LMFDB - Embedded newform 124.2.f.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,2,Mod(33,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	124.f (of order $5$, 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:	$0.990144985064$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			109.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	124.109
Dual form			124.2.f.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 - 0.951057i) q^{3} +2.00000 q^{5} +(0.809017 - 2.48990i) q^{7} +(-0.118034 - 0.363271i) q^{9} +O(q^{10})$	\(q+(-1.30902 - 0.951057i) q^{3} +2.00000 q^{5} +(0.809017 - 2.48990i) q^{7} +(-0.118034 - 0.363271i) q^{9} +(0.809017 - 2.48990i) q^{11} +(1.30902 + 0.951057i) q^{13} +(-2.61803 - 1.90211i) q^{15} +(1.42705 + 4.39201i) q^{17} +(-3.92705 + 2.85317i) q^{19} +(-3.42705 + 2.48990i) q^{21} +(1.66312 + 5.11855i) q^{23} -1.00000 q^{25} +(-1.69098 + 5.20431i) q^{27} +(-0.690983 + 0.502029i) q^{29} +(3.23607 - 4.53077i) q^{31} +(-3.42705 + 2.48990i) q^{33} +(1.61803 - 4.97980i) q^{35} -4.47214 q^{37} +(-0.809017 - 2.48990i) q^{39} +(9.78115 - 7.10642i) q^{41} +(-7.16312 + 5.20431i) q^{43} +(-0.236068 - 0.726543i) q^{45} +(0.690983 + 0.502029i) q^{47} +(0.118034 + 0.0857567i) q^{49} +(2.30902 - 7.10642i) q^{51} +(2.66312 + 8.19624i) q^{53} +(1.61803 - 4.97980i) q^{55} +7.85410 q^{57} +(7.16312 + 5.20431i) q^{59} -13.4164 q^{61} -1.00000 q^{63} +(2.61803 + 1.90211i) q^{65} +1.52786 q^{67} +(2.69098 - 8.28199i) q^{69} +(-1.28115 - 3.94298i) q^{71} +(3.89919 - 12.0005i) q^{73} +(1.30902 + 0.951057i) q^{75} +(-5.54508 - 4.02874i) q^{77} +(1.19098 + 3.66547i) q^{79} +(6.23607 - 4.53077i) q^{81} +(2.54508 - 1.84911i) q^{83} +(2.85410 + 8.78402i) q^{85} +1.38197 q^{87} +(-2.57295 + 7.91872i) q^{89} +(3.42705 - 2.48990i) q^{91} +(-8.54508 + 2.85317i) q^{93} +(-7.85410 + 5.70634i) q^{95} +(5.13525 - 15.8047i) q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} + 8 q^{5} + q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 3 * q^3 + 8 * q^5 + q^7 + 4 * q^9	$ 4 q - 3 q^{3} + 8 q^{5} + q^{7} + 4 q^{9} + q^{11} + 3 q^{13} - 6 q^{15} - q^{17} - 9 q^{19} - 7 q^{21} - 9 q^{23} - 4 q^{25} - 9 q^{27} - 5 q^{29} + 4 q^{31} - 7 q^{33} + 2 q^{35} - q^{39} + 19 q^{41} - 13 q^{43} + 8 q^{45} + 5 q^{47} - 4 q^{49} + 7 q^{51} - 5 q^{53} + 2 q^{55} + 18 q^{57} + 13 q^{59} - 4 q^{63} + 6 q^{65} + 24 q^{67} + 13 q^{69} + 15 q^{71} - 9 q^{73} + 3 q^{75} - 11 q^{77} + 7 q^{79} + 16 q^{81} - q^{83} - 2 q^{85} + 10 q^{87} - 17 q^{89} + 7 q^{91} - 23 q^{93} - 18 q^{95} - 13 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q - 3 * q^3 + 8 * q^5 + q^7 + 4 * q^9 + q^11 + 3 * q^13 - 6 * q^15 - q^17 - 9 * q^19 - 7 * q^21 - 9 * q^23 - 4 * q^25 - 9 * q^27 - 5 * q^29 + 4 * q^31 - 7 * q^33 + 2 * q^35 - q^39 + 19 * q^41 - 13 * q^43 + 8 * q^45 + 5 * q^47 - 4 * q^49 + 7 * q^51 - 5 * q^53 + 2 * q^55 + 18 * q^57 + 13 * q^59 - 4 * q^63 + 6 * q^65 + 24 * q^67 + 13 * q^69 + 15 * q^71 - 9 * q^73 + 3 * q^75 - 11 * q^77 + 7 * q^79 + 16 * q^81 - q^83 - 2 * q^85 + 10 * q^87 - 17 * q^89 + 7 * q^91 - 23 * q^93 - 18 * q^95 - 13 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.30902	−	0.951057i	−0.755761	−	0.549093i	0.141846	−	0.989889i	$-0.454696\pi$
$3$	−1.30902	−	0.951057i	−0.755761	−	0.549093i	−0.897607	+	0.440796i	$0.854696\pi$
$4$		0			0
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		0			0
$7$	0.809017	−	2.48990i	0.305780	−	0.941093i	−0.673605	−	0.739091i	$-0.735255\pi$
$7$	0.809017	−	2.48990i	0.305780	−	0.941093i	0.979385	−	0.202002i	$-0.0647447\pi$
$8$		0			0
$9$	−0.118034	−	0.363271i	−0.0393447	−	0.121090i
$10$		0			0
$11$	0.809017	−	2.48990i	0.243928	−	0.750733i	−0.751883	−	0.659296i	$-0.770854\pi$
$11$	0.809017	−	2.48990i	0.243928	−	0.750733i	0.995811	−	0.0914362i	$-0.0291457\pi$
$12$		0			0
$13$	1.30902	+	0.951057i	0.363056	+	0.263776i	0.754326	−	0.656500i	$-0.227964\pi$
$13$	1.30902	+	0.951057i	0.363056	+	0.263776i	−0.391270	+	0.920276i	$0.627964\pi$
$14$		0			0
$15$	−2.61803	−	1.90211i	−0.675973	−	0.491123i
$16$		0			0
$17$	1.42705	+	4.39201i	0.346111	+	1.06522i	0.960987	+	0.276595i	$0.0892061\pi$
$17$	1.42705	+	4.39201i	0.346111	+	1.06522i	−0.614876	+	0.788624i	$0.710794\pi$
$18$		0			0
$19$	−3.92705	+	2.85317i	−0.900927	+	0.654562i	−0.938704	−	0.344724i	$-0.887972\pi$
$19$	−3.92705	+	2.85317i	−0.900927	+	0.654562i	0.0377767	+	0.999286i	$0.487972\pi$
$20$		0			0
$21$	−3.42705	+	2.48990i	−0.747844	+	0.543340i
$22$		0			0
$23$	1.66312	+	5.11855i	0.346784	+	1.06729i	0.960622	+	0.277860i	$0.0896251\pi$
$23$	1.66312	+	5.11855i	0.346784	+	1.06729i	−0.613837	+	0.789433i	$0.710375\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−1.69098	+	5.20431i	−0.325430	+	1.00157i
$28$		0			0
$29$	−0.690983	+	0.502029i	−0.128312	+	0.0932244i	−0.650090	−	0.759857i	$-0.725269\pi$
$29$	−0.690983	+	0.502029i	−0.128312	+	0.0932244i	0.521778	+	0.853081i	$0.325269\pi$
$30$		0			0
$31$	3.23607	−	4.53077i	0.581215	−	0.813750i
$31$	3.23607	−	4.53077i	0.581215	−	0.813750i
$32$		0			0
$33$	−3.42705	+	2.48990i	−0.596573	+	0.433436i
$34$		0			0
$35$	1.61803	−	4.97980i	0.273498	−	0.841739i
$36$		0			0
$37$	−4.47214			−0.735215			−0.367607	−	0.929981i	$-0.619823\pi$
$37$	−4.47214			−0.735215			−0.367607	+	0.929981i	$0.619823\pi$
$38$		0			0
$39$	−0.809017	−	2.48990i	−0.129546	−	0.398703i
$40$		0			0
$41$	9.78115	−	7.10642i	1.52756	−	1.10984i	0.569983	−	0.821656i	$-0.306950\pi$
$41$	9.78115	−	7.10642i	1.52756	−	1.10984i	0.957576	−	0.288181i	$-0.0930504\pi$
$42$		0			0
$43$	−7.16312	+	5.20431i	−1.09237	+	0.793650i	−0.979797	−	0.199994i	$-0.935908\pi$
$43$	−7.16312	+	5.20431i	−1.09237	+	0.793650i	−0.112568	+	0.993644i	$0.535908\pi$
$44$		0			0
$45$	−0.236068	−	0.726543i	−0.0351909	−	0.108307i
$46$		0			0
$47$	0.690983	+	0.502029i	0.100790	+	0.0732284i	0.637039	−	0.770832i	$-0.280159\pi$
$47$	0.690983	+	0.502029i	0.100790	+	0.0732284i	−0.536249	+	0.844060i	$0.680159\pi$
$48$		0			0
$49$	0.118034	+	0.0857567i	0.0168620	+	0.0122510i
$50$		0			0
$51$	2.30902	−	7.10642i	0.323327	−	0.995098i
$52$		0			0
$53$	2.66312	+	8.19624i	0.365808	+	1.12584i	0.949474	+	0.313846i	$0.101618\pi$
$53$	2.66312	+	8.19624i	0.365808	+	1.12584i	−0.583666	+	0.811994i	$0.698382\pi$
$54$		0			0
$55$	1.61803	−	4.97980i	0.218176	−	0.671476i
$56$		0			0
$57$	7.85410			1.04030
$58$		0			0
$59$	7.16312	+	5.20431i	0.932559	+	0.677544i	0.946618	−	0.322358i	$-0.104475\pi$
$59$	7.16312	+	5.20431i	0.932559	+	0.677544i	−0.0140593	+	0.999901i	$0.504475\pi$
$60$		0			0
$61$	−13.4164			−1.71780			−0.858898	−	0.512148i	$-0.828850\pi$
$61$	−13.4164			−1.71780			−0.858898	+	0.512148i	$0.828850\pi$
$62$		0			0
$63$	−1.00000			−0.125988
$64$		0			0
$65$	2.61803	+	1.90211i	0.324727	+	0.235928i
$66$		0			0
$67$	1.52786			0.186658			0.0933292	−	0.995635i	$-0.470249\pi$
$67$	1.52786			0.186658			0.0933292	+	0.995635i	$0.470249\pi$
$68$		0			0
$69$	2.69098	−	8.28199i	0.323956	−	0.997035i
$70$		0			0
$71$	−1.28115	−	3.94298i	−0.152045	−	0.467946i	0.845805	−	0.533493i	$-0.179121\pi$
$71$	−1.28115	−	3.94298i	−0.152045	−	0.467946i	−0.997849	+	0.0655468i	$0.979121\pi$
$72$		0			0
$73$	3.89919	−	12.0005i	0.456365	−	1.40455i	−0.413159	−	0.910659i	$-0.635575\pi$
$73$	3.89919	−	12.0005i	0.456365	−	1.40455i	0.869525	−	0.493889i	$-0.164425\pi$
$74$		0			0
$75$	1.30902	+	0.951057i	0.151152	+	0.109819i
$76$		0			0
$77$	−5.54508	−	4.02874i	−0.631921	−	0.459118i
$78$		0			0
$79$	1.19098	+	3.66547i	0.133996	+	0.412397i	0.995433	−	0.0954679i	$-0.0304347\pi$
$79$	1.19098	+	3.66547i	0.133996	+	0.412397i	−0.861436	+	0.507865i	$0.830435\pi$
$80$		0			0
$81$	6.23607	−	4.53077i	0.692896	−	0.503419i
$82$		0			0
$83$	2.54508	−	1.84911i	0.279359	−	0.202966i	−0.439279	−	0.898351i	$-0.644766\pi$
$83$	2.54508	−	1.84911i	0.279359	−	0.202966i	0.718638	+	0.695384i	$0.244766\pi$
$84$		0			0
$85$	2.85410	+	8.78402i	0.309571	+	0.952761i
$86$		0			0
$87$	1.38197			0.148162
$88$		0			0
$89$	−2.57295	+	7.91872i	−0.272732	+	0.839383i	0.717079	+	0.696992i	$0.245479\pi$
$89$	−2.57295	+	7.91872i	−0.272732	+	0.839383i	−0.989811	+	0.142391i	$0.954521\pi$
$90$		0			0
$91$	3.42705	−	2.48990i	0.359253	−	0.261012i
$92$		0			0
$93$	−8.54508	+	2.85317i	−0.886084	+	0.295860i
$94$		0			0
$95$	−7.85410	+	5.70634i	−0.805814	+	0.585458i
$96$		0			0
$97$	5.13525	−	15.8047i	0.521406	−	1.60472i	−0.249909	−	0.968269i	$-0.580401\pi$
$97$	5.13525	−	15.8047i	0.521406	−	1.60472i	0.771315	−	0.636454i	$-0.219599\pi$
$98$		0			0
$99$	−1.00000			−0.100504
$100$		0			0
$101$	−2.57295	−	7.91872i	−0.256018	−	0.787942i	−0.993627	−	0.112715i	$-0.964045\pi$
$101$	−2.57295	−	7.91872i	−0.256018	−	0.787942i	0.737609	−	0.675228i	$-0.235955\pi$
$102$		0			0
$103$	−14.3992	+	10.4616i	−1.41879	+	1.03081i	−0.426825	+	0.904334i	$0.640368\pi$
$103$	−14.3992	+	10.4616i	−1.41879	+	1.03081i	−0.991969	+	0.126480i	$0.959632\pi$
$104$		0			0
$105$	−6.85410	+	4.97980i	−0.668892	+	0.485978i
$106$		0			0
$107$	3.95492	+	12.1720i	0.382336	+	1.17671i	0.938394	+	0.345566i	$0.112313\pi$
$107$	3.95492	+	12.1720i	0.382336	+	1.17671i	−0.556058	+	0.831143i	$0.687687\pi$
$108$		0			0
$109$	−6.39919	−	4.64928i	−0.612931	−	0.445320i	0.237514	−	0.971384i	$-0.423667\pi$
$109$	−6.39919	−	4.64928i	−0.612931	−	0.445320i	−0.850445	+	0.526064i	$0.823667\pi$
$110$		0			0
$111$	5.85410	+	4.25325i	0.555647	+	0.403701i
$112$		0			0
$113$	−3.33688	+	10.2699i	−0.313907	+	0.966108i	0.662294	+	0.749244i	$0.269583\pi$
$113$	−3.33688	+	10.2699i	−0.313907	+	0.966108i	−0.976202	+	0.216864i	$0.930417\pi$
$114$		0			0
$115$	3.32624	+	10.2371i	0.310173	+	0.954615i
$116$		0			0
$117$	0.190983	−	0.587785i	0.0176564	−	0.0543408i
$118$		0			0
$119$	12.0902			1.10830
$120$		0			0
$121$	3.35410	+	2.43690i	0.304918	+	0.221536i
$122$		0			0
$123$	−19.5623			−1.76387
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	2.69098	+	1.95511i	0.238786	+	0.173488i	0.700742	−	0.713414i	$-0.252852\pi$
$127$	2.69098	+	1.95511i	0.238786	+	0.173488i	−0.461956	+	0.886903i	$0.652852\pi$
$128$		0			0
$129$	14.3262			1.26135
$130$		0			0
$131$	4.33688	−	13.3475i	0.378915	−	1.16618i	−0.561884	−	0.827216i	$-0.689923\pi$
$131$	4.33688	−	13.3475i	0.378915	−	1.16618i	0.940799	−	0.338965i	$-0.110077\pi$
$132$		0			0
$133$	3.92705	+	12.0862i	0.340519	+	1.04801i
$134$		0			0
$135$	−3.38197	+	10.4086i	−0.291073	+	0.895831i
$136$		0			0
$137$	−10.3992	−	7.55545i	−0.888462	−	0.645506i	0.0470142	−	0.998894i	$-0.485029\pi$
$137$	−10.3992	−	7.55545i	−0.888462	−	0.645506i	−0.935477	+	0.353388i	$0.885029\pi$
$138$		0			0
$139$	6.39919	+	4.64928i	0.542772	+	0.394347i	0.825113	−	0.564967i	$-0.191111\pi$
$139$	6.39919	+	4.64928i	0.542772	+	0.394347i	−0.282342	+	0.959314i	$0.591111\pi$
$140$		0			0
$141$	−0.427051	−	1.31433i	−0.0359642	−	0.110686i
$142$		0			0
$143$	3.42705	−	2.48990i	0.286584	−	0.208216i
$144$		0			0
$145$	−1.38197	+	1.00406i	−0.114766	+	0.0833824i
$146$		0			0
$147$	−0.0729490	−	0.224514i	−0.00601673	−	0.0185176i
$148$		0			0
$149$	−21.4164			−1.75450			−0.877250	−	0.480033i	$-0.840625\pi$
$149$	−21.4164			−1.75450			−0.877250	+	0.480033i	$0.840625\pi$
$150$		0			0
$151$	−3.66312	+	11.2739i	−0.298100	+	0.917459i	0.684062	+	0.729424i	$0.260212\pi$
$151$	−3.66312	+	11.2739i	−0.298100	+	0.917459i	−0.982162	+	0.188035i	$0.939788\pi$
$152$		0			0
$153$	1.42705	−	1.03681i	0.115370	−	0.0838214i
$154$		0			0
$155$	6.47214	−	9.06154i	0.519854	−	0.727840i
$156$		0			0
$157$	8.54508	−	6.20837i	0.681972	−	0.495482i	−0.192039	−	0.981387i	$-0.561510\pi$
$157$	8.54508	−	6.20837i	0.681972	−	0.495482i	0.874011	+	0.485906i	$0.161510\pi$
$158$		0			0
$159$	4.30902	−	13.2618i	0.341727	−	1.05173i
$160$		0			0
$161$	14.0902			1.11046
$162$		0			0
$163$	−5.57295	−	17.1518i	−0.436507	−	1.34343i	−0.891534	−	0.452953i	$-0.850371\pi$
$163$	−5.57295	−	17.1518i	−0.436507	−	1.34343i	0.455027	−	0.890477i	$-0.349629\pi$
$164$		0			0
$165$	−6.85410	+	4.97980i	−0.533591	+	0.387677i
$166$		0			0
$167$	4.07295	−	2.95917i	0.315174	−	0.228988i	−0.418939	−	0.908014i	$-0.637598\pi$
$167$	4.07295	−	2.95917i	0.315174	−	0.228988i	0.734114	+	0.679027i	$0.237598\pi$
$168$		0			0
$169$	−3.20820	−	9.87384i	−0.246785	−	0.759526i
$170$		0			0
$171$	1.50000	+	1.08981i	0.114708	+	0.0833401i
$172$		0			0
$173$	−3.92705	−	2.85317i	−0.298568	−	0.216922i	0.428408	−	0.903586i	$-0.359075\pi$
$173$	−3.92705	−	2.85317i	−0.298568	−	0.216922i	−0.726976	+	0.686663i	$0.759075\pi$
$174$		0			0
$175$	−0.809017	+	2.48990i	−0.0611559	+	0.188219i
$176$		0			0
$177$	−4.42705	−	13.6251i	−0.332758	−	1.02412i
$178$		0			0
$179$	5.57295	−	17.1518i	0.416542	−	1.28198i	−0.494323	−	0.869278i	$-0.664584\pi$
$179$	5.57295	−	17.1518i	0.416542	−	1.28198i	0.910865	−	0.412705i	$-0.135416\pi$
$180$		0			0
$181$	24.4721			1.81900			0.909500	−	0.415704i	$-0.136465\pi$
$181$	24.4721			1.81900			0.909500	+	0.415704i	$0.136465\pi$
$182$		0			0
$183$	17.5623	+	12.7598i	1.29824	+	0.943229i
$184$		0			0
$185$	−8.94427			−0.657596
$186$		0			0
$187$	12.0902			0.884121
$188$		0			0
$189$	11.5902	+	8.42075i	0.843061	+	0.612520i
$190$		0			0
$191$	−7.41641			−0.536632			−0.268316	−	0.963331i	$-0.586467\pi$
$191$	−7.41641			−0.536632			−0.268316	+	0.963331i	$0.586467\pi$
$192$		0			0
$193$	−4.75329	+	14.6291i	−0.342149	+	1.05303i	0.620943	+	0.783856i	$0.286750\pi$
$193$	−4.75329	+	14.6291i	−0.342149	+	1.05303i	−0.963092	+	0.269171i	$0.913250\pi$
$194$		0			0
$195$	−1.61803	−	4.97980i	−0.115870	−	0.356611i
$196$		0			0
$197$	1.89919	−	5.84510i	0.135311	−	0.416446i	−0.860327	−	0.509743i	$-0.829741\pi$
$197$	1.89919	−	5.84510i	0.135311	−	0.416446i	0.995638	+	0.0932969i	$0.0297406\pi$
$198$		0			0
$199$	−11.7812	−	8.55951i	−0.835144	−	0.606767i	0.0858661	−	0.996307i	$-0.472634\pi$
$199$	−11.7812	−	8.55951i	−0.835144	−	0.606767i	−0.921010	+	0.389539i	$0.872634\pi$
$200$		0			0
$201$	−2.00000	−	1.45309i	−0.141069	−	0.102493i
$202$		0			0
$203$	0.690983	+	2.12663i	0.0484975	+	0.149260i
$204$		0			0
$205$	19.5623	−	14.2128i	1.36629	−	0.992668i
$206$		0			0
$207$	1.66312	−	1.20833i	0.115595	−	0.0839845i
$208$		0			0
$209$	3.92705	+	12.0862i	0.271640	+	0.836021i
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	−2.07295	+	6.37988i	−0.142036	+	0.437142i
$214$		0			0
$215$	−14.3262	+	10.4086i	−0.977041	+	0.709862i
$216$		0			0
$217$	−8.66312	−	11.7229i	−0.588091	−	0.795806i
$218$		0			0
$219$	−16.5172	+	12.0005i	−1.11613	+	0.810916i
$220$		0			0
$221$	−2.30902	+	7.10642i	−0.155321	+	0.478030i
$222$		0			0
$223$	0.944272			0.0632331			0.0316166	−	0.999500i	$-0.489934\pi$
$223$	0.944272			0.0632331			0.0316166	+	0.999500i	$0.489934\pi$
$224$		0			0
$225$	0.118034	+	0.363271i	0.00786893	+	0.0242181i
$226$		0			0
$227$	−3.16312	+	2.29814i	−0.209944	+	0.152533i	−0.687788	−	0.725911i	$-0.741418\pi$
$227$	−3.16312	+	2.29814i	−0.209944	+	0.152533i	0.477845	+	0.878444i	$0.341418\pi$
$228$		0			0
$229$	0.0729490	−	0.0530006i	0.00482061	−	0.00350238i	−0.585372	−	0.810765i	$-0.699052\pi$
$229$	0.0729490	−	0.0530006i	0.00482061	−	0.00350238i	0.590193	+	0.807262i	$0.299052\pi$
$230$		0			0
$231$	3.42705	+	10.5474i	0.225483	+	0.693967i
$232$		0			0
$233$	12.5451	+	9.11454i	0.821856	+	0.597113i	0.917243	−	0.398327i	$-0.130409\pi$
$233$	12.5451	+	9.11454i	0.821856	+	0.597113i	−0.0953876	+	0.995440i	$0.530409\pi$
$234$		0			0
$235$	1.38197	+	1.00406i	0.0901495	+	0.0654975i
$236$		0			0
$237$	1.92705	−	5.93085i	0.125175	−	0.385250i
$238$		0			0
$239$	−8.33688	−	25.6583i	−0.539268	−	1.65970i	−0.734242	−	0.678888i	$-0.762462\pi$
$239$	−8.33688	−	25.6583i	−0.539268	−	1.65970i	0.194974	−	0.980808i	$-0.437538\pi$
$240$		0			0
$241$	0.190983	−	0.587785i	0.0123023	−	0.0378626i	−0.944717	−	0.327887i	$-0.893663\pi$
$241$	0.190983	−	0.587785i	0.0123023	−	0.0378626i	0.957019	+	0.290024i	$0.0936635\pi$
$242$		0			0
$243$	3.94427			0.253025
$244$		0			0
$245$	0.236068	+	0.171513i	0.0150818	+	0.0109576i
$246$		0			0
$247$	−7.85410			−0.499745
$248$		0			0
$249$	−5.09017			−0.322576
$250$		0			0
$251$	−2.07295	−	1.50609i	−0.130843	−	0.0950633i	0.520439	−	0.853899i	$-0.325768\pi$
$251$	−2.07295	−	1.50609i	−0.130843	−	0.0950633i	−0.651282	+	0.758836i	$0.725768\pi$
$252$		0			0
$253$	14.0902			0.885841
$254$		0			0
$255$	4.61803	−	14.2128i	0.289193	−	0.890043i
$256$		0			0
$257$	8.19098	+	25.2093i	0.510939	+	1.57251i	0.790551	+	0.612397i	$0.209794\pi$
$257$	8.19098	+	25.2093i	0.510939	+	1.57251i	−0.279611	+	0.960113i	$0.590206\pi$
$258$		0			0
$259$	−3.61803	+	11.1352i	−0.224814	+	0.691905i
$260$		0			0
$261$	0.263932	+	0.191758i	0.0163370	+	0.0118695i
$262$		0			0
$263$	−17.0172	−	12.3637i	−1.04933	−	0.762381i	−0.0772425	−	0.997012i	$-0.524612\pi$
$263$	−17.0172	−	12.3637i	−1.04933	−	0.762381i	−0.972084	+	0.234632i	$0.924612\pi$
$264$		0			0
$265$	5.32624	+	16.3925i	0.327188	+	1.00698i
$266$		0			0
$267$	10.8992	−	7.91872i	0.667019	−	0.484618i
$268$		0			0
$269$	−12.3992	+	9.00854i	−0.755992	+	0.549260i	−0.897678	−	0.440651i	$-0.854747\pi$
$269$	−12.3992	+	9.00854i	−0.755992	+	0.549260i	0.141687	+	0.989912i	$0.454747\pi$
$270$		0			0
$271$	−7.10081	−	21.8541i	−0.431344	−	1.32754i	−0.896787	−	0.442462i	$-0.854105\pi$
$271$	−7.10081	−	21.8541i	−0.431344	−	1.32754i	0.465444	−	0.885078i	$-0.345895\pi$
$272$		0			0
$273$	−6.85410			−0.414829
$274$		0			0
$275$	−0.809017	+	2.48990i	−0.0487856	+	0.150147i
$276$		0			0
$277$	−14.3992	+	10.4616i	−0.865163	+	0.628578i	−0.929285	−	0.369364i	$-0.879576\pi$
$277$	−14.3992	+	10.4616i	−0.865163	+	0.628578i	0.0641214	+	0.997942i	$0.479576\pi$
$278$		0			0
$279$	−2.02786	−	0.640786i	−0.121405	−	0.0383628i
$280$		0			0
$281$	−15.6353	+	11.3597i	−0.932721	+	0.677662i	−0.946658	−	0.322241i	$-0.895564\pi$
$281$	−15.6353	+	11.3597i	−0.932721	+	0.677662i	0.0139364	+	0.999903i	$0.495564\pi$
$282$		0			0
$283$	−5.48278	+	16.8743i	−0.325917	+	1.00307i	0.645107	+	0.764092i	$0.276813\pi$
$283$	−5.48278	+	16.8743i	−0.325917	+	1.00307i	−0.971025	+	0.238979i	$0.923187\pi$
$284$		0			0
$285$	15.7082			0.930474
$286$		0			0
$287$	−9.78115	−	30.1033i	−0.577363	−	1.77694i
$288$		0			0
$289$	−3.50000	+	2.54290i	−0.205882	+	0.149582i
$290$		0			0
$291$	−21.7533	+	15.8047i	−1.27520	+	0.926487i
$292$		0			0
$293$	−1.33688	−	4.11450i	−0.0781014	−	0.240371i	0.904381	−	0.426725i	$-0.140333\pi$
$293$	−1.33688	−	4.11450i	−0.0781014	−	0.240371i	−0.982483	+	0.186354i	$0.940333\pi$
$294$		0			0
$295$	14.3262	+	10.4086i	0.834106	+	0.606013i
$296$		0			0
$297$	11.5902	+	8.42075i	0.672530	+	0.488622i
$298$		0			0
$299$	−2.69098	+	8.28199i	−0.155624	+	0.478960i
$300$		0			0
$301$	7.16312	+	22.0458i	0.412875	+	1.27070i
$302$		0			0
$303$	−4.16312	+	12.8128i	−0.239165	+	0.736074i
$304$		0			0
$305$	−26.8328			−1.53644
$306$		0			0
$307$	6.69098	+	4.86128i	0.381875	+	0.277448i	0.762118	−	0.647438i	$-0.224160\pi$
$307$	6.69098	+	4.86128i	0.381875	+	0.277448i	−0.380243	+	0.924887i	$0.624160\pi$
$308$		0			0
$309$	28.7984			1.63828
$310$		0			0
$311$	21.8885			1.24119			0.620593	−	0.784133i	$-0.286892\pi$
$311$	21.8885			1.24119			0.620593	+	0.784133i	$0.286892\pi$
$312$		0			0
$313$	−1.92705	−	1.40008i	−0.108923	−	0.0791375i	0.531990	−	0.846751i	$-0.321444\pi$
$313$	−1.92705	−	1.40008i	−0.108923	−	0.0791375i	−0.640914	+	0.767613i	$0.721444\pi$
$314$		0			0
$315$	−2.00000			−0.112687
$316$		0			0
$317$	−0.572949	+	1.76336i	−0.0321800	+	0.0990399i	−0.965856	−	0.259078i	$-0.916581\pi$
$317$	−0.572949	+	1.76336i	−0.0321800	+	0.0990399i	0.933676	+	0.358118i	$0.116581\pi$
$318$		0			0
$319$	0.690983	+	2.12663i	0.0386876	+	0.119068i
$320$		0			0
$321$	6.39919	−	19.6947i	0.357168	−	1.09925i
$322$		0			0
$323$	−18.1353	−	13.1760i	−1.00907	−	0.733134i
$324$		0			0
$325$	−1.30902	−	0.951057i	−0.0726112	−	0.0527551i
$326$		0			0
$327$	3.95492	+	12.1720i	0.218707	+	0.673112i
$328$		0			0
$329$	1.80902	−	1.31433i	0.0997343	−	0.0724612i
$330$		0			0
$331$	8.54508	−	6.20837i	0.469680	−	0.341243i	−0.327636	−	0.944804i	$-0.606252\pi$
$331$	8.54508	−	6.20837i	0.469680	−	0.341243i	0.797317	+	0.603561i	$0.206252\pi$
$332$		0			0
$333$	0.527864	+	1.62460i	0.0289268	+	0.0890274i
$334$		0			0
$335$	3.05573			0.166952
$336$		0			0
$337$	3.13525	−	9.64932i	0.170788	−	0.525632i	−0.828628	−	0.559800i	$-0.810878\pi$
$337$	3.13525	−	9.64932i	0.170788	−	0.525632i	0.999416	+	0.0341677i	$0.0108780\pi$
$338$		0			0
$339$	14.1353	−	10.2699i	0.767722	−	0.557782i
$340$		0			0
$341$	−8.66312	−	11.7229i	−0.469134	−	0.634833i
$342$		0			0
$343$	15.1353	−	10.9964i	0.817227	−	0.593750i
$344$		0			0
$345$	5.38197	−	16.5640i	0.289755	−	0.891775i
$346$		0			0
$347$	−22.8328			−1.22573			−0.612865	−	0.790188i	$-0.709983\pi$
$347$	−22.8328			−1.22573			−0.612865	+	0.790188i	$0.709983\pi$
$348$		0			0
$349$	−2.28115	−	7.02067i	−0.122107	−	0.375808i	0.871256	−	0.490829i	$-0.163306\pi$
$349$	−2.28115	−	7.02067i	−0.122107	−	0.375808i	−0.993363	+	0.115022i	$0.963306\pi$
$350$		0			0
$351$	−7.16312	+	5.20431i	−0.382339	+	0.277786i
$352$		0			0
$353$	13.7812	−	10.0126i	0.733497	−	0.532917i	−0.157171	−	0.987571i	$-0.550237\pi$
$353$	13.7812	−	10.0126i	0.733497	−	0.532917i	0.890668	+	0.454655i	$0.150237\pi$
$354$		0			0
$355$	−2.56231	−	7.88597i	−0.135993	−	0.418544i
$356$		0			0
$357$	−15.8262	−	11.4984i	−0.837613	−	0.608562i
$358$		0			0
$359$	9.63525	+	7.00042i	0.508529	+	0.369468i	0.812265	−	0.583288i	$-0.198234\pi$
$359$	9.63525	+	7.00042i	0.508529	+	0.369468i	−0.303736	+	0.952756i	$0.598234\pi$
$360$		0			0
$361$	1.40983	−	4.33901i	0.0742016	−	0.228369i
$362$		0			0
$363$	−2.07295	−	6.37988i	−0.108802	−	0.334857i
$364$		0			0
$365$	7.79837	−	24.0009i	0.408186	−	1.25627i
$366$		0			0
$367$	20.9443			1.09328			0.546641	−	0.837367i	$-0.315906\pi$
$367$	20.9443			1.09328			0.546641	+	0.837367i	$0.315906\pi$
$368$		0			0
$369$	−3.73607	−	2.71441i	−0.194492	−	0.141307i
$370$		0			0
$371$	22.5623			1.17138
$372$		0			0
$373$	−2.94427			−0.152449			−0.0762243	−	0.997091i	$-0.524287\pi$
$373$	−2.94427			−0.152449			−0.0762243	+	0.997091i	$0.524287\pi$
$374$		0			0
$375$	15.7082	+	11.4127i	0.811168	+	0.589348i
$376$		0			0
$377$	−1.38197			−0.0711749
$378$		0			0
$379$	5.57295	−	17.1518i	0.286263	−	0.881027i	−0.699754	−	0.714384i	$-0.746707\pi$
$379$	5.57295	−	17.1518i	0.286263	−	0.881027i	0.986017	−	0.166644i	$-0.0532929\pi$
$380$		0			0
$381$	−1.66312	−	5.11855i	−0.0852042	−	0.262231i
$382$		0			0
$383$	1.86475	−	5.73910i	0.0952840	−	0.293254i	−0.892044	−	0.451949i	$-0.850729\pi$
$383$	1.86475	−	5.73910i	0.0952840	−	0.293254i	0.987328	+	0.158695i	$0.0507288\pi$
$384$		0			0
$385$	−11.0902	−	8.05748i	−0.565207	−	0.410647i
$386$		0			0
$387$	2.73607	+	1.98787i	0.139082	+	0.101049i
$388$		0			0
$389$	4.37132	+	13.4535i	0.221635	+	0.682122i	0.998616	+	0.0525978i	$0.0167501\pi$
$389$	4.37132	+	13.4535i	0.221635	+	0.682122i	−0.776981	+	0.629524i	$0.783250\pi$
$390$		0			0
$391$	−20.1074	+	14.6089i	−1.01687	+	0.738803i
$392$		0			0
$393$	−18.3713	+	13.3475i	−0.926711	+	0.673295i
$394$		0			0
$395$	2.38197	+	7.33094i	0.119850	+	0.368860i
$396$		0			0
$397$	1.41641			0.0710875			0.0355437	−	0.999368i	$-0.488684\pi$
$397$	1.41641			0.0710875			0.0355437	+	0.999368i	$0.488684\pi$
$398$		0			0
$399$	6.35410	−	19.5559i	0.318103	−	0.979020i
$400$		0			0
$401$	−13.1631	+	9.56357i	−0.657335	+	0.477582i	−0.865762	−	0.500456i	$-0.833166\pi$
$401$	−13.1631	+	9.56357i	−0.657335	+	0.477582i	0.208427	+	0.978038i	$0.433166\pi$
$402$		0			0
$403$	8.54508	−	2.85317i	0.425661	−	0.142126i
$404$		0			0
$405$	12.4721	−	9.06154i	0.619745	−	0.450271i
$406$		0			0
$407$	−3.61803	+	11.1352i	−0.179339	+	0.551950i
$408$		0			0
$409$	−12.4721			−0.616707			−0.308354	−	0.951272i	$-0.599778\pi$
$409$	−12.4721			−0.616707			−0.308354	+	0.951272i	$0.599778\pi$
$410$		0			0
$411$	6.42705	+	19.7804i	0.317023	+	0.975697i
$412$		0			0
$413$	18.7533	−	13.6251i	0.922789	−	0.670445i
$414$		0			0
$415$	5.09017	−	3.69822i	0.249867	−	0.181539i
$416$		0			0
$417$	−3.95492	−	12.1720i	−0.193673	−	0.596064i
$418$		0			0
$419$	16.8713	+	12.2577i	0.824218	+	0.598829i	0.917918	−	0.396771i	$-0.129869\pi$
$419$	16.8713	+	12.2577i	0.824218	+	0.598829i	−0.0936995	+	0.995601i	$0.529869\pi$
$420$		0			0
$421$	13.0172	+	9.45756i	0.634421	+	0.460933i	0.857929	−	0.513769i	$-0.171751\pi$
$421$	13.0172	+	9.45756i	0.634421	+	0.460933i	−0.223508	+	0.974702i	$0.571751\pi$
$422$		0			0
$423$	0.100813	−	0.310271i	0.00490170	−	0.0150859i
$424$		0			0
$425$	−1.42705	−	4.39201i	−0.0692221	−	0.213044i
$426$		0			0
$427$	−10.8541	+	33.4055i	−0.525267	+	1.61661i
$428$		0			0
$429$	−6.85410			−0.330919
$430$		0			0
$431$	−5.01722	−	3.64522i	−0.241671	−	0.175584i	0.460356	−	0.887734i	$-0.347722\pi$
$431$	−5.01722	−	3.64522i	−0.241671	−	0.175584i	−0.702027	+	0.712150i	$0.747722\pi$
$432$		0			0
$433$	−23.8885			−1.14801			−0.574005	−	0.818852i	$-0.694611\pi$
$433$	−23.8885			−1.14801			−0.574005	+	0.818852i	$0.694611\pi$
$434$		0			0
$435$	2.76393			0.132520
$436$		0			0
$437$	−21.1353	−	15.3557i	−1.01104	−	0.734561i
$438$		0			0
$439$	−31.4164			−1.49942			−0.749712	−	0.661765i	$-0.769808\pi$
$439$	−31.4164			−1.49942			−0.749712	+	0.661765i	$0.769808\pi$
$440$		0			0
$441$	0.0172209	−	0.0530006i	0.000820044	−	0.00252384i
$442$		0			0
$443$	2.42705	+	7.46969i	0.115313	+	0.354896i	0.992012	−	0.126143i	$-0.0402597\pi$
$443$	2.42705	+	7.46969i	0.115313	+	0.354896i	−0.876699	+	0.481039i	$0.840260\pi$
$444$		0			0
$445$	−5.14590	+	15.8374i	−0.243939	+	0.750767i
$446$		0			0
$447$	28.0344	+	20.3682i	1.32598	+	0.963383i
$448$		0			0
$449$	25.0172	+	18.1761i	1.18064	+	0.857782i	0.992243	−	0.124312i	$-0.0396723\pi$
$449$	25.0172	+	18.1761i	1.18064	+	0.857782i	0.188392	+	0.982094i	$0.439672\pi$
$450$		0			0
$451$	−9.78115	−	30.1033i	−0.460577	−	1.41751i
$452$		0			0
$453$	15.5172	−	11.2739i	0.729063	−	0.529695i
$454$		0			0
$455$	6.85410	−	4.97980i	0.321325	−	0.233456i
$456$		0			0
$457$	0.663119	+	2.04087i	0.0310194	+	0.0954679i	0.965368	−	0.260894i	$-0.0840172\pi$
$457$	0.663119	+	2.04087i	0.0310194	+	0.0954679i	−0.934348	+	0.356361i	$0.884017\pi$
$458$		0			0
$459$	−25.2705			−1.17953
$460$		0			0
$461$	−8.57295	+	26.3848i	−0.399282	+	1.22886i	0.526294	+	0.850303i	$0.323581\pi$
$461$	−8.57295	+	26.3848i	−0.399282	+	1.22886i	−0.925576	+	0.378561i	$0.876419\pi$
$462$		0			0
$463$	9.30902	−	6.76340i	0.432627	−	0.314322i	−0.350072	−	0.936723i	$-0.613843\pi$
$463$	9.30902	−	6.76340i	0.432627	−	0.314322i	0.782698	+	0.622401i	$0.213843\pi$
$464$		0			0
$465$	−17.0902	+	5.70634i	−0.792538	+	0.264625i
$466$		0			0
$467$	−5.45492	+	3.96323i	−0.252423	+	0.183396i	−0.706800	−	0.707413i	$-0.749862\pi$
$467$	−5.45492	+	3.96323i	−0.252423	+	0.183396i	0.454377	+	0.890810i	$0.349862\pi$
$468$		0			0
$469$	1.23607	−	3.80423i	0.0570763	−	0.175663i
$470$		0			0
$471$	−17.0902			−0.787473
$472$		0			0
$473$	7.16312	+	22.0458i	0.329361	+	1.01367i
$474$		0			0
$475$	3.92705	−	2.85317i	0.180185	−	0.130912i
$476$		0			0
$477$	2.66312	−	1.93487i	0.121936	−	0.0885916i
$478$		0			0
$479$	5.84346	+	17.9843i	0.266994	+	0.821724i	0.991227	+	0.132169i	$0.0421941\pi$
$479$	5.84346	+	17.9843i	0.266994	+	0.821724i	−0.724233	+	0.689556i	$0.757806\pi$
$480$		0			0
$481$	−5.85410	−	4.25325i	−0.266924	−	0.193932i
$482$		0			0
$483$	−18.4443	−	13.4005i	−0.839243	−	0.609746i
$484$		0			0
$485$	10.2705	−	31.6094i	0.466360	−	1.43531i
$486$		0			0
$487$	7.19098	+	22.1316i	0.325855	+	1.00288i	0.971053	+	0.238862i	$0.0767745\pi$
$487$	7.19098	+	22.1316i	0.325855	+	1.00288i	−0.645199	+	0.764015i	$0.723225\pi$
$488$		0			0
$489$	−9.01722	+	27.7522i	−0.407773	+	1.25500i
$490$		0			0
$491$	8.36068			0.377312			0.188656	−	0.982043i	$-0.439587\pi$
$491$	8.36068			0.377312			0.188656	+	0.982043i	$0.439587\pi$
$492$		0			0
$493$	−3.19098	−	2.31838i	−0.143715	−	0.104415i
$494$		0			0
$495$	−2.00000			−0.0898933
$496$		0			0
$497$	−10.8541			−0.486873
$498$		0			0
$499$	−1.30902	−	0.951057i	−0.0585996	−	0.0425751i	0.558100	−	0.829774i	$-0.311531\pi$
$499$	−1.30902	−	0.951057i	−0.0585996	−	0.0425751i	−0.616699	+	0.787199i	$0.711531\pi$
$500$		0			0
$501$	−8.14590			−0.363932
$502$		0			0
$503$	−5.19098	+	15.9762i	−0.231454	+	0.712344i	0.766117	+	0.642701i	$0.222186\pi$
$503$	−5.19098	+	15.9762i	−0.231454	+	0.712344i	−0.997572	+	0.0696431i	$0.977814\pi$
$504$		0			0
$505$	−5.14590	−	15.8374i	−0.228989	−	0.704757i
$506$		0			0
$507$	−5.19098	+	15.9762i	−0.230540	+	0.709528i
$508$		0			0
$509$	17.0172	+	12.3637i	0.754275	+	0.548013i	0.897149	−	0.441728i	$-0.145634\pi$
$509$	17.0172	+	12.3637i	0.754275	+	0.548013i	−0.142874	+	0.989741i	$0.545634\pi$
$510$		0			0
$511$	−26.7254	−	19.4172i	−1.18226	−	0.858964i
$512$		0			0
$513$	−8.20820	−	25.2623i	−0.362401	−	1.11536i
$514$		0			0
$515$	−28.7984	+	20.9232i	−1.26901	+	0.921988i
$516$		0			0
$517$	1.80902	−	1.31433i	0.0795605	−	0.0578041i
$518$		0			0
$519$	2.42705	+	7.46969i	0.106536	+	0.327883i
$520$		0			0
$521$	34.3607			1.50537			0.752684	−	0.658382i	$-0.228759\pi$
$521$	34.3607			1.50537			0.752684	+	0.658382i	$0.228759\pi$
$522$		0			0
$523$	9.86475	−	30.3606i	0.431355	−	1.32757i	−0.465421	−	0.885090i	$-0.654097\pi$
$523$	9.86475	−	30.3606i	0.431355	−	1.32757i	0.896776	−	0.442485i	$-0.145903\pi$
$524$		0			0
$525$	3.42705	−	2.48990i	0.149569	−	0.108668i
$526$		0			0
$527$	24.5172	+	7.74721i	1.06799	+	0.337474i
$528$		0			0
$529$	−4.82624	+	3.50647i	−0.209836	+	0.152455i
$530$		0			0
$531$	1.04508	−	3.21644i	0.0453528	−	0.139582i
$532$		0			0
$533$	19.5623			0.847338
$534$		0			0
$535$	7.90983	+	24.3440i	0.341972	+	1.05248i
$536$		0			0
$537$	−23.6074	+	17.1518i	−1.01873	+	0.740154i
$538$		0			0
$539$	0.309017	−	0.224514i	0.0133103	−	0.00967050i
$540$		0			0
$541$	−11.0451	−	33.9933i	−0.474865	−	1.46149i	−0.846139	−	0.532962i	$-0.821079\pi$
$541$	−11.0451	−	33.9933i	−0.474865	−	1.46149i	0.371274	−	0.928523i	$-0.378921\pi$
$542$		0			0
$543$	−32.0344	−	23.2744i	−1.37473	−	0.998799i
$544$		0			0
$545$	−12.7984	−	9.29856i	−0.548222	−	0.398307i
$546$		0			0
$547$	−5.84346	+	17.9843i	−0.249848	+	0.768954i	0.744953	+	0.667117i	$0.232472\pi$
$547$	−5.84346	+	17.9843i	−0.249848	+	0.768954i	−0.994801	+	0.101837i	$0.967528\pi$
$548$		0			0
$549$	1.58359	+	4.87380i	0.0675861	+	0.208009i
$550$		0			0
$551$	1.28115	−	3.94298i	0.0545790	−	0.167977i
$552$		0			0
$553$	10.0902			0.429078
$554$		0			0
$555$	11.7082	+	8.50651i	0.496986	+	0.361081i
$556$		0			0
$557$	26.3607			1.11694			0.558469	−	0.829525i	$-0.311389\pi$
$557$	26.3607			1.11694			0.558469	+	0.829525i	$0.311389\pi$
$558$		0			0
$559$	−14.3262			−0.605935
$560$		0			0
$561$	−15.8262	−	11.4984i	−0.668184	−	0.485464i
$562$		0			0
$563$	28.9443			1.21986			0.609928	−	0.792457i	$-0.291198\pi$
$563$	28.9443			1.21986			0.609928	+	0.792457i	$0.291198\pi$
$564$		0			0
$565$	−6.67376	+	20.5397i	−0.280767	+	0.864113i
$566$		0			0
$567$	−6.23607	−	19.1926i	−0.261890	−	0.806015i
$568$		0			0
$569$	6.01064	−	18.4989i	0.251979	−	0.775512i	−0.742431	−	0.669923i	$-0.766327\pi$
$569$	6.01064	−	18.4989i	0.251979	−	0.775512i	0.994410	−	0.105589i	$-0.0336729\pi$
$570$		0			0
$571$	20.1074	+	14.6089i	0.841468	+	0.611362i	0.922780	−	0.385326i	$-0.125911\pi$
$571$	20.1074	+	14.6089i	0.841468	+	0.611362i	−0.0813123	+	0.996689i	$0.525911\pi$
$572$		0			0
$573$	9.70820	+	7.05342i	0.405566	+	0.294661i
$574$		0			0
$575$	−1.66312	−	5.11855i	−0.0693569	−	0.213458i
$576$		0			0
$577$	−9.92705	+	7.21242i	−0.413269	+	0.300257i	−0.774924	−	0.632055i	$-0.782212\pi$
$577$	−9.92705	+	7.21242i	−0.413269	+	0.300257i	0.361655	+	0.932312i	$0.382212\pi$
$578$		0			0
$579$	20.1353	−	14.6291i	0.836793	−	0.607965i
$580$		0			0
$581$	−2.54508	−	7.83297i	−0.105588	−	0.324966i
$582$		0			0
$583$	22.5623			0.934435
$584$		0			0
$585$	0.381966	−	1.17557i	0.0157924	−	0.0486039i
$586$		0			0
$587$	17.0172	−	12.3637i	0.702376	−	0.510306i	−0.178329	−	0.983971i	$-0.557069\pi$
$587$	17.0172	−	12.3637i	0.702376	−	0.510306i	0.880705	+	0.473665i	$0.157069\pi$
$588$		0			0
$589$	0.218847	+	27.0256i	0.00901744	+	1.11357i
$590$		0			0
$591$	−8.04508	+	5.84510i	−0.330931	+	0.240435i
$592$		0			0
$593$	−1.69756	+	5.22455i	−0.0697105	+	0.214547i	−0.979842	−	0.199772i	$-0.935980\pi$
$593$	−1.69756	+	5.22455i	−0.0697105	+	0.214547i	0.910132	+	0.414318i	$0.135980\pi$
$594$		0			0
$595$	24.1803			0.991297
$596$		0			0
$597$	7.28115	+	22.4091i	0.297998	+	0.917143i
$598$		0			0
$599$	21.4894	−	15.6129i	0.878031	−	0.637927i	−0.0546986	−	0.998503i	$-0.517420\pi$
$599$	21.4894	−	15.6129i	0.878031	−	0.637927i	0.932730	+	0.360576i	$0.117420\pi$
$600$		0			0
$601$	4.54508	−	3.30220i	0.185398	−	0.134699i	−0.491215	−	0.871038i	$-0.663447\pi$
$601$	4.54508	−	3.30220i	0.185398	−	0.134699i	0.676613	+	0.736339i	$0.263447\pi$
$602$		0			0
$603$	−0.180340	−	0.555029i	−0.00734401	−	0.0226025i
$604$		0			0
$605$	6.70820	+	4.87380i	0.272727	+	0.198148i
$606$		0			0
$607$	−5.30902	−	3.85723i	−0.215486	−	0.156560i	0.474806	−	0.880090i	$-0.342518\pi$
$607$	−5.30902	−	3.85723i	−0.215486	−	0.156560i	−0.690293	+	0.723530i	$0.742518\pi$
$608$		0			0
$609$	1.11803	−	3.44095i	0.0453050	−	0.139435i
$610$		0			0
$611$	0.427051	+	1.31433i	0.0172766	+	0.0531720i
$612$		0			0
$613$	10.9549	−	33.7158i	0.442465	−	1.36177i	−0.442775	−	0.896633i	$-0.646006\pi$
$613$	10.9549	−	33.7158i	0.442465	−	1.36177i	0.885240	−	0.465134i	$-0.153994\pi$
$614$		0			0
$615$	−39.1246			−1.57766
$616$		0			0
$617$	−37.3435	−	27.1316i	−1.50339	−	1.09228i	−0.969006	−	0.247036i	$-0.920543\pi$
$617$	−37.3435	−	27.1316i	−1.50339	−	1.09228i	−0.534385	−	0.845241i	$-0.679457\pi$
$618$		0			0
$619$	−11.0557			−0.444367			−0.222184	−	0.975005i	$-0.571318\pi$
$619$	−11.0557			−0.444367			−0.222184	+	0.975005i	$0.571318\pi$
$620$		0			0
$621$	−29.4508			−1.18182
$622$		0			0
$623$	17.6353	+	12.8128i	0.706542	+	0.513332i
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	6.35410	−	19.5559i	0.253758	−	0.780988i
$628$		0			0
$629$	−6.38197	−	19.6417i	−0.254466	−	0.783165i
$630$		0			0
$631$	−3.37132	+	10.3759i	−0.134210	+	0.413057i	−0.995466	−	0.0951145i	$-0.969678\pi$
$631$	−3.37132	+	10.3759i	−0.134210	+	0.413057i	0.861256	+	0.508171i	$0.169678\pi$
$632$		0			0
$633$	5.23607	+	3.80423i	0.208115	+	0.151204i
$634$		0			0
$635$	5.38197	+	3.91023i	0.213577	+	0.155173i
$636$		0			0
$637$	0.0729490	+	0.224514i	0.00289035	+	0.00889557i
$638$		0			0
$639$	−1.28115	+	0.930812i	−0.0506816	+	0.0368224i
$640$		0			0
$641$	2.83688	−	2.06111i	0.112050	−	0.0814091i	−0.530349	−	0.847779i	$-0.677939\pi$
$641$	2.83688	−	2.06111i	0.112050	−	0.0814091i	0.642399	+	0.766370i	$0.277939\pi$
$642$		0			0
$643$	−7.93363	−	24.4172i	−0.312872	−	0.962920i	−0.976622	−	0.214966i	$-0.931036\pi$
$643$	−7.93363	−	24.4172i	−0.312872	−	0.962920i	0.663750	−	0.747955i	$-0.268964\pi$
$644$		0			0
$645$	28.6525			1.12819
$646$		0			0
$647$	3.10081	−	9.54332i	0.121906	−	0.375187i	−0.871419	−	0.490539i	$-0.836800\pi$
$647$	3.10081	−	9.54332i	0.121906	−	0.375187i	0.993325	+	0.115353i	$0.0367998\pi$
$648$		0			0
$649$	18.7533	−	13.6251i	0.736131	−	0.534830i
$650$		0			0
$651$	0.190983	+	23.5847i	0.00748521	+	0.924356i
$652$		0			0
$653$	35.9615	−	26.1276i	1.40728	−	1.02245i	0.413571	−	0.910472i	$-0.364281\pi$
$653$	35.9615	−	26.1276i	1.40728	−	1.02245i	0.993711	−	0.111978i	$-0.0357188\pi$
$654$		0			0
$655$	8.67376	−	26.6951i	0.338912	−	1.04306i
$656$		0			0
$657$	−4.81966			−0.188033
$658$		0			0
$659$	−4.62868	−	14.2456i	−0.180308	−	0.554930i	0.819528	−	0.573039i	$-0.194236\pi$
$659$	−4.62868	−	14.2456i	−0.180308	−	0.554930i	−0.999836	+	0.0181087i	$0.994236\pi$
$660$		0			0
$661$	24.7254	−	17.9641i	0.961708	−	0.698721i	0.00816087	−	0.999967i	$-0.497402\pi$
$661$	24.7254	−	17.9641i	0.961708	−	0.698721i	0.953547	+	0.301245i	$0.0974023\pi$
$662$		0			0
$663$	9.78115	−	7.10642i	0.379869	−	0.275991i
$664$		0			0
$665$	7.85410	+	24.1724i	0.304569	+	0.937367i
$666$		0			0
$667$	−3.71885	−	2.70190i	−0.143994	−	0.104618i
$668$		0			0
$669$	−1.23607	−	0.898056i	−0.0477891	−	0.0347208i
$670$		0			0
$671$	−10.8541	+	33.4055i	−0.419018	+	1.28960i
$672$		0			0
$673$	2.30244	+	7.08618i	0.0887525	+	0.273152i	0.985575	−	0.169238i	$-0.0541307\pi$
$673$	2.30244	+	7.08618i	0.0887525	+	0.273152i	−0.896823	+	0.442390i	$0.854131\pi$
$674$		0			0
$675$	1.69098	−	5.20431i	0.0650860	−	0.200314i
$676$		0			0
$677$	−47.3050			−1.81808			−0.909038	−	0.416712i	$-0.863182\pi$
$677$	−47.3050			−1.81808			−0.909038	+	0.416712i	$0.863182\pi$
$678$		0			0
$679$	−35.1976	−	25.5725i	−1.35076	−	0.981383i
$680$		0			0
$681$	6.32624			0.242422
$682$		0			0
$683$	48.7214			1.86427			0.932136	−	0.362110i	$-0.117943\pi$
$683$	48.7214			1.86427			0.932136	+	0.362110i	$0.117943\pi$
$684$		0			0
$685$	−20.7984	−	15.1109i	−0.794665	−	0.577358i
$686$		0			0
$687$	−0.145898			−0.00556636
$688$		0			0
$689$	−4.30902	+	13.2618i	−0.164160	+	0.505234i
$690$		0			0
$691$	−1.39261	−	4.28601i	−0.0529773	−	0.163048i	0.921067	−	0.389403i	$-0.127319\pi$
$691$	−1.39261	−	4.28601i	−0.0529773	−	0.163048i	−0.974045	+	0.226356i	$0.927319\pi$
$692$		0			0
$693$	−0.809017	+	2.48990i	−0.0307320	+	0.0945834i
$694$		0			0
$695$	12.7984	+	9.29856i	0.485470	+	0.352715i
$696$		0			0
$697$	45.1697	+	32.8177i	1.71092	+	1.24306i
$698$		0			0
$699$	−7.75329	−	23.8622i	−0.293256	−	0.902550i
$700$		0			0
$701$	−23.1631	+	16.8290i	−0.874859	+	0.635622i	−0.931886	−	0.362750i	$-0.881838\pi$
$701$	−23.1631	+	16.8290i	−0.874859	+	0.635622i	0.0570274	+	0.998373i	$0.481838\pi$
$702$		0			0
$703$	17.5623	−	12.7598i	0.662375	−	0.481244i
$704$		0			0
$705$	−0.854102	−	2.62866i	−0.0321673	−	0.0990009i
$706$		0			0
$707$	−21.7984			−0.819812
$708$		0			0
$709$	−12.4615	+	38.3525i	−0.468001	+	1.44036i	0.387167	+	0.922009i	$0.373454\pi$
$709$	−12.4615	+	38.3525i	−0.468001	+	1.44036i	−0.855169	+	0.518350i	$0.826546\pi$
$710$		0			0
$711$	1.19098	−	0.865300i	0.0446654	−	0.0324513i
$712$		0			0
$713$	28.5729	+	9.02878i	1.07007	+	0.338131i
$714$		0			0
$715$	6.85410	−	4.97980i	0.256329	−	0.186234i
$716$		0			0
$717$	−13.4894	+	41.5160i	−0.503769	+	1.55044i
$718$		0			0
$719$	−32.9443			−1.22861			−0.614307	−	0.789067i	$-0.710564\pi$
$719$	−32.9443			−1.22861			−0.614307	+	0.789067i	$0.710564\pi$
$720$		0			0
$721$	14.3992	+	44.3161i	0.536254	+	1.65042i
$722$		0			0
$723$	−0.809017	+	0.587785i	−0.0300877	+	0.0218600i
$724$		0			0
$725$	0.690983	−	0.502029i	0.0256625	−	0.0186449i
$726$		0			0
$727$	10.3156	+	31.7481i	0.382584	+	1.17747i	0.938218	+	0.346046i	$0.112476\pi$
$727$	10.3156	+	31.7481i	0.382584	+	1.17747i	−0.555633	+	0.831427i	$0.687524\pi$
$728$		0			0
$729$	−23.8713	−	17.3435i	−0.884123	−	0.642353i
$730$		0			0
$731$	−33.0795	−	24.0337i	−1.22349	−	0.888918i
$732$		0			0
$733$	−2.86475	+	8.81678i	−0.105812	+	0.325655i	−0.989920	−	0.141627i	$-0.954767\pi$
$733$	−2.86475	+	8.81678i	−0.105812	+	0.325655i	0.884108	+	0.467282i	$0.154767\pi$
$734$		0			0
$735$	−0.145898	−	0.449028i	−0.00538153	−	0.0165626i
$736$		0			0
$737$	1.23607	−	3.80423i	0.0455311	−	0.140130i
$738$		0			0
$739$	−41.5279			−1.52763			−0.763814	−	0.645437i	$-0.776675\pi$
$739$	−41.5279			−1.52763			−0.763814	+	0.645437i	$0.776675\pi$
$740$		0			0
$741$	10.2812	+	7.46969i	0.377688	+	0.274406i
$742$		0			0
$743$	−23.0557			−0.845833			−0.422916	−	0.906169i	$-0.638994\pi$
$743$	−23.0557			−0.845833			−0.422916	+	0.906169i	$0.638994\pi$
$744$		0			0
$745$	−42.8328			−1.56927
$746$		0			0
$747$	−0.972136	−	0.706298i	−0.0355686	−	0.0258421i
$748$		0			0
$749$	33.5066			1.22430
$750$		0			0
$751$	−15.0106	+	46.1980i	−0.547746	+	1.68579i	0.166623	+	0.986021i	$0.446714\pi$
$751$	−15.0106	+	46.1980i	−0.547746	+	1.68579i	−0.714370	+	0.699769i	$0.753286\pi$
$752$		0			0
$753$	1.28115	+	3.94298i	0.0466878	+	0.143690i
$754$		0			0
$755$	−7.32624	+	22.5478i	−0.266629	+	0.820600i
$756$		0			0
$757$	−14.1074	−	10.2496i	−0.512742	−	0.372529i	0.301121	−	0.953586i	$-0.402639\pi$
$757$	−14.1074	−	10.2496i	−0.512742	−	0.372529i	−0.813863	+	0.581057i	$0.802639\pi$
$758$		0			0
$759$	−18.4443	−	13.4005i	−0.669485	−	0.486409i
$760$		0			0
$761$	14.0795	+	43.3323i	0.510382	+	1.57080i	0.791529	+	0.611131i	$0.209285\pi$
$761$	14.0795	+	43.3323i	0.510382	+	1.57080i	−0.281147	+	0.959665i	$0.590715\pi$
$762$		0			0
$763$	−16.7533	+	12.1720i	−0.606510	+	0.440655i
$764$		0			0
$765$	2.85410	−	2.07363i	0.103190	−	0.0749721i
$766$		0			0
$767$	4.42705	+	13.6251i	0.159852	+	0.491972i
$768$		0			0
$769$	36.8328			1.32823			0.664113	−	0.747633i	$-0.268810\pi$
$769$	36.8328			1.32823			0.664113	+	0.747633i	$0.268810\pi$
$770$		0			0
$771$	13.2533	−	40.7894i	0.477306	−	1.46900i
$772$		0			0
$773$	−4.39919	+	3.19620i	−0.158228	+	0.114959i	−0.664082	−	0.747660i	$-0.731177\pi$
$773$	−4.39919	+	3.19620i	−0.158228	+	0.114959i	0.505854	+	0.862619i	$0.331177\pi$
$774$		0			0
$775$	−3.23607	+	4.53077i	−0.116243	+	0.162750i
$776$		0			0
$777$	15.3262	−	11.1352i	0.549826	−	0.399472i
$778$		0			0
$779$	−18.1353	+	55.8146i	−0.649763	+	1.99976i
$780$		0			0
$781$	−10.8541			−0.388390
$782$		0			0
$783$	−1.44427	−	4.44501i	−0.0516141	−	0.158852i
$784$		0			0
$785$	17.0902	−	12.4167i	0.609974	−	0.443172i
$786$		0			0
$787$	9.48936	−	6.89442i	0.338259	−	0.245760i	−0.405668	−	0.914021i	$-0.632961\pi$
$787$	9.48936	−	6.89442i	0.338259	−	0.245760i	0.743927	+	0.668261i	$0.232961\pi$
$788$		0			0
$789$	10.5172	+	32.3687i	0.374423	+	1.15236i
$790$		0			0
$791$	22.8713	+	16.6170i	0.813211	+	0.590832i
$792$		0			0
$793$	−17.5623	−	12.7598i	−0.623656	−	0.453112i
$794$		0			0
$795$	8.61803	−	26.5236i	0.305650	−	0.940694i
$796$		0			0
$797$	−8.46149	−	26.0418i	−0.299721	−	0.922448i	−0.981594	−	0.190977i	$-0.938834\pi$
$797$	−8.46149	−	26.0418i	−0.299721	−	0.922448i	0.681873	−	0.731471i	$-0.261166\pi$
$798$		0			0
$799$	−1.21885	+	3.75123i	−0.0431197	+	0.132709i
$800$		0			0
$801$	3.18034			0.112372
$802$		0			0
$803$	−26.7254	−	19.4172i	−0.943120	−	0.685217i
$804$		0			0
$805$	28.1803			0.993226
$806$		0			0
$807$	24.7984			0.872944
$808$		0			0
$809$	6.25329	+	4.54328i	0.219854	+	0.159733i	0.692261	−	0.721647i	$-0.256615\pi$
$809$	6.25329	+	4.54328i	0.219854	+	0.159733i	−0.472407	+	0.881381i	$0.656615\pi$
$810$		0			0
$811$	−26.4721			−0.929562			−0.464781	−	0.885426i	$-0.653867\pi$
$811$	−26.4721			−0.929562			−0.464781	+	0.885426i	$0.653867\pi$
$812$		0			0
$813$	−11.4894	+	35.3606i	−0.402949	+	1.24015i
$814$		0			0
$815$	−11.1459	−	34.3035i	−0.390424	−	1.20160i
$816$		0			0
$817$	13.2812	−	40.8752i	0.464649	−	1.43004i
$818$		0			0
$819$	−1.30902	−	0.951057i	−0.0457408	−	0.0332326i
$820$		0			0
$821$	−25.8156	−	18.7561i	−0.900970	−	0.654593i	0.0377446	−	0.999287i	$-0.487983\pi$
$821$	−25.8156	−	18.7561i	−0.900970	−	0.654593i	−0.938715	+	0.344694i	$0.887983\pi$
$822$		0			0
$823$	−15.1697	−	46.6875i	−0.528782	−	1.62742i	−0.756713	−	0.653747i	$-0.773196\pi$
$823$	−15.1697	−	46.6875i	−0.528782	−	1.62742i	0.227930	−	0.973677i	$-0.426804\pi$
$824$		0			0
$825$	3.42705	−	2.48990i	0.119315	−	0.0866871i
$826$		0			0
$827$	−32.2877	+	23.4584i	−1.12275	+	0.815729i	−0.984624	−	0.174685i	$-0.944109\pi$
$827$	−32.2877	+	23.4584i	−1.12275	+	0.815729i	−0.138130	+	0.990414i	$0.544109\pi$
$828$		0			0
$829$	3.53851	+	10.8904i	0.122897	+	0.378239i	0.993512	−	0.113726i	$-0.0362786\pi$
$829$	3.53851	+	10.8904i	0.122897	+	0.378239i	−0.870615	+	0.491965i	$0.836279\pi$
$830$		0			0
$831$	28.7984			0.999005
$832$		0			0
$833$	−0.208204	+	0.640786i	−0.00721384	+	0.0222019i
$834$		0			0
$835$	8.14590	−	5.91834i	0.281900	−	0.204813i
$836$		0			0
$837$	18.1074	+	24.5030i	0.625883	+	0.846946i
$838$		0			0
$839$	31.6697	−	23.0094i	1.09336	−	0.794372i	0.113396	−	0.993550i	$-0.463827\pi$
$839$	31.6697	−	23.0094i	1.09336	−	0.794372i	0.979963	+	0.199178i	$0.0638271\pi$
$840$		0			0
$841$	−8.73607	+	26.8869i	−0.301244	+	0.927133i
$842$		0			0
$843$	31.2705			1.07701
$844$		0			0
$845$	−6.41641	−	19.7477i	−0.220731	−	0.679341i
$846$		0			0
$847$	8.78115	−	6.37988i	0.301724	−	0.219215i
$848$		0			0
$849$	23.2254	−	16.8743i	0.797095	−	0.579123i
$850$		0			0
$851$	−7.43769	−	22.8909i	−0.254961	−	0.784689i
$852$		0			0
$853$	−28.1074	−	20.4212i	−0.962379	−	0.699209i	−0.00867675	−	0.999962i	$-0.502762\pi$
$853$	−28.1074	−	20.4212i	−0.962379	−	0.699209i	−0.953702	+	0.300753i	$0.902762\pi$
$854$		0			0
$855$	3.00000	+	2.17963i	0.102598	+	0.0745417i
$856$		0			0
$857$	5.60739	−	17.2578i	0.191545	−	0.589514i	−0.808455	−	0.588558i	$-0.799696\pi$
$857$	5.60739	−	17.2578i	0.191545	−	0.589514i	1.00000		0.000955970i	$-0.000304295\pi$
$858$		0			0
$859$	−3.75329	−	11.5514i	−0.128061	−	0.394130i	0.866386	−	0.499375i	$-0.166437\pi$
$859$	−3.75329	−	11.5514i	−0.128061	−	0.394130i	−0.994446	+	0.105246i	$0.966437\pi$
$860$		0			0
$861$	−15.8262	+	48.7082i	−0.539357	+	1.65997i
$862$		0			0
$863$	−28.3607			−0.965409			−0.482704	−	0.875783i	$-0.660345\pi$
$863$	−28.3607			−0.965409			−0.482704	+	0.875783i	$0.660345\pi$
$864$		0			0
$865$	−7.85410	−	5.70634i	−0.267047	−	0.194021i
$866$		0			0
$867$	7.00000			0.237732
$868$		0			0
$869$	10.0902			0.342286
$870$		0			0
$871$	2.00000	+	1.45309i	0.0677674	+	0.0492359i
$872$		0			0
$873$	−6.34752			−0.214831
$874$		0			0
$875$	−9.70820	+	29.8788i	−0.328197	+	1.01009i
$876$		0			0
$877$	1.42705	+	4.39201i	0.0481881	+	0.148308i	0.972255	−	0.233922i	$-0.0751562\pi$
$877$	1.42705	+	4.39201i	0.0481881	+	0.148308i	−0.924067	+	0.382230i	$0.875156\pi$
$878$		0			0
$879$	−2.16312	+	6.65740i	−0.0729602	+	0.224548i
$880$		0			0
$881$	8.25329	+	5.99637i	0.278060	+	0.202023i	0.718071	−	0.695970i	$-0.245025\pi$
$881$	8.25329	+	5.99637i	0.278060	+	0.202023i	−0.440011	+	0.897993i	$0.645025\pi$
$882$		0			0
$883$	36.1074	+	26.2336i	1.21511	+	0.882829i	0.995685	−	0.0927998i	$-0.0295817\pi$
$883$	36.1074	+	26.2336i	1.21511	+	0.882829i	0.219426	+	0.975629i	$0.429582\pi$
$884$		0			0
$885$	−8.85410	−	27.2501i	−0.297627	−	0.916003i
$886$		0			0
$887$	−19.3435	+	14.0538i	−0.649490	+	0.471882i	−0.863097	−	0.505038i	$-0.831479\pi$
$887$	−19.3435	+	14.0538i	−0.649490	+	0.471882i	0.213608	+	0.976920i	$0.431479\pi$
$888$		0			0
$889$	7.04508	−	5.11855i	0.236285	−	0.171671i
$890$		0			0
$891$	−6.23607	−	19.1926i	−0.208916	−	0.642978i
$892$		0			0
$893$	−4.14590			−0.138737
$894$		0			0
$895$	11.1459	−	34.3035i	0.372566	−	1.14664i
$896$		0			0
$897$	11.3992	−	8.28199i	0.380608	−	0.276528i
$898$		0			0
$899$	0.0385072	+	4.75528i	0.00128429	+	0.158598i
$900$		0			0
$901$	−32.1976	+	23.3929i	−1.07266	+	0.779330i
$902$		0			0
$903$	11.5902	−	35.6709i	0.385697	−	1.18705i
$904$		0			0
$905$	48.9443			1.62696
$906$		0			0
$907$	3.66312	+	11.2739i	0.121632	+	0.374344i	0.993272	−	0.115801i	$-0.0369436\pi$
$907$	3.66312	+	11.2739i	0.121632	+	0.374344i	−0.871641	+	0.490146i	$0.836944\pi$
$908$		0			0
$909$	−2.57295	+	1.86936i	−0.0853393	+	0.0620027i
$910$		0			0
$911$	−20.1074	+	14.6089i	−0.666188	+	0.484014i	−0.868747	−	0.495256i	$-0.835074\pi$
$911$	−20.1074	+	14.6089i	−0.666188	+	0.484014i	0.202559	+	0.979270i	$0.435074\pi$
$912$		0			0
$913$	−2.54508	−	7.83297i	−0.0842300	−	0.259233i
$914$		0			0
$915$	35.1246	+	25.5195i	1.16118	+	0.843649i
$916$		0			0
$917$	−29.7254	−	21.5968i	−0.981620	−	0.713189i
$918$		0			0
$919$	0.628677	−	1.93487i	0.0207381	−	0.0638254i	−0.940152	−	0.340756i	$-0.889317\pi$
$919$	0.628677	−	1.93487i	0.0207381	−	0.0638254i	0.960890	+	0.276930i	$0.0893171\pi$
$920$		0			0
$921$	−4.13525	−	12.7270i	−0.136261	−	0.419369i
$922$		0			0
$923$	2.07295	−	6.37988i	0.0682319	−	0.209996i
$924$		0			0
$925$	4.47214			0.147043
$926$		0			0
$927$	5.50000	+	3.99598i	0.180644	+	0.131245i
$928$		0			0
$929$	50.3607			1.65228			0.826140	−	0.563465i	$-0.190532\pi$
$929$	50.3607			1.65228			0.826140	+	0.563465i	$0.190532\pi$
$930$		0			0
$931$	−0.708204			−0.0232104
$932$		0			0
$933$	−28.6525	−	20.8172i	−0.938040	−	0.681526i
$934$		0			0
$935$	24.1803			0.790782
$936$		0			0
$937$	9.60739	−	29.5685i	0.313860	−	0.965961i	−0.662361	−	0.749184i	$-0.730446\pi$
$937$	9.60739	−	29.5685i	0.313860	−	0.965961i	0.976221	−	0.216777i	$-0.0695543\pi$
$938$		0			0
$939$	1.19098	+	3.66547i	0.0388663	+	0.119618i
$940$		0			0
$941$	−4.46149	+	13.7311i	−0.145441	+	0.447620i	−0.997067	−	0.0765287i	$-0.975616\pi$
$941$	−4.46149	+	13.7311i	−0.145441	+	0.447620i	0.851627	+	0.524149i	$0.175616\pi$
$942$		0			0
$943$	52.6418	+	38.2465i	1.71425	+	1.24548i
$944$		0			0
$945$	23.1803	+	16.8415i	0.754057	+	0.547854i
$946$		0			0
$947$	6.89919	+	21.2335i	0.224193	+	0.689996i	0.998372	+	0.0570298i	$0.0181630\pi$
$947$	6.89919	+	21.2335i	0.224193	+	0.689996i	−0.774179	+	0.632967i	$0.781837\pi$
$948$		0			0
$949$	16.5172	−	12.0005i	0.536172	−	0.389552i
$950$		0			0
$951$	2.42705	−	1.76336i	0.0787025	−	0.0571807i
$952$		0			0
$953$	−16.1697	−	49.7652i	−0.523788	−	1.61205i	−0.766700	−	0.642005i	$-0.778103\pi$
$953$	−16.1697	−	49.7652i	−0.523788	−	1.61205i	0.242913	−	0.970048i	$-0.421897\pi$
$954$		0			0
$955$	−14.8328			−0.479979
$956$		0			0
$957$	1.11803	−	3.44095i	0.0361409	−	0.111230i
$958$		0			0
$959$	−27.2254	+	19.7804i	−0.879155	+	0.638743i
$960$		0			0
$961$	−10.0557	−	29.3238i	−0.324378	−	0.945927i
$962$		0			0
$963$	3.95492	−	2.87341i	0.127445	−	0.0925945i
$964$		0			0
$965$	−9.50658	+	29.2582i	−0.306028	+	0.941856i
$966$		0			0
$967$	−23.4164			−0.753021			−0.376510	−	0.926412i	$-0.622876\pi$
$967$	−23.4164			−0.753021			−0.376510	+	0.926412i	$0.622876\pi$
$968$		0			0
$969$	11.2082	+	34.4953i	0.360059	+	1.10815i
$970$		0			0
$971$	33.4894	−	24.3314i	1.07472	−	0.780833i	0.0979691	−	0.995189i	$-0.468765\pi$
$971$	33.4894	−	24.3314i	1.07472	−	0.780833i	0.976756	+	0.214356i	$0.0687654\pi$
$972$		0			0
$973$	16.7533	−	12.1720i	0.537086	−	0.390216i
$974$		0			0
$975$	0.809017	+	2.48990i	0.0259093	+	0.0797406i
$976$		0			0
$977$	−7.45492	−	5.41631i	−0.238504	−	0.173283i	0.462113	−	0.886821i	$-0.347092\pi$
$977$	−7.45492	−	5.41631i	−0.238504	−	0.173283i	−0.700616	+	0.713538i	$0.747092\pi$
$978$		0			0
$979$	17.6353	+	12.8128i	0.563625	+	0.409498i
$980$		0			0
$981$	−0.933629	+	2.87341i	−0.0298085	+	0.0917410i
$982$		0			0
$983$	−14.8090	−	45.5775i	−0.472334	−	1.45370i	−0.849519	−	0.527558i	$-0.823108\pi$
$983$	−14.8090	−	45.5775i	−0.472334	−	1.45370i	0.377185	−	0.926138i	$-0.376892\pi$
$984$		0			0
$985$	3.79837	−	11.6902i	0.121026	−	0.372481i
$986$		0			0
$987$	−3.61803			−0.115163
$988$		0			0
$989$	−38.5517	−	28.0094i	−1.22587	−	0.890648i
$990$		0			0
$991$	55.7771			1.77182			0.885909	−	0.463859i	$-0.153536\pi$
$991$	55.7771			1.77182			0.885909	+	0.463859i	$0.153536\pi$
$992$		0			0
$993$	−17.0902			−0.542340
$994$		0			0
$995$	−23.5623	−	17.1190i	−0.746975	−	0.542709i
$996$		0			0
$997$	−26.0000			−0.823428			−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000			−0.823428			−0.411714	+	0.911313i	$0.635070\pi$
$998$		0			0
$999$	7.56231	−	23.2744i	0.239261	−	0.736369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.2.f.a.109.1	yes	4
3.2	odd	2		1116.2.m.a.109.1		4
4.3	odd	2		496.2.n.c.481.1		4
31.2	even	5	inner	124.2.f.a.33.1	✓	4
31.8	even	5		3844.2.a.h.1.2		2
31.23	odd	10		3844.2.a.e.1.1		2
93.2	odd	10		1116.2.m.a.901.1		4
124.95	odd	10		496.2.n.c.33.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.2.f.a.33.1	✓	4	31.2	even	5	inner
124.2.f.a.109.1	yes	4	1.1	even	1	trivial
496.2.n.c.33.1		4	124.95	odd	10
496.2.n.c.481.1		4	4.3	odd	2
1116.2.m.a.109.1		4	3.2	odd	2
1116.2.m.a.901.1		4	93.2	odd	10
3844.2.a.e.1.1		2	31.23	odd	10
3844.2.a.h.1.2		2	31.8	even	5

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 - 0.951057i) q^{3} +2.00000 q^{5} +(0.809017 - 2.48990i) q^{7} +(-0.118034 - 0.363271i) q^{9} +O(q^{10})\)	\(q+(-1.30902 - 0.951057i) q^{3} +2.00000 q^{5} +(0.809017 - 2.48990i) q^{7} +(-0.118034 - 0.363271i) q^{9} +(0.809017 - 2.48990i) q^{11} +(1.30902 + 0.951057i) q^{13} +(-2.61803 - 1.90211i) q^{15} +(1.42705 + 4.39201i) q^{17} +(-3.92705 + 2.85317i) q^{19} +(-3.42705 + 2.48990i) q^{21} +(1.66312 + 5.11855i) q^{23} -1.00000 q^{25} +(-1.69098 + 5.20431i) q^{27} +(-0.690983 + 0.502029i) q^{29} +(3.23607 - 4.53077i) q^{31} +(-3.42705 + 2.48990i) q^{33} +(1.61803 - 4.97980i) q^{35} -4.47214 q^{37} +(-0.809017 - 2.48990i) q^{39} +(9.78115 - 7.10642i) q^{41} +(-7.16312 + 5.20431i) q^{43} +(-0.236068 - 0.726543i) q^{45} +(0.690983 + 0.502029i) q^{47} +(0.118034 + 0.0857567i) q^{49} +(2.30902 - 7.10642i) q^{51} +(2.66312 + 8.19624i) q^{53} +(1.61803 - 4.97980i) q^{55} +7.85410 q^{57} +(7.16312 + 5.20431i) q^{59} -13.4164 q^{61} -1.00000 q^{63} +(2.61803 + 1.90211i) q^{65} +1.52786 q^{67} +(2.69098 - 8.28199i) q^{69} +(-1.28115 - 3.94298i) q^{71} +(3.89919 - 12.0005i) q^{73} +(1.30902 + 0.951057i) q^{75} +(-5.54508 - 4.02874i) q^{77} +(1.19098 + 3.66547i) q^{79} +(6.23607 - 4.53077i) q^{81} +(2.54508 - 1.84911i) q^{83} +(2.85410 + 8.78402i) q^{85} +1.38197 q^{87} +(-2.57295 + 7.91872i) q^{89} +(3.42705 - 2.48990i) q^{91} +(-8.54508 + 2.85317i) q^{93} +(-7.85410 + 5.70634i) q^{95} +(5.13525 - 15.8047i) q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} + 8 q^{5} + q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 3 * q^3 + 8 * q^5 + q^7 + 4 * q^9	\( 4 q - 3 q^{3} + 8 q^{5} + q^{7} + 4 q^{9} + q^{11} + 3 q^{13} - 6 q^{15} - q^{17} - 9 q^{19} - 7 q^{21} - 9 q^{23} - 4 q^{25} - 9 q^{27} - 5 q^{29} + 4 q^{31} - 7 q^{33} + 2 q^{35} - q^{39} + 19 q^{41} - 13 q^{43} + 8 q^{45} + 5 q^{47} - 4 q^{49} + 7 q^{51} - 5 q^{53} + 2 q^{55} + 18 q^{57} + 13 q^{59} - 4 q^{63} + 6 q^{65} + 24 q^{67} + 13 q^{69} + 15 q^{71} - 9 q^{73} + 3 q^{75} - 11 q^{77} + 7 q^{79} + 16 q^{81} - q^{83} - 2 q^{85} + 10 q^{87} - 17 q^{89} + 7 q^{91} - 23 q^{93} - 18 q^{95} - 13 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q - 3 * q^3 + 8 * q^5 + q^7 + 4 * q^9 + q^11 + 3 * q^13 - 6 * q^15 - q^17 - 9 * q^19 - 7 * q^21 - 9 * q^23 - 4 * q^25 - 9 * q^27 - 5 * q^29 + 4 * q^31 - 7 * q^33 + 2 * q^35 - q^39 + 19 * q^41 - 13 * q^43 + 8 * q^45 + 5 * q^47 - 4 * q^49 + 7 * q^51 - 5 * q^53 + 2 * q^55 + 18 * q^57 + 13 * q^59 - 4 * q^63 + 6 * q^65 + 24 * q^67 + 13 * q^69 + 15 * q^71 - 9 * q^73 + 3 * q^75 - 11 * q^77 + 7 * q^79 + 16 * q^81 - q^83 - 2 * q^85 + 10 * q^87 - 17 * q^89 + 7 * q^91 - 23 * q^93 - 18 * q^95 - 13 * q^97 - 4 * q^99

Introduction

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