LMFDB - Embedded newform 225.2.h.b.181.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	225.181
Dual form			225.2.h.b.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 1.53884i) q^{2} +(-0.500000 + 0.363271i) q^{4} +(0.690983 - 2.12663i) q^{5} +0.618034 q^{7} +(1.80902 + 1.31433i) q^{8} +O(q^{10})$	\(q+(0.500000 + 1.53884i) q^{2} +(-0.500000 + 0.363271i) q^{4} +(0.690983 - 2.12663i) q^{5} +0.618034 q^{7} +(1.80902 + 1.31433i) q^{8} +3.61803 q^{10} +(1.61803 + 4.97980i) q^{11} +(0.572949 - 1.76336i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.50000 + 4.61653i) q^{16} +(-4.23607 - 3.07768i) q^{17} +(-0.690983 - 0.502029i) q^{19} +(0.427051 + 1.31433i) q^{20} +(-6.85410 + 4.97980i) q^{22} +(-1.16312 - 3.57971i) q^{23} +(-4.04508 - 2.93893i) q^{25} +3.00000 q^{26} +(-0.309017 + 0.224514i) q^{28} +(-2.92705 + 2.12663i) q^{29} +(2.42705 + 1.76336i) q^{31} -3.38197 q^{32} +(2.61803 - 8.05748i) q^{34} +(0.427051 - 1.31433i) q^{35} +(-0.0729490 + 0.224514i) q^{37} +(0.427051 - 1.31433i) q^{38} +(4.04508 - 2.93893i) q^{40} +(0.236068 - 0.726543i) q^{41} -4.85410 q^{43} +(-2.61803 - 1.90211i) q^{44} +(4.92705 - 3.57971i) q^{46} +(0.500000 - 0.363271i) q^{47} -6.61803 q^{49} +(2.50000 - 7.69421i) q^{50} +(0.354102 + 1.08981i) q^{52} +(-2.80902 + 2.04087i) q^{53} +11.7082 q^{55} +(1.11803 + 0.812299i) q^{56} +(-4.73607 - 3.44095i) q^{58} +(3.35410 - 10.3229i) q^{59} +(2.69098 + 8.28199i) q^{61} +(-1.50000 + 4.61653i) q^{62} +(1.30902 + 4.02874i) q^{64} +(-3.35410 - 2.43690i) q^{65} +(-3.85410 - 2.80017i) q^{67} +3.23607 q^{68} +2.23607 q^{70} +(-5.35410 + 3.88998i) q^{71} +(-2.78115 - 8.55951i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(1.00000 + 3.07768i) q^{77} +(6.54508 - 4.75528i) q^{79} +(8.78115 + 6.37988i) q^{80} +1.23607 q^{82} +(-5.04508 - 3.66547i) q^{83} +(-9.47214 + 6.88191i) q^{85} +(-2.42705 - 7.46969i) q^{86} +(-3.61803 + 11.1352i) q^{88} +(2.76393 + 8.50651i) q^{89} +(0.354102 - 1.08981i) q^{91} +(1.88197 + 1.36733i) q^{92} +(0.809017 + 0.587785i) q^{94} +(-1.54508 + 1.12257i) q^{95} +(3.11803 - 2.26538i) q^{97} +(-3.30902 - 10.1841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 5 * q^5 - 2 * q^7 + 5 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8} + 10 q^{10} + 2 q^{11} + 9 q^{13} - q^{14} - 6 q^{16} - 8 q^{17} - 5 q^{19} - 5 q^{20} - 14 q^{22} + 11 q^{23} - 5 q^{25} + 12 q^{26} + q^{28} - 5 q^{29} + 3 q^{31} - 18 q^{32} + 6 q^{34} - 5 q^{35} - 7 q^{37} - 5 q^{38} + 5 q^{40} - 8 q^{41} - 6 q^{43} - 6 q^{44} + 13 q^{46} + 2 q^{47} - 22 q^{49} + 10 q^{50} - 12 q^{52} - 9 q^{53} + 20 q^{55} - 10 q^{58} + 13 q^{61} - 6 q^{62} + 3 q^{64} - 2 q^{67} + 4 q^{68} - 8 q^{71} + 9 q^{73} - 6 q^{74} + 20 q^{76} + 4 q^{77} + 15 q^{79} + 15 q^{80} - 4 q^{82} - 9 q^{83} - 20 q^{85} - 3 q^{86} - 10 q^{88} + 20 q^{89} - 12 q^{91} + 12 q^{92} + q^{94} + 5 q^{95} + 8 q^{97} - 11 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 5 * q^5 - 2 * q^7 + 5 * q^8 + 10 * q^10 + 2 * q^11 + 9 * q^13 - q^14 - 6 * q^16 - 8 * q^17 - 5 * q^19 - 5 * q^20 - 14 * q^22 + 11 * q^23 - 5 * q^25 + 12 * q^26 + q^28 - 5 * q^29 + 3 * q^31 - 18 * q^32 + 6 * q^34 - 5 * q^35 - 7 * q^37 - 5 * q^38 + 5 * q^40 - 8 * q^41 - 6 * q^43 - 6 * q^44 + 13 * q^46 + 2 * q^47 - 22 * q^49 + 10 * q^50 - 12 * q^52 - 9 * q^53 + 20 * q^55 - 10 * q^58 + 13 * q^61 - 6 * q^62 + 3 * q^64 - 2 * q^67 + 4 * q^68 - 8 * q^71 + 9 * q^73 - 6 * q^74 + 20 * q^76 + 4 * q^77 + 15 * q^79 + 15 * q^80 - 4 * q^82 - 9 * q^83 - 20 * q^85 - 3 * q^86 - 10 * q^88 + 20 * q^89 - 12 * q^91 + 12 * q^92 + q^94 + 5 * q^95 + 8 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.500000	+	1.53884i	0.353553	+	1.08813i	0.956844	+	0.290604i	$0.0938561\pi$
$2$	0.500000	+	1.53884i	0.353553	+	1.08813i	−0.603290	+	0.797522i	$0.706144\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	0.690983	−	2.12663i	0.309017	−	0.951057i
$5$	0.690983	−	2.12663i	0.309017	−	0.951057i
$6$		0			0
$7$	0.618034			0.233595			0.116797	−	0.993156i	$-0.462737\pi$
$7$	0.618034			0.233595			0.116797	+	0.993156i	$0.462737\pi$
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$		0			0
$10$	3.61803			1.14412
$11$	1.61803	+	4.97980i	0.487856	+	1.50147i	0.827802	+	0.561020i	$0.189591\pi$
$11$	1.61803	+	4.97980i	0.487856	+	1.50147i	−0.339946	+	0.940445i	$0.610409\pi$
$12$		0			0
$13$	0.572949	−	1.76336i	0.158907	−	0.489067i	−0.839628	−	0.543161i	$-0.817227\pi$
$13$	0.572949	−	1.76336i	0.158907	−	0.489067i	0.998536	+	0.0540944i	$0.0172272\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$		0			0
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	−4.23607	−	3.07768i	−1.02740	−	0.746448i	−0.0596113	−	0.998222i	$-0.518986\pi$
$17$	−4.23607	−	3.07768i	−1.02740	−	0.746448i	−0.967786	+	0.251774i	$0.918986\pi$
$18$		0			0
$19$	−0.690983	−	0.502029i	−0.158522	−	0.115173i	0.505696	−	0.862712i	$-0.331236\pi$
$19$	−0.690983	−	0.502029i	−0.158522	−	0.115173i	−0.664219	+	0.747538i	$0.731236\pi$
$20$	0.427051	+	1.31433i	0.0954915	+	0.293893i
$21$		0			0
$22$	−6.85410	+	4.97980i	−1.46130	+	1.06170i
$23$	−1.16312	−	3.57971i	−0.242527	−	0.746422i	−0.996033	−	0.0889808i	$-0.971639\pi$
$23$	−1.16312	−	3.57971i	−0.242527	−	0.746422i	0.753506	−	0.657441i	$-0.228361\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$	3.00000			0.588348
$27$		0			0
$28$	−0.309017	+	0.224514i	−0.0583987	+	0.0424292i
$29$	−2.92705	+	2.12663i	−0.543540	+	0.394905i	−0.825398	−	0.564551i	$-0.809049\pi$
$29$	−2.92705	+	2.12663i	−0.543540	+	0.394905i	0.281858	+	0.959456i	$0.409049\pi$
$30$		0			0
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	0.784008	−	0.620750i	$-0.213172\pi$
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	−0.348097	+	0.937459i	$0.613172\pi$
$32$	−3.38197			−0.597853
$33$		0			0
$34$	2.61803	−	8.05748i	0.448989	−	1.38185i
$35$	0.427051	−	1.31433i	0.0721848	−	0.222162i
$36$		0			0
$37$	−0.0729490	+	0.224514i	−0.0119927	+	0.0369099i	−0.956874	−	0.290504i	$-0.906177\pi$
$37$	−0.0729490	+	0.224514i	−0.0119927	+	0.0369099i	0.944881	+	0.327414i	$0.106177\pi$
$38$	0.427051	−	1.31433i	0.0692768	−	0.213212i
$39$		0			0
$40$	4.04508	−	2.93893i	0.639584	−	0.464685i
$41$	0.236068	−	0.726543i	0.0368676	−	0.113467i	−0.930929	−	0.365200i	$-0.881001\pi$
$41$	0.236068	−	0.726543i	0.0368676	−	0.113467i	0.967797	+	0.251733i	$0.0810006\pi$
$42$		0			0
$43$	−4.85410			−0.740244			−0.370122	−	0.928983i	$-0.620684\pi$
$43$	−4.85410			−0.740244			−0.370122	+	0.928983i	$0.620684\pi$
$44$	−2.61803	−	1.90211i	−0.394683	−	0.286754i
$45$		0			0
$46$	4.92705	−	3.57971i	0.726454	−	0.527800i
$47$	0.500000	−	0.363271i	0.0729325	−	0.0529886i	−0.550722	−	0.834689i	$-0.685647\pi$
$47$	0.500000	−	0.363271i	0.0729325	−	0.0529886i	0.623654	+	0.781700i	$0.285647\pi$
$48$		0			0
$49$	−6.61803			−0.945433
$50$	2.50000	−	7.69421i	0.353553	−	1.08813i
$51$		0			0
$52$	0.354102	+	1.08981i	0.0491051	+	0.151130i
$53$	−2.80902	+	2.04087i	−0.385848	+	0.280335i	−0.763752	−	0.645510i	$-0.776645\pi$
$53$	−2.80902	+	2.04087i	−0.385848	+	0.280335i	0.377904	+	0.925845i	$0.376645\pi$
$54$		0			0
$55$	11.7082			1.57873
$56$	1.11803	+	0.812299i	0.149404	+	0.108548i
$57$		0			0
$58$	−4.73607	−	3.44095i	−0.621876	−	0.451820i
$59$	3.35410	−	10.3229i	0.436667	−	1.34392i	−0.454702	−	0.890644i	$-0.650254\pi$
$59$	3.35410	−	10.3229i	0.436667	−	1.34392i	0.891369	−	0.453279i	$-0.149746\pi$
$60$		0			0
$61$	2.69098	+	8.28199i	0.344545	+	1.06040i	0.961827	+	0.273659i	$0.0882338\pi$
$61$	2.69098	+	8.28199i	0.344545	+	1.06040i	−0.617282	+	0.786742i	$0.711766\pi$
$62$	−1.50000	+	4.61653i	−0.190500	+	0.586299i
$63$		0			0
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	−3.35410	−	2.43690i	−0.416025	−	0.302260i
$66$		0			0
$67$	−3.85410	−	2.80017i	−0.470853	−	0.342095i	0.326920	−	0.945052i	$-0.393989\pi$
$67$	−3.85410	−	2.80017i	−0.470853	−	0.342095i	−0.797774	+	0.602957i	$0.793989\pi$
$68$	3.23607			0.392431
$69$		0			0
$70$	2.23607			0.267261
$71$	−5.35410	+	3.88998i	−0.635415	+	0.461656i	−0.858272	−	0.513195i	$-0.828462\pi$
$71$	−5.35410	+	3.88998i	−0.635415	+	0.461656i	0.222857	+	0.974851i	$0.428462\pi$
$72$		0			0
$73$	−2.78115	−	8.55951i	−0.325509	−	1.00181i	−0.971210	−	0.238224i	$-0.923435\pi$
$73$	−2.78115	−	8.55951i	−0.325509	−	1.00181i	0.645701	−	0.763590i	$-0.276565\pi$
$74$	−0.381966			−0.0444026
$75$		0			0
$76$	0.527864			0.0605502
$77$	1.00000	+	3.07768i	0.113961	+	0.350735i
$78$		0			0
$79$	6.54508	−	4.75528i	0.736380	−	0.535011i	−0.155196	−	0.987884i	$-0.549601\pi$
$79$	6.54508	−	4.75528i	0.736380	−	0.535011i	0.891575	+	0.452873i	$0.149601\pi$
$80$	8.78115	+	6.37988i	0.981763	+	0.713292i
$81$		0			0
$82$	1.23607			0.136501
$83$	−5.04508	−	3.66547i	−0.553770	−	0.402337i	0.275404	−	0.961329i	$-0.411189\pi$
$83$	−5.04508	−	3.66547i	−0.553770	−	0.402337i	−0.829174	+	0.558991i	$0.811189\pi$
$84$		0			0
$85$	−9.47214	+	6.88191i	−1.02740	+	0.746448i
$86$	−2.42705	−	7.46969i	−0.261716	−	0.805478i
$87$		0			0
$88$	−3.61803	+	11.1352i	−0.385684	+	1.18701i
$89$	2.76393	+	8.50651i	0.292976	+	0.901688i	0.983894	+	0.178754i	$0.0572068\pi$
$89$	2.76393	+	8.50651i	0.292976	+	0.901688i	−0.690918	+	0.722934i	$0.742793\pi$
$90$		0			0
$91$	0.354102	−	1.08981i	0.0371200	−	0.114244i
$92$	1.88197	+	1.36733i	0.196209	+	0.142554i
$93$		0			0
$94$	0.809017	+	0.587785i	0.0834437	+	0.0606254i
$95$	−1.54508	+	1.12257i	−0.158522	+	0.115173i
$96$		0			0
$97$	3.11803	−	2.26538i	0.316588	−	0.230015i	−0.418130	−	0.908387i	$-0.637314\pi$
$97$	3.11803	−	2.26538i	0.316588	−	0.230015i	0.734718	+	0.678372i	$0.237314\pi$
$98$	−3.30902	−	10.1841i	−0.334261	−	1.02875i
$99$		0			0
$100$	3.09017			0.309017
$101$	−1.47214			−0.146483			−0.0732415	−	0.997314i	$-0.523334\pi$
$101$	−1.47214			−0.146483			−0.0732415	+	0.997314i	$0.523334\pi$
$102$		0			0
$103$	−6.92705	+	5.03280i	−0.682543	+	0.495896i	−0.874200	−	0.485566i	$-0.838614\pi$
$103$	−6.92705	+	5.03280i	−0.682543	+	0.495896i	0.191658	+	0.981462i	$0.438614\pi$
$104$	3.35410	−	2.43690i	0.328897	−	0.238957i
$105$		0			0
$106$	−4.54508	−	3.30220i	−0.441458	−	0.320738i
$107$	16.4164			1.58703			0.793517	−	0.608548i	$-0.208248\pi$
$107$	16.4164			1.58703			0.793517	+	0.608548i	$0.208248\pi$
$108$		0			0
$109$	3.09017	−	9.51057i	0.295985	−	0.910947i	−0.686904	−	0.726748i	$-0.741031\pi$
$109$	3.09017	−	9.51057i	0.295985	−	0.910947i	0.982889	−	0.184199i	$-0.0589691\pi$
$110$	5.85410	+	18.0171i	0.558167	+	1.71786i
$111$		0			0
$112$	−0.927051	+	2.85317i	−0.0875981	+	0.269599i
$113$	−5.20820	+	16.0292i	−0.489947	+	1.50790i	0.334740	+	0.942311i	$0.391352\pi$
$113$	−5.20820	+	16.0292i	−0.489947	+	1.50790i	−0.824687	+	0.565590i	$0.808648\pi$
$114$		0			0
$115$	−8.41641			−0.784834
$116$	0.690983	−	2.12663i	0.0641562	−	0.197452i
$117$		0			0
$118$	17.5623			1.61674
$119$	−2.61803	−	1.90211i	−0.239995	−	0.174366i
$120$		0			0
$121$	−13.2812	+	9.64932i	−1.20738	+	0.877211i
$122$	−11.3992	+	8.28199i	−1.03203	+	0.749817i
$123$		0			0
$124$	−1.85410			−0.166503
$125$	−9.04508	+	6.57164i	−0.809017	+	0.587785i
$126$		0			0
$127$	6.14590	+	18.9151i	0.545360	+	1.67845i	0.720132	+	0.693837i	$0.244081\pi$
$127$	6.14590	+	18.9151i	0.545360	+	1.67845i	−0.174772	+	0.984609i	$0.555919\pi$
$128$	−11.0172	+	8.00448i	−0.973794	+	0.707503i
$129$		0			0
$130$	2.07295	−	6.37988i	0.181810	−	0.559553i
$131$	5.50000	+	3.99598i	0.480537	+	0.349131i	0.801534	−	0.597950i	$-0.204018\pi$
$131$	5.50000	+	3.99598i	0.480537	+	0.349131i	−0.320996	+	0.947080i	$0.604018\pi$
$132$		0			0
$133$	−0.427051	−	0.310271i	−0.0370300	−	0.0269039i
$134$	2.38197	−	7.33094i	0.205771	−	0.633297i
$135$		0			0
$136$	−3.61803	−	11.1352i	−0.310244	−	0.954832i
$137$	3.69098	−	11.3597i	0.315342	−	0.970523i	−0.660271	−	0.751027i	$-0.729559\pi$
$137$	3.69098	−	11.3597i	0.315342	−	0.970523i	0.975613	−	0.219496i	$-0.0704412\pi$
$138$		0			0
$139$	1.54508	+	4.75528i	0.131052	+	0.403338i	0.994955	−	0.100321i	$-0.0319869\pi$
$139$	1.54508	+	4.75528i	0.131052	+	0.403338i	−0.863903	+	0.503659i	$0.831987\pi$
$140$	0.263932	+	0.812299i	0.0223063	+	0.0686518i
$141$		0			0
$142$	−8.66312	−	6.29412i	−0.726993	−	0.528191i
$143$	9.70820			0.811841
$144$		0			0
$145$	2.50000	+	7.69421i	0.207614	+	0.638969i
$146$	11.7812	−	8.55951i	0.975015	−	0.708390i
$147$		0			0
$148$	−0.0450850	−	0.138757i	−0.00370596	−	0.0114058i
$149$	3.94427			0.323127			0.161564	−	0.986862i	$-0.448346\pi$
$149$	3.94427			0.323127			0.161564	+	0.986862i	$0.448346\pi$
$150$		0			0
$151$	14.5623			1.18506			0.592532	−	0.805547i	$-0.298128\pi$
$151$	14.5623			1.18506			0.592532	+	0.805547i	$0.298128\pi$
$152$	−0.590170	−	1.81636i	−0.0478691	−	0.147326i
$153$		0			0
$154$	−4.23607	+	3.07768i	−0.341352	+	0.248007i
$155$	5.42705	−	3.94298i	0.435911	−	0.316708i
$156$		0			0
$157$	13.1803			1.05191			0.525953	−	0.850514i	$-0.323709\pi$
$157$	13.1803			1.05191			0.525953	+	0.850514i	$0.323709\pi$
$158$	10.5902	+	7.69421i	0.842509	+	0.612118i
$159$		0			0
$160$	−2.33688	+	7.19218i	−0.184747	+	0.568592i
$161$	−0.718847	−	2.21238i	−0.0566531	−	0.174360i
$162$		0			0
$163$	3.39919	−	10.4616i	0.266245	−	0.819417i	−0.725159	−	0.688581i	$-0.758234\pi$
$163$	3.39919	−	10.4616i	0.266245	−	0.819417i	0.991404	−	0.130836i	$-0.0417662\pi$
$164$	0.145898	+	0.449028i	0.0113927	+	0.0350632i
$165$		0			0
$166$	3.11803	−	9.59632i	0.242006	−	0.744819i
$167$	11.7812	+	8.55951i	0.911653	+	0.662355i	0.941432	−	0.337202i	$-0.109480\pi$
$167$	11.7812	+	8.55951i	0.911653	+	0.662355i	−0.0297794	+	0.999556i	$0.509480\pi$
$168$		0			0
$169$	7.73607	+	5.62058i	0.595082	+	0.432352i
$170$	−15.3262	−	11.1352i	−1.17547	−	0.854028i
$171$		0			0
$172$	2.42705	−	1.76336i	0.185061	−	0.134455i
$173$	−5.83688	−	17.9641i	−0.443770	−	1.36578i	−0.883827	−	0.467813i	$-0.845042\pi$
$173$	−5.83688	−	17.9641i	−0.443770	−	1.36578i	0.440057	−	0.897970i	$-0.354958\pi$
$174$		0			0
$175$	−2.50000	−	1.81636i	−0.188982	−	0.137304i
$176$	−25.4164			−1.91583
$177$		0			0
$178$	−11.7082	+	8.50651i	−0.877567	+	0.637590i
$179$	−0.427051	+	0.310271i	−0.0319193	+	0.0231907i	−0.603631	−	0.797264i	$-0.706280\pi$
$179$	−0.427051	+	0.310271i	−0.0319193	+	0.0231907i	0.571711	+	0.820455i	$0.306280\pi$
$180$		0			0
$181$	−0.236068	−	0.171513i	−0.0175468	−	0.0127485i	0.578977	−	0.815344i	$-0.303452\pi$
$181$	−0.236068	−	0.171513i	−0.0175468	−	0.0127485i	−0.596524	+	0.802595i	$0.703452\pi$
$182$	1.85410			0.137435
$183$		0			0
$184$	2.60081	−	8.00448i	0.191734	−	0.590098i
$185$	0.427051	+	0.310271i	0.0313974	+	0.0228116i
$186$		0			0
$187$	8.47214	−	26.0746i	0.619544	−	1.90676i
$188$	−0.118034	+	0.363271i	−0.00860851	+	0.0264943i
$189$		0			0
$190$	−2.50000	−	1.81636i	−0.181369	−	0.131772i
$191$	0.562306	−	1.73060i	0.0406870	−	0.125222i	−0.928650	−	0.370958i	$-0.879030\pi$
$191$	0.562306	−	1.73060i	0.0406870	−	0.125222i	0.969337	+	0.245736i	$0.0790295\pi$
$192$		0			0
$193$	7.70820			0.554849			0.277424	−	0.960747i	$-0.410519\pi$
$193$	7.70820			0.554849			0.277424	+	0.960747i	$0.410519\pi$
$194$	5.04508	+	3.66547i	0.362216	+	0.263165i
$195$		0			0
$196$	3.30902	−	2.40414i	0.236358	−	0.171724i
$197$	3.00000	−	2.17963i	0.213741	−	0.155292i	−0.475764	−	0.879573i	$-0.657828\pi$
$197$	3.00000	−	2.17963i	0.213741	−	0.155292i	0.689505	+	0.724281i	$0.257828\pi$
$198$		0			0
$199$	−17.5623			−1.24496			−0.622479	−	0.782636i	$-0.713875\pi$
$199$	−17.5623			−1.24496			−0.622479	+	0.782636i	$0.713875\pi$
$200$	−3.45492	−	10.6331i	−0.244299	−	0.751876i
$201$		0			0
$202$	−0.736068	−	2.26538i	−0.0517896	−	0.159392i
$203$	−1.80902	+	1.31433i	−0.126968	+	0.0922477i
$204$		0			0
$205$	−1.38197	−	1.00406i	−0.0965207	−	0.0701264i
$206$	−11.2082	−	8.14324i	−0.780913	−	0.567366i
$207$		0			0
$208$	7.28115	+	5.29007i	0.504857	+	0.366800i
$209$	1.38197	−	4.25325i	0.0955926	−	0.294204i
$210$		0			0
$211$	−2.83688	−	8.73102i	−0.195299	−	0.601068i	−0.999973	−	0.00735149i	$-0.997660\pi$
$211$	−2.83688	−	8.73102i	−0.195299	−	0.601068i	0.804674	−	0.593717i	$-0.202340\pi$
$212$	0.663119	−	2.04087i	0.0455432	−	0.140168i
$213$		0			0
$214$	8.20820	+	25.2623i	0.561101	+	1.72689i
$215$	−3.35410	+	10.3229i	−0.228748	+	0.704014i
$216$		0			0
$217$	1.50000	+	1.08981i	0.101827	+	0.0739814i
$218$	16.1803			1.09587
$219$		0			0
$220$	−5.85410	+	4.25325i	−0.394683	+	0.286754i
$221$	−7.85410	+	5.70634i	−0.528324	+	0.383850i
$222$		0			0
$223$	−0.0557281	−	0.171513i	−0.00373183	−	0.0114854i	0.949173	−	0.314754i	$-0.101922\pi$
$223$	−0.0557281	−	0.171513i	−0.00373183	−	0.0114854i	−0.952905	+	0.303269i	$0.901922\pi$
$224$	−2.09017			−0.139655
$225$		0			0
$226$	−27.2705			−1.81401
$227$	−4.56231	−	14.0413i	−0.302811	−	0.931956i	−0.980485	−	0.196594i	$-0.937012\pi$
$227$	−4.56231	−	14.0413i	−0.302811	−	0.931956i	0.677674	−	0.735362i	$-0.262988\pi$
$228$		0			0
$229$	−17.5623	+	12.7598i	−1.16055	+	0.843189i	−0.989847	−	0.142134i	$-0.954604\pi$
$229$	−17.5623	+	12.7598i	−1.16055	+	0.843189i	−0.170702	+	0.985323i	$0.554604\pi$
$230$	−4.20820	−	12.9515i	−0.277481	−	0.853998i
$231$		0			0
$232$	−8.09017			−0.531146
$233$	−2.38197	−	1.73060i	−0.156048	−	0.113375i	0.507021	−	0.861933i	$-0.330746\pi$
$233$	−2.38197	−	1.73060i	−0.156048	−	0.113375i	−0.663069	+	0.748558i	$0.730746\pi$
$234$		0			0
$235$	−0.427051	−	1.31433i	−0.0278577	−	0.0857373i
$236$	2.07295	+	6.37988i	0.134937	+	0.415295i
$237$		0			0
$238$	1.61803	−	4.97980i	0.104882	−	0.322792i
$239$	6.34346	+	19.5232i	0.410324	+	1.26285i	0.916367	+	0.400340i	$0.131108\pi$
$239$	6.34346	+	19.5232i	0.410324	+	1.26285i	−0.506043	+	0.862508i	$0.668892\pi$
$240$		0			0
$241$	0.781153	−	2.40414i	0.0503185	−	0.154864i	−0.922740	−	0.385423i	$-0.874055\pi$
$241$	0.781153	−	2.40414i	0.0503185	−	0.154864i	0.973058	+	0.230559i	$0.0740554\pi$
$242$	−21.4894	−	15.6129i	−1.38139	−	1.00364i
$243$		0			0
$244$	−4.35410	−	3.16344i	−0.278743	−	0.202519i
$245$	−4.57295	+	14.0741i	−0.292155	+	0.899161i
$246$		0			0
$247$	−1.28115	+	0.930812i	−0.0815178	+	0.0592262i
$248$	2.07295	+	6.37988i	0.131632	+	0.405123i
$249$		0			0
$250$	−14.6353	−	10.6331i	−0.925615	−	0.672499i
$251$	29.1803			1.84185			0.920923	−	0.389744i	$-0.127436\pi$
$251$	29.1803			1.84185			0.920923	+	0.389744i	$0.127436\pi$
$252$		0			0
$253$	15.9443	−	11.5842i	1.00241	−	0.728292i
$254$	−26.0344	+	18.9151i	−1.63355	+	1.18684i
$255$		0			0
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	−22.8541			−1.42560			−0.712800	−	0.701367i	$-0.752573\pi$
$257$	−22.8541			−1.42560			−0.712800	+	0.701367i	$0.752573\pi$
$258$		0			0
$259$	−0.0450850	+	0.138757i	−0.00280144	+	0.00862196i
$260$	2.56231			0.158907
$261$		0			0
$262$	−3.39919	+	10.4616i	−0.210002	+	0.646321i
$263$	3.37132	−	10.3759i	0.207885	−	0.639803i	−0.791698	−	0.610913i	$-0.790803\pi$
$263$	3.37132	−	10.3759i	0.207885	−	0.639803i	0.999583	−	0.0288905i	$-0.00919740\pi$
$264$		0			0
$265$	2.39919	+	7.38394i	0.147381	+	0.453592i
$266$	0.263932	−	0.812299i	0.0161827	−	0.0498053i
$267$		0			0
$268$	2.94427			0.179850
$269$	−10.3262	−	7.50245i	−0.629602	−	0.457433i	0.226660	−	0.973974i	$-0.427219\pi$
$269$	−10.3262	−	7.50245i	−0.629602	−	0.457433i	−0.856262	+	0.516541i	$0.827219\pi$
$270$		0			0
$271$	6.47214	−	4.70228i	0.393154	−	0.285643i	−0.373593	−	0.927593i	$-0.621874\pi$
$271$	6.47214	−	4.70228i	0.393154	−	0.285643i	0.766747	+	0.641950i	$0.221874\pi$
$272$	20.5623	−	14.9394i	1.24677	−	0.905834i
$273$		0			0
$274$	19.3262			1.16754
$275$	8.09017	−	24.8990i	0.487856	−	1.50147i
$276$		0			0
$277$	−7.63525	−	23.4989i	−0.458758	−	1.41191i	−0.866666	−	0.498889i	$-0.833742\pi$
$277$	−7.63525	−	23.4989i	−0.458758	−	1.41191i	0.407908	−	0.913023i	$-0.366258\pi$
$278$	−6.54508	+	4.75528i	−0.392548	+	0.285203i
$279$		0			0
$280$	2.50000	−	1.81636i	0.149404	−	0.108548i
$281$	8.16312	+	5.93085i	0.486971	+	0.353805i	0.804018	−	0.594605i	$-0.202691\pi$
$281$	8.16312	+	5.93085i	0.486971	+	0.353805i	−0.317047	+	0.948410i	$0.602691\pi$
$282$		0			0
$283$	24.1525	+	17.5478i	1.43572	+	1.04311i	0.988916	+	0.148474i	$0.0474362\pi$
$283$	24.1525	+	17.5478i	1.43572	+	1.04311i	0.446799	+	0.894634i	$0.352564\pi$
$284$	1.26393	−	3.88998i	0.0750006	−	0.230828i
$285$		0			0
$286$	4.85410	+	14.9394i	0.287029	+	0.883385i
$287$	0.145898	−	0.449028i	0.00861209	−	0.0265053i
$288$		0			0
$289$	3.21885	+	9.90659i	0.189344	+	0.582741i
$290$	−10.5902	+	7.69421i	−0.621876	+	0.451820i
$291$		0			0
$292$	4.50000	+	3.26944i	0.263343	+	0.191330i
$293$	19.5279			1.14083			0.570415	−	0.821357i	$-0.306782\pi$
$293$	19.5279			1.14083			0.570415	+	0.821357i	$0.306782\pi$
$294$		0			0
$295$	−19.6353	−	14.2658i	−1.14321	−	0.830590i
$296$	−0.427051	+	0.310271i	−0.0248218	+	0.0180341i
$297$		0			0
$298$	1.97214	+	6.06961i	0.114243	+	0.351603i
$299$	−6.97871			−0.403589
$300$		0			0
$301$	−3.00000			−0.172917
$302$	7.28115	+	22.4091i	0.418983	+	1.28950i
$303$		0			0
$304$	3.35410	−	2.43690i	0.192371	−	0.139766i
$305$	19.4721			1.11497
$306$		0			0
$307$	9.23607			0.527130			0.263565	−	0.964642i	$-0.415102\pi$
$307$	9.23607			0.527130			0.263565	+	0.964642i	$0.415102\pi$
$308$	−1.61803	−	1.17557i	−0.0921960	−	0.0669843i
$309$		0			0
$310$	8.78115	+	6.37988i	0.498736	+	0.362353i
$311$	−2.62868	−	8.09024i	−0.149059	−	0.458755i	0.848452	−	0.529272i	$-0.177535\pi$
$311$	−2.62868	−	8.09024i	−0.149059	−	0.458755i	−0.997511	+	0.0705172i	$0.977535\pi$
$312$		0			0
$313$	−5.18034	+	15.9434i	−0.292810	+	0.901177i	0.691138	+	0.722723i	$0.257110\pi$
$313$	−5.18034	+	15.9434i	−0.292810	+	0.901177i	−0.983948	+	0.178454i	$0.942890\pi$
$314$	6.59017	+	20.2825i	0.371905	+	1.14461i
$315$		0			0
$316$	−1.54508	+	4.75528i	−0.0869178	+	0.267506i
$317$	6.19098	+	4.49801i	0.347720	+	0.252634i	0.747912	−	0.663798i	$-0.231056\pi$
$317$	6.19098	+	4.49801i	0.347720	+	0.252634i	−0.400192	+	0.916431i	$0.631056\pi$
$318$		0			0
$319$	−15.3262	−	11.1352i	−0.858105	−	0.623449i
$320$	9.47214			0.529508
$321$		0			0
$322$	3.04508	−	2.21238i	0.169696	−	0.123291i
$323$	1.38197	+	4.25325i	0.0768946	+	0.236657i
$324$		0			0
$325$	−7.50000	+	5.44907i	−0.416025	+	0.302260i
$326$	17.7984			0.985761
$327$		0			0
$328$	1.38197	−	1.00406i	0.0763063	−	0.0554398i
$329$	0.309017	−	0.224514i	0.0170367	−	0.0123779i
$330$		0			0
$331$	18.7082	+	13.5923i	1.02830	+	0.747101i	0.967967	−	0.251078i	$-0.0807850\pi$
$331$	18.7082	+	13.5923i	1.02830	+	0.747101i	0.0603290	+	0.998179i	$0.480785\pi$
$332$	3.85410			0.211521
$333$		0			0
$334$	−7.28115	+	22.4091i	−0.398407	+	1.22617i
$335$	−8.61803	+	6.26137i	−0.470853	+	0.342095i
$336$		0			0
$337$	2.42705	−	7.46969i	0.132210	−	0.406900i	−0.862936	−	0.505314i	$-0.831377\pi$
$337$	2.42705	−	7.46969i	0.132210	−	0.406900i	0.995146	+	0.0984135i	$0.0313768\pi$
$338$	−4.78115	+	14.7149i	−0.260060	+	0.800384i
$339$		0			0
$340$	2.23607	−	6.88191i	0.121268	−	0.373224i
$341$	−4.85410	+	14.9394i	−0.262864	+	0.809013i
$342$		0			0
$343$	−8.41641			−0.454443
$344$	−8.78115	−	6.37988i	−0.473448	−	0.343980i
$345$		0			0
$346$	24.7254	−	17.9641i	1.32925	−	0.965755i
$347$	−16.1074	+	11.7027i	−0.864690	+	0.628234i	−0.929157	−	0.369686i	$-0.879465\pi$
$347$	−16.1074	+	11.7027i	−0.864690	+	0.628234i	0.0644668	+	0.997920i	$0.479465\pi$
$348$		0			0
$349$	21.7082			1.16201			0.581007	−	0.813899i	$-0.302659\pi$
$349$	21.7082			1.16201			0.581007	+	0.813899i	$0.302659\pi$
$350$	1.54508	−	4.75528i	0.0825883	−	0.254181i
$351$		0			0
$352$	−5.47214	−	16.8415i	−0.291666	−	0.897655i
$353$	10.4443	−	7.58821i	0.555893	−	0.403880i	−0.274061	−	0.961712i	$-0.588367\pi$
$353$	10.4443	−	7.58821i	0.555893	−	0.403880i	0.829953	+	0.557833i	$0.188367\pi$
$354$		0			0
$355$	4.57295	+	14.0741i	0.242707	+	0.746975i
$356$	−4.47214	−	3.24920i	−0.237023	−	0.172207i
$357$		0			0
$358$	−0.690983	−	0.502029i	−0.0365196	−	0.0265330i
$359$	−4.24671	+	13.0700i	−0.224133	+	0.689810i	0.774246	+	0.632885i	$0.218130\pi$
$359$	−4.24671	+	13.0700i	−0.224133	+	0.689810i	−0.998378	+	0.0569247i	$0.981870\pi$
$360$		0			0
$361$	−5.64590	−	17.3763i	−0.297153	−	0.914541i
$362$	0.145898	−	0.449028i	0.00766823	−	0.0236004i
$363$		0			0
$364$	0.218847	+	0.673542i	0.0114707	+	0.0353032i
$365$	−20.1246			−1.05337
$366$		0			0
$367$	20.6803	+	15.0251i	1.07950	+	0.784306i	0.977597	−	0.210488i	$-0.0675051\pi$
$367$	20.6803	+	15.0251i	1.07950	+	0.784306i	0.101908	+	0.994794i	$0.467505\pi$
$368$	18.2705			0.952416
$369$		0			0
$370$	−0.263932	+	0.812299i	−0.0137212	+	0.0422294i
$371$	−1.73607	+	1.26133i	−0.0901322	+	0.0654848i
$372$		0			0
$373$	−8.73607	−	26.8869i	−0.452336	−	1.39215i	−0.874234	−	0.485505i	$-0.838636\pi$
$373$	−8.73607	−	26.8869i	−0.452336	−	1.39215i	0.421897	−	0.906644i	$-0.361364\pi$
$374$	44.3607			2.29384
$375$		0			0
$376$	1.38197			0.0712695
$377$	2.07295	+	6.37988i	0.106762	+	0.328581i
$378$		0			0
$379$	−11.8090	+	8.57975i	−0.606588	+	0.440712i	−0.848211	−	0.529658i	$-0.822320\pi$
$379$	−11.8090	+	8.57975i	−0.606588	+	0.440712i	0.241623	+	0.970370i	$0.422320\pi$
$380$	0.364745	−	1.12257i	0.0187110	−	0.0575866i
$381$		0			0
$382$	2.94427			0.150642
$383$	26.9894	+	19.6089i	1.37909	+	1.00197i	0.996964	+	0.0778591i	$0.0248084\pi$
$383$	26.9894	+	19.6089i	1.37909	+	1.00197i	0.382127	+	0.924110i	$0.375192\pi$
$384$		0			0
$385$	7.23607			0.368784
$386$	3.85410	+	11.8617i	0.196169	+	0.603745i
$387$		0			0
$388$	−0.736068	+	2.26538i	−0.0373682	+	0.115007i
$389$	−4.63525	−	14.2658i	−0.235017	−	0.723307i	−0.997119	−	0.0758507i	$-0.975833\pi$
$389$	−4.63525	−	14.2658i	−0.235017	−	0.723307i	0.762102	−	0.647456i	$-0.224167\pi$
$390$		0			0
$391$	−6.09017	+	18.7436i	−0.307993	+	0.947905i
$392$	−11.9721	−	8.69827i	−0.604684	−	0.439329i
$393$		0			0
$394$	4.85410	+	3.52671i	0.244546	+	0.177673i
$395$	−5.59017	−	17.2048i	−0.281272	−	0.865666i
$396$		0			0
$397$	−23.4894	+	17.0660i	−1.17890	+	0.856519i	−0.992047	−	0.125870i	$-0.959828\pi$
$397$	−23.4894	+	17.0660i	−1.17890	+	0.856519i	−0.186850	+	0.982388i	$0.559828\pi$
$398$	−8.78115	−	27.0256i	−0.440159	−	1.35467i
$399$		0			0
$400$	19.6353	−	14.2658i	0.981763	−	0.713292i
$401$	−26.5967			−1.32818			−0.664089	−	0.747653i	$-0.731180\pi$
$401$	−26.5967			−1.32818			−0.664089	+	0.747653i	$0.731180\pi$
$402$		0			0
$403$	4.50000	−	3.26944i	0.224161	−	0.162862i
$404$	0.736068	−	0.534785i	0.0366208	−	0.0266065i
$405$		0			0
$406$	−2.92705	−	2.12663i	−0.145267	−	0.105543i
$407$	−1.23607			−0.0612696
$408$		0			0
$409$	0.489357	−	1.50609i	0.0241971	−	0.0744711i	−0.938229	−	0.346016i	$-0.887534\pi$
$409$	0.489357	−	1.50609i	0.0241971	−	0.0744711i	0.962426	+	0.271544i	$0.0875344\pi$
$410$	0.854102	−	2.62866i	0.0421811	−	0.129820i
$411$		0			0
$412$	1.63525	−	5.03280i	0.0805632	−	0.247948i
$413$	2.07295	−	6.37988i	0.102003	−	0.313933i
$414$		0			0
$415$	−11.2812	+	8.19624i	−0.553770	+	0.402337i
$416$	−1.93769	+	5.96361i	−0.0950033	+	0.292390i
$417$		0			0
$418$	7.23607			0.353928
$419$	−7.66312	−	5.56758i	−0.374368	−	0.271994i	0.384652	−	0.923062i	$-0.374321\pi$
$419$	−7.66312	−	5.56758i	−0.374368	−	0.271994i	−0.759020	+	0.651068i	$0.774321\pi$
$420$		0			0
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.998841	−	0.0481252i	$-0.984675\pi$
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.262889	+	0.964826i	$0.584675\pi$
$422$	12.0172	−	8.73102i	0.584989	−	0.425020i
$423$		0			0
$424$	−7.76393			−0.377050
$425$	8.09017	+	24.8990i	0.392431	+	1.20778i
$426$		0			0
$427$	1.66312	+	5.11855i	0.0804840	+	0.247704i
$428$	−8.20820	+	5.96361i	−0.396759	+	0.288262i
$429$		0			0
$430$	−17.5623			−0.846930
$431$	−24.1353	−	17.5353i	−1.16255	−	0.844645i	−0.172456	−	0.985017i	$-0.555170\pi$
$431$	−24.1353	−	17.5353i	−1.16255	−	0.844645i	−0.990099	+	0.140372i	$0.955170\pi$
$432$		0			0
$433$	−21.7254	−	15.7844i	−1.04406	−	0.758552i	−0.0729839	−	0.997333i	$-0.523252\pi$
$433$	−21.7254	−	15.7844i	−1.04406	−	0.758552i	−0.971073	+	0.238781i	$0.923252\pi$
$434$	−0.927051	+	2.85317i	−0.0444999	+	0.136957i
$435$		0			0
$436$	1.90983	+	5.87785i	0.0914643	+	0.281498i
$437$	−0.993422	+	3.05744i	−0.0475218	+	0.146257i
$438$		0			0
$439$	−12.6631	−	38.9731i	−0.604378	−	1.86008i	−0.501013	−	0.865440i	$-0.667039\pi$
$439$	−12.6631	−	38.9731i	−0.604378	−	1.86008i	−0.103365	−	0.994644i	$-0.532961\pi$
$440$	21.1803	+	15.3884i	1.00973	+	0.733614i
$441$		0			0
$442$	−12.7082	−	9.23305i	−0.604468	−	0.439171i
$443$	−29.9443			−1.42270			−0.711348	−	0.702840i	$-0.751915\pi$
$443$	−29.9443			−1.42270			−0.711348	+	0.702840i	$0.751915\pi$
$444$		0			0
$445$	20.0000			0.948091
$446$	0.236068	−	0.171513i	0.0111781	−	0.00812140i
$447$		0			0
$448$	0.809017	+	2.48990i	0.0382225	+	0.117637i
$449$	−4.67376			−0.220568			−0.110284	−	0.993900i	$-0.535176\pi$
$449$	−4.67376			−0.220568			−0.110284	+	0.993900i	$0.535176\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−3.21885	−	9.90659i	−0.151402	−	0.465967i
$453$		0			0
$454$	19.3262	−	14.0413i	0.907025	−	0.658992i
$455$	−2.07295	−	1.50609i	−0.0971813	−	0.0706064i
$456$		0			0
$457$	−21.4164			−1.00182			−0.500909	−	0.865500i	$-0.667001\pi$
$457$	−21.4164			−1.00182			−0.500909	+	0.865500i	$0.667001\pi$
$458$	−28.4164	−	20.6457i	−1.32781	−	0.964712i
$459$		0			0
$460$	4.20820	−	3.05744i	0.196209	−	0.142554i
$461$	−0.253289	−	0.779543i	−0.0117968	−	0.0363069i	0.944985	−	0.327114i	$-0.106076\pi$
$461$	−0.253289	−	0.779543i	−0.0117968	−	0.0363069i	−0.956782	+	0.290807i	$0.906076\pi$
$462$		0			0
$463$	−7.45492	+	22.9439i	−0.346459	+	1.06629i	0.614339	+	0.789042i	$0.289423\pi$
$463$	−7.45492	+	22.9439i	−0.346459	+	1.06629i	−0.960798	+	0.277250i	$0.910577\pi$
$464$	−5.42705	−	16.7027i	−0.251945	−	0.775405i
$465$		0			0
$466$	1.47214	−	4.53077i	0.0681954	−	0.209884i
$467$	22.2082	+	16.1352i	1.02767	+	0.746648i	0.967842	−	0.251560i	$-0.0809437\pi$
$467$	22.2082	+	16.1352i	1.02767	+	0.746648i	0.0598315	+	0.998208i	$0.480944\pi$
$468$		0			0
$469$	−2.38197	−	1.73060i	−0.109989	−	0.0799117i
$470$	1.80902	−	1.31433i	0.0834437	−	0.0606254i
$471$		0			0
$472$	19.6353	−	14.2658i	0.903786	−	0.656639i
$473$	−7.85410	−	24.1724i	−0.361132	−	1.11145i
$474$		0			0
$475$	1.31966	+	4.06150i	0.0605502	+	0.186354i
$476$	2.00000			0.0916698
$477$		0			0
$478$	−26.8713	+	19.5232i	−1.22907	+	0.892969i
$479$	−8.78115	+	6.37988i	−0.401221	+	0.291504i	−0.770038	−	0.637998i	$-0.779763\pi$
$479$	−8.78115	+	6.37988i	−0.401221	+	0.291504i	0.368817	+	0.929502i	$0.379763\pi$
$480$		0			0
$481$	0.354102	+	0.257270i	0.0161457	+	0.0117305i
$482$	4.09017			0.186302
$483$		0			0
$484$	3.13525	−	9.64932i	0.142512	−	0.438606i
$485$	−2.66312	−	8.19624i	−0.120926	−	0.372172i
$486$		0			0
$487$	−11.2533	+	34.6341i	−0.509935	+	1.56942i	0.282377	+	0.959303i	$0.408877\pi$
$487$	−11.2533	+	34.6341i	−0.509935	+	1.56942i	−0.792312	+	0.610116i	$0.791123\pi$
$488$	−6.01722	+	18.5191i	−0.272387	+	0.838320i
$489$		0			0
$490$	−23.9443			−1.08169
$491$	13.3647	−	41.1325i	0.603143	−	1.85628i	0.0940550	−	0.995567i	$-0.470017\pi$
$491$	13.3647	−	41.1325i	0.603143	−	1.85628i	0.509088	−	0.860715i	$-0.329983\pi$
$492$		0			0
$493$	18.9443			0.853207
$494$	−2.07295	−	1.50609i	−0.0932664	−	0.0677620i
$495$		0			0
$496$	−11.7812	+	8.55951i	−0.528989	+	0.384333i
$497$	−3.30902	+	2.40414i	−0.148430	+	0.107840i
$498$		0			0
$499$	7.56231			0.338535			0.169268	−	0.985570i	$-0.445860\pi$
$499$	7.56231			0.338535			0.169268	+	0.985570i	$0.445860\pi$
$500$	2.13525	−	6.57164i	0.0954915	−	0.293893i
$501$		0			0
$502$	14.5902	+	44.9039i	0.651191	+	2.00416i
$503$	−30.2705	+	21.9928i	−1.34970	+	0.980611i	−0.350669	+	0.936500i	$0.614046\pi$
$503$	−30.2705	+	21.9928i	−1.34970	+	0.980611i	−0.999027	+	0.0441115i	$0.985954\pi$
$504$		0			0
$505$	−1.01722	+	3.13068i	−0.0452657	+	0.139314i
$506$	25.7984	+	18.7436i	1.14688	+	0.833255i
$507$		0			0
$508$	−9.94427	−	7.22494i	−0.441206	−	0.320555i
$509$	6.28115	−	19.3314i	0.278407	−	0.856849i	−0.709891	−	0.704312i	$-0.751256\pi$
$509$	6.28115	−	19.3314i	0.278407	−	0.856849i	0.988298	−	0.152537i	$-0.0487444\pi$
$510$		0			0
$511$	−1.71885	−	5.29007i	−0.0760373	−	0.234019i
$512$	−1.63525	+	5.03280i	−0.0722687	+	0.222420i
$513$		0			0
$514$	−11.4271	−	35.1688i	−0.504026	−	1.55123i
$515$	5.91641	+	18.2088i	0.260708	+	0.802377i
$516$		0			0
$517$	2.61803	+	1.90211i	0.115141	+	0.0836548i
$518$	−0.236068			−0.0103722
$519$		0			0
$520$	−2.86475	−	8.81678i	−0.125627	−	0.386641i
$521$	23.7533	−	17.2578i	1.04065	−	0.756077i	0.0702381	−	0.997530i	$-0.477624\pi$
$521$	23.7533	−	17.2578i	1.04065	−	0.756077i	0.970412	+	0.241453i	$0.0776241\pi$
$522$		0			0
$523$	−4.06231	−	12.5025i	−0.177632	−	0.546696i	0.822112	−	0.569326i	$-0.192796\pi$
$523$	−4.06231	−	12.5025i	−0.177632	−	0.546696i	−0.999744	+	0.0226305i	$0.992796\pi$
$524$	−4.20163			−0.183549
$525$		0			0
$526$	17.6525			0.769685
$527$	−4.85410	−	14.9394i	−0.211448	−	0.650770i
$528$		0			0
$529$	7.14590	−	5.19180i	0.310691	−	0.225730i
$530$	−10.1631	+	7.38394i	−0.441458	+	0.320738i
$531$		0			0
$532$	0.326238			0.0141442
$533$	−1.14590	−	0.832544i	−0.0496344	−	0.0360615i
$534$		0			0
$535$	11.3435	−	34.9116i	0.490420	−	1.50936i
$536$	−3.29180	−	10.1311i	−0.142184	−	0.437597i
$537$		0			0
$538$	6.38197	−	19.6417i	0.275146	−	0.846813i
$539$	−10.7082	−	32.9565i	−0.461235	−	1.41954i
$540$		0			0
$541$	8.38197	−	25.7970i	0.360369	−	1.10910i	−0.592462	−	0.805599i	$-0.701844\pi$
$541$	8.38197	−	25.7970i	0.360369	−	1.10910i	0.952831	−	0.303503i	$-0.0981561\pi$
$542$	10.4721	+	7.60845i	0.449817	+	0.326811i
$543$		0			0
$544$	14.3262	+	10.4086i	0.614232	+	0.446266i
$545$	−18.0902	−	13.1433i	−0.774898	−	0.562996i
$546$		0			0
$547$	17.2254	−	12.5150i	0.736506	−	0.535103i	−0.155109	−	0.987897i	$-0.549573\pi$
$547$	17.2254	−	12.5150i	0.736506	−	0.535103i	0.891615	+	0.452794i	$0.149573\pi$
$548$	2.28115	+	7.02067i	0.0974460	+	0.299908i
$549$		0			0
$550$	42.3607			1.80627
$551$	3.09017			0.131646
$552$		0			0
$553$	4.04508	−	2.93893i	0.172015	−	0.124976i
$554$	32.3435	−	23.4989i	1.37414	−	0.998373i
$555$		0			0
$556$	−2.50000	−	1.81636i	−0.106024	−	0.0770307i
$557$	−4.76393			−0.201854			−0.100927	−	0.994894i	$-0.532181\pi$
$557$	−4.76393			−0.201854			−0.100927	+	0.994894i	$0.532181\pi$
$558$		0			0
$559$	−2.78115	+	8.55951i	−0.117630	+	0.362029i
$560$	5.42705	+	3.94298i	0.229335	+	0.166621i
$561$		0			0
$562$	−5.04508	+	15.5272i	−0.212814	+	0.654974i
$563$	−2.28115	+	7.02067i	−0.0961391	+	0.295886i	−0.987549	−	0.157312i	$-0.949717\pi$
$563$	−2.28115	+	7.02067i	−0.0961391	+	0.295886i	0.891410	+	0.453198i	$0.149717\pi$
$564$		0			0
$565$	30.4894	+	22.1518i	1.28270	+	0.931934i
$566$	−14.9271	+	45.9407i	−0.627431	+	1.93103i
$567$		0			0
$568$	−14.7984			−0.620926
$569$	16.6074	+	12.0660i	0.696218	+	0.505832i	0.878698	−	0.477377i	$-0.158413\pi$
$569$	16.6074	+	12.0660i	0.696218	+	0.505832i	−0.182480	+	0.983210i	$0.558413\pi$
$570$		0			0
$571$	6.57295	−	4.77553i	0.275069	−	0.199850i	−0.441695	−	0.897165i	$-0.645623\pi$
$571$	6.57295	−	4.77553i	0.275069	−	0.199850i	0.716764	+	0.697316i	$0.245623\pi$
$572$	−4.85410	+	3.52671i	−0.202960	+	0.147459i
$573$		0			0
$574$	0.763932			0.0318859
$575$	−5.81559	+	17.8986i	−0.242527	+	0.746422i
$576$		0			0
$577$	−10.4377	−	32.1239i	−0.434527	−	1.33734i	−0.893571	−	0.448923i	$-0.851808\pi$
$577$	−10.4377	−	32.1239i	−0.434527	−	1.33734i	0.459044	−	0.888414i	$-0.348192\pi$
$578$	−13.6353	+	9.90659i	−0.567152	+	0.412060i
$579$		0			0
$580$	−4.04508	−	2.93893i	−0.167963	−	0.122032i
$581$	−3.11803	−	2.26538i	−0.129358	−	0.0939840i
$582$		0			0
$583$	−14.7082	−	10.6861i	−0.609152	−	0.442575i
$584$	6.21885	−	19.1396i	0.257338	−	0.792004i
$585$		0			0
$586$	9.76393	+	30.0503i	0.403344	+	1.24137i
$587$	−1.63525	+	5.03280i	−0.0674942	+	0.207726i	−0.979115	−	0.203306i	$-0.934831\pi$
$587$	−1.63525	+	5.03280i	−0.0674942	+	0.207726i	0.911621	+	0.411032i	$0.134831\pi$
$588$		0			0
$589$	−0.791796	−	2.43690i	−0.0326254	−	0.100411i
$590$	12.1353	−	37.3485i	0.499601	−	1.53761i
$591$		0			0
$592$	−0.927051	−	0.673542i	−0.0381016	−	0.0276824i
$593$	10.9098			0.448013			0.224007	−	0.974588i	$-0.428086\pi$
$593$	10.9098			0.448013			0.224007	+	0.974588i	$0.428086\pi$
$594$		0			0
$595$	−5.85410	+	4.25325i	−0.239995	+	0.174366i
$596$	−1.97214	+	1.43284i	−0.0807818	+	0.0586914i
$597$		0			0
$598$	−3.48936	−	10.7391i	−0.142690	−	0.439156i
$599$	9.47214			0.387021			0.193510	−	0.981098i	$-0.438013\pi$
$599$	9.47214			0.387021			0.193510	+	0.981098i	$0.438013\pi$
$600$		0			0
$601$	2.72949			0.111338			0.0556691	−	0.998449i	$-0.482271\pi$
$601$	2.72949			0.111338			0.0556691	+	0.998449i	$0.482271\pi$
$602$	−1.50000	−	4.61653i	−0.0611354	−	0.188156i
$603$		0			0
$604$	−7.28115	+	5.29007i	−0.296266	+	0.215250i
$605$	11.3435	+	34.9116i	0.461177	+	1.41936i
$606$		0			0
$607$	−35.5623			−1.44343			−0.721715	−	0.692191i	$-0.756646\pi$
$607$	−35.5623			−1.44343			−0.721715	+	0.692191i	$0.756646\pi$
$608$	2.33688	+	1.69784i	0.0947730	+	0.0688566i
$609$		0			0
$610$	9.73607	+	29.9645i	0.394202	+	1.21323i
$611$	−0.354102	−	1.08981i	−0.0143254	−	0.0440891i
$612$		0			0
$613$	−4.62868	+	14.2456i	−0.186951	+	0.575374i	−0.999977	−	0.00685287i	$-0.997819\pi$
$613$	−4.62868	+	14.2456i	−0.186951	+	0.575374i	0.813026	+	0.582227i	$0.197819\pi$
$614$	4.61803	+	14.2128i	0.186369	+	0.573584i
$615$		0			0
$616$	−2.23607	+	6.88191i	−0.0900937	+	0.277280i
$617$	11.5172	+	8.36775i	0.463666	+	0.336873i	0.794968	−	0.606652i	$-0.207488\pi$
$617$	11.5172	+	8.36775i	0.463666	+	0.336873i	−0.331302	+	0.943525i	$0.607488\pi$
$618$		0			0
$619$	−24.6976	−	17.9438i	−0.992679	−	0.721223i	−0.0321727	−	0.999482i	$-0.510243\pi$
$619$	−24.6976	−	17.9438i	−0.992679	−	0.721223i	−0.960506	+	0.278259i	$0.910243\pi$
$620$	−1.28115	+	3.94298i	−0.0514523	+	0.158354i
$621$		0			0
$622$	11.1353	−	8.09024i	0.446483	−	0.324389i
$623$	1.70820	+	5.25731i	0.0684377	+	0.210630i
$624$		0			0
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$	−27.1246			−1.08412
$627$		0			0
$628$	−6.59017	+	4.78804i	−0.262976	+	0.191064i
$629$	1.00000	−	0.726543i	0.0398726	−	0.0289691i
$630$		0			0
$631$	8.28115	+	6.01661i	0.329667	+	0.239517i	0.740290	−	0.672288i	$-0.234688\pi$
$631$	8.28115	+	6.01661i	0.329667	+	0.239517i	−0.410622	+	0.911806i	$0.634688\pi$
$632$	18.0902			0.719588
$633$		0			0
$634$	−3.82624	+	11.7759i	−0.151959	+	0.467683i
$635$	44.4721			1.76482
$636$		0			0
$637$	−3.79180	+	11.6699i	−0.150236	+	0.462380i
$638$	9.47214	−	29.1522i	0.375005	−	1.15415i
$639$		0			0
$640$	9.40983	+	28.9605i	0.371956	+	1.14476i
$641$	0.336881	−	1.03681i	0.0133060	−	0.0409517i	−0.944183	−	0.329421i	$-0.893146\pi$
$641$	0.336881	−	1.03681i	0.0133060	−	0.0409517i	0.957489	+	0.288470i	$0.0931464\pi$
$642$		0			0
$643$	−30.8328			−1.21593			−0.607964	−	0.793965i	$-0.708013\pi$
$643$	−30.8328			−1.21593			−0.607964	+	0.793965i	$0.708013\pi$
$644$	1.16312	+	0.845055i	0.0458333	+	0.0332998i
$645$		0			0
$646$	−5.85410	+	4.25325i	−0.230327	+	0.167342i
$647$	−29.5623	+	21.4783i	−1.16221	+	0.844398i	−0.990056	−	0.140671i	$-0.955074\pi$
$647$	−29.5623	+	21.4783i	−1.16221	+	0.844398i	−0.172158	+	0.985069i	$0.555074\pi$
$648$		0			0
$649$	56.8328			2.23088
$650$	−12.1353	−	8.81678i	−0.475984	−	0.345823i
$651$		0			0
$652$	2.10081	+	6.46564i	0.0822742	+	0.253214i
$653$	15.4443	−	11.2209i	0.604381	−	0.439109i	−0.243050	−	0.970014i	$-0.578148\pi$
$653$	15.4443	−	11.2209i	0.604381	−	0.439109i	0.847431	+	0.530905i	$0.178148\pi$
$654$		0			0
$655$	12.2984	−	8.93529i	0.480537	−	0.349131i
$656$	3.00000	+	2.17963i	0.117130	+	0.0851002i
$657$		0			0
$658$	0.500000	+	0.363271i	0.0194920	+	0.0141618i
$659$	−4.79837	+	14.7679i	−0.186918	+	0.575275i	−0.999976	−	0.00690786i	$-0.997801\pi$
$659$	−4.79837	+	14.7679i	−0.186918	+	0.575275i	0.813058	+	0.582183i	$0.197801\pi$
$660$		0			0
$661$	6.08359	+	18.7234i	0.236624	+	0.728255i	0.996902	+	0.0786563i	$0.0250630\pi$
$661$	6.08359	+	18.7234i	0.236624	+	0.728255i	−0.760277	+	0.649598i	$0.774937\pi$
$662$	−11.5623	+	35.5851i	−0.449382	+	1.38305i
$663$		0			0
$664$	−4.30902	−	13.2618i	−0.167222	−	0.514657i
$665$	−0.954915	+	0.693786i	−0.0370300	+	0.0269039i
$666$		0			0
$667$	11.0172	+	8.00448i	0.426588	+	0.309935i
$668$	−9.00000			−0.348220
$669$		0			0
$670$	−13.9443	−	10.1311i	−0.538714	−	0.391399i
$671$	−36.8885	+	26.8011i	−1.42407	+	1.03464i
$672$		0			0
$673$	3.76393	+	11.5842i	0.145089	+	0.446538i	0.997022	−	0.0771122i	$-0.0245700\pi$
$673$	3.76393	+	11.5842i	0.145089	+	0.446538i	−0.851934	+	0.523650i	$0.824570\pi$
$674$	12.7082			0.489502
$675$		0			0
$676$	−5.90983			−0.227301
$677$	−3.28115	−	10.0984i	−0.126105	−	0.388111i	0.867996	−	0.496571i	$-0.165408\pi$
$677$	−3.28115	−	10.0984i	−0.126105	−	0.388111i	−0.994101	+	0.108460i	$0.965408\pi$
$678$		0			0
$679$	1.92705	−	1.40008i	0.0739534	−	0.0537303i
$680$	−26.1803			−1.00397
$681$		0			0
$682$	−25.4164			−0.973245
$683$	−10.8992	−	7.91872i	−0.417046	−	0.303002i	0.359402	−	0.933183i	$-0.382981\pi$
$683$	−10.8992	−	7.91872i	−0.417046	−	0.303002i	−0.776448	+	0.630181i	$0.782981\pi$
$684$		0			0
$685$	−21.6074	−	15.6987i	−0.825576	−	0.599816i
$686$	−4.20820	−	12.9515i	−0.160670	−	0.494491i
$687$		0			0
$688$	7.28115	−	22.4091i	0.277591	−	0.854338i
$689$	1.98936	+	6.12261i	0.0757885	+	0.233253i
$690$		0			0
$691$	11.2082	−	34.4953i	0.426380	−	1.31226i	−0.475286	−	0.879831i	$-0.657656\pi$
$691$	11.2082	−	34.4953i	0.426380	−	1.31226i	0.901667	−	0.432432i	$-0.142344\pi$
$692$	9.44427	+	6.86167i	0.359017	+	0.260841i
$693$		0			0
$694$	−26.0623	−	18.9354i	−0.989312	−	0.718777i
$695$	11.1803			0.424094
$696$		0			0
$697$	−3.23607	+	2.35114i	−0.122575	+	0.0890558i
$698$	10.8541	+	33.4055i	0.410834	+	1.26442i
$699$		0			0
$700$	1.90983			0.0721848
$701$	41.0132			1.54905			0.774523	−	0.632546i	$-0.217990\pi$
$701$	41.0132			1.54905			0.774523	+	0.632546i	$0.217990\pi$
$702$		0			0
$703$	0.163119	−	0.118513i	0.00615215	−	0.00446980i
$704$	−17.9443	+	13.0373i	−0.676300	+	0.491361i
$705$		0			0
$706$	16.8992	+	12.2780i	0.636009	+	0.462088i
$707$	−0.909830			−0.0342177
$708$		0			0
$709$	−10.3647	+	31.8994i	−0.389256	+	1.19801i	0.544089	+	0.839027i	$0.316875\pi$
$709$	−10.3647	+	31.8994i	−0.389256	+	1.19801i	−0.933345	+	0.358980i	$0.883125\pi$
$710$	−19.3713	+	14.0741i	−0.726993	+	0.528191i
$711$		0			0
$712$	−6.18034	+	19.0211i	−0.231618	+	0.712847i
$713$	3.48936	−	10.7391i	0.130677	−	0.402184i
$714$		0			0
$715$	6.70820	−	20.6457i	0.250873	−	0.772106i
$716$	0.100813	−	0.310271i	0.00376756	−	0.0115954i
$717$		0			0
$718$	−22.2361			−0.829843
$719$	−18.8435	−	13.6906i	−0.702742	−	0.510572i	0.178082	−	0.984016i	$-0.443011\pi$
$719$	−18.8435	−	13.6906i	−0.702742	−	0.510572i	−0.880824	+	0.473443i	$0.843011\pi$
$720$		0			0
$721$	−4.28115	+	3.11044i	−0.159438	+	0.115839i
$722$	23.9164	−	17.3763i	0.890077	−	0.646678i
$723$		0			0
$724$	0.180340			0.00670228
$725$	18.0902			0.671852
$726$		0			0
$727$	7.59017	+	23.3601i	0.281504	+	0.866380i	0.987425	+	0.158089i	$0.0505333\pi$
$727$	7.59017	+	23.3601i	0.281504	+	0.866380i	−0.705921	+	0.708291i	$0.749467\pi$
$728$	2.07295	−	1.50609i	0.0768286	−	0.0558192i
$729$		0			0
$730$	−10.0623	−	30.9686i	−0.372423	−	1.14620i
$731$	20.5623	+	14.9394i	0.760524	+	0.552553i
$732$		0			0
$733$	16.1631	+	11.7432i	0.596998	+	0.433745i	0.844812	−	0.535063i	$-0.179712\pi$
$733$	16.1631	+	11.7432i	0.596998	+	0.433745i	−0.247814	+	0.968808i	$0.579712\pi$
$734$	−12.7812	+	39.3363i	−0.471761	+	1.45193i
$735$		0			0
$736$	3.93363	+	12.1065i	0.144995	+	0.446250i
$737$	7.70820	−	23.7234i	0.283935	−	0.873863i
$738$		0			0
$739$	4.93769	+	15.1967i	0.181636	+	0.559018i	0.999874	−	0.0158612i	$-0.00504898\pi$
$739$	4.93769	+	15.1967i	0.181636	+	0.559018i	−0.818238	+	0.574879i	$0.805049\pi$
$740$	−0.326238			−0.0119927
$741$		0			0
$742$	−2.80902	−	2.04087i	−0.103122	−	0.0749227i
$743$	−28.3607			−1.04045			−0.520226	−	0.854029i	$-0.674152\pi$
$743$	−28.3607			−1.04045			−0.520226	+	0.854029i	$0.674152\pi$
$744$		0			0
$745$	2.72542	−	8.38800i	0.0998518	−	0.307312i
$746$	37.0066	−	26.8869i	1.35491	−	0.984398i
$747$		0			0
$748$	5.23607	+	16.1150i	0.191450	+	0.589221i
$749$	10.1459			0.370723
$750$		0			0
$751$	−5.11146			−0.186520			−0.0932598	−	0.995642i	$-0.529729\pi$
$751$	−5.11146			−0.186520			−0.0932598	+	0.995642i	$0.529729\pi$
$752$	0.927051	+	2.85317i	0.0338061	+	0.104044i
$753$		0			0
$754$	−8.78115	+	6.37988i	−0.319791	+	0.232342i
$755$	10.0623	−	30.9686i	0.366205	−	1.12706i
$756$		0			0
$757$	30.4164			1.10550			0.552752	−	0.833346i	$-0.313578\pi$
$757$	30.4164			1.10550			0.552752	+	0.833346i	$0.313578\pi$
$758$	−19.1074	−	13.8823i	−0.694012	−	0.504229i
$759$		0			0
$760$	−4.27051			−0.154908
$761$	5.70163	+	17.5478i	0.206684	+	0.636107i	0.999640	+	0.0268287i	$0.00854087\pi$
$761$	5.70163	+	17.5478i	0.206684	+	0.636107i	−0.792956	+	0.609279i	$0.791459\pi$
$762$		0			0
$763$	1.90983	−	5.87785i	0.0691405	−	0.212793i
$764$	0.347524	+	1.06957i	0.0125730	+	0.0386957i
$765$		0			0
$766$	−16.6803	+	51.3368i	−0.602685	+	1.85487i
$767$	−16.2812	−	11.8290i	−0.587878	−	0.427119i
$768$		0			0
$769$	−10.8541	−	7.88597i	−0.391409	−	0.284375i	0.374624	−	0.927177i	$-0.377772\pi$
$769$	−10.8541	−	7.88597i	−0.391409	−	0.284375i	−0.766033	+	0.642802i	$0.777772\pi$
$770$	3.61803	+	11.1352i	0.130385	+	0.401283i
$771$		0			0
$772$	−3.85410	+	2.80017i	−0.138712	+	0.100780i
$773$	11.1738	+	34.3893i	0.401892	+	1.23690i	0.923462	+	0.383689i	$0.125346\pi$
$773$	11.1738	+	34.3893i	0.401892	+	1.23690i	−0.521570	+	0.853208i	$0.674654\pi$
$774$		0			0
$775$	−4.63525	−	14.2658i	−0.166503	−	0.512444i
$776$	8.61803			0.309369
$777$		0			0
$778$	19.6353	−	14.2658i	0.703958	−	0.511455i
$779$	−0.527864	+	0.383516i	−0.0189127	+	0.0137409i
$780$		0			0
$781$	−28.0344	−	20.3682i	−1.00315	−	0.728832i
$782$	−31.8885			−1.14033
$783$		0			0
$784$	9.92705	−	30.5523i	0.354538	−	1.09115i
$785$	9.10739	−	28.0297i	0.325057	−	1.00042i
$786$		0			0
$787$	−3.65248	+	11.2412i	−0.130197	+	0.400704i	−0.994812	−	0.101730i	$-0.967562\pi$
$787$	−3.65248	+	11.2412i	−0.130197	+	0.400704i	0.864615	+	0.502434i	$0.167562\pi$
$788$	−0.708204	+	2.17963i	−0.0252287	+	0.0776460i
$789$		0			0
$790$	23.6803	−	17.2048i	0.842509	−	0.612118i
$791$	−3.21885	+	9.90659i	−0.114449	+	0.352238i
$792$		0			0
$793$	16.1459			0.573358
$794$	−38.0066	−	27.6134i	−1.34880	−	0.979963i
$795$		0			0
$796$	8.78115	−	6.37988i	0.311240	−	0.226129i
$797$	7.89919	−	5.73910i	0.279804	−	0.203289i	−0.439028	−	0.898473i	$-0.644677\pi$
$797$	7.89919	−	5.73910i	0.279804	−	0.203289i	0.718832	+	0.695184i	$0.244677\pi$
$798$		0			0
$799$	−3.23607			−0.114484
$800$	13.6803	+	9.93935i	0.483673	+	0.351409i
$801$		0			0
$802$	−13.2984	−	40.9282i	−0.469582	−	1.44522i
$803$	38.1246	−	27.6992i	1.34539	−	0.977482i
$804$		0			0
$805$	−5.20163			−0.183333
$806$	7.28115	+	5.29007i	0.256468	+	0.186335i
$807$		0			0
$808$	−2.66312	−	1.93487i	−0.0936882	−	0.0680685i
$809$	−9.57295	+	29.4625i	−0.336567	+	1.03585i	0.629378	+	0.777099i	$0.283310\pi$
$809$	−9.57295	+	29.4625i	−0.336567	+	1.03585i	−0.965945	+	0.258747i	$0.916690\pi$
$810$		0			0
$811$	−4.54508	−	13.9883i	−0.159600	−	0.491197i	0.838998	−	0.544134i	$-0.183142\pi$
$811$	−4.54508	−	13.9883i	−0.159600	−	0.491197i	−0.998598	+	0.0529372i	$0.983142\pi$
$812$	0.427051	−	1.31433i	0.0149866	−	0.0461239i
$813$		0			0
$814$	−0.618034	−	1.90211i	−0.0216621	−	0.0666690i
$815$	−19.8992	−	14.4576i	−0.697038	−	0.506428i
$816$		0			0
$817$	3.35410	+	2.43690i	0.117345	+	0.0852563i
$818$	2.56231			0.0895889
$819$		0			0
$820$	1.05573			0.0368676
$821$	−32.9164	+	23.9152i	−1.14879	+	0.834645i	−0.988320	−	0.152395i	$-0.951301\pi$
$821$	−32.9164	+	23.9152i	−1.14879	+	0.834645i	−0.160471	+	0.987041i	$0.551301\pi$
$822$		0			0
$823$	14.7426	+	45.3732i	0.513896	+	1.58161i	0.785281	+	0.619139i	$0.212518\pi$
$823$	14.7426	+	45.3732i	0.513896	+	1.58161i	−0.271385	+	0.962471i	$0.587482\pi$
$824$	−19.1459			−0.666979
$825$		0			0
$826$	10.8541			0.377663
$827$	0.298374	+	0.918300i	0.0103755	+	0.0319324i	0.956110	−	0.293007i	$-0.0946560\pi$
$827$	0.298374	+	0.918300i	0.0103755	+	0.0319324i	−0.945735	+	0.324940i	$0.894656\pi$
$828$		0			0
$829$	29.0066	−	21.0745i	1.00744	−	0.731948i	0.0437695	−	0.999042i	$-0.486063\pi$
$829$	29.0066	−	21.0745i	1.00744	−	0.731948i	0.963671	+	0.267094i	$0.0860633\pi$
$830$	−18.2533	−	13.2618i	−0.633581	−	0.460323i
$831$		0			0
$832$	7.85410			0.272292
$833$	28.0344	+	20.3682i	0.971336	+	0.705717i
$834$		0			0
$835$	26.3435	−	19.1396i	0.911653	−	0.662355i
$836$	0.854102	+	2.62866i	0.0295397	+	0.0909140i
$837$		0			0
$838$	4.73607	−	14.5761i	0.163605	−	0.503524i
$839$	−3.35410	−	10.3229i	−0.115796	−	0.356385i	0.876316	−	0.481737i	$-0.159994\pi$
$839$	−3.35410	−	10.3229i	−0.115796	−	0.356385i	−0.992112	+	0.125352i	$0.959994\pi$
$840$		0			0
$841$	−4.91641	+	15.1311i	−0.169531	+	0.521764i
$842$	−41.8885	−	30.4338i	−1.44357	−	1.04882i
$843$		0			0
$844$	4.59017	+	3.33495i	0.158000	+	0.114794i
$845$	17.2984	−	12.5680i	0.595082	−	0.432352i
$846$		0			0
$847$	−8.20820	+	5.96361i	−0.282037	+	0.204912i
$848$	−5.20820	−	16.0292i	−0.178850	−	0.550445i
$849$		0			0
$850$	−34.2705	+	24.8990i	−1.17547	+	0.854028i
$851$	0.888544			0.0304589
$852$		0			0
$853$	12.3820	−	8.99602i	0.423950	−	0.308018i	−0.355275	−	0.934762i	$-0.615613\pi$
$853$	12.3820	−	8.99602i	0.423950	−	0.308018i	0.779225	+	0.626744i	$0.215613\pi$
$854$	−7.04508	+	5.11855i	−0.241078	+	0.175153i
$855$		0			0
$856$	29.6976	+	21.5765i	1.01504	+	0.737471i
$857$	−19.6869			−0.672492			−0.336246	−	0.941774i	$-0.609157\pi$
$857$	−19.6869			−0.672492			−0.336246	+	0.941774i	$0.609157\pi$
$858$		0			0
$859$	−0.489357	+	1.50609i	−0.0166966	+	0.0513870i	−0.959058	−	0.283211i	$-0.908600\pi$
$859$	−0.489357	+	1.50609i	−0.0166966	+	0.0513870i	0.942361	+	0.334598i	$0.108600\pi$
$860$	−2.07295	−	6.37988i	−0.0706870	−	0.217552i
$861$		0			0
$862$	14.9164	−	45.9080i	0.508055	−	1.56363i
$863$	6.62461	−	20.3885i	0.225504	−	0.694031i	−0.772736	−	0.634728i	$-0.781112\pi$
$863$	6.62461	−	20.3885i	0.225504	−	0.694031i	0.998240	−	0.0593032i	$-0.0188879\pi$
$864$		0			0
$865$	−42.2361			−1.43607
$866$	13.4271	−	41.3242i	0.456270	−	1.40425i
$867$		0			0
$868$	−1.14590			−0.0388943
$869$	34.2705	+	24.8990i	1.16255	+	0.844640i
$870$		0			0
$871$	−7.14590	+	5.19180i	−0.242130	+	0.175917i
$872$	18.0902	−	13.1433i	0.612610	−	0.445088i
$873$		0			0
$874$	−5.20163			−0.175948
$875$	−5.59017	+	4.06150i	−0.188982	+	0.137304i
$876$		0			0
$877$	−11.2918	−	34.7526i	−0.381297	−	1.17351i	−0.939131	−	0.343559i	$-0.888368\pi$
$877$	−11.2918	−	34.7526i	−0.381297	−	1.17351i	0.557834	−	0.829952i	$-0.311632\pi$
$878$	53.6418	−	38.9731i	1.81032	−	1.31528i
$879$		0			0
$880$	−17.5623	+	54.0512i	−0.592025	+	1.82207i
$881$	−32.6525	−	23.7234i	−1.10009	−	0.799262i	−0.119015	−	0.992892i	$-0.537974\pi$
$881$	−32.6525	−	23.7234i	−1.10009	−	0.799262i	−0.981075	+	0.193630i	$0.937974\pi$
$882$		0			0
$883$	16.6525	+	12.0987i	0.560400	+	0.407155i	0.831605	−	0.555367i	$-0.187422\pi$
$883$	16.6525	+	12.0987i	0.560400	+	0.407155i	−0.271205	+	0.962522i	$0.587422\pi$
$884$	1.85410	−	5.70634i	0.0623602	−	0.191925i
$885$		0			0
$886$	−14.9721	−	46.0795i	−0.502999	−	1.54807i
$887$	−9.23607	+	28.4257i	−0.310117	+	0.954441i	0.667601	+	0.744519i	$0.267321\pi$
$887$	−9.23607	+	28.4257i	−0.310117	+	0.954441i	−0.977718	+	0.209922i	$0.932679\pi$
$888$		0			0
$889$	3.79837	+	11.6902i	0.127393	+	0.392076i
$890$	10.0000	+	30.7768i	0.335201	+	1.03164i
$891$		0			0
$892$	0.0901699	+	0.0655123i	0.00301911	+	0.00219351i
$893$	−0.527864			−0.0176643
$894$		0			0
$895$	0.364745	+	1.12257i	0.0121921	+	0.0375234i
$896$	−6.80902	+	4.94704i	−0.227473	+	0.165269i
$897$		0			0
$898$	−2.33688	−	7.19218i	−0.0779827	−	0.240006i
$899$	−10.8541			−0.362005
$900$		0			0
$901$	18.1803			0.605675
$902$	2.00000	+	6.15537i	0.0665927	+	0.204951i
$903$		0			0
$904$	−30.4894	+	22.1518i	−1.01406	+	0.736758i
$905$	−0.527864	+	0.383516i	−0.0175468	+	0.0127485i
$906$		0			0
$907$	−33.2492			−1.10402			−0.552011	−	0.833837i	$-0.686139\pi$
$907$	−33.2492			−1.10402			−0.552011	+	0.833837i	$0.686139\pi$
$908$	7.38197	+	5.36331i	0.244979	+	0.177988i
$909$		0			0
$910$	1.28115	−	3.94298i	0.0424698	−	0.130709i
$911$	12.4336	+	38.2668i	0.411944	+	1.26783i	0.914955	+	0.403555i	$0.132226\pi$
$911$	12.4336	+	38.2668i	0.411944	+	1.26783i	−0.503011	+	0.864280i	$0.667774\pi$
$912$		0			0
$913$	10.0902	−	31.0543i	0.333936	−	1.02775i
$914$	−10.7082	−	32.9565i	−0.354196	−	1.09010i
$915$		0			0
$916$	4.14590	−	12.7598i	0.136984	−	0.421594i
$917$	3.39919	+	2.46965i	0.112251	+	0.0815552i
$918$		0			0
$919$	43.0517	+	31.2789i	1.42014	+	1.03179i	0.991748	+	0.128203i	$0.0409209\pi$
$919$	43.0517	+	31.2789i	1.42014	+	1.03179i	0.428395	+	0.903591i	$0.359079\pi$
$920$	−15.2254	−	11.0619i	−0.501967	−	0.364701i
$921$		0			0
$922$	1.07295	−	0.779543i	0.0353357	−	0.0256729i
$923$	3.79180	+	11.6699i	0.124808	+	0.384121i
$924$		0			0
$925$	0.954915	−	0.693786i	0.0313974	−	0.0228116i
$926$	−39.0344			−1.28275
$927$		0			0
$928$	9.89919	−	7.19218i	0.324957	−	0.236095i
$929$	33.6803	−	24.4702i	1.10502	−	0.802841i	0.123145	−	0.992389i	$-0.460702\pi$
$929$	33.6803	−	24.4702i	1.10502	−	0.802841i	0.981872	+	0.189548i	$0.0607021\pi$
$930$		0			0
$931$	4.57295	+	3.32244i	0.149872	+	0.108889i
$932$	1.81966			0.0596049
$933$		0			0
$934$	−13.7254	+	42.2425i	−0.449110	+	1.38222i
$935$	−49.5967	−	36.0341i	−1.62199	−	1.17844i
$936$		0			0
$937$	5.47871	−	16.8617i	0.178982	−	0.550849i	−0.820811	−	0.571200i	$-0.806478\pi$
$937$	5.47871	−	16.8617i	0.178982	−	0.550849i	0.999793	+	0.0203504i	$0.00647819\pi$
$938$	1.47214	−	4.53077i	0.0480669	−	0.147935i
$939$		0			0
$940$	0.690983	+	0.502029i	0.0225374	+	0.0163744i
$941$	14.3435	−	44.1446i	0.467583	−	1.43907i	−0.388121	−	0.921608i	$-0.626876\pi$
$941$	14.3435	−	44.1446i	0.467583	−	1.43907i	0.855704	−	0.517465i	$-0.173124\pi$
$942$		0			0
$943$	−2.87539			−0.0936355
$944$	42.6246	+	30.9686i	1.38731	+	1.00794i
$945$		0			0
$946$	33.2705	−	24.1724i	1.08172	−	0.785914i
$947$	2.14590	−	1.55909i	0.0697323	−	0.0506635i	−0.552373	−	0.833597i	$-0.686278\pi$
$947$	2.14590	−	1.55909i	0.0697323	−	0.0506635i	0.622105	+	0.782934i	$0.286278\pi$
$948$		0			0
$949$	−16.6869			−0.541680
$950$	−5.59017	+	4.06150i	−0.181369	+	0.131772i
$951$		0			0
$952$	−2.23607	−	6.88191i	−0.0724714	−	0.223044i
$953$	−6.26393	+	4.55101i	−0.202909	+	0.147422i	−0.684599	−	0.728919i	$-0.740023\pi$
$953$	−6.26393	+	4.55101i	−0.202909	+	0.147422i	0.481691	+	0.876341i	$0.340023\pi$
$954$		0			0
$955$	−3.29180	−	2.39163i	−0.106520	−	0.0773913i
$956$	−10.2639	−	7.45718i	−0.331959	−	0.241183i
$957$		0			0
$958$	−14.2082	−	10.3229i	−0.459046	−	0.333517i
$959$	2.28115	−	7.02067i	0.0736623	−	0.226709i
$960$		0			0
$961$	−6.79837	−	20.9232i	−0.219302	−	0.674943i
$962$	−0.218847	+	0.673542i	−0.00705591	+	0.0217159i
$963$		0			0
$964$	0.482779	+	1.48584i	0.0155493	+	0.0478557i
$965$	5.32624	−	16.3925i	0.171458	−	0.527692i
$966$		0			0
$967$	−3.32624	−	2.41665i	−0.106965	−	0.0777143i	0.533017	−	0.846104i	$-0.321058\pi$
$967$	−3.32624	−	2.41665i	−0.106965	−	0.0777143i	−0.639982	+	0.768390i	$0.721058\pi$
$968$	−36.7082			−1.17985
$969$		0			0
$970$	11.2812	−	8.19624i	0.362216	−	0.263165i
$971$	4.54508	−	3.30220i	0.145859	−	0.105973i	−0.512463	−	0.858709i	$-0.671267\pi$
$971$	4.54508	−	3.30220i	0.145859	−	0.105973i	0.658321	+	0.752737i	$0.271267\pi$
$972$		0			0
$973$	0.954915	+	2.93893i	0.0306132	+	0.0942177i
$974$	−58.9230			−1.88801
$975$		0			0
$976$	−42.2705			−1.35305
$977$	0.725425	+	2.23263i	0.0232084	+	0.0714281i	0.961990	−	0.273085i	$-0.0880440\pi$
$977$	0.725425	+	2.23263i	0.0232084	+	0.0714281i	−0.938782	+	0.344513i	$0.888044\pi$
$978$		0			0
$979$	−37.8885	+	27.5276i	−1.21092	+	0.879787i
$980$	−2.82624	−	8.69827i	−0.0902809	−	0.277856i
$981$		0			0
$982$	69.9787			2.23311
$983$	7.78115	+	5.65334i	0.248180	+	0.180313i	0.704920	−	0.709287i	$-0.250983\pi$
$983$	7.78115	+	5.65334i	0.248180	+	0.180313i	−0.456740	+	0.889600i	$0.650983\pi$
$984$		0			0
$985$	−2.56231	−	7.88597i	−0.0816419	−	0.251268i
$986$	9.47214	+	29.1522i	0.301654	+	0.928396i
$987$		0			0
$988$	0.302439	−	0.930812i	0.00962187	−	0.0296131i
$989$	5.64590	+	17.3763i	0.179529	+	0.552534i
$990$		0			0
$991$	−4.74671	+	14.6089i	−0.150784	+	0.464066i	−0.997709	−	0.0676459i	$-0.978451\pi$
$991$	−4.74671	+	14.6089i	−0.150784	+	0.464066i	0.846925	+	0.531712i	$0.178451\pi$
$992$	−8.20820	−	5.96361i	−0.260611	−	0.189345i
$993$		0			0
$994$	−5.35410	−	3.88998i	−0.169822	−	0.123383i
$995$	−12.1353	+	37.3485i	−0.384713	+	1.18403i
$996$		0			0
$997$	−20.1353	+	14.6291i	−0.637690	+	0.463309i	−0.859056	−	0.511882i	$-0.828949\pi$
$997$	−20.1353	+	14.6291i	−0.637690	+	0.463309i	0.221366	+	0.975191i	$0.428949\pi$
$998$	3.78115	+	11.6372i	0.119690	+	0.368369i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.b.181.1		4
3.2	odd	2		25.2.d.a.6.1	✓	4
12.11	even	2		400.2.u.b.81.1		4
15.2	even	4		125.2.e.a.99.2		8
15.8	even	4		125.2.e.a.99.1		8
15.14	odd	2		125.2.d.a.26.1		4
25.11	even	5		5625.2.a.f.1.2		2
25.14	even	10		5625.2.a.d.1.1		2
25.21	even	5	inner	225.2.h.b.46.1		4
75.2	even	20		625.2.b.a.624.1		4
75.8	even	20		625.2.e.c.249.2		8
75.11	odd	10		625.2.a.b.1.1		2
75.14	odd	10		625.2.a.c.1.2		2
75.17	even	20		625.2.e.c.249.1		8
75.23	even	20		625.2.b.a.624.4		4
75.29	odd	10		125.2.d.a.101.1		4
75.38	even	20		625.2.e.c.374.1		8
75.41	odd	10		625.2.d.h.251.1		4
75.44	odd	10		625.2.d.b.376.1		4
75.47	even	20		125.2.e.a.24.1		8
75.53	even	20		125.2.e.a.24.2		8
75.56	odd	10		625.2.d.h.376.1		4
75.59	odd	10		625.2.d.b.251.1		4
75.62	even	20		625.2.e.c.374.2		8
75.71	odd	10		25.2.d.a.21.1	yes	4
300.11	even	10		10000.2.a.c.1.1		2
300.71	even	10		400.2.u.b.321.1		4
300.239	even	10		10000.2.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.6.1	✓	4	3.2	odd	2
25.2.d.a.21.1	yes	4	75.71	odd	10
125.2.d.a.26.1		4	15.14	odd	2
125.2.d.a.101.1		4	75.29	odd	10
125.2.e.a.24.1		8	75.47	even	20
125.2.e.a.24.2		8	75.53	even	20
125.2.e.a.99.1		8	15.8	even	4
125.2.e.a.99.2		8	15.2	even	4
225.2.h.b.46.1		4	25.21	even	5	inner
225.2.h.b.181.1		4	1.1	even	1	trivial
400.2.u.b.81.1		4	12.11	even	2
400.2.u.b.321.1		4	300.71	even	10
625.2.a.b.1.1		2	75.11	odd	10
625.2.a.c.1.2		2	75.14	odd	10
625.2.b.a.624.1		4	75.2	even	20
625.2.b.a.624.4		4	75.23	even	20
625.2.d.b.251.1		4	75.59	odd	10
625.2.d.b.376.1		4	75.44	odd	10
625.2.d.h.251.1		4	75.41	odd	10
625.2.d.h.376.1		4	75.56	odd	10
625.2.e.c.249.1		8	75.17	even	20
625.2.e.c.249.2		8	75.8	even	20
625.2.e.c.374.1		8	75.38	even	20
625.2.e.c.374.2		8	75.62	even	20
5625.2.a.d.1.1		2	25.14	even	10
5625.2.a.f.1.2		2	25.11	even	5
10000.2.a.c.1.1		2	300.11	even	10
10000.2.a.l.1.2		2	300.239	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 1.53884i) q^{2} +(-0.500000 + 0.363271i) q^{4} +(0.690983 - 2.12663i) q^{5} +0.618034 q^{7} +(1.80902 + 1.31433i) q^{8} +O(q^{10})\)	\(q+(0.500000 + 1.53884i) q^{2} +(-0.500000 + 0.363271i) q^{4} +(0.690983 - 2.12663i) q^{5} +0.618034 q^{7} +(1.80902 + 1.31433i) q^{8} +3.61803 q^{10} +(1.61803 + 4.97980i) q^{11} +(0.572949 - 1.76336i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.50000 + 4.61653i) q^{16} +(-4.23607 - 3.07768i) q^{17} +(-0.690983 - 0.502029i) q^{19} +(0.427051 + 1.31433i) q^{20} +(-6.85410 + 4.97980i) q^{22} +(-1.16312 - 3.57971i) q^{23} +(-4.04508 - 2.93893i) q^{25} +3.00000 q^{26} +(-0.309017 + 0.224514i) q^{28} +(-2.92705 + 2.12663i) q^{29} +(2.42705 + 1.76336i) q^{31} -3.38197 q^{32} +(2.61803 - 8.05748i) q^{34} +(0.427051 - 1.31433i) q^{35} +(-0.0729490 + 0.224514i) q^{37} +(0.427051 - 1.31433i) q^{38} +(4.04508 - 2.93893i) q^{40} +(0.236068 - 0.726543i) q^{41} -4.85410 q^{43} +(-2.61803 - 1.90211i) q^{44} +(4.92705 - 3.57971i) q^{46} +(0.500000 - 0.363271i) q^{47} -6.61803 q^{49} +(2.50000 - 7.69421i) q^{50} +(0.354102 + 1.08981i) q^{52} +(-2.80902 + 2.04087i) q^{53} +11.7082 q^{55} +(1.11803 + 0.812299i) q^{56} +(-4.73607 - 3.44095i) q^{58} +(3.35410 - 10.3229i) q^{59} +(2.69098 + 8.28199i) q^{61} +(-1.50000 + 4.61653i) q^{62} +(1.30902 + 4.02874i) q^{64} +(-3.35410 - 2.43690i) q^{65} +(-3.85410 - 2.80017i) q^{67} +3.23607 q^{68} +2.23607 q^{70} +(-5.35410 + 3.88998i) q^{71} +(-2.78115 - 8.55951i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(1.00000 + 3.07768i) q^{77} +(6.54508 - 4.75528i) q^{79} +(8.78115 + 6.37988i) q^{80} +1.23607 q^{82} +(-5.04508 - 3.66547i) q^{83} +(-9.47214 + 6.88191i) q^{85} +(-2.42705 - 7.46969i) q^{86} +(-3.61803 + 11.1352i) q^{88} +(2.76393 + 8.50651i) q^{89} +(0.354102 - 1.08981i) q^{91} +(1.88197 + 1.36733i) q^{92} +(0.809017 + 0.587785i) q^{94} +(-1.54508 + 1.12257i) q^{95} +(3.11803 - 2.26538i) q^{97} +(-3.30902 - 10.1841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 5 * q^5 - 2 * q^7 + 5 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8} + 10 q^{10} + 2 q^{11} + 9 q^{13} - q^{14} - 6 q^{16} - 8 q^{17} - 5 q^{19} - 5 q^{20} - 14 q^{22} + 11 q^{23} - 5 q^{25} + 12 q^{26} + q^{28} - 5 q^{29} + 3 q^{31} - 18 q^{32} + 6 q^{34} - 5 q^{35} - 7 q^{37} - 5 q^{38} + 5 q^{40} - 8 q^{41} - 6 q^{43} - 6 q^{44} + 13 q^{46} + 2 q^{47} - 22 q^{49} + 10 q^{50} - 12 q^{52} - 9 q^{53} + 20 q^{55} - 10 q^{58} + 13 q^{61} - 6 q^{62} + 3 q^{64} - 2 q^{67} + 4 q^{68} - 8 q^{71} + 9 q^{73} - 6 q^{74} + 20 q^{76} + 4 q^{77} + 15 q^{79} + 15 q^{80} - 4 q^{82} - 9 q^{83} - 20 q^{85} - 3 q^{86} - 10 q^{88} + 20 q^{89} - 12 q^{91} + 12 q^{92} + q^{94} + 5 q^{95} + 8 q^{97} - 11 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 5 * q^5 - 2 * q^7 + 5 * q^8 + 10 * q^10 + 2 * q^11 + 9 * q^13 - q^14 - 6 * q^16 - 8 * q^17 - 5 * q^19 - 5 * q^20 - 14 * q^22 + 11 * q^23 - 5 * q^25 + 12 * q^26 + q^28 - 5 * q^29 + 3 * q^31 - 18 * q^32 + 6 * q^34 - 5 * q^35 - 7 * q^37 - 5 * q^38 + 5 * q^40 - 8 * q^41 - 6 * q^43 - 6 * q^44 + 13 * q^46 + 2 * q^47 - 22 * q^49 + 10 * q^50 - 12 * q^52 - 9 * q^53 + 20 * q^55 - 10 * q^58 + 13 * q^61 - 6 * q^62 + 3 * q^64 - 2 * q^67 + 4 * q^68 - 8 * q^71 + 9 * q^73 - 6 * q^74 + 20 * q^76 + 4 * q^77 + 15 * q^79 + 15 * q^80 - 4 * q^82 - 9 * q^83 - 20 * q^85 - 3 * q^86 - 10 * q^88 + 20 * q^89 - 12 * q^91 + 12 * q^92 + q^94 + 5 * q^95 + 8 * q^97 - 11 * q^98

Introduction

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