LMFDB - Embedded newform 225.2.h.a.136.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(46,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	225.136
Dual form			225.2.h.a.91.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +4.47214 q^{7} +(0.927051 + 2.85317i) q^{8} +(-1.80902 - 1.31433i) q^{10} +(2.61803 - 1.90211i) q^{11} +(-2.73607 - 1.98787i) q^{13} +(3.61803 - 2.62866i) q^{14} +(0.809017 + 0.587785i) q^{16} +(0.881966 + 2.71441i) q^{17} +(-1.00000 - 3.07768i) q^{19} +2.23607 q^{20} +(1.00000 - 3.07768i) q^{22} +(-3.61803 + 2.62866i) q^{23} +(-4.04508 + 2.93893i) q^{25} -3.38197 q^{26} +(-1.38197 + 4.25325i) q^{28} +(-1.35410 + 4.16750i) q^{29} +(2.23607 + 6.88191i) q^{31} -5.00000 q^{32} +(2.30902 + 1.67760i) q^{34} +(-3.09017 - 9.51057i) q^{35} +(-6.54508 - 4.75528i) q^{37} +(-2.61803 - 1.90211i) q^{38} +(5.42705 - 3.94298i) q^{40} +(-1.11803 - 0.812299i) q^{41} -5.70820 q^{43} +(1.00000 + 3.07768i) q^{44} +(-1.38197 + 4.25325i) q^{46} +(1.61803 - 4.97980i) q^{47} +13.0000 q^{49} +(-1.54508 + 4.75528i) q^{50} +(2.73607 - 1.98787i) q^{52} +(-0.427051 + 1.31433i) q^{53} +(-5.85410 - 4.25325i) q^{55} +(4.14590 + 12.7598i) q^{56} +(1.35410 + 4.16750i) q^{58} +(-3.23607 - 2.35114i) q^{59} +(0.500000 - 0.363271i) q^{61} +(5.85410 + 4.25325i) q^{62} +(-5.66312 + 4.11450i) q^{64} +(-2.33688 + 7.19218i) q^{65} +(1.61803 + 4.97980i) q^{67} -2.85410 q^{68} +(-8.09017 - 5.87785i) q^{70} +(0.236068 - 0.726543i) q^{71} +(-2.50000 + 1.81636i) q^{73} -8.09017 q^{74} +3.23607 q^{76} +(11.7082 - 8.50651i) q^{77} +(0.690983 - 2.12663i) q^{80} -1.38197 q^{82} +(-1.09017 - 3.35520i) q^{83} +(5.16312 - 3.75123i) q^{85} +(-4.61803 + 3.35520i) q^{86} +(7.85410 + 5.70634i) q^{88} +(6.16312 - 4.47777i) q^{89} +(-12.2361 - 8.89002i) q^{91} +(-1.38197 - 4.25325i) q^{92} +(-1.61803 - 4.97980i) q^{94} +(-5.85410 + 4.25325i) q^{95} +(2.73607 - 8.42075i) q^{97} +(10.5172 - 7.64121i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} - 5 q^{5} - 3 q^{8} - 5 q^{10} + 6 q^{11} - 2 q^{13} + 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{19} + 4 q^{22} - 10 q^{23} - 5 q^{25} - 18 q^{26} - 10 q^{28} + 8 q^{29} - 20 q^{32} + 7 q^{34}+ \cdots + 13 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 - 5 * q^5 - 3 * q^8 - 5 * q^10 + 6 * q^11 - 2 * q^13 + 10 * q^14 + q^16 + 8 * q^17 - 4 * q^19 + 4 * q^22 - 10 * q^23 - 5 * q^25 - 18 * q^26 - 10 * q^28 + 8 * q^29 - 20 * q^32 + 7 * q^34 + 10 * q^35 - 15 * q^37 - 6 * q^38 + 15 * q^40 + 4 * q^43 + 4 * q^44 - 10 * q^46 + 2 * q^47 + 52 * q^49 + 5 * q^50 + 2 * q^52 + 5 * q^53 - 10 * q^55 + 30 * q^56 - 8 * q^58 - 4 * q^59 + 2 * q^61 + 10 * q^62 - 7 * q^64 - 25 * q^65 + 2 * q^67 + 2 * q^68 - 10 * q^70 - 8 * q^71 - 10 * q^73 - 10 * q^74 + 4 * q^76 + 20 * q^77 + 5 * q^80 - 10 * q^82 + 18 * q^83 + 5 * q^85 - 14 * q^86 + 18 * q^88 + 9 * q^89 - 40 * q^91 - 10 * q^92 - 2 * q^94 - 10 * q^95 + 2 * q^97 + 13 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i	−0.263792	−	0.964580i	$-0.584973\pi$
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i	0.835853	+	0.548953i	$0.184973\pi$
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$6$		0			0
$7$	4.47214			1.69031			0.845154	−	0.534522i	$-0.179509\pi$
$7$	4.47214			1.69031			0.845154	+	0.534522i	$0.179509\pi$
$8$	0.927051	+	2.85317i	0.327762	+	1.00875i
$9$		0			0
$10$	−1.80902	−	1.31433i	−0.572061	−	0.415627i
$11$	2.61803	−	1.90211i	0.789367	−	0.573509i	−0.118409	−	0.992965i	$-0.537779\pi$
$11$	2.61803	−	1.90211i	0.789367	−	0.573509i	0.907776	+	0.419456i	$0.137779\pi$
$12$		0			0
$13$	−2.73607	−	1.98787i	−0.758849	−	0.551336i	0.139708	−	0.990193i	$-0.455384\pi$
$13$	−2.73607	−	1.98787i	−0.758849	−	0.551336i	−0.898557	+	0.438857i	$0.855384\pi$
$14$	3.61803	−	2.62866i	0.966960	−	0.702538i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	0.881966	+	2.71441i	0.213908	+	0.658342i	0.999229	+	0.0392530i	$0.0124978\pi$
$17$	0.881966	+	2.71441i	0.213908	+	0.658342i	−0.785321	+	0.619089i	$0.787502\pi$
$18$		0			0
$19$	−1.00000	−	3.07768i	−0.229416	−	0.706069i	−0.997813	−	0.0660962i	$-0.978946\pi$
$19$	−1.00000	−	3.07768i	−0.229416	−	0.706069i	0.768398	−	0.639973i	$-0.221054\pi$
$20$	2.23607			0.500000
$21$		0			0
$22$	1.00000	−	3.07768i	0.213201	−	0.656164i
$23$	−3.61803	+	2.62866i	−0.754412	+	0.548113i	−0.897191	−	0.441642i	$-0.854396\pi$
$23$	−3.61803	+	2.62866i	−0.754412	+	0.548113i	0.142779	+	0.989755i	$0.454396\pi$
$24$		0			0
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	−3.38197			−0.663258
$27$		0			0
$28$	−1.38197	+	4.25325i	−0.261167	+	0.803789i
$29$	−1.35410	+	4.16750i	−0.251450	+	0.773885i	0.743058	+	0.669227i	$0.233375\pi$
$29$	−1.35410	+	4.16750i	−0.251450	+	0.773885i	−0.994508	+	0.104658i	$0.966625\pi$
$30$		0			0
$31$	2.23607	+	6.88191i	0.401610	+	1.23603i	0.923693	+	0.383133i	$0.125155\pi$
$31$	2.23607	+	6.88191i	0.401610	+	1.23603i	−0.522083	+	0.852894i	$0.674845\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	2.30902	+	1.67760i	0.395993	+	0.287706i
$35$	−3.09017	−	9.51057i	−0.522334	−	1.60758i
$36$		0			0
$37$	−6.54508	−	4.75528i	−1.07601	−	0.781764i	−0.0990233	−	0.995085i	$-0.531572\pi$
$37$	−6.54508	−	4.75528i	−1.07601	−	0.781764i	−0.976982	+	0.213321i	$0.931572\pi$
$38$	−2.61803	−	1.90211i	−0.424701	−	0.308563i
$39$		0			0
$40$	5.42705	−	3.94298i	0.858092	−	0.623440i
$41$	−1.11803	−	0.812299i	−0.174608	−	0.126860i	0.497049	−	0.867722i	$-0.334417\pi$
$41$	−1.11803	−	0.812299i	−0.174608	−	0.126860i	−0.671657	+	0.740863i	$0.734417\pi$
$42$		0			0
$43$	−5.70820			−0.870493			−0.435246	−	0.900311i	$-0.643339\pi$
$43$	−5.70820			−0.870493			−0.435246	+	0.900311i	$0.643339\pi$
$44$	1.00000	+	3.07768i	0.150756	+	0.463978i
$45$		0			0
$46$	−1.38197	+	4.25325i	−0.203760	+	0.627108i
$47$	1.61803	−	4.97980i	0.236015	−	0.726378i	−0.760971	−	0.648786i	$-0.775277\pi$
$47$	1.61803	−	4.97980i	0.236015	−	0.726378i	0.996985	−	0.0775917i	$-0.0247231\pi$
$48$		0			0
$49$	13.0000			1.85714
$50$	−1.54508	+	4.75528i	−0.218508	+	0.672499i
$51$		0			0
$52$	2.73607	−	1.98787i	0.379424	−	0.275668i
$53$	−0.427051	+	1.31433i	−0.0586600	+	0.180537i	−0.976093	−	0.217354i	$-0.930258\pi$
$53$	−0.427051	+	1.31433i	−0.0586600	+	0.180537i	0.917433	+	0.397890i	$0.130258\pi$
$54$		0			0
$55$	−5.85410	−	4.25325i	−0.789367	−	0.573509i
$56$	4.14590	+	12.7598i	0.554019	+	1.70509i
$57$		0			0
$58$	1.35410	+	4.16750i	0.177802	+	0.547219i
$59$	−3.23607	−	2.35114i	−0.421300	−	0.306092i	0.356861	−	0.934158i	$-0.383847\pi$
$59$	−3.23607	−	2.35114i	−0.421300	−	0.306092i	−0.778161	+	0.628065i	$0.783847\pi$
$60$		0			0
$61$	0.500000	−	0.363271i	0.0640184	−	0.0465121i	−0.555316	−	0.831640i	$-0.687403\pi$
$61$	0.500000	−	0.363271i	0.0640184	−	0.0465121i	0.619334	+	0.785127i	$0.287403\pi$
$62$	5.85410	+	4.25325i	0.743472	+	0.540164i
$63$		0			0
$64$	−5.66312	+	4.11450i	−0.707890	+	0.514312i
$65$	−2.33688	+	7.19218i	−0.289854	+	0.892080i
$66$		0			0
$67$	1.61803	+	4.97980i	0.197674	+	0.608379i	0.999935	+	0.0114051i	$0.00363042\pi$
$67$	1.61803	+	4.97980i	0.197674	+	0.608379i	−0.802261	+	0.596974i	$0.796370\pi$
$68$	−2.85410			−0.346111
$69$		0			0
$70$	−8.09017	−	5.87785i	−0.966960	−	0.702538i
$71$	0.236068	−	0.726543i	0.0280161	−	0.0862247i	−0.936071	−	0.351812i	$-0.885566\pi$
$71$	0.236068	−	0.726543i	0.0280161	−	0.0862247i	0.964087	+	0.265587i	$0.0855657\pi$
$72$		0			0
$73$	−2.50000	+	1.81636i	−0.292603	+	0.212588i	−0.724396	−	0.689384i	$-0.757881\pi$
$73$	−2.50000	+	1.81636i	−0.292603	+	0.212588i	0.431793	+	0.901973i	$0.357881\pi$
$74$	−8.09017			−0.940463
$75$		0			0
$76$	3.23607			0.371202
$77$	11.7082	−	8.50651i	1.33427	−	0.969407i
$78$		0			0
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$	0.690983	−	2.12663i	0.0772542	−	0.237764i
$81$		0			0
$82$	−1.38197			−0.152613
$83$	−1.09017	−	3.35520i	−0.119662	−	0.368281i	0.873229	−	0.487310i	$-0.162022\pi$
$83$	−1.09017	−	3.35520i	−0.119662	−	0.368281i	−0.992891	+	0.119029i	$0.962022\pi$
$84$		0			0
$85$	5.16312	−	3.75123i	0.560019	−	0.406878i
$86$	−4.61803	+	3.35520i	−0.497975	+	0.361800i
$87$		0			0
$88$	7.85410	+	5.70634i	0.837250	+	0.608298i
$89$	6.16312	−	4.47777i	0.653289	−	0.474642i	−0.211101	−	0.977464i	$-0.567705\pi$
$89$	6.16312	−	4.47777i	0.653289	−	0.474642i	0.864390	+	0.502822i	$0.167705\pi$
$90$		0			0
$91$	−12.2361	−	8.89002i	−1.28269	−	0.931928i
$92$	−1.38197	−	4.25325i	−0.144080	−	0.443432i
$93$		0			0
$94$	−1.61803	−	4.97980i	−0.166887	−	0.513627i
$95$	−5.85410	+	4.25325i	−0.600618	+	0.436375i
$96$		0			0
$97$	2.73607	−	8.42075i	0.277806	−	0.854998i	−0.710658	−	0.703538i	$-0.751603\pi$
$97$	2.73607	−	8.42075i	0.277806	−	0.854998i	0.988463	−	0.151460i	$-0.0483974\pi$
$98$	10.5172	−	7.64121i	1.06240	−	0.771879i
$99$		0			0
$100$	−1.54508	−	4.75528i	−0.154508	−	0.475528i
$101$	16.5623			1.64801			0.824006	−	0.566582i	$-0.191734\pi$
$101$	16.5623			1.64801			0.824006	+	0.566582i	$0.191734\pi$
$102$		0			0
$103$	−0.381966	+	1.17557i	−0.0376362	+	0.115832i	−0.968110	−	0.250527i	$-0.919396\pi$
$103$	−0.381966	+	1.17557i	−0.0376362	+	0.115832i	0.930473	+	0.366360i	$0.119396\pi$
$104$	3.13525	−	9.64932i	0.307437	−	0.946194i
$105$		0			0
$106$	0.427051	+	1.31433i	0.0414789	+	0.127659i
$107$	−16.4721			−1.59242			−0.796211	−	0.605019i	$-0.793165\pi$
$107$	−16.4721			−1.59242			−0.796211	+	0.605019i	$0.793165\pi$
$108$		0			0
$109$	15.4443	+	11.2209i	1.47929	+	1.07477i	0.977784	+	0.209617i	$0.0672217\pi$
$109$	15.4443	+	11.2209i	1.47929	+	1.07477i	0.501509	+	0.865152i	$0.332778\pi$
$110$	−7.23607			−0.689932
$111$		0			0
$112$	3.61803	+	2.62866i	0.341872	+	0.248385i
$113$	2.16312	+	1.57160i	0.203489	+	0.147843i	0.684863	−	0.728672i	$-0.259862\pi$
$113$	2.16312	+	1.57160i	0.203489	+	0.147843i	−0.481374	+	0.876515i	$0.659862\pi$
$114$		0			0
$115$	8.09017	+	5.87785i	0.754412	+	0.548113i
$116$	−3.54508	−	2.57565i	−0.329153	−	0.239144i
$117$		0			0
$118$	−4.00000			−0.368230
$119$	3.94427	+	12.1392i	0.361571	+	1.11280i
$120$		0			0
$121$	−0.163119	+	0.502029i	−0.0148290	+	0.0456390i
$122$	0.190983	−	0.587785i	0.0172908	−	0.0532156i
$123$		0			0
$124$	−7.23607			−0.649818
$125$	9.04508	+	6.57164i	0.809017	+	0.587785i
$126$		0			0
$127$	−7.85410	+	5.70634i	−0.696939	+	0.506356i	−0.878934	−	0.476944i	$-0.841745\pi$
$127$	−7.85410	+	5.70634i	−0.696939	+	0.506356i	0.181995	+	0.983299i	$0.441745\pi$
$128$	0.927051	−	2.85317i	0.0819405	−	0.252187i
$129$		0			0
$130$	2.33688	+	7.19218i	0.204958	+	0.630796i
$131$	−4.38197	−	13.4863i	−0.382854	−	1.17830i	−0.938025	−	0.346568i	$-0.887347\pi$
$131$	−4.38197	−	13.4863i	−0.382854	−	1.17830i	0.555171	−	0.831736i	$-0.312653\pi$
$132$		0			0
$133$	−4.47214	−	13.7638i	−0.387783	−	1.19347i
$134$	4.23607	+	3.07768i	0.365941	+	0.265871i
$135$		0			0
$136$	−6.92705	+	5.03280i	−0.593990	+	0.431559i
$137$	−4.35410	−	3.16344i	−0.371996	−	0.270271i	0.386042	−	0.922481i	$-0.373842\pi$
$137$	−4.35410	−	3.16344i	−0.371996	−	0.270271i	−0.758038	+	0.652210i	$0.773842\pi$
$138$		0			0
$139$	4.09017	−	2.97168i	0.346924	−	0.252055i	−0.400654	−	0.916230i	$-0.631217\pi$
$139$	4.09017	−	2.97168i	0.346924	−	0.252055i	0.747577	+	0.664175i	$0.231217\pi$
$140$	10.0000			0.845154
$141$		0			0
$142$	−0.236068	−	0.726543i	−0.0198104	−	0.0609701i
$143$	−10.9443			−0.915206
$144$		0			0
$145$	9.79837			0.813711
$146$	−0.954915	+	2.93893i	−0.0790293	+	0.243227i
$147$		0			0
$148$	6.54508	−	4.75528i	0.538003	−	0.390882i
$149$	12.1459			0.995031			0.497515	−	0.867455i	$-0.334246\pi$
$149$	12.1459			0.995031			0.497515	+	0.867455i	$0.334246\pi$
$150$		0			0
$151$	16.4721			1.34048			0.670242	−	0.742143i	$-0.266190\pi$
$151$	16.4721			1.34048			0.670242	+	0.742143i	$0.266190\pi$
$152$	7.85410	−	5.70634i	0.637052	−	0.462845i
$153$		0			0
$154$	4.47214	−	13.7638i	0.360375	−	1.10912i
$155$	13.0902	−	9.51057i	1.05143	−	0.763907i
$156$		0			0
$157$	−13.7984			−1.10123			−0.550615	−	0.834759i	$-0.685607\pi$
$157$	−13.7984			−1.10123			−0.550615	+	0.834759i	$0.685607\pi$
$158$		0			0
$159$		0			0
$160$	3.45492	+	10.6331i	0.273135	+	0.840623i
$161$	−16.1803	+	11.7557i	−1.27519	+	0.926479i
$162$		0			0
$163$	−2.38197	−	1.73060i	−0.186570	−	0.135551i	0.490580	−	0.871396i	$-0.336785\pi$
$163$	−2.38197	−	1.73060i	−0.186570	−	0.135551i	−0.677150	+	0.735845i	$0.736785\pi$
$164$	1.11803	−	0.812299i	0.0873038	−	0.0634299i
$165$		0			0
$166$	−2.85410	−	2.07363i	−0.221521	−	0.160945i
$167$	7.23607	+	22.2703i	0.559944	+	1.72333i	0.682517	+	0.730870i	$0.260886\pi$
$167$	7.23607	+	22.2703i	0.559944	+	1.72333i	−0.122573	+	0.992460i	$0.539114\pi$
$168$		0			0
$169$	−0.482779	−	1.48584i	−0.0371369	−	0.114295i
$170$	1.97214	−	6.06961i	0.151256	−	0.465518i
$171$		0			0
$172$	1.76393	−	5.42882i	0.134499	−	0.413944i
$173$	8.01722	−	5.82485i	0.609538	−	0.442855i	−0.239714	−	0.970844i	$-0.577054\pi$
$173$	8.01722	−	5.82485i	0.609538	−	0.442855i	0.849252	+	0.527988i	$0.177054\pi$
$174$		0			0
$175$	−18.0902	+	13.1433i	−1.36749	+	0.993538i
$176$	3.23607			0.243928
$177$		0			0
$178$	2.35410	−	7.24518i	0.176447	−	0.543049i
$179$	−1.90983	+	5.87785i	−0.142747	+	0.439331i	−0.996714	−	0.0809958i	$-0.974190\pi$
$179$	−1.90983	+	5.87785i	−0.142747	+	0.439331i	0.853967	+	0.520327i	$0.174190\pi$
$180$		0			0
$181$	−3.02786	−	9.31881i	−0.225059	−	0.692661i	−0.998286	−	0.0585312i	$-0.981358\pi$
$181$	−3.02786	−	9.31881i	−0.225059	−	0.692661i	0.773226	−	0.634130i	$-0.218642\pi$
$182$	−15.1246			−1.12111
$183$		0			0
$184$	−10.8541	−	7.88597i	−0.800175	−	0.581361i
$185$	−5.59017	+	17.2048i	−0.410997	+	1.26492i
$186$		0			0
$187$	7.47214	+	5.42882i	0.546417	+	0.396995i
$188$	4.23607	+	3.07768i	0.308947	+	0.224463i
$189$		0			0
$190$	−2.23607	+	6.88191i	−0.162221	+	0.499266i
$191$	−19.9443	−	14.4904i	−1.44312	−	1.04849i	−0.987380	−	0.158371i	$-0.949376\pi$
$191$	−19.9443	−	14.4904i	−1.44312	−	1.04849i	−0.455737	−	0.890114i	$-0.650624\pi$
$192$		0			0
$193$	7.67376			0.552369			0.276185	−	0.961105i	$-0.410930\pi$
$193$	7.67376			0.552369			0.276185	+	0.961105i	$0.410930\pi$
$194$	−2.73607	−	8.42075i	−0.196438	−	0.604575i
$195$		0			0
$196$	−4.01722	+	12.3637i	−0.286944	+	0.883124i
$197$	−1.66312	+	5.11855i	−0.118492	+	0.364682i	−0.992659	−	0.120943i	$-0.961408\pi$
$197$	−1.66312	+	5.11855i	−0.118492	+	0.364682i	0.874167	+	0.485625i	$0.161408\pi$
$198$		0			0
$199$	−18.6525			−1.32224			−0.661119	−	0.750281i	$-0.729918\pi$
$199$	−18.6525			−1.32224			−0.661119	+	0.750281i	$0.729918\pi$
$200$	−12.1353	−	8.81678i	−0.858092	−	0.623440i
$201$		0			0
$202$	13.3992	−	9.73508i	0.942764	−	0.684958i
$203$	−6.05573	+	18.6376i	−0.425029	+	1.30810i
$204$		0			0
$205$	−0.954915	+	2.93893i	−0.0666942	+	0.205264i
$206$	0.381966	+	1.17557i	0.0266128	+	0.0819059i
$207$		0			0
$208$	−1.04508	−	3.21644i	−0.0724636	−	0.223020i
$209$	−8.47214	−	6.15537i	−0.586030	−	0.425776i
$210$		0			0
$211$	14.4721	−	10.5146i	0.996303	−	0.723856i	0.0350106	−	0.999387i	$-0.488854\pi$
$211$	14.4721	−	10.5146i	0.996303	−	0.723856i	0.961292	+	0.275530i	$0.0888535\pi$
$212$	−1.11803	−	0.812299i	−0.0767869	−	0.0557889i
$213$		0			0
$214$	−13.3262	+	9.68208i	−0.910963	+	0.661853i
$215$	3.94427	+	12.1392i	0.268997	+	0.827888i
$216$		0			0
$217$	10.0000	+	30.7768i	0.678844	+	2.08927i
$218$	19.0902			1.29295
$219$		0			0
$220$	5.85410	−	4.25325i	0.394683	−	0.286754i
$221$	2.98278	−	9.18005i	0.200643	−	0.617517i
$222$		0			0
$223$	11.4721	−	8.33499i	0.768231	−	0.558153i	−0.133193	−	0.991090i	$-0.542523\pi$
$223$	11.4721	−	8.33499i	0.768231	−	0.558153i	0.901424	+	0.432938i	$0.142523\pi$
$224$	−22.3607			−1.49404
$225$		0			0
$226$	2.67376			0.177856
$227$	−16.1803	+	11.7557i	−1.07393	+	0.780254i	−0.976614	−	0.215000i	$-0.931025\pi$
$227$	−16.1803	+	11.7557i	−1.07393	+	0.780254i	−0.0973129	+	0.995254i	$0.531025\pi$
$228$		0			0
$229$	−7.71885	+	23.7562i	−0.510076	+	1.56985i	0.281991	+	0.959417i	$0.409005\pi$
$229$	−7.71885	+	23.7562i	−0.510076	+	1.56985i	−0.792067	+	0.610435i	$0.790995\pi$
$230$	10.0000			0.659380
$231$		0			0
$232$	−13.1459			−0.863070
$233$	−4.51722	−	13.9026i	−0.295933	−	0.910788i	−0.982906	−	0.184106i	$-0.941061\pi$
$233$	−4.51722	−	13.9026i	−0.295933	−	0.910788i	0.686973	−	0.726682i	$-0.258939\pi$
$234$		0			0
$235$	−11.7082			−0.763759
$236$	3.23607	−	2.35114i	0.210650	−	0.153046i
$237$		0			0
$238$	10.3262	+	7.50245i	0.669351	+	0.486312i
$239$	−5.70820	+	4.14725i	−0.369233	+	0.268263i	−0.756893	−	0.653539i	$-0.773284\pi$
$239$	−5.70820	+	4.14725i	−0.369233	+	0.268263i	0.387660	+	0.921803i	$0.373284\pi$
$240$		0			0
$241$	0.836881	+	0.608030i	0.0539082	+	0.0391666i	0.614413	−	0.788985i	$-0.289393\pi$
$241$	0.836881	+	0.608030i	0.0539082	+	0.0391666i	−0.560505	+	0.828151i	$0.689393\pi$
$242$	0.163119	+	0.502029i	0.0104857	+	0.0322716i
$243$		0			0
$244$	0.190983	+	0.587785i	0.0122264	+	0.0376291i
$245$	−8.98278	−	27.6462i	−0.573889	−	1.76625i
$246$		0			0
$247$	−3.38197	+	10.4086i	−0.215189	+	0.662285i
$248$	−17.5623	+	12.7598i	−1.11521	+	0.810246i
$249$		0			0
$250$	11.1803			0.707107
$251$	26.9443			1.70071			0.850354	−	0.526212i	$-0.176388\pi$
$251$	26.9443			1.70071			0.850354	+	0.526212i	$0.176388\pi$
$252$		0			0
$253$	−4.47214	+	13.7638i	−0.281161	+	0.865324i
$254$	−3.00000	+	9.23305i	−0.188237	+	0.579333i
$255$		0			0
$256$	−5.25329	−	16.1680i	−0.328331	−	1.01050i
$257$	12.7984			0.798341			0.399170	−	0.916877i	$-0.369298\pi$
$257$	12.7984			0.798341			0.399170	+	0.916877i	$0.369298\pi$
$258$		0			0
$259$	−29.2705	−	21.2663i	−1.81878	−	1.32142i
$260$	−6.11803	−	4.44501i	−0.379424	−	0.275668i
$261$		0			0
$262$	−11.4721	−	8.33499i	−0.708751	−	0.514938i
$263$	9.61803	+	6.98791i	0.593073	+	0.430893i	0.843414	−	0.537265i	$-0.180542\pi$
$263$	9.61803	+	6.98791i	0.593073	+	0.430893i	−0.250340	+	0.968158i	$0.580542\pi$
$264$		0			0
$265$	3.09017			0.189828
$266$	−11.7082	−	8.50651i	−0.717876	−	0.521567i
$267$		0			0
$268$	−5.23607			−0.319844
$269$	0.0450850	+	0.138757i	0.00274888	+	0.00846018i	0.952422	−	0.304784i	$-0.0985842\pi$
$269$	0.0450850	+	0.138757i	0.00274888	+	0.00846018i	−0.949673	+	0.313244i	$0.898584\pi$
$270$		0			0
$271$	6.85410	−	21.0948i	0.416357	−	1.28142i	−0.494674	−	0.869078i	$-0.664713\pi$
$271$	6.85410	−	21.0948i	0.416357	−	1.28142i	0.911031	−	0.412337i	$-0.135287\pi$
$272$	−0.881966	+	2.71441i	−0.0534770	+	0.164585i
$273$		0			0
$274$	−5.38197			−0.325136
$275$	−5.00000	+	15.3884i	−0.301511	+	0.927957i
$276$		0			0
$277$	4.69098	−	3.40820i	0.281854	−	0.204779i	−0.437872	−	0.899037i	$-0.644268\pi$
$277$	4.69098	−	3.40820i	0.281854	−	0.204779i	0.719726	+	0.694259i	$0.244268\pi$
$278$	1.56231	−	4.80828i	0.0937009	−	0.288382i
$279$		0			0
$280$	24.2705	−	17.6336i	1.45044	−	1.05381i
$281$	5.37132	+	16.5312i	0.320426	+	0.986171i	0.973463	+	0.228844i	$0.0734947\pi$
$281$	5.37132	+	16.5312i	0.320426	+	0.986171i	−0.653037	+	0.757326i	$0.726505\pi$
$282$		0			0
$283$	0.0901699	+	0.277515i	0.00536005	+	0.0164965i	0.953701	−	0.300757i	$-0.0972393\pi$
$283$	0.0901699	+	0.277515i	0.00536005	+	0.0164965i	−0.948341	+	0.317254i	$0.897239\pi$
$284$	0.618034	+	0.449028i	0.0366736	+	0.0266449i
$285$		0			0
$286$	−8.85410	+	6.43288i	−0.523554	+	0.380384i
$287$	−5.00000	−	3.63271i	−0.295141	−	0.214432i
$288$		0			0
$289$	7.16312	−	5.20431i	0.421360	−	0.306136i
$290$	7.92705	−	5.75934i	0.465492	−	0.338200i
$291$		0			0
$292$	−0.954915	−	2.93893i	−0.0558822	−	0.171988i
$293$	−3.79837			−0.221903			−0.110952	−	0.993826i	$-0.535390\pi$
$293$	−3.79837			−0.221903			−0.110952	+	0.993826i	$0.535390\pi$
$294$		0			0
$295$	−2.76393	+	8.50651i	−0.160922	+	0.495268i
$296$	7.50000	−	23.0826i	0.435929	−	1.34165i
$297$		0			0
$298$	9.82624	−	7.13918i	0.569219	−	0.413562i
$299$	15.1246			0.874679
$300$		0			0
$301$	−25.5279			−1.47140
$302$	13.3262	−	9.68208i	0.766839	−	0.557141i
$303$		0			0
$304$	1.00000	−	3.07768i	0.0573539	−	0.176517i
$305$	−1.11803	−	0.812299i	−0.0640184	−	0.0465121i
$306$		0			0
$307$	1.34752			0.0769073			0.0384536	−	0.999260i	$-0.487757\pi$
$307$	1.34752			0.0769073			0.0384536	+	0.999260i	$0.487757\pi$
$308$	4.47214	+	13.7638i	0.254824	+	0.784266i
$309$		0			0
$310$	5.00000	−	15.3884i	0.283981	−	0.874003i
$311$	3.47214	−	2.52265i	0.196887	−	0.143047i	−0.484974	−	0.874529i	$-0.661171\pi$
$311$	3.47214	−	2.52265i	0.196887	−	0.143047i	0.681861	+	0.731482i	$0.261171\pi$
$312$		0			0
$313$	−6.85410	−	4.97980i	−0.387417	−	0.281475i	0.376979	−	0.926222i	$-0.376963\pi$
$313$	−6.85410	−	4.97980i	−0.387417	−	0.281475i	−0.764396	+	0.644747i	$0.776963\pi$
$314$	−11.1631	+	8.11048i	−0.629971	+	0.457701i
$315$		0			0
$316$		0			0
$317$	7.67376	+	23.6174i	0.431001	+	1.32649i	0.897129	+	0.441768i	$0.145649\pi$
$317$	7.67376	+	23.6174i	0.431001	+	1.32649i	−0.466128	+	0.884717i	$0.654351\pi$
$318$		0			0
$319$	4.38197	+	13.4863i	0.245343	+	0.755088i
$320$	12.6631	+	9.20029i	0.707890	+	0.514312i
$321$		0			0
$322$	−6.18034	+	19.0211i	−0.344417	+	1.06001i
$323$	7.47214	−	5.42882i	0.415761	−	0.302068i
$324$		0			0
$325$	16.9098			0.937989
$326$	−2.94427			−0.163068
$327$		0			0
$328$	1.28115	−	3.94298i	0.0707398	−	0.217715i
$329$	7.23607	−	22.2703i	0.398937	−	1.22780i
$330$		0			0
$331$	3.38197	+	10.4086i	0.185890	+	0.572110i	0.999963	−	0.00865315i	$-0.00275442\pi$
$331$	3.38197	+	10.4086i	0.185890	+	0.572110i	−0.814073	+	0.580763i	$0.802754\pi$
$332$	3.52786			0.193617
$333$		0			0
$334$	18.9443	+	13.7638i	1.03658	+	0.753123i
$335$	9.47214	−	6.88191i	0.517518	−	0.375999i
$336$		0			0
$337$	12.0902	+	8.78402i	0.658594	+	0.478496i	0.866188	−	0.499719i	$-0.166563\pi$
$337$	12.0902	+	8.78402i	0.658594	+	0.478496i	−0.207594	+	0.978215i	$0.566563\pi$
$338$	−1.26393	−	0.918300i	−0.0687488	−	0.0499490i
$339$		0			0
$340$	1.97214	+	6.06961i	0.106954	+	0.329171i
$341$	18.9443	+	13.7638i	1.02589	+	0.745353i
$342$		0			0
$343$	26.8328			1.44884
$344$	−5.29180	−	16.2865i	−0.285315	−	0.878108i
$345$		0			0
$346$	3.06231	−	9.42481i	0.164631	−	0.506681i
$347$	10.4164	−	32.0584i	0.559182	−	1.72099i	−0.125453	−	0.992100i	$-0.540038\pi$
$347$	10.4164	−	32.0584i	0.559182	−	1.72099i	0.684635	−	0.728886i	$-0.259962\pi$
$348$		0			0
$349$	25.0344			1.34006			0.670031	−	0.742333i	$-0.266281\pi$
$349$	25.0344			1.34006			0.670031	+	0.742333i	$0.266281\pi$
$350$	−6.90983	+	21.2663i	−0.369346	+	1.13673i
$351$		0			0
$352$	−13.0902	+	9.51057i	−0.697708	+	0.506915i
$353$	9.38197	−	28.8747i	0.499352	−	1.53685i	−0.310712	−	0.950504i	$-0.600567\pi$
$353$	9.38197	−	28.8747i	0.499352	−	1.53685i	0.810063	−	0.586342i	$-0.199433\pi$
$354$		0			0
$355$	−1.70820			−0.0906621
$356$	2.35410	+	7.24518i	0.124767	+	0.383994i
$357$		0			0
$358$	1.90983	+	5.87785i	0.100938	+	0.310654i
$359$	−8.56231	−	6.22088i	−0.451901	−	0.328325i	0.338445	−	0.940986i	$-0.390099\pi$
$359$	−8.56231	−	6.22088i	−0.451901	−	0.328325i	−0.790346	+	0.612661i	$0.790099\pi$
$360$		0			0
$361$	6.89919	−	5.01255i	0.363115	−	0.263819i
$362$	−7.92705	−	5.75934i	−0.416637	−	0.302704i
$363$		0			0
$364$	12.2361	−	8.89002i	0.641344	−	0.465964i
$365$	5.59017	+	4.06150i	0.292603	+	0.212588i
$366$		0			0
$367$	−1.85410	−	5.70634i	−0.0967833	−	0.297868i	0.890931	−	0.454139i	$-0.150053\pi$
$367$	−1.85410	−	5.70634i	−0.0967833	−	0.297868i	−0.987714	+	0.156270i	$0.950053\pi$
$368$	−4.47214			−0.233126
$369$		0			0
$370$	5.59017	+	17.2048i	0.290619	+	0.894434i
$371$	−1.90983	+	5.87785i	−0.0991534	+	0.305163i
$372$		0			0
$373$	−23.7984	+	17.2905i	−1.23223	+	0.895270i	−0.997056	−	0.0766827i	$-0.975567\pi$
$373$	−23.7984	+	17.2905i	−1.23223	+	0.895270i	−0.235178	+	0.971952i	$0.575567\pi$
$374$	9.23607			0.477586
$375$		0			0
$376$	15.7082			0.810089
$377$	11.9894	−	8.71078i	0.617483	−	0.448628i
$378$		0			0
$379$	7.23607	−	22.2703i	0.371692	−	1.14395i	−0.573992	−	0.818861i	$-0.694606\pi$
$379$	7.23607	−	22.2703i	0.371692	−	1.14395i	0.945684	−	0.325089i	$-0.105394\pi$
$380$	−2.23607	−	6.88191i	−0.114708	−	0.353035i
$381$		0			0
$382$	−24.6525			−1.26133
$383$	−6.43769	−	19.8132i	−0.328951	−	1.01241i	−0.969626	−	0.244594i	$-0.921345\pi$
$383$	−6.43769	−	19.8132i	−0.328951	−	1.01241i	0.640675	−	0.767812i	$-0.278655\pi$
$384$		0			0
$385$	−26.1803	−	19.0211i	−1.33427	−	0.969407i
$386$	6.20820	−	4.51052i	0.315989	−	0.229580i
$387$		0			0
$388$	7.16312	+	5.20431i	0.363652	+	0.264209i
$389$	−30.0066	+	21.8011i	−1.52139	+	1.10536i	−0.560603	+	0.828085i	$0.689430\pi$
$389$	−30.0066	+	21.8011i	−1.52139	+	1.10536i	−0.960791	+	0.277272i	$0.910570\pi$
$390$		0			0
$391$	−10.3262	−	7.50245i	−0.522220	−	0.379415i
$392$	12.0517	+	37.0912i	0.608701	+	1.87339i
$393$		0			0
$394$	1.66312	+	5.11855i	0.0837867	+	0.257869i
$395$		0			0
$396$		0			0
$397$	3.38197	−	10.4086i	0.169736	−	0.522394i	−0.829618	−	0.558331i	$-0.811442\pi$
$397$	3.38197	−	10.4086i	0.169736	−	0.522394i	0.999354	+	0.0359377i	$0.0114418\pi$
$398$	−15.0902	+	10.9637i	−0.756402	+	0.549558i
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−33.4508			−1.67046			−0.835228	−	0.549904i	$-0.814664\pi$
$401$	−33.4508			−1.67046			−0.835228	+	0.549904i	$0.814664\pi$
$402$		0			0
$403$	7.56231	−	23.2744i	0.376705	−	1.15938i
$404$	−5.11803	+	15.7517i	−0.254632	+	0.783676i
$405$		0			0
$406$	6.05573	+	18.6376i	0.300541	+	0.924969i
$407$	−26.1803			−1.29771
$408$		0			0
$409$	−20.8713	−	15.1639i	−1.03202	−	0.749807i	−0.0633084	−	0.997994i	$-0.520165\pi$
$409$	−20.8713	−	15.1639i	−1.03202	−	0.749807i	−0.968712	+	0.248187i	$0.920165\pi$
$410$	0.954915	+	2.93893i	0.0471599	+	0.145143i
$411$		0			0
$412$	−1.00000	−	0.726543i	−0.0492665	−	0.0357942i
$413$	−14.4721	−	10.5146i	−0.712127	−	0.517391i
$414$		0			0
$415$	−6.38197	+	4.63677i	−0.313278	+	0.227610i
$416$	13.6803	+	9.93935i	0.670734	+	0.487317i
$417$		0			0
$418$	−10.4721			−0.512209
$419$	−10.1803	−	31.3319i	−0.497342	−	1.53066i	−0.813275	−	0.581880i	$-0.802317\pi$
$419$	−10.1803	−	31.3319i	−0.497342	−	1.53066i	0.315932	−	0.948782i	$-0.397683\pi$
$420$		0			0
$421$	7.15248	−	22.0131i	0.348590	−	1.07285i	−0.611043	−	0.791597i	$-0.709250\pi$
$421$	7.15248	−	22.0131i	0.348590	−	1.07285i	0.959634	−	0.281253i	$-0.0907502\pi$
$422$	5.52786	−	17.0130i	0.269092	−	0.828181i
$423$		0			0
$424$	−4.14590			−0.201343
$425$	−11.5451	−	8.38800i	−0.560019	−	0.406878i
$426$		0			0
$427$	2.23607	−	1.62460i	0.108211	−	0.0786198i
$428$	5.09017	−	15.6659i	0.246043	−	0.757241i
$429$		0			0
$430$	10.3262	+	7.50245i	0.497975	+	0.361800i
$431$	3.29180	+	10.1311i	0.158560	+	0.487998i	0.998504	−	0.0546749i	$-0.0174122\pi$
$431$	3.29180	+	10.1311i	0.158560	+	0.487998i	−0.839944	+	0.542673i	$0.817412\pi$
$432$		0			0
$433$	7.71885	+	23.7562i	0.370944	+	1.14165i	0.946174	+	0.323657i	$0.104912\pi$
$433$	7.71885	+	23.7562i	0.370944	+	1.14165i	−0.575230	+	0.817991i	$0.695088\pi$
$434$	26.1803	+	19.0211i	1.25670	+	0.913043i
$435$		0			0
$436$	−15.4443	+	11.2209i	−0.739646	+	0.537385i
$437$	11.7082	+	8.50651i	0.560079	+	0.406921i
$438$		0			0
$439$	5.00000	−	3.63271i	0.238637	−	0.173380i	−0.462039	−	0.886860i	$-0.652882\pi$
$439$	5.00000	−	3.63271i	0.238637	−	0.173380i	0.700676	+	0.713480i	$0.252882\pi$
$440$	6.70820	−	20.6457i	0.319801	−	0.984247i
$441$		0			0
$442$	−2.98278	−	9.18005i	−0.141876	−	0.436650i
$443$	30.7639			1.46164			0.730819	−	0.682571i	$-0.239138\pi$
$443$	30.7639			1.46164			0.730819	+	0.682571i	$0.239138\pi$
$444$		0			0
$445$	−13.7812	−	10.0126i	−0.653289	−	0.474642i
$446$	4.38197	−	13.4863i	0.207492	−	0.638595i
$447$		0			0
$448$	−25.3262	+	18.4006i	−1.19655	+	0.869346i
$449$	7.79837			0.368028			0.184014	−	0.982924i	$-0.441091\pi$
$449$	7.79837			0.368028			0.184014	+	0.982924i	$0.441091\pi$
$450$		0			0
$451$	−4.47214			−0.210585
$452$	−2.16312	+	1.57160i	−0.101745	+	0.0739217i
$453$		0			0
$454$	−6.18034	+	19.0211i	−0.290058	+	0.892706i
$455$	−10.4508	+	32.1644i	−0.489943	+	1.50789i
$456$		0			0
$457$	22.3607			1.04599			0.522994	−	0.852336i	$-0.324815\pi$
$457$	22.3607			1.04599			0.522994	+	0.852336i	$0.324815\pi$
$458$	7.71885	+	23.7562i	0.360678	+	1.11005i
$459$		0			0
$460$	−8.09017	+	5.87785i	−0.377206	+	0.274056i
$461$	−6.63525	+	4.82079i	−0.309035	+	0.224527i	−0.731482	−	0.681861i	$-0.761171\pi$
$461$	−6.63525	+	4.82079i	−0.309035	+	0.224527i	0.422448	+	0.906387i	$0.361171\pi$
$462$		0			0
$463$	−18.7984	−	13.6578i	−0.873635	−	0.634733i	0.0579252	−	0.998321i	$-0.481552\pi$
$463$	−18.7984	−	13.6578i	−0.873635	−	0.634733i	−0.931560	+	0.363588i	$0.881552\pi$
$464$	−3.54508	+	2.57565i	−0.164576	+	0.119572i
$465$		0			0
$466$	−11.8262	−	8.59226i	−0.547840	−	0.398029i
$467$	−1.79837	−	5.53483i	−0.0832188	−	0.256121i	0.900786	−	0.434263i	$-0.142991\pi$
$467$	−1.79837	−	5.53483i	−0.0832188	−	0.256121i	−0.984005	+	0.178142i	$0.942991\pi$
$468$		0			0
$469$	7.23607	+	22.2703i	0.334131	+	1.02835i
$470$	−9.47214	+	6.88191i	−0.436917	+	0.317439i
$471$		0			0
$472$	3.70820	−	11.4127i	0.170684	−	0.525311i
$473$	−14.9443	+	10.8576i	−0.687138	+	0.499235i
$474$		0			0
$475$	13.0902	+	9.51057i	0.600618	+	0.436375i
$476$	−12.7639			−0.585034
$477$		0			0
$478$	−2.18034	+	6.71040i	−0.0997264	+	0.306926i
$479$	−0.326238	+	1.00406i	−0.0149062	+	0.0458765i	−0.958233	−	0.285989i	$-0.907678\pi$
$479$	−0.326238	+	1.00406i	−0.0149062	+	0.0458765i	0.943327	+	0.331865i	$0.107678\pi$
$480$		0			0
$481$	8.45492	+	26.0216i	0.385511	+	1.18648i
$482$	1.03444			0.0471175
$483$		0			0
$484$	−0.427051	−	0.310271i	−0.0194114	−	0.0141032i
$485$	−19.7984			−0.898998
$486$		0			0
$487$	3.00000	+	2.17963i	0.135943	+	0.0987684i	0.653679	−	0.756772i	$-0.273225\pi$
$487$	3.00000	+	2.17963i	0.135943	+	0.0987684i	−0.517736	+	0.855541i	$0.673225\pi$
$488$	1.50000	+	1.08981i	0.0679018	+	0.0493336i
$489$		0			0
$490$	−23.5172	−	17.0863i	−1.06240	−	0.771879i
$491$	−24.1803	−	17.5680i	−1.09124	−	0.792835i	−0.111635	−	0.993749i	$-0.535609\pi$
$491$	−24.1803	−	17.5680i	−1.09124	−	0.792835i	−0.979609	+	0.200915i	$0.935609\pi$
$492$		0			0
$493$	−12.5066			−0.563268
$494$	3.38197	+	10.4086i	0.152162	+	0.468306i
$495$		0			0
$496$	−2.23607	+	6.88191i	−0.100402	+	0.309007i
$497$	1.05573	−	3.24920i	0.0473559	−	0.145746i
$498$		0			0
$499$	−6.00000			−0.268597			−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000			−0.268597			−0.134298	+	0.990941i	$0.542878\pi$
$500$	−9.04508	+	6.57164i	−0.404508	+	0.293893i
$501$		0			0
$502$	21.7984	−	15.8374i	0.972909	−	0.706860i
$503$	−10.9443	+	33.6830i	−0.487981	+	1.50185i	0.339636	+	0.940557i	$0.389696\pi$
$503$	−10.9443	+	33.6830i	−0.487981	+	1.50185i	−0.827617	+	0.561294i	$0.810304\pi$
$504$		0			0
$505$	−11.4443	−	35.2218i	−0.509263	−	1.56735i
$506$	4.47214	+	13.7638i	0.198811	+	0.611876i
$507$		0			0
$508$	−3.00000	−	9.23305i	−0.133103	−	0.409650i
$509$	21.7254	+	15.7844i	0.962963	+	0.699633i	0.953837	−	0.300325i	$-0.0970952\pi$
$509$	21.7254	+	15.7844i	0.962963	+	0.699633i	0.00912564	+	0.999958i	$0.497095\pi$
$510$		0			0
$511$	−11.1803	+	8.12299i	−0.494589	+	0.359340i
$512$	−8.89919	−	6.46564i	−0.393292	−	0.285744i
$513$		0			0
$514$	10.3541	−	7.52270i	0.456700	−	0.331812i
$515$	2.76393			0.121793
$516$		0			0
$517$	−5.23607	−	16.1150i	−0.230282	−	0.708735i
$518$	−36.1803			−1.58967
$519$		0			0
$520$	−22.6869			−0.994887
$521$	−0.628677	+	1.93487i	−0.0275428	+	0.0847682i	−0.963883	−	0.266326i	$-0.914190\pi$
$521$	−0.628677	+	1.93487i	−0.0275428	+	0.0847682i	0.936340	+	0.351094i	$0.114190\pi$
$522$		0			0
$523$	9.94427	−	7.22494i	0.434833	−	0.315924i	−0.348746	−	0.937217i	$-0.613392\pi$
$523$	9.94427	−	7.22494i	0.434833	−	0.315924i	0.783578	+	0.621293i	$0.213392\pi$
$524$	14.1803			0.619471
$525$		0			0
$526$	11.8885			0.518365
$527$	−16.7082	+	12.1392i	−0.727821	+	0.528793i
$528$		0			0
$529$	−0.927051	+	2.85317i	−0.0403066	+	0.124051i
$530$	2.50000	−	1.81636i	0.108593	−	0.0788975i
$531$		0			0
$532$	14.4721			0.627447
$533$	1.44427	+	4.44501i	0.0625584	+	0.192535i
$534$		0			0
$535$	11.3820	+	35.0301i	0.492085	+	1.51448i
$536$	−12.7082	+	9.23305i	−0.548911	+	0.398807i
$537$		0			0
$538$	0.118034	+	0.0857567i	0.00508881	+	0.00369723i
$539$	34.0344	−	24.7275i	1.46597	−	1.06509i
$540$		0			0
$541$	28.5795	+	20.7642i	1.22873	+	0.892724i	0.996794	−	0.0800067i	$-0.0254942\pi$
$541$	28.5795	+	20.7642i	1.22873	+	0.892724i	0.231936	+	0.972731i	$0.425494\pi$
$542$	−6.85410	−	21.0948i	−0.294409	−	0.906097i
$543$		0			0
$544$	−4.40983	−	13.5721i	−0.189070	−	0.581897i
$545$	13.1910	−	40.5977i	0.565040	−	1.73901i
$546$		0			0
$547$	−0.729490	+	2.24514i	−0.0311907	+	0.0959952i	−0.965440	−	0.260626i	$-0.916071\pi$
$547$	−0.729490	+	2.24514i	−0.0311907	+	0.0959952i	0.934249	+	0.356621i	$0.116071\pi$
$548$	4.35410	−	3.16344i	0.185998	−	0.135135i
$549$		0			0
$550$	5.00000	+	15.3884i	0.213201	+	0.656164i
$551$	14.1803			0.604103
$552$		0			0
$553$		0			0
$554$	1.79180	−	5.51458i	0.0761261	−	0.234292i
$555$		0			0
$556$	1.56231	+	4.80828i	0.0662565	+	0.203917i
$557$	−22.2705			−0.943632			−0.471816	−	0.881697i	$-0.656401\pi$
$557$	−22.2705			−0.943632			−0.471816	+	0.881697i	$0.656401\pi$
$558$		0			0
$559$	15.6180	+	11.3472i	0.660572	+	0.479934i
$560$	3.09017	−	9.51057i	0.130584	−	0.401895i
$561$		0			0
$562$	14.0623	+	10.2169i	0.593183	+	0.430972i
$563$	−14.1803	−	10.3026i	−0.597630	−	0.434204i	0.247407	−	0.968912i	$-0.420422\pi$
$563$	−14.1803	−	10.3026i	−0.597630	−	0.434204i	−0.845037	+	0.534708i	$0.820422\pi$
$564$		0			0
$565$	1.84752	−	5.68609i	0.0777259	−	0.239216i
$566$	0.236068	+	0.171513i	0.00992268	+	0.00720925i
$567$		0			0
$568$	2.29180			0.0961616
$569$	9.35410	+	28.7890i	0.392144	+	1.20690i	0.931163	+	0.364603i	$0.118795\pi$
$569$	9.35410	+	28.7890i	0.392144	+	1.20690i	−0.539019	+	0.842294i	$0.681205\pi$
$570$		0			0
$571$	−6.56231	+	20.1967i	−0.274624	+	0.845206i	0.714695	+	0.699437i	$0.246566\pi$
$571$	−6.56231	+	20.1967i	−0.274624	+	0.845206i	−0.989319	+	0.145769i	$0.953434\pi$
$572$	3.38197	−	10.4086i	0.141407	−	0.435206i
$573$		0			0
$574$	−6.18034			−0.257962
$575$	6.90983	−	21.2663i	0.288160	−	0.886865i
$576$		0			0
$577$	25.0344	−	18.1886i	1.04220	−	0.757201i	0.0714842	−	0.997442i	$-0.477226\pi$
$577$	25.0344	−	18.1886i	1.04220	−	0.757201i	0.970713	+	0.240241i	$0.0772265\pi$
$578$	2.73607	−	8.42075i	0.113805	−	0.350257i
$579$		0			0
$580$	−3.02786	+	9.31881i	−0.125725	+	0.386942i
$581$	−4.87539	−	15.0049i	−0.202265	−	0.622508i
$582$		0			0
$583$	1.38197	+	4.25325i	0.0572352	+	0.176152i
$584$	−7.50000	−	5.44907i	−0.310352	−	0.225484i
$585$		0			0
$586$	−3.07295	+	2.23263i	−0.126942	+	0.0922290i
$587$	−11.7984	−	8.57202i	−0.486971	−	0.353805i	0.317047	−	0.948410i	$-0.397309\pi$
$587$	−11.7984	−	8.57202i	−0.486971	−	0.353805i	−0.804018	+	0.594605i	$0.797309\pi$
$588$		0			0
$589$	18.9443	−	13.7638i	0.780585	−	0.567128i
$590$	2.76393	+	8.50651i	0.113789	+	0.350207i
$591$		0			0
$592$	−2.50000	−	7.69421i	−0.102749	−	0.316230i
$593$	32.7426			1.34458			0.672290	−	0.740288i	$-0.265311\pi$
$593$	32.7426			1.34458			0.672290	+	0.740288i	$0.265311\pi$
$594$		0			0
$595$	23.0902	−	16.7760i	0.946605	−	0.687749i
$596$	−3.75329	+	11.5514i	−0.153741	+	0.473165i
$597$		0			0
$598$	12.2361	−	8.89002i	0.500370	−	0.363540i
$599$	12.4721			0.509598			0.254799	−	0.966994i	$-0.417991\pi$
$599$	12.4721			0.509598			0.254799	+	0.966994i	$0.417991\pi$
$600$		0			0
$601$	−24.3262			−0.992288			−0.496144	−	0.868240i	$-0.665251\pi$
$601$	−24.3262			−0.992288			−0.496144	+	0.868240i	$0.665251\pi$
$602$	−20.6525	+	15.0049i	−0.841732	+	0.611554i
$603$		0			0
$604$	−5.09017	+	15.6659i	−0.207116	+	0.637438i
$605$	1.18034			0.0479876
$606$		0			0
$607$	−39.2361			−1.59254			−0.796271	−	0.604940i	$-0.793197\pi$
$607$	−39.2361			−1.59254			−0.796271	+	0.604940i	$0.793197\pi$
$608$	5.00000	+	15.3884i	0.202777	+	0.624083i
$609$		0			0
$610$	−1.38197			−0.0559542
$611$	−14.3262	+	10.4086i	−0.579578	+	0.421088i
$612$		0			0
$613$	−31.9615	−	23.2214i	−1.29091	−	0.937903i	−0.291089	−	0.956696i	$-0.594018\pi$
$613$	−31.9615	−	23.2214i	−1.29091	−	0.937903i	−0.999823	+	0.0187931i	$0.994018\pi$
$614$	1.09017	−	0.792055i	0.0439957	−	0.0319647i
$615$		0			0
$616$	35.1246	+	25.5195i	1.41521	+	1.02821i
$617$	−8.33688	−	25.6583i	−0.335630	−	1.03296i	−0.966411	−	0.257002i	$-0.917265\pi$
$617$	−8.33688	−	25.6583i	−0.335630	−	1.03296i	0.630781	−	0.775961i	$-0.282735\pi$
$618$		0			0
$619$	8.76393	+	26.9726i	0.352252	+	1.08412i	0.957586	+	0.288149i	$0.0930398\pi$
$619$	8.76393	+	26.9726i	0.352252	+	1.08412i	−0.605333	+	0.795972i	$0.706960\pi$
$620$	5.00000	+	15.3884i	0.200805	+	0.618014i
$621$		0			0
$622$	1.32624	−	4.08174i	0.0531773	−	0.163663i
$623$	27.5623	−	20.0252i	1.10426	−	0.802292i
$624$		0			0
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	−8.47214			−0.338615
$627$		0			0
$628$	4.26393	−	13.1230i	0.170149	−	0.523666i
$629$	7.13525	−	21.9601i	0.284501	−	0.875605i
$630$		0			0
$631$	3.18034	+	9.78808i	0.126607	+	0.389657i	0.994190	−	0.107635i	$-0.0343277\pi$
$631$	3.18034	+	9.78808i	0.126607	+	0.389657i	−0.867583	+	0.497292i	$0.834328\pi$
$632$		0			0
$633$		0			0
$634$	20.0902	+	14.5964i	0.797883	+	0.579696i
$635$	17.5623	+	12.7598i	0.696939	+	0.506356i
$636$		0			0
$637$	−35.5689	−	25.8423i	−1.40929	−	1.02391i
$638$	11.4721	+	8.33499i	0.454186	+	0.329986i
$639$		0			0
$640$	−6.70820			−0.265165
$641$	31.5066	+	22.8909i	1.24444	+	0.904135i	0.997886	−	0.0649953i	$-0.0207032\pi$
$641$	31.5066	+	22.8909i	1.24444	+	0.904135i	0.246549	+	0.969130i	$0.420703\pi$
$642$		0			0
$643$	13.8885			0.547711			0.273855	−	0.961771i	$-0.411701\pi$
$643$	13.8885			0.547711			0.273855	+	0.961771i	$0.411701\pi$
$644$	−6.18034	−	19.0211i	−0.243540	−	0.749538i
$645$		0			0
$646$	2.85410	−	8.78402i	0.112293	−	0.345603i
$647$	−3.20163	+	9.85359i	−0.125869	+	0.387385i	−0.994058	−	0.108848i	$-0.965284\pi$
$647$	−3.20163	+	9.85359i	−0.125869	+	0.387385i	0.868189	+	0.496233i	$0.165284\pi$
$648$		0			0
$649$	−12.9443			−0.508107
$650$	13.6803	−	9.93935i	0.536587	−	0.389853i
$651$		0			0
$652$	2.38197	−	1.73060i	0.0932850	−	0.0677755i
$653$	−13.9377	+	42.8958i	−0.545424	+	1.67864i	0.174555	+	0.984647i	$0.444151\pi$
$653$	−13.9377	+	42.8958i	−0.545424	+	1.67864i	−0.719979	+	0.693995i	$0.755849\pi$
$654$		0			0
$655$	−25.6525	+	18.6376i	−1.00233	+	0.728232i
$656$	−0.427051	−	1.31433i	−0.0166735	−	0.0513159i
$657$		0			0
$658$	−7.23607	−	22.2703i	−0.282091	−	0.868188i
$659$	−5.32624	−	3.86974i	−0.207481	−	0.150744i	0.479192	−	0.877710i	$-0.340930\pi$
$659$	−5.32624	−	3.86974i	−0.207481	−	0.150744i	−0.686673	+	0.726966i	$0.740930\pi$
$660$		0			0
$661$	−20.5623	+	14.9394i	−0.799781	+	0.581075i	−0.910850	−	0.412738i	$-0.864573\pi$
$661$	−20.5623	+	14.9394i	−0.799781	+	0.581075i	0.111069	+	0.993813i	$0.464573\pi$
$662$	8.85410	+	6.43288i	0.344124	+	0.250021i
$663$		0			0
$664$	8.56231	−	6.22088i	0.332282	−	0.241417i
$665$	−26.1803	+	19.0211i	−1.01523	+	0.737608i
$666$		0			0
$667$	−6.05573	−	18.6376i	−0.234479	−	0.721651i
$668$	−23.4164			−0.906008
$669$		0			0
$670$	3.61803	−	11.1352i	0.139777	−	0.430189i
$671$	0.618034	−	1.90211i	0.0238589	−	0.0734303i
$672$		0			0
$673$	−24.1074	+	17.5150i	−0.929272	+	0.675155i	−0.945814	−	0.324708i	$-0.894734\pi$
$673$	−24.1074	+	17.5150i	−0.929272	+	0.675155i	0.0165428	+	0.999863i	$0.494734\pi$
$674$	14.9443			0.575632
$675$		0			0
$676$	1.56231			0.0600887
$677$	30.2705	−	21.9928i	1.16339	−	0.845252i	0.173187	−	0.984889i	$-0.444593\pi$
$677$	30.2705	−	21.9928i	1.16339	−	0.845252i	0.990203	+	0.139636i	$0.0445934\pi$
$678$		0			0
$679$	12.2361	−	37.6587i	0.469577	−	1.44521i
$680$	15.4894	+	11.2537i	0.593990	+	0.431559i
$681$		0			0
$682$	23.4164			0.896661
$683$	−2.29180	−	7.05342i	−0.0876931	−	0.269892i	0.897588	−	0.440836i	$-0.145318\pi$
$683$	−2.29180	−	7.05342i	−0.0876931	−	0.269892i	−0.985281	+	0.170945i	$0.945318\pi$
$684$		0			0
$685$	−3.71885	+	11.4454i	−0.142090	+	0.437308i
$686$	21.7082	−	15.7719i	0.828823	−	0.602175i
$687$		0			0
$688$	−4.61803	−	3.35520i	−0.176061	−	0.127916i
$689$	3.78115	−	2.74717i	0.144050	−	0.104659i
$690$		0			0
$691$	17.1803	+	12.4822i	0.653571	+	0.474847i	0.864486	−	0.502657i	$-0.167644\pi$
$691$	17.1803	+	12.4822i	0.653571	+	0.474847i	−0.210915	+	0.977504i	$0.567644\pi$
$692$	3.06231	+	9.42481i	0.116411	+	0.358277i
$693$		0			0
$694$	−10.4164	−	32.0584i	−0.395401	−	1.21692i
$695$	−9.14590	−	6.64488i	−0.346924	−	0.252055i
$696$		0			0
$697$	1.21885	−	3.75123i	0.0461671	−	0.142088i
$698$	20.2533	−	14.7149i	0.766598	−	0.556966i
$699$		0			0
$700$	−6.90983	−	21.2663i	−0.261167	−	0.803789i
$701$	−0.437694			−0.0165315			−0.00826574	−	0.999966i	$-0.502631\pi$
$701$	−0.437694			−0.0165315			−0.00826574	+	0.999966i	$0.502631\pi$
$702$		0			0
$703$	−8.09017	+	24.8990i	−0.305127	+	0.939083i
$704$	−7.00000	+	21.5438i	−0.263822	+	0.811962i
$705$		0			0
$706$	−9.38197	−	28.8747i	−0.353095	−	1.08671i
$707$	74.0689			2.78565
$708$		0			0
$709$	5.44427	+	3.95550i	0.204464	+	0.148552i	0.685305	−	0.728256i	$-0.259669\pi$
$709$	5.44427	+	3.95550i	0.204464	+	0.148552i	−0.480841	+	0.876808i	$0.659669\pi$
$710$	−1.38197	+	1.00406i	−0.0518643	+	0.0376816i
$711$		0			0
$712$	18.4894	+	13.4333i	0.692918	+	0.503434i
$713$	−26.1803	−	19.0211i	−0.980461	−	0.712347i
$714$		0			0
$715$	7.56231	+	23.2744i	0.282814	+	0.870413i
$716$	−5.00000	−	3.63271i	−0.186859	−	0.135761i
$717$		0			0
$718$	−10.5836			−0.394976
$719$	11.0902	+	34.1320i	0.413594	+	1.27291i	0.913503	+	0.406832i	$0.133367\pi$
$719$	11.0902	+	34.1320i	0.413594	+	1.27291i	−0.499909	+	0.866078i	$0.666633\pi$
$720$		0			0
$721$	−1.70820	+	5.25731i	−0.0636168	+	0.195792i
$722$	2.63525	−	8.11048i	0.0980740	−	0.301841i
$723$		0			0
$724$	9.79837			0.364154
$725$	−6.77051	−	20.8375i	−0.251450	−	0.773885i
$726$		0			0
$727$	−12.4164	+	9.02105i	−0.460499	+	0.334572i	−0.793727	−	0.608274i	$-0.791862\pi$
$727$	−12.4164	+	9.02105i	−0.460499	+	0.334572i	0.333228	+	0.942846i	$0.391862\pi$
$728$	14.0213	−	43.1531i	0.519663	−	1.59936i
$729$		0			0
$730$	6.90983			0.255744
$731$	−5.03444	−	15.4944i	−0.186206	−	0.573082i
$732$		0			0
$733$	0.798374	+	2.45714i	0.0294886	+	0.0907566i	0.964718	−	0.263287i	$-0.0848065\pi$
$733$	0.798374	+	2.45714i	0.0294886	+	0.0907566i	−0.935229	+	0.354043i	$0.884807\pi$
$734$	−4.85410	−	3.52671i	−0.179168	−	0.130173i
$735$		0			0
$736$	18.0902	−	13.1433i	0.666813	−	0.484468i
$737$	13.7082	+	9.95959i	0.504948	+	0.366866i
$738$		0			0
$739$	−14.3262	+	10.4086i	−0.526999	+	0.382887i	−0.819234	−	0.573459i	$-0.805601\pi$
$739$	−14.3262	+	10.4086i	−0.526999	+	0.382887i	0.292235	+	0.956347i	$0.405601\pi$
$740$	−14.6353	−	10.6331i	−0.538003	−	0.390882i
$741$		0			0
$742$	1.90983	+	5.87785i	0.0701121	+	0.215783i
$743$	−0.875388			−0.0321149			−0.0160574	−	0.999871i	$-0.505111\pi$
$743$	−0.875388			−0.0321149			−0.0160574	+	0.999871i	$0.505111\pi$
$744$		0			0
$745$	−8.39261	−	25.8298i	−0.307481	−	0.946330i
$746$	−9.09017	+	27.9767i	−0.332815	+	1.02430i
$747$		0			0
$748$	−7.47214	+	5.42882i	−0.273208	+	0.198497i
$749$	−73.6656			−2.69168
$750$		0			0
$751$	5.34752			0.195134			0.0975670	−	0.995229i	$-0.468894\pi$
$751$	5.34752			0.195134			0.0975670	+	0.995229i	$0.468894\pi$
$752$	4.23607	−	3.07768i	0.154474	−	0.112232i
$753$		0			0
$754$	4.57953	−	14.0943i	0.166777	−	0.513285i
$755$	−11.3820	−	35.0301i	−0.414232	−	1.27488i
$756$		0			0
$757$	27.3820			0.995214			0.497607	−	0.867402i	$-0.334212\pi$
$757$	27.3820			0.995214			0.497607	+	0.867402i	$0.334212\pi$
$758$	−7.23607	−	22.2703i	−0.262826	−	0.808895i
$759$		0			0
$760$	−17.5623	−	12.7598i	−0.637052	−	0.462845i
$761$	−7.88197	+	5.72658i	−0.285721	+	0.207588i	−0.721409	−	0.692509i	$-0.756505\pi$
$761$	−7.88197	+	5.72658i	−0.285721	+	0.207588i	0.435688	+	0.900098i	$0.356505\pi$
$762$		0			0
$763$	69.0689	+	50.1815i	2.50046	+	1.81669i
$764$	19.9443	−	14.4904i	0.721558	−	0.524243i
$765$		0			0
$766$	−16.8541	−	12.2452i	−0.608963	−	0.442438i
$767$	4.18034	+	12.8658i	0.150943	+	0.464556i
$768$		0			0
$769$	−1.74265	−	5.36331i	−0.0628414	−	0.193406i	0.914707	−	0.404118i	$-0.132422\pi$
$769$	−1.74265	−	5.36331i	−0.0628414	−	0.193406i	−0.977548	+	0.210712i	$0.932422\pi$
$770$	−32.3607			−1.16620
$771$		0			0
$772$	−2.37132	+	7.29818i	−0.0853458	+	0.262667i
$773$	−29.0623	+	21.1150i	−1.04530	+	0.759454i	−0.971313	−	0.237805i	$-0.923572\pi$
$773$	−29.0623	+	21.1150i	−1.04530	+	0.759454i	−0.0739857	+	0.997259i	$0.523572\pi$
$774$		0			0
$775$	−29.2705	−	21.2663i	−1.05143	−	0.763907i
$776$	26.5623			0.953531
$777$		0			0
$778$	−11.4615	+	35.2748i	−0.410914	+	1.26466i
$779$	−1.38197	+	4.25325i	−0.0495141	+	0.152389i
$780$		0			0
$781$	−0.763932	−	2.35114i	−0.0273356	−	0.0841304i
$782$	−12.7639			−0.456437
$783$		0			0
$784$	10.5172	+	7.64121i	0.375615	+	0.272900i
$785$	9.53444	+	29.3440i	0.340299	+	1.04733i
$786$		0			0
$787$	−6.61803	−	4.80828i	−0.235907	−	0.171397i	0.463551	−	0.886070i	$-0.346575\pi$
$787$	−6.61803	−	4.80828i	−0.235907	−	0.171397i	−0.699458	+	0.714674i	$0.746575\pi$
$788$	−4.35410	−	3.16344i	−0.155108	−	0.112693i
$789$		0			0
$790$		0			0
$791$	9.67376	+	7.02840i	0.343959	+	0.249901i
$792$		0			0
$793$	−2.09017			−0.0742241
$794$	−3.38197	−	10.4086i	−0.120021	−	0.369388i
$795$		0			0
$796$	5.76393	−	17.7396i	0.204297	−	0.628762i
$797$	−11.7746	+	36.2384i	−0.417077	+	1.28363i	0.493303	+	0.869857i	$0.335789\pi$
$797$	−11.7746	+	36.2384i	−0.417077	+	1.28363i	−0.910380	+	0.413773i	$0.864211\pi$
$798$		0			0
$799$	14.9443			0.528690
$800$	20.2254	−	14.6946i	0.715077	−	0.519534i
$801$		0			0
$802$	−27.0623	+	19.6619i	−0.955603	+	0.694286i
$803$	−3.09017	+	9.51057i	−0.109050	+	0.335621i
$804$		0			0
$805$	36.1803	+	26.2866i	1.27519	+	0.926479i
$806$	−7.56231	−	23.2744i	−0.266371	−	0.819805i
$807$		0			0
$808$	15.3541	+	47.2551i	0.540155	+	1.66243i
$809$	−18.7812	−	13.6453i	−0.660310	−	0.479743i	0.206457	−	0.978456i	$-0.433806\pi$
$809$	−18.7812	−	13.6453i	−0.660310	−	0.479743i	−0.866768	+	0.498712i	$0.833806\pi$
$810$		0			0
$811$	−7.47214	+	5.42882i	−0.262382	+	0.190632i	−0.711197	−	0.702993i	$-0.751846\pi$
$811$	−7.47214	+	5.42882i	−0.262382	+	0.190632i	0.448814	+	0.893625i	$0.351846\pi$
$812$	−15.8541	−	11.5187i	−0.556370	−	0.404226i
$813$		0			0
$814$	−21.1803	+	15.3884i	−0.742371	+	0.539364i
$815$	−2.03444	+	6.26137i	−0.0712634	+	0.219326i
$816$		0			0
$817$	5.70820	+	17.5680i	0.199705	+	0.614628i
$818$	−25.7984			−0.902019
$819$		0			0
$820$	−2.50000	−	1.81636i	−0.0873038	−	0.0634299i
$821$	−1.56231	+	4.80828i	−0.0545249	+	0.167810i	−0.974611	−	0.223907i	$-0.928119\pi$
$821$	−1.56231	+	4.80828i	−0.0545249	+	0.167810i	0.920086	+	0.391717i	$0.128119\pi$
$822$		0			0
$823$	11.9443	−	8.67802i	0.416351	−	0.302497i	−0.359817	−	0.933023i	$-0.617161\pi$
$823$	11.9443	−	8.67802i	0.416351	−	0.302497i	0.776168	+	0.630526i	$0.217161\pi$
$824$	−3.70820			−0.129181
$825$		0			0
$826$	−17.8885			−0.622422
$827$	17.8541	−	12.9718i	0.620848	−	0.451072i	−0.232370	−	0.972628i	$-0.574648\pi$
$827$	17.8541	−	12.9718i	0.620848	−	0.451072i	0.853218	+	0.521555i	$0.174648\pi$
$828$		0			0
$829$	−8.19098	+	25.2093i	−0.284485	+	0.875554i	0.702068	+	0.712110i	$0.252260\pi$
$829$	−8.19098	+	25.2093i	−0.284485	+	0.875554i	−0.986553	+	0.163444i	$0.947740\pi$
$830$	−2.43769	+	7.50245i	−0.0846136	+	0.260414i
$831$		0			0
$832$	23.6738			0.820740
$833$	11.4656	+	35.2874i	0.397258	+	1.22263i
$834$		0			0
$835$	42.3607	−	30.7768i	1.46595	−	1.06508i
$836$	8.47214	−	6.15537i	0.293015	−	0.212888i
$837$		0			0
$838$	−26.6525	−	19.3642i	−0.920695	−	0.668924i
$839$	−35.6525	+	25.9030i	−1.23086	+	0.894272i	−0.996954	−	0.0779870i	$-0.975151\pi$
$839$	−35.6525	+	25.9030i	−1.23086	+	0.894272i	−0.233906	+	0.972259i	$0.575151\pi$
$840$		0			0
$841$	7.92705	+	5.75934i	0.273347	+	0.198598i
$842$	−7.15248	−	22.0131i	−0.246491	−	0.758620i
$843$		0			0
$844$	5.52786	+	17.0130i	0.190277	+	0.585612i
$845$	−2.82624	+	2.05338i	−0.0972255	+	0.0706385i
$846$		0			0
$847$	−0.729490	+	2.24514i	−0.0250656	+	0.0771439i
$848$	−1.11803	+	0.812299i	−0.0383934	+	0.0278945i
$849$		0			0
$850$	−14.2705			−0.489474
$851$	36.1803			1.24025
$852$		0			0
$853$	9.22542	−	28.3929i	0.315873	−	0.972156i	−0.659521	−	0.751686i	$-0.729241\pi$
$853$	9.22542	−	28.3929i	0.315873	−	0.972156i	0.975394	−	0.220470i	$-0.0707590\pi$
$854$	0.854102	−	2.62866i	0.0292268	−	0.0899507i
$855$		0			0
$856$	−15.2705	−	46.9978i	−0.521935	−	1.60635i
$857$	3.52786			0.120510			0.0602548	−	0.998183i	$-0.480809\pi$
$857$	3.52786			0.120510			0.0602548	+	0.998183i	$0.480809\pi$
$858$		0			0
$859$	−2.76393	−	2.00811i	−0.0943041	−	0.0685160i	0.539634	−	0.841900i	$-0.318563\pi$
$859$	−2.76393	−	2.00811i	−0.0943041	−	0.0685160i	−0.633938	+	0.773384i	$0.718563\pi$
$860$	−12.7639			−0.435246
$861$		0			0
$862$	8.61803	+	6.26137i	0.293531	+	0.213263i
$863$	41.3607	+	30.0503i	1.40793	+	1.02292i	0.993619	+	0.112790i	$0.0359788\pi$
$863$	41.3607	+	30.0503i	1.40793	+	1.02292i	0.414315	+	0.910134i	$0.364021\pi$
$864$		0			0
$865$	−17.9271	−	13.0248i	−0.609538	−	0.442855i
$866$	20.2082	+	14.6821i	0.686703	+	0.498919i
$867$		0			0
$868$	−32.3607			−1.09839
$869$		0			0
$870$		0			0
$871$	5.47214	−	16.8415i	0.185416	−	0.570653i
$872$	−17.6976	+	54.4675i	−0.599315	+	1.84450i
$873$		0			0
$874$	14.4721			0.489527
$875$	40.4508	+	29.3893i	1.36749	+	0.993538i
$876$		0			0
$877$	−14.7361	+	10.7064i	−0.497602	+	0.361529i	−0.808100	−	0.589045i	$-0.799504\pi$
$877$	−14.7361	+	10.7064i	−0.497602	+	0.361529i	0.310499	+	0.950574i	$0.399504\pi$
$878$	1.90983	−	5.87785i	0.0644536	−	0.198368i
$879$		0			0
$880$	−2.23607	−	6.88191i	−0.0753778	−	0.231989i
$881$	−7.74265	−	23.8294i	−0.260856	−	0.802833i	−0.992619	−	0.121274i	$-0.961302\pi$
$881$	−7.74265	−	23.8294i	−0.260856	−	0.802833i	0.731763	−	0.681559i	$-0.238698\pi$
$882$		0			0
$883$	−0.0557281	−	0.171513i	−0.00187540	−	0.00577189i	0.950114	−	0.311902i	$-0.100966\pi$
$883$	−0.0557281	−	0.171513i	−0.00187540	−	0.00577189i	−0.951990	+	0.306130i	$0.900966\pi$
$884$	7.80902	+	5.67358i	0.262646	+	0.190823i
$885$		0			0
$886$	24.8885	−	18.0826i	0.836147	−	0.607496i
$887$	13.8541	+	10.0656i	0.465175	+	0.337970i	0.795558	−	0.605877i	$-0.207178\pi$
$887$	13.8541	+	10.0656i	0.465175	+	0.337970i	−0.330383	+	0.943847i	$0.607178\pi$
$888$		0			0
$889$	−35.1246	+	25.5195i	−1.17804	+	0.855897i
$890$	−17.0344			−0.570996
$891$		0			0
$892$	4.38197	+	13.4863i	0.146719	+	0.451555i
$893$	−16.9443			−0.567018
$894$		0			0
$895$	13.8197			0.461940
$896$	4.14590	−	12.7598i	0.138505	−	0.426274i
$897$		0			0
$898$	6.30902	−	4.58377i	0.210535	−	0.152962i
$899$	−31.7082			−1.05753
$900$		0			0
$901$	−3.94427			−0.131403
$902$	−3.61803	+	2.62866i	−0.120467	+	0.0875247i
$903$		0			0
$904$	−2.47871	+	7.62870i	−0.0824408	+	0.253727i
$905$	−17.7254	+	12.8783i	−0.589213	+	0.428088i
$906$		0			0
$907$	−33.1246			−1.09988			−0.549942	−	0.835203i	$-0.685350\pi$
$907$	−33.1246			−1.09988			−0.549942	+	0.835203i	$0.685350\pi$
$908$	−6.18034	−	19.0211i	−0.205102	−	0.631238i
$909$		0			0
$910$	10.4508	+	32.1644i	0.346442	+	1.06624i
$911$	−3.38197	+	2.45714i	−0.112050	+	0.0814088i	−0.642399	−	0.766370i	$-0.722061\pi$
$911$	−3.38197	+	2.45714i	−0.112050	+	0.0814088i	0.530349	+	0.847779i	$0.322061\pi$
$912$		0			0
$913$	−9.23607	−	6.71040i	−0.305669	−	0.222082i
$914$	18.0902	−	13.1433i	0.598370	−	0.434741i
$915$		0			0
$916$	−20.2082	−	14.6821i	−0.667698	−	0.485111i
$917$	−19.5967	−	60.3126i	−0.647142	−	1.99170i
$918$		0			0
$919$	−15.2016	−	46.7858i	−0.501455	−	1.54332i	−0.806649	−	0.591031i	$-0.798721\pi$
$919$	−15.2016	−	46.7858i	−0.501455	−	1.54332i	0.305194	−	0.952290i	$-0.401279\pi$
$920$	−9.27051	+	28.5317i	−0.305640	+	0.940662i
$921$		0			0
$922$	−2.53444	+	7.80021i	−0.0834674	+	0.256886i
$923$	−2.09017	+	1.51860i	−0.0687988	+	0.0499852i
$924$		0			0
$925$	40.4508			1.33002
$926$	−23.2361			−0.763585
$927$		0			0
$928$	6.77051	−	20.8375i	0.222253	−	0.684024i
$929$	−0.645898	+	1.98787i	−0.0211912	+	0.0652199i	−0.961093	−	0.276225i	$-0.910916\pi$
$929$	−0.645898	+	1.98787i	−0.0211912	+	0.0652199i	0.939902	+	0.341445i	$0.110916\pi$
$930$		0			0
$931$	−13.0000	−	40.0099i	−0.426058	−	1.31127i
$932$	14.6180			0.478830
$933$		0			0
$934$	−4.70820	−	3.42071i	−0.154057	−	0.111929i
$935$	6.38197	−	19.6417i	0.208713	−	0.642351i
$936$		0			0
$937$	−9.45492	−	6.86940i	−0.308879	−	0.224413i	0.422537	−	0.906346i	$-0.361140\pi$
$937$	−9.45492	−	6.86940i	−0.308879	−	0.224413i	−0.731415	+	0.681932i	$0.761140\pi$
$938$	18.9443	+	13.7638i	0.618552	+	0.449405i
$939$		0			0
$940$	3.61803	−	11.1352i	0.118007	−	0.363189i
$941$	4.30902	+	3.13068i	0.140470	+	0.102057i	0.655801	−	0.754934i	$-0.272331\pi$
$941$	4.30902	+	3.13068i	0.140470	+	0.102057i	−0.515331	+	0.856991i	$0.672331\pi$
$942$		0			0
$943$	6.18034			0.201260
$944$	−1.23607	−	3.80423i	−0.0402306	−	0.123817i
$945$		0			0
$946$	−5.70820	+	17.5680i	−0.185590	+	0.571186i
$947$	−9.09017	+	27.9767i	−0.295391	+	0.909120i	0.687699	+	0.725996i	$0.258621\pi$
$947$	−9.09017	+	27.9767i	−0.295391	+	0.909120i	−0.983090	+	0.183124i	$0.941379\pi$
$948$		0			0
$949$	10.4508			0.339249
$950$	16.1803			0.524960
$951$		0			0
$952$	−30.9787	+	22.5074i	−1.00403	+	0.729468i
$953$	−3.11803	+	9.59632i	−0.101003	+	0.310855i	−0.988772	−	0.149435i	$-0.952255\pi$
$953$	−3.11803	+	9.59632i	−0.101003	+	0.310855i	0.887769	+	0.460290i	$0.152255\pi$
$954$		0			0
$955$	−17.0344	+	52.4266i	−0.551222	+	1.69649i
$956$	−2.18034	−	6.71040i	−0.0705172	−	0.217030i
$957$		0			0
$958$	0.326238	+	1.00406i	0.0105403	+	0.0324396i
$959$	−19.4721	−	14.1473i	−0.628788	−	0.456841i
$960$		0			0
$961$	−17.2812	+	12.5555i	−0.557457	+	0.405016i
$962$	22.1353	+	16.0822i	0.713669	+	0.518511i
$963$		0			0
$964$	−0.836881	+	0.608030i	−0.0269541	+	0.0195833i
$965$	−5.30244	−	16.3192i	−0.170692	−	0.525335i
$966$		0			0
$967$	10.7639	+	33.1280i	0.346145	+	1.06532i	0.960968	+	0.276659i	$0.0892273\pi$
$967$	10.7639	+	33.1280i	0.346145	+	1.06532i	−0.614823	+	0.788665i	$0.710773\pi$
$968$	−1.58359			−0.0508986
$969$		0			0
$970$	−16.0172	+	11.6372i	−0.514282	+	0.373648i
$971$	2.03444	−	6.26137i	0.0652883	−	0.200937i	−0.913091	−	0.407756i	$-0.866311\pi$
$971$	2.03444	−	6.26137i	0.0652883	−	0.200937i	0.978379	+	0.206819i	$0.0663113\pi$
$972$		0			0
$973$	18.2918	−	13.2898i	0.586408	−	0.426050i
$974$	3.70820			0.118819
$975$		0			0
$976$	0.618034			0.0197828
$977$	−37.0066	+	26.8869i	−1.18395	+	0.860187i	−0.992611	−	0.121338i	$-0.961281\pi$
$977$	−37.0066	+	26.8869i	−1.18395	+	0.860187i	−0.191334	+	0.981525i	$0.561281\pi$
$978$		0			0
$979$	7.61803	−	23.4459i	0.243473	−	0.749334i
$980$	29.0689			0.928571
$981$		0			0
$982$	−29.8885			−0.953782
$983$	−6.70820	−	20.6457i	−0.213958	−	0.658496i	−0.999226	−	0.0393397i	$-0.987475\pi$
$983$	−6.70820	−	20.6457i	−0.213958	−	0.658496i	0.785267	−	0.619157i	$-0.212525\pi$
$984$		0			0
$985$	12.0344			0.383449
$986$	−10.1180	+	7.35118i	−0.322224	+	0.234109i
$987$		0			0
$988$	−8.85410	−	6.43288i	−0.281687	−	0.204657i
$989$	20.6525	−	15.0049i	0.656711	−	0.477128i
$990$		0			0
$991$	2.52786	+	1.83660i	0.0803002	+	0.0583415i	0.627211	−	0.778849i	$-0.284196\pi$
$991$	2.52786	+	1.83660i	0.0803002	+	0.0583415i	−0.546911	+	0.837191i	$0.684196\pi$
$992$	−11.1803	−	34.4095i	−0.354976	−	1.09250i
$993$		0			0
$994$	−1.05573	−	3.24920i	−0.0334857	−	0.103058i
$995$	12.8885	+	39.6669i	0.408594	+	1.25752i
$996$		0			0
$997$	2.90983	−	8.95554i	0.0921552	−	0.283625i	−0.894347	−	0.447375i	$-0.852359\pi$
$997$	2.90983	−	8.95554i	0.0921552	−	0.283625i	0.986502	+	0.163750i	$0.0523590\pi$
$998$	−4.85410	+	3.52671i	−0.153654	+	0.111636i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.a.136.1		4
3.2	odd	2		75.2.g.a.61.1	yes	4
15.2	even	4		375.2.i.a.199.1		8
15.8	even	4		375.2.i.a.199.2		8
15.14	odd	2		375.2.g.a.301.1		4
25.4	even	10		5625.2.a.h.1.1		2
25.16	even	5	inner	225.2.h.a.91.1		4
25.21	even	5		5625.2.a.a.1.2		2
75.29	odd	10		1875.2.a.a.1.1		2
75.38	even	20		375.2.i.a.49.1		8
75.41	odd	10		75.2.g.a.16.1	✓	4
75.47	even	20		1875.2.b.b.1249.4		4
75.53	even	20		1875.2.b.b.1249.1		4
75.59	odd	10		375.2.g.a.76.1		4
75.62	even	20		375.2.i.a.49.2		8
75.71	odd	10		1875.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.a.16.1	✓	4	75.41	odd	10
75.2.g.a.61.1	yes	4	3.2	odd	2
225.2.h.a.91.1		4	25.16	even	5	inner
225.2.h.a.136.1		4	1.1	even	1	trivial
375.2.g.a.76.1		4	75.59	odd	10
375.2.g.a.301.1		4	15.14	odd	2
375.2.i.a.49.1		8	75.38	even	20
375.2.i.a.49.2		8	75.62	even	20
375.2.i.a.199.1		8	15.2	even	4
375.2.i.a.199.2		8	15.8	even	4
1875.2.a.a.1.1		2	75.29	odd	10
1875.2.a.d.1.2		2	75.71	odd	10
1875.2.b.b.1249.1		4	75.53	even	20
1875.2.b.b.1249.4		4	75.47	even	20
5625.2.a.a.1.2		2	25.21	even	5
5625.2.a.h.1.1		2	25.4	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} +4.47214 q^{7} +(0.927051 + 2.85317i) q^{8} +(-1.80902 - 1.31433i) q^{10} +(2.61803 - 1.90211i) q^{11} +(-2.73607 - 1.98787i) q^{13} +(3.61803 - 2.62866i) q^{14} +(0.809017 + 0.587785i) q^{16} +(0.881966 + 2.71441i) q^{17} +(-1.00000 - 3.07768i) q^{19} +2.23607 q^{20} +(1.00000 - 3.07768i) q^{22} +(-3.61803 + 2.62866i) q^{23} +(-4.04508 + 2.93893i) q^{25} -3.38197 q^{26} +(-1.38197 + 4.25325i) q^{28} +(-1.35410 + 4.16750i) q^{29} +(2.23607 + 6.88191i) q^{31} -5.00000 q^{32} +(2.30902 + 1.67760i) q^{34} +(-3.09017 - 9.51057i) q^{35} +(-6.54508 - 4.75528i) q^{37} +(-2.61803 - 1.90211i) q^{38} +(5.42705 - 3.94298i) q^{40} +(-1.11803 - 0.812299i) q^{41} -5.70820 q^{43} +(1.00000 + 3.07768i) q^{44} +(-1.38197 + 4.25325i) q^{46} +(1.61803 - 4.97980i) q^{47} +13.0000 q^{49} +(-1.54508 + 4.75528i) q^{50} +(2.73607 - 1.98787i) q^{52} +(-0.427051 + 1.31433i) q^{53} +(-5.85410 - 4.25325i) q^{55} +(4.14590 + 12.7598i) q^{56} +(1.35410 + 4.16750i) q^{58} +(-3.23607 - 2.35114i) q^{59} +(0.500000 - 0.363271i) q^{61} +(5.85410 + 4.25325i) q^{62} +(-5.66312 + 4.11450i) q^{64} +(-2.33688 + 7.19218i) q^{65} +(1.61803 + 4.97980i) q^{67} -2.85410 q^{68} +(-8.09017 - 5.87785i) q^{70} +(0.236068 - 0.726543i) q^{71} +(-2.50000 + 1.81636i) q^{73} -8.09017 q^{74} +3.23607 q^{76} +(11.7082 - 8.50651i) q^{77} +(0.690983 - 2.12663i) q^{80} -1.38197 q^{82} +(-1.09017 - 3.35520i) q^{83} +(5.16312 - 3.75123i) q^{85} +(-4.61803 + 3.35520i) q^{86} +(7.85410 + 5.70634i) q^{88} +(6.16312 - 4.47777i) q^{89} +(-12.2361 - 8.89002i) q^{91} +(-1.38197 - 4.25325i) q^{92} +(-1.61803 - 4.97980i) q^{94} +(-5.85410 + 4.25325i) q^{95} +(2.73607 - 8.42075i) q^{97} +(10.5172 - 7.64121i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} - 5 q^{5} - 3 q^{8} - 5 q^{10} + 6 q^{11} - 2 q^{13} + 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{19} + 4 q^{22} - 10 q^{23} - 5 q^{25} - 18 q^{26} - 10 q^{28} + 8 q^{29} - 20 q^{32} + 7 q^{34}+ \cdots + 13 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 - 5 * q^5 - 3 * q^8 - 5 * q^10 + 6 * q^11 - 2 * q^13 + 10 * q^14 + q^16 + 8 * q^17 - 4 * q^19 + 4 * q^22 - 10 * q^23 - 5 * q^25 - 18 * q^26 - 10 * q^28 + 8 * q^29 - 20 * q^32 + 7 * q^34 + 10 * q^35 - 15 * q^37 - 6 * q^38 + 15 * q^40 + 4 * q^43 + 4 * q^44 - 10 * q^46 + 2 * q^47 + 52 * q^49 + 5 * q^50 + 2 * q^52 + 5 * q^53 - 10 * q^55 + 30 * q^56 - 8 * q^58 - 4 * q^59 + 2 * q^61 + 10 * q^62 - 7 * q^64 - 25 * q^65 + 2 * q^67 + 2 * q^68 - 10 * q^70 - 8 * q^71 - 10 * q^73 - 10 * q^74 + 4 * q^76 + 20 * q^77 + 5 * q^80 - 10 * q^82 + 18 * q^83 + 5 * q^85 - 14 * q^86 + 18 * q^88 + 9 * q^89 - 40 * q^91 - 10 * q^92 - 2 * q^94 - 10 * q^95 + 2 * q^97 + 13 * q^98

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