LMFDB - Embedded newform 99.2.j.a.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(8,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.j (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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 $ x^16 + 2x^14 - 16x^12 - 72x^10 + 26x^8 + 360x^6 + 725x^4 + 1000*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			35.3
Root			$-1.90184 + 0.0324487i$ of defining polynomial
Character	$\chi$	$=$	99.35
Dual form			99.2.j.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212694 - 0.654604i) q^{2} +(1.23477 + 0.897110i) q^{4} +(-0.0381457 + 0.0123943i) q^{5} +(0.145094 - 0.199704i) q^{7} +(1.96356 - 1.42661i) q^{8} +0.0276065i q^{10} +(-3.12033 - 1.12407i) q^{11} +(-2.18888 - 0.711209i) q^{13} +(-0.0998667 - 0.137455i) q^{14} +(0.427051 + 1.31433i) q^{16} +(1.32142 + 4.06692i) q^{17} +(-3.64429 - 5.01593i) q^{19} +(-0.0582200 - 0.0189168i) q^{20} +(-1.39949 + 1.80350i) q^{22} +6.79984i q^{23} +(-4.04378 + 2.93798i) q^{25} +(-0.931121 + 1.28158i) q^{26} +(0.358314 - 0.116423i) q^{28} +(-4.52705 - 3.28909i) q^{29} +(1.48247 - 4.56258i) q^{31} +5.80538 q^{32} +2.94328 q^{34} +(-0.00305951 + 0.00941619i) q^{35} +(3.26102 + 2.36927i) q^{37} +(-4.05857 + 1.31871i) q^{38} +(-0.0572194 + 0.0787558i) q^{40} +(7.76893 - 5.64446i) q^{41} -1.03166i q^{43} +(-2.84447 - 4.18724i) q^{44} +(4.45120 + 1.44628i) q^{46} +(-6.53982 - 9.00129i) q^{47} +(2.14429 + 6.59944i) q^{49} +(1.06313 + 3.27197i) q^{50} +(-2.06472 - 2.84184i) q^{52} +(8.52885 + 2.77119i) q^{53} +(0.132959 + 0.00420408i) q^{55} -0.599123i q^{56} +(-3.11593 + 2.26385i) q^{58} +(1.63893 - 2.25580i) q^{59} +(8.06923 - 2.62185i) q^{61} +(-2.67137 - 1.94086i) q^{62} +(0.380665 - 1.17156i) q^{64} +0.0923111 q^{65} +7.94588 q^{67} +(-2.01683 + 6.20715i) q^{68} +(0.00551314 + 0.00400553i) q^{70} +(-3.16559 + 1.02856i) q^{71} +(-6.96743 + 9.58984i) q^{73} +(2.24453 - 1.63075i) q^{74} -9.46284i q^{76} +(-0.677222 + 0.460048i) q^{77} +(-2.86363 - 0.930451i) q^{79} +(-0.0325803 - 0.0448429i) q^{80} +(-2.04248 - 6.28611i) q^{82} +(1.63587 + 5.03470i) q^{83} +(-0.100813 - 0.138757i) q^{85} +(-0.675331 - 0.219428i) q^{86} +(-7.73055 + 2.24432i) q^{88} +8.54422i q^{89} +(-0.459624 + 0.333936i) q^{91} +(-6.10021 + 8.39621i) q^{92} +(-7.28326 + 2.36647i) q^{94} +(0.201183 + 0.146168i) q^{95} +(-0.935778 + 2.88003i) q^{97} +4.77610 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70}+ \cdots + 60 q^{97}+O(q^{100}) $ 16 * q - 4 * q^4 - 20 * q^16 - 48 * q^22 - 32 * q^25 + 40 * q^28 + 16 * q^31 + 40 * q^34 - 12 * q^37 + 60 * q^40 - 40 * q^46 - 24 * q^49 - 40 * q^52 + 16 * q^55 + 12 * q^58 + 36 * q^64 + 96 * q^67 + 76 * q^70 - 20 * q^73 - 12 * q^82 - 100 * q^85 - 12 * q^88 - 72 * q^91 - 80 * q^94 + 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

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 $

$2$	0.212694	−	0.654604i	0.150397	−	0.462875i	−0.847268	−	0.531165i	$-0.821754\pi$
$2$	0.212694	−	0.654604i	0.150397	−	0.462875i	0.997665	+	0.0682903i	$0.0217544\pi$
$3$		0			0
$3$		0			0
$4$	1.23477	+	0.897110i	0.617383	+	0.448555i
$5$	−0.0381457	+	0.0123943i	−0.0170593	+	0.00554289i	−0.317534	−	0.948247i	$-0.602855\pi$
$5$	−0.0381457	+	0.0123943i	−0.0170593	+	0.00554289i	0.300475	+	0.953790i	$0.402855\pi$
$6$		0			0
$7$	0.145094	−	0.199704i	0.0548403	−	0.0754811i	−0.780716	−	0.624886i	$-0.785145\pi$
$7$	0.145094	−	0.199704i	0.0548403	−	0.0754811i	0.835556	+	0.549405i	$0.185145\pi$
$8$	1.96356	−	1.42661i	0.694222	−	0.504382i
$9$		0			0
$10$			0.0276065i			0.00872994i
$11$	−3.12033	−	1.12407i	−0.940815	−	0.338919i
$11$	−3.12033	−	1.12407i	−0.940815	−	0.338919i
$12$		0			0
$13$	−2.18888	−	0.711209i	−0.607085	−	0.197254i	−0.0106874	−	0.999943i	$-0.503402\pi$
$13$	−2.18888	−	0.711209i	−0.607085	−	0.197254i	−0.596398	+	0.802689i	$0.703402\pi$
$14$	−0.0998667	−	0.137455i	−0.0266905	−	0.0367363i
$15$		0			0
$16$	0.427051	+	1.31433i	0.106763	+	0.328582i
$17$	1.32142	+	4.06692i	0.320492	+	0.986372i	0.973435	+	0.228965i	$0.0735342\pi$
$17$	1.32142	+	4.06692i	0.320492	+	0.986372i	−0.652943	+	0.757407i	$0.726466\pi$
$18$		0			0
$19$	−3.64429	−	5.01593i	−0.836057	−	1.15073i	−0.986765	−	0.162156i	$-0.948155\pi$
$19$	−3.64429	−	5.01593i	−0.836057	−	1.15073i	0.150708	−	0.988578i	$-0.451845\pi$
$20$	−0.0582200	−	0.0189168i	−0.0130184	−	0.00422993i
$21$		0			0
$22$	−1.39949	+	1.80350i	−0.298373	+	0.384507i
$23$			6.79984i			1.41786i	0.705277	+	0.708932i	$0.250823\pi$
$23$			6.79984i			1.41786i	−0.705277	+	0.708932i	$0.749177\pi$
$24$		0			0
$25$	−4.04378	+	2.93798i	−0.808757	+	0.587596i
$26$	−0.931121	+	1.28158i	−0.182608	+	0.251338i
$27$		0			0
$28$	0.358314	−	0.116423i	0.0677149	−	0.0220019i
$29$	−4.52705	−	3.28909i	−0.840652	−	0.610769i	0.0819007	−	0.996640i	$-0.473901\pi$
$29$	−4.52705	−	3.28909i	−0.840652	−	0.610769i	−0.922553	+	0.385871i	$0.873901\pi$
$30$		0			0
$31$	1.48247	−	4.56258i	0.266260	−	0.819463i	−0.725141	−	0.688601i	$-0.758225\pi$
$31$	1.48247	−	4.56258i	0.266260	−	0.819463i	0.991401	−	0.130863i	$-0.0417747\pi$
$32$	5.80538			1.02626
$33$		0			0
$34$	2.94328			0.504768
$35$	−0.00305951	+	0.00941619i	−0.000517151	+	0.00159163i
$36$		0			0
$37$	3.26102	+	2.36927i	0.536109	+	0.389506i	0.822638	−	0.568566i	$-0.192502\pi$
$37$	3.26102	+	2.36927i	0.536109	+	0.389506i	−0.286529	+	0.958072i	$0.592502\pi$
$38$	−4.05857	+	1.31871i	−0.658386	+	0.213923i
$39$		0			0
$40$	−0.0572194	+	0.0787558i	−0.00904719	+	0.0124524i
$41$	7.76893	−	5.64446i	1.21330	−	0.881517i	0.217777	−	0.975999i	$-0.430119\pi$
$41$	7.76893	−	5.64446i	1.21330	−	0.881517i	0.995527	+	0.0944820i	$0.0301195\pi$
$42$		0			0
$43$		−	1.03166i		−	0.157327i	−0.996901	−	0.0786636i	$-0.974935\pi$
$43$		−	1.03166i		−	0.157327i	0.996901	−	0.0786636i	$-0.0250653\pi$
$44$	−2.84447	−	4.18724i	−0.428820	−	0.631251i
$45$		0			0
$46$	4.45120	+	1.44628i	0.656294	+	0.213243i
$47$	−6.53982	−	9.00129i	−0.953931	−	1.31297i	−0.949759	−	0.312982i	$-0.898672\pi$
$47$	−6.53982	−	9.00129i	−0.953931	−	1.31297i	−0.00417211	−	0.999991i	$-0.501328\pi$
$48$		0			0
$49$	2.14429	+	6.59944i	0.306327	+	0.942778i
$50$	1.06313	+	3.27197i	0.150349	+	0.462726i
$51$		0			0
$52$	−2.06472	−	2.84184i	−0.286325	−	0.394093i
$53$	8.52885	+	2.77119i	1.17153	+	0.380652i	0.829213	−	0.558933i	$-0.188789\pi$
$53$	8.52885	+	2.77119i	1.17153	+	0.380652i	0.342314	+	0.939585i	$0.388789\pi$
$54$		0			0
$55$	0.132959	+	0.00420408i	0.0179282	+	0.000566878i
$56$		−	0.599123i		−	0.0800611i
$57$		0			0
$58$	−3.11593	+	2.26385i	−0.409141	+	0.297259i
$59$	1.63893	−	2.25580i	0.213371	−	0.293680i	−0.688894	−	0.724862i	$-0.741903\pi$
$59$	1.63893	−	2.25580i	0.213371	−	0.293680i	0.902265	+	0.431182i	$0.141903\pi$
$60$		0			0
$61$	8.06923	−	2.62185i	1.03316	−	0.335694i	0.257121	−	0.966379i	$-0.417226\pi$
$61$	8.06923	−	2.62185i	1.03316	−	0.335694i	0.776039	+	0.630685i	$0.217226\pi$
$62$	−2.67137	−	1.94086i	−0.339264	−	0.246490i
$63$		0			0
$64$	0.380665	−	1.17156i	0.0475831	−	0.146446i
$65$	0.0923111			0.0114498
$66$		0			0
$67$	7.94588			0.970744			0.485372	−	0.874308i	$-0.338684\pi$
$67$	7.94588			0.970744			0.485372	+	0.874308i	$0.338684\pi$
$68$	−2.01683	+	6.20715i	−0.244576	+	0.752728i
$69$		0			0
$70$	0.00551314	+	0.00400553i	0.000658946	+	0.000478752i
$71$	−3.16559	+	1.02856i	−0.375687	+	0.122068i	−0.490773	−	0.871288i	$-0.663286\pi$
$71$	−3.16559	+	1.02856i	−0.375687	+	0.122068i	0.115086	+	0.993355i	$0.463286\pi$
$72$		0			0
$73$	−6.96743	+	9.58984i	−0.815476	+	1.12241i	0.174980	+	0.984572i	$0.444014\pi$
$73$	−6.96743	+	9.58984i	−0.815476	+	1.12241i	−0.990455	+	0.137834i	$0.955986\pi$
$74$	2.24453	−	1.63075i	0.260922	−	0.189571i
$75$		0			0
$76$		−	9.46284i		−	1.08546i
$77$	−0.677222	+	0.460048i	−0.0771766	+	0.0524274i
$78$		0			0
$79$	−2.86363	−	0.930451i	−0.322184	−	0.104684i	0.143460	−	0.989656i	$-0.454177\pi$
$79$	−2.86363	−	0.930451i	−0.322184	−	0.104684i	−0.465644	+	0.884972i	$0.654177\pi$
$80$	−0.0325803	−	0.0448429i	−0.00364259	−	0.00501359i
$81$		0			0
$82$	−2.04248	−	6.28611i	−0.225554	−	0.694185i
$83$	1.63587	+	5.03470i	0.179560	+	0.552630i	0.999812	−	0.0193724i	$-0.00616680\pi$
$83$	1.63587	+	5.03470i	0.179560	+	0.552630i	−0.820252	+	0.572002i	$0.806167\pi$
$84$		0			0
$85$	−0.100813	−	0.138757i	−0.0109347	−	0.0150503i
$86$	−0.675331	−	0.219428i	−0.0728228	−	0.0236616i
$87$		0			0
$88$	−7.73055	+	2.24432i	−0.824080	+	0.239245i
$89$			8.54422i			0.905686i	0.891590	+	0.452843i	$0.149590\pi$
$89$			8.54422i			0.905686i	−0.891590	+	0.452843i	$0.850410\pi$
$90$		0			0
$91$	−0.459624	+	0.333936i	−0.0481817	+	0.0350060i
$92$	−6.10021	+	8.39621i	−0.635991	+	0.875366i
$93$		0			0
$94$	−7.28326	+	2.36647i	−0.751211	+	0.244083i
$95$	0.201183	+	0.146168i	0.0206409	+	0.0149965i
$96$		0			0
$97$	−0.935778	+	2.88003i	−0.0950139	+	0.292423i	−0.987257	−	0.159132i	$-0.949130\pi$
$97$	−0.935778	+	2.88003i	−0.0950139	+	0.292423i	0.892243	+	0.451555i	$0.149130\pi$
$98$	4.77610			0.482459
$99$		0			0
$100$	−7.62882			−0.762882
$101$	2.14828	−	6.61172i	0.213762	−	0.657891i	−0.785477	−	0.618890i	$-0.787583\pi$
$101$	2.14828	−	6.61172i	0.213762	−	0.657891i	0.999239	−	0.0390007i	$-0.0124175\pi$
$102$		0			0
$103$	−10.6138	−	7.71139i	−1.04581	−	0.759826i	−0.0743996	−	0.997229i	$-0.523704\pi$
$103$	−10.6138	−	7.71139i	−1.04581	−	0.759826i	−0.971411	+	0.237402i	$0.923704\pi$
$104$	−5.31260	+	1.72617i	−0.520944	+	0.169265i
$105$		0			0
$106$	3.62806	−	4.99360i	0.352389	−	0.485021i
$107$	1.10712	−	0.804368i	0.107029	−	0.0777612i	−0.532983	−	0.846126i	$-0.678929\pi$
$107$	1.10712	−	0.804368i	0.107029	−	0.0777612i	0.640012	+	0.768365i	$0.278929\pi$
$108$		0			0
$109$			7.34454i			0.703480i	0.936098	+	0.351740i	$0.114410\pi$
$109$			7.34454i			0.703480i	−0.936098	+	0.351740i	$0.885590\pi$
$110$	0.0310316	−	0.0861414i	0.00295875	−	0.00821326i
$111$		0			0
$112$	0.324439	+	0.105417i	0.0306566	+	0.00996094i
$113$	−0.310669	−	0.427600i	−0.0292253	−	0.0402252i	0.794154	−	0.607716i	$-0.207914\pi$
$113$	−0.310669	−	0.427600i	−0.0292253	−	0.0402252i	−0.823380	+	0.567491i	$0.807914\pi$
$114$		0			0
$115$	−0.0842791	−	0.259385i	−0.00785907	−	0.0241877i
$116$	−2.63917	−	8.12253i	−0.245041	−	0.754158i
$117$		0			0
$118$	−1.12806	−	1.55265i	−0.103847	−	0.142933i
$119$	1.00391	+	0.326190i	0.0920284	+	0.0299018i
$120$		0			0
$121$	8.47294	+	7.01493i	0.770267	+	0.637721i
$122$		−	5.83980i		−	0.528711i
$123$		0			0
$124$	5.92364	−	4.30378i	0.531959	−	0.386491i
$125$	0.235715	−	0.324434i	0.0210830	−	0.0290183i
$126$		0			0
$127$	12.1468	−	3.94673i	1.07785	−	0.350215i	0.284311	−	0.958732i	$-0.408235\pi$
$127$	12.1468	−	3.94673i	1.07785	−	0.350215i	0.793541	+	0.608517i	$0.208235\pi$
$128$	8.70735	+	6.32626i	0.769628	+	0.559168i
$129$		0			0
$130$	0.0196340	−	0.0604272i	0.00172202	−	0.00529982i
$131$	−18.1534			−1.58607			−0.793033	−	0.609178i	$-0.791499\pi$
$131$	−18.1534			−1.58607			−0.793033	+	0.609178i	$0.791499\pi$
$132$		0			0
$133$	−1.53047			−0.132708
$134$	1.69004	−	5.20140i	0.145997	−	0.449333i
$135$		0			0
$136$	8.39658	+	6.10048i	0.720001	+	0.523111i
$137$	15.2863	−	4.96682i	1.30600	−	0.424344i	0.428334	−	0.903621i	$-0.359101\pi$
$137$	15.2863	−	4.96682i	1.30600	−	0.424344i	0.877664	+	0.479276i	$0.159101\pi$
$138$		0			0
$139$	2.26727	−	3.12062i	0.192307	−	0.264688i	−0.701965	−	0.712211i	$-0.747694\pi$
$139$	2.26727	−	3.12062i	0.192307	−	0.264688i	0.894272	+	0.447523i	$0.147694\pi$
$140$	−0.0122251	+	0.00888208i	−0.00103321	+	0.000750673i
$141$		0			0
$142$			2.29098i			0.192255i
$143$	6.03057	+	4.67966i	0.504302	+	0.391333i
$144$		0			0
$145$	0.213453	+	0.0693552i	0.0177263	+	0.00575964i
$146$	4.79562	+	6.60060i	0.396888	+	0.546270i
$147$		0			0
$148$	1.90110	+	5.85099i	0.156270	+	0.480949i
$149$	−3.17360	−	9.76734i	−0.259992	−	0.800172i	−0.992805	−	0.119742i	$-0.961793\pi$
$149$	−3.17360	−	9.76734i	−0.259992	−	0.800172i	0.732813	−	0.680430i	$-0.238207\pi$
$150$		0			0
$151$	5.15512	+	7.09542i	0.419518	+	0.577417i	0.965508	−	0.260375i	$-0.0838462\pi$
$151$	5.15512	+	7.09542i	0.419518	+	0.577417i	−0.545990	+	0.837792i	$0.683846\pi$
$152$	−14.3115	−	4.65010i	−1.16082	−	0.377173i
$153$		0			0
$154$	0.157109	+	0.541161i	0.0126602	+	0.0436080i
$155$			0.192417i			0.0154553i
$156$		0			0
$157$	10.5422	−	7.65934i	0.841357	−	0.611282i	−0.0813923	−	0.996682i	$-0.525937\pi$
$157$	10.5422	−	7.65934i	0.841357	−	0.611282i	0.922749	+	0.385400i	$0.125937\pi$
$158$	−1.21815	+	1.67664i	−0.0969111	+	0.133387i
$159$		0			0
$160$	−0.221450	+	0.0719535i	−0.0175072	+	0.00568842i
$161$	1.35796	+	0.986614i	0.107022	+	0.0777561i
$162$		0			0
$163$	−2.83608	+	8.72855i	−0.222139	+	0.683673i	0.776431	+	0.630203i	$0.217028\pi$
$163$	−2.83608	+	8.72855i	−0.222139	+	0.683673i	−0.998569	+	0.0534700i	$0.982972\pi$
$164$	14.6565			1.14448
$165$		0			0
$166$	3.64367			0.282804
$167$	2.35141	−	7.23691i	0.181958	−	0.560009i	−0.817925	−	0.575325i	$-0.804876\pi$
$167$	2.35141	−	7.23691i	0.181958	−	0.560009i	0.999883	+	0.0153164i	$0.00487554\pi$
$168$		0			0
$169$	−6.23186	−	4.52771i	−0.479374	−	0.348285i
$170$	−0.112273	+	0.0364798i	−0.00861097	+	0.00279787i
$171$		0			0
$172$	0.925516	−	1.27386i	0.0705699	−	0.0971312i
$173$	−13.4462	+	9.76923i	−1.02230	+	0.742741i	−0.966752	−	0.255715i	$-0.917689\pi$
$173$	−13.4462	+	9.76923i	−1.02230	+	0.742741i	−0.0555432	+	0.998456i	$0.517689\pi$
$174$		0			0
$175$			1.23384i			0.0932698i
$176$	0.144854	−	4.58117i	0.0109188	−	0.345319i
$177$		0			0
$178$	5.59308	+	1.81730i	0.419219	+	0.136213i
$179$	4.14376	+	5.70340i	0.309719	+	0.426292i	0.935294	−	0.353872i	$-0.115135\pi$
$179$	4.14376	+	5.70340i	0.309719	+	0.426292i	−0.625574	+	0.780165i	$0.715135\pi$
$180$		0			0
$181$	−6.52756	−	20.0898i	−0.485189	−	1.49326i	−0.831706	−	0.555216i	$-0.812636\pi$
$181$	−6.52756	−	20.0898i	−0.485189	−	1.49326i	0.346517	−	0.938044i	$-0.387364\pi$
$182$	0.120837	+	0.371898i	0.00895702	+	0.0275669i
$183$		0			0
$184$	9.70070	+	13.3519i	0.715145	+	0.984313i
$185$	−0.153759	−	0.0499594i	−0.0113046	−	0.00367309i
$186$		0			0
$187$	0.448220	−	14.1755i	0.0327771	−	1.03662i
$188$		−	16.9814i		−	1.23850i
$189$		0			0
$190$	0.138472	−	0.100606i	0.0100458	−	0.00729873i
$191$	8.03400	−	11.0579i	0.581320	−	0.800118i	−0.412519	−	0.910949i	$-0.635351\pi$
$191$	8.03400	−	11.0579i	0.581320	−	0.800118i	0.993839	+	0.110831i	$0.0353511\pi$
$192$		0			0
$193$	−23.8096	+	7.73620i	−1.71385	+	0.556864i	−0.990967	−	0.134105i	$-0.957184\pi$
$193$	−23.8096	+	7.73620i	−1.71385	+	0.556864i	−0.722884	+	0.690969i	$0.757184\pi$
$194$	1.68624	+	1.22513i	0.121065	+	0.0879590i
$195$		0			0
$196$	−3.27273	+	10.0724i	−0.233767	+	0.719460i
$197$	−21.0442			−1.49934			−0.749668	−	0.661814i	$-0.769787\pi$
$197$	−21.0442			−1.49934			−0.749668	+	0.661814i	$0.769787\pi$
$198$		0			0
$199$	−10.3709			−0.735176			−0.367588	−	0.929989i	$-0.619816\pi$
$199$	−10.3709			−0.735176			−0.367588	+	0.929989i	$0.619816\pi$
$200$	−3.74885	+	11.5378i	−0.265084	+	0.815845i
$201$		0			0
$202$	−3.87113	−	2.81254i	−0.272372	−	0.197890i
$203$	−1.31369	+	0.426845i	−0.0922031	+	0.0299586i
$204$		0			0
$205$	−0.226392	+	0.311602i	−0.0158119	+	0.0217632i
$206$	−7.30540	+	5.30768i	−0.508991	+	0.369804i
$207$		0			0
$208$		−	3.18062i		−	0.220537i
$209$	5.73314	+	19.7478i	0.396569	+	1.36598i
$210$		0			0
$211$	−17.8262	−	5.79210i	−1.22721	−	0.398744i	−0.377506	−	0.926007i	$-0.623218\pi$
$211$	−17.8262	−	5.79210i	−1.22721	−	0.398744i	−0.849702	+	0.527263i	$0.823218\pi$
$212$	8.04507	+	11.0731i	0.552538	+	0.760503i
$213$		0			0
$214$	−0.291066	−	0.895808i	−0.0198968	−	0.0612361i
$215$	0.0127867	+	0.0393535i	0.000872048	+	0.00268389i
$216$		0			0
$217$	−0.696069	−	0.958057i	−0.0472523	−	0.0650372i
$218$	4.80776	+	1.56214i	0.325623	+	0.105801i
$219$		0			0
$220$	0.160402	+	0.124470i	0.0108143	+	0.00839178i
$221$		−	9.84179i		−	0.662031i
$222$		0			0
$223$	−7.82233	+	5.68326i	−0.523822	+	0.380579i	−0.818042	−	0.575159i	$-0.804940\pi$
$223$	−7.82233	+	5.68326i	−0.523822	+	0.380579i	0.294220	+	0.955738i	$0.404940\pi$
$224$	0.842323	−	1.15936i	0.0562801	−	0.0774629i
$225$		0			0
$226$	−0.345986	+	0.112418i	−0.0230146	+	0.00747791i
$227$	9.47859	+	6.88660i	0.629116	+	0.457080i	0.856094	−	0.516820i	$-0.172884\pi$
$227$	9.47859	+	6.88660i	0.629116	+	0.457080i	−0.226978	+	0.973900i	$0.572884\pi$
$228$		0			0
$229$	6.32872	−	19.4778i	0.418214	−	1.28713i	−0.491131	−	0.871086i	$-0.663416\pi$
$229$	6.32872	−	19.4778i	0.418214	−	1.28713i	0.909345	−	0.416044i	$-0.136584\pi$
$230$	−0.187720			−0.0123779
$231$		0			0
$232$	−13.5814			−0.891661
$233$	−4.98842	+	15.3528i	−0.326802	+	1.00579i	0.643818	+	0.765178i	$0.277349\pi$
$233$	−4.98842	+	15.3528i	−0.326802	+	1.00579i	−0.970621	+	0.240615i	$0.922651\pi$
$234$		0			0
$235$	0.361031	+	0.262304i	0.0235510	+	0.0171108i
$236$	4.04740	−	1.31508i	0.263463	−	0.0856044i
$237$		0			0
$238$	0.427051	−	0.587785i	0.0276816	−	0.0381005i
$239$	−22.9660	+	16.6858i	−1.48555	+	1.07931i	−0.509830	+	0.860275i	$0.670292\pi$
$239$	−22.9660	+	16.6858i	−1.48555	+	1.07931i	−0.975716	+	0.219038i	$0.929708\pi$
$240$		0			0
$241$			14.3654i			0.925357i	0.886526	+	0.462679i	$0.153112\pi$
$241$			14.3654i			0.925357i	−0.886526	+	0.462679i	$0.846888\pi$
$242$	6.39414	−	4.05439i	0.411031	−	0.260626i
$243$		0			0
$244$	12.3157	+	4.00162i	0.788433	+	0.256177i
$245$	−0.163591	−	0.225163i	−0.0104514	−	0.0143852i
$246$		0			0
$247$	4.40952	+	13.5711i	0.280571	+	0.863509i
$248$	−3.59809	−	11.0738i	−0.228479	−	0.703186i
$249$		0			0
$250$	−0.162241	−	0.223305i	−0.0102610	−	0.0141231i
$251$	−6.60298	−	2.14544i	−0.416776	−	0.135419i	0.0931196	−	0.995655i	$-0.470316\pi$
$251$	−6.60298	−	2.14544i	−0.416776	−	0.135419i	−0.509896	+	0.860236i	$0.670316\pi$
$252$		0			0
$253$	7.64348	−	21.2178i	0.480542	−	1.33395i
$254$		−	8.79077i		−	0.551582i
$255$		0			0
$256$	7.98638	−	5.80244i	0.499149	−	0.362653i
$257$	6.12372	−	8.42858i	0.381987	−	0.525760i	−0.574122	−	0.818769i	$-0.694657\pi$
$257$	6.12372	−	8.42858i	0.381987	−	0.525760i	0.956110	+	0.293009i	$0.0946567\pi$
$258$		0			0
$259$	0.946307	−	0.307474i	0.0588007	−	0.0191055i
$260$	0.113983	+	0.0828133i	0.00706891	+	0.00513586i
$261$		0			0
$262$	−3.86110	+	11.8833i	−0.238540	+	0.734150i
$263$	4.26110			0.262751			0.131375	−	0.991333i	$-0.458061\pi$
$263$	4.26110			0.262751			0.131375	+	0.991333i	$0.458061\pi$
$264$		0			0
$265$	−0.359686			−0.0220953
$266$	−0.325521	+	1.00185i	−0.0199589	+	0.0614273i
$267$		0			0
$268$	9.81131	+	7.12833i	0.599321	+	0.435432i
$269$	10.5223	−	3.41889i	0.641553	−	0.208453i	0.0298672	−	0.999554i	$-0.490492\pi$
$269$	10.5223	−	3.41889i	0.641553	−	0.208453i	0.611686	+	0.791101i	$0.290492\pi$
$270$		0			0
$271$	9.34327	−	12.8599i	0.567563	−	0.781184i	−0.424700	−	0.905334i	$-0.639621\pi$
$271$	9.34327	−	12.8599i	0.567563	−	0.781184i	0.992263	+	0.124150i	$0.0396205\pi$
$272$	−4.78095	+	3.47356i	−0.289888	+	0.210616i
$273$		0			0
$274$		−	11.0629i		−	0.668334i
$275$	15.9204	−	4.62198i	0.960038	−	0.278716i
$276$		0			0
$277$	10.7860	+	3.50458i	0.648066	+	0.210570i	0.614561	−	0.788869i	$-0.289333\pi$
$277$	10.7860	+	3.50458i	0.648066	+	0.210570i	0.0335051	+	0.999439i	$0.489333\pi$
$278$	−1.56054	−	2.14790i	−0.0935949	−	0.128822i
$279$		0			0
$280$	0.00742570	+	0.0228539i	0.000443770	+	0.00136578i
$281$	−0.482158	−	1.48393i	−0.0287631	−	0.0885238i	0.935644	−	0.352944i	$-0.114819\pi$
$281$	−0.482158	−	1.48393i	−0.0287631	−	0.0885238i	−0.964408	+	0.264420i	$0.914819\pi$
$282$		0			0
$283$	15.6148	+	21.4919i	0.928202	+	1.27756i	0.960557	+	0.278084i	$0.0896993\pi$
$283$	15.6148	+	21.4919i	0.928202	+	1.27756i	−0.0323551	+	0.999476i	$0.510301\pi$
$284$	−4.83150	−	1.56985i	−0.286697	−	0.0931534i
$285$		0			0
$286$	4.34599	−	2.95230i	0.256984	−	0.174573i
$287$		−	2.37046i		−	0.139924i
$288$		0			0
$289$	−1.04038	+	0.755878i	−0.0611986	+	0.0444634i
$290$	0.0908004	−	0.124976i	0.00533198	−	0.00733884i
$291$		0			0
$292$	−17.2063	+	5.59066i	−1.00692	+	0.327169i
$293$	−21.3051	−	15.4791i	−1.24466	−	0.904296i	−0.246757	−	0.969077i	$-0.579365\pi$
$293$	−21.3051	−	15.4791i	−1.24466	−	0.904296i	−0.997900	+	0.0647811i	$0.979365\pi$
$294$		0			0
$295$	−0.0345592	+	0.106362i	−0.00201211	+	0.00619265i
$296$	9.78322			0.568638
$297$		0			0
$298$	−7.06874			−0.409481
$299$	4.83611	−	14.8840i	0.279679	−	0.860765i
$300$		0			0
$301$	−0.206028	−	0.149688i	−0.0118752	−	0.00862786i
$302$	5.74115	−	1.86541i	0.330366	−	0.107342i
$303$		0			0
$304$	5.03628	−	6.93185i	0.288851	−	0.397569i
$305$	−0.275310	+	0.200025i	−0.0157642	+	0.0114534i
$306$		0			0
$307$			26.0083i			1.48437i	0.670195	+	0.742185i	$0.266211\pi$
$307$			26.0083i			1.48437i	−0.670195	+	0.742185i	$0.733789\pi$
$308$	−1.24892	−	0.0394902i	−0.0711641	−	0.00225016i
$309$		0			0
$310$	0.125957	+	0.0409258i	0.00715387	+	0.00232443i
$311$	7.83210	+	10.7800i	0.444118	+	0.611276i	0.971121	−	0.238588i	$-0.0766844\pi$
$311$	7.83210	+	10.7800i	0.444118	+	0.611276i	−0.527003	+	0.849863i	$0.676684\pi$
$312$		0			0
$313$	−3.47592	−	10.6978i	−0.196471	−	0.604675i	−0.999956	−	0.00935037i	$-0.997024\pi$
$313$	−3.47592	−	10.6978i	−0.196471	−	0.604675i	0.803486	−	0.595324i	$-0.202976\pi$
$314$	−2.77158	−	8.53004i	−0.156409	−	0.481378i
$315$		0			0
$316$	−2.70120	−	3.71788i	−0.151954	−	0.209147i
$317$	−10.4166	−	3.38455i	−0.585053	−	0.190095i	0.00151019	−	0.999999i	$-0.499519\pi$
$317$	−10.4166	−	3.38455i	−0.585053	−	0.190095i	−0.586563	+	0.809904i	$0.699519\pi$
$318$		0			0
$319$	10.4287	+	15.3518i	0.583897	+	0.859535i
$320$			0.0494082i			0.00276200i
$321$		0			0
$322$	0.934670	−	0.679077i	0.0520871	−	0.0378435i
$323$	15.5837	−	21.4492i	0.867103	−	1.19346i
$324$		0			0
$325$	10.9409	−	3.55490i	0.606890	−	0.197191i
$326$	5.11052	+	3.71301i	0.283046	+	0.205645i
$327$		0			0
$328$	7.20231	−	22.1664i	0.397681	−	1.22394i
$329$	−2.74648			−0.151419
$330$		0			0
$331$	4.23285			0.232659			0.116329	−	0.993211i	$-0.462887\pi$
$331$	4.23285			0.232659			0.116329	+	0.993211i	$0.462887\pi$
$332$	−2.49676	+	7.68424i	−0.137027	+	0.421727i
$333$		0			0
$334$	−4.23718	−	3.07849i	−0.231848	−	0.168447i
$335$	−0.303101	+	0.0984835i	−0.0165602	+	0.00538073i
$336$		0			0
$337$	−1.56491	+	2.15391i	−0.0852460	+	0.117331i	−0.849510	−	0.527572i	$-0.823102\pi$
$337$	−1.56491	+	2.15391i	−0.0852460	+	0.117331i	0.764264	+	0.644903i	$0.223102\pi$
$338$	−4.28933	+	3.11638i	−0.233309	+	0.169509i
$339$		0			0
$340$		−	0.261773i		−	0.0141966i
$341$	−9.75446	+	12.5704i	−0.528233	+	0.680723i
$342$		0			0
$343$	3.27243	+	1.06328i	0.176694	+	0.0574115i
$344$	−1.47178	−	2.02573i	−0.0793530	−	0.109220i
$345$		0			0
$346$	3.53506	+	10.8798i	0.190046	+	0.584901i
$347$	5.13066	+	15.7905i	0.275428	+	0.847681i	0.989106	+	0.147207i	$0.0470282\pi$
$347$	5.13066	+	15.7905i	0.275428	+	0.847681i	−0.713678	+	0.700474i	$0.752972\pi$
$348$		0			0
$349$	−8.09660	−	11.1440i	−0.433401	−	0.596525i	0.535329	−	0.844644i	$-0.320188\pi$
$349$	−8.09660	−	11.1440i	−0.433401	−	0.596525i	−0.968730	+	0.248118i	$0.920188\pi$
$350$	0.807679	+	0.262431i	0.0431722	+	0.0140275i
$351$		0			0
$352$	−18.1147	−	6.52564i	−0.965517	−	0.347818i
$353$		−	11.0249i		−	0.586795i	−0.955990	−	0.293398i	$-0.905214\pi$
$353$		−	11.0249i		−	0.586795i	0.955990	−	0.293398i	$-0.0947860\pi$
$354$		0			0
$355$	0.108005	−	0.0784705i	0.00573233	−	0.00416478i
$356$	−7.66511	+	10.5501i	−0.406250	+	0.559155i
$357$		0			0
$358$	4.61482	−	1.49945i	0.243901	−	0.0792482i
$359$	15.3828	+	11.1763i	0.811875	+	0.589862i	0.914374	−	0.404871i	$-0.132684\pi$
$359$	15.3828	+	11.1763i	0.811875	+	0.589862i	−0.102499	+	0.994733i	$0.532684\pi$
$360$		0			0
$361$	−6.00743	+	18.4890i	−0.316180	+	0.973103i
$362$	−14.5392			−0.764163
$363$		0			0
$364$	−0.867106			−0.0454487
$365$	0.146918	−	0.452167i	0.00769004	−	0.0236675i
$366$		0			0
$367$	4.60911	+	3.34872i	0.240594	+	0.174802i	0.701548	−	0.712622i	$-0.252493\pi$
$367$	4.60911	+	3.34872i	0.240594	+	0.174802i	−0.460954	+	0.887424i	$0.652493\pi$
$368$	−8.93722	+	2.90388i	−0.465885	+	0.151375i
$369$		0			0
$370$	−0.0654073	+	0.0900254i	−0.00340036	+	0.00468020i
$371$	1.79090	−	1.30117i	0.0929789	−	0.0675531i
$372$		0			0
$373$		−	22.1594i		−	1.14737i	−0.819076	−	0.573684i	$-0.805514\pi$
$373$		−	22.1594i		−	1.14737i	0.819076	−	0.573684i	$-0.194486\pi$
$374$	−9.18400	−	3.30845i	−0.474893	−	0.171076i
$375$		0			0
$376$	−25.6826	−	8.34479i	−1.32448	−	0.430350i
$377$	7.56992	+	10.4191i	0.389871	+	0.536611i
$378$		0			0
$379$	−0.117844	−	0.362687i	−0.00605325	−	0.0186300i	0.947984	−	0.318317i	$-0.103118\pi$
$379$	−0.117844	−	0.362687i	−0.00605325	−	0.0186300i	−0.954038	+	0.299687i	$0.903118\pi$
$380$	0.117285	+	0.360966i	0.00601660	+	0.0185172i
$381$		0			0
$382$	−5.52973	−	7.61102i	−0.282926	−	0.389414i
$383$	12.0446	+	3.91352i	0.615450	+	0.199972i	0.600119	−	0.799911i	$-0.295120\pi$
$383$	12.0446	+	3.91352i	0.615450	+	0.199972i	0.0153308	+	0.999882i	$0.495120\pi$
$384$		0			0
$385$	0.0201311	−	0.0259425i	0.00102598	−	0.00132215i
$386$			17.2313i			0.877049i
$387$		0			0
$388$	−3.73917	+	2.71667i	−0.189828	+	0.137918i
$389$	−13.9885	+	19.2535i	−0.709243	+	0.976190i	0.290570	+	0.956854i	$0.406155\pi$
$389$	−13.9885	+	19.2535i	−0.709243	+	0.976190i	−0.999813	+	0.0193359i	$0.993845\pi$
$390$		0			0
$391$	−27.6544	+	8.98546i	−1.39854	+	0.454414i
$392$	13.6253	+	9.89933i	0.688179	+	0.499991i
$393$		0			0
$394$	−4.47597	+	13.7756i	−0.225496	+	0.694005i
$395$	0.120768			0.00607647
$396$		0			0
$397$	5.00497			0.251192			0.125596	−	0.992081i	$-0.459916\pi$
$397$	5.00497			0.251192			0.125596	+	0.992081i	$0.459916\pi$
$398$	−2.20583	+	6.78886i	−0.110568	+	0.340295i
$399$		0			0
$400$	−5.58837	−	4.06019i	−0.279419	−	0.203009i
$401$	4.03643	−	1.31151i	0.201570	−	0.0654939i	−0.206492	−	0.978448i	$-0.566205\pi$
$401$	4.03643	−	1.31151i	0.201570	−	0.0654939i	0.408062	+	0.912954i	$0.366205\pi$
$402$		0			0
$403$	−6.48990	+	8.93258i	−0.323285	+	0.444963i
$404$	8.58407	−	6.23669i	0.427073	−	0.310287i
$405$		0			0
$406$			0.950735i			0.0471842i
$407$	−7.51225	−	11.0585i	−0.372368	−	0.548151i
$408$		0			0
$409$	−11.2278	−	3.64812i	−0.555177	−	0.180388i	0.0179728	−	0.999838i	$-0.494279\pi$
$409$	−11.2278	−	3.64812i	−0.555177	−	0.180388i	−0.573150	+	0.819450i	$0.694279\pi$
$410$	0.155824	+	0.214473i	0.00769559	+	0.0105921i
$411$		0			0
$412$	−6.18762	−	19.0435i	−0.304842	−	0.938208i
$413$	−0.212694	−	0.654604i	−0.0104660	−	0.0322109i
$414$		0			0
$415$	−0.124803	−	0.171777i	−0.00612634	−	0.00843218i
$416$	−12.7073	−	4.12884i	−0.623024	−	0.202433i
$417$		0			0
$418$	14.1464	+	0.447299i	0.691923	+	0.0218781i
$419$			20.9795i			1.02492i	0.858712	+	0.512459i	$0.171265\pi$
$419$			20.9795i			1.02492i	−0.858712	+	0.512459i	$0.828735\pi$
$420$		0			0
$421$	2.24889	−	1.63391i	0.109604	−	0.0796320i	−0.531633	−	0.846975i	$-0.678421\pi$
$421$	2.24889	−	1.63391i	0.109604	−	0.0796320i	0.641237	+	0.767343i	$0.278421\pi$
$422$	−7.58306	+	10.4372i	−0.369137	+	0.508074i
$423$		0			0
$424$	20.7003	−	6.72593i	1.00529	−	0.326640i
$425$	−17.2921	−	12.5634i	−0.838789	−	0.609416i
$426$		0			0
$427$	0.647200	−	1.99188i	0.0313202	−	0.0963936i
$428$	2.08864			0.100958
$429$		0			0
$430$	0.0284806			0.00137346
$431$	8.63060	−	26.5623i	0.415722	−	1.27946i	−0.495882	−	0.868390i	$-0.665155\pi$
$431$	8.63060	−	26.5623i	0.415722	−	1.27946i	0.911604	−	0.411070i	$-0.134845\pi$
$432$		0			0
$433$	7.41714	+	5.38887i	0.356445	+	0.258973i	0.751568	−	0.659656i	$-0.229298\pi$
$433$	7.41714	+	5.38887i	0.356445	+	0.258973i	−0.395123	+	0.918628i	$0.629298\pi$
$434$	−0.775198	+	0.251877i	−0.0372107	+	0.0120905i
$435$		0			0
$436$	−6.58887	+	9.06879i	−0.315549	+	0.434317i
$437$	34.1075	−	24.7806i	1.63159	−	1.18542i
$438$		0			0
$439$			2.93111i			0.139894i	0.997551	+	0.0699472i	$0.0222831\pi$
$439$			2.93111i			0.139894i	−0.997551	+	0.0699472i	$0.977717\pi$
$440$	0.267071	−	0.181426i	0.0127321	−	0.00864913i
$441$		0			0
$442$	−6.44247	−	2.09329i	−0.306437	−	0.0995675i
$443$	−21.0670	−	28.9963i	−1.00093	−	1.37766i	−0.924756	−	0.380561i	$-0.875731\pi$
$443$	−21.0670	−	28.9963i	−1.00093	−	1.37766i	−0.0761695	−	0.997095i	$-0.524269\pi$
$444$		0			0
$445$	−0.105900	−	0.325925i	−0.00502012	−	0.0154503i
$446$	2.05652	+	6.32932i	0.0973791	+	0.299702i
$447$		0			0
$448$	−0.178735	−	0.246007i	−0.00844441	−	0.0116227i
$449$	13.5184	+	4.39241i	0.637974	+	0.207290i	0.610104	−	0.792321i	$-0.291128\pi$
$449$	13.5184	+	4.39241i	0.637974	+	0.207290i	0.0278700	+	0.999612i	$0.491128\pi$
$450$		0			0
$451$	−30.5864	+	8.87978i	−1.44026	+	0.418132i
$452$		−	0.806691i		−	0.0379435i
$453$		0			0
$454$	6.52403	−	4.73999i	0.306188	−	0.222459i
$455$	0.0133938	−	0.0184349i	0.000627909	−	0.000864243i
$456$		0			0
$457$	19.4009	−	6.30372i	0.907534	−	0.294876i	0.182191	−	0.983263i	$-0.441681\pi$
$457$	19.4009	−	6.30372i	0.907534	−	0.294876i	0.725343	+	0.688387i	$0.241681\pi$
$458$	−11.4042	−	8.28561i	−0.532882	−	0.387161i
$459$		0			0
$460$	0.128631	−	0.395887i	0.00599747	−	0.0184583i
$461$	0.770354			0.0358790			0.0179395	−	0.999839i	$-0.494289\pi$
$461$	0.770354			0.0358790			0.0179395	+	0.999839i	$0.494289\pi$
$462$		0			0
$463$	37.7948			1.75647			0.878236	−	0.478228i	$-0.158721\pi$
$463$	37.7948			1.75647			0.878236	+	0.478228i	$0.158721\pi$
$464$	2.38967	−	7.35464i	0.110937	−	0.341431i
$465$		0			0
$466$	8.98898	+	6.53088i	0.416406	+	0.302537i
$467$	−16.7411	+	5.43950i	−0.774684	+	0.251710i	−0.669569	−	0.742750i	$-0.733521\pi$
$467$	−16.7411	+	5.43950i	−0.774684	+	0.251710i	−0.105115	+	0.994460i	$0.533521\pi$
$468$		0			0
$469$	1.15290	−	1.58683i	0.0532358	−	0.0732728i
$470$	0.248494	−	0.180542i	0.0114622	−	0.00832776i
$471$		0			0
$472$		−	6.76750i		−	0.311499i
$473$	−1.15966	+	3.21913i	−0.0533212	+	0.148016i
$474$		0			0
$475$	29.4734	+	9.57650i	1.35233	+	0.439400i
$476$	0.946967	+	1.30339i	0.0434042	+	0.0597407i
$477$		0			0
$478$	6.03785	+	18.5826i	0.276165	+	0.849948i
$479$	−0.743452	−	2.28811i	−0.0339692	−	0.104546i	0.932634	−	0.360823i	$-0.117504\pi$
$479$	−0.743452	−	2.28811i	−0.0339692	−	0.104546i	−0.966603	+	0.256277i	$0.917504\pi$
$480$		0			0
$481$	−5.45293	−	7.50531i	−0.248632	−	0.342213i
$482$	9.40365	+	3.05543i	0.428325	+	0.139171i
$483$		0			0
$484$	4.16893	+	16.2630i	0.189497	+	0.739226i
$485$		−	0.121459i		−	0.00551517i
$486$		0			0
$487$	−11.8099	+	8.58039i	−0.535157	+	0.388815i	−0.822283	−	0.569078i	$-0.807300\pi$
$487$	−11.8099	+	8.58039i	−0.535157	+	0.388815i	0.287126	+	0.957893i	$0.407300\pi$
$488$	12.1040	−	16.6598i	0.547924	−	0.754153i
$489$		0			0
$490$	−0.182187	+	0.0591963i	−0.00823039	+	0.00267422i
$491$	20.2597	+	14.7195i	0.914307	+	0.664283i	0.942101	−	0.335331i	$-0.108848\pi$
$491$	20.2597	+	14.7195i	0.914307	+	0.664283i	−0.0277932	+	0.999614i	$0.508848\pi$
$492$		0			0
$493$	7.39433	−	22.7574i	0.333024	−	1.02494i
$494$	9.82158			0.441894
$495$		0			0
$496$	6.62982			0.297688
$497$	−0.253899	+	0.781420i	−0.0113889	+	0.0350515i
$498$		0			0
$499$	−18.3740	−	13.3495i	−0.822535	−	0.597607i	0.0949025	−	0.995487i	$-0.469746\pi$
$499$	−18.3740	−	13.3495i	−0.822535	−	0.597607i	−0.917438	+	0.397880i	$0.869746\pi$
$500$	0.582107	−	0.189138i	0.0260326	−	0.00845851i
$501$		0			0
$502$	−2.80882	+	3.86601i	−0.125364	+	0.172549i
$503$	8.41953	−	6.11715i	0.375408	−	0.272750i	−0.384042	−	0.923316i	$-0.625468\pi$
$503$	8.41953	−	6.11715i	0.375408	−	0.272750i	0.759450	+	0.650566i	$0.225468\pi$
$504$		0			0
$505$			0.278835i			0.0124080i
$506$	−12.2635	−	9.51634i	−0.545179	−	0.423053i
$507$		0			0
$508$	18.5391	+	6.02371i	0.822539	+	0.267259i
$509$	−4.75254	−	6.54130i	−0.210652	−	0.289938i	0.690596	−	0.723241i	$-0.257348\pi$
$509$	−4.75254	−	6.54130i	−0.210652	−	0.289938i	−0.901249	+	0.433302i	$0.857348\pi$
$510$		0			0
$511$	0.904203	+	2.78285i	0.0399996	+	0.123106i
$512$	4.55217	+	14.0102i	0.201180	+	0.619167i
$513$		0			0
$514$	−4.21490	−	5.80132i	−0.185911	−	0.255885i
$515$	0.500449	+	0.162606i	0.0220524	+	0.00716526i
$516$		0			0
$517$	10.2883	+	35.4382i	0.452481	+	1.55857i
$518$		−	0.684854i		−	0.0300908i
$519$		0			0
$520$	0.181258	−	0.131692i	0.00794870	−	0.00577507i
$521$	−20.5846	+	28.3323i	−0.901828	+	1.24126i	0.0680535	+	0.997682i	$0.478321\pi$
$521$	−20.5846	+	28.3323i	−0.901828	+	1.24126i	−0.969881	+	0.243578i	$0.921679\pi$
$522$		0			0
$523$	41.1766	−	13.3791i	1.80052	−	0.585026i	0.800625	−	0.599166i	$-0.204501\pi$
$523$	41.1766	−	13.3791i	1.80052	−	0.585026i	0.999900	+	0.0141400i	$0.00450104\pi$
$524$	−22.4152	−	16.2856i	−0.979211	−	0.711438i
$525$		0			0
$526$	0.906309	−	2.78933i	0.0395169	−	0.121621i
$527$	20.5146			0.893630
$528$		0			0
$529$	−23.2378			−1.01034
$530$	−0.0765028	+	0.235452i	−0.00332307	+	0.0102274i
$531$		0			0
$532$	−1.88977	−	1.37300i	−0.0819319	−	0.0595270i
$533$	−21.0196	+	6.82969i	−0.910461	+	0.295827i
$534$		0			0
$535$	−0.0322622	+	0.0444051i	−0.00139482	+	0.00191980i
$536$	15.6022	−	11.3357i	0.673912	−	0.489626i
$537$		0			0
$538$		−	7.61509i		−	0.328310i
$539$	0.727333	−	23.0028i	0.0313284	−	0.990800i
$540$		0			0
$541$	−0.215252	−	0.0699396i	−0.00925440	−	0.00300694i	0.304386	−	0.952549i	$-0.401549\pi$
$541$	−0.215252	−	0.0699396i	−0.00925440	−	0.00300694i	−0.313641	+	0.949542i	$0.601549\pi$
$542$	−6.43089	−	8.85136i	−0.276230	−	0.380198i
$543$		0			0
$544$	7.67135	+	23.6100i	0.328906	+	1.01227i
$545$	−0.0910303	−	0.280163i	−0.00389931	−	0.0120008i
$546$		0			0
$547$	−9.67686	−	13.3191i	−0.413753	−	0.569482i	0.550376	−	0.834917i	$-0.314484\pi$
$547$	−9.67686	−	13.3191i	−0.413753	−	0.569482i	−0.964129	+	0.265435i	$0.914484\pi$
$548$	23.3308	+	7.58064i	0.996643	+	0.323829i
$549$		0			0
$550$	0.360607	−	11.4046i	0.0153763	−	0.486296i
$551$			34.6938i			1.47801i
$552$		0			0
$553$	−0.601310	+	0.436877i	−0.0255703	+	0.0185779i
$554$	4.58822	−	6.31514i	0.194935	−	0.268305i
$555$		0			0
$556$	5.59909	−	1.81925i	0.237454	−	0.0771535i
$557$	−21.2624	−	15.4481i	−0.900919	−	0.654556i	0.0377832	−	0.999286i	$-0.487970\pi$
$557$	−21.2624	−	15.4481i	−0.900919	−	0.654556i	−0.938702	+	0.344730i	$0.887970\pi$
$558$		0			0
$559$	−0.733729	+	2.25818i	−0.0310334	+	0.0955110i
$560$	−0.0136825			−0.000578192
$561$		0			0
$562$	−1.07394			−0.0453013
$563$	−11.2376	+	34.5859i	−0.473610	+	1.45762i	0.374213	+	0.927343i	$0.377913\pi$
$563$	−11.2376	+	34.5859i	−0.473610	+	1.45762i	−0.847823	+	0.530279i	$0.822087\pi$
$564$		0			0
$565$	0.0171505	+	0.0124606i	0.000721527	+	0.000524220i
$566$	17.3898	−	5.65030i	0.730949	−	0.237500i
$567$		0			0
$568$	−4.74846	+	6.53570i	−0.199241	+	0.274232i
$569$	16.3670	−	11.8913i	0.686138	−	0.498509i	−0.189250	−	0.981929i	$-0.560606\pi$
$569$	16.3670	−	11.8913i	0.686138	−	0.498509i	0.875388	+	0.483420i	$0.160606\pi$
$570$		0			0
$571$		−	24.4002i		−	1.02112i	−0.859843	−	0.510558i	$-0.829439\pi$
$571$		−	24.4002i		−	1.02112i	0.859843	−	0.510558i	$-0.170561\pi$
$572$	3.24818	+	11.1884i	0.135813	+	0.467809i
$573$		0			0
$574$	−1.55172	−	0.504183i	−0.0647673	−	0.0210442i
$575$	−19.9778	−	27.4971i	−0.833132	−	1.14671i
$576$		0			0
$577$	−5.96494	−	18.3582i	−0.248324	−	0.764262i	−0.995072	−	0.0991553i	$-0.968386\pi$
$577$	−5.96494	−	18.3582i	−0.248324	−	0.764262i	0.746748	−	0.665107i	$-0.231614\pi$
$578$	0.273519	+	0.841805i	0.0113769	+	0.0350145i
$579$		0			0
$580$	0.201346	+	0.277129i	0.00836043	+	0.0115071i
$581$	1.24281	+	0.403812i	0.0515603	+	0.0167530i
$582$		0			0
$583$	−23.4978	−	18.2340i	−0.973180	−	0.755177i
$584$			28.7700i			1.19051i
$585$		0			0
$586$	−14.6641	+	10.6541i	−0.605769	+	0.440117i
$587$	−11.2480	+	15.4816i	−0.464256	+	0.638994i	−0.975385	−	0.220510i	$-0.929228\pi$
$587$	−11.2480	+	15.4816i	−0.464256	+	0.638994i	0.511128	+	0.859504i	$0.329228\pi$
$588$		0			0
$589$	−28.2882	+	9.19138i	−1.16559	+	0.378724i
$590$	0.0622746	+	0.0452452i	0.00256381	+	0.00186271i
$591$		0			0
$592$	−1.72138	+	5.29785i	−0.0707481	+	0.217740i
$593$	14.9885			0.615503			0.307751	−	0.951467i	$-0.400423\pi$
$593$	14.9885			0.615503			0.307751	+	0.951467i	$0.400423\pi$
$594$		0			0
$595$	−0.0423378			−0.00173568
$596$	4.84373	−	14.9075i	0.198407	−	0.610633i
$597$		0			0
$598$	−8.71452	−	6.33147i	−0.356363	−	0.258913i
$599$	−31.7090	+	10.3029i	−1.29560	+	0.420965i	−0.874047	−	0.485841i	$-0.838513\pi$
$599$	−31.7090	+	10.3029i	−1.29560	+	0.420965i	−0.421549	+	0.906806i	$0.638513\pi$
$600$		0			0
$601$	−24.8474	+	34.1996i	−1.01355	+	1.39503i	−0.0969178	+	0.995292i	$0.530898\pi$
$601$	−24.8474	+	34.1996i	−1.01355	+	1.39503i	−0.916630	+	0.399737i	$0.869102\pi$
$602$	−0.141807	+	0.103029i	−0.00577962	+	0.00419914i
$603$		0			0
$604$			13.3859i			0.544664i
$605$	−0.410151	−	0.162573i	−0.0166750	−	0.00660955i
$606$		0			0
$607$	−29.3742	−	9.54427i	−1.19226	−	0.387390i	−0.355354	−	0.934732i	$-0.615640\pi$
$607$	−29.3742	−	9.54427i	−1.19226	−	0.387390i	−0.836909	+	0.547342i	$0.815640\pi$
$608$	−21.1565	−	29.1194i	−0.858008	−	1.18095i
$609$		0			0
$610$	0.0723802	+	0.222763i	0.00293059	+	0.00901942i
$611$	7.91306	+	24.3539i	0.320128	+	0.985254i
$612$		0			0
$613$	−9.38958	−	12.9237i	−0.379242	−	0.521981i	0.576142	−	0.817350i	$-0.304558\pi$
$613$	−9.38958	−	12.9237i	−0.379242	−	0.521981i	−0.955383	+	0.295368i	$0.904558\pi$
$614$	17.0251	+	5.53179i	0.687078	+	0.223245i
$615$		0			0
$616$	−0.673455	+	1.86946i	−0.0271343	+	0.0753227i
$617$			2.63374i			0.106030i	0.998594	+	0.0530151i	$0.0168831\pi$
$617$			2.63374i			0.106030i	−0.998594	+	0.0530151i	$0.983117\pi$
$618$		0			0
$619$	−16.3822	+	11.9023i	−0.658454	+	0.478395i	−0.866141	−	0.499800i	$-0.833407\pi$
$619$	−16.3822	+	11.9023i	−0.658454	+	0.478395i	0.207686	+	0.978196i	$0.433407\pi$
$620$	−0.172619	+	0.237590i	−0.00693255	+	0.00954184i
$621$		0			0
$622$	8.72244	−	2.83409i	0.349738	−	0.113637i
$623$	1.70632	+	1.23971i	0.0683622	+	0.0496680i
$624$		0			0
$625$	7.71797	−	23.7535i	0.308719	−	0.950139i
$626$	−7.74212			−0.309437
$627$		0			0
$628$	19.8884			0.793633
$629$	−5.32645	+	16.3931i	−0.212379	+	0.653636i
$630$		0			0
$631$	−6.82846	−	4.96116i	−0.271837	−	0.197501i	0.443512	−	0.896268i	$-0.353732\pi$
$631$	−6.82846	−	4.96116i	−0.271837	−	0.197501i	−0.715349	+	0.698767i	$0.753732\pi$
$632$	−6.95030	+	2.25829i	−0.276468	+	0.0898299i
$633$		0			0
$634$	−4.43107	+	6.09885i	−0.175980	+	0.242216i
$635$	−0.414430	+	0.301101i	−0.0164462	+	0.0119488i
$636$		0			0
$637$		−	15.9704i		−	0.632771i
$638$	12.2675	−	3.56146i	0.485673	−	0.141000i
$639$		0			0
$640$	−0.410557	−	0.133398i	−0.0162287	−	0.00527302i
$641$	18.9940	+	26.1429i	0.750216	+	1.03258i	0.997965	+	0.0637599i	$0.0203092\pi$
$641$	18.9940	+	26.1429i	0.750216	+	1.03258i	−0.247749	+	0.968824i	$0.579691\pi$
$642$		0			0
$643$	4.25724	+	13.1024i	0.167889	+	0.516709i	0.999238	−	0.0390421i	$-0.0124306\pi$
$643$	4.25724	+	13.1024i	0.167889	+	0.516709i	−0.831349	+	0.555751i	$0.812431\pi$
$644$	0.791659	+	2.43648i	0.0311957	+	0.0960106i
$645$		0			0
$646$	−10.7262	−	14.7633i	−0.422015	−	0.580854i
$647$	−8.11003	−	2.63511i	−0.318838	−	0.103597i	0.145226	−	0.989399i	$-0.453609\pi$
$647$	−8.11003	−	2.63511i	−0.318838	−	0.103597i	−0.464064	+	0.885802i	$0.653609\pi$
$648$		0			0
$649$	−7.64968	+	5.19656i	−0.300276	+	0.203983i
$650$		−	7.91804i		−	0.310571i
$651$		0			0
$652$	−11.3324	+	8.23344i	−0.443810	+	0.322447i
$653$	−0.710037	+	0.977282i	−0.0277859	+	0.0382440i	−0.822684	−	0.568499i	$-0.807524\pi$
$653$	−0.710037	+	0.977282i	−0.0277859	+	0.0382440i	0.794898	+	0.606743i	$0.207524\pi$
$654$		0			0
$655$	0.692472	−	0.224998i	0.0270571	−	0.00879139i
$656$	10.7364	+	7.80045i	0.419186	+	0.304556i
$657$		0			0
$658$	−0.584160	+	1.79786i	−0.0227729	+	0.0700878i
$659$	9.41054			0.366583			0.183291	−	0.983059i	$-0.441325\pi$
$659$	9.41054			0.366583			0.183291	+	0.983059i	$0.441325\pi$
$660$		0			0
$661$	15.1027			0.587425			0.293713	−	0.955894i	$-0.405109\pi$
$661$	15.1027			0.587425			0.293713	+	0.955894i	$0.405109\pi$
$662$	0.900300	−	2.77084i	0.0349912	−	0.107692i
$663$		0			0
$664$	10.3947	+	7.55217i	0.403391	+	0.293081i
$665$	0.0583807	−	0.0189690i	0.00226391	−	0.000735588i
$666$		0			0
$667$	22.3653	−	30.7832i	0.865988	−	1.19193i
$668$	9.39575	−	6.82641i	0.363533	−	0.264122i
$669$		0			0
$670$			0.219358i			0.00847453i
$671$	−28.1258	−	0.889320i	−1.08579	−	0.0343318i
$672$		0			0
$673$	39.5629	+	12.8548i	1.52504	+	0.495514i	0.947201	−	0.320639i	$-0.103898\pi$
$673$	39.5629	+	12.8548i	1.52504	+	0.495514i	0.577835	+	0.816153i	$0.303898\pi$
$674$	1.07711	+	1.48252i	0.0414888	+	0.0571045i
$675$		0			0
$676$	−3.63303	−	11.1813i	−0.139732	−	0.430051i
$677$	1.39693	+	4.29931i	0.0536884	+	0.165236i	0.974305	−	0.225231i	$-0.0723137\pi$
$677$	1.39693	+	4.29931i	0.0536884	+	0.165236i	−0.920617	+	0.390467i	$0.872314\pi$
$678$		0			0
$679$	0.439379	+	0.604753i	0.0168618	+	0.0232083i
$680$	−0.395904	−	0.128637i	−0.0151822	−	0.00493301i
$681$		0			0
$682$	6.15389	+	9.05894i	0.235645	+	0.346885i
$683$		−	34.7783i		−	1.33075i	−0.746507	−	0.665377i	$-0.768271\pi$
$683$		−	34.7783i		−	1.33075i	0.746507	−	0.665377i	$-0.231729\pi$
$684$		0			0
$685$	−0.521547	+	0.378926i	−0.0199273	+	0.0144780i
$686$	1.39205	−	1.91599i	0.0531487	−	0.0731528i
$687$		0			0
$688$	1.35594	−	0.440573i	0.0516949	−	0.0167967i
$689$	−16.6977	−	12.1316i	−0.636132	−	0.462177i
$690$		0			0
$691$	−5.52630	+	17.0082i	−0.210230	+	0.647023i	0.789228	+	0.614101i	$0.210481\pi$
$691$	−5.52630	+	17.0082i	−0.210230	+	0.647023i	−0.999458	+	0.0329217i	$0.989519\pi$
$692$	−25.3670			−0.964308
$693$		0			0
$694$	11.4278			0.433794
$695$	−0.0478085	+	0.147139i	−0.00181348	+	0.00558132i
$696$		0			0
$697$	33.2216	+	24.1369i	1.25836	+	0.914250i
$698$	−9.01701	+	2.92980i	−0.341299	+	0.110895i
$699$		0			0
$700$	−1.10689	+	1.52351i	−0.0418367	+	0.0575832i
$701$	14.1345	−	10.2693i	0.533852	−	0.387866i	−0.287945	−	0.957647i	$-0.592972\pi$
$701$	14.1345	−	10.2693i	0.533852	−	0.387866i	0.821797	+	0.569781i	$0.192972\pi$
$702$		0			0
$703$		−	24.9914i		−	0.942568i
$704$	−2.50472	+	3.22778i	−0.0944001	+	0.121651i
$705$		0			0
$706$	−7.21693	−	2.34492i	−0.271613	−	0.0882523i
$707$	−1.00869	−	1.38834i	−0.0379356	−	0.0522139i
$708$		0			0
$709$	2.57673	+	7.93037i	0.0967713	+	0.297831i	0.987711	−	0.156290i	$-0.0499533\pi$
$709$	2.57673	+	7.93037i	0.0967713	+	0.297831i	−0.890940	+	0.454121i	$0.849953\pi$
$710$	−0.0283950	−	0.0873909i	−0.00106565	−	0.00327972i
$711$		0			0
$712$	12.1893	+	16.7771i	0.456812	+	0.628747i
$713$	31.0248	+	10.0806i	1.16189	+	0.377520i
$714$		0			0
$715$	−0.288041	−	0.103764i	−0.0107721	−	0.00388056i
$716$			10.7598i			0.402112i
$717$		0			0
$718$	10.5879	−	7.69254i	0.395136	−	0.287083i
$719$	13.8736	−	19.0953i	0.517397	−	0.712136i	−0.467748	−	0.883862i	$-0.654934\pi$
$719$	13.8736	−	19.0953i	0.517397	−	0.712136i	0.985145	+	0.171726i	$0.0549344\pi$
$720$		0			0
$721$	−3.08000	+	1.00075i	−0.114705	+	0.0372699i
$722$	10.8252	+	7.86497i	0.402872	+	0.292704i
$723$		0			0
$724$	9.96272	−	30.6621i	0.370262	−	1.13955i
$725$	27.9697			1.03877
$726$		0			0
$727$	1.90462			0.0706386			0.0353193	−	0.999376i	$-0.488755\pi$
$727$	1.90462			0.0706386			0.0353193	+	0.999376i	$0.488755\pi$
$728$	−0.426102	+	1.31141i	−0.0157924	+	0.0486039i
$729$		0			0
$730$	−0.264742	−	0.192346i	−0.00979854	−	0.00711905i
$731$	4.19569	−	1.36326i	0.155183	−	0.0504221i
$732$		0			0
$733$	−10.3520	+	14.2482i	−0.382358	+	0.526271i	−0.956207	−	0.292690i	$-0.905450\pi$
$733$	−10.3520	+	14.2482i	−0.382358	+	0.526271i	0.573849	+	0.818961i	$0.305450\pi$
$734$	3.17241	−	2.30489i	0.117096	−	0.0850751i
$735$		0			0
$736$			39.4756i			1.45509i
$737$	−24.7938	−	8.93171i	−0.913291	−	0.329004i
$738$		0			0
$739$	−4.54355	−	1.47629i	−0.167137	−	0.0543062i	0.224253	−	0.974531i	$-0.428006\pi$
$739$	−4.54355	−	1.47629i	−0.167137	−	0.0543062i	−0.391390	+	0.920225i	$0.628006\pi$
$740$	−0.145038	−	0.199627i	−0.00533169	−	0.00733845i
$741$		0			0
$742$	−0.470834	−	1.44908i	−0.0172849	−	0.0531974i
$743$	−0.567901	−	1.74782i	−0.0208343	−	0.0641212i	0.940099	−	0.340902i	$-0.110732\pi$
$743$	−0.567901	−	1.74782i	−0.0208343	−	0.0641212i	−0.960933	+	0.276781i	$0.910732\pi$
$744$		0			0
$745$	0.242118	+	0.333247i	0.00887053	+	0.0122092i
$746$	−14.5056	−	4.71316i	−0.531088	−	0.172561i
$747$		0			0
$748$	13.2704	−	17.1013i	0.485215	−	0.625287i
$749$		−	0.337805i		−	0.0123431i
$750$		0			0
$751$	30.6978	−	22.3033i	1.12018	−	0.813857i	0.135942	−	0.990717i	$-0.456594\pi$
$751$	30.6978	−	22.3033i	1.12018	−	0.813857i	0.984236	+	0.176859i	$0.0565938\pi$
$752$	9.03781	−	12.4395i	0.329575	−	0.453621i
$753$		0			0
$754$	8.43046	−	2.73922i	0.307019	−	0.0997566i
$755$	−0.284588	−	0.206765i	−0.0103572	−	0.00752497i
$756$		0			0
$757$	−9.46409	+	29.1275i	−0.343978	+	1.05866i	0.618150	+	0.786060i	$0.287882\pi$
$757$	−9.46409	+	29.1275i	−0.343978	+	1.05866i	−0.962128	+	0.272596i	$0.912118\pi$
$758$	−0.262481			−0.00953373
$759$		0			0
$760$	0.603558			0.0218934
$761$	9.53788	−	29.3546i	0.345748	−	1.06410i	−0.615434	−	0.788188i	$-0.711019\pi$
$761$	9.53788	−	29.3546i	0.345748	−	1.06410i	0.961182	−	0.275914i	$-0.0889806\pi$
$762$		0			0
$763$	1.46674	+	1.06565i	0.0530994	+	0.0385790i
$764$	19.8402	−	6.44648i	0.717794	−	0.233225i
$765$		0			0
$766$	5.12362	−	7.05205i	0.185124	−	0.254801i
$767$	−5.19177	+	3.77204i	−0.187464	+	0.136200i
$768$		0			0
$769$			19.3154i			0.696532i	0.937396	+	0.348266i	$0.113229\pi$
$769$			19.3154i			0.696532i	−0.937396	+	0.348266i	$0.886771\pi$
$770$	−0.0127003	−	0.0186957i	−0.000457688	−	0.000673747i
$771$		0			0
$772$	−36.3395	−	11.8074i	−1.30789	−	0.424958i
$773$	1.72928	+	2.38015i	0.0621980	+	0.0856082i	0.838983	−	0.544158i	$-0.183151\pi$
$773$	1.72928	+	2.38015i	0.0621980	+	0.0856082i	−0.776785	+	0.629766i	$0.783151\pi$
$774$		0			0
$775$	7.40997	+	22.8056i	0.266174	+	0.819200i
$776$	2.27122	+	6.99009i	0.0815320	+	0.250930i
$777$		0			0
$778$	9.62814	+	13.2520i	0.345185	+	0.475107i
$779$	−56.6245	−	18.3984i	−2.02878	−	0.659191i
$780$		0			0
$781$	11.0339	+	0.348884i	0.394823	+	0.0124840i
$782$			20.0138i			0.715693i
$783$		0			0
$784$	−7.75811	+	5.63660i	−0.277075	+	0.201307i
$785$	−0.307206	+	0.422833i	−0.0109647	+	0.0150916i
$786$		0			0
$787$	−7.65190	+	2.48625i	−0.272761	+	0.0886254i	−0.442204	−	0.896915i	$-0.645803\pi$
$787$	−7.65190	+	2.48625i	−0.272761	+	0.0886254i	0.169443	+	0.985540i	$0.445803\pi$
$788$	−25.9847	−	18.8790i	−0.925665	−	0.672535i
$789$		0			0
$790$	0.0256865	−	0.0790549i	0.000913884	−	0.00281265i
$791$	−0.130470			−0.00463897
$792$		0			0
$793$	−19.5272			−0.693433
$794$	1.06452	−	3.27627i	0.0377786	−	0.116270i
$795$		0			0
$796$	−12.8057	−	9.30388i	−0.453886	−	0.329767i
$797$	52.2338	−	16.9718i	1.85022	−	0.601172i	0.853418	−	0.521227i	$-0.174526\pi$
$797$	52.2338	−	16.9718i	1.85022	−	0.601172i	0.996799	−	0.0799446i	$-0.0254743\pi$
$798$		0			0
$799$	27.9657	−	38.4914i	0.989354	−	1.36173i
$800$	−23.4757	+	17.0561i	−0.829991	+	0.603024i
$801$		0			0
$802$		−	2.92121i		−	0.103152i
$803$	32.5203	−	22.0916i	1.14762	−	0.779596i
$804$		0			0
$805$	−0.0640286	−	0.0208041i	−0.00225671	−	0.000733250i
$806$	4.46694	+	6.14821i	0.157341	+	0.216562i
$807$		0			0
$808$	−5.21407	−	16.0472i	−0.183430	−	0.564540i
$809$	−7.52538	−	23.1607i	−0.264578	−	0.814288i	−0.991790	−	0.127875i	$-0.959184\pi$
$809$	−7.52538	−	23.1607i	−0.264578	−	0.814288i	0.727212	−	0.686413i	$-0.240816\pi$
$810$		0			0
$811$	−12.2026	−	16.7955i	−0.428493	−	0.589770i	0.539114	−	0.842233i	$-0.318759\pi$
$811$	−12.2026	−	16.7955i	−0.428493	−	0.589770i	−0.967607	+	0.252463i	$0.918759\pi$
$812$	−2.00503	−	0.651474i	−0.0703628	−	0.0228623i
$813$		0			0
$814$	−8.83676	+	2.56547i	−0.309728	+	0.0899196i
$815$		−	0.368107i		−	0.0128942i
$816$		0			0
$817$	−5.17476	+	3.75968i	−0.181042	+	0.131535i
$818$	−4.77615	+	6.57380i	−0.166994	+	0.229848i
$819$		0			0
$820$	−0.559083	+	0.181657i	−0.0195240	+	0.00634374i
$821$	23.1681	+	16.8326i	0.808571	+	0.587461i	0.913416	−	0.407027i	$-0.133435\pi$
$821$	23.1681	+	16.8326i	0.808571	+	0.587461i	−0.104845	+	0.994489i	$0.533435\pi$
$822$		0			0
$823$	0.768785	−	2.36608i	0.0267982	−	0.0824763i	−0.936763	−	0.349964i	$-0.886194\pi$
$823$	0.768785	−	2.36608i	0.0267982	−	0.0824763i	0.963561	+	0.267488i	$0.0861936\pi$
$824$	−31.8420			−1.10927
$825$		0			0
$826$	−0.473745			−0.0164837
$827$	7.36490	−	22.6668i	0.256103	−	0.788202i	−0.737508	−	0.675338i	$-0.763998\pi$
$827$	7.36490	−	22.6668i	0.256103	−	0.788202i	0.993610	−	0.112864i	$-0.0360024\pi$
$828$		0			0
$829$	32.8736	+	23.8841i	1.14175	+	0.829528i	0.987362	−	0.158482i	$-0.0506601\pi$
$829$	32.8736	+	23.8841i	1.14175	+	0.829528i	0.154386	+	0.988011i	$0.450660\pi$
$830$	−0.138990	+	0.0451607i	−0.00482443	+	0.00156755i
$831$		0			0
$832$	−1.66646	+	2.29368i	−0.0577740	+	0.0795190i
$833$	−24.0059	+	17.4413i	−0.831755	+	0.604305i
$834$		0			0
$835$			0.305201i			0.0105619i
$836$	−10.6369	+	29.5272i	−0.367884	+	1.02122i
$837$		0			0
$838$	13.7333	+	4.46221i	0.474408	+	0.154145i
$839$	33.6349	+	46.2945i	1.16121	+	1.59826i	0.706683	+	0.707531i	$0.250191\pi$
$839$	33.6349	+	46.2945i	1.16121	+	1.59826i	0.454525	+	0.890734i	$0.349809\pi$
$840$		0			0
$841$	0.714546	+	2.19915i	0.0246395	+	0.0758327i
$842$	−0.591241	−	1.81965i	−0.0203755	−	0.0627094i
$843$		0			0
$844$	−16.8151	−	23.1440i	−0.578799	−	0.796649i
$845$	0.293836	+	0.0954731i	0.0101083	+	0.00328438i
$846$		0			0
$847$	2.63028	−	0.674260i	0.0903776	−	0.0231679i
$848$			12.3931i			0.425582i
$849$		0			0
$850$	−11.9020	+	8.64729i	−0.408234	+	0.296600i
$851$	−16.1107	+	22.1744i	−0.552266	+	0.760130i
$852$		0			0
$853$	−29.0464	+	9.43774i	−0.994529	+	0.323142i	−0.760677	−	0.649130i	$-0.775133\pi$
$853$	−29.0464	+	9.43774i	−0.994529	+	0.323142i	−0.233852	+	0.972272i	$0.575133\pi$
$854$	−1.16623	−	0.847318i	−0.0399077	−	0.0289946i
$855$		0			0
$856$	1.02637	−	3.15885i	0.0350807	−	0.107967i
$857$	6.14781			0.210005			0.105003	−	0.994472i	$-0.466515\pi$
$857$	6.14781			0.210005			0.105003	+	0.994472i	$0.466515\pi$
$858$		0			0
$859$	−27.5988			−0.941660			−0.470830	−	0.882224i	$-0.656045\pi$
$859$	−27.5988			−0.941660			−0.470830	+	0.882224i	$0.656045\pi$
$860$	−0.0195158	+	0.0600635i	−0.000665484	+	0.00204815i
$861$		0			0
$862$	−15.5521	−	11.2993i	−0.529706	−	0.384854i
$863$	−40.7061	+	13.2262i	−1.38565	+	0.450226i	−0.904523	−	0.426424i	$-0.859773\pi$
$863$	−40.7061	+	13.2262i	−1.38565	+	0.450226i	−0.481129	+	0.876650i	$0.659773\pi$
$864$		0			0
$865$	0.391832	−	0.539310i	0.0133227	−	0.0183371i
$866$	5.10515	−	3.70911i	0.173480	−	0.126041i
$867$		0			0
$868$		−	1.80743i		−	0.0613481i
$869$	7.88960	+	6.12224i	0.267636	+	0.207683i
$870$		0			0
$871$	−17.3926	−	5.65118i	−0.589324	−	0.191483i
$872$	10.4778	+	14.4214i	0.354822	+	0.488371i
$873$		0			0
$874$	−8.96700	−	27.5976i	−0.303313	−	0.933503i
$875$	−0.0305901	−	0.0941467i	−0.00103414	−	0.00318274i
$876$		0			0
$877$	6.60112	+	9.08566i	0.222904	+	0.306801i	0.905792	−	0.423722i	$-0.139277\pi$
$877$	6.60112	+	9.08566i	0.222904	+	0.306801i	−0.682889	+	0.730523i	$0.739277\pi$
$878$	1.91872	+	0.623429i	0.0647536	+	0.0210397i
$879$		0			0
$880$	0.0512548	+	0.176547i	0.00172780	+	0.00595141i
$881$		−	47.3136i		−	1.59403i	−0.603957	−	0.797017i	$-0.706410\pi$
$881$		−	47.3136i		−	1.59403i	0.603957	−	0.797017i	$-0.293590\pi$
$882$		0			0
$883$	−14.7740	+	10.7340i	−0.497186	+	0.361227i	−0.807941	−	0.589263i	$-0.799418\pi$
$883$	−14.7740	+	10.7340i	−0.497186	+	0.361227i	0.310755	+	0.950490i	$0.399418\pi$
$884$	8.82917	−	12.1523i	0.296957	−	0.408727i
$885$		0			0
$886$	−23.4619	+	7.62324i	−0.788218	+	0.256108i
$887$	32.9354	+	23.9289i	1.10586	+	0.803455i	0.982007	−	0.188845i	$-0.0604744\pi$
$887$	32.9354	+	23.9289i	1.10586	+	0.803455i	0.123854	+	0.992300i	$0.460474\pi$
$888$		0			0
$889$	0.974242	−	2.99841i	0.0326750	−	0.100563i
$890$	−0.235876			−0.00790658
$891$		0			0
$892$	−14.7573			−0.494110
$893$	−21.3169	+	65.6066i	−0.713342	+	2.19544i
$894$		0			0
$895$	−0.228756	−	0.166201i	−0.00764648	−	0.00555549i
$896$	2.52676	−	0.820995i	0.0844132	−	0.0274275i
$897$		0			0
$898$	5.75057	−	7.91498i	0.191899	−	0.264126i
$899$	−21.7180	+	15.7790i	−0.724335	+	0.526260i
$900$		0			0
$901$			38.3480i			1.27756i
$902$	−0.692800	+	21.9106i	−0.0230677	+	0.729545i
$903$		0			0
$904$	−1.22003	−	0.396413i	−0.0405777	−	0.0131845i
$905$	0.497996	+	0.685433i	0.0165540	+	0.0227846i
$906$		0			0
$907$	0.365168	+	1.12387i	0.0121252	+	0.0373176i	0.956936	−	0.290299i	$-0.0937547\pi$
$907$	0.365168	+	1.12387i	0.0121252	+	0.0373176i	−0.944811	+	0.327616i	$0.893755\pi$
$908$	5.52581	+	17.0067i	0.183380	+	0.564387i
$909$		0			0
$910$	−0.00921881	−	0.0126886i	−0.000305601	−	0.000420623i
$911$	−20.1283	−	6.54007i	−0.666879	−	0.216682i	−0.0440370	−	0.999030i	$-0.514022\pi$
$911$	−20.1283	−	6.54007i	−0.666879	−	0.216682i	−0.622842	+	0.782348i	$0.714022\pi$
$912$		0			0
$913$	0.554880	−	17.5488i	0.0183639	−	0.580779i
$914$		−	14.0406i		−	0.464423i
$915$		0			0
$916$	25.2882	−	18.3730i	0.835547	−	0.607060i
$917$	−2.63394	+	3.62530i	−0.0869803	+	0.119718i
$918$		0			0
$919$	−13.4009	+	4.35422i	−0.442055	+	0.143633i	−0.521584	−	0.853200i	$-0.674659\pi$
$919$	−13.4009	+	4.35422i	−0.442055	+	0.143633i	0.0795283	+	0.996833i	$0.474659\pi$
$920$	−0.535527	−	0.389083i	−0.0176558	−	0.0128277i
$921$		0			0
$922$	0.163849	−	0.504277i	0.00539610	−	0.0166075i
$923$	7.66061			0.252152
$924$		0			0
$925$	−20.1477			−0.662454
$926$	8.03871	−	24.7406i	0.264168	−	0.813027i
$927$		0			0
$928$	−26.2812	−	19.0944i	−0.862723	−	0.626805i
$929$	32.4174	−	10.5331i	1.06358	−	0.345578i	0.275596	−	0.961273i	$-0.411125\pi$
$929$	32.4174	−	10.5331i	1.06358	−	0.345578i	0.787985	+	0.615695i	$0.211125\pi$
$930$		0			0
$931$	25.2880	−	34.8059i	0.828780	−	1.14072i
$932$	−19.9327	+	14.4819i	−0.652916	+	0.474371i
$933$		0			0
$934$			12.1157i			0.396438i
$935$	0.158598	+	0.546290i	0.00518669	+	0.0178656i
$936$		0			0
$937$	6.41974	+	2.08590i	0.209724	+	0.0681434i	0.411995	−	0.911186i	$-0.364832\pi$
$937$	6.41974	+	2.08590i	0.209724	+	0.0681434i	−0.202271	+	0.979330i	$0.564832\pi$
$938$	−0.793529	−	1.09220i	−0.0259096	−	0.0356616i
$939$		0			0
$940$	0.210473	+	0.647768i	0.00686486	+	0.0211279i
$941$	−10.2896	−	31.6682i	−0.335432	−	1.03235i	−0.966509	−	0.256633i	$-0.917387\pi$
$941$	−10.2896	−	31.6682i	−0.335432	−	1.03235i	0.631077	−	0.775720i	$-0.282613\pi$
$942$		0			0
$943$	38.3814	+	52.8275i	1.24987	+	1.72030i
$944$	3.66476	+	1.19075i	0.119278	+	0.0387557i
$945$		0			0
$946$	1.86060	+	1.44381i	0.0604934	+	0.0469422i
$947$		−	0.751232i		−	0.0244117i	−0.999926	−	0.0122059i	$-0.996115\pi$
$947$		−	0.751232i		−	0.0244117i	0.999926	−	0.0122059i	$-0.00388535\pi$
$948$		0			0
$949$	22.0712	−	16.0357i	0.716462	−	0.520540i
$950$	12.5376	−	17.2566i	0.406774	−	0.559877i
$951$		0			0
$952$	2.43658	−	0.791694i	0.0789701	−	0.0256589i
$953$	3.76491	+	2.73537i	0.121957	+	0.0886073i	0.647092	−	0.762412i	$-0.275985\pi$
$953$	3.76491	+	2.73537i	0.121957	+	0.0886073i	−0.525134	+	0.851019i	$0.675985\pi$
$954$		0			0
$955$	−0.169408	+	0.521385i	−0.00548192	+	0.0168716i
$956$	−43.3266			−1.40128
$957$		0			0
$958$	−1.65593			−0.0535007
$959$	1.22605	−	3.77340i	0.0395913	−	0.121849i
$960$		0			0
$961$	6.46012	+	4.69355i	0.208391	+	0.151405i
$962$	−6.07281	+	1.97318i	−0.195795	+	0.0636177i
$963$		0			0
$964$	−12.8874	+	17.7379i	−0.415074	+	0.571300i
$965$	0.812348	−	0.590205i	0.0261504	−	0.0189994i
$966$		0			0
$967$		−	21.7529i		−	0.699525i	−0.936838	−	0.349763i	$-0.886262\pi$
$967$		−	21.7529i		−	0.699525i	0.936838	−	0.349763i	$-0.113738\pi$
$968$	26.6447	+	1.68666i	0.856392	+	0.0542113i
$969$		0			0
$970$	−0.0795075	−	0.0258336i	−0.00255283	−	0.000829465i
$971$	−3.45215	−	4.75147i	−0.110785	−	0.152482i	0.750024	−	0.661410i	$-0.230042\pi$
$971$	−3.45215	−	4.75147i	−0.110785	−	0.152482i	−0.860809	+	0.508928i	$0.830042\pi$
$972$		0			0
$973$	−0.294236	−	0.905565i	−0.00943277	−	0.0290311i
$974$	3.10487	+	9.55579i	0.0994863	+	0.306187i
$975$		0			0
$976$	6.89195	+	9.48595i	0.220606	+	0.303638i
$977$	0.874965	+	0.284293i	0.0279926	+	0.00909535i	0.322980	−	0.946406i	$-0.395315\pi$
$977$	0.874965	+	0.284293i	0.0279926	+	0.00909535i	−0.294987	+	0.955501i	$0.595315\pi$
$978$		0			0
$979$	9.60429	−	26.6608i	0.306954	−	0.852083i
$980$		−	0.424783i		−	0.0135692i
$981$		0			0
$982$	13.9446	−	10.1313i	0.444989	−	0.323304i
$983$	27.4119	−	37.7293i	0.874304	−	1.20338i	−0.103662	−	0.994613i	$-0.533056\pi$
$983$	27.4119	−	37.7293i	0.874304	−	1.20338i	0.977966	−	0.208764i	$-0.0669440\pi$
$984$		0			0
$985$	0.802745	−	0.260828i	0.0255776	−	0.00831066i
$986$	−13.3244	−	9.68072i	−0.424334	−	0.308297i
$987$		0			0
$988$	−6.73006	+	20.7130i	−0.214112	+	0.658968i
$989$	7.01515			0.223069
$990$		0			0
$991$	6.21090			0.197296			0.0986478	−	0.995122i	$-0.468548\pi$
$991$	6.21090			0.197296			0.0986478	+	0.995122i	$0.468548\pi$
$992$	8.60631	−	26.4875i	0.273250	−	0.840978i
$993$		0			0
$994$	0.457518	+	0.332406i	0.0145116	+	0.0105433i
$995$	0.395607	−	0.128540i	0.0125416	−	0.00407500i
$996$		0			0
$997$	−16.7911	+	23.1110i	−0.531781	+	0.731933i	−0.987400	−	0.158241i	$-0.949418\pi$
$997$	−16.7911	+	23.1110i	−0.531781	+	0.731933i	0.455620	+	0.890174i	$0.349418\pi$
$998$	−12.6467	+	9.18836i	−0.400324	+	0.290852i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.j.a.35.3	yes	16
3.2	odd	2	inner	99.2.j.a.35.2	yes	16
4.3	odd	2		1584.2.cd.c.1025.2		16
9.2	odd	6		891.2.u.c.134.3		32
9.4	even	3		891.2.u.c.431.3		32
9.5	odd	6		891.2.u.c.431.2		32
9.7	even	3		891.2.u.c.134.2		32
11.4	even	5		1089.2.d.g.1088.12		16
11.6	odd	10	inner	99.2.j.a.17.2	✓	16
11.7	odd	10		1089.2.d.g.1088.6		16
12.11	even	2		1584.2.cd.c.1025.3		16
33.17	even	10	inner	99.2.j.a.17.3	yes	16
33.26	odd	10		1089.2.d.g.1088.5		16
33.29	even	10		1089.2.d.g.1088.11		16
44.39	even	10		1584.2.cd.c.17.3		16
99.50	even	30		891.2.u.c.512.2		32
99.61	odd	30		891.2.u.c.215.2		32
99.83	even	30		891.2.u.c.215.3		32
99.94	odd	30		891.2.u.c.512.3		32
132.83	odd	10		1584.2.cd.c.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.2	✓	16	11.6	odd	10	inner
99.2.j.a.17.3	yes	16	33.17	even	10	inner
99.2.j.a.35.2	yes	16	3.2	odd	2	inner
99.2.j.a.35.3	yes	16	1.1	even	1	trivial
891.2.u.c.134.2		32	9.7	even	3
891.2.u.c.134.3		32	9.2	odd	6
891.2.u.c.215.2		32	99.61	odd	30
891.2.u.c.215.3		32	99.83	even	30
891.2.u.c.431.2		32	9.5	odd	6
891.2.u.c.431.3		32	9.4	even	3
891.2.u.c.512.2		32	99.50	even	30
891.2.u.c.512.3		32	99.94	odd	30
1089.2.d.g.1088.5		16	33.26	odd	10
1089.2.d.g.1088.6		16	11.7	odd	10
1089.2.d.g.1088.11		16	33.29	even	10
1089.2.d.g.1088.12		16	11.4	even	5
1584.2.cd.c.17.2		16	132.83	odd	10
1584.2.cd.c.17.3		16	44.39	even	10
1584.2.cd.c.1025.2		16	4.3	odd	2
1584.2.cd.c.1025.3		16	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.212694 - 0.654604i) q^{2} +(1.23477 + 0.897110i) q^{4} +(-0.0381457 + 0.0123943i) q^{5} +(0.145094 - 0.199704i) q^{7} +(1.96356 - 1.42661i) q^{8} +0.0276065i q^{10} +(-3.12033 - 1.12407i) q^{11} +(-2.18888 - 0.711209i) q^{13} +(-0.0998667 - 0.137455i) q^{14} +(0.427051 + 1.31433i) q^{16} +(1.32142 + 4.06692i) q^{17} +(-3.64429 - 5.01593i) q^{19} +(-0.0582200 - 0.0189168i) q^{20} +(-1.39949 + 1.80350i) q^{22} +6.79984i q^{23} +(-4.04378 + 2.93798i) q^{25} +(-0.931121 + 1.28158i) q^{26} +(0.358314 - 0.116423i) q^{28} +(-4.52705 - 3.28909i) q^{29} +(1.48247 - 4.56258i) q^{31} +5.80538 q^{32} +2.94328 q^{34} +(-0.00305951 + 0.00941619i) q^{35} +(3.26102 + 2.36927i) q^{37} +(-4.05857 + 1.31871i) q^{38} +(-0.0572194 + 0.0787558i) q^{40} +(7.76893 - 5.64446i) q^{41} -1.03166i q^{43} +(-2.84447 - 4.18724i) q^{44} +(4.45120 + 1.44628i) q^{46} +(-6.53982 - 9.00129i) q^{47} +(2.14429 + 6.59944i) q^{49} +(1.06313 + 3.27197i) q^{50} +(-2.06472 - 2.84184i) q^{52} +(8.52885 + 2.77119i) q^{53} +(0.132959 + 0.00420408i) q^{55} -0.599123i q^{56} +(-3.11593 + 2.26385i) q^{58} +(1.63893 - 2.25580i) q^{59} +(8.06923 - 2.62185i) q^{61} +(-2.67137 - 1.94086i) q^{62} +(0.380665 - 1.17156i) q^{64} +0.0923111 q^{65} +7.94588 q^{67} +(-2.01683 + 6.20715i) q^{68} +(0.00551314 + 0.00400553i) q^{70} +(-3.16559 + 1.02856i) q^{71} +(-6.96743 + 9.58984i) q^{73} +(2.24453 - 1.63075i) q^{74} -9.46284i q^{76} +(-0.677222 + 0.460048i) q^{77} +(-2.86363 - 0.930451i) q^{79} +(-0.0325803 - 0.0448429i) q^{80} +(-2.04248 - 6.28611i) q^{82} +(1.63587 + 5.03470i) q^{83} +(-0.100813 - 0.138757i) q^{85} +(-0.675331 - 0.219428i) q^{86} +(-7.73055 + 2.24432i) q^{88} +8.54422i q^{89} +(-0.459624 + 0.333936i) q^{91} +(-6.10021 + 8.39621i) q^{92} +(-7.28326 + 2.36647i) q^{94} +(0.201183 + 0.146168i) q^{95} +(-0.935778 + 2.88003i) q^{97} +4.77610 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70}+ \cdots + 60 q^{97}+O(q^{100}) \) 16 * q - 4 * q^4 - 20 * q^16 - 48 * q^22 - 32 * q^25 + 40 * q^28 + 16 * q^31 + 40 * q^34 - 12 * q^37 + 60 * q^40 - 40 * q^46 - 24 * q^49 - 40 * q^52 + 16 * q^55 + 12 * q^58 + 36 * q^64 + 96 * q^67 + 76 * q^70 - 20 * q^73 - 12 * q^82 - 100 * q^85 - 12 * q^88 - 72 * q^91 - 80 * q^94 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more