LMFDB - Embedded newform 207.2.i.e.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			100.1
Character	$\chi$	$=$	207.100
Dual form			207.2.i.e.118.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.226138 + 1.57283i) q^{2} +(-0.503658 - 0.147887i) q^{4} +(-0.696899 - 0.804264i) q^{5} +(2.72743 + 1.75281i) q^{7} +(-0.973691 + 2.13209i) q^{8} +O(q^{10})$	\(q+(-0.226138 + 1.57283i) q^{2} +(-0.503658 - 0.147887i) q^{4} +(-0.696899 - 0.804264i) q^{5} +(2.72743 + 1.75281i) q^{7} +(-0.973691 + 2.13209i) q^{8} +(1.42256 - 0.914226i) q^{10} +(0.457998 + 3.18545i) q^{11} +(-1.93077 + 1.24083i) q^{13} +(-3.37365 + 3.89340i) q^{14} +(-4.01640 - 2.58118i) q^{16} +(3.24262 - 0.952119i) q^{17} +(-0.217369 - 0.0638252i) q^{19} +(0.232058 + 0.508137i) q^{20} -5.11373 q^{22} +(-0.206512 - 4.79138i) q^{23} +(0.550401 - 3.82813i) q^{25} +(-1.51499 - 3.31737i) q^{26} +(-1.11447 - 1.28617i) q^{28} +(1.61033 - 0.472836i) q^{29} +(-2.36160 + 5.17119i) q^{31} +(1.89816 - 2.19059i) q^{32} +(0.764238 + 5.31539i) q^{34} +(-0.491019 - 3.41511i) q^{35} +(4.43585 - 5.11925i) q^{37} +(0.149541 - 0.327450i) q^{38} +(2.39333 - 0.702744i) q^{40} +(-1.80269 - 2.08041i) q^{41} +(-0.140028 - 0.306619i) q^{43} +(0.240413 - 1.67211i) q^{44} +(7.58271 + 0.758707i) q^{46} +13.3242 q^{47} +(1.45862 + 3.19393i) q^{49} +(5.89651 + 1.73137i) q^{50} +(1.15595 - 0.339419i) q^{52} +(-10.1284 - 6.50915i) q^{53} +(2.24276 - 2.58829i) q^{55} +(-6.39283 + 4.10842i) q^{56} +(0.379532 + 2.63970i) q^{58} +(7.00588 - 4.50240i) q^{59} +(-4.40688 + 9.64972i) q^{61} +(-7.59933 - 4.88380i) q^{62} +(-3.23683 - 3.73551i) q^{64} +(2.34351 + 0.688117i) q^{65} +(1.74834 - 12.1600i) q^{67} -1.77398 q^{68} +5.48241 q^{70} +(2.22709 - 15.4898i) q^{71} +(4.91808 + 1.44408i) q^{73} +(7.04857 + 8.13448i) q^{74} +(0.100041 + 0.0642921i) q^{76} +(-4.33434 + 9.49088i) q^{77} +(-6.85430 + 4.40499i) q^{79} +(0.723071 + 5.02907i) q^{80} +(3.67978 - 2.36485i) q^{82} +(-5.07198 + 5.85338i) q^{83} +(-3.02553 - 1.94439i) q^{85} +(0.513924 - 0.150902i) q^{86} +(-7.23760 - 2.12515i) q^{88} +(3.52658 + 7.72212i) q^{89} -7.44100 q^{91} +(-0.604574 + 2.44376i) q^{92} +(-3.01312 + 20.9567i) q^{94} +(0.100152 + 0.219301i) q^{95} +(-8.49290 - 9.80133i) q^{97} +(-5.35335 + 1.57188i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4} + 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^4 + 8 * q^7	$ 40 q - 4 q^{4} + 8 q^{7} - 56 q^{16} - 14 q^{19} - 28 q^{22} - 48 q^{25} - 64 q^{28} - 22 q^{31} - 10 q^{34} + 52 q^{37} + 6 q^{40} + 68 q^{43} + 84 q^{46} + 4 q^{49} + 110 q^{52} + 50 q^{55} + 18 q^{58} + 36 q^{61} + 116 q^{64} - 18 q^{67} + 96 q^{70} + 14 q^{73} + 34 q^{76} - 36 q^{79} - 72 q^{82} - 238 q^{85} - 160 q^{88} - 176 q^{91} - 206 q^{94} - 92 q^{97}+O(q^{100}) $ 40 * q - 4 * q^4 + 8 * q^7 - 56 * q^16 - 14 * q^19 - 28 * q^22 - 48 * q^25 - 64 * q^28 - 22 * q^31 - 10 * q^34 + 52 * q^37 + 6 * q^40 + 68 * q^43 + 84 * q^46 + 4 * q^49 + 110 * q^52 + 50 * q^55 + 18 * q^58 + 36 * q^61 + 116 * q^64 - 18 * q^67 + 96 * q^70 + 14 * q^73 + 34 * q^76 - 36 * q^79 - 72 * q^82 - 238 * q^85 - 160 * q^88 - 176 * q^91 - 206 * q^94 - 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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 $

$2$	−0.226138	+	1.57283i	−0.159904	+	1.11216i	0.738903	+	0.673812i	$0.235344\pi$
$2$	−0.226138	+	1.57283i	−0.159904	+	1.11216i	−0.898807	+	0.438345i	$0.855565\pi$
$3$		0			0
$3$		0			0
$4$	−0.503658	−	0.147887i	−0.251829	−	0.0739437i
$5$	−0.696899	−	0.804264i	−0.311663	−	0.359678i	0.578209	−	0.815889i	$-0.303752\pi$
$5$	−0.696899	−	0.804264i	−0.311663	−	0.359678i	−0.889872	+	0.456211i	$0.849206\pi$
$6$		0			0
$7$	2.72743	+	1.75281i	1.03087	+	0.662501i	0.942713	−	0.333605i	$-0.108265\pi$
$7$	2.72743	+	1.75281i	1.03087	+	0.662501i	0.0881590	+	0.996106i	$0.471902\pi$
$8$	−0.973691	+	2.13209i	−0.344252	+	0.753806i
$9$		0			0
$10$	1.42256	−	0.914226i	0.449854	−	0.289104i
$11$	0.457998	+	3.18545i	0.138092	+	0.960449i	0.934569	+	0.355781i	$0.115785\pi$
$11$	0.457998	+	3.18545i	0.138092	+	0.960449i	−0.796478	+	0.604668i	$0.793306\pi$
$12$		0			0
$13$	−1.93077	+	1.24083i	−0.535500	+	0.344145i	−0.780277	−	0.625435i	$-0.784922\pi$
$13$	−1.93077	+	1.24083i	−0.535500	+	0.344145i	0.244777	+	0.969580i	$0.421285\pi$
$14$	−3.37365	+	3.89340i	−0.901645	+	1.04055i
$15$		0			0
$16$	−4.01640	−	2.58118i	−1.00410	−	0.645295i
$17$	3.24262	−	0.952119i	0.786451	−	0.230923i	0.136239	−	0.990676i	$-0.456498\pi$
$17$	3.24262	−	0.952119i	0.786451	−	0.230923i	0.650212	+	0.759753i	$0.274680\pi$
$18$		0			0
$19$	−0.217369	−	0.0638252i	−0.0498678	−	0.0146425i	0.256704	−	0.966490i	$-0.417364\pi$
$19$	−0.217369	−	0.0638252i	−0.0498678	−	0.0146425i	−0.306571	+	0.951848i	$0.599182\pi$
$20$	0.232058	+	0.508137i	0.0518898	+	0.113623i
$21$		0			0
$22$	−5.11373			−1.09025
$23$	−0.206512	−	4.79138i	−0.0430608	−	0.999072i
$23$	−0.206512	−	4.79138i	−0.0430608	−	0.999072i
$24$		0			0
$25$	0.550401	−	3.82813i	0.110080	−	0.765625i
$26$	−1.51499	−	3.31737i	−0.297114	−	0.650590i
$27$		0			0
$28$	−1.11447	−	1.28617i	−0.210616	−	0.243064i
$29$	1.61033	−	0.472836i	0.299031	−	0.0878035i	−0.128775	−	0.991674i	$-0.541105\pi$
$29$	1.61033	−	0.472836i	0.299031	−	0.0878035i	0.427807	+	0.903870i	$0.359286\pi$
$30$		0			0
$31$	−2.36160	+	5.17119i	−0.424156	+	0.928773i	0.570083	+	0.821587i	$0.306911\pi$
$31$	−2.36160	+	5.17119i	−0.424156	+	0.928773i	−0.994239	+	0.107186i	$0.965816\pi$
$32$	1.89816	−	2.19059i	0.335550	−	0.387245i
$33$		0			0
$34$	0.764238	+	5.31539i	0.131066	+	0.911582i
$35$	−0.491019	−	3.41511i	−0.0829973	−	0.577259i
$36$		0			0
$37$	4.43585	−	5.11925i	0.729250	−	0.841599i	−0.263137	−	0.964758i	$-0.584757\pi$
$37$	4.43585	−	5.11925i	0.729250	−	0.841599i	0.992387	+	0.123159i	$0.0393026\pi$
$38$	0.149541	−	0.327450i	0.0242588	−	0.0531193i
$39$		0			0
$40$	2.39333	−	0.702744i	0.378418	−	0.111114i
$41$	−1.80269	−	2.08041i	−0.281532	−	0.324906i	0.597317	−	0.802005i	$-0.296233\pi$
$41$	−1.80269	−	2.08041i	−0.281532	−	0.324906i	−0.878849	+	0.477100i	$0.841688\pi$
$42$		0			0
$43$	−0.140028	−	0.306619i	−0.0213541	−	0.0467589i	0.898654	−	0.438657i	$-0.144546\pi$
$43$	−0.140028	−	0.306619i	−0.0213541	−	0.0467589i	−0.920009	+	0.391898i	$0.871818\pi$
$44$	0.240413	−	1.67211i	0.0362436	−	0.252080i
$45$		0			0
$46$	7.58271	+	0.758707i	1.11801	+	0.111865i
$47$	13.3242			1.94354			0.971769	−	0.235936i	$-0.0758155\pi$
$47$	13.3242			1.94354			0.971769	+	0.235936i	$0.0758155\pi$
$48$		0			0
$49$	1.45862	+	3.19393i	0.208374	+	0.456276i
$50$	5.89651	+	1.73137i	0.833892	+	0.244853i
$51$		0			0
$52$	1.15595	−	0.339419i	0.160302	−	0.0470689i
$53$	−10.1284	−	6.50915i	−1.39125	−	0.894100i	−0.391586	−	0.920141i	$-0.628074\pi$
$53$	−10.1284	−	6.50915i	−1.39125	−	0.894100i	−0.999661	+	0.0260409i	$0.991710\pi$
$54$		0			0
$55$	2.24276	−	2.58829i	0.302414	−	0.349005i
$56$	−6.39283	+	4.10842i	−0.854277	+	0.549011i
$57$		0			0
$58$	0.379532	+	2.63970i	0.0498349	+	0.346610i
$59$	7.00588	−	4.50240i	0.912087	−	0.586163i	0.00173565	−	0.999998i	$-0.499448\pi$
$59$	7.00588	−	4.50240i	0.912087	−	0.586163i	0.910352	+	0.413836i	$0.135811\pi$
$60$		0			0
$61$	−4.40688	+	9.64972i	−0.564243	+	1.23552i	0.385563	+	0.922681i	$0.374007\pi$
$61$	−4.40688	+	9.64972i	−0.564243	+	1.23552i	−0.949806	+	0.312839i	$0.898720\pi$
$62$	−7.59933	−	4.88380i	−0.965116	−	0.620243i
$63$		0			0
$64$	−3.23683	−	3.73551i	−0.404604	−	0.466938i
$65$	2.34351	+	0.688117i	0.290677	+	0.0853504i
$66$		0			0
$67$	1.74834	−	12.1600i	0.213594	−	1.48558i	−0.547428	−	0.836853i	$-0.684393\pi$
$67$	1.74834	−	12.1600i	0.213594	−	1.48558i	0.761022	−	0.648726i	$-0.224698\pi$
$68$	−1.77398			−0.215127
$69$		0			0
$70$	5.48241			0.655273
$71$	2.22709	−	15.4898i	0.264308	−	1.83830i	−0.235148	−	0.971960i	$-0.575557\pi$
$71$	2.22709	−	15.4898i	0.264308	−	1.83830i	0.499455	−	0.866340i	$-0.333533\pi$
$72$		0			0
$73$	4.91808	+	1.44408i	0.575617	+	0.169016i	0.556568	−	0.830802i	$-0.312118\pi$
$73$	4.91808	+	1.44408i	0.575617	+	0.169016i	0.0190493	+	0.999819i	$0.493936\pi$
$74$	7.04857	+	8.13448i	0.819380	+	0.945615i
$75$		0			0
$76$	0.100041	+	0.0642921i	0.0114754	+	0.00737481i
$77$	−4.33434	+	9.49088i	−0.493944	+	1.08159i
$78$		0			0
$79$	−6.85430	+	4.40499i	−0.771169	+	0.495600i	−0.866092	−	0.499884i	$-0.833376\pi$
$79$	−6.85430	+	4.40499i	−0.771169	+	0.495600i	0.0949231	+	0.995485i	$0.469739\pi$
$80$	0.723071	+	5.02907i	0.0808418	+	0.562267i
$81$		0			0
$82$	3.67978	−	2.36485i	0.406364	−	0.261154i
$83$	−5.07198	+	5.85338i	−0.556722	+	0.642491i	−0.962436	−	0.271509i	$-0.912477\pi$
$83$	−5.07198	+	5.85338i	−0.556722	+	0.642491i	0.405714	+	0.914000i	$0.367023\pi$
$84$		0			0
$85$	−3.02553	−	1.94439i	−0.328165	−	0.210899i
$86$	0.513924	−	0.150902i	0.0554178	−	0.0162721i
$87$		0			0
$88$	−7.23760	−	2.12515i	−0.771531	−	0.226542i
$89$	3.52658	+	7.72212i	0.373816	+	0.818543i	0.999267	+	0.0382798i	$0.0121878\pi$
$89$	3.52658	+	7.72212i	0.373816	+	0.818543i	−0.625451	+	0.780264i	$0.715085\pi$
$90$		0			0
$91$	−7.44100			−0.780028
$92$	−0.604574	+	2.44376i	−0.0630312	+	0.254780i
$93$		0			0
$94$	−3.01312	+	20.9567i	−0.310779	+	2.16152i
$95$	0.100152	+	0.219301i	0.0102753	+	0.0224999i
$96$		0			0
$97$	−8.49290	−	9.80133i	−0.862324	−	0.995174i	−0.999989	−	0.00469568i	$-0.998505\pi$
$97$	−8.49290	−	9.80133i	−0.862324	−	0.995174i	0.137665	−	0.990479i	$-0.456040\pi$
$98$	−5.35335	+	1.57188i	−0.540770	+	0.158784i
$99$		0			0
$100$	−0.843346	+	1.84667i	−0.0843346	+	0.184667i
$101$	−11.3062	+	13.0481i	−1.12501	+	1.29833i	−0.175542	+	0.984472i	$0.556168\pi$
$101$	−11.3062	+	13.0481i	−1.12501	+	1.29833i	−0.949469	+	0.313861i	$0.898378\pi$
$102$		0			0
$103$	−0.0331061	−	0.230258i	−0.00326204	−	0.0226880i	0.988125	−	0.153649i	$-0.0491027\pi$
$103$	−0.0331061	−	0.230258i	−0.00326204	−	0.0226880i	−0.991387	+	0.130962i	$0.958194\pi$
$104$	−0.765585	−	5.32476i	−0.0750718	−	0.522136i
$105$		0			0
$106$	12.5282	−	14.4583i	1.21685	−	1.40431i
$107$	0.0351820	−	0.0770378i	0.00340117	−	0.00744752i	−0.907924	−	0.419135i	$-0.862333\pi$
$107$	0.0351820	−	0.0770378i	0.00340117	−	0.00744752i	0.911325	+	0.411688i	$0.135061\pi$
$108$		0			0
$109$	−9.21436	+	2.70558i	−0.882575	+	0.259147i	−0.691455	−	0.722419i	$-0.743030\pi$
$109$	−9.21436	+	2.70558i	−0.882575	+	0.259147i	−0.191120	+	0.981567i	$0.561212\pi$
$110$	3.56375	+	4.11279i	0.339790	+	0.392139i
$111$		0			0
$112$	−6.43011	−	14.0800i	−0.607589	−	1.33043i
$113$	−1.46793	+	10.2097i	−0.138091	+	0.960444i	0.796479	+	0.604666i	$0.206693\pi$
$113$	−1.46793	+	10.2097i	−0.138091	+	0.960444i	−0.934570	+	0.355778i	$0.884216\pi$
$114$		0			0
$115$	−3.70962	+	3.50520i	−0.345924	+	0.326862i
$116$	−0.880984			−0.0817973
$117$		0			0
$118$	5.49720	+	12.0372i	0.506058	+	1.10811i
$119$	10.5129	+	3.08687i	0.963717	+	0.282973i
$120$		0			0
$121$	0.617101	−	0.181197i	0.0561001	−	0.0164725i
$122$	−14.1808	−	9.11343i	−1.28387	−	0.825091i
$123$		0			0
$124$	1.95420	−	2.25526i	0.175492	−	0.202528i
$125$	−7.93868	+	5.10188i	−0.710057	+	0.456326i
$126$		0			0
$127$	−1.08836	−	7.56968i	−0.0965760	−	0.671701i	−0.979390	−	0.201978i	$-0.935263\pi$
$127$	−1.08836	−	7.56968i	−0.0965760	−	0.671701i	0.882814	−	0.469723i	$-0.155646\pi$
$128$	11.4841	−	7.38040i	1.01506	−	0.652341i
$129$		0			0
$130$	−1.61225	+	3.53033i	−0.141403	+	0.309630i
$131$	−2.49137	−	1.60111i	−0.217672	−	0.139889i	0.427261	−	0.904128i	$-0.359478\pi$
$131$	−2.49137	−	1.60111i	−0.217672	−	0.139889i	−0.644933	+	0.764239i	$0.723115\pi$
$132$		0			0
$133$	−0.480984	−	0.555085i	−0.0417066	−	0.0481320i
$134$	18.7302	+	5.49968i	1.61804	+	0.475100i
$135$		0			0
$136$	−1.12731	+	7.84062i	−0.0966661	+	0.672327i
$137$	−13.8811			−1.18594			−0.592971	−	0.805224i	$-0.702045\pi$
$137$	−13.8811			−1.18594			−0.592971	+	0.805224i	$0.702045\pi$
$138$		0			0
$139$	14.8326			1.25809			0.629044	−	0.777370i	$-0.283447\pi$
$139$	14.8326			1.25809			0.629044	+	0.777370i	$0.283447\pi$
$140$	−0.257746	+	1.79266i	−0.0217835	+	0.151508i
$141$		0			0
$142$	23.8591	+	7.00567i	2.00221	+	0.587902i
$143$	−4.83690	−	5.58208i	−0.404482	−	0.466797i
$144$		0			0
$145$	−1.50252	−	0.965614i	−0.124778	−	0.0801899i
$146$	−3.38345	+	7.40872i	−0.280016	+	0.613150i
$147$		0			0
$148$	−2.99123	+	1.92234i	−0.245877	+	0.158016i
$149$	2.70073	+	18.7840i	0.221252	+	1.53884i	0.733311	+	0.679894i	$0.237974\pi$
$149$	2.70073	+	18.7840i	0.221252	+	1.53884i	−0.512058	+	0.858951i	$0.671117\pi$
$150$		0			0
$151$	9.63071	−	6.18928i	0.783736	−	0.503677i	−0.0865355	−	0.996249i	$-0.527580\pi$
$151$	9.63071	−	6.18928i	0.783736	−	0.503677i	0.870272	+	0.492572i	$0.163943\pi$
$152$	0.347731	−	0.401302i	0.0282047	−	0.0325499i
$153$		0			0
$154$	−13.9473	−	8.96341i	−1.12391	−	0.722292i
$155$	5.80480	−	1.70444i	0.466253	−	0.136904i
$156$		0			0
$157$	21.6447	+	6.35545i	1.72743	+	0.507220i	0.986416	−	0.164265i	$-0.0525251\pi$
$157$	21.6447	+	6.35545i	1.72743	+	0.507220i	0.741018	+	0.671485i	$0.234343\pi$
$158$	−5.37827	−	11.7768i	−0.427872	−	0.936909i
$159$		0			0
$160$	−3.08463			−0.243862
$161$	7.83515	−	13.4301i	0.617496	−	1.05844i
$162$		0			0
$163$	−2.69441	+	18.7400i	−0.211042	+	1.46783i	0.558643	+	0.829408i	$0.311322\pi$
$163$	−2.69441	+	18.7400i	−0.211042	+	1.46783i	−0.769685	+	0.638424i	$0.779587\pi$
$164$	0.600271	+	1.31441i	0.0468733	+	0.102638i
$165$		0			0
$166$	−8.05937	−	9.30101i	−0.625529	−	0.721899i
$167$	6.33721	−	1.86077i	0.490388	−	0.143991i	−0.0271841	−	0.999630i	$-0.508654\pi$
$167$	6.33721	−	1.86077i	0.490388	−	0.143991i	0.517572	+	0.855639i	$0.326836\pi$
$168$		0			0
$169$	−3.21218	+	7.03368i	−0.247090	+	0.541053i
$170$	3.74238	−	4.31894i	0.287028	−	0.331247i
$171$		0			0
$172$	0.0251812	+	0.175139i	0.00192005	+	0.0133543i
$173$	−2.36967	−	16.4814i	−0.180162	−	1.25306i	−0.856377	−	0.516352i	$-0.827290\pi$
$173$	−2.36967	−	16.4814i	−0.180162	−	1.25306i	0.676214	−	0.736705i	$-0.263619\pi$
$174$		0			0
$175$	8.21117	−	9.47620i	0.620706	−	0.716333i
$176$	6.38272	−	13.9762i	0.481116	−	1.05350i
$177$		0			0
$178$	−12.9431	+	3.80042i	−0.970123	+	0.284854i
$179$	−2.74910	−	3.17263i	−0.205477	−	0.237134i	0.643652	−	0.765318i	$-0.277418\pi$
$179$	−2.74910	−	3.17263i	−0.205477	−	0.237134i	−0.849130	+	0.528185i	$0.822873\pi$
$180$		0			0
$181$	−1.78504	−	3.90869i	−0.132681	−	0.290531i	0.831617	−	0.555349i	$-0.187415\pi$
$181$	−1.78504	−	3.90869i	−0.132681	−	0.290531i	−0.964298	+	0.264818i	$0.914688\pi$
$182$	1.68269	−	11.7034i	0.124730	−	0.867513i
$183$		0			0
$184$	10.4167	+	4.22503i	0.767931	+	0.311473i
$185$	−7.20857			−0.529985
$186$		0			0
$187$	4.51804	+	9.89313i	0.330392	+	0.723457i
$188$	−6.71085	−	1.97048i	−0.489439	−	0.143712i
$189$		0			0
$190$	−0.367571	+	0.107929i	−0.0266664	+	0.00782997i
$191$	1.08297	+	0.695984i	0.0783611	+	0.0503596i	0.579235	−	0.815161i	$-0.303351\pi$
$191$	1.08297	+	0.695984i	0.0783611	+	0.0503596i	−0.500874	+	0.865520i	$0.666988\pi$
$192$		0			0
$193$	14.2680	−	16.4661i	1.02703	−	1.18526i	0.0445280	−	0.999008i	$-0.485822\pi$
$193$	14.2680	−	16.4661i	1.02703	−	1.18526i	0.982503	−	0.186248i	$-0.0596329\pi$
$194$	17.3364	−	11.1414i	1.24468	−	0.799906i
$195$		0			0
$196$	−0.262303	−	1.82436i	−0.0187360	−	0.130311i
$197$	−10.9019	+	7.00620i	−0.776725	+	0.499171i	−0.867945	−	0.496660i	$-0.834560\pi$
$197$	−10.9019	+	7.00620i	−0.776725	+	0.499171i	0.0912203	+	0.995831i	$0.470923\pi$
$198$		0			0
$199$	−4.63932	+	10.1587i	−0.328873	+	0.720131i	−0.999771	−	0.0214190i	$-0.993182\pi$
$199$	−4.63932	+	10.1587i	−0.328873	+	0.720131i	0.670898	+	0.741550i	$0.265909\pi$
$200$	7.62597	+	4.90092i	0.539238	+	0.346547i
$201$		0			0
$202$	−17.9656	−	20.7334i	−1.26405	−	1.45880i
$203$	5.22086	+	1.53298i	0.366433	+	0.107594i
$204$		0			0
$205$	−0.416910	+	2.89967i	−0.0291183	+	0.202522i
$206$	0.369642			0.0257542
$207$		0			0
$208$	10.9576			0.759770
$209$	0.103757	−	0.721648i	0.00717704	−	0.0499174i
$210$		0			0
$211$	−11.1712	−	3.28017i	−0.769060	−	0.225816i	−0.126412	−	0.991978i	$-0.540346\pi$
$211$	−11.1712	−	3.28017i	−0.769060	−	0.225816i	−0.642648	+	0.766161i	$0.722164\pi$
$212$	4.13865	+	4.77626i	0.284244	+	0.328035i
$213$		0			0
$214$	0.113211	+	0.0727563i	0.00773895	+	0.00497352i
$215$	−0.149017	+	0.326302i	−0.0101629	+	0.0222536i
$216$		0			0
$217$	−15.5052	+	9.96461i	−1.05256	+	0.676442i
$218$	−2.17169	−	15.1044i	−0.147085	−	1.02300i
$219$		0			0
$220$	−1.51236	+	0.971936i	−0.101963	+	0.0655279i
$221$	−5.07934	+	5.86187i	−0.341674	+	0.394312i
$222$		0			0
$223$	−16.8077	−	10.8016i	−1.12552	−	0.723331i	−0.160904	−	0.986970i	$-0.551441\pi$
$223$	−16.8077	−	10.8016i	−1.12552	−	0.723331i	−0.964621	+	0.263639i	$0.915077\pi$
$224$	9.01678	−	2.64757i	0.602459	−	0.176898i
$225$		0			0
$226$	−15.7261	−	4.61759i	−1.04608	−	0.307158i
$227$	4.61542	+	10.1064i	0.306336	+	0.670783i	0.998711	−	0.0507551i	$-0.0161628\pi$
$227$	4.61542	+	10.1064i	0.306336	+	0.670783i	−0.692375	+	0.721538i	$0.743436\pi$
$228$		0			0
$229$	−3.11850			−0.206076			−0.103038	−	0.994677i	$-0.532856\pi$
$229$	−3.11850			−0.206076			−0.103038	+	0.994677i	$0.532856\pi$
$230$	−4.67418	−	6.62725i	−0.308207	−	0.436988i
$231$		0			0
$232$	−0.559839	+	3.89377i	−0.0367552	+	0.255638i
$233$	0.0526472	+	0.115281i	0.00344903	+	0.00755233i	0.911349	−	0.411635i	$-0.135042\pi$
$233$	0.0526472	+	0.115281i	0.00344903	+	0.00755233i	−0.907900	+	0.419188i	$0.862315\pi$
$234$		0			0
$235$	−9.28564	−	10.7162i	−0.605728	−	0.699047i
$236$	−4.19442	+	1.23159i	−0.273033	+	0.0801698i
$237$		0			0
$238$	−7.23248	+	15.8369i	−0.468812	+	1.02656i
$239$	−0.650360	+	0.750555i	−0.0420683	+	0.0485494i	−0.776394	−	0.630248i	$-0.782953\pi$
$239$	−0.650360	+	0.750555i	−0.0420683	+	0.0485494i	0.734325	+	0.678798i	$0.237499\pi$
$240$		0			0
$241$	1.51073	+	10.5073i	0.0973145	+	0.676837i	0.978829	+	0.204680i	$0.0656154\pi$
$241$	1.51073	+	10.5073i	0.0973145	+	0.676837i	−0.881514	+	0.472157i	$0.843475\pi$
$242$	0.145442	+	1.01157i	0.00934934	+	0.0650261i
$243$		0			0
$244$	3.64663	−	4.20844i	0.233452	−	0.269418i
$245$	1.55225	−	3.39896i	0.0991698	−	0.217152i
$246$		0			0
$247$	0.498886	−	0.146486i	0.0317433	−	0.00932068i
$248$	−8.72595	−	10.0703i	−0.554098	−	0.639464i
$249$		0			0
$250$	−6.22913	−	13.6399i	−0.393965	−	0.862663i
$251$	0.477080	−	3.31816i	0.0301130	−	0.209441i	−0.969210	−	0.246236i	$-0.920806\pi$
$251$	0.477080	−	3.31816i	0.0301130	−	0.209441i	0.999323	+	0.0367959i	$0.0117151\pi$
$252$		0			0
$253$	15.1681	−	2.85228i	0.953612	−	0.179321i
$254$	12.1519			0.762479
$255$		0			0
$256$	4.90448	+	10.7393i	0.306530	+	0.671207i
$257$	5.52597	+	1.62257i	0.344701	+	0.101213i	0.449500	−	0.893280i	$-0.351602\pi$
$257$	5.52597	+	1.62257i	0.344701	+	0.101213i	−0.104800	+	0.994493i	$0.533420\pi$
$258$		0			0
$259$	21.0716	−	6.18717i	1.30932	−	0.384452i
$260$	−1.07856	−	0.693152i	−0.0668898	−	0.0429874i
$261$		0			0
$262$	3.08165	−	3.55642i	0.190385	−	0.219716i
$263$	−17.6314	+	11.3310i	−1.08720	+	0.698701i	−0.956210	−	0.292683i	$-0.905452\pi$
$263$	−17.6314	+	11.3310i	−1.08720	+	0.698701i	−0.130990	+	0.991384i	$0.541816\pi$
$264$		0			0
$265$	1.82342	+	12.6822i	0.112012	+	0.779059i
$266$	0.981821	−	0.630978i	0.0601993	−	0.0386878i
$267$		0			0
$268$	−2.67888	+	5.86592i	−0.163638	+	0.358318i
$269$	0.912355	+	0.586335i	0.0556272	+	0.0357495i	0.568159	−	0.822919i	$-0.307656\pi$
$269$	0.912355	+	0.586335i	0.0556272	+	0.0357495i	−0.512532	+	0.858668i	$0.671292\pi$
$270$		0			0
$271$	17.8258	+	20.5721i	1.08284	+	1.24967i	0.966558	+	0.256449i	$0.0825527\pi$
$271$	17.8258	+	20.5721i	1.08284	+	1.24967i	0.116284	+	0.993216i	$0.462902\pi$
$272$	−15.4812	−	4.54570i	−0.938688	−	0.275624i
$273$		0			0
$274$	3.13905	−	21.8325i	0.189637	−	1.31895i
$275$	12.4464			0.750545
$276$		0			0
$277$	−6.26139			−0.376211			−0.188105	−	0.982149i	$-0.560235\pi$
$277$	−6.26139			−0.376211			−0.188105	+	0.982149i	$0.560235\pi$
$278$	−3.35423	+	23.3292i	−0.201173	+	1.39919i
$279$		0			0
$280$	7.75941	+	2.27837i	0.463713	+	0.136159i
$281$	0.510782	+	0.589474i	0.0304707	+	0.0351650i	0.770780	−	0.637101i	$-0.219867\pi$
$281$	0.510782	+	0.589474i	0.0304707	+	0.0351650i	−0.740310	+	0.672266i	$0.765321\pi$
$282$		0			0
$283$	9.65682	+	6.20606i	0.574038	+	0.368912i	0.795220	−	0.606321i	$-0.207355\pi$
$283$	9.65682	+	6.20606i	0.574038	+	0.368912i	−0.221182	+	0.975233i	$0.570992\pi$
$284$	−3.41244	+	7.47220i	−0.202491	+	0.443393i
$285$		0			0
$286$	9.87345	−	6.34528i	0.583829	−	0.375204i
$287$	−1.27013	−	8.83395i	−0.0749734	−	0.521452i
$288$		0			0
$289$	−4.69325	+	3.01617i	−0.276074	+	0.177422i
$290$	1.85852	−	2.14485i	0.109136	−	0.125950i
$291$		0			0
$292$	−2.26347	−	1.45464i	−0.132460	−	0.0851266i
$293$	−32.6841	+	9.59693i	−1.90943	+	0.560659i	−0.926630	+	0.375974i	$0.877308\pi$
$293$	−32.6841	+	9.59693i	−1.90943	+	0.560659i	−0.982798	+	0.184685i	$0.940874\pi$
$294$		0			0
$295$	−8.50351	−	2.49686i	−0.495093	−	0.145373i
$296$	6.59553	+	14.4422i	0.383357	+	0.839435i
$297$		0			0
$298$	−30.1547			−1.74681
$299$	6.34403	+	8.99483i	0.366885	+	0.520184i
$300$		0			0
$301$	0.155528	−	1.08172i	0.00896451	−	0.0623495i
$302$	7.55679	+	16.5471i	0.434845	+	0.952177i
$303$		0			0
$304$	0.708294	+	0.817415i	0.0406234	+	0.0468820i
$305$	10.8321	−	3.18058i	0.620243	−	0.182120i
$306$		0			0
$307$	6.19970	−	13.5754i	0.353835	−	0.774791i	−0.646098	−	0.763254i	$-0.723600\pi$
$307$	6.19970	−	13.5754i	0.353835	−	0.774791i	0.999933	−	0.0115369i	$-0.00367240\pi$
$308$	3.58661	−	4.13916i	0.204366	−	0.235851i
$309$		0			0
$310$	1.36811	+	9.51539i	0.0777032	+	0.540438i
$311$	2.75775	+	19.1806i	0.156378	+	1.08763i	0.905239	+	0.424903i	$0.139692\pi$
$311$	2.75775	+	19.1806i	0.156378	+	1.08763i	−0.748861	+	0.662727i	$0.769399\pi$
$312$		0			0
$313$	18.4515	−	21.2941i	1.04294	−	1.20361i	0.0643198	−	0.997929i	$-0.479512\pi$
$313$	18.4515	−	21.2941i	1.04294	−	1.20361i	0.978618	−	0.205685i	$-0.0659423\pi$
$314$	−14.8907	+	32.6061i	−0.840332	+	1.84007i
$315$		0			0
$316$	4.10367	−	1.20495i	0.230849	−	0.0677835i
$317$	−5.10427	−	5.89064i	−0.286684	−	0.330851i	0.594080	−	0.804406i	$-0.297516\pi$
$317$	−5.10427	−	5.89064i	−0.286684	−	0.330851i	−0.880764	+	0.473555i	$0.842971\pi$
$318$		0			0
$319$	2.24373	+	4.91307i	0.125625	+	0.275079i
$320$	−0.748588	+	5.20654i	−0.0418473	+	0.291054i
$321$		0			0
$322$	19.3515	+	15.3604i	1.07841	+	0.856002i
$323$	−0.765613			−0.0425998
$324$		0			0
$325$	3.68736	+	8.07420i	0.204538	+	0.447876i
$326$	−28.8655	−	8.47568i	−1.59871	−	0.469424i
$327$		0			0
$328$	6.19088	−	1.81781i	0.341834	−	0.100372i
$329$	36.3409	+	23.3549i	2.00354	+	1.28760i
$330$		0			0
$331$	−8.22221	+	9.48894i	−0.451934	+	0.521559i	−0.935299	−	0.353860i	$-0.884869\pi$
$331$	−8.22221	+	9.48894i	−0.451934	+	0.521559i	0.483365	+	0.875419i	$0.339415\pi$
$332$	3.42019	−	2.19802i	0.187707	−	0.120632i
$333$		0			0
$334$	1.49359	+	10.3881i	0.0817255	+	0.568413i
$335$	−10.9983	+	7.06816i	−0.600899	+	0.386175i
$336$		0			0
$337$	2.34826	−	5.14196i	0.127918	−	0.280101i	−0.834827	−	0.550512i	$-0.814432\pi$
$337$	2.34826	−	5.14196i	0.127918	−	0.280101i	0.962745	+	0.270411i	$0.0871597\pi$
$338$	−10.3364	−	6.64278i	−0.562224	−	0.361320i
$339$		0			0
$340$	1.23628	+	1.42675i	0.0670469	+	0.0773763i
$341$	−17.5542	−	5.15437i	−0.950612	−	0.279125i
$342$		0			0
$343$	1.60972	−	11.1958i	0.0869165	−	0.604517i
$344$	0.790082			0.0425983
$345$		0			0
$346$	26.4582			1.42240
$347$	2.20688	−	15.3492i	0.118471	−	0.823986i	−0.840769	−	0.541394i	$-0.817897\pi$
$347$	2.20688	−	15.3492i	0.118471	−	0.823986i	0.959240	−	0.282592i	$-0.0911942\pi$
$348$		0			0
$349$	−15.3307	−	4.50149i	−0.820633	−	0.240959i	−0.155644	−	0.987813i	$-0.549745\pi$
$349$	−15.3307	−	4.50149i	−0.820633	−	0.240959i	−0.664988	+	0.746854i	$0.731564\pi$
$350$	13.0476	+	15.0577i	0.697421	+	0.804867i
$351$		0			0
$352$	7.84736	+	5.04319i	0.418266	+	0.268803i
$353$	12.2741	−	26.8765i	0.653284	−	1.43049i	−0.235367	−	0.971907i	$-0.575629\pi$
$353$	12.2741	−	26.8765i	0.653284	−	1.43049i	0.888650	−	0.458585i	$-0.151644\pi$
$354$		0			0
$355$	−14.0099	+	9.00364i	−0.743570	+	0.477864i
$356$	−0.634184	−	4.41085i	−0.0336117	−	0.233774i
$357$		0			0
$358$	5.61167	−	3.60640i	0.296586	−	0.190604i
$359$	12.6350	−	14.5815i	0.666849	−	0.769585i	−0.317031	−	0.948415i	$-0.602686\pi$
$359$	12.6350	−	14.5815i	0.666849	−	0.769585i	0.983880	+	0.178831i	$0.0572314\pi$
$360$		0			0
$361$	−15.9406	−	10.2444i	−0.838981	−	0.539180i
$362$	6.55136	−	1.92365i	0.344332	−	0.101105i
$363$		0			0
$364$	3.74772	+	1.10043i	0.196434	+	0.0576782i
$365$	−2.26598	−	4.96181i	−0.118607	−	0.259713i
$366$		0			0
$367$	−20.2508			−1.05708			−0.528541	−	0.848908i	$-0.677261\pi$
$367$	−20.2508			−1.05708			−0.528541	+	0.848908i	$0.677261\pi$
$368$	−11.5380	+	19.7771i	−0.601460	+	1.03095i
$369$		0			0
$370$	1.63013	−	11.3378i	0.0847466	−	0.589426i
$371$	−16.2153	−	35.5065i	−0.841855	−	1.84341i
$372$		0			0
$373$	−6.89393	−	7.95602i	−0.356954	−	0.411947i	0.548663	−	0.836044i	$-0.315137\pi$
$373$	−6.89393	−	7.95602i	−0.356954	−	0.411947i	−0.905617	+	0.424097i	$0.860592\pi$
$374$	−16.5819	+	4.86888i	−0.857429	+	0.251764i
$375$		0			0
$376$	−12.9737	+	28.4084i	−0.669066	+	1.46505i
$377$	−2.52248	+	2.91109i	−0.129914	+	0.149929i
$378$		0			0
$379$	0.410647	+	2.85611i	0.0210935	+	0.146709i	0.997646	−	0.0685692i	$-0.0218434\pi$
$379$	0.410647	+	2.85611i	0.0210935	+	0.146709i	−0.976553	+	0.215278i	$0.930934\pi$
$380$	−0.0180103	−	0.125264i	−0.000923907	−	0.00642592i
$381$		0			0
$382$	−1.33956	+	1.54594i	−0.0685380	+	0.0790971i
$383$	−1.09872	+	2.40587i	−0.0561422	+	0.122934i	−0.935624	−	0.352998i	$-0.885162\pi$
$383$	−1.09872	+	2.40587i	−0.0561422	+	0.122934i	0.879482	+	0.475933i	$0.157889\pi$
$384$		0			0
$385$	10.6538	−	3.12823i	0.542966	−	0.159429i
$386$	22.6718	+	26.1647i	1.15396	+	1.33175i
$387$		0			0
$388$	2.82803	+	6.19252i	0.143571	+	0.314377i
$389$	−0.385843	+	2.68360i	−0.0195630	+	0.136064i	−0.997262	−	0.0739464i	$-0.976441\pi$
$389$	−0.385843	+	2.68360i	−0.0195630	+	0.136064i	0.977699	+	0.210010i	$0.0673497\pi$
$390$		0			0
$391$	−5.23161	−	15.3400i	−0.264574	−	0.775778i
$392$	−8.22998			−0.415677
$393$		0			0
$394$	−8.55420	−	18.7311i	−0.430955	−	0.943659i
$395$	8.31953	+	2.44284i	0.418601	+	0.122912i
$396$		0			0
$397$	−24.1065	+	7.07830i	−1.20987	+	0.355250i	−0.823619	−	0.567144i	$-0.808048\pi$
$397$	−24.1065	+	7.07830i	−1.20987	+	0.355250i	−0.386251	+	0.922394i	$0.626230\pi$
$398$	−14.9287	−	9.59412i	−0.748310	−	0.480910i
$399$		0			0
$400$	−12.0917	+	13.9546i	−0.604586	+	0.697729i
$401$	20.4369	−	13.1340i	1.02057	−	0.655882i	0.0804635	−	0.996758i	$-0.474360\pi$
$401$	20.4369	−	13.1340i	1.02057	−	0.655882i	0.940108	+	0.340876i	$0.110724\pi$
$402$		0			0
$403$	−1.85686	−	12.9147i	−0.0924968	−	0.643329i
$404$	7.62412	−	4.89973i	0.379314	−	0.243770i
$405$		0			0
$406$	−3.59176	+	7.86485i	−0.178256	+	0.390326i
$407$	18.3387	+	11.7856i	0.909016	+	0.584189i
$408$		0			0
$409$	−11.2436	−	12.9758i	−0.555958	−	0.641610i	0.406303	−	0.913739i	$-0.366818\pi$
$409$	−11.2436	−	12.9758i	−0.555958	−	0.641610i	−0.962261	+	0.272128i	$0.912272\pi$
$410$	−4.46640	−	1.31145i	−0.220580	−	0.0647681i
$411$		0			0
$412$	−0.0173781	+	0.120867i	−0.000856157	+	0.00595470i
$413$	26.9999			1.32858
$414$		0			0
$415$	8.24232			0.404599
$416$	−0.946754	+	6.58482i	−0.0464184	+	0.322847i
$417$		0			0
$418$	1.11156	+	0.326385i	0.0543684	+	0.0159640i
$419$	−22.4722	−	25.9343i	−1.09784	−	1.26697i	−0.961050	−	0.276374i	$-0.910867\pi$
$419$	−22.4722	−	25.9343i	−1.09784	−	1.26697i	−0.136789	−	0.990600i	$-0.543678\pi$
$420$		0			0
$421$	−9.39658	−	6.03882i	−0.457961	−	0.294314i	0.291248	−	0.956648i	$-0.405930\pi$
$421$	−9.39658	−	6.03882i	−0.457961	−	0.294314i	−0.749209	+	0.662334i	$0.769566\pi$
$422$	7.68539	−	16.8287i	0.374119	−	0.819206i
$423$		0			0
$424$	23.7400	−	15.2568i	1.15292	−	0.740935i
$425$	−1.86009	−	12.9372i	−0.0902276	−	0.627547i
$426$		0			0
$427$	−28.9336	+	18.5945i	−1.40020	+	0.899851i
$428$	−0.0291126	+	0.0335978i	−0.00140721	+	0.00162401i
$429$		0			0
$430$	−0.479518	−	0.308167i	−0.0231244	−	0.0148611i
$431$	−6.28531	+	1.84553i	−0.302753	+	0.0888963i	−0.429581	−	0.903028i	$-0.641339\pi$
$431$	−6.28531	+	1.84553i	−0.302753	+	0.0888963i	0.126828	+	0.991925i	$0.459520\pi$
$432$		0			0
$433$	3.65865	+	1.07428i	0.175824	+	0.0516264i	0.368459	−	0.929644i	$-0.379885\pi$
$433$	3.65865	+	1.07428i	0.175824	+	0.0516264i	−0.192636	+	0.981270i	$0.561704\pi$
$434$	−12.1663	−	26.6404i	−0.584000	−	1.27878i
$435$		0			0
$436$	5.04101			0.241421
$437$	−0.260921	+	1.05468i	−0.0124816	+	0.0504520i
$438$		0			0
$439$	−1.92515	+	13.3897i	−0.0918826	+	0.639058i	0.890887	+	0.454224i	$0.150084\pi$
$439$	−1.92515	+	13.3897i	−0.0918826	+	0.639058i	−0.982770	+	0.184833i	$0.940826\pi$
$440$	3.33469	+	7.30196i	0.158975	+	0.348107i
$441$		0			0
$442$	−8.07108	−	9.31452i	−0.383902	−	0.443046i
$443$	14.5824	−	4.28178i	0.692831	−	0.203433i	0.0836855	−	0.996492i	$-0.473331\pi$
$443$	14.5824	−	4.28178i	0.692831	−	0.203433i	0.609145	+	0.793059i	$0.291513\pi$
$444$		0			0
$445$	3.75296	−	8.21784i	0.177907	−	0.389563i
$446$	20.7900	−	23.9929i	0.984433	−	1.13610i
$447$		0			0
$448$	−2.28060	−	15.8619i	−0.107748	−	0.749404i
$449$	1.05035	+	7.30534i	0.0495690	+	0.344760i	0.999480	+	0.0322400i	$0.0102641\pi$
$449$	1.05035	+	7.30534i	0.0495690	+	0.344760i	−0.949911	+	0.312520i	$0.898827\pi$
$450$		0			0
$451$	5.80142	−	6.69519i	0.273178	−	0.315264i
$452$	2.24922	−	4.92509i	0.105794	−	0.231657i
$453$		0			0
$454$	−16.9393	+	4.97382i	−0.795000	+	0.233433i
$455$	5.18562	+	5.98453i	0.243106	+	0.280559i
$456$		0			0
$457$	13.5558	+	29.6831i	0.634113	+	1.38851i	0.904796	+	0.425846i	$0.140023\pi$
$457$	13.5558	+	29.6831i	0.634113	+	1.38851i	−0.270682	+	0.962669i	$0.587249\pi$
$458$	0.705212	−	4.90486i	0.0329524	−	0.229189i
$459$		0			0
$460$	2.38676	−	1.21682i	0.111283	−	0.0567344i
$461$	−32.0815			−1.49418			−0.747092	−	0.664721i	$-0.768551\pi$
$461$	−32.0815			−1.49418			−0.747092	+	0.664721i	$0.768551\pi$
$462$		0			0
$463$	−2.11428	−	4.62962i	−0.0982588	−	0.215157i	0.854119	−	0.520078i	$-0.174097\pi$
$463$	−2.11428	−	4.62962i	−0.0982588	−	0.215157i	−0.952378	+	0.304921i	$0.901370\pi$
$464$	−7.68821	−	2.25746i	−0.356916	−	0.104800i
$465$		0			0
$466$	−0.193223	+	0.0567354i	−0.00895089	+	0.00262822i
$467$	24.0314	+	15.4440i	1.11204	+	0.714665i	0.961737	−	0.273975i	$-0.0883386\pi$
$467$	24.0314	+	15.4440i	1.11204	+	0.714665i	0.150303	+	0.988640i	$0.451975\pi$
$468$		0			0
$469$	26.0827	−	30.1010i	1.20439	−	1.38994i
$470$	18.9546	−	12.1814i	0.874308	−	0.561884i
$471$		0			0
$472$	2.77795	+	19.3211i	0.127866	+	0.889325i
$473$	0.912585	−	0.586483i	0.0419607	−	0.0269665i
$474$		0			0
$475$	−0.363971	+	0.796984i	−0.0167001	+	0.0365682i
$476$	−4.83841	−	3.10945i	−0.221768	−	0.142522i
$477$		0			0
$478$	−1.03342	−	1.19263i	−0.0472676	−	0.0545497i
$479$	−23.9008	−	7.01790i	−1.09205	−	0.320656i	−0.314363	−	0.949303i	$-0.601791\pi$
$479$	−23.9008	−	7.01790i	−1.09205	−	0.320656i	−0.777691	+	0.628647i	$0.783609\pi$
$480$		0			0
$481$	−2.21250	+	15.3883i	−0.100881	+	0.701644i
$482$	−16.8679			−0.768310
$483$		0			0
$484$	−0.337605			−0.0153457
$485$	−1.96417	+	13.6611i	−0.0891882	+	0.620318i
$486$		0			0
$487$	25.4561	+	7.47459i	1.15353	+	0.338706i	0.801914	−	0.597439i	$-0.203815\pi$
$487$	25.4561	+	7.47459i	1.15353	+	0.338706i	0.351613	+	0.936145i	$0.385633\pi$
$488$	−16.2831	−	18.7917i	−0.737101	−	0.850660i
$489$		0			0
$490$	4.99495	+	3.21006i	0.225649	+	0.145016i
$491$	10.8772	−	23.8178i	0.490882	−	1.07488i	−0.488444	−	0.872595i	$-0.662435\pi$
$491$	10.8772	−	23.8178i	0.490882	−	1.07488i	0.979326	−	0.202287i	$-0.0648374\pi$
$492$		0			0
$493$	4.77150	−	3.06646i	0.214898	−	0.138106i
$494$	0.117580	+	0.817786i	0.00529017	+	0.0367940i
$495$		0			0
$496$	22.8329	−	14.6738i	1.02523	−	0.658874i
$497$	33.2249	−	38.3436i	1.49034	−	1.71995i
$498$		0			0
$499$	1.07724	+	0.692303i	0.0482241	+	0.0309917i	0.564531	−	0.825412i	$-0.309057\pi$
$499$	1.07724	+	0.692303i	0.0482241	+	0.0309917i	−0.516307	+	0.856404i	$0.672694\pi$
$500$	4.75289	−	1.39557i	0.212556	−	0.0624120i
$501$		0			0
$502$	5.11101	+	1.50073i	0.228115	+	0.0669807i
$503$	−9.44975	−	20.6921i	−0.421343	−	0.922613i	−0.994653	−	0.103274i	$-0.967068\pi$
$503$	−9.44975	−	20.6921i	−0.421343	−	0.922613i	0.573310	−	0.819339i	$-0.305659\pi$
$504$		0			0
$505$	18.3734			0.817606
$506$	1.05605	+	24.5018i	0.0469471	+	1.08924i
$507$		0			0
$508$	−0.571301	+	3.97349i	−0.0253474	+	0.176295i
$509$	11.2136	+	24.5544i	0.497036	+	1.08836i	0.977421	+	0.211299i	$0.0677694\pi$
$509$	11.2136	+	24.5544i	0.497036	+	1.08836i	−0.480386	+	0.877057i	$0.659503\pi$
$510$		0			0
$511$	10.8825	+	12.5591i	0.481414	+	0.555581i
$512$	8.19633	−	2.40666i	0.362230	−	0.106360i
$513$		0			0
$514$	−3.80166	+	8.32447i	−0.167684	+	0.367177i
$515$	−0.162117	+	0.187092i	−0.00714371	+	0.00824428i
$516$		0			0
$517$	6.10247	+	42.4436i	0.268386	+	1.86667i
$518$	4.96626	+	34.5411i	0.218205	+	1.51765i
$519$		0			0
$520$	−3.74898	+	4.32655i	−0.164404	+	0.189732i
$521$	7.06984	−	15.4808i	0.309735	−	0.678226i	−0.689190	−	0.724581i	$-0.742033\pi$
$521$	7.06984	−	15.4808i	0.309735	−	0.678226i	0.998925	+	0.0463551i	$0.0147606\pi$
$522$		0			0
$523$	16.9628	−	4.98073i	0.741731	−	0.217792i	0.111029	−	0.993817i	$-0.464585\pi$
$523$	16.9628	−	4.98073i	0.741731	−	0.217792i	0.630702	+	0.776025i	$0.282767\pi$
$524$	1.01802	+	1.17485i	0.0444722	+	0.0513236i
$525$		0			0
$526$	−13.8346	−	30.2935i	−0.603217	−	1.32086i
$527$	−2.73419	+	19.0167i	−0.119103	+	0.828382i
$528$		0			0
$529$	−22.9147	+	1.97896i	−0.996292	+	0.0860418i
$530$	−20.3592			−0.884346
$531$		0			0
$532$	0.160161	+	0.350705i	0.00694388	+	0.0152050i
$533$	6.06202	+	1.77997i	0.262575	+	0.0770990i
$534$		0			0
$535$	−0.0864770	+	0.0253919i	−0.00373873	+	0.00109779i
$536$	24.2238	+	15.5677i	1.04631	+	0.672422i
$537$		0			0
$538$	−1.12852	+	1.30238i	−0.0486540	+	0.0561497i
$539$	−9.50605	+	6.10917i	−0.409455	+	0.263141i
$540$		0			0
$541$	−3.89579	−	27.0958i	−0.167493	−	1.16494i	−0.884044	−	0.467404i	$-0.845189\pi$
$541$	−3.89579	−	27.0958i	−0.167493	−	1.16494i	0.716551	−	0.697535i	$-0.245720\pi$
$542$	−36.3874	+	23.3848i	−1.56297	+	1.00446i
$543$		0			0
$544$	4.06930	−	8.91052i	0.174470	−	0.382035i
$545$	8.59748	+	5.52526i	0.368275	+	0.236676i
$546$		0			0
$547$	9.02260	+	10.4126i	0.385779	+	0.445212i	0.915111	−	0.403202i	$-0.132103\pi$
$547$	9.02260	+	10.4126i	0.385779	+	0.445212i	−0.529332	+	0.848415i	$0.677557\pi$
$548$	6.99133	+	2.05284i	0.298655	+	0.0876929i
$549$		0			0
$550$	−2.81460	+	19.5760i	−0.120015	+	0.834723i
$551$	−0.380214			−0.0161977
$552$		0			0
$553$	−26.4158			−1.12331
$554$	1.41594	−	9.84808i	0.0601576	−	0.418405i
$555$		0			0
$556$	−7.47058	−	2.19356i	−0.316823	−	0.0930277i
$557$	−17.5030	−	20.1995i	−0.741625	−	0.855881i	0.252104	−	0.967700i	$-0.418878\pi$
$557$	−17.5030	−	20.1995i	−0.741625	−	0.855881i	−0.993729	+	0.111820i	$0.964332\pi$
$558$		0			0
$559$	0.650825	+	0.418260i	0.0275270	+	0.0176905i
$560$	−6.84289	+	14.9838i	−0.289165	+	0.633183i
$561$		0			0
$562$	−1.04265	+	0.670069i	−0.0439814	+	0.0282651i
$563$	0.157188	+	1.09327i	0.00662468	+	0.0460757i	0.992866	−	0.119238i	$-0.0380453\pi$
$563$	0.157188	+	1.09327i	0.00662468	+	0.0460757i	−0.986241	+	0.165314i	$0.947136\pi$
$564$		0			0
$565$	9.23426	−	5.93450i	0.388488	−	0.249666i
$566$	−11.9448	+	13.7851i	−0.502079	+	0.579430i
$567$		0			0
$568$	30.8571	+	19.8306i	1.29473	+	0.832075i
$569$	27.9001	−	8.19221i	1.16963	−	0.343435i	0.361465	−	0.932386i	$-0.382277\pi$
$569$	27.9001	−	8.19221i	1.16963	−	0.343435i	0.808169	+	0.588950i	$0.200459\pi$
$570$		0			0
$571$	0.0109909	+	0.00322721i	0.000459953	+	0.000135054i	0.281963	−	0.959425i	$-0.409015\pi$
$571$	0.0109909	+	0.00322721i	0.000459953	+	0.000135054i	−0.281503	+	0.959560i	$0.590833\pi$
$572$	1.61063	+	3.52678i	0.0673436	+	0.147462i
$573$		0			0
$574$	14.1815			0.591924
$575$	−18.4557	−	1.84663i	−0.769655	−	0.0770097i
$576$		0			0
$577$	2.05333	−	14.2813i	0.0854814	−	0.594536i	−0.901388	−	0.433013i	$-0.857450\pi$
$577$	2.05333	−	14.2813i	0.0854814	−	0.594536i	0.986869	−	0.161523i	$-0.0516406\pi$
$578$	−3.68259	−	8.06375i	−0.153176	−	0.335408i
$579$		0			0
$580$	0.613957	+	0.708544i	0.0254932	+	0.0294207i
$581$	−24.0933	+	7.07444i	−0.999560	+	0.293497i
$582$		0			0
$583$	16.0958	−	35.2448i	0.666618	−	1.45969i
$584$	−7.86759	+	9.07968i	−0.325563	+	0.375720i
$585$		0			0
$586$	−7.70317	−	53.5767i	−0.318215	−	2.21323i
$587$	4.11524	+	28.6221i	0.169854	+	1.18136i	0.879183	+	0.476484i	$0.158089\pi$
$587$	4.11524	+	28.6221i	0.169854	+	1.18136i	−0.709329	+	0.704877i	$0.751002\pi$
$588$		0			0
$589$	0.843390	−	0.973324i	0.0347513	−	0.0401051i
$590$	5.85009	−	12.8099i	0.240844	−	0.527376i
$591$		0			0
$592$	−31.0299	+	9.11119i	−1.27532	+	0.374467i
$593$	0.147933	+	0.170723i	0.00607487	+	0.00701077i	0.758779	−	0.651348i	$-0.225796\pi$
$593$	0.147933	+	0.170723i	0.00607487	+	0.00701077i	−0.752704	+	0.658359i	$0.771251\pi$
$594$		0			0
$595$	−4.84378	−	10.6064i	−0.198576	−	0.434820i
$596$	1.41767	−	9.86012i	0.0580701	−	0.403886i
$597$		0			0
$598$	−15.5819	+	7.94399i	−0.637192	+	0.324854i
$599$	−8.69708			−0.355353			−0.177677	−	0.984089i	$-0.556858\pi$
$599$	−8.69708			−0.355353			−0.177677	+	0.984089i	$0.556858\pi$
$600$		0			0
$601$	15.8088	+	34.6163i	0.644853	+	1.41203i	0.895988	+	0.444078i	$0.146469\pi$
$601$	15.8088	+	34.6163i	0.644853	+	1.41203i	−0.251135	+	0.967952i	$0.580804\pi$
$602$	1.66619	+	0.489238i	0.0679090	+	0.0199399i
$603$		0			0
$604$	−5.76590	+	1.69302i	−0.234611	+	0.0688881i
$605$	−0.575788	−	0.370036i	−0.0234091	−	0.0150441i
$606$		0			0
$607$	−22.9785	+	26.5186i	−0.932668	+	1.07636i	0.0642517	+	0.997934i	$0.479534\pi$
$607$	−22.9785	+	26.5186i	−0.932668	+	1.07636i	−0.996920	+	0.0784230i	$0.975012\pi$
$608$	−0.552414	+	0.355015i	−0.0224033	+	0.0143978i
$609$		0			0
$610$	2.55296	+	17.7562i	0.103366	+	0.718929i
$611$	−25.7260	+	16.5331i	−1.04076	+	0.668859i
$612$		0			0
$613$	−8.00302	+	17.5242i	−0.323239	+	0.707794i	−0.999586	−	0.0287892i	$-0.990835\pi$
$613$	−8.00302	+	17.5242i	−0.323239	+	0.707794i	0.676347	+	0.736583i	$0.263562\pi$
$614$	19.9498	+	12.8210i	0.805109	+	0.517412i
$615$		0			0
$616$	−16.0151	−	18.4824i	−0.645265	−	0.744676i
$617$	−2.16926	−	0.636952i	−0.0873311	−	0.0256427i	0.237775	−	0.971320i	$-0.423582\pi$
$617$	−2.16926	−	0.636952i	−0.0873311	−	0.0256427i	−0.325106	+	0.945678i	$0.605400\pi$
$618$		0			0
$619$	4.06800	−	28.2936i	0.163507	−	1.13721i	−0.728452	−	0.685097i	$-0.759760\pi$
$619$	4.06800	−	28.2936i	0.163507	−	1.13721i	0.891958	−	0.452118i	$-0.149331\pi$
$620$	−3.17570			−0.127539
$621$		0			0
$622$	−30.7913			−1.23462
$623$	−3.91695	+	27.2430i	−0.156929	+	1.09147i
$624$		0			0
$625$	−8.91843	−	2.61869i	−0.356737	−	0.104747i
$626$	29.3194	+	33.8364i	1.17184	+	1.35237i
$627$		0			0
$628$	−9.96164	−	6.40196i	−0.397513	−	0.255466i
$629$	9.50965	−	20.8232i	0.379175	−	0.830277i
$630$		0			0
$631$	−30.5528	+	19.6351i	−1.21629	+	0.781661i	−0.981700	−	0.190434i	$-0.939011\pi$
$631$	−30.5528	+	19.6351i	−1.21629	+	0.781661i	−0.234588	+	0.972095i	$0.575374\pi$
$632$	−2.71785	−	18.9031i	−0.108110	−	0.751924i
$633$		0			0
$634$	10.4192	−	6.69603i	0.413800	−	0.265933i
$635$	−5.32955	+	6.15063i	−0.211497	+	0.244080i
$636$		0			0
$637$	−6.77939	−	4.35685i	−0.268609	−	0.172625i
$638$	−8.23480	+	2.41796i	−0.326019	+	0.0957278i
$639$		0			0
$640$	−13.9391	−	4.09288i	−0.550990	−	0.161785i
$641$	6.72976	+	14.7361i	0.265810	+	0.582042i	0.994727	−	0.102560i	$-0.0327033\pi$
$641$	6.72976	+	14.7361i	0.265810	+	0.582042i	−0.728917	+	0.684602i	$0.759976\pi$
$642$		0			0
$643$	39.4841			1.55710			0.778551	−	0.627582i	$-0.215955\pi$
$643$	39.4841			1.55710			0.778551	+	0.627582i	$0.215955\pi$
$644$	−5.93239	+	5.60548i	−0.233769	+	0.220887i
$645$		0			0
$646$	0.173134	−	1.20418i	0.00681188	−	0.0473777i
$647$	13.8146	+	30.2497i	0.543106	+	1.18924i	0.959928	+	0.280248i	$0.0904168\pi$
$647$	13.8146	+	30.2497i	0.543106	+	1.18924i	−0.416821	+	0.908988i	$0.636856\pi$
$648$		0			0
$649$	17.5509	+	20.2548i	0.688931	+	0.795069i
$650$	−13.5332	+	3.97370i	−0.530814	+	0.155861i
$651$		0			0
$652$	4.12848	−	9.04010i	0.161684	−	0.354038i
$653$	1.61801	−	1.86729i	0.0633177	−	0.0730725i	−0.723207	−	0.690631i	$-0.757333\pi$
$653$	1.61801	−	1.86729i	0.0633177	−	0.0730725i	0.786525	+	0.617559i	$0.211878\pi$
$654$		0			0
$655$	0.448520	+	3.11953i	0.0175251	+	0.121890i
$656$	1.87039	+	13.0088i	0.0730263	+	0.507909i
$657$		0			0
$658$	−44.9512	+	51.8765i	−1.75238	+	2.02236i
$659$	−13.5875	+	29.7526i	−0.529296	+	1.15900i	0.436503	+	0.899703i	$0.356217\pi$
$659$	−13.5875	+	29.7526i	−0.529296	+	1.15900i	−0.965799	+	0.259293i	$0.916510\pi$
$660$		0			0
$661$	13.6988	−	4.02232i	0.532820	−	0.156450i	−0.00424500	−	0.999991i	$-0.501351\pi$
$661$	13.6988	−	4.02232i	0.532820	−	0.156450i	0.537065	+	0.843541i	$0.319533\pi$
$662$	−13.0651	−	15.0779i	−0.507790	−	0.586020i
$663$		0			0
$664$	−7.54136	−	16.5133i	−0.292662	−	0.640839i
$665$	−0.111238	+	0.773676i	−0.00431362	+	0.0300019i
$666$		0			0
$667$	−2.59809	−	7.61807i	−0.100599	−	0.294973i
$668$	−3.46698			−0.134141
$669$		0			0
$670$	−8.62985	−	18.8967i	−0.333400	−	0.730045i
$671$	−32.7570	−	9.61833i	−1.26457	−	0.371312i
$672$		0			0
$673$	−13.6730	+	4.01477i	−0.527057	+	0.154758i	−0.534427	−	0.845215i	$-0.679472\pi$
$673$	−13.6730	+	4.01477i	−0.527057	+	0.154758i	0.00736944	+	0.999973i	$0.497654\pi$
$674$	7.55639	+	4.85619i	0.291061	+	0.187054i
$675$		0			0
$676$	2.65803	−	3.06753i	0.102232	−	0.117982i
$677$	−21.7756	+	13.9943i	−0.836904	+	0.537846i	−0.887465	−	0.460875i	$-0.847536\pi$
$677$	−21.7756	+	13.9943i	−0.836904	+	0.537846i	0.0505605	+	0.998721i	$0.483899\pi$
$678$		0			0
$679$	−5.98390	−	41.6189i	−0.229641	−	1.59719i
$680$	7.09155	−	4.55746i	0.271949	−	0.174771i
$681$		0			0
$682$	12.0766	−	26.4441i	0.462437	−	1.01260i
$683$	22.1881	+	14.2594i	0.849005	+	0.545623i	0.891264	−	0.453484i	$-0.149819\pi$
$683$	22.1881	+	14.2594i	0.849005	+	0.545623i	−0.0422591	+	0.999107i	$0.513455\pi$
$684$		0			0
$685$	9.67372	+	11.1641i	0.369614	+	0.426557i
$686$	17.2451	+	5.06361i	0.658419	+	0.193329i
$687$		0			0
$688$	−0.229030	+	1.59294i	−0.00873169	+	0.0607303i
$689$	27.6325			1.05271
$690$		0			0
$691$	−2.77076			−0.105405			−0.0527023	−	0.998610i	$-0.516783\pi$
$691$	−2.77076			−0.105405			−0.0527023	+	0.998610i	$0.516783\pi$
$692$	−1.24389	+	8.65143i	−0.0472855	+	0.328878i
$693$		0			0
$694$	23.6425	+	6.94206i	0.897457	+	0.263517i
$695$	−10.3368	−	11.9294i	−0.392099	−	0.452506i
$696$		0			0
$697$	−7.82623	−	5.02961i	−0.296439	−	0.190510i
$698$	10.5469	−	23.0945i	0.399207	−	0.874141i
$699$		0			0
$700$	−5.53703	+	3.55844i	−0.209280	+	0.134496i
$701$	−5.52393	−	38.4198i	−0.208636	−	1.45109i	−0.777614	−	0.628742i	$-0.783570\pi$
$701$	−5.52393	−	38.4198i	−0.208636	−	1.45109i	0.568978	−	0.822353i	$-0.307339\pi$
$702$		0			0
$703$	−1.29095	+	0.829644i	−0.0486892	+	0.0312906i
$704$	10.4168	−	12.0216i	0.392598	−	0.453082i
$705$		0			0
$706$	39.4964	+	25.3828i	1.48647	+	0.955295i
$707$	−53.7078	+	15.7700i	−2.01989	+	0.593093i
$708$		0			0
$709$	18.5850	+	5.45704i	0.697973	+	0.204943i	0.611423	−	0.791304i	$-0.290597\pi$
$709$	18.5850	+	5.45704i	0.697973	+	0.204943i	0.0865504	+	0.996247i	$0.472416\pi$
$710$	−10.9930	−	24.0713i	−0.412559	−	0.903379i
$711$		0			0
$712$	−19.8980			−0.745710
$713$	25.2649	+	10.2474i	0.946176	+	0.383769i
$714$		0			0
$715$	−1.11864	+	7.78029i	−0.0418346	+	0.290966i
$716$	0.915415	+	2.00448i	0.0342107	+	0.0749109i
$717$		0			0
$718$	20.0770	+	23.1701i	0.749267	+	0.864700i
$719$	−8.32297	+	2.44384i	−0.310394	+	0.0911400i	−0.433220	−	0.901288i	$-0.642623\pi$
$719$	−8.32297	+	2.44384i	−0.310394	+	0.0911400i	0.122826	+	0.992428i	$0.460804\pi$
$720$		0			0
$721$	0.313304	−	0.686041i	0.0116681	−	0.0255495i
$722$	19.7175	−	22.7552i	0.733809	−	0.846861i
$723$		0			0
$724$	0.321004	+	2.23263i	0.0119300	+	0.0829751i
$725$	−0.923747	−	6.42480i	−0.0343071	−	0.238611i
$726$		0			0
$727$	−13.9774	+	16.1307i	−0.518392	+	0.598256i	−0.953227	−	0.302254i	$-0.902261\pi$
$727$	−13.9774	+	16.1307i	−0.518392	+	0.598256i	0.434836	+	0.900510i	$0.356806\pi$
$728$	7.24523	−	15.8648i	0.268526	−	0.587990i
$729$		0			0
$730$	8.31649	−	2.44194i	0.307807	−	0.0903803i
$731$	−0.745995	−	0.860924i	−0.0275916	−	0.0318424i
$732$		0			0
$733$	3.28417	+	7.19133i	0.121304	+	0.265618i	0.960536	−	0.278155i	$-0.0897227\pi$
$733$	3.28417	+	7.19133i	0.121304	+	0.265618i	−0.839233	+	0.543772i	$0.816995\pi$
$734$	4.57947	−	31.8509i	0.169031	−	1.17564i
$735$		0			0
$736$	−10.8879	−	8.64241i	−0.401335	−	0.318563i
$737$	39.5358			1.45632
$738$		0			0
$739$	−4.45570	−	9.75661i	−0.163905	−	0.358903i	0.809803	−	0.586702i	$-0.199574\pi$
$739$	−4.45570	−	9.75661i	−0.163905	−	0.358903i	−0.973708	+	0.227800i	$0.926847\pi$
$740$	3.63066	+	1.06606i	0.133466	+	0.0391890i
$741$		0			0
$742$	59.5125	−	17.4744i	2.18477	−	0.641507i
$743$	19.7327	+	12.6815i	0.723923	+	0.465237i	0.850000	−	0.526783i	$-0.176602\pi$
$743$	19.7327	+	12.6815i	0.723923	+	0.465237i	−0.126076	+	0.992021i	$0.540238\pi$
$744$		0			0
$745$	13.2252	−	15.2626i	0.484532	−	0.559180i
$746$	14.0724	−	9.04379i	0.515228	−	0.331117i
$747$		0			0
$748$	−0.812480	−	5.65092i	−0.0297072	−	0.206618i
$749$	0.230989	−	0.148448i	0.00844016	−	0.00542416i
$750$		0			0
$751$	−0.220694	+	0.483253i	−0.00805325	+	0.0176342i	−0.913616	−	0.406578i	$-0.866722\pi$
$751$	−0.220694	+	0.483253i	−0.00805325	+	0.0176342i	0.905563	+	0.424213i	$0.139449\pi$
$752$	−53.5154	−	34.3922i	−1.95150	−	1.25416i
$753$		0			0
$754$	−4.00821	−	4.62573i	−0.145971	−	0.168459i
$755$	−11.6894	−	3.43233i	−0.425423	−	0.124915i
$756$		0			0
$757$	−2.82214	+	19.6284i	−0.102572	+	0.713406i	0.872028	+	0.489456i	$0.162804\pi$
$757$	−2.82214	+	19.6284i	−0.102572	+	0.713406i	−0.974601	+	0.223950i	$0.928105\pi$
$758$	−4.58503			−0.166536
$759$		0			0
$760$	−0.565086			−0.0204978
$761$	5.67806	−	39.4918i	0.205830	−	1.43158i	−0.580747	−	0.814084i	$-0.697240\pi$
$761$	5.67806	−	39.4918i	0.205830	−	1.43158i	0.786577	−	0.617492i	$-0.211851\pi$
$762$		0			0
$763$	−29.8739	−	8.77177i	−1.08151	−	0.317559i
$764$	−0.442521	−	0.510696i	−0.0160098	−	0.0184763i
$765$		0			0
$766$	−3.53555	−	2.27216i	−0.127745	−	0.0820966i
$767$	−7.94003	+	17.3862i	−0.286698	+	0.627781i
$768$		0			0
$769$	8.19385	−	5.26586i	0.295478	−	0.189892i	−0.384500	−	0.923125i	$-0.625626\pi$
$769$	8.19385	−	5.26586i	0.295478	−	0.189892i	0.679977	+	0.733233i	$0.261990\pi$
$770$	2.51094	+	17.4639i	0.0904878	+	0.629357i
$771$		0			0
$772$	−9.62131	+	6.18324i	−0.346279	+	0.222540i
$773$	−2.41090	+	2.78232i	−0.0867139	+	0.100073i	−0.797448	−	0.603387i	$-0.793817\pi$
$773$	−2.41090	+	2.78232i	−0.0867139	+	0.100073i	0.710734	+	0.703460i	$0.248363\pi$
$774$		0			0
$775$	18.4961	+	11.8867i	0.664401	+	0.426984i
$776$	29.1668	−	8.56413i	1.04703	−	0.307434i
$777$		0			0
$778$	−4.13358	−	1.21373i	−0.148196	−	0.0435143i
$779$	0.259065	+	0.567273i	0.00928196	+	0.0203246i
$780$		0			0
$781$	50.3619			1.80209
$782$	25.3102	−	4.75945i	0.905092	−	0.170198i
$783$		0			0
$784$	2.38572	−	16.5930i	0.0852043	−	0.592609i
$785$	−9.97270	−	21.8372i	−0.355941	−	0.779402i
$786$		0			0
$787$	8.75049	+	10.0986i	0.311921	+	0.359976i	0.889965	−	0.456030i	$-0.150729\pi$
$787$	8.75049	+	10.0986i	0.311921	+	0.359976i	−0.578043	+	0.816006i	$0.696183\pi$
$788$	6.52694	−	1.91648i	0.232513	−	0.0682718i
$789$		0			0
$790$	−5.72352	+	12.5328i	−0.203634	+	0.445896i
$791$	−21.8993	+	25.2731i	−0.778650	+	0.898610i
$792$		0			0
$793$	−3.46500	−	24.0996i	−0.123046	−	0.855802i
$794$	−5.68154	−	39.5160i	−0.201630	−	1.40237i
$795$		0			0
$796$	3.83898	−	4.43041i	0.136069	−	0.157032i
$797$	−10.5566	+	23.1157i	−0.373933	+	0.818799i	0.625328	+	0.780362i	$0.284965\pi$
$797$	−10.5566	+	23.1157i	−0.373933	+	0.818799i	−0.999261	+	0.0384370i	$0.987762\pi$
$798$		0			0
$799$	43.2054	−	12.6862i	1.52850	−	0.448807i
$800$	−7.34110	−	8.47208i	−0.259547	−	0.299533i
$801$		0			0
$802$	16.0360	+	35.1139i	0.566249	+	1.23991i
$803$	−2.34756	+	16.3277i	−0.0828437	+	0.576191i
$804$		0			0
$805$	−16.2617	+	3.05792i	−0.573149	+	0.107778i
$806$	20.7326			0.730273
$807$		0			0
$808$	−16.8109	−	36.8107i	−0.591404	−	1.29499i
$809$	−0.567334	−	0.166584i	−0.0199464	−	0.00585679i	0.271744	−	0.962370i	$-0.412400\pi$
$809$	−0.567334	−	0.166584i	−0.0199464	−	0.00585679i	−0.291691	+	0.956513i	$0.594218\pi$
$810$		0			0
$811$	−40.2155	+	11.8083i	−1.41216	+	0.414647i	−0.896841	−	0.442352i	$-0.854144\pi$
$811$	−40.2155	+	11.8083i	−1.41216	+	0.414647i	−0.515317	+	0.857000i	$0.672326\pi$
$812$	−2.40282	−	1.54420i	−0.0843225	−	0.0541908i
$813$		0			0
$814$	−22.6838	+	26.1784i	−0.795065	+	0.917554i
$815$	16.9497	−	10.8929i	0.593721	−	0.381561i
$816$		0			0
$817$	0.0108677	+	0.0755866i	0.000380213	+	0.00264444i
$818$	22.9512	−	14.7499i	0.802471	−	0.515717i
$819$		0			0
$820$	0.638805	−	1.39879i	0.0223080	−	0.0488478i
$821$	22.3689	+	14.3756i	0.780679	+	0.501712i	0.869259	−	0.494357i	$-0.164596\pi$
$821$	22.3689	+	14.3756i	0.780679	+	0.501712i	−0.0885797	+	0.996069i	$0.528233\pi$
$822$		0			0
$823$	21.2560	+	24.5307i	0.740937	+	0.855087i	0.993657	−	0.112452i	$-0.0358705\pi$
$823$	21.2560	+	24.5307i	0.740937	+	0.855087i	−0.252720	+	0.967540i	$0.581325\pi$
$824$	0.523165	+	0.153615i	0.0182253	+	0.00535143i
$825$		0			0
$826$	−6.10571	+	42.4662i	−0.212445	+	1.47759i
$827$	−16.7672			−0.583054			−0.291527	−	0.956563i	$-0.594163\pi$
$827$	−16.7672			−0.583054			−0.291527	+	0.956563i	$0.594163\pi$
$828$		0			0
$829$	−30.5689			−1.06170			−0.530851	−	0.847465i	$-0.678128\pi$
$829$	−30.5689			−1.06170			−0.530851	+	0.847465i	$0.678128\pi$
$830$	−1.86390	+	12.9637i	−0.0646970	+	0.449978i
$831$		0			0
$832$	10.8847	+	3.19604i	0.377360	+	0.110803i
$833$	7.77075	+	8.96792i	0.269240	+	0.310720i
$834$		0			0
$835$	−5.91295	−	3.80002i	−0.204626	−	0.131505i
$836$	−0.158981	+	0.348120i	−0.00549847	+	0.0120400i
$837$		0			0
$838$	45.8720	−	29.4801i	1.58462	−	1.01837i
$839$	0.378151	+	2.63010i	0.0130552	+	0.0908011i	0.995307	−	0.0967645i	$-0.0308494\pi$
$839$	0.378151	+	2.63010i	0.0130552	+	0.0908011i	−0.982252	+	0.187566i	$0.939940\pi$
$840$		0			0
$841$	−22.0268	+	14.1557i	−0.759543	+	0.488129i
$842$	11.6229	−	13.4136i	0.400553	−	0.462263i
$843$		0			0
$844$	5.14139	+	3.30417i	0.176974	+	0.113734i
$845$	7.89550	−	2.31833i	0.271614	−	0.0797529i
$846$		0			0
$847$	2.00071	+	0.587460i	0.0687451	+	0.0201854i
$848$	23.8785	+	52.2867i	0.819992	+	1.79553i
$849$		0			0
$850$	20.7686			0.712358
$851$	−25.4443	−	20.1967i	−0.872221	−	0.692333i
$852$		0			0
$853$	3.35592	−	23.3409i	0.114905	−	0.799179i	−0.848128	−	0.529792i	$-0.822270\pi$
$853$	3.35592	−	23.3409i	0.114905	−	0.799179i	0.963032	−	0.269387i	$-0.0868209\pi$
$854$	−22.7029	−	49.7125i	−0.776878	−	1.70113i
$855$		0			0
$856$	0.129995	+	0.150022i	0.00444313	+	0.00512765i
$857$	38.0244	−	11.1650i	1.29889	−	0.381388i	0.442058	−	0.896987i	$-0.354249\pi$
$857$	38.0244	−	11.1650i	1.29889	−	0.381388i	0.856830	+	0.515599i	$0.172430\pi$
$858$		0			0
$859$	10.9229	−	23.9179i	0.372686	−	0.816069i	−0.626638	−	0.779310i	$-0.715570\pi$
$859$	10.9229	−	23.9179i	0.372686	−	0.816069i	0.999324	−	0.0367582i	$-0.0117031\pi$
$860$	0.123310	−	0.142307i	0.00420482	−	0.00485262i
$861$		0			0
$862$	−1.48136	−	10.3031i	−0.0504552	−	0.350923i
$863$	−4.93539	−	34.3264i	−0.168003	−	1.16848i	−0.883006	−	0.469362i	$-0.844484\pi$
$863$	−4.93539	−	34.3264i	−0.168003	−	1.16848i	0.715003	−	0.699121i	$-0.246425\pi$
$864$		0			0
$865$	−11.6040	+	13.3917i	−0.394547	+	0.455332i
$866$	−2.51701	+	5.51149i	−0.0855315	+	0.187288i
$867$		0			0
$868$	9.28298	−	2.72573i	0.315085	−	0.0925173i
$869$	−17.1711	−	19.8165i	−0.582491	−	0.672230i
$870$		0			0
$871$	11.7129	+	25.6476i	0.396875	+	0.869035i
$872$	3.20341	−	22.2802i	0.108481	−	0.754503i
$873$		0			0
$874$	−1.59982	−	0.648887i	−0.0541147	−	0.0219489i
$875$	−30.5949			−1.03429
$876$		0			0
$877$	−21.2780	−	46.5924i	−0.718509	−	1.57331i	−0.815983	−	0.578076i	$-0.803804\pi$
$877$	−21.2780	−	46.5924i	−0.718509	−	1.57331i	0.0974742	−	0.995238i	$-0.468924\pi$
$878$	−20.6244	−	6.05587i	−0.696039	−	0.204376i
$879$		0			0
$880$	−15.6887	+	4.60661i	−0.528865	+	0.155289i
$881$	−31.3619	−	20.1551i	−1.05661	−	0.679041i	−0.107569	−	0.994198i	$-0.534307\pi$
$881$	−31.3619	−	20.1551i	−1.05661	−	0.679041i	−0.949040	+	0.315156i	$0.897943\pi$
$882$		0			0
$883$	−5.21161	+	6.01452i	−0.175385	+	0.202405i	−0.836635	−	0.547760i	$-0.815481\pi$
$883$	−5.21161	+	6.01452i	−0.175385	+	0.202405i	0.661251	+	0.750165i	$0.270026\pi$
$884$	3.42515	−	2.20121i	0.115200	−	0.0740347i
$885$		0			0
$886$	3.43685	+	23.9039i	0.115463	+	0.803066i
$887$	36.7862	−	23.6411i	1.23516	−	0.793789i	0.250473	−	0.968123i	$-0.419414\pi$
$887$	36.7862	−	23.6411i	1.23516	−	0.793789i	0.984687	+	0.174334i	$0.0557774\pi$
$888$		0			0
$889$	10.2998	−	22.5535i	0.345445	−	0.756419i
$890$	12.0765	+	7.76112i	0.404807	+	0.260153i
$891$		0			0
$892$	6.86790	+	7.92598i	0.229954	+	0.265381i
$893$	−2.89627	−	0.850420i	−0.0969198	−	0.0284582i
$894$		0			0
$895$	−0.635789	+	4.42201i	−0.0212521	+	0.147811i
$896$	44.2586			1.47858
$897$		0			0
$898$	−11.7275			−0.391353
$899$	−1.35784	+	9.44399i	−0.0452865	+	0.314975i
$900$		0			0
$901$	−39.0402	−	11.4632i	−1.30062	−	0.381895i
$902$	9.21845	+	10.6387i	0.306941	+	0.354229i
$903$		0			0
$904$	−20.3386	−	13.0708i	−0.676451	−	0.434729i
$905$	−1.89963	+	4.15961i	−0.0631458	+	0.138270i
$906$		0			0
$907$	−13.2217	+	8.49704i	−0.439018	+	0.282140i	−0.741421	−	0.671041i	$-0.765848\pi$
$907$	−13.2217	+	8.49704i	−0.439018	+	0.282140i	0.302403	+	0.953180i	$0.402211\pi$
$908$	−0.829991	−	5.77272i	−0.0275442	−	0.191574i
$909$		0			0
$910$	−10.5853	+	6.80275i	−0.350899	+	0.225509i
$911$	−18.3827	+	21.2148i	−0.609047	+	0.702877i	−0.973589	−	0.228310i	$-0.926680\pi$
$911$	−18.3827	+	21.2148i	−0.609047	+	0.702877i	0.364542	+	0.931187i	$0.381226\pi$
$912$		0			0
$913$	−20.9686	−	13.4757i	−0.693959	−	0.445980i
$914$	−49.7518	+	14.6084i	−1.64564	+	0.483204i
$915$		0			0
$916$	1.57066	+	0.461187i	0.0518960	+	0.0152380i
$917$	−3.98860	−	8.73381i	−0.131715	−	0.288416i
$918$		0			0
$919$	−40.9693			−1.35145			−0.675726	−	0.737153i	$-0.736170\pi$
$919$	−40.9693			−1.35145			−0.675726	+	0.737153i	$0.736170\pi$
$920$	−3.86137	−	11.3222i	−0.127305	−	0.373282i
$921$		0			0
$922$	7.25485	−	50.4586i	0.238926	−	1.66177i
$923$	14.9202	+	32.6707i	0.491105	+	1.07537i
$924$		0			0
$925$	−17.1556	−	19.7986i	−0.564073	−	0.650975i
$926$	7.75971	−	2.27846i	0.255000	−	0.0748747i
$927$		0			0
$928$	2.02087	−	4.42509i	0.0663384	−	0.145261i
$929$	−9.17914	+	10.5933i	−0.301158	+	0.347555i	−0.886078	−	0.463536i	$-0.846580\pi$
$929$	−9.17914	+	10.5933i	−0.301158	+	0.347555i	0.584920	+	0.811091i	$0.301126\pi$
$930$		0			0
$931$	−0.113205	−	0.787356i	−0.00371014	−	0.0258046i
$932$	−0.00946755	−	0.0658483i	−0.000310120	−	0.00215693i
$933$		0			0
$934$	−29.7252	+	34.3047i	−0.972639	+	1.12248i
$935$	4.80807	−	10.5282i	0.157241	−	0.344309i
$936$		0			0
$937$	−39.1522	+	11.4961i	−1.27905	+	0.375562i	−0.849551	−	0.527506i	$-0.823127\pi$
$937$	−39.1522	+	11.4961i	−1.27905	+	0.375562i	−0.429496	+	0.903069i	$0.641309\pi$
$938$	41.4454	+	47.8305i	1.35324	+	1.56172i
$939$		0			0
$940$	3.09200	+	6.77053i	0.100850	+	0.220830i
$941$	−5.38862	+	37.4787i	−0.175664	+	1.22177i	0.690991	+	0.722863i	$0.257174\pi$
$941$	−5.38862	+	37.4787i	−0.175664	+	1.22177i	−0.866655	+	0.498908i	$0.833735\pi$
$942$		0			0
$943$	−9.59577	+	9.06699i	−0.312481	+	0.295262i
$944$	−39.7599			−1.29407
$945$		0			0
$946$	0.716065	+	1.56796i	0.0232813	+	0.0509789i
$947$	29.8765	+	8.77252i	0.970855	+	0.285069i	0.728444	−	0.685105i	$-0.240244\pi$
$947$	29.8765	+	8.77252i	0.970855	+	0.285069i	0.242410	+	0.970174i	$0.422062\pi$
$948$		0			0
$949$	−11.2875	+	3.31432i	−0.366409	+	0.107587i
$950$	−1.17121	−	0.752691i	−0.0379991	−	0.0244205i
$951$		0			0
$952$	−16.8178	+	19.4088i	−0.545068	+	0.629042i
$953$	9.83827	−	6.32267i	0.318693	−	0.204811i	−0.371507	−	0.928430i	$-0.621159\pi$
$953$	9.83827	−	6.32267i	0.318693	−	0.204811i	0.690200	+	0.723619i	$0.257523\pi$
$954$		0			0
$955$	−0.194967	−	1.35603i	−0.00630899	−	0.0438800i
$956$	0.438557	−	0.281843i	0.0141839	−	0.00911547i
$957$		0			0
$958$	16.4428	−	36.0047i	0.531243	−	1.16326i
$959$	−37.8597	−	24.3310i	−1.22255	−	0.785687i
$960$		0			0
$961$	−0.863351	−	0.996360i	−0.0278500	−	0.0321407i
$962$	−23.7027	−	6.95975i	−0.764206	−	0.224391i
$963$		0			0
$964$	0.793013	−	5.51553i	0.0255412	−	0.177643i
$965$	−23.1864			−0.746398
$966$		0			0
$967$	6.26021			0.201315			0.100657	−	0.994921i	$-0.467905\pi$
$967$	6.26021			0.201315			0.100657	+	0.994921i	$0.467905\pi$
$968$	−0.214538	+	1.49214i	−0.00689551	+	0.0479593i
$969$		0			0
$970$	−21.0423	−	6.17859i	−0.675628	−	0.198382i
$971$	12.9539	+	14.9496i	0.415710	+	0.479754i	0.924525	−	0.381121i	$-0.124462\pi$
$971$	12.9539	+	14.9496i	0.415710	+	0.479754i	−0.508815	+	0.860876i	$0.669916\pi$
$972$		0			0
$973$	40.4550	+	25.9988i	1.29693	+	0.833484i
$974$	−17.5128	+	38.3478i	−0.561148	+	1.22874i
$975$		0			0
$976$	42.6075	−	27.3821i	1.36383	−	0.876481i
$977$	8.37841	+	58.2731i	0.268049	+	1.86432i	0.466925	+	0.884297i	$0.345362\pi$
$977$	8.37841	+	58.2731i	0.268049	+	1.86432i	−0.198876	+	0.980025i	$0.563729\pi$
$978$		0			0
$979$	−22.9833	+	14.7704i	−0.734548	+	0.472065i
$980$	−1.28447	+	1.48236i	−0.0410309	+	0.0473521i
$981$		0			0
$982$	35.0015	+	22.4941i	1.11694	+	0.717816i
$983$	29.8565	−	8.76667i	0.952275	−	0.279613i	0.231541	−	0.972825i	$-0.425623\pi$
$983$	29.8565	−	8.76667i	0.952275	−	0.279613i	0.720734	+	0.693212i	$0.243805\pi$
$984$		0			0
$985$	13.2323	+	3.88536i	0.421617	+	0.123798i
$986$	3.74399	+	8.19819i	0.119233	+	0.261083i
$987$		0			0
$988$	−0.272931			−0.00868310
$989$	−1.44021	+	0.734249i	−0.0457960	+	0.0233477i
$990$		0			0
$991$	3.81376	−	26.5253i	0.121148	−	0.842603i	−0.835111	−	0.550082i	$-0.814597\pi$
$991$	3.81376	−	26.5253i	0.121148	−	0.842603i	0.956259	−	0.292521i	$-0.0944943\pi$
$992$	6.84526	+	14.9890i	0.217337	+	0.475902i
$993$		0			0
$994$	52.7944	+	60.9280i	1.67454	+	1.93252i
$995$	11.4034	−	3.34834i	0.361513	−	0.106150i
$996$		0			0
$997$	19.1978	−	42.0372i	0.607999	−	1.33133i	−0.315935	−	0.948781i	$-0.602318\pi$
$997$	19.1978	−	42.0372i	0.607999	−	1.33133i	0.923934	−	0.382552i	$-0.124955\pi$
$998$	−1.33248	+	1.53776i	−0.0421789	+	0.0486770i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.e.100.1	✓	40
3.2	odd	2	inner	207.2.i.e.100.4	yes	40
23.3	even	11	inner	207.2.i.e.118.1	yes	40
23.7	odd	22		4761.2.a.bx.1.16		20
23.16	even	11		4761.2.a.bw.1.16		20
69.26	odd	22	inner	207.2.i.e.118.4	yes	40
69.53	even	22		4761.2.a.bx.1.5		20
69.62	odd	22		4761.2.a.bw.1.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.i.e.100.1	✓	40	1.1	even	1	trivial
207.2.i.e.100.4	yes	40	3.2	odd	2	inner
207.2.i.e.118.1	yes	40	23.3	even	11	inner
207.2.i.e.118.4	yes	40	69.26	odd	22	inner
4761.2.a.bw.1.5		20	69.62	odd	22
4761.2.a.bw.1.16		20	23.16	even	11
4761.2.a.bx.1.5		20	69.53	even	22
4761.2.a.bx.1.16		20	23.7	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.226138 + 1.57283i) q^{2} +(-0.503658 - 0.147887i) q^{4} +(-0.696899 - 0.804264i) q^{5} +(2.72743 + 1.75281i) q^{7} +(-0.973691 + 2.13209i) q^{8} +O(q^{10})\)	\(q+(-0.226138 + 1.57283i) q^{2} +(-0.503658 - 0.147887i) q^{4} +(-0.696899 - 0.804264i) q^{5} +(2.72743 + 1.75281i) q^{7} +(-0.973691 + 2.13209i) q^{8} +(1.42256 - 0.914226i) q^{10} +(0.457998 + 3.18545i) q^{11} +(-1.93077 + 1.24083i) q^{13} +(-3.37365 + 3.89340i) q^{14} +(-4.01640 - 2.58118i) q^{16} +(3.24262 - 0.952119i) q^{17} +(-0.217369 - 0.0638252i) q^{19} +(0.232058 + 0.508137i) q^{20} -5.11373 q^{22} +(-0.206512 - 4.79138i) q^{23} +(0.550401 - 3.82813i) q^{25} +(-1.51499 - 3.31737i) q^{26} +(-1.11447 - 1.28617i) q^{28} +(1.61033 - 0.472836i) q^{29} +(-2.36160 + 5.17119i) q^{31} +(1.89816 - 2.19059i) q^{32} +(0.764238 + 5.31539i) q^{34} +(-0.491019 - 3.41511i) q^{35} +(4.43585 - 5.11925i) q^{37} +(0.149541 - 0.327450i) q^{38} +(2.39333 - 0.702744i) q^{40} +(-1.80269 - 2.08041i) q^{41} +(-0.140028 - 0.306619i) q^{43} +(0.240413 - 1.67211i) q^{44} +(7.58271 + 0.758707i) q^{46} +13.3242 q^{47} +(1.45862 + 3.19393i) q^{49} +(5.89651 + 1.73137i) q^{50} +(1.15595 - 0.339419i) q^{52} +(-10.1284 - 6.50915i) q^{53} +(2.24276 - 2.58829i) q^{55} +(-6.39283 + 4.10842i) q^{56} +(0.379532 + 2.63970i) q^{58} +(7.00588 - 4.50240i) q^{59} +(-4.40688 + 9.64972i) q^{61} +(-7.59933 - 4.88380i) q^{62} +(-3.23683 - 3.73551i) q^{64} +(2.34351 + 0.688117i) q^{65} +(1.74834 - 12.1600i) q^{67} -1.77398 q^{68} +5.48241 q^{70} +(2.22709 - 15.4898i) q^{71} +(4.91808 + 1.44408i) q^{73} +(7.04857 + 8.13448i) q^{74} +(0.100041 + 0.0642921i) q^{76} +(-4.33434 + 9.49088i) q^{77} +(-6.85430 + 4.40499i) q^{79} +(0.723071 + 5.02907i) q^{80} +(3.67978 - 2.36485i) q^{82} +(-5.07198 + 5.85338i) q^{83} +(-3.02553 - 1.94439i) q^{85} +(0.513924 - 0.150902i) q^{86} +(-7.23760 - 2.12515i) q^{88} +(3.52658 + 7.72212i) q^{89} -7.44100 q^{91} +(-0.604574 + 2.44376i) q^{92} +(-3.01312 + 20.9567i) q^{94} +(0.100152 + 0.219301i) q^{95} +(-8.49290 - 9.80133i) q^{97} +(-5.35335 + 1.57188i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4} + 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^4 + 8 * q^7	\( 40 q - 4 q^{4} + 8 q^{7} - 56 q^{16} - 14 q^{19} - 28 q^{22} - 48 q^{25} - 64 q^{28} - 22 q^{31} - 10 q^{34} + 52 q^{37} + 6 q^{40} + 68 q^{43} + 84 q^{46} + 4 q^{49} + 110 q^{52} + 50 q^{55} + 18 q^{58} + 36 q^{61} + 116 q^{64} - 18 q^{67} + 96 q^{70} + 14 q^{73} + 34 q^{76} - 36 q^{79} - 72 q^{82} - 238 q^{85} - 160 q^{88} - 176 q^{91} - 206 q^{94} - 92 q^{97}+O(q^{100}) \) 40 * q - 4 * q^4 + 8 * q^7 - 56 * q^16 - 14 * q^19 - 28 * q^22 - 48 * q^25 - 64 * q^28 - 22 * q^31 - 10 * q^34 + 52 * q^37 + 6 * q^40 + 68 * q^43 + 84 * q^46 + 4 * q^49 + 110 * q^52 + 50 * q^55 + 18 * q^58 + 36 * q^61 + 116 * q^64 - 18 * q^67 + 96 * q^70 + 14 * q^73 + 34 * q^76 - 36 * q^79 - 72 * q^82 - 238 * q^85 - 160 * q^88 - 176 * q^91 - 206 * q^94 - 92 * q^97

Introduction

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