LMFDB - Embedded newform 375.2.g.a.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(76,375)] 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("375.76"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not 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:	$2.99439007580$
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			151.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	375.151
Dual form			375.2.g.a.226.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} +4.47214 q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.381966 - 1.17557i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-1.73607 + 5.34307i) q^{13} +(-1.38197 - 4.25325i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(3.11803 + 2.26538i) q^{17} -1.00000 q^{18} +(-1.00000 - 0.726543i) q^{19} +(3.61803 - 2.62866i) q^{21} +(-1.00000 + 0.726543i) q^{22} +(-1.38197 - 4.25325i) q^{23} -3.00000 q^{24} +5.61803 q^{26} +(-0.309017 - 0.951057i) q^{27} +(3.61803 - 2.62866i) q^{28} +(-5.35410 + 3.88998i) q^{29} +(-2.23607 - 1.62460i) q^{31} -5.00000 q^{32} +(-1.00000 - 0.726543i) q^{33} +(1.19098 - 3.66547i) q^{34} +(-0.309017 - 0.951057i) q^{36} +(0.954915 - 2.93893i) q^{37} +(-0.381966 + 1.17557i) q^{38} +(1.73607 + 5.34307i) q^{39} +(-1.11803 + 3.44095i) q^{41} +(-3.61803 - 2.62866i) q^{42} -7.70820 q^{43} +(-1.00000 - 0.726543i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(-0.618034 + 0.449028i) q^{47} +(0.309017 + 0.951057i) q^{48} +13.0000 q^{49} +3.85410 q^{51} +(1.73607 + 5.34307i) q^{52} +(2.92705 - 2.12663i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-10.8541 - 7.88597i) q^{56} -1.23607 q^{57} +(5.35410 + 3.88998i) q^{58} +(-1.23607 + 3.80423i) q^{59} +(0.500000 + 1.53884i) q^{61} +(-0.854102 + 2.62866i) q^{62} +(1.38197 - 4.25325i) q^{63} +(2.16312 + 6.65740i) q^{64} +(-0.381966 + 1.17557i) q^{66} +(0.618034 + 0.449028i) q^{67} +3.85410 q^{68} +(-3.61803 - 2.62866i) q^{69} +(4.23607 - 3.07768i) q^{71} +(-2.42705 + 1.76336i) q^{72} +(2.50000 + 7.69421i) q^{73} -3.09017 q^{74} -1.23607 q^{76} +(-1.70820 - 5.25731i) q^{77} +(4.54508 - 3.30220i) q^{78} +(-0.809017 - 0.587785i) q^{81} +3.61803 q^{82} +(10.0902 + 7.33094i) q^{83} +(1.38197 - 4.25325i) q^{84} +(2.38197 + 7.33094i) q^{86} +(-2.04508 + 6.29412i) q^{87} +(-1.14590 + 3.52671i) q^{88} +(1.66312 + 5.11855i) q^{89} +(-7.76393 + 23.8949i) q^{91} +(-3.61803 - 2.62866i) q^{92} -2.76393 q^{93} +(0.618034 + 0.449028i) q^{94} +(-4.04508 + 2.93893i) q^{96} +(1.73607 - 1.26133i) q^{97} +(-4.01722 - 12.3637i) q^{98} -1.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + q^{4} - q^{6} - 3 q^{8} - q^{9} - 6 q^{11} - q^{12} + 2 q^{13} - 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 10 q^{21} - 4 q^{22} - 10 q^{23} - 12 q^{24} + 18 q^{26}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 + q^4 - q^6 - 3 * q^8 - q^9 - 6 * q^11 - q^12 + 2 * q^13 - 10 * q^14 + q^16 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 10 * q^21 - 4 * q^22 - 10 * q^23 - 12 * q^24 + 18 * q^26 + q^27 + 10 * q^28 - 8 * q^29 - 20 * q^32 - 4 * q^33 + 7 * q^34 + q^36 + 15 * q^37 - 6 * q^38 - 2 * q^39 - 10 * q^42 - 4 * q^43 - 4 * q^44 - 10 * q^46 + 2 * q^47 - q^48 + 52 * q^49 + 2 * q^51 - 2 * q^52 + 5 * q^53 - q^54 - 30 * q^56 + 4 * q^57 + 8 * q^58 + 4 * q^59 + 2 * q^61 + 10 * q^62 + 10 * q^63 - 7 * q^64 - 6 * q^66 - 2 * q^67 + 2 * q^68 - 10 * q^69 + 8 * q^71 - 3 * q^72 + 10 * q^73 + 10 * q^74 + 4 * q^76 + 20 * q^77 + 7 * q^78 - q^81 + 10 * q^82 + 18 * q^83 + 10 * q^84 + 14 * q^86 + 3 * q^87 - 18 * q^88 - 9 * q^89 - 40 * q^91 - 10 * q^92 - 20 * q^93 - 2 * q^94 - 5 * q^96 - 2 * q^97 + 13 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i	−0.998886	−	0.0471903i	$-0.984973\pi$
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i	0.780378	−	0.625308i	$-0.215027\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	4.47214			1.69031			0.845154	−	0.534522i	$-0.179509\pi$
$7$	4.47214			1.69031			0.845154	+	0.534522i	$0.179509\pi$
$8$	−2.42705	−	1.76336i	−0.858092	−	0.623440i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−0.381966	−	1.17557i	−0.115167	−	0.354448i	0.876815	−	0.480828i	$-0.159664\pi$
$11$	−0.381966	−	1.17557i	−0.115167	−	0.354448i	−0.991982	+	0.126380i	$0.959664\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	−1.73607	+	5.34307i	−0.481499	+	1.48190i	0.355490	+	0.934680i	$0.384314\pi$
$13$	−1.73607	+	5.34307i	−0.481499	+	1.48190i	−0.836989	+	0.547220i	$0.815686\pi$
$14$	−1.38197	−	4.25325i	−0.369346	−	1.13673i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	3.11803	+	2.26538i	0.756234	+	0.549436i	0.897753	−	0.440499i	$-0.145199\pi$
$17$	3.11803	+	2.26538i	0.756234	+	0.549436i	−0.141519	+	0.989936i	$0.545199\pi$
$18$	−1.00000			−0.235702
$19$	−1.00000	−	0.726543i	−0.229416	−	0.166680i	0.467139	−	0.884184i	$-0.345285\pi$
$19$	−1.00000	−	0.726543i	−0.229416	−	0.166680i	−0.696555	+	0.717504i	$0.745285\pi$
$20$		0			0
$21$	3.61803	−	2.62866i	0.789520	−	0.573620i
$22$	−1.00000	+	0.726543i	−0.213201	+	0.154899i
$23$	−1.38197	−	4.25325i	−0.288160	−	0.886865i	−0.985434	−	0.170060i	$-0.945604\pi$
$23$	−1.38197	−	4.25325i	−0.288160	−	0.886865i	0.697274	−	0.716805i	$-0.254396\pi$
$24$	−3.00000			−0.612372
$25$		0			0
$26$	5.61803			1.10179
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	3.61803	−	2.62866i	0.683744	−	0.496769i
$29$	−5.35410	+	3.88998i	−0.994232	+	0.722352i	−0.960844	−	0.277091i	$-0.910630\pi$
$29$	−5.35410	+	3.88998i	−0.994232	+	0.722352i	−0.0333880	+	0.999442i	$0.510630\pi$
$30$		0			0
$31$	−2.23607	−	1.62460i	−0.401610	−	0.291787i	0.368587	−	0.929593i	$-0.379842\pi$
$31$	−2.23607	−	1.62460i	−0.401610	−	0.291787i	−0.770196	+	0.637807i	$0.779842\pi$
$32$	−5.00000			−0.883883
$33$	−1.00000	−	0.726543i	−0.174078	−	0.126475i
$34$	1.19098	−	3.66547i	0.204252	−	0.628623i
$35$		0			0
$36$	−0.309017	−	0.951057i	−0.0515028	−	0.158509i
$37$	0.954915	−	2.93893i	0.156987	−	0.483157i	−0.841370	−	0.540460i	$-0.818250\pi$
$37$	0.954915	−	2.93893i	0.156987	−	0.483157i	0.998357	+	0.0573034i	$0.0182503\pi$
$38$	−0.381966	+	1.17557i	−0.0619631	+	0.190703i
$39$	1.73607	+	5.34307i	0.277993	+	0.855576i
$40$		0			0
$41$	−1.11803	+	3.44095i	−0.174608	+	0.537387i	−0.999615	−	0.0277346i	$-0.991171\pi$
$41$	−1.11803	+	3.44095i	−0.174608	+	0.537387i	0.825008	+	0.565121i	$0.191171\pi$
$42$	−3.61803	−	2.62866i	−0.558275	−	0.405610i
$43$	−7.70820			−1.17549			−0.587745	−	0.809046i	$-0.699984\pi$
$43$	−7.70820			−1.17549			−0.587745	+	0.809046i	$0.699984\pi$
$44$	−1.00000	−	0.726543i	−0.150756	−	0.109530i
$45$		0			0
$46$	−3.61803	+	2.62866i	−0.533450	+	0.387574i
$47$	−0.618034	+	0.449028i	−0.0901495	+	0.0654975i	−0.631947	−	0.775012i	$-0.717744\pi$
$47$	−0.618034	+	0.449028i	−0.0901495	+	0.0654975i	0.541797	+	0.840509i	$0.317744\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	13.0000			1.85714
$50$		0			0
$51$	3.85410			0.539682
$52$	1.73607	+	5.34307i	0.240749	+	0.740950i
$53$	2.92705	−	2.12663i	0.402061	−	0.292115i	−0.368319	−	0.929700i	$-0.620066\pi$
$53$	2.92705	−	2.12663i	0.402061	−	0.292115i	0.770380	+	0.637585i	$0.220066\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$		0			0
$56$	−10.8541	−	7.88597i	−1.45044	−	1.05381i
$57$	−1.23607			−0.163721
$58$	5.35410	+	3.88998i	0.703028	+	0.510780i
$59$	−1.23607	+	3.80423i	−0.160922	+	0.495268i	−0.998713	−	0.0507240i	$-0.983847\pi$
$59$	−1.23607	+	3.80423i	−0.160922	+	0.495268i	0.837790	+	0.545992i	$0.183847\pi$
$60$		0			0
$61$	0.500000	+	1.53884i	0.0640184	+	0.197028i	0.977950	−	0.208840i	$-0.0669689\pi$
$61$	0.500000	+	1.53884i	0.0640184	+	0.197028i	−0.913931	+	0.405869i	$0.866969\pi$
$62$	−0.854102	+	2.62866i	−0.108471	+	0.333840i
$63$	1.38197	−	4.25325i	0.174111	−	0.535860i
$64$	2.16312	+	6.65740i	0.270390	+	0.832174i
$65$		0			0
$66$	−0.381966	+	1.17557i	−0.0470168	+	0.144703i
$67$	0.618034	+	0.449028i	0.0755049	+	0.0548575i	0.624897	−	0.780707i	$-0.285141\pi$
$67$	0.618034	+	0.449028i	0.0755049	+	0.0548575i	−0.549392	+	0.835564i	$0.685141\pi$
$68$	3.85410			0.467379
$69$	−3.61803	−	2.62866i	−0.435560	−	0.316453i
$70$		0			0
$71$	4.23607	−	3.07768i	0.502729	−	0.365254i	−0.307330	−	0.951603i	$-0.599435\pi$
$71$	4.23607	−	3.07768i	0.502729	−	0.365254i	0.810058	+	0.586349i	$0.199435\pi$
$72$	−2.42705	+	1.76336i	−0.286031	+	0.207813i
$73$	2.50000	+	7.69421i	0.292603	+	0.900539i	0.984016	+	0.178080i	$0.0569884\pi$
$73$	2.50000	+	7.69421i	0.292603	+	0.900539i	−0.691413	+	0.722460i	$0.743012\pi$
$74$	−3.09017			−0.359225
$75$		0			0
$76$	−1.23607			−0.141787
$77$	−1.70820	−	5.25731i	−0.194668	−	0.599126i
$78$	4.54508	−	3.30220i	0.514630	−	0.373900i
$79$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$79$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	3.61803			0.399545
$83$	10.0902	+	7.33094i	1.10754	+	0.804675i	0.982274	−	0.187448i	$-0.0600217\pi$
$83$	10.0902	+	7.33094i	1.10754	+	0.804675i	0.125266	+	0.992123i	$0.460022\pi$
$84$	1.38197	−	4.25325i	0.150785	−	0.464068i
$85$		0			0
$86$	2.38197	+	7.33094i	0.256854	+	0.790515i
$87$	−2.04508	+	6.29412i	−0.219256	+	0.674801i
$88$	−1.14590	+	3.52671i	−0.122153	+	0.375949i
$89$	1.66312	+	5.11855i	0.176290	+	0.542566i	0.999690	−	0.0248961i	$-0.00792549\pi$
$89$	1.66312	+	5.11855i	0.176290	+	0.542566i	−0.823400	+	0.567462i	$0.807925\pi$
$90$		0			0
$91$	−7.76393	+	23.8949i	−0.813881	+	2.50487i
$92$	−3.61803	−	2.62866i	−0.377206	−	0.274056i
$93$	−2.76393			−0.286606
$94$	0.618034	+	0.449028i	0.0637453	+	0.0463137i
$95$		0			0
$96$	−4.04508	+	2.93893i	−0.412850	+	0.299953i
$97$	1.73607	−	1.26133i	0.176271	−	0.128068i	−0.496151	−	0.868236i	$-0.665254\pi$
$97$	1.73607	−	1.26133i	0.176271	−	0.128068i	0.672422	+	0.740168i	$0.265254\pi$
$98$	−4.01722	−	12.3637i	−0.405801	−	1.24893i
$99$	−1.23607			−0.124230
$100$		0			0
$101$	3.56231			0.354463			0.177231	−	0.984169i	$-0.443286\pi$
$101$	3.56231			0.354463			0.177231	+	0.984169i	$0.443286\pi$
$102$	−1.19098	−	3.66547i	−0.117925	−	0.362935i
$103$	2.61803	−	1.90211i	0.257963	−	0.187421i	−0.451286	−	0.892379i	$-0.649034\pi$
$103$	2.61803	−	1.90211i	0.257963	−	0.187421i	0.709248	+	0.704959i	$0.249034\pi$
$104$	13.6353	−	9.90659i	1.33705	−	0.971421i
$105$		0			0
$106$	−2.92705	−	2.12663i	−0.284300	−	0.206556i
$107$	−7.52786			−0.727746			−0.363873	−	0.931449i	$-0.618546\pi$
$107$	−7.52786			−0.727746			−0.363873	+	0.931449i	$0.618546\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	−2.44427	+	7.52270i	−0.234119	+	0.720544i	0.763118	+	0.646259i	$0.223667\pi$
$109$	−2.44427	+	7.52270i	−0.234119	+	0.720544i	−0.997237	+	0.0742847i	$0.976333\pi$
$110$		0			0
$111$	−0.954915	−	2.93893i	−0.0906365	−	0.278951i
$112$	−1.38197	+	4.25325i	−0.130584	+	0.401895i
$113$	−5.66312	+	17.4293i	−0.532741	+	1.63961i	0.215738	+	0.976451i	$0.430784\pi$
$113$	−5.66312	+	17.4293i	−0.532741	+	1.63961i	−0.748479	+	0.663158i	$0.769216\pi$
$114$	0.381966	+	1.17557i	0.0357744	+	0.110102i
$115$		0			0
$116$	−2.04508	+	6.29412i	−0.189881	+	0.584395i
$117$	4.54508	+	3.30220i	0.420193	+	0.305288i
$118$	4.00000			0.368230
$119$	13.9443	+	10.1311i	1.27827	+	0.928717i
$120$		0			0
$121$	7.66312	−	5.56758i	0.696647	−	0.506144i
$122$	1.30902	−	0.951057i	0.118513	−	0.0861046i
$123$	1.11803	+	3.44095i	0.100810	+	0.310260i
$124$	−2.76393			−0.248208
$125$		0			0
$126$	−4.47214			−0.398410
$127$	1.14590	+	3.52671i	0.101682	+	0.312945i	0.988937	−	0.148333i	$-0.0473909\pi$
$127$	1.14590	+	3.52671i	0.101682	+	0.312945i	−0.887255	+	0.461279i	$0.847391\pi$
$128$	−2.42705	+	1.76336i	−0.214523	+	0.155860i
$129$	−6.23607	+	4.53077i	−0.549055	+	0.398912i
$130$		0			0
$131$	6.61803	+	4.80828i	0.578220	+	0.420102i	0.838082	−	0.545544i	$-0.183677\pi$
$131$	6.61803	+	4.80828i	0.578220	+	0.420102i	−0.259862	+	0.965646i	$0.583677\pi$
$132$	−1.23607			−0.107586
$133$	−4.47214	−	3.24920i	−0.387783	−	0.281741i
$134$	0.236068	−	0.726543i	0.0203932	−	0.0627637i
$135$		0			0
$136$	−3.57295	−	10.9964i	−0.306378	−	0.942934i
$137$	2.35410	−	7.24518i	0.201125	−	0.618998i	−0.798726	−	0.601695i	$-0.794492\pi$
$137$	2.35410	−	7.24518i	0.201125	−	0.618998i	0.999850	−	0.0173024i	$-0.00550780\pi$
$138$	−1.38197	+	4.25325i	−0.117641	+	0.362061i
$139$	−7.09017	−	21.8213i	−0.601380	−	1.85086i	−0.519983	−	0.854177i	$-0.674062\pi$
$139$	−7.09017	−	21.8213i	−0.601380	−	1.85086i	−0.0813976	−	0.996682i	$-0.525938\pi$
$140$		0			0
$141$	−0.236068	+	0.726543i	−0.0198805	+	0.0611859i
$142$	−4.23607	−	3.07768i	−0.355483	−	0.258273i
$143$	6.94427			0.580709
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$		0			0
$146$	6.54508	−	4.75528i	0.541675	−	0.393550i
$147$	10.5172	−	7.64121i	0.867446	−	0.630236i
$148$	−0.954915	−	2.93893i	−0.0784935	−	0.241578i
$149$	−18.8541			−1.54459			−0.772294	−	0.635265i	$-0.780891\pi$
$149$	−18.8541			−1.54459			−0.772294	+	0.635265i	$0.780891\pi$
$150$		0			0
$151$	7.52786			0.612609			0.306304	−	0.951934i	$-0.400907\pi$
$151$	7.52786			0.612609			0.306304	+	0.951934i	$0.400907\pi$
$152$	1.14590	+	3.52671i	0.0929446	+	0.286054i
$153$	3.11803	−	2.26538i	0.252078	−	0.183145i
$154$	−4.47214	+	3.24920i	−0.360375	+	0.261828i
$155$		0			0
$156$	4.54508	+	3.30220i	0.363898	+	0.264387i
$157$	−10.7984			−0.861804			−0.430902	−	0.902399i	$-0.641805\pi$
$157$	−10.7984			−0.861804			−0.430902	+	0.902399i	$0.641805\pi$
$158$		0			0
$159$	1.11803	−	3.44095i	0.0886659	−	0.272885i
$160$		0			0
$161$	−6.18034	−	19.0211i	−0.487079	−	1.49908i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	4.61803	−	14.2128i	0.361712	−	1.11324i	−0.590302	−	0.807183i	$-0.700991\pi$
$163$	4.61803	−	14.2128i	0.361712	−	1.11324i	0.952014	−	0.306054i	$-0.0990087\pi$
$164$	1.11803	+	3.44095i	0.0873038	+	0.268693i
$165$		0			0
$166$	3.85410	−	11.8617i	0.299136	−	0.920647i
$167$	2.76393	+	2.00811i	0.213879	+	0.155393i	0.689567	−	0.724222i	$-0.257801\pi$
$167$	2.76393	+	2.00811i	0.213879	+	0.155393i	−0.475688	+	0.879614i	$0.657801\pi$
$168$	−13.4164			−1.03510
$169$	−15.0172	−	10.9106i	−1.15517	−	0.839281i
$170$		0			0
$171$	−1.00000	+	0.726543i	−0.0764719	+	0.0555601i
$172$	−6.23607	+	4.53077i	−0.475496	+	0.345468i
$173$	−6.51722	−	20.0579i	−0.495495	−	1.52498i	−0.816184	−	0.577793i	$-0.803914\pi$
$173$	−6.51722	−	20.0579i	−0.495495	−	1.52498i	0.320689	−	0.947185i	$-0.396086\pi$
$174$	6.61803			0.501712
$175$		0			0
$176$	1.23607			0.0931721
$177$	1.23607	+	3.80423i	0.0929086	+	0.285943i
$178$	4.35410	−	3.16344i	0.326354	−	0.237110i
$179$	13.0902	−	9.51057i	0.978405	−	0.710853i	0.0210536	−	0.999778i	$-0.493298\pi$
$179$	13.0902	−	9.51057i	0.978405	−	0.710853i	0.957352	+	0.288925i	$0.0932979\pi$
$180$		0			0
$181$	−11.9721	−	8.69827i	−0.889882	−	0.646537i	0.0459654	−	0.998943i	$-0.485364\pi$
$181$	−11.9721	−	8.69827i	−0.889882	−	0.646537i	−0.935847	+	0.352406i	$0.885364\pi$
$182$	25.1246			1.86236
$183$	1.30902	+	0.951057i	0.0967653	+	0.0703041i
$184$	−4.14590	+	12.7598i	−0.305640	+	0.940662i
$185$		0			0
$186$	0.854102	+	2.62866i	0.0626258	+	0.192742i
$187$	1.47214	−	4.53077i	0.107653	−	0.331323i
$188$	−0.236068	+	0.726543i	−0.0172170	+	0.0529886i
$189$	−1.38197	−	4.25325i	−0.100523	−	0.309379i
$190$		0			0
$191$	2.05573	−	6.32688i	0.148747	−	0.457797i	−0.848727	−	0.528832i	$-0.822630\pi$
$191$	2.05573	−	6.32688i	0.148747	−	0.457797i	0.997474	+	0.0710349i	$0.0226302\pi$
$192$	5.66312	+	4.11450i	0.408700	+	0.296938i
$193$	−23.3262			−1.67906			−0.839530	−	0.543314i	$-0.817169\pi$
$193$	−23.3262			−1.67906			−0.839530	+	0.543314i	$0.817169\pi$
$194$	−1.73607	−	1.26133i	−0.124642	−	0.0905580i
$195$		0			0
$196$	10.5172	−	7.64121i	0.751230	−	0.545801i
$197$	6.16312	−	4.47777i	0.439104	−	0.319028i	−0.346175	−	0.938170i	$-0.612520\pi$
$197$	6.16312	−	4.47777i	0.439104	−	0.319028i	0.785279	+	0.619142i	$0.212520\pi$
$198$	0.381966	+	1.17557i	0.0271451	+	0.0835442i
$199$	12.6525			0.896910			0.448455	−	0.893805i	$-0.351974\pi$
$199$	12.6525			0.896910			0.448455	+	0.893805i	$0.351974\pi$
$200$		0			0
$201$	0.763932			0.0538836
$202$	−1.10081	−	3.38795i	−0.0774529	−	0.238376i
$203$	−23.9443	+	17.3965i	−1.68056	+	1.22100i
$204$	3.11803	−	2.26538i	0.218306	−	0.158609i
$205$		0			0
$206$	−2.61803	−	1.90211i	−0.182407	−	0.132526i
$207$	−4.47214			−0.310835
$208$	−4.54508	−	3.30220i	−0.315145	−	0.228966i
$209$	−0.472136	+	1.45309i	−0.0326583	+	0.100512i
$210$		0			0
$211$	5.52786	+	17.0130i	0.380554	+	1.17122i	0.939655	+	0.342125i	$0.111146\pi$
$211$	5.52786	+	17.0130i	0.380554	+	1.17122i	−0.559101	+	0.829100i	$0.688854\pi$
$212$	1.11803	−	3.44095i	0.0767869	−	0.236326i
$213$	1.61803	−	4.97980i	0.110866	−	0.341210i
$214$	2.32624	+	7.15942i	0.159018	+	0.489408i
$215$		0			0
$216$	−0.927051	+	2.85317i	−0.0630778	+	0.194134i
$217$	−10.0000	−	7.26543i	−0.678844	−	0.493209i
$218$	7.90983			0.535721
$219$	6.54508	+	4.75528i	0.442276	+	0.321332i
$220$		0			0
$221$	−17.5172	+	12.7270i	−1.17834	+	0.856111i
$222$	−2.50000	+	1.81636i	−0.167789	+	0.121906i
$223$	−2.52786	−	7.77997i	−0.169278	−	0.520985i	0.830048	−	0.557692i	$-0.188313\pi$
$223$	−2.52786	−	7.77997i	−0.169278	−	0.520985i	−0.999326	+	0.0367073i	$0.988313\pi$
$224$	−22.3607			−1.49404
$225$		0			0
$226$	18.3262			1.21904
$227$	6.18034	+	19.0211i	0.410204	+	1.26248i	0.916471	+	0.400100i	$0.131025\pi$
$227$	6.18034	+	19.0211i	0.410204	+	1.26248i	−0.506268	+	0.862376i	$0.668975\pi$
$228$	−1.00000	+	0.726543i	−0.0662266	+	0.0481165i
$229$	−17.7812	+	12.9188i	−1.17501	+	0.853696i	−0.991600	−	0.129340i	$-0.958714\pi$
$229$	−17.7812	+	12.9188i	−1.17501	+	0.853696i	−0.183411	+	0.983036i	$0.558714\pi$
$230$		0			0
$231$	−4.47214	−	3.24920i	−0.294245	−	0.213781i
$232$	19.8541			1.30349
$233$	10.0172	+	7.27794i	0.656250	+	0.476794i	0.865394	−	0.501091i	$-0.167068\pi$
$233$	10.0172	+	7.27794i	0.656250	+	0.476794i	−0.209144	+	0.977885i	$0.567068\pi$
$234$	1.73607	−	5.34307i	0.113490	−	0.349287i
$235$		0			0
$236$	1.23607	+	3.80423i	0.0804612	+	0.247634i
$237$		0			0
$238$	5.32624	−	16.3925i	0.345249	−	1.06257i
$239$	−7.70820	−	23.7234i	−0.498602	−	1.53454i	−0.811267	−	0.584676i	$-0.801222\pi$
$239$	−7.70820	−	23.7234i	−0.498602	−	1.53454i	0.312664	−	0.949864i	$-0.398778\pi$
$240$		0			0
$241$	8.66312	−	26.6623i	0.558041	−	1.71747i	−0.129735	−	0.991549i	$-0.541413\pi$
$241$	8.66312	−	26.6623i	0.558041	−	1.71747i	0.687775	−	0.725923i	$-0.258587\pi$
$242$	−7.66312	−	5.56758i	−0.492604	−	0.357898i
$243$	−1.00000			−0.0641500
$244$	1.30902	+	0.951057i	0.0838012	+	0.0608852i
$245$		0			0
$246$	2.92705	−	2.12663i	0.186622	−	0.135589i
$247$	5.61803	−	4.08174i	0.357467	−	0.259715i
$248$	2.56231	+	7.88597i	0.162707	+	0.500759i
$249$	12.4721			0.790390
$250$		0			0
$251$	−9.05573			−0.571592			−0.285796	−	0.958290i	$-0.592258\pi$
$251$	−9.05573			−0.571592			−0.285796	+	0.958290i	$0.592258\pi$
$252$	−1.38197	−	4.25325i	−0.0870557	−	0.267930i
$253$	−4.47214	+	3.24920i	−0.281161	+	0.204275i
$254$	3.00000	−	2.17963i	0.188237	−	0.136762i
$255$		0			0
$256$	13.7533	+	9.99235i	0.859581	+	0.624522i
$257$	−11.7984			−0.735962			−0.367981	−	0.929833i	$-0.619951\pi$
$257$	−11.7984			−0.735962			−0.367981	+	0.929833i	$0.619951\pi$
$258$	6.23607	+	4.53077i	0.388241	+	0.282073i
$259$	4.27051	−	13.1433i	0.265357	−	0.816684i
$260$		0			0
$261$	2.04508	+	6.29412i	0.126588	+	0.389597i
$262$	2.52786	−	7.77997i	0.156172	−	0.480648i
$263$	7.38197	−	22.7194i	0.455192	−	1.40094i	−0.415719	−	0.909493i	$-0.636470\pi$
$263$	7.38197	−	22.7194i	0.455192	−	1.40094i	0.870910	−	0.491442i	$-0.163530\pi$
$264$	1.14590	+	3.52671i	0.0705251	+	0.217054i
$265$		0			0
$266$	−1.70820	+	5.25731i	−0.104737	+	0.322346i
$267$	4.35410	+	3.16344i	0.266467	+	0.193599i
$268$	0.763932			0.0466646
$269$	5.54508	+	4.02874i	0.338090	+	0.245637i	0.743855	−	0.668341i	$-0.232995\pi$
$269$	5.54508	+	4.02874i	0.338090	+	0.245637i	−0.405766	+	0.913977i	$0.632995\pi$
$270$		0			0
$271$	0.145898	−	0.106001i	0.00886267	−	0.00643911i	−0.583345	−	0.812224i	$-0.698256\pi$
$271$	0.145898	−	0.106001i	0.00886267	−	0.00643911i	0.592208	+	0.805785i	$0.298256\pi$
$272$	−3.11803	+	2.26538i	−0.189059	+	0.137359i
$273$	7.76393	+	23.8949i	0.469895	+	1.44619i
$274$	−7.61803			−0.460222
$275$		0			0
$276$	−4.47214			−0.269191
$277$	−5.80902	−	17.8783i	−0.349030	−	1.07420i	−0.959391	−	0.282080i	$-0.908976\pi$
$277$	−5.80902	−	17.8783i	−0.349030	−	1.07420i	0.610361	−	0.792124i	$-0.291024\pi$
$278$	−18.5623	+	13.4863i	−1.11329	+	0.808855i
$279$	−2.23607	+	1.62460i	−0.133870	+	0.0972622i
$280$		0			0
$281$	15.8713	+	11.5312i	0.946804	+	0.687893i	0.950049	−	0.312102i	$-0.101033\pi$
$281$	15.8713	+	11.5312i	0.946804	+	0.687893i	−0.00324500	+	0.999995i	$0.501033\pi$
$282$	0.763932			0.0454915
$283$	11.0902	+	8.05748i	0.659242	+	0.478967i	0.866407	−	0.499339i	$-0.166424\pi$
$283$	11.0902	+	8.05748i	0.659242	+	0.478967i	−0.207165	+	0.978306i	$0.566424\pi$
$284$	1.61803	−	4.97980i	0.0960127	−	0.295497i
$285$		0			0
$286$	−2.14590	−	6.60440i	−0.126890	−	0.390526i
$287$	−5.00000	+	15.3884i	−0.295141	+	0.908350i
$288$	−1.54508	+	4.75528i	−0.0910450	+	0.280208i
$289$	−0.663119	−	2.04087i	−0.0390070	−	0.120051i
$290$		0			0
$291$	0.663119	−	2.04087i	0.0388727	−	0.119638i
$292$	6.54508	+	4.75528i	0.383022	+	0.278282i
$293$	20.7984			1.21505			0.607527	−	0.794299i	$-0.292162\pi$
$293$	20.7984			1.21505			0.607527	+	0.794299i	$0.292162\pi$
$294$	−10.5172	−	7.64121i	−0.613377	−	0.445644i
$295$		0			0
$296$	−7.50000	+	5.44907i	−0.435929	+	0.316721i
$297$	−1.00000	+	0.726543i	−0.0580259	+	0.0421583i
$298$	5.82624	+	17.9313i	0.337505	+	1.03873i
$299$	25.1246			1.45299
$300$		0			0
$301$	−34.4721			−1.98694
$302$	−2.32624	−	7.15942i	−0.133860	−	0.411979i
$303$	2.88197	−	2.09387i	0.165565	−	0.120290i
$304$	1.00000	−	0.726543i	0.0573539	−	0.0416701i
$305$		0			0
$306$	−3.11803	−	2.26538i	−0.178246	−	0.129503i
$307$	−32.6525			−1.86358			−0.931788	−	0.363004i	$-0.881751\pi$
$307$	−32.6525			−1.86358			−0.931788	+	0.363004i	$0.881751\pi$
$308$	−4.47214	−	3.24920i	−0.254824	−	0.185140i
$309$	1.00000	−	3.07768i	0.0568880	−	0.175083i
$310$		0			0
$311$	5.47214	+	16.8415i	0.310296	+	0.954994i	0.977647	+	0.210251i	$0.0674280\pi$
$311$	5.47214	+	16.8415i	0.310296	+	0.954994i	−0.667351	+	0.744743i	$0.732572\pi$
$312$	5.20820	−	16.0292i	0.294856	−	0.907475i
$313$	0.145898	−	0.449028i	0.00824664	−	0.0253806i	−0.946849	−	0.321680i	$-0.895753\pi$
$313$	0.145898	−	0.449028i	0.00824664	−	0.0253806i	0.955095	+	0.296299i	$0.0957526\pi$
$314$	3.33688	+	10.2699i	0.188311	+	0.579562i
$315$		0			0
$316$		0			0
$317$	23.3262	+	16.9475i	1.31013	+	0.951867i	0.999999	+	0.00117338i	$0.000373499\pi$
$317$	23.3262	+	16.9475i	1.31013	+	0.951867i	0.310133	+	0.950693i	$0.399627\pi$
$318$	−3.61803			−0.202889
$319$	6.61803	+	4.80828i	0.370539	+	0.269212i
$320$		0			0
$321$	−6.09017	+	4.42477i	−0.339920	+	0.246966i
$322$	−16.1803	+	11.7557i	−0.901695	+	0.655120i
$323$	−1.47214	−	4.53077i	−0.0819118	−	0.252099i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−14.9443			−0.827687
$327$	2.44427	+	7.52270i	0.135169	+	0.416006i
$328$	8.78115	−	6.37988i	0.484858	−	0.352270i
$329$	−2.76393	+	2.00811i	−0.152381	+	0.110711i
$330$		0			0
$331$	5.61803	+	4.08174i	0.308795	+	0.224353i	0.731379	−	0.681971i	$-0.238877\pi$
$331$	5.61803	+	4.08174i	0.308795	+	0.224353i	−0.422584	+	0.906324i	$0.638877\pi$
$332$	12.4721			0.684497
$333$	−2.50000	−	1.81636i	−0.136999	−	0.0995357i
$334$	1.05573	−	3.24920i	0.0577669	−	0.177788i
$335$		0			0
$336$	1.38197	+	4.25325i	0.0753924	+	0.232034i
$337$	−0.909830	+	2.80017i	−0.0495616	+	0.152535i	−0.972774	−	0.231754i	$-0.925553\pi$
$337$	−0.909830	+	2.80017i	−0.0495616	+	0.152535i	0.923213	+	0.384289i	$0.125553\pi$
$338$	−5.73607	+	17.6538i	−0.312001	+	0.960240i
$339$	5.66312	+	17.4293i	0.307578	+	0.946629i
$340$		0			0
$341$	−1.05573	+	3.24920i	−0.0571709	+	0.175954i
$342$	1.00000	+	0.726543i	0.0540738	+	0.0392869i
$343$	26.8328			1.44884
$344$	18.7082	+	13.5923i	1.00868	+	0.732848i
$345$		0			0
$346$	−17.0623	+	12.3965i	−0.917275	+	0.666439i
$347$	−16.4164	+	11.9272i	−0.881279	+	0.640287i	−0.933590	−	0.358344i	$-0.883341\pi$
$347$	−16.4164	+	11.9272i	−0.881279	+	0.640287i	0.0523106	+	0.998631i	$0.483341\pi$
$348$	2.04508	+	6.29412i	0.109628	+	0.337400i
$349$	−4.03444			−0.215959			−0.107979	−	0.994153i	$-0.534438\pi$
$349$	−4.03444			−0.215959			−0.107979	+	0.994153i	$0.534438\pi$
$350$		0			0
$351$	5.61803			0.299868
$352$	1.90983	+	5.87785i	0.101794	+	0.313291i
$353$	11.6180	−	8.44100i	0.618366	−	0.449269i	−0.233985	−	0.972240i	$-0.575177\pi$
$353$	11.6180	−	8.44100i	0.618366	−	0.449269i	0.852350	+	0.522971i	$0.175177\pi$
$354$	3.23607	−	2.35114i	0.171995	−	0.124962i
$355$		0			0
$356$	4.35410	+	3.16344i	0.230767	+	0.167662i
$357$	17.2361			0.912229
$358$	−13.0902	−	9.51057i	−0.691837	−	0.502649i
$359$	−11.5623	+	35.5851i	−0.610235	+	1.87811i	−0.154507	+	0.987992i	$0.549379\pi$
$359$	−11.5623	+	35.5851i	−0.610235	+	1.87811i	−0.455728	+	0.890119i	$0.650621\pi$
$360$		0			0
$361$	−5.39919	−	16.6170i	−0.284168	−	0.874578i
$362$	−4.57295	+	14.0741i	−0.240349	+	0.739718i
$363$	2.92705	−	9.00854i	0.153630	−	0.472826i
$364$	7.76393	+	23.8949i	0.406941	+	1.25243i
$365$		0			0
$366$	0.500000	−	1.53884i	0.0261354	−	0.0804365i
$367$	−4.85410	−	3.52671i	−0.253382	−	0.184093i	0.453842	−	0.891082i	$-0.350053\pi$
$367$	−4.85410	−	3.52671i	−0.253382	−	0.184093i	−0.707224	+	0.706989i	$0.750053\pi$
$368$	4.47214			0.233126
$369$	2.92705	+	2.12663i	0.152376	+	0.110708i
$370$		0			0
$371$	13.0902	−	9.51057i	0.679608	−	0.493764i
$372$	−2.23607	+	1.62460i	−0.115935	+	0.0842315i
$373$	−0.798374	−	2.45714i	−0.0413382	−	0.127226i	0.928258	−	0.371938i	$-0.121307\pi$
$373$	−0.798374	−	2.45714i	−0.0413382	−	0.127226i	−0.969596	+	0.244712i	$0.921307\pi$
$374$	−4.76393			−0.246337
$375$		0			0
$376$	2.29180			0.118190
$377$	−11.4894	−	35.3606i	−0.591732	−	1.82116i
$378$	−3.61803	+	2.62866i	−0.186092	+	0.135203i
$379$	2.76393	−	2.00811i	0.141974	−	0.103150i	−0.514531	−	0.857472i	$-0.672034\pi$
$379$	2.76393	−	2.00811i	0.141974	−	0.103150i	0.656505	+	0.754322i	$0.272034\pi$
$380$		0			0
$381$	3.00000	+	2.17963i	0.153695	+	0.111666i
$382$	−6.65248			−0.340370
$383$	−26.5623	−	19.2986i	−1.35727	−	0.986115i	−0.998613	−	0.0526453i	$-0.983235\pi$
$383$	−26.5623	−	19.2986i	−1.35727	−	0.986115i	−0.358657	−	0.933469i	$-0.616765\pi$
$384$	−0.927051	+	2.85317i	−0.0473084	+	0.145600i
$385$		0			0
$386$	7.20820	+	22.1846i	0.366888	+	1.12916i
$387$	−2.38197	+	7.33094i	−0.121082	+	0.372652i
$388$	0.663119	−	2.04087i	0.0336648	−	0.103609i
$389$	−8.00658	−	24.6417i	−0.405950	−	1.24938i	−0.920100	−	0.391684i	$-0.871893\pi$
$389$	−8.00658	−	24.6417i	−0.405950	−	1.24938i	0.514150	−	0.857700i	$-0.328107\pi$
$390$		0			0
$391$	5.32624	−	16.3925i	0.269359	−	0.829003i
$392$	−31.5517	−	22.9236i	−1.59360	−	1.15782i
$393$	8.18034			0.412644
$394$	−6.16312	−	4.47777i	−0.310493	−	0.225587i
$395$		0			0
$396$	−1.00000	+	0.726543i	−0.0502519	+	0.0365101i
$397$	−5.61803	+	4.08174i	−0.281961	+	0.204857i	−0.719772	−	0.694210i	$-0.755754\pi$
$397$	−5.61803	+	4.08174i	−0.281961	+	0.204857i	0.437811	+	0.899067i	$0.355754\pi$
$398$	−3.90983	−	12.0332i	−0.195982	−	0.603171i
$399$	−5.52786			−0.276739
$400$		0			0
$401$	−22.4508			−1.12114			−0.560571	−	0.828106i	$-0.689418\pi$
$401$	−22.4508			−1.12114			−0.560571	+	0.828106i	$0.689418\pi$
$402$	−0.236068	−	0.726543i	−0.0117740	−	0.0362366i
$403$	12.5623	−	9.12705i	0.625773	−	0.454651i
$404$	2.88197	−	2.09387i	0.143383	−	0.104174i
$405$		0			0
$406$	23.9443	+	17.3965i	1.18833	+	0.863375i
$407$	−3.81966			−0.189334
$408$	−9.35410	−	6.79615i	−0.463097	−	0.336460i
$409$	0.371323	−	1.14281i	0.0183607	−	0.0565085i	−0.941456	−	0.337135i	$-0.890542\pi$
$409$	0.371323	−	1.14281i	0.0183607	−	0.0565085i	0.959817	+	0.280626i	$0.0905422\pi$
$410$		0			0
$411$	−2.35410	−	7.24518i	−0.116119	−	0.357378i
$412$	1.00000	−	3.07768i	0.0492665	−	0.151627i
$413$	−5.52786	+	17.0130i	−0.272008	+	0.837156i
$414$	1.38197	+	4.25325i	0.0679199	+	0.209036i
$415$		0			0
$416$	8.68034	−	26.7153i	0.425589	−	1.30983i
$417$	−18.5623	−	13.4863i	−0.909000	−	0.660427i
$418$	1.52786			0.0747303
$419$	−12.1803	−	8.84953i	−0.595049	−	0.432328i	0.249069	−	0.968486i	$-0.419875\pi$
$419$	−12.1803	−	8.84953i	−0.595049	−	0.432328i	−0.844118	+	0.536158i	$0.819875\pi$
$420$		0			0
$421$	−24.1525	+	17.5478i	−1.17712	+	0.855227i	−0.991844	−	0.127459i	$-0.959318\pi$
$421$	−24.1525	+	17.5478i	−1.17712	+	0.855227i	−0.185276	+	0.982687i	$0.559318\pi$
$422$	14.4721	−	10.5146i	0.704493	−	0.511844i
$423$	0.236068	+	0.726543i	0.0114780	+	0.0353257i
$424$	−10.8541			−0.527122
$425$		0			0
$426$	−5.23607			−0.253688
$427$	2.23607	+	6.88191i	0.108211	+	0.333039i
$428$	−6.09017	+	4.42477i	−0.294379	+	0.213879i
$429$	5.61803	−	4.08174i	0.271241	−	0.197068i
$430$		0			0
$431$	−16.7082	−	12.1392i	−0.804806	−	0.584726i	0.107514	−	0.994204i	$-0.465711\pi$
$431$	−16.7082	−	12.1392i	−0.804806	−	0.584726i	−0.912320	+	0.409478i	$0.865711\pi$
$432$	1.00000			0.0481125
$433$	−17.7812	−	12.9188i	−0.854508	−	0.620836i	0.0718775	−	0.997413i	$-0.477101\pi$
$433$	−17.7812	−	12.9188i	−0.854508	−	0.620836i	−0.926385	+	0.376577i	$0.877101\pi$
$434$	−3.81966	+	11.7557i	−0.183350	+	0.564292i
$435$		0			0
$436$	2.44427	+	7.52270i	0.117059	+	0.360272i
$437$	−1.70820	+	5.25731i	−0.0817145	+	0.251491i
$438$	2.50000	−	7.69421i	0.119455	−	0.367644i
$439$	5.00000	+	15.3884i	0.238637	+	0.734449i	0.996618	+	0.0821726i	$0.0261859\pi$
$439$	5.00000	+	15.3884i	0.238637	+	0.734449i	−0.757981	+	0.652276i	$0.773814\pi$
$440$		0			0
$441$	4.01722	−	12.3637i	0.191296	−	0.588749i
$442$	17.5172	+	12.7270i	0.833209	+	0.605362i
$443$	35.2361			1.67412			0.837058	−	0.547114i	$-0.184274\pi$
$443$	35.2361			1.67412			0.837058	+	0.547114i	$0.184274\pi$
$444$	−2.50000	−	1.81636i	−0.118645	−	0.0862005i
$445$		0			0
$446$	−6.61803	+	4.80828i	−0.313373	+	0.227679i
$447$	−15.2533	+	11.0822i	−0.721456	+	0.524168i
$448$	9.67376	+	29.7728i	0.457042	+	1.40663i
$449$	16.7984			0.792764			0.396382	−	0.918086i	$-0.370266\pi$
$449$	16.7984			0.792764			0.396382	+	0.918086i	$0.370266\pi$
$450$		0			0
$451$	4.47214			0.210585
$452$	5.66312	+	17.4293i	0.266371	+	0.819805i
$453$	6.09017	−	4.42477i	0.286141	−	0.207894i
$454$	16.1803	−	11.7557i	0.759381	−	0.551723i
$455$		0			0
$456$	3.00000	+	2.17963i	0.140488	+	0.102070i
$457$	22.3607			1.04599			0.522994	−	0.852336i	$-0.324815\pi$
$457$	22.3607			1.04599			0.522994	+	0.852336i	$0.324815\pi$
$458$	17.7812	+	12.9188i	0.830859	+	0.603654i
$459$	1.19098	−	3.66547i	0.0555903	−	0.171089i
$460$		0			0
$461$	−10.1353	−	31.1931i	−0.472046	−	1.45281i	−0.849901	−	0.526943i	$-0.823338\pi$
$461$	−10.1353	−	31.1931i	−0.472046	−	1.45281i	0.377855	−	0.925865i	$-0.376662\pi$
$462$	−1.70820	+	5.25731i	−0.0794728	+	0.244592i
$463$	−5.79837	+	17.8456i	−0.269473	+	0.829353i	0.721156	+	0.692773i	$0.243611\pi$
$463$	−5.79837	+	17.8456i	−0.269473	+	0.829353i	−0.990629	+	0.136580i	$0.956389\pi$
$464$	−2.04508	−	6.29412i	−0.0949407	−	0.292197i
$465$		0			0
$466$	3.82624	−	11.7759i	0.177247	−	0.545510i
$467$	22.7984	+	16.5640i	1.05498	+	0.766490i	0.973154	−	0.230156i	$-0.0739238\pi$
$467$	22.7984	+	16.5640i	1.05498	+	0.766490i	0.0818293	+	0.996646i	$0.473924\pi$
$468$	5.61803			0.259694
$469$	2.76393	+	2.00811i	0.127627	+	0.0927261i
$470$		0			0
$471$	−8.73607	+	6.34712i	−0.402537	+	0.292460i
$472$	9.70820	−	7.05342i	0.446856	−	0.324660i
$473$	2.94427	+	9.06154i	0.135378	+	0.416650i
$474$		0			0
$475$		0			0
$476$	17.2361			0.790014
$477$	−1.11803	−	3.44095i	−0.0511913	−	0.157550i
$478$	−20.1803	+	14.6619i	−0.923027	+	0.670619i
$479$	−15.3262	+	11.1352i	−0.700274	+	0.508779i	−0.880021	−	0.474934i	$-0.842472\pi$
$479$	−15.3262	+	11.1352i	−0.700274	+	0.508779i	0.179748	+	0.983713i	$0.442472\pi$
$480$		0			0
$481$	14.0451	+	10.2044i	0.640401	+	0.465278i
$482$	−28.0344			−1.27693
$483$	−16.1803	−	11.7557i	−0.736231	−	0.534903i
$484$	2.92705	−	9.00854i	0.133048	−	0.409479i
$485$		0			0
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	−3.00000	+	9.23305i	−0.135943	+	0.418389i	−0.995736	−	0.0922541i	$-0.970593\pi$
$487$	−3.00000	+	9.23305i	−0.135943	+	0.418389i	0.859793	+	0.510644i	$0.170593\pi$
$488$	1.50000	−	4.61653i	0.0679018	−	0.208980i
$489$	−4.61803	−	14.2128i	−0.208835	−	0.642727i
$490$		0			0
$491$	1.81966	−	5.60034i	0.0821201	−	0.252740i	−0.901563	−	0.432647i	$-0.857580\pi$
$491$	1.81966	−	5.60034i	0.0821201	−	0.252740i	0.983684	+	0.179907i	$0.0575797\pi$
$492$	2.92705	+	2.12663i	0.131962	+	0.0958758i
$493$	−25.5066			−1.14876
$494$	−5.61803	−	4.08174i	−0.252767	−	0.183646i
$495$		0			0
$496$	2.23607	−	1.62460i	0.100402	−	0.0729466i
$497$	18.9443	−	13.7638i	0.849767	−	0.617392i
$498$	−3.85410	−	11.8617i	−0.172706	−	0.531536i
$499$	−6.00000			−0.268597			−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000			−0.268597			−0.134298	+	0.990941i	$0.542878\pi$
$500$		0			0
$501$	3.41641			0.152634
$502$	2.79837	+	8.61251i	0.124898	+	0.384395i
$503$	6.94427	−	5.04531i	0.309630	−	0.224959i	−0.422108	−	0.906546i	$-0.638710\pi$
$503$	6.94427	−	5.04531i	0.309630	−	0.224959i	0.731738	+	0.681586i	$0.238710\pi$
$504$	−10.8541	+	7.88597i	−0.483480	+	0.351269i
$505$		0			0
$506$	4.47214	+	3.24920i	0.198811	+	0.144444i
$507$	−18.5623			−0.824381
$508$	3.00000	+	2.17963i	0.133103	+	0.0967053i
$509$	6.22542	−	19.1599i	0.275937	−	0.849247i	−0.713033	−	0.701131i	$-0.752679\pi$
$509$	6.22542	−	19.1599i	0.275937	−	0.849247i	0.988970	−	0.148116i	$-0.0473210\pi$
$510$		0			0
$511$	11.1803	+	34.4095i	0.494589	+	1.52219i
$512$	3.39919	−	10.4616i	0.150224	−	0.462343i
$513$	−0.381966	+	1.17557i	−0.0168642	+	0.0519027i
$514$	3.64590	+	11.2209i	0.160814	+	0.494934i
$515$		0			0
$516$	−2.38197	+	7.33094i	−0.104860	+	0.322727i
$517$	0.763932	+	0.555029i	0.0335977	+	0.0244102i
$518$	−13.8197			−0.607201
$519$	−17.0623	−	12.3965i	−0.748952	−	0.544146i
$520$		0			0
$521$	21.8713	−	15.8904i	0.958200	−	0.696173i	0.00546804	−	0.999985i	$-0.498259\pi$
$521$	21.8713	−	15.8904i	0.958200	−	0.696173i	0.952732	+	0.303812i	$0.0982595\pi$
$522$	5.35410	−	3.88998i	0.234343	−	0.170260i
$523$	7.94427	+	24.4500i	0.347379	+	1.06912i	0.960298	+	0.278976i	$0.0899951\pi$
$523$	7.94427	+	24.4500i	0.347379	+	1.06912i	−0.612919	+	0.790146i	$0.710005\pi$
$524$	8.18034			0.357360
$525$		0			0
$526$	−23.8885			−1.04159
$527$	−3.29180	−	10.1311i	−0.143393	−	0.441318i
$528$	1.00000	−	0.726543i	0.0435194	−	0.0316187i
$529$	2.42705	−	1.76336i	0.105524	−	0.0766676i
$530$		0			0
$531$	3.23607	+	2.35114i	0.140433	+	0.102031i
$532$	−5.52786			−0.239663
$533$	−16.4443	−	11.9475i	−0.712280	−	0.517502i
$534$	1.66312	−	5.11855i	0.0719702	−	0.221501i
$535$		0			0
$536$	−0.708204	−	2.17963i	−0.0305898	−	0.0941456i
$537$	5.00000	−	15.3884i	0.215766	−	0.664059i
$538$	2.11803	−	6.51864i	0.0913149	−	0.281038i
$539$	−4.96556	−	15.2824i	−0.213882	−	0.658260i
$540$		0			0
$541$	−6.07953	+	18.7109i	−0.261379	+	0.804443i	0.731126	+	0.682242i	$0.238995\pi$
$541$	−6.07953	+	18.7109i	−0.261379	+	0.804443i	−0.992505	+	0.122200i	$0.961005\pi$
$542$	−0.145898	−	0.106001i	−0.00626686	−	0.00455314i
$543$	−14.7984			−0.635059
$544$	−15.5902	−	11.3269i	−0.668423	−	0.485638i
$545$		0			0
$546$	20.3262	−	14.7679i	0.869883	−	0.632007i
$547$	34.2705	−	24.8990i	1.46530	−	1.06460i	0.483359	−	0.875422i	$-0.339417\pi$
$547$	34.2705	−	24.8990i	1.46530	−	1.06460i	0.981942	−	0.189181i	$-0.0605834\pi$
$548$	−2.35410	−	7.24518i	−0.100562	−	0.309499i
$549$	1.61803			0.0690560
$550$		0			0
$551$	8.18034			0.348494
$552$	4.14590	+	12.7598i	0.176461	+	0.543092i
$553$		0			0
$554$	−15.2082	+	11.0494i	−0.646135	+	0.469444i
$555$		0			0
$556$	−18.5623	−	13.4863i	−0.787217	−	0.571947i
$557$	11.2705			0.477547			0.238773	−	0.971075i	$-0.423255\pi$
$557$	11.2705			0.477547			0.238773	+	0.971075i	$0.423255\pi$
$558$	2.23607	+	1.62460i	0.0946603	+	0.0687747i
$559$	13.3820	−	41.1855i	0.565997	−	1.74196i
$560$		0			0
$561$	−1.47214	−	4.53077i	−0.0621536	−	0.191289i
$562$	6.06231	−	18.6579i	0.255723	−	0.787034i
$563$	8.18034	−	25.1765i	0.344760	−	1.06106i	−0.616952	−	0.787001i	$-0.711633\pi$
$563$	8.18034	−	25.1765i	0.344760	−	1.06106i	0.961712	−	0.274062i	$-0.0883673\pi$
$564$	0.236068	+	0.726543i	0.00994026	+	0.0305930i
$565$		0			0
$566$	4.23607	−	13.0373i	0.178055	−	0.547998i
$567$	−3.61803	−	2.62866i	−0.151943	−	0.110393i
$568$	−15.7082			−0.659102
$569$	−2.64590	−	1.92236i	−0.110922	−	0.0805894i	0.530942	−	0.847408i	$-0.321838\pi$
$569$	−2.64590	−	1.92236i	−0.110922	−	0.0805894i	−0.641863	+	0.766819i	$0.721838\pi$
$570$		0			0
$571$	13.5623	−	9.85359i	0.567565	−	0.412360i	−0.266655	−	0.963792i	$-0.585918\pi$
$571$	13.5623	−	9.85359i	0.567565	−	0.412360i	0.834220	+	0.551432i	$0.185918\pi$
$572$	5.61803	−	4.08174i	0.234902	−	0.170666i
$573$	−2.05573	−	6.32688i	−0.0858793	−	0.264309i
$574$	16.1803			0.675354
$575$		0			0
$576$	7.00000			0.291667
$577$	4.03444	+	12.4167i	0.167956	+	0.516915i	0.999242	−	0.0389296i	$-0.0123948\pi$
$577$	4.03444	+	12.4167i	0.167956	+	0.516915i	−0.831286	+	0.555845i	$0.812395\pi$
$578$	−1.73607	+	1.26133i	−0.0722109	+	0.0524643i
$579$	−18.8713	+	13.7108i	−0.784265	+	0.569802i
$580$		0			0
$581$	45.1246	+	32.7849i	1.87208	+	1.36015i
$582$	−2.14590			−0.0889503
$583$	−3.61803	−	2.62866i	−0.149844	−	0.108868i
$584$	7.50000	−	23.0826i	0.310352	−	0.955166i
$585$		0			0
$586$	−6.42705	−	19.7804i	−0.265499	−	0.817122i
$587$	12.7984	−	39.3893i	0.528245	−	1.62577i	−0.229562	−	0.973294i	$-0.573729\pi$
$587$	12.7984	−	39.3893i	0.528245	−	1.62577i	0.757807	−	0.652478i	$-0.226271\pi$
$588$	4.01722	−	12.3637i	0.165667	−	0.509872i
$589$	1.05573	+	3.24920i	0.0435005	+	0.133881i
$590$		0			0
$591$	2.35410	−	7.24518i	0.0968348	−	0.298027i
$592$	2.50000	+	1.81636i	0.102749	+	0.0746518i
$593$	−9.74265			−0.400083			−0.200041	−	0.979787i	$-0.564108\pi$
$593$	−9.74265			−0.400083			−0.200041	+	0.979787i	$0.564108\pi$
$594$	1.00000	+	0.726543i	0.0410305	+	0.0298104i
$595$		0			0
$596$	−15.2533	+	11.0822i	−0.624799	+	0.453943i
$597$	10.2361	−	7.43694i	0.418934	−	0.304374i
$598$	−7.76393	−	23.8949i	−0.317491	−	0.977136i
$599$	−3.52786			−0.144145			−0.0720723	−	0.997399i	$-0.522961\pi$
$599$	−3.52786			−0.144145			−0.0720723	+	0.997399i	$0.522961\pi$
$600$		0			0
$601$	−8.67376			−0.353810			−0.176905	−	0.984228i	$-0.556609\pi$
$601$	−8.67376			−0.353810			−0.176905	+	0.984228i	$0.556609\pi$
$602$	10.6525	+	32.7849i	0.434163	+	1.33621i
$603$	0.618034	−	0.449028i	0.0251683	−	0.0182858i
$604$	6.09017	−	4.42477i	0.247806	−	0.180041i
$605$		0			0
$606$	−2.88197	−	2.09387i	−0.117072	−	0.0850577i
$607$	34.7639			1.41102			0.705512	−	0.708698i	$-0.250717\pi$
$607$	34.7639			1.41102			0.705512	+	0.708698i	$0.250717\pi$
$608$	5.00000	+	3.63271i	0.202777	+	0.147326i
$609$	−9.14590	+	28.1482i	−0.370610	+	1.14062i
$610$		0			0
$611$	−1.32624	−	4.08174i	−0.0536538	−	0.165130i
$612$	1.19098	−	3.66547i	0.0481426	−	0.148168i
$613$	−0.461493	+	1.42033i	−0.0186395	+	0.0573665i	−0.959944	−	0.280193i	$-0.909601\pi$
$613$	−0.461493	+	1.42033i	−0.0186395	+	0.0573665i	0.941304	+	0.337560i	$0.109601\pi$
$614$	10.0902	+	31.0543i	0.407206	+	1.25325i
$615$		0			0
$616$	−5.12461	+	15.7719i	−0.206476	+	0.635469i
$617$	−16.1631	−	11.7432i	−0.650703	−	0.472763i	0.212808	−	0.977094i	$-0.431739\pi$
$617$	−16.1631	−	11.7432i	−0.650703	−	0.472763i	−0.863510	+	0.504331i	$0.831739\pi$
$618$	−3.23607			−0.130174
$619$	13.2361	+	9.61657i	0.532002	+	0.386522i	0.821106	−	0.570775i	$-0.193357\pi$
$619$	13.2361	+	9.61657i	0.532002	+	0.386522i	−0.289104	+	0.957298i	$0.593357\pi$
$620$		0			0
$621$	−3.61803	+	2.62866i	−0.145187	+	0.105484i
$622$	14.3262	−	10.4086i	0.574430	−	0.417348i
$623$	7.43769	+	22.8909i	0.297985	+	0.917103i
$624$	−5.61803			−0.224901
$625$		0			0
$626$	−0.472136			−0.0188703
$627$	0.472136	+	1.45309i	0.0188553	+	0.0580306i
$628$	−8.73607	+	6.34712i	−0.348607	+	0.253278i
$629$	9.63525	−	7.00042i	0.384183	−	0.279125i
$630$		0			0
$631$	−19.1803	−	13.9353i	−0.763557	−	0.554757i	0.136442	−	0.990648i	$-0.456433\pi$
$631$	−19.1803	−	13.9353i	−0.763557	−	0.554757i	−0.899999	+	0.435891i	$0.856433\pi$
$632$		0			0
$633$	14.4721	+	10.5146i	0.575216	+	0.417919i
$634$	8.90983	−	27.4216i	0.353855	−	1.08905i
$635$		0			0
$636$	−1.11803	−	3.44095i	−0.0443329	−	0.136443i
$637$	−22.5689	+	69.4599i	−0.894212	+	2.75210i
$638$	2.52786	−	7.77997i	0.100079	−	0.308012i
$639$	−1.61803	−	4.97980i	−0.0640084	−	0.196998i
$640$		0			0
$641$	6.50658	−	20.0252i	0.256994	−	0.790947i	−0.736436	−	0.676507i	$-0.763493\pi$
$641$	6.50658	−	20.0252i	0.256994	−	0.790947i	0.993430	−	0.114440i	$-0.0365073\pi$
$642$	6.09017	+	4.42477i	0.240360	+	0.174632i
$643$	21.8885			0.863200			0.431600	−	0.902065i	$-0.357949\pi$
$643$	21.8885			0.863200			0.431600	+	0.902065i	$0.357949\pi$
$644$	−16.1803	−	11.7557i	−0.637595	−	0.463240i
$645$		0			0
$646$	−3.85410	+	2.80017i	−0.151638	+	0.110171i
$647$	−27.7984	+	20.1967i	−1.09287	+	0.794014i	−0.979881	−	0.199582i	$-0.936041\pi$
$647$	−27.7984	+	20.1967i	−1.09287	+	0.794014i	−0.112986	+	0.993597i	$0.536041\pi$
$648$	0.927051	+	2.85317i	0.0364180	+	0.112083i
$649$	4.94427			0.194080
$650$		0			0
$651$	−12.3607			−0.484453
$652$	−4.61803	−	14.2128i	−0.180856	−	0.556618i
$653$	−34.0623	+	24.7477i	−1.33296	+	0.968453i	−0.333289	+	0.942825i	$0.608159\pi$
$653$	−34.0623	+	24.7477i	−1.33296	+	0.968453i	−0.999672	+	0.0256283i	$0.991841\pi$
$654$	6.39919	−	4.64928i	0.250228	−	0.181801i
$655$		0			0
$656$	−2.92705	−	2.12663i	−0.114282	−	0.0830308i
$657$	8.09017			0.315628
$658$	2.76393	+	2.00811i	0.107749	+	0.0782844i
$659$	−10.3262	+	31.7809i	−0.402253	+	1.23801i	0.520914	+	0.853609i	$0.325591\pi$
$659$	−10.3262	+	31.7809i	−0.402253	+	1.23801i	−0.923167	+	0.384399i	$0.874409\pi$
$660$		0			0
$661$	−0.437694	−	1.34708i	−0.0170243	−	0.0523955i	0.942183	−	0.335097i	$-0.108769\pi$
$661$	−0.437694	−	1.34708i	−0.0170243	−	0.0523955i	−0.959208	+	0.282702i	$0.908769\pi$
$662$	2.14590	−	6.60440i	0.0834027	−	0.256687i
$663$	−6.69098	+	20.5927i	−0.259856	+	0.799755i
$664$	−11.5623	−	35.5851i	−0.448704	−	1.38097i
$665$		0			0
$666$	−0.954915	+	2.93893i	−0.0370022	+	0.113881i
$667$	23.9443	+	17.3965i	0.927126	+	0.673596i
$668$	3.41641			0.132185
$669$	−6.61803	−	4.80828i	−0.255868	−	0.185899i
$670$		0			0
$671$	1.61803	−	1.17557i	0.0624635	−	0.0453824i
$672$	−18.0902	+	13.1433i	−0.697843	+	0.507013i
$673$	−1.60739	−	4.94704i	−0.0619604	−	0.190694i	0.915285	−	0.402807i	$-0.131966\pi$
$673$	−1.60739	−	4.94704i	−0.0619604	−	0.190694i	−0.977245	+	0.212113i	$0.931966\pi$
$674$	2.94427			0.113409
$675$		0			0
$676$	−18.5623			−0.713935
$677$	−3.27051	−	10.0656i	−0.125696	−	0.386852i	0.868331	−	0.495985i	$-0.165193\pi$
$677$	−3.27051	−	10.0656i	−0.125696	−	0.386852i	−0.994027	+	0.109132i	$0.965193\pi$
$678$	14.8262	−	10.7719i	0.569398	−	0.413692i
$679$	7.76393	−	5.64083i	0.297952	−	0.216475i
$680$		0			0
$681$	16.1803	+	11.7557i	0.620032	+	0.450480i
$682$	3.41641			0.130821
$683$	−15.7082	−	11.4127i	−0.601058	−	0.436694i	0.245196	−	0.969473i	$-0.421148\pi$
$683$	−15.7082	−	11.4127i	−0.601058	−	0.436694i	−0.846254	+	0.532779i	$0.821148\pi$
$684$	−0.381966	+	1.17557i	−0.0146048	+	0.0449491i
$685$		0			0
$686$	−8.29180	−	25.5195i	−0.316582	−	0.974340i
$687$	−6.79180	+	20.9030i	−0.259123	+	0.797499i
$688$	2.38197	−	7.33094i	0.0908116	−	0.279489i
$689$	6.28115	+	19.3314i	0.239293	+	0.736468i
$690$		0			0
$691$	−5.18034	+	15.9434i	−0.197069	+	0.606517i	0.802877	+	0.596145i	$0.203302\pi$
$691$	−5.18034	+	15.9434i	−0.197069	+	0.606517i	−0.999946	+	0.0103723i	$0.996698\pi$
$692$	−17.0623	−	12.3965i	−0.648612	−	0.471244i
$693$	−5.52786			−0.209986
$694$	16.4164	+	11.9272i	0.623158	+	0.452751i
$695$		0			0
$696$	16.0623	−	11.6699i	0.608840	−	0.442348i
$697$	−11.2812	+	8.19624i	−0.427304	+	0.310455i
$698$	1.24671	+	3.83698i	0.0471887	+	0.145232i
$699$	12.3820			0.468329
$700$		0			0
$701$	20.5623			0.776628			0.388314	−	0.921527i	$-0.373058\pi$
$701$	20.5623			0.776628			0.388314	+	0.921527i	$0.373058\pi$
$702$	−1.73607	−	5.34307i	−0.0655237	−	0.201661i
$703$	−3.09017	+	2.24514i	−0.116548	+	0.0846771i
$704$	7.00000	−	5.08580i	0.263822	−	0.191678i
$705$		0			0
$706$	−11.6180	−	8.44100i	−0.437250	−	0.317681i
$707$	15.9311			0.599151
$708$	3.23607	+	2.35114i	0.121619	+	0.0883613i
$709$	−12.4443	+	38.2995i	−0.467354	+	1.43837i	0.388643	+	0.921389i	$0.372944\pi$
$709$	−12.4443	+	38.2995i	−0.467354	+	1.43837i	−0.855997	+	0.516981i	$0.827056\pi$
$710$		0			0
$711$		0			0
$712$	4.98936	−	15.3557i	0.186984	−	0.575478i
$713$	−3.81966	+	11.7557i	−0.143047	+	0.440255i
$714$	−5.32624	−	16.3925i	−0.199329	−	0.613473i
$715$		0			0
$716$	5.00000	−	15.3884i	0.186859	−	0.575092i
$717$	−20.1803	−	14.6619i	−0.753649	−	0.547558i
$718$	37.4164			1.39637
$719$	0.0901699	+	0.0655123i	0.00336277	+	0.00244320i	0.589465	−	0.807794i	$-0.299338\pi$
$719$	0.0901699	+	0.0655123i	0.00336277	+	0.00244320i	−0.586103	+	0.810237i	$0.699338\pi$
$720$		0			0
$721$	11.7082	−	8.50651i	0.436036	−	0.316799i
$722$	−14.1353	+	10.2699i	−0.526060	+	0.382205i
$723$	−8.66312	−	26.6623i	−0.322185	−	0.991583i
$724$	−14.7984			−0.549977
$725$		0			0
$726$	−9.47214			−0.351544
$727$	−14.4164	−	44.3691i	−0.534675	−	1.64556i	−0.744350	−	0.667789i	$-0.767241\pi$
$727$	−14.4164	−	44.3691i	−0.534675	−	1.64556i	0.209675	−	0.977771i	$-0.432759\pi$
$728$	60.9787	−	44.3036i	2.26002	−	1.64200i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−24.0344	−	17.4620i	−0.888946	−	0.645857i
$732$	1.61803			0.0598043
$733$	23.7984	+	17.2905i	0.879013	+	0.638640i	0.932990	−	0.359902i	$-0.117190\pi$
$733$	23.7984	+	17.2905i	0.879013	+	0.638640i	−0.0539772	+	0.998542i	$0.517190\pi$
$734$	−1.85410	+	5.70634i	−0.0684362	+	0.210625i
$735$		0			0
$736$	6.90983	+	21.2663i	0.254700	+	0.783885i
$737$	0.291796	−	0.898056i	0.0107484	−	0.0330803i
$738$	1.11803	−	3.44095i	0.0411554	−	0.126663i
$739$	1.32624	+	4.08174i	0.0487865	+	0.150149i	0.972482	−	0.232978i	$-0.0748470\pi$
$739$	1.32624	+	4.08174i	0.0487865	+	0.150149i	−0.923696	+	0.383127i	$0.874847\pi$
$740$		0			0
$741$	2.14590	−	6.60440i	0.0788315	−	0.242619i
$742$	−13.0902	−	9.51057i	−0.480555	−	0.349144i
$743$	−41.1246			−1.50872			−0.754358	−	0.656463i	$-0.772052\pi$
$743$	−41.1246			−1.50872			−0.754358	+	0.656463i	$0.772052\pi$
$744$	6.70820	+	4.87380i	0.245935	+	0.178682i
$745$		0			0
$746$	−2.09017	+	1.51860i	−0.0765266	+	0.0555998i
$747$	10.0902	−	7.33094i	0.369180	−	0.268225i
$748$	−1.47214	−	4.53077i	−0.0538266	−	0.165661i
$749$	−33.6656			−1.23012
$750$		0			0
$751$	36.6525			1.33747			0.668734	−	0.743502i	$-0.266837\pi$
$751$	36.6525			1.33747			0.668734	+	0.743502i	$0.266837\pi$
$752$	−0.236068	−	0.726543i	−0.00860851	−	0.0264943i
$753$	−7.32624	+	5.32282i	−0.266983	+	0.193974i
$754$	−30.0795	+	21.8541i	−1.09543	+	0.795878i
$755$		0			0
$756$	−3.61803	−	2.62866i	−0.131587	−	0.0956033i
$757$	−29.6180			−1.07649			−0.538243	−	0.842790i	$-0.680912\pi$
$757$	−29.6180			−1.07649			−0.538243	+	0.842790i	$0.680912\pi$
$758$	−2.76393	−	2.00811i	−0.100391	−	0.0729380i
$759$	−1.70820	+	5.25731i	−0.0620039	+	0.190828i
$760$		0			0
$761$	10.1180	+	31.1401i	0.366778	+	1.12883i	0.948860	+	0.315697i	$0.102238\pi$
$761$	10.1180	+	31.1401i	0.366778	+	1.12883i	−0.582081	+	0.813130i	$0.697762\pi$
$762$	1.14590	−	3.52671i	0.0415115	−	0.127759i
$763$	−10.9311	+	33.6425i	−0.395733	+	1.21794i
$764$	−2.05573	−	6.32688i	−0.0743736	−	0.228899i
$765$		0			0
$766$	−10.1459	+	31.2259i	−0.366586	+	1.12824i
$767$	−18.1803	−	13.2088i	−0.656454	−	0.476942i
$768$	17.0000			0.613435
$769$	40.7426	+	29.6013i	1.46922	+	1.06745i	0.980840	+	0.194817i	$0.0624112\pi$
$769$	40.7426	+	29.6013i	1.46922	+	1.06745i	0.488378	+	0.872632i	$0.337589\pi$
$770$		0			0
$771$	−9.54508	+	6.93491i	−0.343758	+	0.249755i
$772$	−18.8713	+	13.7108i	−0.679194	+	0.493463i
$773$	−8.93769	−	27.5074i	−0.321467	−	0.989372i	−0.973010	−	0.230761i	$-0.925878\pi$
$773$	−8.93769	−	27.5074i	−0.321467	−	0.989372i	0.651544	−	0.758611i	$-0.274122\pi$
$774$	7.70820			0.277066
$775$		0			0
$776$	−6.43769			−0.231100
$777$	−4.27051	−	13.1433i	−0.153204	−	0.471512i
$778$	−20.9615	+	15.2294i	−0.751506	+	0.546001i
$779$	3.61803	−	2.62866i	0.129630	−	0.0941814i
$780$		0			0
$781$	−5.23607	−	3.80423i	−0.187361	−	0.136126i
$782$	−17.2361			−0.616361
$783$	5.35410	+	3.88998i	0.191340	+	0.139017i
$784$	−4.01722	+	12.3637i	−0.143472	+	0.441562i
$785$		0			0
$786$	−2.52786	−	7.77997i	−0.0901659	−	0.277502i
$787$	4.38197	−	13.4863i	0.156200	−	0.480735i	−0.842080	−	0.539352i	$-0.818669\pi$
$787$	4.38197	−	13.4863i	0.156200	−	0.480735i	0.998281	+	0.0586173i	$0.0186692\pi$
$788$	2.35410	−	7.24518i	0.0838614	−	0.258099i
$789$	−7.38197	−	22.7194i	−0.262805	−	0.808830i
$790$		0			0
$791$	−25.3262	+	77.9461i	−0.900497	+	2.77145i
$792$	3.00000	+	2.17963i	0.106600	+	0.0774497i
$793$	−9.09017			−0.322801
$794$	5.61803	+	4.08174i	0.199377	+	0.144856i
$795$		0			0
$796$	10.2361	−	7.43694i	0.362808	−	0.263595i
$797$	−39.7254	+	28.8622i	−1.40715	+	1.02235i	−0.413417	+	0.910542i	$0.635665\pi$
$797$	−39.7254	+	28.8622i	−1.40715	+	1.02235i	−0.993730	+	0.111810i	$0.964335\pi$
$798$	1.70820	+	5.25731i	0.0604698	+	0.186107i
$799$	−2.94427			−0.104161
$800$		0			0
$801$	5.38197			0.190162
$802$	6.93769	+	21.3520i	0.244978	+	0.753966i
$803$	8.09017	−	5.87785i	0.285496	−	0.207425i
$804$	0.618034	−	0.449028i	0.0217964	−	0.0158360i
$805$		0			0
$806$	−12.5623	−	9.12705i	−0.442488	−	0.321487i
$807$	6.85410			0.241276
$808$	−8.64590	−	6.28161i	−0.304162	−	0.220986i
$809$	8.71885	−	26.8339i	0.306538	−	0.943428i	−0.672560	−	0.740042i	$-0.734805\pi$
$809$	8.71885	−	26.8339i	0.306538	−	0.943428i	0.979099	−	0.203386i	$-0.0651945\pi$
$810$		0			0
$811$	1.47214	+	4.53077i	0.0516937	+	0.159097i	0.973571	−	0.228386i	$-0.0733447\pi$
$811$	1.47214	+	4.53077i	0.0516937	+	0.159097i	−0.921877	+	0.387483i	$0.873345\pi$
$812$	−9.14590	+	28.1482i	−0.320958	+	0.987807i
$813$	0.0557281	−	0.171513i	0.00195447	−	0.00601524i
$814$	1.18034	+	3.63271i	0.0413709	+	0.127327i
$815$		0			0
$816$	−1.19098	+	3.66547i	−0.0416927	+	0.128317i
$817$	7.70820	+	5.60034i	0.269676	+	0.195931i
$818$	−1.20163			−0.0420139
$819$	20.3262	+	14.7679i	0.710256	+	0.516031i
$820$		0			0
$821$	−18.5623	+	13.4863i	−0.647829	+	0.470675i	−0.862531	−	0.506004i	$-0.831122\pi$
$821$	−18.5623	+	13.4863i	−0.647829	+	0.470675i	0.214702	+	0.976680i	$0.431122\pi$
$822$	−6.16312	+	4.47777i	−0.214963	+	0.156180i
$823$	5.94427	+	18.2946i	0.207204	+	0.637709i	0.999616	+	0.0277222i	$0.00882537\pi$
$823$	5.94427	+	18.2946i	0.207204	+	0.637709i	−0.792411	+	0.609987i	$0.791175\pi$
$824$	−9.70820			−0.338201
$825$		0			0
$826$	17.8885			0.622422
$827$	11.1459	+	34.3035i	0.387581	+	1.19285i	0.934591	+	0.355725i	$0.115766\pi$
$827$	11.1459	+	34.3035i	0.387581	+	1.19285i	−0.547010	+	0.837126i	$0.684234\pi$
$828$	−3.61803	+	2.62866i	−0.125735	+	0.0913521i
$829$	−9.30902	+	6.76340i	−0.323316	+	0.234902i	−0.737589	−	0.675250i	$-0.764036\pi$
$829$	−9.30902	+	6.76340i	−0.323316	+	0.234902i	0.414273	+	0.910152i	$0.364036\pi$
$830$		0			0
$831$	−15.2082	−	11.0494i	−0.527567	−	0.383300i
$832$	−39.3262			−1.36339
$833$	40.5344	+	29.4500i	1.40444	+	1.02038i
$834$	−7.09017	+	21.8213i	−0.245513	+	0.755610i
$835$		0			0
$836$	0.472136	+	1.45309i	0.0163292	+	0.0502560i
$837$	−0.854102	+	2.62866i	−0.0295221	+	0.0908596i
$838$	−4.65248	+	14.3188i	−0.160717	+	0.494636i
$839$	4.34752	+	13.3803i	0.150093	+	0.461939i	0.997631	−	0.0687961i	$-0.0219158\pi$
$839$	4.34752	+	13.3803i	0.150093	+	0.461939i	−0.847538	+	0.530735i	$0.821916\pi$
$840$		0			0
$841$	4.57295	−	14.0741i	0.157688	−	0.485313i
$842$	24.1525	+	17.5478i	0.832349	+	0.604737i
$843$	19.6180			0.675681
$844$	14.4721	+	10.5146i	0.498151	+	0.361928i
$845$		0			0
$846$	0.618034	−	0.449028i	0.0212484	−	0.0154379i
$847$	34.2705	−	24.8990i	1.17755	−	0.855539i
$848$	1.11803	+	3.44095i	0.0383934	+	0.118163i
$849$	13.7082			0.470464
$850$		0			0
$851$	−13.8197			−0.473732
$852$	−1.61803	−	4.97980i	−0.0554329	−	0.170605i
$853$	18.7254	−	13.6048i	0.641146	−	0.465820i	−0.219097	−	0.975703i	$-0.570311\pi$
$853$	18.7254	−	13.6048i	0.641146	−	0.465820i	0.860244	+	0.509883i	$0.170311\pi$
$854$	5.85410	−	4.25325i	0.200323	−	0.145543i
$855$		0			0
$856$	18.2705	+	13.2743i	0.624473	+	0.453706i
$857$	12.4721			0.426040			0.213020	−	0.977048i	$-0.431670\pi$
$857$	12.4721			0.426040			0.213020	+	0.977048i	$0.431670\pi$
$858$	−5.61803	−	4.08174i	−0.191797	−	0.139348i
$859$	−7.23607	+	22.2703i	−0.246891	+	0.759854i	0.748428	+	0.663216i	$0.230809\pi$
$859$	−7.23607	+	22.2703i	−0.246891	+	0.759854i	−0.995320	+	0.0966379i	$0.969191\pi$
$860$		0			0
$861$	5.00000	+	15.3884i	0.170400	+	0.524436i
$862$	−6.38197	+	19.6417i	−0.217371	+	0.668998i
$863$	−3.36068	+	10.3431i	−0.114399	+	0.352084i	−0.991821	−	0.127635i	$-0.959261\pi$
$863$	−3.36068	+	10.3431i	−0.114399	+	0.352084i	0.877422	+	0.479719i	$0.159261\pi$
$864$	1.54508	+	4.75528i	0.0525649	+	0.161778i
$865$		0			0
$866$	−6.79180	+	20.9030i	−0.230795	+	0.710313i
$867$	−1.73607	−	1.26133i	−0.0589600	−	0.0428369i
$868$	−12.3607			−0.419549
$869$		0			0
$870$		0			0
$871$	−3.47214	+	2.52265i	−0.117649	+	0.0854769i
$872$	19.1976	−	13.9478i	0.650111	−	0.472334i
$873$	−0.663119	−	2.04087i	−0.0224432	−	0.0690730i
$874$	5.52786			0.186983
$875$		0			0
$876$	8.09017			0.273342
$877$	10.2639	+	31.5891i	0.346588	+	1.06669i	0.960728	+	0.277492i	$0.0895032\pi$
$877$	10.2639	+	31.5891i	0.346588	+	1.06669i	−0.614140	+	0.789197i	$0.710497\pi$
$878$	13.0902	−	9.51057i	0.441772	−	0.320966i
$879$	16.8262	−	12.2250i	0.567535	−	0.412338i
$880$		0			0
$881$	−34.7426	−	25.2420i	−1.17051	−	0.850425i	−0.179440	−	0.983769i	$-0.557428\pi$
$881$	−34.7426	−	25.2420i	−1.17051	−	0.850425i	−0.991070	+	0.133344i	$0.957428\pi$
$882$	−13.0000			−0.437733
$883$	17.9443	+	13.0373i	0.603873	+	0.438739i	0.847251	−	0.531192i	$-0.178256\pi$
$883$	17.9443	+	13.0373i	0.603873	+	0.438739i	−0.243379	+	0.969931i	$0.578256\pi$
$884$	−6.69098	+	20.5927i	−0.225042	+	0.692608i
$885$		0			0
$886$	−10.8885	−	33.5115i	−0.365808	−	1.12584i
$887$	7.14590	−	21.9928i	0.239936	−	0.738446i	−0.756492	−	0.654002i	$-0.773089\pi$
$887$	7.14590	−	21.9928i	0.239936	−	0.738446i	0.996428	−	0.0844440i	$-0.0269114\pi$
$888$	−2.86475	+	8.81678i	−0.0961346	+	0.295872i
$889$	5.12461	+	15.7719i	0.171874	+	0.528974i
$890$		0			0
$891$	−0.381966	+	1.17557i	−0.0127963	+	0.0393831i
$892$	−6.61803	−	4.80828i	−0.221588	−	0.160993i
$893$	0.944272			0.0315989
$894$	15.2533	+	11.0822i	0.510146	+	0.370643i
$895$		0			0
$896$	−10.8541	+	7.88597i	−0.362610	+	0.263452i
$897$	20.3262	−	14.7679i	0.678673	−	0.493085i
$898$	−5.19098	−	15.9762i	−0.173225	−	0.533133i
$899$	18.2918			0.610066
$900$		0			0
$901$	13.9443			0.464551
$902$	−1.38197	−	4.25325i	−0.0460144	−	0.141618i
$903$	−27.8885	+	20.2622i	−0.928073	+	0.674284i
$904$	44.4787	−	32.3157i	1.47934	−	1.07480i
$905$		0			0
$906$	−6.09017	−	4.42477i	−0.202332	−	0.147003i
$907$	−7.12461			−0.236569			−0.118284	−	0.992980i	$-0.537739\pi$
$907$	−7.12461			−0.236569			−0.118284	+	0.992980i	$0.537739\pi$
$908$	16.1803	+	11.7557i	0.536963	+	0.390127i
$909$	1.10081	−	3.38795i	0.0365117	−	0.112371i
$910$		0			0
$911$	5.61803	+	17.2905i	0.186134	+	0.572861i	0.999966	−	0.00823898i	$-0.00262258\pi$
$911$	5.61803	+	17.2905i	0.186134	+	0.572861i	−0.813832	+	0.581100i	$0.802623\pi$
$912$	0.381966	−	1.17557i	0.0126482	−	0.0389270i
$913$	4.76393	−	14.6619i	0.157663	−	0.485237i
$914$	−6.90983	−	21.2663i	−0.228557	−	0.703426i
$915$		0			0
$916$	−6.79180	+	20.9030i	−0.224407	+	0.690655i
$917$	29.5967	+	21.5033i	0.977371	+	0.710101i
$918$	−3.85410			−0.127204
$919$	−39.7984	−	28.9152i	−1.31283	−	0.953825i	−0.999992	−	0.00401741i	$-0.998721\pi$
$919$	−39.7984	−	28.9152i	−1.31283	−	0.953825i	−0.312835	−	0.949807i	$-0.601279\pi$
$920$		0			0
$921$	−26.4164	+	19.1926i	−0.870450	+	0.632419i
$922$	−26.5344	+	19.2784i	−0.873865	+	0.634900i
$923$	9.09017	+	27.9767i	0.299207	+	0.920863i
$924$	−5.52786			−0.181853
$925$		0			0
$926$	18.7639			0.616621
$927$	−1.00000	−	3.07768i	−0.0328443	−	0.101084i
$928$	26.7705	−	19.4499i	0.878785	−	0.638475i
$929$	7.35410	−	5.34307i	0.241280	−	0.175300i	−0.460573	−	0.887622i	$-0.652356\pi$
$929$	7.35410	−	5.34307i	0.241280	−	0.175300i	0.701853	+	0.712321i	$0.252356\pi$
$930$		0			0
$931$	−13.0000	−	9.44505i	−0.426058	−	0.309549i
$932$	12.3820			0.405585
$933$	14.3262	+	10.4086i	0.469020	+	0.340763i
$934$	8.70820	−	26.8011i	0.284941	−	0.876959i
$935$		0			0
$936$	−5.20820	−	16.0292i	−0.170235	−	0.523931i
$937$	15.0451	−	46.3040i	0.491502	−	1.51269i	−0.330837	−	0.943688i	$-0.607331\pi$
$937$	15.0451	−	46.3040i	0.491502	−	1.51269i	0.822339	−	0.568998i	$-0.192669\pi$
$938$	1.05573	−	3.24920i	0.0344707	−	0.106090i
$939$	−0.145898	−	0.449028i	−0.00476120	−	0.0146535i
$940$		0			0
$941$	−3.19098	+	9.82084i	−0.104023	+	0.320150i	−0.989500	−	0.144533i	$-0.953832\pi$
$941$	−3.19098	+	9.82084i	−0.104023	+	0.320150i	0.885477	+	0.464683i	$0.153832\pi$
$942$	8.73607	+	6.34712i	0.284636	+	0.206801i
$943$	16.1803			0.526904
$944$	−3.23607	−	2.35114i	−0.105325	−	0.0765231i
$945$		0			0
$946$	7.70820	−	5.60034i	0.250615	−	0.182083i
$947$	2.09017	−	1.51860i	0.0679214	−	0.0493478i	−0.553306	−	0.832978i	$-0.686634\pi$
$947$	2.09017	−	1.51860i	0.0679214	−	0.0493478i	0.621228	+	0.783630i	$0.286634\pi$
$948$		0			0
$949$	−45.4508			−1.47540
$950$		0			0
$951$	28.8328			0.934968
$952$	−15.9787	−	49.1774i	−0.517873	−	1.59385i
$953$	−0.881966	+	0.640786i	−0.0285697	+	0.0207571i	−0.601978	−	0.798512i	$-0.705621\pi$
$953$	−0.881966	+	0.640786i	−0.0285697	+	0.0207571i	0.573409	+	0.819269i	$0.305621\pi$
$954$	−2.92705	+	2.12663i	−0.0947668	+	0.0688521i
$955$		0			0
$956$	−20.1803	−	14.6619i	−0.652679	−	0.474199i
$957$	8.18034			0.264433
$958$	15.3262	+	11.1352i	0.495168	+	0.359761i
$959$	10.5279	−	32.4014i	0.339962	−	1.04630i
$960$		0			0
$961$	−7.21885	−	22.2173i	−0.232866	−	0.716688i
$962$	5.36475	−	16.5110i	0.172966	−	0.532336i
$963$	−2.32624	+	7.15942i	−0.0749620	+	0.230709i
$964$	−8.66312	−	26.6623i	−0.279020	−	0.858736i
$965$		0			0
$966$	−6.18034	+	19.0211i	−0.198849	+	0.611995i
$967$	−15.2361	−	11.0697i	−0.489959	−	0.355976i	0.315210	−	0.949022i	$-0.397925\pi$
$967$	−15.2361	−	11.0697i	−0.489959	−	0.355976i	−0.805169	+	0.593046i	$0.797925\pi$
$968$	−28.4164			−0.913338
$969$	−3.85410	−	2.80017i	−0.123812	−	0.0899544i
$970$		0			0
$971$	27.0344	−	19.6417i	0.867577	−	0.630331i	−0.0623590	−	0.998054i	$-0.519862\pi$
$971$	27.0344	−	19.6417i	0.867577	−	0.630331i	0.929936	+	0.367723i	$0.119862\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	−31.7082	−	97.5878i	−1.01652	−	3.12852i
$974$	9.70820			0.311071
$975$		0			0
$976$	−1.61803			−0.0517920
$977$	1.00658	+	3.09793i	0.0322033	+	0.0991115i	0.965866	−	0.259041i	$-0.0834066\pi$
$977$	1.00658	+	3.09793i	0.0322033	+	0.0991115i	−0.933663	+	0.358153i	$0.883407\pi$
$978$	−12.0902	+	8.78402i	−0.386601	+	0.280882i
$979$	5.38197	−	3.91023i	0.172008	−	0.124971i
$980$		0			0
$981$	6.39919	+	4.64928i	0.204310	+	0.148440i
$982$	−5.88854			−0.187911
$983$	6.70820	+	4.87380i	0.213958	+	0.155450i	0.689603	−	0.724188i	$-0.257785\pi$
$983$	6.70820	+	4.87380i	0.213958	+	0.155450i	−0.475644	+	0.879638i	$0.657785\pi$
$984$	3.35410	−	10.3229i	0.106925	−	0.329081i
$985$		0			0
$986$	7.88197	+	24.2582i	0.251013	+	0.772538i
$987$	−1.05573	+	3.24920i	−0.0336042	+	0.103423i
$988$	2.14590	−	6.60440i	0.0682701	−	0.210114i
$989$	10.6525	+	32.7849i	0.338729	+	1.04250i
$990$		0			0
$991$	11.4721	−	35.3076i	0.364424	−	1.12158i	−0.585916	−	0.810372i	$-0.699265\pi$
$991$	11.4721	−	35.3076i	0.364424	−	1.12158i	0.950341	−	0.311211i	$-0.100735\pi$
$992$	11.1803	+	8.12299i	0.354976	+	0.257905i
$993$	6.94427			0.220370
$994$	−18.9443	−	13.7638i	−0.600876	−	0.436562i
$995$		0			0
$996$	10.0902	−	7.33094i	0.319719	−	0.232290i
$997$	−14.0902	+	10.2371i	−0.446240	+	0.324212i	−0.788110	−	0.615535i	$-0.788940\pi$
$997$	−14.0902	+	10.2371i	−0.446240	+	0.324212i	0.341869	+	0.939747i	$0.388940\pi$
$998$	1.85410	+	5.70634i	0.0586906	+	0.180631i
$999$	−3.09017			−0.0977687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.a.151.1		4
5.2	odd	4		375.2.i.a.349.2		8
5.3	odd	4		375.2.i.a.349.1		8
5.4	even	2		75.2.g.a.31.1	✓	4
15.14	odd	2		225.2.h.a.181.1		4
25.2	odd	20		1875.2.b.b.1249.2		4
25.3	odd	20		375.2.i.a.274.2		8
25.4	even	10		75.2.g.a.46.1	yes	4
25.11	even	5		1875.2.a.a.1.2		2
25.14	even	10		1875.2.a.d.1.1		2
25.21	even	5	inner	375.2.g.a.226.1		4
25.22	odd	20		375.2.i.a.274.1		8
25.23	odd	20		1875.2.b.b.1249.3		4
75.11	odd	10		5625.2.a.h.1.2		2
75.14	odd	10		5625.2.a.a.1.1		2
75.29	odd	10		225.2.h.a.46.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.a.31.1	✓	4	5.4	even	2
75.2.g.a.46.1	yes	4	25.4	even	10
225.2.h.a.46.1		4	75.29	odd	10
225.2.h.a.181.1		4	15.14	odd	2
375.2.g.a.151.1		4	1.1	even	1	trivial
375.2.g.a.226.1		4	25.21	even	5	inner
375.2.i.a.274.1		8	25.22	odd	20
375.2.i.a.274.2		8	25.3	odd	20
375.2.i.a.349.1		8	5.3	odd	4
375.2.i.a.349.2		8	5.2	odd	4
1875.2.a.a.1.2		2	25.11	even	5
1875.2.a.d.1.1		2	25.14	even	10
1875.2.b.b.1249.2		4	25.2	odd	20
1875.2.b.b.1249.3		4	25.23	odd	20
5625.2.a.a.1.1		2	75.14	odd	10
5625.2.a.h.1.2		2	75.11	odd	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} +4.47214 q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.381966 - 1.17557i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-1.73607 + 5.34307i) q^{13} +(-1.38197 - 4.25325i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(3.11803 + 2.26538i) q^{17} -1.00000 q^{18} +(-1.00000 - 0.726543i) q^{19} +(3.61803 - 2.62866i) q^{21} +(-1.00000 + 0.726543i) q^{22} +(-1.38197 - 4.25325i) q^{23} -3.00000 q^{24} +5.61803 q^{26} +(-0.309017 - 0.951057i) q^{27} +(3.61803 - 2.62866i) q^{28} +(-5.35410 + 3.88998i) q^{29} +(-2.23607 - 1.62460i) q^{31} -5.00000 q^{32} +(-1.00000 - 0.726543i) q^{33} +(1.19098 - 3.66547i) q^{34} +(-0.309017 - 0.951057i) q^{36} +(0.954915 - 2.93893i) q^{37} +(-0.381966 + 1.17557i) q^{38} +(1.73607 + 5.34307i) q^{39} +(-1.11803 + 3.44095i) q^{41} +(-3.61803 - 2.62866i) q^{42} -7.70820 q^{43} +(-1.00000 - 0.726543i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(-0.618034 + 0.449028i) q^{47} +(0.309017 + 0.951057i) q^{48} +13.0000 q^{49} +3.85410 q^{51} +(1.73607 + 5.34307i) q^{52} +(2.92705 - 2.12663i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-10.8541 - 7.88597i) q^{56} -1.23607 q^{57} +(5.35410 + 3.88998i) q^{58} +(-1.23607 + 3.80423i) q^{59} +(0.500000 + 1.53884i) q^{61} +(-0.854102 + 2.62866i) q^{62} +(1.38197 - 4.25325i) q^{63} +(2.16312 + 6.65740i) q^{64} +(-0.381966 + 1.17557i) q^{66} +(0.618034 + 0.449028i) q^{67} +3.85410 q^{68} +(-3.61803 - 2.62866i) q^{69} +(4.23607 - 3.07768i) q^{71} +(-2.42705 + 1.76336i) q^{72} +(2.50000 + 7.69421i) q^{73} -3.09017 q^{74} -1.23607 q^{76} +(-1.70820 - 5.25731i) q^{77} +(4.54508 - 3.30220i) q^{78} +(-0.809017 - 0.587785i) q^{81} +3.61803 q^{82} +(10.0902 + 7.33094i) q^{83} +(1.38197 - 4.25325i) q^{84} +(2.38197 + 7.33094i) q^{86} +(-2.04508 + 6.29412i) q^{87} +(-1.14590 + 3.52671i) q^{88} +(1.66312 + 5.11855i) q^{89} +(-7.76393 + 23.8949i) q^{91} +(-3.61803 - 2.62866i) q^{92} -2.76393 q^{93} +(0.618034 + 0.449028i) q^{94} +(-4.04508 + 2.93893i) q^{96} +(1.73607 - 1.26133i) q^{97} +(-4.01722 - 12.3637i) q^{98} -1.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + q^{4} - q^{6} - 3 q^{8} - q^{9} - 6 q^{11} - q^{12} + 2 q^{13} - 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 10 q^{21} - 4 q^{22} - 10 q^{23} - 12 q^{24} + 18 q^{26}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 + q^4 - q^6 - 3 * q^8 - q^9 - 6 * q^11 - q^12 + 2 * q^13 - 10 * q^14 + q^16 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 10 * q^21 - 4 * q^22 - 10 * q^23 - 12 * q^24 + 18 * q^26 + q^27 + 10 * q^28 - 8 * q^29 - 20 * q^32 - 4 * q^33 + 7 * q^34 + q^36 + 15 * q^37 - 6 * q^38 - 2 * q^39 - 10 * q^42 - 4 * q^43 - 4 * q^44 - 10 * q^46 + 2 * q^47 - q^48 + 52 * q^49 + 2 * q^51 - 2 * q^52 + 5 * q^53 - q^54 - 30 * q^56 + 4 * q^57 + 8 * q^58 + 4 * q^59 + 2 * q^61 + 10 * q^62 + 10 * q^63 - 7 * q^64 - 6 * q^66 - 2 * q^67 + 2 * q^68 - 10 * q^69 + 8 * q^71 - 3 * q^72 + 10 * q^73 + 10 * q^74 + 4 * q^76 + 20 * q^77 + 7 * q^78 - q^81 + 10 * q^82 + 18 * q^83 + 10 * q^84 + 14 * q^86 + 3 * q^87 - 18 * q^88 - 9 * q^89 - 40 * q^91 - 10 * q^92 - 20 * q^93 - 2 * q^94 - 5 * q^96 - 2 * q^97 + 13 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more