LMFDB - Embedded newform 99.2.j.a.8.4

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			8.4
Root			$0.0783900 + 1.17295i$ of defining polynomial
Character	$\chi$	$=$	99.8
Dual form			99.2.j.a.62.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97102 - 1.43203i) q^{2} +(1.21618 - 3.74302i) q^{4} +(-2.23109 + 3.07083i) q^{5} +(-0.349790 - 0.113654i) q^{7} +(-1.45728 - 4.48505i) q^{8} +O(q^{10})$	\(q+(1.97102 - 1.43203i) q^{2} +(1.21618 - 3.74302i) q^{4} +(-2.23109 + 3.07083i) q^{5} +(-0.349790 - 0.113654i) q^{7} +(-1.45728 - 4.48505i) q^{8} +9.24768i q^{10} +(-2.97756 - 1.46086i) q^{11} +(-0.557375 - 0.767161i) q^{13} +(-0.852201 + 0.276897i) q^{14} +(-2.92705 - 2.12663i) q^{16} +(2.77873 + 2.01886i) q^{17} +(4.05368 - 1.31712i) q^{19} +(8.78079 + 12.0857i) q^{20} +(-7.96085 + 1.38457i) q^{22} -4.96800i q^{23} +(-2.90717 - 8.94734i) q^{25} +(-2.19720 - 0.713913i) q^{26} +(-0.850818 + 1.17105i) q^{28} +(-0.767418 + 2.36187i) q^{29} +(-2.84281 + 2.06543i) q^{31} +0.617031 q^{32} +8.36801 q^{34} +(1.12943 - 0.820576i) q^{35} +(-2.21947 + 6.83082i) q^{37} +(6.10374 - 8.40108i) q^{38} +(17.0242 + 5.53148i) q^{40} +(-0.840249 - 2.58602i) q^{41} +1.88749i q^{43} +(-9.08931 + 9.36841i) q^{44} +(-7.11434 - 9.79205i) q^{46} +(0.0195991 - 0.00636813i) q^{47} +(-5.55368 - 4.03499i) q^{49} +(-18.5430 - 13.4723i) q^{50} +(-3.54937 + 1.15326i) q^{52} +(-3.25941 - 4.48619i) q^{53} +(11.1293 - 5.88428i) q^{55} +1.73445i q^{56} +(1.86968 + 5.75427i) q^{58} +(6.29998 + 2.04699i) q^{59} +(-5.73238 + 7.88994i) q^{61} +(-2.64550 + 8.14200i) q^{62} +(7.07028 - 5.13686i) q^{64} +3.59938 q^{65} +4.46351 q^{67} +(10.9361 - 7.94554i) q^{68} +(1.05103 - 3.23475i) q^{70} +(6.06985 - 8.35443i) q^{71} +(-4.18072 - 1.35840i) q^{73} +(5.40733 + 16.6420i) q^{74} -16.7749i q^{76} +(0.875490 + 0.849407i) q^{77} +(6.42867 + 8.84831i) q^{79} +(13.0610 - 4.24379i) q^{80} +(-5.35942 - 3.89384i) q^{82} +(7.42940 + 5.39778i) q^{83} +(-12.3992 + 4.02874i) q^{85} +(2.70294 + 3.72028i) q^{86} +(-2.21290 + 15.4834i) q^{88} +3.04837i q^{89} +(0.107774 + 0.331693i) q^{91} +(-18.5954 - 6.04200i) q^{92} +(0.0295109 - 0.0406183i) q^{94} +(-4.99948 + 15.3868i) q^{95} +(12.2055 - 8.86782i) q^{97} -16.7247 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4}+O(q^{10}) $ 16 * q - 4 * q^4	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

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 $

$2$	1.97102	−	1.43203i	1.39372	−	1.01260i	0.398279	−	0.917264i	$-0.369608\pi$
$2$	1.97102	−	1.43203i	1.39372	−	1.01260i	0.995445	−	0.0953352i	$-0.0303923\pi$
$3$		0			0
$3$		0			0
$4$	1.21618	−	3.74302i	0.608091	−	1.87151i
$5$	−2.23109	+	3.07083i	−0.997774	+	1.37332i	−0.0710932	+	0.997470i	$0.522649\pi$
$5$	−2.23109	+	3.07083i	−0.997774	+	1.37332i	−0.926681	+	0.375849i	$0.877351\pi$
$6$		0			0
$7$	−0.349790	−	0.113654i	−0.132208	−	0.0429571i	0.242165	−	0.970235i	$-0.422142\pi$
$7$	−0.349790	−	0.113654i	−0.132208	−	0.0429571i	−0.374374	+	0.927278i	$0.622142\pi$
$8$	−1.45728	−	4.48505i	−0.515226	−	1.58570i
$9$		0			0
$10$			9.24768i			2.92437i
$11$	−2.97756	−	1.46086i	−0.897769	−	0.440467i
$11$	−2.97756	−	1.46086i	−0.897769	−	0.440467i
$12$		0			0
$13$	−0.557375	−	0.767161i	−0.154588	−	0.212772i	0.724698	−	0.689067i	$-0.241979\pi$
$13$	−0.557375	−	0.767161i	−0.154588	−	0.212772i	−0.879286	+	0.476295i	$0.841979\pi$
$14$	−0.852201	+	0.276897i	−0.227760	+	0.0740038i
$15$		0			0
$16$	−2.92705	−	2.12663i	−0.731763	−	0.531657i
$17$	2.77873	+	2.01886i	0.673940	+	0.489646i	0.871342	−	0.490676i	$-0.163250\pi$
$17$	2.77873	+	2.01886i	0.673940	+	0.489646i	−0.197402	+	0.980323i	$0.563250\pi$
$18$		0			0
$19$	4.05368	−	1.31712i	0.929979	−	0.302168i	0.195425	−	0.980719i	$-0.437391\pi$
$19$	4.05368	−	1.31712i	0.929979	−	0.302168i	0.734554	+	0.678550i	$0.237391\pi$
$20$	8.78079	+	12.0857i	1.96344	+	2.70245i
$21$		0			0
$22$	−7.96085	+	1.38457i	−1.69726	+	0.295191i
$23$		−	4.96800i		−	1.03590i	−0.855411	−	0.517950i	$-0.826695\pi$
$23$		−	4.96800i		−	1.03590i	0.855411	−	0.517950i	$-0.173305\pi$
$24$		0			0
$25$	−2.90717	−	8.94734i	−0.581433	−	1.78947i
$26$	−2.19720	−	0.713913i	−0.430906	−	0.140010i
$27$		0			0
$28$	−0.850818	+	1.17105i	−0.160789	+	0.221308i
$29$	−0.767418	+	2.36187i	−0.142506	+	0.438588i	−0.996682	−	0.0813958i	$-0.974062\pi$
$29$	−0.767418	+	2.36187i	−0.142506	+	0.438588i	0.854176	+	0.519984i	$0.174062\pi$
$30$		0			0
$31$	−2.84281	+	2.06543i	−0.510585	+	0.370961i	−0.813045	−	0.582200i	$-0.802192\pi$
$31$	−2.84281	+	2.06543i	−0.510585	+	0.370961i	0.302461	+	0.953162i	$0.402192\pi$
$32$	0.617031			0.109077
$33$		0			0
$34$	8.36801			1.43510
$35$	1.12943	−	0.820576i	0.190908	−	0.138703i
$36$		0			0
$37$	−2.21947	+	6.83082i	−0.364878	+	1.12298i	0.585179	+	0.810904i	$0.301024\pi$
$37$	−2.21947	+	6.83082i	−0.364878	+	1.12298i	−0.950057	+	0.312075i	$0.898976\pi$
$38$	6.10374	−	8.40108i	0.990158	−	1.36284i
$39$		0			0
$40$	17.0242	+	5.53148i	2.69176	+	0.874604i
$41$	−0.840249	−	2.58602i	−0.131225	−	0.403869i	0.863759	−	0.503905i	$-0.168104\pi$
$41$	−0.840249	−	2.58602i	−0.131225	−	0.403869i	−0.994984	+	0.100037i	$0.968104\pi$
$42$		0			0
$43$			1.88749i			0.287839i	0.989589	+	0.143919i	$0.0459706\pi$
$43$			1.88749i			0.287839i	−0.989589	+	0.143919i	$0.954029\pi$
$44$	−9.08931	+	9.36841i	−1.37026	+	1.41234i
$45$		0			0
$46$	−7.11434	−	9.79205i	−1.04895	−	1.44376i
$47$	0.0195991	−	0.00636813i	0.00285882	−	0.000928888i	−0.307587	−	0.951520i	$-0.599522\pi$
$47$	0.0195991	−	0.00636813i	0.00285882	−	0.000928888i	0.310446	+	0.950591i	$0.399522\pi$
$48$		0			0
$49$	−5.55368	−	4.03499i	−0.793383	−	0.576427i
$50$	−18.5430	−	13.4723i	−2.62237	−	1.90526i
$51$		0			0
$52$	−3.54937	+	1.15326i	−0.492209	+	0.159928i
$53$	−3.25941	−	4.48619i	−0.447714	−	0.616226i	0.524190	−	0.851601i	$-0.324368\pi$
$53$	−3.25941	−	4.48619i	−0.447714	−	0.616226i	−0.971905	+	0.235375i	$0.924368\pi$
$54$		0			0
$55$	11.1293	−	5.88428i	1.50067	−	0.793436i
$56$			1.73445i			0.231776i
$57$		0			0
$58$	1.86968	+	5.75427i	0.245500	+	0.755573i
$59$	6.29998	+	2.04699i	0.820187	+	0.266495i	0.688906	−	0.724850i	$-0.258091\pi$
$59$	6.29998	+	2.04699i	0.820187	+	0.266495i	0.131281	+	0.991345i	$0.458091\pi$
$60$		0			0
$61$	−5.73238	+	7.88994i	−0.733956	+	1.01020i	0.264988	+	0.964252i	$0.414632\pi$
$61$	−5.73238	+	7.88994i	−0.733956	+	1.01020i	−0.998944	+	0.0459514i	$0.985368\pi$
$62$	−2.64550	+	8.14200i	−0.335978	+	1.03404i
$63$		0			0
$64$	7.07028	−	5.13686i	0.883786	−	0.642108i
$65$	3.59938			0.446448
$66$		0			0
$67$	4.46351			0.545305			0.272652	−	0.962113i	$-0.412099\pi$
$67$	4.46351			0.545305			0.272652	+	0.962113i	$0.412099\pi$
$68$	10.9361	−	7.94554i	1.32620	−	0.963538i
$69$		0			0
$70$	1.05103	−	3.23475i	0.125623	−	0.386626i
$71$	6.06985	−	8.35443i	0.720359	−	0.991489i	−0.279153	−	0.960247i	$-0.590054\pi$
$71$	6.06985	−	8.35443i	0.720359	−	0.991489i	0.999512	−	0.0312420i	$-0.00994626\pi$
$72$		0			0
$73$	−4.18072	−	1.35840i	−0.489317	−	0.158989i	0.0539588	−	0.998543i	$-0.482816\pi$
$73$	−4.18072	−	1.35840i	−0.489317	−	0.158989i	−0.543275	+	0.839555i	$0.682816\pi$
$74$	5.40733	+	16.6420i	0.628589	+	1.93460i
$75$		0			0
$76$		−	16.7749i		−	1.92421i
$77$	0.875490	+	0.849407i	0.0997714	+	0.0967989i
$78$		0			0
$79$	6.42867	+	8.84831i	0.723282	+	0.995513i	0.999408	+	0.0343911i	$0.0109492\pi$
$79$	6.42867	+	8.84831i	0.723282	+	0.995513i	−0.276126	+	0.961121i	$0.589051\pi$
$80$	13.0610	−	4.24379i	1.46027	−	0.474470i
$81$		0			0
$82$	−5.35942	−	3.89384i	−0.591848	−	0.430003i
$83$	7.42940	+	5.39778i	0.815483	+	0.592483i	0.915415	−	0.402511i	$-0.131863\pi$
$83$	7.42940	+	5.39778i	0.815483	+	0.592483i	−0.0999323	+	0.994994i	$0.531863\pi$
$84$		0			0
$85$	−12.3992	+	4.02874i	−1.34488	+	0.436978i
$86$	2.70294	+	3.72028i	0.291466	+	0.401168i
$87$		0			0
$88$	−2.21290	+	15.4834i	−0.235896	+	1.65054i
$89$			3.04837i			0.323127i	0.986862	+	0.161563i	$0.0516536\pi$
$89$			3.04837i			0.323127i	−0.986862	+	0.161563i	$0.948346\pi$
$90$		0			0
$91$	0.107774	+	0.331693i	0.0112978	+	0.0347709i
$92$	−18.5954	−	6.04200i	−1.93870	−	0.629922i
$93$		0			0
$94$	0.0295109	−	0.0406183i	0.00304382	−	0.00418946i
$95$	−4.99948	+	15.3868i	−0.512935	+	1.57865i
$96$		0			0
$97$	12.2055	−	8.86782i	1.23928	−	0.900391i	0.241732	−	0.970343i	$-0.422285\pi$
$97$	12.2055	−	8.86782i	1.23928	−	0.900391i	0.997550	+	0.0699519i	$0.0222846\pi$
$98$	−16.7247			−1.68945
$99$		0			0
$100$	−37.0257			−3.70257
$101$	−14.1253	+	10.2626i	−1.40552	+	1.02117i	−0.411562	+	0.911382i	$0.635017\pi$
$101$	−14.1253	+	10.2626i	−1.40552	+	1.02117i	−0.993955	+	0.109787i	$0.964983\pi$
$102$		0			0
$103$	−2.87868	+	8.85967i	−0.283645	+	0.872969i	0.703157	+	0.711035i	$0.251773\pi$
$103$	−2.87868	+	8.85967i	−0.283645	+	0.872969i	−0.986802	+	0.161934i	$0.948227\pi$
$104$	−2.62850	+	3.61782i	−0.257746	+	0.354757i
$105$		0			0
$106$	−12.8487	−	4.17481i	−1.24798	−	0.405493i
$107$	−4.76675	−	14.6705i	−0.460819	−	1.41825i	−0.864166	−	0.503207i	$-0.832153\pi$
$107$	−4.76675	−	14.6705i	−0.460819	−	1.41825i	0.403347	−	0.915047i	$-0.367847\pi$
$108$		0			0
$109$			10.6286i			1.01803i	0.860757	+	0.509016i	$0.169991\pi$
$109$			10.6286i			1.01803i	−0.860757	+	0.509016i	$0.830009\pi$
$110$	13.5096	−	27.5355i	1.28809	−	2.62541i
$111$		0			0
$112$	0.782155	+	1.07654i	0.0739067	+	0.101724i
$113$	−0.995774	+	0.323547i	−0.0936746	+	0.0304367i	−0.355479	−	0.934684i	$-0.615682\pi$
$113$	−0.995774	+	0.323547i	−0.0936746	+	0.0304367i	0.261805	+	0.965121i	$0.415682\pi$
$114$		0			0
$115$	15.2559	+	11.0841i	1.42262	+	1.03359i
$116$	7.90722	+	5.74493i	0.734167	+	0.533404i
$117$		0			0
$118$	15.3487	−	4.98711i	1.41297	−	0.459101i
$119$	−0.742521	−	1.02199i	−0.0680668	−	0.0936859i
$120$		0			0
$121$	6.73176	+	8.69962i	0.611978	+	0.790875i
$122$			23.7602i			2.15115i
$123$		0			0
$124$	4.27356	+	13.1527i	0.383777	+	1.18114i
$125$	15.9120	+	5.17013i	1.42321	+	0.462430i
$126$		0			0
$127$	10.3127	−	14.1942i	0.915101	−	1.25953i	−0.0502930	−	0.998735i	$-0.516016\pi$
$127$	10.3127	−	14.1942i	0.915101	−	1.25953i	0.965394	−	0.260794i	$-0.0839845\pi$
$128$	6.19820	−	19.0761i	0.547848	−	1.68610i
$129$		0			0
$130$	7.09446	−	5.15442i	0.622225	−	0.452073i
$131$	−13.8890			−1.21349			−0.606744	−	0.794897i	$-0.707525\pi$
$131$	−13.8890			−1.21349			−0.606744	+	0.794897i	$0.707525\pi$
$132$		0			0
$133$	−1.56764			−0.135931
$134$	8.79769	−	6.39189i	0.760004	−	0.552176i
$135$		0			0
$136$	5.00531	−	15.4048i	0.429202	−	1.32095i
$137$	−0.609963	+	0.839541i	−0.0521126	+	0.0717269i	−0.834278	−	0.551344i	$-0.814115\pi$
$137$	−0.609963	+	0.839541i	−0.0521126	+	0.0717269i	0.782165	+	0.623071i	$0.214115\pi$
$138$		0			0
$139$	−18.8643	−	6.12938i	−1.60005	−	0.519887i	−0.632928	−	0.774210i	$-0.718147\pi$
$139$	−18.8643	−	6.12938i	−1.60005	−	0.519887i	−0.967119	+	0.254324i	$0.918147\pi$
$140$	−1.69785	−	5.22544i	−0.143494	−	0.441630i
$141$		0			0
$142$		−	25.1590i		−	2.11130i
$143$	0.538902	+	3.09852i	0.0450652	+	0.259111i
$144$		0			0
$145$	−5.54073	−	7.62616i	−0.460133	−	0.633318i
$146$	−10.1856	+	3.30949i	−0.842964	+	0.273896i
$147$		0			0
$148$	22.8686	+	16.6150i	1.87979	+	1.36575i
$149$	6.50125	+	4.72344i	0.532603	+	0.386959i	0.821331	−	0.570452i	$-0.193232\pi$
$149$	6.50125	+	4.72344i	0.532603	+	0.386959i	−0.288727	+	0.957411i	$0.593232\pi$
$150$		0			0
$151$	−9.58050	+	3.11289i	−0.779650	+	0.253324i	−0.671691	−	0.740832i	$-0.734432\pi$
$151$	−9.58050	+	3.11289i	−0.779650	+	0.253324i	−0.107959	+	0.994155i	$0.534432\pi$
$152$	−11.8147	−	16.2615i	−0.958299	−	1.31899i
$153$		0			0
$154$	2.94199	+	0.420471i	0.237072	+	0.0338826i
$155$		−	13.3380i		−	1.07133i
$156$		0			0
$157$	−5.00062	−	15.3903i	−0.399093	−	1.22828i	−0.925728	−	0.378190i	$-0.876547\pi$
$157$	−5.00062	−	15.3903i	−0.399093	−	1.22828i	0.526635	−	0.850091i	$-0.323453\pi$
$158$	25.3421	+	8.23416i	2.01611	+	0.655074i
$159$		0			0
$160$	−1.37665	+	1.89480i	−0.108834	+	0.149797i
$161$	−0.564633	+	1.73776i	−0.0444993	+	0.136955i
$162$		0			0
$163$	−3.45923	+	2.51328i	−0.270948	+	0.196855i	−0.714959	−	0.699166i	$-0.753555\pi$
$163$	−3.45923	+	2.51328i	−0.270948	+	0.196855i	0.444012	+	0.896021i	$0.353555\pi$
$164$	−10.7014			−0.835642
$165$		0			0
$166$	22.3733			1.73651
$167$	14.8478	−	10.7875i	1.14896	−	0.834765i	0.160614	−	0.987017i	$-0.448653\pi$
$167$	14.8478	−	10.7875i	1.14896	−	0.834765i	0.988342	+	0.152252i	$0.0486526\pi$
$168$		0			0
$169$	3.73935	−	11.5085i	0.287642	−	0.885272i
$170$	−18.6698	+	25.6968i	−1.43191	+	1.97085i
$171$		0			0
$172$	7.06490	+	2.29553i	0.538694	+	0.175032i
$173$	1.91046	+	5.87980i	0.145250	+	0.447033i	0.997043	−	0.0768452i	$-0.0244847\pi$
$173$	1.91046	+	5.87980i	0.145250	+	0.447033i	−0.851793	+	0.523878i	$0.824485\pi$
$174$		0			0
$175$			3.46010i			0.261559i
$176$	5.60877	+	10.6082i	0.422777	+	0.799622i
$177$		0			0
$178$	4.36536	+	6.00841i	0.327198	+	0.450349i
$179$	8.77414	−	2.85089i	0.655810	−	0.213086i	0.0378357	−	0.999284i	$-0.487954\pi$
$179$	8.77414	−	2.85089i	0.655810	−	0.213086i	0.617974	+	0.786198i	$0.287954\pi$
$180$		0			0
$181$	3.38790	+	2.46145i	0.251821	+	0.182958i	0.706533	−	0.707680i	$-0.250258\pi$
$181$	3.38790	+	2.46145i	0.251821	+	0.182958i	−0.454713	+	0.890638i	$0.650258\pi$
$182$	0.687420	+	0.499440i	0.0509550	+	0.0370209i
$183$		0			0
$184$	−22.2817	+	7.23977i	−1.64263	+	0.533723i
$185$	−16.0245	−	22.0558i	−1.17814	−	1.62157i
$186$		0			0
$187$	−5.32455	−	10.0706i	−0.389370	−	0.736438i
$188$		−	0.0811047i		−	0.00591517i
$189$		0			0
$190$	12.1803	+	37.4872i	0.883653	+	2.71960i
$191$	−19.1951	−	6.23688i	−1.38891	−	0.451285i	−0.483323	−	0.875442i	$-0.660570\pi$
$191$	−19.1951	−	6.23688i	−1.38891	−	0.451285i	−0.905589	+	0.424157i	$0.860570\pi$
$192$		0			0
$193$	4.71049	−	6.48343i	0.339068	−	0.466687i	−0.605101	−	0.796149i	$-0.706867\pi$
$193$	4.71049	−	6.48343i	0.339068	−	0.466687i	0.944169	+	0.329462i	$0.106867\pi$
$194$	11.3583	−	34.9574i	0.815481	−	2.50979i
$195$		0			0
$196$	−21.8573	+	15.8803i	−1.56124	+	1.13431i
$197$	21.1710			1.50837			0.754187	−	0.656659i	$-0.228031\pi$
$197$	21.1710			1.50837			0.754187	+	0.656659i	$0.228031\pi$
$198$		0			0
$199$	−10.5160			−0.745457			−0.372729	−	0.927940i	$-0.621578\pi$
$199$	−10.5160			−0.745457			−0.372729	+	0.927940i	$0.621578\pi$
$200$	−35.8927	+	26.0775i	−2.53799	+	1.84396i
$201$		0			0
$202$	−13.1449	+	40.4557i	−0.924869	+	2.84645i
$203$	0.536871	−	0.738940i	0.0376810	−	0.0518634i
$204$		0			0
$205$	9.81591	+	3.18938i	0.685573	+	0.222756i
$206$	7.01339	+	21.5850i	0.488646	+	1.50390i
$207$		0			0
$208$			3.43085i			0.237886i
$209$	−13.9942	−	2.00007i	−0.968001	−	0.138347i
$210$		0			0
$211$	−2.17376	−	2.99193i	−0.149648	−	0.205973i	0.727611	−	0.685990i	$-0.240631\pi$
$211$	−2.17376	−	2.99193i	−0.149648	−	0.205973i	−0.877259	+	0.480017i	$0.840631\pi$
$212$	−20.7560	+	6.74402i	−1.42553	+	0.463181i
$213$		0			0
$214$	−30.4041	−	22.0898i	−2.07838	−	1.51003i
$215$	−5.79615	−	4.21115i	−0.395294	−	0.287198i
$216$		0			0
$217$	1.22913	−	0.399369i	0.0834390	−	0.0271110i
$218$	15.2205	+	20.9492i	1.03086	+	1.41886i
$219$		0			0
$220$	−8.48976	−	48.8135i	−0.572380	−	3.29101i
$221$		−	3.25699i		−	0.219089i
$222$		0			0
$223$	−5.53051	−	17.0212i	−0.370351	−	1.13982i	−0.946562	−	0.322521i	$-0.895470\pi$
$223$	−5.53051	−	17.0212i	−0.370351	−	1.13982i	0.576212	−	0.817301i	$-0.304530\pi$
$224$	−0.215832	−	0.0701279i	−0.0144209	−	0.00468562i
$225$		0			0
$226$	−1.49936	+	2.06370i	−0.0997363	+	0.137275i
$227$	−5.37022	+	16.5278i	−0.356434	+	1.09699i	0.598740	+	0.800944i	$0.295668\pi$
$227$	−5.37022	+	16.5278i	−0.356434	+	1.09699i	−0.955173	+	0.296047i	$0.904332\pi$
$228$		0			0
$229$	−3.45989	+	2.51375i	−0.228636	+	0.166114i	−0.696205	−	0.717843i	$-0.745130\pi$
$229$	−3.45989	+	2.51375i	−0.228636	+	0.166114i	0.467570	+	0.883956i	$0.345130\pi$
$230$	45.9425			3.02936
$231$		0			0
$232$	11.7114			0.768894
$233$	−18.9171	+	13.7441i	−1.23930	+	0.900404i	−0.997552	−	0.0699355i	$-0.977721\pi$
$233$	−18.9171	+	13.7441i	−1.23930	+	0.900404i	−0.241748	+	0.970339i	$0.577721\pi$
$234$		0			0
$235$	−0.0241719	+	0.0743935i	−0.00157680	+	0.00485289i
$236$	15.3238	−	21.0915i	0.997497	−	1.37294i
$237$		0			0
$238$	−2.92705	−	0.951057i	−0.189733	−	0.0616478i
$239$	6.17902	+	19.0171i	0.399687	+	1.23011i	0.925251	+	0.379356i	$0.123855\pi$
$239$	6.17902	+	19.0171i	0.399687	+	1.23011i	−0.525563	+	0.850754i	$0.676145\pi$
$240$		0			0
$241$			2.32570i			0.149811i	0.997191	+	0.0749057i	$0.0238656\pi$
$241$			2.32570i			0.149811i	−0.997191	+	0.0749057i	$0.976134\pi$
$242$	25.7266	+	7.50707i	1.65377	+	0.482573i
$243$		0			0
$244$	22.5606	+	31.0520i	1.44430	+	1.98790i
$245$	24.7815	−	8.05201i	1.58323	−	0.514424i
$246$		0			0
$247$	−3.26987	−	2.37570i	−0.208057	−	0.151162i
$248$	13.4063	+	9.74025i	0.851301	+	0.618507i
$249$		0			0
$250$	38.7668	−	12.5961i	2.45182	−	0.796646i
$251$	1.88681	+	2.59698i	0.119095	+	0.163920i	0.864402	−	0.502801i	$-0.167697\pi$
$251$	1.88681	+	2.59698i	0.119095	+	0.163920i	−0.745307	+	0.666721i	$0.767697\pi$
$252$		0			0
$253$	−7.25758	+	14.7925i	−0.456280	+	0.929999i
$254$		−	42.7451i		−	2.68207i
$255$		0			0
$256$	−9.69957	−	29.8522i	−0.606223	−	1.86576i
$257$	−17.1597	−	5.57552i	−1.07039	−	0.347792i	−0.279752	−	0.960072i	$-0.590252\pi$
$257$	−17.1597	−	5.57552i	−1.07039	−	0.347792i	−0.790641	+	0.612281i	$0.790252\pi$
$258$		0			0
$259$	1.55270	−	2.13710i	0.0964798	−	0.132793i
$260$	4.37750	−	13.4726i	0.271481	−	0.835533i
$261$		0			0
$262$	−27.3756	+	19.8895i	−1.69127	+	1.22878i
$263$	2.05966			0.127004			0.0635019	−	0.997982i	$-0.479773\pi$
$263$	2.05966			0.127004			0.0635019	+	0.997982i	$0.479773\pi$
$264$		0			0
$265$	21.0484			1.29299
$266$	−3.08985	+	2.24490i	−0.189451	+	0.137644i
$267$		0			0
$268$	5.42845	−	16.7070i	0.331595	−	1.02054i
$269$	1.69280	−	2.32994i	0.103212	−	0.142059i	−0.754287	−	0.656545i	$-0.772017\pi$
$269$	1.69280	−	2.32994i	0.103212	−	0.142059i	0.857499	+	0.514486i	$0.172017\pi$
$270$		0			0
$271$	9.67272	+	3.14286i	0.587576	+	0.190915i	0.587692	−	0.809085i	$-0.300037\pi$
$271$	9.67272	+	3.14286i	0.587576	+	0.190915i	−0.000115761		1.00000i	$0.500037\pi$
$272$	−3.84011	−	11.8186i	−0.232841	−	0.716610i
$273$		0			0
$274$			2.52824i			0.152737i
$275$	−4.41457	+	30.8882i	−0.266208	+	1.86263i
$276$		0			0
$277$	4.29714	+	5.91450i	0.258190	+	0.355368i	0.918358	−	0.395750i	$-0.129515\pi$
$277$	4.29714	+	5.91450i	0.258190	+	0.355368i	−0.660169	+	0.751117i	$0.729515\pi$
$278$	−45.9594	+	14.9331i	−2.75646	+	0.895629i
$279$		0			0
$280$	−5.32621	−	3.86972i	−0.318302	−	0.231260i
$281$	−1.86513	−	1.35510i	−0.111264	−	0.0808384i	0.530762	−	0.847521i	$-0.321906\pi$
$281$	−1.86513	−	1.35510i	−0.111264	−	0.0808384i	−0.642026	+	0.766683i	$0.721906\pi$
$282$		0			0
$283$	23.2370	−	7.55016i	1.38130	−	0.448810i	0.478200	−	0.878251i	$-0.341289\pi$
$283$	23.2370	−	7.55016i	1.38130	−	0.448810i	0.903095	+	0.429441i	$0.141289\pi$
$284$	−23.8888	−	32.8801i	−1.41754	−	1.95108i
$285$		0			0
$286$	5.49936	+	5.33553i	0.325184	+	0.315496i
$287$			1.00006i			0.0590318i
$288$		0			0
$289$	−1.60777	−	4.94822i	−0.0945749	−	0.291072i
$290$	−21.8418	−	7.09684i	−1.28260	−	0.416741i
$291$		0			0
$292$	−10.1690	+	13.9965i	−0.595098	+	0.819082i
$293$	3.29456	−	10.1396i	0.192470	−	0.592362i	−0.807527	−	0.589831i	$-0.799194\pi$
$293$	3.29456	−	10.1396i	0.192470	−	0.592362i	0.999997	−	0.00253112i	$-0.000805683\pi$
$294$		0			0
$295$	−20.3418	+	14.7792i	−1.18434	+	0.860476i
$296$	33.8709			1.96871
$297$		0			0
$298$	19.5782			1.13414
$299$	−3.81126	+	2.76904i	−0.220411	+	0.160138i
$300$		0			0
$301$	0.214520	−	0.660224i	0.0123647	−	0.0380547i
$302$	−14.4256	+	19.8552i	−0.830102	+	1.14254i
$303$		0			0
$304$	−14.6664	−	4.76539i	−0.841174	−	0.273314i
$305$	−11.4392	−	35.2063i	−0.655009	−	2.01591i
$306$		0			0
$307$			4.56848i			0.260737i	0.991466	+	0.130369i	$0.0416160\pi$
$307$			4.56848i			0.260737i	−0.991466	+	0.130369i	$0.958384\pi$
$308$	4.24411	−	2.24395i	0.241830	−	0.127861i
$309$		0			0
$310$	−19.1004	−	26.2894i	−1.08483	−	1.49314i
$311$	−8.92302	+	2.89926i	−0.505978	+	0.164402i	−0.550872	−	0.834590i	$-0.685705\pi$
$311$	−8.92302	+	2.89926i	−0.505978	+	0.164402i	0.0448944	+	0.998992i	$0.485705\pi$
$312$		0			0
$313$	4.05804	+	2.94834i	0.229374	+	0.166650i	0.696536	−	0.717522i	$-0.254724\pi$
$313$	4.05804	+	2.94834i	0.229374	+	0.166650i	−0.467162	+	0.884172i	$0.654724\pi$
$314$	−31.8958	−	23.1736i	−1.79998	−	1.30776i
$315$		0			0
$316$	40.9379	−	13.3015i	2.30294	−	0.748269i
$317$	6.86310	+	9.44624i	0.385470	+	0.530554i	0.957023	−	0.290011i	$-0.0936590\pi$
$317$	6.86310	+	9.44624i	0.385470	+	0.530554i	−0.571553	+	0.820565i	$0.693659\pi$
$318$		0			0
$319$	5.73541	−	5.91153i	0.321121	−	0.330982i
$320$			33.1725i			1.85440i
$321$		0			0
$322$	1.37562	+	4.23374i	0.0766606	+	0.235937i
$323$	13.9232	+	4.52391i	0.774706	+	0.251717i
$324$		0			0
$325$	−5.24366	+	7.21728i	−0.290866	+	0.400343i
$326$	−3.21912	+	9.90745i	−0.178291	+	0.548723i
$327$		0			0
$328$	−10.3739	+	7.53711i	−0.572805	+	0.416167i
$329$	−0.00757934			−0.000417863
$330$		0			0
$331$	−29.0516			−1.59682			−0.798411	−	0.602113i	$-0.794326\pi$
$331$	−29.0516			−1.59682			−0.798411	+	0.602113i	$0.794326\pi$
$332$	29.2395	−	21.2438i	1.60473	−	1.16590i
$333$		0			0
$334$	13.8172	−	42.5250i	0.756044	−	2.32686i
$335$	−9.95850	+	13.7067i	−0.544091	+	0.748877i
$336$		0			0
$337$	27.4668	+	8.92451i	1.49621	+	0.486149i	0.938911	−	0.344161i	$-0.111837\pi$
$337$	27.4668	+	8.92451i	1.49621	+	0.486149i	0.557302	+	0.830310i	$0.311837\pi$
$338$	−9.11025	−	28.0385i	−0.495532	−	1.52509i
$339$		0			0
$340$			51.3101i			2.78268i
$341$	11.4820	−	1.99697i	0.621783	−	0.108142i
$342$		0			0
$343$	2.99731	+	4.12544i	0.161840	+	0.222753i
$344$	8.46546	−	2.75060i	0.456427	−	0.148302i
$345$		0			0
$346$	12.1856	+	8.85338i	0.655103	+	0.475961i
$347$	17.9141	+	13.0153i	0.961678	+	0.698700i	0.953540	−	0.301267i	$-0.0974096\pi$
$347$	17.9141	+	13.0153i	0.961678	+	0.698700i	0.00813801	+	0.999967i	$0.497410\pi$
$348$		0			0
$349$	−14.8959	+	4.83997i	−0.797359	+	0.259078i	−0.679235	−	0.733921i	$-0.737688\pi$
$349$	−14.8959	+	4.83997i	−0.797359	+	0.259078i	−0.118125	+	0.992999i	$0.537688\pi$
$350$	4.95498	+	6.81994i	0.264855	+	0.364541i
$351$		0			0
$352$	−1.83725	−	0.901398i	−0.0979257	−	0.0480447i
$353$			11.1636i			0.594180i	0.954850	+	0.297090i	$0.0960161\pi$
$353$			11.1636i			0.594180i	−0.954850	+	0.297090i	$0.903984\pi$
$354$		0			0
$355$	12.1127	+	37.2790i	0.642874	+	1.97856i
$356$	11.4101	+	3.70737i	0.604735	+	0.196490i
$357$		0			0
$358$	13.2115	−	18.1840i	0.698248	−	0.961055i
$359$	5.11867	−	15.7536i	0.270153	−	0.831445i	−0.720308	−	0.693654i	$-0.756000\pi$
$359$	5.11867	−	15.7536i	0.270153	−	0.831445i	0.990461	−	0.137791i	$-0.0440002\pi$
$360$		0			0
$361$	−0.673787	+	0.489535i	−0.0354625	+	0.0257650i
$362$	10.2025			0.536232
$363$		0			0
$364$	1.37261			0.0719442
$365$	13.4990	−	9.80759i	0.706569	−	0.513353i
$366$		0			0
$367$	3.03154	−	9.33012i	0.158245	−	0.487028i	−0.840230	−	0.542230i	$-0.817580\pi$
$367$	3.03154	−	9.33012i	0.158245	−	0.487028i	0.998475	+	0.0552016i	$0.0175801\pi$
$368$	−10.5651	+	14.5416i	−0.550743	+	0.758033i
$369$		0			0
$370$	−63.1692	−	20.5249i	−3.28401	−	1.06704i
$371$	0.630238	+	1.93967i	0.0327203	+	0.100703i
$372$		0			0
$373$		−	12.6350i		−	0.654216i	−0.944987	−	0.327108i	$-0.893926\pi$
$373$		−	12.6350i		−	0.654216i	0.944987	−	0.327108i	$-0.106074\pi$
$374$	−24.9163	−	12.2245i	−1.28839	−	0.632115i
$375$		0			0
$376$	−0.0571228	−	0.0786227i	−0.00294588	−	0.00405466i
$377$	2.23967	−	0.727714i	0.115349	−	0.0374792i
$378$		0			0
$379$	−28.3981	−	20.6325i	−1.45871	−	1.05982i	−0.983695	−	0.179843i	$-0.942441\pi$
$379$	−28.3981	−	20.6325i	−1.45871	−	1.05982i	−0.475019	−	0.879975i	$-0.657559\pi$
$380$	51.5129	+	37.4263i	2.64256	+	1.91993i
$381$		0			0
$382$	−46.7655	+	15.1950i	−2.39273	+	0.777445i
$383$	13.2760	+	18.2729i	0.678374	+	0.933701i	0.999913	−	0.0131951i	$-0.00420024\pi$
$383$	13.2760	+	18.2729i	0.678374	+	0.933701i	−0.321539	+	0.946896i	$0.604200\pi$
$384$		0			0
$385$	−4.56169	+	0.793379i	−0.232485	+	0.0404344i
$386$		−	19.5246i		−	0.993774i
$387$		0			0
$388$	−18.3484	−	56.4704i	−0.931497	−	2.86685i
$389$	6.99867	+	2.27401i	0.354847	+	0.115297i	0.481015	−	0.876712i	$-0.340268\pi$
$389$	6.99867	+	2.27401i	0.354847	+	0.115297i	−0.126169	+	0.992009i	$0.540268\pi$
$390$		0			0
$391$	10.0297	−	13.8047i	0.507225	−	0.698135i
$392$	−10.0038	+	30.7886i	−0.505270	+	1.55506i
$393$		0			0
$394$	41.7286	−	30.3176i	2.10226	−	1.52738i
$395$	−41.5146			−2.08883
$396$		0			0
$397$	16.7327			0.839790			0.419895	−	0.907573i	$-0.362067\pi$
$397$	16.7327			0.839790			0.419895	+	0.907573i	$0.362067\pi$
$398$	−20.7272	+	15.0592i	−1.03896	+	0.754850i
$399$		0			0
$400$	−10.5182	+	32.3718i	−0.525911	+	1.61859i
$401$	−2.98209	+	4.10449i	−0.148918	+	0.204968i	−0.876959	−	0.480566i	$-0.840431\pi$
$401$	−2.98209	+	4.10449i	−0.148918	+	0.204968i	0.728040	+	0.685534i	$0.240431\pi$
$402$		0			0
$403$	3.16903	+	1.02968i	0.157860	+	0.0512920i
$404$	21.2343	+	65.3525i	1.05645	+	3.25141i
$405$		0			0
$406$		−	2.22528i		−	0.110439i
$407$	16.5875	−	17.0968i	0.822211	−	0.847459i
$408$		0			0
$409$	19.0135	+	26.1698i	0.940156	+	1.29401i	0.955764	+	0.294136i	$0.0950319\pi$
$409$	19.0135	+	26.1698i	0.940156	+	1.29401i	−0.0156071	+	0.999878i	$0.504968\pi$
$410$	23.9147	−	7.77035i	1.18106	−	0.383750i
$411$		0			0
$412$	29.6610	+	21.5500i	1.46129	+	1.06169i
$413$	−1.97102	−	1.43203i	−0.0969877	−	0.0704657i
$414$		0			0
$415$	−33.1513	+	10.7715i	−1.62734	+	0.528753i
$416$	−0.343918	−	0.473362i	−0.0168619	−	0.0232085i
$417$		0			0
$418$	−30.4471	+	16.0980i	−1.48922	+	0.787379i
$419$		−	27.9075i		−	1.36337i	−0.731645	−	0.681686i	$-0.761247\pi$
$419$		−	27.9075i		−	1.36337i	0.731645	−	0.681686i	$-0.238753\pi$
$420$		0			0
$421$	8.25960	+	25.4204i	0.402549	+	1.23892i	0.922925	+	0.384980i	$0.125792\pi$
$421$	8.25960	+	25.4204i	0.402549	+	1.23892i	−0.520376	+	0.853937i	$0.674208\pi$
$422$	−8.56907	−	2.78426i	−0.417136	−	0.135536i
$423$		0			0
$424$	−15.3709	+	21.1562i	−0.746478	+	1.02744i
$425$	9.98523	−	30.7314i	0.484355	−	1.49069i
$426$		0			0
$427$	2.90185	−	2.10832i	0.140430	−	0.102029i
$428$	−60.7094			−2.93450
$429$		0			0
$430$	−17.4549			−0.841748
$431$	−0.579760	+	0.421220i	−0.0279260	+	0.0202895i	−0.601661	−	0.798752i	$-0.705494\pi$
$431$	−0.579760	+	0.421220i	−0.0279260	+	0.0202895i	0.573735	+	0.819041i	$0.305494\pi$
$432$		0			0
$433$	3.53281	−	10.8729i	0.169776	−	0.522517i	−0.829580	−	0.558387i	$-0.811420\pi$
$433$	3.53281	−	10.8729i	0.169776	−	0.522517i	0.999356	+	0.0358703i	$0.0114203\pi$
$434$	1.85074	−	2.54732i	0.0888383	−	0.122275i
$435$		0			0
$436$	39.7830	+	12.9263i	1.90526	+	0.619056i
$437$	−6.54346	−	20.1387i	−0.313016	−	0.963365i
$438$		0			0
$439$			8.57525i			0.409274i	0.978838	+	0.204637i	$0.0656015\pi$
$439$			8.57525i			0.409274i	−0.978838	+	0.204637i	$0.934399\pi$
$440$	−42.6097	−	41.3403i	−2.03134	−	1.97082i
$441$		0			0
$442$	−4.66412	−	6.41961i	−0.221850	−	0.305350i
$443$	13.2928	−	4.31910i	0.631561	−	0.205207i	0.0242947	−	0.999705i	$-0.492266\pi$
$443$	13.2928	−	4.31910i	0.631561	−	0.205207i	0.607267	+	0.794498i	$0.292266\pi$
$444$		0			0
$445$	−9.36104	−	6.80119i	−0.443756	−	0.322407i
$446$	−35.2756	−	25.6292i	−1.67035	−	1.21358i
$447$		0			0
$448$	−3.05694	+	0.993261i	−0.144427	+	0.0469271i
$449$	12.7008	+	17.4811i	0.599388	+	0.824986i	0.995652	−	0.0931501i	$-0.0296936\pi$
$449$	12.7008	+	17.4811i	0.599388	+	0.824986i	−0.396264	+	0.918136i	$0.629694\pi$
$450$		0			0
$451$	−1.27593	+	8.92753i	−0.0600811	+	0.420381i
$452$			4.12070i			0.193821i
$453$		0			0
$454$	13.0836	+	40.2671i	0.614042	+	1.88983i
$455$	−1.25903	−	0.409083i	−0.0590241	−	0.0191781i
$456$		0			0
$457$	5.76327	−	7.93246i	0.269594	−	0.371065i	−0.652658	−	0.757652i	$-0.726346\pi$
$457$	5.76327	−	7.93246i	0.269594	−	0.371065i	0.922253	+	0.386587i	$0.126346\pi$
$458$	−3.21974	+	9.90934i	−0.150449	+	0.463033i
$459$		0			0
$460$	60.0419	−	43.6230i	2.79947	−	2.03393i
$461$	−12.3585			−0.575595			−0.287797	−	0.957691i	$-0.592923\pi$
$461$	−12.3585			−0.575595			−0.287797	+	0.957691i	$0.592923\pi$
$462$		0			0
$463$	−33.8717			−1.57415			−0.787076	−	0.616856i	$-0.788406\pi$
$463$	−33.8717			−1.57415			−0.787076	+	0.616856i	$0.788406\pi$
$464$	7.26909	−	5.28130i	0.337459	−	0.245178i
$465$		0			0
$466$	−17.6041	+	54.1797i	−0.815493	+	2.50983i
$467$	9.24994	−	12.7315i	0.428036	−	0.589142i	−0.539465	−	0.842008i	$-0.681373\pi$
$467$	9.24994	−	12.7315i	0.428036	−	0.589142i	0.967501	+	0.252867i	$0.0813734\pi$
$468$		0			0
$469$	−1.56129	−	0.507295i	−0.0720939	−	0.0234247i
$470$	0.0588904	+	0.181246i	0.00271641	+	0.00836026i
$471$		0			0
$472$		−	31.2387i		−	1.43788i
$473$	2.75736	−	5.62011i	0.126783	−	0.258413i
$474$		0			0
$475$	−23.5695	−	32.4406i	−1.08144	−	1.48848i
$476$	−4.72838	+	1.53634i	−0.216725	+	0.0704182i
$477$		0			0
$478$	39.4120	+	28.6345i	1.80266	+	1.30971i
$479$	10.0877	+	7.32913i	0.460918	+	0.334877i	0.793891	−	0.608060i	$-0.208052\pi$
$479$	10.0877	+	7.32913i	0.460918	+	0.334877i	−0.332973	+	0.942936i	$0.608052\pi$
$480$		0			0
$481$	6.47741	−	2.10464i	0.295344	−	0.0959632i
$482$	3.33048	+	4.58401i	0.151699	+	0.208796i
$483$		0			0
$484$	40.7499	−	14.6168i	1.85227	−	0.664400i
$485$			57.2660i			2.60032i
$486$		0			0
$487$	−2.14955	−	6.61563i	−0.0974054	−	0.299783i	0.890468	−	0.455046i	$-0.150377\pi$
$487$	−2.14955	−	6.61563i	−0.0974054	−	0.299783i	−0.987873	+	0.155263i	$0.950377\pi$
$488$	43.7404	+	14.2121i	1.98004	+	0.643353i
$489$		0			0
$490$	37.3143	−	51.3587i	1.68569	−	2.32015i
$491$	0.0932984	−	0.287143i	0.00421050	−	0.0129586i	−0.948929	−	0.315489i	$-0.897831\pi$
$491$	0.0932984	−	0.287143i	0.00421050	−	0.0129586i	0.953140	+	0.302531i	$0.0978314\pi$
$492$		0			0
$493$	−6.90074	+	5.01368i	−0.310794	+	0.225805i
$494$	−9.84705			−0.443040
$495$		0			0
$496$	12.7135			0.570851
$497$	−3.07269	+	2.23244i	−0.137829	+	0.100139i
$498$		0			0
$499$	2.04468	−	6.29287i	0.0915323	−	0.281707i	−0.894802	−	0.446463i	$-0.852683\pi$
$499$	2.04468	−	6.29287i	0.0915323	−	0.281707i	0.986334	+	0.164755i	$0.0526835\pi$
$500$	38.7038	−	53.2713i	1.73089	−	2.38236i
$501$		0			0
$502$	7.43791	+	2.41672i	0.331970	+	0.107864i
$503$	−3.19188	−	9.82361i	−0.142319	−	0.438013i	0.854337	−	0.519719i	$-0.173963\pi$
$503$	−3.19188	−	9.82361i	−0.142319	−	0.438013i	−0.996657	+	0.0817056i	$0.973963\pi$
$504$		0			0
$505$		−	66.2732i		−	2.94912i
$506$	6.87855	+	39.5495i	0.305789	+	1.75819i
$507$		0			0
$508$	−40.5870	−	55.8633i	−1.80076	−	2.47853i
$509$	19.3302	−	6.28078i	0.856798	−	0.278390i	0.152507	−	0.988302i	$-0.451265\pi$
$509$	19.3302	−	6.28078i	0.856798	−	0.278390i	0.704291	+	0.709912i	$0.251265\pi$
$510$		0			0
$511$	1.30799	+	0.950310i	0.0578621	+	0.0420392i
$512$	−29.4132	−	21.3699i	−1.29989	−	0.944427i
$513$		0			0
$514$	−41.8065	+	13.5838i	−1.84401	+	0.599154i
$515$	−20.7840	−	28.6067i	−0.915851	−	1.26056i
$516$		0			0
$517$	−0.0676605	−	0.00967009i	−0.00297571	−	0.000425290i
$518$		−	6.43579i		−	0.282772i
$519$		0			0
$520$	−5.24530	−	16.1434i	−0.230022	−	0.707934i
$521$	11.4110	+	3.70764i	0.499923	+	0.162435i	0.548115	−	0.836403i	$-0.315346\pi$
$521$	11.4110	+	3.70764i	0.499923	+	0.162435i	−0.0481915	+	0.998838i	$0.515346\pi$
$522$		0			0
$523$	−22.2395	+	30.6101i	−0.972466	+	1.33848i	−0.0316743	+	0.999498i	$0.510084\pi$
$523$	−22.2395	+	30.6101i	−0.972466	+	1.33848i	−0.940791	+	0.338986i	$0.889916\pi$
$524$	−16.8916	+	51.9869i	−0.737912	+	2.27106i
$525$		0			0
$526$	4.05963	−	2.94949i	0.177008	−	0.128604i
$527$	−12.0692			−0.525743
$528$		0			0
$529$	−1.68106			−0.0730898
$530$	41.4869	−	30.1420i	1.80207	−	1.30928i
$531$		0			0
$532$	−1.90653	+	5.86770i	−0.0826586	+	0.254397i
$533$	−1.51556	+	2.08599i	−0.0656462	+	0.0903542i
$534$		0			0
$535$	55.6858	+	18.0934i	2.40751	+	0.782247i
$536$	−6.50459	−	20.0191i	−0.280955	−	0.864692i
$537$		0			0
$538$		−	7.01652i		−	0.302504i
$539$	10.6419	+	20.1276i	0.458378	+	0.866957i
$540$		0			0
$541$	21.6491	+	29.7975i	0.930769	+	1.28109i	0.959559	+	0.281508i	$0.0908345\pi$
$541$	21.6491	+	29.7975i	0.930769	+	1.28109i	−0.0287904	+	0.999585i	$0.509166\pi$
$542$	23.5658	−	7.65700i	1.01224	−	0.328896i
$543$		0			0
$544$	1.71456	+	1.24570i	0.0735112	+	0.0534090i
$545$	−32.6386	−	23.7133i	−1.39808	−	1.01577i
$546$		0			0
$547$	34.8795	−	11.3330i	1.49134	−	0.484565i	0.553860	−	0.832610i	$-0.313154\pi$
$547$	34.8795	−	11.3330i	1.49134	−	0.484565i	0.937478	+	0.348044i	$0.113154\pi$
$548$	2.40060	+	3.30414i	0.102548	+	0.141146i
$549$		0			0
$550$	35.5317	+	67.2032i	1.51508	+	2.86555i
$551$			10.5851i			0.450939i
$552$		0			0
$553$	−1.24304	−	3.82570i	−0.0528596	−	0.162685i
$554$	16.9395	+	5.50398i	0.719691	+	0.233842i
$555$		0			0
$556$	−45.8848	+	63.1550i	−1.94595	+	2.67837i
$557$	−2.30765	+	7.10223i	−0.0977784	+	0.300931i	−0.987968	−	0.154660i	$-0.950572\pi$
$557$	−2.30765	+	7.10223i	−0.0977784	+	0.300931i	0.890189	+	0.455591i	$0.150572\pi$
$558$		0			0
$559$	1.44800	−	1.05204i	0.0612441	−	0.0444964i
$560$	−5.05095			−0.213441
$561$		0			0
$562$	−5.61676			−0.236929
$563$	3.16715	−	2.30107i	0.133479	−	0.0969784i	−0.519042	−	0.854749i	$-0.673711\pi$
$563$	3.16715	−	2.30107i	0.133479	−	0.0969784i	0.652521	+	0.757770i	$0.273711\pi$
$564$		0			0
$565$	1.22811	−	3.77972i	0.0516668	−	0.159014i
$566$	34.9886	−	48.1576i	1.47068	−	2.02422i
$567$		0			0
$568$	−46.3155	−	15.0488i	−1.94335	−	0.631434i
$569$	11.6410	+	35.8274i	0.488017	+	1.50196i	0.827563	+	0.561373i	$0.189727\pi$
$569$	11.6410	+	35.8274i	0.488017	+	1.50196i	−0.339546	+	0.940590i	$0.610273\pi$
$570$		0			0
$571$		−	30.3411i		−	1.26974i	−0.772621	−	0.634868i	$-0.781054\pi$
$571$		−	30.3411i		−	1.26974i	0.772621	−	0.634868i	$-0.218946\pi$
$572$	12.2532	+	1.75124i	0.512333	+	0.0732231i
$573$		0			0
$574$	1.43212	+	1.97115i	0.0597756	+	0.0822741i
$575$	−44.4504	+	14.4428i	−1.85371	+	0.602307i
$576$		0			0
$577$	2.68563	+	1.95122i	0.111804	+	0.0812305i	0.642282	−	0.766468i	$-0.277988\pi$
$577$	2.68563	+	1.95122i	0.111804	+	0.0812305i	−0.530478	+	0.847699i	$0.677988\pi$
$578$	−10.2550	−	7.45067i	−0.426550	−	0.309907i
$579$		0			0
$580$	−35.2835	+	11.4643i	−1.46507	+	0.476029i
$581$	−1.98526	−	2.73247i	−0.0823623	−	0.113362i
$582$		0			0
$583$	3.15138	+	18.1195i	0.130517	+	0.750432i
$584$			20.7303i			0.857826i
$585$		0			0
$586$	−8.02659	−	24.7033i	−0.331576	−	1.02048i
$587$	−38.9053	−	12.6411i	−1.60579	−	0.521754i	−0.637263	−	0.770647i	$-0.719933\pi$
$587$	−38.9053	−	12.6411i	−1.60579	−	0.521754i	−0.968531	+	0.248893i	$0.919933\pi$
$588$		0			0
$589$	−8.80345	+	12.1169i	−0.362740	+	0.499269i
$590$	−18.9299	+	58.2601i	−0.779330	+	2.39853i
$591$		0			0
$592$	21.0231	−	15.2742i	0.864044	−	0.627764i
$593$	4.62924			0.190100			0.0950500	−	0.995472i	$-0.469699\pi$
$593$	4.62924			0.190100			0.0950500	+	0.995472i	$0.469699\pi$
$594$		0			0
$595$	4.79500			0.196576
$596$	25.5866	−	18.5898i	1.04807	−	0.761467i
$597$		0			0
$598$	−3.54672	+	10.9157i	−0.145036	+	0.446376i
$599$	−17.9738	+	24.7388i	−0.734390	+	1.01080i	0.264532	+	0.964377i	$0.414782\pi$
$599$	−17.9738	+	24.7388i	−0.734390	+	1.01080i	−0.998922	+	0.0464237i	$0.985218\pi$
$600$		0			0
$601$	−29.7015	−	9.65061i	−1.21155	−	0.393657i	−0.367552	−	0.930003i	$-0.619804\pi$
$601$	−29.7015	−	9.65061i	−1.21155	−	0.393657i	−0.843998	+	0.536346i	$0.819804\pi$
$602$	−0.522639	−	1.60852i	−0.0213012	−	0.0655583i
$603$		0			0
$604$			39.6459i			1.61317i
$605$	−41.7343	+	1.26245i	−1.69674	+	0.0513259i
$606$		0			0
$607$	−18.0842	−	24.8908i	−0.734016	−	1.01029i	−0.998941	−	0.0460167i	$-0.985347\pi$
$607$	−18.0842	−	24.8908i	−0.734016	−	1.01029i	0.264925	−	0.964269i	$-0.414653\pi$
$608$	2.50125	−	0.812705i	0.101439	−	0.0329595i
$609$		0			0
$610$	−72.9636	−	53.0112i	−2.95421	−	2.14636i
$611$	−0.0158094	−	0.0114862i	−0.000639581	−	0.000464683i
$612$		0			0
$613$	24.2244	−	7.87097i	0.978413	−	0.317906i	0.224205	−	0.974542i	$-0.428021\pi$
$613$	24.2244	−	7.87097i	0.978413	−	0.317906i	0.754207	+	0.656636i	$0.228021\pi$
$614$	6.54221	+	9.00458i	0.264022	+	0.363395i
$615$		0			0
$616$	2.53380	−	5.16444i	0.102090	−	0.208081i
$617$		−	4.20930i		−	0.169460i	−0.996404	−	0.0847300i	$-0.972997\pi$
$617$		−	4.20930i		−	0.169460i	0.996404	−	0.0847300i	$-0.0270028\pi$
$618$		0			0
$619$	11.8981	+	36.6187i	0.478227	+	1.47183i	0.841556	+	0.540170i	$0.181640\pi$
$619$	11.8981	+	36.6187i	0.478227	+	1.47183i	−0.363329	+	0.931661i	$0.618360\pi$
$620$	−49.9243	−	16.2214i	−2.00501	−	0.651467i
$621$		0			0
$622$	−13.4356	+	18.4926i	−0.538720	+	0.741484i
$623$	0.346459	−	1.06629i	0.0138806	−	0.0427200i
$624$		0			0
$625$	−13.3225	+	9.67935i	−0.532899	+	0.387174i
$626$	12.2206			0.488433
$627$		0			0
$628$	−63.6880			−2.54143
$629$	−19.9578	+	14.5002i	−0.795769	+	0.578160i
$630$		0			0
$631$	−3.65655	+	11.2537i	−0.145565	+	0.448003i	−0.997083	−	0.0763220i	$-0.975682\pi$
$631$	−3.65655	+	11.2537i	−0.145565	+	0.448003i	0.851518	+	0.524325i	$0.175682\pi$
$632$	30.3167	−	41.7274i	1.20593	−	1.65983i
$633$		0			0
$634$	27.0547	+	8.79059i	1.07448	+	0.349119i
$635$	20.5794	+	63.3370i	0.816670	+	2.51345i
$636$		0			0
$637$			6.50957i			0.257918i
$638$	2.83913	−	19.8650i	0.112402	−	0.786465i
$639$		0			0
$640$	44.7507	+	61.5941i	1.76893	+	2.43472i
$641$	34.1810	−	11.1061i	1.35007	−	0.438664i	0.457354	−	0.889285i	$-0.348797\pi$
$641$	34.1810	−	11.1061i	1.35007	−	0.438664i	0.892716	+	0.450620i	$0.148797\pi$
$642$		0			0
$643$	−2.63357	−	1.91340i	−0.103858	−	0.0754571i	0.534644	−	0.845077i	$-0.320446\pi$
$643$	−2.63357	−	1.91340i	−0.103858	−	0.0754571i	−0.638502	+	0.769620i	$0.720446\pi$
$644$	5.81778	+	4.22687i	0.229253	+	0.166562i
$645$		0			0
$646$	33.9213	−	11.0217i	1.33461	−	0.433643i
$647$	7.14454	+	9.83361i	0.280881	+	0.386599i	0.926025	−	0.377461i	$-0.123203\pi$
$647$	7.14454	+	9.83361i	0.280881	+	0.386599i	−0.645145	+	0.764060i	$0.723203\pi$
$648$		0			0
$649$	−15.7682	−	15.2984i	−0.618956	−	0.600516i
$650$			21.7345i			0.852498i
$651$		0			0
$652$	5.20020	+	16.0046i	0.203656	+	0.626787i
$653$	−24.2713	−	7.88623i	−0.949811	−	0.308612i	−0.207172	−	0.978305i	$-0.566426\pi$
$653$	−24.2713	−	7.88623i	−0.949811	−	0.308612i	−0.742639	+	0.669692i	$0.766426\pi$
$654$		0			0
$655$	30.9877	−	42.6508i	1.21079	−	1.66651i
$656$	−3.04005	+	9.35631i	−0.118694	+	0.365303i
$657$		0			0
$658$	−0.0149391	+	0.0108539i	−0.000582385	+	0.000423127i
$659$	27.9441			1.08855			0.544273	−	0.838908i	$-0.316806\pi$
$659$	27.9441			1.08855			0.544273	+	0.838908i	$0.316806\pi$
$660$		0			0
$661$	−27.3798			−1.06495			−0.532475	−	0.846446i	$-0.678738\pi$
$661$	−27.3798			−1.06495			−0.532475	+	0.846446i	$0.678738\pi$
$662$	−57.2615	+	41.6029i	−2.22553	+	1.61694i
$663$		0			0
$664$	13.3826	−	41.1873i	0.519344	−	1.59838i
$665$	3.49754	−	4.81395i	0.135629	−	0.186677i
$666$		0			0
$667$	11.7338	+	3.81254i	0.454334	+	0.147622i
$668$	−22.3204	−	68.6952i	−0.863603	−	2.65790i
$669$		0			0
$670$			41.2771i			1.59467i
$671$	28.5946	−	15.1186i	1.10388	−	0.583646i
$672$		0			0
$673$	−7.96377	−	10.9612i	−0.306981	−	0.422523i	0.627456	−	0.778652i	$-0.284096\pi$
$673$	−7.96377	−	10.9612i	−0.306981	−	0.422523i	−0.934437	+	0.356129i	$0.884096\pi$
$674$	66.9179	−	21.7429i	2.57758	−	0.837507i
$675$		0			0
$676$	−38.5290	−	27.9930i	−1.48189	−	1.07665i
$677$	−29.6885	−	21.5700i	−1.14102	−	0.829001i	−0.153760	−	0.988108i	$-0.549138\pi$
$677$	−29.6885	−	21.5700i	−1.14102	−	0.829001i	−0.987261	+	0.159107i	$0.949138\pi$
$678$		0			0
$679$	−5.27723	+	1.71468i	−0.202522	+	0.0658033i
$680$	36.1382	+	49.7399i	1.38584	+	1.90744i
$681$		0			0
$682$	19.7715	−	20.3786i	0.757089	−	0.780337i
$683$		−	30.8347i		−	1.17986i	−0.807455	−	0.589929i	$-0.799156\pi$
$683$		−	30.8347i		−	1.17986i	0.807455	−	0.589929i	$-0.200844\pi$
$684$		0			0
$685$	−1.21721	−	3.74619i	−0.0465072	−	0.143134i
$686$	11.8155	+	3.83910i	0.451119	+	0.146578i
$687$		0			0
$688$	4.01398	−	5.52477i	0.153031	−	0.210630i
$689$	−1.62492	+	5.00098i	−0.0619045	+	0.190522i
$690$		0			0
$691$	38.6062	−	28.0491i	1.46865	−	1.06704i	0.487649	−	0.873040i	$-0.337855\pi$
$691$	38.6062	−	28.0491i	1.46865	−	1.06704i	0.981002	−	0.193997i	$-0.0621452\pi$
$692$	24.3317			0.924953
$693$		0			0
$694$	53.9474			2.04782
$695$	60.9102	−	44.2539i	2.31046	−	1.67864i
$696$		0			0
$697$	2.88600	−	8.88220i	0.109315	−	0.336437i
$698$	−22.4292	+	30.8711i	−0.848957	+	1.16849i
$699$		0			0
$700$	12.9512	+	4.20812i	0.489511	+	0.159052i
$701$	−4.34678	−	13.3780i	−0.164176	−	0.505281i	0.834799	−	0.550555i	$-0.185584\pi$
$701$	−4.34678	−	13.3780i	−0.164176	−	0.505281i	−0.998975	+	0.0452742i	$0.985584\pi$
$702$		0			0
$703$			30.6133i			1.15460i
$704$	−28.5565	+	4.96661i	−1.07626	+	0.187186i
$705$		0			0
$706$	15.9867	+	22.0038i	0.601666	+	0.828122i
$707$	6.10727	−	1.98437i	0.229688	−	0.0746300i
$708$		0			0
$709$	7.34115	+	5.33366i	0.275703	+	0.200310i	0.717041	−	0.697031i	$-0.245496\pi$
$709$	7.34115	+	5.33366i	0.275703	+	0.200310i	−0.441338	+	0.897341i	$0.645496\pi$
$710$	77.2591	+	56.1320i	2.89948	+	2.10660i
$711$		0			0
$712$	13.6721	−	4.44233i	0.512383	−	0.166483i
$713$	10.2610	+	14.1231i	0.384279	+	0.528915i
$714$		0			0
$715$	−10.7174	−	5.25820i	−0.400807	−	0.196645i
$716$		−	36.3090i		−	1.35693i
$717$		0			0
$718$	−12.4707	−	38.3809i	−0.465402	−	1.43236i
$719$	−32.2802	−	10.4885i	−1.20385	−	0.391155i	−0.362674	−	0.931916i	$-0.618136\pi$
$719$	−32.2802	−	10.4885i	−1.20385	−	0.391155i	−0.841176	+	0.540761i	$0.818136\pi$
$720$		0			0
$721$	2.01387	−	2.77186i	0.0750005	−	0.103229i
$722$	−0.627020	+	1.92977i	−0.0233353	+	0.0718186i
$723$		0			0
$724$	13.3336	−	9.68741i	0.495539	−	0.360030i
$725$	23.3635			0.867697
$726$		0			0
$727$	30.8992			1.14599			0.572993	−	0.819560i	$-0.305782\pi$
$727$	30.8992			1.14599			0.572993	+	0.819560i	$0.305782\pi$
$728$	1.33060	−	0.966740i	0.0493154	−	0.0358298i
$729$		0			0
$730$	12.5620	−	38.6620i	0.464942	−	1.43094i
$731$	−3.81058	+	5.24481i	−0.140939	+	0.193986i
$732$		0			0
$733$	−39.5648	−	12.8554i	−1.46136	−	0.474825i	−0.532876	−	0.846194i	$-0.678889\pi$
$733$	−39.5648	−	12.8554i	−1.46136	−	0.474825i	−0.928485	+	0.371369i	$0.878889\pi$
$734$	−7.38580	−	22.7312i	−0.272615	−	0.839022i
$735$		0			0
$736$		−	3.06541i		−	0.112993i
$737$	−13.2904	−	6.52058i	−0.489558	−	0.240189i
$738$		0			0
$739$	−8.44687	−	11.6261i	−0.310723	−	0.427674i	0.624883	−	0.780718i	$-0.285146\pi$
$739$	−8.44687	−	11.6261i	−0.310723	−	0.427674i	−0.935607	+	0.353044i	$0.885146\pi$
$740$	−102.044	+	33.1561i	−3.75121	+	1.21884i
$741$		0			0
$742$	4.01989	+	2.92062i	0.147575	+	0.107219i
$743$	10.8649	+	7.89384i	0.398596	+	0.289597i	0.768969	−	0.639286i	$-0.220770\pi$
$743$	10.8649	+	7.89384i	0.398596	+	0.289597i	−0.370373	+	0.928883i	$0.620770\pi$
$744$		0			0
$745$	−29.0098	+	9.42585i	−1.06284	+	0.345336i
$746$	−18.0937	−	24.9039i	−0.662459	−	0.911796i
$747$		0			0
$748$	−44.1703	+	7.68220i	−1.61502	+	0.280889i
$749$			5.67337i			0.207301i
$750$		0			0
$751$	−11.2373	−	34.5847i	−0.410054	−	1.26202i	−0.916601	−	0.399803i	$-0.869078\pi$
$751$	−11.2373	−	34.5847i	−0.410054	−	1.26202i	0.506547	−	0.862212i	$-0.330922\pi$
$752$	−0.0709102	−	0.0230401i	−0.00258583	−	0.000840187i
$753$		0			0
$754$	3.37234	−	4.64163i	0.122813	−	0.169038i
$755$	11.8158	−	36.3653i	0.430021	−	1.32347i
$756$		0			0
$757$	−32.2811	+	23.4536i	−1.17328	+	0.852435i	−0.991397	−	0.130887i	$-0.958218\pi$
$757$	−32.2811	+	23.4536i	−1.17328	+	0.852435i	−0.181878	+	0.983321i	$0.558218\pi$
$758$	−85.5197			−3.10622
$759$		0			0
$760$	76.2962			2.76755
$761$	2.75887	−	2.00443i	0.100009	−	0.0726607i	−0.536657	−	0.843801i	$-0.680313\pi$
$761$	2.75887	−	2.00443i	0.100009	−	0.0726607i	0.636666	+	0.771140i	$0.280313\pi$
$762$		0			0
$763$	1.20798	−	3.71777i	0.0437317	−	0.134592i
$764$	−46.6896	+	64.2627i	−1.68917	+	2.32494i
$765$		0			0
$766$	52.3347	+	17.0046i	1.89093	+	0.614401i
$767$	−1.94108	−	5.97403i	−0.0700884	−	0.215710i
$768$		0			0
$769$			21.4154i			0.772260i	0.922444	+	0.386130i	$0.126188\pi$
$769$			21.4154i			0.772260i	−0.922444	+	0.386130i	$0.873812\pi$
$770$	−7.85505	+	8.09625i	−0.283076	+	0.291769i
$771$		0			0
$772$	−18.5388	−	25.5165i	−0.667227	−	0.918359i
$773$	−34.1302	+	11.0896i	−1.22758	+	0.398864i	−0.849836	−	0.527048i	$-0.823299\pi$
$773$	−34.1302	+	11.0896i	−1.22758	+	0.398864i	−0.377741	+	0.925911i	$0.623299\pi$
$774$		0			0
$775$	26.7446	+	19.4311i	0.960694	+	0.697985i
$776$	−57.5595	−	41.8194i	−2.06626	−	1.50123i
$777$		0			0
$778$	17.0510	−	5.54020i	0.611308	−	0.198626i
$779$	−6.81221	−	9.37620i	−0.244073	−	0.335937i
$780$		0			0
$781$	−30.2780	+	16.0086i	−1.08343	+	0.572833i
$782$		−	41.5723i		−	1.48662i
$783$		0			0
$784$	7.67500	+	23.6212i	0.274107	+	0.843615i
$785$	58.4180	+	18.9811i	2.08503	+	0.677466i
$786$		0			0
$787$	−28.2510	+	38.8842i	−1.00704	+	1.38607i	−0.0861340	+	0.996284i	$0.527451\pi$
$787$	−28.2510	+	38.8842i	−1.00704	+	1.38607i	−0.920905	+	0.389787i	$0.872549\pi$
$788$	25.7479	−	79.2437i	0.917229	−	2.82294i
$789$		0			0
$790$	−81.8263	+	59.4503i	−2.91125	+	2.11515i
$791$	0.385085			0.0136920
$792$		0			0
$793$	9.24793			0.328404
$794$	32.9805	−	23.9618i	1.17044	−	0.850371i
$795$		0			0
$796$	−12.7893	+	39.3615i	−0.453306	+	1.39513i
$797$	3.55363	−	4.89115i	0.125876	−	0.173253i	−0.741428	−	0.671033i	$-0.765851\pi$
$797$	3.55363	−	4.89115i	0.125876	−	0.173253i	0.867304	+	0.497779i	$0.165851\pi$
$798$		0			0
$799$	0.0673169	+	0.0218726i	0.00238150	+	0.000773797i
$800$	−1.79381	−	5.52078i	−0.0634208	−	0.195189i
$801$		0			0
$802$			12.3605i			0.436464i
$803$	10.4639	+	10.1522i	0.369264	+	0.358263i
$804$		0			0
$805$	−4.07663	−	5.61099i	−0.143682	−	0.197762i
$806$	7.72076	−	2.50863i	0.271952	−	0.0883626i
$807$		0			0
$808$	66.6128	+	48.3970i	2.34343	+	1.70260i
$809$	−6.01444	−	4.36974i	−0.211456	−	0.153632i	0.477016	−	0.878895i	$-0.341718\pi$
$809$	−6.01444	−	4.36974i	−0.211456	−	0.153632i	−0.688472	+	0.725263i	$0.741718\pi$
$810$		0			0
$811$	27.7357	−	9.01188i	0.973933	−	0.316450i	0.221530	−	0.975154i	$-0.428895\pi$
$811$	27.7357	−	9.01188i	0.973933	−	0.316450i	0.752402	+	0.658704i	$0.228895\pi$
$812$	−2.11294	−	2.90821i	−0.0741495	−	0.102058i
$813$		0			0
$814$	8.21110	−	57.4521i	0.287799	−	2.01369i
$815$		−	16.2301i		−	0.568514i
$816$		0			0
$817$	2.48605	+	7.65127i	0.0869758	+	0.267684i
$818$	74.9521	+	24.3534i	2.62064	+	0.851497i
$819$		0			0
$820$	23.8759	−	32.8623i	0.833782	−	1.14760i
$821$	−0.331389	+	1.01991i	−0.0115656	+	0.0355952i	−0.956673	−	0.291165i	$-0.905957\pi$
$821$	−0.331389	+	1.01991i	−0.0115656	+	0.0355952i	0.945107	+	0.326760i	$0.105957\pi$
$822$		0			0
$823$	7.23762	−	5.25844i	0.252288	−	0.183298i	−0.454452	−	0.890771i	$-0.650165\pi$
$823$	7.23762	−	5.25844i	0.252288	−	0.183298i	0.706740	+	0.707473i	$0.250165\pi$
$824$	43.9311			1.53041
$825$		0			0
$826$	−5.93565			−0.206528
$827$	−28.5608	+	20.7507i	−0.993157	+	0.721571i	−0.960610	−	0.277899i	$-0.910362\pi$
$827$	−28.5608	+	20.7507i	−0.993157	+	0.721571i	−0.0325471	+	0.999470i	$0.510362\pi$
$828$		0			0
$829$	8.36614	−	25.7483i	0.290568	−	0.894276i	−0.694106	−	0.719873i	$-0.744200\pi$
$829$	8.36614	−	25.7483i	0.290568	−	0.894276i	0.984674	−	0.174404i	$-0.0557998\pi$
$830$	−49.9169	+	68.7047i	−1.73264	+	2.38478i
$831$		0			0
$832$	−7.88160	−	2.56089i	−0.273245	−	0.0887828i
$833$	−7.28608	−	22.4243i	−0.252448	−	0.776954i
$834$		0			0
$835$			69.6630i			2.41079i
$836$	−24.5058	+	49.9483i	−0.847552	+	1.72750i
$837$		0			0
$838$	−39.9645	−	55.0064i	−1.38055	−	1.90016i
$839$	−35.4106	+	11.5056i	−1.22251	+	0.397218i	−0.847996	−	0.530003i	$-0.822191\pi$
$839$	−35.4106	+	11.5056i	−1.22251	+	0.397218i	−0.374515	+	0.927221i	$0.622191\pi$
$840$		0			0
$841$	18.4720	+	13.4207i	0.636965	+	0.462782i
$842$	52.6828	+	38.2763i	1.81557	+	1.31909i
$843$		0			0
$844$	−13.8425	+	4.49772i	−0.476480	+	0.154818i
$845$	26.9980	+	37.1595i	0.928759	+	1.27833i
$846$		0			0
$847$	−1.36596	−	3.80813i	−0.0469349	−	0.130849i
$848$			20.0629i			0.688962i
$849$		0			0
$850$	−24.3272	−	74.8714i	−0.834416	−	2.56807i
$851$	33.9355	+	11.0263i	1.16329	+	0.377977i
$852$		0			0
$853$	20.6424	−	28.4118i	0.706782	−	0.972802i	−0.293078	−	0.956089i	$-0.594680\pi$
$853$	20.6424	−	28.4118i	0.706782	−	0.972802i	0.999860	−	0.0167139i	$-0.00532045\pi$
$854$	2.70044	−	8.31109i	0.0924070	−	0.284400i
$855$		0			0
$856$	−58.8516	+	42.7582i	−2.01151	+	1.46144i
$857$	29.9637			1.02354			0.511770	−	0.859122i	$-0.328990\pi$
$857$	29.9637			1.02354			0.511770	+	0.859122i	$0.328990\pi$
$858$		0			0
$859$	17.2684			0.589189			0.294595	−	0.955622i	$-0.404815\pi$
$859$	17.2684			0.589189			0.294595	+	0.955622i	$0.404815\pi$
$860$	−22.8116	+	16.5736i	−0.777870	+	0.565156i
$861$		0			0
$862$	−0.539519	+	1.66047i	−0.0183761	+	0.0565558i
$863$	20.4637	−	28.1659i	0.696593	−	0.958778i	−0.303389	−	0.952867i	$-0.598118\pi$
$863$	20.4637	−	28.1659i	0.696593	−	0.958778i	0.999983	−	0.00591175i	$-0.00188178\pi$
$864$		0			0
$865$	−22.3183	−	7.25166i	−0.758845	−	0.246564i
$866$	−8.60705	−	26.4898i	−0.292480	−	0.900159i
$867$		0			0
$868$		−	5.08638i		−	0.172643i
$869$	−6.21560	−	35.7378i	−0.210850	−	1.21232i
$870$		0			0
$871$	−2.48785	−	3.42423i	−0.0842976	−	0.116026i
$872$	47.6696	−	15.4888i	1.61430	−	0.524517i
$873$		0			0
$874$	−41.7366	−	30.3234i	−1.41176	−	1.02570i
$875$	−4.97827	−	3.61692i	−0.168296	−	0.122274i
$876$		0			0
$877$	−1.88584	+	0.612748i	−0.0636804	+	0.0206910i	−0.340684	−	0.940178i	$-0.610659\pi$
$877$	−1.88584	+	0.612748i	−0.0636804	+	0.0206910i	0.277004	+	0.960869i	$0.410659\pi$
$878$	12.2800	+	16.9020i	0.414431	+	0.570416i
$879$		0			0
$880$	−45.0896	−	6.44424i	−1.51997	−	0.217235i
$881$			48.9571i			1.64941i	0.565566	+	0.824703i	$0.308658\pi$
$881$			48.9571i			1.64941i	−0.565566	+	0.824703i	$0.691342\pi$
$882$		0			0
$883$	10.7400	+	33.0542i	0.361429	+	1.11236i	0.952187	+	0.305515i	$0.0988286\pi$
$883$	10.7400	+	33.0542i	0.361429	+	1.11236i	−0.590758	+	0.806848i	$0.701171\pi$
$884$	−12.1910	−	3.96110i	−0.410028	−	0.133226i
$885$		0			0
$886$	20.0154	−	27.5488i	0.672430	−	0.925520i
$887$	4.47860	−	13.7837i	0.150377	−	0.462812i	−0.847287	−	0.531136i	$-0.821765\pi$
$887$	4.47860	−	13.7837i	0.150377	−	0.462812i	0.997663	+	0.0683244i	$0.0217653\pi$
$888$		0			0
$889$	−5.22049	+	3.79291i	−0.175090	+	0.127210i
$890$	−28.1903			−0.944943
$891$		0			0
$892$	−70.4368			−2.35840
$893$	0.0710609	−	0.0516288i	0.00237796	−	0.00172769i
$894$		0			0
$895$	−10.8213	+	33.3045i	−0.361716	+	1.11325i
$896$	−4.33614	+	5.96818i	−0.144860	+	0.199383i
$897$		0			0
$898$	50.0671	+	16.2678i	1.67076	+	0.542863i
$899$	−2.69664	−	8.29941i	−0.0899380	−	0.276801i
$900$		0			0
$901$		−	19.0462i		−	0.634521i
$902$	10.2696	+	19.4235i	0.341941	+	0.646733i
$903$		0			0
$904$	2.90224	+	3.99460i	0.0965272	+	0.132858i
$905$	−15.1174	+	4.91195i	−0.502520	+	0.163279i
$906$		0			0
$907$	−18.4206	−	13.3834i	−0.611647	−	0.444387i	0.238347	−	0.971180i	$-0.423394\pi$
$907$	−18.4206	−	13.3834i	−0.611647	−	0.444387i	−0.849994	+	0.526793i	$0.823394\pi$
$908$	55.3329	+	40.2017i	1.83629	+	1.33414i
$909$		0			0
$910$	−3.06739	+	0.996656i	−0.101683	+	0.0330388i
$911$	−13.3395	−	18.3602i	−0.441956	−	0.608300i	0.528689	−	0.848815i	$-0.322684\pi$
$911$	−13.3395	−	18.3602i	−0.441956	−	0.608300i	−0.970645	+	0.240515i	$0.922684\pi$
$912$		0			0
$913$	−14.2361	−	26.9256i	−0.471146	−	0.891106i
$914$		−	23.8883i		−	0.790153i
$915$		0			0
$916$	5.20119	+	16.0076i	0.171852	+	0.528907i
$917$	4.85824	+	1.57854i	0.160433	+	0.0521280i
$918$		0			0
$919$	−0.737746	+	1.01542i	−0.0243360	+	0.0334956i	−0.821012	−	0.570911i	$-0.806590\pi$
$919$	−0.737746	+	1.01542i	−0.0243360	+	0.0334956i	0.796676	+	0.604407i	$0.206590\pi$
$920$	27.4804	−	84.5761i	0.906003	−	2.78839i
$921$		0			0
$922$	−24.3590	+	17.6978i	−0.802220	+	0.582847i
$923$	−9.79237			−0.322320
$924$		0			0
$925$	67.5699			2.22169
$926$	−66.7619	+	48.5054i	−2.19393	+	1.59399i
$927$		0			0
$928$	−0.473521	+	1.45735i	−0.0155441	+	0.0478398i
$929$	−1.68995	+	2.32602i	−0.0554456	+	0.0763143i	−0.835839	−	0.548974i	$-0.815019\pi$
$929$	−1.68995	+	2.32602i	−0.0554456	+	0.0763143i	0.780394	+	0.625288i	$0.215019\pi$
$930$		0			0
$931$	−27.8274	−	9.04168i	−0.912007	−	0.296329i
$932$	28.4377	+	87.5224i	0.931509	+	2.86689i
$933$		0			0
$934$		−	38.3402i		−	1.25453i
$935$	42.8048	+	6.11769i	1.39987	+	0.200070i
$936$		0			0
$937$	18.1303	+	24.9542i	0.592291	+	0.815219i	0.994975	−	0.100120i	$-0.0319227\pi$
$937$	18.1303	+	24.9542i	0.592291	+	0.815219i	−0.402684	+	0.915339i	$0.631923\pi$
$938$	−3.80381	+	1.23593i	−0.124199	+	0.0403546i
$939$		0			0
$940$	0.249059	+	0.180952i	0.00812341	+	0.00590200i
$941$	5.29167	+	3.84462i	0.172503	+	0.125331i	0.670687	−	0.741741i	$-0.265999\pi$
$941$	5.29167	+	3.84462i	0.172503	+	0.125331i	−0.498184	+	0.867072i	$0.665999\pi$
$942$		0			0
$943$	−12.8474	+	4.17436i	−0.418368	+	0.135936i
$944$	−14.0872	−	19.3893i	−0.458498	−	0.631069i
$945$		0			0
$946$	−2.61336	−	15.0260i	−0.0849675	−	0.488537i
$947$		−	33.2579i		−	1.08074i	−0.841429	−	0.540368i	$-0.818285\pi$
$947$		−	33.2579i		−	1.08074i	0.841429	−	0.540368i	$-0.181715\pi$
$948$		0			0
$949$	1.28812	+	3.96442i	0.0418141	+	0.128691i
$950$	−92.9119	−	30.1889i	−3.01446	−	0.979457i
$951$		0			0
$952$	−3.50162	+	4.81957i	−0.113488	+	0.156203i
$953$	−16.9820	+	52.2651i	−0.550100	+	1.69303i	0.158445	+	0.987368i	$0.449352\pi$
$953$	−16.9820	+	52.2651i	−0.550100	+	1.69303i	−0.708545	+	0.705666i	$0.750648\pi$
$954$		0			0
$955$	61.9785	−	45.0300i	2.00558	−	1.45714i
$956$	78.6961			2.54521
$957$		0			0
$958$	30.3786			0.981488
$959$	0.308776	−	0.224339i	0.00997090	−	0.00724428i
$960$		0			0
$961$	−5.76392	+	17.7395i	−0.185933	+	0.572242i
$962$	9.75321	−	13.4241i	0.314456	−	0.432812i
$963$		0			0
$964$	8.70515	+	2.82847i	0.280374	+	0.0910990i
$965$	9.40000	+	28.9302i	0.302597	+	0.931297i
$966$		0			0
$967$			34.0395i			1.09464i	0.836925	+	0.547318i	$0.184351\pi$
$967$			34.0395i			1.09464i	−0.836925	+	0.547318i	$0.815649\pi$
$968$	29.2082	−	42.8700i	0.938786	−	1.37790i
$969$		0			0
$970$	82.0068	+	112.873i	2.63308	+	3.62412i
$971$	−36.2008	+	11.7624i	−1.16174	+	0.377472i	−0.825554	−	0.564323i	$-0.809137\pi$
$971$	−36.2008	+	11.7624i	−1.16174	+	0.377472i	−0.336186	+	0.941796i	$0.609137\pi$
$972$		0			0
$973$	5.90192	+	4.28799i	0.189207	+	0.137467i
$974$	−13.7106	−	9.96134i	−0.439316	−	0.319182i
$975$		0			0
$976$	33.5579	−	10.9036i	1.07416	−	0.349017i
$977$	18.8682	+	25.9699i	0.603648	+	0.830850i	0.996036	−	0.0889499i	$-0.0283511\pi$
$977$	18.8682	+	25.9699i	0.603648	+	0.830850i	−0.392388	+	0.919800i	$0.628351\pi$
$978$		0			0
$979$	4.45325	−	9.07671i	0.142327	−	0.290093i
$980$		−	102.551i		−	3.27586i
$981$		0			0
$982$	−0.227305	−	0.699572i	−0.00725358	−	0.0223242i
$983$	−20.3816	−	6.62238i	−0.650071	−	0.211221i	−0.0346258	−	0.999400i	$-0.511024\pi$
$983$	−20.3816	−	6.62238i	−0.650071	−	0.211221i	−0.615446	+	0.788179i	$0.711024\pi$
$984$		0			0
$985$	−47.2345	+	65.0128i	−1.50502	+	2.07148i
$986$	−6.42177	+	19.7642i	−0.204511	+	0.629419i
$987$		0			0
$988$	−12.8690	+	9.34991i	−0.409419	+	0.297460i
$989$	9.37704			0.298172
$990$		0			0
$991$	−29.3068			−0.930962			−0.465481	−	0.885058i	$-0.654119\pi$
$991$	−29.3068			−0.930962			−0.465481	+	0.885058i	$0.654119\pi$
$992$	−1.75410	+	1.27443i	−0.0556929	+	0.0404632i
$993$		0			0
$994$	−2.85942	+	8.80038i	−0.0906952	+	0.279131i
$995$	23.4621	−	32.2928i	0.743798	−	1.02375i
$996$		0			0
$997$	−31.1587	−	10.1241i	−0.986807	−	0.320633i	−0.229225	−	0.973373i	$-0.573619\pi$
$997$	−31.1587	−	10.1241i	−0.986807	−	0.320633i	−0.757582	+	0.652740i	$0.773619\pi$
$998$	−4.98148	−	15.3314i	−0.157686	−	0.485308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.j.a.8.4	yes	16
3.2	odd	2	inner	99.2.j.a.8.1	✓	16
4.3	odd	2		1584.2.cd.c.305.1		16
9.2	odd	6		891.2.u.c.701.4		32
9.4	even	3		891.2.u.c.107.4		32
9.5	odd	6		891.2.u.c.107.1		32
9.7	even	3		891.2.u.c.701.1		32
11.2	odd	10		1089.2.d.g.1088.15		16
11.7	odd	10	inner	99.2.j.a.62.1	yes	16
11.9	even	5		1089.2.d.g.1088.1		16
12.11	even	2		1584.2.cd.c.305.4		16
33.2	even	10		1089.2.d.g.1088.2		16
33.20	odd	10		1089.2.d.g.1088.16		16
33.29	even	10	inner	99.2.j.a.62.4	yes	16
44.7	even	10		1584.2.cd.c.161.4		16
99.7	odd	30		891.2.u.c.458.1		32
99.29	even	30		891.2.u.c.458.4		32
99.40	odd	30		891.2.u.c.755.4		32
99.95	even	30		891.2.u.c.755.1		32
132.95	odd	10		1584.2.cd.c.161.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.8.1	✓	16	3.2	odd	2	inner
99.2.j.a.8.4	yes	16	1.1	even	1	trivial
99.2.j.a.62.1	yes	16	11.7	odd	10	inner
99.2.j.a.62.4	yes	16	33.29	even	10	inner
891.2.u.c.107.1		32	9.5	odd	6
891.2.u.c.107.4		32	9.4	even	3
891.2.u.c.458.1		32	99.7	odd	30
891.2.u.c.458.4		32	99.29	even	30
891.2.u.c.701.1		32	9.7	even	3
891.2.u.c.701.4		32	9.2	odd	6
891.2.u.c.755.1		32	99.95	even	30
891.2.u.c.755.4		32	99.40	odd	30
1089.2.d.g.1088.1		16	11.9	even	5
1089.2.d.g.1088.2		16	33.2	even	10
1089.2.d.g.1088.15		16	11.2	odd	10
1089.2.d.g.1088.16		16	33.20	odd	10
1584.2.cd.c.161.1		16	132.95	odd	10
1584.2.cd.c.161.4		16	44.7	even	10
1584.2.cd.c.305.1		16	4.3	odd	2
1584.2.cd.c.305.4		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.97102 - 1.43203i) q^{2} +(1.21618 - 3.74302i) q^{4} +(-2.23109 + 3.07083i) q^{5} +(-0.349790 - 0.113654i) q^{7} +(-1.45728 - 4.48505i) q^{8} +O(q^{10})\)	\(q+(1.97102 - 1.43203i) q^{2} +(1.21618 - 3.74302i) q^{4} +(-2.23109 + 3.07083i) q^{5} +(-0.349790 - 0.113654i) q^{7} +(-1.45728 - 4.48505i) q^{8} +9.24768i q^{10} +(-2.97756 - 1.46086i) q^{11} +(-0.557375 - 0.767161i) q^{13} +(-0.852201 + 0.276897i) q^{14} +(-2.92705 - 2.12663i) q^{16} +(2.77873 + 2.01886i) q^{17} +(4.05368 - 1.31712i) q^{19} +(8.78079 + 12.0857i) q^{20} +(-7.96085 + 1.38457i) q^{22} -4.96800i q^{23} +(-2.90717 - 8.94734i) q^{25} +(-2.19720 - 0.713913i) q^{26} +(-0.850818 + 1.17105i) q^{28} +(-0.767418 + 2.36187i) q^{29} +(-2.84281 + 2.06543i) q^{31} +0.617031 q^{32} +8.36801 q^{34} +(1.12943 - 0.820576i) q^{35} +(-2.21947 + 6.83082i) q^{37} +(6.10374 - 8.40108i) q^{38} +(17.0242 + 5.53148i) q^{40} +(-0.840249 - 2.58602i) q^{41} +1.88749i q^{43} +(-9.08931 + 9.36841i) q^{44} +(-7.11434 - 9.79205i) q^{46} +(0.0195991 - 0.00636813i) q^{47} +(-5.55368 - 4.03499i) q^{49} +(-18.5430 - 13.4723i) q^{50} +(-3.54937 + 1.15326i) q^{52} +(-3.25941 - 4.48619i) q^{53} +(11.1293 - 5.88428i) q^{55} +1.73445i q^{56} +(1.86968 + 5.75427i) q^{58} +(6.29998 + 2.04699i) q^{59} +(-5.73238 + 7.88994i) q^{61} +(-2.64550 + 8.14200i) q^{62} +(7.07028 - 5.13686i) q^{64} +3.59938 q^{65} +4.46351 q^{67} +(10.9361 - 7.94554i) q^{68} +(1.05103 - 3.23475i) q^{70} +(6.06985 - 8.35443i) q^{71} +(-4.18072 - 1.35840i) q^{73} +(5.40733 + 16.6420i) q^{74} -16.7749i q^{76} +(0.875490 + 0.849407i) q^{77} +(6.42867 + 8.84831i) q^{79} +(13.0610 - 4.24379i) q^{80} +(-5.35942 - 3.89384i) q^{82} +(7.42940 + 5.39778i) q^{83} +(-12.3992 + 4.02874i) q^{85} +(2.70294 + 3.72028i) q^{86} +(-2.21290 + 15.4834i) q^{88} +3.04837i q^{89} +(0.107774 + 0.331693i) q^{91} +(-18.5954 - 6.04200i) q^{92} +(0.0295109 - 0.0406183i) q^{94} +(-4.99948 + 15.3868i) q^{95} +(12.2055 - 8.86782i) q^{97} -16.7247 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4}+O(q^{10}) \) 16 * q - 4 * q^4	\( 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70} - 20 q^{73} - 12 q^{82} - 100 q^{85} - 12 q^{88} - 72 q^{91} - 80 q^{94} + 60 q^{97}+O(q^{100}) \) 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

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