LMFDB - Embedded newform 288.2.w.a.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(35,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("288.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			251.3
Character	$\chi$	$=$	288.251
Dual form			288.2.w.a.179.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.850468 - 1.12991i) q^{2} +(-0.553410 + 1.92191i) q^{4} +(0.352978 - 0.852163i) q^{5} +(-3.43393 + 3.43393i) q^{7} +(2.64225 - 1.00922i) q^{8} +O(q^{10})$	\(q+(-0.850468 - 1.12991i) q^{2} +(-0.553410 + 1.92191i) q^{4} +(0.352978 - 0.852163i) q^{5} +(-3.43393 + 3.43393i) q^{7} +(2.64225 - 1.00922i) q^{8} +(-1.26307 + 0.325903i) q^{10} +(-1.44650 + 3.49216i) q^{11} +(-0.258636 + 0.107131i) q^{13} +(6.80049 + 0.959599i) q^{14} +(-3.38747 - 2.12721i) q^{16} -5.30575 q^{17} +(2.72546 + 6.57983i) q^{19} +(1.44244 + 1.14999i) q^{20} +(5.17604 - 1.33555i) q^{22} +(2.23882 - 2.23882i) q^{23} +(2.93394 + 2.93394i) q^{25} +(0.341010 + 0.201126i) q^{26} +(-4.69934 - 8.50008i) q^{28} +(-3.16953 + 1.31286i) q^{29} -3.46749i q^{31} +(0.477376 + 5.63668i) q^{32} +(4.51237 + 5.99504i) q^{34} +(1.71417 + 4.13837i) q^{35} +(1.27512 + 0.528171i) q^{37} +(5.11673 - 8.67547i) q^{38} +(0.0726377 - 2.60786i) q^{40} +(5.28251 + 5.28251i) q^{41} +(2.46955 + 1.02292i) q^{43} +(-5.91111 - 4.71264i) q^{44} +(-4.43371 - 0.625628i) q^{46} -0.423698i q^{47} -16.5838i q^{49} +(0.819880 - 5.81033i) q^{50} +(-0.0627636 - 0.556363i) q^{52} +(-12.5563 - 5.20097i) q^{53} +(2.46531 + 2.46531i) q^{55} +(-5.60772 + 12.5389i) q^{56} +(4.17901 + 2.46475i) q^{58} +(-5.24194 - 2.17128i) q^{59} +(0.0138304 + 0.0333895i) q^{61} +(-3.91796 + 2.94899i) q^{62} +(5.96296 - 5.33320i) q^{64} +0.258215i q^{65} +(-9.82224 + 4.06850i) q^{67} +(2.93626 - 10.1972i) q^{68} +(3.21816 - 5.45642i) q^{70} +(4.64969 + 4.64969i) q^{71} +(3.96752 - 3.96752i) q^{73} +(-0.487659 - 1.88997i) q^{74} +(-14.1541 + 1.59674i) q^{76} +(-7.02466 - 16.9590i) q^{77} -12.7319 q^{79} +(-3.00843 + 2.13583i) q^{80} +(1.47618 - 10.4614i) q^{82} +(-0.867335 + 0.359262i) q^{83} +(-1.87281 + 4.52137i) q^{85} +(-0.944460 - 3.66034i) q^{86} +(-0.297669 + 10.6870i) q^{88} +(4.82033 - 4.82033i) q^{89} +(0.520260 - 1.25602i) q^{91} +(3.06382 + 5.54178i) q^{92} +(-0.478742 + 0.360341i) q^{94} +6.56912 q^{95} +8.78058 q^{97} +(-18.7382 + 14.1040i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) $ 32 * q - 4 * q^2 - 4 * q^8	$ 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) $ 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.850468	−	1.12991i	−0.601371	−	0.798970i
$2$	−0.850468	−	1.12991i	−0.601371	−	0.798970i
$3$		0			0
$3$		0			0
$4$	−0.553410	+	1.92191i	−0.276705	+	0.960955i
$5$	0.352978	−	0.852163i	0.157856	−	0.381099i	−0.825087	−	0.565005i	$-0.808874\pi$
$5$	0.352978	−	0.852163i	0.157856	−	0.381099i	0.982944	+	0.183906i	$0.0588742\pi$
$6$		0			0
$7$	−3.43393	+	3.43393i	−1.29790	+	1.29790i	−0.368130	+	0.929774i	$0.620002\pi$
$7$	−3.43393	+	3.43393i	−1.29790	+	1.29790i	−0.929774	+	0.368130i	$0.879998\pi$
$8$	2.64225	−	1.00922i	0.934176	−	0.356812i
$9$		0			0
$10$	−1.26307	+	0.325903i	−0.399417	+	0.103060i
$11$	−1.44650	+	3.49216i	−0.436136	+	1.05293i	0.541135	+	0.840936i	$0.317995\pi$
$11$	−1.44650	+	3.49216i	−0.436136	+	1.05293i	−0.977272	+	0.211991i	$0.932005\pi$
$12$		0			0
$13$	−0.258636	+	0.107131i	−0.0717328	+	0.0297127i	−0.418261	−	0.908327i	$-0.637360\pi$
$13$	−0.258636	+	0.107131i	−0.0717328	+	0.0297127i	0.346529	+	0.938039i	$0.387360\pi$
$14$	6.80049	+	0.959599i	1.81751	+	0.256464i
$15$		0			0
$16$	−3.38747	−	2.12721i	−0.846869	−	0.531802i
$17$	−5.30575			−1.28683			−0.643417	−	0.765516i	$-0.722484\pi$
$17$	−5.30575			−1.28683			−0.643417	+	0.765516i	$0.722484\pi$
$18$		0			0
$19$	2.72546	+	6.57983i	0.625263	+	1.50952i	0.845447	+	0.534059i	$0.179334\pi$
$19$	2.72546	+	6.57983i	0.625263	+	1.50952i	−0.220185	+	0.975458i	$0.570666\pi$
$20$	1.44244	+	1.14999i	0.322539	+	0.257145i
$21$		0			0
$22$	5.17604	−	1.33555i	1.10354	−	0.284740i
$23$	2.23882	−	2.23882i	0.466825	−	0.466825i	−0.434059	−	0.900884i	$-0.642919\pi$
$23$	2.23882	−	2.23882i	0.466825	−	0.466825i	0.900884	+	0.434059i	$0.142919\pi$
$24$		0			0
$25$	2.93394	+	2.93394i	0.586789	+	0.586789i
$26$	0.341010	+	0.201126i	0.0668776	+	0.0394440i
$27$		0			0
$28$	−4.69934	−	8.50008i	−0.888091	−	1.60636i
$29$	−3.16953	+	1.31286i	−0.588568	+	0.243793i	−0.657034	−	0.753861i	$-0.728189\pi$
$29$	−3.16953	+	1.31286i	−0.588568	+	0.243793i	0.0684666	+	0.997653i	$0.478189\pi$
$30$		0			0
$31$		−	3.46749i		−	0.622779i	−0.950282	−	0.311390i	$-0.899206\pi$
$31$		−	3.46749i		−	0.622779i	0.950282	−	0.311390i	$-0.100794\pi$
$32$	0.477376	+	5.63668i	0.0843889	+	0.996433i
$33$		0			0
$34$	4.51237	+	5.99504i	0.773865	+	1.02814i
$35$	1.71417	+	4.13837i	0.289748	+	0.699513i
$36$		0			0
$37$	1.27512	+	0.528171i	0.209628	+	0.0868308i	0.485027	−	0.874499i	$-0.338810\pi$
$37$	1.27512	+	0.528171i	0.209628	+	0.0868308i	−0.275399	+	0.961330i	$0.588810\pi$
$38$	5.11673	−	8.67547i	0.830044	−	1.40735i
$39$		0			0
$40$	0.0726377	−	2.60786i	0.0114850	−	0.412339i
$41$	5.28251	+	5.28251i	0.824989	+	0.824989i	0.986819	−	0.161830i	$-0.0517396\pi$
$41$	5.28251	+	5.28251i	0.824989	+	0.824989i	−0.161830	+	0.986819i	$0.551740\pi$
$42$		0			0
$43$	2.46955	+	1.02292i	0.376603	+	0.155994i	0.562952	−	0.826489i	$-0.309666\pi$
$43$	2.46955	+	1.02292i	0.376603	+	0.155994i	−0.186349	+	0.982484i	$0.559666\pi$
$44$	−5.91111	−	4.71264i	−0.891134	−	0.710457i
$45$		0			0
$46$	−4.43371	−	0.625628i	−0.653715	−	0.0922439i
$47$		−	0.423698i		−	0.0618027i	−0.999522	−	0.0309013i	$-0.990162\pi$
$47$		−	0.423698i		−	0.0618027i	0.999522	−	0.0309013i	$-0.00983776\pi$
$48$		0			0
$49$		−	16.5838i		−	2.36911i
$50$	0.819880	−	5.81033i	0.115948	−	0.821705i
$51$		0			0
$52$	−0.0627636	−	0.556363i	−0.00870374	−	0.0771536i
$53$	−12.5563	−	5.20097i	−1.72474	−	0.714409i	−0.999669	−	0.0257295i	$-0.991809\pi$
$53$	−12.5563	−	5.20097i	−1.72474	−	0.714409i	−0.725066	−	0.688679i	$-0.758191\pi$
$54$		0			0
$55$	2.46531	+	2.46531i	0.332422	+	0.332422i
$56$	−5.60772	+	12.5389i	−0.749364	+	1.67558i
$57$		0			0
$58$	4.17901	+	2.46475i	0.548731	+	0.323638i
$59$	−5.24194	−	2.17128i	−0.682442	−	0.282677i	0.0144054	−	0.999896i	$-0.495414\pi$
$59$	−5.24194	−	2.17128i	−0.682442	−	0.282677i	−0.696847	+	0.717220i	$0.745414\pi$
$60$		0			0
$61$	0.0138304	+	0.0333895i	0.00177080	+	0.00427509i	0.924762	−	0.380545i	$-0.124264\pi$
$61$	0.0138304	+	0.0333895i	0.00177080	+	0.00427509i	−0.922992	+	0.384820i	$0.874264\pi$
$62$	−3.91796	+	2.94899i	−0.497582	+	0.374522i
$63$		0			0
$64$	5.96296	−	5.33320i	0.745371	−	0.666650i
$65$			0.258215i			0.0320276i
$66$		0			0
$67$	−9.82224	+	4.06850i	−1.19998	+	0.497047i	−0.890992	−	0.454020i	$-0.849990\pi$
$67$	−9.82224	+	4.06850i	−1.19998	+	0.497047i	−0.308986	+	0.951067i	$0.599990\pi$
$68$	2.93626	−	10.1972i	0.356073	−	1.23659i
$69$		0			0
$70$	3.21816	−	5.45642i	0.384643	−	0.652166i
$71$	4.64969	+	4.64969i	0.551817	+	0.551817i	0.926965	−	0.375148i	$-0.122408\pi$
$71$	4.64969	+	4.64969i	0.551817	+	0.551817i	−0.375148	+	0.926965i	$0.622408\pi$
$72$		0			0
$73$	3.96752	−	3.96752i	0.464363	−	0.464363i	−0.435720	−	0.900082i	$-0.643506\pi$
$73$	3.96752	−	3.96752i	0.464363	−	0.464363i	0.900082	+	0.435720i	$0.143506\pi$
$74$	−0.487659	−	1.88997i	−0.0566892	−	0.219704i
$75$		0			0
$76$	−14.1541	+	1.59674i	−1.62359	+	0.183158i
$77$	−7.02466	−	16.9590i	−0.800534	−	1.93266i
$78$		0			0
$79$	−12.7319			−1.43245			−0.716224	−	0.697870i	$-0.754131\pi$
$79$	−12.7319			−1.43245			−0.716224	+	0.697870i	$0.754131\pi$
$80$	−3.00843	+	2.13583i	−0.336353	+	0.238793i
$81$		0			0
$82$	1.47618	−	10.4614i	0.163016	−	1.15527i
$83$	−0.867335	+	0.359262i	−0.0952024	+	0.0394341i	−0.429776	−	0.902935i	$-0.641408\pi$
$83$	−0.867335	+	0.359262i	−0.0952024	+	0.0394341i	0.334574	+	0.942369i	$0.391408\pi$
$84$		0			0
$85$	−1.87281	+	4.52137i	−0.203135	+	0.490411i
$86$	−0.944460	−	3.66034i	−0.101844	−	0.394705i
$87$		0			0
$88$	−0.297669	+	10.6870i	−0.0317316	+	1.13924i
$89$	4.82033	−	4.82033i	0.510954	−	0.510954i	−0.403865	−	0.914819i	$-0.632333\pi$
$89$	4.82033	−	4.82033i	0.510954	−	0.510954i	0.914819	+	0.403865i	$0.132333\pi$
$90$		0			0
$91$	0.520260	−	1.25602i	0.0545381	−	0.131667i
$92$	3.06382	+	5.54178i	0.319425	+	0.577771i
$93$		0			0
$94$	−0.478742	+	0.360341i	−0.0493784	+	0.0371663i
$95$	6.56912			0.673977
$96$		0			0
$97$	8.78058			0.891532			0.445766	−	0.895149i	$-0.352931\pi$
$97$	8.78058			0.891532			0.445766	+	0.895149i	$0.352931\pi$
$98$	−18.7382	+	14.1040i	−1.89285	+	1.42472i
$99$		0			0
$100$	−7.26245	+	4.01510i	−0.726245	+	0.401510i
$101$	−4.37141	+	10.5535i	−0.434972	+	1.05011i	0.542691	+	0.839933i	$0.317406\pi$
$101$	−4.37141	+	10.5535i	−0.434972	+	1.05011i	−0.977662	+	0.210182i	$0.932594\pi$
$102$		0			0
$103$	2.54327	−	2.54327i	0.250596	−	0.250596i	−0.570619	−	0.821215i	$-0.693297\pi$
$103$	2.54327	−	2.54327i	0.250596	−	0.250596i	0.821215	+	0.570619i	$0.193297\pi$
$104$	−0.575264	+	0.544086i	−0.0564092	+	0.0533520i
$105$		0			0
$106$	4.80204	+	18.6108i	0.466415	+	1.80764i
$107$	−1.34953	+	3.25806i	−0.130464	+	0.314968i	−0.975590	−	0.219599i	$-0.929525\pi$
$107$	−1.34953	+	3.25806i	−0.130464	+	0.314968i	0.845126	+	0.534567i	$0.179525\pi$
$108$		0			0
$109$	11.5904	−	4.80089i	1.11016	−	0.459842i	0.249165	−	0.968461i	$-0.419844\pi$
$109$	11.5904	−	4.80089i	1.11016	−	0.459842i	0.860992	+	0.508619i	$0.169844\pi$
$110$	0.688921	−	4.88225i	0.0656861	−	0.465505i
$111$		0			0
$112$	18.9370	−	4.32767i	1.78938	−	0.408926i
$113$	16.5004			1.55223			0.776115	−	0.630591i	$-0.217188\pi$
$113$	16.5004			1.55223			0.776115	+	0.630591i	$0.217188\pi$
$114$		0			0
$115$	−1.11758	−	2.69809i	−0.104215	−	0.251598i
$116$	−0.769155	−	6.81811i	−0.0714142	−	0.633046i
$117$		0			0
$118$	2.00474	+	7.76954i	0.184551	+	0.715244i
$119$	18.2196	−	18.2196i	1.67019	−	1.67019i
$120$		0			0
$121$	−2.32465	−	2.32465i	−0.211332	−	0.211332i
$122$	0.0259650	−	0.0440238i	0.00235076	−	0.00398573i
$123$		0			0
$124$	6.66420	+	1.91894i	0.598463	+	0.172326i
$125$	7.79663	−	3.22947i	0.697352	−	0.288853i
$126$		0			0
$127$		−	9.43014i		−	0.836790i	−0.908265	−	0.418395i	$-0.862593\pi$
$127$		−	9.43014i		−	0.836790i	0.908265	−	0.418395i	$-0.137407\pi$
$128$	−11.0974	−	2.20192i	−0.980878	−	0.194624i
$129$		0			0
$130$	0.291761	−	0.219604i	0.0255891	−	0.0192605i
$131$	6.19791	+	14.9631i	0.541514	+	1.30733i	0.923654	+	0.383227i	$0.125187\pi$
$131$	6.19791	+	14.9631i	0.541514	+	1.30733i	−0.382140	+	0.924104i	$0.624813\pi$
$132$		0			0
$133$	−31.9537	−	13.2357i	−2.77074	−	1.14768i
$134$	12.9506	+	7.63815i	1.11876	+	0.659836i
$135$		0			0
$136$	−14.0191	+	5.35465i	−1.20213	+	0.459158i
$137$	5.01737	+	5.01737i	0.428663	+	0.428663i	0.888173	−	0.459510i	$-0.151975\pi$
$137$	5.01737	+	5.01737i	0.428663	+	0.428663i	−0.459510	+	0.888173i	$0.651975\pi$
$138$		0			0
$139$	19.0610	+	7.89534i	1.61674	+	0.669674i	0.993654	−	0.112482i	$-0.0358800\pi$
$139$	19.0610	+	7.89534i	1.61674	+	0.669674i	0.623083	+	0.782156i	$0.285880\pi$
$140$	−8.90222	+	1.00426i	−0.752375	+	0.0848758i
$141$		0			0
$142$	1.29934	−	9.20816i	0.109038	−	0.772731i
$143$		−	1.05816i		−	0.0884881i
$144$		0			0
$145$			3.16437i			0.262787i
$146$	−7.85720	−	1.10871i	−0.650266	−	0.0917573i
$147$		0			0
$148$	−1.72076	+	2.15837i	−0.141446	+	0.177417i
$149$	20.8124	+	8.62076i	1.70502	+	0.706240i	0.999996	−	0.00294754i	$-0.000938232\pi$
$149$	20.8124	+	8.62076i	1.70502	+	0.706240i	0.705019	+	0.709188i	$0.250938\pi$
$150$		0			0
$151$	4.68070	+	4.68070i	0.380910	+	0.380910i	0.871430	−	0.490520i	$-0.163193\pi$
$151$	4.68070	+	4.68070i	0.380910	+	0.380910i	−0.490520	+	0.871430i	$0.663193\pi$
$152$	13.8418	+	14.6350i	1.12272	+	1.18705i
$153$		0			0
$154$	−13.1880	+	22.3604i	−1.06272	+	1.80185i
$155$	−2.95487	−	1.22395i	−0.237341	−	0.0983097i
$156$		0			0
$157$	6.17384	+	14.9050i	0.492726	+	1.18955i	0.953327	+	0.301939i	$0.0976340\pi$
$157$	6.17384	+	14.9050i	0.492726	+	1.18955i	−0.460601	+	0.887607i	$0.652366\pi$
$158$	10.8280	+	14.3859i	0.861433	+	1.14448i
$159$		0			0
$160$	4.97187	+	1.58282i	0.393061	+	0.125133i
$161$			15.3759i			1.21179i
$162$		0			0
$163$	−2.13457	+	0.884169i	−0.167193	+	0.0692534i	−0.464710	−	0.885463i	$-0.653841\pi$
$163$	−2.13457	+	0.884169i	−0.167193	+	0.0692534i	0.297517	+	0.954716i	$0.403841\pi$
$164$	−13.0759	+	7.22911i	−1.02106	+	0.564498i
$165$		0			0
$166$	1.14358	+	0.674473i	0.0887587	+	0.0523493i
$167$	−14.2052	−	14.2052i	−1.09923	−	1.09923i	−0.994500	−	0.104733i	$-0.966601\pi$
$167$	−14.2052	−	14.2052i	−1.09923	−	1.09923i	−0.104733	−	0.994500i	$-0.533399\pi$
$168$		0			0
$169$	−9.13697	+	9.13697i	−0.702844	+	0.702844i
$170$	6.70152	−	1.72916i	0.513983	−	0.132621i
$171$		0			0
$172$	−3.33264	+	4.18016i	−0.254111	+	0.318734i
$173$	−4.53353	−	10.9449i	−0.344678	−	0.832127i	−0.997230	−	0.0743825i	$-0.976301\pi$
$173$	−4.53353	−	10.9449i	−0.344678	−	0.832127i	0.652552	−	0.757744i	$-0.273699\pi$
$174$		0			0
$175$	−20.1499			−1.52319
$176$	12.3285	−	8.75260i	0.929299	−	0.659752i
$177$		0			0
$178$	−9.54609	−	1.34702i	−0.715510	−	0.100964i
$179$	−9.00945	+	3.73184i	−0.673398	+	0.278931i	−0.693064	−	0.720876i	$-0.743740\pi$
$179$	−9.00945	+	3.73184i	−0.673398	+	0.278931i	0.0196661	+	0.999807i	$0.493740\pi$
$180$		0			0
$181$	−5.75935	+	13.9043i	−0.428089	+	1.03350i	0.551804	+	0.833974i	$0.313940\pi$
$181$	−5.75935	+	13.9043i	−0.428089	+	1.03350i	−0.979893	+	0.199524i	$0.936060\pi$
$182$	−1.86166	+	0.480354i	−0.137995	+	0.0356062i
$183$		0			0
$184$	3.65606	−	8.17496i	0.269528	−	0.602666i
$185$	0.900176	−	0.900176i	0.0661823	−	0.0661823i
$186$		0			0
$187$	7.67477	−	18.5285i	0.561235	−	1.35494i
$188$	0.814309	+	0.234478i	0.0593896	+	0.0171011i
$189$		0			0
$190$	−5.58682	−	7.42254i	−0.405311	−	0.538487i
$191$	−6.18207			−0.447319			−0.223660	−	0.974667i	$-0.571800\pi$
$191$	−6.18207			−0.447319			−0.223660	+	0.974667i	$0.571800\pi$
$192$		0			0
$193$	−11.2515			−0.809899			−0.404949	−	0.914339i	$-0.632711\pi$
$193$	−11.2515			−0.809899			−0.404949	+	0.914339i	$0.632711\pi$
$194$	−7.46759	−	9.92129i	−0.536142	−	0.712307i
$195$		0			0
$196$	31.8725	+	9.17763i	2.27661	+	0.655545i
$197$	2.59303	−	6.26014i	0.184746	−	0.446016i	−0.804187	−	0.594376i	$-0.797399\pi$
$197$	2.59303	−	6.26014i	0.184746	−	0.446016i	0.988934	+	0.148359i	$0.0473992\pi$
$198$		0			0
$199$	8.67622	−	8.67622i	0.615041	−	0.615041i	−0.329214	−	0.944255i	$-0.606784\pi$
$199$	8.67622	−	8.67622i	0.615041	−	0.615041i	0.944255	+	0.329214i	$0.106784\pi$
$200$	10.7132	+	4.79123i	0.757538	+	0.338791i
$201$		0			0
$202$	15.6423	−	4.03611i	1.10059	−	0.283980i
$203$	6.37568	−	15.3922i	0.447485	−	1.08032i
$204$		0			0
$205$	6.36616	−	2.63695i	0.444632	−	0.184173i
$206$	−5.03665	−	0.710708i	−0.350920	−	0.0495174i
$207$		0			0
$208$	1.10401	+	0.187271i	0.0765495	+	0.0129849i
$209$	−26.9202			−1.86211
$210$		0			0
$211$	3.18497	+	7.68919i	0.219262	+	0.529345i	0.994787	−	0.101971i	$-0.0325149\pi$
$211$	3.18497	+	7.68919i	0.219262	+	0.529345i	−0.775525	+	0.631317i	$0.782515\pi$
$212$	16.9446	−	21.2537i	1.16376	−	1.45971i
$213$		0			0
$214$	4.82906	−	1.24602i	0.330108	−	0.0851760i
$215$	1.74339	−	1.74339i	0.118898	−	0.118898i
$216$		0			0
$217$	11.9071	+	11.9071i	0.808308	+	0.808308i
$218$	−15.2818	−	9.01313i	−1.03502	−	0.610446i
$219$		0			0
$220$	−6.10243	+	3.37378i	−0.411426	+	0.227460i
$221$	1.37226	−	0.568409i	0.0923082	−	0.0382353i
$222$		0			0
$223$		−	12.9728i		−	0.868722i	−0.900739	−	0.434361i	$-0.856974\pi$
$223$		−	12.9728i		−	0.868722i	0.900739	−	0.434361i	$-0.143026\pi$
$224$	−20.9952	−	17.7167i	−1.40280	−	1.18375i
$225$		0			0
$226$	−14.0331	−	18.6441i	−0.933467	−	1.24018i
$227$	3.79613	+	9.16468i	0.251958	+	0.608281i	0.998362	−	0.0572122i	$-0.0182212\pi$
$227$	3.79613	+	9.16468i	0.251958	+	0.608281i	−0.746404	+	0.665493i	$0.768221\pi$
$228$		0			0
$229$	4.91823	+	2.03720i	0.325006	+	0.134622i	0.539220	−	0.842165i	$-0.318719\pi$
$229$	4.91823	+	2.03720i	0.325006	+	0.134622i	−0.214214	+	0.976787i	$0.568719\pi$
$230$	−2.09814	+	3.55741i	−0.138347	+	0.234569i
$231$		0			0
$232$	−7.04974	+	6.66766i	−0.462838	+	0.437753i
$233$	10.8493	+	10.8493i	0.710759	+	0.710759i	0.966694	−	0.255935i	$-0.0823834\pi$
$233$	10.8493	+	10.8493i	0.710759	+	0.710759i	−0.255935	+	0.966694i	$0.582383\pi$
$234$		0			0
$235$	−0.361060	−	0.149556i	−0.0235529	−	0.00975594i
$236$	7.07394	−	8.87292i	0.460475	−	0.577578i
$237$		0			0
$238$	−36.0817	−	5.09140i	−2.33883	−	0.330026i
$239$			7.69444i			0.497712i	0.968540	+	0.248856i	$0.0800546\pi$
$239$			7.69444i			0.497712i	−0.968540	+	0.248856i	$0.919945\pi$
$240$		0			0
$241$		−	14.5669i		−	0.938338i	−0.883108	−	0.469169i	$-0.844553\pi$
$241$		−	14.5669i		−	0.938338i	0.883108	−	0.469169i	$-0.155447\pi$
$242$	−0.649615	+	4.60370i	−0.0417588	+	0.295937i
$243$		0			0
$244$	−0.0718255	+	0.00810267i	−0.00459815	+	0.000518720i
$245$	−14.1321	−	5.85370i	−0.902866	−	0.373979i
$246$		0			0
$247$	−1.40980	−	1.40980i	−0.0897037	−	0.0897037i
$248$	−3.49945	−	9.16197i	−0.222215	−	0.581786i
$249$		0			0
$250$	−10.2798	−	6.06296i	−0.650152	−	0.383455i
$251$	−14.1528	−	5.86227i	−0.893315	−	0.370023i	−0.111669	−	0.993745i	$-0.535620\pi$
$251$	−14.1528	−	5.86227i	−0.893315	−	0.370023i	−0.781646	+	0.623722i	$0.785620\pi$
$252$		0			0
$253$	4.57986	+	11.0568i	0.287933	+	0.695132i
$254$	−10.6552	+	8.02003i	−0.668570	+	0.503221i
$255$		0			0
$256$	6.94997	+	14.4117i	0.434373	+	0.900733i
$257$		−	19.4990i		−	1.21632i	−0.793816	−	0.608159i	$-0.791908\pi$
$257$		−	19.4990i		−	1.21632i	0.793816	−	0.608159i	$-0.208092\pi$
$258$		0			0
$259$	−6.19237	+	2.56496i	−0.384775	+	0.159379i
$260$	−0.496266	−	0.142899i	−0.0307771	−	0.00886221i
$261$		0			0
$262$	11.6359	−	19.7287i	0.718867	−	1.21884i
$263$	9.65433	+	9.65433i	0.595312	+	0.595312i	0.939061	−	0.343750i	$-0.111697\pi$
$263$	9.65433	+	9.65433i	0.595312	+	0.595312i	−0.343750	+	0.939061i	$0.611697\pi$
$264$		0			0
$265$	−8.86416	+	8.86416i	−0.544521	+	0.544521i
$266$	12.2204	+	47.3615i	0.749284	+	2.90392i
$267$		0			0
$268$	−2.38357	−	21.1290i	−0.145600	−	1.29066i
$269$	7.95451	+	19.2039i	0.484995	+	1.17088i	0.957209	+	0.289397i	$0.0934549\pi$
$269$	7.95451	+	19.2039i	0.484995	+	1.17088i	−0.472214	+	0.881484i	$0.656545\pi$
$270$		0			0
$271$	19.1213			1.16154			0.580770	−	0.814068i	$-0.302752\pi$
$271$	19.1213			1.16154			0.580770	+	0.814068i	$0.302752\pi$
$272$	17.9731	+	11.2864i	1.08978	+	0.684341i
$273$		0			0
$274$	1.40208	−	9.93630i	0.0847030	−	0.600274i
$275$	−14.4898	+	6.00186i	−0.873765	+	0.361926i
$276$		0			0
$277$	−0.609964	+	1.47258i	−0.0366492	+	0.0884789i	−0.941144	−	0.338005i	$-0.890248\pi$
$277$	−0.609964	+	1.47258i	−0.0366492	+	0.0884789i	0.904495	+	0.426484i	$0.140248\pi$
$278$	−7.28974	−	28.2521i	−0.437210	−	1.69445i
$279$		0			0
$280$	8.70578	+	9.20464i	0.520270	+	0.550083i
$281$	8.76628	−	8.76628i	0.522953	−	0.522953i	−0.395509	−	0.918462i	$-0.629432\pi$
$281$	8.76628	−	8.76628i	0.522953	−	0.522953i	0.918462	+	0.395509i	$0.129432\pi$
$282$		0			0
$283$	7.64026	−	18.4452i	0.454166	−	1.09645i	−0.516557	−	0.856253i	$-0.672787\pi$
$283$	7.64026	−	18.4452i	0.454166	−	1.09645i	0.970723	−	0.240201i	$-0.0772134\pi$
$284$	−11.5095	+	6.36310i	−0.682961	+	0.377580i
$285$		0			0
$286$	−1.19563	+	0.899934i	−0.0706993	+	0.0532142i
$287$	−36.2795			−2.14151
$288$		0			0
$289$	11.1510			0.655942
$290$	3.57547	−	2.69120i	0.209959	−	0.158032i
$291$		0			0
$292$	5.42955	+	9.82087i	0.317740	+	0.574723i
$293$	−8.73727	+	21.0936i	−0.510437	+	1.23230i	0.433194	+	0.901301i	$0.357387\pi$
$293$	−8.73727	+	21.0936i	−0.510437	+	1.23230i	−0.943630	+	0.331002i	$0.892613\pi$
$294$		0			0
$295$	−3.70057	+	3.70057i	−0.215456	+	0.215456i
$296$	3.90222	+	0.108690i	0.226812	+	0.00631748i
$297$		0			0
$298$	−7.95952	−	30.8479i	−0.461083	−	1.78697i
$299$	−0.339193	+	0.818885i	−0.0196160	+	0.0473573i
$300$		0			0
$301$	−11.9929	+	4.96763i	−0.691260	+	0.286329i
$302$	1.30800	−	9.26957i	0.0752671	−	0.533404i
$303$		0			0
$304$	4.76426	−	28.0866i	0.273249	−	1.61088i
$305$	0.0333351			0.00190876
$306$		0			0
$307$	2.29860	+	5.54931i	0.131188	+	0.316716i	0.975801	−	0.218662i	$-0.0701693\pi$
$307$	2.29860	+	5.54931i	0.131188	+	0.316716i	−0.844613	+	0.535378i	$0.820169\pi$
$308$	36.4812	−	4.11547i	2.07871	−	0.234501i
$309$		0			0
$310$	1.13007	+	4.37967i	0.0641834	+	0.248749i
$311$	−12.3351	+	12.3351i	−0.699460	+	0.699460i	−0.964294	−	0.264834i	$-0.914683\pi$
$311$	−12.3351	+	12.3351i	−0.699460	+	0.699460i	0.264834	+	0.964294i	$0.414683\pi$
$312$		0			0
$313$	9.07712	+	9.07712i	0.513069	+	0.513069i	0.915465	−	0.402397i	$-0.131823\pi$
$313$	9.07712	+	9.07712i	0.513069	+	0.513069i	−0.402397	+	0.915465i	$0.631823\pi$
$314$	11.5907	−	19.6521i	0.654100	−	1.10903i
$315$		0			0
$316$	7.04595	−	24.4695i	0.396366	−	1.37652i
$317$	−14.7317	+	6.10208i	−0.827416	+	0.342727i	−0.755879	−	0.654711i	$-0.772790\pi$
$317$	−14.7317	+	6.10208i	−0.827416	+	0.342727i	−0.0715366	+	0.997438i	$0.522790\pi$
$318$		0			0
$319$		−	12.9676i		−	0.726045i
$320$	−2.43997	−	6.96392i	−0.136398	−	0.389295i
$321$		0			0
$322$	17.3734	−	13.0767i	0.968183	−	0.728735i
$323$	−14.4606	−	34.9110i	−0.804609	−	1.94250i
$324$		0			0
$325$	−1.07314	−	0.444509i	−0.0595271	−	0.0246569i
$326$	2.81442	+	1.65993i	0.155876	+	0.0919348i
$327$		0			0
$328$	19.2889	+	8.62651i	1.06505	+	0.476319i
$329$	1.45495	+	1.45495i	0.0802139	+	0.0802139i
$330$		0			0
$331$	−20.7207	−	8.58281i	−1.13892	−	0.471754i	−0.268113	−	0.963387i	$-0.586400\pi$
$331$	−20.7207	−	8.58281i	−1.13892	−	0.471754i	−0.870802	+	0.491633i	$0.836400\pi$
$332$	−0.210477	−	1.86576i	−0.0115514	−	0.102397i
$333$		0			0
$334$	−3.96960	+	28.1318i	−0.217207	+	1.53930i
$335$			9.80624i			0.535772i
$336$		0			0
$337$		−	12.9981i		−	0.708052i	−0.935236	−	0.354026i	$-0.884812\pi$
$337$		−	12.9981i		−	0.708052i	0.935236	−	0.354026i	$-0.115188\pi$
$338$	18.0947	+	2.55329i	0.984221	+	0.138881i
$339$		0			0
$340$	−7.65323	−	6.10155i	−0.415055	−	0.330903i
$341$	12.1090	+	5.01573i	0.655741	+	0.271617i
$342$		0			0
$343$	32.9100	+	32.9100i	1.77697	+	1.77697i
$344$	7.55752	+	0.210502i	0.407474	+	0.0113495i
$345$		0			0
$346$	−8.51119	+	14.4308i	−0.457564	+	0.775805i
$347$	−24.4093	−	10.1107i	−1.31036	−	0.542769i	−0.385372	−	0.922762i	$-0.625927\pi$
$347$	−24.4093	−	10.1107i	−1.31036	−	0.542769i	−0.924990	+	0.379992i	$0.875927\pi$
$348$		0			0
$349$	−3.82444	−	9.23301i	−0.204717	−	0.494231i	0.787859	−	0.615856i	$-0.211190\pi$
$349$	−3.82444	−	9.23301i	−0.204717	−	0.494231i	−0.992576	+	0.121624i	$0.961190\pi$
$350$	17.1369	+	22.7677i	0.916004	+	1.21698i
$351$		0			0
$352$	−20.3747	−	6.48638i	−1.08598	−	0.345725i
$353$			24.4035i			1.29887i	0.760418	+	0.649434i	$0.224994\pi$
$353$			24.4035i			1.29887i	−0.760418	+	0.649434i	$0.775006\pi$
$354$		0			0
$355$	5.60353	−	2.32106i	0.297405	−	0.123189i
$356$	6.59662	+	11.9319i	0.349620	+	0.632387i
$357$		0			0
$358$	11.8789	+	7.00609i	0.627819	+	0.370284i
$359$	6.52733	+	6.52733i	0.344500	+	0.344500i	0.858056	−	0.513556i	$-0.171672\pi$
$359$	6.52733	+	6.52733i	0.344500	+	0.344500i	−0.513556	+	0.858056i	$0.671672\pi$
$360$		0			0
$361$	−22.4311	+	22.4311i	−1.18058	+	1.18058i
$362$	20.6088	−	5.31758i	1.08317	−	0.279486i
$363$		0			0
$364$	2.12604	+	1.69499i	0.111435	+	0.0888414i
$365$	−1.98053	−	4.78142i	−0.103666	−	0.250271i
$366$		0			0
$367$	19.4291			1.01419			0.507096	−	0.861889i	$-0.330719\pi$
$367$	19.4291			1.01419			0.507096	+	0.861889i	$0.330719\pi$
$368$	−12.3464	+	2.82150i	−0.643598	+	0.147081i
$369$		0			0
$370$	−1.78269	−	0.251551i	−0.0926778	−	0.0130775i
$371$	60.9771	−	25.2576i	3.16577	−	1.31131i
$372$		0			0
$373$	−4.15808	+	10.0385i	−0.215297	+	0.519773i	−0.994222	−	0.107344i	$-0.965765\pi$
$373$	−4.15808	+	10.0385i	−0.215297	+	0.519773i	0.778925	+	0.627117i	$0.215765\pi$
$374$	−27.4628	+	7.08609i	−1.42007	+	0.366413i
$375$		0			0
$376$	−0.427603	−	1.11951i	−0.0220519	−	0.0577346i
$377$	0.679109	−	0.679109i	0.0349759	−	0.0349759i
$378$		0			0
$379$	1.96668	−	4.74798i	0.101021	−	0.243887i	−0.865286	−	0.501279i	$-0.832863\pi$
$379$	1.96668	−	4.74798i	0.101021	−	0.243887i	0.966307	+	0.257392i	$0.0828631\pi$
$380$	−3.63542	+	12.6253i	−0.186493	+	0.647662i
$381$		0			0
$382$	5.25765	+	6.98521i	0.269005	+	0.357394i
$383$	−6.30106			−0.321969			−0.160985	−	0.986957i	$-0.551467\pi$
$383$	−6.30106			−0.321969			−0.160985	+	0.986957i	$0.551467\pi$
$384$		0			0
$385$	−16.9314			−0.862905
$386$	9.56901	+	12.7132i	0.487050	+	0.647085i
$387$		0			0
$388$	−4.85926	+	16.8755i	−0.246691	+	0.856722i
$389$	−0.331782	+	0.800993i	−0.0168220	+	0.0406119i	−0.932067	−	0.362285i	$-0.881997\pi$
$389$	−0.331782	+	0.800993i	−0.0168220	+	0.0406119i	0.915245	+	0.402897i	$0.131997\pi$
$390$		0			0
$391$	−11.8786	+	11.8786i	−0.600727	+	0.600727i
$392$	−16.7366	−	43.8185i	−0.845327	−	2.21317i
$393$		0			0
$394$	−9.27871	+	2.39414i	−0.467455	+	0.120615i
$395$	−4.49407	+	10.8496i	−0.226121	+	0.545905i
$396$		0			0
$397$	11.2798	−	4.67225i	0.566118	−	0.234494i	−0.0812209	−	0.996696i	$-0.525882\pi$
$397$	11.2798	−	4.67225i	0.566118	−	0.234494i	0.647339	+	0.762202i	$0.275882\pi$
$398$	−17.1822	−	2.42454i	−0.861267	−	0.121531i
$399$		0			0
$400$	−3.69755	−	16.1798i	−0.184878	−	0.808989i
$401$	−10.7890			−0.538777			−0.269388	−	0.963032i	$-0.586822\pi$
$401$	−10.7890			−0.538777			−0.269388	+	0.963032i	$0.586822\pi$
$402$		0			0
$403$	0.371474	+	0.896819i	0.0185045	+	0.0446737i
$404$	−17.8637	−	14.2419i	−0.888754	−	0.708560i
$405$		0			0
$406$	−22.8142	+	5.88664i	−1.13225	+	0.292149i
$407$	−3.68892	+	3.68892i	−0.182853	+	0.182853i
$408$		0			0
$409$	−0.0980818	−	0.0980818i	−0.00484983	−	0.00484983i	0.704678	−	0.709528i	$-0.251092\pi$
$409$	−0.0980818	−	0.0980818i	−0.00484983	−	0.00484983i	−0.709528	+	0.704678i	$0.751092\pi$
$410$	−8.39374	−	4.95057i	−0.414537	−	0.244491i
$411$		0			0
$412$	3.48047	+	6.29541i	0.171470	+	0.310153i
$413$	25.4565	−	10.5444i	1.25263	−	0.518857i
$414$		0			0
$415$			0.865923i			0.0425065i
$416$	−0.727328	−	1.40671i	−0.0356602	−	0.0689695i
$417$		0			0
$418$	22.8948	+	30.4175i	1.11982	+	1.48777i
$419$	11.5665	+	27.9241i	0.565063	+	1.36418i	0.905673	+	0.423977i	$0.139366\pi$
$419$	11.5665	+	27.9241i	0.565063	+	1.36418i	−0.340610	+	0.940205i	$0.610634\pi$
$420$		0			0
$421$	18.0670	+	7.48361i	0.880533	+	0.364729i	0.776703	−	0.629867i	$-0.216890\pi$
$421$	18.0670	+	7.48361i	0.880533	+	0.364729i	0.103829	+	0.994595i	$0.466890\pi$
$422$	5.97941	−	10.1381i	0.291073	−	0.493517i
$423$		0			0
$424$	−38.4257	−	1.07028i	−1.86612	−	0.0519776i
$425$	−15.5668	−	15.5668i	−0.755100	−	0.755100i
$426$		0			0
$427$	−0.162150	−	0.0671647i	−0.00784698	−	0.00325033i
$428$	−5.51485	−	4.39672i	−0.266570	−	0.212523i
$429$		0			0
$430$	−3.45258	−	0.487185i	−0.166498	−	0.0234941i
$431$		−	10.6345i		−	0.512245i	−0.966644	−	0.256123i	$-0.917555\pi$
$431$		−	10.6345i		−	0.512245i	0.966644	−	0.256123i	$-0.0824451\pi$
$432$		0			0
$433$			11.8688i			0.570377i	0.958471	+	0.285189i	$0.0920562\pi$
$433$			11.8688i			0.570377i	−0.958471	+	0.285189i	$0.907944\pi$
$434$	3.32740	−	23.5806i	0.159720	−	1.13191i
$435$		0			0
$436$	2.81265	+	24.9325i	0.134702	+	1.19405i
$437$	20.8328	+	8.62924i	0.996569	+	0.412793i
$438$		0			0
$439$	−11.2613	−	11.2613i	−0.537471	−	0.537471i	0.385314	−	0.922785i	$-0.374093\pi$
$439$	−11.2613	−	11.2613i	−0.537471	−	0.537471i	−0.922785	+	0.385314i	$0.874093\pi$
$440$	9.00199	+	4.02593i	0.429153	+	0.191929i
$441$		0			0
$442$	−1.80932	−	1.06712i	−0.0860604	−	0.0507578i
$443$	17.1370	+	7.09839i	0.814204	+	0.337255i	0.750630	−	0.660723i	$-0.229750\pi$
$443$	17.1370	+	7.09839i	0.814204	+	0.337255i	0.0635743	+	0.997977i	$0.479750\pi$
$444$		0			0
$445$	−2.40624	−	5.80918i	−0.114067	−	0.275381i
$446$	−14.6581	+	11.0329i	−0.694083	+	0.522425i
$447$		0			0
$448$	−2.16256	+	38.7903i	−0.102171	+	1.83267i
$449$		−	38.4537i		−	1.81474i	−0.420331	−	0.907371i	$-0.638086\pi$
$449$		−	38.4537i		−	1.81474i	0.420331	−	0.907371i	$-0.361914\pi$
$450$		0			0
$451$	−26.0885	+	10.8062i	−1.22846	+	0.508845i
$452$	−9.13150	+	31.7123i	−0.429510	+	1.49162i
$453$		0			0
$454$	7.12681	−	12.0836i	0.334478	−	0.567110i
$455$	−0.886693	−	0.886693i	−0.0415688	−	0.0415688i
$456$		0			0
$457$	−11.6258	+	11.6258i	−0.543833	+	0.543833i	−0.924650	−	0.380817i	$-0.875643\pi$
$457$	−11.6258	+	11.6258i	−0.543833	+	0.543833i	0.380817	+	0.924650i	$0.375643\pi$
$458$	−1.88094	−	7.28974i	−0.0878904	−	0.340627i
$459$		0			0
$460$	5.80397	−	0.654748i	0.270611	−	0.0305278i
$461$	1.95672	+	4.72395i	0.0911337	+	0.220016i	0.962874	−	0.269953i	$-0.0870081\pi$
$461$	1.95672	+	4.72395i	0.0911337	+	0.220016i	−0.871740	+	0.489969i	$0.837008\pi$
$462$		0			0
$463$	−24.2082			−1.12505			−0.562524	−	0.826781i	$-0.690170\pi$
$463$	−24.2082			−1.12505			−0.562524	+	0.826781i	$0.690170\pi$
$464$	13.5295	+	2.29496i	0.628089	+	0.106541i
$465$		0			0
$466$	3.03178	−	21.4857i	0.140445	−	0.995304i
$467$	−5.35140	+	2.21662i	−0.247633	+	0.102573i	−0.503048	−	0.864259i	$-0.667788\pi$
$467$	−5.35140	+	2.21662i	−0.247633	+	0.102573i	0.255415	+	0.966832i	$0.417788\pi$
$468$		0			0
$469$	19.7579	−	47.6999i	0.912336	−	2.20257i
$470$	0.138084	+	0.535159i	0.00636936	+	0.0246850i
$471$		0			0
$472$	−16.0418	−	0.446818i	−0.738383	−	0.0205665i
$473$	−7.14442	+	7.14442i	−0.328501	+	0.328501i
$474$		0			0
$475$	−11.3085	+	27.3012i	−0.518871	+	1.25267i
$476$	24.9335	+	45.0993i	1.14283	+	2.06712i
$477$		0			0
$478$	8.69406	−	6.54388i	0.397657	−	0.299310i
$479$	26.4282			1.20754			0.603768	−	0.797160i	$-0.293665\pi$
$479$	26.4282			1.20754			0.603768	+	0.797160i	$0.293665\pi$
$480$		0			0
$481$	−0.386375			−0.0176172
$482$	−16.4594	+	12.3887i	−0.749704	+	0.564290i
$483$		0			0
$484$	5.75426	−	3.18129i	0.261557	−	0.144604i
$485$	3.09935	−	7.48249i	0.140734	−	0.339762i
$486$		0			0
$487$	−9.32733	+	9.32733i	−0.422662	+	0.422662i	−0.886119	−	0.463457i	$-0.846609\pi$
$487$	−9.32733	+	9.32733i	−0.422662	+	0.422662i	0.463457	+	0.886119i	$0.346609\pi$
$488$	0.0702406	+	0.0742655i	0.00317964	+	0.00336184i
$489$		0			0
$490$	5.40470	+	20.9464i	0.244160	+	0.946263i
$491$	2.97593	−	7.18453i	0.134302	−	0.324233i	−0.842394	−	0.538862i	$-0.818854\pi$
$491$	2.97593	−	7.18453i	0.134302	−	0.324233i	0.976696	+	0.214629i	$0.0688543\pi$
$492$		0			0
$493$	16.8168	−	6.96573i	0.757389	−	0.313721i
$494$	−0.393964	+	2.79195i	−0.0177253	+	0.125616i
$495$		0			0
$496$	−7.37607	+	11.7460i	−0.331195	+	0.527412i
$497$	−31.9334			−1.43241
$498$		0			0
$499$	−10.3839	−	25.0689i	−0.464846	−	1.12224i	−0.966384	−	0.257103i	$-0.917232\pi$
$499$	−10.3839	−	25.0689i	−0.464846	−	1.12224i	0.501538	−	0.865136i	$-0.332768\pi$
$500$	1.89202	+	16.7716i	0.0846136	+	0.750051i
$501$		0			0
$502$	5.41261	+	20.9771i	0.241577	+	0.936253i
$503$	3.53224	−	3.53224i	0.157495	−	0.157495i	−0.623961	−	0.781456i	$-0.714478\pi$
$503$	3.53224	−	3.53224i	0.157495	−	0.157495i	0.781456	+	0.623961i	$0.214478\pi$
$504$		0			0
$505$	7.45031	+	7.45031i	0.331535	+	0.331535i
$506$	8.59816	−	14.5783i	0.382235	−	0.648082i
$507$		0			0
$508$	18.1239	+	5.21873i	0.804117	+	0.231544i
$509$	19.0074	−	7.87311i	0.842487	−	0.348969i	0.0806532	−	0.996742i	$-0.474299\pi$
$509$	19.0074	−	7.87311i	0.842487	−	0.348969i	0.761834	+	0.647773i	$0.224299\pi$
$510$		0			0
$511$			27.2484i			1.20540i
$512$	10.3733	−	20.1096i	0.458439	−	0.888726i
$513$		0			0
$514$	−22.0322	+	16.5833i	−0.971800	+	0.731458i
$515$	−1.26957	−	3.06500i	−0.0559437	−	0.135060i
$516$		0			0
$517$	1.47962	+	0.612879i	0.0650736	+	0.0269544i
$518$	8.16460	+	4.81543i	0.358732	+	0.211578i
$519$		0			0
$520$	0.260595	+	0.682269i	0.0114278	+	0.0299195i
$521$	−12.5687	−	12.5687i	−0.550643	−	0.550643i	0.375984	−	0.926626i	$-0.377305\pi$
$521$	−12.5687	−	12.5687i	−0.550643	−	0.550643i	−0.926626	+	0.375984i	$0.877305\pi$
$522$		0			0
$523$	9.66162	+	4.00197i	0.422473	+	0.174994i	0.583783	−	0.811910i	$-0.301572\pi$
$523$	9.66162	+	4.00197i	0.422473	+	0.174994i	−0.161310	+	0.986904i	$0.551572\pi$
$524$	−32.1877	+	3.63111i	−1.40613	+	0.158626i
$525$		0			0
$526$	2.69787	−	19.1193i	0.117633	−	0.833639i
$527$			18.3976i			0.801414i
$528$		0			0
$529$			12.9754i			0.564148i
$530$	17.5544	+	2.47706i	0.762515	+	0.107596i
$531$		0			0
$532$	43.1213	−	54.0874i	1.86954	−	2.34499i
$533$	−1.93217	−	0.800329i	−0.0836914	−	0.0346661i
$534$		0			0
$535$	2.30004	+	2.30004i	0.0994395	+	0.0994395i
$536$	−21.8468	+	20.6628i	−0.943638	+	0.892496i
$537$		0			0
$538$	14.9337	−	25.3202i	0.643837	−	1.09163i
$539$	57.9132	+	23.9884i	2.49450	+	1.03326i
$540$		0			0
$541$	−14.6046	−	35.2587i	−0.627901	−	1.51589i	−0.842225	−	0.539125i	$-0.818755\pi$
$541$	−14.6046	−	35.2587i	−0.627901	−	1.51589i	0.214324	−	0.976763i	$-0.431245\pi$
$542$	−16.2621	−	21.6055i	−0.698516	−	0.928034i
$543$		0			0
$544$	−2.53284	−	29.9068i	−0.108595	−	1.28224i
$545$		−	11.5715i		−	0.495669i
$546$		0			0
$547$	−9.22367	+	3.82057i	−0.394376	+	0.163356i	−0.571053	−	0.820913i	$-0.693465\pi$
$547$	−9.22367	+	3.82057i	−0.394376	+	0.163356i	0.176677	+	0.984269i	$0.443465\pi$
$548$	−12.4196	+	6.86627i	−0.530538	+	0.293312i
$549$		0			0
$550$	19.1046	+	11.2678i	0.814625	+	0.480460i
$551$	−17.2769	−	17.2769i	−0.736019	−	0.736019i
$552$		0			0
$553$	43.7204	−	43.7204i	1.85918	−	1.85918i
$554$	2.18265	−	0.563178i	0.0927317	−	0.0239271i
$555$		0			0
$556$	−25.7227	+	32.2642i	−1.09089	+	1.36831i
$557$	8.65349	+	20.8914i	0.366660	+	0.885196i	0.994293	+	0.106686i	$0.0340241\pi$
$557$	8.65349	+	20.8914i	0.366660	+	0.885196i	−0.627632	+	0.778510i	$0.715976\pi$
$558$		0			0
$559$	−0.748302			−0.0316498
$560$	2.99647	−	17.6650i	0.126624	−	0.746484i
$561$		0			0
$562$	−17.3606	−	2.44970i	−0.732312	−	0.103335i
$563$	−3.53958	+	1.46614i	−0.149175	+	0.0617905i	−0.456022	−	0.889969i	$-0.650726\pi$
$563$	−3.53958	+	1.46614i	−0.149175	+	0.0617905i	0.306847	+	0.951759i	$0.400726\pi$
$564$		0			0
$565$	5.82428	−	14.0611i	0.245029	−	0.591553i
$566$	−27.3393	+	7.05422i	−1.14916	+	0.296511i
$567$		0			0
$568$	16.9782	+	7.59310i	0.712389	+	0.318599i
$569$	0.855711	−	0.855711i	0.0358733	−	0.0358733i	−0.688943	−	0.724816i	$-0.741925\pi$
$569$	0.855711	−	0.855711i	0.0358733	−	0.0358733i	0.724816	+	0.688943i	$0.241925\pi$
$570$		0			0
$571$	4.33854	−	10.4742i	0.181562	−	0.438330i	−0.806726	−	0.590925i	$-0.798763\pi$
$571$	4.33854	−	10.4742i	0.181562	−	0.438330i	0.988289	+	0.152595i	$0.0487629\pi$
$572$	2.03370	+	0.585599i	0.0850331	+	0.0244851i
$573$		0			0
$574$	30.8546	+	40.9927i	1.28784	+	1.71100i
$575$	13.1371			0.547856
$576$		0			0
$577$	−2.91000			−0.121145			−0.0605724	−	0.998164i	$-0.519293\pi$
$577$	−2.91000			−0.121145			−0.0605724	+	0.998164i	$0.519293\pi$
$578$	−9.48357	−	12.5997i	−0.394465	−	0.524078i
$579$		0			0
$580$	−6.08164	−	1.75120i	−0.252526	−	0.0727144i
$581$	1.74469	−	4.21205i	0.0723819	−	0.174745i
$582$		0			0
$583$	36.3253	−	36.3253i	1.50444	−	1.50444i
$584$	6.47909	−	14.4873i	0.268107	−	0.599487i
$585$		0			0
$586$	31.2647	−	8.06709i	1.29153	−	0.333248i
$587$	18.1052	−	43.7099i	0.747283	−	1.80410i	0.173996	−	0.984746i	$-0.444332\pi$
$587$	18.1052	−	43.7099i	0.747283	−	1.80410i	0.573287	−	0.819355i	$-0.305668\pi$
$588$		0			0
$589$	22.8155	−	9.45049i	0.940096	−	0.389401i
$590$	7.32854	+	1.03411i	0.301711	+	0.0425737i
$591$		0			0
$592$	−3.19590	−	4.50161i	−0.131351	−	0.185015i
$593$	30.7464			1.26260			0.631301	−	0.775538i	$-0.282521\pi$
$593$	30.7464			1.26260			0.631301	+	0.775538i	$0.282521\pi$
$594$		0			0
$595$	−9.09496	−	21.9572i	−0.372857	−	0.900157i
$596$	−28.0861	+	35.2287i	−1.15045	+	1.44302i
$597$		0			0
$598$	1.21374	−	0.313176i	0.0496336	−	0.0128067i
$599$	−19.3435	+	19.3435i	−0.790354	+	0.790354i	−0.981552	−	0.191198i	$-0.938763\pi$
$599$	−19.3435	+	19.3435i	−0.790354	+	0.790354i	0.191198	+	0.981552i	$0.438763\pi$
$600$		0			0
$601$	−28.4893	−	28.4893i	−1.16210	−	1.16210i	−0.984015	−	0.178087i	$-0.943009\pi$
$601$	−28.4893	−	28.4893i	−1.16210	−	1.16210i	−0.178087	−	0.984015i	$-0.556991\pi$
$602$	15.8126	+	9.32615i	0.644473	+	0.380106i
$603$		0			0
$604$	−11.5862	+	6.40553i	−0.471437	+	0.260638i
$605$	−2.80153	+	1.16043i	−0.113899	+	0.0471783i
$606$		0			0
$607$			31.5078i			1.27886i	0.768848	+	0.639432i	$0.220830\pi$
$607$			31.5078i			1.27886i	−0.768848	+	0.639432i	$0.779170\pi$
$608$	−35.7873	+	18.5036i	−1.45137	+	0.750419i
$609$		0			0
$610$	−0.0283504	−	0.0376658i	−0.00114788	−	0.00152504i
$611$	0.0453910	+	0.109584i	0.00183632	+	0.00443328i
$612$		0			0
$613$	−40.5414	−	16.7928i	−1.63745	−	0.678254i	−0.641413	−	0.767196i	$-0.721651\pi$
$613$	−40.5414	−	16.7928i	−1.63745	−	0.678254i	−0.996037	+	0.0889418i	$0.971651\pi$
$614$	4.31535	−	7.31672i	0.174154	−	0.295279i
$615$		0			0
$616$	−35.6762	−	37.7206i	−1.43744	−	1.51981i
$617$	−14.1405	−	14.1405i	−0.569276	−	0.569276i	0.362650	−	0.931926i	$-0.381872\pi$
$617$	−14.1405	−	14.1405i	−0.569276	−	0.569276i	−0.931926	+	0.362650i	$0.881872\pi$
$618$		0			0
$619$	−17.7763	−	7.36320i	−0.714491	−	0.295952i	−0.00432943	−	0.999991i	$-0.501378\pi$
$619$	−17.7763	−	7.36320i	−0.714491	−	0.295952i	−0.710162	+	0.704039i	$0.751378\pi$
$620$	3.98757	−	5.00164i	0.160145	−	0.200871i
$621$		0			0
$622$	24.4282	+	3.44700i	0.979483	+	0.138212i
$623$			33.1054i			1.32634i
$624$		0			0
$625$			12.9622i			0.518487i
$626$	2.53657	−	17.9761i	0.101382	−	0.718471i
$627$		0			0
$628$	−32.0627	+	3.61701i	−1.27944	+	0.144334i
$629$	−6.76546	−	2.80235i	−0.269757	−	0.111737i
$630$		0			0
$631$	−14.1654	−	14.1654i	−0.563915	−	0.563915i	0.366502	−	0.930417i	$-0.380555\pi$
$631$	−14.1654	−	14.1654i	−0.563915	−	0.563915i	−0.930417	+	0.366502i	$0.880555\pi$
$632$	−33.6408	+	12.8492i	−1.33816	+	0.511115i
$633$		0			0
$634$	19.4237	+	11.4560i	0.771413	+	0.454974i
$635$	−8.03602	−	3.32863i	−0.318900	−	0.132093i
$636$		0			0
$637$	1.77663	+	4.28917i	0.0703927	+	0.169943i
$638$	−14.6522	+	11.0285i	−0.580088	+	0.436623i
$639$		0			0
$640$	−5.79352	+	8.67954i	−0.229009	+	0.343089i
$641$			3.51722i			0.138922i	0.997585	+	0.0694610i	$0.0221279\pi$
$641$			3.51722i			0.138922i	−0.997585	+	0.0694610i	$0.977872\pi$
$642$		0			0
$643$	28.4159	−	11.7702i	1.12061	−	0.464173i	0.256032	−	0.966668i	$-0.417585\pi$
$643$	28.4159	−	11.7702i	1.12061	−	0.464173i	0.864580	+	0.502496i	$0.167585\pi$
$644$	−29.5511	−	8.50916i	−1.16447	−	0.335308i
$645$		0			0
$646$	−27.1481	+	46.0299i	−1.06813	+	1.81102i
$647$	22.2793	+	22.2793i	0.875889	+	0.875889i	0.993106	−	0.117217i	$-0.0373973\pi$
$647$	22.2793	+	22.2793i	0.875889	+	0.875889i	−0.117217	+	0.993106i	$0.537397\pi$
$648$		0			0
$649$	15.1649	−	15.1649i	0.595275	−	0.595275i
$650$	0.410414	+	1.59060i	0.0160978	+	0.0623883i
$651$		0			0
$652$	−0.517999	−	4.59176i	−0.0202864	−	0.179827i
$653$	−1.57865	−	3.81119i	−0.0617772	−	0.149143i	0.889976	−	0.456007i	$-0.150721\pi$
$653$	−1.57865	−	3.81119i	−0.0617772	−	0.149143i	−0.951754	+	0.306863i	$0.900721\pi$
$654$		0			0
$655$	14.9387			0.583704
$656$	−6.65737	−	29.1313i	−0.259926	−	1.13739i
$657$		0			0
$658$	0.406580	−	2.88135i	0.0158501	−	0.112327i
$659$	−13.2385	+	5.48357i	−0.515699	+	0.213610i	−0.625327	−	0.780363i	$-0.715034\pi$
$659$	−13.2385	+	5.48357i	−0.515699	+	0.213610i	0.109627	+	0.993973i	$0.465034\pi$
$660$		0			0
$661$	−9.61142	+	23.2040i	−0.373841	+	0.902532i	0.619251	+	0.785193i	$0.287436\pi$
$661$	−9.61142	+	23.2040i	−0.373841	+	0.902532i	−0.993092	+	0.117339i	$0.962564\pi$
$662$	7.92448	+	30.7121i	0.307994	+	1.19366i
$663$		0			0
$664$	−1.92914	+	1.82459i	−0.0748653	+	0.0708078i
$665$	−22.5579	+	22.5579i	−0.874758	+	0.874758i
$666$		0			0
$667$	−4.15674	+	10.0353i	−0.160950	+	0.388567i
$668$	35.1625	−	19.4399i	1.36048	−	0.752151i
$669$		0			0
$670$	11.0802	−	8.33989i	0.428066	−	0.322198i
$671$	−0.136607			−0.00527366
$672$		0			0
$673$	−12.4509			−0.479947			−0.239974	−	0.970779i	$-0.577139\pi$
$673$	−12.4509			−0.479947			−0.239974	+	0.970779i	$0.577139\pi$
$674$	−14.6867	+	11.0545i	−0.565712	+	0.425802i
$675$		0			0
$676$	−12.5039	−	22.6169i	−0.480921	−	0.869882i
$677$	−6.84859	+	16.5340i	−0.263213	+	0.635451i	−0.999134	−	0.0416159i	$-0.986749\pi$
$677$	−6.84859	+	16.5340i	−0.263213	+	0.635451i	0.735921	+	0.677067i	$0.236749\pi$
$678$		0			0
$679$	−30.1519	+	30.1519i	−1.15712	+	1.15712i
$680$	−0.385397	+	13.8367i	−0.0147793	+	0.530612i
$681$		0			0
$682$	−4.63100	−	17.9479i	−0.177330	−	0.687260i
$683$	9.54777	−	23.0504i	0.365335	−	0.881997i	−0.629166	−	0.777271i	$-0.716603\pi$
$683$	9.54777	−	23.0504i	0.365335	−	0.881997i	0.994501	−	0.104726i	$-0.0333966\pi$
$684$		0			0
$685$	6.04663	−	2.50460i	0.231030	−	0.0956958i
$686$	9.19658	−	65.1744i	0.351127	−	2.48837i
$687$		0			0
$688$	−6.18958	−	8.71837i	−0.235975	−	0.332385i
$689$	3.80469			0.144947
$690$		0			0
$691$	−0.714680	−	1.72539i	−0.0271877	−	0.0656369i	0.909703	−	0.415260i	$-0.136310\pi$
$691$	−0.714680	−	1.72539i	−0.0271877	−	0.0656369i	−0.936890	+	0.349623i	$0.886310\pi$
$692$	23.5440	−	2.65602i	0.895010	−	0.100967i
$693$		0			0
$694$	9.33515	+	36.1792i	0.354357	+	1.37334i
$695$	13.4562	−	13.4562i	0.510424	−	0.510424i
$696$		0			0
$697$	−28.0277	−	28.0277i	−1.06162	−	1.06162i
$698$	−7.17994	+	12.1737i	−0.271765	+	0.460780i
$699$		0			0
$700$	11.1512	−	38.7264i	0.421475	−	1.46372i
$701$	−23.2566	+	9.63319i	−0.878388	+	0.363840i	−0.775872	−	0.630891i	$-0.782690\pi$
$701$	−23.2566	+	9.63319i	−0.878388	+	0.363840i	−0.102517	+	0.994731i	$0.532690\pi$
$702$		0			0
$703$			9.82957i			0.370729i
$704$	9.99897	+	28.5381i	0.376851	+	1.07557i
$705$		0			0
$706$	27.5738	−	20.7544i	1.03776	−	0.781102i
$707$	−21.2289	−	51.2512i	−0.798396	−	1.92750i
$708$		0			0
$709$	37.2006	+	15.4090i	1.39710	+	0.578698i	0.948997	−	0.315285i	$-0.102100\pi$
$709$	37.2006	+	15.4090i	1.39710	+	0.578698i	0.448102	+	0.893982i	$0.352100\pi$
$710$	−7.38822	−	4.35752i	−0.277275	−	0.163535i
$711$		0			0
$712$	7.87176	−	17.6013i	0.295007	−	0.659636i
$713$	−7.76307	−	7.76307i	−0.290729	−	0.290729i
$714$		0			0
$715$	−0.901729	−	0.373508i	−0.0337227	−	0.0139684i
$716$	−2.18633	−	19.3806i	−0.0817071	−	0.724286i
$717$		0			0
$718$	1.82404	−	12.9266i	0.0680725	−	0.482417i
$719$		−	10.2965i		−	0.383996i	−0.981395	−	0.191998i	$-0.938503\pi$
$719$		−	10.2965i		−	0.383996i	0.981395	−	0.191998i	$-0.0614968\pi$
$720$		0			0
$721$			17.4669i			0.650500i
$722$	44.4221	+	6.26828i	1.65322	+	0.233281i
$723$		0			0
$724$	−23.5355	−	18.7637i	−0.874691	−	0.697348i
$725$	−13.1511	−	5.44737i	−0.488420	−	0.202310i
$726$		0			0
$727$	13.6565	+	13.6565i	0.506493	+	0.506493i	0.913448	−	0.406955i	$-0.133409\pi$
$727$	13.6565	+	13.6565i	0.506493	+	0.506493i	−0.406955	+	0.913448i	$0.633409\pi$
$728$	0.107062	−	3.84377i	0.00396798	−	0.142460i
$729$		0			0
$730$	−3.71821	+	6.30427i	−0.137617	+	0.233331i
$731$	−13.1028	−	5.42737i	−0.484626	−	0.200739i
$732$		0			0
$733$	12.2351	+	29.5382i	0.451915	+	1.09102i	0.971593	+	0.236657i	$0.0760517\pi$
$733$	12.2351	+	29.5382i	0.451915	+	1.09102i	−0.519678	+	0.854362i	$0.673948\pi$
$734$	−16.5238	−	21.9532i	−0.609906	−	0.810309i
$735$		0			0
$736$	13.6882	+	11.5507i	0.504555	+	0.425765i
$737$		−	40.1859i		−	1.48027i
$738$		0			0
$739$	−5.26176	+	2.17949i	−0.193557	+	0.0801739i	−0.477356	−	0.878710i	$-0.658405\pi$
$739$	−5.26176	+	2.17949i	−0.193557	+	0.0801739i	0.283800	+	0.958884i	$0.408405\pi$
$740$	1.23189	+	2.22822i	0.0452852	+	0.0819112i
$741$		0			0
$742$	−80.3979	−	47.4182i	−2.95150	−	1.74078i
$743$	−17.0314	−	17.0314i	−0.624823	−	0.624823i	0.321938	−	0.946761i	$-0.395666\pi$
$743$	−17.0314	−	17.0314i	−0.624823	−	0.624823i	−0.946761	+	0.321938i	$0.895666\pi$
$744$		0			0
$745$	14.6926	−	14.6926i	0.538295	−	0.538295i
$746$	14.8789	−	3.83914i	0.544757	−	0.140561i
$747$		0			0
$748$	31.3629	+	25.0041i	1.14674	+	0.914241i
$749$	−6.55375	−	15.8221i	−0.239469	−	0.578129i
$750$		0			0
$751$	5.21219			0.190196			0.0950978	−	0.995468i	$-0.469684\pi$
$751$	5.21219			0.190196			0.0950978	+	0.995468i	$0.469684\pi$
$752$	−0.901293	+	1.43527i	−0.0328668	+	0.0523387i
$753$		0			0
$754$	−1.34489	−	0.189774i	−0.0489781	−	0.00691117i
$755$	5.64090	−	2.33654i	0.205293	−	0.0850353i
$756$		0			0
$757$	5.99669	−	14.4773i	0.217953	−	0.526186i	−0.776650	−	0.629932i	$-0.783083\pi$
$757$	5.99669	−	14.4773i	0.217953	−	0.526186i	0.994604	+	0.103746i	$0.0330828\pi$
$758$	−7.03740	+	1.81583i	−0.255610	+	0.0659537i
$759$		0			0
$760$	17.3572	−	6.62966i	0.629614	−	0.240483i
$761$	16.7870	−	16.7870i	0.608528	−	0.608528i	−0.334033	−	0.942561i	$-0.608410\pi$
$761$	16.7870	−	16.7870i	0.608528	−	0.608528i	0.942561	+	0.334033i	$0.108410\pi$
$762$		0			0
$763$	−23.3146	+	56.2865i	−0.844046	+	2.03771i
$764$	3.42122	−	11.8814i	0.123775	−	0.429854i
$765$		0			0
$766$	5.35885	+	7.11965i	0.193623	+	0.257244i
$767$	1.58837			0.0573526
$768$		0			0
$769$	33.1933			1.19698			0.598491	−	0.801129i	$-0.295767\pi$
$769$	33.1933			1.19698			0.598491	+	0.801129i	$0.295767\pi$
$770$	14.3996	+	19.1310i	0.518926	+	0.689435i
$771$		0			0
$772$	6.22668	−	21.6243i	0.224103	−	0.778276i
$773$	5.41657	−	13.0767i	0.194820	−	0.470338i	−0.796038	−	0.605247i	$-0.793074\pi$
$773$	5.41657	−	13.0767i	0.194820	−	0.470338i	0.990858	+	0.134909i	$0.0430743\pi$
$774$		0			0
$775$	10.1734	−	10.1734i	0.365440	−	0.365440i
$776$	23.2005	−	8.86150i	0.832848	−	0.318109i
$777$		0			0
$778$	1.18722	−	0.306333i	0.0425640	−	0.0109826i
$779$	−20.3608	+	49.1552i	−0.729500	+	1.76117i
$780$		0			0
$781$	−22.9632	+	9.51169i	−0.821689	+	0.340355i
$782$	23.5242	+	3.31943i	0.841222	+	0.118703i
$783$		0			0
$784$	−35.2771	+	56.1771i	−1.25990	+	2.00633i
$785$	14.8807			0.531115
$786$		0			0
$787$	18.2278	+	44.0057i	0.649750	+	1.56864i	0.813136	+	0.582073i	$0.197758\pi$
$787$	18.2278	+	44.0057i	0.649750	+	1.56864i	−0.163387	+	0.986562i	$0.552242\pi$
$788$	10.5964	+	8.44800i	0.377482	+	0.300948i
$789$		0			0
$790$	16.0812	−	4.14936i	0.572144	−	0.147628i
$791$	−56.6614	+	56.6614i	−2.01465	+	2.01465i
$792$		0			0
$793$	−0.00715408	−	0.00715408i	−0.000254049	−	0.000254049i
$794$	−14.8724	−	8.77162i	−0.527800	−	0.311293i
$795$		0			0
$796$	11.8734	+	21.4764i	0.420842	+	0.761212i
$797$	−33.3377	+	13.8089i	−1.18088	+	0.489138i	−0.884776	−	0.466017i	$-0.845689\pi$
$797$	−33.3377	+	13.8089i	−1.18088	+	0.489138i	−0.296107	+	0.955155i	$0.595689\pi$
$798$		0			0
$799$			2.24803i			0.0795298i
$800$	−15.1371	+	17.9383i	−0.535177	+	0.634214i
$801$		0			0
$802$	9.17569	+	12.1906i	0.324005	+	0.430466i
$803$	8.11619	+	19.5942i	0.286414	+	0.691465i
$804$		0			0
$805$	13.1028	+	5.42734i	0.461812	+	0.191289i
$806$	0.697401	−	1.18245i	0.0245649	−	0.0416500i
$807$		0			0
$808$	−0.899573	+	32.2967i	−0.0316469	+	1.13620i
$809$	−13.3585	−	13.3585i	−0.469661	−	0.469661i	0.432144	−	0.901805i	$-0.357757\pi$
$809$	−13.3585	−	13.3585i	−0.469661	−	0.469661i	−0.901805	+	0.432144i	$0.857757\pi$
$810$		0			0
$811$	−24.9118	−	10.3188i	−0.874772	−	0.362343i	−0.100305	−	0.994957i	$-0.531982\pi$
$811$	−24.9118	−	10.3188i	−0.874772	−	0.362343i	−0.774467	+	0.632614i	$0.781982\pi$
$812$	26.0542	+	20.7717i	0.914321	+	0.728944i
$813$		0			0
$814$	7.30547	+	1.03085i	0.256056	+	0.0361314i
$815$			2.13110i			0.0746490i
$816$		0			0
$817$			19.0372i			0.666026i
$818$	−0.0274086	+	0.194239i	−0.000958319	+	0.00679142i
$819$		0			0
$820$	1.54488	+	13.6945i	0.0539497	+	0.478233i
$821$	39.1686	+	16.2242i	1.36699	+	0.566228i	0.940972	−	0.338485i	$-0.109914\pi$
$821$	39.1686	+	16.2242i	1.36699	+	0.566228i	0.426023	+	0.904712i	$0.359914\pi$
$822$		0			0
$823$	−26.6538	−	26.6538i	−0.929095	−	0.929095i	0.0685527	−	0.997647i	$-0.478162\pi$
$823$	−26.6538	−	26.6538i	−0.929095	−	0.929095i	−0.997647	+	0.0685527i	$0.978162\pi$
$824$	4.15325	−	9.28667i	0.144685	−	0.323517i
$825$		0			0
$826$	−33.5642	−	19.7959i	−1.16785	−	0.688789i
$827$	25.4095	+	10.5250i	0.883576	+	0.365989i	0.777883	−	0.628410i	$-0.216294\pi$
$827$	25.4095	+	10.5250i	0.883576	+	0.365989i	0.105693	+	0.994399i	$0.466294\pi$
$828$		0			0
$829$	−5.57539	−	13.4602i	−0.193641	−	0.467491i	0.797001	−	0.603979i	$-0.206419\pi$
$829$	−5.57539	−	13.4602i	−0.193641	−	0.467491i	−0.990642	+	0.136487i	$0.956419\pi$
$830$	0.978418	−	0.736439i	0.0339614	−	0.0255622i
$831$		0			0
$832$	−0.970889	+	2.01818i	−0.0336595	+	0.0699677i
$833$			87.9894i			3.04865i
$834$		0			0
$835$	−17.1193	+	7.09105i	−0.592438	+	0.245396i
$836$	14.8979	−	51.7382i	0.515255	−	1.78940i
$837$		0			0
$838$	21.7149	−	36.8177i	0.750128	−	1.27185i
$839$	20.3694	+	20.3694i	0.703231	+	0.703231i	0.965103	−	0.261872i	$-0.0843397\pi$
$839$	20.3694	+	20.3694i	0.703231	+	0.703231i	−0.261872	+	0.965103i	$0.584340\pi$
$840$		0			0
$841$	−12.1838	+	12.1838i	−0.420130	+	0.420130i
$842$	−6.90959	−	26.7787i	−0.238120	−	0.922856i
$843$		0			0
$844$	−16.5405	+	1.86594i	−0.569348	+	0.0642284i
$845$	4.56105	+	11.0113i	0.156905	+	0.378802i
$846$		0			0
$847$	15.9654			0.548577
$848$	31.4705	+	44.3279i	1.08070	+	1.52223i
$849$		0			0
$850$	−4.35008	+	30.8282i	−0.149206	+	1.05740i
$851$	4.03723	−	1.67228i	0.138395	−	0.0573249i
$852$		0			0
$853$	2.58123	−	6.23163i	0.0883795	−	0.213367i	−0.873510	−	0.486807i	$-0.838161\pi$
$853$	2.58123	−	6.23163i	0.0883795	−	0.213367i	0.961889	+	0.273440i	$0.0881615\pi$
$854$	0.0620129	+	0.240337i	0.00212204	+	0.00822415i
$855$		0			0
$856$	−0.277714	+	9.97057i	−0.00949207	+	0.340787i
$857$	−11.2096	+	11.2096i	−0.382911	+	0.382911i	−0.872150	−	0.489239i	$-0.837275\pi$
$857$	−11.2096	+	11.2096i	−0.382911	+	0.382911i	0.489239	+	0.872150i	$0.337275\pi$
$858$		0			0
$859$	−2.70400	+	6.52804i	−0.0922594	+	0.222734i	−0.963272	−	0.268526i	$-0.913463\pi$
$859$	−2.70400	+	6.52804i	−0.0922594	+	0.222734i	0.871013	+	0.491260i	$0.163463\pi$
$860$	2.38583	+	4.31546i	0.0813562	+	0.147156i
$861$		0			0
$862$	−12.0161	+	9.04429i	−0.409269	+	0.308050i
$863$	17.1544			0.583943			0.291972	−	0.956427i	$-0.405689\pi$
$863$	17.1544			0.583943			0.291972	+	0.956427i	$0.405689\pi$
$864$		0			0
$865$	−10.9271			−0.371532
$866$	13.4107	−	10.0940i	0.455714	−	0.343008i
$867$		0			0
$868$	−29.4739	+	16.2949i	−1.00041	+	0.553085i
$869$	18.4167	−	44.4618i	0.624743	−	1.50826i
$870$		0			0
$871$	2.10453	−	2.10453i	0.0713091	−	0.0713091i
$872$	25.7795	−	24.3824i	0.873005	−	0.825691i
$873$		0			0
$874$	−7.96735	−	30.8782i	−0.269500	−	1.04447i
$875$	−15.6833	+	37.8629i	−0.530193	+	1.28000i
$876$		0			0
$877$	−46.9641	+	19.4532i	−1.58586	+	0.656886i	−0.989329	−	0.145700i	$-0.953456\pi$
$877$	−46.9641	+	19.4532i	−1.58586	+	0.656886i	−0.596535	+	0.802587i	$0.703456\pi$
$878$	−3.14692	+	22.3016i	−0.106203	+	0.752643i
$879$		0			0
$880$	−3.10695	−	13.5954i	−0.104735	−	0.458301i
$881$	24.1442			0.813438			0.406719	−	0.913553i	$-0.366673\pi$
$881$	24.1442			0.813438			0.406719	+	0.913553i	$0.366673\pi$
$882$		0			0
$883$	−16.3495	−	39.4712i	−0.550205	−	1.32831i	−0.917325	−	0.398140i	$-0.869656\pi$
$883$	−16.3495	−	39.4712i	−0.550205	−	1.32831i	0.367120	−	0.930174i	$-0.380344\pi$
$884$	0.333008	+	2.95192i	0.0112003	+	0.0992839i
$885$		0			0
$886$	−6.55392	−	25.4003i	−0.220183	−	0.853340i
$887$	22.4225	−	22.4225i	0.752872	−	0.752872i	−0.222142	−	0.975014i	$-0.571305\pi$
$887$	22.4225	−	22.4225i	0.752872	−	0.752872i	0.975014	+	0.222142i	$0.0713049\pi$
$888$		0			0
$889$	32.3825	+	32.3825i	1.08607	+	1.08607i
$890$	−4.51744	+	7.65936i	−0.151425	+	0.256742i
$891$		0			0
$892$	24.9325	+	7.17927i	0.834803	+	0.240380i
$893$	2.78786	−	1.15477i	0.0932922	−	0.0386429i
$894$		0			0
$895$			8.99478i			0.300662i
$896$	45.6688	−	30.5464i	1.52569	−	1.02048i
$897$		0			0
$898$	−43.4493	+	32.7036i	−1.44992	+	1.09133i
$899$	4.55234	+	10.9903i	0.151829	+	0.366548i
$900$		0			0
$901$	66.6204	+	27.5951i	2.21945	+	0.919325i
$902$	34.3975	+	20.2874i	1.14531	+	0.675497i
$903$		0			0
$904$	43.5983	−	16.6525i	1.45006	−	0.553854i
$905$	9.81581	+	9.81581i	0.326289	+	0.326289i
$906$		0			0
$907$	16.7879	+	6.95376i	0.557431	+	0.230896i	0.643570	−	0.765388i	$-0.277453\pi$
$907$	16.7879	+	6.95376i	0.557431	+	0.230896i	−0.0861382	+	0.996283i	$0.527453\pi$
$908$	−19.7145	+	2.22400i	−0.654249	+	0.0738062i
$909$		0			0
$910$	−0.247783	+	1.75599i	−0.00821393	+	0.0582105i
$911$		−	51.4718i		−	1.70534i	−0.522451	−	0.852669i	$-0.674982\pi$
$911$		−	51.4718i		−	1.70534i	0.522451	−	0.852669i	$-0.325018\pi$
$912$		0			0
$913$		−	3.54855i		−	0.117440i
$914$	23.0236	+	3.24879i	0.761552	+	0.107460i
$915$		0			0
$916$	−6.63710	+	8.32499i	−0.219296	+	0.275065i
$917$	−72.6654	−	30.0990i	−2.39962	−	0.993957i
$918$		0			0
$919$	−24.8706	−	24.8706i	−0.820407	−	0.820407i	0.165760	−	0.986166i	$-0.446992\pi$
$919$	−24.8706	−	24.8706i	−0.820407	−	0.820407i	−0.986166	+	0.165760i	$0.946992\pi$
$920$	−5.67589	−	6.00114i	−0.187129	−	0.197852i
$921$		0			0
$922$	3.67352	−	6.22849i	0.120981	−	0.205124i
$923$	−1.70070	−	0.704454i	−0.0559793	−	0.0231874i
$924$		0			0
$925$	2.19150	+	5.29075i	0.0720561	+	0.173959i
$926$	20.5882	+	27.3531i	0.676572	+	0.898879i
$927$		0			0
$928$	−8.91325	−	17.2389i	−0.292592	−	0.565895i
$929$		−	10.4466i		−	0.342740i	−0.985207	−	0.171370i	$-0.945181\pi$
$929$		−	10.4466i		−	0.342740i	0.985207	−	0.171370i	$-0.0548194\pi$
$930$		0			0
$931$	109.118	−	45.1984i	3.57621	−	1.48132i
$932$	−26.8554	+	14.8472i	−0.879677	+	0.486337i
$933$		0			0
$934$	7.05578	+	4.16145i	0.230872	+	0.136167i
$935$	−13.0803	−	13.0803i	−0.427772	−	0.427772i
$936$		0			0
$937$	−32.5899	+	32.5899i	−1.06466	+	1.06466i	−0.0669050	+	0.997759i	$0.521312\pi$
$937$	−32.5899	+	32.5899i	−1.06466	+	1.06466i	−0.997759	+	0.0669050i	$0.978688\pi$
$938$	−70.7002	+	18.2424i	−2.30844	+	0.595636i
$939$		0			0
$940$	0.487247	−	0.611158i	0.0158922	−	0.0199338i
$941$	20.8677	+	50.3791i	0.680268	+	1.64231i	0.763520	+	0.645785i	$0.223470\pi$
$941$	20.8677	+	50.3791i	0.680268	+	1.64231i	−0.0832512	+	0.996529i	$0.526530\pi$
$942$		0			0
$943$	23.6531			0.770251
$944$	13.1382	+	18.5058i	0.427611	+	0.602314i
$945$		0			0
$946$	14.1487	+	1.99648i	0.460013	+	0.0649112i
$947$	−3.61124	+	1.49582i	−0.117349	+	0.0486077i	−0.440586	−	0.897711i	$-0.645229\pi$
$947$	−3.61124	+	1.49582i	−0.117349	+	0.0486077i	0.323236	+	0.946318i	$0.395229\pi$
$948$		0			0
$949$	−0.601101	+	1.45119i	−0.0195126	+	0.0471075i
$950$	40.4655	−	10.4411i	1.31288	−	0.338755i
$951$		0			0
$952$	29.7532	−	66.5282i	0.964307	−	2.15619i
$953$	−29.6527	+	29.6527i	−0.960544	+	0.960544i	−0.999251	−	0.0387065i	$-0.987676\pi$
$953$	−29.6527	+	29.6527i	−0.960544	+	0.960544i	0.0387065	+	0.999251i	$0.487676\pi$
$954$		0			0
$955$	−2.18213	+	5.26814i	−0.0706122	+	0.170473i
$956$	−14.7880	−	4.25818i	−0.478279	−	0.137719i
$957$		0			0
$958$	−22.4763	−	29.8616i	−0.726177	−	0.964784i
$959$	−34.4586			−1.11273
$960$		0			0
$961$	18.9765			0.612146
$962$	0.328600	+	0.436571i	0.0105945	+	0.0140756i
$963$		0			0
$964$	27.9963	+	8.06148i	0.901701	+	0.259643i
$965$	−3.97152	+	9.58810i	−0.127848	+	0.308652i
$966$		0			0
$967$	−15.0414	+	15.0414i	−0.483697	+	0.483697i	−0.906310	−	0.422613i	$-0.861113\pi$
$967$	−15.0414	+	15.0414i	−0.483697	+	0.483697i	0.422613	+	0.906310i	$0.361113\pi$
$968$	−8.48839	−	3.79623i	−0.272827	−	0.122016i
$969$		0			0
$970$	−11.0905	+	2.86162i	−0.356093	+	0.0918810i
$971$	−0.522995	+	1.26262i	−0.0167837	+	0.0405195i	−0.932049	−	0.362332i	$-0.881981\pi$
$971$	−0.522995	+	1.26262i	−0.0167837	+	0.0405195i	0.915266	+	0.402851i	$0.131981\pi$
$972$		0			0
$973$	−92.5664	+	38.3423i	−2.96754	+	1.22920i
$974$	18.4717	+	2.60649i	0.591871	+	0.0835173i
$975$		0			0
$976$	0.0241763	−	0.142526i	0.000773866	−	0.00456215i
$977$	−6.54082			−0.209259			−0.104630	−	0.994511i	$-0.533366\pi$
$977$	−6.54082			−0.209259			−0.104630	+	0.994511i	$0.533366\pi$
$978$		0			0
$979$	9.86076	+	23.8060i	0.315151	+	0.760843i
$980$	19.0711	−	23.9211i	0.609205	−	0.764131i
$981$		0			0
$982$	−10.6488	+	2.74766i	−0.339818	+	0.0876815i
$983$	11.2187	−	11.2187i	0.357820	−	0.357820i	−0.505189	−	0.863009i	$-0.668577\pi$
$983$	11.2187	−	11.2187i	0.357820	−	0.357820i	0.863009	+	0.505189i	$0.168577\pi$
$984$		0			0
$985$	−4.41938	−	4.41938i	−0.140813	−	0.140813i
$986$	−22.1728	−	13.0774i	−0.706125	−	0.416468i
$987$		0			0
$988$	3.48972	−	1.92932i	0.111023	−	0.0613797i
$989$	7.81900	−	3.23874i	0.248630	−	0.102986i
$990$		0			0
$991$			18.7152i			0.594507i	0.954799	+	0.297254i	$0.0960707\pi$
$991$			18.7152i			0.594507i	−0.954799	+	0.297254i	$0.903929\pi$
$992$	19.5451	−	1.65530i	0.620558	−	0.0525557i
$993$		0			0
$994$	27.1583	+	36.0820i	0.861410	+	1.14445i
$995$	−4.33105	−	10.4561i	−0.137303	−	0.331480i
$996$		0			0
$997$	−5.03956	−	2.08745i	−0.159604	−	0.0661103i	0.301451	−	0.953482i	$-0.402529\pi$
$997$	−5.03956	−	2.08745i	−0.159604	−	0.0661103i	−0.461055	+	0.887371i	$0.652529\pi$
$998$	−19.4946	+	33.0532i	−0.617089	+	1.04628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.251.3	yes	32
3.2	odd	2		288.2.w.b.251.6	yes	32
4.3	odd	2		1152.2.w.b.143.5		32
12.11	even	2		1152.2.w.a.143.4		32
32.13	even	8		1152.2.w.a.1007.4		32
32.19	odd	8		288.2.w.b.179.6	yes	32
96.77	odd	8		1152.2.w.b.1007.5		32
96.83	even	8	inner	288.2.w.a.179.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.3	✓	32	96.83	even	8	inner
288.2.w.a.251.3	yes	32	1.1	even	1	trivial
288.2.w.b.179.6	yes	32	32.19	odd	8
288.2.w.b.251.6	yes	32	3.2	odd	2
1152.2.w.a.143.4		32	12.11	even	2
1152.2.w.a.1007.4		32	32.13	even	8
1152.2.w.b.143.5		32	4.3	odd	2
1152.2.w.b.1007.5		32	96.77	odd	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.850468 - 1.12991i) q^{2} +(-0.553410 + 1.92191i) q^{4} +(0.352978 - 0.852163i) q^{5} +(-3.43393 + 3.43393i) q^{7} +(2.64225 - 1.00922i) q^{8} +O(q^{10})\)	\(q+(-0.850468 - 1.12991i) q^{2} +(-0.553410 + 1.92191i) q^{4} +(0.352978 - 0.852163i) q^{5} +(-3.43393 + 3.43393i) q^{7} +(2.64225 - 1.00922i) q^{8} +(-1.26307 + 0.325903i) q^{10} +(-1.44650 + 3.49216i) q^{11} +(-0.258636 + 0.107131i) q^{13} +(6.80049 + 0.959599i) q^{14} +(-3.38747 - 2.12721i) q^{16} -5.30575 q^{17} +(2.72546 + 6.57983i) q^{19} +(1.44244 + 1.14999i) q^{20} +(5.17604 - 1.33555i) q^{22} +(2.23882 - 2.23882i) q^{23} +(2.93394 + 2.93394i) q^{25} +(0.341010 + 0.201126i) q^{26} +(-4.69934 - 8.50008i) q^{28} +(-3.16953 + 1.31286i) q^{29} -3.46749i q^{31} +(0.477376 + 5.63668i) q^{32} +(4.51237 + 5.99504i) q^{34} +(1.71417 + 4.13837i) q^{35} +(1.27512 + 0.528171i) q^{37} +(5.11673 - 8.67547i) q^{38} +(0.0726377 - 2.60786i) q^{40} +(5.28251 + 5.28251i) q^{41} +(2.46955 + 1.02292i) q^{43} +(-5.91111 - 4.71264i) q^{44} +(-4.43371 - 0.625628i) q^{46} -0.423698i q^{47} -16.5838i q^{49} +(0.819880 - 5.81033i) q^{50} +(-0.0627636 - 0.556363i) q^{52} +(-12.5563 - 5.20097i) q^{53} +(2.46531 + 2.46531i) q^{55} +(-5.60772 + 12.5389i) q^{56} +(4.17901 + 2.46475i) q^{58} +(-5.24194 - 2.17128i) q^{59} +(0.0138304 + 0.0333895i) q^{61} +(-3.91796 + 2.94899i) q^{62} +(5.96296 - 5.33320i) q^{64} +0.258215i q^{65} +(-9.82224 + 4.06850i) q^{67} +(2.93626 - 10.1972i) q^{68} +(3.21816 - 5.45642i) q^{70} +(4.64969 + 4.64969i) q^{71} +(3.96752 - 3.96752i) q^{73} +(-0.487659 - 1.88997i) q^{74} +(-14.1541 + 1.59674i) q^{76} +(-7.02466 - 16.9590i) q^{77} -12.7319 q^{79} +(-3.00843 + 2.13583i) q^{80} +(1.47618 - 10.4614i) q^{82} +(-0.867335 + 0.359262i) q^{83} +(-1.87281 + 4.52137i) q^{85} +(-0.944460 - 3.66034i) q^{86} +(-0.297669 + 10.6870i) q^{88} +(4.82033 - 4.82033i) q^{89} +(0.520260 - 1.25602i) q^{91} +(3.06382 + 5.54178i) q^{92} +(-0.478742 + 0.360341i) q^{94} +6.56912 q^{95} +8.78058 q^{97} +(-18.7382 + 14.1040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 32 * q - 4 * q^2 - 4 * q^8	\( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

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