
$947$	29.6207	+	21.5207i	0.962544	+	0.699329i	0.953740	−	0.300632i	$-0.0971975\pi$
$947$	29.6207	+	21.5207i	0.962544	+	0.699329i	0.00880418	+	0.999961i	$0.497198\pi$
$948$		0			0
$949$	6.07711			0.197271
$950$	−32.9641	−	18.0762i	−1.06950	−	0.586470i
$951$		0			0
$952$	25.6295	−	78.8796i	0.830658	−	2.55650i
$953$	35.5383	+	25.8201i	1.15120	+	0.836394i	0.988640	−	0.150305i	$-0.0480256\pi$
$953$	35.5383	+	25.8201i	1.15120	+	0.836394i	0.162558	+	0.986699i	$0.448026\pi$
$954$		0			0
$955$	−18.1557	+	15.0360i	−0.587503	+	0.486555i
$956$	−22.9251	+	16.6561i	−0.741450	+	0.538695i
$957$		0			0
$958$	55.4010	−	40.2512i	1.78993	−	1.30046i
$959$	8.76068	+	26.9626i	0.282897	+	0.870668i
$960$		0			0
$961$	7.53541	−	23.1916i	0.243078	−	0.748116i
$962$	−14.0346	−	43.1940i	−0.452493	−	1.39263i
$963$		0			0
$964$	−15.3530	+	47.2517i	−0.494487	+	1.52188i
$965$	0.562897	+	1.41950i	0.0181203	+	0.0456952i
$966$		0			0
$967$	−19.8059	+	14.3899i	−0.636916	+	0.462747i	−0.858789	−	0.512329i	$-0.828783\pi$
$967$	−19.8059	+	14.3899i	−0.636916	+	0.462747i	0.221873	+	0.975076i	$0.428783\pi$
$968$	1.57227			0.0505348
$969$		0			0
$970$	49.0962	+	31.1206i	1.57639	+	0.999221i
$971$	−15.8773	−	11.5355i	−0.509526	−	0.370192i	0.303118	−	0.952953i	$-0.401972\pi$
$971$	−15.8773	−	11.5355i	−0.509526	−	0.370192i	−0.812644	+	0.582761i	$0.801972\pi$
$972$		0			0
$973$	−8.57257	+	26.3837i	−0.274824	+	0.845822i
$974$	37.1344			1.18986
$975$		0			0
$976$	29.2438			0.936070
$977$	−9.43236	+	29.0298i	−0.301768	+	0.928746i	0.679096	+	0.734050i	$0.262372\pi$
$977$	−9.43236	+	29.0298i	−0.301768	+	0.928746i	−0.980864	+	0.194696i	$0.937628\pi$
$978$		0			0
$979$	22.5526	+	16.3854i	0.720785	+	0.523681i
$980$	−10.6127	+	41.4259i	−0.339011	+	1.32330i
$981$		0			0
$982$	20.2356			0.645743
$983$	8.38590	−	6.09271i	0.267469	−	0.194327i	−0.445964	−	0.895051i	$-0.647139\pi$
$983$	8.38590	−	6.09271i	0.267469	−	0.194327i	0.713433	+	0.700723i	$0.247139\pi$
$984$		0			0
$985$	−12.9283	+	50.4644i	−0.411929	+	1.60793i
$986$	−11.8977	+	36.6173i	−0.378899	+	1.16613i
$987$		0			0
$988$	12.1709	+	37.4582i	0.387208	+	1.19170i
$989$	−1.21048	+	3.72546i	−0.0384909	+	0.118463i
$990$		0			0
$991$	−3.12376	−	9.61395i	−0.0992295	−	0.305397i	0.889103	−	0.457707i	$-0.151329\pi$
$991$	−3.12376	−	9.61395i	−0.0992295	−	0.305397i	−0.988333	+	0.152309i	$0.951329\pi$
$992$	−2.61591	+	1.90057i	−0.0830552	+	0.0603431i
$993$		0			0
$994$	−4.84921	+	3.52316i	−0.153808	+	0.111748i
$995$	−8.40308	−	21.1906i	−0.266395	−	0.671787i
$996$		0			0
$997$	−17.2838	−	12.5574i	−0.547382	−	0.397697i	0.279437	−	0.960164i	$-0.409852\pi$
$997$	−17.2838	−	12.5574i	−0.547382	−	0.397697i	−0.826819	+	0.562467i	$0.809852\pi$
$998$	18.4002	−	56.6300i	0.582448	−	1.79259i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.d.46.1		12
3.2	odd	2		75.2.g.c.46.3	yes	12
15.2	even	4		375.2.i.d.274.5		24
15.8	even	4		375.2.i.d.274.2		24
15.14	odd	2		375.2.g.c.226.1		12
25.6	even	5	inner	225.2.h.d.181.1		12
25.9	even	10		5625.2.a.q.1.6		6
25.16	even	5		5625.2.a.p.1.1		6
75.8	even	20		375.2.i.d.349.5		24
75.17	even	20		375.2.i.d.349.2		24
75.38	even	20		1875.2.b.f.1249.2		12
75.41	odd	10		1875.2.a.j.1.6		6
75.44	odd	10		375.2.g.c.151.1		12
75.56	odd	10		75.2.g.c.31.3	✓	12
75.59	odd	10		1875.2.a.k.1.1		6
75.62	even	20		1875.2.b.f.1249.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.3	✓	12	75.56	odd	10
75.2.g.c.46.3	yes	12	3.2	odd	2
225.2.h.d.46.1		12	1.1	even	1	trivial
225.2.h.d.181.1		12	25.6	even	5	inner
375.2.g.c.151.1		12	75.44	odd	10
375.2.g.c.226.1		12	15.14	odd	2
375.2.i.d.274.2		24	15.8	even	4
375.2.i.d.274.5		24	15.2	even	4
375.2.i.d.349.2		24	75.17	even	20
375.2.i.d.349.5		24	75.8	even	20
1875.2.a.j.1.6		6	75.41	odd	10
1875.2.a.k.1.1		6	75.59	odd	10
1875.2.b.f.1249.2		12	75.38	even	20
1875.2.b.f.1249.11		12	75.62	even	20
5625.2.a.p.1.1		6	25.16	even	5
5625.2.a.q.1.6		6	25.9	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.754089 + 2.32085i) q^{2} +(-3.19965 - 2.32468i) q^{4} +(-0.824264 - 2.07860i) q^{5} -3.44028 q^{7} +(3.85959 - 2.80415i) q^{8} +O(q^{10})\)	\(q+(-0.754089 + 2.32085i) q^{2} +(-3.19965 - 2.32468i) q^{4} +(-0.824264 - 2.07860i) q^{5} -3.44028 q^{7} +(3.85959 - 2.80415i) q^{8} +(5.44569 - 0.345540i) q^{10} +(1.00942 - 3.10669i) q^{11} +(-0.998755 - 3.07385i) q^{13} +(2.59428 - 7.98437i) q^{14} +(1.15323 + 3.54927i) q^{16} +(-4.08826 + 2.97030i) q^{17} +(2.49274 - 1.81108i) q^{19} +(-2.19473 + 8.56695i) q^{20} +(6.44895 + 4.68544i) q^{22} +(-0.478250 + 1.47190i) q^{23} +(-3.64118 + 3.42664i) q^{25} +7.88709 q^{26} +(11.0077 + 7.99756i) q^{28} +(-2.52590 - 1.83517i) q^{29} +(-6.02080 + 4.37437i) q^{31} +0.434479 q^{32} +(-3.81069 - 11.7281i) q^{34} +(2.83570 + 7.15098i) q^{35} +(-1.77944 - 5.47655i) q^{37} +(2.32349 + 7.15098i) q^{38} +(-9.01004 - 5.71118i) q^{40} +(-1.67476 - 5.15437i) q^{41} +2.53106 q^{43} +(-10.4519 + 7.59371i) q^{44} +(-3.05541 - 2.21989i) q^{46} +(5.72106 + 4.15659i) q^{47} +4.83555 q^{49} +(-5.20693 - 11.0346i) q^{50} +(-3.95006 + 12.1570i) q^{52} +(-8.21277 - 5.96693i) q^{53} +(-7.28960 + 0.462540i) q^{55} +(-13.2781 + 9.64708i) q^{56} +(6.16391 - 4.47834i) q^{58} +(-0.534773 - 1.64586i) q^{59} +(2.42149 - 7.45259i) q^{61} +(-5.61202 - 17.2720i) q^{62} +(-2.63409 + 8.10689i) q^{64} +(-5.56608 + 4.60968i) q^{65} +(1.49595 - 1.08687i) q^{67} +19.9860 q^{68} +(-18.7347 + 1.18876i) q^{70} +(-0.577613 - 0.419660i) q^{71} +(-0.581036 + 1.78825i) q^{73} +14.0521 q^{74} -12.1861 q^{76} +(-3.47270 + 10.6879i) q^{77} +(10.7868 + 7.83708i) q^{79} +(6.42695 - 5.32263i) q^{80} +13.2254 q^{82} +(3.20166 - 2.32614i) q^{83} +(9.54388 + 6.04956i) q^{85} +(-1.90864 + 5.87419i) q^{86} +(-4.81567 - 14.8211i) q^{88} +(-2.63713 + 8.11624i) q^{89} +(3.43600 + 10.5749i) q^{91} +(4.95193 - 3.59779i) q^{92} +(-13.9610 + 10.1433i) q^{94} +(-5.81919 - 3.68860i) q^{95} +(8.61831 + 6.26157i) q^{97} +(-3.64643 + 11.2226i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

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