LMFDB - Embedded newform 288.2.v.c.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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([0, 1, 0]))

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (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			181.1
Character	$\chi$	$=$	288.181
Dual form			288.2.v.c.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39967 - 0.202304i) q^{2} +(1.91815 + 0.566318i) q^{4} +(1.53803 - 3.71314i) q^{5} +(-1.56292 - 1.56292i) q^{7} +(-2.57020 - 1.18071i) q^{8} +O(q^{10})$	\(q+(-1.39967 - 0.202304i) q^{2} +(1.91815 + 0.566318i) q^{4} +(1.53803 - 3.71314i) q^{5} +(-1.56292 - 1.56292i) q^{7} +(-2.57020 - 1.18071i) q^{8} +(-2.90392 + 4.88602i) q^{10} +(-3.83882 - 1.59009i) q^{11} +(1.23456 + 2.98048i) q^{13} +(1.87138 + 2.50375i) q^{14} +(3.35857 + 2.17256i) q^{16} +3.82597i q^{17} +(-2.98611 - 7.20912i) q^{19} +(5.05299 - 6.25133i) q^{20} +(5.05140 + 3.00221i) q^{22} +(-0.793733 + 0.793733i) q^{23} +(-7.88633 - 7.88633i) q^{25} +(-1.12501 - 4.42144i) q^{26} +(-2.11280 - 3.88301i) q^{28} +(1.97925 - 0.819832i) q^{29} +2.27008 q^{31} +(-4.26137 - 3.72032i) q^{32} +(0.774009 - 5.35509i) q^{34} +(-8.20716 + 3.39952i) q^{35} +(2.48712 - 6.00445i) q^{37} +(2.72114 + 10.6945i) q^{38} +(-8.33718 + 7.72755i) q^{40} +(3.72376 - 3.72376i) q^{41} +(6.59936 + 2.73354i) q^{43} +(-6.46293 - 5.22402i) q^{44} +(1.27154 - 0.950389i) q^{46} +2.53270i q^{47} -2.11457i q^{49} +(9.44282 + 12.6337i) q^{50} +(0.680159 + 6.41615i) q^{52} +(5.60929 + 2.32344i) q^{53} +(-11.8085 + 11.8085i) q^{55} +(2.17167 + 5.86236i) q^{56} +(-2.93615 + 0.747083i) q^{58} +(2.52261 - 6.09012i) q^{59} +(-3.34769 + 1.38666i) q^{61} +(-3.17736 - 0.459246i) q^{62} +(5.21187 + 6.06930i) q^{64} +12.9657 q^{65} +(9.88289 - 4.09363i) q^{67} +(-2.16671 + 7.33876i) q^{68} +(12.1750 - 3.09786i) q^{70} +(2.08330 + 2.08330i) q^{71} +(-3.11317 + 3.11317i) q^{73} +(-4.69587 + 7.90108i) q^{74} +(-1.64515 - 15.5192i) q^{76} +(3.51458 + 8.48495i) q^{77} +3.53047i q^{79} +(13.2326 - 9.12937i) q^{80} +(-5.96536 + 4.45869i) q^{82} +(6.34581 + 15.3201i) q^{83} +(14.2064 + 5.88446i) q^{85} +(-8.68391 - 5.16114i) q^{86} +(7.98912 + 8.61938i) q^{88} +(-6.94955 - 6.94955i) q^{89} +(2.72874 - 6.58776i) q^{91} +(-1.97200 + 1.07299i) q^{92} +(0.512376 - 3.54495i) q^{94} -31.3612 q^{95} -6.02915 q^{97} +(-0.427786 + 2.95970i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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 $

$2$	−1.39967	−	0.202304i	−0.989715	−	0.143051i
$2$	−1.39967	−	0.202304i	−0.989715	−	0.143051i
$3$		0			0
$3$		0			0
$4$	1.91815	+	0.566318i	0.959073	+	0.283159i
$5$	1.53803	−	3.71314i	0.687829	−	1.66057i	−0.0612799	−	0.998121i	$-0.519518\pi$
$5$	1.53803	−	3.71314i	0.687829	−	1.66057i	0.749109	−	0.662446i	$-0.230482\pi$
$6$		0			0
$7$	−1.56292	−	1.56292i	−0.590728	−	0.590728i	0.347100	−	0.937828i	$-0.387166\pi$
$7$	−1.56292	−	1.56292i	−0.590728	−	0.590728i	−0.937828	+	0.347100i	$0.887166\pi$
$8$	−2.57020	−	1.18071i	−0.908703	−	0.417443i
$9$		0			0
$10$	−2.90392	+	4.88602i	−0.918300	+	1.54509i
$11$	−3.83882	−	1.59009i	−1.15745	−	0.479431i	−0.280424	−	0.959876i	$-0.590475\pi$
$11$	−3.83882	−	1.59009i	−1.15745	−	0.479431i	−0.877025	+	0.480445i	$0.840475\pi$
$12$		0			0
$13$	1.23456	+	2.98048i	0.342404	+	0.826637i	0.997472	+	0.0710662i	$0.0226402\pi$
$13$	1.23456	+	2.98048i	0.342404	+	0.826637i	−0.655068	+	0.755570i	$0.727360\pi$
$14$	1.87138	+	2.50375i	0.500148	+	0.669156i
$15$		0			0
$16$	3.35857	+	2.17256i	0.839642	+	0.543140i
$17$			3.82597i			0.927933i	0.885853	+	0.463967i	$0.153574\pi$
$17$			3.82597i			0.927933i	−0.885853	+	0.463967i	$0.846426\pi$
$18$		0			0
$19$	−2.98611	−	7.20912i	−0.685061	−	1.65388i	−0.754501	−	0.656299i	$-0.772121\pi$
$19$	−2.98611	−	7.20912i	−0.685061	−	1.65388i	0.0694399	−	0.997586i	$-0.477879\pi$
$20$	5.05299	−	6.25133i	1.12988	−	1.39784i
$21$		0			0
$22$	5.05140	+	3.00221i	1.07696	+	0.640074i
$23$	−0.793733	+	0.793733i	−0.165505	+	0.165505i	−0.785000	−	0.619495i	$-0.787337\pi$
$23$	−0.793733	+	0.793733i	−0.165505	+	0.165505i	0.619495	+	0.785000i	$0.287337\pi$
$24$		0			0
$25$	−7.88633	−	7.88633i	−1.57727	−	1.57727i
$26$	−1.12501	−	4.42144i	−0.220632	−	0.867116i
$27$		0			0
$28$	−2.11280	−	3.88301i	−0.399281	−	0.733821i
$29$	1.97925	−	0.819832i	0.367537	−	0.152239i	−0.191268	−	0.981538i	$-0.561260\pi$
$29$	1.97925	−	0.819832i	0.367537	−	0.152239i	0.558805	+	0.829299i	$0.311260\pi$
$30$		0			0
$31$	2.27008			0.407718			0.203859	−	0.979000i	$-0.434652\pi$
$31$	2.27008			0.407718			0.203859	+	0.979000i	$0.434652\pi$
$32$	−4.26137	−	3.72032i	−0.753310	−	0.657665i
$33$		0			0
$34$	0.774009	−	5.35509i	0.132741	−	0.918390i
$35$	−8.20716	+	3.39952i	−1.38726	+	0.574623i
$36$		0			0
$37$	2.48712	−	6.00445i	0.408881	−	0.987125i	−0.576552	−	0.817060i	$-0.695602\pi$
$37$	2.48712	−	6.00445i	0.408881	−	0.987125i	0.985433	−	0.170065i	$-0.0543978\pi$
$38$	2.72114	+	10.6945i	0.441427	+	1.73487i
$39$		0			0
$40$	−8.33718	+	7.72755i	−1.31822	+	1.22183i
$41$	3.72376	−	3.72376i	0.581553	−	0.581553i	−0.353777	−	0.935330i	$-0.615103\pi$
$41$	3.72376	−	3.72376i	0.581553	−	0.581553i	0.935330	+	0.353777i	$0.115103\pi$
$42$		0			0
$43$	6.59936	+	2.73354i	1.00639	+	0.416862i	0.824138	−	0.566390i	$-0.191660\pi$
$43$	6.59936	+	2.73354i	1.00639	+	0.416862i	0.182255	+	0.983251i	$0.441660\pi$
$44$	−6.46293	−	5.22402i	−0.974323	−	0.787551i
$45$		0			0
$46$	1.27154	−	0.950389i	0.187478	−	0.140127i
$47$			2.53270i			0.369433i	0.982792	+	0.184716i	$0.0591367\pi$
$47$			2.53270i			0.369433i	−0.982792	+	0.184716i	$0.940863\pi$
$48$		0			0
$49$		−	2.11457i		−	0.302082i
$50$	9.44282	+	12.6337i	1.33542	+	1.78667i
$51$		0			0
$52$	0.680159	+	6.41615i	0.0943211	+	0.889760i
$53$	5.60929	+	2.32344i	0.770495	+	0.319150i	0.733073	−	0.680150i	$-0.238085\pi$
$53$	5.60929	+	2.32344i	0.770495	+	0.319150i	0.0374223	+	0.999300i	$0.488085\pi$
$54$		0			0
$55$	−11.8085	+	11.8085i	−1.59225	+	1.59225i
$56$	2.17167	+	5.86236i	0.290201	+	0.783391i
$57$		0			0
$58$	−2.93615	+	0.747083i	−0.385535	+	0.0980968i
$59$	2.52261	−	6.09012i	0.328416	−	0.792866i	−0.670295	−	0.742095i	$-0.733832\pi$
$59$	2.52261	−	6.09012i	0.328416	−	0.792866i	0.998710	−	0.0507706i	$-0.0161677\pi$
$60$		0			0
$61$	−3.34769	+	1.38666i	−0.428628	+	0.177543i	−0.586559	−	0.809907i	$-0.699518\pi$
$61$	−3.34769	+	1.38666i	−0.428628	+	0.177543i	0.157931	+	0.987450i	$0.449518\pi$
$62$	−3.17736	−	0.459246i	−0.403525	−	0.0583243i
$63$		0			0
$64$	5.21187	+	6.06930i	0.651483	+	0.758663i
$65$	12.9657			1.60820
$66$		0			0
$67$	9.88289	−	4.09363i	1.20739	−	0.500116i	0.314008	−	0.949420i	$-0.398328\pi$
$67$	9.88289	−	4.09363i	1.20739	−	0.500116i	0.893379	+	0.449304i	$0.148328\pi$
$68$	−2.16671	+	7.33876i	−0.262752	+	0.889956i
$69$		0			0
$70$	12.1750	−	3.09786i	1.45520	−	0.370265i
$71$	2.08330	+	2.08330i	0.247242	+	0.247242i	0.819838	−	0.572596i	$-0.194063\pi$
$71$	2.08330	+	2.08330i	0.247242	+	0.247242i	−0.572596	+	0.819838i	$0.694063\pi$
$72$		0			0
$73$	−3.11317	+	3.11317i	−0.364369	+	0.364369i	−0.865418	−	0.501050i	$-0.832947\pi$
$73$	−3.11317	+	3.11317i	−0.364369	+	0.364369i	0.501050	+	0.865418i	$0.332947\pi$
$74$	−4.69587	+	7.90108i	−0.545884	+	0.918482i
$75$		0			0
$76$	−1.64515	−	15.5192i	−0.188712	−	1.78018i
$77$	3.51458	+	8.48495i	0.400524	+	0.966950i
$78$		0			0
$79$			3.53047i			0.397209i	0.980080	+	0.198604i	$0.0636409\pi$
$79$			3.53047i			0.397209i	−0.980080	+	0.198604i	$0.936359\pi$
$80$	13.2326	−	9.12937i	1.47945	−	1.02069i
$81$		0			0
$82$	−5.96536	+	4.45869i	−0.658764	+	0.492380i
$83$	6.34581	+	15.3201i	0.696543	+	1.68160i	0.731162	+	0.682204i	$0.238978\pi$
$83$	6.34581	+	15.3201i	0.696543	+	1.68160i	−0.0346184	+	0.999401i	$0.511022\pi$
$84$		0			0
$85$	14.2064	+	5.88446i	1.54090	+	0.638260i
$86$	−8.68391	−	5.16114i	−0.936410	−	0.556540i
$87$		0			0
$88$	7.98912	+	8.61938i	0.851643	+	0.918829i
$89$	−6.94955	−	6.94955i	−0.736651	−	0.736651i	0.235277	−	0.971928i	$-0.424400\pi$
$89$	−6.94955	−	6.94955i	−0.736651	−	0.736651i	−0.971928	+	0.235277i	$0.924400\pi$
$90$		0			0
$91$	2.72874	−	6.58776i	0.286050	−	0.690585i
$92$	−1.97200	+	1.07299i	−0.205595	+	0.111867i
$93$		0			0
$94$	0.512376	−	3.54495i	0.0528476	−	0.365633i
$95$	−31.3612			−3.21759
$96$		0			0
$97$	−6.02915			−0.612167			−0.306083	−	0.952005i	$-0.599019\pi$
$97$	−6.02915			−0.612167			−0.306083	+	0.952005i	$0.599019\pi$
$98$	−0.427786	+	2.95970i	−0.0432129	+	0.298975i
$99$		0			0
$100$	−10.6610	−	19.5933i	−1.06610	−	1.95933i
$101$	3.29131	−	7.94593i	0.327498	−	0.790649i	−0.671279	−	0.741205i	$-0.734255\pi$
$101$	3.29131	−	7.94593i	0.327498	−	0.790649i	0.998777	−	0.0494446i	$-0.0157451\pi$
$102$		0			0
$103$	2.08556	+	2.08556i	0.205497	+	0.205497i	0.802350	−	0.596854i	$-0.203583\pi$
$103$	2.08556	+	2.08556i	0.205497	+	0.205497i	−0.596854	+	0.802350i	$0.703583\pi$
$104$	0.346015	−	9.11808i	0.0339296	−	0.894101i
$105$		0			0
$106$	−7.38111	−	4.38684i	−0.716917	−	0.426087i
$107$	0.399228	+	0.165366i	0.0385949	+	0.0159865i	0.401897	−	0.915685i	$-0.368351\pi$
$107$	0.399228	+	0.165366i	0.0385949	+	0.0159865i	−0.363303	+	0.931671i	$0.618351\pi$
$108$		0			0
$109$	6.81530	+	16.4536i	0.652787	+	1.57597i	0.808716	+	0.588199i	$0.200163\pi$
$109$	6.81530	+	16.4536i	0.652787	+	1.57597i	−0.155929	+	0.987768i	$0.549837\pi$
$110$	18.9169	−	14.1391i	1.80365	−	1.34811i
$111$		0			0
$112$	−1.85364	−	8.64470i	−0.175152	−	0.816848i
$113$		−	2.50087i		−	0.235262i	−0.993057	−	0.117631i	$-0.962470\pi$
$113$		−	2.50087i		−	0.235262i	0.993057	−	0.117631i	$-0.0375300\pi$
$114$		0			0
$115$	1.72646	+	4.16803i	0.160993	+	0.388671i
$116$	4.26078	−	0.451674i	0.395603	−	0.0419369i
$117$		0			0
$118$	−4.76287	+	8.01381i	−0.438458	+	0.737731i
$119$	5.97967	−	5.97967i	0.548156	−	0.548156i
$120$		0			0
$121$	4.43000	+	4.43000i	0.402727	+	0.402727i
$122$	4.96619	−	1.26361i	0.449617	−	0.114402i
$123$		0			0
$124$	4.35434	+	1.28558i	0.391031	+	0.115449i
$125$	−22.8468	+	9.46346i	−2.04348	+	0.846438i
$126$		0			0
$127$	−12.6224			−1.12006			−0.560029	−	0.828473i	$-0.689210\pi$
$127$	−12.6224			−1.12006			−0.560029	+	0.828473i	$0.689210\pi$
$128$	−6.06704	−	9.54940i	−0.536256	−	0.844055i
$129$		0			0
$130$	−18.1477	−	2.62302i	−1.59166	−	0.230054i
$131$	8.95878	−	3.71085i	0.782732	−	0.324218i	0.0447146	−	0.999000i	$-0.485762\pi$
$131$	8.95878	−	3.71085i	0.782732	−	0.324218i	0.738018	+	0.674782i	$0.235762\pi$
$132$		0			0
$133$	−6.60021	+	15.9343i	−0.572311	+	1.38168i
$134$	−14.6609	+	3.73037i	−1.26651	+	0.322255i
$135$		0			0
$136$	4.51734	−	9.83350i	0.387359	−	0.843216i
$137$	−0.282264	+	0.282264i	−0.0241154	+	0.0241154i	−0.719062	−	0.694946i	$-0.755428\pi$
$137$	−0.282264	+	0.282264i	−0.0241154	+	0.0241154i	0.694946	+	0.719062i	$0.255428\pi$
$138$		0			0
$139$	−9.47722	−	3.92559i	−0.803847	−	0.332964i	−0.0573510	−	0.998354i	$-0.518265\pi$
$139$	−9.47722	−	3.92559i	−0.803847	−	0.332964i	−0.746496	+	0.665390i	$0.768265\pi$
$140$	−17.6677	+	1.87291i	−1.49320	+	0.158290i
$141$		0			0
$142$	−2.49447	−	3.33739i	−0.209331	−	0.280068i
$143$		−	13.4046i		−	1.12095i
$144$		0			0
$145$		−	8.61016i		−	0.715035i
$146$	4.98721	−	3.72760i	0.412744	−	0.308498i
$147$		0			0
$148$	8.17109	−	10.1089i	0.671660	−	0.830947i
$149$	9.00905	+	3.73167i	0.738050	+	0.305711i	0.719856	−	0.694124i	$-0.244208\pi$
$149$	9.00905	+	3.73167i	0.738050	+	0.305711i	0.0181950	+	0.999834i	$0.494208\pi$
$150$		0			0
$151$	4.98517	−	4.98517i	0.405687	−	0.405687i	−0.474544	−	0.880232i	$-0.657387\pi$
$151$	4.98517	−	4.98517i	0.405687	−	0.405687i	0.880232	+	0.474544i	$0.157387\pi$
$152$	−0.836934	+	22.0546i	−0.0678843	+	1.78886i
$153$		0			0
$154$	−3.20271	−	12.5871i	−0.258082	−	1.01430i
$155$	3.49145	−	8.42911i	0.280440	−	0.677043i
$156$		0			0
$157$	18.7301	−	7.75827i	1.49483	−	0.619177i	0.522465	−	0.852661i	$-0.325012\pi$
$157$	18.7301	−	7.75827i	1.49483	−	0.619177i	0.972361	+	0.233483i	$0.0750125\pi$
$158$	0.714228	−	4.94149i	0.0568210	−	0.393124i
$159$		0			0
$160$	−20.3682	+	10.1011i	−1.61025	+	0.798561i
$161$	2.48108			0.195537
$162$		0			0
$163$	2.34679	−	0.972073i	0.183815	−	0.0761387i	−0.288878	−	0.957366i	$-0.593282\pi$
$163$	2.34679	−	0.972073i	0.183815	−	0.0761387i	0.472693	+	0.881227i	$0.343282\pi$
$164$	9.25154	−	5.03388i	0.722424	−	0.393080i
$165$		0			0
$166$	−5.78271	−	22.7269i	−0.448825	−	1.76395i
$167$	12.1836	+	12.1836i	0.942798	+	0.942798i	0.998450	−	0.0556519i	$-0.0177237\pi$
$167$	12.1836	+	12.1836i	0.942798	+	0.942798i	−0.0556519	+	0.998450i	$0.517724\pi$
$168$		0			0
$169$	1.83325	−	1.83325i	0.141019	−	0.141019i
$170$	−18.6937	−	11.1103i	−1.43374	−	0.852121i
$171$		0			0
$172$	11.1105	+	8.98067i	0.847166	+	0.684770i
$173$	−4.17177	−	10.0715i	−0.317174	−	0.765725i	−0.999402	−	0.0345858i	$-0.988989\pi$
$173$	−4.17177	−	10.0715i	−0.317174	−	0.765725i	0.682228	−	0.731140i	$-0.261011\pi$
$174$		0			0
$175$			24.6514i			1.86347i
$176$	−9.43838	−	13.6805i	−0.711445	−	1.03121i
$177$		0			0
$178$	8.32115	+	11.1330i	0.623697	+	0.834453i
$179$	−3.98101	−	9.61101i	−0.297555	−	0.718361i	−0.999978	−	0.00660153i	$-0.997899\pi$
$179$	−3.98101	−	9.61101i	−0.297555	−	0.718361i	0.702423	−	0.711759i	$-0.252101\pi$
$180$		0			0
$181$	−0.272088	−	0.112703i	−0.0202242	−	0.00837713i	0.372548	−	0.928013i	$-0.378484\pi$
$181$	−0.272088	−	0.112703i	−0.0202242	−	0.00837713i	−0.392773	+	0.919636i	$0.628484\pi$
$182$	−5.15206	+	8.66864i	−0.381896	+	0.642563i
$183$		0			0
$184$	2.97722	−	1.10289i	0.219484	−	0.0813060i
$185$	−18.4701	−	18.4701i	−1.35795	−	1.35795i
$186$		0			0
$187$	6.08364	−	14.6872i	0.444880	−	1.07404i
$188$	−1.43431	+	4.85810i	−0.104608	+	0.354313i
$189$		0			0
$190$	43.8953	+	6.34450i	3.18450	+	0.460279i
$191$	18.2329			1.31929			0.659644	−	0.751578i	$-0.270707\pi$
$191$	18.2329			1.31929			0.659644	+	0.751578i	$0.270707\pi$
$192$		0			0
$193$	−20.4986			−1.47552			−0.737762	−	0.675061i	$-0.764117\pi$
$193$	−20.4986			−1.47552			−0.737762	+	0.675061i	$0.764117\pi$
$194$	8.43881	+	1.21972i	0.605871	+	0.0875709i
$195$		0			0
$196$	1.19752	−	4.05606i	0.0855370	−	0.289718i
$197$	3.95929	−	9.55857i	0.282088	−	0.681020i	−0.717796	−	0.696253i	$-0.754849\pi$
$197$	3.95929	−	9.55857i	0.282088	−	0.681020i	0.999884	+	0.0152331i	$0.00484905\pi$
$198$		0			0
$199$	11.7743	+	11.7743i	0.834659	+	0.834659i	0.988150	−	0.153491i	$-0.0490516\pi$
$199$	11.7743	+	11.7743i	0.834659	+	0.834659i	−0.153491	+	0.988150i	$0.549052\pi$
$200$	10.9580	+	29.5809i	0.774849	+	2.09169i
$201$		0			0
$202$	−6.21424	+	10.4558i	−0.437232	+	0.735669i
$203$	−4.37474	−	1.81208i	−0.307046	−	0.127183i
$204$		0			0
$205$	−8.09957	−	19.5541i	−0.565699	−	1.36572i
$206$	−2.49718	−	3.34102i	−0.173987	−	0.232780i
$207$		0			0
$208$	−2.32893	+	12.6923i	−0.161482	+	0.880052i
$209$			32.4227i			2.24273i
$210$		0			0
$211$	6.68934	+	16.1495i	0.460513	+	1.11178i	0.968187	+	0.250228i	$0.0805055\pi$
$211$	6.68934	+	16.1495i	0.460513	+	1.11178i	−0.507674	+	0.861549i	$0.669495\pi$
$212$	9.44363	+	7.63335i	0.648591	+	0.524260i
$213$		0			0
$214$	−0.525333	−	0.312223i	−0.0359110	−	0.0213431i
$215$	20.3001	−	20.3001i	1.38445	−	1.38445i
$216$		0			0
$217$	−3.54795	−	3.54795i	−0.240850	−	0.240850i
$218$	−6.21053	−	24.4083i	−0.420630	−	1.65314i
$219$		0			0
$220$	−29.3377	+	15.9630i	−1.97795	+	1.07623i
$221$	−11.4032	+	4.72337i	−0.767063	+	0.317728i
$222$		0			0
$223$	−11.6491			−0.780084			−0.390042	−	0.920797i	$-0.627540\pi$
$223$	−11.6491			−0.780084			−0.390042	+	0.920797i	$0.627540\pi$
$224$	0.845617	+	12.4747i	0.0565002	+	0.833502i
$225$		0			0
$226$	−0.505936	+	3.50038i	−0.0336543	+	0.232842i
$227$	−22.5984	+	9.36057i	−1.49991	+	0.621283i	−0.973446	−	0.228915i	$-0.926482\pi$
$227$	−22.5984	+	9.36057i	−1.49991	+	0.621283i	−0.526463	+	0.850198i	$0.676482\pi$
$228$		0			0
$229$	−7.47834	+	18.0543i	−0.494182	+	1.19306i	0.458390	+	0.888751i	$0.348426\pi$
$229$	−7.47834	+	18.0543i	−0.494182	+	1.19306i	−0.952573	+	0.304311i	$0.901574\pi$
$230$	−1.57326	−	6.18314i	−0.103737	−	0.407704i
$231$		0			0
$232$	−6.05505	−	0.229779i	−0.397534	−	0.0150857i
$233$	−17.0428	+	17.0428i	−1.11651	+	1.11651i	−0.124259	+	0.992250i	$0.539656\pi$
$233$	−17.0428	+	17.0428i	−1.11651	+	1.11651i	−0.992250	+	0.124259i	$0.960344\pi$
$234$		0			0
$235$	9.40429	+	3.89538i	0.613468	+	0.254107i
$236$	8.28767	−	10.2531i	0.539482	−	0.667422i
$237$		0			0
$238$	−9.57928	+	7.15985i	−0.620932	+	0.464104i
$239$			29.1889i			1.88807i	0.329839	+	0.944037i	$0.393005\pi$
$239$			29.1889i			1.88807i	−0.329839	+	0.944037i	$0.606995\pi$
$240$		0			0
$241$		−	3.63850i		−	0.234376i	−0.993110	−	0.117188i	$-0.962612\pi$
$241$		−	3.63850i		−	0.234376i	0.993110	−	0.117188i	$-0.0373881\pi$
$242$	−5.30432	−	7.09674i	−0.340975	−	0.456195i
$243$		0			0
$244$	−7.20665	+	0.763958i	−0.461358	+	0.0489074i
$245$	−7.85170	−	3.25228i	−0.501627	−	0.207781i
$246$		0			0
$247$	17.8001	−	17.8001i	1.13259	−	1.13259i
$248$	−5.83455	−	2.68029i	−0.370495	−	0.170199i
$249$		0			0
$250$	33.8925	−	8.62371i	2.14355	−	0.545411i
$251$	9.41099	−	22.7201i	0.594016	−	1.43408i	−0.285577	−	0.958356i	$-0.592185\pi$
$251$	9.41099	−	22.7201i	0.594016	−	1.43408i	0.879593	−	0.475727i	$-0.157815\pi$
$252$		0			0
$253$	4.30911	−	1.78489i	0.270912	−	0.112215i
$254$	17.6672	+	2.55357i	1.10854	+	0.160225i
$255$		0			0
$256$	6.55997	+	14.5934i	0.409998	+	0.912086i
$257$	5.22343			0.325829			0.162914	−	0.986640i	$-0.447911\pi$
$257$	5.22343			0.325829			0.162914	+	0.986640i	$0.447911\pi$
$258$		0			0
$259$	−13.2716	+	5.49729i	−0.824659	+	0.341585i
$260$	24.8702	+	7.34272i	1.54238	+	0.455376i
$261$		0			0
$262$	−13.2900	+	3.38156i	−0.821062	+	0.208913i
$263$	17.0256	+	17.0256i	1.04984	+	1.04984i	0.998691	+	0.0511500i	$0.0162887\pi$
$263$	17.0256	+	17.0256i	1.04984	+	1.04984i	0.0511500	+	0.998691i	$0.483711\pi$
$264$		0			0
$265$	17.2546	−	17.2546i	1.05994	−	1.05994i
$266$	12.4617	−	20.9675i	0.764075	−	1.28560i
$267$		0			0
$268$	21.2751	−	2.25532i	1.29958	−	0.137766i
$269$	3.76182	+	9.08184i	0.229362	+	0.553729i	0.996100	−	0.0882310i	$-0.0281214\pi$
$269$	3.76182	+	9.08184i	0.229362	+	0.553729i	−0.766738	+	0.641960i	$0.778121\pi$
$270$		0			0
$271$		−	23.5235i		−	1.42895i	−0.699660	−	0.714476i	$-0.746665\pi$
$271$		−	23.5235i		−	1.42895i	0.699660	−	0.714476i	$-0.253335\pi$
$272$	−8.31214	+	12.8498i	−0.503998	+	0.779132i
$273$		0			0
$274$	0.452179	−	0.337973i	0.0273171	−	0.0204177i
$275$	17.7342	+	42.8143i	1.06942	+	2.58180i
$276$		0			0
$277$	−18.6101	−	7.70855i	−1.11817	−	0.463162i	−0.254427	−	0.967092i	$-0.581887\pi$
$277$	−18.6101	−	7.70855i	−1.11817	−	0.463162i	−0.863744	+	0.503930i	$0.831887\pi$
$278$	12.4708	+	7.41181i	0.747949	+	0.444531i
$279$		0			0
$280$	25.1079	+	0.952801i	1.50048	+	0.0569407i
$281$	−2.95752	−	2.95752i	−0.176431	−	0.176431i	0.613367	−	0.789798i	$-0.289815\pi$
$281$	−2.95752	−	2.95752i	−0.176431	−	0.176431i	−0.789798	+	0.613367i	$0.789815\pi$
$282$		0			0
$283$	−1.30585	+	3.15261i	−0.0776250	+	0.187403i	−0.957928	−	0.287008i	$-0.907339\pi$
$283$	−1.30585	+	3.15261i	−0.0776250	+	0.187403i	0.880303	+	0.474412i	$0.157339\pi$
$284$	2.81627	+	5.17589i	0.167115	+	0.307132i
$285$		0			0
$286$	−2.71181	+	18.7620i	−0.160352	+	1.10942i
$287$	−11.6399			−0.687079
$288$		0			0
$289$	2.36198			0.138940
$290$	−1.74187	+	12.0514i	−0.102286	+	0.707681i
$291$		0			0
$292$	−7.73455	+	4.20847i	−0.452630	+	0.246282i
$293$	7.17905	−	17.3317i	0.419404	−	1.01253i	−0.563116	−	0.826378i	$-0.690398\pi$
$293$	7.17905	−	17.3317i	0.419404	−	1.01253i	0.982521	−	0.186154i	$-0.0596023\pi$
$294$		0			0
$295$	−18.7336	−	18.7336i	−1.09071	−	1.09071i
$296$	−13.4819	+	12.4961i	−0.783619	+	0.726320i
$297$		0			0
$298$	−11.8548	−	7.04567i	−0.686728	−	0.408145i
$299$	−3.34561	−	1.38580i	−0.193482	−	0.0801428i
$300$		0			0
$301$	−6.04196	−	14.5866i	−0.348253	−	0.840756i
$302$	−7.98610	+	5.96906i	−0.459549	+	0.343481i
$303$		0			0
$304$	5.63317	−	30.6998i	0.323084	−	1.76076i
$305$			14.5632i			0.833885i
$306$		0			0
$307$	−8.59001	−	20.7381i	−0.490258	−	1.18359i	−0.954589	−	0.297926i	$-0.903705\pi$
$307$	−8.59001	−	20.7381i	−0.490258	−	1.18359i	0.464331	−	0.885662i	$-0.346295\pi$
$308$	1.93631	+	18.2658i	0.110331	+	1.04079i
$309$		0			0
$310$	−6.59212	+	11.0916i	−0.374407	+	0.629962i
$311$	4.35643	−	4.35643i	0.247030	−	0.247030i	−0.572720	−	0.819751i	$-0.694112\pi$
$311$	4.35643	−	4.35643i	0.247030	−	0.247030i	0.819751	+	0.572720i	$0.194112\pi$
$312$		0			0
$313$	11.2066	+	11.2066i	0.633435	+	0.633435i	0.948928	−	0.315493i	$-0.102170\pi$
$313$	11.2066	+	11.2066i	0.633435	+	0.633435i	−0.315493	+	0.948928i	$0.602170\pi$
$314$	−27.7855	+	7.06983i	−1.56803	+	0.398973i
$315$		0			0
$316$	−1.99937	+	6.77195i	−0.112473	+	0.380952i
$317$	−6.62695	+	2.74497i	−0.372206	+	0.154173i	−0.560942	−	0.827855i	$-0.689561\pi$
$317$	−6.62695	+	2.74497i	−0.372206	+	0.154173i	0.188736	+	0.982028i	$0.439561\pi$
$318$		0			0
$319$	−8.90160			−0.498394
$320$	30.5522	−	10.0176i	1.70792	−	0.560001i
$321$		0			0
$322$	−3.47269	−	0.501933i	−0.193526	−	0.0279716i
$323$	27.5818	−	11.4248i	1.53469	−	0.635691i
$324$		0			0
$325$	13.7689	−	33.2412i	0.763764	−	1.84389i
$326$	−3.48139	+	0.885815i	−0.192816	+	0.0490608i
$327$		0			0
$328$	−13.9675	+	5.17414i	−0.771224	+	0.285694i
$329$	3.95841	−	3.95841i	0.218234	−	0.218234i
$330$		0			0
$331$	−23.8874	−	9.89449i	−1.31297	−	0.543850i	−0.387221	−	0.921987i	$-0.626565\pi$
$331$	−23.8874	−	9.89449i	−1.31297	−	0.543850i	−0.925750	+	0.378137i	$0.876565\pi$
$332$	3.49613	+	32.9800i	0.191875	+	1.81001i
$333$		0			0
$334$	−14.5883	−	19.5179i	−0.798234	−	1.06797i
$335$		−	42.9927i		−	2.34894i
$336$		0			0
$337$			10.9267i			0.595215i	0.954688	+	0.297608i	$0.0961887\pi$
$337$			10.9267i			0.595215i	−0.954688	+	0.297608i	$0.903811\pi$
$338$	−2.93682	+	2.19507i	−0.159742	+	0.119396i
$339$		0			0
$340$	23.9174	+	19.3326i	1.29710	+	1.04846i
$341$	−8.71442	−	3.60963i	−0.471913	−	0.195473i
$342$		0			0
$343$	−14.2453	+	14.2453i	−0.769176	+	0.769176i
$344$	−13.7342	−	14.8177i	−0.740497	−	0.798915i
$345$		0			0
$346$	3.80158	+	14.9408i	0.204374	+	0.803222i
$347$	7.71651	−	18.6293i	0.414244	−	1.00007i	−0.569741	−	0.821824i	$-0.692957\pi$
$347$	7.71651	−	18.6293i	0.414244	−	1.00007i	0.983985	−	0.178249i	$-0.0570434\pi$
$348$		0			0
$349$	−15.8436	+	6.56263i	−0.848088	+	0.351290i	−0.764037	−	0.645172i	$-0.776786\pi$
$349$	−15.8436	+	6.56263i	−0.848088	+	0.351290i	−0.0840506	+	0.996461i	$0.526786\pi$
$350$	4.98708	−	34.5038i	0.266571	−	1.84431i
$351$		0			0
$352$	10.4430	+	21.0576i	0.556613	+	1.12237i
$353$	−20.5654			−1.09458			−0.547292	−	0.836942i	$-0.684341\pi$
$353$	−20.5654			−1.09458			−0.547292	+	0.836942i	$0.684341\pi$
$354$		0			0
$355$	10.9398	−	4.53140i	0.580623	−	0.240502i
$356$	−9.39461	−	17.2659i	−0.497913	−	0.915092i
$357$		0			0
$358$	3.62775	+	14.2576i	0.191733	+	0.753538i
$359$	−3.24218	−	3.24218i	−0.171115	−	0.171115i	0.616354	−	0.787469i	$-0.288609\pi$
$359$	−3.24218	−	3.24218i	−0.171115	−	0.171115i	−0.787469	+	0.616354i	$0.788609\pi$
$360$		0			0
$361$	−29.6195	+	29.6195i	−1.55892	+	1.55892i
$362$	0.358033	+	0.212791i	0.0188178	+	0.0111841i
$363$		0			0
$364$	8.96488	−	11.0909i	0.469888	−	0.581324i
$365$	6.77147	+	16.3478i	0.354435	+	0.855682i
$366$		0			0
$367$		−	18.5178i		−	0.966620i	−0.875449	−	0.483310i	$-0.839434\pi$
$367$		−	18.5178i		−	0.966620i	0.875449	−	0.483310i	$-0.160566\pi$
$368$	−4.39024	+	0.941375i	−0.228857	+	0.0490726i
$369$		0			0
$370$	22.1154	+	29.5886i	1.14973	+	1.53824i
$371$	−5.13551	−	12.3982i	−0.266622	−	0.643684i
$372$		0			0
$373$	8.15655	+	3.37855i	0.422330	+	0.174935i	0.583719	−	0.811956i	$-0.301597\pi$
$373$	8.15655	+	3.37855i	0.422330	+	0.174935i	−0.161388	+	0.986891i	$0.551597\pi$
$374$	−11.4864	+	19.3265i	−0.593946	+	0.999349i
$375$		0			0
$376$	2.99038	−	6.50956i	0.154217	−	0.335705i
$377$	4.88699	+	4.88699i	0.251693	+	0.251693i
$378$		0			0
$379$	−1.24397	+	3.00322i	−0.0638987	+	0.154265i	−0.952603	−	0.304215i	$-0.901606\pi$
$379$	−1.24397	+	3.00322i	−0.0638987	+	0.154265i	0.888705	+	0.458480i	$0.151606\pi$
$380$	−60.1554	−	17.7604i	−3.08591	−	0.911089i
$381$		0			0
$382$	−25.5200	−	3.68859i	−1.30572	−	0.188725i
$383$	−1.29297			−0.0660676			−0.0330338	−	0.999454i	$-0.510517\pi$
$383$	−1.29297			−0.0660676			−0.0330338	+	0.999454i	$0.510517\pi$
$384$		0			0
$385$	36.9114			1.88118
$386$	28.6913	+	4.14696i	1.46035	+	0.211075i
$387$		0			0
$388$	−11.5648	−	3.41441i	−0.587113	−	0.173340i
$389$	−3.57521	+	8.63132i	−0.181270	+	0.437626i	−0.988229	−	0.152983i	$-0.951112\pi$
$389$	−3.57521	+	8.63132i	−0.181270	+	0.437626i	0.806958	+	0.590608i	$0.201112\pi$
$390$		0			0
$391$	−3.03680	−	3.03680i	−0.153577	−	0.153577i
$392$	−2.49669	+	5.43487i	−0.126102	+	0.274502i
$393$		0			0
$394$	−7.47543	+	12.5779i	−0.376607	+	0.633663i
$395$	13.1091	+	5.42998i	0.659592	+	0.273212i
$396$		0			0
$397$	4.98334	+	12.0308i	0.250107	+	0.603811i	0.998212	−	0.0597689i	$-0.0190364\pi$
$397$	4.98334	+	12.0308i	0.250107	+	0.603811i	−0.748106	+	0.663580i	$0.769036\pi$
$398$	−14.0982	−	18.8621i	−0.706677	−	0.945474i
$399$		0			0
$400$	−9.35326	−	43.6203i	−0.467663	−	2.18102i
$401$		−	30.1043i		−	1.50334i	−0.659541	−	0.751669i	$-0.729249\pi$
$401$		−	30.1043i		−	1.50334i	0.659541	−	0.751669i	$-0.270751\pi$
$402$		0			0
$403$	2.80254	+	6.76592i	0.139604	+	0.337034i
$404$	10.8131	−	13.3775i	0.537973	−	0.665556i
$405$		0			0
$406$	5.75659	+	3.42133i	0.285695	+	0.169798i
$407$	−19.0953	+	19.0953i	−0.946517	+	0.946517i
$408$		0			0
$409$	7.91512	+	7.91512i	0.391377	+	0.391377i	0.875178	−	0.483801i	$-0.160744\pi$
$409$	7.91512	+	7.91512i	0.391377	+	0.391377i	−0.483801	+	0.875178i	$0.660744\pi$
$410$	7.38084	+	29.0078i	0.364514	+	1.43259i
$411$		0			0
$412$	2.81932	+	5.18151i	0.138898	+	0.255275i
$413$	−13.4610	+	5.57572i	−0.662372	+	0.274363i
$414$		0			0
$415$	66.6459			3.27152
$416$	5.82744	−	17.2939i	0.285714	−	0.847901i
$417$		0			0
$418$	6.55925	−	45.3811i	0.320823	−	2.21966i
$419$	−25.3304	+	10.4922i	−1.23747	+	0.512577i	−0.902923	−	0.429802i	$-0.858583\pi$
$419$	−25.3304	+	10.4922i	−1.23747	+	0.512577i	−0.334547	+	0.942379i	$0.608583\pi$
$420$		0			0
$421$	6.15064	−	14.8490i	0.299764	−	0.723694i	−0.700189	−	0.713958i	$-0.746901\pi$
$421$	6.15064	−	14.8490i	0.299764	−	0.723694i	0.999953	−	0.00973641i	$-0.00309924\pi$
$422$	−6.09575	−	23.9572i	−0.296737	−	1.16622i
$423$		0			0
$424$	−11.6737	−	12.5946i	−0.566925	−	0.611650i
$425$	30.1729	−	30.1729i	1.46360	−	1.46360i
$426$		0			0
$427$	7.39940	+	3.06493i	0.358082	+	0.148323i
$428$	0.672129	+	0.543286i	0.0324886	+	0.0262607i
$429$		0			0
$430$	−32.5202	+	24.3066i	−1.56826	+	1.17217i
$431$			18.6405i			0.897880i	0.893562	+	0.448940i	$0.148198\pi$
$431$			18.6405i			0.897880i	−0.893562	+	0.448940i	$0.851802\pi$
$432$		0			0
$433$			4.81838i			0.231556i	0.993275	+	0.115778i	$0.0369362\pi$
$433$			4.81838i			0.231556i	−0.993275	+	0.115778i	$0.963064\pi$
$434$	4.24818	+	5.68371i	0.203919	+	0.272827i
$435$		0			0
$436$	3.75478	+	35.4200i	0.179821	+	1.69631i
$437$	8.09230	+	3.35194i	0.387107	+	0.160345i
$438$		0			0
$439$	4.83818	−	4.83818i	0.230914	−	0.230914i	−0.582160	−	0.813074i	$-0.697792\pi$
$439$	4.83818	−	4.83818i	0.230914	−	0.230914i	0.813074	+	0.582160i	$0.197792\pi$
$440$	44.2925	−	16.4078i	2.11156	−	0.782212i
$441$		0			0
$442$	16.9163	−	4.30423i	0.804626	−	0.204731i
$443$	−6.74507	+	16.2840i	−0.320468	+	0.773678i	0.678759	+	0.734361i	$0.262518\pi$
$443$	−6.74507	+	16.2840i	−0.320468	+	0.773678i	−0.999227	+	0.0393167i	$0.987482\pi$
$444$		0			0
$445$	−36.4933	+	15.1160i	−1.72995	+	0.716568i
$446$	16.3049	+	2.35667i	0.772061	+	0.111592i
$447$		0			0
$448$	1.34010	−	17.6316i	0.0633140	−	0.833013i
$449$	6.74899			0.318504			0.159252	−	0.987238i	$-0.449092\pi$
$449$	6.74899			0.318504			0.159252	+	0.987238i	$0.449092\pi$
$450$		0			0
$451$	−20.2160	+	8.37373i	−0.951933	+	0.394303i
$452$	1.41628	−	4.79703i	0.0666164	−	0.225633i
$453$		0			0
$454$	33.5240	−	8.52995i	1.57336	−	0.400330i
$455$	−20.2644	−	20.2644i	−0.950009	−	0.950009i
$456$		0			0
$457$	12.3926	−	12.3926i	0.579700	−	0.579700i	−0.355121	−	0.934820i	$-0.615560\pi$
$457$	12.3926	−	12.3926i	0.579700	−	0.579700i	0.934820	+	0.355121i	$0.115560\pi$
$458$	14.1197	−	23.7571i	0.659768	−	1.11010i
$459$		0			0
$460$	0.951164	+	8.97262i	0.0443482	+	0.418350i
$461$	−1.88308	−	4.54616i	−0.0877039	−	0.211736i	0.873942	−	0.486031i	$-0.161556\pi$
$461$	−1.88308	−	4.54616i	−0.0877039	−	0.211736i	−0.961646	+	0.274295i	$0.911556\pi$
$462$		0			0
$463$		−	15.8534i		−	0.736769i	−0.929674	−	0.368384i	$-0.879911\pi$
$463$		−	15.8534i		−	0.736769i	0.929674	−	0.368384i	$-0.120089\pi$
$464$	8.42858	+	1.54658i	0.391287	+	0.0717980i
$465$		0			0
$466$	27.3021	−	20.4064i	1.26474	−	0.945309i
$467$	3.23415	+	7.80793i	0.149659	+	0.361308i	0.980874	−	0.194642i	$-0.0623546\pi$
$467$	3.23415	+	7.80793i	0.149659	+	0.361308i	−0.831216	+	0.555950i	$0.812355\pi$
$468$		0			0
$469$	−21.8441	−	9.04814i	−1.00867	−	0.417804i
$470$	−12.3748	−	7.35477i	−0.570809	−	0.339250i
$471$		0			0
$472$	−13.6742	+	12.6744i	−0.629408	+	0.583385i
$473$	−20.9872	−	20.9872i	−0.964992	−	0.964992i
$474$		0			0
$475$	−33.3040	+	80.4030i	−1.52809	+	3.68914i
$476$	14.8563	−	8.08349i	0.680937	−	0.370506i
$477$		0			0
$478$	5.90504	−	40.8548i	0.270090	−	1.86866i
$479$	−30.5401			−1.39541			−0.697707	−	0.716383i	$-0.745796\pi$
$479$	−30.5401			−1.39541			−0.697707	+	0.716383i	$0.745796\pi$
$480$		0			0
$481$	20.9666			0.955996
$482$	−0.736083	+	5.09269i	−0.0335277	+	0.231966i
$483$		0			0
$484$	5.98860	+	11.0062i	0.272209	+	0.500280i
$485$	−9.27303	+	22.3871i	−0.421066	+	1.01654i
$486$		0			0
$487$	17.5491	+	17.5491i	0.795225	+	0.795225i	0.982338	−	0.187114i	$-0.0599132\pi$
$487$	17.5491	+	17.5491i	0.795225	+	0.795225i	−0.187114	+	0.982338i	$0.559913\pi$
$488$	10.2415	+	0.388646i	0.463610	+	0.0175932i
$489$		0			0
$490$	10.3318	+	6.14055i	0.466744	+	0.277402i
$491$	−15.1022	−	6.25552i	−0.681551	−	0.282308i	0.0149241	−	0.999889i	$-0.495249\pi$
$491$	−15.1022	−	6.25552i	−0.681551	−	0.282308i	−0.696475	+	0.717581i	$0.745249\pi$
$492$		0			0
$493$	3.13665	+	7.57254i	0.141268	+	0.341050i
$494$	−28.5153	+	21.3132i	−1.28296	+	0.958927i
$495$		0			0
$496$	7.62421	+	4.93188i	0.342337	+	0.221448i
$497$		−	6.51206i		−	0.292106i
$498$		0			0
$499$	4.19611	+	10.1303i	0.187844	+	0.453495i	0.989544	−	0.144231i	$-0.0460709\pi$
$499$	4.19611	+	10.1303i	0.187844	+	0.453495i	−0.801700	+	0.597726i	$0.796071\pi$
$500$	−49.1829	+	5.21375i	−2.19952	+	0.233166i
$501$		0			0
$502$	−17.7686	+	29.8968i	−0.793054	+	1.33436i
$503$	2.86687	−	2.86687i	0.127828	−	0.127828i	−0.640299	−	0.768126i	$-0.721189\pi$
$503$	2.86687	−	2.86687i	0.127828	−	0.127828i	0.768126	+	0.640299i	$0.221189\pi$
$504$		0			0
$505$	−24.4422	−	24.4422i	−1.08766	−	1.08766i
$506$	−6.39242	+	1.62651i	−0.284178	+	0.0723071i
$507$		0			0
$508$	−24.2116	−	7.14829i	−1.07422	−	0.317154i
$509$	17.9175	−	7.42167i	0.794179	−	0.328960i	0.0515568	−	0.998670i	$-0.483582\pi$
$509$	17.9175	−	7.42167i	0.794179	−	0.328960i	0.742623	+	0.669710i	$0.233582\pi$
$510$		0			0
$511$	9.73125			0.430485
$512$	−6.22948	−	21.7530i	−0.275307	−	0.961356i
$513$		0			0
$514$	−7.31107	−	1.05672i	−0.322478	−	0.0466100i
$515$	10.9517	−	4.53633i	0.482588	−	0.199894i
$516$		0			0
$517$	4.02723	−	9.72260i	0.177118	−	0.427600i
$518$	19.6880	−	5.00948i	0.865042	−	0.220104i
$519$		0			0
$520$	−33.3245	−	15.3087i	−1.46138	−	0.671332i
$521$	−4.92906	+	4.92906i	−0.215946	+	0.215946i	−0.806788	−	0.590841i	$-0.798796\pi$
$521$	−4.92906	+	4.92906i	−0.215946	+	0.215946i	0.590841	+	0.806788i	$0.298796\pi$
$522$		0			0
$523$	24.0680	+	9.96931i	1.05242	+	0.435928i	0.840756	−	0.541414i	$-0.182111\pi$
$523$	24.0680	+	9.96931i	1.05242	+	0.435928i	0.211666	+	0.977342i	$0.432111\pi$
$524$	19.2858	−	2.04443i	0.842503	−	0.0893115i
$525$		0			0
$526$	−20.3858	−	27.2745i	−0.888863	−	1.18922i
$527$			8.68524i			0.378335i
$528$		0			0
$529$			21.7400i			0.945216i
$530$	−27.6413	+	20.6600i	−1.20066	+	0.897413i
$531$		0			0
$532$	−21.6840	+	26.8265i	−0.940123	+	1.16308i
$533$	15.6958	+	6.50140i	0.679859	+	0.281607i
$534$		0			0
$535$	1.22805	−	1.22805i	0.0530934	−	0.0530934i
$536$	−30.2344	−	1.14734i	−1.30593	−	0.0495576i
$537$		0			0
$538$	−3.42801	−	13.4726i	−0.147792	−	0.580845i
$539$	−3.36236	+	8.11746i	−0.144827	+	0.349644i
$540$		0			0
$541$	−1.32720	+	0.549745i	−0.0570609	+	0.0236354i	−0.411031	−	0.911621i	$-0.634831\pi$
$541$	−1.32720	+	0.549745i	−0.0570609	+	0.0236354i	0.353970	+	0.935257i	$0.384831\pi$
$542$	−4.75891	+	32.9252i	−0.204413	+	1.41426i
$543$		0			0
$544$	14.2338	−	16.3038i	0.610269	−	0.699022i
$545$	71.5766			3.06600
$546$		0			0
$547$	−22.4773	+	9.31040i	−0.961060	+	0.398084i	−0.807377	−	0.590036i	$-0.799113\pi$
$547$	−22.4773	+	9.31040i	−0.961060	+	0.398084i	−0.153683	+	0.988120i	$0.549113\pi$
$548$	−0.701275	+	0.381572i	−0.0299570	+	0.0163000i
$549$		0			0
$550$	−16.1606	−	63.5135i	−0.689089	−	2.70822i
$551$	−11.8205	−	11.8205i	−0.503571	−	0.503571i
$552$		0			0
$553$	5.51783	−	5.51783i	0.234642	−	0.234642i
$554$	24.4885	+	14.5543i	1.04042	+	0.618353i
$555$		0			0
$556$	−15.9556	−	12.8970i	−0.676666	−	0.546954i
$557$	0.129470	+	0.312569i	0.00548583	+	0.0132440i	0.926599	−	0.376052i	$-0.122718\pi$
$557$	0.129470	+	0.312569i	0.00548583	+	0.0132440i	−0.921113	+	0.389296i	$0.872718\pi$
$558$		0			0
$559$			23.0440i			0.974656i
$560$	−34.9500	−	6.41303i	−1.47691	−	0.271000i
$561$		0			0
$562$	3.54123	+	4.73787i	0.149378	+	0.199855i
$563$	−6.38297	−	15.4098i	−0.269010	−	0.649447i	0.730427	−	0.682990i	$-0.239321\pi$
$563$	−6.38297	−	15.4098i	−0.269010	−	0.649447i	−0.999437	+	0.0335430i	$0.989321\pi$
$564$		0			0
$565$	−9.28607	−	3.84642i	−0.390668	−	0.161820i
$566$	2.46555	−	4.14843i	0.103635	−	0.174372i
$567$		0			0
$568$	−2.89474	−	7.81427i	−0.121460	−	0.327880i
$569$	12.2789	+	12.2789i	0.514760	+	0.514760i	0.915981	−	0.401222i	$-0.131414\pi$
$569$	12.2789	+	12.2789i	0.514760	+	0.514760i	−0.401222	+	0.915981i	$0.631414\pi$
$570$		0			0
$571$	7.13555	−	17.2267i	0.298613	−	0.720916i	−0.701354	−	0.712813i	$-0.747421\pi$
$571$	7.13555	−	17.2267i	0.298613	−	0.720916i	0.999967	−	0.00810312i	$-0.00257933\pi$
$572$	7.59126	−	25.7120i	0.317406	−	1.07507i
$573$		0			0
$574$	16.2919	+	2.35479i	0.680013	+	0.0982871i
$575$	12.5193			0.522091
$576$		0			0
$577$	17.7610			0.739402			0.369701	−	0.929151i	$-0.379460\pi$
$577$	17.7610			0.739402			0.369701	+	0.929151i	$0.379460\pi$
$578$	−3.30599	−	0.477838i	−0.137511	−	0.0198755i
$579$		0			0
$580$	4.87609	−	16.5155i	0.202468	−	0.685771i
$581$	14.0262	−	33.8621i	0.581903	−	1.40484i
$582$		0			0
$583$	−17.8386	−	17.8386i	−0.738799	−	0.738799i
$584$	11.6772	−	4.32573i	0.483206	−	0.179000i
$585$		0			0
$586$	−13.5546	+	22.8064i	−0.559934	+	0.942122i
$587$	6.40407	+	2.65265i	0.264324	+	0.109487i	0.510910	−	0.859634i	$-0.329309\pi$
$587$	6.40407	+	2.65265i	0.264324	+	0.109487i	−0.246585	+	0.969121i	$0.579309\pi$
$588$		0			0
$589$	−6.77871	−	16.3652i	−0.279312	−	0.674318i
$590$	22.4310	+	30.0107i	0.923468	+	1.23552i
$591$		0			0
$592$	21.3982	−	14.7629i	0.879461	−	0.606753i
$593$			8.59336i			0.352887i	0.984311	+	0.176443i	$0.0564593\pi$
$593$			8.59336i			0.352887i	−0.984311	+	0.176443i	$0.943541\pi$
$594$		0			0
$595$	−13.0064	−	31.4003i	−0.533212	−	1.28729i
$596$	15.1674	+	12.2599i	0.621280	+	0.502184i
$597$		0			0
$598$	4.40240	+	2.61649i	0.180028	+	0.106996i
$599$	0.890765	−	0.890765i	0.0363957	−	0.0363957i	−0.688675	−	0.725070i	$-0.741807\pi$
$599$	0.890765	−	0.890765i	0.0363957	−	0.0363957i	0.725070	+	0.688675i	$0.241807\pi$
$600$		0			0
$601$	27.1147	+	27.1147i	1.10603	+	1.10603i	0.993667	+	0.112364i	$0.0358421\pi$
$601$	27.1147	+	27.1147i	1.10603	+	1.10603i	0.112364	+	0.993667i	$0.464158\pi$
$602$	5.50581	+	21.6387i	0.224400	+	0.881927i
$603$		0			0
$604$	12.3855	−	6.73909i	0.503957	−	0.274210i
$605$	23.2627	−	9.63572i	0.945763	−	0.391748i
$606$		0			0
$607$	17.5545			0.712517			0.356258	−	0.934387i	$-0.384052\pi$
$607$	17.5545			0.712517			0.356258	+	0.934387i	$0.384052\pi$
$608$	−14.0953	+	41.8300i	−0.571639	+	1.69643i
$609$		0			0
$610$	2.94619	−	20.3836i	0.119288	−	0.825309i
$611$	−7.54867	+	3.12676i	−0.305387	+	0.126495i
$612$		0			0
$613$	−3.50194	+	8.45444i	−0.141442	+	0.341472i	−0.978687	−	0.205356i	$-0.934165\pi$
$613$	−3.50194	+	8.45444i	−0.141442	+	0.341472i	0.837245	+	0.546828i	$0.184165\pi$
$614$	7.82777	+	30.7643i	0.315903	+	1.24155i
$615$		0			0
$616$	0.985051	−	25.9577i	0.0396888	−	1.04587i
$617$	−23.8371	+	23.8371i	−0.959644	+	0.959644i	−0.999217	−	0.0395730i	$-0.987400\pi$
$617$	−23.8371	+	23.8371i	−0.959644	+	0.959644i	0.0395730	+	0.999217i	$0.487400\pi$
$618$		0			0
$619$	26.8694	+	11.1297i	1.07997	+	0.447340i	0.850500	−	0.525975i	$-0.176300\pi$
$619$	26.8694	+	11.1297i	1.07997	+	0.447340i	0.229474	+	0.973315i	$0.426300\pi$
$620$	11.4707	−	14.1910i	0.460673	−	0.569924i
$621$		0			0
$622$	−6.97888	+	5.21623i	−0.279828	+	0.209152i
$623$			21.7232i			0.870321i
$624$		0			0
$625$			43.6237i			1.74495i
$626$	−13.4184	−	17.9527i	−0.536307	−	0.717534i
$627$		0			0
$628$	40.3207	−	4.27430i	1.60897	−	0.170563i
$629$	22.9728	+	9.51565i	0.915986	+	0.379414i
$630$		0			0
$631$	1.25875	−	1.25875i	0.0501101	−	0.0501101i	−0.681608	−	0.731718i	$-0.738719\pi$
$631$	1.25875	−	1.25875i	0.0501101	−	0.0501101i	0.731718	+	0.681608i	$0.238719\pi$
$632$	4.16845	−	9.07401i	0.165812	−	0.360945i
$633$		0			0
$634$	9.83085	−	2.50139i	0.390433	−	0.0993430i
$635$	−19.4137	+	46.8688i	−0.770409	+	1.85993i
$636$		0			0
$637$	6.30244	−	2.61055i	0.249712	−	0.103434i
$638$	12.4593	+	1.80083i	0.493268	+	0.0712956i
$639$		0			0
$640$	−44.7896	+	7.84049i	−1.77046	+	0.309923i
$641$	−45.9869			−1.81638			−0.908188	−	0.418563i	$-0.862534\pi$
$641$	−45.9869			−1.81638			−0.908188	+	0.418563i	$0.862534\pi$
$642$		0			0
$643$	−1.81578	+	0.752121i	−0.0716074	+	0.0296607i	−0.418200	−	0.908355i	$-0.637339\pi$
$643$	−1.81578	+	0.752121i	−0.0716074	+	0.0296607i	0.346592	+	0.938016i	$0.387339\pi$
$644$	4.75908	+	1.40508i	0.187534	+	0.0553679i
$645$		0			0
$646$	−40.9167	+	10.4110i	−1.60985	+	0.409614i
$647$	15.9718	+	15.9718i	0.627915	+	0.627915i	0.947543	−	0.319628i	$-0.103558\pi$
$647$	15.9718	+	15.9718i	0.627915	+	0.627915i	−0.319628	+	0.947543i	$0.603558\pi$
$648$		0			0
$649$	−19.3677	+	19.3677i	−0.760249	+	0.760249i
$650$	−25.9968	+	43.7411i	−1.01968	+	1.71567i
$651$		0			0
$652$	5.05199	−	0.535549i	0.197851	−	0.0209737i
$653$	−14.3858	−	34.7304i	−0.562960	−	1.35911i	−0.907388	−	0.420294i	$-0.861927\pi$
$653$	−14.3858	−	34.7304i	−0.562960	−	1.35911i	0.344428	−	0.938813i	$-0.388073\pi$
$654$		0			0
$655$		−	38.9726i		−	1.52279i
$656$	20.5966	−	4.41641i	0.804161	−	0.172432i
$657$		0			0
$658$	−6.34127	+	4.73966i	−0.247208	+	0.184771i
$659$	−15.8345	−	38.2279i	−0.616826	−	1.48915i	−0.855370	−	0.518017i	$-0.826670\pi$
$659$	−15.8345	−	38.2279i	−0.616826	−	1.48915i	0.238545	−	0.971132i	$-0.423330\pi$
$660$		0			0
$661$	4.75915	+	1.97131i	0.185110	+	0.0766749i	0.473313	−	0.880894i	$-0.343058\pi$
$661$	4.75915	+	1.97131i	0.185110	+	0.0766749i	−0.288203	+	0.957569i	$0.593058\pi$
$662$	31.4328	+	18.6815i	1.22167	+	0.726078i
$663$		0			0
$664$	1.77858	−	46.8684i	0.0690221	−	1.81885i
$665$	49.0150	+	49.0150i	1.90072	+	1.90072i
$666$		0			0
$667$	−0.920269	+	2.22173i	−0.0356329	+	0.0860255i
$668$	16.4702	+	30.2698i	0.637251	+	1.17117i
$669$		0			0
$670$	−8.69760	+	60.1755i	−0.336017	+	2.32478i
$671$	15.0561			0.581235
$672$		0			0
$673$	9.43631			0.363743			0.181872	−	0.983322i	$-0.441784\pi$
$673$	9.43631			0.363743			0.181872	+	0.983322i	$0.441784\pi$
$674$	2.21052	−	15.2938i	0.0851459	−	0.589094i
$675$		0			0
$676$	4.55465	−	2.47824i	0.175179	−	0.0953170i
$677$	−3.77807	+	9.12108i	−0.145203	+	0.350552i	−0.979702	−	0.200458i	$-0.935757\pi$
$677$	−3.77807	+	9.12108i	−0.145203	+	0.350552i	0.834499	+	0.551009i	$0.185757\pi$
$678$		0			0
$679$	9.42306	+	9.42306i	0.361624	+	0.361624i
$680$	−29.5654	−	31.8978i	−1.13378	−	1.22322i
$681$		0			0
$682$	11.4671	+	6.81525i	0.439097	+	0.260970i
$683$	−8.51669	−	3.52773i	−0.325882	−	0.134985i	0.213744	−	0.976890i	$-0.431434\pi$
$683$	−8.51669	−	3.52773i	−0.325882	−	0.134985i	−0.539626	+	0.841905i	$0.681434\pi$
$684$		0			0
$685$	0.613954	+	1.48222i	0.0234580	+	0.0566326i
$686$	22.8206	−	17.0569i	0.871296	−	0.651234i
$687$		0			0
$688$	16.2256	+	23.5183i	0.618596	+	0.896627i
$689$			19.5868i			0.746198i
$690$		0			0
$691$	12.5830	+	30.3780i	0.478679	+	1.15563i	0.960229	+	0.279214i	$0.0900740\pi$
$691$	12.5830	+	30.3780i	0.478679	+	1.15563i	−0.481550	+	0.876419i	$0.659926\pi$
$692$	−2.29837	−	21.6812i	−0.0873710	−	0.824197i
$693$		0			0
$694$	−14.5693	+	24.5138i	−0.553045	+	0.930530i
$695$	−29.1526	+	29.1526i	−1.10582	+	1.10582i
$696$		0			0
$697$	14.2470	+	14.2470i	0.539642	+	0.539642i
$698$	23.5034	−	5.98029i	0.889618	−	0.226357i
$699$		0			0
$700$	−13.9605	+	47.2850i	−0.527658	+	1.78720i
$701$	47.4874	−	19.6699i	1.79357	−	0.742923i	0.804793	−	0.593555i	$-0.202276\pi$
$701$	47.4874	−	19.6699i	1.79357	−	0.742923i	0.988782	−	0.149368i	$-0.0477238\pi$
$702$		0			0
$703$	−50.7136			−1.91270
$704$	−10.3567	−	31.5863i	−0.390332	−	1.19045i
$705$		0			0
$706$	28.7847	+	4.16046i	1.08333	+	0.156581i
$707$	−17.5629	+	7.27479i	−0.660520	+	0.273596i
$708$		0			0
$709$	−8.88558	+	21.4517i	−0.333705	+	0.805635i	0.664587	+	0.747211i	$0.268608\pi$
$709$	−8.88558	+	21.4517i	−0.333705	+	0.805635i	−0.998292	+	0.0584243i	$0.981392\pi$
$710$	−16.2288	+	4.12930i	−0.609056	+	0.154970i
$711$		0			0
$712$	9.65637	+	26.0671i	0.361888	+	0.976907i
$713$	−1.80184	+	1.80184i	−0.0674793	+	0.0674793i
$714$		0			0
$715$	−49.7732	−	20.6167i	−1.86141	−	0.771021i
$716$	−2.19328	−	20.6898i	−0.0819666	−	0.773216i
$717$		0			0
$718$	3.88207	+	5.19388i	0.144877	+	0.193834i
$719$		−	31.1909i		−	1.16322i	−0.813467	−	0.581612i	$-0.802422\pi$
$719$		−	31.1909i		−	1.16322i	0.813467	−	0.581612i	$-0.197578\pi$
$720$		0			0
$721$		−	6.51913i		−	0.242785i
$722$	47.4496	−	35.4653i	1.76589	−	1.31988i
$723$		0			0
$724$	−0.458080	−	0.370269i	−0.0170244	−	0.0137609i
$725$	−22.0745	−	9.14356i	−0.819826	−	0.339583i
$726$		0			0
$727$	30.4350	−	30.4350i	1.12877	−	1.12877i	0.138397	−	0.990377i	$-0.455805\pi$
$727$	30.4350	−	30.4350i	1.12877	−	1.12877i	0.990377	−	0.138397i	$-0.0441948\pi$
$728$	−14.7916	+	13.7100i	−0.548214	+	0.508127i
$729$		0			0
$730$	−6.17060	−	24.2514i	−0.228384	−	0.897584i
$731$	−10.4585	+	25.2489i	−0.386820	+	0.933866i
$732$		0			0
$733$	20.5901	−	8.52870i	0.760513	−	0.315015i	0.0314898	−	0.999504i	$-0.489975\pi$
$733$	20.5901	−	8.52870i	0.760513	−	0.315015i	0.729023	+	0.684489i	$0.239975\pi$
$734$	−3.74622	+	25.9188i	−0.138276	+	0.956679i
$735$		0			0
$736$	6.33533	−	0.429449i	0.233523	−	0.0158297i
$737$	−44.4479			−1.63726
$738$		0			0
$739$	−15.5441	+	6.43858i	−0.571800	+	0.236847i	−0.649799	−	0.760106i	$-0.725147\pi$
$739$	−15.5441	+	6.43858i	−0.571800	+	0.236847i	0.0779992	+	0.996953i	$0.475147\pi$
$740$	−24.9684	−	45.8883i	−0.917856	−	1.68689i
$741$		0			0
$742$	4.67980	+	18.3923i	0.171801	+	0.675204i
$743$	18.6351	+	18.6351i	0.683656	+	0.683656i	0.960822	−	0.277166i	$-0.0893951\pi$
$743$	18.6351	+	18.6351i	0.683656	+	0.683656i	−0.277166	+	0.960822i	$0.589395\pi$
$744$		0			0
$745$	27.7125	−	27.7125i	1.01531	−	1.01531i
$746$	−10.7330	−	6.37896i	−0.392962	−	0.233550i
$747$		0			0
$748$	19.9869	−	24.7269i	0.730795	−	0.904107i
$749$	−0.365508	−	0.882415i	−0.0133554	−	0.0322427i
$750$		0			0
$751$			41.7048i			1.52183i	0.648852	+	0.760915i	$0.275250\pi$
$751$			41.7048i			1.52183i	−0.648852	+	0.760915i	$0.724750\pi$
$752$	−5.50245	+	8.50626i	−0.200654	+	0.310191i
$753$		0			0
$754$	−5.85151	−	7.82882i	−0.213099	−	0.285109i
$755$	−10.8433	−	26.1780i	−0.394627	−	0.952714i
$756$		0			0
$757$	−2.80030	−	1.15992i	−0.101779	−	0.0421581i	0.331213	−	0.943556i	$-0.392542\pi$
$757$	−2.80030	−	1.15992i	−0.101779	−	0.0421581i	−0.432992	+	0.901398i	$0.642542\pi$
$758$	2.34872	−	3.95185i	0.0853092	−	0.143538i
$759$		0			0
$760$	80.6046	+	37.0284i	2.92384	+	1.34316i
$761$	26.7048	+	26.7048i	0.968047	+	0.968047i	0.999505	−	0.0314581i	$-0.0100151\pi$
$761$	26.7048	+	26.7048i	0.968047	+	0.968047i	−0.0314581	+	0.999505i	$0.510015\pi$
$762$		0			0
$763$	15.0639	−	36.3674i	0.545348	−	1.31659i
$764$	34.9734	+	10.3256i	1.26529	+	0.373568i
$765$		0			0
$766$	1.80973	+	0.261573i	0.0653881	+	0.00945101i
$767$	21.2658			0.767863
$768$		0			0
$769$	−39.4692			−1.42329			−0.711647	−	0.702537i	$-0.752051\pi$
$769$	−39.4692			−1.42329			−0.711647	+	0.702537i	$0.752051\pi$
$770$	−51.6637	−	7.46732i	−1.86183	−	0.269104i
$771$		0			0
$772$	−39.3194	−	11.6087i	−1.41514	−	0.417808i
$773$	−15.3645	+	37.0931i	−0.552622	+	1.33415i	0.362881	+	0.931836i	$0.381793\pi$
$773$	−15.3645	+	37.0931i	−0.552622	+	1.33415i	−0.915503	+	0.402312i	$0.868207\pi$
$774$		0			0
$775$	−17.9026	−	17.9026i	−0.643080	−	0.643080i
$776$	15.4961	+	7.11865i	0.556278	+	0.255545i
$777$		0			0
$778$	6.75027	−	11.3577i	0.242009	−	0.407194i
$779$	−37.9646	−	15.7254i	−1.36022	−	0.563422i
$780$		0			0
$781$	−4.68478	−	11.3101i	−0.167635	−	0.404706i
$782$	3.63615	+	4.86487i	0.130029	+	0.173967i
$783$		0			0
$784$	4.59403	−	7.10193i	0.164073	−	0.253640i
$785$		−	81.4800i		−	2.90815i
$786$		0			0
$787$	0.557658	+	1.34631i	0.0198784	+	0.0479906i	0.933507	−	0.358559i	$-0.116732\pi$
$787$	0.557658	+	1.34631i	0.0198784	+	0.0479906i	−0.913629	+	0.406550i	$0.866732\pi$
$788$	13.0077	−	16.0925i	0.463380	−	0.573272i
$789$		0			0
$790$	−17.2499	−	10.2522i	−0.613725	−	0.364757i
$791$	−3.90865	+	3.90865i	−0.138976	+	0.138976i
$792$		0			0
$793$	−8.26582	−	8.26582i	−0.293528	−	0.293528i
$794$	−4.54113	−	17.8473i	−0.161159	−	0.633379i
$795$		0			0
$796$	15.9169	+	29.2529i	0.564158	+	1.03684i
$797$	−3.39245	+	1.40520i	−0.120167	+	0.0497748i	−0.441957	−	0.897036i	$-0.645716\pi$
$797$	−3.39245	+	1.40520i	−0.120167	+	0.0497748i	0.321790	+	0.946811i	$0.395716\pi$
$798$		0			0
$799$	−9.69004			−0.342809
$800$	4.26690	+	62.9462i	0.150858	+	2.22549i
$801$		0			0
$802$	−6.09023	+	42.1361i	−0.215053	+	1.48788i
$803$	16.9011	−	7.00067i	0.596428	−	0.247048i
$804$		0			0
$805$	3.81599	−	9.21261i	0.134496	−	0.324702i
$806$	−2.55385	−	10.0370i	−0.0899555	−	0.353539i
$807$		0			0
$808$	−17.8411	+	16.5366i	−0.627649	+	0.581754i
$809$	20.7155	−	20.7155i	0.728317	−	0.728317i	−0.241967	−	0.970284i	$-0.577793\pi$
$809$	20.7155	−	20.7155i	0.728317	−	0.728317i	0.970284	+	0.241967i	$0.0777926\pi$
$810$		0			0
$811$	−15.4630	−	6.40499i	−0.542979	−	0.224909i	0.0942978	−	0.995544i	$-0.469939\pi$
$811$	−15.4630	−	6.40499i	−0.542979	−	0.224909i	−0.637277	+	0.770635i	$0.719939\pi$
$812$	−7.36517	−	5.95332i	−0.258467	−	0.208920i
$813$		0			0
$814$	30.5901	−	22.8640i	1.07218	−	0.801383i
$815$		−	10.2091i		−	0.357608i
$816$		0			0
$817$		−	55.7382i		−	1.95003i
$818$	−9.47728	−	12.6798i	−0.331365	−	0.443339i
$819$		0			0
$820$	−4.46233	−	42.0945i	−0.155831	−	1.47001i
$821$	−23.6506	−	9.79640i	−0.825412	−	0.341897i	−0.0703270	−	0.997524i	$-0.522404\pi$
$821$	−23.6506	−	9.79640i	−0.825412	−	0.341897i	−0.755085	+	0.655627i	$0.772404\pi$
$822$		0			0
$823$	0.780666	−	0.780666i	0.0272123	−	0.0272123i	−0.693370	−	0.720582i	$-0.743875\pi$
$823$	0.780666	−	0.780666i	0.0272123	−	0.0272123i	0.720582	+	0.693370i	$0.243875\pi$
$824$	−2.89788	−	7.82276i	−0.100952	−	0.272519i
$825$		0			0
$826$	19.9689	−	5.08095i	0.694808	−	0.176789i
$827$	9.19757	−	22.2049i	0.319831	−	0.772140i	−0.679431	−	0.733739i	$-0.737774\pi$
$827$	9.19757	−	22.2049i	0.319831	−	0.772140i	0.999262	−	0.0384012i	$-0.0122265\pi$
$828$		0			0
$829$	43.9551	−	18.2068i	1.52662	−	0.632348i	0.547718	−	0.836663i	$-0.315497\pi$
$829$	43.9551	−	18.2068i	1.52662	−	0.632348i	0.978905	+	0.204315i	$0.0654968\pi$
$830$	−93.2822	−	13.4827i	−3.23787	−	0.467993i
$831$		0			0
$832$	−11.6551	+	23.0268i	−0.404068	+	0.798309i
$833$	8.09028			0.280311
$834$		0			0
$835$	63.9784	−	26.5007i	2.21406	−	0.917095i
$836$	−18.3616	+	62.1915i	−0.635048	+	2.15094i
$837$		0			0
$838$	37.5768	−	9.56115i	1.29807	−	0.330284i
$839$	−35.8149	−	35.8149i	−1.23647	−	1.23647i	−0.961435	−	0.275032i	$-0.911312\pi$
$839$	−35.8149	−	35.8149i	−1.23647	−	1.23647i	−0.275032	−	0.961435i	$-0.588688\pi$
$840$		0			0
$841$	−17.2608	+	17.2608i	−0.595200	+	0.595200i
$842$	−11.6129	+	19.5393i	−0.400206	+	0.673370i
$843$		0			0
$844$	3.68539	+	34.7654i	0.126856	+	1.19667i
$845$	−3.98752	−	9.62673i	−0.137175	−	0.331169i
$846$		0			0
$847$		−	13.8475i		−	0.475804i
$848$	13.7914	+	19.9900i	0.473598	+	0.686458i
$849$		0			0
$850$	−48.3361	+	36.1279i	−1.65791	+	1.23918i
$851$	2.79182	+	6.74005i	0.0957023	+	0.231046i
$852$		0			0
$853$	−16.7262	−	6.92820i	−0.572693	−	0.237217i	0.0774923	−	0.996993i	$-0.475309\pi$
$853$	−16.7262	−	6.92820i	−0.572693	−	0.237217i	−0.650185	+	0.759776i	$0.725309\pi$
$854$	−9.73667	−	5.78682i	−0.333182	−	0.198021i
$855$		0			0
$856$	−0.830849	−	0.896395i	−0.0283978	−	0.0306381i
$857$	−12.7211	−	12.7211i	−0.434544	−	0.434544i	0.455627	−	0.890171i	$-0.349415\pi$
$857$	−12.7211	−	12.7211i	−0.434544	−	0.434544i	−0.890171	+	0.455627i	$0.849415\pi$
$858$		0			0
$859$	−0.171560	+	0.414182i	−0.00585354	+	0.0141317i	−0.926779	−	0.375606i	$-0.877434\pi$
$859$	−0.171560	+	0.414182i	−0.00585354	+	0.0141317i	0.920926	+	0.389738i	$0.127434\pi$
$860$	50.4348	−	27.4422i	1.71981	−	0.935772i
$861$		0			0
$862$	3.77104	−	26.0905i	0.128442	−	0.888645i
$863$	37.7195			1.28399			0.641993	−	0.766711i	$-0.278108\pi$
$863$	37.7195			1.28399			0.641993	+	0.766711i	$0.278108\pi$
$864$		0			0
$865$	−43.8134			−1.48970
$866$	0.974778	−	6.74413i	0.0331243	−	0.229175i
$867$		0			0
$868$	−4.79621	−	8.81474i	−0.162794	−	0.299192i
$869$	5.61377	−	13.5528i	0.190434	−	0.459749i
$870$		0			0
$871$	24.4019	+	24.4019i	0.826828	+	0.826828i
$872$	1.91016	−	50.3359i	0.0646862	−	1.70459i
$873$		0			0
$874$	−10.6484	−	6.32871i	−0.360188	−	0.214072i
$875$	50.4983	+	20.9171i	1.70716	+	0.707127i
$876$		0			0
$877$	−20.8026	−	50.2220i	−0.702455	−	1.69588i	−0.718044	−	0.695998i	$-0.754962\pi$
$877$	−20.8026	−	50.2220i	−0.702455	−	1.69588i	0.0155888	−	0.999878i	$-0.495038\pi$
$878$	−7.75063	+	5.79306i	−0.261571	+	0.195506i
$879$		0			0
$880$	−65.3142	+	14.0050i	−2.20174	+	0.472107i
$881$		−	18.3109i		−	0.616912i	−0.951239	−	0.308456i	$-0.900188\pi$
$881$		−	18.3109i		−	0.616912i	0.951239	−	0.308456i	$-0.0998122\pi$
$882$		0			0
$883$	12.0402	+	29.0675i	0.405184	+	0.978201i	0.986387	+	0.164442i	$0.0525824\pi$
$883$	12.0402	+	29.0675i	0.405184	+	0.978201i	−0.581203	+	0.813759i	$0.697418\pi$
$884$	−24.5480	+	2.60227i	−0.825637	+	0.0875237i
$885$		0			0
$886$	12.7352	−	21.4277i	0.427847	−	0.719878i
$887$	19.1203	−	19.1203i	0.641996	−	0.641996i	−0.309050	−	0.951046i	$-0.600011\pi$
$887$	19.1203	−	19.1203i	0.641996	−	0.641996i	0.951046	+	0.309050i	$0.100011\pi$
$888$		0			0
$889$	19.7278	+	19.7278i	0.661649	+	0.661649i
$890$	54.1366	−	13.7747i	1.81466	−	0.461728i
$891$		0			0
$892$	−22.3448	−	6.59711i	−0.748158	−	0.220888i
$893$	18.2586	−	7.56294i	0.610999	−	0.253084i
$894$		0			0
$895$	−41.8100			−1.39755
$896$	−5.44264	+	24.4072i	−0.181826	+	0.815388i
$897$		0			0
$898$	−9.44635	−	1.36535i	−0.315229	−	0.0455622i
$899$	4.49305	−	1.86108i	0.149852	−	0.0620706i
$900$		0			0
$901$	−8.88942	+	21.4610i	−0.296150	+	0.714968i
$902$	29.9897	−	7.63067i	0.998548	−	0.254074i
$903$		0			0
$904$	−2.95279	+	6.42773i	−0.0982082	+	0.213783i
$905$	−0.836962	+	0.836962i	−0.0278216	+	0.0278216i
$906$		0			0
$907$	−26.5121	−	10.9817i	−0.880319	−	0.364640i	−0.103699	−	0.994609i	$-0.533068\pi$
$907$	−26.5121	−	10.9817i	−0.880319	−	0.364640i	−0.776621	+	0.629969i	$0.783068\pi$
$908$	−48.6481	+	5.15706i	−1.61444	+	0.171143i
$909$		0			0
$910$	24.2639	+	32.4630i	0.804339	+	1.07614i
$911$			49.8398i			1.65127i	0.564207	+	0.825634i	$0.309182\pi$
$911$			49.8398i			1.65127i	−0.564207	+	0.825634i	$0.690818\pi$
$912$		0			0
$913$		−	68.9018i		−	2.28032i
$914$	−19.8526	+	14.8384i	−0.656664	+	0.490811i
$915$		0			0
$916$	−24.5690	+	30.3957i	−0.811783	+	1.00430i
$917$	−19.8016	−	8.20209i	−0.653906	−	0.270857i
$918$		0			0
$919$	−2.32403	+	2.32403i	−0.0766625	+	0.0766625i	−0.744398	−	0.667736i	$-0.767264\pi$
$919$	−2.32403	+	2.32403i	−0.0766625	+	0.0766625i	0.667736	+	0.744398i	$0.267264\pi$
$920$	0.483883	−	12.7511i	0.0159532	−	0.420392i
$921$		0			0
$922$	1.71598	+	6.74408i	0.0565129	+	0.222104i
$923$	−3.63729	+	8.78119i	−0.119723	+	0.289036i
$924$		0			0
$925$	−66.9674	+	27.7388i	−2.20187	+	0.912046i
$926$	−3.20720	+	22.1895i	−0.105395	+	0.729191i
$927$		0			0
$928$	−11.4843	−	3.86983i	−0.376992	−	0.127033i
$929$	4.20840			0.138073			0.0690366	−	0.997614i	$-0.478007\pi$
$929$	4.20840			0.138073			0.0690366	+	0.997614i	$0.478007\pi$
$930$		0			0
$931$	−15.2442	+	6.31435i	−0.499608	+	0.206944i
$932$	−42.3422	+	23.0389i	−1.38696	+	0.754664i
$933$		0			0
$934$	−2.94716	−	11.5828i	−0.0964341	−	0.379001i
$935$	−45.1788	−	45.1788i	−1.47751	−	1.47751i
$936$		0			0
$937$	22.9897	−	22.9897i	0.751041	−	0.751041i	−0.223633	−	0.974673i	$-0.571792\pi$
$937$	22.9897	−	22.9897i	0.751041	−	0.751041i	0.974673	+	0.223633i	$0.0717917\pi$
$938$	28.7441	+	17.0836i	0.938528	+	0.557798i
$939$		0			0
$940$	15.8328	+	12.7977i	0.516408	+	0.417416i
$941$	14.2932	+	34.5068i	0.465945	+	1.12489i	0.965918	+	0.258850i	$0.0833434\pi$
$941$	14.2932	+	34.5068i	0.465945	+	1.12489i	−0.499973	+	0.866041i	$0.666657\pi$
$942$		0			0
$943$			5.91134i			0.192500i
$944$	21.7035	−	14.9736i	0.706389	−	0.487348i
$945$		0			0
$946$	25.1293	+	33.6209i	0.817025	+	1.09311i
$947$	1.07193	+	2.58787i	0.0348331	+	0.0840945i	0.940339	−	0.340240i	$-0.110508\pi$
$947$	1.07193	+	2.58787i	0.0348331	+	0.0840945i	−0.905506	+	0.424334i	$0.860508\pi$
$948$		0			0
$949$	−13.1221	−	5.43536i	−0.425962	−	0.176439i
$950$	62.8804	−	105.800i	2.04011	−	3.43261i
$951$		0			0
$952$	−22.4292	+	8.30873i	−0.726935	+	0.269287i
$953$	−38.5523	−	38.5523i	−1.24883	−	1.24883i	−0.956236	−	0.292595i	$-0.905481\pi$
$953$	−38.5523	−	38.5523i	−1.24883	−	1.24883i	−0.292595	−	0.956236i	$-0.594519\pi$
$954$		0			0
$955$	28.0428	−	67.7014i	0.907445	−	2.19077i
$956$	−16.5302	+	55.9886i	−0.534625	+	1.81080i
$957$		0			0
$958$	42.7461	+	6.17839i	1.38106	+	0.199615i
$959$	0.882311			0.0284913
$960$		0			0
$961$	−25.8468			−0.833766
$962$	−29.3463	−	4.24164i	−0.946164	−	0.136756i
$963$		0			0
$964$	2.06055	−	6.97917i	0.0663657	−	0.224784i
$965$	−31.5276	+	76.1143i	−1.01491	+	2.45021i
$966$		0			0
$967$	5.77350	+	5.77350i	0.185663	+	0.185663i	0.793818	−	0.608155i	$-0.208090\pi$
$967$	5.77350	+	5.77350i	0.185663	+	0.185663i	−0.608155	+	0.793818i	$0.708090\pi$
$968$	−6.15546	−	16.6165i	−0.197844	−	0.534075i
$969$		0			0
$970$	17.5082	−	29.4585i	0.562153	−	0.945856i
$971$	37.7352	+	15.6304i	1.21098	+	0.501604i	0.894531	−	0.447006i	$-0.147510\pi$
$971$	37.7352	+	15.6304i	1.21098	+	0.501604i	0.316448	+	0.948610i	$0.397510\pi$
$972$		0			0
$973$	8.67674	+	20.9475i	0.278163	+	0.671546i
$974$	−21.0127	−	28.1132i	−0.673289	−	0.900804i
$975$		0			0
$976$	−14.2560	−	2.61587i	−0.456325	−	0.0837319i
$977$			41.0213i			1.31239i	0.754593	+	0.656194i	$0.227835\pi$
$977$			41.0213i			1.31239i	−0.754593	+	0.656194i	$0.772165\pi$
$978$		0			0
$979$	15.6277	+	37.7285i	0.499463	+	1.20581i
$980$	−13.2189	−	10.6849i	−0.422262	−	0.341317i
$981$		0			0
$982$	19.8725	+	11.8109i	0.634157	+	0.376901i
$983$	−25.9049	+	25.9049i	−0.826238	+	0.826238i	−0.986994	−	0.160756i	$-0.948607\pi$
$983$	−25.9049	+	25.9049i	−0.826238	+	0.826238i	0.160756	+	0.986994i	$0.448607\pi$
$984$		0			0
$985$	−29.4028	−	29.4028i	−0.936851	−	0.936851i
$986$	−2.85831	−	11.2336i	−0.0910273	−	0.357751i
$987$		0			0
$988$	44.2237	−	24.0627i	1.40694	−	0.765536i
$989$	−7.40784	+	3.06843i	−0.235556	+	0.0975703i
$990$		0			0
$991$	25.2589			0.802375			0.401187	−	0.915996i	$-0.368598\pi$
$991$	25.2589			0.802375			0.401187	+	0.915996i	$0.368598\pi$
$992$	−9.67363	−	8.44540i	−0.307138	−	0.268142i
$993$		0			0
$994$	−1.31742	+	9.11473i	−0.0417859	+	0.289102i
$995$	61.8290	−	25.6104i	1.96011	−	0.811904i
$996$		0			0
$997$	−1.85169	+	4.47039i	−0.0586438	+	0.141579i	−0.950485	−	0.310769i	$-0.899413\pi$
$997$	−1.85169	+	4.47039i	−0.0586438	+	0.141579i	0.891842	+	0.452348i	$0.149413\pi$
$998$	−3.82377	−	15.0280i	−0.121039	−	0.475702i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.c.181.1	✓	32
3.2	odd	2	inner	288.2.v.c.181.8	yes	32
4.3	odd	2		1152.2.v.d.433.8		32
12.11	even	2		1152.2.v.d.433.1		32
32.3	odd	8		1152.2.v.d.721.8		32
32.29	even	8	inner	288.2.v.c.253.1	yes	32
96.29	odd	8	inner	288.2.v.c.253.8	yes	32
96.35	even	8		1152.2.v.d.721.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.v.c.181.1	✓	32	1.1	even	1	trivial
288.2.v.c.181.8	yes	32	3.2	odd	2	inner
288.2.v.c.253.1	yes	32	32.29	even	8	inner
288.2.v.c.253.8	yes	32	96.29	odd	8	inner
1152.2.v.d.433.1		32	12.11	even	2
1152.2.v.d.433.8		32	4.3	odd	2
1152.2.v.d.721.1		32	96.35	even	8
1152.2.v.d.721.8		32	32.3	odd	8

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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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39967 - 0.202304i) q^{2} +(1.91815 + 0.566318i) q^{4} +(1.53803 - 3.71314i) q^{5} +(-1.56292 - 1.56292i) q^{7} +(-2.57020 - 1.18071i) q^{8} +O(q^{10})\)	\(q+(-1.39967 - 0.202304i) q^{2} +(1.91815 + 0.566318i) q^{4} +(1.53803 - 3.71314i) q^{5} +(-1.56292 - 1.56292i) q^{7} +(-2.57020 - 1.18071i) q^{8} +(-2.90392 + 4.88602i) q^{10} +(-3.83882 - 1.59009i) q^{11} +(1.23456 + 2.98048i) q^{13} +(1.87138 + 2.50375i) q^{14} +(3.35857 + 2.17256i) q^{16} +3.82597i q^{17} +(-2.98611 - 7.20912i) q^{19} +(5.05299 - 6.25133i) q^{20} +(5.05140 + 3.00221i) q^{22} +(-0.793733 + 0.793733i) q^{23} +(-7.88633 - 7.88633i) q^{25} +(-1.12501 - 4.42144i) q^{26} +(-2.11280 - 3.88301i) q^{28} +(1.97925 - 0.819832i) q^{29} +2.27008 q^{31} +(-4.26137 - 3.72032i) q^{32} +(0.774009 - 5.35509i) q^{34} +(-8.20716 + 3.39952i) q^{35} +(2.48712 - 6.00445i) q^{37} +(2.72114 + 10.6945i) q^{38} +(-8.33718 + 7.72755i) q^{40} +(3.72376 - 3.72376i) q^{41} +(6.59936 + 2.73354i) q^{43} +(-6.46293 - 5.22402i) q^{44} +(1.27154 - 0.950389i) q^{46} +2.53270i q^{47} -2.11457i q^{49} +(9.44282 + 12.6337i) q^{50} +(0.680159 + 6.41615i) q^{52} +(5.60929 + 2.32344i) q^{53} +(-11.8085 + 11.8085i) q^{55} +(2.17167 + 5.86236i) q^{56} +(-2.93615 + 0.747083i) q^{58} +(2.52261 - 6.09012i) q^{59} +(-3.34769 + 1.38666i) q^{61} +(-3.17736 - 0.459246i) q^{62} +(5.21187 + 6.06930i) q^{64} +12.9657 q^{65} +(9.88289 - 4.09363i) q^{67} +(-2.16671 + 7.33876i) q^{68} +(12.1750 - 3.09786i) q^{70} +(2.08330 + 2.08330i) q^{71} +(-3.11317 + 3.11317i) q^{73} +(-4.69587 + 7.90108i) q^{74} +(-1.64515 - 15.5192i) q^{76} +(3.51458 + 8.48495i) q^{77} +3.53047i q^{79} +(13.2326 - 9.12937i) q^{80} +(-5.96536 + 4.45869i) q^{82} +(6.34581 + 15.3201i) q^{83} +(14.2064 + 5.88446i) q^{85} +(-8.68391 - 5.16114i) q^{86} +(7.98912 + 8.61938i) q^{88} +(-6.94955 - 6.94955i) q^{89} +(2.72874 - 6.58776i) q^{91} +(-1.97200 + 1.07299i) q^{92} +(0.512376 - 3.54495i) q^{94} -31.3612 q^{95} -6.02915 q^{97} +(-0.427786 + 2.95970i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

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