LMFDB - Embedded newform 99.2.j.a.17.3

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			17.3
Root			$-1.90184 - 0.0324487i$ of defining polynomial
Character	$\chi$	$=$	99.17
Dual form			99.2.j.a.35.3

$q$-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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

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	0.997665	−	0.0682903i	$-0.0217544\pi$
$2$	0.212694	+	0.654604i	0.150397	+	0.462875i	−0.847268	+	0.531165i	$0.821754\pi$
$3$		0			0
$3$		0			0
$4$	1.23477	−	0.897110i	0.617383	−	0.448555i
$5$	−0.0381457	−	0.0123943i	−0.0170593	−	0.00554289i	0.300475	−	0.953790i	$-0.402855\pi$
$5$	−0.0381457	−	0.0123943i	−0.0170593	−	0.00554289i	−0.317534	+	0.948247i	$0.602855\pi$
$6$		0			0
$7$	0.145094	+	0.199704i	0.0548403	+	0.0754811i	0.835556	−	0.549405i	$-0.185145\pi$
$7$	0.145094	+	0.199704i	0.0548403	+	0.0754811i	−0.780716	+	0.624886i	$0.785145\pi$
$8$	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	−0.596398	−	0.802689i	$-0.703402\pi$
$13$	−2.18888	+	0.711209i	−0.607085	+	0.197254i	−0.0106874	+	0.999943i	$0.503402\pi$
$14$	−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	−0.652943	−	0.757407i	$-0.726466\pi$
$17$	1.32142	−	4.06692i	0.320492	−	0.986372i	0.973435	−	0.228965i	$-0.0735342\pi$
$18$		0			0
$19$	−3.64429	+	5.01593i	−0.836057	+	1.15073i	0.150708	+	0.988578i	$0.451845\pi$
$19$	−3.64429	+	5.01593i	−0.836057	+	1.15073i	−0.986765	+	0.162156i	$0.948155\pi$
$20$	−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	$-0.749177\pi$
$23$		−	6.79984i		−	1.41786i	0.705277	−	0.708932i	$-0.250823\pi$
$24$		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	−0.922553	−	0.385871i	$-0.873901\pi$
$29$	−4.52705	+	3.28909i	−0.840652	+	0.610769i	0.0819007	+	0.996640i	$0.473901\pi$
$30$		0			0
$31$	1.48247	+	4.56258i	0.266260	+	0.819463i	0.991401	+	0.130863i	$0.0417747\pi$
$31$	1.48247	+	4.56258i	0.266260	+	0.819463i	−0.725141	+	0.688601i	$0.758225\pi$
$32$	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	−0.286529	−	0.958072i	$-0.592502\pi$
$37$	3.26102	−	2.36927i	0.536109	−	0.389506i	0.822638	+	0.568566i	$0.192502\pi$
$38$	−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	0.995527	−	0.0944820i	$-0.0301195\pi$
$41$	7.76893	+	5.64446i	1.21330	+	0.881517i	0.217777	+	0.975999i	$0.430119\pi$
$42$		0			0
$43$			1.03166i			0.157327i	0.996901	+	0.0786636i	$0.0250653\pi$
$43$			1.03166i			0.157327i	−0.996901	+	0.0786636i	$0.974935\pi$
$44$	−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	−0.00417211	+	0.999991i	$0.501328\pi$
$47$	−6.53982	+	9.00129i	−0.953931	+	1.31297i	−0.949759	+	0.312982i	$0.898672\pi$
$48$		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	0.342314	−	0.939585i	$-0.388789\pi$
$53$	8.52885	−	2.77119i	1.17153	−	0.380652i	0.829213	+	0.558933i	$0.188789\pi$
$54$		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	0.902265	−	0.431182i	$-0.141903\pi$
$59$	1.63893	+	2.25580i	0.213371	+	0.293680i	−0.688894	+	0.724862i	$0.741903\pi$
$60$		0			0
$61$	8.06923	+	2.62185i	1.03316	+	0.335694i	0.776039	−	0.630685i	$-0.217226\pi$
$61$	8.06923	+	2.62185i	1.03316	+	0.335694i	0.257121	+	0.966379i	$0.417226\pi$
$62$	−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	0.115086	−	0.993355i	$-0.463286\pi$
$71$	−3.16559	−	1.02856i	−0.375687	−	0.122068i	−0.490773	+	0.871288i	$0.663286\pi$
$72$		0			0
$73$	−6.96743	−	9.58984i	−0.815476	−	1.12241i	−0.990455	−	0.137834i	$-0.955986\pi$
$73$	−6.96743	−	9.58984i	−0.815476	−	1.12241i	0.174980	−	0.984572i	$-0.444014\pi$
$74$	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	−0.465644	−	0.884972i	$-0.654177\pi$
$79$	−2.86363	+	0.930451i	−0.322184	+	0.104684i	0.143460	+	0.989656i	$0.454177\pi$
$80$	−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	−0.820252	−	0.572002i	$-0.806167\pi$
$83$	1.63587	−	5.03470i	0.179560	−	0.552630i	0.999812	+	0.0193724i	$0.00616680\pi$
$84$		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	$-0.850410\pi$
$89$		−	8.54422i		−	0.905686i	0.891590	−	0.452843i	$-0.149590\pi$
$90$		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	0.892243	−	0.451555i	$-0.149130\pi$
$97$	−0.935778	−	2.88003i	−0.0950139	−	0.292423i	−0.987257	+	0.159132i	$0.949130\pi$
$98$	4.77610			0.482459
$99$		0			0
$100$	−7.62882			−0.762882
$101$	2.14828	+	6.61172i	0.213762	+	0.657891i	0.999239	+	0.0390007i	$0.0124175\pi$
$101$	2.14828	+	6.61172i	0.213762	+	0.657891i	−0.785477	+	0.618890i	$0.787583\pi$
$102$		0			0
$103$	−10.6138	+	7.71139i	−1.04581	+	0.759826i	−0.971411	−	0.237402i	$-0.923704\pi$
$103$	−10.6138	+	7.71139i	−1.04581	+	0.759826i	−0.0743996	+	0.997229i	$0.523704\pi$
$104$	−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	0.640012	−	0.768365i	$-0.278929\pi$
$107$	1.10712	+	0.804368i	0.107029	+	0.0777612i	−0.532983	+	0.846126i	$0.678929\pi$
$108$		0			0
$109$		−	7.34454i		−	0.703480i	−0.936098	−	0.351740i	$-0.885590\pi$
$109$		−	7.34454i		−	0.703480i	0.936098	−	0.351740i	$-0.114410\pi$
$110$	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	−0.823380	−	0.567491i	$-0.807914\pi$
$113$	−0.310669	+	0.427600i	−0.0292253	+	0.0402252i	0.794154	+	0.607716i	$0.207914\pi$
$114$		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	0.793541	−	0.608517i	$-0.208235\pi$
$127$	12.1468	+	3.94673i	1.07785	+	0.350215i	0.284311	+	0.958732i	$0.408235\pi$
$128$	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	0.877664	−	0.479276i	$-0.159101\pi$
$137$	15.2863	+	4.96682i	1.30600	+	0.424344i	0.428334	+	0.903621i	$0.359101\pi$
$138$		0			0
$139$	2.26727	+	3.12062i	0.192307	+	0.264688i	0.894272	−	0.447523i	$-0.147694\pi$
$139$	2.26727	+	3.12062i	0.192307	+	0.264688i	−0.701965	+	0.712211i	$0.747694\pi$
$140$	−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	0.732813	+	0.680430i	$0.238207\pi$
$149$	−3.17360	+	9.76734i	−0.259992	+	0.800172i	−0.992805	+	0.119742i	$0.961793\pi$
$150$		0			0
$151$	5.15512	−	7.09542i	0.419518	−	0.577417i	−0.545990	−	0.837792i	$-0.683846\pi$
$151$	5.15512	−	7.09542i	0.419518	−	0.577417i	0.965508	+	0.260375i	$0.0838462\pi$
$152$	−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	0.922749	−	0.385400i	$-0.125937\pi$
$157$	10.5422	+	7.65934i	0.841357	+	0.611282i	−0.0813923	+	0.996682i	$0.525937\pi$
$158$	−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	−0.998569	−	0.0534700i	$-0.982972\pi$
$163$	−2.83608	−	8.72855i	−0.222139	−	0.683673i	0.776431	−	0.630203i	$-0.217028\pi$
$164$	14.6565			1.14448
$165$		0			0
$166$	3.64367			0.282804
$167$	2.35141	+	7.23691i	0.181958	+	0.560009i	0.999883	−	0.0153164i	$-0.00487554\pi$
$167$	2.35141	+	7.23691i	0.181958	+	0.560009i	−0.817925	+	0.575325i	$0.804876\pi$
$168$		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	−0.0555432	−	0.998456i	$-0.517689\pi$
$173$	−13.4462	−	9.76923i	−1.02230	−	0.742741i	−0.966752	+	0.255715i	$0.917689\pi$
$174$		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	−0.625574	−	0.780165i	$-0.715135\pi$
$179$	4.14376	−	5.70340i	0.309719	−	0.426292i	0.935294	+	0.353872i	$0.115135\pi$
$180$		0			0
$181$	−6.52756	+	20.0898i	−0.485189	+	1.49326i	0.346517	+	0.938044i	$0.387364\pi$
$181$	−6.52756	+	20.0898i	−0.485189	+	1.49326i	−0.831706	+	0.555216i	$0.812636\pi$
$182$	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	0.993839	−	0.110831i	$-0.0353511\pi$
$191$	8.03400	+	11.0579i	0.581320	+	0.800118i	−0.412519	+	0.910949i	$0.635351\pi$
$192$		0			0
$193$	−23.8096	−	7.73620i	−1.71385	−	0.556864i	−0.722884	−	0.690969i	$-0.757184\pi$
$193$	−23.8096	−	7.73620i	−1.71385	−	0.556864i	−0.990967	+	0.134105i	$0.957184\pi$
$194$	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	−0.849702	−	0.527263i	$-0.823218\pi$
$211$	−17.8262	+	5.79210i	−1.22721	+	0.398744i	−0.377506	+	0.926007i	$0.623218\pi$
$212$	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	0.294220	−	0.955738i	$-0.404940\pi$
$223$	−7.82233	−	5.68326i	−0.523822	−	0.380579i	−0.818042	+	0.575159i	$0.804940\pi$
$224$	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	−0.226978	−	0.973900i	$-0.572884\pi$
$227$	9.47859	−	6.88660i	0.629116	−	0.457080i	0.856094	+	0.516820i	$0.172884\pi$
$228$		0			0
$229$	6.32872	+	19.4778i	0.418214	+	1.28713i	0.909345	+	0.416044i	$0.136584\pi$
$229$	6.32872	+	19.4778i	0.418214	+	1.28713i	−0.491131	+	0.871086i	$0.663416\pi$
$230$	−0.187720			−0.0123779
$231$		0			0
$232$	−13.5814			−0.891661
$233$	−4.98842	−	15.3528i	−0.326802	−	1.00579i	−0.970621	−	0.240615i	$-0.922651\pi$
$233$	−4.98842	−	15.3528i	−0.326802	−	1.00579i	0.643818	−	0.765178i	$-0.277349\pi$
$234$		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	−0.975716	−	0.219038i	$-0.929708\pi$
$239$	−22.9660	−	16.6858i	−1.48555	−	1.07931i	−0.509830	−	0.860275i	$-0.670292\pi$
$240$		0			0
$241$		−	14.3654i		−	0.925357i	−0.886526	−	0.462679i	$-0.846888\pi$
$241$		−	14.3654i		−	0.925357i	0.886526	−	0.462679i	$-0.153112\pi$
$242$	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	−0.509896	−	0.860236i	$-0.670316\pi$
$251$	−6.60298	+	2.14544i	−0.416776	+	0.135419i	0.0931196	+	0.995655i	$0.470316\pi$
$252$		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	0.956110	−	0.293009i	$-0.0946567\pi$
$257$	6.12372	+	8.42858i	0.381987	+	0.525760i	−0.574122	+	0.818769i	$0.694657\pi$
$258$		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	0.611686	−	0.791101i	$-0.290492\pi$
$269$	10.5223	+	3.41889i	0.641553	+	0.208453i	0.0298672	+	0.999554i	$0.490492\pi$
$270$		0			0
$271$	9.34327	+	12.8599i	0.567563	+	0.781184i	0.992263	−	0.124150i	$-0.0396205\pi$
$271$	9.34327	+	12.8599i	0.567563	+	0.781184i	−0.424700	+	0.905334i	$0.639621\pi$
$272$	−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	0.0335051	−	0.999439i	$-0.489333\pi$
$277$	10.7860	−	3.50458i	0.648066	−	0.210570i	0.614561	+	0.788869i	$0.289333\pi$
$278$	−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	−0.964408	−	0.264420i	$-0.914819\pi$
$281$	−0.482158	+	1.48393i	−0.0287631	+	0.0885238i	0.935644	+	0.352944i	$0.114819\pi$
$282$		0			0
$283$	15.6148	−	21.4919i	0.928202	−	1.27756i	−0.0323551	−	0.999476i	$-0.510301\pi$
$283$	15.6148	−	21.4919i	0.928202	−	1.27756i	0.960557	−	0.278084i	$-0.0896993\pi$
$284$	−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	−0.997900	−	0.0647811i	$-0.979365\pi$
$293$	−21.3051	+	15.4791i	−1.24466	+	0.904296i	−0.246757	+	0.969077i	$0.579365\pi$
$294$		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	$-0.733789\pi$
$307$		−	26.0083i		−	1.48437i	0.670195	−	0.742185i	$-0.266211\pi$
$308$	−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	−0.527003	−	0.849863i	$-0.676684\pi$
$311$	7.83210	−	10.7800i	0.444118	−	0.611276i	0.971121	+	0.238588i	$0.0766844\pi$
$312$		0			0
$313$	−3.47592	+	10.6978i	−0.196471	+	0.604675i	0.803486	+	0.595324i	$0.202976\pi$
$313$	−3.47592	+	10.6978i	−0.196471	+	0.604675i	−0.999956	+	0.00935037i	$0.997024\pi$
$314$	−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	−0.586563	−	0.809904i	$-0.699519\pi$
$317$	−10.4166	+	3.38455i	−0.585053	+	0.190095i	0.00151019	+	0.999999i	$0.499519\pi$
$318$		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	0.764264	−	0.644903i	$-0.223102\pi$
$337$	−1.56491	−	2.15391i	−0.0852460	−	0.117331i	−0.849510	+	0.527572i	$0.823102\pi$
$338$	−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	−0.713678	−	0.700474i	$-0.752972\pi$
$347$	5.13066	−	15.7905i	0.275428	−	0.847681i	0.989106	−	0.147207i	$-0.0470282\pi$
$348$		0			0
$349$	−8.09660	+	11.1440i	−0.433401	+	0.596525i	−0.968730	−	0.248118i	$-0.920188\pi$
$349$	−8.09660	+	11.1440i	−0.433401	+	0.596525i	0.535329	+	0.844644i	$0.320188\pi$
$350$	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	$0.0947860\pi$
$353$			11.0249i			0.586795i	−0.955990	+	0.293398i	$0.905214\pi$
$354$		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	−0.102499	−	0.994733i	$-0.532684\pi$
$359$	15.3828	−	11.1763i	0.811875	−	0.589862i	0.914374	+	0.404871i	$0.132684\pi$
$360$		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	−0.460954	−	0.887424i	$-0.652493\pi$
$367$	4.60911	−	3.34872i	0.240594	−	0.174802i	0.701548	+	0.712622i	$0.252493\pi$
$368$	−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	$0.194486\pi$
$373$			22.1594i			1.14737i	−0.819076	+	0.573684i	$0.805514\pi$
$374$	−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	−0.954038	−	0.299687i	$-0.903118\pi$
$379$	−0.117844	+	0.362687i	−0.00605325	+	0.0186300i	0.947984	+	0.318317i	$0.103118\pi$
$380$	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	0.0153308	−	0.999882i	$-0.495120\pi$
$383$	12.0446	−	3.91352i	0.615450	−	0.199972i	0.600119	+	0.799911i	$0.295120\pi$
$384$		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	−0.999813	−	0.0193359i	$-0.993845\pi$
$389$	−13.9885	−	19.2535i	−0.709243	−	0.976190i	0.290570	−	0.956854i	$-0.406155\pi$
$390$		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	0.408062	−	0.912954i	$-0.366205\pi$
$401$	4.03643	+	1.31151i	0.201570	+	0.0654939i	−0.206492	+	0.978448i	$0.566205\pi$
$402$		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	−0.573150	−	0.819450i	$-0.694279\pi$
$409$	−11.2278	+	3.64812i	−0.555177	+	0.180388i	0.0179728	+	0.999838i	$0.494279\pi$
$410$	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	$-0.828735\pi$
$419$		−	20.9795i		−	1.02492i	0.858712	−	0.512459i	$-0.171265\pi$
$420$		0			0
$421$	2.24889	+	1.63391i	0.109604	+	0.0796320i	0.641237	−	0.767343i	$-0.278421\pi$
$421$	2.24889	+	1.63391i	0.109604	+	0.0796320i	−0.531633	+	0.846975i	$0.678421\pi$
$422$	−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	0.911604	+	0.411070i	$0.134845\pi$
$431$	8.63060	+	26.5623i	0.415722	+	1.27946i	−0.495882	+	0.868390i	$0.665155\pi$
$432$		0			0
$433$	7.41714	−	5.38887i	0.356445	−	0.258973i	−0.395123	−	0.918628i	$-0.629298\pi$
$433$	7.41714	−	5.38887i	0.356445	−	0.258973i	0.751568	+	0.659656i	$0.229298\pi$
$434$	−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	$-0.977717\pi$
$439$		−	2.93111i		−	0.139894i	0.997551	−	0.0699472i	$-0.0222831\pi$
$440$	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	−0.0761695	+	0.997095i	$0.524269\pi$
$443$	−21.0670	+	28.9963i	−1.00093	+	1.37766i	−0.924756	+	0.380561i	$0.875731\pi$
$444$		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	0.0278700	−	0.999612i	$-0.491128\pi$
$449$	13.5184	−	4.39241i	0.637974	−	0.207290i	0.610104	+	0.792321i	$0.291128\pi$
$450$		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	0.725343	−	0.688387i	$-0.241681\pi$
$457$	19.4009	+	6.30372i	0.907534	+	0.294876i	0.182191	+	0.983263i	$0.441681\pi$
$458$	−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	−0.105115	−	0.994460i	$-0.533521\pi$
$467$	−16.7411	−	5.43950i	−0.774684	−	0.251710i	−0.669569	+	0.742750i	$0.733521\pi$
$468$		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	−0.966603	−	0.256277i	$-0.917504\pi$
$479$	−0.743452	+	2.28811i	−0.0339692	+	0.104546i	0.932634	+	0.360823i	$0.117504\pi$
$480$		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	0.287126	−	0.957893i	$-0.407300\pi$
$487$	−11.8099	−	8.58039i	−0.535157	−	0.388815i	−0.822283	+	0.569078i	$0.807300\pi$
$488$	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	−0.0277932	−	0.999614i	$-0.508848\pi$
$491$	20.2597	−	14.7195i	0.914307	−	0.664283i	0.942101	+	0.335331i	$0.108848\pi$
$492$		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	−0.917438	−	0.397880i	$-0.869746\pi$
$499$	−18.3740	+	13.3495i	−0.822535	+	0.597607i	0.0949025	+	0.995487i	$0.469746\pi$
$500$	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	0.759450	−	0.650566i	$-0.225468\pi$
$503$	8.41953	+	6.11715i	0.375408	+	0.272750i	−0.384042	+	0.923316i	$0.625468\pi$
$504$		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	−0.901249	−	0.433302i	$-0.857348\pi$
$509$	−4.75254	+	6.54130i	−0.210652	+	0.289938i	0.690596	+	0.723241i	$0.257348\pi$
$510$		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	−0.969881	−	0.243578i	$-0.921679\pi$
$521$	−20.5846	−	28.3323i	−0.901828	−	1.24126i	0.0680535	−	0.997682i	$-0.478321\pi$
$522$		0			0
$523$	41.1766	+	13.3791i	1.80052	+	0.585026i	0.999900	−	0.0141400i	$-0.00450104\pi$
$523$	41.1766	+	13.3791i	1.80052	+	0.585026i	0.800625	+	0.599166i	$0.204501\pi$
$524$	−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	−0.313641	−	0.949542i	$-0.601549\pi$
$541$	−0.215252	+	0.0699396i	−0.00925440	+	0.00300694i	0.304386	+	0.952549i	$0.401549\pi$
$542$	−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	−0.964129	−	0.265435i	$-0.914484\pi$
$547$	−9.67686	+	13.3191i	−0.413753	+	0.569482i	0.550376	+	0.834917i	$0.314484\pi$
$548$	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	−0.938702	−	0.344730i	$-0.887970\pi$
$557$	−21.2624	+	15.4481i	−0.900919	+	0.654556i	0.0377832	+	0.999286i	$0.487970\pi$
$558$		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	−0.847823	−	0.530279i	$-0.822087\pi$
$563$	−11.2376	−	34.5859i	−0.473610	−	1.45762i	0.374213	−	0.927343i	$-0.377913\pi$
$564$		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	0.875388	−	0.483420i	$-0.160606\pi$
$569$	16.3670	+	11.8913i	0.686138	+	0.498509i	−0.189250	+	0.981929i	$0.560606\pi$
$570$		0			0
$571$			24.4002i			1.02112i	0.859843	+	0.510558i	$0.170561\pi$
$571$			24.4002i			1.02112i	−0.859843	+	0.510558i	$0.829439\pi$
$572$	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	0.746748	+	0.665107i	$0.231614\pi$
$577$	−5.96494	+	18.3582i	−0.248324	+	0.764262i	−0.995072	+	0.0991553i	$0.968386\pi$
$578$	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	0.511128	−	0.859504i	$-0.329228\pi$
$587$	−11.2480	−	15.4816i	−0.464256	−	0.638994i	−0.975385	+	0.220510i	$0.929228\pi$
$588$		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	−0.421549	−	0.906806i	$-0.638513\pi$
$599$	−31.7090	−	10.3029i	−1.29560	−	0.420965i	−0.874047	+	0.485841i	$0.838513\pi$
$600$		0			0
$601$	−24.8474	−	34.1996i	−1.01355	−	1.39503i	−0.916630	−	0.399737i	$-0.869102\pi$
$601$	−24.8474	−	34.1996i	−1.01355	−	1.39503i	−0.0969178	−	0.995292i	$-0.530898\pi$
$602$	−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	−0.836909	−	0.547342i	$-0.815640\pi$
$607$	−29.3742	+	9.54427i	−1.19226	+	0.387390i	−0.355354	+	0.934732i	$0.615640\pi$
$608$	−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	−0.955383	−	0.295368i	$-0.904558\pi$
$613$	−9.38958	+	12.9237i	−0.379242	+	0.521981i	0.576142	+	0.817350i	$0.304558\pi$
$614$	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	$-0.983117\pi$
$617$		−	2.63374i		−	0.106030i	0.998594	−	0.0530151i	$-0.0168831\pi$
$618$		0			0
$619$	−16.3822	−	11.9023i	−0.658454	−	0.478395i	0.207686	−	0.978196i	$-0.433407\pi$
$619$	−16.3822	−	11.9023i	−0.658454	−	0.478395i	−0.866141	+	0.499800i	$0.833407\pi$
$620$	−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	−0.715349	−	0.698767i	$-0.753732\pi$
$631$	−6.82846	+	4.96116i	−0.271837	+	0.197501i	0.443512	+	0.896268i	$0.353732\pi$
$632$	−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	−0.247749	−	0.968824i	$-0.579691\pi$
$641$	18.9940	−	26.1429i	0.750216	−	1.03258i	0.997965	−	0.0637599i	$-0.0203092\pi$
$642$		0			0
$643$	4.25724	−	13.1024i	0.167889	−	0.516709i	−0.831349	−	0.555751i	$-0.812431\pi$
$643$	4.25724	−	13.1024i	0.167889	−	0.516709i	0.999238	+	0.0390421i	$0.0124306\pi$
$644$	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	−0.464064	−	0.885802i	$-0.653609\pi$
$647$	−8.11003	+	2.63511i	−0.318838	+	0.103597i	0.145226	+	0.989399i	$0.453609\pi$
$648$		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	0.794898	−	0.606743i	$-0.207524\pi$
$653$	−0.710037	−	0.977282i	−0.0277859	−	0.0382440i	−0.822684	+	0.568499i	$0.807524\pi$
$654$		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	0.577835	−	0.816153i	$-0.303898\pi$
$673$	39.5629	−	12.8548i	1.52504	−	0.495514i	0.947201	+	0.320639i	$0.103898\pi$
$674$	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	−0.920617	−	0.390467i	$-0.872314\pi$
$677$	1.39693	−	4.29931i	0.0536884	−	0.165236i	0.974305	+	0.225231i	$0.0723137\pi$
$678$		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	$0.231729\pi$
$683$			34.7783i			1.33075i	−0.746507	+	0.665377i	$0.768271\pi$
$684$		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	−0.999458	−	0.0329217i	$-0.989519\pi$
$691$	−5.52630	−	17.0082i	−0.210230	−	0.647023i	0.789228	−	0.614101i	$-0.210481\pi$
$692$	−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	0.821797	−	0.569781i	$-0.192972\pi$
$701$	14.1345	+	10.2693i	0.533852	+	0.387866i	−0.287945	+	0.957647i	$0.592972\pi$
$702$		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	−0.890940	−	0.454121i	$-0.849953\pi$
$709$	2.57673	−	7.93037i	0.0967713	−	0.297831i	0.987711	+	0.156290i	$0.0499533\pi$
$710$	−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	0.985145	−	0.171726i	$-0.0549344\pi$
$719$	13.8736	+	19.0953i	0.517397	+	0.712136i	−0.467748	+	0.883862i	$0.654934\pi$
$720$		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	0.573849	−	0.818961i	$-0.305450\pi$
$733$	−10.3520	−	14.2482i	−0.382358	−	0.526271i	−0.956207	+	0.292690i	$0.905450\pi$
$734$	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	−0.391390	−	0.920225i	$-0.628006\pi$
$739$	−4.54355	+	1.47629i	−0.167137	+	0.0543062i	0.224253	+	0.974531i	$0.428006\pi$
$740$	−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	−0.960933	−	0.276781i	$-0.910732\pi$
$743$	−0.567901	+	1.74782i	−0.0208343	+	0.0641212i	0.940099	+	0.340902i	$0.110732\pi$
$744$		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	0.984236	−	0.176859i	$-0.0565938\pi$
$751$	30.6978	+	22.3033i	1.12018	+	0.813857i	0.135942	+	0.990717i	$0.456594\pi$
$752$	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	−0.962128	−	0.272596i	$-0.912118\pi$
$757$	−9.46409	−	29.1275i	−0.343978	−	1.05866i	0.618150	−	0.786060i	$-0.287882\pi$
$758$	−0.262481			−0.00953373
$759$		0			0
$760$	0.603558			0.0218934
$761$	9.53788	+	29.3546i	0.345748	+	1.06410i	0.961182	+	0.275914i	$0.0889806\pi$
$761$	9.53788	+	29.3546i	0.345748	+	1.06410i	−0.615434	+	0.788188i	$0.711019\pi$
$762$		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	$-0.886771\pi$
$769$		−	19.3154i		−	0.696532i	0.937396	−	0.348266i	$-0.113229\pi$
$770$	−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	−0.776785	−	0.629766i	$-0.783151\pi$
$773$	1.72928	−	2.38015i	0.0621980	−	0.0856082i	0.838983	+	0.544158i	$0.183151\pi$
$774$		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	0.169443	−	0.985540i	$-0.445803\pi$
$787$	−7.65190	−	2.48625i	−0.272761	−	0.0886254i	−0.442204	+	0.896915i	$0.645803\pi$
$788$	−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	0.996799	+	0.0799446i	$0.0254743\pi$
$797$	52.2338	+	16.9718i	1.85022	+	0.601172i	0.853418	+	0.521227i	$0.174526\pi$
$798$		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	0.727212	+	0.686413i	$0.240816\pi$
$809$	−7.52538	+	23.1607i	−0.264578	+	0.814288i	−0.991790	+	0.127875i	$0.959184\pi$
$810$		0			0
$811$	−12.2026	+	16.7955i	−0.428493	+	0.589770i	−0.967607	−	0.252463i	$-0.918759\pi$
$811$	−12.2026	+	16.7955i	−0.428493	+	0.589770i	0.539114	+	0.842233i	$0.318759\pi$
$812$	−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	−0.104845	−	0.994489i	$-0.533435\pi$
$821$	23.1681	−	16.8326i	0.808571	−	0.587461i	0.913416	+	0.407027i	$0.133435\pi$
$822$		0			0
$823$	0.768785	+	2.36608i	0.0267982	+	0.0824763i	0.963561	−	0.267488i	$-0.0861936\pi$
$823$	0.768785	+	2.36608i	0.0267982	+	0.0824763i	−0.936763	+	0.349964i	$0.886194\pi$
$824$	−31.8420			−1.10927
$825$		0			0
$826$	−0.473745			−0.0164837
$827$	7.36490	+	22.6668i	0.256103	+	0.788202i	0.993610	+	0.112864i	$0.0360024\pi$
$827$	7.36490	+	22.6668i	0.256103	+	0.788202i	−0.737508	+	0.675338i	$0.763998\pi$
$828$		0			0
$829$	32.8736	−	23.8841i	1.14175	−	0.829528i	0.154386	−	0.988011i	$-0.450660\pi$
$829$	32.8736	−	23.8841i	1.14175	−	0.829528i	0.987362	+	0.158482i	$0.0506601\pi$
$830$	−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	0.454525	−	0.890734i	$-0.349809\pi$
$839$	33.6349	−	46.2945i	1.16121	−	1.59826i	0.706683	−	0.707531i	$-0.250191\pi$
$840$		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	−0.233852	−	0.972272i	$-0.575133\pi$
$853$	−29.0464	−	9.43774i	−0.994529	−	0.323142i	−0.760677	+	0.649130i	$0.775133\pi$
$854$	−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	−0.481129	−	0.876650i	$-0.659773\pi$
$863$	−40.7061	−	13.2262i	−1.38565	−	0.450226i	−0.904523	+	0.426424i	$0.859773\pi$
$864$		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	−0.682889	−	0.730523i	$-0.739277\pi$
$877$	6.60112	−	9.08566i	0.222904	−	0.306801i	0.905792	+	0.423722i	$0.139277\pi$
$878$	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	$0.293590\pi$
$881$			47.3136i			1.59403i	−0.603957	+	0.797017i	$0.706410\pi$
$882$		0			0
$883$	−14.7740	−	10.7340i	−0.497186	−	0.361227i	0.310755	−	0.950490i	$-0.399418\pi$
$883$	−14.7740	−	10.7340i	−0.497186	−	0.361227i	−0.807941	+	0.589263i	$0.799418\pi$
$884$	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	0.123854	−	0.992300i	$-0.460474\pi$
$887$	32.9354	−	23.9289i	1.10586	−	0.803455i	0.982007	+	0.188845i	$0.0604744\pi$
$888$		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	−0.944811	−	0.327616i	$-0.893755\pi$
$907$	0.365168	−	1.12387i	0.0121252	−	0.0373176i	0.956936	+	0.290299i	$0.0937547\pi$
$908$	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	−0.622842	−	0.782348i	$-0.714022\pi$
$911$	−20.1283	+	6.54007i	−0.666879	+	0.216682i	−0.0440370	+	0.999030i	$0.514022\pi$
$912$		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	0.0795283	−	0.996833i	$-0.474659\pi$
$919$	−13.4009	−	4.35422i	−0.442055	−	0.143633i	−0.521584	+	0.853200i	$0.674659\pi$
$920$	−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	0.787985	−	0.615695i	$-0.211125\pi$
$929$	32.4174	+	10.5331i	1.06358	+	0.345578i	0.275596	+	0.961273i	$0.411125\pi$
$930$		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	−0.202271	−	0.979330i	$-0.564832\pi$
$937$	6.41974	−	2.08590i	0.209724	−	0.0681434i	0.411995	+	0.911186i	$0.364832\pi$
$938$	−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	0.631077	+	0.775720i	$0.282613\pi$
$941$	−10.2896	+	31.6682i	−0.335432	+	1.03235i	−0.966509	+	0.256633i	$0.917387\pi$
$942$		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	$0.00388535\pi$
$947$			0.751232i			0.0244117i	−0.999926	+	0.0122059i	$0.996115\pi$
$948$		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	−0.525134	−	0.851019i	$-0.675985\pi$
$953$	3.76491	−	2.73537i	0.121957	−	0.0886073i	0.647092	+	0.762412i	$0.275985\pi$
$954$		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	$0.113738\pi$
$967$			21.7529i			0.699525i	−0.936838	+	0.349763i	$0.886262\pi$
$968$	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	−0.860809	−	0.508928i	$-0.830042\pi$
$971$	−3.45215	+	4.75147i	−0.110785	+	0.152482i	0.750024	+	0.661410i	$0.230042\pi$
$972$		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	−0.294987	−	0.955501i	$-0.595315\pi$
$977$	0.874965	−	0.284293i	0.0279926	−	0.00909535i	0.322980	+	0.946406i	$0.395315\pi$
$978$		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	0.977966	+	0.208764i	$0.0669440\pi$
$983$	27.4119	+	37.7293i	0.874304	+	1.20338i	−0.103662	+	0.994613i	$0.533056\pi$
$984$		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	0.455620	−	0.890174i	$-0.349418\pi$
$997$	−16.7911	−	23.1110i	−0.531781	−	0.731933i	−0.987400	+	0.158241i	$0.949418\pi$
$998$	−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.17.3	yes	16
3.2	odd	2	inner	99.2.j.a.17.2	✓	16
4.3	odd	2		1584.2.cd.c.17.2		16
9.2	odd	6		891.2.u.c.215.2		32
9.4	even	3		891.2.u.c.512.2		32
9.5	odd	6		891.2.u.c.512.3		32
9.7	even	3		891.2.u.c.215.3		32
11.2	odd	10	inner	99.2.j.a.35.2	yes	16
11.3	even	5		1089.2.d.g.1088.11		16
11.8	odd	10		1089.2.d.g.1088.5		16
12.11	even	2		1584.2.cd.c.17.3		16
33.2	even	10	inner	99.2.j.a.35.3	yes	16
33.8	even	10		1089.2.d.g.1088.12		16
33.14	odd	10		1089.2.d.g.1088.6		16
44.35	even	10		1584.2.cd.c.1025.3		16
99.2	even	30		891.2.u.c.134.2		32
99.13	odd	30		891.2.u.c.431.2		32
99.68	even	30		891.2.u.c.431.3		32
99.79	odd	30		891.2.u.c.134.3		32
132.35	odd	10		1584.2.cd.c.1025.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.2	✓	16	3.2	odd	2	inner
99.2.j.a.17.3	yes	16	1.1	even	1	trivial
99.2.j.a.35.2	yes	16	11.2	odd	10	inner
99.2.j.a.35.3	yes	16	33.2	even	10	inner
891.2.u.c.134.2		32	99.2	even	30
891.2.u.c.134.3		32	99.79	odd	30
891.2.u.c.215.2		32	9.2	odd	6
891.2.u.c.215.3		32	9.7	even	3
891.2.u.c.431.2		32	99.13	odd	30
891.2.u.c.431.3		32	99.68	even	30
891.2.u.c.512.2		32	9.4	even	3
891.2.u.c.512.3		32	9.5	odd	6
1089.2.d.g.1088.5		16	11.8	odd	10
1089.2.d.g.1088.6		16	33.14	odd	10
1089.2.d.g.1088.11		16	11.3	even	5
1089.2.d.g.1088.12		16	33.8	even	10
1584.2.cd.c.17.2		16	4.3	odd	2
1584.2.cd.c.17.3		16	12.11	even	2
1584.2.cd.c.1025.2		16	132.35	odd	10
1584.2.cd.c.1025.3		16	44.35	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
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