LMFDB - Embedded newform 704.2.w.c.97.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,2,Mod(97,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("704.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			97.15
Character	$\chi$	$=$	704.97
Dual form			704.2.w.c.225.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.77223 + 2.43927i) q^{3} +(-2.80893 + 0.912676i) q^{5} +(-2.83314 - 2.05840i) q^{7} +(-1.88217 + 5.79272i) q^{9} +O(q^{10})$	\(q+(1.77223 + 2.43927i) q^{3} +(-2.80893 + 0.912676i) q^{5} +(-2.83314 - 2.05840i) q^{7} +(-1.88217 + 5.79272i) q^{9} +(-2.62904 + 2.02192i) q^{11} +(3.24840 + 1.05547i) q^{13} +(-7.20433 - 5.23425i) q^{15} +(-1.70655 - 5.25221i) q^{17} +(-1.43071 - 1.96920i) q^{19} -10.5588i q^{21} -0.764022 q^{23} +(3.01202 - 2.18836i) q^{25} +(-8.86303 + 2.87977i) q^{27} +(-4.44933 + 6.12397i) q^{29} +(-2.65498 + 8.17119i) q^{31} +(-9.59126 - 2.82962i) q^{33} +(9.83675 + 3.19615i) q^{35} +(2.99886 - 4.12757i) q^{37} +(3.18235 + 9.79426i) q^{39} +(-0.325508 + 0.236495i) q^{41} -1.38711i q^{43} -17.9891i q^{45} +(-6.40473 + 4.65331i) q^{47} +(1.62658 + 5.00609i) q^{49} +(9.78714 - 13.4708i) q^{51} +(0.735950 + 0.239125i) q^{53} +(5.53943 - 8.07888i) q^{55} +(2.26786 - 6.97975i) q^{57} +(-4.91020 + 6.75831i) q^{59} +(9.41096 - 3.05780i) q^{61} +(17.2562 - 12.5373i) q^{63} -10.0878 q^{65} +12.6972i q^{67} +(-1.35402 - 1.86365i) q^{69} +(-0.174133 - 0.535927i) q^{71} +(5.33230 + 3.87415i) q^{73} +(10.6760 + 3.46883i) q^{75} +(11.6104 - 0.316770i) q^{77} +(-1.17086 + 3.60353i) q^{79} +(-7.94913 - 5.77538i) q^{81} +(-4.61808 + 1.50050i) q^{83} +(9.58713 + 13.1955i) q^{85} -22.8232 q^{87} +2.42355 q^{89} +(-7.03061 - 9.67681i) q^{91} +(-24.6369 + 8.00503i) q^{93} +(5.81599 + 4.22556i) q^{95} +(-2.07586 + 6.38884i) q^{97} +(-6.76410 - 19.0349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 12 q^{9}+O(q^{10}) $ 64 * q - 12 * q^9	$ 64 q - 12 q^{9} - 20 q^{17} + 12 q^{25} - 96 q^{33} - 36 q^{41} + 68 q^{49} + 96 q^{57} + 168 q^{65} + 4 q^{73} + 8 q^{81} - 24 q^{89} - 152 q^{97}+O(q^{100}) $ 64 * q - 12 * q^9 - 20 * q^17 + 12 * q^25 - 96 * q^33 - 36 * q^41 + 68 * q^49 + 96 * q^57 + 168 * q^65 + 4 * q^73 + 8 * q^81 - 24 * q^89 - 152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$	$1$

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			0
$2$		0			0
$3$	1.77223	+	2.43927i	1.02320	+	1.40831i	0.909937	+	0.414746i	$0.136130\pi$
$3$	1.77223	+	2.43927i	1.02320	+	1.40831i	0.113261	+	0.993565i	$0.463870\pi$
$4$		0			0
$5$	−2.80893	+	0.912676i	−1.25619	+	0.408161i	−0.860136	−	0.510065i	$-0.829621\pi$
$5$	−2.80893	+	0.912676i	−1.25619	+	0.408161i	−0.396055	+	0.918227i	$0.629621\pi$
$6$		0			0
$7$	−2.83314	−	2.05840i	−1.07083	−	0.778002i	−0.0947668	−	0.995499i	$-0.530211\pi$
$7$	−2.83314	−	2.05840i	−1.07083	−	0.778002i	−0.976061	+	0.217498i	$0.930211\pi$
$8$		0			0
$9$	−1.88217	+	5.79272i	−0.627389	+	1.93091i
$10$		0			0
$11$	−2.62904	+	2.02192i	−0.792685	+	0.609631i
$11$	−2.62904	+	2.02192i	−0.792685	+	0.609631i
$12$		0			0
$13$	3.24840	+	1.05547i	0.900945	+	0.292735i	0.722627	−	0.691238i	$-0.242934\pi$
$13$	3.24840	+	1.05547i	0.900945	+	0.292735i	0.178318	+	0.983973i	$0.442934\pi$
$14$		0			0
$15$	−7.20433	−	5.23425i	−1.86015	−	1.35148i
$16$		0			0
$17$	−1.70655	−	5.25221i	−0.413898	−	1.27385i	−0.913233	−	0.407438i	$-0.866422\pi$
$17$	−1.70655	−	5.25221i	−0.413898	−	1.27385i	0.499335	−	0.866409i	$-0.333578\pi$
$18$		0			0
$19$	−1.43071	−	1.96920i	−0.328226	−	0.451765i	0.612730	−	0.790292i	$-0.290071\pi$
$19$	−1.43071	−	1.96920i	−0.328226	−	0.451765i	−0.940957	+	0.338527i	$0.890071\pi$
$20$		0			0
$21$		−	10.5588i		−	2.30411i
$22$		0			0
$23$	−0.764022			−0.159310			−0.0796548	−	0.996823i	$-0.525382\pi$
$23$	−0.764022			−0.159310			−0.0796548	+	0.996823i	$0.525382\pi$
$24$		0			0
$25$	3.01202	−	2.18836i	0.602403	−	0.437672i
$26$		0			0
$27$	−8.86303	+	2.87977i	−1.70569	+	0.554212i
$28$		0			0
$29$	−4.44933	+	6.12397i	−0.826219	+	1.13719i	0.162396	+	0.986726i	$0.448078\pi$
$29$	−4.44933	+	6.12397i	−0.826219	+	1.13719i	−0.988615	+	0.150468i	$0.951922\pi$
$30$		0			0
$31$	−2.65498	+	8.17119i	−0.476849	+	1.46759i	0.366600	+	0.930379i	$0.380522\pi$
$31$	−2.65498	+	8.17119i	−0.476849	+	1.46759i	−0.843448	+	0.537210i	$0.819478\pi$
$32$		0			0
$33$	−9.59126	−	2.82962i	−1.66962	−	0.492574i
$34$		0			0
$35$	9.83675	+	3.19615i	1.66271	+	0.540249i
$36$		0			0
$37$	2.99886	−	4.12757i	0.493009	−	0.678569i	−0.487930	−	0.872883i	$-0.662248\pi$
$37$	2.99886	−	4.12757i	0.493009	−	0.678569i	0.980939	+	0.194314i	$0.0622479\pi$
$38$		0			0
$39$	3.18235	+	9.79426i	0.509583	+	1.56834i
$40$		0			0
$41$	−0.325508	+	0.236495i	−0.0508358	+	0.0369344i	−0.612913	−	0.790150i	$-0.710002\pi$
$41$	−0.325508	+	0.236495i	−0.0508358	+	0.0369344i	0.562077	+	0.827085i	$0.310002\pi$
$42$		0			0
$43$		−	1.38711i		−	0.211533i	−0.994391	−	0.105766i	$-0.966270\pi$
$43$		−	1.38711i		−	0.211533i	0.994391	−	0.105766i	$-0.0337296\pi$
$44$		0			0
$45$		−	17.9891i		−	2.68166i
$46$		0			0
$47$	−6.40473	+	4.65331i	−0.934226	+	0.678755i	−0.947024	−	0.321163i	$-0.895926\pi$
$47$	−6.40473	+	4.65331i	−0.934226	+	0.678755i	0.0127977	+	0.999918i	$0.495926\pi$
$48$		0			0
$49$	1.62658	+	5.00609i	0.232368	+	0.715155i
$50$		0			0
$51$	9.78714	−	13.4708i	1.37047	−	1.88630i
$52$		0			0
$53$	0.735950	+	0.239125i	0.101090	+	0.0328463i	0.359126	−	0.933289i	$-0.383075\pi$
$53$	0.735950	+	0.239125i	0.101090	+	0.0328463i	−0.258035	+	0.966136i	$0.583075\pi$
$54$		0			0
$55$	5.53943	−	8.07888i	0.746936	−	1.08936i
$56$		0			0
$57$	2.26786	−	6.97975i	0.300385	−	0.924490i
$58$		0			0
$59$	−4.91020	+	6.75831i	−0.639253	+	0.879856i	−0.998575	−	0.0533571i	$-0.983008\pi$
$59$	−4.91020	+	6.75831i	−0.639253	+	0.879856i	0.359322	+	0.933213i	$0.383008\pi$
$60$		0			0
$61$	9.41096	−	3.05780i	1.20495	−	0.391512i	0.363370	−	0.931645i	$-0.381626\pi$
$61$	9.41096	−	3.05780i	1.20495	−	0.391512i	0.841580	+	0.540133i	$0.181626\pi$
$62$		0			0
$63$	17.2562	−	12.5373i	2.17407	−	1.57956i
$64$		0			0
$65$	−10.0878			−1.25124
$66$		0			0
$67$			12.6972i			1.55121i	0.631218	+	0.775605i	$0.282555\pi$
$67$			12.6972i			1.55121i	−0.631218	+	0.775605i	$0.717445\pi$
$68$		0			0
$69$	−1.35402	−	1.86365i	−0.163005	−	0.224357i
$70$		0			0
$71$	−0.174133	−	0.535927i	−0.0206658	−	0.0636029i	0.940192	−	0.340646i	$-0.110646\pi$
$71$	−0.174133	−	0.535927i	−0.0206658	−	0.0636029i	−0.960858	+	0.277043i	$0.910646\pi$
$72$		0			0
$73$	5.33230	+	3.87415i	0.624099	+	0.453434i	0.854351	−	0.519697i	$-0.173955\pi$
$73$	5.33230	+	3.87415i	0.624099	+	0.453434i	−0.230252	+	0.973131i	$0.573955\pi$
$74$		0			0
$75$	10.6760	+	3.46883i	1.23276	+	0.400547i
$76$		0			0
$77$	11.6104	−	0.316770i	1.32312	−	0.0360992i
$78$		0			0
$79$	−1.17086	+	3.60353i	−0.131732	+	0.405428i	−0.995067	−	0.0992017i	$-0.968371\pi$
$79$	−1.17086	+	3.60353i	−0.131732	+	0.405428i	0.863336	+	0.504630i	$0.168371\pi$
$80$		0			0
$81$	−7.94913	−	5.77538i	−0.883236	−	0.641709i
$82$		0			0
$83$	−4.61808	+	1.50050i	−0.506900	+	0.164702i	−0.551292	−	0.834312i	$-0.685865\pi$
$83$	−4.61808	+	1.50050i	−0.506900	+	0.164702i	0.0443920	+	0.999014i	$0.485865\pi$
$84$		0			0
$85$	9.58713	+	13.1955i	1.03987	+	1.43126i
$86$		0			0
$87$	−22.8232			−2.44691
$88$		0			0
$89$	2.42355			0.256896			0.128448	−	0.991716i	$-0.459000\pi$
$89$	2.42355			0.256896			0.128448	+	0.991716i	$0.459000\pi$
$90$		0			0
$91$	−7.03061	−	9.67681i	−0.737009	−	1.01441i
$92$		0			0
$93$	−24.6369	+	8.00503i	−2.55473	+	0.830083i
$94$		0			0
$95$	5.81599	+	4.22556i	0.596708	+	0.433534i
$96$		0			0
$97$	−2.07586	+	6.38884i	−0.210772	+	0.648688i	0.788655	+	0.614836i	$0.210778\pi$
$97$	−2.07586	+	6.38884i	−0.210772	+	0.648688i	−0.999427	+	0.0338526i	$0.989222\pi$
$98$		0			0
$99$	−6.76410	−	19.0349i	−0.679818	−	1.91308i
$100$		0			0
$101$	−2.43855	−	0.792334i	−0.242645	−	0.0788402i	0.185170	−	0.982707i	$-0.440717\pi$
$101$	−2.43855	−	0.792334i	−0.242645	−	0.0788402i	−0.427815	+	0.903866i	$0.640717\pi$
$102$		0			0
$103$	−7.01547	−	5.09704i	−0.691255	−	0.502226i	0.185818	−	0.982584i	$-0.440507\pi$
$103$	−7.01547	−	5.09704i	−0.691255	−	0.502226i	−0.877072	+	0.480358i	$0.840507\pi$
$104$		0			0
$105$	9.63672	+	29.6588i	0.940448	+	2.89440i
$106$		0			0
$107$	0.0634476	+	0.0873281i	0.00613371	+	0.00844233i	0.812073	−	0.583556i	$-0.198339\pi$
$107$	0.0634476	+	0.0873281i	0.00613371	+	0.00844233i	−0.805939	+	0.591998i	$0.798339\pi$
$108$		0			0
$109$			18.7229i			1.79333i	0.442714	+	0.896663i	$0.354016\pi$
$109$			18.7229i			1.79333i	−0.442714	+	0.896663i	$0.645984\pi$
$110$		0			0
$111$	15.3829			1.46008
$112$		0			0
$113$	11.8221	−	8.58922i	1.11213	−	0.808006i	0.129128	−	0.991628i	$-0.458782\pi$
$113$	11.8221	−	8.58922i	1.11213	−	0.808006i	0.982997	+	0.183622i	$0.0587821\pi$
$114$		0			0
$115$	2.14608	−	0.697304i	0.200123	−	0.0650240i
$116$		0			0
$117$	−12.2281	+	16.8305i	−1.13049	+	1.55598i
$118$		0			0
$119$	−5.97625	+	18.3930i	−0.547842	+	1.68608i
$120$		0			0
$121$	2.82370	−	10.6314i	0.256700	−	0.966491i
$122$		0			0
$123$	−1.15375	−	0.374876i	−0.104030	−	0.0338015i
$124$		0			0
$125$	2.21679	−	3.05115i	0.198276	−	0.272903i
$126$		0			0
$127$	−3.04232	−	9.36328i	−0.269962	−	0.830857i	−0.990509	−	0.137451i	$-0.956109\pi$
$127$	−3.04232	−	9.36328i	−0.269962	−	0.830857i	0.720547	−	0.693406i	$-0.243891\pi$
$128$		0			0
$129$	3.38354	−	2.45828i	0.297904	−	0.216440i
$130$		0			0
$131$			18.3757i			1.60549i	0.596322	+	0.802745i	$0.296628\pi$
$131$			18.3757i			1.60549i	−0.596322	+	0.802745i	$0.703372\pi$
$132$		0			0
$133$			8.52398i			0.739123i
$134$		0			0
$135$	22.2673	−	16.1781i	1.91647	−	1.39239i
$136$		0			0
$137$	1.49184	+	4.59140i	0.127456	+	0.392270i	0.994341	−	0.106239i	$-0.0338810\pi$
$137$	1.49184	+	4.59140i	0.127456	+	0.392270i	−0.866884	+	0.498509i	$0.833881\pi$
$138$		0			0
$139$	−1.13113	+	1.55686i	−0.0959408	+	0.132051i	−0.854289	−	0.519799i	$-0.826007\pi$
$139$	−1.13113	+	1.55686i	−0.0959408	+	0.132051i	0.758348	+	0.651850i	$0.226007\pi$
$140$		0			0
$141$	−22.7013	−	7.37611i	−1.91180	−	0.621180i
$142$		0			0
$143$	−10.6743	+	3.79313i	−0.892626	+	0.317198i
$144$		0			0
$145$	6.90864	−	21.2626i	0.573731	−	1.76576i
$146$		0			0
$147$	−9.32851	+	12.8396i	−0.769403	+	1.05899i
$148$		0			0
$149$	−17.8963	+	5.81487i	−1.46612	+	0.476372i	−0.929934	−	0.367725i	$-0.880137\pi$
$149$	−17.8963	+	5.81487i	−1.46612	+	0.476372i	−0.536189	+	0.844098i	$0.680137\pi$
$150$		0			0
$151$	17.5819	−	12.7740i	1.43080	−	1.03953i	0.440929	−	0.897542i	$-0.354649\pi$
$151$	17.5819	−	12.7740i	1.43080	−	1.03953i	0.989868	−	0.141993i	$-0.0453509\pi$
$152$		0			0
$153$	33.6366			2.71935
$154$		0			0
$155$		−	25.3754i		−	2.03820i
$156$		0			0
$157$	−3.15748	−	4.34590i	−0.251994	−	0.346840i	0.664214	−	0.747542i	$-0.268766\pi$
$157$	−3.15748	−	4.34590i	−0.251994	−	0.346840i	−0.916208	+	0.400702i	$0.868766\pi$
$158$		0			0
$159$	0.720984	+	2.21896i	0.0571778	+	0.175975i
$160$		0			0
$161$	2.16458	+	1.57266i	0.170593	+	0.123943i
$162$		0			0
$163$	−15.7034	−	5.10233i	−1.22998	−	0.399646i	−0.379275	−	0.925284i	$-0.623827\pi$
$163$	−15.7034	−	5.10233i	−1.22998	−	0.399646i	−0.850708	+	0.525638i	$0.823827\pi$
$164$		0			0
$165$	29.5237	−	0.805505i	2.29842	−	0.0627085i
$166$		0			0
$167$	−0.128336	+	0.394979i	−0.00993097	+	0.0305644i	−0.955899	−	0.293695i	$-0.905115\pi$
$167$	−0.128336	+	0.394979i	−0.00993097	+	0.0305644i	0.945968	+	0.324259i	$0.105115\pi$
$168$		0			0
$169$	−1.07911	−	0.784021i	−0.0830086	−	0.0603093i
$170$		0			0
$171$	14.0998	−	4.58131i	1.07824	−	0.350342i
$172$		0			0
$173$	5.63464	+	7.75542i	0.428394	+	0.589634i	0.967584	−	0.252551i	$-0.0812695\pi$
$173$	5.63464	+	7.75542i	0.428394	+	0.589634i	−0.539190	+	0.842184i	$0.681269\pi$
$174$		0			0
$175$	−13.0380			−0.985579
$176$		0			0
$177$	−25.1873			−1.89319
$178$		0			0
$179$	1.11818	+	1.53905i	0.0835769	+	0.115034i	0.848758	−	0.528781i	$-0.177351\pi$
$179$	1.11818	+	1.53905i	0.0835769	+	0.115034i	−0.765181	+	0.643815i	$0.777351\pi$
$180$		0			0
$181$	8.84361	−	2.87346i	0.657340	−	0.213583i	0.0386922	−	0.999251i	$-0.487681\pi$
$181$	8.84361	−	2.87346i	0.657340	−	0.213583i	0.618648	+	0.785668i	$0.287681\pi$
$182$		0			0
$183$	24.1372	+	17.5367i	1.78427	+	1.29635i
$184$		0			0
$185$	−4.65644	+	14.3310i	−0.342348	+	1.05364i
$186$		0			0
$187$	15.1061	+	10.3578i	1.10467	+	0.757435i
$188$		0			0
$189$	31.0380	+	10.0848i	2.25768	+	0.733564i
$190$		0			0
$191$	3.64772	+	2.65022i	0.263940	+	0.191764i	0.711882	−	0.702299i	$-0.247843\pi$
$191$	3.64772	+	2.65022i	0.263940	+	0.191764i	−0.447942	+	0.894062i	$0.647843\pi$
$192$		0			0
$193$	−6.98403	−	21.4946i	−0.502721	−	1.54722i	−0.804568	−	0.593860i	$-0.797603\pi$
$193$	−6.98403	−	21.4946i	−0.502721	−	1.54722i	0.301847	−	0.953356i	$-0.402397\pi$
$194$		0			0
$195$	−17.8780	−	24.6069i	−1.28027	−	1.76214i
$196$		0			0
$197$			10.1753i			0.724957i	0.931992	+	0.362478i	$0.118069\pi$
$197$			10.1753i			0.724957i	−0.931992	+	0.362478i	$0.881931\pi$
$198$		0			0
$199$	2.68722			0.190492			0.0952459	−	0.995454i	$-0.469636\pi$
$199$	2.68722			0.190492			0.0952459	+	0.995454i	$0.469636\pi$
$200$		0			0
$201$	−30.9719	+	22.5024i	−2.18459	+	1.58720i
$202$		0			0
$203$	25.2112	−	8.19160i	1.76948	−	0.574938i
$204$		0			0
$205$	0.698485	−	0.961382i	0.0487843	−	0.0671459i
$206$		0			0
$207$	1.43802	−	4.42576i	0.0999491	−	0.307612i
$208$		0			0
$209$	7.74294	+	2.28433i	0.535590	+	0.158010i
$210$		0			0
$211$	7.22032	+	2.34602i	0.497067	+	0.161507i	0.546813	−	0.837255i	$-0.315841\pi$
$211$	7.22032	+	2.34602i	0.497067	+	0.161507i	−0.0497454	+	0.998762i	$0.515841\pi$
$212$		0			0
$213$	0.998665	−	1.37455i	0.0684274	−	0.0941823i
$214$		0			0
$215$	1.26598	+	3.89630i	0.0863394	+	0.265725i
$216$		0			0
$217$	24.3415	−	17.6851i	1.65241	−	1.20055i
$218$		0			0
$219$			19.8728i			1.34288i
$220$		0			0
$221$		−	18.8625i		−	1.26883i
$222$		0			0
$223$	12.3850	−	8.99820i	0.829358	−	0.602564i	−0.0900194	−	0.995940i	$-0.528693\pi$
$223$	12.3850	−	8.99820i	0.829358	−	0.602564i	0.919378	+	0.393376i	$0.128693\pi$
$224$		0			0
$225$	7.00742	+	21.5666i	0.467161	+	1.43777i
$226$		0			0
$227$	7.91118	−	10.8888i	0.525083	−	0.722715i	−0.461288	−	0.887250i	$-0.652613\pi$
$227$	7.91118	−	10.8888i	0.525083	−	0.722715i	0.986371	+	0.164535i	$0.0526125\pi$
$228$		0			0
$229$	1.57226	+	0.510858i	0.103898	+	0.0337585i	0.360505	−	0.932757i	$-0.382605\pi$
$229$	1.57226	+	0.510858i	0.103898	+	0.0337585i	−0.256607	+	0.966516i	$0.582605\pi$
$230$		0			0
$231$	21.3489	+	27.7594i	1.40466	+	1.82643i
$232$		0			0
$233$	−4.77266	+	14.6887i	−0.312667	+	0.962290i	0.664037	+	0.747700i	$0.268842\pi$
$233$	−4.77266	+	14.6887i	−0.312667	+	0.962290i	−0.976704	+	0.214591i	$0.931158\pi$
$234$		0			0
$235$	13.7435	−	18.9163i	0.896525	−	1.23396i
$236$		0			0
$237$	−10.8650	+	3.53025i	−0.705757	+	0.229314i
$238$		0			0
$239$	10.6410	−	7.73113i	0.688308	−	0.500085i	−0.187795	−	0.982208i	$-0.560134\pi$
$239$	10.6410	−	7.73113i	0.688308	−	0.500085i	0.876104	+	0.482123i	$0.160134\pi$
$240$		0			0
$241$	−27.1737			−1.75041			−0.875207	−	0.483748i	$-0.839275\pi$
$241$	−27.1737			−1.75041			−0.875207	+	0.483748i	$0.839275\pi$
$242$		0			0
$243$		−	1.66792i		−	0.106997i
$244$		0			0
$245$	−9.13787	−	12.5772i	−0.583797	−	0.803528i
$246$		0			0
$247$	−2.56908	−	7.90682i	−0.163467	−	0.503099i
$248$		0			0
$249$	−11.8444	−	8.60548i	−0.750610	−	0.545350i
$250$		0			0
$251$	4.51205	+	1.46605i	0.284798	+	0.0925365i	0.447933	−	0.894067i	$-0.352160\pi$
$251$	4.51205	+	1.46605i	0.284798	+	0.0925365i	−0.163134	+	0.986604i	$0.552160\pi$
$252$		0			0
$253$	2.00864	−	1.54479i	0.126282	−	0.0971201i
$254$		0			0
$255$	−15.1969	+	46.7711i	−0.951664	+	2.92892i
$256$		0			0
$257$	17.9285	+	13.0258i	1.11835	+	0.812527i	0.983958	−	0.178402i	$-0.0570927\pi$
$257$	17.9285	+	13.0258i	1.11835	+	0.812527i	0.134389	+	0.990929i	$0.457093\pi$
$258$		0			0
$259$	−16.9924	+	5.52116i	−1.05586	+	0.343068i
$260$		0			0
$261$	−27.1001	−	37.3000i	−1.67745	−	2.30881i
$262$		0			0
$263$	−5.79252			−0.357182			−0.178591	−	0.983923i	$-0.557154\pi$
$263$	−5.79252			−0.357182			−0.178591	+	0.983923i	$0.557154\pi$
$264$		0			0
$265$	−2.28547			−0.140396
$266$		0			0
$267$	4.29510	+	5.91169i	0.262856	+	0.361790i
$268$		0			0
$269$	12.5326	−	4.07207i	0.764123	−	0.248279i	0.0990758	−	0.995080i	$-0.468411\pi$
$269$	12.5326	−	4.07207i	0.764123	−	0.248279i	0.665047	+	0.746801i	$0.268411\pi$
$270$		0			0
$271$	4.75377	+	3.45382i	0.288771	+	0.209804i	0.722734	−	0.691126i	$-0.242885\pi$
$271$	4.75377	+	3.45382i	0.288771	+	0.209804i	−0.433963	+	0.900931i	$0.642885\pi$
$272$		0			0
$273$	11.1444	−	34.2991i	0.674493	−	2.07588i
$274$		0			0
$275$	−3.49403	+	11.8433i	−0.210698	+	0.714179i
$276$		0			0
$277$	22.8241	+	7.41599i	1.37136	+	0.445583i	0.899821	−	0.436259i	$-0.143697\pi$
$277$	22.8241	+	7.41599i	1.37136	+	0.445583i	0.471544	+	0.881843i	$0.343697\pi$
$278$		0			0
$279$	−42.3363	−	30.7591i	−2.53461	−	1.84150i
$280$		0			0
$281$	−7.34571	−	22.6078i	−0.438208	−	1.34867i	−0.889763	−	0.456423i	$-0.849130\pi$
$281$	−7.34571	−	22.6078i	−0.438208	−	1.34867i	0.451554	−	0.892244i	$-0.350870\pi$
$282$		0			0
$283$	−10.6480	−	14.6558i	−0.632960	−	0.871194i	0.365256	−	0.930907i	$-0.380982\pi$
$283$	−10.6480	−	14.6558i	−0.632960	−	0.871194i	−0.998216	+	0.0597127i	$0.980982\pi$
$284$		0			0
$285$			21.6754i			1.28394i
$286$		0			0
$287$	1.40901			0.0831714
$288$		0			0
$289$	−10.9201	+	7.93391i	−0.642358	+	0.466700i
$290$		0			0
$291$	−19.2630	+	6.25892i	−1.12922	+	0.366905i
$292$		0			0
$293$	−0.972059	+	1.33792i	−0.0567883	+	0.0781623i	−0.836467	−	0.548018i	$-0.815383\pi$
$293$	−0.972059	+	1.33792i	−0.0567883	+	0.0781623i	0.779678	+	0.626180i	$0.215383\pi$
$294$		0			0
$295$	7.62425	−	23.4650i	0.443901	−	1.36619i
$296$		0			0
$297$	17.4786	−	25.4913i	1.01421	−	1.47916i
$298$		0			0
$299$	−2.48185	−	0.806402i	−0.143529	−	0.0466355i
$300$		0			0
$301$	−2.85523	+	3.92989i	−0.164573	+	0.226515i
$302$		0			0
$303$	−2.38897	−	7.35248i	−0.137243	−	0.422389i
$304$		0			0
$305$	−23.6439	+	17.1783i	−1.35385	+	0.983627i
$306$		0			0
$307$			0.240107i			0.0137036i	0.999977	+	0.00685182i	$0.00218102\pi$
$307$			0.240107i			0.0137036i	−0.999977	+	0.00685182i	$0.997819\pi$
$308$		0			0
$309$		−	26.1457i		−	1.48738i
$310$		0			0
$311$	−5.73061	+	4.16354i	−0.324953	+	0.236092i	−0.738286	−	0.674488i	$-0.764365\pi$
$311$	−5.73061	+	4.16354i	−0.324953	+	0.236092i	0.413333	+	0.910580i	$0.364365\pi$
$312$		0			0
$313$	−3.35102	−	10.3134i	−0.189411	−	0.582946i	0.810586	−	0.585620i	$-0.199149\pi$
$313$	−3.35102	−	10.3134i	−0.189411	−	0.582946i	−0.999996	+	0.00267401i	$0.999149\pi$
$314$		0			0
$315$	−37.0288	+	50.9658i	−2.08634	+	2.87160i
$316$		0			0
$317$	−10.2668	−	3.33590i	−0.576644	−	0.187363i	0.00615277	−	0.999981i	$-0.498041\pi$
$317$	−10.2668	−	3.33590i	−0.576644	−	0.187363i	−0.582796	+	0.812618i	$0.698041\pi$
$318$		0			0
$319$	−0.684712	−	25.0963i	−0.0383365	−	1.40513i
$320$		0			0
$321$	−0.100573	+	0.309531i	−0.00561343	+	0.0172763i
$322$		0			0
$323$	−7.90107	+	10.8749i	−0.439627	+	0.605095i
$324$		0			0
$325$	12.0940	−	3.92958i	0.670854	−	0.217974i
$326$		0			0
$327$	−45.6701	+	33.1812i	−2.52556	+	1.83493i
$328$		0			0
$329$	27.7239			1.52847
$330$		0			0
$331$		−	8.98328i		−	0.493766i	−0.969045	−	0.246883i	$-0.920594\pi$
$331$		−	8.98328i		−	0.493766i	0.969045	−	0.246883i	$-0.0794063\pi$
$332$		0			0
$333$	18.2655	+	25.1403i	1.00094	+	1.37768i
$334$		0			0
$335$	−11.5884	−	35.6655i	−0.633144	−	1.94862i
$336$		0			0
$337$	28.3027	+	20.5631i	1.54175	+	1.12014i	0.949228	+	0.314588i	$0.101866\pi$
$337$	28.3027	+	20.5631i	1.54175	+	1.12014i	0.592518	+	0.805557i	$0.298134\pi$
$338$		0			0
$339$	41.9028	+	13.6150i	2.27585	+	0.739468i
$340$		0			0
$341$	−9.54142	−	26.8505i	−0.516697	−	1.45404i
$342$		0			0
$343$	−1.87895	+	5.78282i	−0.101454	+	0.312243i
$344$		0			0
$345$	5.50426	+	3.99908i	0.296340	+	0.215303i
$346$		0			0
$347$	−4.49534	+	1.46062i	−0.241322	+	0.0784104i	−0.427181	−	0.904166i	$-0.640493\pi$
$347$	−4.49534	+	1.46062i	−0.241322	+	0.0784104i	0.185859	+	0.982576i	$0.440493\pi$
$348$		0			0
$349$	−9.07261	−	12.4874i	−0.485646	−	0.668434i	0.493932	−	0.869501i	$-0.335559\pi$
$349$	−9.07261	−	12.4874i	−0.485646	−	0.668434i	−0.979578	+	0.201066i	$0.935559\pi$
$350$		0			0
$351$	−31.8302			−1.69897
$352$		0			0
$353$	−0.0739588			−0.00393643			−0.00196822	−	0.999998i	$-0.500627\pi$
$353$	−0.0739588			−0.00393643			−0.00196822	+	0.999998i	$0.500627\pi$
$354$		0			0
$355$	0.978257	+	1.34645i	0.0519205	+	0.0714624i
$356$		0			0
$357$	−55.4567	+	18.0190i	−2.93508	+	0.953666i
$358$		0			0
$359$	−28.1572	−	20.4574i	−1.48608	−	1.07970i	−0.975533	−	0.219852i	$-0.929443\pi$
$359$	−28.1572	−	20.4574i	−1.48608	−	1.07970i	−0.510548	−	0.859849i	$-0.670557\pi$
$360$		0			0
$361$	4.04050	−	12.4354i	0.212658	−	0.654494i
$362$		0			0
$363$	30.9371	−	11.9535i	1.62378	−	0.627398i
$364$		0			0
$365$	−18.5139	−	6.01553i	−0.969062	−	0.314867i
$366$		0			0
$367$	20.0550	+	14.5708i	1.04686	+	0.760589i	0.971613	−	0.236576i	$-0.0760251\pi$
$367$	20.0550	+	14.5708i	1.04686	+	0.760589i	0.0752481	+	0.997165i	$0.476025\pi$
$368$		0			0
$369$	−0.757291	−	2.33070i	−0.0394230	−	0.121331i
$370$		0			0
$371$	−1.59284	−	2.19235i	−0.0826960	−	0.113821i
$372$		0			0
$373$			2.43652i			0.126158i	0.998009	+	0.0630791i	$0.0200920\pi$
$373$			2.43652i			0.126158i	−0.998009	+	0.0630791i	$0.979908\pi$
$374$		0			0
$375$	11.3712			0.587208
$376$		0			0
$377$	−20.9169	+	15.1970i	−1.07727	+	0.782686i
$378$		0			0
$379$	−33.7387	+	10.9624i	−1.73304	+	0.563099i	−0.993883	−	0.110435i	$-0.964775\pi$
$379$	−33.7387	+	10.9624i	−1.73304	+	0.563099i	−0.739156	+	0.673534i	$0.764775\pi$
$380$		0			0
$381$	17.4479	−	24.0149i	0.893881	−	1.23032i
$382$		0			0
$383$	−4.27361	+	13.1528i	−0.218371	+	0.672078i	0.780526	+	0.625124i	$0.214952\pi$
$383$	−4.27361	+	13.1528i	−0.218371	+	0.672078i	−0.998897	+	0.0469544i	$0.985048\pi$
$384$		0			0
$385$	−32.3236	+	11.4863i	−1.64736	+	0.585395i
$386$		0			0
$387$	8.03515	+	2.61078i	0.408450	+	0.132713i
$388$		0			0
$389$	−20.3320	+	27.9846i	−1.03087	+	1.41888i	−0.126585	+	0.991956i	$0.540402\pi$
$389$	−20.3320	+	27.9846i	−1.03087	+	1.41888i	−0.904289	+	0.426921i	$0.859598\pi$
$390$		0			0
$391$	1.30384	+	4.01280i	0.0659379	+	0.202936i
$392$		0			0
$393$	−44.8232	+	32.5659i	−2.26103	+	1.64273i
$394$		0			0
$395$		−	11.1907i		−	0.563063i
$396$		0			0
$397$			13.7497i			0.690080i	0.938588	+	0.345040i	$0.112135\pi$
$397$			13.7497i			0.690080i	−0.938588	+	0.345040i	$0.887865\pi$
$398$		0			0
$399$	−20.7923	+	15.1065i	−1.04092	+	0.756269i
$400$		0			0
$401$	11.1612	+	34.3507i	0.557365	+	1.71539i	0.689613	+	0.724178i	$0.257781\pi$
$401$	11.1612	+	34.3507i	0.557365	+	1.71539i	−0.132248	+	0.991217i	$0.542219\pi$
$402$		0			0
$403$	−17.2489	+	23.7411i	−0.859229	+	1.18263i
$404$		0			0
$405$	27.5996	+	8.96764i	1.37143	+	0.445606i
$406$		0			0
$407$	0.461498	+	16.9150i	0.0228756	+	0.838446i
$408$		0			0
$409$	−0.0131078	+	0.0403415i	−0.000648137	+	0.00199476i	−0.951380	−	0.308019i	$-0.900334\pi$
$409$	−0.0131078	+	0.0403415i	−0.000648137	+	0.00199476i	0.950732	+	0.310014i	$0.100334\pi$
$410$		0			0
$411$	−8.55577	+	11.7760i	−0.422025	+	0.580868i
$412$		0			0
$413$	27.8226	−	9.04011i	1.36906	−	0.444834i
$414$		0			0
$415$	11.6024	−	8.42962i	0.569538	−	0.413794i
$416$		0			0
$417$	−5.80221			−0.284136
$418$		0			0
$419$		−	13.5033i		−	0.659682i	−0.944037	−	0.329841i	$-0.893005\pi$
$419$		−	13.5033i		−	0.659682i	0.944037	−	0.329841i	$-0.106995\pi$
$420$		0			0
$421$	−3.73068	−	5.13484i	−0.181822	−	0.250257i	0.708371	−	0.705841i	$-0.249431\pi$
$421$	−3.73068	−	5.13484i	−0.181822	−	0.250257i	−0.890193	+	0.455584i	$0.849431\pi$
$422$		0			0
$423$	−14.9005	−	45.8591i	−0.724489	−	2.22975i
$424$		0			0
$425$	−16.6338	−	12.0852i	−0.806860	−	0.586218i
$426$		0			0
$427$	−32.9568	−	10.7083i	−1.59489	−	0.518211i
$428$		0			0
$429$	−28.1697	−	19.3151i	−1.36005	−	0.932539i
$430$		0			0
$431$	−4.16282	+	12.8118i	−0.200516	+	0.617124i	0.799352	+	0.600863i	$0.205176\pi$
$431$	−4.16282	+	12.8118i	−0.200516	+	0.617124i	−0.999868	+	0.0162612i	$0.994824\pi$
$432$		0			0
$433$	−1.56603	−	1.13778i	−0.0752584	−	0.0546784i	0.549520	−	0.835481i	$-0.314811\pi$
$433$	−1.56603	−	1.13778i	−0.0752584	−	0.0546784i	−0.624778	+	0.780802i	$0.714811\pi$
$434$		0			0
$435$	64.1088	−	20.8302i	3.07378	−	0.998733i
$436$		0			0
$437$	1.09309	+	1.50451i	0.0522896	+	0.0719705i
$438$		0			0
$439$	21.6136			1.03156			0.515781	−	0.856720i	$-0.327502\pi$
$439$	21.6136			1.03156			0.515781	+	0.856720i	$0.327502\pi$
$440$		0			0
$441$	−32.0603			−1.52668
$442$		0			0
$443$	−2.72061	−	3.74460i	−0.129260	−	0.177911i	0.739482	−	0.673177i	$-0.235071\pi$
$443$	−2.72061	−	3.74460i	−0.129260	−	0.177911i	−0.868742	+	0.495266i	$0.835071\pi$
$444$		0			0
$445$	−6.80759	+	2.21192i	−0.322711	+	0.104855i
$446$		0			0
$447$	−45.9004	−	33.3486i	−2.17102	−	1.57733i
$448$		0			0
$449$	8.00767	−	24.6451i	0.377906	−	1.16307i	−0.563592	−	0.826053i	$-0.690581\pi$
$449$	8.00767	−	24.6451i	0.377906	−	1.16307i	0.941497	−	0.337020i	$-0.109419\pi$
$450$		0			0
$451$	0.377599	−	1.27991i	0.0177805	−	0.0602684i
$452$		0			0
$453$	62.3185	+	20.2485i	2.92798	+	0.951357i
$454$		0			0
$455$	28.5803	+	20.7648i	1.33986	+	0.973469i
$456$		0			0
$457$	9.98787	+	30.7395i	0.467213	+	1.43793i	0.856178	+	0.516681i	$0.172833\pi$
$457$	9.98787	+	30.7395i	0.467213	+	1.43793i	−0.388965	+	0.921252i	$0.627167\pi$
$458$		0			0
$459$	30.2503	+	41.6360i	1.41196	+	1.94340i
$460$		0			0
$461$		−	27.9486i		−	1.30170i	−0.759208	−	0.650848i	$-0.774413\pi$
$461$		−	27.9486i		−	1.30170i	0.759208	−	0.650848i	$-0.225587\pi$
$462$		0			0
$463$	24.4361			1.13564			0.567821	−	0.823152i	$-0.307787\pi$
$463$	24.4361			1.13564			0.567821	+	0.823152i	$0.307787\pi$
$464$		0			0
$465$	61.8974	−	44.9711i	2.87042	−	2.08549i
$466$		0			0
$467$	10.7326	−	3.48725i	0.496648	−	0.161371i	−0.0499736	−	0.998751i	$-0.515914\pi$
$467$	10.7326	−	3.48725i	0.496648	−	0.161371i	0.546621	+	0.837380i	$0.315914\pi$
$468$		0			0
$469$	26.1359	−	35.9730i	1.20684	−	1.66108i
$470$		0			0
$471$	5.00502	−	15.4039i	0.230619	−	0.709772i
$472$		0			0
$473$	2.80463	+	3.64677i	0.128957	+	0.167679i
$474$		0			0
$475$	−8.61862	−	2.80036i	−0.395449	−	0.128489i
$476$		0			0
$477$	−2.77036	+	3.81308i	−0.126846	+	0.174589i
$478$		0			0
$479$	−0.00730331	−	0.0224773i	−0.000333697	−	0.00102701i	0.950890	−	0.309530i	$-0.100172\pi$
$479$	−0.00730331	−	0.0224773i	−0.000333697	−	0.00102701i	−0.951223	+	0.308503i	$0.900172\pi$
$480$		0			0
$481$	14.0980	−	10.2428i	0.642815	−	0.467033i
$482$		0			0
$483$			8.06712i			0.367066i
$484$		0			0
$485$		−	19.8404i		−	0.900905i
$486$		0			0
$487$	−22.8411	+	16.5950i	−1.03503	+	0.751993i	−0.969309	−	0.245845i	$-0.920935\pi$
$487$	−22.8411	+	16.5950i	−1.03503	+	0.751993i	−0.0657208	+	0.997838i	$0.520935\pi$
$488$		0			0
$489$	−15.3840	−	47.3472i	−0.695691	−	2.14112i
$490$		0			0
$491$	1.45897	−	2.00811i	0.0658426	−	0.0906246i	−0.774826	−	0.632175i	$-0.782162\pi$
$491$	1.45897	−	2.00811i	0.0658426	−	0.0906246i	0.840668	+	0.541550i	$0.182162\pi$
$492$		0			0
$493$	39.7574	+	12.9179i	1.79058	+	0.581795i
$494$		0			0
$495$	36.3726	+	47.2942i	1.63482	+	2.12571i
$496$		0			0
$497$	−0.609808	+	1.87680i	−0.0273536	+	0.0841858i
$498$		0			0
$499$	4.19712	−	5.77684i	0.187889	−	0.258607i	−0.704673	−	0.709533i	$-0.748906\pi$
$499$	4.19712	−	5.77684i	0.187889	−	0.258607i	0.892561	+	0.450926i	$0.148906\pi$
$500$		0			0
$501$	−1.19090	+	0.386947i	−0.0532055	+	0.0172875i
$502$		0			0
$503$	18.0047	−	13.0812i	0.802791	−	0.583262i	−0.108941	−	0.994048i	$-0.534746\pi$
$503$	18.0047	−	13.0812i	0.802791	−	0.583262i	0.911732	+	0.410787i	$0.134746\pi$
$504$		0			0
$505$	7.57287			0.336988
$506$		0			0
$507$		−	4.02171i		−	0.178610i
$508$		0			0
$509$	−19.6881	−	27.0983i	−0.872658	−	1.20111i	−0.978401	−	0.206717i	$-0.933722\pi$
$509$	−19.6881	−	27.0983i	−0.872658	−	1.20111i	0.105743	−	0.994393i	$-0.466278\pi$
$510$		0			0
$511$	−7.13264	−	21.9520i	−0.315530	−	0.971100i
$512$		0			0
$513$	18.3512	+	13.3329i	0.810226	+	0.588664i
$514$		0			0
$515$	24.3579	+	7.91436i	1.07334	+	0.348748i
$516$		0			0
$517$	7.42968	−	25.1836i	0.326757	−	1.10757i
$518$		0			0
$519$	−8.93165	+	27.4888i	−0.392056	+	1.20662i
$520$		0			0
$521$	−20.9131	−	15.1943i	−0.916222	−	0.665674i	0.0263591	−	0.999653i	$-0.491609\pi$
$521$	−20.9131	−	15.1943i	−0.916222	−	0.665674i	−0.942581	+	0.333979i	$0.891609\pi$
$522$		0			0
$523$	−9.59952	+	3.11907i	−0.419758	+	0.136388i	−0.511278	−	0.859416i	$-0.670828\pi$
$523$	−9.59952	+	3.11907i	−0.419758	+	0.136388i	0.0915197	+	0.995803i	$0.470828\pi$
$524$		0			0
$525$	−23.1063	−	31.8031i	−1.00844	−	1.38800i
$526$		0			0
$527$	47.4476			2.06685
$528$		0			0
$529$	−22.4163			−0.974620
$530$		0			0
$531$	−29.9071	−	41.1636i	−1.29786	−	1.78635i
$532$		0			0
$533$	−1.30700	+	0.424669i	−0.0566123	+	0.0183944i
$534$		0			0
$535$	−0.257922	−	0.187391i	−0.0111509	−	0.00810163i
$536$		0			0
$537$	−1.77247	+	5.45509i	−0.0764876	+	0.235404i
$538$		0			0
$539$	−14.3982	−	9.87240i	−0.620176	−	0.425234i
$540$		0			0
$541$	−21.9221	−	7.12294i	−0.942507	−	0.306239i	−0.202840	−	0.979212i	$-0.565017\pi$
$541$	−21.9221	−	7.12294i	−0.942507	−	0.306239i	−0.739667	+	0.672973i	$0.765017\pi$
$542$		0			0
$543$	22.6820	+	16.4795i	0.973380	+	0.707202i
$544$		0			0
$545$	−17.0879	−	52.5912i	−0.731966	−	2.25276i
$546$		0			0
$547$	24.5057	+	33.7293i	1.04779	+	1.44216i	0.890710	+	0.454573i	$0.150208\pi$
$547$	24.5057	+	33.7293i	1.04779	+	1.44216i	0.157080	+	0.987586i	$0.449792\pi$
$548$		0			0
$549$			60.2703i			2.57227i
$550$		0			0
$551$	18.4250			0.784931
$552$		0			0
$553$	10.7347	−	7.79922i	0.456486	−	0.331656i
$554$		0			0
$555$	−43.2095	+	14.0396i	−1.83414	+	0.595949i
$556$		0			0
$557$	−16.5362	+	22.7601i	−0.700660	+	0.964376i	0.299288	+	0.954163i	$0.403251\pi$
$557$	−16.5362	+	22.7601i	−0.700660	+	0.964376i	−0.999948	+	0.0102132i	$0.996749\pi$
$558$		0			0
$559$	1.46406	−	4.50590i	0.0619230	−	0.190579i
$560$		0			0
$561$	1.50615	+	55.2042i	0.0635899	+	2.33072i
$562$		0			0
$563$	−10.6068	−	3.44635i	−0.447022	−	0.145246i	0.0768509	−	0.997043i	$-0.475513\pi$
$563$	−10.6068	−	3.44635i	−0.447022	−	0.145246i	−0.523873	+	0.851796i	$0.675513\pi$
$564$		0			0
$565$	−25.3681	+	34.9162i	−1.06724	+	1.46894i
$566$		0			0
$567$	10.6330	+	32.7249i	0.446543	+	1.37432i
$568$		0			0
$569$	−29.6925	+	21.5729i	−1.24477	+	0.904382i	−0.997907	−	0.0646673i	$-0.979401\pi$
$569$	−29.6925	+	21.5729i	−1.24477	+	0.904382i	−0.246868	+	0.969049i	$0.579401\pi$
$570$		0			0
$571$		−	32.6986i		−	1.36839i	−0.729297	−	0.684197i	$-0.760153\pi$
$571$		−	32.6986i		−	1.36839i	0.729297	−	0.684197i	$-0.239847\pi$
$572$		0			0
$573$			13.5946i			0.567922i
$574$		0			0
$575$	−2.30125	+	1.67195i	−0.0959686	+	0.0697253i
$576$		0			0
$577$	4.15026	+	12.7732i	0.172777	+	0.531754i	0.999525	−	0.0308188i	$-0.00981150\pi$
$577$	4.15026	+	12.7732i	0.172777	+	0.531754i	−0.826748	+	0.562573i	$0.809811\pi$
$578$		0			0
$579$	40.0538	−	55.1293i	1.66458	−	2.29110i
$580$		0			0
$581$	16.1723	+	5.25470i	0.670941	+	0.218002i
$582$		0			0
$583$	−2.41833	+	0.859362i	−0.100157	+	0.0355911i
$584$		0			0
$585$	18.9870	−	58.4360i	0.785016	−	2.41603i
$586$		0			0
$587$	15.8452	−	21.8091i	0.654003	−	0.900157i	−0.345262	−	0.938506i	$-0.612210\pi$
$587$	15.8452	−	21.8091i	0.654003	−	0.900157i	0.999264	+	0.0383490i	$0.0122099\pi$
$588$		0			0
$589$	19.8892	−	6.46239i	0.819519	−	0.266278i
$590$		0			0
$591$	−24.8201	+	18.0329i	−1.02096	+	0.741774i
$592$		0			0
$593$	26.0759			1.07081			0.535404	−	0.844596i	$-0.320159\pi$
$593$	26.0759			1.07081			0.535404	+	0.844596i	$0.320159\pi$
$594$		0			0
$595$		−	57.1190i		−	2.34165i
$596$		0			0
$597$	4.76237	+	6.55484i	0.194911	+	0.268272i
$598$		0			0
$599$	9.01041	+	27.7312i	0.368156	+	1.13307i	0.947981	+	0.318326i	$0.103121\pi$
$599$	9.01041	+	27.7312i	0.368156	+	1.13307i	−0.579826	+	0.814740i	$0.696879\pi$
$600$		0			0
$601$	−13.5822	−	9.86802i	−0.554028	−	0.402525i	0.275240	−	0.961375i	$-0.411243\pi$
$601$	−13.5822	−	9.86802i	−0.554028	−	0.402525i	−0.829268	+	0.558850i	$0.811243\pi$
$602$		0			0
$603$	−73.5513	−	23.8983i	−2.99524	−	0.973213i
$604$		0			0
$605$	1.77146	+	32.4400i	0.0720201	+	1.31887i
$606$		0			0
$607$	0.825515	−	2.54068i	0.0335066	−	0.103123i	−0.932904	−	0.360124i	$-0.882734\pi$
$607$	0.825515	−	2.54068i	0.0335066	−	0.103123i	0.966411	+	0.257001i	$0.0827344\pi$
$608$		0			0
$609$	64.6615	+	46.9793i	2.62022	+	1.90370i
$610$		0			0
$611$	−25.7166	+	8.35583i	−1.04038	+	0.338041i
$612$		0			0
$613$	−20.5851	−	28.3329i	−0.831423	−	1.14436i	−0.987656	−	0.156636i	$-0.949935\pi$
$613$	−20.5851	−	28.3329i	−0.831423	−	1.14436i	0.156233	−	0.987720i	$-0.450065\pi$
$614$		0			0
$615$	3.58294			0.144478
$616$		0			0
$617$	12.6938			0.511032			0.255516	−	0.966805i	$-0.417755\pi$
$617$	12.6938			0.511032			0.255516	+	0.966805i	$0.417755\pi$
$618$		0			0
$619$	16.2613	+	22.3817i	0.653595	+	0.899597i	0.999248	−	0.0387655i	$-0.0123425\pi$
$619$	16.2613	+	22.3817i	0.653595	+	0.899597i	−0.345653	+	0.938362i	$0.612343\pi$
$620$		0			0
$621$	6.77155	−	2.20021i	0.271733	−	0.0882913i
$622$		0			0
$623$	−6.86628	−	4.98864i	−0.275092	−	0.199866i
$624$		0			0
$625$	−9.19453	+	28.2979i	−0.367781	+	1.13191i
$626$		0			0
$627$	8.15018	+	22.9354i	0.325487	+	0.915953i
$628$		0			0
$629$	−26.7966	−	8.70673i	−1.06845	−	0.347160i
$630$		0			0
$631$	−13.1222	−	9.53383i	−0.522386	−	0.379536i	0.295116	−	0.955461i	$-0.404642\pi$
$631$	−13.1222	−	9.53383i	−0.522386	−	0.379536i	−0.817502	+	0.575926i	$0.804642\pi$
$632$		0			0
$633$	7.07349	+	21.7700i	0.281146	+	0.865279i
$634$		0			0
$635$	17.0913	+	23.5241i	0.678247	+	0.933527i
$636$		0			0
$637$			17.9786i			0.712338i
$638$		0			0
$639$	3.43222			0.135777
$640$		0			0
$641$	−16.6654	+	12.1081i	−0.658245	+	0.478243i	−0.866070	−	0.499923i	$-0.833362\pi$
$641$	−16.6654	+	12.1081i	−0.658245	+	0.478243i	0.207825	+	0.978166i	$0.433362\pi$
$642$		0			0
$643$	−14.7618	+	4.79639i	−0.582147	+	0.189151i	−0.585262	−	0.810844i	$-0.699008\pi$
$643$	−14.7618	+	4.79639i	−0.582147	+	0.189151i	0.00311490	+	0.999995i	$0.499008\pi$
$644$		0			0
$645$	−7.26050	+	9.99322i	−0.285882	+	0.393482i
$646$		0			0
$647$	13.9849	−	43.0412i	0.549805	−	1.69213i	−0.159478	−	0.987201i	$-0.550981\pi$
$647$	13.9849	−	43.0412i	0.549805	−	1.69213i	0.709283	−	0.704924i	$-0.249019\pi$
$648$		0			0
$649$	−0.755636	−	27.6959i	−0.0296613	−	1.08716i
$650$		0			0
$651$	86.2775	+	28.0333i	3.38148	+	1.09871i
$652$		0			0
$653$	−26.2935	+	36.1898i	−1.02894	+	1.41622i	−0.123204	+	0.992381i	$0.539317\pi$
$653$	−26.2935	+	36.1898i	−1.02894	+	1.41622i	−0.905739	+	0.423837i	$0.860683\pi$
$654$		0			0
$655$	−16.7710	−	51.6159i	−0.655299	−	2.01680i
$656$		0			0
$657$	−32.4781	+	23.5967i	−1.26709	+	0.920596i
$658$		0			0
$659$			15.3059i			0.596234i	0.954529	+	0.298117i	$0.0963585\pi$
$659$			15.3059i			0.596234i	−0.954529	+	0.298117i	$0.903642\pi$
$660$		0			0
$661$			41.0459i			1.59650i	0.602327	+	0.798250i	$0.294240\pi$
$661$			41.0459i			1.59650i	−0.602327	+	0.798250i	$0.705760\pi$
$662$		0			0
$663$	46.0107	−	33.4287i	1.78691	−	1.29826i
$664$		0			0
$665$	−7.77964	−	23.9433i	−0.301681	−	0.928480i
$666$		0			0
$667$	3.39938	−	4.67885i	0.131625	−	0.181166i
$668$		0			0
$669$	43.8980	+	14.2633i	1.69720	+	0.551452i
$670$		0			0
$671$	−18.5591	+	27.0673i	−0.716468	+	1.04492i
$672$		0			0
$673$	−5.10643	+	15.7160i	−0.196838	+	0.605806i	0.803112	+	0.595828i	$0.203176\pi$
$673$	−5.10643	+	15.7160i	−0.196838	+	0.605806i	−0.999950	+	0.00997788i	$0.996824\pi$
$674$		0			0
$675$	−20.3936	+	28.0694i	−0.784950	+	1.08039i
$676$		0			0
$677$	21.7161	−	7.05598i	0.834617	−	0.271184i	0.139628	−	0.990204i	$-0.455409\pi$
$677$	21.7161	−	7.05598i	0.834617	−	0.271184i	0.694989	+	0.719020i	$0.255409\pi$
$678$		0			0
$679$	19.0320	−	13.8276i	0.730381	−	0.530653i
$680$		0			0
$681$	40.5811			1.55507
$682$		0			0
$683$			6.70806i			0.256677i	0.991730	+	0.128338i	$0.0409644\pi$
$683$			6.70806i			0.256677i	−0.991730	+	0.128338i	$0.959036\pi$
$684$		0			0
$685$	−8.38093	−	11.5354i	−0.320219	−	0.440743i
$686$		0			0
$687$	1.54029	+	4.74052i	0.0587657	+	0.180862i
$688$		0			0
$689$	2.13827	+	1.55355i	0.0814617	+	0.0591854i
$690$		0			0
$691$	23.8987	+	7.76517i	0.909150	+	0.295401i	0.726009	−	0.687686i	$-0.241373\pi$
$691$	23.8987	+	7.76517i	0.909150	+	0.295401i	0.183142	+	0.983087i	$0.441373\pi$
$692$		0			0
$693$	−20.0177	+	67.8517i	−0.760409	+	2.57747i
$694$		0			0
$695$	1.75634	−	5.40546i	0.0666218	−	0.205041i
$696$		0			0
$697$	1.79762	+	1.30605i	0.0680896	+	0.0494700i
$698$		0			0
$699$	−44.2880	+	14.3900i	−1.67512	+	0.544281i
$700$		0			0
$701$	8.07222	+	11.1105i	0.304884	+	0.419636i	0.933777	−	0.357855i	$-0.116492\pi$
$701$	8.07222	+	11.1105i	0.304884	+	0.419636i	−0.628894	+	0.777491i	$0.716492\pi$
$702$		0			0
$703$	−12.4185			−0.468372
$704$		0			0
$705$	70.4984			2.65512
$706$		0			0
$707$	5.27783	+	7.26431i	0.198493	+	0.273203i
$708$		0			0
$709$	5.42513	−	1.76273i	0.203745	−	0.0662008i	−0.205367	−	0.978685i	$-0.565839\pi$
$709$	5.42513	−	1.76273i	0.203745	−	0.0662008i	0.409112	+	0.912484i	$0.365839\pi$
$710$		0			0
$711$	−18.6705	−	13.5649i	−0.700197	−	0.508723i
$712$		0			0
$713$	2.02846	−	6.24297i	0.0759665	−	0.233801i
$714$		0			0
$715$	26.5213	−	20.3968i	0.991841	−	0.762796i
$716$		0			0
$717$	37.7166	+	12.2549i	1.40855	+	0.457666i
$718$		0			0
$719$	−11.8130	−	8.58261i	−0.440549	−	0.320077i	0.345304	−	0.938491i	$-0.387776\pi$
$719$	−11.8130	−	8.58261i	−0.440549	−	0.320077i	−0.785853	+	0.618413i	$0.787776\pi$
$720$		0			0
$721$	9.38410	+	28.8813i	0.349482	+	1.07559i
$722$		0			0
$723$	−48.1581	−	66.2840i	−1.79102	−	2.46513i
$724$		0			0
$725$			28.1822i			1.04666i
$726$		0			0
$727$	6.24163			0.231489			0.115745	−	0.993279i	$-0.463075\pi$
$727$	6.24163			0.231489			0.115745	+	0.993279i	$0.463075\pi$
$728$		0			0
$729$	−19.7789	+	14.3702i	−0.732551	+	0.532229i
$730$		0			0
$731$	−7.28540	+	2.36717i	−0.269460	+	0.0875530i
$732$		0			0
$733$	16.9124	−	23.2780i	0.624675	−	0.859792i	−0.373007	−	0.927828i	$-0.621673\pi$
$733$	16.9124	−	23.2780i	0.624675	−	0.859792i	0.997683	+	0.0680364i	$0.0216734\pi$
$734$		0			0
$735$	14.4847	−	44.5794i	0.534277	−	1.64434i
$736$		0			0
$737$	−25.6727	−	33.3815i	−0.945666	−	1.22962i
$738$		0			0
$739$	5.80395	+	1.88582i	0.213502	+	0.0693709i	0.413815	−	0.910361i	$-0.364196\pi$
$739$	5.80395	+	1.88582i	0.213502	+	0.0693709i	−0.200313	+	0.979732i	$0.564196\pi$
$740$		0			0
$741$	14.7338	−	20.2794i	0.541261	−	0.744981i
$742$		0			0
$743$	−0.402431	−	1.23856i	−0.0147638	−	0.0454382i	0.943403	−	0.331648i	$-0.107605\pi$
$743$	−0.402431	−	1.23856i	−0.0147638	−	0.0454382i	−0.958167	+	0.286210i	$0.907605\pi$
$744$		0			0
$745$	44.9624	−	32.6671i	1.64729	−	1.19683i
$746$		0			0
$747$		−	29.5754i		−	1.08211i
$748$		0			0
$749$		−	0.378014i		−	0.0138123i
$750$		0			0
$751$	−2.68437	+	1.95031i	−0.0979541	+	0.0711678i	−0.635684	−	0.771949i	$-0.719282\pi$
$751$	−2.68437	+	1.95031i	−0.0979541	+	0.0711678i	0.537730	+	0.843117i	$0.319282\pi$
$752$		0			0
$753$	4.42030	+	13.6043i	0.161085	+	0.495768i
$754$		0			0
$755$	−37.7278	+	51.9279i	−1.37306	+	1.88985i
$756$		0			0
$757$	−44.0405	−	14.3096i	−1.60068	−	0.520093i	−0.633405	−	0.773820i	$-0.718343\pi$
$757$	−44.0405	−	14.3096i	−1.60068	−	0.520093i	−0.967276	+	0.253728i	$0.918343\pi$
$758$		0			0
$759$	7.32793	+	2.16189i	0.265987	+	0.0784718i
$760$		0			0
$761$	−15.1914	+	46.7544i	−0.550689	+	1.69485i	0.156375	+	0.987698i	$0.450019\pi$
$761$	−15.1914	+	46.7544i	−0.550689	+	1.69485i	−0.707064	+	0.707149i	$0.749981\pi$
$762$		0			0
$763$	38.5391	−	53.0446i	1.39521	−	1.92034i
$764$		0			0
$765$	−94.4827	+	30.6993i	−3.41603	+	1.10993i
$766$		0			0
$767$	−23.0835	+	16.7711i	−0.833497	+	0.605571i
$768$		0			0
$769$	7.45393			0.268796			0.134398	−	0.990927i	$-0.457090\pi$
$769$	7.45393			0.268796			0.134398	+	0.990927i	$0.457090\pi$
$770$		0			0
$771$			66.8170i			2.40636i
$772$		0			0
$773$	−5.06918	−	6.97713i	−0.182326	−	0.250950i	0.708065	−	0.706148i	$-0.249569\pi$
$773$	−5.06918	−	6.97713i	−0.182326	−	0.250950i	−0.890390	+	0.455198i	$0.849569\pi$
$774$		0			0
$775$	9.88464	+	30.4218i	0.355067	+	1.09278i
$776$		0			0
$777$	−43.5820	−	31.6642i	−1.56350	−	1.13595i
$778$		0			0
$779$	0.931413	+	0.302634i	0.0333713	+	0.0108430i
$780$		0			0
$781$	1.54140	+	1.05689i	0.0551558	+	0.0378185i
$782$		0			0
$783$	21.7989	−	67.0900i	0.779028	−	2.39760i
$784$		0			0
$785$	12.8355	+	9.32555i	0.458120	+	0.332843i
$786$		0			0
$787$	−16.7867	+	5.45433i	−0.598381	+	0.194426i	−0.592518	−	0.805557i	$-0.701866\pi$
$787$	−16.7867	+	5.45433i	−0.598381	+	0.194426i	−0.00586299	+	0.999983i	$0.501866\pi$
$788$		0			0
$789$	−10.2657	−	14.1295i	−0.365468	−	0.503024i
$790$		0			0
$791$	−51.1736			−1.81952
$792$		0			0
$793$	33.7980			1.20020
$794$		0			0
$795$	−4.05039	−	5.57488i	−0.143652	−	0.197721i
$796$		0			0
$797$	6.35405	−	2.06456i	0.225072	−	0.0731303i	−0.194310	−	0.980940i	$-0.562247\pi$
$797$	6.35405	−	2.06456i	0.225072	−	0.0731303i	0.419382	+	0.907810i	$0.362247\pi$
$798$		0			0
$799$	35.3701	+	25.6979i	1.25130	+	0.909126i
$800$		0			0
$801$	−4.56153	+	14.0390i	−0.161174	+	0.496042i
$802$		0			0
$803$	−21.8520	+	0.596197i	−0.771142	+	0.0210393i
$804$		0			0
$805$	−7.51549	−	2.44193i	−0.264886	−	0.0860668i
$806$		0			0
$807$	32.1434	+	23.3536i	1.13150	+	0.822085i
$808$		0			0
$809$	5.48389	+	16.8777i	0.192803	+	0.593387i	0.999995	+	0.00309827i	$0.000986212\pi$
$809$	5.48389	+	16.8777i	0.192803	+	0.593387i	−0.807192	+	0.590289i	$0.799014\pi$
$810$		0			0
$811$	10.5724	+	14.5516i	0.371246	+	0.510976i	0.953239	−	0.302218i	$-0.0977270\pi$
$811$	10.5724	+	14.5516i	0.371246	+	0.510976i	−0.581993	+	0.813194i	$0.697727\pi$
$812$		0			0
$813$			17.7167i			0.621351i
$814$		0			0
$815$	48.7664			1.70821
$816$		0			0
$817$	−2.73150	+	1.98455i	−0.0955630	+	0.0694306i
$818$		0			0
$819$	69.2878	−	22.5130i	2.42111	−	0.786667i
$820$		0			0
$821$	5.56382	−	7.65794i	0.194179	−	0.267264i	−0.700815	−	0.713343i	$-0.747180\pi$
$821$	5.56382	−	7.65794i	0.194179	−	0.267264i	0.894993	+	0.446079i	$0.147180\pi$
$822$		0			0
$823$	−10.2922	+	31.6763i	−0.358765	+	1.10417i	0.595029	+	0.803704i	$0.297141\pi$
$823$	−10.2922	+	31.6763i	−0.358765	+	1.10417i	−0.953794	+	0.300461i	$0.902859\pi$
$824$		0			0
$825$	−35.0813	+	12.4662i	−1.22137	+	0.434019i
$826$		0			0
$827$	2.47115	+	0.802925i	0.0859303	+	0.0279204i	0.351667	−	0.936125i	$-0.385615\pi$
$827$	2.47115	+	0.802925i	0.0859303	+	0.0279204i	−0.265736	+	0.964046i	$0.585615\pi$
$828$		0			0
$829$	−16.9864	+	23.3798i	−0.589963	+	0.812015i	−0.994743	−	0.102399i	$-0.967348\pi$
$829$	−16.9864	+	23.3798i	−0.589963	+	0.812015i	0.404780	+	0.914414i	$0.367348\pi$
$830$		0			0
$831$	22.3599	+	68.8168i	0.775658	+	2.38723i
$832$		0			0
$833$	23.5172	−	17.0862i	0.814822	−	0.592003i
$834$		0			0
$835$		−	1.22660i		−	0.0424481i
$836$		0			0
$837$		−	80.0672i		−	2.76753i
$838$		0			0
$839$	36.0851	−	26.2174i	1.24580	−	0.905124i	0.247826	−	0.968805i	$-0.420284\pi$
$839$	36.0851	−	26.2174i	1.24580	−	0.905124i	0.997970	+	0.0636808i	$0.0202839\pi$
$840$		0			0
$841$	−8.74505	−	26.9145i	−0.301553	−	0.928086i
$842$		0			0
$843$	42.1281	−	57.9844i	1.45097	−	1.99709i
$844$		0			0
$845$	3.74670	+	1.21738i	0.128891	+	0.0418791i
$846$		0			0
$847$	−29.8836	+	24.3080i	−1.02681	+	0.835232i
$848$		0			0
$849$	16.8785	−	51.9468i	0.579270	−	1.78281i
$850$		0			0
$851$	−2.29119	+	3.15356i	−0.0785411	+	0.108103i
$852$		0			0
$853$	9.90332	−	3.21778i	0.339083	−	0.110175i	−0.134526	−	0.990910i	$-0.542951\pi$
$853$	9.90332	−	3.21778i	0.339083	−	0.110175i	0.473609	+	0.880735i	$0.342951\pi$
$854$		0			0
$855$	−35.4242	+	25.7372i	−1.21148	+	0.880192i
$856$		0			0
$857$	−7.40316			−0.252887			−0.126444	−	0.991974i	$-0.540356\pi$
$857$	−7.40316			−0.252887			−0.126444	+	0.991974i	$0.540356\pi$
$858$		0			0
$859$			41.8774i			1.42884i	0.699719	+	0.714419i	$0.253309\pi$
$859$			41.8774i			1.42884i	−0.699719	+	0.714419i	$0.746691\pi$
$860$		0			0
$861$	2.49710	+	3.43696i	0.0851008	+	0.117131i
$862$		0			0
$863$	6.88730	+	21.1969i	0.234446	+	0.721551i	0.997194	+	0.0748557i	$0.0238496\pi$
$863$	6.88730	+	21.1969i	0.234446	+	0.721551i	−0.762748	+	0.646696i	$0.776150\pi$
$864$		0			0
$865$	−22.9055	−	16.6418i	−0.778810	−	0.565839i
$866$		0			0
$867$	−38.7058	−	12.5763i	−1.31452	−	0.427113i
$868$		0			0
$869$	−4.20780	−	11.8412i	−0.142740	−	0.401685i
$870$		0			0
$871$	−13.4015	+	41.2456i	−0.454093	+	1.39756i
$872$		0			0
$873$	−33.1016	−	24.0497i	−1.12032	−	0.813960i
$874$		0			0
$875$	−12.5610	+	4.08131i	−0.424638	+	0.137973i
$876$		0			0
$877$	1.86882	+	2.57221i	0.0631055	+	0.0868573i	0.839403	−	0.543509i	$-0.182905\pi$
$877$	1.86882	+	2.57221i	0.0631055	+	0.0868573i	−0.776298	+	0.630366i	$0.782905\pi$
$878$		0			0
$879$	−4.98626			−0.168183
$880$		0			0
$881$	38.8297			1.30821			0.654103	−	0.756405i	$-0.273046\pi$
$881$	38.8297			1.30821			0.654103	+	0.756405i	$0.273046\pi$
$882$		0			0
$883$	11.6689	+	16.0608i	0.392689	+	0.540489i	0.958890	−	0.283777i	$-0.0915876\pi$
$883$	11.6689	+	16.0608i	0.392689	+	0.540489i	−0.566202	+	0.824267i	$0.691588\pi$
$884$		0			0
$885$	70.7493	−	22.9879i	2.37821	−	0.772728i
$886$		0			0
$887$	−33.4294	−	24.2879i	−1.12245	−	0.815508i	−0.137872	−	0.990450i	$-0.544026\pi$
$887$	−33.4294	−	24.2879i	−1.12245	−	0.815508i	−0.984579	+	0.174942i	$0.944026\pi$
$888$		0			0
$889$	−10.6541	+	32.7898i	−0.357326	+	1.09974i
$890$		0			0
$891$	32.5759	−	0.888780i	1.09133	−	0.0297752i
$892$		0			0
$893$	18.3266	+	5.95467i	0.613275	+	0.199265i
$894$		0			0
$895$	−4.54554	−	3.30253i	−0.151941	−	0.110391i
$896$		0			0
$897$	−2.43138	−	7.48303i	−0.0811815	−	0.249851i
$898$		0			0
$899$	−38.2273	−	52.6153i	−1.27495	−	1.75482i
$900$		0			0
$901$		−	4.27344i		−	0.142369i
$902$		0			0
$903$	−14.6462			−0.487394
$904$		0			0
$905$	−22.2185	+	16.1427i	−0.738568	+	0.536601i
$906$		0			0
$907$	−22.3241	+	7.25354i	−0.741260	+	0.240850i	−0.655216	−	0.755442i	$-0.727422\pi$
$907$	−22.3241	+	7.25354i	−0.741260	+	0.240850i	−0.0860435	+	0.996291i	$0.527422\pi$
$908$		0			0
$909$	9.17954	−	12.6345i	0.304466	−	0.419062i
$910$		0			0
$911$	−10.5363	+	32.4276i	−0.349085	+	1.07437i	0.610276	+	0.792189i	$0.291059\pi$
$911$	−10.5363	+	32.4276i	−0.349085	+	1.07437i	−0.959360	+	0.282184i	$0.908941\pi$
$912$		0			0
$913$	9.10722	−	13.2823i	0.301405	−	0.439579i
$914$		0			0
$915$	−83.8050	−	27.2299i	−2.77051	−	0.900192i
$916$		0			0
$917$	37.8245	−	52.0609i	1.24907	−	1.71920i
$918$		0			0
$919$	−15.7236	−	48.3923i	−0.518674	−	1.59632i	−0.776495	−	0.630123i	$-0.783004\pi$
$919$	−15.7236	−	48.3923i	−0.518674	−	1.59632i	0.257821	−	0.966193i	$-0.416996\pi$
$920$		0			0
$921$	−0.585685	+	0.425525i	−0.0192990	+	0.0140215i
$922$		0			0
$923$		−	1.92470i		−	0.0633523i
$924$		0			0
$925$		−	18.9949i		−	0.624548i
$926$		0			0
$927$	42.7300	−	31.0452i	1.40344	−	1.01966i
$928$		0			0
$929$	0.432862	+	1.33221i	0.0142017	+	0.0437085i	0.957906	−	0.287081i	$-0.0926849\pi$
$929$	0.432862	+	1.33221i	0.0142017	+	0.0437085i	−0.943705	+	0.330790i	$0.892685\pi$
$930$		0			0
$931$	7.53082	−	10.3653i	0.246813	−	0.339709i
$932$		0			0
$933$	−20.3119	−	6.59975i	−0.664983	−	0.216066i
$934$		0			0
$935$	−51.8852	−	15.3072i	−1.69683	−	0.500600i
$936$		0			0
$937$	−1.11285	+	3.42500i	−0.0363552	+	0.111890i	−0.967587	−	0.252537i	$-0.918735\pi$
$937$	−1.11285	+	3.42500i	−0.0363552	+	0.111890i	0.931232	+	0.364427i	$0.118735\pi$
$938$		0			0
$939$	19.2183	−	26.4517i	0.627165	−	0.863218i
$940$		0			0
$941$	23.4359	−	7.61478i	0.763988	−	0.248235i	0.0989988	−	0.995088i	$-0.468436\pi$
$941$	23.4359	−	7.61478i	0.763988	−	0.248235i	0.664989	+	0.746853i	$0.268436\pi$
$942$		0			0
$943$	0.248695	−	0.180688i	0.00809863	−	0.00588400i
$944$		0			0
$945$	−96.3876			−3.13549
$946$		0			0
$947$		−	25.2088i		−	0.819177i	−0.912270	−	0.409589i	$-0.865672\pi$
$947$		−	25.2088i		−	0.819177i	0.912270	−	0.409589i	$-0.134328\pi$
$948$		0			0
$949$	13.2324	+	18.2129i	0.429543	+	0.591215i
$950$		0			0
$951$	−10.0581	−	30.9556i	−0.326155	−	1.00380i
$952$		0			0
$953$	−13.2178	−	9.60326i	−0.428165	−	0.311080i	0.352750	−	0.935718i	$-0.385247\pi$
$953$	−13.2178	−	9.60326i	−0.428165	−	0.311080i	−0.780915	+	0.624638i	$0.785247\pi$
$954$		0			0
$955$	−12.6650	−	4.11510i	−0.409829	−	0.133162i
$956$		0			0
$957$	60.0032	−	46.1467i	1.93963	−	1.49171i
$958$		0			0
$959$	5.22435	−	16.0789i	0.168703	−	0.519215i
$960$		0			0
$961$	−34.6399	−	25.1673i	−1.11742	−	0.811850i
$962$		0			0
$963$	−0.625286	+	0.203168i	−0.0201496	+	0.00654699i
$964$		0			0
$965$	39.2353	+	54.0027i	1.26303	+	1.73841i
$966$		0			0
$967$	15.3536			0.493739			0.246869	−	0.969049i	$-0.420598\pi$
$967$	15.3536			0.493739			0.246869	+	0.969049i	$0.420598\pi$
$968$		0			0
$969$	−40.5293			−1.30199
$970$		0			0
$971$	3.85567	+	5.30688i	0.123734	+	0.170306i	0.866390	−	0.499367i	$-0.166434\pi$
$971$	3.85567	+	5.30688i	0.123734	+	0.170306i	−0.742656	+	0.669673i	$0.766434\pi$
$972$		0			0
$973$	6.40928	−	2.08250i	0.205472	−	0.0667619i
$974$		0			0
$975$	31.0186	+	22.5364i	0.993391	+	0.721741i
$976$		0			0
$977$	10.6624	−	32.8154i	0.341119	−	1.04986i	−0.622509	−	0.782612i	$-0.713887\pi$
$977$	10.6624	−	32.8154i	0.341119	−	1.04986i	0.963629	−	0.267245i	$-0.0861133\pi$
$978$		0			0
$979$	−6.37162	+	4.90023i	−0.203638	+	0.156612i
$980$		0			0
$981$	−108.456	−	35.2396i	−3.46274	−	1.12511i
$982$		0			0
$983$	43.4103	+	31.5395i	1.38457	+	1.00595i	0.996436	+	0.0843513i	$0.0268818\pi$
$983$	43.4103	+	31.5395i	1.38457	+	1.00595i	0.388139	+	0.921601i	$0.373118\pi$
$984$		0			0
$985$	−9.28671	−	28.5815i	−0.295899	−	0.910684i
$986$		0			0
$987$	49.1331	+	67.6260i	1.56393	+	2.15256i
$988$		0			0
$989$			1.05978i			0.0336992i
$990$		0			0
$991$	−41.5423			−1.31963			−0.659817	−	0.751427i	$-0.729366\pi$
$991$	−41.5423			−1.31963			−0.659817	+	0.751427i	$0.729366\pi$
$992$		0			0
$993$	21.9126	−	15.9204i	0.695375	−	0.505220i
$994$		0			0
$995$	−7.54820	+	2.45256i	−0.239294	+	0.0777514i
$996$		0			0
$997$	−8.54127	+	11.7561i	−0.270505	+	0.372318i	−0.922560	−	0.385854i	$-0.873907\pi$
$997$	−8.54127	+	11.7561i	−0.270505	+	0.372318i	0.652055	+	0.758171i	$0.273907\pi$
$998$		0			0
$999$	−14.6925	+	45.2188i	−0.464850	+	1.43066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.w.c.97.15	yes	64
4.3	odd	2	inner	704.2.w.c.97.1	✓	64
8.3	odd	2	inner	704.2.w.c.97.16	yes	64
8.5	even	2	inner	704.2.w.c.97.2	yes	64
11.5	even	5	inner	704.2.w.c.225.2	yes	64
44.27	odd	10	inner	704.2.w.c.225.16	yes	64
88.5	even	10	inner	704.2.w.c.225.15	yes	64
88.27	odd	10	inner	704.2.w.c.225.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
704.2.w.c.97.1	✓	64	4.3	odd	2	inner
704.2.w.c.97.2	yes	64	8.5	even	2	inner
704.2.w.c.97.15	yes	64	1.1	even	1	trivial
704.2.w.c.97.16	yes	64	8.3	odd	2	inner
704.2.w.c.225.1	yes	64	88.27	odd	10	inner
704.2.w.c.225.2	yes	64	11.5	even	5	inner
704.2.w.c.225.15	yes	64	88.5	even	10	inner
704.2.w.c.225.16	yes	64	44.27	odd	10	inner

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:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.77223 + 2.43927i) q^{3} +(-2.80893 + 0.912676i) q^{5} +(-2.83314 - 2.05840i) q^{7} +(-1.88217 + 5.79272i) q^{9} +O(q^{10})\)	\(q+(1.77223 + 2.43927i) q^{3} +(-2.80893 + 0.912676i) q^{5} +(-2.83314 - 2.05840i) q^{7} +(-1.88217 + 5.79272i) q^{9} +(-2.62904 + 2.02192i) q^{11} +(3.24840 + 1.05547i) q^{13} +(-7.20433 - 5.23425i) q^{15} +(-1.70655 - 5.25221i) q^{17} +(-1.43071 - 1.96920i) q^{19} -10.5588i q^{21} -0.764022 q^{23} +(3.01202 - 2.18836i) q^{25} +(-8.86303 + 2.87977i) q^{27} +(-4.44933 + 6.12397i) q^{29} +(-2.65498 + 8.17119i) q^{31} +(-9.59126 - 2.82962i) q^{33} +(9.83675 + 3.19615i) q^{35} +(2.99886 - 4.12757i) q^{37} +(3.18235 + 9.79426i) q^{39} +(-0.325508 + 0.236495i) q^{41} -1.38711i q^{43} -17.9891i q^{45} +(-6.40473 + 4.65331i) q^{47} +(1.62658 + 5.00609i) q^{49} +(9.78714 - 13.4708i) q^{51} +(0.735950 + 0.239125i) q^{53} +(5.53943 - 8.07888i) q^{55} +(2.26786 - 6.97975i) q^{57} +(-4.91020 + 6.75831i) q^{59} +(9.41096 - 3.05780i) q^{61} +(17.2562 - 12.5373i) q^{63} -10.0878 q^{65} +12.6972i q^{67} +(-1.35402 - 1.86365i) q^{69} +(-0.174133 - 0.535927i) q^{71} +(5.33230 + 3.87415i) q^{73} +(10.6760 + 3.46883i) q^{75} +(11.6104 - 0.316770i) q^{77} +(-1.17086 + 3.60353i) q^{79} +(-7.94913 - 5.77538i) q^{81} +(-4.61808 + 1.50050i) q^{83} +(9.58713 + 13.1955i) q^{85} -22.8232 q^{87} +2.42355 q^{89} +(-7.03061 - 9.67681i) q^{91} +(-24.6369 + 8.00503i) q^{93} +(5.81599 + 4.22556i) q^{95} +(-2.07586 + 6.38884i) q^{97} +(-6.76410 - 19.0349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 12 q^{9}+O(q^{10}) \) 64 * q - 12 * q^9	\( 64 q - 12 q^{9} - 20 q^{17} + 12 q^{25} - 96 q^{33} - 36 q^{41} + 68 q^{49} + 96 q^{57} + 168 q^{65} + 4 q^{73} + 8 q^{81} - 24 q^{89} - 152 q^{97}+O(q^{100}) \) 64 * q - 12 * q^9 - 20 * q^17 + 12 * q^25 - 96 * q^33 - 36 * q^41 + 68 * q^49 + 96 * q^57 + 168 * q^65 + 4 * q^73 + 8 * q^81 - 24 * q^89 - 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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